LMFDB - Embedded newform 260.2.j.a.31.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(31,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("260.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.j (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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.18
Character	$\chi$	$=$	260.31
Dual form			260.2.j.a.151.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.400070 - 1.35645i) q^{2} -2.57103i q^{3} +(-1.67989 - 1.08535i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-3.48746 - 1.02859i) q^{6} +(3.59259 - 3.59259i) q^{7} +(-2.14428 + 1.84446i) q^{8} -3.61018 q^{9} +O(q^{10})$	\(q+(0.400070 - 1.35645i) q^{2} -2.57103i q^{3} +(-1.67989 - 1.08535i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-3.48746 - 1.02859i) q^{6} +(3.59259 - 3.59259i) q^{7} +(-2.14428 + 1.84446i) q^{8} -3.61018 q^{9} +(0.676260 + 1.24204i) q^{10} +(-3.05830 + 3.05830i) q^{11} +(-2.79045 + 4.31904i) q^{12} +(3.27029 + 1.51828i) q^{13} +(-3.43587 - 6.31044i) q^{14} +(1.81799 + 1.81799i) q^{15} +(1.64405 + 3.64652i) q^{16} -2.76630i q^{17} +(-1.44432 + 4.89701i) q^{18} +(1.96423 + 1.96423i) q^{19} +(1.95532 - 0.420406i) q^{20} +(-9.23664 - 9.23664i) q^{21} +(2.92488 + 5.37194i) q^{22} -3.63848 q^{23} +(4.74216 + 5.51301i) q^{24} -1.00000i q^{25} +(3.36781 - 3.82856i) q^{26} +1.56878i q^{27} +(-9.93435 + 2.13595i) q^{28} +5.48514 q^{29} +(3.19333 - 1.73868i) q^{30} +(-0.232457 - 0.232457i) q^{31} +(5.60404 - 0.771205i) q^{32} +(7.86296 + 7.86296i) q^{33} +(-3.75233 - 1.10671i) q^{34} +5.08069i q^{35} +(6.06469 + 3.91829i) q^{36} +(-1.59052 - 1.59052i) q^{37} +(3.45020 - 1.87854i) q^{38} +(3.90353 - 8.40801i) q^{39} +(0.212005 - 2.82047i) q^{40} +(-0.376964 + 0.376964i) q^{41} +(-16.2243 + 8.83370i) q^{42} +2.31562 q^{43} +(8.45690 - 1.81829i) q^{44} +(2.55278 - 2.55278i) q^{45} +(-1.45565 + 4.93540i) q^{46} +(1.51890 - 1.51890i) q^{47} +(9.37529 - 4.22690i) q^{48} -18.8134i q^{49} +(-1.35645 - 0.400070i) q^{50} -7.11222 q^{51} +(-3.84587 - 6.09994i) q^{52} -9.54628 q^{53} +(2.12796 + 0.627620i) q^{54} -4.32508i q^{55} +(-1.07713 + 14.3299i) q^{56} +(5.05009 - 5.05009i) q^{57} +(2.19444 - 7.44029i) q^{58} +(5.39264 - 5.39264i) q^{59} +(-1.08087 - 5.02717i) q^{60} +2.11653 q^{61} +(-0.408314 + 0.222316i) q^{62} +(-12.9699 + 12.9699i) q^{63} +(1.19591 - 7.91011i) q^{64} +(-3.38603 + 1.23886i) q^{65} +(13.8114 - 7.51994i) q^{66} +(8.28906 + 8.28906i) q^{67} +(-3.00239 + 4.64707i) q^{68} +9.35463i q^{69} +(6.89168 + 2.03263i) q^{70} +(-0.0524499 - 0.0524499i) q^{71} +(7.74124 - 6.65884i) q^{72} +(2.86601 + 2.86601i) q^{73} +(-2.79377 + 1.52113i) q^{74} -2.57103 q^{75} +(-1.16782 - 5.43156i) q^{76} +21.9744i q^{77} +(-9.84333 - 8.65872i) q^{78} +7.92711i q^{79} +(-3.74100 - 1.41596i) q^{80} -6.79716 q^{81} +(0.360519 + 0.662143i) q^{82} +(7.11999 + 7.11999i) q^{83} +(5.49159 + 25.5415i) q^{84} +(1.95607 + 1.95607i) q^{85} +(0.926409 - 3.14101i) q^{86} -14.1024i q^{87} +(0.916939 - 12.1988i) q^{88} +(1.71088 + 1.71088i) q^{89} +(-2.44142 - 4.48400i) q^{90} +(17.2034 - 6.29427i) q^{91} +(6.11224 + 3.94901i) q^{92} +(-0.597653 + 0.597653i) q^{93} +(-1.45264 - 2.66797i) q^{94} -2.77784 q^{95} +(-1.98279 - 14.4081i) q^{96} +(1.75502 - 1.75502i) q^{97} +(-25.5194 - 7.52667i) q^{98} +(11.0410 - 11.0410i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9}+O(q^{10}) $ 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9	$ 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 40 q^{24} - 16 q^{26} - 44 q^{28} + 40 q^{32} - 4 q^{34} + 16 q^{37} + 8 q^{41} + 8 q^{42} + 28 q^{44} - 12 q^{46} + 104 q^{48} + 56 q^{52} - 16 q^{53} + 20 q^{54} - 48 q^{57} - 4 q^{58} + 16 q^{61} - 8 q^{65} + 64 q^{66} + 24 q^{68} - 8 q^{70} - 32 q^{72} + 48 q^{73} - 136 q^{74} - 88 q^{76} + 52 q^{78} - 32 q^{80} + 56 q^{81} - 20 q^{84} - 64 q^{86} - 8 q^{89} - 88 q^{92} - 48 q^{93} - 16 q^{94} - 4 q^{96} - 32 q^{97} + 16 q^{98}+O(q^{100}) $ 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9 + 16 * q^14 - 12 * q^18 - 8 * q^20 - 16 * q^21 - 40 * q^24 - 16 * q^26 - 44 * q^28 + 40 * q^32 - 4 * q^34 + 16 * q^37 + 8 * q^41 + 8 * q^42 + 28 * q^44 - 12 * q^46 + 104 * q^48 + 56 * q^52 - 16 * q^53 + 20 * q^54 - 48 * q^57 - 4 * q^58 + 16 * q^61 - 8 * q^65 + 64 * q^66 + 24 * q^68 - 8 * q^70 - 32 * q^72 + 48 * q^73 - 136 * q^74 - 88 * q^76 + 52 * q^78 - 32 * q^80 + 56 * q^81 - 20 * q^84 - 64 * q^86 - 8 * q^89 - 88 * q^92 - 48 * q^93 - 16 * q^94 - 4 * q^96 - 32 * q^97 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.400070	−	1.35645i	0.282892	−	0.959152i
$2$	0.400070	−	1.35645i	0.282892	−	0.959152i
$3$		−	2.57103i		−	1.48438i	−0.670188	−	0.742191i	$-0.733787\pi$
$3$		−	2.57103i		−	1.48438i	0.670188	−	0.742191i	$-0.266213\pi$
$4$	−1.67989	−	1.08535i	−0.839944	−	0.542673i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	−3.48746	−	1.02859i	−1.42375	−	0.419920i
$7$	3.59259	−	3.59259i	1.35787	−	1.35787i	0.481334	−	0.876537i	$-0.340152\pi$
$7$	3.59259	−	3.59259i	1.35787	−	1.35787i	0.876537	−	0.481334i	$-0.159848\pi$
$8$	−2.14428	+	1.84446i	−0.758119	+	0.652116i
$9$	−3.61018			−1.20339
$10$	0.676260	+	1.24204i	0.213852	+	0.392769i
$11$	−3.05830	+	3.05830i	−0.922111	+	0.922111i	−0.997178	−	0.0750678i	$-0.976083\pi$
$11$	−3.05830	+	3.05830i	−0.922111	+	0.922111i	0.0750678	+	0.997178i	$0.476083\pi$
$12$	−2.79045	+	4.31904i	−0.805534	+	1.24680i
$13$	3.27029	+	1.51828i	0.907017	+	0.421095i
$13$	3.27029	+	1.51828i	0.907017	+	0.421095i
$14$	−3.43587	−	6.31044i	−0.918274	−	1.68654i
$15$	1.81799	+	1.81799i	0.469403	+	0.469403i
$16$	1.64405	+	3.64652i	0.411013	+	0.911630i
$17$		−	2.76630i		−	0.670926i	−0.942053	−	0.335463i	$-0.891107\pi$
$17$		−	2.76630i		−	0.670926i	0.942053	−	0.335463i	$-0.108893\pi$
$18$	−1.44432	+	4.89701i	−0.340430	+	1.15424i
$19$	1.96423	+	1.96423i	0.450625	+	0.450625i	0.895562	−	0.444937i	$-0.146774\pi$
$19$	1.96423	+	1.96423i	0.450625	+	0.450625i	−0.444937	+	0.895562i	$0.646774\pi$
$20$	1.95532	−	0.420406i	0.437222	−	0.0940056i
$21$	−9.23664	−	9.23664i	−2.01560	−	2.01560i
$22$	2.92488	+	5.37194i	0.623586	+	1.14530i
$23$	−3.63848			−0.758676			−0.379338	−	0.925258i	$-0.623848\pi$
$23$	−3.63848			−0.758676			−0.379338	+	0.925258i	$0.623848\pi$
$24$	4.74216	+	5.51301i	0.967990	+	1.12534i
$25$		−	1.00000i		−	0.200000i
$26$	3.36781	−	3.82856i	0.660482	−	0.750842i
$27$			1.56878i			0.301912i
$28$	−9.93435	+	2.13595i	−1.87742	+	0.403657i
$29$	5.48514			1.01856			0.509282	−	0.860599i	$-0.329911\pi$
$29$	5.48514			1.01856			0.509282	+	0.860599i	$0.329911\pi$
$30$	3.19333	−	1.73868i	0.583019	−	0.317438i
$31$	−0.232457	−	0.232457i	−0.0417505	−	0.0417505i	0.685923	−	0.727674i	$-0.259399\pi$
$31$	−0.232457	−	0.232457i	−0.0417505	−	0.0417505i	−0.727674	+	0.685923i	$0.759399\pi$
$32$	5.60404	−	0.771205i	0.990663	−	0.136331i
$33$	7.86296	+	7.86296i	1.36877	+	1.36877i
$34$	−3.75233	−	1.10671i	−0.643520	−	0.189799i
$35$			5.08069i			0.858793i
$36$	6.06469	+	3.91829i	1.01078	+	0.653048i
$37$	−1.59052	−	1.59052i	−0.261480	−	0.261480i	0.564175	−	0.825655i	$-0.309194\pi$
$37$	−1.59052	−	1.59052i	−0.261480	−	0.261480i	−0.825655	+	0.564175i	$0.809194\pi$
$38$	3.45020	−	1.87854i	0.559697	−	0.304740i
$39$	3.90353	−	8.40801i	0.625066	−	1.34636i
$40$	0.212005	−	2.82047i	0.0335209	−	0.445956i
$41$	−0.376964	+	0.376964i	−0.0588719	+	0.0588719i	−0.735930	−	0.677058i	$-0.763255\pi$
$41$	−0.376964	+	0.376964i	−0.0588719	+	0.0588719i	0.677058	+	0.735930i	$0.263255\pi$
$42$	−16.2243	+	8.83370i	−2.50346	+	1.36307i
$43$	2.31562			0.353129			0.176564	−	0.984289i	$-0.443502\pi$
$43$	2.31562			0.353129			0.176564	+	0.984289i	$0.443502\pi$
$44$	8.45690	−	1.81829i	1.27493	−	0.274117i
$45$	2.55278	−	2.55278i	0.380546	−	0.380546i
$46$	−1.45565	+	4.93540i	−0.214623	+	0.727685i
$47$	1.51890	−	1.51890i	0.221554	−	0.221554i	−0.587598	−	0.809153i	$-0.699927\pi$
$47$	1.51890	−	1.51890i	0.221554	−	0.221554i	0.809153	+	0.587598i	$0.199927\pi$
$48$	9.37529	−	4.22690i	1.35321	−	0.610100i
$49$		−	18.8134i		−	2.68763i
$50$	−1.35645	−	0.400070i	−0.191830	−	0.0565784i
$51$	−7.11222			−0.995911
$52$	−3.84587	−	6.09994i	−0.533327	−	0.845909i
$53$	−9.54628			−1.31128			−0.655641	−	0.755072i	$-0.727602\pi$
$53$	−9.54628			−1.31128			−0.655641	+	0.755072i	$0.727602\pi$
$54$	2.12796	+	0.627620i	0.289579	+	0.0854083i
$55$		−	4.32508i		−	0.583194i
$56$	−1.07713	+	14.3299i	−0.143938	+	1.91492i
$57$	5.05009	−	5.05009i	0.668901	−	0.668901i
$58$	2.19444	−	7.44029i	0.288144	−	0.976958i
$59$	5.39264	−	5.39264i	0.702062	−	0.702062i	−0.262790	−	0.964853i	$-0.584643\pi$
$59$	5.39264	−	5.39264i	0.702062	−	0.702062i	0.964853	+	0.262790i	$0.0846428\pi$
$60$	−1.08087	−	5.02717i	−0.139540	−	0.649005i
$61$	2.11653			0.270993			0.135497	−	0.990778i	$-0.456737\pi$
$61$	2.11653			0.270993			0.135497	+	0.990778i	$0.456737\pi$
