LMFDB - Embedded newform 375.2.i.a.49.1

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			49.1
Root			$-0.587785 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	375.49
Dual form			375.2.i.a.199.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.309017 - 0.951057i) q^{6} -4.47214i q^{7} +(-2.85317 - 0.927051i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-2.61803 - 1.90211i) q^{11} +(-0.587785 - 0.809017i) q^{12} +(-1.98787 - 2.73607i) q^{13} +(3.61803 + 2.62866i) q^{14} +(0.809017 - 0.587785i) q^{16} +(2.71441 + 0.881966i) q^{17} +1.00000i q^{18} +(1.00000 - 3.07768i) q^{19} +(1.38197 + 4.25325i) q^{21} +(3.07768 - 1.00000i) q^{22} +(-2.62866 + 3.61803i) q^{23} +3.00000 q^{24} +3.38197 q^{26} +(-0.587785 + 0.809017i) q^{27} +(4.25325 - 1.38197i) q^{28} +(-1.35410 - 4.16750i) q^{29} +(2.23607 - 6.88191i) q^{31} -5.00000i q^{32} +(3.07768 + 1.00000i) q^{33} +(-2.30902 + 1.67760i) q^{34} +(0.809017 + 0.587785i) q^{36} +(4.75528 + 6.54508i) q^{37} +(1.90211 + 2.61803i) q^{38} +(2.73607 + 1.98787i) q^{39} +(1.11803 - 0.812299i) q^{41} +(-4.25325 - 1.38197i) q^{42} -5.70820i q^{43} +(1.00000 - 3.07768i) q^{44} +(-1.38197 - 4.25325i) q^{46} +(-4.97980 + 1.61803i) q^{47} +(-0.587785 + 0.809017i) q^{48} -13.0000 q^{49} -2.85410 q^{51} +(1.98787 - 2.73607i) q^{52} +(-1.31433 + 0.427051i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-4.14590 + 12.7598i) q^{56} +3.23607i q^{57} +(4.16750 + 1.35410i) q^{58} +(-3.23607 + 2.35114i) q^{59} +(0.500000 + 0.363271i) q^{61} +(4.25325 + 5.85410i) q^{62} +(-2.62866 - 3.61803i) q^{63} +(5.66312 + 4.11450i) q^{64} +(-2.61803 + 1.90211i) q^{66} +(-4.97980 - 1.61803i) q^{67} +2.85410i q^{68} +(1.38197 - 4.25325i) q^{69} +(-0.236068 - 0.726543i) q^{71} +(-2.85317 + 0.927051i) q^{72} +(1.81636 - 2.50000i) q^{73} -8.09017 q^{74} +3.23607 q^{76} +(-8.50651 + 11.7082i) q^{77} +(-3.21644 + 1.04508i) q^{78} +(0.309017 - 0.951057i) q^{81} +1.38197i q^{82} +(3.35520 + 1.09017i) q^{83} +(-3.61803 + 2.62866i) q^{84} +(4.61803 + 3.35520i) q^{86} +(2.57565 + 3.54508i) q^{87} +(5.70634 + 7.85410i) q^{88} +(6.16312 + 4.47777i) q^{89} +(-12.2361 + 8.89002i) q^{91} +(-4.25325 - 1.38197i) q^{92} +7.23607i q^{93} +(1.61803 - 4.97980i) q^{94} +(1.54508 + 4.75528i) q^{96} +(8.42075 - 2.73607i) q^{97} +(7.64121 - 10.5172i) q^{98} -3.23607 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 $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$

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 $

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i	−0.964580	−	0.263792i	$-0.915027\pi$
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i	0.548953	+	0.835853i	$0.315027\pi$
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$		0			0
$5$		0			0
$6$	0.309017	−	0.951057i	0.126156	−	0.388267i
$7$		−	4.47214i		−	1.69031i	−0.534522	−	0.845154i	$-0.679509\pi$
$7$		−	4.47214i		−	1.69031i	0.534522	−	0.845154i	$-0.320491\pi$
$8$	−2.85317	−	0.927051i	−1.00875	−	0.327762i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$		0			0
$11$	−2.61803	−	1.90211i	−0.789367	−	0.573509i	0.118409	−	0.992965i	$-0.462221\pi$
$11$	−2.61803	−	1.90211i	−0.789367	−	0.573509i	−0.907776	+	0.419456i	$0.862221\pi$
$12$	−0.587785	−	0.809017i	−0.169679	−	0.233543i
$13$	−1.98787	−	2.73607i	−0.551336	−	0.758849i	0.438857	−	0.898557i	$-0.355384\pi$
$13$	−1.98787	−	2.73607i	−0.551336	−	0.758849i	−0.990193	+	0.139708i	$0.955384\pi$
$14$	3.61803	+	2.62866i	0.966960	+	0.702538i
$15$		0			0
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	2.71441	+	0.881966i	0.658342	+	0.213908i	0.619089	−	0.785321i	$-0.287502\pi$
$17$	2.71441	+	0.881966i	0.658342	+	0.213908i	0.0392530	+	0.999229i	$0.487502\pi$
$18$			1.00000i			0.235702i
$19$	1.00000	−	3.07768i	0.229416	−	0.706069i	−0.768398	−	0.639973i	$-0.778946\pi$
$19$	1.00000	−	3.07768i	0.229416	−	0.706069i	0.997813	−	0.0660962i	$-0.0210544\pi$
$20$		0			0
$21$	1.38197	+	4.25325i	0.301570	+	0.928136i
$22$	3.07768	−	1.00000i	0.656164	−	0.213201i
$23$	−2.62866	+	3.61803i	−0.548113	+	0.754412i	−0.989755	−	0.142779i	$-0.954396\pi$
$23$	−2.62866	+	3.61803i	−0.548113	+	0.754412i	0.441642	+	0.897191i	$0.354396\pi$
$24$	3.00000			0.612372
$25$		0			0
$26$	3.38197			0.663258
$27$	−0.587785	+	0.809017i	−0.113119	+	0.155695i
$28$	4.25325	−	1.38197i	0.803789	−	0.261167i
$29$	−1.35410	−	4.16750i	−0.251450	−	0.773885i	−0.994508	−	0.104658i	$-0.966625\pi$
$29$	−1.35410	−	4.16750i	−0.251450	−	0.773885i	0.743058	−	0.669227i	$-0.233375\pi$
$30$		0			0
$31$	2.23607	−	6.88191i	0.401610	−	1.23603i	−0.522083	−	0.852894i	$-0.674845\pi$
$31$	2.23607	−	6.88191i	0.401610	−	1.23603i	0.923693	−	0.383133i	$-0.125155\pi$
$32$		−	5.00000i		−	0.883883i
$33$	3.07768	+	1.00000i	0.535756	+	0.174078i
$34$	−2.30902	+	1.67760i	−0.395993	+	0.287706i
$35$		0			0
$36$	0.809017	+	0.587785i	0.134836	+	0.0979642i
$37$	4.75528	+	6.54508i	0.781764	+	1.07601i	0.995085	+	0.0990233i	$0.0315718\pi$
$37$	4.75528	+	6.54508i	0.781764	+	1.07601i	−0.213321	+	0.976982i	$0.568428\pi$
$38$	1.90211	+	2.61803i	0.308563	+	0.424701i
$39$	2.73607	+	1.98787i	0.438122	+	0.318314i
$40$		0			0
$41$	1.11803	−	0.812299i	0.174608	−	0.126860i	−0.497049	−	0.867722i	$-0.665583\pi$
$41$	1.11803	−	0.812299i	0.174608	−	0.126860i	0.671657	+	0.740863i	$0.265583\pi$
$42$	−4.25325	−	1.38197i	−0.656291	−	0.213242i
$43$		−	5.70820i		−	0.870493i	−0.900311	−	0.435246i	$-0.856661\pi$
$43$		−	5.70820i		−	0.870493i	0.900311	−	0.435246i	$-0.143339\pi$
$44$	1.00000	−	3.07768i	0.150756	−	0.463978i
$45$		0			0
$46$	−1.38197	−	4.25325i	−0.203760	−	0.627108i
$47$	−4.97980	+	1.61803i	−0.726378	+	0.236015i	−0.648786	−	0.760971i	$-0.724723\pi$
$47$	−4.97980	+	1.61803i	−0.726378	+	0.236015i	−0.0775917	+	0.996985i	$0.524723\pi$
$48$	−0.587785	+	0.809017i	−0.0848395	+	0.116772i
$49$	−13.0000			−1.85714
$50$		0			0
$51$	−2.85410			−0.399654
$52$	1.98787	−	2.73607i	0.275668	−	0.379424i
$53$	−1.31433	+	0.427051i	−0.180537	+	0.0586600i	−0.397890	−	0.917433i	$-0.630258\pi$
$53$	−1.31433	+	0.427051i	−0.180537	+	0.0586600i	0.217354	+	0.976093i	$0.430258\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$		0			0
$56$	−4.14590	+	12.7598i	−0.554019	+	1.70509i
$57$			3.23607i			0.428628i
$58$	4.16750	+	1.35410i	0.547219	+	0.177802i
$59$	−3.23607	+	2.35114i	−0.421300	+	0.306092i	−0.778161	−	0.628065i	$-0.783847\pi$
$59$	−3.23607	+	2.35114i	−0.421300	+	0.306092i	0.356861	+	0.934158i	$0.383847\pi$
$60$		0			0
$61$	0.500000	+	0.363271i	0.0640184	+	0.0465121i	0.619334	−	0.785127i	$-0.287403\pi$
$61$	0.500000	+	0.363271i	0.0640184	+	0.0465121i	−0.555316	+	0.831640i	$0.687403\pi$
$62$	4.25325	+	5.85410i	0.540164	+	0.743472i
$63$	−2.62866	−	3.61803i	−0.331179	−	0.455829i
$64$	5.66312	+	4.11450i	0.707890	+	0.514312i
$65$		0			0
$66$	−2.61803	+	1.90211i	−0.322258	+	0.234134i
$67$	−4.97980	−	1.61803i	−0.608379	−	0.197674i	−0.0114051	−	0.999935i	$-0.503630\pi$
$67$	−4.97980	−	1.61803i	−0.608379	−	0.197674i	−0.596974	+	0.802261i	$0.703630\pi$
$68$			2.85410i			0.346111i
$69$	1.38197	−	4.25325i	0.166369	−	0.512032i
$70$		0			0
$71$	−0.236068	−	0.726543i	−0.0280161	−	0.0862247i	0.936071	−	0.351812i	$-0.114434\pi$
$71$	−0.236068	−	0.726543i	−0.0280161	−	0.0862247i	−0.964087	+	0.265587i	$0.914434\pi$
$72$	−2.85317	+	0.927051i	−0.336249	+	0.109254i
$73$	1.81636	−	2.50000i	0.212588	−	0.292603i	−0.689384	−	0.724396i	$-0.742119\pi$
$73$	1.81636	−	2.50000i	0.212588	−	0.292603i	0.901973	+	0.431793i	$0.142119\pi$
$74$	−8.09017			−0.940463
$75$		0			0
$76$	3.23607			0.371202
$77$	−8.50651	+	11.7082i	−0.969407	+	1.33427i
$78$	−3.21644	+	1.04508i	−0.364190	+	0.118333i
$79$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$79$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$			1.38197i			0.152613i
$83$	3.35520	+	1.09017i	0.368281	+	0.119662i	0.487310	−	0.873229i	$-0.337978\pi$
