LMFDB - Embedded newform 456.2.bk.a.253.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [456,2,Mod(61,456)] 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("456.61"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(456, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bk (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:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			253.12
Character	$\chi$	$=$	456.253
Dual form			456.2.bk.a.301.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.898327 - 1.09225i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(-0.386016 + 1.96239i) q^{4} +(3.60963 - 0.636475i) q^{5} +(1.33362 - 0.470580i) q^{6} +(-0.686638 + 1.18929i) q^{7} +(2.49019 - 1.34125i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(-3.93782 - 3.37085i) q^{10} +(1.75591 - 1.01378i) q^{11} +(-1.71202 - 1.03391i) q^{12} +(-0.0200547 - 0.0551000i) q^{13} +(1.91583 - 0.318394i) q^{14} +(-0.636475 + 3.60963i) q^{15} +(-3.70198 - 1.51503i) q^{16} +(-0.334054 + 0.280304i) q^{17} +(-0.0139254 + 1.41415i) q^{18} +(3.22669 + 2.93061i) q^{19} +(-0.144359 + 7.32921i) q^{20} +(-0.882725 - 1.05199i) q^{21} +(-2.68468 - 1.00719i) q^{22} +(-1.46664 + 8.31776i) q^{23} +(0.408665 + 2.79875i) q^{24} +(7.92587 - 2.88478i) q^{25} +(-0.0421672 + 0.0714026i) q^{26} +(0.866025 - 0.500000i) q^{27} +(-2.06881 - 1.80654i) q^{28} +(1.82717 - 2.17753i) q^{29} +(4.51438 - 2.54744i) q^{30} +(2.08584 - 3.61278i) q^{31} +(1.67080 + 5.40448i) q^{32} +(0.352081 + 1.99675i) q^{33} +(0.606252 + 0.113065i) q^{34} +(-1.72156 + 4.72993i) q^{35} +(1.55711 - 1.25516i) q^{36} -9.42746i q^{37} +(0.302341 - 6.15700i) q^{38} +0.0586362 q^{39} +(8.13500 - 6.42635i) q^{40} +(4.55055 + 1.65626i) q^{41} +(-0.356060 + 1.90919i) q^{42} +(-3.48899 + 0.615202i) q^{43} +(1.31162 + 3.83712i) q^{44} +(-3.17426 - 1.83266i) q^{45} +(10.4026 - 5.87013i) q^{46} +(3.66354 + 3.07407i) q^{47} +(2.68982 - 2.96056i) q^{48} +(2.55706 + 4.42895i) q^{49} +(-10.2709 - 6.06554i) q^{50} +(-0.149147 - 0.409778i) q^{51} +(0.115869 - 0.0180859i) q^{52} +(9.46348 + 1.66867i) q^{53} +(-1.32410 - 0.496752i) q^{54} +(5.69295 - 4.77695i) q^{55} +(-0.114726 + 3.88252i) q^{56} +(-3.85747 + 2.02976i) q^{57} +(-4.01980 - 0.0395839i) q^{58} +(-0.840408 - 1.00156i) q^{59} +(-6.83783 - 2.64239i) q^{60} +(-9.78309 - 1.72502i) q^{61} +(-5.81983 + 0.967205i) q^{62} +(1.29046 - 0.469688i) q^{63} +(4.40211 - 6.67993i) q^{64} +(-0.107460 - 0.186126i) q^{65} +(1.86466 - 2.17829i) q^{66} +(-5.03340 + 5.99857i) q^{67} +(-0.421118 - 0.763747i) q^{68} +(-7.31451 - 4.22303i) q^{69} +(6.71279 - 2.36866i) q^{70} +(-2.32739 - 13.1993i) q^{71} +(-2.76973 - 0.573209i) q^{72} +(4.37981 + 1.59412i) q^{73} +(-10.2971 + 8.46895i) q^{74} +8.43453i q^{75} +(-6.99657 + 5.20077i) q^{76} +2.78439i q^{77} +(-0.0526745 - 0.0640453i) q^{78} +(-5.63803 - 2.05207i) q^{79} +(-14.3271 - 3.11248i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-2.27883 - 6.45819i) q^{82} +(6.46743 + 3.73397i) q^{83} +(2.40517 - 1.32617i) q^{84} +(-1.02740 + 1.22441i) q^{85} +(3.80621 + 3.25819i) q^{86} +(1.42128 + 2.46174i) q^{87} +(3.01283 - 4.87961i) q^{88} +(-14.5073 + 5.28024i) q^{89} +(0.849803 + 5.11340i) q^{90} +(0.0793003 + 0.0139828i) q^{91} +(-15.7566 - 6.08892i) q^{92} +(2.68151 + 3.19570i) q^{93} +(0.0665969 - 6.76302i) q^{94} +(13.5124 + 8.52473i) q^{95} +(-5.65000 - 0.278400i) q^{96} +(-5.92525 + 4.97188i) q^{97} +(2.54044 - 6.77159i) q^{98} +(-1.99675 - 0.352081i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$	$1$	$1$

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 $

$2$	−0.898327	−	1.09225i	−0.635213	−	0.772337i
$2$	−0.898327	−	1.09225i	−0.635213	−	0.772337i
$3$	−0.342020	+	0.939693i	−0.197465	+	0.542532i
$3$	−0.342020	+	0.939693i	−0.197465	+	0.542532i
$4$	−0.386016	+	1.96239i	−0.193008	+	0.981197i
$5$	3.60963	−	0.636475i	1.61428	−	0.284640i	0.707646	−	0.706567i	$-0.249757\pi$
$5$	3.60963	−	0.636475i	1.61428	−	0.284640i	0.906630	+	0.421927i	$0.138646\pi$
$6$	1.33362	−	0.470580i	0.544450	−	0.192114i
$7$	−0.686638	+	1.18929i	−0.259525	+	0.449510i	−0.966115	−	0.258113i	$-0.916899\pi$
$7$	−0.686638	+	1.18929i	−0.259525	+	0.449510i	0.706590	+	0.707623i	$0.250233\pi$
$8$	2.49019	−	1.34125i	0.880416	−	0.474203i
$9$	−0.766044	−	0.642788i	−0.255348	−	0.214263i
$10$	−3.93782	−	3.37085i	−1.24525	−	1.06596i
$11$	1.75591	−	1.01378i	0.529427	−	0.305665i	−0.211356	−	0.977409i	$-0.567788\pi$
$11$	1.75591	−	1.01378i	0.529427	−	0.305665i	0.740783	+	0.671744i	$0.234455\pi$
$12$	−1.71202	−	1.03391i	−0.494218	−	0.298465i
$13$	−0.0200547	−	0.0551000i	−0.00556219	−	0.0152820i	0.936880	−	0.349650i	$-0.113699\pi$
$13$	−0.0200547	−	0.0551000i	−0.00556219	−	0.0152820i	−0.942443	+	0.334368i	$0.891477\pi$
$14$	1.91583	−	0.318394i	0.512027	−	0.0850944i
$15$	−0.636475	+	3.60963i	−0.164337	+	0.932003i
$16$	−3.70198	−	1.51503i	−0.925496	−	0.378758i
$17$	−0.334054	+	0.280304i	−0.0810200	+	0.0679838i	−0.682398	−	0.730981i	$-0.739063\pi$
$17$	−0.334054	+	0.280304i	−0.0810200	+	0.0679838i	0.601378	+	0.798964i	$0.294619\pi$
$18$	−0.0139254	+	1.41415i	−0.00328225	+	0.333317i
$19$	3.22669	+	2.93061i	0.740252	+	0.672329i
$19$	3.22669	+	2.93061i	0.740252	+	0.672329i
$20$	−0.144359	+	7.32921i	−0.0322796	+	1.63886i
$21$	−0.882725	−	1.05199i	−0.192626	−	0.229563i
$22$	−2.68468	−	1.00719i	−0.572375	−	0.214733i
$23$	−1.46664	+	8.31776i	−0.305817	+	1.73437i	0.313820	+	0.949483i	$0.398391\pi$
$23$	−1.46664	+	8.31776i	−0.305817	+	1.73437i	−0.619636	+	0.784889i	$0.712720\pi$
$24$	0.408665	+	2.79875i	0.0834183	+	0.571292i
$25$	7.92587	−	2.88478i	1.58517	−	0.576956i
$26$	−0.0421672	+	0.0714026i	−0.00826966	+	0.0140032i
$27$	0.866025	−	0.500000i	0.166667	−	0.0962250i
$28$	−2.06881	−	1.80654i	−0.390968	−	0.341404i
$29$	1.82717	−	2.17753i	0.339297	−	0.404358i	−0.569235	−	0.822175i	$-0.692760\pi$
$29$	1.82717	−	2.17753i	0.339297	−	0.404358i	0.908531	+	0.417817i	$0.137205\pi$
$30$	4.51438	−	2.54744i	0.824209	−	0.465097i
$31$	2.08584	−	3.61278i	0.374628	−	0.648875i	−0.615643	−	0.788025i	$-0.711104\pi$
$31$	2.08584	−	3.61278i	0.374628	−	0.648875i	0.990271	+	0.139150i	$0.0444370\pi$
$32$	1.67080	+	5.40448i	0.295359	+	0.955386i
$33$	0.352081	+	1.99675i	0.0612894	+	0.347589i
$34$	0.606252	+	0.113065i	0.103971	+	0.0193905i
$35$	−1.72156	+	4.72993i	−0.290996	+	0.799505i
$36$	1.55711	−	1.25516i	0.259518	−	0.209193i
$37$		−	9.42746i		−	1.54987i	−0.632044	−	0.774933i	$-0.717784\pi$
$37$		−	9.42746i		−	1.54987i	0.632044	−	0.774933i	$-0.282216\pi$
$38$	0.302341	−	6.15700i	0.0490463	−	0.998797i
$39$	0.0586362			0.00938930
$40$	8.13500	−	6.42635i	1.28626	−	1.01610i
$41$	4.55055	+	1.65626i	0.710676	+	0.258665i	0.671962	−	0.740586i	$-0.265452\pi$
$41$	4.55055	+	1.65626i	0.710676	+	0.258665i	0.0387136	+	0.999250i	$0.487674\pi$
$42$	−0.356060	+	1.90919i	−0.0549412	+	0.294594i
$43$	−3.48899	+	0.615202i	−0.532065	+	0.0938175i	−0.433225	−	0.901286i	$-0.642624\pi$
$43$	−3.48899	+	0.615202i	−0.532065	+	0.0938175i	−0.0988403	+	0.995103i	$0.531513\pi$
$44$	1.31162	+	3.83712i	0.197734	+	0.578468i
$45$	−3.17426	−	1.83266i	−0.473190	−	0.273196i
$46$	10.4026	−	5.87013i	1.53378	−	0.865503i
$47$	3.66354	+	3.07407i	0.534382	+	0.448399i	0.869611	−	0.493737i	$-0.164369\pi$
$47$	3.66354	+	3.07407i	0.534382	+	0.448399i	−0.335230	+	0.942136i	$0.608814\pi$
$48$	2.68982	−	2.96056i	0.388241	−	0.427319i
$49$	2.55706	+	4.42895i	0.365294	+	0.632707i
$50$	−10.2709	−	6.06554i	−1.45253	−	0.857798i
$51$	−0.149147	−	0.409778i	−0.0208847	−	0.0573804i
$52$	0.115869	−	0.0180859i	0.0160682	−	0.00250806i
$53$	9.46348	+	1.66867i	1.29991	+	0.229209i	0.780413	−	0.625264i	$-0.215009\pi$
$53$	9.46348	+	1.66867i	1.29991	+	0.229209i	0.519496	+	0.854473i	$0.326120\pi$
$54$	−1.32410	−	0.496752i	−0.180187	−	0.0675993i
$55$	5.69295	−	4.77695i	0.767637	−	0.644124i
$56$	−0.114726	+	3.88252i	−0.0153309	+	0.518823i
$57$	−3.85747	+	2.02976i	−0.510934	+	0.268849i
$58$	−4.01980	−	0.0395839i	−0.527826	−	0.00519762i
$59$	−0.840408	−	1.00156i	−0.109412	−	0.130392i	0.708559	−	0.705651i	$-0.249346\pi$
