LMFDB - Embedded newform 680.2.t.a.523.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(523,680)] 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, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.523"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.t (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			523.8
Character	$\chi$	$=$	680.523
Dual form			680.2.t.a.667.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37567 + 0.327922i) q^{2} -1.51555i q^{3} +(1.78493 - 0.902224i) q^{4} +(-1.48529 - 1.67150i) q^{5} +(0.496982 + 2.08490i) q^{6} -3.71705 q^{7} +(-2.15962 + 1.82648i) q^{8} +0.703111 q^{9} +(2.59139 + 1.81238i) q^{10} +(-1.30000 + 1.30000i) q^{11} +(-1.36737 - 2.70516i) q^{12} +(-3.07440 + 3.07440i) q^{13} +(5.11343 - 1.21890i) q^{14} +(-2.53325 + 2.25102i) q^{15} +(2.37198 - 3.22082i) q^{16} +(3.38853 + 2.34901i) q^{17} +(-0.967248 + 0.230565i) q^{18} -0.903308 q^{19} +(-4.15921 - 1.64347i) q^{20} +5.63337i q^{21} +(1.36207 - 2.21467i) q^{22} +5.70159i q^{23} +(2.76812 + 3.27301i) q^{24} +(-0.587854 + 4.96532i) q^{25} +(3.22119 - 5.23752i) q^{26} -5.61225i q^{27} +(-6.63469 + 3.35361i) q^{28} +(3.08022 + 3.08022i) q^{29} +(2.74675 - 3.92737i) q^{30} +(5.23093 - 5.23093i) q^{31} +(-2.20689 + 5.20861i) q^{32} +(1.97021 + 1.97021i) q^{33} +(-5.43179 - 2.12029i) q^{34} +(5.52088 + 6.21307i) q^{35} +(1.25501 - 0.634363i) q^{36} -9.78412i q^{37} +(1.24265 - 0.296214i) q^{38} +(4.65940 + 4.65940i) q^{39} +(6.26063 + 0.896970i) q^{40} +(2.00614 - 2.00614i) q^{41} +(-1.84731 - 7.74966i) q^{42} +(-1.94236 + 1.94236i) q^{43} +(-1.14752 + 3.49330i) q^{44} +(-1.04432 - 1.17525i) q^{45} +(-1.86968 - 7.84351i) q^{46} +(3.82456 + 3.82456i) q^{47} +(-4.88132 - 3.59486i) q^{48} +6.81646 q^{49} +(-0.819545 - 7.02341i) q^{50} +(3.56004 - 5.13549i) q^{51} +(-2.71380 + 8.26140i) q^{52} +(5.50671 + 5.50671i) q^{53} +(1.84038 + 7.72060i) q^{54} +(4.10382 + 0.242084i) q^{55} +(8.02742 - 6.78912i) q^{56} +1.36901i q^{57} +(-5.24743 - 3.22729i) q^{58} -12.8744 q^{59} +(-2.49075 + 6.30349i) q^{60} +(0.657148 + 0.657148i) q^{61} +(-5.48069 + 8.91137i) q^{62} -2.61350 q^{63} +(1.32793 - 7.88902i) q^{64} +(9.70523 + 0.572511i) q^{65} +(-3.35643 - 2.06428i) q^{66} +(-3.11523 + 3.11523i) q^{67} +(8.16764 + 1.13561i) q^{68} +8.64105 q^{69} +(-9.63231 - 6.73671i) q^{70} +(-10.9681 + 10.9681i) q^{71} +(-1.51845 + 1.28422i) q^{72} +8.17185i q^{73} +(3.20843 + 13.4597i) q^{74} +(7.52519 + 0.890922i) q^{75} +(-1.61235 + 0.814986i) q^{76} +(4.83216 - 4.83216i) q^{77} +(-7.93772 - 4.88188i) q^{78} +(-5.00743 + 5.00743i) q^{79} +(-8.90669 + 0.819063i) q^{80} -6.39630 q^{81} +(-2.10193 + 3.41764i) q^{82} +(-1.45842 + 1.45842i) q^{83} +(5.08257 + 10.0552i) q^{84} +(-1.10656 - 9.15290i) q^{85} +(2.03510 - 3.30898i) q^{86} +(4.66822 - 4.66822i) q^{87} +(0.433081 - 5.18193i) q^{88} +17.1717i q^{89} +(1.82203 + 1.27430i) q^{90} +(11.4277 - 11.4277i) q^{91} +(5.14412 + 10.1770i) q^{92} +(-7.92773 - 7.92773i) q^{93} +(-6.51549 - 4.00718i) q^{94} +(1.34167 + 1.50988i) q^{95} +(7.89391 + 3.34464i) q^{96} +5.70880 q^{97} +(-9.37720 + 2.23527i) q^{98} +(-0.914042 + 0.914042i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 208 q - 8 q^{6} - 192 q^{9} + 2 q^{10} - 8 q^{11} + 8 q^{12} - 16 q^{14} - 16 q^{16} - 12 q^{18} - 10 q^{20} + 4 q^{22} + 16 q^{24} + 12 q^{28} - 24 q^{30} + 20 q^{32} - 8 q^{33} - 4 q^{34} - 8 q^{35} - 12 q^{38}+ \cdots + 24 q^{99}+O(q^{100}) $ 208 * q - 8 * q^6 - 192 * q^9 + 2 * q^10 - 8 * q^11 + 8 * q^12 - 16 * q^14 - 16 * q^16 - 12 * q^18 - 10 * q^20 + 4 * q^22 + 16 * q^24 + 12 * q^28 - 24 * q^30 + 20 * q^32 - 8 * q^33 - 4 * q^34 - 8 * q^35 - 12 * q^38 - 42 * q^40 - 8 * q^41 - 32 * q^42 + 8 * q^44 - 16 * q^46 + 160 * q^49 + 16 * q^50 - 8 * q^51 - 20 * q^52 + 36 * q^54 + 4 * q^56 - 56 * q^58 - 64 * q^59 + 32 * q^60 - 48 * q^65 - 8 * q^67 - 56 * q^68 - 28 * q^70 - 56 * q^72 + 8 * q^74 + 8 * q^75 - 12 * q^78 + 6 * q^80 + 128 * q^81 + 44 * q^82 + 8 * q^86 - 82 * q^90 + 24 * q^91 + 64 * q^94 - 48 * q^96 - 16 * q^97 - 40 * q^98 + 24 * q^99

Character values

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

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

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 $

$2$	−1.37567	+	0.327922i	−0.972745	+	0.231876i
$2$	−1.37567	+	0.327922i	−0.972745	+	0.231876i
$3$		−	1.51555i		−	0.875003i	−0.899218	−	0.437501i	$-0.855864\pi$
$3$		−	1.51555i		−	0.875003i	0.899218	−	0.437501i	$-0.144136\pi$
$4$	1.78493	−	0.902224i	0.892467	−	0.451112i
$5$	−1.48529	−	1.67150i	−0.664240	−	0.747519i
$5$	−1.48529	−	1.67150i	−0.664240	−	0.747519i
$6$	0.496982	+	2.08490i	0.202892	+	0.851155i
$7$	−3.71705			−1.40491			−0.702456	−	0.711727i	$-0.747913\pi$
$7$	−3.71705			−1.40491			−0.702456	+	0.711727i	$0.747913\pi$
$8$	−2.15962	+	1.82648i	−0.763541	+	0.645759i
$9$	0.703111			0.234370
$10$	2.59139	+	1.81238i	0.819468	+	0.573125i
$11$	−1.30000	+	1.30000i	−0.391964	+	0.391964i	−0.875387	−	0.483423i	$-0.839393\pi$
$11$	−1.30000	+	1.30000i	−0.391964	+	0.391964i	0.483423	+	0.875387i	$0.339393\pi$
$12$	−1.36737	−	2.70516i	−0.394724	−	0.780911i
$13$	−3.07440	+	3.07440i	−0.852685	+	0.852685i	−0.990463	−	0.137779i	$-0.956004\pi$
$13$	−3.07440	+	3.07440i	−0.852685	+	0.852685i	0.137779	+	0.990463i	$0.456004\pi$
$14$	5.11343	−	1.21890i	1.36662	−	0.325765i
$15$	−2.53325	+	2.25102i	−0.654082	+	0.581212i
$16$	2.37198	−	3.22082i	0.592996	−	0.805206i
$17$	3.38853	+	2.34901i	0.821840	+	0.569718i
$17$	3.38853	+	2.34901i	0.821840	+	0.569718i
$18$	−0.967248	+	0.230565i	−0.227983	+	0.0543448i
$19$	−0.903308			−0.207233			−0.103617	−	0.994617i	$-0.533041\pi$
$19$	−0.903308			−0.207233			−0.103617	+	0.994617i	$0.533041\pi$
$20$	−4.15921	−	1.64347i	−0.930027	−	0.367490i
$21$			5.63337i			1.22930i
$22$	1.36207	−	2.21467i	0.290394	−	0.472168i
$23$			5.70159i			1.18886i	0.804146	+	0.594432i	$0.202623\pi$
$23$			5.70159i			1.18886i	−0.804146	+	0.594432i	$0.797377\pi$
$24$	2.76812	+	3.27301i	0.565041	+	0.668101i
$25$	−0.587854	+	4.96532i	−0.117571	+	0.993065i
$26$	3.22119	−	5.23752i	0.631728	−	1.02716i
$27$		−	5.61225i		−	1.08008i
$28$	−6.63469	+	3.35361i	−1.25384	+	0.633773i
$29$	3.08022	+	3.08022i	0.571982	+	0.571982i	0.932682	−	0.360700i	$-0.117462\pi$
$29$	3.08022	+	3.08022i	0.571982	+	0.571982i	−0.360700	+	0.932682i	$0.617462\pi$
$30$	2.74675	−	3.92737i	0.501486	−	0.717037i
$31$	5.23093	−	5.23093i	0.939503	−	0.939503i	−0.0587691	−	0.998272i	$-0.518718\pi$
$31$	5.23093	−	5.23093i	0.939503	−	0.939503i	0.998272	+	0.0587691i	$0.0187176\pi$
$32$	−2.20689	+	5.20861i	−0.390126	+	0.920761i
$33$	1.97021	+	1.97021i	0.342970	+	0.342970i
$34$	−5.43179	−	2.12029i	−0.931545	−	0.363626i
$35$	5.52088	+	6.21307i	0.933199	+	1.05020i
$36$	1.25501	−	0.634363i	0.209168	−	0.105727i
$37$		−	9.78412i		−	1.60850i	−0.594292	−	0.804250i	$-0.702567\pi$
$37$		−	9.78412i		−	1.60850i	0.594292	−	0.804250i	$-0.297433\pi$
$38$	1.24265	−	0.296214i	0.201585	−	0.0480523i
$39$	4.65940	+	4.65940i	0.746101	+	0.746101i
$40$	6.26063	+	0.896970i	0.989892	+	0.141823i
$41$	2.00614	−	2.00614i	0.313306	−	0.313306i	−0.532883	−	0.846189i	$-0.678891\pi$
$41$	2.00614	−	2.00614i	0.313306	−	0.313306i	0.846189	+	0.532883i	$0.178891\pi$
$42$	−1.84731	−	7.74966i	−0.285045	−	1.19580i
$43$	−1.94236	+	1.94236i	−0.296207	+	0.296207i	−0.839526	−	0.543319i	$-0.817167\pi$
$43$	−1.94236	+	1.94236i	−0.296207	+	0.296207i	0.543319	+	0.839526i	$0.317167\pi$
$44$	−1.14752	+	3.49330i	−0.172995	+	0.526635i
$45$	−1.04432	−	1.17525i	−0.155678	−	0.175196i
$46$	−1.86968	−	7.84351i	−0.275669	−	1.15646i
$47$	3.82456	+	3.82456i	0.557870	+	0.557870i	0.928700	−	0.370831i	$-0.120927\pi$
$47$	3.82456	+	3.82456i	0.557870	+	0.557870i	−0.370831	+	0.928700i	$0.620927\pi$
$48$	−4.88132	−	3.59486i	−0.704557	−	0.518873i
$49$	6.81646			0.973780
$50$	−0.819545	−	7.02341i	−0.115901	−	0.993261i
$51$	3.56004	−	5.13549i	0.498505	−	0.719112i
$52$	−2.71380	+	8.26140i	−0.376337	+	1.14565i
$53$	5.50671	+	5.50671i	0.756405	+	0.756405i	0.975666	−	0.219261i	$-0.0703646\pi$
$53$	5.50671	+	5.50671i	0.756405	+	0.756405i	−0.219261	+	0.975666i	$0.570365\pi$
$54$	1.84038	+	7.72060i	0.250444	+	1.05064i
$55$	4.10382	+	0.242084i	0.553359	+	0.0326426i
$56$	8.02742	−	6.78912i	1.07271	−	0.907235i
$57$			1.36901i			0.181329i
$58$	−5.24743	−	3.22729i	−0.689022	−	0.423764i
$59$	−12.8744			−1.67611			−0.838055	−	0.545586i	$-0.816307\pi$
$59$	−12.8744			−1.67611			−0.838055	+	0.545586i	$0.816307\pi$
$60$	−2.49075	+	6.30349i	−0.321555	+	0.813777i
$61$	0.657148	+	0.657148i	0.0841391	+	0.0841391i	0.747924	−	0.663785i	$-0.231051\pi$
$61$	0.657148	+	0.657148i	0.0841391	+	0.0841391i	−0.663785	+	0.747924i	$0.731051\pi$
$62$	−5.48069	+	8.91137i	−0.696049	+	1.13174i
$63$	−2.61350			−0.329270
$64$	1.32793	−	7.88902i	0.165991	−	0.986127i
$65$	9.70523	+	0.572511i	1.20379	+	0.0710113i
$66$	−3.35643	−	2.06428i	−0.413149	−	0.254096i
