LMFDB - Embedded newform 375.2.i.a.349.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [375,2,Mod(49,375)] 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("375.49"); 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, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.i (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			349.2
Root			$0.951057 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	375.349
Dual form			375.2.i.a.274.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.951057 - 0.309017i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.809017 - 0.587785i) q^{6} +4.47214i q^{7} +(-1.76336 + 2.42705i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-0.381966 - 1.17557i) q^{11} +(0.951057 + 0.309017i) q^{12} +(5.34307 + 1.73607i) q^{13} +(1.38197 + 4.25325i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-2.26538 + 3.11803i) q^{17} +1.00000i q^{18} +(1.00000 + 0.726543i) q^{19} +(3.61803 - 2.62866i) q^{21} +(-0.726543 - 1.00000i) q^{22} +(-4.25325 + 1.38197i) q^{23} +3.00000 q^{24} +5.61803 q^{26} +(0.951057 - 0.309017i) q^{27} +(-2.62866 - 3.61803i) q^{28} +(5.35410 - 3.88998i) q^{29} +(-2.23607 - 1.62460i) q^{31} -5.00000i q^{32} +(-0.726543 + 1.00000i) q^{33} +(-1.19098 + 3.66547i) q^{34} +(-0.309017 - 0.951057i) q^{36} +(2.93893 + 0.954915i) q^{37} +(1.17557 + 0.381966i) q^{38} +(-1.73607 - 5.34307i) q^{39} +(-1.11803 + 3.44095i) q^{41} +(2.62866 - 3.61803i) q^{42} +7.70820i q^{43} +(1.00000 + 0.726543i) q^{44} +(-3.61803 + 2.62866i) q^{46} +(-0.449028 - 0.618034i) q^{47} +(0.951057 - 0.309017i) q^{48} -13.0000 q^{49} +3.85410 q^{51} +(-5.34307 + 1.73607i) q^{52} +(-2.12663 - 2.92705i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-10.8541 - 7.88597i) q^{56} -1.23607i q^{57} +(3.88998 - 5.35410i) q^{58} +(1.23607 - 3.80423i) q^{59} +(0.500000 + 1.53884i) q^{61} +(-2.62866 - 0.854102i) q^{62} +(-4.25325 - 1.38197i) q^{63} +(-2.16312 - 6.65740i) q^{64} +(-0.381966 + 1.17557i) q^{66} +(-0.449028 + 0.618034i) q^{67} -3.85410i q^{68} +(3.61803 + 2.62866i) q^{69} +(4.23607 - 3.07768i) q^{71} +(-1.76336 - 2.42705i) q^{72} +(7.69421 - 2.50000i) q^{73} +3.09017 q^{74} -1.23607 q^{76} +(5.25731 - 1.70820i) q^{77} +(-3.30220 - 4.54508i) q^{78} +(-0.809017 - 0.587785i) q^{81} +3.61803i q^{82} +(7.33094 - 10.0902i) q^{83} +(-1.38197 + 4.25325i) q^{84} +(2.38197 + 7.33094i) q^{86} +(-6.29412 - 2.04508i) q^{87} +(3.52671 + 1.14590i) q^{88} +(-1.66312 - 5.11855i) q^{89} +(-7.76393 + 23.8949i) q^{91} +(2.62866 - 3.61803i) q^{92} +2.76393i q^{93} +(-0.618034 - 0.449028i) q^{94} +(-4.04508 + 2.93893i) q^{96} +(1.26133 + 1.73607i) q^{97} +(-12.3637 + 4.01722i) q^{98} +1.23607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} - 2 q^{6} + 2 q^{9} - 12 q^{11} + 20 q^{14} + 2 q^{16} + 8 q^{19} + 20 q^{21} + 24 q^{24} + 36 q^{26} + 16 q^{29} - 14 q^{34} + 2 q^{36} + 4 q^{39} + 8 q^{44} - 20 q^{46} - 104 q^{49} + 4 q^{51}+ \cdots - 8 q^{99}+O(q^{100}) $ 8 * q - 2 * q^4 - 2 * q^6 + 2 * q^9 - 12 * q^11 + 20 * q^14 + 2 * q^16 + 8 * q^19 + 20 * q^21 + 24 * q^24 + 36 * q^26 + 16 * q^29 - 14 * q^34 + 2 * q^36 + 4 * q^39 + 8 * q^44 - 20 * q^46 - 104 * q^49 + 4 * q^51 + 2 * q^54 - 60 * q^56 - 8 * q^59 + 4 * q^61 + 14 * q^64 - 12 * q^66 + 20 * q^69 + 16 * q^71 - 20 * q^74 + 8 * q^76 - 2 * q^81 - 20 * q^84 + 28 * q^86 + 18 * q^89 - 80 * q^91 + 4 * q^94 - 10 * q^96 - 8 * q^99

Character values

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

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	0.951057	−	0.309017i	0.672499	−	0.218508i	0.0471903	−	0.998886i	$-0.484973\pi$
$2$	0.951057	−	0.309017i	0.672499	−	0.218508i	0.625308	+	0.780378i	$0.284973\pi$
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$		0			0
$5$		0			0
$6$	−0.809017	−	0.587785i	−0.330280	−	0.239962i
$7$			4.47214i			1.69031i	0.534522	+	0.845154i	$0.320491\pi$
$7$			4.47214i			1.69031i	−0.534522	+	0.845154i	$0.679509\pi$
$8$	−1.76336	+	2.42705i	−0.623440	+	0.858092i
$9$	−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	$0.959664\pi$
$12$	0.951057	+	0.309017i	0.274546	+	0.0892055i
$13$	5.34307	+	1.73607i	1.48190	+	0.481499i	0.934680	−	0.355490i	$-0.115686\pi$
$13$	5.34307	+	1.73607i	1.48190	+	0.481499i	0.547220	+	0.836989i	$0.315686\pi$
$14$	1.38197	+	4.25325i	0.369346	+	1.13673i
$15$		0			0
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	−2.26538	+	3.11803i	−0.549436	+	0.756234i	−0.989936	−	0.141519i	$-0.954801\pi$
$17$	−2.26538	+	3.11803i	−0.549436	+	0.756234i	0.440499	+	0.897753i	$0.354801\pi$
$18$			1.00000i			0.235702i
$19$	1.00000	+	0.726543i	0.229416	+	0.166680i	0.696555	−	0.717504i	$-0.254715\pi$
$19$	1.00000	+	0.726543i	0.229416	+	0.166680i	−0.467139	+	0.884184i	$0.654715\pi$
$20$		0			0
$21$	3.61803	−	2.62866i	0.789520	−	0.573620i
$22$	−0.726543	−	1.00000i	−0.154899	−	0.213201i
$23$	−4.25325	+	1.38197i	−0.886865	+	0.288160i	−0.716805	−	0.697274i	$-0.754396\pi$
$23$	−4.25325	+	1.38197i	−0.886865	+	0.288160i	−0.170060	+	0.985434i	$0.554396\pi$
$24$	3.00000			0.612372
$25$		0			0
$26$	5.61803			1.10179
$27$	0.951057	−	0.309017i	0.183031	−	0.0594703i
$28$	−2.62866	−	3.61803i	−0.496769	−	0.683744i
$29$	5.35410	−	3.88998i	0.994232	−	0.722352i	0.0333880	−	0.999442i	$-0.489370\pi$
$29$	5.35410	−	3.88998i	0.994232	−	0.722352i	0.960844	+	0.277091i	$0.0893703\pi$
$30$		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	$0.779842\pi$
$32$		−	5.00000i		−	0.883883i
$33$	−0.726543	+	1.00000i	−0.126475	+	0.174078i
$34$	−1.19098	+	3.66547i	−0.204252	+	0.628623i
$35$		0			0
$36$	−0.309017	−	0.951057i	−0.0515028	−	0.158509i
$37$	2.93893	+	0.954915i	0.483157	+	0.156987i	0.540460	−	0.841370i	$-0.318250\pi$
$37$	2.93893	+	0.954915i	0.483157	+	0.156987i	−0.0573034	+	0.998357i	$0.518250\pi$
$38$	1.17557	+	0.381966i	0.190703	+	0.0619631i
$39$	−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	$0.191171\pi$
$42$	2.62866	−	3.61803i	0.405610	−	0.558275i
$43$			7.70820i			1.17549i	0.809046	+	0.587745i	$0.199984\pi$
$43$			7.70820i			1.17549i	−0.809046	+	0.587745i	$0.800016\pi$
$44$	1.00000	+	0.726543i	0.150756	+	0.109530i
$45$		0			0
$46$	−3.61803	+	2.62866i	−0.533450	+	0.387574i
$47$	−0.449028	−	0.618034i	−0.0654975	−	0.0901495i	0.775012	−	0.631947i	$-0.217744\pi$
$47$	−0.449028	−	0.618034i	−0.0654975	−	0.0901495i	−0.840509	+	0.541797i	$0.817744\pi$
$48$	0.951057	−	0.309017i	0.137273	−	0.0446028i
$49$	−13.0000			−1.85714
$50$		0			0
$51$	3.85410			0.539682
$52$	−5.34307	+	1.73607i	−0.740950	+	0.240749i
$53$	−2.12663	−	2.92705i	−0.292115	−	0.402061i	0.637585	−	0.770380i	$-0.279934\pi$
$53$	−2.12663	−	2.92705i	−0.292115	−	0.402061i	−0.929700	+	0.368319i	$0.879934\pi$
$54$	0.809017	−	0.587785i	0.110093	−	0.0799874i
$55$		0			0
$56$	−10.8541	−	7.88597i	−1.45044	−	1.05381i
$57$		−	1.23607i		−	0.163721i
$58$	3.88998	−	5.35410i	0.510780	−	0.703028i
$59$	1.23607	−	3.80423i	0.160922	−	0.495268i	−0.837790	−	0.545992i	$-0.816153\pi$
$59$	1.23607	−	3.80423i	0.160922	−	0.495268i	0.998713	+	0.0507240i	$0.0161529\pi$
$60$		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	$0.866969\pi$
$62$	−2.62866	−	0.854102i	−0.333840	−	0.108471i
$63$	−4.25325	−	1.38197i	−0.535860	−	0.174111i
$64$	−2.16312	−	6.65740i	−0.270390	−	0.832174i
$65$		0			0
$66$	−0.381966	+	1.17557i	−0.0470168	+	0.144703i
$67$	−0.449028	+	0.618034i	−0.0548575	+	0.0755049i	−0.835564	−	0.549392i	$-0.814859\pi$
