LMFDB - Embedded newform 280.2.bf.a.109.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(109,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 4]))

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

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

chi := DirichletCharacter("280.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bf (of order $6$, 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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			109.16
Character	$\chi$	$=$	280.109
Dual form			280.2.bf.a.149.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.603821 - 1.27883i) q^{2} +(1.22223 - 2.11697i) q^{3} +(-1.27080 + 1.54437i) q^{4} +(-2.23601 - 0.0158492i) q^{5} +(-3.44524 - 0.284754i) q^{6} +(-2.60788 + 0.446057i) q^{7} +(2.74231 + 0.692614i) q^{8} +(-1.48770 - 2.57677i) q^{9} +O(q^{10})$	\(q+(-0.603821 - 1.27883i) q^{2} +(1.22223 - 2.11697i) q^{3} +(-1.27080 + 1.54437i) q^{4} +(-2.23601 - 0.0158492i) q^{5} +(-3.44524 - 0.284754i) q^{6} +(-2.60788 + 0.446057i) q^{7} +(2.74231 + 0.692614i) q^{8} +(-1.48770 - 2.57677i) q^{9} +(1.32988 + 2.86904i) q^{10} +(-2.04343 - 1.17977i) q^{11} +(1.71616 + 4.57781i) q^{12} -3.45538 q^{13} +(2.14512 + 3.06569i) q^{14} +(-2.76648 + 4.71419i) q^{15} +(-0.770132 - 3.92516i) q^{16} +(-4.52699 - 2.61366i) q^{17} +(-2.39694 + 3.45842i) q^{18} +(2.01367 - 1.16259i) q^{19} +(2.86600 - 3.43308i) q^{20} +(-2.24314 + 6.06598i) q^{21} +(-0.274863 + 3.32556i) q^{22} +(8.12915 - 4.69337i) q^{23} +(4.81798 - 4.95885i) q^{24} +(4.99950 + 0.0708782i) q^{25} +(2.08643 + 4.41884i) q^{26} +0.0601457 q^{27} +(2.62522 - 4.59437i) q^{28} -4.47908i q^{29} +(7.69909 + 0.691319i) q^{30} +(-3.61091 + 6.25428i) q^{31} +(-4.55458 + 3.35496i) q^{32} +(-4.99508 + 2.88391i) q^{33} +(-0.608928 + 7.36743i) q^{34} +(5.83832 - 0.956056i) q^{35} +(5.87004 + 0.977008i) q^{36} +(-3.64447 - 6.31241i) q^{37} +(-2.70266 - 1.87314i) q^{38} +(-4.22327 + 7.31492i) q^{39} +(-6.12087 - 1.59216i) q^{40} +2.84003 q^{41} +(9.11180 - 0.794171i) q^{42} -4.52926 q^{43} +(4.41879 - 1.65654i) q^{44} +(3.28567 + 5.78526i) q^{45} +(-10.9106 - 7.56183i) q^{46} +(-0.730882 + 0.421975i) q^{47} +(-9.25072 - 3.16711i) q^{48} +(6.60207 - 2.32653i) q^{49} +(-2.92816 - 6.43629i) q^{50} +(-11.0661 + 6.38900i) q^{51} +(4.39110 - 5.33637i) q^{52} +(3.21940 - 5.57616i) q^{53} +(-0.0363172 - 0.0769160i) q^{54} +(4.55043 + 2.67037i) q^{55} +(-7.46057 - 0.583026i) q^{56} -5.68384i q^{57} +(-5.72797 + 2.70456i) q^{58} +(-0.976313 - 0.563675i) q^{59} +(-3.76480 - 10.2632i) q^{60} +(-3.84112 + 2.21767i) q^{61} +(10.1785 + 0.841267i) q^{62} +(5.02912 + 6.05630i) q^{63} +(7.04057 + 3.79873i) q^{64} +(7.72627 + 0.0547652i) q^{65} +(6.70416 + 4.64648i) q^{66} +(-4.40206 + 7.62460i) q^{67} +(9.78935 - 3.66989i) q^{68} -22.9455i q^{69} +(-4.74793 - 6.88892i) q^{70} +8.72538 q^{71} +(-2.29503 - 8.09671i) q^{72} +(-10.4440 - 6.02984i) q^{73} +(-5.87187 + 8.47221i) q^{74} +(6.26059 - 10.4971i) q^{75} +(-0.763505 + 4.58727i) q^{76} +(5.85526 + 2.16522i) q^{77} +(11.9046 + 0.983934i) q^{78} +(-3.31473 - 5.74128i) q^{79} +(1.65981 + 8.78891i) q^{80} +(4.53660 - 7.85763i) q^{81} +(-1.71487 - 3.63191i) q^{82} +0.00442057 q^{83} +(-6.51750 - 11.1729i) q^{84} +(10.0810 + 5.91593i) q^{85} +(2.73486 + 5.79215i) q^{86} +(-9.48206 - 5.47447i) q^{87} +(-4.78659 - 4.65062i) q^{88} +(-1.59643 - 2.76511i) q^{89} +(5.41440 - 7.69507i) q^{90} +(9.01121 - 1.54130i) q^{91} +(-3.08225 + 18.5187i) q^{92} +(8.82674 + 15.2884i) q^{93} +(0.980955 + 0.679875i) q^{94} +(-4.52102 + 2.56766i) q^{95} +(1.53559 + 13.7424i) q^{96} -2.37150i q^{97} +(-6.96169 - 7.03810i) q^{98} +7.02058i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 2 q^{4} - 40 q^{9}+O(q^{10}) $ 88 * q - 2 * q^4 - 40 * q^9	$ 88 q - 2 q^{4} - 40 q^{9} + 6 q^{10} - 6 q^{14} + 4 q^{15} + 2 q^{16} - 24 q^{20} - 8 q^{24} - 2 q^{25} - 14 q^{26} + 14 q^{30} - 28 q^{31} + 24 q^{34} + 60 q^{36} - 16 q^{39} - 32 q^{40} - 16 q^{41} - 2 q^{44} - 42 q^{46} - 8 q^{49} - 12 q^{50} + 8 q^{54} - 28 q^{55} + 36 q^{56} + 10 q^{60} + 52 q^{64} - 12 q^{65} - 44 q^{66} - 48 q^{70} + 16 q^{71} - 42 q^{74} - 36 q^{76} - 4 q^{79} - 40 q^{80} - 20 q^{81} + 12 q^{84} - 24 q^{86} + 4 q^{89} - 96 q^{90} - 22 q^{94} - 34 q^{95} + 80 q^{96}+O(q^{100}) $ 88 * q - 2 * q^4 - 40 * q^9 + 6 * q^10 - 6 * q^14 + 4 * q^15 + 2 * q^16 - 24 * q^20 - 8 * q^24 - 2 * q^25 - 14 * q^26 + 14 * q^30 - 28 * q^31 + 24 * q^34 + 60 * q^36 - 16 * q^39 - 32 * q^40 - 16 * q^41 - 2 * q^44 - 42 * q^46 - 8 * q^49 - 12 * q^50 + 8 * q^54 - 28 * q^55 + 36 * q^56 + 10 * q^60 + 52 * q^64 - 12 * q^65 - 44 * q^66 - 48 * q^70 + 16 * q^71 - 42 * q^74 - 36 * q^76 - 4 * q^79 - 40 * q^80 - 20 * q^81 + 12 * q^84 - 24 * q^86 + 4 * q^89 - 96 * q^90 - 22 * q^94 - 34 * q^95 + 80 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.603821	−	1.27883i	−0.426966	−	0.904268i
$2$	−0.603821	−	1.27883i	−0.426966	−	0.904268i
$3$	1.22223	−	2.11697i	0.705655	−	1.22223i	−0.260799	−	0.965393i	$-0.583986\pi$
$3$	1.22223	−	2.11697i	0.705655	−	1.22223i	0.966454	−	0.256838i	$-0.0826807\pi$
$4$	−1.27080	+	1.54437i	−0.635400	+	0.772183i
$5$	−2.23601	−	0.0158492i	−0.999975	−	0.00708800i
$5$	−2.23601	−	0.0158492i	−0.999975	−	0.00708800i
$6$	−3.44524	−	0.284754i	−1.40651	−	0.116250i
$7$	−2.60788	+	0.446057i	−0.985686	+	0.168594i
$7$	−2.60788	+	0.446057i	−0.985686	+	0.168594i
$8$	2.74231	+	0.692614i	0.969554	+	0.244876i
$9$	−1.48770	−	2.57677i	−0.495899	−	0.858923i
$10$	1.32988	+	2.86904i	0.420546	+	0.907271i
$11$	−2.04343	−	1.17977i	−0.616117	−	0.355715i	0.159239	−	0.987240i	$-0.449096\pi$
$11$	−2.04343	−	1.17977i	−0.616117	−	0.355715i	−0.775355	+	0.631525i	$0.782429\pi$
$12$	1.71616	+	4.57781i	0.495412	+	1.32150i
$13$	−3.45538			−0.958350			−0.479175	−	0.877719i	$-0.659064\pi$
$13$	−3.45538			−0.958350			−0.479175	+	0.877719i	$0.659064\pi$
$14$	2.14512	+	3.06569i	0.573308	+	0.819340i
$15$	−2.76648	+	4.71419i	−0.714301	+	1.21720i
$16$	−0.770132	−	3.92516i	−0.192533	−	0.981290i
$17$	−4.52699	−	2.61366i	−1.09796	−	0.633906i	−0.162274	−	0.986746i	$-0.551883\pi$
$17$	−4.52699	−	2.61366i	−1.09796	−	0.633906i	−0.935684	+	0.352840i	$0.885216\pi$
$18$	−2.39694	+	3.45842i	−0.564964	+	0.815156i
$19$	2.01367	−	1.16259i	0.461968	−	0.266717i	−0.250903	−	0.968012i	$-0.580728\pi$
$19$	2.01367	−	1.16259i	0.461968	−	0.266717i	0.712871	+	0.701295i	$0.247394\pi$
$20$	2.86600	−	3.43308i	0.640858	−	0.767660i
$21$	−2.24314	+	6.06598i	−0.489494	+	1.32370i
$22$	−0.274863	+	3.32556i	−0.0586009	+	0.709012i
$23$	8.12915	−	4.69337i	1.69505	−	0.978635i	0.744720	−	0.667377i	$-0.232583\pi$
$23$	8.12915	−	4.69337i	1.69505	−	0.978635i	0.950326	−	0.311257i	$-0.100750\pi$
$24$	4.81798	−	4.95885i	0.983467	−	1.01222i
$25$	4.99950	+	0.0708782i	0.999900	+	0.0141756i
$26$	2.08643	+	4.41884i	0.409183	+	0.866605i
$27$	0.0601457			0.0115750
$28$	2.62522	−	4.59437i	0.496120	−	0.868254i
$29$		−	4.47908i		−	0.831744i	−0.909423	−	0.415872i	$-0.863476\pi$
$29$		−	4.47908i		−	0.831744i	0.909423	−	0.415872i	$-0.136524\pi$
$30$	7.69909	+	0.691319i	1.40566	+	0.126217i
$31$	−3.61091	+	6.25428i	−0.648539	+	1.12330i	0.334933	+	0.942242i	$0.391286\pi$
$31$	−3.61091	+	6.25428i	−0.648539	+	1.12330i	−0.983472	+	0.181061i	$0.942047\pi$
$32$	−4.55458	+	3.35496i	−0.805144	+	0.593079i
$33$	−4.99508	+	2.88391i	−0.869532	+	0.502024i
$34$	−0.608928	+	7.36743i	−0.104430	+	1.26350i
$35$	5.83832	−	0.956056i	0.986856	−	0.161603i
$36$	5.87004	+	0.977008i	0.978340	+	0.162835i
$37$	−3.64447	−	6.31241i	−0.599147	−	1.03775i	−0.992947	−	0.118557i	$-0.962173\pi$
$37$	−3.64447	−	6.31241i	−0.599147	−	1.03775i	0.393800	−	0.919196i	$-0.371160\pi$
$38$	−2.70266	−	1.87314i	−0.438429	−	0.303864i
$39$	−4.22327	+	7.31492i	−0.676265	+	1.17133i
$40$	−6.12087	−	1.59216i	−0.967794	−	0.251742i
$41$	2.84003			0.443538			0.221769	−	0.975099i	$-0.428817\pi$
$41$	2.84003			0.443538			0.221769	+	0.975099i	$0.428817\pi$
$42$	9.11180	−	0.794171i	1.40598	−	0.122543i
$43$	−4.52926			−0.690706			−0.345353	−	0.938473i	$-0.612241\pi$
$43$	−4.52926			−0.690706			−0.345353	+	0.938473i	$0.612241\pi$
$44$	4.41879	−	1.65654i	0.666158	−	0.249733i
$45$	3.28567	+	5.78526i	0.489799	+	0.862416i
$46$	−10.9106	−	7.56183i	−1.60867	−	1.11493i
$47$	−0.730882	+	0.421975i	−0.106610	+	0.0615513i	−0.552357	−	0.833608i	$-0.686271\pi$
$47$	−0.730882	+	0.421975i	−0.106610	+	0.0615513i	0.445747	+	0.895159i	$0.352938\pi$
$48$	−9.25072	−	3.16711i	−1.33523	−	0.457133i
$49$	6.60207	−	2.32653i	0.943152	−	0.332361i
$50$	−2.92816	−	6.43629i	−0.414104	−	0.910229i
$51$	−11.0661	+	6.38900i	−1.54956	+	0.894638i
$52$	4.39110	−	5.33637i	0.608936	−	0.740021i
$53$	3.21940	−	5.57616i	0.442218	−	0.765944i	−0.555636	−	0.831426i	$-0.687525\pi$
$53$	3.21940	−	5.57616i	0.442218	−	0.765944i	0.997854	+	0.0654818i	$0.0208584\pi$
$54$	−0.0363172	−	0.0769160i	−0.00494215	−	0.0104669i
$55$	4.55043	+	2.67037i	0.613580	+	0.360073i
$56$	−7.46057	−	0.583026i	−0.996960	−	0.0779101i
$57$		−	5.68384i		−	0.752843i
$58$	−5.72797	+	2.70456i	−0.752119	+	0.355126i
$59$	−0.976313	−	0.563675i	−0.127105	−	0.0733842i	0.435099	−	0.900382i	$-0.356713\pi$
$59$	−0.976313	−	0.563675i	−0.127105	−	0.0733842i	−0.562204	+	0.826998i	$0.690047\pi$
$60$	−3.76480	−	10.2632i	−0.486033	−	1.32498i
$61$	−3.84112	+	2.21767i	−0.491805	+	0.283944i	−0.725323	−	0.688409i	$-0.758310\pi$
$61$	−3.84112	+	2.21767i	−0.491805	+	0.283944i	0.233518	+	0.972353i	$0.424976\pi$
