LMFDB - Embedded newform 400.2.l.g.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(101,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("400.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.4767670494822400.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + \cdots + 64 $ x^12 - 4x^11 + 7x^10 - 4x^9 - 8x^8 + 24x^7 - 38x^6 + 48x^5 - 32x^4 - 32x^3 + 112x^2 - 128*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			101.4
Root			$0.719139 - 1.21772i$ of defining polynomial
Character	$\chi$	$=$	400.101
Dual form			400.2.l.g.301.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.719139 - 1.21772i) q^{2} +(-1.66783 + 1.66783i) q^{3} +(-0.965679 - 1.75142i) q^{4} +(0.831547 + 3.23035i) q^{6} +1.87372i q^{7} +(-2.82719 - 0.0835873i) q^{8} -2.56332i q^{9} +O(q^{10})$	\(q+(0.719139 - 1.21772i) q^{2} +(-1.66783 + 1.66783i) q^{3} +(-0.965679 - 1.75142i) q^{4} +(0.831547 + 3.23035i) q^{6} +1.87372i q^{7} +(-2.82719 - 0.0835873i) q^{8} -2.56332i q^{9} +(-3.29695 - 3.29695i) q^{11} +(4.53166 + 1.31048i) q^{12} +(-1.90022 + 1.90022i) q^{13} +(2.28166 + 1.34746i) q^{14} +(-2.13493 + 3.38261i) q^{16} -2.57148 q^{17} +(-3.12140 - 1.84338i) q^{18} +(-5.76636 + 5.76636i) q^{19} +(-3.12504 - 3.12504i) q^{21} +(-6.38572 + 1.64379i) q^{22} +7.58574i q^{23} +(4.85469 - 4.57587i) q^{24} +(0.947414 + 3.68046i) q^{26} +(-0.728312 - 0.728312i) q^{27} +(3.28166 - 1.80941i) q^{28} +(6.45786 - 6.45786i) q^{29} -0.799135 q^{31} +(2.58376 + 5.03231i) q^{32} +10.9975 q^{33} +(-1.84925 + 3.13134i) q^{34} +(-4.48944 + 2.47534i) q^{36} +(-2.69652 - 2.69652i) q^{37} +(2.87499 + 11.1686i) q^{38} -6.33850i q^{39} +0.946984i q^{41} +(-6.05276 + 1.55808i) q^{42} +(-0.829986 - 0.829986i) q^{43} +(-2.59054 + 8.95813i) q^{44} +(9.23730 + 5.45520i) q^{46} -1.52421 q^{47} +(-2.08093 - 9.20233i) q^{48} +3.48919 q^{49} +(4.28879 - 4.28879i) q^{51} +(5.16309 + 1.49308i) q^{52} +(-6.97225 - 6.97225i) q^{53} +(-1.41064 + 0.363122i) q^{54} +(0.156619 - 5.29735i) q^{56} -19.2346i q^{57} +(-3.21976 - 12.5080i) q^{58} +(6.84418 + 6.84418i) q^{59} +(-6.87247 + 6.87247i) q^{61} +(-0.574689 + 0.973121i) q^{62} +4.80293 q^{63} +(7.98603 + 0.472635i) q^{64} +(7.90874 - 13.3919i) q^{66} +(3.73647 - 3.73647i) q^{67} +(2.48322 + 4.50373i) q^{68} +(-12.6517 - 12.6517i) q^{69} -9.34417i q^{71} +(-0.214261 + 7.24699i) q^{72} +0.886316i q^{73} +(-5.22277 + 1.34443i) q^{74} +(15.6678 + 4.53086i) q^{76} +(6.17755 - 6.17755i) q^{77} +(-7.71851 - 4.55826i) q^{78} +3.07575 q^{79} +10.1194 q^{81} +(1.15316 + 0.681013i) q^{82} +(0.989393 - 0.989393i) q^{83} +(-2.45547 + 8.49104i) q^{84} +(-1.60756 + 0.413814i) q^{86} +21.5412i q^{87} +(9.04553 + 9.59670i) q^{88} +10.0942i q^{89} +(-3.56048 - 3.56048i) q^{91} +(13.2858 - 7.32539i) q^{92} +(1.33282 - 1.33282i) q^{93} +(-1.09612 + 1.85606i) q^{94} +(-12.7023 - 4.08377i) q^{96} +7.16829 q^{97} +(2.50921 - 4.24885i) q^{98} +(-8.45113 + 8.45113i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 2 q^{3} + 2 q^{4} + 6 q^{6} - 8 q^{8}+O(q^{10}) $ 12 * q + 4 * q^2 + 2 * q^3 + 2 * q^4 + 6 * q^6 - 8 * q^8	$ 12 q + 4 q^{2} + 2 q^{3} + 2 q^{4} + 6 q^{6} - 8 q^{8} - 2 q^{11} + 8 q^{12} - 4 q^{13} + 14 q^{14} + 2 q^{16} - 8 q^{17} + 18 q^{18} - 14 q^{19} - 20 q^{21} + 2 q^{22} - 14 q^{24} - 16 q^{26} - 10 q^{27} + 26 q^{28} - 4 q^{31} - 16 q^{32} + 28 q^{33} - 6 q^{34} + 2 q^{36} + 8 q^{37} + 10 q^{38} + 10 q^{42} - 44 q^{44} - 10 q^{46} + 8 q^{47} - 28 q^{48} + 4 q^{49} + 10 q^{51} - 12 q^{52} - 16 q^{53} + 10 q^{54} + 6 q^{56} - 60 q^{58} + 20 q^{59} + 4 q^{61} - 18 q^{62} - 8 q^{63} + 38 q^{64} + 32 q^{66} + 50 q^{67} - 60 q^{68} - 14 q^{72} + 10 q^{74} + 60 q^{76} - 8 q^{77} + 4 q^{78} + 12 q^{79} - 8 q^{81} + 42 q^{82} - 2 q^{83} + 34 q^{84} + 6 q^{86} + 30 q^{88} - 2 q^{92} - 44 q^{93} + 32 q^{94} - 34 q^{96} + 64 q^{98} + 12 q^{99}+O(q^{100}) $ 12 * q + 4 * q^2 + 2 * q^3 + 2 * q^4 + 6 * q^6 - 8 * q^8 - 2 * q^11 + 8 * q^12 - 4 * q^13 + 14 * q^14 + 2 * q^16 - 8 * q^17 + 18 * q^18 - 14 * q^19 - 20 * q^21 + 2 * q^22 - 14 * q^24 - 16 * q^26 - 10 * q^27 + 26 * q^28 - 4 * q^31 - 16 * q^32 + 28 * q^33 - 6 * q^34 + 2 * q^36 + 8 * q^37 + 10 * q^38 + 10 * q^42 - 44 * q^44 - 10 * q^46 + 8 * q^47 - 28 * q^48 + 4 * q^49 + 10 * q^51 - 12 * q^52 - 16 * q^53 + 10 * q^54 + 6 * q^56 - 60 * q^58 + 20 * q^59 + 4 * q^61 - 18 * q^62 - 8 * q^63 + 38 * q^64 + 32 * q^66 + 50 * q^67 - 60 * q^68 - 14 * q^72 + 10 * q^74 + 60 * q^76 - 8 * q^77 + 4 * q^78 + 12 * q^79 - 8 * q^81 + 42 * q^82 - 2 * q^83 + 34 * q^84 + 6 * q^86 + 30 * q^88 - 2 * q^92 - 44 * q^93 + 32 * q^94 - 34 * q^96 + 64 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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 $

$2$	0.719139	−	1.21772i	0.508508	−	0.861057i
$2$	0.719139	−	1.21772i	0.508508	−	0.861057i
$3$	−1.66783	+	1.66783i	−0.962922	+	0.962922i	−0.999337	−	0.0364144i	$-0.988406\pi$
$3$	−1.66783	+	1.66783i	−0.962922	+	0.962922i	0.0364144	+	0.999337i	$0.488406\pi$
$4$	−0.965679	−	1.75142i	−0.482839	−	0.875709i
$5$		0			0
$5$		0			0
$6$	0.831547	+	3.23035i	0.339478	+	1.31879i
$7$			1.87372i			0.708198i	0.935208	+	0.354099i	$0.115212\pi$
$7$			1.87372i			0.708198i	−0.935208	+	0.354099i	$0.884788\pi$
$8$	−2.82719	−	0.0835873i	−0.999563	−	0.0295526i
$9$		−	2.56332i		−	0.854439i
$10$		0			0
$11$	−3.29695	−	3.29695i	−0.994068	−	0.994068i	0.00591443	−	0.999983i	$-0.498117\pi$
$11$	−3.29695	−	3.29695i	−0.994068	−	0.994068i	−0.999983	+	0.00591443i	$0.998117\pi$
$12$	4.53166	+	1.31048i	1.30818	+	0.378303i
$13$	−1.90022	+	1.90022i	−0.527027	+	0.527027i	−0.919685	−	0.392658i	$-0.871556\pi$
$13$	−1.90022	+	1.90022i	−0.527027	+	0.527027i	0.392658	+	0.919685i	$0.371556\pi$
$14$	2.28166	+	1.34746i	0.609799	+	0.360124i
$15$		0			0
$16$	−2.13493	+	3.38261i	−0.533732	+	0.845653i
$17$	−2.57148			−0.623675			−0.311838	−	0.950135i	$-0.600944\pi$
$17$	−2.57148			−0.623675			−0.311838	+	0.950135i	$0.600944\pi$
$18$	−3.12140	−	1.84338i	−0.735721	−	0.434489i
$19$	−5.76636	+	5.76636i	−1.32289	+	1.32289i	−0.411472	+	0.911422i	$0.634985\pi$
$19$	−5.76636	+	5.76636i	−1.32289	+	1.32289i	−0.911422	+	0.411472i	$0.865015\pi$
$20$		0			0
$21$	−3.12504	−	3.12504i	−0.681940	−	0.681940i
$22$	−6.38572	+	1.64379i	−1.36144	+	0.350458i
$23$			7.58574i			1.58174i	0.611987	+	0.790868i	$0.290371\pi$
$23$			7.58574i			1.58174i	−0.611987	+	0.790868i	$0.709629\pi$
$24$	4.85469	−	4.57587i	0.990959	−	0.934045i
$25$		0			0
$26$	0.947414	+	3.68046i	0.185803	+	0.721798i
$27$	−0.728312	−	0.728312i	−0.140164	−	0.140164i
$28$	3.28166	−	1.80941i	0.620175	−	0.341946i
$29$	6.45786	−	6.45786i	1.19919	−	1.19919i	0.224787	−	0.974408i	$-0.427831\pi$
$29$	6.45786	−	6.45786i	1.19919	−	1.19919i	0.974408	−	0.224787i	$-0.0721685\pi$
$30$		0			0
$31$	−0.799135			−0.143529			−0.0717644	−	0.997422i	$-0.522863\pi$
$31$	−0.799135			−0.143529			−0.0717644	+	0.997422i	$0.522863\pi$
$32$	2.58376	+	5.03231i	0.456749	+	0.889596i
$33$	10.9975			1.91442
$34$	−1.84925	+	3.13134i	−0.317144	+	0.537020i
$35$		0			0
$36$	−4.48944	+	2.47534i	−0.748240	+	0.412557i
$37$	−2.69652	−	2.69652i	−0.443305	−	0.443305i	0.449816	−	0.893121i	$-0.351489\pi$
$37$	−2.69652	−	2.69652i	−0.443305	−	0.443305i	−0.893121	+	0.449816i	$0.851489\pi$
$38$	2.87499	+	11.1686i	0.466386	+	1.81179i
$39$		−	6.33850i		−	1.01497i
$40$		0			0
$41$			0.946984i			0.147894i	0.997262	+	0.0739471i	$0.0235596\pi$
$41$			0.946984i			0.147894i	−0.997262	+	0.0739471i	$0.976440\pi$
$42$	−6.05276	+	1.55808i	−0.933961	+	0.240417i
$43$	−0.829986	−	0.829986i	−0.126572	−	0.126572i	0.640983	−	0.767555i	$-0.278527\pi$
$43$	−0.829986	−	0.829986i	−0.126572	−	0.126572i	−0.767555	+	0.640983i	$0.778527\pi$
$44$	−2.59054	+	8.95813i	−0.390539	+	1.35049i
$45$		0			0
$46$	9.23730	+	5.45520i	1.36197	+	0.804325i
$47$	−1.52421			−0.222329			−0.111165	−	0.993802i	$-0.535458\pi$
$47$	−1.52421			−0.222329			−0.111165	+	0.993802i	$0.535458\pi$
$48$	−2.08093	−	9.20233i	−0.300356	−	1.32824i
$49$	3.48919			0.498456
$50$		0			0
$51$	4.28879	−	4.28879i	0.600551	−	0.600551i
$52$	5.16309	+	1.49308i	0.715992	+	0.207053i
$53$	−6.97225	−	6.97225i	−0.957712	−	0.957712i	0.0414296	−	0.999141i	$-0.486809\pi$
