LMFDB - Embedded newform 560.2.bd.a.141.11

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:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			141.11
Character	$\chi$	$=$	560.141
Dual form			560.2.bd.a.421.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.551277 - 1.30234i) q^{2} +(-1.16279 - 1.16279i) q^{3} +(-1.39219 + 1.43590i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.873327 + 2.15536i) q^{6} -1.00000i q^{7} +(2.63752 + 1.02152i) q^{8} -0.295857i q^{9} +O(q^{10})$	\(q+(-0.551277 - 1.30234i) q^{2} +(-1.16279 - 1.16279i) q^{3} +(-1.39219 + 1.43590i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.873327 + 2.15536i) q^{6} -1.00000i q^{7} +(2.63752 + 1.02152i) q^{8} -0.295857i q^{9} +(-1.31071 - 0.531083i) q^{10} +(3.97270 - 3.97270i) q^{11} +(3.28846 - 0.0508310i) q^{12} +(-1.48922 - 1.48922i) q^{13} +(-1.30234 + 0.551277i) q^{14} -1.64443 q^{15} +(-0.123630 - 3.99809i) q^{16} -6.33574 q^{17} +(-0.385307 + 0.163099i) q^{18} +(4.80932 + 4.80932i) q^{19} +(0.0309111 + 1.99976i) q^{20} +(-1.16279 + 1.16279i) q^{21} +(-7.36387 - 2.98376i) q^{22} -4.65754i q^{23} +(-1.87905 - 4.25468i) q^{24} -1.00000i q^{25} +(-1.11850 + 2.76045i) q^{26} +(-3.83238 + 3.83238i) q^{27} +(1.43590 + 1.39219i) q^{28} +(-4.24816 - 4.24816i) q^{29} +(0.906535 + 2.14161i) q^{30} -0.0294487 q^{31} +(-5.13872 + 2.36506i) q^{32} -9.23880 q^{33} +(3.49275 + 8.25130i) q^{34} +(-0.707107 - 0.707107i) q^{35} +(0.424822 + 0.411889i) q^{36} +(-5.73990 + 5.73990i) q^{37} +(3.61211 - 8.91465i) q^{38} +3.46329i q^{39} +(2.58733 - 1.14268i) q^{40} -0.919426i q^{41} +(2.15536 + 0.873327i) q^{42} +(-3.37767 + 3.37767i) q^{43} +(0.173666 + 11.2352i) q^{44} +(-0.209203 - 0.209203i) q^{45} +(-6.06571 + 2.56760i) q^{46} +12.5540 q^{47} +(-4.50517 + 4.79268i) q^{48} -1.00000 q^{49} +(-1.30234 + 0.551277i) q^{50} +(7.36711 + 7.36711i) q^{51} +(4.21165 - 0.0651011i) q^{52} +(0.0243993 - 0.0243993i) q^{53} +(7.10377 + 2.87836i) q^{54} -5.61825i q^{55} +(1.02152 - 2.63752i) q^{56} -11.1844i q^{57} +(-3.19064 + 7.87447i) q^{58} +(-5.91263 + 5.91263i) q^{59} +(2.28935 - 2.36124i) q^{60} +(1.34761 + 1.34761i) q^{61} +(0.0162344 + 0.0383522i) q^{62} -0.295857 q^{63} +(5.91298 + 5.38857i) q^{64} -2.10608 q^{65} +(5.09314 + 12.0321i) q^{66} +(-9.68994 - 9.68994i) q^{67} +(8.82054 - 9.09750i) q^{68} +(-5.41572 + 5.41572i) q^{69} +(-0.531083 + 1.31071i) q^{70} -11.0515i q^{71} +(0.302225 - 0.780329i) q^{72} -10.5102i q^{73} +(10.6396 + 4.31104i) q^{74} +(-1.16279 + 1.16279i) q^{75} +(-13.6012 + 0.210239i) q^{76} +(-3.97270 - 3.97270i) q^{77} +(4.51038 - 1.90923i) q^{78} -4.67417 q^{79} +(-2.91450 - 2.73966i) q^{80} +8.02490 q^{81} +(-1.19741 + 0.506858i) q^{82} +(4.38372 + 4.38372i) q^{83} +(-0.0508310 - 3.28846i) q^{84} +(-4.48005 + 4.48005i) q^{85} +(6.26091 + 2.53685i) q^{86} +9.87940i q^{87} +(14.5363 - 6.41986i) q^{88} +10.3471i q^{89} +(-0.157125 + 0.387782i) q^{90} +(-1.48922 + 1.48922i) q^{91} +(6.68777 + 6.48417i) q^{92} +(0.0342425 + 0.0342425i) q^{93} +(-6.92073 - 16.3496i) q^{94} +6.80141 q^{95} +(8.72530 + 3.22517i) q^{96} +0.578738 q^{97} +(0.551277 + 1.30234i) q^{98} +(-1.17535 - 1.17535i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 12 q^{4} + 12 q^{6}+O(q^{10}) $ 44 * q + 12 * q^4 + 12 * q^6	$ 44 q + 12 q^{4} + 12 q^{6} - 4 q^{10} + 12 q^{11} - 16 q^{12} + 4 q^{14} + 8 q^{15} - 8 q^{16} - 20 q^{18} + 8 q^{19} - 36 q^{22} + 12 q^{24} + 44 q^{26} - 24 q^{27} - 4 q^{28} + 12 q^{29} - 40 q^{32} - 16 q^{34} + 4 q^{36} + 28 q^{37} - 16 q^{38} + 4 q^{42} - 44 q^{43} - 32 q^{44} - 16 q^{46} - 32 q^{48} - 44 q^{49} + 4 q^{50} - 8 q^{51} + 16 q^{52} - 12 q^{53} - 80 q^{54} + 8 q^{56} + 4 q^{58} + 24 q^{59} - 16 q^{61} + 28 q^{63} + 72 q^{64} - 40 q^{65} - 20 q^{66} - 28 q^{67} + 56 q^{68} + 40 q^{69} + 12 q^{72} + 24 q^{74} - 12 q^{77} + 84 q^{78} - 16 q^{79} + 20 q^{81} + 48 q^{82} + 16 q^{85} - 64 q^{86} + 28 q^{88} - 36 q^{90} - 16 q^{92} + 88 q^{93} + 96 q^{94} - 32 q^{95} + 48 q^{96} + 28 q^{99}+O(q^{100}) $ 44 * q + 12 * q^4 + 12 * q^6 - 4 * q^10 + 12 * q^11 - 16 * q^12 + 4 * q^14 + 8 * q^15 - 8 * q^16 - 20 * q^18 + 8 * q^19 - 36 * q^22 + 12 * q^24 + 44 * q^26 - 24 * q^27 - 4 * q^28 + 12 * q^29 - 40 * q^32 - 16 * q^34 + 4 * q^36 + 28 * q^37 - 16 * q^38 + 4 * q^42 - 44 * q^43 - 32 * q^44 - 16 * q^46 - 32 * q^48 - 44 * q^49 + 4 * q^50 - 8 * q^51 + 16 * q^52 - 12 * q^53 - 80 * q^54 + 8 * q^56 + 4 * q^58 + 24 * q^59 - 16 * q^61 + 28 * q^63 + 72 * q^64 - 40 * q^65 - 20 * q^66 - 28 * q^67 + 56 * q^68 + 40 * q^69 + 12 * q^72 + 24 * q^74 - 12 * q^77 + 84 * q^78 - 16 * q^79 + 20 * q^81 + 48 * q^82 + 16 * q^85 - 64 * q^86 + 28 * q^88 - 36 * q^90 - 16 * q^92 + 88 * q^93 + 96 * q^94 - 32 * q^95 + 48 * q^96 + 28 * 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 $

$2$	−0.551277	−	1.30234i	−0.389812	−	0.920895i
$2$	−0.551277	−	1.30234i	−0.389812	−	0.920895i
$3$	−1.16279	−	1.16279i	−0.671335	−	0.671335i	0.286689	−	0.958024i	$-0.407445\pi$
$3$	−1.16279	−	1.16279i	−0.671335	−	0.671335i	−0.958024	+	0.286689i	$0.907445\pi$
$4$	−1.39219	+	1.43590i	−0.696094	+	0.717951i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	−0.873327	+	2.15536i	−0.356534	+	0.879923i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	2.63752	+	1.02152i	0.932503	+	0.361163i
$9$		−	0.295857i		−	0.0986191i
$10$	−1.31071	−	0.531083i	−0.414482	−	0.167943i
$11$	3.97270	−	3.97270i	1.19781	−	1.19781i	0.222995	−	0.974820i	$-0.428417\pi$
$11$	3.97270	−	3.97270i	1.19781	−	1.19781i	0.974820	−	0.222995i	$-0.0715834\pi$
$12$	3.28846	−	0.0508310i	0.949297	−	0.0146737i
$13$	−1.48922	−	1.48922i	−0.413035	−	0.413035i	0.469759	−	0.882795i	$-0.344341\pi$
$13$	−1.48922	−	1.48922i	−0.413035	−	0.413035i	−0.882795	+	0.469759i	$0.844341\pi$
$14$	−1.30234	+	0.551277i	−0.348065	+	0.147335i
$15$	−1.64443			−0.424589
$16$	−0.123630	−	3.99809i	−0.0309074	−	0.999522i
$17$	−6.33574			−1.53664			−0.768321	−	0.640064i	$-0.778908\pi$
$17$	−6.33574			−1.53664			−0.768321	+	0.640064i	$0.778908\pi$
$18$	−0.385307	+	0.163099i	−0.0908178	+	0.0384429i
$19$	4.80932	+	4.80932i	1.10333	+	1.10333i	0.994006	+	0.109329i	$0.0348701\pi$
$19$	4.80932	+	4.80932i	1.10333	+	1.10333i	0.109329	+	0.994006i	$0.465130\pi$
$20$	0.0309111	+	1.99976i	0.00691193	+	0.447160i
$21$	−1.16279	+	1.16279i	−0.253741	+	0.253741i
$22$	−7.36387	−	2.98376i	−1.56998	−	0.636139i
$23$		−	4.65754i		−	0.971165i	−0.874191	−	0.485582i	$-0.838608\pi$
$23$		−	4.65754i		−	0.971165i	0.874191	−	0.485582i	$-0.161392\pi$
$24$	−1.87905	−	4.25468i	−0.383560	−	0.868483i
$25$		−	1.00000i		−	0.200000i
$26$	−1.11850	+	2.76045i	−0.219356	+	0.541368i
$27$	−3.83238	+	3.83238i	−0.737541	+	0.737541i
$28$	1.43590	+	1.39219i	0.271360	+	0.263099i
$29$	−4.24816	−	4.24816i	−0.788863	−	0.788863i	0.192444	−	0.981308i	$-0.438358\pi$
$29$	−4.24816	−	4.24816i	−0.788863	−	0.788863i	−0.981308	+	0.192444i	$0.938358\pi$
$30$	0.906535	+	2.14161i	0.165510	+	0.391002i
$31$	−0.0294487			−0.00528914			−0.00264457	−	0.999997i	$-0.500842\pi$
$31$	−0.0294487			−0.00528914			−0.00264457	+	0.999997i	$0.500842\pi$
$32$	−5.13872	+	2.36506i	−0.908407	+	0.418088i
$33$	−9.23880			−1.60827
$34$	3.49275	+	8.25130i	0.599001	+	1.41509i
$35$	−0.707107	−	0.707107i	−0.119523	−	0.119523i
$36$	0.424822	+	0.411889i	0.0708037	+	0.0686482i
$37$	−5.73990	+	5.73990i	−0.943634	+	0.943634i	−0.998494	−	0.0548603i	$-0.982529\pi$
$37$	−5.73990	+	5.73990i	−0.943634	+	0.943634i	0.0548603	+	0.998494i	$0.482529\pi$
$38$	3.61211	−	8.91465i	0.585962	−	1.44615i
$39$			3.46329i			0.554570i
$40$	2.58733	−	1.14268i	0.409093	−	0.180673i
$41$		−	0.919426i		−	0.143590i	−0.997419	−	0.0717951i	$-0.977127\pi$
$41$		−	0.919426i		−	0.143590i	0.997419	−	0.0717951i	$-0.0228728\pi$
$42$	2.15536	+	0.873327i	0.332580	+	0.134757i
$43$	−3.37767	+	3.37767i	−0.515090	+	0.515090i	−0.916082	−	0.400992i	$-0.868666\pi$
$43$	−3.37767	+	3.37767i	−0.515090	+	0.515090i	0.400992	+	0.916082i	$0.368666\pi$
$44$	0.173666	+	11.2352i	0.0261812	+	1.69376i
$45$	−0.209203	−	0.209203i	−0.0311861	−	0.0311861i
$46$	−6.06571	+	2.56760i	−0.894340	+	0.378571i
$47$	12.5540			1.83119			0.915594	−	0.402104i	$-0.131721\pi$
$47$	12.5540			1.83119			0.915594	+	0.402104i	$0.131721\pi$
$48$	−4.50517	+	4.79268i	−0.650265	+	0.691763i
$49$	−1.00000			−0.142857
$50$	−1.30234	+	0.551277i	−0.184179	+	0.0779623i
$51$	7.36711	+	7.36711i	1.03160	+	1.03160i
$52$	4.21165	−	0.0651011i	0.584050	−	0.00902789i
$53$	0.0243993	−	0.0243993i	0.00335151	−	0.00335151i	−0.705429	−	0.708781i	$-0.749246\pi$
$53$	0.0243993	−	0.0243993i	0.00335151	−	0.00335151i	0.708781	+	0.705429i	$0.249246\pi$
$54$	7.10377	+	2.87836i	0.966700	+	0.391695i
$55$		−	5.61825i		−	0.757565i
$56$	1.02152	−	2.63752i	0.136507	−	0.352453i
$57$		−	11.1844i		−	1.48141i
$58$	−3.19064	+	7.87447i	−0.418952	+	1.03397i
$59$	−5.91263	+	5.91263i	−0.769759	+	0.769759i	−0.978064	−	0.208305i	$-0.933205\pi$
$59$	−5.91263	+	5.91263i	−0.769759	+	0.769759i	0.208305	+	0.978064i	$0.433205\pi$
