LMFDB - Embedded newform 859.2.f.a.100.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [859,2,Mod(100,859)] 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("859.100"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(859, base_ring=CyclotomicField(26)) chi = DirichletCharacter(H, H._module([22])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	859.f (of order $13$, degree $12$, 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:	$6.85914953363$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$70$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			100.5
Character	$\chi$	$=$	859.100
Dual form			859.2.f.a.524.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.15874 + 1.13300i) q^{2} +(-0.194366 + 0.281587i) q^{3} +(2.24036 - 3.24573i) q^{4} +(0.305534 + 0.442643i) q^{5} +(0.100548 - 0.828091i) q^{6} +(0.433769 + 3.57241i) q^{7} +(-0.571237 + 4.70456i) q^{8} +(1.02230 + 2.69559i) q^{9} +(-1.16108 - 0.609383i) q^{10} +(0.341319 + 2.81102i) q^{11} +(0.478506 + 1.26172i) q^{12} -4.25487 q^{13} +(-4.98392 - 7.22045i) q^{14} -0.184028 q^{15} +(-1.30008 - 3.42802i) q^{16} +(0.361157 - 0.0890173i) q^{17} +(-5.26097 - 4.66082i) q^{18} +6.16228 q^{19} +2.12120 q^{20} +(-1.09025 - 0.572210i) q^{21} +(-3.92169 - 5.68155i) q^{22} +(2.87074 + 1.50668i) q^{23} +(-1.21372 - 1.07526i) q^{24} +(1.67044 - 4.40460i) q^{25} +(9.18516 - 4.82075i) q^{26} +(-1.95438 - 0.481711i) q^{27} +(12.5669 + 6.59560i) q^{28} +(-1.38712 + 3.65753i) q^{29} +(0.397269 - 0.208503i) q^{30} +(1.56209 + 1.38389i) q^{31} +(-0.404091 - 0.357993i) q^{32} +(-0.857888 - 0.450254i) q^{33} +(-0.678790 + 0.601355i) q^{34} +(-1.44877 + 1.28350i) q^{35} +(11.0395 + 2.72098i) q^{36} +(-1.12904 - 2.97703i) q^{37} +(-13.3028 + 6.98184i) q^{38} +(0.827000 - 1.19812i) q^{39} +(-2.25697 + 1.18455i) q^{40} +(-4.61584 + 6.68720i) q^{41} +3.00189 q^{42} +1.45920 q^{43} +(9.88847 + 5.18987i) q^{44} +(-0.880833 + 1.27611i) q^{45} -7.90426 q^{46} +(-3.20711 + 2.84125i) q^{47} +(1.21798 + 0.300205i) q^{48} +(-5.77735 + 1.42399i) q^{49} +(1.38433 + 11.4010i) q^{50} +(-0.0451305 + 0.118999i) q^{51} +(-9.53245 + 13.8101i) q^{52} +(-1.10464 - 0.272270i) q^{53} +(4.76478 - 1.17441i) q^{54} +(-1.13999 + 1.00994i) q^{55} -17.0544 q^{56} +(-1.19774 + 1.73522i) q^{57} +(-1.14953 - 9.46727i) q^{58} +(-1.71991 + 0.902679i) q^{59} +(-0.412290 + 0.597305i) q^{60} +9.12747 q^{61} +(-4.94009 - 1.21762i) q^{62} +(-9.18629 + 4.82134i) q^{63} +(8.39740 + 2.06977i) q^{64} +(-1.30001 - 1.88338i) q^{65} +2.36210 q^{66} +(-3.30205 - 8.70679i) q^{67} +(0.520198 - 1.37165i) q^{68} +(-0.982237 + 0.515518i) q^{69} +(1.67332 - 4.41219i) q^{70} +(0.532254 + 0.131189i) q^{71} +(-13.2655 + 3.26966i) q^{72} +(0.690438 - 5.68627i) q^{73} +(5.81027 + 5.14745i) q^{74} +(0.915602 + 1.32648i) q^{75} +(13.8058 - 20.0011i) q^{76} +(-9.89404 + 2.43866i) q^{77} +(-0.427820 + 3.52342i) q^{78} +(1.72526 - 2.49947i) q^{79} +(1.12017 - 1.62285i) q^{80} +(-5.95820 + 5.27851i) q^{81} +(2.38784 - 19.6657i) q^{82} +(0.382100 + 3.14688i) q^{83} +(-4.29981 + 2.25671i) q^{84} +(0.149749 + 0.132666i) q^{85} +(-3.15005 + 1.65327i) q^{86} +(-0.760306 - 1.10149i) q^{87} -13.4196 q^{88} +(-9.11848 - 2.24750i) q^{89} +(0.455669 - 3.75277i) q^{90} +(-1.84563 - 15.2001i) q^{91} +(11.3218 - 5.94213i) q^{92} +(-0.693302 + 0.170884i) q^{93} +(3.70420 - 9.76718i) q^{94} +(1.88279 + 2.72769i) q^{95} +(0.179348 - 0.0442053i) q^{96} +(-13.3940 + 3.30133i) q^{97} +(10.8584 - 9.61973i) q^{98} +(-7.22841 + 3.79376i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 10 q^{2} - 5 q^{3} - 74 q^{4} - 20 q^{5} + 5 q^{6} - 3 q^{7} + 2 q^{8} - 69 q^{9} + 7 q^{10} - 25 q^{11} - 58 q^{12} - 10 q^{13} + 9 q^{14} - 148 q^{15} - 40 q^{16} - q^{17} + 5 q^{18} - 38 q^{19}+ \cdots - 121 q^{99}+O(q^{100}) $ 840 * q - 10 * q^2 - 5 * q^3 - 74 * q^4 - 20 * q^5 + 5 * q^6 - 3 * q^7 + 2 * q^8 - 69 * q^9 + 7 * q^10 - 25 * q^11 - 58 * q^12 - 10 * q^13 + 9 * q^14 - 148 * q^15 - 40 * q^16 - q^17 + 5 * q^18 - 38 * q^19 - 92 * q^20 + 17 * q^21 + 15 * q^22 - 18 * q^23 + 27 * q^24 - 66 * q^25 + 7 * q^26 - 17 * q^27 + 29 * q^28 + 7 * q^29 - 5 * q^30 + 27 * q^31 + 20 * q^32 + 49 * q^33 + 5 * q^34 + 43 * q^35 + 32 * q^36 - 86 * q^37 - 13 * q^38 + 2 * q^39 + 59 * q^40 + 9 * q^41 + 72 * q^42 + 40 * q^43 + 44 * q^44 - 49 * q^45 + 52 * q^46 - 22 * q^47 + 159 * q^48 - 11 * q^49 - 73 * q^50 + 65 * q^51 + 73 * q^52 + 25 * q^53 + 11 * q^54 + 81 * q^55 - 302 * q^56 - 192 * q^57 + 27 * q^58 - 23 * q^59 - 62 * q^60 + 26 * q^61 + 79 * q^62 + 93 * q^63 - 78 * q^64 + 10 * q^65 + 74 * q^66 + 65 * q^67 + 69 * q^68 - 57 * q^69 + 19 * q^70 + 21 * q^71 - 234 * q^72 - 95 * q^73 + 25 * q^74 - 120 * q^75 - 18 * q^76 - 95 * q^77 - 3 * q^78 - 13 * q^79 - 244 * q^80 - 95 * q^81 - 19 * q^82 - 16 * q^83 - 48 * q^84 + 99 * q^85 + 45 * q^86 - 123 * q^87 + 110 * q^88 + 49 * q^89 + 217 * q^90 - 82 * q^91 + 3 * q^92 - 57 * q^93 - 77 * q^94 - 12 * q^95 + 56 * q^96 + 5 * q^97 + 5 * q^98 - 121 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/859\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{13}\right)$

Coefficient data

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

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

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

$2$	−2.15874	+	1.13300i	−1.52646	+	0.801149i	−0.998832	−	0.0483249i	$-0.984612\pi$
$2$	−2.15874	+	1.13300i	−1.52646	+	0.801149i	−0.527630	+	0.849474i	$0.676919\pi$
$3$	−0.194366	+	0.281587i	−0.112217	+	0.162575i	−0.875068	−	0.484000i	$-0.839184\pi$
$3$	−0.194366	+	0.281587i	−0.112217	+	0.162575i	0.762851	+	0.646574i	$0.223799\pi$
$4$	2.24036	−	3.24573i	1.12018	−	1.62286i
$5$	0.305534	+	0.442643i	0.136639	+	0.197956i	0.885330	−	0.464964i	$-0.153933\pi$
$5$	0.305534	+	0.442643i	0.136639	+	0.197956i	−0.748691	+	0.662919i	$0.769317\pi$
$6$	0.100548	−	0.828091i	0.0410487	−	0.338067i
$7$	0.433769	+	3.57241i	0.163949	+	1.35024i	0.809767	+	0.586752i	$0.199593\pi$
$7$	0.433769	+	3.57241i	0.163949	+	1.35024i	−0.645818	+	0.763492i	$0.723483\pi$
$8$	−0.571237	+	4.70456i	−0.201963	+	1.66331i
$9$	1.02230	+	2.69559i	0.340767	+	0.898529i
$10$	−1.16108	−	0.609383i	−0.367166	−	0.192704i
$11$	0.341319	+	2.81102i	0.102912	+	0.847553i	0.949166	+	0.314775i	$0.101929\pi$
$11$	0.341319	+	2.81102i	0.102912	+	0.847553i	−0.846255	+	0.532778i	$0.821148\pi$
$12$	0.478506	+	1.26172i	0.138133	+	0.364226i
$13$	−4.25487			−1.18009			−0.590044	−	0.807371i	$-0.700890\pi$
$13$	−4.25487			−1.18009			−0.590044	+	0.807371i	$0.700890\pi$
$14$	−4.98392	−	7.22045i	−1.33201	−	1.92975i
$15$	−0.184028			−0.0475158
$16$	−1.30008	−	3.42802i	−0.325019	−	0.857006i
$17$	0.361157	−	0.0890173i	0.0875935	−	0.0215899i	−0.195275	−	0.980748i	$-0.562560\pi$
$17$	0.361157	−	0.0890173i	0.0875935	−	0.0215899i	0.282869	+	0.959159i	$0.408714\pi$
$18$	−5.26097	−	4.66082i	−1.24002	−	1.09857i
$19$	6.16228			1.41372			0.706862	−	0.707351i	$-0.250110\pi$
$19$	6.16228			1.41372			0.706862	+	0.707351i	$0.250110\pi$
$20$	2.12120			0.474316
$21$	−1.09025	−	0.572210i	−0.237913	−	0.124866i
$22$	−3.92169	−	5.68155i	−0.836107	−	1.21131i
$23$	2.87074	+	1.50668i	0.598591	+	0.314165i	0.736666	−	0.676257i	$-0.236399\pi$
$23$	2.87074	+	1.50668i	0.598591	+	0.314165i	−0.138075	+	0.990422i	$0.544091\pi$
$24$	−1.21372	−	1.07526i	−0.247749	−	0.219486i
$25$	1.67044	−	4.40460i	0.334089	−	0.880919i
$26$	9.18516	−	4.82075i	1.80136	−	0.945426i
$27$	−1.95438	−	0.481711i	−0.376121	−	0.0927054i
$28$	12.5669	+	6.59560i	2.37491	+	1.24645i
$29$	−1.38712	+	3.65753i	−0.257581	+	0.679186i	0.742376	+	0.669983i	$0.233699\pi$
$29$	−1.38712	+	3.65753i	−0.257581	+	0.679186i	−0.999958	+	0.00920312i	$0.997071\pi$
$30$	0.397269	−	0.208503i	0.0725311	−	0.0380673i
$31$	1.56209	+	1.38389i	0.280559	+	0.248554i	0.791653	−	0.610971i	$-0.209221\pi$
$31$	1.56209	+	1.38389i	0.280559	+	0.248554i	−0.511093	+	0.859525i	$0.670759\pi$
$32$	−0.404091	−	0.357993i	−0.0714338	−	0.0632848i
$33$	−0.857888	−	0.450254i	−0.149339	−	0.0783792i
$34$	−0.678790	+	0.601355i	−0.116411	+	0.103132i
$35$	−1.44877	+	1.28350i	−0.244887	+	0.216951i
$36$	11.0395	+	2.72098i	1.83991	+	0.453497i
$37$	−1.12904	−	2.97703i	−0.185613	−	0.489421i	0.809619	−	0.586955i	$-0.199674\pi$
$37$	−1.12904	−	2.97703i	−0.185613	−	0.489421i	−0.995232	+	0.0975344i	$0.968904\pi$
$38$	−13.3028	+	6.98184i	−2.15800	+	1.13260i
$39$	0.827000	−	1.19812i	0.132426	−	0.191852i
$40$	−2.25697	+	1.18455i	−0.356859	+	0.187294i
$41$	−4.61584	+	6.68720i	−0.720873	+	1.04436i	0.275667	+	0.961253i	$0.411101\pi$
$41$	−4.61584	+	6.68720i	−0.720873	+	1.04436i	−0.996540	+	0.0831115i	$0.973514\pi$
$42$	3.00189			0.463202
$43$	1.45920			0.222527			0.111263	−	0.993791i	$-0.464510\pi$
$43$	1.45920			0.222527			0.111263	+	0.993791i	$0.464510\pi$
$44$	9.88847	+	5.18987i	1.49074	+	0.782402i
$45$	−0.880833	+	1.27611i	−0.131307	+	0.190231i
$46$	−7.90426			−1.16542
$47$	−3.20711	+	2.84125i	−0.467805	+	0.414439i	−0.863817	−	0.503806i	$-0.831932\pi$
$47$	−3.20711	+	2.84125i	−0.467805	+	0.414439i	0.396012	+	0.918246i	$0.370394\pi$
$48$	1.21798	+	0.300205i	0.175800	+	0.0433308i
$49$	−5.77735	+	1.42399i	−0.825335	+	0.203427i
$50$	1.38433	+	11.4010i	0.195774	+	1.61234i
$51$	−0.0451305	+	0.118999i	−0.00631953	+	0.0166632i
$52$	−9.53245	+	13.8101i	−1.32191	+	1.91512i
$53$	−1.10464	−	0.272270i	−0.151734	−	0.0373992i	0.162717	−	0.986673i	$-0.447974\pi$
$53$	−1.10464	−	0.272270i	−0.151734	−	0.0373992i	−0.314451	+	0.949274i	$0.601820\pi$
$54$	4.76478	−	1.17441i	0.648405	−	0.159817i
$55$	−1.13999	+	1.00994i	−0.153716	+	0.136181i
