LMFDB - Embedded newform 510.2.l.g.137.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [510,2,Mod(137,510)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(510, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("510.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 510 = 2 \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	510.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.07237050309$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			137.11
Character	$\chi$	$=$	510.137
Dual form			510.2.l.g.443.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{2} +(0.318145 + 1.70258i) q^{3} -1.00000i q^{4} +(-2.18694 + 0.466155i) q^{5} +(1.42887 + 0.978944i) q^{6} +(-2.68155 - 2.68155i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.79757 + 1.08334i) q^{9} +(-1.21678 + 1.87602i) q^{10} +4.10569i q^{11} +(1.70258 - 0.318145i) q^{12} +(-4.65342 + 4.65342i) q^{13} -3.79229 q^{14} +(-1.48943 - 3.57514i) q^{15} -1.00000 q^{16} +(0.707107 - 0.707107i) q^{17} +(-1.21214 + 2.74421i) q^{18} +2.50536i q^{19} +(0.466155 + 2.18694i) q^{20} +(3.71243 - 5.41868i) q^{21} +(2.90316 + 2.90316i) q^{22} +(-0.106861 - 0.106861i) q^{23} +(0.978944 - 1.42887i) q^{24} +(4.56540 - 2.03890i) q^{25} +6.58093i q^{26} +(-2.73450 - 4.41843i) q^{27} +(-2.68155 + 2.68155i) q^{28} +5.15029 q^{29} +(-3.58119 - 1.47482i) q^{30} -9.65153 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-6.99028 + 1.30621i) q^{33} -1.00000i q^{34} +(7.11440 + 4.61437i) q^{35} +(1.08334 + 2.79757i) q^{36} +(-6.88398 - 6.88398i) q^{37} +(1.77156 + 1.77156i) q^{38} +(-9.40330 - 6.44237i) q^{39} +(1.87602 + 1.21678i) q^{40} +2.12724i q^{41} +(-1.20650 - 6.45667i) q^{42} +(4.80824 - 4.80824i) q^{43} +4.10569 q^{44} +(5.61310 - 3.67329i) q^{45} -0.151124 q^{46} +(3.75510 - 3.75510i) q^{47} +(-0.318145 - 1.70258i) q^{48} +7.38143i q^{49} +(1.78650 - 4.66995i) q^{50} +(1.42887 + 0.978944i) q^{51} +(4.65342 + 4.65342i) q^{52} +(3.13924 + 3.13924i) q^{53} +(-5.05789 - 1.19071i) q^{54} +(-1.91389 - 8.97890i) q^{55} +3.79229i q^{56} +(-4.26558 + 0.797070i) q^{57} +(3.64180 - 3.64180i) q^{58} +3.38536 q^{59} +(-3.57514 + 1.48943i) q^{60} -4.42559 q^{61} +(-6.82466 + 6.82466i) q^{62} +(10.4068 + 4.59679i) q^{63} +1.00000i q^{64} +(8.00753 - 12.3460i) q^{65} +(-4.01925 + 5.86650i) q^{66} +(7.73282 + 7.73282i) q^{67} +(-0.707107 - 0.707107i) q^{68} +(0.147942 - 0.215937i) q^{69} +(8.29349 - 1.76779i) q^{70} +12.4321i q^{71} +(2.74421 + 1.21214i) q^{72} +(-2.67504 + 2.67504i) q^{73} -9.73542 q^{74} +(4.92386 + 7.12430i) q^{75} +2.50536 q^{76} +(11.0096 - 11.0096i) q^{77} +(-11.2046 + 2.09369i) q^{78} +8.13948i q^{79} +(2.18694 - 0.466155i) q^{80} +(6.65276 - 6.06142i) q^{81} +(1.50419 + 1.50419i) q^{82} +(3.24742 + 3.24742i) q^{83} +(-5.41868 - 3.71243i) q^{84} +(-1.21678 + 1.87602i) q^{85} -6.79988i q^{86} +(1.63854 + 8.76878i) q^{87} +(2.90316 - 2.90316i) q^{88} -12.9925 q^{89} +(1.37165 - 6.56647i) q^{90} +24.9568 q^{91} +(-0.106861 + 0.106861i) q^{92} +(-3.07059 - 16.4325i) q^{93} -5.31052i q^{94} +(-1.16789 - 5.47907i) q^{95} +(-1.42887 - 0.978944i) q^{96} +(-5.96585 - 5.96585i) q^{97} +(5.21946 + 5.21946i) q^{98} +(-4.44785 - 11.4860i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{7} - 12 q^{10} - 8 q^{13} + 8 q^{15} - 28 q^{16} - 16 q^{18} + 48 q^{21} + 20 q^{22} + 40 q^{25} - 36 q^{27} + 4 q^{28} - 12 q^{30} + 16 q^{31} + 8 q^{33} + 8 q^{37} - 8 q^{40} - 48 q^{42} + 48 q^{43}+ \cdots + 60 q^{97}+O(q^{100}) $ 28 * q + 4 * q^7 - 12 * q^10 - 8 * q^13 + 8 * q^15 - 28 * q^16 - 16 * q^18 + 48 * q^21 + 20 * q^22 + 40 * q^25 - 36 * q^27 + 4 * q^28 - 12 * q^30 + 16 * q^31 + 8 * q^33 + 8 * q^37 - 8 * q^40 - 48 * q^42 + 48 * q^43 + 36 * q^45 - 64 * q^46 + 8 * q^52 - 36 * q^55 - 32 * q^57 + 20 * q^58 + 12 * q^60 - 16 * q^61 - 56 * q^63 + 32 * q^66 + 112 * q^67 - 28 * q^70 + 16 * q^72 + 12 * q^73 + 16 * q^75 - 8 * q^76 - 32 * q^78 - 48 * q^81 + 24 * q^82 - 12 * q^85 - 44 * q^87 + 20 * q^88 - 20 * q^90 - 80 * q^91 + 28 * q^93 + 60 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/510\mathbb{Z}\right)^\times$.

$n$	$241$	$307$	$341$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	0.318145	+	1.70258i	0.183681	+	0.982986i
$3$	0.318145	+	1.70258i	0.183681	+	0.982986i
$4$		−	1.00000i		−	0.500000i
$5$	−2.18694	+	0.466155i	−0.978029	+	0.208471i
$5$	−2.18694	+	0.466155i	−0.978029	+	0.208471i
$6$	1.42887	+	0.978944i	0.583334	+	0.399652i
$7$	−2.68155	−	2.68155i	−1.01353	−	1.01353i	−0.999907	−	0.0136237i	$-0.995663\pi$
$7$	−2.68155	−	2.68155i	−1.01353	−	1.01353i	−0.0136237	−	0.999907i	$-0.504337\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.79757	+	1.08334i	−0.932522	+	0.361112i
$10$	−1.21678	+	1.87602i	−0.384779	+	0.593250i
$11$			4.10569i			1.23791i	0.785425	+	0.618957i	$0.212444\pi$
$11$			4.10569i			1.23791i	−0.785425	+	0.618957i	$0.787556\pi$
$12$	1.70258	−	0.318145i	0.491493	−	0.0918407i
$13$	−4.65342	+	4.65342i	−1.29063	+	1.29063i	−0.356228	+	0.934399i	$0.615937\pi$
$13$	−4.65342	+	4.65342i	−1.29063	+	1.29063i	−0.934399	+	0.356228i	$0.884063\pi$
$14$	−3.79229			−1.01353
$15$	−1.48943	−	3.57514i	−0.384569	−	0.923096i
$16$	−1.00000			−0.250000
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i
$18$	−1.21214	+	2.74421i	−0.285705	+	0.646817i
$19$			2.50536i			0.574769i	0.957815	+	0.287385i	$0.0927858\pi$
$19$			2.50536i			0.574769i	−0.957815	+	0.287385i	$0.907214\pi$
$20$	0.466155	+	2.18694i	0.104235	+	0.489014i
$21$	3.71243	−	5.41868i	0.810120	−	1.18245i
$22$	2.90316	+	2.90316i	0.618957	+	0.618957i
$23$	−0.106861	−	0.106861i	−0.0222820	−	0.0222820i	0.695878	−	0.718160i	$-0.255015\pi$
$23$	−0.106861	−	0.106861i	−0.0222820	−	0.0222820i	−0.718160	+	0.695878i	$0.755015\pi$
$24$	0.978944	−	1.42887i	0.199826	−	0.291667i
$25$	4.56540	−	2.03890i	0.913080	−	0.407781i
$26$			6.58093i			1.29063i
$27$	−2.73450	−	4.41843i	−0.526255	−	0.850327i
$28$	−2.68155	+	2.68155i	−0.506765	+	0.506765i
$29$	5.15029			0.956384			0.478192	−	0.878255i	$-0.341292\pi$
$29$	5.15029			0.956384			0.478192	+	0.878255i	$0.341292\pi$
$30$	−3.58119	−	1.47482i	−0.653833	−	0.269263i
$31$	−9.65153			−1.73347			−0.866733	−	0.498772i	$-0.833785\pi$
$31$	−9.65153			−1.73347			−0.866733	+	0.498772i	$0.833785\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−6.99028	+	1.30621i	−1.21685	+	0.227382i
$34$		−	1.00000i		−	0.171499i
$35$	7.11440	+	4.61437i	1.20255	+	0.779971i
$36$	1.08334	+	2.79757i	0.180556	+	0.466261i
$37$	−6.88398	−	6.88398i	−1.13172	−	1.13172i	−0.989891	−	0.141828i	$-0.954702\pi$
$37$	−6.88398	−	6.88398i	−1.13172	−	1.13172i	−0.141828	−	0.989891i	$-0.545298\pi$
$38$	1.77156	+	1.77156i	0.287385	+	0.287385i
$39$	−9.40330	−	6.44237i	−1.50573	−	1.03160i
$40$	1.87602	+	1.21678i	0.296625	+	0.192389i
$41$			2.12724i			0.332220i	0.986107	+	0.166110i	$0.0531206\pi$
$41$			2.12724i			0.332220i	−0.986107	+	0.166110i	$0.946879\pi$
$42$	−1.20650	−	6.45667i	−0.186167	−	0.996286i
$43$	4.80824	−	4.80824i	0.733250	−	0.733250i	−0.238012	−	0.971262i	$-0.576496\pi$
$43$	4.80824	−	4.80824i	0.733250	−	0.733250i	0.971262	+	0.238012i	$0.0764958\pi$
$44$	4.10569			0.618957
$45$	5.61310	−	3.67329i	0.836752	−	0.547582i
$46$	−0.151124			−0.0222820
$47$	3.75510	−	3.75510i	0.547738	−	0.547738i	−0.378048	−	0.925786i	$-0.623405\pi$
$47$	3.75510	−	3.75510i	0.547738	−	0.547738i	0.925786	+	0.378048i	$0.123405\pi$
$48$	−0.318145	−	1.70258i	−0.0459203	−	0.245746i
$49$			7.38143i			1.05449i
$50$	1.78650	−	4.66995i	0.252650	−	0.660430i
$51$	1.42887	+	0.978944i	0.200082	+	0.137080i
$52$	4.65342	+	4.65342i	0.645314	+	0.645314i
$53$	3.13924	+	3.13924i	0.431208	+	0.431208i	0.889039	−	0.457831i	$-0.151374\pi$
$53$	3.13924	+	3.13924i	0.431208	+	0.431208i	−0.457831	+	0.889039i	$0.651374\pi$
$54$	−5.05789	−	1.19071i	−0.688291	−	0.162036i
$55$	−1.91389	−	8.97890i	−0.258069	−	1.21071i
$56$			3.79229i			0.506765i
$57$	−4.26558	+	0.797070i	−0.564990	+	0.105574i
$58$	3.64180	−	3.64180i	0.478192	−	0.478192i
$59$	3.38536			0.440736			0.220368	−	0.975417i	$-0.429274\pi$
$59$	3.38536			0.440736			0.220368	+	0.975417i	$0.429274\pi$
$60$	−3.57514	+	1.48943i	−0.461548	+	0.192285i
$61$	−4.42559			−0.566638			−0.283319	−	0.959026i	$-0.591436\pi$
$61$	−4.42559			−0.566638			−0.283319	+	0.959026i	$0.591436\pi$
$62$	−6.82466	+	6.82466i	−0.866733	+	0.866733i
$63$	10.4068	+	4.59679i	1.31114	+	0.579142i
$64$			1.00000i			0.125000i
$65$	8.00753	−	12.3460i	0.993212	−	1.53133i
$66$	−4.01925	+	5.86650i	−0.494735	+	0.722117i
$67$	7.73282	+	7.73282i	0.944714	+	0.944714i	0.998550	−	0.0538356i	$-0.0171447\pi$
$67$	7.73282	+	7.73282i	0.944714	+	0.944714i	−0.0538356	+	0.998550i	$0.517145\pi$
$68$	−0.707107	−	0.707107i	−0.0857493	−	0.0857493i
