LMFDB - Embedded newform 450.2.p.e.293.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(257,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("450.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.p (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			293.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	450.293
Dual form			450.2.p.e.407.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-1.22474 + 1.22474i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.866025 - 1.50000i) q^{6} +(-4.57081 - 1.22474i) q^{7} +(0.707107 - 0.707107i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.22474 + 1.22474i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.866025 - 1.50000i) q^{6} +(-4.57081 - 1.22474i) q^{7} +(0.707107 - 0.707107i) q^{8} -3.00000i q^{9} +(3.00000 - 1.73205i) q^{11} +(1.67303 - 0.448288i) q^{12} +(4.57081 - 1.22474i) q^{13} +(2.36603 - 4.09808i) q^{14} +(0.500000 + 0.866025i) q^{16} +(2.89778 + 0.776457i) q^{18} +3.19615i q^{19} +(7.09808 - 4.09808i) q^{21} +(0.896575 + 3.34607i) q^{22} +(-0.568406 - 2.12132i) q^{23} +1.73205i q^{24} +4.73205i q^{26} +(3.67423 + 3.67423i) q^{27} +(3.34607 + 3.34607i) q^{28} +(-5.36603 - 9.29423i) q^{29} +(-0.0980762 + 0.169873i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-1.55291 + 5.79555i) q^{33} +(-1.50000 + 2.59808i) q^{36} +(5.79555 - 5.79555i) q^{37} +(-3.08725 - 0.827225i) q^{38} +(-4.09808 + 7.09808i) q^{39} +(-1.50000 - 0.866025i) q^{41} +(2.12132 + 7.91688i) q^{42} +(-0.120118 + 0.448288i) q^{43} -3.46410 q^{44} +2.19615 q^{46} +(1.55291 - 5.79555i) q^{47} +(-1.67303 - 0.448288i) q^{48} +(13.3301 + 7.69615i) q^{49} +(-4.57081 - 1.22474i) q^{52} +(5.79555 - 5.79555i) q^{53} +(-4.50000 + 2.59808i) q^{54} +(-4.09808 + 2.36603i) q^{56} +(-3.91447 - 3.91447i) q^{57} +(10.3664 - 2.77766i) q^{58} +(2.76795 - 4.79423i) q^{59} +(2.00000 + 3.46410i) q^{61} +(-0.138701 - 0.138701i) q^{62} +(-3.67423 + 13.7124i) q^{63} -1.00000i q^{64} +(-5.19615 - 3.00000i) q^{66} +(-1.43280 - 5.34727i) q^{67} +(3.29423 + 1.90192i) q^{69} -7.26795i q^{71} +(-2.12132 - 2.12132i) q^{72} +(-3.67423 - 3.67423i) q^{73} +(4.09808 + 7.09808i) q^{74} +(1.59808 - 2.76795i) q^{76} +(-15.8338 + 4.24264i) q^{77} +(-5.79555 - 5.79555i) q^{78} +(-8.66025 + 5.00000i) q^{79} -9.00000 q^{81} +(1.22474 - 1.22474i) q^{82} +(-16.6102 - 4.45069i) q^{83} -8.19615 q^{84} +(-0.401924 - 0.232051i) q^{86} +(17.9551 + 4.81105i) q^{87} +(0.896575 - 3.34607i) q^{88} +8.66025 q^{89} -22.3923 q^{91} +(-0.568406 + 2.12132i) q^{92} +(-0.0879327 - 0.328169i) q^{93} +(5.19615 + 3.00000i) q^{94} +(0.866025 - 1.50000i) q^{96} +(-2.56961 - 0.688524i) q^{97} +(-10.8840 + 10.8840i) q^{98} +(-5.19615 - 9.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q + 24 q^{11} + 12 q^{14} + 4 q^{16} + 36 q^{21} - 36 q^{29} + 20 q^{31} - 12 q^{36} - 12 q^{39} - 12 q^{41} - 24 q^{46} + 72 q^{49} - 36 q^{54} - 12 q^{56} + 36 q^{59} + 16 q^{61} - 36 q^{69} + 12 q^{74} - 8 q^{76} - 72 q^{81} - 24 q^{84} - 24 q^{86} - 96 q^{91}+O(q^{100}) $ 8 * q + 24 * q^11 + 12 * q^14 + 4 * q^16 + 36 * q^21 - 36 * q^29 + 20 * q^31 - 12 * q^36 - 12 * q^39 - 12 * q^41 - 24 * q^46 + 72 * q^49 - 36 * q^54 - 12 * q^56 + 36 * q^59 + 16 * q^61 - 36 * q^69 + 12 * q^74 - 8 * q^76 - 72 * q^81 - 24 * q^84 - 24 * q^86 - 96 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	−1.22474	+	1.22474i	−0.707107	+	0.707107i
$3$	−1.22474	+	1.22474i	−0.707107	+	0.707107i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$	−0.866025	−	1.50000i	−0.353553	−	0.612372i
$7$	−4.57081	−	1.22474i	−1.72760	−	0.462910i	−0.747975	−	0.663727i	$-0.768974\pi$
$7$	−4.57081	−	1.22474i	−1.72760	−	0.462910i	−0.979629	+	0.200817i	$0.935640\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		−	3.00000i		−	1.00000i
$10$		0			0
$11$	3.00000	−	1.73205i	0.904534	−	0.522233i	0.0258656	−	0.999665i	$-0.491766\pi$
$11$	3.00000	−	1.73205i	0.904534	−	0.522233i	0.878668	+	0.477432i	$0.158432\pi$
$12$	1.67303	−	0.448288i	0.482963	−	0.129410i
$13$	4.57081	−	1.22474i	1.26771	−	0.339683i	0.438560	−	0.898702i	$-0.355489\pi$
$13$	4.57081	−	1.22474i	1.26771	−	0.339683i	0.829155	+	0.559019i	$0.188822\pi$
$14$	2.36603	−	4.09808i	0.632347	−	1.09526i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$17$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$18$	2.89778	+	0.776457i	0.683013	+	0.183013i
$19$			3.19615i			0.733248i	0.930369	+	0.366624i	$0.119486\pi$
$19$			3.19615i			0.733248i	−0.930369	+	0.366624i	$0.880514\pi$
$20$		0			0
$21$	7.09808	−	4.09808i	1.54893	−	0.894274i
$22$	0.896575	+	3.34607i	0.191151	+	0.713384i
$23$	−0.568406	−	2.12132i	−0.118521	−	0.442326i	0.881005	−	0.473106i	$-0.156867\pi$
$23$	−0.568406	−	2.12132i	−0.118521	−	0.442326i	−0.999526	+	0.0307805i	$0.990201\pi$
$24$			1.73205i			0.353553i
$25$		0			0
$26$			4.73205i			0.928032i
$27$	3.67423	+	3.67423i	0.707107	+	0.707107i
$28$	3.34607	+	3.34607i	0.632347	+	0.632347i
$29$	−5.36603	−	9.29423i	−0.996446	−	1.72589i	−0.571173	−	0.820830i	$-0.693511\pi$
$29$	−5.36603	−	9.29423i	−0.996446	−	1.72589i	−0.425273	−	0.905065i	$-0.639822\pi$
$30$		0			0
$31$	−0.0980762	+	0.169873i	−0.0176150	+	0.0305101i	−0.874699	−	0.484667i	$-0.838941\pi$
$31$	−0.0980762	+	0.169873i	−0.0176150	+	0.0305101i	0.857084	+	0.515177i	$0.172274\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−1.55291	+	5.79555i	−0.270328	+	1.00888i
$34$		0			0
$35$		0			0
$36$	−1.50000	+	2.59808i	−0.250000	+	0.433013i
$37$	5.79555	−	5.79555i	0.952783	−	0.952783i	−0.0461511	−	0.998934i	$-0.514696\pi$
$37$	5.79555	−	5.79555i	0.952783	−	0.952783i	0.998934	+	0.0461511i	$0.0146956\pi$
$38$	−3.08725	−	0.827225i	−0.500817	−	0.134194i
$39$	−4.09808	+	7.09808i	−0.656217	+	1.13660i
$40$		0			0
$41$	−1.50000	−	0.866025i	−0.234261	−	0.135250i	0.378275	−	0.925693i	$-0.376517\pi$
$41$	−1.50000	−	0.866025i	−0.234261	−	0.135250i	−0.612536	+	0.790443i	$0.709851\pi$
$42$	2.12132	+	7.91688i	0.327327	+	1.22160i
$43$	−0.120118	+	0.448288i	−0.0183179	+	0.0683632i	−0.974480	−	0.224475i	$-0.927933\pi$
$43$	−0.120118	+	0.448288i	−0.0183179	+	0.0683632i	0.956162	+	0.292839i	$0.0945999\pi$
$44$	−3.46410			−0.522233
$45$		0			0
$46$	2.19615			0.323805
$47$	1.55291	−	5.79555i	0.226516	−	0.845369i	−0.755276	−	0.655407i	$-0.772497\pi$
$47$	1.55291	−	5.79555i	0.226516	−	0.845369i	0.981792	−	0.189961i	$-0.0608363\pi$
$48$	−1.67303	−	0.448288i	−0.241481	−	0.0647048i
$49$	13.3301	+	7.69615i	1.90430	+	1.09945i
$50$		0			0
$51$		0			0
$52$	−4.57081	−	1.22474i	−0.633857	−	0.169842i
$53$	5.79555	−	5.79555i	0.796081	−	0.796081i	−0.186394	−	0.982475i	$-0.559680\pi$
$53$	5.79555	−	5.79555i	0.796081	−	0.796081i	0.982475	+	0.186394i	$0.0596802\pi$
$54$	−4.50000	+	2.59808i	−0.612372	+	0.353553i
$55$		0			0
$56$	−4.09808	+	2.36603i	−0.547628	+	0.316173i
$57$	−3.91447	−	3.91447i	−0.518484	−	0.518484i
$58$	10.3664	−	2.77766i	1.36117	−	0.364725i
$59$	2.76795	−	4.79423i	0.360356	−	0.624155i	−0.627663	−	0.778485i	$-0.715988\pi$
$59$	2.76795	−	4.79423i	0.360356	−	0.624155i	0.988019	+	0.154330i	$0.0493218\pi$
$60$		0			0
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	0.965187	−	0.261562i	$-0.0842377\pi$
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	−0.709113	+	0.705095i	$0.750904\pi$
$62$	−0.138701	−	0.138701i	−0.0176150	−	0.0176150i
$63$	−3.67423	+	13.7124i	−0.462910	+	1.72760i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	−5.19615	−	3.00000i	−0.639602	−	0.369274i
$67$	−1.43280	−	5.34727i	−0.175044	−	0.653273i	−0.996544	−	0.0830646i	$-0.973529\pi$
$67$	−1.43280	−	5.34727i	−0.175044	−	0.653273i	0.821500	−	0.570208i	$-0.193137\pi$
$68$		0			0
$69$	3.29423	+	1.90192i	0.396579	+	0.228965i
$70$		0			0
$71$		−	7.26795i		−	0.862547i	−0.902221	−	0.431273i	$-0.858064\pi$
$71$		−	7.26795i		−	0.862547i	0.902221	−	0.431273i	$-0.141936\pi$
$72$	−2.12132	−	2.12132i	−0.250000	−	0.250000i
$73$	−3.67423	−	3.67423i	−0.430037	−	0.430037i	0.458604	−	0.888641i	$-0.348350\pi$