$62$	10.1785	+	0.841267i	1.29267	+	0.106841i
$63$	5.02912	+	6.05630i	0.633610	+	0.763022i
$64$	7.04057	+	3.79873i	0.880071	+	0.474842i
$65$	7.72627	+	0.0547652i	0.958326	+	0.00679278i
$66$	6.70416	+	4.64648i	0.825225	+	0.571942i
$67$	−4.40206	+	7.62460i	−0.537797	+	0.931493i	0.461225	+	0.887283i	$0.347410\pi$
$67$	−4.40206	+	7.62460i	−0.537797	+	0.931493i	−0.999022	+	0.0442092i	$0.985923\pi$
$68$	9.78935	−	3.66989i	1.18713	−	0.445040i
$69$		−	22.9455i		−	2.76232i
$70$	−4.74793	−	6.88892i	−0.567486	−	0.823383i
$71$	8.72538			1.03551			0.517756	−	0.855528i	$-0.326768\pi$
$71$	8.72538			1.03551			0.517756	+	0.855528i	$0.326768\pi$
$72$	−2.29503	−	8.09671i	−0.270472	−	0.954206i
$73$	−10.4440	−	6.02984i	−1.22238	−	0.705739i	−0.256952	−	0.966424i	$-0.582718\pi$
$73$	−10.4440	−	6.02984i	−1.22238	−	0.705739i	−0.965424	+	0.260685i	$0.916052\pi$
$74$	−5.87187	+	8.47221i	−0.682592	+	0.984875i
$75$	6.26059	−	10.4971i	0.722910	−	1.21211i
$76$	−0.763505	+	4.58727i	−0.0875800	+	0.526196i
$77$	5.85526	+	2.16522i	0.667269	+	0.246750i
$78$	11.9046	+	0.983934i	1.34793	+	0.111409i
$79$	−3.31473	−	5.74128i	−0.372937	−	0.645945i	0.617079	−	0.786901i	$-0.288316\pi$
$79$	−3.31473	−	5.74128i	−0.372937	−	0.645945i	−0.990016	+	0.140956i	$0.954982\pi$
$80$	1.65981	+	8.78891i	0.185573	+	0.982631i
$81$	4.53660	−	7.85763i	0.504067	−	0.873070i
$82$	−1.71487	−	3.63191i	−0.189376	−	0.401077i
$83$	0.00442057			0.000485220			0.000242610	−	1.00000i	$-0.499923\pi$
$83$	0.00442057			0.000485220			0.000242610		1.00000i	$0.499923\pi$
$84$	−6.51750	−	11.1729i	−0.711118	−	1.21906i
$85$	10.0810	+	5.91593i	1.09344	+	0.641672i
$86$	2.73486	+	5.79215i	0.294908	+	0.624583i
$87$	−9.48206	−	5.47447i	−1.01658	−	0.586925i
$88$	−4.78659	−	4.65062i	−0.510252	−	0.495757i
$89$	−1.59643	−	2.76511i	−0.169222	−	0.293101i	0.768925	−	0.639339i	$-0.220792\pi$
$89$	−1.59643	−	2.76511i	−0.169222	−	0.293101i	−0.938146	+	0.346239i	$0.887459\pi$
$90$	5.41440	−	7.69507i	0.570728	−	0.811131i
$91$	9.01121	−	1.54130i	0.944632	−	0.161572i
$92$	−3.08225	+	18.5187i	−0.321347	+	1.93071i
$93$	8.82674	+	15.2884i	0.915290	+	1.58533i
$94$	0.980955	+	0.679875i	0.101178	+	0.0701237i
$95$	−4.52102	+	2.56766i	−0.463847	+	0.263436i
$96$	1.53559	+	13.7424i	0.156725	+	1.40258i
$97$		−	2.37150i		−	0.240789i	−0.992726	−	0.120394i	$-0.961584\pi$
$97$		−	2.37150i		−	0.240789i	0.992726	−	0.120394i	$-0.0384159\pi$
$98$	−6.96169	−	7.03810i	−0.703237	−	0.710955i
$99$			7.02058i			0.705595i
$100$	−6.46283	+	7.63098i	−0.646283	+	0.763098i
$101$	−3.65970	−	2.11293i	−0.364153	−	0.210244i	0.306748	−	0.951791i	$-0.400759\pi$
$101$	−3.65970	−	2.11293i	−0.364153	−	0.210244i	−0.670901	+	0.741547i	$0.734093\pi$
$102$	14.8523	+	10.2938i	1.47060	+	1.01924i
$103$	7.01248	−	4.04866i	0.690960	−	0.398926i	−0.113012	−	0.993594i	$-0.536050\pi$
$103$	7.01248	−	4.04866i	0.690960	−	0.398926i	0.803972	+	0.594668i	$0.202716\pi$
$104$	−9.47574	−	2.39325i	−0.929172	−	0.234677i
$105$	5.11183	−	13.5280i	0.498864	−	1.32020i
$106$	−9.07488	−	0.750052i	−0.881430	−	0.0728515i
$107$	1.12822	+	1.95414i	0.109069	+	0.188913i	0.915393	−	0.402560i	$-0.131880\pi$
$107$	1.12822	+	1.95414i	0.109069	+	0.188913i	−0.806324	+	0.591474i	$0.798546\pi$
$108$	−0.0764332	+	0.0928870i	−0.00735479	+	0.00893806i
$109$	11.8407	+	6.83621i	1.13413	+	0.654790i	0.944970	−	0.327156i	$-0.106090\pi$
$109$	11.8407	+	6.83621i	1.13413	+	0.654790i	0.189159	+	0.981946i	$0.439424\pi$
$110$	0.667304	−	7.43164i	0.0636249	−	0.708579i
$111$	−17.8175			−1.69117
$112$	3.75926	+	9.89282i	0.355217	+	0.934784i
$113$			6.99411i			0.657950i	0.944339	+	0.328975i	$0.106703\pi$
$113$			6.99411i			0.657950i	−0.944339	+	0.328975i	$0.893297\pi$
$114$	−7.26865	+	3.43202i	−0.680771	+	0.321438i
$115$	−18.2513	+	10.3656i	−1.70194	+	0.966596i
$116$	6.91734	+	5.69202i	0.642259	+	0.528490i
$117$	5.14056	+	8.90371i	0.475245	+	0.823148i
$118$	−0.131324	+	1.58889i	−0.0120894	+	0.146270i
$119$	12.9717	+	4.79681i	1.18911	+	0.439723i
$120$	−10.8517	+	11.0117i	−0.990616	+	1.00523i
$121$	−2.71627	−	4.70472i	−0.246934	−	0.427702i
$122$	5.15537	+	3.57306i	0.466745	+	0.323489i
$123$	3.47117	−	6.01224i	0.312985	−	0.542106i
$124$	−5.07015	−	13.5245i	−0.455313	−	1.21454i
$125$	−11.1778	−	0.237723i	−0.999774	−	0.0212626i
$126$	4.70828	−	10.0883i	0.419447	−	0.898737i
$127$			5.75642i			0.510800i	0.966836	+	0.255400i	$0.0822071\pi$
$127$			5.75642i			0.510800i	−0.966836	+	0.255400i	$0.917793\pi$
$128$	0.606680	−	11.2974i	0.0536234	−	0.998561i
$129$	−5.53581	+	9.58830i	−0.487401	+	0.844203i
$130$	−4.59525	−	9.91364i	−0.403030	−	0.869483i
$131$	11.9360	−	6.89125i	1.04285	−	0.602091i	0.122213	−	0.992504i	$-0.461001\pi$
$131$	11.9360	−	6.89125i	1.04285	−	0.602091i	0.920640	+	0.390413i	$0.127668\pi$
$132$	1.89394	−	11.3791i	0.164846	−	0.990424i
$133$	−4.73283	+	3.93012i	−0.410389	+	0.340785i
$134$	12.4086	+	1.02559i	1.07194	+	0.0885974i
$135$	−0.134487		0.000953264i	−0.0115748		8.20439e-5i
$136$	−10.6042	−	10.3029i	−0.909301	−	0.883470i
$137$	−3.00595	−	1.73549i	−0.256816	−	0.148273i	0.366065	−	0.930589i	$-0.380705\pi$
$137$	−3.00595	−	1.73549i	−0.256816	−	0.148273i	−0.622881	+	0.782316i	$0.714038\pi$
$138$	−29.3434	+	13.8550i	−2.49787	+	1.17941i
$139$			20.8436i			1.76793i	0.467554	+	0.883964i	$0.345135\pi$
$139$			20.8436i			1.76793i	−0.467554	+	0.883964i	$0.654865\pi$
$140$	−5.94284	+	10.2315i	−0.502261	+	0.864716i
$141$			2.06300i			0.173736i
$142$	−5.26857	−	11.1583i	−0.442128	−	0.936380i
$143$	7.06082	+	4.07656i	0.590455	+	0.340899i
$144$	−8.96851	+	7.82391i	−0.747376	+	0.651992i
$145$	−0.0709900	+	10.0153i	−0.00589540	+	0.831723i
$146$	−1.40483	+	16.9970i	−0.116264	+	1.40668i
$147$	3.14407	−	16.8199i	0.259319	−	1.38728i
$148$	14.3801	+	2.39342i	1.18203	+	0.196738i
$149$	−4.53569	+	2.61868i	−0.371578	+	0.214531i	−0.674148	−	0.738597i	$-0.735489\pi$
$149$	−4.53569	+	2.61868i	−0.371578	+	0.214531i	0.302570	+	0.953127i	$0.402156\pi$
$150$	−17.2043	−	1.66782i	−1.40473	−	0.136177i
$151$	6.75176	−	11.6944i	0.549450	−	0.951676i	−0.448862	−	0.893601i	$-0.648171\pi$
$151$	6.75176	−	11.6944i	0.549450	−	0.951676i	0.998312	−	0.0580746i	$-0.0184961\pi$
$152$	6.32735	−	1.79350i	0.513216	−	0.145472i
$153$			15.5533i			1.25741i
$154$	−0.766583	−	8.79527i	−0.0617730	−	0.708743i
$155$	8.17317	−	13.9274i	0.656485	−	1.11868i
$156$	−5.92998	−	15.8181i	−0.474778	−	1.26646i
$157$	−6.99733	+	12.1197i	−0.558448	+	0.967260i	0.439179	+	0.898400i	$0.355270\pi$
$157$	−6.99733	+	12.1197i	−0.558448	+	0.967260i	−0.997626	+	0.0688600i	$0.978064\pi$
$158$	−5.34061	+	7.70568i	−0.424876	+	0.613031i
$159$	−7.86969	−	13.6307i	−0.624107	−	1.08099i
$160$	10.2373	−	7.42955i	0.809328	−	0.587357i
$161$	−19.1063	+	15.8658i	−1.50579	+	1.25040i
$162$	−12.7879	−	1.05693i	−1.00471	−	0.0830406i
$163$	9.05729	+	15.6877i	0.709422	+	1.22875i	0.965072	+	0.261985i	$0.0843771\pi$
$163$	9.05729	+	15.6877i	0.709422	+	1.22875i	−0.255650	+	0.966769i	$0.582290\pi$
$164$	−3.60911	+	4.38604i	−0.281824	+	0.342492i
$165$	11.2148	−	6.36929i	0.873068	−	0.495849i
$166$	−0.00266923	−	0.00565314i	−0.000207172	−	0.000438769i
$167$		−	11.5185i		−	0.891331i	−0.895200	−	0.445665i	$-0.852967\pi$
$167$		−	11.5185i		−	0.891331i	0.895200	−	0.445665i	$-0.147033\pi$
$168$	−10.3528	+	15.0812i	−0.798735	+	1.16354i
$169$	−1.06035			−0.0815654
$170$	1.47834	−	16.4640i	0.113383	−	1.26273i
$171$	−5.99147	−	3.45918i	−0.458179	−	0.264530i
$172$	5.75579	−	6.99484i	0.438875	−	0.533352i
$173$	−6.56480	−	11.3706i	−0.499112	−	0.864488i	0.500887	−	0.865513i	$-0.333007\pi$
$173$	−6.56480	−	11.3706i	−0.499112	−	0.864488i	−0.999999	+	0.00102457i	$0.999674\pi$
$174$	−1.27544	+	15.4315i	−0.0966906	+	1.16986i
$175$	−13.0697	+	2.04522i	−0.987977	+	0.154604i
$176$	−3.05709	+	8.92936i	−0.230437	+	0.673076i
$177$	−2.38656	+	1.37788i	−0.179385	+	0.103568i
$178$	−2.57213	+	3.71119i	−0.192789	+	0.278166i
$179$	9.47906	+	5.47274i	0.708498	+	0.409052i	0.810505	−	0.585732i	$-0.199193\pi$
$179$	9.47906	+	5.47274i	0.708498	+	0.409052i	−0.102006	+	0.994784i	$0.532526\pi$
$180$	−13.1100	−	2.27764i	−0.977161	−	0.169765i
$181$		−	5.38277i		−	0.400098i	−0.979786	−	0.200049i	$-0.935890\pi$
$181$		−	5.38277i		−	0.400098i	0.979786	−	0.200049i	$-0.0641102\pi$
$182$	−7.41221	−	10.5931i	−0.549430	−	0.785214i
$183$			10.8420i			0.801466i
$184$	25.5434	−	7.24032i	1.88308	−	0.533764i
$185$	8.04903	+	14.1724i	0.591777	+	1.04197i
$186$	14.2214	−	20.5193i	1.04276	−	1.50455i
$187$	6.16705	+	10.6817i	0.450980	+	0.781120i
$188$	0.277121	−	1.66499i	0.0202112	−	0.121432i
$189$	−0.156853	+	0.0268284i	−0.0114094	+	0.00195148i
$190$	6.01348	+	4.23120i	0.436264	+	0.306964i
$191$	7.10904	+	12.3132i	0.514392	+	0.890953i	0.999861	+	0.0166988i	$0.00531563\pi$
$191$	7.10904	+	12.3132i	0.514392	+	0.890953i	−0.485469	+	0.874254i	$0.661351\pi$
$192$	16.6470	−	10.2617i	1.20139	−	0.740576i
$193$	16.6971	+	9.64007i	1.20188	+	0.693907i	0.960974	−	0.276640i	$-0.0892210\pi$
$193$	16.6971	+	9.64007i	1.20188	+	0.693907i	0.240909	+	0.970548i	$0.422554\pi$
$194$	−3.03273	+	1.43196i	−0.217738	+	0.102809i
$195$	9.55922	−	16.2893i	0.684550	−	1.16650i
$196$	−4.79690	+	13.1526i	−0.342636	+	0.939468i
$197$	−6.71991			−0.478774			−0.239387	−	0.970924i	$-0.576946\pi$
$197$	−6.71991			−0.478774			−0.239387	+	0.970924i	$0.576946\pi$
$198$	8.97812	−	4.23918i	0.638047	−	0.301265i
$199$	−0.404997	+	0.701475i	−0.0287095	+	0.0497263i	−0.880023	−	0.474931i	$-0.842473\pi$