$60$	2.28935	−	2.36124i	0.295554	−	0.304834i
$61$	1.34761	+	1.34761i	0.172543	+	0.172543i	0.788096	−	0.615552i	$-0.211067\pi$
$61$	1.34761	+	1.34761i	0.172543	+	0.172543i	−0.615552	+	0.788096i	$0.711067\pi$
$62$	0.0162344	+	0.0383522i	0.00206177	+	0.00487074i
$63$	−0.295857			−0.0372745
$64$	5.91298	+	5.38857i	0.739122	+	0.673571i
$65$	−2.10608			−0.261226
$66$	5.09314	+	12.0321i	0.626922	+	1.48105i
$67$	−9.68994	−	9.68994i	−1.18381	−	1.18381i	−0.978748	−	0.205067i	$-0.934259\pi$
$67$	−9.68994	−	9.68994i	−1.18381	−	1.18381i	−0.205067	−	0.978748i	$-0.565741\pi$
$68$	8.82054	−	9.09750i	1.06965	−	1.10323i
$69$	−5.41572	+	5.41572i	−0.651977	+	0.651977i
$70$	−0.531083	+	1.31071i	−0.0634765	+	0.156659i
$71$		−	11.0515i		−	1.31157i	−0.754948	−	0.655784i	$-0.772338\pi$
$71$		−	11.0515i		−	1.31157i	0.754948	−	0.655784i	$-0.227662\pi$
$72$	0.302225	−	0.780329i	0.0356176	−	0.0919626i
$73$		−	10.5102i		−	1.23012i	−0.788480	−	0.615060i	$-0.789132\pi$
$73$		−	10.5102i		−	1.23012i	0.788480	−	0.615060i	$-0.210868\pi$
$74$	10.6396	+	4.31104i	1.23683	+	0.501148i
$75$	−1.16279	+	1.16279i	−0.134267	+	0.134267i
$76$	−13.6012	+	0.210239i	−1.56016	+	0.0241161i
$77$	−3.97270	−	3.97270i	−0.452731	−	0.452731i
$78$	4.51038	−	1.90923i	0.510700	−	0.216178i
$79$	−4.67417			−0.525885			−0.262943	−	0.964811i	$-0.584693\pi$
$79$	−4.67417			−0.525885			−0.262943	+	0.964811i	$0.584693\pi$
$80$	−2.91450	−	2.73966i	−0.325850	−	0.306303i
$81$	8.02490			0.891655
$82$	−1.19741	+	0.506858i	−0.132231	+	0.0559732i
$83$	4.38372	+	4.38372i	0.481175	+	0.481175i	0.905507	−	0.424331i	$-0.139491\pi$
$83$	4.38372	+	4.38372i	0.481175	+	0.481175i	−0.424331	+	0.905507i	$0.639491\pi$
$84$	−0.0508310	−	3.28846i	−0.00554612	−	0.358801i
$85$	−4.48005	+	4.48005i	−0.485929	+	0.485929i
$86$	6.26091	+	2.53685i	0.675132	+	0.273555i
$87$			9.87940i			1.05918i
$88$	14.5363	−	6.41986i	1.54957	−	0.684359i
$89$			10.3471i			1.09679i	0.836220	+	0.548394i	$0.184761\pi$
$89$			10.3471i			1.09679i	−0.836220	+	0.548394i	$0.815239\pi$
$90$	−0.157125	+	0.387782i	−0.0165624	+	0.0408758i
$91$	−1.48922	+	1.48922i	−0.156113	+	0.156113i
$92$	6.68777	+	6.48417i	0.697249	+	0.676021i
$93$	0.0342425	+	0.0342425i	0.00355078	+	0.00355078i
$94$	−6.92073	−	16.3496i	−0.713819	−	1.68633i
$95$	6.80141			0.697810
$96$	8.72530	+	3.22517i	0.890522	+	0.329168i
$97$	0.578738			0.0587619			0.0293810	−	0.999568i	$-0.490646\pi$
$97$	0.578738			0.0587619			0.0293810	+	0.999568i	$0.490646\pi$
$98$	0.551277	+	1.30234i	0.0556874	+	0.131556i
$99$	−1.17535	−	1.17535i	−0.118127	−	0.118127i
$100$	1.43590	+	1.39219i	0.143590	+	0.139219i
$101$	−1.30170	+	1.30170i	−0.129524	+	0.129524i	−0.768897	−	0.639373i	$-0.779194\pi$
$101$	−1.30170	+	1.30170i	−0.129524	+	0.129524i	0.639373	+	0.768897i	$0.279194\pi$
$102$	5.53318	−	13.6558i	0.547866	−	1.35213i
$103$		−	12.6795i		−	1.24935i	−0.780885	−	0.624675i	$-0.785231\pi$
$103$		−	12.6795i		−	1.24935i	0.780885	−	0.624675i	$-0.214769\pi$
$104$	−2.40657	−	5.44911i	−0.235983	−	0.534330i
$105$			1.64443i			0.160480i
$106$	−0.0452271	−	0.0183255i	−0.00439284	−	0.00177993i
$107$	7.36414	−	7.36414i	0.711919	−	0.711919i	−0.255018	−	0.966936i	$-0.582081\pi$
$107$	7.36414	−	7.36414i	0.711919	−	0.711919i	0.966936	+	0.255018i	$0.0820813\pi$
$108$	−0.167532	−	10.8383i	−0.0161208	−	1.04292i
$109$	−4.86515	−	4.86515i	−0.465997	−	0.465997i	0.434618	−	0.900615i	$-0.356883\pi$
$109$	−4.86515	−	4.86515i	−0.465997	−	0.465997i	−0.900615	+	0.434618i	$0.856883\pi$
$110$	−7.31688	+	3.09721i	−0.697637	+	0.295308i
$111$	13.3486			1.26699
$112$	−3.99809	+	0.123630i	−0.377784	+	0.0116819i
$113$	9.99365			0.940124			0.470062	−	0.882633i	$-0.344232\pi$
$113$	9.99365			0.940124			0.470062	+	0.882633i	$0.344232\pi$
$114$	−14.5659	+	6.16572i	−1.36423	+	0.577472i
$115$	−3.29338	−	3.29338i	−0.307109	−	0.307109i
$116$	12.0142	−	0.185708i	1.11549	−	0.0172425i
$117$	−0.440597	+	0.440597i	−0.0407332	+	0.0407332i
$118$	10.9598	+	4.44077i	1.00893	+	0.408806i
$119$			6.33574i			0.580796i
$120$	−4.33720	−	1.67982i	−0.395931	−	0.153346i
$121$		−	20.5647i		−	1.86952i
$122$	1.01214	−	2.49795i	0.0916348	−	0.226154i
$123$	−1.06910	+	1.06910i	−0.0963971	+	0.0963971i
$124$	0.0409981	−	0.0422854i	0.00368173	−	0.00379734i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	0.163099	+	0.385307i	0.0145301	+	0.0343259i
$127$	2.74622			0.243687			0.121844	−	0.992549i	$-0.461119\pi$
$127$	2.74622			0.243687			0.121844	+	0.992549i	$0.461119\pi$
$128$	3.75807	−	10.6713i	0.332169	−	0.943220i
$129$	7.85502			0.691596
$130$	1.16103	+	2.74283i	0.101829	+	0.240562i
$131$	5.19885	+	5.19885i	0.454226	+	0.454226i	0.896754	−	0.442529i	$-0.145919\pi$
$131$	5.19885	+	5.19885i	0.454226	+	0.454226i	−0.442529	+	0.896754i	$0.645919\pi$
$132$	12.8621	−	13.2660i	1.11951	−	1.15466i
$133$	4.80932	−	4.80932i	0.417021	−	0.417021i
$134$	−7.27777	+	17.9615i	−0.628704	+	1.55163i
$135$			5.41980i			0.466462i
$136$	−16.7106	−	6.47211i	−1.43292	−	0.554979i
$137$			12.8527i			1.09808i	0.835796	+	0.549041i	$0.185007\pi$
$137$			12.8527i			1.09808i	−0.835796	+	0.549041i	$0.814993\pi$
$138$	10.0387	+	4.06756i	0.854550	+	0.346254i
$139$	3.68042	−	3.68042i	0.312169	−	0.312169i	−0.533580	−	0.845749i	$-0.679154\pi$
$139$	3.68042	−	3.68042i	0.312169	−	0.312169i	0.845749	+	0.533580i	$0.179154\pi$
$140$	1.99976	−	0.0309111i	0.169011	−	0.00261246i
$141$	−14.5976	−	14.5976i	−1.22934	−	1.22934i
$142$	−14.3928	+	6.09242i	−1.20782	+	0.511265i
$143$	−11.8325			−0.989480
$144$	−1.18286	+	0.0365767i	−0.0985720	+	0.00304806i
$145$	−6.00781			−0.498921
$146$	−13.6878	+	5.79401i	−1.13281	+	0.479516i
$147$	1.16279	+	1.16279i	0.0959050	+	0.0959050i
$148$	−0.250919	−	16.2329i	−0.0206254	−	1.33434i
$149$	5.25342	−	5.25342i	0.430377	−	0.430377i	−0.458380	−	0.888756i	$-0.651570\pi$
$149$	5.25342	−	5.25342i	0.430377	−	0.430377i	0.888756	+	0.458380i	$0.151570\pi$
$150$	2.15536	+	0.873327i	0.175985	+	0.0713069i
$151$		−	17.1127i		−	1.39261i	−0.717745	−	0.696306i	$-0.754826\pi$
$151$		−	17.1127i		−	1.39261i	0.717745	−	0.696306i	$-0.245174\pi$
$152$	7.77183	+	17.5975i	0.630379	+	1.42735i
$153$			1.87448i			0.151542i
$154$	−2.98376	+	7.36387i	−0.240438	+	0.593398i
$155$	−0.0208234	+	0.0208234i	−0.00167257	+	0.00167257i
$156$	−4.97294	−	4.82155i	−0.398154	−	0.386033i
$157$	9.91207	+	9.91207i	0.791069	+	0.791069i	0.981668	−	0.190599i	$-0.0610430\pi$
$157$	9.91207	+	9.91207i	0.791069	+	0.791069i	−0.190599	+	0.981668i	$0.561043\pi$
$158$	2.57676	+	6.08737i	0.204996	+	0.484285i
$159$	−0.0567424			−0.00449997
$160$	−1.96127	+	5.30598i	−0.155052	+	0.419474i
$161$	−4.65754			−0.367066
$162$	−4.42394	−	10.4512i	−0.347578	−	0.821120i
$163$	16.7175	+	16.7175i	1.30942	+	1.30942i	0.921836	+	0.387580i	$0.126689\pi$
$163$	16.7175	+	16.7175i	1.30942	+	1.30942i	0.387580	+	0.921836i	$0.373311\pi$
$164$	1.32021	+	1.28001i	0.103091	+	0.0999522i
$165$	−6.53282	+	6.53282i	−0.508579	+	0.508579i
$166$	3.29245	−	8.12574i	0.255544	−	0.630680i
$167$		−	20.9113i		−	1.61817i	−0.587695	−	0.809083i	$-0.699964\pi$
$167$		−	20.9113i		−	1.61817i	0.587695	−	0.809083i	$-0.300036\pi$
$168$	−4.25468	+	1.87905i	−0.328256	+	0.144972i
$169$		−	8.56445i		−	0.658804i
$170$	8.30430	+	3.36480i	0.636910	+	0.258069i
$171$	1.42287	−	1.42287i	0.108810	−	0.108810i
$172$	−0.147654	−	9.55236i	−0.0112585	−	0.728360i
$173$	−2.68169	−	2.68169i	−0.203885	−	0.203885i	0.597777	−	0.801662i	$-0.296051\pi$
$173$	−2.68169	−	2.68169i	−0.203885	−	0.203885i	−0.801662	+	0.597777i	$0.796051\pi$
$174$	12.8664	−	5.44629i	0.975396	−	0.412882i
$175$	−1.00000			−0.0755929
$176$	−16.3744	−	15.3921i	−1.23426	−	1.16022i
$177$	13.7502			1.03353
$178$	13.4754	−	5.70411i	1.01003	−	0.427541i
$179$	8.19420	+	8.19420i	0.612464	+	0.612464i	0.943587	−	0.331124i	$-0.107428\pi$
$179$	8.19420	+	8.19420i	0.612464	+	0.612464i	−0.331124	+	0.943587i	$0.607428\pi$
$180$	0.591644	−	0.00914527i	0.0440986	−	0.000681649i
$181$	6.86243	−	6.86243i	0.510080	−	0.510080i	−0.404471	−	0.914551i	$-0.632544\pi$
$181$	6.86243	−	6.86243i	0.510080	−	0.510080i	0.914551	+	0.404471i	$0.132544\pi$
$182$	2.76045	+	1.11850i	0.204618	+	0.0829088i
$183$		−	3.13396i		−	0.231669i
$184$	4.75779	−	12.2843i	0.350749	−	0.905614i
$185$			8.11744i			0.596806i
$186$	0.0257183	−	0.0634725i	0.00188576	−	0.00465403i
$187$	−25.1700	+	25.1700i	−1.84061	+	1.84061i
$188$	−17.4775	+	18.0263i	−1.27468	+	1.31470i
$189$	3.83238	+	3.83238i	0.278764	+	0.278764i
$190$	−3.74946	−	8.85776i	−0.272015	−	0.642609i
$191$	13.7694			0.996319			0.498159	−	0.867085i	$-0.334009\pi$
$191$	13.7694			0.996319			0.498159	+	0.867085i	$0.334009\pi$
$192$	−0.609778	−	13.1413i	−0.0440070	−	0.948390i
$193$	−12.6996			−0.914140			−0.457070	−	0.889431i	$-0.651101\pi$
$193$	−12.6996			−0.914140			−0.457070	+	0.889431i	$0.651101\pi$
$194$	−0.319045	−	0.753714i	−0.0229061	−	0.0541135i
$195$	2.44891	+	2.44891i	0.175370	+	0.175370i
$196$	1.39219	−	1.43590i	0.0994419	−	0.102564i
$197$	18.9643	−	18.9643i	1.35115	−	1.35115i	0.466768	−	0.884380i	$-0.345418\pi$
