LMFDB - Embedded newform 680.2.bl.a.387.36

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(123,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 3, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.123"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.bl (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$208$
Relative dimension:	$104$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			387.36
Character	$\chi$	$=$	680.387
Dual form			680.2.bl.a.123.36

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.738875 + 1.20585i) q^{2} +2.74346 q^{3} +(-0.908129 - 1.78194i) q^{4} +(-0.584289 - 2.15838i) q^{5} +(-2.02707 + 3.30818i) q^{6} -1.18693i q^{7} +(2.81974 + 0.221566i) q^{8} +4.52655 q^{9} +(3.03439 + 0.890211i) q^{10} +(0.557635 - 0.557635i) q^{11} +(-2.49141 - 4.88867i) q^{12} +(-2.54503 - 2.54503i) q^{13} +(1.43125 + 0.876993i) q^{14} +(-1.60297 - 5.92142i) q^{15} +(-2.35061 + 3.23646i) q^{16} +(2.10422 - 3.54574i) q^{17} +(-3.34455 + 5.45832i) q^{18} -3.23494 q^{19} +(-3.31549 + 3.00125i) q^{20} -3.25629i q^{21} +(0.260399 + 1.08444i) q^{22} -0.472228 q^{23} +(7.73582 + 0.607856i) q^{24} +(-4.31721 + 2.52223i) q^{25} +(4.94938 - 1.18846i) q^{26} +4.18802 q^{27} +(-2.11504 + 1.07789i) q^{28} +(0.887208 + 0.887208i) q^{29} +(8.32472 + 2.44225i) q^{30} +(3.45960 - 3.45960i) q^{31} +(-2.16587 - 5.22580i) q^{32} +(1.52985 - 1.52985i) q^{33} +(2.72085 + 5.15722i) q^{34} +(-2.56185 + 0.693510i) q^{35} +(-4.11069 - 8.06603i) q^{36} +9.40220 q^{37} +(2.39022 - 3.90084i) q^{38} +(-6.98219 - 6.98219i) q^{39} +(-1.16932 - 6.21552i) q^{40} +(4.79693 - 4.79693i) q^{41} +(3.92658 + 2.40599i) q^{42} +(5.51569 + 5.51569i) q^{43} +(-1.50007 - 0.487267i) q^{44} +(-2.64481 - 9.77001i) q^{45} +(0.348917 - 0.569434i) q^{46} +(-4.67838 + 4.67838i) q^{47} +(-6.44878 + 8.87908i) q^{48} +5.59120 q^{49} +(0.148453 - 7.06951i) q^{50} +(5.77284 - 9.72757i) q^{51} +(-2.22388 + 6.84631i) q^{52} +(-6.53086 + 6.53086i) q^{53} +(-3.09442 + 5.05010i) q^{54} +(-1.52941 - 0.877769i) q^{55} +(0.262983 - 3.34683i) q^{56} -8.87492 q^{57} +(-1.72537 + 0.414301i) q^{58} -6.07501 q^{59} +(-9.09590 + 8.23380i) q^{60} +(4.43972 + 4.43972i) q^{61} +(1.61553 + 6.72796i) q^{62} -5.37270i q^{63} +(7.90182 + 1.24951i) q^{64} +(-4.00612 + 6.98019i) q^{65} +(0.714394 + 2.97512i) q^{66} +(-1.65991 - 1.65991i) q^{67} +(-8.22919 - 0.529613i) q^{68} -1.29554 q^{69} +(1.05662 - 3.60161i) q^{70} +(-1.62888 + 1.62888i) q^{71} +(12.7637 + 1.00293i) q^{72} +4.91927 q^{73} +(-6.94705 + 11.3376i) q^{74} +(-11.8441 + 6.91964i) q^{75} +(2.93774 + 5.76447i) q^{76} +(-0.661874 - 0.661874i) q^{77} +(13.5784 - 3.26048i) q^{78} +(2.30907 - 2.30907i) q^{79} +(8.35894 + 3.18248i) q^{80} -2.09000 q^{81} +(2.24003 + 9.32869i) q^{82} +(10.0536 + 10.0536i) q^{83} +(-5.80251 + 2.95713i) q^{84} +(-8.88252 - 2.46998i) q^{85} +(-10.7265 + 2.57567i) q^{86} +(2.43402 + 2.43402i) q^{87} +(1.69594 - 1.44883i) q^{88} +4.84722i q^{89} +(13.7353 + 4.02958i) q^{90} +(-3.02078 + 3.02078i) q^{91} +(0.428844 + 0.841481i) q^{92} +(9.49126 - 9.49126i) q^{93} +(-2.18467 - 9.09814i) q^{94} +(1.89014 + 6.98224i) q^{95} +(-5.94196 - 14.3368i) q^{96} +3.62936i q^{97} +(-4.13119 + 6.74212i) q^{98} +(2.52416 - 2.52416i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 208 q - 8 q^{3} - 8 q^{6} + 192 q^{9} - 6 q^{10} - 8 q^{11} + 16 q^{14} - 16 q^{16} - 12 q^{18} - 10 q^{20} - 16 q^{24} - 32 q^{27} - 24 q^{30} - 20 q^{32} - 8 q^{33} + 4 q^{34} - 8 q^{35} - 12 q^{38} + 38 q^{40}+ \cdots - 24 q^{99}+O(q^{100}) $ 208 * q - 8 * q^3 - 8 * q^6 + 192 * q^9 - 6 * q^10 - 8 * q^11 + 16 * q^14 - 16 * q^16 - 12 * q^18 - 10 * q^20 - 16 * q^24 - 32 * q^27 - 24 * q^30 - 20 * q^32 - 8 * q^33 + 4 * q^34 - 8 * q^35 - 12 * q^38 + 38 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^44 - 16 * q^46 + 68 * q^48 - 160 * q^49 + 16 * q^50 - 8 * q^51 - 20 * q^52 - 36 * q^54 + 4 * q^56 - 32 * q^57 + 64 * q^59 - 32 * q^60 - 72 * q^62 + 32 * q^65 - 8 * q^67 - 28 * q^68 + 28 * q^70 - 56 * q^72 + 32 * q^73 - 8 * q^74 - 16 * q^75 - 10 * q^80 + 128 * q^81 + 8 * q^86 - 16 * q^88 - 118 * q^90 + 24 * q^91 - 56 * q^92 - 64 * q^94 - 48 * q^96 - 40 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$

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 $

$2$	−0.738875	+	1.20585i	−0.522463	+	0.852662i
$2$	−0.738875	+	1.20585i	−0.522463	+	0.852662i
$3$	2.74346			1.58393			0.791967	−	0.610563i	$-0.209057\pi$
$3$	2.74346			1.58393			0.791967	+	0.610563i	$0.209057\pi$
$4$	−0.908129	−	1.78194i	−0.454064	−	0.890969i
$5$	−0.584289	−	2.15838i	−0.261302	−	0.965257i
$5$	−0.584289	−	2.15838i	−0.261302	−	0.965257i
$6$	−2.02707	+	3.30818i	−0.827548	+	1.35056i
$7$		−	1.18693i		−	0.448617i	−0.974518	−	0.224309i	$-0.927988\pi$
$7$		−	1.18693i		−	0.448617i	0.974518	−	0.224309i	$-0.0720124\pi$
$8$	2.81974	+	0.221566i	0.996927	+	0.0783353i
$9$	4.52655			1.50885
$10$	3.03439	+	0.890211i	0.959558	+	0.281509i
$11$	0.557635	−	0.557635i	0.168133	−	0.168133i	−0.618025	−	0.786158i	$-0.712067\pi$
$11$	0.557635	−	0.557635i	0.168133	−	0.168133i	0.786158	+	0.618025i	$0.212067\pi$
$12$	−2.49141	−	4.88867i	−0.719208	−	1.41124i
$13$	−2.54503	−	2.54503i	−0.705866	−	0.705866i	0.259797	−	0.965663i	$-0.416344\pi$
$13$	−2.54503	−	2.54503i	−0.705866	−	0.705866i	−0.965663	+	0.259797i	$0.916344\pi$
$14$	1.43125	+	0.876993i	0.382519	+	0.234386i
$15$	−1.60297	−	5.92142i	−0.413885	−	1.52890i
$16$	−2.35061	+	3.23646i	−0.587651	+	0.809114i
$17$	2.10422	−	3.54574i	0.510349	−	0.859967i
$17$	2.10422	−	3.54574i	0.510349	−	0.859967i
$18$	−3.34455	+	5.45832i	−0.788318	+	1.28654i
$19$	−3.23494			−0.742147			−0.371073	−	0.928604i	$-0.621010\pi$
$19$	−3.23494			−0.742147			−0.371073	+	0.928604i	$0.621010\pi$
$20$	−3.31549	+	3.00125i	−0.741366	+	0.671101i
$21$		−	3.25629i		−	0.710581i
$22$	0.260399	+	1.08444i	0.0555174	+	0.231204i
$23$	−0.472228			−0.0984663			−0.0492332	−	0.998787i	$-0.515678\pi$
$23$	−0.472228			−0.0984663			−0.0492332	+	0.998787i	$0.515678\pi$
$24$	7.73582	+	0.607856i	1.57907	+	0.124078i
$25$	−4.31721	+	2.52223i	−0.863443	+	0.504447i
$26$	4.94938	−	1.18846i	0.970654	−	0.233076i
$27$	4.18802			0.805984
$28$	−2.11504	+	1.07789i	−0.399704	+	0.203701i
$29$	0.887208	+	0.887208i	0.164750	+	0.164750i	0.784667	−	0.619917i	$-0.212834\pi$
$29$	0.887208	+	0.887208i	0.164750	+	0.164750i	−0.619917	+	0.784667i	$0.712834\pi$
$30$	8.32472	+	2.44225i	1.51988	+	0.445892i
$31$	3.45960	−	3.45960i	0.621363	−	0.621363i	−0.324517	−	0.945880i	$-0.605202\pi$
$31$	3.45960	−	3.45960i	0.621363	−	0.621363i	0.945880	+	0.324517i	$0.105202\pi$
$32$	−2.16587	−	5.22580i	−0.382875	−	0.923800i
$33$	1.52985	−	1.52985i	0.266312	−	0.266312i
$34$	2.72085	+	5.15722i	0.466622	+	0.884457i
$35$	−2.56185	+	0.693510i	−0.433031	+	0.117225i
$36$	−4.11069	−	8.06603i	−0.685115	−	1.34434i
$37$	9.40220			1.54571			0.772856	−	0.634582i	$-0.218828\pi$
$37$	9.40220			1.54571			0.772856	+	0.634582i	$0.218828\pi$
$38$	2.39022	−	3.90084i	0.387744	−	0.632800i
$39$	−6.98219	−	6.98219i	−1.11805	−	1.11805i
$40$	−1.16932	−	6.21552i	−0.184885	−	0.982760i
$41$	4.79693	−	4.79693i	0.749154	−	0.749154i	−0.225166	−	0.974320i	$-0.572292\pi$
$41$	4.79693	−	4.79693i	0.749154	−	0.749154i	0.974320	+	0.225166i	$0.0722924\pi$
$42$	3.92658	+	2.40599i	0.605885	+	0.371252i
$43$	5.51569	+	5.51569i	0.841135	+	0.841135i	0.989007	−	0.147871i	$-0.0472422\pi$
$43$	5.51569	+	5.51569i	0.841135	+	0.841135i	−0.147871	+	0.989007i	$0.547242\pi$
$44$	−1.50007	−	0.487267i	−0.226145	−	0.0734582i
$45$	−2.64481	−	9.77001i	−0.394265	−	1.45643i
$46$	0.348917	−	0.569434i	0.0514450	−	0.0839585i
$47$	−4.67838	+	4.67838i	−0.682411	+	0.682411i	−0.960543	−	0.278132i	$-0.910285\pi$
$47$	−4.67838	+	4.67838i	−0.682411	+	0.682411i	0.278132	+	0.960543i	$0.410285\pi$
$48$	−6.44878	+	8.87908i	−0.930801	+	1.28158i
$49$	5.59120			0.798742
$50$	0.148453	−	7.06951i	0.0209945	−	0.999780i
$51$	5.77284	−	9.72757i	0.808360	−	1.36213i
$52$	−2.22388	+	6.84631i	−0.308396	+	0.949413i
$53$	−6.53086	+	6.53086i	−0.897083	+	0.897083i	−0.995177	−	0.0980943i	$-0.968725\pi$
$53$	−6.53086	+	6.53086i	−0.897083	+	0.897083i	0.0980943	+	0.995177i	$0.468725\pi$
$54$	−3.09442	+	5.05010i	−0.421097	+	0.687232i
$55$	−1.52941	−	0.877769i	−0.206225	−	0.118358i
$56$	0.262983	−	3.34683i	0.0351426	−	0.447239i
$57$	−8.87492			−1.17551
$58$	−1.72537	+	0.414301i	−0.226552	+	0.0544004i
$59$	−6.07501			−0.790899			−0.395450	−	0.918488i	$-0.629411\pi$
$59$	−6.07501			−0.790899			−0.395450	+	0.918488i	$0.629411\pi$
$60$	−9.09590	+	8.23380i	−1.17428	+	1.06298i
$61$	4.43972	+	4.43972i	0.568448	+	0.568448i	0.931693	−	0.363246i	$-0.118331\pi$
$61$	4.43972	+	4.43972i	0.568448	+	0.568448i	−0.363246	+	0.931693i	$0.618331\pi$
$62$	1.61553	+	6.72796i	0.205173	+	0.854451i
$63$		−	5.37270i		−	0.676896i
$64$	7.90182	+	1.24951i	0.987727	+	0.156189i
$65$	−4.00612	+	6.98019i	−0.496898	+	0.865786i
$66$	0.714394	+	2.97512i	0.0879359	+	0.366212i