$69$	0.147942	−	0.215937i	0.0178101	−	0.0259957i
$70$	8.29349	−	1.76779i	0.991262	−	0.211292i
$71$			12.4321i			1.47542i	0.675117	+	0.737711i	$0.264093\pi$
$71$			12.4321i			1.47542i	−0.675117	+	0.737711i	$0.735907\pi$
$72$	2.74421	+	1.21214i	0.323409	+	0.142852i
$73$	−2.67504	+	2.67504i	−0.313090	+	0.313090i	−0.846106	−	0.533015i	$-0.821059\pi$
$73$	−2.67504	+	2.67504i	−0.313090	+	0.313090i	0.533015	+	0.846106i	$0.321059\pi$
$74$	−9.73542			−1.13172
$75$	4.92386	+	7.12430i	0.568558	+	0.822643i
$76$	2.50536			0.287385
$77$	11.0096	−	11.0096i	1.25466	−	1.25466i
$78$	−11.2046	+	2.09369i	−1.26867	+	0.237064i
$79$			8.13948i			0.915764i	0.889013	+	0.457882i	$0.151392\pi$
$79$			8.13948i			0.915764i	−0.889013	+	0.457882i	$0.848608\pi$
$80$	2.18694	−	0.466155i	0.244507	−	0.0521177i
$81$	6.65276	−	6.06142i	0.739196	−	0.673491i
$82$	1.50419	+	1.50419i	0.166110	+	0.166110i
$83$	3.24742	+	3.24742i	0.356450	+	0.356450i	0.862503	−	0.506052i	$-0.168896\pi$
$83$	3.24742	+	3.24742i	0.356450	+	0.356450i	−0.506052	+	0.862503i	$0.668896\pi$
$84$	−5.41868	−	3.71243i	−0.591227	−	0.405060i
$85$	−1.21678	+	1.87602i	−0.131978	+	0.203483i
$86$		−	6.79988i		−	0.733250i
$87$	1.63854	+	8.76878i	0.175670	+	0.940112i
$88$	2.90316	−	2.90316i	0.309478	−	0.309478i
$89$	−12.9925			−1.37720			−0.688602	−	0.725140i	$-0.741775\pi$
$89$	−12.9925			−1.37720			−0.688602	+	0.725140i	$0.741775\pi$
$90$	1.37165	−	6.56647i	0.144585	−	0.692167i
$91$	24.9568			2.61618
$92$	−0.106861	+	0.106861i	−0.0111410	+	0.0111410i
$93$	−3.07059	−	16.4325i	−0.318406	−	1.70397i
$94$		−	5.31052i		−	0.547738i
$95$	−1.16789	−	5.47907i	−0.119823	−	0.562141i
$96$	−1.42887	−	0.978944i	−0.145833	−	0.0999131i
$97$	−5.96585	−	5.96585i	−0.605740	−	0.605740i	0.336090	−	0.941830i	$-0.390896\pi$
$97$	−5.96585	−	5.96585i	−0.605740	−	0.605740i	−0.941830	+	0.336090i	$0.890896\pi$
$98$	5.21946	+	5.21946i	0.527245	+	0.527245i
$99$	−4.44785	−	11.4860i	−0.447026	−	1.15438i
$100$	−2.03890	−	4.56540i	−0.203890	−	0.456540i
$101$			1.25938i			0.125313i	0.998035	+	0.0626563i	$0.0199572\pi$
$101$			1.25938i			0.125313i	−0.998035	+	0.0626563i	$0.980043\pi$
$102$	1.70258	−	0.318145i	0.168581	−	0.0315011i
$103$	−5.47938	+	5.47938i	−0.539900	+	0.539900i	−0.923499	−	0.383600i	$-0.874684\pi$
$103$	−5.47938	+	5.47938i	−0.539900	+	0.539900i	0.383600	+	0.923499i	$0.374684\pi$
$104$	6.58093			0.645314
$105$	−5.59292	+	13.5809i	−0.545813	+	1.32536i
$106$	4.43956			0.431208
$107$	−0.869345	+	0.869345i	−0.0840427	+	0.0840427i	−0.747878	−	0.663836i	$-0.768927\pi$
$107$	−0.869345	+	0.869345i	−0.0840427	+	0.0840427i	0.663836	+	0.747878i	$0.268927\pi$
$108$	−4.41843	+	2.73450i	−0.425163	+	0.263128i
$109$			8.86411i			0.849027i	0.905422	+	0.424514i	$0.139555\pi$
$109$			8.86411i			0.849027i	−0.905422	+	0.424514i	$0.860445\pi$
$110$	−7.70237	−	4.99572i	−0.734392	−	0.476323i
$111$	9.53043	−	13.9106i	0.904588	−	1.32034i
$112$	2.68155	+	2.68155i	0.253383	+	0.253383i
$113$	−0.684800	−	0.684800i	−0.0644205	−	0.0644205i	0.674163	−	0.738583i	$-0.264505\pi$
$113$	−0.684800	−	0.684800i	−0.0644205	−	0.0644205i	−0.738583	+	0.674163i	$0.764505\pi$
$114$	−2.45261	+	3.57984i	−0.229708	+	0.335282i
$115$	0.283512	+	0.183884i	0.0264376	+	0.0171473i
$116$		−	5.15029i		−	0.478192i
$117$	7.97704	−	18.0595i	0.737477	−	1.66960i
$118$	2.39381	−	2.39381i	0.220368	−	0.220368i
$119$	−3.79229			−0.347638
$120$	−1.47482	+	3.58119i	−0.134632	+	0.326916i
$121$	−5.85673			−0.532430
$122$	−3.12936	+	3.12936i	−0.283319	+	0.283319i
$123$	−3.62180	+	0.676773i	−0.326567	+	0.0610225i
$124$			9.65153i			0.866733i
$125$	−9.03380	+	6.58714i	−0.808008	+	0.589172i
$126$	10.6092	−	4.10832i	0.945140	−	0.365999i
$127$	−1.70292	−	1.70292i	−0.151110	−	0.151110i	0.627504	−	0.778614i	$-0.284077\pi$
$127$	−1.70292	−	1.70292i	−0.151110	−	0.151110i	−0.778614	+	0.627504i	$0.784077\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	9.71614	+	6.65670i	0.855459	+	0.586090i
$130$	−3.06773	−	14.3921i	−0.269058	−	1.26227i
$131$			5.59261i			0.488629i	0.969696	+	0.244314i	$0.0785629\pi$
$131$			5.59261i			0.488629i	−0.969696	+	0.244314i	$0.921437\pi$
$132$	1.30621	+	6.99028i	0.113691	+	0.608426i
$133$	6.71825	−	6.71825i	0.582547	−	0.582547i
$134$	10.9359			0.944714
$135$	8.03986	+	8.38813i	0.691961	+	0.721935i
$136$	−1.00000			−0.0857493
$137$	−11.7917	+	11.7917i	−1.00743	+	1.00743i	−0.00745772	+	0.999972i	$0.502374\pi$
$137$	−11.7917	+	11.7917i	−1.00743	+	1.00743i	−0.999972	+	0.00745772i	$0.997626\pi$
$138$	−0.0480794	−	0.257301i	−0.00409279	−	0.0219029i
$139$			6.47789i			0.549448i	0.961523	+	0.274724i	$0.0885864\pi$
$139$			6.47789i			0.549448i	−0.961523	+	0.274724i	$0.911414\pi$
$140$	4.61437	−	7.11440i	0.389985	−	0.601277i
$141$	7.58804	+	5.19870i	0.639028	+	0.437809i
$142$	8.79084	+	8.79084i	0.737711	+	0.737711i
$143$	−19.1055	−	19.1055i	−1.59768	−	1.59768i
$144$	2.79757	−	1.08334i	0.233131	−	0.0902781i
$145$	−11.2634	+	2.40083i	−0.935371	+	0.199378i
$146$			3.78308i			0.313090i
$147$	−12.5675	+	2.34837i	−1.03655	+	0.193690i
$148$	−6.88398	+	6.88398i	−0.565860	+	0.565860i
$149$	−0.129049			−0.0105721			−0.00528607	−	0.999986i	$-0.501683\pi$
$149$	−0.129049			−0.0105721			−0.00528607	+	0.999986i	$0.501683\pi$
$150$	8.51933	+	1.55594i	0.695601	+	0.127042i
$151$	2.28103			0.185627			0.0928137	−	0.995683i	$-0.470414\pi$
$151$	2.28103			0.185627			0.0928137	+	0.995683i	$0.470414\pi$
$152$	1.77156	−	1.77156i	0.143692	−	0.143692i
$153$	−1.21214	+	2.74421i	−0.0979960	+	0.221857i
$154$		−	15.5700i		−	1.25466i
$155$	21.1073	−	4.49911i	1.69538	−	0.361377i
$156$	−6.44237	+	9.40330i	−0.515802	+	0.752866i
$157$	−15.2974	−	15.2974i	−1.22086	−	1.22086i	−0.967326	−	0.253537i	$-0.918406\pi$
$157$	−15.2974	−	15.2974i	−1.22086	−	1.22086i	−0.253537	−	0.967326i	$-0.581594\pi$
$158$	5.75548	+	5.75548i	0.457882	+	0.457882i
$159$	−4.34608	+	6.34355i	−0.344666	+	0.503076i
$160$	1.21678	−	1.87602i	0.0961947	−	0.148312i
$161$			0.573105i			0.0451670i
$162$	0.418144	−	8.99028i	0.0328525	−	0.706343i
$163$	−4.78667	+	4.78667i	−0.374921	+	0.374921i	−0.869266	−	0.494345i	$-0.835408\pi$
$163$	−4.78667	+	4.78667i	−0.374921	+	0.374921i	0.494345	+	0.869266i	$0.335408\pi$
$164$	2.12724			0.166110
$165$	14.6784	−	6.11515i	1.14271	−	0.476064i
$166$	4.59254			0.356450
$167$	−0.157313	+	0.157313i	−0.0121732	+	0.0121732i	−0.713167	−	0.700994i	$-0.752740\pi$
$167$	−0.157313	+	0.157313i	−0.0121732	+	0.0121732i	0.700994	+	0.713167i	$0.252740\pi$
$168$	−6.45667	+	1.20650i	−0.498143	+	0.0930834i
$169$		−	30.3087i		−	2.33144i
$170$	0.466155	+	2.18694i	0.0357524	+	0.167731i
$171$	−2.71415	−	7.00892i	−0.207556	−	0.535985i
$172$	−4.80824	−	4.80824i	−0.366625	−	0.366625i
$173$	−17.2500	−	17.2500i	−1.31149	−	1.31149i	−0.920315	−	0.391178i	$-0.872068\pi$
$173$	−17.2500	−	17.2500i	−1.31149	−	1.31149i	−0.391178	−	0.920315i	$-0.627932\pi$
$174$	7.35909	+	5.04184i	0.557891	+	0.382221i
$175$	−17.7098	−	6.77493i	−1.33873	−	0.512136i
$176$		−	4.10569i		−	0.309478i
$177$	1.07704	+	5.76384i	0.0809550	+	0.433237i
$178$	−9.18709	+	9.18709i	−0.688602	+	0.688602i
$179$	22.2732			1.66478			0.832389	−	0.554191i	$-0.186972\pi$
$179$	22.2732			1.66478			0.832389	+	0.554191i	$0.186972\pi$
$180$	−3.67329	−	5.61310i	−0.273791	−	0.418376i
$181$	9.38448			0.697543			0.348772	−	0.937208i	$-0.386599\pi$
$181$	9.38448			0.697543			0.348772	+	0.937208i	$0.386599\pi$
$182$	17.6471	−	17.6471i	1.30809	−	1.30809i
$183$	−1.40798	−	7.53492i	−0.104081	−	0.556998i
$184$			0.151124i			0.0111410i
$185$	18.2638	+	11.8458i	1.34278	+	0.870923i
$186$	−13.7908	−	9.44831i	−1.01119	−	0.692784i
$187$	2.90316	+	2.90316i	0.212300	+	0.212300i
$188$	−3.75510	−	3.75510i	−0.273869	−	0.273869i
$189$	−4.51553	+	19.1809i	−0.328456	+	1.39521i
$190$	−4.70011	−	3.04847i	−0.340982	−	0.221159i
$191$			4.09953i			0.296632i	0.988940	+	0.148316i	$0.0473852\pi$
$191$			4.09953i			0.296632i	−0.988940	+	0.148316i	$0.952615\pi$
$192$	−1.70258	+	0.318145i	−0.122873	+	0.0229602i
$193$	15.4487	−	15.4487i	1.11202	−	1.11202i	0.119146	−	0.992877i	$-0.461984\pi$
$193$	15.4487	−	15.4487i	1.11202	−	1.11202i	0.992877	−	0.119146i	$-0.0380157\pi$
$194$	−8.43699			−0.605740
$195$	23.5676	+	9.70567i	1.68771	+	0.695037i
$196$	7.38143			0.527245
$197$	−17.5206	+	17.5206i	−1.24829	+	1.24829i	−0.291821	+	0.956473i	$0.594261\pi$
$197$	−17.5206	+	17.5206i	−1.24829	+	1.24829i	−0.956473	+	0.291821i	$0.905739\pi$
$198$	−11.2669	−	4.97669i	−0.800704	−	0.353678i
$199$		−	1.60140i		−	0.113521i	−0.998388	−	0.0567603i	$-0.981923\pi$
$199$		−	1.60140i		−	0.113521i	0.998388	−	0.0567603i	$-0.0180771\pi$
$200$	−4.66995	−	1.78650i	−0.330215	−	0.126325i