$53$	−6.97225	−	6.97225i	−0.957712	−	0.957712i	−0.999141	+	0.0414296i	$0.986809\pi$
$54$	−1.41064	+	0.363122i	−0.191963	+	0.0494147i
$55$		0			0
$56$	0.156619	−	5.29735i	0.0209291	−	0.707889i
$57$		−	19.2346i		−	2.54769i
$58$	−3.21976	−	12.5080i	−0.422775	−	1.64238i
$59$	6.84418	+	6.84418i	0.891036	+	0.891036i	0.994621	−	0.103585i	$-0.0330313\pi$
$59$	6.84418	+	6.84418i	0.891036	+	0.891036i	−0.103585	+	0.994621i	$0.533031\pi$
$60$		0			0
$61$	−6.87247	+	6.87247i	−0.879930	+	0.879930i	−0.993527	−	0.113597i	$-0.963763\pi$
$61$	−6.87247	+	6.87247i	−0.879930	+	0.879930i	0.113597	+	0.993527i	$0.463763\pi$
$62$	−0.574689	+	0.973121i	−0.0729856	+	0.123587i
$63$	4.80293			0.605112
$64$	7.98603	+	0.472635i	0.998253	+	0.0590793i
$65$		0			0
$66$	7.90874	−	13.3919i	0.973498	−	1.64843i
$67$	3.73647	−	3.73647i	0.456483	−	0.456483i	−0.441016	−	0.897499i	$-0.645382\pi$
$67$	3.73647	−	3.73647i	0.456483	−	0.456483i	0.897499	+	0.441016i	$0.145382\pi$
$68$	2.48322	+	4.50373i	0.301135	+	0.546158i
$69$	−12.6517	−	12.6517i	−1.52309	−	1.52309i
$70$		0			0
$71$		−	9.34417i		−	1.10895i	−0.832201	−	0.554475i	$-0.812919\pi$
$71$		−	9.34417i		−	1.10895i	0.832201	−	0.554475i	$-0.187081\pi$
$72$	−0.214261	+	7.24699i	−0.0252509	+	0.854066i
$73$			0.886316i			0.103735i	0.998654	+	0.0518677i	$0.0165174\pi$
$73$			0.886316i			0.103735i	−0.998654	+	0.0518677i	$0.983483\pi$
$74$	−5.22277	+	1.34443i	−0.607135	+	0.156287i
$75$		0			0
$76$	15.6678	+	4.53086i	1.79722	+	0.519725i
$77$	6.17755	−	6.17755i	0.703997	−	0.703997i
$78$	−7.71851	−	4.55826i	−0.873949	−	0.516122i
$79$	3.07575			0.346049			0.173024	−	0.984918i	$-0.444646\pi$
$79$	3.07575			0.346049			0.173024	+	0.984918i	$0.444646\pi$
$80$		0			0
$81$	10.1194			1.12437
$82$	1.15316	+	0.681013i	0.127345	+	0.0752053i
$83$	0.989393	−	0.989393i	0.108600	−	0.108600i	−0.650719	−	0.759319i	$-0.725532\pi$
$83$	0.989393	−	0.989393i	0.108600	−	0.108600i	0.759319	+	0.650719i	$0.225532\pi$
$84$	−2.45547	+	8.49104i	−0.267913	+	0.926448i
$85$		0			0
$86$	−1.60756	+	0.413814i	−0.173348	+	0.0446227i
$87$			21.5412i			2.30946i
$88$	9.04553	+	9.59670i	0.964257	+	1.02301i
$89$			10.0942i			1.06998i	0.844859	+	0.534990i	$0.179684\pi$
$89$			10.0942i			1.06998i	−0.844859	+	0.534990i	$0.820316\pi$
$90$		0			0
$91$	−3.56048	−	3.56048i	−0.373239	−	0.373239i
$92$	13.2858	−	7.32539i	1.38514	−	0.763725i
$93$	1.33282	−	1.33282i	0.138207	−	0.138207i
$94$	−1.09612	+	1.85606i	−0.113056	+	0.191438i
$95$		0			0
$96$	−12.7023	−	4.08377i	−1.29643	−	0.416798i
$97$	7.16829			0.727830			0.363915	−	0.931432i	$-0.381440\pi$
$97$	7.16829			0.727830			0.363915	+	0.931432i	$0.381440\pi$
$98$	2.50921	−	4.24885i	0.253469	−	0.429199i
$99$	−8.45113	+	8.45113i	−0.849371	+	0.849371i
$100$		0			0
$101$	−1.05091	−	1.05091i	−0.104570	−	0.104570i	0.652886	−	0.757456i	$-0.273558\pi$
$101$	−1.05091	−	1.05091i	−0.104570	−	0.104570i	−0.757456	+	0.652886i	$0.773558\pi$
$102$	−2.13831	−	8.30678i	−0.211724	−	0.822493i
$103$		−	8.20690i		−	0.808649i	−0.914616	−	0.404325i	$-0.867507\pi$
$103$		−	8.20690i		−	0.808649i	0.914616	−	0.404325i	$-0.132493\pi$
$104$	5.53113	−	5.21346i	0.542372	−	0.511222i
$105$		0			0
$106$	−13.5043	+	3.47622i	−1.31165	+	0.337641i
$107$	2.85743	+	2.85743i	0.276238	+	0.276238i	0.831605	−	0.555367i	$-0.187422\pi$
$107$	2.85743	+	2.85743i	0.276238	+	0.276238i	−0.555367	+	0.831605i	$0.687422\pi$
$108$	−0.572264	+	1.97889i	−0.0550661	+	0.190419i
$109$	−11.3735	+	11.3735i	−1.08939	+	1.08939i	−0.0937940	+	0.995592i	$0.529900\pi$
$109$	−11.3735	+	11.3735i	−1.08939	+	1.08939i	−0.995592	+	0.0937940i	$0.970100\pi$
$110$		0			0
$111$	8.99467			0.853736
$112$	−6.33806	−	4.00025i	−0.598890	−	0.377988i
$113$	3.54221			0.333223			0.166611	−	0.986023i	$-0.446717\pi$
$113$	3.54221			0.333223			0.166611	+	0.986023i	$0.446717\pi$
$114$	−23.4224	−	13.8324i	−2.19371	−	1.29552i
$115$		0			0
$116$	−17.5466	−	5.07419i	−1.62916	−	0.471127i
$117$	4.87088	+	4.87088i	0.450313	+	0.450313i
$118$	13.2562	−	3.41237i	1.22033	−	0.314134i
$119$		−	4.81822i		−	0.441685i
$120$		0			0
$121$			10.7398i			0.976343i
$122$	3.42648	+	13.3110i	0.310219	+	1.20512i
$123$	−1.57941	−	1.57941i	−0.142411	−	0.142411i
$124$	0.771707	+	1.39962i	0.0693014	+	0.125689i
$125$		0			0
$126$	3.45397	−	5.84862i	0.307704	−	0.521036i
$127$	−18.0693			−1.60339			−0.801693	−	0.597735i	$-0.796067\pi$
$127$	−18.0693			−1.60339			−0.801693	+	0.597735i	$0.796067\pi$
$128$	6.31860	−	9.38485i	0.558490	−	0.829511i
$129$	2.76855			0.243757
$130$		0			0
$131$	−6.39614	+	6.39614i	−0.558834	+	0.558834i	−0.928975	−	0.370142i	$-0.879309\pi$
$131$	−6.39614	+	6.39614i	−0.558834	+	0.558834i	0.370142	+	0.928975i	$0.379309\pi$
$132$	−10.6201	−	19.2612i	−0.924358	−	1.67648i
$133$	−10.8045	−	10.8045i	−0.936871	−	0.936871i
$134$	−1.86293	−	7.23702i	−0.160933	−	0.625183i
$135$		0			0
$136$	7.27006	+	0.214943i	0.623403	+	0.0184312i
$137$			10.7357i			0.917212i	0.888640	+	0.458606i	$0.151651\pi$
$137$			10.7357i			0.917212i	−0.888640	+	0.458606i	$0.848349\pi$
$138$	−24.5046	+	6.30790i	−2.08597	+	0.536964i
$139$	−2.31086	−	2.31086i	−0.196005	−	0.196005i	0.602280	−	0.798285i	$-0.294259\pi$
$139$	−2.31086	−	2.31086i	−0.196005	−	0.196005i	−0.798285	+	0.602280i	$0.794259\pi$
$140$		0			0
$141$	2.54213	−	2.54213i	0.214086	−	0.214086i
$142$	−11.3786	−	6.71976i	−0.954869	−	0.563909i
$143$	12.5299			1.04780
$144$	8.67071	+	5.47250i	0.722559	+	0.456042i
$145$		0			0
$146$	1.07928	+	0.637384i	0.0893221	+	0.0527503i
$147$	−5.81938	+	5.81938i	−0.479974	+	0.479974i
$148$	−2.11876	+	7.32670i	−0.174161	+	0.602251i
$149$	1.38743	+	1.38743i	0.113663	+	0.113663i	0.761651	−	0.647988i	$-0.224389\pi$
$149$	1.38743	+	1.38743i	0.113663	+	0.113663i	−0.647988	+	0.761651i	$0.724389\pi$
$150$		0			0
$151$		−	5.68590i		−	0.462712i	−0.972869	−	0.231356i	$-0.925684\pi$
$151$		−	5.68590i		−	0.462712i	0.972869	−	0.231356i	$-0.0743163\pi$
$152$	16.7846	−	15.8206i	1.36141	−	1.28322i
$153$			6.59152i			0.532892i
$154$	−3.08000	−	11.9650i	−0.248194	−	0.964170i
$155$		0			0
$156$	−11.1014	+	6.12096i	−0.888820	+	0.490069i
$157$	2.48874	−	2.48874i	0.198623	−	0.198623i	−0.600787	−	0.799409i	$-0.705146\pi$
$157$	2.48874	−	2.48874i	0.198623	−	0.198623i	0.799409	+	0.600787i	$0.205146\pi$
$158$	2.21189	−	3.74540i	0.175969	−	0.297968i
$159$	23.2571			1.84440
$160$		0			0
$161$	−14.2135			−1.12018
$162$	7.27722	−	12.3225i	0.571753	−	0.968149i
$163$	−12.7091	+	12.7091i	−0.995451	+	0.995451i	−0.999990	−	0.00453842i	$-0.998555\pi$
$163$	−12.7091	+	12.7091i	−0.995451	+	0.995451i	0.00453842	+	0.999990i	$0.498555\pi$
$164$	1.65857	−	0.914483i	0.129512	−	0.0714091i
$165$		0			0
$166$	−0.493292	−	1.91631i	−0.0382868	−	0.148735i
$167$			5.00982i			0.387672i	0.981034	+	0.193836i	$0.0620929\pi$
$167$			5.00982i			0.387672i	−0.981034	+	0.193836i	$0.937907\pi$
$168$	8.57387	+	9.09630i	0.661489	+	0.701795i
$169$			5.77830i			0.444485i
$170$		0			0
$171$	14.7810	+	14.7810i	1.13033	+	1.13033i
$172$	−0.652152	+	2.25515i	−0.0497261	+	0.171954i
$173$	−6.19546	+	6.19546i	−0.471032	+	0.471032i	−0.902249	−	0.431216i	$-0.858085\pi$
$173$	−6.19546	+	6.19546i	−0.471032	+	0.471032i	0.431216	+	0.902249i	$0.358085\pi$
$174$	26.2312	+	15.4911i	1.98858	+	1.17438i
$175$		0			0
$176$	18.1911	−	4.11356i	1.37120	−	0.310071i
$177$	−22.8299			−1.71600
$178$	12.2919	+	7.25911i	0.921313	+	0.544093i
$179$	−5.51628	+	5.51628i	−0.412306	+	0.412306i	−0.882541	−	0.470235i	$-0.844169\pi$
$179$	−5.51628	+	5.51628i	−0.412306	+	0.412306i	0.470235	+	0.882541i	$0.344169\pi$
$180$		0			0
$181$	11.8993	+	11.8993i	0.884470	+	0.884470i	0.993985	−	0.109515i	$-0.0349298\pi$
$181$	11.8993	+	11.8993i	0.884470	+	0.884470i	−0.109515	+	0.993985i	$0.534930\pi$
$182$	−6.89614	+	1.77518i	−0.511176	+	0.131585i
$183$		−	22.9242i		−	1.69461i
$184$	0.634072	−	21.4463i	0.0467444	−	1.58105i
$185$		0			0
$186$	−0.664518	−	2.58149i	−0.0487248	−	0.189284i
$187$	8.47804	+	8.47804i	0.619976	+	0.619976i
$188$	1.47190	+	2.66954i	0.107349	+	0.194696i
$189$	1.36465	−	1.36465i	0.0992637	−	0.0992637i
$190$		0			0
$191$	11.1278			0.805180			0.402590	−	0.915380i	$-0.368110\pi$
$191$	11.1278			0.805180			0.402590	+	0.915380i	$0.368110\pi$
$192$	−14.1076	+	12.5311i	−1.01813	+	0.904352i
