LMFDB - Embedded newform 400.2.q.g.149.6

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			149.6
Root			$1.38652 + 0.278517i$ of defining polynomial
Character	$\chi$	$=$	400.149
Dual form			400.2.q.g.349.6

$q$-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 $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.139945	+	1.40727i	0.0989564	+	0.995092i
$2$	0.139945	+	1.40727i	0.0989564	+	0.995092i
$3$	2.32624	+	2.32624i	1.34306	+	1.34306i	0.893000	+	0.450058i	$0.148597\pi$
$3$	2.32624	+	2.32624i	1.34306	+	1.34306i	0.450058	+	0.893000i	$0.351403\pi$
$4$	−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	0.418037	−	0.908430i	$-0.362718\pi$
$11$	−1.62645	−	1.62645i	−0.490393	−	0.490393i	−0.908430	+	0.418037i	$0.862718\pi$
$12$	−5.47764	−	3.64510i	−1.58126	−	1.05225i
$13$	0.690562	+	0.690562i	0.191528	+	0.191528i	0.796356	−	0.604828i	$-0.206758\pi$
$13$	0.690562	+	0.690562i	0.191528	+	0.191528i	−0.604828	+	0.796356i	$0.706758\pi$
$14$	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	$-0.914207\pi$
$17$		−	2.19577i		−	0.532552i	0.963897	−	0.266276i	$-0.0857933\pi$
$18$	−11.0088	+	1.09477i	−2.59481	+	0.258039i
$19$	−1.92659	+	1.92659i	−0.441991	+	0.441991i	−0.892681	−	0.450690i	$-0.851178\pi$
$19$	−1.92659	+	1.92659i	−0.441991	+	0.441991i	0.450690	+	0.892681i	$0.351178\pi$
$20$		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	−0.0208314	−	0.999783i	$-0.506631\pi$
$29$	5.27182	−	5.27182i	0.978952	−	0.978952i	0.999783	+	0.0208314i	$0.00663132\pi$
$30$		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	−0.0457583	−	0.998953i	$-0.514570\pi$
$37$	5.79805	−	5.79805i	0.953194	−	0.953194i	0.998953	+	0.0457583i	$0.0145704\pi$
$38$	−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	$0.0993218\pi$
$41$			3.93139i			0.613980i	−0.951713	+	0.306990i	$0.900678\pi$
$42$	−2.89508	+	3.53446i	−0.446720	+	0.545379i
$43$	−0.507592	+	0.507592i	−0.0774071	+	0.0774071i	−0.744750	−	0.667343i	$-0.767431\pi$
$43$	−0.507592	+	0.507592i	−0.0774071	+	0.0774071i	0.667343	+	0.744750i	$0.267431\pi$
$44$	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	$-0.765260\pi$
$47$		−	9.21960i		−	1.34482i	0.740180	−	0.672409i	$-0.234740\pi$
$48$	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	−0.127367	−	0.991856i	$-0.540653\pi$
$53$	6.29357	−	6.29357i	0.864488	−	0.864488i	0.991856	+	0.127367i	$0.0406527\pi$
$54$	−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	0.972420	−	0.233237i	$-0.0749317\pi$
$59$	5.67778	+	5.67778i	0.739183	+	0.739183i	−0.233237	+	0.972420i	$0.574932\pi$
$60$		0			0
$61$	−3.60301	+	3.60301i	−0.461318	+	0.461318i	−0.899087	−	0.437770i	$-0.855769\pi$
$61$	−3.60301	+	3.60301i	−0.461318	+	0.461318i	0.437770	+	0.899087i	$0.355769\pi$
$62$	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	0.927626	−	0.373510i	$-0.121846\pi$
$67$	4.53563	+	4.53563i	0.554116	+	0.554116i	−0.373510	+	0.927626i	$0.621846\pi$
$68$	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	$0.211665\pi$
$71$			10.3984i			1.23407i	−0.786937	+	0.617033i	$0.788335\pi$
$72$	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	0.743610	−	0.668614i	$-0.233112\pi$
$83$	0.683244	+	0.683244i	0.0749957	+	0.0749957i	−0.668614	+	0.743610i	$0.733112\pi$
$84$	−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	$-0.906833\pi$
$89$		−	5.44401i		−	0.577064i	0.957470	−	0.288532i	$-0.0931672\pi$
$90$		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	$0.0908402\pi$