$62$	−0.408314	+	0.222316i	−0.0518560	+	0.0282342i
$63$	−12.9699	+	12.9699i	−1.63405	+	1.63405i
$64$	1.19591	−	7.91011i	0.149488	−	0.988763i
$65$	−3.38603	+	1.23886i	−0.419986	+	0.153662i
$66$	13.8114	−	7.51994i	1.70007	−	0.925641i
$67$	8.28906	+	8.28906i	1.01267	+	1.01267i	0.999919	+	0.0127517i	$0.00405911\pi$
$67$	8.28906	+	8.28906i	1.01267	+	1.01267i	0.0127517	+	0.999919i	$0.495941\pi$
$68$	−3.00239	+	4.64707i	−0.364093	+	0.563540i
$69$			9.35463i			1.12616i
$70$	6.89168	+	2.03263i	0.823713	+	0.242946i
$71$	−0.0524499	−	0.0524499i	−0.00622465	−	0.00622465i	0.703988	−	0.710212i	$-0.251401\pi$
$71$	−0.0524499	−	0.0524499i	−0.00622465	−	0.00622465i	−0.710212	+	0.703988i	$0.751401\pi$
$72$	7.74124	−	6.65884i	0.912314	−	0.784752i
$73$	2.86601	+	2.86601i	0.335441	+	0.335441i	0.854648	−	0.519208i	$-0.173773\pi$
$73$	2.86601	+	2.86601i	0.335441	+	0.335441i	−0.519208	+	0.854648i	$0.673773\pi$
$74$	−2.79377	+	1.52113i	−0.324769	+	0.176828i
$75$	−2.57103			−0.296877
$76$	−1.16782	−	5.43156i	−0.133958	−	0.623042i
$77$			21.9744i			2.50422i
$78$	−9.84333	−	8.65872i	−1.11454	−	0.980407i
$79$			7.92711i			0.891869i	0.895065	+	0.445935i	$0.147129\pi$
$79$			7.92711i			0.891869i	−0.895065	+	0.445935i	$0.852871\pi$
$80$	−3.74100	−	1.41596i	−0.418256	−	0.158309i
$81$	−6.79716			−0.755240
$82$	0.360519	+	0.662143i	0.0398127	+	0.0731215i
$83$	7.11999	+	7.11999i	0.781520	+	0.781520i	0.980087	−	0.198567i	$-0.0636287\pi$
$83$	7.11999	+	7.11999i	0.781520	+	0.781520i	−0.198567	+	0.980087i	$0.563629\pi$
$84$	5.49159	+	25.5415i	0.599181	+	2.78680i
$85$	1.95607	+	1.95607i	0.212165	+	0.212165i
$86$	0.926409	−	3.14101i	0.0998973	−	0.338704i
$87$		−	14.1024i		−	1.51194i
$88$	0.916939	−	12.1988i	0.0977460	−	1.30039i
$89$	1.71088	+	1.71088i	0.181353	+	0.181353i	0.791945	−	0.610592i	$-0.209068\pi$
$89$	1.71088	+	1.71088i	0.181353	+	0.181353i	−0.610592	+	0.791945i	$0.709068\pi$
$90$	−2.44142	−	4.48400i	−0.257348	−	0.472655i
$91$	17.2034	−	6.29427i	1.80340	−	0.659819i
$92$	6.11224	+	3.94901i	0.637245	+	0.411712i
$93$	−0.597653	+	0.597653i	−0.0619737	+	0.0619737i
$94$	−1.45264	−	2.66797i	−0.149828	−	0.275180i
$95$	−2.77784			−0.285001
$96$	−1.98279	−	14.4081i	−0.202368	−	1.47052i
$97$	1.75502	−	1.75502i	0.178195	−	0.178195i	−0.612373	−	0.790569i	$-0.709785\pi$
$97$	1.75502	−	1.75502i	0.178195	−	0.178195i	0.790569	+	0.612373i	$0.209785\pi$
$98$	−25.5194	−	7.52667i	−2.57784	−	0.760309i
$99$	11.0410	−	11.0410i	1.10966	−	1.10966i
$100$	−1.08535	+	1.67989i	−0.108535	+	0.167989i
$101$			17.0242i			1.69398i	0.531612	+	0.846988i	$0.321586\pi$
$101$			17.0242i			1.69398i	−0.531612	+	0.846988i	$0.678414\pi$
$102$	−2.84538	+	9.64734i	−0.281735	+	0.955229i
$103$	−16.5641			−1.63211			−0.816055	−	0.577974i	$-0.803843\pi$
$103$	−16.5641			−1.63211			−0.816055	+	0.577974i	$0.803843\pi$
$104$	−9.81285	+	2.77632i	−0.962229	+	0.272241i
$105$	13.0626			1.27478
$106$	−3.81918	+	12.9490i	−0.370951	+	1.25772i
$107$			0.769862i			0.0744254i	0.999307	+	0.0372127i	$0.0118479\pi$
$107$			0.769862i			0.0744254i	−0.999307	+	0.0372127i	$0.988152\pi$
$108$	1.70267	−	2.63537i	0.163839	−	0.253589i
$109$	−13.5091	+	13.5091i	−1.29393	+	1.29393i	−0.361599	+	0.932334i	$0.617769\pi$
$109$	−13.5091	+	13.5091i	−1.29393	+	1.29393i	−0.932334	+	0.361599i	$0.882231\pi$
$110$	−5.86674	−	1.73033i	−0.559372	−	0.164981i
$111$	−4.08927	+	4.08927i	−0.388136	+	0.388136i
$112$	19.0068	+	7.19404i	1.79598	+	0.679773i
$113$	16.1229			1.51671			0.758357	−	0.651840i	$-0.226002\pi$
$113$	16.1229			1.51671			0.758357	+	0.651840i	$0.226002\pi$
$114$	−4.82978	−	8.87056i	−0.452351	−	0.830804i
$115$	2.57279	−	2.57279i	0.239914	−	0.239914i
$116$	−9.21442	−	5.95327i	−0.855538	−	0.552747i
$117$	−11.8063	−	5.48125i	−1.09150	−	0.506742i
$118$	−5.15739	−	9.47226i	−0.474777	−	0.871992i
$119$	−9.93817	−	9.93817i	−0.911031	−	0.911031i
$120$	−7.25150	−	0.545070i	−0.661969	−	0.0497579i
$121$		−	7.70634i		−	0.700576i
$122$	0.846758	−	2.87095i	0.0766618	−	0.259924i
$123$	0.969185	+	0.969185i	0.0873884	+	0.0873884i
$124$	0.138206	+	0.642798i	0.0124112	+	0.0577250i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	12.4041	+	22.7818i	1.10504	+	2.02956i
$127$	−2.34571			−0.208148			−0.104074	−	0.994570i	$-0.533188\pi$
$127$	−2.34571			−0.208148			−0.104074	+	0.994570i	$0.533188\pi$
$128$	−10.2512	−	4.78678i	−0.906085	−	0.423095i
$129$		−	5.95352i		−	0.524178i
$130$	0.325800	+	5.08860i	0.0285746	+	0.446300i
$131$			1.00189i			0.0875354i	0.999042	+	0.0437677i	$0.0139361\pi$
$131$			1.00189i			0.0875354i	−0.999042	+	0.0437677i	$0.986064\pi$
$132$	−4.67487	−	21.7429i	−0.406895	−	1.89248i
$133$	14.1134			1.22378
$134$	14.5599	−	7.92746i	1.25778	−	0.684828i
$135$	−1.10929	−	1.10929i	−0.0954728	−	0.0954728i
$136$	5.10234	+	5.93173i	0.437522	+	0.508641i
$137$	−2.60305	−	2.60305i	−0.222394	−	0.222394i	0.587112	−	0.809506i	$-0.300265\pi$
$137$	−2.60305	−	2.60305i	−0.222394	−	0.222394i	−0.809506	+	0.587112i	$0.800265\pi$
$138$	12.6890	+	3.74250i	1.08016	+	0.318583i
$139$			21.3031i			1.80691i	0.428684	+	0.903455i	$0.358978\pi$
$139$			21.3031i			1.80691i	−0.428684	+	0.903455i	$0.641022\pi$
$140$	5.51430	−	8.53499i	0.466044	−	0.721338i
$141$	−3.90513	−	3.90513i	−0.328871	−	0.328871i
$142$	−0.0921290	+	0.0501618i	−0.00773129	+	0.00420948i
$143$	−14.6449	+	5.35818i	−1.22467	+	0.448074i
$144$	−5.93532	−	13.1646i	−0.494610	−	1.09705i
$145$	−3.87858	+	3.87858i	−0.322098	+	0.322098i
$146$	5.03418	−	2.74098i	0.416632	−	0.226845i
$147$	−48.3698			−3.98947
$148$	0.945633	+	4.39816i	0.0777305	+	0.361526i
$149$	6.82112	−	6.82112i	0.558808	−	0.558808i	−0.370160	−	0.928968i	$-0.620697\pi$
$149$	6.82112	−	6.82112i	0.558808	−	0.558808i	0.928968	+	0.370160i	$0.120697\pi$
$150$	−1.02859	+	3.48746i	−0.0839840	+	0.284750i
$151$	6.56341	−	6.56341i	0.534122	−	0.534122i	−0.387674	−	0.921796i	$-0.626721\pi$
$151$	6.56341	−	6.56341i	0.534122	−	0.534122i	0.921796	+	0.387674i	$0.126721\pi$
$152$	−7.83482	−	0.588916i	−0.635488	−	0.0477674i
$153$			9.98682i			0.807387i
$154$	29.8071	+	8.79129i	2.40192	+	0.708422i
$155$	0.328744			0.0264053
$156$	−15.6831	+	9.88784i	−1.25565	+	0.791661i
$157$	−12.3257			−0.983694			−0.491847	−	0.870682i	$-0.663678\pi$
$157$	−12.3257			−0.983694			−0.491847	+	0.870682i	$0.663678\pi$
$158$	10.7527	+	3.17140i	0.855438	+	0.252303i
$159$			24.5437i			1.94645i
$160$	−3.41733	+	4.50798i	−0.270164	+	0.356387i
$161$	−13.0716	+	13.0716i	−1.03018	+	1.03018i
$162$	−2.71934	+	9.21997i	−0.213651	+	0.724390i
$163$	10.7347	−	10.7347i	0.840808	−	0.840808i	−0.148156	−	0.988964i	$-0.547334\pi$
$163$	10.7347	−	10.7347i	0.840808	−	0.840808i	0.988964	+	0.148156i	$0.0473337\pi$
$164$	1.04239	−	0.224122i	0.0813973	−	0.0175010i
$165$	−11.1199			−0.865683
$166$	12.5064	−	6.80939i	0.970682	−	0.528511i
$167$	5.58527	−	5.58527i	0.432201	−	0.432201i	−0.457175	−	0.889377i	$-0.651139\pi$
$167$	5.58527	−	5.58527i	0.432201	−	0.432201i	0.889377	+	0.457175i	$0.151139\pi$
$168$	36.8426	+	2.76933i	2.84247	+	0.213659i
$169$	8.38966	+	9.93044i	0.645358	+	0.763880i
$170$	3.43586	−	1.87074i	0.263519	−	0.143479i
$171$	−7.09122	−	7.09122i	−0.542279	−	0.542279i
$172$	−3.88998	−	2.51325i	−0.296608	−	0.191633i
$173$			16.5070i			1.25501i	0.778614	+	0.627504i	$0.215923\pi$
$173$			16.5070i			1.25501i	−0.778614	+	0.627504i	$0.784077\pi$
$174$	−19.1292	−	5.64196i	−1.45018	−	0.427716i
$175$	−3.59259	−	3.59259i	−0.271574	−	0.271574i
$176$	−16.1801	−	6.12413i	−1.21962	−	0.461624i
$177$	−13.8646	−	13.8646i	−1.04213	−	1.04213i
$178$	3.00519	−	1.63625i	0.225249	−	0.122642i
$179$	−18.7832			−1.40392			−0.701962	−	0.712215i	$-0.747692\pi$
$179$	−18.7832			−1.40392			−0.701962	+	0.712215i	$0.747692\pi$
$180$	−7.05903	+	1.51774i	−0.526149	+	0.113126i
$181$		−	8.58896i		−	0.638412i	−0.947685	−	0.319206i	$-0.896584\pi$
$181$		−	8.58896i		−	0.638412i	0.947685	−	0.319206i	$-0.103416\pi$
$182$	−1.65529	−	25.8536i	−0.122698	−	1.91640i
$183$		−	5.44164i		−	0.402258i
$184$	7.80193	−	6.71104i	0.575166	−	0.494745i
$185$	2.24933			0.165374
$186$	0.571581	+	1.04979i	0.0419103	+	0.0769741i
$187$	8.46016	+	8.46016i	0.618668	+	0.618668i
$188$	−4.20011	+	0.903052i	−0.306325	+	0.0658618i
$189$	5.63598	+	5.63598i	0.409957	+	0.409957i
$190$	−1.11133	+	3.76799i	−0.0806244	+	0.273359i
$191$		−	14.2936i		−	1.03425i	−0.855910	−	0.517124i	$-0.827003\pi$
$191$		−	14.2936i		−	1.03425i	0.855910	−	0.517124i	$-0.172997\pi$
$192$	−20.3371	−	3.07471i	−1.46770	−	0.221898i
$193$	−4.31470	−	4.31470i	−0.310579	−	0.310579i	0.534555	−	0.845134i	$-0.320479\pi$
$193$	−4.31470	−	4.31470i	−0.310579	−	0.310579i	−0.845134	+	0.534555i	$0.820479\pi$
$194$	−1.67846	−	3.08272i	−0.120506	−	0.221326i
$195$	3.18515	+	8.70558i	0.228093	+	0.623420i
$196$	−20.4190	+	31.6044i	−1.45850	+	2.25746i
$197$	12.3367	−	12.3367i	0.878955	−	0.878955i	−0.114472	−	0.993426i	$-0.536518\pi$
$197$	12.3367	−	12.3367i	0.878955	−	0.878955i	0.993426	+	0.114472i	$0.0365176\pi$