$56$	−17.0544			−2.27899
$57$	−1.19774	+	1.73522i	−0.158644	+	0.229836i
$58$	−1.14953	−	9.46727i	−0.150941	−	1.24311i
$59$	−1.71991	+	0.902679i	−0.223913	+	0.117519i	−0.572950	−	0.819590i	$-0.694201\pi$
$59$	−1.71991	+	0.902679i	−0.223913	+	0.117519i	0.349037	+	0.937109i	$0.386509\pi$
$60$	−0.412290	+	0.597305i	−0.0532264	+	0.0771117i
$61$	9.12747			1.16865			0.584326	−	0.811519i	$-0.301359\pi$
$61$	9.12747			1.16865			0.584326	+	0.811519i	$0.301359\pi$
$62$	−4.94009	−	1.21762i	−0.627392	−	0.154638i
$63$	−9.18629	+	4.82134i	−1.15736	+	0.607431i
$64$	8.39740	+	2.06977i	1.04968	+	0.258722i
$65$	−1.30001	−	1.88338i	−0.161246	−	0.233605i
$66$	2.36210			0.290754
$67$	−3.30205	−	8.70679i	−0.403409	−	1.06370i	−0.970723	−	0.240201i	$-0.922786\pi$
$67$	−3.30205	−	8.70679i	−0.403409	−	1.06370i	0.567314	−	0.823502i	$-0.307983\pi$
$68$	0.520198	−	1.37165i	0.0630833	−	0.166337i
$69$	−0.982237	+	0.515518i	−0.118247	+	0.0620610i
$70$	1.67332	−	4.41219i	0.200000	−	0.527357i
$71$	0.532254	+	0.131189i	0.0631669	+	0.0155692i	0.270772	−	0.962643i	$-0.412721\pi$
$71$	0.532254	+	0.131189i	0.0631669	+	0.0155692i	−0.207606	+	0.978213i	$0.566567\pi$
$72$	−13.2655	+	3.26966i	−1.56336	+	0.385333i
$73$	0.690438	−	5.68627i	0.0808096	−	0.665527i	−0.894870	−	0.446326i	$-0.852732\pi$
$73$	0.690438	−	5.68627i	0.0808096	−	0.665527i	0.975680	−	0.219201i	$-0.0703449\pi$
$74$	5.81027	+	5.14745i	0.675430	+	0.598379i
$75$	0.915602	+	1.32648i	0.105725	+	0.153169i
$76$	13.8058	−	20.0011i	1.58363	−	2.29428i
$77$	−9.89404	+	2.43866i	−1.12753	+	0.277911i
$78$	−0.427820	+	3.52342i	−0.0484411	+	0.398948i
$79$	1.72526	−	2.49947i	0.194107	−	0.281212i	−0.713830	−	0.700319i	$-0.753041\pi$
$79$	1.72526	−	2.49947i	0.194107	−	0.281212i	0.907937	+	0.419106i	$0.137657\pi$
$80$	1.12017	−	1.62285i	0.125239	−	0.181440i
$81$	−5.95820	+	5.27851i	−0.662023	+	0.586501i
$82$	2.38784	−	19.6657i	0.263693	−	2.17171i
$83$	0.382100	+	3.14688i	0.0419410	+	0.345415i	0.998540	+	0.0540090i	$0.0172000\pi$
$83$	0.382100	+	3.14688i	0.0419410	+	0.345415i	−0.956599	+	0.291406i	$0.905877\pi$
$84$	−4.29981	+	2.25671i	−0.469147	+	0.246227i
$85$	0.149749	+	0.132666i	0.0162425	+	0.0143896i
$86$	−3.15005	+	1.65327i	−0.339678	+	0.178277i
$87$	−0.760306	−	1.10149i	−0.0815134	−	0.118093i
$88$	−13.4196			−1.43053
$89$	−9.11848	−	2.24750i	−0.966557	−	0.238235i	−0.275714	−	0.961240i	$-0.588914\pi$
$89$	−9.11848	−	2.24750i	−0.966557	−	0.238235i	−0.690843	+	0.723005i	$0.742760\pi$
$90$	0.455669	−	3.75277i	0.0480317	−	0.395577i
$91$	−1.84563	−	15.2001i	−0.193474	−	1.59340i
$92$	11.3218	−	5.94213i	1.18038	−	0.619510i
$93$	−0.693302	+	0.170884i	−0.0718921	+	0.0177198i
$94$	3.70420	−	9.76718i	0.382059	−	1.00741i
$95$	1.88279	+	2.72769i	0.193170	+	0.279855i
$96$	0.179348	−	0.0442053i	0.0183046	−	0.00451168i
$97$	−13.3940	+	3.30133i	−1.35996	+	0.335199i	−0.850807	−	0.525479i	$-0.823886\pi$
$97$	−13.3940	+	3.30133i	−1.35996	+	0.335199i	−0.509149	+	0.860678i	$0.670040\pi$
$98$	10.8584	−	9.61973i	1.09687	−	0.971740i
$99$	−7.22841	+	3.79376i	−0.726482	+	0.381287i
$100$	−10.5537	−	15.2897i	−1.05537	−	1.52897i
$101$	3.26529	+	0.804822i	0.324908	+	0.0800827i	0.398396	−	0.917213i	$-0.369567\pi$
$101$	3.26529	+	0.804822i	0.324908	+	0.0800827i	−0.0734879	+	0.997296i	$0.523413\pi$
$102$	−0.0374006	−	0.308022i	−0.00370321	−	0.0304987i
$103$	−5.27309	−	4.67155i	−0.519573	−	0.460301i	0.362116	−	0.932133i	$-0.382054\pi$
$103$	−5.27309	−	4.67155i	−0.519573	−	0.460301i	−0.881689	+	0.471832i	$0.843593\pi$
$104$	2.43054	−	20.0173i	0.238334	−	1.96286i
$105$	−0.0798256	−	0.657423i	−0.00779018	−	0.0641579i
$106$	2.69312	−	0.663795i	0.261579	−	0.0644735i
$107$	−5.67529	−	2.97862i	−0.548651	−	0.287954i	0.167532	−	0.985867i	$-0.446420\pi$
$107$	−5.67529	−	2.97862i	−0.548651	−	0.287954i	−0.716183	+	0.697912i	$0.754112\pi$
$108$	−5.94203	+	5.26418i	−0.571772	+	0.506545i
$109$	1.29427	+	10.6593i	0.123969	+	1.02098i	0.913379	+	0.407110i	$0.133463\pi$
$109$	1.29427	+	10.6593i	0.123969	+	1.02098i	−0.789410	+	0.613866i	$0.789614\pi$
$110$	1.31669	−	3.47181i	0.125541	−	0.331024i
$111$	1.05774	+	0.260710i	0.100396	+	0.0247455i
$112$	11.6824	−	6.13138i	1.10388	−	0.579361i
$113$	1.13696	+	0.596722i	0.106956	+	0.0561349i	0.517353	−	0.855772i	$-0.326917\pi$
$113$	1.13696	+	0.596722i	0.106956	+	0.0561349i	−0.410397	+	0.911907i	$0.634610\pi$
$114$	0.619608	−	5.10293i	0.0580316	−	0.477933i
$115$	0.210188	+	1.73105i	0.0196001	+	0.161422i
$116$	8.76370	+	12.6964i	0.813689	+	1.17883i
$117$	−4.34975	−	11.4694i	−0.402135	−	1.06034i
$118$	2.69011	−	3.89730i	0.247645	−	0.358776i
$119$	0.474665	+	1.25159i	0.0435124	+	0.114733i
$120$	0.105124	−	0.865771i	0.00959643	−	0.0790337i
$121$	2.89505	−	0.713565i	0.263186	−	0.0648695i
$122$	−19.7039	+	10.3414i	−1.78390	+	0.936265i
$123$	−0.985870	−	2.59952i	−0.0888929	−	0.234391i
$124$	7.99137	−	1.96970i	0.717646	−	0.176884i
$125$	5.07115	−	1.24993i	0.453577	−	0.111797i
$126$	14.3683	−	20.8161i	1.28003	−	1.85444i
$127$	0.648872	+	1.71093i	0.0575780	+	0.151821i	0.960719	−	0.277524i	$-0.0895138\pi$
$127$	0.648872	+	1.71093i	0.0575780	+	0.151821i	−0.903141	+	0.429345i	$0.858745\pi$
$128$	−19.4245	+	4.78772i	−1.71690	+	0.423179i
$129$	−0.283620	+	0.410894i	−0.0249713	+	0.0361772i
$130$	4.94025	+	2.59284i	0.433288	+	0.227407i
$131$	−17.2094			−1.50359			−0.751797	−	0.659395i	$-0.770812\pi$
$131$	−17.2094			−1.50359			−0.751797	+	0.659395i	$0.770812\pi$
$132$	−3.38338	+	1.77574i	−0.294486	+	0.154558i
$133$	2.67301	+	22.0142i	0.231779	+	1.90887i
$134$	16.9930	+	15.0545i	1.46797	+	1.30051i
$135$	−0.383904	−	1.01227i	−0.0330412	−	0.0871224i
$136$	0.212481	+	1.74994i	0.0182201	+	0.150056i
$137$	−17.5828	+	9.22816i	−1.50220	+	0.788415i	−0.997205	−	0.0747087i	$-0.976197\pi$
$137$	−17.5828	+	9.22816i	−1.50220	+	0.788415i	−0.504993	+	0.863123i	$0.668505\pi$
$138$	1.53632	−	2.22574i	0.130780	−	0.189468i
$139$	−3.24999	−	0.801051i	−0.275661	−	0.0679443i	0.0990618	−	0.995081i	$-0.468416\pi$
$139$	−3.24999	−	0.801051i	−0.275661	−	0.0679443i	−0.374722	+	0.927137i	$0.622262\pi$
$140$	0.920112	+	7.57781i	0.0777637	+	0.640442i
$141$	−0.176708	−	1.45532i	−0.0148815	−	0.122560i
$142$	−1.29764	+	0.319839i	−0.108895	+	0.0268403i
$143$	−1.45227	−	11.9605i	−0.121445	−	1.00019i
$144$	7.91146	−	7.00894i	0.659289	−	0.584079i
$145$	−2.04279	+	0.503503i	−0.169645	+	0.0418136i
$146$	4.95204	+	13.0575i	0.409834	+	1.08064i
$147$	0.721941	−	1.90360i	0.0595447	−	0.157007i
$148$	−12.1921	−	3.00508i	−1.00218	−	0.247016i
$149$	12.9387	+	11.4626i	1.05998	+	0.939056i	0.998256	−	0.0590370i	$-0.0188030\pi$
$149$	12.9387	+	11.4626i	1.05998	+	0.939056i	0.0617199	+	0.998094i	$0.480341\pi$
$150$	−3.47945	−	1.82615i	−0.284096	−	0.149105i
$151$	−10.5192	−	9.31922i	−0.856042	−	0.758387i	0.115986	−	0.993251i	$-0.462997\pi$
$151$	−10.5192	−	9.31922i	−0.856042	−	0.758387i	−0.972028	+	0.234863i	$0.924536\pi$
$152$	−3.52013	+	28.9909i	−0.285520	+	2.35147i
$153$	0.609165	+	0.882528i	0.0492481	+	0.0713482i
$154$	18.5957	−	16.4744i	1.49848	−	1.32754i
$155$	−0.135297	+	1.11427i	−0.0108673	+	0.0895005i
$156$	−2.03598	−	5.36844i	−0.163009	−	0.429819i
$157$	14.1734	−	3.49344i	1.13116	−	0.278807i	0.371060	−	0.928609i	$-0.378994\pi$
$157$	14.1734	−	3.49344i	1.13116	−	0.278807i	0.760103	+	0.649802i	$0.225148\pi$
$158$	−0.892503	+	7.35042i	−0.0710037	+	0.584768i
$159$	0.291373	−	0.258134i	0.0231074	−	0.0204713i
$160$	0.0349995	−	0.288247i	0.00276695	−	0.0227879i
$161$	−4.13724	+	10.9090i	−0.326060	+	0.859750i
$162$	6.88171	−	18.1456i	0.540678	−	1.42565i
$163$	0.914635	−	0.480037i	0.0716397	−	0.0375994i	−0.428523	−	0.903531i	$-0.640966\pi$
$163$	0.914635	−	0.480037i	0.0716397	−	0.0375994i	0.500163	+	0.865931i	$0.333274\pi$
$164$	11.3637	+	29.9635i	0.887353	+	2.33976i
$165$	−0.0628123	−	0.517306i	−0.00488993	−	0.0402722i
$166$	−4.39026	−	6.36039i	−0.340750	−	0.493662i
$167$	−1.07559	+	0.265108i	−0.0832313	+	0.0205147i	−0.280711	−	0.959792i	$-0.590570\pi$
$167$	−1.07559	+	0.265108i	−0.0832313	+	0.0205147i	0.197480	+	0.980307i	$0.436724\pi$
$168$	3.31479	−	4.80231i	0.255742	−	0.370506i
$169$	5.10388			0.392607
$170$	−0.473579	−	0.116727i	−0.0363218	−	0.00895253i
$171$	6.29971	+	16.6110i	0.481751	+	1.27027i
$172$	3.26915	−	4.73618i	0.249270	−	0.361130i
$173$	8.65792	+	7.67025i	0.658250	+	0.583158i	0.924703	−	0.380690i	$-0.124313\pi$
$173$	8.65792	+	7.67025i	0.658250	+	0.583158i	−0.266453	+	0.963848i	$0.585852\pi$
$174$	2.88929	+	1.51642i	0.219037	+	0.114959i
$175$	16.4596	+	4.05693i	1.24423	+	0.306675i
$176$	9.19249	−	4.82459i	0.692910	−	0.363667i
$177$	0.0801088	−	0.659755i	0.00602135	−	0.0495902i
$178$	22.2309	−	5.47942i	1.66627	−	0.410700i
$179$	15.3271	−	13.5786i	1.14560	−	1.01491i	0.145928	−	0.989295i	$-0.453383\pi$
$179$	15.3271	−	13.5786i	1.14560	−	1.01491i	0.999672	−	0.0256176i	$-0.00815522\pi$
$180$	2.16851	+	5.71789i	0.161631	+	0.426186i
$181$	−3.49737	+	5.06682i	−0.259958	+	0.376614i	−0.931130	−	0.364688i	$-0.881176\pi$
$181$	−3.49737	+	5.06682i	−0.259958	+	0.376614i	0.671172	+	0.741301i	$0.265791\pi$
$182$	21.2059	+	30.7221i	1.57189	+	2.27727i
$183$	−1.77407	+	2.57018i	−0.131143	+	0.189993i
$184$	−8.72815	+	12.6449i	−0.643448	+	0.932196i
$185$	0.972801	−	1.40935i	0.0715217	−	0.103617i
$186$	1.30305	−	1.15440i	0.0955444	−	0.0846449i
$187$	0.373499	+	0.984836i	0.0273129	+	0.0720183i
$188$	2.03683	+	16.7748i	0.148551	+	1.22343i
$189$	0.873120	−	7.19079i	0.0635101	−	0.523053i
$190$	−7.15492	−	3.75519i	−0.519072	−	0.272430i
$191$	5.77466	−	15.2265i	0.417840	−	1.10175i	−0.546587	−	0.837402i	$-0.684073\pi$