$97$			5.54540i			0.563050i	−0.959554	+	0.281525i	$0.909160\pi$
$98$	−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	0.692466	−	0.721451i	$-0.256524\pi$
$101$	−0.291294	−	0.291294i	−0.0289848	−	0.0289848i	−0.721451	+	0.692466i	$0.756524\pi$
$102$	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	−0.319361	−	0.947633i	$-0.603468\pi$
$107$	6.49890	−	6.49890i	0.628272	−	0.628272i	0.947633	+	0.319361i	$0.103468\pi$
$108$	17.5796	−	26.4176i	1.69160	−	2.54204i
$109$	2.51950	−	2.51950i	0.241324	−	0.241324i	−0.576074	−	0.817398i	$-0.695416\pi$
$109$	2.51950	−	2.51950i	0.241324	−	0.241324i	0.817398	+	0.576074i	$0.195416\pi$
$110$		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	$-0.918549\pi$
$113$		−	5.38101i		−	0.506203i	0.967440	−	0.253102i	$-0.0814507\pi$
$114$	−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	$0.0692634\pi$
$127$			4.86578i			0.431768i	−0.976419	+	0.215884i	$0.930737\pi$
$128$	−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	−0.264825	−	0.964296i	$-0.585314\pi$
$131$	8.00581	−	8.00581i	0.699471	−	0.699471i	0.964296	+	0.264825i	$0.0853143\pi$
$132$	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	0.266168	−	0.963927i	$-0.414242\pi$
$139$	−8.22645	−	8.22645i	−0.697758	−	0.697758i	−0.963927	+	0.266168i	$0.914242\pi$
$140$		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	−0.999357	−	0.0358519i	$-0.988586\pi$
$149$	−12.6363	−	12.6363i	−1.03521	−	1.03521i	−0.0358519	−	0.999357i	$-0.511414\pi$
$150$		0			0
$151$			15.1562i			1.23339i	0.787201	+	0.616696i	$0.211529\pi$
$151$			15.1562i			1.23339i	−0.787201	+	0.616696i	$0.788471\pi$
$152$	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	0.633460	−	0.773776i	$-0.281634\pi$
$157$	−1.75816	−	1.75816i	−0.140316	−	0.140316i	−0.773776	+	0.633460i	$0.781634\pi$
$158$	−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	0.995576	+	0.0939562i	$0.0299514\pi$
$163$	13.9102	+	13.9102i	1.08953	+	1.08953i	0.0939562	+	0.995576i	$0.470049\pi$
$164$	−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	−0.966933	−	0.255031i	$-0.917914\pi$
$173$	−16.0724	−	16.0724i	−1.22196	−	1.22196i	−0.255031	−	0.966933i	$-0.582086\pi$
$174$	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	−0.263749	+	0.964591i	$0.584959\pi$
$179$	−16.4341	+	16.4341i	−1.22834	+	1.22834i	−0.964591	+	0.263749i	$0.915041\pi$
$180$		0			0
$181$	−15.4539	−	15.4539i	−1.14868	−	1.14868i	−0.986812	−	0.161870i	$-0.948247\pi$
$181$	−15.4539	−	15.4539i	−1.14868	−	1.14868i	−0.161870	−	0.986812i	$-0.551753\pi$
$182$	−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	$0.133209\pi$
$193$			11.2912i			0.812758i	−0.913705	+	0.406379i	$0.866791\pi$
$194$	−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	−0.219345	−	0.975647i	$-0.570392\pi$
$197$	10.6152	−	10.6152i	0.756302	−	0.756302i	0.975647	+	0.219345i	$0.0703920\pi$
$198$	19.6859	+	16.1247i	1.39901	+	1.14593i
$199$			4.68789i			0.332316i	0.986099	+	0.166158i	$0.0531361\pi$
$199$			4.68789i			0.332316i	−0.986099	+	0.166158i	$0.946864\pi$
$200$		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	−0.791881	−	0.610676i	$-0.790898\pi$
$211$	−2.63215	+	2.63215i	−0.181205	+	0.181205i	0.610676	+	0.791881i	$0.290898\pi$
$212$	−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	$-0.963079\pi$
$223$		−	3.45644i		−	0.231461i	0.993281	−	0.115730i	$-0.0369208\pi$
$224$	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	0.531862	−	0.846831i	$-0.321493\pi$