$67$	−3.11523	+	3.11523i	−0.380586	+	0.380586i	−0.871313	−	0.490728i	$-0.836731\pi$
$67$	−3.11523	+	3.11523i	−0.380586	+	0.380586i	0.490728	+	0.871313i	$0.336731\pi$
$68$	8.16764	+	1.13561i	0.990472	+	0.137713i
$69$	8.64105			1.04026
$70$	−9.63231	−	6.73671i	−1.15128	−	0.805191i
$71$	−10.9681	+	10.9681i	−1.30168	+	1.30168i	−0.374418	+	0.927260i	$0.622157\pi$
$71$	−10.9681	+	10.9681i	−1.30168	+	1.30168i	−0.927260	+	0.374418i	$0.877843\pi$
$72$	−1.51845	+	1.28422i	−0.178951	+	0.151347i
$73$			8.17185i			0.956443i	0.878239	+	0.478222i	$0.158718\pi$
$73$			8.17185i			0.956443i	−0.878239	+	0.478222i	$0.841282\pi$
$74$	3.20843	+	13.4597i	0.372972	+	1.56466i
$75$	7.52519	+	0.890922i	0.868934	+	0.102875i
$76$	−1.61235	+	0.814986i	−0.184949	+	0.0934853i
$77$	4.83216	−	4.83216i	0.550675	−	0.550675i
$78$	−7.93772	−	4.88188i	−0.898769	−	0.552764i
$79$	−5.00743	+	5.00743i	−0.563380	+	0.563380i	−0.930266	−	0.366886i	$-0.880424\pi$
$79$	−5.00743	+	5.00743i	−0.563380	+	0.563380i	0.366886	+	0.930266i	$0.380424\pi$
$80$	−8.90669	+	0.819063i	−0.995798	+	0.0915740i
$81$	−6.39630			−0.710700
$82$	−2.10193	+	3.41764i	−0.232119	+	0.377415i
$83$	−1.45842	+	1.45842i	−0.160082	+	0.160082i	−0.782603	−	0.622521i	$-0.786109\pi$
$83$	−1.45842	+	1.45842i	−0.160082	+	0.160082i	0.622521	+	0.782603i	$0.286109\pi$
$84$	5.08257	+	10.0552i	0.554553	+	1.09711i
$85$	−1.10656	−	9.15290i	−0.120023	−	0.992771i
$86$	2.03510	−	3.30898i	0.219451	−	0.356817i
$87$	4.66822	−	4.66822i	0.500486	−	0.500486i
$88$	0.433081	−	5.18193i	0.0461665	−	0.552395i
$89$			17.1717i			1.82020i	0.414392	+	0.910098i	$0.363994\pi$
$89$			17.1717i			1.82020i	−0.414392	+	0.910098i	$0.636006\pi$
$90$	1.82203	+	1.27430i	0.192059	+	0.134323i
$91$	11.4277	−	11.4277i	1.19795	−	1.19795i
$92$	5.14412	+	10.1770i	0.536311	+	1.06102i
$93$	−7.92773	−	7.92773i	−0.822067	−	0.822067i
$94$	−6.51549	−	4.00718i	−0.672021	−	0.413309i
$95$	1.34167	+	1.50988i	0.137652	+	0.154911i
$96$	7.89391	+	3.34464i	0.805669	+	0.341361i
$97$	5.70880			0.579641			0.289820	−	0.957081i	$-0.406404\pi$
$97$	5.70880			0.579641			0.289820	+	0.957081i	$0.406404\pi$
$98$	−9.37720	+	2.23527i	−0.947240	+	0.225796i
$99$	−0.914042	+	0.914042i	−0.0918647	+	0.0918647i
$100$	3.43055	+	9.39315i	0.343055	+	0.939315i
$101$			17.4566i			1.73700i	0.495689	+	0.868500i	$0.334916\pi$
$101$			17.4566i			1.73700i	−0.495689	+	0.868500i	$0.665084\pi$
$102$	−3.21340	+	8.23215i	−0.318174	+	0.815104i
$103$	2.75583	−	2.75583i	0.271540	−	0.271540i	−0.558180	−	0.829720i	$-0.688500\pi$
$103$	2.75583	−	2.75583i	0.271540	−	0.271540i	0.829720	+	0.558180i	$0.188500\pi$
$104$	1.02420	−	12.2549i	0.100431	−	1.20169i
$105$	9.41621	−	8.36717i	0.918928	−	0.816552i
$106$	−9.38119	−	5.76965i	−0.911182	−	0.560398i
$107$	0.0918138			0.00887598			0.00443799	−	0.999990i	$-0.498587\pi$
$107$	0.0918138			0.00887598			0.00443799	+	0.999990i	$0.498587\pi$
$108$	−5.06351	−	10.0175i	−0.487236	−	0.963934i
$109$	−4.29101	+	4.29101i	−0.411005	+	0.411005i	−0.882088	−	0.471084i	$-0.843863\pi$
$109$	−4.29101	+	4.29101i	−0.411005	+	0.411005i	0.471084	+	0.882088i	$0.343863\pi$
$110$	−5.72489	+	1.01270i	−0.545846	+	0.0965576i
$111$	−14.8283			−1.40744
$112$	−8.81678	+	11.9720i	−0.833107	+	1.13124i
$113$	−18.5515			−1.74518			−0.872591	−	0.488451i	$-0.837562\pi$
$113$	−18.5515			−1.74518			−0.872591	+	0.488451i	$0.837562\pi$
$114$	−0.448927	−	1.88330i	−0.0420459	−	0.176387i
$115$	9.53024	−	8.46849i	0.888699	−	0.789691i
$116$	8.27704	+	2.71894i	0.768504	+	0.252447i
$117$	−2.16164	+	2.16164i	−0.199844	+	0.199844i
$118$	17.7110	−	4.22181i	1.63043	−	0.388649i
$119$	−12.5953	−	8.73138i	−1.15461	−	0.800405i
$120$	1.35940	−	9.48829i	0.124096	−	0.866158i
$121$			7.62001i			0.692728i
$122$	−1.11951	−	0.688525i	−0.101356	−	0.0623361i
$123$	−3.04040	−	3.04040i	−0.274144	−	0.274144i
$124$	4.61739	−	14.0563i	0.414654	−	1.26230i
$125$	9.17269	−	6.39232i	0.820430	−	0.571747i
$126$	3.59531	−	0.857023i	0.320296	−	0.0763497i
$127$	−5.38968	+	5.38968i	−0.478257	+	0.478257i	−0.904574	−	0.426317i	$-0.859811\pi$
$127$	−5.38968	+	5.38968i	−0.478257	+	0.478257i	0.426317	+	0.904574i	$0.359811\pi$
$128$	0.760191	+	11.2881i	0.0671920	+	0.997740i
$129$	2.94374	+	2.94374i	0.259182	+	0.259182i
$130$	−13.5389	+	2.39497i	−1.18744	+	0.210053i
$131$	3.41720	+	3.41720i	0.298562	+	0.298562i	0.840451	−	0.541888i	$-0.182290\pi$
$131$	3.41720	+	3.41720i	0.298562	+	0.298562i	−0.541888	+	0.840451i	$0.682290\pi$
$132$	5.29427	+	1.73913i	0.460807	+	0.151371i
$133$	3.35764			0.291144
$134$	3.26397	−	5.30707i	0.281964	−	0.458461i
$135$	−9.38089	+	8.33579i	−0.807379	+	0.717430i
$136$	−11.6084	+	1.11612i	−0.995410	+	0.0957068i
$137$	5.03637	−	5.03637i	0.430286	−	0.430286i	−0.458440	−	0.888726i	$-0.651591\pi$
$137$	5.03637	−	5.03637i	0.430286	−	0.430286i	0.888726	+	0.458440i	$0.151591\pi$
$138$	−11.8872	+	2.83359i	−1.01191	+	0.241211i
$139$	6.33813	−	6.33813i	0.537593	−	0.537593i	−0.385228	−	0.922821i	$-0.625877\pi$
$139$	6.33813	−	6.33813i	0.537593	−	0.537593i	0.922821	+	0.385228i	$0.125877\pi$
$140$	15.4600	+	6.10884i	1.30661	+	0.516291i
$141$	5.79631	−	5.79631i	0.488137	−	0.488137i
$142$	11.4918	−	18.6852i	0.964374	−	1.56803i
$143$		−	7.99342i		−	0.668443i
$144$	1.66777	−	2.26459i	0.138980	−	0.188716i
$145$	0.573595	−	9.72360i	0.0476345	−	0.807501i
$146$	−2.67973	−	11.2418i	−0.221776	−	0.930376i
$147$		−	10.3307i		−	0.852060i
$148$	−8.82747	−	17.4640i	−0.725614	−	1.43553i
$149$	8.14759			0.667477			0.333738	−	0.942666i	$-0.391690\pi$
$149$	8.14759			0.667477			0.333738	+	0.942666i	$0.391690\pi$
$150$	−10.6443	+	1.24206i	−0.869106	+	0.101414i
$151$	−16.1970			−1.31810			−0.659049	−	0.752100i	$-0.729041\pi$
$151$	−16.1970			−1.31810			−0.659049	+	0.752100i	$0.729041\pi$
$152$	1.95080	−	1.64988i	0.158231	−	0.133823i
$153$	2.38251	+	1.65161i	0.192615	+	0.133525i
$154$	−5.06288	+	8.23202i	−0.407979	+	0.663355i
$155$	−16.5129	−	0.974098i	−1.32635	−	0.0782414i
$156$	12.5206	+	4.11290i	1.00245	+	0.329296i
$157$	−16.6722	−	16.6722i	−1.33059	−	1.33059i	−0.904842	−	0.425747i	$-0.860011\pi$
$157$	−16.6722	−	16.6722i	−1.33059	−	1.33059i	−0.425747	−	0.904842i	$-0.639989\pi$
$158$	5.24652	−	8.53061i	0.417391	−	0.678659i
$159$	8.34569	−	8.34569i	0.661857	−	0.661857i
$160$	11.9841	−	4.04746i	0.947424	−	0.319980i
$161$		−	21.1931i		−	1.67025i
$162$	8.79920	−	2.09749i	0.691331	−	0.164794i
$163$	−8.64336			−0.677000			−0.338500	−	0.940966i	$-0.609920\pi$
$163$	−8.64336			−0.677000			−0.338500	+	0.940966i	$0.609920\pi$
$164$	1.77084	−	5.39081i	0.138279	−	0.420951i
$165$	0.366891	−	6.21954i	0.0285624	−	0.484191i
$166$	1.52805	−	2.48455i	0.118600	−	0.192838i
$167$		−	13.1486i		−	1.01747i	−0.860924	−	0.508734i	$-0.830114\pi$
$167$		−	13.1486i		−	1.01747i	0.860924	−	0.508734i	$-0.169886\pi$
$168$	−10.2893	−	12.1660i	−0.793833	−	0.938623i
$169$		−	5.90384i		−	0.454142i
$170$	4.52370	+	12.2285i	0.346952	+	0.937883i
$171$	−0.635125			−0.0485692
$172$	−1.71454	+	5.21942i	−0.130732	+	0.397977i
$173$	−2.10963			−0.160392			−0.0801962	−	0.996779i	$-0.525555\pi$
$173$	−2.10963			−0.160392			−0.0801962	+	0.996779i	$0.525555\pi$
$174$	−4.89112	+	7.95275i	−0.370795	+	0.602896i
$175$	2.18508	−	18.4564i	0.165177	−	1.39517i
$176$	1.10349	+	7.27064i	0.0831788	+	0.548045i
$177$			19.5118i			1.46660i
$178$	−5.63098	−	23.6226i	−0.422059	−	1.77059i
$179$	7.91777			0.591802			0.295901	−	0.955219i	$-0.404380\pi$
$179$	7.91777			0.591802			0.295901	+	0.955219i	$0.404380\pi$
$180$	−2.92438	−	1.15554i	−0.217971	−	0.0861287i
$181$	6.21876	+	6.21876i	0.462237	+	0.462237i	0.899388	−	0.437151i	$-0.144013\pi$
$181$	6.21876	+	6.21876i	0.462237	+	0.462237i	−0.437151	+	0.899388i	$0.644013\pi$
$182$	−11.9733	+	19.4681i	−0.887523	+	1.44307i
$183$	0.995940	−	0.995940i	0.0736220	−	0.0736220i
$184$	−10.4139	−	12.3133i	−0.767720	−	0.907747i
$185$	−16.3542	+	14.5322i	−1.20238	+	1.06843i
$186$	13.5056	+	8.30626i	0.990280	+	0.609045i
$187$	−7.45879	+	1.35138i	−0.545441	+	0.0988226i
$188$	10.2772	+	3.37598i	0.749542	+	0.246219i
$189$			20.8610i			1.51741i
$190$	−2.34082	−	1.63714i	−0.169821	−	0.118770i
$191$		−	19.6175i		−	1.41948i	−0.704466	−	0.709738i	$-0.748813\pi$
$191$		−	19.6175i		−	1.41948i	0.704466	−	0.709738i	$-0.251187\pi$
$192$	−11.9562	−	2.01254i	−0.862864	−	0.145243i
$193$	2.26114			0.162760			0.0813801	−	0.996683i	$-0.474067\pi$
$193$	2.26114			0.162760			0.0813801	+	0.996683i	$0.474067\pi$
$194$	−7.85342	+	1.87204i	−0.563843	+	0.134405i
$195$	0.867669	−	14.7088i	0.0621350	−	1.05332i
$196$	12.1669	−	6.14998i	0.869067	−	0.439284i
$197$	23.1161			1.64696			0.823479	−	0.567347i	$-0.192030\pi$
$197$	23.1161			1.64696			0.823479	+	0.567347i	$0.192030\pi$
$198$	0.957686	−	1.55715i	0.0680598	−	0.110662i
$199$	15.5461	+	15.5461i	1.10203	+	1.10203i	0.994165	+	0.107869i	$0.0344028\pi$
$199$	15.5461	+	15.5461i	1.10203	+	1.10203i	0.107869	+	0.994165i	$0.465597\pi$
$200$	−7.79953	−	11.7969i	−0.551510	−	0.834168i
$201$	4.72128	+	4.72128i	0.333013	+	0.333013i