$197$	18.9643	−	18.9643i	1.35115	−	1.35115i	0.884380	−	0.466768i	$-0.154582\pi$
$198$	−0.882766	+	2.17866i	−0.0627355	+	0.154830i
$199$			15.7513i			1.11658i	0.829645	+	0.558291i	$0.188543\pi$
$199$			15.7513i			1.11658i	−0.829645	+	0.558291i	$0.811457\pi$
$200$	1.02152	−	2.63752i	0.0722326	−	0.186501i
$201$			22.5347i			1.58947i
$202$	2.41286	+	0.977662i	0.169768	+	0.0687880i
$203$	−4.24816	+	4.24816i	−0.298162	+	0.298162i
$204$	−20.8348	+	0.322052i	−1.45873	+	0.0225482i
$205$	−0.650132	−	0.650132i	−0.0454072	−	0.0454072i
$206$	−16.5131	+	6.98993i	−1.15052	+	0.487012i
$207$	−1.37797			−0.0957754
$208$	−5.76992	+	6.13815i	−0.400072	+	0.425604i
$209$	38.2120			2.64318
$210$	2.14161	−	0.906535i	0.147785	−	0.0625569i
$211$	17.8595	+	17.8595i	1.22950	+	1.22950i	0.964155	+	0.265341i	$0.0854846\pi$
$211$	17.8595	+	17.8595i	1.22950	+	1.22950i	0.265341	+	0.964155i	$0.414515\pi$
$212$	0.00106661	+	0.0690035i	7.32553e−5	+	0.00473918i
$213$	−12.8505	+	12.8505i	−0.880502	+	0.880502i
$214$	−13.6503	−	5.53095i	−0.933116	−	0.378088i
$215$			4.77675i			0.325772i
$216$	−14.0228	+	6.19309i	−0.954132	+	0.421387i
$217$			0.0294487i			0.00199911i
$218$	−3.65404	+	9.01813i	−0.247483	+	0.610785i
$219$	−12.2211	+	12.2211i	−0.825823	+	0.825823i
$220$	8.06726	+	7.82165i	0.543894	+	0.527336i
$221$	9.43531	+	9.43531i	0.634688	+	0.634688i
$222$	−7.35875	−	17.3844i	−0.493887	−	1.16676i
$223$	−13.5902			−0.910070			−0.455035	−	0.890473i	$-0.650373\pi$
$223$	−13.5902			−0.910070			−0.455035	+	0.890473i	$0.650373\pi$
$224$	2.36506	+	5.13872i	0.158022	+	0.343345i
$225$	−0.295857			−0.0197238
$226$	−5.50927	−	13.0151i	−0.366471	−	0.865755i
$227$	7.80140	+	7.80140i	0.517797	+	0.517797i	0.916904	−	0.399107i	$-0.130680\pi$
$227$	7.80140	+	7.80140i	0.517797	+	0.517797i	−0.399107	+	0.916904i	$0.630680\pi$
$228$	16.0597	+	15.5708i	1.06358	+	1.03120i
$229$	−10.9217	+	10.9217i	−0.721728	+	0.721728i	−0.968957	−	0.247229i	$-0.920480\pi$
$229$	−10.9217	+	10.9217i	−0.721728	+	0.721728i	0.247229	+	0.968957i	$0.420480\pi$
$230$	−2.47354	+	6.10467i	−0.163100	+	0.402530i
$231$			9.23880i			0.607869i
$232$	−6.86499	−	15.5442i	−0.450709	−	1.02053i
$233$		−	3.44271i		−	0.225539i	−0.993621	−	0.112770i	$-0.964028\pi$
$233$		−	3.44271i		−	0.225539i	0.993621	−	0.112770i	$-0.0359722\pi$
$234$	0.816698	+	0.330917i	0.0533892	+	0.0216327i
$235$	8.87701	−	8.87701i	0.579072	−	0.579072i
$236$	−0.258470	−	16.7214i	−0.0168250	−	1.08847i
$237$	5.43506	+	5.43506i	0.353045	+	0.353045i
$238$	8.25130	−	3.49275i	0.534852	−	0.226401i
$239$	−5.82823			−0.376997			−0.188498	−	0.982073i	$-0.560362\pi$
$239$	−5.82823			−0.376997			−0.188498	+	0.982073i	$0.560362\pi$
$240$	0.203300	+	6.57457i	0.0131230	+	0.424387i
$241$	−9.14801			−0.589275			−0.294637	−	0.955609i	$-0.595199\pi$
$241$	−9.14801			−0.589275			−0.294637	+	0.955609i	$0.595199\pi$
$242$	−26.7823	+	11.3369i	−1.72163	+	0.728761i
$243$	2.16589	+	2.16589i	0.138942	+	0.138942i
$244$	−3.81115	+	0.0589105i	−0.243984	+	0.00377136i
$245$	−0.707107	+	0.707107i	−0.0451754	+	0.0451754i
$246$	1.98170	+	0.802960i	0.126348	+	0.0511948i
$247$		−	14.3243i		−	0.911432i
$248$	−0.0776713	−	0.0300825i	−0.00493213	−	0.00191024i
$249$		−	10.1946i		−	0.646060i
$250$	−0.531083	+	1.31071i	−0.0335886	+	0.0828963i
$251$	2.71270	−	2.71270i	0.171224	−	0.171224i	−0.616293	−	0.787517i	$-0.711366\pi$
$251$	2.71270	−	2.71270i	0.171224	−	0.171224i	0.787517	+	0.616293i	$0.211366\pi$
$252$	0.411889	−	0.424822i	0.0259466	−	0.0267613i
$253$	−18.5030	−	18.5030i	−1.16328	−	1.16328i
$254$	−1.51393	−	3.57651i	−0.0949922	−	0.224410i
$255$	10.4187			0.652442
$256$	−15.9694	+	0.988564i	−0.998089	+	0.0617853i
$257$	20.6688			1.28929			0.644643	−	0.764484i	$-0.277006\pi$
$257$	20.6688			1.28929			0.644643	+	0.764484i	$0.277006\pi$
$258$	−4.33029	−	10.2299i	−0.269592	−	0.636887i
$259$	5.73990	+	5.73990i	0.356660	+	0.356660i
$260$	2.93205	−	3.02412i	0.181838	−	0.187548i
$261$	−1.25685	+	1.25685i	−0.0777970	+	0.0777970i
$262$	3.90467	−	9.63668i	0.241231	−	0.595356i
$263$			0.726418i			0.0447929i	0.999749	+	0.0223964i	$0.00712960\pi$
$263$			0.726418i			0.0447929i	−0.999749	+	0.0223964i	$0.992870\pi$
$264$	−24.3675	−	9.43765i	−1.49972	−	0.580847i
$265$		−	0.0345059i		−	0.00211968i
$266$	−8.91465	−	3.61211i	−0.546592	−	0.221473i
$267$	12.0314	−	12.0314i	0.736312	−	0.736312i
$268$	27.4040	−	0.423595i	1.67397	−	0.0258752i
$269$	−21.3362	−	21.3362i	−1.30089	−	1.30089i	−0.927792	−	0.373098i	$-0.878296\pi$
$269$	−21.3362	−	21.3362i	−1.30089	−	1.30089i	−0.373098	−	0.927792i	$-0.621704\pi$
$270$	7.05843	−	2.98781i	0.429562	−	0.181832i
$271$	12.5537			0.762580			0.381290	−	0.924455i	$-0.375480\pi$
$271$	12.5537			0.762580			0.381290	+	0.924455i	$0.375480\pi$
$272$	0.783285	+	25.3309i	0.0474936	+	1.53591i
$273$	3.46329			0.209608
$274$	16.7386	−	7.08540i	1.01122	−	0.428045i
$275$	−3.97270	−	3.97270i	−0.239563	−	0.239563i
$276$	−0.236748	−	15.3162i	−0.0142505	−	0.921924i
$277$	−12.8485	+	12.8485i	−0.771994	+	0.771994i	−0.978455	−	0.206461i	$-0.933805\pi$
$277$	−12.8485	+	12.8485i	−0.771994	+	0.771994i	0.206461	+	0.978455i	$0.433805\pi$
$278$	−6.82210	−	2.76423i	−0.409162	−	0.165788i
$279$			0.00871261i			0.000521610i
$280$	−1.14268	−	2.58733i	−0.0682881	−	0.154623i
$281$			11.9678i			0.713941i	0.934116	+	0.356970i	$0.116190\pi$
$281$			11.9678i			0.713941i	−0.934116	+	0.356970i	$0.883810\pi$
$282$	−10.9637	+	27.0584i	−0.652881	+	1.61130i
$283$	−9.50022	+	9.50022i	−0.564730	+	0.564730i	−0.930647	−	0.365918i	$-0.880755\pi$
$283$	−9.50022	+	9.50022i	−0.564730	+	0.564730i	0.365918	+	0.930647i	$0.380755\pi$
$284$	15.8688	+	15.3857i	0.941642	+	0.912975i
$285$	−7.90858	−	7.90858i	−0.468464	−	0.468464i
$286$	6.52296	+	15.4099i	0.385711	+	0.911206i
$287$	−0.919426			−0.0542720
$288$	0.699721	+	1.52033i	0.0412315	+	0.0895863i
$289$	23.1416			1.36127
$290$	3.31197	+	7.82421i	0.194485	+	0.459454i
$291$	−0.672948	−	0.672948i	−0.0394489	−	0.0394489i
$292$	15.0916	+	14.6321i	0.883166	+	0.856279i
$293$	−8.77462	+	8.77462i	−0.512619	+	0.512619i	−0.915328	−	0.402709i	$-0.868069\pi$
$293$	−8.77462	+	8.77462i	−0.512619	+	0.512619i	0.402709	+	0.915328i	$0.368069\pi$
$294$	0.873327	−	2.15536i	0.0509335	−	0.125703i
$295$			8.36172i			0.486838i
$296$	−21.0025	+	9.27563i	−1.22075	+	0.539135i
$297$			30.4498i			1.76688i
$298$	−9.73783	−	3.94565i	−0.564097	−	0.228566i
$299$	−6.93610	+	6.93610i	−0.401125	+	0.401125i
$300$	−0.0508310	−	3.28846i	−0.00293473	−	0.189859i
$301$	3.37767	+	3.37767i	0.194686	+	0.194686i
$302$	−22.2866	+	9.43384i	−1.28245	+	0.542856i
$303$	3.02720			0.173908
$304$	18.6335	−	19.8227i	1.06871	−	1.13691i
$305$	1.90580			0.109126
$306$	2.44121	−	1.03336i	0.139555	−	0.0590730i
$307$	−4.72956	−	4.72956i	−0.269930	−	0.269930i	0.559142	−	0.829072i	$-0.311131\pi$
$307$	−4.72956	−	4.72956i	−0.269930	−	0.269930i	−0.829072	+	0.559142i	$0.811131\pi$
$308$	11.2352	−	0.173666i	0.640182	−	0.00989555i
$309$	−14.7436	+	14.7436i	−0.838733	+	0.838733i
$310$	0.0385986	+	0.0156397i	0.00219225	+	0.000888274i
$311$		−	18.2568i		−	1.03525i	−0.855608	−	0.517625i	$-0.826816\pi$
$311$		−	18.2568i		−	1.03525i	0.855608	−	0.517625i	$-0.173184\pi$
$312$	−3.53783	+	9.13448i	−0.200290	+	0.517138i
$313$			1.15335i			0.0651914i	0.999469	+	0.0325957i	$0.0103774\pi$
$313$			1.15335i			0.0651914i	−0.999469	+	0.0325957i	$0.989623\pi$
$314$	7.44460	−	18.3732i	0.420123	−	1.03686i
$315$	−0.209203	+	0.209203i	−0.0117872	+	0.0117872i
$316$	6.50732	−	6.71165i	0.366065	−	0.377560i
$317$	8.28593	+	8.28593i	0.465384	+	0.465384i	0.900415	−	0.435031i	$-0.143263\pi$
$317$	8.28593	+	8.28593i	0.465384	+	0.465384i	−0.435031	+	0.900415i	$0.643263\pi$
$318$	0.0312808	+	0.0738980i	0.00175414	+	0.00414399i
$319$	−33.7533			−1.88982
$320$	7.99140	−	0.370815i	0.446733	−	0.0207292i
$321$	−17.1258			−0.955872
$322$	2.56760	+	6.06571i	0.143087	+	0.338029i
$323$	−30.4706	−	30.4706i	−1.69543	−	1.69543i
$324$	−11.1722	+	11.5230i	−0.620675	+	0.640165i
$325$	−1.48922	+	1.48922i	−0.0826071	+	0.0826071i
$326$	12.5559	−	30.9879i	0.695409	−	1.71626i
$327$			11.3142i			0.625679i
$328$	0.939215	−	2.42500i	0.0518595	−	0.133898i
$329$		−	12.5540i		−	0.692124i
$330$	12.1094	+	4.90657i	0.666598	+	0.270098i
$331$	10.4064	−	10.4064i	0.571989	−	0.571989i	−0.360695	−	0.932684i	$-0.617460\pi$
$331$	10.4064	−	10.4064i	0.571989	−	0.571989i	0.932684	+	0.360695i	$0.117460\pi$
$332$	−12.3975	+	0.191634i	−0.680404	+	0.0105173i
$333$	1.69819	+	1.69819i	0.0930603	+	0.0930603i
$334$	−27.2337	+	11.5279i	−1.49016	+	0.630780i
$335$	−13.7036			−0.748710
$336$	4.79268	+	4.50517i	0.261462	+	0.245777i
$337$	12.3663			0.673637			0.336819	−	0.941570i	$-0.390649\pi$
$337$	12.3663			0.673637			0.336819	+	0.941570i	$0.390649\pi$
$338$	−11.1538	+	4.72138i	−0.606689	+	0.256809i
$339$	−11.6205	−	11.6205i	−0.631138	−	0.631138i
$340$	−0.195845	−	12.6700i	−0.0106212	−	0.687125i
$341$	−0.116991	+	0.116991i	−0.00633541	+	0.00633541i
