LMFDB - Embedded newform 720.2.t.c.541.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [720,2,Mod(181,720)] 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("720.181"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(720, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.t (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.74922894553$
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^{5} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			541.5
Root			$1.32070 - 0.505727i$ of defining polynomial
Character	$\chi$	$=$	720.541
Dual form			720.2.t.c.181.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.257150 + 1.39064i) q^{2} +(-1.86775 + 0.715205i) q^{4} +(0.707107 - 0.707107i) q^{5} -2.89402i q^{7} +(-1.47488 - 2.41345i) q^{8} +(1.16516 + 0.801497i) q^{10} +(-1.84462 + 1.84462i) q^{11} +(-3.08011 - 3.08011i) q^{13} +(4.02454 - 0.744198i) q^{14} +(2.97696 - 2.67165i) q^{16} -7.29875 q^{17} +(-1.23593 - 1.23593i) q^{19} +(-0.814970 + 1.82642i) q^{20} +(-3.03955 - 2.09086i) q^{22} -4.60490i q^{23} -1.00000i q^{25} +(3.49126 - 5.07536i) q^{26} +(2.06982 + 5.40530i) q^{28} +(-4.24680 - 4.24680i) q^{29} +2.06299 q^{31} +(4.48082 + 3.45286i) q^{32} +(-1.87688 - 10.1499i) q^{34} +(-2.04638 - 2.04638i) q^{35} +(-1.17899 + 1.17899i) q^{37} +(1.40091 - 2.03655i) q^{38} +(-2.74946 - 0.663664i) q^{40} +4.61484i q^{41} +(3.03019 - 3.03019i) q^{43} +(2.12601 - 4.76458i) q^{44} +(6.40375 - 1.18415i) q^{46} +11.7111 q^{47} -1.37537 q^{49} +(1.39064 - 0.257150i) q^{50} +(7.95577 + 3.54995i) q^{52} +(-2.73048 + 2.73048i) q^{53} +2.60869i q^{55} +(-6.98457 + 4.26835i) q^{56} +(4.81369 - 6.99782i) q^{58} +(-3.11306 + 3.11306i) q^{59} +(2.34962 + 2.34962i) q^{61} +(0.530498 + 2.86887i) q^{62} +(-3.64944 + 7.11910i) q^{64} -4.35593 q^{65} +(8.24311 + 8.24311i) q^{67} +(13.6322 - 5.22011i) q^{68} +(2.31955 - 3.37201i) q^{70} -3.25937i q^{71} -12.6877i q^{73} +(-1.94272 - 1.33637i) q^{74} +(3.19235 + 1.42446i) q^{76} +(5.33839 + 5.33839i) q^{77} -0.113885 q^{79} +(0.215891 - 3.99417i) q^{80} +(-6.41758 + 1.18671i) q^{82} +(-9.76813 - 9.76813i) q^{83} +(-5.16100 + 5.16100i) q^{85} +(4.99310 + 3.43468i) q^{86} +(7.17251 + 1.73129i) q^{88} -3.74593i q^{89} +(-8.91390 + 8.91390i) q^{91} +(3.29345 + 8.60080i) q^{92} +(3.01150 + 16.2858i) q^{94} -1.74787 q^{95} -13.9853 q^{97} +(-0.353676 - 1.91264i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} + 4 q^{10} + 8 q^{11} - 4 q^{14} + 16 q^{16} - 8 q^{19} - 8 q^{20} - 20 q^{22} + 16 q^{26} - 4 q^{28} + 16 q^{29} + 16 q^{34} - 16 q^{37} - 20 q^{38} + 8 q^{43} - 40 q^{44} - 4 q^{46} + 40 q^{47}+ \cdots - 60 q^{98}+O(q^{100}) $ 16 * q - 4 * q^4 + 4 * q^10 + 8 * q^11 - 4 * q^14 + 16 * q^16 - 8 * q^19 - 8 * q^20 - 20 * q^22 + 16 * q^26 - 4 * q^28 + 16 * q^29 + 16 * q^34 - 16 * q^37 - 20 * q^38 + 8 * q^43 - 40 * q^44 - 4 * q^46 + 40 * q^47 - 16 * q^49 + 4 * q^50 + 56 * q^52 - 16 * q^53 - 16 * q^56 - 12 * q^58 + 8 * q^59 + 16 * q^61 + 8 * q^62 - 16 * q^64 + 40 * q^67 + 48 * q^68 - 8 * q^70 + 72 * q^74 - 16 * q^77 + 16 * q^79 - 16 * q^80 - 76 * q^82 - 40 * q^83 - 16 * q^85 - 28 * q^86 + 32 * q^91 + 52 * q^92 - 36 * q^94 - 32 * q^95 - 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$1$

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 $

$2$	0.257150	+	1.39064i	0.181833	+	0.983329i
$2$	0.257150	+	1.39064i	0.181833	+	0.983329i
$3$		0			0
$3$		0			0
$4$	−1.86775	+	0.715205i	−0.933874	+	0.357603i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$		0			0
$7$		−	2.89402i		−	1.09384i	−0.837186	−	0.546919i	$-0.815801\pi$
$7$		−	2.89402i		−	1.09384i	0.837186	−	0.546919i	$-0.184199\pi$
$8$	−1.47488	−	2.41345i	−0.521450	−	0.853282i
$9$		0			0
$10$	1.16516	+	0.801497i	0.368457	+	0.253456i
$11$	−1.84462	+	1.84462i	−0.556175	+	0.556175i	−0.928216	−	0.372041i	$-0.878658\pi$
$11$	−1.84462	+	1.84462i	−0.556175	+	0.556175i	0.372041	+	0.928216i	$0.378658\pi$
$12$		0			0
$13$	−3.08011	−	3.08011i	−0.854268	−	0.854268i	0.136388	−	0.990656i	$-0.456451\pi$
$13$	−3.08011	−	3.08011i	−0.854268	−	0.854268i	−0.990656	+	0.136388i	$0.956451\pi$
$14$	4.02454	−	0.744198i	1.07560	−	0.198895i
$15$		0			0
$16$	2.97696	−	2.67165i	0.744241	−	0.667912i
$17$	−7.29875			−1.77021			−0.885104	−	0.465393i	$-0.845913\pi$
$17$	−7.29875			−1.77021			−0.885104	+	0.465393i	$0.845913\pi$
$18$		0			0
$19$	−1.23593	−	1.23593i	−0.283542	−	0.283542i	0.550978	−	0.834520i	$-0.314255\pi$
$19$	−1.23593	−	1.23593i	−0.283542	−	0.283542i	−0.834520	+	0.550978i	$0.814255\pi$
$20$	−0.814970	+	1.82642i	−0.182233	+	0.408401i
$21$		0			0
$22$	−3.03955	−	2.09086i	−0.648034	−	0.445773i
$23$		−	4.60490i		−	0.960189i	−0.877217	−	0.480094i	$-0.840602\pi$
$23$		−	4.60490i		−	0.960189i	0.877217	−	0.480094i	$-0.159398\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$	3.49126	−	5.07536i	0.684693	−	0.995360i
$27$		0			0
$28$	2.06982	+	5.40530i	0.391159	+	1.02151i
$29$	−4.24680	−	4.24680i	−0.788611	−	0.788611i	0.192656	−	0.981266i	$-0.438290\pi$
$29$	−4.24680	−	4.24680i	−0.788611	−	0.788611i	−0.981266	+	0.192656i	$0.938290\pi$
$30$		0			0
$31$	2.06299			0.370524			0.185262	−	0.982689i	$-0.440687\pi$
$31$	2.06299			0.370524			0.185262	+	0.982689i	$0.440687\pi$
$32$	4.48082	+	3.45286i	0.792104	+	0.610386i
$33$		0			0
$34$	−1.87688	−	10.1499i	−0.321882	−	1.74070i
$35$	−2.04638	−	2.04638i	−0.345902	−	0.345902i
$36$		0			0
$37$	−1.17899	+	1.17899i	−0.193825	+	0.193825i	−0.797346	−	0.603522i	$-0.793764\pi$
$37$	−1.17899	+	1.17899i	−0.193825	+	0.193825i	0.603522	+	0.797346i	$0.293764\pi$
$38$	1.40091	−	2.03655i	0.227258	−	0.330373i
$39$		0			0
$40$	−2.74946	−	0.663664i	−0.434728	−	0.104934i
$41$			4.61484i			0.720717i	0.932814	+	0.360359i	$0.117346\pi$
$41$			4.61484i			0.720717i	−0.932814	+	0.360359i	$0.882654\pi$
$42$		0			0
$43$	3.03019	−	3.03019i	0.462099	−	0.462099i	−0.437244	−	0.899343i	$-0.644045\pi$
$43$	3.03019	−	3.03019i	0.462099	−	0.462099i	0.899343	+	0.437244i	$0.144045\pi$
$44$	2.12601	−	4.76458i	0.320508	−	0.718287i
$45$		0			0
$46$	6.40375	−	1.18415i	0.944182	−	0.174594i
$47$	11.7111			1.70823			0.854117	−	0.520081i	$-0.174098\pi$
$47$	11.7111			1.70823			0.854117	+	0.520081i	$0.174098\pi$
$48$		0			0
$49$	−1.37537			−0.196481
$50$	1.39064	−	0.257150i	0.196666	−	0.0363665i
$51$		0			0
$52$	7.95577	+	3.54995i	1.10327	+	0.492290i
$53$	−2.73048	+	2.73048i	−0.375061	+	0.375061i	−0.869316	−	0.494256i	$-0.835441\pi$
$53$	−2.73048	+	2.73048i	−0.375061	+	0.375061i	0.494256	+	0.869316i	$0.335441\pi$
$54$		0			0
$55$			2.60869i			0.351756i
$56$	−6.98457	+	4.26835i	−0.933352	+	0.570382i
$57$		0			0
$58$	4.81369	−	6.99782i	0.632069	−	0.918859i
$59$	−3.11306	+	3.11306i	−0.405285	+	0.405285i	−0.880091	−	0.474805i	$-0.842518\pi$
$59$	−3.11306	+	3.11306i	−0.405285	+	0.405285i	0.474805	+	0.880091i	$0.342518\pi$
$60$		0			0
$61$	2.34962	+	2.34962i	0.300838	+	0.300838i	0.841342	−	0.540503i	$-0.181766\pi$
$61$	2.34962	+	2.34962i	0.300838	+	0.300838i	−0.540503	+	0.841342i	$0.681766\pi$
$62$	0.530498	+	2.86887i	0.0673733	+	0.364347i
$63$		0			0
$64$	−3.64944	+	7.11910i	−0.456180	+	0.889888i
$65$	−4.35593			−0.540286
$66$		0			0
$67$	8.24311	+	8.24311i	1.00706	+	1.00706i	0.999975	+	0.00708173i	$0.00225420\pi$
$67$	8.24311	+	8.24311i	1.00706	+	1.00706i	0.00708173	+	0.999975i	$0.497746\pi$
$68$	13.6322	−	5.22011i	1.65315	−	0.633031i
$69$		0			0
$70$	2.31955	−	3.37201i	0.277239	−	0.403032i
$71$		−	3.25937i		−	0.386816i	−0.981118	−	0.193408i	$-0.938046\pi$