$198$	−10.5593	−	19.3937i	−0.750419	−	1.37825i
$199$	2.17568			0.154230			0.0771151	−	0.997022i	$-0.475429\pi$
$199$	2.17568			0.154230			0.0771151	+	0.997022i	$0.475429\pi$
$200$	1.84446	+	2.14428i	0.130423	+	0.151624i
$201$	21.3114	−	21.3114i	1.50319	−	1.50319i
$202$	23.0925	+	6.81088i	1.62478	+	0.479212i
$203$	19.7059	−	19.7059i	1.38308	−	1.38308i
$204$	11.9477	+	7.71922i	0.836509	+	0.540453i
$205$		−	0.533108i		−	0.0372339i
$206$	−6.62679	+	22.4683i	−0.461711	+	1.56544i
$207$	13.1356			0.912984
$208$	−0.159898	+	14.4213i	−0.0110869	+	0.999939i
$209$	−12.0144			−0.831053
$210$	5.22594	−	17.7187i	0.360624	−	1.22271i
$211$		−	14.6097i		−	1.00578i	−0.864352	−	0.502888i	$-0.832271\pi$
$211$		−	14.6097i		−	1.00578i	0.864352	−	0.502888i	$-0.167729\pi$
$212$	16.0367	+	10.3610i	1.10140	+	0.711597i
$213$	−0.134850	+	0.134850i	−0.00923977	+	0.00923977i
$214$	1.04428	+	0.307998i	0.0713852	+	0.0210543i
$215$	−1.63739	+	1.63739i	−0.111669	+	0.111669i
$216$	−2.89355	−	3.36391i	−0.196881	−	0.228885i
$217$	−1.67025			−0.113384
$218$	12.9197	+	23.7289i	0.875035	+	1.60712i
$219$	7.36857	−	7.36857i	0.497922	−	0.497922i
$220$	−4.69421	+	7.26566i	−0.316483	+	0.489850i
$221$	4.20001	−	9.04661i	0.282523	−	0.608541i
$222$	3.91088	+	7.18286i	0.262481	+	0.482082i
$223$	11.4194	+	11.4194i	0.764700	+	0.764700i	0.977168	−	0.212468i	$-0.0681502\pi$
$223$	11.4194	+	11.4194i	0.764700	+	0.764700i	−0.212468	+	0.977168i	$0.568150\pi$
$224$	17.3624	−	22.9036i	1.16007	−	1.53031i
$225$			3.61018i			0.240678i
$226$	6.45028	−	21.8698i	0.429066	−	1.45476i
$227$	1.31638	+	1.31638i	0.0873712	+	0.0873712i	0.749442	−	0.662070i	$-0.230322\pi$
$227$	1.31638	+	1.31638i	0.0873712	+	0.0873712i	−0.662070	+	0.749442i	$0.730322\pi$
$228$	−13.9647	+	3.00250i	−0.924833	+	0.198845i
$229$	−17.1004	−	17.1004i	−1.13002	−	1.13002i	−0.990172	−	0.139852i	$-0.955337\pi$
$229$	−17.1004	−	17.1004i	−1.13002	−	1.13002i	−0.139852	−	0.990172i	$-0.544663\pi$
$230$	−2.46056	−	4.51915i	−0.162244	−	0.297984i
$231$	56.4968			3.71721
$232$	−11.7617	+	10.1171i	−0.772193	+	0.664223i
$233$			12.1762i			0.797687i	0.917019	+	0.398843i	$0.130588\pi$
$233$			12.1762i			0.797687i	−0.917019	+	0.398843i	$0.869412\pi$
$234$	−12.1584	+	13.8218i	−0.794818	+	0.903558i
$235$			2.14805i			0.140123i
$236$	−14.9119	+	3.20616i	−0.970683	+	0.208703i
$237$	20.3808			1.32388
$238$	−17.4566	+	9.50463i	−1.13154	+	0.616094i
$239$	5.17121	+	5.17121i	0.334498	+	0.334498i	0.854292	−	0.519794i	$-0.173991\pi$
$239$	5.17121	+	5.17121i	0.334498	+	0.334498i	−0.519794	+	0.854292i	$0.673991\pi$
$240$	−3.64046	+	9.61820i	−0.234991	+	0.620852i
$241$	3.99736	+	3.99736i	0.257492	+	0.257492i	0.824034	−	0.566541i	$-0.191719\pi$
$241$	3.99736	+	3.99736i	0.257492	+	0.257492i	−0.566541	+	0.824034i	$0.691719\pi$
$242$	−10.4532	−	3.08307i	−0.671959	−	0.198187i
$243$			22.1820i			1.42298i
$244$	−3.55553	−	2.29716i	−0.227619	−	0.147061i
$245$	13.3031	+	13.3031i	0.849903	+	0.849903i
$246$	1.70239	−	0.926905i	0.108540	−	0.0590973i
$247$	3.44136	+	9.40587i	0.218969	+	0.598481i
$248$	0.927212	+	0.0696953i	0.0588780	+	0.00442566i
$249$	18.3057	−	18.3057i	1.16008	−	1.16008i
$250$	1.24204	−	0.676260i	0.0785537	−	0.0427704i
$251$	−25.9009			−1.63485			−0.817425	−	0.576035i	$-0.804599\pi$
$251$	−25.9009			−1.63485			−0.817425	+	0.576035i	$0.804599\pi$
$252$	35.8648	−	7.71116i	2.25927	−	0.485757i
$253$	11.1275	−	11.1275i	0.699583	−	0.699583i
$254$	−0.938446	+	3.18182i	−0.0588833	+	0.199645i
$255$	5.02910	−	5.02910i	0.314935	−	0.314935i
$256$	−10.5942	+	11.9901i	−0.662137	+	0.749383i
$257$			3.57554i			0.223036i	0.993762	+	0.111518i	$0.0355713\pi$
$257$			3.57554i			0.223036i	−0.993762	+	0.111518i	$0.964429\pi$
$258$	−8.07562	−	2.38182i	−0.502766	−	0.148286i
$259$	−11.4282			−0.710112
$260$	7.03275	+	1.59386i	0.436153	+	0.0988472i
$261$	−19.8023			−1.22573
$262$	1.35901	+	0.400825i	0.0839597	+	0.0247630i
$263$			12.2258i			0.753872i	0.926239	+	0.376936i	$0.123022\pi$
$263$			12.2258i			0.753872i	−0.926239	+	0.376936i	$0.876978\pi$
$264$	−31.3634	−	2.35747i	−1.93028	−	0.145092i
$265$	6.75024	−	6.75024i	0.414664	−	0.414664i
$266$	5.64632	−	19.1440i	0.346198	−	1.17379i
$267$	4.39873	−	4.39873i	0.269198	−	0.269198i
$268$	−4.92821	−	22.9212i	−0.301038	−	1.40014i
$269$	−29.8653			−1.82092			−0.910461	−	0.413594i	$-0.864273\pi$
$269$	−29.8653			−1.82092			−0.910461	+	0.413594i	$0.864273\pi$
$270$	−1.94849	+	1.06090i	−0.118581	+	0.0645644i
$271$	−2.94297	+	2.94297i	−0.178773	+	0.178773i	−0.790821	−	0.612048i	$-0.790346\pi$
$271$	−2.94297	+	2.94297i	−0.178773	+	0.178773i	0.612048	+	0.790821i	$0.290346\pi$
$272$	10.0874	−	4.54794i	0.611636	−	0.275759i
$273$	−16.1827	−	44.2303i	−0.979424	−	2.67694i
$274$	−4.57230	+	2.48950i	−0.276223	+	0.150396i
$275$	3.05830	+	3.05830i	0.184422	+	0.184422i
$276$	10.1530	−	15.7147i	0.611139	−	0.945916i
$277$		−	5.02752i		−	0.302074i	−0.988528	−	0.151037i	$-0.951739\pi$
$277$		−	5.02752i		−	0.302074i	0.988528	−	0.151037i	$-0.0482613\pi$
$278$	28.8966	+	8.52274i	1.73310	+	0.511160i
$279$	0.839211	+	0.839211i	0.0502422	+	0.0502422i
$280$	−9.37115	−	10.8944i	−0.560033	−	0.651067i
$281$	0.863791	+	0.863791i	0.0515294	+	0.0515294i	0.732402	−	0.680873i	$-0.238399\pi$
$281$	0.863791	+	0.863791i	0.0515294	+	0.0515294i	−0.680873	+	0.732402i	$0.738399\pi$
$282$	−6.85942	+	3.73477i	−0.408472	+	0.222402i
$283$	5.99944			0.356629			0.178315	−	0.983974i	$-0.442935\pi$
$283$	5.99944			0.356629			0.178315	+	0.983974i	$0.442935\pi$
$284$	0.0311837	+	0.145036i	0.00185041	+	0.00860631i
$285$			7.14190i			0.423050i
$286$	1.40911	+	22.0086i	0.0833226	+	1.30140i
$287$			2.70855i			0.159881i
$288$	−20.2316	+	2.78419i	−1.19216	+	0.164060i
$289$	9.34760			0.549859
$290$	3.70938	+	6.81278i	0.217822	+	0.400060i
$291$	−4.51220	−	4.51220i	−0.264510	−	0.264510i
$292$	−1.70396	−	7.92517i	−0.0997170	−	0.463786i
$293$	−1.53216	−	1.53216i	−0.0895098	−	0.0895098i	0.660934	−	0.750444i	$-0.270160\pi$
$293$	−1.53216	−	1.53216i	−0.0895098	−	0.0895098i	−0.750444	+	0.660934i	$0.770160\pi$
$294$	−19.3513	+	65.6109i	−1.12859	+	3.82651i
$295$			7.62635i			0.444023i
$296$	6.34418	+	0.476870i	0.368748	+	0.0277175i
$297$	−4.79779	−	4.79779i	−0.278396	−	0.278396i
$298$	−6.52355	−	11.9814i	−0.377899	−	0.694063i
$299$	−11.8989	−	5.52423i	−0.688131	−	0.319474i
$300$	4.31904	+	2.79045i	0.249360	+	0.161107i
$301$	8.31907	−	8.31907i	0.479503	−	0.479503i
$302$	−6.27708	−	11.5287i	−0.361206	−	0.663403i
$303$	43.7698			2.51451
$304$	−3.93331	+	10.3919i	−0.225591	+	0.596016i
$305$	−1.49661	+	1.49661i	−0.0856956	+	0.0856956i
$306$	13.5466	+	3.99542i	0.774406	+	0.228403i
$307$	−8.35408	+	8.35408i	−0.476793	+	0.476793i	−0.904104	−	0.427312i	$-0.859461\pi$
$307$	−8.35408	+	8.35408i	−0.476793	+	0.476793i	0.427312	+	0.904104i	$0.359461\pi$
$308$	23.8498	−	36.9145i	1.35897	−	2.10340i
$309$			42.5867i			2.42268i
$310$	0.131520	−	0.445923i	0.00746986	−	0.0253267i
$311$	8.47627			0.480645			0.240322	−	0.970693i	$-0.422747\pi$
$311$	8.47627			0.480645			0.240322	+	0.970693i	$0.422747\pi$
$312$	7.13799	+	25.2291i	0.404109	+	1.42832i
$313$	−8.79326			−0.497025			−0.248512	−	0.968629i	$-0.579942\pi$
$313$	−8.79326			−0.497025			−0.248512	+	0.968629i	$0.579942\pi$
$314$	−4.93112	+	16.7191i	−0.278279	+	0.943512i
$315$		−	18.3422i		−	1.03346i
$316$	8.60365	−	13.3167i	0.483993	−	0.749121i
$317$	−0.556029	+	0.556029i	−0.0312297	+	0.0312297i	−0.722549	−	0.691320i	$-0.757030\pi$
$317$	−0.556029	+	0.556029i	−0.0312297	+	0.0312297i	0.691320	+	0.722549i	$0.257030\pi$
$318$	33.2922	+	9.81920i	1.86694	+	0.550634i
$319$	−16.7752	+	16.7752i	−0.939229	+	0.939229i
$320$	4.74766	+	6.43892i	0.265402	+	0.359947i
$321$	1.97934			0.110476
$322$	12.5013	+	22.9604i	0.696672	+	1.27953i
$323$	5.43365	−	5.43365i	0.302336	−	0.302336i
$324$	11.4185	+	7.37726i	0.634359	+	0.409848i
$325$	1.51828	−	3.27029i	0.0842190	−	0.181403i
$326$	−10.2664	−	18.8557i	−0.568605	−	1.04432i
$327$	34.7321	+	34.7321i	1.92069	+	1.92069i
$328$	0.113021	−	1.50361i	0.00624057	−	0.0830232i
$329$		−	10.9136i		−	0.601684i
$330$	−4.44873	+	15.0835i	−0.244895	+	0.830321i
$331$	12.3394	+	12.3394i	0.678233	+	0.678233i	0.959600	−	0.281367i	$-0.0907879\pi$
$331$	12.3394	+	12.3394i	0.678233	+	0.678233i	−0.281367	+	0.959600i	$0.590788\pi$
$332$	−4.23314	−	19.6884i	−0.232324	−	1.08054i
$333$	5.74205	+	5.74205i	0.314663	+	0.314663i
$334$	−5.34162	−	9.81062i	−0.292280	−	0.536813i
$335$	−11.7225			−0.640469
$336$	18.4961	−	48.8671i	1.00904	−	2.66592i
$337$			5.63331i			0.306866i	0.988159	+	0.153433i	$0.0490329\pi$
$337$			5.63331i			0.306866i	−0.988159	+	0.153433i	$0.950967\pi$
$338$	16.8265	−	7.40725i	0.915244	−	0.402901i
$339$		−	41.4524i		−	2.25138i
$340$	−1.16297	−	5.40899i	−0.0630708	−	0.293343i
$341$	1.42184			0.0769972
$342$	−12.4558	+	6.78187i	−0.673534	+	0.366722i