$202$	−5.72441	−	24.0146i	−0.402768	−	1.68966i
$203$	−11.4493	−	11.4493i	−0.803585	−	0.803585i
$204$	1.72107	−	12.3785i	0.120499	−	0.866666i
$205$	−6.33295	−	0.373581i	−0.442313	−	0.0260920i
$206$	−2.88742	+	4.69481i	−0.201176	+	0.327103i
$207$			4.00885i			0.278634i
$208$	2.60967	+	17.1945i	0.180948	+	1.19222i
$209$	1.17430	−	1.17430i	0.0812279	−	0.0812279i
$210$	−10.2098	+	14.5982i	−0.704544	+	1.00737i
$211$	−5.51839	+	5.51839i	−0.379902	+	0.379902i	−0.871067	−	0.491165i	$-0.836571\pi$
$211$	−5.51839	+	5.51839i	−0.379902	+	0.379902i	0.491165	+	0.871067i	$0.336571\pi$
$212$	14.7974	+	4.86083i	1.01629	+	0.333843i
$213$	16.6227	+	16.6227i	1.13897	+	1.13897i
$214$	−0.126305	+	0.0301078i	−0.00863406	+	0.00205812i
$215$	6.13162	+	0.361704i	0.418173	+	0.0246680i
$216$	10.2507	+	12.1203i	0.697469	+	0.824684i
$217$	−19.4436	+	19.4436i	−1.31992	+	1.31992i
$218$	4.49590	−	7.31014i	0.304501	−	0.495105i
$219$	12.3848			0.836890
$220$	7.54346	−	3.27046i	0.508580	−	0.220495i
$221$	−17.6395	+	3.19591i	−1.18656	+	0.214980i
$222$	20.3989	−	4.86253i	1.36908	−	0.326352i
$223$	6.23609	+	6.23609i	0.417600	+	0.417600i	0.884376	−	0.466776i	$-0.154585\pi$
$223$	6.23609	+	6.23609i	0.417600	+	0.417600i	−0.466776	+	0.884376i	$0.654585\pi$
$224$	8.20311	−	19.3607i	0.548093	−	1.29359i
$225$	−0.413326	+	3.49117i	−0.0275551	+	0.232745i
$226$	25.5208	−	6.08346i	1.69762	−	0.404666i
$227$			17.4600i			1.15886i	0.815022	+	0.579430i	$0.196725\pi$
$227$			17.4600i			1.15886i	−0.815022	+	0.579430i	$0.803275\pi$
$228$	1.23515	+	2.44359i	0.0817999	+	0.161831i
$229$		−	8.31383i		−	0.549394i	−0.961531	−	0.274697i	$-0.911423\pi$
$229$		−	8.31383i		−	0.549394i	0.961531	−	0.274697i	$-0.0885775\pi$
$230$	−10.3335	+	14.7750i	−0.681368	+	0.974236i
$231$	−7.32337	−	7.32337i	−0.481843	−	0.481843i
$232$	−12.2781	−	1.02614i	−0.806095	−	0.0673695i
$233$			5.75838i			0.377244i	0.982050	+	0.188622i	$0.0604021\pi$
$233$			5.75838i			0.377244i	−0.982050	+	0.188622i	$0.939598\pi$
$234$	2.26486	−	3.68255i	0.148058	−	0.240736i
$235$	0.712206	−	12.0733i	0.0464592	−	0.787577i
$236$	−22.9800	+	11.6156i	−1.49587	+	0.756113i
$237$	7.58901	+	7.58901i	0.492959	+	0.492959i
$238$	20.1902	+	7.88121i	1.30874	+	0.510863i
$239$	1.80116			0.116507			0.0582537	−	0.998302i	$-0.481447\pi$
$239$	1.80116			0.116507			0.0582537	+	0.998302i	$0.481447\pi$
$240$	1.24133	+	13.4985i	0.0801275	+	0.871326i
$241$	−8.07085	−	8.07085i	−0.519889	−	0.519889i	0.397649	−	0.917538i	$-0.369826\pi$
$241$	−8.07085	−	8.07085i	−0.519889	−	0.519889i	−0.917538	+	0.397649i	$0.869826\pi$
$242$	−2.49877	−	10.4826i	−0.160627	−	0.673848i
$243$		−	7.14283i		−	0.458212i
$244$	1.76586	+	0.580071i	0.113048	+	0.0371352i
$245$	−10.1244	−	11.3937i	−0.646823	−	0.727920i
$246$	5.17960	+	3.18557i	0.330239	+	0.203105i
$247$	2.77713	−	2.77713i	0.176704	−	0.176704i
$248$	−1.74263	+	20.8510i	−0.110657	+	1.32404i
$249$	2.21030	+	2.21030i	0.140072	+	0.140072i
$250$	−10.5224	+	11.8016i	−0.665496	+	0.746402i
$251$	−28.3150			−1.78723			−0.893613	−	0.448839i	$-0.851838\pi$
$251$	−28.3150			−1.78723			−0.893613	+	0.448839i	$0.851838\pi$
$252$	−4.66492	+	2.35796i	−0.293862	+	0.148538i
$253$	−7.41206	−	7.41206i	−0.465992	−	0.465992i
$254$	5.64703	−	9.18182i	0.354326	−	0.576119i
$255$	−13.8717	+	1.67705i	−0.868677	+	0.105021i
$256$	−4.74740	−	15.2795i	−0.296712	−	0.954967i
$257$	4.04023	+	4.04023i	0.252023	+	0.252023i	0.821800	−	0.569777i	$-0.192970\pi$
$257$	4.04023	+	4.04023i	0.252023	+	0.252023i	−0.569777	+	0.821800i	$0.692970\pi$
$258$	−5.01493	−	3.08430i	−0.312216	−	0.192020i
$259$			36.3681i			2.25980i
$260$	17.8397	−	7.73440i	1.10637	−	0.479667i
$261$	2.16573	+	2.16573i	0.134056	+	0.134056i
$262$	−5.82151	−	3.58036i	−0.359654	−	0.221196i
$263$	−6.89242	−	6.89242i	−0.425005	−	0.425005i	0.461918	−	0.886923i	$-0.347161\pi$
$263$	−6.89242	−	6.89242i	−0.425005	−	0.425005i	−0.886923	+	0.461918i	$0.847161\pi$
$264$	−7.85346	−	0.656355i	−0.483347	−	0.0403959i
$265$	1.02545	−	17.3835i	0.0629931	−	1.06786i
$266$	−4.61900	+	1.10104i	−0.283209	+	0.0675093i
$267$	26.0246			1.59268
$268$	−2.74984	+	8.37111i	−0.167973	+	0.511347i
$269$	−1.79035	−	1.79035i	−0.109160	−	0.109160i	0.650417	−	0.759577i	$-0.274594\pi$
$269$	−1.79035	−	1.79035i	−0.109160	−	0.109160i	−0.759577	+	0.650417i	$0.774594\pi$
$270$	10.1715	−	14.5435i	0.619019	−	0.885089i
$271$		−	15.2942i		−	0.929054i	−0.885559	−	0.464527i	$-0.846224\pi$
$271$		−	15.2942i		−	0.929054i	0.885559	−	0.464527i	$-0.153776\pi$
$272$	15.6033	−	5.34206i	0.946088	−	0.323910i
$273$	−17.3192	−	17.3192i	−1.04821	−	1.04821i
$274$	−5.27684	+	8.57991i	−0.318786	+	0.518331i
$275$	−5.69070	−	7.21912i	−0.343162	−	0.435329i
$276$	15.4237	−	7.79616i	0.928398	−	0.469274i
$277$		−	8.71801i		−	0.523815i	−0.965093	−	0.261907i	$-0.915649\pi$
$277$		−	8.71801i		−	0.523815i	0.965093	−	0.261907i	$-0.0843515\pi$
$278$	−6.64076	+	10.7976i	−0.398286	+	0.647596i
$279$	3.67792	−	3.67792i	0.220191	−	0.220191i
$280$	−23.2711	−	3.33408i	−1.39071	−	0.199249i
$281$			8.21781i			0.490233i	0.969494	+	0.245117i	$0.0788263\pi$
$281$			8.21781i			0.490233i	−0.969494	+	0.245117i	$0.921174\pi$
$282$	−6.07307	+	9.87454i	−0.361646	+	0.588021i
$283$	−0.561393			−0.0333714			−0.0166857	−	0.999861i	$-0.505311\pi$
$283$	−0.561393			−0.0333714			−0.0166857	+	0.999861i	$0.505311\pi$
$284$	−9.68168	+	29.4731i	−0.574502	+	1.74891i
$285$	2.28830	−	2.03337i	0.135547	−	0.120446i
$286$	2.62122	+	10.9963i	0.154996	+	0.650225i
$287$	−7.45691	+	7.45691i	−0.440168	+	0.440168i
$288$	−1.55168	+	3.66223i	−0.0914339	+	0.215799i
$289$	5.96431	+	15.9194i	0.350842	+	0.936435i
$290$	2.39950	+	13.5646i	0.140904	+	0.796538i
$291$		−	8.65196i		−	0.507187i
$292$	7.37285	+	14.5862i	0.431463	+	0.853594i
$293$	5.48283	−	5.48283i	0.320310	−	0.320310i	−0.528576	−	0.848886i	$-0.677274\pi$
$293$	5.48283	−	5.48283i	0.320310	−	0.320310i	0.848886	+	0.528576i	$0.177274\pi$
$294$	3.38766	+	14.2116i	0.197572	+	0.828838i
$295$	19.1222	+	21.5197i	1.11334	+	1.25292i
$296$	17.8705	+	21.1300i	1.03870	+	1.22816i
$297$	7.29591	+	7.29591i	0.423352	+	0.423352i
$298$	−11.2084	+	2.67177i	−0.649285	+	0.154772i
$299$	−17.5290	−	17.5290i	−1.01373	−	1.01373i
$300$	14.2358	−	5.19917i	0.821903	−	0.300174i
$301$	7.21984	−	7.21984i	0.416145	−	0.416145i
$302$	22.2818	−	5.31137i	1.28217	−	0.305635i
$303$	26.4564			1.51988
$304$	−2.14263	+	2.90939i	−0.122888	+	0.166865i
$305$	0.122373	−	2.07448i	0.00700708	−	0.118784i
$306$	−3.81915	−	1.49080i	−0.218326	−	0.0852231i
$307$	0.746565	−	0.746565i	0.0426087	−	0.0426087i	−0.685481	−	0.728090i	$-0.740408\pi$
$307$	0.746565	−	0.746565i	0.0426087	−	0.0426087i	0.728090	+	0.685481i	$0.240408\pi$
$308$	4.26539	−	12.9848i	0.243043	−	0.739876i
$309$	−4.17660	−	4.17660i	−0.237598	−	0.237598i
$310$	23.0358	−	4.07492i	1.30834	−	0.231440i
$311$	−4.45125	+	4.45125i	−0.252407	+	0.252407i	−0.821957	−	0.569550i	$-0.807118\pi$
$311$	−4.45125	+	4.45125i	−0.252407	+	0.252407i	0.569550	+	0.821957i	$0.307118\pi$
$312$	−18.5729	−	1.55223i	−1.05148	−	0.0878777i
$313$	−1.44042			−0.0814175			−0.0407087	−	0.999171i	$-0.512962\pi$
$313$	−1.44042			−0.0814175			−0.0407087	+	0.999171i	$0.512962\pi$
$314$	28.4027	+	17.4683i	1.60286	+	0.985793i
$315$	3.88179	+	4.36847i	0.218714	+	0.246135i
$316$	−4.42011	+	13.4558i	−0.248651	+	0.756946i
$317$	−15.2405			−0.855993			−0.427997	−	0.903780i	$-0.640781\pi$
$317$	−15.2405			−0.855993			−0.427997	+	0.903780i	$0.640781\pi$
$318$	−8.74418	+	14.2177i	−0.490349	+	0.797287i
$319$	−8.00856			−0.448393
$320$	−15.1589	+	9.49781i	−0.847407	+	0.530944i
$321$		−	0.139148i		−	0.00776650i
$322$	6.94968	+	29.1547i	0.387291	+	1.62473i
$323$	−3.06089	−	2.12188i	−0.170312	−	0.118064i
$324$	−11.4170	+	5.77090i	−0.634277	+	0.320606i
$325$	−13.4581	−	17.0727i	−0.746520	−	0.947022i
$326$	11.8904	−	2.83435i	0.658549	−	0.156980i
$327$	6.50324	+	6.50324i	0.359630	+	0.359630i
$328$	−0.668323	+	7.99667i	−0.0369020	+	0.441542i
$329$	−14.2161	−	14.2161i	−0.783758	−	0.783758i
$330$	1.53480	+	8.67635i	0.0844882	+	0.477617i
$331$			10.9948i			0.604328i	0.953256	+	0.302164i	$0.0977091\pi$
$331$			10.9948i			0.604328i	−0.953256	+	0.302164i	$0.902291\pi$
$332$	−1.28736	+	3.91900i	−0.0706530	+	0.215083i
$333$		−	6.87932i		−	0.376984i
$334$	4.31171	+	18.0881i	0.235926	+	0.989737i
$335$	9.83412	+	0.580114i	0.537295	+	0.0316950i
$336$	18.1441	+	13.3623i	0.989841	+	0.728971i
$337$	−9.83453			−0.535721			−0.267860	−	0.963458i	$-0.586317\pi$
$337$	−9.83453			−0.535721			−0.267860	+	0.963458i	$0.586317\pi$
$338$	1.93600	+	8.12174i	0.105304	+	0.441764i
$339$			28.1158i			1.52704i
$340$	−10.2331	−	15.3390i	−0.554968	−	0.831872i
$341$			13.6004i			0.736503i
$342$	0.873723	−	0.208271i	0.0472455	−	0.0112620i
$343$	0.682227			0.0368368
$344$	0.647076	−	7.74244i	0.0348880	−	0.417444i
$345$	−12.8344	−	14.4435i	−0.690982	−	0.777614i
$346$	2.90216	−	0.691795i	0.156021	−	0.0371911i
$347$		−	33.9561i		−	1.82286i	−0.411456	−	0.911429i	$-0.634980\pi$
