LMFDB - Embedded newform 510.2.l.g.443.1

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			443.1
Character	$\chi$	$=$	510.443
Dual form			510.2.l.g.137.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-1.70258 + 0.318145i) q^{3} +1.00000i q^{4} +(2.18694 + 0.466155i) q^{5} +(1.42887 + 0.978944i) q^{6} +(-2.68155 + 2.68155i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.79757 - 1.08334i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.70258 + 0.318145i) 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} +(-0.318145 - 1.70258i) q^{12} +(-4.65342 - 4.65342i) q^{13} +3.79229 q^{14} +(-3.87175 - 0.0979018i) q^{15} -1.00000 q^{16} +(-0.707107 - 0.707107i) q^{17} +(-2.74421 - 1.21214i) 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} +(-4.41843 + 2.73450i) q^{27} +(-2.68155 - 2.68155i) q^{28} -5.15029 q^{29} +(2.66851 + 2.80696i) q^{30} -9.65153 q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.30621 - 6.99028i) 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} +(-6.45667 + 1.20650i) q^{42} +(4.80824 + 4.80824i) q^{43} -4.10569 q^{44} +(6.62311 - 1.06509i) q^{45} -0.151124 q^{46} +(-3.75510 - 3.75510i) q^{47} +(1.70258 - 0.318145i) 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} +(0.797070 + 4.26558i) q^{57} +(3.64180 + 3.64180i) q^{58} -3.38536 q^{59} +(0.0979018 - 3.87175i) q^{60} -4.42559 q^{61} +(6.82466 + 6.82466i) q^{62} +(-4.59679 + 10.4068i) 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} +(1.21214 - 2.74421i) q^{72} +(-2.67504 - 2.67504i) q^{73} +9.73542 q^{74} +(-8.42163 - 2.01894i) q^{75} +2.50536 q^{76} +(-11.0096 - 11.0096i) q^{77} +(-2.09369 - 11.2046i) 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} +(8.76878 - 1.63854i) q^{87} +(2.90316 + 2.90316i) q^{88} +12.9925 q^{89} +(-5.43638 - 3.93011i) q^{90} +24.9568 q^{91} +(0.106861 + 0.106861i) q^{92} +(16.4325 - 3.07059i) 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}+O(q^{10}) $ 28 * q + 4 * q^7	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$241$	$307$	$341$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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
$3$	−1.70258	+	0.318145i	−0.982986	+	0.183681i
$3$	−1.70258	+	0.318145i	−0.982986	+	0.183681i
$4$			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	−0.0136237	+	0.999907i	$0.504337\pi$
$7$	−2.68155	+	2.68155i	−1.01353	+	1.01353i	−0.999907	+	0.0136237i	$0.995663\pi$
$8$	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	$0.787556\pi$
$12$	−0.318145	−	1.70258i	−0.0918407	−	0.491493i
$13$	−4.65342	−	4.65342i	−1.29063	−	1.29063i	−0.934399	−	0.356228i	$-0.884063\pi$
$13$	−4.65342	−	4.65342i	−1.29063	−	1.29063i	−0.356228	−	0.934399i	$-0.615937\pi$
$14$	3.79229			1.01353
$15$	−3.87175	−	0.0979018i	−0.999680	−	0.0252781i
$16$	−1.00000			−0.250000
$17$	−0.707107	−	0.707107i	−0.171499	−	0.171499i
$17$	−0.707107	−	0.707107i	−0.171499	−	0.171499i
$18$	−2.74421	−	1.21214i	−0.646817	−	0.285705i
$19$		−	2.50536i		−	0.574769i	−0.957815	−	0.287385i	$-0.907214\pi$
$19$		−	2.50536i		−	0.574769i	0.957815	−	0.287385i	$-0.0927858\pi$
$20$	−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	$-0.744985\pi$
$23$	0.106861	−	0.106861i	0.0222820	−	0.0222820i	0.718160	+	0.695878i	$0.244985\pi$
$24$	−0.978944	+	1.42887i	−0.199826	+	0.291667i
$25$	4.56540	+	2.03890i	0.913080	+	0.407781i
$26$			6.58093i			1.29063i
$27$	−4.41843	+	2.73450i	−0.850327	+	0.526255i
$28$	−2.68155	−	2.68155i	−0.506765	−	0.506765i
$29$	−5.15029			−0.956384			−0.478192	−	0.878255i	$-0.658708\pi$
$29$	−5.15029			−0.956384			−0.478192	+	0.878255i	$0.658708\pi$
$30$	2.66851	+	2.80696i	0.487201	+	0.512479i
$31$	−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
$33$	−1.30621	−	6.99028i	−0.227382	−	1.21685i
$34$			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	−0.141828	+	0.989891i	$0.545298\pi$
$37$	−6.88398	+	6.88398i	−1.13172	+	1.13172i	−0.989891	+	0.141828i	$0.954702\pi$
$38$	−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	$0.946879\pi$
$42$	−6.45667	+	1.20650i	−0.996286	+	0.186167i
$43$	4.80824	+	4.80824i	0.733250	+	0.733250i	0.971262	−	0.238012i	$-0.0764958\pi$
$43$	4.80824	+	4.80824i	0.733250	+	0.733250i	−0.238012	+	0.971262i	$0.576496\pi$
$44$	−4.10569			−0.618957
$45$	6.62311	−	1.06509i	0.987315	−	0.158775i
$46$	−0.151124			−0.0222820
$47$	−3.75510	−	3.75510i	−0.547738	−	0.547738i	0.378048	−	0.925786i	$-0.376595\pi$
$47$	−3.75510	−	3.75510i	−0.547738	−	0.547738i	−0.925786	+	0.378048i	$0.876595\pi$
$48$	1.70258	−	0.318145i	0.245746	−	0.0459203i
$49$		−	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	$-0.848626\pi$
$53$	−3.13924	+	3.13924i	−0.431208	+	0.431208i	0.457831	+	0.889039i	$0.348626\pi$
$54$	5.05789	+	1.19071i	0.688291	+	0.162036i
$55$	−1.91389	+	8.97890i	−0.258069	+	1.21071i
$56$			3.79229i			0.506765i
$57$	0.797070	+	4.26558i	0.105574	+	0.564990i
$58$	3.64180	+	3.64180i	0.478192	+	0.478192i
$59$	−3.38536			−0.440736			−0.220368	−	0.975417i	$-0.570726\pi$
$59$	−3.38536			−0.440736			−0.220368	+	0.975417i	$0.570726\pi$
$60$	0.0979018	−	3.87175i	0.0126391	−	0.499840i
$61$	−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
$63$	−4.59679	+	10.4068i	−0.579142	+	1.31114i
$64$		−	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	−0.0538356	−	0.998550i	$-0.517145\pi$
$67$	7.73282	−	7.73282i	0.944714	−	0.944714i	0.998550	+	0.0538356i	$0.0171447\pi$
$68$	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	$0.735907\pi$
$72$	1.21214	−	2.74421i	0.142852	−	0.323409i
$73$	−2.67504	−	2.67504i	−0.313090	−	0.313090i	0.533015	−	0.846106i	$-0.321059\pi$
$73$	−2.67504	−	2.67504i	−0.313090	−	0.313090i	−0.846106	+	0.533015i	$0.821059\pi$
$74$	9.73542			1.13172
$75$	−8.42163	−	2.01894i	−0.972446	−	0.233127i
$76$	2.50536			0.287385
$77$	−11.0096	−	11.0096i	−1.25466	−	1.25466i
$78$	−2.09369	−	11.2046i	−0.237064	−	1.26867i
$79$		−	8.13948i		−	0.915764i	−0.889013	−	0.457882i	$-0.848608\pi$