$67$	−0.449028	+	0.618034i	−0.0548575	+	0.0755049i	0.780707	+	0.624897i	$0.214859\pi$
$68$		−	3.85410i		−	0.467379i
$69$	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	$0.199435\pi$
$72$	−1.76336	−	2.42705i	−0.207813	−	0.286031i
$73$	7.69421	−	2.50000i	0.900539	−	0.292603i	0.178080	−	0.984016i	$-0.443012\pi$
$73$	7.69421	−	2.50000i	0.900539	−	0.292603i	0.722460	+	0.691413i	$0.243012\pi$
$74$	3.09017			0.359225
$75$		0			0
$76$	−1.23607			−0.141787
$77$	5.25731	−	1.70820i	0.599126	−	0.194668i
$78$	−3.30220	−	4.54508i	−0.373900	−	0.514630i
$79$		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
$82$			3.61803i			0.399545i
$83$	7.33094	−	10.0902i	0.804675	−	1.10754i	−0.187448	−	0.982274i	$-0.560022\pi$
$83$	7.33094	−	10.0902i	0.804675	−	1.10754i	0.992123	−	0.125266i	$-0.0399783\pi$
$84$	−1.38197	+	4.25325i	−0.150785	+	0.464068i
$85$		0			0
$86$	2.38197	+	7.33094i	0.256854	+	0.790515i
$87$	−6.29412	−	2.04508i	−0.674801	−	0.219256i
$88$	3.52671	+	1.14590i	0.375949	+	0.122153i
$89$	−1.66312	−	5.11855i	−0.176290	−	0.542566i	0.823400	−	0.567462i	$-0.192075\pi$
$89$	−1.66312	−	5.11855i	−0.176290	−	0.542566i	−0.999690	+	0.0248961i	$0.992075\pi$
$90$		0			0
$91$	−7.76393	+	23.8949i	−0.813881	+	2.50487i
$92$	2.62866	−	3.61803i	0.274056	−	0.377206i
$93$			2.76393i			0.286606i
$94$	−0.618034	−	0.449028i	−0.0637453	−	0.0463137i
$95$		0			0
$96$	−4.04508	+	2.93893i	−0.412850	+	0.299953i
$97$	1.26133	+	1.73607i	0.128068	+	0.176271i	0.868236	−	0.496151i	$-0.165254\pi$
$97$	1.26133	+	1.73607i	0.128068	+	0.176271i	−0.740168	+	0.672422i	$0.765254\pi$
$98$	−12.3637	+	4.01722i	−1.24893	+	0.405801i
$99$	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	$0.443286\pi$
$102$	3.66547	−	1.19098i	0.362935	−	0.117925i
$103$	−1.90211	−	2.61803i	−0.187421	−	0.257963i	0.704959	−	0.709248i	$-0.250966\pi$
$103$	−1.90211	−	2.61803i	−0.187421	−	0.257963i	−0.892379	+	0.451286i	$0.850966\pi$
$104$	−13.6353	+	9.90659i	−1.33705	+	0.971421i
$105$		0			0
$106$	−2.92705	−	2.12663i	−0.284300	−	0.206556i
$107$		−	7.52786i		−	0.727746i	−0.931449	−	0.363873i	$-0.881454\pi$
$107$		−	7.52786i		−	0.727746i	0.931449	−	0.363873i	$-0.118546\pi$
$108$	−0.587785	+	0.809017i	−0.0565597	+	0.0778477i
$109$	2.44427	−	7.52270i	0.234119	−	0.720544i	−0.763118	−	0.646259i	$-0.776333\pi$
$109$	2.44427	−	7.52270i	0.234119	−	0.720544i	0.997237	−	0.0742847i	$-0.0236674\pi$
$110$		0			0
$111$	−0.954915	−	2.93893i	−0.0906365	−	0.278951i
$112$	−4.25325	−	1.38197i	−0.401895	−	0.130584i
$113$	17.4293	+	5.66312i	1.63961	+	0.532741i	0.976451	−	0.215738i	$-0.0692157\pi$
$113$	17.4293	+	5.66312i	1.63961	+	0.532741i	0.663158	+	0.748479i	$0.269216\pi$
$114$	−0.381966	−	1.17557i	−0.0357744	−	0.110102i
$115$		0			0
$116$	−2.04508	+	6.29412i	−0.189881	+	0.584395i
$117$	−3.30220	+	4.54508i	−0.305288	+	0.420193i
$118$		−	4.00000i		−	0.368230i
$119$	−13.9443	−	10.1311i	−1.27827	−	0.928717i
$120$		0			0
$121$	7.66312	−	5.56758i	0.696647	−	0.506144i
$122$	0.951057	+	1.30902i	0.0861046	+	0.118513i
$123$	3.44095	−	1.11803i	0.310260	−	0.100810i
$124$	2.76393			0.248208
$125$		0			0
$126$	−4.47214			−0.398410
$127$	−3.52671	+	1.14590i	−0.312945	+	0.101682i	−0.461279	−	0.887255i	$-0.652609\pi$
$127$	−3.52671	+	1.14590i	−0.312945	+	0.101682i	0.148333	+	0.988937i	$0.452609\pi$
$128$	1.76336	+	2.42705i	0.155860	+	0.214523i
$129$	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	$0.583677\pi$
$132$		−	1.23607i		−	0.107586i
$133$	−3.24920	+	4.47214i	−0.281741	+	0.387783i
$134$	−0.236068	+	0.726543i	−0.0203932	+	0.0627637i
$135$		0			0
$136$	−3.57295	−	10.9964i	−0.306378	−	0.942934i
$137$	7.24518	+	2.35410i	0.618998	+	0.201125i	0.601695	−	0.798726i	$-0.294492\pi$
$137$	7.24518	+	2.35410i	0.618998	+	0.201125i	0.0173024	+	0.999850i	$0.494492\pi$
$138$	4.25325	+	1.38197i	0.362061	+	0.117641i
$139$	7.09017	+	21.8213i	0.601380	+	1.85086i	0.519983	+	0.854177i	$0.325938\pi$
$139$	7.09017	+	21.8213i	0.601380	+	1.85086i	0.0813976	+	0.996682i	$0.474062\pi$
$140$		0			0
$141$	−0.236068	+	0.726543i	−0.0198805	+	0.0611859i
$142$	3.07768	−	4.23607i	0.258273	−	0.355483i
$143$		−	6.94427i		−	0.580709i
$144$	−0.809017	−	0.587785i	−0.0674181	−	0.0489821i
$145$		0			0
$146$	6.54508	−	4.75528i	0.541675	−	0.393550i
$147$	7.64121	+	10.5172i	0.630236	+	0.867446i
$148$	−2.93893	+	0.954915i	−0.241578	+	0.0784935i
$149$	18.8541			1.54459			0.772294	−	0.635265i	$-0.219109\pi$
$149$	18.8541			1.54459			0.772294	+	0.635265i	$0.219109\pi$
$150$		0			0
$151$	7.52786			0.612609			0.306304	−	0.951934i	$-0.400907\pi$
$151$	7.52786			0.612609			0.306304	+	0.951934i	$0.400907\pi$
$152$	−3.52671	+	1.14590i	−0.286054	+	0.0929446i
$153$	−2.26538	−	3.11803i	−0.183145	−	0.252078i
$154$	4.47214	−	3.24920i	0.360375	−	0.261828i
$155$		0			0
$156$	4.54508	+	3.30220i	0.363898	+	0.264387i
$157$		−	10.7984i		−	0.861804i	−0.902399	−	0.430902i	$-0.858195\pi$
$157$		−	10.7984i		−	0.861804i	0.902399	−	0.430902i	$-0.141805\pi$
$158$		0			0
$159$	−1.11803	+	3.44095i	−0.0886659	+	0.272885i
$160$		0			0
$161$	−6.18034	−	19.0211i	−0.487079	−	1.49908i
$162$	−0.951057	−	0.309017i	−0.0747221	−	0.0242787i
$163$	−14.2128	−	4.61803i	−1.11324	−	0.361712i	−0.306054	−	0.952014i	$-0.599009\pi$
$163$	−14.2128	−	4.61803i	−1.11324	−	0.361712i	−0.807183	+	0.590302i	$0.799009\pi$
$164$	−1.11803	−	3.44095i	−0.0873038	−	0.268693i
$165$		0			0
$166$	3.85410	−	11.8617i	0.299136	−	0.920647i
$167$	−2.00811	+	2.76393i	−0.155393	+	0.213879i	−0.879614	−	0.475688i	$-0.842199\pi$
$167$	−2.00811	+	2.76393i	−0.155393	+	0.213879i	0.724222	+	0.689567i	$0.242199\pi$
$168$			13.4164i			1.03510i
$169$	15.0172	+	10.9106i	1.15517	+	0.839281i
$170$		0			0
$171$	−1.00000	+	0.726543i	−0.0764719	+	0.0555601i
$172$	−4.53077	−	6.23607i	−0.345468	−	0.475496i
$173$	−20.0579	+	6.51722i	−1.52498	+	0.495495i	−0.947185	−	0.320689i	$-0.896086\pi$
$173$	−20.0579	+	6.51722i	−1.52498	+	0.495495i	−0.577793	+	0.816184i	$0.696086\pi$
$174$	−6.61803			−0.501712
$175$		0			0
$176$	1.23607			0.0931721
$177$	−3.80423	+	1.23607i	−0.285943	+	0.0929086i
$178$	−3.16344	−	4.35410i	−0.237110	−	0.326354i
$179$	−13.0902	+	9.51057i	−0.978405	+	0.710853i	−0.957352	−	0.288925i	$-0.906702\pi$
$179$	−13.0902	+	9.51057i	−0.978405	+	0.710853i	−0.0210536	+	0.999778i	$0.506702\pi$
$180$		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	$0.885364\pi$
$182$			25.1246i			1.86236i
$183$	0.951057	−	1.30902i	0.0703041	−	0.0967653i
$184$	4.14590	−	12.7598i	0.305640	−	0.940662i
$185$		0			0
$186$	0.854102	+	2.62866i	0.0626258	+	0.192742i
$187$	4.53077	+	1.47214i	0.331323	+	0.107653i
$188$	0.726543	+	0.236068i	0.0529886	+	0.0172170i
$189$	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	$0.0226302\pi$
$192$	−4.11450	+	5.66312i	−0.296938	+	0.408700i
$193$			23.3262i			1.67906i	0.543314	+	0.839530i	$0.317169\pi$
$193$			23.3262i			1.67906i	−0.543314	+	0.839530i	$0.682831\pi$
$194$	1.73607	+	1.26133i	0.124642	+	0.0905580i
$195$		0			0
$196$	10.5172	−	7.64121i	0.751230	−	0.545801i
$197$	4.47777	+	6.16312i	0.319028	+	0.439104i	0.938170	−	0.346175i	$-0.112520\pi$
$197$	4.47777	+	6.16312i	0.319028	+	0.439104i	−0.619142	+	0.785279i	$0.712520\pi$
$198$	1.17557	−	0.381966i	0.0835442	−	0.0271451i
$199$	−12.6525			−0.896910			−0.448455	−	0.893805i	$-0.648026\pi$
$199$	−12.6525			−0.896910			−0.448455	+	0.893805i	$0.648026\pi$