$59$	−0.840408	−	1.00156i	−0.109412	−	0.130392i	−0.817971	+	0.575259i	$0.804901\pi$
$60$	−6.83783	−	2.64239i	−0.882760	−	0.341131i
$61$	−9.78309	−	1.72502i	−1.25260	−	0.220867i	−0.492290	−	0.870431i	$-0.663840\pi$
$61$	−9.78309	−	1.72502i	−1.25260	−	0.220867i	−0.760306	+	0.649565i	$0.774951\pi$
$62$	−5.81983	+	0.967205i	−0.739119	+	0.122835i
$63$	1.29046	−	0.469688i	0.162582	−	0.0591752i
$64$	4.40211	−	6.67993i	0.550264	−	0.834991i
$65$	−0.107460	−	0.186126i	−0.0133288	−	0.0230861i
$66$	1.86466	−	2.17829i	0.229524	−	0.268129i
$67$	−5.03340	+	5.99857i	−0.614927	+	0.732842i	−0.980189	−	0.198063i	$-0.936535\pi$
$67$	−5.03340	+	5.99857i	−0.614927	+	0.732842i	0.365262	+	0.930905i	$0.380979\pi$
$68$	−0.421118	−	0.763747i	−0.0510680	−	0.0926180i
$69$	−7.31451	−	4.22303i	−0.880564	−	0.508394i
$70$	6.71279	−	2.36866i	0.802331	−	0.283109i
$71$	−2.32739	−	13.1993i	−0.276210	−	1.56646i	−0.735092	−	0.677967i	$-0.762861\pi$
$71$	−2.32739	−	13.1993i	−0.276210	−	1.56646i	0.458882	−	0.888497i	$-0.348250\pi$
$72$	−2.76973	−	0.573209i	−0.326416	−	0.0675534i
$73$	4.37981	+	1.59412i	0.512618	+	0.186578i	0.585361	−	0.810773i	$-0.300953\pi$
$73$	4.37981	+	1.59412i	0.512618	+	0.186578i	−0.0727428	+	0.997351i	$0.523175\pi$
$74$	−10.2971	+	8.46895i	−1.19702	+	0.984495i
$75$			8.43453i			0.973936i
$76$	−6.99657	+	5.20077i	−0.802562	+	0.596569i
$77$			2.78439i			0.317310i
$78$	−0.0526745	−	0.0640453i	−0.00596421	−	0.00725170i
$79$	−5.63803	−	2.05207i	−0.634328	−	0.230876i	0.00478608	−	0.999989i	$-0.498477\pi$
$79$	−5.63803	−	2.05207i	−0.634328	−	0.230876i	−0.639114	+	0.769112i	$0.720699\pi$
$80$	−14.3271	−	3.11248i	−1.60182	−	0.347986i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	−2.27883	−	6.45819i	−0.251654	−	0.713188i
$83$	6.46743	+	3.73397i	0.709893	+	0.409857i	0.811021	−	0.585017i	$-0.198912\pi$
$83$	6.46743	+	3.73397i	0.709893	+	0.409857i	−0.101129	+	0.994873i	$0.532245\pi$
$84$	2.40517	−	1.32617i	0.262425	−	0.144697i
$85$	−1.02740	+	1.22441i	−0.111438	+	0.132806i
$86$	3.80621	+	3.25819i	0.410434	+	0.351339i
$87$	1.42128	+	2.46174i	0.152378	+	0.263926i
$88$	3.01283	−	4.87961i	0.321169	−	0.520168i
$89$	−14.5073	+	5.28024i	−1.53777	+	0.559704i	−0.965510	−	0.260366i	$-0.916157\pi$
$89$	−14.5073	+	5.28024i	−1.53777	+	0.559704i	−0.572264	+	0.820070i	$0.693935\pi$
$90$	0.849803	+	5.11340i	0.0895771	+	0.539000i
$91$	0.0793003	+	0.0139828i	0.00831293	+	0.00146579i
$92$	−15.7566	−	6.08892i	−1.64274	−	0.634814i
$93$	2.68151	+	3.19570i	0.278059	+	0.331378i
$94$	0.0665969	−	6.76302i	0.00686894	−	0.697552i
$95$	13.5124	+	8.52473i	1.38634	+	0.874619i
$96$	−5.65000	−	0.278400i	−0.576651	−	0.0284141i
$97$	−5.92525	+	4.97188i	−0.601618	+	0.504818i	−0.891965	−	0.452104i	$-0.850674\pi$
$97$	−5.92525	+	4.97188i	−0.601618	+	0.504818i	0.290347	+	0.956921i	$0.406229\pi$
$98$	2.54044	−	6.77159i	0.256624	−	0.684034i
$99$	−1.99675	−	0.352081i	−0.200681	−	0.0353854i
$100$	2.60157	+	16.6673i	0.260157	+	1.66673i
$101$	−1.91713	−	5.26728i	−0.190762	−	0.524114i	0.807031	−	0.590508i	$-0.201073\pi$
$101$	−1.91713	−	5.26728i	−0.190762	−	0.524114i	−0.997793	+	0.0663941i	$0.978851\pi$
$102$	−0.313597	+	0.531020i	−0.0310507	+	0.0525788i
$103$	−5.98945	−	10.3740i	−0.590158	−	1.02218i	−0.994211	−	0.107448i	$-0.965732\pi$
$103$	−5.98945	−	10.3740i	−0.590158	−	1.02218i	0.404053	−	0.914736i	$-0.367601\pi$
$104$	−0.123843	−	0.110311i	−0.0121438	−	0.0108169i
$105$	−3.85588	−	3.23547i	−0.376295	−	0.315749i
$106$	−6.67870	−	11.8355i	−0.648693	−	1.14956i
$107$	−10.3330	−	5.96577i	−0.998931	−	0.576733i	−0.0909992	−	0.995851i	$-0.529006\pi$
$107$	−10.3330	−	5.96577i	−0.998931	−	0.576733i	−0.907932	+	0.419118i	$0.862339\pi$
$108$	0.646898	+	1.89249i	0.0622478	+	0.182105i
$109$	7.13908	−	1.25881i	0.683800	−	0.120572i	0.179052	−	0.983840i	$-0.442697\pi$
$109$	7.13908	−	1.25881i	0.683800	−	0.120572i	0.504747	+	0.863267i	$0.331586\pi$
$110$	−10.3317	−	1.92685i	−0.985093	−	0.183718i
$111$	8.85892	+	3.22438i	0.840851	+	0.306045i
$112$	4.34374	−	3.36246i	0.410445	−	0.317723i
$113$	3.68163			0.346339			0.173170	−	0.984892i	$-0.444599\pi$
$113$	3.68163			0.346339			0.173170	+	0.984892i	$0.444599\pi$
$114$	5.68228	+	2.38992i	0.532194	+	0.223837i
$115$			30.9575i			2.88680i
$116$	3.56786	+	4.42619i	0.331268	+	0.410961i
$117$	−0.0200547	+	0.0551000i	−0.00185406	+	0.00509399i
$118$	−0.338991	+	1.81766i	−0.0312066	+	0.167329i
$119$	−0.103990	−	0.589755i	−0.00953273	−	0.0540628i
$120$	3.25646	+	9.84234i	0.297273	+	0.898479i
$121$	−3.44452	+	5.96608i	−0.313138	+	0.542371i
$122$	6.90426	+	12.2352i	0.625083	+	1.10772i
$123$	−3.11276	+	3.70964i	−0.280668	+	0.334487i
$124$	6.28454	+	5.48784i	0.564368	+	0.492822i
$125$	10.9021	−	6.29432i	0.975112	−	0.562981i
$126$	−1.67227	−	0.987567i	−0.148978	−	0.0879795i
$127$	−14.2829	+	5.19856i	−1.26740	+	0.461297i	−0.886247	−	0.463213i	$-0.846696\pi$
$127$	−14.2829	+	5.19856i	−1.26740	+	0.461297i	−0.381157	+	0.924510i	$0.624474\pi$
$128$	−11.2507	+	1.19256i	−0.994429	+	0.105408i
$129$	0.615202	−	3.48899i	0.0541655	−	0.307188i
$130$	−0.106762	+	0.284575i	−0.00936364	+	0.0249589i
$131$	4.30581	+	5.13147i	0.376200	+	0.448338i	0.920611	−	0.390481i	$-0.127691\pi$
$131$	4.30581	+	5.13147i	0.376200	+	0.448338i	−0.544411	+	0.838819i	$0.683247\pi$
$132$	−4.05432	−	0.0798552i	−0.352883	−	0.00695050i
$133$	−5.70092	+	1.82520i	−0.494333	+	0.158265i
$134$	11.0736	+	0.109044i	0.956611	+	0.00941995i
$135$	2.80779	−	2.35602i	0.241656	−	0.202774i
$136$	−0.455900	+	1.14606i	−0.0390931	+	0.0982739i
$137$	−1.67558	+	9.50269i	−0.143154	+	0.811869i	0.825676	+	0.564145i	$0.190794\pi$
$137$	−1.67558	+	9.50269i	−0.143154	+	0.811869i	−0.968830	+	0.247725i	$0.920317\pi$
$138$	1.95822	+	11.7829i	0.166695	+	1.00303i
$139$	−7.22250	−	19.8436i	−0.612604	−	1.68312i	−0.724396	−	0.689384i	$-0.757881\pi$
$139$	−7.22250	−	19.8436i	−0.612604	−	1.68312i	0.111791	−	0.993732i	$-0.464341\pi$
$140$	−8.61745	−	5.20420i	−0.728307	−	0.439835i
$141$	−4.14169	+	2.39120i	−0.348793	+	0.201376i
$142$	−12.3261	+	14.3993i	−1.03439	+	1.20837i
$143$	−0.0910734	−	0.0764196i	−0.00761594	−	0.00639053i
$144$	1.86204	+	3.54017i	0.155170	+	0.295014i
$145$	5.20945	−	9.02304i	0.432622	−	0.749323i
$146$	−2.19333	−	6.21588i	−0.181521	−	0.514430i
$147$	−5.03642	+	0.888056i	−0.415397	+	0.0732456i
$148$	18.5004	+	3.63915i	1.52072	+	0.299136i
$149$	6.38158	−	17.5332i	0.522799	−	1.43638i	−0.344592	−	0.938752i	$-0.611983\pi$
$149$	6.38158	−	17.5332i	0.522799	−	1.43638i	0.867391	−	0.497626i	$-0.165795\pi$
$150$	9.21261	−	7.57697i	0.752206	−	0.618657i
$151$	−7.93770			−0.645961			−0.322980	−	0.946406i	$-0.604685\pi$
$151$	−7.93770			−0.645961			−0.322980	+	0.946406i	$0.604685\pi$
$152$	11.9657	+	2.97001i	0.970550	+	0.240900i
$153$	0.436076			0.0352547
$154$	3.04125	−	2.50129i	0.245071	−	0.201560i
$155$	5.22967	−	14.3684i	0.420057	−	1.15410i
$156$	−0.0226345	+	0.115067i	−0.00181221	+	0.00921276i
$157$	−17.0370	+	3.00408i	−1.35970	+	0.239752i	−0.805483	−	0.592620i	$-0.798094\pi$
$157$	−17.0370	+	3.00408i	−1.35970	+	0.239752i	−0.554218	+	0.832371i	$0.686983\pi$
$158$	2.82342	+	8.00157i	0.224619	+	0.636570i
$159$	−4.80473	+	8.32204i	−0.381040	+	0.659981i
$160$	9.47080	+	18.4448i	0.748733	+	1.45819i
$161$	−8.88519	−	7.45556i	−0.700251	−	0.587580i
$162$	0.919662	−	1.07435i	0.0722555	−	0.0844087i
$163$	3.50912	−	2.02599i	0.274855	−	0.158688i	−0.356237	−	0.934396i	$-0.615940\pi$
$163$	3.50912	−	2.02599i	0.274855	−	0.158688i	0.631092	+	0.775708i	$0.282607\pi$
$164$	−5.00682	+	8.29062i	−0.390967	+	0.647389i
$165$	2.54176	+	6.98343i	0.197876	+	0.543659i
$166$	−1.73144	−	10.4184i	−0.134386	−	0.808623i
$167$	0.366931	−	2.08097i	0.0283940	−	0.161030i	−0.967314	−	0.253582i	$-0.918391\pi$
$167$	0.366931	−	2.08097i	0.0283940	−	0.161030i	0.995708	+	0.0925518i	$0.0295024\pi$
$168$	−3.60913	−	1.43571i	−0.278451	−	0.110767i
$169$	9.95594	−	8.35403i	0.765842	−	0.642618i
$170$	2.26031	+	0.0222577i	0.173358	+	0.00170709i
$171$	−0.588021	−	4.31905i	−0.0449671	−	0.330286i
