LMFDB - Embedded newform 820.2.bv.c.103.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(103,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 15, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.103"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bv (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [960,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$960$
Relative dimension:	$120$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			103.4
Character	$\chi$	$=$	820.103
Dual form			820.2.bv.c.207.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41297 - 0.0593411i) q^{2} +2.23336 q^{3} +(1.99296 + 0.167694i) q^{4} +(-0.983161 + 2.00833i) q^{5} +(-3.15566 - 0.132530i) q^{6} +(-3.76737 + 1.22409i) q^{7} +(-2.80603 - 0.355211i) q^{8} +1.98789 q^{9} +(1.50835 - 2.77937i) q^{10} +(0.259122 - 1.63603i) q^{11} +(4.45099 + 0.374521i) q^{12} +(-5.87435 - 1.90869i) q^{13} +(5.39581 - 1.50604i) q^{14} +(-2.19575 + 4.48532i) q^{15} +(3.94376 + 0.668415i) q^{16} +(0.889430 + 1.22420i) q^{17} +(-2.80883 - 0.117964i) q^{18} +(3.09361 + 1.57627i) q^{19} +(-2.29618 + 3.83765i) q^{20} +(-8.41388 + 2.73383i) q^{21} +(-0.463216 + 2.29629i) q^{22} +(-3.35446 - 6.58351i) q^{23} +(-6.26688 - 0.793314i) q^{24} +(-3.06679 - 3.94902i) q^{25} +(8.18700 + 3.04551i) q^{26} -2.26040 q^{27} +(-7.71347 + 1.80780i) q^{28} +(-8.67047 + 1.37327i) q^{29} +(3.36869 - 6.20732i) q^{30} +(2.81243 + 3.87098i) q^{31} +(-5.53274 - 1.17848i) q^{32} +(0.578713 - 3.65385i) q^{33} +(-1.18409 - 1.78253i) q^{34} +(1.24554 - 8.76960i) q^{35} +(3.96178 + 0.333358i) q^{36} +(5.76174 - 0.912570i) q^{37} +(-4.27763 - 2.41080i) q^{38} +(-13.1195 - 4.26279i) q^{39} +(3.47216 - 5.28622i) q^{40} +(-3.48858 - 5.36934i) q^{41} +(12.0508 - 3.36353i) q^{42} +(-4.87565 + 2.48427i) q^{43} +(0.790773 - 3.21709i) q^{44} +(-1.95442 + 3.99234i) q^{45} +(4.34908 + 9.50134i) q^{46} +(-2.80251 + 8.62524i) q^{47} +(8.80782 + 1.49281i) q^{48} +(7.03152 - 5.10870i) q^{49} +(4.09894 + 5.76183i) q^{50} +(1.98642 + 2.73407i) q^{51} +(-11.3872 - 4.78904i) q^{52} +(2.27216 - 3.12736i) q^{53} +(3.19388 + 0.134135i) q^{54} +(3.03094 + 2.12889i) q^{55} +(11.0062 - 2.09663i) q^{56} +(6.90913 + 3.52038i) q^{57} +(12.3326 - 1.42587i) q^{58} +(-1.23643 + 3.80535i) q^{59} +(-5.12820 + 8.57084i) q^{60} +(1.30986 - 0.425600i) q^{61} +(-3.74417 - 5.63646i) q^{62} +(-7.48911 + 2.43336i) q^{63} +(7.74765 + 1.99347i) q^{64} +(9.60871 - 9.92109i) q^{65} +(-1.03453 + 5.12843i) q^{66} +(5.15113 + 3.74251i) q^{67} +(1.56731 + 2.58892i) q^{68} +(-7.49172 - 14.7033i) q^{69} +(-2.28031 + 12.3172i) q^{70} +(-1.54751 + 9.77059i) q^{71} +(-5.57809 - 0.706121i) q^{72} +(1.72464 - 1.72464i) q^{73} +(-8.19531 + 0.947524i) q^{74} +(-6.84924 - 8.81959i) q^{75} +(5.90109 + 3.66022i) q^{76} +(1.02645 + 6.48073i) q^{77} +(18.2845 + 6.80172i) q^{78} +(-1.06927 - 1.06927i) q^{79} +(-5.21975 + 7.26321i) q^{80} -11.0120 q^{81} +(4.61063 + 7.79372i) q^{82} +(0.379034 - 0.379034i) q^{83} +(-17.2269 + 4.03746i) q^{84} +(-3.33304 + 0.582690i) q^{85} +(7.03655 - 3.22086i) q^{86} +(-19.3643 + 3.06700i) q^{87} +(-1.30824 + 4.49872i) q^{88} +(-0.948782 - 0.483429i) q^{89} +(2.99844 - 5.52508i) q^{90} +24.4672 q^{91} +(-5.58129 - 13.6832i) q^{92} +(6.28117 + 8.64528i) q^{93} +(4.47169 - 12.0209i) q^{94} +(-6.20718 + 4.66326i) q^{95} +(-12.3566 - 2.63196i) q^{96} +(-2.06341 + 2.84004i) q^{97} +(-10.2385 + 6.80117i) q^{98} +(0.515107 - 3.25226i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 960 q - 10 q^{2} - 20 q^{5} - 16 q^{6} + 2 q^{8} + 960 q^{9} - 60 q^{10} - 40 q^{12} - 20 q^{13} - 8 q^{14} - 28 q^{16} - 20 q^{17} - 48 q^{18} - 34 q^{20} - 40 q^{21} - 10 q^{22} - 48 q^{24} - 4 q^{25}+ \cdots - 38 q^{98}+O(q^{100}) $ 960 * q - 10 * q^2 - 20 * q^5 - 16 * q^6 + 2 * q^8 + 960 * q^9 - 60 * q^10 - 40 * q^12 - 20 * q^13 - 8 * q^14 - 28 * q^16 - 20 * q^17 - 48 * q^18 - 34 * q^20 - 40 * q^21 - 10 * q^22 - 48 * q^24 - 4 * q^25 - 20 * q^26 - 10 * q^28 - 10 * q^30 - 56 * q^33 - 20 * q^34 - 100 * q^36 + 88 * q^37 - 16 * q^40 - 24 * q^41 - 104 * q^42 - 100 * q^45 - 20 * q^46 - 40 * q^48 + 224 * q^49 - 12 * q^50 - 38 * q^52 - 20 * q^53 - 52 * q^54 + 96 * q^56 - 72 * q^57 - 38 * q^58 - 14 * q^60 - 40 * q^61 - 10 * q^62 - 120 * q^64 - 60 * q^65 - 12 * q^66 - 116 * q^68 - 104 * q^69 - 96 * q^70 - 24 * q^72 - 72 * q^73 - 28 * q^74 - 40 * q^76 - 76 * q^77 - 44 * q^78 - 90 * q^80 + 592 * q^81 - 130 * q^82 - 92 * q^84 - 64 * q^85 - 12 * q^86 - 104 * q^88 + 136 * q^89 - 364 * q^90 - 220 * q^92 - 32 * q^94 - 44 * q^96 + 80 * q^97 - 38 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.41297	−	0.0593411i	−0.999119	−	0.0419605i
$2$	−1.41297	−	0.0593411i	−0.999119	−	0.0419605i
$3$	2.23336			1.28943			0.644715	−	0.764423i	$-0.276976\pi$
$3$	2.23336			1.28943			0.644715	+	0.764423i	$0.276976\pi$
$4$	1.99296	+	0.167694i	0.996479	+	0.0838471i
$5$	−0.983161	+	2.00833i	−0.439683	+	0.898153i
$5$	−0.983161	+	2.00833i	−0.439683	+	0.898153i
$6$	−3.15566	−	0.132530i	−1.28829	−	0.0541052i
$7$	−3.76737	+	1.22409i	−1.42393	+	0.462663i	−0.916849	−	0.399235i	$-0.869276\pi$
$7$	−3.76737	+	1.22409i	−1.42393	+	0.462663i	−0.507082	+	0.861898i	$0.669276\pi$
$8$	−2.80603	−	0.355211i	−0.992083	−	0.125586i
$9$	1.98789			0.662630
$10$	1.50835	−	2.77937i	0.476983	−	0.878913i
$11$	0.259122	−	1.63603i	0.0781283	−	0.493283i	−0.917333	−	0.398120i	$-0.869663\pi$
$11$	0.259122	−	1.63603i	0.0781283	−	0.493283i	0.995462	−	0.0951628i	$-0.0303372\pi$
$12$	4.45099	+	0.374521i	1.28489	+	0.108115i
$13$	−5.87435	−	1.90869i	−1.62925	−	0.529376i	−0.655152	−	0.755497i	$-0.727395\pi$
$13$	−5.87435	−	1.90869i	−1.62925	−	0.529376i	−0.974099	+	0.226121i	$0.927395\pi$
$14$	5.39581	−	1.50604i	1.44209	−	0.402507i
$15$	−2.19575	+	4.48532i	−0.566940	+	1.15811i
$16$	3.94376	+	0.668415i	0.985939	+	0.167104i
$17$	0.889430	+	1.22420i	0.215719	+	0.296911i	0.903139	−	0.429349i	$-0.141257\pi$
$17$	0.889430	+	1.22420i	0.215719	+	0.296911i	−0.687420	+	0.726260i	$0.741257\pi$
$18$	−2.80883	−	0.117964i	−0.662047	−	0.0278043i
$19$	3.09361	+	1.57627i	0.709722	+	0.361621i	0.771292	−	0.636481i	$-0.219611\pi$
$19$	3.09361	+	1.57627i	0.709722	+	0.361621i	−0.0615703	+	0.998103i	$0.519611\pi$
$20$	−2.29618	+	3.83765i	−0.513442	+	0.858124i
$21$	−8.41388	+	2.73383i	−1.83606	+	0.596572i
$22$	−0.463216	+	2.29629i	−0.0987579	+	0.489570i
$23$	−3.35446	−	6.58351i	−0.699454	−	1.37276i	−0.917863	−	0.396898i	$-0.870087\pi$
$23$	−3.35446	−	6.58351i	−0.699454	−	1.37276i	0.218409	−	0.975857i	$-0.429913\pi$
$24$	−6.26688	−	0.793314i	−1.27922	−	0.161934i
$25$	−3.06679	−	3.94902i	−0.613358	−	0.789805i
$26$	8.18700	+	3.04551i	1.60560	+	0.597274i
$27$	−2.26040			−0.435015
$28$	−7.71347	+	1.80780i	−1.45771	+	0.341641i
$29$	−8.67047	+	1.37327i	−1.61007	+	0.255009i	−0.895665	−	0.444729i	$-0.853300\pi$
$29$	−8.67047	+	1.37327i	−1.61007	+	0.255009i	−0.714400	+	0.699738i	$0.753300\pi$
$30$	3.36869	−	6.20732i	0.615036	−	1.13330i
$31$	2.81243	+	3.87098i	0.505128	+	0.695248i	0.983088	−	0.183133i	$-0.0586239\pi$
$31$	2.81243	+	3.87098i	0.505128	+	0.695248i	−0.477961	+	0.878381i	$0.658624\pi$
$32$	−5.53274	−	1.17848i	−0.978059	−	0.208327i
$33$	0.578713	−	3.65385i	0.100741	−	0.636054i
$34$	−1.18409	−	1.78253i	−0.203070	−	0.305701i
$35$	1.24554	−	8.76960i	0.210535	−	1.48233i
$36$	3.96178	+	0.333358i	0.660297	+	0.0555596i
$37$	5.76174	−	0.912570i	0.947225	−	0.150026i	0.336336	−	0.941742i	$-0.390812\pi$
$37$	5.76174	−	0.912570i	0.947225	−	0.150026i	0.610889	+	0.791716i	$0.290812\pi$
$38$	−4.27763	−	2.41080i	−0.693923	−	0.391083i
$39$	−13.1195	−	4.26279i	−2.10081	−	0.682593i
$40$	3.47216	−	5.28622i	0.548997	−	0.835824i
$41$	−3.48858	−	5.36934i	−0.544824	−	0.838550i
$41$	−3.48858	−	5.36934i	−0.544824	−	0.838550i
$42$	12.0508	−	3.36353i	1.85947	−	0.519004i
$43$	−4.87565	+	2.48427i	−0.743529	+	0.378847i	−0.784349	−	0.620319i	$-0.787003\pi$
$43$	−4.87565	+	2.48427i	−0.743529	+	0.378847i	0.0408201	+	0.999167i	$0.487003\pi$
$44$	0.790773	−	3.21709i	0.119214	−	0.484995i
$45$	−1.95442	+	3.99234i	−0.291347	+	0.595143i
$46$	4.34908	+	9.50134i	0.641236	+	1.40090i
$47$	−2.80251	+	8.62524i	−0.408788	+	1.25812i	0.508902	+	0.860824i	$0.330051\pi$
$47$	−2.80251	+	8.62524i	−0.408788	+	1.25812i	−0.917690	+	0.397296i	$0.869949\pi$
$48$	8.80782	+	1.49281i	1.27130	+	0.215469i
$49$	7.03152	−	5.10870i	1.00450	−	0.729814i
$50$	4.09894	+	5.76183i	0.579677	+	0.814846i
$51$	1.98642	+	2.73407i	0.278154	+	0.382846i
$52$	−11.3872	−	4.78904i	−1.57913	−	0.664120i
$53$	2.27216	−	3.12736i	0.312105	−	0.429576i	−0.623931	−	0.781479i	$-0.714465\pi$
$53$	2.27216	−	3.12736i	0.312105	−	0.429576i	0.936036	+	0.351903i	$0.114465\pi$
$54$	3.19388	+	0.134135i	0.434632	+	0.0182535i
$55$	3.03094	+	2.12889i	0.408692	+	0.287059i
$56$	11.0062	−	2.09663i	1.47076	−	0.280174i
$57$	6.90913	+	3.52038i	0.915137	+	0.466285i
$58$	12.3326	−	1.42587i	1.61935	−	0.187225i
$59$	−1.23643	+	3.80535i	−0.160970	+	0.495414i	−0.998717	−	0.0506448i	$-0.983872\pi$
$59$	−1.23643	+	3.80535i	−0.160970	+	0.495414i	0.837747	+	0.546058i	$0.183872\pi$
$60$	−5.12820	+	8.57084i	−0.662048	+	1.10649i
$61$	1.30986	−	0.425600i	0.167711	−	0.0544925i	−0.223958	−	0.974599i	$-0.571898\pi$
$61$	1.30986	−	0.425600i	0.167711	−	0.0544925i	0.391669	+	0.920106i	$0.371898\pi$
$62$	−3.74417	−	5.63646i	−0.475510	−	0.715831i
$63$	−7.48911	+	2.43336i	−0.943539	+	0.306574i
$64$	7.74765	+	1.99347i	0.968456	+	0.249184i
$65$	9.60871	−	9.92109i	1.19181	−	1.23056i
$66$	−1.03453	+	5.12843i	−0.127341	+	0.631266i