$71$		−	3.25937i		−	0.386816i	0.981118	−	0.193408i	$-0.0619541\pi$
$72$		0			0
$73$		−	12.6877i		−	1.48499i	−0.669853	−	0.742494i	$-0.733643\pi$
$73$		−	12.6877i		−	1.48499i	0.669853	−	0.742494i	$-0.266357\pi$
$74$	−1.94272	−	1.33637i	−0.225837	−	0.155350i
$75$		0			0
$76$	3.19235	+	1.42446i	0.366188	+	0.163397i
$77$	5.33839	+	5.33839i	0.608365	+	0.608365i
$78$		0			0
$79$	−0.113885			−0.0128130			−0.00640652	−	0.999979i	$-0.502039\pi$
$79$	−0.113885			−0.0128130			−0.00640652	+	0.999979i	$0.502039\pi$
$80$	0.215891	−	3.99417i	0.0241373	−	0.446562i
$81$		0			0
$82$	−6.41758	+	1.18671i	−0.708703	+	0.131050i
$83$	−9.76813	−	9.76813i	−1.07219	−	1.07219i	−0.997183	−	0.0750089i	$-0.976101\pi$
$83$	−9.76813	−	9.76813i	−1.07219	−	1.07219i	−0.0750089	−	0.997183i	$-0.523899\pi$
$84$		0			0
$85$	−5.16100	+	5.16100i	−0.559789	+	0.559789i
$86$	4.99310	+	3.43468i	0.538420	+	0.370371i
$87$		0			0
$88$	7.17251	+	1.73129i	0.764592	+	0.184557i
$89$		−	3.74593i		−	0.397068i	−0.980094	−	0.198534i	$-0.936382\pi$
$89$		−	3.74593i		−	0.397068i	0.980094	−	0.198534i	$-0.0636180\pi$
$90$		0			0
$91$	−8.91390	+	8.91390i	−0.934430	+	0.934430i
$92$	3.29345	+	8.60080i	0.343366	+	0.896695i
$93$		0			0
$94$	3.01150	+	16.2858i	0.310613	+	1.67976i
$95$	−1.74787			−0.179328
$96$		0			0
$97$	−13.9853			−1.41999			−0.709995	−	0.704206i	$-0.751303\pi$
$97$	−13.9853			−1.41999			−0.709995	+	0.704206i	$0.751303\pi$
$98$	−0.353676	−	1.91264i	−0.0357267	−	0.193206i
$99$		0			0
$100$	0.715205	+	1.86775i	0.0715205	+	0.186775i
$101$	−3.52228	+	3.52228i	−0.350480	+	0.350480i	−0.860288	−	0.509808i	$-0.829716\pi$
$101$	−3.52228	+	3.52228i	−0.350480	+	0.350480i	0.509808	+	0.860288i	$0.329716\pi$
$102$		0			0
$103$		−	0.150216i		−	0.0148013i	−0.999973	−	0.00740063i	$-0.997644\pi$
$103$		−	0.150216i		−	0.0148013i	0.999973	−	0.00740063i	$-0.00235572\pi$
$104$	−2.89087	+	11.9765i	−0.283473	+	1.17439i
$105$		0			0
$106$	−4.49926	−	3.09497i	−0.437006	−	0.300610i
$107$	2.75062	−	2.75062i	0.265912	−	0.265912i	−0.561539	−	0.827451i	$-0.689790\pi$
$107$	2.75062	−	2.75062i	0.265912	−	0.265912i	0.827451	+	0.561539i	$0.189790\pi$
$108$		0			0
$109$	−6.90778	−	6.90778i	−0.661646	−	0.661646i	0.294122	−	0.955768i	$-0.404973\pi$
$109$	−6.90778	−	6.90778i	−0.661646	−	0.661646i	−0.955768	+	0.294122i	$0.904973\pi$
$110$	−3.62775	+	0.670826i	−0.345892	+	0.0639607i
$111$		0			0
$112$	−7.73181	−	8.61540i	−0.730587	−	0.814078i
$113$	3.49507			0.328788			0.164394	−	0.986395i	$-0.447433\pi$
$113$	3.49507			0.328788			0.164394	+	0.986395i	$0.447433\pi$
$114$		0			0
$115$	−3.25616	−	3.25616i	−0.303638	−	0.303638i
$116$	10.9693	+	4.89461i	1.01847	+	0.454454i
$117$		0			0
$118$	−5.12966	−	3.52861i	−0.472223	−	0.324835i
$119$			21.1228i			1.93632i
$120$		0			0
$121$			4.19472i			0.381338i
$122$	−2.66327	+	3.87168i	−0.241121	+	0.350526i
$123$		0			0
$124$	−3.85314	+	1.47546i	−0.346022	+	0.132500i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$		0			0
$127$	6.25357			0.554915			0.277458	−	0.960738i	$-0.410508\pi$
$127$	6.25357			0.554915			0.277458	+	0.960738i	$0.410508\pi$
$128$	−10.8385	−	3.24437i	−0.958001	−	0.286764i
$129$		0			0
$130$	−1.12013	−	6.05752i	−0.0982417	−	0.531280i
$131$	5.16490	+	5.16490i	0.451259	+	0.451259i	0.895772	−	0.444513i	$-0.146623\pi$
$131$	5.16490	+	5.16490i	0.451259	+	0.451259i	−0.444513	+	0.895772i	$0.646623\pi$
$132$		0			0
$133$	−3.57681	+	3.57681i	−0.310149	+	0.310149i
$134$	−9.34347	+	13.5829i	−0.807153	+	1.17338i
$135$		0			0
$136$	10.7648	+	17.6151i	0.923075	+	1.51049i
$137$		−	18.9408i		−	1.61823i	−0.587654	−	0.809113i	$-0.699948\pi$
$137$		−	18.9408i		−	1.61823i	0.587654	−	0.809113i	$-0.300052\pi$
$138$		0			0
$139$	2.79057	−	2.79057i	0.236693	−	0.236693i	−0.578786	−	0.815479i	$-0.696473\pi$
$139$	2.79057	−	2.79057i	0.236693	−	0.236693i	0.815479	+	0.578786i	$0.196473\pi$
$140$	5.28571	+	2.35854i	0.446724	+	0.199333i
$141$		0			0
$142$	4.53260	−	0.838147i	0.380367	−	0.0703357i
$143$	11.3633			0.950245
$144$		0			0
$145$	−6.00588			−0.498761
$146$	17.6441	−	3.26265i	1.46023	−	0.270019i
$147$		0			0
$148$	1.35883	−	3.04527i	0.111696	−	0.250320i
$149$	1.60372	−	1.60372i	0.131382	−	0.131382i	−0.638358	−	0.769740i	$-0.720386\pi$
$149$	1.60372	−	1.60372i	0.131382	−	0.131382i	0.769740	+	0.638358i	$0.220386\pi$
$150$		0			0
$151$		−	2.53754i		−	0.206502i	−0.994655	−	0.103251i	$-0.967076\pi$
$151$		−	2.53754i		−	0.206502i	0.994655	−	0.103251i	$-0.0329245\pi$
$152$	−1.16000	+	4.80571i	−0.0940883	+	0.389794i
$153$		0			0
$154$	−6.05099	+	8.79653i	−0.487603	+	0.708844i
$155$	1.45875	−	1.45875i	0.117170	−	0.117170i
$156$		0			0
$157$	10.2405	+	10.2405i	0.817278	+	0.817278i	0.985713	−	0.168435i	$-0.0538712\pi$
$157$	10.2405	+	10.2405i	0.817278	+	0.817278i	−0.168435	+	0.985713i	$0.553871\pi$
$158$	−0.0292855	−	0.158373i	−0.00232983	−	0.0125994i
$159$		0			0
$160$	5.60996	−	0.726875i	0.443506	−	0.0574645i
$161$	−13.3267			−1.05029
$162$		0			0
$163$	8.02607	+	8.02607i	0.628650	+	0.628650i	0.947728	−	0.319078i	$-0.103373\pi$
$163$	8.02607	+	8.02607i	0.628650	+	0.628650i	−0.319078	+	0.947728i	$0.603373\pi$
$164$	−3.30056	−	8.61936i	−0.257731	−	0.673059i
$165$		0			0
$166$	11.0721	−	16.0958i	0.859358	−	1.24928i
$167$		−	6.82611i		−	0.528221i	−0.964492	−	0.264110i	$-0.914922\pi$
$167$		−	6.82611i		−	0.528221i	0.964492	−	0.264110i	$-0.0850783\pi$
$168$		0			0
$169$			5.97411i			0.459547i
$170$	−8.50423	−	5.84993i	−0.652245	−	0.448669i
$171$		0			0
$172$	−3.49242	+	7.82683i	−0.266294	+	0.596790i
$173$	−5.08901	−	5.08901i	−0.386910	−	0.386910i	0.486674	−	0.873584i	$-0.338210\pi$
$173$	−5.08901	−	5.08901i	−0.386910	−	0.386910i	−0.873584	+	0.486674i	$0.838210\pi$
$174$		0			0
$175$	−2.89402			−0.218768
$176$	−0.563193	+	10.4196i	−0.0424523	+	0.785404i
$177$		0			0
$178$	5.20924	−	0.963267i	0.390449	−	0.0721999i
$179$	−1.63797	−	1.63797i	−0.122428	−	0.122428i	0.643238	−	0.765666i	$-0.277590\pi$
$179$	−1.63797	−	1.63797i	−0.122428	−	0.122428i	−0.765666	+	0.643238i	$0.777590\pi$
$180$		0			0
$181$	−16.7757	+	16.7757i	−1.24693	+	1.24693i	−0.289855	+	0.957071i	$0.593607\pi$
$181$	−16.7757	+	16.7757i	−1.24693	+	1.24693i	−0.957071	+	0.289855i	$0.906393\pi$
$182$	−14.6882	−	10.1038i	−1.08876	−	0.748943i
$183$		0			0
$184$	−11.1137	+	6.79170i	−0.819312	+	0.500691i
$185$			1.66734i			0.122585i
$186$		0			0
$187$	13.4635	−	13.4635i	0.984546	−	0.984546i
$188$	−21.8733	+	8.37582i	−1.59527	+	0.610869i
$189$		0			0
$190$	−0.449465	−	2.43066i	−0.0326076	−	0.176338i
$191$	−5.85815			−0.423881			−0.211940	−	0.977283i	$-0.567978\pi$
$191$	−5.85815			−0.423881			−0.211940	+	0.977283i	$0.567978\pi$
$192$		0			0
$193$	−0.0241155			−0.00173587			−0.000867935	−	1.00000i	$-0.500276\pi$
$193$	−0.0241155			−0.00173587			−0.000867935		1.00000i	$0.500276\pi$
$194$	−3.59632	−	19.4485i	−0.258201	−	1.39632i
$195$		0			0
$196$	2.56884	−	0.983671i	0.183489	−	0.0702622i
$197$	−14.9086	+	14.9086i	−1.06219	+	1.06219i	−0.0642576	+	0.997933i	$0.520468\pi$
$197$	−14.9086	+	14.9086i	−1.06219	+	1.06219i	−0.997933	+	0.0642576i	$0.979532\pi$
$198$		0			0
$199$		−	13.6525i		−	0.967801i	−0.875123	−	0.483900i	$-0.839220\pi$
$199$		−	13.6525i		−	0.967801i	0.875123	−	0.483900i	$-0.160780\pi$
$200$	−2.41345	+	1.47488i	−0.170656	+	0.104290i
$201$		0			0
$202$	−5.80397	−	3.99246i	−0.408366	−	0.280909i
$203$	−12.2903	+	12.2903i	−0.862612	+	0.862612i
$204$		0			0
