LMFDB - Embedded newform 171.2.x.a.110.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [171,2,Mod(14,171)] 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("171.14"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(171, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([15, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.x (of order $18$, degree $6$, 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:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			110.1
Character	$\chi$	$=$	171.110
Dual form			171.2.x.a.14.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.02450 + 1.69876i) q^{2} +(1.43995 - 0.962572i) q^{3} +(0.865531 - 4.90867i) q^{4} +(-0.259455 + 0.712848i) q^{5} +(-1.28000 + 4.39486i) q^{6} +(-1.63029 - 2.82374i) q^{7} +(3.94358 + 6.83047i) q^{8} +(1.14691 - 2.77211i) q^{9} +(-0.685689 - 1.88391i) q^{10} -6.35073i q^{11} +(-3.47862 - 7.90137i) q^{12} +(0.295627 + 0.812229i) q^{13} +(8.09738 + 2.94721i) q^{14} +(0.312564 + 1.27621i) q^{15} +(-10.2195 - 3.71960i) q^{16} +(-0.818892 + 2.24989i) q^{17} +(2.38722 + 7.56047i) q^{18} +(4.31029 + 0.649145i) q^{19} +(3.27457 + 1.89057i) q^{20} +(-5.06559 - 2.49678i) q^{21} +(10.7884 + 12.8571i) q^{22} +(0.245272 + 0.0432481i) q^{23} +(12.2534 + 6.03957i) q^{24} +(3.38939 + 2.84403i) q^{25} +(-1.97828 - 1.14216i) q^{26} +(-1.01686 - 5.09568i) q^{27} +(-15.2719 + 5.55851i) q^{28} +(-0.803768 + 4.55839i) q^{29} +(-2.80076 - 2.05272i) q^{30} -1.49225i q^{31} +(12.1851 - 4.43503i) q^{32} +(-6.11304 - 9.14474i) q^{33} +(-2.16417 - 5.94600i) q^{34} +(2.43589 - 0.429513i) q^{35} +(-12.6147 - 8.02916i) q^{36} -4.34331i q^{37} +(-9.82894 + 6.00795i) q^{38} +(1.20752 + 0.885007i) q^{39} +(-5.89227 + 1.03897i) q^{40} +(1.48330 - 1.24464i) q^{41} +(14.4967 - 3.55048i) q^{42} +(0.639011 + 3.62401i) q^{43} +(-31.1736 - 5.49675i) q^{44} +(1.67852 + 1.53681i) q^{45} +(-0.570023 + 0.329103i) q^{46} +(-7.25185 - 1.27870i) q^{47} +(-18.2960 + 4.48098i) q^{48} +(-1.81568 + 3.14486i) q^{49} -11.6931 q^{50} +(0.986514 + 4.02797i) q^{51} +(4.24284 - 0.748127i) q^{52} +(7.32359 + 6.14522i) q^{53} +(10.7150 + 8.58883i) q^{54} +(4.52711 + 1.64773i) q^{55} +(12.8583 - 22.2713i) q^{56} +(6.83145 - 3.21423i) q^{57} +(-6.11638 - 10.5939i) q^{58} +(-0.645657 - 3.66171i) q^{59} +(6.53502 - 0.429676i) q^{60} +(-5.85826 + 2.13223i) q^{61} +(2.53497 + 3.02106i) q^{62} +(-9.69752 + 1.28075i) q^{63} +(-6.25941 + 10.8416i) q^{64} -0.655698 q^{65} +(27.9106 + 8.12897i) q^{66} +(-1.22085 + 1.45495i) q^{67} +(10.3352 + 5.96701i) q^{68} +(0.394809 - 0.173817i) q^{69} +(-4.20182 + 5.00753i) q^{70} +(-0.638887 + 0.536090i) q^{71} +(23.4578 - 3.09807i) q^{72} +(1.84550 + 10.4663i) q^{73} +(7.37823 + 8.79303i) q^{74} +(7.61813 + 0.832739i) q^{75} +(6.91713 - 20.5959i) q^{76} +(-17.9328 + 10.3535i) q^{77} +(-3.94804 + 0.259582i) q^{78} +(-4.52777 + 12.4400i) q^{79} +(5.30302 - 6.31989i) q^{80} +(-6.36918 - 6.35873i) q^{81} +(-0.888607 + 5.03954i) q^{82} +(6.20911 - 3.58483i) q^{83} +(-16.6403 + 22.7043i) q^{84} +(-1.39136 - 1.16749i) q^{85} +(-7.45000 - 6.25129i) q^{86} +(3.23039 + 7.33754i) q^{87} +(43.3785 - 25.0446i) q^{88} +(2.93290 - 16.6333i) q^{89} +(-6.00884 - 0.259880i) q^{90} +(1.81157 - 2.15894i) q^{91} +(0.424581 - 1.16653i) q^{92} +(-1.43639 - 2.14876i) q^{93} +(16.8536 - 9.73042i) q^{94} +(-1.58107 + 2.90416i) q^{95} +(13.2770 - 18.1153i) q^{96} +(7.16659 + 8.54081i) q^{97} +(-1.66650 - 9.45118i) q^{98} +(-17.6049 - 7.28373i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23}+ \cdots + 39 q^{99}+O(q^{100}) $ 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−2.02450	+	1.69876i	−1.43154	+	1.20120i	−0.486743	+	0.873545i	$0.661815\pi$
$2$	−2.02450	+	1.69876i	−1.43154	+	1.20120i	−0.944796	+	0.327659i	$0.893740\pi$
$3$	1.43995	−	0.962572i	0.831356	−	0.555741i
$3$	1.43995	−	0.962572i	0.831356	−	0.555741i
$4$	0.865531	−	4.90867i	0.432765	−	2.45433i
$5$	−0.259455	+	0.712848i	−0.116032	+	0.318795i	−0.984091	−	0.177666i	$-0.943145\pi$
$5$	−0.259455	+	0.712848i	−0.116032	+	0.318795i	0.868059	+	0.496461i	$0.165368\pi$
$6$	−1.28000	+	4.39486i	−0.522560	+	1.79419i
$7$	−1.63029	−	2.82374i	−0.616191	−	1.06727i	−0.990174	−	0.139839i	$-0.955342\pi$
$7$	−1.63029	−	2.82374i	−0.616191	−	1.06727i	0.373983	−	0.927436i	$-0.377992\pi$
$8$	3.94358	+	6.83047i	1.39426	+	2.41494i
$9$	1.14691	−	2.77211i	0.382304	−	0.924037i
$10$	−0.685689	−	1.88391i	−0.216834	−	0.595746i
$11$		−	6.35073i		−	1.91482i	−0.288734	−	0.957409i	$-0.593234\pi$
$11$		−	6.35073i		−	1.91482i	0.288734	−	0.957409i	$-0.406766\pi$
$12$	−3.47862	−	7.90137i	−1.00419	−	2.28093i
$13$	0.295627	+	0.812229i	0.0819923	+	0.225272i	0.973914	−	0.226918i	$-0.0728650\pi$
$13$	0.295627	+	0.812229i	0.0819923	+	0.225272i	−0.891922	+	0.452190i	$0.850643\pi$
$14$	8.09738	+	2.94721i	2.16412	+	0.787674i
$15$	0.312564	+	1.27621i	0.0807038	+	0.329516i
$16$	−10.2195	−	3.71960i	−2.55488	−	0.929900i
$17$	−0.818892	+	2.24989i	−0.198610	+	0.545678i	−0.998517	−	0.0544473i	$-0.982660\pi$
$17$	−0.818892	+	2.24989i	−0.198610	+	0.545678i	0.799906	+	0.600125i	$0.204883\pi$
$18$	2.38722	+	7.56047i	0.562673	+	1.78202i
$19$	4.31029	+	0.649145i	0.988849	+	0.148924i
$19$	4.31029	+	0.649145i	0.988849	+	0.148924i
$20$	3.27457	+	1.89057i	0.732216	+	0.422745i
$21$	−5.06559	−	2.49678i	−1.10540	−	0.544842i
$22$	10.7884	+	12.8571i	2.30009	+	2.74114i
$23$	0.245272	+	0.0432481i	0.0511428	+	0.00901786i	0.199161	−	0.979967i	$-0.436178\pi$
$23$	0.245272	+	0.0432481i	0.0511428	+	0.00901786i	−0.148018	+	0.988985i	$0.547289\pi$
$24$	12.2534	+	6.03957i	2.50121	+	1.23282i
$25$	3.38939	+	2.84403i	0.677877	+	0.568807i
$26$	−1.97828	−	1.14216i	−0.387973	−	0.223996i
$27$	−1.01686	−	5.09568i	−0.195694	−	0.980665i
$28$	−15.2719	+	5.55851i	−2.88611	+	1.05046i
$29$	−0.803768	+	4.55839i	−0.149256	+	0.846473i	0.814595	+	0.580030i	$0.196959\pi$
$29$	−0.803768	+	4.55839i	−0.149256	+	0.846473i	−0.963851	+	0.266442i	$0.914152\pi$
$30$	−2.80076	−	2.05272i	−0.511347	−	0.374773i
$31$		−	1.49225i		−	0.268015i	−0.990980	−	0.134008i	$-0.957215\pi$
$31$		−	1.49225i		−	0.268015i	0.990980	−	0.134008i	$-0.0427847\pi$
$32$	12.1851	−	4.43503i	2.15405	−	0.784009i
$33$	−6.11304	−	9.14474i	−1.06414	−	1.59189i
$34$	−2.16417	−	5.94600i	−0.371152	−	1.01973i
$35$	2.43589	−	0.429513i	0.411740	−	0.0726009i
$36$	−12.6147	−	8.02916i	−2.10245	−	1.33819i
$37$		−	4.34331i		−	0.714035i	−0.934098	−	0.357017i	$-0.883794\pi$
$37$		−	4.34331i		−	0.714035i	0.934098	−	0.357017i	$-0.116206\pi$
$38$	−9.82894	+	6.00795i	−1.59446	+	0.974618i
$39$	1.20752	+	0.885007i	0.193358	+	0.141715i
$40$	−5.89227	+	1.03897i	−0.931650	+	0.164275i
$41$	1.48330	−	1.24464i	0.231653	−	0.194380i	−0.519571	−	0.854427i	$-0.673908\pi$
$41$	1.48330	−	1.24464i	0.231653	−	0.194380i	0.751224	+	0.660048i	$0.229464\pi$
$42$	14.4967	−	3.55048i	2.23689	−	0.547851i
$43$	0.639011	+	3.62401i	0.0974482	+	0.552656i	0.993970	+	0.109656i	$0.0349749\pi$
$43$	0.639011	+	3.62401i	0.0974482	+	0.552656i	−0.896521	+	0.443000i	$0.853914\pi$
$44$	−31.1736	−	5.49675i	−4.69960	−	0.828667i
$45$	1.67852	+	1.53681i	0.250219	+	0.229095i
$46$	−0.570023	+	0.329103i	−0.0840452	+	0.0485235i
$47$	−7.25185	−	1.27870i	−1.05779	−	0.186517i	−0.382415	−	0.923991i	$-0.624907\pi$
$47$	−7.25185	−	1.27870i	−1.05779	−	0.186517i	−0.675376	+	0.737474i	$0.736019\pi$
$48$	−18.2960	+	4.48098i	−2.64080	+	0.646773i
$49$	−1.81568	+	3.14486i	−0.259383	+	0.449265i
$50$	−11.6931			−1.65366
$51$	0.986514	+	4.02797i	0.138140	+	0.564028i
$52$	4.24284	−	0.748127i	0.588376	−	0.103747i
$53$	7.32359	+	6.14522i	1.00597	+	0.844111i	0.987801	−	0.155724i	$-0.0497710\pi$
$53$	7.32359	+	6.14522i	1.00597	+	0.844111i	0.0181718	+	0.999835i	$0.494215\pi$
$54$	10.7150	+	8.58883i	1.45812	+	1.16879i
$55$	4.52711	+	1.64773i	0.610435	+	0.222180i
$56$	12.8583	−	22.2713i	1.71827	−	2.97613i
$57$	6.83145	−	3.21423i	0.904848	−	0.425735i
$58$	−6.11638	−	10.5939i	−0.803121	−	1.39105i
$59$	−0.645657	−	3.66171i	−0.0840574	−	0.476713i	−0.997556	−	0.0698715i	$-0.977741\pi$
$59$	−0.645657	−	3.66171i	−0.0840574	−	0.476713i	0.913499	−	0.406842i	$-0.133370\pi$
$60$	6.53502	−	0.429676i	0.843668	−	0.0554709i
$61$	−5.85826	+	2.13223i	−0.750073	+	0.273004i	−0.688636	−	0.725107i	$-0.741790\pi$
$61$	−5.85826	+	2.13223i	−0.750073	+	0.273004i	−0.0614365	+	0.998111i	$0.519568\pi$
$62$	2.53497	+	3.02106i	0.321941	+	0.383675i
$63$	−9.69752	+	1.28075i	−1.22177	+	0.161360i
$64$	−6.25941	+	10.8416i	−0.782426	+	1.35520i
$65$	−0.655698			−0.0813293
$66$	27.9106	+	8.12897i	3.43555	+	1.00061i
$67$	−1.22085	+	1.45495i	−0.149151	+	0.177751i	−0.835447	−	0.549571i	$-0.814791\pi$
$67$	−1.22085	+	1.45495i	−0.149151	+	0.177751i	0.686296	+	0.727322i	$0.259235\pi$
$68$	10.3352	+	5.96701i	1.25332	+	0.723607i
$69$	0.394809	−	0.173817i	0.0475295	−	0.0209251i
$70$	−4.20182	+	5.00753i	−0.502214	+	0.598515i
$71$	−0.638887	+	0.536090i	−0.0758220	+	0.0636222i	−0.679911	−	0.733295i	$-0.737982\pi$
$71$	−0.638887	+	0.536090i	−0.0758220	+	0.0636222i	0.604089	+	0.796917i	$0.293537\pi$
$72$	23.4578	−	3.09807i	2.76452	−	0.365111i
$73$	1.84550	+	10.4663i	0.215999	+	1.22499i	0.879165	+	0.476518i	$0.158101\pi$
$73$	1.84550	+	10.4663i	0.215999	+	1.22499i	−0.663166	+	0.748472i	$0.730788\pi$
