LMFDB - Embedded newform 560.2.bd.b.141.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(141,560)]

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([0, 3, 0, 0]))

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

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

chi := DirichletCharacter("560.141");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bd (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:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			141.5
Character	$\chi$	$=$	560.141
Dual form			560.2.bd.b.421.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30240 - 0.551150i) q^{2} +(-1.24266 - 1.24266i) q^{3} +(1.39247 + 1.43563i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.933546 + 2.30334i) q^{6} +1.00000i q^{7} +(-1.02229 - 2.63722i) q^{8} +0.0884307i q^{9} +O(q^{10})$	\(q+(-1.30240 - 0.551150i) q^{2} +(-1.24266 - 1.24266i) q^{3} +(1.39247 + 1.43563i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.933546 + 2.30334i) q^{6} +1.00000i q^{7} +(-1.02229 - 2.63722i) q^{8} +0.0884307i q^{9} +(1.31065 - 0.531211i) q^{10} +(-1.60005 + 1.60005i) q^{11} +(0.0536375 - 3.51438i) q^{12} +(-1.80583 - 1.80583i) q^{13} +(0.551150 - 1.30240i) q^{14} +1.75739 q^{15} +(-0.122070 + 3.99814i) q^{16} +2.11216 q^{17} +(0.0487386 - 0.115172i) q^{18} +(5.91638 + 5.91638i) q^{19} +(-1.99977 - 0.0305211i) q^{20} +(1.24266 - 1.24266i) q^{21} +(2.96577 - 1.20203i) q^{22} +0.874774i q^{23} +(-2.00681 + 4.54755i) q^{24} -1.00000i q^{25} +(1.35662 + 3.34720i) q^{26} +(-3.61810 + 3.61810i) q^{27} +(-1.43563 + 1.39247i) q^{28} +(-0.225174 - 0.225174i) q^{29} +(-2.28882 - 0.968587i) q^{30} +9.29821 q^{31} +(2.36256 - 5.13988i) q^{32} +3.97666 q^{33} +(-2.75087 - 1.16412i) q^{34} +(-0.707107 - 0.707107i) q^{35} +(-0.126954 + 0.123137i) q^{36} +(3.04745 - 3.04745i) q^{37} +(-4.44465 - 10.9663i) q^{38} +4.48809i q^{39} +(2.58767 + 1.14192i) q^{40} -6.94259i q^{41} +(-2.30334 + 0.933546i) q^{42} +(2.78693 - 2.78693i) q^{43} +(-4.52511 - 0.0690637i) q^{44} +(-0.0625299 - 0.0625299i) q^{45} +(0.482132 - 1.13930i) q^{46} +11.2096 q^{47} +(5.12004 - 4.81665i) q^{48} -1.00000 q^{49} +(-0.551150 + 1.30240i) q^{50} +(-2.62471 - 2.62471i) q^{51} +(0.0779458 - 5.10708i) q^{52} +(4.93538 - 4.93538i) q^{53} +(6.70632 - 2.71808i) q^{54} -2.26282i q^{55} +(2.63722 - 1.02229i) q^{56} -14.7041i q^{57} +(0.169161 + 0.417370i) q^{58} +(-9.96255 + 9.96255i) q^{59} +(2.44711 + 2.52297i) q^{60} +(4.88247 + 4.88247i) q^{61} +(-12.1099 - 5.12471i) q^{62} -0.0884307 q^{63} +(-5.90983 + 5.39203i) q^{64} +2.55384 q^{65} +(-5.17919 - 2.19174i) q^{66} +(-2.26158 - 2.26158i) q^{67} +(2.94112 + 3.03229i) q^{68} +(1.08705 - 1.08705i) q^{69} +(0.531211 + 1.31065i) q^{70} -10.0793i q^{71} +(0.233211 - 0.0904022i) q^{72} +5.50912i q^{73} +(-5.64858 + 2.28938i) q^{74} +(-1.24266 + 1.24266i) q^{75} +(-0.255371 + 16.7321i) q^{76} +(-1.60005 - 1.60005i) q^{77} +(2.47361 - 5.84527i) q^{78} +14.4524 q^{79} +(-2.74079 - 2.91343i) q^{80} +9.25747 q^{81} +(-3.82641 + 9.04200i) q^{82} +(3.95460 + 3.95460i) q^{83} +(3.51438 + 0.0536375i) q^{84} +(-1.49353 + 1.49353i) q^{85} +(-5.16570 + 2.09367i) q^{86} +0.559632i q^{87} +(5.85542 + 2.58396i) q^{88} -0.0282999i q^{89} +(0.0469753 + 0.115902i) q^{90} +(1.80583 - 1.80583i) q^{91} +(-1.25585 + 1.21809i) q^{92} +(-11.5546 - 11.5546i) q^{93} +(-14.5993 - 6.17817i) q^{94} -8.36702 q^{95} +(-9.32301 + 3.45128i) q^{96} +12.3154 q^{97} +(1.30240 + 0.551150i) q^{98} +(-0.141494 - 0.141494i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 8 q^{4} + 12 q^{6}+O(q^{10}) $ 52 * q - 8 * q^4 + 12 * q^6	$ 52 q - 8 q^{4} + 12 q^{6} - 4 q^{10} - 4 q^{11} + 40 q^{12} + 8 q^{15} - 4 q^{16} + 8 q^{19} + 32 q^{22} + 12 q^{24} - 12 q^{26} - 24 q^{27} + 4 q^{28} + 4 q^{29} - 16 q^{34} + 4 q^{36} - 12 q^{37} + 16 q^{38} - 4 q^{42} + 36 q^{43} + 28 q^{44} - 16 q^{46} + 32 q^{48} - 52 q^{49} - 8 q^{51} - 80 q^{52} - 4 q^{53} + 48 q^{54} - 12 q^{56} - 56 q^{58} + 24 q^{59} - 16 q^{61} - 72 q^{62} - 68 q^{63} + 4 q^{64} + 40 q^{65} - 12 q^{66} - 12 q^{67} - 72 q^{69} - 8 q^{72} + 68 q^{74} - 4 q^{77} - 4 q^{78} - 16 q^{79} - 32 q^{80} - 116 q^{81} + 104 q^{82} + 16 q^{85} - 68 q^{86} - 48 q^{88} + 36 q^{90} + 64 q^{92} + 8 q^{93} - 72 q^{94} - 32 q^{95} - 52 q^{99}+O(q^{100}) $ 52 * q - 8 * q^4 + 12 * q^6 - 4 * q^10 - 4 * q^11 + 40 * q^12 + 8 * q^15 - 4 * q^16 + 8 * q^19 + 32 * q^22 + 12 * q^24 - 12 * q^26 - 24 * q^27 + 4 * q^28 + 4 * q^29 - 16 * q^34 + 4 * q^36 - 12 * q^37 + 16 * q^38 - 4 * q^42 + 36 * q^43 + 28 * q^44 - 16 * q^46 + 32 * q^48 - 52 * q^49 - 8 * q^51 - 80 * q^52 - 4 * q^53 + 48 * q^54 - 12 * q^56 - 56 * q^58 + 24 * q^59 - 16 * q^61 - 72 * q^62 - 68 * q^63 + 4 * q^64 + 40 * q^65 - 12 * q^66 - 12 * q^67 - 72 * q^69 - 8 * q^72 + 68 * q^74 - 4 * q^77 - 4 * q^78 - 16 * q^79 - 32 * q^80 - 116 * q^81 + 104 * q^82 + 16 * q^85 - 68 * q^86 - 48 * q^88 + 36 * q^90 + 64 * q^92 + 8 * q^93 - 72 * q^94 - 32 * q^95 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.30240	−	0.551150i	−0.920933	−	0.389722i
$2$	−1.30240	−	0.551150i	−0.920933	−	0.389722i
$3$	−1.24266	−	1.24266i	−0.717453	−	0.717453i	0.250630	−	0.968083i	$-0.419362\pi$
$3$	−1.24266	−	1.24266i	−0.717453	−	0.717453i	−0.968083	+	0.250630i	$0.919362\pi$
$4$	1.39247	+	1.43563i	0.696234	+	0.717815i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	0.933546	+	2.30334i	0.381119	+	0.940333i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−1.02229	−	2.63722i	−0.361436	−	0.932397i
$9$			0.0884307i			0.0294769i
$10$	1.31065	−	0.531211i	0.414465	−	0.167984i
$11$	−1.60005	+	1.60005i	−0.482435	+	0.482435i	−0.905908	−	0.423474i	$-0.860811\pi$
$11$	−1.60005	+	1.60005i	−0.482435	+	0.482435i	0.423474	+	0.905908i	$0.360811\pi$
$12$	0.0536375	−	3.51438i	0.0154838	−	1.01451i
$13$	−1.80583	−	1.80583i	−0.500848	−	0.500848i	0.410853	−	0.911702i	$-0.365231\pi$
$13$	−1.80583	−	1.80583i	−0.500848	−	0.500848i	−0.911702	+	0.410853i	$0.865231\pi$
$14$	0.551150	−	1.30240i	0.147301	−	0.348080i
$15$	1.75739			0.453757
$16$	−0.122070	+	3.99814i	−0.0305175	+	0.999534i
$17$	2.11216			0.512275			0.256138	−	0.966640i	$-0.417550\pi$
$17$	2.11216			0.512275			0.256138	+	0.966640i	$0.417550\pi$
$18$	0.0487386	−	0.115172i	0.0114878	−	0.0271462i
$19$	5.91638	+	5.91638i	1.35731	+	1.35731i	0.877218	+	0.480092i	$0.159397\pi$
$19$	5.91638	+	5.91638i	1.35731	+	1.35731i	0.480092	+	0.877218i	$0.340603\pi$
$20$	−1.99977	−	0.0305211i	−0.447162	−	0.00682472i
$21$	1.24266	−	1.24266i	0.271172	−	0.271172i
$22$	2.96577	−	1.20203i	0.632305	−	0.256274i
$23$			0.874774i			0.182403i	0.995832	+	0.0912015i	$0.0290707\pi$
$23$			0.874774i			0.182403i	−0.995832	+	0.0912015i	$0.970929\pi$
$24$	−2.00681	+	4.54755i	−0.409638	+	0.928264i
$25$		−	1.00000i		−	0.200000i
$26$	1.35662	+	3.34720i	0.266056	+	0.656439i
$27$	−3.61810	+	3.61810i	−0.696304	+	0.696304i
$28$	−1.43563	+	1.39247i	−0.271309	+	0.263152i
$29$	−0.225174	−	0.225174i	−0.0418138	−	0.0418138i	0.685891	−	0.727705i	$-0.259413\pi$
$29$	−0.225174	−	0.225174i	−0.0418138	−	0.0418138i	−0.727705	+	0.685891i	$0.759413\pi$
$30$	−2.28882	−	0.968587i	−0.417880	−	0.176839i
$31$	9.29821			1.67001			0.835004	−	0.550244i	$-0.185465\pi$
$31$	9.29821			1.67001			0.835004	+	0.550244i	$0.185465\pi$
$32$	2.36256	−	5.13988i	0.417645	−	0.908610i
$33$	3.97666			0.692248
$34$	−2.75087	−	1.16412i	−0.471771	−	0.199645i
$35$	−0.707107	−	0.707107i	−0.119523	−	0.119523i
$36$	−0.126954	+	0.123137i	−0.0211590	+	0.0205228i
$37$	3.04745	−	3.04745i	0.500997	−	0.500997i	−0.410751	−	0.911748i	$-0.634733\pi$
$37$	3.04745	−	3.04745i	0.500997	−	0.500997i	0.911748	+	0.410751i	$0.134733\pi$
$38$	−4.44465	−	10.9663i	−0.721018	−	1.77896i
$39$			4.48809i			0.718670i
$40$	2.58767	+	1.14192i	0.409146	+	0.180554i
$41$		−	6.94259i		−	1.08425i	−0.840298	−	0.542125i	$-0.817620\pi$
$41$		−	6.94259i		−	1.08425i	0.840298	−	0.542125i	$-0.182380\pi$
$42$	−2.30334	+	0.933546i	−0.355412	+	0.144049i
$43$	2.78693	−	2.78693i	0.425003	−	0.425003i	−0.461919	−	0.886922i	$-0.652839\pi$
$43$	2.78693	−	2.78693i	0.425003	−	0.425003i	0.886922	+	0.461919i	$0.152839\pi$
$44$	−4.52511	−	0.0690637i	−0.682186	−	0.0104117i
$45$	−0.0625299	−	0.0625299i	−0.00932141	−	0.00932141i
$46$	0.482132	−	1.13930i	0.0710865	−	0.167981i
$47$	11.2096			1.63509			0.817543	−	0.575867i	$-0.195335\pi$
$47$	11.2096			1.63509			0.817543	+	0.575867i	$0.195335\pi$
$48$	5.12004	−	4.81665i	0.739013	−	0.695224i
$49$	−1.00000			−0.142857
$50$	−0.551150	+	1.30240i	−0.0779444	+	0.184187i
$51$	−2.62471	−	2.62471i	−0.367533	−	0.367533i
$52$	0.0779458	−	5.10708i	0.0108091	−	0.708224i
$53$	4.93538	−	4.93538i	0.677926	−	0.677926i	−0.281605	−	0.959531i	$-0.590867\pi$
$53$	4.93538	−	4.93538i	0.677926	−	0.677926i	0.959531	+	0.281605i	$0.0908666\pi$
$54$	6.70632	−	2.71808i	0.912615	−	0.369884i
$55$		−	2.26282i		−	0.305118i
$56$	2.63722	−	1.02229i	0.352413	−	0.136610i
$57$		−	14.7041i		−	1.94761i
$58$	0.169161	+	0.417370i	0.0222119	+	0.0548034i