$200$		0			0
$201$	0.763932			0.0538836
$202$	3.38795	−	1.10081i	0.238376	−	0.0774529i
$203$	17.3965	+	23.9443i	1.22100	+	1.68056i
$204$	−3.11803	+	2.26538i	−0.218306	+	0.158609i
$205$		0			0
$206$	−2.61803	−	1.90211i	−0.182407	−	0.132526i
$207$		−	4.47214i		−	0.310835i
$208$	−3.30220	+	4.54508i	−0.228966	+	0.315145i
$209$	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	$0.688854\pi$
$212$	3.44095	+	1.11803i	0.236326	+	0.0767869i
$213$	−4.97980	−	1.61803i	−0.341210	−	0.110866i
$214$	−2.32624	−	7.15942i	−0.159018	−	0.489408i
$215$		0			0
$216$	−0.927051	+	2.85317i	−0.0630778	+	0.194134i
$217$	7.26543	−	10.0000i	0.493209	−	0.678844i
$218$		−	7.90983i		−	0.535721i
$219$	−6.54508	−	4.75528i	−0.442276	−	0.321332i
$220$		0			0
$221$	−17.5172	+	12.7270i	−1.17834	+	0.856111i
$222$	−1.81636	−	2.50000i	−0.121906	−	0.167789i
$223$	−7.77997	+	2.52786i	−0.520985	+	0.169278i	−0.557692	−	0.830048i	$-0.688313\pi$
$223$	−7.77997	+	2.52786i	−0.520985	+	0.169278i	0.0367073	+	0.999326i	$0.488313\pi$
$224$	22.3607			1.49404
$225$		0			0
$226$	18.3262			1.21904
$227$	−19.0211	+	6.18034i	−1.26248	+	0.410204i	−0.862376	−	0.506268i	$-0.831025\pi$
$227$	−19.0211	+	6.18034i	−1.26248	+	0.410204i	−0.400100	+	0.916471i	$0.631025\pi$
$228$	0.726543	+	1.00000i	0.0481165	+	0.0662266i
$229$	17.7812	−	12.9188i	1.17501	−	0.853696i	0.183411	−	0.983036i	$-0.441286\pi$
$229$	17.7812	−	12.9188i	1.17501	−	0.853696i	0.991600	+	0.129340i	$0.0412860\pi$
$230$		0			0
$231$	−4.47214	−	3.24920i	−0.294245	−	0.213781i
$232$			19.8541i			1.30349i
$233$	7.27794	−	10.0172i	0.476794	−	0.656250i	−0.501091	−	0.865394i	$-0.667068\pi$
$233$	7.27794	−	10.0172i	0.476794	−	0.656250i	0.977885	+	0.209144i	$0.0670679\pi$
$234$	−1.73607	+	5.34307i	−0.113490	+	0.349287i
$235$		0			0
$236$	1.23607	+	3.80423i	0.0804612	+	0.247634i
$237$		0			0
$238$	−16.3925	−	5.32624i	−1.06257	−	0.345249i
$239$	7.70820	+	23.7234i	0.498602	+	1.53454i	0.811267	+	0.584676i	$0.198778\pi$
$239$	7.70820	+	23.7234i	0.498602	+	1.53454i	−0.312664	+	0.949864i	$0.601222\pi$
$240$		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	$-0.258587\pi$
$242$	5.56758	−	7.66312i	0.357898	−	0.492604i
$243$			1.00000i			0.0641500i
$244$	−1.30902	−	0.951057i	−0.0838012	−	0.0608852i
$245$		0			0
$246$	2.92705	−	2.12663i	0.186622	−	0.135589i
$247$	4.08174	+	5.61803i	0.259715	+	0.357467i
$248$	7.88597	−	2.56231i	0.500759	−	0.162707i
$249$	−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	$0.592258\pi$
$252$	4.25325	−	1.38197i	0.267930	−	0.0870557i
$253$	3.24920	+	4.47214i	0.204275	+	0.281161i
$254$	−3.00000	+	2.17963i	−0.188237	+	0.136762i
$255$		0			0
$256$	13.7533	+	9.99235i	0.859581	+	0.624522i
$257$		−	11.7984i		−	0.735962i	−0.929833	−	0.367981i	$-0.880049\pi$
$257$		−	11.7984i		−	0.735962i	0.929833	−	0.367981i	$-0.119951\pi$
$258$	4.53077	−	6.23607i	0.282073	−	0.388241i
$259$	−4.27051	+	13.1433i	−0.265357	+	0.816684i
$260$		0			0
$261$	2.04508	+	6.29412i	0.126588	+	0.389597i
$262$	7.77997	+	2.52786i	0.480648	+	0.156172i
$263$	−22.7194	−	7.38197i	−1.40094	−	0.455192i	−0.491442	−	0.870910i	$-0.663530\pi$
$263$	−22.7194	−	7.38197i	−1.40094	−	0.455192i	−0.909493	+	0.415719i	$0.863530\pi$
$264$	−1.14590	−	3.52671i	−0.0705251	−	0.217054i
$265$		0			0
$266$	−1.70820	+	5.25731i	−0.104737	+	0.322346i
$267$	−3.16344	+	4.35410i	−0.193599	+	0.266467i
$268$		−	0.763932i		−	0.0466646i
$269$	−5.54508	−	4.02874i	−0.338090	−	0.245637i	0.405766	−	0.913977i	$-0.367005\pi$
$269$	−5.54508	−	4.02874i	−0.338090	−	0.245637i	−0.743855	+	0.668341i	$0.767005\pi$
$270$		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	$0.298256\pi$
$272$	−2.26538	−	3.11803i	−0.137359	−	0.189059i
$273$	23.8949	−	7.76393i	1.44619	−	0.469895i
$274$	7.61803			0.460222
$275$		0			0
$276$	−4.47214			−0.269191
$277$	17.8783	−	5.80902i	1.07420	−	0.349030i	0.282080	−	0.959391i	$-0.408976\pi$
$277$	17.8783	−	5.80902i	1.07420	−	0.349030i	0.792124	+	0.610361i	$0.208976\pi$
$278$	13.4863	+	18.5623i	0.808855	+	1.11329i
$279$	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	$0.501033\pi$
$282$			0.763932i			0.0454915i
$283$	8.05748	−	11.0902i	0.478967	−	0.659242i	−0.499339	−	0.866407i	$-0.666424\pi$
$283$	8.05748	−	11.0902i	0.478967	−	0.659242i	0.978306	+	0.207165i	$0.0664236\pi$
$284$	−1.61803	+	4.97980i	−0.0960127	+	0.295497i
$285$		0			0
$286$	−2.14590	−	6.60440i	−0.126890	−	0.390526i
$287$	−15.3884	−	5.00000i	−0.908350	−	0.295141i
$288$	4.75528	+	1.54508i	0.280208	+	0.0910450i
$289$	0.663119	+	2.04087i	0.0390070	+	0.120051i
$290$		0			0
$291$	0.663119	−	2.04087i	0.0388727	−	0.119638i
$292$	−4.75528	+	6.54508i	−0.278282	+	0.383022i
$293$		−	20.7984i		−	1.21505i	−0.794299	−	0.607527i	$-0.792162\pi$
$293$		−	20.7984i		−	1.21505i	0.794299	−	0.607527i	$-0.207838\pi$
$294$	10.5172	+	7.64121i	0.613377	+	0.445644i
$295$		0			0
$296$	−7.50000	+	5.44907i	−0.435929	+	0.316721i
$297$	−0.726543	−	1.00000i	−0.0421583	−	0.0580259i
$298$	17.9313	−	5.82624i	1.03873	−	0.337505i
$299$	−25.1246			−1.45299
$300$		0			0
$301$	−34.4721			−1.98694
$302$	7.15942	−	2.32624i	0.411979	−	0.133860i
$303$	−2.09387	−	2.88197i	−0.120290	−	0.165565i
$304$	−1.00000	+	0.726543i	−0.0573539	+	0.0416701i
$305$		0			0
$306$	−3.11803	−	2.26538i	−0.178246	−	0.129503i
$307$		−	32.6525i		−	1.86358i	−0.363004	−	0.931788i	$-0.618249\pi$
$307$		−	32.6525i		−	1.86358i	0.363004	−	0.931788i	$-0.381751\pi$
$308$	−3.24920	+	4.47214i	−0.185140	+	0.254824i
$309$	−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	$0.732572\pi$
$312$	16.0292	+	5.20820i	0.907475	+	0.294856i
$313$	−0.449028	−	0.145898i	−0.0253806	−	0.00824664i	0.296299	−	0.955095i	$-0.404247\pi$
$313$	−0.449028	−	0.145898i	−0.0253806	−	0.00824664i	−0.321680	+	0.946849i	$0.604247\pi$
$314$	−3.33688	−	10.2699i	−0.188311	−	0.579562i
$315$		0			0
$316$		0			0
$317$	−16.9475	+	23.3262i	−0.951867	+	1.31013i	−0.00117338	+	0.999999i	$0.500373\pi$
$317$	−16.9475	+	23.3262i	−0.951867	+	1.31013i	−0.950693	+	0.310133i	$0.899627\pi$
$318$			3.61803i			0.202889i
$319$	−6.61803	−	4.80828i	−0.370539	−	0.269212i
$320$		0			0
$321$	−6.09017	+	4.42477i	−0.339920	+	0.246966i
$322$	−11.7557	−	16.1803i	−0.655120	−	0.901695i
$323$	−4.53077	+	1.47214i	−0.252099	+	0.0819118i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−14.9443			−0.827687
$327$	−7.52270	+	2.44427i	−0.416006	+	0.135169i
$328$	−6.37988	−	8.78115i	−0.352270	−	0.484858i
$329$	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	$0.638877\pi$
$332$			12.4721i			0.684497i
$333$	−1.81636	+	2.50000i	−0.0995357	+	0.136999i
$334$	−1.05573	+	3.24920i	−0.0577669	+	0.177788i
$335$		0			0
$336$	1.38197	+	4.25325i	0.0753924	+	0.232034i
$337$	−2.80017	−	0.909830i	−0.152535	−	0.0495616i	0.231754	−	0.972774i	$-0.425553\pi$
$337$	−2.80017	−	0.909830i	−0.152535	−	0.0495616i	−0.384289	+	0.923213i	$0.625553\pi$
$338$	17.6538	+	5.73607i	0.960240	+	0.312001i
$339$	−5.66312	−	17.4293i	−0.307578	−	0.946629i
$340$		0			0
$341$	−1.05573	+	3.24920i	−0.0571709	+	0.175954i
$342$	−0.726543	+	1.00000i	−0.0392869	+	0.0540738i
$343$		−	26.8328i		−	1.44884i
$344$	−18.7082	−	13.5923i	−1.00868	−	0.732848i
$345$		0			0
$346$	−17.0623	+	12.3965i	−0.917275	+	0.666439i
$347$	−11.9272	−	16.4164i	−0.640287	−	0.881279i	0.358344	−	0.933590i	$-0.383341\pi$
$347$	−11.9272	−	16.4164i	−0.640287	−	0.881279i	−0.998631	+	0.0523106i	$0.983341\pi$