$67$	5.15113	+	3.74251i	0.629310	+	0.457221i	0.856161	−	0.516709i	$-0.172843\pi$
$67$	5.15113	+	3.74251i	0.629310	+	0.457221i	−0.226851	+	0.973929i	$0.572843\pi$
$68$	1.56731	+	2.58892i	0.190064	+	0.313953i
$69$	−7.49172	−	14.7033i	−0.901897	−	1.77007i
$70$	−2.28031	+	12.3172i	−0.272549	+	1.47219i
$71$	−1.54751	+	9.77059i	−0.183656	+	1.15956i	0.707788	+	0.706425i	$0.249693\pi$
$71$	−1.54751	+	9.77059i	−0.183656	+	1.15956i	−0.891444	+	0.453131i	$0.850307\pi$
$72$	−5.57809	−	0.706121i	−0.657384	−	0.0832171i
$73$	1.72464	−	1.72464i	0.201854	−	0.201854i	−0.598940	−	0.800794i	$-0.704411\pi$
$73$	1.72464	−	1.72464i	0.201854	−	0.201854i	0.800794	+	0.598940i	$0.204411\pi$
$74$	−8.19531	+	0.947524i	−0.952686	+	0.110147i
$75$	−6.84924	−	8.81959i	−0.790882	−	1.01840i
$76$	5.90109	+	3.66022i	0.676902	+	0.419856i
$77$	1.02645	+	6.48073i	0.116974	+	0.738547i
$78$	18.2845	+	6.80172i	2.07031	+	0.770143i
$79$	−1.06927	−	1.06927i	−0.120302	−	0.120302i	0.644393	−	0.764695i	$-0.277110\pi$
$79$	−1.06927	−	1.06927i	−0.120302	−	0.120302i	−0.764695	+	0.644393i	$0.777110\pi$
$80$	−5.21975	+	7.26321i	−0.583585	+	0.812052i
$81$	−11.0120			−1.22355
$82$	4.61063	+	7.79372i	0.509158	+	0.860673i
$83$	0.379034	−	0.379034i	0.0416044	−	0.0416044i	−0.685999	−	0.727603i	$-0.740634\pi$
$83$	0.379034	−	0.379034i	0.0416044	−	0.0416044i	0.727603	+	0.685999i	$0.240634\pi$
$84$	−17.2269	+	4.03746i	−1.87961	+	0.440523i
$85$	−3.33304	+	0.582690i	−0.361519	+	0.0632016i
$86$	7.03655	−	3.22086i	0.758771	−	0.347314i
$87$	−19.3643	+	3.06700i	−2.07607	+	0.328817i
$88$	−1.30824	+	4.49872i	−0.139459	+	0.479565i
$89$	−0.948782	−	0.483429i	−0.100571	−	0.0512433i	0.402982	−	0.915208i	$-0.367974\pi$
$89$	−0.948782	−	0.483429i	−0.100571	−	0.0512433i	−0.503552	+	0.863965i	$0.667974\pi$
$90$	2.99844	−	5.52508i	0.316063	−	0.582394i
$91$	24.4672			2.56486
$92$	−5.58129	−	13.6832i	−0.581889	−	1.42657i
$93$	6.28117	+	8.64528i	0.651327	+	0.896474i
$94$	4.47169	−	12.0209i	0.461219	−	1.23986i
$95$	−6.20718	+	4.66326i	−0.636844	+	0.478440i
$96$	−12.3566	−	2.63196i	−1.26114	−	0.268623i
$97$	−2.06341	+	2.84004i	−0.209508	+	0.288363i	−0.900819	−	0.434194i	$-0.857033\pi$
$97$	−2.06341	+	2.84004i	−0.209508	+	0.288363i	0.691312	+	0.722557i	$0.257033\pi$
$98$	−10.2385	+	6.80117i	−1.03424	+	0.687022i
$99$	0.515107	−	3.25226i	0.0517702	−	0.326864i
$100$	−5.44975	−	8.38452i	−0.544975	−	0.838452i
$101$	−13.1878	−	6.71950i	−1.31223	−	0.668615i	−0.348958	−	0.937138i	$-0.613465\pi$
$101$	−13.1878	−	6.71950i	−1.31223	−	0.668615i	−0.963273	+	0.268523i	$0.913465\pi$
$102$	−2.64450	−	3.98103i	−0.261845	−	0.394180i
$103$	4.71668	−	9.25700i	0.464748	−	0.912120i	−0.533068	−	0.846072i	$-0.678961\pi$
$103$	4.71668	−	9.25700i	0.464748	−	0.912120i	0.997816	−	0.0660475i	$-0.0210389\pi$
$104$	15.8056	+	7.44249i	1.54987	+	0.729796i
$105$	2.78175	−	19.5857i	0.271471	−	1.91136i
$106$	−3.39607	+	4.28403i	−0.329856	+	0.416102i
$107$	−4.02915	+	7.90764i	−0.389512	+	0.764461i	−0.999612	−	0.0278640i	$-0.991129\pi$
$107$	−4.02915	+	7.90764i	−0.389512	+	0.764461i	0.610099	+	0.792325i	$0.291129\pi$
$108$	−4.50489	−	0.379057i	−0.433483	−	0.0364747i
$109$	3.92313	+	3.92313i	0.375768	+	0.375768i	0.869573	−	0.493805i	$-0.164394\pi$
$109$	3.92313	+	3.92313i	0.375768	+	0.375768i	−0.493805	+	0.869573i	$0.664394\pi$
$110$	−4.15629	−	3.18791i	−0.396287	−	0.303955i
$111$	12.8680	−	2.03810i	1.22138	−	0.193448i
$112$	−15.6758	+	2.30935i	−1.48122	+	0.218214i
$113$	−18.4352	−	2.91985i	−1.73424	−	0.274676i	−0.792219	−	0.610237i	$-0.791074\pi$
$113$	−18.4352	−	2.91985i	−1.73424	−	0.274676i	−0.942019	+	0.335560i	$0.891074\pi$
$114$	−9.55348	−	5.38418i	−0.894765	−	0.504274i
$115$	16.5198	−	0.264231i	1.54048	−	0.0246397i
$116$	−17.5102	+	1.28287i	−1.62578	+	0.119112i
$117$	−11.6776	−	3.79427i	−1.07959	−	0.350780i
$118$	1.97285	−	5.30346i	0.181616	−	0.488223i
$119$	−4.84934	−	3.52325i	−0.444538	−	0.322976i
$120$	7.75459	−	11.8060i	0.707894	−	1.07774i
$121$	7.85216	+	2.55132i	0.713833	+	0.231938i
$122$	−1.87605	+	0.523630i	−0.169849	+	0.0474073i
$123$	−7.79125	−	11.9917i	−0.702513	−	1.08125i
$124$	4.95591	+	8.18632i	0.445054	+	0.735154i
$125$	10.9461	−	2.27661i	0.979049	−	0.203626i
$126$	10.7263	−	2.99385i	0.955572	−	0.266713i
$127$	3.23429	+	20.4205i	0.286997	+	1.81203i	0.536775	+	0.843726i	$0.319642\pi$
$127$	3.23429	+	20.4205i	0.286997	+	1.81203i	−0.249778	+	0.968303i	$0.580358\pi$
$128$	−10.8289	−	3.27646i	−0.957147	−	0.289601i
$129$	−10.8891	+	5.54826i	−0.958729	+	0.488497i
$130$	−14.1655	+	13.4480i	−1.24240	+	1.17947i
$131$	−11.0511	+	8.02907i	−0.965536	+	0.701503i	−0.954430	−	0.298435i	$-0.903535\pi$
$131$	−11.0511	+	8.02907i	−0.965536	+	0.701503i	−0.0111061	+	0.999938i	$0.503535\pi$
$132$	1.76608	−	7.18492i	0.153718	−	0.625367i
$133$	−13.5842	−	2.15153i	−1.17790	−	0.186561i
$134$	−7.05629	−	5.59372i	−0.609571	−	0.483224i
$135$	2.22234	−	4.53964i	0.191269	−	0.390710i
$136$	−2.06092	−	3.75107i	−0.176723	−	0.321652i
$137$			10.4655i			0.894124i	0.894503	+	0.447062i	$0.147530\pi$
$137$			10.4655i			0.894124i	−0.894503	+	0.447062i	$0.852470\pi$
$138$	9.71305	+	21.2199i	0.826830	+	1.80636i
$139$	3.83827	+	11.8130i	0.325558	+	1.00197i	0.971188	+	0.238315i	$0.0765949\pi$
$139$	3.83827	+	11.8130i	0.325558	+	1.00197i	−0.645630	+	0.763650i	$0.723405\pi$
$140$	3.95293	−	17.2686i	0.334083	−	1.45946i
$141$	−6.25901	+	19.2632i	−0.527104	+	1.62226i
$142$	2.76638	−	13.7137i	0.232149	−	1.15083i
$143$	−4.64486	+	9.11605i	−0.388423	+	0.762322i
$144$	7.83976	+	1.32874i	0.653313	+	0.110728i
$145$	5.76649	−	18.7633i	0.478881	−	1.55821i
$146$	−2.53921	+	2.33453i	−0.210147	+	0.193207i
$147$	15.7039	−	11.4096i	1.29524	−	0.941045i
$148$	11.6359	−	0.852503i	0.956468	−	0.0700753i
$149$	0.893586	+	5.64188i	0.0732054	+	0.462201i	0.996874	+	0.0790084i	$0.0251754\pi$
$149$	0.893586	+	5.64188i	0.0732054	+	0.462201i	−0.923669	+	0.383192i	$0.874825\pi$
$150$	9.15440	+	12.8682i	0.747453	+	1.05069i
$151$	−2.00594	−	3.93687i	−0.163241	−	0.320378i	0.794868	−	0.606782i	$-0.207540\pi$
$151$	−2.00594	−	3.93687i	−0.163241	−	0.320378i	−0.958109	+	0.286404i	$0.907540\pi$
$152$	−8.12085	−	5.52195i	−0.658688	−	0.447889i
$153$	1.76809	+	2.43357i	0.142942	+	0.196742i
$154$	−1.06576	−	9.21797i	−0.0858815	−	0.742805i
$155$	−10.5393	+	1.84250i	−0.846535	+	0.147993i
$156$	−25.4318	−	10.6956i	−2.03617	−	0.856336i
$157$	−5.92134	−	18.2240i	−0.472574	−	1.45443i	−0.849201	−	0.528070i	$-0.822916\pi$
$157$	−5.92134	−	18.2240i	−0.472574	−	1.45443i	0.376627	−	0.926365i	$-0.377084\pi$
$158$	1.44739	+	1.57430i	0.115148	+	0.125244i
$159$	5.07455	−	6.98452i	0.402438	−	0.553908i
$160$	7.80634	−	9.95294i	0.617145	−	0.786849i
$161$	20.6963	+	20.6963i	1.63110	+	1.63110i
$162$	15.5596	+	0.653462i	1.22247	+	0.0513409i
$163$	−11.3720	+	11.3720i	−0.890721	+	0.890721i	−0.994591	−	0.103870i	$-0.966877\pi$
$163$	−11.3720	+	11.3720i	−0.890721	+	0.890721i	0.103870	+	0.994591i	$0.466877\pi$
$164$	−6.05218	−	11.2859i	−0.472596	−	0.881279i
$165$	6.76917	+	4.75457i	0.526979	+	0.370143i
$166$	−0.558055	+	0.513071i	−0.0433135	+	0.0398220i
$167$		−	5.70105i		−	0.441161i	−0.975369	−	0.220580i	$-0.929205\pi$
$167$		−	5.70105i		−	0.441161i	0.975369	−	0.220580i	$-0.0707951\pi$
$168$	24.5807	−	4.68253i	1.89644	−	0.361265i
$169$	20.3476	+	14.7834i	1.56520	+	1.13719i
$170$	4.74406	−	0.625535i	0.363853	−	0.0479764i
$171$	6.14975	+	3.13345i	0.470283	+	0.239621i
$172$	−10.1336	+	4.13342i	−0.772676	+	0.315170i
$173$	14.2852	−	14.2852i	1.08608	−	1.08608i	0.0901547	−	0.995928i	$-0.471264\pi$
$173$	14.2852	−	14.2852i	1.08608	−	1.08608i	0.995928	−	0.0901547i	$-0.0287361\pi$
$174$	27.5431	−	3.18447i	2.08804	−	0.241414i
$175$	16.3877	+	11.1234i	1.23879	+	0.840849i
$176$	2.11546	−	6.27892i	0.159459	−	0.473291i
$177$	−2.76140	+	8.49870i	−0.207559	+	0.638801i
$178$	1.31191	+	0.739371i	0.0983319	+	0.0554182i
$179$	15.7353	−	2.49223i	1.17611	−	0.186278i	0.462370	−	0.886687i	$-0.346999\pi$
$179$	15.7353	−	2.49223i	1.17611	−	0.186278i	0.713742	+	0.700409i	$0.246999\pi$
$180$	−4.56456	+	7.62882i	−0.340222	+	0.568619i
$181$	1.55046	−	9.78922i	0.115245	−	0.727627i	−0.860619	−	0.509249i	$-0.829923\pi$
$181$	1.55046	−	9.78922i	0.115245	−	0.727627i	0.975864	−	0.218378i	$-0.0700767\pi$
$182$	−34.5714	−	1.45191i	−2.56260	−	0.107623i
$183$	2.92539	−	0.950517i	0.216251	−	0.0702643i
$184$	7.07420	+	19.6651i	0.521517	+	1.44973i
$185$	−3.83198	+	12.4687i	−0.281732	+	0.916717i
$186$	−8.36207	−	12.5882i	−0.613136	−	0.923015i
$187$	2.23330	−	1.13792i	0.163315	−	0.0832131i
$188$	−7.03169	+	16.7198i	−0.512838	+	1.21941i
$189$	8.51576	−	2.76694i	0.619431	−	0.201265i
$190$	9.04728	−	6.22069i	0.656358	−	0.451296i
$191$	6.07782	+	6.07782i	0.439776	+	0.439776i	0.891936	−	0.452161i	$-0.149347\pi$
$191$	6.07782	+	6.07782i	0.439776	+	0.439776i	−0.452161	+	0.891936i	$0.649347\pi$
$192$	17.3033	+	4.45213i	1.24876	+	0.321305i
$193$	−8.80629	+	12.1208i	−0.633891	+	0.872476i	−0.998271	−	0.0587742i	$-0.981281\pi$
$193$	−8.80629	+	12.1208i	−0.633891	+	0.872476i	0.364380	+	0.931250i	$0.381281\pi$
$194$	3.08407	−	3.89045i	0.221423	−	0.279318i
$195$	21.4597	−	22.1573i	1.53676	−	1.58672i
$196$	14.8702	−	9.00228i	1.06216	−	0.643020i
$197$	7.53066	+	1.19274i	0.536537	+	0.0849792i	0.418822	−	0.908068i	$-0.362443\pi$
$197$	7.53066	+	1.19274i	0.536537	+	0.0849792i	0.117715	+	0.993047i	$0.462443\pi$
$198$	−0.920822	+	4.56477i	−0.0654400	+	0.324404i
$199$	3.96890	+	7.78941i	0.281348	+	0.552176i	0.987827	−	0.155558i	$-0.0497175\pi$
