LMFDB - Embedded newform 680.2.bl.a.123.18

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			123.18
Character	$\chi$	$=$	680.123
Dual form			680.2.bl.a.387.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.20585 - 0.738875i) q^{2} +2.74346 q^{3} +(0.908129 + 1.78194i) q^{4} +(0.584289 - 2.15838i) q^{5} +(-3.30818 - 2.02707i) q^{6} -1.18693i q^{7} +(0.221566 - 2.81974i) q^{8} +4.52655 q^{9} +(-2.29933 + 2.17096i) q^{10} +(0.557635 + 0.557635i) q^{11} +(2.49141 + 4.88867i) q^{12} +(2.54503 - 2.54503i) q^{13} +(-0.876993 + 1.43125i) q^{14} +(1.60297 - 5.92142i) q^{15} +(-2.35061 + 3.23646i) q^{16} +(2.10422 + 3.54574i) q^{17} +(-5.45832 - 3.34455i) q^{18} -3.23494 q^{19} +(4.37671 - 0.918921i) q^{20} -3.25629i q^{21} +(-0.260399 - 1.08444i) q^{22} +0.472228 q^{23} +(0.607856 - 7.73582i) 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} +(-6.30812 + 5.95593i) q^{30} +(-3.45960 - 3.45960i) q^{31} +(5.22580 - 2.16587i) q^{32} +(1.52985 + 1.52985i) q^{33} +(0.0824844 - 5.83037i) q^{34} +(-2.56185 - 0.693510i) q^{35} +(4.11069 + 8.06603i) q^{36} -9.40220 q^{37} +(3.90084 + 2.39022i) q^{38} +(6.98219 - 6.98219i) q^{39} +(-5.95660 - 2.12576i) q^{40} +(4.79693 + 4.79693i) q^{41} +(-2.40599 + 3.92658i) q^{42} +(5.51569 - 5.51569i) q^{43} +(-0.487267 + 1.50007i) q^{44} +(2.64481 - 9.77001i) q^{45} +(-0.569434 - 0.348917i) q^{46} +(4.67838 + 4.67838i) q^{47} +(-6.44878 + 8.87908i) q^{48} +5.59120 q^{49} +(3.34228 + 6.23131i) q^{50} +(5.77284 + 9.72757i) q^{51} +(6.84631 + 2.22388i) q^{52} +(6.53086 + 6.53086i) q^{53} +(-5.05010 - 3.09442i) q^{54} +(1.52941 - 0.877769i) q^{55} +(-3.34683 - 0.262983i) q^{56} -8.87492 q^{57} +(1.72537 - 0.414301i) q^{58} -6.07501 q^{59} +(12.0073 - 2.52102i) 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} +(-4.40737 + 6.96958i) q^{68} +1.29554 q^{69} +(2.57678 + 2.72915i) q^{70} +(1.62888 + 1.62888i) q^{71} +(1.00293 - 12.7637i) q^{72} +4.91927 q^{73} +(11.3376 + 6.94705i) 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} +(5.61207 + 6.96453i) 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} +(-10.4081 + 9.82695i) 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} +(14.3368 - 5.94196i) q^{96} -3.62936i q^{97} +(-6.74212 - 4.13119i) 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 $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.20585	−	0.738875i	−0.852662	−	0.522463i
$2$	−1.20585	−	0.738875i	−0.852662	−	0.522463i
$3$	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
$6$	−3.30818	−	2.02707i	−1.35056	−	0.827548i
$7$		−	1.18693i		−	0.448617i	−0.974518	−	0.224309i	$-0.927988\pi$
$7$		−	1.18693i		−	0.448617i	0.974518	−	0.224309i	$-0.0720124\pi$
$8$	0.221566	−	2.81974i	0.0783353	−	0.996927i
$9$	4.52655			1.50885
$10$	−2.29933	+	2.17096i	−0.727114	+	0.686517i
$11$	0.557635	+	0.557635i	0.168133	+	0.168133i	0.786158	−	0.618025i	$-0.212067\pi$
$11$	0.557635	+	0.557635i	0.168133	+	0.168133i	−0.618025	+	0.786158i	$0.712067\pi$
$12$	2.49141	+	4.88867i	0.719208	+	1.41124i
$13$	2.54503	−	2.54503i	0.705866	−	0.705866i	−0.259797	−	0.965663i	$-0.583656\pi$
$13$	2.54503	−	2.54503i	0.705866	−	0.705866i	0.965663	+	0.259797i	$0.0836558\pi$
$14$	−0.876993	+	1.43125i	−0.234386	+	0.382519i
$15$	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
$18$	−5.45832	−	3.34455i	−1.28654	−	0.788318i
$19$	−3.23494			−0.742147			−0.371073	−	0.928604i	$-0.621010\pi$
$19$	−3.23494			−0.742147			−0.371073	+	0.928604i	$0.621010\pi$
$20$	4.37671	−	0.918921i	0.978662	−	0.205477i
$21$		−	3.25629i		−	0.710581i
$22$	−0.260399	−	1.08444i	−0.0555174	−	0.231204i
$23$	0.472228			0.0984663			0.0492332	−	0.998787i	$-0.484322\pi$
$23$	0.472228			0.0984663			0.0492332	+	0.998787i	$0.484322\pi$
$24$	0.607856	−	7.73582i	0.124078	−	1.57907i
$25$	−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	$-0.787166\pi$
$29$	−0.887208	+	0.887208i	−0.164750	+	0.164750i	0.619917	+	0.784667i	$0.287166\pi$
$30$	−6.30812	+	5.95593i	−1.15170	+	1.08740i
$31$	−3.45960	−	3.45960i	−0.621363	−	0.621363i	0.324517	−	0.945880i	$-0.394798\pi$
$31$	−3.45960	−	3.45960i	−0.621363	−	0.621363i	−0.945880	+	0.324517i	$0.894798\pi$
$32$	5.22580	−	2.16587i	0.923800	−	0.382875i
$33$	1.52985	+	1.52985i	0.266312	+	0.266312i
$34$	0.0824844	−	5.83037i	0.0141460	−	0.999900i
$35$	−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	$-0.781172\pi$
$37$	−9.40220			−1.54571			−0.772856	+	0.634582i	$0.781172\pi$
$38$	3.90084	+	2.39022i	0.632800	+	0.387744i
$39$	6.98219	−	6.98219i	1.11805	−	1.11805i
$40$	−5.95660	−	2.12576i	−0.941822	−	0.336113i
$41$	4.79693	+	4.79693i	0.749154	+	0.749154i	0.974320	−	0.225166i	$-0.0722924\pi$
$41$	4.79693	+	4.79693i	0.749154	+	0.749154i	−0.225166	+	0.974320i	$0.572292\pi$
$42$	−2.40599	+	3.92658i	−0.371252	+	0.605885i
$43$	5.51569	−	5.51569i	0.841135	−	0.841135i	−0.147871	−	0.989007i	$-0.547242\pi$
$43$	5.51569	−	5.51569i	0.841135	−	0.841135i	0.989007	+	0.147871i	$0.0472422\pi$
$44$	−0.487267	+	1.50007i	−0.0734582	+	0.226145i
$45$	2.64481	−	9.77001i	0.394265	−	1.45643i
$46$	−0.569434	−	0.348917i	−0.0839585	−	0.0514450i
$47$	4.67838	+	4.67838i	0.682411	+	0.682411i	0.960543	−	0.278132i	$-0.0897151\pi$
$47$	4.67838	+	4.67838i	0.682411	+	0.682411i	−0.278132	+	0.960543i	$0.589715\pi$
$48$	−6.44878	+	8.87908i	−0.930801	+	1.28158i
$49$	5.59120			0.798742
$50$	3.34228	+	6.23131i	0.472670	+	0.881240i
$51$	5.77284	+	9.72757i	0.808360	+	1.36213i
$52$	6.84631	+	2.22388i	0.949413	+	0.308396i
$53$	6.53086	+	6.53086i	0.897083	+	0.897083i	0.995177	−	0.0980943i	$-0.0312747\pi$
$53$	6.53086	+	6.53086i	0.897083	+	0.897083i	−0.0980943	+	0.995177i	$0.531275\pi$
$54$	−5.05010	−	3.09442i	−0.687232	−	0.421097i
$55$	1.52941	−	0.877769i	0.206225	−	0.118358i
$56$	−3.34683	−	0.262983i	−0.447239	−	0.0351426i
$57$	−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	$0.629411\pi$
$60$	12.0073	−	2.52102i	1.55014	−	0.325462i
$61$	−4.43972	+	4.43972i	−0.568448	+	0.568448i	−0.931693	−	0.363246i	$-0.881669\pi$
$61$	−4.43972	+	4.43972i	−0.568448	+	0.568448i	0.363246	+	0.931693i	$0.381669\pi$
$62$	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	−0.801194	−	0.598404i	$-0.795802\pi$
$67$	−1.65991	+	1.65991i	−0.202790	+	0.202790i	0.598404	+	0.801194i	$0.295802\pi$
$68$	−4.40737	+	6.96958i	−0.534473	+	0.845186i
$69$	1.29554			0.155964
$70$	2.57678	+	2.72915i	0.307984	+	0.326196i
$71$	1.62888	+	1.62888i	0.193313	+	0.193313i	0.797126	−	0.603813i	$-0.206353\pi$
$71$	1.62888	+	1.62888i	0.193313	+	0.193313i	−0.603813	+	0.797126i	$0.706353\pi$
$72$	1.00293	−	12.7637i	0.118196	−	1.50421i
$73$	4.91927			0.575757			0.287879	−	0.957667i	$-0.407050\pi$
$73$	4.91927			0.575757			0.287879	+	0.957667i	$0.407050\pi$
$74$	11.3376	+	6.94705i	1.31797	+	0.807578i
$75$	−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	$-0.308807\pi$
$79$	−2.30907	−	2.30907i	−0.259790	−	0.259790i	−0.824969	+	0.565178i	$0.808807\pi$