$348$	6.29412	−	2.04508i	0.337400	−	0.109628i
$349$	4.03444			0.215959			0.107979	−	0.994153i	$-0.465562\pi$
$349$	4.03444			0.215959			0.107979	+	0.994153i	$0.465562\pi$
$350$		0			0
$351$	5.61803			0.299868
$352$	−5.87785	+	1.90983i	−0.313291	+	0.101794i
$353$	−8.44100	−	11.6180i	−0.449269	−	0.618366i	0.522971	−	0.852350i	$-0.324823\pi$
$353$	−8.44100	−	11.6180i	−0.449269	−	0.618366i	−0.972240	+	0.233985i	$0.924823\pi$
$354$	−3.23607	+	2.35114i	−0.171995	+	0.124962i
$355$		0			0
$356$	4.35410	+	3.16344i	0.230767	+	0.167662i
$357$			17.2361i			0.912229i
$358$	−9.51057	+	13.0902i	−0.502649	+	0.691837i
$359$	11.5623	−	35.5851i	0.610235	−	1.87811i	0.154507	−	0.987992i	$-0.450621\pi$
$359$	11.5623	−	35.5851i	0.610235	−	1.87811i	0.455728	−	0.890119i	$-0.349379\pi$
$360$		0			0
$361$	−5.39919	−	16.6170i	−0.284168	−	0.874578i
$362$	−14.0741	−	4.57295i	−0.739718	−	0.240349i
$363$	−9.00854	−	2.92705i	−0.472826	−	0.153630i
$364$	−7.76393	−	23.8949i	−0.406941	−	1.25243i
$365$		0			0
$366$	0.500000	−	1.53884i	0.0261354	−	0.0804365i
$367$	3.52671	−	4.85410i	0.184093	−	0.253382i	−0.706989	−	0.707224i	$-0.749947\pi$
$367$	3.52671	−	4.85410i	0.184093	−	0.253382i	0.891082	+	0.453842i	$0.149947\pi$
$368$		−	4.47214i		−	0.233126i
$369$	−2.92705	−	2.12663i	−0.152376	−	0.110708i
$370$		0			0
$371$	13.0902	−	9.51057i	0.679608	−	0.493764i
$372$	−1.62460	−	2.23607i	−0.0842315	−	0.115935i
$373$	−2.45714	+	0.798374i	−0.127226	+	0.0413382i	−0.371938	−	0.928258i	$-0.621307\pi$
$373$	−2.45714	+	0.798374i	−0.127226	+	0.0413382i	0.244712	+	0.969596i	$0.421307\pi$
$374$	4.76393			0.246337
$375$		0			0
$376$	2.29180			0.118190
$377$	35.3606	−	11.4894i	1.82116	−	0.591732i
$378$	2.62866	+	3.61803i	0.135203	+	0.186092i
$379$	−2.76393	+	2.00811i	−0.141974	+	0.103150i	−0.656505	−	0.754322i	$-0.727966\pi$
$379$	−2.76393	+	2.00811i	−0.141974	+	0.103150i	0.514531	+	0.857472i	$0.327966\pi$
$380$		0			0
$381$	3.00000	+	2.17963i	0.153695	+	0.111666i
$382$		−	6.65248i		−	0.340370i
$383$	−19.2986	+	26.5623i	−0.986115	+	1.35727i	−0.0526453	+	0.998613i	$0.516765\pi$
$383$	−19.2986	+	26.5623i	−0.986115	+	1.35727i	−0.933469	+	0.358657i	$0.883235\pi$
$384$	0.927051	−	2.85317i	0.0473084	−	0.145600i
$385$		0			0
$386$	7.20820	+	22.1846i	0.366888	+	1.12916i
$387$	−7.33094	−	2.38197i	−0.372652	−	0.121082i
$388$	−2.04087	−	0.663119i	−0.103609	−	0.0336648i
$389$	8.00658	+	24.6417i	0.405950	+	1.24938i	0.920100	+	0.391684i	$0.128107\pi$
$389$	8.00658	+	24.6417i	0.405950	+	1.24938i	−0.514150	+	0.857700i	$0.671893\pi$
$390$		0			0
$391$	5.32624	−	16.3925i	0.269359	−	0.829003i
$392$	22.9236	−	31.5517i	1.15782	−	1.59360i
$393$		−	8.18034i		−	0.412644i
$394$	6.16312	+	4.47777i	0.310493	+	0.225587i
$395$		0			0
$396$	−1.00000	+	0.726543i	−0.0502519	+	0.0365101i
$397$	−4.08174	−	5.61803i	−0.204857	−	0.281961i	0.694210	−	0.719772i	$-0.255754\pi$
$397$	−4.08174	−	5.61803i	−0.204857	−	0.281961i	−0.899067	+	0.437811i	$0.855754\pi$
$398$	−12.0332	+	3.90983i	−0.603171	+	0.195982i
$399$	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	$0.689418\pi$
$402$	0.726543	−	0.236068i	0.0362366	−	0.0117740i
$403$	−9.12705	−	12.5623i	−0.454651	−	0.625773i
$404$	−2.88197	+	2.09387i	−0.143383	+	0.104174i
$405$		0			0
$406$	23.9443	+	17.3965i	1.18833	+	0.863375i
$407$		−	3.81966i		−	0.189334i
$408$	−6.79615	+	9.35410i	−0.336460	+	0.463097i
$409$	−0.371323	+	1.14281i	−0.0183607	+	0.0565085i	−0.959817	−	0.280626i	$-0.909458\pi$
$409$	−0.371323	+	1.14281i	−0.0183607	+	0.0565085i	0.941456	+	0.337135i	$0.109458\pi$
$410$		0			0
$411$	−2.35410	−	7.24518i	−0.116119	−	0.357378i
$412$	3.07768	+	1.00000i	0.151627	+	0.0492665i
$413$	17.0130	+	5.52786i	0.837156	+	0.272008i
$414$	−1.38197	−	4.25325i	−0.0679199	−	0.209036i
$415$		0			0
$416$	8.68034	−	26.7153i	0.425589	−	1.30983i
$417$	13.4863	−	18.5623i	0.660427	−	0.909000i
$418$		−	1.52786i		−	0.0747303i
$419$	12.1803	+	8.84953i	0.595049	+	0.432328i	0.844118	−	0.536158i	$-0.180125\pi$
$419$	12.1803	+	8.84953i	0.595049	+	0.432328i	−0.249069	+	0.968486i	$0.580125\pi$
$420$		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	$0.559318\pi$
$422$	10.5146	+	14.4721i	0.511844	+	0.704493i
$423$	0.726543	−	0.236068i	0.0353257	−	0.0114780i
$424$	10.8541			0.527122
$425$		0			0
$426$	−5.23607			−0.253688
$427$	−6.88191	+	2.23607i	−0.333039	+	0.108211i
$428$	4.42477	+	6.09017i	0.213879	+	0.294379i
$429$	−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	$0.865711\pi$
$432$			1.00000i			0.0481125i
$433$	−12.9188	+	17.7812i	−0.620836	+	0.854508i	−0.997413	−	0.0718775i	$-0.977101\pi$
$433$	−12.9188	+	17.7812i	−0.620836	+	0.854508i	0.376577	+	0.926385i	$0.377101\pi$
$434$	3.81966	−	11.7557i	0.183350	−	0.564292i
$435$		0			0
$436$	2.44427	+	7.52270i	0.117059	+	0.360272i
$437$	−5.25731	−	1.70820i	−0.251491	−	0.0817145i
$438$	−7.69421	−	2.50000i	−0.367644	−	0.119455i
$439$	−5.00000	−	15.3884i	−0.238637	−	0.734449i	−0.996618	−	0.0821726i	$-0.973814\pi$
$439$	−5.00000	−	15.3884i	−0.238637	−	0.734449i	0.757981	−	0.652276i	$-0.226186\pi$
$440$		0			0
$441$	4.01722	−	12.3637i	0.191296	−	0.588749i
$442$	−12.7270	+	17.5172i	−0.605362	+	0.833209i
$443$		−	35.2361i		−	1.67412i	−0.547114	−	0.837058i	$-0.684274\pi$
$443$		−	35.2361i		−	1.67412i	0.547114	−	0.837058i	$-0.315726\pi$
$444$	2.50000	+	1.81636i	0.118645	+	0.0862005i
$445$		0			0
$446$	−6.61803	+	4.80828i	−0.313373	+	0.227679i
$447$	−11.0822	−	15.2533i	−0.524168	−	0.721456i
$448$	29.7728	−	9.67376i	1.40663	−	0.457042i
$449$	−16.7984			−0.792764			−0.396382	−	0.918086i	$-0.629734\pi$
$449$	−16.7984			−0.792764			−0.396382	+	0.918086i	$0.629734\pi$
$450$		0			0
$451$	4.47214			0.210585
$452$	−17.4293	+	5.66312i	−0.819805	+	0.266371i
$453$	−4.42477	−	6.09017i	−0.207894	−	0.286141i
$454$	−16.1803	+	11.7557i	−0.759381	+	0.551723i
$455$		0			0
$456$	3.00000	+	2.17963i	0.140488	+	0.102070i
$457$			22.3607i			1.04599i	0.852336	+	0.522994i	$0.175185\pi$
$457$			22.3607i			1.04599i	−0.852336	+	0.522994i	$0.824815\pi$
$458$	12.9188	−	17.7812i	0.603654	−	0.830859i
$459$	−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	$-0.376662\pi$
$462$	−5.25731	−	1.70820i	−0.244592	−	0.0794728i
$463$	17.8456	+	5.79837i	0.829353	+	0.269473i	0.692773	−	0.721156i	$-0.256389\pi$
$463$	17.8456	+	5.79837i	0.829353	+	0.269473i	0.136580	+	0.990629i	$0.456389\pi$
$464$	2.04508	+	6.29412i	0.0949407	+	0.292197i
$465$		0			0
$466$	3.82624	−	11.7759i	0.177247	−	0.545510i
$467$	−16.5640	+	22.7984i	−0.766490	+	1.05498i	0.230156	+	0.973154i	$0.426076\pi$
$467$	−16.5640	+	22.7984i	−0.766490	+	1.05498i	−0.996646	+	0.0818293i	$0.973924\pi$
$468$		−	5.61803i		−	0.259694i
$469$	−2.76393	−	2.00811i	−0.127627	−	0.0927261i
$470$		0			0
$471$	−8.73607	+	6.34712i	−0.402537	+	0.292460i
$472$	7.05342	+	9.70820i	0.324660	+	0.446856i
$473$	9.06154	−	2.94427i	0.416650	−	0.135378i
$474$		0			0
$475$		0			0
$476$	17.2361			0.790014
$477$	3.44095	−	1.11803i	0.157550	−	0.0511913i
$478$	14.6619	+	20.1803i	0.670619	+	0.923027i
$479$	15.3262	−	11.1352i	0.700274	−	0.508779i	−0.179748	−	0.983713i	$-0.557528\pi$
$479$	15.3262	−	11.1352i	0.700274	−	0.508779i	0.880021	+	0.474934i	$0.157528\pi$
$480$		0			0
$481$	14.0451	+	10.2044i	0.640401	+	0.465278i
$482$		−	28.0344i		−	1.27693i
$483$	−11.7557	+	16.1803i	−0.534903	+	0.736231i
$484$	−2.92705	+	9.00854i	−0.133048	+	0.409479i
