LMFDB - Embedded newform 403.2.r.a.218.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [403,2,Mod(218,403)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("403.218"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(403, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.r (of order $6$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			218.16
Character	$\chi$	$=$	403.218
Dual form			403.2.r.a.342.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.441172 + 0.254711i) q^{2} +(-1.38443 - 2.39789i) q^{3} +(-0.870245 + 1.50731i) q^{4} +1.59074i q^{5} +(1.22154 + 0.705256i) q^{6} +(0.253842 + 0.146556i) q^{7} -1.90549i q^{8} +(-2.33327 + 4.04134i) q^{9} +(-0.405179 - 0.701791i) q^{10} +(1.95980 - 1.13149i) q^{11} +4.81916 q^{12} +(3.01316 - 1.98013i) q^{13} -0.149317 q^{14} +(3.81444 - 2.20227i) q^{15} +(-1.25514 - 2.17397i) q^{16} +(1.26912 - 2.19819i) q^{17} -2.37723i q^{18} +(-6.32788 - 3.65340i) q^{19} +(-2.39774 - 1.38434i) q^{20} -0.811582i q^{21} +(-0.576406 + 0.998365i) q^{22} +(-2.81628 - 4.87794i) q^{23} +(-4.56915 + 2.63800i) q^{24} +2.46953 q^{25} +(-0.824960 + 1.64106i) q^{26} +4.61438 q^{27} +(-0.441809 + 0.255079i) q^{28} +(0.708957 + 1.22795i) q^{29} +(-1.12188 + 1.94316i) q^{30} -1.00000i q^{31} +(4.40786 + 2.54488i) q^{32} +(-5.42640 - 3.13293i) q^{33} +1.29304i q^{34} +(-0.233133 + 0.403798i) q^{35} +(-4.06103 - 7.03390i) q^{36} +(-2.75450 + 1.59031i) q^{37} +3.72224 q^{38} +(-8.91962 - 4.48389i) q^{39} +3.03114 q^{40} +(3.80791 - 2.19850i) q^{41} +(0.206718 + 0.358047i) q^{42} +(5.79062 - 10.0296i) q^{43} +3.93870i q^{44} +(-6.42873 - 3.71163i) q^{45} +(2.48492 + 1.43467i) q^{46} -7.44680i q^{47} +(-3.47530 + 6.01940i) q^{48} +(-3.45704 - 5.98777i) q^{49} +(-1.08949 + 0.629016i) q^{50} -7.02803 q^{51} +(0.362477 + 6.26495i) q^{52} +11.8092 q^{53} +(-2.03573 + 1.17533i) q^{54} +(1.79991 + 3.11754i) q^{55} +(0.279260 - 0.483692i) q^{56} +20.2315i q^{57} +(-0.625543 - 0.361158i) q^{58} +(4.18154 + 2.41421i) q^{59} +7.66604i q^{60} +(-0.654509 + 1.13364i) q^{61} +(0.254711 + 0.441172i) q^{62} +(-1.18456 + 0.683907i) q^{63} +2.42774 q^{64} +(3.14987 + 4.79316i) q^{65} +3.19196 q^{66} +(2.75326 - 1.58960i) q^{67} +(2.20890 + 3.82593i) q^{68} +(-7.79785 + 13.5063i) q^{69} -0.237525i q^{70} +(1.23777 + 0.714626i) q^{71} +(7.70070 + 4.44600i) q^{72} +3.52098i q^{73} +(0.810138 - 1.40320i) q^{74} +(-3.41888 - 5.92168i) q^{75} +(11.0136 - 6.35871i) q^{76} +0.663306 q^{77} +(5.07718 - 0.293755i) q^{78} -10.4024 q^{79} +(3.45823 - 1.99661i) q^{80} +(0.611537 + 1.05921i) q^{81} +(-1.11996 + 1.93983i) q^{82} +16.5617i q^{83} +(1.22330 + 0.706275i) q^{84} +(3.49676 + 2.01885i) q^{85} +5.89973i q^{86} +(1.96300 - 3.40001i) q^{87} +(-2.15604 - 3.73437i) q^{88} +(-2.00679 + 1.15862i) q^{89} +3.78157 q^{90} +(1.05506 - 0.0610438i) q^{91} +9.80341 q^{92} +(-2.39789 + 1.38443i) q^{93} +(1.89678 + 3.28532i) q^{94} +(5.81163 - 10.0660i) q^{95} -14.0928i q^{96} +(-8.02444 - 4.63291i) q^{97} +(3.05030 + 1.76109i) q^{98} +10.5603i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 32 q^{4} - 34 q^{9} + 8 q^{10} - 12 q^{11} - 16 q^{12} + 6 q^{13} - 8 q^{14} - 36 q^{16} - 6 q^{17} + 12 q^{19} - 12 q^{20} - 20 q^{22} - 8 q^{23} + 48 q^{24} - 72 q^{25} - 12 q^{27} - 6 q^{28} + 32 q^{30}+ \cdots - 168 q^{98}+O(q^{100}) $ 68 * q + 32 * q^4 - 34 * q^9 + 8 * q^10 - 12 * q^11 - 16 * q^12 + 6 * q^13 - 8 * q^14 - 36 * q^16 - 6 * q^17 + 12 * q^19 - 12 * q^20 - 20 * q^22 - 8 * q^23 + 48 * q^24 - 72 * q^25 - 12 * q^27 - 6 * q^28 + 32 * q^30 + 6 * q^33 + 30 * q^35 + 40 * q^36 - 42 * q^37 - 36 * q^38 - 14 * q^39 + 8 * q^40 + 18 * q^41 - 16 * q^42 + 12 * q^43 + 60 * q^45 + 30 * q^46 - 46 * q^48 + 22 * q^49 + 56 * q^51 + 20 * q^53 - 114 * q^54 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 6 * q^59 + 6 * q^61 - 8 * q^62 - 30 * q^63 + 24 * q^64 + 24 * q^65 + 8 * q^66 - 48 * q^67 + 58 * q^68 - 28 * q^69 - 30 * q^71 + 72 * q^72 + 8 * q^74 - 4 * q^75 - 12 * q^76 - 20 * q^77 + 26 * q^78 + 16 * q^79 + 42 * q^80 - 58 * q^81 - 42 * q^82 - 72 * q^84 + 30 * q^85 - 20 * q^87 + 64 * q^88 + 18 * q^89 + 52 * q^90 - 22 * q^91 + 48 * q^92 + 8 * q^94 - 32 * q^95 - 168 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.441172	+	0.254711i	−0.311956	+	0.180108i	−0.647801	−	0.761809i	$-0.724311\pi$
$2$	−0.441172	+	0.254711i	−0.311956	+	0.180108i	0.335846	+	0.941917i	$0.390978\pi$
$3$	−1.38443	−	2.39789i	−0.799298	−	1.38443i	−0.920074	−	0.391745i	$-0.871871\pi$
$3$	−1.38443	−	2.39789i	−0.799298	−	1.38443i	0.120775	−	0.992680i	$-0.461462\pi$
$4$	−0.870245	+	1.50731i	−0.435122	+	0.753654i
$5$			1.59074i			0.711402i	0.934600	+	0.355701i	$0.115758\pi$
$5$			1.59074i			0.711402i	−0.934600	+	0.355701i	$0.884242\pi$
$6$	1.22154	+	0.705256i	0.498691	+	0.287919i
$7$	0.253842	+	0.146556i	0.0959432	+	0.0553928i	0.547204	−	0.836999i	$-0.315692\pi$
$7$	0.253842	+	0.146556i	0.0959432	+	0.0553928i	−0.451261	+	0.892392i	$0.649026\pi$
$8$		−	1.90549i		−	0.673691i
$9$	−2.33327	+	4.04134i	−0.777755	+	1.34711i
$10$	−0.405179	−	0.701791i	−0.128129	−	0.221926i
$11$	1.95980	−	1.13149i	0.590902	−	0.341158i	−0.174552	−	0.984648i	$-0.555848\pi$
$11$	1.95980	−	1.13149i	0.590902	−	0.341158i	0.765454	+	0.643490i	$0.222514\pi$
$12$	4.81916			1.39117
$13$	3.01316	−	1.98013i	0.835699	−	0.549188i
$13$	3.01316	−	1.98013i	0.835699	−	0.549188i
$14$	−0.149317			−0.0399067
$15$	3.81444	−	2.20227i	0.984883	−	0.568623i
$16$	−1.25514	−	2.17397i	−0.313786	−	0.543493i
$17$	1.26912	−	2.19819i	0.307808	−	0.533139i	−0.670075	−	0.742294i	$-0.733738\pi$
$17$	1.26912	−	2.19819i	0.307808	−	0.533139i	0.977883	+	0.209155i	$0.0670712\pi$
$18$		−	2.37723i		−	0.560319i
$19$	−6.32788	−	3.65340i	−1.45172	−	0.838148i	−0.453136	−	0.891441i	$-0.649695\pi$
$19$	−6.32788	−	3.65340i	−1.45172	−	0.838148i	−0.998579	+	0.0532930i	$0.983028\pi$
$20$	−2.39774	−	1.38434i	−0.536151	−	0.309547i
$21$		−	0.811582i		−	0.177102i
$22$	−0.576406	+	0.998365i	−0.122890	+	0.212852i
$23$	−2.81628	−	4.87794i	−0.587234	−	1.01712i	−0.994593	−	0.103852i	$-0.966883\pi$
$23$	−2.81628	−	4.87794i	−0.587234	−	1.01712i	0.407358	−	0.913268i	$-0.366450\pi$
$24$	−4.56915	+	2.63800i	−0.932674	+	0.538480i
$25$	2.46953			0.493907
$26$	−0.824960	+	1.64106i	−0.161788	+	0.321838i
$27$	4.61438			0.888038
$28$	−0.441809	+	0.255079i	−0.0834941	+	0.0482053i
$29$	0.708957	+	1.22795i	0.131650	+	0.228024i	0.924313	−	0.381636i	$-0.124639\pi$
$29$	0.708957	+	1.22795i	0.131650	+	0.228024i	−0.792663	+	0.609660i	$0.791306\pi$
$30$	−1.12188	+	1.94316i	−0.204827	+	0.354770i
$31$		−	1.00000i		−	0.179605i
$31$		−	1.00000i		−	0.179605i
$32$	4.40786	+	2.54488i	0.779208	+	0.449876i
$33$	−5.42640	−	3.13293i	−0.944614	−	0.545373i
$34$			1.29304i			0.221754i
$35$	−0.233133	+	0.403798i	−0.0394066	+	0.0682542i
$36$	−4.06103	−	7.03390i	−0.676838	−	1.17232i
$37$	−2.75450	+	1.59031i	−0.452837	+	0.261446i	−0.709028	−	0.705181i	$-0.750866\pi$
$37$	−2.75450	+	1.59031i	−0.452837	+	0.261446i	0.256191	+	0.966626i	$0.417533\pi$
$38$	3.72224			0.603827
$39$	−8.91962	−	4.48389i	−1.42828	−	0.717998i
$40$	3.03114			0.479265
$41$	3.80791	−	2.19850i	0.594696	−	0.343348i	−0.172256	−	0.985052i	$-0.555106\pi$
$41$	3.80791	−	2.19850i	0.594696	−	0.343348i	0.766952	+	0.641704i	$0.221772\pi$
$42$	0.206718	+	0.358047i	0.0318973	+	0.0552478i
$43$	5.79062	−	10.0296i	0.883061	−	1.52951i	0.0351416	−	0.999382i	$-0.488812\pi$
$43$	5.79062	−	10.0296i	0.883061	−	1.52951i	0.847920	−	0.530125i	$-0.177855\pi$
$44$			3.93870i			0.593781i
$45$	−6.42873	−	3.71163i	−0.958339	−	0.553297i
$46$	2.48492	+	1.43467i	0.366382	+	0.211531i
$47$		−	7.44680i		−	1.08623i	−0.839659	−	0.543113i	$-0.817245\pi$
$47$		−	7.44680i		−	1.08623i	0.839659	−	0.543113i	$-0.182755\pi$
$48$	−3.47530	+	6.01940i	−0.501617	+	0.868826i
$49$	−3.45704	−	5.98777i	−0.493863	−	0.855396i
$50$	−1.08949	+	0.629016i	−0.154077	+	0.0889563i
$51$	−7.02803			−0.984122
$52$	0.362477	+	6.26495i	0.0502665	+	0.868792i
$53$	11.8092			1.62212			0.811059	−	0.584964i	$-0.198891\pi$
$53$	11.8092			1.62212			0.811059	+	0.584964i	$0.198891\pi$
$54$	−2.03573	+	1.17533i	−0.277028	+	0.159942i
$55$	1.79991	+	3.11754i	0.242700	+	0.420369i
$56$	0.279260	−	0.483692i	0.0373176	−	0.0646361i
$57$			20.2315i			2.67972i
$58$	−0.625543	−	0.361158i	−0.0821379	−	0.0474223i
$59$	4.18154	+	2.41421i	0.544390	+	0.314304i	0.746856	−	0.664986i	$-0.231562\pi$
$59$	4.18154	+	2.41421i	0.544390	+	0.314304i	−0.202466	+	0.979289i	$0.564896\pi$
$60$			7.66604i			0.989682i
$61$	−0.654509	+	1.13364i	−0.0838012	+	0.145148i	−0.904880	−	0.425667i	$-0.860039\pi$
$61$	−0.654509	+	1.13364i	−0.0838012	+	0.145148i	0.821079	+	0.570815i	$0.193373\pi$
$62$	0.254711	+	0.441172i	0.0323483	+	0.0560289i