$172$	0.139534	−	7.08424i	0.0106393	−	0.540168i
$173$	−8.51700	−	10.1502i	−0.647536	−	0.771703i	0.338005	−	0.941144i	$-0.390248\pi$
$173$	−8.51700	−	10.1502i	−0.647536	−	0.771703i	−0.985540	+	0.169441i	$0.945804\pi$
$174$	1.41205	−	3.76384i	0.107047	−	0.285336i
$175$	−2.01136	+	11.4070i	−0.152044	+	0.862286i
$176$	−8.03625	+	1.09272i	−0.605755	+	0.0823671i
$177$	1.22859	−	0.447172i	0.0923468	−	0.0336115i
$178$	18.7997	+	11.1022i	1.40909	+	0.832148i
$179$	11.7670	−	6.79368i	0.879506	−	0.507783i	0.00901080	−	0.999959i	$-0.497132\pi$
$179$	11.7670	−	6.79368i	0.879506	−	0.507783i	0.870496	+	0.492176i	$0.163798\pi$
$180$	4.82171	−	5.52171i	0.359389	−	0.411564i
$181$	12.6242	−	15.0450i	0.938352	−	1.11828i	−0.0544497	−	0.998517i	$-0.517340\pi$
$181$	12.6242	−	15.0450i	0.938352	−	1.11828i	0.992802	−	0.119768i	$-0.0382151\pi$
$182$	−0.0559650	−	0.0991768i	−0.00414840	−	0.00735148i
$183$	4.96701	−	8.60311i	0.367172	−	0.635960i
$184$	7.50394	+	22.6799i	0.553198	+	1.67199i
$185$	−6.00035	−	34.0297i	−0.441154	−	2.50191i
$186$	1.08162	−	5.79965i	0.0793085	−	0.425251i
$187$	−0.302403	+	0.830845i	−0.0221139	+	0.0607574i
$188$	−7.44672	+	6.00266i	−0.543108	+	0.437789i
$189$			1.37328i			0.0998912i
$190$	−2.82743	−	22.4169i	−0.205124	−	1.62629i
$191$	6.61899			0.478933			0.239467	−	0.970905i	$-0.423027\pi$
$191$	6.61899			0.478933			0.239467	+	0.970905i	$0.423027\pi$
$192$	4.77147	+	6.42130i	0.344351	+	0.463417i
$193$	−14.4651	−	5.26485i	−1.04122	−	0.378972i	−0.235876	−	0.971783i	$-0.575796\pi$
$193$	−14.4651	−	5.26485i	−1.04122	−	0.378972i	−0.805342	+	0.592811i	$0.798018\pi$
$194$	10.7533	+	2.00548i	0.772045	+	0.143985i
$195$	0.211655	−	0.0373205i	0.0151569	−	0.00267257i
$196$	−9.67841	+	3.30831i	−0.691315	+	0.236308i
$197$	−17.2691	−	9.97031i	−1.23037	−	0.710355i	−0.263264	−	0.964724i	$-0.584799\pi$
$197$	−17.2691	−	9.97031i	−1.23037	−	0.710355i	−0.967107	+	0.254368i	$0.918132\pi$
$198$	1.40917	+	2.49723i	0.100146	+	0.177470i
$199$	−12.0578	−	10.1177i	−0.854758	−	0.717227i	0.106074	−	0.994358i	$-0.466172\pi$
$199$	−12.0578	−	10.1177i	−0.854758	−	0.717227i	−0.960832	+	0.277131i	$0.910616\pi$
$200$	15.8677	−	17.8142i	1.12202	−	1.25965i
$201$	−3.91529	−	6.78148i	−0.276163	−	0.478329i
$202$	−4.03097	+	6.82573i	−0.283618	+	0.480257i
$203$	1.33512	+	3.66821i	0.0937071	+	0.257458i
$204$	0.861718	−	0.134504i	0.0603324	−	0.00941719i
$205$	17.4800	+	3.08219i	1.22085	+	0.215269i
$206$	−5.95054	+	15.8612i	−0.414594	+	1.10511i
$207$	6.47006	−	5.42903i	0.449701	−	0.377344i
$208$	−0.00923576	+	0.234363i	−0.000640385	+	0.0162501i
$209$	8.63676	+	1.87476i	0.597417	+	0.129680i
$210$	−0.0700933	+	7.11809i	−0.00483690	+	0.491195i
$211$	−15.5936	−	18.5837i	−1.07351	−	1.27936i	−0.958222	−	0.286025i	$-0.907666\pi$
$211$	−15.5936	−	18.5837i	−1.07351	−	1.27936i	−0.115286	−	0.993332i	$-0.536778\pi$
$212$	−6.92763	+	17.9269i	−0.475792	+	1.23123i
$213$	13.1993	+	2.32739i	0.904399	+	0.159470i
$214$	2.76633	+	16.6455i	0.189102	+	1.13786i
$215$	−12.2024	+	4.44131i	−0.832196	+	0.302895i
$216$	1.48595	−	2.40665i	0.101106	−	0.163752i
$217$	2.86444	+	4.96135i	0.194451	+	0.336799i
$218$	−7.78816	−	6.66682i	−0.527481	−	0.451534i
$219$	−2.99597	+	3.57045i	−0.202449	+	0.241269i
$220$	7.17669	+	13.0158i	0.483852	+	0.877524i
$221$	0.0221441	+	0.0127849i	0.00148958	+	0.000860007i
$222$	−4.43638	−	12.5727i	−0.297750	−	0.843824i
$223$	−0.287032	−	1.62784i	−0.0192211	−	0.109008i	0.973688	−	0.227886i	$-0.0731814\pi$
$223$	−0.287032	−	1.62784i	−0.0192211	−	0.109008i	−0.992909	+	0.118878i	$0.962070\pi$
$224$	−7.57475	−	1.72385i	−0.506109	−	0.115180i
$225$	−7.92587	−	2.88478i	−0.528391	−	0.192319i
$226$	−3.30731	−	4.02126i	−0.219999	−	0.267490i
$227$			27.8353i			1.84749i	0.383003	+	0.923747i	$0.374890\pi$
$227$			27.8353i			1.84749i	−0.383003	+	0.923747i	$0.625110\pi$
$228$	−2.49415	−	8.35339i	−0.165179	−	0.553217i
$229$			24.5496i			1.62228i	0.584851	+	0.811141i	$0.301153\pi$
$229$			24.5496i			1.62228i	−0.584851	+	0.811141i	$0.698847\pi$
$230$	33.8133	−	27.8100i	2.22958	−	1.83374i
$231$	−2.61647	−	0.952317i	−0.172151	−	0.0626579i
$232$	1.62939	−	7.87316i	0.106974	−	0.516898i
$233$	−3.81443	−	21.6327i	−0.249891	−	1.41720i	−0.808853	−	0.588011i	$-0.799911\pi$
$233$	−3.81443	−	21.6327i	−0.249891	−	1.41720i	0.558962	−	0.829193i	$-0.311200\pi$
$234$	0.0781986	−	0.0275930i	0.00511200	−	0.00180381i
$235$	15.1806	+	8.76451i	0.990272	+	0.571734i
$236$	2.28986	−	1.26259i	0.149058	−	0.0821879i
$237$	3.85664	−	4.59616i	0.250516	−	0.298553i
$238$	−0.550743	+	0.643376i	−0.0356994	+	0.0417039i
$239$	−5.79538	−	10.0379i	−0.374872	−	0.649298i	0.615436	−	0.788187i	$-0.288980\pi$
$239$	−5.79538	−	10.0379i	−0.374872	−	0.649298i	−0.990308	+	0.138890i	$0.955647\pi$
$240$	7.82492	−	12.3985i	0.505096	−	0.800321i
$241$	−3.66437	+	1.33372i	−0.236043	+	0.0859127i	−0.457333	−	0.889295i	$-0.651195\pi$
$241$	−3.66437	+	1.33372i	−0.236043	+	0.0859127i	0.221290	+	0.975208i	$0.428973\pi$
$242$	9.61075	−	1.59722i	0.617802	−	0.102673i
$243$	−0.984808	−	0.173648i	−0.0631754	−	0.0111395i
$244$	7.16160	−	18.5324i	0.458475	−	1.18642i
$245$	12.0489	+	14.3594i	0.769779	+	0.917387i
$246$	6.84812	+	0.0674349i	0.436620	+	0.00429949i
$247$	0.0967664	−	0.236563i	0.00615710	−	0.0150521i
$248$	0.348509	−	11.7942i	0.0221303	−	0.748930i
$249$	−5.72078	+	4.80030i	−0.362540	+	0.304207i
$250$	−16.6686	−	6.25343i	−1.05422	−	0.395502i
$251$	25.3595	+	4.47156i	1.60068	+	0.282242i	0.901524	−	0.432730i	$-0.142450\pi$
$251$	25.3595	+	4.47156i	1.60068	+	0.282242i	0.699153	+	0.714972i	$0.253561\pi$
$252$	0.423577	+	2.71369i	0.0266828	+	0.170947i
$253$	5.85704	+	16.0921i	0.368229	+	1.01170i
$254$	18.5088	+	10.9305i	1.16135	+	0.685840i
$255$	−0.799178	−	1.38422i	−0.0500465	−	0.0866831i
$256$	11.4094	+	11.2172i	0.713085	+	0.701077i
$257$	10.0402	+	8.42470i	0.626288	+	0.525518i	0.899773	−	0.436358i	$-0.143732\pi$
$257$	10.0402	+	8.42470i	0.626288	+	0.525518i	−0.273485	+	0.961876i	$0.588176\pi$
$258$	−4.36349	+	2.46230i	−0.271659	+	0.153296i
$259$	11.2120	+	6.47326i	0.696680	+	0.402229i
$260$	0.406734	−	0.139031i	0.0252246	−	0.00862235i
$261$	−2.79938	+	0.493607i	−0.173277	+	0.0305535i
$262$	1.73681	−	9.31275i	0.107300	−	0.575344i
$263$	7.89503	+	2.87355i	0.486828	+	0.177191i	0.573760	−	0.819023i	$-0.305484\pi$
$263$	7.89503	+	2.87355i	0.486828	+	0.177191i	−0.0869322	+	0.996214i	$0.527706\pi$
$264$	3.55488	+	4.50006i	0.218788	+	0.276959i
$265$	35.2217			2.16365
$266$	7.11487	+	4.58720i	0.436241	+	0.281259i
$267$		−	15.4384i		−	0.944813i
$268$	−9.82859	−	12.1931i	−0.600377	−	0.744809i
$269$	−6.43389	+	17.6770i	−0.392281	+	1.07778i	0.573676	+	0.819082i	$0.305517\pi$
$269$	−6.43389	+	17.6770i	−0.392281	+	1.07778i	−0.965957	+	0.258702i	$0.916705\pi$
$270$	−5.09568	−	0.950334i	−0.310113	−	0.0578355i
$271$	−0.234529	−	1.33008i	−0.0142466	−	0.0807967i	0.976855	−	0.213900i	$-0.0686168\pi$
$271$	−0.234529	−	1.33008i	−0.0142466	−	0.0807967i	−0.991102	+	0.133104i	$0.957506\pi$
$272$	1.66133	−	0.531581i	0.100733	−	0.0322318i
$273$	−0.0402618	+	0.0697355i	−0.00243676	+	0.00422059i
$274$	11.8845	−	6.70637i	0.717970	−	0.405147i
$275$	10.9926	−	13.1005i	0.662879	−	0.789988i
$276$	11.1108	−	12.7238i	0.668790	−	0.765883i
$277$	0.690127	−	0.398445i	0.0414657	−	0.0239403i	−0.479124	−	0.877747i	$-0.659046\pi$
$277$	0.690127	−	0.398445i	0.0414657	−	0.0239403i	0.520590	+	0.853807i	$0.325712\pi$
$278$	−15.1860	+	25.7149i	−0.910798	+	1.54227i
$279$	−3.92010	+	1.42680i	−0.234690	+	0.0854203i
$280$	2.05701	+	14.0875i	0.122930	+	0.841888i
$281$	−2.58001	+	14.6320i	−0.153911	+	0.872871i	0.805864	+	0.592100i	$0.201701\pi$
$281$	−2.58001	+	14.6320i	−0.153911	+	0.872871i	−0.959775	+	0.280771i	$0.909410\pi$
$282$	6.33238	+	2.37567i	0.377088	+	0.141469i
$283$	−5.49662	−	6.55061i	−0.326740	−	0.389394i	0.577520	−	0.816377i	$-0.304021\pi$
$283$	−5.49662	−	6.55061i	−0.326740	−	0.389394i	−0.904259	+	0.426983i	$0.859576\pi$
$284$	26.8006	+	0.527873i	1.59032	+	0.0313235i
$285$	−12.6321	+	9.78188i	−0.748264	+	0.579428i
