LMFDB - Embedded newform 510.2.l.d.443.2

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:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.4030726144.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 4x^{6} - 16x^{5} + 18x^{4} - 8x^{3} + 172x^{2} + 184x + 274 $ x^8 - 4x^7 + 4x^6 - 16x^5 + 18x^4 - 8x^3 + 172x^2 + 184*x + 274
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			443.2
Root			$0.487323 - 2.17650i$ of defining polynomial
Character	$\chi$	$=$	510.443
Dual form			510.2.l.d.137.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-1.00000 + 1.41421i) q^{3} +1.00000i q^{4} +(1.90154 + 1.17650i) q^{5} +(1.70711 - 0.292893i) q^{6} +(2.66383 - 2.66383i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.00000 + 1.41421i) q^{3} +1.00000i q^{4} +(1.90154 + 1.17650i) q^{5} +(1.70711 - 0.292893i) q^{6} +(2.66383 - 2.66383i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.00000 - 2.82843i) q^{9} +(-0.512677 - 2.17650i) q^{10} -1.41421i q^{11} +(-1.41421 - 1.00000i) q^{12} +(1.02535 + 1.02535i) q^{13} -3.76722 q^{14} +(-3.56536 + 1.51268i) q^{15} -1.00000 q^{16} +(0.707107 + 0.707107i) q^{17} +(-1.29289 + 2.70711i) q^{18} -5.57029i q^{19} +(-1.17650 + 1.90154i) q^{20} +(1.10339 + 6.43104i) q^{21} +(-1.00000 + 1.00000i) q^{22} +(1.05269 - 1.05269i) q^{23} +(0.292893 + 1.70711i) q^{24} +(2.23168 + 4.47433i) q^{25} -1.45007i q^{26} +(5.00000 + 1.41421i) q^{27} +(2.66383 + 2.66383i) q^{28} -1.85378 q^{29} +(3.59072 + 1.45147i) q^{30} +9.92330 q^{31} +(0.707107 + 0.707107i) q^{32} +(2.00000 + 1.41421i) q^{33} -1.00000i q^{34} +(8.19936 - 1.93137i) q^{35} +(2.82843 - 1.00000i) q^{36} +(-6.88111 + 6.88111i) q^{37} +(-3.93879 + 3.93879i) q^{38} +(-2.47542 + 0.424715i) q^{39} +(2.17650 - 0.512677i) q^{40} -9.48373i q^{41} +(3.76722 - 5.32765i) q^{42} +(6.21729 + 6.21729i) q^{43} +1.41421 q^{44} +(1.42611 - 6.55486i) q^{45} -1.48872 q^{46} +(6.00000 + 6.00000i) q^{47} +(1.00000 - 1.41421i) q^{48} -7.19193i q^{49} +(1.58579 - 4.74186i) q^{50} +(-1.70711 + 0.292893i) q^{51} +(-1.02535 + 1.02535i) q^{52} +(2.35300 - 2.35300i) q^{53} +(-2.53553 - 4.53553i) q^{54} +(1.66383 - 2.68918i) q^{55} -3.76722i q^{56} +(7.87758 + 5.57029i) q^{57} +(1.31082 + 1.31082i) q^{58} +1.60615 q^{59} +(-1.51268 - 3.56536i) q^{60} -13.0083 q^{61} +(-7.01683 - 7.01683i) q^{62} +(-10.1983 - 4.87061i) q^{63} -1.00000i q^{64} +(0.743417 + 3.15608i) q^{65} +(-0.414214 - 2.41421i) q^{66} +(-2.86428 + 2.86428i) q^{67} +(-0.707107 + 0.707107i) q^{68} +(0.436037 + 2.54141i) q^{69} +(-7.16350 - 4.43214i) q^{70} -7.81793i q^{71} +(-2.70711 - 1.29289i) q^{72} +(4.70601 + 4.70601i) q^{73} +9.73136 q^{74} +(-8.55934 - 1.31825i) q^{75} +5.57029 q^{76} +(-3.76722 - 3.76722i) q^{77} +(2.05071 + 1.45007i) q^{78} +10.5449i q^{79} +(-1.90154 - 1.17650i) q^{80} +(-7.00000 + 5.65685i) q^{81} +(-6.70601 + 6.70601i) q^{82} +(-2.21729 + 2.21729i) q^{83} +(-6.43104 + 1.10339i) q^{84} +(0.512677 + 2.17650i) q^{85} -8.79257i q^{86} +(1.85378 - 2.62164i) q^{87} +(-1.00000 - 1.00000i) q^{88} -3.29180 q^{89} +(-5.64340 + 3.62657i) q^{90} +5.46273 q^{91} +(1.05269 + 1.05269i) q^{92} +(-9.92330 + 14.0337i) q^{93} -8.48528i q^{94} +(6.55346 - 10.5921i) q^{95} +(-1.70711 + 0.292893i) q^{96} +(-0.514076 + 0.514076i) q^{97} +(-5.08547 + 5.08547i) q^{98} +(-4.00000 + 1.41421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{3} + 4 q^{5} + 8 q^{6} + 8 q^{7} - 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^3 + 4 * q^5 + 8 * q^6 + 8 * q^7 - 8 * q^9	$ 8 q - 8 q^{3} + 4 q^{5} + 8 q^{6} + 8 q^{7} - 8 q^{9} - 4 q^{10} + 8 q^{13} + 8 q^{14} - 4 q^{15} - 8 q^{16} - 16 q^{18} + 4 q^{20} - 16 q^{21} - 8 q^{22} - 16 q^{23} + 8 q^{24} + 8 q^{25} + 40 q^{27} + 8 q^{28} + 8 q^{29} + 4 q^{30} - 8 q^{31} + 16 q^{33} + 24 q^{35} - 8 q^{37} - 16 q^{38} - 24 q^{39} + 4 q^{40} - 8 q^{42} + 16 q^{43} - 4 q^{45} + 8 q^{46} + 48 q^{47} + 8 q^{48} + 24 q^{50} - 8 q^{51} - 8 q^{52} - 8 q^{53} + 8 q^{54} + 32 q^{57} + 24 q^{58} - 32 q^{59} - 12 q^{60} - 24 q^{61} - 16 q^{62} + 8 q^{63} - 24 q^{65} + 8 q^{66} - 16 q^{67} + 8 q^{69} - 16 q^{72} - 16 q^{73} + 24 q^{74} - 32 q^{75} - 16 q^{76} + 8 q^{77} + 16 q^{78} - 4 q^{80} - 56 q^{81} + 16 q^{83} + 4 q^{85} - 8 q^{87} - 8 q^{88} + 16 q^{89} + 4 q^{90} - 64 q^{91} - 16 q^{92} + 8 q^{93} + 32 q^{95} - 8 q^{96} + 16 q^{97} - 8 q^{98} - 32 q^{99}+O(q^{100}) $ 8 * q - 8 * q^3 + 4 * q^5 + 8 * q^6 + 8 * q^7 - 8 * q^9 - 4 * q^10 + 8 * q^13 + 8 * q^14 - 4 * q^15 - 8 * q^16 - 16 * q^18 + 4 * q^20 - 16 * q^21 - 8 * q^22 - 16 * q^23 + 8 * q^24 + 8 * q^25 + 40 * q^27 + 8 * q^28 + 8 * q^29 + 4 * q^30 - 8 * q^31 + 16 * q^33 + 24 * q^35 - 8 * q^37 - 16 * q^38 - 24 * q^39 + 4 * q^40 - 8 * q^42 + 16 * q^43 - 4 * q^45 + 8 * q^46 + 48 * q^47 + 8 * q^48 + 24 * q^50 - 8 * q^51 - 8 * q^52 - 8 * q^53 + 8 * q^54 + 32 * q^57 + 24 * q^58 - 32 * q^59 - 12 * q^60 - 24 * q^61 - 16 * q^62 + 8 * q^63 - 24 * q^65 + 8 * q^66 - 16 * q^67 + 8 * q^69 - 16 * q^72 - 16 * q^73 + 24 * q^74 - 32 * q^75 - 16 * q^76 + 8 * q^77 + 16 * q^78 - 4 * q^80 - 56 * q^81 + 16 * q^83 + 4 * q^85 - 8 * q^87 - 8 * q^88 + 16 * q^89 + 4 * q^90 - 64 * q^91 - 16 * q^92 + 8 * q^93 + 32 * q^95 - 8 * q^96 + 16 * q^97 - 8 * q^98 - 32 * q^99

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
$3$	−1.00000	+	1.41421i	−0.577350	+	0.816497i
$3$	−1.00000	+	1.41421i	−0.577350	+	0.816497i
$4$			1.00000i			0.500000i
$5$	1.90154	+	1.17650i	0.850393	+	0.526148i
$5$	1.90154	+	1.17650i	0.850393	+	0.526148i
$6$	1.70711	−	0.292893i	0.696923	−	0.119573i
$7$	2.66383	−	2.66383i	1.00683	−	1.00683i	0.00685493	−	0.999977i	$-0.497818\pi$
$7$	2.66383	−	2.66383i	1.00683	−	1.00683i	0.999977	−	0.00685493i	$-0.00218201\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.00000	−	2.82843i	−0.333333	−	0.942809i
$10$	−0.512677	−	2.17650i	−0.162123	−	0.688270i
$11$		−	1.41421i		−	0.426401i	−0.977008	−	0.213201i	$-0.931611\pi$
$11$		−	1.41421i		−	0.426401i	0.977008	−	0.213201i	$-0.0683888\pi$
$12$	−1.41421	−	1.00000i	−0.408248	−	0.288675i
$13$	1.02535	+	1.02535i	0.284382	+	0.284382i	0.834854	−	0.550472i	$-0.185552\pi$
$13$	1.02535	+	1.02535i	0.284382	+	0.284382i	−0.550472	+	0.834854i	$0.685552\pi$
$14$	−3.76722			−1.00683
$15$	−3.56536	+	1.51268i	−0.920573	+	0.390571i
$16$	−1.00000			−0.250000
$17$	0.707107	+	0.707107i	0.171499	+	0.171499i
$17$	0.707107	+	0.707107i	0.171499	+	0.171499i
$18$	−1.29289	+	2.70711i	−0.304738	+	0.638071i
$19$		−	5.57029i		−	1.27791i	−0.769243	−	0.638956i	$-0.779366\pi$
$19$		−	5.57029i		−	1.27791i	0.769243	−	0.638956i	$-0.220634\pi$
$20$	−1.17650	+	1.90154i	−0.263074	+	0.425197i
$21$	1.10339	+	6.43104i	0.240780	+	1.40337i
$22$	−1.00000	+	1.00000i	−0.213201	+	0.213201i
$23$	1.05269	−	1.05269i	0.219500	−	0.219500i	−0.588788	−	0.808288i	$-0.700395\pi$
$23$	1.05269	−	1.05269i	0.219500	−	0.219500i	0.808288	+	0.588788i	$0.200395\pi$
$24$	0.292893	+	1.70711i	0.0597866	+	0.348462i
$25$	2.23168	+	4.47433i	0.446337	+	0.894865i
$26$		−	1.45007i		−	0.284382i
$27$	5.00000	+	1.41421i	0.962250	+	0.272166i
$28$	2.66383	+	2.66383i	0.503416	+	0.503416i
$29$	−1.85378			−0.344238			−0.172119	−	0.985076i	$-0.555061\pi$
$29$	−1.85378			−0.344238			−0.172119	+	0.985076i	$0.555061\pi$
$30$	3.59072	+	1.45147i	0.655572	+	0.265001i
$31$	9.92330			1.78228			0.891138	−	0.453732i	$-0.149908\pi$
$31$	9.92330			1.78228			0.891138	+	0.453732i	$0.149908\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	2.00000	+	1.41421i	0.348155	+	0.246183i
$34$		−	1.00000i		−	0.171499i
$35$	8.19936	−	1.93137i	1.38594	−	0.326460i
$36$	2.82843	−	1.00000i	0.471405	−	0.166667i
$37$	−6.88111	+	6.88111i	−1.13125	+	1.13125i	−0.141278	+	0.989970i	$0.545121\pi$
$37$	−6.88111	+	6.88111i	−1.13125	+	1.13125i	−0.989970	+	0.141278i	$0.954879\pi$
$38$	−3.93879	+	3.93879i	−0.638956	+	0.638956i
$39$	−2.47542	+	0.424715i	−0.396385	+	0.0680089i
$40$	2.17650	−	0.512677i	0.344135	−	0.0810613i
$41$		−	9.48373i		−	1.48111i	−0.671996	−	0.740555i	$-0.734563\pi$
$41$		−	9.48373i		−	1.48111i	0.671996	−	0.740555i	$-0.265437\pi$
$42$	3.76722	−	5.32765i	0.581294	−	0.822074i
$43$	6.21729	+	6.21729i	0.948127	+	0.948127i	0.998719	−	0.0505920i	$-0.0161108\pi$
$43$	6.21729	+	6.21729i	0.948127	+	0.948127i	−0.0505920	+	0.998719i	$0.516111\pi$
$44$	1.41421			0.213201
$45$	1.42611	−	6.55486i	0.212593	−	0.977141i
$46$	−1.48872			−0.219500
$47$	6.00000	+	6.00000i	0.875190	+	0.875190i	0.993032	−	0.117842i	$-0.0375978\pi$
$47$	6.00000	+	6.00000i	0.875190	+	0.875190i	−0.117842	+	0.993032i	$0.537598\pi$
$48$	1.00000	−	1.41421i	0.144338	−	0.204124i
$49$		−	7.19193i		−	1.02742i
$50$	1.58579	−	4.74186i	0.224264	−	0.670601i
$51$	−1.70711	+	0.292893i	−0.239043	+	0.0410133i
$52$	−1.02535	+	1.02535i	−0.142191	+	0.142191i
$53$	2.35300	−	2.35300i	0.323210	−	0.323210i	−0.526787	−	0.849997i	$-0.676604\pi$
$53$	2.35300	−	2.35300i	0.323210	−	0.323210i	0.849997	+	0.526787i	$0.176604\pi$
$54$	−2.53553	−	4.53553i	−0.345042	−	0.617208i
