LMFDB - Embedded newform 400.2.q.g.349.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [400,2,Mod(149,400)] 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("400.149"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(400, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.q (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 $ x^16 - 4x^15 + 4x^14 + 7x^12 - 8x^11 - 28x^10 + 28x^9 + 17x^8 + 56x^7 - 112x^6 - 64x^5 + 112x^4 + 256x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			349.6
Root			$1.38652 - 0.278517i$ of defining polynomial
Character	$\chi$	$=$	400.349
Dual form			400.2.q.g.149.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.139945 - 1.40727i) q^{2} +(2.32624 - 2.32624i) q^{3} +(-1.96083 - 0.393883i) q^{4} +(-2.94811 - 3.59920i) q^{6} +0.982011 q^{7} +(-0.828709 + 2.70430i) q^{8} -7.82281i q^{9} +(-1.62645 + 1.62645i) q^{11} +(-5.47764 + 3.64510i) q^{12} +(0.690562 - 0.690562i) q^{13} +(0.137428 - 1.38196i) q^{14} +(3.68971 + 1.54467i) q^{16} +2.19577i q^{17} +(-11.0088 - 1.09477i) q^{18} +(-1.92659 - 1.92659i) q^{19} +(2.28440 - 2.28440i) q^{21} +(2.06124 + 2.51647i) q^{22} +2.01442 q^{23} +(4.36308 + 8.21864i) q^{24} +(-0.875168 - 1.06845i) q^{26} +(-11.2190 - 11.2190i) q^{27} +(-1.92556 - 0.386797i) q^{28} +(5.27182 + 5.27182i) q^{29} +0.435286 q^{31} +(2.69014 - 4.97626i) q^{32} +7.56703i q^{33} +(3.09004 + 0.307288i) q^{34} +(-3.08127 + 15.3392i) q^{36} +(5.79805 + 5.79805i) q^{37} +(-2.98086 + 2.44162i) q^{38} -3.21283i q^{39} -3.93139i q^{41} +(-2.89508 - 3.53446i) q^{42} +(-0.507592 - 0.507592i) q^{43} +(3.82982 - 2.54856i) q^{44} +(0.281909 - 2.83484i) q^{46} +9.21960i q^{47} +(12.1765 - 4.98988i) q^{48} -6.03565 q^{49} +(5.10789 + 5.10789i) q^{51} +(-1.62608 + 1.08208i) q^{52} +(6.29357 + 6.29357i) q^{53} +(-17.3583 + 14.2182i) q^{54} +(-0.813802 + 2.65565i) q^{56} -8.96345 q^{57} +(8.15665 - 6.68111i) q^{58} +(5.67778 - 5.67778i) q^{59} +(-3.60301 - 3.60301i) q^{61} +(0.0609163 - 0.612566i) q^{62} -7.68209i q^{63} +(-6.62648 - 4.48216i) q^{64} +(10.6489 + 1.05897i) q^{66} +(4.53563 - 4.53563i) q^{67} +(0.864875 - 4.30553i) q^{68} +(4.68603 - 4.68603i) q^{69} -10.3984i q^{71} +(21.1552 + 6.48284i) q^{72} -9.24439 q^{73} +(8.97085 - 7.34803i) q^{74} +(3.01887 + 4.53658i) q^{76} +(-1.59719 + 1.59719i) q^{77} +(-4.52133 - 0.449621i) q^{78} -15.4493 q^{79} -28.7280 q^{81} +(-5.53253 - 0.550180i) q^{82} +(0.683244 - 0.683244i) q^{83} +(-5.37910 + 3.57953i) q^{84} +(-0.785356 + 0.643285i) q^{86} +24.5271 q^{87} +(-3.05055 - 5.74626i) q^{88} +5.44401i q^{89} +(0.678140 - 0.678140i) q^{91} +(-3.94994 - 0.793445i) q^{92} +(1.01258 - 1.01258i) q^{93} +(12.9745 + 1.29024i) q^{94} +(-5.31808 - 17.8339i) q^{96} -5.54540i q^{97} +(-0.844662 + 8.49381i) q^{98} +(12.7234 + 12.7234i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 4 q^{4} - 12 q^{6} - 8 q^{7} + 8 q^{8} - 8 q^{11} - 20 q^{12} - 4 q^{14} + 16 q^{16} - 12 q^{18} + 8 q^{19} + 20 q^{22} - 24 q^{23} - 8 q^{24} - 16 q^{26} - 24 q^{27} - 20 q^{28} + 16 q^{29}+ \cdots + 8 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 + 4 * q^4 - 12 * q^6 - 8 * q^7 + 8 * q^8 - 8 * q^11 - 20 * q^12 - 4 * q^14 + 16 * q^16 - 12 * q^18 + 8 * q^19 + 20 * q^22 - 24 * q^23 - 8 * q^24 - 16 * q^26 - 24 * q^27 - 20 * q^28 + 16 * q^29 - 24 * q^32 - 16 * q^34 - 4 * q^36 + 16 * q^37 + 20 * q^38 + 20 * q^42 + 8 * q^43 - 40 * q^44 - 4 * q^46 + 16 * q^49 - 32 * q^51 + 16 * q^52 + 16 * q^53 - 32 * q^54 + 16 * q^56 + 28 * q^58 + 8 * q^59 + 16 * q^61 - 48 * q^62 + 16 * q^64 + 40 * q^67 + 8 * q^68 - 16 * q^69 + 96 * q^72 + 72 * q^74 + 16 * q^77 - 24 * q^78 - 16 * q^79 - 16 * q^81 - 44 * q^82 - 40 * q^83 + 64 * q^84 + 28 * q^86 + 16 * q^88 + 32 * q^91 - 20 * q^92 + 48 * q^93 + 36 * q^94 + 8 * q^96 + 32 * q^98 + 8 * q^99

Character values

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

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	0.139945	−	1.40727i	0.0989564	−	0.995092i
$2$	0.139945	−	1.40727i	0.0989564	−	0.995092i
$3$	2.32624	−	2.32624i	1.34306	−	1.34306i	0.450058	−	0.893000i	$-0.351403\pi$
$3$	2.32624	−	2.32624i	1.34306	−	1.34306i	0.893000	−	0.450058i	$-0.148597\pi$
$4$	−1.96083	−	0.393883i	−0.980415	−	0.196941i
$5$		0			0
$5$		0			0
$6$	−2.94811	−	3.59920i	−1.20356	−	1.46937i
$7$	0.982011			0.371165			0.185583	−	0.982629i	$-0.440583\pi$
$7$	0.982011			0.371165			0.185583	+	0.982629i	$0.440583\pi$
$8$	−0.828709	+	2.70430i	−0.292993	+	0.956115i
$9$		−	7.82281i		−	2.60760i
$10$		0			0
$11$	−1.62645	+	1.62645i	−0.490393	+	0.490393i	−0.908430	−	0.418037i	$-0.862718\pi$
$11$	−1.62645	+	1.62645i	−0.490393	+	0.490393i	0.418037	+	0.908430i	$0.362718\pi$
$12$	−5.47764	+	3.64510i	−1.58126	+	1.05225i
$13$	0.690562	−	0.690562i	0.191528	−	0.191528i	−0.604828	−	0.796356i	$-0.706758\pi$
$13$	0.690562	−	0.690562i	0.191528	−	0.191528i	0.796356	+	0.604828i	$0.206758\pi$
$14$	0.137428	−	1.38196i	0.0367292	−	0.369344i
$15$		0			0
$16$	3.68971	+	1.54467i	0.922428	+	0.386169i
$17$			2.19577i			0.532552i	0.963897	+	0.266276i	$0.0857933\pi$
$17$			2.19577i			0.532552i	−0.963897	+	0.266276i	$0.914207\pi$
$18$	−11.0088	−	1.09477i	−2.59481	−	0.258039i
$19$	−1.92659	−	1.92659i	−0.441991	−	0.441991i	0.450690	−	0.892681i	$-0.351178\pi$
$19$	−1.92659	−	1.92659i	−0.441991	−	0.441991i	−0.892681	+	0.450690i	$0.851178\pi$
$20$		0			0
$21$	2.28440	−	2.28440i	0.498496	−	0.498496i
$22$	2.06124	+	2.51647i	0.439458	+	0.536513i
$23$	2.01442			0.420035			0.210018	−	0.977698i	$-0.432648\pi$
$23$	2.01442			0.420035			0.210018	+	0.977698i	$0.432648\pi$
$24$	4.36308	+	8.21864i	0.890610	+	1.67762i
$25$		0			0
$26$	−0.875168	−	1.06845i	−0.171635	−	0.209540i
$27$	−11.2190	−	11.2190i	−2.15911	−	2.15911i
$28$	−1.92556	−	0.386797i	−0.363896	−	0.0730978i
$29$	5.27182	+	5.27182i	0.978952	+	0.978952i	0.999783	−	0.0208314i	$-0.00663132\pi$
$29$	5.27182	+	5.27182i	0.978952	+	0.978952i	−0.0208314	+	0.999783i	$0.506631\pi$
$30$		0			0
$31$	0.435286			0.0781797			0.0390898	−	0.999236i	$-0.487554\pi$
$31$	0.435286			0.0781797			0.0390898	+	0.999236i	$0.487554\pi$
$32$	2.69014	−	4.97626i	0.475553	−	0.879687i
$33$			7.56703i			1.31725i
$34$	3.09004	+	0.307288i	0.529938	+	0.0526994i
$35$		0			0
$36$	−3.08127	+	15.3392i	−0.513545	+	2.55654i
$37$	5.79805	+	5.79805i	0.953194	+	0.953194i	0.998953	−	0.0457583i	$-0.0145704\pi$
$37$	5.79805	+	5.79805i	0.953194	+	0.953194i	−0.0457583	+	0.998953i	$0.514570\pi$
$38$	−2.98086	+	2.44162i	−0.483559	+	0.396084i
$39$		−	3.21283i		−	0.514465i
$40$		0			0
$41$		−	3.93139i		−	0.613980i	−0.951713	−	0.306990i	$-0.900678\pi$
$41$		−	3.93139i		−	0.613980i	0.951713	−	0.306990i	$-0.0993218\pi$
$42$	−2.89508	−	3.53446i	−0.446720	−	0.545379i
$43$	−0.507592	−	0.507592i	−0.0774071	−	0.0774071i	0.667343	−	0.744750i	$-0.267431\pi$
$43$	−0.507592	−	0.507592i	−0.0774071	−	0.0774071i	−0.744750	+	0.667343i	$0.767431\pi$
$44$	3.82982	−	2.54856i	0.577367	−	0.384210i
$45$		0			0
$46$	0.281909	−	2.83484i	0.0415652	−	0.417974i
$47$			9.21960i			1.34482i	0.740180	+	0.672409i	$0.234740\pi$
$47$			9.21960i			1.34482i	−0.740180	+	0.672409i	$0.765260\pi$
$48$	12.1765	−	4.98988i	1.75752	−	0.720227i
$49$	−6.03565			−0.862236
$50$		0			0
$51$	5.10789	+	5.10789i	0.715248	+	0.715248i
$52$	−1.62608	+	1.08208i	−0.225496	+	0.150057i
$53$	6.29357	+	6.29357i	0.864488	+	0.864488i	0.991856	−	0.127367i	$-0.0406527\pi$
$53$	6.29357	+	6.29357i	0.864488	+	0.864488i	−0.127367	+	0.991856i	$0.540653\pi$
$54$	−17.3583	+	14.2182i	−2.36216	+	1.93485i
$55$		0			0
$56$	−0.813802	+	2.65565i	−0.108749	+	0.354877i
$57$	−8.96345			−1.18724
$58$	8.15665	−	6.68111i	1.07102	−	0.877273i
$59$	5.67778	−	5.67778i	0.739183	−	0.739183i	−0.233237	−	0.972420i	$-0.574932\pi$
$59$	5.67778	−	5.67778i	0.739183	−	0.739183i	0.972420	+	0.233237i	$0.0749317\pi$
$60$		0			0
$61$	−3.60301	−	3.60301i	−0.461318	−	0.461318i	0.437770	−	0.899087i	$-0.355769\pi$
$61$	−3.60301	−	3.60301i	−0.461318	−	0.461318i	−0.899087	+	0.437770i	$0.855769\pi$
$62$	0.0609163	−	0.612566i	0.00773637	−	0.0777959i
$63$		−	7.68209i		−	0.967852i
$64$	−6.62648	−	4.48216i	−0.828310	−	0.560270i