$59$	−9.96255	+	9.96255i	−1.29701	+	1.29701i	−0.366657	+	0.930356i	$0.619498\pi$
$59$	−9.96255	+	9.96255i	−1.29701	+	1.29701i	−0.930356	+	0.366657i	$0.880502\pi$
$60$	2.44711	+	2.52297i	0.315921	+	0.325714i
$61$	4.88247	+	4.88247i	0.625136	+	0.625136i	0.946840	−	0.321704i	$-0.104256\pi$
$61$	4.88247	+	4.88247i	0.625136	+	0.625136i	−0.321704	+	0.946840i	$0.604256\pi$
$62$	−12.1099	−	5.12471i	−1.53796	−	0.650839i
$63$	−0.0884307			−0.0111412
$64$	−5.90983	+	5.39203i	−0.738728	+	0.674003i
$65$	2.55384			0.316764
$66$	−5.17919	−	2.19174i	−0.637514	−	0.269784i
$67$	−2.26158	−	2.26158i	−0.276296	−	0.276296i	0.555333	−	0.831628i	$-0.312591\pi$
$67$	−2.26158	−	2.26158i	−0.276296	−	0.276296i	−0.831628	+	0.555333i	$0.812591\pi$
$68$	2.94112	+	3.03229i	0.356663	+	0.367719i
$69$	1.08705	−	1.08705i	0.130866	−	0.130866i
$70$	0.531211	+	1.31065i	0.0634918	+	0.156653i
$71$		−	10.0793i		−	1.19619i	−0.801425	−	0.598096i	$-0.795924\pi$
$71$		−	10.0793i		−	1.19619i	0.801425	−	0.598096i	$-0.204076\pi$
$72$	0.233211	−	0.0904022i	0.0274842	−	0.0106540i
$73$			5.50912i			0.644794i	0.946605	+	0.322397i	$0.104489\pi$
$73$			5.50912i			0.644794i	−0.946605	+	0.322397i	$0.895511\pi$
$74$	−5.64858	+	2.28938i	−0.656634	+	0.266135i
$75$	−1.24266	+	1.24266i	−0.143491	+	0.143491i
$76$	−0.255371	+	16.7321i	−0.0292930	+	1.91930i
$77$	−1.60005	−	1.60005i	−0.182343	−	0.182343i
$78$	2.47361	−	5.84527i	0.280082	−	0.661847i
$79$	14.4524			1.62602			0.813012	−	0.582248i	$-0.197827\pi$
$79$	14.4524			1.62602			0.813012	+	0.582248i	$0.197827\pi$
$80$	−2.74079	−	2.91343i	−0.306430	−	0.325731i
$81$	9.25747			1.02861
$82$	−3.82641	+	9.04200i	−0.422556	+	0.998522i
$83$	3.95460	+	3.95460i	0.434073	+	0.434073i	0.890012	−	0.455938i	$-0.150696\pi$
$83$	3.95460	+	3.95460i	0.434073	+	0.434073i	−0.455938	+	0.890012i	$0.650696\pi$
$84$	3.51438	+	0.0536375i	0.383450	+	0.00585234i
$85$	−1.49353	+	1.49353i	−0.161996	+	0.161996i
$86$	−5.16570	+	2.09367i	−0.557032	+	0.225766i
$87$			0.559632i			0.0599988i
$88$	5.85542	+	2.58396i	0.624190	+	0.275451i
$89$		−	0.0282999i		−	0.00299978i	−0.999999	−	0.00149989i	$-0.999523\pi$
$89$		−	0.0282999i		−	0.00299978i	0.999999	−	0.00149989i	$-0.000477430\pi$
$90$	0.0469753	+	0.115902i	0.00495163	+	0.0122171i
$91$	1.80583	−	1.80583i	0.189303	−	0.189303i
$92$	−1.25585	+	1.21809i	−0.130932	+	0.126995i
$93$	−11.5546	−	11.5546i	−1.19815	−	1.19815i
$94$	−14.5993	−	6.17817i	−1.50580	−	0.637229i
$95$	−8.36702			−0.858438
$96$	−9.32301	+	3.45128i	−0.951526	+	0.352244i
$97$	12.3154			1.25044			0.625220	−	0.780448i	$-0.285009\pi$
$97$	12.3154			1.25044			0.625220	+	0.780448i	$0.285009\pi$
$98$	1.30240	+	0.551150i	0.131562	+	0.0556746i
$99$	−0.141494	−	0.141494i	−0.0142207	−	0.0142207i
$100$	1.43563	−	1.39247i	0.143563	−	0.139247i
$101$	7.19126	−	7.19126i	0.715557	−	0.715557i	−0.252135	−	0.967692i	$-0.581133\pi$
$101$	7.19126	−	7.19126i	0.715557	−	0.715557i	0.967692	+	0.252135i	$0.0811327\pi$
$102$	1.97180	+	4.86502i	0.195238	+	0.481709i
$103$			17.9142i			1.76513i	0.470186	+	0.882567i	$0.344187\pi$
$103$			17.9142i			1.76513i	−0.470186	+	0.882567i	$0.655813\pi$
$104$	−2.91628	+	6.60847i	−0.285965	+	0.648014i
$105$			1.75739i			0.171504i
$106$	−9.14794	+	3.70768i	−0.888527	+	0.360122i
$107$	−5.77938	+	5.77938i	−0.558713	+	0.558713i	−0.928941	−	0.370228i	$-0.879280\pi$
$107$	−5.77938	+	5.77938i	−0.558713	+	0.558713i	0.370228	+	0.928941i	$0.379280\pi$
$108$	−10.2324	−	0.156169i	−0.984609	−	0.0150274i
$109$	5.40994	+	5.40994i	0.518178	+	0.518178i	0.917020	−	0.398841i	$-0.130588\pi$
$109$	5.40994	+	5.40994i	0.518178	+	0.518178i	−0.398841	+	0.917020i	$0.630588\pi$
$110$	−1.24715	+	2.94709i	−0.118911	+	0.280994i
$111$	−7.57391			−0.718883
$112$	−3.99814	−	0.122070i	−0.377788	−	0.0115345i
$113$	−8.18060			−0.769566			−0.384783	−	0.923007i	$-0.625724\pi$
$113$	−8.18060			−0.769566			−0.384783	+	0.923007i	$0.625724\pi$
$114$	−8.10419	+	19.1506i	−0.759027	+	1.79362i
$115$	−0.618559	−	0.618559i	−0.0576809	−	0.0576809i
$116$	0.00971926	−	0.636814i	0.000902411	−	0.0591267i
$117$	0.159691	−	0.159691i	0.0147635	−	0.0147635i
$118$	18.4660	−	7.48432i	1.69994	−	0.688987i
$119$			2.11216i			0.193622i
$120$	−1.79657	−	4.63463i	−0.164004	−	0.423082i
$121$			5.87965i			0.534514i
$122$	−3.66793	−	9.04988i	−0.332079	−	0.819337i
$123$	−8.62731	+	8.62731i	−0.777899	+	0.777899i
$124$	12.9475	+	13.3488i	1.16272	+	1.19876i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	0.115172	+	0.0487386i	0.0102603	+	0.00434198i
$127$	−16.2385			−1.44093			−0.720466	−	0.693491i	$-0.756072\pi$
$127$	−16.2385			−1.44093			−0.720466	+	0.693491i	$0.756072\pi$
$128$	10.6687	−	3.76535i	0.942993	−	0.332813i
$129$	−6.92644			−0.609839
$130$	−3.32610	−	1.40755i	−0.291719	−	0.123450i
$131$	−0.899662	−	0.899662i	−0.0786038	−	0.0786038i	0.666712	−	0.745316i	$-0.267701\pi$
$131$	−0.899662	−	0.899662i	−0.0786038	−	0.0786038i	−0.745316	+	0.666712i	$0.767701\pi$
$132$	5.53737	+	5.70902i	0.481966	+	0.496906i
$133$	−5.91638	+	5.91638i	−0.513015	+	0.513015i
$134$	1.69900	+	4.19194i	0.146771	+	0.362128i
$135$		−	5.11677i		−	0.440382i
$136$	−2.15925	−	5.57023i	−0.185155	−	0.477644i
$137$			14.3079i			1.22240i	0.791475	+	0.611202i	$0.209314\pi$
$137$			14.3079i			1.22240i	−0.791475	+	0.611202i	$0.790686\pi$
$138$	−2.01490	+	0.816642i	−0.171520	+	0.0695172i
$139$	−10.1651	+	10.1651i	−0.862193	+	0.862193i	−0.991592	−	0.129400i	$-0.958695\pi$
$139$	−10.1651	+	10.1651i	−0.862193	+	0.862193i	0.129400	+	0.991592i	$0.458695\pi$
$140$	0.0305211	−	1.99977i	0.00257950	−	0.169011i
$141$	−13.9298	−	13.9298i	−1.17310	−	1.17310i
$142$	−5.55520	+	13.1272i	−0.466182	+	1.10161i
$143$	5.77887			0.483253
$144$	−0.353558	−	0.0107947i	−0.0294632	−	0.000899562i
$145$	0.318444			0.0264453
$146$	3.03635	−	7.17505i	0.251290	−	0.593811i
$147$	1.24266	+	1.24266i	0.102493	+	0.102493i
$148$	8.61847	+	0.131538i	0.708434	+	0.0108123i
$149$	−6.15851	+	6.15851i	−0.504525	+	0.504525i	−0.912841	−	0.408316i	$-0.866116\pi$
$149$	−6.15851	+	6.15851i	−0.504525	+	0.504525i	0.408316	+	0.912841i	$0.366116\pi$
$150$	2.30334	−	0.933546i	0.188067	−	0.0762237i
$151$		−	20.2711i		−	1.64963i	−0.565399	−	0.824817i	$-0.691278\pi$
$151$		−	20.2711i		−	1.64963i	0.565399	−	0.824817i	$-0.308722\pi$
$152$	9.55449	−	21.6511i	0.774971	−	1.75613i
$153$			0.186780i			0.0151003i
$154$	1.20203	+	2.96577i	0.0968626	+	0.238989i
$155$	−6.57483	+	6.57483i	−0.528103	+	0.528103i
$156$	−6.44324	+	6.24952i	−0.515872	+	0.500362i
$157$	−1.91142	−	1.91142i	−0.152548	−	0.152548i	0.626707	−	0.779255i	$-0.284402\pi$
$157$	−1.91142	−	1.91142i	−0.152548	−	0.152548i	−0.779255	+	0.626707i	$0.784402\pi$
$158$	−18.8227	−	7.96545i	−1.49746	−	0.633697i
$159$	−12.2660			−0.972760
$160$	1.96386	+	5.30502i	0.155257	+	0.419399i
$161$	−0.874774			−0.0689419
$162$	−12.0569	−	5.10226i	−0.947279	−	0.400871i
$163$	−3.08252	−	3.08252i	−0.241442	−	0.241442i	0.576005	−	0.817446i	$-0.304611\pi$
$163$	−3.08252	−	3.08252i	−0.241442	−	0.241442i	−0.817446	+	0.576005i	$0.804611\pi$
$164$	9.96700	−	9.66733i	0.778292	−	0.754892i
$165$	−2.81193	+	2.81193i	−0.218908	+	0.218908i
$166$	−2.97087	−	7.33003i	−0.230584	−	0.568920i
$167$			4.20859i			0.325671i	0.986653	+	0.162835i	$0.0520639\pi$
$167$			4.20859i			0.325671i	−0.986653	+	0.162835i	$0.947936\pi$
$168$	−4.54755	−	2.00681i	−0.350851	−	0.154828i
$169$		−	6.47792i		−	0.498302i
$170$	2.76832	−	1.12200i	0.212320	−	0.0860538i
$171$	−0.523189	+	0.523189i	−0.0400093	+	0.0400093i
$172$	7.88171	+	0.120293i	0.600975	+	0.00917226i
$173$	−0.620913	−	0.620913i	−0.0472071	−	0.0472071i	0.683109	−	0.730316i	$-0.260627\pi$
$173$	−0.620913	−	0.620913i	−0.0472071	−	0.0472071i	−0.730316	+	0.683109i	$0.760627\pi$
$174$	0.308441	−	0.728862i	0.0233828	−	0.0552549i
$175$	1.00000			0.0755929
$176$	−6.20192	−	6.59256i	−0.467487	−	0.496933i
$177$	24.7602			1.86109
$178$	−0.0155975	+	0.0368577i	−0.00116908	+	0.00276260i
$179$	−1.30281	−	1.30281i	−0.0973764	−	0.0973764i	0.656740	−	0.754117i	$-0.271935\pi$
$179$	−1.30281	−	1.30281i	−0.0973764	−	0.0973764i	−0.754117	+	0.656740i	$0.771935\pi$
$180$	0.00269900	−	0.176841i	0.000201172	−	0.0131809i
$181$	9.13481	−	9.13481i	0.678985	−	0.678985i	−0.280785	−	0.959771i	$-0.590595\pi$
$181$	9.13481	−	9.13481i	0.678985	−	0.678985i	0.959771	+	0.280785i	$0.0905949\pi$
$182$	−3.34720	+	1.35662i	−0.248111	+	0.100560i
$183$		−	12.1345i		−	0.897011i
$184$	2.30697	−	0.894278i	0.170072	−	0.0659270i
$185$			4.30974i			0.316858i
$186$	8.68031	+	21.4169i	0.636471	+	1.57036i
$187$	−3.37958	+	3.37958i	−0.247139	+	0.247139i
$188$	15.6090	+	16.0928i	1.13840	+	1.17369i
$189$	−3.61810	−	3.61810i	−0.263178	−	0.263178i
$190$	10.8972	+	4.61148i	0.790564	+	0.334552i
$191$	8.50784			0.615606			0.307803	−	0.951450i	$-0.400406\pi$
$191$	8.50784			0.615606			0.307803	+	0.951450i	$0.400406\pi$
$192$	14.0444	+	0.643451i	1.01357	+	0.0464370i
$193$	6.69214			0.481711			0.240855	−	0.970561i	$-0.422572\pi$
$193$	6.69214			0.481711			0.240855	+	0.970561i	$0.422572\pi$