$199$	3.96890	+	7.78941i	0.281348	+	0.552176i	−0.706479	+	0.707734i	$0.749717\pi$
$200$	7.20278	+	12.1705i	0.509313	+	0.860581i
$201$	11.5043	+	8.35837i	0.811452	+	0.589554i
$202$	18.2351	+	10.2770i	1.28302	+	0.723088i
$203$	30.9838	−	15.7870i	2.17464	−	1.10803i
$204$	3.50036	+	5.78199i	0.245074	+	0.404820i
$205$	14.2132	−	1.72730i	0.992696	−	0.120640i
$206$	−7.21384	+	12.8000i	−0.502612	+	0.891815i
$207$	−6.66831	−	13.0873i	−0.463479	−	0.909629i
$208$	−21.8912	−	11.4539i	−1.51788	−	0.794186i
$209$	3.38045	−	4.65279i	0.233831	−	0.321841i
$210$	−5.09276	+	27.5088i	−0.351433	+	1.89829i
$211$	8.75002	−	4.45836i	0.602376	−	0.306926i	−0.126078	−	0.992020i	$-0.540239\pi$
$211$	8.75002	−	4.45836i	0.602376	−	0.306926i	0.728454	+	0.685094i	$0.240239\pi$
$212$	5.05276	−	5.85167i	0.347025	−	0.401894i
$213$	−3.45614	+	21.8212i	−0.236811	+	1.49517i
$214$	6.16230	−	10.9342i	0.421246	−	0.747443i
$215$	−0.195686	−	12.2343i	−0.0133457	−	0.834376i
$216$	6.34277	+	0.802920i	0.431571	+	0.0546318i
$217$	−15.3339	−	11.1407i	−1.04093	−	0.756281i
$218$	−5.31045	−	5.77606i	−0.359669	−	0.391204i
$219$	3.85175	−	3.85175i	0.260277	−	0.260277i
$220$	5.68353	+	4.75105i	0.383183	+	0.320316i
$221$	−2.88821	−	8.88900i	−0.194282	−	0.597939i
$222$	−18.3031	+	2.11616i	−1.22842	+	0.142027i
$223$	3.27544	+	6.42842i	0.219340	+	0.430479i	0.974288	−	0.225306i	$-0.0723381\pi$
$223$	3.27544	+	6.42842i	0.219340	+	0.430479i	−0.754948	+	0.655784i	$0.772338\pi$
$224$	22.2864	−	2.33283i	1.48907	−	0.155868i
$225$	−6.09644	−	7.85023i	−0.406430	−	0.523349i
$226$	25.8751	+	5.21962i	1.72118	+	0.347204i
$227$	−1.91469	−	5.89281i	−0.127082	−	0.391119i	0.867192	−	0.497973i	$-0.165922\pi$
$227$	−1.91469	−	5.89281i	−0.127082	−	0.391119i	−0.994275	+	0.106854i	$0.965922\pi$
$228$	13.1793	+	8.17458i	0.872817	+	0.541375i
$229$	−22.3754	−	3.54392i	−1.47861	−	0.234189i	−0.635571	−	0.772043i	$-0.719235\pi$
$229$	−22.3754	−	3.54392i	−1.47861	−	0.234189i	−0.843038	+	0.537854i	$0.819235\pi$
$230$	−23.3577	−	0.606956i	−1.54016	−	0.0400215i
$231$	2.29242	+	14.4738i	0.150830	+	0.952305i
$232$	24.8174	−	0.773588i	1.62934	−	0.0507885i
$233$	8.19907	+	2.66404i	0.537139	+	0.174527i	0.565009	−	0.825085i	$-0.308873\pi$
$233$	8.19907	+	2.66404i	0.537139	+	0.174527i	−0.0278705	+	0.999612i	$0.508873\pi$
$234$	16.2749	+	6.05414i	1.06392	+	0.395772i
$235$	−14.5670	−	14.1084i	−0.950248	−	0.920328i
$236$	−3.10229	+	7.37655i	−0.201942	+	0.480172i
$237$	−2.38806	−	2.38806i	−0.155121	−	0.155121i
$238$	6.64288	+	5.26600i	0.430594	+	0.341344i
$239$	7.26553	−	14.2594i	0.469968	−	0.922365i	−0.527383	−	0.849628i	$-0.676827\pi$
$239$	7.26553	−	14.2594i	0.469968	−	0.922365i	0.997351	−	0.0727369i	$-0.0231734\pi$
$240$	−11.6576	+	16.2214i	−0.752493	+	1.04708i
$241$	−3.27172	+	4.50313i	−0.210750	+	0.290072i	−0.901285	−	0.433227i	$-0.857375\pi$
$241$	−3.27172	+	4.50313i	−0.210750	+	0.290072i	0.690535	+	0.723299i	$0.257375\pi$
$242$	−10.9435	−	4.07089i	−0.703472	−	0.261687i
$243$	−17.8125			−1.14267
$244$	2.68187	−	0.628546i	0.171689	−	0.0402385i
$245$	3.34685	+	19.1443i	0.213822	+	1.22308i
$246$	10.2972	+	17.4062i	0.656524	+	1.10978i
$247$	−15.1643	−	15.1643i	−0.964881	−	0.964881i
$248$	−6.51676	−	11.8611i	−0.413815	−	0.753181i
$249$	0.846519	−	0.846519i	0.0536459	−	0.0536459i
$250$	−15.6016	+	2.56722i	−0.986731	+	0.162365i
$251$	−21.4300	−	15.5698i	−1.35265	−	0.982757i	−0.998875	−	0.0474255i	$-0.984898\pi$
$251$	−21.4300	−	15.5698i	−1.35265	−	0.982757i	−0.353774	−	0.935331i	$-0.615102\pi$
$252$	−15.3335	+	3.59370i	−0.965922	+	0.226382i
$253$	−11.6401	+	3.78208i	−0.731804	+	0.237777i
$254$	−3.35818	−	29.0455i	−0.210711	−	1.82248i
$255$	−7.44388	+	1.30136i	−0.466154	+	0.0814940i
$256$	15.1064	+	5.27213i	0.944153	+	0.329508i
$257$	−14.4166	+	10.4743i	−0.899286	+	0.653369i	−0.938282	−	0.345870i	$-0.887584\pi$
$257$	−14.4166	+	10.4743i	−0.899286	+	0.653369i	0.0389968	+	0.999239i	$0.487584\pi$
$258$	15.7151	−	7.19334i	0.978382	−	0.447838i
$259$	−20.5895	+	10.4909i	−1.27937	+	0.651872i
$260$	20.8135	−	18.1610i	1.29080	−	1.12630i
$261$	−17.2359	+	2.72990i	−1.06688	+	0.168977i
$262$	16.0913	−	10.6890i	0.994121	−	0.660371i
$263$	2.42900	+	3.34323i	0.149779	+	0.206152i	0.877313	−	0.479919i	$-0.159334\pi$
$263$	2.42900	+	3.34323i	0.149779	+	0.206152i	−0.727534	+	0.686071i	$0.759334\pi$
$264$	−2.92178	+	10.0473i	−0.179823	+	0.618366i
$265$	4.04688	+	7.63795i	0.248598	+	0.469196i
$266$	19.0664	+	3.84615i	1.16904	+	0.235823i
$267$	−2.11897	−	1.07967i	−0.129679	−	0.0660747i
$268$	9.63838	+	8.32248i	0.588758	+	0.508376i
$269$	−1.56932	−	0.509904i	−0.0956833	−	0.0310894i	0.260784	−	0.965397i	$-0.416019\pi$
$269$	−1.56932	−	0.509904i	−0.0956833	−	0.0310894i	−0.356467	+	0.934308i	$0.616019\pi$
$270$	−3.40948	+	6.28249i	−0.207494	+	0.382340i
$271$	4.93651	−	1.60397i	0.299872	−	0.0974343i	−0.155217	−	0.987880i	$-0.549608\pi$
$271$	4.93651	−	1.60397i	0.299872	−	0.0974343i	0.455089	+	0.890446i	$0.349608\pi$
$272$	2.68943	+	5.42244i	0.163070	+	0.328784i
$273$	54.6441			3.30721
$274$	0.621032	−	14.7873i	0.0375179	−	0.893336i
$275$	−7.25541	+	3.99409i	−0.437518	+	0.240853i
$276$	−12.4650	−	30.5594i	−0.750306	−	1.83946i
$277$	−0.799831	+	5.04993i	−0.0480572	+	0.303421i	−0.999996	−	0.00286747i	$-0.999087\pi$
$277$	−0.799831	+	5.04993i	−0.0480572	+	0.303421i	0.951939	+	0.306289i	$0.0990873\pi$
$278$	−4.72236	−	16.9191i	−0.283228	−	1.01474i
$279$	5.59081	+	7.69508i	0.334713	+	0.460693i
$280$	−6.61010	+	24.1654i	−0.395029	+	1.44416i
$281$	−9.35562	−	18.3614i	−0.558110	−	1.09535i	−0.981866	−	0.189576i	$-0.939289\pi$
$281$	−9.35562	−	18.3614i	−0.558110	−	1.09535i	0.423757	−	0.905776i	$-0.360711\pi$
$282$	9.98688	−	26.8469i	0.594710	−	1.59871i
$283$	24.3190	−	3.85175i	1.44562	−	0.228963i	0.616198	−	0.787591i	$-0.288672\pi$
$283$	24.3190	−	3.85175i	1.44562	−	0.228963i	0.829418	+	0.558628i	$0.188672\pi$
$284$	−4.72259	+	19.2129i	−0.280234	+	1.14007i
$285$	−13.8629	+	10.4147i	−0.821165	+	0.616915i
$286$	7.10399	−	12.6051i	0.420068	−	0.745352i
$287$	19.7153	+	15.9579i	1.16376	+	0.941967i
$288$	−10.9985	−	2.34268i	−0.648092	−	0.138044i
$289$	4.54572	−	13.9903i	0.267395	−	0.822958i
$290$	−9.26130	+	26.1698i	−0.543842	+	1.53674i
$291$	−4.60834	+	6.34284i	−0.270146	+	0.371824i
$292$	3.72636	−	3.14793i	0.218069	−	0.184219i
$293$	−5.82625	+	17.9314i	−0.340373	+	1.04756i	0.623641	+	0.781711i	$0.285653\pi$
$293$	−5.82625	+	17.9314i	−0.340373	+	1.04756i	−0.964014	+	0.265850i	$0.914347\pi$
$294$	−22.8662	+	15.1895i	−1.33358	+	0.885867i
$295$	−6.42678	−	6.22443i	−0.374182	−	0.362400i
$296$	−16.4918	+	0.514069i	−0.958566	+	0.0298796i
$297$	−0.585721	+	3.69810i	−0.0339870	+	0.214585i
$298$	−0.927813	−	8.02482i	−0.0537468	−	0.464866i
$299$	7.13941	+	45.0764i	0.412883	+	2.60684i
$300$	−12.1713	−	18.7256i	−0.702708	−	1.08113i
$301$	15.3274	−	15.3274i	0.883455	−	0.883455i
$302$	2.60070	+	5.68171i	0.149654	+	0.326945i
$303$	−29.4530	−	15.0071i	−1.69203	−	0.862133i
$304$	11.1468	+	8.28424i	0.639314	+	0.475134i
$305$	−0.433059	+	3.04907i	−0.0247969	+	0.174589i
$306$	−2.35384	−	3.54347i	−0.134560	−	0.202567i
$307$	−17.4188	−	8.87530i	−0.994141	−	0.506540i	−0.120292	−	0.992739i	$-0.538383\pi$
$307$	−17.4188	−	8.87530i	−0.994141	−	0.506540i	−0.873848	+	0.486199i	$0.838383\pi$
$308$	0.958883	+	13.0879i	0.0546374	+	0.745754i
$309$	10.5340	−	20.6742i	0.599260	−	1.17611i
$310$	15.0010	−	1.97798i	0.852000	−	0.112342i
$311$	−5.98001	−	0.947141i	−0.339095	−	0.0537074i	−0.0154353	−	0.999881i	$-0.504913\pi$
$311$	−5.98001	−	0.947141i	−0.339095	−	0.0537074i	−0.323660	+	0.946173i	$0.604913\pi$
$312$	35.2996	+	16.6217i	1.99845	+	0.941021i
$313$	−8.21177	−	5.96620i	−0.464157	−	0.337230i	0.331003	−	0.943630i	$-0.392613\pi$
$313$	−8.21177	−	5.96620i	−0.464157	−	0.337230i	−0.795160	+	0.606400i	$0.792613\pi$
$314$	7.28523	+	26.1013i	0.411129	+	1.47298i
$315$	2.47601	−	17.4330i	0.139507	−	0.982238i
$316$	−1.95170	−	2.31032i	−0.109792	−	0.129966i
$317$	−1.13401	+	0.823905i	−0.0636923	+	0.0462751i	−0.619176	−	0.785252i	$-0.712533\pi$
$317$	−1.13401	+	0.823905i	−0.0636923	+	0.0462751i	0.555484	+	0.831528i	$0.312533\pi$
$318$	−7.58465	+	9.56777i	−0.425326	+	0.536534i
$319$			14.5410i			0.814141i
$320$	−11.6207	+	13.6000i	−0.649619	+	0.760260i
$321$	−8.99853	+	17.6606i	−0.502249	+	0.985719i
$322$	−28.0151	−	30.4714i	−1.56122	−	1.69810i
$323$	0.821883	+	5.18916i	0.0457308	+	0.288733i
$324$	−21.9464	−	1.84664i	−1.21924	−	0.102591i
$325$	10.4779	+	29.0515i	0.581211	+	1.61149i
$326$	16.7430	−	15.3934i	0.927312	−	0.852561i
$327$	8.76175	+	8.76175i	0.484526	+	0.484526i
$328$	7.88182	+	16.3057i	0.435201	+	0.900334i
$329$		−	35.9250i		−	1.98061i
$330$	−9.28248	−	7.11974i	−0.510984	−	0.391929i
$331$	7.43942	−	7.43942i	0.408908	−	0.408908i	−0.472450	−	0.881358i	$-0.656630\pi$
$331$	7.43942	−	7.43942i	0.408908	−	0.408908i	0.881358	+	0.472450i	$0.156630\pi$
$332$	0.818960	−	0.691837i	0.0449463	−	0.0379695i
$333$	11.4537	−	1.81409i	0.627660	−	0.0994115i
$334$	−0.338307	+	8.05540i	−0.0185113	+	0.440772i
$335$	−12.5806	+	6.66568i	−0.687351	+	0.364185i
$336$	−35.0096	+	5.15762i	−1.90993	+	0.281371i
$337$	0.213185	+	0.213185i	0.0116129	+	0.0116129i	0.712889	−	0.701276i	$-0.247386\pi$
$337$	0.213185	+	0.213185i	0.0116129	+	0.0116129i	−0.701276	+	0.712889i	$0.747386\pi$
$338$	−27.8733	−	22.0960i	−1.51611	−	1.20186i
$339$	−41.1724	−	6.52107i	−2.23618	−	0.354176i
$340$	−6.74033	+	0.602343i	−0.365546	+	0.0326667i
$341$	7.06182	−	3.59817i	0.382419	−	0.194852i
$342$	−8.50345	−	4.79240i	−0.459814	−	0.259143i
$343$	−3.93828	+	5.42058i	−0.212647	+	0.292684i