$67$	−1.65991	−	1.65991i	−0.202790	−	0.202790i	0.598404	−	0.801194i	$-0.295802\pi$
$67$	−1.65991	−	1.65991i	−0.202790	−	0.202790i	−0.801194	+	0.598404i	$0.795802\pi$
$68$	−8.22919	−	0.529613i	−0.997935	−	0.0642250i
$69$	−1.29554			−0.155964
$70$	1.05662	−	3.60161i	0.126290	−	0.430475i
$71$	−1.62888	+	1.62888i	−0.193313	+	0.193313i	−0.797126	−	0.603813i	$-0.793647\pi$
$71$	−1.62888	+	1.62888i	−0.193313	+	0.193313i	0.603813	+	0.797126i	$0.293647\pi$
$72$	12.7637	+	1.00293i	1.50421	+	0.118196i
$73$	4.91927			0.575757			0.287879	−	0.957667i	$-0.407050\pi$
$73$	4.91927			0.575757			0.287879	+	0.957667i	$0.407050\pi$
$74$	−6.94705	+	11.3376i	−0.807578	+	1.31797i
$75$	−11.8441	+	6.91964i	−1.36764	+	0.799011i
$76$	2.93774	+	5.76447i	0.336982	+	0.661230i
$77$	−0.661874	−	0.661874i	−0.0754275	−	0.0754275i
$78$	13.5784	−	3.26048i	1.53745	−	0.369177i
$79$	2.30907	−	2.30907i	0.259790	−	0.259790i	−0.565178	−	0.824969i	$-0.691193\pi$
$79$	2.30907	−	2.30907i	0.259790	−	0.259790i	0.824969	+	0.565178i	$0.191193\pi$
$80$	8.35894	+	3.18248i	0.934558	+	0.355812i
$81$	−2.09000			−0.232223
$82$	2.24003	+	9.32869i	0.247370	+	1.03018i
$83$	10.0536	+	10.0536i	1.10353	+	1.10353i	0.993981	+	0.109549i	$0.0349407\pi$
$83$	10.0536	+	10.0536i	1.10353	+	1.10353i	0.109549	+	0.993981i	$0.465059\pi$
$84$	−5.80251	+	2.95713i	−0.633105	+	0.322649i
$85$	−8.88252	−	2.46998i	−0.963445	−	0.267907i
$86$	−10.7265	+	2.57567i	−1.15667	+	0.277742i
$87$	2.43402	+	2.43402i	0.260954	+	0.260954i
$88$	1.69594	−	1.44883i	0.180787	−	0.154446i
$89$			4.84722i			0.513804i	0.966437	+	0.256902i	$0.0827017\pi$
$89$			4.84722i			0.513804i	−0.966437	+	0.256902i	$0.917298\pi$
$90$	13.7353	+	4.02958i	1.44783	+	0.424755i
$91$	−3.02078	+	3.02078i	−0.316664	+	0.316664i
$92$	0.428844	+	0.841481i	0.0447100	+	0.0877304i
$93$	9.49126	−	9.49126i	0.984198	−	0.984198i
$94$	−2.18467	−	9.09814i	−0.225331	−	0.938401i
$95$	1.89014	+	6.98224i	0.193924	+	0.716362i
$96$	−5.94196	−	14.3368i	−0.606448	−	1.46324i
$97$			3.62936i			0.368506i	0.982879	+	0.184253i	$0.0589865\pi$
$97$			3.62936i			0.368506i	−0.982879	+	0.184253i	$0.941013\pi$
$98$	−4.13119	+	6.74212i	−0.417314	+	0.681057i
$99$	2.52416	−	2.52416i	0.253688	−	0.253688i
$100$	8.41505	+	5.40249i	0.841505	+	0.540249i
$101$		−	11.1782i		−	1.11228i	−0.831090	−	0.556138i	$-0.812283\pi$
$101$		−	11.1782i		−	1.11228i	0.831090	−	0.556138i	$-0.187717\pi$
$102$	7.46454	+	14.1486i	0.739100	+	1.40092i
$103$	12.5477	+	12.5477i	1.23636	+	1.23636i	0.961476	+	0.274888i	$0.0886407\pi$
$103$	12.5477	+	12.5477i	1.23636	+	1.23636i	0.274888	+	0.961476i	$0.411359\pi$
$104$	−6.61243	−	7.74022i	−0.648402	−	0.758991i
$105$	−7.02831	+	1.90261i	−0.685893	+	0.185676i
$106$	−3.04972	−	12.7007i	−0.296215	−	1.23360i
$107$		−	4.31495i		−	0.417142i	−0.978007	−	0.208571i	$-0.933119\pi$
$107$		−	4.31495i		−	0.417142i	0.978007	−	0.208571i	$-0.0668812\pi$
$108$	−3.80326	−	7.46279i	−0.365969	−	0.718107i
$109$	−7.66591	+	7.66591i	−0.734261	+	0.734261i	−0.971461	−	0.237200i	$-0.923770\pi$
$109$	−7.66591	+	7.66591i	−0.734261	+	0.734261i	0.237200	+	0.971461i	$0.423770\pi$
$110$	2.18849	−	1.19567i	0.208665	−	0.114003i
$111$	25.7945			2.44831
$112$	3.84145	+	2.79000i	0.362983	+	0.263631i
$113$		−	17.7291i		−	1.66781i	−0.551905	−	0.833907i	$-0.686099\pi$
$113$		−	17.7291i		−	1.66781i	0.551905	−	0.833907i	$-0.313901\pi$
$114$	6.55745	−	10.7018i	0.614162	−	1.00231i
$115$	0.275917	+	1.01925i	0.0257294	+	0.0950453i
$116$	0.775251	−	2.38665i	0.0719802	−	0.221595i
$117$	−11.5202	−	11.5202i	−1.06505	−	1.06505i
$118$	4.48867	−	7.32553i	0.413216	−	0.674370i
$119$	−4.20854	−	2.49757i	−0.385796	−	0.228952i
$120$	−3.20797	−	17.0520i	−0.292846	−	1.55663i
$121$			10.3781i			0.943462i
$122$	−8.63401	+	2.07322i	−0.781686	+	0.187701i
$123$	13.1602	−	13.1602i	1.18661	−	1.18661i
$124$	−9.30656	−	3.02303i	−0.835753	−	0.271476i
$125$	7.96644	+	7.84448i	0.712540	+	0.701631i
$126$	6.47864	+	3.96975i	0.577163	+	0.353653i
$127$	13.5467	+	13.5467i	1.20208	+	1.20208i	0.973533	+	0.228545i	$0.0733968\pi$
$127$	13.5467	+	13.5467i	1.20208	+	1.20208i	0.228545	+	0.973533i	$0.426603\pi$
$128$	−7.34517	+	8.60514i	−0.649228	+	0.760594i
$129$	15.1321	+	15.1321i	1.33230	+	1.33230i
$130$	−5.45701	−	9.98825i	−0.478612	−	0.876027i
$131$	−3.62682	−	3.62682i	−0.316877	−	0.316877i	0.530689	−	0.847566i	$-0.321933\pi$
$131$	−3.62682	−	3.62682i	−0.316877	−	0.316877i	−0.847566	+	0.530689i	$0.821933\pi$
$132$	−4.11539	−	1.33679i	−0.358199	−	0.116353i
$133$			3.83965i			0.332940i
$134$	3.22806	−	0.775129i	0.278862	−	0.0669609i
$135$	−2.44701	−	9.03934i	−0.210605	−	0.777982i
$136$	6.71897	−	9.53181i	0.576147	−	0.817346i
$137$	−9.09793	−	9.09793i	−0.777289	−	0.777289i	0.202080	−	0.979369i	$-0.435230\pi$
$137$	−9.09793	−	9.09793i	−0.777289	−	0.777289i	−0.979369	+	0.202080i	$0.935230\pi$
$138$	0.957239	−	1.56222i	0.0814856	−	0.132985i
$139$	−5.75698	+	5.75698i	−0.488301	+	0.488301i	−0.907770	−	0.419469i	$-0.862216\pi$
$139$	−5.75698	+	5.75698i	−0.488301	+	0.488301i	0.419469	+	0.907770i	$0.362216\pi$
$140$	3.56228	+	3.93526i	0.301067	+	0.332590i
$141$	−12.8349	+	12.8349i	−1.08090	+	1.08090i
$142$	−0.760642	−	3.16772i	−0.0638317	−	0.265830i
$143$	−2.83840			−0.237359
$144$	−10.6401	+	14.6500i	−0.886677	+	1.22083i
$145$	1.39655	−	2.43332i	0.115977	−	0.202076i
$146$	−3.63472	+	5.93188i	−0.300812	+	0.490926i
$147$	15.3392			1.26516
$148$	−8.53840	−	16.7541i	−0.701852	−	1.37718i
$149$	−20.7473			−1.69969			−0.849844	−	0.527034i	$-0.823304\pi$
$149$	−20.7473			−1.69969			−0.849844	+	0.527034i	$0.823304\pi$
$150$	0.407275	−	19.3949i	0.0332539	−	1.58359i
$151$	6.77920			0.551684			0.275842	−	0.961203i	$-0.411043\pi$
$151$	6.77920			0.551684			0.275842	+	0.961203i	$0.411043\pi$
$152$	−9.12168	−	0.716752i	−0.739866	−	0.0581363i
$153$	9.52487	−	16.0499i	0.770040	−	1.29756i
$154$	1.28716	−	0.309076i	0.103722	−	0.0249060i
$155$	−9.48854	−	5.44573i	−0.762138	−	0.437412i
$156$	−6.10110	+	18.7826i	−0.488479	+	1.50381i
$157$	−10.3523	+	10.3523i	−0.826203	+	0.826203i	−0.986989	−	0.160787i	$-0.948597\pi$
$157$	−10.3523	+	10.3523i	−0.826203	+	0.826203i	0.160787	+	0.986989i	$0.448597\pi$
$158$	1.07827	+	4.49049i	0.0857823	+	0.357244i
$159$	−17.9171	+	17.9171i	−1.42092	+	1.42092i
$160$	−10.0138	+	7.72814i	−0.791659	+	0.610963i
$161$			0.560502i			0.0441737i
$162$	1.54425	−	2.52022i	0.121328	−	0.198007i
$163$			4.34001i			0.339936i	0.985450	+	0.169968i	$0.0543665\pi$
$163$			4.34001i			0.339936i	−0.985450	+	0.169968i	$0.945634\pi$
$164$	−12.9041	−	4.19160i	−1.00764	−	0.327309i
$165$	−4.19586	−	2.40812i	−0.326648	−	0.187472i
$166$	−19.5515	+	4.69476i	−1.51749	+	0.364384i
$167$	6.25000			0.483640			0.241820	−	0.970321i	$-0.422256\pi$
$167$	6.25000			0.483640			0.241820	+	0.970321i	$0.422256\pi$
$168$	0.721482	−	9.18188i	0.0556636	−	0.708397i
$169$		−	0.0455960i		−	0.00350738i
$170$	9.54149	−	8.88594i	0.731799	−	0.681521i
$171$	−14.6431			−1.11979
$172$	4.81966	−	14.8376i	0.367496	−	1.13135i
$173$			25.2426i			1.91916i	0.281436	+	0.959580i	$0.409189\pi$
$173$			25.2426i			1.91916i	−0.281436	+	0.959580i	$0.590811\pi$
$174$	−4.73348	+	1.13662i	−0.358844	+	0.0861666i
$175$	2.99372	+	5.12423i	0.226304	+	0.387355i
$176$	0.493982	+	3.11554i	0.0372353	+	0.234843i
$177$	−16.6665			−1.25273
$178$	−5.84500	−	3.58149i	−0.438101	−	0.268444i
$179$	−19.5352			−1.46013			−0.730066	−	0.683377i	$-0.760511\pi$
$179$	−19.5352			−1.46013			−0.730066	+	0.683377i	$0.760511\pi$
$180$	−15.0077	+	13.5853i	−1.11861	+	1.01259i
$181$	−17.1034	−	17.1034i	−1.27129	−	1.27129i	−0.945413	−	0.325875i	$-0.894341\pi$
$181$	−17.1034	−	17.1034i	−1.27129	−	1.27129i	−0.325875	−	0.945413i	$-0.605659\pi$
$182$	−1.41062	−	5.87457i	−0.104562	−	0.435452i
$183$	12.1802	+	12.1802i	0.900384	+	0.900384i
$184$	−1.33156	−	0.104630i	−0.0981638	−	0.00771339i
$185$	−5.49360	−	20.2935i	−0.403897	−	1.49201i
$186$	4.43215	+	18.4579i	0.324981	+	1.35340i
$187$	−0.803837	−	3.15061i	−0.0587824	−	0.230396i
$188$	12.5851	+	4.08801i	0.917866	+	0.298149i
$189$		−	4.97088i		−	0.361579i
$190$	−9.81608	−	2.87978i	−0.712133	−	0.208921i
$191$			1.60952i			0.116461i	0.998303	+	0.0582306i	$0.0185459\pi$
$191$			1.60952i			0.116461i	−0.998303	+	0.0582306i	$0.981454\pi$
$192$	21.6783	+	3.42798i	1.56450	+	0.247393i
$193$		−	12.0974i		−	0.870789i	−0.900240	−	0.435394i	$-0.856609\pi$
$193$		−	12.0974i		−	0.870789i	0.900240	−	0.435394i	$-0.143391\pi$
$194$	−4.37645	−	2.68164i	−0.314211	−	0.192531i
$195$	−10.9906	+	19.1498i	−0.787054	+	1.37135i
$196$	−5.07753	−	9.96317i	−0.362680	−	0.711655i
$197$		−	27.2727i		−	1.94310i	−0.236835	−	0.971550i	$-0.576110\pi$
$197$		−	27.2727i		−	1.94310i	0.236835	−	0.971550i	$-0.423890\pi$
$198$	1.17871	+	4.90879i	0.0837673	+	0.348852i
$199$	14.7893	+	14.7893i	1.04839	+	1.04839i	0.998768	+	0.0496211i	$0.0158014\pi$
$199$	14.7893	+	14.7893i	1.04839	+	1.04839i	0.0496211	+	0.998768i	$0.484199\pi$
$200$	−12.7322	+	6.15549i	−0.900305	+	0.435259i