$80$	5.61207	+	6.96453i	0.627449	+	0.778658i
$81$	−2.09000			−0.232223
$82$	−2.24003	−	9.32869i	−0.247370	−	1.03018i
$83$	10.0536	−	10.0536i	1.10353	−	1.10353i	0.109549	−	0.993981i	$-0.465059\pi$
$83$	10.0536	−	10.0536i	1.10353	−	1.10353i	0.993981	−	0.109549i	$-0.0349407\pi$
$84$	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	$-0.917298\pi$
$89$		−	4.84722i		−	0.513804i	0.966437	−	0.256902i	$-0.0827017\pi$
$90$	−10.4081	+	9.82695i	−1.09710	+	1.03585i
$91$	−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
$96$	14.3368	−	5.94196i	1.46324	−	0.606448i
$97$		−	3.62936i		−	0.368506i	−0.982879	−	0.184253i	$-0.941013\pi$
$97$		−	3.62936i		−	0.368506i	0.982879	−	0.184253i	$-0.0589865\pi$
$98$	−6.74212	−	4.13119i	−0.681057	−	0.417314i
$99$	2.52416	+	2.52416i	0.253688	+	0.253688i
$100$	0.573881	−	9.98352i	0.0573881	−	0.998352i
$101$		−	11.1782i		−	1.11228i	−0.831090	−	0.556138i	$-0.812283\pi$
$101$		−	11.1782i		−	1.11228i	0.831090	−	0.556138i	$-0.187717\pi$
$102$	0.226292	−	15.9954i	0.0224063	−	1.58378i
$103$	−12.5477	+	12.5477i	−1.23636	+	1.23636i	−0.274888	+	0.961476i	$0.588641\pi$
$103$	−12.5477	+	12.5477i	−1.23636	+	1.23636i	−0.961476	+	0.274888i	$0.911359\pi$
$104$	−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	$0.0668812\pi$
$107$			4.31495i			0.417142i	−0.978007	+	0.208571i	$0.933119\pi$
$108$	3.80326	+	7.46279i	0.365969	+	0.718107i
$109$	7.66591	+	7.66591i	0.734261	+	0.734261i	0.971461	−	0.237200i	$-0.0762296\pi$
$109$	7.66591	+	7.66591i	0.734261	+	0.734261i	−0.237200	+	0.971461i	$0.576230\pi$
$110$	−2.49279	−	0.0715873i	−0.237678	−	0.00682558i
$111$	−25.7945			−2.44831
$112$	3.84145	+	2.79000i	0.362983	+	0.263631i
$113$			17.7291i			1.66781i	0.551905	+	0.833907i	$0.313901\pi$
$113$			17.7291i			1.66781i	−0.551905	+	0.833907i	$0.686099\pi$
$114$	10.7018	+	6.55745i	1.00231	+	0.614162i
$115$	0.275917	−	1.01925i	0.0257294	−	0.0950453i
$116$	−2.38665	−	0.775251i	−0.221595	−	0.0719802i
$117$	11.5202	−	11.5202i	1.06505	−	1.06505i
$118$	7.32553	+	4.48867i	0.674370	+	0.413216i
$119$	4.20854	−	2.49757i	0.385796	−	0.228952i
$120$	−16.3417	−	5.83194i	−1.49178	−	0.532380i
$121$		−	10.3781i		−	0.943462i
$122$	8.63401	−	2.07322i	0.781686	−	0.187701i
$123$	13.1602	+	13.1602i	1.18661	+	1.18661i
$124$	3.02303	−	9.30656i	0.271476	−	0.835753i
$125$	−7.96644	+	7.84448i	−0.712540	+	0.701631i
$126$	−3.96975	+	6.47864i	−0.353653	+	0.577163i
$127$	−13.5467	+	13.5467i	−1.20208	+	1.20208i	−0.228545	+	0.973533i	$0.573397\pi$
$127$	−13.5467	+	13.5467i	−1.20208	+	1.20208i	−0.973533	+	0.228545i	$0.926603\pi$
$128$	8.60514	+	7.34517i	0.760594	+	0.649228i
$129$	15.1321	−	15.1321i	1.33230	−	1.33230i
$130$	−0.326723	+	11.3771i	−0.0286555	+	0.997833i
$131$	−3.62682	+	3.62682i	−0.316877	+	0.316877i	−0.847566	−	0.530689i	$-0.821933\pi$
$131$	−3.62682	+	3.62682i	−0.316877	+	0.316877i	0.530689	+	0.847566i	$0.321933\pi$
$132$	−1.33679	+	4.11539i	−0.116353	+	0.358199i
$133$			3.83965i			0.332940i
$134$	3.22806	−	0.775129i	0.278862	−	0.0669609i
$135$	2.44701	−	9.03934i	0.210605	−	0.777982i
$136$	10.4643	−	5.14774i	0.897303	−	0.441415i
$137$	−9.09793	+	9.09793i	−0.777289	+	0.777289i	−0.979369	−	0.202080i	$-0.935230\pi$
$137$	−9.09793	+	9.09793i	−0.777289	+	0.777289i	0.202080	+	0.979369i	$0.435230\pi$
$138$	−1.56222	−	0.957239i	−0.132985	−	0.0814856i
$139$	−5.75698	−	5.75698i	−0.488301	−	0.488301i	0.419469	−	0.907770i	$-0.362216\pi$
$139$	−5.75698	−	5.75698i	−0.488301	−	0.488301i	−0.907770	+	0.419469i	$0.862216\pi$
$140$	−1.09069	−	5.19485i	−0.0921805	−	0.439045i
$141$	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
$146$	−5.93188	−	3.63472i	−0.490926	−	0.300812i
$147$	15.3392			1.26516
$148$	−8.53840	−	16.7541i	−0.701852	−	1.37718i
$149$	20.7473			1.69969			0.849844	−	0.527034i	$-0.176696\pi$
$149$	20.7473			1.69969			0.849844	+	0.527034i	$0.176696\pi$
$150$	9.16939	+	17.0953i	0.748678	+	1.39583i
$151$	−6.77920			−0.551684			−0.275842	−	0.961203i	$-0.588957\pi$
$151$	−6.77920			−0.551684			−0.275842	+	0.961203i	$0.588957\pi$
$152$	−0.716752	+	9.12168i	−0.0581363	+	0.739866i
$153$	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
$156$	18.7826	+	6.10110i	1.50381	+	0.488479i
$157$	10.3523	+	10.3523i	0.826203	+	0.826203i	0.986989	−	0.160787i	$-0.0514031\pi$
$157$	10.3523	+	10.3523i	0.826203	+	0.826203i	−0.160787	+	0.986989i	$0.551403\pi$
$158$	1.07827	+	4.49049i	0.0857823	+	0.357244i
$159$	17.9171	+	17.9171i	1.42092	+	1.42092i
$160$	−1.62139	−	12.5448i	−0.128182	−	0.991751i
$161$		−	0.560502i		−	0.0441737i
$162$	2.52022	+	1.54425i	0.198007	+	0.121328i
$163$		−	4.34001i		−	0.339936i	−0.985450	−	0.169968i	$-0.945634\pi$
$163$		−	4.34001i		−	0.339936i	0.985450	−	0.169968i	$-0.0543665\pi$
$164$	−4.19160	+	12.9041i	−0.327309	+	1.00764i
$165$	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	$-0.577744\pi$
$167$	−6.25000			−0.483640			−0.241820	+	0.970321i	$0.577744\pi$
$168$	−9.18188	−	0.721482i	−0.708397	−	0.0556636i
$169$			0.0455960i			0.00350738i
$170$	−12.5360	−	3.58465i	−0.961464	−	0.274930i
$171$	−14.6431			−1.11979
$172$	14.8376	+	4.81966i	1.13135	+	0.367496i
$173$			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
$176$	−3.11554	+	0.493982i	−0.234843	+	0.0372353i
$177$	−16.6665			−1.25273
$178$	−3.58149	+	5.84500i	−0.268444	+	0.438101i
$179$	−19.5352			−1.46013			−0.730066	−	0.683377i	$-0.760511\pi$
$179$	−19.5352			−1.46013			−0.730066	+	0.683377i	$0.760511\pi$
$180$	19.8114	−	4.15954i	1.47665	−	0.310034i
$181$	17.1034	−	17.1034i	1.27129	−	1.27129i	0.325875	−	0.945413i	$-0.394341\pi$
$181$	17.1034	−	17.1034i	1.27129	−	1.27129i	0.945413	−	0.325875i	$-0.105659\pi$
$182$	1.41062	+	5.87457i	0.104562	+	0.435452i
$183$	−12.1802	+	12.1802i	−0.900384	+	0.900384i
$184$	0.104630	−	1.33156i	0.00771339	−	0.0981638i
$185$	−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
$188$	−4.08801	+	12.5851i	−0.298149	+	0.917866i
$189$		−	4.97088i		−	0.361579i
$190$	7.43822	−	7.02293i	0.539625	−	0.509497i
$191$			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	$0.143391\pi$
$193$			12.0974i			0.870789i	−0.900240	+	0.435394i	$0.856609\pi$
$194$	−2.68164	+	4.37645i	−0.192531	+	0.314211i
$195$	−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	−0.0496211	+	0.998768i	$0.515801\pi$
$199$	−14.7893	+	14.7893i	−1.04839	+	1.04839i	−0.998768	+	0.0496211i	$0.984199\pi$
$200$	−8.06858	+	11.6146i	−0.570535	+	0.821273i
$201$	−4.55388	+	4.55388i	−0.321206	+	0.321206i
$202$	−8.25931	+	13.4792i	−0.581123	+	0.948395i
$203$	1.05305	+	1.05305i	0.0739099	+	0.0739099i
$204$	−12.0914	+	19.1207i	−0.846570	+	1.33872i
$205$	13.1564	−	7.55081i	0.918882	−	0.527371i
$206$	24.4018	−	5.85943i	1.70016	−	0.408246i
$207$	2.13756			0.148571
$208$	2.25452	+	14.2193i	0.156323	+	0.985929i
$209$	−1.80392	−	1.80392i	−0.124780	−	0.124780i
$210$	7.06927	+	7.48730i	0.487826	+	0.516673i
