LMFDB - Embedded newform 380.2.bj.a.283.38

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(23,380)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 27, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("380.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bj (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$56$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			283.38
Character	$\chi$	$=$	380.283
Dual form			380.2.bj.a.47.38

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.744093 + 1.20263i) q^{2} +(2.39174 - 0.209250i) q^{3} +(-0.892653 + 1.78974i) q^{4} +(0.685314 - 2.12846i) q^{5} +(2.03132 + 2.72068i) q^{6} +(0.693673 - 2.58882i) q^{7} +(-2.81662 + 0.258199i) q^{8} +(2.72219 - 0.479996i) q^{9} +O(q^{10})$	\(q+(0.744093 + 1.20263i) q^{2} +(2.39174 - 0.209250i) q^{3} +(-0.892653 + 1.78974i) q^{4} +(0.685314 - 2.12846i) q^{5} +(2.03132 + 2.72068i) q^{6} +(0.693673 - 2.58882i) q^{7} +(-2.81662 + 0.258199i) q^{8} +(2.72219 - 0.479996i) q^{9} +(3.06969 - 0.759591i) q^{10} +(3.81160 + 2.20063i) q^{11} +(-1.76049 + 4.46737i) q^{12} +(-5.36419 - 0.469306i) q^{13} +(3.62956 - 1.09209i) q^{14} +(1.19371 - 5.23412i) q^{15} +(-2.40634 - 3.19523i) q^{16} +(1.78579 + 2.55038i) q^{17} +(2.60282 + 2.91663i) q^{18} +(0.355971 + 4.34434i) q^{19} +(3.19765 + 3.12651i) q^{20} +(1.11737 - 6.33693i) q^{21} +(0.189635 + 6.22142i) q^{22} +(-2.99779 + 1.39789i) q^{23} +(-6.68258 + 1.20692i) q^{24} +(-4.06069 - 2.91733i) q^{25} +(-3.42705 - 6.80036i) q^{26} +(-0.546872 + 0.146534i) q^{27} +(4.01411 + 3.55241i) q^{28} +(-4.64203 + 0.818515i) q^{29} +(7.18295 - 2.45907i) q^{30} +(1.94331 - 1.12197i) q^{31} +(2.05215 - 5.27150i) q^{32} +(9.57681 + 4.46574i) q^{33} +(-1.73837 + 4.04537i) q^{34} +(-5.03482 - 3.25061i) q^{35} +(-1.57090 + 5.30048i) q^{36} +(-5.98188 + 5.98188i) q^{37} +(-4.95977 + 3.66069i) q^{38} -12.9279 q^{39} +(-1.38070 + 6.17201i) q^{40} +(-1.53945 - 1.29175i) q^{41} +(8.45242 - 3.37147i) q^{42} +(4.79853 - 10.2905i) q^{43} +(-7.34098 + 4.85738i) q^{44} +(0.843902 - 6.12302i) q^{45} +(-3.91179 - 2.56508i) q^{46} +(-0.159040 + 0.227133i) q^{47} +(-6.42394 - 7.13863i) q^{48} +(-0.158636 - 0.0915883i) q^{49} +(0.486944 - 7.05428i) q^{50} +(4.80481 + 5.72615i) q^{51} +(5.62830 - 9.18159i) q^{52} +(1.43669 + 3.08099i) q^{53} +(-0.583150 - 0.548652i) q^{54} +(7.29609 - 6.60472i) q^{55} +(-1.28538 + 7.47082i) q^{56} +(1.76044 + 10.3160i) q^{57} +(-4.43847 - 4.97360i) q^{58} +(0.983136 - 5.57564i) q^{59} +(8.30214 + 6.80868i) q^{60} +(7.29760 + 2.65611i) q^{61} +(2.79532 + 1.50224i) q^{62} +(0.645686 - 7.38022i) q^{63} +(7.86667 - 1.45450i) q^{64} +(-4.67506 + 11.0959i) q^{65} +(1.75539 + 14.8403i) q^{66} +(-3.82455 + 5.46202i) q^{67} +(-6.15861 + 0.919506i) q^{68} +(-6.87742 + 3.97068i) q^{69} +(0.162918 - 8.47380i) q^{70} +(-4.30197 - 11.8196i) q^{71} +(-7.54343 + 2.05483i) q^{72} +(0.171811 + 1.96381i) q^{73} +(-11.6451 - 2.74294i) q^{74} +(-10.3225 - 6.12778i) q^{75} +(-8.09300 - 3.24089i) q^{76} +(8.34103 - 8.34103i) q^{77} +(-9.61958 - 15.5476i) q^{78} +(12.5002 + 10.4889i) q^{79} +(-8.45003 + 2.93207i) q^{80} +(-9.06976 + 3.30112i) q^{81} +(0.408010 - 2.81258i) q^{82} +(3.75641 + 1.00653i) q^{83} +(10.3440 + 7.65648i) q^{84} +(6.65220 - 2.05318i) q^{85} +(15.9462 - 1.88620i) q^{86} +(-10.9312 + 2.92901i) q^{87} +(-11.3040 - 5.21417i) q^{88} +(4.22723 + 5.03782i) q^{89} +(7.99169 - 3.54119i) q^{90} +(-4.93594 + 13.5614i) q^{91} +(0.174120 - 6.61311i) q^{92} +(4.41310 - 3.09009i) q^{93} +(-0.391498 - 0.0222591i) q^{94} +(9.49071 + 2.21957i) q^{95} +(3.80514 - 13.0374i) q^{96} +(-2.62711 - 3.75190i) q^{97} +(-0.00789244 - 0.258931i) q^{98} +(11.4322 + 4.16097i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.744093	+	1.20263i	0.526153	+	0.850390i
$2$	0.744093	+	1.20263i	0.526153	+	0.850390i
$3$	2.39174	−	0.209250i	1.38087	−	0.120810i	0.627607	−	0.778531i	$-0.284035\pi$
$3$	2.39174	−	0.209250i	1.38087	−	0.120810i	0.753262	+	0.657720i	$0.228479\pi$
$4$	−0.892653	+	1.78974i	−0.446326	+	0.894870i
$5$	0.685314	−	2.12846i	0.306482	−	0.951877i
$5$	0.685314	−	2.12846i	0.306482	−	0.951877i
$6$	2.03132	+	2.72068i	0.829284	+	1.11071i
$7$	0.693673	−	2.58882i	0.262184	−	0.978482i	−0.701768	−	0.712405i	$-0.747606\pi$
$7$	0.693673	−	2.58882i	0.262184	−	0.978482i	0.963952	−	0.266077i	$-0.0857276\pi$
$8$	−2.81662	+	0.258199i	−0.995825	+	0.0912872i
$9$	2.72219	−	0.479996i	0.907397	−	0.159999i
$10$	3.06969	−	0.759591i	0.970723	−	0.240204i
$11$	3.81160	+	2.20063i	1.14924	+	0.663514i	0.948702	−	0.316172i	$-0.102398\pi$
$11$	3.81160	+	2.20063i	1.14924	+	0.663514i	0.200538	+	0.979686i	$0.435731\pi$
$12$	−1.76049	+	4.46737i	−0.508209	+	1.28962i
$13$	−5.36419	−	0.469306i	−1.48776	−	0.130162i	−0.685909	−	0.727687i	$-0.740595\pi$
$13$	−5.36419	−	0.469306i	−1.48776	−	0.130162i	−0.801850	+	0.597525i	$0.796151\pi$
$14$	3.62956	−	1.09209i	0.970040	−	0.291873i
$15$	1.19371	−	5.23412i	0.308214	−	1.35144i
$16$	−2.40634	−	3.19523i	−0.601586	−	0.798808i
$17$	1.78579	+	2.55038i	0.433118	+	0.618557i	0.975082	−	0.221845i	$-0.0712078\pi$
$17$	1.78579	+	2.55038i	0.433118	+	0.618557i	−0.541964	+	0.840402i	$0.682319\pi$
$18$	2.60282	+	2.91663i	0.613490	+	0.687457i
$19$	0.355971	+	4.34434i	0.0816653	+	0.996660i
$19$	0.355971	+	4.34434i	0.0816653	+	0.996660i
$20$	3.19765	+	3.12651i	0.715015	+	0.699109i
$21$	1.11737	−	6.33693i	0.243830	−	1.38283i
$22$	0.189635	+	6.22142i	0.0404303	+	1.32641i
$23$	−2.99779	+	1.39789i	−0.625083	+	0.291481i	−0.709235	−	0.704972i	$-0.750960\pi$
$23$	−2.99779	+	1.39789i	−0.625083	+	0.291481i	0.0841520	+	0.996453i	$0.473182\pi$
$24$	−6.68258	+	1.20692i	−1.36408	+	0.246362i
$25$	−4.06069	−	2.91733i	−0.812138	−	0.583465i
$26$	−3.42705	−	6.80036i	−0.672100	−	1.33366i
$27$	−0.546872	+	0.146534i	−0.105246	+	0.0282005i
$28$	4.01411	+	3.55241i	0.758595	+	0.671343i
$29$	−4.64203	+	0.818515i	−0.862003	+	0.151994i	−0.587136	−	0.809488i	$-0.699745\pi$
$29$	−4.64203	+	0.818515i	−0.862003	+	0.151994i	−0.274866	+	0.961482i	$0.588634\pi$
$30$	7.18295	−	2.45907i	1.31142	−	0.448963i
$31$	1.94331	−	1.12197i	0.349028	−	0.201512i	−0.315229	−	0.949016i	$-0.602081\pi$
$31$	1.94331	−	1.12197i	0.349028	−	0.201512i	0.664257	+	0.747504i	$0.268748\pi$
$32$	2.05215	−	5.27150i	0.362772	−	0.931878i
$33$	9.57681	+	4.46574i	1.66711	+	0.777386i
$34$	−1.73837	+	4.04537i	−0.298128	+	0.693775i
$35$	−5.03482	−	3.25061i	−0.851040	−	0.549453i
$36$	−1.57090	+	5.30048i	−0.261817	+	0.883414i
$37$	−5.98188	+	5.98188i	−0.983415	+	0.983415i	−0.999865	−	0.0164493i	$-0.994764\pi$
$37$	−5.98188	+	5.98188i	−0.983415	+	0.983415i	0.0164493	+	0.999865i	$0.494764\pi$
$38$	−4.95977	+	3.66069i	−0.804581	+	0.593843i
$39$	−12.9279			−2.07013
$40$	−1.38070	+	6.17201i	−0.218308	+	0.975880i
$41$	−1.53945	−	1.29175i	−0.240422	−	0.201738i	0.514613	−	0.857423i	$-0.327936\pi$
$41$	−1.53945	−	1.29175i	−0.240422	−	0.201738i	−0.755035	+	0.655685i	$0.772380\pi$
$42$	8.45242	−	3.37147i	1.30424	−	0.520229i
$43$	4.79853	−	10.2905i	0.731769	−	1.56928i	−0.0876909	−	0.996148i	$-0.527949\pi$
$43$	4.79853	−	10.2905i	0.731769	−	1.56928i	0.819460	−	0.573136i	$-0.194273\pi$
$44$	−7.34098	+	4.85738i	−1.10669	+	0.732277i
$45$	0.843902	−	6.12302i	0.125802	−	0.912766i
$46$	−3.91179	−	2.56508i	−0.576762	−	0.378201i
$47$	−0.159040	+	0.227133i	−0.0231984	+	0.0331307i	−0.830584	−	0.556894i	$-0.811993\pi$
$47$	−0.159040	+	0.227133i	−0.0231984	+	0.0331307i	0.807385	+	0.590025i	$0.200882\pi$
$48$	−6.42394	−	7.13863i	−0.927215	−	1.03037i
$49$	−0.158636	−	0.0915883i	−0.0226622	−	0.0130840i
$50$	0.486944	−	7.05428i	0.0688643	−	0.997626i
$51$	4.80481	+	5.72615i	0.672808	+	0.801821i
$52$	5.62830	−	9.18159i	0.780504	−	1.27326i
$53$	1.43669	+	3.08099i	0.197344	+	0.423206i	0.979931	−	0.199335i	$-0.0638781\pi$
$53$	1.43669	+	3.08099i	0.197344	+	0.423206i	−0.782587	+	0.622541i	$0.786100\pi$
$54$	−0.583150	−	0.548652i	−0.0793567	−	0.0746621i
$55$	7.29609	−	6.60472i	0.983804	−	0.890580i
$56$	−1.28538	+	7.47082i	−0.171766	+	0.998331i
$57$	1.76044	+	10.3160i	0.233176	+	1.36639i
$58$	−4.43847	−	4.97360i	−0.582800	−	0.653066i
$59$	0.983136	−	5.57564i	0.127993	−	0.725887i	−0.851491	−	0.524369i	$-0.824301\pi$
$59$	0.983136	−	5.57564i	0.127993	−	0.725887i	0.979485	−	0.201518i	$-0.0645875\pi$
$60$	8.30214	+	6.80868i	1.07180	+	0.878997i
$61$	7.29760	+	2.65611i	0.934362	+	0.340080i	0.763937	−	0.645291i	$-0.223264\pi$
$61$	7.29760	+	2.65611i	0.934362	+	0.340080i	0.170425	+	0.985371i	$0.445486\pi$
$62$	2.79532	+	1.50224i	0.355006	+	0.190784i
$63$	0.645686	−	7.38022i	0.0813488	−	0.929821i
$64$	7.86667	−	1.45450i	0.983333	−	0.181812i
$65$	−4.67506	+	11.0959i	−0.579869	+	1.37627i
$66$	1.75539	+	14.8403i	0.216073	+	1.82672i
$67$	−3.82455	+	5.46202i	−0.467243	+	0.667292i	−0.981746	−	0.190196i	$-0.939088\pi$
$67$	−3.82455	+	5.46202i	−0.467243	+	0.667292i	0.514503	+	0.857489i	$0.327976\pi$
$68$	−6.15861	+	0.919506i	−0.746841	+	0.111506i
$69$	−6.87742	+	3.97068i	−0.827944	+	0.478014i
$70$	0.162918	−	8.47380i	0.0194724	−	1.01281i
$71$	−4.30197	−	11.8196i	−0.510550	−	1.40272i	−0.880665	−	0.473739i	$-0.842904\pi$
$71$	−4.30197	−	11.8196i	−0.510550	−	1.40272i	0.370116	−	0.928986i	$-0.379318\pi$
$72$	−7.54343	+	2.05483i	−0.889002	+	0.242164i
$73$	0.171811	+	1.96381i	0.0201089	+	0.229846i	0.999598	+	0.0283491i	$0.00902502\pi$
$73$	0.171811	+	1.96381i	0.0201089	+	0.229846i	−0.979489	+	0.201497i	$0.935419\pi$
