LMFDB - Embedded newform 560.2.bc.a.251.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(251,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("560.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bc (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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$64$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			251.2
Character	$\chi$	$=$	560.251
Dual form			560.2.bc.a.531.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40740 + 0.138663i) q^{2} +(0.176544 - 0.176544i) q^{3} +(1.96155 - 0.390307i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.223988 + 0.272948i) q^{6} +(-2.53089 - 0.771085i) q^{7} +(-2.70656 + 0.821311i) q^{8} +2.93766i q^{9} +O(q^{10})$	\(q+(-1.40740 + 0.138663i) q^{2} +(0.176544 - 0.176544i) q^{3} +(1.96155 - 0.390307i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.223988 + 0.272948i) q^{6} +(-2.53089 - 0.771085i) q^{7} +(-2.70656 + 0.821311i) q^{8} +2.93766i q^{9} +(-0.897132 + 1.09323i) q^{10} +(0.978755 - 0.978755i) q^{11} +(0.277393 - 0.415206i) q^{12} +(2.57707 + 2.57707i) q^{13} +(3.66890 + 0.734285i) q^{14} -0.249671i q^{15} +(3.69532 - 1.53121i) q^{16} +7.40385i q^{17} +(-0.407344 - 4.13447i) q^{18} +(1.84697 - 1.84697i) q^{19} +(1.11103 - 1.66301i) q^{20} +(-0.582946 + 0.310684i) q^{21} +(-1.24178 + 1.51322i) q^{22} +3.59564 q^{23} +(-0.332830 + 0.622825i) q^{24} -1.00000i q^{25} +(-3.98432 - 3.26963i) q^{26} +(1.04826 + 1.04826i) q^{27} +(-5.26542 - 0.524693i) q^{28} +(3.00471 - 3.00471i) q^{29} +(0.0346201 + 0.351387i) q^{30} +10.5897 q^{31} +(-4.98847 + 2.66743i) q^{32} -0.345587i q^{33} +(-1.02664 - 10.4202i) q^{34} +(-2.33485 + 1.24437i) q^{35} +(1.14659 + 5.76236i) q^{36} +(-6.74670 - 6.74670i) q^{37} +(-2.34331 + 2.85552i) q^{38} +0.909936 q^{39} +(-1.33307 + 2.49458i) q^{40} -6.05682 q^{41} +(0.777357 - 0.518090i) q^{42} +(1.28129 - 1.28129i) q^{43} +(1.53786 - 2.30189i) q^{44} +(2.07724 + 2.07724i) q^{45} +(-5.06051 + 0.498581i) q^{46} +3.23567 q^{47} +(0.382062 - 0.922714i) q^{48} +(5.81085 + 3.90307i) q^{49} +(0.138663 + 1.40740i) q^{50} +(1.30711 + 1.30711i) q^{51} +(6.06090 + 4.04920i) q^{52} +(6.09045 + 6.09045i) q^{53} +(-1.62068 - 1.32997i) q^{54} -1.38417i q^{55} +(7.48331 + 0.00833549i) q^{56} -0.652143i q^{57} +(-3.81218 + 4.64546i) q^{58} +(9.72909 + 9.72909i) q^{59} +(-0.0974485 - 0.489742i) q^{60} +(8.74709 + 8.74709i) q^{61} +(-14.9040 + 1.46840i) q^{62} +(2.26519 - 7.43492i) q^{63} +(6.65090 - 4.44585i) q^{64} +3.64453 q^{65} +(0.0479200 + 0.486379i) q^{66} +(-2.29246 - 2.29246i) q^{67} +(2.88978 + 14.5230i) q^{68} +(0.634791 - 0.634791i) q^{69} +(3.11352 - 2.07509i) q^{70} -10.7355 q^{71} +(-2.41273 - 7.95095i) q^{72} +4.00333 q^{73} +(10.4308 + 8.55978i) q^{74} +(-0.176544 - 0.176544i) q^{75} +(2.90202 - 4.34379i) q^{76} +(-3.23183 + 1.72242i) q^{77} +(-1.28064 + 0.126174i) q^{78} +1.12435i q^{79} +(1.53026 - 3.69572i) q^{80} -8.44286 q^{81} +(8.52437 - 0.839854i) q^{82} +(-1.73594 + 1.73594i) q^{83} +(-1.02221 + 0.836949i) q^{84} +(5.23531 + 5.23531i) q^{85} +(-1.62562 + 1.98095i) q^{86} -1.06093i q^{87} +(-1.84519 + 3.45292i) q^{88} -7.69624 q^{89} +(-3.21154 - 2.63547i) q^{90} +(-4.53516 - 8.50945i) q^{91} +(7.05302 - 1.40341i) q^{92} +(1.86956 - 1.86956i) q^{93} +(-4.55388 + 0.448667i) q^{94} -2.61200i q^{95} +(-0.409767 + 1.35161i) q^{96} -10.9023i q^{97} +(-8.71940 - 4.68743i) q^{98} +(2.87525 + 2.87525i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 4 q^{4}+O(q^{10}) $ 128 * q - 4 * q^4	$ 128 q - 4 q^{4} + 8 q^{11} - 8 q^{14} + 20 q^{16} + 20 q^{18} - 52 q^{22} - 16 q^{23} + 44 q^{28} + 16 q^{29} + 40 q^{32} + 16 q^{37} + 60 q^{42} - 8 q^{43} - 108 q^{44} - 40 q^{46} - 4 q^{50} + 80 q^{51} + 16 q^{53} + 12 q^{56} - 76 q^{58} - 56 q^{60} - 52 q^{64} + 40 q^{67} - 8 q^{70} - 64 q^{71} - 36 q^{72} + 60 q^{74} - 48 q^{78} - 128 q^{81} - 32 q^{84} + 76 q^{86} + 20 q^{88} - 32 q^{91} + 64 q^{92} - 76 q^{98} - 40 q^{99}+O(q^{100}) $ 128 * q - 4 * q^4 + 8 * q^11 - 8 * q^14 + 20 * q^16 + 20 * q^18 - 52 * q^22 - 16 * q^23 + 44 * q^28 + 16 * q^29 + 40 * q^32 + 16 * q^37 + 60 * q^42 - 8 * q^43 - 108 * q^44 - 40 * q^46 - 4 * q^50 + 80 * q^51 + 16 * q^53 + 12 * q^56 - 76 * q^58 - 56 * q^60 - 52 * q^64 + 40 * q^67 - 8 * q^70 - 64 * q^71 - 36 * q^72 + 60 * q^74 - 48 * q^78 - 128 * q^81 - 32 * q^84 + 76 * q^86 + 20 * q^88 - 32 * q^91 + 64 * q^92 - 76 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.40740	+	0.138663i	−0.995182	+	0.0980492i
$2$	−1.40740	+	0.138663i	−0.995182	+	0.0980492i
$3$	0.176544	−	0.176544i	0.101928	−	0.101928i	−0.654304	−	0.756232i	$-0.727038\pi$
$3$	0.176544	−	0.176544i	0.101928	−	0.101928i	0.756232	+	0.654304i	$0.227038\pi$
$4$	1.96155	−	0.390307i	0.980773	−	0.195154i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	−0.223988	+	0.272948i	−0.0914428	+	0.111431i
$7$	−2.53089	−	0.771085i	−0.956588	−	0.291443i
$7$	−2.53089	−	0.771085i	−0.956588	−	0.291443i
$8$	−2.70656	+	0.821311i	−0.956912	+	0.290377i
$9$			2.93766i			0.979221i
$10$	−0.897132	+	1.09323i	−0.283698	+	0.345710i
$11$	0.978755	−	0.978755i	0.295106	−	0.295106i	−0.543988	−	0.839093i	$-0.683086\pi$
$11$	0.978755	−	0.978755i	0.295106	−	0.295106i	0.839093	+	0.543988i	$0.183086\pi$
$12$	0.277393	−	0.415206i	0.0800765	−	0.119860i
$13$	2.57707	+	2.57707i	0.714752	+	0.714752i	0.967525	−	0.252774i	$-0.0813428\pi$
$13$	2.57707	+	2.57707i	0.714752	+	0.714752i	−0.252774	+	0.967525i	$0.581343\pi$
$14$	3.66890	+	0.734285i	0.980555	+	0.196246i
$15$		−	0.249671i		−	0.0644649i
$16$	3.69532	−	1.53121i	0.923830	−	0.382802i
$17$			7.40385i			1.79570i	0.440304	+	0.897849i	$0.354871\pi$
$17$			7.40385i			1.79570i	−0.440304	+	0.897849i	$0.645129\pi$
$18$	−0.407344	−	4.13447i	−0.0960119	−	0.974503i
$19$	1.84697	−	1.84697i	0.423723	−	0.423723i	−0.462760	−	0.886483i	$-0.653141\pi$
$19$	1.84697	−	1.84697i	0.423723	−	0.423723i	0.886483	+	0.462760i	$0.153141\pi$
$20$	1.11103	−	1.66301i	0.248435	−	0.371861i
$21$	−0.582946	+	0.310684i	−0.127209	+	0.0677969i
$22$	−1.24178	+	1.51322i	−0.264749	+	0.322619i
$23$	3.59564			0.749744			0.374872	−	0.927077i	$-0.377687\pi$
$23$	3.59564			0.749744			0.374872	+	0.927077i	$0.377687\pi$
$24$	−0.332830	+	0.622825i	−0.0679385	+	0.127134i
$25$		−	1.00000i		−	0.200000i
$26$	−3.98432	−	3.26963i	−0.781389	−	0.641227i
$27$	1.04826	+	1.04826i	0.201738	+	0.201738i
$28$	−5.26542	−	0.524693i	−0.995072	−	0.0991576i
$29$	3.00471	−	3.00471i	0.557960	−	0.557960i	−0.370766	−	0.928726i	$-0.620905\pi$
$29$	3.00471	−	3.00471i	0.557960	−	0.557960i	0.928726	+	0.370766i	$0.120905\pi$
$30$	0.0346201	+	0.351387i	0.00632073	+	0.0641543i
$31$	10.5897			1.90197			0.950985	−	0.309237i	$-0.100074\pi$
$31$	10.5897			1.90197			0.950985	+	0.309237i	$0.100074\pi$
$32$	−4.98847	+	2.66743i	−0.881845	+	0.471539i
$33$		−	0.345587i		−	0.0601590i
$34$	−1.02664	−	10.4202i	−0.176067	−	1.78705i
$35$	−2.33485	+	1.24437i	−0.394662	+	0.210337i
$36$	1.14659	+	5.76236i	0.191098	+	0.960394i
$37$	−6.74670	−	6.74670i	−1.10915	−	1.10915i	−0.993262	−	0.115888i	$-0.963029\pi$
$37$	−6.74670	−	6.74670i	−1.10915	−	1.10915i	−0.115888	−	0.993262i	$-0.536971\pi$
$38$	−2.34331	+	2.85552i	−0.380136	+	0.463227i
$39$	0.909936			0.145706
$40$	−1.33307	+	2.49458i	−0.210777	+	0.394428i
$41$	−6.05682			−0.945917			−0.472958	−	0.881085i	$-0.656814\pi$
$41$	−6.05682			−0.945917			−0.472958	+	0.881085i	$0.656814\pi$
$42$	0.777357	−	0.518090i	0.119949	−	0.0799430i
$43$	1.28129	−	1.28129i	0.195395	−	0.195395i	−0.602628	−	0.798022i	$-0.705880\pi$
$43$	1.28129	−	1.28129i	0.195395	−	0.195395i	0.798022	+	0.602628i	$0.205880\pi$
$44$	1.53786	−	2.30189i	0.231841	−	0.347023i
$45$	2.07724	+	2.07724i	0.309657	+	0.309657i
$46$	−5.06051	+	0.498581i	−0.746131	+	0.0735118i
$47$	3.23567			0.471971			0.235986	−	0.971757i	$-0.424168\pi$
$47$	3.23567			0.471971			0.235986	+	0.971757i	$0.424168\pi$
$48$	0.382062	−	0.922714i	0.0551458	−	0.133182i
$49$	5.81085	+	3.90307i	0.830122	+	0.557582i
$50$	0.138663	+	1.40740i	0.0196098	+	0.199036i
$51$	1.30711	+	1.30711i	0.183032	+	0.183032i
$52$	6.06090	+	4.04920i	0.840495	+	0.561523i
$53$	6.09045	+	6.09045i	0.836588	+	0.836588i	0.988408	−	0.151820i	$-0.0485135\pi$
$53$	6.09045	+	6.09045i	0.836588	+	0.836588i	−0.151820	+	0.988408i	$0.548514\pi$
$54$	−1.62068	−	1.32997i	−0.220546	−	0.180986i
$55$		−	1.38417i		−	0.186641i
$56$	7.48331	+	0.00833549i	0.999999	+	0.00111388i
$57$		−	0.652143i		−	0.0863784i
$58$	−3.81218	+	4.64546i	−0.500564	+	0.609979i
$59$	9.72909	+	9.72909i	1.26662	+	1.26662i	0.947823	+	0.318797i	$0.103279\pi$
$59$	9.72909	+	9.72909i	1.26662	+	1.26662i	0.318797	+	0.947823i	$0.396721\pi$
$60$	−0.0974485	−	0.489742i	−0.0125805	−	0.0632254i
$61$	8.74709	+	8.74709i	1.11995	+	1.11995i	0.991748	+	0.128202i	$0.0409206\pi$
$61$	8.74709	+	8.74709i	1.11995	+	1.11995i	0.128202	+	0.991748i	$0.459079\pi$
$62$	−14.9040	+	1.46840i	−1.89281	+	0.186487i