$73$	−3.67423	−	3.67423i	−0.430037	−	0.430037i	−0.888641	+	0.458604i	$0.848350\pi$
$74$	4.09808	+	7.09808i	0.476392	+	0.825135i
$75$		0			0
$76$	1.59808	−	2.76795i	0.183312	−	0.317506i
$77$	−15.8338	+	4.24264i	−1.80442	+	0.483494i
$78$	−5.79555	−	5.79555i	−0.656217	−	0.656217i
$79$	−8.66025	+	5.00000i	−0.974355	+	0.562544i	−0.900561	−	0.434730i	$-0.856844\pi$
$79$	−8.66025	+	5.00000i	−0.974355	+	0.562544i	−0.0737937	+	0.997274i	$0.523511\pi$
$80$		0			0
$81$	−9.00000			−1.00000
$82$	1.22474	−	1.22474i	0.135250	−	0.135250i
$83$	−16.6102	−	4.45069i	−1.82321	−	0.488527i	−0.826031	−	0.563625i	$-0.809406\pi$
$83$	−16.6102	−	4.45069i	−1.82321	−	0.488527i	−0.997176	+	0.0750978i	$0.976073\pi$
$84$	−8.19615			−0.894274
$85$		0			0
$86$	−0.401924	−	0.232051i	−0.0433406	−	0.0250227i
$87$	17.9551	+	4.81105i	1.92499	+	0.515798i
$88$	0.896575	−	3.34607i	0.0955753	−	0.356692i
$89$	8.66025			0.917985			0.458993	−	0.888440i	$-0.348210\pi$
$89$	8.66025			0.917985			0.458993	+	0.888440i	$0.348210\pi$
$90$		0			0
$91$	−22.3923			−2.34735
$92$	−0.568406	+	2.12132i	−0.0592604	+	0.221163i
$93$	−0.0879327	−	0.328169i	−0.00911820	−	0.0340296i
$94$	5.19615	+	3.00000i	0.535942	+	0.309426i
$95$		0			0
$96$	0.866025	−	1.50000i	0.0883883	−	0.153093i
$97$	−2.56961	−	0.688524i	−0.260904	−	0.0699091i	0.125996	−	0.992031i	$-0.459787\pi$
$97$	−2.56961	−	0.688524i	−0.260904	−	0.0699091i	−0.386900	+	0.922122i	$0.626454\pi$
$98$	−10.8840	+	10.8840i	−1.09945	+	1.09945i
$99$	−5.19615	−	9.00000i	−0.522233	−	0.904534i
$100$		0			0
$101$	6.29423	−	3.63397i	0.626299	−	0.361594i	−0.153018	−	0.988223i	$-0.548899\pi$
$101$	6.29423	−	3.63397i	0.626299	−	0.361594i	0.779317	+	0.626629i	$0.215566\pi$
$102$		0			0
$103$	−10.0382	+	2.68973i	−0.989093	+	0.265027i	−0.716869	−	0.697207i	$-0.754426\pi$
$103$	−10.0382	+	2.68973i	−0.989093	+	0.265027i	−0.272223	+	0.962234i	$0.587759\pi$
$104$	2.36603	−	4.09808i	0.232008	−	0.401849i
$105$		0			0
$106$	4.09808	+	7.09808i	0.398040	+	0.689426i
$107$	7.91688	+	7.91688i	0.765353	+	0.765353i	0.977285	−	0.211931i	$-0.0679753\pi$
$107$	7.91688	+	7.91688i	0.765353	+	0.765353i	−0.211931	+	0.977285i	$0.567975\pi$
$108$	−1.34486	−	5.01910i	−0.129410	−	0.482963i
$109$		−	1.80385i		−	0.172777i	−0.996262	−	0.0863886i	$-0.972467\pi$
$109$		−	1.80385i		−	0.172777i	0.996262	−	0.0863886i	$-0.0275327\pi$
$110$		0			0
$111$			14.1962i			1.34744i
$112$	−1.22474	−	4.57081i	−0.115728	−	0.431901i
$113$	−3.46618	−	12.9360i	−0.326071	−	1.21691i	−0.913231	−	0.407443i	$-0.866421\pi$
$113$	−3.46618	−	12.9360i	−0.326071	−	1.21691i	0.587160	−	0.809471i	$-0.300246\pi$
$114$	4.79423	−	2.76795i	0.449021	−	0.259242i
$115$		0			0
$116$			10.7321i			0.996446i
$117$	−3.67423	−	13.7124i	−0.339683	−	1.26771i
$118$	3.91447	+	3.91447i	0.360356	+	0.360356i
$119$		0			0
$120$		0			0
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	−3.86370	+	1.03528i	−0.349803	+	0.0937295i
$123$	2.89778	−	0.776457i	0.261284	−	0.0700108i
$124$	0.169873	−	0.0980762i	0.0152550	−	0.00880750i
$125$		0			0
$126$	−12.2942	−	7.09808i	−1.09526	−	0.632347i
$127$	5.79555	−	5.79555i	0.514272	−	0.514272i	−0.401560	−	0.915833i	$-0.631532\pi$
$127$	5.79555	−	5.79555i	0.514272	−	0.514272i	0.915833	+	0.401560i	$0.131532\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	−0.401924	−	0.696152i	−0.0353874	−	0.0612928i
$130$		0			0
$131$	−6.00000	−	3.46410i	−0.524222	−	0.302660i	0.214438	−	0.976738i	$-0.431208\pi$
$131$	−6.00000	−	3.46410i	−0.524222	−	0.302660i	−0.738661	+	0.674078i	$0.764541\pi$
$132$	4.24264	−	4.24264i	0.369274	−	0.369274i
$133$	3.91447	−	14.6090i	0.339428	−	1.26676i
$134$	5.53590			0.478229
$135$		0			0
$136$		0			0
$137$	−3.46618	+	12.9360i	−0.296136	+	1.10519i	0.644175	+	0.764878i	$0.277201\pi$
$137$	−3.46618	+	12.9360i	−0.296136	+	1.10519i	−0.940311	+	0.340317i	$0.889466\pi$
$138$	−2.68973	+	2.68973i	−0.228965	+	0.228965i
$139$	6.92820	+	4.00000i	0.587643	+	0.339276i	0.764165	−	0.645021i	$-0.223151\pi$
$139$	6.92820	+	4.00000i	0.587643	+	0.339276i	−0.176522	+	0.984297i	$0.556485\pi$
$140$		0			0
$141$	5.19615	+	9.00000i	0.437595	+	0.757937i
$142$	7.02030	+	1.88108i	0.589130	+	0.157857i
$143$	11.5911	−	11.5911i	0.969297	−	0.969297i
$144$	2.59808	−	1.50000i	0.216506	−	0.125000i
$145$		0			0
$146$	4.50000	−	2.59808i	0.372423	−	0.215018i
$147$	−25.7518	+	6.90018i	−2.12397	+	0.569117i
$148$	−7.91688	+	2.12132i	−0.650763	+	0.174371i
$149$	−9.00000	+	15.5885i	−0.737309	+	1.27706i	0.216394	+	0.976306i	$0.430570\pi$
$149$	−9.00000	+	15.5885i	−0.737309	+	1.27706i	−0.953703	+	0.300750i	$0.902763\pi$
$150$		0			0
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	0.981617	−	0.190864i	$-0.0611289\pi$
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	−0.656101	+	0.754673i	$0.727796\pi$
$152$	2.26002	+	2.26002i	0.183312	+	0.183312i
$153$		0			0
$154$		−	16.3923i		−	1.32093i
$155$		0			0
$156$	7.09808	−	4.09808i	0.568301	−	0.328109i
$157$	5.13922	+	19.1798i	0.410154	+	1.53072i	0.794348	+	0.607463i	$0.207813\pi$
$157$	5.13922	+	19.1798i	0.410154	+	1.53072i	−0.384194	+	0.923253i	$0.625520\pi$
$158$	−2.58819	−	9.65926i	−0.205905	−	0.768449i
$159$			14.1962i			1.12583i
$160$		0			0
$161$			10.3923i			0.819028i
$162$	2.32937	−	8.69333i	0.183013	−	0.683013i
$163$	10.1261	+	10.1261i	0.793140	+	0.793140i	0.982003	−	0.188864i	$-0.0604804\pi$
$163$	10.1261	+	10.1261i	0.793140	+	0.793140i	−0.188864	+	0.982003i	$0.560480\pi$
$164$	0.866025	+	1.50000i	0.0676252	+	0.117130i
$165$		0			0
$166$	8.59808	−	14.8923i	0.667340	−	1.15587i
$167$	15.8338	−	4.24264i	1.22525	−	0.328305i	0.412523	−	0.910947i	$-0.364648\pi$
$167$	15.8338	−	4.24264i	1.22525	−	0.328305i	0.812729	+	0.582642i	$0.197981\pi$
$168$	2.12132	−	7.91688i	0.163663	−	0.610800i
$169$	8.13397	−	4.69615i	0.625690	−	0.361242i
$170$		0			0
$171$	9.58846			0.733248
$172$	0.328169	−	0.328169i	0.0250227	−	0.0250227i
$173$	15.8338	+	4.24264i	1.20382	+	0.322562i	0.804334	−	0.594178i	$-0.202523\pi$
$173$	15.8338	+	4.24264i	1.20382	+	0.322562i	0.399484	+	0.916740i	$0.369189\pi$
$174$	−9.29423	+	16.0981i	−0.704594	+	1.22039i
$175$		0			0
$176$	3.00000	+	1.73205i	0.226134	+	0.130558i
$177$	2.48168	+	9.26174i	0.186534	+	0.696155i
$178$	−2.24144	+	8.36516i	−0.168003	+	0.626995i
$179$	−22.8564			−1.70837			−0.854184	−	0.519971i	$-0.825943\pi$
$179$	−22.8564			−1.70837			−0.854184	+	0.519971i	$0.825943\pi$
$180$		0			0
$181$	−12.3923			−0.921113			−0.460556	−	0.887630i	$-0.652350\pi$
$181$	−12.3923			−0.921113			−0.460556	+	0.887630i	$0.652350\pi$
$182$	5.79555	−	21.6293i	0.429595	−	1.60327i
$183$	−6.69213	−	1.79315i	−0.494697	−	0.132554i
$184$	−1.90192	−	1.09808i	−0.140212	−	0.0809513i
$185$		0			0
$186$	0.339746			0.0249114
$187$		0			0
$188$	−4.24264	+	4.24264i	−0.309426	+	0.309426i
$189$	−12.2942	−	21.2942i	−0.894274	−	1.54893i
$190$		0			0
$191$	3.00000	−	1.73205i	0.217072	−	0.125327i	−0.387522	−	0.921861i	$-0.626669\pi$
$191$	3.00000	−	1.73205i	0.217072	−	0.125327i	0.604594	+	0.796534i	$0.293335\pi$
$192$	1.22474	+	1.22474i	0.0883883	+	0.0883883i
$193$	−10.6945	+	2.86559i	−0.769809	+	0.206270i	−0.622287	−	0.782789i	$-0.713796\pi$
$193$	−10.6945	+	2.86559i	−0.769809	+	0.206270i	−0.147522	+	0.989059i	$0.547130\pi$
$194$	1.33013	−	2.30385i	0.0954976	−	0.165407i
$195$		0			0
$196$	−7.69615	−	13.3301i	−0.549725	−	0.952152i
$197$	−10.0382	−	10.0382i	−0.715192	−	0.715192i	0.252425	−	0.967617i	$-0.418772\pi$
$197$	−10.0382	−	10.0382i	−0.715192	−	0.715192i	−0.967617	+	0.252425i	$0.918772\pi$
$198$	10.0382	−	2.68973i	0.713384	−	0.191151i
$199$		−	20.3923i		−	1.44557i	−0.691072	−	0.722786i	$-0.742861\pi$
$199$		−	20.3923i		−	1.44557i	0.691072	−	0.722786i	$-0.257139\pi$
$200$		0			0
$201$	8.30385	+	4.79423i	0.585708	+	0.338159i
$202$	1.88108	+	7.02030i	0.132353	+	0.493947i
$203$	13.1440	+	49.0542i	0.922530	+	3.44293i
$204$		0			0
$205$		0			0
$206$		−	10.3923i		−	0.724066i
$207$	−6.36396	+	1.70522i	−0.442326	+	0.118521i
$208$	3.34607	+	3.34607i	0.232008	+	0.232008i