$201$	−10.7056	+	15.6259i	−0.755114	+	1.10217i
$202$	0.890513	+	0.890513i	0.0626563	+	0.0626563i
$203$	−13.8108	−	13.8108i	−0.969325	−	0.969325i
$204$	0.978944	−	1.42887i	0.0685398	−	0.100041i
$205$	−0.991624	−	4.65215i	−0.0692580	−	0.324920i
$206$			7.74902i			0.539900i
$207$	0.414717	+	0.183184i	0.0288248	+	0.0127322i
$208$	4.65342	−	4.65342i	0.322657	−	0.322657i
$209$	−10.2863			−0.711515
$210$	5.64835	+	13.5579i	0.389773	+	0.935586i
$211$	−9.57018			−0.658838			−0.329419	−	0.944184i	$-0.606853\pi$
$211$	−9.57018			−0.658838			−0.329419	+	0.944184i	$0.606853\pi$
$212$	3.13924	−	3.13924i	0.215604	−	0.215604i
$213$	−21.1667	+	3.95522i	−1.45032	+	0.271007i
$214$			1.22944i			0.0840427i
$215$	−8.27394	+	12.7567i	−0.564278	+	0.870001i
$216$	−1.19071	+	5.05789i	−0.0810178	+	0.344145i
$217$	25.8811	+	25.8811i	1.75692	+	1.75692i
$218$	6.26787	+	6.26787i	0.424514	+	0.424514i
$219$	−5.40553	−	3.70343i	−0.365272	−	0.250254i
$220$	−8.97890	+	1.91389i	−0.605357	+	0.129034i
$221$			6.58093i			0.442681i
$222$	−3.09728	−	16.5753i	−0.207876	−	1.11246i
$223$	17.8329	−	17.8329i	1.19418	−	1.19418i	0.218299	−	0.975882i	$-0.429949\pi$
$223$	17.8329	−	17.8329i	1.19418	−	1.19418i	0.975882	−	0.218299i	$-0.0700509\pi$
$224$	3.79229			0.253383
$225$	−10.5632	+	10.6498i	−0.704213	+	0.709989i
$226$	−0.968453			−0.0644205
$227$	−3.28982	+	3.28982i	−0.218353	+	0.218353i	−0.807804	−	0.589451i	$-0.799344\pi$
$227$	−3.28982	+	3.28982i	−0.218353	+	0.218353i	0.589451	+	0.807804i	$0.299344\pi$
$228$	0.797070	+	4.26558i	0.0527872	+	0.282495i
$229$			6.78275i			0.448217i	0.974564	+	0.224108i	$0.0719470\pi$
$229$			6.78275i			0.448217i	−0.974564	+	0.224108i	$0.928053\pi$
$230$	0.330499	−	0.0704472i	0.0217925	−	0.00464515i
$231$	22.2475	+	15.2421i	1.46377	+	1.00286i
$232$	−3.64180	−	3.64180i	−0.239096	−	0.239096i
$233$	−6.89977	−	6.89977i	−0.452019	−	0.452019i	0.444005	−	0.896024i	$-0.353557\pi$
$233$	−6.89977	−	6.89977i	−0.452019	−	0.452019i	−0.896024	+	0.444005i	$0.853557\pi$
$234$	−7.12937	−	18.4106i	−0.466061	−	1.20354i
$235$	−6.46172	+	9.96264i	−0.421516	+	0.649891i
$236$		−	3.38536i		−	0.220368i
$237$	−13.8581	+	2.58954i	−0.900183	+	0.168209i
$238$	−2.68155	+	2.68155i	−0.173819	+	0.173819i
$239$	10.3093			0.666854			0.333427	−	0.942776i	$-0.391795\pi$
$239$	10.3093			0.666854			0.333427	+	0.942776i	$0.391795\pi$
$240$	1.48943	+	3.57514i	0.0961424	+	0.230774i
$241$	−14.8673			−0.957685			−0.478842	−	0.877901i	$-0.658943\pi$
$241$	−14.8673			−0.957685			−0.478842	+	0.877901i	$0.658943\pi$
$242$	−4.14133	+	4.14133i	−0.266215	+	0.266215i
$243$	12.4366	+	9.39846i	0.797808	+	0.602911i
$244$			4.42559i			0.283319i
$245$	−3.44089	−	16.1427i	−0.219830	−	1.03132i
$246$	−2.08245	+	3.03955i	−0.132772	+	0.193795i
$247$	−11.6585	−	11.6585i	−0.741813	−	0.741813i
$248$	6.82466	+	6.82466i	0.433367	+	0.433367i
$249$	−4.49584	+	6.56214i	−0.284912	+	0.415859i
$250$	−1.73005	+	11.0457i	−0.109418	+	0.698590i
$251$			19.2583i			1.21557i	0.794102	+	0.607785i	$0.207942\pi$
$251$			19.2583i			1.21557i	−0.794102	+	0.607785i	$0.792058\pi$
$252$	4.59679	−	10.4068i	0.289571	−	0.655569i
$253$	0.438738	−	0.438738i	0.0275832	−	0.0275832i
$254$	−2.40829			−0.151110
$255$	−3.58119	−	1.47482i	−0.224263	−	0.0923566i
$256$	1.00000			0.0625000
$257$	−20.5292	+	20.5292i	−1.28058	+	1.28058i	−0.340240	+	0.940339i	$0.610508\pi$
$257$	−20.5292	+	20.5292i	−1.28058	+	1.28058i	−0.940339	+	0.340240i	$0.889492\pi$
$258$	11.5773	−	2.16335i	0.720774	−	0.134684i
$259$			36.9195i			2.29406i
$260$	−12.3460	−	8.00753i	−0.765664	−	0.496606i
$261$	−14.4083	+	5.57950i	−0.891850	+	0.345362i
$262$	3.95457	+	3.95457i	0.244314	+	0.244314i
$263$	9.67629	+	9.67629i	0.596666	+	0.596666i	0.939424	−	0.342758i	$-0.111361\pi$
$263$	9.67629	+	9.67629i	0.596666	+	0.596666i	−0.342758	+	0.939424i	$0.611361\pi$
$264$	5.86650	+	4.01925i	0.361058	+	0.247367i
$265$	−8.32870	−	5.40195i	−0.511628	−	0.331839i
$266$		−	9.50105i		−	0.582547i
$267$	−4.13351	−	22.1208i	−0.252967	−	1.35377i
$268$	7.73282	−	7.73282i	0.472357	−	0.472357i
$269$	10.8355			0.660652			0.330326	−	0.943867i	$-0.392841\pi$
$269$	10.8355			0.660652			0.330326	+	0.943867i	$0.392841\pi$
$270$	11.6163	+	0.246261i	0.706948	+	0.0149869i
$271$	26.0695			1.58361			0.791805	−	0.610774i	$-0.209141\pi$
$271$	26.0695			1.58361			0.791805	+	0.610774i	$0.209141\pi$
$272$	−0.707107	+	0.707107i	−0.0428746	+	0.0428746i
$273$	7.93989	+	42.4909i	0.480544	+	2.57167i
$274$			16.6759i			1.00743i
$275$	8.37111	+	18.7441i	0.504797	+	1.13031i
$276$	−0.215937	−	0.147942i	−0.0129979	−	0.00890506i
$277$	2.68254	+	2.68254i	0.161178	+	0.161178i	0.783088	−	0.621910i	$-0.213643\pi$
$277$	2.68254	+	2.68254i	0.161178	+	0.161178i	−0.621910	+	0.783088i	$0.713643\pi$
$278$	4.58056	+	4.58056i	0.274724	+	0.274724i
$279$	27.0008	−	10.4559i	1.61650	−	0.625976i
$280$	−1.76779	−	8.29349i	−0.105646	−	0.495631i
$281$		−	19.6537i		−	1.17244i	−0.810152	−	0.586220i	$-0.800615\pi$
$281$		−	19.6537i		−	1.17244i	0.810152	−	0.586220i	$-0.199385\pi$
$282$	9.04159	−	1.68952i	0.538419	−	0.100609i
$283$	−7.74608	+	7.74608i	−0.460457	+	0.460457i	−0.898805	−	0.438349i	$-0.855564\pi$
$283$	−7.74608	+	7.74608i	−0.460457	+	0.460457i	0.438349	+	0.898805i	$0.355564\pi$
$284$	12.4321			0.737711
$285$	8.95701	−	3.73156i	0.530567	−	0.221039i
$286$	−27.0193			−1.59768
$287$	5.70431	−	5.70431i	0.336715	−	0.336715i
$288$	1.21214	−	2.74421i	0.0714262	−	0.161704i
$289$		−	1.00000i		−	0.0588235i
$290$	−6.26675	+	9.66204i	−0.367997	+	0.567375i
$291$	8.25934	−	12.0554i	0.484171	−	0.706698i
$292$	2.67504	+	2.67504i	0.156545	+	0.156545i
$293$	6.15446	+	6.15446i	0.359547	+	0.359547i	0.863646	−	0.504099i	$-0.168175\pi$
$293$	6.15446	+	6.15446i	0.359547	+	0.359547i	−0.504099	+	0.863646i	$0.668175\pi$
$294$	−7.22600	+	10.5471i	−0.421429	+	0.615119i
$295$	−7.40356	+	1.57810i	−0.431052	+	0.0918805i
$296$			9.73542i			0.565860i
$297$	18.1407	−	11.2270i	1.05263	−	0.651459i
$298$	−0.0912517	+	0.0912517i	−0.00528607	+	0.00528607i
$299$	0.994537			0.0575156
$300$	7.12430	−	4.92386i	0.411321	−	0.284279i
$301$	−25.7871			−1.48634
$302$	1.61293	−	1.61293i	0.0928137	−	0.0928137i
$303$	−2.14419	+	0.400665i	−0.123180	+	0.0230176i
$304$		−	2.50536i		−	0.143692i
$305$	9.67849	−	2.06301i	0.554189	−	0.118128i
$306$	1.08334	+	2.79757i	0.0619303	+	0.159926i
$307$	−1.40907	−	1.40907i	−0.0804197	−	0.0804197i	0.665753	−	0.746172i	$-0.268111\pi$
$307$	−1.40907	−	1.40907i	−0.0804197	−	0.0804197i	−0.746172	+	0.665753i	$0.768111\pi$
$308$	−11.0096	−	11.0096i	−0.627332	−	0.627332i
$309$	−11.0723	−	7.58585i	−0.629883	−	0.431544i
$310$	11.7438	−	18.1065i	0.667001	−	1.02838i
$311$		−	1.72157i		−	0.0976211i	−0.998808	−	0.0488106i	$-0.984457\pi$
$311$		−	1.72157i		−	0.0976211i	0.998808	−	0.0488106i	$-0.0155431\pi$
$312$	2.09369	+	11.2046i	0.118532	+	0.634334i
$313$	3.06674	−	3.06674i	0.173342	−	0.173342i	−0.615104	−	0.788446i	$-0.710886\pi$
$313$	3.06674	−	3.06674i	0.173342	−	0.173342i	0.788446	+	0.615104i	$0.210886\pi$
$314$	−21.6337			−1.22086
$315$	−24.9019	−	5.20171i	−1.40307	−	0.293083i
$316$	8.13948			0.457882
$317$	−0.177452	+	0.177452i	−0.00996668	+	0.00996668i	−0.712073	−	0.702106i	$-0.752243\pi$
$317$	−0.177452	+	0.177452i	−0.00996668	+	0.00996668i	0.702106	+	0.712073i	$0.252243\pi$
$318$	1.41242	+	7.55871i	0.0792048	+	0.423871i
$319$			21.1455i			1.18392i
$320$	−0.466155	−	2.18694i	−0.0260588	−	0.122254i
$321$	−1.75671	−	1.20355i	−0.0980499	−	0.0671757i
$322$	0.405247	+	0.405247i	0.0225835	+	0.0225835i
$323$	1.77156	+	1.77156i	0.0985721	+	0.0985721i
$324$	−6.06142	−	6.65276i	−0.336745	−	0.369598i
$325$	−11.7569	+	30.7326i	−0.652153	+	1.70474i
$326$			6.76938i			0.374921i
$327$	−15.0919	+	2.82008i	−0.834582	+	0.155951i
$328$	1.50419	−	1.50419i	0.0830549	−	0.0830549i
$329$	−20.1390			−1.11030
$330$	6.05514	−	14.7033i	0.333325	−	0.809388i
$331$	−24.3775			−1.33991			−0.669953	−	0.742403i	$-0.733686\pi$
$331$	−24.3775			−1.33991			−0.669953	+	0.742403i	$0.733686\pi$
$332$	3.24742	−	3.24742i	0.178225	−	0.178225i
$333$	26.7161	+	11.8007i	1.46403	+	0.646675i
$334$			0.222474i			0.0121732i
$335$	−20.5159	−	13.3065i	−1.12090	−	0.727012i
$336$	−3.71243	+	5.41868i	−0.202530	+	0.295613i
$337$	−0.685998	−	0.685998i	−0.0373687	−	0.0373687i	0.688176	−	0.725544i	$-0.258412\pi$
$337$	−0.685998	−	0.685998i	−0.0373687	−	0.0373687i	−0.725544	+	0.688176i	$0.758412\pi$
$338$	−21.4315	−	21.4315i	−1.16572	−	1.16572i
$339$	0.948061	−	1.38379i	0.0514916	−	0.0751573i
$340$	1.87602	+	1.21678i	0.101741	+	0.0659890i
$341$		−	39.6262i		−	2.14588i
$342$	−6.87525	−	3.03686i	−0.371771	−	0.164214i
$343$	1.02282	−	1.02282i	0.0552269	−	0.0552269i
$344$	−6.79988			−0.366625