$65$		0			0
$66$	10.6489	+	1.05897i	1.31079	+	0.130350i
$67$	4.53563	−	4.53563i	0.554116	−	0.554116i	−0.373510	−	0.927626i	$-0.621846\pi$
$67$	4.53563	−	4.53563i	0.554116	−	0.554116i	0.927626	+	0.373510i	$0.121846\pi$
$68$	0.864875	−	4.30553i	0.104882	−	0.522122i
$69$	4.68603	−	4.68603i	0.564132	−	0.564132i
$70$		0			0
$71$		−	10.3984i		−	1.23407i	−0.786937	−	0.617033i	$-0.788335\pi$
$71$		−	10.3984i		−	1.23407i	0.786937	−	0.617033i	$-0.211665\pi$
$72$	21.1552	+	6.48284i	2.49317	+	0.764010i
$73$	−9.24439			−1.08197			−0.540987	−	0.841031i	$-0.681949\pi$
$73$	−9.24439			−1.08197			−0.540987	+	0.841031i	$0.681949\pi$
$74$	8.97085	−	7.34803i	1.04284	−	0.854191i
$75$		0			0
$76$	3.01887	+	4.53658i	0.346288	+	0.520381i
$77$	−1.59719	+	1.59719i	−0.182017	+	0.182017i
$78$	−4.52133	−	0.449621i	−0.511940	−	0.0509096i
$79$	−15.4493			−1.73818			−0.869091	−	0.494653i	$-0.835295\pi$
$79$	−15.4493			−1.73818			−0.869091	+	0.494653i	$0.835295\pi$
$80$		0			0
$81$	−28.7280			−3.19200
$82$	−5.53253	−	0.550180i	−0.610966	−	0.0607572i
$83$	0.683244	−	0.683244i	0.0749957	−	0.0749957i	−0.668614	−	0.743610i	$-0.733112\pi$
$83$	0.683244	−	0.683244i	0.0749957	−	0.0749957i	0.743610	+	0.668614i	$0.233112\pi$
$84$	−5.37910	+	3.57953i	−0.586908	+	0.390559i
$85$		0			0
$86$	−0.785356	+	0.643285i	−0.0846871	+	0.0693672i
$87$	24.5271			2.62958
$88$	−3.05055	−	5.74626i	−0.325190	−	0.612553i
$89$			5.44401i			0.577064i	0.957470	+	0.288532i	$0.0931672\pi$
$89$			5.44401i			0.577064i	−0.957470	+	0.288532i	$0.906833\pi$
$90$		0			0
$91$	0.678140	−	0.678140i	0.0710884	−	0.0710884i
$92$	−3.94994	−	0.793445i	−0.411809	−	0.0827223i
$93$	1.01258	−	1.01258i	0.105000	−	0.105000i
$94$	12.9745	+	1.29024i	1.33822	+	0.133078i
$95$		0			0
$96$	−5.31808	−	17.8339i	−0.542775	−	1.82016i
$97$		−	5.54540i		−	0.563050i	−0.959554	−	0.281525i	$-0.909160\pi$
$97$		−	5.54540i		−	0.563050i	0.959554	−	0.281525i	$-0.0908402\pi$
$98$	−0.844662	+	8.49381i	−0.0853238	+	0.858004i
$99$	12.7234	+	12.7234i	1.27875	+	1.27875i
$100$		0			0
$101$	−0.291294	+	0.291294i	−0.0289848	+	0.0289848i	−0.721451	−	0.692466i	$-0.756524\pi$
$101$	−0.291294	+	0.291294i	−0.0289848	+	0.0289848i	0.692466	+	0.721451i	$0.256524\pi$
$102$	7.90302	−	6.47337i	0.782516	−	0.640959i
$103$	4.50219			0.443614			0.221807	−	0.975091i	$-0.428805\pi$
$103$	4.50219			0.443614			0.221807	+	0.975091i	$0.428805\pi$
$104$	1.29521	+	2.43976i	0.127006	+	0.239239i
$105$		0			0
$106$	9.73752	−	7.97601i	0.945792	−	0.774698i
$107$	6.49890	+	6.49890i	0.628272	+	0.628272i	0.947633	−	0.319361i	$-0.103468\pi$
$107$	6.49890	+	6.49890i	0.628272	+	0.628272i	−0.319361	+	0.947633i	$0.603468\pi$
$108$	17.5796	+	26.4176i	1.69160	+	2.54204i
$109$	2.51950	+	2.51950i	0.241324	+	0.241324i	0.817398	−	0.576074i	$-0.195416\pi$
$109$	2.51950	+	2.51950i	0.241324	+	0.241324i	−0.576074	+	0.817398i	$0.695416\pi$
$110$		0			0
$111$	26.9754			2.56039
$112$	3.62334	+	1.51689i	0.342373	+	0.143332i
$113$			5.38101i			0.506203i	0.967440	+	0.253102i	$0.0814507\pi$
$113$			5.38101i			0.506203i	−0.967440	+	0.253102i	$0.918549\pi$
$114$	−1.25439	+	12.6140i	−0.117485	+	1.18141i
$115$		0			0
$116$	−8.26066	−	12.4136i	−0.766983	−	1.15258i
$117$	−5.40214	−	5.40214i	−0.499428	−	0.499428i
$118$	−7.19560	−	8.78476i	−0.662408	−	0.808702i
$119$			2.15627i			0.197665i
$120$		0			0
$121$			5.70933i			0.519030i
$122$	−5.57464	+	4.56619i	−0.504704	+	0.413403i
$123$	−9.14536	−	9.14536i	−0.824610	−	0.824610i
$124$	−0.853522	−	0.171452i	−0.0766485	−	0.0153968i
$125$		0			0
$126$	−10.8108	−	1.07507i	−0.963102	−	0.0957751i
$127$		−	4.86578i		−	0.431768i	−0.976419	−	0.215884i	$-0.930737\pi$
$127$		−	4.86578i		−	0.431768i	0.976419	−	0.215884i	$-0.0692634\pi$
$128$	−7.23496	+	8.69801i	−0.639486	+	0.768802i
$129$	−2.36157			−0.207924
$130$		0			0
$131$	8.00581	+	8.00581i	0.699471	+	0.699471i	0.964296	−	0.264825i	$-0.0853143\pi$
$131$	8.00581	+	8.00581i	0.699471	+	0.699471i	−0.264825	+	0.964296i	$0.585314\pi$
$132$	2.98052	−	14.8377i	0.259421	−	1.29145i
$133$	−1.89194	−	1.89194i	−0.164052	−	0.164052i
$134$	−5.74813	−	7.01761i	−0.496563	−	0.606229i
$135$		0			0
$136$	−5.93802	−	1.81965i	−0.509181	−	0.156034i
$137$	13.5567			1.15822			0.579112	−	0.815248i	$-0.303399\pi$
$137$	13.5567			1.15822			0.579112	+	0.815248i	$0.303399\pi$
$138$	−5.93873	−	7.25031i	−0.505538	−	0.617187i
$139$	−8.22645	+	8.22645i	−0.697758	+	0.697758i	−0.963927	−	0.266168i	$-0.914242\pi$
$139$	−8.22645	+	8.22645i	−0.697758	+	0.697758i	0.266168	+	0.963927i	$0.414242\pi$
$140$		0			0
$141$	21.4470	+	21.4470i	1.80617	+	1.80617i
$142$	−14.6334	−	1.45521i	−1.22801	−	0.122119i
$143$			2.24633i			0.187847i
$144$	12.0837	−	28.8639i	1.00697	−	2.40533i
$145$		0			0
$146$	−1.29371	+	13.0094i	−0.107068	+	1.07666i
$147$	−14.0404	+	14.0404i	−1.15803	+	1.15803i
$148$	−9.08525	−	13.6528i	−0.746803	−	1.12225i
$149$	−12.6363	+	12.6363i	−1.03521	+	1.03521i	−0.0358519	+	0.999357i	$0.511414\pi$
$149$	−12.6363	+	12.6363i	−1.03521	+	1.03521i	−0.999357	+	0.0358519i	$0.988586\pi$
$150$		0			0
$151$		−	15.1562i		−	1.23339i	−0.787201	−	0.616696i	$-0.788471\pi$
$151$		−	15.1562i		−	1.23339i	0.787201	−	0.616696i	$-0.211529\pi$
$152$	6.80667	−	3.61350i	0.552094	−	0.293094i
$153$	17.1771			1.38869
$154$	2.02416	+	2.47120i	0.163112	+	0.199135i
$155$		0			0
$156$	−1.26548	+	6.29982i	−0.101319	+	0.504389i
$157$	−1.75816	+	1.75816i	−0.140316	+	0.140316i	−0.773776	−	0.633460i	$-0.781634\pi$
$157$	−1.75816	+	1.75816i	−0.140316	+	0.140316i	0.633460	+	0.773776i	$0.281634\pi$
$158$	−2.16206	+	21.7414i	−0.172004	+	1.72965i
$159$	29.2807			2.32211
$160$		0			0
$161$	1.97818			0.155903
$162$	−4.02035	+	40.4281i	−0.315868	+	3.17633i
$163$	13.9102	−	13.9102i	1.08953	−	1.08953i	0.0939562	−	0.995576i	$-0.470049\pi$
$163$	13.9102	−	13.9102i	1.08953	−	1.08953i	0.995576	−	0.0939562i	$-0.0299514\pi$
$164$	−1.54851	+	7.70879i	−0.120918	+	0.601955i
$165$		0			0
$166$	−0.865893	−	1.05713i	−0.0672063	−	0.0820490i
$167$	−18.8620			−1.45958			−0.729792	−	0.683669i	$-0.760383\pi$
$167$	−18.8620			−1.45958			−0.729792	+	0.683669i	$0.760383\pi$
$168$	4.28459	+	8.07079i	0.330564	+	0.622675i
$169$			12.0462i			0.926634i
$170$		0			0
$171$	−15.0714	+	15.0714i	−1.15254	+	1.15254i
$172$	0.795370	+	1.19523i	0.0606464	+	0.0911357i
$173$	−16.0724	+	16.0724i	−1.22196	+	1.22196i	−0.255031	+	0.966933i	$0.582086\pi$
$173$	−16.0724	+	16.0724i	−1.22196	+	1.22196i	−0.966933	+	0.255031i	$0.917914\pi$
$174$	3.43245	−	34.5162i	0.260213	−	2.61667i
$175$		0			0
$176$	−8.51346	+	3.48879i	−0.641726	+	0.262978i
$177$		−	26.4158i		−	1.98553i
$178$	7.66121	+	0.761865i	0.574232	+	0.0571042i
$179$	−16.4341	−	16.4341i	−1.22834	−	1.22834i	−0.964591	−	0.263749i	$-0.915041\pi$
$179$	−16.4341	−	16.4341i	−1.22834	−	1.22834i	−0.263749	−	0.964591i	$-0.584959\pi$
$180$		0			0
$181$	−15.4539	+	15.4539i	−1.14868	+	1.14868i	−0.161870	+	0.986812i	$0.551753\pi$
$181$	−15.4539	+	15.4539i	−1.14868	+	1.14868i	−0.986812	+	0.161870i	$0.948247\pi$
$182$	−0.859425	−	1.04923i	−0.0637048	−	0.0777741i
$183$	−16.7629			−1.23915
$184$	−1.66937	+	5.44760i	−0.123067	+	0.401602i
$185$		0			0
$186$	−1.28327	−	1.56668i	−0.0940940	−	0.114875i
$187$	−3.57130	−	3.57130i	−0.261160	−	0.261160i
$188$	3.63144	−	18.0781i	0.264850	−	1.31848i
$189$	−11.0172	−	11.0172i	−0.801385	−	0.801385i
$190$		0			0
$191$	−14.7872			−1.06997			−0.534983	−	0.844863i	$-0.679682\pi$
$191$	−14.7872			−1.06997			−0.534983	+	0.844863i	$0.679682\pi$
$192$	−25.8414	+	4.98822i	−1.86494	+	0.359994i
$193$		−	11.2912i		−	0.812758i	−0.913705	−	0.406379i	$-0.866791\pi$
$193$		−	11.2912i		−	0.812758i	0.913705	−	0.406379i	$-0.133209\pi$
$194$	−7.80388	−	0.776053i	−0.560286	−	0.0557173i
$195$		0			0
$196$	11.8349	+	2.37734i	0.845350	+	0.169810i
$197$	10.6152	+	10.6152i	0.756302	+	0.756302i	0.975647	−	0.219345i	$-0.0703920\pi$
$197$	10.6152	+	10.6152i	0.756302	+	0.756302i	−0.219345	+	0.975647i	$0.570392\pi$
$198$	19.6859	−	16.1247i	1.39901	−	1.14593i
$199$		−	4.68789i		−	0.332316i	−0.986099	−	0.166158i	$-0.946864\pi$
$199$		−	4.68789i		−	0.332316i	0.986099	−	0.166158i	$-0.0531361\pi$