$191$	5.77466	−	15.2265i	0.417840	−	1.10175i	0.964427	−	0.264350i	$-0.0851575\pi$
$192$	−2.21499	+	1.96231i	−0.159853	+	0.141618i
$193$	4.95115	−	13.0551i	0.356391	−	0.939727i	−0.630188	−	0.776443i	$-0.717022\pi$
$193$	4.95115	−	13.0551i	0.356391	−	0.939727i	0.986579	−	0.163284i	$-0.0522086\pi$
$194$	25.1738	−	22.3021i	1.80738	−	1.60120i
$195$	0.783014			0.0560728
$196$	−8.32148	+	21.9419i	−0.594391	+	1.56728i
$197$	3.15954	+	8.33103i	0.225108	+	0.593562i	0.999220	−	0.0394873i	$-0.0125725\pi$
$197$	3.15954	+	8.33103i	0.225108	+	0.593562i	−0.774112	+	0.633049i	$0.781803\pi$
$198$	11.3060	−	16.3795i	0.803480	−	1.16404i
$199$	−5.49488	−	2.88394i	−0.389522	−	0.204437i	0.258581	−	0.965990i	$-0.416745\pi$
$199$	−5.49488	−	2.88394i	−0.389522	−	0.204437i	−0.648103	+	0.761553i	$0.724437\pi$
$200$	19.7675	+	10.3748i	1.39777	+	0.733608i
$201$	3.09353	+	0.762486i	0.218201	+	0.0537816i
$202$	−7.96078	+	1.96216i	−0.560119	+	0.138057i
$203$	−13.6679	−	3.36883i	−0.959297	−	0.236445i
$204$	0.285131	+	0.413083i	0.0199631	+	0.0289216i
$205$	−4.37033			−0.305237
$206$	16.6761	+	4.11029i	1.16188	+	0.286377i
$207$	−1.12663	+	9.27862i	−0.0783061	+	0.644908i
$208$	5.53166	+	14.5858i	0.383551	+	1.01134i
$209$	2.10331	+	17.3223i	0.145489	+	1.19821i
$210$	0.917180	+	1.32877i	0.0632915	+	0.0916935i
$211$	11.0043	+	15.9424i	0.757564	+	1.09752i	0.992104	+	0.125415i	$0.0400263\pi$
$211$	11.0043	+	15.9424i	0.757564	+	1.09752i	−0.234540	+	0.972106i	$0.575358\pi$
$212$	−3.35852	+	2.97539i	−0.230664	+	0.204350i
$213$	−0.140393	+	0.124377i	−0.00961958	+	0.00852220i
$214$	15.6263			1.06819
$215$	0.445837	+	0.645906i	0.0304058	+	0.0440504i
$216$	3.38266	−	8.91933i	0.230161	−	0.606884i
$217$	−4.26623	+	6.18070i	−0.289611	+	0.419573i
$218$	−14.8709	−	21.5443i	−1.00719	−	1.45916i
$219$	1.46698	+	1.29963i	0.0991296	+	0.0878211i
$220$	0.724008	+	5.96274i	0.0488126	+	0.402008i
$221$	−1.53668	+	0.378757i	−0.103368	+	0.0254779i
$222$	−2.57878	+	0.635611i	−0.173076	+	0.0426594i
$223$	1.92998	+	15.8948i	0.129241	+	1.06440i	0.902615	+	0.430448i	$0.141644\pi$
$223$	1.92998	+	15.8948i	0.129241	+	1.06440i	−0.773374	+	0.633950i	$0.781433\pi$
$224$	1.10362	−	1.59886i	0.0737384	−	0.106828i
$225$	13.5807			0.905378
$226$	−3.13049			−0.208237
$227$	10.8896	+	9.64730i	0.722765	+	0.640314i	0.942099	−	0.335336i	$-0.108850\pi$
$227$	10.8896	+	9.64730i	0.722765	+	0.640314i	−0.219334	+	0.975650i	$0.570388\pi$
$228$	2.94869	+	7.77506i	0.195282	+	0.514916i
$229$	10.1820			0.672843			0.336422	−	0.941711i	$-0.390783\pi$
$229$	10.1820			0.672843			0.336422	+	0.941711i	$0.390783\pi$
$230$	−2.41502	−	3.49876i	−0.159242	−	0.230701i
$231$	1.23637	−	3.26003i	0.0813470	−	0.214494i
$232$	−16.4147	−	8.61511i	−1.07768	−	0.565609i
$233$	−0.361905	+	0.189943i	−0.0237092	+	0.0124435i	−0.476536	−	0.879155i	$-0.658108\pi$
$233$	−0.361905	+	0.189943i	−0.0237092	+	0.0124435i	0.452827	+	0.891598i	$0.350416\pi$
$234$	22.3847	+	19.8312i	1.46334	+	1.29640i
$235$	−2.23754	−	0.551504i	−0.145961	−	0.0359762i
$236$	−0.923377	+	7.60469i	−0.0601067	+	0.495023i
$237$	0.368488	+	0.971623i	0.0239359	+	0.0631137i
$238$	−2.44272	−	2.16406i	−0.158338	−	0.140275i
$239$	−10.8278	−	9.59258i	−0.700391	−	0.620492i	0.235875	−	0.971783i	$-0.424204\pi$
$239$	−10.8278	−	9.59258i	−0.700391	−	0.620492i	−0.936266	+	0.351291i	$0.885743\pi$
$240$	0.239251	+	0.630852i	0.0154436	+	0.0407213i
$241$	−3.48608	+	3.08840i	−0.224558	+	0.198941i	−0.767899	−	0.640571i	$-0.778698\pi$
$241$	−3.48608	+	3.08840i	−0.224558	+	0.198941i	0.543341	+	0.839512i	$0.317159\pi$
$242$	−5.44120	+	4.82048i	−0.349773	+	0.309872i
$243$	−1.05616	−	8.69830i	−0.0677530	−	0.557996i
$244$	20.4489	−	29.6253i	1.30910	−	1.89656i
$245$	−2.39549	−	2.12222i	−0.153042	−	0.135584i
$246$	5.07349	+	4.49472i	0.323474	+	0.286573i
$247$	−26.2197			−1.66832
$248$	−7.40292	+	6.55841i	−0.470086	+	0.416460i
$249$	−0.960389	−	0.504051i	−0.0608622	−	0.0319429i
$250$	−9.53115	+	8.44386i	−0.602803	+	0.534037i
$251$	−17.0596	−	15.1135i	−1.07679	−	0.953954i	−0.0777169	−	0.996975i	$-0.524763\pi$
$251$	−17.0596	−	15.1135i	−1.07679	−	0.953954i	−0.999074	+	0.0430219i	$0.986301\pi$
$252$	−4.93189	+	40.6177i	−0.310680	+	2.55868i
$253$	−3.25547	+	8.58396i	−0.204669	+	0.539669i
$254$	−3.33923	−	2.95830i	−0.209522	−	0.185620i
$255$	−0.0664630	+	0.0163817i	−0.00416208	+	0.00102586i
$256$	23.5608	−	20.8731i	1.47255	−	1.30457i
$257$	−9.70551	−	14.0609i	−0.605413	−	0.877092i	0.393698	−	0.919240i	$-0.371195\pi$
$257$	−9.70551	−	14.0609i	−0.605413	−	0.877092i	−0.999111	+	0.0421473i	$0.986580\pi$
$258$	0.146721	−	1.20835i	0.00913443	−	0.0752288i
$259$	10.1454	−	5.32473i	0.630406	−	0.330863i
$260$	−9.02544			−0.559734
$261$	−11.2772			−0.698044
$262$	37.1507	−	19.4982i	2.29518	−	1.20460i
$263$	29.1173	−	7.17677i	1.79545	−	0.442539i	0.806555	−	0.591159i	$-0.201329\pi$
$263$	29.1173	−	7.17677i	1.79545	−	0.442539i	0.988894	+	0.148620i	$0.0474831\pi$
$264$	2.60831	−	3.77879i	0.160530	−	0.232568i
$265$	−0.216988	−	0.572150i	−0.0133295	−	0.0351469i
$266$	−30.7123	−	44.4945i	−1.88309	−	2.72813i
$267$	2.40519	−	2.13081i	0.147195	−	0.130404i
$268$	−35.6576	−	8.78882i	−2.17814	−	0.536863i
$269$	23.7817			1.45000			0.724998	−	0.688751i	$-0.241841\pi$
$269$	23.7817			1.45000			0.724998	+	0.688751i	$0.241841\pi$
$270$	1.97565	+	1.75027i	0.120234	+	0.106518i
$271$	15.0586	+	21.8161i	0.914744	+	1.32524i	0.945470	+	0.325708i	$0.105603\pi$
$271$	15.0586	+	21.8161i	0.914744	+	1.32524i	−0.0307260	+	0.999528i	$0.509782\pi$
$272$	−0.774686	−	1.12233i	−0.0469722	−	0.0680510i
$273$	4.63889	+	2.43468i	0.280758	+	0.147353i
$274$	27.5013	−	39.8424i	1.66141	−	2.40697i
$275$	12.9515	+	3.19227i	0.781008	+	0.192501i
$276$	−0.527338	+	4.34302i	−0.0317420	+	0.261419i
$277$	−1.16119	−	9.56325i	−0.0697691	−	0.574600i	−0.985111	−	0.171922i	$-0.945002\pi$
$277$	−1.16119	−	9.56325i	−0.0697691	−	0.574600i	0.915342	−	0.402678i	$-0.131921\pi$
$278$	7.92349	−	1.95296i	0.475219	−	0.117131i
$279$	−2.13347	+	5.62550i	−0.127727	+	0.336790i
$280$	−5.21070	−	7.54900i	−0.311399	−	0.451139i
$281$	−7.39944	+	10.7199i	−0.441414	+	0.639498i	−0.979036	−	0.203688i	$-0.934707\pi$
$281$	−7.39944	+	10.7199i	−0.441414	+	0.639498i	0.537622	+	0.843186i	$0.319323\pi$
$282$	2.03034	+	2.94146i	0.120905	+	0.175161i
$283$	3.04391	+	25.0688i	0.180941	+	1.49019i	0.746448	+	0.665444i	$0.231758\pi$
$283$	3.04391	+	25.0688i	0.180941	+	1.49019i	−0.565507	+	0.824744i	$0.691319\pi$
$284$	1.61825	−	1.43364i	0.0960252	−	0.0850709i
$285$	−1.13403			−0.0671743
$286$	16.6863	+	24.1742i	0.986680	+	1.42945i
$287$	−25.8916	−	13.5890i	−1.52833	−	0.802131i
$288$	0.551899	−	1.45524i	0.0325210	−	0.0857507i
$289$	−14.9302	+	7.83600i	−0.878250	+	0.460941i
$290$	3.83939	−	3.40141i	0.225457	−	0.199737i
$291$	1.67373	−	4.41325i	0.0981155	−	0.258709i
$292$	−16.9092	−	14.9803i	−0.989538	−	0.876654i
$293$	19.1337	+	27.7200i	1.11780	+	1.61942i	0.706122	+	0.708090i	$0.250443\pi$
$293$	19.1337	+	27.7200i	1.11780	+	1.61942i	0.411681	+	0.911328i	$0.364942\pi$
$294$	0.598288	+	4.92735i	0.0348929	+	0.287369i
$295$	−0.925055	−	0.485507i	−0.0538588	−	0.0282673i
$296$	14.6506	−	3.61105i	0.851548	−	0.209888i
$297$	0.687031	−	5.65821i	0.0398656	−	0.328323i
$298$	−40.9184	−	10.0855i	−2.37034	−	0.584236i
$299$	−12.2146	−	6.41073i	−0.706390	−	0.370742i
$300$	6.35667			0.367003
$301$	0.632957	+	5.21287i	0.0364831	+	0.300465i
$302$	33.2669	+	8.19957i	1.91430	+	0.471832i
$303$	−0.861288	+	0.763035i	−0.0494797	+	0.0438352i
$304$	−8.01145	−	21.1245i	−0.459488	−	1.21157i
$305$	2.78875	+	4.04021i	0.159684	+	0.231342i
$306$	−2.31493	−	1.21497i	−0.132336	−	0.0694552i
$307$	−7.70495	−	20.3163i	−0.439745	−	1.15951i	−0.953452	−	0.301546i	$-0.902497\pi$
$307$	−7.70495	−	20.3163i	−0.439745	−	1.15951i	0.513707	−	0.857966i	$-0.328272\pi$
$308$	−14.2510	+	37.5769i	−0.812027	+	2.14114i
$309$	2.34036	−	0.576846i	0.133138	−	0.0328156i
$310$	−0.970394	−	2.55872i	−0.0551147	−	0.145325i
$311$	0.223870	−	1.84373i	0.0126945	−	0.104548i	−0.984984	−	0.172644i	$-0.944769\pi$
$311$	0.223870	−	1.84373i	0.0126945	−	0.104548i	0.997679	+	0.0680952i	$0.0216922\pi$
$312$	5.16420	+	4.57509i	0.292366	+	0.259013i
$313$	28.7753			1.62647			0.813237	−	0.581933i	$-0.197703\pi$
$313$	28.7753			1.62647			0.813237	+	0.581933i	$0.197703\pi$
$314$	−26.6388	+	23.5999i	−1.50331	+	1.33182i
$315$	−4.94085	−	2.59316i	−0.278386	−	0.146108i
$316$	−4.24739	−	11.1994i	−0.238934	−	0.630018i
$317$	−3.27578	−	1.71926i	−0.183986	−	0.0965634i	0.370215	−	0.928946i	$-0.379284\pi$
$317$	−3.27578	−	1.71926i	−0.183986	−	0.0965634i	−0.554201	+	0.832383i	$0.686976\pi$
$318$	−0.336534	+	0.887368i	−0.0188719	+	0.0497611i
$319$	−10.7548	−	2.65083i	−0.602155	−	0.148418i
$320$	1.64952	+	4.34943i	0.0922111	+	0.243141i
$321$	1.94182	−	1.01915i	0.108382	−	0.0568833i
$322$	−3.42862	−	28.2372i	−0.191070	−	1.57360i
$323$	2.22555	−	0.548550i	0.123833	−	0.0305221i
$324$	3.78405	+	31.1645i	0.210225	+	1.73136i
$325$	−7.10751	+	18.7410i	−0.394254	+	1.03956i
$326$	−1.43058	+	2.07255i	−0.0792326	+	0.114788i
$327$	−3.25309	−	1.70735i	−0.179896	−	0.0944168i
$328$	−28.8236	−	25.5355i	−1.59152	−	1.40996i
$329$	−11.5413	−	10.2247i	−0.636290	−	0.563704i
$330$	0.721701	+	1.04556i	0.0397283	+	0.0575564i
$331$	2.66811	−	21.9739i	0.146653	−	1.20779i	−0.714570	−	0.699564i	$-0.753377\pi$
$331$	2.66811	−	21.9739i	0.146653	−	1.20779i	0.861222	−	0.508229i	$-0.169700\pi$
$332$	11.0700	+	5.80996i	0.607543	+	0.318863i
$333$	6.87063	−	6.08685i	0.376508	−	0.333557i
$334$	2.02155	−	1.79093i	0.110614	−	0.0979955i