$63$	−1.18456	+	0.683907i	−0.149241	+	0.0861642i
$64$	2.42774			0.303467
$65$	3.14987	+	4.79316i	0.390694	+	0.594518i
$66$	3.19196			0.392904
$67$	2.75326	−	1.58960i	0.336365	−	0.194200i	−0.322299	−	0.946638i	$-0.604456\pi$
$67$	2.75326	−	1.58960i	0.336365	−	0.194200i	0.658663	+	0.752438i	$0.271122\pi$
$68$	2.20890	+	3.82593i	0.267868	+	0.463962i
$69$	−7.79785	+	13.5063i	−0.938751	+	1.62596i
$70$		−	0.237525i		−	0.0283897i
$71$	1.23777	+	0.714626i	0.146896	+	0.0848106i	0.571647	−	0.820500i	$-0.306305\pi$
$71$	1.23777	+	0.714626i	0.146896	+	0.0848106i	−0.424750	+	0.905310i	$0.639638\pi$
$72$	7.70070	+	4.44600i	0.907537	+	0.523967i
$73$			3.52098i			0.412099i	0.978542	+	0.206050i	$0.0660609\pi$
$73$			3.52098i			0.412099i	−0.978542	+	0.206050i	$0.933939\pi$
$74$	0.810138	−	1.40320i	0.0941767	−	0.163119i
$75$	−3.41888	−	5.92168i	−0.394779	−	0.683777i
$76$	11.0136	−	6.35871i	1.26335	−	0.729394i
$77$	0.663306			0.0755908
$78$	5.07718	−	0.293755i	0.574877	−	0.0332612i
$79$	−10.4024			−1.17037			−0.585184	−	0.810901i	$-0.698978\pi$
$79$	−10.4024			−1.17037			−0.585184	+	0.810901i	$0.698978\pi$
$80$	3.45823	−	1.99661i	0.386642	−	0.223228i
$81$	0.611537	+	1.05921i	0.0679485	+	0.117690i
$82$	−1.11996	+	1.93983i	−0.123679	+	0.214218i
$83$			16.5617i			1.81788i	0.416929	+	0.908939i	$0.363106\pi$
$83$			16.5617i			1.81788i	−0.416929	+	0.908939i	$0.636894\pi$
$84$	1.22330	+	0.706275i	0.133473	+	0.0770609i
$85$	3.49676	+	2.01885i	0.379276	+	0.218975i
$86$			5.89973i			0.636184i
$87$	1.96300	−	3.40001i	0.210455	−	0.364519i
$88$	−2.15604	−	3.73437i	−0.229835	−	0.398085i
$89$	−2.00679	+	1.15862i	−0.212719	+	0.122813i	−0.602574	−	0.798063i	$-0.705858\pi$
$89$	−2.00679	+	1.15862i	−0.212719	+	0.122813i	0.389855	+	0.920876i	$0.372525\pi$
$90$	3.78157			0.398612
$91$	1.05506	−	0.0610438i	0.110601	−	0.00639912i
$92$	9.80341			1.02208
$93$	−2.39789	+	1.38443i	−0.248650	+	0.143558i
$94$	1.89678	+	3.28532i	0.195638	+	0.338854i
$95$	5.81163	−	10.0660i	0.596261	−	1.03275i
$96$		−	14.0928i		−	1.43834i
$97$	−8.02444	−	4.63291i	−0.814758	−	0.470401i	0.0338474	−	0.999427i	$-0.489224\pi$
$97$	−8.02444	−	4.63291i	−0.814758	−	0.470401i	−0.848605	+	0.529026i	$0.822557\pi$
$98$	3.05030	+	1.76109i	0.308127	+	0.177897i
$99$			10.5603i			1.06135i
$100$	−2.14910	+	3.72235i	−0.214910	+	0.372235i
$101$	−8.80947	−	15.2584i	−0.876575	−	1.51827i	−0.855075	−	0.518504i	$-0.826489\pi$
$101$	−8.80947	−	15.2584i	−0.876575	−	1.51827i	−0.0214996	−	0.999769i	$-0.506844\pi$
$102$	3.10057	−	1.79012i	0.307002	−	0.177248i
$103$	−9.30004			−0.916360			−0.458180	−	0.888859i	$-0.651499\pi$
$103$	−9.30004			−0.916360			−0.458180	+	0.888859i	$0.651499\pi$
$104$	−3.77310	−	5.74152i	−0.369983	−	0.563003i
$105$	1.29102			0.125991
$106$	−5.20989	+	3.00793i	−0.506029	+	0.292156i
$107$	3.14228	+	5.44258i	0.303775	+	0.526154i	0.976988	−	0.213295i	$-0.0684194\pi$
$107$	3.14228	+	5.44258i	0.303775	+	0.526154i	−0.673213	+	0.739449i	$0.735086\pi$
$108$	−4.01564	+	6.95529i	−0.386405	+	0.669273i
$109$		−	5.56390i		−	0.532925i	−0.963845	−	0.266462i	$-0.914145\pi$
$109$		−	5.56390i		−	0.532925i	0.963845	−	0.266462i	$-0.0858548\pi$
$110$	−1.58814	−	0.916914i	−0.151423	−	0.0874244i
$111$	7.62680	+	4.40333i	0.723904	+	0.417946i
$112$		−	0.735793i		−	0.0695259i
$113$	−5.96095	+	10.3247i	−0.560759	+	0.971263i	0.436672	+	0.899621i	$0.356157\pi$
$113$	−5.96095	+	10.3247i	−0.560759	+	0.971263i	−0.997430	+	0.0716417i	$0.977176\pi$
$114$	−5.15317	−	8.92555i	−0.482638	−	0.835954i
$115$	7.75955	−	4.47998i	0.723582	−	0.417760i
$116$	−2.46786			−0.229135
$117$	0.971858	+	16.7973i	0.0898483	+	1.55291i
$118$	−2.45970			−0.226434
$119$	0.644314	−	0.371995i	0.0590642	−	0.0341007i
$120$	−4.19639	−	7.26835i	−0.383076	−	0.663507i
$121$	−2.93945	+	5.09128i	−0.267223	+	0.462844i
$122$		−	0.666841i		−	0.0603730i
$123$	−10.5435	−	6.08731i	−0.950679	−	0.548875i
$124$	1.50731	+	0.870245i	0.135360	+	0.0781503i
$125$			11.8821i			1.06277i
$126$	0.348397	−	0.603441i	0.0310376	−	0.0537588i
$127$	−1.79324	−	3.10598i	−0.159124	−	0.275611i	0.775429	−	0.631435i	$-0.217534\pi$
$127$	−1.79324	−	3.10598i	−0.159124	−	0.275611i	−0.934553	+	0.355824i	$0.884200\pi$
$128$	−9.88678	+	5.70813i	−0.873876	+	0.504532i
$129$	−32.0667			−2.82332
$130$	−2.61050	−	1.31230i	−0.228956	−	0.115096i
$131$	0.428946			0.0374772			0.0187386	−	0.999824i	$-0.494035\pi$
$131$	0.428946			0.0374772			0.0187386	+	0.999824i	$0.494035\pi$
$132$	9.44459	−	5.45284i	0.822046	−	0.474608i
$133$	−1.07085	−	1.85477i	−0.0928548	−	0.160829i
$134$	−0.809775	+	1.40257i	−0.0699539	+	0.121164i
$135$			7.34030i			0.631752i
$136$	−4.18862	−	2.41830i	−0.359171	−	0.207367i
$137$	8.94515	+	5.16449i	0.764236	+	0.441232i	0.830815	−	0.556549i	$-0.187875\pi$
$137$	8.94515	+	5.16449i	0.764236	+	0.441232i	−0.0665786	+	0.997781i	$0.521208\pi$
$138$		−	7.94478i		−	0.676305i
$139$	5.45025	−	9.44010i	0.462284	−	0.800699i	−0.536791	−	0.843716i	$-0.680363\pi$
$139$	5.45025	−	9.44010i	0.462284	−	0.800699i	0.999074	+	0.0430165i	$0.0136968\pi$
$140$	−0.405765	−	0.702806i	−0.0342934	−	0.0593979i
$141$	−17.8566	+	10.3095i	−1.50380	+	0.868219i
$142$	−0.728092			−0.0611001
$143$	3.66469	−	7.29001i	0.306457	−	0.609622i
$144$	11.7143			0.976194
$145$	−1.95335	+	1.12777i	−0.162217	+	0.0936561i
$146$	−0.896831	−	1.55336i	−0.0742222	−	0.128557i
$147$	−9.57203	+	16.5792i	−0.789488	+	1.36743i
$148$		−	5.53584i		−	0.455043i
$149$	8.29885	+	4.79134i	0.679868	+	0.392522i	0.799805	−	0.600259i	$-0.204936\pi$
$149$	8.29885	+	4.79134i	0.679868	+	0.392522i	−0.119937	+	0.992781i	$0.538269\pi$
$150$	3.01663	+	1.74165i	0.246307	+	0.142205i
$151$		−	15.5089i		−	1.26210i	−0.775744	−	0.631048i	$-0.782625\pi$
$151$		−	15.5089i		−	1.26210i	0.775744	−	0.631048i	$-0.217375\pi$
$152$	−6.96151	+	12.0577i	−0.564653	+	0.978007i
$153$	5.92241	+	10.2579i	0.478799	+	0.829304i
$154$	−0.292632	+	0.168951i	−0.0235810	+	0.0136145i
$155$	1.59074			0.127772
$156$	14.5209	−	9.54253i	1.16260	−	0.764014i
$157$	−13.1727			−1.05129			−0.525647	−	0.850703i	$-0.676177\pi$
$157$	−13.1727			−1.05129			−0.525647	+	0.850703i	$0.676177\pi$
$158$	4.58927	−	2.64961i	0.365102	−	0.210792i
$159$	−16.3490	−	28.3172i	−1.29656	−	2.24570i
$160$	−4.04826	+	7.01178i	−0.320043	+	0.554330i
$161$		−	1.65097i		−	0.130114i
$162$	−0.539586	−	0.311530i	−0.0423938	−	0.0244761i
$163$	15.4403	+	8.91447i	1.20938	+	0.698235i	0.962624	−	0.270842i	$-0.0873022\pi$
$163$	15.4403	+	8.91447i	1.20938	+	0.698235i	0.246756	+	0.969078i	$0.420636\pi$
$164$			7.65293i			0.597593i
$165$	4.98369	−	8.63201i	0.387980	−	0.672001i
$166$	−4.21843	−	7.30654i	−0.327414	−	0.567097i
$167$	5.89062	−	3.40095i	0.455830	−	0.263174i	−0.254459	−	0.967084i	$-0.581897\pi$
$167$	5.89062	−	3.40095i	0.455830	−	0.263174i	0.710289	+	0.703910i	$0.248564\pi$
$168$	−1.54646			−0.119312
$169$	5.15821	−	11.9328i	0.396785	−	0.917911i
$170$	−2.05689			−0.157757
$171$	29.5293	−	17.0487i	2.25816	−	1.30375i
$172$	10.0785	+	17.4565i	0.768480	+	1.33105i
$173$	8.22159	−	14.2402i	0.625076	−	1.08266i	−0.363450	−	0.931614i	$-0.618401\pi$
$173$	8.22159	−	14.2402i	0.625076	−	1.08266i	0.988526	−	0.151050i	$-0.0482653\pi$
$174$			1.99998i			0.151618i
$175$	0.626871	+	0.361924i	0.0473870	+	0.0273589i
$176$	−4.91966	−	2.84037i	−0.370833	−	0.214101i
$177$		−	13.3692i		−	1.00489i
$178$	0.590225	−	1.02230i	0.0442393	−	0.0766246i
$179$	6.56290	+	11.3673i	0.490534	+	0.849630i	0.999941	−	0.0108957i	$-0.00346829\pi$
$179$	6.56290	+	11.3673i	0.490534	+	0.849630i	−0.509406	+	0.860526i	$0.670135\pi$
$180$	11.1891	−	6.46005i	0.833989	−	0.481504i
$181$	−8.13161			−0.604418			−0.302209	−	0.953242i	$-0.597724\pi$
$181$	−8.13161			−0.604418			−0.302209	+	0.953242i	$0.597724\pi$
$182$	−0.449916	+	0.295667i	−0.0333500	+	0.0219163i
$183$	3.62447			0.267929
$184$	−9.29483	+	5.36638i	−0.685224	+	0.395614i
$185$	−2.52978	−	4.38171i	−0.185993	−	0.322149i
$186$	0.705256	−	1.22154i	0.0517119	−	0.0895676i
$187$		−	5.74402i		−	0.420044i
$188$	11.2246	+	6.48054i	0.818640	+	0.472642i
$189$	1.17132	+	0.676263i	0.0852012	+	0.0491909i
$190$			5.92114i			0.429564i
$191$	−4.68231	+	8.11001i	−0.338800	+	0.586819i	−0.984207	−	0.177019i	$-0.943354\pi$
$191$	−4.68231	+	8.11001i	−0.338800	+	0.586819i	0.645407	+	0.763839i	$0.276688\pi$
$192$	−3.36102	−	5.82146i	−0.242561	−	0.420128i
$193$	−18.9403	+	10.9352i	−1.36336	+	0.787134i	−0.990069	−	0.140582i	$-0.955103\pi$
$193$	−18.9403	+	10.9352i	−1.36336	+	0.787134i	−0.373287	+	0.927716i	$0.621769\pi$
$194$	4.72021			0.338891
$195$	7.13273	−	14.1888i	0.510785	−	1.01608i
$196$	12.0339			0.859564
$197$	8.01941	−	4.63001i	0.571359	−	0.329875i	−0.186333	−	0.982487i	$-0.559660\pi$