$344$	14.5637	−	5.23905i	0.785220	−	0.282471i
$345$	36.8947	−	0.590123i	1.98635	−	0.0317712i
$346$	−21.0322	+	19.3368i	−1.13070	+	1.03955i
$347$	−10.1089	−	31.1119i	−0.542673	−	1.67017i	−0.726460	−	0.687209i	$-0.758836\pi$
$347$	−10.1089	−	31.1119i	−0.542673	−	1.67017i	0.183788	−	0.982966i	$-0.441164\pi$
$348$	−39.1065	+	2.86512i	−2.09633	+	0.153587i
$349$	−9.61091	−	29.5793i	−0.514460	−	1.58335i	−0.784262	−	0.620430i	$-0.786958\pi$
$349$	−9.61091	−	29.5793i	−0.514460	−	1.58335i	0.269801	−	0.962916i	$-0.413042\pi$
$350$	−22.4952	−	16.6895i	−1.20242	−	0.892089i
$351$	13.2784	+	4.31441i	0.708748	+	0.230286i
$352$	−3.36168	+	8.74638i	−0.179178	+	0.466183i
$353$	15.3466	−	30.1193i	0.816815	−	1.60309i	0.0192826	−	0.999814i	$-0.493862\pi$
$353$	15.3466	−	30.1193i	0.816815	−	1.60309i	0.797533	−	0.603276i	$-0.206138\pi$
$354$	4.40609	−	11.8445i	0.234181	−	0.629530i
$355$	−18.1011	−	12.7140i	−0.960708	−	0.674787i
$356$	−1.80981	−	1.12256i	−0.0959200	−	0.0594955i
$357$	−10.8303	−	7.86868i	−0.573201	−	0.416455i
$358$	−22.3814	+	2.58769i	−1.18289	+	0.136763i
$359$	19.5221	−	14.1836i	1.03034	−	0.748583i	0.0619600	−	0.998079i	$-0.480265\pi$
$359$	19.5221	−	14.1836i	1.03034	−	0.748583i	0.968376	+	0.249496i	$0.0802649\pi$
$360$	6.90228	−	10.5084i	0.363782	−	0.553842i
$361$	−4.08216	−	5.61861i	−0.214850	−	0.295716i
$362$	−2.77166	+	13.7399i	−0.145675	+	0.722151i
$363$	17.5367	+	5.69802i	0.920437	+	0.299068i
$364$	48.7621	+	4.10301i	2.55583	+	0.215056i
$365$	1.76806	+	5.15926i	0.0925443	+	0.270048i
$366$	−4.18989	+	1.16945i	−0.219009	+	0.0611284i
$367$	−3.74499	−	7.34995i	−0.195487	−	0.383664i	0.772368	−	0.635176i	$-0.219072\pi$
$367$	−3.74499	−	7.34995i	−0.195487	−	0.383664i	−0.967854	+	0.251511i	$0.919072\pi$
$368$	−8.82868	−	28.2059i	−0.460227	−	1.47034i
$369$	−6.93491	−	10.6737i	−0.361017	−	0.555649i
$370$	6.15437	−	17.3905i	0.319950	−	0.904088i
$371$	−4.73188	+	14.5632i	−0.245667	+	0.756086i
$372$	11.0683	+	18.2830i	0.573866	+	0.947929i
$373$	4.88412	+	30.8371i	0.252890	+	1.59669i	0.707974	+	0.706238i	$0.249609\pi$
$373$	4.88412	+	30.8371i	0.252890	+	1.59669i	−0.455084	+	0.890448i	$0.650391\pi$
$374$	−3.22310	+	1.47532i	−0.166663	+	0.0762870i
$375$	24.4466	−	5.08448i	1.26242	−	0.262561i
$376$	10.9277	−	23.2072i	0.563554	−	1.19682i
$377$	53.5545	+	8.48220i	2.75820	+	0.436855i
$378$	−12.1967	+	3.40426i	−0.627330	+	0.175096i
$379$	−4.43841	+	3.22469i	−0.227986	+	0.165641i	−0.695914	−	0.718125i	$-0.745001\pi$
$379$	−4.43841	+	3.22469i	−0.227986	+	0.165641i	0.467928	+	0.883766i	$0.345001\pi$
$380$	−13.1527	+	8.25276i	−0.674717	+	0.423358i
$381$	7.22334	+	45.6064i	0.370063	+	2.33648i
$382$	−8.22710	−	8.94843i	−0.420935	−	0.457842i
$383$			12.4495i			0.636140i	0.948067	+	0.318070i	$0.103035\pi$
$383$			12.4495i			0.636140i	−0.948067	+	0.318070i	$0.896965\pi$
$384$	−24.1848	−	7.31751i	−1.23417	−	0.373420i
$385$	−14.0246	−	4.31015i	−0.714760	−	0.219666i
$386$	13.1623	−	16.6038i	0.669942	−	0.845109i
$387$	−9.69225	+	4.93845i	−0.492685	+	0.251035i
$388$	−4.58855	+	5.31406i	−0.232948	+	0.269781i
$389$	10.4674	+	32.2154i	0.530719	+	1.63339i	0.752722	+	0.658339i	$0.228741\pi$
$389$	10.4674	+	32.2154i	0.530719	+	1.63339i	−0.222003	+	0.975046i	$0.571259\pi$
$390$	−31.6367	+	30.0342i	−1.60199	+	1.52084i
$391$	5.07594	−	9.96209i	0.256701	−	0.503805i
$392$	−21.5454	+	11.8375i	−1.08820	+	0.597885i
$393$	−24.6810	+	17.9318i	−1.24499	+	0.904539i
$394$	−10.5698	−	2.13218i	−0.532499	−	0.107418i
$395$	3.19871	−	1.09618i	0.160945	−	0.0551550i
$396$	1.57197	−	6.39523i	0.0789945	−	0.321372i
$397$	−8.16720	+	25.1361i	−0.409900	+	1.26154i	0.506833	+	0.862044i	$0.330816\pi$
$397$	−8.16720	+	25.1361i	−0.409900	+	1.26154i	−0.916734	+	0.399499i	$0.869184\pi$
$398$	−5.14570	−	11.2417i	−0.257930	−	0.563496i
$399$	−30.3385	−	4.80514i	−1.51882	−	0.240558i
$400$	−9.45509	−	17.6239i	−0.472754	−	0.881194i
$401$			9.53530i			0.476170i	0.971244	+	0.238085i	$0.0765197\pi$
$401$			9.53530i			0.476170i	−0.971244	+	0.238085i	$0.923480\pi$
$402$	−15.7592	−	12.4928i	−0.785999	−	0.623084i
$403$	−9.13269	−	28.1075i	−0.454932	−	1.40014i
$404$	−25.1558	−	15.6032i	−1.25155	−	0.776288i
$405$	10.8265	−	22.1157i	0.537975	−	1.09894i
$406$	−44.7160	+	20.4680i	−2.21922	+	1.01581i
$407$		−	9.66287i		−	0.478971i
$408$	−4.60278	−	8.37749i	−0.227872	−	0.414747i
$409$		−	5.01149i		−	0.247802i	−0.992295	−	0.123901i	$-0.960459\pi$
$409$		−	5.01149i		−	0.247802i	0.992295	−	0.123901i	$-0.0395406\pi$
$410$	−20.1854	+	1.59718i	−0.996884	+	0.0788792i
$411$			23.3731i			1.15291i
$412$	10.9525	−	17.6579i	0.539590	−	0.869940i
$413$		−	15.8496i		−	0.779909i
$414$	8.64549	+	18.8876i	0.424903	+	0.928276i
$415$	0.388575	+	1.13388i	0.0190744	+	0.0556598i
$416$	30.2519	+	17.4831i	1.48322	+	0.857178i
$417$	8.57224	+	26.3827i	0.419785	+	1.29196i
$418$	−5.05257	+	6.37365i	−0.247130	+	0.311745i
$419$		−	3.64669i		−	0.178152i	−0.996025	−	0.0890762i	$-0.971609\pi$
$419$		−	3.64669i		−	0.178152i	0.996025	−	0.0890762i	$-0.0283915\pi$
$420$	8.82831	−	38.5669i	0.430777	−	1.88187i
$421$	3.12265	+	0.494580i	0.152189	+	0.0241043i	0.232064	−	0.972701i	$-0.425452\pi$
$421$	3.12265	+	0.494580i	0.152189	+	0.0241043i	−0.0798751	+	0.996805i	$0.525452\pi$
$422$	−12.6281	+	5.78028i	−0.614724	+	0.281380i
$423$	−5.57108	+	17.1460i	−0.270875	+	0.833668i
$424$	−7.48663	+	7.96838i	−0.363583	+	0.386979i
$425$	2.10668	−	7.26674i	0.102189	−	0.352488i
$426$	6.17832	−	30.6276i	0.299340	−	1.48391i
$427$	−4.41376	+	3.20678i	−0.213597	+	0.155187i
$428$	−9.35598	+	15.0839i	−0.452238	+	0.729109i
$429$	−10.3736	+	20.3594i	−0.500844	+	0.982961i
$430$	−0.449502	+	17.2984i	−0.0216769	+	0.834201i
$431$	−7.06433	−	21.7418i	−0.340277	−	1.04726i	−0.964064	−	0.265670i	$-0.914407\pi$
$431$	−7.06433	−	21.7418i	−0.340277	−	1.04726i	0.623787	−	0.781594i	$-0.285593\pi$
$432$	−8.91448	−	1.51089i	−0.428898	−	0.0726926i
$433$	15.0326	−	7.65951i	0.722422	−	0.368093i	−0.0538001	−	0.998552i	$-0.517133\pi$
$433$	15.0326	−	7.65951i	0.722422	−	0.368093i	0.776222	+	0.630459i	$0.217133\pi$
$434$	21.0052	+	16.6514i	1.00828	+	0.799293i
$435$	12.8786	−	41.9052i	0.617483	−	2.00920i
$436$	7.16074	+	8.47651i	0.342937	+	0.405951i
$437$		−	25.6543i		−	1.22721i
$438$	−5.67097	+	5.21383i	−0.270969	+	0.249127i
$439$	−0.622671	−	3.93139i	−0.0297185	−	0.187635i	0.968363	−	0.249545i	$-0.0802810\pi$
$439$	−0.622671	−	3.93139i	−0.0297185	−	0.187635i	−0.998082	+	0.0619096i	$0.980281\pi$
$440$	−7.74871	−	7.05035i	−0.369405	−	0.336112i
$441$	13.9779	−	10.1555i	0.665614	−	0.483597i
$442$	3.55347	+	12.7313i	0.169021	+	0.605565i
$443$	29.4982	+	4.67205i	1.40150	+	0.221976i	0.810993	−	0.585056i	$-0.198928\pi$
$443$	29.4982	+	4.67205i	1.40150	+	0.221976i	0.590507	+	0.807032i	$0.298928\pi$
$444$	25.9872	−	1.90394i	1.23330	−	0.0903572i
$445$	1.90369	−	1.43018i	0.0902436	−	0.0677971i
$446$	−4.24662	−	9.27751i	−0.201083	−	0.439303i
$447$	1.99570	+	12.6003i	0.0943933	+	0.595976i
$448$	−31.6284	+	1.97371i	−1.49430	+	0.0932489i
$449$	−1.22197	+	3.76083i	−0.0576682	+	0.177485i	−0.975741	−	0.218927i	$-0.929744\pi$
$449$	−1.22197	+	3.76083i	−0.0576682	+	0.177485i	0.918073	+	0.396411i	$0.129744\pi$
$450$	8.14824	+	11.4539i	0.384112	+	0.539942i
$451$	−9.68839	+	4.31611i	−0.456208	+	0.203238i
$452$	−36.2509	−	8.91061i	−1.70510	−	0.419120i
$453$	−4.47997	−	8.79244i	−0.210488	−	0.413105i
$454$	2.35571	+	8.43997i	0.110559	+	0.396107i
$455$	−24.0552	+	49.1383i	−1.12773	+	2.30364i
$456$	−18.1368	−	12.3325i	−0.849332	−	0.577522i
$457$	−19.3008	−	6.27120i	−0.902852	−	0.293354i	−0.179438	−	0.983769i	$-0.557428\pi$
$457$	−19.3008	−	6.27120i	−0.902852	−	0.293354i	−0.723414	+	0.690415i	$0.757428\pi$
$458$	31.4054	+	6.33522i	1.46748	+	0.296026i
$459$	−2.01047	−	2.76718i	−0.0938408	−	0.129161i
$460$	32.9676	+	2.24368i	1.53712	+	0.104612i
$461$	−13.7082	+	9.95962i	−0.638457	+	0.463866i	−0.859320	−	0.511439i	$-0.829113\pi$
$461$	−13.7082	+	9.95962i	−0.638457	+	0.463866i	0.220863	+	0.975305i	$0.429113\pi$
$462$	−2.38023	−	20.5870i	−0.110738	−	0.957795i
$463$	−1.29514	−	0.940973i	−0.0601902	−	0.0437307i	0.557283	−	0.830322i	$-0.311844\pi$
$463$	−1.29514	−	0.940973i	−0.0601902	−	0.0437307i	−0.617473	+	0.786592i	$0.711844\pi$
$464$	−35.1121	−	0.379639i	−1.63004	−	0.0176243i
$465$	−23.5380	+	4.11496i	−1.09155	+	0.190827i
$466$	−11.4269	−	4.25074i	−0.529342	−	0.196912i
$467$	9.28740	−	18.2275i	0.429770	−	0.843470i	−0.569992	−	0.821650i	$-0.693054\pi$
$467$	9.28740	−	18.2275i	0.429770	−	0.843470i	0.999762	−	0.0218203i	$-0.00694618\pi$
$468$	−22.6366	−	9.52008i	−1.04638	−	0.440066i
$469$	−23.9874	−	7.79396i	−1.10763	−	0.359892i
$470$	19.7455	+	20.7991i	0.910793	+	0.959390i
$471$	−13.2245	−	40.7008i	−0.609352	−	1.87539i
$472$	4.82117	−	10.2387i	0.221912	−	0.471276i
$473$	2.80095	+	8.62045i	0.128788	+	0.396369i
$474$	3.23255	+	3.51597i	0.148476	+	0.161494i
$475$	−3.26271	−	17.0508i	−0.149703	−	0.782345i
$476$	−9.07369	−	7.83489i	−0.415892	−	0.359112i
$477$	4.51681	−	6.21685i	0.206810	−	0.284650i
$478$	−11.1121	+	19.7169i	−0.508257	+	0.901832i
$479$	−11.9433	+	6.08544i	−0.545705	+	0.278051i	−0.705032	−	0.709175i	$-0.749068\pi$
$479$	−11.9433	+	6.08544i	−0.545705	+	0.278051i	0.159327	+	0.987226i	$0.449068\pi$
$480$	17.4344	−	22.2285i	0.795766	−	1.01459i
$481$	−35.5883	−	5.63663i	−1.62269	−	0.257008i
$482$	4.89005	−	6.16863i	0.222736	−	0.280974i
$483$	46.2223	+	46.2223i	2.10319	+	2.10319i
$484$	15.2212	+	6.40144i	0.691872	+	0.290974i
$485$	−3.67508	−	6.93623i	−0.166877	−	0.314958i
$486$	25.1684	+	1.05701i	1.14166	+	0.0479470i