$342$	−2.63747	−	1.06867i	−0.142618	−	0.0577871i
$343$			1.00000i			0.0539949i
$344$	−12.3590	+	5.45829i	−0.666354	+	0.294291i
$345$			7.65899i			0.412346i
$346$	−2.01412	+	4.97082i	−0.108280	+	0.267233i
$347$	11.8205	−	11.8205i	0.634556	−	0.634556i	−0.314651	−	0.949207i	$-0.601887\pi$
$347$	11.8205	−	11.8205i	0.634556	−	0.634556i	0.949207	+	0.314651i	$0.101887\pi$
$348$	−14.1859	−	13.7540i	−0.760442	−	0.737291i
$349$	6.12765	+	6.12765i	0.328006	+	0.328006i	0.851828	−	0.523822i	$-0.175494\pi$
$349$	6.12765	+	6.12765i	0.328006	+	0.328006i	−0.523822	+	0.851828i	$0.675494\pi$
$350$	0.551277	+	1.30234i	0.0294670	+	0.0696131i
$351$	11.4145			0.609261
$352$	−11.0189	+	29.8103i	−0.587311	+	1.58889i
$353$	13.4244			0.714510			0.357255	−	0.934007i	$-0.383713\pi$
$353$	13.4244			0.714510			0.357255	+	0.934007i	$0.383713\pi$
$354$	−7.58020	−	17.9075i	−0.402883	−	0.951774i
$355$	−7.81457	−	7.81457i	−0.414754	−	0.414754i
$356$	−14.8574	−	14.4051i	−0.787440	−	0.763467i
$357$	7.36711	−	7.36711i	0.389909	−	0.389909i
$358$	6.15438	−	15.1889i	0.325269	−	0.802760i
$359$		−	10.4387i		−	0.550934i	−0.961310	−	0.275467i	$-0.911167\pi$
$359$		−	10.4387i		−	0.550934i	0.961310	−	0.275467i	$-0.0888325\pi$
$360$	−0.338070	−	0.765481i	−0.0178179	−	0.0403444i
$361$			27.2592i			1.43469i
$362$	−12.7203	−	5.15412i	−0.668565	−	0.270895i
$363$	−23.9124	+	23.9124i	−1.25507	+	1.25507i
$364$	−0.0651011	−	4.21165i	−0.00341222	−	0.220750i
$365$	−7.43180	−	7.43180i	−0.388998	−	0.388998i
$366$	−4.08148	+	1.72768i	−0.213343	+	0.0903072i
$367$	−9.04263			−0.472022			−0.236011	−	0.971750i	$-0.575840\pi$
$367$	−9.04263			−0.472022			−0.236011	+	0.971750i	$0.575840\pi$
$368$	−18.6213	+	0.575810i	−0.970701	+	0.0300162i
$369$	−0.272019			−0.0141607
$370$	10.5717	−	4.47496i	0.549596	−	0.232642i
$371$	−0.0243993	−	0.0243993i	−0.00126675	−	0.00126675i
$372$	−0.0968408	+	0.00149691i	−0.00502096	+	7.76110e-5i
$373$	23.2031	−	23.2031i	1.20141	−	1.20141i	0.227673	−	0.973738i	$-0.426888\pi$
$373$	23.2031	−	23.2031i	1.20141	−	1.20141i	0.973738	−	0.227673i	$-0.0731119\pi$
$374$	46.6556	+	18.9043i	2.41250	+	0.977518i
$375$			1.64443i			0.0849179i
$376$	33.1114	+	12.8242i	1.70759	+	0.661357i
$377$			12.6529i			0.651657i
$378$	2.87836	−	7.10377i	0.148047	−	0.365378i
$379$	14.5814	−	14.5814i	0.748998	−	0.748998i	−0.225293	−	0.974291i	$-0.572334\pi$
$379$	14.5814	−	14.5814i	0.748998	−	0.748998i	0.974291	+	0.225293i	$0.0723340\pi$
$380$	−9.46884	+	9.76616i	−0.485741	+	0.500993i
$381$	−3.19326	−	3.19326i	−0.163596	−	0.163596i
$382$	−7.59075	−	17.9325i	−0.388377	−	0.917505i
$383$	−11.5921			−0.592331			−0.296165	−	0.955137i	$-0.595708\pi$
$383$	−11.5921			−0.592331			−0.296165	+	0.955137i	$0.595708\pi$
$384$	−16.7783	+	8.03863i	−0.856213	+	0.410219i
$385$	−5.61825			−0.286332
$386$	7.00102	+	16.5393i	0.356343	+	0.841827i
$387$	0.999309	+	0.999309i	0.0507977	+	0.0507977i
$388$	−0.805711	+	0.831011i	−0.0409038	+	0.0421882i
$389$	−12.4619	+	12.4619i	−0.631845	+	0.631845i	−0.948530	−	0.316686i	$-0.897430\pi$
$389$	−12.4619	+	12.4619i	−0.631845	+	0.631845i	0.316686	+	0.948530i	$0.397430\pi$
$390$	1.83929	−	4.53935i	0.0931362	−	0.229859i
$391$			29.5090i			1.49233i
$392$	−2.63752	−	1.02152i	−0.133215	−	0.0515947i
$393$		−	12.0903i		−	0.609875i
$394$	−35.1525	−	14.2434i	−1.77096	−	0.717571i
$395$	−3.30514	+	3.30514i	−0.166300	+	0.166300i
$396$	3.32400	−	0.0513804i	0.167037	−	0.00258196i
$397$	−21.1537	−	21.1537i	−1.06168	−	1.06168i	−0.997969	−	0.0637068i	$-0.979708\pi$
$397$	−21.1537	−	21.1537i	−1.06168	−	1.06168i	−0.0637068	−	0.997969i	$-0.520292\pi$
$398$	20.5136	−	8.68334i	1.02825	−	0.435257i
$399$	−11.1844			−0.559922
$400$	−3.99809	+	0.123630i	−0.199904	+	0.00618148i
$401$	−17.7733			−0.887554			−0.443777	−	0.896137i	$-0.646362\pi$
$401$	−17.7733			−0.887554			−0.443777	+	0.896137i	$0.646362\pi$
$402$	29.3478	−	12.4228i	1.46374	−	0.619595i
$403$	0.0438555	+	0.0438555i	0.00218460	+	0.00218460i
$404$	−0.0569037	−	3.68133i	−0.00283107	−	0.183153i
$405$	5.67446	−	5.67446i	0.281966	−	0.281966i
$406$	7.87447	+	3.19064i	0.390803	+	0.158349i
$407$			45.6058i			2.26060i
$408$	11.9052	+	26.9565i	0.589395	+	1.33455i
$409$		−	28.5404i		−	1.41123i	−0.708594	−	0.705616i	$-0.750670\pi$
$409$		−	28.5404i		−	1.41123i	0.708594	−	0.705616i	$-0.249330\pi$
$410$	−0.488291	+	1.20510i	−0.0241150	+	0.0595155i
$411$	14.9450	−	14.9450i	0.737180	−	0.737180i
$412$	18.2066	+	17.6523i	0.896973	+	0.869665i
$413$	5.91263	+	5.91263i	0.290941	+	0.290941i
$414$	0.759642	+	1.79459i	0.0373344	+	0.0881991i
$415$	6.19951			0.304322
$416$	11.1748	+	4.13059i	0.547889	+	0.202519i
$417$	−8.55908			−0.419140
$418$	−21.0654	−	49.7651i	−1.03034	−	2.43409i
$419$	4.72914	+	4.72914i	0.231034	+	0.231034i	0.813124	−	0.582090i	$-0.197765\pi$
$419$	4.72914	+	4.72914i	0.231034	+	0.231034i	−0.582090	+	0.813124i	$0.697765\pi$
$420$	−2.36124	−	2.28935i	−0.115217	−	0.111709i
$421$	−17.0941	+	17.0941i	−0.833115	+	0.833115i	−0.987942	−	0.154827i	$-0.950518\pi$
$421$	−17.0941	+	17.0941i	−0.833115	+	0.833115i	0.154827	+	0.987942i	$0.450518\pi$
$422$	13.4136	−	33.1046i	0.652964	−	1.61151i
$423$		−	3.71419i		−	0.180590i
$424$	0.0892781	−	0.0394291i	0.00433573	−	0.00191485i
$425$			6.33574i			0.307329i
$426$	23.8199	+	9.65155i	1.15408	+	0.467619i
$427$	1.34761	−	1.34761i	0.0652153	−	0.0652153i
$428$	0.321923	+	20.8265i	0.0155607	+	1.00668i
$429$	13.7586	+	13.7586i	0.664272	+	0.664272i
$430$	6.22096	−	2.63331i	0.300001	−	0.126990i
$431$	2.55164			0.122908			0.0614541	−	0.998110i	$-0.480426\pi$
$431$	2.55164			0.122908			0.0614541	+	0.998110i	$0.480426\pi$
$432$	15.7960	+	14.8484i	0.759984	+	0.714393i
$433$	7.58358			0.364444			0.182222	−	0.983257i	$-0.441671\pi$
$433$	7.58358			0.364444			0.182222	+	0.983257i	$0.441671\pi$
$434$	0.0383522	−	0.0162344i	0.00184097	−	0.000779275i
$435$	6.98579	+	6.98579i	0.334943	+	0.334943i
$436$	13.7591	−	0.212679i	0.658940	−	0.0101855i
$437$	22.3996	−	22.3996i	1.07152	−	1.07152i
$438$	22.6532	+	9.17881i	1.08241	+	0.438580i
$439$		−	36.9647i		−	1.76423i	−0.471036	−	0.882114i	$-0.656120\pi$
$439$		−	36.9647i		−	1.76423i	0.471036	−	0.882114i	$-0.343880\pi$
$440$	5.73917	−	14.8182i	0.273604	−	0.706431i
$441$			0.295857i			0.0140884i
$442$	7.08653	−	17.4895i	0.337072	−	0.831889i
$443$	19.2301	−	19.2301i	0.913652	−	0.913652i	−0.0829058	−	0.996557i	$-0.526420\pi$
$443$	19.2301	−	19.2301i	0.913652	−	0.913652i	0.996557	+	0.0829058i	$0.0264201\pi$
$444$	−18.5837	+	19.1672i	−0.881942	+	0.909636i
$445$	7.31649	+	7.31649i	0.346835	+	0.346835i
$446$	7.49199	+	17.6991i	0.354756	+	0.838079i
$447$	−12.2172			−0.577854
$448$	5.38857	−	5.91298i	0.254586	−	0.279362i
$449$	25.1219			1.18557			0.592787	−	0.805359i	$-0.298028\pi$
$449$	25.1219			1.18557			0.592787	+	0.805359i	$0.298028\pi$
$450$	0.163099	+	0.385307i	0.00768858	+	0.0181636i
$451$	−3.65261	−	3.65261i	−0.171994	−	0.171994i
$452$	−13.9130	+	14.3499i	−0.654414	+	0.674963i
$453$	−19.8984	+	19.8984i	−0.934909	+	0.934909i
$454$	5.85935	−	14.4608i	0.274993	−	0.678680i
$455$			2.10608i			0.0987343i
$456$	11.4252	−	29.4991i	0.535032	−	1.38142i
$457$		−	16.1744i		−	0.756605i	−0.925682	−	0.378302i	$-0.876508\pi$
$457$		−	16.1744i		−	0.756605i	0.925682	−	0.378302i	$-0.123492\pi$
$458$	20.2447	+	8.20292i	0.945974	+	0.383297i
$459$	24.2809	−	24.2809i	1.13334	−	1.13334i
$460$	9.31397	−	0.143970i	0.434266	−	0.00671262i
$461$	6.33074	+	6.33074i	0.294852	+	0.294852i	0.838993	−	0.544142i	$-0.183145\pi$
$461$	6.33074	+	6.33074i	0.294852	+	0.294852i	−0.544142	+	0.838993i	$0.683145\pi$
$462$	12.0321	−	5.09314i	0.559783	−	0.236954i
$463$	12.3492			0.573917			0.286959	−	0.957943i	$-0.407356\pi$
$463$	12.3492			0.573917			0.286959	+	0.957943i	$0.407356\pi$
$464$	−16.4593	+	17.5097i	−0.764105	+	0.812868i
$465$	0.0484262			0.00224571
$466$	−4.48358	+	1.89789i	−0.207698	+	0.0879179i
$467$	−4.79813	−	4.79813i	−0.222031	−	0.222031i	0.587322	−	0.809353i	$-0.300182\pi$
$467$	−4.79813	−	4.79813i	−0.222031	−	0.222031i	−0.809353	+	0.587322i	$0.800182\pi$
$468$	−0.0192606	−	1.24605i	−0.000890323	−	0.0575985i
$469$	−9.68994	+	9.68994i	−0.447440	+	0.447440i
$470$	−16.4546	−	6.66721i	−0.758994	−	0.307535i
$471$		−	23.0512i		−	1.06214i
$472$	−21.6345	+	9.55477i	−0.995811	+	0.439794i
$473$			26.8370i			1.23396i
$474$	4.08208	−	10.0745i	0.187496	−	0.462739i
$475$	4.80932	−	4.80932i	0.220667	−	0.220667i
$476$	−9.09750	−	8.82054i	−0.416983	−	0.404289i
$477$	−0.00721872	−	0.00721872i	−0.000330523	−	0.000330523i
$478$	3.21297	+	7.59035i	0.146958	+	0.347174i
$479$	23.0029			1.05103			0.525514	−	0.850785i	$-0.323873\pi$
$479$	23.0029			1.05103			0.525514	+	0.850785i	$0.323873\pi$
$480$	8.45026	−	3.88917i	0.385700	−	0.177516i
$481$	17.0959			0.779508
$482$	5.04309	+	11.9138i	0.229706	+	0.542660i
$483$	5.41572	+	5.41572i	0.246424	+	0.246424i
$484$	29.5289	+	28.6299i	1.34222	+	1.30136i
$485$	0.409229	−	0.409229i	0.0185822	−	0.0185822i
$486$	1.62673	−	4.01474i	0.0737898	−	0.182112i