$194$	−16.0395	−	6.78764i	−1.15157	−	0.487324i
$195$	−3.17356	−	3.17356i	−0.227263	−	0.227263i
$196$	−1.39247	−	1.43563i	−0.0994619	−	0.102545i
$197$	−11.1723	+	11.1723i	−0.795993	+	0.795993i	−0.982461	−	0.186468i	$-0.940296\pi$
$197$	−11.1723	+	11.1723i	−0.795993	+	0.795993i	0.186468	+	0.982461i	$0.440296\pi$
$198$	0.106297	+	0.262265i	0.00755417	+	0.0186384i
$199$			7.79863i			0.552830i	0.961038	+	0.276415i	$0.0891465\pi$
$199$			7.79863i			0.552830i	−0.961038	+	0.276415i	$0.910854\pi$
$200$	−2.63722	+	1.02229i	−0.186479	+	0.0722872i
$201$			5.62077i			0.396458i
$202$	−13.3293	+	5.40240i	−0.937848	+	0.380112i
$203$	0.225174	−	0.225174i	0.0158041	−	0.0158041i
$204$	0.113291	−	7.42294i	0.00793198	−	0.519710i
$205$	4.90915	+	4.90915i	0.342870	+	0.342870i
$206$	9.87339	−	23.3313i	0.687912	−	1.62557i
$207$	−0.0773569			−0.00537668
$208$	7.44041	−	6.99954i	0.515900	−	0.485330i
$209$	−18.9331			−1.30963
$210$	0.968587	−	2.28882i	0.0668389	−	0.157944i
$211$	−4.18091	−	4.18091i	−0.287826	−	0.287826i	0.548394	−	0.836220i	$-0.315239\pi$
$211$	−4.18091	−	4.18091i	−0.287826	−	0.287826i	−0.836220	+	0.548394i	$0.815239\pi$
$212$	13.9577	+	0.213027i	0.958621	+	0.0146308i
$213$	−12.5252	+	12.5252i	−0.858211	+	0.858211i
$214$	10.7123	−	4.34173i	0.732280	−	0.296795i
$215$			3.94131i			0.268795i
$216$	13.2405	+	5.84296i	0.900902	+	0.397563i
$217$			9.29821i			0.631204i
$218$	−4.06419	−	10.0276i	−0.275262	−	0.679153i
$219$	6.84599	−	6.84599i	0.462609	−	0.462609i
$220$	3.24857	−	3.15090i	0.219019	−	0.212434i
$221$	−3.81422	−	3.81422i	−0.256572	−	0.256572i
$222$	9.86422	+	4.17436i	0.662043	+	0.280165i
$223$	−5.03406			−0.337105			−0.168553	−	0.985693i	$-0.553909\pi$
$223$	−5.03406			−0.337105			−0.168553	+	0.985693i	$0.553909\pi$
$224$	5.13988	+	2.36256i	0.343422	+	0.157855i
$225$	0.0884307			0.00589538
$226$	10.6544	+	4.50874i	0.708718	+	0.299917i
$227$	1.13782	+	1.13782i	0.0755200	+	0.0755200i	0.743858	−	0.668338i	$-0.232994\pi$
$227$	1.13782	+	1.13782i	0.0755200	+	0.0755200i	−0.668338	+	0.743858i	$0.732994\pi$
$228$	21.1097	−	20.4750i	1.39803	−	1.35599i
$229$	−5.36562	+	5.36562i	−0.354570	+	0.354570i	−0.861807	−	0.507237i	$-0.830667\pi$
$229$	−5.36562	+	5.36562i	−0.354570	+	0.354570i	0.507237	+	0.861807i	$0.330667\pi$
$230$	0.464690	+	1.14653i	0.0306407	+	0.0755998i
$231$			3.97666i			0.261645i
$232$	−0.363638	+	0.824027i	−0.0238740	+	0.0541000i
$233$			6.42088i			0.420646i	0.977632	+	0.210323i	$0.0674516\pi$
$233$			6.42088i			0.420646i	−0.977632	+	0.210323i	$0.932548\pi$
$234$	−0.295995	+	0.119967i	−0.0193498	+	0.00784250i
$235$	−7.92638	+	7.92638i	−0.517060	+	0.517060i
$236$	−28.1751	−	0.430017i	−1.83404	−	0.0279917i
$237$	−17.9595	−	17.9595i	−1.16659	−	1.16659i
$238$	1.16412	−	2.75087i	0.0754587	−	0.178313i
$239$	27.8512			1.80154			0.900772	−	0.434293i	$-0.143002\pi$
$239$	27.8512			1.80154			0.900772	+	0.434293i	$0.143002\pi$
$240$	−0.214525	+	7.02630i	−0.0138475	+	0.453546i
$241$	10.2211			0.658398			0.329199	−	0.944261i	$-0.393221\pi$
$241$	10.2211			0.658398			0.329199	+	0.944261i	$0.393221\pi$
$242$	3.24057	−	7.65763i	0.208312	−	0.492251i
$243$	−0.649620	−	0.649620i	−0.0416732	−	0.0416732i
$244$	−0.210744	+	13.8081i	−0.0134915	+	0.883973i
$245$	0.707107	−	0.707107i	0.0451754	−	0.0451754i
$246$	15.9911	−	6.48123i	1.01956	−	0.413228i
$247$		−	21.3680i		−	1.35961i
$248$	−9.50551	−	24.5214i	−0.603601	−	1.55711i
$249$		−	9.82848i		−	0.622854i
$250$	−0.531211	−	1.31065i	−0.0335967	−	0.0828931i
$251$	13.7069	−	13.7069i	0.865169	−	0.865169i	−0.126764	−	0.991933i	$-0.540459\pi$
$251$	13.7069	−	13.7069i	0.865169	−	0.865169i	0.991933	+	0.126764i	$0.0404591\pi$
$252$	−0.123137	−	0.126954i	−0.00775689	−	0.00799734i
$253$	−1.39969	−	1.39969i	−0.0879976	−	0.0879976i
$254$	21.1489	+	8.94983i	1.32700	+	0.561563i
$255$	3.71190			0.232448
$256$	−15.9702	−	0.976106i	−0.998137	−	0.0610066i
$257$	13.7371			0.856899			0.428449	−	0.903566i	$-0.359060\pi$
$257$	13.7371			0.856899			0.428449	+	0.903566i	$0.359060\pi$
$258$	9.02096	+	3.81751i	0.561620	+	0.237668i
$259$	3.04745	+	3.04745i	0.189359	+	0.189359i
$260$	3.55613	+	3.66636i	0.220542	+	0.227378i
$261$	0.0199123	−	0.0199123i	0.00123254	−	0.00123254i
$262$	0.675867	+	1.66756i	0.0417552	+	0.103022i
$263$			11.8875i			0.733016i	0.930415	+	0.366508i	$0.119447\pi$
$263$			11.8875i			0.733016i	−0.930415	+	0.366508i	$0.880553\pi$
$264$	−4.06532	−	10.4873i	−0.250203	−	0.645450i
$265$			6.97968i			0.428758i
$266$	10.9663	−	4.44465i	0.672385	−	0.272519i
$267$	−0.0351673	+	0.0351673i	−0.00215220	+	0.00215220i
$268$	0.0976172	−	6.39596i	0.00596292	−	0.390696i
$269$	−4.74383	−	4.74383i	−0.289237	−	0.289237i	0.547542	−	0.836778i	$-0.315564\pi$
$269$	−4.74383	−	4.74383i	−0.289237	−	0.289237i	−0.836778	+	0.547542i	$0.815564\pi$
$270$	−2.82011	+	6.66406i	−0.171626	+	0.405562i
$271$	−29.2013			−1.77385			−0.886925	−	0.461913i	$-0.847163\pi$
$271$	−29.2013			−1.77385			−0.886925	+	0.461913i	$0.847163\pi$
$272$	−0.257832	+	8.44472i	−0.0156334	+	0.512036i
$273$	−4.48809			−0.271632
$274$	7.88579	−	18.6345i	0.476398	−	1.12575i
$275$	1.60005	+	1.60005i	0.0964869	+	0.0964869i
$276$	3.07429	+	0.0469208i	0.185050	+	0.00282430i
$277$	12.5655	−	12.5655i	0.754987	−	0.754987i	−0.220418	−	0.975405i	$-0.570742\pi$
$277$	12.5655	−	12.5655i	0.754987	−	0.754987i	0.975405	+	0.220418i	$0.0707423\pi$
$278$	18.8415	−	7.63648i	1.13004	−	0.458006i
$279$			0.822247i			0.0492266i
$280$	−1.14192	+	2.58767i	−0.0682429	+	0.154643i
$281$		−	2.46295i		−	0.146927i	−0.997298	−	0.0734635i	$-0.976595\pi$
$281$		−	2.46295i		−	0.146927i	0.997298	−	0.0734635i	$-0.0234052\pi$
$282$	10.4647	+	25.8194i	0.623162	+	1.53753i
$283$	−4.67312	+	4.67312i	−0.277788	+	0.277788i	−0.832225	−	0.554437i	$-0.812933\pi$
$283$	−4.67312	+	4.67312i	−0.277788	+	0.277788i	0.554437	+	0.832225i	$0.312933\pi$
$284$	14.4701	−	14.0351i	0.858645	−	0.832829i
$285$	10.3974	+	10.3974i	0.615889	+	0.615889i
$286$	−7.52637	−	3.18502i	−0.445044	−	0.188334i
$287$	6.94259			0.409808
$288$	0.454523	+	0.208922i	0.0267830	+	0.0123109i
$289$	−12.5388			−0.737574
$290$	−0.414740	−	0.175511i	−0.0243544	−	0.0103063i
$291$	−15.3039	−	15.3039i	−0.897132	−	0.897132i
$292$	−7.90906	+	7.67127i	−0.462843	+	0.448927i
$293$	7.58448	−	7.58448i	0.443090	−	0.443090i	−0.449959	−	0.893049i	$-0.648561\pi$
$293$	7.58448	−	7.58448i	0.443090	−	0.443090i	0.893049	+	0.449959i	$0.148561\pi$
$294$	−0.933546	−	2.30334i	−0.0544455	−	0.134333i
$295$		−	14.0892i		−	0.820303i
$296$	−11.1522	−	4.92139i	−0.648206	−	0.286050i
$297$		−	11.5783i		−	0.671843i
$298$	11.4151	−	4.62655i	0.661258	−	0.268009i
$299$	1.57970	−	1.57970i	0.0913563	−	0.0913563i
$300$	−3.51438	−	0.0536375i	−0.202903	−	0.00309676i
$301$	2.78693	+	2.78693i	0.160636	+	0.160636i
$302$	−11.1724	+	26.4009i	−0.642899	+	1.51920i
$303$	−17.8727			−1.02676
$304$	−24.3767	+	22.9323i	−1.39810	+	1.31526i
$305$	−6.90485			−0.395371
$306$	0.102944	−	0.243262i	0.00588491	−	0.0139063i
$307$	18.1548	+	18.1548i	1.03615	+	1.03615i	0.999322	+	0.0368277i	$0.0117253\pi$
$307$	18.1548	+	18.1548i	1.03615	+	1.03615i	0.0368277	+	0.999322i	$0.488275\pi$
$308$	0.0690637	−	4.52511i	0.00393527	−	0.257842i
$309$	22.2613	−	22.2613i	1.26640	−	1.26640i
$310$	12.1867	−	4.93931i	0.692160	−	0.280534i
$311$		−	1.86178i		−	0.105572i	−0.998606	−	0.0527858i	$-0.983190\pi$
$311$		−	1.86178i		−	0.105572i	0.998606	−	0.0527858i	$-0.0168101\pi$
$312$	11.8361	−	4.58816i	0.670086	−	0.259753i
$313$			12.9382i			0.731309i	0.930751	+	0.365655i	$0.119155\pi$
$313$			12.9382i			0.731309i	−0.930751	+	0.365655i	$0.880845\pi$
$314$	1.43595	+	3.54291i	0.0810352	+	0.199938i
$315$	0.0625299	−	0.0625299i	0.00352316	−	0.00352316i
$316$	20.1245	+	20.7483i	1.13209	+	1.16718i
$317$	−16.2943	−	16.2943i	−0.915180	−	0.915180i	0.0814937	−	0.996674i	$-0.474031\pi$
$317$	−16.2943	−	16.2943i	−0.915180	−	0.915180i	−0.996674	+	0.0814937i	$0.974031\pi$
$318$	15.9752	+	6.76043i	0.895846	+	0.379106i
$319$	0.720582			0.0403448
$320$	0.366139	−	7.99162i	0.0204678	−	0.446745i
$321$	14.3637			0.801701
$322$	1.13930	+	0.482132i	0.0634908	+	0.0268682i
$323$	12.4964	+	12.4964i	0.695316	+	0.695316i
$324$	12.8907	+	13.2903i	0.716151	+	0.738351i
$325$	−1.80583	+	1.80583i	−0.100170	+	0.100170i
$326$	2.31573	+	5.71359i	0.128256	+	0.316447i
$327$		−	13.4455i		−	0.743537i
$328$	−18.3091	+	7.09738i	−1.01095	+	0.391887i
$329$			11.2096i			0.618005i
$330$	5.21203	−	2.11245i	0.286913	−	0.116286i
$331$	11.1674	−	11.1674i	0.613813	−	0.613813i	−0.330124	−	0.943938i	$-0.607091\pi$
$331$	11.1674	−	11.1674i	0.613813	−	0.613813i	0.943938	+	0.330124i	$0.107091\pi$
$332$	−0.170694	+	11.1840i	−0.00936803	+	0.613801i
$333$	0.269488	+	0.269488i	0.0147678	+	0.0147678i
$334$	2.31957	−	5.48125i	0.126921	−	0.299921i
$335$	3.19835			0.174745
$336$	4.81665	+	5.12004i	0.262770	+	0.279321i
$337$	−25.9873			−1.41562			−0.707809	−	0.706404i	$-0.750316\pi$
$337$	−25.9873			−1.41562			−0.707809	+	0.706404i	$0.750316\pi$