$193$	−20.7821			−1.49593			−0.747965	−	0.663738i	$-0.768969\pi$
$193$	−20.7821			−1.49593			−0.747965	+	0.663738i	$0.768969\pi$
$194$	5.15500	−	8.72896i	0.370107	−	0.626703i
$195$		0			0
$196$	−3.36944	−	6.11103i	−0.240674	−	0.436502i
$197$	14.0309	+	14.0309i	0.999663	+	0.999663i	1.00000		0.000337236i	$-0.000107346\pi$
$197$	14.0309	+	14.0309i	0.999663	+	0.999663i	−0.000337236		1.00000i	$0.500107\pi$
$198$	4.21357	+	16.3686i	0.299445	+	1.16327i
$199$		−	3.24727i		−	0.230193i	−0.993354	−	0.115096i	$-0.963282\pi$
$199$		−	3.24727i		−	0.230193i	0.993354	−	0.115096i	$-0.0367177\pi$
$200$		0			0
$201$			12.4636i			0.879115i
$202$	−2.03547	+	0.523964i	−0.143215	+	0.0368660i
$203$	12.1002	+	12.1002i	0.849267	+	0.849267i
$204$	−11.6531	−	3.36987i	−0.815877	−	0.235938i
$205$		0			0
$206$	−9.99369	−	5.90190i	−0.696294	−	0.411205i
$207$	19.4447			1.35150
$208$	−2.37088	−	10.4846i	−0.164391	−	0.726974i
$209$	38.0228			2.63009
$210$		0			0
$211$	−10.1821	+	10.1821i	−0.700964	+	0.700964i	−0.964617	−	0.263654i	$-0.915072\pi$
$211$	−10.1821	+	10.1821i	−0.700964	+	0.700964i	0.263654	+	0.964617i	$0.415072\pi$
$212$	−5.47837	+	18.9443i	−0.376256	+	1.30110i
$213$	15.5845	+	15.5845i	1.06783	+	1.06783i
$214$	5.53443	−	1.42466i	0.378326	−	0.0973876i
$215$		0			0
$216$	1.99820	+	2.11996i	0.135960	+	0.144245i
$217$		−	1.49735i		−	0.101647i
$218$	5.67061	+	22.0289i	0.384062	+	1.49198i
$219$	−1.47822	−	1.47822i	−0.0998892	−	0.0998892i
$220$		0			0
$221$	4.88638	−	4.88638i	0.328694	−	0.328694i
$222$	6.46842	−	10.9530i	0.434132	−	0.735116i
$223$	−24.0469			−1.61030			−0.805151	−	0.593070i	$-0.797916\pi$
$223$	−24.0469			−1.61030			−0.805151	+	0.593070i	$0.797916\pi$
$224$	−9.42912	+	4.84124i	−0.630010	+	0.323469i
$225$		0			0
$226$	2.54734	−	4.31341i	0.169446	−	0.286924i
$227$	11.9863	−	11.9863i	0.795562	−	0.795562i	−0.186830	−	0.982392i	$-0.559821\pi$
$227$	11.9863	−	11.9863i	0.795562	−	0.795562i	0.982392	+	0.186830i	$0.0598215\pi$
$228$	−33.6879	+	18.5745i	−2.23103	+	1.23012i
$229$	−20.1972	−	20.1972i	−1.33467	−	1.33467i	−0.901140	−	0.433529i	$-0.857268\pi$
$229$	−20.1972	−	20.1972i	−1.33467	−	1.33467i	−0.433529	−	0.901140i	$-0.642732\pi$
$230$		0			0
$231$			20.6062i			1.35579i
$232$	−18.7974	+	17.7178i	−1.23411	+	1.16323i
$233$		−	10.0655i		−	0.659410i	−0.944084	−	0.329705i	$-0.893051\pi$
$233$		−	10.0655i		−	0.659410i	0.944084	−	0.329705i	$-0.106949\pi$
$234$	9.43419	−	2.42852i	0.616733	−	0.158757i
$235$		0			0
$236$	5.37774	−	18.5963i	0.350061	−	1.21052i
$237$	−5.12983	+	5.12983i	−0.333218	+	0.333218i
$238$	−5.86724	−	3.46497i	−0.380316	−	0.224601i
$239$	0.992801			0.0642189			0.0321095	−	0.999484i	$-0.489777\pi$
$239$	0.992801			0.0642189			0.0321095	+	0.999484i	$0.489777\pi$
$240$		0			0
$241$	14.1229			0.909738			0.454869	−	0.890558i	$-0.349686\pi$
$241$	14.1229			0.909738			0.454869	+	0.890558i	$0.349686\pi$
$242$	13.0780	+	7.72339i	0.840687	+	0.496478i
$243$	−14.6924	+	14.6924i	−0.942520	+	0.942520i
$244$	18.6732	+	5.39997i	1.19543	+	0.345698i
$245$		0			0
$246$	−3.05909	+	0.787462i	−0.195041	+	0.0502068i
$247$		−	21.9148i		−	1.39440i
$248$	2.25931	+	0.0667975i	0.143466	+	0.00424165i
$249$			3.30028i			0.209147i
$250$		0			0
$251$	1.56681	+	1.56681i	0.0988961	+	0.0988961i	0.754824	−	0.655928i	$-0.227722\pi$
$251$	1.56681	+	1.56681i	0.0988961	+	0.0988961i	−0.655928	+	0.754824i	$0.727722\pi$
$252$	−4.63809	−	8.41193i	−0.292172	−	0.529902i
$253$	25.0098	−	25.0098i	1.57235	−	1.57235i
$254$	−12.9943	+	22.0033i	−0.815335	+	1.38061i
$255$		0			0
$256$	−6.88415	−	14.4433i	−0.430260	−	0.902705i
$257$	−10.2593			−0.639960			−0.319980	−	0.947424i	$-0.603676\pi$
$257$	−10.2593			−0.639960			−0.319980	+	0.947424i	$0.603676\pi$
$258$	1.99097	−	3.37132i	0.123953	−	0.209889i
$259$	5.05251	−	5.05251i	0.313948	−	0.313948i
$260$		0			0
$261$	−16.5535	−	16.5535i	−1.02464	−	1.02464i
$262$	3.18899	+	12.3884i	0.197016	+	0.765359i
$263$		−	19.0630i		−	1.17548i	−0.809051	−	0.587739i	$-0.800018\pi$
$263$		−	19.0630i		−	1.17548i	0.809051	−	0.587739i	$-0.199982\pi$
$264$	−31.0921	−	0.919252i	−1.91358	−	0.0565761i
$265$		0			0
$266$	−20.9268	+	5.38692i	−1.28311	+	0.330293i
$267$	−16.8354	−	16.8354i	−1.03031	−	1.03031i
$268$	−10.1524	−	2.93589i	−0.620154	−	0.179338i
$269$	3.48459	−	3.48459i	0.212459	−	0.212459i	−0.592852	−	0.805311i	$-0.701998\pi$
$269$	3.48459	−	3.48459i	0.212459	−	0.212459i	0.805311	+	0.592852i	$0.201998\pi$
$270$		0			0
$271$	−30.0045			−1.82264			−0.911322	−	0.411695i	$-0.864937\pi$
$271$	−30.0045			−1.82264			−0.911322	+	0.411695i	$0.864937\pi$
$272$	5.48992	−	8.69832i	0.332876	−	0.527413i
$273$	11.8765			0.718801
$274$	13.0731	+	7.72045i	0.789772	+	0.466409i
$275$		0			0
$276$	−9.94096	+	34.3760i	−0.598375	+	2.06919i
$277$	8.43732	+	8.43732i	0.506949	+	0.506949i	0.913589	−	0.406639i	$-0.133299\pi$
$277$	8.43732	+	8.43732i	0.506949	+	0.506949i	−0.406639	+	0.913589i	$0.633299\pi$
$278$	−4.47581	+	1.15215i	−0.268441	+	0.0691014i
$279$			2.04844i			0.122637i
$280$		0			0
$281$		−	6.44714i		−	0.384604i	−0.981336	−	0.192302i	$-0.938405\pi$
$281$		−	6.44714i		−	0.384604i	0.981336	−	0.192302i	$-0.0615954\pi$
$282$	−1.26746	−	4.92375i	−0.0754759	−	0.293205i
$283$	2.61000	+	2.61000i	0.155148	+	0.155148i	0.780413	−	0.625264i	$-0.215009\pi$
$283$	2.61000	+	2.61000i	0.155148	+	0.155148i	−0.625264	+	0.780413i	$0.715009\pi$
$284$	−16.3656	+	9.02347i	−0.971117	+	0.535444i
$285$		0			0
$286$	9.01073	−	15.2579i	0.532815	−	0.902217i
$287$	−1.77438			−0.104738
$288$	12.8994	−	6.62300i	0.760105	−	0.390264i
$289$	−10.3875			−0.611029
$290$		0			0
$291$	−11.9555	+	11.9555i	−0.700844	+	0.700844i
$292$	1.55231	−	0.855896i	0.0908420	−	0.0500875i
$293$	−7.52428	−	7.52428i	−0.439573	−	0.439573i	0.452295	−	0.891868i	$-0.350605\pi$
$293$	−7.52428	−	7.52428i	−0.439573	−	0.439573i	−0.891868	+	0.452295i	$0.850605\pi$
$294$	2.90143	+	11.2713i	0.169215	+	0.657356i
$295$		0			0
$296$	7.39818	+	7.84897i	0.430010	+	0.456212i
$297$			4.80242i			0.278665i
$298$	2.68726	−	0.691746i	0.155669	−	0.0400718i
$299$	−14.4146	−	14.4146i	−0.833618	−	0.833618i
$300$		0			0
$301$	1.55516	−	1.55516i	0.0896377	−	0.0896377i
$302$	−6.92383	−	4.08895i	−0.398422	−	0.235293i
$303$	3.50549			0.201385
$304$	−7.19460	−	31.8162i	−0.412639	−	1.82478i
$305$		0			0
$306$	8.02661	+	4.74021i	0.458851	+	0.270980i
$307$	12.7130	−	12.7130i	0.725571	−	0.725571i	−0.244163	−	0.969734i	$-0.578513\pi$
$307$	12.7130	−	12.7130i	0.725571	−	0.725571i	0.969734	+	0.244163i	$0.0785133\pi$
$308$	−16.7850	−	4.85394i	−0.956414	−	0.276579i
$309$	13.6877	+	13.6877i	0.778667	+	0.778667i
$310$		0			0
$311$		−	11.9313i		−	0.676563i	−0.941045	−	0.338281i	$-0.890154\pi$
$311$		−	11.9313i		−	0.676563i	0.941045	−	0.338281i	$-0.109846\pi$
$312$	−0.529818	+	17.9202i	−0.0299951	+	1.01453i
$313$			34.3458i			1.94134i	0.240414	+	0.970670i	$0.422717\pi$
$313$			34.3458i			1.94134i	−0.240414	+	0.970670i	$0.577283\pi$
$314$	−1.24083	−	4.82033i	−0.0700244	−	0.272027i
$315$		0			0
$316$	−2.97019	−	5.38692i	−0.167086	−	0.303038i
$317$	−17.1112	+	17.1112i	−0.961060	+	0.961060i	−0.999270	−	0.0382097i	$-0.987835\pi$
$317$	−17.1112	+	17.1112i	−0.961060	+	0.961060i	0.0382097	+	0.999270i	$0.487835\pi$
$318$	16.7251	−	28.3206i	0.937894	−	1.58814i
$319$	−42.5825			−2.38416
$320$		0			0
$321$	−9.53141			−0.531992
$322$	−10.2215	+	17.3081i	−0.569622	+	0.964541i
$323$	14.8281	−	14.8281i	0.825056	−	0.825056i
$324$	−9.77205	−	17.7232i	−0.542891	−	0.984623i
$325$		0			0
$326$	6.33649	+	24.6157i	0.350946	+	1.36334i
$327$		−	37.9382i		−	2.09799i
$328$	0.0791559	−	2.67731i	0.00437065	−	0.147830i
$329$		−	2.85594i		−	0.157453i
$330$		0			0
$331$	9.80246	+	9.80246i	0.538792	+	0.538792i	0.923174	−	0.384382i	$-0.125585\pi$
$331$	9.80246	+	9.80246i	0.538792	+	0.538792i	−0.384382	+	0.923174i	$0.625585\pi$
$332$	−2.68828	−	0.777405i	−0.147538	−	0.0426656i
$333$	−6.91203	+	6.91203i	−0.378777	+	0.378777i
$334$	6.10056	+	3.60276i	0.333808	+	0.197134i
$335$		0			0
$336$	17.2425	−	3.89906i	0.940658	−	0.212711i
$337$	6.07501			0.330927			0.165463	−	0.986216i	$-0.447088\pi$
$337$	6.07501			0.330927			0.165463	+	0.986216i	$0.447088\pi$