$74$	7.37823	+	8.79303i	0.857702	+	1.02217i
$75$	7.61813	+	0.832739i	0.879666	+	0.0961564i
$76$	6.91713	−	20.5959i	0.793449	−	2.36252i
$77$	−17.9328	+	10.3535i	−2.04364	+	1.17989i
$78$	−3.94804	+	0.259582i	−0.447027	+	0.0293919i
$79$	−4.52777	+	12.4400i	−0.509414	+	1.39960i	0.372429	+	0.928061i	$0.378525\pi$
$79$	−4.52777	+	12.4400i	−0.509414	+	1.39960i	−0.881843	+	0.471543i	$0.843697\pi$
$80$	5.30302	−	6.31989i	0.592895	−	0.706585i
$81$	−6.36918	−	6.35873i	−0.707687	−	0.706526i
$82$	−0.888607	+	5.03954i	−0.0981302	+	0.556524i
$83$	6.20911	−	3.58483i	0.681538	−	0.393486i	−0.118896	−	0.992907i	$-0.537936\pi$
$83$	6.20911	−	3.58483i	0.681538	−	0.393486i	0.800434	+	0.599420i	$0.204602\pi$
$84$	−16.6403	+	22.7043i	−1.81560	+	2.47724i
$85$	−1.39136	−	1.16749i	−0.150914	−	0.126632i
$86$	−7.45000	−	6.25129i	−0.803354	−	0.674094i
$87$	3.23039	+	7.33754i	0.346335	+	0.786667i
$88$	43.3785	−	25.0446i	4.62417	−	2.66976i
$89$	2.93290	−	16.6333i	0.310886	−	1.76312i	−0.283527	−	0.958964i	$-0.591504\pi$
$89$	2.93290	−	16.6333i	0.310886	−	1.76312i	0.594413	−	0.804160i	$-0.297384\pi$
$90$	−6.00884	−	0.259880i	−0.633388	−	0.0273938i
$91$	1.81157	−	2.15894i	0.189904	−	0.226319i
$92$	0.424581	−	1.16653i	0.0442657	−	0.121619i
$93$	−1.43639	−	2.14876i	−0.148947	−	0.222816i
$94$	16.8536	−	9.73042i	1.73831	−	1.00362i
$95$	−1.58107	+	2.90416i	−0.162214	+	0.297960i
$96$	13.2770	−	18.1153i	1.35507	−	1.84888i
$97$	7.16659	+	8.54081i	0.727657	+	0.867188i	0.995351	−	0.0963164i	$-0.0307061\pi$
$97$	7.16659	+	8.54081i	0.727657	+	0.867188i	−0.267694	+	0.963504i	$0.586262\pi$
$98$	−1.66650	−	9.45118i	−0.168342	−	0.954713i
$99$	−17.6049	−	7.28373i	−1.76936	−	0.732043i
$100$	16.8940	−	14.1758i	1.68940	−	1.41758i
$101$	3.47382	−	4.13993i	0.345658	−	0.411939i	−0.565006	−	0.825087i	$-0.691126\pi$
$101$	3.47382	−	4.13993i	0.345658	−	0.411939i	0.910664	+	0.413148i	$0.135571\pi$
$102$	−8.83974	−	6.47878i	−0.875265	−	0.641495i
$103$	10.1146	+	5.83968i	0.996623	+	0.575401i	0.907247	−	0.420597i	$-0.138179\pi$
$103$	10.1146	+	5.83968i	0.996623	+	0.575401i	0.0893757	+	0.995998i	$0.471513\pi$
$104$	−4.38208	+	5.22236i	−0.429698	+	0.512095i
$105$	3.09412	−	2.96319i	0.301955	−	0.289178i
$106$	−25.2659			−2.45404
$107$	−4.78301	+	8.28441i	−0.462391	+	0.800884i	−0.999080	−	0.0428960i	$-0.986342\pi$
$107$	−4.78301	+	8.28441i	−0.462391	+	0.800884i	0.536689	+	0.843780i	$0.319675\pi$
$108$	−25.8931	+	0.580945i	−2.49157	+	0.0559015i
$109$	−3.37261	−	4.01931i	−0.323037	−	0.384980i	0.579947	−	0.814654i	$-0.303073\pi$
$109$	−3.37261	−	4.01931i	−0.323037	−	0.384980i	−0.902984	+	0.429673i	$0.858629\pi$
$110$	−11.9642	+	4.35463i	−1.14075	+	0.415197i
$111$	−4.18074	−	6.25414i	−0.396818	−	0.593617i
$112$	6.15757	+	34.9213i	0.581835	+	3.29975i
$113$	4.97218	+	8.61206i	0.467743	+	0.810155i	0.999321	−	0.0368549i	$-0.0117339\pi$
$113$	4.97218	+	8.61206i	0.467743	+	0.810155i	−0.531578	+	0.847010i	$0.678401\pi$
$114$	−8.37009	+	18.1122i	−0.783931	+	1.69636i
$115$	−0.0944666	+	0.163621i	−0.00880905	+	0.0152577i
$116$	21.6800	+	7.89086i	2.01293	+	0.732648i
$117$	2.59065	+	0.112044i	0.239505	+	0.0103585i
$118$	7.52749	+	6.31631i	0.692962	+	0.581464i
$119$	7.68813	−	1.35563i	0.704770	−	0.124270i
$120$	−7.48450	+	7.16779i	−0.683238	+	0.654327i
$121$	−29.3318			−2.66653
$122$	8.23791	−	14.2685i	0.745825	−	1.29181i
$123$	0.937826	−	3.22000i	0.0845610	−	0.290337i
$124$	−7.32494	−	1.29158i	−0.657799	−	0.115988i
$125$	−6.19158	+	3.57471i	−0.553792	+	0.319732i
$126$	17.4570	−	19.0666i	1.55519	−	1.69859i
$127$	11.0562	+	1.94951i	0.981082	+	0.172991i	0.641114	−	0.767446i	$-0.278473\pi$
$127$	11.0562	+	1.94951i	0.981082	+	0.172991i	0.339968	+	0.940437i	$0.389584\pi$
$128$	−1.24166	−	7.04181i	−0.109748	−	0.622414i
$129$	4.40851	+	4.60330i	0.388148	+	0.405298i
$130$	1.32746	−	1.11387i	0.116426	−	0.0976931i
$131$	13.6658	−	2.40966i	1.19399	−	0.210533i	0.458891	−	0.888493i	$-0.348247\pi$
$131$	13.6658	−	2.40966i	1.19399	−	0.210533i	0.735099	+	0.677960i	$0.237136\pi$
$132$	−50.1795	+	22.0918i	−4.36757	+	1.92285i
$133$	−5.19400	−	13.2294i	−0.450377	−	1.14714i
$134$		−	5.01949i		−	0.433618i
$135$	3.89628	+	0.597238i	0.335338	+	0.0514021i
$136$	−18.5972	+	3.27918i	−1.59469	+	0.281187i
$137$	0.340121	+	0.934475i	0.0290585	+	0.0798376i	0.953374	−	0.301793i	$-0.0975850\pi$
$137$	0.340121	+	0.934475i	0.0290585	+	0.0798376i	−0.924315	+	0.381630i	$0.875363\pi$
$138$	−0.504019	+	1.02258i	−0.0429050	+	0.0870477i
$139$	9.56750	−	3.48228i	0.811504	−	0.295363i	0.0972593	−	0.995259i	$-0.468992\pi$
$139$	9.56750	−	3.48228i	0.811504	−	0.295363i	0.714245	+	0.699896i	$0.246770\pi$
$140$		−	12.3287i		−	1.04197i
$141$	−11.6731	+	5.13916i	−0.983055	+	0.432796i
$142$	0.382741	−	2.17063i	0.0321189	−	0.182155i
$143$	5.15825	−	1.87745i	0.431355	−	0.157000i
$144$	−22.0320	+	24.0636i	−1.83600	+	2.00530i
$145$	−3.04090	−	1.75566i	−0.252533	−	0.145800i
$146$	−21.5160	−	18.0540i	−1.78067	−	1.49416i
$147$	0.412655	+	6.27616i	0.0340352	+	0.517649i
$148$	−21.3198	−	3.75926i	−1.75248	−	0.309010i
$149$	13.5782	+	16.1819i	1.11237	+	1.32567i	0.940207	+	0.340604i	$0.110632\pi$
$149$	13.5782	+	16.1819i	1.11237	+	1.32567i	0.172164	+	0.985068i	$0.444924\pi$
$150$	−16.8376	+	11.2555i	−1.37478	+	0.919007i
$151$	6.03093	+	3.48196i	0.490790	+	0.283358i	0.724902	−	0.688852i	$-0.241885\pi$
$151$	6.03093	+	3.48196i	0.490790	+	0.283358i	−0.234112	+	0.972210i	$0.575218\pi$
$152$	12.5640	+	32.0013i	1.01907	+	2.59565i
$153$	5.29774	+	4.85048i	0.428297	+	0.392138i
$154$	18.7169	−	51.4243i	1.50825	−	4.14389i
$155$	1.06374	+	0.387172i	0.0854421	+	0.0310984i
$156$	5.38935	−	5.16130i	0.431493	−	0.413235i
$157$	−14.8903	−	5.41962i	−1.18837	−	0.432533i	−0.329221	−	0.944253i	$-0.606786\pi$
$157$	−14.8903	−	5.41962i	−1.18837	−	0.432533i	−0.859152	+	0.511720i	$0.829008\pi$
$158$	−11.9660	−	32.8763i	−0.951964	−	2.61550i
$159$	16.4608	+	1.79933i	1.30543	+	0.142696i
$160$			9.83684i			0.777670i
$161$	−0.277743	−	0.763093i	−0.0218892	−	0.0601402i
$162$	23.6964	+	2.05356i	1.86176	+	0.161343i
$163$	0.484740	+	0.839594i	0.0379678	+	0.0657621i	0.884385	−	0.466758i	$-0.154578\pi$
$163$	0.484740	+	0.839594i	0.0379678	+	0.0657621i	−0.846417	+	0.532521i	$0.821245\pi$
$164$	−4.82567	−	8.35830i	−0.376821	−	0.652673i
$165$	8.10487	−	1.98501i	0.630963	−	0.154533i
$166$	−6.48059	+	17.8053i	−0.502991	+	1.38196i
$167$	1.36206	−	7.72464i	0.105400	−	0.597751i	−0.885660	−	0.464334i	$-0.846294\pi$
$167$	1.36206	−	7.72464i	0.105400	−	0.597751i	0.991060	−	0.133417i	$-0.0425950\pi$
$168$	−2.92235	−	44.4466i	−0.225464	−	3.42913i
$169$	9.38626	−	7.87600i	0.722020	−	0.605847i
$170$	4.80010			0.368151
$171$	6.74303	−	11.2041i	0.515652	−	0.856798i
$172$	18.3421			1.39857
$173$	2.32775	−	1.95321i	0.176975	−	0.148500i	−0.549997	−	0.835167i	$-0.685371\pi$
$173$	2.32775	−	1.95321i	0.176975	−	0.148500i	0.726973	+	0.686667i	$0.240927\pi$
$174$	−19.0047	−	9.36721i	−1.44074	−	0.710126i
$175$	2.50514	−	14.2074i	0.189371	−	1.07398i
$176$	−23.6222	+	64.9014i	−1.78059	+	4.89213i
$177$	−4.45437	−	4.65118i	−0.334811	−	0.349604i
$178$	22.3183	+	38.6564i	1.67283	+	2.89742i
$179$	−1.02579	−	1.77672i	−0.0766712	−	0.132798i	0.825141	−	0.564927i	$-0.191096\pi$
$179$	−1.02579	−	1.77672i	−0.0766712	−	0.132798i	−0.901812	+	0.432129i	$0.857763\pi$
$180$	8.99652	−	6.90914i	0.670561	−	0.514977i
$181$	−0.313953	−	0.862578i	−0.0233359	−	0.0641149i	0.927478	−	0.373879i	$-0.121972\pi$
$181$	−0.313953	−	0.862578i	−0.0233359	−	0.0641149i	−0.950814	+	0.309764i	$0.899750\pi$
$182$			7.44821i			0.552098i
$183$	−6.38317	+	8.70930i	−0.471858	+	0.643810i
$184$	0.671845	+	1.84588i	0.0495291	+	0.136080i
$185$	3.09612	+	1.12689i	0.227631	+	0.0828509i
$186$	6.55821	+	1.91008i	0.480871	+	0.140054i
$187$	14.2884	+	5.20056i	1.04487	+	0.380303i
$188$	−12.5534	+	34.4902i	−0.915550	+	2.51545i
$189$	−12.7311	+	11.1788i	−0.926054	+	0.813137i
$190$	−1.73258	−	8.56533i	−0.125695	−	0.621395i
$191$	13.9129	+	8.03263i	1.00670	+	0.581221i	0.910225	−	0.414114i	$-0.135908\pi$
$191$	13.9129	+	8.03263i	1.00670	+	0.581221i	0.0964794	+	0.995335i	$0.469242\pi$
$192$	1.42259	+	21.6365i	0.102667	+	1.56148i
$193$	−11.8242	−	14.0915i	−0.851122	−	1.01433i	−0.999677	−	0.0254233i	$-0.991907\pi$
$193$	−11.8242	−	14.0915i	−0.851122	−	1.01433i	0.148555	−	0.988904i	$-0.452538\pi$
$194$	−29.0175	−	5.11658i	−2.08334	−	0.367349i
$195$	−0.944172	+	0.631156i	−0.0676136	+	0.0451980i
$196$	13.8655	+	11.6346i	0.990394	+	0.831040i
$197$	−5.05018	−	2.91572i	−0.359810	−	0.207736i	0.309187	−	0.951001i	$-0.399943\pi$
$197$	−5.05018	−	2.91572i	−0.359810	−	0.207736i	−0.668997	+	0.743265i	$0.733276\pi$
$198$	48.0145	−	15.1606i	3.41224	−	1.07742i
$199$	−17.1618	+	6.24637i	−1.21656	+	0.442793i	−0.868976	−	0.494854i	$-0.835222\pi$
$199$	−17.1618	+	6.24637i	−1.21656	+	0.442793i	−0.347588	+	0.937647i	$0.612999\pi$
$200$	−6.05979	+	34.3668i	−0.428492	+	2.43010i
$201$	−0.357468	+	3.27022i	−0.0252138	+	0.230663i
$202$			14.2825i			1.00491i
$203$	14.1821	−	5.16186i	0.995389	−	0.362292i
$204$	20.6258	−	1.35614i	1.44410	−	0.0949488i
$205$	0.502386	+	1.38030i	0.0350882	+	0.0964040i
$206$	−30.3973	+	5.35986i	−2.11788	+	0.373439i