$487$	29.9558	−	4.74454i	1.35743	−	0.214995i	0.565065	−	0.825046i	$-0.308851\pi$
$487$	29.9558	−	4.74454i	1.35743	−	0.214995i	0.792362	+	0.610051i	$0.208851\pi$
$488$	−3.82669	+	0.728970i	−0.173226	+	0.0329989i
$489$	−25.3977	+	25.3977i	−1.14852	+	1.14852i
$490$	−3.59294	−	27.2489i	−0.162313	−	1.23098i
$491$			21.1626i			0.955056i	0.878617	+	0.477528i	$0.158467\pi$
$491$			21.1626i			0.955056i	−0.878617	+	0.477528i	$0.841533\pi$
$492$	−13.5167	−	25.2054i	−0.609379	−	1.13635i
$493$	−9.39292	−	9.39292i	−0.423036	−	0.423036i
$494$	20.5268	+	22.3265i	0.923545	+	1.00452i
$495$	6.02517	+	4.23199i	0.270811	+	0.190214i
$496$	8.50412	+	17.1461i	0.381846	+	0.769881i
$497$	−6.13006	−	38.7037i	−0.274971	−	1.73610i
$498$	−1.24634	+	1.14587i	−0.0558497	+	0.0513477i
$499$	−10.7065	+	21.0128i	−0.479290	+	0.940661i	0.517112	+	0.855918i	$0.327007\pi$
$499$	−10.7065	+	21.0128i	−0.479290	+	0.940661i	−0.996403	+	0.0847430i	$0.972993\pi$
$500$	22.1969	−	2.70158i	0.992675	−	0.120818i
$501$		−	12.7325i		−	0.568846i
$502$	29.3559	+	23.2713i	1.31022	+	1.03865i
$503$	−12.5925	+	9.14895i	−0.561470	+	0.407932i	−0.831997	−	0.554781i	$-0.812802\pi$
$503$	−12.5925	+	9.14895i	−0.561470	+	0.407932i	0.270527	+	0.962712i	$0.412802\pi$
$504$	21.8791	−	4.16787i	0.974570	−	0.185652i
$505$	26.4607	−	19.8791i	1.17748	−	0.884606i
$506$	16.6715	−	4.65323i	0.741137	−	0.206861i
$507$	45.4436	+	33.0167i	2.01822	+	1.46632i
$508$	3.02140	+	41.2396i	0.134053	+	1.82971i
$509$	−38.5231	−	6.10146i	−1.70751	−	0.270442i	−0.775095	−	0.631844i	$-0.782298\pi$
$509$	−38.5231	−	6.10146i	−1.70751	−	0.270442i	−0.932410	+	0.361402i	$0.882298\pi$
$510$	10.5952	−	1.39704i	0.469163	−	0.0618622i
$511$	−4.38624	+	8.60849i	−0.194036	+	0.380817i
$512$	−21.0321	−	8.34579i	−0.929495	−	0.368835i
$513$	−6.99280	−	3.56301i	−0.308739	−	0.157311i
$514$	20.9918	−	13.9444i	0.925909	−	0.615059i
$515$	13.9539	+	18.5738i	0.614881	+	0.818458i
$516$	−22.6319	+	9.23140i	−0.996312	+	0.406390i
$517$	13.3850	+	6.81999i	0.588671	+	0.299943i
$518$	29.7149	−	13.6015i	1.30560	−	0.597615i
$519$	31.9039	−	31.9039i	1.40043	−	1.40043i
$520$	−30.4865	+	24.4258i	−1.33692	+	1.07114i
$521$	−6.95049	−	43.8837i	−0.304507	−	1.92258i	−0.379080	−	0.925364i	$-0.623759\pi$
$521$	−6.95049	−	43.8837i	−0.304507	−	1.92258i	0.0745728	−	0.997216i	$-0.476241\pi$
$522$	24.5158	−	2.83447i	1.07303	−	0.124061i
$523$	−1.91926	+	12.1177i	−0.0839235	+	0.529872i	0.909530	+	0.415638i	$0.136442\pi$
$523$	−1.91926	+	12.1177i	−0.0839235	+	0.529872i	−0.993454	+	0.114235i	$0.963558\pi$
$524$	−23.3707	+	14.1484i	−1.02095	+	0.618075i
$525$	36.5996	+	24.8425i	1.59734	+	1.08422i
$526$	−3.23371	−	4.86802i	−0.140996	−	0.212256i
$527$	−2.23738	+	6.88593i	−0.0974616	+	0.299956i
$528$	4.72459	−	14.0231i	0.205611	−	0.610276i
$529$	−18.5711	+	25.5609i	−0.807437	+	1.11134i
$530$	−5.26487	−	11.0323i	−0.228691	−	0.479214i
$531$	−2.45789	+	7.56461i	−0.106663	+	0.328276i
$532$	−26.7120	−	6.56591i	−1.15811	−	0.284668i
$533$	10.2447	+	38.2000i	0.443747	+	1.65463i
$534$	2.92997	+	1.65128i	0.126792	+	0.0714579i
$535$	−11.9199	−	15.8663i	−0.515341	−	0.685962i
$536$	−13.1249	−	12.3314i	−0.566907	−	0.532633i
$537$	35.1426	−	5.56604i	1.51651	−	0.240192i
$538$	2.18714	+	0.813603i	0.0942945	+	0.0350769i
$539$	−6.53598	−	12.8276i	−0.281525	−	0.552523i
$540$	5.19030	−	8.67463i	0.223355	−	0.373297i
$541$	13.9504	+	19.2011i	0.599776	+	0.825520i	0.995688	−	0.0927682i	$-0.0295715\pi$
$541$	13.9504	+	19.2011i	0.599776	+	0.825520i	−0.395912	+	0.918288i	$0.629572\pi$
$542$	−7.07032	+	1.97342i	−0.303696	+	0.0847657i
$543$	3.46273	−	21.8628i	0.148600	−	0.938225i
$544$	−3.47830	−	7.82133i	−0.149131	−	0.335337i
$545$	−11.7360	+	4.02188i	−0.502715	+	0.172278i
$546$	−77.2104	−	3.24264i	−3.30430	−	0.138772i
$547$	−11.6484			−0.498050			−0.249025	−	0.968497i	$-0.580110\pi$
$547$	−11.6484			−0.498050			−0.249025	+	0.968497i	$0.580110\pi$
$548$	−1.75500	+	20.8572i	−0.0749697	+	0.890975i
$549$	2.60386	−	0.846046i	0.111130	−	0.0361084i
$550$	10.4887	−	5.21298i	0.447239	−	0.222282i
$551$	−28.9876	−	9.41865i	−1.23491	−	0.401248i
$552$	15.7992	+	43.9192i	0.672460	+	1.86932i
$553$	5.33721	+	2.71945i	0.226961	+	0.115643i
$554$	1.42980	−	7.08793i	0.0607466	−	0.301137i
$555$	−8.55817	+	27.8471i	−0.363274	+	1.18204i
$556$	5.66855	+	24.1864i	0.240400	+	1.02573i
$557$	14.2703	+	19.6414i	0.604652	+	0.832233i	0.996124	−	0.0879575i	$-0.0280340\pi$
$557$	14.2703	+	19.6414i	0.604652	+	0.832233i	−0.391472	+	0.920190i	$0.628034\pi$
$558$	−7.44299	−	11.2047i	−0.315087	−	0.474332i
$559$	33.3829	−	5.28734i	1.41195	−	0.223631i
$560$	10.7739	−	33.7526i	0.455278	−	1.42631i
$561$	4.98775	−	2.54139i	0.210583	−	0.107297i
$562$	12.1296	+	26.4993i	0.511657	+	1.11781i
$563$	−14.1297	+	10.2659i	−0.595498	+	0.432654i	−0.844278	−	0.535906i	$-0.819970\pi$
$563$	−14.1297	+	10.2659i	−0.595498	+	0.432654i	0.248780	+	0.968560i	$0.419970\pi$
$564$	−15.7043	+	37.3412i	−0.661269	+	1.57235i
$565$	23.9888	−	34.1533i	1.00922	−	1.43684i
$566$	−34.5906	+	3.99929i	−1.45395	+	0.168103i
$567$	41.4861	−	13.4796i	1.74225	−	0.566092i
$568$	7.81298	−	26.8669i	0.327826	−	1.12731i
$569$	−22.1717	−	16.1087i	−0.929487	−	0.675312i	0.0163802	−	0.999866i	$-0.494786\pi$
$569$	−22.1717	−	16.1087i	−0.929487	−	0.675312i	−0.945867	+	0.324554i	$0.894786\pi$
$570$	20.2058	−	13.8930i	0.846328	−	0.581915i
$571$	−27.6858	+	27.6858i	−1.15861	+	1.15861i	−0.173839	+	0.984774i	$0.555617\pi$
$571$	−27.6858	+	27.6858i	−1.15861	+	1.15861i	−0.984774	+	0.173839i	$0.944383\pi$
$572$	−10.7857	+	17.3890i	−0.450973	+	0.727070i
$573$	13.5740	+	13.5740i	0.567060	+	0.567060i
$574$	−26.9101	−	23.7180i	−1.12321	−	0.989969i
$575$	−15.7110	+	33.4371i	−0.655194	+	1.39442i
$576$	15.4015	+	3.96280i	0.641728	+	0.165117i
$577$	6.29920			0.262239			0.131120	−	0.991367i	$-0.458143\pi$
$577$	6.29920			0.262239			0.131120	+	0.991367i	$0.458143\pi$
$578$	−7.25316	+	19.4981i	−0.301692	+	0.811013i
$579$	−19.6676	+	27.0701i	−0.817358	+	1.12500i
$580$	14.6389	−	36.4275i	0.607846	−	1.51257i
$581$	−0.963987	+	1.89193i	−0.0399929	+	0.0784905i
$582$	6.88783	−	8.68876i	0.285510	−	0.360161i
$583$	−4.52770	−	4.52770i	−0.187518	−	0.187518i
$584$	−5.45202	+	4.22680i	−0.225606	+	0.174906i
$585$	19.1011	−	19.7220i	0.789732	−	0.815406i
$586$	9.29637	−	24.9907i	0.384030	−	1.03236i
$587$	16.1134	+	5.23556i	0.665071	+	0.216095i	0.622048	−	0.782979i	$-0.286301\pi$
$587$	16.1134	+	5.23556i	0.665071	+	0.216095i	0.0430233	+	0.999074i	$0.486301\pi$
$588$	33.2105	−	20.1053i	1.36958	−	0.829129i
$589$	2.59884	+	16.4084i	0.107083	+	0.676098i
$590$	8.71147	+	9.17629i	0.358646	+	0.377782i
$591$	16.8187	+	2.66381i	0.691827	+	0.109575i
$592$	23.3329	+	0.252280i	0.958976	+	0.0103686i
$593$	−1.58365	−	4.87396i	−0.0650325	−	0.200150i	0.913260	−	0.407376i	$-0.133556\pi$
$593$	−1.58365	−	4.87396i	−0.0650325	−	0.200150i	−0.978293	+	0.207227i	$0.933556\pi$
$594$	1.04705	−	5.19053i	0.0429611	−	0.212970i
$595$	11.8435	−	6.27516i	0.485537	−	0.257256i
$596$	0.834768	+	11.3939i	0.0341934	+	0.466711i
$597$	8.86398	+	17.3965i	0.362778	+	0.711993i
$598$	−7.41287	−	64.1152i	−0.303135	−	2.62187i
$599$	−6.83087	−	21.0232i	−0.279102	−	0.858986i	−0.988105	−	0.153781i	$-0.950855\pi$
$599$	−6.83087	−	21.0232i	−0.279102	−	0.858986i	0.709003	−	0.705205i	$-0.249145\pi$
$600$	16.0864	+	27.1810i	0.656724	+	1.10966i
$601$	−11.9766	+	11.9766i	−0.488535	+	0.488535i	−0.907844	−	0.419309i	$-0.862273\pi$
$601$	−11.9766	+	11.9766i	−0.488535	+	0.488535i	0.419309	+	0.907844i	$0.362273\pi$
$602$	−22.5666	+	20.7475i	−0.919747	+	0.845607i
$603$	10.2399	+	7.43971i	0.417000	+	0.302968i
$604$	−3.33755	−	8.18240i	−0.135803	−	0.332937i
$605$	−12.8438	+	13.2614i	−0.522176	+	0.539152i
$606$	40.7256	+	22.9523i	1.65437	+	0.932372i
$607$	−2.01432	+	12.7179i	−0.0817589	+	0.516205i	0.912489	+	0.409101i	$0.134158\pi$
$607$	−2.01432	+	12.7179i	−0.0817589	+	0.516205i	−0.994248	+	0.107104i	$0.965842\pi$
$608$	−15.2585	−	12.3668i	−0.618814	−	0.501541i
$609$	69.1980	−	35.2581i	2.80404	−	1.42873i
$610$	0.792834	−	4.28254i	0.0321009	−	0.173395i
$611$	32.9258	−	45.3185i	1.33204	−	1.83339i
$612$	3.11563	+	5.14650i	0.125942	+	0.208035i
$613$	−14.4031	−	28.2677i	−0.581737	−	1.14172i	−0.974981	−	0.222288i	$-0.928647\pi$
$613$	−14.4031	−	28.2677i	−0.581737	−	1.14172i	0.393244	−	0.919434i	$-0.371353\pi$
$614$	24.0855	+	13.5742i	0.972010	+	0.547809i
$615$	31.7433	−	3.85767i	1.28001	−	0.155556i
$616$	−0.578217	−	18.5497i	−0.0232970	−	0.747390i
$617$	−18.1514	+	9.24862i	−0.730749	+	0.372335i	−0.779439	−	0.626479i	$-0.784496\pi$
$617$	−18.1514	+	9.24862i	−0.730749	+	0.372335i	0.0486893	+	0.998814i	$0.484496\pi$
$618$	−16.1111	+	28.5869i	−0.648083	+	1.14993i
$619$	−16.4029	−	11.9174i	−0.659287	−	0.479000i	0.207135	−	0.978312i	$-0.433586\pi$
$619$	−16.4029	−	11.9174i	−0.659287	−	0.479000i	−0.866422	+	0.499313i	$0.833586\pi$
$620$	−21.3133	+	1.90465i	−0.855963	+	0.0764924i
$621$	7.58244	+	14.8814i	0.304273	+	0.597169i
$622$	8.39336	+	1.69314i	0.336543	+	0.0678887i
$623$	4.16617	+	0.659856i	0.166914	+	0.0264366i
$624$	−48.8909	−	25.5807i	−1.95720	−	1.02405i
$625$	−6.18959	+	24.2217i	−0.247584	+	0.968866i
$626$	11.2489	+	8.91735i	0.449598	+	0.356409i
$627$	7.54976	−	10.3914i	0.301509	−	0.414991i
$628$	−8.74492	−	37.3127i	−0.348960	−	1.48894i
$629$	6.24184	+	6.24184i	0.248878	+	0.248878i
$630$	−4.53301	+	24.4853i	−0.180599	+	0.975519i
$631$	27.6967	−	8.99919i	1.10259	−	0.358252i	0.299489	−	0.954100i	$-0.403184\pi$
$631$	27.6967	−	8.99919i	1.10259	−	0.358252i	0.803097	+	0.595848i	$0.203184\pi$