$74$	−11.6451	−	2.74294i	−1.35371	−	0.318860i
$75$	−10.3225	−	6.12778i	−1.19195	−	0.707575i
$76$	−8.09300	−	3.24089i	−0.928331	−	0.371756i
$77$	8.34103	−	8.34103i	0.950548	−	0.950548i
$78$	−9.61958	−	15.5476i	−1.08920	−	1.76041i
$79$	12.5002	+	10.4889i	1.40638	+	1.18009i	0.958182	+	0.286160i	$0.0923788\pi$
$79$	12.5002	+	10.4889i	1.40638	+	1.18009i	0.448199	+	0.893934i	$0.352066\pi$
$80$	−8.45003	+	2.93207i	−0.944742	+	0.327815i
$81$	−9.06976	+	3.30112i	−1.00775	+	0.366791i
$82$	0.408010	−	2.81258i	0.0450572	−	0.310597i
$83$	3.75641	+	1.00653i	0.412320	+	0.110481i	0.459015	−	0.888428i	$-0.348202\pi$
$83$	3.75641	+	1.00653i	0.412320	+	0.110481i	−0.0466955	+	0.998909i	$0.514869\pi$
$84$	10.3440	+	7.65648i	1.12863	+	0.835390i
$85$	6.65220	−	2.05318i	0.721533	−	0.222699i
$86$	15.9462	−	1.88620i	1.71953	−	0.203394i
$87$	−10.9312	+	2.92901i	−1.17195	+	0.314023i
$88$	−11.3040	−	5.21417i	−1.20501	−	0.555833i
$89$	4.22723	+	5.03782i	0.448086	+	0.534008i	0.942049	−	0.335475i	$-0.108897\pi$
$89$	4.22723	+	5.03782i	0.448086	+	0.534008i	−0.493963	+	0.869483i	$0.664452\pi$
$90$	7.99169	−	3.54119i	0.842398	−	0.373274i
$91$	−4.93594	+	13.5614i	−0.517427	+	1.42162i
$92$	0.174120	−	6.61311i	0.0181533	−	0.689464i
$93$	4.41310	−	3.09009i	0.457618	−	0.320427i
$94$	−0.391498	−	0.0222591i	−0.0403799	−	0.00229585i
$95$	9.49071	+	2.21957i	0.973726	+	0.227723i
$96$	3.80514	−	13.0374i	0.388361	−	1.33063i
$97$	−2.62711	−	3.75190i	−0.266743	−	0.380948i	0.663328	−	0.748329i	$-0.269143\pi$
$97$	−2.62711	−	3.75190i	−0.266743	−	0.380948i	−0.930071	+	0.367381i	$0.880255\pi$
$98$	−0.00789244	−	0.258931i	−0.000797257	−	0.0261559i
$99$	11.4322	+	4.16097i	1.14898	+	0.418194i
$100$	8.84604	−	4.66342i	0.884604	−	0.466342i
$101$	11.4532	−	9.61039i	1.13964	−	0.956269i	0.140210	−	0.990122i	$-0.455222\pi$
$101$	11.4532	−	9.61039i	1.13964	−	0.956269i	0.999427	+	0.0338526i	$0.0107777\pi$
$102$	−3.31123	+	10.0392i	−0.327861	+	0.994030i
$103$	−2.05297	−	7.66178i	−0.202285	−	0.754938i	−0.990260	−	0.139231i	$-0.955537\pi$
$103$	−2.05297	−	7.66178i	−0.202285	−	0.754938i	0.787975	−	0.615707i	$-0.211130\pi$
$104$	15.2301	−	0.0631746i	1.49343	−	0.00619478i
$105$	−12.7221	−	6.72106i	−1.24155	−	0.655909i
$106$	−2.63627	+	4.02035i	−0.256057	+	0.390491i
$107$	3.39951	−	12.6871i	0.328643	−	1.22651i	−0.581955	−	0.813221i	$-0.697712\pi$
$107$	3.39951	−	12.6871i	0.328643	−	1.22651i	0.910599	−	0.413292i	$-0.135621\pi$
$108$	0.225909	−	1.10956i	0.0217381	−	0.106768i
$109$	−4.36881	−	12.0032i	−0.418456	−	1.14970i	−0.952579	−	0.304292i	$-0.901580\pi$
$109$	−4.36881	−	12.0032i	−0.418456	−	1.14970i	0.534122	−	0.845407i	$-0.320642\pi$
$110$	13.3720	+	3.86000i	1.27497	+	0.368036i
$111$	−13.0554	+	15.5588i	−1.23916	+	1.47677i
$112$	−9.94110	+	4.01315i	−0.939346	+	0.379207i
$113$	−12.6528	−	12.6528i	−1.19027	−	1.19027i	−0.976991	−	0.213280i	$-0.931585\pi$
$113$	−12.6528	−	12.6528i	−1.19027	−	1.19027i	−0.213280	−	0.976991i	$-0.568415\pi$
$114$	−11.0965	+	9.79324i	−1.03928	+	0.917221i
$115$	0.920934	+	7.33868i	0.0858775	+	0.684336i
$116$	2.67879	−	9.03867i	0.248719	−	0.839220i
$117$	−14.8276	+	1.29725i	−1.37081	+	0.119931i
$118$	7.43700	−	2.96644i	0.684631	−	0.273083i
$119$	7.84122	−	2.85397i	0.718804	−	0.261623i
$120$	−2.01078	+	15.0507i	−0.183558	+	1.37394i
$121$	4.18552	+	7.24953i	0.380501	+	0.659048i
$122$	2.23577	+	10.7527i	0.202417	+	0.973506i
$123$	−3.95226	−	2.76740i	−0.356363	−	0.249528i
$124$	0.273335	+	4.47954i	0.0245462	+	0.402275i
$125$	−8.99226	+	6.64374i	−0.804292	+	0.594234i
$126$	9.35615	−	4.71505i	0.833512	−	0.420050i
$127$	0.432517	+	0.0378404i	0.0383797	+	0.00335779i	0.106329	−	0.994331i	$-0.466090\pi$
$127$	0.432517	+	0.0378404i	0.0383797	+	0.00335779i	−0.0679497	+	0.997689i	$0.521646\pi$
$128$	7.60275	+	8.37843i	0.671995	+	0.740556i
$129$	9.32354	−	25.6162i	0.820892	−	2.25538i
$130$	−16.8229	+	2.63397i	−1.47547	+	0.231014i
$131$	−3.06882	−	0.541116i	−0.268124	−	0.0472775i	0.0379695	−	0.999279i	$-0.487911\pi$
$131$	−3.06882	−	0.541116i	−0.268124	−	0.0472775i	−0.306094	+	0.952001i	$0.599022\pi$
$132$	−16.5413	+	13.1537i	−1.43973	+	1.14488i
$133$	11.4936	+	2.09200i	0.996625	+	0.181400i
$134$	−9.41463	−	0.535279i	−0.813300	−	0.0462411i
$135$	−0.0628873	+	1.26442i	−0.00541247	+	0.108824i
$136$	−5.68840	−	6.72234i	−0.487776	−	0.576436i
$137$	0.597624	−	0.278676i	0.0510584	−	0.0238089i	−0.396921	−	0.917853i	$-0.629921\pi$
$137$	0.597624	−	0.278676i	0.0510584	−	0.0238089i	0.447980	+	0.894044i	$0.352144\pi$
$138$	−9.89271	−	5.31646i	−0.842124	−	0.452567i
$139$	−6.04686	+	5.07392i	−0.512888	+	0.430364i	−0.862144	−	0.506663i	$-0.830879\pi$
$139$	−6.04686	+	5.07392i	−0.512888	+	0.430364i	0.349256	+	0.937027i	$0.386434\pi$
$140$	10.3121	−	6.10936i	0.871531	−	0.516335i
$141$	−0.332854	+	0.576521i	−0.0280314	+	0.0485518i
$142$	11.0135	−	13.9685i	0.924235	−	1.17221i
$143$	−19.4134	−	13.5934i	−1.62343	−	1.13674i
$144$	−8.08422	−	7.54300i	−0.673685	−	0.628583i
$145$	−1.43907	+	10.4413i	−0.119508	+	0.867104i
$146$	−2.23389	+	1.66788i	−0.184878	+	0.138035i
$147$	−0.398579	−	0.185861i	−0.0328743	−	0.0153295i
$148$	−5.36628	−	16.0458i	−0.441105	−	1.31895i
$149$	0.796092	−	0.948746i	0.0652184	−	0.0777243i	−0.732449	−	0.680822i	$-0.761623\pi$
$149$	0.796092	−	0.948746i	0.0652184	−	0.0777243i	0.797667	+	0.603098i	$0.206067\pi$
$150$	−0.311465	−	16.9739i	−0.0254310	−	1.38591i
$151$			13.6339i			1.10951i	0.832014	+	0.554754i	$0.187188\pi$
$151$			13.6339i			1.10951i	−0.832014	+	0.554754i	$0.812812\pi$
$152$	−2.12434	−	12.1444i	−0.172307	−	0.985043i
$153$	6.08544	+	6.08544i	0.491978	+	0.491978i
$154$	16.2377	+	3.82470i	1.30847	+	0.308203i
$155$	−1.05629	−	4.90515i	−0.0848434	−	0.393991i
$156$	11.5402	−	23.1376i	0.923952	−	1.85249i
$157$	−0.716848	+	1.53728i	−0.0572107	+	0.122689i	−0.932835	−	0.360305i	$-0.882673\pi$
$157$	−0.716848	+	1.53728i	−0.0572107	+	0.122689i	0.875624	+	0.482993i	$0.160450\pi$
$158$	−3.31300	+	22.8379i	−0.263568	+	1.81688i
$159$	4.08087	+	7.06828i	0.323634	+	0.560551i
$160$	−9.81381	−	7.98055i	−0.775849	−	0.630918i
$161$	1.53941	+	8.73044i	0.121323	+	0.688055i
$162$	−10.7188	−	8.45125i	−0.842147	−	0.663993i
$163$	4.27116	+	15.9402i	0.334543	+	1.24853i	0.904364	+	0.426762i	$0.140346\pi$
$163$	4.27116	+	15.9402i	0.334543	+	1.24853i	−0.569821	+	0.821769i	$0.692988\pi$
$164$	3.68610	−	1.60213i	0.287836	−	0.125105i
$165$	16.0683	−	17.3234i	1.25091	−	1.34863i
$166$	1.58463	+	5.26653i	0.122991	+	0.408762i
$167$	−0.0206845	−	0.0443580i	−0.00160061	−	0.00343252i	0.905506	−	0.424334i	$-0.139492\pi$
$167$	−0.0206845	−	0.0443580i	−0.00160061	−	0.00343252i	−0.907106	+	0.420901i	$0.861714\pi$
$168$	−1.51102	+	18.1372i	−0.116578	+	1.39932i
$169$	15.7518	+	2.77747i	1.21168	+	0.213652i
$170$	7.41908	+	6.47240i	0.569018	+	0.496411i
$171$	3.05428	+	11.6553i	0.233567	+	0.891299i
$172$	14.1339	+	17.7740i	1.07770	+	1.35525i
$173$	−4.64685	+	3.25376i	−0.353294	+	0.247379i	−0.736728	−	0.676189i	$-0.763630\pi$
$173$	−4.64685	+	3.25376i	−0.353294	+	0.247379i	0.383434	+	0.923568i	$0.374741\pi$
$174$	−11.6564	−	10.9668i	−0.883667	−	0.831391i
$175$	−10.3692	+	8.48873i	−0.783840	+	0.641688i
$176$	−2.14049	−	17.4744i	−0.161346	−	1.31718i
$177$	1.18470	−	13.5412i	0.0890475	−	1.01782i
$178$	−2.91320	+	8.83242i	−0.218353	+	0.662018i
$179$	8.01182	−	13.8769i	0.598832	−	1.03721i	−0.394162	−	0.919041i	$-0.628965\pi$
$179$	8.01182	−	13.8769i	0.598832	−	1.03721i	0.992994	−	0.118166i	$-0.0377014\pi$
$180$	10.2053	+	6.97610i	0.760659	+	0.519968i
$181$	1.98785	+	11.2737i	0.147756	+	0.837965i	0.965113	+	0.261834i	$0.0843272\pi$
$181$	1.98785	+	11.2737i	0.147756	+	0.837965i	−0.817357	+	0.576131i	$0.804562\pi$
$182$	−19.9822	+	4.15480i	−1.48118	+	0.307974i
$183$	18.0097	+	4.82569i	1.33132	+	0.356725i
$184$	8.08271	−	4.71136i	0.595865	−	0.347326i
$185$	8.63274	+	16.8317i	0.634691	+	1.23749i
$186$	7.00000	+	3.00803i	0.513265	+	0.220560i
$187$	1.19430	+	13.6509i	0.0873356	+	0.998251i
$188$	−0.264541	−	0.487391i	−0.0192936	−	0.0355466i
$189$			1.51740i			0.110375i
$190$	4.39264	+	13.0654i	0.318676	+	0.947864i
$191$			6.68271i			0.483544i	0.970333	+	0.241772i	$0.0777286\pi$
$191$			6.68271i			0.483544i	−0.970333	+	0.241772i	$0.922271\pi$
$192$	18.5106	−	5.12487i	1.33589	−	0.369856i
$193$	−0.196645	−	2.24766i	−0.0141548	−	0.161790i	0.985827	−	0.167763i	$-0.0536543\pi$
$193$	−0.196645	−	2.24766i	−0.0141548	−	0.161790i	−0.999982	+	0.00597286i	$0.998099\pi$
$194$	2.55735	−	5.95121i	0.183607	−	0.427272i
$195$	−8.85969	+	27.5166i	−0.634456	+	1.97050i
$196$	0.305526	−	0.202160i	0.0218233	−	0.0144400i
$197$	3.00380	+	0.804865i	0.214012	+	0.0573443i	0.364232	−	0.931308i	$-0.381332\pi$
$197$	3.00380	+	0.804865i	0.214012	+	0.0573443i	−0.150220	+	0.988653i	$0.547998\pi$
$198$	3.50248	+	16.8449i	0.248910	+	1.19711i
$199$	3.24236	+	18.3883i	0.229844	+	1.30351i	0.853204	+	0.521577i	$0.174656\pi$
$199$	3.24236	+	18.3883i	0.229844	+	1.30351i	−0.623359	+	0.781935i	$0.714233\pi$
$200$	12.1907	+	7.16853i	0.862010	+	0.506891i
$201$	−8.00438	+	13.8640i	−0.564586	+	0.977891i
$202$	20.0800	+	6.62299i	1.41283	+	0.465992i
$203$	−1.10106	+	12.5852i	−0.0772792	+	0.883305i
$204$	−14.5373	+	3.48790i	−1.01782	+	0.244202i
$205$	−3.80445	+	2.39140i	−0.265714	+	0.167023i
$206$	7.68672	−	8.17004i	0.535559	−	0.569234i
$207$	−7.48958	+	5.24426i	−0.520562	+	0.364501i
$208$	11.4085	+	18.2692i	0.791040	+	1.26674i
$209$	−8.20345	+	17.3422i	−0.567445	+	1.19959i