$199$	−0.404997	+	0.701475i	−0.0287095	+	0.0497263i	0.851314	+	0.524657i	$0.175806\pi$
$200$	13.6611	+	3.65709i	0.965986	+	0.258596i
$201$	10.7607	+	18.6380i	0.758999	+	1.31463i
$202$	−0.492268	+	5.95595i	−0.0346358	+	0.419059i
$203$	1.99793	+	11.6809i	0.140227	+	0.819838i
$204$	4.19581	−	25.2092i	0.293766	−	1.76500i
$205$	−6.35034	−	0.0450123i	−0.443527	−	0.00314379i
$206$	−9.41181	−	6.52309i	−0.655752	−	0.454485i
$207$	−24.1874	−	13.9646i	−1.68114	−	0.970608i
$208$	2.66110	+	13.5629i	0.184514	+	0.940420i
$209$	−5.48639			−0.379502
$210$	−20.3867	+	1.63136i	−1.40681	+	0.112575i
$211$		−	16.4689i		−	1.13376i	−0.823799	−	0.566882i	$-0.808149\pi$
$211$		−	16.4689i		−	1.13376i	0.823799	−	0.566882i	$-0.191851\pi$
$212$	4.52042	+	12.0581i	0.310463	+	0.828154i
$213$	10.6644	−	18.4713i	0.730715	−	1.26563i
$214$	1.81776	−	2.62275i	0.124260	−	0.179287i
$215$	10.1275	+	0.0717854i	0.690689	+	0.00489572i
$216$	0.164938	+	0.0416578i	0.0112226	+	0.00283445i
$217$	6.62706	−	17.9211i	0.449874	−	1.21656i
$218$	1.59269	−	19.2700i	0.107871	−	1.30513i
$219$	−25.5299	+	14.7397i	−1.72515	+	0.996017i
$220$	−9.90672	+	3.63402i	−0.667911	+	0.245005i
$221$	15.6425	+	9.03119i	1.05223	+	0.607504i
$222$	10.7586	+	22.7856i	0.722070	+	1.52927i
$223$		−	11.9314i		−	0.798984i	−0.916737	−	0.399492i	$-0.869186\pi$
$223$		−	11.9314i		−	0.798984i	0.916737	−	0.399492i	$-0.130814\pi$
$224$	10.3813	−	10.7809i	0.693630	−	0.720332i
$225$	−7.25510	−	12.9880i	−0.483674	−	0.865866i
$226$	8.94426	−	4.22319i	0.594963	−	0.280922i
$227$	5.36296	−	9.28892i	0.355952	−	0.616528i	−0.631328	−	0.775516i	$-0.717490\pi$
$227$	5.36296	−	9.28892i	0.355952	−	0.616528i	0.987280	+	0.158988i	$0.0508232\pi$
$228$	8.77792	+	7.22302i	0.581332	+	0.478356i
$229$	3.82171	−	2.20647i	0.252546	−	0.145807i	−0.368384	−	0.929674i	$-0.620089\pi$
$229$	3.82171	−	2.20647i	0.252546	−	0.145807i	0.620929	+	0.783866i	$0.286755\pi$
$230$	24.2763	+	17.0813i	1.60073	+	1.12631i
$231$	11.7402	−	9.74898i	0.772447	−	0.641436i
$232$	3.10227	−	12.2830i	0.203674	−	0.806421i
$233$	−0.450962	+	0.260363i	−0.0295435	+	0.0170569i	−0.514699	−	0.857371i	$-0.672096\pi$
$233$	−0.450962	+	0.260363i	−0.0295435	+	0.0170569i	0.485156	+	0.874428i	$0.338763\pi$
$234$	8.28233	−	11.9501i	0.541433	−	0.781205i
$235$	1.64095	−	0.931957i	0.107044	−	0.0607942i
$236$	2.11122	−	0.791467i	0.137429	−	0.0515201i
$237$	−16.2055			−1.05266
$238$	−1.69828	−	19.4850i	−0.110083	−	1.26302i
$239$	12.3076			0.796113			0.398057	−	0.917361i	$-0.369685\pi$
$239$	12.3076			0.796113			0.398057	+	0.917361i	$0.369685\pi$
$240$	20.6345	+	7.22831i	1.33195	+	0.466586i
$241$	8.31611	−	14.4039i	0.535688	−	0.927838i	−0.463442	−	0.886127i	$-0.653386\pi$
$241$	8.31611	−	14.4039i	0.535688	−	0.927838i	0.999130	−	0.0417108i	$-0.0132808\pi$
$242$	−4.37638	+	6.31445i	−0.281325	+	0.405908i
$243$	−10.9993	−	19.0514i	−0.705608	−	1.22215i
$244$	1.45640	−	8.75032i	0.0932365	−	0.560182i
$245$	−14.7992	+	5.09750i	−0.945484	+	0.325668i
$246$	−9.78459	−	0.808710i	−0.623843	−	0.0515615i
$247$	−6.95800	+	4.01721i	−0.442727	+	0.255609i
$248$	−14.2341	+	14.6502i	−0.903864	+	0.930291i
$249$	0.00540295	−	0.00935819i	0.000342398	−	0.000593051i
$250$	6.44539	+	14.4380i	0.407642	+	0.913142i
$251$		−	6.29796i		−	0.397524i	−0.980048	−	0.198762i	$-0.936308\pi$
$251$		−	6.29796i		−	0.397524i	0.980048	−	0.198762i	$-0.0636920\pi$
$252$	−15.7442	+	0.0704537i	−0.991788	+	0.00443817i
$253$	−22.1484			−1.39246
$254$	7.36147	−	3.47585i	0.461900	−	0.218094i
$255$	24.8451	−	14.1105i	1.55586	−	0.883633i
$256$	−14.8138	+	6.04579i	−0.925862	+	0.377862i
$257$	−20.5797	+	11.8817i	−1.28372	+	0.741158i	−0.977527	−	0.210810i	$-0.932390\pi$
$257$	−20.5797	+	11.8817i	−1.28372	+	0.741158i	−0.306197	+	0.951968i	$0.599057\pi$
$258$	15.6044	+	1.28973i	0.971489	+	0.0802949i
$259$	12.3200	+	14.8364i	0.765530	+	0.921886i
$260$	−9.90313	+	11.8626i	−0.614166	+	0.735687i
$261$	−11.5415	+	6.66352i	−0.714404	+	0.412461i
$262$	−16.0199	−	11.1030i	−0.989714	−	0.685946i
$263$	−22.6161	−	13.0574i	−1.39457	−	0.805154i	−0.400751	−	0.916187i	$-0.631251\pi$
$263$	−22.6161	−	13.0574i	−1.39457	−	0.805154i	−0.993817	+	0.111033i	$0.964584\pi$
$264$	−15.6955	+	4.44892i	−0.965992	+	0.273812i
$265$	−7.28698	+	12.4173i	−0.447636	+	0.762790i
$266$	7.88373	+	3.67939i	0.483382	+	0.225598i
$267$	−7.80485			−0.477649
$268$	−6.18102	−	16.4877i	−0.377566	−	1.00715i
$269$	−14.0095	−	8.08840i	−0.854175	−	0.493158i	0.00788200	−	0.999969i	$-0.497491\pi$
$269$	−14.0095	−	8.08840i	−0.854175	−	0.493158i	−0.862057	+	0.506810i	$0.830824\pi$
$270$	0.0799867	+	0.172561i	0.00486784	+	0.0105017i
$271$	−3.38733	−	5.86703i	−0.205766	−	0.356396i	0.744611	−	0.667499i	$-0.232635\pi$
$271$	−3.38733	−	5.86703i	−0.205766	−	0.356396i	−0.950376	+	0.311102i	$0.899302\pi$
$272$	−6.77266	+	19.7820i	−0.410653	+	1.19946i
$273$	7.75091	−	20.9603i	0.469106	−	1.26857i
$274$	−0.404333	+	4.89202i	−0.0244266	+	0.295538i
$275$	−10.1325	−	6.04311i	−0.611012	−	0.364413i
$276$	35.4363	+	29.1592i	2.13301	+	1.75518i
$277$	8.07045	−	13.9784i	0.484907	−	0.839883i	−0.514943	−	0.857224i	$-0.672187\pi$
$277$	8.07045	−	13.9784i	0.484907	−	0.839883i	0.999850	+	0.0173415i	$0.00552025\pi$
$278$	26.6553	−	12.5858i	1.59868	−	0.754845i
$279$	21.4878			1.28644
$280$	16.6727	+	1.42190i	0.996383	+	0.0849746i
$281$	−9.13231			−0.544788			−0.272394	−	0.962186i	$-0.587815\pi$
$281$	−9.13231			−0.544788			−0.272394	+	0.962186i	$0.587815\pi$
$282$	2.63823	−	1.24568i	0.157104	−	0.0741794i
$283$	4.31520	−	7.47415i	0.256512	−	0.444292i	−0.708793	−	0.705416i	$-0.750760\pi$
$283$	4.31520	−	7.47415i	0.256512	−	0.444292i	0.965305	+	0.261125i	$0.0840934\pi$
$284$	−11.0882	+	13.4752i	−0.657965	+	0.799605i
$285$	−0.0900845	+	12.7091i	−0.00533615	+	0.752824i
$286$	0.949754	−	11.4911i	0.0561602	−	0.679482i
$287$	−7.40645	+	1.26681i	−0.437189	+	0.0747777i
$288$	15.4208	+	6.74494i	0.908679	+	0.397449i
$289$	5.16245	+	8.94162i	0.303673	+	0.525978i
$290$	12.8507	−	5.95665i	0.754618	−	0.349786i
$291$	−5.02038	−	2.89852i	−0.294300	−	0.169914i
$292$	22.5845	−	8.46661i	1.32166	−	0.495471i
$293$	25.7079			1.50187			0.750934	−	0.660377i	$-0.229603\pi$
$293$	25.7079			1.50187			0.750934	+	0.660377i	$0.229603\pi$
$294$	−23.4082	+	6.13548i	−1.36519	+	0.357829i
$295$	2.17411	+	1.27586i	0.126582	+	0.0742833i
$296$	−5.62222	−	19.8348i	−0.326785	−	1.15288i
$297$	−0.122903	−	0.0709583i	−0.00713158	−	0.00411742i
$298$	6.08759	+	4.21915i	0.352644	+	0.244409i
$299$	−28.0893	+	16.2174i	−1.62445	+	0.937875i
$300$	8.25546	+	23.0084i	0.476629	+	1.32839i
$301$	11.8118	−	2.02031i	0.680819	−	0.116449i
$302$	−19.0320	−	1.57302i	−1.09517	−	0.0905170i
$303$	−8.94599	+	5.16497i	−0.513934	+	0.296720i
$304$	−6.11417	−	7.00864i	−0.350671	−	0.401973i
$305$	8.62394	−	4.89786i	0.493805	−	0.280451i
$306$	19.8901	−	9.39144i	1.13704	−	0.536873i
$307$	−21.0935			−1.20387			−0.601934	−	0.798546i	$-0.705603\pi$
$307$	−21.0935			−1.20387			−0.601934	+	0.798546i	$0.705603\pi$
$308$	−10.7848	+	6.29110i	−0.614519	+	0.358469i
$309$		−	19.7936i		−	1.12602i
$310$	−22.7459	−	2.04241i	−1.29188	−	0.116001i
$311$	8.70925	−	15.0849i	0.493856	−	0.855384i	−0.506119	−	0.862464i	$-0.668920\pi$
$311$	8.70925	−	15.0849i	0.493856	−	0.855384i	0.999975	+	0.00707961i	$0.00225353\pi$
$312$	−16.6480	+	17.1347i	−0.942505	+	0.970062i
$313$	1.68712	−	0.974058i	0.0953616	−	0.0550570i	−0.451561	−	0.892240i	$-0.649133\pi$
$313$	1.68712	−	0.974058i	0.0953616	−	0.0550570i	0.546922	+	0.837183i	$0.315799\pi$
$314$	19.7242	+	1.63023i	1.11310	+	0.0919993i
$315$	−11.1492	−	13.6217i	−0.628185	−	0.767494i
$316$	13.0790	+	2.17687i	0.735752	+	0.122458i
$317$	−3.76685	−	6.52437i	−0.211567	−	0.366445i	0.740638	−	0.671904i	$-0.234523\pi$
$317$	−3.76685	−	6.52437i	−0.211567	−	0.366445i	−0.952205	+	0.305459i	$0.901190\pi$
$318$	−12.6794	+	18.2945i	−0.711027	+	1.02590i
$319$	−5.28430	+	9.15267i	−0.295864	+	0.512451i
$320$	−15.6826	−	8.60560i	−0.876684	−	0.481068i
$321$	5.51579			0.307861
$322$	31.8264	+	14.8536i	1.77362	+	0.827759i
$323$	−12.1545			−0.676295
$324$	6.36994	+	16.9917i	0.353885	+	0.943981i
$325$	−17.2752	−	0.244911i	−0.958254	−	0.0135852i
$326$	14.5929	−	21.0553i	0.808224	−	1.16614i
$327$	28.9440	−	16.7109i	1.60061	−	0.924112i
$328$	7.78825	+	1.96704i	0.430034	+	0.108612i
$329$	1.71783	−	1.42647i	0.0947068	−	0.0786441i
$330$	−14.9169	−	10.4958i	−0.821150	−	0.577777i
$331$	27.3735	−	15.8041i	1.50458	−	0.868670i	0.504595	−	0.863356i	$-0.331642\pi$
$331$	27.3735	−	15.8041i	1.50458	−	0.868670i	0.999986	−	0.00531427i	$-0.00169159\pi$
$332$	−0.00561766	+	0.00682697i	−0.000308309	+	0.000374679i
$333$	−10.8437	+	18.7819i	−0.594233	+	1.02924i
$334$	−14.7302	+	6.95513i	−0.806002	+	0.380568i
$335$	9.96391	−	16.9789i	0.544386	−	0.927657i
$336$	25.5375	+	4.13309i	1.39318	+	0.225479i
$337$			1.95397i			0.106440i	0.998583	+	0.0532198i	$0.0169484\pi$
$337$			1.95397i			0.106440i	−0.998583	+	0.0532198i	$0.983052\pi$
$338$	0.640262	+	1.35601i	0.0348256	+	0.0737570i
$339$	14.8063	+	8.54841i	0.804167	+	0.464286i
$340$	−21.9473	+	8.05077i	−1.19026	+	0.436614i
$341$	14.7573	−	8.52012i	0.799151	−	0.461390i
$342$	−0.805916	+	9.75078i	−0.0435790	+	0.527262i
$343$	−16.1796	+	9.01220i	−0.873618	+	0.486613i
$344$	−12.4207	−	3.13703i	−0.669677	−	0.169137i
$345$	−0.363669	+	51.3065i	−0.0195793	+	2.76225i
$346$	−10.5770	+	15.2610i	−0.568625	+	0.820438i