$83$	3.35520	+	1.09017i	0.368281	+	0.119662i	−0.119029	+	0.992891i	$0.537978\pi$
$84$	−3.61803	+	2.62866i	−0.394760	+	0.286810i
$85$		0			0
$86$	4.61803	+	3.35520i	0.497975	+	0.361800i
$87$	2.57565	+	3.54508i	0.276139	+	0.380073i
$88$	5.70634	+	7.85410i	0.608298	+	0.837250i
$89$	6.16312	+	4.47777i	0.653289	+	0.474642i	0.864390	−	0.502822i	$-0.167705\pi$
$89$	6.16312	+	4.47777i	0.653289	+	0.474642i	−0.211101	+	0.977464i	$0.567705\pi$
$90$		0			0
$91$	−12.2361	+	8.89002i	−1.28269	+	0.931928i
$92$	−4.25325	−	1.38197i	−0.443432	−	0.144080i
$93$			7.23607i			0.750345i
$94$	1.61803	−	4.97980i	0.166887	−	0.513627i
$95$		0			0
$96$	1.54508	+	4.75528i	0.157695	+	0.485334i
$97$	8.42075	−	2.73607i	0.854998	−	0.277806i	0.151460	−	0.988463i	$-0.451603\pi$
$97$	8.42075	−	2.73607i	0.854998	−	0.277806i	0.703538	+	0.710658i	$0.251603\pi$
$98$	7.64121	−	10.5172i	0.771879	−	1.06240i
$99$	−3.23607			−0.325237
$100$		0			0
$101$	−16.5623			−1.64801			−0.824006	−	0.566582i	$-0.808266\pi$
$101$	−16.5623			−1.64801			−0.824006	+	0.566582i	$0.808266\pi$
$102$	1.67760	−	2.30902i	0.166107	−	0.228627i
$103$	1.17557	−	0.381966i	0.115832	−	0.0376362i	−0.250527	−	0.968110i	$-0.580604\pi$
$103$	1.17557	−	0.381966i	0.115832	−	0.0376362i	0.366360	+	0.930473i	$0.380604\pi$
$104$	3.13525	+	9.64932i	0.307437	+	0.946194i
$105$		0			0
$106$	0.427051	−	1.31433i	0.0414789	−	0.127659i
$107$		−	16.4721i		−	1.59242i	−0.605019	−	0.796211i	$-0.706835\pi$
$107$		−	16.4721i		−	1.59242i	0.605019	−	0.796211i	$-0.293165\pi$
$108$	−0.951057	−	0.309017i	−0.0915155	−	0.0297352i
$109$	−15.4443	+	11.2209i	−1.47929	+	1.07477i	−0.501509	+	0.865152i	$0.667222\pi$
$109$	−15.4443	+	11.2209i	−1.47929	+	1.07477i	−0.977784	+	0.209617i	$0.932778\pi$
$110$		0			0
$111$	−6.54508	−	4.75528i	−0.621232	−	0.451351i
$112$	−2.62866	−	3.61803i	−0.248385	−	0.341872i
$113$	−1.57160	−	2.16312i	−0.147843	−	0.203489i	0.728672	−	0.684863i	$-0.240138\pi$
$113$	−1.57160	−	2.16312i	−0.147843	−	0.203489i	−0.876515	+	0.481374i	$0.840138\pi$
$114$	−2.61803	−	1.90211i	−0.245201	−	0.178149i
$115$		0			0
$116$	3.54508	−	2.57565i	0.329153	−	0.239144i
$117$	−3.21644	−	1.04508i	−0.297360	−	0.0966181i
$118$		−	4.00000i		−	0.368230i
$119$	3.94427	−	12.1392i	0.361571	−	1.11280i
$120$		0			0
$121$	−0.163119	−	0.502029i	−0.0148290	−	0.0456390i
$122$	−0.587785	+	0.190983i	−0.0532156	+	0.0172908i
$123$	−0.812299	+	1.11803i	−0.0732426	+	0.100810i
$124$	7.23607			0.649818
$125$		0			0
$126$	4.47214			0.398410
$127$	−5.70634	+	7.85410i	−0.506356	+	0.696939i	−0.983299	−	0.181995i	$-0.941745\pi$
$127$	−5.70634	+	7.85410i	−0.506356	+	0.696939i	0.476944	+	0.878934i	$0.341745\pi$
$128$	2.85317	−	0.927051i	0.252187	−	0.0819405i
$129$	1.76393	+	5.42882i	0.155306	+	0.477981i
$130$		0			0
$131$	4.38197	−	13.4863i	0.382854	−	1.17830i	−0.555171	−	0.831736i	$-0.687347\pi$
$131$	4.38197	−	13.4863i	0.382854	−	1.17830i	0.938025	−	0.346568i	$-0.112653\pi$
$132$			3.23607i			0.281664i
$133$	−13.7638	−	4.47214i	−1.19347	−	0.387783i
$134$	4.23607	−	3.07768i	0.365941	−	0.265871i
$135$		0			0
$136$	−6.92705	−	5.03280i	−0.593990	−	0.431559i
$137$	−3.16344	−	4.35410i	−0.270271	−	0.371996i	0.652210	−	0.758038i	$-0.273842\pi$
$137$	−3.16344	−	4.35410i	−0.270271	−	0.371996i	−0.922481	+	0.386042i	$0.873842\pi$
$138$	2.62866	+	3.61803i	0.223766	+	0.307988i
$139$	−4.09017	−	2.97168i	−0.346924	−	0.252055i	0.400654	−	0.916230i	$-0.368783\pi$
$139$	−4.09017	−	2.97168i	−0.346924	−	0.252055i	−0.747577	+	0.664175i	$0.768783\pi$
$140$		0			0
$141$	4.23607	−	3.07768i	0.356741	−	0.259188i
$142$	0.726543	+	0.236068i	0.0609701	+	0.0198104i
$143$			10.9443i			0.915206i
$144$	0.309017	−	0.951057i	0.0257514	−	0.0792547i
$145$		0			0
$146$	0.954915	+	2.93893i	0.0790293	+	0.243227i
$147$	12.3637	−	4.01722i	1.01974	−	0.331335i
$148$	−4.75528	+	6.54508i	−0.390882	+	0.538003i
$149$	12.1459			0.995031			0.497515	−	0.867455i	$-0.334246\pi$
$149$	12.1459			0.995031			0.497515	+	0.867455i	$0.334246\pi$
$150$		0			0
$151$	16.4721			1.34048			0.670242	−	0.742143i	$-0.266190\pi$
$151$	16.4721			1.34048			0.670242	+	0.742143i	$0.266190\pi$
$152$	−5.70634	+	7.85410i	−0.462845	+	0.637052i
$153$	2.71441	−	0.881966i	0.219447	−	0.0713027i
$154$	−4.47214	−	13.7638i	−0.360375	−	1.10912i
$155$		0			0
$156$	−1.04508	+	3.21644i	−0.0836738	+	0.257521i
$157$			13.7984i			1.10123i	0.834759	+	0.550615i	$0.185607\pi$
$157$			13.7984i			1.10123i	−0.834759	+	0.550615i	$0.814393\pi$
$158$		0			0
$159$	1.11803	−	0.812299i	0.0886659	−	0.0644195i
$160$		0			0
$161$	16.1803	+	11.7557i	1.27519	+	0.926479i
$162$	0.587785	+	0.809017i	0.0461808	+	0.0635624i
$163$	−1.73060	−	2.38197i	−0.135551	−	0.186570i	0.735845	−	0.677150i	$-0.236785\pi$
$163$	−1.73060	−	2.38197i	−0.135551	−	0.186570i	−0.871396	+	0.490580i	$0.836785\pi$
$164$	1.11803	+	0.812299i	0.0873038	+	0.0634299i
$165$		0			0
$166$	−2.85410	+	2.07363i	−0.221521	+	0.160945i
$167$	22.2703	+	7.23607i	1.72333	+	0.559944i	0.992460	−	0.122573i	$-0.0391145\pi$
$167$	22.2703	+	7.23607i	1.72333	+	0.559944i	0.730870	+	0.682517i	$0.239114\pi$
$168$		−	13.4164i		−	1.03510i
$169$	0.482779	−	1.48584i	0.0371369	−	0.114295i
$170$		0			0
$171$	−1.00000	−	3.07768i	−0.0764719	−	0.235356i
$172$	5.42882	−	1.76393i	0.413944	−	0.134499i
$173$	5.82485	−	8.01722i	0.442855	−	0.609538i	−0.527988	−	0.849252i	$-0.677054\pi$
$173$	5.82485	−	8.01722i	0.442855	−	0.609538i	0.970844	+	0.239714i	$0.0770535\pi$
$174$	−4.38197			−0.332196
$175$		0			0
$176$	−3.23607			−0.243928
$177$	2.35114	−	3.23607i	0.176723	−	0.243238i
$178$	−7.24518	+	2.35410i	−0.543049	+	0.176447i
$179$	−1.90983	−	5.87785i	−0.142747	−	0.439331i	0.853967	−	0.520327i	$-0.174190\pi$
$179$	−1.90983	−	5.87785i	−0.142747	−	0.439331i	−0.996714	+	0.0809958i	$0.974190\pi$
$180$		0			0
$181$	−3.02786	+	9.31881i	−0.225059	+	0.692661i	0.773226	+	0.634130i	$0.218642\pi$
$181$	−3.02786	+	9.31881i	−0.225059	+	0.692661i	−0.998286	+	0.0585312i	$0.981358\pi$
$182$		−	15.1246i		−	1.12111i
$183$	−0.587785	−	0.190983i	−0.0434503	−	0.0141179i
$184$	10.8541	−	7.88597i	0.800175	−	0.581361i
$185$		0			0
$186$	−5.85410	−	4.25325i	−0.429244	−	0.311864i
$187$	−5.42882	−	7.47214i	−0.396995	−	0.546417i
$188$	−3.07768	−	4.23607i	−0.224463	−	0.308947i
$189$	3.61803	+	2.62866i	0.263173	+	0.191207i
$190$		0			0
$191$	19.9443	−	14.4904i	1.44312	−	1.04849i	0.455737	−	0.890114i	$-0.349376\pi$
$191$	19.9443	−	14.4904i	1.44312	−	1.04849i	0.987380	−	0.158371i	$-0.0506243\pi$
$192$	−6.65740	−	2.16312i	−0.480456	−	0.156110i
$193$			7.67376i			0.552369i	0.961105	+	0.276185i	$0.0890702\pi$
$193$			7.67376i			0.552369i	−0.961105	+	0.276185i	$0.910930\pi$
$194$	−2.73607	+	8.42075i	−0.196438	+	0.604575i
$195$		0			0
$196$	−4.01722	−	12.3637i	−0.286944	−	0.883124i
$197$	5.11855	−	1.66312i	0.364682	−	0.118492i	−0.120943	−	0.992659i	$-0.538592\pi$
$197$	5.11855	−	1.66312i	0.364682	−	0.118492i	0.485625	+	0.874167i	$0.338592\pi$
$198$	1.90211	−	2.61803i	0.135177	−	0.186056i
$199$	18.6525			1.32224			0.661119	−	0.750281i	$-0.270082\pi$
$199$	18.6525			1.32224			0.661119	+	0.750281i	$0.270082\pi$
$200$		0			0
$201$	5.23607			0.369324
$202$	9.73508	−	13.3992i	0.684958	−	0.942764i
$203$	−18.6376	+	6.05573i	−1.30810	+	0.425029i
$204$	−0.881966	−	2.71441i	−0.0617500	−	0.190047i
$205$		0			0
$206$	−0.381966	+	1.17557i	−0.0266128	+	0.0819059i
$207$			4.47214i			0.310835i
$208$	−3.21644	−	1.04508i	−0.223020	−	0.0724636i
$209$	−8.47214	+	6.15537i	−0.586030	+	0.425776i
$210$		0			0
$211$	14.4721	+	10.5146i	0.996303	+	0.723856i	0.961292	−	0.275530i	$-0.0888535\pi$
$211$	14.4721	+	10.5146i	0.996303	+	0.723856i	0.0350106	+	0.999387i	$0.488854\pi$
$212$	−0.812299	−	1.11803i	−0.0557889	−	0.0767869i
$213$	0.449028	+	0.618034i	0.0307669	+	0.0423470i
$214$	13.3262	+	9.68208i	0.910963	+	0.661853i
$215$		0			0
$216$	2.42705	−	1.76336i	0.165140	−	0.119981i