$210$	−1.38348	−	20.3012i	−0.0954694	−	1.40091i
$211$	14.0281	+	2.47353i	0.965734	+	0.170285i	0.634209	−	0.773161i	$-0.281326\pi$
$211$	14.0281	+	2.47353i	0.965734	+	0.170285i	0.331525	+	0.943446i	$0.392437\pi$
$212$	−6.79663	−	0.178952i	−0.466795	−	0.0122905i
$213$	−12.7624	−	27.3691i	−0.874466	−	1.87530i
$214$	17.7875	−	5.35205i	1.21593	−	0.365858i
$215$	−18.6144	−	17.2657i	−1.26949	−	1.17751i
$216$	1.50250	−	0.553932i	0.102232	−	0.0376903i
$217$	−1.55656	−	5.80915i	−0.105666	−	0.394351i
$218$	11.1847	−	14.1856i	0.757521	−	0.960769i
$219$	0.821851	+	4.66095i	0.0555356	+	0.314958i
$220$	5.30786	+	18.9538i	0.357856	+	1.27787i
$221$	−8.38243	−	14.5188i	−0.563863	−	0.976640i
$222$	−28.4259	−	4.12365i	−1.90782	−	0.276761i
$223$	7.17087	−	15.3780i	0.480197	−	1.02979i	−0.505743	−	0.862684i	$-0.668781\pi$
$223$	7.17087	−	15.3780i	0.480197	−	1.02979i	0.985940	−	0.167102i	$-0.0534408\pi$
$224$	−12.2234	−	8.96934i	−0.816713	−	0.599290i
$225$	−12.4543	−	5.99240i	−0.830285	−	0.399494i
$226$	5.80180	−	24.6314i	0.385930	−	1.63846i
$227$	−2.58965	−	2.58965i	−0.171881	−	0.171881i	0.615924	−	0.787806i	$-0.288783\pi$
$227$	−2.58965	−	2.58965i	−0.171881	−	0.171881i	−0.787806	+	0.615924i	$0.788783\pi$
$228$	−20.0345	−	6.05789i	−1.32682	−	0.401194i
$229$			23.8907i			1.57874i	0.613918	+	0.789370i	$0.289593\pi$
$229$			23.8907i			1.57874i	−0.613918	+	0.789370i	$0.710407\pi$
$230$	−8.14048	+	6.56821i	−0.536768	+	0.433095i
$231$	18.2042	−	21.6949i	1.19775	−	1.42742i
$232$	12.8635	−	3.50401i	0.844529	−	0.230050i
$233$	−0.465685	−	0.217152i	−0.0305080	−	0.0142261i	0.407304	−	0.913292i	$-0.366469\pi$
$233$	−0.465685	−	0.217152i	−0.0305080	−	0.0142261i	−0.437812	+	0.899066i	$0.644247\pi$
$234$	−12.5932	−	16.8669i	−0.823245	−	1.10262i
$235$	0.374451	+	0.494168i	0.0244265	+	0.0322359i
$236$	9.10136	+	6.73667i	0.592448	+	0.438520i
$237$	32.0919	+	22.4710i	2.08460	+	1.45965i
$238$	9.26688	+	7.30650i	0.600682	+	0.473610i
$239$	9.76471	−	16.9130i	0.631627	−	1.09401i	−0.355592	−	0.934641i	$-0.615721\pi$
$239$	9.76471	−	16.9130i	0.631627	−	1.09401i	0.987219	−	0.159369i	$-0.0509458\pi$
$240$	−19.5967	+	8.78090i	−1.26496	+	0.566805i
$241$	3.08135	−	2.58556i	0.198487	−	0.166550i	−0.538127	−	0.842864i	$-0.680868\pi$
$241$	3.08135	−	2.58556i	0.198487	−	0.166550i	0.736614	+	0.676313i	$0.236423\pi$
$242$	−5.60411	+	10.4280i	−0.360246	+	0.670334i
$243$	−19.4624	+	9.07545i	−1.24851	+	0.582190i
$244$	−11.2680	+	10.6898i	−0.721358	+	0.684346i
$245$	−0.303657	+	0.274883i	−0.0194000	+	0.0175616i
$246$	0.387322	−	6.81232i	0.0246947	−	0.434337i
$247$	0.129329	−	23.4709i	0.00822901	−	1.49342i
$248$	−5.18386	+	3.66192i	−0.329175	+	0.232532i
$249$	9.19495	+	1.62132i	0.582707	+	0.102747i
$250$	−14.6811	−	5.87084i	−0.928511	−	0.371304i
$251$	−7.47424	+	20.5353i	−0.471770	+	1.29618i	0.444558	+	0.895750i	$0.353361\pi$
$251$	−7.47424	+	20.5353i	−0.471770	+	1.29618i	−0.916328	+	0.400428i	$0.868862\pi$
$252$	12.6323	+	7.74358i	0.795761	+	0.487800i
$253$	−14.5026	−	1.26882i	−0.911773	−	0.0797698i
$254$	0.276325	+	0.548316i	0.0173382	+	0.0344044i
$255$	15.4807	−	6.30264i	0.969438	−	0.394687i
$256$	−4.41903	+	15.3777i	−0.276189	+	0.961103i
$257$	−21.8482	−	15.2983i	−1.36285	−	0.954279i	−0.999746	−	0.0225314i	$-0.992827\pi$
$257$	−21.8482	−	15.2983i	−1.36285	−	0.954279i	−0.363106	−	0.931748i	$-0.618284\pi$
$258$	37.7445	−	7.84803i	2.34987	−	0.488597i
$259$	11.3366	+	19.6355i	0.704419	+	1.22009i
$260$	−15.6855	−	18.2719i	−0.972773	−	1.13317i
$261$	−12.2436	+	4.45630i	−0.757860	+	0.275838i
$262$	−1.63272	−	4.09331i	−0.100870	−	0.252885i
$263$	22.5835	−	1.97580i	1.39256	−	0.121833i	0.633946	−	0.773378i	$-0.281434\pi$
$263$	22.5835	−	1.97580i	1.39256	−	0.121833i	0.758610	+	0.651545i	$0.225879\pi$
$264$	−28.1273	−	10.1056i	−1.73111	−	0.621954i
$265$	7.54235	−	0.946491i	0.463323	−	0.0581425i
$266$	6.03642	+	15.3793i	0.370117	+	0.942964i
$267$	11.1646	+	11.1646i	0.683262	+	0.683262i
$268$	−6.36161	−	11.7206i	−0.388597	−	0.715952i
$269$	−17.1451	+	20.4327i	−1.04535	+	1.24580i	−0.0767881	+	0.997047i	$0.524467\pi$
$269$	−17.1451	+	20.4327i	−1.04535	+	1.24580i	−0.968566	+	0.248757i	$0.919978\pi$
$270$	−1.56743	+	0.865214i	−0.0953905	+	0.0526552i
$271$	−4.60802	−	12.6604i	−0.279917	−	0.769067i	−0.997371	−	0.0724607i	$-0.976915\pi$
$271$	−4.60802	−	12.6604i	−0.279917	−	0.769067i	0.717454	−	0.696606i	$-0.245307\pi$
$272$	3.85182	−	11.8431i	0.233551	−	0.718094i
$273$	−8.96775	+	33.4681i	−0.542753	+	2.02558i
$274$	0.779833	+	0.511361i	0.0471114	+	0.0308924i
$275$	−9.05777	−	20.0557i	−0.546204	−	1.20941i
$276$	−0.967342	−	15.8532i	−0.0582271	−	0.954253i
$277$	−1.85886	−	6.93737i	−0.111688	−	0.416826i	0.887330	−	0.461136i	$-0.152558\pi$
$277$	−1.85886	−	6.93737i	−0.111688	−	0.416826i	−0.999018	+	0.0443094i	$0.985891\pi$
$278$	−10.6015	−	3.49669i	−0.635835	−	0.209717i
$279$	4.75151	−	3.98699i	0.284465	−	0.238695i
$280$	15.0205	+	7.85574i	0.897645	+	0.469470i
$281$	0.330669	+	0.120354i	0.0197261	+	0.00717970i	0.351864	−	0.936051i	$-0.385548\pi$
$281$	0.330669	+	0.120354i	0.0197261	+	0.00717970i	−0.332138	+	0.943231i	$0.607770\pi$
$282$	−0.941017	+	0.0286831i	−0.0560368	+	0.00170805i
$283$	15.1747	+	21.6717i	0.902041	+	1.28825i	0.957098	+	0.289765i	$0.0935770\pi$
$283$	15.1747	+	21.6717i	0.902041	+	1.28825i	−0.0550572	+	0.998483i	$0.517534\pi$
$284$	24.9941	+	2.85136i	1.48313	+	0.169197i
$285$	23.1637	+	3.32269i	1.37210	+	0.196819i
$286$	1.90251	−	33.4619i	0.112498	−	1.97864i
$287$	−4.41199	+	3.08931i	−0.260432	+	0.182356i
$288$	3.05605	−	15.3350i	0.180079	−	0.903626i
$289$	2.49898	−	6.86589i	0.146999	−	0.403876i
$290$	−13.6279	+	6.03863i	−0.800256	+	0.354601i
$291$	−7.06844	−	8.42383i	−0.414359	−	0.493814i
$292$	−3.66807	−	1.44550i	−0.214657	−	0.0845914i
$293$	3.84290	−	1.02970i	0.224505	−	0.0601559i	−0.144813	−	0.989459i	$-0.546258\pi$
$293$	3.84290	−	1.02970i	0.224505	−	0.0601559i	0.369318	+	0.929303i	$0.379591\pi$
$294$	−0.0730578	−	0.617642i	−0.00426082	−	0.0360216i
$295$	−11.1938	−	5.91363i	−0.651727	−	0.344305i
$296$	15.3042	−	18.3932i	0.889536	−	1.06908i
$297$	−2.40692	−	0.644933i	−0.139664	−	0.0374228i
$298$	1.73336	+	0.251452i	0.100411	+	0.0145662i
$299$	16.7368	−	6.09169i	0.967914	−	0.352292i
$300$	20.1816	−	13.0047i	1.16518	−	0.750827i
$301$	−23.3116	−	19.5608i	−1.34366	−	1.12746i
$302$	−16.3965	+	10.1449i	−0.943515	+	0.583771i
$303$	25.3821	−	25.3821i	1.45816	−	1.45816i
$304$	13.0246	−	11.5914i	0.747011	−	0.664811i
$305$	10.6546	−	13.7124i	0.610079	−	0.785169i
$306$	−2.79042	+	11.8467i	−0.159518	+	0.677229i
$307$	0.489823	+	5.59870i	0.0279557	+	0.319535i	0.997278	+	0.0737398i	$0.0234934\pi$
$307$	0.489823	+	5.59870i	0.0279557	+	0.319535i	−0.969322	+	0.245795i	$0.920951\pi$
$308$	7.48264	+	22.3739i	0.426363	+	1.27487i
$309$	−6.51338	−	17.8954i	−0.370534	−	1.01803i
$310$	5.11312	−	4.92022i	0.290406	−	0.279450i
$311$	−20.7872	+	12.0015i	−1.17874	+	0.680544i	−0.955722	−	0.294271i	$-0.904923\pi$
$311$	−20.7872	+	12.0015i	−1.17874	+	0.680544i	−0.223014	+	0.974815i	$0.571590\pi$
$312$	36.4130	−	3.33798i	2.06148	−	0.188976i
$313$	11.3379	−	16.1922i	0.640854	−	0.915235i	−0.358982	−	0.933345i	$-0.616876\pi$
$313$	11.3379	−	16.1922i	0.640854	−	0.915235i	0.999836	+	0.0181096i	$0.00576479\pi$
$314$	−2.38219	+	0.281777i	−0.134435	+	0.0159016i
$315$	−15.2660	−	6.43208i	−0.860143	−	0.362407i
$316$	−29.9307	+	13.0091i	−1.68374	+	0.731822i
$317$	0.101031	−	1.15479i	0.00567445	−	0.0648592i	−0.992829	−	0.119539i	$-0.961858\pi$
$317$	0.101031	−	1.15479i	0.00567445	−	0.0648592i	0.998504	+	0.0546799i	$0.0174139\pi$
$318$	−5.46400	+	10.1673i	−0.306406	+	0.570151i
$319$	−19.4948	−	7.09552i	−1.09150	−	0.397273i
$320$	2.29530	−	17.7407i	0.128311	−	0.991734i
$321$	5.47595	−	31.0556i	0.305638	−	1.73336i
$322$	−9.35405	+	8.34760i	−0.521281	+	0.465194i
$323$	−10.4440	+	8.66595i	−0.581120	+	0.482186i
$324$	2.18799	−	19.1793i	0.121555	−	1.06552i
$325$	20.4132	+	17.5548i	1.13232	+	0.973766i
$326$	−15.9920	+	16.9976i	−0.885717	+	0.941410i
$327$	−12.9607	−	27.7943i	−0.716729	−	1.53703i
$328$	4.66957	+	3.24089i	0.257834	+	0.178948i
$329$	0.477684	+	0.569282i	0.0263356	+	0.0313855i
$330$	32.7900	+	6.43400i	1.80503	+	0.354180i
$331$	−12.0851	−	6.97732i	−0.664256	−	0.383508i	0.129641	−	0.991561i	$-0.458618\pi$
$331$	−12.0851	−	6.97732i	−0.664256	−	0.383508i	−0.793897	+	0.608053i	$0.791951\pi$
$332$	−5.15459	+	5.82452i	−0.282895	+	0.319662i
$333$	−13.4125	+	19.1551i	−0.735003	+	1.04969i
$334$	0.0379552	−	0.0578823i	0.00207682	−	0.00316718i
$335$	9.00468	+	11.8836i	0.491978	+	0.649270i
$336$	−22.9367	+	11.6786i	−1.25130	+	0.637117i
$337$	8.66752	−	18.5876i	0.472150	−	1.01253i	−0.515650	−	0.856799i	$-0.672449\pi$
$337$	8.66752	−	18.5876i	0.472150	−	1.01253i	0.987800	−	0.155729i	$-0.0497728\pi$
$338$	8.38054	+	21.0104i	0.455841	+	1.14281i
$339$	−32.9096	−	27.6145i	−1.78741	−	1.49981i
$340$	−2.26344	+	13.7385i	−0.122753	+	0.745075i
$341$	9.87614			0.534823
$342$	−11.7443	+	12.3458i	−0.635060	+	0.667583i
$343$	12.9189	−	12.9189i	0.697555	−	0.697555i
$344$	−10.8586	+	30.2233i	−0.585458	+	1.62953i
$345$	3.73825	+	17.3595i	0.201261	+	0.934603i
$346$	−7.37077	−	3.16736i	−0.396255	−	0.170278i
$347$	−5.45074	−	2.54172i	−0.292611	−	0.136447i	0.270770	−	0.962644i	$-0.412722\pi$
$347$	−5.45074	−	2.54172i	−0.292611	−	0.136447i	−0.563381	+	0.826197i	$0.690500\pi$
$348$	4.51561	−	22.1787i	0.242062	−	1.18890i