$79$		−	8.13948i		−	0.915764i	0.889013	−	0.457882i	$-0.151392\pi$
$80$	−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	$-0.831104\pi$
$83$	−3.24742	+	3.24742i	−0.356450	+	0.356450i	0.506052	+	0.862503i	$0.331104\pi$
$84$	5.41868	+	3.71243i	0.591227	+	0.405060i
$85$	−1.21678	−	1.87602i	−0.131978	−	0.203483i
$86$		−	6.79988i		−	0.733250i
$87$	8.76878	−	1.63854i	0.940112	−	0.175670i
$88$	2.90316	+	2.90316i	0.309478	+	0.309478i
$89$	12.9925			1.37720			0.688602	−	0.725140i	$-0.258225\pi$
$89$	12.9925			1.37720			0.688602	+	0.725140i	$0.258225\pi$
$90$	−5.43638	−	3.93011i	−0.573045	−	0.414270i
$91$	24.9568			2.61618
$92$	0.106861	+	0.106861i	0.0111410	+	0.0111410i
$93$	16.4325	−	3.07059i	1.70397	−	0.318406i
$94$			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	−0.941830	−	0.336090i	$-0.890896\pi$
$97$	−5.96585	+	5.96585i	−0.605740	+	0.605740i	0.336090	+	0.941830i	$0.390896\pi$
$98$	−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	$0.980043\pi$
$102$	−0.318145	−	1.70258i	−0.0315011	−	0.168581i
$103$	−5.47938	−	5.47938i	−0.539900	−	0.539900i	0.383600	−	0.923499i	$-0.374684\pi$
$103$	−5.47938	−	5.47938i	−0.539900	−	0.539900i	−0.923499	+	0.383600i	$0.874684\pi$
$104$	−6.58093			−0.645314
$105$	10.6448	−	10.1198i	1.03883	−	0.987587i
$106$	4.43956			0.431208
$107$	0.869345	+	0.869345i	0.0840427	+	0.0840427i	0.747878	−	0.663836i	$-0.231073\pi$
$107$	0.869345	+	0.869345i	0.0840427	+	0.0840427i	−0.663836	+	0.747878i	$0.731073\pi$
$108$	−2.73450	−	4.41843i	−0.263128	−	0.425163i
$109$		−	8.86411i		−	0.849027i	−0.905422	−	0.424514i	$-0.860445\pi$
$109$		−	8.86411i		−	0.849027i	0.905422	−	0.424514i	$-0.139555\pi$
$110$	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	$-0.735495\pi$
$113$	0.684800	−	0.684800i	0.0644205	−	0.0644205i	0.738583	+	0.674163i	$0.235495\pi$
$114$	2.45261	−	3.57984i	0.229708	−	0.335282i
$115$	0.283512	−	0.183884i	0.0264376	−	0.0171473i
$116$		−	5.15029i		−	0.478192i
$117$	−18.0595	−	7.97704i	−1.66960	−	0.737477i
$118$	2.39381	+	2.39381i	0.220368	+	0.220368i
$119$	3.79229			0.347638
$120$	−2.80696	+	2.66851i	−0.256240	+	0.243601i
$121$	−5.85673			−0.532430
$122$	3.12936	+	3.12936i	0.283319	+	0.283319i
$123$	−0.676773	−	3.62180i	−0.0610225	−	0.326567i
$124$		−	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	−0.778614	−	0.627504i	$-0.784077\pi$
$127$	−1.70292	+	1.70292i	−0.151110	+	0.151110i	0.627504	+	0.778614i	$0.284077\pi$
$128$	−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	$0.921437\pi$
$132$	6.99028	−	1.30621i	0.608426	−	0.113691i
$133$	6.71825	+	6.71825i	0.582547	+	0.582547i
$134$	−10.9359			−0.944714
$135$	−10.9375	+	3.92052i	−0.941353	+	0.337425i
$136$	−1.00000			−0.0857493
$137$	11.7917	+	11.7917i	1.00743	+	1.00743i	0.999972	+	0.00745772i	$0.00237389\pi$
$137$	11.7917	+	11.7917i	1.00743	+	1.00743i	0.00745772	+	0.999972i	$0.497626\pi$
$138$	0.257301	−	0.0480794i	0.0219029	−	0.00409279i
$139$		−	6.47789i		−	0.549448i	−0.961523	−	0.274724i	$-0.911414\pi$
$139$		−	6.47789i		−	0.549448i	0.961523	−	0.274724i	$-0.0885864\pi$
$140$	−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
$147$	2.34837	+	12.5675i	0.193690	+	1.03655i
$148$	−6.88398	−	6.88398i	−0.565860	−	0.565860i
$149$	0.129049			0.0105721			0.00528607	−	0.999986i	$-0.498317\pi$
$149$	0.129049			0.0105721			0.00528607	+	0.999986i	$0.498317\pi$
$150$	4.52739	+	7.38260i	0.369660	+	0.602787i
$151$	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
$153$	−2.74421	−	1.21214i	−0.221857	−	0.0979960i
$154$			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	−0.253537	+	0.967326i	$0.581594\pi$
$157$	−15.2974	+	15.2974i	−1.22086	+	1.22086i	−0.967326	+	0.253537i	$0.918406\pi$
$158$	−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
$162$	−8.99028	−	0.418144i	−0.706343	−	0.0328525i
$163$	−4.78667	−	4.78667i	−0.374921	−	0.374921i	0.494345	−	0.869266i	$-0.335408\pi$
$163$	−4.78667	−	4.78667i	−0.374921	−	0.374921i	−0.869266	+	0.494345i	$0.835408\pi$
$164$	−2.12724			−0.166110
$165$	0.401955	−	15.8962i	0.0312921	−	1.23752i
$166$	4.59254			0.356450
$167$	0.157313	+	0.157313i	0.0121732	+	0.0121732i	0.713167	−	0.700994i	$-0.247260\pi$
$167$	0.157313	+	0.157313i	0.0121732	+	0.0121732i	−0.700994	+	0.713167i	$0.747260\pi$
$168$	−1.20650	−	6.45667i	−0.0930834	−	0.498143i
$169$			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	0.391178	−	0.920315i	$-0.372068\pi$
$173$	17.2500	−	17.2500i	1.31149	−	1.31149i	0.920315	−	0.391178i	$-0.127932\pi$
$174$	−7.35909	−	5.04184i	−0.557891	−	0.382221i
$175$	−17.7098	+	6.77493i	−1.33873	+	0.512136i
$176$		−	4.10569i		−	0.309478i
$177$	5.76384	−	1.07704i	0.433237	−	0.0809550i
$178$	−9.18709	−	9.18709i	−0.688602	−	0.688602i
$179$	−22.2732			−1.66478			−0.832389	−	0.554191i	$-0.813028\pi$
$179$	−22.2732			−1.66478			−0.832389	+	0.554191i	$0.813028\pi$
$180$	1.06509	+	6.62311i	0.0793873	+	0.493657i
$181$	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
$183$	7.53492	−	1.40798i	0.556998	−	0.104081i
$184$		−	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	$0.952615\pi$
$192$	0.318145	+	1.70258i	0.0229602	+	0.122873i
$193$	15.4487	+	15.4487i	1.11202	+	1.11202i	0.992877	+	0.119146i	$0.0380157\pi$
$193$	15.4487	+	15.4487i	1.11202	+	1.11202i	0.119146	+	0.992877i	$0.461984\pi$
$194$	8.43699			0.605740
$195$	17.5613	+	18.4724i	1.25759	+	1.32284i
$196$	7.38143			0.527245
$197$	17.5206	+	17.5206i	1.24829	+	1.24829i	0.956473	+	0.291821i	$0.0942612\pi$
$197$	17.5206	+	17.5206i	1.24829	+	1.24829i	0.291821	+	0.956473i	$0.405739\pi$
$198$	4.97669	−	11.2669i	0.353678	−	0.800704i
$199$			1.60140i			0.113521i	0.998388	+	0.0567603i	$0.0180771\pi$
$199$			1.60140i			0.113521i	−0.998388	+	0.0567603i	$0.981923\pi$
$200$	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
$207$	0.183184	−	0.414717i	0.0127322	−	0.0288248i
$208$	4.65342	+	4.65342i	0.322657	+	0.322657i