$347$		−	33.9561i		−	1.82286i	0.411456	−	0.911429i	$-0.365020\pi$
$348$	4.12069	−	12.5443i	0.220892	−	0.672443i
$349$			10.3032i			0.551519i	0.961227	+	0.275759i	$0.0889293\pi$
$349$			10.3032i			0.551519i	−0.961227	+	0.275759i	$0.911071\pi$
$350$	3.04629	+	26.1064i	0.162831	+	1.39544i
$351$	17.2543	+	17.2543i	0.920965	+	0.920965i
$352$	−3.90224	−	9.64013i	−0.207990	−	0.513821i
$353$	14.5146	+	14.5146i	0.772535	+	0.772535i	0.978549	−	0.206014i	$-0.0660493\pi$
$353$	14.5146	+	14.5146i	0.772535	+	0.772535i	−0.206014	+	0.978549i	$0.566049\pi$
$354$	−6.39836	−	26.8419i	−0.340069	−	1.42663i
$355$	34.6241	+	2.04247i	1.83766	+	0.108403i
$356$	15.4927	+	30.6504i	0.821113	+	1.62447i
$357$	−13.2328	+	19.0889i	−0.700356	+	1.01029i
$358$	−10.8922	+	2.59641i	−0.575672	+	0.137224i
$359$			20.5335i			1.08372i	0.840470	+	0.541858i	$0.182279\pi$
$359$			20.5335i			1.08372i	−0.840470	+	0.541858i	$0.817721\pi$
$360$	4.40191	+	0.630669i	0.232001	+	0.0332392i
$361$	−18.1840			−0.957054
$362$	−10.5942	−	6.51569i	−0.556820	−	0.342457i
$363$	11.5485			0.606139
$364$	10.0873	−	30.7080i	0.528720	−	1.60954i
$365$	13.6593	−	12.1375i	0.714960	−	0.635308i
$366$	−1.04349	+	1.69667i	−0.0545443	+	0.0886866i
$367$	−0.314519			−0.0164178			−0.00820889	−	0.999966i	$-0.502613\pi$
$367$	−0.314519			−0.0164178			−0.00820889	+	0.999966i	$0.502613\pi$
$368$	18.3638	+	13.5241i	0.957280	+	0.704991i
$369$	1.41054	−	1.41054i	0.0734296	−	0.0734296i
$370$	17.7325	−	25.3544i	0.921871	−	1.31811i
$371$	−20.4687	−	20.4687i	−1.06268	−	1.06268i
$372$	−21.3031	−	6.99789i	−1.10451	−	0.362824i
$373$	−14.2125	+	14.2125i	−0.735895	+	0.735895i	−0.971781	−	0.235886i	$-0.924201\pi$
$373$	−14.2125	+	14.2125i	−0.735895	+	0.735895i	0.235886	+	0.971781i	$0.424201\pi$
$374$	9.81769	−	4.30495i	0.507661	−	0.222604i
$375$	−9.68788	−	13.9017i	−0.500280	−	0.717879i
$376$	−15.2451	−	1.27411i	−0.786206	−	0.0657073i
$377$	−18.9396			−0.975441
$378$	−6.84078	−	28.6978i	−0.351852	−	1.47606i
$379$	−12.1204	+	12.1204i	−0.622585	+	0.622585i	−0.946192	−	0.323607i	$-0.895105\pi$
$379$	−12.1204	+	12.1204i	−0.622585	+	0.622585i	0.323607	+	0.946192i	$0.395105\pi$
$380$	3.75705	+	1.48455i	0.192732	+	0.0761561i
$381$	8.16833	+	8.16833i	0.418476	+	0.418476i
$382$	6.43302	+	26.9873i	0.329142	+	1.38079i
$383$	18.0098	+	18.0098i	0.920257	+	0.920257i	0.997047	−	0.0767901i	$-0.0244671\pi$
$383$	18.0098	+	18.0098i	0.920257	+	0.920257i	−0.0767901	+	0.997047i	$0.524467\pi$
$384$	17.1077	−	1.15211i	0.873025	−	0.0587932i
$385$	−15.2541	−	0.899839i	−0.777421	−	0.0458600i
$386$	−3.11058	+	0.741476i	−0.158324	+	0.0377401i
$387$	−1.36569	+	1.36569i	−0.0694220	+	0.0694220i
$388$	10.1898	−	5.15062i	0.517310	−	0.261483i
$389$			3.61983i			0.183533i	0.995781	+	0.0917663i	$0.0292513\pi$
$389$			3.61983i			0.183533i	−0.995781	+	0.0917663i	$0.970749\pi$
$390$	3.62970	+	20.5189i	0.183797	+	1.03902i
$391$	−13.3931	+	19.3200i	−0.677318	+	0.977056i
$392$	−14.7210	+	12.4501i	−0.743521	+	0.628827i
$393$	5.17894	−	5.17894i	0.261243	−	0.261243i
$394$	−31.8002	+	7.58029i	−1.60207	+	0.381889i
$395$	15.8074	+	0.932478i	0.795357	+	0.0469181i
$396$	−0.806834	+	2.45618i	−0.0405450	+	0.123428i
$397$	−21.8199			−1.09511			−0.547555	−	0.836770i	$-0.684441\pi$
$397$	−21.8199			−1.09511			−0.547555	+	0.836770i	$0.684441\pi$
$398$	−26.4842	−	16.2884i	−1.32753	−	0.816464i
$399$		−	5.08867i		−	0.254752i
$400$	14.5980	+	13.6710i	0.729902	+	0.683552i
$401$	22.4858	−	22.4858i	1.12289	−	1.12289i	0.131585	−	0.991305i	$-0.457993\pi$
$401$	22.4858	−	22.4858i	1.12289	−	1.12289i	0.991305	−	0.131585i	$-0.0420065\pi$
$402$	−8.04313	−	4.94671i	−0.401155	−	0.246720i
$403$			32.1639i			1.60220i
$404$	15.7498	+	31.1589i	0.783582	+	1.55022i
$405$	9.50034	+	10.6915i	0.472076	+	0.531262i
$406$	19.5050	+	11.9960i	0.968016	+	0.595352i
$407$	12.7193	+	12.7193i	0.630474	+	0.630474i
$408$	1.69154	+	17.5931i	0.0837437	+	0.870986i
$409$		−	35.8757i		−	1.77394i	−0.461827	−	0.886970i	$-0.652806\pi$
$409$		−	35.8757i		−	1.77394i	0.461827	−	0.886970i	$-0.347194\pi$
$410$	8.83456	−	1.56279i	0.436308	−	0.0771807i
$411$	−7.63286	−	7.63286i	−0.376501	−	0.376501i
$412$	2.43260	−	7.40536i	0.119846	−	0.364836i
$413$	47.8549			2.35479
$414$	−1.31459	−	5.51485i	−0.0646086	−	0.271040i
$415$	4.60392	+	0.271585i	0.225997	+	0.0133316i
$416$	−9.22850	−	22.7982i	−0.452465	−	1.11777i
$417$	−9.60574	−	9.60574i	−0.470395	−	0.470395i
$418$	−1.23037	+	2.00052i	−0.0601793	+	0.0978489i
$419$	−21.6697	−	21.6697i	−1.05864	−	1.05864i	−0.998170	−	0.0604656i	$-0.980741\pi$
$419$	−21.6697	−	21.6697i	−1.05864	−	1.05864i	−0.0604656	−	0.998170i	$-0.519259\pi$
$420$	9.25825	−	23.4304i	0.451756	−	1.14329i
$421$		−	16.7158i		−	0.814680i	−0.913277	−	0.407340i	$-0.866456\pi$
$421$		−	16.7158i		−	0.814680i	0.913277	−	0.407340i	$-0.133544\pi$
$422$	5.78188	−	9.40109i	0.281458	−	0.457638i
$423$	2.68909	+	2.68909i	0.130748	+	0.130748i
$424$	−21.9503	−	1.83450i	−1.06600	−	0.0890914i
$425$	−13.6556	+	15.4443i	−0.662392	+	0.749158i
$426$	−28.3184	−	17.4164i	−1.37203	−	0.843830i
$427$	−2.44265	−	2.44265i	−0.118208	−	0.118208i
$428$	0.163882	−	0.0828367i	0.00792152	−	0.00400406i
$429$	−12.1144			−0.584890
$430$	−8.55369	+	1.51311i	−0.412495	+	0.0729684i
$431$	6.57830	+	6.57830i	0.316866	+	0.316866i	0.847562	−	0.530696i	$-0.178070\pi$
$431$	6.57830	+	6.57830i	0.316866	+	0.316866i	−0.530696	+	0.847562i	$0.678070\pi$
$432$	−18.0761	−	13.3121i	−0.869684	−	0.640481i
$433$	20.9132	−	20.9132i	1.00502	−	1.00502i	0.00503702	−	0.999987i	$-0.498397\pi$
$433$	20.9132	−	20.9132i	1.00502	−	1.00502i	0.999987	−	0.00503702i	$-0.00160334\pi$
$434$	20.3720	−	33.1240i	0.977888	−	1.59000i
$435$	−14.7366	−	0.869311i	−0.706566	−	0.0416803i
$436$	−3.78772	+	11.5306i	−0.181399	+	0.552217i
$437$		−	5.15029i		−	0.246372i
$438$	−17.0375	+	4.06126i	−0.814081	+	0.194055i
$439$	−7.88355	−	7.88355i	−0.376261	−	0.376261i	0.493490	−	0.869751i	$-0.335721\pi$
$439$	−7.88355	−	7.88355i	−0.376261	−	0.376261i	−0.869751	+	0.493490i	$0.835721\pi$
$440$	−9.30486	+	6.97274i	−0.443592	+	0.332412i
$441$	4.79272			0.228225
$442$	23.2181	−	10.1809i	1.10437	−	0.484256i
$443$	5.63993	+	5.63993i	0.267961	+	0.267961i	0.828278	−	0.560317i	$-0.189321\pi$
$443$	5.63993	+	5.63993i	0.267961	+	0.267961i	−0.560317	+	0.828278i	$0.689321\pi$
$444$	−26.4676	+	13.3785i	−1.25610	+	0.634914i
$445$	28.7026	−	25.5049i	1.36063	−	1.20905i
$446$	−10.6238	−	6.53386i	−0.503050	−	0.309387i
$447$		−	12.3481i		−	0.584044i
$448$	−4.93598	+	29.3239i	−0.233203	+	1.38542i
$449$	−15.8239	−	15.8239i	−0.746777	−	0.746777i	0.227095	−	0.973873i	$-0.427077\pi$
$449$	−15.8239	−	15.8239i	−0.746777	−	0.746777i	−0.973873	+	0.227095i	$0.927077\pi$
$450$	−0.576231	−	4.93824i	−0.0271638	−	0.232791i
$451$			5.21595i			0.245609i
$452$	−33.1133	+	16.7377i	−1.55752	+	0.787273i
$453$			24.5474i			1.15334i
$454$	−5.72551	−	24.0192i	−0.268712	−	1.12728i
$455$	−36.0748	−	2.12805i	−1.69121	−	0.0997646i
$456$	−2.50047	−	2.95654i	−0.117095	−	0.138453i
$457$	1.74011	+	1.74011i	0.0813989	+	0.0813989i	0.746634	−	0.665235i	$-0.231669\pi$
$457$	1.74011	+	1.74011i	0.0813989	+	0.0813989i	−0.665235	+	0.746634i	$0.731669\pi$
$458$	2.72629	+	11.4371i	0.127391	+	0.534420i
$459$	13.1832	−	19.0173i	0.615340	−	0.887651i
$460$	9.37037	−	23.7141i	0.436896	−	1.10568i
$461$	−12.9627			−0.603733			−0.301867	−	0.953350i	$-0.597610\pi$
$461$	−12.9627			−0.603733			−0.301867	+	0.953350i	$0.597610\pi$
$462$	12.4760	+	7.67305i	0.580438	+	0.356982i
$463$	19.9650	−	19.9650i	0.927854	−	0.927854i	−0.0697132	−	0.997567i	$-0.522208\pi$
$463$	19.9650	−	19.9650i	0.927854	−	0.927854i	0.997567	+	0.0697132i	$0.0222084\pi$
$464$	17.2271	−	2.61461i	0.799746	−	0.121380i
$465$	−1.47629	+	25.0262i	−0.0684615	+	1.16056i
$466$	−1.88830	−	7.92163i	−0.0874737	−	0.366962i
$467$	17.6270	+	17.6270i	0.815680	+	0.815680i	0.985479	−	0.169798i	$-0.0543116\pi$
$467$	17.6270	+	17.6270i	0.815680	+	0.815680i	−0.169798	+	0.985479i	$0.554312\pi$
$468$	−1.90810	+	5.80867i	−0.0882021	+	0.268506i
$469$	11.5795	−	11.5795i	0.534690	−	0.534690i
$470$	2.97935	+	16.8425i	0.137427	+	0.776885i
$471$	−25.2676	+	25.2676i	−1.16427	+	1.16427i
$472$	27.8039	−	23.5149i	1.27978	−	1.08236i
$473$		−	5.05012i		−	0.232205i
$474$	−12.9286	−	7.95136i	−0.593829	−	0.365218i
$475$	0.531013	−	4.48521i	0.0243646	−	0.205796i
$476$	−30.3595	−	4.22112i	−1.39153	−	0.193475i
$477$	3.87183	+	3.87183i	0.177279	+	0.177279i
$478$	−2.47780	+	0.590640i	−0.113332	+	0.0270153i
$479$	−13.0574	−	13.0574i	−0.596610	−	0.596610i	0.342799	−	0.939409i	$-0.388625\pi$
$479$	−13.0574	−	13.0574i	−0.596610	−	0.596610i	−0.939409	+	0.342799i	$0.888625\pi$
$480$	−6.13412	−	18.1625i	−0.279983	−	0.828999i
$481$	30.0803	+	30.0803i	1.37154	+	1.37154i
$482$	13.7494	+	8.45622i	0.626269	+	0.385170i
$483$	−32.1192			−1.46147
$484$	6.87496	+	13.6012i	0.312498	+	0.618237i
$485$	−8.47919	−	9.54228i	−0.385020	−	0.433293i
$486$	2.34229	+	9.82617i	0.106248	+	0.445724i