$217$	−30.7768	−	10.0000i	−2.08927	−	0.678844i
$218$		−	19.0902i		−	1.29295i
$219$	−0.954915	+	2.93893i	−0.0645272	+	0.198594i
$220$		0			0
$221$	−2.98278	−	9.18005i	−0.200643	−	0.617517i
$222$	7.69421	−	2.50000i	0.516401	−	0.167789i
$223$	−8.33499	+	11.4721i	−0.558153	+	0.768231i	−0.991090	−	0.133193i	$-0.957477\pi$
$223$	−8.33499	+	11.4721i	−0.558153	+	0.768231i	0.432938	+	0.901424i	$0.357477\pi$
$224$	−22.3607			−1.49404
$225$		0			0
$226$	2.67376			0.177856
$227$	11.7557	−	16.1803i	0.780254	−	1.07393i	−0.215000	−	0.976614i	$-0.568975\pi$
$227$	11.7557	−	16.1803i	0.780254	−	1.07393i	0.995254	−	0.0973129i	$-0.0310248\pi$
$228$	−3.07768	+	1.00000i	−0.203825	+	0.0662266i
$229$	7.71885	+	23.7562i	0.510076	+	1.56985i	0.792067	+	0.610435i	$0.209005\pi$
$229$	7.71885	+	23.7562i	0.510076	+	1.56985i	−0.281991	+	0.959417i	$0.590995\pi$
$230$		0			0
$231$	4.47214	−	13.7638i	0.294245	−	0.905593i
$232$			13.1459i			0.863070i
$233$	13.9026	+	4.51722i	0.910788	+	0.295933i	0.726682	−	0.686973i	$-0.241061\pi$
$233$	13.9026	+	4.51722i	0.910788	+	0.295933i	0.184106	+	0.982906i	$0.441061\pi$
$234$	2.73607	−	1.98787i	0.178862	−	0.129951i
$235$		0			0
$236$	−3.23607	−	2.35114i	−0.210650	−	0.153046i
$237$		0			0
$238$	7.50245	+	10.3262i	0.486312	+	0.669351i
$239$	−5.70820	−	4.14725i	−0.369233	−	0.268263i	0.387660	−	0.921803i	$-0.373284\pi$
$239$	−5.70820	−	4.14725i	−0.369233	−	0.268263i	−0.756893	+	0.653539i	$0.773284\pi$
$240$		0			0
$241$	0.836881	−	0.608030i	0.0539082	−	0.0391666i	−0.560505	−	0.828151i	$-0.689393\pi$
$241$	0.836881	−	0.608030i	0.0539082	−	0.0391666i	0.614413	+	0.788985i	$0.289393\pi$
$242$	0.502029	+	0.163119i	0.0322716	+	0.0104857i
$243$			1.00000i			0.0641500i
$244$	−0.190983	+	0.587785i	−0.0122264	+	0.0376291i
$245$		0			0
$246$	−0.427051	−	1.31433i	−0.0272278	−	0.0837985i
$247$	−10.4086	+	3.38197i	−0.662285	+	0.215189i
$248$	−12.7598	+	17.5623i	−0.810246	+	1.11521i
$249$	−3.52786			−0.223569
$250$		0			0
$251$	−26.9443			−1.70071			−0.850354	−	0.526212i	$-0.823612\pi$
$251$	−26.9443			−1.70071			−0.850354	+	0.526212i	$0.823612\pi$
$252$	2.62866	−	3.61803i	0.165590	−	0.227915i
$253$	13.7638	−	4.47214i	0.865324	−	0.281161i
$254$	−3.00000	−	9.23305i	−0.188237	−	0.579333i
$255$		0			0
$256$	−5.25329	+	16.1680i	−0.328331	+	1.01050i
$257$			12.7984i			0.798341i	0.916877	+	0.399170i	$0.130702\pi$
$257$			12.7984i			0.798341i	−0.916877	+	0.399170i	$0.869298\pi$
$258$	−5.42882	−	1.76393i	−0.337984	−	0.109818i
$259$	29.2705	−	21.2663i	1.81878	−	1.32142i
$260$		0			0
$261$	−3.54508	−	2.57565i	−0.219435	−	0.159429i
$262$	8.33499	+	11.4721i	0.514938	+	0.708751i
$263$	−6.98791	−	9.61803i	−0.430893	−	0.593073i	0.537265	−	0.843414i	$-0.319458\pi$
$263$	−6.98791	−	9.61803i	−0.430893	−	0.593073i	−0.968158	+	0.250340i	$0.919458\pi$
$264$	−7.85410	−	5.70634i	−0.483387	−	0.351201i
$265$		0			0
$266$	11.7082	−	8.50651i	0.717876	−	0.521567i
$267$	−7.24518	−	2.35410i	−0.443398	−	0.144069i
$268$		−	5.23607i		−	0.319844i
$269$	0.0450850	−	0.138757i	0.00274888	−	0.00846018i	−0.949673	−	0.313244i	$-0.898584\pi$
$269$	0.0450850	−	0.138757i	0.00274888	−	0.00846018i	0.952422	+	0.304784i	$0.0985842\pi$
$270$		0			0
$271$	6.85410	+	21.0948i	0.416357	+	1.28142i	0.911031	+	0.412337i	$0.135287\pi$
$271$	6.85410	+	21.0948i	0.416357	+	1.28142i	−0.494674	+	0.869078i	$0.664713\pi$
$272$	2.71441	−	0.881966i	0.164585	−	0.0534770i
$273$	8.89002	−	12.2361i	0.538049	−	0.740561i
$274$	5.38197			0.325136
$275$		0			0
$276$	4.47214			0.269191
$277$	3.40820	−	4.69098i	0.204779	−	0.281854i	−0.694259	−	0.719726i	$-0.744268\pi$
$277$	3.40820	−	4.69098i	0.204779	−	0.281854i	0.899037	+	0.437872i	$0.144268\pi$
$278$	4.80828	−	1.56231i	0.288382	−	0.0937009i
$279$	−2.23607	−	6.88191i	−0.133870	−	0.412009i
$280$		0			0
$281$	−5.37132	+	16.5312i	−0.320426	+	0.986171i	0.653037	+	0.757326i	$0.273495\pi$
$281$	−5.37132	+	16.5312i	−0.320426	+	0.986171i	−0.973463	+	0.228844i	$0.926505\pi$
$282$			5.23607i			0.311803i
$283$	0.277515	+	0.0901699i	0.0164965	+	0.00536005i	0.317254	−	0.948341i	$-0.397239\pi$
$283$	0.277515	+	0.0901699i	0.0164965	+	0.00536005i	−0.300757	+	0.953701i	$0.597239\pi$
$284$	0.618034	−	0.449028i	0.0366736	−	0.0266449i
$285$		0			0
$286$	−8.85410	−	6.43288i	−0.523554	−	0.380384i
$287$	−3.63271	−	5.00000i	−0.214432	−	0.295141i
$288$	−2.93893	−	4.04508i	−0.173178	−	0.238359i
$289$	−7.16312	−	5.20431i	−0.421360	−	0.306136i
$290$		0			0
$291$	−7.16312	+	5.20431i	−0.419909	+	0.305082i
$292$	2.93893	+	0.954915i	0.171988	+	0.0558822i
$293$			3.79837i			0.221903i	0.993826	+	0.110952i	$0.0353899\pi$
$293$			3.79837i			0.221903i	−0.993826	+	0.110952i	$0.964610\pi$
$294$	−4.01722	+	12.3637i	−0.234289	+	0.721068i
$295$		0			0
$296$	−7.50000	−	23.0826i	−0.435929	−	1.34165i
$297$	3.07768	−	1.00000i	0.178585	−	0.0580259i
$298$	−7.13918	+	9.82624i	−0.413562	+	0.569219i
$299$	15.1246			0.874679
$300$		0			0
$301$	−25.5279			−1.47140
$302$	−9.68208	+	13.3262i	−0.557141	+	0.766839i
$303$	15.7517	−	5.11803i	0.904911	−	0.294023i
$304$	−1.00000	−	3.07768i	−0.0573539	−	0.176517i
$305$		0			0
$306$	−0.881966	+	2.71441i	−0.0504186	+	0.155173i
$307$		−	1.34752i		−	0.0769073i	−0.999260	−	0.0384536i	$-0.987757\pi$
$307$		−	1.34752i		−	0.0769073i	0.999260	−	0.0384536i	$-0.0122432\pi$
$308$	−13.7638	−	4.47214i	−0.784266	−	0.254824i
$309$	−1.00000	+	0.726543i	−0.0568880	+	0.0413316i
$310$		0			0
$311$	−3.47214	−	2.52265i	−0.196887	−	0.143047i	0.484974	−	0.874529i	$-0.338829\pi$
$311$	−3.47214	−	2.52265i	−0.196887	−	0.143047i	−0.681861	+	0.731482i	$0.738829\pi$
$312$	−5.96361	−	8.20820i	−0.337623	−	0.464698i
$313$	−4.97980	−	6.85410i	−0.281475	−	0.387417i	0.644747	−	0.764396i	$-0.276963\pi$
$313$	−4.97980	−	6.85410i	−0.281475	−	0.387417i	−0.926222	+	0.376979i	$0.876963\pi$
$314$	−11.1631	−	8.11048i	−0.629971	−	0.457701i
$315$		0			0
$316$		0			0
$317$	23.6174	+	7.67376i	1.32649	+	0.431001i	0.884717	−	0.466128i	$-0.154351\pi$
$317$	23.6174	+	7.67376i	1.32649	+	0.431001i	0.441768	+	0.897129i	$0.354351\pi$
$318$			1.38197i			0.0774968i
$319$	−4.38197	+	13.4863i	−0.245343	+	0.755088i
$320$		0			0
$321$	5.09017	+	15.6659i	0.284106	+	0.874387i
$322$	−19.0211	+	6.18034i	−1.06001	+	0.344417i
$323$	5.42882	−	7.47214i	0.302068	−	0.415761i
$324$	1.00000			0.0555556
$325$		0			0
$326$	2.94427			0.163068
$327$	11.2209	−	15.4443i	0.620518	−	0.854070i
$328$	−3.94298	+	1.28115i	−0.217715	+	0.0707398i
$329$	7.23607	+	22.2703i	0.398937	+	1.22780i
$330$		0			0
$331$	3.38197	−	10.4086i	0.185890	−	0.572110i	−0.814073	−	0.580763i	$-0.802754\pi$
$331$	3.38197	−	10.4086i	0.185890	−	0.572110i	0.999963	+	0.00865315i	$0.00275442\pi$
$332$			3.52786i			0.193617i
$333$	7.69421	+	2.50000i	0.421640	+	0.136999i
$334$	−18.9443	+	13.7638i	−1.03658	+	0.753123i
$335$		0			0
$336$	3.61803	+	2.62866i	0.197380	+	0.143405i
$337$	−8.78402	−	12.0902i	−0.478496	−	0.658594i	0.499719	−	0.866188i	$-0.333437\pi$
$337$	−8.78402	−	12.0902i	−0.478496	−	0.658594i	−0.978215	+	0.207594i	$0.933437\pi$
$338$	0.918300	+	1.26393i	0.0499490	+	0.0687488i
$339$	2.16312	+	1.57160i	0.117484	+	0.0853575i
$340$		0			0
$341$	−18.9443	+	13.7638i	−1.02589	+	0.745353i
$342$	3.07768	+	1.00000i	0.166422	+	0.0540738i
$343$			26.8328i			1.44884i
$344$	−5.29180	+	16.2865i	−0.285315	+	0.878108i
$345$		0			0
$346$	3.06231	+	9.42481i	0.164631	+	0.506681i
$347$	−32.0584	+	10.4164i	−1.72099	+	0.559182i	−0.992100	−	0.125453i	$-0.959962\pi$
$347$	−32.0584	+	10.4164i	−1.72099	+	0.559182i	−0.728886	+	0.684635i	$0.759962\pi$
$348$	−2.57565	+	3.54508i	−0.138070	+	0.190037i
$349$	−25.0344			−1.34006			−0.670031	−	0.742333i	$-0.733719\pi$
$349$	−25.0344			−1.34006			−0.670031	+	0.742333i	$0.733719\pi$
$350$		0			0
$351$	3.38197			0.180516
$352$	−9.51057	+	13.0902i	−0.506915	+	0.697708i
$353$	28.8747	−	9.38197i	1.53685	−	0.499352i	0.586342	−	0.810063i	$-0.300567\pi$