$63$	2.26519	−	7.43492i	0.285387	−	0.936712i
$64$	6.65090	−	4.44585i	0.831362	−	0.555731i
$65$	3.64453			0.452049
$66$	0.0479200	+	0.486379i	0.00589854	+	0.0598692i
$67$	−2.29246	−	2.29246i	−0.280069	−	0.280069i	0.553068	−	0.833136i	$-0.313457\pi$
$67$	−2.29246	−	2.29246i	−0.280069	−	0.280069i	−0.833136	+	0.553068i	$0.813457\pi$
$68$	2.88978	+	14.5230i	0.350437	+	1.76117i
$69$	0.634791	−	0.634791i	0.0764198	−	0.0764198i
$70$	3.11352	−	2.07509i	0.372137	−	0.248020i
$71$	−10.7355			−1.27407			−0.637034	−	0.770835i	$-0.719839\pi$
$71$	−10.7355			−1.27407			−0.637034	+	0.770835i	$0.719839\pi$
$72$	−2.41273	−	7.95095i	−0.284344	−	0.937029i
$73$	4.00333			0.468554			0.234277	−	0.972170i	$-0.424728\pi$
$73$	4.00333			0.468554			0.234277	+	0.972170i	$0.424728\pi$
$74$	10.4308	+	8.55978i	1.21256	+	0.995055i
$75$	−0.176544	−	0.176544i	−0.0203856	−	0.0203856i
$76$	2.90202	−	4.34379i	0.332885	−	0.498267i
$77$	−3.23183	+	1.72242i	−0.368301	+	0.196288i
$78$	−1.28064	+	0.126174i	−0.145004	+	0.0142864i
$79$			1.12435i			0.126499i	0.997998	+	0.0632494i	$0.0201464\pi$
$79$			1.12435i			0.126499i	−0.997998	+	0.0632494i	$0.979854\pi$
$80$	1.53026	−	3.69572i	0.171088	−	0.413194i
$81$	−8.44286			−0.938096
$82$	8.52437	−	0.839854i	0.941359	−	0.0927464i
$83$	−1.73594	+	1.73594i	−0.190544	+	0.190544i	−0.795931	−	0.605387i	$-0.793018\pi$
$83$	−1.73594	+	1.73594i	−0.190544	+	0.190544i	0.605387	+	0.795931i	$0.293018\pi$
$84$	−1.02221	+	0.836949i	−0.111533	+	0.0913187i
$85$	5.23531	+	5.23531i	0.567849	+	0.567849i
$86$	−1.62562	+	1.98095i	−0.175295	+	0.213611i
$87$		−	1.06093i		−	0.113743i
$88$	−1.84519	+	3.45292i	−0.196698	+	0.368082i
$89$	−7.69624			−0.815800			−0.407900	−	0.913027i	$-0.633739\pi$
$89$	−7.69624			−0.815800			−0.407900	+	0.913027i	$0.633739\pi$
$90$	−3.21154	−	2.63547i	−0.338527	−	0.277803i
$91$	−4.53516	−	8.50945i	−0.475414	−	0.892033i
$92$	7.05302	−	1.40341i	0.735328	−	0.146315i
$93$	1.86956	−	1.86956i	0.193864	−	0.193864i
$94$	−4.55388	+	0.448667i	−0.469697	+	0.0462764i
$95$		−	2.61200i		−	0.267986i
$96$	−0.409767	+	1.35161i	−0.0418217	+	0.137948i
$97$		−	10.9023i		−	1.10696i	−0.832864	−	0.553478i	$-0.813300\pi$
$97$		−	10.9023i		−	1.10696i	0.832864	−	0.553478i	$-0.186700\pi$
$98$	−8.71940	−	4.68743i	−0.880793	−	0.473502i
$99$	2.87525	+	2.87525i	0.288974	+	0.288974i
$100$	−0.390307	−	1.96155i	−0.0390307	−	0.196155i
$101$	−7.36104	+	7.36104i	−0.732451	+	0.732451i	−0.971105	−	0.238654i	$-0.923294\pi$
$101$	−7.36104	+	7.36104i	−0.732451	+	0.732451i	0.238654	+	0.971105i	$0.423294\pi$
$102$	−2.02087	−	1.65838i	−0.200096	−	0.164204i
$103$		−	12.6931i		−	1.25069i	−0.780349	−	0.625344i	$-0.784959\pi$
$103$		−	12.6931i		−	1.25069i	0.780349	−	0.625344i	$-0.215041\pi$
$104$	−9.09158	−	4.85842i	−0.891502	−	0.476407i
$105$	−0.192518	+	0.631892i	−0.0187878	+	0.0616663i
$106$	−9.41621	−	7.72718i	−0.914583	−	0.750530i
$107$	−5.21896	+	5.21896i	−0.504536	+	0.504536i	−0.912844	−	0.408308i	$-0.866119\pi$
$107$	−5.21896	+	5.21896i	−0.504536	+	0.504536i	0.408308	+	0.912844i	$0.366119\pi$
$108$	2.46536	+	1.64707i	0.237229	+	0.158489i
$109$	9.35887	−	9.35887i	0.896417	−	0.896417i	−0.0987000	−	0.995117i	$-0.531468\pi$
$109$	9.35887	−	9.35887i	0.896417	−	0.896417i	0.995117	+	0.0987000i	$0.0314684\pi$
$110$	0.191932	+	1.94808i	0.0183000	+	0.185742i
$111$	−2.38218			−0.226107
$112$	−10.5332	+	1.02592i	−0.995290	+	0.0969406i
$113$	−9.83245			−0.924959			−0.462480	−	0.886630i	$-0.653040\pi$
$113$	−9.83245			−0.924959			−0.462480	+	0.886630i	$0.653040\pi$
$114$	0.0904278	+	0.917825i	0.00846933	+	0.0859622i
$115$	2.54250	−	2.54250i	0.237090	−	0.237090i
$116$	4.72111	−	7.06662i	0.438344	−	0.656119i
$117$	−7.57058	+	7.57058i	−0.699900	+	0.699900i
$118$	−15.0418	−	12.3437i	−1.38471	−	1.13633i
$119$	5.70900	−	18.7384i	0.523343	−	1.71774i
$120$	0.205058	+	0.675750i	0.0187191	+	0.0616872i
$121$			9.08408i			0.825825i
$122$	−13.5235	−	11.0978i	−1.22436	−	1.00474i
$123$	−1.06930	+	1.06930i	−0.0964153	+	0.0964153i
$124$	20.7722	−	4.13324i	1.86540	−	0.371176i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	−2.15708	+	10.7780i	−0.192168	+	0.960180i
$127$			12.0507i			1.06933i	0.845065	+	0.534664i	$0.179562\pi$
$127$			12.0507i			1.06933i	−0.845065	+	0.534664i	$0.820438\pi$
$128$	−8.74400	+	7.17931i	−0.772867	+	0.634568i
$129$		−	0.452408i		−	0.0398323i
$130$	−5.12931	+	0.505360i	−0.449871	+	0.0443230i
$131$	−6.27543	+	6.27543i	−0.548287	+	0.548287i	−0.925945	−	0.377658i	$-0.876729\pi$
$131$	−6.27543	+	6.27543i	−0.548287	+	0.548287i	0.377658	+	0.925945i	$0.376729\pi$
$132$	−0.134885	−	0.677885i	−0.0117402	−	0.0590023i
$133$	−6.09864	+	3.25031i	−0.528820	+	0.281837i
$134$	3.54429	+	2.90853i	0.306180	+	0.251259i
$135$	1.48246			0.127590
$136$	−6.08086	−	20.0389i	−0.521430	−	1.71833i
$137$			2.07590i			0.177356i	0.996060	+	0.0886781i	$0.0282642\pi$
$137$			2.07590i			0.177356i	−0.996060	+	0.0886781i	$0.971736\pi$
$138$	−0.805382	+	0.981426i	−0.0685587	+	0.0835445i
$139$	−12.2922	−	12.2922i	−1.04261	−	1.04261i	−0.999051	−	0.0435635i	$-0.986129\pi$
$139$	−12.2922	−	12.2922i	−1.04261	−	1.04261i	−0.0435635	−	0.999051i	$-0.513871\pi$
$140$	−4.09423	+	3.35220i	−0.346026	+	0.283313i
$141$	0.571240	−	0.571240i	0.0481071	−	0.0481071i
$142$	15.1091	−	1.48861i	1.26793	−	0.124921i
$143$	5.04465			0.421855
$144$	4.49818	+	10.8556i	0.374848	+	0.904634i
$145$		−	4.24929i		−	0.352885i
$146$	−5.63428	+	0.555112i	−0.466297	+	0.0459414i
$147$	1.71494	−	0.336808i	0.141446	−	0.0277795i
$148$	−15.8672	−	10.6007i	−1.30428	−	0.871370i
$149$	4.08134	+	4.08134i	0.334356	+	0.334356i	0.854238	−	0.519882i	$-0.174024\pi$
$149$	4.08134	+	4.08134i	0.334356	+	0.334356i	−0.519882	+	0.854238i	$0.674024\pi$
$150$	0.272948	+	0.223988i	0.0222861	+	0.0182886i
$151$	−20.7250			−1.68657			−0.843286	−	0.537465i	$-0.819382\pi$
$151$	−20.7250			−1.68657			−0.843286	+	0.537465i	$0.819382\pi$
$152$	−3.48199	+	6.51585i	−0.282426	+	0.528505i
$153$	−21.7500			−1.75839
$154$	4.30964	−	2.87227i	0.347281	−	0.231454i
$155$	7.48806	−	7.48806i	0.601456	−	0.601456i
$156$	1.78488	−	0.355154i	0.142905	−	0.0284351i
$157$	9.66337	+	9.66337i	0.771221	+	0.771221i	0.978320	−	0.207099i	$-0.0664022\pi$
$157$	9.66337	+	9.66337i	0.771221	+	0.771221i	−0.207099	+	0.978320i	$0.566402\pi$
$158$	−0.155905	−	1.58240i	−0.0124031	−	0.125889i
$159$	2.15047			0.170543
$160$	−1.64123	+	5.41354i	−0.129750	+	0.427978i
$161$	−9.10020	−	2.77255i	−0.717196	−	0.218507i
$162$	11.8825	−	1.17071i	0.933576	−	0.0919796i
$163$	−1.58658	−	1.58658i	−0.124270	−	0.124270i	0.642236	−	0.766507i	$-0.278007\pi$
$163$	−1.58658	−	1.58658i	−0.124270	−	0.124270i	−0.766507	+	0.642236i	$0.778007\pi$
$164$	−11.8807	+	2.36402i	−0.927730	+	0.184599i
$165$	−0.244367	−	0.244367i	−0.0190240	−	0.0190240i
$166$	2.20245	−	2.68386i	0.170943	−	0.208308i
$167$		−	13.4079i		−	1.03754i	−0.854914	−	0.518769i	$-0.826391\pi$
$167$		−	13.4079i		−	1.03754i	0.854914	−	0.518769i	$-0.173609\pi$
$168$	1.32261	−	1.31966i	0.102041	−	0.101814i
$169$			0.282627i			0.0217405i
$170$	−8.09412	−	6.64223i	−0.620791	−	0.509436i
$171$	5.42577	+	5.42577i	0.414919	+	0.414919i
$172$	2.01321	−	3.01340i	0.153506	−	0.229770i
$173$	2.90615	+	2.90615i	0.220951	+	0.220951i	0.808899	−	0.587948i	$-0.200064\pi$
$173$	2.90615	+	2.90615i	0.220951	+	0.220951i	−0.587948	+	0.808899i	$0.700064\pi$
$174$	0.147111	+	1.49315i	0.0111524	+	0.113195i
$175$	−0.771085	+	2.53089i	−0.0582886	+	0.191318i
$176$	2.11813	−	5.11549i	0.159660	−	0.385595i
$177$	3.43523			0.258208
$178$	10.8317	−	1.06718i	0.811869	−	0.0799885i
$179$	3.28164	+	3.28164i	0.245281	+	0.245281i	0.819031	−	0.573750i	$-0.194512\pi$
$179$	3.28164	+	3.28164i	0.245281	+	0.245281i	−0.573750	+	0.819031i	$0.694512\pi$
$180$	4.88537	+	3.26384i	0.364134	+	0.243272i
$181$	12.9371	−	12.9371i	0.961607	−	0.961607i	−0.0376831	−	0.999290i	$-0.511998\pi$
$181$	12.9371	−	12.9371i	0.961607	−	0.961607i	0.999290	+	0.0376831i	$0.0119978\pi$
$182$	7.56272	+	11.3473i	0.560586	+	0.841120i
$183$	3.08850			0.228308
$184$	−9.73182	+	2.95314i	−0.717439	+	0.217708i
$185$	−9.54127			−0.701488
$186$	−2.37197	+	2.89045i	−0.173922	+	0.211938i
$187$	7.24656	+	7.24656i	0.529921	+	0.529921i
$188$	6.34692	−	1.26291i	0.462897	−	0.0921069i
$189$	−1.84474	−	3.46134i	−0.134185	−	0.251775i
$190$	0.362187	+	3.67613i	0.0262758	+	0.266695i
$191$		−	17.0926i		−	1.23677i	−0.785874	−	0.618387i	$-0.787786\pi$
$191$		−	17.0926i		−	1.23677i	0.785874	−	0.618387i	$-0.212214\pi$
$192$	0.389289	−	1.95907i	0.0280945	−	0.141384i
$193$	18.8951			1.36010			0.680050	−	0.733166i	$-0.261958\pi$
$193$	18.8951			1.36010			0.680050	+	0.733166i	$0.261958\pi$
$194$	1.51173	+	15.3438i	0.108536	+	1.10162i
$195$	0.643422	−	0.643422i	0.0460764	−	0.0460764i
$196$	12.9217	+	5.38803i	0.922975	+	0.384860i
$197$	−2.93046	−	2.93046i	−0.208786	−	0.208786i	0.594965	−	0.803751i	$-0.297166\pi$
$197$	−2.93046	−	2.93046i	−0.208786	−	0.208786i	−0.803751	+	0.594965i	$0.797166\pi$