$201$	−4.55388	−	4.55388i	−0.321206	−	0.321206i
$202$	13.4792	+	8.25931i	0.948395	+	0.581123i
$203$	1.05305	−	1.05305i	0.0739099	−	0.0739099i
$204$	−22.5764	−	1.45297i	−1.58066	−	0.101728i
$205$	−13.1564	−	7.55081i	−0.918882	−	0.527371i
$206$	−24.4018	+	5.85943i	−1.70016	+	0.408246i
$207$	−2.13756			−0.148571
$208$	14.2193	−	2.25452i	0.985929	−	0.156323i
$209$	−1.80392	+	1.80392i	−0.124780	+	0.124780i
$210$	2.89878	−	9.88085i	0.200035	−	0.681844i
$211$	12.0624	−	12.0624i	0.830408	−	0.830408i	−0.157164	−	0.987572i	$-0.550235\pi$
$211$	12.0624	−	12.0624i	0.830408	−	0.830408i	0.987572	+	0.157164i	$0.0502352\pi$
$212$	17.5685	+	5.70673i	1.20661	+	0.391940i
$213$	−4.46877	+	4.46877i	−0.306195	+	0.306195i
$214$	5.20316	+	3.18820i	0.355681	+	0.217941i
$215$	8.68221	−	15.1277i	0.592122	−	1.03170i
$216$	11.8091	+	0.927921i	0.803508	+	0.0631370i
$217$	−4.10630	−	4.10630i	−0.278754	−	0.278754i
$218$	−3.57976	−	14.9081i	−0.242452	−	1.00970i
$219$	13.4958			0.911962
$220$	−0.175230	+	3.52244i	−0.0118140	+	0.237483i
$221$	−14.3793	+	3.66870i	−0.967259	+	0.246783i
$222$	−19.0589	+	31.1042i	−1.27915	+	2.08758i
$223$	−1.96944	+	1.96944i	−0.131883	+	0.131883i	−0.769967	−	0.638084i	$-0.779727\pi$
$223$	−1.96944	+	1.96944i	−0.131883	+	0.131883i	0.638084	+	0.769967i	$0.279727\pi$
$224$	−6.20266	+	2.57073i	−0.414433	+	0.171764i
$225$	−19.5421	+	11.4170i	−1.30281	+	0.761135i
$226$	21.3786	+	13.0996i	1.42208	+	0.871372i
$227$	13.7782			0.914493			0.457247	−	0.889340i	$-0.348836\pi$
$227$	13.7782			0.914493			0.457247	+	0.889340i	$0.348836\pi$
$228$	8.05957	+	15.8146i	0.533758	+	1.04734i
$229$		−	17.9808i		−	1.18821i	−0.804388	−	0.594104i	$-0.797507\pi$
$229$		−	17.9808i		−	1.18821i	0.804388	−	0.594104i	$-0.202493\pi$
$230$	−1.43292	−	0.420382i	−0.0944842	−	0.0277192i
$231$	−1.81582	−	1.81582i	−0.119472	−	0.119472i
$232$	2.30512	+	2.69827i	0.151338	+	0.177150i
$233$	14.6545			0.960048			0.480024	−	0.877255i	$-0.340628\pi$
$233$	14.6545			0.960048			0.480024	+	0.877255i	$0.340628\pi$
$234$	22.4036	−	5.37961i	1.46457	−	0.351676i
$235$	12.8312	+	7.36419i	0.837018	+	0.480387i
$236$	5.51689	+	10.8253i	0.359119	+	0.704667i
$237$	6.33482	−	6.33482i	0.411491	−	0.411491i
$238$	6.12126	−	3.22946i	0.396783	−	0.209335i
$239$	24.8818			1.60947			0.804734	−	0.593636i	$-0.202308\pi$
$239$	24.8818			1.60947			0.804734	+	0.593636i	$0.202308\pi$
$240$	22.9324	+	8.73098i	1.48028	+	0.563582i
$241$	−1.57909	−	1.57909i	−0.101718	−	0.101718i	0.654416	−	0.756134i	$-0.272914\pi$
$241$	−1.57909	−	1.57909i	−0.101718	−	0.101718i	−0.756134	+	0.654416i	$0.772914\pi$
$242$	−12.5144	−	7.66811i	−0.804454	−	0.492924i
$243$	−18.2979			−1.17381
$244$	3.87947	−	11.9431i	0.248357	−	0.764581i
$245$	−3.26687	−	12.0679i	−0.208713	−	0.770992i
$246$	6.14542	+	25.5928i	0.391817	+	1.63174i
$247$	8.23304	+	8.23304i	0.523856	+	0.523856i
$248$	10.5217	−	8.98863i	0.668128	−	0.570779i
$249$	27.5817	+	27.5817i	1.74792	+	1.74792i
$250$	−15.3454	+	3.81022i	−0.970530	+	0.240979i
$251$	−27.3206			−1.72446			−0.862232	−	0.506514i	$-0.830934\pi$
$251$	−27.3206			−1.72446			−0.862232	+	0.506514i	$0.830934\pi$
$252$	−9.57381	+	4.87910i	−0.603093	+	0.307354i
$253$	−0.263331	+	0.263331i	−0.0165555	+	0.0165555i
$254$	−26.3446	+	6.32593i	−1.65301	+	0.396924i
$255$	−24.3688	−	6.77629i	−1.52603	−	0.424348i
$256$	−4.94931	−	15.2153i	−0.309332	−	0.950954i
$257$	−5.63189	+	5.63189i	−0.351308	+	0.351308i	−0.860596	−	0.509288i	$-0.829909\pi$
$257$	−5.63189	+	5.63189i	−0.351308	+	0.351308i	0.509288	+	0.860596i	$0.329909\pi$
$258$	−29.4276	+	7.06623i	−1.83208	+	0.439925i
$259$		−	11.1598i		−	0.693433i
$260$	16.0763	+	0.799746i	0.997012	+	0.0495982i
$261$	4.01599	+	4.01599i	0.248584	+	0.248584i
$262$	7.05316	−	1.69362i	0.435746	−	0.104632i
$263$	−8.73122	+	8.73122i	−0.538390	+	0.538390i	−0.923056	−	0.384666i	$-0.874317\pi$
$263$	−8.73122	+	8.73122i	−0.538390	+	0.538390i	0.384666	+	0.923056i	$0.374317\pi$
$264$	4.65272	−	3.97480i	0.286355	−	0.244632i
$265$	17.9120	+	10.2802i	1.10033	+	0.631506i
$266$	−4.63003	−	2.83702i	−0.283885	−	0.173949i
$267$			13.2981i			0.813832i
$268$	−1.45044	+	4.46526i	−0.0885999	+	0.272759i
$269$	8.44539	+	8.44539i	0.514925	+	0.514925i	0.916031	−	0.401107i	$-0.131374\pi$
$269$	8.44539	+	8.44539i	0.514925	+	0.514925i	−0.401107	+	0.916031i	$0.631374\pi$
$270$	12.7081	+	3.72822i	0.773389	+	0.226892i
$271$		−	4.62963i		−	0.281230i	−0.990064	−	0.140615i	$-0.955092\pi$
$271$		−	4.62963i		−	0.281230i	0.990064	−	0.140615i	$-0.0449080\pi$
$272$	6.52942	+	15.1449i	0.395904	+	0.918292i
$273$	−8.28737	+	8.28737i	−0.501575	+	0.501575i
$274$	17.6929	−	4.24847i	1.06887	−	0.256660i
$275$	−1.00094	+	3.81392i	−0.0603591	+	0.229988i
$276$	1.17651	+	2.30857i	0.0708178	+	0.138959i
$277$	3.60475			0.216588			0.108294	−	0.994119i	$-0.465461\pi$
$277$	3.60475			0.216588			0.108294	+	0.994119i	$0.465461\pi$
$278$	−2.68835	−	11.1957i	−0.161236	−	0.671475i
$279$	15.6601	−	15.6601i	0.937543	−	0.937543i
$280$	−7.37739	+	1.38790i	−0.440883	+	0.0829427i
$281$		−	5.60340i		−	0.334271i	−0.985934	−	0.167135i	$-0.946548\pi$
$281$		−	5.60340i		−	0.334271i	0.985934	−	0.167135i	$-0.0534517\pi$
$282$	−5.99354	−	24.9603i	−0.356910	−	1.48637i
$283$		−	1.56049i		−	0.0927615i	−0.998924	−	0.0463808i	$-0.985231\pi$
$283$		−	1.56049i		−	0.0927615i	0.998924	−	0.0463808i	$-0.0147688\pi$
$284$	4.38181	+	1.42333i	0.260012	+	0.0844594i
$285$	5.18552	+	19.1555i	0.307163	+	1.13467i
$286$	2.09722	−	3.42267i	0.124011	−	0.202387i
$287$	−5.69362	−	5.69362i	−0.336084	−	0.336084i
$288$	−9.80390	−	23.6549i	−0.577700	−	1.39388i
$289$	−8.14448	−	14.9220i	−0.479087	−	0.877767i
$290$	1.90233	+	3.48194i	0.111709	+	0.204466i
$291$			9.95699i			0.583689i
$292$	−4.46733	−	8.76584i	−0.261431	−	0.512982i
$293$	1.52126	+	1.52126i	0.0888731	+	0.0888731i	0.750146	−	0.661273i	$-0.229983\pi$
$293$	1.52126	+	1.52126i	0.0888731	+	0.0888731i	−0.661273	+	0.750146i	$0.729983\pi$
$294$	−11.3337	+	18.4967i	−0.660998	+	1.07875i
$295$	3.54956	+	13.1122i	0.206663	+	0.763421i
$296$	26.5117	+	2.08320i	1.54096	+	0.121084i
$297$	2.33539	−	2.33539i	0.135513	−	0.135513i
$298$	15.3297	−	25.0181i	0.888025	−	1.44926i
$299$	1.20184	+	1.20184i	0.0695040	+	0.0695040i
$300$	23.0863	+	14.8215i	1.33289	+	0.855720i
$301$	6.54674	−	6.54674i	0.377348	−	0.377348i
$302$	−5.00898	+	8.17467i	−0.288235	+	0.470400i
$303$		−	30.6670i		−	1.76177i
$304$	7.60407	−	10.4698i	0.436123	−	0.600482i
$305$	6.98852	−	12.1767i	0.400162	−	0.697234i
$306$	12.3161	+	23.3444i	0.704063	+	1.33451i
$307$	15.1392	+	15.1392i	0.864042	+	0.864042i	0.991805	−	0.127763i	$-0.0407796\pi$
$307$	15.1392	+	15.1392i	0.864042	+	0.864042i	−0.127763	+	0.991805i	$0.540780\pi$
$308$	−0.578351	+	1.78048i	−0.0329546	+	0.101452i
$309$	34.4241	+	34.4241i	1.95832	+	1.95832i
$310$	13.5776	−	7.41801i	0.771153	−	0.421314i
$311$	−13.2017	+	13.2017i	−0.748597	+	0.748597i	−0.974216	−	0.225618i	$-0.927560\pi$
$311$	−13.2017	+	13.2017i	−0.748597	+	0.748597i	0.225618	+	0.974216i	$0.427560\pi$
$312$	−18.1409	−	21.2349i	−1.02703	−	1.20219i
$313$			3.52888i			0.199464i	0.995014	+	0.0997321i	$0.0317986\pi$
$313$			3.52888i			0.199464i	−0.995014	+	0.0997321i	$0.968201\pi$
$314$	−4.83422	−	20.1323i	−0.272811	−	1.13613i
$315$	−11.5963	+	3.13921i	−0.653379	+	0.176874i
$316$	−6.21154	−	2.01768i	−0.349426	−	0.113504i
$317$			2.68127i			0.150595i	0.997161	+	0.0752975i	$0.0239907\pi$
$317$			2.68127i			0.150595i	−0.997161	+	0.0752975i	$0.976009\pi$
$318$	−8.36678	−	34.8438i	−0.469186	−	1.95394i
$319$	0.989477			0.0554001
$320$	−1.92002	−	17.7852i	−0.107332	−	0.994223i
$321$		−	11.8379i		−	0.660725i
$322$	−0.675878	−	0.414140i	−0.0376652	−	0.0230791i
$323$	−6.80704	+	11.4703i	−0.378754	+	0.638222i
$324$	1.89799	+	3.72426i	0.105444	+	0.206903i
$325$	17.4066	+	4.56828i	0.965546	+	0.253403i
$326$	−5.23339	−	3.20673i	−0.289851	−	0.177604i
$327$	−21.0311	+	21.0311i	−1.16302	+	1.16302i
$328$	14.5889	−	12.4632i	0.805538	−	0.688167i
$329$	5.55291	+	5.55291i	0.306142	+	0.306142i
$330$	6.00404	−	3.28027i	0.330511	−	0.180573i
$331$			0.0382552i			0.00210269i	0.999999	+	0.00105135i	$0.000334654\pi$
$331$			0.0382552i			0.00210269i	−0.999999	+	0.00105135i	$0.999665\pi$
$332$	8.78497	−	27.0450i	0.482138	−	1.48429i
$333$	42.5595			2.33225
$334$	−4.61797	+	7.53654i	−0.252684	+	0.412381i
$335$	−2.61285	+	4.55258i	−0.142755	+	0.248734i
$336$	10.5388	+	7.65425i	0.574941	+	0.417574i
$337$			28.9062i			1.57462i	0.616556	+	0.787311i	$0.288527\pi$
$337$			28.9062i			1.57462i	−0.616556	+	0.787311i	$0.711473\pi$
$338$	0.0549817	+	0.0336897i	0.00299061	+	0.00183248i
$339$		−	48.6390i		−	2.64171i
$340$	3.66511	+	18.0712i	0.198769	+	0.980046i
$341$		−	3.85839i		−	0.208943i
$342$	10.8194	−	17.6574i	0.585048	−	0.954800i
$343$		−	14.9449i		−	0.806947i
$344$	14.3307	+	16.7749i	0.772660	+	0.904441i
$345$	0.756967	+	2.79626i	0.0407537	+	0.150546i
$346$	−30.4387	−	18.6511i	−1.63639	−	1.00269i