$353$	28.8747	−	9.38197i	1.53685	−	0.499352i	0.950504	+	0.310712i	$0.100567\pi$
$354$	1.23607	+	3.80423i	0.0656963	+	0.202192i
$355$		0			0
$356$	−2.35410	+	7.24518i	−0.124767	+	0.383994i
$357$			12.7639i			0.675539i
$358$	5.87785	+	1.90983i	0.310654	+	0.100938i
$359$	−8.56231	+	6.22088i	−0.451901	+	0.328325i	−0.790346	−	0.612661i	$-0.790099\pi$
$359$	−8.56231	+	6.22088i	−0.451901	+	0.328325i	0.338445	+	0.940986i	$0.390099\pi$
$360$		0			0
$361$	6.89919	+	5.01255i	0.363115	+	0.263819i
$362$	−5.75934	−	7.92705i	−0.302704	−	0.416637i
$363$	0.310271	+	0.427051i	0.0162850	+	0.0224144i
$364$	−12.2361	−	8.89002i	−0.641344	−	0.465964i
$365$		0			0
$366$	0.500000	−	0.363271i	0.0261354	−	0.0189885i
$367$	5.70634	+	1.85410i	0.297868	+	0.0967833i	0.454139	−	0.890931i	$-0.349947\pi$
$367$	5.70634	+	1.85410i	0.297868	+	0.0967833i	−0.156270	+	0.987714i	$0.549947\pi$
$368$			4.47214i			0.233126i
$369$	0.427051	−	1.31433i	0.0222314	−	0.0684212i
$370$		0			0
$371$	1.90983	+	5.87785i	0.0991534	+	0.305163i
$372$	−6.88191	+	2.23607i	−0.356810	+	0.115935i
$373$	17.2905	−	23.7984i	0.895270	−	1.23223i	−0.0766827	−	0.997056i	$-0.524433\pi$
$373$	17.2905	−	23.7984i	0.895270	−	1.23223i	0.971952	−	0.235178i	$-0.0755672\pi$
$374$	9.23607			0.477586
$375$		0			0
$376$	15.7082			0.810089
$377$	−8.71078	+	11.9894i	−0.448628	+	0.617483i
$378$	−4.25325	+	1.38197i	−0.218764	+	0.0710807i
$379$	−7.23607	−	22.2703i	−0.371692	−	1.14395i	−0.945684	−	0.325089i	$-0.894606\pi$
$379$	−7.23607	−	22.2703i	−0.371692	−	1.14395i	0.573992	−	0.818861i	$-0.305394\pi$
$380$		0			0
$381$	3.00000	−	9.23305i	0.153695	−	0.473024i
$382$			24.6525i			1.26133i
$383$	19.8132	+	6.43769i	1.01241	+	0.328951i	0.767812	−	0.640675i	$-0.221345\pi$
$383$	19.8132	+	6.43769i	1.01241	+	0.328951i	0.244594	+	0.969626i	$0.421345\pi$
$384$	−2.42705	+	1.76336i	−0.123855	+	0.0899859i
$385$		0			0
$386$	−6.20820	−	4.51052i	−0.315989	−	0.229580i
$387$	−3.35520	−	4.61803i	−0.170554	−	0.234748i
$388$	5.20431	+	7.16312i	0.264209	+	0.363652i
$389$	−30.0066	−	21.8011i	−1.52139	−	1.10536i	−0.960791	−	0.277272i	$-0.910570\pi$
$389$	−30.0066	−	21.8011i	−1.52139	−	1.10536i	−0.560603	−	0.828085i	$-0.689430\pi$
$390$		0			0
$391$	−10.3262	+	7.50245i	−0.522220	+	0.379415i
$392$	37.0912	+	12.0517i	1.87339	+	0.608701i
$393$			14.1803i			0.715304i
$394$	−1.66312	+	5.11855i	−0.0837867	+	0.257869i
$395$		0			0
$396$	−1.00000	−	3.07768i	−0.0502519	−	0.154659i
$397$	10.4086	−	3.38197i	0.522394	−	0.169736i	−0.0359377	−	0.999354i	$-0.511442\pi$
$397$	10.4086	−	3.38197i	0.522394	−	0.169736i	0.558331	+	0.829618i	$0.311442\pi$
$398$	−10.9637	+	15.0902i	−0.549558	+	0.756402i
$399$	14.4721			0.724513
$400$		0			0
$401$	33.4508			1.67046			0.835228	−	0.549904i	$-0.185336\pi$
$401$	33.4508			1.67046			0.835228	+	0.549904i	$0.185336\pi$
$402$	−3.07768	+	4.23607i	−0.153501	+	0.211276i
$403$	−23.2744	+	7.56231i	−1.15938	+	0.376705i
$404$	−5.11803	−	15.7517i	−0.254632	−	0.783676i
$405$		0			0
$406$	6.05573	−	18.6376i	0.300541	−	0.924969i
$407$		−	26.1803i		−	1.29771i
$408$	8.14324	+	2.64590i	0.403150	+	0.130991i
$409$	20.8713	−	15.1639i	1.03202	−	0.749807i	0.0633084	−	0.997994i	$-0.479835\pi$
$409$	20.8713	−	15.1639i	1.03202	−	0.749807i	0.968712	+	0.248187i	$0.0798348\pi$
$410$		0			0
$411$	4.35410	+	3.16344i	0.214772	+	0.156041i
$412$	0.726543	+	1.00000i	0.0357942	+	0.0492665i
$413$	10.5146	+	14.4721i	0.517391	+	0.712127i
$414$	−3.61803	−	2.62866i	−0.177817	−	0.129191i
$415$		0			0
$416$	−13.6803	+	9.93935i	−0.670734	+	0.487317i
$417$	4.80828	+	1.56231i	0.235463	+	0.0765064i
$418$		−	10.4721i		−	0.512209i
$419$	−10.1803	+	31.3319i	−0.497342	+	1.53066i	0.315932	+	0.948782i	$0.397683\pi$
$419$	−10.1803	+	31.3319i	−0.497342	+	1.53066i	−0.813275	+	0.581880i	$0.802317\pi$
$420$		0			0
$421$	7.15248	+	22.0131i	0.348590	+	1.07285i	0.959634	+	0.281253i	$0.0907502\pi$
$421$	7.15248	+	22.0131i	0.348590	+	1.07285i	−0.611043	+	0.791597i	$0.709250\pi$
$422$	−17.0130	+	5.52786i	−0.828181	+	0.269092i
$423$	−3.07768	+	4.23607i	−0.149642	+	0.205965i
$424$	4.14590			0.201343
$425$		0			0
$426$	−0.763932			−0.0370126
$427$	1.62460	−	2.23607i	0.0786198	−	0.108211i
$428$	15.6659	−	5.09017i	0.757241	−	0.246043i
$429$	−3.38197	−	10.4086i	−0.163283	−	0.502533i
$430$		0			0
$431$	−3.29180	+	10.1311i	−0.158560	+	0.487998i	−0.998504	−	0.0546749i	$-0.982588\pi$
$431$	−3.29180	+	10.1311i	−0.158560	+	0.487998i	0.839944	+	0.542673i	$0.182588\pi$
$432$			1.00000i			0.0481125i
$433$	23.7562	+	7.71885i	1.14165	+	0.370944i	0.817991	−	0.575230i	$-0.195088\pi$
$433$	23.7562	+	7.71885i	1.14165	+	0.370944i	0.323657	+	0.946174i	$0.395088\pi$
$434$	26.1803	−	19.0211i	1.25670	−	0.913043i
$435$		0			0
$436$	−15.4443	−	11.2209i	−0.739646	−	0.537385i
$437$	8.50651	+	11.7082i	0.406921	+	0.560079i
$438$	−1.81636	−	2.50000i	−0.0867889	−	0.119455i
$439$	−5.00000	−	3.63271i	−0.238637	−	0.173380i	0.462039	−	0.886860i	$-0.347118\pi$
$439$	−5.00000	−	3.63271i	−0.238637	−	0.173380i	−0.700676	+	0.713480i	$0.747118\pi$
$440$		0			0
$441$	−10.5172	+	7.64121i	−0.500820	+	0.363867i
$442$	9.18005	+	2.98278i	0.436650	+	0.141876i
$443$		−	30.7639i		−	1.46164i	−0.682571	−	0.730819i	$-0.739138\pi$
$443$		−	30.7639i		−	1.46164i	0.682571	−	0.730819i	$-0.260862\pi$
$444$	2.50000	−	7.69421i	0.118645	−	0.365151i
$445$		0			0
$446$	−4.38197	−	13.4863i	−0.207492	−	0.638595i
$447$	−11.5514	+	3.75329i	−0.546364	+	0.177524i
$448$	18.4006	−	25.3262i	0.869346	−	1.19655i
$449$	7.79837			0.368028			0.184014	−	0.982924i	$-0.441091\pi$
$449$	7.79837			0.368028			0.184014	+	0.982924i	$0.441091\pi$
$450$		0			0
$451$	−4.47214			−0.210585
$452$	1.57160	−	2.16312i	0.0739217	−	0.101745i
$453$	−15.6659	+	5.09017i	−0.736050	+	0.239157i
$454$	6.18034	+	19.0211i	0.290058	+	0.892706i
$455$		0			0
$456$	3.00000	−	9.23305i	0.140488	−	0.432377i
$457$		−	22.3607i		−	1.04599i	−0.852336	−	0.522994i	$-0.824815\pi$
$457$		−	22.3607i		−	1.04599i	0.852336	−	0.522994i	$-0.175185\pi$
$458$	−23.7562	−	7.71885i	−1.11005	−	0.360678i
$459$	−2.30902	+	1.67760i	−0.107776	+	0.0783036i
$460$		0			0
$461$	6.63525	+	4.82079i	0.309035	+	0.224527i	0.731482	−	0.681861i	$-0.238829\pi$
$461$	6.63525	+	4.82079i	0.309035	+	0.224527i	−0.422448	+	0.906387i	$0.638829\pi$
$462$	8.50651	+	11.7082i	0.395759	+	0.544715i
$463$	−13.6578	−	18.7984i	−0.634733	−	0.873635i	0.363588	−	0.931560i	$-0.381552\pi$
$463$	−13.6578	−	18.7984i	−0.634733	−	0.873635i	−0.998321	+	0.0579252i	$0.981552\pi$
$464$	−3.54508	−	2.57565i	−0.164576	−	0.119572i
$465$		0			0
$466$	−11.8262	+	8.59226i	−0.547840	+	0.398029i
$467$	−5.53483	−	1.79837i	−0.256121	−	0.0832188i	0.178142	−	0.984005i	$-0.442991\pi$
$467$	−5.53483	−	1.79837i	−0.256121	−	0.0832188i	−0.434263	+	0.900786i	$0.642991\pi$
$468$		−	3.38197i		−	0.156331i
$469$	−7.23607	+	22.2703i	−0.334131	+	1.02835i
$470$		0			0
$471$	−4.26393	−	13.1230i	−0.196472	−	0.604677i
$472$	11.4127	−	3.70820i	0.525311	−	0.170684i
$473$	−10.8576	+	14.9443i	−0.499235	+	0.687138i
$474$		0			0
$475$		0			0
$476$	12.7639			0.585034
$477$	−0.812299	+	1.11803i	−0.0371926	+	0.0511913i
$478$	6.71040	−	2.18034i	0.306926	−	0.0997264i
$479$	−0.326238	−	1.00406i	−0.0149062	−	0.0458765i	0.943327	−	0.331865i	$-0.107678\pi$
$479$	−0.326238	−	1.00406i	−0.0149062	−	0.0458765i	−0.958233	+	0.285989i	$0.907678\pi$
$480$		0			0
$481$	8.45492	−	26.0216i	0.385511	−	1.18648i
$482$			1.03444i			0.0471175i
$483$	−19.0211	−	6.18034i	−0.865491	−	0.281215i
$484$	0.427051	−	0.310271i	0.0194114	−	0.0141032i
$485$		0			0
$486$	−0.809017	−	0.587785i	−0.0366978	−	0.0266625i
$487$	−2.17963	−	3.00000i	−0.0987684	−	0.135943i	0.756772	−	0.653679i	$-0.226775\pi$
$487$	−2.17963	−	3.00000i	−0.0987684	−	0.135943i	−0.855541	+	0.517736i	$0.826775\pi$
$488$	−1.08981	−	1.50000i	−0.0493336	−	0.0679018i
$489$	2.38197	+	1.73060i	0.107716	+	0.0782604i
$490$		0			0