$485$		0			0
$486$	0.309017	+	0.951057i	0.0140173	+	0.0431408i
$487$	−9.23305	−	3.00000i	−0.418389	−	0.135943i	0.0922541	−	0.995736i	$-0.470593\pi$
$487$	−9.23305	−	3.00000i	−0.418389	−	0.135943i	−0.510644	+	0.859793i	$0.670593\pi$
$488$	−4.61653	−	1.50000i	−0.208980	−	0.0679018i
$489$	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	$0.0575797\pi$
$492$	−2.12663	+	2.92705i	−0.0958758	+	0.131962i
$493$			25.5066i			1.14876i
$494$	5.61803	+	4.08174i	0.252767	+	0.183646i
$495$		0			0
$496$	2.23607	−	1.62460i	0.100402	−	0.0729466i
$497$	13.7638	+	18.9443i	0.617392	+	0.849767i
$498$	−11.8617	+	3.85410i	−0.531536	+	0.172706i
$499$	6.00000			0.268597			0.134298	−	0.990941i	$-0.457122\pi$
$499$	6.00000			0.268597			0.134298	+	0.990941i	$0.457122\pi$
$500$		0			0
$501$	3.41641			0.152634
$502$	−8.61251	+	2.79837i	−0.384395	+	0.124898i
$503$	−5.04531	−	6.94427i	−0.224959	−	0.309630i	0.681586	−	0.731738i	$-0.261290\pi$
$503$	−5.04531	−	6.94427i	−0.224959	−	0.309630i	−0.906546	+	0.422108i	$0.861290\pi$
$504$	10.8541	−	7.88597i	0.483480	−	0.351269i
$505$		0			0
$506$	4.47214	+	3.24920i	0.198811	+	0.144444i
$507$		−	18.5623i		−	0.824381i
$508$	2.17963	−	3.00000i	0.0967053	−	0.133103i
$509$	−6.22542	+	19.1599i	−0.275937	+	0.849247i	0.713033	+	0.701131i	$0.247321\pi$
$509$	−6.22542	+	19.1599i	−0.275937	+	0.849247i	−0.988970	+	0.148116i	$0.952679\pi$
$510$		0			0
$511$	11.1803	+	34.4095i	0.494589	+	1.52219i
$512$	10.4616	+	3.39919i	0.462343	+	0.150224i
$513$	1.17557	+	0.381966i	0.0519027	+	0.0168642i
$514$	−3.64590	−	11.2209i	−0.160814	−	0.494934i
$515$		0			0
$516$	−2.38197	+	7.33094i	−0.104860	+	0.322727i
$517$	−0.555029	+	0.763932i	−0.0244102	+	0.0335977i
$518$			13.8197i			0.607201i
$519$	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	$0.0982595\pi$
$522$	3.88998	+	5.35410i	0.170260	+	0.234343i
$523$	24.4500	−	7.94427i	1.06912	−	0.347379i	0.278976	−	0.960298i	$-0.410005\pi$
$523$	24.4500	−	7.94427i	1.06912	−	0.347379i	0.790146	+	0.612919i	$0.210005\pi$
$524$	−8.18034			−0.357360
$525$		0			0
$526$	−23.8885			−1.04159
$527$	10.1311	−	3.29180i	0.441318	−	0.143393i
$528$	−0.726543	−	1.00000i	−0.0316187	−	0.0435194i
$529$	−2.42705	+	1.76336i	−0.105524	+	0.0766676i
$530$		0			0
$531$	3.23607	+	2.35114i	0.140433	+	0.102031i
$532$		−	5.52786i		−	0.239663i
$533$	−11.9475	+	16.4443i	−0.517502	+	0.712280i
$534$	−1.66312	+	5.11855i	−0.0719702	+	0.221501i
$535$		0			0
$536$	−0.708204	−	2.17963i	−0.0305898	−	0.0941456i
$537$	15.3884	+	5.00000i	0.664059	+	0.215766i
$538$	−6.51864	−	2.11803i	−0.281038	−	0.0913149i
$539$	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	$0.961005\pi$
$542$	0.106001	−	0.145898i	0.00455314	−	0.00626686i
$543$			14.7984i			0.635059i
$544$	15.5902	+	11.3269i	0.668423	+	0.485638i
$545$		0			0
$546$	20.3262	−	14.7679i	0.869883	−	0.632007i
$547$	24.8990	+	34.2705i	1.06460	+	1.46530i	0.875422	+	0.483359i	$0.160583\pi$
$547$	24.8990	+	34.2705i	1.06460	+	1.46530i	0.189181	+	0.981942i	$0.439417\pi$
$548$	−7.24518	+	2.35410i	−0.309499	+	0.100562i
$549$	−1.61803			−0.0690560
$550$		0			0
$551$	8.18034			0.348494
$552$	−12.7598	+	4.14590i	−0.543092	+	0.176461i
$553$		0			0
$554$	15.2082	−	11.0494i	0.646135	−	0.469444i
$555$		0			0
$556$	−18.5623	−	13.4863i	−0.787217	−	0.571947i
$557$			11.2705i			0.477547i	0.971075	+	0.238773i	$0.0767453\pi$
$557$			11.2705i			0.477547i	−0.971075	+	0.238773i	$0.923255\pi$
$558$	1.62460	−	2.23607i	0.0687747	−	0.0946603i
$559$	−13.3820	+	41.1855i	−0.565997	+	1.74196i
$560$		0			0
$561$	−1.47214	−	4.53077i	−0.0621536	−	0.191289i
$562$	18.6579	+	6.06231i	0.787034	+	0.255723i
$563$	−25.1765	−	8.18034i	−1.06106	−	0.344760i	−0.274062	−	0.961712i	$-0.588367\pi$
$563$	−25.1765	−	8.18034i	−1.06106	−	0.344760i	−0.787001	+	0.616952i	$0.788367\pi$
$564$	−0.236068	−	0.726543i	−0.00994026	−	0.0305930i
$565$		0			0
$566$	4.23607	−	13.0373i	0.178055	−	0.547998i
$567$	2.62866	−	3.61803i	0.110393	−	0.151943i
$568$			15.7082i			0.659102i
$569$	2.64590	+	1.92236i	0.110922	+	0.0805894i	0.641863	−	0.766819i	$-0.278162\pi$
$569$	2.64590	+	1.92236i	0.110922	+	0.0805894i	−0.530942	+	0.847408i	$0.678162\pi$
$570$		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	$0.185918\pi$
$572$	4.08174	+	5.61803i	0.170666	+	0.234902i
$573$	−6.32688	+	2.05573i	−0.264309	+	0.0858793i
$574$	−16.1803			−0.675354
$575$		0			0
$576$	7.00000			0.291667
$577$	−12.4167	+	4.03444i	−0.516915	+	0.167956i	−0.555845	−	0.831286i	$-0.687605\pi$
$577$	−12.4167	+	4.03444i	−0.516915	+	0.167956i	0.0389296	+	0.999242i	$0.487605\pi$
$578$	1.26133	+	1.73607i	0.0524643	+	0.0722109i
$579$	18.8713	−	13.7108i	0.784265	−	0.569802i
$580$		0			0
$581$	45.1246	+	32.7849i	1.87208	+	1.36015i
$582$		−	2.14590i		−	0.0889503i
$583$	−2.62866	+	3.61803i	−0.108868	+	0.149844i
$584$	−7.50000	+	23.0826i	−0.310352	+	0.955166i
$585$		0			0
$586$	−6.42705	−	19.7804i	−0.265499	−	0.817122i
$587$	39.3893	+	12.7984i	1.62577	+	0.528245i	0.973294	−	0.229562i	$-0.0737294\pi$
$587$	39.3893	+	12.7984i	1.62577	+	0.528245i	0.652478	+	0.757807i	$0.273729\pi$
$588$	−12.3637	−	4.01722i	−0.509872	−	0.165667i
$589$	−1.05573	−	3.24920i	−0.0435005	−	0.133881i
$590$		0			0
$591$	2.35410	−	7.24518i	0.0968348	−	0.298027i
$592$	−1.81636	+	2.50000i	−0.0746518	+	0.102749i
$593$			9.74265i			0.400083i	0.979787	+	0.200041i	$0.0641076\pi$
$593$			9.74265i			0.400083i	−0.979787	+	0.200041i	$0.935892\pi$
$594$	−1.00000	−	0.726543i	−0.0410305	−	0.0298104i
$595$		0			0
$596$	−15.2533	+	11.0822i	−0.624799	+	0.453943i
$597$	7.43694	+	10.2361i	0.304374	+	0.418934i
$598$	−23.8949	+	7.76393i	−0.977136	+	0.317491i
$599$	3.52786			0.144145			0.0720723	−	0.997399i	$-0.477039\pi$
$599$	3.52786			0.144145			0.0720723	+	0.997399i	$0.477039\pi$
$600$		0			0
$601$	−8.67376			−0.353810			−0.176905	−	0.984228i	$-0.556609\pi$
$601$	−8.67376			−0.353810			−0.176905	+	0.984228i	$0.556609\pi$
$602$	−32.7849	+	10.6525i	−1.33621	+	0.434163i
$603$	−0.449028	−	0.618034i	−0.0182858	−	0.0251683i
$604$	−6.09017	+	4.42477i	−0.247806	+	0.180041i
$605$		0			0
$606$	−2.88197	−	2.09387i	−0.117072	−	0.0850577i
$607$			34.7639i			1.41102i	0.708698	+	0.705512i	$0.249283\pi$
$607$			34.7639i			1.41102i	−0.708698	+	0.705512i	$0.750717\pi$
$608$	3.63271	−	5.00000i	0.147326	−	0.202777i
$609$	9.14590	−	28.1482i	0.370610	−	1.14062i
$610$		0			0
$611$	−1.32624	−	4.08174i	−0.0536538	−	0.165130i
$612$	3.66547	+	1.19098i	0.148168	+	0.0481426i
$613$	1.42033	+	0.461493i	0.0573665	+	0.0186395i	0.337560	−	0.941304i	$-0.390399\pi$
$613$	1.42033	+	0.461493i	0.0573665	+	0.0186395i	−0.280193	+	0.959944i	$0.590399\pi$
$614$	−10.0902	−	31.0543i	−0.407206	−	1.25325i
$615$		0			0
$616$	−5.12461	+	15.7719i	−0.206476	+	0.635469i
$617$	11.7432	−	16.1631i	0.472763	−	0.650703i	−0.504331	−	0.863510i	$-0.668261\pi$
$617$	11.7432	−	16.1631i	0.472763	−	0.650703i	0.977094	+	0.212808i	$0.0682608\pi$
$618$			3.23607i			0.130174i
$619$	−13.2361	−	9.61657i	−0.532002	−	0.386522i	0.289104	−	0.957298i	$-0.406643\pi$
$619$	−13.2361	−	9.61657i	−0.532002	−	0.386522i	−0.821106	+	0.570775i	$0.806643\pi$
$620$		0			0
$621$	−3.61803	+	2.62866i	−0.145187	+	0.105484i
$622$	10.4086	+	14.3262i	0.417348	+	0.574430i
$623$	22.8909	−	7.43769i	0.917103	−	0.297985i
$624$	5.61803			0.224901
$625$		0			0
$626$	−0.472136			−0.0188703
$627$	−1.45309	+	0.472136i	−0.0580306	+	0.0188553i