$343$	−42.4407	−	42.4407i	−2.29158	−	2.29158i
$344$	−4.96535	+	4.27108i	−0.267714	+	0.230281i
$345$	−6.61472	−	6.61472i	−0.356125	−	0.356125i
$346$	22.3909	+	6.60397i	1.20374	+	0.355031i
$347$		−	9.75415i		−	0.523630i	−0.965118	−	0.261815i	$-0.915679\pi$
$347$		−	9.75415i		−	0.523630i	0.965118	−	0.261815i	$-0.0843211\pi$
$348$	−15.3060	+	23.6905i	−0.820488	+	1.26995i
$349$	18.5602	+	18.5602i	0.993506	+	0.993506i	0.999979	−	0.00647329i	$-0.00206053\pi$
$349$	18.5602	+	18.5602i	0.993506	+	0.993506i	−0.00647329	+	0.999979i	$0.502061\pi$
$350$	−6.31044	+	3.43587i	−0.337307	+	0.183655i
$351$	−2.38184	+	5.13037i	−0.127133	+	0.273839i
$352$	−14.7802	+	19.4974i	−0.787789	+	1.03921i
$353$	6.50938	−	6.50938i	0.346460	−	0.346460i	−0.512329	−	0.858789i	$-0.671217\pi$
$353$	6.50938	−	6.50938i	0.346460	−	0.346460i	0.858789	+	0.512329i	$0.171217\pi$
$354$	−24.3534	+	13.2598i	−1.29437	+	0.704750i
$355$	0.0741753			0.00393682
$356$	−1.01719	−	4.73099i	−0.0539112	−	0.250742i
$357$	−25.5513	+	25.5513i	−1.35232	+	1.35232i
$358$	−7.51459	+	25.4784i	−0.397159	+	1.34658i
$359$	−1.28987	+	1.28987i	−0.0680766	+	0.0680766i	−0.740325	−	0.672249i	$-0.765329\pi$
$359$	−1.28987	+	1.28987i	−0.0680766	+	0.0680766i	0.672249	+	0.740325i	$0.265329\pi$
$360$	−0.765375	+	10.1824i	−0.0403388	+	0.536659i
$361$		−	11.2836i		−	0.593873i
$362$	−11.6504	−	3.43618i	−0.612334	−	0.180602i
$363$	−19.8132			−1.03992
$364$	−35.7312	−	8.09793i	−1.87283	−	0.424447i
$365$	−4.05314			−0.212151
$366$	−7.38129	−	2.17704i	−0.385826	−	0.113795i
$367$		−	20.6014i		−	1.07539i	−0.843141	−	0.537693i	$-0.819296\pi$
$367$		−	20.6014i		−	1.07539i	0.843141	−	0.537693i	$-0.180704\pi$
$368$	−5.98185	−	13.2678i	−0.311825	−	0.691631i
$369$	1.36091	−	1.36091i	0.0708460	−	0.0708460i
$370$	0.899890	−	3.05110i	0.0467830	−	0.158619i
$371$	−34.2959	+	34.2959i	−1.78055	+	1.78055i
$372$	1.65265	−	0.355331i	0.0856859	−	0.0184230i
$373$	−33.6227			−1.74092			−0.870460	−	0.492239i	$-0.836178\pi$
$373$	−33.6227			−1.74092			−0.870460	+	0.492239i	$0.836178\pi$
$374$	14.8604	−	8.09109i	0.768412	−	0.418380i
$375$	1.81799	−	1.81799i	0.0938806	−	0.0938806i
$376$	−0.455397	+	6.05851i	−0.0234853	+	0.312444i
$377$	17.9380	+	8.32797i	0.923855	+	0.428912i
$378$	9.89968	−	5.39011i	0.509184	−	0.277237i
$379$	−18.6069	−	18.6069i	−0.955774	−	0.955774i	0.0432886	−	0.999063i	$-0.486217\pi$
$379$	−18.6069	−	18.6069i	−0.955774	−	0.955774i	−0.999063	+	0.0432886i	$0.986217\pi$
$380$	4.66647	+	3.01492i	0.239385	+	0.154662i
$381$			6.03087i			0.308971i
$382$	−19.3885	−	5.71843i	−0.992001	−	0.292580i
$383$	3.36439	+	3.36439i	0.171912	+	0.171912i	0.787819	−	0.615907i	$-0.211210\pi$
$383$	3.36439	+	3.36439i	0.171912	+	0.171912i	−0.615907	+	0.787819i	$0.711210\pi$
$384$	−12.3069	+	26.3561i	−0.628035	+	1.34498i
$385$	−15.5382	−	15.5382i	−0.791902	−	0.791902i
$386$	−7.57884	+	4.12648i	−0.385753	+	0.210032i
$387$	−8.35979			−0.424952
$388$	−4.85304	+	1.04344i	−0.246376	+	0.0529724i
$389$		−	24.0545i		−	1.21961i	−0.792550	−	0.609807i	$-0.791247\pi$
$389$		−	24.0545i		−	1.21961i	0.792550	−	0.609807i	$-0.208753\pi$
$390$	13.0829	−	0.837641i	0.662480	−	0.0424156i
$391$			10.0651i			0.509015i
$392$	34.7006	+	40.3413i	1.75265	+	2.03754i
$393$	2.57588			0.129936
$394$	−11.7985	−	21.6696i	−0.594402	−	1.09170i
$395$	−5.60531	−	5.60531i	−0.282034	−	0.282034i
$396$	−30.5309	+	6.56434i	−1.53424	+	0.329871i
$397$	−21.0435	−	21.0435i	−1.05614	−	1.05614i	−0.998327	−	0.0578139i	$-0.981587\pi$
$397$	−21.0435	−	21.0435i	−1.05614	−	1.05614i	−0.0578139	−	0.998327i	$-0.518413\pi$
$398$	0.870425	−	2.95120i	0.0436305	−	0.147930i
$399$		−	36.2858i		−	1.81656i
$400$	3.64652	−	1.64405i	0.182326	−	0.0822026i
$401$	4.80943	+	4.80943i	0.240172	+	0.240172i	0.816921	−	0.576749i	$-0.195679\pi$
$401$	4.80943	+	4.80943i	0.240172	+	0.240172i	−0.576749	+	0.816921i	$0.695679\pi$
$402$	−20.3817	−	37.4338i	−1.01655	−	1.86703i
$403$	−0.407268	−	1.11314i	−0.0202875	−	0.0554493i
$404$	18.4772	−	28.5988i	0.919274	−	1.42285i
$405$	4.80632	−	4.80632i	0.238828	−	0.238828i
$406$	−18.8462	−	34.6136i	−0.935321	−	1.71785i
$407$	9.72855			0.482226
$408$	15.2506	−	13.1182i	0.755019	−	0.649450i
$409$	−1.18836	+	1.18836i	−0.0587606	+	0.0587606i	−0.735876	−	0.677116i	$-0.763230\pi$
$409$	−1.18836	+	1.18836i	−0.0587606	+	0.0587606i	0.677116	+	0.735876i	$0.263230\pi$
$410$	−0.723132	−	0.213280i	−0.0357129	−	0.0105332i
$411$	−6.69252	+	6.69252i	−0.330117	+	0.330117i
$412$	27.8259	+	17.9778i	1.37088	+	0.885701i
$413$		−	38.7471i		−	1.90662i
$414$	5.25514	−	17.8177i	0.258276	−	0.875690i
$415$	−10.0692			−0.494277
$416$	19.4978	+	5.98642i	0.955956	+	0.293509i
$417$	54.7710			2.68215
$418$	−4.80659	+	16.2969i	−0.235098	+	0.797106i
$419$			26.4250i			1.29095i	0.763783	+	0.645474i	$0.223340\pi$
$419$			26.4250i			1.29095i	−0.763783	+	0.645474i	$0.776660\pi$
$420$	−21.9437	−	14.1774i	−1.07074	−	0.691787i
$421$	−2.28690	+	2.28690i	−0.111457	+	0.111457i	−0.760636	−	0.649179i	$-0.775113\pi$
$421$	−2.28690	+	2.28690i	−0.111457	+	0.111457i	0.649179	+	0.760636i	$0.275113\pi$
$422$	−19.8173	−	5.84491i	−0.964691	−	0.284526i
$423$	−5.48349	+	5.48349i	−0.266617	+	0.266617i
$424$	20.4699	−	17.6078i	0.994108	−	0.855109i
$425$	−2.76630			−0.134185
$426$	0.128967	+	0.236866i	0.00624849	+	0.0114762i
$427$	7.60381	−	7.60381i	0.367974	−	0.367974i
$428$	0.835566	−	1.29328i	0.0403886	−	0.0625132i
$429$	13.7760	+	37.6523i	0.665113	+	1.81787i
$430$	1.56596	+	2.87610i	0.0755173	+	0.138698i
$431$	−17.9170	−	17.9170i	−0.863032	−	0.863032i	0.128657	−	0.991689i	$-0.458933\pi$
$431$	−17.9170	−	17.9170i	−0.863032	−	0.863032i	−0.991689	+	0.128657i	$0.958933\pi$
$432$	−5.72058	+	2.57915i	−0.275231	+	0.124090i
$433$			31.7594i			1.52626i	0.646244	+	0.763130i	$0.276339\pi$
$433$			31.7594i			1.52626i	−0.646244	+	0.763130i	$0.723661\pi$
$434$	−0.668214	+	2.26560i	−0.0320753	+	0.108752i
$435$	9.97193	+	9.97193i	0.478117	+	0.478117i
$436$	37.3557	−	8.03172i	1.78901	−	0.384650i
$437$	−7.14682	−	7.14682i	−0.341879	−	0.341879i
$438$	−7.04713	−	12.9430i	−0.336725	−	0.618441i
$439$	−11.0336			−0.526606			−0.263303	−	0.964713i	$-0.584812\pi$
$439$	−11.0336			−0.526606			−0.263303	+	0.964713i	$0.584812\pi$
$440$	7.97746	+	9.27420i	0.380310	+	0.442130i
$441$			67.9197i			3.23427i
$442$	−10.5909	−	9.31636i	−0.503759	−	0.443134i
$443$		−	18.7557i		−	0.891112i	−0.895254	−	0.445556i	$-0.853006\pi$
$443$		−	18.7557i		−	0.891112i	0.895254	−	0.445556i	$-0.146994\pi$
$444$	11.3078	−	2.43125i	0.536643	−	0.115382i
$445$	−2.41955			−0.114698
$446$	20.0583	−	10.9212i	0.949790	−	0.517136i
$447$	−17.5373	−	17.5373i	−0.829484	−	0.829484i
$448$	−24.1214	−	32.7142i	−1.13963	−	1.54560i
$449$	12.4793	+	12.4793i	0.588937	+	0.588937i	0.937343	−	0.348407i	$-0.113277\pi$
$449$	12.4793	+	12.4793i	0.588937	+	0.588937i	−0.348407	+	0.937343i	$0.613277\pi$
$450$	4.89701	+	1.44432i	0.230847	+	0.0680860i
$451$		−	2.30573i		−	0.108573i
$452$	−27.0847	−	17.4989i	−1.27396	−	0.823079i
$453$	−16.8747	−	16.8747i	−0.792842	−	0.792842i
$454$	2.31224	−	1.25895i	0.108519	−	0.0590857i
$455$	−7.71390	+	16.6154i	−0.361633	+	0.778940i
$456$	−1.51412	+	20.1435i	−0.0709051	+	0.943307i
$457$	−19.9648	+	19.9648i	−0.933915	+	0.933915i	−0.997948	−	0.0640326i	$-0.979604\pi$
$457$	−19.9648	+	19.9648i	−0.933915	+	0.933915i	0.0640326	+	0.997948i	$0.479604\pi$
$458$	−30.0371	+	16.3544i	−1.40354	+	0.764190i
$459$	4.33971			0.202560
$460$	−7.11438	+	1.52964i	−0.331710	+	0.0713197i
$461$	−17.1270	+	17.1270i	−0.797686	+	0.797686i	−0.982730	−	0.185044i	$-0.940757\pi$
$461$	−17.1270	+	17.1270i	−0.797686	+	0.797686i	0.185044	+	0.982730i	$0.440757\pi$
$462$	22.6026	−	76.6348i	1.05157	−	3.56537i
$463$	−13.2556	+	13.2556i	−0.616041	+	0.616041i	−0.944514	−	0.328472i	$-0.893466\pi$
$463$	−13.2556	+	13.2556i	−0.616041	+	0.616041i	0.328472	+	0.944514i	$0.393466\pi$
$464$	9.01785	+	20.0017i	0.418643	+	0.928554i
$465$		−	0.845209i		−	0.0391956i
$466$	16.5163	+	4.87131i	0.765103	+	0.225659i
$467$	4.56140			0.211076			0.105538	−	0.994415i	$-0.466343\pi$
$467$	4.56140			0.211076			0.105538	+	0.994415i	$0.466343\pi$
$468$	13.8843	+	22.0219i	0.641801	+	1.01796i
$469$	59.5584			2.75015
$470$	2.91371	+	0.859369i	0.134399	+	0.0396397i
$471$			31.6896i			1.46018i
$472$	−1.61682	+	21.5099i	−0.0744203	+	0.990073i
$473$	−7.08185	+	7.08185i	−0.325624	+	0.325624i
$474$	8.15374	−	27.6455i	0.374514	−	1.26980i
$475$	1.96423	−	1.96423i	0.0901251	−	0.0901251i
$476$	5.90868	+	27.4814i	0.270824	+	1.25961i
$477$	34.4638			1.57799
$478$	9.08331	−	4.94562i	0.415461	−	0.226207i
$479$	−2.16255	+	2.16255i	−0.0988096	+	0.0988096i	−0.754784	−	0.655974i	$-0.772258\pi$
$479$	−2.16255	+	2.16255i	−0.0988096	+	0.0988096i	0.655974	+	0.754784i	$0.272258\pi$
$480$	11.5901	+	8.78604i	0.529015	+	0.401026i
$481$	−2.78661	−	7.61632i	−0.127059	−	0.347274i
$482$	7.02142	−	3.82298i	0.319817	−	0.174132i