$205$	3.26319	+	3.26319i	0.227911	+	0.227911i
$206$	0.208897	−	0.0386282i	0.0145545	−	0.00269135i
$207$		0			0
$208$	−17.3983	−	0.940405i	−1.20636	−	0.0652053i
$209$	4.55966			0.315398
$210$		0			0
$211$	−2.45103	−	2.45103i	−0.168736	−	0.168736i	0.617688	−	0.786424i	$-0.288070\pi$
$211$	−2.45103	−	2.45103i	−0.168736	−	0.168736i	−0.786424	+	0.617688i	$0.788070\pi$
$212$	3.14700	−	7.05271i	0.216137	−	0.484382i
$213$		0			0
$214$	4.53243	+	3.11779i	0.309831	+	0.213128i
$215$		−	4.28533i		−	0.292257i
$216$		0			0
$217$		−	5.97033i		−	0.405293i
$218$	7.82989	−	11.3826i	0.530307	−	0.770924i
$219$		0			0
$220$	−1.86575	−	4.87238i	−0.125789	−	0.328496i
$221$	22.4809	+	22.4809i	1.51223	+	1.51223i
$222$		0			0
$223$	13.9483			0.934045			0.467023	−	0.884245i	$-0.345327\pi$
$223$	13.9483			0.934045			0.467023	+	0.884245i	$0.345327\pi$
$224$	9.99266	−	12.9676i	0.667663	−	0.866434i
$225$		0			0
$226$	0.898758	+	4.86038i	0.0597845	+	0.323307i
$227$	−4.43883	−	4.43883i	−0.294616	−	0.294616i	0.544285	−	0.838901i	$-0.316801\pi$
$227$	−4.43883	−	4.43883i	−0.294616	−	0.294616i	−0.838901	+	0.544285i	$0.816801\pi$
$228$		0			0
$229$	−5.35068	+	5.35068i	−0.353583	+	0.353583i	−0.861441	−	0.507858i	$-0.830438\pi$
$229$	−5.35068	+	5.35068i	−0.353583	+	0.353583i	0.507858	+	0.861441i	$0.330438\pi$
$230$	3.69082	−	5.36546i	0.243365	−	0.353788i
$231$		0			0
$232$	−3.98588	+	16.5129i	−0.261686	+	1.08413i
$233$		−	11.9370i		−	0.782019i	−0.920387	−	0.391010i	$-0.872126\pi$
$233$		−	11.9370i		−	0.782019i	0.920387	−	0.391010i	$-0.127874\pi$
$234$		0			0
$235$	8.28097	−	8.28097i	0.540191	−	0.540191i
$236$	3.58793	−	8.04088i	0.233554	−	0.523416i
$237$		0			0
$238$	−29.3741	+	5.43172i	−1.90404	+	0.352086i
$239$	16.7720			1.08489			0.542445	−	0.840091i	$-0.317499\pi$
$239$	16.7720			1.08489			0.542445	+	0.840091i	$0.317499\pi$
$240$		0			0
$241$	−22.0294			−1.41904			−0.709519	−	0.704686i	$-0.751088\pi$
$241$	−22.0294			−1.41904			−0.709519	+	0.704686i	$0.751088\pi$
$242$	−5.83334	+	1.07867i	−0.374981	+	0.0693397i
$243$		0			0
$244$	−6.06897	−	2.70804i	−0.388526	−	0.173365i
$245$	−0.972532	+	0.972532i	−0.0621328	+	0.0621328i
$246$		0			0
$247$			7.61360i			0.484442i
$248$	−3.04267	−	4.97891i	−0.193210	−	0.316161i
$249$		0			0
$250$	0.801497	−	1.16516i	0.0506911	−	0.0736913i
$251$	−6.63925	+	6.63925i	−0.419066	+	0.419066i	−0.884882	−	0.465816i	$-0.845761\pi$
$251$	−6.63925	+	6.63925i	−0.419066	+	0.419066i	0.465816	+	0.884882i	$0.345761\pi$
$252$		0			0
$253$	8.49432	+	8.49432i	0.534033	+	0.534033i
$254$	1.60811	+	8.69646i	0.100902	+	0.545664i
$255$		0			0
$256$	1.72461	−	15.9068i	0.107788	−	0.994174i
$257$	7.25821			0.452755			0.226377	−	0.974040i	$-0.427312\pi$
$257$	7.25821			0.452755			0.226377	+	0.974040i	$0.427312\pi$
$258$		0			0
$259$	3.41202	+	3.41202i	0.212013	+	0.212013i
$260$	8.13577	−	3.11538i	0.504559	−	0.193208i
$261$		0			0
$262$	−5.85435	+	8.51066i	−0.361683	+	0.525790i
$263$		−	9.27431i		−	0.571878i	−0.958248	−	0.285939i	$-0.907694\pi$
$263$		−	9.27431i		−	0.571878i	0.958248	−	0.285939i	$-0.0923055\pi$
$264$		0			0
$265$			3.86149i			0.237209i
$266$	−5.89383	−	4.05428i	−0.361374	−	0.248584i
$267$		0			0
$268$	−21.2916	−	9.50054i	−1.30059	−	0.580338i
$269$	13.4195	+	13.4195i	0.818199	+	0.818199i	0.985847	−	0.167648i	$-0.0536173\pi$
$269$	13.4195	+	13.4195i	0.818199	+	0.818199i	−0.167648	+	0.985847i	$0.553617\pi$
$270$		0			0
$271$	22.5999			1.37285			0.686423	−	0.727202i	$-0.259180\pi$
$271$	22.5999			1.37285			0.686423	+	0.727202i	$0.259180\pi$
$272$	−21.7281	+	19.4997i	−1.31746	+	1.18234i
$273$		0			0
$274$	26.3399	−	4.87064i	1.59125	−	0.294246i
$275$	1.84462	+	1.84462i	0.111235	+	0.111235i
$276$		0			0
$277$	16.2015	−	16.2015i	0.973451	−	0.973451i	−0.0262056	−	0.999657i	$-0.508342\pi$
$277$	16.2015	−	16.2015i	0.973451	−	0.973451i	0.999657	+	0.0262056i	$0.00834245\pi$
$278$	4.59827	+	3.16308i	0.275786	+	0.189709i
$279$		0			0
$280$	−1.92066	+	7.95701i	−0.114781	+	0.475522i
$281$		−	8.84793i		−	0.527824i	−0.964547	−	0.263912i	$-0.914987\pi$
$281$		−	8.84793i		−	0.527824i	0.964547	−	0.263912i	$-0.0850128\pi$
$282$		0			0
$283$	−20.3062	+	20.3062i	−1.20708	+	1.20708i	−0.235109	+	0.971969i	$0.575545\pi$
$283$	−20.3062	+	20.3062i	−1.20708	+	1.20708i	−0.971969	+	0.235109i	$0.924455\pi$
$284$	2.33112	+	6.08768i	0.138326	+	0.361237i
$285$		0			0
$286$	2.92207	+	15.8022i	0.172786	+	0.934404i
$287$	13.3555			0.788348
$288$		0			0
$289$	36.2718			2.13364
$290$	−1.54441	−	8.35200i	−0.0906910	−	0.490447i
$291$		0			0
$292$	9.07434	+	23.6975i	0.531036	+	1.38679i
$293$	7.16936	−	7.16936i	0.418839	−	0.418839i	−0.465965	−	0.884803i	$-0.654293\pi$
$293$	7.16936	−	7.16936i	0.418839	−	0.418839i	0.884803	+	0.465965i	$0.154293\pi$
$294$		0			0
$295$			4.40253i			0.256325i
$296$	4.58430	+	1.10655i	0.266457	+	0.0643172i
$297$		0			0
$298$	2.64259	+	1.81779i	0.153081	+	0.105302i
$299$	−14.1836	+	14.1836i	−0.820258	+	0.820258i
$300$		0			0
$301$	−8.76943	−	8.76943i	−0.505461	−	0.505461i
$302$	3.52880	−	0.652528i	0.203059	−	0.0375488i
$303$		0			0
$304$	−6.98129	−	0.377349i	−0.400405	−	0.0216425i
$305$	3.32287			0.190267
$306$		0			0
$307$	−18.4308	−	18.4308i	−1.05190	−	1.05190i	−0.998577	−	0.0533241i	$-0.983018\pi$
$307$	−18.4308	−	18.4308i	−1.05190	−	1.05190i	−0.0533241	−	0.998577i	$-0.516982\pi$
$308$	−13.7888	−	6.15271i	−0.785690	−	0.350583i
$309$		0			0
$310$	2.40372	+	1.65348i	0.136522	+	0.0939113i
$311$			7.08961i			0.402015i	0.979590	+	0.201007i	$0.0644215\pi$
$311$			7.08961i			0.402015i	−0.979590	+	0.201007i	$0.935578\pi$
$312$		0			0
$313$		−	22.0477i		−	1.24621i	−0.782139	−	0.623104i	$-0.785871\pi$
$313$		−	22.0477i		−	1.24621i	0.782139	−	0.623104i	$-0.214129\pi$
$314$	−11.6074	+	16.8741i	−0.655046	+	0.952262i
$315$		0			0
$316$	0.212708	−	0.0814510i	0.0119658	−	0.00458198i
$317$	6.19670	+	6.19670i	0.348042	+	0.348042i	0.859380	−	0.511338i	$-0.170850\pi$
$317$	6.19670	+	6.19670i	0.348042	+	0.348042i	−0.511338	+	0.859380i	$0.670850\pi$
$318$		0			0
$319$	15.6675			0.877211
$320$	2.45342	+	7.61451i	0.137150	+	0.425664i
$321$		0			0
$322$	−3.42696	−	18.5326i	−0.190977	−	1.03278i
$323$	9.02076	+	9.02076i	0.501929	+	0.501929i
$324$		0			0
$325$	−3.08011	+	3.08011i	−0.170854	+	0.170854i
$326$	−9.09745	+	13.2253i	−0.503861	+	0.732479i
$327$		0			0
$328$	11.1377	−	6.80636i	0.614975	−	0.375818i
$329$		−	33.8921i		−	1.86853i
$330$		0			0
$331$	−18.6174	+	18.6174i	−1.02330	+	1.02330i	−0.0235823	+	0.999722i	$0.507507\pi$
$331$	−18.6174	+	18.6174i	−1.02330	+	1.02330i	−0.999722	+	0.0235823i	$0.992493\pi$
$332$	25.2306	+	11.2582i	1.38471	+	0.617873i
$333$		0			0
$334$	9.49265	−	1.75534i	0.519415	−	0.0960477i
$335$	11.6575			0.636919
$336$		0			0
$337$	14.2577			0.776666			0.388333	−	0.921519i	$-0.373051\pi$
$337$	14.2577			0.776666			0.388333	+	0.921519i	$0.373051\pi$
$338$	−8.30782	+	1.53624i	−0.451886	+	0.0835606i
$339$		0			0
$340$	5.94827	−	13.3306i	0.322590	−	0.722954i
$341$	−3.80544	+	3.80544i	−0.206076	+	0.206076i
$342$		0			0
$343$		−	16.2778i		−	0.878919i
$344$	−11.7824	−	2.84402i	−0.635262	−	0.153339i
$345$		0			0
$346$	5.76833	−	8.38561i	0.310107	−	0.450813i
$347$	23.5395	−	23.5395i	1.26367	−	1.26367i	0.314363	−	0.949303i	$-0.398209\pi$
$347$	23.5395	−	23.5395i	1.26367	−	1.26367i	0.949303	−	0.314363i	$-0.101791\pi$
$348$		0			0
$349$	−1.56682	−	1.56682i	−0.0838701	−	0.0838701i	0.663927	−	0.747797i	$-0.268888\pi$
$349$	−1.56682	−	1.56682i	−0.0838701	−	0.0838701i	−0.747797	+	0.663927i	$0.768888\pi$