$55$	1.66383	−	2.68918i	0.224350	−	0.362609i
$56$		−	3.76722i		−	0.503416i
$57$	7.87758	+	5.57029i	1.04341	+	0.737803i
$58$	1.31082	+	1.31082i	0.172119	+	0.172119i
$59$	1.60615			0.209103			0.104551	−	0.994519i	$-0.466659\pi$
$59$	1.60615			0.209103			0.104551	+	0.994519i	$0.466659\pi$
$60$	−1.51268	−	3.56536i	−0.195286	−	0.460286i
$61$	−13.0083			−1.66554			−0.832772	−	0.553617i	$-0.813247\pi$
$61$	−13.0083			−1.66554			−0.832772	+	0.553617i	$0.813247\pi$
$62$	−7.01683	−	7.01683i	−0.891138	−	0.891138i
$63$	−10.1983	−	4.87061i	−1.28486	−	0.613639i
$64$		−	1.00000i		−	0.125000i
$65$	0.743417	+	3.15608i	0.0922095	+	0.391463i
$66$	−0.414214	−	2.41421i	−0.0509862	−	0.297169i
$67$	−2.86428	+	2.86428i	−0.349928	+	0.349928i	−0.860083	−	0.510155i	$-0.829588\pi$
$67$	−2.86428	+	2.86428i	−0.349928	+	0.349928i	0.510155	+	0.860083i	$0.329588\pi$
$68$	−0.707107	+	0.707107i	−0.0857493	+	0.0857493i
$69$	0.436037	+	2.54141i	0.0524926	+	0.305950i
$70$	−7.16350	−	4.43214i	−0.856203	−	0.529742i
$71$		−	7.81793i		−	0.927817i	−0.885883	−	0.463909i	$-0.846447\pi$
$71$		−	7.81793i		−	0.927817i	0.885883	−	0.463909i	$-0.153553\pi$
$72$	−2.70711	−	1.29289i	−0.319036	−	0.152369i
$73$	4.70601	+	4.70601i	0.550797	+	0.550797i	0.926671	−	0.375874i	$-0.122657\pi$
$73$	4.70601	+	4.70601i	0.550797	+	0.550797i	−0.375874	+	0.926671i	$0.622657\pi$
$74$	9.73136			1.13125
$75$	−8.55934	−	1.31825i	−0.988347	−	0.152218i
$76$	5.57029			0.638956
$77$	−3.76722	−	3.76722i	−0.429314	−	0.429314i
$78$	2.05071	+	1.45007i	0.232197	+	0.164188i
$79$			10.5449i			1.18640i	0.805056	+	0.593199i	$0.202135\pi$
$79$			10.5449i			1.18640i	−0.805056	+	0.593199i	$0.797865\pi$
$80$	−1.90154	−	1.17650i	−0.212598	−	0.131537i
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$	−6.70601	+	6.70601i	−0.740555	+	0.740555i
$83$	−2.21729	+	2.21729i	−0.243379	+	0.243379i	−0.818246	−	0.574868i	$-0.805054\pi$
$83$	−2.21729	+	2.21729i	−0.243379	+	0.243379i	0.574868	+	0.818246i	$0.305054\pi$
$84$	−6.43104	+	1.10339i	−0.701684	+	0.120390i
$85$	0.512677	+	2.17650i	0.0556076	+	0.236075i
$86$		−	8.79257i		−	0.948127i
$87$	1.85378	−	2.62164i	0.198746	−	0.281069i
$88$	−1.00000	−	1.00000i	−0.106600	−	0.106600i
$89$	−3.29180			−0.348930			−0.174465	−	0.984663i	$-0.555820\pi$
$89$	−3.29180			−0.348930			−0.174465	+	0.984663i	$0.555820\pi$
$90$	−5.64340	+	3.62657i	−0.594867	+	0.382274i
$91$	5.46273			0.572649
$92$	1.05269	+	1.05269i	0.109750	+	0.109750i
$93$	−9.92330	+	14.0337i	−1.02900	+	1.45522i
$94$		−	8.48528i		−	0.875190i
$95$	6.55346	−	10.5921i	0.672371	−	1.08673i
$96$	−1.70711	+	0.292893i	−0.174231	+	0.0298933i
$97$	−0.514076	+	0.514076i	−0.0521965	+	0.0521965i	−0.732723	−	0.680527i	$-0.761751\pi$
$97$	−0.514076	+	0.514076i	−0.0521965	+	0.0521965i	0.680527	+	0.732723i	$0.261751\pi$
$98$	−5.08547	+	5.08547i	−0.513710	+	0.513710i
$99$	−4.00000	+	1.41421i	−0.402015	+	0.142134i
$100$	−4.47433	+	2.23168i	−0.447433	+	0.223168i
$101$			9.82688i			0.977811i	0.872337	+	0.488905i	$0.162604\pi$
$101$			9.82688i			0.977811i	−0.872337	+	0.488905i	$0.837396\pi$
$102$	1.41421	+	1.00000i	0.140028	+	0.0990148i
$103$	−11.8129	−	11.8129i	−1.16396	−	1.16396i	−0.983600	−	0.180363i	$-0.942273\pi$
$103$	−11.8129	−	11.8129i	−1.16396	−	1.16396i	−0.180363	−	0.983600i	$-0.557727\pi$
$104$	1.45007			0.142191
$105$	−5.46800	+	13.5270i	−0.533622	+	1.32010i
$106$	−3.32765			−0.323210
$107$	1.62164	+	1.62164i	0.156770	+	0.156770i	0.781134	−	0.624364i	$-0.214642\pi$
$107$	1.62164	+	1.62164i	0.156770	+	0.156770i	−0.624364	+	0.781134i	$0.714642\pi$
$108$	−1.41421	+	5.00000i	−0.136083	+	0.481125i
$109$		−	2.35300i		−	0.225377i	−0.993630	−	0.112688i	$-0.964054\pi$
$109$		−	2.35300i		−	0.225377i	0.993630	−	0.112688i	$-0.0359462\pi$
$110$	−3.07804	+	0.725034i	−0.293480	+	0.0691293i
$111$	−2.85025	−	16.6125i	−0.270534	−	1.57679i
$112$	−2.66383	+	2.66383i	−0.251708	+	0.251708i
$113$	−2.86428	+	2.86428i	−0.269449	+	0.269449i	−0.828878	−	0.559429i	$-0.811020\pi$
$113$	−2.86428	+	2.86428i	−0.269449	+	0.269449i	0.559429	+	0.828878i	$0.311020\pi$
$114$	−1.63150	−	9.50908i	−0.152804	−	0.890607i
$115$	3.24021	−	0.763233i	0.302151	−	0.0711719i
$116$		−	1.85378i		−	0.172119i
$117$	1.87478	−	3.92549i	0.173324	−	0.362912i
$118$	−1.13572	−	1.13572i	−0.104551	−	0.104551i
$119$	3.76722			0.345340
$120$	−1.45147	+	3.59072i	−0.132500	+	0.327786i
$121$	9.00000			0.818182
$122$	9.19826	+	9.19826i	0.832772	+	0.832772i
$123$	13.4120	+	9.48373i	1.20932	+	0.855119i
$124$			9.92330i			0.891138i
$125$	−1.02042	+	11.1337i	−0.0912695	+	0.995826i
$126$	3.76722	+	10.6553i	0.335610	+	0.949250i
$127$	8.48528	−	8.48528i	0.752947	−	0.752947i	−0.222081	−	0.975028i	$-0.571285\pi$
$127$	8.48528	−	8.48528i	0.752947	−	0.752947i	0.975028	+	0.222081i	$0.0712850\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−15.0099	+	2.57528i	−1.32154	+	0.226741i
$130$	1.70601	−	2.75736i	0.149627	−	0.241836i
$131$		−	13.0711i		−	1.14202i	−0.820942	−	0.571012i	$-0.806551\pi$
$131$		−	13.0711i		−	1.14202i	0.820942	−	0.571012i	$-0.193449\pi$
$132$	−1.41421	+	2.00000i	−0.123091	+	0.174078i
$133$	−14.8383	−	14.8383i	−1.28664	−	1.28664i
$134$	4.05071			0.349928
$135$	7.84386	+	8.57169i	0.675092	+	0.737734i
$136$	1.00000			0.0857493
$137$	−5.82843	−	5.82843i	−0.497956	−	0.497956i	0.412845	−	0.910801i	$-0.364535\pi$
$137$	−5.82843	−	5.82843i	−0.497956	−	0.497956i	−0.910801	+	0.412845i	$0.864535\pi$
$138$	1.48872	−	2.10537i	0.126728	−	0.179221i
$139$			12.8979i			1.09399i	0.837136	+	0.546995i	$0.184228\pi$
$139$			12.8979i			1.09399i	−0.837136	+	0.546995i	$0.815772\pi$
$140$	1.93137	+	8.19936i	0.163230	+	0.692972i
$141$	−14.4853	+	2.48528i	−1.21988	+	0.209298i
$142$	−5.52811	+	5.52811i	−0.463909	+	0.463909i
$143$	1.45007	−	1.45007i	0.121261	−	0.121261i
$144$	1.00000	+	2.82843i	0.0833333	+	0.235702i
$145$	−3.52503	−	2.18098i	−0.292738	−	0.181120i
$146$		−	6.65530i		−	0.550797i
$147$	10.1709	+	7.19193i	0.838884	+	0.593181i
$148$	−6.88111	−	6.88111i	−0.565624	−	0.565624i
$149$	3.25594			0.266737			0.133369	−	0.991067i	$-0.457421\pi$
$149$	3.25594			0.266737			0.133369	+	0.991067i	$0.457421\pi$
$150$	5.12022	+	6.98451i	0.418064	+	0.570282i
$151$	−18.7904			−1.52914			−0.764570	−	0.644541i	$-0.777048\pi$
$151$	−18.7904			−1.52914			−0.764570	+	0.644541i	$0.777048\pi$
$152$	−3.93879	−	3.93879i	−0.319478	−	0.319478i
$153$	1.29289	−	2.70711i	0.104524	−	0.218857i
$154$			5.32765i			0.429314i
$155$	18.8695	+	11.6748i	1.51564	+	0.937741i
$156$	−0.424715	−	2.47542i	−0.0340044	−	0.198192i
$157$	2.46337	−	2.46337i	0.196598	−	0.196598i	−0.601942	−	0.798540i	$-0.705606\pi$
$157$	2.46337	−	2.46337i	0.196598	−	0.196598i	0.798540	+	0.601942i	$0.205606\pi$
$158$	7.45640	−	7.45640i	0.593199	−	0.593199i
$159$	0.974646	+	5.68066i	0.0772945	+	0.450505i
$160$	0.512677	+	2.17650i	0.0405307	+	0.172068i
$161$		−	5.60834i		−	0.441999i
$162$	8.94975	+	0.949747i	0.703159	+	0.0746192i
$163$	−11.2933	−	11.2933i	−0.884563	−	0.884563i	0.109431	−	0.993994i	$-0.465097\pi$
$163$	−11.2933	−	11.2933i	−0.884563	−	0.884563i	−0.993994	+	0.109431i	$0.965097\pi$
$164$	9.48373			0.740555
$165$	2.13925	+	5.04218i	0.166540	+	0.392533i
$166$	3.13572			0.243379
$167$	−10.0372	−	10.0372i	−0.776701	−	0.776701i	0.202567	−	0.979268i	$-0.435072\pi$
$167$	−10.0372	−	10.0372i	−0.776701	−	0.776701i	−0.979268	+	0.202567i	$0.935072\pi$
$168$	5.32765	+	3.76722i	0.411037	+	0.290647i
$169$		−	10.8973i		−	0.838254i
$170$	1.17650	−	1.90154i	0.0902336	−	0.145841i
$171$	−15.7552	+	5.57029i	−1.20483	+	0.425971i
$172$	−6.21729	+	6.21729i	−0.474064	+	0.474064i
$173$	−8.80660	+	8.80660i	−0.669554	+	0.669554i	−0.957613	−	0.288059i	$-0.906990\pi$
$173$	−8.80660	+	8.80660i	−0.669554	+	0.669554i	0.288059	+	0.957613i	$0.406990\pi$
$174$	−3.16460	+	0.542960i	−0.239908	+	0.0411617i
$175$	17.8636	+	5.97400i	1.35036	+	0.451592i
$176$			1.41421i			0.106600i
$177$	−1.60615	+	2.27144i	−0.120725	+	0.170732i
$178$	2.32765	+	2.32765i	0.174465	+	0.174465i
$179$	−24.0525			−1.79777			−0.898883	−	0.438189i	$-0.855620\pi$
$179$	−24.0525			−1.79777			−0.898883	+	0.438189i	$0.855620\pi$
$180$	6.55486	+	1.42611i	0.488570	+	0.106296i
$181$	−12.1152			−0.900518			−0.450259	−	0.892898i	$-0.648668\pi$
$181$	−12.1152			−0.900518			−0.450259	+	0.892898i	$0.648668\pi$
$182$	−3.86273	−	3.86273i	−0.286325	−	0.286325i
$183$	13.0083	−	18.3965i	0.961602	−	1.35991i
$184$		−	1.48872i		−	0.109750i
$185$	−21.1803	+	4.98904i	−1.55721	+	0.366802i
$186$	16.9401	−	2.90647i	1.24211	−	0.213112i
$187$	1.00000	−	1.00000i	0.0731272	−	0.0731272i
$188$	−6.00000	+	6.00000i	−0.437595	+	0.437595i
$189$	17.0863	−	9.55191i	1.24285	−	0.694799i
$190$	−12.1238	+	2.85576i	−0.879550	+	0.207179i
$191$		−	24.8114i		−	1.79529i	−0.440721	−	0.897644i	$-0.645277\pi$
$191$		−	24.8114i		−	1.79529i	0.440721	−	0.897644i	$-0.354723\pi$
$192$	1.41421	+	1.00000i	0.102062	+	0.0721688i
$193$	5.42907	+	5.42907i	0.390793	+	0.390793i	0.874970	−	0.484177i	$-0.160881\pi$