$483$	33.6073	+	33.6073i	1.52919	+	1.52919i
$484$	−8.36404	+	12.9458i	−0.380183	+	0.588445i
$485$			2.48197i			0.112701i
$486$	30.0887	+	8.87435i	1.36485	+	0.402549i
$487$	−4.47820	−	4.47820i	−0.202926	−	0.202926i	0.598326	−	0.801253i	$-0.295833\pi$
$487$	−4.47820	−	4.47820i	−0.202926	−	0.202926i	−0.801253	+	0.598326i	$0.795833\pi$
$488$	−4.53843	+	3.90385i	−0.205445	+	0.176719i
$489$	−27.5992	−	27.5992i	−1.24808	−	1.24808i
$490$	23.3671	−	12.7227i	1.05562	−	0.574755i
$491$	−19.7269			−0.890262			−0.445131	−	0.895465i	$-0.646843\pi$
$491$	−19.7269			−0.890262			−0.445131	+	0.895465i	$0.646843\pi$
$492$	−0.576222	−	2.68002i	−0.0259781	−	0.120825i
$493$		−	15.1735i		−	0.683381i
$494$	14.1353	−	0.905022i	0.635978	−	0.0407189i
$495$			15.6143i			0.701811i
$496$	0.465487	−	1.22983i	0.0209010	−	0.0552210i
$497$	−0.376862			−0.0169046
$498$	−17.5071	−	32.1542i	−0.784512	−	1.44086i
$499$	1.69594	+	1.69594i	0.0759206	+	0.0759206i	0.744047	−	0.668127i	$-0.232904\pi$
$499$	1.69594	+	1.69594i	0.0759206	+	0.0759206i	−0.668127	+	0.744047i	$0.732904\pi$
$500$	−0.420406	−	1.95532i	−0.0188011	−	0.0874444i
$501$	−14.3599	−	14.3599i	−0.641552	−	0.641552i
$502$	−10.3622	+	35.1331i	−0.462486	+	1.56807i
$503$		−	13.2958i		−	0.592830i	−0.955059	−	0.296415i	$-0.904209\pi$
$503$		−	13.2958i		−	0.592830i	0.955059	−	0.296415i	$-0.0957911\pi$
$504$	3.88863	−	51.7336i	0.173213	−	2.30440i
$505$	−12.0380	−	12.0380i	−0.535682	−	0.535682i
$506$	−10.6421	−	19.5457i	−0.473100	−	0.868912i
$507$	25.5314	−	21.5700i	1.13389	−	0.957959i
$508$	3.94052	+	2.54590i	0.174833	+	0.112956i
$509$	−23.9865	+	23.9865i	−1.06318	+	1.06318i	−0.0653173	+	0.997865i	$0.520806\pi$
$509$	−23.9865	+	23.9865i	−1.06318	+	1.06318i	−0.997865	+	0.0653173i	$0.979194\pi$
$510$	−4.80971	−	8.83369i	−0.212978	−	0.391163i
$511$	20.5928			0.910970
$512$	12.0255	+	19.1673i	0.531459	+	0.847084i
$513$	−3.08144	+	3.08144i	−0.136049	+	0.136049i
$514$	4.85003	+	1.43047i	0.213926	+	0.0630951i
$515$	11.7126	−	11.7126i	0.516118	−	0.516118i
$516$	−6.46162	+	10.0012i	−0.284457	+	0.440280i
$517$			9.29048i			0.408595i
$518$	−4.57206	+	15.5017i	−0.200885	+	0.681105i
$519$	42.4400			1.86291
$520$	4.97558	−	8.90189i	0.218194	−	0.390374i
$521$	5.69937			0.249694			0.124847	−	0.992176i	$-0.460156\pi$
$521$	5.69937			0.249694			0.124847	+	0.992176i	$0.460156\pi$
$522$	−7.92231	+	26.8608i	−0.346750	+	1.17566i
$523$		−	6.79654i		−	0.297192i	−0.988898	−	0.148596i	$-0.952525\pi$
$523$		−	6.79654i		−	0.297192i	0.988898	−	0.148596i	$-0.0474754\pi$
$524$	1.08739	−	1.68306i	0.0475030	−	0.0735248i
$525$	−9.23664	+	9.23664i	−0.403120	+	0.403120i
$526$	16.5836	+	4.89115i	0.723078	+	0.213264i
$527$	−0.643045	+	0.643045i	−0.0280115	+	0.0280115i
$528$	−15.7453	+	41.5995i	−0.685227	+	1.81039i
$529$	−9.76146			−0.424411
$530$	−6.45577	−	11.8569i	−0.280421	−	0.515031i
$531$	−19.4684	+	19.4684i	−0.844856	+	0.844856i
$532$	−23.7089	−	15.3179i	−1.02791	−	0.664113i
$533$	−1.80512	+	0.660447i	−0.0781884	+	0.0286071i
$534$	−4.20684	−	7.72643i	−0.182048	−	0.334355i
$535$	−0.544375	−	0.544375i	−0.0235354	−	0.0235354i
$536$	−33.0630	−	2.48523i	−1.42810	−	0.107346i
$537$			48.2921i			2.08396i
$538$	−11.9482	+	40.5107i	−0.515124	+	1.74654i
$539$	57.5369	+	57.5369i	2.47829	+	2.47829i
$540$	0.659523	+	3.06746i	0.0283814	+	0.132002i
$541$	24.1166	+	24.1166i	1.03685	+	1.03685i	0.999294	+	0.0375586i	$0.0119581\pi$
$541$	24.1166	+	24.1166i	1.03685	+	1.03685i	0.0375586	+	0.999294i	$0.488042\pi$
$542$	2.81458	+	5.16937i	0.120897	+	0.222043i
$543$	−22.0824			−0.947648
$544$	−2.13338	−	15.5024i	−0.0914681	−	0.664662i
$545$		−	19.1047i		−	0.818355i
$546$	−66.4703	+	4.25580i	−2.84467	+	0.182131i
$547$		−	24.8477i		−	1.06241i	−0.847243	−	0.531205i	$-0.821739\pi$
$547$		−	24.8477i		−	1.06241i	0.847243	−	0.531205i	$-0.178261\pi$
$548$	1.54763	+	7.19805i	0.0661114	+	0.307485i
$549$	−7.64103			−0.326111
$550$	5.37194	−	2.92488i	0.229060	−	0.124717i
$551$	10.7741	+	10.7741i	0.458991	+	0.458991i
$552$	−17.2543	−	20.0590i	−0.734391	−	0.853767i
$553$	28.4789	+	28.4789i	1.21104	+	1.21104i
$554$	−6.81955	−	2.01136i	−0.289735	−	0.0854543i
$555$		−	5.78310i		−	0.245479i
$556$	23.1213	−	35.7869i	0.980560	−	1.51770i
$557$	28.2899	+	28.2899i	1.19868	+	1.19868i	0.974561	+	0.224122i	$0.0719513\pi$
$557$	28.2899	+	28.2899i	1.19868	+	1.19868i	0.224122	+	0.974561i	$0.428049\pi$
$558$	1.47409	−	0.802601i	0.0624030	−	0.0339768i
$559$	7.57276	+	3.51576i	0.320294	+	0.148701i
$560$	−18.5268	+	8.35292i	−0.782901	+	0.352975i
$561$	21.7513	−	21.7513i	0.918340	−	0.918340i
$562$	1.51726	−	0.826109i	0.0640018	−	0.0348473i
$563$	28.4369			1.19847			0.599236	−	0.800572i	$-0.295471\pi$
$563$	28.4369			1.19847			0.599236	+	0.800572i	$0.295471\pi$
$564$	2.32177	+	10.7986i	0.0977641	+	0.454703i
$565$	−11.4006	+	11.4006i	−0.479627	+	0.479627i
$566$	2.40019	−	8.13791i	0.100888	−	0.342062i
$567$	−24.4194	+	24.4194i	−1.02552	+	1.02552i
$568$	0.209209	+	0.0157255i	0.00877823	+	0.000659829i
$569$		−	18.3722i		−	0.770202i	−0.922874	−	0.385101i	$-0.874167\pi$
$569$		−	18.3722i		−	0.770202i	0.922874	−	0.385101i	$-0.125833\pi$
$570$	9.68760	+	2.85726i	0.405769	+	0.119677i
$571$	20.9691			0.877530			0.438765	−	0.898602i	$-0.355416\pi$
$571$	20.9691			0.877530			0.438765	+	0.898602i	$0.355416\pi$
$572$	30.4172	+	6.89359i	1.27181	+	0.288236i
$573$	−36.7492			−1.53522
$574$	3.67401	+	1.08361i	0.153350	+	0.0452290i
$575$			3.63848i			0.151735i
$576$	−4.31744	+	28.5569i	−0.179893	+	1.18987i
$577$	−16.1707	+	16.1707i	−0.673194	+	0.673194i	−0.958451	−	0.285257i	$-0.907921\pi$
$577$	−16.1707	+	16.1707i	−0.673194	+	0.673194i	0.285257	+	0.958451i	$0.407921\pi$
$578$	3.73969	−	12.6795i	0.155551	−	0.527398i
$579$	−11.0932	+	11.0932i	−0.461018	+	0.461018i
$580$	10.7252	−	2.30598i	0.445339	−	0.0957508i
$581$	51.1584			2.12241
$582$	−7.92576	+	4.31536i	−0.328533	+	0.178878i
$583$	29.1953	−	29.1953i	1.20915	−	1.20915i
$584$	−11.4318	−	0.859286i	−0.473050	−	0.0355575i
$585$	12.2242	−	4.47251i	0.505407	−	0.184916i
$586$	−2.69126	+	1.46532i	−0.111175	+	0.0605319i
$587$	−15.0363	−	15.0363i	−0.620615	−	0.620615i	0.325074	−	0.945689i	$-0.394611\pi$
$587$	−15.0363	−	15.0363i	−0.620615	−	0.620615i	−0.945689	+	0.325074i	$0.894611\pi$
$588$	81.2558	+	52.4979i	3.35093	+	2.16498i
$589$		−	0.913198i		−	0.0376277i
$590$	10.3447	+	3.05107i	0.425886	+	0.125611i
$591$	−31.7180	−	31.7180i	−1.30470	−	1.30470i
$592$	3.18496	−	8.41475i	0.130901	−	0.345844i
$593$	13.5836	+	13.5836i	0.557811	+	0.557811i	0.928684	−	0.370873i	$-0.120941\pi$
$593$	13.5836	+	13.5836i	0.557811	+	0.557811i	−0.370873	+	0.928684i	$0.620941\pi$
$594$	−8.42738	+	4.58849i	−0.345780	+	0.188268i
$595$	14.0547			0.576187
$596$	−18.8620	+	4.05545i	−0.772617	+	0.166118i
$597$		−	5.59374i		−	0.228937i
$598$	−12.2537	+	13.9301i	−0.501091	+	0.569646i
$599$		−	0.945070i		−	0.0386145i	−0.999814	−	0.0193073i	$-0.993854\pi$
$599$		−	0.945070i		−	0.0386145i	0.999814	−	0.0193073i	$-0.00614607\pi$
$600$	5.51301	−	4.74216i	0.225068	−	0.193598i
$601$	13.5765			0.553796			0.276898	−	0.960899i	$-0.410694\pi$
$601$	13.5765			0.553796			0.276898	+	0.960899i	$0.410694\pi$
$602$	−7.95616	−	14.6126i	−0.324269	−	0.595564i
$603$	−29.9250	−	29.9250i	−1.21864	−	1.21864i
$604$	−18.1494	+	3.90223i	−0.738487	+	0.158779i
$605$	5.44920	+	5.44920i	0.221542	+	0.221542i
$606$	17.5110	−	59.3713i	0.711334	−	2.41180i
$607$		−	22.2429i		−	0.902813i	−0.892319	−	0.451406i	$-0.850923\pi$
$607$		−	22.2429i		−	0.902813i	0.892319	−	0.451406i	$-0.149077\pi$
$608$	12.5225	+	9.49280i	0.507852	+	0.384984i
$609$	−50.6643	−	50.6643i	−2.05302	−	2.05302i
$610$	1.43132	+	2.62882i	0.0579525	+	0.106438i
$611$	7.27336	−	2.66114i	0.294249	−	0.107658i
$612$	10.8391	−	16.7767i	0.438147	−	0.678160i
$613$	−2.55715	+	2.55715i	−0.103282	+	0.103282i	−0.756860	−	0.653577i	$-0.773267\pi$
$613$	−2.55715	+	2.55715i	−0.103282	+	0.103282i	0.653577	+	0.756860i	$0.273267\pi$
$614$	7.98964	+	14.6741i	0.322436	+	0.592197i
$615$	−1.37063			−0.0552693
$616$	−40.5310	−	47.1194i	−1.63304	−	1.89849i
$617$	25.0426	−	25.0426i	1.00818	−	1.00818i	0.00821104	−	0.999966i	$-0.497386\pi$
$617$	25.0426	−	25.0426i	1.00818	−	1.00818i	0.999966	−	0.00821104i	$-0.00261368\pi$
$618$	57.7666	+	17.0377i	2.32371	+	0.685355i
$619$	−18.6915	+	18.6915i	−0.751276	+	0.751276i	−0.974717	−	0.223441i	$-0.928271\pi$
$619$	−18.6915	+	18.6915i	−0.751276	+	0.751276i	0.223441	+	0.974717i	$0.428271\pi$
$620$	−0.552253	−	0.356801i	−0.0221790	−	0.0143295i
$621$		−	5.70797i		−	0.229053i
$622$	3.39110	−	11.4976i	0.135971	−	0.461011i
$623$	12.2930			0.492509
$624$	37.0776	+	0.411101i	1.48429	+	0.0164572i
$625$	−1.00000			−0.0400000
$626$	−3.51792	+	11.9276i	−0.140604	+	0.476722i
$627$			30.8893i			1.23360i
$628$	20.7057	+	13.3776i	0.826248	+	0.533824i
$629$	−4.39985	+	4.39985i	−0.175433	+	0.175433i
$630$	−24.8802	−	7.33815i	−0.991250	−	0.292359i