$209$	5.53590	+	9.58846i	0.382926	+	0.663247i
$210$		0			0
$211$	−0.598076	+	1.03590i	−0.0411733	+	0.0713142i	−0.885878	−	0.463919i	$-0.846443\pi$
$211$	−0.598076	+	1.03590i	−0.0411733	+	0.0713142i	0.844704	+	0.535233i	$0.179776\pi$
$212$	−7.91688	+	2.12132i	−0.543733	+	0.145693i
$213$	8.90138	+	8.90138i	0.609913	+	0.609913i
$214$	−9.69615	+	5.59808i	−0.662815	+	0.382677i
$215$		0			0
$216$	5.19615			0.353553
$217$	0.656339	−	0.656339i	0.0445552	−	0.0445552i
$218$	1.74238	+	0.466870i	0.118009	+	0.0316204i
$219$	9.00000			0.608164
$220$		0			0
$221$		0			0
$222$	−13.7124	−	3.67423i	−0.920318	−	0.246598i
$223$	−0.656339	+	2.44949i	−0.0439517	+	0.164030i	−0.984414	−	0.175869i	$-0.943726\pi$
$223$	−0.656339	+	2.44949i	−0.0439517	+	0.164030i	0.940462	+	0.339899i	$0.110393\pi$
$224$	4.73205			0.316173
$225$		0			0
$226$	13.3923			0.890843
$227$	−3.31388	+	12.3676i	−0.219950	+	0.820864i	0.764415	+	0.644724i	$0.223028\pi$
$227$	−3.31388	+	12.3676i	−0.219950	+	0.820864i	−0.984365	+	0.176140i	$0.943639\pi$
$228$	1.43280	+	5.34727i	0.0948892	+	0.354131i
$229$	5.02628	+	2.90192i	0.332146	+	0.191765i	0.656793	−	0.754071i	$-0.271912\pi$
$229$	5.02628	+	2.90192i	0.332146	+	0.191765i	−0.324648	+	0.945835i	$0.605246\pi$
$230$		0			0
$231$	14.1962	−	24.5885i	0.934038	−	1.61780i
$232$	−10.3664	−	2.77766i	−0.680585	−	0.182362i
$233$	3.25813	−	3.25813i	0.213447	−	0.213447i	−0.592283	−	0.805730i	$-0.701773\pi$
$233$	3.25813	−	3.25813i	0.213447	−	0.213447i	0.805730	+	0.592283i	$0.201773\pi$
$234$	14.1962			0.928032
$235$		0			0
$236$	−4.79423	+	2.76795i	−0.312078	+	0.180178i
$237$	4.48288	−	16.7303i	0.291194	−	1.08675i
$238$		0			0
$239$	1.90192	−	3.29423i	0.123025	−	0.213086i	−0.797934	−	0.602745i	$-0.794074\pi$
$239$	1.90192	−	3.29423i	0.123025	−	0.213086i	0.920959	+	0.389659i	$0.127407\pi$
$240$		0			0
$241$	−4.69615	−	8.13397i	−0.302506	−	0.523955i	0.674197	−	0.738551i	$-0.264490\pi$
$241$	−4.69615	−	8.13397i	−0.302506	−	0.523955i	−0.976703	+	0.214596i	$0.931156\pi$
$242$	0.707107	+	0.707107i	0.0454545	+	0.0454545i
$243$	11.0227	−	11.0227i	0.707107	−	0.707107i
$244$		−	4.00000i		−	0.256074i
$245$		0			0
$246$			3.00000i			0.191273i
$247$	3.91447	+	14.6090i	0.249072	+	0.929549i
$248$	0.0507680	+	0.189469i	0.00322377	+	0.0120313i
$249$	25.7942	−	14.8923i	1.63464	−	0.943761i
$250$		0			0
$251$		−	9.00000i		−	0.568075i	−0.958813	−	0.284037i	$-0.908326\pi$
$251$		−	9.00000i		−	0.568075i	0.958813	−	0.284037i	$-0.0916740\pi$
$252$	10.0382	−	10.0382i	0.632347	−	0.632347i
$253$	−5.37945	−	5.37945i	−0.338203	−	0.338203i
$254$	4.09808	+	7.09808i	0.257136	+	0.445373i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	24.5271	−	6.57201i	1.52996	−	0.409951i	0.606952	−	0.794738i	$-0.292392\pi$
$257$	24.5271	−	6.57201i	1.52996	−	0.409951i	0.923005	+	0.384787i	$0.125725\pi$
$258$	0.776457	−	0.208051i	0.0483401	−	0.0129527i
$259$	−33.5885	+	19.3923i	−2.08709	+	1.20498i
$260$		0			0
$261$	−27.8827	+	16.0981i	−1.72589	+	0.996446i
$262$	4.89898	−	4.89898i	0.302660	−	0.302660i
$263$	12.1595	+	3.25813i	0.749788	+	0.200905i	0.613424	−	0.789754i	$-0.289792\pi$
$263$	12.1595	+	3.25813i	0.749788	+	0.200905i	0.136364	+	0.990659i	$0.456458\pi$
$264$	3.00000	+	5.19615i	0.184637	+	0.319801i
$265$		0			0
$266$	13.0981	+	7.56218i	0.803095	+	0.463667i
$267$	−10.6066	+	10.6066i	−0.649113	+	0.649113i
$268$	−1.43280	+	5.34727i	−0.0875219	+	0.326636i
$269$	10.0526			0.612915			0.306458	−	0.951884i	$-0.400856\pi$
$269$	10.0526			0.612915			0.306458	+	0.951884i	$0.400856\pi$
$270$		0			0
$271$	26.5885			1.61513			0.807567	−	0.589776i	$-0.200784\pi$
$271$	26.5885			1.61513			0.807567	+	0.589776i	$0.200784\pi$
$272$		0			0
$273$	27.4249	−	27.4249i	1.65983	−	1.65983i
$274$	−11.5981	−	6.69615i	−0.700665	−	0.404529i
$275$		0			0
$276$	−1.90192	−	3.29423i	−0.114482	−	0.198289i
$277$	−18.8516	−	5.05128i	−1.13269	−	0.303502i	−0.356679	−	0.934227i	$-0.616091\pi$
$277$	−18.8516	−	5.05128i	−1.13269	−	0.303502i	−0.776007	+	0.630725i	$0.782758\pi$
$278$	−5.65685	+	5.65685i	−0.339276	+	0.339276i
$279$	0.509619	+	0.294229i	0.0305101	+	0.0176150i
$280$		0			0
$281$	9.00000	−	5.19615i	0.536895	−	0.309976i	−0.206925	−	0.978357i	$-0.566345\pi$
$281$	9.00000	−	5.19615i	0.536895	−	0.309976i	0.743820	+	0.668380i	$0.233012\pi$
$282$	−10.0382	+	2.68973i	−0.597766	+	0.160171i
$283$	3.79435	−	1.01669i	0.225551	−	0.0604362i	−0.144274	−	0.989538i	$-0.546085\pi$
$283$	3.79435	−	1.01669i	0.225551	−	0.0604362i	0.369824	+	0.929102i	$0.379418\pi$
$284$	−3.63397	+	6.29423i	−0.215637	+	0.373494i
$285$		0			0
$286$	8.19615	+	14.1962i	0.484649	+	0.839436i
$287$	5.79555	+	5.79555i	0.342101	+	0.342101i
$288$	0.776457	+	2.89778i	0.0457532	+	0.170753i
$289$		−	17.0000i		−	1.00000i
$290$		0			0
$291$	3.99038	−	2.30385i	0.233920	−	0.135054i
$292$	1.34486	+	5.01910i	0.0787022	+	0.293720i
$293$	−0.984508	−	3.67423i	−0.0575156	−	0.214651i	0.931187	−	0.364542i	$-0.118774\pi$
$293$	−0.984508	−	3.67423i	−0.0575156	−	0.214651i	−0.988703	+	0.149891i	$0.952108\pi$
$294$		−	26.6603i		−	1.55486i
$295$		0			0
$296$		−	8.19615i		−	0.476392i
$297$	17.3867	+	4.65874i	1.00888	+	0.270328i
$298$	−12.7279	−	12.7279i	−0.737309	−	0.737309i
$299$	−5.19615	−	9.00000i	−0.300501	−	0.520483i
$300$		0			0
$301$	1.09808	−	1.90192i	0.0632921	−	0.109625i
$302$	−7.72741	+	2.07055i	−0.444662	+	0.119147i
$303$	−3.25813	+	12.1595i	−0.187175	+	0.698546i
$304$	−2.76795	+	1.59808i	−0.158753	+	0.0916560i
$305$		0			0
$306$		0			0
$307$	2.44949	−	2.44949i	0.139800	−	0.139800i	−0.633743	−	0.773543i	$-0.718483\pi$
$307$	2.44949	−	2.44949i	0.139800	−	0.139800i	0.773543	+	0.633743i	$0.218483\pi$
$308$	15.8338	+	4.24264i	0.902212	+	0.241747i
$309$	9.00000	−	15.5885i	0.511992	−	0.886796i
$310$		0			0
$311$	−9.58846	−	5.53590i	−0.543712	−	0.313912i	0.202870	−	0.979206i	$-0.434973\pi$
$311$	−9.58846	−	5.53590i	−0.543712	−	0.313912i	−0.746582	+	0.665294i	$0.768306\pi$
$312$	2.12132	+	7.91688i	0.120096	+	0.448205i
$313$	−5.34727	+	19.9563i	−0.302245	+	1.12800i	0.633045	+	0.774115i	$0.281805\pi$
$313$	−5.34727	+	19.9563i	−0.302245	+	1.12800i	−0.935291	+	0.353880i	$0.884862\pi$
$314$	−19.8564			−1.12056
$315$		0			0
$316$	10.0000			0.562544
$317$	1.70522	−	6.36396i	0.0957746	−	0.357436i	−0.901361	−	0.433068i	$-0.857431\pi$
$317$	1.70522	−	6.36396i	0.0957746	−	0.357436i	0.997136	+	0.0756325i	$0.0240976\pi$
$318$	−13.7124	−	3.67423i	−0.768955	−	0.206041i
$319$	−32.1962	−	18.5885i	−1.80264	−	1.04075i
$320$		0			0
$321$	−19.3923			−1.08237
$322$	−10.0382	−	2.68973i	−0.559407	−	0.149893i
$323$		0			0
$324$	7.79423	+	4.50000i	0.433013	+	0.250000i
$325$		0			0
$326$	−12.4019	+	7.16025i	−0.686879	+	0.396570i
$327$	2.20925	+	2.20925i	0.122172	+	0.122172i
$328$	−1.67303	+	0.448288i	−0.0923778	+	0.0247525i
$329$	−14.1962	+	24.5885i	−0.782659	+	1.35561i
$330$		0			0
$331$	6.79423	+	11.7679i	0.373445	+	0.646825i	0.990093	−	0.140414i	$-0.0448433\pi$
$331$	6.79423	+	11.7679i	0.373445	+	0.646825i	−0.616648	+	0.787239i	$0.711510\pi$
$332$	12.1595	+	12.1595i	0.667340	+	0.667340i
$333$	−17.3867	−	17.3867i	−0.952783	−	0.952783i
$334$			16.3923i			0.896947i
$335$		0			0
$336$	7.09808	+	4.09808i	0.387232	+	0.223568i
$337$	5.31508	+	19.8362i	0.289531	+	1.08054i	0.945464	+	0.325725i	$0.105609\pi$
$337$	5.31508	+	19.8362i	0.289531	+	1.08054i	−0.655933	+	0.754819i	$0.727725\pi$
$338$	2.43091	+	9.07227i	0.132224	+	0.493466i
$339$	20.0885	+	11.5981i	1.09106	+	0.629921i
$340$		0			0
$341$			0.679492i			0.0367966i
$342$	−2.48168	+	9.26174i	−0.134194	+	0.500817i
$343$	−28.0812	−	28.0812i	−1.51624	−	1.51624i
$344$	0.232051	+	0.401924i	0.0125113	+	0.0216703i
$345$		0			0
$346$	−8.19615	+	14.1962i	−0.440628	+	0.763190i
$347$	8.48528	−	2.27362i	0.455514	−	0.122055i	−0.0237644	−	0.999718i	$-0.507565\pi$
$347$	8.48528	−	2.27362i	0.455514	−	0.122055i	0.479278	+	0.877663i	$0.340898\pi$
$348$	−13.1440	−	13.1440i	−0.704594	−	0.704594i
$349$	−1.73205	+	1.00000i	−0.0927146	+	0.0535288i	−0.545640	−	0.838019i	$-0.683714\pi$