$338$	−3.57031	+	8.43682i	−0.194199	+	0.458902i
$339$	10.1657	+	10.1657i	0.552127	+	0.552127i
$340$	−4.22384	−	0.0644655i	−0.229070	−	0.00349613i
$341$	−14.8776	+	14.8776i	−0.805670	+	0.805670i
$342$	0.969755	−	0.393043i	0.0524383	−	0.0212534i
$343$		−	1.00000i		−	0.0539949i
$344$	−10.1988	−	4.50067i	−0.549882	−	0.242660i
$345$			1.53732i			0.0827667i
$346$	0.466458	+	1.15089i	0.0250769	+	0.0618722i
$347$	−11.0080	+	11.0080i	−0.590939	+	0.590939i	−0.937885	−	0.346946i	$-0.887219\pi$
$347$	−11.0080	+	11.0080i	−0.590939	+	0.590939i	0.346946	+	0.937885i	$0.387219\pi$
$348$	−0.803424	+	0.779269i	−0.0430681	+	0.0417732i
$349$	−6.19146	−	6.19146i	−0.331421	−	0.331421i	0.521705	−	0.853126i	$-0.325296\pi$
$349$	−6.19146	−	6.19146i	−0.331421	−	0.331421i	−0.853126	+	0.521705i	$0.825296\pi$
$350$	−1.30240	−	0.551150i	−0.0696160	−	0.0294602i
$351$	13.0674			0.697486
$352$	4.44386	+	12.0043i	0.236859	+	0.639832i
$353$	−20.2766			−1.07921			−0.539606	−	0.841918i	$-0.681427\pi$
$353$	−20.2766			−1.07921			−0.539606	+	0.841918i	$0.681427\pi$
$354$	−32.2476	−	13.6466i	−1.71394	−	0.725308i
$355$	7.12714	+	7.12714i	0.378269	+	0.378269i
$356$	0.0406282	−	0.0394067i	0.00215329	−	0.00208855i
$357$	2.62471	−	2.62471i	0.138914	−	0.138914i
$358$	0.978728	+	2.41481i	0.0517274	+	0.127627i
$359$		−	17.5817i		−	0.927927i	−0.885854	−	0.463964i	$-0.846427\pi$
$359$		−	17.5817i		−	0.927927i	0.885854	−	0.463964i	$-0.153573\pi$
$360$	−0.100981	+	0.228829i	−0.00532216	+	0.0120603i
$361$			51.0070i			2.68458i
$362$	−16.9318	+	6.86248i	−0.889915	+	0.360684i
$363$	7.30643	−	7.30643i	0.383488	−	0.383488i
$364$	5.10708	+	0.0779458i	0.267684	+	0.00408547i
$365$	−3.89554	−	3.89554i	−0.203902	−	0.203902i
$366$	−6.68795	+	15.8040i	−0.349585	+	0.826087i
$367$	3.16094			0.165000			0.0824999	−	0.996591i	$-0.473710\pi$
$367$	3.16094			0.165000			0.0824999	+	0.996591i	$0.473710\pi$
$368$	−3.49747	−	0.106784i	−0.182318	−	0.00556649i
$369$	0.613938			0.0319603
$370$	2.37531	−	5.61298i	0.123487	−	0.291805i
$371$	4.93538	+	4.93538i	0.256232	+	0.256232i
$372$	0.498733	−	32.6774i	0.0258581	−	1.69425i
$373$	21.3458	−	21.3458i	1.10525	−	1.10525i	0.111478	−	0.993767i	$-0.464441\pi$
$373$	21.3458	−	21.3458i	1.10525	−	1.10525i	0.993767	−	0.111478i	$-0.0355585\pi$
$374$	6.26420	−	2.53889i	0.323914	−	0.131283i
$375$		−	1.75739i		−	0.0907514i
$376$	−11.4595	−	29.5621i	−0.590979	−	1.52455i
$377$			0.813254i			0.0418847i
$378$	2.71808	+	6.70632i	0.139803	+	0.344936i
$379$	8.77455	−	8.77455i	0.450719	−	0.450719i	−0.444874	−	0.895593i	$-0.646752\pi$
$379$	8.77455	−	8.77455i	0.450719	−	0.450719i	0.895593	+	0.444874i	$0.146752\pi$
$380$	−11.6508	−	12.0120i	−0.597674	−	0.616200i
$381$	20.1790	+	20.1790i	1.03380	+	1.03380i
$382$	−11.0806	−	4.68910i	−0.566932	−	0.239915i
$383$	−13.2550			−0.677301			−0.338650	−	0.940912i	$-0.609970\pi$
$383$	−13.2550			−0.677301			−0.338650	+	0.940912i	$0.609970\pi$
$384$	−17.9367	−	8.57861i	−0.915330	−	0.437775i
$385$	2.26282			0.115324
$386$	−8.71581	−	3.68837i	−0.443623	−	0.187733i
$387$	0.246450	+	0.246450i	0.0125278	+	0.0125278i
$388$	17.1488	+	17.6804i	0.870599	+	0.897585i
$389$	15.6426	−	15.6426i	0.793113	−	0.793113i	−0.188886	−	0.981999i	$-0.560488\pi$
$389$	15.6426	−	15.6426i	0.793113	−	0.793113i	0.981999	+	0.188886i	$0.0604876\pi$
$390$	2.38412	+	5.88234i	0.120725	+	0.297864i
$391$			1.84767i			0.0934406i
$392$	1.02229	+	2.63722i	0.0516337	+	0.133200i
$393$			2.23596i			0.112789i
$394$	20.7084	−	8.39314i	1.04327	−	0.422840i
$395$	−10.2194	+	10.2194i	−0.514194	+	0.514194i
$396$	0.00610735	−	0.400159i	0.000306906	−	0.0201087i
$397$	−18.9490	−	18.9490i	−0.951021	−	0.951021i	0.0478340	−	0.998855i	$-0.484768\pi$
$397$	−18.9490	−	18.9490i	−0.951021	−	0.951021i	−0.998855	+	0.0478340i	$0.984768\pi$
$398$	4.29822	−	10.1569i	0.215450	−	0.509119i
$399$	14.7041			0.736128
$400$	3.99814	+	0.122070i	0.199907	+	0.00610351i
$401$	6.72679			0.335920			0.167960	−	0.985794i	$-0.446282\pi$
$401$	6.72679			0.335920			0.167960	+	0.985794i	$0.446282\pi$
$402$	3.09789	−	7.32046i	0.154508	−	0.365111i
$403$	−16.7910	−	16.7910i	−0.836421	−	0.836421i
$404$	20.3376	+	0.310399i	1.01183	+	0.0154429i
$405$	−6.54602	+	6.54602i	−0.325274	+	0.325274i
$406$	−0.417370	+	0.169161i	−0.0207137	+	0.00839532i
$407$			9.75216i			0.483397i
$408$	−4.23870	+	9.60516i	−0.209847	+	0.475526i
$409$		−	30.5015i		−	1.50820i	−0.656758	−	0.754102i	$-0.728073\pi$
$409$		−	30.5015i		−	1.50820i	0.656758	−	0.754102i	$-0.271927\pi$
$410$	−3.68798	−	9.09934i	−0.182136	−	0.449384i
$411$	17.7799	−	17.7799i	0.877017	−	0.877017i
$412$	−25.7181	+	24.9449i	−1.26704	+	1.22895i
$413$	−9.96255	−	9.96255i	−0.490225	−	0.490225i
$414$	0.100749	+	0.0426353i	0.00495156	+	0.00209541i
$415$	−5.59265			−0.274532
$416$	−13.5482	+	5.01538i	−0.664253	+	0.245899i
$417$	25.2636			1.23716
$418$	24.6583	+	10.4350i	1.20608	+	0.510390i
$419$	−19.7672	−	19.7672i	−0.965693	−	0.965693i	0.0337378	−	0.999431i	$-0.489259\pi$
$419$	−19.7672	−	19.7672i	−0.965693	−	0.965693i	−0.999431	+	0.0337378i	$0.989259\pi$
$420$	−2.52297	+	2.44711i	−0.123108	+	0.119407i
$421$	−10.6486	+	10.6486i	−0.518980	+	0.518980i	−0.917263	−	0.398283i	$-0.869606\pi$
$421$	−10.6486	+	10.6486i	−0.518980	+	0.518980i	0.398283	+	0.917263i	$0.369606\pi$
$422$	3.14089	+	7.74951i	0.152896	+	0.377240i
$423$			0.991272i			0.0481973i
$424$	−18.0611	−	7.97025i	−0.877123	−	0.387069i
$425$		−	2.11216i		−	0.102455i
$426$	23.2160	−	9.40948i	1.12482	−	0.455891i
$427$	−4.88247	+	4.88247i	−0.236279	+	0.236279i
$428$	−16.3446	−	0.249457i	−0.790048	−	0.0120580i
$429$	−7.18120	−	7.18120i	−0.346711	−	0.346711i
$430$	2.17225	−	5.13315i	0.104755	−	0.247542i
$431$	6.27900			0.302449			0.151224	−	0.988499i	$-0.451678\pi$
$431$	6.27900			0.302449			0.151224	+	0.988499i	$0.451678\pi$
$432$	−14.0240	−	14.9073i	−0.674731	−	0.717230i
$433$	32.7293			1.57287			0.786436	−	0.617672i	$-0.211924\pi$
$433$	32.7293			1.57287			0.786436	+	0.617672i	$0.211924\pi$
$434$	5.12471	−	12.1099i	0.245994	−	0.581296i
$435$	−0.395719	−	0.395719i	−0.0189733	−	0.0189733i
$436$	−0.233511	+	15.2998i	−0.0111832	+	0.732730i
$437$	−5.17550	+	5.17550i	−0.247578	+	0.247578i
$438$	−12.6893	+	5.14302i	−0.606321	+	0.245743i
$439$		−	3.82702i		−	0.182654i	−0.995821	−	0.0913268i	$-0.970889\pi$
$439$		−	3.82702i		−	0.182654i	0.995821	−	0.0913268i	$-0.0291108\pi$
$440$	−5.96755	+	2.31327i	−0.284492	+	0.110281i
$441$		−	0.0884307i		−	0.00421098i
$442$	2.86541	+	7.06983i	0.136294	+	0.336277i
$443$	−7.04111	+	7.04111i	−0.334533	+	0.334533i	−0.854305	−	0.519772i	$-0.826017\pi$
$443$	−7.04111	+	7.04111i	−0.334533	+	0.334533i	0.519772	+	0.854305i	$0.326017\pi$
$444$	−10.5464	−	10.8733i	−0.500511	−	0.516025i
$445$	0.0200110	+	0.0200110i	0.000948615	+	0.000948615i
$446$	6.55633	+	2.77452i	0.310451	+	0.131377i
$447$	15.3059			0.723945
$448$	−5.39203	−	5.90983i	−0.254749	−	0.279213i
$449$	−34.7021			−1.63769			−0.818846	−	0.574014i	$-0.805386\pi$
$449$	−34.7021			−1.63769			−0.818846	+	0.574014i	$0.805386\pi$
$450$	−0.115172	−	0.0487386i	−0.00542925	−	0.00229756i
$451$	11.1085	+	11.1085i	0.523080	+	0.523080i
$452$	−11.3912	−	11.7443i	−0.535798	−	0.552406i
$453$	−25.1901	+	25.1901i	−1.18354	+	1.18354i
$454$	−0.854784	−	2.10901i	−0.0401170	−	0.0989806i
$455$			2.55384i			0.119726i
$456$	−38.7780	+	15.0320i	−1.81595	+	0.703937i
$457$		−	17.7929i		−	0.832318i	−0.909292	−	0.416159i	$-0.863376\pi$
$457$		−	17.7929i		−	0.832318i	0.909292	−	0.416159i	$-0.136624\pi$
$458$	9.94542	−	4.03090i	0.464719	−	0.188351i
$459$	−7.64203	+	7.64203i	−0.356699	+	0.356699i
$460$	0.0266991	−	1.74935i	0.00124485	−	0.0815636i
$461$	4.86365	+	4.86365i	0.226523	+	0.226523i	0.811238	−	0.584716i	$-0.198794\pi$
$461$	4.86365	+	4.86365i	0.226523	+	0.226523i	−0.584716	+	0.811238i	$0.698794\pi$
$462$	2.19174	−	5.17919i	0.101969	−	0.240958i
$463$	8.18756			0.380508			0.190254	−	0.981735i	$-0.439069\pi$
$463$	8.18756			0.380508			0.190254	+	0.981735i	$0.439069\pi$
$464$	0.927764	−	0.872790i	0.0430703	−	0.0405182i
$465$	16.3406			0.757778
$466$	3.53887	−	8.36253i	0.163935	−	0.387387i
$467$	25.1409	+	25.1409i	1.16338	+	1.16338i	0.983730	+	0.179653i	$0.0574976\pi$
$467$	25.1409	+	25.1409i	1.16338	+	1.16338i	0.179653	+	0.983730i	$0.442502\pi$
$468$	0.451622	+	0.00689280i	0.0208762	+	0.000318620i
$469$	2.26158	−	2.26158i	0.104430	−	0.104430i
$470$	14.6919	−	5.95465i	0.677687	−	0.274668i
$471$			4.75052i			0.218892i
$472$	36.4581	+	16.0887i	1.67812	+	0.740544i
$473$			8.91848i			0.410072i
$474$	13.4920	+	33.2887i	0.619707	+	1.52900i
$475$	5.91638	−	5.91638i	0.271462	−	0.271462i
$476$	−3.03229	+	2.94112i	−0.138985	+	0.134806i
$477$	0.436439	+	0.436439i	0.0199832	+	0.0199832i
$478$	−36.2732	−	15.3502i	−1.65910	−	0.702101i
$479$	13.8450			0.632593			0.316297	−	0.948660i	$-0.397561\pi$
$479$	13.8450			0.632593			0.316297	+	0.948660i	$0.397561\pi$
$480$	4.15194	−	9.03278i	0.189509	−	0.412288i
$481$	−11.0064			−0.501847
$482$	−13.3119	−	5.63335i	−0.606340	−	0.256592i