$347$	−2.53653	+	4.39339i	−0.136168	+	0.235850i	−0.926043	−	0.377418i	$-0.876812\pi$
$347$	−2.53653	+	4.39339i	−0.136168	+	0.235850i	0.789875	+	0.613268i	$0.210145\pi$
$348$	20.5044	−	7.68681i	1.09915	−	0.412056i
$349$		−	0.256705i		−	0.0137411i	−0.999976	−	0.00687055i	$-0.997813\pi$
$349$		−	0.256705i		−	0.0137411i	0.999976	−	0.00687055i	$-0.00218698\pi$
$350$	10.5072	+	15.4789i	0.561636	+	0.827385i
$351$	−0.207826			−0.0110929
$352$	13.2651	−	1.48224i	0.707030	−	0.0790038i
$353$	23.9299	+	13.8160i	1.27366	+	0.735349i	0.975675	−	0.219221i	$-0.0703515\pi$
$353$	23.9299	+	13.8160i	1.27366	+	0.735349i	0.297987	+	0.954570i	$0.403685\pi$
$354$	3.20313	+	2.22001i	0.170244	+	0.117992i
$355$	−19.5101	−	0.138291i	−1.03549	−	0.00733971i
$356$	6.29908	+	1.04842i	0.333851	+	0.0555661i
$357$	26.0091	−	21.5978i	1.37655	−	1.14308i
$358$	1.27503	−	15.4266i	0.0673876	−	0.815323i
$359$	−11.0806	−	19.1922i	−0.584813	−	1.01293i	−0.994899	−	0.100879i	$-0.967834\pi$
$359$	−11.0806	−	19.1922i	−0.584813	−	1.01293i	0.410085	−	0.912047i	$-0.365499\pi$
$360$	5.00338	+	18.1407i	0.263701	+	0.956099i
$361$	−6.79675	+	11.7723i	−0.357724	+	0.619595i
$362$	−6.88364	+	3.25023i	−0.361796	+	0.170828i
$363$	−13.2796			−0.697000
$364$	−9.07113	+	15.8753i	−0.475456	+	0.832091i
$365$	23.2573	+	13.6483i	1.21734	+	0.714386i
$366$	13.8651	−	6.54665i	0.724740	−	0.342199i
$367$	27.3396	+	15.7845i	1.42711	+	0.823944i	0.996892	−	0.0787790i	$-0.0251022\pi$
$367$	27.3396	+	15.7845i	1.42711	+	0.823944i	0.430221	+	0.902723i	$0.358435\pi$
$368$	−24.6827	−	28.2937i	−1.28668	−	1.47491i
$369$	−4.22510	−	7.31809i	−0.219950	−	0.380965i
$370$	13.2639	−	18.8509i	0.689555	−	0.980012i
$371$	−5.90851	+	15.9780i	−0.306754	+	0.829535i
$372$	−34.8279	−	5.79674i	−1.80574	−	0.300547i
$373$	4.00325	+	6.93383i	0.207280	+	0.359020i	0.950857	−	0.309631i	$-0.100205\pi$
$373$	4.00325	+	6.93383i	0.207280	+	0.359020i	−0.743577	+	0.668651i	$0.766872\pi$
$374$	9.93620	−	14.3364i	0.513788	−	0.741318i
$375$	−14.1651	+	23.3725i	−0.731484	+	1.20695i
$376$	−2.29657	+	0.650968i	−0.118437	+	0.0335711i
$377$			15.4769i			0.797102i
$378$	0.129020	+	0.184388i	0.00663607	+	0.00948390i
$379$			10.9382i			0.561856i	0.959729	+	0.280928i	$0.0906422\pi$
$379$			10.9382i			0.561856i	−0.959729	+	0.280928i	$0.909358\pi$
$380$	1.77991	−	10.2451i	0.0913075	−	0.525562i
$381$	12.1861	+	7.03568i	0.624315	+	0.360449i
$382$	11.4539	−	16.5262i	0.586032	−	0.845554i
$383$	−16.3968	+	9.46670i	−0.837838	+	0.483726i	−0.856529	−	0.516099i	$-0.827384\pi$
$383$	−16.3968	+	9.46670i	−0.837838	+	0.483726i	0.0186907	+	0.999825i	$0.494050\pi$
$384$	−23.1748	−	15.0924i	−1.18263	−	0.770180i
$385$	−13.0581	−	4.93426i	−0.665503	−	0.251473i
$386$	2.24594	−	27.1736i	0.114315	−	1.38310i
$387$	6.73817	+	11.6709i	0.342521	+	0.593263i
$388$	3.66246	+	3.01370i	0.185933	+	0.152997i
$389$	−29.3054	−	16.9195i	−1.48584	−	0.857851i	−0.485971	−	0.873975i	$-0.661534\pi$
$389$	−29.3054	−	16.9195i	−1.48584	−	0.857851i	−0.999870	+	0.0161245i	$0.994867\pi$
$390$	−26.6033	−	2.38877i	−1.34711	−	0.120960i
$391$	−49.0675			−2.48145
$392$	19.7163	−	1.80738i	0.995825	−	0.0912865i
$393$		−	33.6908i		−	1.69948i
$394$	4.05762	+	8.59361i	0.204420	+	0.432940i
$395$	7.32079	+	12.8901i	0.368349	+	0.648572i
$396$	−10.8423	−	8.92176i	−0.544849	−	0.448335i
$397$	13.8264	+	23.9479i	0.693925	+	1.20191i	0.970542	+	0.240933i	$0.0774534\pi$
$397$	13.8264	+	23.9479i	0.693925	+	1.20191i	−0.276617	+	0.960980i	$0.589213\pi$
$398$	1.14161	+	0.0943558i	0.0572238	+	0.00472963i
$399$	2.53532	+	14.8228i	0.126925	+	0.742066i
$400$	−3.57207	−	19.6784i	−0.178603	−	0.983921i
$401$	−12.4894	−	21.6322i	−0.623689	−	1.08026i	−0.988793	−	0.149295i	$-0.952300\pi$
$401$	−12.4894	−	21.6322i	−0.623689	−	1.08026i	0.365103	−	0.930967i	$-0.381034\pi$
$402$	17.3373	−	25.0151i	0.864707	−	1.24764i
$403$	12.4771	−	21.6109i	0.621527	−	1.07652i
$404$	7.91388	−	2.96680i	0.393730	−	0.147604i
$405$	−10.2684	+	17.4979i	−0.510243	+	0.869475i
$406$	13.7315	−	9.60817i	0.681481	−	0.476846i
$407$			17.1986i			0.852503i
$408$	−34.7717	+	9.85612i	−1.72146	+	0.487950i
$409$	−15.9607	+	27.6447i	−0.789205	+	1.36694i	0.137249	+	0.990537i	$0.456174\pi$
$409$	−15.9607	+	27.6447i	−0.789205	+	1.36694i	−0.926454	+	0.376407i	$0.877159\pi$
$410$	3.77690	+	8.14816i	0.186528	+	0.402409i
$411$	−7.34794	+	4.24234i	−0.362447	+	0.209259i
$412$	−2.65885	+	15.9749i	−0.130992	+	0.787025i
$413$	2.79754	+	1.03450i	0.137658	+	0.0509046i
$414$	−3.25347	+	39.3637i	−0.159899	+	1.93462i
$415$	−0.00988444		7.00626e-5i	−0.000485208		3.43924e-6i
$416$	15.7378	−	11.5927i	0.771610	−	0.568377i
$417$	44.1251	+	25.4757i	2.16082	+	1.24755i
$418$	3.31280	+	7.01615i	0.162034	+	0.343171i
$419$		−	33.6443i		−	1.64363i	−0.569752	−	0.821817i	$-0.692961\pi$
$419$		−	33.6443i		−	1.64363i	0.569752	−	0.821817i	$-0.307039\pi$
$420$	14.3961	+	25.0860i	0.702459	+	1.22407i
$421$			13.0935i			0.638136i	0.947732	+	0.319068i	$0.103370\pi$
$421$			13.0935i			0.638136i	−0.947732	+	0.319068i	$0.896630\pi$
$422$	−21.0609	+	9.94425i	−1.02523	+	0.484079i
$423$	2.17466	+	1.25554i	0.105736	+	0.0610465i
$424$	12.6907	−	13.0618i	0.616316	−	0.634336i
$425$	−22.4474	−	13.3879i	−1.08886	−	0.649406i
$426$	−30.0611	−	2.48459i	−1.45646	−	0.120379i
$427$	9.02797	−	7.49678i	0.436894	−	0.362795i
$428$	−4.45165	−	0.740931i	−0.215178	−	0.0358143i
$429$	17.2599	−	9.96501i	0.833316	−	0.481115i
$430$	−6.02339	−	12.9947i	−0.290474	−	0.626658i
$431$	1.88463	−	3.26427i	0.0907794	−	0.157235i	−0.817060	−	0.576553i	$-0.804398\pi$
$431$	1.88463	−	3.26427i	0.0907794	−	0.157235i	0.907839	+	0.419318i	$0.137731\pi$
$432$	−0.0463202	−	0.236082i	−0.00222858	−	0.0113585i
$433$		−	40.8966i		−	1.96536i	−0.185303	−	0.982681i	$-0.559327\pi$
$433$		−	40.8966i		−	1.96536i	0.185303	−	0.982681i	$-0.440673\pi$
$434$	−26.9195	+	2.34627i	−1.29218	+	0.112625i
$435$	21.1152	+	12.3913i	1.01240	+	0.594116i
$436$	−25.6047	+	9.59886i	−1.22624	+	0.459702i
$437$	10.9130	−	18.9018i	0.522038	−	0.904196i
$438$	34.2651	+	23.7482i	1.63725	+	1.13473i
$439$	−2.59501	−	4.49469i	−0.123853	−	0.214520i	0.797431	−	0.603410i	$-0.206192\pi$
$439$	−2.59501	−	4.49469i	−0.123853	−	0.214520i	−0.921284	+	0.388890i	$0.872859\pi$
$440$	10.6292	+	10.4747i	0.506726	+	0.499362i
$441$	−15.8168	−	13.5508i	−0.753181	−	0.645277i
$442$	2.10408	−	25.4573i	0.100081	−	1.21088i
$443$	−7.85278	−	13.6014i	−0.373097	−	0.646223i	0.616943	−	0.787008i	$-0.288371\pi$
$443$	−7.85278	−	13.6014i	−0.373097	−	0.646223i	−0.990040	+	0.140785i	$0.955037\pi$
$444$	22.6425	−	27.5168i	1.07457	−	1.30589i
$445$	3.52582	+	6.20811i	0.167140	+	0.294293i
$446$	−15.2582	+	7.20442i	−0.722496	+	0.341139i
$447$			12.8025i			0.605539i
$448$	−20.0554	−	6.76614i	−0.947529	−	0.319670i
$449$	−37.5438			−1.77180			−0.885900	−	0.463877i	$-0.846458\pi$
$449$	−37.5438			−1.77180			−0.885900	+	0.463877i	$0.846458\pi$
$450$	−12.2286	+	17.1204i	−0.576463	+	0.807066i
$451$	−5.80339	−	3.35059i	−0.273271	−	0.157773i
$452$	−10.8015	−	8.88811i	−0.508058	−	0.418062i
$453$	−16.5044	−	28.5865i	−0.775445	−	1.34311i
$454$	−15.1172	−	1.24946i	−0.709486	−	0.0586400i
$455$	−20.1736	+	3.30354i	−0.945753	+	0.154872i
$456$	3.93671	−	15.5869i	0.184353	−	0.729922i
$457$	−16.3639	+	9.44771i	−0.765472	+	0.441945i	−0.831257	−	0.555889i	$-0.812378\pi$
$457$	−16.3639	+	9.44771i	−0.765472	+	0.441945i	0.0657852	+	0.997834i	$0.479045\pi$
$458$	−5.12932	−	3.55500i	−0.239677	−	0.166114i
$459$	−0.272279	−	0.157201i	−0.0127089	−	0.00733749i
$460$	7.18546	−	41.3592i	0.335024	−	1.92838i
$461$			10.1965i			0.474897i	0.971400	+	0.237448i	$0.0763111\pi$
$461$			10.1965i			0.474897i	−0.971400	+	0.237448i	$0.923689\pi$
$462$	−19.5562	−	9.12702i	−0.909838	−	0.424628i
$463$		−	7.88473i		−	0.366434i	−0.983072	−	0.183217i	$-0.941349\pi$
$463$		−	7.88473i		−	0.366434i	0.983072	−	0.183217i	$-0.0586512\pi$
$464$	−17.5811	+	3.44948i	−0.816183	+	0.160138i
$465$	−19.4944	−	34.3249i	−0.904031	−	1.59178i
$466$	0.605259	+	0.419490i	0.0280381	+	0.0194325i
$467$	4.30815	+	7.46194i	0.199357	+	0.345297i	0.948320	−	0.317315i	$-0.102781\pi$
$467$	4.30815	+	7.46194i	0.199357	+	0.345297i	−0.748963	+	0.662612i	$0.769448\pi$
$468$	−20.2832	−	3.37594i	−0.937592	−	0.156053i
$469$	8.07904	−	21.8476i	0.373055	−	1.00883i
$470$	−2.18265	−	1.53576i	−0.100678	−	0.0708391i
$471$	17.1047	+	29.6262i	0.788143	+	1.36510i
$472$	−2.28695	−	2.22198i	−0.105265	−	0.102275i
$473$	9.25522	+	5.34350i	0.425556	+	0.245695i
$474$	9.78521	+	20.7240i	0.449449	+	0.951885i
$475$	10.1498	−	5.66966i	0.465703	−	0.260142i
$476$	−23.8925	+	13.9372i	−1.09511	+	0.638813i
$477$	−19.1579			−0.877182
$478$	−7.43159	−	15.7393i	−0.339913	−	0.719899i
$479$	−7.28280	+	12.6142i	−0.332760	+	0.576357i	−0.983052	−	0.183327i	$-0.941313\pi$
$479$	−7.28280	+	12.6142i	−0.332760	+	0.576357i	0.650292	+	0.759684i	$0.274646\pi$
$480$	−3.21578	−	30.7526i	−0.146780	−	1.40366i
$481$	12.5930	+	21.8118i	0.574193	+	0.994531i
$482$	−23.4416	−	1.93748i	−1.06773	−	0.0882498i
$483$	10.2350	+	59.8391i	0.465709	+	2.72278i
$484$	10.7176	+	1.78384i	0.487166	+	0.0810838i
$485$	−0.0375864	+	5.30269i	−0.00170671	+	0.240783i
$486$	−17.7218	+	25.5699i	−0.803879	+	1.15987i
$487$	21.7499	+	12.5573i	0.985581	+	0.569026i	0.903950	−	0.427637i	$-0.140654\pi$
$487$	21.7499	+	12.5573i	0.985581	+	0.569026i	0.0816306	+	0.996663i	$0.473987\pi$
$488$	−12.0696	+	3.42114i	−0.546363	+	0.154868i