$211$	12.0624	+	12.0624i	0.830408	+	0.830408i	0.987572	−	0.157164i	$-0.0502352\pi$
$211$	12.0624	+	12.0624i	0.830408	+	0.830408i	−0.157164	+	0.987572i	$0.550235\pi$
$212$	−5.70673	+	17.5685i	−0.391940	+	1.20661i
$213$	4.46877	+	4.46877i	0.306195	+	0.306195i
$214$	3.18820	−	5.20316i	0.217941	−	0.355681i
$215$	−8.68221	−	15.1277i	−0.592122	−	1.03170i
$216$	0.927921	−	11.8091i	0.0631370	−	0.803508i
$217$	−4.10630	+	4.10630i	−0.278754	+	0.278754i
$218$	−3.57976	−	14.9081i	−0.242452	−	1.00970i
$219$	13.4958			0.911962
$220$	2.95303	+	1.92818i	0.199093	+	0.129998i
$221$	14.3793	+	3.66870i	0.967259	+	0.246783i
$222$	31.1042	+	19.0589i	2.08758	+	1.27915i
$223$	1.96944	+	1.96944i	0.131883	+	0.131883i	0.769967	−	0.638084i	$-0.220273\pi$
$223$	1.96944	+	1.96944i	0.131883	+	0.131883i	−0.638084	+	0.769967i	$0.720273\pi$
$224$	−2.57073	−	6.20266i	−0.171764	−	0.414433i
$225$	−19.5421	−	11.4170i	−1.30281	−	0.761135i
$226$	13.0996	−	21.3786i	0.871372	−	1.42208i
$227$	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	$-0.202493\pi$
$230$	−1.08581	+	1.02519i	−0.0715962	+	0.0675988i
$231$	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
$238$	−6.92024	−	0.0979033i	−0.448573	−	0.00634613i
$239$	−24.8818			−1.60947			−0.804734	−	0.593636i	$-0.797692\pi$
$239$	−24.8818			−1.60947			−0.804734	+	0.593636i	$0.797692\pi$
$240$	15.3965	+	19.1069i	0.993838	+	1.23334i
$241$	−1.57909	+	1.57909i	−0.101718	+	0.101718i	−0.756134	−	0.654416i	$-0.772914\pi$
$241$	−1.57909	+	1.57909i	−0.101718	+	0.101718i	0.654416	+	0.756134i	$0.272914\pi$
$242$	−7.66811	+	12.5144i	−0.492924	+	0.804454i
$243$	−18.2979			−1.17381
$244$	−11.9431	−	3.87947i	−0.764581	−	0.248357i
$245$	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
$250$	15.4024	−	3.57303i	0.974132	−	0.225978i
$251$	−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	0.509288	−	0.860596i	$-0.329909\pi$
$257$	−5.63189	−	5.63189i	−0.351308	−	0.351308i	−0.860596	+	0.509288i	$0.829909\pi$
$258$	−29.4276	+	7.06623i	−1.83208	+	0.439925i
$259$			11.1598i			0.693433i
$260$	8.80019	−	13.4776i	0.545765	−	0.835843i
$261$	−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	$-0.125683\pi$
$263$	8.73122	+	8.73122i	0.538390	+	0.538390i	−0.384666	+	0.923056i	$0.625683\pi$
$264$	4.65272	−	3.97480i	0.286355	−	0.244632i
$265$	17.9120	−	10.2802i	1.10033	−	0.631506i
$266$	2.83702	−	4.63003i	0.173949	−	0.283885i
$267$		−	13.2981i		−	0.813832i
$268$	−4.46526	−	1.45044i	−0.272759	−	0.0885999i
$269$	−8.44539	+	8.44539i	−0.514925	+	0.514925i	−0.916031	−	0.401107i	$-0.868626\pi$
$269$	−8.44539	+	8.44539i	−0.514925	+	0.514925i	0.401107	+	0.916031i	$0.368626\pi$
$270$	−9.62966	+	9.09201i	−0.586042	+	0.553322i
$271$		−	4.62963i		−	0.281230i	−0.990064	−	0.140615i	$-0.955092\pi$
$271$		−	4.62963i		−	0.281230i	0.990064	−	0.140615i	$-0.0449080\pi$
$272$	−16.4218	−	1.52439i	−0.995719	−	0.0924300i
$273$	−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	$-0.534539\pi$
$277$	−3.60475			−0.216588			−0.108294	+	0.994119i	$0.534539\pi$
$278$	2.68835	+	11.1957i	0.161236	+	0.671475i
$279$	−15.6601	−	15.6601i	−0.937543	−	0.937543i
$280$	−2.52313	+	7.07007i	−0.150786	+	0.422518i
$281$			5.60340i			0.334271i	0.985934	+	0.167135i	$0.0534517\pi$
$281$			5.60340i			0.334271i	−0.985934	+	0.167135i	$0.946548\pi$
$282$	−5.99354	−	24.9603i	−0.356910	−	1.48637i
$283$			1.56049i			0.0927615i	0.998924	+	0.0463808i	$0.0147688\pi$
$283$			1.56049i			0.0927615i	−0.998924	+	0.0463808i	$0.985231\pi$
$284$	−1.42333	+	4.38181i	−0.0844594	+	0.260012i
$285$	−5.18552	+	19.1555i	−0.307163	+	1.13467i
$286$	−3.42267	−	2.09722i	−0.202387	−	0.124011i
$287$	5.69362	−	5.69362i	0.336084	−	0.336084i
$288$	23.6549	−	9.80390i	1.39388	−	0.577700i
$289$	−8.14448	+	14.9220i	−0.479087	+	0.877767i
$290$	0.113897	−	3.96608i	0.00668825	−	0.232896i
$291$		−	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	$-0.770017\pi$
$293$	−1.52126	+	1.52126i	−0.0888731	+	0.0888731i	0.661273	+	0.750146i	$0.270017\pi$
$294$	−18.4967	−	11.3337i	−1.07875	−	0.660998i
$295$	−3.54956	+	13.1122i	−0.206663	+	0.763421i
$296$	−2.08320	+	26.5117i	−0.121084	+	1.54096i
$297$	2.33539	+	2.33539i	0.135513	+	0.135513i
$298$	−25.0181	−	15.3297i	−1.44926	−	0.888025i
$299$	1.20184	−	1.20184i	0.0695040	−	0.0695040i
$300$	1.57442	−	27.3893i	0.0908990	−	1.58132i
$301$	−6.54674	−	6.54674i	−0.377348	−	0.377348i
$302$	8.17467	+	5.00898i	0.470400	+	0.288235i
$303$		−	30.6670i		−	1.76177i
$304$	7.60407	−	10.4698i	0.436123	−	0.600482i
$305$	6.98852	+	12.1767i	0.400162	+	0.697234i
$306$	0.373370	−	26.3914i	0.0213441	−	1.50870i
$307$	15.1392	−	15.1392i	0.864042	−	0.864042i	−0.127763	−	0.991805i	$-0.540780\pi$
$307$	15.1392	−	15.1392i	0.864042	−	0.864042i	0.991805	+	0.127763i	$0.0407796\pi$
$308$	1.78048	+	0.578351i	0.101452	+	0.0329546i
$309$	−34.4241	+	34.4241i	−1.95832	+	1.95832i
$310$	15.4654	+	0.444132i	0.878377	+	0.0252250i
$311$	13.2017	+	13.2017i	0.748597	+	0.748597i	0.974216	−	0.225618i	$-0.0724403\pi$
$311$	13.2017	+	13.2017i	0.748597	+	0.748597i	−0.225618	+	0.974216i	$0.572440\pi$
$312$	−18.1409	−	21.2349i	−1.02703	−	1.20219i
$313$		−	3.52888i		−	0.199464i	−0.995014	−	0.0997321i	$-0.968201\pi$
$313$		−	3.52888i		−	0.199464i	0.995014	−	0.0997321i	$-0.0317986\pi$
$314$	−4.83422	−	20.1323i	−0.272811	−	1.13613i
$315$	−11.5963	−	3.13921i	−0.653379	−	0.176874i
$316$	2.01768	−	6.21154i	0.113504	−	0.349426i
$317$			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
$320$	−7.31387	+	16.3251i	−0.408858	+	0.912598i
$321$			11.8379i			0.660725i
$322$	−0.414140	+	0.675878i	−0.0230791	+	0.0376652i
$323$	−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
$326$	−3.20673	+	5.23339i	−0.177604	+	0.289851i
$327$	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
$330$	−6.83886	−	0.196396i	−0.376467	−	0.0108113i
$331$		−	0.0382552i		−	0.00210269i	−0.999999	−	0.00105135i	$-0.999665\pi$
$331$		−	0.0382552i		−	0.00210269i	0.999999	−	0.00105135i	$-0.000334654\pi$
$332$	27.0450	+	8.78497i	1.48429	+	0.482138i
$333$	−42.5595			−2.33225
$334$	7.53654	+	4.61797i	0.412381	+	0.252684i
$335$	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	$-0.711473\pi$
$337$		−	28.9062i		−	1.57462i	0.616556	−	0.787311i	$-0.288527\pi$
$338$	0.0336897	−	0.0549817i	0.00183248	−	0.00299061i
$339$			48.6390i			2.64171i
$340$	12.4678	+	13.5850i	0.676163	+	0.736752i
$341$		−	3.85839i		−	0.208943i
$342$	17.6574	+	10.8194i	0.954800	+	0.585048i
$343$		−	14.9449i		−	0.806947i
$344$	−14.3307	−	16.7749i	−0.772660	−	0.904441i
$345$	0.756967	−	2.79626i	0.0407537	−	0.150546i
$346$	18.6511	−	30.4387i	1.00269	−	1.63639i
$347$	10.7142			0.575168			0.287584	−	0.957755i	$-0.407148\pi$
$347$	10.7142			0.575168			0.287584	+	0.957755i	$0.407148\pi$
$348$	−6.54767	−	2.12687i	−0.350992	−	0.114012i
$349$			4.56718i			0.244475i	0.992501	+	0.122238i	$0.0390070\pi$
$349$			4.56718i			0.244475i	−0.992501	+	0.122238i	$0.960993\pi$