$347$	10.7142			0.575168			0.287584	−	0.957755i	$-0.407148\pi$
$347$	10.7142			0.575168			0.287584	+	0.957755i	$0.407148\pi$
$348$	2.12687	−	6.54767i	0.114012	−	0.350992i
$349$			4.56718i			0.244475i	0.992501	+	0.122238i	$0.0390070\pi$
$349$			4.56718i			0.244475i	−0.992501	+	0.122238i	$0.960993\pi$
$350$	−8.39101	−	0.176204i	−0.448519	−	0.00941848i
$351$	−10.6587	−	10.6587i	−0.568917	−	0.568917i
$352$	−4.12185	−	1.70633i	−0.219696	−	0.0909476i
$353$	−4.41530	+	4.41530i	−0.235003	+	0.235003i	−0.814777	−	0.579774i	$-0.803141\pi$
$353$	−4.41530	+	4.41530i	−0.235003	+	0.235003i	0.579774	+	0.814777i	$0.303141\pi$
$354$	12.3145	−	20.0973i	0.654507	−	1.06816i
$355$	4.46749	+	2.56401i	0.237110	+	0.136084i
$356$	8.63744	−	4.40190i	0.457783	−	0.233300i
$357$	−11.5459	−	6.85196i	−0.611076	−	0.362644i
$358$	14.4341	−	23.5565i	0.762865	−	1.24500i
$359$		−	28.8563i		−	1.52298i	−0.648178	−	0.761489i	$-0.724469\pi$
$359$		−	28.8563i		−	1.52298i	0.648178	−	0.761489i	$-0.275531\pi$
$360$	−5.29297	−	28.1349i	−0.278964	−	1.48284i
$361$	−8.53515			−0.449218
$362$	33.2614	−	7.98681i	1.74818	−	0.419777i
$363$			28.4718i			1.49438i
$364$	8.12609	+	2.63958i	0.425923	+	0.138352i
$365$	−2.87427	−	10.6177i	−0.150446	−	0.555754i
$366$	−23.6870	+	5.68779i	−1.23814	+	0.297305i
$367$		−	13.6218i		−	0.711050i	−0.934667	−	0.355525i	$-0.884302\pi$
$367$		−	13.6218i		−	0.711050i	0.934667	−	0.355525i	$-0.115698\pi$
$368$	1.11002	−	1.52835i	0.0578639	−	0.0796705i
$369$	21.7135	−	21.7135i	1.13036	−	1.13036i
$370$	28.5299	+	8.36994i	1.48320	+	0.435132i
$371$	7.75168	+	7.75168i	0.402447	+	0.402447i
$372$	−25.5321	−	8.29355i	−1.32378	−	0.430001i
$373$	−18.8307	−	18.8307i	−0.975017	−	0.975017i	0.0246788	−	0.999695i	$-0.492144\pi$
$373$	−18.8307	−	18.8307i	−0.975017	−	0.975017i	−0.999695	+	0.0246788i	$0.992144\pi$
$374$	4.39309	+	1.35861i	0.227161	+	0.0702518i
$375$	21.8556	+	21.5210i	1.12862	+	1.11134i
$376$	−14.2284	+	12.1552i	−0.733771	+	0.626857i
$377$		−	4.51595i		−	0.232583i
$378$	5.99412	+	3.67286i	0.308304	+	0.188912i
$379$	−4.91018	+	4.91018i	−0.252219	+	0.252219i	−0.821880	−	0.569661i	$-0.807075\pi$
$379$	−4.91018	+	4.91018i	−0.252219	+	0.252219i	0.569661	+	0.821880i	$0.307075\pi$
$380$	10.7254	−	9.70888i	0.550203	−	0.498055i
$381$	37.1649	+	37.1649i	1.90401	+	1.90401i
$382$	−1.94084	−	1.18924i	−0.0993019	−	0.0608466i
$383$	−3.89730	+	3.89730i	−0.199143	+	0.199143i	−0.799632	−	0.600490i	$-0.794972\pi$
$383$	−3.89730	+	3.89730i	−0.199143	+	0.199143i	0.600490	+	0.799632i	$0.294972\pi$
$384$	−20.1512	+	23.6078i	−1.02833	+	1.20473i
$385$	−1.04185	+	1.81530i	−0.0530976	+	0.0925163i
$386$	14.5876	+	8.93845i	0.742488	+	0.454955i
$387$	24.9670	+	24.9670i	1.26915	+	1.26915i
$388$	6.46729	−	3.29592i	0.328327	−	0.167325i
$389$			0.662332i			0.0335815i	0.999859	+	0.0167908i	$0.00534492\pi$
$389$			0.662332i			0.0335815i	−0.999859	+	0.0167908i	$0.994655\pi$
$390$	−14.9711	−	27.4023i	−0.758090	−	1.38757i
$391$	−0.993673	+	1.67440i	−0.0502522	+	0.0846778i
$392$	15.7657	+	1.23882i	0.796288	+	0.0625697i
$393$	−9.95003	−	9.95003i	−0.501913	−	0.501913i
$394$	32.8867	+	20.1511i	1.65681	+	1.01520i
$395$	−6.33300	−	3.63468i	−0.318648	−	0.182881i
$396$	−6.79016	−	2.20564i	−0.341218	−	0.110837i
$397$			20.6467i			1.03623i	0.855312	+	0.518114i	$0.173366\pi$
$397$			20.6467i			1.03623i	−0.855312	+	0.518114i	$0.826634\pi$
$398$	−28.7612	+	6.90620i	−1.44167	+	0.346177i
$399$			10.5339i			0.527355i
$400$	1.98496	−	19.9013i	0.0992480	−	0.995063i
$401$	8.23865	−	8.23865i	0.411418	−	0.411418i	−0.470814	−	0.882232i	$-0.656040\pi$
$401$	8.23865	−	8.23865i	0.411418	−	0.411418i	0.882232	+	0.470814i	$0.156040\pi$
$402$	8.85603	−	2.12653i	0.441699	−	0.106062i
$403$	−17.6096			−0.877197
$404$	−19.9189	+	10.1513i	−0.991003	+	0.505045i
$405$	1.22117	+	4.51102i	0.0606802	+	0.224155i
$406$	0.491746	+	2.04790i	0.0244049	+	0.101635i
$407$	5.24299	−	5.24299i	0.259886	−	0.259886i
$408$	18.4332	−	26.1501i	0.912579	−	1.29462i
$409$		−	17.7959i		−	0.879948i	−0.898010	−	0.439974i	$-0.854988\pi$
$409$		−	17.7959i		−	0.879948i	0.898010	−	0.439974i	$-0.145012\pi$
$410$	18.8260	−	10.2855i	0.929751	−	0.507964i
$411$	−24.9598	−	24.9598i	−1.23117	−	1.23117i
$412$	10.9643	−	33.7542i	0.540173	−	1.66295i
$413$			7.21061i			0.354811i
$414$	1.57939	−	2.57757i	0.0776228	−	0.126681i
$415$	15.8254	−	27.5738i	0.776836	−	1.35355i
$416$	−7.78765	+	18.8121i	−0.381821	+	0.922337i
$417$	−15.7940	+	15.7940i	−0.773437	+	0.773437i
$418$	−0.842377	−	3.50811i	−0.0412020	−	0.171587i
$419$	20.5726	+	20.5726i	1.00504	+	1.00504i	0.999987	+	0.00504921i	$0.00160722\pi$
$419$	20.5726	+	20.5726i	1.00504	+	1.00504i	0.00504921	+	0.999987i	$0.498393\pi$
$420$	9.77295	+	10.7962i	0.476871	+	0.526801i
$421$		−	10.0185i		−	0.488270i	−0.969741	−	0.244135i	$-0.921496\pi$
$421$		−	10.0185i		−	0.488270i	0.969741	−	0.244135i	$-0.0785039\pi$
$422$	5.63278	+	23.4579i	0.274200	+	1.14191i
$423$	−21.1769	+	21.1769i	−1.02966	+	1.02966i
$424$	−19.8623	+	16.9683i	−0.964599	+	0.824053i
$425$	−0.141206	+	20.6150i	−0.00684952	+	0.999977i
$426$	−2.08679	−	8.69051i	−0.101105	−	0.421057i
$427$	5.26963	−	5.26963i	0.255015	−	0.255015i
$428$	−7.68897	+	3.91853i	−0.371660	+	0.189409i
$429$	−7.78703			−0.375961
$430$	11.8266	+	21.6469i	0.570331	+	1.04391i
$431$	−2.55950	−	2.55950i	−0.123287	−	0.123287i	0.642771	−	0.766058i	$-0.277785\pi$
$431$	−2.55950	−	2.55950i	−0.123287	−	0.123287i	−0.766058	+	0.642771i	$0.777785\pi$
$432$	−9.84438	+	13.5543i	−0.473638	+	0.652134i
$433$	24.3763	+	24.3763i	1.17145	+	1.17145i	0.981864	+	0.189585i	$0.0607143\pi$
$433$	24.3763	+	24.3763i	1.17145	+	1.17145i	0.189585	+	0.981864i	$0.439286\pi$
$434$	7.98562	−	1.91753i	0.383322	−	0.0920442i
$435$	3.83137	−	6.67570i	0.183700	−	0.320075i
$436$	20.6218	+	6.69854i	0.987605	+	0.320802i
$437$	1.52763			0.0730765
$438$	−9.97171	+	16.2739i	−0.476467	+	0.777595i
$439$	16.6455	+	16.6455i	0.794446	+	0.794446i	0.982214	−	0.187767i	$-0.0601251\pi$
$439$	16.6455	+	16.6455i	0.794446	+	0.794446i	−0.187767	+	0.982214i	$0.560125\pi$
$440$	−4.11804	−	2.81394i	−0.196320	−	0.134149i
$441$	25.3088			1.20518
$442$	6.20065	−	20.0500i	0.294935	−	0.953680i
$443$	−23.3454	+	23.3454i	−1.10918	+	1.10918i	−0.115917	+	0.993259i	$0.536981\pi$
$443$	−23.3454	+	23.3454i	−1.10918	+	1.10918i	−0.993259	+	0.115917i	$0.963019\pi$
$444$	−23.4247	−	45.9642i	−1.11169	−	2.18137i
$445$	10.4621	−	2.83217i	0.495953	−	0.134258i
$446$	−0.919672	−	3.83001i	−0.0435477	−	0.181356i
$447$	−56.9194			−2.69220
$448$	1.48309	−	9.37890i	0.0700692	−	0.443112i
$449$	12.7750	+	12.7750i	0.602891	+	0.602891i	0.941079	−	0.338188i	$-0.109814\pi$
$449$	12.7750	+	12.7750i	0.602891	+	0.602891i	−0.338188	+	0.941079i	$0.609814\pi$
$450$	0.671981	−	32.0005i	0.0316775	−	1.50852i
$451$		−	5.34987i		−	0.251916i
$452$	−31.5922	+	16.1003i	−1.48597	+	0.757295i
$453$	18.5984			0.873831
$454$	−10.1804	+	16.6144i	−0.477789	+	0.779754i
$455$	8.28500	+	4.75498i	0.388407	+	0.222917i
$456$	−25.0249	−	1.96638i	−1.17190	−	0.0920841i
$457$	−18.4516	+	18.4516i	−0.863128	+	0.863128i	−0.991700	−	0.128573i	$-0.958960\pi$
$457$	−18.4516	+	18.4516i	−0.863128	+	0.863128i	0.128573	+	0.991700i	$0.458960\pi$
$458$	21.6821	+	13.2856i	1.01314	+	0.620795i
$459$	8.81253	−	14.8496i	0.411334	−	0.693120i
$460$	1.56567	−	1.41728i	0.0729996	−	0.0660808i
$461$	19.1015			0.889644			0.444822	−	0.895619i	$-0.353267\pi$
$461$	19.1015			0.889644			0.444822	+	0.895619i	$0.353267\pi$
$462$	3.53126	−	0.847936i	0.164289	−	0.0394496i
$463$	24.7437	+	24.7437i	1.14994	+	1.14994i	0.986564	+	0.163375i	$0.0522380\pi$
$463$	24.7437	+	24.7437i	1.14994	+	1.14994i	0.163375	+	0.986564i	$0.447762\pi$
$464$	−4.95689	+	0.785935i	−0.230118	+	0.0364861i
$465$	−26.0314	−	14.9401i	−1.20718	−	0.692831i
$466$	−10.8278	+	17.6711i	−0.501590	+	0.818596i
$467$	21.9192	−	21.9192i	1.01430	−	1.01430i	0.0144021	−	0.999896i	$-0.495415\pi$
$467$	21.9192	−	21.9192i	1.01430	−	1.01430i	0.999896	−	0.0144021i	$-0.00458451\pi$
$468$	−10.0665	+	30.9902i	−0.465323	+	1.43252i
$469$	−1.97019	+	1.97019i	−0.0909751	+	0.0909751i
$470$	−18.3608	+	10.0313i	−0.846919	+	0.462708i
$471$	−28.4010	+	28.4010i	−1.30865	+	1.30865i
$472$	−17.1299	−	1.34601i	−0.788469	−	0.0619553i
$473$	6.15148			0.282846
$474$	2.95818	+	12.3195i	0.135874	+	0.565851i
$475$	13.9659	−	8.15928i	0.640801	−	0.374374i
$476$	−0.628613	+	9.76747i	−0.0288124	+	0.447691i
$477$	−29.5623	+	29.5623i	−1.35356	+	1.35356i
$478$	−18.3845	+	30.0036i	−0.840887	+	1.37233i
$479$	−29.4006	−	29.4006i	−1.34335	−	1.34335i	−0.892703	−	0.450645i	$-0.851194\pi$
$479$	−29.4006	−	29.4006i	−1.34335	−	1.34335i	−0.450645	−	0.892703i	$-0.648806\pi$
$480$	−27.4724	+	21.2018i	−1.25394	+	0.967726i
$481$	−23.9289	−	23.9289i	−1.09106	−	1.09106i
$482$	3.07088	−	0.737388i	0.139875	−	0.0335871i
$483$			1.53771i			0.0699683i
$484$	18.4931	−	9.42464i	0.840596	−	0.428393i
$485$	7.83354	−	2.12059i	0.355703	−	0.0962912i
$486$	13.5198	−	22.0644i	0.613273	−	1.00086i