$198$	−4.44532	−	3.64794i	−0.315915	−	0.259248i
$199$		−	17.4475i		−	1.23682i	−0.785857	−	0.618408i	$-0.787778\pi$
$199$		−	17.4475i		−	1.23682i	0.785857	−	0.618408i	$-0.212222\pi$
$200$	0.821311	+	2.70656i	0.0580754	+	0.191382i
$201$	−0.809443			−0.0570937
$202$	9.33922	−	11.3806i	0.657105	−	0.800738i
$203$	−9.92148	+	5.28771i	−0.696351	+	0.371124i
$204$	3.07413	+	2.05378i	0.215232	+	0.143793i
$205$	−4.28282	+	4.28282i	−0.299125	+	0.299125i
$206$	1.76006	+	17.8642i	0.122629	+	1.24466i
$207$			10.5628i			0.734165i
$208$	13.4692	+	5.57708i	0.933918	+	0.386701i
$209$		−	3.61545i		−	0.250086i
$210$	0.183330	−	0.916019i	0.0126510	−	0.0632113i
$211$	−13.1176	−	13.1176i	−0.903055	−	0.903055i	0.0926446	−	0.995699i	$-0.470468\pi$
$211$	−13.1176	−	13.1176i	−0.903055	−	0.903055i	−0.995699	+	0.0926446i	$0.970468\pi$
$212$	14.3238	+	9.56955i	0.983765	+	0.657239i
$213$	−1.89529	+	1.89529i	−0.129863	+	0.129863i
$214$	6.62149	−	8.06884i	0.452636	−	0.551574i
$215$		−	1.81201i		−	0.123578i
$216$	−3.69813	−	1.97623i	−0.251626	−	0.134465i
$217$	−26.8015	−	8.16558i	−1.81940	−	0.554316i
$218$	−11.8739	+	14.4694i	−0.804205	+	0.979991i
$219$	0.706765	−	0.706765i	0.0477588	−	0.0477588i
$220$	−0.540251	−	2.71511i	−0.0364237	−	0.183053i
$221$	−19.0803	+	19.0803i	−1.28348	+	1.28348i
$222$	3.35268	−	0.330319i	0.225017	−	0.0221696i
$223$	3.49894			0.234307			0.117153	−	0.993114i	$-0.462623\pi$
$223$	3.49894			0.234307			0.117153	+	0.993114i	$0.462623\pi$
$224$	14.6821	−	2.90444i	0.980989	−	0.194061i
$225$	2.93766			0.195844
$226$	13.8382	−	1.36339i	0.920502	−	0.0906915i
$227$	−3.37074	+	3.37074i	−0.223724	+	0.223724i	−0.810065	−	0.586341i	$-0.800568\pi$
$227$	−3.37074	+	3.37074i	−0.223724	+	0.223724i	0.586341	+	0.810065i	$0.300568\pi$
$228$	−0.254536	−	1.27921i	−0.0168571	−	0.0847176i
$229$	−4.60318	+	4.60318i	−0.304186	+	0.304186i	−0.842649	−	0.538463i	$-0.819005\pi$
$229$	−4.60318	+	4.60318i	−0.304186	+	0.304186i	0.538463	+	0.842649i	$0.319005\pi$
$230$	−3.22577	+	3.93087i	−0.212701	+	0.259194i
$231$	−0.266477	+	0.874645i	−0.0175329	+	0.0575474i
$232$	−5.66461	+	10.6002i	−0.371900	+	0.695937i
$233$		−	1.89297i		−	0.124012i	−0.998076	−	0.0620062i	$-0.980250\pi$
$233$		−	1.89297i		−	0.124012i	0.998076	−	0.0620062i	$-0.0197499\pi$
$234$	9.60507	−	11.7046i	0.627903	−	0.765153i
$235$	2.28797	−	2.28797i	0.149250	−	0.149250i
$236$	22.8814	+	15.2867i	1.48945	+	0.995081i
$237$	0.198497	+	0.198497i	0.0128938	+	0.0128938i
$238$	−5.43653	+	27.1640i	−0.352398	+	1.76078i
$239$		−	11.1410i		−	0.720651i	−0.932827	−	0.360325i	$-0.882666\pi$
$239$		−	11.1410i		−	0.720651i	0.932827	−	0.360325i	$-0.117334\pi$
$240$	−0.382299	−	0.922616i	−0.0246773	−	0.0595546i
$241$			15.5869i			1.00404i	0.864856	+	0.502020i	$0.167410\pi$
$241$			15.5869i			1.00404i	−0.864856	+	0.502020i	$0.832590\pi$
$242$	−1.25962	−	12.7849i	−0.0809715	−	0.821846i
$243$	−4.63532	+	4.63532i	−0.297356	+	0.297356i
$244$	20.5719	+	13.7438i	1.31698	+	0.879854i
$245$	6.86878	−	1.34901i	0.438830	−	0.0861849i
$246$	1.35666	−	1.65320i	0.0864973	−	0.105404i
$247$	9.51954			0.605714
$248$	−28.6617	+	8.69745i	−1.82002	+	0.552289i
$249$			0.612939i			0.0388435i
$250$	1.09323	+	0.897132i	0.0691420	+	0.0567396i
$251$	2.76100	+	2.76100i	0.174273	+	0.174273i	0.788854	−	0.614581i	$-0.210675\pi$
$251$	2.76100	+	2.76100i	0.174273	+	0.174273i	−0.614581	+	0.788854i	$0.710675\pi$
$252$	1.54137	−	15.4680i	0.0970973	−	0.974396i
$253$	3.51926	−	3.51926i	0.221254	−	0.221254i
$254$	−1.67098	−	16.9602i	−0.104847	−	1.06418i
$255$	1.84853			0.115759
$256$	11.3108	−	11.3166i	0.706925	−	0.707289i
$257$		−	16.3721i		−	1.02126i	−0.859800	−	0.510631i	$-0.829412\pi$
$257$		−	16.3721i		−	1.02126i	0.859800	−	0.510631i	$-0.170588\pi$
$258$	0.0627320	+	0.636719i	0.00390553	+	0.0396404i
$259$	11.8729	+	22.2775i	0.737746	+	1.38425i
$260$	7.14892	−	1.42249i	0.443357	−	0.0882189i
$261$	8.82681	+	8.82681i	0.546366	+	0.546366i
$262$	7.96187	−	9.70220i	0.491886	−	0.599404i
$263$	10.3460			0.637965			0.318982	−	0.947761i	$-0.396659\pi$
$263$	10.3460			0.637965			0.318982	+	0.947761i	$0.396659\pi$
$264$	0.283834	+	0.935352i	0.0174688	+	0.0575669i
$265$	8.61320			0.529105
$266$	8.13253	−	5.42013i	0.498638	−	0.332330i
$267$	−1.35873	+	1.35873i	−0.0831528	+	0.0831528i
$268$	−5.39153	−	3.60201i	−0.329340	−	0.220027i
$269$	9.06161	+	9.06161i	0.552496	+	0.552496i	0.927160	−	0.374664i	$-0.122242\pi$
$269$	9.06161	+	9.06161i	0.552496	+	0.552496i	−0.374664	+	0.927160i	$0.622242\pi$
$270$	−2.08642	+	0.205562i	−0.126975	+	0.0125101i
$271$	−22.1493			−1.34548			−0.672738	−	0.739881i	$-0.734882\pi$
$271$	−22.1493			−1.34548			−0.672738	+	0.739881i	$0.734882\pi$
$272$	11.3369	+	27.3596i	0.687398	+	1.65892i
$273$	−2.30295	−	0.701638i	−0.139381	−	0.0424651i
$274$	−0.287850	−	2.92162i	−0.0173896	−	0.176502i
$275$	−0.978755	−	0.978755i	−0.0590211	−	0.0590211i
$276$	0.997408	−	1.49293i	0.0600369	−	0.0898641i
$277$	−18.1242	−	18.1242i	−1.08898	−	1.08898i	−0.995634	−	0.0933421i	$-0.970245\pi$
$277$	−18.1242	−	18.1242i	−1.08898	−	1.08898i	−0.0933421	−	0.995634i	$-0.529755\pi$
$278$	19.0046	+	15.5956i	1.13982	+	0.935363i
$279$			31.1090i			1.86245i
$280$	5.29739	−	5.28561i	0.316580	−	0.315875i
$281$			9.63776i			0.574940i	0.957790	+	0.287470i	$0.0928142\pi$
$281$			9.63776i			0.574940i	−0.957790	+	0.287470i	$0.907186\pi$
$282$	−0.724753	+	0.883172i	−0.0431584	+	0.0525921i
$283$	1.09319	+	1.09319i	0.0649833	+	0.0649833i	0.738852	−	0.673868i	$-0.235368\pi$
$283$	1.09319	+	1.09319i	0.0649833	+	0.0649833i	−0.673868	+	0.738852i	$0.735368\pi$
$284$	−21.0582	+	4.19014i	−1.24957	+	0.248639i
$285$	−0.461135	−	0.461135i	−0.0273153	−	0.0273153i
$286$	−7.09984	+	0.699504i	−0.419822	+	0.0413625i
$287$	15.3292	+	4.67033i	0.904853	+	0.275681i
$288$	−7.83600	−	14.6545i	−0.461741	−	0.863522i
$289$	−37.8170			−2.22453
$290$	0.589218	+	5.98045i	0.0346001	+	0.351184i
$291$	−1.92473	−	1.92473i	−0.112830	−	0.112830i
$292$	7.85271	−	1.56253i	0.459545	−	0.0914400i
$293$	23.1027	−	23.1027i	1.34967	−	1.34967i	0.463658	−	0.886014i	$-0.346537\pi$
$293$	23.1027	−	23.1027i	1.34967	−	1.34967i	0.886014	−	0.463658i	$-0.153463\pi$
$294$	−2.36690	+	0.711822i	−0.138040	+	0.0415143i
$295$	13.7590			0.801081
$296$	23.8015	+	12.7192i	1.38343	+	0.739288i
$297$	2.05198			0.119068
$298$	−6.31000	−	5.17815i	−0.365529	−	0.299962i
$299$	9.26624	+	9.26624i	0.535881	+	0.535881i
$300$	−0.415206	−	0.277393i	−0.0239719	−	0.0160153i
$301$	−4.23079	+	2.25482i	−0.243858	+	0.129966i
$302$	29.1683	−	2.87377i	1.67845	−	0.165367i
$303$			2.59910i			0.149314i
$304$	3.99704	−	9.65322i	0.229246	−	0.553650i
$305$	12.3703			0.708319
$306$	30.6110	−	3.01591i	1.74991	−	0.172408i
$307$	−23.0642	+	23.0642i	−1.31634	+	1.31634i	−0.399697	+	0.916647i	$0.630885\pi$
$307$	−23.0642	+	23.0642i	−1.31634	+	1.31634i	−0.916647	+	0.399697i	$0.869115\pi$
$308$	−5.66711	+	4.64001i	−0.322913	+	0.264389i
$309$	−2.24089	−	2.24089i	−0.127480	−	0.127480i
$310$	−9.50038	+	11.5770i	−0.539585	+	0.657530i
$311$		−	14.9822i		−	0.849565i	−0.905295	−	0.424782i	$-0.860351\pi$
$311$		−	14.9822i		−	0.849565i	0.905295	−	0.424782i	$-0.139649\pi$
$312$	−2.46279	+	0.747340i	−0.139428	+	0.0423098i
$313$	2.43405			0.137581			0.0687904	−	0.997631i	$-0.478086\pi$
$313$	2.43405			0.137581			0.0687904	+	0.997631i	$0.478086\pi$
$314$	−14.9402	−	12.2603i	−0.843122	−	0.691887i
$315$	−3.65555	−	6.85901i	−0.205967	−	0.386462i
$316$	0.438840	+	2.20546i	0.0246867	+	0.124067i
$317$	7.09234	−	7.09234i	0.398345	−	0.398345i	−0.479304	−	0.877649i	$-0.659111\pi$
$317$	7.09234	−	7.09234i	0.398345	−	0.398345i	0.877649	+	0.479304i	$0.159111\pi$
$318$	−3.02657	+	0.298189i	−0.169722	+	0.0167216i
$319$		−	5.88174i		−	0.329314i
$320$	1.55921	−	7.84658i	0.0871623	−	0.438637i
$321$			1.84276i			0.102853i
$322$	13.1921	+	2.64023i	0.735165	+	0.147134i
$323$	13.6747	+	13.6747i	0.760879	+	0.760879i
$324$	−16.5611	+	3.29531i	−0.920059	+	0.183073i
$325$	2.57707	−	2.57707i	0.142950	−	0.142950i
$326$	2.45295	+	2.01295i	0.135856	+	0.111487i
$327$		−	3.30451i		−	0.182740i
$328$	16.3931	−	4.97453i	0.905160	−	0.274673i
$329$	−8.18915	−	2.49498i	−0.451482	−	0.137553i
$330$	0.377807	+	0.310038i	0.0207976	+	0.0170670i
$331$	3.73150	−	3.73150i	0.205102	−	0.205102i	−0.597080	−	0.802182i	$-0.703673\pi$
$331$	3.73150	−	3.73150i	0.205102	−	0.205102i	0.802182	+	0.597080i	$0.203673\pi$
$332$	−2.72757	+	4.08267i	−0.149695	+	0.224065i
$333$	19.8195	−	19.8195i	1.08610	−	1.08610i
$334$	1.85918	+	18.8703i	0.101730	+	1.03254i
$335$	−3.24203			−0.177131
$336$	−1.67845	+	2.04069i	−0.0915669	+	0.111329i
$337$	11.1971			0.609945			0.304973	−	0.952361i	$-0.401353\pi$
$337$	11.1971			0.609945			0.304973	+	0.952361i	$0.401353\pi$
$338$	−0.0391897	−	0.397769i	−0.00213164	−	0.0216358i
$339$	−1.73586	+	1.73586i	−0.0942792	+	0.0942792i
$340$	12.3127	+	8.22593i	0.667749	+	0.446113i
$341$	10.3647	−	10.3647i	0.561282	−	0.561282i
$342$	−8.38857	−	6.88387i	−0.453602	−	0.372237i