$335$	2.84511	−	4.12185i	0.155445	−	0.225201i
$336$	−0.544133	+	4.48134i	−0.0296849	+	0.244477i
$337$	−23.3047	+	12.2312i	−1.26949	+	0.666278i	−0.958759	−	0.284220i	$-0.908265\pi$
$337$	−23.3047	+	12.2312i	−1.26949	+	0.666278i	−0.310728	+	0.950499i	$0.600573\pi$
$338$	−11.0180	+	5.78268i	−0.599299	+	0.314536i
$339$	−0.389015	+	0.204171i	−0.0211284	+	0.0110890i
$340$	0.766089	−	0.188824i	0.0415470	−	0.0102404i
$341$	−3.35696	+	4.86340i	−0.181790	+	0.263368i
$342$	−32.4196	−	28.7213i	−1.75305	−	1.55307i
$343$	1.33958	+	3.53219i	0.0723308	+	0.190721i
$344$	−0.833552	+	6.86492i	−0.0449421	+	0.370132i
$345$	−0.528297	−	0.277272i	−0.0284425	−	0.0149278i
$346$	−27.3806	−	6.74871i	−1.47199	−	0.362813i
$347$	12.1821	−	32.1216i	0.653971	−	1.72438i	−0.0347935	−	0.999395i	$-0.511077\pi$
$347$	12.1821	−	32.1216i	0.653971	−	1.72438i	0.688764	−	0.724985i	$-0.258153\pi$
$348$	−5.27851			−0.282958
$349$	15.0834	−	13.3627i	0.807394	−	0.715289i	−0.154713	−	0.987959i	$-0.549445\pi$
$349$	15.0834	−	13.3627i	0.807394	−	0.715289i	0.962107	+	0.272671i	$0.0879069\pi$
$350$	−40.1285	+	9.89079i	−2.14496	+	0.528685i
$351$	8.31562	+	2.04962i	0.443855	+	0.109400i
$352$	0.868400	−	1.25810i	0.0462859	−	0.0670567i
$353$	1.69124	+	13.9286i	0.0900154	+	0.741344i	0.965917	+	0.258853i	$0.0833446\pi$
$353$	1.69124	+	13.9286i	0.0900154	+	0.741344i	−0.875901	+	0.482490i	$0.839732\pi$
$354$	0.574566	+	1.51501i	0.0305378	+	0.0805216i
$355$	0.104552	+	0.275681i	0.00554904	+	0.0146316i
$356$	−27.7235	+	24.5609i	−1.46934	+	1.30172i
$357$	−0.444690	−	0.109606i	−0.0235355	−	0.00580098i
$358$	−17.7027	+	46.6783i	−0.935618	+	2.46702i
$359$	7.94336	−	20.9449i	0.419234	−	1.10543i	−0.544546	−	0.838731i	$-0.683298\pi$
$359$	7.94336	−	20.9449i	0.419234	−	1.10543i	0.963780	−	0.266699i	$-0.0859329\pi$
$360$	−5.50036	−	4.87290i	−0.289895	−	0.256824i
$361$	18.9737			0.998618
$362$	1.80924	−	14.9005i	0.0950918	−	0.783151i
$363$	−0.361767	+	0.953901i	−0.0189878	+	0.0500668i
$364$	−53.4703	−	28.0634i	−2.80261	−	1.47092i
$365$	2.72794	−	1.43173i	0.142787	−	0.0749402i
$366$	0.917753	−	7.55837i	0.0479717	−	0.395083i
$367$	21.1957	+	5.22428i	1.10641	+	0.272705i	0.749876	−	0.661578i	$-0.230113\pi$
$367$	21.1957	+	5.22428i	1.10641	+	0.272705i	0.356532	+	0.934283i	$0.383959\pi$
$368$	1.43275	−	11.7998i	0.0746873	−	0.615106i
$369$	−22.7447	−	5.60606i	−1.18404	−	0.291840i
$370$	−0.503245	+	4.14459i	−0.0261625	+	0.215467i
$371$	0.493500	−	4.06434i	0.0256212	−	0.211010i
$372$	−0.998608	+	2.63311i	−0.0517754	+	0.136521i
$373$	−15.1881	−	22.0037i	−0.786409	−	1.13931i	−0.987170	−	0.159670i	$-0.948957\pi$
$373$	−15.1881	−	22.0037i	−0.786409	−	1.13931i	0.200761	−	0.979640i	$-0.435658\pi$
$374$	−1.92210	−	1.70284i	−0.0993896	−	0.0880515i
$375$	−0.633694	+	1.67091i	−0.0327238	+	0.0862857i
$376$	−11.5348	−	16.7111i	−0.594863	−	0.861808i
$377$	5.90200	−	15.5623i	0.303969	−	0.801499i
$378$	6.26230	+	16.5123i	0.322098	+	0.849302i
$379$	10.1364	+	8.98009i	0.520673	+	0.461276i	0.882058	−	0.471140i	$-0.156158\pi$
$379$	10.1364	+	8.98009i	0.520673	+	0.461276i	−0.361385	+	0.932417i	$0.617696\pi$
$380$	13.0715			0.670552
$381$	−0.607896	−	0.149833i	−0.0311435	−	0.00767617i
$382$	4.78558	+	39.4128i	0.244852	+	2.01654i
$383$	7.02086	+	1.73049i	0.358749	+	0.0884237i	0.414571	−	0.910017i	$-0.363932\pi$
$383$	7.02086	+	1.73049i	0.358749	+	0.0884237i	−0.0558217	+	0.998441i	$0.517778\pi$
$384$	2.42730	−	6.40028i	0.123868	−	0.326613i
$385$	−4.10242	−	3.63443i	−0.209079	−	0.185228i
$386$	4.10312	+	33.7922i	0.208843	+	1.71998i
$387$	1.49175	+	3.93341i	0.0758298	+	0.199947i
$388$	−19.2923	+	50.8695i	−0.979416	+	2.58251i
$389$	35.0163	−	8.63073i	1.77540	−	0.437596i	0.790747	−	0.612144i	$-0.209693\pi$
$389$	35.0163	−	8.63073i	1.77540	−	0.437596i	0.984649	+	0.174548i	$0.0558464\pi$
$390$	−1.69033	+	0.887152i	−0.0855930	+	0.0449227i
$391$	1.17091	+	0.288603i	0.0592155	+	0.0145953i
$392$	−3.39901	−	27.9933i	−0.171676	−	1.41388i
$393$	3.34492	−	4.84595i	0.168729	−	0.244446i
$394$	−16.2597	−	14.4048i	−0.819150	−	0.725704i
$395$	1.63350			0.0821901
$396$	−3.88075	+	31.9608i	−0.195015	+	1.60609i
$397$	−1.55924	−	12.8415i	−0.0782559	−	0.644496i	−0.978078	−	0.208239i	$-0.933227\pi$
$397$	−1.55924	−	12.8415i	−0.0782559	−	0.644496i	0.899822	−	0.436257i	$-0.143696\pi$
$398$	15.1295			0.758375
$399$	−6.71846	−	3.52612i	−0.336344	−	0.176527i
$400$	−17.2708			−0.863538
$401$	3.85199	−	2.02168i	0.192359	−	0.100958i	−0.365794	−	0.930696i	$-0.619202\pi$
$401$	3.85199	−	2.02168i	0.192359	−	0.100958i	0.558153	+	0.829738i	$0.311510\pi$
$402$	−7.54203	+	1.85894i	−0.376162	+	0.0927156i
$403$	−6.64648	−	5.88826i	−0.331085	−	0.293315i
$404$	9.92767	−	8.79515i	0.493920	−	0.437575i
$405$	−4.15693	−	1.02459i	−0.206559	−	0.0509123i
$406$	33.3223	−	8.21321i	1.65376	−	0.407615i
$407$	7.98312	−	4.18987i	0.395709	−	0.207684i
$408$	−0.534060	−	0.280296i	−0.0264399	−	0.0138767i
$409$	−2.87526	+	1.50905i	−0.142172	+	0.0746179i	−0.534309	−	0.845289i	$-0.679428\pi$
$409$	−2.87526	+	1.50905i	−0.142172	+	0.0746179i	0.392137	+	0.919907i	$0.371736\pi$
$410$	9.43443	−	4.95157i	0.465933	−	0.244541i
$411$	0.818959	−	6.74473i	0.0403962	−	0.332693i
$412$	−26.9762	+	6.64904i	−1.32902	+	0.327575i
$413$	−3.97078	−	5.75267i	−0.195389	−	0.283070i
$414$	−8.08053	−	21.3066i	−0.397137	−	1.04716i
$415$	−1.27620	+	1.13061i	−0.0626461	+	0.0554996i
$416$	1.71935	+	1.52321i	0.0842981	+	0.0746816i
$417$	0.857253	−	0.759460i	0.0419799	−	0.0371909i
$418$	−24.1666	−	35.0113i	−1.18203	−	1.71246i
$419$	−11.2122	−	16.2436i	−0.547750	−	0.793553i	0.447146	−	0.894461i	$-0.352441\pi$
$419$	−11.2122	−	16.2436i	−0.547750	−	0.793553i	−0.994896	+	0.100908i	$0.967825\pi$
$420$	−2.31265	−	1.21377i	−0.112846	−	0.0592261i
$421$	8.61547	+	2.12352i	0.419892	+	0.103494i	0.443600	−	0.896225i	$-0.353701\pi$
$421$	8.61547	+	2.12352i	0.419892	+	0.103494i	−0.0237079	+	0.999719i	$0.507547\pi$
$422$	−41.8181	−	21.9478i	−2.03567	−	1.06840i
$423$	−10.9375	−	5.74043i	−0.531798	−	0.279109i
$424$	1.91193	−	5.04133i	0.0928513	−	0.244829i
$425$	0.211208	−	1.73945i	0.0102451	−	0.0843757i
$426$	0.162154	−	0.427564i	0.00785636	−	0.0207155i
$427$	3.95921	+	32.6070i	0.191600	+	1.57797i
$428$	−22.3825	+	11.7472i	−1.08190	+	0.567825i
$429$	3.65020	+	1.91577i	0.176233	+	0.0924943i
$430$	−1.69426	−	0.889214i	−0.0817043	−	0.0428817i
$431$	−14.0991	+	7.39978i	−0.679130	+	0.356435i	−0.768757	−	0.639540i	$-0.779125\pi$
$431$	−14.0991	+	7.39978i	−0.679130	+	0.356435i	0.0896274	+	0.995975i	$0.471432\pi$
$432$	0.889528	+	7.32592i	0.0427974	+	0.352469i
$433$	−7.64287	+	20.1526i	−0.367293	+	0.968471i	0.616211	+	0.787581i	$0.288667\pi$
$433$	−7.64287	+	20.1526i	−0.367293	+	0.968471i	−0.983503	+	0.180890i	$0.942102\pi$
$434$	2.20699	−	18.1762i	0.105939	−	0.872484i
$435$	0.255269	−	0.673088i	0.0122392	−	0.0322721i
$436$	37.4968	+	19.6799i	1.79577	+	0.942494i
$437$	17.6903	+	9.28460i	0.846243	+	0.444143i
$438$	−4.63932	−	1.14349i	−0.221675	−	0.0546381i
$439$	−6.05958	−	3.18031i	−0.289208	−	0.151788i	0.313880	−	0.949463i	$-0.398371\pi$
$439$	−6.05958	−	3.18031i	−0.289208	−	0.151788i	−0.603088	+	0.797675i	$0.706063\pi$
$440$	−4.10014	−	5.94008i	−0.195466	−	0.283182i
$441$	−9.74467	−	14.1176i	−0.464032	−	0.672266i
$442$	2.88816	−	2.55869i	0.137376	−	0.121704i
$443$	0.535699	+	0.474588i	0.0254518	+	0.0225483i	0.675753	−	0.737128i	$-0.263819\pi$
$443$	0.535699	+	0.474588i	0.0254518	+	0.0225483i	−0.650301	+	0.759677i	$0.725357\pi$
$444$	3.21592	−	2.84906i	0.152621	−	0.135210i
$445$	−1.79117	−	4.72292i	−0.0849094	−	0.223888i
$446$	−22.1751	−	32.1262i	−1.05002	−	1.52122i
$447$	−5.74257	+	1.41542i	−0.271614	+	0.0669469i
$448$	−3.75154	+	30.8968i	−0.177244	+	1.45973i
$449$	12.7836	−	6.70937i	0.603297	−	0.316635i	−0.135276	−	0.990808i	$-0.543192\pi$
$449$	12.7836	−	6.70937i	0.603297	−	0.316635i	0.738573	+	0.674173i	$0.235500\pi$
$450$	−29.3172	+	15.3868i	−1.38203	+	0.725343i
$451$	−20.3733	−	10.6927i	−0.959341	−	0.503501i
$452$	4.48400	−	2.35338i	0.210909	−	0.110694i
$453$	4.66875	−	1.15074i	0.219357	−	0.0540667i
$454$	−34.4381	−	8.48823i	−1.61626	−	0.398372i
$455$	6.16431	−	5.46111i	0.288988	−	0.256021i
$456$	−7.47927	−	6.62606i	−0.350249	−	0.310293i
$457$	29.7627	−	7.33585i	1.39224	−	0.343157i	0.529289	−	0.848442i	$-0.322459\pi$
$457$	29.7627	−	7.33585i	1.39224	−	0.343157i	0.862953	+	0.505285i	$0.168613\pi$
$458$	−21.9803	+	11.5361i	−1.02707	+	0.539048i
$459$	−0.748719			−0.0349472
$460$	6.08943	+	3.19598i	0.283921	+	0.149013i
$461$	−20.5791			−0.958466			−0.479233	−	0.877688i	$-0.659085\pi$
$461$	−20.5791			−0.958466			−0.479233	+	0.877688i	$0.659085\pi$
$462$	1.02460	+	8.43837i	0.0476689	+	0.392588i
$463$	−0.558325	+	4.59822i	−0.0259476	+	0.213697i	−0.999916	−	0.0129877i	$-0.995866\pi$
$463$	−0.558325	+	4.59822i	−0.0259476	+	0.213697i	0.973968	+	0.226685i	$0.0727888\pi$
$464$	14.3415			0.665786
$465$	−0.287468	−	0.254674i	−0.0133310	−	0.0118102i
$466$	0.566056	−	0.820074i	0.0262221	−	0.0379892i
$467$	1.88573	+	15.5304i	0.0872613	+	0.718661i	0.969024	+	0.246968i	$0.0794341\pi$
$467$	1.88573	+	15.5304i	0.0872613	+	0.718661i	−0.881762	+	0.471694i	$0.843643\pi$
$468$	−46.9715	−	11.5774i	−2.17126	−	0.535167i
$469$	29.6719	−	15.5730i	1.37012	−	0.719094i
$470$	5.45513	−	1.34457i	0.251626	−	0.0620203i
$471$	−1.77112	+	4.67007i	−0.0816090	+	0.215185i
$472$	−3.26423	−	8.60707i	−0.150249	−	0.396173i
$473$	0.498055	+	4.10185i	0.0229006	+	0.188603i
$474$	−1.89632	−	1.67999i	−0.0871007	−	0.0771644i
$475$	10.2937	−	27.1424i	0.472309	−	1.24538i
$476$	5.12574	+	1.26338i	0.234938	+	0.0579069i