$487$		−	1.90977i		−	0.0865399i	−0.999063	−	0.0432700i	$-0.986222\pi$
$487$		−	1.90977i		−	0.0865399i	0.999063	−	0.0432700i	$-0.0137776\pi$
$488$	2.17772	+	4.93095i	0.0985809	+	0.223214i
$489$		−	38.8778i		−	1.75811i
$490$	1.31071	+	0.531083i	0.0592117	+	0.0239919i
$491$	−10.8069	+	10.8069i	−0.487710	+	0.487710i	−0.907583	−	0.419873i	$-0.862075\pi$
$491$	−10.8069	+	10.8069i	−0.487710	+	0.487710i	0.419873	+	0.907583i	$0.362075\pi$
$492$	−0.0467354	−	3.02350i	−0.00210699	−	0.136310i
$493$	26.9152	+	26.9152i	1.21220	+	1.21220i
$494$	−18.6551	+	7.89665i	−0.839333	+	0.355287i
$495$	−1.66220			−0.0747104
$496$	0.00364073	+	0.117738i	0.000163473	+	0.00528661i
$497$	−11.0515			−0.495726
$498$	−13.2769	+	5.62008i	−0.594953	+	0.251842i
$499$	−17.2482	−	17.2482i	−0.772136	−	0.772136i	0.206344	−	0.978480i	$-0.433844\pi$
$499$	−17.2482	−	17.2482i	−0.772136	−	0.772136i	−0.978480	+	0.206344i	$0.933844\pi$
$500$	1.99976	−	0.0309111i	0.0894320	−	0.00138239i
$501$	−24.3154	+	24.3154i	−1.08633	+	1.08633i
$502$	−5.02832	−	2.03741i	−0.224425	−	0.0909343i
$503$		−	28.2064i		−	1.25766i	−0.777543	−	0.628830i	$-0.783534\pi$
$503$		−	28.2064i		−	1.25766i	0.777543	−	0.628830i	$-0.216466\pi$
$504$	−0.780329	−	0.302225i	−0.0347586	−	0.0134622i
$505$			1.84088i			0.0819183i
$506$	−13.8970	+	34.2976i	−0.617795	+	1.52471i
$507$	−9.95862	+	9.95862i	−0.442278	+	0.442278i
$508$	−3.82325	+	3.94330i	−0.169629	+	0.174956i
$509$	0.695650	+	0.695650i	0.0308341	+	0.0308341i	0.722356	−	0.691522i	$-0.243059\pi$
$509$	0.695650	+	0.695650i	0.0308341	+	0.0308341i	−0.691522	+	0.722356i	$0.743059\pi$
$510$	−5.74357	−	13.5687i	−0.254330	−	0.600831i
$511$	−10.5102			−0.464942
$512$	10.0910	+	20.2527i	0.445965	+	0.895051i
$513$	−36.8623			−1.62751
$514$	−11.3942	−	26.9179i	−0.502579	−	1.18730i
$515$	−8.96578	−	8.96578i	−0.395079	−	0.395079i
$516$	−10.9357	+	11.2790i	−0.481415	+	0.496532i
$517$	49.8733	−	49.8733i	2.19342	−	2.19342i
$518$	4.31104	−	10.6396i	0.189416	−	0.467477i
$519$			6.23645i			0.273750i
$520$	−5.55481	−	2.15141i	−0.243594	−	0.0943454i
$521$		−	28.9638i		−	1.26893i	−0.772952	−	0.634464i	$-0.781221\pi$
$521$		−	28.9638i		−	1.26893i	0.772952	−	0.634464i	$-0.218779\pi$
$522$	2.32972	+	0.943975i	0.101969	+	0.0413167i
$523$	−24.6703	+	24.6703i	−1.07876	+	1.07876i	−0.0821360	+	0.996621i	$0.526174\pi$
$523$	−24.6703	+	24.6703i	−1.07876	+	1.07876i	−0.996621	+	0.0821360i	$0.973826\pi$
$524$	−14.7028	+	0.227267i	−0.642295	+	0.00992821i
$525$	1.16279	+	1.16279i	0.0507481	+	0.0507481i
$526$	0.946045	−	0.400458i	0.0412495	−	0.0174608i
$527$	0.186579			0.00812751
$528$	1.14219	+	36.9376i	0.0497074	+	1.60750i
$529$	1.30731			0.0568394
$530$	−0.0449384	+	0.0190223i	−0.00195200	+	0.000826276i
$531$	1.74930	+	1.74930i	0.0759130	+	0.0759130i
$532$	0.210239	+	13.6012i	0.00911502	+	0.589687i
$533$	−1.36923	+	1.36923i	−0.0593078	+	0.0593078i
$534$	−22.3017	−	9.03638i	−0.965089	−	0.391043i
$535$		−	10.4145i		−	0.450257i
$536$	−15.6589	−	35.4559i	−0.676360	−	1.53146i
$537$		−	19.0562i		−	0.822336i
$538$	−16.0248	+	39.5491i	−0.690880	+	1.70508i
$539$	−3.97270	+	3.97270i	−0.171116	+	0.171116i
$540$	−7.78230	−	7.54538i	−0.334897	−	0.324701i
$541$	−1.88528	−	1.88528i	−0.0810547	−	0.0810547i	0.665417	−	0.746472i	$-0.268254\pi$
$541$	−1.88528	−	1.88528i	−0.0810547	−	0.0810547i	−0.746472	+	0.665417i	$0.768254\pi$
$542$	−6.92054	−	16.3491i	−0.297263	−	0.702256i
$543$	−15.9591			−0.684869
$544$	32.5576	−	14.9844i	1.39590	−	0.642452i
$545$	−6.88036			−0.294722
$546$	−1.90923	−	4.51038i	−0.0817076	−	0.193027i
$547$	−7.58192	−	7.58192i	−0.324179	−	0.324179i	0.526189	−	0.850368i	$-0.323621\pi$
$547$	−7.58192	−	7.58192i	−0.324179	−	0.324179i	−0.850368	+	0.526189i	$0.823621\pi$
$548$	−18.4552	−	17.8934i	−0.788369	−	0.764367i
$549$	0.398700	−	0.398700i	0.0170161	−	0.0170161i
$550$	−2.98376	+	7.36387i	−0.127228	+	0.313997i
$551$		−	40.8615i		−	1.74076i
$552$	−19.8163	+	8.75177i	−0.843440	+	0.372500i
$553$			4.67417i			0.198766i
$554$	23.8163	+	9.65009i	1.01186	+	0.409993i
$555$	9.43885	−	9.43885i	0.400657	−	0.400657i
$556$	0.160889	+	10.4086i	0.00682322	+	0.441421i
$557$	10.8760	+	10.8760i	0.460832	+	0.460832i	0.898928	−	0.438096i	$-0.144347\pi$
$557$	10.8760	+	10.8760i	0.460832	+	0.460832i	−0.438096	+	0.898928i	$0.644347\pi$
$558$	0.0113468	−	0.00480306i	0.000480348	−	0.000203330i
$559$	10.0602			0.425501
$560$	−2.73966	+	2.91450i	−0.115772	+	0.123160i
$561$	58.5347			2.47134
$562$	15.5862	−	6.59759i	0.657464	−	0.278303i
$563$	17.4406	+	17.4406i	0.735035	+	0.735035i	0.971613	−	0.236578i	$-0.0760259\pi$
$563$	17.4406	+	17.4406i	0.735035	+	0.735035i	−0.236578	+	0.971613i	$0.576026\pi$
$564$	41.2833	−	0.638133i	1.73834	−	0.0268702i
$565$	7.06658	−	7.06658i	0.297293	−	0.297293i
$566$	17.6098	+	7.13528i	0.740195	+	0.299918i
$567$		−	8.02490i		−	0.337014i
$568$	11.2893	−	29.1484i	0.473690	−	1.22304i
$569$			23.8027i			0.997861i	0.866642	+	0.498931i	$0.166274\pi$
$569$			23.8027i			0.997861i	−0.866642	+	0.498931i	$0.833726\pi$
$570$	−5.93986	+	14.6595i	−0.248793	+	0.614019i
$571$	−11.8136	+	11.8136i	−0.494385	+	0.494385i	−0.909685	−	0.415300i	$-0.863677\pi$
$571$	−11.8136	+	11.8136i	−0.494385	+	0.494385i	0.415300	+	0.909685i	$0.363677\pi$
$572$	16.4730	−	16.9902i	0.688770	−	0.710398i
$573$	−16.0109	−	16.0109i	−0.668864	−	0.668864i
$574$	0.506858	+	1.19741i	0.0211559	+	0.0499788i
$575$	−4.65754			−0.194233
$576$	1.59425	−	1.74940i	0.0664270	−	0.0728916i
$577$	13.0968			0.545226			0.272613	−	0.962124i	$-0.412112\pi$
$577$	13.0968			0.545226			0.272613	+	0.962124i	$0.412112\pi$
$578$	−12.7574	−	30.1383i	−0.530640	−	1.25359i
$579$	14.7670	+	14.7670i	0.613694	+	0.613694i
$580$	8.36399	−	8.62662i	0.347296	−	0.358201i
$581$	4.38372	−	4.38372i	0.181867	−	0.181867i
$582$	−0.505428	+	1.24739i	−0.0209506	+	0.0517060i
$583$		−	0.193863i		−	0.00802897i
$584$	10.7364	−	27.7207i	0.444274	−	1.14709i
$585$			0.623098i			0.0257619i
$586$	16.2648	+	6.59030i	0.671892	+	0.272243i
$587$	−0.220405	+	0.220405i	−0.00909709	+	0.00909709i	−0.711641	−	0.702544i	$-0.752048\pi$
$587$	−0.220405	+	0.220405i	−0.00909709	+	0.00909709i	0.702544	+	0.711641i	$0.252048\pi$
$588$	−3.28846	+	0.0508310i	−0.135614	+	0.00209624i
$589$	−0.141628	−	0.141628i	−0.00583569	−	0.00583569i
$590$	10.8898	−	4.60963i	0.448327	−	0.189775i
$591$	−44.1028			−1.81415
$592$	23.6583	+	22.2390i	0.972348	+	0.914018i
$593$	−14.8744			−0.610819			−0.305409	−	0.952221i	$-0.598793\pi$
$593$	−14.8744			−0.610819			−0.305409	+	0.952221i	$0.598793\pi$
$594$	39.6560	−	16.7863i	1.62711	−	0.688749i
$595$	4.48005	+	4.48005i	0.183664	+	0.183664i
$596$	0.229652	+	14.8571i	0.00940693	+	0.608572i
$597$	18.3154	−	18.3154i	0.749600	−	0.749600i
$598$	12.8569	+	5.20946i	0.525757	+	0.213031i
$599$		−	21.1703i		−	0.864995i	−0.901635	−	0.432497i	$-0.857632\pi$
$599$		−	21.1703i		−	0.864995i	0.901635	−	0.432497i	$-0.142368\pi$
$600$	−4.25468	+	1.87905i	−0.173697	+	0.0767120i
$601$			22.0011i			0.897444i	0.893671	+	0.448722i	$0.148121\pi$
$601$			22.0011i			0.897444i	−0.893671	+	0.448722i	$0.851879\pi$
$602$	2.53685	−	6.26091i	0.103394	−	0.255176i
$603$	−2.86684	+	2.86684i	−0.116747	+	0.116747i
$604$	24.5722	+	23.8241i	0.999827	+	0.969388i
$605$	−14.5415	−	14.5415i	−0.591194	−	0.591194i
$606$	−1.66883	−	3.94245i	−0.0677914	−	0.160151i
$607$	−23.0452			−0.935377			−0.467688	−	0.883893i	$-0.654913\pi$
$607$	−23.0452			−0.935377			−0.467688	+	0.883893i	$0.654913\pi$
$608$	−36.0881	−	13.3394i	−1.46357	−	0.540985i
$609$	9.87940			0.400334
$610$	−1.05063	−	2.48201i	−0.0425386	−	0.100494i
$611$	−18.6957	−	18.6957i	−0.756345	−	0.756345i
$612$	−2.69156	−	2.60962i	−0.108800	−	0.105488i
$613$	3.35701	−	3.35701i	0.135588	−	0.135588i	−0.636055	−	0.771644i	$-0.719435\pi$
$613$	3.35701	−	3.35701i	0.135588	−	0.135588i	0.771644	+	0.636055i	$0.219435\pi$
$614$	−3.55221	+	8.76681i	−0.143355	+	0.353800i
$615$			1.51193i			0.0609669i
$616$	−6.41986	−	14.5363i	−0.258663	−	0.585683i
$617$			38.4016i			1.54599i	0.634411	+	0.772996i	$0.281243\pi$
$617$			38.4016i			1.54599i	−0.634411	+	0.772996i	$0.718757\pi$
$618$	27.3290	+	11.0734i	1.09933	+	0.445436i
$619$	−2.60221	+	2.60221i	−0.104592	+	0.104592i	−0.757466	−	0.652874i	$-0.773563\pi$
$619$	−2.60221	+	2.60221i	−0.104592	+	0.104592i	0.652874	+	0.757466i	$0.273563\pi$
$620$	−0.000910290	−	0.0588903i	−3.65581e−5	−	0.00236509i
$621$	17.8495	+	17.8495i	0.716274	+	0.716274i
$622$	−23.7766	+	10.0646i	−0.953356	+	0.403552i
$623$	10.3471			0.414547
$624$	13.8465	−	0.428165i	0.554305	−	0.0171403i
$625$	−1.00000			−0.0400000
$626$	1.50206	−	0.635818i	0.0600344	−	0.0254124i
$627$	−44.4324	−	44.4324i	−1.77446	−	1.77446i
$628$	−28.0322	+	0.433305i	−1.11861	+	0.0172907i
$629$	36.3665	−	36.3665i	1.45003	−	1.45003i
$630$	0.387782	+	0.157125i	0.0154496	+	0.00626000i
$631$			45.6979i			1.81920i	0.415481	+	0.909602i	$0.363613\pi$
$631$			45.6979i			1.81920i	−0.415481	+	0.909602i	$0.636387\pi$
$632$	−12.3282	−	4.77478i	−0.490390	−	0.189930i