$200$		0			0
$201$		−	21.1020i		−	1.48842i
$202$	0.369165	+	0.450695i	0.0259743	+	0.0317108i
$203$	5.17698	+	5.17698i	0.363353	+	0.363353i
$204$	−8.00380	−	12.0276i	−0.560378	−	0.842102i
$205$		0			0
$206$	0.630061	−	6.33581i	0.0438984	−	0.441437i
$207$		−	15.7584i		−	1.09529i
$208$	3.61467	−	1.48128i	0.250632	−	0.102709i
$209$	6.26701			0.433498
$210$		0			0
$211$	−2.63215	−	2.63215i	−0.181205	−	0.181205i	0.610676	−	0.791881i	$-0.290898\pi$
$211$	−2.63215	−	2.63215i	−0.181205	−	0.181205i	−0.791881	+	0.610676i	$0.790898\pi$
$212$	−9.86169	−	14.8195i	−0.677304	−	1.01781i
$213$	−24.1893	−	24.1893i	−1.65742	−	1.65742i
$214$	10.0552	−	8.23623i	0.687360	−	0.563017i
$215$		0			0
$216$	39.6370	−	21.0423i	2.69695	−	1.43175i
$217$	0.427456			0.0290176
$218$	3.89821	−	3.19303i	0.264020	−	0.216259i
$219$	−21.5047	+	21.5047i	−1.45315	+	1.45315i
$220$		0			0
$221$	1.51632	+	1.51632i	0.101998	+	0.101998i
$222$	3.77508	−	37.9617i	0.253367	−	2.54782i
$223$			3.45644i			0.231461i	0.993281	+	0.115730i	$0.0369208\pi$
$223$			3.45644i			0.231461i	−0.993281	+	0.115730i	$0.963079\pi$
$224$	2.64174	−	4.88674i	0.176509	−	0.326509i
$225$		0			0
$226$	7.57255	+	0.753048i	0.503719	+	0.0500920i
$227$	−4.74550	+	4.74550i	−0.314970	+	0.314970i	−0.846831	−	0.531862i	$-0.821493\pi$
$227$	−4.74550	+	4.74550i	−0.314970	+	0.314970i	0.531862	+	0.846831i	$0.321493\pi$
$228$	17.5758	+	3.53055i	1.16399	+	0.233816i
$229$	13.3576	−	13.3576i	0.882697	−	0.882697i	−0.111111	−	0.993808i	$-0.535441\pi$
$229$	13.3576	−	13.3576i	0.882697	−	0.882697i	0.993808	+	0.111111i	$0.0354410\pi$
$230$		0			0
$231$			7.43091i			0.488918i
$232$	−18.6254	+	9.88777i	−1.22282	+	0.649164i
$233$	−4.82691			−0.316222			−0.158111	−	0.987421i	$-0.550540\pi$
$233$	−4.82691			−0.316222			−0.158111	+	0.987421i	$0.550540\pi$
$234$	−8.35829	+	6.84628i	−0.546399	+	0.447555i
$235$		0			0
$236$	−13.3695	+	8.89678i	−0.870282	+	0.579131i
$237$	−35.9388	+	35.9388i	−2.33448	+	2.33448i
$238$	3.03446	+	0.301760i	0.196695	+	0.0195602i
$239$	8.82497			0.570840			0.285420	−	0.958403i	$-0.407867\pi$
$239$	8.82497			0.570840			0.285420	+	0.958403i	$0.407867\pi$
$240$		0			0
$241$	−3.74147			−0.241009			−0.120504	−	0.992713i	$-0.538451\pi$
$241$	−3.74147			−0.241009			−0.120504	+	0.992713i	$0.538451\pi$
$242$	8.03458	+	0.798995i	0.516483	+	0.0513613i
$243$	−33.1712	+	33.1712i	−2.12793	+	2.12793i
$244$	5.64572	+	8.48405i	0.361430	+	0.543135i
$245$		0			0
$246$	−14.1499	+	11.5902i	−0.902163	+	0.738962i
$247$	−2.66087			−0.169307
$248$	−0.360725	+	1.17714i	−0.0229061	+	0.0747487i
$249$		−	3.17878i		−	0.201447i
$250$		0			0
$251$	−5.99322	+	5.99322i	−0.378289	+	0.378289i	−0.870484	−	0.492196i	$-0.836194\pi$
$251$	−5.99322	+	5.99322i	−0.378289	+	0.378289i	0.492196	+	0.870484i	$0.336194\pi$
$252$	−3.02584	+	15.0633i	−0.190610	+	0.948897i
$253$	−3.27635	+	3.27635i	−0.205982	+	0.205982i
$254$	−6.84748	−	0.680944i	−0.429649	−	0.0427262i
$255$		0			0
$256$	11.2280	+	11.3988i	0.701748	+	0.712426i
$257$			14.7662i			0.921091i	0.887636	+	0.460545i	$0.152346\pi$
$257$			14.7662i			0.921091i	−0.887636	+	0.460545i	$0.847654\pi$
$258$	−0.330490	+	3.32337i	−0.0205754	+	0.206904i
$259$	5.69375	+	5.69375i	0.353793	+	0.353793i
$260$		0			0
$261$	41.2404	−	41.2404i	2.55272	−	2.55272i
$262$	12.3867	−	10.1460i	0.765255	−	0.626821i
$263$	−6.79486			−0.418989			−0.209494	−	0.977810i	$-0.567182\pi$
$263$	−6.79486			−0.418989			−0.209494	+	0.977810i	$0.567182\pi$
$264$	−20.4635	−	6.27087i	−1.25944	−	0.385945i
$265$		0			0
$266$	−2.92724	+	2.39770i	−0.179480	+	0.147013i
$267$	12.6641	+	12.6641i	0.775030	+	0.775030i
$268$	−10.6801	+	7.10710i	−0.652392	+	0.434135i
$269$	6.03990	+	6.03990i	0.368259	+	0.368259i	0.866842	−	0.498583i	$-0.166146\pi$
$269$	6.03990	+	6.03990i	0.368259	+	0.368259i	−0.498583	+	0.866842i	$0.666146\pi$
$270$		0			0
$271$	−24.6221			−1.49568			−0.747842	−	0.663877i	$-0.768910\pi$
$271$	−24.6221			−1.49568			−0.747842	+	0.663877i	$0.768910\pi$
$272$	−3.39175	+	8.10175i	−0.205655	+	0.491241i
$273$		−	3.15504i		−	0.190952i
$274$	1.89719	−	19.0779i	0.114614	−	1.15254i
$275$		0			0
$276$	−11.0343	+	7.34276i	−0.664184	+	0.441982i
$277$	−9.98018	−	9.98018i	−0.599651	−	0.599651i	0.340569	−	0.940220i	$-0.389380\pi$
$277$	−9.98018	−	9.98018i	−0.599651	−	0.599651i	−0.940220	+	0.340569i	$0.889380\pi$
$278$	10.4256	+	12.7281i	0.625286	+	0.763381i
$279$		−	3.40516i		−	0.203862i
$280$		0			0
$281$			14.4611i			0.862675i	0.902191	+	0.431337i	$0.141958\pi$
$281$			14.4611i			0.862675i	−0.902191	+	0.431337i	$0.858042\pi$
$282$	33.1832	−	27.1804i	1.97603	−	1.61857i
$283$	20.0783	+	20.0783i	1.19353	+	1.19353i	0.976069	+	0.217462i	$0.0697777\pi$
$283$	20.0783	+	20.0783i	1.19353	+	1.19353i	0.217462	+	0.976069i	$0.430222\pi$
$284$	−4.09576	+	20.3895i	−0.243039	+	1.20990i
$285$		0			0
$286$	3.16120	+	0.314363i	0.186925	+	0.0185887i
$287$		−	3.86067i		−	0.227888i
$288$	−38.9284	−	21.0444i	−2.29388	−	1.24006i
$289$	12.1786			0.716388
$290$		0			0
$291$	−12.8999	−	12.8999i	−0.756208	−	0.756208i
$292$	18.1267	+	3.64121i	1.06078	+	0.213085i
$293$	15.4038	+	15.4038i	0.899899	+	0.899899i	0.995427	−	0.0955279i	$-0.0304539\pi$
$293$	15.4038	+	15.4038i	0.899899	+	0.899899i	−0.0955279	+	0.995427i	$0.530454\pi$
$294$	17.7938	+	21.7236i	1.03775	+	1.26694i
$295$		0			0
$296$	−20.4846	+	10.8748i	−1.19064	+	0.632084i
$297$	36.4944			2.11762
$298$	16.0144	+	19.5512i	0.927687	+	1.13257i
$299$	1.39108	−	1.39108i	0.0804484	−	0.0804484i
$300$		0			0
$301$	−0.498461	−	0.498461i	−0.0287308	−	0.0287308i
$302$	−21.3289	−	2.12104i	−1.22734	−	0.122052i
$303$			1.35524i			0.0778566i
$304$	−4.13262	−	10.0845i	−0.237022	−	0.578388i
$305$		0			0
$306$	2.40385	−	24.1728i	0.137419	−	1.38187i
$307$	9.12398	−	9.12398i	0.520733	−	0.520733i	−0.397060	−	0.917793i	$-0.629969\pi$
$307$	9.12398	−	9.12398i	0.520733	−	0.520733i	0.917793	+	0.397060i	$0.129969\pi$
$308$	3.76092	−	2.50271i	0.214299	−	0.142605i
$309$	10.4732	−	10.4732i	0.595799	−	0.595799i
$310$		0			0
$311$			0.642911i			0.0364561i	0.999834	+	0.0182281i	$0.00580249\pi$
$311$			0.642911i			0.0364561i	−0.999834	+	0.0182281i	$0.994198\pi$
$312$	8.68846	+	2.66250i	0.491887	+	0.150735i
$313$	−21.3775			−1.20833			−0.604164	−	0.796860i	$-0.706493\pi$
$313$	−21.3775			−1.20833			−0.604164	+	0.796860i	$0.706493\pi$
$314$	2.22816	+	2.72025i	0.125742	+	0.153513i
$315$		0			0
$316$	30.2935	+	6.08521i	1.70414	+	0.342320i
$317$	8.66200	−	8.66200i	0.486507	−	0.486507i	−0.420695	−	0.907202i	$-0.638214\pi$
$317$	8.66200	−	8.66200i	0.486507	−	0.486507i	0.907202	+	0.420695i	$0.138214\pi$
$318$	4.09771	−	41.2060i	0.229788	−	2.31072i
$319$	−17.1487			−0.960141
$320$		0			0
$321$	30.2360			1.68761
$322$	0.276838	−	2.78384i	0.0154276	−	0.155137i
$323$	4.23035	−	4.23035i	0.235383	−	0.235383i
$324$	56.3307	+	11.3155i	3.12948	+	0.628636i
$325$		0			0
$326$	−17.6288	−	21.5221i	−0.976369	−	1.19200i
$327$	11.7219			0.648224
$328$	10.6317	+	3.25798i	0.587035	+	0.179892i
$329$			9.05375i			0.499150i
$330$		0			0
$331$	−8.43941	+	8.43941i	−0.463872	+	0.463872i	−0.899922	−	0.436050i	$-0.856377\pi$
$331$	−8.43941	+	8.43941i	−0.463872	+	0.463872i	0.436050	+	0.899922i	$0.356377\pi$
$332$	−1.60884	+	1.07061i	−0.0882967	+	0.0587572i
$333$	45.3571	−	45.3571i	2.48555	−	2.48555i
$334$	−2.63965	+	26.5440i	−0.144435	+	1.45242i
$335$		0			0
$336$	11.9574	−	4.90012i	0.652330	−	0.267323i
$337$		−	30.7047i		−	1.67259i	−0.548280	−	0.836295i	$-0.684717\pi$
$337$		−	30.7047i		−	1.67259i	0.548280	−	0.836295i	$-0.315283\pi$
$338$	16.9523	+	1.68582i	0.922086	+	0.0916964i
$339$	12.5175	+	12.5175i	0.679860	+	0.679860i
$340$		0			0
$341$	−0.707970	+	0.707970i	−0.0383387	+	0.0383387i
$342$	19.1004	+	23.3187i	1.03283	+	1.26093i
$343$	−12.8012			−0.691197
$344$	1.79333	−	0.952035i	0.0966898	−	0.0513303i
$345$		0			0
$346$	20.3690	+	24.8675i	1.09504	+	1.33689i
$347$	−13.6418	−	13.6418i	−0.732329	−	0.732329i	0.238752	−	0.971081i	$-0.423262\pi$
$347$	−13.6418	−	13.6418i	−0.732329	−	0.732329i	−0.971081	+	0.238752i	$0.923262\pi$