$350$	7.39612	−	3.96705i	0.395339	−	0.212048i
$351$	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	0.579774	−	0.814777i	$-0.303141\pi$
$353$	−4.41530	−	4.41530i	−0.235003	−	0.235003i	−0.814777	+	0.579774i	$0.803141\pi$
$354$	20.0973	+	12.3145i	1.06816	+	0.654507i
$355$	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
$358$	23.5565	+	14.4341i	1.24500	+	0.762865i
$359$		−	28.8563i		−	1.52298i	−0.648178	−	0.761489i	$-0.724469\pi$
$359$		−	28.8563i		−	1.52298i	0.648178	−	0.761489i	$-0.275531\pi$
$360$	−26.9629	−	9.62237i	−1.42107	−	0.507143i
$361$	−8.53515			−0.449218
$362$	−33.2614	+	7.98681i	−1.74818	+	0.419777i
$363$		−	28.4718i		−	1.49438i
$364$	2.63958	−	8.12609i	0.138352	−	0.425923i
$365$	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
$370$	21.6188	−	20.4118i	1.12391	−	1.06116i
$371$	7.75168	−	7.75168i	0.402447	−	0.402447i
$372$	8.29355	−	25.5321i	0.430001	−	1.32378i
$373$	18.8307	−	18.8307i	0.975017	−	0.975017i	−0.0246788	−	0.999695i	$-0.507856\pi$
$373$	18.8307	−	18.8307i	0.975017	−	0.975017i	0.999695	+	0.0246788i	$0.00785631\pi$
$374$	3.29721	−	3.20522i	0.170495	−	0.165738i
$375$	−21.8556	+	21.5210i	−1.12862	+	1.11134i
$376$	14.2284	−	12.1552i	0.733771	−	0.626857i
$377$			4.51595i			0.232583i
$378$	−3.67286	+	5.99412i	−0.188912	+	0.308304i
$379$	−4.91018	−	4.91018i	−0.252219	−	0.252219i	0.569661	−	0.821880i	$-0.307075\pi$
$379$	−4.91018	−	4.91018i	−0.252219	−	0.252219i	−0.821880	+	0.569661i	$0.807075\pi$
$380$	−14.1584	+	2.97266i	−0.726311	+	0.152494i
$381$	−37.1649	+	37.1649i	−1.90401	+	1.90401i
$382$	1.18924	−	1.94084i	0.0608466	−	0.0993019i
$383$	3.89730	+	3.89730i	0.199143	+	0.199143i	0.799632	−	0.600490i	$-0.205028\pi$
$383$	3.89730	+	3.89730i	0.199143	+	0.199143i	−0.600490	+	0.799632i	$0.705028\pi$
$384$	23.6078	+	20.1512i	1.20473	+	1.02833i
$385$	−1.04185	−	1.81530i	−0.0530976	−	0.0925163i
$386$	8.93845	−	14.5876i	0.454955	−	0.742488i
$387$	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	$0.994655\pi$
$390$	−0.896350	+	31.2124i	−0.0453884	+	1.58050i
$391$	0.993673	+	1.67440i	0.0502522	+	0.0846778i
$392$	1.23882	−	15.7657i	0.0625697	−	0.796288i
$393$	−9.95003	+	9.95003i	−0.501913	+	0.501913i
$394$	−20.1511	+	32.8867i	−1.01520	+	1.65681i
$395$	−6.33300	+	3.63468i	−0.318648	+	0.182881i
$396$	−2.20564	+	6.79016i	−0.110837	+	0.341218i
$397$			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
$400$	18.3112	−	8.04370i	0.915558	−	0.402185i
$401$	8.23865	+	8.23865i	0.411418	+	0.411418i	0.882232	−	0.470814i	$-0.156040\pi$
$401$	8.23865	+	8.23865i	0.411418	+	0.411418i	−0.470814	+	0.882232i	$0.656040\pi$
$402$	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
$408$	28.7082	−	14.1226i	1.42127	−	0.699173i
$409$			17.7959i			0.879948i	0.898010	+	0.439974i	$0.145012\pi$
$409$			17.7959i			0.879948i	−0.898010	+	0.439974i	$0.854988\pi$
$410$	−21.4437	−	0.615813i	−1.05903	−	0.0304129i
$411$	−24.9598	+	24.9598i	−1.23117	+	1.23117i
$412$	−33.7542	−	10.9643i	−1.66295	−	0.540173i
$413$			7.21061i			0.354811i
$414$	−2.57757	−	1.57939i	−0.126681	−	0.0776228i
$415$	−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	0.00504921	−	0.999987i	$-0.498393\pi$
$419$	20.5726	−	20.5726i	1.00504	−	1.00504i	0.999987	−	0.00504921i	$-0.00160722\pi$
$420$	−2.99227	−	14.2518i	−0.146008	−	0.695418i
$421$		−	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
$430$	−0.708086	+	24.6568i	−0.0341469	+	1.18905i
$431$	2.55950	−	2.55950i	0.123287	−	0.123287i	−0.642771	−	0.766058i	$-0.722215\pi$
$431$	2.55950	−	2.55950i	0.123287	−	0.123287i	0.766058	+	0.642771i	$0.222215\pi$
$432$	−9.84438	+	13.5543i	−0.473638	+	0.652134i
$433$	24.3763	−	24.3763i	1.17145	−	1.17145i	0.189585	−	0.981864i	$-0.439286\pi$
$433$	24.3763	−	24.3763i	1.17145	−	1.17145i	0.981864	−	0.189585i	$-0.0607143\pi$
$434$	7.98562	−	1.91753i	0.383322	−	0.0920442i
$435$	3.83137	+	6.67570i	0.183700	+	0.320075i
$436$	−6.69854	+	20.6218i	−0.320802	+	0.987605i
$437$	−1.52763			−0.0730765
$438$	−16.2739	−	9.97171i	−0.777595	−	0.476467i
$439$	−16.6455	+	16.6455i	−0.794446	+	0.794446i	−0.982214	−	0.187767i	$-0.939875\pi$
$439$	−16.6455	+	16.6455i	−0.794446	+	0.794446i	0.187767	+	0.982214i	$0.439875\pi$
$440$	−2.13621	−	4.50701i	−0.101840	−	0.214863i
$441$	25.3088			1.20518
$442$	−14.6286	−	15.0484i	−0.695810	−	0.715780i
$443$	−23.3454	−	23.3454i	−1.10918	−	1.10918i	−0.993259	−	0.115917i	$-0.963019\pi$
$443$	−23.3454	−	23.3454i	−1.10918	−	1.10918i	−0.115917	−	0.993259i	$-0.536981\pi$
$444$	−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	−0.338188	−	0.941079i	$-0.609814\pi$
$449$	12.7750	−	12.7750i	0.602891	−	0.602891i	0.941079	+	0.338188i	$0.109814\pi$
$450$	15.1290	+	28.2063i	0.713187	+	1.32966i
$451$			5.34987i			0.251916i
$452$	−31.5922	+	16.1003i	−1.48597	+	0.757295i
$453$	−18.5984			−0.873831
$454$	−16.6144	−	10.1804i	−0.779754	−	0.477789i
$455$	−8.28500	+	4.75498i	−0.388407	+	0.222917i
$456$	−1.96638	+	25.0249i	−0.0920841	+	1.17190i
$457$	−18.4516	−	18.4516i	−0.863128	−	0.863128i	0.128573	−	0.991700i	$-0.458960\pi$
$457$	−18.4516	−	18.4516i	−0.863128	−	0.863128i	−0.991700	+	0.128573i	$0.958960\pi$
$458$	−13.2856	+	21.6821i	−0.620795	+	1.01314i
$459$	8.81253	+	14.8496i	0.411334	+	0.693120i
$460$	2.06680	−	0.433940i	0.0963653	−	0.0202326i
$461$	−19.1015			−0.889644			−0.444822	−	0.895619i	$-0.646733\pi$
$461$	−19.1015			−0.889644			−0.444822	+	0.895619i	$0.646733\pi$
$462$	−3.53126	+	0.847936i	−0.164289	+	0.0394496i
$463$	−24.7437	+	24.7437i	−1.14994	+	1.14994i	−0.163375	+	0.986564i	$0.552238\pi$
$463$	−24.7437	+	24.7437i	−1.14994	+	1.14994i	−0.986564	+	0.163375i	$0.947762\pi$
$464$	−0.785935	−	4.95689i	−0.0364861	−	0.230118i
$465$	−26.0314	+	14.9401i	−1.20718	+	0.692831i
$466$	−17.6711	−	10.8278i	−0.818596	−	0.501590i
$467$	21.9192	+	21.9192i	1.01430	+	1.01430i	0.999896	+	0.0144021i	$0.00458451\pi$
$467$	21.9192	+	21.9192i	1.01430	+	1.01430i	0.0144021	+	0.999896i	$0.495415\pi$
$468$	30.9902	+	10.0665i	1.43252	+	0.465323i
$469$	1.97019	+	1.97019i	0.0909751	+	0.0909751i
$470$	−20.9137	−	0.600594i	−0.964678	−	0.0277033i
$471$	28.4010	+	28.4010i	1.30865	+	1.30865i
$472$	−1.34601	+	17.1299i	−0.0619553	+	0.788469i
$473$	6.15148			0.282846
$474$	2.95818	+	12.3195i	0.135874	+	0.565851i
$475$	13.9659	+	8.15928i	0.640801	+	0.374374i
$476$	8.27240	+	5.23125i	0.379165	+	0.239774i
$477$	29.5623	+	29.5623i	1.35356	+	1.35356i
$478$	30.0036	+	18.3845i	1.37233	+	0.840887i
$479$	29.4006	−	29.4006i	1.34335	−	1.34335i	0.450645	−	0.892703i	$-0.351194\pi$
$479$	29.4006	−	29.4006i	1.34335	−	1.34335i	0.892703	−	0.450645i	$-0.148806\pi$
$480$	−4.44820	−	34.4160i	−0.203032	−	1.57087i
$481$	−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
$486$	22.0644	+	13.5198i	1.00086	+	0.613273i
$487$		−	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
$490$	−12.8560	+	12.1383i	−0.580776	+	0.548350i