$209$	10.2863			0.711515
$210$	−14.6828	−	0.371271i	−1.01321	−	0.0256202i
$211$	−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
$213$	−3.95522	−	21.1667i	−0.271007	−	1.45032i
$214$		−	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
$222$	−16.5753	+	3.09728i	−1.11246	+	0.207876i
$223$	17.8329	+	17.8329i	1.19418	+	1.19418i	0.975882	+	0.218299i	$0.0700509\pi$
$223$	17.8329	+	17.8329i	1.19418	+	1.19418i	0.218299	+	0.975882i	$0.429949\pi$
$224$	−3.79229			−0.253383
$225$	14.9808	+	0.758102i	0.998722	+	0.0505401i
$226$	−0.968453			−0.0644205
$227$	3.28982	+	3.28982i	0.218353	+	0.218353i	0.807804	−	0.589451i	$-0.200656\pi$
$227$	3.28982	+	3.28982i	0.218353	+	0.218353i	−0.589451	+	0.807804i	$0.700656\pi$
$228$	−4.26558	+	0.797070i	−0.282495	+	0.0527872i
$229$		−	6.78275i		−	0.448217i	−0.974564	−	0.224108i	$-0.928053\pi$
$229$		−	6.78275i		−	0.448217i	0.974564	−	0.224108i	$-0.0719470\pi$
$230$	−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	$-0.646443\pi$
$233$	6.89977	−	6.89977i	0.452019	−	0.452019i	0.896024	+	0.444005i	$0.146443\pi$
$234$	7.12937	+	18.4106i	0.466061	+	1.20354i
$235$	−6.46172	−	9.96264i	−0.421516	−	0.649891i
$236$		−	3.38536i		−	0.220368i
$237$	2.58954	+	13.8581i	0.168209	+	0.900183i
$238$	−2.68155	−	2.68155i	−0.173819	−	0.173819i
$239$	−10.3093			−0.666854			−0.333427	−	0.942776i	$-0.608205\pi$
$239$	−10.3093			−0.666854			−0.333427	+	0.942776i	$0.608205\pi$
$240$	3.87175	+	0.0979018i	0.249920	+	0.00631953i
$241$	−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
$243$	−9.39846	+	12.4366i	−0.602911	+	0.797808i
$244$		−	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	$0.792058\pi$
$252$	−10.4068	−	4.59679i	−0.655569	−	0.289571i
$253$	0.438738	+	0.438738i	0.0275832	+	0.0275832i
$254$	2.40829			0.151110
$255$	2.66851	+	2.80696i	0.167109	+	0.175779i
$256$	1.00000			0.0625000
$257$	20.5292	+	20.5292i	1.28058	+	1.28058i	0.940339	+	0.340240i	$0.110508\pi$
$257$	20.5292	+	20.5292i	1.28058	+	1.28058i	0.340240	+	0.940339i	$0.389492\pi$
$258$	2.16335	+	11.5773i	0.134684	+	0.720774i
$259$		−	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	$-0.888639\pi$
$263$	−9.67629	+	9.67629i	−0.596666	+	0.596666i	0.342758	+	0.939424i	$0.388639\pi$
$264$	−5.86650	−	4.01925i	−0.361058	−	0.247367i
$265$	−8.32870	+	5.40195i	−0.511628	+	0.331839i
$266$		−	9.50105i		−	0.582547i
$267$	−22.1208	+	4.13351i	−1.35377	+	0.252967i
$268$	7.73282	+	7.73282i	0.472357	+	0.472357i
$269$	−10.8355			−0.660652			−0.330326	−	0.943867i	$-0.607159\pi$
$269$	−10.8355			−0.660652			−0.330326	+	0.943867i	$0.607159\pi$
$270$	10.5062	+	4.96177i	0.639389	+	0.301964i
$271$	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
$273$	−42.4909	+	7.93989i	−2.57167	+	0.480544i
$274$		−	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	−0.621910	−	0.783088i	$-0.713643\pi$
$277$	2.68254	−	2.68254i	0.161178	−	0.161178i	0.783088	+	0.621910i	$0.213643\pi$
$278$	−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	$-0.199385\pi$
$282$	−1.68952	−	9.04159i	−0.100609	−	0.538419i
$283$	−7.74608	−	7.74608i	−0.460457	−	0.460457i	0.438349	−	0.898805i	$-0.355564\pi$
$283$	−7.74608	−	7.74608i	−0.460457	−	0.460457i	−0.898805	+	0.438349i	$0.855564\pi$
$284$	−12.4321			−0.737711
$285$	−0.245279	+	9.70012i	−0.0145291	+	0.574586i
$286$	−27.0193			−1.59768
$287$	−5.70431	−	5.70431i	−0.336715	−	0.336715i
$288$	2.74421	+	1.21214i	0.161704	+	0.0714262i
$289$			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	$-0.831825\pi$
$293$	−6.15446	+	6.15446i	−0.359547	+	0.359547i	0.504099	+	0.863646i	$0.331825\pi$
$294$	7.22600	−	10.5471i	0.421429	−	0.615119i
$295$	−7.40356	−	1.57810i	−0.431052	−	0.0918805i
$296$			9.73542i			0.565860i
$297$	−11.2270	−	18.1407i	−0.651459	−	1.05263i
$298$	−0.0912517	−	0.0912517i	−0.00528607	−	0.00528607i
$299$	−0.994537			−0.0575156
$300$	2.01894	−	8.42163i	0.116563	−	0.486223i
$301$	−25.7871			−1.48634
$302$	−1.61293	−	1.61293i	−0.0928137	−	0.0928137i
$303$	−0.400665	−	2.14419i	−0.0230176	−	0.123180i
$304$			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	−0.746172	−	0.665753i	$-0.768111\pi$
$307$	−1.40907	+	1.40907i	−0.0804197	+	0.0804197i	0.665753	+	0.746172i	$0.268111\pi$
$308$	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	$-0.0155431\pi$
$312$	11.2046	−	2.09369i	0.634334	−	0.118532i
$313$	3.06674	+	3.06674i	0.173342	+	0.173342i	0.788446	−	0.615104i	$-0.210886\pi$
$313$	3.06674	+	3.06674i	0.173342	+	0.173342i	−0.615104	+	0.788446i	$0.710886\pi$
$314$	21.6337			1.22086
$315$	−14.9041	+	20.6163i	−0.839751	+	1.16160i
$316$	8.13948			0.457882
$317$	0.177452	+	0.177452i	0.00996668	+	0.00996668i	0.712073	−	0.702106i	$-0.247757\pi$
$317$	0.177452	+	0.177452i	0.00996668	+	0.00996668i	−0.702106	+	0.712073i	$0.747757\pi$
$318$	−7.55871	+	1.41242i	−0.423871	+	0.0792048i
$319$		−	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
$327$	2.82008	+	15.0919i	0.155951	+	0.834582i
$328$	1.50419	+	1.50419i	0.0830549	+	0.0830549i
$329$	20.1390			1.11030
$330$	−11.5245	+	10.9561i	−0.634405	+	0.603113i
$331$	−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
$333$	−11.8007	+	26.7161i	−0.646675	+	1.46403i
$334$		−	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	−0.725544	−	0.688176i	$-0.758412\pi$
$337$	−0.685998	+	0.685998i	−0.0373687	+	0.0373687i	0.688176	+	0.725544i	$0.258412\pi$
$338$	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
$342$	−3.03686	+	6.87525i	−0.164214	+	0.371771i
$343$	1.02282	+	1.02282i	0.0552269	+	0.0552269i
$344$	6.79988			0.366625
$345$	−0.424200	+	0.403276i	−0.0228382	+	0.0217117i
$346$	−24.3952			−1.31149
$347$	−19.5689	−	19.5689i	−1.05051	−	1.05051i	−0.998654	−	0.0518581i	$-0.983486\pi$
$347$	−19.5689	−	19.5689i	−1.05051	−	1.05051i	−0.0518581	−	0.998654i	$-0.516514\pi$
$348$	1.63854	+	8.76878i	0.0878350	+	0.470056i
$349$			10.9262i			0.584869i	0.956286	+	0.292434i	$0.0944653\pi$