$345$	−0.222880	+	0.541204i	−0.0119995	+	0.0291374i
$346$	−24.3952			−1.31149
$347$	19.5689	−	19.5689i	1.05051	−	1.05051i	0.0518581	−	0.998654i	$-0.483486\pi$
$347$	19.5689	−	19.5689i	1.05051	−	1.05051i	0.998654	−	0.0518581i	$-0.0165144\pi$
$348$	8.76878	−	1.63854i	0.470056	−	0.0878350i
$349$		−	10.9262i		−	0.584869i	−0.956286	−	0.292434i	$-0.905535\pi$
$349$		−	10.9262i		−	0.584869i	0.956286	−	0.292434i	$-0.0944653\pi$
$350$	−17.3133	+	7.73210i	−0.925435	+	0.413298i
$351$	33.2856	+	7.83601i	1.77665	+	0.418255i
$352$	−2.90316	−	2.90316i	−0.154739	−	0.154739i
$353$	5.82919	+	5.82919i	0.310256	+	0.310256i	0.845009	−	0.534752i	$-0.179595\pi$
$353$	5.82919	+	5.82919i	0.310256	+	0.310256i	−0.534752	+	0.845009i	$0.679595\pi$
$354$	4.83723	+	3.31407i	0.257096	+	0.176141i
$355$	−5.79529	−	27.1883i	−0.307582	−	1.44300i
$356$			12.9925i			0.688602i
$357$	−1.20650	−	6.45667i	−0.0638547	−	0.341723i
$358$	15.7495	−	15.7495i	0.832389	−	0.832389i
$359$	−30.4881			−1.60910			−0.804549	−	0.593886i	$-0.797593\pi$
$359$	−30.4881			−1.60910			−0.804549	+	0.593886i	$0.797593\pi$
$360$	−6.56647	−	1.37165i	−0.346083	−	0.0722926i
$361$	12.7232			0.669640
$362$	6.63583	−	6.63583i	0.348772	−	0.348772i
$363$	−1.86329	−	9.97155i	−0.0977974	−	0.523371i
$364$		−	24.9568i		−	1.30809i
$365$	4.60317	−	7.09714i	0.240941	−	0.371481i
$366$	−6.32359	−	4.33240i	−0.330539	−	0.226458i
$367$	19.2408	+	19.2408i	1.00436	+	1.00436i	0.999990	+	0.00437114i	$0.00139138\pi$
$367$	19.2408	+	19.2408i	1.00436	+	1.00436i	0.00437114	+	0.999990i	$0.498609\pi$
$368$	0.106861	+	0.106861i	0.00557051	+	0.00557051i
$369$	−2.30452	−	5.95110i	−0.119969	−	0.309802i
$370$	21.2908	−	4.53821i	1.10685	−	0.235930i
$371$		−	16.8361i		−	0.874085i
$372$	−16.4325	+	3.07059i	−0.851987	+	0.159203i
$373$	3.79471	−	3.79471i	0.196483	−	0.196483i	−0.602008	−	0.798490i	$-0.705632\pi$
$373$	3.79471	−	3.79471i	0.196483	−	0.196483i	0.798490	+	0.602008i	$0.205632\pi$
$374$	4.10569			0.212300
$375$	−14.0892	−	13.2851i	−0.727563	−	0.686040i
$376$	−5.31052			−0.273869
$377$	−23.9665	+	23.9665i	−1.23434	+	1.23434i
$378$	10.3700	+	16.7559i	0.533376	+	0.861832i
$379$		−	19.1599i		−	0.984179i	−0.870545	−	0.492090i	$-0.836233\pi$
$379$		−	19.1599i		−	0.984179i	0.870545	−	0.492090i	$-0.163767\pi$
$380$	−5.47907	+	1.16789i	−0.281070	+	0.0599113i
$381$	2.35758	−	3.44114i	0.120783	−	0.176295i
$382$	2.89881	+	2.89881i	0.148316	+	0.148316i
$383$	3.11794	+	3.11794i	0.159319	+	0.159319i	0.782265	−	0.622946i	$-0.214064\pi$
$383$	3.11794	+	3.11794i	0.159319	+	0.159319i	−0.622946	+	0.782265i	$0.714064\pi$
$384$	−0.978944	+	1.42887i	−0.0499565	+	0.0729167i
$385$	−18.9452	+	29.2096i	−0.965536	+	1.48866i
$386$		−	21.8478i		−	1.11202i
$387$	−8.24243	+	18.6603i	−0.418986	+	0.948558i
$388$	−5.96585	+	5.96585i	−0.302870	+	0.302870i
$389$	−1.74726			−0.0885897			−0.0442949	−	0.999019i	$-0.514104\pi$
$389$	−1.74726			−0.0885897			−0.0442949	+	0.999019i	$0.514104\pi$
$390$	23.5277	−	9.80185i	1.19137	−	0.496336i
$391$	−0.151124			−0.00764267
$392$	5.21946	−	5.21946i	0.263622	−	0.263622i
$393$	−9.52188	+	1.77926i	−0.480315	+	0.0897520i
$394$			24.7779i			1.24829i
$395$	−3.79426	−	17.8006i	−0.190910	−	0.895643i
$396$	−11.4860	+	4.44785i	−0.577191	+	0.223513i
$397$	13.2172	+	13.2172i	0.663353	+	0.663353i	0.956169	−	0.292816i	$-0.0945922\pi$
$397$	13.2172	+	13.2172i	0.663353	+	0.663353i	−0.292816	+	0.956169i	$0.594592\pi$
$398$	−1.13236	−	1.13236i	−0.0567603	−	0.0567603i
$399$	13.5758	+	9.30099i	0.679638	+	0.465632i
$400$	−4.56540	+	2.03890i	−0.228270	+	0.101945i
$401$		−	10.7765i		−	0.538154i	−0.963119	−	0.269077i	$-0.913281\pi$
$401$		−	10.7765i		−	0.538154i	0.963119	−	0.269077i	$-0.0867186\pi$
$402$	3.47919	+	18.6192i	0.173526	+	0.928641i
$403$	44.9127	−	44.9127i	2.23726	−	2.23726i
$404$	1.25938			0.0626563
$405$	−11.7236	+	16.3572i	−0.582551	+	0.812794i
$406$	−19.5314			−0.969325
$407$	28.2635	−	28.2635i	1.40097	−	1.40097i
$408$	−0.318145	−	1.70258i	−0.0157505	−	0.0842903i
$409$			29.1789i			1.44280i	0.692516	+	0.721402i	$0.256502\pi$
$409$			29.1789i			1.44280i	−0.692516	+	0.721402i	$0.743498\pi$
$410$	−3.99075	−	2.58838i	−0.197089	−	0.127831i
$411$	−23.8277	−	16.3248i	−1.17534	−	0.805243i
$412$	5.47938	+	5.47938i	0.269950	+	0.269950i
$413$	−9.07800	−	9.07800i	−0.446699	−	0.446699i
$414$	0.422780	−	0.163718i	0.0207785	−	0.00804631i
$415$	−8.61570	−	5.58810i	−0.422928	−	0.274309i
$416$		−	6.58093i		−	0.322657i
$417$	−11.0291	+	2.06091i	−0.540099	+	0.100923i
$418$	−7.27348	+	7.27348i	−0.355757	+	0.355757i
$419$	16.5097			0.806549			0.403275	−	0.915079i	$-0.367872\pi$
$419$	16.5097			0.806549			0.403275	+	0.915079i	$0.367872\pi$
$420$	13.5809	+	5.59292i	0.662680	+	0.272907i
$421$	−13.7223			−0.668785			−0.334393	−	0.942434i	$-0.608531\pi$
$421$	−13.7223			−0.668785			−0.334393	+	0.942434i	$0.608531\pi$
$422$	−6.76714	+	6.76714i	−0.329419	+	0.329419i
$423$	−6.43711	+	14.5732i	−0.312983	+	0.708573i
$424$		−	4.43956i		−	0.215604i
$425$	1.78650	−	4.66995i	0.0866581	−	0.226526i
$426$	−12.1704	+	17.7639i	−0.589655	+	0.860663i
$427$	11.8674	+	11.8674i	0.574306	+	0.574306i
$428$	0.869345	+	0.869345i	0.0420214	+	0.0420214i
$429$	26.4504	−	38.6071i	1.27704	−	1.86397i
$430$	3.16980	+	14.8709i	0.152861	+	0.717139i
$431$			27.9472i			1.34617i	0.739565	+	0.673085i	$0.235031\pi$
$431$			27.9472i			1.34617i	−0.739565	+	0.673085i	$0.764969\pi$
$432$	2.73450	+	4.41843i	0.131564	+	0.212582i
$433$	−9.74815	+	9.74815i	−0.468466	+	0.468466i	−0.901417	−	0.432951i	$-0.857472\pi$
$433$	−9.74815	+	9.74815i	−0.468466	+	0.468466i	0.432951	+	0.901417i	$0.357472\pi$
$434$	36.6014			1.75692
$435$	−7.67100	−	18.4130i	−0.367796	−	0.882835i
$436$	8.86411			0.424514
$437$	0.267725	−	0.267725i	0.0128070	−	0.0128070i
$438$	−6.44101	+	1.20357i	−0.307763	+	0.0575089i
$439$		−	12.9879i		−	0.619880i	−0.950756	−	0.309940i	$-0.899691\pi$
$439$		−	12.9879i		−	0.619880i	0.950756	−	0.309940i	$-0.100309\pi$
$440$	−4.99572	+	7.70237i	−0.238162	+	0.367196i
$441$	−7.99657	−	20.6500i	−0.380789	−	0.983335i
$442$	4.65342	+	4.65342i	0.221341	+	0.221341i
$443$	−0.368153	−	0.368153i	−0.0174915	−	0.0174915i	0.698307	−	0.715798i	$-0.253937\pi$
$443$	−0.368153	−	0.368153i	−0.0174915	−	0.0174915i	−0.715798	+	0.698307i	$0.753937\pi$
$444$	−13.9106	−	9.53043i	−0.660170	−	0.452294i
$445$	28.4138	−	6.05652i	1.34694	−	0.287107i
$446$		−	25.2196i		−	1.19418i
$447$	−0.0410565	−	0.219717i	−0.00194190	−	0.0103923i
$448$	2.68155	−	2.68155i	0.126691	−	0.126691i
$449$	0.488249			0.0230419			0.0115209	−	0.999934i	$-0.496333\pi$
$449$	0.488249			0.0230419			0.0115209	+	0.999934i	$0.496333\pi$
$450$	0.0612673	+	14.9999i	0.00288817	+	0.707101i
$451$	−8.73381			−0.411259
$452$	−0.684800	+	0.684800i	−0.0322103	+	0.0322103i
$453$	0.725699	+	3.88364i	0.0340963	+	0.182469i
$454$			4.65251i			0.218353i
$455$	−54.5789	+	11.6337i	−2.55870	+	0.545397i
$456$	3.57984	+	2.45261i	0.167641	+	0.114854i
$457$	−11.5449	−	11.5449i	−0.540047	−	0.540047i	0.383495	−	0.923543i	$-0.374720\pi$
$457$	−11.5449	−	11.5449i	−0.540047	−	0.540047i	−0.923543	+	0.383495i	$0.874720\pi$
$458$	4.79613	+	4.79613i	0.224108	+	0.224108i
$459$	−5.05789	−	1.19071i	−0.236082	−	0.0555778i
$460$	0.183884	−	0.283512i	0.00857365	−	0.0132188i
$461$			26.9391i			1.25468i	0.778746	+	0.627339i	$0.215856\pi$
$461$			26.9391i			1.25468i	−0.778746	+	0.627339i	$0.784144\pi$
$462$	26.5091	−	4.95351i	1.23332	−	0.230458i
$463$	−14.7097	+	14.7097i	−0.683618	+	0.683618i	−0.960814	−	0.277195i	$-0.910595\pi$
$463$	−14.7097	+	14.7097i	−0.683618	+	0.683618i	0.277195	+	0.960814i	$0.410595\pi$
$464$	−5.15029			−0.239096
$465$	14.3753	+	34.5055i	0.666638	+	1.60016i
$466$	−9.75775			−0.452019
$467$	−3.30218	+	3.30218i	−0.152807	+	0.152807i	−0.779370	−	0.626564i	$-0.784461\pi$
$467$	−3.30218	+	3.30218i	−0.152807	+	0.152807i	0.626564	+	0.779370i	$0.284461\pi$
$468$	−18.0595	−	7.97704i	−0.834800	−	0.368739i
$469$		−	41.4719i		−	1.91499i
$470$	2.47552	+	11.6138i	0.114187	+	0.535703i
$471$	21.1782	−	30.9118i	0.975841	−	1.42434i
$472$	−2.39381	−	2.39381i	−0.110184	−	0.110184i
$473$	19.7412	+	19.7412i	0.907700	+	0.907700i
$474$	−7.96810	+	11.6303i	−0.365987	+	0.534196i
$475$	5.10819	+	11.4380i	0.234380	+	0.524810i
$476$			3.79229i			0.173819i
$477$	−12.1831	−	5.38138i	−0.557825	−	0.246396i
$478$	7.28978	−	7.28978i	0.333427	−	0.333427i
$479$	16.2896			0.744289			0.372145	−	0.928175i	$-0.378623\pi$
$479$	16.2896			0.744289			0.372145	+	0.928175i	$0.378623\pi$
$480$	3.58119	+	1.47482i	0.163458	+	0.0673158i
$481$	64.0681			2.92125
$482$	−10.5127	+	10.5127i	−0.478842	+	0.478842i
$483$	−0.975759	+	0.182331i	−0.0443986	+	0.00829634i
$484$			5.85673i			0.266215i
