LMFDB - Embedded newform 560.2.bc.a.251.4

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			251.4
Character	$\chi$	$=$	560.251
Dual form			560.2.bc.a.531.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40603 - 0.151956i) q^{2} +(0.503741 - 0.503741i) q^{3} +(1.95382 + 0.427308i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.784820 + 0.631727i) q^{6} +(1.62955 - 2.08436i) q^{7} +(-2.68219 - 0.897701i) q^{8} +2.49249i q^{9} +O(q^{10})$	\(q+(-1.40603 - 0.151956i) q^{2} +(0.503741 - 0.503741i) q^{3} +(1.95382 + 0.427308i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.784820 + 0.631727i) q^{6} +(1.62955 - 2.08436i) q^{7} +(-2.68219 - 0.897701i) q^{8} +2.49249i q^{9} +(1.10166 - 0.886762i) q^{10} +(-3.83792 + 3.83792i) q^{11} +(1.19947 - 0.768967i) q^{12} +(2.58425 + 2.58425i) q^{13} +(-2.60792 + 2.68305i) q^{14} +0.712398i q^{15} +(3.63482 + 1.66976i) q^{16} +2.62187i q^{17} +(0.378749 - 3.50451i) q^{18} +(2.39277 - 2.39277i) q^{19} +(-1.68371 + 1.07941i) q^{20} +(-0.229107 - 1.87085i) q^{21} +(5.97942 - 4.81303i) q^{22} +2.53426 q^{23} +(-1.80334 + 0.898920i) q^{24} -1.00000i q^{25} +(-3.24083 - 4.02621i) q^{26} +(2.76679 + 2.76679i) q^{27} +(4.07451 - 3.37615i) q^{28} +(-4.44955 + 4.44955i) q^{29} +(0.108253 - 1.00165i) q^{30} -6.69517 q^{31} +(-4.85692 - 2.90006i) q^{32} +3.86664i q^{33} +(0.398409 - 3.68642i) q^{34} +(0.321600 + 2.62613i) q^{35} +(-1.06506 + 4.86987i) q^{36} +(2.88110 + 2.88110i) q^{37} +(-3.72789 + 3.00070i) q^{38} +2.60358 q^{39} +(2.53136 - 1.26182i) q^{40} +10.7555 q^{41} +(0.0378437 + 2.66528i) q^{42} +(-3.75959 + 3.75959i) q^{43} +(-9.13858 + 5.85863i) q^{44} +(-1.76246 - 1.76246i) q^{45} +(-3.56324 - 0.385096i) q^{46} +12.9999 q^{47} +(2.67214 - 0.989877i) q^{48} +(-1.68913 - 6.79315i) q^{49} +(-0.151956 + 1.40603i) q^{50} +(1.32075 + 1.32075i) q^{51} +(3.94488 + 6.15342i) q^{52} +(1.07796 + 1.07796i) q^{53} +(-3.46975 - 4.31061i) q^{54} -5.42764i q^{55} +(-6.24189 + 4.12780i) q^{56} -2.41067i q^{57} +(6.93231 - 5.58004i) q^{58} +(-5.89390 - 5.89390i) q^{59} +(-0.304413 + 1.39190i) q^{60} +(6.59740 + 6.59740i) q^{61} +(9.41359 + 1.01737i) q^{62} +(5.19525 + 4.06164i) q^{63} +(6.38827 + 4.81560i) q^{64} -3.65468 q^{65} +(0.587559 - 5.43660i) q^{66} +(4.41889 + 4.41889i) q^{67} +(-1.12035 + 5.12266i) q^{68} +(1.27661 - 1.27661i) q^{69} +(-0.0531216 - 3.74128i) q^{70} +12.8438 q^{71} +(2.23751 - 6.68533i) q^{72} -10.9703 q^{73} +(-3.61310 - 4.48869i) q^{74} +(-0.503741 - 0.503741i) q^{75} +(5.69748 - 3.65259i) q^{76} +(1.74553 + 14.2537i) q^{77} +(-3.66071 - 0.395630i) q^{78} +12.6491i q^{79} +(-3.75090 + 1.38950i) q^{80} -4.68997 q^{81} +(-15.1225 - 1.63436i) q^{82} +(6.43343 - 6.43343i) q^{83} +(0.351796 - 3.75320i) q^{84} +(-1.85394 - 1.85394i) q^{85} +(5.85738 - 4.71479i) q^{86} +4.48284i q^{87} +(13.7393 - 6.84873i) q^{88} -17.3593 q^{89} +(2.21024 + 2.74588i) q^{90} +(9.59766 - 1.17534i) q^{91} +(4.95149 + 1.08291i) q^{92} +(-3.37264 + 3.37264i) q^{93} +(-18.2781 - 1.97540i) q^{94} +3.38389i q^{95} +(-3.90751 + 0.985746i) q^{96} +1.67254i q^{97} +(1.34270 + 9.80801i) q^{98} +(-9.56599 - 9.56599i) 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 $

$2$	−1.40603	−	0.151956i	−0.994211	−	0.107449i
$2$	−1.40603	−	0.151956i	−0.994211	−	0.107449i
$3$	0.503741	−	0.503741i	0.290835	−	0.290835i	−0.546575	−	0.837410i	$-0.684069\pi$
$3$	0.503741	−	0.503741i	0.290835	−	0.290835i	0.837410	+	0.546575i	$0.184069\pi$
$4$	1.95382	+	0.427308i	0.976909	+	0.213654i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	−0.784820	+	0.631727i	−0.320401	+	0.257901i
$7$	1.62955	−	2.08436i	0.615912	−	0.787815i
$7$	1.62955	−	2.08436i	0.615912	−	0.787815i
$8$	−2.68219	−	0.897701i	−0.948297	−	0.317385i
$9$			2.49249i			0.830830i
$10$	1.10166	−	0.886762i	0.348375	−	0.280419i
$11$	−3.83792	+	3.83792i	−1.15718	+	1.15718i	−0.172098	+	0.985080i	$0.555055\pi$
$11$	−3.83792	+	3.83792i	−1.15718	+	1.15718i	−0.985080	+	0.172098i	$0.944945\pi$
$12$	1.19947	−	0.768967i	0.346258	−	0.221982i
$13$	2.58425	+	2.58425i	0.716741	+	0.716741i	0.967936	−	0.251195i	$-0.0808237\pi$
$13$	2.58425	+	2.58425i	0.716741	+	0.716741i	−0.251195	+	0.967936i	$0.580824\pi$
$14$	−2.60792	+	2.68305i	−0.696996	+	0.717075i
$15$			0.712398i			0.183940i
$16$	3.63482	+	1.66976i	0.908704	+	0.417441i
$17$			2.62187i			0.635897i	0.948108	+	0.317949i	$0.102994\pi$
$17$			2.62187i			0.635897i	−0.948108	+	0.317949i	$0.897006\pi$
$18$	0.378749	−	3.50451i	0.0892719	−	0.826020i
$19$	2.39277	−	2.39277i	0.548939	−	0.548939i	−0.377195	−	0.926134i	$-0.623111\pi$
$19$	2.39277	−	2.39277i	0.548939	−	0.548939i	0.926134	+	0.377195i	$0.123111\pi$
$20$	−1.68371	+	1.07941i	−0.376489	+	0.241363i
$21$	−0.229107	−	1.87085i	−0.0499953	−	0.408253i
$22$	5.97942	−	4.81303i	1.27482	−	1.02614i
$23$	2.53426			0.528430			0.264215	−	0.964464i	$-0.414887\pi$
$23$	2.53426			0.528430			0.264215	+	0.964464i	$0.414887\pi$
$24$	−1.80334	+	0.898920i	−0.368105	+	0.183491i
$25$		−	1.00000i		−	0.200000i
$26$	−3.24083	−	4.02621i	−0.635578	−	0.789605i
$27$	2.76679	+	2.76679i	0.532470	+	0.532470i
$28$	4.07451	−	3.37615i	0.770010	−	0.638032i
$29$	−4.44955	+	4.44955i	−0.826260	+	0.826260i	−0.986997	−	0.160737i	$-0.948613\pi$
$29$	−4.44955	+	4.44955i	−0.826260	+	0.826260i	0.160737	+	0.986997i	$0.448613\pi$
$30$	0.108253	−	1.00165i	0.0197642	−	0.182875i
$31$	−6.69517			−1.20249			−0.601244	−	0.799065i	$-0.705328\pi$
$31$	−6.69517			−1.20249			−0.601244	+	0.799065i	$0.705328\pi$
$32$	−4.85692	−	2.90006i	−0.858589	−	0.512664i
$33$			3.86664i			0.673096i
$34$	0.398409	−	3.68642i	0.0683266	−	0.632216i
$35$	0.321600	+	2.62613i	0.0543603	+	0.443897i
$36$	−1.06506	+	4.86987i	−0.177510	+	0.811645i
$37$	2.88110	+	2.88110i	0.473649	+	0.473649i	0.903093	−	0.429444i	$-0.141291\pi$
$37$	2.88110	+	2.88110i	0.473649	+	0.473649i	−0.429444	+	0.903093i	$0.641291\pi$
$38$	−3.72789	+	3.00070i	−0.604744	+	0.486778i
$39$	2.60358			0.416907
$40$	2.53136	−	1.26182i	0.400244	−	0.199512i
$41$	10.7555			1.67972			0.839861	−	0.542801i	$-0.182636\pi$
$41$	10.7555			1.67972			0.839861	+	0.542801i	$0.182636\pi$
$42$	0.0378437	+	2.66528i	0.00583941	+	0.411262i
$43$	−3.75959	+	3.75959i	−0.573333	+	0.573333i	−0.933058	−	0.359725i	$-0.882870\pi$
$43$	−3.75959	+	3.75959i	−0.573333	+	0.573333i	0.359725	+	0.933058i	$0.382870\pi$
$44$	−9.13858	+	5.85863i	−1.37769	+	0.883222i
$45$	−1.76246	−	1.76246i	−0.262731	−	0.262731i
$46$	−3.56324	−	0.385096i	−0.525371	−	0.0567793i
$47$	12.9999			1.89622			0.948112	−	0.317937i	$-0.102990\pi$
$47$	12.9999			1.89622			0.948112	+	0.317937i	$0.102990\pi$
$48$	2.67214	−	0.989877i	0.385690	−	0.142876i
$49$	−1.68913	−	6.79315i	−0.241304	−	0.970450i
$50$	−0.151956	+	1.40603i	−0.0214898	+	0.198842i
$51$	1.32075	+	1.32075i	0.184941	+	0.184941i
$52$	3.94488	+	6.15342i	0.547056	+	0.853325i
$53$	1.07796	+	1.07796i	0.148069	+	0.148069i	0.777255	−	0.629186i	$-0.216612\pi$
$53$	1.07796	+	1.07796i	0.148069	+	0.148069i	−0.629186	+	0.777255i	$0.716612\pi$
$54$	−3.46975	−	4.31061i	−0.472174	−	0.586600i
$55$		−	5.42764i		−	0.731863i
$56$	−6.24189	+	4.12780i	−0.834108	+	0.551601i
$57$		−	2.41067i		−	0.319301i
$58$	6.93231	−	5.58004i	0.910257	−	0.732696i
$59$	−5.89390	−	5.89390i	−0.767321	−	0.767321i	0.210313	−	0.977634i	$-0.432552\pi$
$59$	−5.89390	−	5.89390i	−0.767321	−	0.767321i	−0.977634	+	0.210313i	$0.932552\pi$
$60$	−0.304413	+	1.39190i	−0.0392996	+	0.179693i
$61$	6.59740	+	6.59740i	0.844711	+	0.844711i	0.989467	−	0.144756i	$-0.0462399\pi$
$61$	6.59740	+	6.59740i	0.844711	+	0.844711i	−0.144756	+	0.989467i	$0.546240\pi$
$62$	9.41359	+	1.01737i	1.19553	+	0.129206i
$63$	5.19525	+	4.06164i	0.654540	+	0.511718i
$64$	6.38827	+	4.81560i	0.798533	+	0.601950i
$65$	−3.65468			−0.453307
$66$	0.587559	−	5.43660i	0.0723235	−	0.669199i
$67$	4.41889	+	4.41889i	0.539853	+	0.539853i	0.923486	−	0.383633i	$-0.125327\pi$
$67$	4.41889	+	4.41889i	0.539853	+	0.539853i	−0.383633	+	0.923486i	$0.625327\pi$
$68$	−1.12035	+	5.12266i	−0.135862	+	0.621214i
$69$	1.27661	−	1.27661i	0.153686	−	0.153686i
$70$	−0.0531216	−	3.74128i	−0.00634925	−	0.447169i
$71$	12.8438			1.52428			0.762140	−	0.647413i	$-0.224149\pi$
$71$	12.8438			1.52428			0.762140	+	0.647413i	$0.224149\pi$
$72$	2.23751	−	6.68533i	0.263693	−	0.787873i
$73$	−10.9703			−1.28398			−0.641991	−	0.766712i	$-0.721891\pi$
$73$	−10.9703			−1.28398			−0.641991	+	0.766712i	$0.721891\pi$
$74$	−3.61310	−	4.48869i	−0.420014	−	0.521800i
$75$	−0.503741	−	0.503741i	−0.0581670	−	0.0581670i
$76$	5.69748	−	3.65259i	0.653546	−	0.418980i
$77$	1.74553	+	14.2537i	0.198922	+	1.62436i
$78$	−3.66071	−	0.395630i	−0.414493	−	0.0447963i