$338$	7.03635	+	4.15540i	0.382727	+	0.226024i
$339$	−5.90780	+	5.90780i	−0.320868	+	0.320868i
$340$		0			0
$341$	2.63471	+	2.63471i	0.142677	+	0.142677i
$342$	28.6287	−	7.36952i	1.54806	−	0.398498i
$343$			19.6538i			1.06120i
$344$	2.27715	+	2.41590i	0.122776	+	0.130257i
$345$		0			0
$346$	3.08894	+	11.9997i	0.166062	+	0.645110i
$347$	5.77231	+	5.77231i	0.309874	+	0.309874i	0.844860	−	0.534987i	$-0.179683\pi$
$347$	5.77231	+	5.77231i	0.309874	+	0.309874i	−0.534987	+	0.844860i	$0.679683\pi$
$348$	37.7277	−	20.8019i	2.02242	−	1.11510i
$349$	−7.58851	+	7.58851i	−0.406203	+	0.406203i	−0.880412	−	0.474209i	$-0.842734\pi$
$349$	−7.58851	+	7.58851i	−0.406203	+	0.406203i	0.474209	+	0.880412i	$0.342734\pi$
$350$		0			0
$351$	2.76791			0.147740
$352$	8.07275	−	25.1098i	0.430279	−	1.33836i
$353$	−16.2285			−0.863753			−0.431877	−	0.901933i	$-0.642148\pi$
$353$	−16.2285			−0.863753			−0.431877	+	0.901933i	$0.642148\pi$
$354$	−16.4178	+	27.8003i	−0.872598	+	1.47757i
$355$		0			0
$356$	17.6791	−	9.74772i	0.936990	−	0.516628i
$357$	8.03597	+	8.03597i	0.425309	+	0.425309i
$358$	2.75031	+	10.6843i	0.145358	+	0.564680i
$359$		−	6.77298i		−	0.357464i	−0.983898	−	0.178732i	$-0.942800\pi$
$359$		−	6.77298i		−	0.357464i	0.983898	−	0.178732i	$-0.0571996\pi$
$360$		0			0
$361$		−	47.5019i		−	2.50010i
$362$	23.0473	−	5.93277i	1.21134	−	0.311819i
$363$	−17.9121	−	17.9121i	−0.940142	−	0.940142i
$364$	−2.79761	+	9.67416i	−0.146634	+	0.507064i
$365$		0			0
$366$	−27.9153	−	16.4857i	−1.45915	−	0.861722i
$367$	−6.35705			−0.331835			−0.165918	−	0.986140i	$-0.553059\pi$
$367$	−6.35705			−0.331835			−0.165918	+	0.986140i	$0.553059\pi$
$368$	−25.6596	−	16.1950i	−1.33760	−	0.844224i
$369$	2.42742			0.126367
$370$		0			0
$371$	13.0640	−	13.0640i	0.678250	−	0.678250i
$372$	−3.62140	−	1.04725i	−0.187761	−	0.0542974i
$373$	9.20937	+	9.20937i	0.476843	+	0.476843i	0.904121	−	0.427278i	$-0.140527\pi$
$373$	9.20937	+	9.20937i	0.476843	+	0.476843i	−0.427278	+	0.904121i	$0.640527\pi$
$374$	16.4208	−	4.22698i	0.849097	−	0.218572i
$375$		0			0
$376$	4.30925	+	0.127405i	0.222232	+	0.00657041i
$377$			24.5428i			1.26402i
$378$	−0.680387	−	2.64313i	−0.0349954	−	0.135948i
$379$	5.41600	+	5.41600i	0.278201	+	0.278201i	0.832391	−	0.554189i	$-0.186972\pi$
$379$	5.41600	+	5.41600i	0.278201	+	0.278201i	−0.554189	+	0.832391i	$0.686972\pi$
$380$		0			0
$381$	30.1365	−	30.1365i	1.54394	−	1.54394i
$382$	8.00244	−	13.5505i	0.409440	−	0.693306i
$383$	28.1626			1.43904			0.719520	−	0.694472i	$-0.244362\pi$
$383$	28.1626			1.43904			0.719520	+	0.694472i	$0.244362\pi$
$384$	5.11398	+	26.1907i	0.260972	+	1.33654i
$385$		0			0
$386$	−14.9452	+	25.3068i	−0.760693	+	1.28808i
$387$	−2.12752	+	2.12752i	−0.108148	+	0.108148i
$388$	−6.92227	−	12.5547i	−0.351425	−	0.637367i
$389$	9.59783	+	9.59783i	0.486629	+	0.486629i	0.907241	−	0.420611i	$-0.138184\pi$
$389$	9.59783	+	9.59783i	0.486629	+	0.486629i	−0.420611	+	0.907241i	$0.638184\pi$
$390$		0			0
$391$		−	19.5066i		−	0.986490i
$392$	−9.86461	−	0.291652i	−0.498238	−	0.0147307i
$393$		−	21.3354i		−	1.07623i
$394$	27.1759	−	6.99554i	1.36910	−	0.352430i
$395$		0			0
$396$	22.9625	+	6.64039i	1.15391	+	0.333692i
$397$	10.4884	−	10.4884i	0.526399	−	0.526399i	−0.393098	−	0.919497i	$-0.628597\pi$
$397$	10.4884	−	10.4884i	0.526399	−	0.526399i	0.919497	+	0.393098i	$0.128597\pi$
$398$	−3.95426	−	2.33524i	−0.198209	−	0.117055i
$399$	36.0402			1.80427
$400$		0			0
$401$	−2.44221			−0.121958			−0.0609791	−	0.998139i	$-0.519422\pi$
$401$	−2.44221			−0.121958			−0.0609791	+	0.998139i	$0.519422\pi$
$402$	15.1772	+	8.96306i	0.756969	+	0.447037i
$403$	1.51853	−	1.51853i	0.0756436	−	0.0756436i
$404$	−0.825743	+	2.85543i	−0.0410823	+	0.142063i
$405$		0			0
$406$	23.4364	−	6.03292i	1.16313	−	0.299409i
$407$			17.7806i			0.881350i
$408$	−12.4837	+	11.7667i	−0.618036	+	0.582541i
$409$			24.6628i			1.21950i	0.792596	+	0.609748i	$0.208729\pi$
$409$			24.6628i			1.21950i	−0.792596	+	0.609748i	$0.791271\pi$
$410$		0			0
$411$	−17.9053	−	17.9053i	−0.883204	−	0.883204i
$412$	−14.3737	+	7.92522i	−0.708142	+	0.390448i
$413$	−12.8240	+	12.8240i	−0.631030	+	0.631030i
$414$	13.9834	−	23.6781i	0.687247	−	1.16372i
$415$		0			0
$416$	−14.4722	−	4.65279i	−0.709560	−	0.228122i
$417$	7.70826			0.377475
$418$	27.3437	−	46.3011i	1.33742	−	2.26466i
$419$	19.1661	−	19.1661i	0.936326	−	0.936326i	−0.0617649	−	0.998091i	$-0.519673\pi$
$419$	19.1661	−	19.1661i	0.936326	−	0.936326i	0.998091	+	0.0617649i	$0.0196729\pi$
$420$		0			0
$421$	−7.43469	−	7.43469i	−0.362345	−	0.362345i	0.502331	−	0.864676i	$-0.332476\pi$
$421$	−7.43469	−	7.43469i	−0.362345	−	0.362345i	−0.864676	+	0.502331i	$0.832476\pi$
$422$	5.07659	+	19.7213i	0.247124	+	0.960016i
$423$			3.90704i			0.189967i
$424$	19.1291	+	20.2947i	0.928991	+	0.985596i
$425$		0			0
$426$	30.1850	−	7.77012i	1.46247	−	0.376464i
$427$	−12.8771	−	12.8771i	−0.623164	−	0.623164i
$428$	2.24519	−	7.76391i	0.108526	−	0.375283i
$429$	−20.8977	+	20.8977i	−1.00895	+	1.00895i
$430$		0			0
$431$	22.5647			1.08690			0.543451	−	0.839441i	$-0.317117\pi$
$431$	22.5647			1.08690			0.543451	+	0.839441i	$0.317117\pi$
$432$	4.01849	−	0.908704i	0.193340	−	0.0437201i
$433$	26.4811			1.27260			0.636301	−	0.771441i	$-0.280464\pi$
$433$	26.4811			1.27260			0.636301	+	0.771441i	$0.280464\pi$
$434$	−1.82335	−	1.07680i	−0.0875237	−	0.0516882i
$435$		0			0
$436$	30.9030	+	8.93662i	1.47998	+	0.427986i
$437$	−43.7421	−	43.7421i	−2.09247	−	2.09247i
$438$	−2.86311	+	0.737013i	−0.136805	+	0.0352159i
$439$			0.765288i			0.0365252i	0.999833	+	0.0182626i	$0.00581349\pi$
$439$			0.765288i			0.0365252i	−0.999833	+	0.0182626i	$0.994187\pi$
$440$		0			0
$441$		−	8.94390i		−	0.425900i
$442$	−2.43625	−	9.46423i	−0.115881	−	0.450167i
$443$	20.2685	+	20.2685i	0.962985	+	0.962985i	0.999339	−	0.0363537i	$-0.0115743\pi$
$443$	20.2685	+	20.2685i	0.962985	+	0.962985i	−0.0363537	+	0.999339i	$0.511574\pi$
$444$	−8.68596	−	15.7534i	−0.412218	−	0.747625i
$445$		0			0
$446$	−17.2931	+	29.2824i	−0.818851	+	1.38656i
$447$	−4.62800			−0.218897
$448$	−0.885583	+	14.9635i	−0.0418399	+	0.706961i
$449$	−35.2717			−1.66457			−0.832287	−	0.554345i	$-0.812969\pi$
$449$	−35.2717			−1.66457			−0.832287	+	0.554345i	$0.812969\pi$
$450$		0			0
$451$	3.12216	−	3.12216i	0.147017	−	0.147017i
$452$	−3.42063	−	6.20388i	−0.160893	−	0.291806i
$453$	9.48312	+	9.48312i	0.445556	+	0.445556i
$454$	−5.97615	−	23.2158i	−0.280475	−	1.08957i
$455$		0			0
$456$	−1.60777	+	54.3800i	−0.0752908	+	2.54658i
$457$			9.01188i			0.421558i	0.977534	+	0.210779i	$0.0676000\pi$
$457$			9.01188i			0.421558i	−0.977534	+	0.210779i	$0.932400\pi$
$458$	−39.1191	+	10.0699i	−1.82792	+	0.470537i
$459$	1.87284	+	1.87284i	0.0874167	+	0.0874167i
$460$		0			0
$461$	−22.8247	+	22.8247i	−1.06305	+	1.06305i	−0.0651807	+	0.997873i	$0.520762\pi$
$461$	−22.8247	+	22.8247i	−1.06305	+	1.06305i	−0.997873	+	0.0651807i	$0.979238\pi$
$462$	25.0926	+	14.8187i	1.16741	+	0.689429i
$463$	3.72721			0.173218			0.0866090	−	0.996242i	$-0.472397\pi$
$463$	3.72721			0.173218			0.0866090	+	0.996242i	$0.472397\pi$
$464$	8.05738	+	35.6315i	0.374054	+	1.65415i
$465$		0			0
$466$	−12.2569	−	7.23846i	−0.567790	−	0.335315i
$467$	−3.23477	+	3.23477i	−0.149687	+	0.149687i	−0.777978	−	0.628291i	$-0.783755\pi$
$467$	−3.23477	+	3.23477i	−0.149687	+	0.149687i	0.628291	+	0.777978i	$0.283755\pi$
$468$	3.82724	−	13.2346i	0.176914	−	0.611771i
$469$	7.00109	+	7.00109i	0.323280	+	0.323280i
$470$		0			0
$471$			8.30158i			0.382517i
$472$	−18.7777	−	19.9219i	−0.864314	−	0.916979i
$473$			5.47284i			0.251642i
$474$	2.55763	+	9.93575i	0.117476	+	0.456364i
$475$		0			0
$476$	−8.43871	+	4.65285i	−0.386788	+	0.213263i
$477$	−17.8721	+	17.8721i	−0.818307	+	0.818307i
$478$	0.713961	−	1.20895i	0.0326558	−	0.0552962i
$479$	−11.0636			−0.505508			−0.252754	−	0.967531i	$-0.581336\pi$
$479$	−11.0636			−0.505508			−0.252754	+	0.967531i	$0.581336\pi$
$480$		0			0
$481$	10.2480			0.467267
$482$	10.1563	−	17.1978i	0.462609	−	0.783336i
$483$	23.7057	−	23.7057i	1.07865	−	1.07865i
$484$	18.8098	−	10.3712i	0.854992	−	0.471417i
$485$		0			0
$486$	7.32536	+	28.4572i	0.332285	+	1.29084i
$487$		−	6.68176i		−	0.302779i	−0.988474	−	0.151390i	$-0.951625\pi$