$197$	8.01941	−	4.63001i	0.571359	−	0.329875i	0.757692	+	0.652612i	$0.226327\pi$
$198$	−2.68982	−	4.65890i	−0.191157	−	0.331094i
$199$	3.21439	−	5.56748i	0.227862	−	0.394669i	−0.729312	−	0.684181i	$-0.760160\pi$
$199$	3.21439	−	5.56748i	0.227862	−	0.394669i	0.957174	+	0.289512i	$0.0934932\pi$
$200$		−	4.70566i		−	0.332740i
$201$	−7.62337	−	4.40136i	−0.537711	−	0.310448i
$202$	7.77298	+	4.48773i	0.546905	+	0.315756i
$203$			0.415607i			0.0291699i
$204$	6.11611	−	10.5934i	0.428213	−	0.741687i
$205$	3.49725	+	6.05741i	0.244258	+	0.423068i
$206$	4.10292	−	2.36882i	0.285864	−	0.165043i
$207$	26.2845			1.82690
$208$	−8.08667	−	4.06517i	−0.560710	−	0.281869i
$209$	−16.5352			−1.14376
$210$	−0.569561	+	0.328836i	−0.0393034	+	0.0226919i
$211$	−0.818680	−	1.41799i	−0.0563602	−	0.0976188i	0.836469	−	0.548015i	$-0.184616\pi$
$211$	−0.818680	−	1.41799i	−0.0563602	−	0.0976188i	−0.892829	+	0.450396i	$0.851283\pi$
$212$	−10.2769	+	17.8001i	−0.705820	+	1.22252i
$213$		−	3.95739i		−	0.271156i
$214$	−2.77257	−	1.60074i	−0.189529	−	0.109424i
$215$	15.9546	+	9.21140i	1.08809	+	0.628212i
$216$		−	8.79263i		−	0.598263i
$217$	0.146556	−	0.253842i	0.00994885	−	0.0172319i
$218$	1.41718	+	2.45464i	0.0959838	+	0.166249i
$219$	8.44294	−	4.87453i	0.570521	−	0.329390i
$220$	−6.26546			−0.422418
$221$	−0.528619	−	9.13651i	−0.0355588	−	0.614588i
$222$	−4.48630			−0.301101
$223$	−18.6955	+	10.7939i	−1.25194	+	0.722810i	−0.971495	−	0.237058i	$-0.923817\pi$
$223$	−18.6955	+	10.7939i	−1.25194	+	0.722810i	−0.280449	+	0.959869i	$0.590483\pi$
$224$	0.745934	+	1.29200i	0.0498398	+	0.0863251i
$225$	−5.76208	+	9.98021i	−0.384139	+	0.665347i
$226$		−	6.07327i		−	0.403988i
$227$	16.3738	+	9.45343i	1.08677	+	0.627446i	0.932714	−	0.360616i	$-0.117434\pi$
$227$	16.3738	+	9.45343i	1.08677	+	0.627446i	0.154054	+	0.988062i	$0.450767\pi$
$228$	−30.4950	−	17.6063i	−2.01958	−	1.16601i
$229$			2.75993i			0.182381i	0.995833	+	0.0911907i	$0.0290673\pi$
$229$			2.75993i			0.182381i	−0.995833	+	0.0911907i	$0.970933\pi$
$230$	−2.28220	+	3.95288i	−0.150484	+	0.260645i
$231$	−0.918298	−	1.59054i	−0.0604196	−	0.104650i
$232$	2.33984	−	1.35091i	0.153618	−	0.0886914i
$233$	20.5820			1.34837			0.674186	−	0.738561i	$-0.264494\pi$
$233$	20.5820			1.34837			0.674186	+	0.738561i	$0.264494\pi$
$234$	−4.70721	−	7.16296i	−0.307720	−	0.468258i
$235$	11.8459			0.772744
$236$	−7.27793	+	4.20191i	−0.473753	+	0.273521i
$237$	14.4014	+	24.9440i	0.935472	+	1.62029i
$238$	−0.189502	+	0.328227i	−0.0122836	+	0.0212758i
$239$			1.41328i			0.0914175i	0.998955	+	0.0457088i	$0.0145546\pi$
$239$			1.41328i			0.0914175i	−0.998955	+	0.0457088i	$0.985445\pi$
$240$	−9.57533	−	5.52832i	−0.618085	−	0.356851i
$241$	−7.04669	−	4.06841i	−0.453917	−	0.262069i	0.255566	−	0.966792i	$-0.417738\pi$
$241$	−7.04669	−	4.06841i	−0.453917	−	0.262069i	−0.709483	+	0.704722i	$0.751072\pi$
$242$		−	2.99484i		−	0.192516i
$243$	8.61482	−	14.9213i	0.552641	−	0.957202i
$244$	−1.13917	−	1.97309i	−0.0729276	−	0.126314i
$245$	9.52502	−	5.49927i	0.608531	−	0.351336i
$246$	6.20201			0.395426
$247$	−26.3011	+	1.52172i	−1.67350	+	0.0968250i
$248$	−1.90549			−0.120998
$249$	39.7131	−	22.9284i	2.51672	−	1.45303i
$250$	−3.02650	−	5.24205i	−0.191413	−	0.331537i
$251$	−10.3533	+	17.9324i	−0.653492	+	1.13188i	0.328778	+	0.944407i	$0.393363\pi$
$251$	−10.3533	+	17.9324i	−0.653492	+	1.13188i	−0.982270	+	0.187474i	$0.939970\pi$
$252$		−	2.38067i		−	0.149968i
$253$	−11.0387	−	6.37319i	−0.693996	−	0.400679i
$254$	1.58225	+	0.913512i	0.0992792	+	0.0573189i
$255$		−	11.1798i		−	0.700107i
$256$	0.480107	−	0.831570i	0.0300067	−	0.0519731i
$257$	−9.35902	−	16.2103i	−0.583799	−	1.01117i	−0.995024	−	0.0996362i	$-0.968232\pi$
$257$	−9.35902	−	16.2103i	−0.583799	−	1.01117i	0.411224	−	0.911534i	$-0.365101\pi$
$258$	14.1469	−	8.16773i	0.880749	−	0.508501i
$259$	−0.932277			−0.0579289
$260$	−9.96593	+	0.576608i	−0.618061	+	0.0357597i
$261$	−6.61674			−0.409566
$262$	−0.189239	+	0.109257i	−0.0116912	+	0.00674992i
$263$	−5.18885	−	8.98735i	−0.319958	−	0.554184i	0.660521	−	0.750808i	$-0.270336\pi$
$263$	−5.18885	−	8.98735i	−0.319958	−	0.554184i	−0.980479	+	0.196624i	$0.937002\pi$
$264$	−5.96975	+	10.3399i	−0.367413	+	0.636378i
$265$			18.7854i			1.15398i
$266$	0.944861	+	0.545516i	0.0579332	+	0.0334477i
$267$	5.55649	+	3.20804i	0.340052	+	0.196329i
$268$			5.53336i			0.338004i
$269$	−3.07985	+	5.33446i	−0.187782	+	0.325248i	−0.944510	−	0.328482i	$-0.893463\pi$
$269$	−3.07985	+	5.33446i	−0.187782	+	0.325248i	0.756729	+	0.653729i	$0.226796\pi$
$270$	−1.86965	−	3.23833i	−0.113783	−	0.197079i
$271$	18.4874	−	10.6737i	1.12303	−	0.648381i	0.180856	−	0.983510i	$-0.442113\pi$
$271$	18.4874	−	10.6737i	1.12303	−	0.648381i	0.942172	+	0.335129i	$0.108780\pi$
$272$	−6.37173			−0.386343
$273$	−1.60703	−	2.44542i	−0.0972621	−	0.148004i
$274$	−5.26180			−0.317877
$275$	4.83979	−	2.79426i	0.291851	−	0.168500i
$276$	−13.5721	−	23.5075i	−0.816943	−	1.41499i
$277$	−0.0985182	+	0.170639i	−0.00591938	+	0.0102527i	−0.868970	−	0.494865i	$-0.835218\pi$
$277$	−0.0985182	+	0.170639i	−0.00591938	+	0.0102527i	0.863051	+	0.505118i	$0.168551\pi$
$278$			5.55294i			0.333043i
$279$	4.04134	+	2.33327i	0.241948	+	0.139689i
$280$	0.769430	+	0.444231i	0.0459822	+	0.0265479i
$281$		−	12.4260i		−	0.741272i	−0.928778	−	0.370636i	$-0.879140\pi$
$281$		−	12.4260i		−	0.741272i	0.928778	−	0.370636i	$-0.120860\pi$
$282$	5.25189	−	9.09655i	0.312746	−	0.541692i
$283$	9.20091	+	15.9364i	0.546937	+	0.947323i	0.998482	+	0.0550746i	$0.0175397\pi$
$283$	9.20091	+	15.9364i	0.546937	+	0.947323i	−0.451545	+	0.892248i	$0.649127\pi$
$284$	−2.15433	+	1.24380i	−0.127836	+	0.0738060i
$285$	−32.1831			−1.90636
$286$	0.240086	+	4.14958i	0.0141966	+	0.245370i
$287$	1.28881			0.0760760
$288$	−20.5694	+	11.8758i	−1.21207	+	0.699787i
$289$	5.27864	+	9.14288i	0.310508	+	0.537816i
$290$	0.574509	−	0.995080i	0.0337364	−	0.0584331i
$291$			25.6557i			1.50396i
$292$	−5.30720	−	3.06411i	−0.310580	−	0.179314i
$293$	4.26855	+	2.46445i	0.249371	+	0.143975i	0.619476	−	0.785015i	$-0.287345\pi$
$293$	4.26855	+	2.46445i	0.249371	+	0.143975i	−0.370105	+	0.928990i	$0.620678\pi$
$294$		−	9.75240i		−	0.568771i
$295$	−3.84039	+	6.65176i	−0.223596	+	0.387280i
$296$	3.03031	+	5.24866i	0.176133	+	0.305072i
$297$	9.04327	−	5.22113i	0.524743	−	0.302961i
$298$	−4.88162			−0.282785
$299$	−18.1448	−	9.12140i	−1.04934	−	0.527504i
$300$	11.9011			0.687108
$301$	2.93980	−	1.69730i	0.169447	−	0.0978306i
$302$	3.95028	+	6.84208i	0.227313	+	0.393718i
$303$	−24.3921	+	42.2484i	−1.40129	+	2.42711i
$304$			18.3422i			1.05200i
$305$	−1.80333	−	1.04116i	−0.103259	−	0.0596164i
$306$	−5.22560	−	3.01700i	−0.298728	−	0.172471i
$307$		−	33.0345i		−	1.88538i	−0.333675	−	0.942688i	$-0.608289\pi$
$307$		−	33.0345i		−	1.88538i	0.333675	−	0.942688i	$-0.391711\pi$
$308$	−0.577239	+	0.999807i	−0.0328912	+	0.0569693i
$309$	12.8752	+	22.3005i	0.732445	+	1.26863i
$310$	−0.701791	+	0.405179i	−0.0398591	+	0.0230126i
$311$	−20.2636			−1.14904			−0.574522	−	0.818489i	$-0.694812\pi$
$311$	−20.2636			−1.14904			−0.574522	+	0.818489i	$0.694812\pi$
$312$	−8.54399	+	16.9962i	−0.483708	+	0.962221i
$313$	−17.2713			−0.976233			−0.488117	−	0.872778i	$-0.662316\pi$
$313$	−17.2713			−0.976233			−0.488117	+	0.872778i	$0.662316\pi$
$314$	5.81141	−	3.35522i	0.327957	−	0.189346i
$315$	−1.08792	−	1.88433i	−0.0612974	−	0.106170i
$316$	9.05268	−	15.6797i	0.509253	−	0.882052i
$317$		−	1.09130i		−	0.0612936i	−0.999530	−	0.0306468i	$-0.990243\pi$
$317$		−	1.09130i		−	0.0612936i	0.999530	−	0.0306468i	$-0.00975671\pi$
$318$	14.4254	+	8.32851i	0.808936	+	0.467039i
$319$	2.77883	+	1.60436i	0.155585	+	0.0898268i
$320$			3.86191i			0.215887i
$321$	8.70049	−	15.0697i	0.485614	−	0.841108i
$322$	0.420519	+	0.728360i	0.0234346	+	0.0405899i
$323$	−16.0617	+	9.27325i	−0.893699	+	0.515977i
$324$	−2.12875			−0.118264
$325$	7.44109	−	4.88998i	0.412757	−	0.271248i
$326$	−9.08244			−0.503030
$327$	−13.3416	+	7.70280i	−0.737795	+	0.425966i
$328$	−4.18921	−	7.25592i	−0.231310	−	0.400641i
$329$	1.09137	−	1.89031i	0.0601692	−	0.104216i
$330$			5.07760i			0.279513i
$331$	9.14208	+	5.27818i	0.502494	+	0.290115i	0.729743	−	0.683722i	$-0.239640\pi$
$331$	9.14208	+	5.27818i	0.502494	+	0.290115i	−0.227249	+	0.973837i	$0.572973\pi$
$332$	−24.9635	−	14.4127i	−1.37005	−	0.791000i
$333$		−	14.8425i		−	0.813363i
$334$	−1.73252	+	3.00081i	−0.0947991	+	0.164197i
$335$	2.52864	+	4.37974i	0.138155	+	0.239291i
$336$	−1.76435	+	1.01865i	−0.0962534	+	0.0555719i
$337$	4.10643			0.223691			0.111846	−	0.993726i	$-0.464324\pi$
$337$	4.10643			0.223691			0.111846	+	0.993726i	$0.464324\pi$
$338$	0.763768	+	6.57829i	0.0415435	+	0.357812i
$339$	33.0099			1.79285
$340$	−6.08607	+	3.51379i	−0.330063	+	0.190562i