$485$	15.8280	+	10.2659i	0.718711	+	0.466152i
$486$	15.4397	−	2.14829i	0.700360	−	0.0974486i
$487$	−4.05412	−	4.05412i	−0.183710	−	0.183710i	0.609260	−	0.792970i	$-0.291466\pi$
$487$	−4.05412	−	4.05412i	−0.183710	−	0.183710i	−0.792970	+	0.609260i	$0.791466\pi$
$488$	3.12936	+	3.12936i	0.141660	+	0.141660i
$489$	−9.67256	−	6.62684i	−0.437408	−	0.299676i
$490$	−13.8477	−	8.98156i	−0.625576	−	0.405745i
$491$		−	9.15619i		−	0.413213i	−0.978424	−	0.206607i	$-0.933758\pi$
$491$		−	9.15619i		−	0.413213i	0.978424	−	0.206607i	$-0.0662420\pi$
$492$	0.676773	+	3.62180i	0.0305113	+	0.163284i
$493$	3.64180	−	3.64180i	0.164019	−	0.164019i
$494$	−16.4876			−0.741813
$495$	15.0814	+	23.0457i	0.677859	+	1.03583i
$496$	9.65153			0.433367
$497$	33.3374	−	33.3374i	1.49539	−	1.49539i
$498$	1.46110	+	7.81917i	0.0654733	+	0.350386i
$499$			9.51732i			0.426054i	0.977046	+	0.213027i	$0.0683322\pi$
$499$			9.51732i			0.426054i	−0.977046	+	0.213027i	$0.931668\pi$
$500$	6.58714	+	9.03380i	0.294586	+	0.404004i
$501$	−0.317886	−	0.217789i	−0.0142021	−	0.00973011i
$502$	13.6176	+	13.6176i	0.607785	+	0.607785i
$503$	−25.6641	−	25.6641i	−1.14430	−	1.14430i	−0.987654	−	0.156650i	$-0.949930\pi$
$503$	−25.6641	−	25.6641i	−1.14430	−	1.14430i	−0.156650	−	0.987654i	$-0.550070\pi$
$504$	−4.10832	−	10.6092i	−0.182999	−	0.472570i
$505$	−0.587064	−	2.75418i	−0.0261240	−	0.122559i
$506$		−	0.620469i		−	0.0275832i
$507$	51.6030	−	9.64257i	2.29177	−	0.428242i
$508$	−1.70292	+	1.70292i	−0.0755549	+	0.0755549i
$509$	35.3731			1.56788			0.783941	−	0.620835i	$-0.213206\pi$
$509$	35.3731			1.56788			0.783941	+	0.620835i	$0.213206\pi$
$510$	−3.57514	+	1.48943i	−0.158310	+	0.0659531i
$511$	14.3465			0.634653
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	11.0698	−	6.85092i	0.488742	−	0.302475i
$514$			29.0327i			1.28058i
$515$	9.42883	−	14.5373i	0.415484	−	0.640591i
$516$	6.65670	−	9.71614i	0.293045	−	0.427729i
$517$	15.4173	+	15.4173i	0.678052	+	0.678052i
$518$	26.1060	+	26.1060i	1.14703	+	1.14703i
$519$	23.8815	−	34.8575i	1.04828	−	1.53008i
$520$	−14.3921	+	3.06773i	−0.631135	+	0.134529i
$521$		−	12.3503i		−	0.541076i	−0.962709	−	0.270538i	$-0.912798\pi$
$521$		−	12.3503i		−	0.541076i	0.962709	−	0.270538i	$-0.0872016\pi$
$522$	−6.24289	+	14.1335i	−0.273244	+	0.618606i
$523$	2.65510	−	2.65510i	0.116099	−	0.116099i	−0.646670	−	0.762770i	$-0.723839\pi$
$523$	2.65510	−	2.65510i	0.116099	−	0.116099i	0.762770	+	0.646670i	$0.223839\pi$
$524$	5.59261			0.244314
$525$	5.90058	−	32.3077i	0.257522	−	1.41003i
$526$	13.6843			0.596666
$527$	−6.82466	+	6.82466i	−0.297287	+	0.297287i
$528$	6.99028	−	1.30621i	0.304213	−	0.0568454i
$529$		−	22.9772i		−	0.999007i
$530$	−9.70904	+	2.06952i	−0.421734	+	0.0898942i
$531$	−9.47076	+	3.66748i	−0.410996	+	0.159155i
$532$	−6.71825	−	6.71825i	−0.291273	−	0.291273i
$533$	−9.89896	−	9.89896i	−0.428772	−	0.428772i
$534$	−18.5646	−	12.7189i	−0.803369	−	0.550402i
$535$	1.49595	−	2.30645i	0.0646758	−	0.0997167i
$536$		−	10.9359i		−	0.472357i
$537$	7.08612	+	37.9220i	0.305789	+	1.63645i
$538$	7.66186	−	7.66186i	0.330326	−	0.330326i
$539$	−30.3059			−1.30537
$540$	8.38813	−	8.03986i	0.360967	−	0.345980i
$541$	−27.6909			−1.19052			−0.595262	−	0.803532i	$-0.702952\pi$
$541$	−27.6909			−1.19052			−0.595262	+	0.803532i	$0.702952\pi$
$542$	18.4339	−	18.4339i	0.791805	−	0.791805i
$543$	2.98563	+	15.9778i	0.128126	+	0.685675i
$544$			1.00000i			0.0428746i
$545$	−4.13204	−	19.3853i	−0.176997	−	0.830373i
$546$	35.6600	+	24.4313i	1.52611	+	1.04556i
$547$	−2.76042	−	2.76042i	−0.118027	−	0.118027i	0.645626	−	0.763654i	$-0.276596\pi$
$547$	−2.76042	−	2.76042i	−0.118027	−	0.118027i	−0.763654	+	0.645626i	$0.776596\pi$
$548$	11.7917	+	11.7917i	0.503715	+	0.503715i
$549$	12.3809	−	4.79440i	0.528403	−	0.204620i
$550$	19.1734	+	7.33483i	0.817556	+	0.312758i
$551$			12.9033i			0.549700i
$552$	−0.257301	+	0.0480794i	−0.0109515	+	0.00204640i
$553$	21.8264	−	21.8264i	0.928155	−	0.928155i
$554$	3.79368			0.161178
$555$	−14.3579	+	34.8644i	−0.609461	+	1.47991i
$556$	6.47789			0.274724
$557$	32.6785	−	32.6785i	1.38463	−	1.38463i	0.548452	−	0.836182i	$-0.315217\pi$
$557$	32.6785	−	32.6785i	1.38463	−	1.38463i	0.836182	−	0.548452i	$-0.184783\pi$
$558$	11.6990	−	26.4859i	0.495260	−	1.12124i
$559$			44.7496i			1.89270i
$560$	−7.11440	−	4.61437i	−0.300638	−	0.194993i
$561$	−4.01925	+	5.86650i	−0.169693	+	0.247684i
$562$	−13.8973	−	13.8973i	−0.586220	−	0.586220i
$563$	−8.56925	−	8.56925i	−0.361151	−	0.361151i	0.503086	−	0.864237i	$-0.332198\pi$
$563$	−8.56925	−	8.56925i	−0.361151	−	0.361151i	−0.864237	+	0.503086i	$0.832198\pi$
$564$	5.19870	−	7.58804i	0.218905	−	0.319514i
$565$	1.81684	+	1.17839i	0.0764349	+	0.0495753i
$566$			10.9546i			0.460457i
$567$	−34.0937	−	1.58572i	−1.43180	−	0.0665940i
$568$	8.79084	−	8.79084i	0.368855	−	0.368855i
$569$	−16.0012			−0.670807			−0.335404	−	0.942075i	$-0.608873\pi$
$569$	−16.0012			−0.670807			−0.335404	+	0.942075i	$0.608873\pi$
$570$	3.69495	−	8.97218i	0.154764	−	0.375803i
$571$	−34.8888			−1.46005			−0.730025	−	0.683420i	$-0.760492\pi$
$571$	−34.8888			−1.46005			−0.730025	+	0.683420i	$0.760492\pi$
$572$	−19.1055	+	19.1055i	−0.798842	+	0.798842i
$573$	−6.97979	+	1.30425i	−0.291585	+	0.0544857i
$574$		−	8.06711i		−	0.336715i
$575$	−0.705741	−	0.269983i	−0.0294314	−	0.0112591i
$576$	−1.08334	−	2.79757i	−0.0451390	−	0.116565i
$577$	−11.9919	−	11.9919i	−0.499229	−	0.499229i	0.411969	−	0.911198i	$-0.364841\pi$
$577$	−11.9919	−	11.9919i	−0.499229	−	0.499229i	−0.911198	+	0.411969i	$0.864841\pi$
$578$	−0.707107	−	0.707107i	−0.0294118	−	0.0294118i
$579$	31.2176	+	21.3878i	1.29736	+	0.888845i
$580$	2.40083	+	11.2634i	0.0996891	+	0.467686i
$581$		−	17.4162i		−	0.722547i
$582$	−2.68419	−	14.3647i	−0.111263	−	0.595434i
$583$	−12.8888	+	12.8888i	−0.533798	+	0.533798i
$584$	3.78308			0.156545
$585$	−9.02677	+	43.2135i	−0.373211	+	1.78666i
$586$	8.70372			0.359547
$587$	−13.3609	+	13.3609i	−0.551465	+	0.551465i	−0.926863	−	0.375399i	$-0.877506\pi$
$587$	−13.3609	+	13.3609i	−0.551465	+	0.551465i	0.375399	+	0.926863i	$0.377506\pi$
$588$	2.34837	+	12.5675i	0.0968451	+	0.518274i
$589$		−	24.1806i		−	0.996344i
$590$	−4.11923	+	6.35100i	−0.169586	+	0.261466i
$591$	−35.4044	−	24.2562i	−1.45634	−	0.997767i
$592$	6.88398	+	6.88398i	0.282930	+	0.282930i
$593$	9.96226	+	9.96226i	0.409101	+	0.409101i	0.881425	−	0.472324i	$-0.156585\pi$
$593$	9.96226	+	9.96226i	0.409101	+	0.409101i	−0.472324	+	0.881425i	$0.656585\pi$
$594$	4.88871	−	20.7661i	0.200586	−	0.852045i
$595$	8.29349	−	1.76779i	0.340000	−	0.0724724i
$596$			0.129049i			0.00528607i
$597$	2.72652	−	0.509479i	0.111589	−	0.0208516i
$598$	0.703244	−	0.703244i	0.0287578	−	0.0287578i
$599$	−24.4461			−0.998839			−0.499419	−	0.866360i	$-0.666453\pi$
$599$	−24.4461			−0.998839			−0.499419	+	0.866360i	$0.666453\pi$
$600$	1.55594	−	8.51933i	0.0635211	−	0.347800i
$601$	24.4345			0.996706			0.498353	−	0.866974i	$-0.333938\pi$
$601$	24.4345			0.996706			0.498353	+	0.866974i	$0.333938\pi$
$602$	−18.2342	+	18.2342i	−0.743171	+	0.743171i
$603$	−30.0103	−	13.2558i	−1.22212	−	0.539819i
$604$		−	2.28103i		−	0.0928137i
$605$	12.8083	−	2.73014i	0.520732	−	0.110996i
$606$	−1.23286	+	1.79948i	−0.0500814	+	0.0730990i
$607$	−11.9863	−	11.9863i	−0.486510	−	0.486510i	0.420693	−	0.907203i	$-0.361787\pi$
$607$	−11.9863	−	11.9863i	−0.486510	−	0.486510i	−0.907203	+	0.420693i	$0.861787\pi$
$608$	−1.77156	−	1.77156i	−0.0718462	−	0.0718462i
$609$	19.1201	−	27.9078i	0.774786	−	1.13088i
$610$	5.38496	−	8.30249i	0.218031	−	0.336158i
$611$			34.9482i			1.41385i
$612$	2.74421	+	1.21214i	0.110928	+	0.0489980i
$613$	15.3999	−	15.3999i	0.621995	−	0.621995i	−0.324047	−	0.946041i	$-0.605043\pi$
$613$	15.3999	−	15.3999i	0.621995	−	0.621995i	0.946041	+	0.324047i	$0.105043\pi$
$614$	−1.99272			−0.0804197
$615$	7.60518	−	3.16838i	0.306671	−	0.127761i
$616$	−15.5700			−0.627332
$617$	−18.1477	+	18.1477i	−0.730599	+	0.730599i	−0.970739	−	0.240139i	$-0.922807\pi$
$617$	−18.1477	+	18.1477i	−0.730599	+	0.730599i	0.240139	+	0.970739i	$0.422807\pi$
$618$	−13.1933	+	2.46531i	−0.530714	+	0.0991695i
$619$			27.6016i			1.10940i	0.832050	+	0.554701i	$0.187167\pi$
$619$			27.6016i			1.10940i	−0.832050	+	0.554701i	$0.812833\pi$
$620$	−4.49911	−	21.1073i	−0.180689	−	0.847690i
$621$	−0.179945	+	0.764368i	−0.00722096	+	0.0306730i
$622$	−1.21733	−	1.21733i	−0.0488106	−	0.0488106i
$623$	34.8401	+	34.8401i	1.39584	+	1.39584i
$624$	9.40330	+	6.44237i	0.376433	+	0.257901i
$625$	16.6857	−	18.6168i	0.667430	−	0.744673i
$626$		−	4.33702i		−	0.173342i
$627$	−3.27252	−	17.5132i	−0.130692	−	0.699409i
$628$	−15.2974	+	15.2974i	−0.610431	+	0.610431i
$629$	−9.73542			−0.388176