$207$	0.401194	−	0.630320i	0.0278849	−	0.0438103i
$208$		−	9.40020i		−	0.651787i
$209$	4.12255	−	27.3735i	0.285163	−	1.89347i
$210$	−1.23030	+	11.2552i	−0.0848989	+	0.776679i
$211$	−14.1345	+	2.49230i	−0.973062	+	0.171577i	−0.637508	−	0.770444i	$-0.720035\pi$
$211$	−14.1345	+	2.49230i	−0.973062	+	0.171577i	−0.335554	+	0.942021i	$0.608924\pi$
$212$	36.5036	−	30.6302i	2.50708	−	2.10369i
$213$	−0.403941	+	1.38692i	−0.0276776	+	0.0950300i
$214$	−4.39001	−	24.8970i	−0.300095	−	1.70192i
$215$	−2.74916	−	0.484751i	−0.187491	−	0.0330598i
$216$	30.7959	−	27.0408i	2.09539	−	1.83990i
$217$	−4.21372	+	2.43279i	−0.286046	+	0.165149i
$218$	13.6557	+	2.40787i	0.924880	+	0.163081i
$219$	12.7320	+	13.2946i	0.860349	+	0.898363i
$220$	12.0065	−	20.7959i	0.809480	−	1.40206i
$221$	−2.06951			−0.139210
$222$	19.0882	+	5.55945i	1.28112	+	0.373126i
$223$	−1.01457	+	0.178897i	−0.0679408	+	0.0119798i	−0.207515	−	0.978232i	$-0.566538\pi$
$223$	−1.01457	+	0.178897i	−0.0679408	+	0.0119798i	0.139574	+	0.990212i	$0.455427\pi$
$224$	−32.3887	−	27.1773i	−2.16406	−	1.81586i
$225$	11.7713	−	6.13390i	0.784753	−	0.408926i
$226$	−24.6960	−	8.98861i	−1.64275	−	0.597913i
$227$	−4.99016	+	8.64322i	−0.331209	+	0.573671i	−0.982749	−	0.184943i	$-0.940790\pi$
$227$	−4.99016	+	8.64322i	−0.331209	+	0.573671i	0.651540	+	0.758614i	$0.274123\pi$
$228$	−9.86474	−	36.3153i	−0.653308	−	2.40504i
$229$	2.44218	+	4.22998i	0.161384	+	0.279525i	0.935365	−	0.353683i	$-0.115071\pi$
$229$	2.44218	+	4.22998i	0.161384	+	0.279525i	−0.773981	+	0.633208i	$0.781738\pi$
$230$	−0.0867047	−	0.491727i	−0.00571714	−	0.0324235i
$231$	−15.8564	+	32.1702i	−1.04327	+	2.11664i
$232$	−34.3057	+	12.4863i	−2.25228	+	0.819763i
$233$	−7.69052	−	9.16520i	−0.503823	−	0.600432i	0.452854	−	0.891585i	$-0.350406\pi$
$233$	−7.69052	−	9.16520i	−0.503823	−	0.600432i	−0.956677	+	0.291152i	$0.905961\pi$
$234$	−5.43511	+	4.17405i	−0.355304	+	0.272866i
$235$	2.79305	−	4.83770i	0.182198	−	0.315577i
$236$	−18.5329			−1.20639
$237$	5.45458	+	22.2712i	0.354313	+	1.44667i
$238$	−13.2618	+	15.8048i	−0.859632	+	1.02447i
$239$	−2.92222	−	1.68714i	−0.189023	−	0.109132i	0.402502	−	0.915419i	$-0.368141\pi$
$239$	−2.92222	−	1.68714i	−0.189023	−	0.109132i	−0.591525	+	0.806287i	$0.701474\pi$
$240$	1.55273	−	14.2049i	0.100229	−	0.916920i
$241$	−9.95753	+	11.8669i	−0.641421	+	0.764416i	−0.984594	−	0.174857i	$-0.944054\pi$
$241$	−9.95753	+	11.8669i	−0.641421	+	0.764416i	0.343173	+	0.939272i	$0.388498\pi$
$242$	59.3823	−	49.8277i	3.81724	−	3.20305i
$243$	−15.2920	−	3.02546i	−0.980985	−	0.194083i
$244$	5.39591	+	30.6017i	0.345438	+	1.95908i
$245$	−1.77072	−	2.11026i	−0.113127	−	0.134819i
$246$	3.57137	+	8.11203i	0.227702	+	0.517204i
$247$	0.746985	+	3.69285i	0.0475295	+	0.234970i
$248$	10.1927	−	5.88479i	0.647240	−	0.373684i
$249$	5.49015	−	11.1387i	0.347924	−	0.705886i
$250$	6.46230	−	17.7550i	0.408711	−	1.12293i
$251$	−3.39453	+	4.04544i	−0.214261	+	0.255346i	−0.862461	−	0.506124i	$-0.831078\pi$
$251$	−3.39453	+	4.04544i	−0.214261	+	0.255346i	0.648200	+	0.761470i	$0.275522\pi$
$252$	−2.10671	+	48.7105i	−0.132710	+	3.06847i
$253$	0.274657	−	1.55766i	0.0172676	−	0.0979292i
$254$	−25.6951	+	14.8351i	−1.61226	+	0.930836i
$255$	−3.12728	−	0.341844i	−0.195838	−	0.0214071i
$256$	−4.70385	−	3.94700i	−0.293991	−	0.246688i
$257$	−12.6067	−	10.5783i	−0.786385	−	0.659855i	0.158463	−	0.987365i	$-0.449346\pi$
$257$	−12.6067	−	10.5783i	−0.786385	−	0.659855i	−0.944848	+	0.327510i	$0.893791\pi$
$258$	−16.7449	−	1.83039i	−1.04249	−	0.113955i
$259$	−12.2644	+	7.08084i	−0.762071	+	0.439982i
$260$	−0.567527	+	3.21860i	−0.0351965	+	0.199609i
$261$	11.7145	+	7.45621i	0.725110	+	0.461528i
$262$	−23.5731	+	28.0933i	−1.45635	+	1.73561i
$263$	1.66589	−	4.57700i	0.102723	−	0.282230i	−0.877675	−	0.479257i	$-0.840906\pi$
$263$	1.66589	−	4.57700i	0.102723	−	0.282230i	0.980398	+	0.197027i	$0.0631286\pi$
$264$	38.3557	−	77.8179i	2.36063	−	4.78936i
$265$	−6.28075	+	3.62620i	−0.385824	+	0.222755i
$266$	32.9889	+	17.9597i	2.02268	+	1.10118i
$267$	−11.7875	−	26.7742i	−0.721383	−	1.63856i
$268$	6.08520	+	7.25206i	0.371713	+	0.442990i
$269$	1.18246	+	6.70608i	0.0720960	+	0.408877i	0.999402	+	0.0345732i	$0.0110072\pi$
$269$	1.18246	+	6.70608i	0.0720960	+	0.408877i	−0.927306	+	0.374304i	$0.877882\pi$
$270$	−8.90259	+	5.40973i	−0.541794	+	0.329226i
$271$	11.0962	−	9.31080i	0.674045	−	0.565591i	−0.240215	−	0.970720i	$-0.577218\pi$
$271$	11.0962	−	9.31080i	0.674045	−	0.565591i	0.914260	+	0.405129i	$0.132773\pi$
$272$	16.7374	−	19.9468i	1.01485	−	1.20945i
$273$	0.530431	−	4.85254i	0.0321031	−	0.293689i
$274$	−2.27602	−	1.31406i	−0.137500	−	0.0793855i
$275$	18.0617	−	21.5251i	1.08916	−	1.29801i
$276$	−0.511490	−	2.08843i	−0.0307881	−	0.125709i
$277$	−8.60584			−0.517075			−0.258537	−	0.966001i	$-0.583240\pi$
$277$	−8.60584			−0.517075			−0.258537	+	0.966001i	$0.583240\pi$
$278$	−13.4539	+	23.3028i	−0.806909	+	1.39761i
$279$	−4.13667	−	1.71148i	−0.247656	−	0.102463i
$280$	12.5399	+	14.9444i	0.749401	+	0.893101i
$281$	−18.1948	+	6.62238i	−1.08541	+	0.395058i	−0.821920	−	0.569603i	$-0.807097\pi$
$281$	−18.1948	+	6.62238i	−1.08541	+	0.395058i	−0.263494	+	0.964661i	$0.584875\pi$
$282$	14.9021	−	30.2341i	0.887406	−	1.80041i
$283$	1.28701	+	7.29900i	0.0765049	+	0.433881i	0.998868	+	0.0475578i	$0.0151438\pi$
$283$	1.28701	+	7.29900i	0.0765049	+	0.433881i	−0.922364	+	0.386323i	$0.873745\pi$
$284$	2.07851	+	3.60009i	0.123337	+	0.213626i
$285$	0.518797	+	5.70374i	0.0307309	+	0.337860i
$286$	−7.25356	+	12.5635i	−0.428912	+	0.742897i
$287$	−5.93274	−	2.15934i	−0.350199	−	0.127462i
$288$	1.68090	−	38.8651i	0.0990480	−	2.29015i
$289$	8.63135	+	7.24256i	0.507726	+	0.426033i
$290$	9.13876	−	1.61141i	0.536646	−	0.0946253i
$291$	18.5407	+	5.39998i	1.08687	+	0.316553i
$292$	52.9730			3.10001
$293$	−9.18804	+	15.9142i	−0.536771	+	0.929715i	0.462304	+	0.886721i	$0.347023\pi$
$293$	−9.18804	+	15.9142i	−0.536771	+	0.929715i	−0.999075	+	0.0429933i	$0.986311\pi$
$294$	−11.4971	−	12.0051i	−0.670525	−	0.700152i
$295$	2.77776	+	0.489794i	0.161727	+	0.0285169i
$296$	29.6668	−	17.1282i	1.72435	−	0.995554i
$297$	−32.3613	+	6.45779i	−1.87780	+	0.374719i
$298$	−54.9783	−	9.69415i	−3.18481	−	0.561567i
$299$	0.0373818	+	0.212003i	0.00216184	+	0.0122604i
$300$	10.6814	−	36.6741i	0.616689	−	2.11738i
$301$	9.19150	−	7.71258i	0.529789	−	0.444546i
$302$	−18.1246	+	3.19586i	−1.04296	+	0.183901i
$303$	1.01714	−	9.30510i	0.0584332	−	0.534564i
$304$	−41.6345	−	22.6665i	−2.38790	−	1.30001i
$305$		−	4.72927i		−	0.270797i
$306$	−18.9651	−	0.820232i	−1.08416	−	0.0468895i
$307$	−3.93086	+	0.693117i	−0.224346	+	0.0395583i	−0.284691	−	0.958619i	$-0.591891\pi$
$307$	−3.93086	+	0.693117i	−0.224346	+	0.0395583i	0.0603450	+	0.998178i	$0.480780\pi$
$308$	35.3006	+	96.9877i	2.01144	+	5.52638i
$309$	20.1857	−	1.32720i	1.14832	−	0.0755017i
$310$	−2.81127	+	1.02322i	−0.159669	+	0.0581148i
$311$		−	24.4621i		−	1.38712i	−0.720400	−	0.693558i	$-0.756042\pi$
$311$		−	24.4621i		−	1.38712i	0.720400	−	0.693558i	$-0.243958\pi$
$312$	−1.28308	+	11.7380i	−0.0726402	+	0.664534i
$313$	5.30576	−	30.0904i	0.299899	−	1.70081i	−0.346695	−	0.937978i	$-0.612696\pi$
$313$	5.30576	−	30.0904i	0.299899	−	1.70081i	0.646594	−	0.762835i	$-0.276193\pi$
$314$	39.3520	−	14.3230i	2.22076	−	0.808292i
$315$	1.60309	−	7.24516i	0.0903240	−	0.408218i
$316$	57.1447	+	32.9925i	3.21464	+	1.85597i
$317$	24.5343	+	20.5867i	1.37798	+	1.15627i	0.969951	+	0.243299i	$0.0782298\pi$
$317$	24.5343	+	20.5867i	1.37798	+	1.15627i	0.408033	+	0.912967i	$0.366215\pi$
$318$	−36.3816	+	24.3202i	−2.04018	+	1.36381i
$319$	28.9491	+	5.10452i	1.62084	+	0.285798i
$320$	−6.10439	−	7.27493i	−0.341246	−	0.406681i
$321$	1.08705	+	16.5331i	0.0606731	+	0.922789i
$322$	1.85860	+	1.07306i	0.103576	+	0.0597996i
$323$	−4.99017	+	9.16609i	−0.277660	+	0.510015i
$324$	−36.7256	+	25.7605i	−2.04031	+	1.43114i
$325$	−1.30801	+	3.59373i	−0.0725554	+	0.199344i
$326$	−2.40763	−	0.876304i	−0.133346	−	0.0485340i
$327$	−8.72526	−	2.54124i	−0.482508	−	0.140531i
$328$	14.3510	+	5.22332i	0.792399	+	0.288410i
$329$	8.21190	+	22.5620i	0.452736	+	1.24388i
$330$	−13.0363	+	17.7869i	−0.717623	+	0.979136i
$331$			19.2433i			1.05771i	0.848714	+	0.528853i	$0.177378\pi$
$331$			19.2433i			1.05771i	−0.848714	+	0.528853i	$0.822622\pi$
$332$	−12.2226	−	33.5812i	−0.670801	−	1.84301i
$333$	−12.0401	−	4.98139i	−0.659794	−	0.272978i
$334$	10.3648	+	17.9524i	0.567137	+	0.982310i
$335$	−0.720404	−	1.24778i	−0.0393599	−	0.0681733i
$336$	42.4808	+	44.3578i	2.31752	+	2.41992i
$337$	7.91681	−	21.7513i	0.431256	−	1.18487i	−0.513786	−	0.857918i	$-0.671758\pi$
$337$	7.91681	−	21.7513i	0.431256	−	1.18487i	0.945042	−	0.326948i	$-0.106020\pi$
$338$	−5.62306	+	31.8900i	−0.305854	+	1.73459i
$339$	15.4494	+	7.61486i	0.839097	+	0.413583i
$340$	−6.93509	+	5.81923i	−0.376108	+	0.315592i
$341$	−9.47686			−0.513201
$342$	5.38177	+	34.1375i	0.291013	+	1.84594i
$343$	−10.9837			−0.593064
$344$	−22.2337	+	18.6563i	−1.19876	+	1.00588i
$345$	0.0214697	+	0.326537i	0.00115589	+	0.0175802i
$346$	−1.39449	+	7.90857i	−0.0749685	+	0.425167i
$347$	2.77917	−	7.63571i	0.149194	−	0.409906i	−0.842473	−	0.538739i	$-0.818901\pi$