$341$	−1.13149	−	1.95980i	−0.0612737	−	0.106129i
$342$	−8.68498	+	15.0428i	−0.469630	+	0.813423i
$343$		−	4.07838i		−	0.220212i
$344$	−19.1113	−	11.0339i	−1.03041	−	0.594910i
$345$	−21.4850	−	12.4044i	−1.15672	−	0.667830i
$346$			8.37650i			0.450324i
$347$	−3.58664	+	6.21224i	−0.192541	+	0.333491i	−0.946092	−	0.323899i	$-0.895006\pi$
$347$	−3.58664	+	6.21224i	−0.192541	+	0.333491i	0.753551	+	0.657390i	$0.228340\pi$
$348$	3.41657	+	5.91768i	0.183148	+	0.317221i
$349$	−5.69276	+	3.28672i	−0.304727	+	0.175934i	−0.644564	−	0.764550i	$-0.722961\pi$
$349$	−5.69276	+	3.28672i	−0.304727	+	0.175934i	0.339838	+	0.940484i	$0.389628\pi$
$350$	−0.368744			−0.0197102
$351$	13.9038	−	9.13705i	0.742132	−	0.487700i
$352$	11.5181			0.613914
$353$	31.9594	−	18.4518i	1.70103	−	0.982088i	0.756302	−	0.654222i	$-0.227004\pi$
$353$	31.9594	−	18.4518i	1.70103	−	0.982088i	0.944724	−	0.327866i	$-0.106329\pi$
$354$	3.40527	+	5.89811i	0.180988	+	0.313481i
$355$	−1.13679	+	1.96897i	−0.0603344	+	0.104502i
$356$		−	4.03313i		−	0.213756i
$357$	−1.78401	−	1.03000i	−0.0944198	−	0.0545133i
$358$	−5.79073	−	3.34328i	−0.306050	−	0.176698i
$359$			16.6122i			0.876761i	0.898790	+	0.438380i	$0.144448\pi$
$359$			16.6122i			0.876761i	−0.898790	+	0.438380i	$0.855552\pi$
$360$	−7.07245	+	12.2499i	−0.372751	+	0.645624i
$361$	17.1947	+	29.7821i	0.904985	+	1.56748i
$362$	3.58744	−	2.07121i	0.188551	−	0.108860i
$363$	16.2778			0.854363
$364$	−0.826152	+	1.64343i	−0.0433021	+	0.0861391i
$365$	−5.60098			−0.293169
$366$	−1.59902	+	0.923192i	−0.0835819	+	0.0482560i
$367$	−8.28982	−	14.3584i	−0.432725	−	0.749502i	0.564382	−	0.825514i	$-0.309115\pi$
$367$	−8.28982	−	14.3584i	−0.432725	−	0.749502i	−0.997107	+	0.0760119i	$0.975781\pi$
$368$	−7.06966	+	12.2450i	−0.368532	+	0.638315i
$369$			20.5187i			1.06816i
$370$	2.23213	+	1.28872i	0.116043	+	0.0669975i
$371$	2.99767	+	1.73071i	0.155631	+	0.0898538i
$372$		−	4.81916i		−	0.249862i
$373$	7.57275	−	13.1164i	0.392102	−	0.679141i	−0.600624	−	0.799531i	$-0.705081\pi$
$373$	7.57275	−	13.1164i	0.392102	−	0.679141i	0.992727	+	0.120390i	$0.0384146\pi$
$374$	1.46306	+	2.53410i	0.0756532	+	0.131035i
$375$	28.4921	−	16.4499i	1.47132	−	0.849469i
$376$	−14.1898			−0.731781
$377$	4.56769	+	2.29618i	0.235248	+	0.118259i
$378$	−0.689006			−0.0354386
$379$	4.17718	−	2.41169i	0.214567	−	0.123880i	−0.388865	−	0.921295i	$-0.627133\pi$
$379$	4.17718	−	2.41169i	0.214567	−	0.123880i	0.603432	+	0.797414i	$0.293799\pi$
$380$	10.1151	+	17.5198i	0.518893	+	0.898749i
$381$	−4.96520	+	8.59998i	−0.254375	+	0.440590i
$382$		−	4.77054i		−	0.244082i
$383$	22.1113	+	12.7660i	1.12984	+	0.652311i	0.943894	−	0.330249i	$-0.107133\pi$
$383$	22.1113	+	12.7660i	1.12984	+	0.652311i	0.185942	+	0.982561i	$0.440466\pi$
$384$	27.3750	+	15.8050i	1.39697	+	0.806544i
$385$			1.05515i			0.0537755i
$386$	5.57063	−	9.64861i	0.283538	−	0.491101i
$387$	27.0221	+	46.8037i	1.37361	+	2.37916i
$388$	13.9665	−	8.06353i	0.709039	−	0.409364i
$389$	−12.8541			−0.651726			−0.325863	−	0.945417i	$-0.605655\pi$
$389$	−12.8541			−0.651726			−0.325863	+	0.945417i	$0.605655\pi$
$390$	0.467289	+	8.07649i	0.0236621	+	0.408969i
$391$	−14.2968			−0.723022
$392$	−11.4096	+	6.58734i	−0.576273	+	0.332711i
$393$	−0.593843	−	1.02857i	−0.0299554	−	0.0518843i
$394$	−2.35863	+	4.08526i	−0.118826	+	0.205812i
$395$		−	16.5476i		−	0.832602i
$396$	−15.9176	−	9.19004i	−0.799890	−	0.461817i
$397$	29.2193	+	16.8698i	1.46648	+	0.846670i	0.999297	−	0.0374922i	$-0.0119369\pi$
$397$	29.2193	+	16.8698i	1.46648	+	0.846670i	0.467179	+	0.884163i	$0.345270\pi$
$398$			3.27496i			0.164159i
$399$	−2.96503	+	5.13559i	−0.148437	+	0.257101i
$400$	−3.09962	−	5.36869i	−0.154981	−	0.268435i
$401$	16.8822	−	9.74696i	0.843058	−	0.486740i	−0.0152444	−	0.999884i	$-0.504853\pi$
$401$	16.8822	−	9.74696i	0.843058	−	0.486740i	0.858303	+	0.513144i	$0.171519\pi$
$402$	4.48429			0.223656
$403$	−1.98013	−	3.01316i	−0.0986371	−	0.150096i
$404$	30.6656			1.52567
$405$	−1.68494	+	0.972799i	−0.0837252	+	0.0483388i
$406$	−0.105859	−	0.183354i	−0.00525372	−	0.00909970i
$407$	−3.59885	+	6.23339i	−0.178388	+	0.308978i
$408$			13.3918i			0.662994i
$409$	17.7640	+	10.2561i	0.878375	+	0.507130i	0.870122	−	0.492836i	$-0.164040\pi$
$409$	17.7640	+	10.2561i	0.878375	+	0.507130i	0.00825274	+	0.999966i	$0.497373\pi$
$410$	−3.08577	−	1.78157i	−0.152396	−	0.0879856i
$411$		−	28.5994i		−	1.41070i
$412$	8.09331	−	14.0180i	0.398729	−	0.690619i
$413$	0.707633	+	1.22566i	0.0348204	+	0.0603106i
$414$	−11.5960	+	6.69494i	−0.569911	+	0.329038i
$415$	−26.3454			−1.29324
$416$	18.3208	−	1.06000i	0.898249	−	0.0519708i
$417$	−30.1818			−1.47801
$418$	7.29486	−	4.21169i	0.356803	−	0.206000i
$419$	6.75246	+	11.6956i	0.329879	+	0.571367i	0.982488	−	0.186328i	$-0.0596587\pi$
$419$	6.75246	+	11.6956i	0.329879	+	0.571367i	−0.652609	+	0.757695i	$0.726325\pi$
$420$	−1.12350	+	1.94596i	−0.0548213	+	0.0949533i
$421$			9.05394i			0.441262i	0.975357	+	0.220631i	$0.0708116\pi$
$421$			9.05394i			0.441262i	−0.975357	+	0.220631i	$0.929188\pi$
$422$	0.722357	+	0.417053i	0.0351638	+	0.0203018i
$423$	30.0950	+	17.3754i	1.46327	+	0.844819i
$424$		−	22.5023i		−	1.09281i
$425$	3.13415	−	5.42850i	0.152028	−	0.263321i
$426$	1.00799	+	1.74589i	0.0488372	+	0.0845885i
$427$	−0.332283	+	0.191844i	−0.0160803	+	0.00928398i
$428$	−10.9382			−0.528718
$429$	−22.5542	+	1.30494i	−1.08893	+	0.0630029i
$430$	−9.38496			−0.452583
$431$	−20.6451	+	11.9195i	−0.994441	+	0.574141i	−0.906599	−	0.421993i	$-0.861331\pi$
$431$	−20.6451	+	11.9195i	−0.994441	+	0.574141i	−0.0878425	+	0.996134i	$0.527997\pi$
$432$	−5.79170	−	10.0315i	−0.278653	−	0.482642i
$433$	13.4441	−	23.2859i	0.646082	−	1.11905i	−0.337968	−	0.941158i	$-0.609740\pi$
$433$	13.4441	−	23.2859i	0.646082	−	1.11905i	0.984050	−	0.177890i	$-0.0569271\pi$
$434$			0.149317i			0.00716745i
$435$	5.40854	+	3.12262i	0.259320	+	0.149718i
$436$	8.38651	+	4.84196i	0.401641	+	0.231888i
$437$			41.1560i			1.96876i
$438$	−2.48319	+	4.30101i	−0.118651	+	0.205510i
$439$	1.21505	+	2.10453i	0.0579913	+	0.100444i	0.893564	−	0.448937i	$-0.148197\pi$
$439$	1.21505	+	2.10453i	0.0579913	+	0.100444i	−0.835572	+	0.549380i	$0.814864\pi$
$440$	5.94043	−	3.42971i	0.283199	−	0.163505i
$441$	32.2648			1.53642
$442$	2.56038	+	3.89613i	0.121785	+	0.185320i
$443$	−18.6848			−0.887741			−0.443870	−	0.896091i	$-0.646395\pi$
$443$	−18.6848			−0.887741			−0.443870	+	0.896091i	$0.646395\pi$
$444$	−13.2744	+	7.66396i	−0.629974	+	0.363715i
$445$	−1.84307	−	3.19229i	−0.0873698	−	0.151329i
$446$	5.49862	−	9.52389i	0.260367	−	0.450969i
$447$		−	26.5330i		−	1.25497i
$448$	0.616261	+	0.355799i	0.0291156	+	0.0168099i
$449$	2.47284	+	1.42770i	0.116701	+	0.0673771i	0.557214	−	0.830369i	$-0.311870\pi$
$449$	2.47284	+	1.42770i	0.116701	+	0.0673771i	−0.440514	+	0.897746i	$0.645204\pi$
$450$		−	5.87065i		−	0.276745i
$451$	4.97517	−	8.61724i	0.234271	−	0.405770i
$452$	−10.3750	−	17.9700i	−0.487998	−	0.845236i
$453$	−37.1887	+	21.4709i	−1.74728	+	1.00879i
$454$	−9.63156			−0.452031
$455$	0.0971050	+	1.67834i	0.00455235	+	0.0786816i
$456$	38.5507			1.80530
$457$	−24.2079	+	13.9765i	−1.13240	+	0.653791i	−0.944537	−	0.328404i	$-0.893489\pi$
$457$	−24.2079	+	13.9765i	−1.13240	+	0.653791i	−0.187863	+	0.982195i	$0.560156\pi$
$458$	−0.702984	−	1.21760i	−0.0328483	−	0.0568949i
$459$	5.85622	−	10.1433i	0.273345	−	0.473448i
$460$			15.5947i			0.727107i
$461$	0.298494	+	0.172336i	0.0139023	+	0.00802648i	0.506935	−	0.861984i	$-0.330778\pi$
$461$	0.298494	+	0.172336i	0.0139023	+	0.00802648i	−0.493033	+	0.870011i	$0.664112\pi$
$462$	0.810254	+	0.467800i	0.0376964	+	0.0217640i
$463$			17.1454i			0.796816i	0.917208	+	0.398408i	$0.130437\pi$
$463$			17.1454i			0.796816i	−0.917208	+	0.398408i	$0.869563\pi$
$464$	1.77968	−	3.08250i	0.0826198	−	0.143102i
$465$	−2.20227	−	3.81444i	−0.102128	−	0.176890i
$466$	−9.08020	+	5.24246i	−0.420632	+	0.242852i
$467$	−27.5932			−1.27686			−0.638430	−	0.769680i	$-0.720416\pi$
$467$	−27.5932			−1.27686			−0.638430	+	0.769680i	$0.720416\pi$
$468$	−26.1645	−	13.1529i	−1.20946	−	0.607993i
$469$	0.931858			0.0430292
$470$	−5.22610	+	3.01729i	−0.241062	+	0.139177i
$471$	18.2366	+	31.5867i	0.840297	+	1.45544i
$472$	4.60025	−	7.96786i	0.211743	−	0.366750i
$473$		−	26.2082i		−	1.20505i
$474$	−12.7070	−	7.33639i	−0.583652	−	0.336971i
$475$	−15.6269	−	9.02220i	−0.717012	−	0.413967i
$476$			1.29491i			0.0593520i
$477$	−27.5540	+	47.7249i	−1.26161	+	2.18517i
$478$	−0.359978	−	0.623499i	−0.0164650	−	0.0285182i
$479$	21.3843	−	12.3462i	0.977074	−	0.564114i	0.0756887	−	0.997131i	$-0.475884\pi$
$479$	21.3843	−	12.3462i	0.977074	−	0.564114i	0.901386	+	0.433017i	$0.142551\pi$