$79$			12.6491i			1.42314i	0.702617	+	0.711568i	$0.252015\pi$
$79$			12.6491i			1.42314i	−0.702617	+	0.711568i	$0.747985\pi$
$80$	−3.75090	+	1.38950i	−0.419364	+	0.155351i
$81$	−4.68997			−0.521108
$82$	−15.1225	−	1.63436i	−1.67000	−	0.180485i
$83$	6.43343	−	6.43343i	0.706161	−	0.706161i	−0.259565	−	0.965726i	$-0.583579\pi$
$83$	6.43343	−	6.43343i	0.706161	−	0.706161i	0.965726	+	0.259565i	$0.0835791\pi$
$84$	0.351796	−	3.75320i	0.0383841	−	0.409508i
$85$	−1.85394	−	1.85394i	−0.201088	−	0.201088i
$86$	5.85738	−	4.71479i	0.631618	−	0.508409i
$87$			4.48284i			0.480611i
$88$	13.7393	−	6.84873i	1.46462	−	0.730077i
$89$	−17.3593			−1.84008			−0.920040	−	0.391824i	$-0.871844\pi$
$89$	−17.3593			−1.84008			−0.920040	+	0.391824i	$0.871844\pi$
$90$	2.21024	+	2.74588i	0.232980	+	0.289441i
$91$	9.59766	−	1.17534i	1.00611	−	0.123210i
$92$	4.95149	+	1.08291i	0.516228	+	0.112901i
$93$	−3.37264	+	3.37264i	−0.349726	+	0.349726i
$94$	−18.2781	−	1.97540i	−1.88525	−	0.203747i
$95$			3.38389i			0.347179i
$96$	−3.90751	+	0.985746i	−0.398809	+	0.100607i
$97$			1.67254i			0.169821i	0.996389	+	0.0849103i	$0.0270604\pi$
$97$			1.67254i			0.169821i	−0.996389	+	0.0849103i	$0.972940\pi$
$98$	1.34270	+	9.80801i	0.135633	+	0.990759i
$99$	−9.56599	−	9.56599i	−0.961418	−	0.961418i
$100$	0.427308	−	1.95382i	0.0427308	−	0.195382i
$101$	−0.777162	+	0.777162i	−0.0773305	+	0.0773305i	−0.744714	−	0.667384i	$-0.767414\pi$
$101$	−0.777162	+	0.777162i	−0.0773305	+	0.0773305i	0.667384	+	0.744714i	$0.267414\pi$
$102$	−1.65631	−	2.05770i	−0.163999	−	0.203742i
$103$		−	13.6684i		−	1.34679i	−0.739284	−	0.673394i	$-0.764836\pi$
$103$		−	13.6684i		−	1.34679i	0.739284	−	0.673394i	$-0.235164\pi$
$104$	−4.61156	−	9.25131i	−0.452200	−	0.907166i
$105$	1.48489	+	1.16089i	0.144911	+	0.113291i
$106$	−1.35183	−	1.67944i	−0.131302	−	0.163121i
$107$	6.74159	−	6.74159i	0.651734	−	0.651734i	−0.301677	−	0.953410i	$-0.597546\pi$
$107$	6.74159	−	6.74159i	0.651734	−	0.651734i	0.953410	+	0.301677i	$0.0975463\pi$
$108$	4.22354	+	6.58809i	0.406410	+	0.633939i
$109$	−4.74149	+	4.74149i	−0.454152	+	0.454152i	−0.896730	−	0.442578i	$-0.854064\pi$
$109$	−4.74149	+	4.74149i	−0.454152	+	0.454152i	0.442578	+	0.896730i	$0.354064\pi$
$110$	−0.824763	+	7.63141i	−0.0786380	+	0.727626i
$111$	2.90265			0.275508
$112$	9.40351	−	4.85530i	0.888548	−	0.458783i
$113$	−13.4508			−1.26535			−0.632674	−	0.774418i	$-0.718043\pi$
$113$	−13.4508			−1.26535			−0.632674	+	0.774418i	$0.718043\pi$
$114$	−0.366316	+	3.38947i	−0.0343086	+	0.317453i
$115$	−1.79199	+	1.79199i	−0.167104	+	0.167104i
$116$	−10.5949	+	6.79228i	−0.983715	+	0.630648i
$117$	−6.44121	+	6.44121i	−0.595490	+	0.595490i
$118$	7.39137	+	9.18260i	0.680431	+	0.845326i
$119$	5.46493	+	4.27247i	0.500969	+	0.391657i
$120$	0.639520	−	1.91078i	0.0583799	−	0.174430i
$121$		−	18.4593i		−	1.67812i
$122$	−8.27361	−	10.2786i	−0.749057	−	0.930584i
$123$	5.41798	−	5.41798i	0.488522	−	0.488522i
$124$	−13.0812	−	2.86090i	−1.17472	−	0.256917i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−6.68747	−	6.50022i	−0.595767	−	0.579085i
$127$		−	10.0803i		−	0.894483i	−0.894413	−	0.447241i	$-0.852406\pi$
$127$		−	10.0803i		−	0.894483i	0.894413	−	0.447241i	$-0.147594\pi$
$128$	−8.25031	−	7.74160i	−0.729231	−	0.684267i
$129$			3.78773i			0.333491i
$130$	5.13857	+	0.555350i	0.450682	+	0.0487074i
$131$	−9.99489	+	9.99489i	−0.873257	+	0.873257i	−0.992826	−	0.119568i	$-0.961849\pi$
$131$	−9.99489	+	9.99489i	−0.873257	+	0.873257i	0.119568	+	0.992826i	$0.461849\pi$
$132$	−1.65225	+	7.55472i	−0.143810	+	0.657554i
$133$	−1.08826	−	8.88653i	−0.0943639	−	0.770560i
$134$	−5.54159	−	6.88454i	−0.478721	−	0.594734i
$135$	−3.91284			−0.336763
$136$	2.35366	−	7.03235i	0.201824	−	0.603019i
$137$		−	14.4238i		−	1.23231i	−0.787626	−	0.616154i	$-0.788690\pi$
$137$		−	14.4238i		−	1.23231i	0.787626	−	0.616154i	$-0.211310\pi$
$138$	−1.98894	+	1.60096i	−0.169310	+	0.136283i
$139$	−0.391142	−	0.391142i	−0.0331762	−	0.0331762i	0.690324	−	0.723500i	$-0.257468\pi$
$139$	−0.391142	−	0.391142i	−0.0331762	−	0.0331762i	−0.723500	+	0.690324i	$0.757468\pi$
$140$	−0.493819	+	5.26841i	−0.0417353	+	0.445262i
$141$	6.54856	−	6.54856i	0.551489	−	0.551489i
$142$	−18.0587	−	1.95169i	−1.51545	−	0.163782i
$143$	−19.8363			−1.65879
$144$	−4.16187	+	9.05974i	−0.346823	+	0.754978i
$145$		−	6.29261i		−	0.522573i
$146$	15.4246	+	1.66701i	1.27655	+	0.137963i
$147$	−4.27287	−	2.57110i	−0.352421	−	0.212061i
$148$	4.39802	+	6.86025i	0.361515	+	0.563909i
$149$	4.57539	+	4.57539i	0.374831	+	0.374831i	0.869233	−	0.494402i	$-0.164613\pi$
$149$	4.57539	+	4.57539i	0.374831	+	0.374831i	−0.494402	+	0.869233i	$0.664613\pi$
$150$	0.631727	+	0.784820i	0.0515803	+	0.0640803i
$151$	8.28025			0.673837			0.336919	−	0.941534i	$-0.390615\pi$
$151$	8.28025			0.673837			0.336919	+	0.941534i	$0.390615\pi$
$152$	−8.56584	+	4.26987i	−0.694782	+	0.346332i
$153$	−6.53499			−0.528323
$154$	−0.288325	−	20.3063i	−0.0232339	−	1.63633i
$155$	4.73420	−	4.73420i	0.380260	−	0.380260i
$156$	5.08693	+	1.11253i	0.407280	+	0.0890738i
$157$	−0.731177	−	0.731177i	−0.0583542	−	0.0583542i	0.677327	−	0.735682i	$-0.263138\pi$
$157$	−0.731177	−	0.731177i	−0.0583542	−	0.0583542i	−0.735682	+	0.677327i	$0.763138\pi$
$158$	1.92211	−	17.7850i	0.152915	−	1.41490i
$159$	1.08602			0.0861272
$160$	5.48501	−	1.38370i	0.433628	−	0.109391i
$161$	4.12971	−	5.28232i	0.325467	−	0.416305i
$162$	6.59422	+	0.712669i	0.518091	+	0.0559926i
$163$	−6.52291	−	6.52291i	−0.510914	−	0.510914i	0.403892	−	0.914806i	$-0.367657\pi$
$163$	−6.52291	−	6.52291i	−0.510914	−	0.510914i	−0.914806	+	0.403892i	$0.867657\pi$
$164$	21.0142	+	4.59590i	1.64094	+	0.358879i
$165$	−2.73413	−	2.73413i	−0.212852	−	0.212852i
$166$	−10.0232	+	8.06798i	−0.777949	+	0.626196i
$167$		−	23.6257i		−	1.82821i	−0.405475	−	0.914106i	$-0.632894\pi$
$167$		−	23.6257i		−	1.82821i	0.405475	−	0.914106i	$-0.367106\pi$
$168$	−1.06496	+	5.22364i	−0.0821631	+	0.403013i
$169$			0.356655i			0.0274350i
$170$	2.32498	+	2.88841i	0.178317	+	0.221531i
$171$	5.96395	+	5.96395i	0.456075	+	0.456075i
$172$	−8.95207	+	5.73906i	−0.682589	+	0.437599i
$173$	−4.66209	−	4.66209i	−0.354452	−	0.354452i	0.507311	−	0.861763i	$-0.330640\pi$
$173$	−4.66209	−	4.66209i	−0.354452	−	0.354452i	−0.861763	+	0.507311i	$0.830640\pi$
$174$	0.681194	−	6.30299i	0.0516412	−	0.477829i
$175$	−2.08436	−	1.62955i	−0.157563	−	0.123182i
$176$	−20.3586	+	7.54172i	−1.53459	+	0.568478i
$177$	−5.93801			−0.446328
$178$	24.4076	+	2.63785i	1.82943	+	0.197715i
$179$	−8.13037	−	8.13037i	−0.607692	−	0.607692i	0.334650	−	0.942342i	$-0.391382\pi$
$179$	−8.13037	−	8.13037i	−0.607692	−	0.607692i	−0.942342	+	0.334650i	$0.891382\pi$
$180$	−2.69041	−	4.19663i	−0.200531	−	0.312798i
$181$	−7.52356	+	7.52356i	−0.559222	+	0.559222i	−0.929086	−	0.369864i	$-0.879404\pi$
$181$	−7.52356	+	7.52356i	−0.559222	+	0.559222i	0.369864	+	0.929086i	$0.379404\pi$
$182$	−13.6732	+	0.194142i	−1.01352	+	0.0143908i
$183$	6.64677			0.491343
$184$	−6.79737	−	2.27501i	−0.501109	−	0.167716i
$185$	−4.07448			−0.299562
$186$	5.25451	−	4.22952i	0.385279	−	0.310124i
$187$	−10.0625	−	10.0625i	−0.735846	−	0.735846i
$188$	25.3994	+	5.55494i	1.85244	+	0.405136i
$189$	10.2756	−	1.25837i	0.747442	−	0.0915328i
$190$	0.514201	−	4.75783i	0.0373041	−	0.345169i
$191$		−	9.00140i		−	0.651319i	−0.945487	−	0.325659i	$-0.894414\pi$
$191$		−	9.00140i		−	0.651319i	0.945487	−	0.325659i	$-0.105586\pi$
$192$	5.64385	−	0.792216i	0.407310	−	0.0571732i
$193$	24.5020			1.76369			0.881845	−	0.471539i	$-0.156301\pi$
$193$	24.5020			1.76369			0.881845	+	0.471539i	$0.156301\pi$
$194$	0.254152	−	2.35163i	0.0182471	−	0.168837i
$195$	−1.84101	+	1.84101i	−0.131838	+	0.131838i
$196$	−0.397486	−	13.9944i	−0.0283918	−	0.999597i
$197$	2.74374	+	2.74374i	0.195484	+	0.195484i	0.798061	−	0.602577i	$-0.205859\pi$
$197$	2.74374	+	2.74374i	0.195484	+	0.195484i	−0.602577	+	0.798061i	$0.705859\pi$
$198$	11.9964	+	14.9036i	0.852548	+	1.05916i
$199$			1.39828i			0.0991214i	0.998771	+	0.0495607i	$0.0157821\pi$
$199$			1.39828i			0.0991214i	−0.998771	+	0.0495607i	$0.984218\pi$
$200$	−0.897701	+	2.68219i	−0.0634770	+	0.189659i
$201$	4.45195			0.314016
$202$	1.21080	−	0.974616i	0.0851919	−	0.0685737i
$203$	2.02370	+	16.5252i	0.142036	+	1.15984i
$204$	2.01613	+	3.14486i	0.141157	+	0.220184i
$205$	−7.60527	+	7.60527i	−0.531175	+	0.531175i
$206$	−2.07699	+	19.2181i	−0.144711	+	1.33899i
$207$			6.31662i			0.439035i
$208$	5.07818	+	13.7083i	0.352108	+	0.950502i
$209$			18.3665i			1.27044i
$210$	−1.91140	−	1.85788i	−0.131899	−	0.128206i