$491$			21.6329i			0.976278i	0.872766	+	0.488139i	$0.162324\pi$
$491$			21.6329i			0.976278i	−0.872766	+	0.488139i	$0.837676\pi$
$492$	−11.4995	+	35.4017i	−0.518436	+	1.59603i
$493$	−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
$496$	19.3290	−	3.06469i	0.867898	−	0.137609i
$497$	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	−0.998351	−	0.0574114i	$-0.981715\pi$
$499$	−21.0190	+	21.0190i	−0.940939	+	0.940939i	0.0574114	+	0.998351i	$0.481715\pi$
$500$	−21.2129	−	7.07191i	−0.948671	−	0.316265i
$501$	−17.1466			−0.766053
$502$	32.9445	+	20.1865i	1.47038	+	0.900969i
$503$	−0.704050			−0.0313920			−0.0156960	−	0.999877i	$-0.504996\pi$
$503$	−0.704050			−0.0313920			−0.0156960	+	0.999877i	$0.504996\pi$
$504$	−15.1496	−	1.19041i	−0.674816	−	0.0530249i
$505$	−24.1269	−	6.53132i	−1.07363	−	0.290640i
$506$	−0.122968	−	0.512105i	−0.00546659	−	0.0227658i
$507$			0.125091i			0.00555547i
$508$	−36.4416	−	11.8373i	−1.61684	−	0.525194i
$509$	−8.81873			−0.390883			−0.195442	−	0.980715i	$-0.562614\pi$
$509$	−8.81873			−0.390883			−0.195442	+	0.980715i	$0.562614\pi$
$510$	−34.3918	−	9.83433i	−1.52290	−	0.435472i
$511$		−	5.83883i		−	0.258295i
$512$	−5.27407	+	22.0042i	−0.233083	+	0.972457i
$513$	−13.5480			−0.598159
$514$	2.62993	+	10.9524i	0.116001	+	0.483092i
$515$	19.7513	+	34.4143i	0.870345	+	1.51647i
$516$	40.7062	+	13.2225i	1.79199	+	0.582090i
$517$			5.21765i			0.229472i
$518$	8.24566	−	13.4569i	0.362293	−	0.591264i
$519$			69.2520i			3.03982i
$520$	−20.5699	+	9.74962i	−0.902050	+	0.427549i
$521$	−21.2780	−	21.2780i	−0.932207	−	0.932207i	0.0656368	−	0.997844i	$-0.479092\pi$
$521$	−21.2780	−	21.2780i	−0.932207	−	0.932207i	−0.997844	+	0.0656368i	$0.979092\pi$
$522$	7.80998	−	1.87535i	0.341834	−	0.0820819i
$523$	16.8090	+	16.8090i	0.735006	+	0.735006i	0.971607	−	0.236601i	$-0.0760333\pi$
$523$	16.8090	+	16.8090i	0.735006	+	0.735006i	−0.236601	+	0.971607i	$0.576033\pi$
$524$	−9.75640	−	3.16915i	−0.426210	−	0.138445i
$525$	−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
$528$	−8.54735	+	1.35522i	−0.371976	+	0.0589783i
$529$	−22.7770			−0.990304
$530$	−29.1949	−	0.838410i	−1.26814	−	0.0364182i
$531$	−27.4988			−1.19335
$532$	−6.84202	+	3.48690i	−0.296639	+	0.151176i
$533$	24.4167			1.05760
$534$	−9.82565	+	16.0355i	−0.425197	+	0.693923i
$535$	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
$540$	18.3297	−	3.84846i	0.788786	−	0.165611i
$541$	−18.5242	−	18.5242i	−0.796419	−	0.796419i	0.186110	−	0.982529i	$-0.440412\pi$
$541$	−18.5242	−	18.5242i	−0.796419	−	0.796419i	−0.982529	+	0.186110i	$0.940412\pi$
$542$	−3.42072	+	5.58262i	−0.146932	+	0.239794i
$543$	46.9225	−	46.9225i	2.01364	−	2.01364i
$544$	18.6758	+	13.9719i	0.800720	+	0.599038i
$545$	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	$-0.914266\pi$
$547$		−	12.4469i		−	0.532190i	0.963947	−	0.266095i	$-0.0857335\pi$
$548$	−24.4740	−	7.94986i	−1.04548	−	0.339601i
$549$	−20.0966	+	20.0966i	−0.857702	+	0.857702i
$550$	−1.61102	+	5.33857i	−0.0686942	+	0.227637i
$551$	2.87007	−	2.87007i	0.122269	−	0.122269i
$552$	0.287046	−	3.65307i	0.0122175	−	0.155485i
$553$	−2.74070	+	2.74070i	−0.116546	+	0.116546i
$554$	4.34677	+	2.66346i	0.184677	+	0.113160i
$555$	−15.0714	+	55.6744i	−0.639747	+	2.36325i
$556$	5.03051	−	15.4867i	0.213341	−	0.656781i
$557$	−10.8212	−	10.8212i	−0.458508	−	0.458508i	0.439658	−	0.898165i	$-0.355100\pi$
$557$	−10.8212	−	10.8212i	−0.458508	−	0.458508i	−0.898165	+	0.439658i	$0.855100\pi$
$558$	7.31279	+	30.4544i	0.309575	+	1.28924i
$559$		−	28.0753i		−	1.18746i
$560$	8.26641	−	6.66114i	0.349319	−	0.281485i
$561$	−2.20529	+	8.64357i	−0.0931075	+	0.364932i
$562$	4.14021	−	6.75683i	0.174644	−	0.285020i
$563$	30.1456	−	30.1456i	1.27048	−	1.27048i	0.324651	−	0.945834i	$-0.394753\pi$
$563$	30.1456	−	30.1456i	1.27048	−	1.27048i	0.945834	−	0.324651i	$-0.105247\pi$
$564$	−11.2153	+	34.5268i	−0.472248	+	1.45384i
$565$	38.2662	+	10.3589i	1.60987	+	0.435803i
$566$	1.15301	−	1.88171i	0.0484645	−	0.0790942i
$567$			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	$0.614113\pi$
$570$	20.4064	−	19.2671i	0.854731	−	0.807009i
$571$	−19.8158	−	19.8158i	−0.829266	−	0.829266i	0.158150	−	0.987415i	$-0.449447\pi$
$571$	−19.8158	−	19.8158i	−0.829266	−	0.829266i	−0.987415	+	0.158150i	$0.949447\pi$
$572$	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	−0.358414	−	0.933563i	$-0.616682\pi$
$577$	13.8155	−	13.8155i	0.575148	−	0.575148i	0.933563	+	0.358414i	$0.116682\pi$
$578$	20.8465	−	11.9759i	0.867101	−	0.498133i
$579$			33.1886i			1.37927i
$580$	−3.06778	+	4.69833i	−0.127383	+	0.195087i
$581$	−11.9330	−	11.9330i	−0.495063	−	0.495063i
$582$	−7.35696	+	12.0066i	−0.304956	+	0.497689i
$583$			7.28367i			0.301659i
$584$	1.08994	−	13.8710i	0.0451021	−	0.573988i
$585$	−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	0.0328203	−	0.999461i	$-0.489551\pi$
$587$	−23.4199	−	23.4199i	−0.966641	−	0.966641i	−0.999461	+	0.0328203i	$0.989551\pi$
$588$	13.9300	+	27.3335i	0.574462	+	1.12721i
$589$	11.1916	+	11.1916i	0.461142	+	0.461142i
$590$	13.9685	−	13.1886i	0.575073	−	0.542966i
$591$		−	74.8215i		−	3.07774i
$592$	22.1009	−	30.4298i	0.908340	−	1.25066i
$593$	15.4067	−	15.4067i	0.632677	−	0.632677i	−0.316062	−	0.948739i	$-0.602361\pi$
$593$	15.4067	−	15.4067i	0.632677	−	0.632677i	0.948739	+	0.316062i	$0.102361\pi$
$594$	−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	$-0.366625\pi$
$599$	19.9151			0.813710			0.406855	+	0.913493i	$0.366625\pi$
$600$	−22.1358	+	31.8640i	−0.903690	+	1.30084i
$601$	24.0776	+	24.0776i	0.982144	+	0.982144i	0.999843	−	0.0176995i	$-0.00563422\pi$
$601$	24.0776	+	24.0776i	0.982144	+	0.982144i	−0.0176995	+	0.999843i	$0.505634\pi$
$602$	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
$606$	−22.6591	+	36.9797i	−0.920461	+	1.50220i
$607$	10.8898			0.442002			0.221001	−	0.975274i	$-0.429068\pi$
$607$	10.8898			0.442002			0.221001	+	0.975274i	$0.429068\pi$
$608$	−16.9052	+	7.00645i	−0.685595	+	0.284149i
$609$	2.88901	+	2.88901i	0.117068	+	0.117068i
$610$	0.569956	−	19.8468i	0.0230768	−	0.803575i
$611$	23.8133			0.963382
$612$	−19.9502	+	31.5481i	−0.806439	+	1.27526i
$613$	14.4866	−	14.4866i	0.585109	−	0.585109i	−0.351193	−	0.936303i	$-0.614224\pi$
$613$	14.4866	−	14.4866i	0.585109	−	0.585109i	0.936303	+	0.351193i	$0.114224\pi$
$614$	−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	$0.145923\pi$
$617$			21.9850i			0.885083i	−0.896748	+	0.442542i	$0.854077\pi$
$618$	66.9453	−	16.0751i	2.69294	−	0.646634i
$619$	23.6274	−	23.6274i	0.949666	−	0.949666i	−0.0491265	−	0.998793i	$-0.515644\pi$
$619$	23.6274	−	23.6274i	0.949666	−	0.949666i	0.998793	+	0.0491265i	$0.0156437\pi$
$620$	−18.3208	−	11.9626i	−0.735780	−	0.480428i
$621$	1.97770			0.0793623
$622$	−6.16479	−	25.6735i	−0.247186	−	1.02941i
$623$	−5.75331			−0.230501
$624$	6.18519	+	39.0099i	0.247606	+	1.56165i