$193$	5.42907	+	5.42907i	0.390793	+	0.390793i	−0.484177	+	0.874970i	$0.660881\pi$
$194$	0.727013			0.0521965
$195$	−5.20679	−	2.10473i	−0.372866	−	0.150723i
$196$	7.19193			0.513710
$197$	10.7995	+	10.7995i	0.769436	+	0.769436i	0.978007	−	0.208572i	$-0.0668814\pi$
$197$	10.7995	+	10.7995i	0.769436	+	0.769436i	−0.208572	+	0.978007i	$0.566881\pi$
$198$	3.82843	+	1.82843i	0.272074	+	0.129941i
$199$			8.21178i			0.582118i	0.956705	+	0.291059i	$0.0940075\pi$
$199$			8.21178i			0.582118i	−0.956705	+	0.291059i	$0.905992\pi$
$200$	4.74186	+	1.58579i	0.335300	+	0.112132i
$201$	−1.18642	−	6.91499i	−0.0836839	−	0.487746i
$202$	6.94865	−	6.94865i	0.488905	−	0.488905i
$203$	−4.93815	+	4.93815i	−0.346590	+	0.346590i
$204$	−0.292893	−	1.70711i	−0.0205066	−	0.119521i
$205$	11.1576	−	18.0337i	0.779283	−	1.25953i
$206$			16.7060i			1.16396i
$207$	−4.03013	−	1.92476i	−0.280113	−	0.133780i
$208$	−1.02535	−	1.02535i	−0.0710955	−	0.0710955i
$209$	−7.87758			−0.544904
$210$	13.4315	−	5.69858i	0.926861	−	0.393240i
$211$	16.8979			1.16330			0.581651	−	0.813438i	$-0.302407\pi$
$211$	16.8979			1.16330			0.581651	+	0.813438i	$0.302407\pi$
$212$	2.35300	+	2.35300i	0.161605	+	0.161605i
$213$	11.0562	+	7.81793i	0.757559	+	0.535675i
$214$		−	2.29335i		−	0.156770i
$215$	4.50775	+	19.1371i	0.307426	+	1.30514i
$216$	4.53553	−	2.53553i	0.308604	−	0.172521i
$217$	26.4339	−	26.4339i	1.79445	−	1.79445i
$218$	−1.66383	+	1.66383i	−0.112688	+	0.112688i
$219$	−11.3613	+	1.94929i	−0.767726	+	0.131721i
$220$	2.68918	+	1.66383i	0.181304	+	0.112175i
$221$			1.45007i			0.0975422i
$222$	−9.73136	+	13.7622i	−0.653126	+	0.923660i
$223$	−15.6807	−	15.6807i	−1.05005	−	1.05005i	−0.998679	−	0.0513750i	$-0.983640\pi$
$223$	−15.6807	−	15.6807i	−1.05005	−	1.05005i	−0.0513750	−	0.998679i	$-0.516360\pi$
$224$	3.76722			0.251708
$225$	10.4236	−	10.7865i	0.694908	−	0.719099i
$226$	4.05071			0.269449
$227$	9.38387	+	9.38387i	0.622829	+	0.622829i	0.946254	−	0.323425i	$-0.104834\pi$
$227$	9.38387	+	9.38387i	0.622829	+	0.622829i	−0.323425	+	0.946254i	$0.604834\pi$
$228$	−5.57029	+	7.87758i	−0.368902	+	0.521706i
$229$			9.15763i			0.605153i	0.953125	+	0.302577i	$0.0978468\pi$
$229$			9.15763i			0.605153i	−0.953125	+	0.302577i	$0.902153\pi$
$230$	−2.83086	−	1.75149i	−0.186661	−	0.115490i
$231$	9.09487	−	1.56043i	0.598398	−	0.102669i
$232$	−1.31082	+	1.31082i	−0.0860596	+	0.0860596i
$233$	−4.67015	+	4.67015i	−0.305952	+	0.305952i	−0.843337	−	0.537385i	$-0.819412\pi$
$233$	−4.67015	+	4.67015i	−0.305952	+	0.305952i	0.537385	+	0.843337i	$0.319412\pi$
$234$	−4.10141	+	1.45007i	−0.268118	+	0.0947940i
$235$	4.35021	+	18.4682i	0.283776	+	1.20473i
$236$			1.60615i			0.104551i
$237$	−14.9128	−	10.5449i	−0.968690	−	0.684967i
$238$	−2.66383	−	2.66383i	−0.172670	−	0.172670i
$239$	−2.44852			−0.158381			−0.0791907	−	0.996859i	$-0.525234\pi$
$239$	−2.44852			−0.158381			−0.0791907	+	0.996859i	$0.525234\pi$
$240$	3.56536	−	1.51268i	0.230143	−	0.0976429i
$241$	1.41202			0.0909561			0.0454781	−	0.998965i	$-0.485519\pi$
$241$	1.41202			0.0909561			0.0454781	+	0.998965i	$0.485519\pi$
$242$	−6.36396	−	6.36396i	−0.409091	−	0.409091i
$243$	−1.00000	−	15.5563i	−0.0641500	−	0.997940i
$244$		−	13.0083i		−	0.832772i
$245$	8.46133	−	13.6757i	0.540574	−	0.873710i
$246$	−2.77772	−	16.1897i	−0.177101	−	1.03222i
$247$	5.71152	−	5.71152i	0.363415	−	0.363415i
$248$	7.01683	−	7.01683i	0.445569	−	0.445569i
$249$	−0.918430	−	5.35300i	−0.0582032	−	0.339233i
$250$	8.59425	−	7.15115i	0.543548	−	0.452278i
$251$		−	16.4704i		−	1.03960i	−0.854287	−	0.519802i	$-0.826006\pi$
$251$		−	16.4704i		−	1.03960i	0.854287	−	0.519802i	$-0.173994\pi$
$252$	4.87061	−	10.1983i	0.306820	−	0.642430i
$253$	−1.48872	−	1.48872i	−0.0935952	−	0.0935952i
$254$	−12.0000			−0.752947
$255$	−3.59072	−	1.45147i	−0.224859	−	0.0908944i
$256$	1.00000			0.0625000
$257$	5.82843	+	5.82843i	0.363567	+	0.363567i	0.865124	−	0.501557i	$-0.167239\pi$
$257$	5.82843	+	5.82843i	0.363567	+	0.363567i	−0.501557	+	0.865124i	$0.667239\pi$
$258$	12.4346	+	8.79257i	0.774143	+	0.547402i
$259$			36.6602i			2.27795i
$260$	−3.15608	+	0.743417i	−0.195732	+	0.0461047i
$261$	1.85378	+	5.24328i	0.114746	+	0.324551i
$262$	−9.24264	+	9.24264i	−0.571012	+	0.571012i
$263$	−2.80463	+	2.80463i	−0.172941	+	0.172941i	−0.788270	−	0.615329i	$-0.789023\pi$
$263$	−2.80463	+	2.80463i	−0.172941	+	0.172941i	0.615329	+	0.788270i	$0.289023\pi$
$264$	2.41421	−	0.414214i	0.148585	−	0.0254931i
$265$	7.24264	−	1.70601i	0.444912	−	0.104799i
$266$			20.9845i			1.28664i
$267$	3.29180	−	4.65530i	0.201455	−	0.284900i
$268$	−2.86428	−	2.86428i	−0.174964	−	0.174964i
$269$	−28.7356			−1.75204			−0.876020	−	0.482275i	$-0.839811\pi$
$269$	−28.7356			−1.75204			−0.876020	+	0.482275i	$0.839811\pi$
$270$	0.514655	−	11.6075i	0.0313209	−	0.706413i
$271$	29.7959			1.80997			0.904986	−	0.425442i	$-0.139881\pi$
$271$	29.7959			1.80997			0.904986	+	0.425442i	$0.139881\pi$
$272$	−0.707107	−	0.707107i	−0.0428746	−	0.0428746i
$273$	−5.46273	+	7.72546i	−0.330619	+	0.467566i
$274$			8.24264i			0.497956i
$275$	6.32765	−	3.15608i	0.381572	−	0.190319i
$276$	−2.54141	+	0.436037i	−0.152975	+	0.0262463i
$277$	0.177901	−	0.177901i	0.0106891	−	0.0106891i	−0.701742	−	0.712431i	$-0.747594\pi$
$277$	0.177901	−	0.177901i	0.0106891	−	0.0106891i	0.712431	+	0.701742i	$0.247594\pi$
$278$	9.12022	−	9.12022i	0.546995	−	0.546995i
$279$	−9.92330	−	28.0673i	−0.594092	−	1.68035i
$280$	4.43214	−	7.16350i	0.264871	−	0.428101i
$281$			10.2902i			0.613864i	0.951731	+	0.306932i	$0.0993025\pi$
$281$			10.2902i			0.613864i	−0.951731	+	0.306932i	$0.900697\pi$
$282$	12.0000	+	8.48528i	0.714590	+	0.505291i
$283$	3.08437	+	3.08437i	0.183347	+	0.183347i	0.792812	−	0.609466i	$-0.208616\pi$
$283$	3.08437	+	3.08437i	0.183347	+	0.183347i	−0.609466	+	0.792812i	$0.708616\pi$
$284$	7.81793			0.463909
$285$	8.42605	+	19.8601i	0.499116	+	1.17641i
$286$	−2.05071			−0.121261
$287$	−25.2630	−	25.2630i	−1.49123	−	1.49123i
$288$	1.29289	−	2.70711i	0.0761845	−	0.159518i
$289$			1.00000i			0.0588235i
$290$	0.950390	+	4.03476i	0.0558088	+	0.236929i
$291$	−0.212937	−	1.24109i	−0.0124826	−	0.0727539i
$292$	−4.70601	+	4.70601i	−0.275398	+	0.275398i
$293$	10.8383	−	10.8383i	0.633179	−	0.633179i	−0.315685	−	0.948864i	$-0.602234\pi$
$293$	10.8383	−	10.8383i	0.633179	−	0.633179i	0.948864	+	0.315685i	$0.102234\pi$
$294$	−2.10647	−	12.2774i	−0.122852	−	0.716032i
$295$	3.05415	+	1.88964i	0.177819	+	0.110019i
$296$			9.73136i			0.565624i
$297$	2.00000	−	7.07107i	0.116052	−	0.410305i
$298$	−2.30230	−	2.30230i	−0.133369	−	0.133369i
$299$	2.15875			0.124844
$300$	1.31825	−	8.55934i	0.0761090	−	0.494173i
$301$	33.1235			1.90921
$302$	13.2868	+	13.2868i	0.764570	+	0.764570i
$303$	−13.8973	−	9.82688i	−0.798379	−	0.564539i
$304$			5.57029i			0.319478i
$305$	−24.7358	−	15.3043i	−1.41637	−	0.876322i
$306$	−2.82843	+	1.00000i	−0.161690	+	0.0571662i
$307$	−4.26799	+	4.26799i	−0.243587	+	0.243587i	−0.818332	−	0.574745i	$-0.805101\pi$
$307$	−4.26799	+	4.26799i	−0.243587	+	0.243587i	0.574745	+	0.818332i	$0.305101\pi$
$308$	3.76722	−	3.76722i	0.214657	−	0.214657i
$309$	28.5189	−	4.89308i	1.62239	−	0.278357i
$310$	−5.08744	−	21.5981i	−0.288947	−	1.22669i
$311$			23.8726i			1.35369i	0.736125	+	0.676845i	$0.236653\pi$
$311$			23.8726i			1.35369i	−0.736125	+	0.676845i	$0.763347\pi$
$312$	−1.45007	+	2.05071i	−0.0820940	+	0.116098i
$313$	1.10692	+	1.10692i	0.0625670	+	0.0625670i	0.737698	−	0.675131i	$-0.235913\pi$
$313$	1.10692	+	1.10692i	0.0625670	+	0.0625670i	−0.675131	+	0.737698i	$0.735913\pi$
$314$	−3.48373			−0.196598
$315$	−13.6621	−	21.2599i	−0.769771	−	1.19786i
$316$	−10.5449			−0.593199
$317$	24.3030	+	24.3030i	1.36499	+	1.36499i	0.867426	+	0.497566i	$0.165773\pi$
$317$	24.3030	+	24.3030i	1.36499	+	1.36499i	0.497566	+	0.867426i	$0.334227\pi$
$318$	3.32765	−	4.70601i	0.186605	−	0.263900i
$319$			2.62164i			0.146784i
$320$	1.17650	−	1.90154i	0.0657685	−	0.106299i
$321$	−3.91499	+	0.671706i	−0.218513	+	0.0374910i
$322$	−3.96570	+	3.96570i	−0.221000	+	0.221000i
$323$	3.93879	−	3.93879i	0.219160	−	0.219160i
$324$	−5.65685	−	7.00000i	−0.314270	−	0.388889i
$325$	−2.29950	+	6.87603i	−0.127553	+	0.381414i
$326$			15.9712i			0.884563i
$327$	3.32765	+	2.35300i	0.184020	+	0.130121i
$328$	−6.70601	−	6.70601i	−0.370277	−	0.370277i
$329$	31.9659			1.76234
$330$	2.05269	−	5.07804i	0.112997	−	0.279537i
$331$	−20.6033			−1.13246			−0.566230	−	0.824247i	$-0.691599\pi$
$331$	−20.6033			−1.13246			−0.566230	+	0.824247i	$0.691599\pi$
$332$	−2.21729	−	2.21729i	−0.121689	−	0.121689i
$333$	26.3438	+	12.5816i	1.44363	+	0.689468i
$334$			14.1947i			0.776701i
$335$	−8.81637	+	2.07670i	−0.481690	+	0.113462i
$336$	−1.10339	−	6.43104i	−0.0601950	−	0.350842i
$337$	−2.92674	+	2.92674i	−0.159430	+	0.159430i	−0.782314	−	0.622884i	$-0.785961\pi$
$337$	−2.92674	+	2.92674i	−0.159430	+	0.159430i	0.622884	+	0.782314i	$0.285961\pi$
$338$	−7.70555	+	7.70555i	−0.419127	+	0.419127i