$480$	22.4180			1.02324
$481$	−5.15072	+	10.2461i	−0.234853	+	0.467182i
$482$	4.14507			0.188803
$483$	−3.95884	+	2.28564i	−0.180134	+	0.104000i
$484$	−5.11609	−	8.86132i	−0.232549	−	0.402787i
$485$	7.36978	−	12.7648i	0.334644	−	0.579621i
$486$			8.77715i			0.398139i
$487$	17.7217	+	10.2317i	0.803049	+	0.463641i	0.844536	−	0.535498i	$-0.179876\pi$
$487$	17.7217	+	10.2317i	0.803049	+	0.463641i	−0.0414871	+	0.999139i	$0.513210\pi$
$488$	2.16014	+	1.24716i	0.0977849	+	0.0564561i
$489$		−	49.3657i		−	2.23239i
$490$	−2.80145	+	4.85225i	−0.126556	+	0.219202i
$491$	−14.4590	−	25.0437i	−0.652525	−	1.13021i	−0.982508	−	0.186220i	$-0.940376\pi$
$491$	−14.4590	−	25.0437i	−0.652525	−	1.13021i	0.329983	−	0.943987i	$-0.392957\pi$
$492$	18.3509	−	10.5949i	0.827323	−	0.477655i
$493$	3.59902			0.162092
$494$	11.2157	−	7.37051i	0.504618	−	0.331615i
$495$	−16.7987			−0.755046
$496$	−2.17397	+	1.25514i	−0.0976142	+	0.0563576i
$497$	0.209465	+	0.362804i	0.00939580	+	0.0162740i
$498$	−11.6802	+	20.2307i	−0.523402	+	0.906560i
$499$			26.4372i			1.18349i	0.806124	+	0.591746i	$0.201561\pi$
$499$			26.4372i			1.18349i	−0.806124	+	0.591746i	$0.798439\pi$
$500$	−17.9100	−	10.3404i	−0.800960	−	0.462435i
$501$	−16.3103	−	9.41673i	−0.728688	−	0.420708i
$502$		−	10.5483i		−	0.470795i
$503$	18.0470	−	31.2583i	0.804675	−	1.39374i	−0.111836	−	0.993727i	$-0.535673\pi$
$503$	18.0470	−	31.2583i	0.804675	−	1.39374i	0.916511	−	0.400011i	$-0.130994\pi$
$504$	1.30317	+	2.25716i	0.0580480	+	0.100542i
$505$	24.2723	−	14.0136i	1.08010	−	0.623598i
$506$	6.49328			0.288661
$507$	−35.7549	+	4.15130i	−1.58793	+	0.184366i
$508$	6.24222			0.276954
$509$	−10.2499	+	5.91780i	−0.454320	+	0.262302i	−0.709653	−	0.704551i	$-0.751148\pi$
$509$	−10.2499	+	5.91780i	−0.454320	+	0.262302i	0.255333	+	0.966853i	$0.417815\pi$
$510$	2.84762	+	4.93221i	0.126095	+	0.218402i
$511$	−0.516020	+	0.893772i	−0.0228274	+	0.0395381i
$512$		−	22.3434i		−	0.987447i
$513$	−29.1992	−	16.8582i	−1.28918	−	0.744307i
$514$	8.25787	+	4.76768i	0.364239	+	0.210293i
$515$		−	14.7940i		−	0.651901i
$516$	27.9059	−	48.3344i	1.22849	−	2.12781i
$517$	−8.42599	−	14.5942i	−0.370575	−	0.641854i
$518$	0.411294	−	0.237461i	0.0180712	−	0.0104334i
$519$	−45.5287			−1.99849
$520$	9.13329	−	6.00204i	0.400521	−	0.263207i
$521$	1.37650			0.0603057			0.0301528	−	0.999545i	$-0.490401\pi$
$521$	1.37650			0.0603057			0.0301528	+	0.999545i	$0.490401\pi$
$522$	2.91912	−	1.68535i	0.127766	−	0.0737659i
$523$	20.2168	+	35.0166i	0.884021	+	1.53117i	0.846832	+	0.531861i	$0.178507\pi$
$523$	20.2168	+	35.0166i	0.884021	+	1.53117i	0.0371895	+	0.999308i	$0.488159\pi$
$524$	−0.373288	+	0.646554i	−0.0163072	+	0.0282448i
$525$		−	2.00423i		−	0.0874717i
$526$	4.57835	+	2.64331i	0.199625	+	0.115254i
$527$	−2.19819	−	1.26912i	−0.0957546	−	0.0552840i
$528$			15.7291i			0.684521i
$529$	−4.36284	+	7.55666i	−0.189689	+	0.328550i
$530$	−4.78485	−	8.28760i	−0.207840	−	0.359990i
$531$	−19.5133	+	11.2660i	−0.846804	+	0.488903i
$532$	3.72762			0.161613
$533$	7.12052	−	14.1646i	0.308424	−	0.613535i
$534$	−3.26849			−0.141441
$535$	−8.65776	+	4.99856i	−0.374307	+	0.216106i
$536$	−3.02895	−	5.24630i	−0.130831	−	0.226606i
$537$	18.1717	−	31.4743i	0.784166	−	1.35822i
$538$		−	3.13788i		−	0.135284i
$539$	−13.5502	−	7.82323i	−0.583650	−	0.336970i
$540$	−11.0641	−	6.38786i	−0.476123	−	0.274890i
$541$			41.6555i			1.79091i	0.445154	+	0.895454i	$0.353149\pi$
$541$			41.6555i			1.79091i	−0.445154	+	0.895454i	$0.646851\pi$
$542$	−5.43741	+	9.41787i	−0.233557	+	0.404532i
$543$	11.2576	+	19.4987i	0.483110	+	0.836771i
$544$	11.1883	−	6.45955i	0.479693	−	0.276951i
$545$	8.85074			0.379124
$546$	1.33185	+	0.669522i	0.0569980	+	0.0286529i
$547$	21.4330			0.916411			0.458205	−	0.888846i	$-0.348492\pi$
$547$	21.4330			0.916411			0.458205	+	0.888846i	$0.348492\pi$
$548$	−15.5689	+	8.98874i	−0.665072	+	0.383980i
$549$	−3.05429	−	5.29018i	−0.130354	−	0.225779i
$550$	−1.42345	+	2.46549i	−0.0606963	+	0.105129i
$551$		−	10.3604i		−	0.441369i
$552$	25.7360	+	14.8587i	1.09540	+	0.632428i
$553$	−2.64058	−	1.52454i	−0.112289	−	0.0648300i
$554$		−	0.100375i		−	0.00426451i
$555$	−7.00458	+	12.1323i	−0.297328	+	0.514987i
$556$	9.48610	+	16.4304i	0.402300	+	0.696804i
$557$	−34.6756	+	20.0199i	−1.46925	+	0.848272i	−0.999406	−	0.0344763i	$-0.989024\pi$
$557$	−34.6756	+	20.0199i	−1.46925	+	0.848272i	−0.469845	+	0.882749i	$0.655690\pi$
$558$	−2.37723			−0.100636
$559$	−2.41192	−	41.6870i	−0.102014	−	1.76317i
$560$	1.17046			0.0494609
$561$	−13.7736	+	7.95216i	−0.581520	+	0.335741i
$562$	3.16503	+	5.48199i	0.133509	+	0.231244i
$563$	12.5886	−	21.8040i	0.530545	−	0.918931i	−0.468820	−	0.883294i	$-0.655321\pi$
$563$	12.5886	−	21.8040i	0.530545	−	0.918931i	0.999365	−	0.0356368i	$-0.0113460\pi$
$564$		−	35.8873i		−	1.51113i
$565$	−16.4239	−	9.48234i	−0.690959	−	0.398925i
$566$	−8.11836	−	4.68714i	−0.341240	−	0.197015i
$567$			0.358497i			0.0150555i
$568$	1.36171	−	2.35855i	0.0571361	−	0.0989626i
$569$	6.12926	+	10.6162i	0.256952	+	0.445054i	0.965424	−	0.260685i	$-0.0839485\pi$
$569$	6.12926	+	10.6162i	0.256952	+	0.445054i	−0.708472	+	0.705739i	$0.750615\pi$
$570$	14.1983	−	8.19737i	0.594700	−	0.343350i
$571$	10.7739			0.450872			0.225436	−	0.974258i	$-0.427619\pi$
$571$	10.7739			0.450872			0.225436	+	0.974258i	$0.427619\pi$
$572$	7.79912	+	11.8679i	0.326098	+	0.496222i
$573$	25.9293			1.08321
$574$	−0.568587	+	0.328274i	−0.0237323	+	0.0137019i
$575$	−6.95489	−	12.0462i	−0.290039	−	0.502362i
$576$	−5.66456	+	9.81130i	−0.236023	+	0.408804i
$577$		−	27.7482i		−	1.15517i	−0.816329	−	0.577587i	$-0.803994\pi$
$577$		−	27.7482i		−	1.15517i	0.816329	−	0.577587i	$-0.196006\pi$
$578$	−4.65758	−	2.68905i	−0.193730	−	0.111850i
$579$	52.4430	+	30.2780i	2.17946	+	1.25831i
$580$		−	3.92574i		−	0.163008i
$581$	−2.42721	+	4.20404i	−0.100697	+	0.174413i
$582$	−6.53477	−	11.3186i	−0.270875	−	0.469169i
$583$	23.1437	−	13.3620i	0.958514	−	0.553398i
$584$	6.70917			0.277628
$585$	−26.7203	+	1.54598i	−1.10475	+	0.0639183i
$586$	−2.51089			−0.103724
$587$	33.5943	−	19.3957i	1.38659	−	0.800546i	0.393657	−	0.919257i	$-0.371210\pi$
$587$	33.5943	−	19.3957i	1.38659	−	0.800546i	0.992929	+	0.118711i	$0.0378763\pi$
$588$	−16.6600	−	28.8560i	−0.687048	−	1.19000i
$589$	−3.65340	+	6.32788i	−0.150536	+	0.260736i
$590$		−	3.91276i		−	0.161086i
$591$	−22.2046	−	12.8198i	−0.913373	−	0.527336i
$592$	6.91458	+	3.99214i	0.284188	+	0.164076i
$593$			33.4309i			1.37284i	0.727205	+	0.686421i	$0.240819\pi$
$593$			33.4309i			1.37284i	−0.727205	+	0.686421i	$0.759181\pi$
$594$	−2.65976	+	4.60683i	−0.109131	+	0.189021i
$595$	0.591749	+	1.02494i	0.0242593	+	0.0420184i
$596$	−14.4441	+	8.33929i	−0.591652	+	0.341590i
$597$	−17.8003			−0.728519
$598$	10.3283	−	0.597573i	0.422355	−	0.0244366i
$599$	−29.7820			−1.21686			−0.608430	−	0.793608i	$-0.708200\pi$
$599$	−29.7820			−1.21686			−0.608430	+	0.793608i	$0.708200\pi$
$600$	−11.2837	+	6.51463i	−0.460654	+	0.265959i
$601$	−19.5144	−	33.7999i	−0.796008	−	1.37873i	−0.922197	−	0.386720i	$-0.873608\pi$
$601$	−19.5144	−	33.7999i	−0.796008	−	1.37873i	0.126189	−	0.992006i	$-0.459725\pi$
$602$	−0.864639	+	1.49760i	−0.0352401	+	0.0610376i
$603$			14.8358i			0.604161i
$604$	23.3767	+	13.4965i	0.951184	+	0.549166i
$605$	−8.09893	−	4.67592i	−0.329268	−	0.190103i
$606$		−	24.8517i		−	1.00953i
$607$	−18.4908	+	32.0270i	−0.750519	+	1.29994i	0.197053	+	0.980393i	$0.436863\pi$
$607$	−18.4908	+	32.0270i	−0.750519	+	1.29994i	−0.947572	+	0.319544i	$0.896470\pi$
$608$	−18.5950	−	32.2074i	−0.754125	−	1.30618i
$609$	0.996581	−	0.575376i	0.0403835	−	0.0233154i
$610$	1.06077			0.0429495
$611$	−14.7456	−	22.4384i	−0.596543	−	0.907759i
$612$	−20.6158			−0.833344
$613$	21.7787	−	12.5739i	0.879632	−	0.507856i	0.00909477	−	0.999959i	$-0.497105\pi$
$613$	21.7787	−	12.5739i	0.879632	−	0.507856i	0.870537	+	0.492103i	$0.163772\pi$
$614$	8.41423	+	14.5739i	0.339571	+	0.588154i
$615$	9.68336	−	16.7721i	0.390471	−	0.676315i
$616$		−	1.26392i		−	0.0509248i
$617$	9.70636	+	5.60397i	0.390763	+	0.225607i	0.682491	−	0.730894i	$-0.260897\pi$
$617$	9.70636	+	5.60397i	0.390763	+	0.225607i	−0.291727	+	0.956501i	$0.594230\pi$
$618$	−11.3604	−	6.55891i	−0.456981	−	0.263838i
$619$			46.7908i			1.88068i	0.340235	+	0.940340i	$0.389493\pi$
$619$			46.7908i			1.88068i	−0.340235	+	0.940340i	$0.610507\pi$
$620$	−1.38434	+	2.39774i	−0.0555963	+	0.0962956i
$621$	−12.9954	−	22.5086i	−0.521486	−	0.903241i
$622$	8.93973	−	5.16135i	0.358450	−	0.206951i
$623$	−0.679209			−0.0272119
$624$	1.44754	+	25.0189i	0.0579480	+	1.00156i
$625$	−6.55374			−0.262150
$626$	7.61962	−	4.39919i	0.304541	−	0.175827i
$627$	22.8917	+	39.6496i	0.914207	+	1.58345i
$628$	11.4635	−	19.8553i	0.457441	−	0.792312i