$349$	−1.73205	+	1.00000i	−0.0927146	+	0.0535288i	0.452926	+	0.891548i	$0.350380\pi$
$350$		0			0
$351$	21.2942	+	12.2942i	1.13660	+	0.656217i
$352$	−2.44949	+	2.44949i	−0.130558	+	0.130558i
$353$	−14.4889	−	3.88229i	−0.771166	−	0.206633i	−0.148279	−	0.988946i	$-0.547373\pi$
$353$	−14.4889	−	3.88229i	−0.771166	−	0.206633i	−0.622886	+	0.782312i	$0.714040\pi$
$354$	−9.58846			−0.509621
$355$		0			0
$356$	−7.50000	−	4.33013i	−0.397499	−	0.229496i
$357$		0			0
$358$	5.91567	−	22.0776i	0.312653	−	1.16684i
$359$	35.3205			1.86415			0.932073	−	0.362272i	$-0.117999\pi$
$359$	35.3205			1.86415			0.932073	+	0.362272i	$0.117999\pi$
$360$		0			0
$361$	8.78461			0.462348
$362$	3.20736	−	11.9700i	0.168575	−	0.629132i
$363$	0.448288	+	1.67303i	0.0235290	+	0.0878114i
$364$	19.3923	+	11.1962i	1.01643	+	0.586838i
$365$		0			0
$366$	3.46410	−	6.00000i	0.181071	−	0.313625i
$367$	−4.00240	−	1.07244i	−0.208924	−	0.0559810i	0.152839	−	0.988251i	$-0.451158\pi$
$367$	−4.00240	−	1.07244i	−0.208924	−	0.0559810i	−0.361763	+	0.932270i	$0.617825\pi$
$368$	1.55291	−	1.55291i	0.0809513	−	0.0809513i
$369$	−2.59808	+	4.50000i	−0.135250	+	0.234261i
$370$		0			0
$371$	−33.5885	+	19.3923i	−1.74383	+	1.00680i
$372$	−0.0879327	+	0.328169i	−0.00455910	+	0.0170148i
$373$	−22.5259	+	6.03579i	−1.16635	+	0.312521i	−0.789498	−	0.613754i	$-0.789659\pi$
$373$	−22.5259	+	6.03579i	−1.16635	+	0.312521i	−0.376848	+	0.926275i	$0.622992\pi$
$374$		0			0
$375$		0			0
$376$	−3.00000	−	5.19615i	−0.154713	−	0.267971i
$377$	−35.9101	−	35.9101i	−1.84947	−	1.84947i
$378$	23.7506	−	6.36396i	1.22160	−	0.327327i
$379$		−	0.392305i		−	0.0201513i	−0.999949	−	0.0100757i	$-0.996793\pi$
$379$		−	0.392305i		−	0.0201513i	0.999949	−	0.0100757i	$-0.00320724\pi$
$380$		0			0
$381$			14.1962i			0.727291i
$382$	0.896575	+	3.34607i	0.0458728	+	0.171200i
$383$	−1.40061	−	5.22715i	−0.0715678	−	0.267095i	0.920865	−	0.389881i	$-0.127484\pi$
$383$	−1.40061	−	5.22715i	−0.0715678	−	0.267095i	−0.992433	+	0.122786i	$0.960817\pi$
$384$	−1.50000	+	0.866025i	−0.0765466	+	0.0441942i
$385$		0			0
$386$		−	11.0718i		−	0.563540i
$387$	1.34486	+	0.360355i	0.0683632	+	0.0183179i
$388$	1.88108	+	1.88108i	0.0954976	+	0.0954976i
$389$	−5.19615	−	9.00000i	−0.263455	−	0.456318i	0.703702	−	0.710495i	$-0.251529\pi$
$389$	−5.19615	−	9.00000i	−0.263455	−	0.456318i	−0.967158	+	0.254177i	$0.918196\pi$
$390$		0			0
$391$		0			0
$392$	14.8678	−	3.98382i	0.750939	−	0.201213i
$393$	11.5911	−	3.10583i	0.584694	−	0.156668i
$394$	12.2942	−	7.09808i	0.619374	−	0.357596i
$395$		0			0
$396$			10.3923i			0.522233i
$397$	−10.9348	+	10.9348i	−0.548800	+	0.548800i	−0.926094	−	0.377293i	$-0.876855\pi$
$397$	−10.9348	+	10.9348i	−0.548800	+	0.548800i	0.377293	+	0.926094i	$0.376855\pi$
$398$	19.6975	+	5.27792i	0.987344	+	0.264558i
$399$	13.0981	+	22.6865i	0.655724	+	1.13575i
$400$		0			0
$401$	9.00000	+	5.19615i	0.449439	+	0.259483i	0.707593	−	0.706620i	$-0.249781\pi$
$401$	9.00000	+	5.19615i	0.449439	+	0.259483i	−0.258154	+	0.966104i	$0.583114\pi$
$402$	−6.78006	+	6.78006i	−0.338159	+	0.338159i
$403$	−0.240237	+	0.896575i	−0.0119670	+	0.0446616i
$404$	−7.26795			−0.361594
$405$		0			0
$406$	−50.7846			−2.52040
$407$	7.34847	−	27.4249i	0.364250	−	1.35940i
$408$		0			0
$409$	18.5263	+	10.6962i	0.916066	+	0.528891i	0.882378	−	0.470542i	$-0.155941\pi$
$409$	18.5263	+	10.6962i	0.916066	+	0.528891i	0.0336878	+	0.999432i	$0.489275\pi$
$410$		0			0
$411$	−11.5981	−	20.0885i	−0.572091	−	0.990891i
$412$	10.0382	+	2.68973i	0.494546	+	0.132513i
$413$	−18.5235	+	18.5235i	−0.911481	+	0.911481i
$414$		−	6.58846i		−	0.323805i
$415$		0			0
$416$	−4.09808	+	2.36603i	−0.200925	+	0.116004i
$417$	−13.3843	+	3.58630i	−0.655430	+	0.175622i
$418$	−10.6945	+	2.86559i	−0.523087	+	0.140161i
$419$	4.50000	−	7.79423i	0.219839	−	0.380773i	−0.734919	−	0.678155i	$-0.762780\pi$
$419$	4.50000	−	7.79423i	0.219839	−	0.380773i	0.954759	+	0.297382i	$0.0961133\pi$
$420$		0			0
$421$	−11.2942	−	19.5622i	−0.550447	−	0.953402i	−0.998242	−	0.0592661i	$-0.981124\pi$
$421$	−11.2942	−	19.5622i	−0.550447	−	0.953402i	0.447795	−	0.894136i	$-0.352209\pi$
$422$	−0.845807	−	0.845807i	−0.0411733	−	0.0411733i
$423$	−17.3867	−	4.65874i	−0.845369	−	0.226516i
$424$		−	8.19615i		−	0.398040i
$425$		0			0
$426$	−10.9019	+	6.29423i	−0.528200	+	0.304956i
$427$	−4.89898	−	18.2832i	−0.237078	−	0.884788i
$428$	−2.89778	−	10.8147i	−0.140069	−	0.522746i
$429$			28.3923i			1.37079i
$430$		0			0
$431$			21.1244i			1.01752i	0.860907	+	0.508762i	$0.169897\pi$
$431$			21.1244i			1.01752i	−0.860907	+	0.508762i	$0.830103\pi$
$432$	−1.34486	+	5.01910i	−0.0647048	+	0.241481i
$433$	12.0716	+	12.0716i	0.580123	+	0.580123i	0.934937	−	0.354814i	$-0.115456\pi$
$433$	12.0716	+	12.0716i	0.580123	+	0.580123i	−0.354814	+	0.934937i	$0.615456\pi$
$434$	0.464102	+	0.803848i	0.0222776	+	0.0385859i
$435$		0			0
$436$	−0.901924	+	1.56218i	−0.0431943	+	0.0748147i
$437$	6.78006	−	1.81671i	0.324334	−	0.0869051i
$438$	−2.32937	+	8.69333i	−0.111302	+	0.415383i
$439$	1.22243	−	0.705771i	0.0583435	−	0.0336846i	−0.470545	−	0.882376i	$-0.655942\pi$
$439$	1.22243	−	0.705771i	0.0583435	−	0.0336846i	0.528888	+	0.848692i	$0.322609\pi$
$440$		0			0
$441$	23.0885	−	39.9904i	1.09945	−	1.90430i
$442$		0			0
$443$	−10.0382	−	2.68973i	−0.476929	−	0.127793i	0.0123433	−	0.999924i	$-0.496071\pi$
$443$	−10.0382	−	2.68973i	−0.476929	−	0.127793i	−0.489272	+	0.872131i	$0.662738\pi$
$444$	7.09808	−	12.2942i	0.336860	−	0.583458i
$445$		0			0
$446$	−2.19615	−	1.26795i	−0.103991	−	0.0600391i
$447$	−8.06918	−	30.1146i	−0.381659	−	1.42437i
$448$	−1.22474	+	4.57081i	−0.0578638	+	0.215950i
$449$	−30.1244			−1.42166			−0.710828	−	0.703366i	$-0.751680\pi$
$449$	−30.1244			−1.42166			−0.710828	+	0.703366i	$0.751680\pi$
$450$		0			0
$451$	−6.00000			−0.282529
$452$	−3.46618	+	12.9360i	−0.163036	+	0.608457i
$453$	−13.3843	−	3.58630i	−0.628847	−	0.168499i
$454$	−11.0885	−	6.40192i	−0.520407	−	0.300457i
$455$		0			0
$456$	−5.53590			−0.259242
$457$	26.6484	+	7.14042i	1.24656	+	0.334015i	0.821007	−	0.570919i	$-0.193413\pi$
$457$	26.6484	+	7.14042i	1.24656	+	0.334015i	0.425553	+	0.904933i	$0.360080\pi$
$458$	−4.10394	+	4.10394i	−0.191765	+	0.191765i
$459$		0			0
$460$		0			0
$461$	−8.70577	+	5.02628i	−0.405468	+	0.234097i	−0.688841	−	0.724913i	$-0.741880\pi$
$461$	−8.70577	+	5.02628i	−0.405468	+	0.234097i	0.283373	+	0.959010i	$0.408547\pi$
$462$	20.0764	+	20.0764i	0.934038	+	0.934038i
$463$	−2.12132	+	0.568406i	−0.0985861	+	0.0264161i	−0.307775	−	0.951459i	$-0.599584\pi$
$463$	−2.12132	+	0.568406i	−0.0985861	+	0.0264161i	0.209189	+	0.977875i	$0.432918\pi$
$464$	5.36603	−	9.29423i	0.249111	−	0.431474i
$465$		0			0
$466$	2.30385	+	3.99038i	0.106724	+	0.184851i
$467$	6.78006	+	6.78006i	0.313744	+	0.313744i	0.846358	−	0.532614i	$-0.178790\pi$
$467$	6.78006	+	6.78006i	0.313744	+	0.313744i	−0.532614	+	0.846358i	$0.678790\pi$
$468$	−3.67423	+	13.7124i	−0.169842	+	0.633857i
$469$			26.1962i			1.20963i
$470$		0			0
$471$	−29.7846	−	17.1962i	−1.37240	−	0.792357i
$472$	−1.43280	−	5.34727i	−0.0659498	−	0.246128i
$473$	0.416102	+	1.55291i	0.0191324	+	0.0714031i
$474$	15.0000	+	8.66025i	0.688973	+	0.397779i
$475$		0			0
$476$		0			0
$477$	−17.3867	−	17.3867i	−0.796081	−	0.796081i
$478$	2.68973	+	2.68973i	0.123025	+	0.123025i
$479$	1.56218	+	2.70577i	0.0713777	+	0.123630i	0.899505	−	0.436910i	$-0.143927\pi$
$479$	1.56218	+	2.70577i	0.0713777	+	0.123630i	−0.828128	+	0.560540i	$0.810594\pi$
$480$		0			0
$481$	19.3923	−	33.5885i	0.884213	−	1.53150i
$482$	9.07227	−	2.43091i	0.413231	−	0.110725i
$483$	−12.7279	−	12.7279i	−0.579141	−	0.579141i
$484$	−0.866025	+	0.500000i	−0.0393648	+	0.0227273i
$485$		0			0
$486$	7.79423	+	13.5000i	0.353553	+	0.612372i
$487$	11.3509	−	11.3509i	0.514357	−	0.514357i	−0.401501	−	0.915858i	$-0.631511\pi$
$487$	11.3509	−	11.3509i	0.514357	−	0.514357i	0.915858	+	0.401501i	$0.131511\pi$
$488$	3.86370	+	1.03528i	0.174902	+	0.0468648i