$347$	2.77917	−	7.63571i	0.149194	−	0.409906i	0.991666	+	0.128833i	$0.0411231\pi$
$348$	38.8136	−	9.50607i	2.08063	−	0.509579i
$349$	7.87884	+	13.6465i	0.421744	+	0.730483i	0.996110	−	0.0881160i	$-0.0280846\pi$
$349$	7.87884	+	13.6465i	0.421744	+	0.730483i	−0.574366	+	0.818599i	$0.694751\pi$
$350$	19.0632	+	33.0184i	1.01897	+	1.76491i
$351$	3.83825	−	2.33234i	0.204871	−	0.124491i
$352$	−28.1657	−	77.3845i	−1.50124	−	4.12461i
$353$		−	17.1465i		−	0.912616i	−0.889822	−	0.456308i	$-0.849172\pi$
$353$		−	17.1465i		−	0.912616i	0.889822	−	0.456308i	$-0.150828\pi$
$354$	16.9191	+	1.84943i	0.899241	+	0.0982961i
$355$	−0.216388	−	0.594521i	−0.0114847	−	0.0315539i
$356$	−79.1087	−	28.7932i	−4.19275	−	1.52604i
$357$	9.76564	−	9.35241i	0.516852	−	0.494982i
$358$	5.09494	+	1.85441i	0.269276	+	0.0980084i
$359$	−1.18280	+	3.24973i	−0.0624260	+	0.171514i	−0.966984	−	0.254836i	$-0.917979\pi$
$359$	−1.18280	+	3.24973i	−0.0624260	+	0.171514i	0.904558	+	0.426350i	$0.140201\pi$
$360$	−3.87779	+	17.5256i	−0.204377	+	0.923682i
$361$	18.1572	+	5.59601i	0.955643	+	0.294527i
$362$	2.10091	+	1.21296i	0.110421	+	0.0637518i
$363$	−42.2364	+	28.2340i	−2.21683	+	1.48190i
$364$	−9.02957	−	10.7610i	−0.473278	−	0.564031i
$365$	−7.93972	−	1.39999i	−0.415584	−	0.0732787i
$366$	−1.87225	−	28.4755i	−0.0978642	−	1.48844i
$367$	−24.4511	−	20.5169i	−1.27634	−	1.07097i	−0.993738	−	0.111733i	$-0.964360\pi$
$367$	−24.4511	−	20.5169i	−1.27634	−	1.07097i	−0.282597	−	0.959239i	$-0.591196\pi$
$368$	−2.34570	−	1.35429i	−0.122278	−	0.0705972i
$369$	−1.74905	−	5.53936i	−0.0910521	−	0.288368i
$370$	−8.18242	+	2.97816i	−0.425384	+	0.154827i
$371$	5.41296	−	30.6984i	0.281027	−	1.59378i
$372$	−11.7908	+	5.19096i	−0.611324	+	0.269139i
$373$		−	10.7974i		−	0.559066i	−0.960136	−	0.279533i	$-0.909820\pi$
$373$		−	10.7974i		−	0.559066i	0.960136	−	0.279533i	$-0.0901796\pi$
$374$	−37.7615	+	13.7441i	−1.95260	+	0.710688i
$375$	−5.47465	+	11.1072i	−0.282710	+	0.573576i
$376$	−19.8641	−	54.5762i	−1.02441	−	2.81455i
$377$	−3.94008	+	0.694742i	−0.202924	+	0.0357810i
$378$	6.78415	−	44.2586i	0.348939	−	2.27642i
$379$		−	32.4777i		−	1.66827i	−0.551561	−	0.834135i	$-0.685967\pi$
$379$		−	32.4777i		−	1.66827i	0.551561	−	0.834135i	$-0.314033\pi$
$380$	12.8871	+	10.2746i	0.661093	+	0.527075i
$381$	17.7970	−	7.83521i	0.911766	−	0.401410i
$382$	−41.8123	+	7.37263i	−2.13930	+	0.377217i
$383$	−21.1197	+	17.7215i	−1.07917	+	0.905527i	−0.995851	−	0.0909961i	$-0.970995\pi$
$383$	−21.1197	+	17.7215i	−1.07917	+	0.905527i	−0.0833141	+	0.996523i	$0.526550\pi$
$384$	−8.56618	−	8.94467i	−0.437141	−	0.456456i
$385$	−2.72772	−	15.4697i	−0.139018	−	0.788407i
$386$	47.8761	+	8.44185i	2.43683	+	0.429679i
$387$	10.7790	+	2.38501i	0.547929	+	0.121237i
$388$	48.1269	−	27.7861i	2.44327	−	1.41062i
$389$	25.1845	+	4.44070i	1.27690	+	0.225152i	0.770664	−	0.637241i	$-0.219924\pi$
$389$	25.1845	+	4.44070i	1.27690	+	0.225152i	0.506238	+	0.862394i	$0.331036\pi$
$390$	0.839297	−	2.88170i	0.0424994	−	0.145920i
$391$	−0.298155	+	0.516419i	−0.0150783	+	0.0261165i
$392$	−28.6411			−1.44660
$393$	17.3587	−	16.6241i	0.875628	−	0.838576i
$394$	15.1772	−	2.67615i	0.764616	−	0.134822i
$395$	−7.69304	−	6.45523i	−0.387079	−	0.324798i
$396$	−50.9910	+	80.1125i	−2.56240	+	4.02580i
$397$	−25.5350	−	9.29398i	−1.28156	−	0.466451i	−0.390615	−	0.920554i	$-0.627738\pi$
$397$	−25.5350	−	9.29398i	−1.28156	−	0.466451i	−0.890949	+	0.454103i	$0.849960\pi$
$398$	24.1329	−	41.7995i	1.20967	−	2.09522i
$399$	−20.2134	−	14.0501i	−1.01194	−	0.703387i
$400$	−24.0592	−	41.6718i	−1.20296	−	2.08359i
$401$	4.53233	+	25.7041i	0.226334	+	1.28360i	0.860119	+	0.510094i	$0.170389\pi$
$401$	4.53233	+	25.7041i	0.226334	+	1.28360i	−0.633785	+	0.773510i	$0.718499\pi$
$402$	−4.83162	−	7.22781i	−0.240979	−	0.360491i
$403$	1.21205	−	0.441149i	0.0603763	−	0.0219752i
$404$	−17.3149	−	20.6351i	−0.861447	−	1.02663i
$405$	6.18533	−	2.89045i	0.307352	−	0.143628i
$406$	−19.9429	+	34.5422i	−0.989752	+	1.71430i
$407$	−27.5832			−1.36725
$408$	−23.6225	+	22.6229i	−1.16949	+	1.12000i
$409$	0.00239955	−	0.00285967i	0.000118650	−	0.000141402i	−0.765985	−	0.642858i	$-0.777748\pi$
$409$	0.00239955	−	0.00285967i	0.000118650	−	0.000141402i	0.766104	+	0.642717i	$0.222193\pi$
$410$	−3.36187	−	1.94098i	−0.166031	−	0.0958581i
$411$	1.38926	+	1.01821i	0.0685270	+	0.0502244i
$412$	37.4196	−	44.5949i	1.84353	−	2.19703i
$413$	−9.28711	+	7.79281i	−0.456989	+	0.383459i
$414$	0.258543	+	1.95762i	0.0127067	+	0.0962116i
$415$	0.944452	+	5.35625i	0.0463613	+	0.262928i
$416$	7.20451	+	8.58601i	0.353230	+	0.420964i
$417$	10.4248	−	14.2237i	0.510503	−	0.696538i
$418$	38.1549	+	62.4210i	1.86622	+	3.05311i
$419$	0.544792	−	0.314536i	0.0266148	−	0.0153661i	−0.486634	−	0.873606i	$-0.661775\pi$
$419$	0.544792	−	0.314536i	0.0266148	−	0.0153661i	0.513248	+	0.858240i	$0.328442\pi$
$420$	−11.8673	−	17.7527i	−0.579064	−	0.866245i
$421$	−2.69819	+	7.41322i	−0.131502	+	0.361298i	−0.987916	−	0.154992i	$-0.950465\pi$
$421$	−2.69819	+	7.41322i	−0.131502	+	0.361298i	0.856414	+	0.516290i	$0.172687\pi$
$422$	24.3816	−	29.0569i	1.18688	−	1.41447i
$423$	−11.8619	+	18.6364i	−0.576746	+	0.906131i
$424$	−13.0936	+	74.2577i	−0.635883	+	3.60627i
$425$	−9.17429	+	5.29678i	−0.445019	+	0.256932i
$426$	−1.53826	−	3.49402i	−0.0745289	−	0.169286i
$427$	15.5715	+	13.0661i	0.753559	+	0.632311i
$428$	36.5256	+	30.6486i	1.76553	+	1.48146i
$429$	5.62045	−	7.66862i	0.271358	−	0.370245i
$430$	6.38916	−	3.68878i	0.308113	−	0.177889i
$431$	0.183471	−	1.04051i	0.00883747	−	0.0501198i	−0.980070	−	0.198652i	$-0.936344\pi$
$431$	0.183471	−	1.04051i	0.00883747	−	0.0501198i	0.988908	+	0.148532i	$0.0474548\pi$
$432$	−8.56211	+	55.8577i	−0.411945	+	2.68746i
$433$	9.40407	−	11.2073i	0.451931	−	0.538590i	−0.491185	−	0.871055i	$-0.663436\pi$
$433$	9.40407	−	11.2073i	0.451931	−	0.538590i	0.943115	+	0.332465i	$0.107880\pi$
$434$	4.39796	−	12.0833i	0.211109	−	0.580017i
$435$	−6.06870	+	0.399015i	−0.290972	+	0.0191313i
$436$	−22.6486	+	13.0762i	−1.08467	+	0.626234i
$437$	1.02912	+	0.345629i	0.0492295	+	0.0165337i
$438$	−48.3602	−	5.28626i	−2.31074	−	0.252587i
$439$	−17.5017	−	20.8577i	−0.835312	−	0.995485i	−0.999958	−	0.00913290i	$-0.997093\pi$
$439$	−17.5017	−	20.8577i	−0.835312	−	0.995485i	0.164647	−	0.986353i	$-0.447352\pi$
$440$	6.59820	+	37.4202i	0.314557	+	1.78394i
$441$	6.63546	+	8.64015i	0.315974	+	0.411436i
$442$	4.18973	−	3.51560i	0.199285	−	0.167220i
$443$	−17.8818	+	21.3107i	−0.849590	+	1.01250i	0.150126	+	0.988667i	$0.452032\pi$
$443$	−17.8818	+	21.3107i	−0.849590	+	1.01250i	−0.999716	+	0.0238348i	$0.992412\pi$
$444$	−34.3181	+	15.1087i	−1.62866	+	0.717028i
$445$	11.0960	+	6.40630i	0.526003	+	0.303688i
$446$	1.75010	−	2.08569i	0.0828698	−	0.0987604i
$447$	35.1282	+	10.2311i	1.66151	+	0.483915i
$448$	40.8186			1.92850
$449$	−5.56243	+	9.63441i	−0.262507	+	0.454676i	−0.966908	−	0.255127i	$-0.917883\pi$
$449$	−5.56243	+	9.63441i	−0.262507	+	0.454676i	0.704400	+	0.709803i	$0.251216\pi$
$450$	−13.4110	+	32.4147i	−0.632201	+	1.52804i
$451$	−7.90436	−	9.42005i	−0.372202	−	0.443573i
$452$	46.5773	−	16.9528i	2.19081	−	0.797391i
$453$	12.0359	−	0.791354i	0.565495	−	0.0371811i
$454$	−4.58015	−	25.9753i	−0.214957	−	1.21908i
$455$	1.06898	+	1.85152i	0.0501144	+	0.0868007i
$456$	48.8950	+	33.9865i	2.28972	+	1.59156i
$457$	−0.723233	+	1.25268i	−0.0338314	+	0.0585978i	−0.882445	−	0.470415i	$-0.844104\pi$
$457$	−0.723233	+	1.25268i	−0.0338314	+	0.0585978i	0.848614	+	0.529013i	$0.177438\pi$
$458$	−12.1299	−	4.41493i	−0.566794	−	0.206296i
$459$	12.2974	+	1.88500i	0.573994	+	0.0879843i
$460$	0.721397	+	0.605324i	0.0336353	+	0.0282234i
$461$	−19.2844	+	3.40036i	−0.898163	+	0.158370i	−0.603624	−	0.797269i	$-0.706277\pi$
$461$	−19.2844	+	3.40036i	−0.898163	+	0.158370i	−0.294539	+	0.955639i	$0.595166\pi$
$462$	−22.5482	−	92.0648i	−1.04904	−	4.28324i
$463$	−0.421291			−0.0195791			−0.00978954	−	0.999952i	$-0.503116\pi$
$463$	−0.421291			−0.0195791			−0.00978954	+	0.999952i	$0.503116\pi$
$464$	25.1695	−	43.5949i	1.16847	−	2.02384i
$465$	1.90442	−	0.466423i	0.0883154	−	0.0216298i
$466$	31.1389	+	5.49064i	1.44248	+	0.254349i
$467$	−11.4110	+	6.58813i	−0.528037	+	0.304862i	−0.740217	−	0.672368i	$-0.765277\pi$
$467$	−11.4110	+	6.58813i	−0.528037	+	0.304862i	0.212180	+	0.977231i	$0.431944\pi$
$468$	2.79227	−	12.6196i	0.129073	−	0.583343i
$469$	6.09876	+	1.07538i	0.281614	+	0.0496562i
$470$	2.56356	+	14.5387i	0.118248	+	0.670618i
$471$	−26.6580	+	6.52898i	−1.22834	+	0.300839i
$472$	22.4650	−	18.8504i	1.03403	−	0.867658i
$473$	23.0151	−	4.05819i	1.05824	−	0.186596i
$474$	−48.8762	−	35.8221i	−2.24496	−	1.64536i
$475$	12.7631	+	14.4588i	0.585609	+	0.663416i
$476$		−	38.9118i		−	1.78352i
$477$	25.4347	−	13.2538i	1.16458	−	0.606848i
$478$	8.78209	−	1.54852i	0.401683	−	0.0708276i
$479$	−5.50056	−	15.1127i	−0.251327	−	0.690516i	−0.999631	−	0.0271598i	$-0.991354\pi$
$479$	−5.50056	−	15.1127i	−0.251327	−	0.690516i	0.748304	−	0.663356i	$-0.230869\pi$
$480$	9.46866	+	14.1646i	0.432183	+	0.646521i
$481$	3.52776	−	1.28400i	0.160852	−	0.0585453i
$482$		−	40.9401i		−	1.86477i
$483$	−1.13447	−	0.831468i	−0.0516201	−	0.0378331i
$484$	−25.3876	+	143.980i	−1.15398	+	6.54455i