$349$	−4.65934	+	2.69007i	−0.249409	+	0.143996i	−0.619493	−	0.785002i	$-0.712662\pi$
$349$	−4.65934	+	2.69007i	−0.249409	+	0.143996i	0.370085	+	0.928998i	$0.379329\pi$
$350$	−17.9245	−	6.15397i	−0.958104	−	0.328944i
$351$	3.00230	−	0.529386i	0.160251	−	0.0282565i
$352$	19.4226	−	15.5768i	1.03523	−	0.830246i
$353$	7.45334	−	1.99712i	0.396701	−	0.106296i	−0.0549528	−	0.998489i	$-0.517501\pi$
$353$	7.45334	−	1.99712i	0.396701	−	0.106296i	0.451654	+	0.892193i	$0.350834\pi$
$354$	17.1666	−	8.65113i	0.912395	−	0.459803i
$355$	−28.1057	+	1.05646i	−1.49169	+	0.0560713i
$356$	−12.7898	+	3.06863i	−0.677861	+	0.162637i
$357$	18.1569	−	8.46672i	0.960967	−	0.448106i
$358$	22.6503	−	0.690403i	1.19711	−	0.0364889i
$359$	4.13448	−	23.4478i	0.218210	−	1.23753i	−0.657040	−	0.753856i	$-0.728192\pi$
$359$	4.13448	−	23.4478i	0.218210	−	1.23753i	0.875249	−	0.483672i	$-0.160697\pi$
$360$	−0.795991	+	17.4641i	−0.0419524	+	0.920439i
$361$	−18.7466	+	3.09292i	−0.986662	+	0.162785i
$362$	−12.0789	+	10.7793i	−0.634855	+	0.566548i
$363$	11.5276	+	16.4631i	0.605042	+	0.864090i
$364$	−19.8653	−	20.9397i	−1.04122	−	1.09754i
$365$	4.29763	+	0.980130i	0.224948	+	0.0513024i
$366$	7.59737	+	25.2498i	0.397121	+	1.31983i
$367$	17.3024	+	1.51376i	0.903175	+	0.0790176i	0.529274	−	0.848451i	$-0.322464\pi$
$367$	17.3024	+	1.51376i	0.903175	+	0.0790176i	0.373901	+	0.927469i	$0.378020\pi$
$368$	11.6803	+	6.21484i	0.608879	+	0.323971i
$369$	−4.81071	−	2.77747i	−0.250436	−	0.144589i
$370$	−13.8188	+	22.9063i	−0.718403	+	1.19084i
$371$	8.97272	−	1.58213i	0.465840	−	0.0821402i
$372$	1.59109	+	10.6567i	0.0824941	+	0.552523i
$373$	−2.94207	+	10.9800i	−0.152335	+	0.568521i	0.846984	+	0.531618i	$0.178416\pi$
$373$	−2.94207	+	10.9800i	−0.152335	+	0.568521i	−0.999319	+	0.0369029i	$0.988251\pi$
$374$	−15.5283	+	11.5938i	−0.802950	+	0.599502i
$375$	−20.1169	+	17.7717i	−1.03883	+	0.917726i
$376$	0.389310	−	0.680810i	0.0200771	−	0.0351101i
$377$	25.2849	−	2.21214i	1.30224	−	0.113931i
$378$	−1.82488	+	1.12909i	−0.0938616	+	0.0580740i
$379$	−4.30222			−0.220990			−0.110495	−	0.993877i	$-0.535244\pi$
$379$	−4.30222			−0.220990			−0.110495	+	0.993877i	$0.535244\pi$
$380$	−12.4444	+	15.0046i	−0.638382	+	0.769720i
$381$	1.04239			0.0534030
$382$	−8.03685	+	4.97256i	−0.411201	+	0.254418i
$383$	−24.9011	+	2.17857i	−1.27239	+	0.111319i	−0.703262	−	0.710931i	$-0.748274\pi$
$383$	−24.9011	+	2.17857i	−1.27239	+	0.111319i	−0.569126	+	0.822251i	$0.692718\pi$
$384$	19.9370	+	18.4481i	1.01740	+	0.941427i
$385$	−12.0373	−	23.4698i	−0.613479	−	1.19613i
$386$	2.55679	−	1.90896i	0.130137	−	0.0971634i
$387$	8.12313	−	30.3159i	0.412922	−	1.54104i
$388$	9.06003	−	1.35270i	0.459953	−	0.0686730i
$389$	33.2089	−	5.85562i	1.68376	−	0.296892i	0.751781	−	0.659413i	$-0.229195\pi$
$389$	33.2089	−	5.85562i	1.68376	−	0.296892i	0.931975	+	0.362522i	$0.118084\pi$
$390$	−39.6848	+	9.81994i	−2.00952	+	0.497252i
$391$	−8.91860	−	5.14916i	−0.451033	−	0.260404i
$392$	0.470464	+	0.217010i	0.0237620	+	0.0109606i
$393$	−7.45304	−	0.652057i	−0.375956	−	0.0328919i
$394$	1.26715	+	4.21136i	0.0638379	+	0.212165i
$395$	30.8918	−	19.4180i	1.55433	−	0.977024i
$396$	−17.6520	+	16.7463i	−0.887048	+	0.841535i
$397$	−2.09332	−	2.98957i	−0.105061	−	0.150042i	0.763179	−	0.646187i	$-0.223637\pi$
$397$	−2.09332	−	2.98957i	−0.105061	−	0.150042i	−0.868240	+	0.496145i	$0.834749\pi$
$398$	−19.7018	+	17.5820i	−0.987561	+	0.881305i
$399$	27.9275	+	2.59848i	1.39812	+	0.130087i
$400$	0.449874	+	19.9949i	0.0224937	+	0.999747i
$401$	−6.47234	+	36.7065i	−0.323213	+	1.83303i	0.198731	+	0.980054i	$0.436318\pi$
$401$	−6.47234	+	36.7065i	−0.323213	+	1.83303i	−0.521944	+	0.852980i	$0.674793\pi$
$402$	−22.6293	+	0.689762i	−1.12865	+	0.0344022i
$403$	−10.9508	+	5.10645i	−0.545499	+	0.254370i
$404$	6.97636	+	29.0770i	0.347087	+	1.44664i
$405$	0.810679	+	21.5669i	0.0402830	+	1.07167i
$406$	−15.9546	+	8.04035i	−0.791814	+	0.399036i
$407$	−35.9644	+	9.63664i	−1.78269	+	0.477670i
$408$	−15.0118	−	14.8878i	−0.743195	−	0.737055i
$409$	−14.9370	+	2.63379i	−0.738586	+	0.130233i	−0.530270	−	0.847829i	$-0.677909\pi$
$409$	−14.9370	+	2.63379i	−0.738586	+	0.130233i	−0.208316	+	0.978062i	$0.566798\pi$
$410$	−5.70685	−	2.79593i	−0.281841	−	0.138081i
$411$	1.37104	−	0.791573i	0.0676286	−	0.0390454i
$412$	15.5452	+	3.16503i	0.765857	+	0.155930i
$413$	−13.7524	−	6.41283i	−0.676710	−	0.315555i
$414$	−11.8799	−	5.10500i	−0.583864	−	0.250897i
$415$	4.71667	−	7.30558i	0.231532	−	0.358617i
$416$	−13.4821	+	27.3142i	−0.661013	+	1.33919i
$417$	−13.4008	+	13.4008i	−0.656239	+	0.656239i
$418$	−26.9605	+	3.03848i	−1.31868	+	0.148617i
$419$	−12.2723			−0.599543			−0.299771	−	0.954011i	$-0.596910\pi$
$419$	−12.2723			−0.599543			−0.299771	+	0.954011i	$0.596910\pi$
$420$	23.3854	−	16.7698i	1.14109	−	0.818281i
$421$	10.6372	+	8.92567i	0.518425	+	0.435011i	0.864082	−	0.503350i	$-0.167899\pi$
$421$	10.6372	+	8.92567i	0.518425	+	0.435011i	−0.345657	+	0.938361i	$0.612344\pi$
$422$	7.46345	+	18.7112i	0.363315	+	0.910847i
$423$	−0.323915	+	0.694637i	−0.0157493	+	0.0337744i
$424$	−4.84211	−	8.30701i	−0.235154	−	0.403424i
$425$	0.188730	−	15.5660i	0.00915476	−	0.755063i
$426$	23.4186	−	35.7136i	1.13463	−	1.73033i
$427$	11.9383	−	17.0497i	0.577737	−	0.825094i
$428$	19.6721	+	17.4095i	0.950888	+	0.841518i
$429$	−49.2761	−	28.4496i	−2.37907	−	1.37356i
$430$	6.91347	−	35.2336i	0.333397	−	1.69911i
$431$	1.14111	+	1.35992i	0.0549654	+	0.0655052i	0.792827	−	0.609447i	$-0.208609\pi$
$431$	1.14111	+	1.35992i	0.0549654	+	0.0655052i	−0.737861	+	0.674952i	$0.764164\pi$
$432$	1.78417	+	1.39477i	0.0858411	+	0.0671061i
$433$	−6.97413	−	14.9561i	−0.335155	−	0.718742i	0.664436	−	0.747345i	$-0.268672\pi$
$433$	−6.97413	−	14.9561i	−0.335155	−	0.718742i	−0.999591	+	0.0286030i	$0.990894\pi$
$434$	5.82806	−	6.19451i	0.279756	−	0.297346i
$435$	−1.25703	+	25.2740i	−0.0602700	+	1.21179i
$436$	25.3825	+	2.89566i	1.21560	+	0.138677i
$437$	−7.14006	−	12.5258i	−0.341555	−	0.599192i
$438$	−4.99388	+	4.45656i	−0.238617	+	0.212943i
$439$	1.04634	−	5.93407i	0.0499389	−	0.283218i	−0.949604	−	0.313452i	$-0.898514\pi$
$439$	1.04634	−	5.93407i	0.0499389	−	0.283218i	0.999543	+	0.0302347i	$0.00962546\pi$
$440$	−18.8450	+	20.4868i	−0.898398	+	0.976670i
$441$	−0.475798	−	0.173176i	−0.0226571	−	0.00824649i
$442$	11.2235	−	20.8843i	0.533847	−	0.993366i
$443$	2.65088	−	30.2997i	0.125947	−	1.43958i	−0.625725	−	0.780044i	$-0.715197\pi$
$443$	2.65088	−	30.2997i	0.125947	−	1.43958i	0.751672	−	0.659537i	$-0.229248\pi$
$444$	−16.1923	−	37.2543i	−0.768452	−	1.76801i
$445$	13.6198	−	5.54501i	0.645640	−	0.262859i
$446$	23.8299	−	2.81872i	1.12838	−	0.133470i
$447$	1.70552	−	2.43573i	0.0806682	−	0.115206i
$448$	1.69146	−	21.3743i	0.0799139	−	1.00984i
$449$	21.7809	−	12.5752i	1.02791	−	0.593462i	0.111522	−	0.993762i	$-0.464428\pi$
$449$	21.7809	−	12.5752i	1.02791	−	0.593462i	0.916384	+	0.400300i	$0.131094\pi$
$450$	−2.06047	−	19.4368i	−0.0971314	−	0.916261i
$451$	−3.02510	−	8.31140i	−0.142446	−	0.391368i
$452$	33.9397	−	11.3506i	1.59639	−	0.533889i
$453$	2.85288	+	32.6086i	0.134040	+	1.53209i
$454$	1.18746	−	5.04135i	0.0557303	−	0.236602i
$455$	25.4822	+	19.7998i	1.19463	+	0.928228i
$456$	−7.62207	−	28.6017i	−0.356936	−	1.33940i
$457$	−20.5277	+	20.5277i	−0.960245	+	0.960245i	−0.999239	−	0.0389946i	$-0.987584\pi$
$457$	−20.5277	+	20.5277i	−0.960245	+	0.960245i	0.0389946	+	0.999239i	$0.487584\pi$
$458$	−28.7317	+	17.7769i	−1.34254	+	0.830659i
$459$	−1.35032	−	1.13305i	−0.0630274	−	0.0528863i
$460$	−13.9564	−	4.90266i	−0.650721	−	0.228588i
$461$	−13.0158	+	4.73738i	−0.606208	+	0.220642i	−0.626843	−	0.779145i	$-0.715653\pi$
$461$	−13.0158	+	4.73738i	−0.606208	+	0.220642i	0.0206351	+	0.999787i	$0.493431\pi$
$462$	39.6366	+	5.74994i	1.84406	+	0.267511i
$463$	1.25910	+	0.337376i	0.0585155	+	0.0156792i	0.287958	−	0.957643i	$-0.407024\pi$
$463$	1.25910	+	0.337376i	0.0585155	+	0.0156792i	−0.229443	+	0.973322i	$0.573690\pi$
$464$	13.7857	+	12.8627i	0.639983	+	0.597137i
$465$	−3.55277	−	11.5108i	−0.164756	−	0.533800i
$466$	−0.0853580	−	0.721630i	−0.00395413	−	0.0334288i
$467$	15.6135	−	4.18363i	0.722507	−	0.193595i	0.121217	−	0.992626i	$-0.461320\pi$
$467$	15.6135	−	4.18363i	0.722507	−	0.193595i	0.601290	+	0.799031i	$0.294654\pi$
$468$	10.9142	−	27.6956i	0.504508	−	1.28023i
$469$	11.4872	+	13.6899i	0.530430	+	0.632142i
$470$	−0.315676	+	0.818033i	−0.0145611	+	0.0377331i
$471$	−1.39283	+	3.82678i	−0.0641784	+	0.176329i
$472$	−1.32949	+	15.9583i	−0.0611948	+	0.734540i
$473$	40.9356	−	28.6634i	1.88222	−	1.31794i
$474$	−3.14502	+	55.3153i	−0.144455	+	2.54072i
$475$	11.2284	−	18.6795i	0.515193	−	0.857074i
$476$	−1.89162	+	16.5814i	−0.0867022	+	0.760006i
$477$	5.38980	+	7.69743i	0.246782	+	0.352441i
$478$	27.6060	−	0.841455i	1.26267	−	0.0384873i
$479$	−19.9614	−	7.26534i	−0.912057	−	0.331962i	−0.156983	−	0.987601i	$-0.550177\pi$
$479$	−19.9614	−	7.26534i	−0.912057	−	0.331962i	−0.755074	+	0.655639i	$0.772399\pi$
$480$	−25.1420	−	17.0338i	−1.14757	−	0.777485i
$481$	34.8953	−	29.2806i	1.59109	−	1.33508i
$482$	5.40229	+	1.78184i	0.246067	+	0.0811605i
$483$	5.50871	+	20.5588i	0.250655	+	0.935456i
$484$	−16.7110	+	1.01968i	−0.759590	+	0.0463491i
$485$	−9.78617	+	3.02047i	−0.444367	+	0.137152i
$486$	−25.3962	−	16.6531i	−1.15200	−	0.755400i
$487$	9.22284	−	34.4201i	0.417927	−	1.55972i	−0.360974	−	0.932576i	$-0.617556\pi$