$628$	6.34712	+	8.73607i	0.253278	+	0.348607i
$629$	−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
$633$	10.5146	−	14.4721i	0.417919	−	0.575216i
$634$	−8.90983	+	27.4216i	−0.353855	+	1.08905i
$635$		0			0
$636$	−1.11803	−	3.44095i	−0.0443329	−	0.136443i
$637$	−69.4599	−	22.5689i	−2.75210	−	0.894212i
$638$	−7.77997	−	2.52786i	−0.308012	−	0.100079i
$639$	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	$-0.0365073\pi$
$642$	−4.42477	+	6.09017i	−0.174632	+	0.240360i
$643$		−	21.8885i		−	0.863200i	−0.902065	−	0.431600i	$-0.857949\pi$
$643$		−	21.8885i		−	0.863200i	0.902065	−	0.431600i	$-0.142051\pi$
$644$	16.1803	+	11.7557i	0.637595	+	0.463240i
$645$		0			0
$646$	−3.85410	+	2.80017i	−0.151638	+	0.110171i
$647$	−20.1967	−	27.7984i	−0.794014	−	1.09287i	−0.993597	−	0.112986i	$-0.963959\pi$
$647$	−20.1967	−	27.7984i	−0.794014	−	1.09287i	0.199582	−	0.979881i	$-0.436041\pi$
$648$	2.85317	−	0.927051i	0.112083	−	0.0364180i
$649$	−4.94427			−0.194080
$650$		0			0
$651$	−12.3607			−0.484453
$652$	14.2128	−	4.61803i	0.556618	−	0.180856i
$653$	24.7477	+	34.0623i	0.968453	+	1.33296i	0.942825	+	0.333289i	$0.108159\pi$
$653$	24.7477	+	34.0623i	0.968453	+	1.33296i	0.0256283	+	0.999672i	$0.491841\pi$
$654$	−6.39919	+	4.64928i	−0.250228	+	0.181801i
$655$		0			0
$656$	−2.92705	−	2.12663i	−0.114282	−	0.0830308i
$657$			8.09017i			0.315628i
$658$	2.00811	−	2.76393i	0.0782844	−	0.107749i
$659$	10.3262	−	31.7809i	0.402253	−	1.23801i	−0.520914	−	0.853609i	$-0.674409\pi$
$659$	10.3262	−	31.7809i	0.402253	−	1.23801i	0.923167	−	0.384399i	$-0.125591\pi$
$660$		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	$0.908769\pi$
$662$	6.60440	+	2.14590i	0.256687	+	0.0834027i
$663$	20.5927	+	6.69098i	0.799755	+	0.259856i
$664$	11.5623	+	35.5851i	0.448704	+	1.38097i
$665$		0			0
$666$	−0.954915	+	2.93893i	−0.0370022	+	0.113881i
$667$	−17.3965	+	23.9443i	−0.673596	+	0.927126i
$668$		−	3.41641i		−	0.132185i
$669$	6.61803	+	4.80828i	0.255868	+	0.185899i
$670$		0			0
$671$	1.61803	−	1.17557i	0.0624635	−	0.0453824i
$672$	−13.1433	−	18.0902i	−0.507013	−	0.697843i
$673$	−4.94704	+	1.60739i	−0.190694	+	0.0619604i	−0.402807	−	0.915285i	$-0.631966\pi$
$673$	−4.94704	+	1.60739i	−0.190694	+	0.0619604i	0.212113	+	0.977245i	$0.431966\pi$
$674$	−2.94427			−0.113409
$675$		0			0
$676$	−18.5623			−0.713935
$677$	10.0656	−	3.27051i	0.386852	−	0.125696i	−0.109132	−	0.994027i	$-0.534807\pi$
$677$	10.0656	−	3.27051i	0.386852	−	0.125696i	0.495985	+	0.868331i	$0.334807\pi$
$678$	−10.7719	−	14.8262i	−0.413692	−	0.569398i
$679$	−7.76393	+	5.64083i	−0.297952	+	0.216475i
$680$		0			0
$681$	16.1803	+	11.7557i	0.620032	+	0.450480i
$682$			3.41641i			0.130821i
$683$	−11.4127	+	15.7082i	−0.436694	+	0.601058i	−0.969473	−	0.245196i	$-0.921148\pi$
$683$	−11.4127	+	15.7082i	−0.436694	+	0.601058i	0.532779	+	0.846254i	$0.321148\pi$
$684$	0.381966	−	1.17557i	0.0146048	−	0.0449491i
$685$		0			0
$686$	−8.29180	−	25.5195i	−0.316582	−	0.974340i
$687$	−20.9030	−	6.79180i	−0.797499	−	0.259123i
$688$	−7.33094	−	2.38197i	−0.279489	−	0.0908116i
$689$	−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	$0.996698\pi$
$692$	12.3965	−	17.0623i	0.471244	−	0.648612i
$693$			5.52786i			0.209986i
$694$	−16.4164	−	11.9272i	−0.623158	−	0.452751i
$695$		0			0
$696$	16.0623	−	11.6699i	0.608840	−	0.442348i
$697$	−8.19624	−	11.2812i	−0.310455	−	0.427304i
$698$	3.83698	−	1.24671i	0.145232	−	0.0471887i
$699$	−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	$0.373058\pi$
$702$	5.34307	−	1.73607i	0.201661	−	0.0655237i
$703$	2.24514	+	3.09017i	0.0846771	+	0.116548i
$704$	−7.00000	+	5.08580i	−0.263822	+	0.191678i
$705$		0			0
$706$	−11.6180	−	8.44100i	−0.437250	−	0.317681i
$707$			15.9311i			0.599151i
$708$	2.35114	−	3.23607i	0.0883613	−	0.121619i
$709$	12.4443	−	38.2995i	0.467354	−	1.43837i	−0.388643	−	0.921389i	$-0.627056\pi$
$709$	12.4443	−	38.2995i	0.467354	−	1.43837i	0.855997	−	0.516981i	$-0.172944\pi$
$710$		0			0
$711$		0			0
$712$	15.3557	+	4.98936i	0.575478	+	0.186984i
$713$	11.7557	+	3.81966i	0.440255	+	0.143047i
$714$	5.32624	+	16.3925i	0.199329	+	0.613473i
$715$		0			0
$716$	5.00000	−	15.3884i	0.186859	−	0.575092i
$717$	14.6619	−	20.1803i	0.547558	−	0.753649i
$718$		−	37.4164i		−	1.39637i
$719$	−0.0901699	−	0.0655123i	−0.00336277	−	0.00244320i	0.586103	−	0.810237i	$-0.300662\pi$
$719$	−0.0901699	−	0.0655123i	−0.00336277	−	0.00244320i	−0.589465	+	0.807794i	$0.700662\pi$
$720$		0			0
$721$	11.7082	−	8.50651i	0.436036	−	0.316799i
$722$	−10.2699	−	14.1353i	−0.382205	−	0.526060i
$723$	−26.6623	+	8.66312i	−0.991583	+	0.322185i
$724$	14.7984			0.549977
$725$		0			0
$726$	−9.47214			−0.351544
$727$	44.3691	−	14.4164i	1.64556	−	0.534675i	0.667789	−	0.744350i	$-0.267241\pi$
$727$	44.3691	−	14.4164i	1.64556	−	0.534675i	0.977771	+	0.209675i	$0.0672407\pi$
$728$	−44.3036	−	60.9787i	−1.64200	−	2.26002i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$		0			0
$731$	−24.0344	−	17.4620i	−0.888946	−	0.645857i
$732$			1.61803i			0.0598043i
$733$	17.2905	−	23.7984i	0.638640	−	0.879013i	−0.359902	−	0.932990i	$-0.617190\pi$
$733$	17.2905	−	23.7984i	0.638640	−	0.879013i	0.998542	+	0.0539772i	$0.0171898\pi$
$734$	1.85410	−	5.70634i	0.0684362	−	0.210625i
$735$		0			0
$736$	6.90983	+	21.2663i	0.254700	+	0.783885i
$737$	0.898056	+	0.291796i	0.0330803	+	0.0107484i
$738$	−3.44095	−	1.11803i	−0.126663	−	0.0411554i
$739$	−1.32624	−	4.08174i	−0.0487865	−	0.150149i	0.923696	−	0.383127i	$-0.125153\pi$
$739$	−1.32624	−	4.08174i	−0.0487865	−	0.150149i	−0.972482	+	0.232978i	$0.925153\pi$
$740$		0			0
$741$	2.14590	−	6.60440i	0.0788315	−	0.242619i
$742$	9.51057	−	13.0902i	0.349144	−	0.480555i
$743$			41.1246i			1.50872i	0.656463	+	0.754358i	$0.272052\pi$
$743$			41.1246i			1.50872i	−0.656463	+	0.754358i	$0.727948\pi$
$744$	−6.70820	−	4.87380i	−0.245935	−	0.178682i
$745$		0			0
$746$	−2.09017	+	1.51860i	−0.0765266	+	0.0555998i
$747$	7.33094	+	10.0902i	0.268225	+	0.369180i
$748$	−4.53077	+	1.47214i	−0.165661	+	0.0538266i
$749$	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	$0.266837\pi$
$752$	0.726543	−	0.236068i	0.0264943	−	0.00860851i
$753$	5.32282	+	7.32624i	0.193974	+	0.266983i
$754$	30.0795	−	21.8541i	1.09543	−	0.795878i
$755$		0			0
$756$	−3.61803	−	2.62866i	−0.131587	−	0.0956033i
$757$		−	29.6180i		−	1.07649i	−0.842790	−	0.538243i	$-0.819088\pi$
$757$		−	29.6180i		−	1.07649i	0.842790	−	0.538243i	$-0.180912\pi$
$758$	−2.00811	+	2.76393i	−0.0729380	+	0.100391i
$759$	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	$0.697762\pi$
$762$	3.52671	+	1.14590i	0.127759	+	0.0415115i
$763$	33.6425	+	10.9311i	1.21794	+	0.395733i
$764$	2.05573	+	6.32688i	0.0743736	+	0.228899i
$765$		0			0
$766$	−10.1459	+	31.2259i	−0.366586	+	1.12824i
$767$	13.2088	−	18.1803i	0.476942	−	0.656454i
$768$		−	17.0000i		−	0.613435i
$769$	−40.7426	−	29.6013i	−1.46922	−	1.06745i	−0.980840	−	0.194817i	$-0.937589\pi$
$769$	−40.7426	−	29.6013i	−1.46922	−	1.06745i	−0.488378	−	0.872632i	$-0.662411\pi$
$770$		0			0
$771$	−9.54508	+	6.93491i	−0.343758	+	0.249755i
$772$	−13.7108	−	18.8713i	−0.493463	−	0.679194i
$773$	−27.5074	+	8.93769i	−0.989372	+	0.321467i	−0.758611	−	0.651544i	$-0.774122\pi$
$773$	−27.5074	+	8.93769i	−0.989372	+	0.321467i	−0.230761	+	0.973010i	$0.574122\pi$
$774$	−7.70820			−0.277066
$775$		0			0
$776$	−6.43769			−0.231100