$339$	−1.18642	−	6.91499i	−0.0644377	−	0.375571i
$340$	−2.17650	+	0.512677i	−0.118037	+	0.0278038i
$341$		−	14.0337i		−	0.759965i
$342$	15.0794	+	7.20179i	0.815399	+	0.389428i
$343$	−0.511278	−	0.511278i	−0.0276064	−	0.0276064i
$344$	8.79257			0.474064
$345$	−2.16083	+	5.34558i	−0.116335	+	0.287796i
$346$	12.4544			0.669554
$347$	0.587338	+	0.587338i	0.0315300	+	0.0315300i	0.722696	−	0.691166i	$-0.242903\pi$
$347$	0.587338	+	0.587338i	0.0315300	+	0.0315300i	−0.691166	+	0.722696i	$0.742903\pi$
$348$	2.62164	+	1.85378i	0.140535	+	0.0993731i
$349$		−	3.72856i		−	0.199586i	−0.995008	−	0.0997928i	$-0.968182\pi$
$349$		−	3.72856i		−	0.199586i	0.995008	−	0.0997928i	$-0.0318180\pi$
$350$	−8.40724	−	16.8558i	−0.449386	−	0.900978i
$351$	3.67670	+	6.57684i	0.196248	+	0.351046i
$352$	1.00000	−	1.00000i	0.0533002	−	0.0533002i
$353$	−20.2624	+	20.2624i	−1.07846	+	1.07846i	−0.0818085	+	0.996648i	$0.526070\pi$
$353$	−20.2624	+	20.2624i	−1.07846	+	1.07846i	−0.996648	+	0.0818085i	$0.973930\pi$
$354$	2.74186	−	0.470430i	0.145728	−	0.0250031i
$355$	9.19781	−	14.8661i	0.488169	−	0.789009i
$356$		−	3.29180i		−	0.174465i
$357$	−3.76722	+	5.32765i	−0.199382	+	0.281969i
$358$	17.0077	+	17.0077i	0.898883	+	0.898883i
$359$	17.2052			0.908057			0.454029	−	0.890987i	$-0.349986\pi$
$359$	17.2052			0.908057			0.454029	+	0.890987i	$0.349986\pi$
$360$	−3.62657	−	5.64340i	−0.191137	−	0.297433i
$361$	−12.0282			−0.633061
$362$	8.56676	+	8.56676i	0.450259	+	0.450259i
$363$	−9.00000	+	12.7279i	−0.472377	+	0.668043i
$364$			5.46273i			0.286325i
$365$	3.41202	+	14.4853i	0.178593	+	0.758194i
$366$	−22.2066	+	3.81004i	−1.16076	+	0.199154i
$367$	−15.0724	+	15.0724i	−0.786773	+	0.786773i	−0.980964	−	0.194191i	$-0.937792\pi$
$367$	−15.0724	+	15.0724i	−0.786773	+	0.786773i	0.194191	+	0.980964i	$0.437792\pi$
$368$	−1.05269	+	1.05269i	−0.0548750	+	0.0548750i
$369$	−26.8240	+	9.48373i	−1.39640	+	0.493703i
$370$	18.5045	+	11.4490i	0.962005	+	0.595204i
$371$		−	12.5360i		−	0.650836i
$372$	−14.0337	−	9.92330i	−0.727611	−	0.514499i
$373$	−13.6299	−	13.6299i	−0.705732	−	0.705732i	0.259903	−	0.965635i	$-0.416309\pi$
$373$	−13.6299	−	13.6299i	−0.705732	−	0.705732i	−0.965635	+	0.259903i	$0.916309\pi$
$374$	−1.41421			−0.0731272
$375$	−14.7250	−	12.5768i	−0.760394	−	0.649462i
$376$	8.48528			0.437595
$377$	−1.90078	−	1.90078i	−0.0978952	−	0.0978952i
$378$	−18.8361	−	5.32765i	−0.968824	−	0.274025i
$379$			15.0501i			0.773070i	0.922275	+	0.386535i	$0.126328\pi$
$379$			15.0501i			0.773070i	−0.922275	+	0.386535i	$0.873672\pi$
$380$	10.5921	+	6.55346i	0.543364	+	0.336185i
$381$	3.51472	+	20.4853i	0.180064	+	1.04949i
$382$	−17.5443	+	17.5443i	−0.897644	+	0.897644i
$383$	−26.0982	+	26.0982i	−1.33355	+	1.33355i	−0.431389	+	0.902166i	$0.641976\pi$
$383$	−26.0982	+	26.0982i	−1.33355	+	1.33355i	−0.902166	+	0.431389i	$0.858024\pi$
$384$	−0.292893	−	1.70711i	−0.0149466	−	0.0871154i
$385$	−2.73136	−	11.5956i	−0.139203	−	0.590969i
$386$		−	7.67786i		−	0.390793i
$387$	11.3679	−	23.8024i	0.577861	−	1.20995i
$388$	−0.514076	−	0.514076i	−0.0260982	−	0.0260982i
$389$	37.5344			1.90307			0.951536	−	0.307538i	$-0.0995052\pi$
$389$	37.5344			1.90307			0.951536	+	0.307538i	$0.0995052\pi$
$390$	2.19349	+	5.17002i	0.111071	+	0.261794i
$391$	1.48872			0.0752879
$392$	−5.08547	−	5.08547i	−0.256855	−	0.256855i
$393$	18.4853	+	13.0711i	0.932459	+	0.659348i
$394$		−	15.2729i		−	0.769436i
$395$	−12.4061	+	20.0516i	−0.624221	+	1.00890i
$396$	−1.41421	−	4.00000i	−0.0710669	−	0.201008i
$397$	−1.28203	+	1.28203i	−0.0643431	+	0.0643431i	−0.738546	−	0.674203i	$-0.764487\pi$
$397$	−1.28203	+	1.28203i	−0.0643431	+	0.0643431i	0.674203	+	0.738546i	$0.264487\pi$
$398$	5.80660	−	5.80660i	0.291059	−	0.291059i
$399$	35.8228	−	6.14622i	1.79338	−	0.307696i
$400$	−2.23168	−	4.47433i	−0.111584	−	0.223716i
$401$			38.4543i			1.92032i	0.279458	+	0.960158i	$0.409845\pi$
$401$			38.4543i			1.92032i	−0.279458	+	0.960158i	$0.590155\pi$
$402$	−4.05071	+	5.72856i	−0.202031	+	0.285715i
$403$	10.1749	+	10.1749i	0.506847	+	0.506847i
$404$	−9.82688			−0.488905
$405$	−19.9661	+	2.52120i	−0.992121	+	0.125279i
$406$	6.98360			0.346590
$407$	9.73136	+	9.73136i	0.482366	+	0.482366i
$408$	−1.00000	+	1.41421i	−0.0495074	+	0.0700140i
$409$			11.6380i			0.575464i	0.957711	+	0.287732i	$0.0929013\pi$
$409$			11.6380i			0.575464i	−0.957711	+	0.287732i	$0.907099\pi$
$410$	−20.6414	+	4.86209i	−1.01940	+	0.240121i
$411$	14.0711	−	2.41421i	0.694075	−	0.119084i
$412$	11.8129	−	11.8129i	0.581981	−	0.581981i
$413$	4.27850	−	4.27850i	0.210531	−	0.210531i
$414$	1.48872	+	4.21074i	0.0731667	+	0.206947i
$415$	−6.82490	+	1.60761i	−0.335021	+	0.0789144i
$416$			1.45007i			0.0710955i
$417$	−18.2404	−	12.8979i	−0.893238	−	0.631615i
$418$	5.57029	+	5.57029i	0.272452	+	0.272452i
$419$	2.49307			0.121795			0.0608973	−	0.998144i	$-0.480604\pi$
$419$	2.49307			0.121795			0.0608973	+	0.998144i	$0.480604\pi$
$420$	−13.5270	−	5.46800i	−0.660051	−	0.266811i
$421$	−16.7341			−0.815569			−0.407784	−	0.913078i	$-0.633699\pi$
$421$	−16.7341			−0.815569			−0.407784	+	0.913078i	$0.633699\pi$
$422$	−11.9487	−	11.9487i	−0.581651	−	0.581651i
$423$	10.9706	−	22.9706i	0.533407	−	1.11687i
$424$		−	3.32765i		−	0.161605i
$425$	−1.58579	+	4.74186i	−0.0769219	+	0.230014i
$426$	−2.28982	−	13.3460i	−0.110942	−	0.646617i
$427$	−34.6519	+	34.6519i	−1.67692	+	1.67692i
$428$	−1.62164	+	1.62164i	−0.0783850	+	0.0783850i
$429$	0.600638	+	3.50078i	0.0289991	+	0.169019i
$430$	10.3445	−	16.7194i	0.498855	−	0.806281i
$431$			12.5956i			0.606711i	0.952877	+	0.303355i	$0.0981069\pi$
$431$			12.5956i			0.606711i	−0.952877	+	0.303355i	$0.901893\pi$
$432$	−5.00000	−	1.41421i	−0.240563	−	0.0680414i
$433$	−25.4627	−	25.4627i	−1.22366	−	1.22366i	−0.966321	−	0.257339i	$-0.917154\pi$
$433$	−25.4627	−	25.4627i	−1.22366	−	1.22366i	−0.257339	−	0.966321i	$-0.582846\pi$
$434$	−37.3832			−1.79445
$435$	6.60940	−	2.80417i	0.316896	−	0.134450i
$436$	2.35300			0.112688
$437$	−5.86377	−	5.86377i	−0.280502	−	0.280502i
$438$	9.41202	+	6.65530i	0.449724	+	0.318003i
$439$		−	17.0639i		−	0.814415i	−0.913336	−	0.407207i	$-0.866503\pi$
$439$		−	17.0639i		−	0.814415i	0.913336	−	0.407207i	$-0.133497\pi$
$440$	−0.725034	−	3.07804i	−0.0345647	−	0.146740i
$441$	−20.3419	+	7.19193i	−0.968660	+	0.342473i
$442$	1.02535	−	1.02535i	0.0487711	−	0.0487711i
$443$	13.8059	−	13.8059i	0.655937	−	0.655937i	−0.298479	−	0.954416i	$-0.596479\pi$
$443$	13.8059	−	13.8059i	0.655937	−	0.655937i	0.954416	+	0.298479i	$0.0964794\pi$
$444$	16.6125	−	2.85025i	0.788393	−	0.135267i
$445$	−6.25947	−	3.87281i	−0.296727	−	0.183589i
$446$			22.1758i			1.05005i
$447$	−3.25594	+	4.60460i	−0.154001	+	0.217790i
$448$	−2.66383	−	2.66383i	−0.125854	−	0.125854i
$449$	−7.33471			−0.346146			−0.173073	−	0.984909i	$-0.555370\pi$
$449$	−7.33471			−0.346146			−0.173073	+	0.984909i	$0.555370\pi$
$450$	−14.9978	+	0.256583i	−0.707003	+	0.0120955i
$451$	−13.4120			−0.631547
$452$	−2.86428	−	2.86428i	−0.134725	−	0.134725i
$453$	18.7904	−	26.5736i	0.882849	−	1.24854i
$454$		−	13.2708i		−	0.622829i
$455$	10.3876	+	6.42691i	0.486977	+	0.301298i
$456$	9.50908	−	1.63150i	0.445304	−	0.0764020i
$457$	9.77927	−	9.77927i	0.457455	−	0.457455i	−0.440364	−	0.897819i	$-0.645151\pi$
$457$	9.77927	−	9.77927i	0.457455	−	0.457455i	0.897819	+	0.440364i	$0.145151\pi$
$458$	6.47542	−	6.47542i	0.302577	−	0.302577i
$459$	2.53553	+	4.53553i	0.118349	+	0.211701i
$460$	0.763233	+	3.24021i	0.0355859	+	0.151075i
$461$			29.5415i			1.37588i	0.725765	+	0.687942i	$0.241486\pi$
$461$			29.5415i			1.37588i	−0.725765	+	0.687942i	$0.758514\pi$
$462$	−7.53444	−	5.32765i	−0.350534	−	0.247865i
$463$	−12.0000	−	12.0000i	−0.557687	−	0.557687i	0.370961	−	0.928648i	$-0.379028\pi$
$463$	−12.0000	−	12.0000i	−0.557687	−	0.557687i	−0.928648	+	0.370961i	$0.879028\pi$
$464$	1.85378			0.0860596
$465$	−35.3801	+	15.0107i	−1.64072	+	0.696106i
$466$	6.60460			0.305952
$467$	−26.7616	−	26.7616i	−1.23838	−	1.23838i	−0.960664	−	0.277715i	$-0.910423\pi$
$467$	−26.7616	−	26.7616i	−1.23838	−	1.23838i	−0.277715	−	0.960664i	$-0.589577\pi$
$468$	3.92549	+	1.87478i	0.181456	+	0.0866619i
$469$			15.2599i			0.704637i
$470$	9.98295	−	16.1351i	0.460479	−	0.744256i
$471$	1.02036	+	5.94710i	0.0470157	+	0.274028i
$472$	1.13572	−	1.13572i	0.0522756	−	0.0522756i
$473$	8.79257	−	8.79257i	0.404283	−	0.404283i
$474$	3.08854	+	18.0013i	0.141861	+	0.826829i
$475$	24.9233	−	12.4311i	1.14356	−	0.570380i
$476$			3.76722i			0.172670i
$477$	−9.00831	−	4.30230i	−0.412462	−	0.196989i
$478$	1.73136	+	1.73136i	0.0791907	+	0.0791907i
$479$	20.0457			0.915912			0.457956	−	0.888975i	$-0.348582\pi$
$479$	20.0457			0.915912			0.457956	+	0.888975i	$0.348582\pi$
$480$	−3.59072	−	1.45147i	−0.163893	−	0.0662501i
$481$	−14.1111			−0.643413
$482$	−0.998448	−	0.998448i	−0.0454781	−	0.0454781i
$483$	7.93139	+	5.60834i	0.360891	+	0.255188i
$484$			9.00000i			0.409091i