$487$		−	0.342177i		−	0.0155055i	−0.999970	−	0.00775277i	$-0.997532\pi$
$487$		−	0.342177i		−	0.0155055i	0.999970	−	0.00775277i	$-0.00246781\pi$
$488$	11.5351	+	13.5025i	0.522171	+	0.611230i
$489$			11.9066i			0.538437i
$490$	16.9659	+	4.97734i	0.766440	+	0.224853i
$491$		−	21.6329i		−	0.976278i	−0.872766	−	0.488139i	$-0.837676\pi$
$491$		−	21.6329i		−	0.976278i	0.872766	−	0.488139i	$-0.162324\pi$
$492$	−35.4017	−	11.4995i	−1.59603	−	0.518436i
$493$	5.01269	−	1.27892i	0.225760	−	0.0575997i
$494$	−16.0110	+	3.84459i	−0.720367	+	0.172976i
$495$	−6.92294	−	3.97326i	−0.311163	−	0.178585i
$496$	3.06469	+	19.3290i	0.137609	+	0.867898i
$497$	1.93337	+	1.93337i	0.0867236	+	0.0867236i
$498$	−53.6387	+	12.8799i	−2.40361	+	0.577161i
$499$	−21.0190	−	21.0190i	−0.940939	−	0.940939i	0.0574114	−	0.998351i	$-0.481715\pi$
$499$	−21.0190	−	21.0190i	−0.940939	−	0.940939i	−0.998351	+	0.0574114i	$0.981715\pi$
$500$	6.74382	−	21.3195i	0.301593	−	0.953437i
$501$	17.1466			0.766053
$502$	20.1865	−	32.9445i	0.900969	−	1.47038i
$503$	0.704050			0.0313920			0.0156960	−	0.999877i	$-0.495004\pi$
$503$	0.704050			0.0313920			0.0156960	+	0.999877i	$0.495004\pi$
$504$	1.19041	−	15.1496i	0.0530249	−	0.674816i
$505$	−24.1269	+	6.53132i	−1.07363	+	0.290640i
$506$	−0.122968	−	0.512105i	−0.00546659	−	0.0227658i
$507$		−	0.125091i		−	0.00555547i
$508$	11.8373	−	36.4416i	0.525194	−	1.61684i
$509$	8.81873			0.390883			0.195442	−	0.980715i	$-0.437386\pi$
$509$	8.81873			0.390883			0.195442	+	0.980715i	$0.437386\pi$
$510$	26.1766	−	24.3782i	1.15912	−	1.07948i
$511$		−	5.83883i		−	0.258295i
$512$	22.0042	+	5.27407i	0.972457	+	0.233083i
$513$	−13.5480			−0.598159
$514$	−2.62993	−	10.9524i	−0.116001	−	0.483092i
$515$	19.7513	−	34.4143i	0.870345	−	1.51647i
$516$	13.2225	−	40.7062i	0.582090	−	1.79199i
$517$			5.21765i			0.229472i
$518$	13.4569	+	8.24566i	0.591264	+	0.362293i
$519$			69.2520i			3.03982i
$520$	−12.8428	+	18.7947i	−0.563193	+	0.824201i
$521$	−21.2780	+	21.2780i	−0.932207	+	0.932207i	−0.997844	−	0.0656368i	$-0.979092\pi$
$521$	−21.2780	+	21.2780i	−0.932207	+	0.932207i	0.0656368	+	0.997844i	$0.479092\pi$
$522$	−7.80998	+	1.87535i	−0.341834	+	0.0820819i
$523$	16.8090	−	16.8090i	0.735006	−	0.735006i	−0.236601	−	0.971607i	$-0.576033\pi$
$523$	16.8090	−	16.8090i	0.735006	−	0.735006i	0.971607	+	0.236601i	$0.0760333\pi$
$524$	−3.16915	+	9.75640i	−0.138445	+	0.426210i
$525$	8.21313	+	14.0581i	0.358450	+	0.613546i
$526$	−4.07723	−	16.9798i	−0.177776	−	0.740353i
$527$	−4.98706	−	19.5466i	−0.217240	−	0.851464i
$528$	1.35522	+	8.54735i	0.0589783	+	0.371976i
$529$	−22.7770			−0.990304
$530$	−25.6310	+	14.0033i	−1.11334	+	0.608266i
$531$	−27.4988			−1.19335
$532$	6.84202	−	3.48690i	0.296639	−	0.151176i
$533$	−24.4167			−1.05760
$534$	−16.0355	−	9.82565i	−0.693923	−	0.425197i
$535$	−9.31330	+	2.52117i	−0.402649	+	0.109000i
$536$	−4.31272	−	5.04828i	−0.186281	−	0.218052i
$537$	−53.5940			−2.31275
$538$	−16.4239	+	3.94376i	−0.708086	+	0.170027i
$539$	3.11785	−	3.11785i	0.134295	−	0.134295i
$540$	−13.8853	+	12.5693i	−0.597530	+	0.540897i
$541$	18.5242	−	18.5242i	0.796419	−	0.796419i	−0.186110	−	0.982529i	$-0.559588\pi$
$541$	18.5242	−	18.5242i	0.796419	−	0.796419i	0.982529	+	0.186110i	$0.0595882\pi$
$542$	5.58262	+	3.42072i	0.239794	+	0.146932i
$543$	−46.9225	−	46.9225i	−2.01364	−	2.01364i
$544$	−23.0868	−	3.31667i	−0.989838	−	0.142201i
$545$	21.0251	+	12.0668i	0.900614	+	0.516887i
$546$	−3.86996	−	16.1166i	−0.165619	−	0.689728i
$547$			12.4469i			0.532190i	0.963947	+	0.266095i	$0.0857335\pi$
$547$			12.4469i			0.532190i	−0.963947	+	0.266095i	$0.914266\pi$
$548$	−7.94986	+	24.4740i	−0.339601	+	1.04548i
$549$	20.0966	+	20.0966i	0.857702	+	0.857702i
$550$	−3.85942	−	4.02499i	−0.164566	−	0.171626i
$551$	−2.87007	−	2.87007i	−0.122269	−	0.122269i
$552$	−3.65307	−	0.287046i	−0.155485	−	0.0122175i
$553$	−2.74070	−	2.74070i	−0.116546	−	0.116546i
$554$	−2.66346	+	4.34677i	−0.113160	+	0.184677i
$555$	−15.0714	−	55.6744i	−0.639747	−	2.36325i
$556$	15.4867	+	5.03051i	0.656781	+	0.213341i
$557$	10.8212	−	10.8212i	0.458508	−	0.458508i	−0.439658	−	0.898165i	$-0.644900\pi$
$557$	10.8212	−	10.8212i	0.458508	−	0.458508i	0.898165	+	0.439658i	$0.144900\pi$
$558$	7.31279	+	30.4544i	0.309575	+	1.28924i
$559$		−	28.0753i		−	1.18746i
$560$	3.77738	−	9.92148i	0.159623	−	0.419259i
$561$	−2.20529	−	8.64357i	−0.0931075	−	0.364932i
$562$	6.75683	+	4.14021i	0.285020	+	0.174644i
$563$	30.1456	+	30.1456i	1.27048	+	1.27048i	0.945834	+	0.324651i	$0.105247\pi$
$563$	30.1456	+	30.1456i	1.27048	+	1.27048i	0.324651	+	0.945834i	$0.394753\pi$
$564$	34.5268	+	11.2153i	1.45384	+	0.472248i
$565$	−38.2662	+	10.3589i	−1.60987	+	0.435803i
$566$	1.88171	+	1.15301i	0.0790942	+	0.0484645i
$567$			2.48069i			0.104179i
$568$	−4.95393	+	4.23212i	−0.207862	+	0.177576i
$569$	−16.7390			−0.701736			−0.350868	−	0.936425i	$-0.614113\pi$
$569$	−16.7390			−0.701736			−0.350868	+	0.936425i	$0.614113\pi$
$570$	−26.9300	−	7.90055i	−1.12797	−	0.330918i
$571$	−19.8158	+	19.8158i	−0.829266	+	0.829266i	−0.987415	−	0.158150i	$-0.949447\pi$
$571$	−19.8158	+	19.8158i	−0.829266	+	0.829266i	0.158150	+	0.987415i	$0.449447\pi$
$572$	2.57763	+	5.05785i	0.107776	+	0.211479i
$573$			4.41566i			0.184467i
$574$	11.0725	−	2.65876i	0.462157	−	0.110974i
$575$	2.03871	−	1.19107i	0.0850200	−	0.0496710i
$576$	35.7680	+	5.65598i	1.49033	+	0.235666i
$577$	13.8155	+	13.8155i	0.575148	+	0.575148i	0.933563	−	0.358414i	$-0.116682\pi$
$577$	13.8155	+	13.8155i	0.575148	+	0.575148i	−0.358414	+	0.933563i	$0.616682\pi$
$578$	24.0114	+	1.20453i	0.998744	+	0.0501018i
$579$		−	33.1886i		−	1.37927i
$580$	−5.60427	−	0.278794i	−0.232705	−	0.0115763i
$581$	11.9330	−	11.9330i	0.495063	−	0.495063i
$582$	−12.0066	−	7.35696i	−0.497689	−	0.304956i
$583$			7.28367i			0.301659i
$584$	13.8710	+	1.08994i	0.573988	+	0.0451021i
$585$	−18.1339	+	31.5962i	−0.749744	+	1.30634i
$586$	−2.95843	+	0.710386i	−0.122212	+	0.0293458i
$587$	−23.4199	+	23.4199i	−0.966641	+	0.966641i	−0.999461	−	0.0328203i	$-0.989551\pi$
$587$	−23.4199	+	23.4199i	−0.966641	+	0.966641i	0.0328203	+	0.999461i	$0.489551\pi$
$588$	−13.9300	−	27.3335i	−0.574462	−	1.12721i
$589$	−11.1916	+	11.1916i	−0.461142	+	0.461142i
$590$	−18.4340	−	5.40804i	−0.758914	−	0.222645i
$591$		−	74.8215i		−	3.07774i
$592$	−22.1009	+	30.4298i	−0.908340	+	1.25066i
$593$	15.4067	+	15.4067i	0.632677	+	0.632677i	0.948739	−	0.316062i	$-0.102361\pi$
$593$	15.4067	+	15.4067i	0.632677	+	0.632677i	−0.316062	+	0.948739i	$0.602361\pi$
$594$	1.09056	+	4.54167i	0.0447461	+	0.186347i
$595$	−2.93170	+	10.5429i	−0.120188	+	0.432218i
$596$	18.8413	+	36.9705i	0.771768	+	1.51437i
$597$	40.5739	+	40.5739i	1.66058	+	1.66058i
$598$	−2.33724	+	0.561223i	−0.0955767	+	0.0229501i
$599$	−19.9151			−0.813710			−0.406855	−	0.913493i	$-0.633375\pi$
$599$	−19.9151			−0.813710			−0.406855	+	0.913493i	$0.633375\pi$
$600$	−34.9303	+	16.8873i	−1.42603	+	0.689422i
$601$	24.0776	−	24.0776i	0.982144	−	0.982144i	−0.0176995	−	0.999843i	$-0.505634\pi$
$601$	24.0776	−	24.0776i	0.982144	−	0.982144i	0.999843	+	0.0176995i	$0.00563422\pi$
$602$	3.05714	+	12.7316i	0.124600	+	0.518900i
$603$	−7.51365	−	7.51365i	−0.305980	−	0.305980i
$604$	−6.15639	−	12.0801i	−0.250500	−	0.491533i
$605$	22.3999	−	6.06380i	0.910684	−	0.246528i
$606$	36.9797	+	22.6591i	1.50220	+	0.920461i
$607$	−10.8898			−0.442002			−0.221001	−	0.975274i	$-0.570932\pi$
$607$	−10.8898			−0.442002			−0.221001	+	0.975274i	$0.570932\pi$
$608$	7.00645	+	16.9052i	0.284149	+	0.685595i
$609$	2.88901	−	2.88901i	0.117068	−	0.117068i
$610$	9.51955	+	17.4241i	0.385435	+	0.705482i
$611$	23.8133			0.963382
$612$	−37.2498	−	2.39732i	−1.50573	−	0.0969058i
$613$	−14.4866	−	14.4866i	−0.585109	−	0.585109i	0.351193	−	0.936303i	$-0.385776\pi$
$613$	−14.4866	−	14.4866i	−0.585109	−	0.585109i	−0.936303	+	0.351193i	$0.885776\pi$
$614$	−29.4416	+	7.06959i	−1.18817	+	0.285305i
$615$	−36.0940	−	20.7153i	−1.45545	−	0.835322i
$616$	−1.71966	−	2.01296i	−0.0692871	−	0.0811044i
$617$		−	21.9850i		−	0.885083i	−0.896748	−	0.442542i	$-0.854077\pi$
$617$		−	21.9850i		−	0.885083i	0.896748	−	0.442542i	$-0.145923\pi$
$618$	−66.9453	+	16.0751i	−2.69294	+	0.646634i
$619$	23.6274	+	23.6274i	0.949666	+	0.949666i	0.998793	−	0.0491265i	$-0.0156437\pi$
$619$	23.6274	+	23.6274i	0.949666	+	0.949666i	−0.0491265	+	0.998793i	$0.515644\pi$
$620$	−1.08714	+	21.8534i	−0.0436605	+	0.877654i
$621$	−1.97770			−0.0793623
$622$	−6.16479	−	25.6735i	−0.247186	−	1.02941i
$623$	5.75331			0.230501
$624$	39.0099	−	6.18519i	1.56165	−	0.247606i
$625$	12.2767	−	21.7781i	0.491067	−	0.871122i
$626$	−4.25529	−	2.60740i	−0.170076	−	0.104213i
$627$	−4.94897	+	4.94897i	−0.197643	+	0.197643i
$628$	27.8483	+	9.04593i	1.11127	+	0.360972i
$629$	19.7843	−	33.3377i	0.788853	−	1.32926i
$630$	4.78283	−	16.3029i	0.190553	−	0.649521i
$631$	13.8266			0.550428			0.275214	−	0.961383i	$-0.411251\pi$
$631$	13.8266			0.550428			0.275214	+	0.961383i	$0.411251\pi$