$489$	−24.8038			−1.12167
$490$		0			0
$491$	−16.2058	−	9.35641i	−0.731356	−	0.422249i	0.0875619	−	0.996159i	$-0.472092\pi$
$491$	−16.2058	−	9.35641i	−0.731356	−	0.422249i	−0.818918	+	0.573910i	$0.805426\pi$
$492$	−2.89778	−	0.776457i	−0.130642	−	0.0350054i
$493$		0			0
$494$	−15.1244			−0.680477
$495$		0			0
$496$	−0.196152			−0.00880750
$497$	−8.90138	+	33.2204i	−0.399282	+	1.49014i
$498$	7.70882	+	28.7697i	0.345441	+	1.28920i
$499$	−10.0359	−	5.79423i	−0.449269	−	0.259385i	0.258253	−	0.966077i	$-0.416853\pi$
$499$	−10.0359	−	5.79423i	−0.449269	−	0.259385i	−0.707521	+	0.706692i	$0.750187\pi$
$500$		0			0
$501$	−14.1962	+	24.5885i	−0.634237	+	1.09853i
$502$	8.69333	+	2.32937i	0.388002	+	0.103965i
$503$	3.82654	−	3.82654i	0.170617	−	0.170617i	−0.616633	−	0.787250i	$-0.711504\pi$
$503$	3.82654	−	3.82654i	0.170617	−	0.170617i	0.787250	+	0.616633i	$0.211504\pi$
$504$	7.09808	+	12.2942i	0.316173	+	0.547628i
$505$		0			0
$506$	6.58846	−	3.80385i	0.292893	−	0.169102i
$507$	−4.21046	+	15.7136i	−0.186993	+	0.697867i
$508$	−7.91688	+	2.12132i	−0.351255	+	0.0941184i
$509$	−10.3923	+	18.0000i	−0.460631	+	0.797836i	−0.998992	−	0.0448779i	$-0.985710\pi$
$509$	−10.3923	+	18.0000i	−0.460631	+	0.797836i	0.538362	+	0.842714i	$0.319043\pi$
$510$		0			0
$511$	12.2942	+	21.2942i	0.543865	+	0.942001i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−11.7434	+	11.7434i	−0.518484	+	0.518484i
$514$			25.3923i			1.12001i
$515$		0			0
$516$			0.803848i			0.0353874i
$517$	−5.37945	−	20.0764i	−0.236588	−	0.882959i
$518$	−10.0382	−	37.4631i	−0.441053	−	1.64603i
$519$	−24.5885	+	14.1962i	−1.07931	+	0.623142i
$520$		0			0
$521$		−	2.78461i		−	0.121996i	−0.998138	−	0.0609980i	$-0.980572\pi$
$521$		−	2.78461i		−	0.121996i	0.998138	−	0.0609980i	$-0.0194283\pi$
$522$	−8.33298	−	31.0991i	−0.364725	−	1.36117i
$523$	23.9909	+	23.9909i	1.04905	+	1.04905i	0.998733	+	0.0503137i	$0.0160221\pi$
$523$	23.9909	+	23.9909i	1.04905	+	1.04905i	0.0503137	+	0.998733i	$0.483978\pi$
$524$	3.46410	+	6.00000i	0.151330	+	0.262111i
$525$		0			0
$526$	−6.29423	+	10.9019i	−0.274441	+	0.475346i
$527$		0			0
$528$	−5.79555	+	1.55291i	−0.252219	+	0.0675819i
$529$	15.7417	−	9.08846i	0.684420	−	0.395150i
$530$		0			0
$531$	−14.3827	−	8.30385i	−0.624155	−	0.360356i
$532$	−10.6945	+	10.6945i	−0.463667	+	0.463667i
$533$	−7.91688	−	2.12132i	−0.342918	−	0.0918846i
$534$	−7.50000	−	12.9904i	−0.324557	−	0.562149i
$535$		0			0
$536$	−4.79423	−	2.76795i	−0.207079	−	0.119557i
$537$	27.9933	−	27.9933i	1.20800	−	1.20800i
$538$	−2.60179	+	9.71003i	−0.112171	+	0.418629i
$539$	53.3205			2.29668
$540$		0			0
$541$	−8.39230			−0.360813			−0.180407	−	0.983592i	$-0.557741\pi$
$541$	−8.39230			−0.360813			−0.180407	+	0.983592i	$0.557741\pi$
$542$	−6.88160	+	25.6825i	−0.295590	+	1.10316i
$543$	15.1774	−	15.1774i	0.651325	−	0.651325i
$544$		0			0
$545$		0			0
$546$	19.3923	+	33.5885i	0.829914	+	1.43745i
$547$	−38.8079	−	10.3986i	−1.65931	−	0.444610i	−0.697110	−	0.716964i	$-0.745531\pi$
$547$	−38.8079	−	10.3986i	−1.65931	−	0.444610i	−0.962197	+	0.272354i	$0.912198\pi$
$548$	9.46979	−	9.46979i	0.404529	−	0.404529i
$549$	10.3923	−	6.00000i	0.443533	−	0.256074i
$550$		0			0
$551$	29.7058	−	17.1506i	1.26551	−	0.730642i
$552$	3.67423	−	0.984508i	0.156386	−	0.0419035i
$553$	45.7081	−	12.2474i	1.94371	−	0.520814i
$554$	9.75833	−	16.9019i	0.414592	−	0.718094i
$555$		0			0
$556$	−4.00000	−	6.92820i	−0.169638	−	0.293821i
$557$	3.10583	+	3.10583i	0.131598	+	0.131598i	0.769838	−	0.638240i	$-0.220337\pi$
$557$	3.10583	+	3.10583i	0.131598	+	0.131598i	−0.638240	+	0.769838i	$0.720337\pi$
$558$	−0.416102	+	0.416102i	−0.0176150	+	0.0176150i
$559$			2.19615i			0.0928874i
$560$		0			0
$561$		0			0
$562$	2.68973	+	10.0382i	0.113459	+	0.423436i
$563$	0.624153	+	2.32937i	0.0263049	+	0.0981713i	0.977830	−	0.209399i	$-0.0671507\pi$
$563$	0.624153	+	2.32937i	0.0263049	+	0.0981713i	−0.951525	+	0.307570i	$0.900484\pi$
$564$		−	10.3923i		−	0.437595i
$565$		0			0
$566$			3.92820i			0.165115i
$567$	41.1373	+	11.0227i	1.72760	+	0.462910i
$568$	−5.13922	−	5.13922i	−0.215637	−	0.215637i
$569$	12.4641	+	21.5885i	0.522522	+	0.905035i	0.999657	+	0.0262048i	$0.00834220\pi$
$569$	12.4641	+	21.5885i	0.522522	+	0.905035i	−0.477134	+	0.878830i	$0.658324\pi$
$570$		0			0
$571$	−9.59808	+	16.6244i	−0.401667	+	0.695708i	−0.993927	−	0.110039i	$-0.964902\pi$
$571$	−9.59808	+	16.6244i	−0.401667	+	0.695708i	0.592260	+	0.805747i	$0.298236\pi$
$572$	−15.8338	+	4.24264i	−0.662042	+	0.177394i
$573$	−1.55291	+	5.79555i	−0.0648739	+	0.242113i
$574$	−7.09808	+	4.09808i	−0.296268	+	0.171050i
$575$		0			0
$576$	−3.00000			−0.125000
$577$	−15.9217	+	15.9217i	−0.662828	+	0.662828i	−0.956046	−	0.293217i	$-0.905274\pi$
$577$	−15.9217	+	15.9217i	−0.662828	+	0.662828i	0.293217	+	0.956046i	$0.405274\pi$
$578$	16.4207	+	4.39992i	0.683013	+	0.183013i
$579$	9.58846	−	16.6077i	0.398483	−	0.690192i
$580$		0			0
$581$	70.4711	+	40.6865i	2.92364	+	1.68796i
$582$	1.19256	+	4.45069i	0.0494332	+	0.184487i
$583$	7.34847	−	27.4249i	0.304342	−	1.13582i
$584$	−5.19615			−0.215018
$585$		0			0
$586$	3.80385			0.157135
$587$	−1.13681	+	4.24264i	−0.0469213	+	0.175113i	−0.985410	−	0.170197i	$-0.945559\pi$
$587$	−1.13681	+	4.24264i	−0.0469213	+	0.175113i	0.938489	+	0.345310i	$0.112226\pi$
$588$	25.7518	+	6.90018i	1.06199	+	0.284559i
$589$	−0.542940	−	0.313467i	−0.0223715	−	0.0129162i
$590$		0			0
$591$	24.5885			1.01143
$592$	7.91688	+	2.12132i	0.325382	+	0.0871857i
$593$	−14.8492	+	14.8492i	−0.609785	+	0.609785i	−0.942890	−	0.333105i	$-0.891904\pi$
$593$	−14.8492	+	14.8492i	−0.609785	+	0.609785i	0.333105	+	0.942890i	$0.391904\pi$
$594$	−9.00000	+	15.5885i	−0.369274	+	0.639602i
$595$		0			0
$596$	15.5885	−	9.00000i	0.638528	−	0.368654i
$597$	24.9754	+	24.9754i	1.02217	+	1.02217i
$598$	10.0382	−	2.68973i	0.410492	−	0.109991i
$599$	3.63397	−	6.29423i	0.148480	−	0.257175i	−0.782186	−	0.623045i	$-0.785895\pi$
$599$	3.63397	−	6.29423i	0.148480	−	0.257175i	0.930666	+	0.365870i	$0.119229\pi$
$600$		0			0
$601$	14.3923	+	24.9282i	0.587074	+	1.01684i	0.994613	+	0.103655i	$0.0330537\pi$
$601$	14.3923	+	24.9282i	0.587074	+	1.01684i	−0.407539	+	0.913188i	$0.633613\pi$
$602$	1.55291	+	1.55291i	0.0632921	+	0.0632921i
$603$	−16.0418	+	4.29839i	−0.653273	+	0.175044i
$604$		−	8.00000i		−	0.325515i
$605$		0			0
$606$	−10.9019	−	6.29423i	−0.442860	−	0.255686i
$607$	−12.5756	−	46.9328i	−0.510429	−	1.90495i	−0.415864	−	0.909427i	$-0.636521\pi$
$607$	−12.5756	−	46.9328i	−0.510429	−	1.90495i	−0.0945643	−	0.995519i	$-0.530146\pi$
$608$	−0.827225	−	3.08725i	−0.0335484	−	0.125204i
$609$	−76.1769	−	43.9808i	−3.08684	−	1.78219i
$610$		0			0
$611$		−	28.3923i		−	1.14863i
$612$		0			0
$613$	10.0382	+	10.0382i	0.405439	+	0.405439i	0.880145	−	0.474706i	$-0.157445\pi$
$613$	10.0382	+	10.0382i	0.405439	+	0.405439i	−0.474706	+	0.880145i	$0.657445\pi$
$614$	1.73205	+	3.00000i	0.0698999	+	0.121070i
$615$		0			0
$616$	−8.19615	+	14.1962i	−0.330232	+	0.571979i
$617$	−11.3831	+	3.05008i	−0.458265	+	0.122792i	−0.480564	−	0.876960i	$-0.659568\pi$
$617$	−11.3831	+	3.05008i	−0.458265	+	0.122792i	0.0222993	+	0.999751i	$0.492901\pi$
$618$	12.7279	+	12.7279i	0.511992	+	0.511992i
$619$	41.2128	−	23.7942i	1.65648	−	0.956371i	0.682164	−	0.731200i	$-0.261039\pi$
$619$	41.2128	−	23.7942i	1.65648	−	0.956371i	0.974319	−	0.225171i	$-0.0722941\pi$
$620$		0			0
$621$	5.70577	−	9.88269i	0.228965	−	0.396579i
$622$	7.82894	−	7.82894i	0.313912	−	0.313912i
$623$	−39.5844	−	10.6066i	−1.58591	−	0.424945i
$624$	−8.19615			−0.328109
$625$		0			0
$626$	−17.8923	−	10.3301i	−0.715120	−	0.412875i
$627$	−18.5235	−	4.96335i	−0.739756	−	0.198217i
$628$	5.13922	−	19.1798i	0.205077	−	0.765358i
$629$		0			0
$630$		0			0
$631$	−0.784610			−0.0312348			−0.0156174	−	0.999878i	$-0.504971\pi$
$631$	−0.784610			−0.0312348			−0.0156174	+	0.999878i	$0.504971\pi$
$632$	−2.58819	+	9.65926i	−0.102953	+	0.384225i
$633$	−0.536220	−	2.00120i	−0.0213128	−	0.0795406i