$211$	−2.04301	−	2.04301i	−0.140647	−	0.140647i	0.633278	−	0.773925i	$-0.281709\pi$
$211$	−2.04301	−	2.04301i	−0.140647	−	0.140647i	−0.773925	+	0.633278i	$0.781709\pi$
$212$	1.64551	+	2.56675i	0.113014	+	0.176285i
$213$	6.46996	−	6.46996i	0.443314	−	0.443314i
$214$	−10.5033	+	8.45442i	−0.717989	+	0.577932i
$215$		−	5.31687i		−	0.362607i
$216$	−4.93731	−	9.90481i	−0.335941	−	0.673937i
$217$	−10.9101	+	13.9552i	−0.740628	+	0.947338i
$218$	7.38716	−	5.94616i	0.500321	−	0.402725i
$219$	−5.52622	+	5.52622i	−0.373427	+	0.373427i
$220$	2.31928	−	10.6046i	0.156366	−	0.714964i
$221$	−6.77556	+	6.77556i	−0.455774	+	0.455774i
$222$	−4.08121	−	0.441075i	−0.273913	−	0.0296030i
$223$	1.19992			0.0803526			0.0401763	−	0.999193i	$-0.487208\pi$
$223$	1.19992			0.0803526			0.0401763	+	0.999193i	$0.487208\pi$
$224$	−13.9594	+	5.39777i	−0.932700	+	0.360653i
$225$	2.49249			0.166166
$226$	18.9122	+	2.04394i	1.25802	+	0.135961i
$227$	−4.27313	+	4.27313i	−0.283618	+	0.283618i	−0.834550	−	0.550932i	$-0.814272\pi$
$227$	−4.27313	+	4.27313i	−0.283618	+	0.283618i	0.550932	+	0.834550i	$0.314272\pi$
$228$	1.03010	−	4.71002i	0.0682200	−	0.311929i
$229$	7.21229	−	7.21229i	0.476602	−	0.476602i	−0.427441	−	0.904043i	$-0.640585\pi$
$229$	7.21229	−	7.21229i	0.476602	−	0.476602i	0.904043	+	0.427441i	$0.140585\pi$
$230$	2.79189	−	2.24729i	0.184092	−	0.148182i
$231$	8.05948	+	6.30089i	0.530275	+	0.414568i
$232$	15.9289	−	7.94016i	1.04578	−	0.521297i
$233$		−	2.64422i		−	0.173229i	−0.996242	−	0.0866144i	$-0.972395\pi$
$233$		−	2.64422i		−	0.173229i	0.996242	−	0.0866144i	$-0.0276048\pi$
$234$	10.0353	−	8.07772i	0.656027	−	0.528057i
$235$	−9.19229	+	9.19229i	−0.599639	+	0.599639i
$236$	−8.99711	−	14.0341i	−0.585662	−	0.913544i
$237$	6.37188	+	6.37188i	0.413898	+	0.413898i
$238$	−7.03461	−	6.83764i	−0.455986	−	0.443218i
$239$			19.4374i			1.25730i	0.777689	+	0.628650i	$0.216392\pi$
$239$			19.4374i			1.25730i	−0.777689	+	0.628650i	$0.783608\pi$
$240$	−1.18954	+	2.58943i	−0.0767843	+	0.167147i
$241$		−	0.461714i		−	0.0297416i	−0.999889	−	0.0148708i	$-0.995266\pi$
$241$		−	0.461714i		−	0.0297416i	0.999889	−	0.0148708i	$-0.00473369\pi$
$242$	−2.80500	+	25.9543i	−0.180312	+	1.66841i
$243$	−10.6629	+	10.6629i	−0.684026	+	0.684026i
$244$	10.0710	+	15.7093i	0.644730	+	1.00568i
$245$	5.99787	+	3.60909i	0.383190	+	0.230576i
$246$	−8.44111	+	6.79452i	−0.538185	+	0.433203i
$247$	12.3670			0.786894
$248$	17.9577	+	6.01026i	1.14032	+	0.381652i
$249$		−	6.48157i		−	0.410753i
$250$	−0.886762	−	1.10166i	−0.0560837	−	0.0696751i
$251$	8.96190	+	8.96190i	0.565670	+	0.565670i	0.930912	−	0.365242i	$-0.119014\pi$
$251$	8.96190	+	8.96190i	0.565670	+	0.565670i	−0.365242	+	0.930912i	$0.619014\pi$
$252$	8.41501	+	10.1557i	0.530096	+	0.639747i
$253$	−9.72630	+	9.72630i	−0.611487	+	0.611487i
$254$	−1.53176	+	14.1732i	−0.0961114	+	0.889304i
$255$	−1.86782			−0.116967
$256$	10.4238	+	12.1386i	0.651486	+	0.758661i
$257$			4.24334i			0.264692i	0.991204	+	0.132346i	$0.0422510\pi$
$257$			4.24334i			0.264692i	−0.991204	+	0.132346i	$0.957749\pi$
$258$	0.575567	−	5.32564i	0.0358333	−	0.331560i
$259$	10.7001	−	1.31035i	0.664874	−	0.0814215i
$260$	−7.14057	−	1.56167i	−0.442840	−	0.0968508i
$261$	−11.0904	−	11.0904i	−0.686482	−	0.686482i
$262$	15.5719	−	12.5343i	0.962033	−	0.774371i
$263$	2.94050			0.181319			0.0906594	−	0.995882i	$-0.471103\pi$
$263$	2.94050			0.181319			0.0906594	+	0.995882i	$0.471103\pi$
$264$	3.47109	−	10.3711i	0.213631	−	0.638295i
$265$	−1.52446			−0.0936469
$266$	0.179758	+	12.6601i	0.0110216	+	0.776238i
$267$	−8.74459	+	8.74459i	−0.535160	+	0.535160i
$268$	6.74548	+	10.5219i	0.412046	+	0.642729i
$269$	−18.1024	−	18.1024i	−1.10372	−	1.10372i	−0.993958	−	0.109762i	$-0.964991\pi$
$269$	−18.1024	−	18.1024i	−1.10372	−	1.10372i	−0.109762	−	0.993958i	$-0.535009\pi$
$270$	5.50155	+	0.594579i	0.334814	+	0.0361849i
$271$	2.82906			0.171853			0.0859265	−	0.996301i	$-0.472615\pi$
$271$	2.82906			0.171853			0.0859265	+	0.996301i	$0.472615\pi$
$272$	−4.37791	+	9.53002i	−0.265450	+	0.577842i
$273$	4.24267	−	5.42681i	0.256778	−	0.328445i
$274$	−2.19178	+	20.2802i	−0.132410	+	1.22517i
$275$	3.83792	+	3.83792i	0.231436	+	0.231436i
$276$	3.03978	−	1.94876i	0.182973	−	0.117302i
$277$	8.04117	+	8.04117i	0.483147	+	0.483147i	0.906135	−	0.422988i	$-0.139019\pi$
$277$	8.04117	+	8.04117i	0.483147	+	0.483147i	−0.422988	+	0.906135i	$0.639019\pi$
$278$	0.490519	+	0.609392i	0.0294194	+	0.0365489i
$279$		−	16.6877i		−	0.999064i
$280$	1.49489	−	7.33248i	0.0893367	−	0.438200i
$281$		−	15.2503i		−	0.909757i	−0.890554	−	0.454878i	$-0.849683\pi$
$281$		−	15.2503i		−	0.909757i	0.890554	−	0.454878i	$-0.150317\pi$
$282$	−10.2025	+	8.21236i	−0.607553	+	0.489039i
$283$	−3.07009	−	3.07009i	−0.182498	−	0.182498i	0.609946	−	0.792443i	$-0.291191\pi$
$283$	−3.07009	−	3.07009i	−0.182498	−	0.182498i	−0.792443	+	0.609946i	$0.791191\pi$
$284$	25.0945	+	5.48826i	1.48908	+	0.325668i
$285$	1.70460	+	1.70460i	0.100972	+	0.100972i
$286$	27.8903	+	3.01424i	1.64919	+	0.178236i
$287$	17.5266	−	22.4183i	1.03456	−	1.32331i
$288$	7.22838	−	12.1058i	0.425936	−	0.713342i
$289$	10.1258			0.595635
$290$	−0.956199	+	8.84757i	−0.0561500	+	0.519547i
$291$	0.842527	+	0.842527i	0.0493898	+	0.0493898i
$292$	−21.4341	−	4.68772i	−1.25433	−	0.274328i
$293$	−12.7032	+	12.7032i	−0.742131	+	0.742131i	−0.972988	−	0.230857i	$-0.925847\pi$
$293$	−12.7032	+	12.7032i	−0.742131	+	0.742131i	0.230857	+	0.972988i	$0.425847\pi$
$294$	5.61708	+	4.26433i	0.327595	+	0.248701i
$295$	8.33524			0.485296
$296$	−5.14128	−	10.3140i	−0.298831	−	0.599489i
$297$	−21.2375			−1.23232
$298$	−5.73786	−	7.12838i	−0.332386	−	0.412936i
$299$	6.54916	+	6.54916i	0.378747	+	0.378747i
$300$	−0.768967	−	1.19947i	−0.0443963	−	0.0692515i
$301$	1.70991	+	13.9628i	0.0985573	+	0.804803i
$302$	−11.6422	−	1.25823i	−0.669936	−	0.0724032i
$303$			0.782977i			0.0449809i
$304$	12.6926	−	4.70191i	0.727972	−	0.269673i
$305$	−9.33014			−0.534242
$306$	9.18836	+	0.993030i	0.525264	+	0.0567678i
$307$	−2.33540	+	2.33540i	−0.133288	+	0.133288i	−0.770603	−	0.637315i	$-0.780045\pi$
$307$	−2.33540	+	2.33540i	−0.133288	+	0.133288i	0.637315	+	0.770603i	$0.280045\pi$
$308$	−2.68028	+	28.5951i	−0.152723	+	1.62935i
$309$	−6.88534	−	6.88534i	−0.391693	−	0.391693i
$310$	−7.37580	+	5.93702i	−0.418917	+	0.337200i
$311$		−	3.17427i		−	0.179996i	−0.995942	−	0.0899980i	$-0.971314\pi$
$311$		−	3.17427i		−	0.179996i	0.995942	−	0.0899980i	$-0.0286861\pi$
$312$	−6.98330	−	2.33724i	−0.395351	−	0.132320i
$313$	11.4877			0.649323			0.324661	−	0.945830i	$-0.394750\pi$
$313$	11.4877			0.649323			0.324661	+	0.945830i	$0.394750\pi$
$314$	0.916947	+	1.13916i	0.0517463	+	0.0642865i
$315$	−6.54561	+	0.801585i	−0.368803	+	0.0451642i
$316$	−5.40507	+	24.7141i	−0.304059	+	1.39028i
$317$	17.6398	−	17.6398i	0.990747	−	0.990747i	−0.00921047	−	0.999958i	$-0.502932\pi$
$317$	17.6398	−	17.6398i	0.990747	−	0.990747i	0.999958	+	0.00921047i	$0.00293182\pi$
$318$	−1.52698	−	0.165028i	−0.0856285	−	0.00925428i
$319$		−	34.1540i		−	1.91226i
$320$	−7.92233	+	1.11204i	−0.442872	+	0.0621650i
$321$		−	6.79203i		−	0.379094i
$322$	−6.60916	+	6.79954i	−0.368314	+	0.378924i
$323$	6.27353	+	6.27353i	0.349069	+	0.349069i
$324$	−9.16336	−	2.00406i	−0.509075	−	0.111337i
$325$	2.58425	−	2.58425i	0.143348	−	0.143348i
$326$	8.18019	+	10.1626i	0.453059	+	0.562853i
$327$			4.77697i			0.264167i
$328$	−28.8482	−	9.65519i	−1.59288	−	0.533119i
$329$	21.1839	−	27.0964i	1.16791	−	1.49387i
$330$	3.42879	+	4.25972i	0.188749	+	0.234490i
$331$	2.69551	−	2.69551i	0.148159	−	0.148159i	−0.629136	−	0.777295i	$-0.716591\pi$
$331$	2.69551	−	2.69551i	0.148159	−	0.148159i	0.777295	+	0.629136i	$0.216591\pi$
$332$	15.3188	−	9.82071i	0.840730	−	0.538981i
$333$	−7.18110	+	7.18110i	−0.393522	+	0.393522i
$334$	−3.59007	+	33.2184i	−0.196440	+	1.81763i
$335$	−6.24925			−0.341433
$336$	2.29112	−	7.18275i	0.124991	−	0.391851i
$337$	−4.00673			−0.218261			−0.109130	−	0.994027i	$-0.534807\pi$
$337$	−4.00673			−0.218261			−0.109130	+	0.994027i	$0.534807\pi$
$338$	0.0541958	−	0.501466i	0.00294787	−	0.0272762i
$339$	−6.77574	+	6.77574i	−0.368008	+	0.368008i
$340$	−2.83006	−	4.41447i	−0.153482	−	0.239409i
$341$	25.6956	−	25.6956i	1.39149	−	1.39149i
$342$	−7.47921	−	9.29173i	−0.404429	−	0.502439i
$343$	−16.9119	−	7.54902i	−0.913157	−	0.407609i
$344$	13.4589	−	6.70895i	0.725657	−	0.361722i
$345$			1.80540i			0.0971996i
$346$	5.84659	+	7.26346i	0.314315	+	0.390486i
$347$	−11.8846	+	11.8846i	−0.637996	+	0.637996i	−0.950061	−	0.312065i	$-0.898979\pi$
$347$	−11.8846	+	11.8846i	−0.637996	+	0.637996i	0.312065	+	0.950061i	$0.398979\pi$