$487$	24.8028			1.12392			0.561960	−	0.827164i	$-0.310047\pi$
$487$	24.8028			1.12392			0.561960	+	0.827164i	$0.310047\pi$
$488$	−2.61946	−	0.218922i	−0.118577	−	0.00991012i
$489$			13.0994i			0.592377i
$490$	17.6641	+	12.3540i	0.797981	+	0.558098i
$491$			40.9044i			1.84599i	0.384811	+	0.922996i	$0.374267\pi$
$491$			40.9044i			1.84599i	−0.384811	+	0.922996i	$0.625733\pi$
$492$	−8.17004	−	2.68379i	−0.368334	−	0.120995i
$493$	3.20196	+	17.6729i	0.144209	+	0.795947i
$494$	−2.90973	+	4.73109i	−0.130915	+	0.212862i
$495$	2.88544	+	0.170212i	0.129691	+	0.00765046i
$496$	−4.44022	−	29.2556i	−0.199372	−	1.31361i
$497$	40.7691	−	40.7691i	1.82874	−	1.82874i
$498$	−3.76545	−	2.31584i	−0.168734	−	0.103775i
$499$	−0.108545	−	0.108545i	−0.00485913	−	0.00485913i	0.704673	−	0.709532i	$-0.251094\pi$
$499$	−0.108545	−	0.108545i	−0.00485913	−	0.00485913i	−0.709532	+	0.704673i	$0.751094\pi$
$500$	10.6053	−	19.6857i	0.474285	−	0.880371i
$501$	−19.9273			−0.890287
$502$	38.9521	−	9.28510i	1.73852	−	0.414414i
$503$		−	5.66034i		−	0.252382i	−0.992006	−	0.126191i	$-0.959725\pi$
$503$		−	5.66034i		−	0.252382i	0.992006	−	0.126191i	$-0.0402753\pi$
$504$	5.64416	−	4.77350i	0.251411	−	0.212629i
$505$	29.1788	−	25.9281i	1.29844	−	1.15378i
$506$	12.6271	+	7.76597i	0.561344	+	0.345239i
$507$	−8.94757			−0.397375
$508$	−4.75753	+	14.4829i	−0.211081	+	0.642576i
$509$	−5.13864			−0.227766			−0.113883	−	0.993494i	$-0.536329\pi$
$509$	−5.13864			−0.227766			−0.113883	+	0.993494i	$0.536329\pi$
$510$	18.5329	−	6.85588i	0.820650	−	0.303584i
$511$		−	30.3752i		−	1.34372i
$512$	11.5413	+	19.4627i	0.510059	+	0.860139i
$513$			5.06959i			0.223828i
$514$	−6.88291	−	4.23315i	−0.303592	−	0.186716i
$515$	−8.69958	−	0.513188i	−0.383349	−	0.0226138i
$516$	7.91029	+	2.59847i	0.348231	+	0.114391i
$517$	−9.94384			−0.437330
$518$	−11.9259	−	50.0304i	−0.523993	−	2.19821i
$519$			3.19725i			0.140344i
$520$	−22.0053	+	16.4900i	−0.964996	+	0.723135i
$521$	29.6119	−	29.6119i	1.29732	−	1.29732i	0.367168	−	0.930155i	$-0.380327\pi$
$521$	29.6119	−	29.6119i	1.29732	−	1.29732i	0.930155	−	0.367168i	$-0.119673\pi$
$522$	−3.68953	−	2.26914i	−0.161486	−	0.0993177i
$523$	18.7631	+	18.7631i	0.820451	+	0.820451i	0.986173	−	0.165722i	$-0.0529953\pi$
$523$	18.7631	+	18.7631i	0.820451	+	0.820451i	−0.165722	+	0.986173i	$0.552995\pi$
$524$	9.18256	+	3.01640i	0.401142	+	0.131772i
$525$	−27.9715	−	3.31160i	−1.22078	−	0.144530i
$526$	11.7419	+	7.22152i	0.511970	+	0.314873i
$527$	30.0127	−	5.43768i	1.30737	−	0.236869i
$528$	11.0190	−	1.67239i	0.479541	−	0.0727816i
$529$	−9.50817			−0.413399
$530$	4.28976	+	24.2503i	0.186335	+	1.05336i
$531$	−9.05215			−0.392830
$532$	5.99317	−	3.02934i	0.259837	−	0.131339i
$533$			12.3353i			0.534302i
$534$	−35.8012	+	8.53402i	−1.54927	+	0.369303i
$535$	−0.136370	−	0.153467i	−0.00589578	−	0.00663497i
$536$	1.03781	−	12.4176i	0.0448263	−	0.536359i
$537$		−	11.9998i		−	0.517828i
$538$	3.05003	+	1.87584i	0.131496	+	0.0808731i
$539$	−8.86138	+	8.86138i	−0.381687	+	0.381687i
$540$	−9.22353	+	23.3425i	−0.396918	+	1.00450i
$541$	−23.9023	+	23.9023i	−1.02764	+	1.02764i	−0.0280350	+	0.999607i	$0.508925\pi$
$541$	−23.9023	+	23.9023i	−1.02764	+	1.02764i	−0.999607	+	0.0280350i	$0.991075\pi$
$542$	5.01529	+	21.0397i	0.215425	+	0.903733i
$543$	9.42484	−	9.42484i	0.404458	−	0.404458i
$544$	−19.7132	+	12.4656i	−0.845196	+	0.534457i
$545$	13.5458	+	0.799068i	0.580240	+	0.0342283i
$546$	29.5049	+	18.1462i	1.26269	+	0.776585i
$547$	−6.46473			−0.276412			−0.138206	−	0.990404i	$-0.544134\pi$
$547$	−6.46473			−0.276412			−0.138206	+	0.990404i	$0.544134\pi$
$548$	4.44565	−	13.5335i	0.189909	−	0.578123i
$549$	0.462047	+	0.462047i	0.0197197	+	0.0197197i
$550$	10.1958	+	8.06502i	0.434752	+	0.343893i
$551$	−2.78239	−	2.78239i	−0.118534	−	0.118534i
$552$	−18.6614	+	15.7827i	−0.794281	+	0.671757i
$553$	18.6129	−	18.6129i	0.791500	−	0.791500i
$554$	2.85883	+	11.9931i	0.121460	+	0.509538i
$555$	22.0243	+	24.7856i	0.934879	+	1.05209i
$556$	5.59473	−	17.0316i	0.237269	−	0.722299i
$557$	−25.3100	−	25.3100i	−1.07242	−	1.07242i	−0.997164	−	0.0752544i	$-0.976023\pi$
$557$	−25.3100	−	25.3100i	−1.07242	−	1.07242i	−0.0752544	−	0.997164i	$-0.523977\pi$
$558$	−3.85353	+	6.26568i	−0.163133	+	0.265247i
$559$		−	11.9432i		−	0.505142i
$560$	33.1066	−	3.04450i	1.39901	−	0.128653i
$561$	2.04808	+	11.3042i	0.0864701	+	0.477262i
$562$	−2.69480	−	11.3050i	−0.113673	−	0.476872i
$563$	24.4415	−	24.4415i	1.03009	−	1.03009i	0.0305539	−	0.999533i	$-0.490273\pi$
$563$	24.4415	−	24.4415i	1.03009	−	1.03009i	0.999533	−	0.0305539i	$-0.00972711\pi$
$564$	5.11646	−	15.5756i	0.215442	−	0.655851i
$565$	27.5543	+	31.0090i	1.15922	+	1.30456i
$566$	0.772292	−	0.184093i	0.0324618	−	0.00773801i
$567$	23.7754			0.998472
$568$	3.65392	−	43.7201i	0.153315	−	1.83445i
$569$	7.01994			0.294291			0.147146	−	0.989115i	$-0.452991\pi$
$569$	7.01994			0.294291			0.147146	+	0.989115i	$0.452991\pi$
$570$	−2.48116	+	3.54763i	−0.103924	+	0.148594i
$571$	−5.66950	+	5.66950i	−0.237261	+	0.237261i	−0.815715	−	0.578454i	$-0.803656\pi$
$571$	−5.66950	+	5.66950i	−0.237261	+	0.237261i	0.578454	+	0.815715i	$0.303656\pi$
$572$	−7.21186	−	14.2677i	−0.301543	−	0.596564i
$573$	−29.7314			−1.24205
$574$	7.81296	−	12.7035i	0.326107	−	0.530235i
$575$	−28.3102	−	3.35170i	−1.18062	−	0.139776i
$576$	0.933680	−	5.54685i	0.0389033	−	0.231119i
$577$	−13.7607	+	13.7607i	−0.572864	+	0.572864i	−0.932928	−	0.360063i	$-0.882755\pi$
$577$	−13.7607	+	13.7607i	−0.572864	+	0.572864i	0.360063	+	0.932928i	$0.382755\pi$
$578$	−13.4252	−	19.9440i	−0.558416	−	0.829561i
$579$		−	3.42686i		−	0.142416i
$580$	−7.74904	−	17.8735i	−0.321761	−	0.742157i
$581$	5.42101	−	5.42101i	0.224901	−	0.224901i
$582$	2.83717	+	11.9022i	0.117604	+	0.493364i
$583$	−14.3174			−0.592967
$584$	−14.9257	−	17.6481i	−0.617632	−	0.730284i
$585$	6.82385	+	0.402539i	0.282131	+	0.0166429i
$586$	−5.74462	+	9.34050i	−0.237308	+	0.385853i
$587$	22.0867	+	22.0867i	0.911614	+	0.911614i	0.996399	−	0.0847853i	$-0.0270205\pi$
$587$	22.0867	+	22.0867i	0.911614	+	0.911614i	−0.0847853	+	0.996399i	$0.527020\pi$
$588$	−9.32059	−	18.4396i	−0.384375	−	0.760436i
$589$	−4.72514	+	4.72514i	−0.194696	+	0.194696i
$590$	−33.3626	−	23.3334i	−1.37352	−	0.960620i
$591$		−	35.0337i		−	1.44109i
$592$	−31.5129	−	23.2078i	−1.29517	−	0.953833i
$593$	−15.8013	+	15.8013i	−0.648882	+	0.648882i	−0.952723	−	0.303841i	$-0.901731\pi$
$593$	−15.8013	+	15.8013i	−0.648882	+	0.648882i	0.303841	+	0.952723i	$0.401731\pi$
$594$	−12.4292	−	7.64427i	−0.509978	−	0.313648i
$595$	4.11314	+	34.0218i	0.168622	+	1.39476i
$596$	14.5429	−	7.35096i	0.595701	−	0.301107i
$597$	23.5609	−	23.5609i	0.964283	−	0.964283i
$598$	29.8622	+	18.3659i	1.22116	+	0.751039i
$599$	−0.415409			−0.0169732			−0.00848658	−	0.999964i	$-0.502701\pi$
$599$	−0.415409			−0.0169732			−0.00848658	+	0.999964i	$0.502701\pi$
$600$	−17.8788	+	11.8206i	−0.729900	+	0.482573i
$601$	21.0815	−	21.0815i	0.859934	−	0.859934i	−0.131396	−	0.991330i	$-0.541946\pi$
$601$	21.0815	−	21.0815i	0.859934	−	0.859934i	0.991330	+	0.131396i	$0.0419459\pi$
$602$	−7.56457	+	12.2997i	−0.308309	+	0.501297i
$603$	−2.19035	+	2.19035i	−0.0891979	+	0.0891979i
$604$	−28.9107	+	14.6134i	−1.17636	+	0.594610i
$605$	12.7369	−	11.3179i	0.517828	−	0.460138i
$606$	−36.3953	+	8.67563i	−1.47846	+	0.352423i
$607$			20.6894i			0.839756i	0.907581	+	0.419878i	$0.137927\pi$
$607$			20.6894i			0.839756i	−0.907581	+	0.419878i	$0.862073\pi$
$608$	1.99350	−	4.70498i	0.0808470	−	0.190812i
$609$	−17.3520	+	17.3520i	−0.703139	+	0.703139i
$610$	0.511921	+	2.89392i	0.0207271	+	0.117172i
$611$	−23.5164			−0.951373
$612$	5.74276	+	0.798460i	0.232137	+	0.0322758i
$613$	−19.5899	+	19.5899i	−0.791228	+	0.791228i	−0.981694	−	0.190466i	$-0.939000\pi$
$613$	−19.5899	+	19.5899i	−0.791228	+	0.791228i	0.190466	+	0.981694i	$0.439000\pi$
$614$	−0.782212	+	1.27184i	−0.0315675	+	0.0513274i
$615$	−0.566180	+	9.59790i	−0.0228306	+	0.387025i
$616$	−1.60978	+	19.2615i	−0.0648600	+	0.776067i
$617$	−46.0849			−1.85531			−0.927655	−	0.373438i	$-0.878179\pi$
$617$	−46.0849			−1.85531			−0.927655	+	0.373438i	$0.878179\pi$
$618$	7.11522	+	4.37602i	0.286216	+	0.176029i
$619$	9.52714	+	9.52714i	0.382928	+	0.382928i	0.872156	−	0.489228i	$-0.162721\pi$
$619$	9.52714	+	9.52714i	0.382928	+	0.382928i	−0.489228	+	0.872156i	$0.662721\pi$
$620$	−30.3534	+	13.1597i	−1.21902	+	0.528505i
$621$	31.9987			1.28407
$622$	4.66379	−	7.58311i	0.187001	−	0.304055i
$623$		−	63.8281i		−	2.55722i
$624$	26.0591	−	3.95509i	1.04320	−	0.158330i
$625$	−24.3089	−	5.83777i	−0.972354	−	0.233511i
$626$	1.98154	−	0.472346i	0.0791985	−	0.0188787i
$627$	−1.77971	−	1.77971i	−0.0710746	−	0.0710746i
$628$	−44.8009	−	14.7167i	−1.78775	−	0.587262i
$629$	22.9830	−	33.1538i	0.916392	−	1.32193i
$630$	−6.77258	−	4.73665i	−0.269826	−	0.188713i
$631$	−15.4948			−0.616837			−0.308419	−	0.951251i	$-0.599800\pi$