$348$	−48.0934	−	9.66078i	−2.57808	−	0.517872i
$349$	−9.97321	−	9.97321i	−0.533854	−	0.533854i	0.387863	−	0.921717i	$-0.373213\pi$
$349$	−9.97321	−	9.97321i	−0.533854	−	0.533854i	−0.921717	+	0.387863i	$0.873213\pi$
$350$		0			0
$351$	−15.4949			−0.827056
$352$	3.71826	+	12.4690i	0.198184	+	0.664600i
$353$		−	26.7843i		−	1.42559i	−0.701374	−	0.712793i	$-0.747430\pi$
$353$		−	26.7843i		−	1.42559i	0.701374	−	0.712793i	$-0.252570\pi$
$354$	−37.1742	−	3.69677i	−1.97579	−	0.196481i
$355$		0			0
$356$	2.14430	−	10.6748i	0.113648	−	0.565763i
$357$	5.01601	+	5.01601i	0.265475	+	0.265475i
$358$	−25.4271	+	20.8273i	−1.34386	+	1.10076i
$359$		−	19.1190i		−	1.00906i	−0.863393	−	0.504532i	$-0.831665\pi$
$359$		−	19.1190i		−	1.00906i	0.863393	−	0.504532i	$-0.168335\pi$
$360$		0			0
$361$		−	11.5765i		−	0.609288i
$362$	19.5852	+	23.9106i	1.02937	+	1.25671i
$363$	13.2813	+	13.2813i	0.697087	+	0.697087i
$364$	−1.59683	+	1.06261i	−0.0836964	+	0.0556959i
$365$		0			0
$366$	−2.34590	+	23.5900i	−0.122622	+	1.23307i
$367$		−	4.24385i		−	0.221527i	−0.993847	−	0.110764i	$-0.964670\pi$
$367$		−	4.24385i		−	0.221527i	0.993847	−	0.110764i	$-0.0353297\pi$
$368$	7.43263	+	3.11162i	0.387453	+	0.162204i
$369$	−30.7545			−1.60102
$370$		0			0
$371$	6.18035	+	6.18035i	0.320868	+	0.320868i
$372$	−2.38434	+	1.58666i	−0.123622	+	0.0822646i
$373$	23.9514	+	23.9514i	1.24016	+	1.24016i	0.959935	+	0.280221i	$0.0904078\pi$
$373$	23.9514	+	23.9514i	1.24016	+	1.24016i	0.280221	+	0.959935i	$0.409592\pi$
$374$	−5.52558	+	4.52601i	−0.285721	+	0.234034i
$375$		0			0
$376$	−24.9326	−	7.64037i	−1.28580	−	0.394022i
$377$	7.28104			0.374992
$378$	−17.0460	+	13.9624i	−0.876754	+	0.718149i
$379$	7.45685	−	7.45685i	0.383033	−	0.383033i	−0.489161	−	0.872194i	$-0.662697\pi$
$379$	7.45685	−	7.45685i	0.383033	−	0.383033i	0.872194	+	0.489161i	$0.162697\pi$
$380$		0			0
$381$	−11.3190	−	11.3190i	−0.579890	−	0.579890i
$382$	−2.06941	+	20.8097i	−0.105880	+	1.06472i
$383$			5.19667i			0.265538i	0.991147	+	0.132769i	$0.0423868\pi$
$383$			5.19667i			0.265538i	−0.991147	+	0.132769i	$0.957613\pi$
$384$	3.40340	+	37.0640i	0.173679	+	1.89141i
$385$		0			0
$386$	−15.8898	−	1.58015i	−0.808768	−	0.0804275i
$387$	−3.97080	+	3.97080i	−0.201847	+	0.201847i
$388$	−2.18424	+	10.8736i	−0.110888	+	0.552022i
$389$	−10.3846	+	10.3846i	−0.526522	+	0.526522i	−0.919534	−	0.393011i	$-0.871433\pi$
$389$	−10.3846	+	10.3846i	−0.526522	+	0.526522i	0.393011	+	0.919534i	$0.371433\pi$
$390$		0			0
$391$			4.42320i			0.223691i
$392$	5.00180	−	16.3222i	0.252629	−	0.824397i
$393$	37.2469			1.87886
$394$	16.4240	−	13.4529i	0.827431	−	0.677749i
$395$		0			0
$396$	−19.9369	−	29.9600i	−1.00187	−	1.50554i
$397$	9.93104	−	9.93104i	0.498425	−	0.498425i	−0.412523	−	0.910947i	$-0.635352\pi$
$397$	9.93104	−	9.93104i	0.498425	−	0.498425i	0.910947	+	0.412523i	$0.135352\pi$
$398$	−6.59714	−	0.656048i	−0.330684	−	0.0328847i
$399$	−8.80221			−0.440662
$400$		0			0
$401$	9.51392			0.475102			0.237551	−	0.971375i	$-0.423655\pi$
$401$	9.51392			0.475102			0.237551	+	0.971375i	$0.423655\pi$
$402$	−29.6962	−	2.95312i	−1.48111	−	0.147288i
$403$	0.300592	−	0.300592i	0.0149736	−	0.0149736i
$404$	0.685914	−	0.456442i	0.0341255	−	0.0227089i
$405$		0			0
$406$	8.00992	−	6.56093i	0.397525	−	0.325613i
$407$	−18.8605			−0.934879
$408$	−18.0462	+	9.58031i	−0.893421	+	0.474296i
$409$			4.81799i			0.238234i	0.992880	+	0.119117i	$0.0380064\pi$
$409$			4.81799i			0.238234i	−0.992880	+	0.119117i	$0.961994\pi$
$410$		0			0
$411$	31.5361	−	31.5361i	1.55556	−	1.55556i
$412$	−8.82803	−	1.77333i	−0.434926	−	0.0873659i
$413$	5.57564	−	5.57564i	0.274359	−	0.274359i
$414$	−22.1764	−	2.20532i	−1.08991	−	0.108386i
$415$		0			0
$416$	−1.57871	−	5.29413i	−0.0774027	−	0.259566i
$417$			38.2734i			1.87426i
$418$	0.877039	−	8.81939i	0.0428974	−	0.431370i
$419$	−21.4380	−	21.4380i	−1.04731	−	1.04731i	−0.998824	−	0.0484914i	$-0.984559\pi$
$419$	−21.4380	−	21.4380i	−1.04731	−	1.04731i	−0.0484914	−	0.998824i	$-0.515441\pi$
$420$		0			0
$421$	−4.80145	+	4.80145i	−0.234008	+	0.234008i	−0.814363	−	0.580355i	$-0.802914\pi$
$421$	−4.80145	+	4.80145i	−0.234008	+	0.234008i	0.580355	+	0.814363i	$0.302914\pi$
$422$	−4.07251	+	3.33579i	−0.198246	+	0.162384i
$423$	72.1232			3.50675
$424$	−22.2352	+	11.8042i	−1.07984	+	0.573261i
$425$		0			0
$426$	−37.4261	+	30.6557i	−1.81330	+	1.48527i
$427$	−3.53819	−	3.53819i	−0.171225	−	0.171225i
$428$	−10.1834	−	15.3030i	−0.492235	−	0.739700i
$429$	5.22551	+	5.22551i	0.252290	+	0.252290i
$430$		0			0
$431$	13.2369			0.637597			0.318799	−	0.947822i	$-0.396721\pi$
$431$	13.2369			0.637597			0.318799	+	0.947822i	$0.396721\pi$
$432$	−24.0653	−	58.7248i	−1.15784	−	2.82540i
$433$		−	1.50709i		−	0.0724259i	−0.999344	−	0.0362129i	$-0.988471\pi$
$433$		−	1.50709i		−	0.0724259i	0.999344	−	0.0362129i	$-0.0115295\pi$
$434$	0.0598204	−	0.601546i	0.00287147	−	0.0288751i
$435$		0			0
$436$	−3.94792	−	5.93270i	−0.189071	−	0.284125i
$437$	−3.88097	−	3.88097i	−0.185652	−	0.185652i
$438$	27.2535	+	33.2725i	1.30222	+	1.58982i
$439$		−	10.3092i		−	0.492033i	−0.969266	−	0.246016i	$-0.920878\pi$
$439$		−	10.3092i		−	0.492033i	0.969266	−	0.246016i	$-0.0791217\pi$
$440$		0			0
$441$			47.2158i			2.24837i
$442$	2.34607	−	1.92167i	0.111591	−	0.0914044i
$443$	−14.2651	−	14.2651i	−0.677755	−	0.677755i	0.281736	−	0.959492i	$-0.409090\pi$
$443$	−14.2651	−	14.2651i	−0.677755	−	0.677755i	−0.959492	+	0.281736i	$0.909090\pi$
$444$	−52.8941	−	10.6251i	−2.51024	−	0.504246i
$445$		0			0
$446$	4.86416	+	0.483713i	0.230324	+	0.0229045i
$447$			58.7904i			2.78069i
$448$	−6.50728	−	4.40153i	−0.307440	−	0.207953i
$449$	19.5711			0.923618			0.461809	−	0.886979i	$-0.347201\pi$
$449$	19.5711			0.923618			0.461809	+	0.886979i	$0.347201\pi$
$450$		0			0
$451$	6.39420	+	6.39420i	0.301091	+	0.301091i
$452$	2.11949	−	10.5513i	0.0996923	−	0.496289i
$453$	−35.2569	−	35.2569i	−1.65652	−	1.65652i
$454$	6.01410	+	7.34232i	0.282256	+	0.344592i
$455$		0			0
$456$	7.42810	−	24.2399i	0.347852	−	1.13514i
$457$	−39.0185			−1.82521			−0.912604	−	0.408845i	$-0.865932\pi$
$457$	−39.0185			−1.82521			−0.912604	+	0.408845i	$0.865932\pi$
$458$	−16.9285	−	20.6672i	−0.791016	−	0.965713i
$459$	24.6344	−	24.6344i	1.14984	−	1.14984i
$460$		0			0
$461$	19.6941	+	19.6941i	0.917245	+	0.917245i	0.996828	−	0.0795833i	$-0.0253590\pi$
$461$	19.6941	+	19.6941i	0.917245	+	0.917245i	−0.0795833	+	0.996828i	$0.525359\pi$
$462$	10.4573	+	1.03992i	0.486518	+	0.0483815i
$463$		−	14.9979i		−	0.697009i	−0.937307	−	0.348505i	$-0.886690\pi$
$463$		−	14.9979i		−	0.697009i	0.937307	−	0.348505i	$-0.113310\pi$
$464$	11.3082	+	27.5947i	0.524972	+	1.28105i
$465$		0			0
$466$	−0.675505	+	6.79278i	−0.0312921	+	0.314670i
$467$	4.88870	−	4.88870i	0.226222	−	0.226222i	−0.584890	−	0.811112i	$-0.698862\pi$
$467$	4.88870	−	4.88870i	0.226222	−	0.226222i	0.811112	+	0.584890i	$0.198862\pi$
$468$	8.46488	+	12.7205i	0.391289	+	0.588005i
$469$	4.45404	−	4.45404i	0.205669	−	0.205669i
$470$		0			0
$471$			8.17980i			0.376905i
$472$	10.6492	+	20.0596i	0.490168	+	0.923320i
$473$	1.65114			0.0759197
$474$	45.5462	+	55.6052i	2.09201	+	2.55403i
$475$		0			0
$476$	0.849317	−	4.22808i	0.0389284	−	0.193794i
$477$	49.2334	−	49.2334i	2.25424	−	2.25424i
$478$	1.23501	−	12.4191i	0.0564883	−	0.568038i
$479$	27.3381			1.24911			0.624555	−	0.780981i	$-0.285280\pi$
$479$	27.3381			1.24911			0.624555	+	0.780981i	$0.285280\pi$
$480$		0			0
$481$	8.00784			0.365126
$482$	−0.523601	+	5.26526i	−0.0238494	+	0.239826i
$483$	4.60173	−	4.60173i	0.209386	−	0.209386i
$484$	2.24881	−	11.1950i	0.102218	−	0.508865i
$485$		0			0
$486$	42.0387	+	51.3230i	1.90691	+	2.32806i
$487$	35.4769			1.60761			0.803806	−	0.594892i	$-0.202805\pi$
$487$	35.4769			1.60761			0.803806	+	0.594892i	$0.202805\pi$
$488$	12.7295	−	6.75777i	0.576235	−	0.305910i
$489$		−	64.7171i		−	2.92661i
$490$		0			0
$491$	3.55614	−	3.55614i	0.160486	−	0.160486i	−0.622296	−	0.782782i	$-0.713800\pi$
$491$	3.55614	−	3.55614i	0.160486	−	0.160486i	0.782782	+	0.622296i	$0.213800\pi$
$492$	14.3303	+	21.5347i	0.646060	+	0.970860i