$286$	−0.00165556	+	0.168125i	−9.78953e−5	+	0.00994142i
$287$	−5.09436	+	4.27468i	−0.300711	+	0.252326i
$288$	2.19402	−	5.21404i	0.129284	−	0.307241i
$289$	−2.91900	+	16.5545i	−0.171706	+	0.973792i
$290$	−14.5352	+	2.41562i	−0.853536	+	0.141850i
$291$	−2.64548	−	7.26840i	−0.155081	−	0.426081i
$292$	−4.81897	+	7.97956i	−0.282009	+	0.466968i
$293$	−20.0878	+	11.5977i	−1.17354	+	0.677546i	−0.954512	−	0.298172i	$-0.903623\pi$
$293$	−20.0878	+	11.5977i	−1.17354	+	0.677546i	−0.219032	+	0.975718i	$0.570290\pi$
$294$	5.49433	+	4.70326i	0.320436	+	0.274299i
$295$	−3.67103	−	3.08036i	−0.213736	−	0.179345i
$296$	−12.6446	−	23.4762i	−0.734950	−	1.36453i
$297$	1.01378	−	1.75591i	0.0588252	−	0.101888i
$298$	−24.8834	+	8.78032i	−1.44146	+	0.508630i
$299$	0.487721	−	0.0859984i	0.0282056	−	0.00497342i
$300$	−16.5519	−	3.25586i	−0.955623	−	0.187977i
$301$	1.66402	−	4.57184i	0.0959123	−	0.263517i
$302$	7.13065	+	8.66995i	0.410323	+	0.498899i
$303$	5.60533			0.322018
$304$	−7.50517	−	15.7376i	−0.430451	−	0.902614i
$305$	−36.4113			−2.08490
$306$	−0.391739	−	0.476304i	−0.0223942	−	0.0272285i
$307$	4.77810	−	13.1277i	0.272701	−	0.749239i	−0.725440	−	0.688286i	$-0.758364\pi$
$307$	4.77810	−	13.1277i	0.272701	−	0.749239i	0.998141	−	0.0609537i	$-0.0194142\pi$
$308$	−5.46407	−	1.07482i	−0.311344	−	0.0612434i
$309$	11.7969	−	2.08011i	0.671103	−	0.118334i
$310$	−20.3918	+	7.19543i	−1.15818	+	0.408673i
$311$	16.7255	−	28.9695i	0.948418	−	1.64271i	0.199659	−	0.979865i	$-0.436016\pi$
$311$	16.7255	−	28.9695i	0.948418	−	1.64271i	0.748759	−	0.662843i	$-0.230650\pi$
$312$	0.146015	−	0.0786456i	0.00826649	−	0.00445243i
$313$	25.9771	+	21.7974i	1.46831	+	1.23206i	0.917683	+	0.397313i	$0.130057\pi$
$313$	25.9771	+	21.7974i	1.46831	+	1.23206i	0.550631	+	0.834749i	$0.314387\pi$
$314$	18.5860	+	15.9100i	1.04887	+	0.897853i
$315$	4.35913	−	2.51675i	0.245609	−	0.141803i
$316$	6.20335	−	10.2719i	0.348966	−	0.577840i
$317$	3.38914	+	9.31160i	0.190353	+	0.522992i	0.997752	−	0.0670148i	$-0.0213475\pi$
$317$	3.38914	+	9.31160i	0.190353	+	0.522992i	−0.807399	+	0.590006i	$0.799125\pi$
$318$	13.4060	−	2.22795i	0.751769	−	0.124937i
$319$	1.00081	−	5.67589i	0.0560348	−	0.317789i
$320$	11.6384	−	26.9139i	0.650605	−	1.50453i
$321$	9.14009	−	7.66945i	0.510150	−	0.428067i
$322$	−0.161518	+	16.4024i	−0.00900103	+	0.914068i
$323$	−1.89935	−	0.0745289i	−0.105683	−	0.00414690i
$324$	−1.99961	−	0.0393850i	−0.111090	−	0.00218806i
$325$	−0.317903	−	0.378862i	−0.0176341	−	0.0210155i
$326$	−5.36522	−	2.01283i	−0.297152	−	0.111480i
$327$	−1.25881	+	7.13908i	−0.0696125	+	0.394792i
$328$	13.5532	−	1.97899i	0.748350	−	0.109272i
$329$	−6.17149	+	2.24624i	−0.340245	+	0.123839i
$330$	5.34431	−	9.04964i	0.294195	−	0.498167i
$331$	−18.8554	+	10.8862i	−1.03639	+	0.598359i	−0.918808	−	0.394704i	$-0.870847\pi$
$331$	−18.8554	+	10.8862i	−1.03639	+	0.598359i	−0.117581	+	0.993063i	$0.537514\pi$
$332$	−9.82406	+	11.2503i	−0.539165	+	0.617439i
$333$	−6.05986	+	7.22186i	−0.332078	+	0.395755i
$334$	−2.60256	+	1.46861i	−0.142406	+	0.0803588i
$335$	−14.3508	+	24.8563i	−0.784066	+	1.35804i
$336$	1.67404	+	5.23181i	0.0913262	+	0.285419i
$337$	−0.651565	−	3.69521i	−0.0354930	−	0.201291i	0.961905	−	0.273384i	$-0.0881431\pi$
$337$	−0.651565	−	3.69521i	−0.0354930	−	0.201291i	−0.997398	+	0.0720936i	$0.977032\pi$
$338$	−18.0684	−	3.36972i	−0.982790	−	0.183288i
$339$	−1.25919	+	3.45961i	−0.0683900	+	0.187900i
$340$	−2.00619	−	2.48881i	−0.108801	−	0.134975i
$341$		−	8.45830i		−	0.458043i
$342$	−4.18925	+	4.52219i	−0.226529	+	0.244532i
$343$	−16.6360			−0.898261
$344$	−7.86310	+	6.21156i	−0.423950	+	0.334905i
$345$	−29.0905	−	10.5881i	−1.56618	−	0.570044i
$346$	−3.43545	+	18.4209i	−0.184691	+	0.990312i
$347$	−4.01644	+	0.708206i	−0.215614	+	0.0380185i	−0.280411	−	0.959880i	$-0.590471\pi$
$347$	−4.01644	+	0.708206i	−0.215614	+	0.0380185i	0.0647978	+	0.997898i	$0.479360\pi$
$348$	−5.37954	+	1.83885i	−0.288373	+	0.0985728i
$349$	−22.2504	−	12.8463i	−1.19103	−	0.687644i	−0.232493	−	0.972598i	$-0.574688\pi$
$349$	−22.2504	−	12.8463i	−1.19103	−	0.687644i	−0.958541	+	0.284954i	$0.908022\pi$
$350$	14.2661	−	8.05030i	0.762556	−	0.430306i
$351$	−0.0449179	−	0.0376906i	−0.00239754	−	0.00201178i
$352$	8.41271	+	7.79597i	0.448399	+	0.415526i
$353$	11.6943	+	20.2552i	0.622427	+	1.07807i	0.989032	+	0.147698i	$0.0471864\pi$
$353$	11.6943	+	20.2552i	0.622427	+	1.07807i	−0.366606	+	0.930376i	$0.619480\pi$
$354$	−1.59210	−	0.940224i	−0.0846193	−	0.0499724i
$355$	−16.8020	−	46.1631i	−0.891758	−	2.45008i
$356$	−4.76185	−	30.5074i	−0.252377	−	1.61689i
$357$	0.589755	+	0.103990i	0.0312132	+	0.00550372i
$358$	−17.9910	−	6.74954i	−0.950854	−	0.356724i
$359$	−4.93607	+	4.14186i	−0.260516	+	0.218599i	−0.763685	−	0.645589i	$-0.776612\pi$
$359$	−4.93607	+	4.14186i	−0.260516	+	0.218599i	0.503169	+	0.864188i	$0.332167\pi$
$360$	−10.3626	−	0.306206i	−0.546154	−	0.0161385i
$361$	1.82299	+	18.9123i	0.0959470	+	0.995386i
$362$	−27.7736	−	0.273492i	−1.45975	−	0.0143744i
$363$	−4.42819	−	5.27731i	−0.232420	−	0.276987i
$364$	−0.0580509	+	0.150221i	−0.00304269	+	0.00787372i
$365$	16.8241	+	2.96654i	0.880614	+	0.155276i
$366$	−13.8587	+	2.30320i	−0.724407	+	0.120390i
$367$	−10.3959	+	3.78380i	−0.542662	+	0.197513i	−0.598783	−	0.800911i	$-0.704349\pi$
$367$	−10.3959	+	3.78380i	−0.542662	+	0.197513i	0.0561213	+	0.998424i	$0.482127\pi$
$368$	18.0311	−	28.5702i	0.939938	−	1.48932i
$369$	−2.42129	−	4.19381i	−0.126048	−	0.218321i
$370$	−31.7786	+	37.1237i	−1.65209	+	1.92997i
$371$	−8.48252	+	10.1091i	−0.440390	+	0.524837i
$372$	−7.30632	+	4.02859i	−0.378815	+	0.208872i
$373$	24.7097	+	14.2661i	1.27942	+	0.738672i	0.976741	−	0.214421i	$-0.0687865\pi$
$373$	24.7097	+	14.2661i	1.27942	+	0.738672i	0.302676	+	0.953093i	$0.402120\pi$
$374$	1.17915	−	0.416072i	0.0609722	−	0.0215146i
$375$	2.18600	+	12.3974i	0.112884	+	0.640199i
$376$	13.2460	+	2.74132i	0.683110	+	0.141373i
$377$	−0.156625	−	0.0570070i	−0.00806662	−	0.00293601i
$378$	1.49996	−	1.23365i	0.0771496	−	0.0634522i
$379$			4.94280i			0.253895i	0.991909	+	0.126947i	$0.0405179\pi$
$379$			4.94280i			0.253895i	−0.991909	+	0.126947i	$0.959482\pi$
$380$	−21.9449	+	23.2260i	−1.12575	+	1.19147i
$381$		−	15.1996i		−	0.778697i
$382$	−5.94602	−	7.22959i	−0.304225	−	0.369898i
$383$	18.2846	+	6.65506i	0.934301	+	0.340058i	0.763913	−	0.645319i	$-0.223276\pi$
$383$	18.2846	+	6.65506i	0.934301	+	0.340058i	0.170388	+	0.985377i	$0.445498\pi$
$384$	2.72732	−	10.9801i	0.139178	−	0.560324i
$385$	1.77219	+	10.0506i	0.0903194	+	0.512227i
$386$	7.24383	+	20.5290i	0.368701	+	1.04490i
$387$	3.06816	+	1.77140i	0.155963	+	0.0900455i
$388$	−7.46954	−	13.5469i	−0.379209	−	0.687740i
$389$	−2.46268	+	2.93491i	−0.124863	+	0.148806i	−0.824854	−	0.565346i	$-0.808743\pi$
$389$	−2.46268	+	2.93491i	−0.124863	+	0.148806i	0.699991	+	0.714151i	$0.253187\pi$
$390$	−0.230899	−	0.197654i	−0.0116920	−	0.0100086i
$391$	−1.84157	−	3.18968i	−0.0931320	−	0.161309i
$392$	12.3079	+	7.59929i	0.621642	+	0.383822i
$393$	−6.29467	+	2.29107i	−0.317524	+	0.115569i
$394$	4.62323	+	27.8188i	0.232915	+	1.40149i
$395$	−21.6573	−	3.81877i	−1.08970	−	0.192143i
$396$	1.46170	−	3.78250i	0.0734530	−	0.190078i
$397$	−2.88731	−	3.44096i	−0.144910	−	0.172697i	0.688707	−	0.725040i	$-0.258179\pi$
$397$	−2.88731	−	3.44096i	−0.144910	−	0.172697i	−0.833617	+	0.552342i	$0.813734\pi$
$398$	−0.219191	+	22.2592i	−0.0109871	+	1.11575i
$399$	0.234704	−	5.98137i	0.0117499	−	0.299443i
$400$	−33.7120	−	1.32852i	−1.68560	−	0.0664260i
$401$	12.4383	−	10.4370i	0.621141	−	0.521199i	−0.277021	−	0.960864i	$-0.589347\pi$
$401$	12.4383	−	10.4370i	0.621141	−	0.521199i	0.898162	+	0.439665i	$0.144903\pi$
$402$	−3.88985	+	10.3685i	−0.194008	+	0.517132i
$403$	−0.240895	−	0.0424764i	−0.0119999	−	0.00211590i
$404$	11.0765	−	1.72892i	0.551078	−	0.0860170i
$405$	1.25361	+	3.44427i	0.0622925	+	0.171147i
$406$	2.80723	−	4.75354i	0.139320	−	0.235914i
$407$	−9.55733	−	16.5538i	−0.473739	−	0.820541i
$408$	−0.921018	−	0.820382i	−0.0455972	−	0.0406150i