$631$	−15.4948			−0.616837			−0.308419	+	0.951251i	$0.599800\pi$
$632$	1.66817	−	19.9601i	0.0663563	−	0.793971i
$633$	8.36340	+	8.36340i	0.332415	+	0.332415i
$634$	20.9659	−	4.99770i	0.832664	−	0.198484i
$635$	17.0141	+	1.00366i	0.675184	+	0.0398291i
$636$	7.36683	−	22.4262i	0.292114	−	0.889257i
$637$	−20.9565	+	20.9565i	−0.830327	+	0.830327i
$638$	11.0171	−	2.62618i	0.436172	−	0.103971i
$639$	−7.71181	+	7.71181i	−0.305074	+	0.305074i
$640$	17.7391	−	18.0368i	0.701199	−	0.712966i
$641$	−27.7337	−	27.7337i	−1.09542	−	1.09542i	−0.994939	−	0.100477i	$-0.967963\pi$
$641$	−27.7337	−	27.7337i	−1.09542	−	1.09542i	−0.100477	−	0.994939i	$-0.532037\pi$
$642$	0.0456298	+	0.191422i	0.00180086	+	0.00755483i
$643$			11.6274i			0.458541i	0.973363	+	0.229271i	$0.0736341\pi$
$643$			11.6274i			0.458541i	−0.973363	+	0.229271i	$0.926366\pi$
$644$	−19.1209	−	37.8283i	−0.753471	−	1.49064i
$645$	0.548180	−	9.29276i	0.0215846	−	0.365902i
$646$	4.90658	+	1.91527i	0.193047	+	0.0753553i
$647$	14.1827	+	14.1827i	0.557578	+	0.557578i	0.928617	−	0.371039i	$-0.120998\pi$
$647$	14.1827	+	14.1827i	0.557578	+	0.557578i	−0.371039	+	0.928617i	$0.620998\pi$
$648$	13.8136	−	11.6827i	0.542649	−	0.458941i
$649$	16.7367	−	16.7367i	0.656975	−	0.656975i
$650$	24.1124	+	19.0732i	0.945765	+	0.748111i
$651$	29.4678	+	29.4678i	1.15493	+	1.15493i
$652$	−15.4278	+	7.79825i	−0.604201	+	0.305403i
$653$		−	29.9896i		−	1.17358i	−0.809738	−	0.586792i	$-0.800391\pi$
$653$		−	29.9896i		−	1.17358i	0.809738	−	0.586792i	$-0.199609\pi$
$654$	−11.0789	−	6.81376i	−0.433218	−	0.266439i
$655$	0.636347	−	10.7874i	0.0248642	−	0.421498i
$656$	−1.70289	−	11.2199i	−0.0664867	−	0.438065i
$657$			5.74572i			0.224162i
$658$	24.2184	+	14.8949i	0.944132	+	0.580663i
$659$		−	9.33759i		−	0.363741i	−0.983323	−	0.181870i	$-0.941785\pi$
$659$		−	9.33759i		−	0.363741i	0.983323	−	0.181870i	$-0.0582151\pi$
$660$	−4.95655	−	11.4325i	−0.192933	−	0.445009i
$661$	−26.0027			−1.01139			−0.505694	−	0.862713i	$-0.668763\pi$
$661$	−26.0027			−1.01139			−0.505694	+	0.862713i	$0.668763\pi$
$662$	−3.60543	−	15.1252i	−0.140129	−	0.587858i
$663$	4.84356	+	26.7335i	0.188108	+	1.03824i
$664$	0.485856	−	5.81340i	0.0188549	−	0.225604i
$665$	−4.98705	−	5.61231i	−0.193390	−	0.217636i
$666$	2.25588	+	9.46367i	0.0874135	+	0.366710i
$667$	−17.5622	+	17.5622i	−0.680009	+	0.680009i
$668$	−11.8630	−	23.4694i	−0.458992	−	0.908057i
$669$	9.45111	−	9.45111i	0.365401	−	0.365401i
$670$	−13.7187	+	2.42678i	−0.530001	+	0.0937546i
$671$	−1.70858			−0.0659590
$672$	−29.3421	−	12.4322i	−1.13189	−	0.479583i
$673$	2.71734			0.104746			0.0523728	−	0.998628i	$-0.483322\pi$
$673$	2.71734			0.104746			0.0523728	+	0.998628i	$0.483322\pi$
$674$	13.5291	−	3.22496i	0.521120	−	0.124221i
$675$	27.8666	+	3.29918i	1.07259	+	0.126986i
$676$	−5.32659	−	10.5380i	−0.204869	−	0.405307i
$677$			17.1643i			0.659678i	0.944037	+	0.329839i	$0.106994\pi$
$677$			17.1643i			0.659678i	−0.944037	+	0.329839i	$0.893006\pi$
$678$	−9.21978	−	38.6780i	−0.354084	−	1.48542i
$679$	−21.2199			−0.814344
$680$	19.1074	+	17.7457i	0.732733	+	0.680516i
$681$	26.4615			1.01401
$682$	−4.45987	−	18.7096i	−0.170777	−	0.716429i
$683$			30.3673i			1.16197i	0.813914	+	0.580985i	$0.197333\pi$
$683$			30.3673i			1.16197i	−0.813914	+	0.580985i	$0.802667\pi$
$684$	−1.13366	+	0.573025i	−0.0433465	+	0.0219102i
$685$	−15.8988	−	0.937867i	−0.607460	−	0.0358341i
$686$	−0.938520	+	0.223717i	−0.0358328	+	0.00854157i
$687$	−12.6000			−0.480721
$688$	1.64875	+	10.8632i	0.0628581	+	0.414157i
$689$	−33.8597			−1.28995
$690$	22.3923	+	15.6609i	0.852459	+	0.596199i
$691$	−1.07060	+	1.07060i	−0.0407275	+	0.0407275i	−0.727177	−	0.686450i	$-0.759168\pi$
$691$	−1.07060	+	1.07060i	−0.0407275	+	0.0407275i	0.686450	+	0.727177i	$0.259168\pi$
$692$	−3.76556	+	1.90336i	−0.143145	+	0.0723550i
$693$	3.39754	−	3.39754i	0.129062	−	0.129062i
$694$	11.1349	+	46.7124i	0.422677	+	1.77318i
$695$	−20.0081	−	1.18028i	−0.758952	−	0.0447705i
$696$	−1.55517	+	18.6080i	−0.0589485	+	0.705335i
$697$	11.5103	−	2.08543i	0.435984	−	0.0789912i
$698$	−3.37865	−	14.1738i	−0.127884	−	0.536487i
$699$	8.72711			0.330090
$700$	−12.7515	−	34.9148i	−0.481963	−	1.31966i
$701$			20.9298i			0.790509i	0.918572	+	0.395254i	$0.129344\pi$
$701$			20.9298i			0.790509i	−0.918572	+	0.395254i	$0.870656\pi$
$702$	−29.3942	−	18.0781i	−1.10941	−	0.682315i
$703$			8.83807i			0.333334i
$704$	8.52940	+	11.9820i	0.321464	+	0.451589i
$705$	−18.2977	−	1.07938i	−0.689132	−	0.0406519i
$706$	−24.7270	−	15.2077i	−0.930612	−	0.572347i
$707$		−	64.8872i		−	2.44033i
$708$	17.6041	+	34.8274i	0.661601	+	1.30889i
$709$	24.3007	+	24.3007i	0.912634	+	0.912634i	0.996479	−	0.0838451i	$-0.0267201\pi$
$709$	24.3007	+	24.3007i	0.912634	+	0.912634i	−0.0838451	+	0.996479i	$0.526720\pi$
$710$	−48.3011	+	8.54423i	−1.81271	+	0.320659i
$711$	−3.52078	+	3.52078i	−0.132039	+	0.132039i
$712$	−31.3638	−	37.0844i	−1.17541	−	1.38980i
$713$	29.8246	+	29.8246i	1.11694	+	1.11694i
$714$	11.9444	−	30.5993i	0.447007	−	1.14515i
$715$	−13.3610	+	11.8725i	−0.499675	+	0.444007i
$716$	14.1327	−	7.14360i	0.528164	−	0.266969i
$717$		−	2.72975i		−	0.101944i
$718$	−6.73337	−	28.2473i	−0.251287	−	1.05418i
$719$	23.3854	+	23.3854i	0.872129	+	0.872129i	0.992704	−	0.120575i	$-0.0384738\pi$
$719$	23.3854	+	23.3854i	0.872129	+	0.872129i	−0.120575	+	0.992704i	$0.538474\pi$
$720$	−6.26239	+	0.575891i	−0.233385	+	0.0214622i
$721$	−10.2436	+	10.2436i	−0.381490	+	0.381490i
$722$	25.0152	−	5.96294i	0.930970	−	0.221918i
$723$	−12.2318	+	12.2318i	−0.454904	+	0.454904i
$724$	16.7108	+	5.48936i	0.621052	+	0.204011i
$725$	−17.1050	+	13.4836i	−0.635264	+	0.500767i
$726$	−15.8869	+	3.78701i	−0.589619	+	0.140549i
$727$	11.5450	+	11.5450i	0.428182	+	0.428182i	0.888009	−	0.459827i	$-0.152088\pi$
$727$	11.5450	+	11.5450i	0.428182	+	0.428182i	−0.459827	+	0.888009i	$0.652088\pi$
$728$	−3.80701	+	45.5520i	−0.141097	+	1.68827i
$729$	−30.0142			−1.11164
$730$	−14.8105	+	21.1764i	−0.548162	+	0.783775i
$731$	−11.1444	+	2.01913i	−0.412189	+	0.0746801i
$732$	0.879126	−	2.67625i	0.0324934	−	0.0989170i
$733$	−9.08578	−	9.08578i	−0.335591	−	0.335591i	0.519114	−	0.854705i	$-0.326262\pi$
$733$	−9.08578	−	9.08578i	−0.335591	−	0.335591i	−0.854705	+	0.519114i	$0.826262\pi$
$734$	0.432675	−	0.103138i	0.0159703	−	0.00380688i
$735$	−17.2678	+	15.3440i	−0.636932	+	0.565972i
$736$	−29.6974	−	12.5828i	−1.09466	−	0.463807i
$737$		−	8.09958i		−	0.298352i
$738$	−1.47789	+	2.40298i	−0.0544017	+	0.0884548i
$739$	4.68350			0.172285			0.0861427	−	0.996283i	$-0.472546\pi$
$739$	4.68350			0.172285			0.0861427	+	0.996283i	$0.472546\pi$
$740$	−16.0799	+	40.6942i	−0.591107	+	1.49595i
$741$	−4.20887	−	4.20887i	−0.154617	−	0.154617i
$742$	34.8704	+	21.4461i	1.28013	+	0.787310i
$743$	−37.5211			−1.37651			−0.688257	−	0.725467i	$-0.741624\pi$
$743$	−37.5211			−1.37651			−0.688257	+	0.725467i	$0.741624\pi$
$744$	31.6007	+	2.64104i	1.15854	+	0.0968252i
$745$	−12.1015	−	13.6187i	−0.443365	−	0.498952i
$746$	14.8911	−	24.2123i	0.545202	−	0.886475i
$747$	−1.02543	+	1.02543i	−0.0375185	+	0.0375185i
$748$	−12.0942	+	9.14163i	−0.442208	+	0.334251i
$749$	−0.341277			−0.0124700
$750$	17.8860	+	15.9472i	0.653104	+	0.582310i
$751$	13.4655	−	13.4655i	0.491364	−	0.491364i	−0.417372	−	0.908736i	$-0.637049\pi$
$751$	13.4655	−	13.4655i	0.491364	−	0.491364i	0.908736	+	0.417372i	$0.137049\pi$
$752$	21.3900	−	3.24644i	0.780014	−	0.118386i
$753$			42.9127i			1.56383i
$754$	26.0547	−	6.21072i	0.948856	−	0.226181i
$755$	24.0572	+	27.0734i	0.875533	+	0.985303i
$756$	18.8213	+	37.2355i	0.684524	+	1.35424i
$757$	−17.5046	+	17.5046i	−0.636215	+	0.636215i	−0.949620	−	0.313405i	$-0.898530\pi$
$757$	−17.5046	+	17.5046i	−0.636215	+	0.636215i	0.313405	+	0.949620i	$0.398530\pi$
$758$	12.6992	−	20.6483i	0.461254	−	0.749979i
$759$	−11.2333	+	11.2333i	−0.407744	+	0.407744i
$760$	−5.65527	−	0.810240i	−0.205138	−	0.0293905i
$761$	−27.5546			−0.998852			−0.499426	−	0.866356i	$-0.666456\pi$
$761$	−27.5546			−0.998852			−0.499426	+	0.866356i	$0.666456\pi$
$762$	−13.9155	−	8.55835i	−0.504105	−	0.310036i
$763$	15.9499	−	15.9499i	0.577426	−	0.577426i
$764$	−17.6994	−	35.0160i	−0.640343	−	1.26684i
$765$	−0.778034	−	6.43550i	−0.0281299	−	0.232676i
$766$	−30.6813	−	18.8697i	−1.10856	−	0.681791i
$767$	39.5811	−	39.5811i	1.42919	−	1.42919i
$768$	−23.1568	+	7.19492i	−0.835599	+	0.259624i
$769$		−	15.2916i		−	0.551429i	−0.961240	−	0.275715i	$-0.911086\pi$
$769$		−	15.2916i		−	0.551429i	0.961240	−	0.275715i	$-0.0889145\pi$
$770$	21.2797	−	3.76427i	0.766867	−	0.135655i
$771$	6.12317	−	6.12317i	0.220521	−	0.220521i
$772$	4.03598	−	2.04005i	0.145258	−	0.0734231i
$773$	−4.32599	−	4.32599i	−0.155595	−	0.155595i	0.625016	−	0.780612i	$-0.285092\pi$
$773$	−4.32599	−	4.32599i	−0.155595	−	0.155595i	−0.780612	+	0.625016i	$0.785092\pi$
$774$	1.43090	−	2.32658i	0.0514327	−	0.0836273i
$775$	22.8982	+	29.0483i	0.822529	+	1.04344i
$776$	−12.3288	+	10.4270i	−0.442580	+	0.374308i