$343$	−11.6971	−	14.3589i	−0.631582	−	0.775309i
$344$	−2.41554	+	4.52021i	−0.130237	+	0.243714i
$345$		−	0.897730i		−	0.0483321i
$346$	−4.49309	−	3.68714i	−0.241550	−	0.198222i
$347$	−1.69866	+	1.69866i	−0.0911889	+	0.0911889i	−0.751230	−	0.660041i	$-0.770539\pi$
$347$	−1.69866	+	1.69866i	−0.0911889	+	0.0911889i	0.660041	+	0.751230i	$0.270539\pi$
$348$	−0.414087	−	2.08106i	−0.0221974	−	0.111556i
$349$	8.68835	+	8.68835i	0.465077	+	0.465077i	0.900315	−	0.435238i	$-0.143336\pi$
$349$	8.68835	+	8.68835i	0.465077	+	0.465077i	−0.435238	+	0.900315i	$0.643336\pi$
$350$	0.734285	−	3.66890i	0.0392492	−	0.196111i
$351$			5.40289i			0.288385i
$352$	−2.27173	+	7.49325i	−0.121084	+	0.399391i
$353$		−	0.340882i		−	0.0181433i	−0.999959	−	0.00907166i	$-0.997112\pi$
$353$		−	0.340882i		−	0.0181433i	0.999959	−	0.00907166i	$-0.00288764\pi$
$354$	−4.83474	+	0.476338i	−0.256964	+	0.0253171i
$355$	−7.59114	+	7.59114i	−0.402896	+	0.402896i
$356$	−15.0965	+	3.00390i	−0.800114	+	0.159206i
$357$	−2.30026	−	4.31604i	−0.121743	−	0.228429i
$358$	−5.07361	−	4.16353i	−0.268149	−	0.220050i
$359$	−25.6134			−1.35182			−0.675912	−	0.736982i	$-0.736250\pi$
$359$	−25.6134			−1.35182			−0.675912	+	0.736982i	$0.736250\pi$
$360$	−7.32824	−	3.91611i	−0.386232	−	0.206397i
$361$			12.1774i			0.640918i
$362$	−16.4138	+	20.0015i	−0.862688	+	1.05126i
$363$	1.60374	+	1.60374i	0.0841746	+	0.0841746i
$364$	−12.2172	−	14.9216i	−0.640356	−	0.782103i
$365$	2.83078	−	2.83078i	0.148170	−	0.148170i
$366$	−4.34675	+	0.428259i	−0.227208	+	0.0223855i
$367$	16.4093			0.856557			0.428278	−	0.903647i	$-0.359120\pi$
$367$	16.4093			0.856557			0.428278	+	0.903647i	$0.359120\pi$
$368$	13.2871	−	5.50569i	0.692636	−	0.287004i
$369$		−	17.7929i		−	0.926262i
$370$	13.4284	−	1.32302i	0.698108	−	0.0687804i
$371$	−10.7180	−	20.1105i	−0.556452	−	1.04409i
$372$	2.93752	−	4.39692i	0.152303	−	0.227970i
$373$	0.461478	+	0.461478i	0.0238944	+	0.0238944i	0.718953	−	0.695059i	$-0.244622\pi$
$373$	0.461478	+	0.461478i	0.0238944	+	0.0238944i	−0.695059	+	0.718953i	$0.744622\pi$
$374$	−11.2036	−	9.19397i	−0.579326	−	0.475409i
$375$	−0.249671			−0.0128930
$376$	−8.75753	+	2.65749i	−0.451635	+	0.137050i
$377$	15.4867			0.797606
$378$	3.07624	+	4.61569i	0.158225	+	0.237405i
$379$	−21.8512	+	21.8512i	−1.12242	+	1.12242i	−0.131044	+	0.991377i	$0.541833\pi$
$379$	−21.8512	+	21.8512i	−1.12242	+	1.12242i	−0.991377	+	0.131044i	$0.958167\pi$
$380$	−1.01948	−	5.12357i	−0.0522984	−	0.262833i
$381$	2.12748	+	2.12748i	0.108994	+	0.108994i
$382$	2.37010	+	24.0561i	0.121265	+	1.23082i
$383$	−16.2481			−0.830241			−0.415120	−	0.909766i	$-0.636261\pi$
$383$	−16.2481			−0.830241			−0.415120	+	0.909766i	$0.636261\pi$
$384$	−0.276236	+	2.81117i	−0.0140966	+	0.143457i
$385$	−1.06731	+	3.50318i	−0.0543953	+	0.178539i
$386$	−26.5930	+	2.62004i	−1.35355	+	0.133357i
$387$	3.76399	+	3.76399i	0.191335	+	0.191335i
$388$	−4.25523	−	21.3853i	−0.216026	−	1.08567i
$389$	−12.7387	−	12.7387i	−0.645878	−	0.645878i	0.306117	−	0.951994i	$-0.400970\pi$
$389$	−12.7387	−	12.7387i	−0.645878	−	0.645878i	−0.951994	+	0.306117i	$0.900970\pi$
$390$	−0.816333	+	0.994770i	−0.0413366	+	0.0503721i
$391$			26.6216i			1.34631i
$392$	−18.9330	−	5.79137i	−0.956263	−	0.292508i
$393$			2.21578i			0.111771i
$394$	4.53066	+	3.71798i	0.228252	+	0.187309i
$395$	0.795033	+	0.795033i	0.0400025	+	0.0400025i
$396$	6.76217	+	4.51771i	0.339812	+	0.227023i
$397$	1.55444	+	1.55444i	0.0780150	+	0.0780150i	0.745038	−	0.667023i	$-0.232432\pi$
$397$	1.55444	+	1.55444i	0.0780150	+	0.0780150i	−0.667023	+	0.745038i	$0.732432\pi$
$398$	2.41931	+	24.5555i	0.121269	+	1.23086i
$399$	−0.502858	+	1.65050i	−0.0251744	+	0.0826286i
$400$	−1.53121	−	3.69532i	−0.0765605	−	0.184766i
$401$	15.4547			0.771769			0.385885	−	0.922547i	$-0.373896\pi$
$401$	15.4547			0.771769			0.385885	+	0.922547i	$0.373896\pi$
$402$	1.13921	−	0.112239i	0.0568186	−	0.00559799i
$403$	27.2905	+	27.2905i	1.35944	+	1.35944i
$404$	−11.5659	+	17.3121i	−0.575427	+	0.861308i
$405$	−5.97001	+	5.97001i	−0.296652	+	0.296652i
$406$	13.2303	−	8.81765i	0.656607	−	0.437613i
$407$	−13.2067			−0.654633
$408$	−4.61130	−	2.46422i	−0.228294	−	0.121997i
$409$	10.5094			0.519656			0.259828	−	0.965655i	$-0.416334\pi$
$409$	10.5094			0.519656			0.259828	+	0.965655i	$0.416334\pi$
$410$	5.43377	−	6.62151i	0.268355	−	0.327013i
$411$	0.366488	+	0.366488i	0.0180775	+	0.0180775i
$412$	−4.95420	−	24.8981i	−0.244076	−	1.22664i
$413$	−17.1213	−	32.1253i	−0.842486	−	1.58078i
$414$	−1.46466	−	14.8661i	−0.0719843	−	0.730628i
$415$			2.45498i			0.120510i
$416$	−19.7298	−	5.98150i	−0.967334	−	0.293267i
$417$	−4.34025			−0.212543
$418$	0.501328	+	5.08839i	0.0245208	+	0.248881i
$419$	−0.488822	+	0.488822i	−0.0238805	+	0.0238805i	−0.718946	−	0.695066i	$-0.755375\pi$
$419$	−0.488822	+	0.488822i	−0.0238805	+	0.0238805i	0.695066	+	0.718946i	$0.255375\pi$
$420$	−0.131001	+	1.31463i	−0.00639219	+	0.0641472i
$421$	14.5806	+	14.5806i	0.710613	+	0.710613i	0.966663	−	0.256051i	$-0.0824214\pi$
$421$	14.5806	+	14.5806i	0.710613	+	0.710613i	−0.256051	+	0.966663i	$0.582421\pi$
$422$	20.2807	+	16.6428i	0.987247	+	0.810160i
$423$			9.50532i			0.462165i
$424$	−21.4863	−	11.4820i	−1.04347	−	0.557615i
$425$	7.40385			0.359140
$426$	2.40462	−	2.93024i	0.116504	−	0.141970i
$427$	−15.3932	−	28.8827i	−0.744930	−	1.39773i
$428$	−8.20023	+	12.2742i	−0.396373	+	0.593297i
$429$	0.890604	−	0.890604i	0.0429988	−	0.0429988i
$430$	0.251258	+	2.55023i	0.0121168	+	0.122983i
$431$		−	35.7322i		−	1.72116i	−0.509316	−	0.860580i	$-0.670101\pi$
$431$		−	35.7322i		−	1.72116i	0.509316	−	0.860580i	$-0.329899\pi$
$432$	5.47877	+	2.26855i	0.263597	+	0.109146i
$433$		−	3.38964i		−	0.162896i	−0.996678	−	0.0814479i	$-0.974046\pi$
$433$		−	3.38964i		−	0.162896i	0.996678	−	0.0814479i	$-0.0259544\pi$
$434$	38.8526	+	7.77587i	1.86499	+	0.373254i
$435$	−0.750189	−	0.750189i	−0.0359688	−	0.0359688i
$436$	14.7050	−	22.0107i	0.704243	−	1.05412i
$437$	6.64103	−	6.64103i	0.317684	−	0.317684i
$438$	−0.896699	+	1.09270i	−0.0428459	+	0.0522114i
$439$			7.38471i			0.352453i	0.984350	+	0.176227i	$0.0563891\pi$
$439$			7.38471i			0.352453i	−0.984350	+	0.176227i	$0.943611\pi$
$440$	1.13683	+	3.74633i	0.0541964	+	0.178599i
$441$	−11.4659	+	17.0703i	−0.545996	+	0.812873i
$442$	24.2078	−	29.4993i	1.15145	−	1.40314i
$443$	18.4426	−	18.4426i	0.876234	−	0.876234i	−0.116908	−	0.993143i	$-0.537298\pi$
$443$	18.4426	−	18.4426i	0.876234	−	0.876234i	0.993143	+	0.116908i	$0.0372984\pi$
$444$	−4.67276	+	0.929783i	−0.221759	+	0.0441255i
$445$	−5.44207	+	5.44207i	−0.257979	+	0.257979i
$446$	−4.92441	+	0.485172i	−0.233178	+	0.0229736i
$447$	1.44107			0.0681605
$448$	−20.2608	+	6.12356i	−0.957235	+	0.289311i
$449$	−18.9231			−0.893035			−0.446517	−	0.894775i	$-0.647336\pi$
$449$	−18.9231			−0.893035			−0.446517	+	0.894775i	$0.647336\pi$
$450$	−4.13447	+	0.407344i	−0.194901	+	0.0192024i
$451$	−5.92815	+	5.92815i	−0.279145	+	0.279145i
$452$	−19.2868	+	3.83767i	−0.907175	+	0.180509i
$453$	−3.65887	+	3.65887i	−0.171909	+	0.171909i
$454$	4.27658	−	5.21137i	0.200710	−	0.244582i
$455$	−9.22393	−	2.81025i	−0.432425	−	0.131746i
$456$	0.535612	+	1.76506i	0.0250823	+	0.0826566i
$457$		−	31.9731i		−	1.49564i	−0.663903	−	0.747819i	$-0.731101\pi$
$457$		−	31.9731i		−	1.49564i	0.663903	−	0.747819i	$-0.268899\pi$
$458$	5.84022	−	7.11679i	0.272895	−	0.332546i
$459$	−7.76117	+	7.76117i	−0.362260	+	0.362260i
$460$	3.99488	−	5.97960i	0.186262	−	0.278800i
$461$	−0.872708	−	0.872708i	−0.0406461	−	0.0406461i	0.686492	−	0.727138i	$-0.259150\pi$
$461$	−0.872708	−	0.872708i	−0.0406461	−	0.0406461i	−0.727138	+	0.686492i	$0.759150\pi$
$462$	0.253759	−	1.26793i	0.0118060	−	0.0589892i
$463$		−	3.59688i		−	0.167161i	−0.996501	−	0.0835805i	$-0.973364\pi$
$463$		−	3.59688i		−	0.167161i	0.996501	−	0.0835805i	$-0.0266356\pi$
$464$	6.50252	−	15.7042i	0.301872	−	0.729048i
$465$		−	2.64395i		−	0.122610i
$466$	0.262484	+	2.66416i	0.0121593	+	0.123415i
$467$	4.76343	−	4.76343i	0.220425	−	0.220425i	−0.588252	−	0.808677i	$-0.700184\pi$
$467$	4.76343	−	4.76343i	0.220425	−	0.220425i	0.808677	+	0.588252i	$0.200184\pi$
$468$	−11.8952	+	17.8049i	−0.549855	+	0.823031i
$469$	4.03430	+	7.56967i	0.186287	+	0.349535i
$470$	−2.90283	+	3.53734i	−0.133897	+	0.163165i
$471$	3.41203			0.157218
$472$	−34.3229	−	18.3417i	−1.57984	−	0.844247i
$473$		−	2.50813i		−	0.115324i
$474$	−0.306889	−	0.251840i	−0.0140959	−	0.0115674i
$475$	−1.84697	−	1.84697i	−0.0847446	−	0.0847446i
$476$	3.88475	−	38.9844i	0.178057	−	1.78685i
$477$	−17.8917	+	17.8917i	−0.819205	+	0.819205i
$478$	1.54484	+	15.6798i	0.0706592	+	0.717178i
$479$	2.53429			0.115795			0.0578974	−	0.998323i	$-0.481560\pi$
$479$	2.53429			0.115795			0.0578974	+	0.998323i	$0.481560\pi$
$480$	0.665980	+	1.24548i	0.0303977	+	0.0568481i
$481$		−	34.7735i		−	1.58553i
$482$	−2.16132	−	21.9370i	−0.0984454	−	0.999203i
$483$	−2.09607	+	1.11711i	−0.0953743	+	0.0508303i