$349$			10.9262i			0.584869i	−0.956286	+	0.292434i	$0.905535\pi$
$350$	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	$-0.820405\pi$
$353$	−5.82919	+	5.82919i	−0.310256	+	0.310256i	0.534752	+	0.845009i	$0.320405\pi$
$354$	−4.83723	−	3.31407i	−0.257096	−	0.176141i
$355$	−5.79529	+	27.1883i	−0.307582	+	1.44300i
$356$			12.9925i			0.688602i
$357$	−6.45667	+	1.20650i	−0.341723	+	0.0638547i
$358$	15.7495	+	15.7495i	0.832389	+	0.832389i
$359$	30.4881			1.60910			0.804549	−	0.593886i	$-0.202407\pi$
$359$	30.4881			1.60910			0.804549	+	0.593886i	$0.202407\pi$
$360$	3.93011	−	5.43638i	0.207135	−	0.286522i
$361$	12.7232			0.669640
$362$	−6.63583	−	6.63583i	−0.348772	−	0.348772i
$363$	9.97155	−	1.86329i	0.523371	−	0.0977974i
$364$			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	0.00437114	−	0.999990i	$-0.498609\pi$
$367$	19.2408	−	19.2408i	1.00436	−	1.00436i	0.999990	−	0.00437114i	$-0.00139138\pi$
$368$	−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
$372$	3.07059	+	16.4325i	0.159203	+	0.851987i
$373$	3.79471	+	3.79471i	0.196483	+	0.196483i	0.798490	−	0.602008i	$-0.205632\pi$
$373$	3.79471	+	3.79471i	0.196483	+	0.196483i	−0.602008	+	0.798490i	$0.705632\pi$
$374$	−4.10569			−0.212300
$375$	−17.4765	−	8.34108i	−0.902480	−	0.430731i
$376$	−5.31052			−0.273869
$377$	23.9665	+	23.9665i	1.23434	+	1.23434i
$378$	−16.7559	+	10.3700i	−0.861832	+	0.533376i
$379$			19.1599i			0.984179i	0.870545	+	0.492090i	$0.163767\pi$
$379$			19.1599i			0.984179i	−0.870545	+	0.492090i	$0.836233\pi$
$380$	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	$-0.785936\pi$
$383$	−3.11794	+	3.11794i	−0.159319	+	0.159319i	0.622946	+	0.782265i	$0.285936\pi$
$384$	0.978944	−	1.42887i	0.0499565	−	0.0729167i
$385$	−18.9452	−	29.2096i	−0.965536	−	1.48866i
$386$		−	21.8478i		−	1.11202i
$387$	18.6603	+	8.24243i	0.948558	+	0.418986i
$388$	−5.96585	−	5.96585i	−0.302870	−	0.302870i
$389$	1.74726			0.0885897			0.0442949	−	0.999019i	$-0.485896\pi$
$389$	1.74726			0.0885897			0.0442949	+	0.999019i	$0.485896\pi$
$390$	0.644285	−	25.4797i	0.0326246	−	1.29021i
$391$	−0.151124			−0.00764267
$392$	−5.21946	−	5.21946i	−0.263622	−	0.263622i
$393$	−1.77926	−	9.52188i	−0.0897520	−	0.480315i
$394$		−	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	−0.292816	−	0.956169i	$-0.594592\pi$
$397$	13.2172	−	13.2172i	0.663353	−	0.663353i	0.956169	+	0.292816i	$0.0945922\pi$
$398$	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	$-0.0867186\pi$
$402$	18.6192	−	3.47919i	0.928641	−	0.173526i
$403$	44.9127	+	44.9127i	2.23726	+	2.23726i
$404$	−1.25938			−0.0626563
$405$	17.3747	−	10.1547i	0.863358	−	0.504593i
$406$	−19.5314			−0.969325
$407$	−28.2635	−	28.2635i	−1.40097	−	1.40097i
$408$	1.70258	−	0.318145i	0.0842903	−	0.0157505i
$409$		−	29.1789i		−	1.44280i	−0.692516	−	0.721402i	$-0.743498\pi$
$409$		−	29.1789i		−	1.44280i	0.692516	−	0.721402i	$-0.256502\pi$
$410$	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
$417$	2.06091	+	11.0291i	0.100923	+	0.540099i
$418$	−7.27348	−	7.27348i	−0.355757	−	0.355757i
$419$	−16.5097			−0.806549			−0.403275	−	0.915079i	$-0.632128\pi$
$419$	−16.5097			−0.806549			−0.403275	+	0.915079i	$0.632128\pi$
$420$	10.1198	+	10.6448i	0.493793	+	0.519414i
$421$	−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
$423$	−14.5732	−	6.43711i	−0.708573	−	0.312983i
$424$			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	$0.764969\pi$
$432$	4.41843	−	2.73450i	0.212582	−	0.131564i
$433$	−9.74815	−	9.74815i	−0.468466	−	0.468466i	0.432951	−	0.901417i	$-0.357472\pi$
$433$	−9.74815	−	9.74815i	−0.468466	−	0.468466i	−0.901417	+	0.432951i	$0.857472\pi$
$434$	−36.6014			−1.75692
$435$	19.9406	+	0.504222i	0.956079	+	0.0241756i
$436$	8.86411			0.424514
$437$	−0.267725	−	0.267725i	−0.0128070	−	0.0128070i
$438$	−1.20357	−	6.44101i	−0.0575089	−	0.307763i
$439$			12.9879i			0.619880i	0.950756	+	0.309940i	$0.100309\pi$
$439$			12.9879i			0.619880i	−0.950756	+	0.309940i	$0.899691\pi$
$440$	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	$-0.746063\pi$
$443$	0.368153	−	0.368153i	0.0174915	−	0.0174915i	0.715798	+	0.698307i	$0.246063\pi$
$444$	13.9106	+	9.53043i	0.660170	+	0.452294i
$445$	28.4138	+	6.05652i	1.34694	+	0.287107i
$446$		−	25.2196i		−	1.19418i
$447$	−0.219717	+	0.0410565i	−0.0103923	+	0.00194190i
$448$	2.68155	+	2.68155i	0.126691	+	0.126691i
$449$	−0.488249			−0.0230419			−0.0115209	−	0.999934i	$-0.503667\pi$
$449$	−0.488249			−0.0230419			−0.0115209	+	0.999934i	$0.503667\pi$
$450$	−10.0570	−	11.1291i	−0.474091	−	0.524631i
$451$	−8.73381			−0.411259
$452$	0.684800	+	0.684800i	0.0322103	+	0.0322103i
$453$	−3.88364	+	0.725699i	−0.182469	+	0.0340963i
$454$		−	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	−0.923543	−	0.383495i	$-0.874720\pi$
$457$	−11.5449	+	11.5449i	−0.540047	+	0.540047i	0.383495	+	0.923543i	$0.374720\pi$
$458$	−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	$0.784144\pi$
$462$	−4.95351	−	26.5091i	−0.230458	−	1.23332i
$463$	−14.7097	−	14.7097i	−0.683618	−	0.683618i	0.277195	−	0.960814i	$-0.410595\pi$
$463$	−14.7097	−	14.7097i	−0.683618	−	0.683618i	−0.960814	+	0.277195i	$0.910595\pi$
$464$	5.15029			0.239096
$465$	37.3683	+	0.944902i	1.73291	+	0.0438188i
$466$	−9.75775			−0.452019
$467$	3.30218	+	3.30218i	0.152807	+	0.152807i	0.779370	−	0.626564i	$-0.215539\pi$
$467$	3.30218	+	3.30218i	0.152807	+	0.152807i	−0.626564	+	0.779370i	$0.715539\pi$
$468$	7.97704	−	18.0595i	0.368739	−	0.834800i
$469$			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
$477$	−5.38138	+	12.1831i	−0.246396	+	0.557825i
$478$	7.28978	+	7.28978i	0.333427	+	0.333427i
$479$	−16.2896			−0.744289			−0.372145	−	0.928175i	$-0.621377\pi$
$479$	−16.2896			−0.744289			−0.372145	+	0.928175i	$0.621377\pi$
$480$	−2.66851	−	2.80696i	−0.121800	−	0.128120i
$481$	64.0681			2.92125
$482$	10.5127	+	10.5127i	0.478842	+	0.478842i
$483$	−0.182331	−	0.975759i	−0.00829634	−	0.0443986i