$483$	1.08705	+	1.08705i	0.0494625	+	0.0494625i
$484$	−8.44100	+	8.18722i	−0.383682	+	0.372146i
$485$	−8.70831	+	8.70831i	−0.395424	+	0.395424i
$486$	0.488024	+	1.20410i	0.0221372	+	0.0546191i
$487$		−	29.5560i		−	1.33931i	−0.742671	−	0.669656i	$-0.766442\pi$
$487$		−	29.5560i		−	1.33931i	0.742671	−	0.669656i	$-0.233558\pi$
$488$	7.88480	−	17.8674i	0.356928	−	0.808821i
$489$			7.66108i			0.346446i
$490$	−1.31065	+	0.531211i	−0.0592093	+	0.0239976i
$491$	−6.60680	+	6.60680i	−0.298161	+	0.298161i	−0.840293	−	0.542132i	$-0.817617\pi$
$491$	−6.60680	+	6.60680i	−0.298161	+	0.298161i	0.542132	+	0.840293i	$0.317617\pi$
$492$	−24.3989	−	0.372384i	−1.09999	−	0.0167883i
$493$	−0.475604	−	0.475604i	−0.0214201	−	0.0214201i
$494$	−11.7770	+	27.8296i	−0.529871	+	1.25211i
$495$	0.200103			0.00899394
$496$	−1.13503	+	37.1755i	−0.0509645	+	1.66923i
$497$	10.0793			0.452118
$498$	−5.41697	+	12.8006i	−0.242740	+	0.573607i
$499$	−28.6459	−	28.6459i	−1.28237	−	1.28237i	−0.939317	−	0.343050i	$-0.888540\pi$
$499$	−28.6459	−	28.6459i	−1.28237	−	1.28237i	−0.343050	−	0.939317i	$-0.611460\pi$
$500$	−0.0305211	+	1.99977i	−0.00136494	+	0.0894323i
$501$	5.22987	−	5.22987i	0.233653	−	0.233653i
$502$	−25.4063	+	10.2972i	−1.13394	+	0.459587i
$503$			26.1515i			1.16604i	0.812458	+	0.583019i	$0.198129\pi$
$503$			26.1515i			1.16604i	−0.812458	+	0.583019i	$0.801871\pi$
$504$	0.0904022	+	0.233211i	0.00402684	+	0.0103880i
$505$			10.1700i			0.452558i
$506$	1.05151	+	2.59438i	0.0467452	+	0.115334i
$507$	−8.04989	+	8.04989i	−0.357508	+	0.357508i
$508$	−22.6115	−	23.3124i	−1.00322	−	1.03432i
$509$	19.6190	+	19.6190i	0.869599	+	0.869599i	0.992428	−	0.122829i	$-0.0391967\pi$
$509$	19.6190	+	19.6190i	0.869599	+	0.869599i	−0.122829	+	0.992428i	$0.539197\pi$
$510$	−4.83436	−	2.04582i	−0.214069	−	0.0905902i
$511$	−5.50912			−0.243709
$512$	20.2615	+	10.0733i	0.895442	+	0.445179i
$513$	−42.8121			−1.89020
$514$	−17.8912	−	7.57122i	−0.789146	−	0.333952i
$515$	−12.6672	−	12.6672i	−0.558184	−	0.558184i
$516$	−9.64483	−	9.94380i	−0.424590	−	0.437751i
$517$	−17.9360	+	17.9360i	−0.788823	+	0.788823i
$518$	−2.28938	−	5.64858i	−0.100590	−	0.248184i
$519$			1.54317i			0.0677378i
$520$	−2.61077	−	6.73502i	−0.114490	−	0.295350i
$521$			40.8090i			1.78788i	0.448190	+	0.893938i	$0.352069\pi$
$521$			40.8090i			1.78788i	−0.448190	+	0.893938i	$0.647931\pi$
$522$	−0.0369083	+	0.0149590i	−0.00161543	+	0.000654738i
$523$	23.1595	−	23.1595i	1.01270	−	1.01270i	0.0127774	−	0.999918i	$-0.495933\pi$
$523$	23.1595	−	23.1595i	1.01270	−	1.01270i	0.999918	−	0.0127774i	$-0.00406728\pi$
$524$	0.0388324	−	2.54433i	0.00169640	−	0.111150i
$525$	−1.24266	−	1.24266i	−0.0542343	−	0.0542343i
$526$	6.55181	−	15.4822i	0.285672	−	0.675058i
$527$	19.6393			0.855503
$528$	−0.485432	+	15.8992i	−0.0211257	+	0.691926i
$529$	22.2348			0.966729
$530$	3.84685	−	9.09030i	0.167096	−	0.394857i
$531$	−0.880995	−	0.880995i	−0.0382319	−	0.0382319i
$532$	−16.7321	−	0.255371i	−0.725428	−	0.0110717i
$533$	−12.5372	+	12.5372i	−0.543045	+	0.543045i
$534$	0.0651841	−	0.0264193i	0.00282079	−	0.00114327i
$535$		−	8.17327i		−	0.353361i
$536$	−3.65227	+	8.27627i	−0.157754	+	0.357480i
$537$			3.23791i			0.139726i
$538$	3.56378	+	8.79291i	0.153646	+	0.379089i
$539$	1.60005	−	1.60005i	0.0689192	−	0.0689192i
$540$	7.34579	−	7.12494i	0.316113	−	0.306608i
$541$	9.33555	+	9.33555i	0.401367	+	0.401367i	0.878714	−	0.477348i	$-0.158402\pi$
$541$	9.33555	+	9.33555i	0.401367	+	0.401367i	−0.477348	+	0.878714i	$0.658402\pi$
$542$	38.0316	+	16.0943i	1.63360	+	0.691308i
$543$	−22.7030			−0.974280
$544$	4.99011	−	10.8563i	0.213949	−	0.465458i
$545$	−7.65081			−0.327725
$546$	5.84527	+	2.47361i	0.250155	+	0.105861i
$547$	11.2640	+	11.2640i	0.481615	+	0.481615i	0.905647	−	0.424032i	$-0.139386\pi$
$547$	11.2640	+	11.2640i	0.481615	+	0.481615i	−0.424032	+	0.905647i	$0.639386\pi$
$548$	−20.5408	+	19.9232i	−0.877460	+	0.851079i
$549$	−0.431760	+	0.431760i	−0.0184271	+	0.0184271i
$550$	−1.20203	−	2.96577i	−0.0512549	−	0.126461i
$551$		−	2.66443i		−	0.113508i
$552$	−3.97808	−	1.75550i	−0.169318	−	0.0747192i
$553$			14.4524i			0.614579i
$554$	−23.2907	+	9.43976i	−0.989527	+	0.401057i
$555$	5.35556	−	5.35556i	0.227331	−	0.227331i
$556$	−28.7479	−	0.438760i	−1.21918	−	0.0186076i
$557$	15.7910	+	15.7910i	0.669086	+	0.669086i	0.957505	−	0.288418i	$-0.0931293\pi$
$557$	15.7910	+	15.7910i	0.669086	+	0.669086i	−0.288418	+	0.957505i	$0.593129\pi$
$558$	0.453182	−	1.07089i	0.0191847	−	0.0453344i
$559$	−10.0655			−0.425724
$560$	2.91343	−	2.74079i	0.123115	−	0.115820i
$561$	8.39936			0.354621
$562$	−1.35745	+	3.20773i	−0.0572607	+	0.135310i
$563$	−12.3874	−	12.3874i	−0.522065	−	0.522065i	0.396130	−	0.918195i	$-0.370353\pi$
$563$	−12.3874	−	12.3874i	−0.522065	−	0.522065i	−0.918195	+	0.396130i	$0.870353\pi$
$564$	0.601255	−	39.3947i	0.0253174	−	1.65882i
$565$	5.78456	−	5.78456i	0.243358	−	0.243358i
$566$	8.66183	−	3.51066i	0.364084	−	0.147564i
$567$			9.25747i			0.388777i
$568$	−26.5813	+	10.3040i	−1.11533	+	0.432347i
$569$			13.7884i			0.578042i	0.957323	+	0.289021i	$0.0933297\pi$
$569$			13.7884i			0.578042i	−0.957323	+	0.289021i	$0.906670\pi$
$570$	−7.81100	−	19.2721i	−0.327167	−	0.807218i
$571$	−26.2815	+	26.2815i	−1.09985	+	1.09985i	−0.105419	+	0.994428i	$0.533618\pi$
$571$	−26.2815	+	26.2815i	−1.09985	+	1.09985i	−0.994428	+	0.105419i	$0.966382\pi$
$572$	8.04688	+	8.29632i	0.336457	+	0.346887i
$573$	−10.5724	−	10.5724i	−0.441668	−	0.441668i
$574$	−9.04200	−	3.82641i	−0.377406	−	0.159711i
$575$	0.874774			0.0364806
$576$	−0.476821	−	0.522610i	−0.0198675	−	0.0217754i
$577$	−45.2487			−1.88373			−0.941865	−	0.335993i	$-0.890928\pi$
$577$	−45.2487			−1.88373			−0.941865	+	0.335993i	$0.890928\pi$
$578$	16.3304	+	6.91074i	0.679256	+	0.287449i
$579$	−8.31609	−	8.31609i	−0.345605	−	0.345605i
$580$	0.443423	+	0.457168i	0.0184121	+	0.0189829i
$581$	−3.95460	+	3.95460i	−0.164064	+	0.164064i
$582$	11.4970	+	28.3665i	0.476566	+	1.17583i
$583$			15.7937i			0.654110i
$584$	14.5287	−	5.63194i	0.601204	−	0.233052i
$585$			0.225837i			0.00933723i
$586$	−14.0582	+	5.69780i	−0.580738	+	0.235374i
$587$	27.0622	−	27.0622i	1.11698	−	1.11698i	0.124794	−	0.992183i	$-0.460173\pi$
$587$	27.0622	−	27.0622i	1.11698	−	1.11698i	0.992183	−	0.124794i	$-0.0398270\pi$
$588$	−0.0536375	+	3.51438i	−0.00221197	+	0.144930i
$589$	55.0117	+	55.0117i	2.26672	+	2.26672i
$590$	−7.76525	+	18.3497i	−0.319690	+	0.755444i
$591$	27.7668			1.14218
$592$	11.8121	+	12.5561i	0.485474	+	0.516053i
$593$	34.8607			1.43156			0.715778	−	0.698328i	$-0.246072\pi$
$593$	34.8607			1.43156			0.715778	+	0.698328i	$0.246072\pi$
$594$	−6.38140	+	15.0796i	−0.261832	+	0.618722i
$595$	−1.49353	−	1.49353i	−0.0612286	−	0.0612286i
$596$	−17.4169	−	0.265822i	−0.713423	−	0.0108885i
$597$	9.69108	−	9.69108i	0.396630	−	0.396630i
$598$	−2.92804	+	1.18674i	−0.119737	+	0.0485294i
$599$			23.5067i			0.960457i	0.877143	+	0.480229i	$0.159446\pi$
$599$			23.5067i			0.960457i	−0.877143	+	0.480229i	$0.840554\pi$
$600$	4.54755	+	2.00681i	0.185653	+	0.0819275i
$601$		−	23.9850i		−	0.978370i	−0.872180	−	0.489185i	$-0.837294\pi$
$601$		−	23.9850i		−	0.978370i	0.872180	−	0.489185i	$-0.162706\pi$
$602$	−2.09367	−	5.16570i	−0.0853315	−	0.210538i
$603$	0.199993	−	0.199993i	0.00814434	−	0.00814434i
$604$	29.1017	−	28.2268i	1.18413	−	1.14853i
$605$	−4.15754	−	4.15754i	−0.169028	−	0.169028i
$606$	23.2773	+	9.85051i	0.945574	+	0.400150i
$607$	−42.4269			−1.72206			−0.861028	−	0.508558i	$-0.830179\pi$
$607$	−42.4269			−1.72206			−0.861028	+	0.508558i	$0.830179\pi$
$608$	44.3872	−	16.4317i	1.80014	−	0.666392i
$609$	−0.559632			−0.0226774
$610$	8.99285	+	3.80561i	0.364110	+	0.154085i
$611$	−20.2427	−	20.2427i	−0.818931	−	0.818931i
$612$	−0.268147	+	0.260085i	−0.0108392	+	0.0105133i
$613$	−8.71130	+	8.71130i	−0.351846	+	0.351846i	−0.860796	−	0.508950i	$-0.830034\pi$
$613$	−8.71130	+	8.71130i	−0.351846	+	0.351846i	0.508950	+	0.860796i	$0.330034\pi$
$614$	−13.6387	−	33.6508i	−0.550414	−	1.35803i
$615$		−	12.2009i		−	0.491986i
$616$	−2.58396	+	5.85542i	−0.104111	+	0.235922i
$617$		−	12.2653i		−	0.493784i	−0.969043	−	0.246892i	$-0.920591\pi$
$617$		−	12.2653i		−	0.493784i	0.969043	−	0.246892i	$-0.0794092\pi$
$618$	−41.2623	+	16.7237i	−1.65981	+	0.672725i
$619$	3.39836	−	3.39836i	0.136592	−	0.136592i	−0.635505	−	0.772097i	$-0.719208\pi$
$619$	3.39836	−	3.39836i	0.136592	−	0.136592i	0.772097	+	0.635505i	$0.219208\pi$
$620$	−18.5943	−	0.283791i	−0.746763	−	0.0113973i
$621$	−3.16503	−	3.16503i	−0.127008	−	0.127008i
$622$	−1.02612	+	2.42477i	−0.0411436	+	0.0972243i
$623$	0.0282999			0.00113381
$624$	−17.9440	−	0.547862i	−0.718335	−	0.0219320i
$625$	−1.00000			−0.0400000
$626$	7.13088	−	16.8506i	0.285007	−	0.673486i
$627$	23.5274	+	23.5274i	0.939595	+	0.939595i
$628$	0.0825034	−	5.40569i	0.00329224	−	0.215711i
$629$	6.43671	−	6.43671i	0.256648	−	0.256648i
$630$	−0.115902	+	0.0469753i	−0.00461765	+	0.00187154i
$631$		−	45.7825i		−	1.82257i	−0.411773	−	0.911287i	$-0.635090\pi$