$489$	44.2804			2.00243
$490$	15.4549	+	15.8476i	0.698180	+	0.715922i
$491$			0.781768i			0.0352807i	0.999844	+	0.0176403i	$0.00561539\pi$
$491$			0.781768i			0.0352807i	−0.999844	+	0.0176403i	$0.994385\pi$
$492$	4.87394	+	13.0011i	0.219734	+	0.586136i
$493$	−11.7068	+	20.2768i	−0.527248	+	0.913219i
$494$	9.33870	+	6.47242i	0.420168	+	0.291208i
$495$	0.111271	−	15.6981i	0.00500126	−	0.705577i
$496$	27.3300	+	9.35679i	1.22715	+	0.420132i
$497$	−22.7547	+	3.89202i	−1.02069	+	0.174581i
$498$	−0.0152299	−	0.00125878i	−0.000682469	−	5.64071e-5i
$499$	11.3635	−	6.56069i	0.508698	−	0.293697i	−0.223600	−	0.974681i	$-0.571781\pi$
$499$	11.3635	−	6.56069i	0.508698	−	0.293697i	0.732298	+	0.680984i	$0.238448\pi$
$500$	14.5719	−	16.9605i	0.651675	−	0.758498i
$501$	−24.3843	−	14.0783i	−1.08941	−	0.628972i
$502$	−8.05401	+	3.80284i	−0.359468	+	0.169729i
$503$			10.9137i			0.486620i	0.969949	+	0.243310i	$0.0782332\pi$
$503$			10.9137i			0.486620i	−0.969949	+	0.243310i	$0.921767\pi$
$504$	9.59675	+	20.0915i	0.427473	+	0.894947i
$505$	8.14964	+	4.78253i	0.362654	+	0.212820i
$506$	13.3737	+	28.3240i	0.594533	+	1.25916i
$507$	−1.29599	+	2.24473i	−0.0575571	+	0.0996918i
$508$	−8.89002	−	7.31526i	−0.394431	−	0.324562i
$509$	32.4201	−	18.7178i	1.43700	−	0.829650i	0.439356	−	0.898313i	$-0.355207\pi$
$509$	32.4201	−	18.7178i	1.43700	−	0.829650i	0.997640	+	0.0686626i	$0.0218732\pi$
$510$	−33.0469	−	23.2524i	−1.46334	−	1.02963i
$511$	29.9263	+	11.0665i	1.32386	+	0.489552i
$512$	16.6764	+	15.2937i	0.737000	+	0.675893i
$513$	0.121114	−	0.0699251i	0.00534731	−	0.00308727i
$514$	27.6210	+	19.1434i	1.21831	+	0.844381i
$515$	−15.7442	+	8.94170i	−0.693770	+	0.394018i
$516$	−7.77294	−	20.7341i	−0.342184	−	0.912769i
$517$	1.99134			0.0875790
$518$	11.5340	−	24.7137i	0.506777	−	1.08586i
$519$	−32.0948			−1.40881
$520$	21.1499	+	5.50151i	0.927486	+	0.241257i
$521$	14.3563	−	24.8659i	0.628961	−	1.08939i	−0.358799	−	0.933415i	$-0.616814\pi$
$521$	14.3563	−	24.8659i	0.628961	−	1.08939i	0.987760	−	0.155978i	$-0.0498530\pi$
$522$	15.4905	+	10.7361i	0.678001	+	0.469905i
$523$	14.2597	+	24.6986i	0.623535	+	1.07999i	0.988822	+	0.149100i	$0.0476375\pi$
$523$	14.2597	+	24.6986i	0.623535	+	1.07999i	−0.365287	+	0.930895i	$0.619029\pi$
$524$	−4.52566	+	27.1909i	−0.197704	+	1.18784i
$525$	−11.6445	+	30.1678i	−0.508209	+	1.31663i
$526$	−3.04210	+	36.8064i	−0.132642	+	1.60484i
$527$	32.6932	−	18.8754i	1.42414	−	0.822226i
$528$	15.1667	+	17.3855i	0.660045	+	0.756607i
$529$	32.5554	−	56.3876i	1.41545	−	2.45164i
$530$	20.2797	+	1.82095i	0.880892	+	0.0790972i
$531$			3.35431i			0.145565i
$532$	−0.0550577	−	12.3036i	−0.00238705	−	0.533430i
$533$	−9.81337			−0.425064
$534$	4.71273	+	9.98105i	0.203940	+	0.431922i
$535$	−2.49174	−	4.38735i	−0.107727	−	0.189682i
$536$	−17.3527	+	17.8601i	−0.749524	+	0.771439i
$537$	23.1712	−	13.3779i	0.999911	−	0.577299i
$538$	−1.88443	+	22.7997i	−0.0812435	+	0.982965i
$539$	−16.2356	−	3.03485i	−0.699317	−	0.130720i
$540$	0.172378	−	0.206485i	0.00741796	−	0.00888570i
$541$	−19.0706	+	11.0104i	−0.819907	+	0.473374i	−0.850384	−	0.526162i	$-0.823631\pi$
$541$	−19.0706	+	11.0104i	−0.819907	+	0.473374i	0.0304773	+	0.999535i	$0.490297\pi$
$542$	−5.45758	+	7.87444i	−0.234423	+	0.338236i
$543$	−11.3951	−	6.57899i	−0.489012	−	0.282331i
$544$	29.3873	−	3.28375i	1.25997	−	0.140790i
$545$	−26.3675	−	15.4735i	−1.12946	−	0.662812i
$546$	−31.4847	+	2.74416i	−1.34742	+	0.117439i
$547$	6.43028			0.274939			0.137469	−	0.990506i	$-0.456103\pi$
$547$	6.43028			0.274939			0.137469	+	0.990506i	$0.456103\pi$
$548$	6.50020	−	2.43683i	0.277675	−	0.104096i
$549$	11.4289	+	6.59845i	0.487772	+	0.281615i
$550$	−1.60988	+	16.6067i	−0.0686457	+	0.708111i
$551$	−5.20735	−	9.01940i	−0.221841	−	0.384239i
$552$	15.8924	−	62.9238i	0.676425	−	2.67822i
$553$	11.2054	+	13.4940i	0.476500	+	0.573824i
$554$	−22.7491	−	1.88025i	−0.966518	−	0.0798841i
$555$	39.8402	+	0.282395i	1.69112	+	0.0119870i
$556$	−32.1901	−	26.4880i	−1.36516	−	1.12334i
$557$	−18.0317	+	31.2319i	−0.764029	+	1.32334i	0.176730	+	0.984259i	$0.443448\pi$
$557$	−18.0317	+	31.2319i	−0.764029	+	1.32334i	−0.940759	+	0.339077i	$0.889885\pi$
$558$	−12.9748	−	27.4792i	−0.549266	−	1.16329i
$559$	15.6503			0.661938
$560$	−8.24895	−	22.1801i	−0.348582	−	0.937278i
$561$	30.1503			1.27295
$562$	5.51428	+	11.6787i	0.232606	+	0.492634i
$563$	5.75434	−	9.96680i	0.242516	−	0.420051i	−0.718914	−	0.695099i	$-0.755361\pi$
$563$	5.75434	−	9.96680i	0.242516	−	0.420051i	0.961430	+	0.275048i	$0.0886939\pi$
$564$	−3.18603	−	2.62167i	−0.134156	−	0.110392i
$565$	0.110851	−	15.6389i	0.00466355	−	0.657934i
$566$	−12.1638	−	1.00535i	−0.511281	−	0.0422581i
$567$	−8.32596	+	22.5153i	−0.349658	+	0.945555i
$568$	23.9277	+	6.04332i	1.00399	+	0.253572i
$569$	−9.54005	−	16.5238i	−0.399940	−	0.692716i	0.593778	−	0.804629i	$-0.297636\pi$
$569$	−9.54005	−	16.5238i	−0.399940	−	0.692716i	−0.993718	+	0.111913i	$0.964302\pi$
$570$	16.3072	−	7.55883i	0.683032	−	0.316605i
$571$	34.0475	+	19.6574i	1.42484	+	0.822635i	0.996708	−	0.0810791i	$-0.0258367\pi$
$571$	34.0475	+	19.6574i	1.42484	+	0.822635i	0.428137	+	0.903714i	$0.359170\pi$
$572$	−15.2686	+	5.72399i	−0.638412	+	0.239332i
$573$	34.7555			1.45193
$574$	6.09221	+	8.70664i	0.254284	+	0.363408i
$575$	40.9743	−	22.8883i	1.70875	−	0.954508i
$576$	−0.685790	−	23.7933i	−0.0285746	−	0.991387i
$577$	1.70285	+	0.983139i	0.0708905	+	0.0409286i	0.535026	−	0.844835i	$-0.320302\pi$
$577$	1.70285	+	0.983139i	0.0708905	+	0.0409286i	−0.464136	+	0.885764i	$0.653635\pi$
$578$	8.31760	−	12.0010i	0.345967	−	0.499177i
$579$	40.8154	−	23.5648i	1.69623	−	0.979319i
$580$	−15.3770	−	12.8370i	−0.638497	−	0.533029i
$581$	−0.0115283	+	0.00197183i	−0.000478275	+	8.18051e-5i
$582$	−0.675294	+	8.17038i	−0.0279918	+	0.338673i
$583$	−13.1572	+	7.59631i	−0.544916	+	0.314607i
$584$	−24.4643	−	23.7694i	−1.01234	−	0.983583i
$585$	−11.3532	−	19.9903i	−0.469399	−	0.826496i
$586$	−15.5229	−	32.8759i	−0.641247	−	1.35809i
$587$	22.8007			0.941084			0.470542	−	0.882378i	$-0.344058\pi$
$587$	22.8007			0.941084			0.470542	+	0.882378i	$0.344058\pi$
$588$	21.9806	+	26.2303i	0.906465	+	1.08172i
$589$			16.7921i			0.691907i
$590$	0.318826	−	3.55071i	0.0131258	−	0.146180i
$591$	−8.21328	+	14.2258i	−0.337849	+	0.585172i
$592$	−21.9705	+	19.1665i	−0.902982	+	0.787739i
$593$	−25.7327	+	14.8568i	−1.05672	+	0.610096i	−0.924522	−	0.381128i	$-0.875536\pi$
$593$	−25.7327	+	14.8568i	−1.05672	+	0.610096i	−0.132195	+	0.991224i	$0.542202\pi$
$594$	−0.0165318	+	0.200018i	−0.000678308	+	0.00820685i
$595$	−28.9288	−	10.9313i	−1.18597	−	0.448141i
$596$	1.71975	−	10.3326i	0.0704439	−	0.423239i
$597$	0.990000	+	1.71473i	0.0405180	+	0.0701792i
$598$	37.7001	+	26.1290i	1.54167	+	1.06849i
$599$	0.567182	−	0.982388i	0.0231744	−	0.0401393i	−0.854206	−	0.519935i	$-0.825956\pi$
$599$	0.567182	−	0.982388i	0.0231744	−	0.0401393i	0.877380	+	0.479796i	$0.159289\pi$
$600$	24.4390	−	24.4503i	0.997717	−	0.998178i
$601$	33.7109			1.37510			0.687548	−	0.726139i	$-0.258687\pi$
$601$	33.7109			1.37510			0.687548	+	0.726139i	$0.258687\pi$
$602$	−9.71582	−	13.8853i	−0.395987	−	0.565923i
$603$	26.1957			1.06677
$604$	9.48028	+	25.2884i	0.385747	+	1.02897i
$605$	5.99905	+	10.5629i	0.243896	+	0.429441i
$606$	12.0069	+	8.32166i	0.487746	+	0.338044i
$607$	10.3329	−	5.96570i	0.419399	−	0.242140i	−0.275421	−	0.961324i	$-0.588817\pi$
$607$	10.3329	−	5.96570i	0.419399	−	0.242140i	0.694820	+	0.719183i	$0.255484\pi$
$608$	−5.27098	+	12.0509i	−0.213767	+	0.488730i
$609$	27.1700	+	10.0472i	1.10098	+	0.407134i
$610$	−11.4708	−	8.07110i	−0.464441	−	0.326789i
$611$	2.52547	−	1.45808i	0.102170	−	0.0589877i
$612$	−24.0201	−	19.7652i	−0.970953	−	0.798961i
$613$	−2.75099	+	4.76486i	−0.111112	+	0.192451i	−0.916219	−	0.400678i	$-0.868774\pi$
$613$	−2.75099	+	4.76486i	−0.111112	+	0.192451i	0.805107	+	0.593129i	$0.202108\pi$
$614$	12.7367	+	26.9749i	0.514010	+	1.08862i
$615$	−7.85687	+	13.3884i	−0.316819	+	0.539874i
$616$	14.5573	+	9.99315i	0.586530	+	0.402635i
$617$		−	40.3808i		−	1.62567i	−0.582493	−	0.812836i	$-0.697923\pi$
$617$		−	40.3808i		−	1.62567i	0.582493	−	0.812836i	$-0.302077\pi$
$618$	−25.3126	+	11.9518i	−1.01822	+	0.480771i
$619$	−12.8352	−	7.41039i	−0.515889	−	0.297849i	0.219362	−	0.975644i	$-0.429602\pi$
$619$	−12.8352	−	7.41039i	−0.515889	−	0.297849i	−0.735251	+	0.677795i	$0.762936\pi$
$620$	11.1226	+	30.3213i	0.446693	+	1.21773i
$621$	0.488934	−	0.282286i	0.0196202	−	0.0113277i
$622$	−24.5498	−	2.02907i	−0.984356	−	0.0813584i
$623$	5.39670	+	6.49896i	0.216214	+	0.260375i
$624$	31.9647	+	10.9436i	1.27961	+	0.438093i
$625$	24.9900	+	0.708711i	0.999598	+	0.0283484i
$626$	−2.26437	−	1.56938i	−0.0905024	−	0.0627249i
$627$	−6.70564	+	11.6145i	−0.267797	+	0.463839i
$628$	−9.82509	−	26.2082i	−0.392064	−	1.04582i
$629$			38.1016i			1.51921i
$630$	−10.6877	+	22.4829i	−0.425806	+	0.895742i
$631$	−27.2082			−1.08314			−0.541570	−	0.840655i	$-0.682170\pi$
$631$	−27.2082			−1.08314			−0.541570	+	0.840655i	$0.682170\pi$
$632$	−5.11354	−	18.0402i	−0.203406	−	0.717602i
$633$	−34.8641	−	20.1288i	−1.38572	−	0.800047i
$634$	−6.06904	+	8.75670i	−0.241032	+	0.347773i
$635$	0.0912349	−	12.8714i	0.00362055	−	0.510787i
$636$	31.0516	+	5.16822i	1.23128	+	0.204933i
$637$	−22.8126	+	8.03903i	−0.903870	+	0.318518i
$638$	14.8955	+	1.23113i	0.589717	+	0.0487409i
$639$	−12.9807	−	22.4833i	−0.513510	−	0.889425i