$630$	−21.2865	+	13.9302i	−0.848074	+	0.554991i
$631$	−1.37990			−0.0549328			−0.0274664	−	0.999623i	$-0.508744\pi$
$631$	−1.37990			−0.0549328			−0.0274664	+	0.999623i	$0.508744\pi$
$632$	5.75548	−	5.75548i	0.228941	−	0.228941i
$633$	−3.04471	−	16.2940i	−0.121016	−	0.647629i
$634$			0.250955i			0.00996668i
$635$	4.51801	+	2.93036i	0.179292	+	0.116288i
$636$	6.34355	+	4.34608i	0.251538	+	0.172333i
$637$	−34.3489	−	34.3489i	−1.36095	−	1.36095i
$638$	14.9521	+	14.9521i	0.591960	+	0.591960i
$639$	−13.4682	−	34.7797i	−0.532793	−	1.37586i
$640$	−1.87602	−	1.21678i	−0.0741562	−	0.0480974i
$641$		−	17.2377i		−	0.680847i	−0.940272	−	0.340424i	$-0.889430\pi$
$641$		−	17.2377i		−	0.680847i	0.940272	−	0.340424i	$-0.110570\pi$
$642$	−2.09322	+	0.391141i	−0.0826128	+	0.0154371i
$643$	0.301754	−	0.301754i	0.0119000	−	0.0119000i	−0.701132	−	0.713032i	$-0.747322\pi$
$643$	0.301754	−	0.301754i	0.0119000	−	0.0119000i	0.713032	+	0.701132i	$0.247322\pi$
$644$	0.573105			0.0225835
$645$	−24.3517	−	10.0286i	−0.958846	−	0.394875i
$646$	2.50536			0.0985721
$647$	−28.9532	+	28.9532i	−1.13827	+	1.13827i	−0.149507	+	0.988761i	$0.547769\pi$
$647$	−28.9532	+	28.9532i	−1.13827	+	1.13827i	−0.988761	+	0.149507i	$0.952231\pi$
$648$	−8.99028	−	0.418144i	−0.353172	−	0.0164262i
$649$			13.8992i			0.545593i
$650$	13.4179	+	30.0446i	0.526293	+	1.17845i
$651$	−35.8307	+	52.2986i	−1.40432	+	2.04974i
$652$	4.78667	+	4.78667i	0.187461	+	0.187461i
$653$	23.5931	+	23.5931i	0.923270	+	0.923270i	0.997259	−	0.0739895i	$-0.0235731\pi$
$653$	23.5931	+	23.5931i	0.923270	+	0.923270i	−0.0739895	+	0.997259i	$0.523573\pi$
$654$	−8.67746	+	12.6657i	−0.339316	+	0.495266i
$655$	−2.60702	−	12.2307i	−0.101865	−	0.477893i
$656$		−	2.12724i		−	0.0830549i
$657$	4.58564	−	10.3816i	0.178903	−	0.405024i
$658$	−14.2404	+	14.2404i	−0.555149	+	0.555149i
$659$	16.1089			0.627514			0.313757	−	0.949503i	$-0.398412\pi$
$659$	16.1089			0.627514			0.313757	+	0.949503i	$0.398412\pi$
$660$	−6.11515	−	14.6784i	−0.238032	−	0.571357i
$661$	−17.9070			−0.696502			−0.348251	−	0.937401i	$-0.613224\pi$
$661$	−17.9070			−0.696502			−0.348251	+	0.937401i	$0.613224\pi$
$662$	−17.2375	+	17.2375i	−0.669953	+	0.669953i
$663$	−11.2046	+	2.09369i	−0.435150	+	0.0813123i
$664$		−	4.59254i		−	0.178225i
$665$	−11.5607	+	17.8242i	−0.448303	+	0.691191i
$666$	27.2355	−	10.5467i	1.05535	−	0.408678i
$667$	−0.550364	−	0.550364i	−0.0213102	−	0.0213102i
$668$	0.157313	+	0.157313i	0.00608661	+	0.00608661i
$669$	36.0355	+	24.6885i	1.39321	+	0.954514i
$670$	−23.9160	+	5.09780i	−0.923957	+	0.196945i
$671$		−	18.1701i		−	0.701449i
$672$	1.20650	+	6.45667i	0.0465417	+	0.249072i
$673$	−19.4682	+	19.4682i	−0.750442	+	0.750442i	−0.974562	−	0.224119i	$-0.928049\pi$
$673$	−19.4682	+	19.4682i	−0.750442	+	0.750442i	0.224119	+	0.974562i	$0.428049\pi$
$674$	−0.970148			−0.0373687
$675$	−21.4928	−	14.5965i	−0.827260	−	0.561819i
$676$	−30.3087			−1.16572
$677$	14.4315	−	14.4315i	0.554648	−	0.554648i	−0.373131	−	0.927779i	$-0.621716\pi$
$677$	14.4315	−	14.4315i	0.554648	−	0.554648i	0.927779	+	0.373131i	$0.121716\pi$
$678$	−0.308109	−	1.64887i	−0.0118329	−	0.0633245i
$679$			31.9955i			1.22787i
$680$	2.18694	−	0.466155i	0.0838653	−	0.0178762i
$681$	−6.64784	−	4.55455i	−0.254746	−	0.174531i
$682$	−28.0200	−	28.0200i	−1.07294	−	1.07294i
$683$	19.4121	+	19.4121i	0.742785	+	0.742785i	0.973113	−	0.230328i	$-0.0739800\pi$
$683$	19.4121	+	19.4121i	0.742785	+	0.742785i	−0.230328	+	0.973113i	$0.573980\pi$
$684$	−7.00892	+	2.71415i	−0.267993	+	0.103778i
$685$	20.2909	−	31.2844i	0.775276	−	1.19531i
$686$		−	1.44648i		−	0.0552269i
$687$	−11.5482	+	2.15790i	−0.440591	+	0.0823291i
$688$	−4.80824	+	4.80824i	−0.183312	+	0.183312i
$689$	−29.2164			−1.11306
$690$	0.225089	+	0.540289i	0.00856899	+	0.0205684i
$691$	8.43576			0.320911			0.160456	−	0.987043i	$-0.448704\pi$
$691$	8.43576			0.320911			0.160456	+	0.987043i	$0.448704\pi$
$692$	−17.2500	+	17.2500i	−0.655747	+	0.655747i
$693$	−18.8730	+	42.7273i	−0.716927	+	1.62308i
$694$		−	27.6746i		−	1.05051i
$695$	−3.01970	−	14.1668i	−0.114544	−	0.537376i
$696$	5.04184	−	7.35909i	0.191111	−	0.278946i
$697$	1.50419	+	1.50419i	0.0569752	+	0.0569752i
$698$	−7.72602	−	7.72602i	−0.292434	−	0.292434i
$699$	9.55229	−	13.9426i	0.361301	−	0.527356i
$700$	−6.77493	+	17.7098i	−0.256068	+	0.669366i
$701$		−	16.8028i		−	0.634631i	−0.948320	−	0.317316i	$-0.897219\pi$
$701$		−	16.8028i		−	0.634631i	0.948320	−	0.317316i	$-0.102781\pi$
$702$	29.0774	−	17.9956i	1.09745	−	0.679199i
$703$	17.2469	−	17.2469i	0.650478	−	0.650478i
$704$	−4.10569			−0.154739
$705$	−19.0180	−	7.83203i	−0.716258	−	0.294971i
$706$	8.24371			0.310256
$707$	3.37708	−	3.37708i	0.127008	−	0.127008i
$708$	5.76384	−	1.07704i	0.216619	−	0.0404775i
$709$		−	24.7534i		−	0.929634i	−0.885407	−	0.464817i	$-0.846120\pi$
$709$		−	24.7534i		−	0.929634i	0.885407	−	0.464817i	$-0.153880\pi$
$710$	−23.3229	−	15.1271i	−0.875293	−	0.567711i
$711$	−8.81781	−	22.7708i	−0.330694	−	0.853970i
$712$	9.18709	+	9.18709i	0.344301	+	0.344301i
$713$	1.03137	+	1.03137i	0.0386251	+	0.0386251i
$714$	−5.41868	−	3.71243i	−0.202789	−	0.138934i
$715$	50.6888	+	32.8765i	1.89565	+	1.22951i
$716$		−	22.2732i		−	0.832389i
$717$	3.27986	+	17.5524i	0.122489	+	0.655508i
$718$	−21.5583	+	21.5583i	−0.804549	+	0.804549i
$719$	43.9400			1.63869			0.819343	−	0.573304i	$-0.194338\pi$
$719$	43.9400			1.63869			0.819343	+	0.573304i	$0.194338\pi$
$720$	−5.61310	+	3.67329i	−0.209188	+	0.136895i
$721$	29.3865			1.09441
$722$	8.99663	−	8.99663i	0.334820	−	0.334820i
$723$	−4.72995	−	25.3127i	−0.175909	−	0.941391i
$724$		−	9.38448i		−	0.348772i
$725$	23.5131	−	10.5009i	0.873255	−	0.389995i
$726$	−8.36850	−	5.73341i	−0.310584	−	0.212787i
$727$	10.2955	+	10.2955i	0.381840	+	0.381840i	0.871765	−	0.489924i	$-0.162976\pi$
$727$	10.2955	+	10.2955i	0.381840	+	0.381840i	−0.489924	+	0.871765i	$0.662976\pi$
$728$	−17.6471	−	17.6471i	−0.654045	−	0.654045i
$729$	−12.0450	+	24.1644i	−0.446111	+	0.894978i
$730$	−1.76350	−	8.27337i	−0.0652702	−	0.306211i
$731$		−	6.79988i		−	0.251503i
$732$	−7.53492	+	1.40798i	−0.278499	+	0.0520405i
$733$	−32.7437	+	32.7437i	−1.20941	+	1.20941i	−0.238198	+	0.971217i	$0.576557\pi$
$733$	−32.7437	+	32.7437i	−1.20941	+	1.20941i	−0.971217	+	0.238198i	$0.923443\pi$
$734$	27.2106			1.00436
$735$	26.3896	−	10.9941i	0.973395	−	0.405524i
$736$	0.151124			0.00557051
$737$	−31.7486	+	31.7486i	−1.16947	+	1.16947i
$738$	−5.83761	−	2.57852i	−0.214885	−	0.0949168i
$739$		−	5.04676i		−	0.185648i	−0.995683	−	0.0928241i	$-0.970411\pi$
$739$		−	5.04676i		−	0.185648i	0.995683	−	0.0928241i	$-0.0295894\pi$
$740$	11.8458	−	18.2638i	0.435462	−	0.671392i
$741$	16.1405	−	23.5587i	0.592934	−	0.865449i
$742$	−11.9049	−	11.9049i	−0.437042	−	0.437042i
$743$	4.48784	+	4.48784i	0.164643	+	0.164643i	0.784620	−	0.619977i	$-0.212858\pi$
$743$	4.48784	+	4.48784i	0.164643	+	0.164643i	−0.619977	+	0.784620i	$0.712858\pi$
$744$	−9.44831	+	13.7908i	−0.346392	+	0.505595i
$745$	0.282223	−	0.0601570i	0.0103399	−	0.00220398i
$746$		−	5.36653i		−	0.196483i
$747$	−12.6029	−	5.56682i	−0.461116	−	0.203679i
$748$	2.90316	−	2.90316i	0.106150	−	0.106150i
$749$	4.66238			0.170360
$750$	−19.3566	+	0.568575i	−0.706802	+	0.0207614i
$751$	19.0153			0.693879			0.346940	−	0.937887i	$-0.387221\pi$
$751$	19.0153			0.693879			0.346940	+	0.937887i	$0.387221\pi$
$752$	−3.75510	+	3.75510i	−0.136934	+	0.136934i
$753$	−32.7887	+	6.12693i	−1.19489	+	0.223278i
$754$			33.8937i			1.23434i
$755$	−4.98847	+	1.06331i	−0.181549	+	0.0386979i
$756$	19.1809	+	4.51553i	0.697604	+	0.164228i
$757$	−4.31391	−	4.31391i	−0.156792	−	0.156792i	0.624352	−	0.781143i	$-0.285363\pi$
$757$	−4.31391	−	4.31391i	−0.156792	−	0.156792i	−0.781143	+	0.624352i	$0.785363\pi$
$758$	−13.5481	−	13.5481i	−0.492090	−	0.492090i
$759$	0.886570	+	0.607405i	0.0321804	+	0.0220474i
$760$	−3.04847	+	4.70011i	−0.110580	+	0.170491i
$761$			31.1782i			1.13021i	0.825019	+	0.565105i	$0.191164\pi$
$761$			31.1782i			1.13021i	−0.825019	+	0.565105i	$0.808836\pi$
$762$	−0.766188	−	4.10032i	−0.0277561	−	0.148539i
$763$	23.7695	−	23.7695i	0.860515	−	0.860515i
$764$	4.09953			0.148316
$765$	1.37165	−	6.56647i	0.0495923	−	0.237411i
$766$	4.40943			0.159319
$767$	−15.7535	+	15.7535i	−0.568826	+	0.568826i
$768$	0.318145	+	1.70258i	0.0114801	+	0.0614366i
$769$		−	40.1055i		−	1.44624i	−0.690721	−	0.723121i	$-0.742707\pi$
$769$		−	40.1055i		−	1.44624i	0.690721	−	0.723121i	$-0.257293\pi$
$770$	7.25801	+	34.0506i	0.261561	+	1.22710i
$771$	−41.4840	−	28.4214i	−1.49401	−	1.02357i
$772$	−15.4487	−	15.4487i	−0.556011	−	0.556011i
$773$	24.1301	+	24.1301i	0.867901	+	0.867901i	0.992240	−	0.124339i	$-0.0396811\pi$