$485$	−1.58235	+	0.372723i	−0.0718506	+	0.0169245i
$486$	−10.2929	+	11.7071i	−0.466895	+	0.531045i
$487$	−30.5611	+	30.5611i	−1.38486	+	1.38486i	−0.549100	+	0.835756i	$0.685030\pi$
$487$	−30.5611	+	30.5611i	−1.38486	+	1.38486i	−0.835756	+	0.549100i	$0.814970\pi$
$488$	−9.19826	+	9.19826i	−0.416386	+	0.416386i
$489$	27.2646	−	4.67786i	1.23295	−	0.211540i
$490$	−15.6533	+	3.68714i	−0.707142	+	0.166568i
$491$		−	8.52802i		−	0.384864i	−0.981310	−	0.192432i	$-0.938363\pi$
$491$		−	8.52802i		−	0.384864i	0.981310	−	0.192432i	$-0.0616375\pi$
$492$	−9.48373	+	13.4120i	−0.427560	+	0.604661i
$493$	−1.31082	−	1.31082i	−0.0590364	−	0.0590364i
$494$	−8.07731			−0.363415
$495$	−9.26997	−	2.01683i	−0.416654	−	0.0906498i
$496$	−9.92330			−0.445569
$497$	−20.8256	−	20.8256i	−0.934155	−	0.934155i
$498$	−3.13572	+	4.43457i	−0.140515	+	0.198718i
$499$		−	13.1694i		−	0.589542i	−0.955568	−	0.294771i	$-0.904757\pi$
$499$		−	13.1694i		−	0.589542i	0.955568	−	0.294771i	$-0.0952434\pi$
$500$	−11.1337	−	1.02042i	−0.497913	−	0.0456348i
$501$	24.2319	−	4.15754i	1.08260	−	0.185745i
$502$	−11.6464	+	11.6464i	−0.519802	+	0.519802i
$503$	−6.42605	+	6.42605i	−0.286523	+	0.286523i	−0.835704	−	0.549180i	$-0.814940\pi$
$503$	−6.42605	+	6.42605i	−0.286523	+	0.286523i	0.549180	+	0.835704i	$0.314940\pi$
$504$	−10.6553	+	3.76722i	−0.474625	+	0.167805i
$505$	−11.5613	+	18.6862i	−0.514473	+	0.831523i
$506$			2.10537i			0.0935952i
$507$	15.4111	+	10.8973i	0.684431	+	0.483966i
$508$	8.48528	+	8.48528i	0.376473	+	0.376473i
$509$	−21.1038			−0.935410			−0.467705	−	0.883885i	$-0.654919\pi$
$509$	−21.1038			−0.935410			−0.467705	+	0.883885i	$0.654919\pi$
$510$	1.51268	+	3.56536i	0.0669825	+	0.157877i
$511$	25.0720			1.10912
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	7.87758	−	27.8515i	0.347804	−	1.22967i
$514$		−	8.24264i		−	0.363567i
$515$	−8.56478	−	36.3607i	−0.377409	−	1.60224i
$516$	−2.57528	−	15.0099i	−0.113371	−	0.660772i
$517$	8.48528	−	8.48528i	0.373182	−	0.373182i
$518$	25.9227	−	25.9227i	1.13898	−	1.13898i
$519$	−3.64781	−	21.2610i	−0.160121	−	0.933255i
$520$	2.75736	+	1.70601i	0.120918	+	0.0748135i
$521$		−	30.2095i		−	1.32350i	−0.749724	−	0.661750i	$-0.769814\pi$
$521$		−	30.2095i		−	1.32350i	0.749724	−	0.661750i	$-0.230186\pi$
$522$	2.39674	−	5.01838i	0.104902	−	0.219649i
$523$	−7.29399	−	7.29399i	−0.318944	−	0.318944i	0.529417	−	0.848361i	$-0.322411\pi$
$523$	−7.29399	−	7.29399i	−0.318944	−	0.318944i	−0.848361	+	0.529417i	$0.822411\pi$
$524$	13.0711			0.571012
$525$	−26.3122	+	19.2890i	−1.14836	+	0.841841i
$526$	3.96634			0.172941
$527$	7.01683	+	7.01683i	0.305658	+	0.305658i
$528$	−2.00000	−	1.41421i	−0.0870388	−	0.0615457i
$529$			20.7837i			0.903639i
$530$	−6.32765	−	3.91499i	−0.274856	−	0.170056i
$531$	−1.60615	−	4.54287i	−0.0697009	−	0.197144i
$532$	14.8383	−	14.8383i	0.643321	−	0.643321i
$533$	9.72418	−	9.72418i	0.421201	−	0.421201i
$534$	−5.61945	+	0.964145i	−0.243177	+	0.0417226i
$535$	1.17575	+	4.99148i	0.0508319	+	0.215800i
$536$			4.05071i			0.174964i
$537$	24.0525	−	34.0153i	1.03794	−	1.46787i
$538$	20.3191	+	20.3191i	0.876020	+	0.876020i
$539$	−10.1709			−0.438093
$540$	−8.57169	+	7.84386i	−0.368867	+	0.337546i
$541$	−29.8157			−1.28188			−0.640939	−	0.767592i	$-0.721455\pi$
$541$	−29.8157			−1.28188			−0.640939	+	0.767592i	$0.721455\pi$
$542$	−21.0689	−	21.0689i	−0.904986	−	0.904986i
$543$	12.1152	−	17.1335i	0.519914	−	0.735270i
$544$			1.00000i			0.0428746i
$545$	2.76832	−	4.47433i	0.118582	−	0.191659i
$546$	9.32546	−	1.60000i	0.399093	−	0.0684735i
$547$	11.5189	−	11.5189i	0.492514	−	0.492514i	−0.416583	−	0.909098i	$-0.636773\pi$
$547$	11.5189	−	11.5189i	0.492514	−	0.492514i	0.909098	+	0.416583i	$0.136773\pi$
$548$	5.82843	−	5.82843i	0.248978	−	0.248978i
$549$	13.0083	+	36.7930i	0.555181	+	1.57029i
$550$	−6.70601	−	2.24264i	−0.285945	−	0.0956265i
$551$			10.3261i			0.439907i
$552$	2.10537	+	1.48872i	0.0896106	+	0.0633642i
$553$	28.0899	+	28.0899i	1.19450	+	1.19450i
$554$	−0.251591			−0.0106891
$555$	14.1248	−	34.9426i	0.599563	−	1.48323i
$556$	−12.8979			−0.546995
$557$	22.1709	+	22.1709i	0.939412	+	0.939412i	0.998267	−	0.0588541i	$-0.0187447\pi$
$557$	22.1709	+	22.1709i	0.939412	+	0.939412i	−0.0588541	+	0.998267i	$0.518745\pi$
$558$	−12.8298	+	26.8634i	−0.543127	+	1.13722i
$559$			12.7498i			0.539261i
$560$	−8.19936	+	1.93137i	−0.346486	+	0.0816151i
$561$	0.414214	+	2.41421i	0.0174881	+	0.101928i
$562$	7.27630	−	7.27630i	0.306932	−	0.306932i
$563$	11.3579	−	11.3579i	0.478677	−	0.478677i	−0.426031	−	0.904708i	$-0.640089\pi$
$563$	11.3579	−	11.3579i	0.478677	−	0.478677i	0.904708	+	0.426031i	$0.140089\pi$
$564$	−2.48528	−	14.4853i	−0.104649	−	0.609940i
$565$	−8.81637	+	2.07670i	−0.370908	+	0.0873676i
$566$		−	4.36195i		−	0.183347i
$567$	−3.57791	+	33.7157i	−0.150258	+	1.41592i
$568$	−5.52811	−	5.52811i	−0.231954	−	0.231954i
$569$	−16.1080			−0.675284			−0.337642	−	0.941275i	$-0.609629\pi$
$569$	−16.1080			−0.675284			−0.337642	+	0.941275i	$0.609629\pi$
$570$	8.08510	−	20.0013i	0.338648	−	0.837764i
$571$	−35.9192			−1.50317			−0.751586	−	0.659635i	$-0.770711\pi$
$571$	−35.9192			−1.50317			−0.751586	+	0.659635i	$0.770711\pi$
$572$	1.45007	+	1.45007i	0.0606304	+	0.0606304i
$573$	35.0886	+	24.8114i	1.46585	+	1.03651i
$574$			35.7273i			1.49123i
$575$	7.05932	+	2.36080i	0.294394	+	0.0984520i
$576$	−2.82843	+	1.00000i	−0.117851	+	0.0416667i
$577$	8.26520	−	8.26520i	0.344085	−	0.344085i	−0.513816	−	0.857900i	$-0.671769\pi$
$577$	8.26520	−	8.26520i	0.344085	−	0.344085i	0.857900	+	0.513816i	$0.171769\pi$
$578$	0.707107	−	0.707107i	0.0294118	−	0.0294118i
$579$	−13.1069	+	2.24879i	−0.544705	+	0.0934566i
$580$	2.18098	−	3.52503i	0.0905602	−	0.146369i
$581$			11.8129i			0.490083i
$582$	−0.727013	+	1.02815i	−0.0301357	+	0.0426183i
$583$	−3.32765	−	3.32765i	−0.137817	−	0.137817i
$584$	6.65530			0.275398
$585$	8.18332	−	5.25878i	0.338339	−	0.217424i
$586$	−15.3277			−0.633179
$587$	−11.6569	−	11.6569i	−0.481130	−	0.481130i	0.424363	−	0.905492i	$-0.360498\pi$
$587$	−11.6569	−	11.6569i	−0.481130	−	0.481130i	−0.905492	+	0.424363i	$0.860498\pi$
$588$	−7.19193	+	10.1709i	−0.296590	+	0.419442i
$589$		−	55.2757i		−	2.27759i
$590$	−0.823434	−	3.49578i	−0.0339003	−	0.143919i
$591$	−26.0724	+	4.47332i	−1.07248	+	0.184008i
$592$	6.88111	−	6.88111i	0.282812	−	0.282812i
$593$	−6.56323	+	6.56323i	−0.269520	+	0.269520i	−0.828907	−	0.559387i	$-0.811037\pi$
$593$	−6.56323	+	6.56323i	−0.269520	+	0.269520i	0.559387	+	0.828907i	$0.311037\pi$
$594$	−6.41421	+	3.58579i	−0.263178	+	0.147127i
$595$	7.16350	+	4.43214i	0.293675	+	0.181700i
$596$			3.25594i			0.133369i
$597$	−11.6132	−	8.21178i	−0.475297	−	0.336086i
$598$	−1.52647	−	1.52647i	−0.0624219	−	0.0624219i
$599$	23.3854			0.955502			0.477751	−	0.878495i	$-0.341452\pi$
$599$	23.3854			0.955502			0.477751	+	0.878495i	$0.341452\pi$
$600$	−6.98451	+	5.12022i	−0.285141	+	0.209032i
$601$	2.15212			0.0877869			0.0438934	−	0.999036i	$-0.486024\pi$
$601$	2.15212			0.0877869			0.0438934	+	0.999036i	$0.486024\pi$
$602$	−23.4219	−	23.4219i	−0.954604	−	0.954604i
$603$	10.9657	+	5.23713i	0.446558	+	0.213272i
$604$		−	18.7904i		−	0.764570i
$605$	17.1138	+	10.5885i	0.695776	+	0.430485i
$606$	2.87823	+	16.7755i	0.116920	+	0.681459i
$607$	−23.1751	+	23.1751i	−0.940648	+	0.940648i	−0.998335	−	0.0576863i	$-0.981628\pi$
$607$	−23.1751	+	23.1751i	−0.940648	+	0.940648i	0.0576863	+	0.998335i	$0.481628\pi$
$608$	3.93879	−	3.93879i	0.159739	−	0.159739i
$609$	−2.04545	−	11.9217i	−0.0828857	−	0.483093i
$610$	6.66906	+	28.3126i	0.270022	+	1.14634i
$611$			12.3042i			0.497776i
$612$	2.70711	+	1.29289i	0.109428	+	0.0522621i
$613$	−1.03430	−	1.03430i	−0.0417751	−	0.0417751i	0.685911	−	0.727686i	$-0.259404\pi$
$613$	−1.03430	−	1.03430i	−0.0417751	−	0.0417751i	−0.727686	+	0.685911i	$0.759404\pi$
$614$	6.03586			0.243587
$615$	14.3458	+	33.8129i	0.578479	+	1.36347i
$616$	−5.32765			−0.214657
$617$	4.05071	+	4.05071i	0.163075	+	0.163075i	0.783928	−	0.620852i	$-0.213213\pi$
$617$	4.05071	+	4.05071i	0.163075	+	0.163075i	−0.620852	+	0.783928i	$0.713213\pi$
$618$	−23.6259	−	16.7060i	−0.950372	−	0.672014i
$619$		−	8.33717i		−	0.335099i	−0.985864	−	0.167550i	$-0.946415\pi$
$619$		−	8.33717i		−	0.335099i	0.985864	−	0.167550i	$-0.0535854\pi$
$620$	−11.6748	+	18.8695i	−0.468871	+	0.757818i
$621$	6.75215	−	3.77471i	0.270954	−	0.151474i
$622$	16.8805	−	16.8805i	0.676845	−	0.676845i
$623$	−8.76877	+	8.76877i	−0.351313	+	0.351313i
$624$	2.47542	−	0.424715i	0.0990962	−	0.0170022i
$625$	−15.0392	+	19.9706i	−0.601567	+	0.798823i
$626$		−	1.56543i		−	0.0625670i
$627$	7.87758	−	11.1406i	0.314600	−	0.444912i
$628$	2.46337	+	2.46337i	0.0982991	+	0.0982991i
$629$	−9.73136			−0.388015
$630$	−5.37248	+	24.6936i	−0.214045	+	0.983816i
$631$	32.2880			1.28537			0.642683	−	0.766132i	$-0.277821\pi$
$631$	32.2880			1.28537			0.642683	+	0.766132i	$0.277821\pi$
$632$	7.45640	+	7.45640i	0.296600	+	0.296600i