$409$	14.0032	+	11.7501i	0.692413	+	0.581004i	0.919604	−	0.392847i	$-0.128510\pi$
$409$	14.0032	+	11.7501i	0.692413	+	0.581004i	−0.227191	+	0.973850i	$0.572954\pi$
$410$	−12.3362	−	21.8613i	−0.609242	−	1.07965i
$411$	−8.35652	−	4.82464i	−0.412197	−	0.237982i
$412$	22.6700	−	7.74912i	1.11687	−	0.381772i
$413$	1.76820	−	0.311782i	0.0870076	−	0.0153418i
$414$	−11.7421	−	2.18988i	−0.577092	−	0.107627i
$415$	25.7216	+	9.36190i	1.26262	+	0.459558i
$416$	0.264279	−	0.200447i	0.0129574	−	0.00982771i
$417$	21.1172			1.03411
$418$	−5.71093	−	11.1176i	−0.279331	−	0.543782i
$419$		−	21.6852i		−	1.05939i	−0.848188	−	0.529696i	$-0.822306\pi$
$419$		−	21.6852i		−	1.05939i	0.848188	−	0.529696i	$-0.177694\pi$
$420$	7.83769	−	6.31781i	0.382440	−	0.308278i
$421$	0.683080	−	1.87675i	0.0332913	−	0.0914670i	−0.921933	−	0.387348i	$-0.873391\pi$
$421$	0.683080	−	1.87675i	0.0332913	−	0.0914670i	0.955225	+	0.295881i	$0.0956133\pi$
$422$	−6.28990	+	33.7264i	−0.306188	+	1.64177i
$423$	−0.830456	−	4.70975i	−0.0403782	−	0.228996i
$424$	25.8040	−	8.53757i	1.25315	−	0.414621i
$425$	−1.83905	+	3.18533i	−0.0892070	+	0.154511i
$426$	−9.31517	−	16.5076i	−0.451322	−	0.799798i
$427$	8.76900	−	10.4505i	0.424362	−	0.505735i
$428$	15.6959	−	17.9746i	0.758690	−	0.868834i
$429$	0.102960	−	0.0594439i	0.00497095	−	0.00286998i
$430$	15.8127	+	9.33830i	0.762559	+	0.450333i
$431$	27.0992	−	9.86330i	1.30532	−	0.475098i	0.406596	−	0.913608i	$-0.366716\pi$
$431$	27.0992	−	9.86330i	1.30532	−	0.475098i	0.898726	+	0.438510i	$0.144494\pi$
$432$	−3.96353	+	0.538937i	−0.190695	+	0.0259296i
$433$	−1.13668	+	6.44643i	−0.0546253	+	0.309796i	−0.999862	−	0.0165889i	$-0.994719\pi$
$433$	−1.13668	+	6.44643i	−0.0546253	+	0.309796i	0.945237	+	0.326385i	$0.105830\pi$
$434$	2.84583	−	7.58560i	0.136604	−	0.364120i
$435$	6.69715	+	7.98135i	0.321104	+	0.382676i
$436$	−0.285510	+	14.4956i	−0.0136735	+	0.694214i
$437$	−29.1085	+	22.5406i	−1.39245	+	1.07826i
$438$	6.59118	+	0.0649048i	0.314939	+	0.00310127i
$439$	18.2069	−	15.2774i	0.868967	−	0.729150i	−0.0949135	−	0.995486i	$-0.530257\pi$
$439$	18.2069	−	15.2774i	0.868967	−	0.729150i	0.963880	+	0.266336i	$0.0858130\pi$
$440$	7.76946	−	19.5312i	0.370394	−	0.931112i
$441$	0.888056	−	5.03642i	0.0422884	−	0.239829i
$442$	−0.00592836	−	0.0356720i	−0.000281984	−	0.00169674i
$443$	−11.7259	−	32.2168i	−0.557116	−	1.53066i	−0.823800	−	0.566880i	$-0.808150\pi$
$443$	−11.7259	−	32.2168i	−0.557116	−	1.53066i	0.266684	−	0.963784i	$-0.414072\pi$
$444$	−9.74719	+	16.1400i	−0.462581	+	0.765972i
$445$	−49.0054	+	28.2933i	−2.32308	+	1.34123i
$446$	−1.52016	+	1.77584i	−0.0719816	+	0.0840887i
$447$	14.2932	+	11.9934i	0.676046	+	0.567270i
$448$	4.92173	+	9.82209i	0.232530	+	0.464050i
$449$	17.0193	−	29.4783i	0.803191	−	1.39117i	−0.114315	−	0.993445i	$-0.536467\pi$
$449$	17.0193	−	29.4783i	0.803191	−	1.39117i	0.917506	−	0.397723i	$-0.130199\pi$
$450$	3.96913	+	11.2485i	0.187106	+	0.530259i
$451$	9.66943	−	1.70498i	0.455316	−	0.0802844i
$452$	−1.42117	+	7.22482i	−0.0668462	+	0.339827i
$453$	2.71485	−	7.45900i	0.127555	−	0.350454i
$454$	30.4031	−	25.0052i	1.42689	−	1.17355i
$455$	0.295145			0.0138366
$456$	−6.88342	+	10.2283i	−0.322346	+	0.478985i
$457$	−9.12554			−0.426875			−0.213437	−	0.976957i	$-0.568466\pi$
$457$	−9.12554			−0.426875			−0.213437	+	0.976957i	$0.568466\pi$
$458$	26.8143	−	22.0536i	1.25295	−	1.03050i
$459$	−0.149147	+	0.409778i	−0.00696158	+	0.0191268i
$460$	−60.7508	−	11.9501i	−2.83252	−	0.557175i
$461$	10.8009	−	1.90449i	0.503049	−	0.0887010i	0.0836352	−	0.996496i	$-0.473347\pi$
$461$	10.8009	−	1.90449i	0.503049	−	0.0887010i	0.419413	+	0.907795i	$0.362236\pi$
$462$	1.31028	+	3.71333i	0.0609597	+	0.172760i
$463$	−15.9834	+	27.6840i	−0.742811	+	1.28659i	0.208400	+	0.978044i	$0.433174\pi$
$463$	−15.9834	+	27.6840i	−0.742811	+	1.28659i	−0.951211	+	0.308542i	$0.900159\pi$
$464$	−10.0632	+	5.29298i	−0.467171	+	0.245720i
$465$	11.7132	+	9.82857i	0.543188	+	0.455789i
$466$	−20.2017	+	23.5995i	−0.935825	+	1.09323i
$467$	−10.5167	+	6.07183i	−0.486656	+	0.280971i	−0.723186	−	0.690653i	$-0.757323\pi$
$467$	−10.5167	+	6.07183i	−0.486656	+	0.280971i	0.236530	+	0.971624i	$0.423990\pi$
$468$	−0.100386	−	0.0606248i	−0.00464036	−	0.00280238i
$469$	−3.67793	−	10.1050i	−0.169831	−	0.466607i
$470$	−4.06410	−	24.4544i	−0.187463	−	1.12800i
$471$	3.00408	−	17.0370i	0.138421	−	0.785024i
$472$	−3.43612	−	1.36688i	−0.158160	−	0.0629157i
$473$	−5.50267	+	4.61729i	−0.253013	+	0.212303i
$474$	−8.48468	−	0.0835505i	−0.389714	−	0.00383760i
$475$	34.0285	+	13.9194i	1.56133	+	0.638665i
$476$	1.19747	+	0.0235859i	0.0548861	+	0.00108106i
$477$	−6.17685	−	7.36128i	−0.282818	−	0.337050i
$478$	−5.75773	+	15.3473i	−0.263352	+	0.701970i
$479$	−4.03772	+	22.8991i	−0.184488	+	1.04629i	0.742123	+	0.670264i	$0.233819\pi$
$479$	−4.03772	+	22.8991i	−0.184488	+	1.04629i	−0.926611	+	0.376021i	$0.877292\pi$
$480$	−20.5716	+	2.59116i	−0.938961	+	0.118270i
$481$	−0.519453	+	0.189065i	−0.0236850	+	0.00862064i
$482$	4.74857	+	2.80429i	0.216291	+	0.127732i
$483$	10.0448	−	5.79939i	0.457056	−	0.263882i
$484$	−10.3782	−	9.06250i	−0.471735	−	0.411932i
$485$	−18.2235	+	21.7179i	−0.827486	+	0.986160i
$486$	0.695013	+	1.23165i	0.0315264	+	0.0558687i
$487$	−0.603863	+	1.04592i	−0.0273637	+	0.0473952i	−0.879383	−	0.476115i	$-0.842045\pi$
$487$	−0.603863	+	1.04592i	−0.0273637	+	0.0473952i	0.852019	+	0.523510i	$0.175378\pi$
$488$	−26.6755	+	8.82591i	−1.20754	+	0.399530i
$489$	0.703619	+	3.99042i	0.0318188	+	0.180453i
$490$	4.86011	−	26.0599i	0.219558	−	1.17726i
$491$	−4.45502	+	12.2401i	−0.201052	+	0.552386i	−0.998713	−	0.0507201i	$-0.983848\pi$
$491$	−4.45502	+	12.2401i	−0.201052	+	0.552386i	0.797661	+	0.603106i	$0.206071\pi$
$492$	−6.07820	−	7.54043i	−0.274026	−	0.339949i
$493$			1.23958i			0.0558277i
$494$	−0.345314	+	0.106818i	−0.0155364	+	0.00480597i
$495$	−7.43161			−0.334026
$496$	−13.1952	+	10.2144i	−0.592483	+	0.458638i
$497$	17.2959	+	6.29518i	0.775825	+	0.282377i
$498$	10.3823	+	1.93627i	0.465240	+	0.0867663i
$499$	20.6357	−	3.63863i	0.923781	−	0.162887i	0.308526	−	0.951216i	$-0.400164\pi$
$499$	20.6357	−	3.63863i	0.923781	−	0.162887i	0.615255	+	0.788328i	$0.289053\pi$
$500$	8.14357	+	23.8239i	0.364191	+	1.06544i
$501$	1.82997	+	1.05654i	0.0817572	+	0.0472025i
$502$	−17.8971	−	31.7158i	−0.798785	−	1.41555i
$503$	14.9252	+	12.5238i	0.665483	+	0.558407i	0.911725	−	0.410802i	$-0.134751\pi$
$503$	14.9252	+	12.5238i	0.665483	+	0.558407i	−0.246242	+	0.969208i	$0.579196\pi$
$504$	2.58352	−	2.90044i	0.115079	−	0.129196i
$505$	−10.2726	−	17.7927i	−0.457127	−	0.791766i
$506$	12.3150	−	20.8533i	0.547470	−	0.927043i
$507$	4.44509	+	12.2128i	0.197413	+	0.542388i
$508$	−4.68819	−	30.0354i	−0.208005	−	1.33261i
$509$	25.9811	+	4.58117i	1.15159	+	0.203057i	0.716671	−	0.697411i	$-0.245665\pi$
$509$	25.9811	+	4.58117i	1.15159	+	0.203057i	0.434922	+	0.900468i	$0.356776\pi$
$510$	−0.793986	+	2.11638i	−0.0351583	+	0.0937150i
$511$	−4.90322	+	4.11429i	−0.216906	+	0.182005i
$512$	2.00266	−	22.5386i	0.0885061	−	0.996076i
$513$	4.25970	+	0.924644i	0.188070	+	0.0408240i
$514$	0.182513	−	18.5345i	0.00805031	−	0.817522i
$515$	−28.2225	−	33.6343i	−1.24363	−	1.48210i
$516$	6.60929	+	2.55407i	0.290958	+	0.112437i
$517$	9.54926	+	1.68379i	0.419976	+	0.0740531i
$518$	−3.00165	−	18.0614i	−0.131885	−	0.793573i
$519$	12.4510	−	4.53180i	0.546539	−	0.198924i
$520$	−0.517237	−	0.319359i	−0.0226824	−	0.0140048i
$521$	11.0907	+	19.2097i	0.485893	+	0.841591i	0.999869	−	0.0162136i	$-0.00516119\pi$
$521$	11.0907	+	19.2097i	0.485893	+	0.841591i	−0.513976	+	0.857805i	$0.671828\pi$
$522$	3.05390	+	2.61420i	0.133666	+	0.114421i
$523$	−3.19064	+	3.80245i	−0.139517	+	0.166270i	−0.831278	−	0.555856i	$-0.812390\pi$
$523$	−3.19064	+	3.80245i	−0.139517	+	0.166270i	0.691762	+	0.722126i	$0.256835\pi$
$524$	−11.7321	+	6.46887i	−0.512518	+	0.282594i
$525$	−10.0311	−	5.79147i	−0.437794	−	0.252761i
$526$	−3.95368	−	11.2047i	−0.172389	−	0.488549i
$527$	0.315896	+	1.79154i	0.0137606	+	0.0780405i
$528$	1.72174	−	7.92534i	0.0749290	−	0.344906i