$633$		−	41.5335i		−	1.65081i
$634$	6.22327	−	15.3590i	0.247158	−	0.609982i
$635$	1.94187	−	1.94187i	0.0770607	−	0.0770607i
$636$	0.0789960	−	0.0814765i	0.00313240	−	0.00323075i
$637$	1.48922	+	1.48922i	0.0590050	+	0.0590050i
$638$	18.6074	+	43.9584i	0.736676	+	1.74033i
$639$	−3.26966			−0.129346
$640$	−4.88840	−	10.2031i	−0.193231	−	0.403313i
$641$	−40.0534			−1.58201			−0.791007	−	0.611807i	$-0.790443\pi$
$641$	−40.0534			−1.58201			−0.791007	+	0.611807i	$0.790443\pi$
$642$	9.44109	+	22.3037i	0.372610	+	0.880257i
$643$	18.6888	+	18.6888i	0.737014	+	0.737014i	0.971999	−	0.234985i	$-0.0755040\pi$
$643$	18.6888	+	18.6888i	0.737014	+	0.737014i	−0.234985	+	0.971999i	$0.575504\pi$
$644$	6.48417	−	6.68777i	0.255512	−	0.263535i
$645$	5.55434	−	5.55434i	0.218702	−	0.218702i
$646$	−22.8854	+	56.4809i	−0.900414	+	2.22221i
$647$			33.7799i			1.32802i	0.747722	+	0.664012i	$0.231148\pi$
$647$			33.7799i			1.32802i	−0.747722	+	0.664012i	$0.768852\pi$
$648$	21.1658	+	8.19762i	0.831471	+	0.322033i
$649$			46.9782i			1.84406i
$650$	2.76045	+	1.11850i	0.108274	+	0.0438712i
$651$	0.0342425	−	0.0342425i	0.00134207	−	0.00134207i
$652$	−47.2786	+	0.730804i	−1.85157	+	0.0286205i
$653$	12.5543	+	12.5543i	0.491289	+	0.491289i	0.908712	−	0.417423i	$-0.137067\pi$
$653$	12.5543	+	12.5543i	0.491289	+	0.491289i	−0.417423	+	0.908712i	$0.637067\pi$
$654$	14.7350	−	6.23729i	0.576185	−	0.243897i
$655$	7.35228			0.287277
$656$	−3.67595	+	0.113668i	−0.143522	+	0.00443800i
$657$	−3.10951			−0.121313
$658$	−16.3496	+	6.92073i	−0.637373	+	0.269798i
$659$	−19.8807	−	19.8807i	−0.774443	−	0.774443i	0.204437	−	0.978880i	$-0.434464\pi$
$659$	−19.8807	−	19.8807i	−0.774443	−	0.774443i	−0.978880	+	0.204437i	$0.934464\pi$
$660$	−0.285581	−	18.4754i	−0.0111162	−	0.719154i
$661$	−10.1929	+	10.1929i	−0.396460	+	0.396460i	−0.876982	−	0.480523i	$-0.840447\pi$
$661$	−10.1929	+	10.1929i	−0.396460	+	0.396460i	0.480523	+	0.876982i	$0.340447\pi$
$662$	−19.2896	−	7.81591i	−0.749710	−	0.303774i
$663$		−	21.9425i		−	0.852176i
$664$	7.08405	+	16.0402i	0.274915	+	0.622480i
$665$		−	6.80141i		−	0.263747i
$666$	1.27545	−	3.14780i	0.0494228	−	0.121975i
$667$	−19.7860	+	19.7860i	−0.766116	+	0.766116i
$668$	30.0266	+	29.1125i	1.16176	+	1.12639i
$669$	15.8026	+	15.8026i	0.610962	+	0.610962i
$670$	7.55451	+	17.8468i	0.291856	+	0.689483i
$671$	10.7073			0.413350
$672$	3.22517	−	8.72530i	0.124414	−	0.336586i
$673$	8.14797			0.314081			0.157041	−	0.987592i	$-0.449805\pi$
$673$	8.14797			0.314081			0.157041	+	0.987592i	$0.449805\pi$
$674$	−6.81728	−	16.1052i	−0.262592	−	0.620349i
$675$	3.83238	+	3.83238i	0.147508	+	0.147508i
$676$	12.2977	+	11.9233i	0.472989	+	0.458589i
$677$	13.7512	−	13.7512i	0.528503	−	0.528503i	−0.391623	−	0.920126i	$-0.628086\pi$
$677$	13.7512	−	13.7512i	0.528503	−	0.528503i	0.920126	+	0.391623i	$0.128086\pi$
$678$	−8.72773	+	21.5399i	−0.335186	+	0.827236i
$679$		−	0.578738i		−	0.0222099i
$680$	−16.3927	+	7.23972i	−0.628630	+	0.277631i
$681$		−	18.1427i		−	0.695230i
$682$	0.216856	+	0.0878676i	0.00830386	+	0.00336463i
$683$	10.9048	−	10.9048i	0.417262	−	0.417262i	−0.466997	−	0.884259i	$-0.654664\pi$
$683$	10.9048	−	10.9048i	0.417262	−	0.417262i	0.884259	+	0.466997i	$0.154664\pi$
$684$	0.0622008	+	4.02401i	0.00237831	+	0.153862i
$685$	9.08824	+	9.08824i	0.347244	+	0.347244i
$686$	1.30234	−	0.551277i	0.0497236	−	0.0210479i
$687$	25.3993			0.969043
$688$	13.9218	+	13.0867i	0.530764	+	0.498924i
$689$	−0.0726719			−0.00276858
$690$	9.97462	−	4.22223i	0.379727	−	0.160737i
$691$	17.5590	+	17.5590i	0.667977	+	0.667977i	0.957247	−	0.289271i	$-0.0934127\pi$
$691$	17.5590	+	17.5590i	0.667977	+	0.667977i	−0.289271	+	0.957247i	$0.593413\pi$
$692$	7.58404	−	0.117230i	0.288302	−	0.00445640i
$693$	−1.17535	+	1.17535i	−0.0446480	+	0.0446480i
$694$	−21.9107	−	8.87794i	−0.831717	−	0.337002i
$695$		−	5.20490i		−	0.197433i
$696$	−10.0920	+	26.0571i	−0.382538	+	0.987691i
$697$			5.82524i			0.220647i
$698$	4.60226	−	11.3583i	0.174198	−	0.429919i
$699$	−4.00314	+	4.00314i	−0.151412	+	0.151412i
$700$	1.39219	−	1.43590i	0.0526197	−	0.0542720i
$701$	14.7247	+	14.7247i	0.556146	+	0.556146i	0.928208	−	0.372062i	$-0.121349\pi$
$701$	14.7247	+	14.7247i	0.556146	+	0.556146i	−0.372062	+	0.928208i	$0.621349\pi$
$702$	−6.29255	−	14.8656i	−0.237497	−	0.561065i
$703$	−55.2101			−2.08229
$704$	44.8977	−	2.08333i	1.69215	−	0.0785185i
$705$	−20.6441			−0.777503
$706$	−7.40057	−	17.4832i	−0.278524	−	0.657988i
$707$	1.30170	+	1.30170i	0.0489555	+	0.0489555i
$708$	−19.1429	+	19.7440i	−0.719435	+	0.742025i
$709$	−4.15445	+	4.15445i	−0.156023	+	0.156023i	−0.780802	−	0.624779i	$-0.785189\pi$
$709$	−4.15445	+	4.15445i	−0.156023	+	0.156023i	0.624779	+	0.780802i	$0.285189\pi$
$710$	−5.86925	+	14.4852i	−0.220269	+	0.543621i
$711$			1.38289i			0.0518624i
$712$	−10.5698	+	27.2906i	−0.396119	+	1.02276i
$713$			0.137158i			0.00513662i
$714$	−13.6558	−	5.53318i	−0.511056	−	0.207074i
$715$	−8.36681	+	8.36681i	−0.312901	+	0.312901i
$716$	−23.1739	+	0.358209i	−0.866051	+	0.0133869i
$717$	6.77699	+	6.77699i	0.253091	+	0.253091i
$718$	−13.5948	+	5.75462i	−0.507352	+	0.214761i
$719$	14.2575			0.531717			0.265858	−	0.964012i	$-0.414345\pi$
$719$	14.2575			0.531717			0.265858	+	0.964012i	$0.414345\pi$
$720$	−0.810548	+	0.862275i	−0.0302073	+	0.0321351i
$721$	−12.6795			−0.472210
$722$	35.5008	−	15.0274i	1.32120	−	0.559260i
$723$	10.6372	+	10.6372i	0.395601	+	0.395601i
$724$	0.299990	+	19.4076i	0.0111490	+	0.721276i
$725$	−4.24816	+	4.24816i	−0.157773	+	0.157773i
$726$	44.3244	+	17.9597i	1.64503	+	0.666548i
$727$			12.2178i			0.453135i	0.973995	+	0.226567i	$0.0727504\pi$
$727$			12.2178i			0.453135i	−0.973995	+	0.226567i	$0.927250\pi$
$728$	−5.44911	+	2.40657i	−0.201958	+	0.0891934i
$729$		−	29.1116i		−	1.07821i
$730$	−5.58176	+	13.7757i	−0.206590	+	0.509863i
$731$	21.4001	−	21.4001i	0.791509	−	0.791509i
$732$	4.50006	+	4.36306i	0.166327	+	0.161263i
$733$	22.9048	+	22.9048i	0.846009	+	0.846009i	0.989632	−	0.143624i	$-0.0458755\pi$
$733$	22.9048	+	22.9048i	0.846009	+	0.846009i	−0.143624	+	0.989632i	$0.545876\pi$
$734$	4.98500	+	11.7766i	0.184000	+	0.434682i
$735$	1.64443			0.0606556
$736$	11.0154	+	23.9338i	0.406032	+	0.882212i
$737$	−76.9905			−2.83598
$738$	0.149958	+	0.354262i	0.00552002	+	0.0130406i
$739$	13.3203	+	13.3203i	0.489997	+	0.489997i	0.908305	−	0.418308i	$-0.137377\pi$
$739$	13.3203	+	13.3203i	0.489997	+	0.489997i	−0.418308	+	0.908305i	$0.637377\pi$
$740$	−11.6559	−	11.3010i	−0.428478	−	0.415433i
$741$	−16.6561	+	16.6561i	−0.611876	+	0.611876i
$742$	−0.0183255	+	0.0452271i	−0.000672749	+	0.00166034i
$743$			1.88792i			0.0692610i	0.999400	+	0.0346305i	$0.0110254\pi$
$743$			1.88792i			0.0692610i	−0.999400	+	0.0346305i	$0.988975\pi$
$744$	0.0553356	+	0.125295i	0.00202870	+	0.00459352i
$745$		−	7.42945i		−	0.272194i
$746$	−43.0097	−	17.4270i	−1.57470	−	0.638049i
$747$	1.29696	−	1.29696i	0.0474531	−	0.0474531i
$748$	−1.10030	−	71.1830i	−0.0402311	−	2.60271i
$749$	−7.36414	−	7.36414i	−0.269080	−	0.269080i
$750$	2.14161	−	0.906535i	0.0782004	−	0.0331020i
$751$	5.29005			0.193037			0.0965183	−	0.995331i	$-0.469229\pi$
$751$	5.29005			0.193037			0.0965183	+	0.995331i	$0.469229\pi$
$752$	−1.55204	−	50.1920i	−0.0565972	−	1.83031i
$753$	−6.30859			−0.229898
$754$	16.4784	−	6.97525i	0.600107	−	0.254024i
$755$	−12.1005	−	12.1005i	−0.440383	−	0.440383i
$756$	−10.8383	+	0.167532i	−0.394185	+	0.00609308i
$757$	26.4798	−	26.4798i	0.962423	−	0.962423i	−0.0368961	−	0.999319i	$-0.511747\pi$
$757$	26.4798	−	26.4798i	0.962423	−	0.962423i	0.999319	+	0.0368961i	$0.0117471\pi$
$758$	−27.0284	−	10.9516i	−0.981716	−	0.397780i
$759$			43.0301i			1.56189i
$760$	17.9388	+	6.94780i	0.650710	+	0.252023i
$761$		−	26.0367i		−	0.943828i	−0.881645	−	0.471914i	$-0.843563\pi$
$761$		−	26.0367i		−	0.943828i	0.881645	−	0.471914i	$-0.156437\pi$
$762$	−2.39835	+	5.91909i	−0.0868829	+	0.214426i
$763$	−4.86515	+	4.86515i	−0.176130	+	0.176130i
$764$	−19.1696	+	19.7715i	−0.693531	+	0.715308i
$765$	1.32545	+	1.32545i	0.0479219	+	0.0479219i
$766$	6.39048	+	15.0969i	0.230897	+	0.545474i
$767$	17.6104			0.635875
$768$	19.7185	+	17.4195i	0.711531	+	0.628574i
$769$	−17.7514			−0.640132			−0.320066	−	0.947395i	$-0.603705\pi$
$769$	−17.7514			−0.640132			−0.320066	+	0.947395i	$0.603705\pi$
$770$	3.09721	+	7.31688i	0.111616	+	0.263682i
$771$	−24.0334	−	24.0334i	−0.865542	−	0.865542i
$772$	17.6803	−	18.2354i	0.636327	−	0.656308i
$773$	−11.6700	+	11.6700i	−0.419740	+	0.419740i	−0.885114	−	0.465374i	$-0.845920\pi$
$773$	−11.6700	+	11.6700i	−0.419740	+	0.419740i	0.465374	+	0.885114i	$0.345920\pi$
$774$	0.750546	−	1.85234i	0.0269778	−	0.0665809i
$775$			0.0294487i			0.00105783i
$776$	1.52643	+	0.591194i	0.0547957	+	0.0212226i
$777$		−	13.3486i		−	0.478877i
$778$	23.0997	+	9.35971i	0.828163	+	0.335562i
$779$	4.42182	−	4.42182i	0.158428	−	0.158428i
$780$	−6.92575	+	0.107054i	−0.247982	+	0.00383315i
$781$	−43.9042	−	43.9042i	−1.57102	−	1.57102i