$629$			8.07322i			0.321900i
$630$	0.959920	+	0.554210i	0.0382441	+	0.0220803i
$631$	−14.8181	−	8.55525i	−0.589900	−	0.340579i	0.175158	−	0.984540i	$-0.443956\pi$
$631$	−14.8181	−	8.55525i	−0.589900	−	0.340579i	−0.765058	+	0.643961i	$0.777290\pi$
$632$			19.8217i			0.788465i
$633$	−2.26680	+	3.92621i	−0.0900973	+	0.156053i
$634$	0.277966	+	0.481452i	0.0110395	+	0.0191209i
$635$	4.94081	−	2.85258i	0.196070	−	0.113201i
$636$	56.9104			2.25664
$637$	−22.2731	−	11.1967i	−0.882494	−	0.443630i
$638$	−1.63459			−0.0647140
$639$	−5.77609	+	3.33483i	−0.228499	+	0.131924i
$640$	−9.08018	−	15.7273i	−0.358926	−	0.621677i
$641$	10.8847	−	18.8528i	0.429919	−	0.744642i	−0.566946	−	0.823755i	$-0.691875\pi$
$641$	10.8847	−	18.8528i	0.429919	−	0.744642i	0.996866	+	0.0791126i	$0.0252087\pi$
$642$			8.86443i			0.349851i
$643$	40.2923	+	23.2628i	1.58897	+	0.917394i	0.993477	+	0.114036i	$0.0363780\pi$
$643$	40.2923	+	23.2628i	1.58897	+	0.917394i	0.595497	+	0.803358i	$0.296955\pi$
$644$	2.48852	+	1.43674i	0.0980612	+	0.0566157i
$645$		−	51.0099i		−	2.00851i
$646$	4.72399	−	8.18219i	0.185863	−	0.321924i
$647$	−17.3945	−	30.1282i	−0.683850	−	1.18446i	−0.973797	−	0.227420i	$-0.926971\pi$
$647$	−17.3945	−	30.1282i	−0.683850	−	1.18446i	0.289947	−	0.957043i	$-0.406362\pi$
$648$	2.01831	−	1.16527i	0.0792869	−	0.0457763i
$649$	10.9266			0.428908
$650$	−2.03727	+	4.05265i	−0.0799081	+	0.158958i
$651$	−0.811582			−0.0318084
$652$	−26.8737	+	15.5156i	−1.05246	+	0.607636i
$653$	−19.7732	−	34.2483i	−0.773787	−	1.34024i	−0.935474	−	0.353396i	$-0.885027\pi$
$653$	−19.7732	−	34.2483i	−0.773787	−	1.34024i	0.161687	−	0.986842i	$-0.448306\pi$
$654$	3.92397	−	6.79652i	0.153439	−	0.265765i
$655$			0.682343i			0.0266613i
$656$	−9.55894	−	5.51886i	−0.373214	−	0.215475i
$657$	−14.2295	−	8.21538i	−0.555144	−	0.320513i
$658$			1.11193i			0.0433477i
$659$	−16.8107	+	29.1170i	−0.654853	+	1.13424i	0.327078	+	0.944997i	$0.393936\pi$
$659$	−16.8107	+	29.1170i	−0.654853	+	1.13424i	−0.981931	+	0.189241i	$0.939397\pi$
$660$	8.67407	+	15.0239i	0.337638	+	0.584805i
$661$	6.64532	−	3.83668i	0.258473	−	0.149230i	−0.365165	−	0.930943i	$-0.618987\pi$
$661$	6.64532	−	3.83668i	0.258473	−	0.149230i	0.623638	+	0.781713i	$0.285654\pi$
$662$	−5.37764			−0.209008
$663$	−21.1766	+	13.9164i	−0.822429	+	0.540468i
$664$	31.5580			1.22469
$665$	2.95047	−	1.70345i	0.114414	−	0.0660571i
$666$	3.78054	+	6.54808i	0.146493	+	0.253733i
$667$	3.99324	−	6.91649i	0.154619	−	0.267808i
$668$			11.8386i			0.458051i
$669$	51.7651	+	29.8866i	2.00135	+	1.15548i
$670$	−2.23113	−	1.28814i	−0.0861961	−	0.0497654i
$671$			2.96228i			0.114358i
$672$	2.06538	−	3.57734i	0.0796737	−	0.137999i
$673$	23.9212	+	41.4328i	0.922095	+	1.59712i	0.796167	+	0.605077i	$0.206857\pi$
$673$	23.9212	+	41.4328i	0.922095	+	1.59712i	0.125928	+	0.992039i	$0.459809\pi$
$674$	−1.81164	+	1.04595i	−0.0697817	+	0.0402885i
$675$	11.3954			0.438608
$676$	13.4976	+	18.1595i	0.519138	+	0.698443i
$677$	50.0405			1.92321			0.961606	−	0.274434i	$-0.0884905\pi$
$677$	50.0405			1.92321			0.961606	+	0.274434i	$0.0884905\pi$
$678$	−14.5631	+	8.40798i	−0.559291	+	0.322907i
$679$	−1.35796	−	2.35205i	−0.0521137	−	0.0902635i
$680$	3.84689	−	6.66302i	0.147522	−	0.255515i
$681$		−	52.3503i		−	2.00607i
$682$	0.998365	+	0.576406i	0.0382294	+	0.0220717i
$683$	30.5727	+	17.6512i	1.16983	+	0.675403i	0.953641	−	0.300947i	$-0.0973029\pi$
$683$	30.5727	+	17.6512i	1.16983	+	0.675403i	0.216192	+	0.976351i	$0.430636\pi$
$684$			59.3463i			2.26916i
$685$	−8.21538	+	14.2294i	−0.313893	+	0.543679i
$686$	1.03881	+	1.79926i	0.0396618	+	0.0686962i
$687$	6.61802	−	3.82092i	0.252493	−	0.145777i
$688$	−29.0722			−1.10837
$689$	35.5830	−	23.3837i	1.35560	−	0.890848i
$690$	12.6381			0.481125
$691$	−19.0334	+	10.9889i	−0.724065	+	0.418039i	−0.816247	−	0.577703i	$-0.803949\pi$
$691$	−19.0334	+	10.9889i	−0.724065	+	0.418039i	0.0921819	+	0.995742i	$0.470616\pi$
$692$	14.3096	+	24.7849i	0.543969	+	0.942182i
$693$	−1.54767	+	2.68064i	−0.0587911	+	0.101829i
$694$		−	3.65422i		−	0.138712i
$695$	15.0168	+	8.66995i	0.569619	+	0.328870i
$696$	−6.47866	−	3.74046i	−0.245573	−	0.141782i
$697$		−	11.1607i		−	0.422741i
$698$	1.67432	−	2.90002i	0.0633741	−	0.109767i
$699$	−28.4943	−	49.3535i	−1.07775	−	1.86672i
$700$	−1.09106	+	0.629925i	−0.0412383	+	0.0238089i
$701$	27.6218			1.04326			0.521631	−	0.853171i	$-0.325324\pi$
$701$	27.6218			1.04326			0.521631	+	0.853171i	$0.325324\pi$
$702$	−3.80668	+	7.57246i	−0.143674	+	0.285804i
$703$	23.2402			0.876521
$704$	4.75788	−	2.74696i	0.179319	−	0.103530i
$705$	−16.3998	−	28.4053i	−0.617653	−	1.06981i
$706$	−9.39972	+	16.2808i	−0.353763	+	0.612736i
$707$		−	5.16431i		−	0.194224i
$708$	20.1515	+	11.6345i	0.757339	+	0.437250i
$709$	14.2618	+	8.23408i	0.535615	+	0.309237i	0.743300	−	0.668958i	$-0.233260\pi$
$709$	14.2618	+	8.23408i	0.535615	+	0.309237i	−0.207685	+	0.978196i	$0.566593\pi$
$710$		−	1.15821i		−	0.0434668i
$711$	24.2717	−	42.0398i	0.910259	−	1.57662i
$712$	2.20773	+	3.82390i	0.0827383	+	0.143307i
$713$	−4.87794	+	2.81628i	−0.182680	+	0.105470i
$714$	1.04941			0.0392730
$715$	11.5965	+	5.82958i	0.433686	+	0.218014i
$716$	−22.8453			−0.853770
$717$	3.38890	−	1.95658i	0.126561	−	0.0730699i
$718$	−4.23131	−	7.32885i	−0.157911	−	0.273510i
$719$	10.1228	−	17.5333i	0.377518	−	0.653880i	−0.613182	−	0.789941i	$-0.710111\pi$
$719$	10.1228	−	17.5333i	0.377518	−	0.653880i	0.990700	+	0.136061i	$0.0434443\pi$
$720$			18.6345i			0.694467i
$721$	−2.36074	−	1.36297i	−0.0879186	−	0.0507598i
$722$	−15.1716	−	8.75935i	−0.564630	−	0.325989i
$723$			22.5296i			0.837886i
$724$	7.07649	−	12.2568i	0.262996	−	0.455522i
$725$	1.75079	+	3.03246i	0.0650228	+	0.112623i
$726$	−7.18131	+	4.14613i	−0.266523	+	0.153877i
$727$	23.2329			0.861659			0.430830	−	0.902433i	$-0.358221\pi$
$727$	23.2329			0.861659			0.430830	+	0.902433i	$0.358221\pi$
$728$	−0.116318	−	2.01041i	−0.00431103	−	0.0745107i
$729$	−44.0371			−1.63100
$730$	2.47099	−	1.42663i	0.0914555	−	0.0528019i
$731$	−14.6980	−	25.4578i	−0.543627	−	0.941589i
$732$	−3.15418	+	5.46320i	−0.116582	+	0.201926i
$733$		−	26.5546i		−	0.980815i	−0.871493	−	0.490408i	$-0.836848\pi$
$733$		−	26.5546i		−	0.980815i	0.871493	−	0.490408i	$-0.163152\pi$
$734$	7.31447	+	4.22301i	0.269982	+	0.155874i
$735$	−26.3733	−	15.2267i	−0.972795	−	0.561644i
$736$		−	28.6684i		−	1.05673i
$737$	3.59723	−	6.23059i	0.132506	−	0.229507i
$738$	−5.22634	−	9.05228i	−0.192384	−	0.333219i
$739$	−13.0136	+	7.51343i	−0.478715	+	0.276386i	−0.719881	−	0.694098i	$-0.755804\pi$
$739$	−13.0136	+	7.51343i	−0.478715	+	0.276386i	0.241166	+	0.970484i	$0.422470\pi$
$740$	8.80611			0.323719
$741$	40.0608	+	60.9605i	1.47167	+	2.23944i
$742$	−1.76332			−0.0647334
$743$	5.17853	−	2.98983i	0.189982	−	0.109686i	−0.401992	−	0.915643i	$-0.631682\pi$
$743$	5.17853	−	2.98983i	0.189982	−	0.109686i	0.591974	+	0.805957i	$0.298349\pi$
$744$	2.63800	+	4.56915i	0.0967138	+	0.167513i
$745$	−7.62180	+	13.2013i	−0.279241	+	0.483660i
$746$			7.71544i			0.282482i
$747$	−66.9312	−	38.6428i	−2.44889	−	1.41386i
$748$	8.65801	+	4.99870i	0.316568	+	0.182771i
$749$			1.84207i			0.0673079i
$750$	−8.37993	+	14.5145i	−0.305992	+	0.529993i
$751$	−24.8886	−	43.1084i	−0.908199	−	1.57305i	−0.816565	−	0.577254i	$-0.804124\pi$
$751$	−24.8886	−	43.1084i	−0.908199	−	1.57305i	−0.0916344	−	0.995793i	$-0.529209\pi$
$752$	−16.1891	+	9.34679i	−0.590356	+	0.340842i
$753$	57.3332			2.08934
$754$	−2.60000	+	0.150430i	−0.0946863	+	0.00547835i
$755$	24.6707			0.897858
$756$	−2.03868	+	1.17703i	−0.0741459	+	0.0428082i
$757$	17.2963	+	29.9581i	0.628645	+	1.08884i	0.987824	+	0.155576i	$0.0497234\pi$
$757$	17.2963	+	29.9581i	0.628645	+	1.08884i	−0.359179	+	0.933269i	$0.616943\pi$
$758$	−1.22857	+	2.12794i	−0.0446236	+	0.0772904i
$759$			35.2928i			1.28105i
$760$	−19.1807	−	11.0740i	−0.695757	−	0.401695i
$761$	−19.0321	−	10.9882i	−0.689913	−	0.398321i	0.113666	−	0.993519i	$-0.463740\pi$
$761$	−19.0321	−	10.9882i	−0.689913	−	0.398321i	−0.803579	+	0.595198i	$0.797074\pi$
$762$		−	5.05876i		−	0.183259i
$763$	0.815421	−	1.41235i	0.0295202	−	0.0511305i
$764$	−8.14952	−	14.1154i	−0.294839	−	0.510677i
$765$	−16.3177	+	9.42104i	−0.589969	+	0.340619i
$766$	−13.0065			−0.469945
$767$	17.3801	−	1.00557i	0.627558	−	0.0363092i
$768$	−2.65869			−0.0959372
$769$	−1.86912	+	1.07914i	−0.0674021	+	0.0389146i	−0.533322	−	0.845912i	$-0.679057\pi$
$769$	−1.86912	+	1.07914i	−0.0674021	+	0.0389146i	0.465920	+	0.884827i	$0.345723\pi$
$770$	−0.268758	−	0.465503i	−0.00968537	−	0.0167756i
$771$	−25.9137	+	44.8839i	−0.933260	+	1.61645i
$772$		−	38.0652i		−	1.37000i
$773$	−22.8756	−	13.2073i	−0.822780	−	0.475032i	0.0285945	−	0.999591i	$-0.490897\pi$