$631$		−	45.7825i		−	1.82257i	0.411773	−	0.911287i	$-0.364910\pi$
$632$	−14.7746	−	38.1141i	−0.587703	−	1.51610i
$633$			10.3909i			0.413003i
$634$	12.2410	+	30.2023i	0.486153	+	1.19948i
$635$	11.4823	−	11.4823i	0.455662	−	0.455662i
$636$	−17.0801	−	17.6095i	−0.677268	−	0.698262i
$637$	1.80583	+	1.80583i	0.0715498	+	0.0715498i
$638$	−0.938482	−	0.397149i	−0.0371549	−	0.0157233i
$639$	0.891319			0.0352600
$640$	−4.88144	+	10.2064i	−0.192956	+	0.403445i
$641$	14.3223			0.565698			0.282849	−	0.959164i	$-0.408720\pi$
$641$	14.3223			0.565698			0.282849	+	0.959164i	$0.408720\pi$
$642$	−18.7072	−	7.91653i	−0.738313	−	0.312440i
$643$	17.2632	+	17.2632i	0.680795	+	0.680795i	0.960179	−	0.279385i	$-0.0901304\pi$
$643$	17.2632	+	17.2632i	0.680795	+	0.680795i	−0.279385	+	0.960179i	$0.590130\pi$
$644$	−1.21809	−	1.25585i	−0.0479997	−	0.0494875i
$645$	4.89773	−	4.89773i	0.192848	−	0.192848i
$646$	−9.38783	−	23.1626i	−0.369359	−	0.911319i
$647$		−	7.86279i		−	0.309118i	−0.987984	−	0.154559i	$-0.950604\pi$
$647$		−	7.86279i		−	0.309118i	0.987984	−	0.154559i	$-0.0493957\pi$
$648$	−9.46387	−	24.4140i	−0.371776	−	0.959071i
$649$		−	31.8812i		−	1.25145i
$650$	3.34720	−	1.35662i	0.131288	−	0.0532112i
$651$	11.5546	−	11.5546i	0.452859	−	0.452859i
$652$	0.133052	−	8.71767i	0.00521071	−	0.341410i
$653$	−13.7676	−	13.7676i	−0.538767	−	0.538767i	0.384400	−	0.923167i	$-0.374408\pi$
$653$	−13.7676	−	13.7676i	−0.538767	−	0.538767i	−0.923167	+	0.384400i	$0.874408\pi$
$654$	−7.41048	+	17.5113i	−0.289773	+	0.684748i
$655$	1.27231			0.0497134
$656$	27.7574	+	0.847483i	1.08375	+	0.0330886i
$657$	−0.487175			−0.0190065
$658$	6.17817	−	14.5993i	0.240850	−	0.569141i
$659$	23.7192	+	23.7192i	0.923969	+	0.923969i	0.997307	−	0.0733382i	$-0.0233652\pi$
$659$	23.7192	+	23.7192i	0.923969	+	0.923969i	−0.0733382	+	0.997307i	$0.523365\pi$
$660$	−7.95240	−	0.121372i	−0.309547	−	0.00472440i
$661$	−15.3164	+	15.3164i	−0.595739	+	0.595739i	−0.939176	−	0.343437i	$-0.888409\pi$
$661$	−15.3164	+	15.3164i	−0.595739	+	0.595739i	0.343437	+	0.939176i	$0.388409\pi$
$662$	−20.6992	+	8.38942i	−0.804497	+	0.326064i
$663$			9.47959i			0.368157i
$664$	6.38637	−	14.4719i	0.247839	−	0.561618i
$665$		−	8.36702i		−	0.324459i
$666$	−0.202451	−	0.499508i	−0.00784483	−	0.0193555i
$667$	0.196976	−	0.196976i	0.00762696	−	0.00762696i
$668$	−6.04198	+	5.86033i	−0.233771	+	0.226743i
$669$	6.25564	+	6.25564i	0.241857	+	0.241857i
$670$	−4.16552	−	1.76277i	−0.160928	−	0.0681019i
$671$	−15.6244			−0.603174
$672$	−3.45128	−	9.32301i	−0.133136	−	0.359643i
$673$	17.5236			0.675485			0.337743	−	0.941239i	$-0.390337\pi$
$673$	17.5236			0.675485			0.337743	+	0.941239i	$0.390337\pi$
$674$	33.8457	+	14.3229i	1.30369	+	0.551698i
$675$	3.61810	+	3.61810i	0.139261	+	0.139261i
$676$	9.29990	−	9.02030i	0.357689	−	0.346934i
$677$	2.69219	−	2.69219i	0.103469	−	0.103469i	−0.653477	−	0.756946i	$-0.726690\pi$
$677$	2.69219	−	2.69219i	0.103469	−	0.103469i	0.756946	+	0.653477i	$0.226690\pi$
$678$	−7.63696	−	18.8427i	−0.293296	−	0.723648i
$679$			12.3154i			0.472622i
$680$	5.46557	+	2.41193i	0.209595	+	0.0924932i
$681$		−	2.82787i		−	0.108364i
$682$	27.5764	−	11.1768i	1.05595	−	0.427980i
$683$	33.6578	−	33.6578i	1.28788	−	1.28788i	0.351809	−	0.936072i	$-0.385567\pi$
$683$	33.6578	−	33.6578i	1.28788	−	1.28788i	0.936072	−	0.351809i	$-0.114433\pi$
$684$	−1.47963	−	0.0225826i	−0.0565751	−	0.000863467i
$685$	−10.1172	−	10.1172i	−0.386558	−	0.386558i
$686$	−0.551150	+	1.30240i	−0.0210430	+	0.0497257i
$687$	13.3353			0.508775
$688$	10.8023	+	11.4827i	0.411835	+	0.437775i
$689$	−17.8249			−0.679076
$690$	0.847296	−	2.00220i	0.0322560	−	0.0762225i
$691$	−25.8896	−	25.8896i	−0.984885	−	0.984885i	0.0150024	−	0.999887i	$-0.495224\pi$
$691$	−25.8896	−	25.8896i	−0.984885	−	0.984885i	−0.999887	+	0.0150024i	$0.995224\pi$
$692$	0.0268007	−	1.75600i	0.00101881	−	0.0667532i
$693$	0.141494	−	0.141494i	0.00537491	−	0.00537491i
$694$	20.4038	−	8.26968i	0.774516	−	0.313913i
$695$		−	14.3756i		−	0.545298i
$696$	1.47587	−	0.572109i	0.0559427	−	0.0216857i
$697$		−	14.6639i		−	0.555435i
$698$	4.65130	+	11.4761i	0.176054	+	0.434379i
$699$	7.97901	−	7.97901i	0.301794	−	0.301794i
$700$	1.39247	+	1.43563i	0.0526303	+	0.0542617i
$701$	31.6107	+	31.6107i	1.19392	+	1.19392i	0.975957	+	0.217961i	$0.0699407\pi$
$701$	31.6107	+	31.6107i	1.19392	+	1.19392i	0.217961	+	0.975957i	$0.430059\pi$
$702$	−17.0189	−	7.20210i	−0.642338	−	0.271826i
$703$	36.0597			1.36002
$704$	0.828507	−	18.0836i	0.0312255	−	0.681551i
$705$	19.6997			0.741932
$706$	26.4081	+	11.1754i	0.993881	+	0.420593i
$707$	7.19126	+	7.19126i	0.270455	+	0.270455i
$708$	34.4778	+	35.5465i	1.29575	+	1.33592i
$709$	5.55361	−	5.55361i	0.208570	−	0.208570i	−0.595089	−	0.803660i	$-0.702883\pi$
$709$	5.55361	−	5.55361i	0.208570	−	0.208570i	0.803660	+	0.595089i	$0.202883\pi$
$710$	−5.35423	−	13.2105i	−0.200941	−	0.495780i
$711$			1.27804i			0.0479301i
$712$	−0.0746330	+	0.0289308i	−0.00279699	+	0.00108423i
$713$			8.13384i			0.304615i
$714$	−4.86502	+	1.97180i	−0.182069	+	0.0737928i
$715$	−4.08628	+	4.08628i	−0.152818	+	0.152818i
$716$	0.0562335	−	3.68447i	0.00210155	−	0.137695i
$717$	−34.6097	−	34.6097i	−1.29252	−	1.29252i
$718$	−9.69016	+	22.8983i	−0.361634	+	0.854558i
$719$	−9.07203			−0.338330			−0.169165	−	0.985588i	$-0.554107\pi$
$719$	−9.07203			−0.338330			−0.169165	+	0.985588i	$0.554107\pi$
$720$	0.257636	−	0.242370i	0.00960154	−	0.00903260i
$721$	−17.9142			−0.667158
$722$	28.1125	−	66.4313i	1.04624	−	2.47232i
$723$	−12.7014	−	12.7014i	−0.472369	−	0.472369i
$724$	25.8341	+	0.394289i	0.960118	+	0.0146536i
$725$	−0.225174	+	0.225174i	−0.00836275	+	0.00836275i
$726$	−13.5428	+	5.48892i	−0.502621	+	0.203713i
$727$		−	11.7394i		−	0.435389i	−0.976017	−	0.217695i	$-0.930146\pi$
$727$		−	11.7394i		−	0.435389i	0.976017	−	0.217695i	$-0.0698537\pi$
$728$	−6.60847	−	2.91628i	−0.244926	−	0.108085i
$729$		−	26.1579i		−	0.968811i
$730$	2.92650	+	7.22055i	0.108315	+	0.267245i
$731$	5.88645	−	5.88645i	0.217718	−	0.217718i
$732$	17.4207	−	16.8969i	0.643888	−	0.624529i
$733$	30.8950	+	30.8950i	1.14113	+	1.14113i	0.988243	+	0.152889i	$0.0488578\pi$
$733$	30.8950	+	30.8950i	1.14113	+	1.14113i	0.152889	+	0.988243i	$0.451142\pi$
$734$	−4.11680	−	1.74215i	−0.151954	−	0.0643041i
$735$	−1.75739			−0.0648224
$736$	4.49623	+	2.06670i	0.165733	+	0.0761797i
$737$	7.23730			0.266589
$738$	−0.799590	−	0.338372i	−0.0294333	−	0.0124556i
$739$	−22.6424	−	22.6424i	−0.832914	−	0.832914i	0.155000	−	0.987914i	$-0.450462\pi$
$739$	−22.6424	−	22.6424i	−0.832914	−	0.832914i	−0.987914	+	0.155000i	$0.950462\pi$
$740$	−6.18719	+	6.00117i	−0.227446	+	0.220607i
$741$	−26.5533	+	26.5533i	−0.975458	+	0.975458i
$742$	−3.70768	−	9.14794i	−0.136113	−	0.335832i
$743$			38.2965i			1.40496i	0.711703	+	0.702481i	$0.247924\pi$
$743$			38.2965i			1.40496i	−0.711703	+	0.702481i	$0.752076\pi$
$744$	−18.6597	+	42.2840i	−0.684098	+	1.55021i
$745$		−	8.70945i		−	0.319089i
$746$	−39.5655	+	16.0360i	−1.44859	+	0.587118i
$747$	−0.349708	+	0.349708i	−0.0127951	+	0.0127951i
$748$	−9.55778	−	0.145874i	−0.349467	−	0.00533368i
$749$	−5.77938	−	5.77938i	−0.211174	−	0.211174i
$750$	−0.968587	+	2.28882i	−0.0353678	+	0.0835759i
$751$	−3.19670			−0.116649			−0.0583247	−	0.998298i	$-0.518576\pi$
$751$	−3.19670			−0.116649			−0.0583247	+	0.998298i	$0.518576\pi$
$752$	−1.36836	+	44.8175i	−0.0498988	+	1.63433i
$753$	−34.0660			−1.24144
$754$	0.448225	−	1.05918i	0.0163234	−	0.0385730i
$755$	14.3338	+	14.3338i	0.521660	+	0.521660i
$756$	0.156169	−	10.2324i	0.00567983	−	0.372147i
$757$	−0.744304	+	0.744304i	−0.0270522	+	0.0270522i	−0.720503	−	0.693451i	$-0.756089\pi$
$757$	−0.744304	+	0.744304i	−0.0270522	+	0.0270522i	0.693451	+	0.720503i	$0.256089\pi$
$758$	−16.2640	+	6.59184i	−0.590736	+	0.239426i
$759$			3.47868i			0.126268i
$760$	8.55356	+	22.0656i	0.310270	+	0.800405i
$761$			14.8684i			0.538981i	0.963003	+	0.269490i	$0.0868553\pi$
$761$			14.8684i			0.538981i	−0.963003	+	0.269490i	$0.913145\pi$
$762$	−15.1594	−	37.4026i	−0.549166	−	1.35495i
$763$	−5.40994	+	5.40994i	−0.195853	+	0.195853i
$764$	11.8469	+	12.2141i	0.428606	+	0.441891i
$765$	−0.132073	−	0.132073i	−0.00477513	−	0.00477513i
$766$	17.2633	+	7.30552i	0.623748	+	0.263959i
$767$	35.9814			1.29921
$768$	18.6326	+	21.0586i	0.672347	+	0.759886i
$769$	−16.5147			−0.595537			−0.297768	−	0.954638i	$-0.596242\pi$
$769$	−16.5147			−0.595537			−0.297768	+	0.954638i	$0.596242\pi$
$770$	−2.94709	−	1.24715i	−0.106206	−	0.0449443i
$771$	−17.0706	−	17.0706i	−0.614784	−	0.614784i
$772$	9.31859	+	9.60744i	0.335383	+	0.345779i
$773$	24.8184	−	24.8184i	0.892656	−	0.892656i	−0.102116	−	0.994772i	$-0.532561\pi$
$773$	24.8184	−	24.8184i	0.892656	−	0.892656i	0.994772	+	0.102116i	$0.0325614\pi$
$774$	−0.185144	−	0.456806i	−0.00665488	−	0.0164196i
$775$		−	9.29821i		−	0.334002i
$776$	−12.5900	−	32.4784i	−0.451954	−	1.16591i
$777$		−	7.57391i		−	0.271712i
$778$	−28.9943	+	11.7515i	−1.03950	+	0.421310i