$632$	2.62059	+	3.38022i	0.104241	+	0.134458i
$633$	19.5419	−	9.95711i	0.776722	−	0.395760i
$634$	1.65121	−	1.09686i	0.0655779	−	0.0435618i
$635$	−44.1910	−	13.5811i	−1.75367	−	0.538951i
$636$	11.2846	−	13.0689i	0.447465	−	0.518215i
$637$	−51.0565	+	16.5893i	−2.02293	+	0.657291i
$638$	0.862881	−	20.5460i	0.0341618	−	0.813424i
$639$	−3.07628	+	19.4229i	−0.121696	+	0.768357i
$640$	17.2268	−	18.5267i	0.680947	−	0.732332i
$641$	43.0787	−	6.82299i	1.70151	−	0.269492i	0.771284	−	0.636491i	$-0.219615\pi$
$641$	43.0787	−	6.82299i	1.70151	−	0.269492i	0.930222	+	0.366998i	$0.119615\pi$
$642$	13.7626	−	24.4199i	0.543168	−	0.963776i
$643$	4.31112	−	13.2683i	0.170014	−	0.523250i	−0.829357	−	0.558720i	$-0.811293\pi$
$643$	4.31112	−	13.2683i	0.170014	−	0.523250i	0.999371	+	0.0354699i	$0.0112928\pi$
$644$	37.7762	+	44.7175i	1.48859	+	1.76212i
$645$	−0.437036	−	27.3237i	−0.0172083	−	1.07587i
$646$	−0.853363	−	7.38089i	−0.0335751	−	0.290397i
$647$	−0.786636	+	0.786636i	−0.0309259	+	0.0309259i	−0.722401	−	0.691475i	$-0.756961\pi$
$647$	−0.786636	+	0.786636i	−0.0309259	+	0.0309259i	0.691475	+	0.722401i	$0.256961\pi$
$648$	30.8999	+	3.91157i	1.21386	+	0.153661i
$649$	5.90529	+	3.00889i	0.231803	+	0.118109i
$650$	−13.0810	−	41.6706i	−0.513080	−	1.63446i
$651$	−34.2461	−	24.8812i	−1.34221	−	0.975172i
$652$	−24.5709	+	20.7568i	−0.962269	+	0.812900i
$653$		−	25.4645i		−	0.996503i	−0.867032	−	0.498252i	$-0.833976\pi$
$653$		−	25.4645i		−	0.996503i	0.867032	−	0.498252i	$-0.166024\pi$
$654$	−11.8601	−	12.9000i	−0.463768	−	0.504430i
$655$	−5.26006	−	30.0881i	−0.205527	−	1.17564i
$656$	−10.1692	−	23.5072i	−0.397039	−	0.917802i
$657$	3.42841	−	3.42841i	0.133755	−	0.133755i
$658$	−2.13183	+	50.7608i	−0.0831073	+	1.97886i
$659$	−1.22147	−	1.22147i	−0.0475819	−	0.0475819i	0.682915	−	0.730497i	$-0.260712\pi$
$659$	−1.22147	−	1.22147i	−0.0475819	−	0.0475819i	−0.730497	+	0.682915i	$0.760712\pi$
$660$	12.6934	+	10.6108i	0.494088	+	0.413025i
$661$	−9.71777	+	13.3754i	−0.377977	+	0.520241i	−0.955047	−	0.296454i	$-0.904196\pi$
$661$	−9.71777	+	13.3754i	−0.377977	+	0.520241i	0.577070	+	0.816695i	$0.304196\pi$
$662$	−10.9531	+	10.0702i	−0.425706	+	0.391390i
$663$	−6.45041	−	19.8523i	−0.250513	−	0.771001i
$664$	−1.19822	+	0.928945i	−0.0464999	+	0.0360501i
$665$	17.6765	−	25.1664i	0.685464	−	0.975909i
$666$	−16.2914	+	1.88357i	−0.631278	+	0.0729870i
$667$	38.1257	+	52.4755i	1.47623	+	2.03186i
$668$	0.956034	−	11.3620i	0.0369901	−	0.439607i
$669$	7.31524	+	14.3570i	0.282823	+	0.555072i
$670$	18.1715	−	8.67184i	0.702027	−	0.335023i
$671$	−0.356881	−	2.25326i	−0.0137773	−	0.0869862i
$672$	49.7735	−	5.21004i	1.92006	−	0.200982i
$673$	11.0962	−	8.06186i	0.427727	−	0.310762i	−0.353012	−	0.935619i	$-0.614843\pi$
$673$	11.0962	−	8.06186i	0.427727	−	0.310762i	0.780739	+	0.624857i	$0.214843\pi$
$674$	−0.288572	−	0.313874i	−0.0111154	−	0.0120900i
$675$	6.93218	+	8.92639i	0.266820	+	0.343577i
$676$	38.0729	+	32.8749i	1.46434	+	1.26442i
$677$	−11.7685	+	23.0970i	−0.452300	+	0.887689i	0.546440	+	0.837498i	$0.315983\pi$
$677$	−11.7685	+	23.0970i	−0.452300	+	0.887689i	−0.998740	+	0.0501903i	$0.984017\pi$
$678$	57.7883	+	11.6573i	2.21935	+	0.447695i
$679$	4.29716	−	13.2253i	0.164910	−	0.507540i
$680$	9.55961	−	0.451113i	0.366594	−	0.0172994i
$681$	−4.27619	−	13.1608i	−0.163864	−	0.504321i
$682$	−10.1916	+	4.66505i	−0.390258	+	0.178634i
$683$		−	9.05126i		−	0.346337i	−0.984892	−	0.173168i	$-0.944599\pi$
$683$		−	9.05126i		−	0.346337i	0.984892	−	0.173168i	$-0.0554005\pi$
$684$	11.7307	+	7.27612i	0.448535	+	0.278209i
$685$	−21.0181	−	10.2892i	−0.803060	−	0.393131i
$686$	5.88633	−	7.42540i	0.224741	−	0.283503i
$687$	−49.9723	−	7.91484i	−1.90656	−	0.301970i
$688$	−20.8889	+	6.53839i	−0.796381	+	0.249274i
$689$	−19.3166	+	14.0344i	−0.735905	+	0.534666i
$690$	−52.1661	−	1.35555i	−1.98593	−	0.0516049i
$691$	−29.3587	+	14.9590i	−1.11686	+	0.569067i	−0.912191	−	0.409765i	$-0.865611\pi$
$691$	−29.3587	+	14.9590i	−1.11686	+	0.569067i	−0.204666	+	0.978832i	$0.565611\pi$
$692$	30.8653	−	26.0742i	1.17332	−	0.991193i
$693$	2.04046	+	12.8830i	0.0775108	+	0.489384i
$694$	12.4373	+	44.5600i	0.472113	+	1.69147i
$695$	−27.4980	−	3.90554i	−1.04306	−	0.148146i
$696$	55.4262	−	1.72770i	2.10092	−	0.0654883i
$697$	3.47028	−	9.04636i	0.131446	−	0.342655i
$698$	11.8246	+	42.3650i	0.447569	+	1.60354i
$699$	18.3115	+	5.94975i	0.692603	+	0.225040i
$700$	30.7946	+	24.9166i	1.16393	+	0.941757i
$701$	−24.2490	−	17.6179i	−0.915871	−	0.665419i	0.0266220	−	0.999646i	$-0.491525\pi$
$701$	−24.2490	−	17.6179i	−0.915871	−	0.665419i	−0.942493	+	0.334226i	$0.891525\pi$
$702$	−18.5059	−	6.88408i	−0.698461	−	0.259823i
$703$	19.2630	+	6.25893i	0.726518	+	0.236060i
$704$	5.26897	−	12.1589i	0.198582	−	0.458254i
$705$	−32.5334	−	31.5090i	−1.22528	−	1.18670i
$706$	−23.4715	+	41.6470i	−0.883362	+	1.56740i
$707$	57.9084	+	9.17179i	2.17787	+	0.344941i
$708$	−6.92853	+	16.4745i	−0.260390	+	0.619149i
$709$	−18.4549	+	2.92297i	−0.693089	+	0.109775i	−0.493034	−	0.870010i	$-0.664112\pi$
$709$	−18.4549	+	2.92297i	−0.693089	+	0.109775i	−0.200055	+	0.979785i	$0.564112\pi$
$710$	24.8219	+	19.0386i	0.931548	+	0.714505i
$711$	−2.12559	−	2.12559i	−0.0797159	−	0.0797159i
$712$	2.49060	+	1.69353i	0.0933390	+	0.0634679i
$713$	16.0504	−	31.5007i	0.601093	−	1.17971i
$714$	14.8359	+	11.7609i	0.555221	+	0.440140i
$715$	−13.7414	−	18.2910i	−0.513899	−	0.684043i
$716$	31.7777	−	2.32818i	1.18759	−	0.0870082i
$717$	16.2265	−	31.8464i	0.605991	−	1.18932i
$718$	−28.4257	+	18.8825i	−1.06084	+	0.704690i
$719$	31.6023	+	16.1022i	1.17857	+	0.600511i	0.929805	−	0.368053i	$-0.119976\pi$
$719$	31.6023	+	16.1022i	1.17857	+	0.600511i	0.248764	+	0.968564i	$0.419976\pi$
$720$	−10.3763	+	14.4385i	−0.386701	+	0.538090i
$721$	−6.43804	+	40.6482i	−0.239765	+	1.51382i
$722$	5.43454	+	8.18115i	0.202253	+	0.304471i
$723$	−7.30692	+	10.0571i	−0.271747	+	0.374028i
$724$	4.73160	−	19.2495i	0.175848	−	0.715402i
$725$	32.0136	+	30.0284i	1.18895	+	1.11523i
$726$	−24.4407	−	9.09176i	−0.907078	−	0.337427i
$727$	−2.56881	−	3.53566i	−0.0952718	−	0.131130i	0.758720	−	0.651417i	$-0.225825\pi$
$727$	−2.56881	−	3.53566i	−0.0952718	−	0.131130i	−0.853992	+	0.520287i	$0.825825\pi$
$728$	−68.6559	−	8.69103i	−2.54456	−	0.322111i
$729$	−6.74570			−0.249841
$730$	−2.19205	−	7.39479i	−0.0811314	−	0.273693i
$731$	−7.37778	−	3.75917i	−0.272877	−	0.139038i
$732$	5.98958	−	1.40377i	0.221381	−	0.0518848i
$733$	33.7221	−	5.34106i	1.24555	−	0.197276i	0.501360	−	0.865239i	$-0.332833\pi$
$733$	33.7221	−	5.34106i	1.24555	−	0.197276i	0.744195	+	0.667963i	$0.232833\pi$
$734$	4.85539	+	10.6075i	0.179216	+	0.391529i
$735$	7.47471	+	42.7561i	0.275709	+	1.57708i
$736$	10.8009	+	40.3780i	0.398125	+	1.48835i
$737$	7.45765	−	7.45765i	0.274706	−	0.274706i
$738$	9.16542	+	15.4931i	0.337384	+	0.570308i
$739$	−25.2086			−0.927315			−0.463658	−	0.886014i	$-0.653463\pi$
$739$	−25.2086			−0.927315			−0.463658	+	0.886014i	$0.653463\pi$
$740$	−9.72789	+	24.2070i	−0.357604	+	0.889866i
$741$	−33.8673	−	33.8673i	−1.24415	−	1.24415i
$742$	7.55020	−	20.2966i	0.277177	−	0.745112i
$743$	0.758139	+	4.78670i	0.0278134	+	0.175607i	0.997685	−	0.0680116i	$-0.0216655\pi$
$743$	0.758139	+	4.78670i	0.0278134	+	0.175607i	−0.969871	+	0.243619i	$0.921665\pi$
$744$	−14.5543	−	26.4901i	−0.533585	−	0.971174i
$745$	−12.2093	−	3.75226i	−0.447314	−	0.137472i
$746$	−5.07120	−	43.8617i	−0.185670	−	1.60589i
$747$	0.753478	−	0.753478i	0.0275683	−	0.0275683i
$748$	4.64169	−	1.89332i	0.169717	−	0.0692266i
$749$	5.49959	−	34.7230i	0.200951	−	1.26875i
$750$	−34.8439	+	5.73352i	−1.27232	+	0.209358i
$751$	8.92059	+	17.5076i	0.325517	+	0.638863i	0.994537	−	0.104381i	$-0.0332861\pi$
$751$	8.92059	+	17.5076i	0.325517	+	0.638863i	−0.669020	+	0.743244i	$0.733286\pi$
$752$	−16.8177	+	32.1426i	−0.613277	+	1.17212i
$753$	−47.8608	−	34.7729i	−1.74415	−	1.26720i
$754$	−75.1674	−	15.1631i	−2.73744	−	0.552206i
$755$	9.87870	−	0.158008i	0.359523	−	0.00575049i
$756$	17.4356	−	4.08635i	0.634125	−	0.148619i
$757$	−19.5045	+	6.33740i	−0.708903	+	0.230337i	−0.641205	−	0.767369i	$-0.721565\pi$
$757$	−19.5045	+	6.33740i	−0.708903	+	0.230337i	−0.0676977	+	0.997706i	$0.521565\pi$
$758$	6.46269	−	4.29301i	0.234735	−	0.155929i
$759$	−25.9964	+	8.44675i	−0.943610	+	0.306597i
$760$	19.0740	−	10.8804i	0.691887	−	0.394673i
$761$	−13.8231	+	42.5431i	−0.501087	+	1.54219i	0.306164	+	0.951979i	$0.400955\pi$
$761$	−13.8231	+	42.5431i	−0.501087	+	1.54219i	−0.807251	+	0.590209i	$0.799045\pi$
$762$	−7.50001	−	64.8690i	−0.271697	−	2.34995i
$763$	−19.5821	−	9.97759i	−0.708921	−	0.361213i
$764$	11.0936	+	13.1321i	0.401353	+	0.475101i
$765$	−6.62573	+	1.15832i	−0.239554	+	0.0418793i
$766$	0.738768	−	17.5908i	0.0266928	−	0.635580i
$767$	14.5265	−	19.9940i	0.524520	−	0.721940i
$768$	33.7381	+	11.7746i	1.21742	+	0.424878i
$769$	−4.26338	−	5.86804i	−0.153741	−	0.211607i	0.725198	−	0.688540i	$-0.241748\pi$
$769$	−4.26338	−	5.86804i	−0.153741	−	0.211607i	−0.878939	+	0.476934i	$0.841748\pi$
$770$	19.5606	+	6.92234i	0.704913	+	0.249464i
$771$	−32.1975	+	23.3929i	−1.15957	+	0.842474i
$772$	−19.5832	+	22.6795i	−0.704813	+	0.816254i
$773$	−7.33245	+	22.5669i	−0.263730	+	0.811677i	0.728254	+	0.685308i	$0.240332\pi$
$773$	−7.33245	+	22.5669i	−0.263730	+	0.811677i	−0.991983	+	0.126369i	$0.959668\pi$
$774$	13.9879	−	6.40272i	0.502785	−	0.230141i
$775$	6.66146	−	22.9778i	0.239287	−	0.825388i
$776$	6.79882	−	7.23631i	0.244063	−	0.259768i