$632$	7.02256	−	5.99934i	0.279343	−	0.238641i
$633$	33.0926	−	33.0926i	1.31531	−	1.31531i
$634$	−3.23320	−	1.98112i	−0.128407	−	0.0786804i
$635$	21.3238	−	37.1542i	0.846209	−	1.47442i
$636$	48.1983	+	15.6562i	1.91119	+	0.620807i
$637$	−14.2298	−	14.2298i	−0.563805	−	0.563805i
$638$	−0.731099	+	1.19316i	−0.0289445	+	0.0472375i
$639$	−7.37322	+	7.37322i	−0.291680	+	0.291680i
$640$	22.8649	+	10.8258i	0.903813	+	0.427927i
$641$	1.51664	+	1.51664i	0.0599038	+	0.0599038i	0.736424	−	0.676520i	$-0.236513\pi$
$641$	1.51664	+	1.51664i	0.0599038	+	0.0599038i	−0.676520	+	0.736424i	$0.736513\pi$
$642$	14.2746	+	8.74670i	0.563375	+	0.345205i
$643$	−29.8655			−1.17778			−0.588890	−	0.808213i	$-0.700435\pi$
$643$	−29.8655			−1.17778			−0.588890	+	0.808213i	$0.700435\pi$
$644$	0.998779	−	0.509007i	0.0393574	−	0.0200577i
$645$	23.8192	−	41.5022i	0.937882	−	1.63415i
$646$	−8.80180	−	16.6833i	−0.346302	−	0.656397i
$647$	2.34060	−	2.34060i	0.0920183	−	0.0920183i	−0.659599	−	0.751618i	$-0.729274\pi$
$647$	2.34060	−	2.34060i	0.0920183	−	0.0920183i	0.751618	+	0.659599i	$0.229274\pi$
$648$	−5.89326	−	0.463073i	−0.231509	−	0.0181912i
$649$	−3.38764	+	3.38764i	−0.132976	+	0.132976i
$650$	−18.3700	+	17.6143i	−0.720529	+	0.690891i
$651$	−11.2655	−	11.2655i	−0.441528	−	0.441528i
$652$	7.73364	−	3.94129i	0.302873	−	0.154353i
$653$	−31.4935			−1.23243			−0.616217	−	0.787576i	$-0.711336\pi$
$653$	−31.4935			−1.23243			−0.616217	+	0.787576i	$0.711336\pi$
$654$	−9.82091	−	40.8996i	−0.384028	−	1.59930i
$655$	−5.70895	+	9.94718i	−0.223067	+	0.388668i
$656$	4.24937	+	26.8007i	0.165910	+	1.04639i
$657$	22.2673			0.868731
$658$	−10.7989	+	2.59305i	−0.420983	+	0.101088i
$659$			4.23508i			0.164975i	0.996592	+	0.0824876i	$0.0262865\pi$
$659$			4.23508i			0.164975i	−0.996592	+	0.0824876i	$0.973714\pi$
$660$	−0.480736	+	9.66365i	−0.0187126	+	0.376157i
$661$	9.54965			0.371438			0.185719	−	0.982603i	$-0.440539\pi$
$661$	9.54965			0.371438			0.185719	+	0.982603i	$0.440539\pi$
$662$	−0.0461298	−	0.0282658i	−0.00179289	−	0.00109858i
$663$	−39.4491	+	10.0649i	−1.53208	+	0.390889i
$664$	26.1211	+	30.5762i	1.01369	+	1.18658i
$665$	8.28743	−	2.24346i	0.321373	−	0.0869978i
$666$	−31.4461	+	51.3202i	−1.21851	+	1.98862i
$667$	−0.418965	−	0.418965i	−0.0162224	−	0.0162224i
$668$	−5.67580	−	11.1371i	−0.219603	−	0.430908i
$669$	−5.40307	+	5.40307i	−0.208895	+	0.208895i
$670$	−3.55914	−	6.51447i	−0.137502	−	0.251676i
$671$	4.95148			0.191150
$672$	−17.0167	+	7.05269i	−0.656435	+	0.272063i
$673$			23.5472i			0.907680i	0.891083	+	0.453840i	$0.149946\pi$
$673$			23.5472i			0.907680i	−0.891083	+	0.453840i	$0.850054\pi$
$674$	−34.8564	−	21.3581i	−1.34262	−	0.822682i
$675$	−18.0806	+	10.5632i	−0.695921	+	0.406576i
$676$	−0.0812492	+	0.0414070i	−0.00312497	+	0.00159258i
$677$	−5.28053			−0.202947			−0.101474	−	0.994838i	$-0.532356\pi$
$677$	−5.28053			−0.202947			−0.101474	+	0.994838i	$0.532356\pi$
$678$	58.6512	+	35.9381i	2.25248	+	1.38020i
$679$	4.30780			0.165318
$680$	−24.4991	−	8.93276i	−0.939498	−	0.342556i
$681$	37.8000			1.44850
$682$	4.65262	+	2.85087i	0.178158	+	0.109165i
$683$	36.7608			1.40661			0.703306	−	0.710887i	$-0.251706\pi$
$683$	36.7608			1.40661			0.703306	+	0.710887i	$0.251706\pi$
$684$	13.2978	+	26.0931i	0.508456	+	0.997696i
$685$	−14.3210	+	24.9526i	−0.547177	+	0.953391i
$686$	18.0212	+	11.0424i	0.688053	+	0.421600i
$687$		−	49.3296i		−	1.88204i
$688$	−30.8165	+	4.88609i	−1.17487	+	0.186280i
$689$	33.2425			1.26644
$690$	−3.93116	−	1.15330i	−0.149657	−	0.0439054i
$691$	−2.78868	+	2.78868i	−0.106086	+	0.106086i	−0.758158	−	0.652071i	$-0.773900\pi$
$691$	−2.78868	+	2.78868i	−0.106086	+	0.106086i	0.652071	+	0.758158i	$0.273900\pi$
$692$	44.9808	−	22.9235i	1.70991	−	0.871422i
$693$	−2.99600	−	2.99600i	−0.113809	−	0.113809i
$694$	−7.91645	+	12.9197i	−0.300504	+	0.490424i
$695$	15.7895	+	9.06202i	0.598930	+	0.343742i
$696$	6.32399	+	7.40258i	0.239710	+	0.280594i
$697$	−6.91483	−	27.1025i	−0.261918	−	1.02658i
$698$	−5.50731	−	3.37457i	−0.208455	−	0.127729i
$699$	40.2039			1.52065
$700$	6.41238	−	9.98808i	0.242365	−	0.377514i
$701$		−	4.28238i		−	0.161743i	−0.996725	−	0.0808717i	$-0.974230\pi$
$701$		−	4.28238i		−	0.161743i	0.996725	−	0.0808717i	$-0.0257704\pi$
$702$	20.7281	−	4.97728i	0.782332	−	0.187855i
$703$	−30.4156			−1.14714
$704$	5.10310	−	3.70956i	0.192330	−	0.139809i
$705$	35.2019	+	20.2033i	1.32578	+	0.760902i
$706$	−2.06182	−	8.58653i	−0.0775976	−	0.323158i
$707$	−13.2678			−0.498986
$708$	15.1353	+	29.6987i	0.568821	+	1.11615i
$709$	−28.4197	−	28.4197i	−1.06733	−	1.06733i	−0.997564	−	0.0697621i	$-0.977776\pi$
$709$	−28.4197	−	28.4197i	−1.06733	−	1.06733i	−0.0697621	−	0.997564i	$-0.522224\pi$
$710$	−6.39272	+	3.49262i	−0.239915	+	0.131076i
$711$	10.4521	−	10.4521i	0.391984	−	0.391984i
$712$	−1.07398	+	13.6679i	−0.0402490	+	0.512225i
$713$	−1.63372	+	1.63372i	−0.0611833	+	0.0611833i
$714$	16.7934	−	8.85989i	0.628478	−	0.331573i
$715$	1.65845	+	6.12635i	0.0620223	+	0.229112i
$716$	17.7405	+	34.8106i	0.662993	+	1.30093i
$717$	68.2620			2.54929
$718$	34.7963	+	21.3212i	1.29859	+	0.795700i
$719$	−22.7796	−	22.7796i	−0.849535	−	0.849535i	0.140540	−	0.990075i	$-0.455116\pi$
$719$	−22.7796	−	22.7796i	−0.849535	−	0.849535i	−0.990075	+	0.140540i	$0.955116\pi$
$720$	37.8371	+	14.4056i	1.41011	+	0.536866i
$721$	14.8933	−	14.8933i	0.554654	−	0.554654i
$722$	6.30640	−	10.2921i	0.234700	−	0.383031i
$723$	−4.33215	−	4.33215i	−0.161115	−	0.161115i
$724$	−14.9451	+	46.0094i	−0.555432	+	1.70992i
$725$	−6.06802	−	1.59252i	−0.225360	−	0.0591447i
$726$	−34.3326	−	21.0371i	−1.27420	−	0.780760i
$727$	36.7379	−	36.7379i	1.36253	−	1.36253i	0.491856	−	0.870677i	$-0.336319\pi$
$727$	36.7379	−	36.7379i	1.36253	−	1.36253i	0.870677	−	0.491856i	$-0.163681\pi$
$728$	−9.18710	+	7.84850i	−0.340496	+	0.290885i
$729$	−43.9294			−1.62702
$730$	14.9270	+	4.37919i	0.552473	+	0.162081i
$731$	31.1634	−	7.95093i	1.15262	−	0.294076i
$732$	10.6431	−	32.7655i	0.393382	−	1.21105i
$733$	10.0360	−	10.0360i	0.370689	−	0.370689i	−0.497039	−	0.867728i	$-0.665579\pi$
$733$	10.0360	−	10.0360i	0.370689	−	0.370689i	0.867728	+	0.497039i	$0.165579\pi$
$734$	16.4257	+	10.0648i	0.606285	+	0.371497i
$735$	−8.96252	−	33.1078i	−0.330588	−	1.22120i
$736$	1.02278	+	2.46777i	0.0377003	+	0.0909632i
$737$	−1.85124			−0.0681915
$738$	10.1396	+	42.2268i	0.373244	+	1.55439i
$739$	−32.6464			−1.20092			−0.600459	−	0.799656i	$-0.705015\pi$
$739$	−32.6464			−1.20092			−0.600459	+	0.799656i	$0.705015\pi$
$740$	−31.1729	+	28.2184i	−1.14594	+	1.03733i
$741$	22.5870	+	22.5870i	0.829754	+	0.829754i
$742$	−15.0748	+	3.61981i	−0.553415	+	0.132887i
$743$		−	2.05470i		−	0.0753796i	−0.999289	−	0.0376898i	$-0.988000\pi$
$743$		−	2.05470i		−	0.0753796i	0.999289	−	0.0376898i	$-0.0119999\pi$
$744$	28.8658	−	24.6599i	1.05827	−	0.904076i
$745$	12.1224	+	44.7807i	0.444132	+	1.64064i
$746$	36.6204	−	8.79339i	1.34077	−	0.321949i
$747$	45.5083	+	45.5083i	1.66506	+	1.66506i
$748$	−4.88421	+	4.29355i	−0.178584	+	0.156988i
$749$	−5.12154			−0.187137
$750$	−42.0995	+	10.4532i	−1.53726	+	0.381695i
$751$	−3.48860	+	3.48860i	−0.127301	+	0.127301i	−0.767887	−	0.640586i	$-0.778692\pi$
$751$	−3.48860	+	3.48860i	−0.127301	+	0.127301i	0.640586	+	0.767887i	$0.278692\pi$
$752$	−4.14435	−	26.1384i	−0.151129	−	0.953169i
$753$	−74.9530			−2.73144
$754$	5.44554	+	3.33672i	0.198315	+	0.121516i
$755$	−3.96101	−	14.6321i	−0.144156	−	0.532517i
$756$	−8.85781	+	4.51420i	−0.322155	+	0.164180i
$757$	−29.1555	−	29.1555i	−1.05968	−	1.05968i	−0.998103	−	0.0615726i	$-0.980388\pi$
$757$	−29.1555	−	29.1555i	−1.05968	−	1.05968i	−0.0615726	−	0.998103i	$-0.519612\pi$
$758$	−2.29291	−	9.54892i	−0.0832823	−	0.346832i
$759$	−0.722436	+	0.722436i	−0.0262228	+	0.0262228i
$760$	3.78267	+	20.1069i	0.137212	+	0.729352i
$761$	22.9265			0.831086			0.415543	−	0.909574i	$-0.363592\pi$
$761$	22.9265			0.831086			0.415543	+	0.909574i	$0.363592\pi$
$762$	−72.2753	+	17.3549i	−2.61826	+	0.628702i
$763$	9.09890	+	9.09890i	0.329402	+	0.329402i
$764$	2.86807	−	1.46166i	0.103763	−	0.0528808i
$765$	−40.2072	−	11.1805i	−1.45369	−	0.404232i
$766$	−1.81993	−	7.57915i	−0.0657566	−	0.273846i
$767$	15.4611	+	15.4611i	0.558269	+	0.558269i
$768$	−13.5782	−	41.7424i	−0.489962	−	1.50625i
$769$		−	22.3026i		−	0.804254i	−0.915584	−	0.402127i	$-0.868271\pi$
$769$		−	22.3026i		−	0.804254i	0.915584	−	0.402127i	$-0.131729\pi$
$770$	−1.41918	−	2.59759i	−0.0511436	−	0.0936106i
$771$	−15.4508	+	15.4508i	−0.556448	+	0.556448i
$772$	−21.5568	+	10.9860i	−0.775846	+	0.395394i
$773$	19.2579	−	19.2579i	0.692658	−	0.692658i	−0.270158	−	0.962816i	$-0.587076\pi$
$773$	19.2579	−	19.2579i	0.692658	−	0.692658i	0.962816	+	0.270158i	$0.0870760\pi$
$774$	−48.5539	+	11.6589i	−1.74523	+	0.419070i
$775$	−6.20991	+	23.6618i	−0.223067	+	0.849956i
$776$	−0.804141	+	10.2338i	−0.0288670	+	0.367373i
$777$		−	30.6163i		−	1.09835i