$640$	−1.53560	+	25.2516i	−0.0606999	+	0.998156i
$641$	−12.5262	+	21.6960i	−0.494755	+	0.856940i	−0.999982	−	0.00604629i	$-0.998075\pi$
$641$	−12.5262	+	21.6960i	−0.494755	+	0.856940i	0.505227	+	0.862986i	$0.331409\pi$
$642$	−3.33055	−	7.05374i	−0.131446	−	0.278389i
$643$	−21.0363			−0.829590			−0.414795	−	0.909915i	$-0.636147\pi$
$643$	−21.0363			−0.829590			−0.414795	+	0.909915i	$0.636147\pi$
$644$	−0.222267	−	49.6694i	−0.00875853	−	1.95725i
$645$	12.5301	−	21.3518i	0.493372	−	0.840727i
$646$	7.33915	+	15.5435i	0.288755	+	0.611552i
$647$	6.34048	+	3.66068i	0.249270	+	0.143916i	0.619430	−	0.785052i	$-0.287364\pi$
$647$	6.34048	+	3.66068i	0.249270	+	0.143916i	−0.370160	+	0.928968i	$0.620697\pi$
$648$	17.8831	−	18.4060i	0.702515	−	0.723055i
$649$	1.33002	+	2.30366i	0.0522077	+	0.0904264i
$650$	10.1179	+	22.2398i	0.396857	+	0.872318i
$651$	−29.8386	−	35.9330i	−1.16947	−	1.40832i
$652$	−35.7375	−	5.94815i	−1.39959	−	0.232947i
$653$	13.0567	+	22.6149i	0.510950	+	0.884991i	0.999919	+	0.0126901i	$0.00403949\pi$
$653$	13.0567	+	22.6149i	0.510950	+	0.884991i	−0.488970	+	0.872301i	$0.662627\pi$
$654$	−38.8473	−	26.9241i	−1.51905	−	1.05282i
$655$	−26.7982	+	15.2197i	−1.04709	+	0.594684i
$656$	−2.18720	−	11.1476i	−0.0853957	−	0.435239i
$657$			35.8823i			1.39990i
$658$	−2.86147	−	1.33547i	−0.111552	−	0.0520620i
$659$			6.78166i			0.264176i	0.991238	+	0.132088i	$0.0421682\pi$
$659$			6.78166i			0.264176i	−0.991238	+	0.132088i	$0.957832\pi$
$660$	−4.41522	+	25.4138i	−0.171862	+	0.989231i
$661$	−19.2177	−	11.0953i	−0.747482	−	0.431559i	0.0773015	−	0.997008i	$-0.475370\pi$
$661$	−19.2177	−	11.0953i	−0.747482	−	0.431559i	−0.824783	+	0.565449i	$0.808703\pi$
$662$	−36.7393	−	25.4631i	−1.42792	−	0.989652i
$663$	38.2375	−	22.0764i	1.48502	−	0.857377i
$664$	0.0121226	+	0.00306175i	0.000470447	+	0.000118819i
$665$	10.6450	−	8.71278i	0.412794	−	0.337867i
$666$	30.5665	+	2.52637i	1.18443	+	0.0978947i
$667$	−21.0220	−	36.4111i	−0.813974	−	1.40984i
$668$	17.7888	+	14.6378i	0.688271	+	0.566352i
$669$	−25.2583	−	14.5829i	−0.976544	−	0.563808i
$670$	−27.7295	−	2.48989i	−1.07128	−	0.0961930i
$671$	10.4654			0.404012
$672$	−10.1345	−	35.1537i	−0.390948	−	1.35608i
$673$		−	2.67172i		−	0.102987i	−0.998673	−	0.0514936i	$-0.983602\pi$
$673$		−	2.67172i		−	0.102987i	0.998673	−	0.0514936i	$-0.0163982\pi$
$674$	2.49879	−	1.17985i	0.0962500	−	0.0454461i
$675$	0.300698	+	0.00426302i	0.0115739	+	0.000164084i
$676$	1.34749	−	1.63757i	0.0518267	−	0.0629834i
$677$	−0.0718818	−	0.124503i	−0.00276264	−	0.00478504i	0.864641	−	0.502391i	$-0.167546\pi$
$677$	−0.0718818	−	0.124503i	−0.00276264	−	0.00478504i	−0.867403	+	0.497606i	$0.834213\pi$
$678$	1.99160	−	24.0964i	0.0764870	−	0.925417i
$679$	1.05782	+	6.18457i	0.0405955	+	0.237342i
$680$	23.5478	+	23.2056i	0.903016	+	0.889893i
$681$	−13.1096	−	22.7064i	−0.502359	−	0.870112i
$682$	−19.8065	−	13.7274i	−0.758431	−	0.525649i
$683$	12.9878	−	22.4955i	0.496964	−	0.860767i	−0.503030	−	0.864269i	$-0.667781\pi$
$683$	12.9878	−	22.4955i	0.496964	−	0.860767i	0.999994	+	0.00350195i	$0.00111471\pi$
$684$	12.9562	−	4.85710i	0.495393	−	0.185716i
$685$	6.69384	+	3.92821i	0.255759	+	0.150089i
$686$	21.2946	+	15.2492i	0.813033	+	0.582217i
$687$		−	10.7873i		−	0.411559i
$688$	3.48813	+	17.7781i	0.132984	+	0.677783i
$689$	−11.1242	+	19.2677i	−0.423800	+	0.734042i
$690$	65.8317	−	30.5148i	2.50617	−	1.16168i
$691$	−26.5744	+	15.3428i	−1.01094	+	0.583666i	−0.911467	−	0.411374i	$-0.865049\pi$
$691$	−26.5744	+	15.3428i	−1.01094	+	0.583666i	−0.0994727	+	0.995040i	$0.531716\pi$
$692$	25.9029	+	4.31127i	0.984679	+	0.163890i
$693$	−3.13158	−	18.3088i	−0.118959	−	0.695495i
$694$	7.15000	+	0.590958i	0.271410	+	0.0224324i
$695$	0.330355	−	46.6065i	0.0125311	−	1.76788i
$696$	−22.2111	−	21.5801i	−0.841909	−	0.817993i
$697$	−12.8568	−	7.42287i	−0.486986	−	0.281161i
$698$	−0.328281	+	0.155004i	−0.0124256	+	0.00586698i
$699$			1.27289i			0.0481453i
$700$	13.4504	−	22.7835i	0.508378	−	0.861134i
$701$		−	14.8235i		−	0.559876i	−0.960018	−	0.279938i	$-0.909686\pi$
$701$		−	14.8235i		−	0.559876i	0.960018	−	0.279938i	$-0.0903140\pi$
$702$	0.125490	+	0.265774i	0.00473631	+	0.0100310i
$703$	−14.6775	−	8.47408i	−0.553574	−	0.319606i
$704$	−9.90525	−	16.0687i	−0.373318	−	0.605612i
$705$	0.0326970	−	4.61290i	0.00123144	−	0.173732i
$706$	3.21883	−	38.9446i	0.121142	−	1.46570i
$707$	10.4865	+	3.87782i	0.394387	+	0.145841i
$708$	0.904889	−	5.43673i	0.0340078	−	0.204325i
$709$	7.03224	−	4.06007i	0.264101	−	0.152479i	−0.362103	−	0.932138i	$-0.617941\pi$
$709$	7.03224	−	4.06007i	0.264101	−	0.152479i	0.626204	+	0.779659i	$0.284608\pi$
$710$	11.6037	+	25.0335i	0.435480	+	0.939490i
$711$	−9.86264	+	17.0826i	−0.369878	+	0.640647i
$712$	−2.46277	−	8.68850i	−0.0922963	−	0.325615i
$713$			67.7894i			2.53873i
$714$	−43.3247	−	20.2199i	−1.62139	−	0.756712i
$715$	−15.7235	−	9.22716i	−0.588024	−	0.345076i
$716$	−20.4979	+	7.68438i	−0.766043	+	0.287179i
$717$	15.0427	−	26.0548i	0.561782	−	0.973034i
$718$	−17.8528	+	25.7589i	−0.666261	+	0.961313i
$719$	18.5331	+	32.1003i	0.691169	+	1.19714i	0.971455	+	0.237224i	$0.0762374\pi$
$719$	18.5331	+	32.1003i	0.691169	+	1.19714i	−0.280286	+	0.959917i	$0.590429\pi$
$720$	20.1777	−	17.3522i	0.751978	−	0.646678i
$721$	−16.4818	+	13.6864i	−0.613813	+	0.509707i
$722$	19.1588	+	1.58350i	0.713016	+	0.0589318i
$723$	−20.3284	−	35.2098i	−0.756022	−	1.30947i
$724$	8.31297	+	6.84043i	0.308949	+	0.254222i
$725$	0.317469	−	22.3931i	0.0117905	−	0.831661i
$726$	8.01852	+	16.9824i	0.297595	+	0.630275i
$727$			0.939460i			0.0348426i	0.999848	+	0.0174213i	$0.00554566\pi$
$727$			0.939460i			0.0348426i	−0.999848	+	0.0174213i	$0.994454\pi$
$728$	25.7791	+	2.01457i	0.955437	+	0.0746651i
$729$	−26.5553			−0.983530
$730$	3.41060	−	37.9832i	0.126232	−	1.40582i
$731$	20.5039	+	11.8380i	0.758366	+	0.437843i
$732$	−16.7441	−	13.7781i	−0.618878	−	0.509252i
$733$	−10.8763	−	18.8382i	−0.401724	−	0.695806i	0.592210	−	0.805784i	$-0.298256\pi$
$733$	−10.8763	−	18.8382i	−0.401724	−	0.695806i	−0.993934	+	0.109977i	$0.964922\pi$
$734$	3.67746	−	44.4936i	0.135738	−	1.64229i
$735$	−7.29676	+	37.5597i	−0.269145	+	1.38541i
$736$	−21.2788	+	48.6493i	−0.784348	+	1.79324i
$737$	17.9906	−	10.3869i	0.662692	−	0.382605i
$738$	−6.80737	+	9.82199i	−0.250583	+	0.361553i
$739$	6.77611	+	3.91219i	0.249263	+	0.143912i	0.619427	−	0.785054i	$-0.287365\pi$
$739$	6.77611	+	3.91219i	0.249263	+	0.143912i	−0.370164	+	0.928967i	$0.620698\pi$
$740$	−32.1161	−	5.57962i	−1.18061	−	0.205111i
$741$			19.6398i			0.721487i
$742$	24.0008	−	2.09187i	0.881096	−	0.0767950i
$743$			38.7632i			1.42208i	0.703150	+	0.711042i	$0.251776\pi$
$743$			38.7632i			1.42208i	−0.703150	+	0.711042i	$0.748224\pi$
$744$	13.6168	+	48.0390i	0.499214	+	1.76120i
$745$	10.1834	−	5.78351i	0.373089	−	0.211892i
$746$	6.44992	−	9.30625i	0.236149	−	0.340726i
$747$	−0.00657647	−	0.0113908i	−0.000240620	−	0.000416767i
$748$	−24.3335	−	4.05006i	−0.889720	−	0.148085i
$749$	−3.81392	−	4.59290i	−0.139358	−	0.167821i
$750$	38.4426	+	4.00194i	1.40373	+	0.146130i
$751$	18.8864	+	32.7123i	0.689176	+	1.19369i	0.972105	+	0.234547i	$0.0753607\pi$
$751$	18.8864	+	32.7123i	0.689176	+	1.19369i	−0.282929	+	0.959141i	$0.591306\pi$
$752$	2.21919	+	2.54385i	0.0809257	+	0.0927648i
$753$	−13.3326	−	7.69756i	−0.485866	−	0.280515i
$754$	19.7923	−	9.34529i	0.720794	−	0.340335i
$755$	−15.2824	+	26.0418i	−0.556182	+	0.947757i
$756$	0.157896	−	0.276332i	0.00574261	−	0.0100501i
$757$	22.8980			0.832242			0.416121	−	0.909309i	$-0.363389\pi$
$757$	22.8980			0.832242			0.416121	+	0.909309i	$0.363389\pi$
$758$	13.9880	−	6.60469i	0.508068	−	0.239893i
$759$	−27.0705	+	46.8875i	−0.982597	+	1.70191i
$760$	−14.1765	+	3.91000i	−0.514234	+	0.141831i
$761$	−9.23194	−	15.9902i	−0.334657	−	0.579644i	0.648761	−	0.760992i	$-0.275287\pi$
$761$	−9.23194	−	15.9902i	−0.334657	−	0.579644i	−0.983419	+	0.181348i	$0.941954\pi$
$762$	1.63917	−	19.8323i	0.0593807	−	0.718447i
$763$	−33.9284	−	12.5464i	−1.22829	−	0.454210i
$764$	−28.0503	−	4.66868i	−1.01482	−	0.168907i
$765$	0.246509	−	34.7775i	0.00891255	−	1.25738i
$766$	22.0070	+	15.2525i	0.795146	+	0.551095i
$767$	3.37353	+	1.94771i	0.121811	+	0.0703277i
$768$	−5.30715	+	38.7496i	−0.191505	+	1.39826i
$769$	−14.0648			−0.507190			−0.253595	−	0.967311i	$-0.581613\pi$
$769$	−14.0648			−0.507190			−0.253595	+	0.967311i	$0.581613\pi$
$770$	1.57469	+	19.6785i	0.0567479	+	0.709163i
$771$			58.0886i			2.09201i
$772$	−36.1065	+	13.5358i	−1.29950	+	0.487165i
$773$	−10.3933	+	18.0018i	−0.373822	+	0.647480i	−0.990150	−	0.140010i	$-0.955286\pi$
$773$	−10.3933	+	18.0018i	−0.373822	+	0.647480i	0.616328	+	0.787490i	$0.288620\pi$
$774$	10.8564	−	15.6641i	0.390224	−	0.563034i
$775$	−18.4960	+	31.0123i	−0.664398	+	1.11400i
$776$	1.64253	−	6.50339i	0.0589635	−	0.233458i
$777$	46.4660	−	7.94764i	1.66696	−	0.285120i
$778$	−3.94188	+	47.6928i	−0.141323	+	1.70987i
$779$	5.71889	−	3.30180i	0.204900	−	0.118299i
$780$	13.0088	+	35.4634i	0.465790	+	1.26979i
$781$	−17.8297	−	10.2940i	−0.637996	−	0.368347i
$782$	29.6280	+	62.7489i	1.05949	+	2.24389i
$783$		−	0.269397i		−	0.00962748i
$784$	−14.2165	−	24.1224i	−0.507731	−	0.861516i
$785$	15.8382	−	26.9890i	0.565290	−	0.963277i
$786$	−43.0847	+	20.3432i	−1.53678	+	0.725618i
$787$	10.3257	−	17.8846i	0.368071	−	0.637518i	−0.621193	−	0.783658i	$-0.713352\pi$
$787$	10.3257	−	17.8846i	0.368071	−	0.637518i	0.989264	+	0.146140i	$0.0466850\pi$