$493$	−11.5757	+	11.5757i	−0.521343	+	0.521343i
$494$	−0.372376	+	3.74456i	−0.0167540	+	0.168476i
$495$		0			0
$496$	1.60608	+	0.672375i	0.0721151	+	0.0301905i
$497$		−	10.2114i		−	0.458042i
$498$	−4.47341	−	0.444856i	−0.200458	−	0.0199345i
$499$	17.6521	+	17.6521i	0.790218	+	0.790218i	0.981529	−	0.191312i	$-0.0612742\pi$
$499$	17.6521	+	17.6521i	0.790218	+	0.790218i	−0.191312	+	0.981529i	$0.561274\pi$
$500$		0			0
$501$	−43.8776	+	43.8776i	−1.96031	+	1.96031i
$502$	7.59537	+	9.27281i	0.338998	+	0.413866i
$503$	−31.8567			−1.42042			−0.710210	−	0.703990i	$-0.751400\pi$
$503$	−31.8567			−1.42042			−0.710210	+	0.703990i	$0.751400\pi$
$504$	20.7747	+	6.36622i	0.925378	+	0.283574i
$505$		0			0
$506$	4.15220	+	5.06923i	0.184588	+	0.225355i
$507$	28.0225	+	28.0225i	1.24452	+	1.24452i
$508$	−1.91655	+	9.54097i	−0.0850330	+	0.423312i
$509$	5.61054	+	5.61054i	0.248683	+	0.248683i	0.820430	−	0.571747i	$-0.193734\pi$
$509$	5.61054	+	5.61054i	0.248683	+	0.248683i	−0.571747	+	0.820430i	$0.693734\pi$
$510$		0			0
$511$	−9.07810			−0.401591
$512$	17.6125	−	14.2056i	0.778371	−	0.627804i
$513$			43.2291i			1.90861i
$514$	20.7801	+	2.06646i	0.916570	+	0.0911478i
$515$		0			0
$516$	4.63063	+	0.930180i	0.203852	+	0.0409489i
$517$	−14.9952	−	14.9952i	−0.659489	−	0.659489i
$518$	8.80948	−	7.21585i	0.387066	−	0.317046i
$519$			74.7767i			3.28233i
$520$		0			0
$521$		−	33.1977i		−	1.45442i	−0.686417	−	0.727208i	$-0.740818\pi$
$521$		−	33.1977i		−	1.45442i	0.686417	−	0.727208i	$-0.259182\pi$
$522$	−52.2651	−	63.8079i	−2.28758	−	2.79280i
$523$	−2.60707	−	2.60707i	−0.113999	−	0.113999i	0.647806	−	0.761805i	$-0.275687\pi$
$523$	−2.60707	−	2.60707i	−0.113999	−	0.113999i	−0.761805	+	0.647806i	$0.775687\pi$
$524$	−12.5447	−	18.8514i	−0.548017	−	0.823527i
$525$		0			0
$526$	−0.950909	+	9.56221i	−0.0414616	+	0.416932i
$527$			0.955787i			0.0416347i
$528$	−11.6886	+	27.9202i	−0.508681	+	1.21507i
$529$	−18.9421			−0.823570
$530$		0			0
$531$	−44.4162	−	44.4162i	−1.92750	−	1.92750i
$532$	2.96457	+	4.45497i	0.128530	+	0.193147i
$533$	−2.71487	−	2.71487i	−0.117594	−	0.117594i
$534$	19.5941	−	16.0496i	0.847921	−	0.694532i
$535$		0			0
$536$	8.50699	+	16.0244i	0.367446	+	0.692150i
$537$	−76.4593			−3.29946
$538$	9.34504	−	7.65452i	0.402893	−	0.330010i
$539$	9.81668	−	9.81668i	0.422834	−	0.422834i
$540$		0			0
$541$	−22.6839	−	22.6839i	−0.975257	−	0.975257i	0.0244439	−	0.999701i	$-0.492218\pi$
$541$	−22.6839	−	22.6839i	−0.975257	−	0.975257i	−0.999701	+	0.0244439i	$0.992218\pi$
$542$	−3.44574	+	34.6499i	−0.148007	+	1.48834i
$543$			71.8992i			3.08549i
$544$	10.9267	+	5.90691i	0.468479	+	0.253257i
$545$		0			0
$546$	−4.44000	−	0.441533i	−0.190014	−	0.0188959i
$547$	−3.02284	+	3.02284i	−0.129248	+	0.129248i	−0.768771	−	0.639524i	$-0.779132\pi$
$547$	−3.02284	+	3.02284i	−0.129248	+	0.129248i	0.639524	+	0.768771i	$0.279132\pi$
$548$	−26.5823	−	5.33974i	−1.13554	−	0.228102i
$549$	−28.1857	+	28.1857i	−1.20293	+	1.20293i
$550$		0			0
$551$		−	20.3133i		−	0.865375i
$552$	8.78907	+	16.5558i	0.374088	+	0.704661i
$553$	−15.1714			−0.645153
$554$	−15.4415	+	12.6481i	−0.656047	+	0.537368i
$555$		0			0
$556$	19.3709	−	12.8904i	0.821510	−	0.546675i
$557$	9.27495	−	9.27495i	0.392992	−	0.392992i	−0.482760	−	0.875753i	$-0.660366\pi$
$557$	9.27495	−	9.27495i	0.392992	−	0.392992i	0.875753	+	0.482760i	$0.160366\pi$
$558$	−4.79199	−	0.476537i	−0.202861	−	0.0201734i
$559$	−0.701048			−0.0296512
$560$		0			0
$561$	−16.6154			−0.701504
$562$	20.3507	+	2.02376i	0.858441	+	0.0853672i
$563$	20.3025	−	20.3025i	0.855649	−	0.855649i	−0.135173	−	0.990822i	$-0.543159\pi$
$563$	20.3025	−	20.3025i	0.855649	−	0.855649i	0.990822	+	0.135173i	$0.0431589\pi$
$564$	−33.6064	−	50.5016i	−1.41508	−	2.12650i
$565$		0			0
$566$	31.0655	−	25.4458i	1.30578	−	1.06956i
$567$	−28.2112			−1.18476
$568$	28.1205	+	8.61727i	1.17991	+	0.361573i
$569$		−	14.3362i		−	0.601005i	−0.953781	−	0.300503i	$-0.902846\pi$
$569$		−	14.3362i		−	0.601005i	0.953781	−	0.300503i	$-0.0971544\pi$
$570$		0			0
$571$	8.54368	−	8.54368i	0.357542	−	0.357542i	−0.505364	−	0.862906i	$-0.668642\pi$
$571$	8.54368	−	8.54368i	0.357542	−	0.357542i	0.862906	+	0.505364i	$0.168642\pi$
$572$	0.884790	−	4.40467i	0.0369949	−	0.184168i
$573$	−34.3987	+	34.3987i	−1.43703	+	1.43703i
$574$	−5.43301	−	0.540283i	−0.226769	−	0.0225510i
$575$		0			0
$576$	−35.0631	+	51.8377i	−1.46096	+	2.15991i
$577$			8.68179i			0.361428i	0.983536	+	0.180714i	$0.0578408\pi$
$577$			8.68179i			0.361428i	−0.983536	+	0.180714i	$0.942159\pi$
$578$	1.70434	−	17.1386i	0.0708912	−	0.712872i
$579$	−26.2661	−	26.2661i	−1.09158	−	1.09158i
$580$		0			0
$581$	0.670953	−	0.670953i	0.0278358	−	0.0278358i
$582$	−19.9590	+	16.3484i	−0.827328	+	0.677665i
$583$	−20.4723			−0.847877
$584$	7.66092	−	24.9996i	0.317011	−	1.03449i
$585$		0			0
$586$	23.8330	−	19.5216i	0.984533	−	0.806431i
$587$	−21.9042	−	21.9042i	−0.904082	−	0.904082i	0.0917043	−	0.995786i	$-0.470769\pi$
$587$	−21.9042	−	21.9042i	−0.904082	−	0.904082i	−0.995786	+	0.0917043i	$0.970769\pi$
$588$	33.0611	−	22.0006i	1.36342	−	0.907288i
$589$	−0.838619	−	0.838619i	−0.0345547	−	0.0345547i
$590$		0			0
$591$	49.3871			2.03151
$592$	12.4371	+	30.3493i	0.511160	+	1.24735i
$593$		−	17.5142i		−	0.719222i	−0.933102	−	0.359611i	$-0.882909\pi$
$593$		−	17.5142i		−	0.719222i	0.933102	−	0.359611i	$-0.117091\pi$
$594$	5.10722	−	51.3575i	0.209552	−	2.10722i
$595$		0			0
$596$	29.7549	−	19.8005i	1.21881	−	0.811059i
$597$	−10.9052	−	10.9052i	−0.446319	−	0.446319i
$598$	−1.76296	−	2.15231i	−0.0720926	−	0.0880144i
$599$		−	19.0276i		−	0.777447i	−0.921354	−	0.388724i	$-0.872916\pi$
$599$		−	19.0276i		−	0.777447i	0.921354	−	0.388724i	$-0.127084\pi$
$600$		0			0
$601$		−	5.52545i		−	0.225388i	−0.993630	−	0.112694i	$-0.964052\pi$
$601$		−	5.52545i		−	0.225388i	0.993630	−	0.112694i	$-0.0359479\pi$
$602$	−0.771228	+	0.631713i	−0.0314329	+	0.0257467i
$603$	−35.4814	−	35.4814i	−1.44491	−	1.44491i
$604$	−5.96975	+	29.7187i	−0.242906	+	1.20924i
$605$		0			0
$606$	1.90719	+	0.189660i	0.0774744	+	0.00770440i
$607$			12.1064i			0.491384i	0.969348	+	0.245692i	$0.0790151\pi$
$607$			12.1064i			0.491384i	−0.969348	+	0.245692i	$0.920985\pi$
$608$	−14.7700	+	4.40443i	−0.599004	+	0.178623i
$609$	24.0858			0.976007
$610$		0			0
$611$	6.36671	+	6.36671i	0.257570	+	0.257570i
$612$	−33.6814	−	6.76576i	−1.36149	−	0.273490i
$613$	17.8073	+	17.8073i	0.719230	+	0.719230i	0.968448	−	0.249218i	$-0.0801734\pi$
$613$	17.8073	+	17.8073i	0.719230	+	0.719230i	−0.249218	+	0.968448i	$0.580173\pi$
$614$	−11.5631	−	14.1168i	−0.466647	−	0.569707i
$615$		0			0
$616$	−2.99568	−	5.64289i	−0.120699	−	0.227358i
$617$	1.10944			0.0446642			0.0223321	−	0.999751i	$-0.492891\pi$
$617$	1.10944			0.0446642			0.0223321	+	0.999751i	$0.492891\pi$
$618$	−13.2730	−	16.2043i	−0.533917	−	0.651833i
$619$	31.8702	−	31.8702i	1.28097	−	1.28097i	0.340859	−	0.940115i	$-0.389282\pi$
$619$	31.8702	−	31.8702i	1.28097	−	1.28097i	0.940115	−	0.340859i	$-0.110718\pi$
$620$		0			0
$621$	−22.5998	−	22.5998i	−0.906901	−	0.906901i
$622$	0.904750	+	0.0899724i	0.0362772	+	0.00360756i
$623$			5.34608i			0.214186i
$624$	4.96278	−	11.8544i	0.198670	−	0.474557i
$625$		0			0
$626$	−2.99168	+	30.0840i	−0.119572	+	1.20240i
$627$	14.5786	−	14.5786i	0.582213	−	0.582213i
$628$	4.13996	−	2.75494i	0.165202	−	0.109934i
$629$	−12.7312	+	12.7312i	−0.507626	+	0.507626i
$630$		0			0
$631$		−	6.80064i		−	0.270729i	−0.990796	−	0.135365i	$-0.956779\pi$
$631$		−	6.80064i		−	0.270729i	0.990796	−	0.135365i	$-0.0432206\pi$
$632$	12.8030	−	41.7795i	0.509275	−	1.66190i
$633$	−12.2460			−0.486736
$634$	−10.9776	−	13.4020i	−0.435976	−	0.532262i
$635$		0			0
$636$	−57.4146	−	11.5332i	−2.27664	−	0.457320i
$637$	−4.16800	+	4.16800i	−0.165142	+	0.165142i
$638$	−2.39988	+	24.1328i	−0.0950121	+	0.955429i
$639$	−81.3449			−3.21796
$640$		0			0
$641$	14.2566			0.563100			0.281550	−	0.959547i	$-0.409151\pi$
$641$	14.2566			0.563100			0.281550	+	0.959547i	$0.409151\pi$
$642$	4.23139	−	42.5503i	0.167000	−	1.67933i
$643$	−14.4137	+	14.4137i	−0.568422	+	0.568422i	−0.931686	−	0.363264i	$-0.881662\pi$