$487$		−	6.68176i		−	0.302779i	0.988474	−	0.151390i	$-0.0483748\pi$
$488$	20.0042	−	18.8553i	0.905550	−	0.853541i
$489$		−	42.3932i		−	1.91708i
$490$		0			0
$491$	−18.4274	−	18.4274i	−0.831618	−	0.831618i	0.156120	−	0.987738i	$-0.450101\pi$
$491$	−18.4274	−	18.4274i	−0.831618	−	0.831618i	−0.987738	+	0.156120i	$0.950101\pi$
$492$	−1.24100	+	4.29141i	−0.0559488	+	0.193472i
$493$	−16.6063	+	16.6063i	−0.747908	+	0.747908i
$494$	−26.6860	−	15.7597i	−1.20066	−	0.709065i
$495$		0			0
$496$	1.70610	−	2.70316i	0.0766060	−	0.121376i
$497$	17.5083			0.785356
$498$	4.01881	+	2.37336i	0.180087	+	0.106353i
$499$	8.84615	−	8.84615i	0.396008	−	0.396008i	−0.480814	−	0.876822i	$-0.659659\pi$
$499$	8.84615	−	8.84615i	0.396008	−	0.396008i	0.876822	+	0.480814i	$0.159659\pi$
$500$		0			0
$501$	−8.35554	−	8.35554i	−0.373298	−	0.373298i
$502$	3.03469	−	0.781180i	0.135445	−	0.0348658i
$503$			16.8746i			0.752401i	0.926538	+	0.376201i	$0.122770\pi$
$503$			16.8746i			0.752401i	−0.926538	+	0.376201i	$0.877230\pi$
$504$	−13.5788	−	0.401464i	−0.604848	−	0.0178826i
$505$		0			0
$506$	−12.4694	−	48.4405i	−0.554332	−	2.15344i
$507$	−9.63723	−	9.63723i	−0.428004	−	0.428004i
$508$	17.4491	+	31.6468i	0.774178	+	1.40410i
$509$	20.5691	−	20.5691i	0.911707	−	0.911707i	−0.0846994	−	0.996407i	$-0.526993\pi$
$509$	20.5691	−	20.5691i	0.911707	−	0.911707i	0.996407	+	0.0846994i	$0.0269930\pi$
$510$		0			0
$511$	−1.66070			−0.0734652
$512$	−22.5385	−	2.00376i	−0.996071	−	0.0885545i
$513$	8.39943			0.370844
$514$	−7.37788	+	12.4930i	−0.325425	+	0.551042i
$515$		0			0
$516$	−2.67353	−	4.84889i	−0.117696	−	0.213460i
$517$	5.02526	+	5.02526i	0.221011	+	0.221011i
$518$	−2.51908	−	9.78599i	−0.110682	−	0.429972i
$519$		−	20.6660i		−	0.907135i
$520$		0			0
$521$			12.6708i			0.555118i	0.960709	+	0.277559i	$0.0895253\pi$
$521$			12.6708i			0.555118i	−0.960709	+	0.277559i	$0.910475\pi$
$522$	−32.0619	+	8.25327i	−1.40331	+	0.361236i
$523$	−27.8509	−	27.8509i	−1.21784	−	1.21784i	−0.968388	−	0.249448i	$-0.919751\pi$
$523$	−27.8509	−	27.8509i	−1.21784	−	1.21784i	−0.249448	−	0.968388i	$-0.580249\pi$
$524$	17.3789	+	5.02570i	0.759202	+	0.219549i
$525$		0			0
$526$	−23.2134	−	13.7090i	−1.01215	−	0.597740i
$527$	2.05496			0.0895154
$528$	−23.4789	+	37.2003i	−1.02179	+	1.61894i
$529$	−34.5435			−1.50189
$530$		0			0
$531$	17.5438	−	17.5438i	0.761336	−	0.761336i
$532$	−8.48954	+	29.3569i	−0.368068	+	1.27278i
$533$	−1.79948	−	1.79948i	−0.0779442	−	0.0779442i
$534$	−32.6077	+	8.39377i	−1.41107	+	0.363234i
$535$		0			0
$536$	−10.8760	+	10.2514i	−0.469774	+	0.442793i
$537$		−	18.4005i		−	0.794038i
$538$	−1.73734	−	6.74915i	−0.0749023	−	0.290976i
$539$	−11.5037	−	11.5037i	−0.495499	−	0.495499i
$540$		0			0
$541$	−23.4122	+	23.4122i	−1.00657	+	1.00657i	−0.00659048	+	0.999978i	$0.502098\pi$
$541$	−23.4122	+	23.4122i	−1.00657	+	1.00657i	−0.999978	+	0.00659048i	$0.997902\pi$
$542$	−21.5774	+	36.5370i	−0.926829	+	1.56940i
$543$	−39.6921			−1.70335
$544$	−6.64409	−	12.9405i	−0.284863	−	0.554819i
$545$		0			0
$546$	8.54089	−	14.4623i	0.365516	−	0.618929i
$547$	17.3745	−	17.3745i	0.742878	−	0.742878i	−0.230253	−	0.973131i	$-0.573955\pi$
$547$	17.3745	−	17.3745i	0.742878	−	0.742878i	0.973131	+	0.230253i	$0.0739552\pi$
$548$	18.8027	−	10.3672i	0.803211	−	0.442866i
$549$	17.6163	+	17.6163i	0.751846	+	0.751846i
$550$		0			0
$551$			74.4767i			3.17282i
$552$	34.7113	+	36.8264i	1.47741	+	1.56744i
$553$			5.76308i			0.245071i
$554$	16.3419	−	4.20668i	0.694300	−	0.178725i
$555$		0			0
$556$	−1.81574	+	6.27884i	−0.0770043	+	0.266282i
$557$	22.8889	−	22.8889i	0.969832	−	0.969832i	−0.0297261	−	0.999558i	$-0.509464\pi$
$557$	22.8889	−	22.8889i	0.969832	−	0.969832i	0.999558	+	0.0297261i	$0.00946351\pi$
$558$	2.49442	+	1.47311i	0.105597	+	0.0623617i
$559$	3.15432			0.133413
$560$		0			0
$561$	−28.2799			−1.19398
$562$	−7.85081	−	4.63639i	−0.331166	−	0.195574i
$563$	19.2489	−	19.2489i	0.811246	−	0.811246i	−0.173574	−	0.984821i	$-0.555532\pi$
$563$	19.2489	−	19.2489i	0.811246	−	0.811246i	0.984821	+	0.173574i	$0.0555317\pi$
$564$	−6.90721	−	1.99745i	−0.290846	−	0.0841079i
$565$		0			0
$566$	5.05520	−	1.30129i	0.212486	−	0.0546975i
$567$			18.9608i			0.796278i
$568$	−0.781054	+	26.4178i	−0.0327723	+	1.10846i
$569$			34.4274i			1.44327i	0.692273	+	0.721635i	$0.256609\pi$
$569$			34.4274i			1.44327i	−0.692273	+	0.721635i	$0.743391\pi$
$570$		0			0
$571$	5.85059	+	5.85059i	0.244840	+	0.244840i	0.818849	−	0.574009i	$-0.194613\pi$
$571$	5.85059	+	5.85059i	0.244840	+	0.244840i	−0.574009	+	0.818849i	$0.694613\pi$
$572$	−12.0998	−	21.9451i	−0.505920	−	0.917569i
$573$	−18.5593	+	18.5593i	−0.775326	+	0.775326i
$574$	−1.27603	+	2.16070i	−0.0532603	+	0.0901857i
$575$		0			0
$576$	1.21151	−	20.4707i	0.0504797	−	0.852947i
$577$	32.5042			1.35317			0.676585	−	0.736365i	$-0.263459\pi$
$577$	32.5042			1.35317			0.676585	+	0.736365i	$0.263459\pi$
$578$	−7.47005	+	12.6491i	−0.310713	+	0.526131i
$579$	34.6611	−	34.6611i	1.44047	−	1.44047i
$580$		0			0
$581$	1.85384	+	1.85384i	0.0769103	+	0.0769103i
$582$	5.96077	+	23.1561i	0.247082	+	0.959851i
$583$			45.9743i			1.90406i
$584$	0.0740848	−	2.50578i	0.00306565	−	0.103690i
$585$		0			0
$586$	−14.5735	+	3.75146i	−0.602024	+	0.154971i
$587$	−14.7519	−	14.7519i	−0.608875	−	0.608875i	0.333777	−	0.942652i	$-0.391677\pi$
$587$	−14.7519	−	14.7519i	−0.608875	−	0.608875i	−0.942652	+	0.333777i	$0.891677\pi$
$588$	15.8118	+	4.57251i	0.652068	+	0.188567i
$589$	4.60810	−	4.60810i	0.189873	−	0.189873i
$590$		0			0
$591$	−46.8024			−1.92520
$592$	14.8782	−	3.36440i	0.611488	−	0.138276i
$593$	−20.5310			−0.843108			−0.421554	−	0.906803i	$-0.638515\pi$
$593$	−20.5310			−0.843108			−0.421554	+	0.906803i	$0.638515\pi$
$594$	5.84800	+	3.45361i	0.239946	+	0.141703i
$595$		0			0
$596$	1.09016	−	3.76979i	0.0446547	−	0.154416i
$597$	5.41590	+	5.41590i	0.221658	+	0.221658i
$598$	−27.9190	+	7.18683i	−1.14169	+	0.293891i
$599$			12.3998i			0.506644i	0.967382	+	0.253322i	$0.0815232\pi$
$599$			12.3998i			0.506644i	−0.967382	+	0.253322i	$0.918477\pi$
$600$		0			0
$601$			12.3980i			0.505723i	0.967502	+	0.252862i	$0.0813718\pi$
$601$			12.3980i			0.505723i	−0.967502	+	0.252862i	$0.918628\pi$
$602$	−0.775370	−	3.01212i	−0.0316017	−	0.122765i
$603$	−9.57777	−	9.57777i	−0.390037	−	0.390037i
$604$	−9.95839	+	5.49076i	−0.405201	+	0.223416i
$605$		0			0
$606$	2.52093	−	4.26870i	0.102406	−	0.173404i
$607$	4.90398			0.199046			0.0995232	−	0.995035i	$-0.468268\pi$
$607$	4.90398			0.199046			0.0995232	+	0.995035i	$0.468268\pi$
$608$	−43.9171	−	14.1192i	−1.78107	−	0.572610i
$609$	−40.3621			−1.63556
$610$		0			0
$611$	2.89635	−	2.89635i	0.117174	−	0.117174i
$612$	11.5445	−	6.36529i	0.466659	−	0.257301i
$613$	−0.408547	−	0.408547i	−0.0165011	−	0.0165011i	0.698808	−	0.715309i	$-0.253714\pi$
$613$	−0.408547	−	0.408547i	−0.0165011	−	0.0165011i	−0.715309	+	0.698808i	$0.753714\pi$
$614$	−6.33846	−	24.6233i	−0.255800	−	0.993717i
$615$		0			0
$616$	−17.9815	+	16.9487i	−0.724494	+	0.682884i
$617$		−	6.17186i		−	0.248470i	−0.992253	−	0.124235i	$-0.960352\pi$
$617$		−	6.17186i		−	0.248470i	0.992253	−	0.124235i	$-0.0396476\pi$
$618$	26.5111	−	6.82442i	1.06643	−	0.274518i
$619$	18.5138	+	18.5138i	0.744132	+	0.744132i	0.973370	−	0.229238i	$-0.0736234\pi$
$619$	18.5138	+	18.5138i	0.744132	+	0.744132i	−0.229238	+	0.973370i	$0.573623\pi$
$620$		0			0
$621$	5.52479	−	5.52479i	0.221702	−	0.221702i
$622$	−14.5290	−	8.58027i	−0.582559	−	0.344037i
$623$	−18.9136			−0.757757
$624$	21.4407	+	13.5323i	0.858315	+	0.541724i
$625$		0			0
$626$	41.8236	+	24.6994i	1.67161	+	0.987187i
$627$	−63.4156	+	63.4156i	−2.53258	+	2.53258i
$628$	−6.76214	−	1.95550i	−0.269839	−	0.0780329i
$629$	6.93404	+	6.93404i	0.276478	+	0.276478i
$630$		0			0
$631$		−	20.7940i		−	0.827795i	−0.910323	−	0.413897i	$-0.864167\pi$
$631$		−	20.7940i		−	0.827795i	0.910323	−	0.413897i	$-0.135833\pi$
$632$	−8.69574	−	0.257094i	−0.345898	−	0.0102266i
$633$		−	33.9640i		−	1.34995i
$634$	8.53130	+	33.1419i	0.338821	+	1.31623i
$635$		0			0
$636$	−22.4588	−	40.7328i	−0.890551	−	1.61516i
$637$	−6.63024	+	6.63024i	−0.262700	+	0.262700i
$638$	−30.6227	+	51.8535i	−1.21237	+	2.05290i