$227$	−4.74550	−	4.74550i	−0.314970	−	0.314970i	−0.846831	+	0.531862i	$0.821493\pi$
$228$	17.5758	−	3.53055i	1.16399	−	0.233816i
$229$	13.3576	+	13.3576i	0.882697	+	0.882697i	0.993808	−	0.111111i	$-0.0354410\pi$
$229$	13.3576	+	13.3576i	0.882697	+	0.882697i	−0.111111	+	0.993808i	$0.535441\pi$
$230$		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	0.492196	−	0.870484i	$-0.336194\pi$
$251$	−5.99322	−	5.99322i	−0.378289	−	0.378289i	−0.870484	+	0.492196i	$0.836194\pi$
$252$	−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	$-0.847654\pi$
$257$		−	14.7662i		−	0.921091i	0.887636	−	0.460545i	$-0.152346\pi$
$258$	−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	−0.498583	−	0.866842i	$-0.666146\pi$
$269$	6.03990	−	6.03990i	0.368259	−	0.368259i	0.866842	+	0.498583i	$0.166146\pi$
$270$		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	−0.940220	−	0.340569i	$-0.889380\pi$
$277$	−9.98018	+	9.98018i	−0.599651	+	0.599651i	0.340569	+	0.940220i	$0.389380\pi$
$278$	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	$-0.858042\pi$
$281$		−	14.4611i		−	0.862675i	0.902191	−	0.431337i	$-0.141958\pi$
$282$	33.1832	+	27.1804i	1.97603	+	1.61857i
$283$	20.0783	−	20.0783i	1.19353	−	1.19353i	0.217462	−	0.976069i	$-0.430222\pi$
$283$	20.0783	−	20.0783i	1.19353	−	1.19353i	0.976069	−	0.217462i	$-0.0697777\pi$
$284$	−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	−0.0955279	−	0.995427i	$-0.530454\pi$
$293$	15.4038	−	15.4038i	0.899899	−	0.899899i	0.995427	+	0.0955279i	$0.0304539\pi$
$294$	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	0.917793	−	0.397060i	$-0.129969\pi$
$307$	9.12398	+	9.12398i	0.520733	+	0.520733i	−0.397060	+	0.917793i	$0.629969\pi$
$308$	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	$-0.994198\pi$
$311$		−	0.642911i		−	0.0364561i	0.999834	−	0.0182281i	$-0.00580249\pi$
$312$	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	0.907202	−	0.420695i	$-0.138214\pi$
$317$	8.66200	+	8.66200i	0.486507	+	0.486507i	−0.420695	+	0.907202i	$0.638214\pi$
$318$	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	0.436050	−	0.899922i	$-0.356377\pi$
$331$	−8.43941	−	8.43941i	−0.463872	−	0.463872i	−0.899922	+	0.436050i	$0.856377\pi$
$332$	−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	$0.315283\pi$
$337$			30.7047i			1.67259i	−0.548280	+	0.836295i	$0.684717\pi$
$338$	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	−0.971081	−	0.238752i	$-0.923262\pi$
$347$	−13.6418	+	13.6418i	−0.732329	+	0.732329i	0.238752	+	0.971081i	$0.423262\pi$
$348$	−48.0934	+	9.66078i	−2.57808	+	0.517872i
$349$	−9.97321	+	9.97321i	−0.533854	+	0.533854i	−0.921717	−	0.387863i	$-0.873213\pi$
$349$	−9.97321	+	9.97321i	−0.533854	+	0.533854i	0.387863	+	0.921717i	$0.373213\pi$
$350$		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	$0.252570\pi$
$353$			26.7843i			1.42559i	−0.701374	+	0.712793i	$0.747430\pi$
$354$	−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	$0.168335\pi$
$359$			19.1190i			1.00906i	−0.863393	+	0.504532i	$0.831665\pi$
$360$		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	$0.0353297\pi$
$367$			4.24385i			0.221527i	−0.993847	+	0.110764i	$0.964670\pi$
$368$	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	0.280221	−	0.959935i	$-0.409592\pi$
$373$	23.9514	−	23.9514i	1.24016	−	1.24016i	0.959935	−	0.280221i	$-0.0904078\pi$