$485$	−7.94771	+	2.89273i	−0.360887	+	0.131352i
$486$	36.0983	−	19.8524i	1.63745	−	0.900525i
$487$	3.71599	+	2.14543i	0.168388	+	0.0972187i	0.581825	−	0.813314i	$-0.302339\pi$
$487$	3.71599	+	2.14543i	0.168388	+	0.0972187i	−0.413438	+	0.910532i	$0.635672\pi$
$488$	−37.6666	−	31.6061i	−1.70509	−	1.43074i
$489$	1.50617	+	0.742377i	0.0681114	+	0.0335714i
$490$	7.16963	+	1.26420i	0.323891	+	0.0571107i
$491$	−6.10276	−	7.27298i	−0.275414	−	0.328225i	0.610552	−	0.791976i	$-0.290948\pi$
$491$	−6.10276	−	7.27298i	−0.275414	−	0.328225i	−0.885966	+	0.463751i	$0.846503\pi$
$492$	−14.9942	−	7.39048i	−0.675990	−	0.333189i
$493$	−9.59767	−	5.54122i	−0.432257	−	0.249564i
$494$	−7.78553	−	6.20724i	−0.350288	−	0.279277i
$495$	9.75989	−	10.6598i	0.438675	−	0.479124i
$496$	−5.55056	+	15.2500i	−0.249227	+	0.684747i
$497$	2.55535	+	0.930072i	0.114623	+	0.0417194i
$498$	7.80712	+	31.8767i	0.349846	+	1.42843i
$499$	−1.43798	−	0.523383i	−0.0643730	−	0.0234299i	0.309633	−	0.950856i	$-0.399794\pi$
$499$	−1.43798	−	0.523383i	−0.0643730	−	0.0234299i	−0.374006	+	0.927426i	$0.622016\pi$
$500$	12.1881	+	33.4864i	0.545067	+	1.49756i
$501$	−5.47422	−	12.4342i	−0.244570	−	0.555518i
$502$		−	13.9565i		−	0.622909i
$503$	−13.9371	−	38.2918i	−0.621424	−	1.70735i	−0.703475	−	0.710720i	$-0.748369\pi$
$503$	−13.9371	−	38.2918i	−0.621424	−	1.70735i	0.0820506	−	0.996628i	$-0.473853\pi$
$504$	−46.9911	−	61.1879i	−2.09315	−	2.72553i
$505$	2.04984	+	3.55043i	0.0912168	+	0.157992i
$506$	2.09004	+	3.62006i	0.0929138	+	0.160931i
$507$	5.93452	−	20.3760i	0.263561	−	0.904930i
$508$	19.1390	−	52.5840i	0.849156	−	2.33304i
$509$	−3.11231	+	17.6508i	−0.137951	+	0.782357i	0.834809	+	0.550540i	$0.185578\pi$
$509$	−3.11231	+	17.6508i	−0.137951	+	0.782357i	−0.972759	+	0.231817i	$0.925533\pi$
$510$	6.91190	−	4.62044i	0.306064	−	0.204596i
$511$	26.5455	−	22.2743i	1.17430	−	0.985358i
$512$	30.5289			1.34920
$513$	−1.07511	−	22.6240i	−0.0474674	−	0.998873i
$514$	43.4923			1.91836
$515$	−6.78710	+	5.69505i	−0.299075	+	0.250954i
$516$	26.4118	−	17.6556i	1.16271	−	0.777245i
$517$	−8.12066	+	46.0546i	−0.357146	+	2.02548i
$518$	12.8006	−	35.1694i	0.562427	−	1.54525i
$519$	1.47173	−	5.05315i	0.0646020	−	0.221809i
$520$	−2.58579	−	4.47873i	−0.113395	−	0.196405i
$521$	16.4560	+	28.5027i	0.720952	+	1.24873i	0.960619	+	0.277870i	$0.0896285\pi$
$521$	16.4560	+	28.5027i	0.720952	+	1.24873i	−0.239667	+	0.970855i	$0.577038\pi$
$522$	−36.3824	+	4.80503i	−1.59241	+	0.210310i
$523$	7.51002	+	20.6336i	0.328390	+	0.902245i	0.988520	+	0.151093i	$0.0482792\pi$
$523$	7.51002	+	20.6336i	0.328390	+	0.902245i	−0.660129	+	0.751152i	$0.729499\pi$
$524$		−	69.1667i		−	3.02156i
$525$	−10.0683	−	22.8693i	−0.439417	−	0.998096i
$526$	4.40262	+	12.0961i	0.191963	+	0.527415i
$527$	3.35739	+	1.22199i	0.146250	+	0.0532307i
$528$	28.4575	+	116.193i	1.23845	+	5.05664i
$529$	−21.5546	−	7.84525i	−0.937158	−	0.341098i
$530$	6.55537	−	18.0107i	0.284747	−	0.782336i
$531$	−10.8912	−	2.40982i	−0.472636	−	0.104577i
$532$	−69.4345	+	14.0451i	−3.01037	+	0.608933i
$533$	1.44943	+	0.836831i	0.0627820	+	0.0362472i
$534$	69.3468	+	34.1803i	3.00093	+	1.47913i
$535$	−4.66455	−	5.55899i	−0.201666	−	0.240336i
$536$	−14.7525	−	2.60127i	−0.637213	−	0.112358i
$537$	−3.18731	−	1.57099i	−0.137543	−	0.0677934i
$538$	−13.7859	−	11.5678i	−0.594353	−	0.498721i
$539$	19.9721	+	11.5309i	0.860261	+	0.496672i
$540$	6.30399	−	18.6086i	0.271281	−	0.800787i
$541$	13.1805	−	4.79731i	0.566675	−	0.206253i	−0.0427650	−	0.999085i	$-0.513617\pi$
$541$	13.1805	−	4.79731i	0.566675	−	0.206253i	0.609440	+	0.792832i	$0.291394\pi$
$542$	−6.64744	+	37.6995i	−0.285532	+	1.61933i
$543$	−1.28237	−	0.939867i	−0.0550317	−	0.0403336i
$544$			31.0470i			1.33113i
$545$	3.74020	−	1.36132i	0.160213	−	0.0583126i
$546$	7.16943	+	10.7250i	0.306823	+	0.458989i
$547$	12.9341	+	35.5361i	0.553021	+	1.51941i	0.829564	+	0.558411i	$0.188589\pi$
$547$	12.9341	+	35.5361i	0.553021	+	1.51941i	−0.276543	+	0.961001i	$0.589189\pi$
$548$	4.88141	−	0.860725i	0.208524	−	0.0367684i
$549$	−0.808128	+	18.6852i	−0.0344900	+	0.797465i
$550$			74.2601i			3.16646i
$551$	−6.42353	+	19.1262i	−0.273652	+	0.814805i
$552$	2.74421	+	2.01127i	0.116801	+	0.0856055i
$553$	42.5088	−	7.49545i	1.80766	−	0.318739i
$554$	17.4225	−	14.6192i	0.740212	−	0.621112i
$555$	5.54297	−	1.35756i	0.235286	−	0.0576253i
$556$	−8.81241	−	49.9777i	−0.373730	−	2.11953i
$557$	−15.3168	−	2.70076i	−0.648993	−	0.114435i	−0.160546	−	0.987028i	$-0.551325\pi$
$557$	−15.3168	−	2.70076i	−0.648993	−	0.114435i	−0.488447	+	0.872594i	$0.662436\pi$
$558$	11.2821	−	3.56232i	0.477609	−	0.150805i
$559$	−2.75462	+	1.59038i	−0.116508	+	0.0672659i
$560$	−26.4912	−	4.67111i	−1.11946	−	0.197390i
$561$	25.5805	−	6.26509i	1.08001	−	0.264512i
$562$	25.5857	−	44.3157i	1.07927	−	1.86934i
$563$	9.04621			0.381252			0.190626	−	0.981663i	$-0.438948\pi$
$563$	9.04621			0.381252			0.190626	+	0.981663i	$0.438948\pi$
$564$	15.1230	+	61.7476i	0.636793	+	2.60004i
$565$	−7.42915	+	1.30996i	−0.312547	+	0.0551104i
$566$	−15.0048	−	12.5905i	−0.630699	−	0.529219i
$567$	−7.57182	+	28.3515i	−0.317986	+	1.19065i
$568$	−6.18125	−	2.24979i	−0.259359	−	0.0943991i
$569$	9.91059	−	17.1656i	0.415473	−	0.719621i	−0.580005	−	0.814613i	$-0.696949\pi$
$569$	9.91059	−	17.1656i	0.415473	−	0.719621i	0.995478	+	0.0949920i	$0.0302826\pi$
$570$	−10.7396	−	10.6659i	−0.449832	−	0.446746i
$571$	15.1317	+	26.2089i	0.633243	+	1.09681i	0.986884	+	0.161428i	$0.0516099\pi$
$571$	15.1317	+	26.2089i	0.633243	+	1.09681i	−0.353642	+	0.935381i	$0.615057\pi$
$572$	−4.75115	−	26.9451i	−0.198656	−	1.12663i
$573$	27.7659	−	1.82560i	1.15994	−	0.0762655i
$574$	15.6791	−	5.70671i	0.654431	−	0.238193i
$575$	0.708324	+	0.844147i	0.0295391	+	0.0352034i
$576$	22.8752	+	29.7862i	0.953132	+	1.24109i
$577$	7.66581	−	13.2776i	0.319132	−	0.552752i	−0.661175	−	0.750231i	$-0.729942\pi$
$577$	7.66581	−	13.2776i	0.319132	−	0.552752i	0.980307	+	0.197479i	$0.0632754\pi$
$578$	−29.7776			−1.23858
$579$	−30.5903	−	8.90944i	−1.27129	−	0.370264i
$580$	−11.2500	+	13.4072i	−0.467129	+	0.556703i
$581$	−20.2453	−	11.6886i	−0.839916	−	0.484926i
$582$	−46.7089	+	20.5638i	−1.93615	+	0.852399i
$583$	39.0267	−	46.5102i	1.61632	−	1.92625i
$584$	−64.2121	+	53.8803i	−2.65711	+	2.22958i
$585$	−0.752028	+	1.81767i	−0.0310925	+	0.0751513i
$586$	−8.43310	−	47.8265i	−0.348368	−	1.97569i
$587$	−3.27414	−	3.90196i	−0.135138	−	0.161051i	0.694231	−	0.719752i	$-0.255744\pi$
$587$	−3.27414	−	3.90196i	−0.135138	−	0.161051i	−0.829369	+	0.558701i	$0.811300\pi$
$588$	31.1647	+	3.40662i	1.28521	+	0.140487i
$589$	0.968685	−	6.43202i	0.0399140	−	0.265027i
$590$	−6.45562	+	3.72715i	−0.265774	+	0.153445i
$591$	−10.0786	+	0.662664i	−0.414578	+	0.0272583i
$592$	−16.1554	+	44.3865i	−0.663981	+	1.82427i
$593$	3.64215	−	4.34055i	0.149565	−	0.178245i	−0.686060	−	0.727545i	$-0.740661\pi$
$593$	3.64215	−	4.34055i	0.149565	−	0.178245i	0.835625	+	0.549300i	$0.185106\pi$
$594$	54.5454	−	68.0479i	2.23802	−	2.79204i
$595$	−1.02837	+	5.83219i	−0.0421592	+	0.239097i
$596$	91.1839	−	52.6451i	3.73504	−	2.15643i
$597$	−18.6995	+	25.5139i	−0.765319	+	1.04421i
$598$	−0.435821	−	0.365697i	−0.0178220	−	0.0149545i
$599$	−27.4211	−	23.0091i	−1.12040	−	0.940125i	−0.121773	−	0.992558i	$-0.538858\pi$
$599$	−27.4211	−	23.0091i	−1.12040	−	0.940125i	−0.998624	+	0.0524331i	$0.983302\pi$
$600$	24.3547	+	55.3194i	0.994276	+	2.25841i
$601$	−0.820033	+	0.473447i	−0.0334499	+	0.0193123i	−0.516632	−	0.856208i	$-0.672814\pi$
$601$	−0.820033	+	0.473447i	−0.0334499	+	0.0193123i	0.483182	+	0.875520i	$0.339481\pi$
$602$	−5.50639	+	31.2283i	−0.224424	+	1.27277i
$603$	2.63308	+	5.05304i	0.107227	+	0.205776i
$604$	22.3117	−	26.5901i	0.907852	−	1.08194i
$605$	7.61030	−	20.9091i	0.309403	−	0.850077i
$606$	13.7479	+	20.5661i	0.558471	+	0.835439i
$607$	1.96702	−	1.13566i	0.0798389	−	0.0460950i	−0.459549	−	0.888152i	$-0.651989\pi$
$607$	1.96702	−	1.13566i	0.0798389	−	0.0460950i	0.539388	+	0.842057i	$0.318656\pi$
$608$	55.4004	−	11.2063i	2.24678	−	0.454477i
$609$	15.4529	−	21.0841i	0.626182	−	0.854372i
$610$	8.03388	+	9.57441i	0.325282	+	0.387657i
$611$	−1.10525	−	6.26818i	−0.0447136	−	0.253583i
$612$	28.3948	−	21.8066i	1.14779	−	0.881479i
$613$	−27.8078	+	23.3335i	−1.12315	+	0.942432i	−0.998759	−	0.0498023i	$-0.984141\pi$
$613$	−27.8078	+	23.3335i	−1.12315	+	0.942432i	−0.124387	+	0.992234i	$0.539696\pi$
$614$	6.78060	−	8.08080i	0.273643	−	0.326115i
$615$	2.05204	+	1.50397i	0.0827464	+	0.0606461i
$616$	−141.439	−	81.6599i	−5.69874	−	3.29017i
$617$	14.2665	−	17.0022i	0.574349	−	0.684483i	−0.398168	−	0.917312i	$-0.630354\pi$
$617$	14.2665	−	17.0022i	0.574349	−	0.684483i	0.972518	+	0.232830i	$0.0747985\pi$
$618$	−38.6113	+	36.9775i	−1.55317	+	1.48745i
$619$	3.09223			0.124287			0.0621436	−	0.998067i	$-0.480206\pi$
$619$	3.09223			0.124287			0.0621436	+	0.998067i	$0.480206\pi$
$620$	2.82120	−	4.88646i	0.113302	−	0.196245i
$621$	−0.0290282	−	1.29381i	−0.00116486	−	0.0519187i
$622$	41.5552	+	49.5235i	1.66621	+	1.98571i
$623$	−51.7496	+	18.8353i	−2.07330	+	0.754621i
$624$	−9.04837	−	13.5358i	−0.362225	−	0.541866i
$625$	2.89977	+	16.4454i	0.115991	+	0.657817i
$626$	40.3749	+	69.9314i	1.61371	+	2.79502i