$477$	−0.395350	−	3.25600i	−0.0181018	−	0.149082i
$478$	34.2428	+	8.44008i	1.56623	+	0.386040i
$479$	38.1490			1.74307			0.871537	−	0.490330i	$-0.163124\pi$
$479$	38.1490			1.74307			0.871537	+	0.490330i	$0.163124\pi$
$480$	0.0743640	+	0.0658807i	0.00339424	+	0.00300703i
$481$	4.80391	+	12.6669i	0.219039	+	0.577560i
$482$	4.02641	−	10.6168i	0.183398	−	0.483580i
$483$	−2.26770	−	3.28533i	−0.103184	−	0.149488i
$484$	4.16992	−	10.9952i	0.189542	−	0.499781i
$485$	−5.55364	−	4.92009i	−0.252178	−	0.223410i
$486$	12.1351	+	17.5808i	0.550461	+	0.797480i
$487$	−11.2077	+	29.5522i	−0.507868	+	1.33914i	0.398702	+	0.917081i	$0.369461\pi$
$487$	−11.2077	+	29.5522i	−0.507868	+	1.33914i	−0.906570	+	0.422056i	$0.861308\pi$
$488$	−5.21395	+	42.9408i	−0.236025	+	1.94384i
$489$	−0.0426012	+	0.350853i	−0.00192649	+	0.0158661i
$490$	7.57572	+	1.86725i	0.342236	+	0.0843537i
$491$	−1.99527	+	16.4325i	−0.0900451	+	0.741588i	0.875837	+	0.482607i	$0.160310\pi$
$491$	−1.99527	+	16.4325i	−0.0900451	+	0.741588i	−0.965882	+	0.258981i	$0.916613\pi$
$492$	−10.6461	−	2.62402i	−0.479961	−	0.118300i
$493$	−0.175385	+	1.44442i	−0.00789892	+	0.0650535i
$494$	56.6016	−	29.7068i	2.54663	−	1.33657i
$495$	−3.88780	−	2.04048i	−0.174744	−	0.0917126i
$496$	2.71317	−	7.15404i	0.121825	−	0.321226i
$497$	−0.237785	+	1.95833i	−0.0106661	+	0.0878433i
$498$	2.64432			0.118495
$499$	−21.2364	−	18.8138i	−0.950672	−	0.842222i	0.0369109	−	0.999319i	$-0.488248\pi$
$499$	−21.2364	−	18.8138i	−0.950672	−	0.842222i	−0.987583	+	0.157096i	$0.949787\pi$
$500$	7.30430	−	19.2599i	0.326658	−	0.861327i
$501$	0.134406	−	0.354399i	0.00600481	−	0.0158334i
$502$	53.9508	+	13.2977i	2.40794	+	0.593504i
$503$	−11.7169	+	10.3803i	−0.522431	+	0.462833i	−0.882648	−	0.470035i	$-0.844241\pi$
$503$	−11.7169	+	10.3803i	−0.522431	+	0.462833i	0.360217	+	0.932869i	$0.382703\pi$
$504$	−17.4347	−	45.9716i	−0.776605	−	2.04774i
$505$	0.641409	+	1.69126i	0.0285423	+	0.0752599i
$506$	−2.69788	−	22.2190i	−0.119935	−	0.987755i
$507$	−0.992021	+	1.43719i	−0.0440572	+	0.0638279i
$508$	7.00693	+	1.72705i	0.310882	+	0.0766256i
$509$	−15.5668	+	3.83688i	−0.689988	+	0.170067i	−0.568693	−	0.822550i	$-0.692551\pi$
$509$	−15.5668	+	3.83688i	−0.689988	+	0.170067i	−0.121295	+	0.992617i	$0.538705\pi$
$510$	0.124916	−	0.110666i	0.00553139	−	0.00490038i
$511$	20.6131			0.911872
$512$	−13.0243	+	34.3423i	−0.575598	+	1.51773i
$513$	−12.0434	−	2.96844i	−0.531731	−	0.131060i
$514$	36.8826	+	19.3575i	1.62682	+	0.853822i
$515$	0.456718	−	3.76141i	0.0201254	−	0.165748i
$516$	0.698238	+	1.84110i	0.0307382	+	0.0810501i
$517$	−9.08145	−	8.04547i	−0.399402	−	0.353839i
$518$	−15.8685	+	22.9895i	−0.697221	+	1.01010i
$519$	−3.84265	+	0.947128i	−0.168674	+	0.0415743i
$520$	9.60312	−	5.04010i	0.421124	−	0.221023i
$521$	−1.50032	+	0.787428i	−0.0657302	+	0.0344979i	−0.497268	−	0.867597i	$-0.665663\pi$
$521$	−1.50032	+	0.787428i	−0.0657302	+	0.0344979i	0.431538	+	0.902095i	$0.357971\pi$
$522$	24.3447	−	12.7771i	1.06554	−	0.559237i
$523$	−5.11755	+	42.1468i	−0.223775	+	1.84295i	0.257372	+	0.966312i	$0.417143\pi$
$523$	−5.11755	+	42.1468i	−0.223775	+	1.84295i	−0.481147	+	0.876640i	$0.659780\pi$
$524$	−38.5553	+	55.8571i	−1.68430	+	2.44013i
$525$	−4.34156	+	3.84629i	−0.189481	+	0.167866i
$526$	−54.7255	+	48.4826i	−2.38615	+	2.11394i
$527$	0.687350	+	0.360749i	0.0299414	+	0.0157145i
$528$	−0.428161	+	3.52622i	−0.0186333	+	0.153459i
$529$	−7.09442	−	10.2780i	−0.308453	−	0.446871i
$530$	1.11666	+	0.989278i	0.0485048	+	0.0429715i
$531$	−4.19152	−	3.71336i	−0.181896	−	0.161146i
$532$	77.4406	+	40.6439i	3.35747	+	1.76214i
$533$	19.6398	−	28.4531i	0.850693	−	1.23244i
$534$	−2.77799	+	7.32495i	−0.120215	+	0.316981i
$535$	−0.415530	−	3.42219i	−0.0179649	−	0.147954i
$536$	42.8479	−	10.5611i	1.85075	−	0.456168i
$537$	0.844506	+	6.95513i	0.0364431	+	0.300136i
$538$	−51.3386	+	26.9446i	−2.21336	+	1.16166i
$539$	−5.97477	−	15.7542i	−0.257352	−	0.678580i
$540$	−4.14564	−	1.02181i	−0.178400	−	0.0439716i
$541$	−3.49129	+	9.20578i	−0.150102	+	0.395787i	−0.988886	−	0.148678i	$-0.952498\pi$
$541$	−3.49129	+	9.20578i	−0.150102	+	0.395787i	0.838783	+	0.544465i	$0.183267\pi$
$542$	−57.2252	−	30.0341i	−2.45803	−	1.29008i
$543$	−0.746983	−	1.96963i	−0.0320561	−	0.0845250i
$544$	−0.177808	−	0.0933208i	−0.00762345	−	0.00400109i
$545$	−4.32281	+	3.82968i	−0.185169	+	0.164045i
$546$	−12.7726			−0.546619
$547$	26.0246	+	23.0558i	1.11273	+	0.985795i	0.999969	−	0.00782735i	$-0.00249155\pi$
$547$	26.0246	+	23.0558i	1.11273	+	0.985795i	0.112763	+	0.993622i	$0.464030\pi$
$548$	−9.43975	+	77.7434i	−0.403246	+	3.32103i
$549$	9.33102	+	24.6039i	0.398238	+	1.05007i
$550$	−31.5759	+	7.78276i	−1.34640	+	0.331858i
$551$	−8.54782	+	22.5387i	−0.364149	+	0.960183i
$552$	−1.86420	−	4.91548i	−0.0793454	−	0.209217i
$553$	9.67749	+	5.07914i	0.411529	+	0.215987i
$554$	13.3418	+	19.3290i	0.566840	+	0.821210i
$555$	0.207775	+	0.547857i	0.00881955	+	0.0232552i
$556$	−9.88116	+	8.75394i	−0.419054	+	0.371250i
$557$	−36.6383	−	9.03053i	−1.55241	−	0.382636i	−0.632438	−	0.774611i	$-0.717946\pi$
$557$	−36.6383	−	9.03053i	−1.55241	−	0.382636i	−0.919976	+	0.391975i	$0.871792\pi$
$558$	−1.76805	−	14.5612i	−0.0748476	−	0.616425i
$559$	−6.20872			−0.262601
$560$	6.28337	+	3.29777i	0.265521	+	0.139356i
$561$	−0.349913	−	0.0862458i	−0.0147733	−	0.00364130i
$562$	3.82785	−	31.5252i	0.161468	−	1.32981i
$563$	6.74708	−	1.66301i	0.284355	−	0.0700873i	−0.0945582	−	0.995519i	$-0.530144\pi$
$563$	6.74708	−	1.66301i	0.284355	−	0.0700873i	0.378914	+	0.925432i	$0.376298\pi$
$564$	−5.11948	−	2.68691i	−0.215569	−	0.113139i
$565$	0.0832451	+	0.685585i	0.00350215	+	0.0288428i
$566$	−34.9739	−	50.6684i	−1.47006	−	2.12975i
$567$	−21.4415	−	18.9955i	−0.900457	−	0.797735i
$568$	−0.921230	+	2.42908i	−0.0386539	+	0.101922i
$569$	28.2139	−	24.9954i	1.18279	−	1.04786i	0.184912	−	0.982755i	$-0.440800\pi$
$569$	28.2139	−	24.9954i	1.18279	−	1.04786i	0.997878	−	0.0651053i	$-0.0207383\pi$
$570$	2.44809	−	1.28485i	0.102539	−	0.0538166i
$571$	3.68225	−	9.70930i	0.154097	−	0.406322i	−0.835629	−	0.549294i	$-0.814897\pi$
$571$	3.68225	−	9.70930i	0.154097	−	0.406322i	0.989727	+	0.142972i	$0.0456660\pi$
$572$	−42.0741	−	22.0822i	−1.75921	−	0.923303i
$573$	3.16520	+	4.58559i	0.132228	+	0.191566i
$574$	71.2895			2.97557
$575$	11.4317	−	10.1276i	0.476736	−	0.422352i
$576$	3.00542	+	24.7519i	0.125226	+	1.03133i
$577$	13.0509	+	18.9076i	0.543318	+	0.787132i	0.994437	−	0.105332i	$-0.0335905\pi$
$577$	13.0509	+	18.9076i	0.543318	+	0.787132i	−0.451119	+	0.892464i	$0.648975\pi$
$578$	23.3524	−	33.8318i	0.971332	−	1.40722i
$579$	2.71382	+	3.93165i	0.112782	+	0.163394i
$580$	−2.94236	+	7.75837i	−0.122175	+	0.322149i
$581$	−11.0762	+	2.73004i	−0.459518	+	0.113261i
$582$	1.38705	+	11.4234i	0.0574952	+	0.473515i
$583$	0.388320	−	3.19810i	0.0160826	−	0.132452i
$584$	26.3570	+	6.49642i	1.09066	+	0.268824i
$585$	3.74783	−	5.42967i	0.154954	−	0.224489i
$586$	−72.7114	−	38.1619i	−3.00368	−	1.57645i
$587$	8.04240	+	11.6514i	0.331945	+	0.480906i	0.953046	−	0.302825i	$-0.0979297\pi$
$587$	8.04240	+	11.6514i	0.331945	+	0.480906i	−0.621101	+	0.783731i	$0.713314\pi$
$588$	−4.56116	−	6.60799i	−0.188099	−	0.272509i
$589$	9.62603	+	8.52792i	0.396634	+	0.351387i
$590$	2.54703			0.104860
$591$	−2.96002	−	0.729580i	−0.121759	−	0.0300109i
$592$	−8.73749	+	7.74074i	−0.359109	+	0.318143i
$593$	14.5161	+	21.0302i	0.596105	+	0.863607i	0.998658	−	0.0517893i	$-0.0164924\pi$
$593$	14.5161	+	21.0302i	0.596105	+	0.863607i	−0.402553	+	0.915397i	$0.631877\pi$
$594$	4.92761	+	12.9930i	0.202182	+	0.533110i
$595$	−0.408980	+	0.592510i	−0.0167665	+	0.0242905i
$596$	66.1919	−	16.3148i	2.71133	−	0.668282i
$597$	1.88010	−	0.986751i	0.0769473	−	0.0403850i
$598$	33.6316			1.37530
$599$	1.25242			0.0511727			0.0255863	−	0.999673i	$-0.491855\pi$
$599$	1.25242			0.0511727			0.0255863	+	0.999673i	$0.491855\pi$
$600$	−6.76353	+	3.54977i	−0.276120	+	0.144919i
$601$	−4.62306	+	38.0744i	−0.188579	+	1.55309i	0.524138	+	0.851633i	$0.324388\pi$
$601$	−4.62306	+	38.0744i	−0.188579	+	1.55309i	−0.712717	+	0.701452i	$0.752536\pi$
$602$	−7.27256	−	10.5361i	−0.296407	−	0.429420i
$603$	20.0942	−	17.8019i	0.818300	−	0.724950i
$604$	−53.8145	+	13.2641i	−2.18968	+	0.539708i
$605$	1.20039	+	1.06345i	0.0488028	+	0.0432355i
$606$	0.994785	−	2.62303i	0.0404104	−	0.106553i
$607$	1.81695	−	14.9640i	0.0737479	−	0.607369i	−0.908243	−	0.418442i	$-0.862576\pi$
$607$	1.81695	−	14.9640i	0.0737479	−	0.607369i	0.981991	−	0.188926i	$-0.0605007\pi$
$608$	−2.49012	−	2.20605i	−0.100988	−	0.0894673i
$609$	3.60519	−	3.19392i	0.146090	−	0.129424i
$610$	−10.5977	−	5.56212i	−0.429090	−	0.225204i
$611$	13.6458	−	12.0891i	0.552051	−	0.489074i
$612$	4.22920			0.170955
$613$	15.7571	+	13.9596i	0.636424	+	0.563822i	0.918427	−	0.395591i	$-0.129460\pi$
$613$	15.7571	+	13.9596i	0.636424	+	0.563822i	−0.282003	+	0.959414i	$0.590999\pi$
$614$	39.6513	+	35.1280i	1.60020	+	1.41765i
$615$	0.849443	−	1.23063i	0.0342529	−	0.0496238i
$616$	−5.82099	−	47.9402i	−0.234535	−	1.93157i
$617$	3.06192	−	2.71262i	0.123268	−	0.109206i	−0.599237	−	0.800572i	$-0.704529\pi$
$617$	3.06192	−	2.71262i	0.123268	−	0.109206i	0.722505	+	0.691366i	$0.242991\pi$
$618$	−4.39867	+	3.89688i	−0.176940	+	0.156755i
$619$	−10.9643	−	28.9105i	−0.440693	−	1.16201i	−0.952936	−	0.303171i	$-0.901955\pi$
$619$	−10.9643	−	28.9105i	−0.440693	−	1.16201i	0.512244	−	0.858840i	$-0.328814\pi$
$620$	3.31351	+	2.93551i	0.133074	+	0.117893i
$621$	−4.88473	−	4.32750i	−0.196018	−	0.173656i
$622$	1.60566	+	4.23379i	0.0643813	+	0.169759i