$633$	−16.8979	+	23.8973i	−0.671633	+	0.949832i
$634$		−	34.3696i		−	1.36499i
$635$	26.1180	−	6.15212i	1.03646	−	0.244139i
$636$	−5.68066	+	0.974646i	−0.225253	+	0.0386472i
$637$	7.37427	−	7.37427i	0.292179	−	0.292179i
$638$	1.85378	−	1.85378i	0.0733919	−	0.0733919i
$639$	−22.1124	+	7.81793i	−0.874754	+	0.309272i
$640$	−2.17650	+	0.512677i	−0.0860338	+	0.0202653i
$641$		−	41.0676i		−	1.62207i	−0.584996	−	0.811036i	$-0.698904\pi$
$641$		−	41.0676i		−	1.62207i	0.584996	−	0.811036i	$-0.301096\pi$
$642$	3.24328	+	2.29335i	0.128002	+	0.0905112i
$643$	−1.29335	−	1.29335i	−0.0510047	−	0.0510047i	0.681144	−	0.732149i	$-0.261483\pi$
$643$	−1.29335	−	1.29335i	−0.0510047	−	0.0510047i	−0.732149	+	0.681144i	$0.761483\pi$
$644$	5.60834			0.221000
$645$	−31.5716	−	12.7621i	−1.24313	−	0.502509i
$646$	−5.57029			−0.219160
$647$	−2.52023	−	2.52023i	−0.0990804	−	0.0990804i	0.655829	−	0.754909i	$-0.272319\pi$
$647$	−2.52023	−	2.52023i	−0.0990804	−	0.0990804i	−0.754909	+	0.655829i	$0.772319\pi$
$648$	−0.949747	+	8.94975i	−0.0373096	+	0.351579i
$649$		−	2.27144i		−	0.0891616i
$650$	6.48808	−	3.23610i	0.254483	−	0.126930i
$651$	10.9493	+	63.8172i	0.429137	+	2.50119i
$652$	11.2933	−	11.2933i	0.442282	−	0.442282i
$653$	26.7039	−	26.7039i	1.04500	−	1.04500i	0.0460661	−	0.998938i	$-0.485332\pi$
$653$	26.7039	−	26.7039i	1.04500	−	1.04500i	0.998938	−	0.0460661i	$-0.0146685\pi$
$654$	−0.689179	−	4.01683i	−0.0269490	−	0.157070i
$655$	15.3781	−	24.8551i	0.600874	−	0.971170i
$656$			9.48373i			0.370277i
$657$	8.60460	−	18.0166i	0.335697	−	0.702895i
$658$	−22.6033	−	22.6033i	−0.881169	−	0.881169i
$659$	39.0855			1.52255			0.761277	−	0.648427i	$-0.224573\pi$
$659$	39.0855			1.52255			0.761277	+	0.648427i	$0.224573\pi$
$660$	−5.04218	+	2.13925i	−0.196267	+	0.0832701i
$661$	26.2701			1.02179			0.510895	−	0.859643i	$-0.329314\pi$
$661$	26.2701			1.02179			0.510895	+	0.859643i	$0.329314\pi$
$662$	14.5687	+	14.5687i	0.566230	+	0.566230i
$663$	−2.05071	−	1.45007i	−0.0796429	−	0.0563160i
$664$			3.13572i			0.121689i
$665$	−10.7583	−	45.6728i	−0.417188	−	1.77112i
$666$	−9.73136	−	27.5245i	−0.377083	−	1.06655i
$667$	−1.95145	+	1.95145i	−0.0755604	+	0.0755604i
$668$	10.0372	−	10.0372i	0.388351	−	0.388351i
$669$	37.8565	−	6.49514i	1.46361	−	0.251117i
$670$	7.70257	+	4.76567i	0.297576	+	0.184114i
$671$			18.3965i			0.710190i
$672$	−3.76722	+	5.32765i	−0.145324	+	0.205519i
$673$	−3.27208	−	3.27208i	−0.126129	−	0.126129i	0.641224	−	0.767354i	$-0.278427\pi$
$673$	−3.27208	−	3.27208i	−0.126129	−	0.126129i	−0.767354	+	0.641224i	$0.778427\pi$
$674$	4.13903			0.159430
$675$	4.83077	+	25.5277i	0.185936	+	0.982562i
$676$	10.8973			0.419127
$677$	22.6604	+	22.6604i	0.870909	+	0.870909i	0.992572	−	0.121662i	$-0.0388225\pi$
$677$	22.6604	+	22.6604i	0.870909	+	0.870909i	−0.121662	+	0.992572i	$0.538822\pi$
$678$	−4.05071	+	5.72856i	−0.155566	+	0.220004i
$679$			2.73882i			0.105106i
$680$	1.90154	+	1.17650i	0.0729206	+	0.0451168i
$681$	−22.6547	+	3.88693i	−0.868128	+	0.148947i
$682$	−9.92330	+	9.92330i	−0.379983	+	0.379983i
$683$	−13.0992	+	13.0992i	−0.501228	+	0.501228i	−0.911819	−	0.410592i	$-0.865322\pi$
$683$	−13.0992	+	13.0992i	−0.501228	+	0.501228i	0.410592	+	0.911819i	$0.365322\pi$
$684$	−5.57029	−	15.7552i	−0.212985	−	0.602414i
$685$	−4.22581	−	17.9401i	−0.161460	−	0.685457i
$686$			0.723056i			0.0276064i
$687$	−12.9508	−	9.15763i	−0.494106	−	0.349385i
$688$	−6.21729	−	6.21729i	−0.237032	−	0.237032i
$689$	4.82532			0.183830
$690$	5.30783	−	2.25196i	0.202066	−	0.0857305i
$691$	3.69977			0.140746			0.0703729	−	0.997521i	$-0.477581\pi$
$691$	3.69977			0.140746			0.0703729	+	0.997521i	$0.477581\pi$
$692$	−8.80660	−	8.80660i	−0.334777	−	0.334777i
$693$	−6.88808	+	14.4225i	−0.261657	+	0.547866i
$694$		−	0.830622i		−	0.0315300i
$695$	−15.1745	+	24.5259i	−0.575600	+	0.930321i
$696$	−0.542960	−	3.16460i	−0.0205808	−	0.119954i
$697$	6.70601	−	6.70601i	0.254008	−	0.254008i
$698$	−2.63649	+	2.63649i	−0.0997928	+	0.0997928i
$699$	−1.93444	−	11.2747i	−0.0731673	−	0.426450i
$700$	−5.97400	+	17.8636i	−0.225796	+	0.675182i
$701$		−	5.12087i		−	0.193412i	−0.995313	−	0.0967062i	$-0.969169\pi$
$701$		−	5.12087i		−	0.193412i	0.995313	−	0.0967062i	$-0.0308307\pi$
$702$	2.05071	−	7.25034i	0.0773990	−	0.273647i
$703$	38.3298	+	38.3298i	1.44564	+	1.44564i
$704$	−1.41421			−0.0533002
$705$	−30.4682	−	12.3161i	−1.14750	−	0.463852i
$706$	28.6553			1.07846
$707$	26.1771	+	26.1771i	0.984490	+	0.984490i
$708$	−2.27144	−	1.60615i	−0.0853658	−	0.0603627i
$709$			2.70321i			0.101521i	0.998711	+	0.0507606i	$0.0161646\pi$
$709$			2.70321i			0.101521i	−0.998711	+	0.0507606i	$0.983835\pi$
$710$	−17.0157	+	4.00807i	−0.638589	+	0.150420i
$711$	29.8256	−	10.5449i	1.11855	−	0.395466i
$712$	−2.32765	+	2.32765i	−0.0872324	+	0.0872324i
$713$	10.4461	−	10.4461i	0.391210	−	0.391210i
$714$	6.43104	−	1.10339i	0.240676	−	0.0412934i
$715$	4.46337	−	1.05135i	0.166921	−	0.0393183i
$716$		−	24.0525i		−	0.898883i
$717$	2.44852	−	3.46273i	0.0914415	−	0.129318i
$718$	−12.1659	−	12.1659i	−0.454029	−	0.454029i
$719$	14.0497			0.523964			0.261982	−	0.965073i	$-0.415624\pi$
$719$	14.0497			0.523964			0.261982	+	0.965073i	$0.415624\pi$
$720$	−1.42611	+	6.55486i	−0.0531481	+	0.244285i
$721$	−62.9352			−2.34383
$722$	8.50519	+	8.50519i	0.316530	+	0.316530i
$723$	−1.41202	+	1.99690i	−0.0525135	+	0.0742654i
$724$		−	12.1152i		−	0.450259i
$725$	−4.13705	−	8.29442i	−0.153646	−	0.308047i
$726$	15.3640	−	2.63604i	0.570210	−	0.0978326i
$727$	4.37005	−	4.37005i	0.162076	−	0.162076i	−0.621410	−	0.783486i	$-0.713440\pi$
$727$	4.37005	−	4.37005i	0.162076	−	0.162076i	0.783486	+	0.621410i	$0.213440\pi$
$728$	3.86273	−	3.86273i	0.143162	−	0.143162i
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$	7.82998	−	12.6553i	0.289801	−	0.468394i
$731$			8.79257i			0.325205i
$732$	18.3965	+	13.0083i	0.679955	+	0.480801i
$733$	25.3325	+	25.3325i	0.935678	+	0.935678i	0.998053	−	0.0623749i	$-0.0198674\pi$
$733$	25.3325	+	25.3325i	0.935678	+	0.935678i	−0.0623749	+	0.998053i	$0.519867\pi$
$734$	21.3156			0.786773
$735$	10.8791	+	25.6418i	0.401281	+	0.945814i
$736$	1.48872			0.0548750
$737$	4.05071	+	4.05071i	0.149210	+	0.149210i
$738$	25.6735	+	12.2614i	0.945053	+	0.451350i
$739$			14.8809i			0.547403i	0.961815	+	0.273701i	$0.0882480\pi$
$739$			14.8809i			0.547403i	−0.961815	+	0.273701i	$0.911752\pi$
$740$	−4.98904	−	21.1803i	−0.183401	−	0.778605i
$741$	2.36579	+	13.7888i	0.0869094	+	0.506545i
$742$	−8.86428	+	8.86428i	−0.325418	+	0.325418i
$743$	−22.6885	+	22.6885i	−0.832362	+	0.832362i	−0.987839	−	0.155478i	$-0.950308\pi$
$743$	−22.6885	+	22.6885i	−0.832362	+	0.832362i	0.155478	+	0.987839i	$0.450308\pi$
$744$	2.90647	+	16.9401i	0.106556	+	0.621055i
$745$	6.19129	+	3.83062i	0.226831	+	0.140343i
$746$			19.2757i			0.705732i
$747$	8.48872	+	4.05415i	0.310586	+	0.148334i
$748$	1.00000	+	1.00000i	0.0365636	+	0.0365636i
$749$	8.63954			0.315682
$750$	1.51901	+	19.3052i	0.0554662	+	0.704928i
$751$	30.2398			1.10347			0.551734	−	0.834020i	$-0.313966\pi$
$751$	30.2398			1.10347			0.551734	+	0.834020i	$0.313966\pi$
$752$	−6.00000	−	6.00000i	−0.218797	−	0.218797i
$753$	23.2927	+	16.4704i	0.848833	+	0.600216i
$754$			2.68811i			0.0978952i
$755$	−35.7306	−	22.1069i	−1.30037	−	0.804553i
$756$	9.55191	+	17.0863i	0.347400	+	0.621424i
$757$	−9.13779	+	9.13779i	−0.332118	+	0.332118i	−0.853391	−	0.521272i	$-0.825458\pi$
$757$	−9.13779	+	9.13779i	−0.332118	+	0.332118i	0.521272	+	0.853391i	$0.325458\pi$
$758$	10.6420	−	10.6420i	0.386535	−	0.386535i
$759$	3.59409	−	0.616649i	0.130457	−	0.0223829i
$760$	−2.85576	−	12.1238i	−0.103589	−	0.439775i
$761$		−	6.34315i		−	0.229939i	−0.993369	−	0.114969i	$-0.963323\pi$
$761$		−	6.34315i		−	0.229939i	0.993369	−	0.114969i	$-0.0366770\pi$
$762$	12.0000	−	16.9706i	0.434714	−	0.614779i
$763$	−6.26799	−	6.26799i	−0.226917	−	0.226917i
$764$	24.8114			0.897644
$765$	5.64340	−	3.62657i	0.204038	−	0.131119i
$766$	36.9084			1.33355
$767$	1.64687	+	1.64687i	0.0594650	+	0.0594650i
$768$	−1.00000	+	1.41421i	−0.0360844	+	0.0510310i
$769$		−	15.6272i		−	0.563529i	−0.959484	−	0.281765i	$-0.909080\pi$
$769$		−	15.6272i		−	0.563529i	0.959484	−	0.281765i	$-0.0909198\pi$
$770$	−6.26799	+	10.1307i	−0.225883	+	0.365086i
$771$	−14.0711	+	2.41421i	−0.506757	+	0.0869458i
$772$	−5.42907	+	5.42907i	−0.195396	+	0.195396i
$773$	1.52269	−	1.52269i	0.0547673	−	0.0547673i	−0.679193	−	0.733960i	$-0.737670\pi$
$773$	1.52269	−	1.52269i	0.0547673	−	0.0547673i	0.733960	+	0.679193i	$0.237670\pi$
$774$	−24.8691	+	8.79257i	−0.893903	+	0.316042i
$775$	22.1457	+	44.4001i	0.795496	+	1.59490i
$776$			0.727013i			0.0260982i
$777$	−51.8453	−	36.6602i	−1.85994	−	1.31518i
$778$	−26.5409	−	26.5409i	−0.951536	−	0.951536i
$779$	−52.8271			−1.89273
$780$	2.10473	−	5.20679i	0.0753614	−	0.186433i
$781$	−11.0562			−0.395623
$782$	−1.05269	−	1.05269i	−0.0376440	−	0.0376440i
$783$	−9.26890	−	2.62164i	−0.331244	−	0.0936898i