$777$	55.1176			1.97733
$778$	−1.18702	−	4.97969i	−0.0425568	−	0.178531i
$779$	−1.81216	+	1.81216i	−0.0649273	+	0.0649273i
$780$	−11.7219	−	27.0370i	−0.419710	−	0.968079i
$781$		−	28.5171i		−	1.02042i
$782$	12.0890	−	30.9699i	0.432302	−	1.10748i
$783$	17.2869	−	17.2869i	0.617785	−	0.617785i
$784$	16.1685	−	21.9546i	0.577447	−	0.784093i
$785$	−3.10469	+	52.6307i	−0.110811	+	1.87847i
$786$	−5.42622	+	8.82279i	−0.193547	+	0.314699i
$787$	36.5735			1.30371			0.651853	−	0.758346i	$-0.273992\pi$
$787$	36.5735			1.30371			0.651853	+	0.758346i	$0.273992\pi$
$788$	41.2608	−	20.8559i	1.46986	−	0.742962i
$789$	−10.4458	+	10.4458i	−0.371880	+	0.371880i
$790$	−22.0515	+	3.90081i	−0.784559	+	0.138785i
$791$	68.9570			2.45183
$792$	0.304504	−	3.64347i	0.0108201	−	0.129465i
$793$	−4.04067			−0.143488
$794$	30.0170	−	7.15523i	1.06526	−	0.253930i
$795$	−26.3456	−	1.55413i	−0.934382	−	0.0551192i
$796$	41.7749	+	13.7227i	1.48067	+	0.486388i
$797$	−26.7083	+	26.7083i	−0.946058	+	0.946058i	−0.998618	−	0.0525598i	$-0.983262\pi$
$797$	−26.7083	+	26.7083i	−0.946058	+	0.946058i	0.0525598	+	0.998618i	$0.483262\pi$
$798$	1.66869	+	7.00033i	0.0590708	+	0.247809i
$799$	3.97572	+	21.9436i	0.140651	+	0.776308i
$800$	−24.5651	−	14.0198i	−0.868508	−	0.495675i
$801$			12.0736i			0.426600i
$802$	−23.5595	+	38.3067i	−0.831915	+	1.35266i
$803$	−10.6234	−	10.6234i	−0.374891	−	0.374891i
$804$	12.6868	+	4.16752i	0.447430	+	0.146977i
$805$	−35.4244	+	31.4778i	−1.24855	+	1.10945i
$806$	−10.5472	−	44.2469i	−0.371511	−	1.55853i
$807$	−2.71337	+	2.71337i	−0.0955151	+	0.0955151i
$808$	−31.8842	−	37.6997i	−1.12168	−	1.32627i
$809$	12.0635	+	12.0635i	0.424130	+	0.424130i	0.886623	−	0.462493i	$-0.153045\pi$
$809$	12.0635	+	12.0635i	0.424130	+	0.424130i	−0.462493	+	0.886623i	$0.653045\pi$
$810$	−16.5753	−	11.5925i	−0.582396	−	0.407320i
$811$	−19.3441	−	19.3441i	−0.679263	−	0.679263i	0.280570	−	0.959833i	$-0.409476\pi$
$811$	−19.3441	−	19.3441i	−0.679263	−	0.679263i	−0.959833	+	0.280570i	$0.909476\pi$
$812$	−30.7662	−	10.1064i	−1.07968	−	0.354666i
$813$	−23.1791			−0.812925
$814$	−21.6686	−	13.3267i	−0.759482	−	0.467099i
$815$	12.8379	+	14.4474i	0.449691	+	0.506071i
$816$	−8.09615	−	23.6475i	−0.283422	−	0.827830i
$817$	1.75455	−	1.75455i	0.0613838	−	0.0613838i
$818$	11.7644	+	49.3532i	0.411334	+	1.72559i
$819$	8.03493	−	8.03493i	0.280763	−	0.280763i
$820$	−11.6410	+	5.04693i	−0.406520	+	0.176246i
$821$	7.82008	−	7.82008i	0.272923	−	0.272923i	−0.557353	−	0.830276i	$-0.688183\pi$
$821$	7.82008	−	7.82008i	0.272923	−	0.272923i	0.830276	+	0.557353i	$0.188183\pi$
$822$	13.0033	+	7.99732i	0.453541	+	0.278938i
$823$			16.6827i			0.581523i	0.956796	+	0.290761i	$0.0939086\pi$
$823$			16.6827i			0.581523i	−0.956796	+	0.290761i	$0.906091\pi$
$824$	−0.918076	+	10.9850i	−0.0319827	+	0.382682i
$825$	−10.9409	+	8.62454i	−0.380914	+	0.300268i
$826$	−65.8326	+	15.6927i	−2.29061	+	0.546018i
$827$			16.6333i			0.578398i	0.957269	+	0.289199i	$0.0933889\pi$
$827$			16.6333i			0.578398i	−0.957269	+	0.289199i	$0.906611\pi$
$828$	3.61688	+	7.15554i	0.125695	+	0.248672i
$829$	23.7611			0.825258			0.412629	−	0.910899i	$-0.364611\pi$
$829$	23.7611			0.825258			0.412629	+	0.910899i	$0.364611\pi$
$830$	−6.42253	+	1.13611i	−0.222929	+	0.0394351i
$831$	−13.2126			−0.458339
$832$	20.1714	+	28.3366i	0.699317	+	0.982393i
$833$	23.0978	+	16.0119i	0.800291	+	0.554780i
$834$	16.3643	+	10.0644i	0.566648	+	0.348502i
$835$	−21.9779	+	19.5294i	−0.760577	+	0.675843i
$836$	1.03656	−	3.15553i	0.0358503	−	0.109136i
$837$	−29.3573	−	29.3573i	−1.01474	−	1.01474i
$838$	36.9164	+	22.7044i	1.27526	+	0.784311i
$839$	0.873046	−	0.873046i	0.0301409	−	0.0301409i	−0.691876	−	0.722017i	$-0.743215\pi$
$839$	0.873046	−	0.873046i	0.0301409	−	0.0301409i	0.722017	+	0.691876i	$0.243215\pi$
$840$	−5.05296	+	35.2684i	−0.174344	+	1.21688i
$841$		−	10.0245i		−	0.345673i
$842$	5.48149	+	22.9955i	0.188905	+	0.792476i
$843$	12.4545			0.428955
$844$	−4.87114	+	14.8288i	−0.167672	+	0.510428i
$845$	−9.86830	+	8.76889i	−0.339480	+	0.301659i
$846$	−4.58111	−	2.81749i	−0.157502	−	0.0968672i
$847$		−	28.3240i		−	0.973223i
$848$	30.7980	−	4.67432i	1.05761	−	0.160517i
$849$			0.850819i			0.0292000i
$850$	13.7210	−	25.7242i	0.470627	−	0.882332i
$851$	55.7851			1.91229
$852$	44.6680	+	14.6731i	1.53030	+	0.502691i
$853$	30.3331			1.03858			0.519292	−	0.854597i	$-0.326196\pi$
$853$	30.3331			1.03858			0.519292	+	0.854597i	$0.326196\pi$
$854$	4.16128	+	2.55928i	0.142396	+	0.0875768i
$855$	0.943342	+	1.06161i	0.0322616	+	0.0363065i
$856$	−0.198283	+	0.167696i	−0.00677718	+	0.00573174i
$857$			48.9530i			1.67220i	0.548576	+	0.836101i	$0.315170\pi$
$857$			48.9530i			1.67220i	−0.548576	+	0.836101i	$0.684830\pi$
$858$	16.6654	−	3.97258i	0.568949	−	0.135622i
$859$	49.4797			1.68822			0.844112	−	0.536167i	$-0.180128\pi$
$859$	49.4797			1.68822			0.844112	+	0.536167i	$0.180128\pi$
$860$	11.2709	−	4.88648i	0.384333	−	0.166627i
$861$	11.3013	+	11.3013i	0.385148	+	0.385148i
$862$	−11.2067	−	6.89241i	−0.381703	−	0.234756i
$863$	−1.26688	+	1.26688i	−0.0431250	+	0.0431250i	−0.728340	−	0.685215i	$-0.759708\pi$
$863$	−1.26688	+	1.26688i	−0.0431250	+	0.0431250i	0.685215	+	0.728340i	$0.259708\pi$
$864$	29.2320	+	12.3856i	0.994494	+	0.421366i
$865$	3.13341	+	3.52626i	0.106539	+	0.119896i
$866$	−21.9118	+	35.6276i	−0.744592	+	1.21067i
$867$	24.1266	−	9.03921i	0.819383	−	0.306988i
$868$	−17.1631	+	52.2481i	−0.582553	+	1.77342i
$869$		−	13.0193i		−	0.441649i
$870$	20.5578	−	3.63657i	0.696973	−	0.123291i
$871$		−	19.1549i		−	0.649039i
$872$	1.42951	−	17.1044i	0.0484092	−	0.579229i
$873$	4.01392			0.135850
$874$	1.68889	+	7.08510i	0.0571277	+	0.239657i
$875$	−34.0953	+	23.7606i	−1.15263	+	0.803254i
$876$	22.1061	−	11.1739i	0.746897	−	0.377532i
$877$	−15.3169			−0.517216			−0.258608	−	0.965982i	$-0.583264\pi$
$877$	−15.3169			−0.517216			−0.258608	+	0.965982i	$0.583264\pi$
$878$	13.4303	+	8.25997i	0.453252	+	0.278761i
$879$	−8.30950	−	8.30950i	−0.280272	−	0.280272i
$880$	10.5139	−	12.6435i	0.354423	−	0.426211i
$881$	−2.69015	−	2.69015i	−0.0906336	−	0.0906336i	0.660336	−	0.750970i	$-0.270414\pi$
$881$	−2.69015	−	2.69015i	−0.0906336	−	0.0906336i	−0.750970	+	0.660336i	$0.770414\pi$
$882$	−6.59321	+	1.57164i	−0.222005	+	0.0529198i
$883$	19.1831	+	19.1831i	0.645562	+	0.645562i	0.951917	−	0.306355i	$-0.0991096\pi$
$883$	19.1831	+	19.1831i	0.645562	+	0.645562i	−0.306355	+	0.951917i	$0.599110\pi$
$884$	−28.6019	+	21.6193i	−0.961986	+	0.727135i
$885$	32.6141	−	28.9807i	1.09631	−	0.974174i
$886$	−9.60813	−	5.90922i	−0.322791	−	0.198524i
$887$			40.6132i			1.36366i	0.731512	+	0.681828i	$0.238815\pi$
$887$			40.6132i			1.36366i	−0.731512	+	0.681828i	$0.761185\pi$
$888$	32.0235	−	27.0836i	1.07464	−	0.908868i
$889$	20.0337	−	20.0337i	0.671909	−	0.671909i
$890$	−31.1217	+	44.4985i	−1.04320	+	1.49159i
$891$	8.31518	−	8.31518i	0.278569	−	0.278569i
$892$	16.7574	+	5.50466i	0.561079	+	0.184310i
$893$	−3.45476	−	3.45476i	−0.115609	−	0.115609i
$894$	4.04920	+	16.9869i	0.135426	+	0.568126i
$895$	−11.7601	−	13.2346i	−0.393098	−	0.442383i
$896$	−2.82567	−	41.9586i	−0.0943989	−	1.40174i
$897$	−26.5660	+	26.5660i	−0.887013	+	0.887013i
$898$	26.9575	+	16.5795i	0.899584	+	0.553265i
$899$	32.2248			1.07476
$900$	2.41206	+	6.60442i	0.0804020	+	0.220147i
$901$	5.72436	+	31.5950i	0.190706	+	1.05258i
$902$	−1.71042	−	7.17542i	−0.0569509	−	0.238915i
$903$	−10.9420	−	10.9420i	−0.364128	−	0.364128i
$904$	40.0643	−	33.8841i	1.33252	−	1.12697i
$905$	1.15805	−	19.6313i	0.0384949	−	0.652567i
$906$	−8.04964	−	33.7692i	−0.267431	−	1.12190i
$907$		−	42.0092i		−	1.39489i	−0.716637	−	0.697446i	$-0.754320\pi$
$907$		−	42.0092i		−	1.39489i	0.716637	−	0.697446i	$-0.245680\pi$
$908$	15.7528	+	31.1649i	0.522776	+	1.03424i
$909$			12.2739i			0.407101i
$910$	50.3249	−	8.90222i	1.66825	−	0.295106i
$911$	−9.54809	−	9.54809i	−0.316342	−	0.316342i	0.531018	−	0.847361i	$-0.321810\pi$
$911$	−9.54809	−	9.54809i	−0.316342	−	0.316342i	−0.847361	+	0.531018i	$0.821810\pi$
$912$	4.40933	+	3.24726i	0.146008	+	0.107528i
$913$		−	3.79188i		−	0.125493i
$914$	−2.96444	−	1.82320i	−0.0980549	−	0.0603060i
$915$	−3.14397	−	0.185463i	−0.103937	−	0.00613121i
$916$	−7.50094	−	14.8396i	−0.247838	−	0.490316i
$917$	−12.7019	−	12.7019i	−0.419454	−	0.419454i
$918$	−11.8996	+	30.4846i	−0.392744	+	1.00614i
$919$	31.0155			1.02311			0.511553	−	0.859252i	$-0.329070\pi$
$919$	31.0155			1.02311			0.511553	+	0.859252i	$0.329070\pi$
$920$	−5.11416	+	35.6955i	−0.168609	+	1.17685i
$921$	−1.13146	−	1.13146i	−0.0372828	−	0.0372828i
$922$	17.8324	−	4.25075i	0.587279	−	0.139991i
$923$		−	67.4408i		−	2.21984i
$924$	−19.6791	−	6.46441i	−0.647394	−	0.212664i
$925$	48.5813	+	5.75163i	1.59734	+	0.189113i
$926$	−20.9183	+	34.0123i	−0.687419	+	1.11771i
$927$	1.93765	−	1.93765i	0.0636409	−	0.0636409i
$928$	−22.8414	+	9.24598i	−0.749804	+	0.303514i