$777$	13.1433	−	4.27051i	0.471512	−	0.153204i
$778$	15.2294	+	20.9615i	0.546001	+	0.751506i
$779$	−3.61803	+	2.62866i	−0.129630	+	0.0941814i
$780$		0			0
$781$	−5.23607	−	3.80423i	−0.187361	−	0.136126i
$782$		−	17.2361i		−	0.616361i
$783$	3.88998	−	5.35410i	0.139017	−	0.191340i
$784$	4.01722	−	12.3637i	0.143472	−	0.441562i
$785$		0			0
$786$	−2.52786	−	7.77997i	−0.0901659	−	0.277502i
$787$	13.4863	+	4.38197i	0.480735	+	0.156200i	0.539352	−	0.842080i	$-0.318669\pi$
$787$	13.4863	+	4.38197i	0.480735	+	0.156200i	−0.0586173	+	0.998281i	$0.518669\pi$
$788$	−7.24518	−	2.35410i	−0.258099	−	0.0838614i
$789$	7.38197	+	22.7194i	0.262805	+	0.808830i
$790$		0			0
$791$	−25.3262	+	77.9461i	−0.900497	+	2.77145i
$792$	−2.17963	+	3.00000i	−0.0774497	+	0.106600i
$793$			9.09017i			0.322801i
$794$	−5.61803	−	4.08174i	−0.199377	−	0.144856i
$795$		0			0
$796$	10.2361	−	7.43694i	0.362808	−	0.263595i
$797$	−28.8622	−	39.7254i	−1.02235	−	1.40715i	−0.910542	−	0.413417i	$-0.864335\pi$
$797$	−28.8622	−	39.7254i	−1.02235	−	1.40715i	−0.111810	−	0.993730i	$-0.535665\pi$
$798$	5.25731	−	1.70820i	0.186107	−	0.0604698i
$799$	2.94427			0.104161
$800$		0			0
$801$	5.38197			0.190162
$802$	−21.3520	+	6.93769i	−0.753966	+	0.244978i
$803$	−5.87785	−	8.09017i	−0.207425	−	0.285496i
$804$	−0.618034	+	0.449028i	−0.0217964	+	0.0158360i
$805$		0			0
$806$	−12.5623	−	9.12705i	−0.442488	−	0.321487i
$807$			6.85410i			0.241276i
$808$	−6.28161	+	8.64590i	−0.220986	+	0.304162i
$809$	−8.71885	+	26.8339i	−0.306538	+	0.943428i	0.672560	+	0.740042i	$0.265195\pi$
$809$	−8.71885	+	26.8339i	−0.306538	+	0.943428i	−0.979099	+	0.203386i	$0.934805\pi$
$810$		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	$0.873345\pi$
$812$	−28.1482	−	9.14590i	−0.987807	−	0.320958i
$813$	−0.171513	−	0.0557281i	−0.00601524	−	0.00195447i
$814$	−1.18034	−	3.63271i	−0.0413709	−	0.127327i
$815$		0			0
$816$	−1.19098	+	3.66547i	−0.0416927	+	0.128317i
$817$	−5.60034	+	7.70820i	−0.195931	+	0.269676i
$818$			1.20163i			0.0420139i
$819$	−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	$0.431122\pi$
$822$	−4.47777	−	6.16312i	−0.156180	−	0.214963i
$823$	18.2946	−	5.94427i	0.637709	−	0.207204i	0.0277222	−	0.999616i	$-0.491175\pi$
$823$	18.2946	−	5.94427i	0.637709	−	0.207204i	0.609987	+	0.792411i	$0.291175\pi$
$824$	9.70820			0.338201
$825$		0			0
$826$	17.8885			0.622422
$827$	−34.3035	+	11.1459i	−1.19285	+	0.387581i	−0.837126	−	0.547010i	$-0.815766\pi$
$827$	−34.3035	+	11.1459i	−1.19285	+	0.387581i	−0.355725	+	0.934591i	$0.615766\pi$
$828$	2.62866	+	3.61803i	0.0913521	+	0.125735i
$829$	9.30902	−	6.76340i	0.323316	−	0.234902i	−0.414273	−	0.910152i	$-0.635964\pi$
$829$	9.30902	−	6.76340i	0.323316	−	0.234902i	0.737589	+	0.675250i	$0.235964\pi$
$830$		0			0
$831$	−15.2082	−	11.0494i	−0.527567	−	0.383300i
$832$		−	39.3262i		−	1.36339i
$833$	29.4500	−	40.5344i	1.02038	−	1.40444i
$834$	7.09017	−	21.8213i	0.245513	−	0.755610i
$835$		0			0
$836$	0.472136	+	1.45309i	0.0163292	+	0.0502560i
$837$	−2.62866	−	0.854102i	−0.0908596	−	0.0295221i
$838$	14.3188	+	4.65248i	0.494636	+	0.160717i
$839$	−4.34752	−	13.3803i	−0.150093	−	0.461939i	0.847538	−	0.530735i	$-0.178084\pi$
$839$	−4.34752	−	13.3803i	−0.150093	−	0.461939i	−0.997631	+	0.0687961i	$0.978084\pi$
$840$		0			0
$841$	4.57295	−	14.0741i	0.157688	−	0.485313i
$842$	−17.5478	+	24.1525i	−0.604737	+	0.832349i
$843$		−	19.6180i		−	0.675681i
$844$	−14.4721	−	10.5146i	−0.498151	−	0.361928i
$845$		0			0
$846$	0.618034	−	0.449028i	0.0212484	−	0.0154379i
$847$	24.8990	+	34.2705i	0.855539	+	1.17755i
$848$	3.44095	−	1.11803i	0.118163	−	0.0383934i
$849$	−13.7082			−0.470464
$850$		0			0
$851$	−13.8197			−0.473732
$852$	4.97980	−	1.61803i	0.170605	−	0.0554329i
$853$	−13.6048	−	18.7254i	−0.465820	−	0.641146i	0.509883	−	0.860244i	$-0.329689\pi$
$853$	−13.6048	−	18.7254i	−0.465820	−	0.641146i	−0.975703	+	0.219097i	$0.929689\pi$
$854$	−5.85410	+	4.25325i	−0.200323	+	0.145543i
$855$		0			0
$856$	18.2705	+	13.2743i	0.624473	+	0.453706i
$857$			12.4721i			0.426040i	0.977048	+	0.213020i	$0.0683300\pi$
$857$			12.4721i			0.426040i	−0.977048	+	0.213020i	$0.931670\pi$
$858$	−4.08174	+	5.61803i	−0.139348	+	0.191797i
$859$	7.23607	−	22.2703i	0.246891	−	0.759854i	−0.748428	−	0.663216i	$-0.769191\pi$
$859$	7.23607	−	22.2703i	0.246891	−	0.759854i	0.995320	−	0.0966379i	$-0.0308089\pi$
$860$		0			0
$861$	5.00000	+	15.3884i	0.170400	+	0.524436i
$862$	−19.6417	−	6.38197i	−0.668998	−	0.217371i
$863$	10.3431	+	3.36068i	0.352084	+	0.114399i	0.479719	−	0.877422i	$-0.340739\pi$
$863$	10.3431	+	3.36068i	0.352084	+	0.114399i	−0.127635	+	0.991821i	$0.540739\pi$
$864$	−1.54508	−	4.75528i	−0.0525649	−	0.161778i
$865$		0			0
$866$	−6.79180	+	20.9030i	−0.230795	+	0.710313i
$867$	1.26133	−	1.73607i	0.0428369	−	0.0589600i
$868$			12.3607i			0.419549i
$869$		0			0
$870$		0			0
$871$	−3.47214	+	2.52265i	−0.117649	+	0.0854769i
$872$	13.9478	+	19.1976i	0.472334	+	0.650111i
$873$	−2.04087	+	0.663119i	−0.0690730	+	0.0224432i
$874$	−5.52786			−0.186983
$875$		0			0
$876$	8.09017			0.273342
$877$	−31.5891	+	10.2639i	−1.06669	+	0.346588i	−0.789197	−	0.614140i	$-0.789503\pi$
$877$	−31.5891	+	10.2639i	−1.06669	+	0.346588i	−0.277492	+	0.960728i	$0.589503\pi$
$878$	−9.51057	−	13.0902i	−0.320966	−	0.441772i
$879$	−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	$0.957428\pi$
$882$		−	13.0000i		−	0.437733i
$883$	13.0373	−	17.9443i	0.438739	−	0.603873i	−0.531192	−	0.847251i	$-0.678256\pi$
$883$	13.0373	−	17.9443i	0.438739	−	0.603873i	0.969931	+	0.243379i	$0.0782557\pi$
$884$	6.69098	−	20.5927i	0.225042	−	0.692608i
$885$		0			0
$886$	−10.8885	−	33.5115i	−0.365808	−	1.12584i
$887$	21.9928	+	7.14590i	0.738446	+	0.239936i	0.654002	−	0.756492i	$-0.273089\pi$
$887$	21.9928	+	7.14590i	0.738446	+	0.239936i	0.0844440	+	0.996428i	$0.473089\pi$
$888$	8.81678	+	2.86475i	0.295872	+	0.0961346i
$889$	−5.12461	−	15.7719i	−0.171874	−	0.528974i
$890$		0			0
$891$	−0.381966	+	1.17557i	−0.0127963	+	0.0393831i
$892$	4.80828	−	6.61803i	0.160993	−	0.221588i
$893$		−	0.944272i		−	0.0315989i
$894$	−15.2533	−	11.0822i	−0.510146	−	0.370643i
$895$		0			0
$896$	−10.8541	+	7.88597i	−0.362610	+	0.263452i
$897$	14.7679	+	20.3262i	0.493085	+	0.678673i
$898$	−15.9762	+	5.19098i	−0.533133	+	0.173225i
$899$	−18.2918			−0.610066
$900$		0			0
$901$	13.9443			0.464551
$902$	4.25325	−	1.38197i	0.141618	−	0.0460144i
$903$	20.2622	+	27.8885i	0.674284	+	0.928073i
$904$	−44.4787	+	32.3157i	−1.47934	+	1.07480i
$905$		0			0
$906$	−6.09017	−	4.42477i	−0.202332	−	0.147003i
$907$		−	7.12461i		−	0.236569i	−0.992980	−	0.118284i	$-0.962261\pi$
$907$		−	7.12461i		−	0.236569i	0.992980	−	0.118284i	$-0.0377395\pi$
$908$	11.7557	−	16.1803i	0.390127	−	0.536963i
$909$	−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	$0.802623\pi$
$912$	1.17557	+	0.381966i	0.0389270	+	0.0126482i
$913$	−14.6619	−	4.76393i	−0.485237	−	0.157663i
$914$	6.90983	+	21.2663i	0.228557	+	0.703426i
$915$		0			0
$916$	−6.79180	+	20.9030i	−0.224407	+	0.690655i
$917$	−21.5033	+	29.5967i	−0.710101	+	0.977371i
$918$			3.85410i			0.127204i
$919$	39.7984	+	28.9152i	1.31283	+	0.953825i	0.999992	+	0.00401741i	$0.00127879\pi$
$919$	39.7984	+	28.9152i	1.31283	+	0.953825i	0.312835	+	0.949807i	$0.398721\pi$
$920$		0			0
$921$	−26.4164	+	19.1926i	−0.870450	+	0.632419i
$922$	−19.2784	−	26.5344i	−0.634900	−	0.873865i