$784$			7.19193i			0.256855i
$785$	7.58235	−	1.78603i	0.270626	−	0.0637460i
$786$	−3.82843	−	22.3137i	−0.136555	−	0.795904i
$787$	−11.9438	+	11.9438i	−0.425750	+	0.425750i	−0.887178	−	0.461428i	$-0.847337\pi$
$787$	−11.9438	+	11.9438i	−0.425750	+	0.425750i	0.461428	+	0.887178i	$0.347337\pi$
$788$	−10.7995	+	10.7995i	−0.384718	+	0.384718i
$789$	−1.16171	−	6.77096i	−0.0413581	−	0.241053i
$790$	22.9511	−	5.40614i	0.816563	−	0.192342i
$791$			15.2599i			0.542579i
$792$	−1.82843	+	3.82843i	−0.0649703	+	0.136037i
$793$	−13.3381	−	13.3381i	−0.473650	−	0.473650i
$794$	1.81306			0.0643431
$795$	−4.82998	+	11.9487i	−0.171302	+	0.423775i
$796$	−8.21178			−0.291059
$797$	12.0365	+	12.0365i	0.426353	+	0.426353i	0.887384	−	0.461031i	$-0.152520\pi$
$797$	12.0365	+	12.0365i	0.426353	+	0.426353i	−0.461031	+	0.887384i	$0.652520\pi$
$798$	−29.6766	−	20.9845i	−1.05054	−	0.742843i
$799$			8.48528i			0.300188i
$800$	−1.58579	+	4.74186i	−0.0560660	+	0.167650i
$801$	3.29180	+	9.31060i	0.116310	+	0.328974i
$802$	27.1913	−	27.1913i	0.960158	−	0.960158i
$803$	6.65530	−	6.65530i	0.234861	−	0.234861i
$804$	6.91499	−	1.18642i	0.243873	−	0.0418420i
$805$	6.59823	−	10.6645i	0.232557	−	0.375873i
$806$		−	14.3895i		−	0.506847i
$807$	28.7356	−	40.6383i	1.01154	−	1.43053i
$808$	6.94865	+	6.94865i	0.244453	+	0.244453i
$809$	−42.2163			−1.48425			−0.742124	−	0.670263i	$-0.766181\pi$
$809$	−42.2163			−1.48425			−0.742124	+	0.670263i	$0.766181\pi$
$810$	15.9009	+	12.3354i	0.558700	+	0.433421i
$811$	−1.80807			−0.0634898			−0.0317449	−	0.999496i	$-0.510106\pi$
$811$	−1.80807			−0.0634898			−0.0317449	+	0.999496i	$0.510106\pi$
$812$	−4.93815	−	4.93815i	−0.173295	−	0.173295i
$813$	−29.7959	+	42.1377i	−1.04499	+	1.47784i
$814$		−	13.7622i		−	0.482366i
$815$	−8.18807	−	34.7614i	−0.286815	−	1.21764i
$816$	1.70711	−	0.292893i	0.0597607	−	0.0102533i
$817$	34.6321	−	34.6321i	1.21162	−	1.21162i
$818$	8.22934	−	8.22934i	0.287732	−	0.287732i
$819$	−5.46273	−	15.4509i	−0.190883	−	0.539899i
$820$	18.0337	+	11.1576i	0.629763	+	0.389641i
$821$		−	15.2895i		−	0.533606i	−0.963751	−	0.266803i	$-0.914033\pi$
$821$		−	15.2895i		−	0.533606i	0.963751	−	0.266803i	$-0.0859674\pi$
$822$	−11.6569	−	8.24264i	−0.406579	−	0.287495i
$823$	7.00508	+	7.00508i	0.244182	+	0.244182i	0.818578	−	0.574396i	$-0.194763\pi$
$823$	7.00508	+	7.00508i	0.244182	+	0.244182i	−0.574396	+	0.818578i	$0.694763\pi$
$824$	−16.7060			−0.581981
$825$	−1.86428	+	12.1047i	−0.0649060	+	0.421433i
$826$	−6.05071			−0.210531
$827$	2.08592	+	2.08592i	0.0725345	+	0.0725345i	0.742443	−	0.669909i	$-0.233667\pi$
$827$	2.08592	+	2.08592i	0.0725345	+	0.0725345i	−0.669909	+	0.742443i	$0.733667\pi$
$828$	1.92476	−	4.03013i	0.0668900	−	0.140057i
$829$		−	12.2194i		−	0.424399i	−0.977226	−	0.212199i	$-0.931937\pi$
$829$		−	12.2194i		−	0.424399i	0.977226	−	0.212199i	$-0.0680626\pi$
$830$	5.96268	+	3.68918i	0.206968	+	0.128053i
$831$	0.0736892	+	0.429492i	0.00255625	+	0.0148989i
$832$	1.02535	−	1.02535i	0.0355477	−	0.0355477i
$833$	5.08547	−	5.08547i	0.176201	−	0.176201i
$834$	3.77772	+	22.0182i	0.130812	+	0.762427i
$835$	−7.27731	−	30.8949i	−0.251842	−	1.06916i
$836$		−	7.87758i		−	0.272452i
$837$	49.6165	+	14.0337i	1.71500	+	0.485074i
$838$	−1.76287	−	1.76287i	−0.0608973	−	0.0608973i
$839$	−35.2466			−1.21685			−0.608423	−	0.793613i	$-0.708198\pi$
$839$	−35.2466			−1.21685			−0.608423	+	0.793613i	$0.708198\pi$
$840$	5.69858	+	13.4315i	0.196620	+	0.463431i
$841$	−25.5635			−0.881500
$842$	11.8328	+	11.8328i	0.407784	+	0.407784i
$843$	−14.5526	−	10.2902i	−0.501218	−	0.354415i
$844$			16.8979i			0.581651i
$845$	12.8207	−	20.7216i	0.441045	−	0.712845i
$846$	−24.0000	+	8.48528i	−0.825137	+	0.291730i
$847$	23.9744	−	23.9744i	0.823771	−	0.823771i
$848$	−2.35300	+	2.35300i	−0.0808025	+	0.0808025i
$849$	−7.44632	+	1.27759i	−0.255557	+	0.0438467i
$850$	4.47433	−	2.23168i	0.153468	−	0.0765461i
$851$			14.4873i			0.496618i
$852$	−7.81793	+	11.0562i	−0.267838	+	0.378780i
$853$	−9.90238	−	9.90238i	−0.339051	−	0.339051i	0.516959	−	0.856010i	$-0.327064\pi$
$853$	−9.90238	−	9.90238i	−0.339051	−	0.339051i	−0.856010	+	0.516959i	$0.827064\pi$
$854$	49.0051			1.67692
$855$	−36.5125	−	7.94387i	−1.24870	−	0.271675i
$856$	2.29335			0.0783850
$857$	34.2117	+	34.2117i	1.16865	+	1.16865i	0.982527	+	0.186121i	$0.0595916\pi$
$857$	34.2117	+	34.2117i	1.16865	+	1.16865i	0.186121	+	0.982527i	$0.440408\pi$
$858$	2.05071	−	2.90014i	0.0700100	−	0.0990091i
$859$			37.9987i			1.29650i	0.761428	+	0.648250i	$0.224499\pi$
$859$			37.9987i			1.29650i	−0.761428	+	0.648250i	$0.775501\pi$
$860$	−19.1371	+	4.50775i	−0.652568	+	0.153713i
$861$	60.9903	−	10.4643i	2.07854	−	0.356622i
$862$	8.90647	−	8.90647i	0.303355	−	0.303355i
$863$	5.14071	−	5.14071i	0.174992	−	0.174992i	−0.614177	−	0.789169i	$-0.710512\pi$
$863$	5.14071	−	5.14071i	0.174992	−	0.174992i	0.789169	+	0.614177i	$0.210512\pi$
$864$	2.53553	+	4.53553i	0.0862606	+	0.154302i
$865$	−27.1071	+	6.38509i	−0.921668	+	0.217100i
$866$			36.0097i			1.22366i
$867$	−1.41421	−	1.00000i	−0.0480292	−	0.0339618i
$868$	26.4339	+	26.4339i	0.897226	+	0.897226i
$869$	14.9128			0.505882
$870$	−6.65640	−	2.69070i	−0.225673	−	0.0912234i
$871$	−5.87380			−0.199026
$872$	−1.66383	−	1.66383i	−0.0563442	−	0.0563442i
$873$	1.96810	+	0.939950i	0.0666102	+	0.0318125i
$874$			8.29262i			0.280502i
$875$	26.9399	+	32.3764i	0.910736	+	1.09452i
$876$	−1.94929	−	11.3613i	−0.0658605	−	0.383863i
$877$	−11.1355	+	11.1355i	−0.376019	+	0.376019i	−0.869664	−	0.493645i	$-0.835664\pi$
$877$	−11.1355	+	11.1355i	−0.376019	+	0.376019i	0.493645	+	0.869664i	$0.335664\pi$
$878$	−12.0660	+	12.0660i	−0.407207	+	0.407207i
$879$	4.48937	+	26.1659i	0.151423	+	0.882555i
$880$	−1.66383	+	2.68918i	−0.0560875	+	0.0906522i
$881$		−	39.8676i		−	1.34317i	−0.740926	−	0.671587i	$-0.765613\pi$
$881$		−	39.8676i		−	1.34317i	0.740926	−	0.671587i	$-0.234387\pi$
$882$	19.4693	+	9.29840i	0.655567	+	0.313093i
$883$	−5.79102	−	5.79102i	−0.194883	−	0.194883i	0.602919	−	0.797802i	$-0.294004\pi$
$883$	−5.79102	−	5.79102i	−0.194883	−	0.194883i	−0.797802	+	0.602919i	$0.794004\pi$
$884$	−1.45007			−0.0487711
$885$	−5.72650	+	2.42958i	−0.192494	+	0.0816695i
$886$	−19.5245			−0.655937
$887$	−27.4066	−	27.4066i	−0.920224	−	0.920224i	0.0768213	−	0.997045i	$-0.475523\pi$
$887$	−27.4066	−	27.4066i	−0.920224	−	0.920224i	−0.997045	+	0.0768213i	$0.975523\pi$
$888$	−13.7622	−	9.73136i	−0.461830	−	0.326563i
$889$		−	45.2066i		−	1.51618i
$890$	1.68763	+	7.16460i	0.0565694	+	0.240158i
$891$	8.00000	+	9.89949i	0.268010	+	0.331646i
$892$	15.6807	−	15.6807i	0.525027	−	0.525027i
$893$	33.4218	−	33.4218i	1.11842	−	1.11842i
$894$	5.55824	−	0.953643i	0.185895	−	0.0318946i
$895$	−45.7367	−	28.2978i	−1.52881	−	0.945891i
$896$			3.76722i			0.125854i
$897$	−2.15875	+	3.05293i	−0.0720786	+	0.101934i
$898$	5.18642	+	5.18642i	0.173073	+	0.173073i
$899$	−18.3956			−0.613528
$900$	10.7865	+	10.4236i	0.359549	+	0.347454i
$901$	3.32765			0.110860
$902$	9.48373	+	9.48373i	0.315774	+	0.315774i
$903$	−33.1235	+	46.8438i	−1.10228	+	1.55886i
$904$			4.05071i			0.134725i
$905$	−23.0376	−	14.2536i	−0.765794	−	0.473806i
$906$	−32.0772	+	5.50357i	−1.06569	+	0.182844i
$907$	16.7115	−	16.7115i	0.554897	−	0.554897i	−0.372953	−	0.927850i	$-0.621655\pi$
$907$	16.7115	−	16.7115i	0.554897	−	0.554897i	0.927850	+	0.372953i	$0.121655\pi$
$908$	−9.38387	+	9.38387i	−0.311415	+	0.311415i
$909$	27.7946	−	9.82688i	0.921889	−	0.325937i
$910$	−2.80061	−	11.8896i	−0.0928394	−	0.394138i
$911$		−	54.7460i		−	1.81382i	−0.421327	−	0.906909i	$-0.638436\pi$
$911$		−	54.7460i		−	1.81382i	0.421327	−	0.906909i	$-0.361564\pi$
$912$	−7.87758	−	5.57029i	−0.260853	−	0.184451i
$913$	3.13572	+	3.13572i	0.103777	+	0.103777i
$914$	−13.8300			−0.457455
$915$	46.3793	−	19.6774i	1.53325	−	0.650514i
$916$	−9.15763			−0.302577
$917$	−34.8190	−	34.8190i	−1.14983	−	1.14983i
$918$	1.41421	−	5.00000i	0.0466760	−	0.165025i
$919$		−	39.5918i		−	1.30601i	−0.757353	−	0.653006i	$-0.773508\pi$
$919$		−	39.5918i		−	1.30601i	0.757353	−	0.653006i	$-0.226492\pi$
$920$	1.75149	−	2.83086i	0.0577448	−	0.0933307i
$921$	−1.76786	−	10.3038i	−0.0582530	−	0.339523i
$922$	20.8890	−	20.8890i	0.687942	−	0.687942i
$923$	8.01614	−	8.01614i	0.263854	−	0.263854i
$924$	1.56043	+	9.09487i	0.0513345	+	0.299199i
$925$	−46.1448	−	15.4319i	−1.51723	−	0.507397i
$926$			16.9706i			0.557687i
$927$	−21.5991	+	45.2250i	−0.709407	+	1.48538i
$928$	−1.31082	−	1.31082i	−0.0430298	−	0.0430298i
$929$	−25.2320			−0.827835			−0.413918	−	0.910314i	$-0.635840\pi$
$929$	−25.2320			−0.827835			−0.413918	+	0.910314i	$0.635840\pi$
$930$	35.6317	+	14.4033i	1.16841	+	0.472304i
$931$	−40.0612			−1.31295
$932$	−4.67015	−	4.67015i	−0.152976	−	0.152976i
$933$	−33.7609	−	23.8726i	−1.10528	−	0.781553i
$934$			37.8466i			1.23838i
$935$	3.07804	−	0.725034i	0.100663	−	0.0237112i
$936$	−1.45007	−	4.10141i	−0.0473970	−	0.134059i
$937$	−12.0288	+	12.0288i	−0.392964	+	0.392964i	−0.875742	−	0.482779i	$-0.839628\pi$