$348$	−1.91555	+	8.75866i	−0.102684	+	0.469513i
$349$	7.73725	+	7.73725i	0.414166	+	0.414166i	0.883187	−	0.469021i	$-0.155393\pi$
$349$	7.73725	+	7.73725i	0.414166	+	0.414166i	−0.469021	+	0.883187i	$0.655393\pi$
$350$	2.68305	+	2.60792i	0.143415	+	0.139399i
$351$			14.3002i			0.763286i
$352$	29.7707	−	7.51024i	1.58678	−	0.400297i
$353$		−	30.0845i		−	1.60124i	−0.599173	−	0.800619i	$-0.704504\pi$
$353$		−	30.0845i		−	1.60124i	0.599173	−	0.800619i	$-0.295496\pi$
$354$	8.34899	+	0.902315i	0.443744	+	0.0479575i
$355$	−9.08194	+	9.08194i	−0.482020	+	0.482020i
$356$	−33.9169	−	7.41776i	−1.79759	−	0.393141i
$357$	4.90513	−	0.600690i	0.259607	−	0.0317919i
$358$	10.1961	+	12.6670i	0.538878	+	0.669470i
$359$	−13.5555			−0.715429			−0.357715	−	0.933831i	$-0.616444\pi$
$359$	−13.5555			−0.715429			−0.357715	+	0.933831i	$0.616444\pi$
$360$	3.14508	+	6.30940i	0.165760	+	0.332534i
$361$			7.54932i			0.397333i
$362$	11.7216	−	9.43507i	0.616072	−	0.495897i
$363$	−9.29872	−	9.29872i	−0.488056	−	0.488056i
$364$	19.2543	+	1.80475i	1.00920	+	0.0945946i
$365$	7.75721	−	7.75721i	0.406031	−	0.406031i
$366$	−9.34553	−	1.01002i	−0.488499	−	0.0527944i
$367$	11.3794			0.594000			0.297000	−	0.954878i	$-0.404014\pi$
$367$	11.3794			0.594000			0.297000	+	0.954878i	$0.404014\pi$
$368$	9.21157	+	4.23162i	0.480186	+	0.220588i
$369$			26.8079i			1.39556i
$370$	5.72883	+	0.619142i	0.297828	+	0.0321877i
$371$	4.00344	−	0.490267i	0.207848	−	0.0254534i
$372$	−8.03067	+	5.14836i	−0.416371	+	0.266930i
$373$	−4.59936	−	4.59936i	−0.238146	−	0.238146i	0.577936	−	0.816082i	$-0.303858\pi$
$373$	−4.59936	−	4.59936i	−0.238146	−	0.238146i	−0.816082	+	0.577936i	$0.803858\pi$
$374$	12.6191	+	15.6773i	0.652520	+	0.810652i
$375$	0.712398			0.0367881
$376$	−34.8681	−	11.6700i	−1.79818	−	0.601833i
$377$	−22.9974			−1.18443
$378$	−14.6390	+	0.207856i	−0.752950	+	0.0106910i
$379$	19.3596	−	19.3596i	0.994434	−	0.994434i	−0.00555091	−	0.999985i	$-0.501767\pi$
$379$	19.3596	−	19.3596i	0.994434	−	0.994434i	0.999985	+	0.00555091i	$0.00176692\pi$
$380$	−1.44596	+	6.61150i	−0.0741763	+	0.339163i
$381$	−5.07787	−	5.07787i	−0.260147	−	0.260147i
$382$	−1.36782	+	12.6562i	−0.0699836	+	0.647548i
$383$	0.782224			0.0399698			0.0199849	−	0.999800i	$-0.493638\pi$
$383$	0.782224			0.0399698			0.0199849	+	0.999800i	$0.493638\pi$
$384$	−8.05579	+	0.256259i	−0.411095	+	0.0130772i
$385$	−11.3132	−	8.84462i	−0.576573	−	0.450764i
$386$	−34.4504	−	3.72322i	−1.75348	−	0.189507i
$387$	−9.37075	−	9.37075i	−0.476342	−	0.476342i
$388$	−0.714689	+	3.26784i	−0.0362828	+	0.165899i
$389$	24.3126	+	24.3126i	1.23270	+	1.23270i	0.962923	+	0.269775i	$0.0869493\pi$
$389$	24.3126	+	24.3126i	1.23270	+	1.23270i	0.269775	+	0.962923i	$0.413051\pi$
$390$	2.86826	−	2.30876i	0.145240	−	0.116908i
$391$			6.64451i			0.336027i
$392$	−1.56765	+	19.7368i	−0.0791783	+	0.996860i
$393$			10.0697i			0.507948i
$394$	−3.44085	−	4.27470i	−0.173347	−	0.215356i
$395$	−8.94428	−	8.94428i	−0.450035	−	0.450035i
$396$	−14.6026	−	22.7778i	−0.733807	−	1.14463i
$397$	17.1708	+	17.1708i	0.861777	+	0.861777i	0.991544	−	0.129767i	$-0.0414231\pi$
$397$	17.1708	+	17.1708i	0.861777	+	0.861777i	−0.129767	+	0.991544i	$0.541423\pi$
$398$	0.212477	−	1.96602i	0.0106505	−	0.0985475i
$399$	−5.02471	−	3.92831i	−0.251550	−	0.196662i
$400$	1.66976	−	3.63482i	0.0834882	−	0.181741i
$401$	27.7212			1.38433			0.692166	−	0.721739i	$-0.256657\pi$
$401$	27.7212			1.38433			0.692166	+	0.721739i	$0.256657\pi$
$402$	−6.25956	−	0.676500i	−0.312198	−	0.0337408i
$403$	−17.3020	−	17.3020i	−0.861873	−	0.861873i
$404$	−1.85052	+	1.18635i	−0.0920669	+	0.0590229i
$405$	3.31631	−	3.31631i	0.164789	−	0.164789i
$406$	−0.334274	−	23.5424i	−0.0165897	−	1.16839i
$407$	−22.1149			−1.09619
$408$	−2.35685	−	4.72812i	−0.116682	−	0.234077i
$409$	−1.47940			−0.0731519			−0.0365759	−	0.999331i	$-0.511645\pi$
$409$	−1.47940			−0.0731519			−0.0365759	+	0.999331i	$0.511645\pi$
$410$	11.8489	−	9.53754i	0.585174	−	0.471026i
$411$	−7.26586	−	7.26586i	−0.358399	−	0.358399i
$412$	5.84062	−	26.7056i	0.287747	−	1.31569i
$413$	−21.8894	+	2.68061i	−1.07711	+	0.131904i
$414$	0.959848	−	8.88133i	0.0471739	−	0.436494i
$415$			9.09825i			0.446615i
$416$	−5.05698	−	20.0459i	−0.247939	−	0.982833i
$417$	−0.394068			−0.0192976
$418$	2.79090	−	25.8238i	0.136508	−	1.26308i
$419$	10.5574	−	10.5574i	0.515764	−	0.515764i	−0.400523	−	0.916287i	$-0.631172\pi$
$419$	10.5574	−	10.5574i	0.515764	−	0.515764i	0.916287	+	0.400523i	$0.131172\pi$
$420$	2.40516	+	2.90267i	0.117360	+	0.141636i
$421$	7.58462	+	7.58462i	0.369652	+	0.369652i	0.867350	−	0.497698i	$-0.165821\pi$
$421$	7.58462	+	7.58462i	0.369652	+	0.369652i	−0.497698	+	0.867350i	$0.665821\pi$
$422$	2.56208	+	3.18298i	0.124720	+	0.154945i
$423$			32.4020i			1.57544i
$424$	−1.92360	−	3.85896i	−0.0934183	−	0.187408i
$425$	2.62187			0.127179
$426$	−10.0801	+	8.11378i	−0.488381	+	0.393114i
$427$	24.5022	−	3.00057i	1.18574	−	0.145208i
$428$	16.0526	−	10.2911i	0.775930	−	0.497439i
$429$	−9.99235	+	9.99235i	−0.482435	+	0.482435i
$430$	−0.807930	+	7.47566i	−0.0389618	+	0.360508i
$431$			18.2577i			0.879443i	0.898134	+	0.439721i	$0.144923\pi$
$431$			18.2577i			0.879443i	−0.898134	+	0.439721i	$0.855077\pi$
$432$	5.43689	+	14.6767i	0.261583	+	0.706132i
$433$		−	0.819589i		−	0.0393870i	−0.999806	−	0.0196935i	$-0.993731\pi$
$433$		−	0.819589i		−	0.0393870i	0.999806	−	0.0196935i	$-0.00626903\pi$
$434$	17.4605	−	17.9635i	0.838130	−	0.862274i
$435$	−3.16985	−	3.16985i	−0.151983	−	0.151983i
$436$	−11.2901	+	7.23794i	−0.540697	+	0.346634i
$437$	6.06390	−	6.06390i	0.290076	−	0.290076i
$438$	8.60975	−	6.93026i	0.411390	−	0.331141i
$439$			14.6925i			0.701234i	0.936519	+	0.350617i	$0.114028\pi$
$439$			14.6925i			0.701234i	−0.936519	+	0.350617i	$0.885972\pi$
$440$	−4.87240	+	14.5580i	−0.232283	+	0.694024i
$441$	16.9318	−	4.21014i	0.806278	−	0.200483i
$442$	10.5562	−	8.49703i	0.502107	−	0.404163i
$443$	−18.1310	+	18.1310i	−0.861429	+	0.861429i	−0.991504	−	0.130075i	$-0.958478\pi$
$443$	−18.1310	+	18.1310i	−0.861429	+	0.861429i	0.130075	+	0.991504i	$0.458478\pi$
$444$	5.67126	+	1.24033i	0.269146	+	0.0588633i
$445$	12.2749	−	12.2749i	0.581885	−	0.581885i
$446$	−1.68712	−	0.182335i	−0.0798874	−	0.00863381i
$447$	4.60963			0.218028
$448$	20.4475	−	5.46819i	0.966052	−	0.258348i
$449$	32.8661			1.55105			0.775523	−	0.631320i	$-0.217486\pi$
$449$	32.8661			1.55105			0.775523	+	0.631320i	$0.217486\pi$
$450$	−3.50451	−	0.378749i	−0.165204	−	0.0178544i
$451$	−41.2787	+	41.2787i	−1.94374	+	1.94374i
$452$	−26.2805	−	5.74765i	−1.23613	−	0.270347i
$453$	4.17110	−	4.17110i	0.195976	−	0.195976i
$454$	6.65746	−	5.35881i	0.312450	−	0.251501i
$455$	−5.95548	+	7.61767i	−0.279197	+	0.357122i
$456$	−2.16406	+	6.46588i	−0.101341	+	0.302792i
$457$			27.6783i			1.29474i	0.762178	+	0.647368i	$0.224130\pi$
$457$			27.6783i			1.29474i	−0.762178	+	0.647368i	$0.775870\pi$
$458$	−11.2366	+	9.04472i	−0.525053	+	0.422632i
$459$	−7.25418	+	7.25418i	−0.338596	+	0.338596i
$460$	−4.26696	+	2.73550i	−0.198948	+	0.127543i
$461$	5.65995	+	5.65995i	0.263610	+	0.263610i	0.826519	−	0.562909i	$-0.190318\pi$
$461$	5.65995	+	5.65995i	0.263610	+	0.263610i	−0.562909	+	0.826519i	$0.690318\pi$
$462$	−10.3744	−	10.0839i	−0.482660	−	0.469145i
$463$		−	18.0765i		−	0.840087i	−0.907504	−	0.420044i	$-0.862015\pi$
$463$		−	18.0765i		−	0.840087i	0.907504	−	0.420044i	$-0.137985\pi$
$464$	−23.6030	+	8.74359i	−1.09574	+	0.405911i
$465$		−	4.76963i		−	0.221186i
$466$	−0.401805	+	3.71785i	−0.0186133	+	0.172226i
$467$	11.2980	−	11.2980i	0.522808	−	0.522808i	−0.395611	−	0.918418i	$-0.629467\pi$
$467$	11.2980	−	11.2980i	0.522808	−	0.522808i	0.918418	+	0.395611i	$0.129467\pi$
$468$	−15.3373	+	9.83257i	−0.708968	+	0.454511i
$469$	16.4114	−	2.00976i	0.757806	−	0.0928020i
$470$	14.3214	−	11.5278i	0.660598	−	0.531736i
$471$	−0.736648			−0.0339429
$472$	10.5176	+	21.0995i	0.484112	+	0.971184i
$473$		−	28.8581i		−	1.32690i
$474$	−7.99079	−	9.92728i	−0.367029	−	0.455975i
$475$	−2.39277	−	2.39277i	−0.109788	−	0.109788i
$476$	8.85182	+	10.6828i	0.405723	+	0.489648i
$477$	−2.68680	+	2.68680i	−0.123020	+	0.123020i
$478$	2.95362	−	27.3295i	0.135096	−	1.25002i
$479$	4.73906			0.216533			0.108267	−	0.994122i	$-0.465470\pi$
$479$	4.73906			0.216533			0.108267	+	0.994122i	$0.465470\pi$
$480$	2.06600	−	3.46006i	0.0942995	−	0.157929i
$481$			14.8909i			0.678967i
$482$	−0.0701601	+	0.649181i	−0.00319571	+	0.0295694i
$483$	−0.580617	−	4.74123i	−0.0264190	−	0.215733i
$484$	7.88782	−	36.0662i	0.358537	−	1.63937i
$485$	−1.18266	−	1.18266i	−0.0537020	−	0.0537020i
$486$	16.6126	−	13.3720i	0.753564	−	0.606568i