$529$	−45.4211	−	16.5319i	−1.97483	−	0.718779i
$530$	−31.6406	−	38.4709i	−1.37438	−	1.67107i
$531$			1.30744i			0.0567382i
$532$	−1.38112	−	11.8920i	−0.0598790	−	0.515584i
$533$		−	0.283951i		−	0.0122993i
$534$	−16.8625	+	13.8687i	−0.729714	+	0.600158i
$535$	−41.0955	−	14.9575i	−1.77671	−	0.646670i
$536$	−4.48856	+	21.6886i	−0.193876	+	0.936806i
$537$	2.35942	+	13.3809i	0.101816	+	0.577430i
$538$	25.0874	−	8.85230i	1.08159	−	0.381650i
$539$	8.97992	+	5.18456i	0.386793	+	0.223315i
$540$	3.53959	+	6.41946i	0.152320	+	0.276250i
$541$	14.0331	−	16.7240i	0.603332	−	0.719023i	−0.374777	−	0.927115i	$-0.622281\pi$
$541$	14.0331	−	16.7240i	0.603332	−	0.719023i	0.978109	+	0.208092i	$0.0667253\pi$
$542$	−1.24210	+	1.45101i	−0.0533526	+	0.0623263i
$543$	9.81991	+	17.0086i	0.421413	+	0.729908i
$544$	−2.07304	−	1.33705i	−0.0888808	−	0.0573257i
$545$	24.9682	−	9.08769i	1.06952	−	0.389274i
$546$	0.112337	−	0.0186694i	0.00480757	−	0.000798977i
$547$	−20.7434	−	3.65762i	−0.886923	−	0.156388i	−0.288415	−	0.957506i	$-0.593128\pi$
$547$	−20.7434	−	3.65762i	−0.886923	−	0.156388i	−0.598508	+	0.801117i	$0.704239\pi$
$548$	−18.0012	−	6.95633i	−0.768974	−	0.297160i
$549$	6.38546	+	7.60989i	0.272525	+	0.324782i
$550$	−24.1839	−	0.238144i	−1.03121	−	0.0101545i
$551$	12.2772	−	1.67149i	0.523027	−	0.0712079i
$552$	−23.8787	−	0.705598i	−1.01634	−	0.0300322i
$553$	6.31180	−	5.29623i	0.268405	−	0.225219i
$554$	−1.05516	−	0.395857i	−0.0448295	−	0.0168183i
$555$	34.0297	+	6.00035i	1.44448	+	0.254701i
$556$	41.7291	−	6.51343i	1.76971	−	0.276231i
$557$	6.81979	+	18.7372i	0.288964	+	0.793922i	0.996212	+	0.0869564i	$0.0277141\pi$
$557$	6.81979	+	18.7372i	0.288964	+	0.793922i	−0.707248	+	0.706965i	$0.750064\pi$
$558$	5.07996	+	2.99999i	0.215052	+	0.127000i
$559$	0.103868	+	0.179905i	0.00439316	+	0.00760918i
$560$	13.5392	−	14.9019i	0.572134	−	0.629722i
$561$	−0.677311	−	0.568332i	−0.0285961	−	0.0239950i
$562$	18.2995	−	10.3263i	0.771917	−	0.435589i
$563$	−19.1810	−	11.0742i	−0.808384	−	0.466721i	0.0380103	−	0.999277i	$-0.487898\pi$
$563$	−19.1810	−	11.0742i	−0.808384	−	0.466721i	−0.846394	+	0.532557i	$0.821231\pi$
$564$	−3.09373	−	9.05066i	−0.130269	−	0.381102i
$565$	13.2893	−	2.34327i	0.559087	−	0.0985821i
$566$	−2.21714	+	11.8883i	−0.0931933	+	0.499701i
$567$	−1.29046	−	0.469688i	−0.0541941	−	0.0197251i
$568$	−23.4991	−	29.7471i	−0.986001	−	1.24816i
$569$	−40.1025			−1.68118			−0.840592	−	0.541669i	$-0.817793\pi$
$569$	−40.1025			−1.68118			−0.840592	+	0.541669i	$0.817793\pi$
$570$	22.0320	+	5.01012i	0.922821	+	0.209851i
$571$			25.1495i			1.05247i	0.850338	+	0.526237i	$0.176398\pi$
$571$			25.1495i			1.05247i	−0.850338	+	0.526237i	$0.823602\pi$
$572$	0.185121	−	0.149223i	0.00774031	−	0.00623931i
$573$	−2.26383	+	6.21982i	−0.0945728	+	0.259837i
$574$	9.24541	+	1.72425i	0.385896	+	0.0719688i
$575$	12.3705	+	70.1564i	0.515884	+	2.92572i
$576$	−7.66599	+	2.28750i	−0.319416	+	0.0953124i
$577$	16.4947	−	28.5697i	0.686683	−	1.18937i	−0.286221	−	0.958164i	$-0.592399\pi$
$577$	16.4947	−	28.5697i	0.686683	−	1.18937i	0.972905	−	0.231207i	$-0.0742675\pi$
$578$	20.7038	−	11.6831i	0.861165	−	0.485951i
$579$	9.89468	−	11.7920i	0.411209	−	0.490060i
$580$	15.6958	+	13.7060i	0.651734	+	0.569112i
$581$	−8.88157	+	5.12778i	−0.368470	+	0.212736i
$582$	−5.56239	+	9.41892i	−0.230569	+	0.390427i
$583$	18.3087	−	6.66381i	0.758268	−	0.275987i
$584$	13.0447	−	1.90474i	0.539792	−	0.0788188i
$585$	−0.0373205	+	0.211655i	−0.00154301	+	0.00875085i
$586$	30.7130	+	11.5224i	1.26874	+	0.475985i
$587$	8.05095	+	9.59475i	0.332298	+	0.396018i	0.906160	−	0.422934i	$-0.139000\pi$
$587$	8.05095	+	9.59475i	0.332298	+	0.396018i	−0.573862	+	0.818952i	$0.694555\pi$
$588$	0.201419	−	10.2262i	0.00830640	−	0.421723i
$589$	17.3180	−	5.54452i	0.713577	−	0.228458i
$590$	−0.0667331	+	6.77685i	−0.00274736	+	0.278999i
$591$	15.2754	−	12.8176i	0.628346	−	0.527245i
$592$	−14.2829	+	34.9003i	−0.587023	+	1.43439i
$593$	2.11950	−	12.0203i	0.0870376	−	0.493615i	−0.909861	−	0.414914i	$-0.863812\pi$
$593$	2.11950	−	12.0203i	0.0870376	−	0.493615i	0.996898	−	0.0787009i	$-0.0250772\pi$
$594$	−2.82859	+	0.470087i	−0.116059	+	0.0192879i
$595$	−0.750729	−	2.06261i	−0.0307769	−	0.0845589i
$596$	31.9437	+	19.2913i	1.30847	+	0.790201i
$597$	13.6316	−	7.87020i	0.557904	−	0.322106i
$598$	−0.532065	−	0.455458i	−0.0217578	−	0.0186251i
$599$	−10.2192	−	8.57489i	−0.417544	−	0.350361i	0.409684	−	0.912227i	$-0.365639\pi$
$599$	−10.2192	−	8.57489i	−0.417544	−	0.350361i	−0.827228	+	0.561867i	$0.810083\pi$
$600$	11.3128	+	21.0036i	0.461843	+	0.857469i
$601$	−7.06611	+	12.2389i	−0.288232	+	0.499233i	−0.973388	−	0.229164i	$-0.926401\pi$
$601$	−7.06611	+	12.2389i	−0.288232	+	0.499233i	0.685155	+	0.728397i	$0.259734\pi$
$602$	−6.48842	+	2.28949i	−0.264448	+	0.0933128i
$603$	7.71161	−	1.35977i	0.314041	−	0.0553739i
$604$	3.06408	−	15.5769i	0.124676	−	0.633815i
$605$	−8.63618	+	23.7277i	−0.351110	+	0.964668i
$606$	−5.03542	−	6.12241i	−0.204550	−	0.248706i
$607$	4.05081			0.164417			0.0822086	−	0.996615i	$-0.473803\pi$
$607$	4.05081			0.164417			0.0822086	+	0.996615i	$0.473803\pi$
$608$	−10.4473	+	22.3350i	−0.423694	+	0.905805i
$609$	−3.90363			−0.158183
$610$	32.7092	+	39.7702i	1.32436	+	1.61025i
$611$	0.0959100	−	0.263510i	0.00388010	−	0.0106605i
$612$	−0.168332	+	0.855754i	−0.00680443	+	0.0345918i
$613$	−0.547387	+	0.0965190i	−0.0221087	+	0.00389837i	−0.184692	−	0.982797i	$-0.559129\pi$
$613$	−0.547387	+	0.0965190i	−0.0221087	+	0.00389837i	0.162583	+	0.986695i	$0.448018\pi$
$614$	−18.6311	+	6.57412i	−0.751888	+	0.265310i
$615$	−8.87481	+	15.3716i	−0.357867	+	0.619843i
$616$	3.73455	+	6.93366i	0.150469	+	0.279365i
$617$	1.74834	+	1.46703i	0.0703856	+	0.0590605i	0.677302	−	0.735705i	$-0.263149\pi$
$617$	1.74834	+	1.46703i	0.0703856	+	0.0590605i	−0.606916	+	0.794766i	$0.707594\pi$
$618$	−12.8695	−	11.0165i	−0.517687	−	0.443150i
$619$	14.6114	−	8.43592i	0.587283	−	0.339068i	−0.176739	−	0.984258i	$-0.556555\pi$
$619$	14.6114	−	8.43592i	0.587283	−	0.339068i	0.764023	+	0.645190i	$0.223222\pi$
$620$	26.1777	+	15.8091i	1.05132	+	0.634909i
$621$	2.88873	+	7.93671i	0.115921	+	0.318489i
$622$	−46.6669	+	7.75563i	−1.87117	+	0.310972i
$623$	3.68154	−	20.8791i	0.147498	−	0.836502i
$624$	−0.217070	−	0.0888356i	−0.00868976	−	0.00355627i
$625$	3.04019	−	2.55102i	0.121607	−	0.102041i
$626$	0.472220	−	47.9547i	0.0188737	−	1.91666i
$627$	−4.71565	+	7.47469i	−0.188325	+	0.298510i
$628$	0.681354	−	34.5929i	0.0271890	−	1.38041i
$629$	2.64256	+	3.14928i	0.105366	+	0.125570i
$630$	−6.66484	−	2.50039i	−0.265534	−	0.0996181i
$631$	−4.11266	+	23.3241i	−0.163723	+	0.928517i	0.786649	+	0.617400i	$0.211814\pi$
$631$	−4.11266	+	23.3241i	−0.163723	+	0.928517i	−0.950372	+	0.311117i	$0.899297\pi$
$632$	−16.7921	+	2.45193i	−0.667954	+	0.0975326i
$633$	22.7963	−	8.29718i	0.906073	−	0.329783i
$634$	7.12602	−	12.0667i	0.283011	−	0.479228i
$635$	−48.2473	+	27.8556i	−1.91464	+	1.10542i
$636$	−14.4764	−	12.6412i	−0.574028	−	0.501257i
$637$	0.192754	−	0.229715i	0.00763719	−	0.00910165i
$638$	−7.09855	+	4.00567i	−0.281034	+	0.158586i
$639$	−6.70144	+	11.6072i	−0.265105	+	0.459175i
$640$	−39.8518	+	11.4655i	−1.57528	+	0.453213i
$641$	0.332931	+	1.88815i	0.0131500	+	0.0745773i	0.990677	−	0.136235i	$-0.0435002\pi$
$641$	0.332931	+	1.88815i	0.0131500	+	0.0745773i	−0.977527	+	0.210812i	$0.932389\pi$
$642$	−16.5877	−	3.09358i	−0.654666	−	0.122094i
$643$	9.07407	−	24.9308i	0.357846	−	0.983175i	−0.621929	−	0.783074i	$-0.713651\pi$
$643$	9.07407	−	24.9308i	0.357846	−	0.983175i	0.979775	−	0.200101i	$-0.0641270\pi$
$644$	18.0606	−	14.5583i	0.711686	−	0.573677i
$645$		−	12.9855i		−	0.511304i
$646$	1.62483	+	2.14152i	0.0639283	+	0.0842568i
$647$	12.5679			0.494094			0.247047	−	0.969004i	$-0.420540\pi$
$647$	12.5679			0.494094			0.247047	+	0.969004i	$0.420540\pi$
$648$	1.75329	+	2.21946i	0.0688757	+	0.0871884i
$649$	−2.49104	−	0.906664i	−0.0977818	−	0.0355897i
$650$	−0.128231	+	0.687571i	−0.00502962	+	0.0269687i