$779$	41.0750	−	41.0750i	1.47166	−	1.47166i
$780$	0.136981	−	8.97514i	0.00490472	−	0.321362i
$781$	16.1274	+	16.1274i	0.577084	+	0.577084i
$782$	1.01834	−	2.40639i	0.0364158	−	0.0860524i
$783$	1.62941			0.0582302
$784$	0.122070	−	3.99814i	0.00435965	−	0.142791i
$785$	2.70316			0.0964799
$786$	1.23235	−	2.91210i	0.0439564	−	0.103871i
$787$	−12.4562	−	12.4562i	−0.444016	−	0.444016i	0.449343	−	0.893359i	$-0.351658\pi$
$787$	−12.4562	−	12.4562i	−0.444016	−	0.444016i	−0.893359	+	0.449343i	$0.851658\pi$
$788$	−31.5964	−	0.482234i	−1.12557	−	0.0171789i
$789$	14.7722	−	14.7722i	0.525904	−	0.525904i
$790$	18.9421	−	7.67727i	0.673930	−	0.273145i
$791$		−	8.18060i		−	0.290869i
$792$	−0.228502	+	0.517799i	−0.00811945	+	0.0183992i
$793$		−	17.6339i		−	0.626197i
$794$	14.2353	+	35.1228i	0.505193	+	1.24646i
$795$	8.67340	−	8.67340i	0.307614	−	0.307614i
$796$	−11.1960	+	10.8593i	−0.396830	+	0.384899i
$797$	−7.93901	−	7.93901i	−0.281214	−	0.281214i	0.552379	−	0.833593i	$-0.313720\pi$
$797$	−7.93901	−	7.93901i	−0.281214	−	0.281214i	−0.833593	+	0.552379i	$0.813720\pi$
$798$	−19.1506	−	8.10419i	−0.677924	−	0.286885i
$799$	23.6765			0.837614
$800$	−5.13988	−	2.36256i	−0.181722	−	0.0835290i
$801$	0.00250258			8.84243e−5
$802$	−8.76094	−	3.70747i	−0.309359	−	0.130915i
$803$	−8.81489	−	8.81489i	−0.311071	−	0.311071i
$804$	−8.06934	+	7.82673i	−0.284584	+	0.276028i
$805$	0.618559	−	0.618559i	0.0218013	−	0.0218013i
$806$	12.6142	+	31.1229i	0.444316	+	1.09626i
$807$			11.7900i			0.415027i
$808$	−26.3165	−	11.6133i	−0.925811	−	0.408555i
$809$			22.1772i			0.779710i	0.920876	+	0.389855i	$0.127475\pi$
$809$			22.1772i			0.779710i	−0.920876	+	0.389855i	$0.872525\pi$
$810$	12.1333	−	4.91767i	0.426322	−	0.172789i
$811$	34.7534	−	34.7534i	1.22036	−	1.22036i	0.252854	−	0.967504i	$-0.418631\pi$
$811$	34.7534	−	34.7534i	1.22036	−	1.22036i	0.967504	−	0.252854i	$-0.0813692\pi$
$812$	0.636814	+	0.00971926i	0.0223478	+	0.000341079i
$813$	36.2874	+	36.2874i	1.27265	+	1.27265i
$814$	5.37490	−	12.7012i	0.188390	−	0.445176i
$815$	4.35934			0.152701
$816$	10.8144	−	10.1736i	0.378578	−	0.356146i
$817$	32.9770			1.15372
$818$	−16.8109	+	39.7250i	−0.587780	+	1.38895i
$819$	0.159691	+	0.159691i	0.00558006	+	0.00558006i
$820$	−0.211895	+	13.8836i	−0.00739971	+	0.484835i
$821$	21.6905	−	21.6905i	0.757004	−	0.757004i	−0.218772	−	0.975776i	$-0.570205\pi$
$821$	21.6905	−	21.6905i	0.757004	−	0.757004i	0.975776	+	0.218772i	$0.0702052\pi$
$822$	−32.9558	+	13.3571i	−1.14947	+	0.465881i
$823$		−	19.8173i		−	0.690789i	−0.938458	−	0.345394i	$-0.887745\pi$
$823$		−	19.8173i		−	0.690789i	0.938458	−	0.345394i	$-0.112255\pi$
$824$	47.2435	−	18.3136i	1.64581	−	0.637983i
$825$		−	3.97666i		−	0.138450i
$826$	7.48432	+	18.4660i	0.260413	+	0.642515i
$827$	−39.2978	+	39.2978i	−1.36652	+	1.36652i	−0.501171	+	0.865348i	$0.667097\pi$
$827$	−39.2978	+	39.2978i	−1.36652	+	1.36652i	−0.865348	+	0.501171i	$0.832903\pi$
$828$	−0.107717	−	0.111056i	−0.00374342	−	0.00385946i
$829$	20.2018	+	20.2018i	0.701639	+	0.701639i	0.964762	−	0.263123i	$-0.0847526\pi$
$829$	20.2018	+	20.2018i	0.701639	+	0.701639i	−0.263123	+	0.964762i	$0.584753\pi$
$830$	7.28383	+	3.08239i	0.252826	+	0.106991i
$831$	−31.2294			−1.08334
$832$	20.4093	+	0.935060i	0.707564	+	0.0324174i
$833$	−2.11216			−0.0731821
$834$	−32.9032	−	13.9240i	−1.13935	−	0.482150i
$835$	−2.97592	−	2.97592i	−0.102986	−	0.102986i
$836$	−26.3637	−	27.1809i	−0.911806	−	0.940070i
$837$	−33.6419	+	33.6419i	−1.16283	+	1.16283i
$838$	14.8500	+	36.6395i	0.512986	+	1.26569i
$839$			20.8107i			0.718464i	0.933248	+	0.359232i	$0.116961\pi$
$839$			20.8107i			0.718464i	−0.933248	+	0.359232i	$0.883039\pi$
$840$	4.63463	−	1.79657i	0.159910	−	0.0619877i
$841$		−	28.8986i		−	0.996503i
$842$	19.7376	−	7.99969i	0.680203	−	0.275688i
$843$	−3.06062	+	3.06062i	−0.105413	+	0.105413i
$844$	0.180462	−	11.8240i	0.00621176	−	0.407000i
$845$	4.58058	+	4.58058i	0.157577	+	0.157577i
$846$	0.546339	−	1.29103i	0.0187835	−	0.0443864i
$847$	−5.87965			−0.202027
$848$	19.1298	+	20.3348i	0.656922	+	0.698299i
$849$	11.6142			0.398599
$850$	−1.16412	+	2.75087i	−0.0399290	+	0.0943542i
$851$	2.66583	+	2.66583i	0.0913834	+	0.0913834i
$852$	−35.4224	−	0.540628i	−1.21355	−	0.0185216i
$853$	18.8726	−	18.8726i	0.646186	−	0.646186i	−0.305883	−	0.952069i	$-0.598952\pi$
$853$	18.8726	−	18.8726i	0.646186	−	0.646186i	0.952069	+	0.305883i	$0.0989515\pi$
$854$	9.04988	−	3.66793i	0.309680	−	0.125514i
$855$		−	0.739901i		−	0.0253041i
$856$	21.1497	+	9.33324i	0.722882	+	0.319004i
$857$		−	10.4227i		−	0.356031i	−0.984028	−	0.178016i	$-0.943032\pi$
$857$		−	10.4227i		−	0.356031i	0.984028	−	0.178016i	$-0.0569678\pi$
$858$	5.39484	+	13.3107i	0.184177	+	0.454419i
$859$	−20.3735	+	20.3735i	−0.695136	+	0.695136i	−0.963357	−	0.268222i	$-0.913564\pi$
$859$	−20.3735	+	20.3735i	−0.695136	+	0.695136i	0.268222	+	0.963357i	$0.413564\pi$
$860$	−5.65827	+	5.48815i	−0.192945	+	0.187144i
$861$	−8.62731	−	8.62731i	−0.294018	−	0.294018i
$862$	−8.17774	−	3.46067i	−0.278535	−	0.117871i
$863$	−24.8089			−0.844505			−0.422252	−	0.906478i	$-0.638760\pi$
$863$	−24.8089			−0.844505			−0.422252	+	0.906478i	$0.638760\pi$
$864$	10.0486	+	27.1446i	0.341861	+	0.923477i
$865$	0.878103			0.0298564
$866$	−42.6265	−	18.0388i	−1.44851	−	0.612983i
$867$	15.5815	+	15.5815i	0.529175	+	0.529175i
$868$	−13.3488	+	12.9475i	−0.453088	+	0.439465i
$869$	−23.1246	+	23.1246i	−0.784450	+	0.784450i
$870$	0.297282	+	0.733484i	0.0100788	+	0.0248674i
$871$			8.16807i			0.276765i
$872$	8.73663	−	19.7977i	0.295860	−	0.670436i
$873$			1.08906i			0.0368591i
$874$	9.59302	−	3.88807i	0.324489	−	0.131516i
$875$	−0.707107	+	0.707107i	−0.0239046	+	0.0239046i
$876$	19.3611	+	0.295496i	0.654152	+	0.00998387i
$877$	−3.28176	−	3.28176i	−0.110817	−	0.110817i	0.649524	−	0.760341i	$-0.274968\pi$
$877$	−3.28176	−	3.28176i	−0.110817	−	0.110817i	−0.760341	+	0.649524i	$0.774968\pi$
$878$	−2.10926	+	4.98429i	−0.0711841	+	0.168212i
$879$	−18.8499			−0.635792
$880$	9.04706	+	0.276223i	0.304976	+	0.00931146i
$881$	−55.0298			−1.85400			−0.927000	−	0.375061i	$-0.877622\pi$
$881$	−55.0298			−1.85400			−0.927000	+	0.375061i	$0.877622\pi$
$882$	−0.0487386	+	0.115172i	−0.00164111	+	0.00387803i
$883$	7.68093	+	7.68093i	0.258484	+	0.258484i	0.824437	−	0.565953i	$-0.191492\pi$
$883$	7.68093	+	7.68093i	0.258484	+	0.258484i	−0.565953	+	0.824437i	$0.691492\pi$
$884$	0.164634	−	10.7870i	0.00553725	−	0.362806i
$885$	−17.5081	+	17.5081i	−0.588529	+	0.588529i
$886$	13.0510	−	5.28960i	0.438457	−	0.177708i
$887$			9.50290i			0.319076i	0.987192	+	0.159538i	$0.0510005\pi$
$887$			9.50290i			0.319076i	−0.987192	+	0.159538i	$0.949000\pi$
$888$	7.74277	+	19.9740i	0.259830	+	0.670285i
$889$		−	16.2385i		−	0.544621i
$890$	−0.0150332	−	0.0370914i	−0.000503914	−	0.00124331i
$891$	−14.8125	+	14.8125i	−0.496236	+	0.496236i
$892$	−7.00976	−	7.22705i	−0.234704	−	0.241979i
$893$	66.3202	+	66.3202i	2.21932	+	2.21932i
$894$	−19.9344	−	8.43586i	−0.666705	−	0.282137i
$895$	1.84245			0.0615863
$896$	3.76535	+	10.6687i	0.125792	+	0.356418i
$897$	−3.92607			−0.131088
$898$	45.1958	+	19.1260i	1.50820	+	0.638244i
$899$	−2.09372	−	2.09372i	−0.0698293	−	0.0698293i
$900$	0.123137	+	0.126954i	0.00410456	+	0.00423179i
$901$	10.4243	−	10.4243i	0.347285	−	0.347285i
$902$	−8.34523	−	20.5902i	−0.277866	−	0.685577i
$903$		−	6.92644i		−	0.230497i
$904$	8.36298	+	21.5740i	0.278149	+	0.717541i
$905$			12.9186i			0.429428i
$906$	46.6910	−	18.9240i	1.55121	−	0.628706i
$907$	−23.6548	+	23.6548i	−0.785446	+	0.785446i	−0.980744	−	0.195298i	$-0.937433\pi$
$907$	−23.6548	+	23.6548i	−0.785446	+	0.785446i	0.195298	+	0.980744i	$0.437433\pi$
$908$	−0.0491122	+	3.21788i	−0.00162985	+	0.106789i
$909$	0.635928	+	0.635928i	0.0210924	+	0.0210924i
$910$	1.40755	−	3.32610i	0.0466597	−	0.110259i
$911$	−36.0167			−1.19329			−0.596643	−	0.802507i	$-0.703499\pi$
$911$	−36.0167			−1.19329			−0.596643	+	0.802507i	$0.703499\pi$
$912$	58.7892	+	1.79494i	1.94670	+	0.0594363i
$913$	−12.6551			−0.418824
$914$	−9.80658	+	23.1734i	−0.324373	+	0.766509i
$915$	8.58042	+	8.58042i	0.283660	+	0.283660i
$916$	−15.1745	−	0.231598i	−0.501380	−	0.00765221i
$917$	0.899662	−	0.899662i	0.0297094	−	0.0297094i
$918$	14.1648	−	5.74104i	0.467510	−	0.189483i
$919$			13.6821i			0.451329i	0.974205	+	0.225665i	$0.0724554\pi$
$919$			13.6821i			0.451329i	−0.974205	+	0.225665i	$0.927545\pi$
$920$	−0.998924	+	2.26362i	−0.0329336	+	0.0746295i
$921$		−	45.1207i		−	1.48678i
$922$	−3.65380	−	9.01500i	−0.120331	−	0.296893i
$923$	−18.2015	+	18.2015i	−0.599111	+	0.599111i
$924$	−5.70902	+	5.53737i	−0.187813	+	0.182166i
$925$	−3.04745	−	3.04745i	−0.100199	−	0.100199i
$926$	−10.6634	−	4.51257i	−0.350422	−	0.148292i
$927$	−1.58416			−0.0520307
$928$	−1.68935	+	0.625380i	−0.0554557	+	0.0205291i
$929$	−41.8318			−1.37246			−0.686229	−	0.727386i	$-0.740735\pi$
$929$	−41.8318			−1.37246			−0.686229	+	0.727386i	$0.740735\pi$
$930$	−21.2819	−	9.00613i	−0.697862	−	0.295323i