$484$		−	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	−0.792970	−	0.609260i	$-0.791466\pi$
$487$	−4.05412	+	4.05412i	−0.183710	+	0.183710i	0.609260	+	0.792970i	$0.291466\pi$
$488$	−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	$-0.0662420\pi$
$492$	3.62180	−	0.676773i	0.163284	−	0.0305113i
$493$	3.64180	+	3.64180i	0.164019	+	0.164019i
$494$	16.4876			0.741813
$495$	4.37295	+	27.1925i	0.196549	+	1.22221i
$496$	9.65153			0.433367
$497$	−33.3374	−	33.3374i	−1.49539	−	1.49539i
$498$	−7.81917	+	1.46110i	−0.350386	+	0.0654733i
$499$		−	9.51732i		−	0.426054i	−0.977046	−	0.213027i	$-0.931668\pi$
$499$		−	9.51732i		−	0.426054i	0.977046	−	0.213027i	$-0.0683322\pi$
$500$	−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	0.156650	−	0.987654i	$-0.449930\pi$
$503$	25.6641	−	25.6641i	1.14430	−	1.14430i	0.987654	−	0.156650i	$-0.0500696\pi$
$504$	4.10832	+	10.6092i	0.182999	+	0.472570i
$505$	−0.587064	+	2.75418i	−0.0261240	+	0.122559i
$506$		−	0.620469i		−	0.0275832i
$507$	−9.64257	−	51.6030i	−0.428242	−	2.29177i
$508$	−1.70292	−	1.70292i	−0.0755549	−	0.0755549i
$509$	−35.3731			−1.56788			−0.783941	−	0.620835i	$-0.786794\pi$
$509$	−35.3731			−1.56788			−0.783941	+	0.620835i	$0.786794\pi$
$510$	0.0979018	−	3.87175i	0.00433516	−	0.171444i
$511$	14.3465			0.634653
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	6.85092	+	11.0698i	0.302475	+	0.488742i
$514$		−	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	$-0.0872016\pi$
$522$	14.1335	+	6.24289i	0.618606	+	0.273244i
$523$	2.65510	+	2.65510i	0.116099	+	0.116099i	0.762770	−	0.646670i	$-0.223839\pi$
$523$	2.65510	+	2.65510i	0.116099	+	0.116099i	−0.646670	+	0.762770i	$0.723839\pi$
$524$	−5.59261			−0.244314
$525$	27.9969	−	17.1691i	1.22189	−	0.749323i
$526$	13.6843			0.596666
$527$	6.82466	+	6.82466i	0.297287	+	0.297287i
$528$	1.30621	+	6.99028i	0.0568454	+	0.304213i
$529$			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
$537$	37.9220	−	7.08612i	1.63645	−	0.305789i
$538$	7.66186	+	7.66186i	0.330326	+	0.330326i
$539$	30.3059			1.30537
$540$	−3.92052	−	10.9375i	−0.168712	−	0.470676i
$541$	−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
$543$	−15.9778	+	2.98563i	−0.685675	+	0.128126i
$544$		−	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	−0.763654	−	0.645626i	$-0.776596\pi$
$547$	−2.76042	+	2.76042i	−0.118027	+	0.118027i	0.645626	+	0.763654i	$0.276596\pi$
$548$	−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
$552$	0.0480794	+	0.257301i	0.00204640	+	0.0109515i
$553$	21.8264	+	21.8264i	0.928155	+	0.928155i
$554$	−3.79368			−0.161178
$555$	27.3270	−	25.9791i	1.15997	−	1.10275i
$556$	6.47789			0.274724
$557$	−32.6785	−	32.6785i	−1.38463	−	1.38463i	−0.836182	−	0.548452i	$-0.815217\pi$
$557$	−32.6785	−	32.6785i	−1.38463	−	1.38463i	−0.548452	−	0.836182i	$-0.684783\pi$
$558$	26.4859	+	11.6990i	1.12124	+	0.495260i
$559$		−	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	$-0.667802\pi$
$563$	8.56925	−	8.56925i	0.361151	−	0.361151i	0.864237	+	0.503086i	$0.167802\pi$
$564$	−5.19870	+	7.58804i	−0.218905	+	0.319514i
$565$	1.81684	−	1.17839i	0.0764349	−	0.0495753i
$566$			10.9546i			0.460457i
$567$	−1.58572	+	34.0937i	−0.0665940	+	1.43180i
$568$	8.79084	+	8.79084i	0.368855	+	0.368855i
$569$	16.0012			0.670807			0.335404	−	0.942075i	$-0.391127\pi$
$569$	16.0012			0.670807			0.335404	+	0.942075i	$0.391127\pi$
$570$	7.03246	−	6.68558i	0.294557	−	0.280028i
$571$	−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
$573$	−1.30425	−	6.97979i	−0.0544857	−	0.291585i
$574$			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	−0.911198	−	0.411969i	$-0.864841\pi$
$577$	−11.9919	+	11.9919i	−0.499229	+	0.499229i	0.411969	+	0.911198i	$0.364841\pi$
$578$	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
$582$	−14.3647	+	2.68419i	−0.595434	+	0.111263i
$583$	−12.8888	−	12.8888i	−0.533798	−	0.533798i
$584$	−3.78308			−0.156545
$585$	−35.7765	−	25.8638i	−1.47917	−	1.06934i
$586$	8.70372			0.359547
$587$	13.3609	+	13.3609i	0.551465	+	0.551465i	0.926863	−	0.375399i	$-0.122494\pi$
$587$	13.3609	+	13.3609i	0.551465	+	0.551465i	−0.375399	+	0.926863i	$0.622494\pi$
$588$	−12.5675	+	2.34837i	−0.518274	+	0.0968451i
$589$			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	$-0.843415\pi$
$593$	−9.96226	+	9.96226i	−0.409101	+	0.409101i	0.472324	+	0.881425i	$0.343415\pi$
$594$	−4.88871	+	20.7661i	−0.200586	+	0.852045i
$595$	8.29349	+	1.76779i	0.340000	+	0.0724724i
$596$			0.129049i			0.00528607i
$597$	−0.509479	−	2.72652i	−0.0208516	−	0.111589i
$598$	0.703244	+	0.703244i	0.0287578	+	0.0287578i
$599$	24.4461			0.998839			0.499419	−	0.866360i	$-0.333547\pi$
$599$	24.4461			0.998839			0.499419	+	0.866360i	$0.333547\pi$
$600$	−7.38260	+	4.52739i	−0.301393	+	0.184830i
$601$	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
$603$	13.2558	−	30.0103i	0.539819	−	1.22212i
$604$			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	−0.907203	−	0.420693i	$-0.861787\pi$
$607$	−11.9863	+	11.9863i	−0.486510	+	0.486510i	0.420693	+	0.907203i	$0.361787\pi$
$608$	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
$612$	1.21214	−	2.74421i	0.0489980	−	0.110928i
$613$	15.3999	+	15.3999i	0.621995	+	0.621995i	0.946041	−	0.324047i	$-0.105043\pi$
$613$	15.3999	+	15.3999i	0.621995	+	0.621995i	−0.324047	+	0.946041i	$0.605043\pi$
$614$	1.99272			0.0804197
$615$	0.208261	−	8.23614i	0.00839789	−	0.332113i
$616$	−15.5700			−0.627332
$617$	18.1477	+	18.1477i	0.730599	+	0.730599i	0.970739	−	0.240139i	$-0.0771930\pi$
$617$	18.1477	+	18.1477i	0.730599	+	0.730599i	−0.240139	+	0.970739i	$0.577193\pi$
$618$	−2.46531	−	13.1933i	−0.0991695	−	0.530714i
$619$		−	27.6016i		−	1.10940i	−0.832050	−	0.554701i	$-0.812833\pi$
$619$		−	27.6016i		−	1.10940i	0.832050	−	0.554701i	$-0.187167\pi$
$620$	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
$627$	−17.5132	+	3.27252i	−0.699409	+	0.130692i