$623$	4.07369	−	33.5498i	0.163209	−	1.34415i
$624$	−5.18234	−	1.27733i	−0.207460	−	0.0511342i
$625$	−15.5274	−	13.7561i	−0.621097	−	0.550244i
$626$	−62.1184	+	32.6022i	−2.48275	+	1.30305i
$627$	−5.28655	−	2.77459i	−0.211124	−	0.110807i
$628$	20.4149	−	53.8297i	0.814643	−	2.14804i
$629$	−0.672768	−	0.974673i	−0.0268250	−	0.0388628i
$630$	13.6041			0.541999
$631$	−3.72049	−	9.81013i	−0.148110	−	0.390535i	0.840344	−	0.542053i	$-0.182353\pi$
$631$	−3.72049	−	9.81013i	−0.148110	−	0.390535i	−0.988454	+	0.151518i	$0.951584\pi$
$632$	10.7734	+	9.54438i	0.428542	+	0.379655i
$633$	−6.62804			−0.263441
$634$	9.01949			0.358210
$635$	−0.559080	+	0.809967i	−0.0221864	+	0.0321425i
$636$	−0.185051	−	1.52403i	−0.00733774	−	0.0604317i
$637$	24.5818	−	6.05888i	0.973968	−	0.240061i
$638$	26.2203	−	6.46272i	1.03807	−	0.255862i
$639$	0.190493	+	1.56885i	0.00753579	+	0.0620628i
$640$	−8.05411	−	7.13532i	−0.318367	−	0.282048i
$641$	21.7756	+	31.5474i	0.860083	+	1.24605i	0.967764	+	0.251860i	$0.0810422\pi$
$641$	21.7756	+	31.5474i	0.860083	+	1.24605i	−0.107681	+	0.994186i	$0.534342\pi$
$642$	−3.03721	+	4.40016i	−0.119869	+	0.173660i
$643$	9.70450	−	25.5887i	0.382708	−	1.00912i	−0.595840	−	0.803103i	$-0.703181\pi$
$643$	9.70450	−	25.5887i	0.382708	−	1.00912i	0.978549	−	0.206016i	$-0.0660498\pi$
$644$	26.1387	+	37.8685i	1.03001	+	1.49223i
$645$	−0.268534			−0.0105735
$646$	−4.18290	+	3.70572i	−0.164574	+	0.145800i
$647$	6.86990	−	6.08620i	0.270084	−	0.239273i	−0.517200	−	0.855865i	$-0.673025\pi$
$647$	6.86990	−	6.08620i	0.270084	−	0.239273i	0.787283	+	0.616592i	$0.211487\pi$
$648$	−21.4295	−	31.0460i	−0.841832	−	1.21960i
$649$	−3.12448	−	4.52660i	−0.122647	−	0.177684i
$650$	−5.89015	−	48.5097i	−0.231031	−	1.90271i
$651$	−0.911199	−	2.40263i	−0.0357127	−	0.0941667i
$652$	0.491044	−	4.04411i	0.0192308	−	0.158380i
$653$	−36.4367	−	8.98083i	−1.42588	−	0.351447i	−0.550479	−	0.834849i	$-0.685555\pi$
$653$	−36.4367	−	8.98083i	−1.42588	−	0.351447i	−0.875398	+	0.483402i	$0.839401\pi$
$654$	8.95700			0.350247
$655$	−5.25806	−	7.61762i	−0.205449	−	0.297645i
$656$	28.9248	+	7.12933i	1.12932	+	0.278353i
$657$	16.0337	−	3.95194i	0.625533	−	0.154180i
$658$	36.4991	+	8.99622i	1.42288	+	0.350709i
$659$	−34.5647	−	18.1410i	−1.34645	−	0.706671i	−0.371361	−	0.928489i	$-0.621109\pi$
$659$	−34.5647	−	18.1410i	−1.34645	−	0.706671i	−0.975088	+	0.221817i	$0.928801\pi$
$660$	−1.81976	−	0.955081i	−0.0708339	−	0.0371765i
$661$	4.49668	−	6.51457i	0.174901	−	0.253387i	−0.725723	−	0.687987i	$-0.758495\pi$
$661$	4.49668	−	6.51457i	0.174901	−	0.253387i	0.900624	+	0.434599i	$0.143110\pi$
$662$	19.1365	+	50.4589i	0.743763	+	1.96114i
$663$	0.192024	−	0.506326i	0.00745760	−	0.0196641i
$664$	−15.0230			−0.583004
$665$	−8.92772	+	7.90927i	−0.346202	+	0.306708i
$666$	−7.93555	+	20.9243i	−0.307496	+	0.810802i
$667$	−9.49279	+	8.40988i	−0.367562	+	0.325632i
$668$	−1.54923	+	4.08499i	−0.0599417	+	0.158053i
$669$	−4.85091	−	2.54596i	−0.187547	−	0.0984323i
$670$	−1.47182	+	12.1215i	−0.0568612	+	0.468295i
$671$	3.11538	+	25.6575i	0.120268	+	0.990496i
$672$	0.235715	+	0.621528i	0.00909289	+	0.0239760i
$673$	−16.1386	+	14.2976i	−0.622098	+	0.551131i	−0.914203	−	0.405255i	$-0.867183\pi$
$673$	−16.1386	+	14.2976i	−0.622098	+	0.551131i	0.292106	+	0.956386i	$0.405644\pi$
$674$	36.4509	−	52.8082i	1.40404	−	2.03410i
$675$	−5.38642	+	7.80358i	−0.207324	+	0.300360i
$676$	11.4346	−	16.5658i	0.439791	−	0.637147i
$677$	24.3383	+	35.2602i	0.935398	+	1.35516i	0.934806	+	0.355158i	$0.115573\pi$
$677$	24.3383	+	35.2602i	0.935398	+	1.35516i	0.000591950		1.00000i	$0.499812\pi$
$678$	0.608459	−	0.881505i	0.0233677	−	0.0338540i
$679$	−17.6036	−	46.4169i	−0.675564	−	1.78132i
$680$	−0.709677	+	0.628719i	−0.0272149	+	0.0241103i
$681$	−4.83312	+	1.19126i	−0.185205	+	0.0456490i
$682$	1.73661	−	14.3023i	0.0664982	−	0.547662i
$683$	37.9053	−	19.8942i	1.45040	−	0.761231i	0.458558	−	0.888665i	$-0.348366\pi$
$683$	37.9053	−	19.8942i	1.45040	−	0.761231i	0.991847	+	0.127433i	$0.0406739\pi$
$684$	68.0283	+	16.7675i	2.60113	+	0.641121i
$685$	−9.45691	−	4.96337i	−0.361330	−	0.189641i
$686$	−6.89378	−	6.10736i	−0.263206	−	0.233180i
$687$	−1.97903	+	2.86711i	−0.0755045	+	0.109387i
$688$	−1.89708	−	5.00219i	−0.0723255	−	0.190707i
$689$	4.70011	+	1.15847i	0.179060	+	0.0441343i
$690$	1.45460			0.0553759
$691$	13.1609	−	19.0669i	0.500665	−	0.725338i	−0.488433	−	0.872602i	$-0.662431\pi$
$691$	13.1609	−	19.0669i	0.500665	−	0.725338i	0.989097	+	0.147264i	$0.0470465\pi$
$692$	44.2924	−	10.9171i	1.68375	−	0.415006i
$693$	−16.6883	−	24.1772i	−0.633937	−	0.918416i
$694$	10.0956	+	83.1447i	0.383223	+	3.15613i
$695$	−0.638404	−	1.68333i	−0.0242160	−	0.0638525i
$696$	5.61636	−	2.94770i	0.212888	−	0.111732i
$697$	−1.07177	+	2.82602i	−0.0405961	+	0.107043i
$698$	−17.4212	+	45.9360i	−0.659403	+	1.73870i
$699$	0.0168566	−	0.138826i	0.000637574	−	0.00525089i
$700$	50.0432	−	44.3344i	1.89145	−	1.67568i
$701$	3.48524	−	28.7035i	0.131636	−	1.08412i	−0.765833	−	0.643040i	$-0.777673\pi$
$701$	3.48524	−	28.7035i	0.131636	−	1.08412i	0.897469	−	0.441078i	$-0.145404\pi$
$702$	−20.2735	+	4.99697i	−0.765174	+	0.188599i
$703$	−6.95746	−	18.3453i	−0.262406	−	0.691907i
$704$	−2.95197	+	24.3117i	−0.111257	+	0.916281i
$705$	0.590198	−	0.522870i	0.0222281	−	0.0196924i
$706$	−19.4320	−	28.1521i	−0.731332	−	1.05952i
$707$	−1.45877	+	12.0141i	−0.0548627	+	0.451835i
$708$	−1.96191	−	1.73810i	−0.0737332	−	0.0653219i
$709$	30.7665	+	16.1475i	1.15546	+	0.606432i	0.929906	−	0.367798i	$-0.119888\pi$
$709$	30.7665	+	16.1475i	1.15546	+	0.606432i	0.225555	+	0.974231i	$0.427581\pi$
$710$	−0.538046	−	0.476667i	−0.0201925	−	0.0178890i
$711$	8.50127	+	2.09538i	0.318823	+	0.0785827i
$712$	15.7823	−	41.6146i	0.591468	−	1.55957i
$713$	2.39927	+	6.32636i	0.0898534	+	0.236924i
$714$	1.08416	−	0.267220i	0.0405735	−	0.0100005i
$715$	4.85051	−	4.29717i	0.181399	−	0.160705i
$716$	−9.73422	−	80.1685i	−0.363785	−	2.99604i
$717$	4.80570	−	1.18450i	0.179472	−	0.0442359i
$718$	6.58283	+	54.2145i	0.245669	+	2.02327i
$719$	−3.34478	−	27.5467i	−0.124739	−	1.02732i	−0.911854	−	0.410514i	$-0.865349\pi$
$719$	−3.34478	−	27.5467i	−0.124739	−	1.02732i	0.787115	−	0.616806i	$-0.211574\pi$
$720$	5.51968	+	1.36048i	0.205706	+	0.0507020i
$721$	14.4014	−	20.8640i	0.536335	−	0.777016i
$722$	−40.9594	+	21.4972i	−1.52435	+	0.800042i
$723$	−0.192079	−	1.58191i	−0.00714350	−	0.0588320i
$724$	8.61013	+	22.7030i	0.319993	+	0.843752i
$725$	13.7928	+	12.2194i	0.512253	+	0.453817i
$726$	−0.299804	−	2.46911i	−0.0111268	−	0.0916372i
$727$	−31.2291	+	16.3903i	−1.15822	+	0.607882i	−0.930661	−	0.365882i	$-0.880767\pi$
$727$	−31.2291	+	16.3903i	−1.15822	+	0.607882i	−0.227561	+	0.973764i	$0.573075\pi$
$728$	72.5642			2.68941
$729$	−18.4903	−	9.70445i	−0.684825	−	0.359424i
$730$	−4.26677	+	6.18148i	−0.157920	+	0.228787i
$731$	0.527003	−	0.129894i	0.0194919	−	0.00480432i
$732$	4.36755	+	11.5163i	0.161429	+	0.425654i
$733$	−20.4372	+	29.6085i	−0.754867	+	1.09361i	0.237631	+	0.971355i	$0.423629\pi$
$733$	−20.4372	+	29.6085i	−0.754867	+	1.09361i	−0.992498	+	0.122258i	$0.960986\pi$
$734$	−51.6752	+	12.7368i	−1.90737	+	0.470124i
$735$	1.06319	−	0.262054i	0.0392165	−	0.00966599i
$736$	−0.620658	−	1.63654i	−0.0228778	−	0.0603237i
$737$	23.3479	−	12.2539i	0.860030	−	0.451378i
$738$	55.4516	−	13.6676i	2.04120	−	0.503111i
$739$	−2.35864	+	19.4251i	−0.0867639	+	0.714565i	0.882804	+	0.469742i	$0.155653\pi$
$739$	−2.35864	+	19.4251i	−0.0867639	+	0.714565i	−0.969568	+	0.244823i	$0.921270\pi$
$740$	−2.39492	−	6.31489i	−0.0880391	−	0.232140i
$741$	5.09621	−	7.38314i	0.187214	−	0.271226i
$742$	3.53954	+	9.33299i	0.129941	+	0.342625i
$743$	14.0481	+	20.3522i	0.515375	+	0.746650i	0.991125	−	0.132930i	$-0.0424387\pi$
$743$	14.0481	+	20.3522i	0.515375	+	0.746650i	−0.475750	+	0.879581i	$0.657823\pi$
$744$	−0.407893	−	3.35930i	−0.0149541	−	0.123158i
$745$	−1.12066	+	9.22943i	−0.0410576	+	0.338140i
$746$	57.7173	+	30.2924i	2.11318	+	1.10908i
$747$	−8.09207	+	4.24704i	−0.296073	+	0.155391i
$748$	4.03328	+	0.994115i	0.147471	+	0.0363484i
$749$	8.17909	−	21.5665i	0.298857	−	0.788022i
$750$	−0.525156	−	4.32505i	−0.0191760	−	0.157928i
$751$	−18.3726	+	16.2767i	−0.670426	+	0.593946i	−0.928120	−	0.372281i	$-0.878576\pi$
$751$	−18.3726	+	16.2767i	−0.670426	+	0.593946i	0.257694	+	0.966227i	$0.417037\pi$
$752$	13.9094	+	7.30020i	0.507222	+	0.266211i
$753$	7.57156	−	1.86622i	0.275923	−	0.0680089i
$754$	4.89112	+	40.2820i	0.178124	+	1.46698i
$755$	0.911101	−	7.50360i	0.0331584	−	0.273084i
$756$	−21.3832	−	18.9439i	−0.777701	−	0.688983i
$757$	4.87735	+	40.1686i	0.177270	+	1.45995i	0.761395	+	0.648288i	$0.224515\pi$
$757$	4.87735	+	40.1686i	0.177270	+	1.45995i	−0.584125	+	0.811663i	$0.698562\pi$
$758$	−32.0563	−	7.90118i	−1.16434	−	0.286984i
$759$	−1.78438	−	2.58513i	−0.0647691	−	0.0938342i
$760$	−13.9081	+	7.29954i	−0.504500	+	0.264782i
$761$	−21.1598	+	18.7459i	−0.767042	+	0.679540i	−0.952984	−	0.303021i	$-0.902005\pi$
$761$	−21.1598	+	18.7459i	−0.767042	+	0.679540i	0.185942	+	0.982561i	$0.440466\pi$
$762$	1.48205	−	0.365293i	0.0536891	−	0.0132332i
$763$	−37.5179	+	9.24734i	−1.35824	+	0.334776i
$764$	−36.4838	−	52.8559i	−1.31994	−	1.91226i
$765$	−0.204524	+	0.539285i	−0.00739457	+	0.0194979i
$766$	−17.1169	+	4.21893i	−0.618458	+	0.152436i
$767$	7.31799	−	3.84078i	0.264237	−	0.138682i
$768$	1.29818	+	10.6914i	0.0468439	+	0.385794i
$769$	−3.05034	+	25.1218i	−0.109998	+	0.905916i	0.828347	+	0.560216i	$0.189282\pi$
$769$	−3.05034	+	25.1218i	−0.109998	+	0.905916i	−0.938345	+	0.345700i	$0.887641\pi$