$937$	−12.0288	+	12.0288i	−0.392964	+	0.392964i	0.482779	+	0.875742i	$0.339628\pi$
$938$	10.7904	−	10.7904i	0.352318	−	0.352318i
$939$	−2.67235	+	0.458503i	−0.0872088	+	0.0149627i
$940$	−18.4682	+	4.35021i	−0.602367	+	0.141888i
$941$		−	9.88167i		−	0.322133i	−0.986944	−	0.161067i	$-0.948507\pi$
$941$		−	9.88167i		−	0.322133i	0.986944	−	0.161067i	$-0.0514934\pi$
$942$	3.48373	−	4.92674i	0.113506	−	0.160522i
$943$	−9.98339	−	9.98339i	−0.325104	−	0.325104i
$944$	−1.60615			−0.0522756
$945$	43.7282	+	1.93882i	1.42248	+	0.0630698i
$946$	−12.4346			−0.404283
$947$	13.8871	+	13.8871i	0.451270	+	0.451270i	0.895776	−	0.444506i	$-0.146621\pi$
$947$	13.8871	+	13.8871i	0.451270	+	0.451270i	−0.444506	+	0.895776i	$0.646621\pi$
$948$	10.5449	−	14.9128i	0.342484	−	0.484345i
$949$			9.65065i			0.313273i
$950$	−26.4136	−	8.83329i	−0.856969	−	0.286590i
$951$	−58.6726	+	10.0666i	−1.90259	+	0.326433i
$952$	2.66383	−	2.66383i	0.0863351	−	0.0863351i
$953$	−4.32214	+	4.32214i	−0.140008	+	0.140008i	−0.773637	−	0.633629i	$-0.781565\pi$
$953$	−4.32214	+	4.32214i	−0.140008	+	0.140008i	0.633629	+	0.773637i	$0.281565\pi$
$954$	3.32765	+	9.41202i	0.107737	+	0.304725i
$955$	29.1906	−	47.1798i	0.944587	−	1.52670i
$956$		−	2.44852i		−	0.0791907i
$957$	−3.70756	−	2.62164i	−0.119848	−	0.0847456i
$958$	−14.1745	−	14.1745i	−0.457956	−	0.457956i
$959$	−31.0518			−1.00272
$960$	1.51268	+	3.56536i	0.0488214	+	0.115072i
$961$	67.4718			2.17651
$962$	9.97809	+	9.97809i	0.321706	+	0.321706i
$963$	2.96505	−	6.20834i	0.0955475	−	0.200061i
$964$			1.41202i			0.0454781i
$965$	3.93626	+	16.7109i	0.126713	+	0.537942i
$966$	−1.64265	−	9.57404i	−0.0528512	−	0.308040i
$967$	22.8719	−	22.8719i	0.735512	−	0.735512i	−0.236194	−	0.971706i	$-0.575900\pi$
$967$	22.8719	−	22.8719i	0.735512	−	0.735512i	0.971706	+	0.236194i	$0.0759000\pi$
$968$	6.36396	−	6.36396i	0.204545	−	0.204545i
$969$	1.63150	+	9.50908i	0.0524114	+	0.305476i
$970$	1.38244	+	0.855333i	0.0443875	+	0.0274631i
$971$			30.9675i			0.993793i	0.867810	+	0.496897i	$0.165527\pi$
$971$			30.9675i			0.993793i	−0.867810	+	0.496897i	$0.834473\pi$
$972$	15.5563	−	1.00000i	0.498970	−	0.0320750i
$973$	34.3579	+	34.3579i	1.10146	+	1.10146i
$974$	43.2200			1.38486
$975$	−7.42468	−	10.1280i	−0.237780	−	0.324356i
$976$	13.0083			0.416386
$977$	−26.0667	−	26.0667i	−0.833947	−	0.833947i	0.154107	−	0.988054i	$-0.450750\pi$
$977$	−26.0667	−	26.0667i	−0.833947	−	0.833947i	−0.988054	+	0.154107i	$0.950750\pi$
$978$	−22.5867	−	15.9712i	−0.722243	−	0.510703i
$979$			4.65530i			0.148784i
$980$	13.6757	+	8.46133i	0.436855	+	0.270287i
$981$	−6.65530	+	2.35300i	−0.212487	+	0.0751257i
$982$	−6.03022	+	6.03022i	−0.192432	+	0.192432i
$983$	−0.337726	+	0.337726i	−0.0107718	+	0.0107718i	−0.712472	−	0.701700i	$-0.752425\pi$
$983$	−0.337726	+	0.337726i	−0.0107718	+	0.0107718i	0.701700	+	0.712472i	$0.252425\pi$
$984$	16.1897	−	2.77772i	0.516110	−	0.0885505i
$985$	7.83004	+	33.2414i	0.249486	+	1.05916i
$986$			1.85378i			0.0590364i
$987$	−31.9659	+	45.2066i	−1.01749	+	1.43894i
$988$	5.71152	+	5.71152i	0.181708	+	0.181708i
$989$	13.0897			0.416228
$990$	5.12875	+	7.98098i	0.163002	+	0.253652i
$991$	24.2621			0.770710			0.385355	−	0.922769i	$-0.374079\pi$
$991$	24.2621			0.770710			0.385355	+	0.922769i	$0.374079\pi$
$992$	7.01683	+	7.01683i	0.222785	+	0.222785i
$993$	20.6033	−	29.1375i	0.653826	−	0.924650i
$994$			29.4518i			0.934155i
$995$	−9.66118	+	15.6150i	−0.306280	+	0.495029i
$996$	5.35300	−	0.918430i	0.169616	−	0.0291016i
$997$	−31.8517	+	31.8517i	−1.00875	+	1.00875i	−0.00879133	+	0.999961i	$0.502798\pi$
$997$	−31.8517	+	31.8517i	−1.00875	+	1.00875i	−0.999961	+	0.00879133i	$0.997202\pi$
$998$	−9.31216	+	9.31216i	−0.294771	+	0.294771i
$999$	−44.1369	+	24.6742i	−1.39643	+	0.780657i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	510.2.l.d.443.2	yes	8
3.2	odd	2		510.2.l.e.443.3	yes	8
5.2	odd	4		510.2.l.e.137.3	yes	8
15.2	even	4	inner	510.2.l.d.137.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.l.d.137.2	✓	8	15.2	even	4	inner
510.2.l.d.443.2	yes	8	1.1	even	1	trivial
510.2.l.e.137.3	yes	8	5.2	odd	4
510.2.l.e.443.3	yes	8	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.00000 + 1.41421i) q^{3} +1.00000i q^{4} +(1.90154 + 1.17650i) q^{5} +(1.70711 - 0.292893i) q^{6} +(2.66383 - 2.66383i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.00000 + 1.41421i) q^{3} +1.00000i q^{4} +(1.90154 + 1.17650i) q^{5} +(1.70711 - 0.292893i) q^{6} +(2.66383 - 2.66383i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.00000 - 2.82843i) q^{9} +(-0.512677 - 2.17650i) q^{10} -1.41421i q^{11} +(-1.41421 - 1.00000i) q^{12} +(1.02535 + 1.02535i) q^{13} -3.76722 q^{14} +(-3.56536 + 1.51268i) q^{15} -1.00000 q^{16} +(0.707107 + 0.707107i) q^{17} +(-1.29289 + 2.70711i) q^{18} -5.57029i q^{19} +(-1.17650 + 1.90154i) q^{20} +(1.10339 + 6.43104i) q^{21} +(-1.00000 + 1.00000i) q^{22} +(1.05269 - 1.05269i) q^{23} +(0.292893 + 1.70711i) q^{24} +(2.23168 + 4.47433i) q^{25} -1.45007i q^{26} +(5.00000 + 1.41421i) q^{27} +(2.66383 + 2.66383i) q^{28} -1.85378 q^{29} +(3.59072 + 1.45147i) q^{30} +9.92330 q^{31} +(0.707107 + 0.707107i) q^{32} +(2.00000 + 1.41421i) q^{33} -1.00000i q^{34} +(8.19936 - 1.93137i) q^{35} +(2.82843 - 1.00000i) q^{36} +(-6.88111 + 6.88111i) q^{37} +(-3.93879 + 3.93879i) q^{38} +(-2.47542 + 0.424715i) q^{39} +(2.17650 - 0.512677i) q^{40} -9.48373i q^{41} +(3.76722 - 5.32765i) q^{42} +(6.21729 + 6.21729i) q^{43} +1.41421 q^{44} +(1.42611 - 6.55486i) q^{45} -1.48872 q^{46} +(6.00000 + 6.00000i) q^{47} +(1.00000 - 1.41421i) q^{48} -7.19193i q^{49} +(1.58579 - 4.74186i) q^{50} +(-1.70711 + 0.292893i) q^{51} +(-1.02535 + 1.02535i) q^{52} +(2.35300 - 2.35300i) q^{53} +(-2.53553 - 4.53553i) q^{54} +(1.66383 - 2.68918i) q^{55} -3.76722i q^{56} +(7.87758 + 5.57029i) q^{57} +(1.31082 + 1.31082i) q^{58} +1.60615 q^{59} +(-1.51268 - 3.56536i) q^{60} -13.0083 q^{61} +(-7.01683 - 7.01683i) q^{62} +(-10.1983 - 4.87061i) q^{63} -1.00000i q^{64} +(0.743417 + 3.15608i) q^{65} +(-0.414214 - 2.41421i) q^{66} +(-2.86428 + 2.86428i) q^{67} +(-0.707107 + 0.707107i) q^{68} +(0.436037 + 2.54141i) q^{69} +(-7.16350 - 4.43214i) q^{70} -7.81793i q^{71} +(-2.70711 - 1.29289i) q^{72} +(4.70601 + 4.70601i) q^{73} +9.73136 q^{74} +(-8.55934 - 1.31825i) q^{75} +5.57029 q^{76} +(-3.76722 - 3.76722i) q^{77} +(2.05071 + 1.45007i) q^{78} +10.5449i q^{79} +(-1.90154 - 1.17650i) q^{80} +(-7.00000 + 5.65685i) q^{81} +(-6.70601 + 6.70601i) q^{82} +(-2.21729 + 2.21729i) q^{83} +(-6.43104 + 1.10339i) q^{84} +(0.512677 + 2.17650i) q^{85} -8.79257i q^{86} +(1.85378 - 2.62164i) q^{87} +(-1.00000 - 1.00000i) q^{88} -3.29180 q^{89} +(-5.64340 + 3.62657i) q^{90} +5.46273 q^{91} +(1.05269 + 1.05269i) q^{92} +(-9.92330 + 14.0337i) q^{93} -8.48528i q^{94} +(6.55346 - 10.5921i) q^{95} +(-1.70711 + 0.292893i) q^{96} +(-0.514076 + 0.514076i) q^{97} +(-5.08547 + 5.08547i) q^{98} +(-4.00000 + 1.41421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3} + 4 q^{5} + 8 q^{6} + 8 q^{7} - 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^3 + 4 * q^5 + 8 * q^6 + 8 * q^7 - 8 * q^9	\( 8 q - 8 q^{3} + 4 q^{5} + 8 q^{6} + 8 q^{7} - 8 q^{9} - 4 q^{10} + 8 q^{13} + 8 q^{14} - 4 q^{15} - 8 q^{16} - 16 q^{18} + 4 q^{20} - 16 q^{21} - 8 q^{22} - 16 q^{23} + 8 q^{24} + 8 q^{25} + 40 q^{27} + 8 q^{28} + 8 q^{29} + 4 q^{30} - 8 q^{31} + 16 q^{33} + 24 q^{35} - 8 q^{37} - 16 q^{38} - 24 q^{39} + 4 q^{40} - 8 q^{42} + 16 q^{43} - 4 q^{45} + 8 q^{46} + 48 q^{47} + 8 q^{48} + 24 q^{50} - 8 q^{51} - 8 q^{52} - 8 q^{53} + 8 q^{54} + 32 q^{57} + 24 q^{58} - 32 q^{59} - 12 q^{60} - 24 q^{61} - 16 q^{62} + 8 q^{63} - 24 q^{65} + 8 q^{66} - 16 q^{67} + 8 q^{69} - 16 q^{72} - 16 q^{73} + 24 q^{74} - 32 q^{75} - 16 q^{76} + 8 q^{77} + 16 q^{78} - 4 q^{80} - 56 q^{81} + 16 q^{83} + 4 q^{85} - 8 q^{87} - 8 q^{88} + 16 q^{89} + 4 q^{90} - 64 q^{91} - 16 q^{92} + 8 q^{93} + 32 q^{95} - 8 q^{96} + 16 q^{97} - 8 q^{98} - 32 q^{99}+O(q^{100}) \) 8 * q - 8 * q^3 + 4 * q^5 + 8 * q^6 + 8 * q^7 - 8 * q^9 - 4 * q^10 + 8 * q^13 + 8 * q^14 - 4 * q^15 - 8 * q^16 - 16 * q^18 + 4 * q^20 - 16 * q^21 - 8 * q^22 - 16 * q^23 + 8 * q^24 + 8 * q^25 + 40 * q^27 + 8 * q^28 + 8 * q^29 + 4 * q^30 - 8 * q^31 + 16 * q^33 + 24 * q^35 - 8 * q^37 - 16 * q^38 - 24 * q^39 + 4 * q^40 - 8 * q^42 + 16 * q^43 - 4 * q^45 + 8 * q^46 + 48 * q^47 + 8 * q^48 + 24 * q^50 - 8 * q^51 - 8 * q^52 - 8 * q^53 + 8 * q^54 + 32 * q^57 + 24 * q^58 - 32 * q^59 - 12 * q^60 - 24 * q^61 - 16 * q^62 + 8 * q^63 - 24 * q^65 + 8 * q^66 - 16 * q^67 + 8 * q^69 - 16 * q^72 - 16 * q^73 + 24 * q^74 - 32 * q^75 - 16 * q^76 + 8 * q^77 + 16 * q^78 - 4 * q^80 - 56 * q^81 + 16 * q^83 + 4 * q^85 - 8 * q^87 - 8 * q^88 + 16 * q^89 + 4 * q^90 - 64 * q^91 - 16 * q^92 + 8 * q^93 + 32 * q^95 - 8 * q^96 + 16 * q^97 - 8 * q^98 - 32 * q^99

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