$777$	−45.9838	+	23.4299i	−1.64966	+	0.840543i
$778$	−12.8784	−	46.1405i	−0.461714	−	1.65422i
$779$	−2.32875	−	22.1096i	−0.0834360	−	0.792157i
$780$	46.4839	−	40.5600i	1.66439	−	1.45228i
$781$	15.5840	+	5.06355i	0.557640	+	0.181188i
$782$	−7.76330	+	13.7749i	−0.277615	+	0.492590i
$783$	19.5988	−	3.10414i	0.700402	−	0.110933i
$784$	31.1454	−	15.4475i	1.11233	−	0.551696i
$785$	42.4215	+	6.02512i	1.51409	+	0.215046i
$786$	35.9375	−	23.8724i	1.28185	−	0.851502i
$787$	−4.71778	+	29.7869i	−0.168171	+	1.06179i	0.748789	+	0.662809i	$0.230636\pi$
$787$	−4.71778	+	29.7869i	−0.168171	+	1.06179i	−0.916960	+	0.398980i	$0.869364\pi$
$788$	14.8083	+	3.63993i	0.527523	+	0.129667i
$789$	5.42483	+	7.46663i	0.193129	+	0.265819i
$790$	−4.58473	+	1.35906i	−0.163117	+	0.0483531i
$791$	73.0263	−	11.5662i	2.59652	−	0.411248i
$792$	−2.60064	+	8.94297i	−0.0924099	+	0.317775i
$793$	−8.50692			−0.302090
$794$	13.0316	−	35.0318i	0.462474	−	1.24323i
$795$	9.03813	+	17.0583i	0.320549	+	0.604995i
$796$	6.60361	+	16.1895i	0.234059	+	0.573822i
$797$	15.0442	+	29.5260i	0.532894	+	1.04586i	0.987859	+	0.155354i	$0.0496518\pi$
$797$	15.0442	+	29.5260i	0.532894	+	1.04586i	−0.454965	+	0.890509i	$0.650348\pi$
$798$	42.5822	+	8.58983i	1.50739	+	0.304077i
$799$	−13.0516	+	4.24073i	−0.461733	+	0.150026i
$800$	12.3139	+	25.4631i	0.435363	+	0.900255i
$801$	−1.88608	−	0.961003i	−0.0666412	−	0.0339554i
$802$	0.565835	−	13.4731i	0.0199803	−	0.475751i
$803$	−2.37468	−	3.26847i	−0.0838007	−	0.115342i
$804$	21.5260	+	18.5871i	0.759162	+	0.655516i
$805$	−61.9128	+	21.2172i	−2.18214	+	0.747810i
$806$	11.2363	+	40.2570i	0.395781	+	1.41799i
$807$	−3.50486	−	1.13880i	−0.123377	−	0.0400876i
$808$	34.6185	+	23.5396i	1.21787	+	0.828120i
$809$	2.64134	−	16.6767i	0.0928645	−	0.586323i	−0.896746	−	0.442546i	$-0.854075\pi$
$809$	2.64134	−	16.6767i	0.0928645	−	0.586323i	0.989610	−	0.143777i	$-0.0459248\pi$
$810$	−16.6099	+	30.6063i	−0.583613	+	1.07539i
$811$	0.301743			0.0105956			0.00529781	−	0.999986i	$-0.498314\pi$
$811$	0.301743			0.0105956			0.00529781	+	0.999986i	$0.498314\pi$
$812$	64.3968	−	26.2671i	2.25988	−	0.921794i
$813$	11.0250	−	3.58224i	0.386664	−	0.125635i
$814$	−0.573406	+	13.6533i	−0.0200979	+	0.478549i
$815$	−11.6582	−	34.0191i	−0.408369	−	1.19164i
$816$	6.00645	+	12.1103i	0.210268	+	0.423944i
$817$	−18.9992			−0.664698
$818$	−0.297388	+	7.08108i	−0.0103979	+	0.247584i
$819$	48.6382			1.69956
$820$	28.6161	−	1.05895i	0.999316	−	0.0369800i
$821$	−34.6624			−1.20972			−0.604862	−	0.796330i	$-0.706772\pi$
$821$	−34.6624			−1.20972			−0.604862	+	0.796330i	$0.706772\pi$
$822$	1.38699	−	33.0255i	0.0483767	−	1.15189i
$823$	20.6558			0.720017			0.360008	−	0.932949i	$-0.382774\pi$
$823$	20.6558			0.720017			0.360008	+	0.932949i	$0.382774\pi$
$824$	−16.5234	+	24.3001i	−0.575618	+	0.846532i
$825$	−16.2039	+	8.92024i	−0.564149	+	0.310563i
$826$	−0.940535	+	22.3950i	−0.0327254	+	0.779222i
$827$	−30.8935	+	10.0379i	−1.07427	+	0.349052i	−0.792150	−	0.610327i	$-0.791038\pi$
$827$	−30.8935	+	10.0379i	−1.07427	+	0.349052i	−0.282122	+	0.959379i	$0.591038\pi$
$828$	−11.0950	−	27.2006i	−0.385577	−	0.945288i
$829$	−47.7823			−1.65955			−0.829774	−	0.558100i	$-0.811531\pi$
$829$	−47.7823			−1.65955			−0.829774	+	0.558100i	$0.811531\pi$
$830$	−0.481758	−	1.62519i	−0.0167221	−	0.0564112i
$831$	−1.78631	+	11.2783i	−0.0619664	+	0.391240i
$832$	−41.7075	−	26.4982i	−1.44595	−	0.918660i
$833$	12.5081	+	4.06413i	0.433380	+	0.140814i
$834$	−10.5467	−	37.7865i	−0.365203	−	1.30844i
$835$	11.4496	+	5.60505i	0.396230	+	0.193971i
$836$	7.51735	−	8.70594i	0.259993	−	0.301101i
$837$	−6.35723	−	8.74997i	−0.219738	−	0.302443i
$838$	−0.216399	+	5.15265i	−0.00747536	+	0.177995i
$839$	14.6508	+	7.46495i	0.505802	+	0.257719i	0.688220	−	0.725502i	$-0.258392\pi$
$839$	14.6508	+	7.46495i	0.505802	+	0.257719i	−0.182418	+	0.983221i	$0.558392\pi$
$840$	−14.7627	+	53.9699i	−0.509362	+	1.86214i
$841$	45.7105	−	14.8522i	1.57622	−	0.512146i
$842$	−4.38286	−	0.884127i	−0.151043	−	0.0304690i
$843$	−20.8945	−	41.0077i	−0.719643	−	1.41238i
$844$	18.1861	−	7.41799i	0.625990	−	0.255338i
$845$	−49.6950	+	26.3303i	−1.70956	+	0.905791i
$846$	8.88923	−	23.8962i	0.305618	−	0.821568i
$847$	−32.7050			−1.12376
$848$	11.0512	−	10.8148i	0.379501	−	0.371382i
$849$	54.3131	−	8.60235i	1.86402	−	0.295232i
$850$	−3.40789	+	10.1427i	−0.116890	+	0.347890i
$851$	−25.3355	−	34.8713i	−0.868489	−	1.19537i
$852$	−10.5472	+	42.9092i	−0.361343	+	1.47005i
$853$	8.45724	−	53.3969i	0.289570	−	1.82828i	−0.229221	−	0.973374i	$-0.573618\pi$
$853$	8.45724	−	53.3969i	0.289570	−	1.82828i	0.518791	−	0.854901i	$-0.326382\pi$
$854$	6.42679	−	4.26916i	0.219920	−	0.146088i
$855$	−12.3392	+	9.27004i	−0.421992	+	0.317029i
$856$	14.1148	−	20.7579i	0.482434	−	0.709491i
$857$	−27.3063	+	4.32489i	−0.932766	+	0.147736i	−0.604279	−	0.796773i	$-0.706539\pi$
$857$	−27.3063	+	4.32489i	−0.932766	+	0.147736i	−0.328487	+	0.944509i	$0.606539\pi$
$858$	15.8658	−	28.1516i	0.541648	−	0.961080i
$859$	−40.3542	−	13.1119i	−1.37687	−	0.447372i	−0.475230	−	0.879861i	$-0.657635\pi$
$859$	−40.3542	−	13.1119i	−1.37687	−	0.447372i	−0.901639	+	0.432490i	$0.857635\pi$
$860$	1.66164	−	24.4153i	0.0566613	−	0.832556i
$861$	44.0314	+	35.6398i	1.50058	+	1.21460i
$862$	8.69149	+	31.1396i	0.296033	+	1.06062i
$863$	2.69083	−	1.37105i	0.0915970	−	0.0466710i	−0.407592	−	0.913164i	$-0.633631\pi$
$863$	2.69083	−	1.37105i	0.0915970	−	0.0466710i	0.499189	+	0.866493i	$0.333631\pi$
$864$	12.5062	+	2.66383i	0.425470	+	0.0906254i
$865$	14.6448	+	42.7340i	0.497937	+	1.45300i
$866$	−21.6952	+	9.93059i	−0.737231	+	0.337455i
$867$	10.1522	−	31.2453i	0.344788	−	1.06115i
$868$	−28.6915	−	24.7744i	−0.973854	−	0.840897i
$869$	−2.02643	+	1.47229i	−0.0687420	+	0.0499440i
$870$	−20.6838	+	58.4465i	−0.701246	+	1.98152i
$871$	−23.1162	−	31.8167i	−0.783263	−	1.07807i
$872$	−9.61489	−	12.4020i	−0.325601	−	0.419984i
$873$	−4.10184	+	5.64570i	−0.138826	+	0.191078i
$874$	−1.52236	+	36.2487i	−0.0514945	+	1.22613i
$875$	−38.4512	+	21.9758i	−1.29989	+	0.742919i
$876$	8.32229	−	7.03046i	0.281184	−	0.237537i
$877$	14.1804	+	7.22525i	0.478837	+	0.243979i	0.676712	−	0.736248i	$-0.263404\pi$
$877$	14.1804	+	7.22525i	0.478837	+	0.243979i	−0.197876	+	0.980227i	$0.563404\pi$
$878$	0.646522	+	5.59188i	0.0218190	+	0.188717i
$879$	−13.0121	+	40.0471i	−0.438887	+	1.35076i
$880$	10.5303	+	10.4217i	0.354977	+	0.351317i
$881$	−27.5857	+	8.96315i	−0.929387	+	0.301976i	−0.734312	−	0.678812i	$-0.762495\pi$
$881$	−27.5857	+	8.96315i	−0.929387	+	0.301976i	−0.195075	+	0.980788i	$0.562495\pi$
$882$	−20.3530	+	13.5200i	−0.685320	+	0.455242i
$883$	−52.2101	+	16.9641i	−1.75701	+	0.570887i	−0.996883	−	0.0788887i	$-0.974863\pi$
$883$	−52.2101	+	16.9641i	−1.75701	+	0.570887i	−0.760126	+	0.649776i	$0.774863\pi$
$884$	−4.26545	−	18.1997i	−0.143463	−	0.612123i
$885$	−14.3533	−	13.9014i	−0.482481	−	0.467290i
$886$	−41.4027	−	8.35191i	−1.39095	−	0.280588i
$887$	1.95260	+	1.41865i	0.0655619	+	0.0476335i	0.620083	−	0.784536i	$-0.287099\pi$
$887$	1.95260	+	1.41865i	0.0655619	+	0.0476335i	−0.554522	+	0.832169i	$0.687099\pi$
$888$	−36.8321	+	1.14810i	−1.23600	+	0.0385277i
$889$	−37.1814	−	72.9725i	−1.24702	−	2.44742i
$890$	−2.77472	+	1.90783i	−0.0930089	+	0.0639507i
$891$	−2.85344	+	18.0159i	−0.0955940	+	0.603557i
$892$	5.44981	+	13.3608i	0.182473	+	0.447354i
$893$	−22.2656	+	22.2656i	−0.745089	+	0.745089i
$894$	−2.07214	−	17.9223i	−0.0693027	−	0.599412i
$895$	−10.4651	+	34.0520i	−0.349810	+	1.13823i
$896$	44.8071	−	0.911919i	1.49690	−	0.0304651i
$897$	15.9449	+	100.672i	0.532383	+	3.36134i
$898$	1.94977	−	5.24142i	0.0650648	−	0.174908i
$899$	−29.7010	−	29.7010i	−0.990583	−	0.990583i
$900$	−10.8335	−	16.6675i	−0.361117	−	0.555584i
$901$	5.84943			0.194873
$902$	13.9455	−	5.52361i	0.464335	−	0.183916i
$903$	34.2315	−	34.2315i	1.13915	−	1.13915i
$904$	50.6926	+	14.7416i	1.68601	+	0.490298i
$905$	18.1357	+	12.7382i	0.602850	+	0.423433i
$906$	5.80831	+	12.6893i	0.192968	+	0.421573i
$907$	17.6639	−	2.79769i	0.586521	−	0.0928959i	0.143881	−	0.989595i	$-0.454042\pi$
$907$	17.6639	−	2.79769i	0.586521	−	0.0928959i	0.442640	+	0.896699i	$0.354042\pi$
$908$	−2.82770	−	12.0652i	−0.0938406	−	0.400398i
$909$	−26.2158	−	13.3576i	−0.869524	−	0.443045i
$910$	36.9052	−	68.0034i	1.22339	−	2.25429i
$911$	−44.5912			−1.47737			−0.738685	−	0.674050i	$-0.764553\pi$
$911$	−44.5912			−1.47737			−0.738685	+	0.674050i	$0.764553\pi$
$912$	24.8949	+	18.5017i	0.824351	+	0.612652i
$913$	−0.521896	−	0.718328i	−0.0172722	−	0.0237732i
$914$	26.8992	+	10.0063i	0.889748	+	0.330980i
$915$	−0.967176	+	6.80967i	−0.0319739	+	0.225121i
$916$	−43.9989	−	10.8151i	−1.45377	−	0.357341i
$917$	31.8051	−	43.7759i	1.05030	−	1.44561i
$918$	2.67652	+	4.02924i	0.0883385	+	0.132985i
$919$	4.05637	−	25.6109i	0.133807	−	0.844826i	−0.825898	−	0.563819i	$-0.809332\pi$
$919$	4.05637	−	25.6109i	0.133807	−	0.844826i	0.959706	−	0.281007i	$-0.0906684\pi$
$920$	−46.4491	−	5.12659i	−1.53138	−	0.169019i
$921$	−38.9023	−	19.8217i	−1.28188	−	0.653148i
$922$	19.9603	−	13.2592i	0.657358	−	0.436667i
$923$	27.7396	−	54.4421i	0.913062	−	1.79198i
$924$	2.14153	+	29.2301i	0.0704511	+	0.961598i
$925$	−21.2738	−	19.9546i	−0.699479	−	0.656103i
$926$	1.77415	+	1.40642i	0.0583022	+	0.0462178i
$927$	9.37624	−	18.4019i	0.307956	−	0.604398i
$928$	49.5898	+	2.62001i	1.62786	+	0.0860061i
$929$	−4.66996	−	4.66996i	−0.153216	−	0.153216i	0.626336	−	0.779553i	$-0.284554\pi$
$929$	−4.66996	−	4.66996i	−0.153216	−	0.153216i	−0.779553	+	0.626336i	$0.784554\pi$