$651$	−5.64184	+	0.994809i	−0.221121	+	0.0389896i
$652$	2.62122	+	7.66834i	0.102655	+	0.300315i
$653$	−7.43086	−	4.29021i	−0.290792	−	0.167889i	0.347507	−	0.937677i	$-0.387028\pi$
$653$	−7.43086	−	4.29021i	−0.290792	−	0.167889i	−0.638299	+	0.769789i	$0.720362\pi$
$654$	8.92847	−	5.03829i	0.349131	−	0.197013i
$655$	18.8084	+	15.7822i	0.734906	+	0.616660i
$656$	−14.3368	−	13.0257i	−0.559756	−	0.508567i
$657$	−2.33045	−	4.03645i	−0.0909194	−	0.157477i
$658$	7.99748	+	4.72295i	0.311774	+	0.184120i
$659$	−0.406103	−	1.11576i	−0.0158195	−	0.0434638i	0.931532	−	0.363661i	$-0.118473\pi$
$659$	−0.406103	−	1.11576i	−0.0158195	−	0.0434638i	−0.947351	+	0.320197i	$0.896251\pi$
$660$	−14.6854	+	2.29222i	−0.571629	+	0.0892247i
$661$	18.9611	+	3.34335i	0.737500	+	0.130041i	0.529766	−	0.848144i	$-0.322280\pi$
$661$	18.9611	+	3.34335i	0.737500	+	0.130041i	0.207735	+	0.978185i	$0.433391\pi$
$662$	28.8288	+	10.8155i	1.12046	+	0.420355i
$663$	−0.0195876	+	0.0164360i	−0.000760721	+	0.000638320i
$664$	21.1133	+	0.623884i	0.819356	+	0.0242114i
$665$	−19.4165	+	10.2168i	−0.752941	+	0.396190i
$666$	13.3318	+	0.131281i	0.516597	+	0.00508704i
$667$	15.4324	+	18.3916i	0.597544	+	0.712126i
$668$	3.94204	+	1.52335i	0.152522	+	0.0589402i
$669$	1.62784	+	0.287032i	0.0629360	+	0.0110973i
$670$	40.0409	−	6.65445i	1.54691	−	0.257084i
$671$	−18.9270	+	6.88887i	−0.730669	+	0.265942i
$672$	4.21060	−	6.52834i	0.162428	−	0.251836i
$673$	20.7172	+	35.8833i	0.798591	+	1.38320i	0.920534	+	0.390663i	$0.127754\pi$
$673$	20.7172	+	35.8833i	0.798591	+	1.38320i	−0.121943	+	0.992537i	$0.538913\pi$
$674$	−3.45077	+	4.03118i	−0.132919	+	0.155275i
$675$	5.42161	−	6.46123i	0.208678	−	0.248693i
$676$	12.5507	+	22.7623i	0.482721	+	0.875472i
$677$	−33.0040	−	19.0549i	−1.26845	−	0.732339i	−0.293754	−	0.955881i	$-0.594905\pi$
$677$	−33.0040	−	19.0549i	−1.26845	−	0.732339i	−0.974694	+	0.223542i	$0.928238\pi$
$678$	4.90992	−	1.73251i	0.188564	−	0.0665365i
$679$	−1.84451	−	10.4607i	−0.0707858	−	0.401446i
$680$	−0.916193	+	4.42702i	−0.0351344	+	0.169769i
$681$	−26.1566	−	9.52024i	−1.00232	−	0.364816i
$682$	−9.23857	+	7.59833i	−0.353763	+	0.290955i
$683$		−	11.1589i		−	0.426984i	−0.976945	−	0.213492i	$-0.931516\pi$
$683$		−	11.1589i		−	0.426984i	0.976945	−	0.213492i	$-0.0684837\pi$
$684$	8.70267	+	0.513293i	0.332755	+	0.0196263i
$685$			35.3676i			1.35133i
$686$	14.9446	+	18.1707i	0.570587	+	0.693760i
$687$	−23.0691	−	8.39645i	−0.880139	−	0.320345i
$688$	13.8482	+	3.00845i	0.527958	+	0.114696i
$689$	−0.0978442	−	0.554902i	−0.00372757	−	0.0211401i
$690$	14.5680	+	41.2857i	0.554594	+	1.57172i
$691$	7.36097	+	4.24986i	0.280024	+	0.161672i	0.633434	−	0.773796i	$-0.281645\pi$
$691$	7.36097	+	4.24986i	0.280024	+	0.161672i	−0.353410	+	0.935468i	$0.614978\pi$
$692$	23.2063	−	12.7956i	0.882172	−	0.486415i
$693$	1.78977	−	2.13297i	0.0679878	−	0.0810246i
$694$	4.38161	+	3.75075i	0.166324	+	0.142376i
$695$	−38.7005	−	67.0313i	−1.46799	−	2.54264i
$696$	6.84107	+	4.22390i	0.259310	+	0.160107i
$697$	−1.98438	+	0.722257i	−0.0751639	+	0.0273574i
$698$	5.95680	+	35.8431i	0.225468	+	1.35668i
$699$	21.6327	+	3.81443i	0.818223	+	0.144275i
$700$	−21.6086	−	8.35035i	−0.816727	−	0.315613i
$701$	−11.5969	−	13.8207i	−0.438011	−	0.522001i	0.501205	−	0.865329i	$-0.332890\pi$
$701$	−11.5969	−	13.8207i	−0.438011	−	0.522001i	−0.939216	+	0.343328i	$0.888446\pi$
$702$	−0.000816531		0.0829200i	−3.08180e−5		0.00312962i
$703$	27.6283	−	30.4195i	1.04202	−	1.14729i
$704$	0.957767	−	16.1921i	0.0360972	−	0.610263i
$705$	−13.4280	+	11.2674i	−0.505728	+	0.424356i
$706$	11.6184	−	30.9689i	0.437263	−	1.16553i
$707$	7.58072	+	1.33669i	0.285102	+	0.0502712i
$708$	0.403271	+	2.58360i	0.0151558	+	0.0970977i
$709$	−14.1577	−	38.8980i	−0.531704	−	1.46084i	−0.857042	−	0.515247i	$-0.827700\pi$
$709$	−14.1577	−	38.8980i	−0.531704	−	1.46084i	0.325338	−	0.945598i	$-0.394522\pi$
$710$	−35.3279	+	59.8216i	−1.32583	+	2.24506i
$711$	2.99993	+	5.19604i	0.112506	+	0.194867i
$712$	−29.0439	+	32.6067i	−1.08847	+	1.22199i
$713$	26.9911	+	22.6482i	1.01082	+	0.848182i
$714$	−0.416211	−	0.737577i	−0.0155763	−	0.0276031i
$715$	−0.377380	−	0.217881i	−0.0141132	−	0.00814827i
$716$	8.78963	+	25.7140i	0.328484	+	0.960975i
$717$	11.4147	−	2.01271i	0.426289	−	0.0751662i
$718$	8.95815	+	1.67068i	0.334315	+	0.0623491i
$719$	−12.3924	−	4.51046i	−0.462158	−	0.168212i	0.100439	−	0.994943i	$-0.467975\pi$
$719$	−12.3924	−	4.51046i	−0.462158	−	0.168212i	−0.562597	+	0.826732i	$0.690198\pi$
$720$	8.97451	+	11.5936i	0.334460	+	0.432067i
$721$	16.4503			0.612643
$722$	19.0193	−	18.9806i	0.707827	−	0.706386i
$723$		−	3.89955i		−	0.145026i
$724$	24.6510	+	30.5813i	0.916148	+	1.13655i
$725$	8.20019	−	22.5298i	0.304547	−	0.836737i
$726$	−1.78617	+	9.57743i	−0.0662911	+	0.355452i
$727$	−4.31118	−	24.4499i	−0.159893	−	0.906797i	−0.954175	−	0.299248i	$-0.903264\pi$
$727$	−4.31118	−	24.4499i	−0.159893	−	0.906797i	0.794283	−	0.607549i	$-0.207847\pi$
$728$	0.216227	−	0.0715415i	0.00801392	−	0.00265151i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	−11.8734	−	21.0410i	−0.439452	−	0.778764i
$731$	0.993065	−	1.18349i	0.0367298	−	0.0437729i
$732$	14.9653	+	13.0682i	0.553135	+	0.483013i
$733$	26.3284	−	15.2007i	0.972463	−	0.561452i	0.0724766	−	0.997370i	$-0.476910\pi$
$733$	26.3284	−	15.2007i	0.972463	−	0.561452i	0.899986	+	0.435919i	$0.143576\pi$
$734$	13.4718	+	7.95582i	0.497252	+	0.293655i
$735$	−17.6144	+	6.41111i	−0.649716	+	0.236477i
$736$	−47.4036	+	5.97088i	−1.74732	+	0.220090i
$737$	−2.75699	+	15.6357i	−0.101555	+	0.575948i
$738$	−2.40556	+	6.41207i	−0.0885500	+	0.236031i
$739$	12.0448	+	14.3544i	0.443074	+	0.528035i	0.940647	−	0.339387i	$-0.110220\pi$
$739$	12.0448	+	14.3544i	0.443074	+	0.528035i	−0.497573	+	0.867422i	$0.665775\pi$
$740$	69.0958	+	1.36094i	2.54001	+	0.0500290i
$741$	0.189200	+	0.171840i	0.00695045	+	0.00631270i
$742$	18.6617	+	0.183766i	0.685093	+	0.00674625i
$743$	−3.58226	+	3.00587i	−0.131420	+	0.110275i	−0.706129	−	0.708084i	$-0.749560\pi$
$743$	−3.58226	+	3.00587i	−0.131420	+	0.110275i	0.574708	+	0.818358i	$0.305116\pi$
$744$	10.9637	+	4.36133i	0.401948	+	0.159894i
$745$	11.8757	−	67.3502i	0.435091	−	2.46752i
$746$	−6.61520	−	39.8048i	−0.242200	−	1.45736i
$747$	−2.55419	−	7.01757i	−0.0934528	−	0.256760i
$748$	−1.51371	−	0.914153i	−0.0553469	−	0.0334247i
$749$	14.1901	−	8.19266i	0.518495	−	0.299353i
$750$	11.5773	−	13.5246i	0.422743	−	0.493847i
$751$	34.4023	+	28.8669i	1.25536	+	1.05337i	0.996161	+	0.0875439i	$0.0279018\pi$
$751$	34.4023	+	28.8669i	1.25536	+	1.05337i	0.259195	+	0.965825i	$0.416543\pi$
$752$	−8.90504	−	16.9305i	−0.324733	−	0.617393i
$753$	−12.8753	+	22.3008i	−0.469204	+	0.812685i
$754$	0.0784351	+	0.222285i	0.00285644	+	0.00809514i
$755$	−28.6522	+	5.05215i	−1.04276	+	0.183867i
$756$	−2.69491	−	0.530106i	−0.0980129	−	0.0192798i
$757$	−2.88932	+	7.93835i	−0.105014	+	0.288524i	−0.981060	−	0.193703i	$-0.937950\pi$
$757$	−2.88932	+	7.93835i	−0.105014	+	0.288524i	0.876046	+	0.482228i	$0.160172\pi$
$758$	5.39877	−	4.44025i	0.196092	−	0.161277i
$759$	−17.1248			−0.621592
$760$	45.0823	+	3.10474i	1.63531	+	0.112621i
$761$	−32.6120			−1.18218			−0.591092	−	0.806604i	$-0.701303\pi$
$761$	−32.6120			−1.18218			−0.591092	+	0.806604i	$0.701303\pi$
$762$	−16.6017	+	13.6542i	−0.601416	+	0.494639i
$763$	−3.40487	+	9.35480i	−0.123264	+	0.338666i
$764$	−2.55503	+	12.9891i	−0.0924379	+	0.469928i
$765$	1.57407	−	0.277552i	0.0569108	−	0.0100349i
$766$	−9.15660	−	25.9498i	−0.330841	−	0.937604i
$767$	−0.0383317	+	0.0663925i	−0.00138408	+	0.00239729i
$768$	−14.4430	+	6.88478i	−0.521166	+	0.248433i
$769$	−30.9106	−	25.9370i	−1.11466	−	0.935314i	−0.116341	−	0.993209i	$-0.537116\pi$
$769$	−30.9106	−	25.9370i	−1.11466	−	0.935314i	−0.998323	+	0.0578959i	$0.981561\pi$
$770$	9.38576	−	10.9644i	0.338239	−	0.395130i
$771$	−11.3506	+	6.55325i	−0.408781	+	0.236010i
$772$	15.9154	−	26.3538i	0.572810	−	0.948495i
$773$	−1.28158	−	3.52112i	−0.0460953	−	0.126646i	0.914509	−	0.404566i	$-0.132577\pi$