$374$	−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	0.872194	−	0.489161i	$-0.162697\pi$
$379$	7.45685	+	7.45685i	0.383033	+	0.383033i	−0.489161	+	0.872194i	$0.662697\pi$
$380$		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	$-0.957613\pi$
$383$		−	5.19667i		−	0.265538i	0.991147	−	0.132769i	$-0.0423868\pi$
$384$	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	0.393011	−	0.919534i	$-0.371433\pi$
$389$	−10.3846	−	10.3846i	−0.526522	−	0.526522i	−0.919534	+	0.393011i	$0.871433\pi$
$390$		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	0.910947	−	0.412523i	$-0.135352\pi$
$397$	9.93104	+	9.93104i	0.498425	+	0.498425i	−0.412523	+	0.910947i	$0.635352\pi$
$398$	−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	$-0.961994\pi$
$409$		−	4.81799i		−	0.238234i	0.992880	−	0.119117i	$-0.0380064\pi$
$410$		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	−0.0484914	+	0.998824i	$0.515441\pi$
$419$	−21.4380	+	21.4380i	−1.04731	+	1.04731i	−0.998824	+	0.0484914i	$0.984559\pi$
$420$		0			0
$421$	−4.80145	−	4.80145i	−0.234008	−	0.234008i	0.580355	−	0.814363i	$-0.302914\pi$
$421$	−4.80145	−	4.80145i	−0.234008	−	0.234008i	−0.814363	+	0.580355i	$0.802914\pi$
$422$	−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	$0.0115295\pi$
$433$			1.50709i			0.0724259i	−0.999344	+	0.0362129i	$0.988471\pi$
$434$	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	$0.0791217\pi$
$439$			10.3092i			0.492033i	−0.969266	+	0.246016i	$0.920878\pi$
$440$		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	−0.959492	−	0.281736i	$-0.909090\pi$
$443$	−14.2651	+	14.2651i	−0.677755	+	0.677755i	0.281736	+	0.959492i	$0.409090\pi$
$444$	−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	−0.0795833	−	0.996828i	$-0.525359\pi$
$461$	19.6941	−	19.6941i	0.917245	−	0.917245i	0.996828	+	0.0795833i	$0.0253590\pi$
$462$	10.4573	−	1.03992i	0.486518	−	0.0483815i
$463$			14.9979i			0.697009i	0.937307	+	0.348505i	$0.113310\pi$
$463$			14.9979i			0.697009i	−0.937307	+	0.348505i	$0.886690\pi$
$464$	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	0.811112	−	0.584890i	$-0.198862\pi$
$467$	4.88870	+	4.88870i	0.226222	+	0.226222i	−0.584890	+	0.811112i	$0.698862\pi$
$468$	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	0.782782	−	0.622296i	$-0.213800\pi$
$491$	3.55614	+	3.55614i	0.160486	+	0.160486i	−0.622296	+	0.782782i	$0.713800\pi$
$492$	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	−0.191312	−	0.981529i	$-0.561274\pi$
$499$	17.6521	−	17.6521i	0.790218	−	0.790218i	0.981529	+	0.191312i	$0.0612742\pi$
$500$		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	−0.571747	−	0.820430i	$-0.693734\pi$
$509$	5.61054	−	5.61054i	0.248683	−	0.248683i	0.820430	+	0.571747i	$0.193734\pi$
$510$		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	$0.259182\pi$
$521$			33.1977i			1.45442i	−0.686417	+	0.727208i	$0.740818\pi$
$522$	−52.2651	+	63.8079i	−2.28758	+	2.79280i
$523$	−2.60707	+	2.60707i	−0.113999	+	0.113999i	−0.761805	−	0.647806i	$-0.775687\pi$
$523$	−2.60707	+	2.60707i	−0.113999	+	0.113999i	0.647806	+	0.761805i	$0.275687\pi$
$524$	−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	−0.999701	−	0.0244439i	$-0.992218\pi$
$541$	−22.6839	+	22.6839i	−0.975257	+	0.975257i	0.0244439	+	0.999701i	$0.492218\pi$
$542$	−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	0.639524	−	0.768771i	$-0.279132\pi$
$547$	−3.02284	−	3.02284i	−0.129248	−	0.129248i	−0.768771	+	0.639524i	$0.779132\pi$