$627$	−20.4127	−	43.3847i	−0.815205	−	1.73262i
$628$	−39.4911	+	68.4006i	−1.57587	+	2.72948i
$629$	9.77195	+	3.55670i	0.389633	+	0.141815i
$630$	9.06232	+	17.3911i	0.361051	+	0.692878i
$631$	−2.58804	−	2.17163i	−0.103028	−	0.0864511i	0.589818	−	0.807536i	$-0.299199\pi$
$631$	−2.58804	−	2.17163i	−0.103028	−	0.0864511i	−0.692847	+	0.721085i	$0.743644\pi$
$632$	−102.826	+	18.1311i	−4.09021	+	0.721215i
$633$	−17.9540	+	17.1943i	−0.713608	+	0.683412i
$634$	−84.6417			−3.36155
$635$	−4.25831	+	7.37560i	−0.168986	+	0.292692i
$636$	23.0797	−	79.2433i	0.915168	−	3.14220i
$637$	−3.09111	−	0.545046i	−0.122474	−	0.0215955i
$638$	−67.2790	+	38.8435i	−2.66360	+	1.53783i
$639$	0.753353	+	2.38591i	0.0298022	+	0.0943853i
$640$	5.34190	+	0.941921i	0.211157	+	0.0372327i
$641$	5.27093	+	29.8929i	0.208189	+	1.18070i	0.892342	+	0.451360i	$0.149061\pi$
$641$	5.27093	+	29.8929i	0.208189	+	1.18070i	−0.684153	+	0.729339i	$0.739828\pi$
$642$	−30.2865	−	31.6247i	−1.19531	−	1.24813i
$643$	−14.3844	+	12.0699i	−0.567264	+	0.475991i	−0.880737	−	0.473606i	$-0.842952\pi$
$643$	−14.3844	+	12.0699i	−0.567264	+	0.475991i	0.313473	+	0.949597i	$0.398508\pi$
$644$	−3.98616	+	0.702868i	−0.157077	+	0.0276969i
$645$	−4.42526	+	1.94825i	−0.174245	+	0.0767122i
$646$	−5.46837	−	27.0339i	−0.215150	−	1.06363i
$647$			1.18300i			0.0465086i	0.999730	+	0.0232543i	$0.00740274\pi$
$647$			1.18300i			0.0465086i	−0.999730	+	0.0232543i	$0.992597\pi$
$648$	18.3158	−	68.5807i	0.719512	−	2.69410i
$649$	−23.2545	+	4.10040i	−0.912820	+	0.160955i
$650$	−3.45681	−	9.49752i	−0.135587	−	0.372523i
$651$	−3.72581	+	7.55911i	−0.146026	+	0.296265i
$652$	4.54085	−	1.65273i	0.177833	−	0.0647260i
$653$			13.7421i			0.537770i	0.963172	+	0.268885i	$0.0866551\pi$
$653$			13.7421i			0.537770i	−0.963172	+	0.268885i	$0.913345\pi$
$654$	21.9813	−	9.67737i	0.859535	−	0.378415i
$655$	−1.82796	+	10.3669i	−0.0714242	+	0.405067i
$656$	−19.7882	+	7.20230i	−0.772598	+	0.281203i
$657$	31.1304	+	6.88804i	1.21451	+	0.268728i
$658$	−54.9524	−	31.7268i	−2.14227	−	1.23684i
$659$	1.60512	+	1.34685i	0.0625265	+	0.0524659i	0.673515	−	0.739173i	$-0.264784\pi$
$659$	1.60512	+	1.34685i	0.0625265	+	0.0524659i	−0.610989	+	0.791639i	$0.709228\pi$
$660$	−2.72876	−	41.5022i	−0.106217	−	1.61547i
$661$	42.5800	+	7.50801i	1.65617	+	0.292028i	0.922073	−	0.387015i	$-0.126494\pi$
$661$	42.5800	+	7.50801i	1.65617	+	0.292028i	0.734098	+	0.679043i	$0.237605\pi$
$662$	−32.6897	−	38.9580i	−1.27052	−	1.51415i
$663$	−2.97999	+	1.99205i	−0.115733	+	0.0773649i
$664$	48.9722	+	28.2741i	1.90049	+	1.09725i
$665$	10.7782	−	0.270080i	0.417961	−	0.0104732i
$666$	32.8374	−	10.3684i	1.27242	−	0.401768i
$667$	−0.394284	+	1.08329i	−0.0152667	+	0.0419450i
$668$	−36.7388	−	13.3718i	−1.42147	−	0.517372i
$669$	−1.28873	+	1.23420i	−0.0498253	+	0.0477170i
$670$	3.57813	+	1.30233i	0.138235	+	0.0503135i
$671$	13.5412	+	37.2042i	0.522754	+	1.43625i
$672$	−72.7982	−	7.95757i	−2.80825	−	0.306970i
$673$		−	30.6064i		−	1.17979i	−0.807480	−	0.589895i	$-0.799169\pi$
$673$		−	30.6064i		−	1.17979i	0.807480	−	0.589895i	$-0.200831\pi$
$674$	20.9225	+	57.4842i	0.805906	+	2.21421i
$675$	11.0458	−	20.1632i	0.425152	−	0.776083i
$676$	−30.5366	−	52.8909i	−1.17448	−	2.03427i
$677$	−0.467835	−	0.810314i	−0.0179804	−	0.0311429i	0.856895	−	0.515491i	$-0.172390\pi$
$677$	−0.467835	−	0.810314i	−0.0179804	−	0.0311429i	−0.874876	+	0.484348i	$0.839057\pi$
$678$	−44.2132	+	10.8285i	−1.69800	+	0.415867i
$679$	12.4334	−	34.1606i	0.477151	−	1.31096i
$680$	2.48758	−	14.1077i	0.0953942	−	0.541007i
$681$	1.13413	+	17.2492i	0.0434599	+	0.660990i
$682$	19.1859	−	16.0989i	0.734667	−	0.616459i
$683$	−17.9300			−0.686071			−0.343035	−	0.939323i	$-0.611455\pi$
$683$	−17.9300			−0.686071			−0.343035	+	0.939323i	$0.611455\pi$
$684$	−49.1608	−	42.7968i	−1.87971	−	1.63638i
$685$	−0.754385			−0.0288236
$686$	22.2365	−	18.6586i	0.848994	−	0.712390i
$687$	7.58828	+	3.74019i	0.289511	+	0.142697i
$688$	6.94948	−	39.4125i	0.264946	−	1.50259i
$689$	−2.82628	+	7.76513i	−0.107673	+	0.295828i
$690$	−0.598173	−	0.624603i	−0.0227720	−	0.0237782i
$691$	−1.17561	−	2.03622i	−0.0447224	−	0.0774614i	0.842798	−	0.538230i	$-0.180907\pi$
$691$	−1.17561	−	2.03622i	−0.0447224	−	0.0774614i	−0.887520	+	0.460769i	$0.847574\pi$
$692$	−7.57294	−	13.1167i	−0.287880	−	0.498623i
$693$	8.13373	+	61.5864i	0.308975	+	2.33947i
$694$	7.34479	+	20.1796i	0.278804	+	0.766009i
$695$			7.72367i			0.292975i
$696$	−37.3796	+	51.0013i	−1.41687	+	1.93320i
$697$	1.58563	+	4.35648i	0.0600600	+	0.165013i
$698$	−39.1329	−	14.2432i	−1.48120	−	0.539114i
$699$	−19.8961	−	5.79476i	−0.752541	−	0.219178i
$700$	−67.5709	−	24.5938i	−2.55394	−	0.929558i
$701$	0.152181	−	0.418113i	0.00574779	−	0.0157919i	−0.936786	−	0.349904i	$-0.886214\pi$
$701$	0.152181	−	0.418113i	0.00574779	−	0.0157919i	0.942533	+	0.334112i	$0.108436\pi$
$702$	−3.80846	+	11.2421i	−0.143741	+	0.424306i
$703$	2.81944	−	18.7209i	0.106337	−	0.706073i
$704$	68.8522	+	39.7519i	2.59497	+	1.49820i
$705$	−0.634784	−	9.65456i	−0.0239073	−	0.363612i
$706$	29.1278	+	34.7131i	1.09624	+	1.30645i
$707$	−17.3534	−	3.05988i	−0.652643	−	0.115079i
$708$	−26.6865	+	17.8393i	−1.00294	+	0.670441i
$709$	14.7171	+	12.3492i	0.552714	+	0.463782i	0.875859	−	0.482567i	$-0.160296\pi$
$709$	14.7171	+	12.3492i	0.552714	+	0.463782i	−0.323145	+	0.946350i	$0.604740\pi$
$710$	1.44803	+	0.836018i	0.0543434	+	0.0313752i
$711$	29.2920	+	26.8190i	1.09853	+	1.00579i
$712$	125.179	−	45.5615i	4.69129	−	1.70749i
$713$	0.0645369	−	0.366007i	0.00241692	−	0.0137071i
$714$	−3.88307	+	35.5234i	−0.145320	+	1.32943i
$715$			4.16416i			0.155731i
$716$	−9.60919	+	3.49746i	−0.359112	+	0.130706i
$717$	−5.83184	+	0.383442i	−0.217794	+	0.0143199i
$718$	−3.12592	−	8.58838i	−0.116658	−	0.320516i
$719$	37.0819	−	6.53854i	1.38292	−	0.243846i	0.567815	−	0.823156i	$-0.307789\pi$
$719$	37.0819	−	6.53854i	1.38292	−	0.243846i	0.815107	+	0.579310i	$0.196678\pi$
$720$	−11.4373	−	21.9489i	−0.426244	−	0.817987i
$721$		−	38.0815i		−	1.41823i
$722$	−46.2656	+	19.5156i	−1.72183	+	0.726296i
$723$	−2.91558	+	26.6726i	−0.108432	+	0.991965i
$724$	−4.50585	+	0.794502i	−0.167458	+	0.0295274i
$725$	−15.6885	+	13.1642i	−0.582656	+	0.488907i
$726$	37.5449	−	128.909i	1.39342	−	4.78427i
$727$	4.79925	+	27.2179i	0.177994	+	1.00946i	0.934630	+	0.355620i	$0.115730\pi$
$727$	4.79925	+	27.2179i	0.177994	+	1.00946i	−0.756636	+	0.653836i	$0.773158\pi$
$728$	21.8907	+	3.85991i	0.811322	+	0.143058i
$729$	−24.9320	+	10.3632i	−0.923407	+	0.383821i
$730$	18.4522	−	10.6534i	0.682947	−	0.394300i
$731$	−8.67689	−	1.52997i	−0.320926	−	0.0565880i
$732$	37.2262	+	38.8710i	1.37592	+	1.43671i
$733$	−22.0709	+	38.2280i	−0.815209	+	1.41198i	0.0939693	+	0.995575i	$0.470044\pi$
$733$	−22.0709	+	38.2280i	−0.815209	+	1.41198i	−0.909178	+	0.416408i	$0.863289\pi$
$734$	84.3545			3.11358
$735$	−4.58101	−	1.33422i	−0.168973	−	0.0492136i
$736$	3.18048	−	0.560805i	0.117234	−	0.0206715i
$737$	9.24002	+	7.75330i	0.340361	+	0.285597i
$738$	12.9510	+	8.24322i	0.476733	+	0.303437i
$739$	−49.3025	−	17.9446i	−1.81362	−	0.660104i	−0.996496	−	0.0836444i	$-0.973344\pi$
$739$	−49.3025	−	17.9446i	−1.81362	−	0.660104i	−0.817126	−	0.576460i	$-0.804434\pi$
$740$	8.21133	−	14.2224i	0.301855	−	0.522827i
$741$	4.63025	+	4.59849i	0.170097	+	0.168930i
$742$	41.1907	+	71.3443i	1.51216	+	2.61913i
$743$	−4.43163	−	25.1330i	−0.162581	−	0.922042i	−0.951524	−	0.307575i	$-0.900482\pi$
$743$	−4.43163	−	25.1330i	−0.162581	−	0.922042i	0.788943	−	0.614467i	$-0.210629\pi$
$744$	9.01252	−	18.2850i	0.330415	−	0.670362i
$745$	−15.0582	+	5.48073i	−0.551689	+	0.200798i
$746$	18.3421	+	21.8593i	0.671552	+	0.800324i
$747$	−2.81624	−	21.3238i	−0.103041	−	0.780198i
$748$	37.8949	−	65.6359i	1.38558	−	2.39989i
$749$	31.1907			1.13968
$750$	−7.78509	−	31.7868i	−0.284271	−	1.16069i
$751$	−28.3064	+	33.7343i	−1.03292	+	1.23098i	−0.0603929	+	0.998175i	$0.519235\pi$
$751$	−28.3064	+	33.7343i	−1.03292	+	1.23098i	−0.972523	+	0.232807i	$0.925209\pi$
$752$	69.3541	+	40.0416i	2.52908	+	1.46017i
$753$	−0.993925	+	9.09271i	−0.0362206	+	0.331357i
$754$	6.79650	−	8.09975i	0.247514	−	0.294975i
$755$	−4.04687	+	3.39572i	−0.147281	+	0.123583i
$756$	43.8537	+	72.1685i	1.59495	+	2.62474i
$757$	5.46508	+	30.9940i	0.198632	+	1.12650i	0.907151	+	0.420805i	$0.138252\pi$
$757$	5.46508	+	30.9940i	0.198632	+	1.12650i	−0.708520	+	0.705691i	$0.750637\pi$
$758$	55.1719	+	65.7513i	2.00393	+	2.38819i
$759$	−1.10387	−	2.50733i	−0.0400678	−	0.0910103i
$760$	−26.0718	+	0.653307i	−0.945725	+	0.0236979i
$761$	−17.5822	+	10.1511i	−0.637355	+	0.367977i	−0.783595	−	0.621272i	$-0.786616\pi$
$761$	−17.5822	+	10.1511i	−0.637355	+	0.367977i	0.146240	+	0.989249i	$0.453283\pi$
$762$	−22.7199	+	46.0952i	−0.823054	+	1.66985i
$763$	−5.85119	+	16.0760i	−0.211827	+	0.581991i
$764$	51.4716	−	61.3415i	1.86218	−	2.21926i
$765$	−4.83218	+	2.51800i	−0.174708	+	0.0910384i
$766$	12.6523	−	71.7545i	0.457145	−	2.59260i
$767$	2.78327	−	1.60692i	0.100498	−	0.0580226i
$768$	−10.5726	−	1.15569i	−0.381505	−	0.0417024i
$769$	−27.7241	−	23.2633i	−0.999756	−	0.838895i	−0.0128057	−	0.999918i	$-0.504076\pi$
$769$	−27.7241	−	23.2633i	−0.999756	−	0.838895i	−0.986951	+	0.161023i	$0.948521\pi$