$350$	−0.744198	−	4.02454i	−0.0397791	−	0.215121i
$351$		0			0
$352$	−14.6347	+	1.89619i	−0.780030	+	0.101068i
$353$	−9.44678			−0.502801			−0.251401	−	0.967883i	$-0.580891\pi$
$353$	−9.44678			−0.502801			−0.251401	+	0.967883i	$0.580891\pi$
$354$		0			0
$355$	−2.30472	−	2.30472i	−0.122322	−	0.122322i
$356$	2.67911	+	6.99646i	0.141993	+	0.370811i
$357$		0			0
$358$	1.85662	−	2.69903i	0.0981256	−	0.142648i
$359$		−	18.0452i		−	0.952392i	−0.879339	−	0.476196i	$-0.842015\pi$
$359$		−	18.0452i		−	0.952392i	0.879339	−	0.476196i	$-0.157985\pi$
$360$		0			0
$361$		−	15.9449i		−	0.839208i
$362$	−27.6427	−	19.0150i	−1.45287	−	0.999407i
$363$		0			0
$364$	10.2736	−	23.0242i	0.538485	−	1.20679i
$365$	−8.97159	−	8.97159i	−0.469594	−	0.469594i
$366$		0			0
$367$	29.1329			1.52073			0.760363	−	0.649498i	$-0.225021\pi$
$367$	29.1329			1.52073			0.760363	+	0.649498i	$0.225021\pi$
$368$	−12.3027	−	13.7086i	−0.641321	−	0.714612i
$369$		0			0
$370$	−2.31867	+	0.428757i	−0.120542	+	0.0222900i
$371$	7.90208	+	7.90208i	0.410255	+	0.410255i
$372$		0			0
$373$	3.35598	−	3.35598i	0.173766	−	0.173766i	−0.614866	−	0.788632i	$-0.710790\pi$
$373$	3.35598	−	3.35598i	0.173766	−	0.173766i	0.788632	+	0.614866i	$0.210790\pi$
$374$	22.1849	+	15.2607i	1.14716	+	0.789110i
$375$		0			0
$376$	−17.2725	−	28.2640i	−0.890759	−	1.45760i
$377$			26.1612i			1.34737i
$378$		0			0
$379$	11.6507	−	11.6507i	0.598457	−	0.598457i	−0.341445	−	0.939902i	$-0.610916\pi$
$379$	11.6507	−	11.6507i	0.598457	−	0.598457i	0.939902	+	0.341445i	$0.110916\pi$
$380$	3.26458	−	1.25009i	0.167470	−	0.0641281i
$381$		0			0
$382$	−1.50642	−	8.14656i	−0.0770753	−	0.416814i
$383$	21.8044			1.11415			0.557077	−	0.830461i	$-0.311923\pi$
$383$	21.8044			1.11415			0.557077	+	0.830461i	$0.311923\pi$
$384$		0			0
$385$	7.54962			0.384764
$386$	−0.00620130	−	0.0335359i	−0.000315638	−	0.00170693i
$387$		0			0
$388$	26.1210	−	10.0024i	1.32609	−	0.507793i
$389$	11.8899	−	11.8899i	0.602842	−	0.602842i	−0.338224	−	0.941066i	$-0.609826\pi$
$389$	11.8899	−	11.8899i	0.602842	−	0.602842i	0.941066	+	0.338224i	$0.109826\pi$
$390$		0			0
$391$			33.6101i			1.69973i
$392$	2.02851	+	3.31938i	0.102455	+	0.167654i
$393$		0			0
$394$	−24.5661	−	16.8987i	−1.23762	−	0.851343i
$395$	−0.0805287	+	0.0805287i	−0.00405184	+	0.00405184i
$396$		0			0
$397$	−9.23905	−	9.23905i	−0.463694	−	0.463694i	0.436170	−	0.899864i	$-0.356335\pi$
$397$	−9.23905	−	9.23905i	−0.463694	−	0.463694i	−0.899864	+	0.436170i	$0.856335\pi$
$398$	18.9857	−	3.51074i	0.951667	−	0.175978i
$399$		0			0
$400$	−2.67165	−	2.97696i	−0.133582	−	0.148848i
$401$	14.4744			0.722818			0.361409	−	0.932407i	$-0.382296\pi$
$401$	14.4744			0.722818			0.361409	+	0.932407i	$0.382296\pi$
$402$		0			0
$403$	−6.35422	−	6.35422i	−0.316526	−	0.316526i
$404$	4.05958	−	9.09789i	0.201972	−	0.452637i
$405$		0			0
$406$	−20.2519	−	13.9309i	−1.00508	−	0.691381i
$407$		−	4.34958i		−	0.215601i
$408$		0			0
$409$			9.54117i			0.471781i	0.971780	+	0.235890i	$0.0758006\pi$
$409$			9.54117i			0.471781i	−0.971780	+	0.235890i	$0.924199\pi$
$410$	−3.69878	+	5.37704i	−0.182670	+	0.265553i
$411$		0			0
$412$	0.107436	+	0.280566i	0.00529297	+	0.0138225i
$413$	9.00925	+	9.00925i	0.443316	+	0.443316i
$414$		0			0
$415$	−13.8142			−0.678114
$416$	−3.16622	−	24.4366i	−0.155237	−	1.19810i
$417$		0			0
$418$	1.17252	+	6.34083i	0.0573497	+	0.310140i
$419$	−0.837667	−	0.837667i	−0.0409227	−	0.0409227i	0.686349	−	0.727272i	$-0.259212\pi$
$419$	−0.837667	−	0.837667i	−0.0409227	−	0.0409227i	−0.727272	+	0.686349i	$0.759212\pi$
$420$		0			0
$421$	17.9679	−	17.9679i	0.875702	−	0.875702i	−0.117385	−	0.993087i	$-0.537451\pi$
$421$	17.9679	−	17.9679i	0.875702	−	0.875702i	0.993087	+	0.117385i	$0.0374511\pi$
$422$	2.77822	−	4.03878i	0.135241	−	0.196605i
$423$		0			0
$424$	10.6170	+	2.56273i	0.515608	+	0.124457i
$425$			7.29875i			0.354042i
$426$		0			0
$427$	6.79986	−	6.79986i	0.329068	−	0.329068i
$428$	−3.17020	+	7.10471i	−0.153237	+	0.343419i
$429$		0			0
$430$	5.95934	−	1.10197i	0.287385	−	0.0531419i
$431$	3.85473			0.185676			0.0928380	−	0.995681i	$-0.470406\pi$
$431$	3.85473			0.185676			0.0928380	+	0.995681i	$0.470406\pi$
$432$		0			0
$433$	−25.5651			−1.22858			−0.614289	−	0.789081i	$-0.710557\pi$
$433$	−25.5651			−1.22858			−0.614289	+	0.789081i	$0.710557\pi$
$434$	8.30257	−	1.53527i	0.398536	−	0.0736954i
$435$		0			0
$436$	17.8425	+	7.96151i	0.854500	+	0.381287i
$437$	−5.69135	+	5.69135i	−0.272254	+	0.272254i
$438$		0			0
$439$			30.1311i			1.43808i	0.694970	+	0.719039i	$0.255418\pi$
$439$			30.1311i			1.43808i	−0.694970	+	0.719039i	$0.744582\pi$
$440$	6.29594	−	3.84752i	0.300147	−	0.183423i
$441$		0			0
$442$	−25.4819	+	37.0438i	−1.21205	+	1.76199i
$443$	−20.1625	+	20.1625i	−0.957948	+	0.957948i	−0.999151	−	0.0412027i	$-0.986881\pi$
$443$	−20.1625	+	20.1625i	−0.957948	+	0.957948i	0.0412027	+	0.999151i	$0.486881\pi$
$444$		0			0
$445$	−2.64877	−	2.64877i	−0.125564	−	0.125564i
$446$	3.58680	+	19.3970i	0.169840	+	0.918474i
$447$		0			0
$448$	20.6028	+	10.5616i	0.973393	+	0.498987i
$449$	36.5827			1.72644			0.863221	−	0.504826i	$-0.168443\pi$
$449$	36.5827			1.72644			0.863221	+	0.504826i	$0.168443\pi$
$450$		0			0
$451$	−8.51265	−	8.51265i	−0.400845	−	0.400845i
$452$	−6.52791	+	2.49969i	−0.307047	+	0.117576i
$453$		0			0
$454$	5.03136	−	7.31426i	0.236134	−	0.343275i
$455$			12.6062i			0.590986i
$456$		0			0
$457$			16.7340i			0.782785i	0.920224	+	0.391392i	$0.128006\pi$
$457$			16.7340i			0.782785i	−0.920224	+	0.391392i	$0.871994\pi$
$458$	−8.81679	−	6.06493i	−0.411982	−	0.283396i
$459$		0			0
$460$	8.41051	+	3.75286i	0.392142	+	0.174978i
$461$	−11.8377	−	11.8377i	−0.551335	−	0.551335i	0.375491	−	0.926826i	$-0.377474\pi$
$461$	−11.8377	−	11.8377i	−0.551335	−	0.551335i	−0.926826	+	0.375491i	$0.877474\pi$
$462$		0			0
$463$	−32.2711			−1.49976			−0.749882	−	0.661572i	$-0.769890\pi$
$463$	−32.2711			−1.49976			−0.749882	+	0.661572i	$0.769890\pi$
$464$	−23.9885	−	1.29661i	−1.11364	−	0.0601938i
$465$		0			0
$466$	16.6000	−	3.06960i	0.768982	−	0.142197i
$467$	−1.22565	−	1.22565i	−0.0567163	−	0.0567163i	0.678180	−	0.734896i	$-0.262769\pi$
$467$	−1.22565	−	1.22565i	−0.0567163	−	0.0567163i	−0.734896	+	0.678180i	$0.762769\pi$
$468$		0			0
$469$	23.8558	−	23.8558i	1.10156	−	1.10156i
$470$	13.6453	+	9.38638i	0.629410	+	0.432961i
$471$		0			0
$472$	12.1046	+	2.92180i	0.557159	+	0.134487i
$473$			11.1791i			0.514016i
$474$		0			0
$475$	−1.23593	+	1.23593i	−0.0567084	+	0.0567084i
$476$	−15.1071	−	39.4520i	−0.692433	−	1.80828i
$477$		0			0
$478$	4.31292	+	23.3238i	0.197268	+	1.06680i
$479$	−28.8399			−1.31773			−0.658865	−	0.752261i	$-0.728963\pi$
$479$	−28.8399			−1.31773			−0.658865	+	0.752261i	$0.728963\pi$
$480$		0			0
$481$	7.26282			0.331156
$482$	−5.66486	−	30.6349i	−0.258027	−	1.39538i
$483$		0			0
$484$	−3.00009	−	7.83468i	−0.136368	−	0.356122i
$485$	−9.88909	+	9.88909i	−0.449041	+	0.449041i
$486$		0			0
$487$		−	32.1668i		−	1.45762i	−0.684718	−	0.728808i	$-0.740075\pi$
$487$		−	32.1668i		−	1.45762i	0.684718	−	0.728808i	$-0.259925\pi$
$488$	2.20527	−	9.13611i	0.0998278	−	0.413572i
$489$		0			0
$490$	−1.60253	−	1.10235i	−0.0723948	−	0.0497993i
$491$	5.43607	−	5.43607i	0.245326	−	0.245326i	−0.573723	−	0.819049i	$-0.694501\pi$
$491$	5.43607	−	5.43607i	0.245326	−	0.245326i	0.819049	+	0.573723i	$0.194501\pi$
$492$		0			0
$493$	30.9963	+	30.9963i	1.39600	+	1.39600i