$484$	3.54558	+	17.8188i	0.161163	+	0.809947i
$485$	−7.70906	−	7.70906i	−0.350050	−	0.350050i
$486$	5.88100	−	7.16650i	0.266768	−	0.325079i
$487$	17.4209			0.789414			0.394707	−	0.918807i	$-0.370846\pi$
$487$	17.4209			0.789414			0.394707	+	0.918807i	$0.370846\pi$
$488$	−30.8586	−	16.4904i	−1.39690	−	0.746486i
$489$	−0.560202			−0.0253332
$490$	−9.48006	+	2.85103i	−0.428266	+	0.128797i
$491$	10.2394	−	10.2394i	0.462098	−	0.462098i	−0.437245	−	0.899343i	$-0.644046\pi$
$491$	10.2394	−	10.2394i	0.462098	−	0.462098i	0.899343	+	0.437245i	$0.144046\pi$
$492$	−1.68012	+	2.51483i	−0.0757457	+	0.113377i
$493$	22.2464	+	22.2464i	1.00193	+	1.00193i
$494$	−13.3978	+	1.32000i	−0.602795	+	0.0593897i
$495$	4.06622			0.182763
$496$	39.1324	−	16.2151i	1.75710	−	0.728079i
$497$	27.1704	+	8.27798i	1.21876	+	0.371318i
$498$	−0.0849917	−	0.862651i	−0.00380857	−	0.0386563i
$499$	−2.70543	−	2.70543i	−0.121112	−	0.121112i	0.643953	−	0.765065i	$-0.277293\pi$
$499$	−2.70543	−	2.70543i	−0.121112	−	0.121112i	−0.765065	+	0.643953i	$0.777293\pi$
$500$	−1.66301	−	1.11103i	−0.0743721	−	0.0496869i
$501$	−2.36710	−	2.36710i	−0.105754	−	0.105754i
$502$	−4.26868	−	3.50299i	−0.190521	−	0.156346i
$503$			19.8860i			0.886671i	0.896356	+	0.443336i	$0.146205\pi$
$503$			19.8860i			0.886671i	−0.896356	+	0.443336i	$0.853795\pi$
$504$	−0.0244869	+	21.9835i	−0.00109073	+	0.979221i
$505$			10.4101i			0.463243i
$506$	−4.46501	+	5.44099i	−0.198494	+	0.241881i
$507$	0.0498962	+	0.0498962i	0.00221597	+	0.00221597i
$508$	4.70348	+	23.6380i	0.208683	+	1.04877i
$509$	−19.1507	−	19.1507i	−0.848840	−	0.848840i	0.141148	−	0.989988i	$-0.454921\pi$
$509$	−19.1507	−	19.1507i	−0.848840	−	0.848840i	−0.989988	+	0.141148i	$0.954921\pi$
$510$	−2.60162	+	0.256322i	−0.115202	+	0.0113501i
$511$	−10.1320	−	3.08691i	−0.448214	−	0.136557i
$512$	−14.3496	+	17.4954i	−0.634169	+	0.773194i
$513$	3.87220			0.170962
$514$	2.27019	+	23.0421i	0.100134	+	1.01634i
$515$	−8.97537	−	8.97537i	−0.395502	−	0.395502i
$516$	−0.176578	−	0.887419i	−0.00777342	−	0.0390664i
$517$	3.16693	−	3.16693i	0.139281	−	0.139281i
$518$	−19.7990	−	29.7070i	−0.869916	−	1.30525i
$519$	1.02613			0.0450421
$520$	−9.86414	+	2.99329i	−0.432571	+	0.131265i
$521$	17.7051			0.775674			0.387837	−	0.921728i	$-0.373222\pi$
$521$	17.7051			0.775674			0.387837	+	0.921728i	$0.373222\pi$
$522$	−13.6468	−	11.1989i	−0.597304	−	0.490163i
$523$	7.11421	+	7.11421i	0.311083	+	0.311083i	0.845329	−	0.534246i	$-0.179405\pi$
$523$	7.11421	+	7.11421i	0.311083	+	0.311083i	−0.534246	+	0.845329i	$0.679405\pi$
$524$	−9.86020	+	14.7589i	−0.430745	+	0.644745i
$525$	0.310684	+	0.582946i	0.0135594	+	0.0254418i
$526$	−14.5610	+	1.43461i	−0.634891	+	0.0625519i
$527$			78.4047i			3.41536i
$528$	−0.529167	−	1.27706i	−0.0230290	−	0.0555767i
$529$	−10.0713			−0.437884
$530$	−12.1222	+	1.19433i	−0.526555	+	0.0518783i
$531$	−28.5808	+	28.5808i	−1.24030	+	1.24030i
$532$	−10.6942	+	8.75597i	−0.463650	+	0.379619i
$533$	−15.6089	−	15.6089i	−0.676096	−	0.676096i
$534$	1.72387	−	2.10068i	0.0745991	−	0.0909052i
$535$			7.38073i			0.319097i
$536$	8.08750	+	4.32186i	0.349327	+	0.186676i
$537$	1.15871			0.0500020
$538$	−14.0098	−	11.4968i	−0.604006	−	0.495662i
$539$	9.50755	−	1.86725i	0.409519	−	0.0804283i
$540$	2.90792	−	0.578616i	0.125137	−	0.0248997i
$541$	−3.16209	+	3.16209i	−0.135949	+	0.135949i	−0.771806	−	0.635857i	$-0.780647\pi$
$541$	−3.16209	+	3.16209i	−0.135949	+	0.135949i	0.635857	+	0.771806i	$0.280647\pi$
$542$	31.1730	−	3.07128i	1.33899	−	0.131923i
$543$		−	4.56794i		−	0.196029i
$544$	−19.7492	−	36.9339i	−0.846741	−	1.58353i
$545$		−	13.2354i		−	0.566944i
$546$	3.33846	+	0.668152i	0.142873	+	0.0285943i
$547$	−25.4712	−	25.4712i	−1.08907	−	1.08907i	−0.995624	−	0.0934460i	$-0.970212\pi$
$547$	−25.4712	−	25.4712i	−1.08907	−	1.08907i	−0.0934460	−	0.995624i	$-0.529788\pi$
$548$	0.810239	+	4.07197i	0.0346117	+	0.173946i
$549$	−25.6960	+	25.6960i	−1.09668	+	1.09668i
$550$	1.51322	+	1.24178i	0.0645237	+	0.0529498i
$551$		−	11.0992i		−	0.472841i
$552$	−1.19674	+	2.23946i	−0.0509365	+	0.0953176i
$553$	0.866967	−	2.84560i	0.0368672	−	0.121007i
$554$	28.0211	+	22.9948i	1.19050	+	0.976956i
$555$	−1.68446	+	1.68446i	−0.0715012	+	0.0715012i
$556$	−28.9095	−	19.3140i	−1.22604	−	0.819098i
$557$	−14.5968	+	14.5968i	−0.618485	+	0.618485i	−0.945143	−	0.326658i	$-0.894078\pi$
$557$	−14.5968	+	14.5968i	−0.618485	+	0.618485i	0.326658	+	0.945143i	$0.394078\pi$
$558$	−4.31366	−	43.7828i	−0.182612	−	1.85348i
$559$	6.60395			0.279317
$560$	−6.72263	+	8.17351i	−0.284083	+	0.345394i
$561$	2.55868			0.108027
$562$	−1.33640	−	13.5642i	−0.0563724	−	0.572170i
$563$	25.5265	−	25.5265i	1.07581	−	1.07581i	0.0789337	−	0.996880i	$-0.474848\pi$
$563$	25.5265	−	25.5265i	1.07581	−	1.07581i	0.996880	−	0.0789337i	$-0.0251515\pi$
$564$	0.897554	−	1.34347i	0.0377938	−	0.0565704i
$565$	−6.95259	+	6.95259i	−0.292498	+	0.292498i
$566$	−1.69014	−	1.38697i	−0.0710417	−	0.0582986i
$567$	21.3680	+	6.51017i	0.897372	+	0.273401i
$568$	29.0562	−	8.81717i	1.21917	−	0.369960i
$569$		−	12.4537i		−	0.522084i	−0.965327	−	0.261042i	$-0.915934\pi$
$569$		−	12.4537i		−	0.522084i	0.965327	−	0.261042i	$-0.0840662\pi$
$570$	0.712943	+	0.585058i	0.0298619	+	0.0245054i
$571$	−15.2950	+	15.2950i	−0.640077	+	0.640077i	−0.950574	−	0.310497i	$-0.899504\pi$
$571$	−15.2950	+	15.2950i	−0.640077	+	0.640077i	0.310497	+	0.950574i	$0.399504\pi$
$572$	9.89531	−	1.96896i	0.413744	−	0.0823264i
$573$	−3.01760	−	3.01760i	−0.126062	−	0.126062i
$574$	−22.2219	−	4.44743i	−0.927523	−	0.185632i
$575$		−	3.59564i		−	0.149949i
$576$	13.0604	+	19.5381i	0.544184	+	0.814088i
$577$		−	6.33648i		−	0.263791i	−0.991264	−	0.131896i	$-0.957894\pi$
$577$		−	6.33648i		−	0.263791i	0.991264	−	0.131896i	$-0.0421064\pi$
$578$	53.2236	−	5.24380i	2.21381	−	0.218113i
$579$	3.33582	−	3.33582i	0.138632	−	0.138632i
$580$	−1.65853	−	8.33518i	−0.0688667	−	0.346100i
$581$	5.73203	−	3.05492i	0.237805	−	0.126739i
$582$	2.97575	+	2.44198i	0.123349	+	0.101223i
$583$	11.9221			0.493764
$584$	−10.8352	+	3.28798i	−0.448365	+	0.136057i
$585$			10.7064i			0.442656i
$586$	−29.3112	+	35.7182i	−1.21083	+	1.47550i
$587$	26.0843	+	26.0843i	1.07662	+	1.07662i	0.996811	+	0.0798046i	$0.0254296\pi$
$587$	26.0843	+	26.0843i	1.07662	+	1.07662i	0.0798046	+	0.996811i	$0.474570\pi$
$588$	3.23247	−	1.33002i	0.133305	−	0.0548490i
$589$	19.5589	−	19.5589i	0.805908	−	0.805908i
$590$	−19.3644	+	1.90786i	−0.797221	+	0.0785453i
$591$	−1.03471			−0.0425623
$592$	−35.2618	−	14.6006i	−1.44925	−	0.600081i
$593$		−	11.6626i		−	0.478925i	−0.970906	−	0.239462i	$-0.923029\pi$
$593$		−	11.6626i		−	0.478925i	0.970906	−	0.239462i	$-0.0769711\pi$
$594$	−2.88796	+	0.284533i	−0.118494	+	0.0116745i
$595$	−9.21315	−	17.2869i	−0.377702	−	0.708694i
$596$	9.59871	+	6.41276i	0.393178	+	0.262677i
$597$	−3.08025	−	3.08025i	−0.126066	−	0.126066i
$598$	−14.3262	−	11.7564i	−0.585841	−	0.480756i
$599$	−4.35971			−0.178133			−0.0890664	−	0.996026i	$-0.528388\pi$
$599$	−4.35971			−0.178133			−0.0890664	+	0.996026i	$0.528388\pi$
$600$	0.622825	+	0.332830i	0.0254267	+	0.0135877i
$601$	39.9253			1.62859			0.814293	−	0.580454i	$-0.197125\pi$
$601$	39.9253			1.62859			0.814293	+	0.580454i	$0.197125\pi$
$602$	5.64175	−	3.76009i	0.229940	−	0.153250i
$603$	6.73449	−	6.73449i	0.274249	−	0.274249i
$604$	−40.6529	+	8.08909i	−1.65414	+	0.329141i
$605$	6.42341	+	6.42341i	0.261149	+	0.261149i
$606$	−0.360398	−	3.65797i	−0.0146402	−	0.148595i
$607$	−31.4255			−1.27552			−0.637761	−	0.770234i	$-0.720139\pi$
$607$	−31.4255			−1.27552			−0.637761	+	0.770234i	$0.720139\pi$
$608$	−4.28689	+	14.1402i	−0.173856	+	0.573460i
$609$	−0.818065	+	2.68510i	−0.0331497	+	0.108806i
$610$	−17.4099	+	1.71529i	−0.704906	+	0.0694501i
$611$	8.33857	+	8.33857i	0.337343	+	0.337343i
$612$	−42.6637	+	8.48919i	−1.72458	+	0.343155i
$613$	27.5057	+	27.5057i	1.11094	+	1.11094i	0.993023	+	0.117921i	$0.0376231\pi$
$613$	27.5057	+	27.5057i	1.11094	+	1.11094i	0.117921	+	0.993023i	$0.462377\pi$
$614$	29.2624	−	35.6587i	1.18094	−	1.43907i
$615$			1.51222i			0.0609784i
$616$	7.33248	−	7.31617i	0.295434	−	0.294777i
$617$		−	13.9785i		−	0.562751i	−0.959598	−	0.281376i	$-0.909209\pi$
$617$		−	13.9785i		−	0.562751i	0.959598	−	0.281376i	$-0.0907907\pi$
$618$	3.46456	+	2.84310i	0.139365	+	0.114366i
$619$	7.34739	+	7.34739i	0.295316	+	0.295316i	0.839176	−	0.543860i	$-0.183038\pi$
$619$	7.34739	+	7.34739i	0.295316	+	0.295316i	−0.543860	+	0.839176i	$0.683038\pi$
$620$	11.7655	−	17.6108i	0.472515	−	0.707267i
$621$	3.76917	+	3.76917i	0.151252	+	0.151252i
$622$	2.07747	+	21.0860i	0.0832992	+	0.845471i
$623$	19.4784	+	5.93446i	0.780385	+	0.237759i
$624$	3.36250	−	1.39330i	0.134608	−	0.0557767i
$625$	−1.00000			−0.0400000
$626$	−3.42569	+	0.337512i	−0.136918	+	0.0134897i
$627$	−0.638288	−	0.638288i	−0.0254908	−	0.0254908i
$628$	22.7268	+	15.1835i	0.906899	+	0.605886i
$629$	49.9516	−	49.9516i	1.99170	−	1.99170i