$782$	38.4308	−	16.2676i	1.37428	−	0.581729i
$783$	32.5611			1.16364
$784$	0.123630	+	3.99809i	0.00441534	+	0.142789i
$785$	14.0178			0.500316
$786$	−15.7457	+	6.66510i	−0.561630	+	0.237736i
$787$	−18.4037	−	18.4037i	−0.656020	−	0.656020i	0.298416	−	0.954436i	$-0.403542\pi$
$787$	−18.4037	−	18.4037i	−0.656020	−	0.656020i	−0.954436	+	0.298416i	$0.903542\pi$
$788$	0.829020	+	53.6326i	0.0295326	+	1.91058i
$789$	0.844669	−	0.844669i	0.0300710	−	0.0300710i
$790$	6.12647	+	2.48237i	0.217970	+	0.0883188i
$791$		−	9.99365i		−	0.355333i
$792$	−1.89936	−	4.30066i	−0.0674909	−	0.152817i
$793$		−	4.01377i		−	0.142533i
$794$	−15.8878	+	39.2110i	−0.563838	+	1.39154i
$795$	−0.0401229	+	0.0401229i	−0.00142301	+	0.00142301i
$796$	−22.6174	−	21.9288i	−0.801651	−	0.777245i
$797$	−6.85581	−	6.85581i	−0.242845	−	0.242845i	0.575181	−	0.818026i	$-0.304932\pi$
$797$	−6.85581	−	6.85581i	−0.242845	−	0.242845i	−0.818026	+	0.575181i	$0.804932\pi$
$798$	6.16572	+	14.5659i	0.218264	+	0.515629i
$799$	−79.5388			−2.81388
$800$	2.36506	+	5.13872i	0.0836176	+	0.181681i
$801$	3.06126			0.108164
$802$	9.79799	+	23.1469i	0.345979	+	0.817344i
$803$	−41.7537	−	41.7537i	−1.47346	−	1.47346i
$804$	−32.3576	−	31.3725i	−1.14116	−	1.10642i
$805$	−3.29338	+	3.29338i	−0.116076	+	0.116076i
$806$	0.0329383	−	0.0812915i	0.00116020	−	0.00286337i
$807$			49.6188i			1.74667i
$808$	−4.76298	+	2.10354i	−0.167561	+	0.0740023i
$809$		−	37.5597i		−	1.32053i	−0.751033	−	0.660264i	$-0.770444\pi$
$809$		−	37.5597i		−	1.32053i	0.751033	−	0.660264i	$-0.229556\pi$
$810$	−10.5183	−	4.26188i	−0.369575	−	0.149747i
$811$	−23.4281	+	23.4281i	−0.822670	+	0.822670i	−0.986490	−	0.163820i	$-0.947618\pi$
$811$	−23.4281	+	23.4281i	−0.822670	+	0.822670i	0.163820	+	0.986490i	$0.447618\pi$
$812$	−0.185708	−	12.0142i	−0.00651707	−	0.421615i
$813$	−14.5972	−	14.5972i	−0.511947	−	0.511947i
$814$	59.3944	−	25.1414i	2.08177	−	0.881207i
$815$	23.6421			0.828148
$816$	28.5436	−	30.3652i	0.999225	−	1.06299i
$817$	−32.4886			−1.13663
$818$	−37.1693	+	15.7337i	−1.29960	+	0.550115i
$819$	0.440597	+	0.440597i	0.0153957	+	0.0153957i
$820$	1.83863	−	0.0284205i	0.0642078	−	0.000992485i
$821$	7.51385	−	7.51385i	0.262235	−	0.262235i	−0.563727	−	0.825962i	$-0.690633\pi$
$821$	7.51385	−	7.51385i	0.262235	−	0.262235i	0.825962	+	0.563727i	$0.190633\pi$
$822$	−27.7022	−	11.2246i	−0.966227	−	0.391504i
$823$			16.8403i			0.587015i	0.955957	+	0.293507i	$0.0948225\pi$
$823$			16.8403i			0.587015i	−0.955957	+	0.293507i	$0.905177\pi$
$824$	12.9524	−	33.4424i	0.451219	−	1.16502i
$825$			9.23880i			0.321654i
$826$	4.44077	−	10.9598i	0.154514	−	0.381339i
$827$	−37.1528	+	37.1528i	−1.29193	+	1.29193i	−0.358336	+	0.933593i	$0.616656\pi$
$827$	−37.1528	+	37.1528i	−1.29193	+	1.29193i	−0.933593	+	0.358336i	$0.883344\pi$
$828$	1.91839	−	1.97863i	0.0666687	−	0.0687621i
$829$	−4.41271	−	4.41271i	−0.153260	−	0.153260i	0.626312	−	0.779572i	$-0.284563\pi$
$829$	−4.41271	−	4.41271i	−0.153260	−	0.153260i	−0.779572	+	0.626312i	$0.784563\pi$
$830$	−3.41765	−	8.07388i	−0.118628	−	0.280249i
$831$	29.8802			1.03653
$832$	−0.780964	−	16.8305i	−0.0270751	−	0.583492i
$833$	6.33574			0.219520
$834$	4.71843	+	11.1468i	0.163386	+	0.385984i
$835$	−14.7865	−	14.7865i	−0.511709	−	0.511709i
$836$	−53.1983	+	54.8687i	−1.83990	+	1.89767i
$837$	0.112858	−	0.112858i	0.00390096	−	0.00390096i
$838$	3.55189	−	8.76603i	0.122698	−	0.302817i
$839$		−	16.3798i		−	0.565493i	−0.959195	−	0.282747i	$-0.908754\pi$
$839$		−	16.3798i		−	0.565493i	0.959195	−	0.282747i	$-0.0912456\pi$
$840$	−1.67982	+	4.33720i	−0.0579593	+	0.149648i
$841$			7.09372i			0.244611i
$842$	31.6859	+	12.8388i	1.09197	+	0.442453i
$843$	13.9160	−	13.9160i	0.479293	−	0.479293i
$844$	−50.5081	+	0.780724i	−1.73856	+	0.0268736i
$845$	−6.05598	−	6.05598i	−0.208332	−	0.208332i
$846$	−4.83715	+	2.04755i	−0.166305	+	0.0703962i
$847$	−20.5647			−0.706612
$848$	−0.100567	−	0.0945342i	−0.00345349	−	0.00324632i
$849$	22.0935			0.758245
$850$	8.25130	−	3.49275i	0.283017	−	0.119800i
$851$	26.7338	+	26.7338i	0.916424	+	0.916424i
$852$	−0.561758	−	36.3424i	−0.0192455	−	1.24507i
$853$	11.3173	−	11.3173i	0.387496	−	0.387496i	−0.486298	−	0.873793i	$-0.661653\pi$
$853$	11.3173	−	11.3173i	0.387496	−	0.387496i	0.873793	+	0.486298i	$0.161653\pi$
$854$	−2.49795	−	1.01214i	−0.0854781	−	0.0346347i
$855$		−	2.01225i		−	0.0688174i
$856$	26.9457	−	11.9004i	0.920985	−	0.406747i
$857$			0.712110i			0.0243252i	0.999926	+	0.0121626i	$0.00387158\pi$
$857$			0.712110i			0.0243252i	−0.999926	+	0.0121626i	$0.996128\pi$
$858$	10.3336	−	25.5032i	0.352783	−	0.870666i
$859$	−16.0220	+	16.0220i	−0.546662	+	0.546662i	−0.925474	−	0.378812i	$-0.876333\pi$
$859$	−16.0220	+	16.0220i	−0.546662	+	0.546662i	0.378812	+	0.925474i	$0.376333\pi$
$860$	−6.85894	−	6.65013i	−0.233888	−	0.226767i
$861$	1.06910	+	1.06910i	0.0364347	+	0.0364347i
$862$	−1.40666	−	3.32311i	−0.0479111	−	0.113186i
$863$	7.70788			0.262379			0.131190	−	0.991357i	$-0.458120\pi$
$863$	7.70788			0.262379			0.131190	+	0.991357i	$0.458120\pi$
$864$	10.6297	−	28.7573i	0.361630	−	0.978344i
$865$	−3.79248			−0.128948
$866$	−4.18065	−	9.87641i	−0.142064	−	0.335614i
$867$	−26.9087	−	26.9087i	−0.913869	−	0.913869i
$868$	−0.0422854	−	0.0409981i	−0.00143526	−	0.00139156i
$869$	−18.5691	+	18.5691i	−0.629913	+	0.629913i
$870$	5.24678	−	12.9490i	0.177883	−	0.439012i
$871$			28.8609i			0.977915i
$872$	−7.86204	−	17.8018i	−0.266242	−	0.602844i
$873$		−	0.171224i		−	0.00579505i
$874$	−41.5204	−	16.8236i	−1.40445	−	0.569066i
$875$	−0.707107	+	0.707107i	−0.0239046	+	0.0239046i
$876$	−0.534242	−	34.5623i	−0.0180504	−	1.16775i
$877$	−11.2828	−	11.2828i	−0.380994	−	0.380994i	0.490466	−	0.871460i	$-0.336827\pi$
$877$	−11.2828	−	11.2828i	−0.380994	−	0.380994i	−0.871460	+	0.490466i	$0.836827\pi$
$878$	−48.1406	+	20.3778i	−1.62467	+	0.687717i
$879$	20.4060			0.688277
$880$	−22.4623	+	0.694582i	−0.757203	+	0.0234143i
$881$	−53.4988			−1.80242			−0.901210	−	0.433383i	$-0.857320\pi$
$881$	−53.4988			−1.80242			−0.901210	+	0.433383i	$0.857320\pi$
$882$	0.385307	−	0.163099i	0.0129740	−	0.00549184i
$883$	24.6980	+	24.6980i	0.831154	+	0.831154i	0.987675	−	0.156521i	$-0.0500278\pi$
$883$	24.6980	+	24.6980i	0.831154	+	0.831154i	−0.156521	+	0.987675i	$0.550028\pi$
$884$	−26.6839	+	0.412464i	−0.897477	+	0.0138726i
$885$	9.72289	−	9.72289i	0.326831	−	0.326831i
$886$	−35.6453	−	14.4431i	−1.19753	−	0.485225i
$887$		−	18.4063i		−	0.618022i	−0.951059	−	0.309011i	$-0.900002\pi$
$887$		−	18.4063i		−	0.618022i	0.951059	−	0.309011i	$-0.0999979\pi$
$888$	35.2070	+	13.6359i	1.18147	+	0.457589i
$889$		−	2.74622i		−	0.0921052i
$890$	5.49515	−	13.5620i	0.184198	−	0.454599i
$891$	31.8805	−	31.8805i	1.06804	−	1.06804i
$892$	18.9202	−	19.5143i	0.633494	−	0.653386i
$893$	60.3762	+	60.3762i	2.02041	+	2.02041i
$894$	6.73506	+	15.9110i	0.225254	+	0.532142i
$895$	11.5884			0.387356
$896$	−10.6713	−	3.75807i	−0.356504	−	0.125548i
$897$	16.1304			0.538579
$898$	−13.8491	−	32.7172i	−0.462151	−	1.09179i
$899$	0.125103	+	0.125103i	0.00417241	+	0.00417241i
$900$	0.411889	−	0.424822i	0.0137296	−	0.0141607i
$901$	−0.154588	+	0.154588i	−0.00515007	+	0.00515007i
$902$	−2.74334	+	6.77054i	−0.0913433	+	0.225434i
$903$		−	7.85502i		−	0.261399i
$904$	26.3584	+	10.2087i	0.876668	+	0.339538i
$905$		−	9.70494i		−	0.322603i
$906$	36.8841	+	14.9450i	1.22539	+	0.496514i
$907$	8.25702	−	8.25702i	0.274170	−	0.274170i	−0.556607	−	0.830776i	$-0.687897\pi$
$907$	8.25702	−	8.25702i	0.274170	−	0.274170i	0.830776	+	0.556607i	$0.187897\pi$
$908$	−22.0630	+	0.341037i	−0.732188	+	0.0113177i
$909$	0.385118	+	0.385118i	0.0127736	+	0.0127736i
$910$	2.74283	−	1.16103i	0.0909239	−	0.0384878i
$911$	37.4980			1.24236			0.621182	−	0.783666i	$-0.286653\pi$
$911$	37.4980			1.24236			0.621182	+	0.783666i	$0.286653\pi$
$912$	−44.7163	+	1.38273i	−1.48071	+	0.0457866i
$913$	34.8304			1.15272
$914$	−21.0645	+	8.91655i	−0.696753	+	0.294933i
$915$	−2.21604	−	2.21604i	−0.0732601	−	0.0732601i
$916$	−0.477442	−	30.8876i	−0.0157751	−	1.02056i
$917$	5.19885	−	5.19885i	0.171681	−	0.171681i
$918$	−45.0076	−	18.2366i	−1.48547	−	0.601896i
$919$		−	1.19070i		−	0.0392775i	−0.999807	−	0.0196388i	$-0.993748\pi$
$919$		−	1.19070i		−	0.0392775i	0.999807	−	0.0196388i	$-0.00625162\pi$
$920$	−5.32208	−	12.0506i	−0.175464	−	0.397297i
$921$			10.9989i			0.362427i
$922$	4.75479	−	11.7348i	0.156591	−	0.386464i
$923$	−16.4581	+	16.4581i	−0.541724	+	0.541724i
$924$	−13.2660	−	12.8621i	−0.436420	−	0.423133i
$925$	5.73990	+	5.73990i	0.188727	+	0.188727i
$926$	−6.80784	−	16.0829i	−0.223720	−	0.528517i
$927$	−3.75133			−0.123210
$928$	31.8773	+	11.7830i	1.04642	+	0.386794i
$929$	−20.5448			−0.674052			−0.337026	−	0.941495i	$-0.609421\pi$
$929$	−20.5448			−0.674052			−0.337026	+	0.941495i	$0.609421\pi$
$930$	−0.0266963	−	0.0630675i	−0.000875405	−	0.00206806i
$931$	−4.80932	−	4.80932i	−0.157619	−	0.157619i
$932$	4.94340	+	4.79290i	0.161926	+	0.156997i