$491$	24.1803	−	17.5680i	1.09124	−	0.792835i	0.111635	−	0.993749i	$-0.464391\pi$
$491$	24.1803	−	17.5680i	1.09124	−	0.792835i	0.979609	+	0.200915i	$0.0643914\pi$
$492$	−1.31433	−	0.427051i	−0.0592545	−	0.0192529i
$493$		−	12.5066i		−	0.563268i
$494$	3.38197	−	10.4086i	0.152162	−	0.468306i
$495$		0			0
$496$	−2.23607	−	6.88191i	−0.100402	−	0.309007i
$497$	−3.24920	+	1.05573i	−0.145746	+	0.0473559i
$498$	2.07363	−	2.85410i	0.0929214	−	0.127895i
$499$	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
$501$	−23.4164			−1.04617
$502$	15.8374	−	21.7984i	0.706860	−	0.972909i
$503$	−33.6830	+	10.9443i	−1.50185	+	0.487981i	−0.940557	−	0.339636i	$-0.889696\pi$
$503$	−33.6830	+	10.9443i	−1.50185	+	0.487981i	−0.561294	+	0.827617i	$0.689696\pi$
$504$	4.14590	+	12.7598i	0.184673	+	0.568365i
$505$		0			0
$506$	−4.47214	+	13.7638i	−0.198811	+	0.611876i
$507$			1.56231i			0.0693844i
$508$	−9.23305	−	3.00000i	−0.409650	−	0.133103i
$509$	21.7254	−	15.7844i	0.962963	−	0.699633i	0.00912564	−	0.999958i	$-0.497095\pi$
$509$	21.7254	−	15.7844i	0.962963	−	0.699633i	0.953837	+	0.300325i	$0.0970952\pi$
$510$		0			0
$511$	−11.1803	−	8.12299i	−0.494589	−	0.359340i
$512$	−6.46564	−	8.89919i	−0.285744	−	0.393292i
$513$	1.90211	+	2.61803i	0.0839803	+	0.115589i
$514$	−10.3541	−	7.52270i	−0.456700	−	0.331812i
$515$		0			0
$516$	−4.61803	+	3.35520i	−0.203298	+	0.147704i
$517$	16.1150	+	5.23607i	0.708735	+	0.230282i
$518$			36.1803i			1.58967i
$519$	−3.06231	+	9.42481i	−0.134420	+	0.413703i
$520$		0			0
$521$	0.628677	+	1.93487i	0.0275428	+	0.0847682i	0.963883	−	0.266326i	$-0.0858097\pi$
$521$	0.628677	+	1.93487i	0.0275428	+	0.0847682i	−0.936340	+	0.351094i	$0.885810\pi$
$522$	4.16750	−	1.35410i	0.182406	−	0.0592674i
$523$	−7.22494	+	9.94427i	−0.315924	+	0.434833i	−0.937217	−	0.348746i	$-0.886608\pi$
$523$	−7.22494	+	9.94427i	−0.315924	+	0.434833i	0.621293	+	0.783578i	$0.286608\pi$
$524$	14.1803			0.619471
$525$		0			0
$526$	11.8885			0.518365
$527$	12.1392	−	16.7082i	0.528793	−	0.727821i
$528$	3.07768	−	1.00000i	0.133939	−	0.0435194i
$529$	0.927051	+	2.85317i	0.0403066	+	0.124051i
$530$		0			0
$531$	−1.23607	+	3.80423i	−0.0536408	+	0.165089i
$532$		−	14.4721i		−	0.627447i
$533$	−4.44501	−	1.44427i	−0.192535	−	0.0625584i
$534$	6.16312	−	4.47777i	0.266704	−	0.193772i
$535$		0			0
$536$	12.7082	+	9.23305i	0.548911	+	0.398807i
$537$	3.63271	+	5.00000i	0.156763	+	0.215766i
$538$	0.0857567	+	0.118034i	0.00369723	+	0.00508881i
$539$	34.0344	+	24.7275i	1.46597	+	1.06509i
$540$		0			0
$541$	28.5795	−	20.7642i	1.22873	−	0.892724i	0.231936	−	0.972731i	$-0.425494\pi$
$541$	28.5795	−	20.7642i	1.22873	−	0.892724i	0.996794	+	0.0800067i	$0.0254942\pi$
$542$	−21.0948	−	6.85410i	−0.906097	−	0.294409i
$543$		−	9.79837i		−	0.420488i
$544$	4.40983	−	13.5721i	0.189070	−	0.581897i
$545$		0			0
$546$	4.67376	+	14.3844i	0.200019	+	0.615594i
$547$	−2.24514	+	0.729490i	−0.0959952	+	0.0311907i	−0.356621	−	0.934249i	$-0.616071\pi$
$547$	−2.24514	+	0.729490i	−0.0959952	+	0.0311907i	0.260626	+	0.965440i	$0.416071\pi$
$548$	3.16344	−	4.35410i	0.135135	−	0.185998i
$549$	0.618034			0.0263770
$550$		0			0
$551$	−14.1803			−0.604103
$552$	−7.88597	+	10.8541i	−0.335649	+	0.461981i
$553$		0			0
$554$	1.79180	+	5.51458i	0.0761261	+	0.234292i
$555$		0			0
$556$	1.56231	−	4.80828i	0.0662565	−	0.203917i
$557$		−	22.2705i		−	0.943632i	−0.881697	−	0.471816i	$-0.843599\pi$
$557$		−	22.2705i		−	0.943632i	0.881697	−	0.471816i	$-0.156401\pi$
$558$	6.88191	+	2.23607i	0.291334	+	0.0946603i
$559$	−15.6180	+	11.3472i	−0.660572	+	0.479934i
$560$		0			0
$561$	7.47214	+	5.42882i	0.315474	+	0.229205i
$562$	−10.2169	−	14.0623i	−0.430972	−	0.593183i
$563$	10.3026	+	14.1803i	0.434204	+	0.597630i	0.968912	−	0.247407i	$-0.0795784\pi$
$563$	10.3026	+	14.1803i	0.434204	+	0.597630i	−0.534708	+	0.845037i	$0.679578\pi$
$564$	4.23607	+	3.07768i	0.178371	+	0.129594i
$565$		0			0
$566$	−0.236068	+	0.171513i	−0.00992268	+	0.00720925i
$567$	−4.25325	−	1.38197i	−0.178620	−	0.0580371i
$568$			2.29180i			0.0961616i
$569$	9.35410	−	28.7890i	0.392144	−	1.20690i	−0.539019	−	0.842294i	$-0.681205\pi$
$569$	9.35410	−	28.7890i	0.392144	−	1.20690i	0.931163	−	0.364603i	$-0.118795\pi$
$570$		0			0
$571$	−6.56231	−	20.1967i	−0.274624	−	0.845206i	−0.989319	−	0.145769i	$-0.953434\pi$
$571$	−6.56231	−	20.1967i	−0.274624	−	0.845206i	0.714695	−	0.699437i	$-0.246566\pi$
$572$	−10.4086	+	3.38197i	−0.435206	+	0.141407i
$573$	−14.4904	+	19.9443i	−0.605344	+	0.833184i
$574$	6.18034			0.257962
$575$		0			0
$576$	7.00000			0.291667
$577$	18.1886	−	25.0344i	0.757201	−	1.04220i	−0.240241	−	0.970713i	$-0.577226\pi$
$577$	18.1886	−	25.0344i	0.757201	−	1.04220i	0.997442	−	0.0714842i	$-0.0227735\pi$
$578$	8.42075	−	2.73607i	0.350257	−	0.113805i
$579$	−2.37132	−	7.29818i	−0.0985488	−	0.303302i
$580$		0			0
$581$	4.87539	−	15.0049i	0.202265	−	0.622508i
$582$		−	8.85410i		−	0.367014i
$583$	4.25325	+	1.38197i	0.176152	+	0.0572352i
$584$	−7.50000	+	5.44907i	−0.310352	+	0.225484i
$585$		0			0
$586$	−3.07295	−	2.23263i	−0.126942	−	0.0922290i
$587$	−8.57202	−	11.7984i	−0.353805	−	0.486971i	0.594605	−	0.804018i	$-0.297309\pi$
$587$	−8.57202	−	11.7984i	−0.353805	−	0.486971i	−0.948410	+	0.317047i	$0.897309\pi$
$588$	7.64121	+	10.5172i	0.315118	+	0.433723i
$589$	−18.9443	−	13.7638i	−0.780585	−	0.567128i
$590$		0			0
$591$	−4.35410	+	3.16344i	−0.179104	+	0.130127i
$592$	7.69421	+	2.50000i	0.316230	+	0.102749i
$593$		−	32.7426i		−	1.34458i	−0.740288	−	0.672290i	$-0.765311\pi$
$593$		−	32.7426i		−	1.34458i	0.740288	−	0.672290i	$-0.234689\pi$
$594$	−1.00000	+	3.07768i	−0.0410305	+	0.126279i
$595$		0			0
$596$	3.75329	+	11.5514i	0.153741	+	0.473165i
$597$	−17.7396	+	5.76393i	−0.726032	+	0.235902i
$598$	−8.89002	+	12.2361i	−0.363540	+	0.500370i
$599$	12.4721			0.509598			0.254799	−	0.966994i	$-0.417991\pi$
$599$	12.4721			0.509598			0.254799	+	0.966994i	$0.417991\pi$
$600$		0			0
$601$	−24.3262			−0.992288			−0.496144	−	0.868240i	$-0.665251\pi$
$601$	−24.3262			−0.992288			−0.496144	+	0.868240i	$0.665251\pi$
$602$	15.0049	−	20.6525i	0.611554	−	0.841732i
$603$	−4.97980	+	1.61803i	−0.202793	+	0.0658914i
$604$	5.09017	+	15.6659i	0.207116	+	0.637438i
$605$		0			0
$606$	−5.11803	+	15.7517i	−0.207906	+	0.639869i
$607$			39.2361i			1.59254i	0.604940	+	0.796271i	$0.293197\pi$
$607$			39.2361i			1.59254i	−0.604940	+	0.796271i	$0.706803\pi$
$608$	−15.3884	−	5.00000i	−0.624083	−	0.202777i
$609$	15.8541	−	11.5187i	0.642441	−	0.466760i
$610$		0			0
$611$	14.3262	+	10.4086i	0.579578	+	0.421088i
$612$	1.67760	+	2.30902i	0.0678129	+	0.0933365i
$613$	−23.2214	−	31.9615i	−0.937903	−	1.29091i	−0.956696	−	0.291089i	$-0.905982\pi$
$613$	−23.2214	−	31.9615i	−0.937903	−	1.29091i	0.0187931	−	0.999823i	$-0.494018\pi$
$614$	1.09017	+	0.792055i	0.0439957	+	0.0319647i
$615$		0			0
$616$	35.1246	−	25.5195i	1.41521	−	1.02821i
$617$	−25.6583	−	8.33688i	−1.03296	−	0.335630i	−0.257002	−	0.966411i	$-0.582735\pi$
$617$	−25.6583	−	8.33688i	−1.03296	−	0.335630i	−0.775961	+	0.630781i	$0.782735\pi$
$618$		−	1.23607i		−	0.0497219i
$619$	−8.76393	+	26.9726i	−0.352252	+	1.08412i	0.605333	+	0.795972i	$0.293040\pi$
$619$	−8.76393	+	26.9726i	−0.352252	+	1.08412i	−0.957586	+	0.288149i	$0.906960\pi$
$620$		0			0
$621$	−1.38197	−	4.25325i	−0.0554564	−	0.170677i
$622$	4.08174	−	1.32624i	0.163663	−	0.0531773i
$623$	20.0252	−	27.5623i	0.802292	−	1.10426i
$624$	3.38197			0.135387
$625$		0			0
$626$	8.47214			0.338615
$627$	6.15537	−	8.47214i	0.245822	−	0.338345i
$628$	−13.1230	+	4.26393i	−0.523666	+	0.170149i
$629$	7.13525	+	21.9601i	0.284501	+	0.875605i
$630$		0			0
$631$	3.18034	−	9.78808i	0.126607	−	0.389657i	−0.867583	−	0.497292i	$-0.834328\pi$
$631$	3.18034	−	9.78808i	0.126607	−	0.389657i	0.994190	+	0.107635i	$0.0343277\pi$
$632$		0			0
$633$	−17.0130	−	5.52786i	−0.676207	−	0.219713i