$639$	−23.9521			−0.947530
$640$		0			0
$641$	16.1179			0.636620			0.318310	−	0.947987i	$-0.396885\pi$
$641$	16.1179			0.636620			0.318310	+	0.947987i	$0.396885\pi$
$642$	−6.85441	+	11.6066i	−0.270522	+	0.458075i
$643$	10.3733	−	10.3733i	0.409082	−	0.409082i	−0.472336	−	0.881419i	$-0.656589\pi$
$643$	10.3733	−	10.3733i	0.409082	−	0.409082i	0.881419	+	0.472336i	$0.156589\pi$
$644$	13.7257	+	24.8938i	0.540868	+	0.980954i
$645$		0			0
$646$	−7.39298	−	28.7199i	−0.290873	−	1.12997i
$647$		−	32.5724i		−	1.28055i	−0.768145	−	0.640276i	$-0.778820\pi$
$647$		−	32.5724i		−	1.28055i	0.768145	−	0.640276i	$-0.221180\pi$
$648$	−28.6094	−	0.845850i	−1.12388	−	0.0332281i
$649$		−	45.1298i		−	1.77150i
$650$		0			0
$651$	2.49733	+	2.49733i	0.0978780	+	0.0978780i
$652$	34.5318	+	9.98601i	1.35237	+	0.391083i
$653$	4.31962	−	4.31962i	0.169040	−	0.169040i	−0.617517	−	0.786557i	$-0.711861\pi$
$653$	4.31962	−	4.31962i	0.169040	−	0.169040i	0.786557	+	0.617517i	$0.211861\pi$
$654$	−46.1981	−	27.2828i	−1.80649	−	1.06684i
$655$		0			0
$656$	−3.20328	−	2.02174i	−0.125067	−	0.0789359i
$657$	2.27191			0.0886356
$658$	−3.47774	−	2.05382i	−0.135576	−	0.0800662i
$659$	−4.19711	+	4.19711i	−0.163496	+	0.163496i	−0.784114	−	0.620617i	$-0.786882\pi$
$659$	−4.19711	+	4.19711i	−0.163496	+	0.163496i	0.620617	+	0.784114i	$0.286882\pi$
$660$		0			0
$661$	21.2310	+	21.2310i	0.825790	+	0.825790i	0.986931	−	0.161141i	$-0.0515175\pi$
$661$	21.2310	+	21.2310i	0.825790	+	0.825790i	−0.161141	+	0.986931i	$0.551518\pi$
$662$	18.9860	−	4.88731i	0.737911	−	0.189951i
$663$			16.2993i			0.633013i
$664$	−2.87990	+	2.71450i	−0.111762	+	0.105343i
$665$		0			0
$666$	3.44620	+	13.3876i	0.133538	+	0.518760i
$667$	48.9877	+	48.9877i	1.89681	+	1.89681i
$668$	8.77429	−	4.83788i	0.339488	−	0.187183i
$669$	40.1062	−	40.1062i	1.55060	−	1.55060i
$670$		0			0
$671$	45.3164			1.74942
$672$	7.65182	−	23.8005i	0.295175	−	0.918126i
$673$	−6.08317			−0.234489			−0.117244	−	0.993103i	$-0.537406\pi$
$673$	−6.08317			−0.234489			−0.117244	+	0.993103i	$0.537406\pi$
$674$	4.36877	−	7.39765i	0.168279	−	0.284947i
$675$		0			0
$676$	10.1202	−	5.57998i	0.389239	−	0.214615i
$677$	−8.42443	−	8.42443i	−0.323777	−	0.323777i	0.526437	−	0.850214i	$-0.323528\pi$
$677$	−8.42443	−	8.42443i	−0.323777	−	0.323777i	−0.850214	+	0.526437i	$0.823528\pi$
$678$	2.94551	+	11.4426i	0.113122	+	0.439449i
$679$			13.4313i			0.515447i
$680$		0			0
$681$			39.9824i			1.53213i
$682$	5.10305	−	1.31361i	0.195406	−	0.0503008i
$683$	14.7609	+	14.7609i	0.564812	+	0.564812i	0.930670	−	0.365859i	$-0.119225\pi$
$683$	14.7609	+	14.7609i	0.564812	+	0.564812i	−0.365859	+	0.930670i	$0.619225\pi$
$684$	11.6140	−	40.1615i	0.444073	−	1.53561i
$685$		0			0
$686$	23.9328	+	14.1338i	0.913757	+	0.539630i
$687$	67.3710			2.57036
$688$	4.57948	−	1.03556i	0.174591	−	0.0394804i
$689$	26.4977			1.00948
$690$		0			0
$691$	−4.06268	+	4.06268i	−0.154552	+	0.154552i	−0.780147	−	0.625596i	$-0.784856\pi$
$691$	−4.06268	+	4.06268i	−0.154552	+	0.154552i	0.625596	+	0.780147i	$0.284856\pi$
$692$	16.8337	+	4.86802i	0.639920	+	0.185054i
$693$	−15.8350	−	15.8350i	−0.601523	−	0.601523i
$694$	11.1801	−	2.87796i	0.424392	−	0.109246i
$695$		0			0
$696$	1.80057	−	60.9012i	0.0682506	−	2.30845i
$697$		−	2.43515i		−	0.0922379i
$698$	3.78348	+	14.6979i	0.143207	+	0.556322i
$699$	16.7875	+	16.7875i	0.634961	+	0.634961i
$700$		0			0
$701$	11.1049	−	11.1049i	0.419428	−	0.419428i	−0.465578	−	0.885007i	$-0.654154\pi$
$701$	11.1049	−	11.1049i	0.419428	−	0.419428i	0.885007	+	0.465578i	$0.154154\pi$
$702$	1.99051	−	3.37054i	0.0751271	−	0.127213i
$703$	31.0982			1.17289
$704$	−24.7713	−	27.8878i	−0.933603	−	1.05106i
$705$		0			0
$706$	−11.6705	+	19.7617i	−0.439225	+	0.743741i
$707$	1.96911	−	1.96911i	0.0740561	−	0.0740561i
$708$	22.0463	+	39.9846i	0.828551	+	1.50271i
$709$	13.0114	+	13.0114i	0.488652	+	0.488652i	0.907881	−	0.419229i	$-0.137700\pi$
$709$	13.0114	+	13.0114i	0.488652	+	0.488652i	−0.419229	+	0.907881i	$0.637700\pi$
$710$		0			0
$711$		−	7.88412i		−	0.295678i
$712$	0.843744	−	28.5381i	0.0316206	−	1.06951i
$713$		−	6.06203i		−	0.227025i
$714$	15.5645	−	4.00658i	0.582488	−	0.149942i
$715$		0			0
$716$	14.9883	+	4.33436i	0.560138	+	0.161983i
$717$	−1.65582	+	1.65582i	−0.0618378	+	0.0618378i
$718$	−8.24759	−	4.87071i	−0.307797	−	0.181773i
$719$	−50.0570			−1.86681			−0.933406	−	0.358821i	$-0.883179\pi$
$719$	−50.0570			−1.86681			−0.933406	+	0.358821i	$0.883179\pi$
$720$		0			0
$721$	15.3774			0.572684
$722$	−57.8439	−	34.1604i	−2.15273	−	1.27132i
$723$	−23.5547	+	23.5547i	−0.876007	+	0.876007i
$724$	9.34977	−	32.3316i	0.347481	−	1.20160i
$725$		0			0
$726$	−34.6932	+	8.93062i	−1.28759	+	0.331447i
$727$			27.7141i			1.02786i	0.857832	+	0.513930i	$0.171811\pi$
$727$			27.7141i			1.02786i	−0.857832	+	0.513930i	$0.828189\pi$
$728$	9.76854	+	10.3638i	0.362046	+	0.384107i
$729$		−	18.6509i		−	0.690775i
$730$		0			0
$731$	2.13429	+	2.13429i	0.0789396	+	0.0789396i
$732$	−40.1499	+	22.1374i	−1.48398	+	0.818224i
$733$	16.8860	−	16.8860i	0.623698	−	0.623698i	−0.322777	−	0.946475i	$-0.604616\pi$
$733$	16.8860	−	16.8860i	0.623698	−	0.623698i	0.946475	+	0.322777i	$0.104616\pi$
$734$	−4.57160	+	7.74110i	−0.168741	+	0.285729i
$735$		0			0
$736$	−38.1738	+	19.5998i	−1.40711	+	0.722457i
$737$	−24.6379			−0.907550
$738$	1.74565	−	2.95592i	0.0642584	−	0.108809i
$739$	−23.6286	+	23.6286i	−0.869193	+	0.869193i	−0.992383	−	0.123190i	$-0.960688\pi$
$739$	−23.6286	+	23.6286i	−0.869193	+	0.869193i	0.123190	+	0.992383i	$0.460688\pi$
$740$		0			0
$741$	36.5501	+	36.5501i	1.34270	+	1.34270i
$742$	−6.51345	−	25.3031i	−0.239116	−	0.928907i
$743$		−	6.53356i		−	0.239693i	−0.992792	−	0.119846i	$-0.961760\pi$
$743$		−	6.53356i		−	0.239693i	0.992792	−	0.119846i	$-0.0382402\pi$
$744$	−3.87955	+	3.65673i	−0.142231	+	0.134062i
$745$		0			0
$746$	17.8372	−	4.59161i	0.653068	−	0.168111i
$747$	−2.53613	−	2.53613i	−0.0927921	−	0.0927921i
$748$	6.66153	−	23.0356i	0.243570	−	0.842267i
$749$	−5.35401	+	5.35401i	−0.195631	+	0.195631i
$750$		0			0
$751$	−22.8483			−0.833746			−0.416873	−	0.908965i	$-0.636874\pi$
$751$	−22.8483			−0.833746			−0.416873	+	0.908965i	$0.636874\pi$
$752$	3.25409	−	5.15583i	0.118664	−	0.188014i
$753$	−5.22634			−0.190459
$754$	29.8862	+	17.6496i	1.08839	+	0.642762i
$755$		0			0
$756$	−3.70789	−	1.07226i	−0.134855	−	0.0389977i
$757$	−24.0190	−	24.0190i	−0.872985	−	0.872985i	0.119811	−	0.992797i	$-0.461771\pi$
$757$	−24.0190	−	24.0190i	−0.872985	−	0.872985i	−0.992797	+	0.119811i	$0.961771\pi$
$758$	10.4900	−	2.70031i	0.381015	−	0.0980797i
$759$			83.4243i			3.02811i
$760$		0			0
$761$		−	5.51772i		−	0.200017i	−0.994987	−	0.100009i	$-0.968113\pi$
$761$		−	5.51772i		−	0.200017i	0.994987	−	0.100009i	$-0.0318871\pi$
$762$	−15.0254	−	58.3700i	−0.544314	−	2.11452i
$763$	−21.3107	−	21.3107i	−0.771501	−	0.771501i
$764$	−10.7459	−	19.4894i	−0.388772	−	0.705103i
$765$		0			0
$766$	20.2528	−	34.2941i	0.731763	−	1.23910i
$767$	−26.0109			−0.939200
$768$	35.5706	+	12.6073i	1.28354	+	0.454928i
$769$	14.0124			0.505299			0.252649	−	0.967558i	$-0.418698\pi$
$769$	14.0124			0.505299			0.252649	+	0.967558i	$0.418698\pi$
$770$		0			0
$771$	17.1108	−	17.1108i	0.616231	−	0.616231i
$772$	20.0689	+	36.3982i	0.722294	+	1.31000i
$773$	0.753043	+	0.753043i	0.0270851	+	0.0270851i	0.720520	−	0.693435i	$-0.243903\pi$
$773$	0.753043	+	0.753043i	0.0270851	+	0.0270851i	−0.693435	+	0.720520i	$0.743903\pi$
$774$	1.06074	+	4.12070i	0.0381274	+	0.148115i
$775$		0			0
$776$	−20.2661	−	0.599178i	−0.727512	−	0.0215092i
$777$			16.8535i			0.604614i
$778$	18.5896	−	4.78529i	0.666471	−	0.171561i
$779$	−5.46066	−	5.46066i	−0.195648	−	0.195648i
$780$		0			0
$781$	−30.8073	+	30.8073i	−1.10237	+	1.10237i
$782$	−23.7535	−	14.0279i	−0.849424	−	0.501638i
$783$	−9.40668			−0.336167
$784$	−7.44917	+	11.8026i	−0.266042	+	0.421521i
$785$		0			0
$786$	−25.9805	−	15.3431i	−0.926693	−	0.547270i
$787$	−29.2752	+	29.2752i	−1.04355	+	1.04355i	−0.0445395	+	0.999008i	$0.514182\pi$
$787$	−29.2752	+	29.2752i	−1.04355	+	1.04355i	−0.999008	+	0.0445395i	$0.985818\pi$
$788$	11.0247	−	38.1234i	0.392737	−	1.35809i