$778$	−0.798670	−	0.489380i	−0.0286337	−	0.0175451i
$779$	−15.5178	+	15.5178i	−0.555982	+	0.555982i
$780$	44.1047	+	2.19407i	1.57920	+	0.0785602i
$781$			1.81665i			0.0650047i
$782$	−1.28486	−	2.43539i	−0.0459466	−	0.0870892i
$783$	3.71564	+	3.71564i	0.132786	+	0.132786i
$784$	−13.1427	+	18.0957i	−0.469382	+	0.646274i
$785$	28.3929	+	16.2955i	1.01339	+	0.581610i
$786$	19.3500	−	4.64638i	0.690193	−	0.165731i
$787$			20.4683i			0.729617i	0.931083	+	0.364809i	$0.118866\pi$
$787$			20.4683i			0.729617i	−0.931083	+	0.364809i	$0.881134\pi$
$788$	−48.5983	+	24.7671i	−1.73124	+	0.882292i
$789$	−23.9537	+	23.9537i	−0.852774	+	0.852774i
$790$	9.06216	−	4.95105i	0.322417	−	0.176151i
$791$	−21.0432			−0.748211
$792$	7.67674	−	6.55820i	0.272781	−	0.233036i
$793$		−	22.5985i		−	0.802495i
$794$	−24.8967	−	15.2553i	−0.883552	−	0.541391i
$795$	49.1408	+	28.2032i	1.74284	+	1.00026i
$796$	12.9231	−	39.7843i	0.458046	−	1.41012i
$797$	−30.0902	−	30.0902i	−1.06585	−	1.06585i	−0.997673	−	0.0681748i	$-0.978282\pi$
$797$	−30.0902	−	30.0902i	−1.06585	−	1.06585i	−0.0681748	−	0.997673i	$-0.521718\pi$
$798$	−12.7023	−	7.78324i	−0.449656	−	0.275524i
$799$	6.74393	+	26.4326i	0.238583	+	0.935120i
$800$	22.5312	+	17.0981i	0.796599	+	0.604509i
$801$			21.9412i			0.775253i
$802$	3.84721	+	16.0219i	0.135850	+	0.565752i
$803$	2.74316	−	2.74316i	0.0968039	−	0.0968039i
$804$	−3.97922	+	12.2502i	−0.140336	+	0.432033i
$805$	1.20978	−	0.327495i	0.0426390	−	0.0115427i
$806$	13.0113	−	21.2345i	0.458303	−	0.747953i
$807$	23.1696	+	23.1696i	0.815607	+	0.815607i
$808$	2.47671	−	31.5197i	0.0871305	−	1.10886i
$809$	2.61310	+	2.61310i	0.0918717	+	0.0918717i	0.751549	−	0.659677i	$-0.229307\pi$
$809$	2.61310	+	2.61310i	0.0918717	+	0.0918717i	−0.659677	+	0.751549i	$0.729307\pi$
$810$	−6.34189	−	1.86054i	−0.222831	−	0.0653728i
$811$	−1.78985	−	1.78985i	−0.0628500	−	0.0628500i	0.674983	−	0.737833i	$-0.264151\pi$
$811$	−1.78985	−	1.78985i	−0.0628500	−	0.0628500i	−0.737833	+	0.674983i	$0.764151\pi$
$812$	−2.83279	−	0.920169i	−0.0994113	−	0.0322916i
$813$		−	12.7012i		−	0.445450i
$814$	2.44833	+	10.1962i	0.0858138	+	0.357375i
$815$	9.36740	−	2.53582i	0.328126	−	0.0888259i
$816$	17.9132	+	41.5492i	0.627087	+	1.45451i
$817$	−17.8429	−	17.8429i	−0.624246	−	0.624246i
$818$	21.4591	+	13.1489i	0.750298	+	0.459741i
$819$	−13.6737	+	13.6737i	−0.477798	+	0.477798i
$820$	−1.50738	+	30.3010i	−0.0526399	+	1.05816i
$821$	−24.4251	+	24.4251i	−0.852444	+	0.852444i	−0.990434	−	0.137990i	$-0.955936\pi$
$821$	−24.4251	+	24.4251i	−0.852444	+	0.852444i	0.137990	+	0.990434i	$0.455936\pi$
$822$	48.5398	−	11.6555i	1.69302	−	0.406532i
$823$	25.4357			0.886632			0.443316	−	0.896365i	$-0.353802\pi$
$823$	25.4357			0.886632			0.443316	+	0.896365i	$0.353802\pi$
$824$	32.6011	+	38.1614i	1.13571	+	1.32942i
$825$	−2.74604	+	10.4633i	−0.0956049	+	0.364286i
$826$	−8.69489	−	5.32774i	−0.302534	−	0.185376i
$827$	−55.7481			−1.93855			−0.969275	−	0.245978i	$-0.920891\pi$
$827$	−55.7481			−1.93855			−0.969275	+	0.245978i	$0.920891\pi$
$828$	1.94118	+	3.80900i	0.0674607	+	0.132372i
$829$	0.274786			0.00954370			0.00477185	−	0.999989i	$-0.498481\pi$
$829$	0.274786			0.00954370			0.00477185	+	0.999989i	$0.498481\pi$
$830$	21.5568	+	39.4565i	0.748248	+	1.36956i
$831$	9.88947			0.343062
$832$	−16.9303	−	23.2905i	−0.586954	−	0.807451i
$833$	11.7651	−	19.8249i	0.407638	−	0.686892i
$834$	−7.37536	−	30.7150i	−0.255388	−	1.06357i
$835$	−3.65180	−	13.4899i	−0.126376	−	0.466836i
$836$	4.85266	+	1.57628i	0.167833	+	0.0545168i
$837$	14.4889	−	14.4889i	0.500809	−	0.500809i
$838$	−40.0079	+	9.60680i	−1.38205	+	0.331862i
$839$	22.2504	−	22.2504i	0.768169	−	0.768169i	−0.209615	−	0.977784i	$-0.567221\pi$
$839$	22.2504	−	22.2504i	0.768169	−	0.768169i	0.977784	+	0.209615i	$0.0672211\pi$
$840$	−20.2395	+	3.80763i	−0.698330	+	0.131376i
$841$		−	27.4257i		−	0.945715i
$842$	12.0807	+	7.40238i	0.416329	+	0.255103i
$843$		−	15.3727i		−	0.529463i
$844$	−32.4486	−	10.5402i	−1.11693	−	0.362809i
$845$	−0.0984135	+	0.0266412i	−0.00338553	+	0.000916486i
$846$	−9.88900	−	41.1832i	−0.339991	−	1.41591i
$847$	12.3181			0.423254
$848$	−5.78538	−	36.4883i	−0.198671	−	1.25301i
$849$		−	4.28114i		−	0.146928i
$850$	−24.7542	−	15.4022i	−0.849063	−	0.528291i
$851$	−4.43998			−0.152201
$852$	12.0213	+	3.90485i	0.411843	+	0.133778i
$853$		−	24.3488i		−	0.833686i	−0.908979	−	0.416843i	$-0.863136\pi$
$853$		−	24.3488i		−	0.833686i	0.908979	−	0.416843i	$-0.136864\pi$
$854$	2.46077	+	10.2480i	0.0842057	+	0.350678i
$855$	8.55581	+	31.6054i	0.292603	+	1.08088i
$856$	0.956044	−	12.1670i	0.0326769	−	0.415860i
$857$	−17.1041			−0.584265			−0.292132	−	0.956378i	$-0.594365\pi$
$857$	−17.1041			−0.584265			−0.292132	+	0.956378i	$0.594365\pi$
$858$	5.75364	−	9.38995i	0.196426	−	0.320568i
$859$	7.55056			0.257622			0.128811	−	0.991669i	$-0.458884\pi$
$859$	7.55056			0.257622			0.128811	+	0.991669i	$0.458884\pi$
$860$	−34.8412	−	1.73324i	−1.18808	−	0.0591030i
$861$	−15.6202	−	15.6202i	−0.532335	−	0.532335i
$862$	4.97751	−	1.19521i	0.169535	−	0.0407091i
$863$	−29.1069	−	29.1069i	−0.990810	−	0.990810i	0.00914807	−	0.999958i	$-0.497088\pi$
$863$	−29.1069	−	29.1069i	−0.990810	−	0.990810i	−0.999958	+	0.00914807i	$0.997088\pi$
$864$	−9.07069	−	21.8858i	−0.308591	−	0.744569i
$865$	54.4831	−	14.7490i	1.85248	−	0.501480i
$866$	−47.4051	+	11.3830i	−1.61089	+	0.386811i
$867$	−22.3440	−	40.9380i	−0.758843	−	1.39033i
$868$	−3.58813	+	11.0462i	−0.121789	+	0.374934i
$869$		−	2.57523i		−	0.0873587i
$870$	5.21897	+	9.55254i	0.176940	+	0.323862i
$871$			8.44904i			0.286285i
$872$	−23.3143	+	19.9173i	−0.789523	+	0.674486i
$873$			16.4285i			0.556019i
$874$	−1.12873	+	1.84209i	−0.0381798	+	0.0623095i
$875$	9.31085	−	9.45561i	0.314764	−	0.319658i
$876$	−12.2559	−	24.0487i	−0.414089	−	0.812530i
$877$			10.9656i			0.370283i	0.982712	+	0.185142i	$0.0592744\pi$
$877$			10.9656i			0.370283i	−0.982712	+	0.185142i	$0.940726\pi$
$878$	−32.3708	+	7.77297i	−1.09246	+	0.262325i
$879$	4.17351	+	4.17351i	0.140769	+	0.140769i
$880$	6.43590	−	2.88658i	0.216954	−	0.0973065i
$881$	−35.2679	−	35.2679i	−1.18821	−	1.18821i	−0.977563	−	0.210642i	$-0.932444\pi$
$881$	−35.2679	−	35.2679i	−1.18821	−	1.18821i	−0.210642	−	0.977563i	$-0.567556\pi$
$882$	−18.7000	+	30.5185i	−0.629663	+	1.02761i
$883$	−29.9632	+	29.9632i	−1.00834	+	1.00834i	−0.00837847	+	0.999965i	$0.502667\pi$
$883$	−29.9632	+	29.9632i	−1.00834	+	1.00834i	−0.999965	+	0.00837847i	$0.997333\pi$
$884$	19.5957	+	22.2914i	0.659074	+	0.749743i
$885$	9.73806	+	35.9727i	0.327341	+	1.20921i
$886$	−10.9017	−	45.4004i	−0.366248	−	1.52526i
$887$	−48.5465			−1.63003			−0.815016	−	0.579439i	$-0.803272\pi$
$887$	−48.5465			−1.63003			−0.815016	+	0.579439i	$0.803272\pi$
$888$	72.7337	+	5.71518i	2.44078	+	0.191789i
$889$	16.0790	−	16.0790i	0.539273	−	0.539273i
$890$	−4.31504	+	14.7083i	−0.144641	+	0.493025i
$891$	−1.16546	+	1.16546i	−0.0390443	+	0.0390443i
$892$	5.29793	+	1.72092i	0.177388	+	0.0576205i
$893$	15.1343	−	15.1343i	0.506449	−	0.506449i
$894$	42.0563	−	68.6361i	1.40657	−	2.29553i
$895$	11.4142	+	42.1645i	0.381535	+	1.40940i
$896$	10.2137	+	8.71821i	0.341216	+	0.291255i
$897$	3.29719	+	3.29719i	0.110090	+	0.110090i
$898$	−24.8439	+	5.96557i	−0.829051	+	0.199074i
$899$	6.13877			0.204740
$900$	38.0911	+	24.4546i	1.26970	+	0.815155i
$901$	9.41431	+	36.8991i	0.313636	+	1.22929i
$902$	6.45112	+	3.95288i	0.214799	+	0.131617i
$903$	17.9607	−	17.9607i	0.597694	−	0.597694i
$904$	3.92816	−	49.9914i	0.130649	−	1.66269i
$905$	−26.9224	+	46.9090i	−0.894930	+	1.55931i
$906$	−13.7419	+	22.4269i	−0.456545	+	0.745082i
$907$	−10.7948			−0.358437			−0.179218	−	0.983809i	$-0.557357\pi$
$907$	−10.7948			−0.358437			−0.179218	+	0.983809i	$0.557357\pi$
$908$	−12.5124	−	24.5520i	−0.415239	−	0.814785i
$909$		−	50.5988i		−	1.67826i
$910$	−11.8553	+	6.47709i	−0.393001	+	0.214714i
$911$	13.9247	+	13.9247i	0.461345	+	0.461345i	0.899096	−	0.437751i	$-0.144225\pi$
$911$	13.9247	+	13.9247i	0.461345	+	0.461345i	−0.437751	+	0.899096i	$0.644225\pi$
$912$	20.8614	−	28.7233i	0.690791	−	0.951124i
$913$	11.2125			0.371080
$914$	−8.61635	−	35.8831i	−0.285003	−	1.18691i
$915$	19.1727	−	33.4062i	0.633830	−	1.10437i
$916$	−32.0407	+	16.3289i	−1.05866	+	0.539522i
$917$	−4.30479	+	4.30479i	−0.142157	+	0.142157i
$918$	11.3950	+	21.5985i	0.376090	+	0.712858i
$919$	47.6999			1.57347			0.786737	−	0.617288i	$-0.211769\pi$
$919$	47.6999			1.57347			0.786737	+	0.617288i	$0.211769\pi$
$920$	0.552184	+	2.93514i	0.0182050	+	0.0967688i
$921$	41.5338	+	41.5338i	1.36859	+	1.36859i
$922$	−14.1136	+	23.0334i	−0.464806	+	0.758565i
$923$	8.29113			0.272906
$924$	−1.58668	+	4.88468i	−0.0521980	+	0.160694i
$925$	−40.5913	+	23.7145i	−1.33463	+	0.779730i
$926$	−48.1197	+	11.5546i	−1.58131	+	0.379708i
$927$	56.7979	+	56.7979i	1.86549	+	1.86549i
$928$	2.71480	−	6.55795i	0.0891177	−	0.215275i
$929$	−26.1971	−	26.1971i	−0.859498	−	0.859498i	0.131781	−	0.991279i	$-0.457930\pi$