$930$	33.5026	−	4.41754i	1.09859	−	0.144857i
$931$	29.8054	−	4.72072i	0.976834	−	0.154715i
$932$	15.8936	+	6.68425i	0.520614	+	0.218950i
$933$	−13.3555	−	2.11530i	−0.437240	−	0.0692520i
$934$	−14.2044	+	25.2038i	−0.464784	+	0.824694i
$935$	0.0896341	+	5.60396i	0.00293135	+	0.183269i
$936$	31.4199	+	14.7948i	1.02699	+	0.483585i
$937$	11.1325	+	3.61718i	0.363684	+	0.118168i	0.485158	−	0.874426i	$-0.338762\pi$
$937$	11.1325	+	3.61718i	0.363684	+	0.118168i	−0.121474	+	0.992595i	$0.538762\pi$
$938$	33.4309	+	12.4361i	1.09156	+	0.406052i
$939$	−18.3398	−	13.3247i	−0.598498	−	0.434834i
$940$	−26.6656	−	30.5602i	−0.869735	−	0.996763i
$941$	21.4728	+	6.97694i	0.699994	+	0.227442i	0.637328	−	0.770593i	$-0.280040\pi$
$941$	21.4728	+	6.97694i	0.699994	+	0.227442i	0.0626659	+	0.998035i	$0.480040\pi$
$942$	16.2705	+	58.2936i	0.530123	+	1.89931i
$943$	−23.6468	+	40.9783i	−0.770045	+	1.33444i
$944$	−7.41974	+	14.1809i	−0.241492	+	0.461549i
$945$	−2.81543	+	19.8228i	−0.0915860	+	0.644837i
$946$	−3.44611	−	12.3466i	−0.112043	−	0.401424i
$947$	1.04784	+	6.61581i	0.0340503	+	0.214985i	0.998847	−	0.0480128i	$-0.0152888\pi$
$947$	1.04784	+	6.61581i	0.0340503	+	0.214985i	−0.964796	+	0.262998i	$0.915289\pi$
$948$	−4.35884	−	5.15977i	−0.141569	−	0.167582i
$949$	−13.4230	+	6.83935i	−0.435728	+	0.222015i
$950$	3.59829	+	24.2859i	0.116744	+	0.787938i
$951$	−2.53265	+	1.84008i	−0.0821267	+	0.0596686i
$952$	12.3559	+	11.6089i	0.400457	+	0.376246i
$953$	50.9146	+	8.06408i	1.64929	+	0.261221i	0.910739	−	0.412982i	$-0.135513\pi$
$953$	50.9146	+	8.06408i	1.64929	+	0.261221i	0.738546	+	0.674203i	$0.235513\pi$
$954$	−6.75102	+	8.51618i	−0.218572	+	0.275722i
$955$	−18.1818	+	6.23080i	−0.588348	+	0.201624i
$956$	16.8711	−	27.2000i	0.545651	−	0.879711i
$957$			32.4753i			1.04978i
$958$	17.2367	−	7.88980i	0.556892	−	0.254908i
$959$	−12.8107	−	39.4272i	−0.413678	−	1.27317i
$960$	−25.9533	+	30.3736i	−0.837638	+	0.980303i
$961$	2.50482	−	7.70903i	0.0808005	−	0.248678i
$962$	49.9506	+	10.0762i	1.61047	+	0.324871i
$963$	−8.00950	+	15.7195i	−0.258103	+	0.506555i
$964$	−7.27554	+	8.42590i	−0.234329	+	0.271380i
$965$	−15.6846	−	29.6027i	−0.504906	−	0.952944i
$966$	−62.5677	−	68.0535i	−2.01308	−	2.18958i
$967$	−32.8911	+	23.8968i	−1.05771	+	0.768470i	−0.973663	−	0.227992i	$-0.926784\pi$
$967$	−32.8911	+	23.8968i	−1.05771	+	0.768470i	−0.0840448	+	0.996462i	$0.526784\pi$
$968$	−21.1272	−	9.94827i	−0.679053	−	0.319749i
$969$	1.83556	+	11.5893i	0.0589666	+	0.372301i
$970$	4.78117	+	10.0188i	0.153514	+	0.321683i
$971$	12.9470	+	25.4100i	0.415490	+	0.815444i	0.999992	+	0.00405211i	$0.00128983\pi$
$971$	12.9470	+	25.4100i	0.415490	+	0.815444i	−0.584502	+	0.811392i	$0.698710\pi$
$972$	−35.4995	−	2.98705i	−1.13865	−	0.0958096i
$973$	−28.9204	−	39.8055i	−0.927144	−	1.27610i
$974$	−42.6082	+	4.92626i	−1.36525	+	0.157848i
$975$	23.4010	+	64.8824i	0.749431	+	2.07790i
$976$	5.45026	−	0.802931i	0.174458	−	0.0257012i
$977$	−0.251011	−	0.772532i	−0.00803055	−	0.0247155i	0.946961	−	0.321349i	$-0.104136\pi$
$977$	−0.251011	−	0.772532i	−0.00803055	−	0.0247155i	−0.954992	+	0.296633i	$0.904136\pi$
$978$	37.3932	−	34.3790i	1.19570	−	1.09932i
$979$	−1.03676	+	1.42697i	−0.0331349	+	0.0456062i
$980$	3.45973	+	38.7150i	0.110517	+	1.23671i
$981$	7.79875	+	7.79875i	0.248995	+	0.248995i
$982$	1.25581	−	29.9021i	0.0400746	−	0.954214i
$983$	−13.2573	+	13.2573i	−0.422843	+	0.422843i	−0.886181	−	0.463339i	$-0.846651\pi$
$983$	−13.2573	+	13.2573i	−0.422843	+	0.422843i	0.463339	+	0.886181i	$0.346651\pi$
$984$	17.6029	+	36.4166i	0.561161	+	1.16092i
$985$	−9.79926	+	13.9514i	−0.312231	+	0.444529i
$986$	12.7145	+	13.8293i	0.404913	+	0.440414i
$987$		−	80.2333i		−	2.55385i
$988$	−27.6788	−	32.7648i	−0.880581	−	1.04239i
$989$	32.7104	+	23.7655i	1.04013	+	0.755698i
$990$	−8.26225	−	6.33721i	−0.262591	−	0.201410i
$991$	−16.1283	−	8.21780i	−0.512334	−	0.261047i	0.178656	−	0.983912i	$-0.442825\pi$
$991$	−16.1283	−	8.21780i	−0.512334	−	0.261047i	−0.690990	+	0.722865i	$0.742825\pi$
$992$	−10.9986	−	24.7315i	−0.349206	−	0.785226i
$993$	16.6149	−	16.6149i	0.527258	−	0.527258i
$994$	6.36486	+	55.0508i	0.201881	+	1.74611i
$995$	−19.5458	+	0.312630i	−0.619643	+	0.00991105i
$996$	1.82903	−	1.54512i	0.0579551	−	0.0489590i
$997$	15.7453	−	48.4590i	0.498658	−	1.53471i	−0.312520	−	0.949911i	$-0.601173\pi$
$997$	15.7453	−	48.4590i	0.498658	−	1.53471i	0.811178	−	0.584800i	$-0.198827\pi$
$998$	16.3749	−	29.0550i	0.518339	−	0.919721i
$999$	−13.0239	+	2.06278i	−0.412057	+	0.0652634i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bv.c.103.4	yes	960
4.3	odd	2	inner	820.2.bv.c.103.40	yes	960
5.2	odd	4		820.2.bk.c.267.64	yes	960
20.7	even	4		820.2.bk.c.267.22	yes	960
41.2	even	20		820.2.bk.c.43.22	✓	960
164.43	odd	20		820.2.bk.c.43.64	yes	960
205.2	odd	20	inner	820.2.bv.c.207.40	yes	960
820.207	even	20	inner	820.2.bv.c.207.4	yes	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bk.c.43.22	✓	960	41.2	even	20
820.2.bk.c.43.64	yes	960	164.43	odd	20
820.2.bk.c.267.22	yes	960	20.7	even	4
820.2.bk.c.267.64	yes	960	5.2	odd	4
820.2.bv.c.103.4	yes	960	1.1	even	1	trivial
820.2.bv.c.103.40	yes	960	4.3	odd	2	inner
820.2.bv.c.207.4	yes	960	820.207	even	20	inner
820.2.bv.c.207.40	yes	960	205.2	odd	20	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:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bv (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41297 - 0.0593411i) q^{2} +2.23336 q^{3} +(1.99296 + 0.167694i) q^{4} +(-0.983161 + 2.00833i) q^{5} +(-3.15566 - 0.132530i) q^{6} +(-3.76737 + 1.22409i) q^{7} +(-2.80603 - 0.355211i) q^{8} +1.98789 q^{9} +(1.50835 - 2.77937i) q^{10} +(0.259122 - 1.63603i) q^{11} +(4.45099 + 0.374521i) q^{12} +(-5.87435 - 1.90869i) q^{13} +(5.39581 - 1.50604i) q^{14} +(-2.19575 + 4.48532i) q^{15} +(3.94376 + 0.668415i) q^{16} +(0.889430 + 1.22420i) q^{17} +(-2.80883 - 0.117964i) q^{18} +(3.09361 + 1.57627i) q^{19} +(-2.29618 + 3.83765i) q^{20} +(-8.41388 + 2.73383i) q^{21} +(-0.463216 + 2.29629i) q^{22} +(-3.35446 - 6.58351i) q^{23} +(-6.26688 - 0.793314i) q^{24} +(-3.06679 - 3.94902i) q^{25} +(8.18700 + 3.04551i) q^{26} -2.26040 q^{27} +(-7.71347 + 1.80780i) q^{28} +(-8.67047 + 1.37327i) q^{29} +(3.36869 - 6.20732i) q^{30} +(2.81243 + 3.87098i) q^{31} +(-5.53274 - 1.17848i) q^{32} +(0.578713 - 3.65385i) q^{33} +(-1.18409 - 1.78253i) q^{34} +(1.24554 - 8.76960i) q^{35} +(3.96178 + 0.333358i) q^{36} +(5.76174 - 0.912570i) q^{37} +(-4.27763 - 2.41080i) q^{38} +(-13.1195 - 4.26279i) q^{39} +(3.47216 - 5.28622i) q^{40} +(-3.48858 - 5.36934i) q^{41} +(12.0508 - 3.36353i) q^{42} +(-4.87565 + 2.48427i) q^{43} +(0.790773 - 3.21709i) q^{44} +(-1.95442 + 3.99234i) q^{45} +(4.34908 + 9.50134i) q^{46} +(-2.80251 + 8.62524i) q^{47} +(8.80782 + 1.49281i) q^{48} +(7.03152 - 5.10870i) q^{49} +(4.09894 + 5.76183i) q^{50} +(1.98642 + 2.73407i) q^{51} +(-11.3872 - 4.78904i) q^{52} +(2.27216 - 3.12736i) q^{53} +(3.19388 + 0.134135i) q^{54} +(3.03094 + 2.12889i) q^{55} +(11.0062 - 2.09663i) q^{56} +(6.90913 + 3.52038i) q^{57} +(12.3326 - 1.42587i) q^{58} +(-1.23643 + 3.80535i) q^{59} +(-5.12820 + 8.57084i) q^{60} +(1.30986 - 0.425600i) q^{61} +(-3.74417 - 5.63646i) q^{62} +(-7.48911 + 2.43336i) q^{63} +(7.74765 + 1.99347i) q^{64} +(9.60871 - 9.92109i) q^{65} +(-1.03453 + 5.12843i) q^{66} +(5.15113 + 3.74251i) q^{67} +(1.56731 + 2.58892i) q^{68} +(-7.49172 - 14.7033i) q^{69} +(-2.28031 + 12.3172i) q^{70} +(-1.54751 + 9.77059i) q^{71} +(-5.57809 - 0.706121i) q^{72} +(1.72464 - 1.72464i) q^{73} +(-8.19531 + 0.947524i) q^{74} +(-6.84924 - 8.81959i) q^{75} +(5.90109 + 3.66022i) q^{76} +(1.02645 + 6.48073i) q^{77} +(18.2845 + 6.80172i) q^{78} +(-1.06927 - 1.06927i) q^{79} +(-5.21975 + 7.26321i) q^{80} -11.0120 q^{81} +(4.61063 + 7.79372i) q^{82} +(0.379034 - 0.379034i) q^{83} +(-17.2269 + 4.03746i) q^{84} +(-3.33304 + 0.582690i) q^{85} +(7.03655 - 3.22086i) q^{86} +(-19.3643 + 3.06700i) q^{87} +(-1.30824 + 4.49872i) q^{88} +(-0.948782 - 0.483429i) q^{89} +(2.99844 - 5.52508i) q^{90} +24.4672 q^{91} +(-5.58129 - 13.6832i) q^{92} +(6.28117 + 8.64528i) q^{93} +(4.47169 - 12.0209i) q^{94} +(-6.20718 + 4.66326i) q^{95} +(-12.3566 - 2.63196i) q^{96} +(-2.06341 + 2.84004i) q^{97} +(-10.2385 + 6.80117i) q^{98} +(0.515107 - 3.25226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 960 q - 10 q^{2} - 20 q^{5} - 16 q^{6} + 2 q^{8} + 960 q^{9} - 60 q^{10} - 40 q^{12} - 20 q^{13} - 8 q^{14} - 28 q^{16} - 20 q^{17} - 48 q^{18} - 34 q^{20} - 40 q^{21} - 10 q^{22} - 48 q^{24} - 4 q^{25}+ \cdots - 38 q^{98}+O(q^{100}) \) 960 * q - 10 * q^2 - 20 * q^5 - 16 * q^6 + 2 * q^8 + 960 * q^9 - 60 * q^10 - 40 * q^12 - 20 * q^13 - 8 * q^14 - 28 * q^16 - 20 * q^17 - 48 * q^18 - 34 * q^20 - 40 * q^21 - 10 * q^22 - 48 * q^24 - 4 * q^25 - 20 * q^26 - 10 * q^28 - 10 * q^30 - 56 * q^33 - 20 * q^34 - 100 * q^36 + 88 * q^37 - 16 * q^40 - 24 * q^41 - 104 * q^42 - 100 * q^45 - 20 * q^46 - 40 * q^48 + 224 * q^49 - 12 * q^50 - 38 * q^52 - 20 * q^53 - 52 * q^54 + 96 * q^56 - 72 * q^57 - 38 * q^58 - 14 * q^60 - 40 * q^61 - 10 * q^62 - 120 * q^64 - 60 * q^65 - 12 * q^66 - 116 * q^68 - 104 * q^69 - 96 * q^70 - 24 * q^72 - 72 * q^73 - 28 * q^74 - 40 * q^76 - 76 * q^77 - 44 * q^78 - 90 * q^80 + 592 * q^81 - 130 * q^82 - 92 * q^84 - 64 * q^85 - 12 * q^86 - 104 * q^88 + 136 * q^89 - 364 * q^90 - 220 * q^92 - 32 * q^94 - 44 * q^96 + 80 * q^97 - 38 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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