$931$	−5.91638	−	5.91638i	−0.193901	−	0.193901i
$932$	−9.21802	+	8.94087i	−0.301946	+	0.292868i
$933$	−2.31356	+	2.31356i	−0.0757426	+	0.0757426i
$934$	−18.8870	−	46.5998i	−0.618002	−	1.52479i
$935$		−	4.77945i		−	0.156305i
$936$	−0.584392	−	0.257889i	−0.0191014	−	0.00842936i
$937$		−	20.5411i		−	0.671049i	−0.942032	−	0.335524i	$-0.891087\pi$
$937$		−	20.5411i		−	0.671049i	0.942032	−	0.335524i	$-0.108913\pi$
$938$	−4.19194	+	1.69900i	−0.136872	+	0.0554743i
$939$	16.0778	−	16.0778i	0.524680	−	0.524680i
$940$	−22.4166	−	0.342129i	−0.731148	−	0.0111590i
$941$	15.6333	+	15.6333i	0.509631	+	0.509631i	0.914413	−	0.404782i	$-0.132653\pi$
$941$	15.6333	+	15.6333i	0.509631	+	0.509631i	−0.404782	+	0.914413i	$0.632653\pi$
$942$	2.61825	−	6.18705i	0.0853071	−	0.201585i
$943$	6.07320			0.197771
$944$	−38.6155	−	41.0477i	−1.25683	−	1.33599i
$945$	5.11677			0.166449
$946$	4.91542	−	11.6154i	0.159814	−	0.377649i
$947$	3.37239	+	3.37239i	0.109588	+	0.109588i	0.759775	−	0.650187i	$-0.225309\pi$
$947$	3.37239	+	3.37239i	0.109588	+	0.109588i	−0.650187	+	0.759775i	$0.725309\pi$
$948$	0.775192	−	50.7912i	0.0251771	−	1.64962i
$949$	9.94856	−	9.94856i	0.322944	−	0.322944i
$950$	−10.9663	+	4.44465i	−0.355793	+	0.144204i
$951$			40.4967i			1.31320i
$952$	5.57023	−	2.15925i	0.180532	−	0.0699818i
$953$		−	46.3477i		−	1.50135i	−0.660671	−	0.750675i	$-0.729728\pi$
$953$		−	46.3477i		−	1.50135i	0.660671	−	0.750675i	$-0.270272\pi$
$954$	−0.327872	−	0.808959i	−0.0106153	−	0.0261910i
$955$	−6.01595	+	6.01595i	−0.194672	+	0.194672i
$956$	38.7819	+	39.9840i	1.25429	+	1.29318i
$957$	−0.895441	−	0.895441i	−0.0289455	−	0.0289455i
$958$	−18.0316	−	7.63066i	−0.582576	−	0.246535i
$959$	−14.3079			−0.462025
$960$	−10.3859	+	9.47591i	−0.335203	+	0.305834i
$961$	55.4567			1.78893
$962$	14.3346	+	6.06616i	0.462167	+	0.195581i
$963$	−0.511074	−	0.511074i	−0.0164691	−	0.0164691i
$964$	14.2325	+	14.6737i	0.458399	+	0.472608i
$965$	−4.73206	+	4.73206i	−0.152330	+	0.152330i
$966$	−0.816642	−	2.01490i	−0.0262750	−	0.0648283i
$967$			1.34940i			0.0433936i	0.999765	+	0.0216968i	$0.00690685\pi$
$967$			1.34940i			0.0433936i	−0.999765	+	0.0216968i	$0.993093\pi$
$968$	15.5059	−	6.01074i	0.498379	−	0.193192i
$969$		−	31.0576i		−	0.997713i
$970$	16.1412	−	6.54208i	0.518264	−	0.210053i
$971$	−9.70260	+	9.70260i	−0.311371	+	0.311371i	−0.845441	−	0.534069i	$-0.820662\pi$
$971$	−9.70260	+	9.70260i	−0.311371	+	0.311371i	0.534069	+	0.845441i	$0.320662\pi$
$972$	0.0280398	−	1.83719i	0.000899376	−	0.0589279i
$973$	−10.1651	−	10.1651i	−0.325878	−	0.325878i
$974$	−16.2898	+	38.4936i	−0.521959	+	1.23342i
$975$	4.48809			0.143734
$976$	−20.1168	+	18.9248i	−0.643922	+	0.605767i
$977$	5.16687			0.165303			0.0826515	−	0.996579i	$-0.473661\pi$
$977$	5.16687			0.165303			0.0826515	+	0.996579i	$0.473661\pi$
$978$	4.22240	−	9.97775i	0.135018	−	0.319053i
$979$	0.0452814	+	0.0452814i	0.00144720	+	0.00144720i
$980$	1.99977	+	0.0305211i	0.0638802	+	0.000974960i
$981$	−0.478405	+	0.478405i	−0.0152743	+	0.0152743i
$982$	12.2460	−	4.96333i	0.390786	−	0.158386i
$983$		−	8.58100i		−	0.273691i	−0.990592	−	0.136846i	$-0.956304\pi$
$983$		−	8.58100i		−	0.273691i	0.990592	−	0.136846i	$-0.0436964\pi$
$984$	31.5718	+	13.9324i	1.00647	+	0.444150i
$985$		−	15.8000i		−	0.503430i
$986$	0.357296	+	0.881554i	0.0113786	+	0.0280744i
$987$	13.9298	−	13.9298i	0.443389	−	0.443389i
$988$	30.6766	−	29.7542i	0.975951	−	0.946608i
$989$	2.43793	+	2.43793i	0.0775218	+	0.0775218i
$990$	−0.260613	−	0.110287i	−0.00828282	−	0.00350514i
$991$	−24.9952			−0.793998			−0.396999	−	0.917819i	$-0.629948\pi$
$991$	−24.9952			−0.793998			−0.396999	+	0.917819i	$0.629948\pi$
$992$	21.9676	−	47.7917i	0.697471	−	1.51739i
$993$	−27.7546			−0.880764
$994$	−13.1272	−	5.55520i	−0.416370	−	0.176200i
$995$	−5.51446	−	5.51446i	−0.174820	−	0.174820i
$996$	14.1101	−	13.6858i	0.447094	−	0.433652i
$997$	−26.8436	+	26.8436i	−0.850146	+	0.850146i	−0.990151	−	0.140005i	$-0.955288\pi$
$997$	−26.8436	+	26.8436i	−0.850146	+	0.850146i	0.140005	+	0.990151i	$0.455288\pi$
$998$	21.5201	+	53.0965i	0.681207	+	1.68074i
$999$			22.0520i			0.697693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bd.b.141.5	✓	52
4.3	odd	2		2240.2.bd.b.1681.20		52
16.5	even	4	inner	560.2.bd.b.421.5	yes	52
16.11	odd	4		2240.2.bd.b.561.20		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.b.141.5	✓	52	1.1	even	1	trivial
560.2.bd.b.421.5	yes	52	16.5	even	4	inner
2240.2.bd.b.561.20		52	16.11	odd	4
2240.2.bd.b.1681.20		52	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.30240 - 0.551150i) q^{2} +(-1.24266 - 1.24266i) q^{3} +(1.39247 + 1.43563i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.933546 + 2.30334i) q^{6} +1.00000i q^{7} +(-1.02229 - 2.63722i) q^{8} +0.0884307i q^{9} +O(q^{10})\)	\(q+(-1.30240 - 0.551150i) q^{2} +(-1.24266 - 1.24266i) q^{3} +(1.39247 + 1.43563i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.933546 + 2.30334i) q^{6} +1.00000i q^{7} +(-1.02229 - 2.63722i) q^{8} +0.0884307i q^{9} +(1.31065 - 0.531211i) q^{10} +(-1.60005 + 1.60005i) q^{11} +(0.0536375 - 3.51438i) q^{12} +(-1.80583 - 1.80583i) q^{13} +(0.551150 - 1.30240i) q^{14} +1.75739 q^{15} +(-0.122070 + 3.99814i) q^{16} +2.11216 q^{17} +(0.0487386 - 0.115172i) q^{18} +(5.91638 + 5.91638i) q^{19} +(-1.99977 - 0.0305211i) q^{20} +(1.24266 - 1.24266i) q^{21} +(2.96577 - 1.20203i) q^{22} +0.874774i q^{23} +(-2.00681 + 4.54755i) q^{24} -1.00000i q^{25} +(1.35662 + 3.34720i) q^{26} +(-3.61810 + 3.61810i) q^{27} +(-1.43563 + 1.39247i) q^{28} +(-0.225174 - 0.225174i) q^{29} +(-2.28882 - 0.968587i) q^{30} +9.29821 q^{31} +(2.36256 - 5.13988i) q^{32} +3.97666 q^{33} +(-2.75087 - 1.16412i) q^{34} +(-0.707107 - 0.707107i) q^{35} +(-0.126954 + 0.123137i) q^{36} +(3.04745 - 3.04745i) q^{37} +(-4.44465 - 10.9663i) q^{38} +4.48809i q^{39} +(2.58767 + 1.14192i) q^{40} -6.94259i q^{41} +(-2.30334 + 0.933546i) q^{42} +(2.78693 - 2.78693i) q^{43} +(-4.52511 - 0.0690637i) q^{44} +(-0.0625299 - 0.0625299i) q^{45} +(0.482132 - 1.13930i) q^{46} +11.2096 q^{47} +(5.12004 - 4.81665i) q^{48} -1.00000 q^{49} +(-0.551150 + 1.30240i) q^{50} +(-2.62471 - 2.62471i) q^{51} +(0.0779458 - 5.10708i) q^{52} +(4.93538 - 4.93538i) q^{53} +(6.70632 - 2.71808i) q^{54} -2.26282i q^{55} +(2.63722 - 1.02229i) q^{56} -14.7041i q^{57} +(0.169161 + 0.417370i) q^{58} +(-9.96255 + 9.96255i) q^{59} +(2.44711 + 2.52297i) q^{60} +(4.88247 + 4.88247i) q^{61} +(-12.1099 - 5.12471i) q^{62} -0.0884307 q^{63} +(-5.90983 + 5.39203i) q^{64} +2.55384 q^{65} +(-5.17919 - 2.19174i) q^{66} +(-2.26158 - 2.26158i) q^{67} +(2.94112 + 3.03229i) q^{68} +(1.08705 - 1.08705i) q^{69} +(0.531211 + 1.31065i) q^{70} -10.0793i q^{71} +(0.233211 - 0.0904022i) q^{72} +5.50912i q^{73} +(-5.64858 + 2.28938i) q^{74} +(-1.24266 + 1.24266i) q^{75} +(-0.255371 + 16.7321i) q^{76} +(-1.60005 - 1.60005i) q^{77} +(2.47361 - 5.84527i) q^{78} +14.4524 q^{79} +(-2.74079 - 2.91343i) q^{80} +9.25747 q^{81} +(-3.82641 + 9.04200i) q^{82} +(3.95460 + 3.95460i) q^{83} +(3.51438 + 0.0536375i) q^{84} +(-1.49353 + 1.49353i) q^{85} +(-5.16570 + 2.09367i) q^{86} +0.559632i q^{87} +(5.85542 + 2.58396i) q^{88} -0.0282999i q^{89} +(0.0469753 + 0.115902i) q^{90} +(1.80583 - 1.80583i) q^{91} +(-1.25585 + 1.21809i) q^{92} +(-11.5546 - 11.5546i) q^{93} +(-14.5993 - 6.17817i) q^{94} -8.36702 q^{95} +(-9.32301 + 3.45128i) q^{96} +12.3154 q^{97} +(1.30240 + 0.551150i) q^{98} +(-0.141494 - 0.141494i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 8 q^{4} + 12 q^{6}+O(q^{10}) \) 52 * q - 8 * q^4 + 12 * q^6	\( 52 q - 8 q^{4} + 12 q^{6} - 4 q^{10} - 4 q^{11} + 40 q^{12} + 8 q^{15} - 4 q^{16} + 8 q^{19} + 32 q^{22} + 12 q^{24} - 12 q^{26} - 24 q^{27} + 4 q^{28} + 4 q^{29} - 16 q^{34} + 4 q^{36} - 12 q^{37} + 16 q^{38} - 4 q^{42} + 36 q^{43} + 28 q^{44} - 16 q^{46} + 32 q^{48} - 52 q^{49} - 8 q^{51} - 80 q^{52} - 4 q^{53} + 48 q^{54} - 12 q^{56} - 56 q^{58} + 24 q^{59} - 16 q^{61} - 72 q^{62} - 68 q^{63} + 4 q^{64} + 40 q^{65} - 12 q^{66} - 12 q^{67} - 72 q^{69} - 8 q^{72} + 68 q^{74} - 4 q^{77} - 4 q^{78} - 16 q^{79} - 32 q^{80} - 116 q^{81} + 104 q^{82} + 16 q^{85} - 68 q^{86} - 48 q^{88} + 36 q^{90} + 64 q^{92} + 8 q^{93} - 72 q^{94} - 32 q^{95} - 52 q^{99}+O(q^{100}) \) 52 * q - 8 * q^4 + 12 * q^6 - 4 * q^10 - 4 * q^11 + 40 * q^12 + 8 * q^15 - 4 * q^16 + 8 * q^19 + 32 * q^22 + 12 * q^24 - 12 * q^26 - 24 * q^27 + 4 * q^28 + 4 * q^29 - 16 * q^34 + 4 * q^36 - 12 * q^37 + 16 * q^38 - 4 * q^42 + 36 * q^43 + 28 * q^44 - 16 * q^46 + 32 * q^48 - 52 * q^49 - 8 * q^51 - 80 * q^52 - 4 * q^53 + 48 * q^54 - 12 * q^56 - 56 * q^58 + 24 * q^59 - 16 * q^61 - 72 * q^62 - 68 * q^63 + 4 * q^64 + 40 * q^65 - 12 * q^66 - 12 * q^67 - 72 * q^69 - 8 * q^72 + 68 * q^74 - 4 * q^77 - 4 * q^78 - 16 * q^79 - 32 * q^80 - 116 * q^81 + 104 * q^82 + 16 * q^85 - 68 * q^86 - 48 * q^88 + 36 * q^90 + 64 * q^92 + 8 * q^93 - 72 * q^94 - 32 * q^95 - 52 * q^99

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