$634$	−20.0902	+	14.5964i	−0.797883	+	0.579696i
$635$		0			0
$636$	1.11803	+	0.812299i	0.0443329	+	0.0322098i
$637$	25.8423	+	35.5689i	1.02391	+	1.40929i
$638$	−8.33499	−	11.4721i	−0.329986	−	0.454186i
$639$	−0.618034	−	0.449028i	−0.0244490	−	0.0177633i
$640$		0			0
$641$	−31.5066	+	22.8909i	−1.24444	+	0.904135i	−0.997886	−	0.0649953i	$-0.979297\pi$
$641$	−31.5066	+	22.8909i	−1.24444	+	0.904135i	−0.246549	+	0.969130i	$0.579297\pi$
$642$	−15.6659	−	5.09017i	−0.618285	−	0.200893i
$643$			13.8885i			0.547711i	0.961771	+	0.273855i	$0.0882990\pi$
$643$			13.8885i			0.547711i	−0.961771	+	0.273855i	$0.911701\pi$
$644$	−6.18034	+	19.0211i	−0.243540	+	0.749538i
$645$		0			0
$646$	2.85410	+	8.78402i	0.112293	+	0.345603i
$647$	9.85359	−	3.20163i	0.387385	−	0.125869i	−0.108848	−	0.994058i	$-0.534716\pi$
$647$	9.85359	−	3.20163i	0.387385	−	0.125869i	0.496233	+	0.868189i	$0.334716\pi$
$648$	−1.76336	+	2.42705i	−0.0692712	+	0.0953436i
$649$	12.9443			0.508107
$650$		0			0
$651$	32.3607			1.26832
$652$	1.73060	−	2.38197i	0.0677755	−	0.0932850i
$653$	−42.8958	+	13.9377i	−1.67864	+	0.545424i	−0.984647	−	0.174555i	$-0.944151\pi$
$653$	−42.8958	+	13.9377i	−1.67864	+	0.545424i	−0.693995	+	0.719979i	$0.744151\pi$
$654$	5.89919	+	18.1558i	0.230676	+	0.709949i
$655$		0			0
$656$	0.427051	−	1.31433i	0.0166735	−	0.0513159i
$657$		−	3.09017i		−	0.120559i
$658$	−22.2703	−	7.23607i	−0.868188	−	0.282091i
$659$	−5.32624	+	3.86974i	−0.207481	+	0.150744i	−0.686673	−	0.726966i	$-0.740930\pi$
$659$	−5.32624	+	3.86974i	−0.207481	+	0.150744i	0.479192	+	0.877710i	$0.340930\pi$
$660$		0			0
$661$	−20.5623	−	14.9394i	−0.799781	−	0.581075i	0.111069	−	0.993813i	$-0.464573\pi$
$661$	−20.5623	−	14.9394i	−0.799781	−	0.581075i	−0.910850	+	0.412738i	$0.864573\pi$
$662$	6.43288	+	8.85410i	0.250021	+	0.344124i
$663$	5.67358	+	7.80902i	0.220344	+	0.303277i
$664$	−8.56231	−	6.22088i	−0.332282	−	0.241417i
$665$		0			0
$666$	−6.54508	+	4.75528i	−0.253617	+	0.184263i
$667$	18.6376	+	6.05573i	0.721651	+	0.234479i
$668$			23.4164i			0.906008i
$669$	4.38197	−	13.4863i	0.169417	−	0.521411i
$670$		0			0
$671$	−0.618034	−	1.90211i	−0.0238589	−	0.0734303i
$672$	21.2663	−	6.90983i	0.820364	−	0.266552i
$673$	17.5150	−	24.1074i	0.675155	−	0.929272i	−0.324708	−	0.945814i	$-0.605266\pi$
$673$	17.5150	−	24.1074i	0.675155	−	0.929272i	0.999863	+	0.0165428i	$0.00526596\pi$
$674$	14.9443			0.575632
$675$		0			0
$676$	1.56231			0.0600887
$677$	−21.9928	+	30.2705i	−0.845252	+	1.16339i	0.139636	+	0.990203i	$0.455407\pi$
$677$	−21.9928	+	30.2705i	−0.845252	+	1.16339i	−0.984889	+	0.173187i	$0.944593\pi$
$678$	−2.54290	+	0.826238i	−0.0976594	+	0.0317315i
$679$	−12.2361	−	37.6587i	−0.469577	−	1.44521i
$680$		0			0
$681$	−6.18034	+	19.0211i	−0.236831	+	0.728891i
$682$		−	23.4164i		−	0.896661i
$683$	7.05342	+	2.29180i	0.269892	+	0.0876931i	0.440836	−	0.897588i	$-0.354682\pi$
$683$	7.05342	+	2.29180i	0.269892	+	0.0876931i	−0.170945	+	0.985281i	$0.554682\pi$
$684$	2.61803	−	1.90211i	0.100103	−	0.0727291i
$685$		0			0
$686$	−21.7082	−	15.7719i	−0.828823	−	0.602175i
$687$	−14.6821	−	20.2082i	−0.560158	−	0.770991i
$688$	−3.35520	−	4.61803i	−0.127916	−	0.176061i
$689$	3.78115	+	2.74717i	0.144050	+	0.104659i
$690$		0			0
$691$	17.1803	−	12.4822i	0.653571	−	0.474847i	−0.210915	−	0.977504i	$-0.567644\pi$
$691$	17.1803	−	12.4822i	0.653571	−	0.474847i	0.864486	+	0.502657i	$0.167644\pi$
$692$	9.42481	+	3.06231i	0.358277	+	0.116411i
$693$			14.4721i			0.549751i
$694$	10.4164	−	32.0584i	0.395401	−	1.21692i
$695$		0			0
$696$	−4.06231	−	12.5025i	−0.153981	−	0.473906i
$697$	3.75123	−	1.21885i	0.142088	−	0.0461671i
$698$	14.7149	−	20.2533i	0.556966	−	0.766598i
$699$	−14.6180			−0.552905
$700$		0			0
$701$	0.437694			0.0165315			0.00826574	−	0.999966i	$-0.497369\pi$
$701$	0.437694			0.0165315			0.00826574	+	0.999966i	$0.497369\pi$
$702$	−1.98787	+	2.73607i	−0.0750273	+	0.103266i
$703$	24.8990	−	8.09017i	0.939083	−	0.305127i
$704$	−7.00000	−	21.5438i	−0.263822	−	0.811962i
$705$		0			0
$706$	−9.38197	+	28.8747i	−0.353095	+	1.08671i
$707$			74.0689i			2.78565i
$708$	3.80423	+	1.23607i	0.142972	+	0.0464543i
$709$	−5.44427	+	3.95550i	−0.204464	+	0.148552i	−0.685305	−	0.728256i	$-0.740331\pi$
$709$	−5.44427	+	3.95550i	−0.204464	+	0.148552i	0.480841	+	0.876808i	$0.340331\pi$
$710$		0			0
$711$		0			0
$712$	−13.4333	−	18.4894i	−0.503434	−	0.692918i
$713$	19.0211	+	26.1803i	0.712347	+	0.980461i
$714$	−10.3262	−	7.50245i	−0.386450	−	0.280772i
$715$		0			0
$716$	5.00000	−	3.63271i	0.186859	−	0.135761i
$717$	6.71040	+	2.18034i	0.250604	+	0.0814263i
$718$		−	10.5836i		−	0.394976i
$719$	11.0902	−	34.1320i	0.413594	−	1.27291i	−0.499909	−	0.866078i	$-0.666633\pi$
$719$	11.0902	−	34.1320i	0.413594	−	1.27291i	0.913503	−	0.406832i	$-0.133367\pi$
$720$		0			0
$721$	−1.70820	−	5.25731i	−0.0636168	−	0.195792i
$722$	−8.11048	+	2.63525i	−0.301841	+	0.0980740i
$723$	−0.608030	+	0.836881i	−0.0226129	+	0.0311239i
$724$	−9.79837			−0.364154
$725$		0			0
$726$	−0.527864			−0.0195909
$727$	−9.02105	+	12.4164i	−0.334572	+	0.460499i	−0.942846	−	0.333228i	$-0.891862\pi$
$727$	−9.02105	+	12.4164i	−0.334572	+	0.460499i	0.608274	+	0.793727i	$0.291862\pi$
$728$	43.1531	−	14.0213i	1.59936	−	0.519663i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$		0			0
$731$	5.03444	−	15.4944i	0.186206	−	0.573082i
$732$		−	0.618034i		−	0.0228432i
$733$	2.45714	+	0.798374i	0.0907566	+	0.0294886i	0.354043	−	0.935229i	$-0.384807\pi$
$733$	2.45714	+	0.798374i	0.0907566	+	0.0294886i	−0.263287	+	0.964718i	$0.584807\pi$
$734$	−4.85410	+	3.52671i	−0.179168	+	0.130173i
$735$		0			0
$736$	18.0902	+	13.1433i	0.666813	+	0.484468i
$737$	9.95959	+	13.7082i	0.366866	+	0.504948i
$738$	0.812299	+	1.11803i	0.0299011	+	0.0411554i
$739$	14.3262	+	10.4086i	0.526999	+	0.382887i	0.819234	−	0.573459i	$-0.194399\pi$
$739$	14.3262	+	10.4086i	0.526999	+	0.382887i	−0.292235	+	0.956347i	$0.594399\pi$
$740$		0			0
$741$	8.85410	−	6.43288i	0.325264	−	0.236318i
$742$	−5.87785	−	1.90983i	−0.215783	−	0.0701121i
$743$			0.875388i			0.0321149i	0.999871	+	0.0160574i	$0.00511146\pi$
$743$			0.875388i			0.0321149i	−0.999871	+	0.0160574i	$0.994889\pi$
$744$	6.70820	−	20.6457i	0.245935	−	0.756909i
$745$		0			0
$746$	9.09017	+	27.9767i	0.332815	+	1.02430i
$747$	3.35520	−	1.09017i	0.122760	−	0.0398872i
$748$	5.42882	−	7.47214i	0.198497	−	0.273208i
$749$	−73.6656			−2.69168
$750$		0			0
$751$	5.34752			0.195134			0.0975670	−	0.995229i	$-0.468894\pi$
$751$	5.34752			0.195134			0.0975670	+	0.995229i	$0.468894\pi$
$752$	−3.07768	+	4.23607i	−0.112232	+	0.154474i
$753$	25.6255	−	8.32624i	0.933846	−	0.303425i
$754$	−4.57953	−	14.0943i	−0.166777	−	0.513285i
$755$		0			0
$756$	−1.38197	+	4.25325i	−0.0502616	+	0.154689i
$757$		−	27.3820i		−	0.995214i	−0.867402	−	0.497607i	$-0.834212\pi$
$757$		−	27.3820i		−	0.995214i	0.867402	−	0.497607i	$-0.165788\pi$
$758$	22.2703	+	7.23607i	0.808895	+	0.262826i
$759$	−11.7082	+	8.50651i	−0.424981	+	0.308767i
$760$		0			0
$761$	7.88197	+	5.72658i	0.285721	+	0.207588i	0.721409	−	0.692509i	$-0.243495\pi$
$761$	7.88197	+	5.72658i	0.285721	+	0.207588i	−0.435688	+	0.900098i	$0.643495\pi$
$762$	5.70634	+	7.85410i	0.206719	+	0.284524i
$763$	50.1815	+	69.0689i	1.81669	+	2.50046i
$764$	19.9443	+	14.4904i	0.721558	+	0.524243i
$765$		0			0
$766$	−16.8541	+	12.2452i	−0.608963	+	0.442438i
$767$	12.8658	+	4.18034i	0.464556	+	0.150943i
$768$		−	17.0000i		−	0.613435i
$769$	1.74265	−	5.36331i	0.0628414	−	0.193406i	−0.914707	−	0.404118i	$-0.867578\pi$
$769$	1.74265	−	5.36331i	0.0628414	−	0.193406i	0.977548	+	0.210712i	$0.0675784\pi$
$770$		0			0
$771$	−3.95492	−	12.1720i	−0.142433	−	0.438363i
$772$	−7.29818	+	2.37132i	−0.262667	+	0.0853458i
$773$	−21.1150	+	29.0623i	−0.759454	+	1.04530i	0.237805	+	0.971313i	$0.423572\pi$
$773$	−21.1150	+	29.0623i	−0.759454	+	1.04530i	−0.997259	+	0.0739857i	$0.976428\pi$