$788$	8.53967	−	10.3780i	0.304213	−	0.369701i
$789$	−55.2842	+	31.9183i	−1.96817	+	1.13632i
$790$	12.0638	−	17.1453i	0.429211	−	0.610004i
$791$	−3.11977	−	18.2398i	−0.110926	−	0.648532i
$792$	−4.86256	+	19.2526i	−0.172783	+	0.684113i
$793$	13.2725	−	7.66290i	0.471321	−	0.272118i
$794$	22.2767	−	32.1418i	0.790569	−	1.14067i
$795$	17.3807	+	30.6031i	0.616429	+	1.08538i
$796$	−0.568664	−	1.51690i	−0.0201558	−	0.0537650i
$797$	12.8680			0.455808			0.227904	−	0.973684i	$-0.426813\pi$
$797$	12.8680			0.455808			0.227904	+	0.973684i	$0.426813\pi$
$798$	17.4249	−	12.1925i	0.616834	−	0.431611i
$799$	4.41160			0.156071
$800$	−23.0084	+	16.4503i	−0.813471	+	0.581606i
$801$	−4.75002	+	8.22728i	−0.167834	+	0.290697i
$802$	−20.1225	+	29.0337i	−0.710552	+	1.02522i
$803$	14.2277	+	24.6431i	0.502084	+	0.869635i
$804$	−42.4586	−	7.06681i	−1.49740	−	0.249227i
$805$	42.9734	−	35.1733i	1.51462	−	1.23970i
$806$	−35.1706	−	2.90690i	−1.23883	−	0.102391i
$807$	−34.2457	+	19.7718i	−1.20551	+	0.696000i
$808$	−8.57259	−	8.32907i	−0.301583	−	0.293016i
$809$	4.90348	−	8.49307i	0.172397	−	0.298601i	−0.766860	−	0.641814i	$-0.778182\pi$
$809$	4.90348	−	8.49307i	0.172397	−	0.298601i	0.939257	+	0.343213i	$0.111515\pi$
$810$	28.5770	+	2.56599i	1.00409	+	0.0901599i
$811$			5.57003i			0.195590i	0.995207	+	0.0977952i	$0.0311790\pi$
$811$			5.57003i			0.195590i	−0.995207	+	0.0977952i	$0.968821\pi$
$812$	−20.5785	−	11.7586i	−0.722165	−	0.412645i
$813$	−16.5604			−0.580798
$814$	21.9940	−	10.3849i	0.770891	−	0.363990i
$815$	−20.0036	−	35.2214i	−0.700694	−	1.23375i
$816$	33.6002	+	38.5157i	1.17624	+	1.34832i
$817$	−9.12045	+	5.26570i	−0.319084	+	0.184223i
$818$	44.9902	+	3.71851i	1.57305	+	0.130015i
$819$	−17.3775	−	20.9268i	−0.607220	−	0.731242i
$820$	8.13952	−	9.75004i	0.284245	−	0.340486i
$821$	38.9299	−	22.4762i	1.35866	−	0.784425i	0.369221	−	0.929342i	$-0.379625\pi$
$821$	38.9299	−	22.4762i	1.35866	−	0.784425i	0.989444	+	0.144916i	$0.0462913\pi$
$822$	9.86206	+	6.83514i	0.343979	+	0.238403i
$823$	11.9462	+	6.89712i	0.416417	+	0.240419i	0.693543	−	0.720415i	$-0.256049\pi$
$823$	11.9462	+	6.89712i	0.416417	+	0.240419i	−0.277126	+	0.960834i	$0.589382\pi$
$824$	22.0346	−	6.24574i	0.767611	−	0.217581i
$825$	−25.1773	+	14.0641i	−0.876561	+	0.489648i
$826$	−0.366260	−	4.20222i	−0.0127438	−	0.146214i
$827$	−42.2773			−1.47012			−0.735062	−	0.677999i	$-0.762847\pi$
$827$	−42.2773			−1.47012			−0.735062	+	0.677999i	$0.762847\pi$
$828$	52.3039	−	19.6080i	1.81769	−	0.681425i
$829$	38.3972	+	22.1686i	1.33359	+	0.769948i	0.985848	−	0.167643i	$-0.0536156\pi$
$829$	38.3972	+	22.1686i	1.33359	+	0.769948i	0.347741	+	0.937591i	$0.386949\pi$
$830$	0.00587883	+	0.0126828i	0.000204057	+	0.000440226i
$831$	−19.7279	−	34.1698i	−0.684354	−	1.18534i
$832$	−24.3278	−	13.1261i	−0.843416	−	0.455064i
$833$	−35.9683	−	6.72339i	−1.24623	−	0.232952i
$834$	5.93530	−	71.8112i	0.205523	−	2.48662i
$835$	−0.182560	+	25.7556i	−0.00631775	+	0.891308i
$836$	6.97211	−	8.47300i	0.241135	−	0.293045i
$837$	−0.217181	+	0.376168i	−0.00750687	+	0.0130023i
$838$	−43.0253	+	20.3152i	−1.48629	+	0.701776i
$839$	23.4170			0.808445			0.404223	−	0.914661i	$-0.367542\pi$
$839$	23.4170			0.808445			0.404223	+	0.914661i	$0.367542\pi$
$840$	23.3880	−	33.5576i	0.806962	−	1.15785i
$841$	8.93785			0.308202
$842$	16.7443	−	7.90610i	0.577046	−	0.272462i
$843$	−11.1618	+	19.3328i	−0.384433	+	0.665857i
$844$	25.4340	+	20.9287i	0.875473	+	0.720394i
$845$	2.37096	+	0.0168058i	0.0815634	+	0.000578135i
$846$	0.292515	−	3.53914i	0.0100569	−	0.121678i
$847$	9.18228	+	11.0577i	0.315507	+	0.379948i
$848$	−24.3667	−	8.34227i	−0.836755	−	0.286475i
$849$	−10.5483	−	18.2703i	−0.362018	−	0.627034i
$850$	−3.56653	+	36.7903i	−0.122331	+	1.26190i
$851$	−59.2529	−	34.2097i	−2.03116	−	1.17269i
$852$	14.9741	+	39.9432i	0.513005	+	1.36843i
$853$	55.8284			1.91153			0.955764	−	0.294133i	$-0.0950309\pi$
$853$	55.8284			1.91153			0.955764	+	0.294133i	$0.0950309\pi$
$854$	−15.0384	−	7.01851i	−0.514602	−	0.240168i
$855$	13.3422	+	7.82972i	0.456293	+	0.267771i
$856$	1.74047	+	6.14028i	0.0594882	+	0.209870i
$857$	−11.4414	−	6.60570i	−0.390831	−	0.225646i	0.291689	−	0.956513i	$-0.405783\pi$
$857$	−11.4414	−	6.60570i	−0.390831	−	0.225646i	−0.682520	+	0.730867i	$0.739116\pi$
$858$	−23.1654	−	16.0554i	−0.790854	−	0.548121i
$859$	−41.6251	+	24.0322i	−1.42023	+	0.819969i	−0.996318	−	0.0857347i	$-0.972676\pi$
$859$	−41.6251	+	24.0322i	−1.42023	+	0.819969i	−0.423911	+	0.905704i	$0.639343\pi$
$860$	−12.9809	+	15.5493i	−0.442644	+	0.530227i
$861$	−6.37059	+	17.2275i	−0.217109	+	0.587113i
$862$	−5.31242	−	0.439079i	−0.180942	−	0.0149551i
$863$	25.5092	−	14.7277i	0.868343	−	0.501338i	0.00154562	−	0.999999i	$-0.499508\pi$
$863$	25.5092	−	14.7277i	0.868343	−	0.501338i	0.866797	+	0.498661i	$0.166175\pi$
$864$	−0.273939	+	0.201787i	−0.00931959	+	0.00686492i
$865$	14.4988	+	25.5288i	0.492972	+	0.868004i
$866$	−52.2996	+	24.6942i	−1.77721	+	0.839143i
$867$	25.2388			0.857155
$868$	19.2551	+	33.0087i	0.653559	+	1.12039i
$869$			15.6425i			0.530637i
$870$	3.09647	−	34.4848i	0.104980	−	1.16915i
$871$	15.2108	−	26.3459i	0.515398	−	0.892696i
$872$	27.7360	+	26.9480i	0.939258	+	0.912576i
$873$	−6.11079	+	3.52807i	−0.206819	+	0.119407i
$874$	−30.7616	−	2.54249i	−1.04053	−	0.0860011i
$875$	29.2564	−	4.36599i	0.989048	−	0.147597i
$876$	9.67994	−	58.1588i	0.327055	−	1.96500i
$877$	−14.3849	−	24.9154i	−0.485744	−	0.841333i	0.514122	−	0.857717i	$-0.328118\pi$
$877$	−14.3849	−	24.9154i	−0.485744	−	0.841333i	−0.999866	+	0.0163841i	$0.994785\pi$
$878$	−4.18102	+	6.03256i	−0.141102	+	0.203589i
$879$	31.4209	−	54.4227i	1.05980	−	1.83563i
$880$	6.97722	−	19.9177i	0.235202	−	0.671426i
$881$	17.3351			0.584034			0.292017	−	0.956413i	$-0.405674\pi$
$881$	17.3351			0.584034			0.292017	+	0.956413i	$0.405674\pi$
$882$	−7.77865	+	28.4092i	−0.261921	+	0.956588i
$883$	8.13010			0.273600			0.136800	−	0.990599i	$-0.456318\pi$
$883$	8.13010			0.273600			0.136800	+	0.990599i	$0.456318\pi$
$884$	−33.8259	+	12.6809i	−1.13769	+	0.426504i
$885$	5.35822	−	3.04313i	0.180114	−	0.102294i
$886$	−12.6522	+	18.2552i	−0.425059	+	0.613294i
$887$	−13.3281	+	7.69500i	−0.447515	+	0.258373i	−0.706780	−	0.707433i	$-0.749853\pi$
$887$	−13.3281	+	7.69500i	−0.447515	+	0.258373i	0.259265	+	0.965806i	$0.416520\pi$
$888$	−48.8613	−	12.3407i	−1.63968	−	0.414126i
$889$	−2.56769	−	15.0120i	−0.0861177	−	0.503488i
$890$	5.81014	−	8.25750i	0.194756	−	0.276792i
$891$	−18.5404	+	10.7043i	−0.621128	+	0.358609i
$892$	18.4264	+	15.1624i	0.616962	+	0.507675i
$893$	−0.981171	+	1.69944i	−0.0328336	+	0.0568695i
$894$	16.3722	−	7.73044i	0.547569	−	0.258545i
$895$	−21.1086	−	12.3873i	−0.705581	−	0.414063i
$896$	3.45715	+	29.7329i	0.115495	+	0.993308i
$897$			79.2855i			2.64727i
$898$	22.6697	+	48.0120i	0.756498	+	1.60218i
$899$	28.0134	+	16.1736i	0.934300	+	0.539419i
$900$	29.2780	+	5.30061i	0.975933	+	0.176687i
$901$	−29.1484	+	16.8288i	−0.971073	+	0.560649i
$902$	−0.780617	+	9.44469i	−0.0259917	+	0.314474i
$903$	10.1598	−	27.4744i	0.338096	−	0.914291i
$904$	−4.84422	+	19.1800i	−0.161116	+	0.637919i
$905$	−0.0853128	+	12.0359i	−0.00283589	+	0.400088i
$906$	−26.5915	+	38.3674i	−0.883443	+	1.27467i
$907$	−1.30397	+	2.25855i	−0.0432977	+	0.0749938i	−0.886862	−	0.462034i	$-0.847120\pi$
$907$	−1.30397	+	2.25855i	−0.0432977	+	0.0749938i	0.843564	+	0.537028i	$0.180453\pi$
$908$	7.53024	+	20.0867i	0.249900	+	0.666602i
$909$			12.5736i			0.417039i
$910$	16.4059	+	23.8038i	0.543850	+	0.789089i
$911$	4.97707			0.164898			0.0824488	−	0.996595i	$-0.473726\pi$
$911$	4.97707			0.164898			0.0824488	+	0.996595i	$0.473726\pi$
$912$	−22.3100	+	4.37731i	−0.738757	+	0.144947i
$913$	−0.00903311	−	0.00521527i	−0.000298952	−	0.000172600i
$914$	21.9629	+	15.2219i	0.726467	+	0.503496i
$915$	0.171838	−	24.2429i	0.00568079	−	0.801446i
$916$	−1.44904	+	8.70610i	−0.0478777	+	0.287658i
$917$	−28.0537	+	23.2957i	−0.926416	+	0.769291i
$918$	−0.0366244	+	0.443119i	−0.00120879	+	0.0146251i
$919$	−25.4107	−	44.0126i	−0.838222	−	1.45184i	−0.891380	−	0.453256i	$-0.850262\pi$
$919$	−25.4107	−	44.0126i	−0.838222	−	1.45184i	0.0531588	−	0.998586i	$-0.483071\pi$
$920$	−57.2301	+	15.7846i	−1.88682	+	0.520403i
$921$	−25.7811	+	44.6542i	−0.849516	+	1.47140i
$922$	13.0395	−	6.15684i	0.429434	−	0.202765i
$923$	−30.1495			−0.992383
$924$	0.136575	+	30.5201i	0.00449299	+	1.00404i
$925$	−17.7731	−	31.8172i	−0.584376	−	1.04614i
$926$	−10.0832	+	4.76097i	−0.331355	+	0.156455i
$927$	−20.8649	−	12.0464i	−0.685293	−	0.395654i
$928$	15.0271	+	20.4003i	0.493290	+	0.669674i
$929$	24.4465	+	42.3426i	0.802064	+	1.38922i	0.918255	+	0.395989i	$0.129598\pi$
$929$	24.4465	+	42.3426i	0.802064	+	1.38922i	−0.116191	+	0.993227i	$0.537068\pi$
$930$	−32.1245	+	45.6560i	−1.05340	+	1.49712i
$931$	10.5896	−	12.3604i	0.347060	−	0.405095i
$932$	0.170987	−	1.02732i	0.00560086	−	0.0336509i
$933$	−21.2894	−	36.8744i	−0.696985	−	1.20721i
$934$	6.94118	−	10.0151i	0.227122	−	0.327703i
$935$	−13.6203	−	23.9820i	−0.445432	−	0.784297i
$936$	7.93019	+	27.9772i	0.259206	+	0.914463i
$937$		−	39.1497i		−	1.27896i	−0.768806	−	0.639482i	$-0.779149\pi$
$937$		−	39.1497i		−	1.27896i	0.768806	−	0.639482i	$-0.220851\pi$
$938$	−32.8176	+	2.86034i	−1.07153	+	0.0933933i
$939$		−	4.76210i		−	0.155405i
$940$	−0.646036	+	3.71856i	−0.0210714	+	0.121286i