$487$	−10.1242			−0.458771			−0.229385	−	0.973336i	$-0.573672\pi$
$487$	−10.1242			−0.458771			−0.229385	+	0.973336i	$0.573672\pi$
$488$	−11.7730	−	23.6180i	−0.532938	−	1.06914i
$489$	−6.57172			−0.297184
$490$	−7.88475	−	5.98588i	−0.356197	−	0.270415i
$491$	−6.31050	+	6.31050i	−0.284789	+	0.284789i	−0.835015	−	0.550227i	$-0.814541\pi$
$491$	−6.31050	+	6.31050i	−0.284789	+	0.284789i	0.550227	+	0.835015i	$0.314541\pi$
$492$	12.9009	−	8.27060i	0.581617	−	0.372867i
$493$	−11.6661	−	11.6661i	−0.525417	−	0.525417i
$494$	−17.3883	−	1.87924i	−0.782338	−	0.0845510i
$495$	13.5283			0.608054
$496$	−24.3357	−	11.1794i	−1.09271	−	0.501968i
$497$	20.9296	−	26.7711i	0.938822	−	1.20085i
$498$	−0.984913	+	9.11326i	−0.0441350	+	0.408375i
$499$	−25.5321	−	25.5321i	−1.14297	−	1.14297i	−0.987903	−	0.155072i	$-0.950439\pi$
$499$	−25.5321	−	25.5321i	−1.14297	−	1.14297i	−0.155072	−	0.987903i	$-0.549561\pi$
$500$	1.07941	+	1.68371i	0.0482725	+	0.0752978i
$501$	−11.9012	−	11.9012i	−0.531708	−	0.531708i
$502$	−11.2389	−	13.9625i	−0.501614	−	0.623176i
$503$		−	23.4233i		−	1.04439i	−0.852825	−	0.522197i	$-0.825112\pi$
$503$		−	23.4233i		−	1.04439i	0.852825	−	0.522197i	$-0.174888\pi$
$504$	−10.2885	−	15.5579i	−0.458286	−	0.693002i
$505$		−	1.09907i		−	0.0489081i
$506$	15.1534	−	12.1975i	0.673651	−	0.542244i
$507$	0.179662	+	0.179662i	0.00797906	+	0.00797906i
$508$	4.30740	−	19.6951i	0.191110	−	0.873829i
$509$	−30.4864	−	30.4864i	−1.35128	−	1.35128i	−0.884227	−	0.467057i	$-0.845314\pi$
$509$	−30.4864	−	30.4864i	−1.35128	−	1.35128i	−0.467057	−	0.884227i	$-0.654686\pi$
$510$	2.62620	+	0.283826i	0.116290	+	0.0125680i
$511$	−17.8767	+	22.8662i	−0.790820	+	1.01154i
$512$	−12.8116	−	18.6511i	−0.566197	−	0.824270i
$513$	13.2406			0.584586
$514$	0.644801	−	5.96625i	0.0284409	−	0.263160i
$515$	9.66502	+	9.66502i	0.425892	+	0.425892i
$516$	−1.61853	+	7.40053i	−0.0712516	+	0.325790i
$517$	−49.8925	+	49.8925i	−2.19427	+	2.19427i
$518$	−15.2438	+	0.216443i	−0.669774	+	0.00950997i
$519$	−4.69698			−0.206174
$520$	9.80253	+	3.28080i	0.429869	+	0.143873i
$521$	4.87201			0.213447			0.106723	−	0.994289i	$-0.465964\pi$
$521$	4.87201			0.213447			0.106723	+	0.994289i	$0.465964\pi$
$522$	13.9082	+	17.2787i	0.608745	+	0.756269i
$523$	−15.5915	−	15.5915i	−0.681770	−	0.681770i	0.278629	−	0.960399i	$-0.410120\pi$
$523$	−15.5915	−	15.5915i	−0.681770	−	0.681770i	−0.960399	+	0.278629i	$0.910120\pi$
$524$	−23.7991	+	15.2573i	−1.03967	+	0.666518i
$525$	−1.87085	+	0.229107i	−0.0816506	+	0.00999906i
$526$	−4.13442	−	0.446826i	−0.180269	−	0.0194825i
$527$		−	17.5539i		−	0.764659i
$528$	−6.45638	+	14.0545i	−0.280978	+	0.611645i
$529$	−16.5775			−0.720762
$530$	2.14343	+	0.231651i	0.0931047	+	0.0100623i
$531$	14.6905	−	14.6905i	0.637513	−	0.637513i
$532$	1.67103	−	17.8277i	0.0724483	−	0.772929i
$533$	27.7948	+	27.7948i	1.20393	+	1.20393i
$534$	13.6239	−	10.9663i	0.589564	−	0.474559i
$535$			9.53404i			0.412193i
$536$	−7.88545	−	15.8191i	−0.340599	−	0.683282i
$537$	−8.19120			−0.353477
$538$	22.7016	+	28.2031i	0.978736	+	1.21592i
$539$	32.5543	+	19.5888i	1.40221	+	0.843751i
$540$	−7.64497	−	1.67199i	−0.328987	−	0.0719508i
$541$	13.5300	−	13.5300i	0.581699	−	0.581699i	−0.353671	−	0.935370i	$-0.615067\pi$
$541$	13.5300	−	13.5300i	0.581699	−	0.581699i	0.935370	+	0.353671i	$0.115067\pi$
$542$	−3.97773	−	0.429892i	−0.170858	−	0.0184654i
$543$			7.57986i			0.325283i
$544$	7.60360	−	12.7342i	0.326002	−	0.545975i
$545$		−	6.70548i		−	0.287231i
$546$	−6.78994	+	6.98554i	−0.290583	+	0.298953i
$547$	−4.57430	−	4.57430i	−0.195583	−	0.195583i	0.602521	−	0.798103i	$-0.294163\pi$
$547$	−4.57430	−	4.57430i	−0.195583	−	0.195583i	−0.798103	+	0.602521i	$0.794163\pi$
$548$	6.16341	−	28.1815i	0.263288	−	1.20385i
$549$	−16.4440	+	16.4440i	−0.701811	+	0.701811i
$550$	−4.81303	−	5.97942i	−0.205228	−	0.254963i
$551$			21.2935i			0.907132i
$552$	−4.57013	+	2.27810i	−0.194518	+	0.0969623i
$553$	26.3653	+	20.6124i	1.12117	+	0.876527i
$554$	−10.0842	−	12.5280i	−0.428436	−	0.532264i
$555$	−2.05249	+	2.05249i	−0.0871232	+	0.0871232i
$556$	−0.597082	−	0.931358i	−0.0253219	−	0.0394984i
$557$	15.0677	−	15.0677i	0.638439	−	0.638439i	−0.311731	−	0.950170i	$-0.600909\pi$
$557$	15.0677	−	15.0677i	0.638439	−	0.638439i	0.950170	+	0.311731i	$0.100909\pi$
$558$	−2.53579	+	23.4633i	−0.107348	+	0.993280i
$559$	−19.4314			−0.821862
$560$	−3.21607	+	10.0825i	−0.135904	+	0.426064i
$561$	−10.1378			−0.428020
$562$	−2.31737	+	21.4423i	−0.0977525	+	0.904490i
$563$	−0.930296	+	0.930296i	−0.0392073	+	0.0392073i	−0.726439	−	0.687231i	$-0.758826\pi$
$563$	−0.930296	+	0.930296i	−0.0392073	+	0.0392073i	0.687231	+	0.726439i	$0.258826\pi$
$564$	15.5930	−	9.99645i	0.656582	−	0.420927i
$565$	9.51118	−	9.51118i	0.400138	−	0.400138i
$566$	3.85011	+	4.78314i	0.161832	+	0.201050i
$567$	−7.64255	+	9.77560i	−0.320957	+	0.410537i
$568$	−34.4495	−	11.5299i	−1.44547	−	0.483784i
$569$			7.83447i			0.328438i	0.986424	+	0.164219i	$0.0525104\pi$
$569$			7.83447i			0.328438i	−0.986424	+	0.164219i	$0.947490\pi$
$570$	−2.13769	−	2.65574i	−0.0895380	−	0.111237i
$571$	−6.15340	+	6.15340i	−0.257512	+	0.257512i	−0.824041	−	0.566530i	$-0.808286\pi$
$571$	−6.15340	+	6.15340i	−0.257512	+	0.257512i	0.566530	+	0.824041i	$0.308286\pi$
$572$	−38.7565	−	8.47620i	−1.62049	−	0.354408i
$573$	−4.53438	−	4.53438i	−0.189426	−	0.189426i
$574$	−28.0494	+	28.8574i	−1.17076	+	1.20449i
$575$		−	2.53426i		−	0.105686i
$576$	−12.0028	+	15.9227i	−0.500118	+	0.663445i
$577$		−	18.8669i		−	0.785439i	−0.919658	−	0.392719i	$-0.871534\pi$
$577$		−	18.8669i		−	0.785439i	0.919658	−	0.392719i	$-0.128466\pi$
$578$	−14.2371	−	1.53867i	−0.592186	−	0.0640004i
$579$	12.3427	−	12.3427i	0.512943	−	0.512943i
$580$	2.68888	−	12.2946i	0.111650	−	0.510506i
$581$	−2.92600	−	23.8932i	−0.121391	−	0.991257i
$582$	−1.05659	−	1.31264i	−0.0437970	−	0.0544107i
$583$	−8.27423			−0.342684
$584$	29.4245	+	9.84809i	1.21760	+	0.407517i
$585$		−	9.10924i		−	0.376621i
$586$	19.7914	−	15.9307i	0.817576	−	0.658093i
$587$	0.393581	+	0.393581i	0.0162448	+	0.0162448i	0.715183	−	0.698938i	$-0.246344\pi$
$587$	0.393581	+	0.393581i	0.0162448	+	0.0162448i	−0.698938	+	0.715183i	$0.746344\pi$
$588$	−7.24976	−	6.84930i	−0.298975	−	0.282461i
$589$	−16.0200	+	16.0200i	−0.660093	+	0.660093i
$590$	−11.7196	−	1.26659i	−0.482487	−	0.0521446i
$591$	2.76427			0.113707
$592$	5.66150	+	15.2830i	0.232686	+	0.628128i
$593$			29.9804i			1.23115i	0.788080	+	0.615573i	$0.211075\pi$
$593$			29.9804i			1.23115i	−0.788080	+	0.615573i	$0.788925\pi$
$594$	29.8605	+	3.22716i	1.22519	+	0.132412i
$595$	−6.88538	+	0.843194i	−0.282273	+	0.0345676i
$596$	6.98439	+	10.8946i	0.286092	+	0.446260i
$597$	0.704371	+	0.704371i	0.0288280	+	0.0288280i
$598$	−8.21310	−	10.2035i	−0.335859	−	0.417251i
$599$	24.5893			1.00469			0.502346	−	0.864667i	$-0.332470\pi$
$599$	24.5893			1.00469			0.502346	+	0.864667i	$0.332470\pi$
$600$	0.898920	+	1.80334i	0.0366983	+	0.0736210i
$601$	17.4395			0.711372			0.355686	−	0.934606i	$-0.384247\pi$
$601$	17.4395			0.711372			0.355686	+	0.934606i	$0.384247\pi$
$602$	−0.282441	−	19.8919i	−0.0115114	−	0.810733i
$603$	−11.0140	+	11.0140i	−0.448526	+	0.448526i
$604$	16.1781	+	3.53822i	0.658278	+	0.143968i
$605$	13.0527	+	13.0527i	0.530668	+	0.530668i
$606$	0.118978	−	1.10089i	0.00483315	−	0.0447205i
$607$	40.3408			1.63738			0.818691	−	0.574234i	$-0.194700\pi$
$607$	40.3408			1.63738			0.818691	+	0.574234i	$0.194700\pi$
$608$	−18.5607	+	4.68229i	−0.752734	+	0.189892i
$609$	9.34386	+	7.30502i	0.378632	+	0.296014i
$610$	13.1184	+	1.41777i	0.531149	+	0.0574038i
$611$	33.5948	+	33.5948i	1.35910	+	1.35910i
$612$	−12.7682	−	2.79245i	−0.516123	−	0.112878i
$613$	−0.447113	−	0.447113i	−0.0180587	−	0.0180587i	0.698020	−	0.716078i	$-0.254065\pi$
$613$	−0.447113	−	0.447113i	−0.0180587	−	0.0180587i	−0.716078	+	0.698020i	$0.754065\pi$
$614$	3.63851	−	2.92875i	0.146838	−	0.118195i
$615$			7.66218i			0.308969i
$616$	8.11373	−	39.7981i	0.326911	−	1.60351i
$617$			31.6077i			1.27248i	0.771492	+	0.636239i	$0.219511\pi$
$617$			31.6077i			1.27248i	−0.771492	+	0.636239i	$0.780489\pi$
$618$	8.63470	+	10.7272i	0.347338	+	0.431513i
$619$	18.9454	+	18.9454i	0.761479	+	0.761479i	0.976590	−	0.215110i	$-0.0690111\pi$
$619$	18.9454	+	18.9454i	0.761479	+	0.761479i	−0.215110	+	0.976590i	$0.569011\pi$
$620$	11.2727	−	7.22681i	0.452724	−	0.290236i
$621$	7.01178	+	7.01178i	0.281373	+	0.281373i
$622$	−0.482348	+	4.46310i	−0.0193404	+	0.178954i
$623$	−28.2878	+	36.1830i	−1.13333	+	1.44964i
$624$	9.46354	+	4.34737i	0.378845	+	0.174034i
$625$	−1.00000			−0.0400000
$626$	−16.1520	−	1.74562i	−0.645563	−	0.0697691i