$923$	27.9767	−	9.09017i	0.920863	−	0.299207i
$924$	5.52786			0.181853
$925$		0			0
$926$	18.7639			0.616621
$927$	3.07768	−	1.00000i	0.101084	−	0.0328443i
$928$	−19.4499	−	26.7705i	−0.638475	−	0.878785i
$929$	−7.35410	+	5.34307i	−0.241280	+	0.175300i	−0.701853	−	0.712321i	$-0.747644\pi$
$929$	−7.35410	+	5.34307i	−0.241280	+	0.175300i	0.460573	+	0.887622i	$0.347644\pi$
$930$		0			0
$931$	−13.0000	−	9.44505i	−0.426058	−	0.309549i
$932$			12.3820i			0.405585i
$933$	10.4086	−	14.3262i	0.340763	−	0.469020i
$934$	−8.70820	+	26.8011i	−0.284941	+	0.876959i
$935$		0			0
$936$	−5.20820	−	16.0292i	−0.170235	−	0.523931i
$937$	46.3040	+	15.0451i	1.51269	+	0.491502i	0.943688	−	0.330837i	$-0.107331\pi$
$937$	46.3040	+	15.0451i	1.51269	+	0.491502i	0.568998	+	0.822339i	$0.307331\pi$
$938$	−3.24920	−	1.05573i	−0.106090	−	0.0344707i
$939$	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	$0.153832\pi$
$942$	−6.34712	+	8.73607i	−0.206801	+	0.284636i
$943$		−	16.1803i		−	0.526904i
$944$	3.23607	+	2.35114i	0.105325	+	0.0765231i
$945$		0			0
$946$	7.70820	−	5.60034i	0.250615	−	0.182083i
$947$	1.51860	+	2.09017i	0.0493478	+	0.0679214i	0.832978	−	0.553306i	$-0.186634\pi$
$947$	1.51860	+	2.09017i	0.0493478	+	0.0679214i	−0.783630	+	0.621228i	$0.786634\pi$
$948$		0			0
$949$	45.4508			1.47540
$950$		0			0
$951$	28.8328			0.934968
$952$	49.1774	−	15.9787i	1.59385	−	0.517873i
$953$	0.640786	+	0.881966i	0.0207571	+	0.0285697i	0.819269	−	0.573409i	$-0.194379\pi$
$953$	0.640786	+	0.881966i	0.0207571	+	0.0285697i	−0.798512	+	0.601978i	$0.794379\pi$
$954$	2.92705	−	2.12663i	0.0947668	−	0.0688521i
$955$		0			0
$956$	−20.1803	−	14.6619i	−0.652679	−	0.474199i
$957$			8.18034i			0.264433i
$958$	11.1352	−	15.3262i	0.359761	−	0.495168i
$959$	−10.5279	+	32.4014i	−0.339962	+	1.04630i
$960$		0			0
$961$	−7.21885	−	22.2173i	−0.232866	−	0.716688i
$962$	16.5110	+	5.36475i	0.532336	+	0.172966i
$963$	7.15942	+	2.32624i	0.230709	+	0.0749620i
$964$	8.66312	+	26.6623i	0.279020	+	0.858736i
$965$		0			0
$966$	−6.18034	+	19.0211i	−0.198849	+	0.611995i
$967$	11.0697	−	15.2361i	0.355976	−	0.489959i	−0.593046	−	0.805169i	$-0.702075\pi$
$967$	11.0697	−	15.2361i	0.355976	−	0.489959i	0.949022	+	0.315210i	$0.102075\pi$
$968$			28.4164i			0.913338i
$969$	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	$0.119862\pi$
$972$	−0.587785	−	0.809017i	−0.0188532	−	0.0259492i
$973$	−97.5878	+	31.7082i	−3.12852	+	1.01652i
$974$	−9.70820			−0.311071
$975$		0			0
$976$	−1.61803			−0.0517920
$977$	−3.09793	+	1.00658i	−0.0991115	+	0.0322033i	−0.358153	−	0.933663i	$-0.616593\pi$
$977$	−3.09793	+	1.00658i	−0.0991115	+	0.0322033i	0.259041	+	0.965866i	$0.416593\pi$
$978$	8.78402	+	12.0902i	0.280882	+	0.386601i
$979$	−5.38197	+	3.91023i	−0.172008	+	0.124971i
$980$		0			0
$981$	6.39919	+	4.64928i	0.204310	+	0.148440i
$982$		−	5.88854i		−	0.187911i
$983$	4.87380	−	6.70820i	0.155450	−	0.213958i	−0.724188	−	0.689603i	$-0.757785\pi$
$983$	4.87380	−	6.70820i	0.155450	−	0.213958i	0.879638	+	0.475644i	$0.157785\pi$
$984$	−3.35410	+	10.3229i	−0.106925	+	0.329081i
$985$		0			0
$986$	7.88197	+	24.2582i	0.251013	+	0.772538i
$987$	−3.24920	−	1.05573i	−0.103423	−	0.0336042i
$988$	−6.60440	−	2.14590i	−0.210114	−	0.0682701i
$989$	−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	$-0.100735\pi$
$992$	−8.12299	+	11.1803i	−0.257905	+	0.354976i
$993$		−	6.94427i		−	0.220370i
$994$	18.9443	+	13.7638i	0.600876	+	0.436562i
$995$		0			0
$996$	10.0902	−	7.33094i	0.319719	−	0.232290i
$997$	−10.2371	−	14.0902i	−0.324212	−	0.446240i	0.615535	−	0.788110i	$-0.288940\pi$
$997$	−10.2371	−	14.0902i	−0.324212	−	0.446240i	−0.939747	+	0.341869i	$0.888940\pi$
$998$	5.70634	−	1.85410i	0.180631	−	0.0586906i
$999$	3.09017			0.0977687

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.a.31.1	✓	4	5.2	odd	4
75.2.g.a.46.1	yes	4	25.22	odd	20
225.2.h.a.46.1		4	75.47	even	20
225.2.h.a.181.1		4	15.2	even	4
375.2.g.a.151.1		4	5.3	odd	4
375.2.g.a.226.1		4	25.3	odd	20
375.2.i.a.274.1		8	25.21	even	5	inner
375.2.i.a.274.2		8	25.4	even	10	inner
375.2.i.a.349.1		8	5.4	even	2	inner
375.2.i.a.349.2		8	1.1	even	1	trivial
1875.2.a.a.1.2		2	25.23	odd	20
1875.2.a.d.1.1		2	25.2	odd	20
1875.2.b.b.1249.2		4	25.11	even	5
1875.2.b.b.1249.3		4	25.14	even	10
5625.2.a.a.1.1		2	75.2	even	20
5625.2.a.h.1.2		2	75.23	even	20

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.i (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.809017 - 0.587785i) q^{6} +4.47214i q^{7} +(-1.76336 + 2.42705i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-0.381966 - 1.17557i) q^{11} +(0.951057 + 0.309017i) q^{12} +(5.34307 + 1.73607i) q^{13} +(1.38197 + 4.25325i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-2.26538 + 3.11803i) q^{17} +1.00000i q^{18} +(1.00000 + 0.726543i) q^{19} +(3.61803 - 2.62866i) q^{21} +(-0.726543 - 1.00000i) q^{22} +(-4.25325 + 1.38197i) q^{23} +3.00000 q^{24} +5.61803 q^{26} +(0.951057 - 0.309017i) q^{27} +(-2.62866 - 3.61803i) q^{28} +(5.35410 - 3.88998i) q^{29} +(-2.23607 - 1.62460i) q^{31} -5.00000i q^{32} +(-0.726543 + 1.00000i) q^{33} +(-1.19098 + 3.66547i) q^{34} +(-0.309017 - 0.951057i) q^{36} +(2.93893 + 0.954915i) q^{37} +(1.17557 + 0.381966i) q^{38} +(-1.73607 - 5.34307i) q^{39} +(-1.11803 + 3.44095i) q^{41} +(2.62866 - 3.61803i) q^{42} +7.70820i q^{43} +(1.00000 + 0.726543i) q^{44} +(-3.61803 + 2.62866i) q^{46} +(-0.449028 - 0.618034i) q^{47} +(0.951057 - 0.309017i) q^{48} -13.0000 q^{49} +3.85410 q^{51} +(-5.34307 + 1.73607i) q^{52} +(-2.12663 - 2.92705i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-10.8541 - 7.88597i) q^{56} -1.23607i q^{57} +(3.88998 - 5.35410i) q^{58} +(1.23607 - 3.80423i) q^{59} +(0.500000 + 1.53884i) q^{61} +(-2.62866 - 0.854102i) q^{62} +(-4.25325 - 1.38197i) q^{63} +(-2.16312 - 6.65740i) q^{64} +(-0.381966 + 1.17557i) q^{66} +(-0.449028 + 0.618034i) q^{67} -3.85410i q^{68} +(3.61803 + 2.62866i) q^{69} +(4.23607 - 3.07768i) q^{71} +(-1.76336 - 2.42705i) q^{72} +(7.69421 - 2.50000i) q^{73} +3.09017 q^{74} -1.23607 q^{76} +(5.25731 - 1.70820i) q^{77} +(-3.30220 - 4.54508i) q^{78} +(-0.809017 - 0.587785i) q^{81} +3.61803i q^{82} +(7.33094 - 10.0902i) q^{83} +(-1.38197 + 4.25325i) q^{84} +(2.38197 + 7.33094i) q^{86} +(-6.29412 - 2.04508i) q^{87} +(3.52671 + 1.14590i) q^{88} +(-1.66312 - 5.11855i) q^{89} +(-7.76393 + 23.8949i) q^{91} +(2.62866 - 3.61803i) q^{92} +2.76393i q^{93} +(-0.618034 - 0.449028i) q^{94} +(-4.04508 + 2.93893i) q^{96} +(1.26133 + 1.73607i) q^{97} +(-12.3637 + 4.01722i) q^{98} +1.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} - 2 q^{6} + 2 q^{9} - 12 q^{11} + 20 q^{14} + 2 q^{16} + 8 q^{19} + 20 q^{21} + 24 q^{24} + 36 q^{26} + 16 q^{29} - 14 q^{34} + 2 q^{36} + 4 q^{39} + 8 q^{44} - 20 q^{46} - 104 q^{49} + 4 q^{51}+ \cdots - 8 q^{99}+O(q^{100}) \) 8 * q - 2 * q^4 - 2 * q^6 + 2 * q^9 - 12 * q^11 + 20 * q^14 + 2 * q^16 + 8 * q^19 + 20 * q^21 + 24 * q^24 + 36 * q^26 + 16 * q^29 - 14 * q^34 + 2 * q^36 + 4 * q^39 + 8 * q^44 - 20 * q^46 - 104 * q^49 + 4 * q^51 + 2 * q^54 - 60 * q^56 - 8 * q^59 + 4 * q^61 + 14 * q^64 - 12 * q^66 + 20 * q^69 + 16 * q^71 - 20 * q^74 + 8 * q^76 - 2 * q^81 - 20 * q^84 + 28 * q^86 + 18 * q^89 - 80 * q^91 + 4 * q^94 - 10 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

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