$789$	31.7939	+	31.7939i	1.13189	+	1.13189i
$790$		0			0
$791$			6.63709i			0.235988i
$792$	24.5994	−	23.1866i	0.874101	−	0.823899i
$793$		−	26.1185i		−	0.927494i
$794$	−5.22932	−	20.3146i	−0.185581	−	0.720937i
$795$		0			0
$796$	−5.68733	+	3.13582i	−0.201582	+	0.111146i
$797$	−6.09658	+	6.09658i	−0.215952	+	0.215952i	−0.806790	−	0.590838i	$-0.798797\pi$
$797$	−6.09658	+	6.09658i	−0.215952	+	0.215952i	0.590838	+	0.806790i	$0.298797\pi$
$798$	25.9179	−	43.8869i	0.917485	−	1.55358i
$799$	3.91948			0.138661
$800$		0			0
$801$	25.8745			0.914232
$802$	−1.75629	+	2.97393i	−0.0620167	+	0.105013i
$803$	2.92214	−	2.92214i	0.103120	−	0.103120i
$804$	21.8290	−	12.0358i	0.769849	−	0.424471i
$805$		0			0
$806$	−0.757111	−	2.94119i	−0.0266681	−	0.103599i
$807$			11.6234i			0.409163i
$808$	2.88329	+	3.05897i	0.101434	+	0.107614i
$809$		−	31.5083i		−	1.10777i	−0.832592	−	0.553886i	$-0.813144\pi$
$809$		−	31.5083i		−	1.10777i	0.832592	−	0.553886i	$-0.186856\pi$
$810$		0			0
$811$	20.2317	+	20.2317i	0.710431	+	0.710431i	0.966625	−	0.256194i	$-0.0824686\pi$
$811$	20.2317	+	20.2317i	0.710431	+	0.710431i	−0.256194	+	0.966625i	$0.582469\pi$
$812$	9.50760	−	32.8774i	0.333651	−	1.15377i
$813$	50.0424	−	50.0424i	1.75506	−	1.75506i
$814$	21.6517	+	12.7867i	0.758893	+	0.448174i
$815$		0			0
$816$	5.35106	+	23.6636i	0.187325	+	0.828391i
$817$	9.57200			0.334882
$818$	30.0323	+	17.7359i	1.05006	+	0.620123i
$819$	−9.12664	+	9.12664i	−0.318910	+	0.318910i
$820$		0			0
$821$	−19.1821	−	19.1821i	−0.669459	−	0.669459i	0.288132	−	0.957591i	$-0.406966\pi$
$821$	−19.1821	−	19.1821i	−0.669459	−	0.669459i	−0.957591	+	0.288132i	$0.906966\pi$
$822$	−34.6800	+	8.92723i	−1.20961	+	0.311373i
$823$		−	11.4746i		−	0.399979i	−0.979798	−	0.199989i	$-0.935909\pi$
$823$		−	11.4746i		−	0.399979i	0.979798	−	0.199989i	$-0.0640907\pi$
$824$	−0.685992	+	23.2025i	−0.0238977	+	0.808296i
$825$		0			0
$826$	6.39381	+	24.8383i	0.222469	+	0.864236i
$827$	17.7573	+	17.7573i	0.617482	+	0.617482i	0.944885	−	0.327403i	$-0.106173\pi$
$827$	17.7573	+	17.7573i	0.617482	+	0.617482i	−0.327403	+	0.944885i	$0.606173\pi$
$828$	−18.7773	−	34.0557i	−0.652556	−	1.18352i
$829$	−20.0071	+	20.0071i	−0.694876	+	0.694876i	−0.963301	−	0.268424i	$-0.913497\pi$
$829$	−20.0071	+	20.0071i	−0.694876	+	0.694876i	0.268424	+	0.963301i	$0.413497\pi$
$830$		0			0
$831$	−28.1440			−0.976306
$832$	−16.0733	+	14.2771i	−0.557243	+	0.494970i
$833$	−8.97238			−0.310874
$834$	5.54331	−	9.38649i	0.191949	−	0.325028i
$835$		0			0
$836$	−36.7178	−	66.5939i	−1.26991	−	2.30320i
$837$	0.582020	+	0.582020i	0.0201175	+	0.0201175i
$838$	−9.55584	−	37.1220i	−0.330101	−	1.28236i
$839$			20.3936i			0.704065i	0.935988	+	0.352033i	$0.114509\pi$
$839$			20.3936i			0.704065i	−0.935988	+	0.352033i	$0.885491\pi$
$840$		0			0
$841$		−	54.4079i		−	1.87614i
$842$	−14.3999	+	3.70679i	−0.496255	+	0.127744i
$843$	10.7527	+	10.7527i	0.370344	+	0.370344i
$844$	27.6657	+	8.00047i	0.952293	+	0.275387i
$845$		0			0
$846$	4.75768	+	2.80971i	0.163572	+	0.0965997i
$847$	−20.1233			−0.691444
$848$	38.4697	−	8.69917i	1.32105	−	0.298731i
$849$	−8.70608			−0.298792
$850$		0			0
$851$	20.4551	−	20.4551i	0.701191	−	0.701191i
$852$	12.2453	−	42.3446i	0.419519	−	1.45070i
$853$	37.4481	+	37.4481i	1.28220	+	1.28220i	0.939414	+	0.342784i	$0.111370\pi$
$853$	37.4481	+	37.4481i	1.28220	+	1.28220i	0.342784	+	0.939414i	$0.388630\pi$
$854$	−24.9410	+	6.42024i	−0.853464	+	0.219696i
$855$		0			0
$856$	−7.83965	−	8.31734i	−0.267954	−	0.284281i
$857$			12.7258i			0.434706i	0.976093	+	0.217353i	$0.0697422\pi$
$857$			12.7258i			0.434706i	−0.976093	+	0.217353i	$0.930258\pi$
$858$	10.4192	+	40.4759i	0.355705	+	1.38183i
$859$	17.4318	+	17.4318i	0.594766	+	0.594766i	0.938915	−	0.344149i	$-0.111833\pi$
$859$	17.4318	+	17.4318i	0.594766	+	0.594766i	−0.344149	+	0.938915i	$0.611833\pi$
$860$		0			0
$861$	2.95936	−	2.95936i	0.100855	−	0.100855i
$862$	16.2271	−	27.4774i	0.552699	−	0.935885i
$863$	−33.6976			−1.14708			−0.573540	−	0.819178i	$-0.694430\pi$
$863$	−33.6976			−1.14708			−0.573540	+	0.819178i	$0.694430\pi$
$864$	1.78331	−	5.54688i	0.0606694	−	0.188709i
$865$		0			0
$866$	19.0436	−	32.2466i	0.647128	−	1.09578i
$867$	17.3246	−	17.3246i	0.588374	−	0.588374i
$868$	−2.62249	+	1.44596i	−0.0890130	+	0.0490791i
$869$	−10.1406	−	10.1406i	−0.343996	−	0.343996i
$870$		0			0
$871$			14.2003i			0.481158i
$872$	33.1058	−	31.2044i	1.12110	−	1.05672i
$873$		−	18.3746i		−	0.621886i
$874$	−84.7223	+	21.8090i	−2.86577	+	0.737699i
$875$		0			0
$876$	−1.16150	+	4.01648i	−0.0392434	+	0.135704i
$877$	−21.8386	+	21.8386i	−0.737436	+	0.737436i	−0.972081	−	0.234645i	$-0.924607\pi$
$877$	−21.8386	+	21.8386i	−0.737436	+	0.737436i	0.234645	+	0.972081i	$0.424607\pi$
$878$	0.931906	+	0.550349i	0.0314503	+	0.0185734i
$879$	25.0985			0.846550
$880$		0			0
$881$	−39.3274			−1.32497			−0.662487	−	0.749073i	$-0.730499\pi$
$881$	−39.3274			−1.32497			−0.662487	+	0.749073i	$0.730499\pi$
$882$	−10.8912	−	6.43191i	−0.366724	−	0.216574i
$883$	−6.80206	+	6.80206i	−0.228907	+	0.228907i	−0.812236	−	0.583329i	$-0.801750\pi$
$883$	−6.80206	+	6.80206i	−0.228907	+	0.228907i	0.583329	+	0.812236i	$0.301750\pi$
$884$	−13.2768	−	3.83942i	−0.446546	−	0.129134i
$885$		0			0
$886$	39.2572	−	10.1055i	1.31887	−	0.339500i
$887$			29.4190i			0.987793i	0.869521	+	0.493897i	$0.164428\pi$
$887$			29.4190i			0.987793i	−0.869521	+	0.493897i	$0.835572\pi$
$888$	−25.4297	−	0.751840i	−0.853363	−	0.0252301i
$889$		−	33.8566i		−	1.13552i
$890$		0			0
$891$	−33.3630	−	33.3630i	−1.11770	−	1.11770i
$892$	23.2216	+	42.1162i	0.777517	+	1.41016i
$893$	8.78917	−	8.78917i	0.294118	−	0.294118i
$894$	−3.32818	+	5.63561i	−0.111311	+	0.188483i
$895$		0			0
$896$	17.5845	+	11.8393i	0.587458	+	0.395522i
$897$	48.0822			1.60542
$898$	−25.3652	+	42.9510i	−0.846449	+	1.43329i
$899$	−5.16070	+	5.16070i	−0.172119	+	0.172119i
$900$		0			0
$901$	17.9290	+	17.9290i	0.597301	+	0.597301i
$902$	−1.55665	−	6.04718i	−0.0518307	−	0.201349i
$903$			5.18748i			0.172628i
$904$	−10.0145	−	0.296084i	−0.333077	−	0.00984759i
$905$		0			0
$906$	18.3675	−	4.72810i	0.610218	−	0.157081i
$907$	16.6137	+	16.6137i	0.551649	+	0.551649i	0.926917	−	0.375267i	$-0.122449\pi$
$907$	16.6137	+	16.6137i	0.551649	+	0.551649i	−0.375267	+	0.926917i	$0.622449\pi$
$908$	−32.5681	−	9.41814i	−1.08081	−	0.312552i
$909$	−2.69382	+	2.69382i	−0.0893485	+	0.0893485i
$910$		0			0
$911$	40.7299			1.34944			0.674721	−	0.738073i	$-0.264264\pi$
$911$	40.7299			1.34944			0.674721	+	0.738073i	$0.264264\pi$
$912$	65.0633	+	41.0646i	2.15446	+	1.35978i
$913$	−6.52396			−0.215912
$914$	10.9739	+	6.48079i	0.362985	+	0.214365i
$915$		0			0
$916$	−15.8697	+	54.8777i	−0.524351	+	1.81321i
$917$	−11.9846	−	11.9846i	−0.395765	−	0.395765i
$918$	3.62742	−	0.933760i	0.119723	−	0.0308187i
$919$			35.6125i			1.17475i	0.809316	+	0.587373i	$0.199838\pi$
$919$			35.6125i			1.17475i	−0.809316	+	0.587373i	$0.800162\pi$
$920$		0			0
$921$			42.4064i			1.39734i
$922$	11.3800	+	44.2083i	0.374779	+	1.45592i
$923$	17.7560	+	17.7560i	0.584446	+	0.584446i
$924$	36.0901	−	19.8990i	1.18728	−	0.654628i
$925$		0			0
$926$	2.68038	−	4.53869i	0.0880828	−	0.149151i
$927$	−21.0369			−0.690942
$928$	49.1836	+	15.8124i	1.61453	+	0.519067i
$929$	−0.570971			−0.0187329			−0.00936647	−	0.999956i	$-0.502981\pi$
$929$	−0.570971			−0.0187329			−0.00936647	+	0.999956i	$0.502981\pi$
$930$		0			0
$931$	−20.1199	+	20.1199i	−0.659404	+	0.659404i
$932$	−17.6288	+	9.72000i	−0.577451	+	0.318389i
$933$	19.8994	+	19.8994i	0.651477	+	0.651477i
$934$	1.61279	+	6.26529i	0.0527722	+	0.205007i
$935$		0			0
$936$	−13.3638	−	14.1780i	−0.436808	−	0.463424i
$937$		−	21.3585i		−	0.697750i	−0.937169	−	0.348875i	$-0.886564\pi$
$937$		−	21.3585i		−	0.697750i	0.937169	−	0.348875i	$-0.113436\pi$
$938$	13.5601	−	3.49060i	0.442753	−	0.113972i
$939$	−57.2830	−	57.2830i	−1.86936	−	1.86936i
$940$		0			0
$941$	33.6914	−	33.6914i	1.09831	−	1.09831i	0.103700	−	0.994609i	$-0.466932\pi$
$941$	33.6914	−	33.6914i	1.09831	−	1.09831i	0.994609	−	0.103700i	$-0.0330681\pi$
$942$	10.1090	+	5.96999i	0.329369	+	0.194513i
$943$	−7.18358			−0.233929
$944$	−37.7630	+	8.53937i	−1.22908	+	0.277933i
$945$		0			0