$630$	6.09591	+	9.14648i	0.242867	+	0.364405i
$631$	30.8802			1.22932			0.614660	−	0.788792i	$-0.289293\pi$
$631$	30.8802			1.22932			0.614660	+	0.788792i	$0.289293\pi$
$632$	−0.923438	−	3.04311i	−0.0367324	−	0.121048i
$633$	−4.63169			−0.184093
$634$	−8.99831	+	10.9652i	−0.357368	+	0.435483i
$635$	8.52114	+	8.52114i	0.338151	+	0.338151i
$636$	4.21824	−	0.839343i	0.167264	−	0.0332821i
$637$	4.91650	+	25.0335i	0.194799	+	0.991864i
$638$	0.815577	+	8.27796i	0.0322890	+	0.327727i
$639$		−	31.5373i		−	1.24760i
$640$	−1.10640	+	11.2595i	−0.0437342	+	0.445070i
$641$	−24.9879			−0.986962			−0.493481	−	0.869756i	$-0.664276\pi$
$641$	−24.9879			−0.986962			−0.493481	+	0.869756i	$0.664276\pi$
$642$	−0.255521	−	2.59349i	−0.0100846	−	0.102357i
$643$	−12.5054	+	12.5054i	−0.493166	+	0.493166i	−0.909302	−	0.416136i	$-0.863384\pi$
$643$	−12.5054	+	12.5054i	−0.493166	+	0.493166i	0.416136	+	0.909302i	$0.363384\pi$
$644$	−18.9326	−	1.88661i	−0.746049	−	0.0743428i
$645$	−0.319901	−	0.319901i	−0.0125961	−	0.0125961i
$646$	−21.1419	−	17.3495i	−0.831816	−	0.682609i
$647$			23.7903i			0.935293i	0.883916	+	0.467647i	$0.154898\pi$
$647$			23.7903i			0.935293i	−0.883916	+	0.467647i	$0.845102\pi$
$648$	22.8511	−	6.93421i	0.897676	−	0.272402i
$649$	19.0448			0.747573
$650$	−3.26963	+	3.98432i	−0.128245	+	0.156278i
$651$	−6.17323	+	3.29006i	−0.241948	+	0.128948i
$652$	−3.73139	−	2.49289i	−0.146133	−	0.0976291i
$653$	−2.86761	+	2.86761i	−0.112218	+	0.112218i	−0.760986	−	0.648768i	$-0.775285\pi$
$653$	−2.86761	+	2.86761i	−0.112218	+	0.112218i	0.648768	+	0.760986i	$0.275285\pi$
$654$	0.458212	+	4.65077i	0.0179175	+	0.181859i
$655$			8.87480i			0.346767i
$656$	−22.3819	+	9.27427i	−0.873867	+	0.362099i
$657$			11.7604i			0.458818i
$658$	11.8714	+	2.37591i	0.462794	+	0.0926224i
$659$	26.6806	+	26.6806i	1.03933	+	1.03933i	0.999194	+	0.0401351i	$0.0127788\pi$
$659$	26.6806	+	26.6806i	1.03933	+	1.03933i	0.0401351	+	0.999194i	$0.487221\pi$
$660$	−0.574715	−	0.383959i	−0.0223708	−	0.0149456i
$661$	2.65709	−	2.65709i	0.103349	−	0.103349i	−0.653542	−	0.756890i	$-0.726718\pi$
$661$	2.65709	−	2.65709i	0.103349	−	0.103349i	0.756890	+	0.653542i	$0.226718\pi$
$662$	−4.73429	+	5.76912i	−0.184003	+	0.224223i
$663$			6.73703i			0.261645i
$664$	3.27267	−	6.12415i	0.127004	−	0.237663i
$665$	−2.01408	+	6.61071i	−0.0781026	+	0.256352i
$666$	−25.1458	+	30.6422i	−0.974379	+	1.18736i
$667$	10.8039	−	10.8039i	0.418327	−	0.418327i
$668$	−5.23321	−	26.3003i	−0.202479	−	1.01759i
$669$	0.617719	−	0.617719i	0.0238824	−	0.0238824i
$670$	4.56283	−	0.449548i	0.176278	−	0.0173676i
$671$	17.1225			0.661007
$672$	2.07928	−	3.10480i	0.0802100	−	0.119770i
$673$	−3.09585			−0.119336			−0.0596681	−	0.998218i	$-0.519004\pi$
$673$	−3.09585			−0.119336			−0.0596681	+	0.998218i	$0.519004\pi$
$674$	−15.7588	+	1.55262i	−0.607006	+	0.0598046i
$675$	1.04826	−	1.04826i	0.0403476	−	0.0403476i
$676$	0.110311	+	0.554385i	0.00424274	+	0.0213225i
$677$	−9.01828	+	9.01828i	−0.346601	+	0.346601i	−0.858842	−	0.512241i	$-0.828815\pi$
$677$	−9.01828	+	9.01828i	−0.346601	+	0.346601i	0.512241	+	0.858842i	$0.328815\pi$
$678$	2.20235	−	2.68375i	0.0845809	−	0.103069i
$679$	−8.40657	+	27.5925i	−0.322614	+	1.05890i
$680$	−18.4695	−	9.86985i	−0.708273	−	0.378492i
$681$			1.19017i			0.0456074i
$682$	−13.1501	+	16.0245i	−0.503544	+	0.613611i
$683$	29.3053	−	29.3053i	1.12134	−	1.12134i	0.129797	−	0.991541i	$-0.458568\pi$
$683$	29.3053	−	29.3053i	1.12134	−	1.12134i	0.991541	−	0.129797i	$-0.0414324\pi$
$684$	12.7606	+	8.52517i	0.487914	+	0.325968i
$685$	1.46788	+	1.46788i	0.0560849	+	0.0560849i
$686$	18.4535	+	18.5868i	0.704557	+	0.709647i
$687$			1.62533i			0.0620102i
$688$	2.77285	−	6.69669i	0.105714	−	0.255309i
$689$			31.3911i			1.19591i
$690$	0.124481	+	1.26346i	0.00473893	+	0.0480993i
$691$	10.1726	−	10.1726i	0.386983	−	0.386983i	−0.486627	−	0.873610i	$-0.661773\pi$
$691$	10.1726	−	10.1726i	0.386983	−	0.386983i	0.873610	+	0.486627i	$0.161773\pi$
$692$	6.83484	+	4.56626i	0.259822	+	0.173583i
$693$	−5.05990	−	9.49403i	−0.192210	−	0.360648i
$694$	2.15515	−	2.62624i	0.0818086	−	0.0996906i
$695$	−17.3839			−0.659407
$696$	0.871351	+	2.87146i	0.0330285	+	0.108842i
$697$		−	44.8438i		−	1.69858i
$698$	−13.4327	−	11.0232i	−0.508436	−	0.417235i
$699$	−0.334193	−	0.334193i	−0.0126403	−	0.0126403i
$700$	−0.524693	+	5.26542i	−0.0198315	+	0.199014i
$701$	20.9837	−	20.9837i	0.792543	−	0.792543i	−0.189364	−	0.981907i	$-0.560643\pi$
$701$	20.9837	−	20.9837i	0.792543	−	0.792543i	0.981907	+	0.189364i	$0.0606426\pi$
$702$	−0.749179	−	7.60403i	−0.0282759	−	0.286996i
$703$	−24.9218			−0.939945
$704$	2.15820	−	10.8610i	0.0813404	−	0.409339i
$705$		−	0.807855i		−	0.0304256i
$706$	0.0472675	+	0.479757i	0.00177894	+	0.0180559i
$707$	24.3060	−	12.9540i	0.914121	−	0.487186i
$708$	6.73836	−	1.34080i	0.253243	−	0.0503902i
$709$	17.1087	+	17.1087i	0.642531	+	0.642531i	0.951177	−	0.308646i	$-0.0998758\pi$
$709$	17.1087	+	17.1087i	0.642531	+	0.642531i	−0.308646	+	0.951177i	$0.599876\pi$
$710$	9.63116	−	11.7364i	0.361451	−	0.440458i
$711$	−3.30295			−0.123870
$712$	20.8303	−	6.32101i	0.780649	−	0.236890i
$713$	38.0769			1.42599
$714$	3.83586	+	5.75544i	0.143553	+	0.215392i
$715$	3.56711	−	3.56711i	0.133402	−	0.133402i
$716$	7.71792	+	5.15623i	0.288432	+	0.192697i
$717$	−1.96688	−	1.96688i	−0.0734544	−	0.0734544i
$718$	36.0483	−	3.55162i	1.34531	−	0.132545i
$719$	−53.3287			−1.98883			−0.994413	−	0.105559i	$-0.966337\pi$
$719$	−53.3287			−1.98883			−0.994413	+	0.105559i	$0.966337\pi$
$720$	10.8568	+	4.49538i	0.404608	+	0.167533i
$721$	−9.78746	+	32.1249i	−0.364504	+	1.19639i
$722$	−1.68855	−	17.1385i	−0.0628414	−	0.637829i
$723$	2.75178	+	2.75178i	0.102340	+	0.102340i
$724$	20.3273	−	30.4261i	0.755457	−	1.13078i
$725$	−3.00471	−	3.00471i	−0.111592	−	0.111592i
$726$	−2.47948	−	2.03473i	−0.0920223	−	0.0755158i
$727$			21.9423i			0.813793i	0.913474	+	0.406897i	$0.133389\pi$
$727$			21.9423i			0.813793i	−0.913474	+	0.406897i	$0.866611\pi$
$728$	19.2636	+	19.3065i	0.713955	+	0.715548i
$729$		−	23.6919i		−	0.877478i
$730$	−3.59152	+	4.37656i	−0.132928	+	0.161984i
$731$	9.48646	+	9.48646i	0.350869	+	0.350869i
$732$	6.05823	−	1.20546i	0.223919	−	0.0445552i
$733$	−23.7073	−	23.7073i	−0.875648	−	0.875648i	0.117433	−	0.993081i	$-0.462533\pi$
$733$	−23.7073	−	23.7073i	−0.875648	−	0.875648i	−0.993081	+	0.117433i	$0.962533\pi$
$734$	−23.0944	+	2.27535i	−0.852430	+	0.0839847i
$735$	0.974485	−	1.45080i	0.0359444	−	0.0535137i
$736$	−17.9368	+	9.59112i	−0.661158	+	0.353533i
$737$	−4.48752			−0.165300
$738$	2.46721	+	25.0417i	0.0908193	+	0.921799i
$739$	4.51925	+	4.51925i	0.166243	+	0.166243i	0.785326	−	0.619083i	$-0.212495\pi$
$739$	4.51925	+	4.51925i	0.166243	+	0.166243i	−0.619083	+	0.785326i	$0.712495\pi$
$740$	−18.7156	+	3.72403i	−0.688001	+	0.136898i
$741$	1.68062	−	1.68062i	0.0617391	−	0.0617391i
$742$	17.8731	+	26.8174i	0.656143	+	0.984497i
$743$	−1.02788			−0.0377093			−0.0188546	−	0.999822i	$-0.506002\pi$
$743$	−1.02788			−0.0377093			−0.0188546	+	0.999822i	$0.506002\pi$
$744$	−3.52457	+	6.59554i	−0.129217	+	0.241804i
$745$	5.77189			0.211466
$746$	−0.713474	−	0.585494i	−0.0261221	−	0.0214365i
$747$	−5.09960	−	5.09960i	−0.186585	−	0.186585i
$748$	17.0428	+	11.3861i	0.623148	+	0.416316i
$749$	17.2329	−	9.18438i	0.629677	−	0.335590i
$750$	0.351387	−	0.0346201i	0.0128309	−	0.00126415i
$751$		−	39.5491i		−	1.44317i	−0.692328	−	0.721583i	$-0.743415\pi$
$751$		−	39.5491i		−	1.44317i	0.692328	−	0.721583i	$-0.256585\pi$
$752$	11.9569	−	4.95450i	0.436022	−	0.180672i
$753$	0.974879			0.0355266
$754$	−21.7960	+	2.14742i	−0.793762	+	0.0782046i
$755$	−14.6548	+	14.6548i	−0.533341	+	0.533341i
$756$	−4.96952	−	6.06955i	−0.180740	−	0.220748i
$757$	−32.2655	−	32.2655i	−1.17271	−	1.17271i	−0.981562	−	0.191146i	$-0.938779\pi$
$757$	−32.2655	−	32.2655i	−1.17271	−	1.17271i	−0.191146	−	0.981562i	$-0.561221\pi$
$758$	27.7234	−	33.7833i	1.00696	−	1.22706i
$759$		−	1.24261i		−	0.0451039i
$760$	2.14527	+	7.06954i	0.0778170	+	0.256439i
$761$	−3.78659			−0.137264			−0.0686320	−	0.997642i	$-0.521863\pi$
$761$	−3.78659			−0.137264			−0.0686320	+	0.997642i	$0.521863\pi$
$762$	−3.28922	−	2.69922i	−0.119156	−	0.0977823i
$763$	−30.9028	+	16.4698i	−1.11876	+	0.596248i
$764$	−6.67135	−	33.5278i	−0.241361	−	1.21299i
$765$	−15.3796	+	15.3796i	−0.556050	+	0.556050i
$766$	22.8676	−	2.25301i	0.826240	−	0.0814044i
$767$			50.1452i			1.81064i
$768$	−0.00102944	−	3.99474i	−3.71467e−5	−	0.144148i
$769$			35.7569i			1.28943i	0.764424	+	0.644714i	$0.223024\pi$
$769$			35.7569i			1.28943i	−0.764424	+	0.644714i	$0.776976\pi$
$770$	1.01637	−	5.07838i	0.0366276	−	0.183012i
$771$	−2.89040	−	2.89040i	−0.104095	−	0.104095i
$772$	37.0636	−	7.37489i	1.33395	−	0.265428i
$773$	−16.9413	+	16.9413i	−0.609337	+	0.609337i	−0.942773	−	0.333436i	$-0.891792\pi$
$773$	−16.9413	+	16.9413i	−0.609337	+	0.609337i	0.333436	+	0.942773i	$0.391792\pi$