$634$	5.70577	+	3.29423i	0.226605	+	0.130831i
$635$		0			0
$636$	7.09808	−	12.2942i	0.281457	−	0.487498i
$637$	70.3553	+	18.8516i	2.78758	+	0.746929i
$638$	26.2880	−	26.2880i	1.04075	−	1.04075i
$639$	−21.8038			−0.862547
$640$		0			0
$641$	−32.0885	+	18.5263i	−1.26742	+	0.731744i	−0.974499	−	0.224393i	$-0.927960\pi$
$641$	−32.0885	+	18.5263i	−1.26742	+	0.731744i	−0.292919	+	0.956137i	$0.594627\pi$
$642$	5.01910	−	18.7315i	0.198088	−	0.739274i
$643$	36.1182	−	9.67784i	1.42436	−	0.381657i	0.537333	−	0.843370i	$-0.319432\pi$
$643$	36.1182	−	9.67784i	1.42436	−	0.381657i	0.887029	+	0.461713i	$0.152765\pi$
$644$	5.19615	−	9.00000i	0.204757	−	0.354650i
$645$		0			0
$646$		0			0
$647$	10.0382	+	10.0382i	0.394642	+	0.394642i	0.876338	−	0.481696i	$-0.159979\pi$
$647$	10.0382	+	10.0382i	0.394642	+	0.394642i	−0.481696	+	0.876338i	$0.659979\pi$
$648$	−6.36396	+	6.36396i	−0.250000	+	0.250000i
$649$		−	19.1769i		−	0.752760i
$650$		0			0
$651$			1.60770i			0.0630105i
$652$	−3.70642	−	13.8325i	−0.145155	−	0.541724i
$653$	2.12132	+	7.91688i	0.0830137	+	0.309811i	0.994931	−	0.100564i	$-0.0320646\pi$
$653$	2.12132	+	7.91688i	0.0830137	+	0.309811i	−0.911917	+	0.410375i	$0.865398\pi$
$654$	−2.70577	+	1.56218i	−0.105804	+	0.0610860i
$655$		0			0
$656$		−	1.73205i		−	0.0676252i
$657$	−11.0227	+	11.0227i	−0.430037	+	0.430037i
$658$	−20.0764	−	20.0764i	−0.782659	−	0.782659i
$659$	−20.0885	−	34.7942i	−0.782535	−	1.35539i	−0.930461	−	0.366392i	$-0.880593\pi$
$659$	−20.0885	−	34.7942i	−0.782535	−	1.35539i	0.147925	−	0.988999i	$-0.452740\pi$
$660$		0			0
$661$	19.5885	−	33.9282i	0.761903	−	1.31965i	−0.179966	−	0.983673i	$-0.557599\pi$
$661$	19.5885	−	33.9282i	0.761903	−	1.31965i	0.941869	−	0.335981i	$-0.109068\pi$
$662$	−13.1254	+	3.51695i	−0.510135	+	0.136690i
$663$		0			0
$664$	−14.8923	+	8.59808i	−0.577934	+	0.333670i
$665$		0			0
$666$	21.2942	−	12.2942i	0.825135	−	0.476392i
$667$	−16.6660	+	16.6660i	−0.645308	+	0.645308i
$668$	−15.8338	−	4.24264i	−0.612626	−	0.164153i
$669$	−2.19615	−	3.80385i	−0.0849082	−	0.147065i
$670$		0			0
$671$	12.0000	+	6.92820i	0.463255	+	0.267460i
$672$	−5.79555	+	5.79555i	−0.223568	+	0.223568i
$673$	−5.79555	+	21.6293i	−0.223402	+	0.833748i	0.759636	+	0.650348i	$0.225377\pi$
$673$	−5.79555	+	21.6293i	−0.223402	+	0.833748i	−0.983038	+	0.183400i	$0.941290\pi$
$674$	−20.5359			−0.791013
$675$		0			0
$676$	−9.39230			−0.361242
$677$	−6.36396	+	23.7506i	−0.244587	+	0.912811i	0.729004	+	0.684510i	$0.239984\pi$
$677$	−6.36396	+	23.7506i	−0.244587	+	0.912811i	−0.973591	+	0.228301i	$0.926683\pi$
$678$	−16.4022	+	16.4022i	−0.629921	+	0.629921i
$679$	10.9019	+	6.29423i	0.418377	+	0.241550i
$680$		0			0
$681$	−11.0885	−	19.2058i	−0.424911	−	0.735967i
$682$	−0.656339	−	0.175865i	−0.0251325	−	0.00673424i
$683$	5.94786	−	5.94786i	0.227588	−	0.227588i	−0.584096	−	0.811685i	$-0.698551\pi$
$683$	5.94786	−	5.94786i	0.227588	−	0.227588i	0.811685	+	0.584096i	$0.198551\pi$
$684$	−8.30385	−	4.79423i	−0.317506	−	0.183312i
$685$		0			0
$686$	34.3923	−	19.8564i	1.31310	−	0.758121i
$687$	−9.71003	+	2.60179i	−0.370461	+	0.0992646i
$688$	−0.448288	+	0.120118i	−0.0170908	+	0.00457947i
$689$	19.3923	−	33.5885i	0.738788	−	1.27962i
$690$		0			0
$691$	−21.7942	−	37.7487i	−0.829092	−	1.43603i	−0.898752	−	0.438458i	$-0.855525\pi$
$691$	−21.7942	−	37.7487i	−0.829092	−	1.43603i	0.0696602	−	0.997571i	$-0.477808\pi$
$692$	−11.5911	−	11.5911i	−0.440628	−	0.440628i
$693$	12.7279	+	47.5013i	0.483494	+	1.80442i
$694$			8.78461i			0.333459i
$695$		0			0
$696$	16.0981	−	9.29423i	0.610196	−	0.352297i
$697$		0			0
$698$	−0.517638	−	1.93185i	−0.0195929	−	0.0731217i
$699$			7.98076i			0.301860i
$700$		0			0
$701$		−	14.5359i		−	0.549013i	−0.961585	−	0.274507i	$-0.911485\pi$
$701$		−	14.5359i		−	0.549013i	0.961585	−	0.274507i	$-0.0885145\pi$
$702$	−17.3867	+	17.3867i	−0.656217	+	0.656217i
$703$	18.5235	+	18.5235i	0.698626	+	0.698626i
$704$	−1.73205	−	3.00000i	−0.0652791	−	0.113067i
$705$		0			0
$706$	7.50000	−	12.9904i	0.282266	−	0.488899i
$707$	−33.2204	+	8.90138i	−1.24938	+	0.334771i
$708$	2.48168	−	9.26174i	0.0932671	−	0.348077i
$709$	31.3468	−	18.0981i	1.17725	−	0.679688i	0.221876	−	0.975075i	$-0.428782\pi$
$709$	31.3468	−	18.0981i	1.17725	−	0.679688i	0.955378	+	0.295387i	$0.0954487\pi$
$710$		0			0
$711$	15.0000	+	25.9808i	0.562544	+	0.974355i
$712$	6.12372	−	6.12372i	0.229496	−	0.229496i
$713$	0.416102	+	0.111494i	0.0155831	+	0.00417549i
$714$		0			0
$715$		0			0
$716$	19.7942	+	11.4282i	0.739745	+	0.427092i
$717$	1.70522	+	6.36396i	0.0636825	+	0.237666i
$718$	−9.14162	+	34.1170i	−0.341162	+	1.27323i
$719$	14.8756			0.554768			0.277384	−	0.960759i	$-0.410533\pi$
$719$	14.8756			0.554768			0.277384	+	0.960759i	$0.410533\pi$
$720$		0			0
$721$	49.1769			1.83144
$722$	−2.27362	+	8.48528i	−0.0846155	+	0.315789i
$723$	15.7136	+	4.21046i	0.584396	+	0.156589i
$724$	10.7321	+	6.19615i	0.398854	+	0.230278i
$725$		0			0
$726$	−1.73205			−0.0642824
$727$	6.69213	+	1.79315i	0.248197	+	0.0665043i	0.380773	−	0.924669i	$-0.375658\pi$
$727$	6.69213	+	1.79315i	0.248197	+	0.0665043i	−0.132575	+	0.991173i	$0.542325\pi$
$728$	−15.8338	+	15.8338i	−0.586838	+	0.586838i
$729$			27.0000i			1.00000i
$730$		0			0
$731$		0			0
$732$	4.89898	+	4.89898i	0.181071	+	0.181071i
$733$	13.1440	−	3.52193i	0.485486	−	0.130085i	−0.00777015	−	0.999970i	$-0.502473\pi$
$733$	13.1440	−	3.52193i	0.485486	−	0.130085i	0.493256	+	0.869884i	$0.335807\pi$
$734$	2.07180	−	3.58846i	0.0764714	−	0.132452i
$735$		0			0
$736$	1.09808	+	1.90192i	0.0404756	+	0.0701058i
$737$	−13.5601	−	13.5601i	−0.499494	−	0.499494i
$738$	−3.67423	−	3.67423i	−0.135250	−	0.135250i
$739$			19.5885i			0.720573i	0.932842	+	0.360287i	$0.117321\pi$
$739$			19.5885i			0.720573i	−0.932842	+	0.360287i	$0.882679\pi$
$740$		0			0
$741$	−22.6865	−	13.0981i	−0.833411	−	0.481170i
$742$	−10.0382	−	37.4631i	−0.368514	−	1.37531i
$743$	−8.63759	−	32.2359i	−0.316882	−	1.18262i	−0.922224	−	0.386655i	$-0.873630\pi$
$743$	−8.63759	−	32.2359i	−0.316882	−	1.18262i	0.605342	−	0.795965i	$-0.293036\pi$
$744$	−0.294229	−	0.169873i	−0.0107869	−	0.00622785i
$745$		0			0
$746$		−	23.3205i		−	0.853824i
$747$	−13.3521	+	49.8306i	−0.488527	+	1.82321i
$748$		0			0
$749$	−26.4904	−	45.8827i	−0.967937	−	1.67652i
$750$		0			0
$751$	−5.29423	+	9.16987i	−0.193189	+	0.334613i	−0.946305	−	0.323274i	$-0.895216\pi$
$751$	−5.29423	+	9.16987i	−0.193189	+	0.334613i	0.753116	+	0.657887i	$0.228550\pi$
$752$	5.79555	−	1.55291i	0.211342	−	0.0566290i
$753$	11.0227	+	11.0227i	0.401690	+	0.401690i
$754$	43.9808	−	25.3923i	1.60168	−	0.924733i
$755$		0			0
$756$			24.5885i			0.894274i
$757$	27.6651	−	27.6651i	1.00551	−	1.00551i	0.00552030	−	0.999985i	$-0.498243\pi$
$757$	27.6651	−	27.6651i	1.00551	−	1.00551i	0.999985	−	0.00552030i	$-0.00175717\pi$
$758$	0.378937	+	0.101536i	0.0137636	+	0.00368795i
$759$	13.1769			0.478292
$760$		0			0
$761$	−41.0885	−	23.7224i	−1.48946	−	0.859937i	−0.489528	−	0.871988i	$-0.662831\pi$
$761$	−41.0885	−	23.7224i	−1.48946	−	0.859937i	−0.999927	+	0.0120501i	$0.996164\pi$
$762$	−13.7124	−	3.67423i	−0.496749	−	0.133103i
$763$	−2.20925	+	8.24504i	−0.0799803	+	0.298491i
$764$	−3.46410			−0.125327
$765$		0			0
$766$	5.41154			0.195527
$767$	6.78006	−	25.3035i	0.244814	−	0.913658i
$768$	−0.448288	−	1.67303i	−0.0161762	−	0.0603704i
$769$	−10.9186	−	6.30385i	−0.393734	−	0.227323i	0.290043	−	0.957014i	$-0.406331\pi$
$769$	−10.9186	−	6.30385i	−0.393734	−	0.227323i	−0.683777	+	0.729691i	$0.739664\pi$
$770$		0			0
$771$	−21.9904	+	38.0885i	−0.791964	+	1.37172i
$772$	10.6945	+	2.86559i	0.384905	+	0.103135i
$773$	35.9101	−	35.9101i	1.29160	−	1.29160i	0.357800	−	0.933798i	$-0.383527\pi$
$773$	35.9101	−	35.9101i	1.29160	−	1.29160i	0.933798	−	0.357800i	$-0.116473\pi$
$774$	−0.696152	+	1.20577i	−0.0250227	+	0.0433406i
$775$		0			0
$776$	−2.30385	+	1.33013i	−0.0827033	+	0.0477488i
$777$	17.3867	−	64.8879i	0.623743	−	2.32784i
$778$	10.0382	−	2.68973i	0.359887	−	0.0964314i