$774$	5.70820			0.205177
$775$		0			0
$776$	−26.5623			−0.953531
$777$	−21.2663	+	29.2705i	−0.762923	+	1.05007i
$778$	35.2748	−	11.4615i	1.26466	−	0.410914i
$779$	−1.38197	−	4.25325i	−0.0495141	−	0.152389i
$780$		0			0
$781$	−0.763932	+	2.35114i	−0.0273356	+	0.0841304i
$782$		−	12.7639i		−	0.456437i
$783$	4.16750	+	1.35410i	0.148934	+	0.0483917i
$784$	−10.5172	+	7.64121i	−0.375615	+	0.272900i
$785$		0			0
$786$	−11.4721	−	8.33499i	−0.409198	−	0.297299i
$787$	4.80828	+	6.61803i	0.171397	+	0.235907i	0.886070	−	0.463551i	$-0.153425\pi$
$787$	4.80828	+	6.61803i	0.171397	+	0.235907i	−0.714674	+	0.699458i	$0.753425\pi$
$788$	3.16344	+	4.35410i	0.112693	+	0.155108i
$789$	9.61803	+	6.98791i	0.342411	+	0.248776i
$790$		0			0
$791$	−9.67376	+	7.02840i	−0.343959	+	0.249901i
$792$	9.23305	+	3.00000i	0.328082	+	0.106600i
$793$		−	2.09017i		−	0.0742241i
$794$	−3.38197	+	10.4086i	−0.120021	+	0.369388i
$795$		0			0
$796$	5.76393	+	17.7396i	0.204297	+	0.628762i
$797$	36.2384	−	11.7746i	1.28363	−	0.417077i	0.413773	−	0.910380i	$-0.364211\pi$
$797$	36.2384	−	11.7746i	1.28363	−	0.417077i	0.869857	+	0.493303i	$0.164211\pi$
$798$	−8.50651	+	11.7082i	−0.301127	+	0.414466i
$799$	−14.9443			−0.528690
$800$		0			0
$801$	7.61803			0.269170
$802$	−19.6619	+	27.0623i	−0.694286	+	0.955603i
$803$	−9.51057	+	3.09017i	−0.335621	+	0.109050i
$804$	1.61803	+	4.97980i	0.0570637	+	0.175624i
$805$		0			0
$806$	7.56231	−	23.2744i	0.266371	−	0.819805i
$807$			0.145898i			0.00513585i
$808$	47.2551	+	15.3541i	1.66243	+	0.540155i
$809$	−18.7812	+	13.6453i	−0.660310	+	0.479743i	−0.866768	−	0.498712i	$-0.833806\pi$
$809$	−18.7812	+	13.6453i	−0.660310	+	0.479743i	0.206457	+	0.978456i	$0.433806\pi$
$810$		0			0
$811$	−7.47214	−	5.42882i	−0.262382	−	0.190632i	0.448814	−	0.893625i	$-0.351846\pi$
$811$	−7.47214	−	5.42882i	−0.262382	−	0.190632i	−0.711197	+	0.702993i	$0.751846\pi$
$812$	−11.5187	−	15.8541i	−0.404226	−	0.556370i
$813$	−13.0373	−	17.9443i	−0.457237	−	0.629333i
$814$	21.1803	+	15.3884i	0.742371	+	0.539364i
$815$		0			0
$816$	−2.30902	+	1.67760i	−0.0808318	+	0.0587277i
$817$	−17.5680	−	5.70820i	−0.614628	−	0.199705i
$818$			25.7984i			0.902019i
$819$	−4.67376	+	14.3844i	−0.163314	+	0.502630i
$820$		0			0
$821$	1.56231	+	4.80828i	0.0545249	+	0.167810i	0.974611	−	0.223907i	$-0.0718812\pi$
$821$	1.56231	+	4.80828i	0.0545249	+	0.167810i	−0.920086	+	0.391717i	$0.871881\pi$
$822$	−5.11855	+	1.66312i	−0.178530	+	0.0580079i
$823$	−8.67802	+	11.9443i	−0.302497	+	0.416351i	−0.933023	−	0.359817i	$-0.882839\pi$
$823$	−8.67802	+	11.9443i	−0.302497	+	0.416351i	0.630526	+	0.776168i	$0.282839\pi$
$824$	−3.70820			−0.129181
$825$		0			0
$826$	−17.8885			−0.622422
$827$	−12.9718	+	17.8541i	−0.451072	+	0.620848i	−0.972628	−	0.232370i	$-0.925352\pi$
$827$	−12.9718	+	17.8541i	−0.451072	+	0.620848i	0.521555	+	0.853218i	$0.325352\pi$
$828$	−4.25325	+	1.38197i	−0.147811	+	0.0480266i
$829$	8.19098	+	25.2093i	0.284485	+	0.875554i	0.986553	+	0.163444i	$0.0522602\pi$
$829$	8.19098	+	25.2093i	0.284485	+	0.875554i	−0.702068	+	0.712110i	$0.747740\pi$
$830$		0			0
$831$	−1.79180	+	5.51458i	−0.0621567	+	0.191299i
$832$		−	23.6738i		−	0.820740i
$833$	−35.2874	−	11.4656i	−1.22263	−	0.397258i
$834$	−4.09017	+	2.97168i	−0.141631	+	0.102901i
$835$		0			0
$836$	−8.47214	−	6.15537i	−0.293015	−	0.212888i
$837$	4.25325	+	5.85410i	0.147014	+	0.202347i
$838$	−19.3642	−	26.6525i	−0.668924	−	0.920695i
$839$	−35.6525	−	25.9030i	−1.23086	−	0.894272i	−0.233906	−	0.972259i	$-0.575151\pi$
$839$	−35.6525	−	25.9030i	−1.23086	−	0.894272i	−0.996954	+	0.0779870i	$0.975151\pi$
$840$		0			0
$841$	7.92705	−	5.75934i	0.273347	−	0.198598i
$842$	−22.0131	−	7.15248i	−0.758620	−	0.246491i
$843$		−	17.3820i		−	0.598667i
$844$	−5.52786	+	17.0130i	−0.190277	+	0.585612i
$845$		0			0
$846$	−1.61803	−	4.97980i	−0.0556292	−	0.171209i
$847$	−2.24514	+	0.729490i	−0.0771439	+	0.0250656i
$848$	−0.812299	+	1.11803i	−0.0278945	+	0.0383934i
$849$	−0.291796			−0.0100144
$850$		0			0
$851$	−36.1803			−1.24025
$852$	−0.449028	+	0.618034i	−0.0153834	+	0.0211735i
$853$	−28.3929	+	9.22542i	−0.972156	+	0.315873i	−0.751686	−	0.659521i	$-0.770759\pi$
$853$	−28.3929	+	9.22542i	−0.972156	+	0.315873i	−0.220470	+	0.975394i	$0.570759\pi$
$854$	0.854102	+	2.62866i	0.0292268	+	0.0899507i
$855$		0			0
$856$	−15.2705	+	46.9978i	−0.521935	+	1.60635i
$857$			3.52786i			0.120510i	0.998183	+	0.0602548i	$0.0191913\pi$
$857$			3.52786i			0.120510i	−0.998183	+	0.0602548i	$0.980809\pi$
$858$	10.4086	+	3.38197i	0.355344	+	0.115458i
$859$	2.76393	−	2.00811i	0.0943041	−	0.0685160i	−0.539634	−	0.841900i	$-0.681437\pi$
$859$	2.76393	−	2.00811i	0.0943041	−	0.0685160i	0.633938	+	0.773384i	$0.281437\pi$
$860$		0			0
$861$	5.00000	+	3.63271i	0.170400	+	0.123803i
$862$	−6.26137	−	8.61803i	−0.213263	−	0.293531i
$863$	−30.0503	−	41.3607i	−1.02292	−	1.40793i	−0.910134	−	0.414315i	$-0.864021\pi$
$863$	−30.0503	−	41.3607i	−1.02292	−	1.40793i	−0.112790	−	0.993619i	$-0.535979\pi$
$864$	4.04508	+	2.93893i	0.137617	+	0.0999843i
$865$		0			0
$866$	−20.2082	+	14.6821i	−0.686703	+	0.498919i
$867$	8.42075	+	2.73607i	0.285984	+	0.0929217i
$868$		−	32.3607i		−	1.09839i
$869$		0			0
$870$		0			0
$871$	5.47214	+	16.8415i	0.185416	+	0.570653i
$872$	54.4675	−	17.6976i	1.84450	−	0.599315i
$873$	5.20431	−	7.16312i	0.176139	−	0.242435i
$874$	−14.4721			−0.489527
$875$		0			0
$876$	−3.09017			−0.104407
$877$	−10.7064	+	14.7361i	−0.361529	+	0.497602i	−0.950574	−	0.310499i	$-0.899504\pi$
$877$	−10.7064	+	14.7361i	−0.361529	+	0.497602i	0.589045	+	0.808100i	$0.299504\pi$
$878$	5.87785	−	1.90983i	0.198368	−	0.0644536i
$879$	−1.17376	−	3.61247i	−0.0395900	−	0.121846i
$880$		0			0
$881$	7.74265	−	23.8294i	0.260856	−	0.802833i	−0.731763	−	0.681559i	$-0.761302\pi$
$881$	7.74265	−	23.8294i	0.260856	−	0.802833i	0.992619	−	0.121274i	$-0.0386979\pi$
$882$		−	13.0000i		−	0.437733i
$883$	−0.171513	−	0.0557281i	−0.00577189	−	0.00187540i	0.306130	−	0.951990i	$-0.400966\pi$
$883$	−0.171513	−	0.0557281i	−0.00577189	−	0.00187540i	−0.311902	+	0.950114i	$0.600966\pi$
$884$	7.80902	−	5.67358i	0.262646	−	0.190823i
$885$		0			0
$886$	24.8885	+	18.0826i	0.836147	+	0.607496i
$887$	10.0656	+	13.8541i	0.337970	+	0.465175i	0.943847	−	0.330383i	$-0.107178\pi$
$887$	10.0656	+	13.8541i	0.337970	+	0.465175i	−0.605877	+	0.795558i	$0.707178\pi$
$888$	14.2658	+	19.6353i	0.478731	+	0.658916i
$889$	35.1246	+	25.5195i	1.17804	+	0.855897i
$890$		0			0
$891$	−2.61803	+	1.90211i	−0.0877074	+	0.0637232i
$892$	−13.4863	−	4.38197i	−0.451555	−	0.146719i
$893$			16.9443i			0.567018i
$894$	3.75329	−	11.5514i	0.125529	−	0.386338i
$895$		0			0
$896$	−4.14590	−	12.7598i	−0.138505	−	0.426274i
$897$	−14.3844	+	4.67376i	−0.480280	+	0.156052i
$898$	−4.58377	+	6.30902i	−0.152962	+	0.210535i
$899$	−31.7082			−1.05753
$900$		0			0
$901$	−3.94427			−0.131403
$902$	2.62866	−	3.61803i	0.0875247	−	0.120467i
$903$	24.2784	−	7.88854i	0.807936	−	0.262514i
$904$	2.47871	+	7.62870i	0.0824408	+	0.253727i
$905$		0			0
$906$	5.09017	−	15.6659i	0.169110	−	0.520466i
$907$			33.1246i			1.09988i	0.835203	+	0.549942i	$0.185350\pi$
$907$			33.1246i			1.09988i	−0.835203	+	0.549942i	$0.814650\pi$
$908$	19.0211	+	6.18034i	0.631238	+	0.205102i
$909$	−13.3992	+	9.73508i	−0.444423	+	0.322892i
$910$		0			0
$911$	3.38197	+	2.45714i	0.112050	+	0.0814088i	0.642399	−	0.766370i	$-0.277939\pi$
$911$	3.38197	+	2.45714i	0.112050	+	0.0814088i	−0.530349	+	0.847779i	$0.677939\pi$
$912$	1.90211	+	2.61803i	0.0629853	+	0.0866918i
$913$	−6.71040	−	9.23607i	−0.222082	−	0.305669i
$914$	18.0902	+	13.1433i	0.598370	+	0.434741i
$915$		0			0
$916$	−20.2082	+	14.6821i	−0.667698	+	0.485111i
$917$	−60.3126	−	19.5967i	−1.99170	−	0.647142i
$918$		−	2.85410i		−	0.0941994i
$919$	15.2016	−	46.7858i	0.501455	−	1.54332i	−0.305194	−	0.952290i	$-0.598721\pi$