$487$	9.22284	−	34.4201i	0.417927	−	1.55972i	0.778900	−	0.627148i	$-0.215778\pi$
$488$	−21.2404	−	5.59701i	−0.961506	−	0.253365i
$489$	13.5510	+	37.2309i	0.612795	+	1.68364i
$490$	−0.556532	−	0.160650i	−0.0251416	−	0.00725742i
$491$	5.06349	−	6.03444i	0.228512	−	0.272330i	−0.639589	−	0.768717i	$-0.720896\pi$
$491$	5.06349	−	6.03444i	0.228512	−	0.272330i	0.868102	+	0.496386i	$0.165340\pi$
$492$	8.48092	−	4.60319i	0.382349	−	0.207528i
$493$	−10.3772	−	10.3772i	−0.467366	−	0.467366i
$494$	28.3232	−	17.3090i	1.27432	−	0.778769i
$495$	16.6911	−	21.4814i	0.750209	−	0.965516i
$496$	−8.26121	−	3.50948i	−0.370939	−	0.157580i
$497$	−33.5829	+	2.93812i	−1.50640	+	0.131793i
$498$	4.89205	+	12.2646i	0.219218	+	0.549588i
$499$	−18.5661	+	6.75751i	−0.831133	+	0.302508i	−0.722324	−	0.691555i	$-0.756926\pi$
$499$	−18.5661	+	6.75751i	−0.831133	+	0.302508i	−0.108809	+	0.994063i	$0.534704\pi$
$500$	−3.86360	−	22.0244i	−0.172785	−	0.984960i
$501$	−0.0587537	−	0.101764i	−0.00262492	−	0.00454650i
$502$	−30.2580	+	6.29140i	−1.35048	+	0.280799i
$503$	−9.27591	−	6.49506i	−0.413592	−	0.289601i	0.348202	−	0.937420i	$-0.386792\pi$
$503$	−9.27591	−	6.49506i	−0.413592	−	0.289601i	−0.761794	+	0.647819i	$0.775681\pi$
$504$	0.0869175	+	20.9540i	0.00387161	+	0.933364i
$505$	−12.6063	−	30.9638i	−0.560972	−	1.37787i
$506$	−9.26538	−	18.3855i	−0.411896	−	0.817333i
$507$	38.2554	+	3.34691i	1.69898	+	0.148642i
$508$	−0.453812	+	0.740315i	−0.0201347	+	0.0328462i
$509$	−1.12631	+	3.09452i	−0.0499230	+	0.137162i	−0.962148	−	0.272527i	$-0.912141\pi$
$509$	−1.12631	+	3.09452i	−0.0499230	+	0.137162i	0.912225	+	0.409689i	$0.134363\pi$
$510$	19.0988	+	13.9278i	0.845710	+	0.616735i
$511$	5.20312	+	0.917451i	0.230172	+	0.0405856i
$512$	−21.7818	+	6.12793i	−0.962630	+	0.270819i
$513$	−0.831264	−	2.32364i	−0.0367012	−	0.102591i
$514$	2.14113	−	37.6587i	0.0944410	−	1.66105i
$515$	−17.7147	−	0.881062i	−0.780604	−	0.0388242i
$516$	37.5237	+	39.5531i	1.65189	+	1.74123i
$517$	−1.10603	+	0.515751i	−0.0486432	+	0.0226827i
$518$	−15.1788	+	28.2443i	−0.666920	+	1.24099i
$519$	−10.4332	+	8.75449i	−0.457966	+	0.384279i
$520$	10.3029	−	32.4599i	0.451812	−	1.42346i
$521$	3.55819	−	6.16297i	0.155887	−	0.270005i	−0.777495	−	0.628890i	$-0.783510\pi$
$521$	3.55819	−	6.16297i	0.155887	−	0.270005i	0.933382	+	0.358885i	$0.116843\pi$
$522$	−14.4697	−	11.4087i	−0.633320	−	0.499343i
$523$	33.2354	+	23.2717i	1.45328	+	1.01760i	0.991429	+	0.130643i	$0.0417042\pi$
$523$	33.2354	+	23.2717i	1.45328	+	1.01760i	0.461853	+	0.886956i	$0.347185\pi$
$524$	3.70785	−	5.00937i	0.161978	−	0.218835i
$525$	−23.0242	+	22.4726i	−1.00486	+	0.980783i
$526$	19.1803	+	25.6894i	0.836303	+	1.12011i
$527$	6.33179	+	2.95256i	0.275817	+	0.128616i
$528$	−8.77601	−	41.3463i	−0.381927	−	1.79936i
$529$	−7.75145	+	9.23782i	−0.337020	+	0.401644i
$530$	6.75048	+	8.36640i	0.293222	+	0.363413i
$531$		−	15.6499i		−	0.679146i
$532$	−14.0040	+	18.7032i	−0.607149	+	0.810887i
$533$	7.65168	+	7.65168i	0.331431	+	0.331431i
$534$	−5.11942	+	21.7344i	−0.221539	+	0.940539i
$535$	−24.6744	−	15.9304i	−1.06677	−	0.688731i
$536$	9.36200	−	16.3719i	0.404377	−	0.707159i
$537$	16.2584	−	34.8663i	0.701603	−	1.50459i
$538$	−37.3306	−	5.41541i	−1.60944	−	0.233475i
$539$	−0.403103	−	0.698195i	−0.0173629	−	0.0300734i
$540$	−2.20684	−	1.24124i	−0.0949674	−	0.0534144i
$541$	0.892552	+	5.06192i	0.0383738	+	0.217629i	0.997965	−	0.0637705i	$-0.0203126\pi$
$541$	0.892552	+	5.06192i	0.0383738	+	0.217629i	−0.959591	+	0.281399i	$0.909201\pi$
$542$	11.7971	−	14.9623i	0.506727	−	0.642686i
$543$	7.11343	+	26.5477i	0.305266	+	1.13927i
$544$	17.1090	−	4.18004i	0.733543	−	0.179218i
$545$	−28.5424	+	1.07288i	−1.22262	+	0.0459571i
$546$	−46.9227	+	14.1185i	−2.00811	+	0.604214i
$547$	18.6470	+	39.9887i	0.797289	+	1.70979i	0.699555	+	0.714579i	$0.253382\pi$
$547$	18.6470	+	39.9887i	0.797289	+	1.70979i	0.0977341	+	0.995213i	$0.468841\pi$
$548$	−0.0347117	+	1.31835i	−0.00148281	+	0.0563172i
$549$	21.1404	+	3.72762i	0.902249	+	0.159091i
$550$	17.3799	−	25.8165i	0.741080	−	1.10082i
$551$	−5.20833	−	19.8752i	−0.221882	−	0.846711i
$552$	18.3458	−	12.9596i	0.780851	−	0.551599i
$553$	35.8249	−	25.0849i	1.52343	−	1.06672i
$554$	6.95995	−	7.39758i	0.295700	−	0.314293i
$555$	24.1692	+	38.4505i	1.02593	+	1.63213i
$556$	−3.68325	−	15.3516i	−0.156205	−	0.651051i
$557$	−3.43824	+	39.2992i	−0.145683	+	1.66516i	0.474162	+	0.880438i	$0.342751\pi$
$557$	−3.43824	+	39.2992i	−0.145683	+	1.66516i	−0.619845	+	0.784725i	$0.712804\pi$
$558$	8.33045	+	2.74763i	0.352656	+	0.116317i
$559$	−30.5696	+	52.9482i	−1.29296	+	2.23947i
$560$	1.72905	+	23.9095i	0.0730657	+	1.01036i
$561$	5.71288	+	32.3994i	0.241198	+	1.36790i
$562$	0.101307	+	0.487228i	0.00427338	+	0.0205525i
$563$	−12.5732	−	3.36897i	−0.529896	−	0.141985i	−0.0160556	−	0.999871i	$-0.505111\pi$
$563$	−12.5732	−	3.36897i	−0.529896	−	0.141985i	−0.513840	+	0.857886i	$0.671778\pi$
$564$	−0.734699	−	1.11036i	−0.0309364	−	0.0467544i
$565$	−35.6020	+	18.2598i	−1.49779	+	0.768195i
$566$	−14.7717	+	34.3753i	−0.620902	+	1.44490i
$567$	2.25457	+	25.7699i	0.0946832	+	1.08223i
$568$	15.1688	+	32.1804i	0.636469	+	1.35026i
$569$		−	40.2912i		−	1.68910i	−0.535480	−	0.844548i	$-0.679869\pi$
$569$		−	40.2912i		−	1.68910i	0.535480	−	0.844548i	$-0.320131\pi$
$570$	13.2400	+	30.3298i	0.554561	+	1.27038i
$571$			27.2858i			1.14188i	0.820993	+	0.570938i	$0.193420\pi$
$571$			27.2858i			1.14188i	−0.820993	+	0.570938i	$0.806580\pi$
$572$	41.6581	−	22.6107i	1.74181	−	0.945402i
$573$	1.39836	+	15.9833i	0.0584171	+	0.667711i
$574$	−6.99823	−	3.00727i	−0.292101	−	0.125521i
$575$	16.2512	+	3.06913i	0.677723	+	0.127992i
$576$	20.7164	−	7.73538i	0.863184	−	0.322308i
$577$	−23.1467	−	6.20215i	−0.963612	−	0.258199i	−0.257483	−	0.966283i	$-0.582893\pi$
$577$	−23.1467	−	6.20215i	−0.963612	−	0.258199i	−0.706128	+	0.708084i	$0.749560\pi$
$578$	10.1166	−	2.10350i	0.420796	−	0.0874941i
$579$	−0.940644	−	5.33466i	−0.0390919	−	0.221701i
$580$	−17.4027	−	11.8960i	−0.722606	−	0.493956i
$581$	5.21144	−	9.02647i	0.216207	−	0.374481i
$582$	4.87121	−	14.7688i	0.201918	−	0.612188i
$583$	−1.30403	+	14.9051i	−0.0540073	+	0.617306i
$584$	−0.990978	−	5.48693i	−0.0410070	−	0.227051i
$585$	−7.40043	+	32.4490i	−0.305970	+	1.34160i
$586$	4.09783	+	3.85541i	0.169280	+	0.159265i
$587$	−7.00499	+	4.90494i	−0.289127	+	0.202449i	−0.709137	−	0.705071i	$-0.750915\pi$
$587$	−7.00499	+	4.90494i	−0.289127	+	0.202449i	0.420010	+	0.907519i	$0.362026\pi$
$588$	0.688435	−	0.547445i	0.0283906	−	0.0225762i
$589$	5.56597	+	8.04300i	0.229342	+	0.331406i
$590$	−1.21728	−	17.8623i	−0.0501146	−	0.735379i
$591$	7.35271	+	1.29648i	0.302450	+	0.0533301i
$592$	33.5080	+	4.71905i	1.37717	+	0.193952i
$593$	−16.6101	−	35.6204i	−0.682093	−	1.46275i	−0.876287	−	0.481790i	$-0.839987\pi$
$593$	−16.6101	−	35.6204i	−0.682093	−	1.46275i	0.194194	−	0.980963i	$-0.437791\pi$
$594$	−1.01536	−	3.37454i	−0.0416606	−	0.138459i
$595$	−0.700869	−	18.6456i	−0.0287328	−	0.764395i
$596$	0.987375	+	2.27170i	0.0404445	+	0.0930524i
$597$	11.6026	+	43.3015i	0.474863	+	1.77221i
$598$	19.7798	+	15.5954i	0.808856	+	0.637745i
$599$	3.35433	+	19.0233i	0.137054	+	0.777273i	0.973407	+	0.229082i	$0.0735723\pi$
$599$	3.35433	+	19.0233i	0.137054	+	0.777273i	−0.836353	+	0.548191i	$0.815317\pi$
$600$	30.6569	+	14.5943i	1.25156	+	0.595811i
$601$	19.9962	+	34.6345i	0.815664	+	1.41277i	0.908850	+	0.417122i	$0.136961\pi$
$601$	19.9962	+	34.6345i	0.815664	+	1.41277i	−0.0931865	+	0.995649i	$0.529705\pi$
$602$	6.17843	−	42.5903i	0.251814	−	1.73585i
$603$	−7.78940	+	16.7044i	−0.317209	+	0.680257i
$604$	−24.4011	−	12.1703i	−0.992866	−	0.495203i
$605$	18.2987	−	3.94051i	0.743949	−	0.160204i
$606$	49.4120	+	11.6387i	2.00722	+	0.472790i
$607$	12.2069	+	12.2069i	0.495464	+	0.495464i	0.910023	−	0.414559i	$-0.136064\pi$
$607$	12.2069	+	12.2069i	0.495464	+	0.495464i	−0.414559	+	0.910023i	$0.636064\pi$
$608$	23.6317	+	7.03874i	0.958391	+	0.285459i
$609$			30.3308i			1.22906i
$610$	24.4190	+	2.61025i	0.988695	+	0.105686i
$611$	0.959717	−	1.14375i	0.0388260	−	0.0462710i
$612$	−16.3235	+	5.45917i	−0.659840	+	0.220674i
$613$	24.6385	+	11.4891i	0.995140	+	0.464042i	0.850802	−	0.525487i	$-0.176117\pi$
$613$	24.6385	+	11.4891i	0.995140	+	0.464042i	0.144339	+	0.989528i	$0.453895\pi$
$614$	−6.36871	+	4.75503i	−0.257020	+	0.191897i
$615$	−8.59884	+	6.51569i	−0.346739	+	0.262738i
$616$	−21.3398	+	25.6471i	−0.859807	+	1.03335i
$617$	−6.98590	−	4.89158i	−0.281242	−	0.196928i	0.424441	−	0.905456i	$-0.360471\pi$
$617$	−6.98590	−	4.89158i	−0.281242	−	0.196928i	−0.705683	+	0.708528i	$0.749360\pi$
$618$	16.6750	−	21.1490i	0.670767	−	0.850739i
$619$	23.7612	−	41.1555i	0.955042	−	1.65418i	0.220769	−	0.975326i	$-0.429143\pi$
$619$	23.7612	−	41.1555i	0.955042	−	1.65418i	0.734273	−	0.678855i	$-0.237523\pi$
$620$	9.72185	+	2.48811i	0.390439	+	0.0999249i
$621$	1.43457	−	1.20375i	0.0575674	−	0.0483048i
$622$	−29.9011	−	16.0692i	−1.19892	−	0.644316i
$623$	15.9743	−	7.44896i	0.639998	−	0.298436i
$624$	31.1090	+	41.3078i	1.24536	+	1.65363i
$625$	7.97841	+	23.6927i	0.319136	+	0.947709i
$626$	27.9097	+	1.58683i	1.11549	+	0.0634227i
$627$	−15.9916	+	43.1946i	−0.638644	+	1.72503i
$628$	−2.11144	−	2.65523i	−0.0842558	−	0.105955i
$629$	−25.9385	−	4.57365i	−1.03423	−	0.182363i
$630$	−3.62389	−	23.1455i	−0.144379	−	0.922138i
$631$	6.51434	−	17.8980i	0.259332	−	0.712509i	−0.739877	−	0.672742i	$-0.765116\pi$