$494$	−10.5878	+	1.95784i	−0.476366	+	0.0880873i
$495$		0			0
$496$	6.14144	−	5.51157i	0.275759	−	0.247477i
$497$	−9.43268			−0.423114
$498$		0			0
$499$	−17.1282	−	17.1282i	−0.766762	−	0.766762i	0.210773	−	0.977535i	$-0.432402\pi$
$499$	−17.1282	−	17.1282i	−0.766762	−	0.766762i	−0.977535	+	0.210773i	$0.932402\pi$
$500$	1.82642	+	0.814970i	0.0816801	+	0.0364466i
$501$		0			0
$502$	−10.9401	−	7.52551i	−0.488280	−	0.335880i
$503$		−	23.5180i		−	1.04862i	−0.851529	−	0.524308i	$-0.824324\pi$
$503$		−	23.5180i		−	1.04862i	0.851529	−	0.524308i	$-0.175676\pi$
$504$		0			0
$505$			4.98126i			0.221663i
$506$	−9.62821	+	13.9968i	−0.428026	+	0.622235i
$507$		0			0
$508$	−11.6801	+	4.47259i	−0.518221	+	0.198439i
$509$	−20.3147	−	20.3147i	−0.900434	−	0.900434i	0.0950391	−	0.995474i	$-0.469702\pi$
$509$	−20.3147	−	20.3147i	−0.900434	−	0.900434i	−0.995474	+	0.0950391i	$0.969702\pi$
$510$		0			0
$511$	−36.7186			−1.62434
$512$	22.5641	−	1.69212i	0.997200	−	0.0747820i
$513$		0			0
$514$	1.86645	+	10.0935i	0.0823256	+	0.445207i
$515$	−0.106219	−	0.106219i	−0.00468057	−	0.00468057i
$516$		0			0
$517$	−21.6025	+	21.6025i	−0.950077	+	0.950077i
$518$	−3.86748	+	5.62229i	−0.169928	+	0.247029i
$519$		0			0
$520$	6.42449	+	10.5128i	0.281732	+	0.461017i
$521$		−	35.5082i		−	1.55564i	−0.628487	−	0.777820i	$-0.716325\pi$
$521$		−	35.5082i		−	1.55564i	0.628487	−	0.777820i	$-0.283675\pi$
$522$		0			0
$523$	0.677766	−	0.677766i	0.0296366	−	0.0296366i	−0.692133	−	0.721770i	$-0.743329\pi$
$523$	0.677766	−	0.677766i	0.0296366	−	0.0296366i	0.721770	+	0.692133i	$0.243329\pi$
$524$	−13.3407	−	5.95276i	−0.582791	−	0.260048i
$525$		0			0
$526$	12.8972	−	2.38489i	0.562345	−	0.103986i
$527$	−15.0572			−0.655904
$528$		0			0
$529$	1.79485			0.0780371
$530$	−5.36993	+	0.992982i	−0.233255	+	0.0431324i
$531$		0			0
$532$	4.12243	−	9.23874i	0.178730	−	0.400550i
$533$	14.2142	−	14.2142i	0.615686	−	0.615686i
$534$		0			0
$535$		−	3.88996i		−	0.168178i
$536$	7.73667	−	32.0519i	0.334173	−	1.38443i
$537$		0			0
$538$	−15.2108	+	22.1124i	−0.655784	+	0.953334i
$539$	2.53704	−	2.53704i	0.109278	−	0.109278i
$540$		0			0
$541$	5.37099	+	5.37099i	0.230917	+	0.230917i	0.813075	−	0.582158i	$-0.197792\pi$
$541$	5.37099	+	5.37099i	0.230917	+	0.230917i	−0.582158	+	0.813075i	$0.697792\pi$
$542$	5.81157	+	31.4283i	0.249628	+	1.34996i
$543$		0			0
$544$	−32.7044	−	25.2016i	−1.40219	−	1.08051i
$545$	−9.76908			−0.418461
$546$		0			0
$547$	8.86782	+	8.86782i	0.379161	+	0.379161i	0.870799	−	0.491639i	$-0.163602\pi$
$547$	8.86782	+	8.86782i	0.379161	+	0.379161i	−0.491639	+	0.870799i	$0.663602\pi$
$548$	13.5466	+	35.3767i	0.578682	+	1.51122i
$549$		0			0
$550$	−2.09086	+	3.03955i	−0.0891545	+	0.129607i
$551$			10.4975i			0.447209i
$552$		0			0
$553$			0.329585i			0.0140154i
$554$	26.6966	+	18.3641i	1.13423	+	0.780218i
$555$		0			0
$556$	−3.21625	+	7.20791i	−0.136399	+	0.305684i
$557$	22.8089	+	22.8089i	0.966446	+	0.966446i	0.999455	−	0.0330091i	$-0.0105090\pi$
$557$	22.8089	+	22.8089i	0.966446	+	0.966446i	−0.0330091	+	0.999455i	$0.510509\pi$
$558$		0			0
$559$	−18.6666			−0.789513
$560$	−11.5592	−	0.624793i	−0.488466	−	0.0264023i
$561$		0			0
$562$	12.3043	−	2.27525i	0.519024	−	0.0959755i
$563$	−20.9711	−	20.9711i	−0.883826	−	0.883826i	0.110095	−	0.993921i	$-0.464884\pi$
$563$	−20.9711	−	20.9711i	−0.883826	−	0.883826i	−0.993921	+	0.110095i	$0.964884\pi$
$564$		0			0
$565$	2.47139	−	2.47139i	0.103972	−	0.103972i
$566$	−33.4603	−	23.0168i	−1.40644	−	0.967469i
$567$		0			0
$568$	−7.86630	+	4.80719i	−0.330063	+	0.201705i
$569$		−	8.05295i		−	0.337597i	−0.985651	−	0.168799i	$-0.946011\pi$
$569$		−	8.05295i		−	0.337597i	0.985651	−	0.168799i	$-0.0539888\pi$
$570$		0			0
$571$	−22.5040	+	22.5040i	−0.941762	+	0.941762i	−0.998395	−	0.0566333i	$-0.981963\pi$
$571$	−22.5040	+	22.5040i	−0.941762	+	0.941762i	0.0566333	+	0.998395i	$0.481963\pi$
$572$	−21.2237	+	8.12708i	−0.887409	+	0.339810i
$573$		0			0
$574$	3.43436	+	18.5726i	0.143347	+	0.775206i
$575$	−4.60490			−0.192038
$576$		0			0
$577$	15.9819			0.665334			0.332667	−	0.943044i	$-0.392051\pi$
$577$	15.9819			0.665334			0.332667	+	0.943044i	$0.392051\pi$
$578$	9.32730	+	50.4410i	0.387965	+	2.09807i
$579$		0			0
$580$	11.2175	−	4.29544i	0.465780	−	0.178358i
$581$	−28.2692	+	28.2692i	−1.17280	+	1.17280i
$582$		0			0
$583$		−	10.0734i		−	0.417199i
$584$	−30.6212	+	18.7129i	−1.26711	+	0.774347i
$585$		0			0
$586$	11.8136	+	8.12638i	0.488015	+	0.335698i
$587$	5.25752	−	5.25752i	0.217001	−	0.217001i	−0.590232	−	0.807233i	$-0.700964\pi$
$587$	5.25752	−	5.25752i	0.217001	−	0.217001i	0.807233	+	0.590232i	$0.200964\pi$
$588$		0			0
$589$	−2.54971	−	2.54971i	−0.105059	−	0.105059i
$590$	−6.12232	+	1.13211i	−0.252052	+	0.0466082i
$591$		0			0
$592$	−0.359964	+	6.65965i	−0.0147944	+	0.273710i
$593$	−3.96571			−0.162852			−0.0814260	−	0.996679i	$-0.525947\pi$
$593$	−3.96571			−0.162852			−0.0814260	+	0.996679i	$0.525947\pi$
$594$		0			0
$595$	14.9360	+	14.9360i	0.612318	+	0.612318i
$596$	−1.84835	+	4.14233i	−0.0757115	+	0.169676i
$597$		0			0
$598$	−23.3716	−	16.0769i	−0.955734	−	0.657435i
$599$			8.31600i			0.339783i	0.985463	+	0.169891i	$0.0543417\pi$
$599$			8.31600i			0.339783i	−0.985463	+	0.169891i	$0.945658\pi$
$600$		0			0
$601$			46.0550i			1.87862i	0.343068	+	0.939310i	$0.388534\pi$
$601$			46.0550i			1.87862i	−0.343068	+	0.939310i	$0.611466\pi$
$602$	9.94004	−	14.4502i	0.405126	−	0.588944i
$603$		0			0
$604$	1.81486	+	4.73948i	0.0738456	+	0.192847i
$605$	2.96612	+	2.96612i	0.120590	+	0.120590i
$606$		0			0
$607$	−5.05760			−0.205282			−0.102641	−	0.994718i	$-0.532729\pi$
$607$	−5.05760			−0.205282			−0.102641	+	0.994718i	$0.532729\pi$
$608$	−1.27048	−	9.80549i	−0.0515249	−	0.397665i
$609$		0			0
$610$	0.854476	+	4.62091i	0.0345967	+	0.187095i
$611$	−36.0713	−	36.0713i	−1.45929	−	1.45929i
$612$		0			0
$613$	31.2000	−	31.2000i	1.26016	−	1.26016i	0.309141	−	0.951016i	$-0.399958\pi$
$613$	31.2000	−	31.2000i	1.26016	−	1.26016i	0.951016	−	0.309141i	$-0.100042\pi$
$614$	20.8911	−	30.3701i	0.843096	−	1.22564i
$615$		0			0
$616$	5.01041	−	20.7574i	0.201875	−	0.836339i
$617$			30.7412i			1.23759i	0.785551	+	0.618796i	$0.212379\pi$
$617$			30.7412i			1.23759i	−0.785551	+	0.618796i	$0.787621\pi$
$618$		0			0
$619$	−16.8766	+	16.8766i	−0.678329	+	0.678329i	−0.959622	−	0.281293i	$-0.909237\pi$
$619$	−16.8766	+	16.8766i	−0.678329	+	0.678329i	0.281293	+	0.959622i	$0.409237\pi$
$620$	−1.68127	+	3.76789i	−0.0675216	+	0.151322i
$621$		0			0
$622$	−9.85908	+	1.82309i	−0.395313	+	0.0730994i
$623$	−10.8408			−0.434328
$624$		0			0
$625$	−1.00000			−0.0400000
$626$	30.6603	−	5.66956i	1.22543	−	0.226601i
$627$		0			0
$628$	−26.4506	−	11.8026i	−1.05550	−	0.470974i
$629$	8.60515	−	8.60515i	0.343110	−	0.343110i
$630$		0			0
$631$		−	30.7318i		−	1.22342i	−0.791084	−	0.611708i	$-0.790483\pi$
$631$		−	30.7318i		−	1.22342i	0.791084	−	0.611708i	$-0.209517\pi$
$632$	0.167967	+	0.274855i	0.00668136	+	0.0109331i
$633$		0			0
$634$	−7.02389	+	10.2109i	−0.278954	+	0.405525i
$635$	4.42195	−	4.42195i	0.175480	−	0.175480i
$636$		0			0
$637$	4.23628	+	4.23628i	0.167848	+	0.167848i
$638$	4.02890	+	21.7878i	0.159506	+	0.862588i
$639$		0			0
$640$	−9.95812	+	5.36989i	−0.393629	+	0.212264i
$641$	−22.1658			−0.875496			−0.437748	−	0.899098i	$-0.644224\pi$
$641$	−22.1658			−0.875496			−0.437748	+	0.899098i	$0.644224\pi$
$642$		0			0