$919$	15.2016	−	46.7858i	0.501455	−	1.54332i	0.806649	−	0.591031i	$-0.201279\pi$
$920$		0			0
$921$	0.416408	+	1.28157i	0.0137211	+	0.0422292i
$922$	−7.80021	+	2.53444i	−0.256886	+	0.0834674i
$923$	−1.51860	+	2.09017i	−0.0499852	+	0.0687988i
$924$	14.4721			0.476098
$925$		0			0
$926$	23.2361			0.763585
$927$	0.726543	−	1.00000i	0.0238628	−	0.0328443i
$928$	−20.8375	+	6.77051i	−0.684024	+	0.222253i
$929$	−0.645898	−	1.98787i	−0.0211912	−	0.0652199i	0.939902	−	0.341445i	$-0.110916\pi$
$929$	−0.645898	−	1.98787i	−0.0211912	−	0.0652199i	−0.961093	+	0.276225i	$0.910916\pi$
$930$		0			0
$931$	−13.0000	+	40.0099i	−0.426058	+	1.31127i
$932$			14.6180i			0.478830i
$933$	4.08174	+	1.32624i	0.133630	+	0.0434191i
$934$	4.70820	−	3.42071i	0.154057	−	0.111929i
$935$		0			0
$936$	8.20820	+	5.96361i	0.268294	+	0.194927i
$937$	6.86940	+	9.45492i	0.224413	+	0.308879i	0.906346	−	0.422537i	$-0.138860\pi$
$937$	6.86940	+	9.45492i	0.224413	+	0.308879i	−0.681932	+	0.731415i	$0.738860\pi$
$938$	−13.7638	−	18.9443i	−0.449405	−	0.618552i
$939$	6.85410	+	4.97980i	0.223675	+	0.162510i
$940$		0			0
$941$	−4.30902	+	3.13068i	−0.140470	+	0.102057i	−0.655801	−	0.754934i	$-0.727669\pi$
$941$	−4.30902	+	3.13068i	−0.140470	+	0.102057i	0.515331	+	0.856991i	$0.327669\pi$
$942$	13.1230	+	4.26393i	0.427572	+	0.138926i
$943$			6.18034i			0.201260i
$944$	−1.23607	+	3.80423i	−0.0402306	+	0.123817i
$945$		0			0
$946$	−5.70820	−	17.5680i	−0.185590	−	0.571186i
$947$	27.9767	−	9.09017i	0.909120	−	0.295391i	0.183124	−	0.983090i	$-0.441379\pi$
$947$	27.9767	−	9.09017i	0.909120	−	0.295391i	0.725996	+	0.687699i	$0.241379\pi$
$948$		0			0
$949$	−10.4508			−0.339249
$950$		0			0
$951$	−24.8328			−0.805259
$952$	−22.5074	+	30.9787i	−0.729468	+	1.00403i
$953$	−9.59632	+	3.11803i	−0.310855	+	0.101003i	−0.460290	−	0.887769i	$-0.652255\pi$
$953$	−9.59632	+	3.11803i	−0.310855	+	0.101003i	0.149435	+	0.988772i	$0.452255\pi$
$954$	−0.427051	−	1.31433i	−0.0138263	−	0.0425529i
$955$		0			0
$956$	2.18034	−	6.71040i	0.0705172	−	0.217030i
$957$		−	14.1803i		−	0.458385i
$958$	1.00406	+	0.326238i	0.0324396	+	0.0105403i
$959$	−19.4721	+	14.1473i	−0.628788	+	0.456841i
$960$		0			0
$961$	−17.2812	−	12.5555i	−0.557457	−	0.405016i
$962$	16.0822	+	22.1353i	0.518511	+	0.713669i
$963$	−9.68208	−	13.3262i	−0.312001	−	0.429432i
$964$	0.836881	+	0.608030i	0.0269541	+	0.0195833i
$965$		0			0
$966$	16.1803	−	11.7557i	0.520594	−	0.378234i
$967$	−33.1280	−	10.7639i	−1.06532	−	0.346145i	−0.276659	−	0.960968i	$-0.589227\pi$
$967$	−33.1280	−	10.7639i	−1.06532	−	0.346145i	−0.788665	+	0.614823i	$0.789227\pi$
$968$			1.58359i			0.0508986i
$969$	−2.85410	+	8.78402i	−0.0916870	+	0.282183i
$970$		0			0
$971$	−2.03444	−	6.26137i	−0.0652883	−	0.200937i	0.913091	−	0.407756i	$-0.133689\pi$
$971$	−2.03444	−	6.26137i	−0.0652883	−	0.200937i	−0.978379	+	0.206819i	$0.933689\pi$
$972$	−0.951057	+	0.309017i	−0.0305052	+	0.00991172i
$973$	−13.2898	+	18.2918i	−0.426050	+	0.586408i
$974$	3.70820			0.118819
$975$		0			0
$976$	0.618034			0.0197828
$977$	26.8869	−	37.0066i	0.860187	−	1.18395i	−0.121338	−	0.992611i	$-0.538719\pi$
$977$	26.8869	−	37.0066i	0.860187	−	1.18395i	0.981525	−	0.191334i	$-0.0612814\pi$
$978$	−2.80017	+	0.909830i	−0.0895395	+	0.0290932i
$979$	−7.61803	−	23.4459i	−0.243473	−	0.749334i
$980$		0			0
$981$	−5.89919	+	18.1558i	−0.188347	+	0.579671i
$982$			29.8885i			0.953782i
$983$	20.6457	+	6.70820i	0.658496	+	0.213958i	0.619157	−	0.785267i	$-0.287475\pi$
$983$	20.6457	+	6.70820i	0.658496	+	0.213958i	0.0393397	+	0.999226i	$0.487475\pi$
$984$	3.35410	−	2.43690i	0.106925	−	0.0776855i
$985$		0			0
$986$	10.1180	+	7.35118i	0.322224	+	0.234109i
$987$	−13.7638	−	18.9443i	−0.438107	−	0.603003i
$988$	−6.43288	−	8.85410i	−0.204657	−	0.281687i
$989$	20.6525	+	15.0049i	0.656711	+	0.477128i
$990$		0			0
$991$	2.52786	−	1.83660i	0.0803002	−	0.0583415i	−0.546911	−	0.837191i	$-0.684196\pi$
$991$	2.52786	−	1.83660i	0.0803002	−	0.0583415i	0.627211	+	0.778849i	$0.284196\pi$
$992$	−34.4095	−	11.1803i	−1.09250	−	0.354976i
$993$			10.9443i			0.347306i
$994$	1.05573	−	3.24920i	0.0334857	−	0.103058i
$995$		0			0
$996$	−1.09017	−	3.35520i	−0.0345434	−	0.106314i
$997$	8.95554	−	2.90983i	0.283625	−	0.0921552i	−0.163750	−	0.986502i	$-0.552359\pi$
$997$	8.95554	−	2.90983i	0.283625	−	0.0921552i	0.447375	+	0.894347i	$0.352359\pi$
$998$	−3.52671	+	4.85410i	−0.111636	+	0.153654i
$999$	−8.09017			−0.255962

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.i.a.49.1		8
5.2	odd	4		75.2.g.a.16.1	✓	4
5.3	odd	4		375.2.g.a.76.1		4
5.4	even	2	inner	375.2.i.a.49.2		8
15.2	even	4		225.2.h.a.91.1		4
25.2	odd	20		75.2.g.a.61.1	yes	4
25.6	even	5		1875.2.b.b.1249.1		4
25.8	odd	20		1875.2.a.a.1.1		2
25.11	even	5	inner	375.2.i.a.199.2		8
25.14	even	10	inner	375.2.i.a.199.1		8
25.17	odd	20		1875.2.a.d.1.2		2
25.19	even	10		1875.2.b.b.1249.4		4
25.23	odd	20		375.2.g.a.301.1		4
75.2	even	20		225.2.h.a.136.1		4
75.8	even	20		5625.2.a.h.1.1		2
75.17	even	20		5625.2.a.a.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.a.16.1	✓	4	5.2	odd	4
75.2.g.a.61.1	yes	4	25.2	odd	20
225.2.h.a.91.1		4	15.2	even	4
225.2.h.a.136.1		4	75.2	even	20
375.2.g.a.76.1		4	5.3	odd	4
375.2.g.a.301.1		4	25.23	odd	20
375.2.i.a.49.1		8	1.1	even	1	trivial
375.2.i.a.49.2		8	5.4	even	2	inner
375.2.i.a.199.1		8	25.14	even	10	inner
375.2.i.a.199.2		8	25.11	even	5	inner
1875.2.a.a.1.1		2	25.8	odd	20
1875.2.a.d.1.2		2	25.17	odd	20
1875.2.b.b.1249.1		4	25.6	even	5
1875.2.b.b.1249.4		4	25.19	even	10
5625.2.a.a.1.2		2	75.17	even	20
5625.2.a.h.1.1		2	75.8	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+(-0.587785 + 0.809017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.309017 - 0.951057i) q^{6} -4.47214i q^{7} +(-2.85317 - 0.927051i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-2.61803 - 1.90211i) q^{11} +(-0.587785 - 0.809017i) q^{12} +(-1.98787 - 2.73607i) q^{13} +(3.61803 + 2.62866i) q^{14} +(0.809017 - 0.587785i) q^{16} +(2.71441 + 0.881966i) q^{17} +1.00000i q^{18} +(1.00000 - 3.07768i) q^{19} +(1.38197 + 4.25325i) q^{21} +(3.07768 - 1.00000i) q^{22} +(-2.62866 + 3.61803i) q^{23} +3.00000 q^{24} +3.38197 q^{26} +(-0.587785 + 0.809017i) q^{27} +(4.25325 - 1.38197i) q^{28} +(-1.35410 - 4.16750i) q^{29} +(2.23607 - 6.88191i) q^{31} -5.00000i q^{32} +(3.07768 + 1.00000i) q^{33} +(-2.30902 + 1.67760i) q^{34} +(0.809017 + 0.587785i) q^{36} +(4.75528 + 6.54508i) q^{37} +(1.90211 + 2.61803i) q^{38} +(2.73607 + 1.98787i) q^{39} +(1.11803 - 0.812299i) q^{41} +(-4.25325 - 1.38197i) q^{42} -5.70820i q^{43} +(1.00000 - 3.07768i) q^{44} +(-1.38197 - 4.25325i) q^{46} +(-4.97980 + 1.61803i) q^{47} +(-0.587785 + 0.809017i) q^{48} -13.0000 q^{49} -2.85410 q^{51} +(1.98787 - 2.73607i) q^{52} +(-1.31433 + 0.427051i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-4.14590 + 12.7598i) q^{56} +3.23607i q^{57} +(4.16750 + 1.35410i) q^{58} +(-3.23607 + 2.35114i) q^{59} +(0.500000 + 0.363271i) q^{61} +(4.25325 + 5.85410i) q^{62} +(-2.62866 - 3.61803i) q^{63} +(5.66312 + 4.11450i) q^{64} +(-2.61803 + 1.90211i) q^{66} +(-4.97980 - 1.61803i) q^{67} +2.85410i q^{68} +(1.38197 - 4.25325i) q^{69} +(-0.236068 - 0.726543i) q^{71} +(-2.85317 + 0.927051i) q^{72} +(1.81636 - 2.50000i) q^{73} -8.09017 q^{74} +3.23607 q^{76} +(-8.50651 + 11.7082i) q^{77} +(-3.21644 + 1.04508i) q^{78} +(0.309017 - 0.951057i) q^{81} +1.38197i q^{82} +(3.35520 + 1.09017i) q^{83} +(-3.61803 + 2.62866i) q^{84} +(4.61803 + 3.35520i) q^{86} +(2.57565 + 3.54508i) q^{87} +(5.70634 + 7.85410i) q^{88} +(6.16312 + 4.47777i) q^{89} +(-12.2361 + 8.89002i) q^{91} +(-4.25325 - 1.38197i) q^{92} +7.23607i q^{93} +(1.61803 - 4.97980i) q^{94} +(1.54508 + 4.75528i) q^{96} +(8.42075 - 2.73607i) q^{97} +(7.64121 - 10.5172i) q^{98} -3.23607 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

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