$770$	31.8015	+	26.6846i	1.14605	+	0.961648i
$771$	−28.3354	−	3.09734i	−1.02047	−	0.111548i
$772$	−79.4046	+	45.8443i	−2.85783	+	1.64997i
$773$	−2.37406	+	13.4640i	−0.0853889	+	0.484265i	0.911883	+	0.410450i	$0.134628\pi$
$773$	−2.37406	+	13.4640i	−0.0853889	+	0.484265i	−0.997272	+	0.0738146i	$0.976483\pi$
$774$	−25.8738	+	13.4825i	−0.930013	+	0.484619i
$775$	4.24400	−	5.05780i	0.152449	−	0.181682i
$776$	−30.0758	+	82.6325i	−1.07966	+	2.96633i
$777$	−10.8443	+	22.0014i	−0.389036	+	0.789296i
$778$	−58.5297	+	33.7921i	−2.09839	+	1.21151i
$779$	7.20141	−	4.40187i	0.258017	−	0.157713i
$780$	2.28093	+	5.18091i	0.0816703	+	0.185506i
$781$	3.40457	+	4.05740i	0.121825	+	0.145185i
$782$	−0.273657	−	1.55199i	−0.00978595	−	0.0554989i
$783$	24.0455	−	0.539490i	0.859314	−	0.0192798i
$784$	30.2530	−	25.3853i	1.08046	−	0.906617i
$785$	7.72673	−	9.20835i	0.275779	−	0.328660i
$786$	−6.90225	+	63.1438i	−0.246195	+	2.25226i
$787$	−17.2254	−	9.94508i	−0.614019	−	0.354504i	0.160518	−	0.987033i	$-0.448684\pi$
$787$	−17.2254	−	9.94508i	−0.614019	−	0.354504i	−0.774537	+	0.632529i	$0.782017\pi$
$788$	−18.6834	+	22.2660i	−0.665568	+	0.793193i
$789$	−2.00689	−	8.19419i	−0.0714471	−	0.291721i
$790$	26.5405			0.944267
$791$	16.2122	−	28.0803i	0.576438	−	0.998420i
$792$	−19.6750	−	148.974i	−0.699122	−	5.29356i
$793$	−3.46372	−	4.12790i	−0.123000	−	0.146586i
$794$	67.4839	−	24.5621i	2.39491	−	0.871677i
$795$	−5.55350	+	11.2672i	−0.196962	+	0.399607i
$796$	15.8073	+	89.6478i	0.560276	+	3.17748i
$797$	−0.398239	−	0.689770i	−0.0141064	−	0.0244329i	0.858886	−	0.512167i	$-0.171157\pi$
$797$	−0.398239	−	0.689770i	−0.0141064	−	0.0244329i	−0.872992	+	0.487734i	$0.837824\pi$
$798$	64.7899	−	5.89312i	2.29354	−	0.208614i
$799$	8.81540	−	15.2687i	0.311866	−	0.540169i
$800$	53.9135	+	19.6229i	1.90613	+	0.693775i
$801$	−42.7455	−	27.2072i	−1.51034	−	0.961320i
$802$	−52.8409	−	44.3388i	−1.86588	−	1.56566i
$803$	66.4688	−	11.7202i	2.34563	−	0.413599i
$804$	15.7430	+	4.58516i	0.555213	+	0.161706i
$805$	0.616031			0.0217122
$806$	−1.70438	+	2.95208i	−0.0600344	+	0.103983i
$807$	8.15777	+	8.51822i	0.287167	+	0.299855i
$808$	41.9770	+	7.40167i	1.47674	+	0.260390i
$809$	37.0520	−	21.3920i	1.30268	−	0.752102i	0.321816	−	0.946802i	$-0.395707\pi$
$809$	37.0520	−	21.3920i	1.30268	−	0.752102i	0.980863	+	0.194700i	$0.0623735\pi$
$810$	−7.61203	+	16.3591i	−0.267460	+	0.574801i
$811$	−21.3317	−	3.76136i	−0.749058	−	0.132079i	−0.213929	−	0.976849i	$-0.568626\pi$
$811$	−21.3317	−	3.76136i	−0.749058	−	0.132079i	−0.535130	+	0.844770i	$0.679737\pi$
$812$	−13.0628	−	74.0830i	−0.458416	−	2.59980i
$813$	7.01564	−	24.0880i	0.246049	−	0.844802i
$814$	55.8422	−	46.8572i	1.95727	−	1.64234i
$815$	−0.724271	+	0.127709i	−0.0253701	+	0.00447344i
$816$	4.90073	−	44.8333i	0.171560	−	1.56948i
$817$	0.401813	+	16.0353i	0.0140577	+	0.561006i
$818$			0.00986566i			0.000344945i
$819$	−3.90712	−	7.49799i	−0.136526	−	0.262001i
$820$	7.21024	−	1.27136i	0.251793	−	0.0443978i
$821$	−7.03183	−	19.3198i	−0.245412	−	0.674265i	−0.999840	−	0.0178820i	$-0.994308\pi$
$821$	−7.03183	−	19.3198i	−0.245412	−	0.674265i	0.754428	−	0.656383i	$-0.227915\pi$
$822$	−4.54224	+	0.298651i	−0.158429	+	0.0104166i
$823$	32.7065	−	11.9042i	1.14008	−	0.414954i	0.298135	−	0.954524i	$-0.403635\pi$
$823$	32.7065	−	11.9042i	1.14008	−	0.414954i	0.841941	+	0.539570i	$0.181413\pi$
$824$			92.1168i			3.20904i
$825$	5.28850	−	48.3807i	0.184122	−	1.68440i
$826$	5.56367	−	31.5531i	0.193585	−	1.09787i
$827$	−30.4794	+	11.0936i	−1.05987	+	0.385762i	−0.812380	−	0.583128i	$-0.801829\pi$
$827$	−30.4794	+	11.0936i	−1.05987	+	0.385762i	−0.247492	+	0.968890i	$0.579606\pi$
$828$	−2.74679	−	2.51489i	−0.0954574	−	0.0873985i
$829$	25.0414	+	14.4577i	0.869724	+	0.502135i	0.867257	−	0.497861i	$-0.165881\pi$
$829$	25.0414	+	14.4577i	0.869724	+	0.502135i	0.00246760	+	0.999997i	$0.499215\pi$
$830$	−11.0110	−	9.23935i	−0.382198	−	0.320703i
$831$	−12.3920	+	8.28373i	−0.429873	+	0.287359i
$832$	−10.6563	−	1.87900i	−0.369442	−	0.0651426i
$833$	−5.58872	−	6.66038i	−0.193638	−	0.230768i
$834$	3.05769	+	46.5051i	0.105879	+	1.61034i
$835$	5.15310	+	2.97514i	0.178330	+	0.102959i
$836$	−130.799	−	43.9288i	−4.52379	−	1.51931i
$837$	−7.60402	+	1.51740i	−0.262833	+	0.0524491i
$838$	−0.568612	+	1.56225i	−0.0196424	+	0.0539670i
$839$	20.4668	+	7.44929i	0.706591	+	0.257178i	0.670222	−	0.742160i	$-0.266199\pi$
$839$	20.4668	+	7.44929i	0.706591	+	0.257178i	0.0363688	+	0.999338i	$0.488421\pi$
$840$	32.4419	+	9.44872i	1.11935	+	0.326012i
$841$	7.11817	+	2.59080i	0.245454	+	0.0893380i
$842$	−7.13078	−	19.5917i	−0.245743	−	0.675173i
$843$	−19.8252	+	27.0497i	−0.682815	+	0.931643i
$844$			71.5389i			2.46247i
$845$	3.17908	+	8.73445i	0.109364	+	0.300474i
$846$	−7.64421	−	57.8799i	−0.262813	−	1.98995i
$847$	47.8193	+	82.8255i	1.64309	+	2.84592i
$848$	−51.9858	−	90.0420i	−1.78520	−	3.09205i
$849$	8.87904	+	9.27136i	0.304728	+	0.318192i
$850$	9.57542	−	26.3083i	0.328434	−	0.902366i
$851$	0.187840	−	1.06529i	0.00643907	−	0.0365178i
$852$	6.45830	+	3.18323i	0.221258	+	0.109056i
$853$	5.48975	−	4.60645i	0.187965	−	0.157722i	−0.543949	−	0.839118i	$-0.683071\pi$
$853$	5.48975	−	4.60645i	0.187965	−	0.157722i	0.731914	+	0.681397i	$0.238627\pi$
$854$	−53.7207			−1.83828
$855$	6.23730	+	7.71372i	0.213311	+	0.263804i
$856$	−75.4486			−2.57878
$857$	2.33414	−	1.95858i	0.0797327	−	0.0669037i	−0.602050	−	0.798458i	$-0.705649\pi$
$857$	2.33414	−	1.95858i	0.0797327	−	0.0669037i	0.681783	+	0.731555i	$0.261205\pi$
$858$	1.64854	+	25.0729i	0.0562801	+	0.855975i
$859$	5.10180	−	28.9337i	0.174071	−	0.987206i	−0.765139	−	0.643865i	$-0.777330\pi$
$859$	5.10180	−	28.9337i	0.174071	−	0.987206i	0.939211	−	0.343342i	$-0.111559\pi$
$860$	−4.75897	+	13.0752i	−0.162279	+	0.445859i
$861$	−10.6214	+	2.60134i	−0.361975	+	0.0886536i
$862$	1.39614	+	2.41819i	0.0475529	+	0.0823640i
$863$	−5.22563	−	9.05105i	−0.177882	−	0.308101i	0.763273	−	0.646077i	$-0.223591\pi$
$863$	−5.22563	−	9.05105i	−0.177882	−	0.308101i	−0.941155	+	0.337975i	$0.890258\pi$
$864$	−34.9900	−	57.5818i	−1.19039	−	1.95897i
$865$	0.788397	+	2.16610i	0.0268063	+	0.0736497i
$866$			38.6645i			1.31387i
$867$	19.4002	+	2.12064i	0.658865	+	0.0720206i
$868$	8.29467	+	22.7894i	0.281539	+	0.773523i
$869$	79.0028	+	28.7547i	2.67999	+	0.975436i
$870$	11.6083	−	11.1171i	0.393557	−	0.376904i
$871$	−1.54267	−	0.561487i	−0.0522715	−	0.0190253i
$872$	14.1537	−	38.8870i	0.479305	−	1.31688i
$873$	31.8955	−	10.0710i	1.07950	−	0.340852i
$874$	−2.67060	+	1.04850i	−0.0903343	+	0.0354661i
$875$	20.1881	+	11.6556i	0.682483	+	0.394032i
$876$	76.2785	−	50.9903i	2.57721	−	1.72280i
$877$	−29.1626	−	34.7547i	−0.984752	−	1.17358i	−0.984819	−	0.173582i	$-0.944466\pi$
$877$	−29.1626	−	34.7547i	−0.984752	−	1.17358i	6.70241e−5	−	1.00000i	$-0.499979\pi$
$878$	70.8645	+	12.4953i	2.39156	+	0.421697i
$879$	2.08819	+	31.7597i	0.0704329	+	1.07123i
$880$	−40.1359	−	33.6780i	−1.35298	−	1.13529i
$881$	−41.1563	−	23.7616i	−1.38659	−	0.800549i	−0.393662	−	0.919255i	$-0.628792\pi$
$881$	−41.1563	−	23.7616i	−1.38659	−	0.800549i	−0.992929	+	0.118706i	$0.962125\pi$
$882$	−28.1110	−	6.21996i	−0.946547	−	0.209437i
$883$	−8.75647	+	3.18710i	−0.294679	+	0.107254i	−0.485129	−	0.874443i	$-0.661227\pi$
$883$	−8.75647	+	3.18710i	−0.294679	+	0.107254i	0.190450	+	0.981697i	$0.439005\pi$
$884$	−1.79122	+	10.1585i	−0.0602454	+	0.341669i
$885$	4.47130	−	1.96851i	0.150301	−	0.0661708i
$886$		−	73.5204i		−	2.46997i
$887$	−38.3310	+	13.9514i	−1.28703	+	0.468441i	−0.892751	−	0.450550i	$-0.851228\pi$
$887$	−38.3310	+	13.9514i	−1.28703	+	0.468441i	−0.394279	+	0.918991i	$0.629006\pi$
$888$	26.2317	−	53.2201i	0.880278	−	1.78595i
$889$	−12.5199	−	34.3982i	−0.419905	−	1.15368i
$890$	−33.3467	+	5.87993i	−1.11779	+	0.197096i
$891$	−40.3826	+	40.4490i	−1.35287	+	1.35509i
$892$			5.13504i			0.171934i
$893$	−30.4275	−	10.2191i	−1.01822	−	0.341968i
$894$	−88.4973	+	38.9614i	−2.95979	+	1.30307i
$895$	1.53268	−	0.270253i	0.0512318	−	0.00903355i
$896$	−17.8600	+	14.9863i	−0.596661	+	0.500658i
$897$	0.257896	+	0.269291i	0.00861089	+	0.00899135i
$898$	−5.10539	−	28.9541i	−0.170369	−	0.966211i
$899$	6.80225	+	1.19942i	0.226868	+	0.0400029i
$900$	−19.9208	−	63.0905i	−0.664028	−	2.10302i
$901$	−19.8233	+	11.4450i	−0.660409	+	0.381287i
$902$	32.0048	+	5.64331i	1.06564	+	0.187902i
$903$	5.81139	−	19.9532i	0.193391	−	0.664001i
$904$	−39.2163	+	67.9246i	−1.30431	+	2.25914i
$905$	0.696344			0.0231473
$906$	−23.0223	+	22.0481i	−0.764866	+	0.732501i
$907$	−7.49873	+	1.32223i	−0.248991	+	0.0439039i	−0.296751	−	0.954955i	$-0.595903\pi$
$907$	−7.49873	+	1.32223i	−0.248991	+	0.0439039i	0.0477594	+	0.998859i	$0.484792\pi$
$908$	38.1075	+	31.9760i	1.26464	+	1.06116i
$909$	−7.49219	−	14.3779i	−0.248500	−	0.476886i
$910$	−5.30944	−	1.93248i	−0.176006	−	0.0640610i
$911$	−20.3397	+	35.2294i	−0.673884	+	1.16720i	0.302910	+	0.953019i	$0.402042\pi$
$911$	−20.3397	+	35.2294i	−0.673884	+	1.16720i	−0.976794	+	0.214182i	$0.931292\pi$
$912$	−81.7697	+	7.43757i	−2.70767	+	0.246283i
$913$	−22.7663	−	39.4324i	−0.753455	−	1.30502i
$914$	−0.663809	−	3.76465i	−0.0219568	−	0.124523i