$773$	24.1301	+	24.1301i	0.867901	+	0.867901i	−0.124339	+	0.992240i	$0.539681\pi$
$774$	7.36656	+	19.0231i	0.264786	+	0.683772i
$775$	−44.0631	+	19.6785i	−1.58279	+	0.706874i
$776$			8.43699i			0.302870i
$777$	−62.8584	+	11.7458i	−2.25503	+	0.421377i
$778$	−1.23550	+	1.23550i	−0.0442949	+	0.0442949i
$779$	−5.32951			−0.190950
$780$	9.70567	−	23.5676i	0.347519	−	0.843854i
$781$	−51.0425			−1.82644
$782$	−0.106861	+	0.106861i	−0.00382134	+	0.00382134i
$783$	−14.0835	−	22.7562i	−0.503302	−	0.813239i
$784$		−	7.38143i		−	0.263622i
$785$	40.5853	+	26.3235i	1.44855	+	0.939525i
$786$	−5.47486	+	7.99112i	−0.195282	+	0.285034i
$787$	24.8399	+	24.8399i	0.885447	+	0.885447i	0.994082	−	0.108635i	$-0.0346479\pi$
$787$	24.8399	+	24.8399i	0.885447	+	0.885447i	−0.108635	+	0.994082i	$0.534648\pi$
$788$	17.5206	+	17.5206i	0.624147	+	0.624147i
$789$	−13.3962	+	19.5531i	−0.476918	+	0.696110i
$790$	−15.2698	−	9.90394i	−0.543276	−	0.352367i
$791$			3.67265i			0.130584i
$792$	−4.97669	+	11.2669i	−0.176839	+	0.400352i
$793$	20.5941	−	20.5941i	0.731319	−	0.731319i
$794$	18.6920			0.663353
$795$	6.54753	−	15.8989i	0.232217	−	0.563876i
$796$	−1.60140			−0.0567603
$797$	19.6674	−	19.6674i	0.696654	−	0.696654i	−0.267033	−	0.963687i	$-0.586043\pi$
$797$	19.6674	−	19.6674i	0.696654	−	0.696654i	0.963687	+	0.267033i	$0.0860433\pi$
$798$	16.1763	−	3.02272i	0.572635	−	0.107003i
$799$		−	5.31052i		−	0.187873i
$800$	−1.78650	+	4.66995i	−0.0631624	+	0.165108i
$801$	36.3474	−	14.0753i	1.28427	−	0.497325i
$802$	−7.62015	−	7.62015i	−0.269077	−	0.269077i
$803$	−10.9829	−	10.9829i	−0.387579	−	0.387579i
$804$	15.6259	+	10.7056i	0.551084	+	0.377557i
$805$	−0.267156	−	1.25335i	−0.00941601	−	0.0441747i
$806$		−	63.5161i		−	2.23726i
$807$	3.44727	+	18.4483i	0.121350	+	0.649412i
$808$	0.890513	−	0.890513i	0.0313281	−	0.0313281i
$809$	−8.25845			−0.290352			−0.145176	−	0.989406i	$-0.546375\pi$
$809$	−8.25845			−0.290352			−0.145176	+	0.989406i	$0.546375\pi$
$810$	3.27641	+	19.8561i	0.115121	+	0.697673i
$811$	−45.8241			−1.60910			−0.804551	−	0.593883i	$-0.797594\pi$
$811$	−45.8241			−1.60910			−0.804551	+	0.593883i	$0.797594\pi$
$812$	−13.8108	+	13.8108i	−0.484662	+	0.484662i
$813$	8.29390	+	44.3855i	0.290880	+	1.55667i
$814$		−	39.9706i		−	1.40097i
$815$	8.23683	−	12.6995i	0.288524	−	0.444844i
$816$	−1.42887	−	0.978944i	−0.0500204	−	0.0342699i
$817$	12.0464	+	12.0464i	0.421450	+	0.421450i
$818$	20.6326	+	20.6326i	0.721402	+	0.721402i
$819$	−69.8183	+	27.0366i	−2.43965	+	0.944735i
$820$	−4.65215	+	0.991624i	−0.162460	+	0.0346290i
$821$		−	27.1005i		−	0.945814i	−0.881112	−	0.472907i	$-0.843205\pi$
$821$		−	27.1005i		−	0.945814i	0.881112	−	0.472907i	$-0.156795\pi$
$822$	−28.3921	+	5.30537i	−0.990289	+	0.185046i
$823$	6.78813	−	6.78813i	0.236619	−	0.236619i	−0.578829	−	0.815449i	$-0.696490\pi$
$823$	6.78813	−	6.78813i	0.236619	−	0.236619i	0.815449	+	0.578829i	$0.196490\pi$
$824$	7.74902			0.269950
$825$	−29.2502	+	20.2159i	−1.01836	+	0.703826i
$826$	−12.8382			−0.446699
$827$	2.55296	−	2.55296i	0.0887750	−	0.0887750i	−0.661325	−	0.750100i	$-0.730005\pi$
$827$	2.55296	−	2.55296i	0.0887750	−	0.0887750i	0.750100	+	0.661325i	$0.230005\pi$
$828$	0.183184	−	0.414717i	0.00636608	−	0.0144124i
$829$		−	13.1146i		−	0.455488i	−0.973721	−	0.227744i	$-0.926865\pi$
$829$		−	13.1146i		−	0.455488i	0.973721	−	0.227744i	$-0.0731350\pi$
$830$	−10.0436	+	2.14083i	−0.348619	+	0.0743095i
$831$	−3.71380	+	5.42067i	−0.128830	+	0.188041i
$832$	−4.65342	−	4.65342i	−0.161328	−	0.161328i
$833$	5.21946	+	5.21946i	0.180843	+	0.180843i
$834$	−6.34150	+	9.25607i	−0.219588	+	0.320511i
$835$	0.270701	−	0.417365i	0.00936800	−	0.0144435i
$836$			10.2863i			0.355757i
$837$	26.3921	+	42.6446i	0.912246	+	1.47401i
$838$	11.6741	−	11.6741i	0.403275	−	0.403275i
$839$	12.9994			0.448790			0.224395	−	0.974498i	$-0.427959\pi$
$839$	12.9994			0.448790			0.224395	+	0.974498i	$0.427959\pi$
$840$	13.5579	−	5.64835i	0.467793	−	0.194886i
$841$	−2.47454			−0.0853291
$842$	−9.70315	+	9.70315i	−0.334393	+	0.334393i
$843$	33.4620	−	6.25273i	1.15249	−	0.215356i
$844$			9.57018i			0.329419i
$845$	14.1285	+	66.2832i	0.486036	+	2.28021i
$846$	5.75308	+	14.8565i	0.197795	+	0.510778i
$847$	15.7051	+	15.7051i	0.539634	+	0.539634i
$848$	−3.13924	−	3.13924i	−0.107802	−	0.107802i
$849$	−15.6527	−	10.7239i	−0.537200	−	0.368045i
$850$	−2.03890	−	4.56540i	−0.0699338	−	0.156592i
$851$			1.47126i			0.0504340i
$852$	3.95522	+	21.1667i	0.135504	+	0.725159i
$853$	−13.0775	+	13.0775i	−0.447765	+	0.447765i	−0.894611	−	0.446846i	$-0.852547\pi$
$853$	−13.0775	+	13.0775i	−0.447765	+	0.447765i	0.446846	+	0.894611i	$0.352547\pi$
$854$	16.7831			0.574306
$855$	9.20292	+	14.0629i	0.314733	+	0.480940i
$856$	1.22944			0.0420214
$857$	−4.02020	+	4.02020i	−0.137328	+	0.137328i	−0.772429	−	0.635101i	$-0.780958\pi$
$857$	−4.02020	+	4.02020i	−0.137328	+	0.137328i	0.635101	+	0.772429i	$0.280958\pi$
$858$	−8.59607	−	46.0026i	−0.293465	−	1.57050i
$859$			6.71895i			0.229248i	0.993409	+	0.114624i	$0.0365663\pi$
$859$			6.71895i			0.229248i	−0.993409	+	0.114624i	$0.963434\pi$
$860$	12.7567	+	8.27394i	0.435000	+	0.282139i
$861$	11.5269	+	7.89725i	0.392834	+	0.269138i
$862$	19.7617	+	19.7617i	0.673085	+	0.673085i
$863$	28.6838	+	28.6838i	0.976408	+	0.976408i	0.999728	−	0.0233202i	$-0.00742372\pi$
$863$	28.6838	+	28.6838i	0.976408	+	0.976408i	−0.0233202	+	0.999728i	$0.507424\pi$
$864$	5.05789	+	1.19071i	0.172073	+	0.0405089i
$865$	45.7659	+	29.6835i	1.55609	+	1.00927i
$866$			13.7860i			0.468466i
$867$	1.70258	−	0.318145i	0.0578227	−	0.0108048i
$868$	25.8811	−	25.8811i	0.878461	−	0.878461i
$869$	−33.4182			−1.13364
$870$	−18.4442	−	7.59573i	−0.625315	−	0.257519i
$871$	−71.9681			−2.43855
$872$	6.26787	−	6.26787i	0.212257	−	0.212257i
$873$	23.1529	+	10.2268i	0.783607	+	0.346126i
$874$		−	0.378620i		−	0.0128070i
$875$	41.8883	+	6.56085i	1.41608	+	0.221797i
$876$	−3.70343	+	5.40553i	−0.125127	+	0.182636i
$877$	36.6209	+	36.6209i	1.23660	+	1.23660i	0.961382	+	0.275218i	$0.0887501\pi$
$877$	36.6209	+	36.6209i	1.23660	+	1.23660i	0.275218	+	0.961382i	$0.411250\pi$
$878$	−9.18385	−	9.18385i	−0.309940	−	0.309940i
$879$	−8.52045	+	12.4365i	−0.287388	+	0.419472i
$880$	1.91389	+	8.97890i	0.0645172	+	0.302679i
$881$		−	22.9253i		−	0.772373i	−0.922421	−	0.386186i	$-0.873792\pi$
$881$		−	22.9253i		−	0.772373i	0.922421	−	0.386186i	$-0.126208\pi$
$882$	−20.2562	−	8.94735i	−0.682062	−	0.301273i
$883$	−27.7206	+	27.7206i	−0.932874	+	0.932874i	−0.997885	−	0.0650109i	$-0.979292\pi$
$883$	−27.7206	+	27.7206i	−0.932874	+	0.932874i	0.0650109	+	0.997885i	$0.479292\pi$
$884$	6.58093			0.221341
$885$	−5.04225	−	12.1031i	−0.169493	−	0.406841i
$886$	−0.520648			−0.0174915
$887$	27.7458	−	27.7458i	0.931612	−	0.931612i	−0.0661947	−	0.997807i	$-0.521086\pi$
$887$	27.7458	−	27.7458i	0.931612	−	0.931612i	0.997807	+	0.0661947i	$0.0210858\pi$
$888$	−16.5753	+	3.09728i	−0.556232	+	0.103938i
$889$			9.13294i			0.306309i
$890$	15.8090	−	24.3742i	0.529919	−	0.817026i
$891$	24.8863	+	27.3142i	0.833723	+	0.915060i
$892$	−17.8329	−	17.8329i	−0.597091	−	0.597091i
$893$	9.40789	+	9.40789i	0.314823	+	0.314823i
$894$	−0.184395	−	0.126332i	−0.00616708	−	0.00422518i
$895$	−48.7102	+	10.3828i	−1.62820	+	0.347058i
$896$		−	3.79229i		−	0.126691i
$897$	0.316408	+	1.69328i	0.0105645	+	0.0565370i
$898$	0.345244	−	0.345244i	0.0115209	−	0.0115209i
$899$	−49.7082			−1.65786
$900$	10.6498	+	10.5632i	0.354995	+	0.352106i
$901$	4.43956			0.147903
$902$	−6.17574	+	6.17574i	−0.205630	+	0.205630i
$903$	−8.20404	−	43.9046i	−0.273014	−	1.46105i
$904$			0.968453i			0.0322103i
$905$	−20.5233	+	4.37462i	−0.682217	+	0.145417i
$906$	3.25929	+	2.23300i	0.108283	+	0.0741864i
$907$	23.9025	+	23.9025i	0.793670	+	0.793670i	0.982089	−	0.188419i	$-0.0603363\pi$
$907$	23.9025	+	23.9025i	0.793670	+	0.793670i	−0.188419	+	0.982089i	$0.560336\pi$
$908$	3.28982	+	3.28982i	0.109177	+	0.109177i
$909$	−1.36433	−	3.52319i	−0.0452519	−	0.116857i
$910$	−30.3669	+	46.8194i	−1.00665	+	1.55205i
$911$			47.8142i			1.58416i	0.610420	+	0.792078i	$0.291001\pi$
$911$			47.8142i			1.58416i	−0.610420	+	0.792078i	$0.708999\pi$
$912$	4.26558	−	0.797070i	0.141248	−	0.0263936i
$913$	−13.3329	+	13.3329i	−0.441255	+	0.441255i
$914$	−16.3269			−0.540047
$915$	6.59161	+	15.8221i	0.217912	+	0.523062i
$916$	6.78275			0.224108
$917$	14.9969	−	14.9969i	0.495240	−	0.495240i
$918$	−4.41843	+	2.73450i	−0.145830	+	0.0902520i
$919$		−	13.8669i		−	0.457426i	−0.973494	−	0.228713i	$-0.926548\pi$
$919$		−	13.8669i		−	0.457426i	0.973494	−	0.228713i	$-0.0734518\pi$
$920$	−0.0704472	−	0.330499i	−0.00232257	−	0.0108962i
$921$	1.95076	−	2.84734i	0.0642798	−	0.0938230i