$774$	−5.81937	−	4.77552i	−0.209173	−	0.171652i
$775$		−	10.5897i		−	0.380394i
$776$	8.95414	+	29.5076i	0.321435	+	1.05926i
$777$	6.02905	+	1.83687i	0.216291	+	0.0658972i
$778$	19.6948	+	16.1621i	0.706093	+	0.579438i
$779$	−11.1867	+	11.1867i	−0.400807	+	0.400807i
$780$	1.01097	−	1.51323i	0.0361985	−	0.0541824i
$781$	−10.5074	+	10.5074i	−0.375985	+	0.375985i
$782$	−3.69142	−	37.4672i	−0.132005	−	1.33983i
$783$	6.29943			0.225123
$784$	27.4494	+	5.52546i	0.980336	+	0.197338i
$785$	13.6661			0.487763
$786$	−0.307246	−	3.11849i	−0.0109591	−	0.111233i
$787$	27.4719	−	27.4719i	0.979267	−	0.979267i	−0.0205228	−	0.999789i	$-0.506533\pi$
$787$	27.4719	−	27.4719i	0.979267	−	0.979267i	0.999789	+	0.0205228i	$0.00653308\pi$
$788$	−6.89200	−	4.60444i	−0.245517	−	0.164027i
$789$	1.82654	−	1.82654i	0.0650264	−	0.0650264i
$790$	−1.22917	−	1.00869i	−0.0437319	−	0.0358875i
$791$	24.8849	+	7.58166i	0.884805	+	0.269573i
$792$	−10.1435	−	5.42056i	−0.360434	−	0.192611i
$793$			45.0838i			1.60097i
$794$	−2.40326	−	1.97217i	−0.0852884	−	0.0699898i
$795$	1.52061	−	1.52061i	0.0539305	−	0.0539305i
$796$	−6.80986	−	34.2240i	−0.241369	−	1.21304i
$797$	−28.5576	−	28.5576i	−1.01156	−	1.01156i	−0.999932	−	0.0116300i	$-0.996298\pi$
$797$	−28.5576	−	28.5576i	−1.01156	−	1.01156i	−0.0116300	−	0.999932i	$-0.503702\pi$
$798$	0.478858	−	2.39265i	0.0169514	−	0.0846988i
$799$			23.9564i			0.847518i
$800$	2.66743	+	4.98847i	0.0943078	+	0.176369i
$801$		−	22.6090i		−	0.798849i
$802$	−21.7509	+	2.14298i	−0.768051	+	0.0756714i
$803$	3.91828	−	3.91828i	0.138273	−	0.138273i
$804$	−1.58776	+	0.315931i	−0.0559959	+	0.0111420i
$805$	−8.39530	+	4.47432i	−0.295895	+	0.157699i
$806$	−42.1928	−	34.6245i	−1.48618	−	1.21959i
$807$	3.19955			0.112630
$808$	13.8774	−	25.9688i	0.488204	−	0.913578i
$809$			33.8337i			1.18953i	0.803900	+	0.594764i	$0.202755\pi$
$809$			33.8337i			1.18953i	−0.803900	+	0.594764i	$0.797245\pi$
$810$	7.57437	−	9.23000i	0.266136	−	0.324309i
$811$	−22.8205	−	22.8205i	−0.801336	−	0.801336i	0.181968	−	0.983304i	$-0.441753\pi$
$811$	−22.8205	−	22.8205i	−0.801336	−	0.801336i	−0.983304	+	0.181968i	$0.941753\pi$
$812$	−17.3976	+	14.2445i	−0.610536	+	0.499884i
$813$	−3.91034	+	3.91034i	−0.137142	+	0.137142i
$814$	18.5871	−	1.83128i	0.651479	−	0.0641863i
$815$	−2.24376			−0.0785954
$816$	6.83164	+	2.82873i	0.239155	+	0.0990252i
$817$		−	4.73299i		−	0.165586i
$818$	−14.7909	+	1.45726i	−0.517152	+	0.0509519i
$819$	24.9979	−	13.3228i	0.873497	−	0.465535i
$820$	−6.72933	+	10.0726i	−0.234999	+	0.351749i
$821$	9.05164	+	9.05164i	0.315904	+	0.315904i	0.847192	−	0.531287i	$-0.178292\pi$
$821$	9.05164	+	9.05164i	0.315904	+	0.315904i	−0.531287	+	0.847192i	$0.678292\pi$
$822$	−0.566614	−	0.464977i	−0.0197629	−	0.0162180i
$823$	−10.9205			−0.380663			−0.190332	−	0.981720i	$-0.560956\pi$
$823$	−10.9205			−0.380663			−0.190332	+	0.981720i	$0.560956\pi$
$824$	10.4250	+	34.3546i	0.363171	+	1.19680i
$825$	−0.345587			−0.0120318
$826$	28.5511	+	42.8390i	0.993421	+	1.49056i
$827$	−13.4654	+	13.4654i	−0.468237	+	0.468237i	−0.901343	−	0.433106i	$-0.857418\pi$
$827$	−13.4654	+	13.4654i	−0.468237	+	0.468237i	0.433106	+	0.901343i	$0.357418\pi$
$828$	4.12273	+	20.7194i	0.143275	+	0.720049i
$829$	−28.8777	−	28.8777i	−1.00296	−	1.00296i	−0.999996	−	0.00296878i	$-0.999055\pi$
$829$	−28.8777	−	28.8777i	−1.00296	−	1.00296i	−0.00296878	−	0.999996i	$-0.500945\pi$
$830$	−0.340414	−	3.45514i	−0.0118160	−	0.119930i
$831$	−6.39944			−0.221994
$832$	28.5971	+	5.68258i	0.991427	+	0.197008i
$833$	−28.8978	+	43.0227i	−1.00125	+	1.49065i
$834$	6.10847	−	0.601830i	0.211519	−	0.0208397i
$835$	−9.48085	−	9.48085i	−0.328098	−	0.328098i
$836$	−1.41114	−	7.09188i	−0.0488052	−	0.245278i
$837$	11.1008	+	11.1008i	0.383699	+	0.383699i
$838$	0.620187	−	0.755749i	0.0214240	−	0.0261069i
$839$			2.25826i			0.0779639i	0.999240	+	0.0389820i	$0.0124115\pi$
$839$			2.25826i			0.0779639i	−0.999240	+	0.0389820i	$0.987589\pi$
$840$	0.00208113	−	1.86837i	7.18060e−5	−	0.0644648i
$841$			10.9435i			0.377362i
$842$	−22.5424	−	18.4989i	−0.776864	−	0.637514i
$843$	1.70149	+	1.70149i	0.0586025	+	0.0586025i
$844$	−30.8507	−	20.6109i	−1.06193	−	0.709457i
$845$	0.199847	+	0.199847i	0.00687496	+	0.00687496i
$846$	−1.31803	−	13.3778i	−0.0453149	−	0.459938i
$847$	7.00460	−	22.9908i	0.240681	−	0.789975i
$848$	31.8319	+	13.1804i	1.09311	+	0.452617i
$849$	0.385992			0.0132472
$850$	−10.4202	+	1.02664i	−0.357409	+	0.0352133i
$851$	−24.2587	−	24.2587i	−0.831579	−	0.831579i
$852$	−2.97795	+	4.45744i	−0.102023	+	0.152709i
$853$	13.3778	−	13.3778i	0.458047	−	0.458047i	−0.439967	−	0.898014i	$-0.645010\pi$
$853$	13.3778	−	13.3778i	0.458047	−	0.458047i	0.898014	+	0.439967i	$0.145010\pi$
$854$	25.6693	+	38.5151i	0.878387	+	1.31796i
$855$	7.67319			0.262418
$856$	9.83903	−	18.4118i	0.336291	−	0.629302i
$857$	−46.6899			−1.59490			−0.797448	−	0.603388i	$-0.793817\pi$
$857$	−46.6899			−1.59490			−0.797448	+	0.603388i	$0.793817\pi$
$858$	−1.12994	+	1.37693i	−0.0385756	+	0.0470076i
$859$	2.79689	+	2.79689i	0.0954288	+	0.0954288i	0.753210	−	0.657781i	$-0.228505\pi$
$859$	2.79689	+	2.79689i	0.0954288	+	0.0954288i	−0.657781	+	0.753210i	$0.728505\pi$
$860$	−0.707242	−	3.55435i	−0.0241167	−	0.121202i
$861$	3.53080	−	1.88176i	0.120329	−	0.0641302i
$862$	4.95472	+	50.2895i	0.168758	+	1.71287i
$863$		−	31.6740i		−	1.07820i	−0.842243	−	0.539099i	$-0.818765\pi$
$863$		−	31.6740i		−	1.07820i	0.842243	−	0.539099i	$-0.181235\pi$
$864$	−8.02538	−	2.43306i	−0.273029	−	0.0827744i
$865$	4.10992			0.139742
$866$	0.470016	+	4.77058i	0.0159718	+	0.162111i
$867$	−6.67638	+	6.67638i	−0.226742	+	0.226742i
$868$	−55.7594	−	5.55635i	−1.89260	−	0.188595i
$869$	1.10046	+	1.10046i	0.0373305	+	0.0373305i
$870$	1.15984	+	0.951792i	0.0393222	+	0.0322688i
$871$		−	11.8157i		−	0.400360i
$872$	−17.6438	+	33.0169i	−0.597494	+	1.11809i
$873$	32.0272			1.08396
$874$	−8.42572	+	10.2674i	−0.285004	+	0.347302i
$875$	1.24437	+	2.33485i	0.0420675	+	0.0789324i
$876$	1.11050	−	1.66221i	0.0375202	−	0.0561608i
$877$	8.47123	−	8.47123i	0.286053	−	0.286053i	−0.549464	−	0.835517i	$-0.685168\pi$
$877$	8.47123	−	8.47123i	0.286053	−	0.286053i	0.835517	+	0.549464i	$0.185168\pi$
$878$	−1.02398	−	10.3932i	−0.0345577	−	0.350755i
$879$		−	8.15729i		−	0.275139i
$880$	−2.11945	−	5.11495i	−0.0714467	−	0.172425i
$881$			6.46468i			0.217801i	0.994053	+	0.108900i	$0.0347329\pi$
$881$			6.46468i			0.217801i	−0.994053	+	0.108900i	$0.965267\pi$
$882$	13.7701	−	25.6147i	0.463663	−	0.862491i
$883$	−1.58594	−	1.58594i	−0.0533710	−	0.0533710i	0.679918	−	0.733289i	$-0.262016\pi$
$883$	−1.58594	−	1.58594i	−0.0533710	−	0.0533710i	−0.733289	+	0.679918i	$0.762016\pi$
$884$	−29.9797	+	44.8740i	−1.00833	+	1.50928i
$885$	2.42908	−	2.42908i	0.0816525	−	0.0816525i
$886$	−23.3988	+	28.5134i	−0.786098	+	0.957926i
$887$		−	19.1490i		−	0.642960i	−0.946916	−	0.321480i	$-0.895820\pi$
$887$		−	19.1490i		−	0.642960i	0.946916	−	0.321480i	$-0.104180\pi$
$888$	6.44751	−	1.95651i	0.216364	−	0.0656562i
$889$	9.29212	−	30.4991i	0.311648	−	1.02291i
$890$	6.90455	−	8.41377i	0.231441	−	0.282030i
$891$	−8.26349	+	8.26349i	−0.276837	+	0.276837i
$892$	6.86334	−	1.36566i	0.229802	−	0.0457258i
$893$	5.97618	−	5.97618i	0.199985	−	0.199985i
$894$	−2.02817	+	0.199823i	−0.0678321	+	0.00668308i
$895$	4.64093			0.155129
$896$	27.6660	−	11.4277i	0.924256	−	0.381773i
$897$	3.27181			0.109242
$898$	26.6323	−	2.62392i	0.888732	−	0.0875613i
$899$	31.8190	−	31.8190i	1.06122	−	1.06122i
$900$	5.76236	−	1.14659i	0.192079	−	0.0382197i
$901$	−45.0928	+	45.0928i	−1.50226	+	1.50226i
$902$	7.52126	−	9.16528i	0.250430	−	0.305170i
$903$	−0.348845	+	1.14500i	−0.0116088	+	0.0381031i
$904$	26.6121	−	8.07550i	0.885105	−	0.268587i
$905$		−	18.2958i		−	0.608173i
$906$	4.64215	−	5.65684i	0.154225	−	0.187936i
$907$	31.5859	−	31.5859i	1.04879	−	1.04879i	0.0500460	−	0.998747i	$-0.484063\pi$
$907$	31.5859	−	31.5859i	1.04879	−	1.04879i	0.998747	−	0.0500460i	$-0.0159368\pi$
$908$	−5.29624	+	7.92749i	−0.175762	+	0.263083i
$909$	−21.6243	−	21.6243i	−0.717231	−	0.717231i
$910$	13.3714	+	2.67613i	0.443259	+	0.0887127i
$911$		−	11.2057i		−	0.371263i	−0.982619	−	0.185631i	$-0.940567\pi$
$911$		−	11.2057i		−	0.371263i	0.982619	−	0.185631i	$-0.0594330\pi$
$912$	−0.998567	−	2.40988i	−0.0330659	−	0.0797990i
$913$			3.39811i			0.112461i
$914$	4.43347	+	44.9989i	0.146646	+	1.48843i
$915$	2.18390	−	2.18390i	0.0721974	−	0.0721974i
$916$	−7.23269	+	10.8260i	−0.238975	+	0.357701i
$917$	20.7213	−	11.0436i	0.684279	−	0.364691i
$918$	9.84688	−	11.9992i	0.324995	−	0.396034i
$919$	−2.37775			−0.0784347			−0.0392174	−	0.999231i	$-0.512486\pi$
$919$	−2.37775			−0.0784347			−0.0392174	+	0.999231i	$0.512486\pi$
$920$	−4.79325	+	8.96962i	−0.158029	+	0.295720i
$921$			8.14371i			0.268345i
$922$	1.34926	+	1.10724i	0.0444355	+	0.0364649i
$923$	−27.6662	−	27.6662i	−0.910643	−	0.910643i
$924$	−0.181327	+	1.81966i	−0.00596523	+	0.0598625i