$946$	6.66438	+	3.93573i	0.216678	+	0.127962i
$947$	0.421834	−	0.421834i	0.0137078	−	0.0137078i	−0.700220	−	0.713927i	$-0.746915\pi$
$947$	0.421834	−	0.421834i	0.0137078	−	0.0137078i	0.713927	+	0.700220i	$0.246915\pi$
$948$	13.9382	+	4.03071i	0.452693	+	0.130911i
$949$	−1.68420	−	1.68420i	−0.0546714	−	0.0546714i
$950$		0			0
$951$		−	57.0771i		−	1.85085i
$952$	−0.402742	+	13.6220i	−0.0130529	+	0.441492i
$953$		−	27.7261i		−	0.898137i	−0.893497	−	0.449069i	$-0.851756\pi$
$953$		−	27.7261i		−	0.898137i	0.893497	−	0.449069i	$-0.148244\pi$
$954$	8.91067	+	34.6157i	0.288493	+	1.12072i
$955$		0			0
$956$	−0.958726	−	1.73881i	−0.0310074	−	0.0562371i
$957$	71.0204	−	71.0204i	2.29576	−	2.29576i
$958$	−7.95625	+	13.4723i	−0.257055	+	0.435271i
$959$	−20.1156			−0.649567
$960$		0			0
$961$	−30.3614			−0.979399
$962$	7.36972	−	12.4792i	0.237609	−	0.402344i
$963$	7.32450	−	7.32450i	0.236029	−	0.236029i
$964$	−13.6382	−	24.7352i	−0.439257	−	0.796666i
$965$		0			0
$966$	−11.8192	−	45.9147i	−0.380277	−	1.47728i
$967$		−	41.9640i		−	1.34947i	−0.738060	−	0.674735i	$-0.764258\pi$
$967$		−	41.9640i		−	1.34947i	0.738060	−	0.674735i	$-0.235742\pi$
$968$	0.897709	−	30.3634i	0.0288534	−	0.975916i
$969$			49.4614i			1.58893i
$970$		0			0
$971$	30.0549	+	30.0549i	0.964508	+	0.964508i	0.999391	−	0.0348833i	$-0.0111059\pi$
$971$	30.0549	+	30.0549i	0.964508	+	0.964508i	−0.0348833	+	0.999391i	$0.511106\pi$
$972$	39.9208	+	11.5444i	1.28046	+	0.370287i
$973$	4.32990	−	4.32990i	0.138810	−	0.138810i
$974$	−8.13651	−	4.80511i	−0.260710	−	0.153966i
$975$		0			0
$976$	−8.57468	−	37.9192i	−0.274469	−	1.21376i
$977$	−44.3389			−1.41853			−0.709263	−	0.704944i	$-0.750972\pi$
$977$	−44.3389			−1.41853			−0.709263	+	0.704944i	$0.750972\pi$
$978$	−51.6229	−	30.4866i	−1.65072	−	0.974853i
$979$	33.2800	−	33.2800i	1.06363	−	1.06363i
$980$		0			0
$981$	29.1539	+	29.1539i	0.930814	+	0.930814i
$982$	−35.6913	+	9.18755i	−1.13896	+	0.293186i
$983$		−	27.0764i		−	0.863604i	−0.901968	−	0.431802i	$-0.857878\pi$
$983$		−	27.0764i		−	0.863604i	0.901968	−	0.431802i	$-0.142122\pi$
$984$	4.33327	+	4.59731i	0.138140	+	0.146557i
$985$		0			0
$986$	8.27955	+	32.1639i	0.263674	+	1.02431i
$987$	4.76323	+	4.76323i	0.151615	+	0.151615i
$988$	−38.3819	+	21.1626i	−1.22109	+	0.673272i
$989$	6.29606	−	6.29606i	0.200203	−	0.200203i
$990$		0			0
$991$	19.3780			0.615564			0.307782	−	0.951457i	$-0.400413\pi$
$991$	19.3780			0.615564			0.307782	+	0.951457i	$0.400413\pi$
$992$	−2.06477	−	4.02150i	−0.0655567	−	0.127683i
$993$	−32.6977			−1.03763
$994$	12.5909	−	21.3202i	0.399360	−	0.676236i
$995$		0			0
$996$	5.78017	−	3.18701i	0.183152	−	0.100984i
$997$	−8.69453	−	8.69453i	−0.275359	−	0.275359i	0.555894	−	0.831253i	$-0.312376\pi$
$997$	−8.69453	−	8.69453i	−0.275359	−	0.275359i	−0.831253	+	0.555894i	$0.812376\pi$
$998$	−4.41051	−	17.1337i	−0.139612	−	0.542359i
$999$			3.92782i			0.124271i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.l.g.101.4	yes	12
4.3	odd	2		1600.2.l.f.1201.6		12
5.2	odd	4		400.2.q.f.149.5		12
5.3	odd	4		400.2.q.e.149.2		12
5.4	even	2		400.2.l.f.101.3	✓	12
16.3	odd	4		1600.2.l.f.401.6		12
16.13	even	4	inner	400.2.l.g.301.4	yes	12
20.3	even	4		1600.2.q.e.49.6		12
20.7	even	4		1600.2.q.f.49.1		12
20.19	odd	2		1600.2.l.g.1201.1		12
80.3	even	4		1600.2.q.f.849.1		12
80.13	odd	4		400.2.q.f.349.5		12
80.19	odd	4		1600.2.l.g.401.1		12
80.29	even	4		400.2.l.f.301.3	yes	12
80.67	even	4		1600.2.q.e.849.6		12
80.77	odd	4		400.2.q.e.349.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.l.f.101.3	✓	12	5.4	even	2
400.2.l.f.301.3	yes	12	80.29	even	4
400.2.l.g.101.4	yes	12	1.1	even	1	trivial
400.2.l.g.301.4	yes	12	16.13	even	4	inner
400.2.q.e.149.2		12	5.3	odd	4
400.2.q.e.349.2		12	80.77	odd	4
400.2.q.f.149.5		12	5.2	odd	4
400.2.q.f.349.5		12	80.13	odd	4
1600.2.l.f.401.6		12	16.3	odd	4
1600.2.l.f.1201.6		12	4.3	odd	2
1600.2.l.g.401.1		12	80.19	odd	4
1600.2.l.g.1201.1		12	20.19	odd	2
1600.2.q.e.49.6		12	20.3	even	4
1600.2.q.e.849.6		12	80.67	even	4
1600.2.q.f.49.1		12	20.7	even	4
1600.2.q.f.849.1		12	80.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.719139 - 1.21772i) q^{2} +(-1.66783 + 1.66783i) q^{3} +(-0.965679 - 1.75142i) q^{4} +(0.831547 + 3.23035i) q^{6} +1.87372i q^{7} +(-2.82719 - 0.0835873i) q^{8} -2.56332i q^{9} +O(q^{10})\)	\(q+(0.719139 - 1.21772i) q^{2} +(-1.66783 + 1.66783i) q^{3} +(-0.965679 - 1.75142i) q^{4} +(0.831547 + 3.23035i) q^{6} +1.87372i q^{7} +(-2.82719 - 0.0835873i) q^{8} -2.56332i q^{9} +(-3.29695 - 3.29695i) q^{11} +(4.53166 + 1.31048i) q^{12} +(-1.90022 + 1.90022i) q^{13} +(2.28166 + 1.34746i) q^{14} +(-2.13493 + 3.38261i) q^{16} -2.57148 q^{17} +(-3.12140 - 1.84338i) q^{18} +(-5.76636 + 5.76636i) q^{19} +(-3.12504 - 3.12504i) q^{21} +(-6.38572 + 1.64379i) q^{22} +7.58574i q^{23} +(4.85469 - 4.57587i) q^{24} +(0.947414 + 3.68046i) q^{26} +(-0.728312 - 0.728312i) q^{27} +(3.28166 - 1.80941i) q^{28} +(6.45786 - 6.45786i) q^{29} -0.799135 q^{31} +(2.58376 + 5.03231i) q^{32} +10.9975 q^{33} +(-1.84925 + 3.13134i) q^{34} +(-4.48944 + 2.47534i) q^{36} +(-2.69652 - 2.69652i) q^{37} +(2.87499 + 11.1686i) q^{38} -6.33850i q^{39} +0.946984i q^{41} +(-6.05276 + 1.55808i) q^{42} +(-0.829986 - 0.829986i) q^{43} +(-2.59054 + 8.95813i) q^{44} +(9.23730 + 5.45520i) q^{46} -1.52421 q^{47} +(-2.08093 - 9.20233i) q^{48} +3.48919 q^{49} +(4.28879 - 4.28879i) q^{51} +(5.16309 + 1.49308i) q^{52} +(-6.97225 - 6.97225i) q^{53} +(-1.41064 + 0.363122i) q^{54} +(0.156619 - 5.29735i) q^{56} -19.2346i q^{57} +(-3.21976 - 12.5080i) q^{58} +(6.84418 + 6.84418i) q^{59} +(-6.87247 + 6.87247i) q^{61} +(-0.574689 + 0.973121i) q^{62} +4.80293 q^{63} +(7.98603 + 0.472635i) q^{64} +(7.90874 - 13.3919i) q^{66} +(3.73647 - 3.73647i) q^{67} +(2.48322 + 4.50373i) q^{68} +(-12.6517 - 12.6517i) q^{69} -9.34417i q^{71} +(-0.214261 + 7.24699i) q^{72} +0.886316i q^{73} +(-5.22277 + 1.34443i) q^{74} +(15.6678 + 4.53086i) q^{76} +(6.17755 - 6.17755i) q^{77} +(-7.71851 - 4.55826i) q^{78} +3.07575 q^{79} +10.1194 q^{81} +(1.15316 + 0.681013i) q^{82} +(0.989393 - 0.989393i) q^{83} +(-2.45547 + 8.49104i) q^{84} +(-1.60756 + 0.413814i) q^{86} +21.5412i q^{87} +(9.04553 + 9.59670i) q^{88} +10.0942i q^{89} +(-3.56048 - 3.56048i) q^{91} +(13.2858 - 7.32539i) q^{92} +(1.33282 - 1.33282i) q^{93} +(-1.09612 + 1.85606i) q^{94} +(-12.7023 - 4.08377i) q^{96} +7.16829 q^{97} +(2.50921 - 4.24885i) q^{98} +(-8.45113 + 8.45113i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 2 q^{3} + 2 q^{4} + 6 q^{6} - 8 q^{8}+O(q^{10}) \) 12 * q + 4 * q^2 + 2 * q^3 + 2 * q^4 + 6 * q^6 - 8 * q^8	\( 12 q + 4 q^{2} + 2 q^{3} + 2 q^{4} + 6 q^{6} - 8 q^{8} - 2 q^{11} + 8 q^{12} - 4 q^{13} + 14 q^{14} + 2 q^{16} - 8 q^{17} + 18 q^{18} - 14 q^{19} - 20 q^{21} + 2 q^{22} - 14 q^{24} - 16 q^{26} - 10 q^{27} + 26 q^{28} - 4 q^{31} - 16 q^{32} + 28 q^{33} - 6 q^{34} + 2 q^{36} + 8 q^{37} + 10 q^{38} + 10 q^{42} - 44 q^{44} - 10 q^{46} + 8 q^{47} - 28 q^{48} + 4 q^{49} + 10 q^{51} - 12 q^{52} - 16 q^{53} + 10 q^{54} + 6 q^{56} - 60 q^{58} + 20 q^{59} + 4 q^{61} - 18 q^{62} - 8 q^{63} + 38 q^{64} + 32 q^{66} + 50 q^{67} - 60 q^{68} - 14 q^{72} + 10 q^{74} + 60 q^{76} - 8 q^{77} + 4 q^{78} + 12 q^{79} - 8 q^{81} + 42 q^{82} - 2 q^{83} + 34 q^{84} + 6 q^{86} + 30 q^{88} - 2 q^{92} - 44 q^{93} + 32 q^{94} - 34 q^{96} + 64 q^{98} + 12 q^{99}+O(q^{100}) \) 12 * q + 4 * q^2 + 2 * q^3 + 2 * q^4 + 6 * q^6 - 8 * q^8 - 2 * q^11 + 8 * q^12 - 4 * q^13 + 14 * q^14 + 2 * q^16 - 8 * q^17 + 18 * q^18 - 14 * q^19 - 20 * q^21 + 2 * q^22 - 14 * q^24 - 16 * q^26 - 10 * q^27 + 26 * q^28 - 4 * q^31 - 16 * q^32 + 28 * q^33 - 6 * q^34 + 2 * q^36 + 8 * q^37 + 10 * q^38 + 10 * q^42 - 44 * q^44 - 10 * q^46 + 8 * q^47 - 28 * q^48 + 4 * q^49 + 10 * q^51 - 12 * q^52 - 16 * q^53 + 10 * q^54 + 6 * q^56 - 60 * q^58 + 20 * q^59 + 4 * q^61 - 18 * q^62 - 8 * q^63 + 38 * q^64 + 32 * q^66 + 50 * q^67 - 60 * q^68 - 14 * q^72 + 10 * q^74 + 60 * q^76 - 8 * q^77 + 4 * q^78 + 12 * q^79 - 8 * q^81 + 42 * q^82 - 2 * q^83 + 34 * q^84 + 6 * q^86 + 30 * q^88 - 2 * q^92 - 44 * q^93 + 32 * q^94 - 34 * q^96 + 64 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more