$643$	0.975773	+	0.975773i	0.0384807	+	0.0384807i	0.726085	−	0.687605i	$-0.241338\pi$
$643$	0.975773	+	0.975773i	0.0384807	+	0.0384807i	−0.687605	+	0.726085i	$0.741338\pi$
$644$	24.8909	−	9.53133i	0.980839	−	0.375587i
$645$		0			0
$646$	−10.2249	+	14.8643i	−0.402294	+	0.584828i
$647$		−	23.2610i		−	0.914484i	−0.889342	−	0.457242i	$-0.848837\pi$
$647$		−	23.2610i		−	0.914484i	0.889342	−	0.457242i	$-0.151163\pi$
$648$		0			0
$649$		−	11.4848i		−	0.450819i
$650$	−5.07536	−	3.49126i	−0.199072	−	0.136939i
$651$		0			0
$652$	−20.7310	−	9.25038i	−0.811887	−	0.362273i
$653$	23.9372	+	23.9372i	0.936735	+	0.936735i	0.998115	−	0.0613792i	$-0.0195499\pi$
$653$	23.9372	+	23.9372i	0.936735	+	0.936735i	−0.0613792	+	0.998115i	$0.519550\pi$
$654$		0			0
$655$	7.30427			0.285401
$656$	12.3292	+	13.7382i	0.481376	+	0.536387i
$657$		0			0
$658$	47.1316	−	8.71535i	1.83738	−	0.339760i
$659$	14.1064	+	14.1064i	0.549508	+	0.549508i	0.926299	−	0.376790i	$-0.122972\pi$
$659$	14.1064	+	14.1064i	0.549508	+	0.549508i	−0.376790	+	0.926299i	$0.622972\pi$
$660$		0			0
$661$	−3.04121	+	3.04121i	−0.118289	+	0.118289i	−0.763774	−	0.645484i	$-0.776656\pi$
$661$	−3.04121	+	3.04121i	−0.118289	+	0.118289i	0.645484	+	0.763774i	$0.276656\pi$
$662$	−30.6775	−	21.1026i	−1.19232	−	0.820175i
$663$		0			0
$664$	−9.16800	+	37.9817i	−0.355787	+	1.47398i
$665$			5.05838i			0.196156i
$666$		0			0
$667$	−19.5561	+	19.5561i	−0.757215	+	0.757215i
$668$	4.88207	+	12.7495i	0.188893	+	0.493291i
$669$		0			0
$670$	2.99773	+	16.2114i	0.115813	+	0.626301i
$671$	−8.66835			−0.334638
$672$		0			0
$673$	−25.3628			−0.977662			−0.488831	−	0.872378i	$-0.662577\pi$
$673$	−25.3628			−0.977662			−0.488831	+	0.872378i	$0.662577\pi$
$674$	3.66637	+	19.8273i	0.141223	+	0.763719i
$675$		0			0
$676$	−4.27271	−	11.1581i	−0.164335	−	0.429159i
$677$	−9.36526	+	9.36526i	−0.359936	+	0.359936i	−0.863789	−	0.503853i	$-0.831915\pi$
$677$	−9.36526	+	9.36526i	−0.359936	+	0.359936i	0.503853	+	0.863789i	$0.331915\pi$
$678$		0			0
$679$			40.4737i			1.55324i
$680$	20.0677	+	4.84392i	0.769560	+	0.185756i
$681$		0			0
$682$	−6.27056	−	4.31342i	−0.240112	−	0.165169i
$683$	−4.20530	+	4.20530i	−0.160911	+	0.160911i	−0.782970	−	0.622059i	$-0.786296\pi$
$683$	−4.20530	+	4.20530i	−0.160911	+	0.160911i	0.622059	+	0.782970i	$0.286296\pi$
$684$		0			0
$685$	−13.3932	−	13.3932i	−0.511728	−	0.511728i
$686$	22.6365	−	4.18584i	0.864267	−	0.159816i
$687$		0			0
$688$	0.925163	−	17.1163i	0.0352715	−	0.652554i
$689$	16.8204			0.640804
$690$		0			0
$691$	5.79295	+	5.79295i	0.220374	+	0.220374i	0.808656	−	0.588282i	$-0.200195\pi$
$691$	5.79295	+	5.79295i	0.220374	+	0.220374i	−0.588282	+	0.808656i	$0.700195\pi$
$692$	13.1447	+	5.86530i	0.499686	+	0.222965i
$693$		0			0
$694$	38.7881	+	26.6817i	1.47238	+	1.01282i
$695$		−	3.94646i		−	0.149698i
$696$		0			0
$697$		−	33.6826i		−	1.27582i
$698$	1.77598	−	2.58179i	0.0672217	−	0.0977223i
$699$		0			0
$700$	5.40530	−	2.06982i	0.204301	−	0.0782319i
$701$	0.258991	+	0.258991i	0.00978196	+	0.00978196i	0.711981	−	0.702199i	$-0.247798\pi$
$701$	0.258991	+	0.258991i	0.00978196	+	0.00978196i	−0.702199	+	0.711981i	$0.747798\pi$
$702$		0			0
$703$	2.91430			0.109915
$704$	−6.40023	−	19.8639i	−0.241218	−	0.748649i
$705$		0			0
$706$	−2.42924	−	13.1370i	−0.0914257	−	0.494419i
$707$	10.1936	+	10.1936i	0.383368	+	0.383368i
$708$		0			0
$709$	−0.751674	+	0.751674i	−0.0282297	+	0.0282297i	−0.721081	−	0.692851i	$-0.756354\pi$
$709$	−0.751674	+	0.751674i	−0.0282297	+	0.0282297i	0.692851	+	0.721081i	$0.256354\pi$
$710$	2.61237	−	3.79769i	0.0980406	−	0.142525i
$711$		0			0
$712$	−9.04060	+	5.52481i	−0.338811	+	0.207051i
$713$		−	9.49986i		−	0.355773i
$714$		0			0
$715$	8.03505	−	8.03505i	0.300494	−	0.300494i
$716$	4.23081	+	1.88783i	0.158113	+	0.0705516i
$717$		0			0
$718$	25.0944	−	4.64034i	0.936515	−	0.173176i
$719$	−39.6557			−1.47891			−0.739455	−	0.673206i	$-0.764917\pi$
$719$	−39.6557			−1.47891			−0.739455	+	0.673206i	$0.764917\pi$
$720$		0			0
$721$	−0.434730			−0.0161902
$722$	22.1736	−	4.10025i	0.825218	−	0.152595i
$723$		0			0
$724$	19.3347	−	43.3308i	0.718567	−	1.61037i
$725$	−4.24680	+	4.24680i	−0.157722	+	0.157722i
$726$		0			0
$727$		−	22.2952i		−	0.826881i	−0.910531	−	0.413441i	$-0.864327\pi$
$727$		−	22.2952i		−	0.826881i	0.910531	−	0.413441i	$-0.135673\pi$
$728$	34.6602	+	8.36625i	1.28459	+	0.310074i
$729$		0			0
$730$	10.1692	−	14.7833i	0.376378	−	0.547154i
$731$	−22.1166	+	22.1166i	−0.818011	+	0.818011i
$732$		0			0
$733$	28.2309	+	28.2309i	1.04273	+	1.04273i	0.999045	+	0.0436851i	$0.0139098\pi$
$733$	28.2309	+	28.2309i	1.04273	+	1.04273i	0.0436851	+	0.999045i	$0.486090\pi$
$734$	7.49154	+	40.5134i	0.276518	+	1.49538i
$735$		0			0
$736$	15.9001	−	20.6337i	0.586086	−	0.760570i
$737$	−30.4109			−1.12020
$738$		0			0
$739$	−5.45140	−	5.45140i	−0.200533	−	0.200533i	0.599695	−	0.800228i	$-0.295288\pi$
$739$	−5.45140	−	5.45140i	−0.200533	−	0.200533i	−0.800228	+	0.599695i	$0.795288\pi$
$740$	−1.19249	−	3.11417i	−0.0438369	−	0.114479i
$741$		0			0
$742$	−8.95691	+	13.0210i	−0.328819	+	0.478014i
$743$			52.5667i			1.92849i	0.265020	+	0.964243i	$0.414621\pi$
$743$			52.5667i			1.92849i	−0.265020	+	0.964243i	$0.585379\pi$
$744$		0			0
$745$		−	2.26800i		−	0.0830931i
$746$	5.52994	+	3.80396i	0.202466	+	0.139273i
$747$		0			0
$748$	−15.5172	+	34.7755i	−0.567365	+	1.27152i
$749$	−7.96035	−	7.96035i	−0.290865	−	0.290865i
$750$		0			0
$751$	31.0189			1.13190			0.565948	−	0.824441i	$-0.308510\pi$
$751$	31.0189			1.13190			0.565948	+	0.824441i	$0.308510\pi$
$752$	34.8634	−	31.2878i	1.27134	−	1.14095i
$753$		0			0
$754$	−36.3807	+	6.72735i	−1.32491	+	0.244996i
$755$	−1.79431	−	1.79431i	−0.0653016	−	0.0653016i
$756$		0			0
$757$	−2.47389	+	2.47389i	−0.0899152	+	0.0899152i	−0.750634	−	0.660719i	$-0.770252\pi$
$757$	−2.47389	+	2.47389i	−0.0899152	+	0.0899152i	0.660719	+	0.750634i	$0.270252\pi$
$758$	19.1979	+	13.2059i	0.697300	+	0.479662i
$759$		0			0
$760$	2.57791	+	4.21839i	0.0935105	+	0.153017i
$761$		−	2.48375i		−	0.0900358i	−0.998986	−	0.0450179i	$-0.985666\pi$
$761$		−	2.48375i		−	0.0900358i	0.998986	−	0.0450179i	$-0.0143345\pi$
$762$		0			0
$763$	−19.9913	+	19.9913i	−0.723733	+	0.723733i
$764$	10.9415	−	4.18978i	0.395851	−	0.151581i
$765$		0			0
$766$	5.60701	+	30.3221i	0.202590	+	1.09558i
$767$	19.1771			0.692444
$768$		0			0
$769$	43.4690			1.56753			0.783767	−	0.621055i	$-0.213296\pi$
$769$	43.4690			1.56753			0.783767	+	0.621055i	$0.213296\pi$
$770$	1.94139	+	10.4988i	0.0699627	+	0.378350i
$771$		0			0
$772$	0.0450416	−	0.0172475i	0.00162108	−	0.000620752i
$773$	−0.297026	+	0.297026i	−0.0106833	+	0.0106833i	−0.712428	−	0.701745i	$-0.752405\pi$
$773$	−0.297026	+	0.297026i	−0.0106833	+	0.0106833i	0.701745	+	0.712428i	$0.252405\pi$
$774$		0			0
$775$		−	2.06299i		−	0.0741047i
$776$	20.6267	+	33.7527i	0.740454	+	1.21165i
$777$		0			0
$778$	19.5920	+	13.4771i	0.702409	+	0.483176i
$779$	5.70363	−	5.70363i	0.204354	−	0.204354i
$780$		0			0
$781$	6.01231	+	6.01231i	0.215137	+	0.215137i
$782$	−46.7394	+	8.64283i	−1.67140	+	0.309067i
$783$		0			0
$784$	−4.09442	+	3.67450i	−0.146229	+	0.131232i
$785$	14.4822			0.516892
$786$		0			0
$787$	−23.6931	−	23.6931i	−0.844567	−	0.844567i	0.144882	−	0.989449i	$-0.453720\pi$
$787$	−23.6931	−	23.6931i	−0.844567	−	0.844567i	−0.989449	+	0.144882i	$0.953720\pi$
$788$	17.1827	−	38.5081i	0.612110	−	1.37179i
$789$		0			0
$790$	−0.132694	−	0.0912783i	−0.00472105	−	0.00324754i