$643$	−14.4137	+	14.4137i	−0.568422	+	0.568422i	0.363264	+	0.931686i	$0.381662\pi$
$644$	−3.87888	−	0.779172i	−0.152849	−	0.0307037i
$645$		0			0
$646$	−5.36124	−	6.54528i	−0.210935	−	0.257520i
$647$	−20.5723			−0.808782			−0.404391	−	0.914586i	$-0.632517\pi$
$647$	−20.5723			−0.808782			−0.404391	+	0.914586i	$0.632517\pi$
$648$	23.8071	−	77.6891i	0.935233	−	3.05192i
$649$			18.4692i			0.724980i
$650$		0			0
$651$	0.994365	−	0.994365i	0.0389723	−	0.0389723i
$652$	−32.7546	+	21.7966i	−1.28277	+	0.853620i
$653$	9.79946	−	9.79946i	0.383482	−	0.383482i	−0.488873	−	0.872355i	$-0.662592\pi$
$653$	9.79946	−	9.79946i	0.383482	−	0.383482i	0.872355	+	0.488873i	$0.162592\pi$
$654$	1.64043	−	16.4960i	0.0641459	−	0.645043i
$655$		0			0
$656$	6.07271	−	14.5057i	0.237100	−	0.566352i
$657$			72.3172i			2.82136i
$658$	12.7411	+	1.26703i	0.496700	+	0.0493940i
$659$	8.70669	+	8.70669i	0.339165	+	0.339165i	0.856053	−	0.516888i	$-0.172910\pi$
$659$	8.70669	+	8.70669i	0.339165	+	0.339165i	−0.516888	+	0.856053i	$0.672910\pi$
$660$		0			0
$661$	19.7899	−	19.7899i	0.769737	−	0.769737i	−0.208323	−	0.978060i	$-0.566801\pi$
$661$	19.7899	−	19.7899i	0.769737	−	0.769737i	0.978060	+	0.208323i	$0.0668006\pi$
$662$	10.6955	+	13.0576i	0.415692	+	0.507498i
$663$	7.05464			0.273979
$664$	1.28149	+	2.41391i	0.0497313	+	0.0936778i
$665$		0			0
$666$	−57.4823	−	70.1773i	−2.22739	−	2.71932i
$667$	10.6196	+	10.6196i	0.411194	+	0.411194i
$668$	36.9852	+	7.42941i	1.43100	+	0.287453i
$669$	8.04053	+	8.04053i	0.310865	+	0.310865i
$670$		0			0
$671$	11.7202			0.452454
$672$	−5.22242	−	17.5131i	−0.201459	−	0.675582i
$673$		−	14.0829i		−	0.542857i	−0.962459	−	0.271429i	$-0.912504\pi$
$673$		−	14.0829i		−	0.542857i	0.962459	−	0.271429i	$-0.0874961\pi$
$674$	−43.2098	−	4.29698i	−1.66438	−	0.165513i
$675$		0			0
$676$	4.74481	−	23.6206i	0.182493	−	0.908487i
$677$	29.8166	+	29.8166i	1.14594	+	1.14594i	0.987343	+	0.158601i	$0.0506984\pi$
$677$	29.8166	+	29.8166i	1.14594	+	1.14594i	0.158601	+	0.987343i	$0.449302\pi$
$678$	19.3674	−	15.8638i	0.743799	−	0.609247i
$679$		−	5.44564i		−	0.208984i
$680$		0			0
$681$			22.0784i			0.846045i
$682$	0.897229	+	1.09538i	0.0343567	+	0.0419444i
$683$	−12.0646	−	12.0646i	−0.461641	−	0.461641i	0.437552	−	0.899193i	$-0.355845\pi$
$683$	−12.0646	−	12.0646i	−0.461641	−	0.461641i	−0.899193	+	0.437552i	$0.855845\pi$
$684$	35.4888	−	23.6161i	1.35695	−	0.902983i
$685$		0			0
$686$	−1.79146	+	18.0147i	−0.0683984	+	0.687805i
$687$		−	62.1462i		−	2.37102i
$688$	−1.08880	−	2.65693i	−0.0415103	−	0.101295i
$689$	8.69221			0.331147
$690$		0			0
$691$	2.58867	+	2.58867i	0.0984776	+	0.0984776i	0.754629	−	0.656152i	$-0.227817\pi$
$691$	2.58867	+	2.58867i	0.0984776	+	0.0984776i	−0.656152	+	0.754629i	$0.727817\pi$
$692$	37.8459	−	25.1847i	1.43869	−	0.957377i
$693$	12.4945	+	12.4945i	0.474628	+	0.474628i
$694$	−21.1068	+	17.2886i	−0.801203	+	0.656266i
$695$		0			0
$696$	−20.3258	+	66.3285i	−0.770447	+	2.51418i
$697$	8.63242			0.326976
$698$	−15.4307	+	12.6393i	−0.584062	+	0.478405i
$699$	−11.2286	+	11.2286i	−0.424704	+	0.424704i
$700$		0			0
$701$	−26.9943	−	26.9943i	−1.01956	−	1.01956i	−0.999805	−	0.0197572i	$-0.993711\pi$
$701$	−26.9943	−	26.9943i	−1.01956	−	1.01956i	−0.0197572	−	0.999805i	$-0.506289\pi$
$702$	−2.16844	+	21.8055i	−0.0818425	+	0.822997i
$703$		−	22.3410i		−	0.842606i
$704$	18.0676	−	3.48763i	0.680949	−	0.131445i
$705$		0			0
$706$	−37.6929	−	3.74835i	−1.41859	−	0.141071i
$707$	−0.286054	+	0.286054i	−0.0107582	+	0.0107582i
$708$	−10.4047	+	51.7969i	−0.391033	+	1.94665i
$709$	35.0639	−	35.0639i	1.31685	−	1.31685i	0.400598	−	0.916254i	$-0.368802\pi$
$709$	35.0639	−	35.0639i	1.31685	−	1.31685i	0.916254	−	0.400598i	$-0.131198\pi$
$710$		0			0
$711$			120.857i			4.53249i
$712$	−14.7223	−	4.51151i	−0.551740	−	0.169076i
$713$	0.876848			0.0328382
$714$	7.76085	−	6.35692i	0.290443	−	0.237902i
$715$		0			0
$716$	25.7513	+	38.6975i	0.962373	+	1.44619i
$717$	20.5290	−	20.5290i	0.766671	−	0.766671i
$718$	−26.9057	−	2.67562i	−1.00411	−	0.0998534i
$719$	0.436840			0.0162914			0.00814568	−	0.999967i	$-0.497407\pi$
$719$	0.436840			0.0162914			0.00814568	+	0.999967i	$0.497407\pi$
$720$		0			0
$721$	4.42120			0.164654
$722$	−16.2913	−	1.62007i	−0.606298	−	0.0602929i
$723$	−8.70356	+	8.70356i	−0.323689	+	0.323689i
$724$	36.3896	−	24.2155i	1.35241	−	0.899963i
$725$		0			0
$726$	20.5491	−	16.8317i	0.762647	−	0.624684i
$727$	−38.8072			−1.43928			−0.719640	−	0.694348i	$-0.755693\pi$
$727$	−38.8072			−1.43928			−0.719640	+	0.694348i	$0.755693\pi$
$728$	1.27191	+	2.39588i	0.0471402	+	0.0887970i
$729$			68.1444i			2.52387i
$730$		0			0
$731$	1.11455	−	1.11455i	0.0412233	−	0.0412233i
$732$	32.8693	+	6.60263i	1.21488	+	0.244040i
$733$	24.3059	−	24.3059i	0.897758	−	0.897758i	−0.0974793	−	0.995238i	$-0.531078\pi$
$733$	24.3059	−	24.3059i	0.897758	−	0.897758i	0.995238	+	0.0974793i	$0.0310780\pi$
$734$	−5.97226	−	0.593908i	−0.220440	−	0.0219215i
$735$		0			0
$736$	5.41906	−	10.0243i	0.199749	−	0.369500i
$737$			14.7539i			0.543469i
$738$	−4.30395	+	43.2800i	−0.158431	+	1.59316i
$739$	27.0262	+	27.0262i	0.994174	+	0.994174i	0.999983	−	0.00580951i	$-0.00184923\pi$
$739$	27.0262	+	27.0262i	0.994174	+	0.994174i	−0.00580951	+	0.999983i	$0.501849\pi$
$740$		0			0
$741$	−6.18982	+	6.18982i	−0.227389	+	0.227389i
$742$	9.56235	−	7.83253i	0.351045	−	0.287541i
$743$	12.1663			0.446337			0.223169	−	0.974780i	$-0.428360\pi$
$743$	12.1663			0.446337			0.223169	+	0.974780i	$0.428360\pi$
$744$	1.89919	+	3.57746i	0.0696276	+	0.131156i
$745$		0			0
$746$	37.0580	−	30.3543i	1.35679	−	1.11135i
$747$	−5.34489	−	5.34489i	−0.195559	−	0.195559i
$748$	5.59605	+	8.40940i	0.204612	+	0.307478i
$749$	6.38199	+	6.38199i	0.233193	+	0.233193i
$750$		0			0
$751$	−40.8606			−1.49102			−0.745512	−	0.666492i	$-0.767795\pi$
$751$	−40.8606			−1.49102			−0.745512	+	0.666492i	$0.767795\pi$
$752$	−14.2413	+	34.0177i	−0.519326	+	1.24050i
$753$			27.8834i			1.01613i
$754$	1.01895	−	10.2464i	0.0371079	−	0.373152i
$755$		0			0
$756$	17.2634	+	25.9424i	0.627864	+	0.943516i
$757$	0.00399171	+	0.00399171i	0.000145081	+	0.000145081i	0.707179	−	0.707034i	$-0.249967\pi$
$757$	0.00399171	+	0.00399171i	0.000145081	+	0.000145081i	−0.707034	+	0.707179i	$0.749967\pi$
$758$	−9.45026	−	11.5374i	−0.343249	−	0.419056i
$759$			15.2432i			0.553292i
$760$		0			0
$761$		−	0.751325i		−	0.0272355i	−0.999907	−	0.0136178i	$-0.995665\pi$
$761$		−	0.751325i		−	0.0272355i	0.999907	−	0.0136178i	$-0.00433480\pi$
$762$	−17.5129	+	14.3449i	−0.634427	+	0.519660i
$763$	2.47418	+	2.47418i	0.0895712	+	0.0895712i
$764$	28.9953	+	5.82443i	1.04901	+	0.210721i
$765$		0			0
$766$	7.31313	+	0.727250i	0.264234	+	0.0262766i
$767$		−	7.84172i		−	0.283148i
$768$	52.6354	+	0.397428i	1.89932	+	0.0143410i
$769$	−35.4522			−1.27844			−0.639219	−	0.769025i	$-0.720742\pi$
$769$	−35.4522			−1.27844			−0.639219	+	0.769025i	$0.720742\pi$
$770$		0			0
$771$	34.3498	+	34.3498i	1.23708	+	1.23708i
$772$	−4.44740	+	22.1401i	−0.160066	+	0.796840i
$773$	−5.50186	−	5.50186i	−0.197888	−	0.197888i	0.601206	−	0.799094i	$-0.294687\pi$
$773$	−5.50186	−	5.50186i	−0.197888	−	0.197888i	−0.799094	+	0.601206i	$0.794687\pi$
$774$	5.03230	+	6.14369i	0.180882	+	0.220830i
$775$		0			0
$776$	14.9964	+	4.59552i	0.538340	+	0.164970i
$777$	26.4901			0.950327
$778$	13.1607	+	16.0673i	0.471835	+	0.576041i
$779$	−7.57419	+	7.57419i	−0.271373	+	0.271373i
$780$		0			0
$781$	16.9125	+	16.9125i	0.605177	+	0.605177i
$782$	6.22464	+	0.619006i	0.222593	+	0.0221356i
$783$		−	118.289i		−	4.22732i
$784$	−22.2698	−	9.32312i	−0.795351	−	0.332969i
$785$		0			0
$786$	5.21254	−	52.4166i	0.185925	−	1.86964i
$787$	28.6944	−	28.6944i	1.02284	−	1.02284i	0.0231107	−	0.999733i	$-0.492643\pi$
$787$	28.6944	−	28.6944i	1.02284	−	1.02284i	0.999733	−	0.0231107i	$-0.00735700\pi$
$788$	−16.6335	−	24.9958i	−0.592543	−	0.890437i
$789$	−15.8065	+	15.8065i	−0.562726	+	0.562726i
$790$		0			0
$791$			5.28422i			0.187885i
$792$	−44.9519	+	23.8639i	−1.59730	+	0.847967i
$793$	−4.97620			−0.176710
$794$	−12.5859	−	15.3655i	−0.446656	−	0.545300i