$548$	−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	0.875753	−	0.482760i	$-0.160366\pi$
$557$	9.27495	+	9.27495i	0.392992	+	0.392992i	−0.482760	+	0.875753i	$0.660366\pi$
$558$	−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	0.990822	−	0.135173i	$-0.0431589\pi$
$563$	20.3025	+	20.3025i	0.855649	+	0.855649i	−0.135173	+	0.990822i	$0.543159\pi$
$564$	−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	$0.0971544\pi$
$569$			14.3362i			0.601005i	−0.953781	+	0.300503i	$0.902846\pi$
$570$		0			0
$571$	8.54368	+	8.54368i	0.357542	+	0.357542i	0.862906	−	0.505364i	$-0.168642\pi$
$571$	8.54368	+	8.54368i	0.357542	+	0.357542i	−0.505364	+	0.862906i	$0.668642\pi$
$572$	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	$-0.942159\pi$
$577$		−	8.68179i		−	0.361428i	0.983536	−	0.180714i	$-0.0578408\pi$
$578$	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	−0.995786	−	0.0917043i	$-0.970769\pi$
$587$	−21.9042	+	21.9042i	−0.904082	+	0.904082i	0.0917043	+	0.995786i	$0.470769\pi$
$588$	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	$0.117091\pi$
$593$			17.5142i			0.719222i	−0.933102	+	0.359611i	$0.882909\pi$
$594$	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	$0.127084\pi$
$599$			19.0276i			0.777447i	−0.921354	+	0.388724i	$0.872916\pi$
$600$		0			0
$601$			5.52545i			0.225388i	0.993630	+	0.112694i	$0.0359479\pi$
$601$			5.52545i			0.225388i	−0.993630	+	0.112694i	$0.964052\pi$
$602$	−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	$-0.920985\pi$
$607$		−	12.1064i		−	0.491384i	0.969348	−	0.245692i	$-0.0790151\pi$
$608$	−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	−0.249218	−	0.968448i	$-0.580173\pi$
$613$	17.8073	−	17.8073i	0.719230	−	0.719230i	0.968448	+	0.249218i	$0.0801734\pi$
$614$	−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	0.940115	+	0.340859i	$0.110718\pi$
$619$	31.8702	+	31.8702i	1.28097	+	1.28097i	0.340859	+	0.940115i	$0.389282\pi$
$620$		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	$0.0432206\pi$
$631$			6.80064i			0.270729i	−0.990796	+	0.135365i	$0.956779\pi$
$632$	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	0.363264	−	0.931686i	$-0.381662\pi$
$643$	−14.4137	−	14.4137i	−0.568422	−	0.568422i	−0.931686	+	0.363264i	$0.881662\pi$
$644$	−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	0.872355	−	0.488873i	$-0.162592\pi$
$653$	9.79946	+	9.79946i	0.383482	+	0.383482i	−0.488873	+	0.872355i	$0.662592\pi$
$654$	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	−0.516888	−	0.856053i	$-0.672910\pi$
$659$	8.70669	−	8.70669i	0.339165	−	0.339165i	0.856053	+	0.516888i	$0.172910\pi$
$660$		0			0
$661$	19.7899	+	19.7899i	0.769737	+	0.769737i	0.978060	−	0.208323i	$-0.0668006\pi$
$661$	19.7899	+	19.7899i	0.769737	+	0.769737i	−0.208323	+	0.978060i	$0.566801\pi$
$662$	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	$0.0874961\pi$
$673$			14.0829i			0.542857i	−0.962459	+	0.271429i	$0.912504\pi$
$674$	−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	0.158601	−	0.987343i	$-0.449302\pi$
$677$	29.8166	−	29.8166i	1.14594	−	1.14594i	0.987343	−	0.158601i	$-0.0506984\pi$
$678$	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	−0.899193	−	0.437552i	$-0.855845\pi$
$683$	−12.0646	+	12.0646i	−0.461641	+	0.461641i	0.437552	+	0.899193i	$0.355845\pi$
$684$	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	−0.656152	−	0.754629i	$-0.727817\pi$