$791$		−	10.1148i		−	0.359641i
$792$		0			0
$793$		−	14.4742i		−	0.513993i
$794$	10.4723	−	15.2240i	0.371650	−	0.540279i
$795$		0			0
$796$	9.76435	+	25.4994i	0.346088	+	0.903804i
$797$	−38.2292	−	38.2292i	−1.35415	−	1.35415i	−0.880963	−	0.473186i	$-0.843104\pi$
$797$	−38.2292	−	38.2292i	−1.35415	−	1.35415i	−0.473186	−	0.880963i	$-0.656896\pi$
$798$		0			0
$799$	−85.4762			−3.02393
$800$	3.45286	−	4.48082i	0.122077	−	0.158421i
$801$		0			0
$802$	3.72210	+	20.1287i	0.131432	+	0.710768i
$803$	23.4041	+	23.4041i	0.825913	+	0.825913i
$804$		0			0
$805$	−9.42340	+	9.42340i	−0.332131	+	0.332131i
$806$	7.20243	−	10.4704i	0.253695	−	0.368804i
$807$		0			0
$808$	13.6958	+	3.30588i	0.481816	+	0.116300i
$809$			53.8310i			1.89260i	0.323296	+	0.946298i	$0.395209\pi$
$809$			53.8310i			1.89260i	−0.323296	+	0.946298i	$0.604791\pi$
$810$		0			0
$811$	27.0549	−	27.0549i	0.950025	−	0.950025i	−0.0487847	−	0.998809i	$-0.515535\pi$
$811$	27.0549	−	27.0549i	0.950025	−	0.950025i	0.998809	+	0.0487847i	$0.0155348\pi$
$812$	14.1651	−	31.7454i	0.497098	−	1.11404i
$813$		0			0
$814$	6.04870	−	1.11850i	0.212007	−	0.0392033i
$815$	11.3506			0.397593
$816$		0			0
$817$	−7.49020			−0.262049
$818$	−13.2683	+	2.45351i	−0.463916	+	0.0857851i
$819$		0			0
$820$	−8.42866	−	3.76096i	−0.294342	−	0.131338i
$821$	24.2170	−	24.2170i	0.845180	−	0.845180i	−0.144347	−	0.989527i	$-0.546108\pi$
$821$	24.2170	−	24.2170i	0.845180	−	0.845180i	0.989527	+	0.144347i	$0.0461082\pi$
$822$		0			0
$823$			41.3013i			1.43967i	0.694144	+	0.719836i	$0.255783\pi$
$823$			41.3013i			1.43967i	−0.694144	+	0.719836i	$0.744217\pi$
$824$	−0.362539	+	0.221552i	−0.0126296	+	0.00771812i
$825$		0			0
$826$	−10.2119	+	14.8453i	−0.355317	+	0.516535i
$827$	−15.7264	+	15.7264i	−0.546862	+	0.546862i	−0.925532	−	0.378670i	$-0.876382\pi$
$827$	−15.7264	+	15.7264i	−0.546862	+	0.546862i	0.378670	+	0.925532i	$0.376382\pi$
$828$		0			0
$829$	−20.7323	−	20.7323i	−0.720061	−	0.720061i	0.248556	−	0.968618i	$-0.420044\pi$
$829$	−20.7323	−	20.7323i	−0.720061	−	0.720061i	−0.968618	+	0.248556i	$0.920044\pi$
$830$	−3.55233	−	19.2106i	−0.123303	−	0.666809i
$831$		0			0
$832$	33.1682	−	10.6869i	1.14990	−	0.370503i
$833$	10.0385			0.347813
$834$		0			0
$835$	−4.82679	−	4.82679i	−0.167038	−	0.167038i
$836$	−8.51629	+	3.26109i	−0.294542	+	0.112787i
$837$		0			0
$838$	0.949485	−	1.38030i	0.0327994	−	0.0476816i
$839$			43.6919i			1.50841i	0.656638	+	0.754206i	$0.271978\pi$
$839$			43.6919i			1.50841i	−0.656638	+	0.754206i	$0.728022\pi$
$840$		0			0
$841$			7.07060i			0.243814i
$842$	29.6073	+	20.3664i	1.02033	+	0.701872i
$843$		0			0
$844$	6.33090	+	2.82492i	0.217919	+	0.0972377i
$845$	4.22433	+	4.22433i	0.145321	+	0.145321i
$846$		0			0
$847$	12.1396			0.417122
$848$	−0.833659	+	15.4234i	−0.0286280	+	0.529643i
$849$		0			0
$850$	−10.1499	+	1.87688i	−0.348140	+	0.0643763i
$851$	5.42913	+	5.42913i	0.186108	+	0.186108i
$852$		0			0
$853$	−35.0610	+	35.0610i	−1.20046	+	1.20046i	−0.226439	+	0.974025i	$0.572708\pi$
$853$	−35.0610	+	35.0610i	−1.20046	+	1.20046i	−0.974025	+	0.226439i	$0.927292\pi$
$854$	11.2047	+	7.70756i	0.383418	+	0.263747i
$855$		0			0
$856$	−10.6953	−	2.58162i	−0.365558	−	0.0882381i
$857$		−	45.3397i		−	1.54878i	−0.632711	−	0.774388i	$-0.718058\pi$
$857$		−	45.3397i		−	1.54878i	0.632711	−	0.774388i	$-0.281942\pi$
$858$		0			0
$859$	32.1229	−	32.1229i	1.09602	−	1.09602i	0.101147	−	0.994871i	$-0.467749\pi$
$859$	32.1229	−	32.1229i	1.09602	−	1.09602i	0.994871	−	0.101147i	$-0.0322514\pi$
$860$	3.06489	+	8.00391i	0.104512	+	0.272931i
$861$		0			0
$862$	0.991245	+	5.36054i	0.0337619	+	0.182581i
$863$	−36.9142			−1.25657			−0.628287	−	0.777981i	$-0.716244\pi$
$863$	−36.9142			−1.25657			−0.628287	+	0.777981i	$0.716244\pi$
$864$		0			0
$865$	−7.19695			−0.244704
$866$	−6.57406	−	35.5517i	−0.223396	−	1.20810i
$867$		0			0
$868$	4.27002	+	11.1511i	0.144934	+	0.378492i
$869$	0.210075	−	0.210075i	0.00712630	−	0.00712630i
$870$		0			0
$871$		−	50.7793i		−	1.72059i
$872$	−6.48338	+	26.8597i	−0.219555	+	0.909585i
$873$		0			0
$874$	−9.37813	−	6.45107i	−0.317220	−	0.218211i
$875$	−2.04638	+	2.04638i	−0.0691804	+	0.0691804i
$876$		0			0
$877$	−15.7178	−	15.7178i	−0.530753	−	0.530753i	0.390044	−	0.920796i	$-0.372460\pi$
$877$	−15.7178	−	15.7178i	−0.530753	−	0.530753i	−0.920796	+	0.390044i	$0.872460\pi$
$878$	−41.9014	+	7.74821i	−1.41410	+	0.261490i
$879$		0			0
$880$	6.96951	+	7.76598i	0.234942	+	0.261791i
$881$	−1.16748			−0.0393335			−0.0196667	−	0.999807i	$-0.506261\pi$
$881$	−1.16748			−0.0393335			−0.0196667	+	0.999807i	$0.506261\pi$
$882$		0			0
$883$	32.2410	+	32.2410i	1.08500	+	1.08500i	0.996035	+	0.0889621i	$0.0283550\pi$
$883$	32.2410	+	32.2410i	1.08500	+	1.08500i	0.0889621	+	0.996035i	$0.471645\pi$
$884$	−58.0672	−	25.9102i	−1.95301	−	0.871455i
$885$		0			0
$886$	−33.2235	−	22.8539i	−1.11616	−	0.767792i
$887$		−	42.7282i		−	1.43467i	−0.696728	−	0.717336i	$-0.745361\pi$
$887$		−	42.7282i		−	1.43467i	0.696728	−	0.717336i	$-0.254639\pi$
$888$		0			0
$889$		−	18.0980i		−	0.606987i
$890$	3.00235	−	4.36462i	0.100639	−	0.146302i
$891$		0			0
$892$	−26.0518	+	9.97588i	−0.872280	+	0.334017i
$893$	−14.4741	−	14.4741i	−0.484356	−	0.484356i
$894$		0			0
$895$	−2.31644			−0.0774302
$896$	−9.38928	+	31.3670i	−0.313674	+	1.04790i
$897$		0			0
$898$	9.40724	+	50.8732i	0.313924	+	1.69766i
$899$	−8.76109	−	8.76109i	−0.292199	−	0.292199i
$900$		0			0
$901$	19.9291	−	19.9291i	0.663935	−	0.663935i
$902$	9.64899	−	14.0270i	0.321276	−	0.467050i
$903$		0			0
$904$	−5.15482	−	8.43516i	−0.171447	−	0.280549i
$905$			23.7244i			0.788625i
$906$		0			0
$907$	1.23335	−	1.23335i	0.0409528	−	0.0409528i	−0.686334	−	0.727287i	$-0.740781\pi$
$907$	1.23335	−	1.23335i	0.0409528	−	0.0409528i	0.727287	+	0.686334i	$0.240781\pi$
$908$	11.4653	+	5.11594i	0.380489	+	0.169779i
$909$		0			0
$910$	−17.5306	+	3.24167i	−0.581134	+	0.107460i
$911$	−23.9284			−0.792785			−0.396392	−	0.918081i	$-0.629738\pi$
$911$	−23.9284			−0.792785			−0.396392	+	0.918081i	$0.629738\pi$
$912$		0			0
$913$	36.0371			1.19265
$914$	−23.2710	+	4.30316i	−0.769735	+	0.142336i
$915$		0			0
$916$	6.16689	−	13.8206i	0.203760	−	0.456644i
$917$	14.9473	−	14.9473i	0.493605	−	0.493605i
$918$		0			0
$919$			45.3844i			1.49709i	0.663082	+	0.748546i	$0.269248\pi$
$919$			45.3844i			1.49709i	−0.663082	+	0.748546i	$0.730752\pi$
$920$	−3.05611	+	12.6610i	−0.100757	+	0.417421i
$921$		0			0
$922$	13.4179	−	19.5060i	0.441893	−	0.642395i
$923$	−10.0392	+	10.0392i	−0.330444	+	0.330444i
$924$		0			0
$925$	1.17899	+	1.17899i	0.0387649	+	0.0387649i
$926$	−8.29851	−	44.8774i	−0.272706	−	1.47476i
$927$		0			0
$928$	−4.36553	−	33.6927i	−0.143305	−	1.10602i
$929$	6.51036			0.213598			0.106799	−	0.994281i	$-0.465940\pi$
$929$	6.51036			0.213598			0.106799	+	0.994281i	$0.465940\pi$
$930$		0			0
$931$	1.69986	+	1.69986i	0.0557107	+	0.0557107i
$932$	8.53741	+	22.2953i	0.279652	+	0.730307i
$933$		0			0
$934$	1.38926	−	2.01961i	0.0454579	−	0.0660837i
$935$		−	19.0402i		−	0.622681i
$936$		0			0
$937$			40.2986i			1.31650i	0.752801	+	0.658248i	$0.228702\pi$
$937$			40.2986i			1.31650i	−0.752801	+	0.658248i	$0.771298\pi$
$938$	39.3092	+	27.0402i	1.28349	+	0.882894i
$939$		0			0
$940$	−9.54417	+	21.3894i	−0.311296	+	0.697644i
$941$	−1.10649	−	1.10649i	−0.0360705	−	0.0360705i	0.688841	−	0.724912i	$-0.258120\pi$
$941$	−1.10649	−	1.10649i	−0.0360705	−	0.0360705i	−0.724912	+	0.688841i	$0.758120\pi$