$625$	12.2767	+	21.7781i	0.491067	+	0.871122i
$626$	−2.60740	+	4.25529i	−0.104213	+	0.170076i
$627$	−4.94897	−	4.94897i	−0.197643	−	0.197643i
$628$	−9.04593	+	27.8483i	−0.360972	+	1.11127i
$629$	−19.7843	−	33.3377i	−0.788853	−	1.32926i
$630$	11.6639	+	12.3536i	0.464701	+	0.492180i
$631$	−13.8266			−0.550428			−0.275214	−	0.961383i	$-0.588749\pi$
$631$	−13.8266			−0.550428			−0.275214	+	0.961383i	$0.588749\pi$
$632$	−7.02256	+	5.99934i	−0.279343	+	0.238641i
$633$	33.0926	+	33.0926i	1.31531	+	1.31531i
$634$	1.98112	−	3.23320i	0.0786804	−	0.128407i
$635$	21.3238	+	37.1542i	0.846209	+	1.47442i
$636$	−15.6562	+	48.1983i	−0.620807	+	1.91119i
$637$	14.2298	−	14.2298i	0.563805	−	0.563805i
$638$	1.19316	+	0.731099i	0.0472375	+	0.0289445i
$639$	7.37322	+	7.37322i	0.291680	+	0.291680i
$640$	20.8816	−	14.2815i	0.825416	−	0.564524i
$641$	1.51664	−	1.51664i	0.0599038	−	0.0599038i	−0.676520	−	0.736424i	$-0.736513\pi$
$641$	1.51664	−	1.51664i	0.0599038	−	0.0599038i	0.736424	+	0.676520i	$0.236513\pi$
$642$	8.74670	−	14.2746i	0.345205	−	0.563375i
$643$	−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
$646$	−0.266832	+	18.8609i	−0.0104984	+	0.742072i
$647$	−2.34060	−	2.34060i	−0.0920183	−	0.0920183i	0.659599	−	0.751618i	$-0.270726\pi$
$647$	−2.34060	−	2.34060i	−0.0920183	−	0.0920183i	−0.751618	+	0.659599i	$0.770726\pi$
$648$	−0.463073	+	5.89326i	−0.0181912	+	0.231509i
$649$	−3.38764	−	3.38764i	−0.132976	−	0.132976i
$650$	24.3651	+	7.35267i	0.955678	+	0.288396i
$651$	−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	$-0.288664\pi$
$653$	31.4935			1.23243			0.616217	+	0.787576i	$0.288664\pi$
$654$	−9.82091	−	40.8996i	−0.384028	−	1.59930i
$655$	5.70895	+	9.94718i	0.223067	+	0.388668i
$656$	−26.8007	+	4.24937i	−1.04639	+	0.165910i
$657$	22.2673			0.868731
$658$	−10.7989	+	2.59305i	−0.420983	+	0.101088i
$659$		−	4.23508i		−	0.164975i	−0.996592	−	0.0824876i	$-0.973714\pi$
$659$		−	4.23508i		−	0.164975i	0.996592	−	0.0824876i	$-0.0262865\pi$
$660$	8.10150	+	5.28989i	0.315351	+	0.205909i
$661$	−9.54965			−0.371438			−0.185719	−	0.982603i	$-0.559461\pi$
$661$	−9.54965			−0.371438			−0.185719	+	0.982603i	$0.559461\pi$
$662$	−0.0282658	+	0.0461298i	−0.00109858	+	0.00179289i
$663$	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
$666$	51.3202	+	31.4461i	1.98862	+	1.21851i
$667$	−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
$670$	0.213093	−	7.42027i	0.00823251	−	0.286670i
$671$	−4.95148			−0.191150
$672$	−7.05269	−	17.0167i	−0.272063	−	0.656435i
$673$		−	23.5472i		−	0.907680i	−0.891083	−	0.453840i	$-0.850054\pi$
$673$		−	23.5472i		−	0.907680i	0.891083	−	0.453840i	$-0.149946\pi$
$674$	−21.3581	+	34.8564i	−0.822682	+	1.34262i
$675$	−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	$-0.467644\pi$
$677$	5.28053			0.202947			0.101474	+	0.994838i	$0.467644\pi$
$678$	35.9381	−	58.6512i	1.38020	−	2.25248i
$679$	−4.30780			−0.165318
$680$	−4.99664	−	25.5936i	−0.191612	−	0.981471i
$681$	37.8000			1.44850
$682$	−2.85087	+	4.65262i	−0.109165	+	0.178158i
$683$	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
$686$	−11.0424	+	18.0212i	−0.421600	+	0.688053i
$687$		−	49.3296i		−	1.88204i
$688$	4.88609	+	30.8165i	0.186280	+	1.17487i
$689$	33.2425			1.26644
$690$	−2.97887	+	2.81256i	−0.113404	+	0.107072i
$691$	−2.78868	−	2.78868i	−0.106086	−	0.106086i	0.652071	−	0.758158i	$-0.273900\pi$
$691$	−2.78868	−	2.78868i	−0.106086	−	0.106086i	−0.758158	+	0.652071i	$0.773900\pi$
$692$	−44.9808	+	22.9235i	−1.70991	+	0.871422i
$693$	2.99600	−	2.99600i	0.113809	−	0.113809i
$694$	−12.9197	−	7.91645i	−0.490424	−	0.300504i
$695$	−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
$698$	3.37457	−	5.50731i	0.127729	−	0.208455i
$699$	40.2039			1.52065
$700$	−11.8497	−	0.681156i	−0.447878	−	0.0257453i
$701$		−	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
$704$	−3.70956	−	5.10310i	−0.139809	−	0.192330i
$705$	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	0.0697621	−	0.997564i	$-0.477776\pi$
$709$	28.4197	−	28.4197i	1.06733	−	1.06733i	0.997564	−	0.0697621i	$-0.0222240\pi$
$710$	−7.28159	−	0.209111i	−0.273273	−	0.00784778i
$711$	−10.4521	−	10.4521i	−0.391984	−	0.391984i
$712$	−13.6679	−	1.07398i	−0.512225	−	0.0402490i
$713$	−1.63372	−	1.63372i	−0.0611833	−	0.0611833i
$714$	−18.9854	−	0.268593i	−0.710510	−	0.0100519i
$715$	1.65845	−	6.12635i	0.0620223	−	0.229112i
$716$	−17.7405	−	34.8106i	−0.662993	−	1.30093i
$717$	−68.2620			−2.54929
$718$	−21.3212	+	34.7963i	−0.795700	+	1.29859i
$719$	22.7796	−	22.7796i	0.849535	−	0.849535i	−0.140540	−	0.990075i	$-0.544884\pi$
$719$	22.7796	−	22.7796i	0.849535	−	0.849535i	0.990075	+	0.140540i	$0.0448840\pi$
$720$	25.4033	+	31.5253i	0.946726	+	1.17488i
$721$	14.8933	+	14.8933i	0.554654	+	0.554654i
$722$	10.2921	+	6.30640i	0.383031	+	0.234700i
$723$	−4.33215	+	4.33215i	−0.161115	+	0.161115i
$724$	46.0094	+	14.9451i	1.70992	+	0.555432i
$725$	6.06802	−	1.59252i	0.225360	−	0.0591447i
$726$	−21.0371	+	34.3326i	−0.780760	+	1.27420i
$727$	−36.7379	−	36.7379i	−1.36253	−	1.36253i	−0.870677	−	0.491856i	$-0.836319\pi$
$727$	−36.7379	−	36.7379i	−1.36253	−	1.36253i	−0.491856	−	0.870677i	$-0.663681\pi$
$728$	−9.18710	+	7.84850i	−0.340496	+	0.290885i
$729$	−43.9294			−1.62702
$730$	−11.3111	+	10.6795i	−0.418641	+	0.395267i
$731$	31.1634	+	7.95093i	1.15262	+	0.294076i
$732$	−32.7655	−	10.6431i	−1.21105	−	0.393382i
$733$	−10.0360	−	10.0360i	−0.370689	−	0.370689i	0.497039	−	0.867728i	$-0.334421\pi$
$733$	−10.0360	−	10.0360i	−0.370689	−	0.370689i	−0.867728	+	0.497039i	$0.834421\pi$
$734$	−10.0648	+	16.4257i	−0.371497	+	0.606285i
$735$	8.96252	−	33.1078i	0.330588	−	1.22120i
$736$	2.46777	−	1.02278i	0.0909632	−	0.0377003i
$737$	−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	$0.705015\pi$
$740$	−41.1507	+	8.63988i	−1.51273	+	0.317608i
$741$	−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
$748$	−6.34419	+	1.42878i	−0.231966	+	0.0522412i
$749$	5.12154			0.187137
$750$	42.2558	−	9.80244i	1.54296	−	0.357935i
$751$	3.48860	+	3.48860i	0.127301	+	0.127301i	0.767887	−	0.640586i	$-0.221308\pi$
$751$	3.48860	+	3.48860i	0.127301	+	0.127301i	−0.640586	+	0.767887i	$0.721308\pi$
$752$	−26.1384	+	4.14435i	−0.953169	+	0.151129i
$753$	−74.9530			−2.73144
$754$	3.33672	−	5.44554i	0.121516	−	0.198315i
$755$	−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	0.0615726	−	0.998103i	$-0.480388\pi$
$757$	29.1555	−	29.1555i	1.05968	−	1.05968i	0.998103	−	0.0615726i	$-0.0196116\pi$
$758$	2.29291	+	9.54892i	0.0832823	+	0.346832i
$759$	0.722436	+	0.722436i	0.0262228	+	0.0262228i
$760$	19.2693	+	6.87672i	0.698970	+	0.249445i
$761$	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	$0.131729\pi$
$769$			22.3026i			0.804254i	−0.915584	+	0.402127i	$0.868271\pi$
$770$	−0.0849691	+	2.95877i	−0.00306207	+	0.106627i
$771$	−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	$-0.412924\pi$