$628$	−15.2974	−	15.2974i	−0.610431	−	0.610431i
$629$	9.73542			0.388176
$630$	25.1167	−	4.03914i	1.00067	−	0.160923i
$631$	−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
$633$	16.2940	−	3.04471i	0.647629	−	0.121016i
$634$		−	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	$-0.110570\pi$
$642$	0.391141	+	2.09322i	0.0154371	+	0.0826128i
$643$	0.301754	+	0.301754i	0.0119000	+	0.0119000i	0.713032	−	0.701132i	$-0.247322\pi$
$643$	0.301754	+	0.301754i	0.0119000	+	0.0119000i	−0.701132	+	0.713032i	$0.747322\pi$
$644$	−0.573105			−0.0225835
$645$	−18.1456	−	19.0870i	−0.714480	−	0.751551i
$646$	2.50536			0.0985721
$647$	28.9532	+	28.9532i	1.13827	+	1.13827i	0.988761	+	0.149507i	$0.0477685\pi$
$647$	28.9532	+	28.9532i	1.13827	+	1.13827i	0.149507	+	0.988761i	$0.452231\pi$
$648$	0.418144	−	8.99028i	0.0164262	−	0.353172i
$649$		−	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	$-0.976427\pi$
$653$	−23.5931	+	23.5931i	−0.923270	+	0.923270i	0.0739895	+	0.997259i	$0.476427\pi$
$654$	8.67746	−	12.6657i	0.339316	−	0.495266i
$655$	−2.60702	+	12.2307i	−0.101865	+	0.477893i
$656$		−	2.12724i		−	0.0830549i
$657$	−10.3816	−	4.58564i	−0.405024	−	0.178903i
$658$	−14.2404	−	14.2404i	−0.555149	−	0.555149i
$659$	−16.1089			−0.627514			−0.313757	−	0.949503i	$-0.601588\pi$
$659$	−16.1089			−0.627514			−0.313757	+	0.949503i	$0.601588\pi$
$660$	15.8962	+	0.401955i	0.618759	+	0.0156461i
$661$	−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
$663$	−2.09369	−	11.2046i	−0.0813123	−	0.435150i
$664$			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
$672$	6.45667	−	1.20650i	0.249072	−	0.0465417i
$673$	−19.4682	−	19.4682i	−0.750442	−	0.750442i	0.224119	−	0.974562i	$-0.428049\pi$
$673$	−19.4682	−	19.4682i	−0.750442	−	0.750442i	−0.974562	+	0.224119i	$0.928049\pi$
$674$	0.970148			0.0373687
$675$	−25.7473	+	3.47535i	−0.991013	+	0.133766i
$676$	−30.3087			−1.16572
$677$	−14.4315	−	14.4315i	−0.554648	−	0.554648i	0.373131	−	0.927779i	$-0.378284\pi$
$677$	−14.4315	−	14.4315i	−0.554648	−	0.554648i	−0.927779	+	0.373131i	$0.878284\pi$
$678$	1.64887	−	0.308109i	0.0633245	−	0.0118329i
$679$		−	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	$-0.926020\pi$
$683$	−19.4121	+	19.4121i	−0.742785	+	0.742785i	0.230328	+	0.973113i	$0.426020\pi$
$684$	7.00892	−	2.71415i	0.267993	−	0.103778i
$685$	20.2909	+	31.2844i	0.775276	+	1.19531i
$686$		−	1.44648i		−	0.0552269i
$687$	2.15790	+	11.5482i	0.0823291	+	0.440591i
$688$	−4.80824	−	4.80824i	−0.183312	−	0.183312i
$689$	29.2164			1.11306
$690$	0.585114	+	0.0147953i	0.0222749	+	0.000563248i
$691$	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
$693$	−42.7273	−	18.8730i	−1.62308	−	0.716927i
$694$			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	$-0.102781\pi$
$702$	−17.9956	−	29.0774i	−0.679199	−	1.09745i
$703$	17.2469	+	17.2469i	0.650478	+	0.650478i
$704$	4.10569			0.154739
$705$	14.1712	+	14.9064i	0.533717	+	0.561409i
$706$	8.24371			0.310256
$707$	−3.37708	−	3.37708i	−0.127008	−	0.127008i
$708$	1.07704	+	5.76384i	0.0404775	+	0.216619i
$709$			24.7534i			0.929634i	0.885407	+	0.464817i	$0.153880\pi$
$709$			24.7534i			0.929634i	−0.885407	+	0.464817i	$0.846120\pi$
$710$	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
$717$	17.5524	−	3.27986i	0.655508	−	0.122489i
$718$	−21.5583	−	21.5583i	−0.804549	−	0.804549i
$719$	−43.9400			−1.63869			−0.819343	−	0.573304i	$-0.805662\pi$
$719$	−43.9400			−1.63869			−0.819343	+	0.573304i	$0.805662\pi$
$720$	−6.62311	+	1.06509i	−0.246829	+	0.0396937i
$721$	29.3865			1.09441
$722$	−8.99663	−	8.99663i	−0.334820	−	0.334820i
$723$	25.3127	−	4.72995i	0.941391	−	0.175909i
$724$			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	−0.489924	−	0.871765i	$-0.662976\pi$
$727$	10.2955	−	10.2955i	0.381840	−	0.381840i	0.871765	+	0.489924i	$0.162976\pi$
$728$	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
$732$	1.40798	+	7.53492i	0.0520405	+	0.278499i
$733$	−32.7437	−	32.7437i	−1.20941	−	1.20941i	−0.971217	−	0.238198i	$-0.923443\pi$
$733$	−32.7437	−	32.7437i	−1.20941	−	1.20941i	−0.238198	−	0.971217i	$-0.576557\pi$
$734$	−27.2106			−1.00436
$735$	−0.722655	+	28.5790i	−0.0266555	+	1.05415i
$736$	0.151124			0.00557051
$737$	31.7486	+	31.7486i	1.16947	+	1.16947i
$738$	2.57852	−	5.83761i	0.0949168	−	0.214885i
$739$			5.04676i			0.185648i	0.995683	+	0.0928241i	$0.0295894\pi$
$739$			5.04676i			0.185648i	−0.995683	+	0.0928241i	$0.970411\pi$
$740$	−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	$-0.787142\pi$
$743$	−4.48784	+	4.48784i	−0.164643	+	0.164643i	0.619977	+	0.784620i	$0.287142\pi$
$744$	9.44831	−	13.7908i	0.346392	−	0.505595i
$745$	0.282223	+	0.0601570i	0.0103399	+	0.00220398i
$746$		−	5.36653i		−	0.196483i
$747$	−5.56682	+	12.6029i	−0.203679	+	0.461116i
$748$	2.90316	+	2.90316i	0.106150	+	0.106150i
$749$	−4.66238			−0.170360
$750$	6.45969	+	18.2558i	0.235874	+	0.666606i
$751$	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
$753$	−6.12693	−	32.7887i	−0.223278	−	1.19489i
$754$		−	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	−0.781143	−	0.624352i	$-0.785363\pi$
$757$	−4.31391	+	4.31391i	−0.156792	+	0.156792i	0.624352	+	0.781143i	$0.285363\pi$
$758$	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	$0.808836\pi$
$762$	−4.10032	+	0.766188i	−0.148539	+	0.0277561i
$763$	23.7695	+	23.7695i	0.860515	+	0.860515i
$764$	−4.09953			−0.148316
$765$	−5.43638	−	3.93011i	−0.196553	−	0.142093i
$766$	4.40943			0.159319
$767$	15.7535	+	15.7535i	0.568826	+	0.568826i
$768$	−1.70258	+	0.318145i	−0.0614366	+	0.0114801i
$769$			40.1055i			1.44624i	0.690721	+	0.723121i	$0.257293\pi$
$769$			40.1055i			1.44624i	−0.690721	+	0.723121i	$0.742707\pi$
$770$	−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	$-0.960319\pi$
$773$	−24.1301	+	24.1301i	−0.867901	+	0.867901i	0.124339	+	0.992240i	$0.460319\pi$
$774$	−7.36656	−	19.0231i	−0.264786	−	0.683772i