$929$	−26.1971	−	26.1971i	−0.859498	−	0.859498i	−0.991279	+	0.131781i	$0.957930\pi$
$930$	37.2494	−	20.3510i	1.22146	−	0.667335i
$931$	−18.0872			−0.592784
$932$	−13.3082	−	26.1134i	−0.435923	−	0.855373i
$933$	−36.2182	+	36.2182i	−1.18573	+	1.18573i
$934$	10.2356	+	42.6267i	0.334920	+	1.39479i
$935$	−6.33055	+	3.57586i	−0.207031	+	0.116943i
$936$	−29.9315	−	35.0365i	−0.978342	−	1.14520i
$937$	16.9484	−	16.9484i	0.553681	−	0.553681i	−0.373820	−	0.927501i	$-0.621952\pi$
$937$	16.9484	−	16.9484i	0.553681	−	0.553681i	0.927501	+	0.373820i	$0.121952\pi$
$938$	−0.920024	−	3.83148i	−0.0300398	−	0.125102i
$939$			9.68133i			0.315938i
$940$	1.47012	−	29.5521i	0.0479501	−	0.963883i
$941$	−2.24164	−	2.24164i	−0.0730755	−	0.0730755i	0.669624	−	0.742700i	$-0.266455\pi$
$941$	−2.24164	−	2.24164i	−0.0730755	−	0.0730755i	−0.742700	+	0.669624i	$0.766455\pi$
$942$	−13.2625	−	55.2321i	−0.432115	−	1.79956i
$943$	−2.26524	+	2.26524i	−0.0737665	+	0.0737665i
$944$	14.2800	−	19.6615i	0.464773	−	0.639928i
$945$	−10.7291	+	2.90443i	−0.349016	+	0.0944812i
$946$	−4.54518	+	7.41774i	−0.147776	+	0.241172i
$947$		−	17.5791i		−	0.571243i	−0.958342	−	0.285622i	$-0.907800\pi$
$947$		−	17.5791i		−	0.571243i	0.958342	−	0.285622i	$-0.0922001\pi$
$948$	−17.0411	−	5.53542i	−0.553469	−	0.179782i
$949$	−12.5197	−	12.5197i	−0.406407	−	0.406407i
$950$	−0.480238	+	22.8695i	−0.0155810	+	0.741983i
$951$			7.35594i			0.238533i
$952$	−11.3136	−	7.97495i	−0.366676	−	0.258469i
$953$	−24.2292	+	24.2292i	−0.784862	+	0.784862i	−0.980647	−	0.195785i	$-0.937275\pi$
$953$	−24.2292	+	24.2292i	−0.784862	+	0.784862i	0.195785	+	0.980647i	$0.437275\pi$
$954$	−13.8047	−	57.4903i	−0.446945	−	1.86132i
$955$	3.47397	−	0.940427i	0.112415	−	0.0304315i
$956$	−22.5958	−	44.3377i	−0.730801	−	1.43399i
$957$	2.71459			0.0877501
$958$	57.1760	−	13.7292i	1.84727	−	0.443572i
$959$	−10.7986	+	10.7986i	−0.348705	+	0.348705i
$960$	−5.26748	−	48.7929i	−0.170007	−	1.57478i
$961$			7.06232i			0.227817i
$962$	46.5351	−	11.1741i	1.50035	−	0.360268i
$963$		−	19.5318i		−	0.629404i
$964$	−1.37982	+	4.24785i	−0.0444410	+	0.136814i
$965$	−26.1108	+	7.06836i	−0.840535	+	0.227539i
$966$	−1.85424	−	1.13618i	−0.0596593	−	0.0365559i
$967$	−10.2794	−	10.2794i	−0.330562	−	0.330562i	0.522238	−	0.852800i	$-0.325097\pi$
$967$	−10.2794	−	10.2794i	−0.330562	−	0.330562i	−0.852800	+	0.522238i	$0.825097\pi$
$968$	−2.29943	+	29.2635i	−0.0739064	+	0.940563i
$969$	−18.6748	+	31.4681i	−0.599922	+	1.01090i
$970$	−3.23089	+	11.0129i	−0.103738	+	0.353603i
$971$			38.7947i			1.24498i	0.782627	+	0.622491i	$0.213879\pi$
$971$			38.7947i			1.24498i	−0.782627	+	0.622491i	$0.786121\pi$
$972$	16.6168	+	32.6057i	0.532985	+	1.04583i
$973$	6.83314	+	6.83314i	0.219060	+	0.219060i
$974$	0.412613	+	0.252826i	0.0132210	+	0.00810107i
$975$	47.7543	+	12.5329i	1.52936	+	0.401373i
$976$	−24.8050	+	3.93293i	−0.793988	+	0.125890i
$977$	32.9960	−	32.9960i	1.05563	−	1.05563i	0.0572759	−	0.998358i	$-0.481759\pi$
$977$	32.9960	−	32.9960i	1.05563	−	1.05563i	0.998358	−	0.0572759i	$-0.0182415\pi$
$978$	−14.3576	−	8.79751i	−0.459104	−	0.281313i
$979$	2.70298	+	2.70298i	0.0863875	+	0.0863875i
$980$	−18.5376	+	16.7806i	−0.592161	+	0.536037i
$981$	−34.7001	+	34.7001i	−1.10789	+	1.10789i
$982$	26.0859	+	15.9840i	0.832435	+	0.510069i
$983$			55.4327i			1.76803i	0.467459	+	0.884015i	$0.345169\pi$
$983$			55.4327i			1.76803i	−0.467459	+	0.884015i	$0.654831\pi$
$984$	40.0240	−	34.1923i	1.27592	−	1.09001i
$985$	−58.8649	+	15.9351i	−1.87559	+	0.507736i
$986$	−2.16157	+	6.98950i	−0.0688384	+	0.222591i
$987$	15.2342	+	15.2342i	0.484908	+	0.484908i
$988$	7.19411	−	22.1474i	0.228875	−	0.704604i
$989$	−2.60466	−	2.60466i	−0.0828235	−	0.0828235i
$990$	9.90633	−	5.41226i	0.314844	−	0.172013i
$991$	−2.78499	+	2.78499i	−0.0884682	+	0.0884682i	−0.749956	−	0.661488i	$-0.769925\pi$
$991$	−2.78499	+	2.78499i	−0.0884682	+	0.0884682i	0.661488	+	0.749956i	$0.269925\pi$
$992$	−25.5722	−	10.5862i	−0.811919	−	0.336111i
$993$			0.104951i			0.00333053i
$994$	−3.75987	+	0.902829i	−0.119256	+	0.0286360i
$995$	23.2798	−	40.5623i	0.738019	−	1.28591i
$996$	24.1012	−	74.1967i	0.763675	−	2.35101i
$997$			25.2309i			0.799069i	0.916718	+	0.399535i	$0.130828\pi$
$997$			25.2309i			0.799069i	−0.916718	+	0.399535i	$0.869172\pi$
$998$	40.8761	−	9.81526i	1.29391	−	0.310697i
$999$	39.3766			1.24582

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.bl.a.387.36	yes	208
5.3	odd	4		680.2.t.a.523.87	yes	208
8.3	odd	2	inner	680.2.bl.a.387.18	yes	208
17.4	even	4		680.2.t.a.667.69	yes	208
40.3	even	4		680.2.t.a.523.69	✓	208
85.38	odd	4	inner	680.2.bl.a.123.18	yes	208
136.123	odd	4		680.2.t.a.667.87	yes	208
680.123	even	4	inner	680.2.bl.a.123.36	yes	208

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.t.a.523.69	✓	208	40.3	even	4
680.2.t.a.523.87	yes	208	5.3	odd	4
680.2.t.a.667.69	yes	208	17.4	even	4
680.2.t.a.667.87	yes	208	136.123	odd	4
680.2.bl.a.123.18	yes	208	85.38	odd	4	inner
680.2.bl.a.123.36	yes	208	680.123	even	4	inner
680.2.bl.a.387.18	yes	208	8.3	odd	2	inner
680.2.bl.a.387.36	yes	208	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.bl (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.738875 + 1.20585i) q^{2} +2.74346 q^{3} +(-0.908129 - 1.78194i) q^{4} +(-0.584289 - 2.15838i) q^{5} +(-2.02707 + 3.30818i) q^{6} -1.18693i q^{7} +(2.81974 + 0.221566i) q^{8} +4.52655 q^{9} +(3.03439 + 0.890211i) q^{10} +(0.557635 - 0.557635i) q^{11} +(-2.49141 - 4.88867i) q^{12} +(-2.54503 - 2.54503i) q^{13} +(1.43125 + 0.876993i) q^{14} +(-1.60297 - 5.92142i) q^{15} +(-2.35061 + 3.23646i) q^{16} +(2.10422 - 3.54574i) q^{17} +(-3.34455 + 5.45832i) q^{18} -3.23494 q^{19} +(-3.31549 + 3.00125i) q^{20} -3.25629i q^{21} +(0.260399 + 1.08444i) q^{22} -0.472228 q^{23} +(7.73582 + 0.607856i) q^{24} +(-4.31721 + 2.52223i) q^{25} +(4.94938 - 1.18846i) q^{26} +4.18802 q^{27} +(-2.11504 + 1.07789i) q^{28} +(0.887208 + 0.887208i) q^{29} +(8.32472 + 2.44225i) q^{30} +(3.45960 - 3.45960i) q^{31} +(-2.16587 - 5.22580i) q^{32} +(1.52985 - 1.52985i) q^{33} +(2.72085 + 5.15722i) q^{34} +(-2.56185 + 0.693510i) q^{35} +(-4.11069 - 8.06603i) q^{36} +9.40220 q^{37} +(2.39022 - 3.90084i) q^{38} +(-6.98219 - 6.98219i) q^{39} +(-1.16932 - 6.21552i) q^{40} +(4.79693 - 4.79693i) q^{41} +(3.92658 + 2.40599i) q^{42} +(5.51569 + 5.51569i) q^{43} +(-1.50007 - 0.487267i) q^{44} +(-2.64481 - 9.77001i) q^{45} +(0.348917 - 0.569434i) q^{46} +(-4.67838 + 4.67838i) q^{47} +(-6.44878 + 8.87908i) q^{48} +5.59120 q^{49} +(0.148453 - 7.06951i) q^{50} +(5.77284 - 9.72757i) q^{51} +(-2.22388 + 6.84631i) q^{52} +(-6.53086 + 6.53086i) q^{53} +(-3.09442 + 5.05010i) q^{54} +(-1.52941 - 0.877769i) q^{55} +(0.262983 - 3.34683i) q^{56} -8.87492 q^{57} +(-1.72537 + 0.414301i) q^{58} -6.07501 q^{59} +(-9.09590 + 8.23380i) q^{60} +(4.43972 + 4.43972i) q^{61} +(1.61553 + 6.72796i) q^{62} -5.37270i q^{63} +(7.90182 + 1.24951i) q^{64} +(-4.00612 + 6.98019i) q^{65} +(0.714394 + 2.97512i) q^{66} +(-1.65991 - 1.65991i) q^{67} +(-8.22919 - 0.529613i) q^{68} -1.29554 q^{69} +(1.05662 - 3.60161i) q^{70} +(-1.62888 + 1.62888i) q^{71} +(12.7637 + 1.00293i) q^{72} +4.91927 q^{73} +(-6.94705 + 11.3376i) q^{74} +(-11.8441 + 6.91964i) q^{75} +(2.93774 + 5.76447i) q^{76} +(-0.661874 - 0.661874i) q^{77} +(13.5784 - 3.26048i) q^{78} +(2.30907 - 2.30907i) q^{79} +(8.35894 + 3.18248i) q^{80} -2.09000 q^{81} +(2.24003 + 9.32869i) q^{82} +(10.0536 + 10.0536i) q^{83} +(-5.80251 + 2.95713i) q^{84} +(-8.88252 - 2.46998i) q^{85} +(-10.7265 + 2.57567i) q^{86} +(2.43402 + 2.43402i) q^{87} +(1.69594 - 1.44883i) q^{88} +4.84722i q^{89} +(13.7353 + 4.02958i) q^{90} +(-3.02078 + 3.02078i) q^{91} +(0.428844 + 0.841481i) q^{92} +(9.49126 - 9.49126i) q^{93} +(-2.18467 - 9.09814i) q^{94} +(1.89014 + 6.98224i) q^{95} +(-5.94196 - 14.3368i) q^{96} +3.62936i q^{97} +(-4.13119 + 6.74212i) q^{98} +(2.52416 - 2.52416i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 208 q - 8 q^{3} - 8 q^{6} + 192 q^{9} - 6 q^{10} - 8 q^{11} + 16 q^{14} - 16 q^{16} - 12 q^{18} - 10 q^{20} - 16 q^{24} - 32 q^{27} - 24 q^{30} - 20 q^{32} - 8 q^{33} + 4 q^{34} - 8 q^{35} - 12 q^{38} + 38 q^{40}+ \cdots - 24 q^{99}+O(q^{100}) \) 208 * q - 8 * q^3 - 8 * q^6 + 192 * q^9 - 6 * q^10 - 8 * q^11 + 16 * q^14 - 16 * q^16 - 12 * q^18 - 10 * q^20 - 16 * q^24 - 32 * q^27 - 24 * q^30 - 20 * q^32 - 8 * q^33 + 4 * q^34 - 8 * q^35 - 12 * q^38 + 38 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^44 - 16 * q^46 + 68 * q^48 - 160 * q^49 + 16 * q^50 - 8 * q^51 - 20 * q^52 - 36 * q^54 + 4 * q^56 - 32 * q^57 + 64 * q^59 - 32 * q^60 - 72 * q^62 + 32 * q^65 - 8 * q^67 - 28 * q^68 + 28 * q^70 - 56 * q^72 + 32 * q^73 - 8 * q^74 - 16 * q^75 - 10 * q^80 + 128 * q^81 + 8 * q^86 - 16 * q^88 - 118 * q^90 + 24 * q^91 - 56 * q^92 - 64 * q^94 - 48 * q^96 - 40 * q^98 - 24 * q^99

Introduction

L-functions

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