$631$	6.51434	−	17.8980i	0.259332	−	0.712509i	0.999209	−	0.0397666i	$-0.0126614\pi$
$632$	−37.9165	−	26.3157i	−1.50824	−	1.04678i
$633$	34.0691	+	2.98066i	1.35412	+	0.118471i
$634$	1.46396	−	0.737764i	0.0581413	−	0.0293004i
$635$	0.376952	−	0.894664i	0.0149589	−	0.0355036i
$636$	−16.2932	+	0.994187i	−0.646067	+	0.0394221i
$637$	0.807969	+	0.565746i	0.0320129	+	0.0224157i
$638$	−5.97262	−	28.7248i	−0.236458	−	1.13723i
$639$	−17.3841	−	30.1102i	−0.687705	−	1.19114i
$640$	23.0434	−	10.4403i	0.910872	−	0.412689i
$641$	15.0614	−	5.48191i	0.594890	−	0.216522i	−0.0269887	−	0.999636i	$-0.508592\pi$
$641$	15.0614	−	5.48191i	0.594890	−	0.216522i	0.621879	+	0.783113i	$0.286370\pi$
$642$	41.4232	−	16.5227i	1.63484	−	0.652100i
$643$	−7.47786	+	0.654228i	−0.294898	+	0.0258002i	−0.233645	−	0.972322i	$-0.575065\pi$
$643$	−7.47786	+	0.654228i	−0.294898	+	0.0258002i	−0.0612533	+	0.998122i	$0.519510\pi$
$644$	−16.9994	−	5.03810i	−0.669869	−	0.198529i
$645$	−48.1335	−	37.3999i	−1.89526	−	1.47262i
$646$	−18.1933	−	6.11204i	−0.715805	−	0.240475i
$647$	−13.3245	−	13.3245i	−0.523841	−	0.523841i	0.394888	−	0.918729i	$-0.370783\pi$
$647$	−13.3245	−	13.3245i	−0.523841	−	0.523841i	−0.918729	+	0.394888i	$0.870783\pi$
$648$	24.6937	−	11.6398i	0.970060	−	0.457255i
$649$	16.0172	−	19.0886i	0.628731	−	0.749293i
$650$	−5.92268	+	37.6120i	−0.232307	+	1.47526i
$651$	−4.93844	−	13.5682i	−0.193553	−	0.531781i
$652$	−32.3414	−	6.58477i	−1.26659	−	0.257880i
$653$	−8.72724	+	32.5705i	−0.341523	+	1.27458i	0.555098	+	0.831785i	$0.312681\pi$
$653$	−8.72724	+	32.5705i	−0.341523	+	1.27458i	−0.896622	+	0.442797i	$0.853986\pi$
$654$	23.7824	−	36.2686i	0.929967	−	1.41821i
$655$	−3.25485	+	6.16103i	−0.127178	+	0.240732i
$656$	−0.423004	+	8.02730i	−0.0165155	+	0.313413i
$657$	1.41032	+	5.26338i	0.0550218	+	0.205344i
$658$	−0.329196	+	0.998078i	−0.0128334	+	0.0389091i
$659$	14.9283	−	12.5263i	0.581522	−	0.487955i	−0.303924	−	0.952696i	$-0.598297\pi$
$659$	14.9283	−	12.5263i	0.581522	−	0.487955i	0.885447	+	0.464741i	$0.153853\pi$
$660$	16.6611	+	44.2219i	0.648531	+	1.72133i
$661$	15.2115	+	5.53655i	0.591660	+	0.215347i	0.620459	−	0.784239i	$-0.286946\pi$
$661$	15.2115	+	5.53655i	0.591660	+	0.215347i	−0.0287993	+	0.999585i	$0.509168\pi$
$662$	−0.601257	−	19.7257i	−0.0233685	−	0.766660i
$663$	−23.0866	−	32.9711i	−0.896610	−	1.28049i
$664$	−10.8403	−	1.86510i	−0.420683	−	0.0723799i
$665$	12.3295	−	23.0301i	0.478118	−	0.893069i
$666$	−33.0167	−	1.87720i	−1.27937	−	0.0727401i
$667$	12.7716	−	8.94280i	0.494520	−	0.346267i
$668$	0.0978534	+	0.00257644i	0.00378606	+	9.96853e-5i
$669$	13.9330	−	38.2806i	0.538681	−	1.48001i
$670$	−7.59129	+	19.6718i	−0.293277	+	0.759989i
$671$	21.9704	+	26.1833i	0.848158	+	1.01080i
$672$	−31.1121	−	18.8945i	−1.20017	−	0.728873i
$673$	−24.0077	+	6.43285i	−0.925430	+	0.247968i	−0.689905	−	0.723900i	$-0.742348\pi$
$673$	−24.0077	+	6.43285i	−0.925430	+	0.247968i	−0.235525	+	0.971868i	$0.575681\pi$
$674$	28.8034	−	3.40702i	1.10947	−	0.131233i
$675$	2.64817	+	1.00038i	0.101928	+	0.0385045i
$676$	−19.0319	+	25.7124i	−0.731995	+	0.988937i
$677$	6.95651	+	1.86399i	0.267361	+	0.0716390i	0.390009	−	0.920811i	$-0.372472\pi$
$677$	6.95651	+	1.86399i	0.267361	+	0.0716390i	−0.122648	+	0.992450i	$0.539139\pi$
$678$	8.72225	−	60.1259i	0.334976	−	2.30912i
$679$	−11.5354	+	4.19853i	−0.442686	+	0.161125i
$680$	−18.2066	+	7.50062i	−0.698191	+	0.287636i
$681$	−6.73565	−	5.65188i	−0.258111	−	0.216581i
$682$	7.34876	+	11.8774i	0.281399	+	0.454808i
$683$	−18.9867	+	18.9867i	−0.726505	+	0.726505i	−0.969922	−	0.243417i	$-0.921732\pi$
$683$	−18.9867	+	18.9867i	−0.726505	+	0.726505i	0.243417	+	0.969922i	$0.421732\pi$
$684$	−23.5863	−	4.93772i	−0.901844	−	0.188798i
$685$	−0.183592	−	1.46300i	−0.00701470	−	0.0558983i
$686$	25.1495	+	5.92384i	0.960214	+	0.226173i
$687$	4.99912	+	57.1402i	0.190728	+	2.18003i
$688$	−44.4274	+	9.43001i	−1.69378	+	0.359516i
$689$	−6.26075	−	17.2013i	−0.238516	−	0.655316i
$690$	−18.0955	+	17.4128i	−0.688884	+	0.662894i
$691$	3.39648	−	1.96096i	0.129208	−	0.0745983i	−0.434003	−	0.900912i	$-0.642899\pi$
$691$	3.39648	−	1.96096i	0.129208	−	0.0745983i	0.563211	+	0.826313i	$0.309566\pi$
$692$	−1.67536	−	11.2211i	−0.0636877	−	0.426564i
$693$	18.7022	−	26.7095i	0.710438	−	1.01461i
$694$	−0.999096	−	8.44652i	−0.0379252	−	0.320625i
$695$	6.65564	+	16.3477i	0.252463	+	0.620105i
$696$	30.0328	−	11.0723i	1.13839	−	0.419696i
$697$	0.545315	−	6.23298i	0.0206553	−	0.236091i
$698$	−6.70214	−	3.60181i	−0.253680	−	0.136331i
$699$	−1.15923	−	0.421927i	−0.0438463	−	0.0159587i
$700$	−5.93651	−	26.1357i	−0.224379	−	0.987837i
$701$	−0.253505	+	1.43770i	−0.00957477	+	0.0543012i	−0.989221	−	0.146432i	$-0.953221\pi$
$701$	−0.253505	+	1.43770i	−0.00957477	+	0.0543012i	0.979646	+	0.200733i	$0.0643323\pi$
$702$	2.87065	+	3.21675i	0.108346	+	0.121408i
$703$	−28.1167	−	23.8580i	−1.06044	−	0.899820i
$704$	33.1854	+	11.7676i	1.25072	+	0.443510i
$705$	0.998992	+	1.10356i	0.0376242	+	0.0415627i
$706$	7.94777	+	7.47759i	0.299118	+	0.281423i
$707$	−16.9348	−	36.3168i	−0.636898	−	1.36583i
$708$	23.1777	+	14.2079i	0.871071	+	0.533965i
$709$	−15.3326	−	18.2727i	−0.575829	−	0.686246i	0.396988	−	0.917824i	$-0.370056\pi$
$709$	−15.3326	−	18.2727i	−0.575829	−	0.686246i	−0.972816	+	0.231578i	$0.925611\pi$
$710$	−22.1838	−	33.0147i	−0.832542	−	1.23902i
$711$	39.0625	+	22.5527i	1.46496	+	0.845794i
$712$	−13.2073	−	13.0981i	−0.494963	−	0.490874i
$713$	−4.25724	+	6.07997i	−0.159435	+	0.227697i
$714$	23.6928	+	15.5361i	0.886681	+	0.581424i
$715$	−42.2373	+	32.0049i	−1.57958	+	1.19691i
$716$	17.6842	+	26.7263i	0.660891	+	0.998809i
$717$	19.8156	−	42.4946i	0.740026	−	1.58699i
$718$	31.2755	−	12.4751i	1.16719	−	0.465566i
$719$	16.5946	+	13.9245i	0.618873	+	0.519296i	0.897449	−	0.441118i	$-0.145418\pi$
$719$	16.5946	+	13.9245i	0.618873	+	0.519296i	−0.278576	+	0.960414i	$0.589862\pi$
$720$	−21.5952	+	12.0376i	−0.804806	+	0.448616i
$721$	−21.2591			−0.791729
$722$	−17.6688	−	20.2438i	−0.657566	−	0.753397i
$723$	6.82874	−	6.82874i	0.253964	−	0.253964i
$724$	−21.9514	−	6.50573i	−0.815817	−	0.241783i
$725$	21.2377	+	10.2186i	0.788749	+	0.379508i
$726$	−11.2215	+	26.1136i	−0.416469	+	0.969166i
$727$	−16.3949	−	7.64505i	−0.608052	−	0.283539i	0.0941042	−	0.995562i	$-0.470001\pi$
$727$	−16.3949	−	7.64505i	−0.608052	−	0.283539i	−0.702156	+	0.712023i	$0.747779\pi$
$728$	10.4011	−	39.4717i	0.385491	−	1.46292i
$729$	−19.5736	+	11.3008i	−0.724947	+	0.418548i
$730$	2.01909	+	5.89777i	0.0747300	+	0.218286i
$731$	34.8138	−	6.13861i	1.28763	−	0.227045i
$732$	−24.7132	+	27.9251i	−0.913425	+	1.03214i
$733$	4.78291	−	1.28158i	0.176661	−	0.0473361i	−0.169404	−	0.985547i	$-0.554184\pi$
$733$	4.78291	−	1.28158i	0.176661	−	0.0473361i	0.346065	+	0.938211i	$0.387518\pi$
$734$	11.0541	+	21.9348i	0.408013	+	0.809627i
$735$	−0.668749	+	0.720987i	−0.0246672	+	0.0265940i
$736$	1.21707	+	18.6716i	0.0448618	+	0.688243i
$737$	−26.5975	+	12.4026i	−0.979732	+	0.456856i
$738$	−0.239343	−	7.85221i	−0.00881033	−	0.289044i
$739$	−0.673753	+	3.82104i	−0.0247844	+	0.140559i	−0.994689	−	0.102926i	$-0.967180\pi$
$739$	−0.673753	+	3.82104i	−0.0247844	+	0.140559i	0.969905	+	0.243485i	$0.0782907\pi$
$740$	−37.8304	+	0.425526i	−1.39067	+	0.0156426i
$741$	−4.60197	−	56.1633i	−0.169057	−	2.06321i
$742$	8.57926	+	9.61364i	0.314954	+	0.352928i
$743$	3.76641	+	5.37899i	0.138176	+	0.197336i	0.882276	−	0.470732i	$-0.156010\pi$
$743$	3.76641	+	5.37899i	0.138176	+	0.197336i	−0.744100	+	0.668068i	$0.767121\pi$
$744$	−11.6322	+	9.84306i	−0.426456	+	0.360864i
$745$	−1.47380	−	2.34464i	−0.0539957	−	0.0859010i
$746$	−15.3940	+	4.63188i	−0.563616	+	0.169585i
$747$	10.7088	+	0.936898i	0.391814	+	0.0342793i
$748$	−25.4976	−	10.0480i	−0.932285	−	0.367391i
$749$	−30.4866	−	17.6014i	−1.11396	−	0.643143i
$750$	−36.3417	−	10.9695i	−1.32701	−	0.400549i
$751$	16.1248	−	2.84324i	0.588402	−	0.103751i	0.128483	−	0.991712i	$-0.458989\pi$
$751$	16.1248	−	2.84324i	0.588402	−	0.103751i	0.459920	+	0.887961i	$0.347878\pi$
$752$	1.10845	−	0.0383892i	0.0404209	−	0.00139991i
$753$	−13.5794	+	50.6790i	−0.494861	+	1.84685i
$754$	21.4747	+	28.7624i	0.782061	+	1.04746i
$755$	29.0192	+	9.34348i	1.05612	+	0.340044i
$756$	−2.71576	−	1.35451i	−0.0987711	−	0.0492631i
$757$	−30.4706	+	2.66583i	−1.10747	+	0.0968912i	−0.626187	−	0.779673i	$-0.715385\pi$
$757$	−30.4706	+	2.66583i	−1.10747	+	0.0968912i	−0.481285	+	0.876564i	$0.659830\pi$
$758$	−3.20125	−	5.17399i	−0.116275	−	0.187928i
$759$	−34.9520			−1.26868
$760$	−27.3048	−	3.80117i	−0.990449	−	0.137883i
$761$	0.835915			0.0303019			0.0151510	−	0.999885i	$-0.495177\pi$
$761$	0.835915			0.0303019			0.0151510	+	0.999885i	$0.495177\pi$
$762$	0.775631	+	1.25361i	0.0280981	+	0.0454134i
$763$	−34.1047	+	2.98378i	−1.23467	+	0.108020i
$764$	−11.9603	−	5.96534i	−0.432709	−	0.215818i
$765$	17.1230	−	8.78218i	0.619085	−	0.317520i
$766$	−21.1487	−	28.3258i	−0.764135	−	1.02345i
$767$	−7.89042	+	29.4474i	−0.284906	+	1.06329i
$768$	−7.35138	+	37.7040i	−0.265270	+	1.36052i
$769$	−17.4555	+	3.07788i	−0.629462	+	0.110991i	−0.479273	−	0.877666i	$-0.659099\pi$
$769$	−17.4555	+	3.07788i	−0.629462	+	0.110991i	−0.150189	+	0.988657i	$0.547988\pi$
$770$	19.2686	−	31.9402i	0.694394	−	1.15104i
$771$	−55.4562	−	32.0177i	−1.99721	−	1.15309i
$772$	4.19826	+	1.65444i	0.151099	+	0.0595445i
$773$	30.6478	+	2.68133i	1.10232	+	0.0964409i	0.623763	−	0.781613i	$-0.285603\pi$