$941$	−11.2736	−	6.50882i	−0.367509	−	0.212182i	0.304860	−	0.952397i	$-0.401390\pi$
$941$	−11.2736	−	6.50882i	−0.367509	−	0.212182i	−0.672370	+	0.740215i	$0.734724\pi$
$942$	27.5587	−	39.7629i	0.897909	−	1.29555i
$943$	23.0870	−	13.3293i	0.751817	−	0.434062i
$944$	−1.46062	+	4.26629i	−0.0475393	+	0.138856i
$945$	0.351150	−	0.0575027i	0.0114229	−	0.00187056i
$946$	1.24492	−	15.0624i	0.0404760	−	0.489719i
$947$	−20.5191	−	35.5401i	−0.666781	−	1.15490i	−0.978799	−	0.204822i	$-0.934338\pi$
$947$	−20.5191	−	35.5401i	−0.666781	−	1.15490i	0.312019	−	0.950076i	$-0.398995\pi$
$948$	20.5939	−	25.0272i	0.668860	−	0.812845i
$949$	36.0879	+	20.8354i	1.17146	+	0.676345i
$950$	−13.3792	−	9.55633i	−0.434077	−	0.310048i
$951$	−18.4158			−0.597174
$952$	32.2501	+	22.1387i	1.04523	+	0.717521i
$953$			29.5295i			0.956555i	0.878209	+	0.478277i	$0.158739\pi$
$953$			29.5295i			0.956555i	−0.878209	+	0.478277i	$0.841261\pi$
$954$	11.5680	+	24.4997i	0.374527	+	0.793207i
$955$	−15.7007	−	27.6452i	−0.508064	−	0.894576i
$956$	−15.6405	+	19.0075i	−0.505850	+	0.614745i
$957$	12.9173	+	22.3734i	0.417556	+	0.723228i
$958$	20.5289	+	1.69674i	0.663258	+	0.0548192i
$959$	8.61329	+	3.18512i	0.278138	+	0.102853i
$960$	−37.3855	+	22.6815i	−1.20661	+	0.732042i
$961$	−10.5774	−	18.3206i	−0.341206	−	0.590986i
$962$	20.2896	−	29.2747i	0.654162	−	0.943855i
$963$	3.35690	−	5.81433i	0.108175	−	0.187364i
$964$	11.6768	+	31.1476i	0.376085	+	1.00320i
$965$	−37.1821	−	21.8199i	−1.19693	−	0.702409i
$966$	70.3438	−	49.2209i	2.26328	−	1.58366i
$967$			16.6899i			0.536710i	0.963320	+	0.268355i	$0.0864801\pi$
$967$			16.6899i			0.536710i	−0.963320	+	0.268355i	$0.913520\pi$
$968$	−4.19031	−	14.7831i	−0.134682	−	0.475148i
$969$	−14.8556	+	25.7307i	−0.477231	+	0.826589i
$970$	6.80393	−	3.15381i	0.218461	−	0.101263i
$971$	−11.8372	+	6.83423i	−0.379875	+	0.219321i	−0.677764	−	0.735280i	$-0.737051\pi$
$971$	−11.8372	+	6.83423i	−0.379875	+	0.219321i	0.297889	+	0.954601i	$0.403717\pi$
$972$	43.4003	+	7.22354i	1.39207	+	0.231695i
$973$	−9.29743	−	54.3575i	−0.298062	−	1.74262i
$974$	2.92559	−	35.3967i	0.0937419	−	1.13418i
$975$	−21.6327	+	36.2716i	−0.692801	+	1.16162i
$976$	11.6629	+	13.3691i	0.373320	+	0.427935i
$977$	16.8802	+	9.74579i	0.540045	+	0.311795i	0.745097	−	0.666956i	$-0.232403\pi$
$977$	16.8802	+	9.74579i	0.540045	+	0.311795i	−0.205052	+	0.978751i	$0.565736\pi$
$978$	−26.7374	−	56.6270i	−0.854969	−	1.81073i
$979$			7.53372i			0.240779i
$980$	10.9344	−	29.3332i	0.349286	−	0.937016i
$981$		−	40.6808i		−	1.29884i
$982$	0.999746	−	0.472048i	0.0319032	−	0.0150636i
$983$	−13.6471	−	7.87913i	−0.435274	−	0.251305i	0.266317	−	0.963885i	$-0.414193\pi$
$983$	−13.6471	−	7.87913i	−0.435274	−	0.251305i	−0.701591	+	0.712580i	$0.747526\pi$
$984$	13.6832	−	14.0833i	0.436205	−	0.448958i
$985$	15.0258	+	0.106506i	0.478762	+	0.00339355i
$986$	32.9993	+	2.72744i	1.05091	+	0.0868593i
$987$	−0.920217	−	5.38006i	−0.0292908	−	0.171249i
$988$	2.63820	−	15.8508i	0.0839323	−	0.504280i
$989$	−36.8191	+	21.2575i	−1.17078	+	0.675949i
$990$	−20.1424	+	9.33655i	−0.640166	+	0.296735i
$991$	16.9044	−	29.2793i	0.536986	−	0.930088i	−0.462078	−	0.886839i	$-0.652896\pi$
$991$	16.9044	−	29.2793i	0.536986	−	0.930088i	0.999064	−	0.0432484i	$-0.0137707\pi$
$992$	−4.53668	−	40.6001i	−0.144040	−	1.28906i
$993$		−	77.2649i		−	2.45193i
$994$	18.7170	+	26.7493i	0.593667	+	0.848436i
$995$	0.916696	−	1.56209i	0.0290612	−	0.0495215i
$996$	0.00758639	+	0.0202365i	0.000240384	+	0.000641219i
$997$	1.94775	−	3.37360i	0.0616859	−	0.106843i	−0.833533	−	0.552469i	$-0.813686\pi$
$997$	1.94775	−	3.37360i	0.0616859	−	0.106843i	0.895219	+	0.445626i	$0.147019\pi$
$998$	−15.2515	−	10.5704i	−0.482777	−	0.334601i
$999$	−0.219199	−	0.379664i	−0.00693516	−	0.0120120i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bf.a.109.16	yes	88
4.3	odd	2		1120.2.bv.a.529.7		88
5.4	even	2	inner	280.2.bf.a.109.29	yes	88
7.2	even	3	inner	280.2.bf.a.149.14	yes	88
8.3	odd	2		1120.2.bv.a.529.38		88
8.5	even	2	inner	280.2.bf.a.109.31	yes	88
20.19	odd	2		1120.2.bv.a.529.37		88
28.23	odd	6		1120.2.bv.a.849.8		88
35.9	even	6	inner	280.2.bf.a.149.31	yes	88
40.19	odd	2		1120.2.bv.a.529.8		88
40.29	even	2	inner	280.2.bf.a.109.14	✓	88
56.37	even	6	inner	280.2.bf.a.149.29	yes	88
56.51	odd	6		1120.2.bv.a.849.37		88
140.79	odd	6		1120.2.bv.a.849.38		88
280.149	even	6	inner	280.2.bf.a.149.16	yes	88
280.219	odd	6		1120.2.bv.a.849.7		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bf.a.109.14	✓	88	40.29	even	2	inner
280.2.bf.a.109.16	yes	88	1.1	even	1	trivial
280.2.bf.a.109.29	yes	88	5.4	even	2	inner
280.2.bf.a.109.31	yes	88	8.5	even	2	inner
280.2.bf.a.149.14	yes	88	7.2	even	3	inner
280.2.bf.a.149.16	yes	88	280.149	even	6	inner
280.2.bf.a.149.29	yes	88	56.37	even	6	inner
280.2.bf.a.149.31	yes	88	35.9	even	6	inner
1120.2.bv.a.529.7		88	4.3	odd	2
1120.2.bv.a.529.8		88	40.19	odd	2
1120.2.bv.a.529.37		88	20.19	odd	2
1120.2.bv.a.529.38		88	8.3	odd	2
1120.2.bv.a.849.7		88	280.219	odd	6
1120.2.bv.a.849.8		88	28.23	odd	6
1120.2.bv.a.849.37		88	56.51	odd	6
1120.2.bv.a.849.38		88	140.79	odd	6

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.603821 - 1.27883i) q^{2} +(1.22223 - 2.11697i) q^{3} +(-1.27080 + 1.54437i) q^{4} +(-2.23601 - 0.0158492i) q^{5} +(-3.44524 - 0.284754i) q^{6} +(-2.60788 + 0.446057i) q^{7} +(2.74231 + 0.692614i) q^{8} +(-1.48770 - 2.57677i) q^{9} +O(q^{10})\)	\(q+(-0.603821 - 1.27883i) q^{2} +(1.22223 - 2.11697i) q^{3} +(-1.27080 + 1.54437i) q^{4} +(-2.23601 - 0.0158492i) q^{5} +(-3.44524 - 0.284754i) q^{6} +(-2.60788 + 0.446057i) q^{7} +(2.74231 + 0.692614i) q^{8} +(-1.48770 - 2.57677i) q^{9} +(1.32988 + 2.86904i) q^{10} +(-2.04343 - 1.17977i) q^{11} +(1.71616 + 4.57781i) q^{12} -3.45538 q^{13} +(2.14512 + 3.06569i) q^{14} +(-2.76648 + 4.71419i) q^{15} +(-0.770132 - 3.92516i) q^{16} +(-4.52699 - 2.61366i) q^{17} +(-2.39694 + 3.45842i) q^{18} +(2.01367 - 1.16259i) q^{19} +(2.86600 - 3.43308i) q^{20} +(-2.24314 + 6.06598i) q^{21} +(-0.274863 + 3.32556i) q^{22} +(8.12915 - 4.69337i) q^{23} +(4.81798 - 4.95885i) q^{24} +(4.99950 + 0.0708782i) q^{25} +(2.08643 + 4.41884i) q^{26} +0.0601457 q^{27} +(2.62522 - 4.59437i) q^{28} -4.47908i q^{29} +(7.69909 + 0.691319i) q^{30} +(-3.61091 + 6.25428i) q^{31} +(-4.55458 + 3.35496i) q^{32} +(-4.99508 + 2.88391i) q^{33} +(-0.608928 + 7.36743i) q^{34} +(5.83832 - 0.956056i) q^{35} +(5.87004 + 0.977008i) q^{36} +(-3.64447 - 6.31241i) q^{37} +(-2.70266 - 1.87314i) q^{38} +(-4.22327 + 7.31492i) q^{39} +(-6.12087 - 1.59216i) q^{40} +2.84003 q^{41} +(9.11180 - 0.794171i) q^{42} -4.52926 q^{43} +(4.41879 - 1.65654i) q^{44} +(3.28567 + 5.78526i) q^{45} +(-10.9106 - 7.56183i) q^{46} +(-0.730882 + 0.421975i) q^{47} +(-9.25072 - 3.16711i) q^{48} +(6.60207 - 2.32653i) q^{49} +(-2.92816 - 6.43629i) q^{50} +(-11.0661 + 6.38900i) q^{51} +(4.39110 - 5.33637i) q^{52} +(3.21940 - 5.57616i) q^{53} +(-0.0363172 - 0.0769160i) q^{54} +(4.55043 + 2.67037i) q^{55} +(-7.46057 - 0.583026i) q^{56} -5.68384i q^{57} +(-5.72797 + 2.70456i) q^{58} +(-0.976313 - 0.563675i) q^{59} +(-3.76480 - 10.2632i) q^{60} +(-3.84112 + 2.21767i) q^{61} +(10.1785 + 0.841267i) q^{62} +(5.02912 + 6.05630i) q^{63} +(7.04057 + 3.79873i) q^{64} +(7.72627 + 0.0547652i) q^{65} +(6.70416 + 4.64648i) q^{66} +(-4.40206 + 7.62460i) q^{67} +(9.78935 - 3.66989i) q^{68} -22.9455i q^{69} +(-4.74793 - 6.88892i) q^{70} +8.72538 q^{71} +(-2.29503 - 8.09671i) q^{72} +(-10.4440 - 6.02984i) q^{73} +(-5.87187 + 8.47221i) q^{74} +(6.26059 - 10.4971i) q^{75} +(-0.763505 + 4.58727i) q^{76} +(5.85526 + 2.16522i) q^{77} +(11.9046 + 0.983934i) q^{78} +(-3.31473 - 5.74128i) q^{79} +(1.65981 + 8.78891i) q^{80} +(4.53660 - 7.85763i) q^{81} +(-1.71487 - 3.63191i) q^{82} +0.00442057 q^{83} +(-6.51750 - 11.1729i) q^{84} +(10.0810 + 5.91593i) q^{85} +(2.73486 + 5.79215i) q^{86} +(-9.48206 - 5.47447i) q^{87} +(-4.78659 - 4.65062i) q^{88} +(-1.59643 - 2.76511i) q^{89} +(5.41440 - 7.69507i) q^{90} +(9.01121 - 1.54130i) q^{91} +(-3.08225 + 18.5187i) q^{92} +(8.82674 + 15.2884i) q^{93} +(0.980955 + 0.679875i) q^{94} +(-4.52102 + 2.56766i) q^{95} +(1.53559 + 13.7424i) q^{96} -2.37150i q^{97} +(-6.96169 - 7.03810i) q^{98} +7.02058i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 2 q^{4} - 40 q^{9}+O(q^{10}) \) 88 * q - 2 * q^4 - 40 * q^9	\( 88 q - 2 q^{4} - 40 q^{9} + 6 q^{10} - 6 q^{14} + 4 q^{15} + 2 q^{16} - 24 q^{20} - 8 q^{24} - 2 q^{25} - 14 q^{26} + 14 q^{30} - 28 q^{31} + 24 q^{34} + 60 q^{36} - 16 q^{39} - 32 q^{40} - 16 q^{41} - 2 q^{44} - 42 q^{46} - 8 q^{49} - 12 q^{50} + 8 q^{54} - 28 q^{55} + 36 q^{56} + 10 q^{60} + 52 q^{64} - 12 q^{65} - 44 q^{66} - 48 q^{70} + 16 q^{71} - 42 q^{74} - 36 q^{76} - 4 q^{79} - 40 q^{80} - 20 q^{81} + 12 q^{84} - 24 q^{86} + 4 q^{89} - 96 q^{90} - 22 q^{94} - 34 q^{95} + 80 q^{96}+O(q^{100}) \) 88 * q - 2 * q^4 - 40 * q^9 + 6 * q^10 - 6 * q^14 + 4 * q^15 + 2 * q^16 - 24 * q^20 - 8 * q^24 - 2 * q^25 - 14 * q^26 + 14 * q^30 - 28 * q^31 + 24 * q^34 + 60 * q^36 - 16 * q^39 - 32 * q^40 - 16 * q^41 - 2 * q^44 - 42 * q^46 - 8 * q^49 - 12 * q^50 + 8 * q^54 - 28 * q^55 + 36 * q^56 + 10 * q^60 + 52 * q^64 - 12 * q^65 - 44 * q^66 - 48 * q^70 + 16 * q^71 - 42 * q^74 - 36 * q^76 - 4 * q^79 - 40 * q^80 - 20 * q^81 + 12 * q^84 - 24 * q^86 + 4 * q^89 - 96 * q^90 - 22 * q^94 - 34 * q^95 + 80 * q^96

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