$691$	2.58867	−	2.58867i	0.0984776	−	0.0984776i	0.754629	+	0.656152i	$0.227817\pi$
$692$	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	−0.0197572	+	0.999805i	$0.506289\pi$
$701$	−26.9943	+	26.9943i	−1.01956	+	1.01956i	−0.999805	+	0.0197572i	$0.993711\pi$
$702$	−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	0.916254	+	0.400598i	$0.131198\pi$
$709$	35.0639	+	35.0639i	1.31685	+	1.31685i	0.400598	+	0.916254i	$0.368802\pi$
$710$		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	0.995238	−	0.0974793i	$-0.0310780\pi$
$733$	24.3059	+	24.3059i	0.897758	+	0.897758i	−0.0974793	+	0.995238i	$0.531078\pi$
$734$	−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	−0.00580951	−	0.999983i	$-0.501849\pi$
$739$	27.0262	−	27.0262i	0.994174	−	0.994174i	0.999983	+	0.00580951i	$0.00184923\pi$
$740$		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	−0.707034	−	0.707179i	$-0.749967\pi$
$757$	0.00399171	−	0.00399171i	0.000145081	−	0.000145081i	0.707179	+	0.707034i	$0.249967\pi$
$758$	−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	$0.00433480\pi$
$761$			0.751325i			0.0272355i	−0.999907	+	0.0136178i	$0.995665\pi$
$762$	−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	−0.799094	−	0.601206i	$-0.794687\pi$
$773$	−5.50186	+	5.50186i	−0.197888	+	0.197888i	0.601206	+	0.799094i	$0.294687\pi$
$774$	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	0.999733	+	0.0231107i	$0.00735700\pi$
$787$	28.6944	+	28.6944i	1.02284	+	1.02284i	0.0231107	+	0.999733i	$0.492643\pi$
$788$	−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	0.586818	−	0.809719i	$-0.300381\pi$
$797$	−6.29277	−	6.29277i	−0.222901	−	0.222901i	−0.809719	+	0.586818i	$0.800381\pi$
$798$	−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	$-0.842040\pi$
$809$		−	27.0850i		−	0.952257i	0.879376	−	0.476128i	$-0.157960\pi$
$810$		0			0
$811$	−14.6690	−	14.6690i	−0.515098	−	0.515098i	0.400986	−	0.916084i	$-0.368668\pi$
$811$	−14.6690	−	14.6690i	−0.515098	−	0.515098i	−0.916084	+	0.400986i	$0.868668\pi$
$812$	−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	0.383553	−	0.923519i	$-0.374700\pi$
$821$	−15.4717	−	15.4717i	−0.539965	−	0.539965i	−0.923519	+	0.383553i	$0.874700\pi$
$822$	−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	−0.693394	−	0.720559i	$-0.743885\pi$
$827$	0.781185	−	0.781185i	0.0271645	−	0.0271645i	0.720559	+	0.693394i	$0.243885\pi$
$828$	−6.20697	−	30.8996i	−0.215707	−	1.07384i
$829$	−28.9122	+	28.9122i	−1.00416	+	1.00416i	−0.00417165	+	0.999991i	$0.501328\pi$
$829$	−28.9122	+	28.9122i	−1.00416	+	1.00416i	−0.999991	+	0.00417165i	$0.998672\pi$
$830$		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	$-0.786787\pi$
$839$		−	35.9665i		−	1.24170i	0.783928	−	0.620851i	$-0.213213\pi$
$840$		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	−0.545798	−	0.837917i	$-0.683773\pi$
$853$	8.53167	−	8.53167i	0.292119	−	0.292119i	0.837917	+	0.545798i	$0.183773\pi$
$854$	−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	0.0884877	−	0.996077i	$-0.471797\pi$
$859$	−26.6003	−	26.6003i	−0.907590	−	0.907590i	−0.996077	+	0.0884877i	$0.971797\pi$
$860$		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	$-0.864327\pi$
$863$		−	24.2911i		−	0.826880i	0.910531	−	0.413440i	$-0.135673\pi$
$864$	−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	0.346198	−	0.938161i	$-0.387472\pi$
$877$	−17.5305	−	17.5305i	−0.591963	−	0.591963i	−0.938161	+	0.346198i	$0.887472\pi$