$770$	12.9739	+	3.19777i	0.467546	+	0.115240i
$771$	5.84578			0.210531
$772$	−31.2809	−	45.3182i	−1.12583	−	1.63104i
$773$	14.1432	−	7.42293i	0.508696	−	0.266984i	−0.190789	−	0.981631i	$-0.561105\pi$
$773$	14.1432	−	7.42293i	0.508696	−	0.266984i	0.699486	+	0.714647i	$0.253412\pi$
$774$	−7.67684	−	6.80109i	−0.275938	−	0.244460i
$775$	8.70485	−	4.56866i	0.312688	−	0.164111i
$776$	−7.88014	−	64.8988i	−0.282881	−	2.32973i
$777$	−0.472547	+	3.89177i	−0.0169525	+	0.139617i
$778$	−65.8126	+	58.3048i	−2.35949	+	2.09033i
$779$	−28.4441	+	41.2084i	−1.01912	+	1.47644i
$780$	1.75424	−	2.54145i	0.0628118	−	0.0909985i
$781$	−0.187105	+	1.54095i	−0.00669516	+	0.0551396i
$782$	−2.85468	+	0.703616i	−0.102083	+	0.0251612i
$783$	4.47283	−	6.48001i	0.159846	−	0.231577i
$784$	12.3925	+	17.9536i	0.442588	+	0.641199i
$785$	5.87681	+	5.20640i	0.209752	+	0.185824i
$786$	−1.73038	+	14.2510i	−0.0617206	+	0.508315i
$787$	31.3735	−	7.73288i	1.11835	−	0.275647i	0.363529	−	0.931583i	$-0.381572\pi$
$787$	31.3735	−	7.73288i	1.11835	−	0.275647i	0.754817	+	0.655936i	$0.227726\pi$
$788$	34.1188	+	8.40953i	1.21543	+	0.299577i
$789$	−3.63852	+	9.59399i	−0.129535	+	0.341555i
$790$	−3.52630	+	1.85075i	−0.125460	+	0.0658466i
$791$	−1.63856	+	4.32052i	−0.0582604	+	0.153620i
$792$	−13.7189	−	36.1736i	−0.487478	−	1.28537i
$793$	−38.8362			−1.37911
$794$	17.9153	+	25.9549i	0.635792	+	0.921104i
$795$	0.203285	+	0.0501053i	0.00720978	+	0.00177705i
$796$	−21.6710	+	11.3738i	−0.768109	+	0.403134i
$797$	27.2754	+	6.72279i	0.966145	+	0.238133i	0.690666	−	0.723174i	$-0.257317\pi$
$797$	27.2754	+	6.72279i	0.966145	+	0.238133i	0.275479	+	0.961307i	$0.411164\pi$
$798$	18.4985			0.654840
$799$	−0.905351	+	1.31163i	−0.0320290	+	0.0464020i
$800$	−2.25183	+	1.18185i	−0.0796140	+	0.0417847i
$801$	−3.26349	−	26.8773i	−0.115310	−	0.949662i
$802$	−6.02491	+	8.72859i	−0.212747	+	0.308217i
$803$	16.2198			0.572386
$804$	9.40545	−	8.33250i	0.331705	−	0.293865i
$805$	−6.09286	+	1.50176i	−0.214745	+	0.0529299i
$806$	21.0194	+	5.18082i	0.740377	+	0.182487i
$807$	−4.62235	+	6.69663i	−0.162714	+	0.235733i
$808$	−5.65159	+	14.9020i	−0.198822	+	0.524251i
$809$	3.28500	+	27.0544i	0.115494	+	0.951181i	0.929116	+	0.369787i	$0.120569\pi$
$809$	3.28500	+	27.0544i	0.115494	+	0.951181i	−0.813622	+	0.581394i	$0.802507\pi$
$810$	10.1346	−	2.49795i	0.356093	−	0.0877691i
$811$	53.0207	+	13.0684i	1.86181	+	0.458895i	0.998918	−	0.0464970i	$-0.0148058\pi$
$811$	53.0207	+	13.0684i	1.86181	+	0.458895i	0.862890	+	0.505392i	$0.168652\pi$
$812$	−41.5553	+	36.8148i	−1.45831	+	1.29195i
$813$	−9.07003			−0.318100
$814$	−12.4864	+	18.0897i	−0.437649	+	0.634043i
$815$	0.491937	+	0.258188i	0.0172318	+	0.00904395i
$816$	0.466605			0.0163345
$817$	8.99203			0.314591
$818$	4.49720	−	6.51532i	0.157241	−	0.227803i
$819$	39.0864	−	20.5141i	1.36579	−	0.716822i
$820$	−9.79114	+	14.1849i	−0.341921	+	0.495359i
$821$	−14.7516	+	7.74222i	−0.514833	+	0.270205i	−0.702068	−	0.712110i	$-0.747740\pi$
$821$	−14.7516	+	7.74222i	−0.514833	+	0.270205i	0.187235	+	0.982315i	$0.440047\pi$
$822$	5.87383	+	15.4880i	0.204873	+	0.540207i
$823$	−31.6174	−	7.79298i	−1.10211	−	0.271646i	−0.354018	−	0.935239i	$-0.615185\pi$
$823$	−31.6174	−	7.79298i	−1.10211	−	0.271646i	−0.748094	+	0.663593i	$0.769031\pi$
$824$	24.9898	−	22.1390i	0.870560	−	0.771249i
$825$	−3.41624	+	3.02653i	−0.118938	+	0.105370i
$826$	15.0896	+	7.91966i	0.525036	+	0.275560i
$827$	17.8474	+	15.8114i	0.620615	+	0.549817i	0.913762	−	0.406251i	$-0.133164\pi$
$827$	17.8474	+	15.8114i	0.620615	+	0.549817i	−0.293147	+	0.956067i	$0.594703\pi$
$828$	27.5918	+	24.4442i	0.958881	+	0.849495i
$829$	1.52875	−	0.802351i	0.0530958	−	0.0278668i	−0.437966	−	0.898991i	$-0.644301\pi$
$829$	1.52875	−	0.802351i	0.0530958	−	0.0278668i	0.491062	+	0.871125i	$0.336609\pi$
$830$	1.47400	−	3.88663i	0.0511634	−	0.134907i
$831$	2.91859	+	1.53179i	0.101245	+	0.0531373i
$832$	−35.7298	−	8.80661i	−1.23871	−	0.305314i
$833$	−1.95977	+	1.02857i	−0.0679020	+	0.0356377i
$834$	−0.990124	+	2.61074i	−0.0342852	+	0.0904027i
$835$	−0.445976	−	0.395100i	−0.0154336	−	0.0136730i
$836$	60.9356	+	31.9815i	2.10750	+	1.10610i
$837$	−2.38628	−	3.45712i	−0.0824818	−	0.119496i
$838$	42.6082	+	22.3625i	1.47187	+	0.772499i
$839$	−18.8812			−0.651850			−0.325925	−	0.945396i	$-0.605676\pi$
$839$	−18.8812			−0.651850			−0.325925	+	0.945396i	$0.605676\pi$
$840$	3.13849			0.108288
$841$	10.2534	+	9.08370i	0.353565	+	0.313231i
$842$	−21.0045	+	5.17715i	−0.723864	+	0.178416i
$843$	−1.58040	−	4.16718i	−0.0544320	−	0.143525i
$844$	76.3983			2.62974
$845$	1.55941	+	2.25920i	0.0536454	+	0.0777187i
$846$	30.1151			1.03538
$847$	3.80492	+	10.0328i	0.130739	+	0.344730i
$848$	0.502774	+	4.14071i	0.0172653	+	0.142193i
$849$	−7.65070	−	4.01540i	−0.262571	−	0.137808i
$850$	1.51485	+	3.99432i	0.0519588	+	0.137004i
$851$	1.24426	−	10.2474i	0.0426526	−	0.351276i
$852$	0.0891636	+	0.734328i	0.00305469	+	0.0251577i
$853$	−3.71948	+	30.6327i	−0.127353	+	1.04884i	0.779208	+	0.626766i	$0.215622\pi$
$853$	−3.71948	+	30.6327i	−0.127353	+	1.04884i	−0.906560	+	0.422077i	$0.861301\pi$
$854$	−45.4906	−	65.9045i	−1.55666	−	2.25520i
$855$	−5.42795	+	7.86374i	−0.185632	+	0.268934i
$856$	17.2551	−	24.9983i	0.589766	−	0.854423i
$857$	6.97440	−	3.66045i	0.238241	−	0.125038i	−0.341378	−	0.939926i	$-0.610894\pi$
$857$	6.97440	−	3.66045i	0.238241	−	0.125038i	0.579619	+	0.814888i	$0.303201\pi$
$858$	−10.0504			−0.343115
$859$	9.54208	−	27.7119i	0.325572	−	0.945517i
$859$	9.54208	−	27.7119i	0.325572	−	0.945517i
$860$	3.09527			0.105548
$861$	8.85892	−	4.64952i	0.301911	−	0.158455i
$862$	22.0524	−	31.9485i	0.751109	−	1.08817i
$863$	2.00500	−	2.90474i	0.0682508	−	0.0988784i	−0.787372	−	0.616478i	$-0.788559\pi$
$863$	2.00500	−	2.90474i	0.0682508	−	0.0988784i	0.855623	+	0.517600i	$0.173174\pi$
$864$	0.617297	+	0.894309i	0.0210009	+	0.0304250i
$865$	−0.749888	+	6.17589i	−0.0254970	+	0.209986i
$866$	−6.33381	−	52.1636i	−0.215232	−	1.77259i
$867$	0.695410	−	5.72722i	0.0236174	−	0.194507i
$868$	10.5030	+	27.6940i	0.356494	+	0.939997i
$869$	7.61491	+	3.99661i	0.258318	+	0.135576i
$870$	0.211547	+	1.74224i	0.00717210	+	0.0590675i
$871$	14.0498	+	37.0462i	0.476058	+	1.25526i
$872$	−50.8867			−1.72324
$873$	−22.5917	−	32.7298i	−0.764614	−	1.10773i
$874$	−48.7083			−1.64758
$875$	6.66495	+	17.5740i	0.225316	+	0.594111i
$876$	7.50484	−	1.84978i	0.253565	−	0.0624981i
$877$	−13.9955	−	12.3989i	−0.472594	−	0.418682i	0.392915	−	0.919575i	$-0.371467\pi$
$877$	−13.9955	−	12.3989i	−0.472594	−	0.418682i	−0.865509	+	0.500893i	$0.833005\pi$
$878$	16.6844			0.563070
$879$	−11.5245			−0.388713
$880$	4.94419	+	2.59491i	0.166668	+	0.0874744i
$881$	−28.7033	−	41.5840i	−0.967040	−	1.40100i	−0.915495	−	0.402328i	$-0.868201\pi$
$881$	−28.7033	−	41.5840i	−0.967040	−	1.40100i	−0.0515443	−	0.998671i	$-0.516414\pi$
$882$	37.0314	+	19.4356i	1.24691	+	0.654430i
$883$	−3.09919	−	2.74564i	−0.104296	−	0.0923981i	0.609363	−	0.792891i	$-0.291425\pi$
$883$	−3.09919	−	2.74564i	−0.104296	−	0.0923981i	−0.713659	+	0.700493i	$0.752964\pi$
$884$	−2.21337	+	5.83618i	−0.0744438	+	0.196292i
$885$	0.316512	−	0.166118i	0.0106394	−	0.00558400i
$886$	−1.69414	−	0.417569i	−0.0569158	−	0.0140285i
$887$	−1.42540	−	0.748106i	−0.0478601	−	0.0251189i	0.440623	−	0.897692i	$-0.354757\pi$
$887$	−1.42540	−	0.748106i	−0.0478601	−	0.0251189i	−0.488483	+	0.872573i	$0.662450\pi$
$888$	−1.83075	+	4.82729i	−0.0614359	+	0.161993i
$889$	−5.83069	+	3.06018i	−0.195555	+	0.102635i
$890$	9.21771	+	8.16618i	0.308978	+	0.273731i
$891$	−16.8716	−	14.9470i	−0.565221	−	0.500742i
$892$	55.9142	+	29.3460i	1.87215	+	0.982578i
$893$	−19.7631	+	17.5086i	−0.661348	+	0.585903i
$894$	10.7931	−	9.56183i	0.360974	−	0.319795i
$895$	10.6934	+	2.63569i	0.357441	+	0.0881014i
$896$	−25.5294	−	67.3156i	−0.852879	−	2.24886i
$897$	4.17929	−	2.19346i	0.139542	−	0.0732374i
$898$	−19.9949	+	28.9676i	−0.667238	+	0.966661i
$899$	−7.22842	+	3.79377i	−0.241081	+	0.126529i
$900$	30.4256	−	44.0791i	1.01419	−	1.46930i
$901$	−0.423187			−0.0140984
$902$	56.0955			1.86778
$903$	−1.59091	−	0.834972i	−0.0529420	−	0.0277861i
$904$	−3.45679	+	5.00802i	−0.114971	+	0.166564i
$905$	−3.31136			−0.110073
$906$	−8.77485	+	7.77384i	−0.291525	+	0.258269i
$907$	18.8418	+	4.64408i	0.625631	+	0.154204i	0.539371	−	0.842068i	$-0.318662\pi$
$907$	18.8418	+	4.64408i	0.625631	+	0.154204i	0.0862605	+	0.996273i	$0.472508\pi$
$908$	55.7091	−	13.7311i	1.84877	−	0.455681i
$909$	1.16864	+	9.62464i	0.0387614	+	0.319229i
$910$	−7.11976	+	18.7733i	−0.236018	+	0.622328i
$911$	17.1868	−	24.8994i	0.569424	−	0.824953i	−0.427443	−	0.904042i	$-0.640586\pi$
$911$	17.1868	−	24.8994i	0.569424	−	0.824953i	0.996868	+	0.0790888i	$0.0252011\pi$
$912$	7.50553	+	1.84995i	0.248533	+	0.0612579i
$913$	−8.71551	+	2.14818i	−0.288441	+	0.0710944i
$914$	−55.9386	+	49.5573i	−1.85028	+	1.63921i
$915$	−1.67971			−0.0555295
$916$	22.8113	−	33.0479i	0.753707	−	1.09193i
$917$	−7.46491	−	61.4790i	−0.246513	−	2.03022i
$918$	1.61629	−	0.848296i	0.0533456	−	0.0279979i
$919$	−3.52167	+	5.10203i	−0.116169	+	0.168300i	−0.876755	−	0.480937i	$-0.840296\pi$
$919$	−3.52167	+	5.10203i	−0.116169	+	0.168300i	0.760586	+	0.649238i	$0.224912\pi$
$920$	−8.26393			−0.272454
$921$	7.21839	+	1.77917i	0.237854	+	0.0586258i
$922$	44.4251	−	23.3161i	1.46306	−	0.767874i
$923$	−2.26467	−	0.558191i	−0.0745425	−	0.0183731i
$924$	−7.81126	−	11.3166i	−0.256972	−	0.372288i
$925$	−14.9986			−0.493152
$926$	−4.00448	−	10.5590i	−0.131596	−	0.346989i