$631$	−34.1938	+	34.1938i	−1.36123	+	1.36123i	−0.488888	+	0.872347i	$0.662597\pi$
$631$	−34.1938	+	34.1938i	−1.36123	+	1.36123i	−0.872347	+	0.488888i	$0.837403\pi$
$632$	−14.6213	−	16.9980i	−0.581603	−	0.676143i
$633$	−37.5620			−1.49296
$634$	0.531772	+	0.976673i	0.0211194	+	0.0387886i
$635$	1.65866	−	1.65866i	0.0658221	−	0.0658221i
$636$	26.6384	−	41.2308i	1.05628	−	1.63491i
$637$	28.5640	−	61.5254i	1.13175	−	2.43772i
$638$	16.0434	+	29.4658i	0.635163	+	1.16656i
$639$	0.189353	+	0.189353i	0.00749070	+	0.00749070i
$640$	10.6334	−	3.86392i	0.420324	−	0.152735i
$641$		−	38.8958i		−	1.53629i	−0.640274	−	0.768147i	$-0.721179\pi$
$641$		−	38.8958i		−	1.53629i	0.640274	−	0.768147i	$-0.278821\pi$
$642$	0.791872	−	2.68486i	0.0312527	−	0.105963i
$643$	−3.60575	−	3.60575i	−0.142197	−	0.142197i	0.632425	−	0.774622i	$-0.282060\pi$
$643$	−3.60575	−	3.60575i	−0.142197	−	0.142197i	−0.774622	+	0.632425i	$0.782060\pi$
$644$	36.1459	−	7.77161i	1.42435	−	0.306245i
$645$	4.20977	+	4.20977i	0.165760	+	0.165760i
$646$	−5.19661	−	9.54428i	−0.204458	−	0.375515i
$647$	−33.9357			−1.33415			−0.667074	−	0.744991i	$-0.732454\pi$
$647$	−33.9357			−1.33415			−0.667074	+	0.744991i	$0.732454\pi$
$648$	14.5750	−	12.5371i	0.572561	−	0.492504i
$649$			32.9846i			1.29476i
$650$	−3.82856	−	3.36781i	−0.150168	−	0.132096i
$651$			4.29424i			0.168305i
$652$	−29.6840	+	6.38226i	−1.16252	+	0.249948i
$653$	6.90318			0.270142			0.135071	−	0.990836i	$-0.456874\pi$
$653$	6.90318			0.270142			0.135071	+	0.990836i	$0.456874\pi$
$654$	61.0075	−	33.2170i	2.38558	−	1.29889i
$655$	−0.708442	−	0.708442i	−0.0276811	−	0.0276811i
$656$	−1.99435	−	0.754858i	−0.0778665	−	0.0294723i
$657$	−10.3468	−	10.3468i	−0.403666	−	0.403666i
$658$	−14.8037	−	4.36618i	−0.577107	−	0.170212i
$659$		−	14.2677i		−	0.555789i	−0.960612	−	0.277895i	$-0.910363\pi$
$659$		−	14.2677i		−	0.555789i	0.960612	−	0.277895i	$-0.0896366\pi$
$660$	18.6802	+	12.0689i	0.727126	+	0.469782i
$661$	−10.1944	−	10.1944i	−0.396518	−	0.396518i	0.480485	−	0.877003i	$-0.340461\pi$
$661$	−10.1944	−	10.1944i	−0.396518	−	0.396518i	−0.877003	+	0.480485i	$0.840461\pi$
$662$	21.6743	−	11.8011i	0.842395	−	0.458662i
$663$	−23.2591	−	10.7983i	−0.903308	−	0.419373i
$664$	−28.3998	−	2.13472i	−1.10213	−	0.0828431i
$665$	−9.97965	+	9.97965i	−0.386994	+	0.386994i
$666$	10.0860	−	5.49156i	0.390825	−	0.212794i
$667$	−19.9576			−0.772760
$668$	−15.4446	+	3.32069i	−0.597569	+	0.128481i
$669$	29.3596	−	29.3596i	1.13511	−	1.13511i
$670$	−4.68982	+	15.9009i	−0.181184	+	0.614307i
$671$	−6.47296	+	6.47296i	−0.249886	+	0.249886i
$672$	−58.8858	−	44.6391i	−2.27157	−	1.72199i
$673$			7.79620i			0.300521i	0.988646	+	0.150261i	$0.0480113\pi$
$673$			7.79620i			0.300521i	−0.988646	+	0.150261i	$0.951989\pi$
$674$	7.64128	+	2.25372i	0.294331	+	0.0868099i
$675$	1.56878			0.0603823
$676$	−3.31574	−	25.7877i	−0.127528	−	0.991835i
$677$	−25.4483			−0.978057			−0.489029	−	0.872268i	$-0.662649\pi$
$677$	−25.4483			−0.978057			−0.489029	+	0.872268i	$0.662649\pi$
$678$	−56.2279	−	16.5838i	−2.15942	−	0.636898i
$679$		−	12.6101i		−	0.483933i
$680$	−7.80226	−	0.586469i	−0.299203	−	0.0224900i
$681$	3.38445	−	3.38445i	0.129692	−	0.129692i
$682$	0.568837	−	1.92865i	0.0217819	−	0.0738520i
$683$	5.43776	−	5.43776i	0.208070	−	0.208070i	−0.595377	−	0.803447i	$-0.702997\pi$
$683$	5.43776	−	5.43776i	0.208070	−	0.208070i	0.803447	+	0.595377i	$0.202997\pi$
$684$	4.21604	+	19.6089i	0.161204	+	0.749764i
$685$	3.68127			0.140654
$686$	−74.5478	+	40.5893i	−2.84625	+	1.54971i
$687$	−43.9655	+	43.9655i	−1.67739	+	1.67739i
$688$	3.80700	+	8.44395i	0.145140	+	0.321923i
$689$	−31.2192	−	14.4939i	−1.18936	−	0.552174i
$690$	−11.6189	+	6.32616i	−0.442322	+	0.240833i
$691$	−16.4214	−	16.4214i	−0.624700	−	0.624700i	0.322029	−	0.946730i	$-0.395635\pi$
$691$	−16.4214	−	16.4214i	−0.624700	−	0.624700i	−0.946730	+	0.322029i	$0.895635\pi$
$692$	17.9158	−	27.7300i	0.681058	−	1.05414i
$693$		−	79.3314i		−	3.01355i
$694$	−13.2310	−	3.90234i	−0.502241	−	0.148131i
$695$	−15.0636	−	15.0636i	−0.571395	−	0.571395i
$696$	26.0114	+	30.2396i	0.985961	+	1.14623i
$697$	1.04280	+	1.04280i	0.0394987	+	0.0394987i
$698$	32.6013	−	17.7505i	1.23398	−	0.671868i
$699$	31.3052			1.18407
$700$	2.13595	+	9.93435i	0.0807314	+	0.375483i
$701$			14.5028i			0.547763i	0.961763	+	0.273882i	$0.0883077\pi$
$701$			14.5028i			0.547763i	−0.961763	+	0.273882i	$0.911692\pi$
$702$	6.00616	+	5.28334i	0.226688	+	0.199407i
$703$		−	6.24829i		−	0.235659i
$704$	20.5340	+	27.8489i	0.773904	+	1.04959i
$705$	5.52269			0.207996
$706$	−6.22542	−	11.4338i	−0.234297	−	0.430318i
$707$	61.1611	+	61.1611i	2.30020	+	2.30020i
$708$	8.24312	+	38.3389i	0.309796	+	1.44087i
$709$	−6.85421	−	6.85421i	−0.257415	−	0.257415i	0.566587	−	0.824002i	$-0.308264\pi$
$709$	−6.85421	−	6.85421i	−0.257415	−	0.257415i	−0.824002	+	0.566587i	$0.808264\pi$
$710$	0.0296753	−	0.100615i	0.00111369	−	0.00377601i
$711$		−	28.6183i		−	1.07327i
$712$	−6.82428	−	0.512957i	−0.255751	−	0.0192239i
$713$	0.845790	+	0.845790i	0.0316751	+	0.0316751i
$714$	24.4367	+	44.8813i	0.914519	+	1.67964i
$715$	6.56668	−	14.1443i	0.245580	−	0.528967i
$716$	31.5537	+	20.3863i	1.17922	+	0.761871i
$717$	13.2953	−	13.2953i	0.496523	−	0.496523i
$718$	1.23360	+	2.26567i	0.0460375	+	0.0845541i
$719$	39.0195			1.45518			0.727591	−	0.686011i	$-0.240640\pi$
$719$	39.0195			1.45518			0.727591	+	0.686011i	$0.240640\pi$
$720$	13.5057	+	5.11186i	0.503326	+	0.190508i
$721$	−59.5080	+	59.5080i	−2.21619	+	2.21619i
$722$	−15.3056	−	4.51422i	−0.569615	−	0.168002i
$723$	10.2773	−	10.2773i	0.382217	−	0.382217i
$724$	−9.32198	+	14.4285i	−0.346449	+	0.536231i
$725$		−	5.48514i		−	0.203713i
$726$	−7.92666	+	26.8755i	−0.294186	+	0.997444i
$727$	−32.9715			−1.22285			−0.611423	−	0.791304i	$-0.709403\pi$
$727$	−32.9715			−1.22285			−0.611423	+	0.791304i	$0.709403\pi$
$728$	−25.2794	+	45.2277i	−0.936916	+	1.67625i
$729$	36.6390			1.35700
$730$	−1.62154	+	5.49787i	−0.0600159	+	0.203485i
$731$		−	6.40569i		−	0.236923i
$732$	−5.90606	+	9.14135i	−0.218294	+	0.337874i
$733$	32.6338	−	32.6338i	1.20536	−	1.20536i	0.232842	−	0.972515i	$-0.425198\pi$
$733$	32.6338	−	32.6338i	1.20536	−	1.20536i	0.972515	−	0.232842i	$-0.0748024\pi$
$734$	−27.9447	−	8.24200i	−1.03146	−	0.304218i
$735$	34.2026	−	34.2026i	1.26158	−	1.26158i
$736$	−20.3902	+	2.80602i	−0.751592	+	0.103431i
$737$	−50.7008			−1.86759
$738$	−1.30154	−	2.39045i	−0.0479103	−	0.0879938i
$739$	22.9813	−	22.9813i	0.845380	−	0.845380i	−0.144173	−	0.989553i	$-0.546052\pi$
$739$	22.9813	−	22.9813i	0.845380	−	0.845380i	0.989553	+	0.144173i	$0.0460521\pi$
$740$	−3.77863	−	2.44130i	−0.138905	−	0.0897441i
$741$	24.1827	−	8.84784i	0.888375	−	0.325033i
$742$	32.7997	+	60.2412i	1.20412	+	2.21152i
$743$	−4.69447	−	4.69447i	−0.172223	−	0.172223i	0.615732	−	0.787955i	$-0.288860\pi$
$743$	−4.69447	−	4.69447i	−0.172223	−	0.172223i	−0.787955	+	0.615732i	$0.788860\pi$
$744$	0.179188	−	2.38389i	0.00656937	−	0.0873975i
$745$			9.64651i			0.353421i
$746$	−13.4514	+	45.6074i	−0.492492	+	1.66981i
$747$	−25.7044	−	25.7044i	−0.940475	−	0.940475i
$748$	−5.02993	−	23.3943i	−0.183912	−	0.855381i
$749$	2.76580	+	2.76580i	0.101060	+	0.101060i
$750$	−1.73868	−	3.19333i	−0.0634877	−	0.116604i
$751$	−6.65662			−0.242904			−0.121452	−	0.992597i	$-0.538755\pi$
$751$	−6.65662			−0.242904			−0.121452	+	0.992597i	$0.538755\pi$
$752$	8.03584	+	3.04154i	0.293037	+	0.110914i
$753$			66.5919i			2.42674i
$754$	18.4729	−	21.0002i	0.672743	−	0.764782i
$755$			9.28206i			0.337809i
$756$	−3.35083	−	15.5848i	−0.121869	−	0.566813i
$757$	−47.8549			−1.73932			−0.869658	−	0.493655i	$-0.835661\pi$
$757$	−47.8549			−1.73932			−0.869658	+	0.493655i	$0.835661\pi$
$758$	−32.6834	+	17.7952i	−1.18711	+	0.646352i
$759$	−28.6092	−	28.6092i	−1.03845	−	1.03845i
$760$	5.95648	−	5.12363i	0.216064	−	0.185854i
$761$	17.5012	+	17.5012i	0.634419	+	0.634419i	0.949173	−	0.314754i	$-0.101922\pi$
$761$	17.5012	+	17.5012i	0.634419	+	0.634419i	−0.314754	+	0.949173i	$0.601922\pi$
$762$	8.18055	+	2.41277i	0.296350	+	0.0874054i
$763$			97.0650i			3.51399i
$764$	−15.5135	+	24.0116i	−0.561258	+	0.868711i
$765$	−7.06175	−	7.06175i	−0.255318	−	0.255318i
$766$	5.90960	−	3.21762i	0.213523	−	0.116257i
$767$	25.8231	−	9.44800i	0.932417	−	0.341147i
$768$	30.8269	+	27.2379i	1.11237	+	0.982864i
$769$	−4.03627	+	4.03627i	−0.145552	+	0.145552i	−0.776128	−	0.630576i	$-0.782819\pi$
$769$	−4.03627	+	4.03627i	−0.145552	+	0.145552i	0.630576	+	0.776128i	$0.282819\pi$
$770$	−27.2932	+	14.8604i	−0.983577	+	0.535532i
$771$	9.19281			0.331071
$772$	2.56528	+	11.9312i	0.0923264	+	0.429412i
$773$	−19.4807	+	19.4807i	−0.700671	+	0.700671i	−0.964555	−	0.263884i	$-0.914996\pi$
$773$	−19.4807	+	19.4807i	−0.700671	+	0.700671i	0.263884	+	0.964555i	$0.414996\pi$
$774$	−3.34450	+	11.3396i	−0.120216	+	0.407594i
$775$	−0.232457	+	0.232457i	−0.00835010	+	0.00835010i