$878$	−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	0.333687	−	0.942684i	$-0.391707\pi$
$883$	−18.0965	−	18.0965i	−0.608997	−	0.608997i	−0.942684	+	0.333687i	$0.891707\pi$
$884$	−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	−0.144664	−	0.989481i	$-0.546210\pi$
$907$	25.4429	−	25.4429i	0.844817	−	0.844817i	0.989481	+	0.144664i	$0.0462100\pi$
$908$	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	$-0.724091\pi$
$919$		−	46.2157i		−	1.52451i	0.647274	−	0.762257i	$-0.275909\pi$
$920$		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	−0.903638	−	0.428297i	$-0.859114\pi$
$941$	−14.5814	+	14.5814i	−0.475341	+	0.475341i	0.428297	+	0.903638i	$0.359114\pi$
$942$	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	−0.965102	−	0.261876i	$-0.915659\pi$
$947$	−37.7582	−	37.7582i	−1.22698	−	1.22698i	−0.261876	−	0.965102i	$-0.584341\pi$
$948$	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	0.897168	−	0.441690i	$-0.145621\pi$
$971$	14.1931	+	14.1931i	0.455478	+	0.455478i	−0.441690	+	0.897168i	$0.645621\pi$
$972$	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	$0.0946419\pi$
$977$			18.3144i			0.585929i	−0.956123	+	0.292965i	$0.905358\pi$
$978$	−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	−0.860868	−	0.508828i	$-0.830079\pi$
$997$	−11.1158	+	11.1158i	−0.352041	+	0.352041i	0.508828	+	0.860868i	$0.330079\pi$
$998$	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.149.6		16
4.3	odd	2		1600.2.q.h.49.1		16
5.2	odd	4		400.2.l.h.101.1		16
5.3	odd	4		80.2.l.a.21.8	✓	16
5.4	even	2		400.2.q.h.149.3		16
15.8	even	4		720.2.t.c.181.1		16
16.3	odd	4		1600.2.q.g.849.8		16
16.13	even	4		400.2.q.h.349.3		16
20.3	even	4		320.2.l.a.241.8		16
20.7	even	4		1600.2.l.i.1201.1		16
20.19	odd	2		1600.2.q.g.49.8		16
40.3	even	4		640.2.l.a.481.1		16
40.13	odd	4		640.2.l.b.481.8		16
60.23	odd	4		2880.2.t.c.2161.3		16
80.3	even	4		320.2.l.a.81.8		16
80.13	odd	4		80.2.l.a.61.8	yes	16
80.19	odd	4		1600.2.q.h.849.1		16
80.29	even	4	inner	400.2.q.g.349.6		16
80.43	even	4		640.2.l.a.161.1		16
80.53	odd	4		640.2.l.b.161.8		16
80.67	even	4		1600.2.l.i.401.1		16
80.77	odd	4		400.2.l.h.301.1		16
160.3	even	8		5120.2.a.u.1.8		8
160.13	odd	8		5120.2.a.v.1.8		8
160.83	even	8		5120.2.a.t.1.1		8
160.93	odd	8		5120.2.a.s.1.1		8
240.83	odd	4		2880.2.t.c.721.2		16
240.173	even	4		720.2.t.c.541.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.8	✓	16	5.3	odd	4
80.2.l.a.61.8	yes	16	80.13	odd	4
320.2.l.a.81.8		16	80.3	even	4
320.2.l.a.241.8		16	20.3	even	4
400.2.l.h.101.1		16	5.2	odd	4
400.2.l.h.301.1		16	80.77	odd	4
400.2.q.g.149.6		16	1.1	even	1	trivial
400.2.q.g.349.6		16	80.29	even	4	inner
400.2.q.h.149.3		16	5.4	even	2
400.2.q.h.349.3		16	16.13	even	4
640.2.l.a.161.1		16	80.43	even	4
640.2.l.a.481.1		16	40.3	even	4
640.2.l.b.161.8		16	80.53	odd	4
640.2.l.b.481.8		16	40.13	odd	4
720.2.t.c.181.1		16	15.8	even	4
720.2.t.c.541.1		16	240.173	even	4
1600.2.l.i.401.1		16	80.67	even	4
1600.2.l.i.1201.1		16	20.7	even	4
1600.2.q.g.49.8		16	20.19	odd	2
1600.2.q.g.849.8		16	16.3	odd	4
1600.2.q.h.49.1		16	4.3	odd	2
1600.2.q.h.849.1		16	80.19	odd	4
2880.2.t.c.721.2		16	240.83	odd	4
2880.2.t.c.2161.3		16	60.23	odd	4
5120.2.a.s.1.1		8	160.93	odd	8
5120.2.a.t.1.1		8	160.83	even	8
5120.2.a.u.1.8		8	160.3	even	8
5120.2.a.v.1.8		8	160.13	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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