$942$		0			0
$943$	21.2509			0.692025
$944$	−0.950465	+	17.5844i	−0.0309350	+	0.572325i
$945$		0			0
$946$	−15.5461	+	2.87471i	−0.505447	+	0.0934649i
$947$	8.83833	+	8.83833i	0.287207	+	0.287207i	0.835975	−	0.548768i	$-0.184903\pi$
$947$	8.83833	+	8.83833i	0.287207	+	0.287207i	−0.548768	+	0.835975i	$0.684903\pi$
$948$		0			0
$949$	−39.0796	+	39.0796i	−1.26858	+	1.26858i
$950$	−2.03655	−	1.40091i	−0.0660745	−	0.0454516i
$951$		0			0
$952$	50.9786	−	31.1536i	1.65223	−	1.00969i
$953$			14.9610i			0.484636i	0.970197	+	0.242318i	$0.0779077\pi$
$953$			14.9610i			0.484636i	−0.970197	+	0.242318i	$0.922092\pi$
$954$		0			0
$955$	−4.14234	+	4.14234i	−0.134043	+	0.134043i
$956$	−31.3258	+	11.9954i	−1.01315	+	0.387959i
$957$		0			0
$958$	−7.41620	−	40.1059i	−0.239606	−	1.29576i
$959$	−54.8152			−1.77008
$960$		0			0
$961$	−26.7441			−0.862712
$962$	1.86764	+	10.1000i	0.0602150	+	0.325636i
$963$		0			0
$964$	41.1453	−	15.7555i	1.32520	−	0.507452i
$965$	−0.0170522	+	0.0170522i	−0.000548930	+	0.000548930i
$966$		0			0
$967$			3.95287i			0.127116i	0.997978	+	0.0635578i	$0.0202447\pi$
$967$			3.95287i			0.127116i	−0.997978	+	0.0635578i	$0.979755\pi$
$968$	10.1237	−	6.18672i	0.325389	−	0.198849i
$969$		0			0
$970$	−16.2951	−	11.2092i	−0.523205	−	0.359905i
$971$	29.0538	−	29.0538i	0.932380	−	0.932380i	−0.0654740	−	0.997854i	$-0.520856\pi$
$971$	29.0538	−	29.0538i	0.932380	−	0.932380i	0.997854	+	0.0654740i	$0.0208560\pi$
$972$		0			0
$973$	−8.07597	−	8.07597i	−0.258904	−	0.258904i
$974$	44.7323	−	8.27169i	1.43332	−	0.265042i
$975$		0			0
$976$	13.2721	+	0.717377i	0.424830	+	0.0229627i
$977$	−25.8962			−0.828494			−0.414247	−	0.910164i	$-0.635955\pi$
$977$	−25.8962			−0.828494			−0.414247	+	0.910164i	$0.635955\pi$
$978$		0			0
$979$	6.90984	+	6.90984i	0.220839	+	0.220839i
$980$	1.12088	−	2.51201i	0.0358053	−	0.0802431i
$981$		0			0
$982$	8.95749	+	6.16172i	0.285845	+	0.196628i
$983$			22.0151i			0.702173i	0.936343	+	0.351087i	$0.114188\pi$
$983$			22.0151i			0.702173i	−0.936343	+	0.351087i	$0.885812\pi$
$984$		0			0
$985$			21.0839i			0.671789i
$986$	−35.1340	+	51.0754i	−1.11889	+	1.62657i
$987$		0			0
$988$	−5.44529	−	14.2203i	−0.173238	−	0.452407i
$989$	−13.9537	−	13.9537i	−0.443702	−	0.443702i
$990$		0			0
$991$	−54.3207			−1.72556			−0.862778	−	0.505583i	$-0.831277\pi$
$991$	−54.3207			−1.72556			−0.862778	+	0.505583i	$0.831277\pi$
$992$	9.24388	+	7.12321i	0.293493	+	0.226162i
$993$		0			0
$994$	−2.42562	−	13.1174i	−0.0769359	−	0.416060i
$995$	−9.65378	−	9.65378i	−0.306045	−	0.306045i
$996$		0			0
$997$	8.14405	−	8.14405i	0.257925	−	0.257925i	−0.566285	−	0.824210i	$-0.691620\pi$
$997$	8.14405	−	8.14405i	0.257925	−	0.257925i	0.824210	+	0.566285i	$0.191620\pi$
$998$	19.4146	−	28.2236i	0.614557	−	0.893402i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.t.c.541.5		16
3.2	odd	2		80.2.l.a.61.4	yes	16
4.3	odd	2		2880.2.t.c.721.7		16
12.11	even	2		320.2.l.a.81.7		16
15.2	even	4		400.2.q.h.349.7		16
15.8	even	4		400.2.q.g.349.2		16
15.14	odd	2		400.2.l.h.301.5		16
16.5	even	4	inner	720.2.t.c.181.5		16
16.11	odd	4		2880.2.t.c.2161.6		16
24.5	odd	2		640.2.l.b.161.7		16
24.11	even	2		640.2.l.a.161.2		16
48.5	odd	4		80.2.l.a.21.4	✓	16
48.11	even	4		320.2.l.a.241.7		16
48.29	odd	4		640.2.l.b.481.7		16
48.35	even	4		640.2.l.a.481.2		16
60.23	odd	4		1600.2.q.h.849.2		16
60.47	odd	4		1600.2.q.g.849.7		16
60.59	even	2		1600.2.l.i.401.2		16
96.5	odd	8		5120.2.a.s.1.8		8
96.11	even	8		5120.2.a.t.1.8		8
96.53	odd	8		5120.2.a.v.1.1		8
96.59	even	8		5120.2.a.u.1.1		8
240.53	even	4		400.2.q.h.149.7		16
240.59	even	4		1600.2.l.i.1201.2		16
240.107	odd	4		1600.2.q.h.49.2		16
240.149	odd	4		400.2.l.h.101.5		16
240.197	even	4		400.2.q.g.149.2		16
240.203	odd	4		1600.2.q.g.49.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.4	✓	16	48.5	odd	4
80.2.l.a.61.4	yes	16	3.2	odd	2
320.2.l.a.81.7		16	12.11	even	2
320.2.l.a.241.7		16	48.11	even	4
400.2.l.h.101.5		16	240.149	odd	4
400.2.l.h.301.5		16	15.14	odd	2
400.2.q.g.149.2		16	240.197	even	4
400.2.q.g.349.2		16	15.8	even	4
400.2.q.h.149.7		16	240.53	even	4
400.2.q.h.349.7		16	15.2	even	4
640.2.l.a.161.2		16	24.11	even	2
640.2.l.a.481.2		16	48.35	even	4
640.2.l.b.161.7		16	24.5	odd	2
640.2.l.b.481.7		16	48.29	odd	4
720.2.t.c.181.5		16	16.5	even	4	inner
720.2.t.c.541.5		16	1.1	even	1	trivial
1600.2.l.i.401.2		16	60.59	even	2
1600.2.l.i.1201.2		16	240.59	even	4
1600.2.q.g.49.7		16	240.203	odd	4
1600.2.q.g.849.7		16	60.47	odd	4
1600.2.q.h.49.2		16	240.107	odd	4
1600.2.q.h.849.2		16	60.23	odd	4
2880.2.t.c.721.7		16	4.3	odd	2
2880.2.t.c.2161.6		16	16.11	odd	4
5120.2.a.s.1.8		8	96.5	odd	8
5120.2.a.t.1.8		8	96.11	even	8
5120.2.a.u.1.1		8	96.59	even	8
5120.2.a.v.1.1		8	96.53	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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.257150 + 1.39064i) q^{2} +(-1.86775 + 0.715205i) q^{4} +(0.707107 - 0.707107i) q^{5} -2.89402i q^{7} +(-1.47488 - 2.41345i) q^{8} +(1.16516 + 0.801497i) q^{10} +(-1.84462 + 1.84462i) q^{11} +(-3.08011 - 3.08011i) q^{13} +(4.02454 - 0.744198i) q^{14} +(2.97696 - 2.67165i) q^{16} -7.29875 q^{17} +(-1.23593 - 1.23593i) q^{19} +(-0.814970 + 1.82642i) q^{20} +(-3.03955 - 2.09086i) q^{22} -4.60490i q^{23} -1.00000i q^{25} +(3.49126 - 5.07536i) q^{26} +(2.06982 + 5.40530i) q^{28} +(-4.24680 - 4.24680i) q^{29} +2.06299 q^{31} +(4.48082 + 3.45286i) q^{32} +(-1.87688 - 10.1499i) q^{34} +(-2.04638 - 2.04638i) q^{35} +(-1.17899 + 1.17899i) q^{37} +(1.40091 - 2.03655i) q^{38} +(-2.74946 - 0.663664i) q^{40} +4.61484i q^{41} +(3.03019 - 3.03019i) q^{43} +(2.12601 - 4.76458i) q^{44} +(6.40375 - 1.18415i) q^{46} +11.7111 q^{47} -1.37537 q^{49} +(1.39064 - 0.257150i) q^{50} +(7.95577 + 3.54995i) q^{52} +(-2.73048 + 2.73048i) q^{53} +2.60869i q^{55} +(-6.98457 + 4.26835i) q^{56} +(4.81369 - 6.99782i) q^{58} +(-3.11306 + 3.11306i) q^{59} +(2.34962 + 2.34962i) q^{61} +(0.530498 + 2.86887i) q^{62} +(-3.64944 + 7.11910i) q^{64} -4.35593 q^{65} +(8.24311 + 8.24311i) q^{67} +(13.6322 - 5.22011i) q^{68} +(2.31955 - 3.37201i) q^{70} -3.25937i q^{71} -12.6877i q^{73} +(-1.94272 - 1.33637i) q^{74} +(3.19235 + 1.42446i) q^{76} +(5.33839 + 5.33839i) q^{77} -0.113885 q^{79} +(0.215891 - 3.99417i) q^{80} +(-6.41758 + 1.18671i) q^{82} +(-9.76813 - 9.76813i) q^{83} +(-5.16100 + 5.16100i) q^{85} +(4.99310 + 3.43468i) q^{86} +(7.17251 + 1.73129i) q^{88} -3.74593i q^{89} +(-8.91390 + 8.91390i) q^{91} +(3.29345 + 8.60080i) q^{92} +(3.01150 + 16.2858i) q^{94} -1.74787 q^{95} -13.9853 q^{97} +(-0.353676 - 1.91264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} + 4 q^{10} + 8 q^{11} - 4 q^{14} + 16 q^{16} - 8 q^{19} - 8 q^{20} - 20 q^{22} + 16 q^{26} - 4 q^{28} + 16 q^{29} + 16 q^{34} - 16 q^{37} - 20 q^{38} + 8 q^{43} - 40 q^{44} - 4 q^{46} + 40 q^{47}+ \cdots - 60 q^{98}+O(q^{100}) \) 16 * q - 4 * q^4 + 4 * q^10 + 8 * q^11 - 4 * q^14 + 16 * q^16 - 8 * q^19 - 8 * q^20 - 20 * q^22 + 16 * q^26 - 4 * q^28 + 16 * q^29 + 16 * q^34 - 16 * q^37 - 20 * q^38 + 8 * q^43 - 40 * q^44 - 4 * q^46 + 40 * q^47 - 16 * q^49 + 4 * q^50 + 56 * q^52 - 16 * q^53 - 16 * q^56 - 12 * q^58 + 8 * q^59 + 16 * q^61 + 8 * q^62 - 16 * q^64 + 40 * q^67 + 48 * q^68 - 8 * q^70 + 72 * q^74 - 16 * q^77 + 16 * q^79 - 16 * q^80 - 76 * q^82 - 40 * q^83 - 16 * q^85 - 28 * q^86 + 32 * q^91 + 52 * q^92 - 36 * q^94 - 32 * q^95 - 60 * q^98

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