$775$	−44.0631	−	19.6785i	−1.58279	−	0.706874i
$776$			8.43699i			0.302870i
$777$	11.7458	+	62.8584i	0.421377	+	2.25503i
$778$	−1.23550	−	1.23550i	−0.0442949	−	0.0442949i
$779$	5.32951			0.190950
$780$	−18.4724	+	17.5613i	−0.661420	+	0.628795i
$781$	−51.0425			−1.82644
$782$	0.106861	+	0.106861i	0.00382134	+	0.00382134i
$783$	22.7562	−	14.0835i	0.813239	−	0.503302i
$784$			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	−0.108635	−	0.994082i	$-0.534648\pi$
$787$	24.8399	−	24.8399i	0.885447	−	0.885447i	0.994082	+	0.108635i	$0.0346479\pi$
$788$	−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
$792$	11.2669	+	4.97669i	0.400352	+	0.176839i
$793$	20.5941	+	20.5941i	0.731319	+	0.731319i
$794$	−18.6920			−0.663353
$795$	12.4617	−	11.8470i	0.441970	−	0.420170i
$796$	−1.60140			−0.0567603
$797$	−19.6674	−	19.6674i	−0.696654	−	0.696654i	0.267033	−	0.963687i	$-0.413957\pi$
$797$	−19.6674	−	19.6674i	−0.696654	−	0.696654i	−0.963687	+	0.267033i	$0.913957\pi$
$798$	3.02272	+	16.1763i	0.107003	+	0.572635i
$799$			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
$807$	18.4483	−	3.44727i	0.649412	−	0.121350i
$808$	0.890513	+	0.890513i	0.0313281	+	0.0313281i
$809$	8.25845			0.290352			0.145176	−	0.989406i	$-0.453625\pi$
$809$	8.25845			0.290352			0.145176	+	0.989406i	$0.453625\pi$
$810$	−19.4663	−	5.10532i	−0.683975	−	0.179383i
$811$	−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
$813$	−44.3855	+	8.29390i	−1.55667	+	0.290880i
$814$			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	$-0.156795\pi$
$822$	5.30537	+	28.3921i	0.185046	+	0.990289i
$823$	6.78813	+	6.78813i	0.236619	+	0.236619i	0.815449	−	0.578829i	$-0.196490\pi$
$823$	6.78813	+	6.78813i	0.236619	+	0.236619i	−0.578829	+	0.815449i	$0.696490\pi$
$824$	−7.74902			−0.269950
$825$	8.28914	−	34.5766i	0.288591	−	1.20380i
$826$	−12.8382			−0.446699
$827$	−2.55296	−	2.55296i	−0.0887750	−	0.0887750i	0.661325	−	0.750100i	$-0.269995\pi$
$827$	−2.55296	−	2.55296i	−0.0887750	−	0.0887750i	−0.750100	+	0.661325i	$0.769995\pi$
$828$	0.414717	+	0.183184i	0.0144124	+	0.00636608i
$829$			13.1146i			0.455488i	0.973721	+	0.227744i	$0.0731350\pi$
$829$			13.1146i			0.455488i	−0.973721	+	0.227744i	$0.926865\pi$
$830$	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
$837$	42.6446	−	26.3921i	1.47401	−	0.912246i
$838$	11.6741	+	11.6741i	0.403275	+	0.403275i
$839$	−12.9994			−0.448790			−0.224395	−	0.974498i	$-0.572041\pi$
$839$	−12.9994			−0.448790			−0.224395	+	0.974498i	$0.572041\pi$
$840$	0.371271	−	14.6828i	0.0128101	−	0.506604i
$841$	−2.47454			−0.0853291
$842$	9.70315	+	9.70315i	0.334393	+	0.334393i
$843$	6.25273	+	33.4620i	0.215356	+	1.15249i
$844$		−	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
$852$	21.1667	−	3.95522i	0.725159	−	0.135504i
$853$	−13.0775	−	13.0775i	−0.447765	−	0.447765i	0.446846	−	0.894611i	$-0.352547\pi$
$853$	−13.0775	−	13.0775i	−0.447765	−	0.447765i	−0.894611	+	0.446846i	$0.852547\pi$
$854$	−16.7831			−0.574306
$855$	−2.66844	−	16.5933i	−0.0912588	−	0.567478i
$856$	1.22944			0.0420214
$857$	4.02020	+	4.02020i	0.137328	+	0.137328i	0.772429	−	0.635101i	$-0.219042\pi$
$857$	4.02020	+	4.02020i	0.137328	+	0.137328i	−0.635101	+	0.772429i	$0.719042\pi$
$858$	46.0026	−	8.59607i	1.57050	−	0.293465i
$859$		−	6.71895i		−	0.229248i	−0.993409	−	0.114624i	$-0.963434\pi$
$859$		−	6.71895i		−	0.229248i	0.993409	−	0.114624i	$-0.0365663\pi$
$860$	−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	$-0.992576\pi$
$863$	−28.6838	+	28.6838i	−0.976408	+	0.976408i	0.0233202	+	0.999728i	$0.492576\pi$
$864$	−5.05789	−	1.19071i	−0.172073	−	0.0405089i
$865$	45.7659	−	29.6835i	1.55609	−	1.00927i
$866$			13.7860i			0.468466i
$867$	−0.318145	−	1.70258i	−0.0108048	−	0.0578227i
$868$	25.8811	+	25.8811i	0.878461	+	0.878461i
$869$	33.4182			1.13364
$870$	−13.7436	−	14.4567i	−0.465952	−	0.490127i
$871$	−71.9681			−2.43855
$872$	−6.26787	−	6.26787i	−0.212257	−	0.212257i
$873$	−10.2268	+	23.1529i	−0.346126	+	0.783607i
$874$			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	0.275218	−	0.961382i	$-0.411250\pi$
$877$	36.6209	−	36.6209i	1.23660	−	1.23660i	0.961382	−	0.275218i	$-0.0887501\pi$
$878$	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	$-0.126208\pi$
$882$	−8.94735	+	20.2562i	−0.301273	+	0.682062i
$883$	−27.7206	−	27.7206i	−0.932874	−	0.932874i	0.0650109	−	0.997885i	$-0.479292\pi$
$883$	−27.7206	−	27.7206i	−0.932874	−	0.932874i	−0.997885	+	0.0650109i	$0.979292\pi$
$884$	−6.58093			−0.221341
$885$	13.1072	+	0.331432i	0.440595	+	0.0111410i
$886$	−0.520648			−0.0174915
$887$	−27.7458	−	27.7458i	−0.931612	−	0.931612i	0.0661947	−	0.997807i	$-0.478914\pi$
$887$	−27.7458	−	27.7458i	−0.931612	−	0.931612i	−0.997807	+	0.0661947i	$0.978914\pi$
$888$	−3.09728	−	16.5753i	−0.103938	−	0.556232i
$889$		−	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
$897$	1.69328	−	0.316408i	0.0565370	−	0.0105645i
$898$	0.345244	+	0.345244i	0.0115209	+	0.0115209i
$899$	49.7082			1.65786
$900$	−0.758102	+	14.9808i	−0.0252701	+	0.499361i
$901$	4.43956			0.147903
$902$	6.17574	+	6.17574i	0.205630	+	0.205630i
$903$	43.9046	−	8.20404i	1.46105	−	0.273014i
$904$		−	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	−0.188419	−	0.982089i	$-0.560336\pi$
$907$	23.9025	−	23.9025i	0.793670	−	0.793670i	0.982089	+	0.188419i	$0.0603363\pi$
$908$	−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	$0.708999\pi$
$912$	−0.797070	−	4.26558i	−0.0263936	−	0.141248i
$913$	−13.3329	−	13.3329i	−0.441255	−	0.441255i
$914$	16.3269			0.540047
$915$	17.1348	+	0.433273i	0.566457	+	0.0143236i
$916$	6.78275			0.224108
$917$	−14.9969	−	14.9969i	−0.495240	−	0.495240i
$918$	−2.73450	−	4.41843i	−0.0902520	−	0.145830i
$919$			13.8669i			0.457426i	0.973494	+	0.228713i	$0.0734518\pi$
$919$			13.8669i			0.457426i	−0.973494	+	0.228713i	$0.926548\pi$
$920$	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