$933$	−21.2288	+	21.2288i	−0.694999	+	0.694999i
$934$	−3.60370	+	8.89390i	−0.117917	+	0.291017i
$935$			35.5958i			1.16411i
$936$	−1.61216	+	0.712001i	−0.0526951	+	0.0232725i
$937$		−	20.6843i		−	0.675727i	−0.941195	−	0.337863i	$-0.890296\pi$
$937$		−	20.6843i		−	0.675727i	0.941195	−	0.337863i	$-0.109704\pi$
$938$	17.9615	+	7.27777i	0.586462	+	0.237628i
$939$	1.34110	−	1.34110i	0.0437653	−	0.0437653i
$940$	0.388058	+	25.1050i	0.0126570	+	0.818834i
$941$	−18.7569	−	18.7569i	−0.611459	−	0.611459i	0.331867	−	0.943326i	$-0.392321\pi$
$941$	−18.7569	−	18.7569i	−0.611459	−	0.611459i	−0.943326	+	0.331867i	$0.892321\pi$
$942$	−30.0206	+	12.7076i	−0.978123	+	0.414036i
$943$	−4.28226			−0.139450
$944$	24.3702	+	22.9082i	0.793182	+	0.745600i
$945$	5.41980			0.176306
$946$	34.9509	−	14.7946i	1.13635	−	0.481014i
$947$	−19.7221	−	19.7221i	−0.640881	−	0.640881i	0.309891	−	0.950772i	$-0.399707\pi$
$947$	−19.7221	−	19.7221i	−0.640881	−	0.640881i	−0.950772	+	0.309891i	$0.899707\pi$
$948$	−15.3708	+	0.237593i	−0.499222	+	0.00771666i
$949$	−15.6519	+	15.6519i	−0.508083	+	0.508083i
$950$	−8.91465	−	3.61211i	−0.289229	−	0.117192i
$951$		−	19.2695i		−	0.624857i
$952$	−6.47211	+	16.7106i	−0.209762	+	0.541594i
$953$			42.2504i			1.36862i	0.729190	+	0.684312i	$0.239897\pi$
$953$			42.2504i			1.36862i	−0.729190	+	0.684312i	$0.760103\pi$
$954$	−0.00542173	+	0.0133808i	−0.000175535	+	0.000433218i
$955$	9.73644	−	9.73644i	0.315064	−	0.315064i
$956$	8.11399	−	8.36877i	0.262425	−	0.270665i
$957$	39.2479	+	39.2479i	1.26870	+	1.26870i
$958$	−12.6809	−	29.9576i	−0.409703	−	0.967886i
$959$	12.8527			0.415036
$960$	−9.72347	−	8.86111i	−0.313824	−	0.285991i
$961$	−30.9991			−0.999972
$962$	−9.42460	−	22.2648i	−0.303861	−	0.717845i
$963$	−2.17874	−	2.17874i	−0.0702088	−	0.0702088i
$964$	12.7357	−	13.1356i	0.410191	−	0.423071i
$965$	−8.98000	+	8.98000i	−0.289077	+	0.289077i
$966$	4.06756	−	10.0387i	0.130872	−	0.322989i
$967$			37.1348i			1.19418i	0.802176	+	0.597088i	$0.203676\pi$
$967$			37.1348i			1.19418i	−0.802176	+	0.597088i	$0.796324\pi$
$968$	21.0073	−	54.2398i	0.675202	−	1.74333i
$969$			70.8616i			2.27640i
$970$	−0.758555	−	0.307358i	−0.0243557	−	0.00986866i
$971$	−6.58118	+	6.58118i	−0.211200	+	0.211200i	−0.804777	−	0.593577i	$-0.797715\pi$
$971$	−6.58118	+	6.58118i	−0.211200	+	0.211200i	0.593577	+	0.804777i	$0.297715\pi$
$972$	−6.12534	+	0.0946818i	−0.196470	+	0.00303692i
$973$	−3.68042	−	3.68042i	−0.117989	−	0.117989i
$974$	−2.48717	+	1.05281i	−0.0796941	+	0.0337343i
$975$	3.46329			0.110914
$976$	5.22125	−	5.55446i	0.167128	−	0.177794i
$977$	33.6155			1.07546			0.537728	−	0.843118i	$-0.319283\pi$
$977$	33.6155			1.07546			0.537728	+	0.843118i	$0.319283\pi$
$978$	−50.6321	+	21.4324i	−1.61904	+	0.685333i
$979$	41.1058	+	41.1058i	1.31375	+	1.31375i
$980$	−0.0309111	−	1.99976i	−0.000987418	−	0.0638800i
$981$	−1.43939	+	1.43939i	−0.0459562	+	0.0459562i
$982$	20.0319	+	8.11671i	0.639245	+	0.259015i
$983$			34.8765i			1.11239i	0.831053	+	0.556193i	$0.187738\pi$
$983$			34.8765i			1.11239i	−0.831053	+	0.556193i	$0.812262\pi$
$984$	−3.91186	+	1.72765i	−0.124706	+	0.0550755i
$985$		−	26.8195i		−	0.854541i
$986$	20.2151	−	49.8906i	0.643779	−	1.58884i
$987$	−14.5976	+	14.5976i	−0.464647	+	0.464647i
$988$	20.5683	+	19.9421i	0.654364	+	0.634442i
$989$	15.7316	+	15.7316i	0.500237	+	0.500237i
$990$	0.916333	+	2.16475i	0.0291230	+	0.0688004i
$991$	22.2085			0.705477			0.352738	−	0.935722i	$-0.385251\pi$
$991$	22.2085			0.705477			0.352738	+	0.935722i	$0.385251\pi$
$992$	0.151329	−	0.0696479i	0.00480469	−	0.00221132i
$993$	−24.2009			−0.767993
$994$	6.09242	+	14.3928i	0.193240	+	0.456512i
$995$	11.1379	+	11.1379i	0.353094	+	0.353094i
$996$	14.6385	+	14.1929i	0.463839	+	0.449718i
$997$	−23.5079	+	23.5079i	−0.744503	+	0.744503i	−0.973441	−	0.228938i	$-0.926475\pi$
$997$	−23.5079	+	23.5079i	−0.744503	+	0.744503i	0.228938	+	0.973441i	$0.426475\pi$
$998$	−12.9545	+	31.9716i	−0.410068	+	1.01204i
$999$		−	43.9949i		−	1.39194i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bd.a.141.11	✓	44
4.3	odd	2		2240.2.bd.a.1681.16		44
16.5	even	4	inner	560.2.bd.a.421.11	yes	44
16.11	odd	4		2240.2.bd.a.561.16		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.a.141.11	✓	44	1.1	even	1	trivial
560.2.bd.a.421.11	yes	44	16.5	even	4	inner
2240.2.bd.a.561.16		44	16.11	odd	4
2240.2.bd.a.1681.16		44	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)

\(f(q)\)	\(=\)	\(q+(-0.551277 - 1.30234i) q^{2} +(-1.16279 - 1.16279i) q^{3} +(-1.39219 + 1.43590i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.873327 + 2.15536i) q^{6} -1.00000i q^{7} +(2.63752 + 1.02152i) q^{8} -0.295857i q^{9} +O(q^{10})\)	\(q+(-0.551277 - 1.30234i) q^{2} +(-1.16279 - 1.16279i) q^{3} +(-1.39219 + 1.43590i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.873327 + 2.15536i) q^{6} -1.00000i q^{7} +(2.63752 + 1.02152i) q^{8} -0.295857i q^{9} +(-1.31071 - 0.531083i) q^{10} +(3.97270 - 3.97270i) q^{11} +(3.28846 - 0.0508310i) q^{12} +(-1.48922 - 1.48922i) q^{13} +(-1.30234 + 0.551277i) q^{14} -1.64443 q^{15} +(-0.123630 - 3.99809i) q^{16} -6.33574 q^{17} +(-0.385307 + 0.163099i) q^{18} +(4.80932 + 4.80932i) q^{19} +(0.0309111 + 1.99976i) q^{20} +(-1.16279 + 1.16279i) q^{21} +(-7.36387 - 2.98376i) q^{22} -4.65754i q^{23} +(-1.87905 - 4.25468i) q^{24} -1.00000i q^{25} +(-1.11850 + 2.76045i) q^{26} +(-3.83238 + 3.83238i) q^{27} +(1.43590 + 1.39219i) q^{28} +(-4.24816 - 4.24816i) q^{29} +(0.906535 + 2.14161i) q^{30} -0.0294487 q^{31} +(-5.13872 + 2.36506i) q^{32} -9.23880 q^{33} +(3.49275 + 8.25130i) q^{34} +(-0.707107 - 0.707107i) q^{35} +(0.424822 + 0.411889i) q^{36} +(-5.73990 + 5.73990i) q^{37} +(3.61211 - 8.91465i) q^{38} +3.46329i q^{39} +(2.58733 - 1.14268i) q^{40} -0.919426i q^{41} +(2.15536 + 0.873327i) q^{42} +(-3.37767 + 3.37767i) q^{43} +(0.173666 + 11.2352i) q^{44} +(-0.209203 - 0.209203i) q^{45} +(-6.06571 + 2.56760i) q^{46} +12.5540 q^{47} +(-4.50517 + 4.79268i) q^{48} -1.00000 q^{49} +(-1.30234 + 0.551277i) q^{50} +(7.36711 + 7.36711i) q^{51} +(4.21165 - 0.0651011i) q^{52} +(0.0243993 - 0.0243993i) q^{53} +(7.10377 + 2.87836i) q^{54} -5.61825i q^{55} +(1.02152 - 2.63752i) q^{56} -11.1844i q^{57} +(-3.19064 + 7.87447i) q^{58} +(-5.91263 + 5.91263i) q^{59} +(2.28935 - 2.36124i) q^{60} +(1.34761 + 1.34761i) q^{61} +(0.0162344 + 0.0383522i) q^{62} -0.295857 q^{63} +(5.91298 + 5.38857i) q^{64} -2.10608 q^{65} +(5.09314 + 12.0321i) q^{66} +(-9.68994 - 9.68994i) q^{67} +(8.82054 - 9.09750i) q^{68} +(-5.41572 + 5.41572i) q^{69} +(-0.531083 + 1.31071i) q^{70} -11.0515i q^{71} +(0.302225 - 0.780329i) q^{72} -10.5102i q^{73} +(10.6396 + 4.31104i) q^{74} +(-1.16279 + 1.16279i) q^{75} +(-13.6012 + 0.210239i) q^{76} +(-3.97270 - 3.97270i) q^{77} +(4.51038 - 1.90923i) q^{78} -4.67417 q^{79} +(-2.91450 - 2.73966i) q^{80} +8.02490 q^{81} +(-1.19741 + 0.506858i) q^{82} +(4.38372 + 4.38372i) q^{83} +(-0.0508310 - 3.28846i) q^{84} +(-4.48005 + 4.48005i) q^{85} +(6.26091 + 2.53685i) q^{86} +9.87940i q^{87} +(14.5363 - 6.41986i) q^{88} +10.3471i q^{89} +(-0.157125 + 0.387782i) q^{90} +(-1.48922 + 1.48922i) q^{91} +(6.68777 + 6.48417i) q^{92} +(0.0342425 + 0.0342425i) q^{93} +(-6.92073 - 16.3496i) q^{94} +6.80141 q^{95} +(8.72530 + 3.22517i) q^{96} +0.578738 q^{97} +(0.551277 + 1.30234i) q^{98} +(-1.17535 - 1.17535i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 12 q^{4} + 12 q^{6}+O(q^{10}) \) 44 * q + 12 * q^4 + 12 * q^6	\( 44 q + 12 q^{4} + 12 q^{6} - 4 q^{10} + 12 q^{11} - 16 q^{12} + 4 q^{14} + 8 q^{15} - 8 q^{16} - 20 q^{18} + 8 q^{19} - 36 q^{22} + 12 q^{24} + 44 q^{26} - 24 q^{27} - 4 q^{28} + 12 q^{29} - 40 q^{32} - 16 q^{34} + 4 q^{36} + 28 q^{37} - 16 q^{38} + 4 q^{42} - 44 q^{43} - 32 q^{44} - 16 q^{46} - 32 q^{48} - 44 q^{49} + 4 q^{50} - 8 q^{51} + 16 q^{52} - 12 q^{53} - 80 q^{54} + 8 q^{56} + 4 q^{58} + 24 q^{59} - 16 q^{61} + 28 q^{63} + 72 q^{64} - 40 q^{65} - 20 q^{66} - 28 q^{67} + 56 q^{68} + 40 q^{69} + 12 q^{72} + 24 q^{74} - 12 q^{77} + 84 q^{78} - 16 q^{79} + 20 q^{81} + 48 q^{82} + 16 q^{85} - 64 q^{86} + 28 q^{88} - 36 q^{90} - 16 q^{92} + 88 q^{93} + 96 q^{94} - 32 q^{95} + 48 q^{96} + 28 q^{99}+O(q^{100}) \) 44 * q + 12 * q^4 + 12 * q^6 - 4 * q^10 + 12 * q^11 - 16 * q^12 + 4 * q^14 + 8 * q^15 - 8 * q^16 - 20 * q^18 + 8 * q^19 - 36 * q^22 + 12 * q^24 + 44 * q^26 - 24 * q^27 - 4 * q^28 + 12 * q^29 - 40 * q^32 - 16 * q^34 + 4 * q^36 + 28 * q^37 - 16 * q^38 + 4 * q^42 - 44 * q^43 - 32 * q^44 - 16 * q^46 - 32 * q^48 - 44 * q^49 + 4 * q^50 - 8 * q^51 + 16 * q^52 - 12 * q^53 - 80 * q^54 + 8 * q^56 + 4 * q^58 + 24 * q^59 - 16 * q^61 + 28 * q^63 + 72 * q^64 - 40 * q^65 - 20 * q^66 - 28 * q^67 + 56 * q^68 + 40 * q^69 + 12 * q^72 + 24 * q^74 - 12 * q^77 + 84 * q^78 - 16 * q^79 + 20 * q^81 + 48 * q^82 + 16 * q^85 - 64 * q^86 + 28 * q^88 - 36 * q^90 - 16 * q^92 + 88 * q^93 + 96 * q^94 - 32 * q^95 + 48 * q^96 + 28 * q^99

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