$779$	2.76795	−	4.79423i	0.0991721	−	0.171771i
$780$		0			0
$781$	−12.5885	−	21.8038i	−0.450450	−	0.780203i
$782$		0			0
$783$	14.4331	−	53.8652i	0.515798	−	1.92499i
$784$			15.3923i			0.549725i
$785$		0			0
$786$			12.0000i			0.428026i
$787$	4.48288	+	16.7303i	0.159797	+	0.596372i	0.998647	+	0.0520081i	$0.0165622\pi$
$787$	4.48288	+	16.7303i	0.159797	+	0.596372i	−0.838849	+	0.544364i	$0.816771\pi$
$788$	3.67423	+	13.7124i	0.130889	+	0.488485i
$789$	−18.8827	+	10.9019i	−0.672241	+	0.388119i
$790$		0			0
$791$			63.3731i			2.25329i
$792$	−10.0382	−	2.68973i	−0.356692	−	0.0955753i
$793$	13.3843	+	13.3843i	0.475289	+	0.475289i
$794$	−7.73205	−	13.3923i	−0.274400	−	0.475275i
$795$		0			0
$796$	−10.1962	+	17.6603i	−0.361393	+	0.625951i
$797$	−39.5844	+	10.6066i	−1.40215	+	0.375705i	−0.879117	−	0.476607i	$-0.841867\pi$
$797$	−39.5844	+	10.6066i	−1.40215	+	0.375705i	−0.523034	+	0.852312i	$0.675200\pi$
$798$	−25.3035	+	6.78006i	−0.895736	+	0.240012i
$799$		0			0
$800$		0			0
$801$		−	25.9808i		−	0.917985i
$802$	−7.34847	+	7.34847i	−0.259483	+	0.259483i
$803$	−17.3867	−	4.65874i	−0.613562	−	0.164403i
$804$	−4.79423	−	8.30385i	−0.169079	−	0.292854i
$805$		0			0
$806$	−0.803848	−	0.464102i	−0.0283143	−	0.0163473i
$807$	−12.3118	+	12.3118i	−0.433397	+	0.433397i
$808$	1.88108	−	7.02030i	0.0661763	−	0.246973i
$809$	1.73205			0.0608957			0.0304478	−	0.999536i	$-0.490307\pi$
$809$	1.73205			0.0608957			0.0304478	+	0.999536i	$0.490307\pi$
$810$		0			0
$811$	34.3731			1.20700			0.603501	−	0.797362i	$-0.293772\pi$
$811$	34.3731			1.20700			0.603501	+	0.797362i	$0.293772\pi$
$812$	13.1440	−	49.0542i	0.461265	−	1.72146i
$813$	−32.5641	+	32.5641i	−1.14207	+	1.14207i
$814$	24.5885	+	14.1962i	0.861825	+	0.497575i
$815$		0			0
$816$		0			0
$817$	−1.43280	−	0.383917i	−0.0501272	−	0.0134315i
$818$	−15.1266	+	15.1266i	−0.528891	+	0.528891i
$819$			67.1769i			2.34735i
$820$		0			0
$821$	12.5885	−	7.26795i	0.439340	−	0.253653i	−0.263978	−	0.964529i	$-0.585034\pi$
$821$	12.5885	−	7.26795i	0.439340	−	0.253653i	0.703318	+	0.710876i	$0.251701\pi$
$822$	22.4058	−	6.00361i	0.781491	−	0.209400i
$823$	39.2562	−	10.5187i	1.36839	−	0.366658i	0.501497	−	0.865160i	$-0.332783\pi$
$823$	39.2562	−	10.5187i	1.36839	−	0.366658i	0.866889	+	0.498502i	$0.166116\pi$
$824$	−5.19615	+	9.00000i	−0.181017	+	0.313530i
$825$		0			0
$826$	−13.0981	−	22.6865i	−0.455740	−	0.789365i
$827$	0.568406	+	0.568406i	0.0197654	+	0.0197654i	0.716920	−	0.697155i	$-0.245551\pi$
$827$	0.568406	+	0.568406i	0.0197654	+	0.0197654i	−0.697155	+	0.716920i	$0.745551\pi$
$828$	6.36396	+	1.70522i	0.221163	+	0.0592604i
$829$			28.5885i			0.992918i	0.868060	+	0.496459i	$0.165367\pi$
$829$			28.5885i			0.992918i	−0.868060	+	0.496459i	$0.834633\pi$
$830$		0			0
$831$	29.2750	−	16.9019i	1.01554	−	0.586321i
$832$	−1.22474	−	4.57081i	−0.0424604	−	0.158464i
$833$		0			0
$834$		−	13.8564i		−	0.479808i
$835$		0			0
$836$		−	11.0718i		−	0.382926i
$837$	−0.984508	+	0.263798i	−0.0340296	+	0.00911820i
$838$	6.36396	+	6.36396i	0.219839	+	0.219839i
$839$	6.75833	+	11.7058i	0.233323	+	0.404128i	0.958784	−	0.284136i	$-0.0917066\pi$
$839$	6.75833	+	11.7058i	0.233323	+	0.404128i	−0.725461	+	0.688264i	$0.758373\pi$
$840$		0			0
$841$	−43.0885	+	74.6314i	−1.48581	+	2.57350i
$842$	21.8188	−	5.84632i	0.751925	−	0.201478i
$843$	−4.65874	+	17.3867i	−0.160456	+	0.598829i
$844$	1.03590	−	0.598076i	0.0356571	−	0.0205866i
$845$		0			0
$846$	9.00000	−	15.5885i	0.309426	−	0.535942i
$847$	−3.34607	+	3.34607i	−0.114972	+	0.114972i
$848$	7.91688	+	2.12132i	0.271867	+	0.0728464i
$849$	−3.40192	+	5.89230i	−0.116754	+	0.202223i
$850$		0			0
$851$	−15.5885	−	9.00000i	−0.534365	−	0.308516i
$852$	−3.25813	−	12.1595i	−0.111622	−	0.416578i
$853$	4.83461	−	18.0430i	0.165534	−	0.617781i	−0.832438	−	0.554119i	$-0.813055\pi$
$853$	4.83461	−	18.0430i	0.165534	−	0.617781i	0.997972	−	0.0636620i	$-0.0202780\pi$
$854$	18.9282			0.647710
$855$		0			0
$856$	11.1962			0.382677
$857$	−10.8147	+	40.3608i	−0.369422	+	1.37870i	0.491905	+	0.870649i	$0.336301\pi$
$857$	−10.8147	+	40.3608i	−0.369422	+	1.37870i	−0.861327	+	0.508051i	$0.830366\pi$
$858$	−27.4249	−	7.34847i	−0.936269	−	0.250873i
$859$	−36.0167	−	20.7942i	−1.22887	−	0.709490i	−0.262079	−	0.965047i	$-0.584408\pi$
$859$	−36.0167	−	20.7942i	−1.22887	−	0.709490i	−0.966794	+	0.255557i	$0.917741\pi$
$860$		0			0
$861$	−14.1962			−0.483804
$862$	−20.4046	−	5.46739i	−0.694982	−	0.186220i
$863$	−33.2204	+	33.2204i	−1.13084	+	1.13084i	−0.140798	+	0.990038i	$0.544967\pi$
$863$	−33.2204	+	33.2204i	−1.13084	+	1.13084i	−0.990038	+	0.140798i	$0.955033\pi$
$864$	−4.50000	−	2.59808i	−0.153093	−	0.0883883i
$865$		0			0
$866$	−14.7846	+	8.53590i	−0.502401	+	0.290062i
$867$	20.8207	+	20.8207i	0.707107	+	0.707107i
$868$	−0.896575	+	0.240237i	−0.0304318	+	0.00815416i
$869$	−17.3205	+	30.0000i	−0.587558	+	1.01768i
$870$		0			0
$871$	−13.0981	−	22.6865i	−0.443811	−	0.768704i
$872$	−1.27551	−	1.27551i	−0.0431943	−	0.0431943i
$873$	−2.06557	+	7.70882i	−0.0699091	+	0.260904i
$874$			7.01924i			0.237429i
$875$		0			0
$876$	−7.79423	−	4.50000i	−0.263343	−	0.152041i
$877$	9.55772	+	35.6699i	0.322741	+	1.20449i	0.916563	+	0.399890i	$0.130952\pi$
$877$	9.55772	+	35.6699i	0.322741	+	1.20449i	−0.593822	+	0.804597i	$0.702382\pi$
$878$	0.365334	+	1.36345i	0.0123294	+	0.0460141i
$879$	5.70577	+	3.29423i	0.192451	+	0.111112i
$880$		0			0
$881$			18.6795i			0.629328i	0.949203	+	0.314664i	$0.101892\pi$
$881$			18.6795i			0.629328i	−0.949203	+	0.314664i	$0.898108\pi$
$882$	32.6520	+	32.6520i	1.09945	+	1.09945i
$883$	−18.2832	−	18.2832i	−0.615280	−	0.615280i	0.329037	−	0.944317i	$-0.393276\pi$
$883$	−18.2832	−	18.2832i	−0.615280	−	0.615280i	−0.944317	+	0.329037i	$0.893276\pi$
$884$		0			0
$885$		0			0
$886$	5.19615	−	9.00000i	0.174568	−	0.302361i
$887$	10.0382	−	2.68973i	0.337050	−	0.0903122i	−0.0863246	−	0.996267i	$-0.527512\pi$
$887$	10.0382	−	2.68973i	0.337050	−	0.0903122i	0.423374	+	0.905955i	$0.360846\pi$
$888$	10.0382	+	10.0382i	0.336860	+	0.336860i
$889$	−33.5885	+	19.3923i	−1.12652	+	0.650397i
$890$		0			0
$891$	−27.0000	+	15.5885i	−0.904534	+	0.522233i
$892$	1.79315	−	1.79315i	0.0600391	−	0.0600391i
$893$	18.5235	+	4.96335i	0.619865	+	0.166092i
$894$	31.1769			1.04271
$895$		0			0
$896$	−4.09808	−	2.36603i	−0.136907	−	0.0790434i
$897$	17.3867	+	4.65874i	0.580524	+	0.155551i
$898$	7.79676	−	29.0979i	0.260181	−	0.971009i
$899$	2.10512			0.0702096
$900$		0			0
$901$		0			0
$902$	1.55291	−	5.79555i	0.0517064	−	0.192971i
$903$	0.984508	+	3.67423i	0.0327624	+	0.122271i
$904$	−11.5981	−	6.69615i	−0.385746	−	0.222711i
$905$		0			0
$906$	6.92820	−	12.0000i	0.230174	−	0.398673i
$907$	−31.8756	−	8.54103i	−1.05841	−	0.283600i	−0.312687	−	0.949856i	$-0.601229\pi$
$907$	−31.8756	−	8.54103i	−1.05841	−	0.283600i	−0.745723	+	0.666256i	$0.767896\pi$
$908$	9.05369	−	9.05369i	0.300457	−	0.300457i
$909$	−10.9019	−	18.8827i	−0.361594	−	0.626299i
$910$		0			0
$911$	33.8827	−	19.5622i	1.12258	−	0.648124i	0.180524	−	0.983571i	$-0.442221\pi$
$911$	33.8827	−	19.5622i	1.12258	−	0.648124i	0.942059	+	0.335447i	$0.108887\pi$
$912$	1.43280	−	5.34727i	0.0474446	−	0.177066i
$913$	−57.5394	+	15.4176i	−1.90428	+	0.510250i
$914$	−13.7942	+	23.8923i	−0.456273	+	0.790287i
$915$		0			0
$916$	−2.90192	−	5.02628i	−0.0958823	−	0.166073i
$917$	23.1822	+	23.1822i	0.765544	+	0.765544i
$918$		0			0
$919$			58.5885i			1.93265i	0.257316	+	0.966327i	$0.417162\pi$
$919$			58.5885i			1.93265i	−0.257316	+	0.966327i	$0.582838\pi$
$920$		0			0
$921$			6.00000i			0.197707i
$922$	−2.60179	−	9.71003i	−0.0856855	−	0.319783i
$923$	−8.90138	−	33.2204i	−0.292993	−	1.09346i
$924$	−24.5885	+	14.1962i	−0.808901	+	0.467019i
$925$		0			0
$926$		−	2.19615i		−	0.0721700i
$927$	8.06918	+	30.1146i	0.265027	+	0.989093i
$928$	7.58871	+	7.58871i	0.249111	+	0.249111i
$929$	15.9282	+	27.5885i	0.522587	+	0.905148i	0.999655	+	0.0262811i	$0.00836650\pi$
$929$	15.9282	+	27.5885i	0.522587	+	0.905148i	−0.477067	+	0.878867i	$0.658300\pi$