$773$	30.6478	+	2.68133i	1.10232	+	0.0964409i	0.478561	+	0.878054i	$0.341159\pi$
$774$	42.5033	−	12.7887i	1.52775	−	0.459681i
$775$	−11.1643	−	1.11329i	−0.401034	−	0.0399907i
$776$	8.36830	+	9.88935i	0.300405	+	0.355007i
$777$	31.2228	+	44.5907i	1.12011	+	1.59968i
$778$	31.7526	+	35.5810i	1.13839	+	1.27564i
$779$	5.06381	−	7.14772i	0.181430	−	0.256094i
$780$	−41.3390	−	40.4193i	−1.48017	−	1.44724i
$781$	9.61307	−	54.5185i	0.343983	−	1.95082i
$782$	−0.443718	−	14.5572i	−0.0158673	−	0.520566i
$783$	2.41866	−	1.12784i	0.0864357	−	0.0403056i
$784$	0.0890857	+	0.727271i	0.00318163	+	0.0259739i
$785$	2.78078	+	2.57930i	0.0992504	+	0.0920593i
$786$	−4.76157	−	9.44846i	−0.169839	−	0.337016i
$787$	0.177034	−	0.0474362i	0.00631059	−	0.00169092i	−0.255662	−	0.966766i	$-0.582294\pi$
$787$	0.177034	−	0.0474362i	0.00631059	−	0.00169092i	0.261973	+	0.965075i	$0.415627\pi$
$788$	−4.12185	+	4.65755i	−0.146835	+	0.165919i
$789$	53.6002	−	9.45117i	1.90822	−	0.336470i
$790$	46.3390	+	22.7027i	1.64867	+	0.807726i
$791$	−41.5326	+	23.9789i	−1.47673	+	0.852590i
$792$	−33.2744	−	8.76809i	−1.18236	−	0.311561i
$793$	−37.8992	−	17.6727i	−1.34584	−	0.627576i
$794$	2.03774	−	4.74202i	0.0723165	−	0.168288i
$795$	17.8412	−	3.84199i	0.632764	−	0.136261i
$796$	−35.8046	−	10.6114i	−1.26906	−	0.376111i
$797$	−8.56781	+	8.56781i	−0.303487	+	0.303487i	−0.842377	−	0.538889i	$-0.818844\pi$
$797$	−8.56781	+	8.56781i	−0.303487	+	0.303487i	0.538889	+	0.842377i	$0.318844\pi$
$798$	17.6556	+	35.5201i	0.625003	+	1.25740i
$799$	−0.863287			−0.0305409
$800$	−23.7118	+	15.4191i	−0.838340	+	0.545148i
$801$	13.9255	+	11.6849i	0.492032	+	0.412864i
$802$	−48.9604	+	19.5292i	−1.72885	+	0.689599i
$803$	−3.66673	+	7.86333i	−0.129396	+	0.277491i
$804$	−17.6678	−	26.7015i	−0.623096	−	0.941689i
$805$	19.6374	+	2.70651i	0.692126	+	0.0953920i
$806$	−14.2896	−	9.37015i	−0.503330	−	0.330049i
$807$	−36.7310	+	52.4572i	−1.29299	+	1.84658i
$808$	−29.7779	+	30.0260i	−1.04758	+	1.05631i
$809$	−34.3659	−	19.8412i	−1.20824	−	0.697579i	−0.245867	−	0.969304i	$-0.579073\pi$
$809$	−34.3659	−	19.8412i	−1.20824	−	0.697579i	−0.962375	+	0.271725i	$0.912406\pi$
$810$	−25.3339	+	17.0227i	−0.890142	+	0.598118i
$811$	−30.5616	−	36.4219i	−1.07316	−	1.27895i	−0.958362	−	0.285556i	$-0.907822\pi$
$811$	−30.5616	−	36.4219i	−1.07316	−	1.27895i	−0.114800	−	0.993389i	$-0.536623\pi$
$812$	−21.5413	−	13.2048i	−0.755952	−	0.463397i
$813$	−13.6704	−	29.3162i	−0.479441	−	1.02816i
$814$	−38.3502	−	36.0814i	−1.34417	−	1.26465i
$815$	36.8551	+	1.83303i	1.29098	+	0.0642083i
$816$	6.73436	−	29.1316i	0.235750	−	1.01981i
$817$	46.4135	+	17.1833i	1.62380	+	0.601169i
$818$	−14.2820	−	16.0039i	−0.499358	−	0.559564i
$819$	−6.92717	+	39.2859i	−0.242055	+	1.37276i
$820$	−0.883941	−	8.94367i	−0.0308685	−	0.312327i
$821$	12.4038	+	4.51460i	0.432894	+	0.157561i	0.549270	−	0.835645i	$-0.314906\pi$
$821$	12.4038	+	4.51460i	0.432894	+	0.157561i	−0.116376	+	0.993205i	$0.537128\pi$
$822$	1.97216	+	1.05986i	0.0687868	+	0.0369669i
$823$	−2.55233	+	29.1733i	−0.0889687	+	1.01692i	0.812180	+	0.583407i	$0.198281\pi$
$823$	−2.55233	+	29.1733i	−0.0889687	+	1.01692i	−0.901149	+	0.433510i	$0.857275\pi$
$824$	7.76069	+	21.0502i	0.270357	+	0.733320i
$825$	−25.8604	−	46.0727i	−0.900345	−	1.60404i
$826$	−2.52075	−	21.3108i	−0.0877080	−	0.741497i
$827$	−7.26051	+	10.3691i	−0.252473	+	0.360569i	−0.925303	−	0.379228i	$-0.876190\pi$
$827$	−7.26051	+	10.3691i	−0.252473	+	0.360569i	0.672830	+	0.739797i	$0.265078\pi$
$828$	−2.70027	−	18.0857i	−0.0938410	−	0.628522i
$829$	−25.2737	+	14.5918i	−0.877792	+	0.506794i	−0.869930	−	0.493175i	$-0.835836\pi$
$829$	−25.2737	+	14.5918i	−0.877792	+	0.506794i	−0.00786251	+	0.999969i	$0.502503\pi$
$830$	12.2956	+	0.236396i	0.426786	+	0.00820541i
$831$	−5.89755	−	16.2034i	−0.204584	−	0.562090i
$832$	−42.8809	+	4.11033i	−1.48663	+	0.142500i
$833$	−0.0497057	−	0.568138i	−0.00172220	−	0.0196848i
$834$	−26.0876	−	6.14480i	−0.903340	−	0.212777i
$835$	−0.108590	+	0.0136269i	−0.00375790	+	0.000471580i
$836$	−23.7153	−	30.1626i	−0.820209	−	1.04320i
$837$	−0.898334	+	0.898334i	−0.0310510	+	0.0310510i
$838$	−9.13176	−	14.7591i	−0.315451	−	0.509845i
$839$	12.8726	+	10.8014i	0.444411	+	0.372905i	0.837357	−	0.546656i	$-0.184100\pi$
$839$	12.8726	+	10.8014i	0.444411	+	0.372905i	−0.392946	+	0.919562i	$0.628544\pi$
$840$	37.5688	+	15.6458i	1.29625	+	0.539832i
$841$	−6.37263	+	2.31945i	−0.219746	+	0.0799810i
$842$	−2.81924	+	19.4342i	−0.0971576	+	0.669746i
$843$	0.816057	+	0.218662i	0.0281065	+	0.00753111i
$844$	−16.9492	+	22.8987i	−0.583416	+	0.788204i
$845$	16.7067	−	31.6237i	0.574727	−	1.08789i
$846$	−1.07642	+	0.127324i	−0.0370079	+	0.00437748i
$847$	21.6711	−	5.80675i	0.744628	−	0.199522i
$848$	6.38731	−	12.0045i	0.219341	−	0.412235i
$849$	40.8286	+	48.6576i	1.40123	+	1.66993i
$850$	18.8607	−	11.3556i	0.646915	−	0.389494i
$851$	9.57041	−	26.2945i	0.328070	−	0.901364i
$852$	60.3760	+	1.58967i	2.06845	+	0.0544613i
$853$	−14.3423	+	10.0426i	−0.491071	+	0.343851i	−0.792739	−	0.609562i	$-0.791345\pi$
$853$	−14.3423	+	10.0426i	−0.491071	+	0.343851i	0.301668	+	0.953413i	$0.402457\pi$
$854$	29.3878	+	1.67088i	1.00563	+	0.0571762i
$855$	26.9009	+	1.48658i	0.919991	+	0.0508400i
$856$	−6.29931	+	36.6126i	−0.215306	+	1.25139i
$857$	−0.445553	−	0.636316i	−0.0152198	−	0.0217362i	0.811470	−	0.584394i	$-0.198668\pi$
$857$	−0.445553	−	0.636316i	−0.0152198	−	0.0217362i	−0.826690	+	0.562658i	$0.809779\pi$
$858$	−2.45158	−	80.4301i	−0.0836957	−	2.74584i
$859$	28.2598	+	10.2857i	0.964213	+	0.350945i	0.775683	−	0.631123i	$-0.217406\pi$
$859$	28.2598	+	10.2857i	0.964213	+	0.350945i	0.188530	+	0.982067i	$0.439628\pi$
$860$	47.5173	−	17.9027i	1.62033	−	0.610476i
$861$	−9.90588	+	8.31202i	−0.337591	+	0.283273i
$862$	−0.786396	+	2.38425i	−0.0267848	+	0.0812078i
$863$	−10.3644	−	38.6806i	−0.352809	−	1.31670i	−0.883219	−	0.468960i	$-0.844629\pi$
$863$	−10.3644	−	38.6806i	−0.352809	−	1.31670i	0.530410	−	0.847741i	$-0.322038\pi$
$864$	−0.349811	+	3.18355i	−0.0119008	+	0.108306i
$865$	3.74095	+	12.1205i	0.127196	+	0.412109i
$866$	12.7973	−	19.5160i	0.434868	−	0.663181i
$867$	4.54021	−	16.9443i	0.154194	−	0.575458i
$868$	11.7863	+	2.39972i	0.400054	+	0.0814518i
$869$	24.5635	+	67.4877i	0.833260	+	2.28936i
$870$	−31.3307	+	17.2944i	−1.06221	+	0.586336i
$871$	23.0790	−	27.5045i	0.782001	−	0.931953i
$872$	15.4045	+	32.6804i	0.521662	+	1.10670i
$873$	−8.95239	−	8.95239i	−0.302992	−	0.302992i
$874$	9.75111	−	17.9072i	0.329836	−	0.605722i
$875$	10.9618	+	27.8879i	0.370575	+	0.942784i
$876$	−9.07552	−	2.68971i	−0.306633	−	0.0908768i
$877$	0.162769	−	0.0142405i	0.00549633	−	0.000480866i	−0.0844072	−	0.996431i	$-0.526900\pi$
$877$	0.162769	−	0.0142405i	0.00549633	−	0.000480866i	0.0899036	+	0.995950i	$0.471344\pi$
$878$	7.91508	−	3.15714i	0.267121	−	0.106548i
$879$	8.97574	−	3.26690i	0.302744	−	0.110190i
$880$	−38.6605	−	7.41949i	−1.30324	−	0.250111i
$881$	−4.74324	−	8.21553i	−0.159804	−	0.276788i	0.774994	−	0.631968i	$-0.217753\pi$
$881$	−4.74324	−	8.21553i	−0.159804	−	0.276788i	−0.934798	+	0.355180i	$0.884419\pi$
$882$	−0.145770	−	0.701070i	−0.00490834	−	0.0236063i
$883$	−40.2953	−	28.2151i	−1.35604	−	0.949512i	−0.999886	−	0.0150867i	$-0.995198\pi$
$883$	−40.2953	−	28.2151i	−1.35604	−	0.949512i	−0.356158	−	0.934426i	$-0.615914\pi$
$884$	33.4675	−	2.04214i	1.12563	−	0.0686845i
$885$	−28.0100	−	11.8015i	−0.941545	−	0.396705i
$886$	38.4119	−	19.3577i	1.29047	−	0.650335i
$887$	−13.5506	−	1.18553i	−0.454986	−	0.0398061i	−0.142640	−	0.989775i	$-0.545559\pi$
$887$	−13.5506	−	1.18553i	−0.454986	−	0.0398061i	−0.312346	+	0.949968i	$0.601115\pi$
$888$	32.7547	−	47.1940i	1.09918	−	1.58373i
$889$	0.397987	−	1.09346i	0.0133481	−	0.0366735i
$890$	16.8030	+	12.2536i	0.563238	+	0.410742i
$891$	−41.8348	−	7.37661i	−1.40152	−	0.247126i
$892$	21.1215	+	26.5612i	0.707200	+	0.889335i
$893$	−1.04336	−	0.610071i	−0.0349146	−	0.0204153i
$894$	4.19835	+	0.238702i	0.140414	+	0.00798339i
$895$	−24.0458	−	26.5629i	−0.803762	−	0.887898i
$896$	26.9641	−	13.8703i	0.900807	−	0.463374i
$897$	38.7553	−	18.0719i	1.29400	−	0.603403i
$898$	31.3304	+	16.8373i	1.04551	+	0.561869i
$899$	−8.10253	+	6.79883i	−0.270235	+	0.226754i
$900$	21.8422	−	16.9408i	0.728073	−	0.564693i
$901$	−5.29205	+	9.16610i	−0.176304	+	0.305367i
$902$	7.74460	−	9.82253i	0.257867	−	0.327055i
$903$	−59.8483	−	41.9062i	−1.99163	−	1.39455i
$904$	38.9049	+	32.3710i	1.29396	+	1.07664i
$905$	25.3579	+	3.49493i	0.842924	+	0.116176i
$906$	−37.0934	+	27.6948i	−1.23235	+	0.920098i
$907$	28.5604	+	13.3179i	0.948332	+	0.442215i	0.834330	−	0.551266i	$-0.185855\pi$
$907$	28.5604	+	13.3179i	0.948332	+	0.442215i	0.114003	+	0.993480i	$0.463633\pi$
$908$	6.94647	−	2.32315i	0.230527	−	0.0770964i
$909$	26.5649	−	31.6588i	0.881101	−	1.05006i
$910$	−4.85073	+	45.3786i	−0.160800	+	1.50429i
$911$		−	20.9909i		−	0.695460i	−0.937595	−	0.347730i	$-0.886953\pi$
$911$		−	20.9909i		−	0.695460i	0.937595	−	0.347730i	$-0.113047\pi$
$912$	28.7259	−	30.4489i	0.951209	−	1.00826i
$913$	12.1029	+	12.1029i	0.400549	+	0.400549i
$914$	−39.9618	−	9.41278i	−1.32182	−	0.311347i
$915$	22.6136	−	35.0259i	0.747583	−	1.15792i
$916$	−42.7581	−	21.3261i	−1.41277	−	0.704633i
$917$	−3.52961	+	7.56928i	−0.116558	+	0.249960i
$918$	0.357883	−	2.46703i	0.0118119	−	0.0814242i
$919$	−10.4041	−	18.0204i	−0.343200	−	0.594439i	0.641825	−	0.766851i	$-0.278177\pi$