$915$	−4.55226	−	6.80991i	−0.150493	−	0.225129i
$916$	22.8774	−	8.32668i	0.755889	−	0.275121i
$917$	−29.0835	−	34.6604i	−0.960422	−	1.14459i
$918$	−28.0983	+	17.0742i	−0.927382	+	0.563531i
$919$	6.55406	−	11.3520i	0.216198	−	0.374467i	−0.737444	−	0.675408i	$-0.763968\pi$
$919$	6.55406	−	11.3520i	0.216198	−	0.374467i	0.953643	+	0.300941i	$0.0973008\pi$
$920$	−1.49014			−0.0491286
$921$	−4.99307	+	4.78179i	−0.164527	+	0.157565i
$922$	33.2649	−	39.6436i	1.09552	−	1.30559i
$923$	−0.624301	−	0.360440i	−0.0205491	−	0.0118640i
$924$	144.189	+	105.678i	4.74346	+	3.47655i
$925$	12.3525	−	14.7211i	0.406148	−	0.484028i
$926$	0.852905	−	0.715673i	0.0280282	−	0.0235185i
$927$	27.7888	−	21.3412i	0.912704	−	0.700938i
$928$	10.4226	+	59.1094i	0.342138	+	1.94036i
$929$	13.0106	+	15.5054i	0.426864	+	0.508716i	0.936015	−	0.351961i	$-0.114485\pi$
$929$	13.0106	+	15.5054i	0.426864	+	0.508716i	−0.509151	+	0.860677i	$0.670041\pi$
$930$	−3.06316	+	4.17942i	−0.100445	+	0.137049i
$931$	−9.86759	+	12.3766i	−0.323397	+	0.405627i
$932$	−51.6453	+	29.8174i	−1.69170	+	0.976703i
$933$	−23.5465	−	35.2242i	−0.770878	−	1.15319i
$934$	11.9099	−	32.7222i	0.389704	−	1.07070i
$935$	−7.41442	+	8.83617i	−0.242478	+	0.288974i
$936$	9.45110	+	18.1372i	0.308919	+	0.592833i
$937$	−5.49239	+	31.1489i	−0.179429	+	1.01759i	0.753478	+	0.657473i	$0.228374\pi$
$937$	−5.49239	+	31.1489i	−0.179429	+	1.01759i	−0.932907	+	0.360117i	$0.882737\pi$
$938$	−14.1737	+	8.18322i	−0.462789	+	0.267192i
$939$	−21.3242	−	48.4359i	−0.695888	−	1.58065i
$940$	−21.3292	−	17.8973i	−0.695682	−	0.583746i
$941$	−35.7924	−	30.0334i	−1.16680	−	0.979060i	−0.166822	−	0.985987i	$-0.553351\pi$
$941$	−35.7924	−	30.0334i	−1.16680	−	0.979060i	−0.999976	+	0.00692694i	$0.997795\pi$
$942$	42.8781	−	58.5035i	1.39704	−	1.90615i
$943$	0.417641	−	0.241125i	0.0136003	−	0.00785211i
$944$	−7.02177	+	39.8224i	−0.228539	+	1.29611i
$945$	−4.66561	−	11.9758i	−0.151772	−	0.389571i
$946$	−39.7003	+	47.3129i	−1.29077	+	1.53828i
$947$	−7.82974	+	21.5120i	−0.254432	+	0.699047i	0.745054	+	0.667004i	$0.232424\pi$
$947$	−7.82974	+	21.5120i	−0.254432	+	0.699047i	−0.999486	+	0.0320429i	$0.989799\pi$
$948$	114.043	−	7.49829i	3.70395	−	0.243533i
$949$	−7.95547	+	4.59310i	−0.258246	+	0.149098i
$950$	−50.4009	−	7.59055i	−1.63522	−	0.246270i
$951$	55.1444	+	6.02784i	1.78818	+	0.195466i
$952$	39.5783	+	47.1676i	1.28274	+	1.52871i
$953$	4.13148	+	23.4308i	0.133832	+	0.758998i	0.975666	+	0.219262i	$0.0703649\pi$
$953$	4.13148	+	23.4308i	0.133832	+	0.758998i	−0.841834	+	0.539736i	$0.818524\pi$
$954$	−28.9777	+	70.0398i	−0.938189	+	2.26762i
$955$	−9.33583	+	7.83369i	−0.302100	+	0.253492i
$956$	−10.8109	+	12.8839i	−0.349649	+	0.416696i
$957$	46.5988	−	20.5154i	1.50632	−	0.663168i
$958$	36.8087	+	21.2515i	1.18924	+	0.686605i
$959$	2.08422	−	2.48388i	0.0673031	−	0.0802087i
$960$	−15.7926	−	4.59962i	−0.509706	−	0.148452i
$961$	28.7732			0.928168
$962$	−4.96075	+	8.59227i	−0.159941	+	0.277026i
$963$	17.4796	+	22.7605i	0.563273	+	0.733447i
$964$	49.6322	+	59.1494i	1.59855	+	1.90507i
$965$	13.1129	−	4.77272i	0.422120	−	0.153639i
$966$	3.70920	−	0.243878i	0.119341	−	0.00784666i
$967$	−5.25014	−	29.7750i	−0.168833	−	0.957500i	−0.945024	−	0.327002i	$-0.893962\pi$
$967$	−5.25014	−	29.7750i	−0.168833	−	0.957500i	0.776191	−	0.630498i	$-0.217149\pi$
$968$	−115.672	−	200.350i	−3.71785	−	6.43950i
$969$	1.63743	+	18.0021i	0.0526017	+	0.578311i
$970$	11.1761	−	19.3576i	0.358843	−	0.621534i
$971$	46.8984	+	17.0696i	1.50504	+	0.547791i	0.957361	−	0.288896i	$-0.0932881\pi$
$971$	46.8984	+	17.0696i	1.50504	+	0.547791i	0.547682	+	0.836686i	$0.315510\pi$
$972$	−28.0867	+	72.4449i	−0.900882	+	2.32367i
$973$	−25.4309	−	21.3390i	−0.815276	−	0.684098i
$974$	−11.1676	+	1.96915i	−0.357833	+	0.0630956i
$975$	1.57575	+	6.43385i	0.0504645	+	0.206048i
$976$	67.7996			2.17021
$977$	10.7428	−	18.6071i	0.343693	−	0.595293i	−0.641423	−	0.767188i	$-0.721655\pi$
$977$	10.7428	−	18.6071i	0.343693	−	0.595293i	0.985115	+	0.171894i	$0.0549888\pi$
$978$	−4.31037	+	1.05568i	−0.137830	+	0.0337568i
$979$	−105.634	−	18.6260i	−3.37606	−	0.595291i
$980$	−11.8912	+	6.86536i	−0.379849	+	0.219306i
$981$	−15.0101	+	4.73943i	−0.479234	+	0.151318i
$982$	24.7101	+	4.35706i	0.788531	+	0.139039i
$983$	−9.65641	−	54.7642i	−0.307992	−	1.74671i	−0.609078	−	0.793110i	$-0.708460\pi$
$983$	−9.65641	−	54.7642i	−0.307992	−	1.74671i	0.301086	−	0.953597i	$-0.402651\pi$
$984$	25.6925	−	6.29250i	0.819047	−	0.200598i
$985$	3.38876	−	2.84351i	0.107975	−	0.0906017i
$986$	28.8437	−	5.08592i	0.918571	−	0.161969i
$987$	33.5423	+	24.5836i	1.06766	+	0.782505i
$988$	18.7735	−	0.470426i	0.597265	−	0.0149662i
$989$			0.916505i			0.0291432i
$990$	−1.65043	+	38.1606i	−0.0524541	+	1.21282i
$991$	5.42317	−	0.956250i	0.172273	−	0.0303763i	−0.0868464	−	0.996222i	$-0.527679\pi$
$991$	5.42317	−	0.956250i	0.172273	−	0.0303763i	0.259119	+	0.965845i	$0.416568\pi$
$992$	−6.61815	−	18.1832i	−0.210127	−	0.577318i
$993$	18.5230	+	27.7093i	0.587810	+	0.879329i
$994$	−6.75328	+	2.45799i	−0.214201	+	0.0779628i
$995$		−	13.8544i		−	0.439213i
$996$	−49.9242	−	36.5902i	−1.58191	−	1.15940i
$997$	6.20121	−	35.1688i	0.196394	−	1.11381i	−0.714025	−	0.700121i	$-0.753130\pi$
$997$	6.20121	−	35.1688i	0.196394	−	1.11381i	0.910419	−	0.413687i	$-0.135759\pi$
$998$	3.80030	−	1.38320i	0.120297	−	0.0437844i
$999$	−22.1321	+	4.41652i	−0.700229	+	0.139733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.x.a.110.1	yes	108
3.2	odd	2		513.2.bo.a.224.18		108
9.4	even	3		513.2.cd.a.395.1		108
9.5	odd	6		171.2.bd.a.167.18	yes	108
19.14	odd	18		171.2.bd.a.128.18	yes	108
57.14	even	18		513.2.cd.a.413.1		108
171.14	even	18	inner	171.2.x.a.14.1	✓	108
171.166	odd	18		513.2.bo.a.71.18		108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.x.a.14.1	✓	108	171.14	even	18	inner
171.2.x.a.110.1	yes	108	1.1	even	1	trivial
171.2.bd.a.128.18	yes	108	19.14	odd	18
171.2.bd.a.167.18	yes	108	9.5	odd	6
513.2.bo.a.71.18		108	171.166	odd	18
513.2.bo.a.224.18		108	3.2	odd	2
513.2.cd.a.395.1		108	9.4	even	3
513.2.cd.a.413.1		108	57.14	even	18

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.02450 + 1.69876i) q^{2} +(1.43995 - 0.962572i) q^{3} +(0.865531 - 4.90867i) q^{4} +(-0.259455 + 0.712848i) q^{5} +(-1.28000 + 4.39486i) q^{6} +(-1.63029 - 2.82374i) q^{7} +(3.94358 + 6.83047i) q^{8} +(1.14691 - 2.77211i) q^{9} +(-0.685689 - 1.88391i) q^{10} -6.35073i q^{11} +(-3.47862 - 7.90137i) q^{12} +(0.295627 + 0.812229i) q^{13} +(8.09738 + 2.94721i) q^{14} +(0.312564 + 1.27621i) q^{15} +(-10.2195 - 3.71960i) q^{16} +(-0.818892 + 2.24989i) q^{17} +(2.38722 + 7.56047i) q^{18} +(4.31029 + 0.649145i) q^{19} +(3.27457 + 1.89057i) q^{20} +(-5.06559 - 2.49678i) q^{21} +(10.7884 + 12.8571i) q^{22} +(0.245272 + 0.0432481i) q^{23} +(12.2534 + 6.03957i) q^{24} +(3.38939 + 2.84403i) q^{25} +(-1.97828 - 1.14216i) q^{26} +(-1.01686 - 5.09568i) q^{27} +(-15.2719 + 5.55851i) q^{28} +(-0.803768 + 4.55839i) q^{29} +(-2.80076 - 2.05272i) q^{30} -1.49225i q^{31} +(12.1851 - 4.43503i) q^{32} +(-6.11304 - 9.14474i) q^{33} +(-2.16417 - 5.94600i) q^{34} +(2.43589 - 0.429513i) q^{35} +(-12.6147 - 8.02916i) q^{36} -4.34331i q^{37} +(-9.82894 + 6.00795i) q^{38} +(1.20752 + 0.885007i) q^{39} +(-5.89227 + 1.03897i) q^{40} +(1.48330 - 1.24464i) q^{41} +(14.4967 - 3.55048i) q^{42} +(0.639011 + 3.62401i) q^{43} +(-31.1736 - 5.49675i) q^{44} +(1.67852 + 1.53681i) q^{45} +(-0.570023 + 0.329103i) q^{46} +(-7.25185 - 1.27870i) q^{47} +(-18.2960 + 4.48098i) q^{48} +(-1.81568 + 3.14486i) q^{49} -11.6931 q^{50} +(0.986514 + 4.02797i) q^{51} +(4.24284 - 0.748127i) q^{52} +(7.32359 + 6.14522i) q^{53} +(10.7150 + 8.58883i) q^{54} +(4.52711 + 1.64773i) q^{55} +(12.8583 - 22.2713i) q^{56} +(6.83145 - 3.21423i) q^{57} +(-6.11638 - 10.5939i) q^{58} +(-0.645657 - 3.66171i) q^{59} +(6.53502 - 0.429676i) q^{60} +(-5.85826 + 2.13223i) q^{61} +(2.53497 + 3.02106i) q^{62} +(-9.69752 + 1.28075i) q^{63} +(-6.25941 + 10.8416i) q^{64} -0.655698 q^{65} +(27.9106 + 8.12897i) q^{66} +(-1.22085 + 1.45495i) q^{67} +(10.3352 + 5.96701i) q^{68} +(0.394809 - 0.173817i) q^{69} +(-4.20182 + 5.00753i) q^{70} +(-0.638887 + 0.536090i) q^{71} +(23.4578 - 3.09807i) q^{72} +(1.84550 + 10.4663i) q^{73} +(7.37823 + 8.79303i) q^{74} +(7.61813 + 0.832739i) q^{75} +(6.91713 - 20.5959i) q^{76} +(-17.9328 + 10.3535i) q^{77} +(-3.94804 + 0.259582i) q^{78} +(-4.52777 + 12.4400i) q^{79} +(5.30302 - 6.31989i) q^{80} +(-6.36918 - 6.35873i) q^{81} +(-0.888607 + 5.03954i) q^{82} +(6.20911 - 3.58483i) q^{83} +(-16.6403 + 22.7043i) q^{84} +(-1.39136 - 1.16749i) q^{85} +(-7.45000 - 6.25129i) q^{86} +(3.23039 + 7.33754i) q^{87} +(43.3785 - 25.0446i) q^{88} +(2.93290 - 16.6333i) q^{89} +(-6.00884 - 0.259880i) q^{90} +(1.81157 - 2.15894i) q^{91} +(0.424581 - 1.16653i) q^{92} +(-1.43639 - 2.14876i) q^{93} +(16.8536 - 9.73042i) q^{94} +(-1.58107 + 2.90416i) q^{95} +(13.2770 - 18.1153i) q^{96} +(7.16659 + 8.54081i) q^{97} +(-1.66650 - 9.45118i) q^{98} +(-17.6049 - 7.28373i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23}+ \cdots + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Introduction

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