$930$		0			0
$931$	−24.5981	+	42.6051i	−0.806169	+	1.39633i
$932$	−4.45069	+	1.19256i	−0.145787	+	0.0390636i
$933$	18.5235	−	4.96335i	0.606431	−	0.162493i
$934$	−8.30385	+	4.79423i	−0.271710	+	0.156872i
$935$		0			0
$936$	−12.2942	−	7.09808i	−0.401849	−	0.232008i
$937$	−17.7148	+	17.7148i	−0.578718	+	0.578718i	−0.934550	−	0.355832i	$-0.884198\pi$
$937$	−17.7148	+	17.7148i	−0.578718	+	0.578718i	0.355832	+	0.934550i	$0.384198\pi$
$938$	−25.3035	−	6.78006i	−0.826190	−	0.221377i
$939$	−17.8923	−	30.9904i	−0.583893	−	1.01133i
$940$		0			0
$941$	9.88269	+	5.70577i	0.322166	+	0.186003i	0.652358	−	0.757911i	$-0.273780\pi$
$941$	9.88269	+	5.70577i	0.322166	+	0.186003i	−0.330191	+	0.943914i	$0.607113\pi$
$942$	24.3190	−	24.3190i	0.792357	−	0.792357i
$943$	−0.984508	+	3.67423i	−0.0320600	+	0.119650i
$944$	5.53590			0.180178
$945$		0			0
$946$	−1.60770			−0.0522707
$947$	10.9670	−	40.9292i	0.356378	−	1.33002i	−0.522363	−	0.852723i	$-0.674949\pi$
$947$	10.9670	−	40.9292i	0.356378	−	1.33002i	0.878741	−	0.477298i	$-0.158384\pi$
$948$	−12.2474	+	12.2474i	−0.397779	+	0.397779i
$949$	−21.2942	−	12.2942i	−0.691240	−	0.399088i
$950$		0			0
$951$	5.70577	+	9.88269i	0.185022	+	0.320468i
$952$		0			0
$953$	−13.8647	+	13.8647i	−0.449123	+	0.449123i	−0.895063	−	0.445940i	$-0.852869\pi$
$953$	−13.8647	+	13.8647i	−0.449123	+	0.449123i	0.445940	+	0.895063i	$0.352869\pi$
$954$	21.2942	−	12.2942i	0.689426	−	0.398040i
$955$		0			0
$956$	−3.29423	+	1.90192i	−0.106543	+	0.0615126i
$957$	62.1982	−	16.6660i	2.01058	−	0.538734i
$958$	−3.01790	+	0.808643i	−0.0975038	+	0.0261261i
$959$	31.6865	−	54.8827i	1.02321	−	1.77225i
$960$		0			0
$961$	15.4808	+	26.8135i	0.499379	+	0.864951i
$962$	27.4249	+	27.4249i	0.884213	+	0.884213i
$963$	23.7506	−	23.7506i	0.765353	−	0.765353i
$964$			9.39230i			0.302506i
$965$		0			0
$966$	15.5885	−	9.00000i	0.501550	−	0.289570i
$967$	−10.7589	−	40.1528i	−0.345983	−	1.29123i	−0.891460	−	0.453100i	$-0.850318\pi$
$967$	−10.7589	−	40.1528i	−0.345983	−	1.29123i	0.545476	−	0.838126i	$-0.316349\pi$
$968$	−0.258819	−	0.965926i	−0.00831876	−	0.0310460i
$969$		0			0
$970$		0			0
$971$			54.0333i			1.73401i	0.498298	+	0.867006i	$0.333959\pi$
$971$			54.0333i			1.73401i	−0.498298	+	0.867006i	$0.666041\pi$
$972$	−15.0573	+	4.03459i	−0.482963	+	0.129410i
$973$	−26.7685	−	26.7685i	−0.858159	−	0.858159i
$974$	8.02628	+	13.9019i	0.257179	+	0.445446i
$975$		0			0
$976$	−2.00000	+	3.46410i	−0.0640184	+	0.110883i
$977$	44.6035	−	11.9515i	1.42699	−	0.382361i	0.539033	−	0.842285i	$-0.318790\pi$
$977$	44.6035	−	11.9515i	1.42699	−	0.382361i	0.887959	+	0.459923i	$0.152123\pi$
$978$	6.41971	−	23.9587i	0.205280	−	0.766114i
$979$	25.9808	−	15.0000i	0.830349	−	0.479402i
$980$		0			0
$981$	−5.41154			−0.172777
$982$	13.2320	−	13.2320i	0.422249	−	0.422249i
$983$	41.7057	+	11.1750i	1.33021	+	0.356427i	0.852792	−	0.522251i	$-0.174908\pi$
$983$	41.7057	+	11.1750i	1.33021	+	0.356427i	0.477414	+	0.878679i	$0.341574\pi$
$984$	1.50000	−	2.59808i	0.0478183	−	0.0828236i
$985$		0			0
$986$		0			0
$987$	−12.7279	−	47.5013i	−0.405134	−	1.51198i
$988$	3.91447	−	14.6090i	0.124536	−	0.464774i
$989$	1.01924			0.0324099
$990$		0			0
$991$	−29.1769			−0.926835			−0.463418	−	0.886140i	$-0.653377\pi$
$991$	−29.1769			−0.926835			−0.463418	+	0.886140i	$0.653377\pi$
$992$	0.0507680	−	0.189469i	0.00161189	−	0.00601564i
$993$	−22.7339	−	6.09154i	−0.721440	−	0.193309i
$994$	−29.7846	−	17.1962i	−0.944710	−	0.545429i
$995$		0			0
$996$	−29.7846			−0.943761
$997$	−21.0609	−	5.64325i	−0.667005	−	0.178724i	−0.0905999	−	0.995887i	$-0.528878\pi$
$997$	−21.0609	−	5.64325i	−0.667005	−	0.178724i	−0.576405	+	0.817164i	$0.695545\pi$
$998$	8.19428	−	8.19428i	0.259385	−	0.259385i
$999$	42.5885			1.34744

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.p.e.293.1	yes	8
3.2	odd	2		1350.2.q.a.1043.2		8
5.2	odd	4		450.2.p.c.257.1	✓	8
5.3	odd	4		450.2.p.c.257.2	yes	8
5.4	even	2	inner	450.2.p.e.293.2	yes	8
9.2	odd	6		450.2.p.c.443.1	yes	8
9.7	even	3		1350.2.q.d.143.2		8
15.2	even	4		1350.2.q.d.557.2		8
15.8	even	4		1350.2.q.d.557.1		8
15.14	odd	2		1350.2.q.a.1043.1		8
45.2	even	12	inner	450.2.p.e.407.1	yes	8
45.7	odd	12		1350.2.q.a.1007.2		8
45.29	odd	6		450.2.p.c.443.2	yes	8
45.34	even	6		1350.2.q.d.143.1		8
45.38	even	12	inner	450.2.p.e.407.2	yes	8
45.43	odd	12		1350.2.q.a.1007.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.p.c.257.1	✓	8	5.2	odd	4
450.2.p.c.257.2	yes	8	5.3	odd	4
450.2.p.c.443.1	yes	8	9.2	odd	6
450.2.p.c.443.2	yes	8	45.29	odd	6
450.2.p.e.293.1	yes	8	1.1	even	1	trivial
450.2.p.e.293.2	yes	8	5.4	even	2	inner
450.2.p.e.407.1	yes	8	45.2	even	12	inner
450.2.p.e.407.2	yes	8	45.38	even	12	inner
1350.2.q.a.1007.1		8	45.43	odd	12
1350.2.q.a.1007.2		8	45.7	odd	12
1350.2.q.a.1043.1		8	15.14	odd	2
1350.2.q.a.1043.2		8	3.2	odd	2
1350.2.q.d.143.1		8	45.34	even	6
1350.2.q.d.143.2		8	9.7	even	3
1350.2.q.d.557.1		8	15.8	even	4
1350.2.q.d.557.2		8	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.22474 + 1.22474i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.866025 - 1.50000i) q^{6} +(-4.57081 - 1.22474i) q^{7} +(0.707107 - 0.707107i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.22474 + 1.22474i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.866025 - 1.50000i) q^{6} +(-4.57081 - 1.22474i) q^{7} +(0.707107 - 0.707107i) q^{8} -3.00000i q^{9} +(3.00000 - 1.73205i) q^{11} +(1.67303 - 0.448288i) q^{12} +(4.57081 - 1.22474i) q^{13} +(2.36603 - 4.09808i) q^{14} +(0.500000 + 0.866025i) q^{16} +(2.89778 + 0.776457i) q^{18} +3.19615i q^{19} +(7.09808 - 4.09808i) q^{21} +(0.896575 + 3.34607i) q^{22} +(-0.568406 - 2.12132i) q^{23} +1.73205i q^{24} +4.73205i q^{26} +(3.67423 + 3.67423i) q^{27} +(3.34607 + 3.34607i) q^{28} +(-5.36603 - 9.29423i) q^{29} +(-0.0980762 + 0.169873i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-1.55291 + 5.79555i) q^{33} +(-1.50000 + 2.59808i) q^{36} +(5.79555 - 5.79555i) q^{37} +(-3.08725 - 0.827225i) q^{38} +(-4.09808 + 7.09808i) q^{39} +(-1.50000 - 0.866025i) q^{41} +(2.12132 + 7.91688i) q^{42} +(-0.120118 + 0.448288i) q^{43} -3.46410 q^{44} +2.19615 q^{46} +(1.55291 - 5.79555i) q^{47} +(-1.67303 - 0.448288i) q^{48} +(13.3301 + 7.69615i) q^{49} +(-4.57081 - 1.22474i) q^{52} +(5.79555 - 5.79555i) q^{53} +(-4.50000 + 2.59808i) q^{54} +(-4.09808 + 2.36603i) q^{56} +(-3.91447 - 3.91447i) q^{57} +(10.3664 - 2.77766i) q^{58} +(2.76795 - 4.79423i) q^{59} +(2.00000 + 3.46410i) q^{61} +(-0.138701 - 0.138701i) q^{62} +(-3.67423 + 13.7124i) q^{63} -1.00000i q^{64} +(-5.19615 - 3.00000i) q^{66} +(-1.43280 - 5.34727i) q^{67} +(3.29423 + 1.90192i) q^{69} -7.26795i q^{71} +(-2.12132 - 2.12132i) q^{72} +(-3.67423 - 3.67423i) q^{73} +(4.09808 + 7.09808i) q^{74} +(1.59808 - 2.76795i) q^{76} +(-15.8338 + 4.24264i) q^{77} +(-5.79555 - 5.79555i) q^{78} +(-8.66025 + 5.00000i) q^{79} -9.00000 q^{81} +(1.22474 - 1.22474i) q^{82} +(-16.6102 - 4.45069i) q^{83} -8.19615 q^{84} +(-0.401924 - 0.232051i) q^{86} +(17.9551 + 4.81105i) q^{87} +(0.896575 - 3.34607i) q^{88} +8.66025 q^{89} -22.3923 q^{91} +(-0.568406 + 2.12132i) q^{92} +(-0.0879327 - 0.328169i) q^{93} +(5.19615 + 3.00000i) q^{94} +(0.866025 - 1.50000i) q^{96} +(-2.56961 - 0.688524i) q^{97} +(-10.8840 + 10.8840i) q^{98} +(-5.19615 - 9.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q + 24 q^{11} + 12 q^{14} + 4 q^{16} + 36 q^{21} - 36 q^{29} + 20 q^{31} - 12 q^{36} - 12 q^{39} - 12 q^{41} - 24 q^{46} + 72 q^{49} - 36 q^{54} - 12 q^{56} + 36 q^{59} + 16 q^{61} - 36 q^{69} + 12 q^{74} - 8 q^{76} - 72 q^{81} - 24 q^{84} - 24 q^{86} - 96 q^{91}+O(q^{100}) \) 8 * q + 24 * q^11 + 12 * q^14 + 4 * q^16 + 36 * q^21 - 36 * q^29 + 20 * q^31 - 12 * q^36 - 12 * q^39 - 12 * q^41 - 24 * q^46 + 72 * q^49 - 36 * q^54 - 12 * q^56 + 36 * q^59 + 16 * q^61 - 36 * q^69 + 12 * q^74 - 8 * q^76 - 72 * q^81 - 24 * q^84 - 24 * q^86 - 96 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more