$929$	−20.9262	−	20.9262i	−0.686568	−	0.686568i	0.274904	−	0.961472i	$-0.411354\pi$
$929$	−20.9262	−	20.9262i	−0.686568	−	0.686568i	−0.961472	+	0.274904i	$0.911354\pi$
$930$	−6.17574	−	34.9119i	−0.202510	−	1.14481i
$931$	−6.15736			−0.201799
$932$	5.19535	+	10.2783i	0.170179	+	0.336678i
$933$	6.74609	+	6.74609i	0.220857	+	0.220857i
$934$	−30.0292	−	18.4687i	−0.982586	−	0.604313i
$935$	13.3373	+	10.4602i	0.436175	+	0.342086i
$936$	0.720128	−	8.61653i	0.0235381	−	0.281640i
$937$	−37.2453	−	37.2453i	−1.21675	−	1.21675i	−0.968763	−	0.247988i	$-0.920231\pi$
$937$	−37.2453	−	37.2453i	−1.21675	−	1.21675i	−0.247988	−	0.968763i	$-0.579769\pi$
$938$	−12.1323	+	19.7267i	−0.396135	+	0.644098i
$939$			2.18303i			0.0712405i
$940$	−9.62162	−	22.1927i	−0.313823	−	0.723845i
$941$	18.6114	+	18.6114i	0.606715	+	0.606715i	0.942086	−	0.335371i	$-0.108862\pi$
$941$	18.6114	+	18.6114i	0.606715	+	0.606715i	−0.335371	+	0.942086i	$0.608862\pi$
$942$	26.4741	−	43.0457i	0.862572	−	1.40250i
$943$	11.4382	+	11.4382i	0.372478	+	0.372478i
$944$	−30.5379	+	41.4663i	−0.993925	+	1.34961i
$945$	34.8693	−	30.9845i	1.13430	−	1.00793i
$946$	1.65605	+	6.94730i	0.0538427	+	0.225876i
$947$	35.3439			1.14852			0.574261	−	0.818672i	$-0.305289\pi$
$947$	35.3439			1.14852			0.574261	+	0.818672i	$0.305289\pi$
$948$	20.3929	+	6.69889i	0.662329	+	0.217570i
$949$	−25.1235	−	25.1235i	−0.815544	−	0.815544i
$950$	0.740301	+	6.34430i	0.0240185	+	0.205836i
$951$			23.0978i			0.748997i
$952$	43.1489	−	4.14869i	1.39846	−	0.134460i
$953$	−2.89722	−	2.89722i	−0.0938502	−	0.0938502i	0.658623	−	0.752473i	$-0.271139\pi$
$953$	−2.89722	−	2.89722i	−0.0938502	−	0.0938502i	−0.752473	+	0.658623i	$0.771139\pi$
$954$	−6.59601	−	4.05670i	−0.213554	−	0.131341i
$955$	−32.7908	+	29.1377i	−1.06109	+	0.942872i
$956$	3.21495	−	1.62505i	0.103979	−	0.0525579i
$957$			12.1374i			0.392345i
$958$	22.2446	+	13.6809i	0.718689	+	0.442010i
$959$	−18.7204	+	18.7204i	−0.604514	+	0.604514i
$960$	14.3944	+	22.9740i	0.464577	+	0.741484i
$961$		−	23.7252i		−	0.765330i
$962$	−51.2445	−	31.5165i	−1.65219	−	1.01613i
$963$	0.0645553			0.00208026
$964$	−21.6877	−	7.12422i	−0.698512	−	0.229456i
$965$	−3.35843	−	3.77950i	−0.108112	−	0.121666i
$966$	44.1854	−	10.5326i	1.42164	−	0.338880i
$967$	24.8158	−	24.8158i	0.798023	−	0.798023i	−0.184761	−	0.982784i	$-0.559151\pi$
$967$	24.8158	−	24.8158i	0.798023	−	0.798023i	0.982784	+	0.184761i	$0.0591510\pi$
$968$	−13.9178	−	16.4563i	−0.447335	−	0.528927i
$969$	−3.21581	+	4.63893i	−0.103307	+	0.149024i
$970$	14.7937	+	10.3465i	0.474997	+	0.332206i
$971$		−	17.4174i		−	0.558952i	−0.960153	−	0.279476i	$-0.909839\pi$
$971$		−	17.4174i		−	0.558952i	0.960153	−	0.279476i	$-0.0901607\pi$
$972$	−6.44443	−	12.7495i	−0.206705	−	0.408940i
$973$	−23.5591	+	23.5591i	−0.755271	+	0.755271i
$974$	−34.1204	+	8.13337i	−1.09329	+	0.260610i
$975$	−25.8745	+	20.3964i	−0.828646	+	0.653207i
$976$	3.67530	−	0.557814i	0.117643	−	0.0178552i
$977$	−18.2967	−	18.2967i	−0.585364	−	0.585364i	0.351008	−	0.936372i	$-0.385839\pi$
$977$	−18.2967	−	18.2967i	−0.585364	−	0.585364i	−0.936372	+	0.351008i	$0.885839\pi$
$978$	−4.29559	−	18.0205i	−0.137358	−	0.576232i
$979$	−22.3232	−	22.3232i	−0.713452	−	0.713452i
$980$	−28.3511	−	11.2026i	−0.905642	−	0.357854i
$981$	−3.01706	+	3.01706i	−0.0963272	+	0.0963272i
$982$	−13.4135	−	56.2710i	−0.428041	−	1.79568i
$983$	−55.1497			−1.75900			−0.879502	−	0.475896i	$-0.842124\pi$
$983$	−55.1497			−1.75900			−0.879502	+	0.475896i	$0.842124\pi$
$984$	12.1193	+	1.01288i	0.386351	+	0.0322893i
$985$	−34.3341	−	38.6387i	−1.09397	−	1.23113i
$986$	−10.2002	−	23.2621i	−0.324839	−	0.740815i
$987$	−21.5452	+	21.5452i	−0.685790	+	0.685790i
$988$	2.45140	−	7.46258i	0.0779894	−	0.237416i
$989$	−11.0745	−	11.0745i	−0.352150	−	0.352150i
$990$	−4.02523	+	0.712043i	−0.127930	+	0.0226302i
$991$	28.4525	−	28.4525i	0.903823	−	0.903823i	−0.0919410	−	0.995764i	$-0.529307\pi$
$991$	28.4525	−	28.4525i	0.903823	−	0.903823i	0.995764	+	0.0919410i	$0.0293071\pi$
$992$	15.7018	+	38.7899i	0.498533	+	1.23158i
$993$	16.6631			0.528789
$994$	−42.7157	+	69.4539i	−1.35486	+	2.20294i
$995$	2.89498	−	49.0758i	0.0917770	−	1.55581i
$996$	5.93944	+	1.95106i	0.188198	+	0.0618216i
$997$	41.8164			1.32434			0.662170	−	0.749354i	$-0.269636\pi$
$997$	41.8164			1.32434			0.662170	+	0.749354i	$0.269636\pi$
$998$	0.184916	+	0.113727i	0.00585341	+	0.00359998i
$999$	−54.9109			−1.73730

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.t.a.523.8	✓	208
5.2	odd	4		680.2.bl.a.387.45	yes	208
8.3	odd	2	inner	680.2.t.a.523.60	yes	208
17.4	even	4		680.2.bl.a.123.97	yes	208
40.27	even	4		680.2.bl.a.387.97	yes	208
85.72	odd	4	inner	680.2.t.a.667.60	yes	208
136.123	odd	4		680.2.bl.a.123.45	yes	208
680.667	even	4	inner	680.2.t.a.667.8	yes	208

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.t.a.523.8	✓	208	1.1	even	1	trivial
680.2.t.a.523.60	yes	208	8.3	odd	2	inner
680.2.t.a.667.8	yes	208	680.667	even	4	inner
680.2.t.a.667.60	yes	208	85.72	odd	4	inner
680.2.bl.a.123.45	yes	208	136.123	odd	4
680.2.bl.a.123.97	yes	208	17.4	even	4
680.2.bl.a.387.45	yes	208	5.2	odd	4
680.2.bl.a.387.97	yes	208	40.27	even	4

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.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37567 + 0.327922i) q^{2} -1.51555i q^{3} +(1.78493 - 0.902224i) q^{4} +(-1.48529 - 1.67150i) q^{5} +(0.496982 + 2.08490i) q^{6} -3.71705 q^{7} +(-2.15962 + 1.82648i) q^{8} +0.703111 q^{9} +(2.59139 + 1.81238i) q^{10} +(-1.30000 + 1.30000i) q^{11} +(-1.36737 - 2.70516i) q^{12} +(-3.07440 + 3.07440i) q^{13} +(5.11343 - 1.21890i) q^{14} +(-2.53325 + 2.25102i) q^{15} +(2.37198 - 3.22082i) q^{16} +(3.38853 + 2.34901i) q^{17} +(-0.967248 + 0.230565i) q^{18} -0.903308 q^{19} +(-4.15921 - 1.64347i) q^{20} +5.63337i q^{21} +(1.36207 - 2.21467i) q^{22} +5.70159i q^{23} +(2.76812 + 3.27301i) q^{24} +(-0.587854 + 4.96532i) q^{25} +(3.22119 - 5.23752i) q^{26} -5.61225i q^{27} +(-6.63469 + 3.35361i) q^{28} +(3.08022 + 3.08022i) q^{29} +(2.74675 - 3.92737i) q^{30} +(5.23093 - 5.23093i) q^{31} +(-2.20689 + 5.20861i) q^{32} +(1.97021 + 1.97021i) q^{33} +(-5.43179 - 2.12029i) q^{34} +(5.52088 + 6.21307i) q^{35} +(1.25501 - 0.634363i) q^{36} -9.78412i q^{37} +(1.24265 - 0.296214i) q^{38} +(4.65940 + 4.65940i) q^{39} +(6.26063 + 0.896970i) q^{40} +(2.00614 - 2.00614i) q^{41} +(-1.84731 - 7.74966i) q^{42} +(-1.94236 + 1.94236i) q^{43} +(-1.14752 + 3.49330i) q^{44} +(-1.04432 - 1.17525i) q^{45} +(-1.86968 - 7.84351i) q^{46} +(3.82456 + 3.82456i) q^{47} +(-4.88132 - 3.59486i) q^{48} +6.81646 q^{49} +(-0.819545 - 7.02341i) q^{50} +(3.56004 - 5.13549i) q^{51} +(-2.71380 + 8.26140i) q^{52} +(5.50671 + 5.50671i) q^{53} +(1.84038 + 7.72060i) q^{54} +(4.10382 + 0.242084i) q^{55} +(8.02742 - 6.78912i) q^{56} +1.36901i q^{57} +(-5.24743 - 3.22729i) q^{58} -12.8744 q^{59} +(-2.49075 + 6.30349i) q^{60} +(0.657148 + 0.657148i) q^{61} +(-5.48069 + 8.91137i) q^{62} -2.61350 q^{63} +(1.32793 - 7.88902i) q^{64} +(9.70523 + 0.572511i) q^{65} +(-3.35643 - 2.06428i) q^{66} +(-3.11523 + 3.11523i) q^{67} +(8.16764 + 1.13561i) q^{68} +8.64105 q^{69} +(-9.63231 - 6.73671i) q^{70} +(-10.9681 + 10.9681i) q^{71} +(-1.51845 + 1.28422i) q^{72} +8.17185i q^{73} +(3.20843 + 13.4597i) q^{74} +(7.52519 + 0.890922i) q^{75} +(-1.61235 + 0.814986i) q^{76} +(4.83216 - 4.83216i) q^{77} +(-7.93772 - 4.88188i) q^{78} +(-5.00743 + 5.00743i) q^{79} +(-8.90669 + 0.819063i) q^{80} -6.39630 q^{81} +(-2.10193 + 3.41764i) q^{82} +(-1.45842 + 1.45842i) q^{83} +(5.08257 + 10.0552i) q^{84} +(-1.10656 - 9.15290i) q^{85} +(2.03510 - 3.30898i) q^{86} +(4.66822 - 4.66822i) q^{87} +(0.433081 - 5.18193i) q^{88} +17.1717i q^{89} +(1.82203 + 1.27430i) q^{90} +(11.4277 - 11.4277i) q^{91} +(5.14412 + 10.1770i) q^{92} +(-7.92773 - 7.92773i) q^{93} +(-6.51549 - 4.00718i) q^{94} +(1.34167 + 1.50988i) q^{95} +(7.89391 + 3.34464i) q^{96} +5.70880 q^{97} +(-9.37720 + 2.23527i) q^{98} +(-0.914042 + 0.914042i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 208 q - 8 q^{6} - 192 q^{9} + 2 q^{10} - 8 q^{11} + 8 q^{12} - 16 q^{14} - 16 q^{16} - 12 q^{18} - 10 q^{20} + 4 q^{22} + 16 q^{24} + 12 q^{28} - 24 q^{30} + 20 q^{32} - 8 q^{33} - 4 q^{34} - 8 q^{35} - 12 q^{38}+ \cdots + 24 q^{99}+O(q^{100}) \) 208 * q - 8 * q^6 - 192 * q^9 + 2 * q^10 - 8 * q^11 + 8 * q^12 - 16 * q^14 - 16 * q^16 - 12 * q^18 - 10 * q^20 + 4 * q^22 + 16 * q^24 + 12 * q^28 - 24 * q^30 + 20 * q^32 - 8 * q^33 - 4 * q^34 - 8 * q^35 - 12 * q^38 - 42 * q^40 - 8 * q^41 - 32 * q^42 + 8 * q^44 - 16 * q^46 + 160 * q^49 + 16 * q^50 - 8 * q^51 - 20 * q^52 + 36 * q^54 + 4 * q^56 - 56 * q^58 - 64 * q^59 + 32 * q^60 - 48 * q^65 - 8 * q^67 - 56 * q^68 - 28 * q^70 - 56 * q^72 + 8 * q^74 + 8 * q^75 - 12 * q^78 + 6 * q^80 + 128 * q^81 + 44 * q^82 + 8 * q^86 - 82 * q^90 + 24 * q^91 + 64 * q^94 - 48 * q^96 - 16 * q^97 - 40 * q^98 + 24 * q^99

Introduction

L-functions

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