$627$	9.25198	+	9.25198i	0.369488	+	0.369488i
$628$	−1.11615	−	1.74102i	−0.0445392	−	0.0694744i
$629$	−7.55386	+	7.55386i	−0.301192	+	0.301192i
$630$	9.32510	−	0.132405i	0.371521	−	0.00527515i
$631$	1.96141			0.0780826			0.0390413	−	0.999238i	$-0.487570\pi$
$631$	1.96141			0.0780826			0.0390413	+	0.999238i	$0.487570\pi$
$632$	11.3551	−	33.9273i	0.451682	−	1.34956i
$633$	−2.05830			−0.0818101
$634$	−27.4824	+	22.1215i	−1.09147	+	0.878556i
$635$	7.12786	+	7.12786i	0.282860	+	0.282860i
$636$	2.12189	+	0.464066i	0.0841384	+	0.0184014i
$637$	13.1900	−	21.9203i	0.522608	−	0.868513i
$638$	−5.18991	+	48.0215i	−0.205471	+	1.90119i
$639$			32.0131i			1.26642i
$640$	11.3080	−	0.359714i	0.446987	−	0.0142189i
$641$	−13.6701			−0.539938			−0.269969	−	0.962869i	$-0.587013\pi$
$641$	−13.6701			−0.539938			−0.269969	+	0.962869i	$0.587013\pi$
$642$	−1.03209	+	9.54977i	−0.0407333	+	0.376899i
$643$	9.56751	−	9.56751i	0.377306	−	0.377306i	−0.492823	−	0.870129i	$-0.664035\pi$
$643$	9.56751	−	9.56751i	0.377306	−	0.377306i	0.870129	+	0.492823i	$0.164035\pi$
$644$	10.3259	−	8.55604i	0.406897	−	0.337155i
$645$	−2.67833	−	2.67833i	−0.105459	−	0.105459i
$646$	−7.86745	−	9.77405i	−0.309541	−	0.384555i
$647$		−	32.9774i		−	1.29648i	−0.761438	−	0.648238i	$-0.775506\pi$
$647$		−	32.9774i		−	1.29648i	0.761438	−	0.648238i	$-0.224494\pi$
$648$	12.5794	+	4.21019i	0.494165	+	0.165392i
$649$	45.2407			1.77585
$650$	−4.02621	+	3.24083i	−0.157921	+	0.127116i
$651$	1.53391	+	12.5257i	0.0601188	+	0.490920i
$652$	−9.95730	−	15.5319i	−0.389958	−	0.608275i
$653$	2.43575	−	2.43575i	0.0953182	−	0.0953182i	−0.657840	−	0.753158i	$-0.728530\pi$
$653$	2.43575	−	2.43575i	0.0953182	−	0.0953182i	0.753158	+	0.657840i	$0.228530\pi$
$654$	0.725889	−	6.71654i	0.0283845	−	0.262638i
$655$		−	14.1349i		−	0.552297i
$656$	39.0942	+	17.9591i	1.52637	+	0.701185i
$657$		−	27.3435i		−	1.06677i
$658$	−33.9026	+	34.8792i	−1.32166	+	1.35973i
$659$	−1.10623	−	1.10623i	−0.0430926	−	0.0430926i	0.685232	−	0.728325i	$-0.259701\pi$
$659$	−1.10623	−	1.10623i	−0.0430926	−	0.0430926i	−0.728325	+	0.685232i	$0.759701\pi$
$660$	−4.17368	−	6.51031i	−0.162460	−	0.253413i
$661$	27.5757	−	27.5757i	1.07257	−	1.07257i	0.0754189	−	0.997152i	$-0.475971\pi$
$661$	27.5757	−	27.5757i	1.07257	−	1.07257i	0.997152	−	0.0754189i	$-0.0240294\pi$
$662$	−4.19956	+	3.38036i	−0.163221	+	0.131381i
$663$			6.82626i			0.265110i
$664$	−23.0310	+	11.4804i	−0.893775	+	0.445525i
$665$	7.05324	+	5.51421i	0.273513	+	0.213832i
$666$	11.1880	−	9.00560i	0.433527	−	0.348960i
$667$	−11.2763	+	11.2763i	−0.436621	+	0.436621i
$668$	10.0955	−	46.1603i	0.390605	−	1.78600i
$669$	0.604449	−	0.604449i	0.0233694	−	0.0233694i
$670$	8.78661	+	0.949610i	0.339456	+	0.0366866i
$671$	−50.6407			−1.95496
$672$	−4.31284	+	9.75099i	−0.166371	+	0.376153i
$673$	−34.0933			−1.31420			−0.657101	−	0.753803i	$-0.728217\pi$
$673$	−34.0933			−1.31420			−0.657101	+	0.753803i	$0.728217\pi$
$674$	5.63357	+	0.608847i	0.216997	+	0.0234519i
$675$	2.76679	−	2.76679i	0.106494	−	0.106494i
$676$	−0.152402	+	0.696839i	−0.00586160	+	0.0268015i
$677$	20.4932	−	20.4932i	0.787619	−	0.787619i	−0.193484	−	0.981103i	$-0.561979\pi$
$677$	20.4932	−	20.4932i	0.787619	−	0.787619i	0.981103	+	0.193484i	$0.0619787\pi$
$678$	10.5565	−	8.49726i	0.405420	−	0.326335i
$679$	3.48618	+	2.72549i	0.133787	+	0.104595i
$680$	3.30834	+	6.63691i	0.126869	+	0.254514i
$681$			4.30511i			0.164972i
$682$	−40.0332	+	32.2240i	−1.53295	+	1.23392i
$683$	26.6262	−	26.6262i	1.01882	−	1.01882i	0.0190044	−	0.999819i	$-0.493950\pi$
$683$	26.6262	−	26.6262i	1.01882	−	1.01882i	0.999819	−	0.0190044i	$-0.00604966\pi$
$684$	9.10403	+	14.2009i	0.348101	+	0.542986i
$685$	10.1992	+	10.1992i	0.389690	+	0.389690i
$686$	22.6315	+	13.1840i	0.864073	+	0.503367i
$687$		−	7.26626i		−	0.277225i
$688$	−19.9431	+	7.38779i	−0.760322	+	0.281657i
$689$			5.57141i			0.212254i
$690$	0.274342	−	2.53844i	0.0104440	−	0.0966369i
$691$	19.7837	−	19.7837i	0.752606	−	0.752606i	−0.222359	−	0.974965i	$-0.571376\pi$
$691$	19.7837	−	19.7837i	0.752606	−	0.752606i	0.974965	+	0.222359i	$0.0713756\pi$
$692$	−7.11674	−	11.1010i	−0.270538	−	0.421998i
$693$	−35.5272	+	4.35072i	−1.34957	+	0.165270i
$694$	18.5159	−	14.9041i	0.702855	−	0.565750i
$695$	0.553158			0.0209825
$696$	4.02425	−	12.0238i	0.152539	−	0.455762i
$697$			28.1995i			1.06813i
$698$	−9.70306	−	12.0545i	−0.367266	−	0.456270i
$699$	−1.33200	−	1.33200i	−0.0503810	−	0.0503810i
$700$	−3.37615	−	4.07451i	−0.127606	−	0.154002i
$701$	32.9611	−	32.9611i	1.24492	−	1.24492i	0.286991	−	0.957933i	$-0.407345\pi$
$701$	32.9611	−	32.9611i	1.24492	−	1.24492i	0.957933	−	0.286991i	$-0.0926549\pi$
$702$	2.17299	−	20.1064i	0.0820143	−	0.758867i
$703$	13.7876			0.520009
$704$	−42.9996	+	6.03576i	−1.62061	+	0.227481i
$705$			9.26107i			0.348792i
$706$	−4.57153	+	42.2997i	−0.172052	+	1.59197i
$707$	0.353462	+	2.88631i	0.0132933	+	0.108551i
$708$	−11.6018	−	2.53736i	−0.436022	−	0.0953597i
$709$	1.96826	+	1.96826i	0.0739196	+	0.0739196i	0.743100	−	0.669180i	$-0.233355\pi$
$709$	1.96826	+	1.96826i	0.0739196	+	0.0739196i	−0.669180	+	0.743100i	$0.733355\pi$
$710$	14.1495	−	11.3894i	0.531021	−	0.427436i
$711$	−31.5278			−1.18238
$712$	46.5609	+	15.5834i	1.74494	+	0.584014i
$713$	−16.9673			−0.635431
$714$	−6.98802	+	0.0992214i	−0.261520	+	0.00371327i
$715$	14.0264	−	14.0264i	0.524556	−	0.524556i
$716$	−12.4111	−	19.3594i	−0.463824	−	0.723496i
$717$	9.79141	+	9.79141i	0.365667	+	0.365667i
$718$	19.0593	+	2.05983i	0.711288	+	0.0768722i
$719$	30.9469			1.15412			0.577062	−	0.816700i	$-0.304199\pi$
$719$	30.9469			1.15412			0.577062	+	0.816700i	$0.304199\pi$
$720$	−3.46332	−	9.34909i	−0.129070	−	0.348420i
$721$	−28.4899	−	22.2734i	−1.06102	−	0.829503i
$722$	1.14716	−	10.6145i	0.0426930	−	0.395032i
$723$	−0.232584	−	0.232584i	−0.00864990	−	0.00864990i
$724$	−17.9146	+	11.4848i	−0.665789	+	0.426829i
$725$	4.44955	+	4.44955i	0.165252	+	0.165252i
$726$	11.6613	+	14.4872i	0.432790	+	0.537672i
$727$		−	5.15786i		−	0.191294i	−0.995415	−	0.0956472i	$-0.969508\pi$
$727$		−	5.15786i		−	0.191294i	0.995415	−	0.0956472i	$-0.0304921\pi$
$728$	−26.7978	−	5.46333i	−0.993194	−	0.202485i
$729$		−	3.32722i		−	0.123230i
$730$	−12.0856	+	9.72808i	−0.447308	+	0.360052i
$731$	−9.85717	−	9.85717i	−0.364581	−	0.364581i
$732$	12.9866	+	2.84022i	0.479998	+	0.104977i
$733$	−13.6663	−	13.6663i	−0.504778	−	0.504778i	0.408141	−	0.912919i	$-0.366177\pi$
$733$	−13.6663	−	13.6663i	−0.504778	−	0.504778i	−0.912919	+	0.408141i	$0.866177\pi$
$734$	−15.9997	−	1.72917i	−0.590561	−	0.0638247i
$735$	4.83942	−	1.20333i	0.178505	−	0.0443856i
$736$	−12.3087	−	7.34952i	−0.453704	−	0.270907i
$737$	−33.9187			−1.24941
$738$	4.07362	−	37.6926i	0.149952	−	1.38748i
$739$	−6.51052	−	6.51052i	−0.239493	−	0.239493i	0.577147	−	0.816640i	$-0.304166\pi$
$739$	−6.51052	−	6.51052i	−0.239493	−	0.239493i	−0.816640	+	0.577147i	$0.804166\pi$
$740$	−7.96080	−	1.74106i	−0.292645	−	0.0640026i
$741$	6.22977	−	6.22977i	0.228856	−	0.228856i
$742$	−5.70343	+	0.0809818i	−0.209380	+	0.00297294i
$743$	9.31278			0.341653			0.170826	−	0.985301i	$-0.445356\pi$
$743$	9.31278			0.341653			0.170826	+	0.985301i	$0.445356\pi$
$744$	12.0737	−	6.01843i	0.442642	−	0.220646i
$745$	−6.47058			−0.237064
$746$	5.76792	+	7.16572i	0.211179	+	0.262356i
$747$	16.0353	+	16.0353i	0.586700	+	0.586700i
$748$	−15.3606	−	23.9602i	−0.561639	−	0.876072i
$749$	−3.06615	−	25.0377i	−0.112035	−	0.914856i
$750$	−1.00165	−	0.108253i	−0.0365751	−	0.00395284i
$751$		−	32.8572i		−	1.19897i	−0.800384	−	0.599487i	$-0.795371\pi$
$751$		−	32.8572i		−	1.19897i	0.800384	−	0.599487i	$-0.204629\pi$
$752$	47.2521	+	21.7067i	1.72311	+	0.791562i
$753$	9.02896			0.329033
$754$	32.3350	+	3.49460i	1.17757	+	0.127266i
$755$	−5.85502	+	5.85502i	−0.213086	+	0.213086i
$756$	20.6144	+	1.93223i	0.749740	+	0.0702747i
$757$	30.1664	+	30.1664i	1.09642	+	1.09642i	0.994826	+	0.101590i	$0.0323930\pi$
$757$	30.1664	+	30.1664i	1.09642	+	1.09642i	0.101590	+	0.994826i	$0.467607\pi$
$758$	−30.1618	+	24.2782i	−1.09553	+	0.881826i
$759$			9.79908i			0.355684i
$760$	3.03772	−	9.07622i	0.110190	−	0.329229i
$761$	−28.2293			−1.02331			−0.511655	−	0.859191i	$-0.670967\pi$
$761$	−28.2293			−1.02331			−0.511655	+	0.859191i	$0.670967\pi$
$762$	6.36800	+	7.91123i	0.230688	+	0.286594i
$763$	2.15648	+	17.6095i	0.0780699	+	0.637506i
$764$	3.84637	−	17.5871i	0.139157	−	0.636279i
$765$	4.62093	−	4.62093i	0.167070	−	0.167070i
$766$	−1.09983	−	0.118864i	−0.0397384	−	0.00429472i
$767$		−	30.4626i		−	1.09994i
$768$	11.3656	+	0.863817i	0.410120	+	0.0311703i