$773$	−19.2579	−	19.2579i	−0.692658	−	0.692658i	−0.962816	+	0.270158i	$0.912924\pi$
$774$	−48.5539	+	11.6589i	−1.74523	+	0.419070i
$775$	6.20991	+	23.6618i	0.223067	+	0.849956i
$776$	−10.2338	−	0.804141i	−0.367373	−	0.0288670i
$777$			30.6163i			1.09835i
$778$	0.489380	−	0.798670i	0.0175451	−	0.0286337i
$779$	−15.5178	−	15.5178i	−0.555982	−	0.555982i
$780$	24.1429	−	36.9751i	0.864456	−	1.32392i
$781$			1.81665i			0.0650047i
$782$	0.0389515	−	2.75326i	0.00139290	−	0.0984565i
$783$	−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	$-0.881134\pi$
$787$		−	20.4683i		−	0.729617i	0.931083	−	0.364809i	$-0.118866\pi$
$788$	48.5983	−	24.7671i	1.73124	−	0.882292i
$789$	23.9537	+	23.9537i	0.852774	+	0.852774i
$790$	10.3222	+	0.296430i	0.367247	+	0.0105465i
$791$	21.0432			0.748211
$792$	7.67674	−	6.55820i	0.272781	−	0.233036i
$793$			22.5985i			0.802495i
$794$	15.2553	−	24.8967i	0.541391	−	0.883552i
$795$	49.1408	−	28.2032i	1.74284	−	1.00026i
$796$	−39.7843	−	12.9231i	−1.41012	−	0.458046i
$797$	30.0902	−	30.0902i	1.06585	−	1.06585i	0.0681748	−	0.997673i	$-0.478282\pi$
$797$	30.0902	−	30.0902i	1.06585	−	1.06585i	0.997673	−	0.0681748i	$-0.0217176\pi$
$798$	7.78324	−	12.7023i	0.275524	−	0.449656i
$799$	−6.74393	+	26.4326i	−0.238583	+	0.935120i
$800$	−28.0237	−	3.83020i	−0.990789	−	0.135418i
$801$		−	21.9412i		−	0.775253i
$802$	−3.84721	−	16.0219i	−0.135850	−	0.565752i
$803$	2.74316	+	2.74316i	0.0968039	+	0.0968039i
$804$	−12.2502	−	3.97922i	−0.432033	−	0.140336i
$805$	−1.20978	−	0.327495i	−0.0426390	−	0.0115427i
$806$	21.2345	+	13.0113i	0.747953	+	0.458303i
$807$	−23.1696	+	23.1696i	−0.815607	+	0.815607i
$808$	−31.5197	−	2.47671i	−1.10886	−	0.0871305i
$809$	2.61310	−	2.61310i	0.0918717	−	0.0918717i	−0.659677	−	0.751549i	$-0.729307\pi$
$809$	2.61310	−	2.61310i	0.0918717	−	0.0918717i	0.751549	+	0.659677i	$0.229307\pi$
$810$	4.80562	−	4.53731i	0.168852	−	0.159425i
$811$	−1.78985	+	1.78985i	−0.0628500	+	0.0628500i	−0.737833	−	0.674983i	$-0.764151\pi$
$811$	−1.78985	+	1.78985i	−0.0628500	+	0.0628500i	0.674983	+	0.737833i	$0.264151\pi$
$812$	−0.920169	+	2.83279i	−0.0322916	+	0.0994113i
$813$		−	12.7012i		−	0.445450i
$814$	2.44833	+	10.1962i	0.0858138	+	0.357375i
$815$	−9.36740	−	2.53582i	−0.328126	−	0.0888259i
$816$	−45.0525	−	4.18211i	−1.57715	−	0.146403i
$817$	−17.8429	+	17.8429i	−0.624246	+	0.624246i
$818$	13.1489	−	21.4591i	0.459741	−	0.750298i
$819$	−13.6737	−	13.6737i	−0.477798	−	0.477798i
$820$	25.4028	+	16.5868i	0.887103	+	0.579235i
$821$	24.4251	+	24.4251i	0.852444	+	0.852444i	0.990434	−	0.137990i	$-0.0440642\pi$
$821$	24.4251	+	24.4251i	0.852444	+	0.852444i	−0.137990	+	0.990434i	$0.544064\pi$
$822$	48.5398	−	11.6555i	1.69302	−	0.406532i
$823$	−25.4357			−0.886632			−0.443316	−	0.896365i	$-0.646198\pi$
$823$	−25.4357			−0.886632			−0.443316	+	0.896365i	$0.646198\pi$
$824$	32.6011	+	38.1614i	1.13571	+	1.32942i
$825$	−2.74604	−	10.4633i	−0.0956049	−	0.364286i
$826$	5.32774	−	8.69489i	0.185376	−	0.302534i
$827$	−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	$-0.501519\pi$
$829$	−0.274786			−0.00954370			−0.00477185	+	0.999989i	$0.501519\pi$
$830$	−1.29065	+	44.9427i	−0.0447992	+	1.55998i
$831$	−9.88947			−0.343062
$832$	−23.2905	+	16.9303i	−0.807451	+	0.586954i
$833$	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
$836$	1.57628	−	4.85266i	0.0545168	−	0.167833i
$837$	−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	$-0.432779\pi$
$839$	−22.2504	−	22.2504i	−0.768169	−	0.768169i	−0.977784	+	0.209615i	$0.932779\pi$
$840$	−6.92210	+	19.3964i	−0.238835	+	0.669240i
$841$			27.4257i			0.945715i
$842$	−7.40238	+	12.0807i	−0.255103	+	0.416329i
$843$			15.3727i			0.529463i
$844$	−10.5402	+	32.4486i	−0.362809	+	1.11693i
$845$	0.0984135	+	0.0266412i	0.00338553	+	0.000916486i
$846$	−9.88900	−	41.1832i	−0.339991	−	1.41591i
$847$	−12.3181			−0.423254
$848$	−36.4883	+	5.78538i	−1.25301	+	0.198671i
$849$			4.28114i			0.146928i
$850$	−15.0617	+	24.9629i	−0.516611	+	0.856220i
$851$	−4.43998			−0.152201
$852$	−3.90485	+	12.0213i	−0.133778	+	0.411843i
$853$		−	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
$856$	12.1670	+	0.956044i	0.415860	+	0.0326769i
$857$	−17.1041			−0.584265			−0.292132	−	0.956378i	$-0.594365\pi$
$857$	−17.1041			−0.584265			−0.292132	+	0.956378i	$0.594365\pi$
$858$	−9.38995	−	5.75364i	−0.320568	−	0.196426i
$859$	7.55056			0.257622			0.128811	−	0.991669i	$-0.458884\pi$
$859$	7.55056			0.257622			0.128811	+	0.991669i	$0.458884\pi$
$860$	19.0721	−	29.2091i	0.650353	−	0.996021i
$861$	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	$-0.502912\pi$
$863$	29.1069	−	29.1069i	0.990810	−	0.990810i	0.999958	+	0.00914807i	$0.00291196\pi$
$864$	21.8858	−	9.07069i	0.744569	−	0.308591i
$865$	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
$868$	−11.0462	−	3.58813i	−0.374934	−	0.121789i
$869$		−	2.57523i		−	0.0873587i
$870$	0.312471	−	10.8808i	0.0105937	−	0.368893i
$871$			8.44904i			0.286285i
$872$	23.3143	−	19.9173i	0.789523	−	0.674486i
$873$		−	16.4285i		−	0.556019i
$874$	1.84209	+	1.12873i	0.0623095	+	0.0381798i
$875$	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
$880$	−0.754174	+	7.01315i	−0.0254232	+	0.236413i
$881$	−35.2679	+	35.2679i	−1.18821	+	1.18821i	−0.210642	+	0.977563i	$0.567556\pi$
$881$	−35.2679	+	35.2679i	−1.18821	+	1.18821i	−0.977563	+	0.210642i	$0.932444\pi$
$882$	−30.5185	−	18.7000i	−1.02761	−	0.629663i
$883$	−29.9632	−	29.9632i	−1.00834	−	1.00834i	−0.999965	−	0.00837847i	$-0.997333\pi$
$883$	−29.9632	−	29.9632i	−1.00834	−	1.00834i	−0.00837847	−	0.999965i	$-0.502667\pi$
$884$	6.52090	+	28.9547i	0.219322	+	0.973853i
$885$	−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	$-0.196728\pi$
$887$	48.5465			1.63003			0.815016	+	0.579439i	$0.196728\pi$
$888$	−5.71518	+	72.7337i	−0.191789	+	2.44078i
$889$	16.0790	+	16.0790i	0.539273	+	0.539273i
$890$	10.5231	+	11.1454i	0.352735	+	0.373594i
$891$	−1.16546	−	1.16546i	−0.0390443	−	0.0390443i
$892$	−1.72092	+	5.29793i	−0.0576205	+	0.177388i
$893$	−15.1343	−	15.1343i	−0.506449	−	0.506449i
$894$	−68.6361	−	42.0563i	−2.29553	−	1.40657i
$895$	−11.4142	+	42.1645i	−0.381535	+	1.40940i
$896$	8.71821	−	10.2137i	0.291255	−	0.341216i
$897$	3.29719	−	3.29719i	0.110090	−	0.110090i
$898$	−24.8439	+	5.96557i	−0.829051	+	0.199074i
$899$	6.13877			0.204740
$900$	2.59770	−	45.1909i	0.0865900	−	1.50636i
$901$	−9.41431	+	36.8991i	−0.313636	+	1.22929i
$902$	3.95288	−	6.45112i	0.131617	−	0.214799i
$903$	−17.9607	−	17.9607i	−0.597694	−	0.597694i
$904$	49.9914	+	3.92816i	1.66269	+	0.130649i
$905$	−26.9224	−	46.9090i	−0.894930	−	1.55931i
$906$	22.4269	+	13.7419i	0.745082	+	0.456545i
$907$	−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
$910$	13.5038	+	0.387797i	0.447645	+	0.0128554i
$911$	−13.9247	+	13.9247i	−0.461345	+	0.461345i	−0.899096	−	0.437751i	$-0.855775\pi$