$776$	−0.526191	+	7.00034i	−0.0188891	+	0.251297i
$777$			29.3821i			1.05408i
$778$	−32.6287	−	9.62349i	−1.16979	−	0.345019i
$779$	−1.48089			−0.0530584
$780$	4.09787	−	18.0814i	0.146727	−	0.647418i
$781$	0.320814			0.0114796
$782$	13.6528	+	4.02675i	0.488223	+	0.143996i
$783$			8.60497i			0.307516i
$784$	68.6034	−	30.9302i	2.45012	−	1.10465i
$785$	8.71555	−	8.71555i	0.311071	−	0.311071i
$786$	1.03053	−	3.49404i	0.0367578	−	0.124628i
$787$	20.6736	−	20.6736i	0.736935	−	0.736935i	−0.235049	−	0.971984i	$-0.575525\pi$
$787$	20.6736	−	20.6736i	0.736935	−	0.736935i	0.971984	+	0.235049i	$0.0755250\pi$
$788$	−34.1139	+	7.33471i	−1.21526	+	0.261288i
$789$	31.4327			1.11903
$790$	−9.84582	+	5.36079i	−0.350298	+	0.190728i
$791$	57.9229	−	57.9229i	2.05950	−	2.05950i
$792$	−3.31031	+	44.0397i	−0.117627	+	1.56488i
$793$	6.92166	+	3.21348i	0.245795	+	0.114114i
$794$	−36.9632	+	20.1255i	−1.31177	+	0.714226i
$795$	−17.3550	−	17.3550i	−0.615520	−	0.615520i
$796$	−3.65491	−	2.36137i	−0.129545	−	0.0836965i
$797$		−	11.0557i		−	0.391614i	−0.980642	−	0.195807i	$-0.937267\pi$
$797$		−	11.0557i		−	0.391614i	0.980642	−	0.195807i	$-0.0627326\pi$
$798$	−49.2197	−	14.5168i	−1.74236	−	0.513891i
$799$	−4.20173	−	4.20173i	−0.148646	−	0.148646i
$800$	−0.771205	−	5.60404i	−0.0272662	−	0.198133i
$801$	−6.17659	−	6.17659i	−0.218239	−	0.218239i
$802$	8.44784	−	4.59963i	0.298304	−	0.162418i
$803$	−17.5302			−0.618627
$804$	−58.9310	+	12.6706i	−2.07834	+	0.446856i
$805$		−	18.4860i		−	0.651545i
$806$	−1.67285	+	0.107105i	−0.0589235	+	0.00377261i
$807$			76.7846i			2.70295i
$808$	−31.4006	−	36.5048i	−1.10467	−	1.28424i
$809$	28.9511			1.01787			0.508934	−	0.860805i	$-0.330040\pi$
$809$	28.9511			1.01787			0.508934	+	0.860805i	$0.330040\pi$
$810$	−4.59664	−	8.44237i	−0.161510	−	0.296635i
$811$	18.4847	+	18.4847i	0.649084	+	0.649084i	0.952772	−	0.303687i	$-0.0982178\pi$
$811$	18.4847	+	18.4847i	0.649084	+	0.649084i	−0.303687	+	0.952772i	$0.598218\pi$
$812$	−54.4913	+	11.7160i	−1.91227	+	0.411151i
$813$	7.56645	+	7.56645i	0.265367	+	0.265367i
$814$	3.89210	−	13.1963i	0.136418	−	0.462528i
$815$			15.1812i			0.531774i
$816$	−11.6929	−	25.9349i	−0.409332	−	0.907902i
$817$	4.54841	+	4.54841i	0.159129	+	0.159129i
$818$	1.13652	+	2.08737i	0.0397374	+	0.0729832i
$819$	−62.1072	+	22.7234i	−2.17020	+	0.794021i
$820$	−0.578606	+	0.895562i	−0.0202058	+	0.0312744i
$821$	12.2771	−	12.2771i	0.428475	−	0.428475i	−0.459634	−	0.888108i	$-0.652019\pi$
$821$	12.2771	−	12.2771i	0.428475	−	0.428475i	0.888108	+	0.459634i	$0.152019\pi$
$822$	6.40056	+	11.7555i	0.223245	+	0.410020i
$823$	9.20129			0.320737			0.160368	−	0.987057i	$-0.448732\pi$
$823$	9.20129			0.320737			0.160368	+	0.987057i	$0.448732\pi$
$824$	35.5181	−	30.5519i	1.23733	−	1.06433i
$825$	7.86296	−	7.86296i	0.273753	−	0.273753i
$826$	−52.5583	−	15.5015i	−1.82874	−	0.539368i
$827$	14.8553	−	14.8553i	0.516569	−	0.516569i	−0.399962	−	0.916532i	$-0.630977\pi$
$827$	14.8553	−	14.8553i	0.516569	−	0.516569i	0.916532	+	0.399962i	$0.130977\pi$
$828$	−22.0663	−	14.2566i	−0.766856	−	0.495451i
$829$			33.7807i			1.17325i	0.809858	+	0.586625i	$0.199544\pi$
$829$			33.7807i			1.17325i	−0.809858	+	0.586625i	$0.800456\pi$
$830$	−4.02838	+	13.6583i	−0.139827	+	0.474087i
$831$	−12.9259			−0.448394
$832$	15.9207	−	24.0527i	0.551952	−	0.833876i
$833$	−52.0435			−1.80320
$834$	21.9122	−	74.2938i	0.758757	−	2.57258i
$835$			7.89877i			0.273348i
$836$	20.1828	+	13.0398i	0.698038	+	0.450990i
$837$	0.364673	−	0.364673i	0.0126050	−	0.0126050i
$838$	35.8441	+	10.5719i	1.23821	+	0.365199i
$839$	23.0964	−	23.0964i	0.797375	−	0.797375i	−0.185306	−	0.982681i	$-0.559327\pi$
$839$	23.0964	−	23.0964i	0.797375	−	0.797375i	0.982681	+	0.185306i	$0.0593275\pi$
$840$	−28.0099	+	24.0935i	−0.966433	+	0.831304i
$841$	1.08675			0.0374743
$842$	2.18713	+	4.01697i	0.0753736	+	0.138434i
$843$	2.22083	−	2.22083i	0.0764894	−	0.0764894i
$844$	−15.8566	+	24.5427i	−0.545807	+	0.844795i
$845$	−12.9543	−	1.08950i	−0.445640	−	0.0374798i
$846$	5.24428	+	9.63184i	0.180302	+	0.331149i
$847$	−27.6857	−	27.6857i	−0.951292	−	0.951292i
$848$	−15.6946	−	34.8107i	−0.538954	−	1.19540i
$849$		−	15.4247i		−	0.529375i
$850$	−1.10671	+	3.75233i	−0.0379599	+	0.128704i
$851$	5.78707	+	5.78707i	0.198378	+	0.198378i
$852$	0.372892	−	0.0801742i	0.0127751	−	0.00274672i
$853$	−23.6760	−	23.6760i	−0.810650	−	0.810650i	0.174081	−	0.984731i	$-0.444305\pi$
$853$	−23.6760	−	23.6760i	−0.810650	−	0.810650i	−0.984731	+	0.174081i	$0.944305\pi$
$854$	−7.27210	−	13.3562i	−0.248846	−	0.457040i
$855$	10.0285			0.342967
$856$	−1.41998	−	1.65080i	−0.0485340	−	0.0564233i
$857$		−	39.8505i		−	1.36127i	−0.732624	−	0.680634i	$-0.761705\pi$
$857$		−	39.8505i		−	1.36127i	0.732624	−	0.680634i	$-0.238295\pi$
$858$	56.5847	−	3.62287i	1.93177	−	0.123683i
$859$			30.6122i			1.04448i	0.852800	+	0.522238i	$0.174903\pi$
$859$			30.6122i			1.04448i	−0.852800	+	0.522238i	$0.825097\pi$
$860$	4.52777	−	0.973500i	0.154396	−	0.0331961i
$861$	6.96377			0.237324
$862$	−31.4715	+	17.1354i	−1.07192	+	0.583634i
$863$	17.3698	+	17.3698i	0.591274	+	0.591274i	0.937976	−	0.346701i	$-0.112698\pi$
$863$	17.3698	+	17.3698i	0.591274	+	0.591274i	−0.346701	+	0.937976i	$0.612698\pi$
$864$	1.20985	+	8.79149i	0.0411599	+	0.299093i
$865$	−11.6722	−	11.6722i	−0.396868	−	0.396868i
$866$	43.0799	+	12.7060i	1.46392	+	0.431767i
$867$		−	24.0329i		−	0.816201i
$868$	2.80583	+	1.81279i	0.0952359	+	0.0615302i
$869$	−24.2434	−	24.2434i	−0.822402	−	0.822402i
$870$	17.5158	−	9.53691i	0.593843	−	0.323332i
$871$	14.5226	+	39.6928i	0.492079	+	1.34494i
$872$	4.05029	−	53.8842i	0.137160	−	1.82475i
$873$	−6.33593	+	6.33593i	−0.214439	+	0.214439i
$874$	−12.5535	+	6.83504i	−0.424628	+	0.231199i
$875$	5.08069			0.171759
$876$	−20.3758	+	4.38094i	−0.688436	+	0.148018i
$877$	9.39543	−	9.39543i	0.317261	−	0.317261i	−0.530453	−	0.847714i	$-0.677978\pi$
$877$	9.39543	−	9.39543i	0.317261	−	0.317261i	0.847714	+	0.530453i	$0.177978\pi$
$878$	−4.41421	+	14.9665i	−0.148973	+	0.505095i
$879$	−3.93923	+	3.93923i	−0.132867	+	0.132867i
$880$	15.7715	−	7.11066i	0.531657	−	0.239700i
$881$			10.6711i			0.359519i	0.983711	+	0.179760i	$0.0575320\pi$
$881$			10.6711i			0.359519i	−0.983711	+	0.179760i	$0.942468\pi$
$882$	92.1294	+	27.1726i	3.10216	+	0.914949i
$883$	−18.9432			−0.637489			−0.318744	−	0.947841i	$-0.603261\pi$
$883$	−18.9432			−0.637489			−0.318744	+	0.947841i	$0.603261\pi$
$884$	−16.8742	+	10.6388i	−0.567542	+	0.357823i
$885$	19.6075			0.659100
$886$	−25.4411	−	7.50360i	−0.854712	−	0.252088i
$887$			21.5418i			0.723302i	0.932314	+	0.361651i	$0.117787\pi$
$887$			21.5418i			0.723302i	−0.932314	+	0.361651i	$0.882213\pi$
$888$	1.22604	−	16.3110i	0.0411434	−	0.547363i
$889$	−8.42716	+	8.42716i	−0.282638	+	0.282638i
$890$	−0.967990	+	3.28199i	−0.0324471	+	0.110013i
$891$	20.7877	−	20.7877i	0.696415	−	0.696415i
$892$	−6.78933	−	31.5773i	−0.227324	−	1.05729i
$893$	5.96694			0.199676
$894$	−30.8045	+	16.7722i	−1.03026	+	0.560947i
$895$	13.2817	−	13.2817i	0.443959	−	0.443959i
$896$	−54.0252	+	19.6314i	−1.80486	+	0.655838i
$897$	−14.2029	+	30.5924i	−0.474222	+	1.02145i
$898$	21.9202	−	11.9349i	0.731485	−	0.398274i
$899$	−1.27506	−	1.27506i	−0.0425256	−	0.0425256i
$900$	3.91829	−	6.06469i	0.130610	−	0.202156i
$901$			26.4079i			0.879773i
$902$	−3.12760	−	0.922454i	−0.104138	−	0.0307144i
$903$	−21.3886	−	21.3886i	−0.711766	−	0.711766i
$904$	−34.5720	+	29.7381i	−1.14985	+	0.989074i
$905$	6.07331	+	6.07331i	0.201884	+	0.201884i
$906$	−29.6406	+	16.1385i	−0.984744	+	0.536167i
$907$	33.4331			1.11013			0.555064	−	0.831808i	$-0.312694\pi$
$907$	33.4331			1.11013			0.555064	+	0.831808i	$0.312694\pi$
$908$	−0.782645	−	3.64010i	−0.0259730	−	0.120801i
$909$		−	61.4605i		−	2.03852i
$910$	19.4517	+	17.1108i	0.644818	+	0.567217i
$911$		−	44.8539i		−	1.48608i	−0.669249	−	0.743039i	$-0.733384\pi$
$911$		−	44.8539i		−	1.48608i	0.669249	−	0.743039i	$-0.266616\pi$
$912$	26.7178	+	10.1126i	0.884716	+	0.334863i
$913$	−43.5501			−1.44130
$914$	19.0939	+	35.0685i	0.631569	+	1.15996i
$915$	3.84782	+	3.84782i	0.127205	+	0.127205i
$916$	10.1669	+	47.2865i	0.335924	+	1.56239i
$917$	3.59937	+	3.59937i	0.118862	+	0.118862i
$918$	1.73619	−	5.88658i	0.0573027	−	0.194286i
$919$		−	38.5678i		−	1.27223i	−0.771592	−	0.636117i	$-0.780539\pi$
$919$		−	38.5678i		−	1.27223i	0.771592	−	0.636117i	$-0.219461\pi$
$920$	−0.771376	+	10.2622i	−0.0254315	+	0.338336i
$921$	21.4786	+	21.4786i	0.707743	+	0.707743i
$922$	16.3799	+	30.0839i	0.539443	+	0.990761i
$923$	−0.0918930	−	0.251160i	−0.00302470	−	0.00826704i
$924$	−94.9083	−	61.3185i	−3.12225	−	2.01723i
$925$	−1.59052	+	1.59052i	−0.0522959	+	0.0522959i
$926$	12.6774	+	23.2837i	0.416604	+	0.765150i
$927$	59.7993			1.96407
$928$	30.7389	−	4.23017i	1.00905	−	0.138862i
$929$	27.0979	−	27.0979i	0.889052	−	0.889052i	−0.105380	−	0.994432i	$-0.533606\pi$