$769$			1.40339i			0.0506077i	0.999680	+	0.0253038i	$0.00805532\pi$
$769$			1.40339i			0.0506077i	−0.999680	+	0.0253038i	$0.991945\pi$
$770$	14.5626	+	14.1549i	0.524801	+	0.510106i
$771$	2.13755	+	2.13755i	0.0769818	+	0.0769818i
$772$	47.8724	+	10.4699i	1.72297	+	0.376820i
$773$	1.73233	−	1.73233i	0.0623075	−	0.0623075i	−0.675266	−	0.737574i	$-0.735971\pi$
$773$	1.73233	−	1.73233i	0.0623075	−	0.0623075i	0.737574	+	0.675266i	$0.235971\pi$
$774$	11.7516	+	14.5995i	0.422402	+	0.524767i
$775$			6.69517i			0.240498i
$776$	1.50144	−	4.48606i	0.0538985	−	0.161040i
$777$	4.73002	−	6.05018i	0.169689	−	0.217049i
$778$	−30.4897	−	37.8786i	−1.09311	−	1.35801i
$779$	25.7354	−	25.7354i	0.922065	−	0.922065i
$780$	−4.38368	+	2.81032i	−0.156961	+	0.100626i
$781$	−49.2936	+	49.2936i	−1.76386	+	1.76386i
$782$	1.00967	−	9.34235i	0.0361058	−	0.334082i
$783$	−24.6220			−0.879917
$784$	5.20329	−	27.5123i	0.185832	−	0.982582i
$785$	1.03404			0.0369065
$786$	1.53015	−	14.1582i	0.0545785	−	0.505007i
$787$	−36.0454	+	36.0454i	−1.28488	+	1.28488i	−0.347025	+	0.937856i	$0.612808\pi$
$787$	−36.0454	+	36.0454i	−1.28488	+	1.28488i	−0.937856	+	0.347025i	$0.887192\pi$
$788$	4.18836	+	6.53320i	0.149204	+	0.232736i
$789$	1.48125	−	1.48125i	0.0527339	−	0.0527339i
$790$	11.2168	+	13.9350i	0.399074	+	0.495786i
$791$	−21.9188	+	28.0364i	−0.779344	+	0.996860i
$792$	17.0704	+	34.2452i	0.606570	+	1.21685i
$793$			34.0986i			1.21088i
$794$	−21.5334	−	26.7518i	−0.764191	−	0.949385i
$795$	−0.767934	+	0.767934i	−0.0272358	+	0.0272358i
$796$	−0.597496	+	2.73198i	−0.0211777	+	0.0968326i
$797$	23.2621	+	23.2621i	0.823984	+	0.823984i	0.986677	−	0.162693i	$-0.0520179\pi$
$797$	23.2621	+	23.2621i	0.823984	+	0.823984i	−0.162693	+	0.986677i	$0.552018\pi$
$798$	6.46795	+	6.28685i	0.228963	+	0.222552i
$799$			34.0840i			1.20580i
$800$	−2.90006	+	4.85692i	−0.102533	+	0.171718i
$801$		−	43.2678i		−	1.52879i
$802$	−38.9768	−	4.21240i	−1.37632	−	0.148745i
$803$	42.1034	−	42.1034i	1.48580	−	1.48580i
$804$	8.69830	+	1.90235i	0.306766	+	0.0670909i
$805$	0.815019	+	6.65531i	0.0287256	+	0.234569i
$806$	21.6979	+	26.9562i	0.764276	+	0.949491i
$807$	−18.2378			−0.642001
$808$	2.78215	−	1.38684i	0.0978759	−	0.0487887i
$809$			49.6502i			1.74561i	0.488072	+	0.872803i	$0.337700\pi$
$809$			49.6502i			1.74561i	−0.488072	+	0.872803i	$0.662300\pi$
$810$	−5.16675	+	4.15889i	−0.181541	+	0.146128i
$811$	−32.3289	−	32.3289i	−1.13522	−	1.13522i	−0.989296	−	0.145925i	$-0.953384\pi$
$811$	−32.3289	−	32.3289i	−1.13522	−	1.13522i	−0.145925	−	0.989296i	$-0.546616\pi$
$812$	−3.10741	+	33.1520i	−0.109049	+	1.16341i
$813$	1.42511	−	1.42511i	0.0499809	−	0.0499809i
$814$	31.0941	+	3.36048i	1.08985	+	0.117785i
$815$	9.22479			0.323130
$816$	2.59533	+	7.00600i	0.0908548	+	0.245259i
$817$			17.9917i			0.629449i
$818$	2.08008	+	0.224804i	0.0727284	+	0.00786010i
$819$	2.92953	+	23.9221i	0.102366	+	0.835905i
$820$	−18.1091	+	11.6095i	−0.632397	+	0.405422i
$821$	11.8776	+	11.8776i	0.414530	+	0.414530i	0.883313	−	0.468783i	$-0.155307\pi$
$821$	11.8776	+	11.8776i	0.414530	+	0.414530i	−0.468783	+	0.883313i	$0.655307\pi$
$822$	9.11190	+	11.3201i	0.317814	+	0.394833i
$823$	−2.62077			−0.0913545			−0.0456772	−	0.998956i	$-0.514545\pi$
$823$	−2.62077			−0.0913545			−0.0456772	+	0.998956i	$0.514545\pi$
$824$	−12.2701	+	36.6612i	−0.427450	+	1.27715i
$825$	3.86664			0.134619
$826$	31.1845	−	0.442781i	1.08505	−	0.0154063i
$827$	−21.7923	+	21.7923i	−0.757793	+	0.757793i	−0.975920	−	0.218127i	$-0.930005\pi$
$827$	−21.7923	+	21.7923i	−0.757793	+	0.757793i	0.218127	+	0.975920i	$0.430005\pi$
$828$	−2.69914	+	12.3415i	−0.0938017	+	0.428898i
$829$	9.86029	+	9.86029i	0.342462	+	0.342462i	0.857292	−	0.514830i	$-0.172145\pi$
$829$	9.86029	+	9.86029i	0.342462	+	0.342462i	−0.514830	+	0.857292i	$0.672145\pi$
$830$	1.38253	−	12.7924i	0.0479884	−	0.444030i
$831$	8.10134			0.281032
$832$	4.06415	+	28.9536i	0.140899	+	1.00378i
$833$	17.8108	−	4.42868i	0.617106	−	0.153445i
$834$	0.554070	+	0.0598810i	0.0191859	+	0.00207351i
$835$	16.7059	+	16.7059i	0.578131	+	0.578131i
$836$	−7.84816	+	35.8849i	−0.271434	+	1.24110i
$837$	−18.5242	−	18.5242i	−0.640289	−	0.640289i
$838$	−16.4483	+	13.2397i	−0.568196	+	0.457359i
$839$			17.8815i			0.617338i	0.951169	+	0.308669i	$0.0998836\pi$
$839$			17.8815i			0.617338i	−0.951169	+	0.308669i	$0.900116\pi$
$840$	−2.94064	−	4.44671i	−0.101462	−	0.153426i
$841$		−	10.5969i		−	0.365412i
$842$	−9.51164	−	11.8167i	−0.327793	−	0.407230i
$843$	−7.68220	−	7.68220i	−0.264589	−	0.264589i
$844$	−3.11868	−	4.86467i	−0.107349	−	0.167449i
$845$	−0.252193	−	0.252193i	−0.00867571	−	0.00867571i
$846$	4.92368	−	45.5581i	0.169279	−	1.56632i
$847$	−38.4759	−	30.0804i	−1.32205	−	1.03357i
$848$	2.11824	+	5.71811i	0.0727406	+	0.196361i
$849$	−3.09306			−0.106154
$850$	−3.68642	−	0.398409i	−0.126443	−	0.0136653i
$851$	7.30145	+	7.30145i	0.250290	+	0.250290i
$852$	15.4058	−	9.87646i	0.527794	−	0.338362i
$853$	6.87815	−	6.87815i	0.235504	−	0.235504i	−0.579482	−	0.814985i	$-0.696745\pi$
$853$	6.87815	−	6.87815i	0.235504	−	0.235504i	0.814985	+	0.579482i	$0.196745\pi$
$854$	−34.9067	+	0.495632i	−1.19448	+	0.0169602i
$855$	−8.43430			−0.288447
$856$	−24.1341	+	12.0303i	−0.824888	+	0.411186i
$857$	17.8550			0.609915			0.304957	−	0.952366i	$-0.401358\pi$
$857$	17.8550			0.609915			0.304957	+	0.952366i	$0.401358\pi$
$858$	15.5679	−	12.5311i	0.531480	−	0.427805i
$859$	−38.9214	−	38.9214i	−1.32798	−	1.32798i	−0.907130	−	0.420850i	$-0.861732\pi$
$859$	−38.9214	−	38.9214i	−1.32798	−	1.32798i	−0.420850	−	0.907130i	$-0.638268\pi$
$860$	2.27194	−	10.3882i	0.0774725	−	0.354235i
$861$	−2.46416	−	20.1219i	−0.0839782	−	0.685752i
$862$	2.77437	−	25.6708i	0.0944953	−	0.874351i
$863$			3.41417i			0.116220i	0.998310	+	0.0581098i	$0.0185073\pi$
$863$			3.41417i			0.116220i	−0.998310	+	0.0581098i	$0.981493\pi$
$864$	−5.41420	−	21.4620i	−0.184195	−	0.730151i
$865$	6.59320			0.224175
$866$	−0.124541	+	1.15236i	−0.00423209	+	0.0391589i
$867$	5.10078	−	5.10078i	0.173231	−	0.173231i
$868$	−27.2796	+	22.6039i	−0.925929	+	0.767226i
$869$	−48.5464	−	48.5464i	−1.64682	−	1.64682i
$870$	3.97521	+	4.93857i	0.134772	+	0.167433i
$871$			22.8390i			0.773869i
$872$	16.9740	−	8.46113i	0.574812	−	0.286530i
$873$	−4.16879			−0.141092
$874$	−9.44745	+	7.60456i	−0.319565	+	0.257228i
$875$	2.62613	−	0.321600i	0.0887795	−	0.0108721i
$876$	−13.1586	+	8.43583i	−0.444589	+	0.285020i
$877$	7.97309	−	7.97309i	0.269232	−	0.269232i	−0.559559	−	0.828791i	$-0.689029\pi$
$877$	7.97309	−	7.97309i	0.269232	−	0.269232i	0.828791	+	0.559559i	$0.189029\pi$
$878$	2.23261	−	20.6580i	0.0753469	−	0.697174i
$879$			12.7983i			0.431675i
$880$	9.06289	−	19.7285i	0.305510	−	0.665047i
$881$			43.2127i			1.45587i	0.685645	+	0.727937i	$0.259520\pi$
$881$			43.2127i			1.45587i	−0.685645	+	0.727937i	$0.740480\pi$
$882$	−24.4464	+	3.34667i	−0.823152	+	0.112688i
$883$	7.88834	+	7.88834i	0.265464	+	0.265464i	0.827269	−	0.561806i	$-0.189893\pi$
$883$	7.88834	+	7.88834i	0.265464	+	0.265464i	−0.561806	+	0.827269i	$0.689893\pi$
$884$	−16.1335	+	10.3430i	−0.542627	+	0.347872i
$885$	4.19880	−	4.19880i	0.141141	−	0.141141i
$886$	28.2478	−	22.7375i	0.949002	−	0.763882i
$887$		−	32.0831i		−	1.07724i	−0.842547	−	0.538622i	$-0.818945\pi$
$887$		−	32.0831i		−	1.07724i	0.842547	−	0.538622i	$-0.181055\pi$
$888$	−7.78546	−	2.60571i	−0.261263	−	0.0874420i
$889$	−21.0110	−	16.4264i	−0.704687	−	0.550923i
$890$	−19.1240	+	15.3935i	−0.641039	+	0.515993i
$891$	17.9998	−	17.9998i	0.603015	−	0.603015i
$892$	2.34443	+	0.512736i	0.0784972	+	0.0171677i
$893$	31.1056	−	31.1056i	1.04091	−	1.04091i
$894$	−6.48126	−	0.700460i	−0.216766	−	0.0234269i
$895$	11.4981			0.384338
$896$	−29.5806	+	4.58131i	−0.988218	+	0.153051i
$897$	6.59816			0.220306
$898$	−46.2105	−	4.99419i	−1.54207	−	0.166658i
$899$	29.7905	−	29.7905i	0.993569	−	0.993569i
$900$	4.86987	+	1.06506i	0.162329	+	0.0355020i
$901$	−2.82626	+	2.82626i	−0.0941565	+	0.0941565i
$902$	64.3115	−	51.7664i	2.14134	−	1.72363i
$903$	7.89499	+	6.17229i	0.262729	+	0.205401i
$904$	36.0777	+	12.0748i	1.19993	+	0.401603i
$905$		−	10.6399i		−	0.353683i
$906$	−6.49850	+	5.23086i	−0.215898	+	0.173784i
$907$	22.8244	−	22.8244i	0.757873	−	0.757873i	−0.218062	−	0.975935i	$-0.569974\pi$
$907$	22.8244	−	22.8244i	0.757873	−	0.757873i	0.975935	+	0.218062i	$0.0699735\pi$
$908$	−10.1749	+	6.52298i	−0.337665	+	0.216473i
$909$	−1.93707	−	1.93707i	−0.0642485	−	0.0642485i
$910$	9.53111	−	9.80567i	0.315953	−	0.325055i
$911$		−	17.9331i		−	0.594150i	−0.954854	−	0.297075i	$-0.903989\pi$
$911$		−	17.9331i		−	0.594150i	0.954854	−	0.297075i	$-0.0960111\pi$