$773$	−22.8756	−	13.2073i	−0.822780	−	0.475032i	−0.851374	+	0.524559i	$0.824230\pi$
$774$	−23.8428	−	13.7656i	−0.857011	−	0.494796i
$775$		−	2.46953i		−	0.0887082i
$776$	−8.82794	+	15.2904i	−0.316905	+	0.548895i
$777$	1.29067	+	2.23550i	0.0463024	+	0.0801982i
$778$	5.67085	−	3.27406i	0.203310	−	0.117381i
$779$	−32.1280			−1.15111
$780$	15.1797	+	23.0990i	0.543521	+	0.827076i
$781$	3.23438			0.115735
$782$	6.30736	−	3.64156i	0.225551	−	0.130222i
$783$	3.27140	+	5.66622i	0.116910	+	0.202494i
$784$	−8.67816	+	15.0310i	−0.309934	+	0.536822i
$785$		−	20.9543i		−	0.747893i
$786$	0.523974	+	0.302516i	0.0186895	+	0.0107904i
$787$	−36.6069	−	21.1350i	−1.30489	−	0.753381i	−0.323656	−	0.946175i	$-0.604912\pi$
$787$	−36.6069	−	21.1350i	−1.30489	−	0.753381i	−0.981239	+	0.192793i	$0.938245\pi$
$788$			16.1170i			0.574143i
$789$	−14.3671	+	24.8846i	−0.511484	+	0.885916i
$790$	4.21486	+	7.30035i	0.149958	+	0.259735i
$791$	−3.02628	+	1.74722i	−0.107602	+	0.0621240i
$792$	20.1225			0.715021
$793$	0.272618	+	4.71185i	0.00968094	+	0.167323i
$794$	−17.1877			−0.609967
$795$	45.0455	−	26.0070i	1.59760	−	0.922373i
$796$	5.59461	+	9.69015i	0.198296	+	0.343458i
$797$	−24.2570	+	42.0144i	−0.859228	+	1.48823i	0.0134393	+	0.999910i	$0.495722\pi$
$797$	−24.2570	+	42.0144i	−0.859228	+	1.48823i	−0.872667	+	0.488316i	$0.837611\pi$
$798$		−	3.02090i		−	0.106939i
$799$	−16.3695	−	9.45092i	−0.579110	−	0.334349i
$800$	10.8854	+	6.28467i	0.384856	+	0.222197i
$801$		−	10.8135i		−	0.382075i
$802$	−4.96531	+	8.60017i	−0.175331	+	0.303682i
$803$	3.98396	+	6.90042i	0.140591	+	0.243511i
$804$	13.2684	−	7.66052i	0.467941	−	0.270166i
$805$	2.62626			0.0925637
$806$	1.64106	+	0.824960i	0.0578038	+	0.0290580i
$807$	17.0553			0.600375
$808$	−29.0747	+	16.7863i	−1.02285	+	0.590540i
$809$	12.9047	+	22.3516i	0.453705	+	0.785841i	0.998613	−	0.0526555i	$-0.0167685\pi$
$809$	12.9047	+	22.3516i	0.453705	+	0.785841i	−0.544907	+	0.838496i	$0.683435\pi$
$810$	0.495564	−	0.858343i	0.0174124	−	0.0301591i
$811$		−	8.08164i		−	0.283785i	−0.989882	−	0.141892i	$-0.954681\pi$
$811$		−	8.08164i		−	0.283785i	0.989882	−	0.141892i	$-0.0453187\pi$
$812$	−0.626447	−	0.361680i	−0.0219840	−	0.0126925i
$813$	−51.1888	−	29.5539i	−1.79527	−	1.03650i
$814$		−	3.66666i		−	0.128516i
$815$	−14.1806	+	24.5616i	−0.496726	+	0.860355i
$816$	8.82119	+	15.2787i	0.308803	+	0.534863i
$817$	−73.2847	+	42.3109i	−2.56391	+	1.48027i
$818$	−10.4493			−0.365352
$819$	−2.21505	+	4.40630i	−0.0774000	+	0.153968i
$820$	−12.1739			−0.425129
$821$	4.79049	−	2.76579i	0.167189	−	0.0965268i	−0.414070	−	0.910245i	$-0.635893\pi$
$821$	4.79049	−	2.76579i	0.167189	−	0.0965268i	0.581260	+	0.813718i	$0.302560\pi$
$822$	7.28457	+	12.6172i	0.254078	+	0.440077i
$823$	5.64137	−	9.77114i	0.196646	−	0.340601i	−0.750793	−	0.660538i	$-0.770328\pi$
$823$	5.64137	−	9.77114i	0.196646	−	0.340601i	0.947439	+	0.319937i	$0.103662\pi$
$824$			17.7211i			0.617343i
$825$	−13.4007	−	7.73688i	−0.466551	−	0.269364i
$826$	−0.624376	−	0.360483i	−0.0217248	−	0.0125428i
$827$		−	15.9781i		−	0.555612i	−0.960637	−	0.277806i	$-0.910393\pi$
$827$		−	15.9781i		−	0.555612i	0.960637	−	0.277806i	$-0.0896073\pi$
$828$	−22.8740	+	39.6189i	−0.794925	+	1.37685i
$829$	4.36246	+	7.55601i	0.151515	+	0.262431i	0.931784	−	0.363012i	$-0.118252\pi$
$829$	4.36246	+	7.55601i	0.151515	+	0.262431i	−0.780270	+	0.625443i	$0.784918\pi$
$830$	11.6228	−	6.71044i	0.403434	−	0.232923i
$831$	0.545564			0.0189254
$832$	7.31515	−	4.80722i	0.253607	−	0.166661i
$833$	−17.5497			−0.608060
$834$	13.3154	−	7.68763i	0.461074	−	0.266201i
$835$	5.41005	+	9.37047i	0.187222	+	0.324279i
$836$	14.3897	−	24.9236i	0.497677	−	0.862002i
$837$		−	4.61438i		−	0.159496i
$838$	−5.95799	−	3.43985i	−0.205815	−	0.118827i
$839$	13.9232	+	8.03854i	0.480681	+	0.277521i	0.720700	−	0.693247i	$-0.243820\pi$
$839$	13.9232	+	8.03854i	0.480681	+	0.277521i	−0.240019	+	0.970768i	$0.577154\pi$
$840$		−	2.46002i		−	0.0848786i
$841$	13.4948	−	23.3736i	0.465337	−	0.805987i
$842$	−2.30613	−	3.99434i	−0.0794746	−	0.137654i
$843$	−29.7962	+	17.2028i	−1.02624	+	0.592497i
$844$	2.84981			0.0980944
$845$	18.9821	+	8.20539i	0.653004	+	0.282274i
$846$	−17.7028			−0.608633
$847$	−1.49231	+	0.861587i	−0.0512765	+	0.0296045i
$848$	−14.8222	−	25.6729i	−0.508998	−	0.881610i
$849$	25.4759	−	44.1256i	0.874332	−	1.51439i
$850$			3.19320i			0.109526i
$851$	15.5149	+	8.95752i	0.531843	+	0.307060i
$852$	5.96500	+	3.44390i	0.204358	+	0.117986i
$853$			17.8246i			0.610304i	0.952304	+	0.305152i	$0.0987073\pi$
$853$			17.8246i			0.610304i	−0.952304	+	0.305152i	$0.901293\pi$
$854$	0.0977294	−	0.169272i	0.00334423	−	0.00579238i
$855$	27.1202	+	46.9735i	0.927490	+	1.60646i
$856$	10.3708	−	5.98756i	0.354465	−	0.204651i
$857$	−19.0093			−0.649347			−0.324673	−	0.945826i	$-0.605254\pi$
$857$	−19.0093			−0.649347			−0.324673	+	0.945826i	$0.605254\pi$
$858$	9.61788	−	6.32049i	0.328349	−	0.215778i
$859$	12.6135			0.430366			0.215183	−	0.976574i	$-0.430965\pi$
$859$	12.6135			0.430366			0.215183	+	0.976574i	$0.430965\pi$
$860$	−27.7688	+	16.0323i	−0.946909	+	0.546698i
$861$	−1.78426	−	3.09043i	−0.0608075	−	0.105322i
$862$	6.07204	−	10.5171i	0.206814	−	0.358213i
$863$		−	32.5106i		−	1.10667i	−0.832958	−	0.553337i	$-0.813354\pi$
$863$		−	32.5106i		−	1.10667i	0.832958	−	0.553337i	$-0.186646\pi$
$864$	20.3396	+	11.7430i	0.691966	+	0.399507i
$865$	22.6525	+	13.0784i	0.770209	+	0.444680i
$866$			13.6974i			0.465457i
$867$	14.6158	−	25.3153i	0.496378	−	0.859751i
$868$	0.255079	+	0.441809i	0.00865794	+	0.0149960i
$869$	−20.3867	+	11.7703i	−0.691573	+	0.399280i
$870$	−3.18146			−0.107862
$871$	5.14841	−	10.2415i	0.174447	−	0.347020i
$872$	−10.6019			−0.359027
$873$	37.4463	−	21.6196i	1.26736	−	0.731713i
$874$	−10.4829	−	18.1569i	−0.354588	−	0.614165i
$875$	−1.74139	+	3.01618i	−0.0588698	+	0.101965i
$876$			16.9681i			0.573301i
$877$	−36.2255	−	20.9148i	−1.22325	−	0.706242i	−0.257638	−	0.966241i	$-0.582944\pi$
$877$	−36.2255	−	20.9148i	−1.22325	−	0.706242i	−0.965609	+	0.259999i	$0.916278\pi$
$878$	−1.07209	−	0.618973i	−0.0361814	−	0.0208893i
$879$		−	13.6474i		−	0.460315i
$880$	4.51830	−	7.82592i	0.152312	−	0.263812i
$881$	−12.3029	−	21.3092i	−0.414495	−	0.717926i	0.580880	−	0.813989i	$-0.302708\pi$
$881$	−12.3029	−	21.3092i	−0.414495	−	0.717926i	−0.995375	+	0.0960626i	$0.969375\pi$
$882$	−14.2343	+	8.21819i	−0.479294	+	0.276721i
$883$	22.6833			0.763353			0.381676	−	0.924296i	$-0.375347\pi$
$883$	22.6833			0.763353			0.381676	+	0.924296i	$0.375347\pi$
$884$	14.2316	+	7.15421i	0.478659	+	0.240622i
$885$	21.2670			0.714881
$886$	8.24320	−	4.75921i	0.276936	−	0.159889i
$887$	5.37723	+	9.31364i	0.180550	+	0.312721i	0.942068	−	0.335422i	$-0.108879\pi$
$887$	5.37723	+	9.31364i	0.180550	+	0.312721i	−0.761518	+	0.648144i	$0.775546\pi$
$888$	8.39049	−	14.5328i	0.281566	−	0.487687i
$889$		−	1.05124i		−	0.0352573i
$890$	1.62622	+	0.938898i	0.0545110	+	0.0314719i
$891$	2.39698	+	1.38390i	0.0803019	+	0.0463623i
$892$		−	37.5732i		−	1.25804i
$893$	−27.2062	+	47.1224i	−0.910419	+	1.57689i
$894$	6.75824	+	11.7056i	0.226029	+	0.391495i
$895$	−18.0824	+	10.4399i	−0.604429	+	0.348967i
$896$	−3.34624			−0.111790
$897$	3.24798	+	56.1372i	0.108447	+	1.87437i
$898$	−1.45460			−0.0485405
$899$	1.22795	−	0.708957i	0.0409544	−	0.0236450i
$900$	−10.0288	−	17.3705i	−0.334295	−	0.579015i
$901$	14.9874	−	25.9589i	0.499301	−	0.864815i
$902$			5.06891i			0.168776i
$903$	−8.13988	−	4.69956i	−0.270878	−	0.156392i
$904$	19.6735	+	11.3585i	0.654331	+	0.377778i
$905$		−	12.9353i		−	0.429984i
$906$	10.9377	−	18.9447i	0.363382	−	0.629396i
$907$	−13.0509	−	22.6048i	−0.433348	−	0.750580i	0.563811	−	0.825904i	$-0.309334\pi$
$907$	−13.0509	−	22.6048i	−0.433348	−	0.750580i	−0.997159	+	0.0753232i	$0.976001\pi$
$908$	−28.4985	+	16.4536i	−0.945755	+	0.546032i
$909$	82.2193			2.72704
$910$	−0.470330	−	0.715701i	−0.0155913	−	0.0237253i
$911$	−18.5256			−0.613781			−0.306890	−	0.951745i	$-0.599288\pi$
$911$	−18.5256			−0.613781			−0.306890	+	0.951745i	$0.599288\pi$
$912$	43.9826	−	25.3934i	1.45641	−	0.840858i
$913$	18.7394	+	32.4576i	0.620183	+	1.07419i
$914$	7.11991	−	12.3320i	0.235506	−	0.407908i
$915$			5.76561i			0.190605i
$916$	−4.16007	−	2.40182i	−0.137453	−	0.0793582i
$917$	0.108884	+	0.0628644i	0.00359568	+	0.00207597i
$918$			5.96657i			0.196926i
$919$	28.3799	−	49.1554i	0.936166	−	1.62149i	0.163625	−	0.986523i	$-0.447681\pi$
$919$	28.3799	−	49.1554i	0.936166	−	1.62149i	0.772541	−	0.634965i	$-0.218985\pi$
$920$	−8.53653	−	14.7857i	−0.281441	−	0.487470i
$921$	−79.2132	+	45.7337i	−2.61016	+	1.50698i
$922$	−0.175583			−0.00578252
$923$	5.14464	−	0.297658i	0.169338	−	0.00979753i