$922$	19.0488	+	19.0488i	0.627339	+	0.627339i
$923$	−57.8519	−	57.8519i	−1.90422	−	1.90422i
$924$	15.2421	−	22.2475i	0.501429	−	0.731887i
$925$	−45.4639	−	17.3923i	−1.49484	−	0.571857i
$926$			20.8027i			0.683618i
$927$	9.39292	−	21.2650i	0.308504	−	0.698433i
$928$	−3.64180	+	3.64180i	−0.119548	+	0.119548i
$929$	−38.1864			−1.25286			−0.626428	−	0.779480i	$-0.715484\pi$
$929$	−38.1864			−1.25286			−0.626428	+	0.779480i	$0.715484\pi$
$930$	34.5640	+	14.2342i	1.13340	+	0.466759i
$931$	−18.4931			−0.606088
$932$	−6.89977	+	6.89977i	−0.226010	+	0.226010i
$933$	2.93111	−	0.547709i	0.0959602	−	0.0179312i
$934$			4.66999i			0.152807i
$935$	−7.70237	−	4.99572i	−0.251894	−	0.163377i
$936$	−18.4106	+	7.12937i	−0.601769	+	0.233031i
$937$	−37.9865	−	37.9865i	−1.24096	−	1.24096i	−0.959602	−	0.281362i	$-0.909214\pi$
$937$	−37.9865	−	37.9865i	−1.24096	−	1.24096i	−0.281362	−	0.959602i	$-0.590786\pi$
$938$	−29.3251	−	29.3251i	−0.957497	−	0.957497i
$939$	6.19704	+	4.24570i	0.202233	+	0.138553i
$940$	9.96264	+	6.46172i	0.324945	+	0.210758i
$941$		−	4.51739i		−	0.147263i	−0.997286	−	0.0736314i	$-0.976541\pi$
$941$		−	4.51739i		−	0.147263i	0.997286	−	0.0736314i	$-0.0234588\pi$
$942$	−6.88268	−	36.8332i	−0.224250	−	1.20009i
$943$	0.227319	−	0.227319i	0.00740252	−	0.00740252i
$944$	−3.38536			−0.110184
$945$	0.933890	−	44.0525i	0.0303795	−	1.43303i
$946$	27.9182			0.907700
$947$	−3.20617	+	3.20617i	−0.104186	+	0.104186i	−0.757279	−	0.653092i	$-0.773471\pi$
$947$	−3.20617	+	3.20617i	−0.104186	+	0.104186i	0.653092	+	0.757279i	$0.273471\pi$
$948$	2.58954	+	13.8581i	0.0841044	+	0.450091i
$949$		−	24.8962i		−	0.808166i
$950$	11.6999	+	4.47584i	0.379595	+	0.145215i
$951$	−0.358581	−	0.245670i	−0.0116278	−	0.00796641i
$952$	2.68155	+	2.68155i	0.0869096	+	0.0869096i
$953$	15.9434	+	15.9434i	0.516458	+	0.516458i	0.916498	−	0.400039i	$-0.131004\pi$
$953$	15.9434	+	15.9434i	0.516458	+	0.516458i	−0.400039	+	0.916498i	$0.631004\pi$
$954$	−12.4200	+	4.80954i	−0.402111	+	0.155714i
$955$	−1.91102	−	8.96542i	−0.0618390	−	0.290114i
$956$		−	10.3093i		−	0.333427i
$957$	−36.0019	+	6.72735i	−1.16378	+	0.217464i
$958$	11.5185	−	11.5185i	0.372145	−	0.372145i
$959$	63.2399			2.04212
$960$	3.57514	−	1.48943i	0.115387	−	0.0480712i
$961$	62.1521			2.00491
$962$	45.3030	−	45.3030i	1.46063	−	1.46063i
$963$	1.49026	−	3.37384i	0.0480229	−	0.108721i
$964$			14.8673i			0.478842i
$965$	−26.5839	+	40.9869i	−0.855766	+	1.31941i
$966$	−0.561038	+	0.818893i	−0.0180511	+	0.0263475i
$967$	−0.705954	−	0.705954i	−0.0227020	−	0.0227020i	0.695665	−	0.718367i	$-0.255110\pi$
$967$	−0.705954	−	0.705954i	−0.0227020	−	0.0227020i	−0.718367	+	0.695665i	$0.755110\pi$
$968$	4.14133	+	4.14133i	0.133107	+	0.133107i
$969$	−2.45261	+	3.57984i	−0.0787892	+	0.115001i
$970$	18.4512	−	3.93294i	0.592432	−	0.126279i
$971$			2.23995i			0.0718835i	0.999354	+	0.0359417i	$0.0114431\pi$
$971$			2.23995i			0.0718835i	−0.999354	+	0.0359417i	$0.988557\pi$
$972$	9.39846	−	12.4366i	0.301456	−	0.398904i
$973$	17.3708	−	17.3708i	0.556882	−	0.556882i
$974$	−5.73339			−0.183710
$975$	−56.0652	−	10.2396i	−1.79552	−	0.327928i
$976$	4.42559			0.141660
$977$	19.5421	−	19.5421i	0.625208	−	0.625208i	−0.321651	−	0.946858i	$-0.604238\pi$
$977$	19.5421	−	19.5421i	0.625208	−	0.625208i	0.946858	+	0.321651i	$0.104238\pi$
$978$	−11.5254	+	2.15365i	−0.368542	+	0.0688661i
$979$		−	53.3433i		−	1.70486i
$980$	−16.1427	+	3.44089i	−0.515661	+	0.109915i
$981$	−9.60282	−	24.7979i	−0.306594	−	0.791737i
$982$	−6.47441	−	6.47441i	−0.206607	−	0.206607i
$983$	−11.7978	−	11.7978i	−0.376292	−	0.376292i	0.493471	−	0.869763i	$-0.335728\pi$
$983$	−11.7978	−	11.7978i	−0.376292	−	0.376292i	−0.869763	+	0.493471i	$0.835728\pi$
$984$	3.03955	+	2.08245i	0.0968974	+	0.0663861i
$985$	30.1492	−	46.4839i	0.960634	−	1.48110i
$986$		−	5.15029i		−	0.164019i
$987$	−6.40713	−	34.2883i	−0.203941	−	1.09141i
$988$	−11.6585	+	11.6585i	−0.370907	+	0.370907i
$989$	−1.02763			−0.0326766
$990$	26.9599	+	5.63160i	0.856843	+	0.178984i
$991$	31.6663			1.00591			0.502957	−	0.864311i	$-0.332245\pi$
$991$	31.6663			1.00591			0.502957	+	0.864311i	$0.332245\pi$
$992$	6.82466	−	6.82466i	0.216683	−	0.216683i
$993$	−7.75558	−	41.5046i	−0.246116	−	1.31711i
$994$		−	47.1462i		−	1.49539i
$995$	0.746502	+	3.50217i	0.0236657	+	0.111026i
$996$	6.56214	+	4.49584i	0.207929	+	0.142456i
$997$	−5.05187	−	5.05187i	−0.159994	−	0.159994i	0.622570	−	0.782564i	$-0.286089\pi$
$997$	−5.05187	−	5.05187i	−0.159994	−	0.159994i	−0.782564	+	0.622570i	$0.786089\pi$
$998$	6.72976	+	6.72976i	0.213027	+	0.213027i
$999$	−11.5921	+	49.2406i	−0.366758	+	1.55790i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	510.2.l.g.137.11	yes	28
3.2	odd	2	inner	510.2.l.g.137.1	✓	28
5.3	odd	4	inner	510.2.l.g.443.1	yes	28
15.8	even	4	inner	510.2.l.g.443.11	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.l.g.137.1	✓	28	3.2	odd	2	inner
510.2.l.g.137.11	yes	28	1.1	even	1	trivial
510.2.l.g.443.1	yes	28	5.3	odd	4	inner
510.2.l.g.443.11	yes	28	15.8	even	4	inner

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:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.318145 + 1.70258i) q^{3} -1.00000i q^{4} +(-2.18694 + 0.466155i) q^{5} +(1.42887 + 0.978944i) q^{6} +(-2.68155 - 2.68155i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.79757 + 1.08334i) q^{9} +(-1.21678 + 1.87602i) q^{10} +4.10569i q^{11} +(1.70258 - 0.318145i) q^{12} +(-4.65342 + 4.65342i) q^{13} -3.79229 q^{14} +(-1.48943 - 3.57514i) q^{15} -1.00000 q^{16} +(0.707107 - 0.707107i) q^{17} +(-1.21214 + 2.74421i) q^{18} +2.50536i q^{19} +(0.466155 + 2.18694i) q^{20} +(3.71243 - 5.41868i) q^{21} +(2.90316 + 2.90316i) q^{22} +(-0.106861 - 0.106861i) q^{23} +(0.978944 - 1.42887i) q^{24} +(4.56540 - 2.03890i) q^{25} +6.58093i q^{26} +(-2.73450 - 4.41843i) q^{27} +(-2.68155 + 2.68155i) q^{28} +5.15029 q^{29} +(-3.58119 - 1.47482i) q^{30} -9.65153 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-6.99028 + 1.30621i) q^{33} -1.00000i q^{34} +(7.11440 + 4.61437i) q^{35} +(1.08334 + 2.79757i) q^{36} +(-6.88398 - 6.88398i) q^{37} +(1.77156 + 1.77156i) q^{38} +(-9.40330 - 6.44237i) q^{39} +(1.87602 + 1.21678i) q^{40} +2.12724i q^{41} +(-1.20650 - 6.45667i) q^{42} +(4.80824 - 4.80824i) q^{43} +4.10569 q^{44} +(5.61310 - 3.67329i) q^{45} -0.151124 q^{46} +(3.75510 - 3.75510i) q^{47} +(-0.318145 - 1.70258i) q^{48} +7.38143i q^{49} +(1.78650 - 4.66995i) q^{50} +(1.42887 + 0.978944i) q^{51} +(4.65342 + 4.65342i) q^{52} +(3.13924 + 3.13924i) q^{53} +(-5.05789 - 1.19071i) q^{54} +(-1.91389 - 8.97890i) q^{55} +3.79229i q^{56} +(-4.26558 + 0.797070i) q^{57} +(3.64180 - 3.64180i) q^{58} +3.38536 q^{59} +(-3.57514 + 1.48943i) q^{60} -4.42559 q^{61} +(-6.82466 + 6.82466i) q^{62} +(10.4068 + 4.59679i) q^{63} +1.00000i q^{64} +(8.00753 - 12.3460i) q^{65} +(-4.01925 + 5.86650i) q^{66} +(7.73282 + 7.73282i) q^{67} +(-0.707107 - 0.707107i) q^{68} +(0.147942 - 0.215937i) q^{69} +(8.29349 - 1.76779i) q^{70} +12.4321i q^{71} +(2.74421 + 1.21214i) q^{72} +(-2.67504 + 2.67504i) q^{73} -9.73542 q^{74} +(4.92386 + 7.12430i) q^{75} +2.50536 q^{76} +(11.0096 - 11.0096i) q^{77} +(-11.2046 + 2.09369i) q^{78} +8.13948i q^{79} +(2.18694 - 0.466155i) q^{80} +(6.65276 - 6.06142i) q^{81} +(1.50419 + 1.50419i) q^{82} +(3.24742 + 3.24742i) q^{83} +(-5.41868 - 3.71243i) q^{84} +(-1.21678 + 1.87602i) q^{85} -6.79988i q^{86} +(1.63854 + 8.76878i) q^{87} +(2.90316 - 2.90316i) q^{88} -12.9925 q^{89} +(1.37165 - 6.56647i) q^{90} +24.9568 q^{91} +(-0.106861 + 0.106861i) q^{92} +(-3.07059 - 16.4325i) q^{93} -5.31052i q^{94} +(-1.16789 - 5.47907i) q^{95} +(-1.42887 - 0.978944i) q^{96} +(-5.96585 - 5.96585i) q^{97} +(5.21946 + 5.21946i) q^{98} +(-4.44785 - 11.4860i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{7} - 12 q^{10} - 8 q^{13} + 8 q^{15} - 28 q^{16} - 16 q^{18} + 48 q^{21} + 20 q^{22} + 40 q^{25} - 36 q^{27} + 4 q^{28} - 12 q^{30} + 16 q^{31} + 8 q^{33} + 8 q^{37} - 8 q^{40} - 48 q^{42} + 48 q^{43}+ \cdots + 60 q^{97}+O(q^{100}) \) 28 * q + 4 * q^7 - 12 * q^10 - 8 * q^13 + 8 * q^15 - 28 * q^16 - 16 * q^18 + 48 * q^21 + 20 * q^22 + 40 * q^25 - 36 * q^27 + 4 * q^28 - 12 * q^30 + 16 * q^31 + 8 * q^33 + 8 * q^37 - 8 * q^40 - 48 * q^42 + 48 * q^43 + 36 * q^45 - 64 * q^46 + 8 * q^52 - 36 * q^55 - 32 * q^57 + 20 * q^58 + 12 * q^60 - 16 * q^61 - 56 * q^63 + 32 * q^66 + 112 * q^67 - 28 * q^70 + 16 * q^72 + 12 * q^73 + 16 * q^75 - 8 * q^76 - 32 * q^78 - 48 * q^81 + 24 * q^82 - 12 * q^85 - 44 * q^87 + 20 * q^88 - 20 * q^90 - 80 * q^91 + 28 * q^93 + 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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