$929$	27.0979	−	27.0979i	0.889052	−	0.889052i	0.994432	+	0.105380i	$0.0336059\pi$
$930$	−1.14648	−	0.338142i	−0.0375946	−	0.0110881i
$931$	36.9539	−	36.9539i	1.21111	−	1.21111i
$932$	13.2153	−	20.4546i	0.432883	−	0.670012i
$933$		−	21.7927i		−	0.713461i
$934$	1.82488	−	6.18729i	0.0597118	−	0.202454i
$935$	−11.9645			−0.391280
$936$	35.4261	−	10.0230i	1.15794	−	0.327612i
$937$	27.6340			0.902763			0.451381	−	0.892331i	$-0.350931\pi$
$937$	27.6340			0.902763			0.451381	+	0.892331i	$0.350931\pi$
$938$	23.8275	−	80.7877i	0.777996	−	2.63781i
$939$			22.6077i			0.737775i
$940$	2.33137	−	3.60848i	0.0760410	−	0.117696i
$941$	−3.20725	+	3.20725i	−0.104553	+	0.104553i	−0.757448	−	0.652895i	$-0.773554\pi$
$941$	−3.20725	+	3.20725i	−0.104553	+	0.104553i	0.652895	+	0.757448i	$0.273554\pi$
$942$	42.9852	+	12.6780i	1.40053	+	0.413073i
$943$	1.37158	−	1.37158i	0.0446647	−	0.0446647i
$944$	28.5302	+	10.7986i	0.928578	+	0.351464i
$945$	−7.97047			−0.259280
$946$	6.77291	+	12.4394i	0.220206	+	0.404439i
$947$	−11.6248	+	11.6248i	−0.377755	+	0.377755i	−0.870292	−	0.492537i	$-0.836070\pi$
$947$	−11.6248	+	11.6248i	−0.377755	+	0.377755i	0.492537	+	0.870292i	$0.336070\pi$
$948$	−34.2375	−	22.1202i	−1.11198	−	0.718431i
$949$	5.02129	+	13.7241i	0.162998	+	0.445502i
$950$	−1.87854	−	3.45020i	−0.0609480	−	0.111939i
$951$	1.42956	+	1.42956i	0.0463568	+	0.0463568i
$952$	39.6409	+	2.97967i	1.28477	+	0.0965715i
$953$		−	51.3443i		−	1.66320i	−0.555372	−	0.831602i	$-0.687424\pi$
$953$		−	51.3443i		−	1.66320i	0.555372	−	0.831602i	$-0.312576\pi$
$954$	13.7879	−	46.7482i	0.446400	−	1.51353i
$955$	10.1071	+	10.1071i	0.327058	+	0.327058i
$956$	−3.07451	−	14.2996i	−0.0994367	−	0.462482i
$957$	43.1294	+	43.1294i	1.39418	+	1.39418i
$958$	2.06821	+	3.79856i	0.0668210	+	0.122726i
$959$	−18.7034			−0.603964
$960$	16.5546	−	12.2064i	0.534299	−	0.393958i
$961$		−	30.8919i		−	0.996514i
$962$	−11.4460	+	0.732834i	−0.369033	+	0.0236275i
$963$		−	2.77934i		−	0.0895629i
$964$	−2.37660	−	11.0536i	−0.0765452	−	0.356013i
$965$	6.10191			0.196427
$966$	59.0318	−	32.1412i	1.89932	−	1.03413i
$967$	6.56284	+	6.56284i	0.211047	+	0.211047i	0.804712	−	0.593665i	$-0.202320\pi$
$967$	6.56284	+	6.56284i	0.211047	+	0.211047i	−0.593665	+	0.804712i	$0.702320\pi$
$968$	14.2141	+	16.5246i	0.456857	+	0.531120i
$969$	−13.9701	−	13.9701i	−0.448783	−	0.448783i
$970$	3.36666	+	0.992962i	0.108097	+	0.0318821i
$971$			9.03014i			0.289791i	0.989447	+	0.144895i	$0.0462846\pi$
$971$			9.03014i			0.289791i	−0.989447	+	0.144895i	$0.953715\pi$
$972$	24.0751	−	37.2633i	0.772210	−	1.19522i
$973$	76.5335	+	76.5335i	2.45355	+	2.45355i
$974$	−7.86602	+	4.28284i	−0.252044	+	0.137231i
$975$	−8.40801	−	3.90353i	−0.269272	−	0.125013i
$976$	3.47968	+	7.71795i	0.111382	+	0.247046i
$977$	35.5250	−	35.5250i	1.13654	−	1.13654i	0.147479	−	0.989065i	$-0.452884\pi$
$977$	35.5250	−	35.5250i	1.13654	−	1.13654i	0.989065	−	0.147479i	$-0.0471159\pi$
$978$	−48.4785	+	26.3953i	−1.55017	+	0.844027i
$979$	−10.4648			−0.334456
$980$	−7.90926	−	36.7861i	−0.252652	−	1.17509i
$981$	48.7701	−	48.7701i	1.55711	−	1.55711i
$982$	−7.89213	+	26.7585i	−0.251848	+	0.853897i
$983$	−37.3707	+	37.3707i	−1.19194	+	1.19194i	−0.215417	+	0.976522i	$0.569111\pi$
$983$	−37.3707	+	37.3707i	−1.19194	+	1.19194i	−0.976522	+	0.215417i	$0.930889\pi$
$984$	−3.86583	−	0.290581i	−0.123238	−	0.00926339i
$985$			17.4467i			0.555900i
$986$	−20.5821	−	6.07047i	−0.655467	−	0.193323i
$987$	−28.0591			−0.893130
$988$	4.42750	−	19.5359i	0.140858	−	0.621519i
$989$	−8.42534			−0.267910
$990$	21.1800	+	6.24681i	0.673143	+	0.198537i
$991$			45.7861i			1.45444i	0.686403	+	0.727222i	$0.259189\pi$
$991$			45.7861i			1.45444i	−0.686403	+	0.727222i	$0.740811\pi$
$992$	−1.48197	−	1.12343i	−0.0470526	−	0.0356688i
$993$	31.7248	−	31.7248i	1.00676	−	1.00676i
$994$	−0.150771	+	0.511192i	−0.00478216	+	0.0162140i
$995$	−1.53844	+	1.53844i	−0.0487719	+	0.0487719i
$996$	−50.6195	+	10.8835i	−1.60394	+	0.344858i
$997$	−9.75676			−0.309000			−0.154500	−	0.987993i	$-0.549377\pi$
$997$	−9.75676			−0.309000			−0.154500	+	0.987993i	$0.549377\pi$
$998$	2.97894	−	1.62195i	0.0942967	−	0.0513421i
$999$	2.49517	−	2.49517i	0.0789437	−	0.0789437i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.j.a.31.18	✓	56
4.3	odd	2	inner	260.2.j.a.31.25	yes	56
13.8	odd	4	inner	260.2.j.a.151.25	yes	56
52.47	even	4	inner	260.2.j.a.151.18	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.j.a.31.18	✓	56	1.1	even	1	trivial
260.2.j.a.31.25	yes	56	4.3	odd	2	inner
260.2.j.a.151.18	yes	56	52.47	even	4	inner
260.2.j.a.151.25	yes	56	13.8	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.400070 - 1.35645i) q^{2} -2.57103i q^{3} +(-1.67989 - 1.08535i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-3.48746 - 1.02859i) q^{6} +(3.59259 - 3.59259i) q^{7} +(-2.14428 + 1.84446i) q^{8} -3.61018 q^{9} +O(q^{10})\)	\(q+(0.400070 - 1.35645i) q^{2} -2.57103i q^{3} +(-1.67989 - 1.08535i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-3.48746 - 1.02859i) q^{6} +(3.59259 - 3.59259i) q^{7} +(-2.14428 + 1.84446i) q^{8} -3.61018 q^{9} +(0.676260 + 1.24204i) q^{10} +(-3.05830 + 3.05830i) q^{11} +(-2.79045 + 4.31904i) q^{12} +(3.27029 + 1.51828i) q^{13} +(-3.43587 - 6.31044i) q^{14} +(1.81799 + 1.81799i) q^{15} +(1.64405 + 3.64652i) q^{16} -2.76630i q^{17} +(-1.44432 + 4.89701i) q^{18} +(1.96423 + 1.96423i) q^{19} +(1.95532 - 0.420406i) q^{20} +(-9.23664 - 9.23664i) q^{21} +(2.92488 + 5.37194i) q^{22} -3.63848 q^{23} +(4.74216 + 5.51301i) q^{24} -1.00000i q^{25} +(3.36781 - 3.82856i) q^{26} +1.56878i q^{27} +(-9.93435 + 2.13595i) q^{28} +5.48514 q^{29} +(3.19333 - 1.73868i) q^{30} +(-0.232457 - 0.232457i) q^{31} +(5.60404 - 0.771205i) q^{32} +(7.86296 + 7.86296i) q^{33} +(-3.75233 - 1.10671i) q^{34} +5.08069i q^{35} +(6.06469 + 3.91829i) q^{36} +(-1.59052 - 1.59052i) q^{37} +(3.45020 - 1.87854i) q^{38} +(3.90353 - 8.40801i) q^{39} +(0.212005 - 2.82047i) q^{40} +(-0.376964 + 0.376964i) q^{41} +(-16.2243 + 8.83370i) q^{42} +2.31562 q^{43} +(8.45690 - 1.81829i) q^{44} +(2.55278 - 2.55278i) q^{45} +(-1.45565 + 4.93540i) q^{46} +(1.51890 - 1.51890i) q^{47} +(9.37529 - 4.22690i) q^{48} -18.8134i q^{49} +(-1.35645 - 0.400070i) q^{50} -7.11222 q^{51} +(-3.84587 - 6.09994i) q^{52} -9.54628 q^{53} +(2.12796 + 0.627620i) q^{54} -4.32508i q^{55} +(-1.07713 + 14.3299i) q^{56} +(5.05009 - 5.05009i) q^{57} +(2.19444 - 7.44029i) q^{58} +(5.39264 - 5.39264i) q^{59} +(-1.08087 - 5.02717i) q^{60} +2.11653 q^{61} +(-0.408314 + 0.222316i) q^{62} +(-12.9699 + 12.9699i) q^{63} +(1.19591 - 7.91011i) q^{64} +(-3.38603 + 1.23886i) q^{65} +(13.8114 - 7.51994i) q^{66} +(8.28906 + 8.28906i) q^{67} +(-3.00239 + 4.64707i) q^{68} +9.35463i q^{69} +(6.89168 + 2.03263i) q^{70} +(-0.0524499 - 0.0524499i) q^{71} +(7.74124 - 6.65884i) q^{72} +(2.86601 + 2.86601i) q^{73} +(-2.79377 + 1.52113i) q^{74} -2.57103 q^{75} +(-1.16782 - 5.43156i) q^{76} +21.9744i q^{77} +(-9.84333 - 8.65872i) q^{78} +7.92711i q^{79} +(-3.74100 - 1.41596i) q^{80} -6.79716 q^{81} +(0.360519 + 0.662143i) q^{82} +(7.11999 + 7.11999i) q^{83} +(5.49159 + 25.5415i) q^{84} +(1.95607 + 1.95607i) q^{85} +(0.926409 - 3.14101i) q^{86} -14.1024i q^{87} +(0.916939 - 12.1988i) q^{88} +(1.71088 + 1.71088i) q^{89} +(-2.44142 - 4.48400i) q^{90} +(17.2034 - 6.29427i) q^{91} +(6.11224 + 3.94901i) q^{92} +(-0.597653 + 0.597653i) q^{93} +(-1.45264 - 2.66797i) q^{94} -2.77784 q^{95} +(-1.98279 - 14.4081i) q^{96} +(1.75502 - 1.75502i) q^{97} +(-25.5194 - 7.52667i) q^{98} +(11.0410 - 11.0410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9}+O(q^{10}) \) 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9	\( 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 40 q^{24} - 16 q^{26} - 44 q^{28} + 40 q^{32} - 4 q^{34} + 16 q^{37} + 8 q^{41} + 8 q^{42} + 28 q^{44} - 12 q^{46} + 104 q^{48} + 56 q^{52} - 16 q^{53} + 20 q^{54} - 48 q^{57} - 4 q^{58} + 16 q^{61} - 8 q^{65} + 64 q^{66} + 24 q^{68} - 8 q^{70} - 32 q^{72} + 48 q^{73} - 136 q^{74} - 88 q^{76} + 52 q^{78} - 32 q^{80} + 56 q^{81} - 20 q^{84} - 64 q^{86} - 8 q^{89} - 88 q^{92} - 48 q^{93} - 16 q^{94} - 4 q^{96} - 32 q^{97} + 16 q^{98}+O(q^{100}) \) 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9 + 16 * q^14 - 12 * q^18 - 8 * q^20 - 16 * q^21 - 40 * q^24 - 16 * q^26 - 44 * q^28 + 40 * q^32 - 4 * q^34 + 16 * q^37 + 8 * q^41 + 8 * q^42 + 28 * q^44 - 12 * q^46 + 104 * q^48 + 56 * q^52 - 16 * q^53 + 20 * q^54 - 48 * q^57 - 4 * q^58 + 16 * q^61 - 8 * q^65 + 64 * q^66 + 24 * q^68 - 8 * q^70 - 32 * q^72 + 48 * q^73 - 136 * q^74 - 88 * q^76 + 52 * q^78 - 32 * q^80 + 56 * q^81 - 20 * q^84 - 64 * q^86 - 8 * q^89 - 88 * q^92 - 48 * q^93 - 16 * q^94 - 4 * q^96 - 32 * q^97 + 16 * q^98

Introduction

L-functions

Modular forms

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