$927$	7.20188	−	18.9898i	0.236541	−	0.623707i
$928$	1.86989	−	0.981395i	0.0613822	−	0.0322159i
$929$	−17.3145	+	45.6545i	−0.568070	+	1.49788i	0.275739	+	0.961233i	$0.411078\pi$
$929$	−17.3145	+	45.6545i	−0.568070	+	1.49788i	−0.843808	+	0.536644i	$0.819692\pi$
$930$	0.909114	+	0.224077i	0.0298110	+	0.00734776i
$931$	−35.6016	+	8.77502i	−1.16680	+	0.287590i
$932$	−0.194298	+	1.60019i	−0.00636443	+	0.0524158i
$933$	0.475659	+	0.421397i	0.0155724	+	0.0137959i
$934$	−21.6667	−	31.3896i	−0.708956	−	1.02710i
$935$	−0.321814	+	0.466227i	−0.0105244	+	0.0152473i
$936$	56.4431	−	13.9120i	1.84490	−	0.454727i
$937$	6.61091	−	54.4457i	0.215969	−	1.77866i	−0.333104	−	0.942890i	$-0.608096\pi$
$937$	6.61091	−	54.4457i	0.215969	−	1.77866i	0.549073	−	0.835775i	$-0.314981\pi$
$938$	−46.4098	+	67.2362i	−1.51533	+	2.19534i
$939$	−5.59293	+	8.10275i	−0.182518	+	0.264423i
$940$	−6.80294	+	6.02688i	−0.221887	+	0.196575i
$941$	−4.26843	+	35.1537i	−0.139147	+	1.14598i	0.741078	+	0.671419i	$0.234315\pi$
$941$	−4.26843	+	35.1537i	−0.139147	+	1.14598i	−0.880224	+	0.474558i	$0.842608\pi$
$942$	−1.46777	−	12.0881i	−0.0478224	−	0.393853i
$943$	−23.3264	+	12.2426i	−0.759611	+	0.398674i
$944$	5.33042	+	4.72234i	0.173490	+	0.153699i
$945$	3.44972	−	1.81055i	0.112219	−	0.0588973i
$946$	−5.72255	−	8.29054i	−0.186056	−	0.269549i
$947$	−54.9613			−1.78600			−0.893000	−	0.450056i	$-0.851404\pi$
$947$	−54.9613			−1.78600			−0.893000	+	0.450056i	$0.851404\pi$
$948$	3.97917	+	0.980777i	0.129237	+	0.0318542i
$949$	−2.93772	+	24.1943i	−0.0953624	+	0.785380i
$950$	8.53065	+	70.2562i	0.276771	+	2.27941i
$951$	1.12082	−	0.588253i	0.0363452	−	0.0190754i
$952$	−6.15932	+	1.51814i	−0.199625	+	0.0492031i
$953$	7.60743	−	20.0592i	0.246429	−	0.649780i	−0.753542	−	0.657400i	$-0.771656\pi$
$953$	7.60743	−	20.0592i	0.246429	−	0.649780i	0.999971	+	0.00762002i	$0.00242555\pi$
$954$	4.54250	+	6.58094i	0.147069	+	0.213066i
$955$	8.50426	−	2.09611i	0.275191	−	0.0678286i
$956$	−55.3931	+	13.6532i	−1.79154	+	0.441575i
$957$	2.83681	−	2.51319i	0.0917011	−	0.0812400i
$958$	−82.3540	+	43.2227i	−2.66074	+	1.39646i
$959$	−40.5936	−	58.8100i	−1.31084	−	1.89907i
$960$	−1.54536	−	0.380896i	−0.0498762	−	0.0122934i
$961$	−3.21167	−	26.4505i	−0.103602	−	0.853241i
$962$	−24.7219	−	21.9017i	−0.797067	−	0.706140i
$963$	2.22728	−	18.3433i	0.0717730	−	0.591104i
$964$	2.21401	+	18.2340i	0.0713084	+	0.587277i
$965$	7.29148	−	1.79719i	0.234721	−	0.0578536i
$966$	8.61766	+	4.52290i	0.277269	+	0.145522i
$967$	42.5155	−	37.6655i	1.36721	−	1.21124i	0.413499	−	0.910505i	$-0.364307\pi$
$967$	42.5155	−	37.6655i	1.36721	−	1.21124i	0.953708	−	0.300734i	$-0.0972318\pi$
$968$	1.70325	+	14.0275i	0.0547446	+	0.450862i
$969$	−0.278107	+	0.733308i	−0.00893408	+	0.0235572i
$970$	17.5633	+	4.32897i	0.563924	+	0.138995i
$971$	−12.3470	+	6.48019i	−0.396233	+	0.207959i	−0.651058	−	0.759028i	$-0.725674\pi$
$971$	−12.3470	+	6.48019i	−0.396233	+	0.207959i	0.254825	+	0.966987i	$0.417982\pi$
$972$	−30.5985	−	16.0593i	−0.981447	−	0.515103i
$973$	1.45194	−	11.9578i	0.0465469	−	0.383348i
$974$	−9.28803	−	76.4938i	−0.297608	−	2.45102i
$975$	−3.89576	−	5.64399i	−0.124764	−	0.180752i
$976$	−11.8664	−	31.2892i	−0.379835	−	1.00154i
$977$	−7.63258	+	11.0577i	−0.244188	+	0.353767i	−0.925844	−	0.377905i	$-0.876645\pi$
$977$	−7.63258	+	11.0577i	−0.244188	+	0.353767i	0.681656	+	0.731672i	$0.261260\pi$
$978$	−0.305549	−	0.805668i	−0.00977039	−	0.0257624i
$979$	3.20546	−	26.3993i	0.102447	−	0.843726i
$980$	−12.2549	+	3.02057i	−0.391469	+	0.0964885i
$981$	−27.4099	+	14.3858i	−0.875132	+	0.459305i
$982$	−14.3107	−	37.7342i	−0.456672	−	1.20415i
$983$	−5.00517	+	1.23366i	−0.159640	+	0.0393477i	−0.318326	−	0.947981i	$-0.603121\pi$
$983$	−5.00517	+	1.23366i	−0.159640	+	0.0393477i	0.158686	+	0.987329i	$0.449274\pi$
$984$	12.7928	−	3.15314i	0.407819	−	0.100518i
$985$	−2.72232	+	3.94396i	−0.0867404	+	0.125665i
$986$	−1.25791	−	3.31685i	−0.0400601	−	0.105630i
$987$	5.12236	−	1.26255i	0.163047	−	0.0401874i
$988$	−58.7417	+	85.1020i	−1.86882	+	2.70745i
$989$	4.18900	+	2.19856i	0.133202	+	0.0699100i
$990$	10.7046			0.340215
$991$	−28.2171	+	14.8095i	−0.896347	+	0.470439i	−0.848972	−	0.528438i	$-0.822778\pi$
$991$	−28.2171	+	14.8095i	−0.896347	+	0.470439i	−0.0473751	+	0.998877i	$0.515086\pi$
$992$	−0.135802	−	1.11843i	−0.00431173	−	0.0355103i
$993$	5.66898	+	5.02228i	0.179900	+	0.159377i
$994$	−1.70547	−	4.49695i	−0.0540941	−	0.142635i
$995$	−0.402321	−	3.31341i	−0.0127544	−	0.105042i
$996$	−3.78763	+	1.98790i	−0.120016	+	0.0629891i
$997$	−15.7981	+	22.8875i	−0.500330	+	0.724854i	−0.989049	−	0.147588i	$-0.952849\pi$
$997$	−15.7981	+	22.8875i	−0.500330	+	0.724854i	0.488719	+	0.872441i	$0.337464\pi$
$998$	67.1599	+	16.5534i	2.12591	+	0.523990i
$999$	0.772501	+	6.36212i	0.0244409	+	0.201289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	859.2.f.a.100.5	✓	840
859.524	even	13	inner	859.2.f.a.524.5	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
859.2.f.a.100.5	✓	840	1.1	even	1	trivial
859.2.f.a.524.5	yes	840	859.524	even	13	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	859.f (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.15874 + 1.13300i) q^{2} +(-0.194366 + 0.281587i) q^{3} +(2.24036 - 3.24573i) q^{4} +(0.305534 + 0.442643i) q^{5} +(0.100548 - 0.828091i) q^{6} +(0.433769 + 3.57241i) q^{7} +(-0.571237 + 4.70456i) q^{8} +(1.02230 + 2.69559i) q^{9} +(-1.16108 - 0.609383i) q^{10} +(0.341319 + 2.81102i) q^{11} +(0.478506 + 1.26172i) q^{12} -4.25487 q^{13} +(-4.98392 - 7.22045i) q^{14} -0.184028 q^{15} +(-1.30008 - 3.42802i) q^{16} +(0.361157 - 0.0890173i) q^{17} +(-5.26097 - 4.66082i) q^{18} +6.16228 q^{19} +2.12120 q^{20} +(-1.09025 - 0.572210i) q^{21} +(-3.92169 - 5.68155i) q^{22} +(2.87074 + 1.50668i) q^{23} +(-1.21372 - 1.07526i) q^{24} +(1.67044 - 4.40460i) q^{25} +(9.18516 - 4.82075i) q^{26} +(-1.95438 - 0.481711i) q^{27} +(12.5669 + 6.59560i) q^{28} +(-1.38712 + 3.65753i) q^{29} +(0.397269 - 0.208503i) q^{30} +(1.56209 + 1.38389i) q^{31} +(-0.404091 - 0.357993i) q^{32} +(-0.857888 - 0.450254i) q^{33} +(-0.678790 + 0.601355i) q^{34} +(-1.44877 + 1.28350i) q^{35} +(11.0395 + 2.72098i) q^{36} +(-1.12904 - 2.97703i) q^{37} +(-13.3028 + 6.98184i) q^{38} +(0.827000 - 1.19812i) q^{39} +(-2.25697 + 1.18455i) q^{40} +(-4.61584 + 6.68720i) q^{41} +3.00189 q^{42} +1.45920 q^{43} +(9.88847 + 5.18987i) q^{44} +(-0.880833 + 1.27611i) q^{45} -7.90426 q^{46} +(-3.20711 + 2.84125i) q^{47} +(1.21798 + 0.300205i) q^{48} +(-5.77735 + 1.42399i) q^{49} +(1.38433 + 11.4010i) q^{50} +(-0.0451305 + 0.118999i) q^{51} +(-9.53245 + 13.8101i) q^{52} +(-1.10464 - 0.272270i) q^{53} +(4.76478 - 1.17441i) q^{54} +(-1.13999 + 1.00994i) q^{55} -17.0544 q^{56} +(-1.19774 + 1.73522i) q^{57} +(-1.14953 - 9.46727i) q^{58} +(-1.71991 + 0.902679i) q^{59} +(-0.412290 + 0.597305i) q^{60} +9.12747 q^{61} +(-4.94009 - 1.21762i) q^{62} +(-9.18629 + 4.82134i) q^{63} +(8.39740 + 2.06977i) q^{64} +(-1.30001 - 1.88338i) q^{65} +2.36210 q^{66} +(-3.30205 - 8.70679i) q^{67} +(0.520198 - 1.37165i) q^{68} +(-0.982237 + 0.515518i) q^{69} +(1.67332 - 4.41219i) q^{70} +(0.532254 + 0.131189i) q^{71} +(-13.2655 + 3.26966i) q^{72} +(0.690438 - 5.68627i) q^{73} +(5.81027 + 5.14745i) q^{74} +(0.915602 + 1.32648i) q^{75} +(13.8058 - 20.0011i) q^{76} +(-9.89404 + 2.43866i) q^{77} +(-0.427820 + 3.52342i) q^{78} +(1.72526 - 2.49947i) q^{79} +(1.12017 - 1.62285i) q^{80} +(-5.95820 + 5.27851i) q^{81} +(2.38784 - 19.6657i) q^{82} +(0.382100 + 3.14688i) q^{83} +(-4.29981 + 2.25671i) q^{84} +(0.149749 + 0.132666i) q^{85} +(-3.15005 + 1.65327i) q^{86} +(-0.760306 - 1.10149i) q^{87} -13.4196 q^{88} +(-9.11848 - 2.24750i) q^{89} +(0.455669 - 3.75277i) q^{90} +(-1.84563 - 15.2001i) q^{91} +(11.3218 - 5.94213i) q^{92} +(-0.693302 + 0.170884i) q^{93} +(3.70420 - 9.76718i) q^{94} +(1.88279 + 2.72769i) q^{95} +(0.179348 - 0.0442053i) q^{96} +(-13.3940 + 3.30133i) q^{97} +(10.8584 - 9.61973i) q^{98} +(-7.22841 + 3.79376i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 10 q^{2} - 5 q^{3} - 74 q^{4} - 20 q^{5} + 5 q^{6} - 3 q^{7} + 2 q^{8} - 69 q^{9} + 7 q^{10} - 25 q^{11} - 58 q^{12} - 10 q^{13} + 9 q^{14} - 148 q^{15} - 40 q^{16} - q^{17} + 5 q^{18} - 38 q^{19}+ \cdots - 121 q^{99}+O(q^{100}) \) 840 * q - 10 * q^2 - 5 * q^3 - 74 * q^4 - 20 * q^5 + 5 * q^6 - 3 * q^7 + 2 * q^8 - 69 * q^9 + 7 * q^10 - 25 * q^11 - 58 * q^12 - 10 * q^13 + 9 * q^14 - 148 * q^15 - 40 * q^16 - q^17 + 5 * q^18 - 38 * q^19 - 92 * q^20 + 17 * q^21 + 15 * q^22 - 18 * q^23 + 27 * q^24 - 66 * q^25 + 7 * q^26 - 17 * q^27 + 29 * q^28 + 7 * q^29 - 5 * q^30 + 27 * q^31 + 20 * q^32 + 49 * q^33 + 5 * q^34 + 43 * q^35 + 32 * q^36 - 86 * q^37 - 13 * q^38 + 2 * q^39 + 59 * q^40 + 9 * q^41 + 72 * q^42 + 40 * q^43 + 44 * q^44 - 49 * q^45 + 52 * q^46 - 22 * q^47 + 159 * q^48 - 11 * q^49 - 73 * q^50 + 65 * q^51 + 73 * q^52 + 25 * q^53 + 11 * q^54 + 81 * q^55 - 302 * q^56 - 192 * q^57 + 27 * q^58 - 23 * q^59 - 62 * q^60 + 26 * q^61 + 79 * q^62 + 93 * q^63 - 78 * q^64 + 10 * q^65 + 74 * q^66 + 65 * q^67 + 69 * q^68 - 57 * q^69 + 19 * q^70 + 21 * q^71 - 234 * q^72 - 95 * q^73 + 25 * q^74 - 120 * q^75 - 18 * q^76 - 95 * q^77 - 3 * q^78 - 13 * q^79 - 244 * q^80 - 95 * q^81 - 19 * q^82 - 16 * q^83 - 48 * q^84 + 99 * q^85 + 45 * q^86 - 123 * q^87 + 110 * q^88 + 49 * q^89 + 217 * q^90 - 82 * q^91 + 3 * q^92 - 57 * q^93 - 77 * q^94 - 12 * q^95 + 56 * q^96 + 5 * q^97 + 5 * q^98 - 121 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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