$795$		0			0
$796$	−1.84648	+	9.19215i	−0.0654467	+	0.325807i
$797$	−6.29277	+	6.29277i	−0.222901	+	0.222901i	−0.809719	−	0.586818i	$-0.800381\pi$
$797$	−6.29277	+	6.29277i	−0.222901	+	0.222901i	0.586818	+	0.809719i	$0.300381\pi$
$798$	−1.23183	+	12.3871i	−0.0436063	+	0.438499i
$799$	−20.2441			−0.716185
$800$		0			0
$801$	42.5875			1.50476
$802$	1.33143	−	13.3887i	0.0470144	−	0.472771i
$803$	15.0355	−	15.0355i	0.530592	−	0.530592i
$804$	−8.31170	+	41.3774i	−0.293131	+	1.45927i
$805$		0			0
$806$	−0.380948	−	0.465081i	−0.0134183	−	0.0163818i
$807$	28.1005			0.989186
$808$	−0.546348	−	1.02914i	−0.0192205	−	0.0362052i
$809$			27.0850i			0.952257i	0.879376	+	0.476128i	$0.157960\pi$
$809$			27.0850i			0.952257i	−0.879376	+	0.476128i	$0.842040\pi$
$810$		0			0
$811$	−14.6690	+	14.6690i	−0.515098	+	0.515098i	−0.916084	−	0.400986i	$-0.868668\pi$
$811$	−14.6690	+	14.6690i	−0.515098	+	0.515098i	0.400986	+	0.916084i	$0.368668\pi$
$812$	−8.11206	−	12.1903i	−0.284677	−	0.427796i
$813$	−57.2769	+	57.2769i	−2.00879	+	2.00879i
$814$	−2.63944	+	26.5418i	−0.0925122	+	0.930290i
$815$		0			0
$816$	10.9566	+	26.7367i	0.383559	+	0.935971i
$817$			1.95585i			0.0684264i
$818$	6.78022	+	0.674256i	0.237065	+	0.0235748i
$819$	−5.30496	−	5.30496i	−0.185370	−	0.185370i
$820$		0			0
$821$	−15.4717	+	15.4717i	−0.539965	+	0.539965i	−0.923519	−	0.383553i	$-0.874700\pi$
$821$	−15.4717	+	15.4717i	−0.539965	+	0.539965i	0.383553	+	0.923519i	$0.374700\pi$
$822$	−39.9666	−	48.7932i	−1.39399	−	1.70186i
$823$	7.64319			0.266425			0.133212	−	0.991088i	$-0.457471\pi$
$823$	7.64319			0.266425			0.133212	+	0.991088i	$0.457471\pi$
$824$	−3.73101	+	12.1753i	−0.129976	+	0.424146i
$825$		0			0
$826$	−7.06616	−	8.62673i	−0.245863	−	0.300162i
$827$	0.781185	+	0.781185i	0.0271645	+	0.0271645i	0.720559	−	0.693394i	$-0.243885\pi$
$827$	0.781185	+	0.781185i	0.0271645	+	0.0271645i	−0.693394	+	0.720559i	$0.743885\pi$
$828$	−6.20697	+	30.8996i	−0.215707	+	1.07384i
$829$	−28.9122	−	28.9122i	−1.00416	−	1.00416i	−0.999991	−	0.00417165i	$-0.998672\pi$
$829$	−28.9122	−	28.9122i	−1.00416	−	1.00416i	−0.00417165	−	0.999991i	$-0.501328\pi$
$830$		0			0
$831$	−46.4326			−1.61073
$832$	−7.67121	+	1.48079i	−0.265951	+	0.0513371i
$833$		−	13.2529i		−	0.459186i
$834$	53.8612	+	5.35619i	1.86506	+	0.185470i
$835$		0			0
$836$	−12.2885	−	2.46847i	−0.425008	−	0.0853737i
$837$	−4.88349	−	4.88349i	−0.168798	−	0.168798i
$838$	−33.1693	+	27.1690i	−1.14581	+	0.938536i
$839$			35.9665i			1.24170i	0.783928	+	0.620851i	$0.213213\pi$
$839$			35.9665i			1.24170i	−0.783928	+	0.620851i	$0.786787\pi$
$840$		0			0
$841$			26.5841i			0.916692i
$842$	6.08500	+	7.42888i	0.209703	+	0.256016i
$843$	33.6400	+	33.6400i	1.15862	+	1.15862i
$844$	4.12444	+	6.19795i	0.141969	+	0.213342i
$845$		0			0
$846$	10.0933	−	101.497i	0.347015	−	3.48954i
$847$			5.60663i			0.192646i
$848$	13.4999	+	32.9430i	0.463590	+	1.13127i
$849$	93.4140			3.20596
$850$		0			0
$851$	11.6797	+	11.6797i	0.400375	+	0.400375i
$852$	37.9033	+	56.9588i	1.29855	+	1.95138i
$853$	8.53167	+	8.53167i	0.292119	+	0.292119i	0.837917	−	0.545798i	$-0.183773\pi$
$853$	8.53167	+	8.53167i	0.292119	+	0.292119i	−0.545798	+	0.837917i	$0.683773\pi$
$854$	−5.47435	+	4.48405i	−0.187329	+	0.153441i
$855$		0			0
$856$	−22.9607	+	12.1893i	−0.784779	+	0.416621i
$857$	20.6681			0.706010			0.353005	−	0.935621i	$-0.385160\pi$
$857$	20.6681			0.706010			0.353005	+	0.935621i	$0.385160\pi$
$858$	8.08500	−	6.62242i	0.276017	−	0.226086i
$859$	−26.6003	+	26.6003i	−0.907590	+	0.907590i	−0.996077	−	0.0884877i	$-0.971797\pi$
$859$	−26.6003	+	26.6003i	−0.907590	+	0.907590i	0.0884877	+	0.996077i	$0.471797\pi$
$860$		0			0
$861$	−8.98085	−	8.98085i	−0.306066	−	0.306066i
$862$	1.85244	−	18.6279i	0.0630943	−	0.634468i
$863$			24.2911i			0.826880i	0.910531	+	0.413440i	$0.135673\pi$
$863$			24.2911i			0.826880i	−0.910531	+	0.413440i	$0.864327\pi$
$864$	−86.0096	+	25.6481i	−2.92611	+	0.872567i
$865$		0			0
$866$	−2.12088	−	0.210910i	−0.0720704	−	0.00716700i
$867$	28.3304	−	28.3304i	0.962150	−	0.962150i
$868$	−0.838168	−	0.168367i	−0.0284493	−	0.00571476i
$869$	25.1275	−	25.1275i	0.852391	−	0.852391i
$870$		0			0
$871$		−	6.26428i		−	0.212257i
$872$	−8.90141	+	4.72555i	−0.301440	+	0.160027i
$873$	−43.3806			−1.46821
$874$	−6.00470	+	4.91845i	−0.203112	+	0.166369i
$875$		0			0
$876$	50.6374	−	33.6968i	1.71088	−	1.13851i
$877$	−17.5305	+	17.5305i	−0.591963	+	0.591963i	−0.938161	−	0.346198i	$-0.887472\pi$
$877$	−17.5305	+	17.5305i	−0.591963	+	0.591963i	0.346198	+	0.938161i	$0.387472\pi$
$878$	−14.5079	−	1.44273i	−0.489618	−	0.0486898i
$879$	71.6659			2.41723
$880$		0			0
$881$	35.1334			1.18367			0.591837	−	0.806058i	$-0.298403\pi$
$881$	35.1334			1.18367			0.591837	+	0.806058i	$0.298403\pi$
$882$	66.4455	+	6.60764i	2.23734	+	0.222491i
$883$	−18.0965	+	18.0965i	−0.608997	+	0.608997i	−0.942684	−	0.333687i	$-0.891707\pi$
$883$	−18.0965	+	18.0965i	−0.608997	+	0.608997i	0.333687	+	0.942684i	$0.391707\pi$
$884$	−2.37599	−	3.57049i	−0.0799131	−	0.120088i
$885$		0			0
$886$	−22.0712	+	18.0785i	−0.741497	+	0.607361i
$887$	−14.6666			−0.492455			−0.246228	−	0.969212i	$-0.579191\pi$
$887$	−14.6666			−0.492455			−0.246228	+	0.969212i	$0.579191\pi$
$888$	−22.3547	+	72.9495i	−0.750176	+	2.44802i
$889$		−	4.77825i		−	0.160257i
$890$		0			0
$891$	46.7246	−	46.7246i	1.56533	−	1.56533i
$892$	1.36143	−	6.77750i	0.0455841	−	0.226927i
$893$	17.7624	−	17.7624i	0.594397	−	0.594397i
$894$	82.7341	+	8.22744i	2.76704	+	0.275167i
$895$		0			0
$896$	−7.10481	+	8.54154i	−0.237355	+	0.285353i
$897$		−	6.47199i		−	0.216094i
$898$	2.73889	−	27.5419i	0.0913979	−	0.919085i
$899$	2.29475	+	2.29475i	0.0765341	+	0.0765341i
$900$		0			0
$901$	−13.8192	+	13.8192i	−0.460385	+	0.460385i
$902$	9.89322	−	8.10354i	0.329408	−	0.269818i
$903$	−2.31908			−0.0771743
$904$	−14.5519	−	4.45930i	−0.483988	−	0.148314i
$905$		0			0
$906$	−54.5502	+	44.6821i	−1.81231	+	1.48446i
$907$	25.4429	+	25.4429i	0.844817	+	0.844817i	0.989481	−	0.144664i	$-0.0462100\pi$
$907$	25.4429	+	25.4429i	0.844817	+	0.844817i	−0.144664	+	0.989481i	$0.546210\pi$
$908$	11.1743	−	7.43595i	0.370832	−	0.246771i
$909$	2.27874	+	2.27874i	0.0755810	+	0.0755810i
$910$		0			0
$911$	14.6852			0.486542			0.243271	−	0.969958i	$-0.421780\pi$
$911$	14.6852			0.486542			0.243271	+	0.969958i	$0.421780\pi$
$912$	−33.0726	−	13.8456i	−1.09514	−	0.458474i
$913$			2.22252i			0.0735547i
$914$	−5.46046	+	54.9096i	−0.180616	+	1.81625i
$915$		0			0
$916$	−31.4534	+	20.9307i	−1.03925	+	0.691570i
$917$	7.86179	+	7.86179i	0.259619	+	0.259619i
$918$	−31.2199	−	38.1148i	−1.03041	−	1.25798i
$919$			46.2157i			1.52451i	0.647274	+	0.762257i	$0.275909\pi$
$919$			46.2157i			1.52451i	−0.647274	+	0.762257i	$0.724091\pi$
$920$		0			0
$921$		−	42.4492i		−	1.39875i
$922$	30.4710	−	24.9588i	1.00351	−	0.821976i
$923$	−7.18076	−	7.18076i	−0.236358	−	0.236358i
$924$	2.92690	−	14.5707i	0.0962881	−	0.479342i
$925$		0			0
$926$	−21.1061	−	2.09888i	−0.693588	−	0.0689735i
$927$		−	35.2198i		−	1.15677i
$928$	40.4158	−	12.0520i	1.32671	−	0.395627i
$929$	−52.0543			−1.70785			−0.853923	−	0.520400i	$-0.825783\pi$
$929$	−52.0543			−1.70785			−0.853923	+	0.520400i	$0.825783\pi$
$930$		0			0
$931$	11.6283	+	11.6283i	0.381101	+	0.381101i
$932$	9.46476	+	1.90124i	0.310029	+	0.0622771i
$933$	1.49557	+	1.49557i	0.0489627	+	0.0489627i
$934$	−6.19558	−	7.56389i	−0.202726	−	0.247498i
$935$		0			0
$936$	19.0858	−	10.1322i	0.623840	−	0.331182i
$937$	33.7454			1.10241			0.551207	−	0.834368i	$-0.314167\pi$
$937$	33.7454			1.10241			0.551207	+	0.834368i	$0.314167\pi$
$938$	−5.64473	−	6.89137i	−0.184307	−	0.225011i
$939$	−49.7293	+	49.7293i	−1.62285	+	1.62285i
$940$		0			0
$941$	−14.5814	−	14.5814i	−0.475341	−	0.475341i	0.428297	−	0.903638i	$-0.359114\pi$
$941$	−14.5814	−	14.5814i	−0.475341	−	0.475341i	−0.903638	+	0.428297i	$0.859114\pi$
$942$	11.5112	+	1.14473i	0.375056	+	0.0372972i
$943$		−	7.91946i		−	0.257893i
$944$	29.7197	−	12.1790i	0.967293	−	0.396394i
$945$		0			0
$946$	0.231070	−	2.32361i	0.00751274	−	0.0755471i