$911$	−13.9247	+	13.9247i	−0.461345	+	0.461345i	0.437751	+	0.899096i	$0.355775\pi$
$912$	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
$918$	0.345446	−	24.4177i	0.0114014	−	0.805904i
$919$	−47.6999			−1.57347			−0.786737	−	0.617288i	$-0.788231\pi$
$919$	−47.6999			−1.57347			−0.786737	+	0.617288i	$0.788231\pi$
$920$	−2.81287	−	1.00384i	−0.0927377	−	0.0330958i
$921$	41.5338	−	41.5338i	1.36859	−	1.36859i
$922$	23.0334	+	14.1136i	0.758565	+	0.464806i
$923$	8.29113			0.272906
$924$	4.88468	+	1.58668i	0.160694	+	0.0521980i
$925$	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	−0.991279	−	0.131781i	$-0.957930\pi$
$929$	−26.1971	+	26.1971i	−0.859498	+	0.859498i	0.131781	+	0.991279i	$0.457930\pi$
$930$	42.4287	+	1.21846i	1.39129	+	0.0399547i
$931$	−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	0.927501	−	0.373820i	$-0.121952\pi$
$937$	16.9484	+	16.9484i	0.553681	+	0.553681i	−0.373820	+	0.927501i	$0.621952\pi$
$938$	−0.920024	−	3.83148i	−0.0300398	−	0.125102i
$939$		−	9.68133i		−	0.315938i
$940$	24.7750	+	16.1768i	0.808070	+	0.527630i
$941$	2.24164	−	2.24164i	0.0730755	−	0.0730755i	−0.669624	−	0.742700i	$-0.733545\pi$
$941$	2.24164	−	2.24164i	0.0730755	−	0.0730755i	0.742700	+	0.669624i	$0.233545\pi$
$942$	−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
$946$	−7.41774	−	4.54518i	−0.241172	−	0.147776i
$947$			17.5791i			0.571243i	0.958342	+	0.285622i	$0.0922001\pi$
$947$			17.5791i			0.571243i	−0.958342	+	0.285622i	$0.907800\pi$
$948$	5.53542	−	17.0411i	0.179782	−	0.553469i
$949$	12.5197	−	12.5197i	0.406407	−	0.406407i
$950$	−10.8121	−	20.1579i	−0.350790	−	0.654009i
$951$			7.35594i			0.238533i
$952$	−6.11001	−	12.4203i	−0.198027	−	0.402546i
$953$	−24.2292	−	24.2292i	−0.784862	−	0.784862i	0.195785	−	0.980647i	$-0.437275\pi$
$953$	−24.2292	−	24.2292i	−0.784862	−	0.784862i	−0.980647	+	0.195785i	$0.937275\pi$
$954$	−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
$960$	−20.0653	+	44.7871i	−0.647604	+	1.44550i
$961$		−	7.06232i		−	0.227817i
$962$	46.5351	−	11.1741i	1.50035	−	0.360268i
$963$			19.5318i			0.629404i
$964$	−4.24785	−	1.37982i	−0.136814	−	0.0444410i
$965$	26.1108	+	7.06836i	0.840535	+	0.227539i
$966$	−1.13618	+	1.85424i	−0.0365559	+	0.0596593i
$967$	10.2794	−	10.2794i	0.330562	−	0.330562i	−0.522238	−	0.852800i	$-0.674903\pi$
$967$	10.2794	−	10.2794i	0.330562	−	0.330562i	0.852800	+	0.522238i	$0.174903\pi$
$968$	−29.2635	−	2.29943i	−0.940563	−	0.0739064i
$969$	−18.6748	−	31.4681i	−0.599922	−	1.01090i
$970$	7.87919	+	8.34511i	0.252985	+	0.267945i
$971$		−	38.7947i		−	1.24498i	−0.782627	−	0.622491i	$-0.786121\pi$
$971$		−	38.7947i		−	1.24498i	0.782627	−	0.622491i	$-0.213879\pi$
$972$	−16.6168	−	32.6057i	−0.532985	−	1.04583i
$973$	−6.83314	+	6.83314i	−0.219060	+	0.219060i
$974$	−0.252826	+	0.412613i	−0.00810107	+	0.0132210i
$975$	−47.7543	+	12.5329i	−1.52936	+	0.401373i
$976$	−3.93293	−	24.8050i	−0.125890	−	0.793988i
$977$	32.9960	+	32.9960i	1.05563	+	1.05563i	0.998358	+	0.0572759i	$0.0182415\pi$
$977$	32.9960	+	32.9960i	1.05563	+	1.05563i	0.0572759	+	0.998358i	$0.481759\pi$
$978$	−8.79751	+	14.3576i	−0.281313	+	0.459104i
$979$	2.70298	−	2.70298i	0.0863875	−	0.0863875i
$980$	24.4710	−	5.13787i	0.781699	−	0.164123i
$981$	34.7001	+	34.7001i	1.10789	+	1.10789i
$982$	15.9840	−	26.0859i	0.510069	−	0.832435i
$983$			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
$986$	5.09957	+	5.24593i	0.162403	+	0.167065i
$987$	15.2342	−	15.2342i	0.484908	−	0.484908i
$988$	−22.1474	−	7.19411i	−0.704604	−	0.228875i
$989$	2.60466	−	2.60466i	0.0828235	−	0.0828235i
$990$	−11.2837	−	0.324043i	−0.358621	−	0.0102988i
$991$	2.78499	+	2.78499i	0.0884682	+	0.0884682i	0.749956	−	0.661488i	$-0.230075\pi$
$991$	2.78499	+	2.78499i	0.0884682	+	0.0884682i	−0.661488	+	0.749956i	$0.730075\pi$
$992$	−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
$996$	74.1967	+	24.1012i	2.35101	+	0.763675i
$997$			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.123.18	yes	208
5.2	odd	4		680.2.t.a.667.69	yes	208
8.3	odd	2	inner	680.2.bl.a.123.36	yes	208
17.13	even	4		680.2.t.a.523.87	yes	208
40.27	even	4		680.2.t.a.667.87	yes	208
85.47	odd	4	inner	680.2.bl.a.387.36	yes	208
136.115	odd	4		680.2.t.a.523.69	✓	208
680.387	even	4	inner	680.2.bl.a.387.18	yes	208

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.t.a.523.69	✓	208	136.115	odd	4
680.2.t.a.523.87	yes	208	17.13	even	4
680.2.t.a.667.69	yes	208	5.2	odd	4
680.2.t.a.667.87	yes	208	40.27	even	4
680.2.bl.a.123.18	yes	208	1.1	even	1	trivial
680.2.bl.a.123.36	yes	208	8.3	odd	2	inner
680.2.bl.a.387.18	yes	208	680.387	even	4	inner
680.2.bl.a.387.36	yes	208	85.47	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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+(-1.20585 - 0.738875i) q^{2} +2.74346 q^{3} +(0.908129 + 1.78194i) q^{4} +(0.584289 - 2.15838i) q^{5} +(-3.30818 - 2.02707i) q^{6} -1.18693i q^{7} +(0.221566 - 2.81974i) q^{8} +4.52655 q^{9} +(-2.29933 + 2.17096i) q^{10} +(0.557635 + 0.557635i) q^{11} +(2.49141 + 4.88867i) q^{12} +(2.54503 - 2.54503i) q^{13} +(-0.876993 + 1.43125i) q^{14} +(1.60297 - 5.92142i) q^{15} +(-2.35061 + 3.23646i) q^{16} +(2.10422 + 3.54574i) q^{17} +(-5.45832 - 3.34455i) q^{18} -3.23494 q^{19} +(4.37671 - 0.918921i) q^{20} -3.25629i q^{21} +(-0.260399 - 1.08444i) q^{22} +0.472228 q^{23} +(0.607856 - 7.73582i) 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} +(-6.30812 + 5.95593i) q^{30} +(-3.45960 - 3.45960i) q^{31} +(5.22580 - 2.16587i) q^{32} +(1.52985 + 1.52985i) q^{33} +(0.0824844 - 5.83037i) q^{34} +(-2.56185 - 0.693510i) q^{35} +(4.11069 + 8.06603i) q^{36} -9.40220 q^{37} +(3.90084 + 2.39022i) q^{38} +(6.98219 - 6.98219i) q^{39} +(-5.95660 - 2.12576i) q^{40} +(4.79693 + 4.79693i) q^{41} +(-2.40599 + 3.92658i) q^{42} +(5.51569 - 5.51569i) q^{43} +(-0.487267 + 1.50007i) q^{44} +(2.64481 - 9.77001i) q^{45} +(-0.569434 - 0.348917i) q^{46} +(4.67838 + 4.67838i) q^{47} +(-6.44878 + 8.87908i) q^{48} +5.59120 q^{49} +(3.34228 + 6.23131i) q^{50} +(5.77284 + 9.72757i) q^{51} +(6.84631 + 2.22388i) q^{52} +(6.53086 + 6.53086i) q^{53} +(-5.05010 - 3.09442i) q^{54} +(1.52941 - 0.877769i) q^{55} +(-3.34683 - 0.262983i) q^{56} -8.87492 q^{57} +(1.72537 - 0.414301i) q^{58} -6.07501 q^{59} +(12.0073 - 2.52102i) 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} +(-4.40737 + 6.96958i) q^{68} +1.29554 q^{69} +(2.57678 + 2.72915i) q^{70} +(1.62888 + 1.62888i) q^{71} +(1.00293 - 12.7637i) q^{72} +4.91927 q^{73} +(11.3376 + 6.94705i) 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} +(5.61207 + 6.96453i) 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} +(-10.4081 + 9.82695i) 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} +(14.3368 - 5.94196i) q^{96} -3.62936i q^{97} +(-6.74212 - 4.13119i) 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

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