$912$	4.02526	−	8.76235i	0.133290	−	0.290150i
$913$			49.3821i			1.63431i
$914$	4.20588	−	38.9164i	0.139118	−	1.28724i
$915$	−4.69997	+	4.69997i	−0.155376	+	0.155376i
$916$	17.1734	−	11.0096i	0.567425	−	0.363769i
$917$	4.54579	+	37.1201i	0.150115	+	1.22582i
$918$	11.3019	−	9.09725i	0.373018	−	0.300254i
$919$	−31.8671			−1.05120			−0.525600	−	0.850732i	$-0.676159\pi$
$919$	−31.8671			−1.05120			−0.525600	+	0.850732i	$0.676159\pi$
$920$	6.41514	−	3.19779i	0.211501	−	0.105428i
$921$			2.35287i			0.0775298i
$922$	−7.09797	−	8.81810i	−0.233759	−	0.290408i
$923$	33.1916	+	33.1916i	1.09251	+	1.09251i
$924$	13.0543	+	15.7547i	0.429456	+	0.518291i
$925$	2.88110	−	2.88110i	0.0947298	−	0.0947298i
$926$	−2.74683	+	25.4161i	−0.0902666	+	0.835223i
$927$	34.0683			1.11895
$928$	34.5150	−	8.70710i	1.13301	−	0.285825i
$929$			33.7843i			1.10843i	0.832374	+	0.554214i	$0.186981\pi$
$929$			33.7843i			1.10843i	−0.832374	+	0.554214i	$0.813019\pi$
$930$	−0.724773	+	6.70622i	−0.0237662	+	0.219906i
$931$	−20.2961	−	12.2127i	−0.665178	−	0.400256i
$932$	1.12990	−	5.16633i	0.0370110	−	0.169229i
$933$	−1.59901	−	1.59901i	−0.0523492	−	0.0523492i
$934$	−17.6020	+	14.1684i	−0.575956	+	0.463606i
$935$	14.2306			0.465390
$936$	23.0588	−	11.4943i	0.753700	−	0.375701i
$937$	23.5999			0.770977			0.385488	−	0.922713i	$-0.374033\pi$
$937$	23.5999			0.770977			0.385488	+	0.922713i	$0.374033\pi$
$938$	−23.3802	+	0.331970i	−0.763390	+	0.0108392i
$939$	5.78682	−	5.78682i	0.188846	−	0.188846i
$940$	−21.8880	+	14.0321i	−0.713908	+	0.457677i
$941$	−33.7721	−	33.7721i	−1.10094	−	1.10094i	−0.994298	−	0.106640i	$-0.965991\pi$
$941$	−33.7721	−	33.7721i	−1.10094	−	1.10094i	−0.106640	−	0.994298i	$-0.534009\pi$
$942$	1.03575	+	0.111938i	0.0337464	+	0.00364714i
$943$	27.2572			0.887616
$944$	−11.5818	−	31.2647i	−0.376956	−	1.01758i
$945$	−6.37617	+	8.15577i	−0.207417	+	0.265307i
$946$	−4.38516	+	40.5752i	−0.142574	+	1.31921i
$947$	34.5344	+	34.5344i	1.12222	+	1.12222i	0.991407	+	0.130811i	$0.0417580\pi$
$947$	34.5344	+	34.5344i	1.12222	+	1.12222i	0.130811	+	0.991407i	$0.458242\pi$
$948$	9.72675	+	15.1723i	0.315910	+	0.492772i
$949$	−28.3501	−	28.3501i	−0.920282	−	0.920282i
$950$	3.00070	+	3.72789i	0.0973555	+	0.120949i
$951$		−	17.7717i		−	0.576288i
$952$	−10.8226	−	16.3654i	−0.350762	−	0.530407i
$953$		−	34.6306i		−	1.12179i	−0.827886	−	0.560897i	$-0.810456\pi$
$953$		−	34.6306i		−	1.12179i	0.827886	−	0.560897i	$-0.189544\pi$
$954$	4.18598	−	3.36943i	0.135526	−	0.109089i
$955$	6.36495	+	6.36495i	0.205965	+	0.205965i
$956$	−8.30575	+	37.9771i	−0.268627	+	1.22827i
$957$	−17.2048	−	17.2048i	−0.556152	−	0.556152i
$958$	−6.66325	−	0.720129i	−0.215280	−	0.0232663i
$959$	−30.0644	−	23.5043i	−0.970831	−	0.758994i
$960$	−3.43063	+	4.55099i	−0.110723	+	0.146882i
$961$	13.8254			0.445979
$962$	2.26276	−	20.9370i	0.0729544	−	0.675037i
$963$	16.8033	+	16.8033i	0.541480	+	0.541480i
$964$	0.197294	−	0.902105i	0.00635441	−	0.0290548i
$965$	−17.3255	+	17.3255i	−0.557728	+	0.557728i
$966$	0.0959059	+	6.75452i	0.00308572	+	0.217323i
$967$	−53.1782			−1.71010			−0.855048	−	0.518549i	$-0.826472\pi$
$967$	−53.1782			−1.71010			−0.855048	+	0.518549i	$0.826472\pi$
$968$	−16.5709	+	49.5114i	−0.532610	+	1.59136i
$969$	6.32047			0.203043
$970$	1.48314	+	1.84257i	0.0476209	+	0.0591613i
$971$	−17.4969	−	17.4969i	−0.561504	−	0.561504i	0.368231	−	0.929734i	$-0.379964\pi$
$971$	−17.4969	−	17.4969i	−0.561504	−	0.561504i	−0.929734	+	0.368231i	$0.879964\pi$
$972$	−25.3897	+	16.2771i	−0.814377	+	0.522087i
$973$	−1.45267	+	0.177896i	−0.0465703	+	0.00570307i
$974$	14.2349	+	1.53843i	0.456115	+	0.0492945i
$975$		−	2.60358i		−	0.0833814i
$976$	12.9642	+	34.9965i	0.414975	+	1.12021i
$977$	−27.5914			−0.882726			−0.441363	−	0.897329i	$-0.645505\pi$
$977$	−27.5914			−0.882726			−0.441363	+	0.897329i	$0.645505\pi$
$978$	9.24001	+	0.998612i	0.295463	+	0.0319321i
$979$	66.6236	−	66.6236i	2.12930	−	2.12930i
$980$	10.1766	+	9.61444i	0.325079	+	0.307122i
$981$	−11.8181	−	11.8181i	−0.377323	−	0.377323i
$982$	9.83165	−	7.91381i	0.313740	−	0.252540i
$983$			13.4939i			0.430387i	0.976571	+	0.215194i	$0.0690382\pi$
$983$			13.4939i			0.430387i	−0.976571	+	0.215194i	$0.930962\pi$
$984$	−19.3958	+	9.66831i	−0.618314	+	0.308215i
$985$	−3.88024			−0.123635
$986$	14.6302	+	18.1756i	0.465919	+	0.578830i
$987$	−2.97836	−	24.3208i	−0.0948022	−	0.774139i
$988$	24.1629	+	5.28452i	0.768724	+	0.168123i
$989$	−9.52779	+	9.52779i	−0.302966	+	0.302966i
$990$	−19.0212	−	2.05571i	−0.604534	−	0.0653348i
$991$			37.3118i			1.18525i	0.805479	+	0.592624i	$0.201908\pi$
$991$			37.3118i			1.18525i	−0.805479	+	0.592624i	$0.798092\pi$
$992$	32.5179	+	19.4164i	1.03244	+	0.616473i
$993$		−	2.71568i		−	0.0861795i
$994$	−33.4956	+	34.4605i	−1.06242	+	1.09302i
$995$	−0.988733	−	0.988733i	−0.0313449	−	0.0313449i
$996$	2.76963	−	12.6638i	0.0877590	−	0.401268i
$997$	−20.3371	+	20.3371i	−0.644081	+	0.644081i	−0.951556	−	0.307475i	$-0.900516\pi$
$997$	−20.3371	+	20.3371i	−0.644081	+	0.644081i	0.307475	+	0.951556i	$0.400516\pi$
$998$	32.0191	+	39.7786i	1.01355	+	1.25917i
$999$			15.9428i			0.504408i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bc.a.251.4	yes	128
7.6	odd	2	inner	560.2.bc.a.251.3	✓	128
16.3	odd	4	inner	560.2.bc.a.531.3	yes	128
112.83	even	4	inner	560.2.bc.a.531.4	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bc.a.251.3	✓	128	7.6	odd	2	inner
560.2.bc.a.251.4	yes	128	1.1	even	1	trivial
560.2.bc.a.531.3	yes	128	16.3	odd	4	inner
560.2.bc.a.531.4	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)

\(f(q)\)	\(=\)	\(q+(-1.40603 - 0.151956i) q^{2} +(0.503741 - 0.503741i) q^{3} +(1.95382 + 0.427308i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.784820 + 0.631727i) q^{6} +(1.62955 - 2.08436i) q^{7} +(-2.68219 - 0.897701i) q^{8} +2.49249i q^{9} +O(q^{10})\)	\(q+(-1.40603 - 0.151956i) q^{2} +(0.503741 - 0.503741i) q^{3} +(1.95382 + 0.427308i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.784820 + 0.631727i) q^{6} +(1.62955 - 2.08436i) q^{7} +(-2.68219 - 0.897701i) q^{8} +2.49249i q^{9} +(1.10166 - 0.886762i) q^{10} +(-3.83792 + 3.83792i) q^{11} +(1.19947 - 0.768967i) q^{12} +(2.58425 + 2.58425i) q^{13} +(-2.60792 + 2.68305i) q^{14} +0.712398i q^{15} +(3.63482 + 1.66976i) q^{16} +2.62187i q^{17} +(0.378749 - 3.50451i) q^{18} +(2.39277 - 2.39277i) q^{19} +(-1.68371 + 1.07941i) q^{20} +(-0.229107 - 1.87085i) q^{21} +(5.97942 - 4.81303i) q^{22} +2.53426 q^{23} +(-1.80334 + 0.898920i) q^{24} -1.00000i q^{25} +(-3.24083 - 4.02621i) q^{26} +(2.76679 + 2.76679i) q^{27} +(4.07451 - 3.37615i) q^{28} +(-4.44955 + 4.44955i) q^{29} +(0.108253 - 1.00165i) q^{30} -6.69517 q^{31} +(-4.85692 - 2.90006i) q^{32} +3.86664i q^{33} +(0.398409 - 3.68642i) q^{34} +(0.321600 + 2.62613i) q^{35} +(-1.06506 + 4.86987i) q^{36} +(2.88110 + 2.88110i) q^{37} +(-3.72789 + 3.00070i) q^{38} +2.60358 q^{39} +(2.53136 - 1.26182i) q^{40} +10.7555 q^{41} +(0.0378437 + 2.66528i) q^{42} +(-3.75959 + 3.75959i) q^{43} +(-9.13858 + 5.85863i) q^{44} +(-1.76246 - 1.76246i) q^{45} +(-3.56324 - 0.385096i) q^{46} +12.9999 q^{47} +(2.67214 - 0.989877i) q^{48} +(-1.68913 - 6.79315i) q^{49} +(-0.151956 + 1.40603i) q^{50} +(1.32075 + 1.32075i) q^{51} +(3.94488 + 6.15342i) q^{52} +(1.07796 + 1.07796i) q^{53} +(-3.46975 - 4.31061i) q^{54} -5.42764i q^{55} +(-6.24189 + 4.12780i) q^{56} -2.41067i q^{57} +(6.93231 - 5.58004i) q^{58} +(-5.89390 - 5.89390i) q^{59} +(-0.304413 + 1.39190i) q^{60} +(6.59740 + 6.59740i) q^{61} +(9.41359 + 1.01737i) q^{62} +(5.19525 + 4.06164i) q^{63} +(6.38827 + 4.81560i) q^{64} -3.65468 q^{65} +(0.587559 - 5.43660i) q^{66} +(4.41889 + 4.41889i) q^{67} +(-1.12035 + 5.12266i) q^{68} +(1.27661 - 1.27661i) q^{69} +(-0.0531216 - 3.74128i) q^{70} +12.8438 q^{71} +(2.23751 - 6.68533i) q^{72} -10.9703 q^{73} +(-3.61310 - 4.48869i) q^{74} +(-0.503741 - 0.503741i) q^{75} +(5.69748 - 3.65259i) q^{76} +(1.74553 + 14.2537i) q^{77} +(-3.66071 - 0.395630i) q^{78} +12.6491i q^{79} +(-3.75090 + 1.38950i) q^{80} -4.68997 q^{81} +(-15.1225 - 1.63436i) q^{82} +(6.43343 - 6.43343i) q^{83} +(0.351796 - 3.75320i) q^{84} +(-1.85394 - 1.85394i) q^{85} +(5.85738 - 4.71479i) q^{86} +4.48284i q^{87} +(13.7393 - 6.84873i) q^{88} -17.3593 q^{89} +(2.21024 + 2.74588i) q^{90} +(9.59766 - 1.17534i) q^{91} +(4.95149 + 1.08291i) q^{92} +(-3.37264 + 3.37264i) q^{93} +(-18.2781 - 1.97540i) q^{94} +3.38389i q^{95} +(-3.90751 + 0.985746i) q^{96} +1.67254i q^{97} +(1.34270 + 9.80801i) q^{98} +(-9.56599 - 9.56599i) 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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