$947$	−37.7582	+	37.7582i	−1.22698	+	1.22698i	−0.261876	+	0.965102i	$0.584341\pi$
$947$	−37.7582	+	37.7582i	−1.22698	+	1.22698i	−0.965102	+	0.261876i	$0.915659\pi$
$948$	84.6256	−	56.3143i	2.74851	−	1.82900i
$949$	−6.38383	+	6.38383i	−0.207228	+	0.207228i
$950$		0			0
$951$		−	40.2998i		−	1.30681i
$952$	−5.83120	−	1.78692i	−0.188990	−	0.0579144i
$953$	48.6441			1.57574			0.787868	−	0.615844i	$-0.211185\pi$
$953$	48.6441			1.57574			0.787868	+	0.615844i	$0.211185\pi$
$954$	−62.3948	−	76.1748i	−2.02011	−	2.46625i
$955$		0			0
$956$	−17.3043	−	3.47600i	−0.559660	−	0.112422i
$957$	−39.8920	+	39.8920i	−1.28952	+	1.28952i
$958$	3.82584	−	38.4721i	0.123607	−	1.24298i
$959$	13.3128			0.429893
$960$		0			0
$961$	−30.8105			−0.993888
$962$	1.12066	−	11.2692i	0.0361315	−	0.363334i
$963$	50.8397	−	50.8397i	1.63829	−	1.63829i
$964$	7.33638	+	1.47370i	0.236289	+	0.0474646i
$965$		0			0
$966$	−5.83190	−	7.11988i	−0.187638	−	0.229078i
$967$	12.4521			0.400433			0.200216	−	0.979752i	$-0.435835\pi$
$967$	12.4521			0.400433			0.200216	+	0.979752i	$0.435835\pi$
$968$	−15.4397	−	4.73138i	−0.496252	−	0.152072i
$969$		−	19.6817i		−	0.632266i
$970$		0			0
$971$	14.1931	−	14.1931i	0.455478	−	0.455478i	−0.441690	−	0.897168i	$-0.645621\pi$
$971$	14.1931	−	14.1931i	0.455478	−	0.455478i	0.897168	+	0.441690i	$0.145621\pi$
$972$	78.1086	−	51.9775i	2.50533	−	1.66718i
$973$	−8.07846	+	8.07846i	−0.258984	+	0.258984i
$974$	4.96483	−	49.9256i	0.159083	−	1.59972i
$975$		0			0
$976$	−7.72859	−	18.8595i	−0.247386	−	0.603679i
$977$		−	18.3144i		−	0.585929i	−0.956123	−	0.292965i	$-0.905358\pi$
$977$		−	18.3144i		−	0.585929i	0.956123	−	0.292965i	$-0.0946419\pi$
$978$	−91.0746	−	9.05686i	−2.91224	−	0.289607i
$979$	−8.85441	−	8.85441i	−0.282988	−	0.282988i
$980$		0			0
$981$	19.7096	−	19.7096i	0.629278	−	0.629278i
$982$	−4.50679	−	5.50212i	−0.143817	−	0.175580i
$983$	−27.0583			−0.863027			−0.431513	−	0.902107i	$-0.642020\pi$
$983$	−27.0583			−0.863027			−0.431513	+	0.902107i	$0.642020\pi$
$984$	32.3107	−	17.1530i	1.03003	−	0.546816i
$985$		0			0
$986$	14.6702	+	17.9101i	0.467194	+	0.570374i
$987$	21.0612	+	21.0612i	0.670386	+	0.670386i
$988$	5.21751	+	1.04807i	0.165991	+	0.0333435i
$989$	−1.02250	−	1.02250i	−0.0325137	−	0.0325137i
$990$		0			0
$991$	25.7759			0.818799			0.409400	−	0.912355i	$-0.365738\pi$
$991$	25.7759			0.818799			0.409400	+	0.912355i	$0.365738\pi$
$992$	1.17098	−	2.16610i	0.0371786	−	0.0687736i
$993$			39.2642i			1.24601i
$994$	−14.3702	−	1.42903i	−0.455794	−	0.0453262i
$995$		0			0
$996$	−1.25207	+	6.23305i	−0.0396733	+	0.197502i
$997$	−11.1158	−	11.1158i	−0.352041	−	0.352041i	0.508828	−	0.860868i	$-0.330079\pi$
$997$	−11.1158	−	11.1158i	−0.352041	−	0.352041i	−0.860868	+	0.508828i	$0.830079\pi$
$998$	27.3117	−	22.3710i	0.864536	−	0.708142i
$999$		−	130.097i		−	4.11609i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.q.g.349.6		16
4.3	odd	2		1600.2.q.h.849.1		16
5.2	odd	4		80.2.l.a.61.8	yes	16
5.3	odd	4		400.2.l.h.301.1		16
5.4	even	2		400.2.q.h.349.3		16
15.2	even	4		720.2.t.c.541.1		16
16.5	even	4		400.2.q.h.149.3		16
16.11	odd	4		1600.2.q.g.49.8		16
20.3	even	4		1600.2.l.i.401.1		16
20.7	even	4		320.2.l.a.81.8		16
20.19	odd	2		1600.2.q.g.849.8		16
40.27	even	4		640.2.l.a.161.1		16
40.37	odd	4		640.2.l.b.161.8		16
60.47	odd	4		2880.2.t.c.721.2		16
80.27	even	4		320.2.l.a.241.8		16
80.37	odd	4		80.2.l.a.21.8	✓	16
80.43	even	4		1600.2.l.i.1201.1		16
80.53	odd	4		400.2.l.h.101.1		16
80.59	odd	4		1600.2.q.h.49.1		16
80.67	even	4		640.2.l.a.481.1		16
80.69	even	4	inner	400.2.q.g.149.6		16
80.77	odd	4		640.2.l.b.481.8		16
160.27	even	8		5120.2.a.t.1.1		8
160.37	odd	8		5120.2.a.v.1.8		8
160.107	even	8		5120.2.a.u.1.8		8
160.117	odd	8		5120.2.a.s.1.1		8
240.107	odd	4		2880.2.t.c.2161.3		16
240.197	even	4		720.2.t.c.181.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.8	✓	16	80.37	odd	4
80.2.l.a.61.8	yes	16	5.2	odd	4
320.2.l.a.81.8		16	20.7	even	4
320.2.l.a.241.8		16	80.27	even	4
400.2.l.h.101.1		16	80.53	odd	4
400.2.l.h.301.1		16	5.3	odd	4
400.2.q.g.149.6		16	80.69	even	4	inner
400.2.q.g.349.6		16	1.1	even	1	trivial
400.2.q.h.149.3		16	16.5	even	4
400.2.q.h.349.3		16	5.4	even	2
640.2.l.a.161.1		16	40.27	even	4
640.2.l.a.481.1		16	80.67	even	4
640.2.l.b.161.8		16	40.37	odd	4
640.2.l.b.481.8		16	80.77	odd	4
720.2.t.c.181.1		16	240.197	even	4
720.2.t.c.541.1		16	15.2	even	4
1600.2.l.i.401.1		16	20.3	even	4
1600.2.l.i.1201.1		16	80.43	even	4
1600.2.q.g.49.8		16	16.11	odd	4
1600.2.q.g.849.8		16	20.19	odd	2
1600.2.q.h.49.1		16	80.59	odd	4
1600.2.q.h.849.1		16	4.3	odd	2
2880.2.t.c.721.2		16	60.47	odd	4
2880.2.t.c.2161.3		16	240.107	odd	4
5120.2.a.s.1.1		8	160.117	odd	8
5120.2.a.t.1.1		8	160.27	even	8
5120.2.a.u.1.8		8	160.107	even	8
5120.2.a.v.1.8		8	160.37	odd	8

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.q (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.139945 - 1.40727i) q^{2} +(2.32624 - 2.32624i) q^{3} +(-1.96083 - 0.393883i) q^{4} +(-2.94811 - 3.59920i) q^{6} +0.982011 q^{7} +(-0.828709 + 2.70430i) q^{8} -7.82281i q^{9} +(-1.62645 + 1.62645i) q^{11} +(-5.47764 + 3.64510i) q^{12} +(0.690562 - 0.690562i) q^{13} +(0.137428 - 1.38196i) q^{14} +(3.68971 + 1.54467i) q^{16} +2.19577i q^{17} +(-11.0088 - 1.09477i) q^{18} +(-1.92659 - 1.92659i) q^{19} +(2.28440 - 2.28440i) q^{21} +(2.06124 + 2.51647i) q^{22} +2.01442 q^{23} +(4.36308 + 8.21864i) q^{24} +(-0.875168 - 1.06845i) q^{26} +(-11.2190 - 11.2190i) q^{27} +(-1.92556 - 0.386797i) q^{28} +(5.27182 + 5.27182i) q^{29} +0.435286 q^{31} +(2.69014 - 4.97626i) q^{32} +7.56703i q^{33} +(3.09004 + 0.307288i) q^{34} +(-3.08127 + 15.3392i) q^{36} +(5.79805 + 5.79805i) q^{37} +(-2.98086 + 2.44162i) q^{38} -3.21283i q^{39} -3.93139i q^{41} +(-2.89508 - 3.53446i) q^{42} +(-0.507592 - 0.507592i) q^{43} +(3.82982 - 2.54856i) q^{44} +(0.281909 - 2.83484i) q^{46} +9.21960i q^{47} +(12.1765 - 4.98988i) q^{48} -6.03565 q^{49} +(5.10789 + 5.10789i) q^{51} +(-1.62608 + 1.08208i) q^{52} +(6.29357 + 6.29357i) q^{53} +(-17.3583 + 14.2182i) q^{54} +(-0.813802 + 2.65565i) q^{56} -8.96345 q^{57} +(8.15665 - 6.68111i) q^{58} +(5.67778 - 5.67778i) q^{59} +(-3.60301 - 3.60301i) q^{61} +(0.0609163 - 0.612566i) q^{62} -7.68209i q^{63} +(-6.62648 - 4.48216i) q^{64} +(10.6489 + 1.05897i) q^{66} +(4.53563 - 4.53563i) q^{67} +(0.864875 - 4.30553i) q^{68} +(4.68603 - 4.68603i) q^{69} -10.3984i q^{71} +(21.1552 + 6.48284i) q^{72} -9.24439 q^{73} +(8.97085 - 7.34803i) q^{74} +(3.01887 + 4.53658i) q^{76} +(-1.59719 + 1.59719i) q^{77} +(-4.52133 - 0.449621i) q^{78} -15.4493 q^{79} -28.7280 q^{81} +(-5.53253 - 0.550180i) q^{82} +(0.683244 - 0.683244i) q^{83} +(-5.37910 + 3.57953i) q^{84} +(-0.785356 + 0.643285i) q^{86} +24.5271 q^{87} +(-3.05055 - 5.74626i) q^{88} +5.44401i q^{89} +(0.678140 - 0.678140i) q^{91} +(-3.94994 - 0.793445i) q^{92} +(1.01258 - 1.01258i) q^{93} +(12.9745 + 1.29024i) q^{94} +(-5.31808 - 17.8339i) q^{96} -5.54540i q^{97} +(-0.844662 + 8.49381i) q^{98} +(12.7234 + 12.7234i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 4 q^{4} - 12 q^{6} - 8 q^{7} + 8 q^{8} - 8 q^{11} - 20 q^{12} - 4 q^{14} + 16 q^{16} - 12 q^{18} + 8 q^{19} + 20 q^{22} - 24 q^{23} - 8 q^{24} - 16 q^{26} - 24 q^{27} - 20 q^{28} + 16 q^{29}+ \cdots + 8 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 4 * q^4 - 12 * q^6 - 8 * q^7 + 8 * q^8 - 8 * q^11 - 20 * q^12 - 4 * q^14 + 16 * q^16 - 12 * q^18 + 8 * q^19 + 20 * q^22 - 24 * q^23 - 8 * q^24 - 16 * q^26 - 24 * q^27 - 20 * q^28 + 16 * q^29 - 24 * q^32 - 16 * q^34 - 4 * q^36 + 16 * q^37 + 20 * q^38 + 20 * q^42 + 8 * q^43 - 40 * q^44 - 4 * q^46 + 16 * q^49 - 32 * q^51 + 16 * q^52 + 16 * q^53 - 32 * q^54 + 16 * q^56 + 28 * q^58 + 8 * q^59 + 16 * q^61 - 48 * q^62 + 16 * q^64 + 40 * q^67 + 8 * q^68 - 16 * q^69 + 96 * q^72 + 72 * q^74 + 16 * q^77 - 24 * q^78 - 16 * q^79 - 16 * q^81 - 44 * q^82 - 40 * q^83 + 64 * q^84 + 28 * q^86 + 16 * q^88 + 32 * q^91 - 20 * q^92 + 48 * q^93 + 36 * q^94 + 8 * q^96 + 32 * q^98 + 8 * q^99

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