$925$	−6.74670	+	6.74670i	−0.221830	+	0.221830i
$926$	0.498752	+	5.06224i	0.0163900	+	0.166356i
$927$	37.2880			1.22470
$928$	−6.97405	+	23.0037i	−0.228935	+	0.755134i
$929$		−	12.3153i		−	0.404051i	−0.979380	−	0.202026i	$-0.935248\pi$
$929$		−	12.3153i		−	0.404051i	0.979380	−	0.202026i	$-0.0647524\pi$
$930$	0.366617	+	3.72109i	0.0120218	+	0.122019i
$931$	17.9413	−	3.52361i	0.588002	−	0.115482i
$932$	−0.738838	−	3.71314i	−0.0242015	−	0.121628i
$933$	−2.64503	−	2.64503i	−0.0865944	−	0.0865944i
$934$	−6.04354	+	7.36455i	−0.197751	+	0.240976i
$935$	10.2482			0.335151
$936$	14.2724	−	26.7080i	0.466508	−	0.872978i
$937$	−3.38760			−0.110668			−0.0553340	−	0.998468i	$-0.517622\pi$
$937$	−3.38760			−0.110668			−0.0553340	+	0.998468i	$0.517622\pi$
$938$	−6.72750	−	10.0941i	−0.219661	−	0.329585i
$939$	0.429719	−	0.429719i	0.0140233	−	0.0140233i
$940$	3.59494	−	5.38096i	0.117254	−	0.175508i
$941$	−3.59002	−	3.59002i	−0.117031	−	0.117031i	0.646166	−	0.763197i	$-0.276371\pi$
$941$	−3.59002	−	3.59002i	−0.117031	−	0.117031i	−0.763197	+	0.646166i	$0.776371\pi$
$942$	−4.80208	+	0.473120i	−0.156460	+	0.0154151i
$943$	−21.7782			−0.709195
$944$	50.8494	+	21.0548i	1.65501	+	0.685276i
$945$	−3.75196	−	1.14311i	−0.122051	−	0.0371853i
$946$	0.347784	+	3.52994i	0.0113074	+	0.114768i
$947$	−24.0700	−	24.0700i	−0.782171	−	0.782171i	0.198026	−	0.980197i	$-0.436547\pi$
$947$	−24.0700	−	24.0700i	−0.782171	−	0.782171i	−0.980197	+	0.198026i	$0.936547\pi$
$948$	0.466836	+	0.311886i	0.0151621	+	0.0101296i
$949$	10.3169	+	10.3169i	0.334900	+	0.334900i
$950$	2.85552	+	2.34331i	0.0926454	+	0.0760271i
$951$		−	2.50422i		−	0.0812050i
$952$	−0.0617148	+	55.4053i	−0.00200019	+	1.79570i
$953$			1.16774i			0.0378269i	0.999821	+	0.0189134i	$0.00602069\pi$
$953$			1.16774i			0.0378269i	−0.999821	+	0.0189134i	$0.993979\pi$
$954$	22.6999	−	27.6617i	0.734935	−	0.895580i
$955$	−12.0863	−	12.0863i	−0.391102	−	0.391102i
$956$	−4.34841	−	21.8536i	−0.140637	−	0.706794i
$957$	−1.03839	−	1.03839i	−0.0335663	−	0.0335663i
$958$	−3.56676	+	0.351411i	−0.115237	+	0.0113536i
$959$	1.60070	−	5.25389i	0.0516892	−	0.169657i
$960$	−1.11000	−	1.66054i	−0.0358251	−	0.0535937i
$961$	81.1422			2.61749
$962$	4.82178	+	48.9402i	0.155460	+	1.57789i
$963$	−15.3316	−	15.3316i	−0.494052	−	0.494052i
$964$	6.08368	+	30.5744i	0.195942	+	0.984736i
$965$	13.3609	−	13.3609i	0.430101	−	0.430101i
$966$	2.79510	−	1.86287i	0.0899309	−	0.0599367i
$967$	−30.7287			−0.988168			−0.494084	−	0.869414i	$-0.664497\pi$
$967$	−30.7287			−0.988168			−0.494084	+	0.869414i	$0.664497\pi$
$968$	−7.46085	−	24.5866i	−0.239801	−	0.790242i
$969$	4.82837			0.155110
$970$	11.9187	+	9.78076i	0.382686	+	0.314041i
$971$	12.6093	+	12.6093i	0.404652	+	0.404652i	0.879869	−	0.475217i	$-0.157630\pi$
$971$	12.6093	+	12.6093i	0.404652	+	0.404652i	−0.475217	+	0.879869i	$0.657630\pi$
$972$	−7.28320	+	10.9016i	−0.233609	+	0.349669i
$973$	21.6320	+	40.5887i	0.693490	+	1.30121i
$974$	−24.5181	+	2.41562i	−0.785611	+	0.0774014i
$975$		−	0.909936i		−	0.0291413i
$976$	45.7169	+	18.9297i	1.46336	+	0.605924i
$977$	52.9758			1.69485			0.847423	−	0.530918i	$-0.178153\pi$
$977$	52.9758			1.69485			0.847423	+	0.530918i	$0.178153\pi$
$978$	0.788428	−	0.0776790i	0.0252111	−	0.00248390i
$979$	−7.53274	+	7.53274i	−0.240747	+	0.240747i
$980$	12.9469	−	5.32707i	0.413574	−	0.170167i
$981$	27.4932	+	27.4932i	0.877791	+	0.877791i
$982$	−12.9911	+	15.8308i	−0.414563	+	0.505180i
$983$			3.97679i			0.126840i	0.997987	+	0.0634199i	$0.0202007\pi$
$983$			3.97679i			0.126840i	−0.997987	+	0.0634199i	$0.979799\pi$
$984$	2.01589	−	3.77234i	0.0642642	−	0.120258i
$985$	−4.14429			−0.132048
$986$	−34.3943	−	28.2248i	−1.09534	−	0.898861i
$987$	−1.88622	+	1.00527i	−0.0600391	+	0.0319982i
$988$	18.6730	−	3.71554i	0.594067	−	0.118207i
$989$	4.60706	−	4.60706i	0.146496	−	0.146496i
$990$	−5.72280	+	0.563833i	−0.181882	+	0.0179198i
$991$			28.1763i			0.895049i	0.894272	+	0.447524i	$0.147694\pi$
$991$			28.1763i			0.895049i	−0.894272	+	0.447524i	$0.852306\pi$
$992$	−52.8265	+	28.2473i	−1.67724	+	0.896853i
$993$		−	1.31755i		−	0.0418111i
$994$	−39.3874	−	7.88291i	−1.24929	−	0.250031i
$995$	−12.3372	−	12.3372i	−0.391116	−	0.391116i
$996$	0.239235	+	1.20231i	0.00758044	+	0.0380966i
$997$	−41.7859	+	41.7859i	−1.32337	+	1.32337i	−0.412348	+	0.911027i	$0.635291\pi$
$997$	−41.7859	+	41.7859i	−1.32337	+	1.32337i	−0.911027	+	0.412348i	$0.864709\pi$
$998$	4.18277	+	3.43248i	0.132403	+	0.108653i
$999$		−	14.1446i		−	0.447515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bc.a.251.2	yes	128
7.6	odd	2	inner	560.2.bc.a.251.1	✓	128
16.3	odd	4	inner	560.2.bc.a.531.1	yes	128
112.83	even	4	inner	560.2.bc.a.531.2	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bc.a.251.1	✓	128	7.6	odd	2	inner
560.2.bc.a.251.2	yes	128	1.1	even	1	trivial
560.2.bc.a.531.1	yes	128	16.3	odd	4	inner
560.2.bc.a.531.2	yes	128	112.83	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40740 + 0.138663i) q^{2} +(0.176544 - 0.176544i) q^{3} +(1.96155 - 0.390307i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.223988 + 0.272948i) q^{6} +(-2.53089 - 0.771085i) q^{7} +(-2.70656 + 0.821311i) q^{8} +2.93766i q^{9} +O(q^{10})\)	\(q+(-1.40740 + 0.138663i) q^{2} +(0.176544 - 0.176544i) q^{3} +(1.96155 - 0.390307i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.223988 + 0.272948i) q^{6} +(-2.53089 - 0.771085i) q^{7} +(-2.70656 + 0.821311i) q^{8} +2.93766i q^{9} +(-0.897132 + 1.09323i) q^{10} +(0.978755 - 0.978755i) q^{11} +(0.277393 - 0.415206i) q^{12} +(2.57707 + 2.57707i) q^{13} +(3.66890 + 0.734285i) q^{14} -0.249671i q^{15} +(3.69532 - 1.53121i) q^{16} +7.40385i q^{17} +(-0.407344 - 4.13447i) q^{18} +(1.84697 - 1.84697i) q^{19} +(1.11103 - 1.66301i) q^{20} +(-0.582946 + 0.310684i) q^{21} +(-1.24178 + 1.51322i) q^{22} +3.59564 q^{23} +(-0.332830 + 0.622825i) q^{24} -1.00000i q^{25} +(-3.98432 - 3.26963i) q^{26} +(1.04826 + 1.04826i) q^{27} +(-5.26542 - 0.524693i) q^{28} +(3.00471 - 3.00471i) q^{29} +(0.0346201 + 0.351387i) q^{30} +10.5897 q^{31} +(-4.98847 + 2.66743i) q^{32} -0.345587i q^{33} +(-1.02664 - 10.4202i) q^{34} +(-2.33485 + 1.24437i) q^{35} +(1.14659 + 5.76236i) q^{36} +(-6.74670 - 6.74670i) q^{37} +(-2.34331 + 2.85552i) q^{38} +0.909936 q^{39} +(-1.33307 + 2.49458i) q^{40} -6.05682 q^{41} +(0.777357 - 0.518090i) q^{42} +(1.28129 - 1.28129i) q^{43} +(1.53786 - 2.30189i) q^{44} +(2.07724 + 2.07724i) q^{45} +(-5.06051 + 0.498581i) q^{46} +3.23567 q^{47} +(0.382062 - 0.922714i) q^{48} +(5.81085 + 3.90307i) q^{49} +(0.138663 + 1.40740i) q^{50} +(1.30711 + 1.30711i) q^{51} +(6.06090 + 4.04920i) q^{52} +(6.09045 + 6.09045i) q^{53} +(-1.62068 - 1.32997i) q^{54} -1.38417i q^{55} +(7.48331 + 0.00833549i) q^{56} -0.652143i q^{57} +(-3.81218 + 4.64546i) q^{58} +(9.72909 + 9.72909i) q^{59} +(-0.0974485 - 0.489742i) q^{60} +(8.74709 + 8.74709i) q^{61} +(-14.9040 + 1.46840i) q^{62} +(2.26519 - 7.43492i) q^{63} +(6.65090 - 4.44585i) q^{64} +3.64453 q^{65} +(0.0479200 + 0.486379i) q^{66} +(-2.29246 - 2.29246i) q^{67} +(2.88978 + 14.5230i) q^{68} +(0.634791 - 0.634791i) q^{69} +(3.11352 - 2.07509i) q^{70} -10.7355 q^{71} +(-2.41273 - 7.95095i) q^{72} +4.00333 q^{73} +(10.4308 + 8.55978i) q^{74} +(-0.176544 - 0.176544i) q^{75} +(2.90202 - 4.34379i) q^{76} +(-3.23183 + 1.72242i) q^{77} +(-1.28064 + 0.126174i) q^{78} +1.12435i q^{79} +(1.53026 - 3.69572i) q^{80} -8.44286 q^{81} +(8.52437 - 0.839854i) q^{82} +(-1.73594 + 1.73594i) q^{83} +(-1.02221 + 0.836949i) q^{84} +(5.23531 + 5.23531i) q^{85} +(-1.62562 + 1.98095i) q^{86} -1.06093i q^{87} +(-1.84519 + 3.45292i) q^{88} -7.69624 q^{89} +(-3.21154 - 2.63547i) q^{90} +(-4.53516 - 8.50945i) q^{91} +(7.05302 - 1.40341i) q^{92} +(1.86956 - 1.86956i) q^{93} +(-4.55388 + 0.448667i) q^{94} -2.61200i q^{95} +(-0.409767 + 1.35161i) q^{96} -10.9023i q^{97} +(-8.71940 - 4.68743i) q^{98} +(2.87525 + 2.87525i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 4 q^{4}+O(q^{10}) \) 128 * q - 4 * q^4	\( 128 q - 4 q^{4} + 8 q^{11} - 8 q^{14} + 20 q^{16} + 20 q^{18} - 52 q^{22} - 16 q^{23} + 44 q^{28} + 16 q^{29} + 40 q^{32} + 16 q^{37} + 60 q^{42} - 8 q^{43} - 108 q^{44} - 40 q^{46} - 4 q^{50} + 80 q^{51} + 16 q^{53} + 12 q^{56} - 76 q^{58} - 56 q^{60} - 52 q^{64} + 40 q^{67} - 8 q^{70} - 64 q^{71} - 36 q^{72} + 60 q^{74} - 48 q^{78} - 128 q^{81} - 32 q^{84} + 76 q^{86} + 20 q^{88} - 32 q^{91} + 64 q^{92} - 76 q^{98} - 40 q^{99}+O(q^{100}) \) 128 * q - 4 * q^4 + 8 * q^11 - 8 * q^14 + 20 * q^16 + 20 * q^18 - 52 * q^22 - 16 * q^23 + 44 * q^28 + 16 * q^29 + 40 * q^32 + 16 * q^37 + 60 * q^42 - 8 * q^43 - 108 * q^44 - 40 * q^46 - 4 * q^50 + 80 * q^51 + 16 * q^53 + 12 * q^56 - 76 * q^58 - 56 * q^60 - 52 * q^64 + 40 * q^67 - 8 * q^70 - 64 * q^71 - 36 * q^72 + 60 * q^74 - 48 * q^78 - 128 * q^81 - 32 * q^84 + 76 * q^86 + 20 * q^88 - 32 * q^91 + 64 * q^92 - 76 * q^98 - 40 * q^99

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