$919$	−10.4041	−	18.0204i	−0.343200	−	0.594439i	−0.985025	+	0.172412i	$0.944844\pi$
$920$	−4.48876	−	20.4325i	−0.147990	−	0.673639i
$921$	2.34305	+	13.2881i	0.0772062	+	0.437858i
$922$	−15.3823	−	12.1282i	−0.506590	−	0.399422i
$923$	17.5296	+	65.4214i	0.576994	+	2.15337i
$924$	22.5782	+	51.9468i	0.742769	+	1.70892i
$925$	41.7417	−	6.83947i	1.37246	−	0.224880i
$926$	0.531150	+	1.76528i	0.0174547	+	0.0580107i
$927$	−9.26619	−	19.8714i	−0.304342	−	0.652663i
$928$	−5.21134	+	26.1501i	−0.171071	+	0.858421i
$929$	−14.4223	−	2.54304i	−0.473181	−	0.0834346i	−0.0680279	−	0.997683i	$-0.521671\pi$
$929$	−14.4223	−	2.54304i	−0.473181	−	0.0834346i	−0.405153	+	0.914249i	$0.632782\pi$
$930$	11.1997	−	12.8378i	0.367252	−	0.420967i
$931$	0.341421	−	0.721770i	0.0111896	−	0.0236550i
$932$	0.804341	−	0.639614i	0.0263471	−	0.0209512i
$933$	−47.2063	+	33.0542i	−1.54546	+	1.08215i
$934$	16.6493	+	15.6643i	0.544781	+	0.512552i
$935$	29.8738	+	6.81312i	0.976978	+	0.222813i
$936$	41.4288	−	7.48233i	1.35414	−	0.244568i
$937$	−3.04946	+	34.8555i	−0.0996215	+	1.13868i	0.767659	+	0.640859i	$0.221422\pi$
$937$	−3.04946	+	34.8555i	−0.0996215	+	1.13868i	−0.867280	+	0.497820i	$0.834134\pi$
$938$	−7.91641	+	24.0015i	−0.258480	+	0.783676i
$939$	23.7290	−	41.0998i	0.774366	−	1.34124i
$940$	−1.21869	+	0.229050i	−0.0397492	+	0.00747078i
$941$	−4.93131	−	27.9669i	−0.160756	−	0.911693i	−0.953333	−	0.301921i	$-0.902372\pi$
$941$	−4.93131	−	27.9669i	−0.160756	−	0.911693i	0.792577	−	0.609772i	$-0.208739\pi$
$942$	−5.63861	+	1.17241i	−0.183716	+	0.0381992i
$943$	6.42069	+	1.72042i	0.209086	+	0.0560245i
$944$	−20.1812	+	10.2756i	−0.656843	+	0.334441i
$945$	3.22973	+	1.03990i	0.105063	+	0.0338278i
$946$	64.9314	+	27.9023i	2.11110	+	0.907181i
$947$	−1.29389	−	14.7893i	−0.0420459	−	0.480587i	−0.987803	−	0.155711i	$-0.950233\pi$
$947$	−1.29389	−	14.7893i	−0.0420459	−	0.480587i	0.945757	−	0.324876i	$-0.105322\pi$
$948$	−68.8642	+	37.3774i	−2.23661	+	1.21396i
$949$		−	10.6149i		−	0.344573i
$950$	30.8195	−	0.395667i	0.999918	−	0.0128371i
$951$		−	2.78308i		−	0.0902476i
$952$	−21.3488	+	10.0631i	−0.691920	+	0.326148i
$953$	4.09291	+	46.7822i	0.132582	+	1.51542i	0.713035	+	0.701129i	$0.247320\pi$
$953$	4.09291	+	46.7822i	0.132582	+	1.51542i	−0.580452	+	0.814294i	$0.697124\pi$
$954$	−5.24668	+	12.2096i	−0.169867	+	0.395299i
$955$	14.2239	+	4.57975i	0.460274	+	0.148197i
$956$	21.5534	+	32.5737i	0.697085	+	1.05351i
$957$	−48.1111	−	12.8913i	−1.55521	−	0.416718i
$958$	−6.11556	−	29.4123i	−0.197585	−	0.950267i
$959$	−0.306888	−	1.74045i	−0.00990994	−	0.0562021i
$960$	1.77751	−	42.9113i	0.0573688	−	1.38496i
$961$	−12.9824	+	22.4861i	−0.418786	+	0.725359i
$962$	61.1792	+	20.1787i	1.97250	+	0.650589i
$963$	3.16434	−	36.1686i	0.101969	−	1.16552i
$964$	1.87691	+	7.82282i	0.0604511	+	0.251956i
$965$	−4.91882	−	1.12180i	−0.158342	−	0.0361121i
$966$	−20.6257	+	21.9226i	−0.663620	+	0.705347i
$967$	10.5969	−	7.42005i	0.340774	−	0.238613i	−0.390644	−	0.920542i	$-0.627748\pi$
$967$	10.5969	−	7.42005i	0.340774	−	0.238613i	0.731418	+	0.681929i	$0.238859\pi$
$968$	−13.6608	−	19.3384i	−0.439075	−	0.621561i
$969$	−23.1660	+	22.9121i	−0.744198	+	0.736042i
$970$	−10.9143	−	9.52166i	−0.350438	−	0.305722i
$971$	−25.7459	−	4.53970i	−0.826226	−	0.145686i	−0.255482	−	0.966814i	$-0.582234\pi$
$971$	−25.7459	−	4.53970i	−0.826226	−	0.145686i	−0.570744	+	0.821128i	$0.693345\pi$
$972$	1.13043	−	42.9338i	0.0362585	−	1.37710i
$973$	8.94092	+	19.1739i	0.286633	+	0.614686i
$974$	48.2574	−	14.5201i	1.54627	−	0.465252i
$975$	52.4963	+	37.7150i	1.68123	+	1.20785i
$976$	−9.07364	−	29.7090i	−0.290440	−	0.950963i
$977$	5.61104	+	20.9407i	0.179513	+	0.669952i	0.995739	+	0.0922190i	$0.0293960\pi$
$977$	5.61104	+	20.9407i	0.179513	+	0.669952i	−0.816226	+	0.577733i	$0.803937\pi$
$978$	−34.6920	+	44.0001i	−1.10933	+	1.40697i
$979$	5.02615	+	28.5047i	0.160636	+	0.911015i
$980$	−0.220909	−	0.788843i	−0.00705667	−	0.0251987i
$981$	−17.6542	−	30.5780i	−0.563656	−	0.976281i
$982$	11.0249	+	1.59935i	0.351819	+	0.0510372i
$983$	−26.0222	+	55.8048i	−0.829980	+	1.77990i	−0.243570	+	0.969883i	$0.578319\pi$
$983$	−26.0222	+	55.8048i	−0.829980	+	1.77990i	−0.586410	+	0.810014i	$0.699459\pi$
$984$	11.8465	+	6.77424i	0.377654	+	0.215955i
$985$	3.77167	−	5.84188i	0.120175	−	0.186138i
$986$	4.75838	−	20.2016i	0.151538	−	0.643350i
$987$	1.26162	+	1.26162i	0.0401577	+	0.0401577i
$988$	41.8914	+	21.1829i	1.33274	+	0.673916i
$989$			37.5566i			1.19423i
$990$	38.2539	+	4.08914i	1.21579	+	0.129961i
$991$	10.2124	−	12.1707i	0.324408	−	0.386614i	−0.579049	−	0.815292i	$-0.696576\pi$
$991$	10.2124	−	12.1707i	0.324408	−	0.386614i	0.903457	+	0.428678i	$0.141021\pi$
$992$	−1.92649	−	12.5466i	−0.0611663	−	0.398354i
$993$	−30.3643	−	14.1591i	−0.963582	−	0.449326i
$994$	−28.5223	−	38.2017i	−0.904671	−	1.21168i
$995$	41.3608	+	5.70054i	1.31123	+	0.180719i
$996$	−11.1096	+	15.0093i	−0.352022	+	0.475588i
$997$	−37.3376	−	26.1441i	−1.18249	−	0.827991i	−0.194261	−	0.980950i	$-0.562231\pi$
$997$	−37.3376	−	26.1441i	−1.18249	−	0.827991i	−0.988233	+	0.152959i	$0.951120\pi$
$998$	−21.9417	−	17.3000i	−0.694552	−	0.547622i
$999$	2.39478	−	4.14788i	0.0757674	−	0.131233i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bj.a.283.38	yes	672
4.3	odd	2	inner	380.2.bj.a.283.39	yes	672
5.2	odd	4	inner	380.2.bj.a.207.12	yes	672
19.9	even	9	inner	380.2.bj.a.123.13	yes	672
20.7	even	4	inner	380.2.bj.a.207.13	yes	672
76.47	odd	18	inner	380.2.bj.a.123.12	yes	672
95.47	odd	36	inner	380.2.bj.a.47.39	yes	672
380.47	even	36	inner	380.2.bj.a.47.38	✓	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bj.a.47.38	✓	672	380.47	even	36	inner
380.2.bj.a.47.39	yes	672	95.47	odd	36	inner
380.2.bj.a.123.12	yes	672	76.47	odd	18	inner
380.2.bj.a.123.13	yes	672	19.9	even	9	inner
380.2.bj.a.207.12	yes	672	5.2	odd	4	inner
380.2.bj.a.207.13	yes	672	20.7	even	4	inner
380.2.bj.a.283.38	yes	672	1.1	even	1	trivial
380.2.bj.a.283.39	yes	672	4.3	odd	2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bj (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.744093 + 1.20263i) q^{2} +(2.39174 - 0.209250i) q^{3} +(-0.892653 + 1.78974i) q^{4} +(0.685314 - 2.12846i) q^{5} +(2.03132 + 2.72068i) q^{6} +(0.693673 - 2.58882i) q^{7} +(-2.81662 + 0.258199i) q^{8} +(2.72219 - 0.479996i) q^{9} +O(q^{10})\)	\(q+(0.744093 + 1.20263i) q^{2} +(2.39174 - 0.209250i) q^{3} +(-0.892653 + 1.78974i) q^{4} +(0.685314 - 2.12846i) q^{5} +(2.03132 + 2.72068i) q^{6} +(0.693673 - 2.58882i) q^{7} +(-2.81662 + 0.258199i) q^{8} +(2.72219 - 0.479996i) q^{9} +(3.06969 - 0.759591i) q^{10} +(3.81160 + 2.20063i) q^{11} +(-1.76049 + 4.46737i) q^{12} +(-5.36419 - 0.469306i) q^{13} +(3.62956 - 1.09209i) q^{14} +(1.19371 - 5.23412i) q^{15} +(-2.40634 - 3.19523i) q^{16} +(1.78579 + 2.55038i) q^{17} +(2.60282 + 2.91663i) q^{18} +(0.355971 + 4.34434i) q^{19} +(3.19765 + 3.12651i) q^{20} +(1.11737 - 6.33693i) q^{21} +(0.189635 + 6.22142i) q^{22} +(-2.99779 + 1.39789i) q^{23} +(-6.68258 + 1.20692i) q^{24} +(-4.06069 - 2.91733i) q^{25} +(-3.42705 - 6.80036i) q^{26} +(-0.546872 + 0.146534i) q^{27} +(4.01411 + 3.55241i) q^{28} +(-4.64203 + 0.818515i) q^{29} +(7.18295 - 2.45907i) q^{30} +(1.94331 - 1.12197i) q^{31} +(2.05215 - 5.27150i) q^{32} +(9.57681 + 4.46574i) q^{33} +(-1.73837 + 4.04537i) q^{34} +(-5.03482 - 3.25061i) q^{35} +(-1.57090 + 5.30048i) q^{36} +(-5.98188 + 5.98188i) q^{37} +(-4.95977 + 3.66069i) q^{38} -12.9279 q^{39} +(-1.38070 + 6.17201i) q^{40} +(-1.53945 - 1.29175i) q^{41} +(8.45242 - 3.37147i) q^{42} +(4.79853 - 10.2905i) q^{43} +(-7.34098 + 4.85738i) q^{44} +(0.843902 - 6.12302i) q^{45} +(-3.91179 - 2.56508i) q^{46} +(-0.159040 + 0.227133i) q^{47} +(-6.42394 - 7.13863i) q^{48} +(-0.158636 - 0.0915883i) q^{49} +(0.486944 - 7.05428i) q^{50} +(4.80481 + 5.72615i) q^{51} +(5.62830 - 9.18159i) q^{52} +(1.43669 + 3.08099i) q^{53} +(-0.583150 - 0.548652i) q^{54} +(7.29609 - 6.60472i) q^{55} +(-1.28538 + 7.47082i) q^{56} +(1.76044 + 10.3160i) q^{57} +(-4.43847 - 4.97360i) q^{58} +(0.983136 - 5.57564i) q^{59} +(8.30214 + 6.80868i) q^{60} +(7.29760 + 2.65611i) q^{61} +(2.79532 + 1.50224i) q^{62} +(0.645686 - 7.38022i) q^{63} +(7.86667 - 1.45450i) q^{64} +(-4.67506 + 11.0959i) q^{65} +(1.75539 + 14.8403i) q^{66} +(-3.82455 + 5.46202i) q^{67} +(-6.15861 + 0.919506i) q^{68} +(-6.87742 + 3.97068i) q^{69} +(0.162918 - 8.47380i) q^{70} +(-4.30197 - 11.8196i) q^{71} +(-7.54343 + 2.05483i) q^{72} +(0.171811 + 1.96381i) q^{73} +(-11.6451 - 2.74294i) q^{74} +(-10.3225 - 6.12778i) q^{75} +(-8.09300 - 3.24089i) q^{76} +(8.34103 - 8.34103i) q^{77} +(-9.61958 - 15.5476i) q^{78} +(12.5002 + 10.4889i) q^{79} +(-8.45003 + 2.93207i) q^{80} +(-9.06976 + 3.30112i) q^{81} +(0.408010 - 2.81258i) q^{82} +(3.75641 + 1.00653i) q^{83} +(10.3440 + 7.65648i) q^{84} +(6.65220 - 2.05318i) q^{85} +(15.9462 - 1.88620i) q^{86} +(-10.9312 + 2.92901i) q^{87} +(-11.3040 - 5.21417i) q^{88} +(4.22723 + 5.03782i) q^{89} +(7.99169 - 3.54119i) q^{90} +(-4.93594 + 13.5614i) q^{91} +(0.174120 - 6.61311i) q^{92} +(4.41310 - 3.09009i) q^{93} +(-0.391498 - 0.0222591i) q^{94} +(9.49071 + 2.21957i) q^{95} +(3.80514 - 13.0374i) q^{96} +(-2.62711 - 3.75190i) q^{97} +(-0.00789244 - 0.258931i) q^{98} +(11.4322 + 4.16097i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

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