$924$	3.19658			0.105160
$925$	−6.80233	+	3.92733i	−0.223659	+	0.129130i
$926$	−4.36712	−	7.56408i	−0.143513	−	0.248571i
$927$	21.6995	−	37.5846i	0.712704	−	1.23444i
$928$			7.21684i			0.236905i
$929$	27.9978	+	16.1645i	0.918578	+	0.530341i	0.883181	−	0.469032i	$-0.155397\pi$
$929$	27.9978	+	16.1645i	0.918578	+	0.530341i	0.0353965	+	0.999373i	$0.488731\pi$
$930$	1.94316	+	1.12188i	0.0637186	+	0.0367879i
$931$			50.5199i			1.65572i
$932$	−17.9114	+	31.0234i	−0.586707	+	1.01621i
$933$	28.0534	+	48.5900i	0.918428	+	1.59076i
$934$	12.1733	−	7.02827i	0.398323	−	0.229972i
$935$	9.13726			0.298820
$936$	32.0071	−	1.85186i	1.04618	−	0.0605300i
$937$	32.1331			1.04974			0.524871	−	0.851182i	$-0.324114\pi$
$937$	32.1331			1.04974			0.524871	+	0.851182i	$0.324114\pi$
$938$	−0.411110	+	0.237354i	−0.0134232	+	0.00774989i
$939$	23.9109	+	41.4148i	0.780301	+	1.35152i
$940$	−10.3089	+	17.8555i	−0.336238	+	0.582382i
$941$			48.4681i			1.58001i	0.613098	+	0.790007i	$0.289923\pi$
$941$			48.4681i			1.58001i	−0.613098	+	0.790007i	$0.710077\pi$
$942$	−16.0909	−	9.29010i	−0.524271	−	0.302688i
$943$	−21.4483	−	12.3832i	−0.698452	−	0.403251i
$944$		−	12.1207i		−	0.394496i
$945$	−1.07576	+	1.86327i	−0.0349945	+	0.0606123i
$946$	6.67550	+	11.5623i	0.217039	+	0.375923i
$947$	−26.5387	+	15.3221i	−0.862393	+	0.497903i	−0.864813	−	0.502094i	$-0.832563\pi$
$947$	−26.5387	+	15.3221i	−0.862393	+	0.497903i	0.00241987	+	0.999997i	$0.499230\pi$
$948$	−50.1310			−1.62818
$949$	6.97198	+	10.6093i	0.226320	+	0.344391i
$950$	9.19220			0.298234
$951$	−2.61683	+	1.51083i	−0.0848565	+	0.0489919i
$952$	−0.708831	−	1.22773i	−0.0229733	−	0.0397910i
$953$	0.916140	−	1.58680i	0.0296767	−	0.0514015i	−0.850806	−	0.525481i	$-0.823886\pi$
$953$	0.916140	−	1.58680i	0.0296767	−	0.0514015i	0.880482	+	0.474079i	$0.157219\pi$
$954$		−	28.0732i		−	0.908903i
$955$	−12.9009	−	7.44836i	−0.417465	−	0.241023i
$956$	−2.13025	−	1.22990i	−0.0688972	−	0.0397778i
$957$		−	8.88445i		−	0.287194i
$958$	−6.28944	+	10.8936i	−0.203202	+	0.351957i
$959$	1.51377	+	2.62193i	0.0488822	+	0.0846664i
$960$	9.26045	−	5.34652i	0.298880	−	0.172558i
$961$	−1.00000			−0.0322581
$962$	−0.337441	−	5.83224i	−0.0108795	−	0.188039i
$963$	−29.3271			−0.945052
$964$	12.2647	−	7.08102i	0.395019	−	0.228064i
$965$	−17.3951	−	30.1292i	−0.559969	−	0.969894i
$966$	1.16435	−	2.01672i	0.0374624	−	0.0648869i
$967$			19.2920i			0.620389i	0.950673	+	0.310194i	$0.100394\pi$
$967$			19.2920i			0.620389i	−0.950673	+	0.310194i	$0.899606\pi$
$968$	9.70136	+	5.60108i	0.311814	+	0.180026i
$969$	44.4726	+	25.6762i	1.42866	+	0.824840i
$970$			7.50864i			0.241088i
$971$	16.1618	−	27.9930i	0.518656	−	0.898338i	−0.481109	−	0.876661i	$-0.659766\pi$
$971$	16.1618	−	27.9930i	0.518656	−	0.898338i	0.999765	−	0.0216773i	$-0.00690064\pi$
$972$	14.9940	+	25.9704i	0.480933	+	0.833001i
$973$	2.76700	−	1.59753i	0.0887060	−	0.0512144i
$974$	−10.4244			−0.334021
$975$	−22.0273	−	11.0731i	−0.705438	−	0.354624i
$976$	3.28601			0.105183
$977$	−13.0912	+	7.55822i	−0.418825	+	0.241809i	−0.694575	−	0.719421i	$-0.744407\pi$
$977$	−13.0912	+	7.55822i	−0.418825	+	0.241809i	0.275749	+	0.961230i	$0.411074\pi$
$978$	12.5740	+	21.7787i	0.402071	+	0.696408i
$979$	−2.62194	+	4.54133i	−0.0837975	+	0.145141i
$980$			19.1429i			0.611496i
$981$	22.4856	+	12.9821i	0.717909	+	0.414485i
$982$	12.7578	+	7.36572i	0.407118	+	0.235049i
$983$			12.8886i			0.411082i	0.978648	+	0.205541i	$0.0658955\pi$
$983$			12.8886i			0.411082i	−0.978648	+	0.205541i	$0.934105\pi$
$984$	−11.5993	+	20.0906i	−0.369772	+	0.640463i
$985$	7.36516	+	12.7568i	0.234674	+	0.406466i
$986$	−1.58779	+	0.916709i	−0.0505654	+	0.0291939i
$987$	−6.04368			−0.192373
$988$	20.5947	−	40.9681i	0.655204	−	1.30337i
$989$	−65.2320			−2.07426
$990$	7.41112	−	4.27881i	0.235541	−	0.135990i
$991$	15.4653	+	26.7866i	0.491270	+	0.850905i	0.999949	−	0.0100512i	$-0.00319946\pi$
$991$	15.4653	+	26.7866i	0.491270	+	0.850905i	−0.508679	+	0.860956i	$0.669866\pi$
$992$	2.54488	−	4.40786i	0.0808001	−	0.139950i
$993$		−	29.2290i		−	0.927554i
$994$	−0.184820	−	0.106706i	−0.00586214	−	0.00338451i
$995$	8.85644	+	5.11327i	0.280768	+	0.162102i
$996$			79.8132i			2.52898i
$997$	−17.4017	+	30.1407i	−0.551119	+	0.954566i	0.447075	+	0.894496i	$0.352466\pi$
$997$	−17.4017	+	30.1407i	−0.551119	+	0.954566i	−0.998194	+	0.0600696i	$0.980868\pi$
$998$	−6.73384	−	11.6634i	−0.213156	−	0.369197i
$999$	−12.7103	+	7.33830i	−0.402136	+	0.232173i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.r.a.218.16	✓	68
13.2	odd	12		5239.2.a.r.1.14		34
13.4	even	6	inner	403.2.r.a.342.16	yes	68
13.11	odd	12		5239.2.a.q.1.21		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.r.a.218.16	✓	68	1.1	even	1	trivial
403.2.r.a.342.16	yes	68	13.4	even	6	inner
5239.2.a.q.1.21		34	13.11	odd	12
5239.2.a.r.1.14		34	13.2	odd	12

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.441172 + 0.254711i) q^{2} +(-1.38443 - 2.39789i) q^{3} +(-0.870245 + 1.50731i) q^{4} +1.59074i q^{5} +(1.22154 + 0.705256i) q^{6} +(0.253842 + 0.146556i) q^{7} -1.90549i q^{8} +(-2.33327 + 4.04134i) q^{9} +(-0.405179 - 0.701791i) q^{10} +(1.95980 - 1.13149i) q^{11} +4.81916 q^{12} +(3.01316 - 1.98013i) q^{13} -0.149317 q^{14} +(3.81444 - 2.20227i) q^{15} +(-1.25514 - 2.17397i) q^{16} +(1.26912 - 2.19819i) q^{17} -2.37723i q^{18} +(-6.32788 - 3.65340i) q^{19} +(-2.39774 - 1.38434i) q^{20} -0.811582i q^{21} +(-0.576406 + 0.998365i) q^{22} +(-2.81628 - 4.87794i) q^{23} +(-4.56915 + 2.63800i) q^{24} +2.46953 q^{25} +(-0.824960 + 1.64106i) q^{26} +4.61438 q^{27} +(-0.441809 + 0.255079i) q^{28} +(0.708957 + 1.22795i) q^{29} +(-1.12188 + 1.94316i) q^{30} -1.00000i q^{31} +(4.40786 + 2.54488i) q^{32} +(-5.42640 - 3.13293i) q^{33} +1.29304i q^{34} +(-0.233133 + 0.403798i) q^{35} +(-4.06103 - 7.03390i) q^{36} +(-2.75450 + 1.59031i) q^{37} +3.72224 q^{38} +(-8.91962 - 4.48389i) q^{39} +3.03114 q^{40} +(3.80791 - 2.19850i) q^{41} +(0.206718 + 0.358047i) q^{42} +(5.79062 - 10.0296i) q^{43} +3.93870i q^{44} +(-6.42873 - 3.71163i) q^{45} +(2.48492 + 1.43467i) q^{46} -7.44680i q^{47} +(-3.47530 + 6.01940i) q^{48} +(-3.45704 - 5.98777i) q^{49} +(-1.08949 + 0.629016i) q^{50} -7.02803 q^{51} +(0.362477 + 6.26495i) q^{52} +11.8092 q^{53} +(-2.03573 + 1.17533i) q^{54} +(1.79991 + 3.11754i) q^{55} +(0.279260 - 0.483692i) q^{56} +20.2315i q^{57} +(-0.625543 - 0.361158i) q^{58} +(4.18154 + 2.41421i) q^{59} +7.66604i q^{60} +(-0.654509 + 1.13364i) q^{61} +(0.254711 + 0.441172i) q^{62} +(-1.18456 + 0.683907i) q^{63} +2.42774 q^{64} +(3.14987 + 4.79316i) q^{65} +3.19196 q^{66} +(2.75326 - 1.58960i) q^{67} +(2.20890 + 3.82593i) q^{68} +(-7.79785 + 13.5063i) q^{69} -0.237525i q^{70} +(1.23777 + 0.714626i) q^{71} +(7.70070 + 4.44600i) q^{72} +3.52098i q^{73} +(0.810138 - 1.40320i) q^{74} +(-3.41888 - 5.92168i) q^{75} +(11.0136 - 6.35871i) q^{76} +0.663306 q^{77} +(5.07718 - 0.293755i) q^{78} -10.4024 q^{79} +(3.45823 - 1.99661i) q^{80} +(0.611537 + 1.05921i) q^{81} +(-1.11996 + 1.93983i) q^{82} +16.5617i q^{83} +(1.22330 + 0.706275i) q^{84} +(3.49676 + 2.01885i) q^{85} +5.89973i q^{86} +(1.96300 - 3.40001i) q^{87} +(-2.15604 - 3.73437i) q^{88} +(-2.00679 + 1.15862i) q^{89} +3.78157 q^{90} +(1.05506 - 0.0610438i) q^{91} +9.80341 q^{92} +(-2.39789 + 1.38443i) q^{93} +(1.89678 + 3.28532i) q^{94} +(5.81163 - 10.0660i) q^{95} -14.0928i q^{96} +(-8.02444 - 4.63291i) q^{97} +(3.05030 + 1.76109i) q^{98} +10.5603i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 32 q^{4} - 34 q^{9} + 8 q^{10} - 12 q^{11} - 16 q^{12} + 6 q^{13} - 8 q^{14} - 36 q^{16} - 6 q^{17} + 12 q^{19} - 12 q^{20} - 20 q^{22} - 8 q^{23} + 48 q^{24} - 72 q^{25} - 12 q^{27} - 6 q^{28} + 32 q^{30}+ \cdots - 168 q^{98}+O(q^{100}) \) 68 * q + 32 * q^4 - 34 * q^9 + 8 * q^10 - 12 * q^11 - 16 * q^12 + 6 * q^13 - 8 * q^14 - 36 * q^16 - 6 * q^17 + 12 * q^19 - 12 * q^20 - 20 * q^22 - 8 * q^23 + 48 * q^24 - 72 * q^25 - 12 * q^27 - 6 * q^28 + 32 * q^30 + 6 * q^33 + 30 * q^35 + 40 * q^36 - 42 * q^37 - 36 * q^38 - 14 * q^39 + 8 * q^40 + 18 * q^41 - 16 * q^42 + 12 * q^43 + 60 * q^45 + 30 * q^46 - 46 * q^48 + 22 * q^49 + 56 * q^51 + 20 * q^53 - 114 * q^54 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 6 * q^59 + 6 * q^61 - 8 * q^62 - 30 * q^63 + 24 * q^64 + 24 * q^65 + 8 * q^66 - 48 * q^67 + 58 * q^68 - 28 * q^69 - 30 * q^71 + 72 * q^72 + 8 * q^74 - 4 * q^75 - 12 * q^76 - 20 * q^77 + 26 * q^78 + 16 * q^79 + 42 * q^80 - 58 * q^81 - 42 * q^82 - 72 * q^84 + 30 * q^85 - 20 * q^87 + 64 * q^88 + 18 * q^89 + 52 * q^90 - 22 * q^91 + 48 * q^92 + 8 * q^94 - 32 * q^95 - 168 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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