$927$	−21.2650	−	9.39292i	−0.698433	−	0.308504i
$928$	−3.64180	−	3.64180i	−0.119548	−	0.119548i
$929$	38.1864			1.25286			0.626428	−	0.779480i	$-0.284516\pi$
$929$	38.1864			1.25286			0.626428	+	0.779480i	$0.284516\pi$
$930$	−25.7552	−	27.0915i	−0.844547	−	0.888366i
$931$	−18.4931			−0.606088
$932$	6.89977	+	6.89977i	0.226010	+	0.226010i
$933$	0.547709	+	2.93111i	0.0179312	+	0.0959602i
$934$		−	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	−0.281362	+	0.959602i	$0.590786\pi$
$937$	−37.9865	+	37.9865i	−1.24096	+	1.24096i	−0.959602	+	0.281362i	$0.909214\pi$
$938$	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	$-0.0234588\pi$
$942$	−36.8332	+	6.88268i	−1.20009	+	0.224250i
$943$	0.227319	+	0.227319i	0.00740252	+	0.00740252i
$944$	3.38536			0.110184
$945$	18.8165	−	39.8426i	0.612100	−	1.29608i
$946$	27.9182			0.907700
$947$	3.20617	+	3.20617i	0.104186	+	0.104186i	0.757279	−	0.653092i	$-0.226529\pi$
$947$	3.20617	+	3.20617i	0.104186	+	0.104186i	−0.653092	+	0.757279i	$0.726529\pi$
$948$	−13.8581	+	2.58954i	−0.450091	+	0.0841044i
$949$			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	$-0.868996\pi$
$953$	−15.9434	+	15.9434i	−0.516458	+	0.516458i	0.400039	+	0.916498i	$0.368996\pi$
$954$	12.4200	−	4.80954i	0.402111	−	0.155714i
$955$	−1.91102	+	8.96542i	−0.0618390	+	0.290114i
$956$		−	10.3093i		−	0.333427i
$957$	6.72735	+	36.0019i	0.217464	+	1.16378i
$958$	11.5185	+	11.5185i	0.372145	+	0.372145i
$959$	−63.2399			−2.04212
$960$	−0.0979018	+	3.87175i	−0.00315977	+	0.124960i
$961$	62.1521			2.00491
$962$	−45.3030	−	45.3030i	−1.46063	−	1.46063i
$963$	3.37384	+	1.49026i	0.108721	+	0.0480229i
$964$		−	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	−0.718367	−	0.695665i	$-0.755110\pi$
$967$	−0.705954	+	0.705954i	−0.0227020	+	0.0227020i	0.695665	+	0.718367i	$0.255110\pi$
$968$	−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	$0.988557\pi$
$972$	−12.4366	−	9.39846i	−0.398904	−	0.301456i
$973$	17.3708	+	17.3708i	0.556882	+	0.556882i
$974$	5.73339			0.183710
$975$	29.7944	+	48.5844i	0.954186	+	1.55595i
$976$	4.42559			0.141660
$977$	−19.5421	−	19.5421i	−0.625208	−	0.625208i	0.321651	−	0.946858i	$-0.395762\pi$
$977$	−19.5421	−	19.5421i	−0.625208	−	0.625208i	−0.946858	+	0.321651i	$0.895762\pi$
$978$	−2.15365	−	11.5254i	−0.0688661	−	0.368542i
$979$			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	$-0.664272\pi$
$983$	11.7978	−	11.7978i	0.376292	−	0.376292i	0.869763	+	0.493471i	$0.164272\pi$
$984$	−3.03955	−	2.08245i	−0.0968974	−	0.0663861i
$985$	30.1492	+	46.4839i	0.960634	+	1.48110i
$986$		−	5.15029i		−	0.164019i
$987$	−34.2883	+	6.40713i	−1.09141	+	0.203941i
$988$	−11.6585	−	11.6585i	−0.370907	−	0.370907i
$989$	1.02763			0.0326766
$990$	16.1358	−	22.3201i	0.512831	−	0.709380i
$991$	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
$993$	41.5046	−	7.75558i	1.31711	−	0.246116i
$994$			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	−0.782564	−	0.622570i	$-0.786089\pi$
$997$	−5.05187	+	5.05187i	−0.159994	+	0.159994i	0.622570	+	0.782564i	$0.286089\pi$
$998$	−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.443.1	yes	28
3.2	odd	2	inner	510.2.l.g.443.11	yes	28
5.2	odd	4	inner	510.2.l.g.137.11	yes	28
15.2	even	4	inner	510.2.l.g.137.1	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.l.g.137.1	✓	28	15.2	even	4	inner
510.2.l.g.137.11	yes	28	5.2	odd	4	inner
510.2.l.g.443.1	yes	28	1.1	even	1	trivial
510.2.l.g.443.11	yes	28	3.2	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.70258 + 0.318145i) q^{3} +1.00000i q^{4} +(2.18694 + 0.466155i) q^{5} +(1.42887 + 0.978944i) q^{6} +(-2.68155 + 2.68155i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.79757 - 1.08334i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.70258 + 0.318145i) 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} +(-0.318145 - 1.70258i) q^{12} +(-4.65342 - 4.65342i) q^{13} +3.79229 q^{14} +(-3.87175 - 0.0979018i) q^{15} -1.00000 q^{16} +(-0.707107 - 0.707107i) q^{17} +(-2.74421 - 1.21214i) 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} +(-4.41843 + 2.73450i) q^{27} +(-2.68155 - 2.68155i) q^{28} -5.15029 q^{29} +(2.66851 + 2.80696i) q^{30} -9.65153 q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.30621 - 6.99028i) 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} +(-6.45667 + 1.20650i) q^{42} +(4.80824 + 4.80824i) q^{43} -4.10569 q^{44} +(6.62311 - 1.06509i) q^{45} -0.151124 q^{46} +(-3.75510 - 3.75510i) q^{47} +(1.70258 - 0.318145i) 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} +(0.797070 + 4.26558i) q^{57} +(3.64180 + 3.64180i) q^{58} -3.38536 q^{59} +(0.0979018 - 3.87175i) q^{60} -4.42559 q^{61} +(6.82466 + 6.82466i) q^{62} +(-4.59679 + 10.4068i) 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} +(1.21214 - 2.74421i) q^{72} +(-2.67504 - 2.67504i) q^{73} +9.73542 q^{74} +(-8.42163 - 2.01894i) q^{75} +2.50536 q^{76} +(-11.0096 - 11.0096i) q^{77} +(-2.09369 - 11.2046i) 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} +(8.76878 - 1.63854i) q^{87} +(2.90316 + 2.90316i) q^{88} +12.9925 q^{89} +(-5.43638 - 3.93011i) q^{90} +24.9568 q^{91} +(0.106861 + 0.106861i) q^{92} +(16.4325 - 3.07059i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{7}+O(q^{10}) \) 28 * q + 4 * q^7	\( 28 q + 4 q^{7} - 12 q^{10} - 8 q^{13} + 8 q^{15} - 28 q^{16} - 16 q^{18} + 48 q^{21} + 20 q^{22} + 40 q^{25} - 36 q^{27} + 4 q^{28} - 12 q^{30} + 16 q^{31} + 8 q^{33} + 8 q^{37} - 8 q^{40} - 48 q^{42} + 48 q^{43} + 36 q^{45} - 64 q^{46} + 8 q^{52} - 36 q^{55} - 32 q^{57} + 20 q^{58} + 12 q^{60} - 16 q^{61} - 56 q^{63} + 32 q^{66} + 112 q^{67} - 28 q^{70} + 16 q^{72} + 12 q^{73} + 16 q^{75} - 8 q^{76} - 32 q^{78} - 48 q^{81} + 24 q^{82} - 12 q^{85} - 44 q^{87} + 20 q^{88} - 20 q^{90} - 80 q^{91} + 28 q^{93} + 60 q^{97}+O(q^{100}) \) 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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