$773$	−1.28158	−	3.52112i	−0.0460953	−	0.126646i	−0.960604	+	0.277920i	$0.910355\pi$
$774$	−0.821400	−	4.94250i	−0.0295246	−	0.177654i
$775$	6.11002	−	34.6517i	0.219478	−	1.24472i
$776$	−8.08650	+	20.3282i	−0.290288	+	0.729738i
$777$	−9.91761	+	8.32186i	−0.355792	+	0.298545i
$778$	5.41794	+	0.0533516i	0.194243	+	0.00191275i
$779$	9.82931	+	18.6801i	0.352171	+	0.669285i
$780$	−0.00846463	+	0.429757i	−0.000303082	+	0.0153878i
$781$	−17.4678	−	20.8173i	−0.625046	−	0.744901i
$782$	−1.82960	+	4.87683i	−0.0654264	+	0.174395i
$783$	0.493607	−	2.79938i	0.0176401	−	0.100042i
$784$	−2.75619	−	20.2699i	−0.0984352	−	0.723926i
$785$	−59.5853	+	21.6873i	−2.12669	+	0.774051i
$786$	8.15710	+	4.81722i	0.290954	+	0.171824i
$787$	−11.6622	+	6.73318i	−0.415713	+	0.240012i	−0.693241	−	0.720706i	$-0.743818\pi$
$787$	−11.6622	+	6.73318i	−0.415713	+	0.240012i	0.277529	+	0.960717i	$0.410485\pi$
$788$	26.2318	−	30.0401i	0.934470	−	1.07013i
$789$	−5.40052	+	6.43608i	−0.192263	+	0.229131i
$790$	15.2843	+	27.0857i	0.543791	+	0.963665i
$791$	−2.52795	+	4.37854i	−0.0898836	+	0.155683i
$792$	−5.44451	+	1.80139i	−0.193462	+	0.0640094i
$793$	0.101149	+	0.573643i	0.00359190	+	0.0203707i
$794$	−1.16464	+	6.24478i	−0.0413315	+	0.221619i
$795$	−12.0465	+	33.0976i	−0.427247	+	1.17385i
$796$	24.5095	−	19.7566i	0.868716	−	0.700256i
$797$		−	30.6309i		−	1.08500i	−0.840056	−	0.542500i	$-0.817478\pi$
$797$		−	30.6309i		−	1.08500i	0.840056	−	0.542500i	$-0.182522\pi$
$798$	−6.74399	+	5.11687i	−0.238735	+	0.181135i
$799$	−2.08549			−0.0737795
$800$	28.8333	+	38.0153i	1.01941	+	1.34404i
$801$	14.5073	+	5.28024i	0.512591	+	0.186568i
$802$	−22.5735	−	4.20991i	−0.797098	−	0.148657i
$803$	9.30663	−	1.64101i	0.328424	−	0.0579100i
$804$	14.8193	−	5.06558i	0.522636	−	0.178649i
$805$	−36.8175	−	21.2566i	−1.29765	−	0.749197i
$806$	0.170008	+	0.301275i	0.00598828	+	0.0106120i
$807$	−14.4104	−	12.0918i	−0.507270	−	0.425650i
$808$	−11.8388	−	10.5452i	−0.416486	−	0.370979i
$809$	13.1578	+	22.7900i	0.462605	+	0.801255i	0.999090	−	0.0426547i	$-0.0135815\pi$
$809$	13.1578	+	22.7900i	0.462605	+	0.801255i	−0.536485	+	0.843910i	$0.680248\pi$
$810$	2.63585	−	4.46334i	0.0926142	−	0.156826i
$811$	5.32655	+	14.6346i	0.187041	+	0.513890i	0.997402	−	0.0720411i	$-0.0229513\pi$
$811$	5.32655	+	14.6346i	0.187041	+	0.513890i	−0.810361	+	0.585931i	$0.800729\pi$
$812$	−7.71386	+	1.20405i	−0.270703	+	0.0422537i
$813$	1.33008	+	0.234529i	0.0466480	+	0.00822530i
$814$	−9.49524	+	25.3097i	−0.332808	+	0.887105i
$815$	11.3771	−	9.54654i	0.398523	−	0.334401i
$816$	−0.0686862	+	1.74295i	−0.00240450	+	0.0610155i
$817$	−13.0608	−	8.23981i	−0.456939	−	0.288274i
$818$	0.254554	−	25.8504i	0.00890028	−	0.903837i
$819$	−0.0517596	−	0.0616847i	−0.00180863	−	0.00215544i
$820$	−12.7960	+	33.1128i	−0.446856	+	1.15635i
$821$	24.4095	+	4.30405i	0.851897	+	0.150213i	0.582514	−	0.812821i	$-0.302069\pi$
$821$	24.4095	+	4.30405i	0.851897	+	0.150213i	0.269383	+	0.963033i	$0.413180\pi$
$822$	2.23718	+	13.4615i	0.0780308	+	0.469524i
$823$	20.6795	−	7.52673i	0.720843	−	0.262365i	0.0445592	−	0.999007i	$-0.485812\pi$
$823$	20.6795	−	7.52673i	0.720843	−	0.262365i	0.676283	+	0.736641i	$0.263589\pi$
$824$	−28.8290	−	17.8000i	−1.00431	−	0.620092i
$825$	8.55072	+	14.8103i	0.297698	+	0.515628i
$826$	−1.92897	−	1.65124i	−0.0671174	−	0.0574538i
$827$	−9.78752	+	11.6643i	−0.340345	+	0.405608i	−0.908884	−	0.417049i	$-0.863064\pi$
$827$	−9.78752	+	11.6643i	−0.340345	+	0.405608i	0.568539	+	0.822656i	$0.307509\pi$
$828$	8.15635	+	14.7925i	0.283453	+	0.514075i
$829$	37.0502	+	21.3909i	1.28681	+	0.742938i	0.978083	−	0.208215i	$-0.0667652\pi$
$829$	37.0502	+	21.3909i	1.28681	+	0.742938i	0.308722	+	0.951152i	$0.400099\pi$
$830$	−12.8809	−	36.5045i	−0.447103	−	1.26709i
$831$	0.138379	+	0.784784i	0.00480030	+	0.0272239i
$832$	−0.456347	−	0.108592i	−0.0158210	−	0.00376475i
$833$	−2.09565	−	0.762754i	−0.0726099	−	0.0264279i
$834$	−18.9701	−	23.0652i	−0.656882	−	0.798683i
$835$		−	7.74507i		−	0.268029i
$836$	−7.01295	+	16.2250i	−0.242548	+	0.561155i
$837$		−	4.17168i		−	0.144195i
$838$	−23.6857	+	19.4804i	−0.818207	+	0.672940i
$839$	−52.1532	−	18.9822i	−1.80053	−	0.655338i	−0.998298	−	0.0583228i	$-0.981425\pi$
$839$	−52.1532	−	18.9822i	−1.80053	−	0.655338i	−0.802230	−	0.597016i	$-0.796353\pi$
$840$	−13.9414	−	2.88524i	−0.481025	−	0.0995504i
$841$	3.63269	+	20.6020i	0.125265	+	0.710413i
$842$	−2.66350	+	0.939839i	−0.0917904	+	0.0323890i
$843$	−12.8672	−	7.42885i	−0.443168	−	0.255863i
$844$	42.4880	−	23.4272i	1.46250	−	0.806397i
$845$	30.6201	−	36.4917i	1.05337	−	1.25535i
$846$	−4.39820	+	5.13796i	−0.151213	+	0.176647i
$847$	−4.73028	−	8.19308i	−0.162534	−	0.281518i
$848$	−32.5056	−	20.5148i	−1.11625	−	0.704482i
$849$	8.03552	−	2.92469i	0.275778	−	0.100375i
$850$	5.13124	−	0.852767i	0.176000	−	0.0292497i
$851$	78.4153	+	13.8267i	2.68804	+	0.473975i
$852$	−9.66237	+	25.0038i	−0.331027	+	0.856614i
$853$	15.4823	+	18.4511i	0.530103	+	0.631753i	0.962939	−	0.269720i	$-0.0869313\pi$
$853$	15.4823	+	18.4511i	0.530103	+	0.631753i	−0.432835	+	0.901473i	$0.642487\pi$
$854$	−19.2920	−	0.189972i	−0.660158	−	0.00650071i
$855$	−4.87151	−	15.2159i	−0.166602	−	0.520374i
$856$	−33.7328	−	0.996780i	−1.15296	−	0.0340692i
$857$	18.5121	−	15.5335i	0.632361	−	0.530614i	−0.269300	−	0.963056i	$-0.586792\pi$
$857$	18.5121	−	15.5335i	0.632361	−	0.530614i	0.901662	+	0.432442i	$0.142348\pi$
$858$	−0.157419	−	0.0590577i	−0.00537420	−	0.00201620i
$859$	−54.3335	−	9.58046i	−1.85383	−	0.326881i	−0.868258	−	0.496113i	$-0.834760\pi$
$859$	−54.3335	−	9.58046i	−1.85383	−	0.326881i	−0.985576	+	0.169232i	$0.945871\pi$
$860$	−4.00528	−	25.6603i	−0.136579	−	0.875009i
$861$	−2.27451	−	6.24916i	−0.0775150	−	0.212971i
$862$	−35.1171	−	20.7386i	−1.19609	−	0.706359i
$863$	−1.45648	−	2.52270i	−0.0495793	−	0.0858738i	0.840171	−	0.542322i	$-0.182455\pi$
$863$	−1.45648	−	2.52270i	−0.0495793	−	0.0858738i	−0.889750	+	0.456448i	$0.849121\pi$
$864$	4.14920	+	3.84502i	0.141159	+	0.130810i
$865$	−37.2036	−	31.2175i	−1.26496	−	1.06143i
$866$	8.06222	−	4.54947i	0.273965	−	0.154597i
$867$	−14.5577	−	8.40492i	−0.494407	−	0.285446i
$868$	−10.8418	+	3.70600i	−0.367996	+	0.125790i
$869$	−11.9802	+	2.11244i	−0.406401	+	0.0716595i
$870$	2.70139	−	14.4848i	0.0915857	−	0.491081i
$871$	0.431465	+	0.157040i	0.0146196	+	0.00532111i
$872$	16.0893	−	12.7100i	0.544852	−	0.430413i
$873$	7.73487			0.261786
$874$	50.7690	+	11.5449i	1.71729	+	0.390513i
$875$			17.2877i			0.584431i
$876$	−5.85015	−	7.25752i	−0.197658	−	0.245209i
$877$	−1.48916	+	4.09142i	−0.0502852	+	0.138158i	−0.962293	−	0.272016i	$-0.912310\pi$
$877$	−1.48916	+	4.09142i	−0.0502852	+	0.138158i	0.912007	+	0.410174i	$0.134532\pi$
$878$	−33.0424	−	6.16235i	−1.11513	−	0.207969i
$879$	−4.02784	−	22.8430i	−0.135856	−	0.770477i
$880$	−28.3124	+	9.05920i	−0.954411	+	0.305386i
$881$	7.15927	−	12.4002i	0.241202	−	0.417774i	−0.719855	−	0.694125i	$-0.755792\pi$
$881$	7.15927	−	12.4002i	0.241202	−	0.417774i	0.961057	+	0.276350i	$0.0891250\pi$
$882$	−6.29879	+	3.55437i	−0.212091	+	0.119682i
$883$	3.38302	−	4.03173i	0.113848	−	0.135678i	−0.706111	−	0.708101i	$-0.749552\pi$
$883$	3.38302	−	4.03173i	0.113848	−	0.135678i	0.819959	+	0.572423i	$0.193996\pi$
$884$	−0.0336370	+	0.0385203i	−0.00113134	+	0.00129558i
$885$	4.15016	−	2.39609i	0.139506	−	0.0805438i
$886$	−24.6550	+	41.7488i	−0.828300	+	1.40258i
$887$	14.0321	−	5.10728i	0.471153	−	0.171486i	−0.0955217	−	0.995427i	$-0.530452\pi$
$887$	14.0321	−	5.10728i	0.471153	−	0.171486i	0.566674	+	0.823942i	$0.308230\pi$
$888$	26.3851	−	3.85267i	0.885426	−	0.129287i
$889$	3.62459	−	20.5561i	0.121565	−	0.689429i
$890$	74.9261	+	28.1094i	2.51153	+	0.942231i
$891$	1.30328	+	1.55319i	0.0436617	+	0.0520340i
$892$	3.30526	+	0.0651016i	0.110668	+	0.00217976i
$893$	2.81216	+	20.6555i	0.0941052	+	0.691209i
$894$	0.259827	−	26.3858i	0.00868990	−	0.882473i
$895$	38.1505	−	32.0121i	1.27523	−	1.07005i
$896$	6.30684	−	14.1992i	0.210697	−	0.474362i
$897$	−0.0859984	+	0.487721i	−0.00287140	+	0.0162845i
$898$	−47.4866	+	7.89185i	−1.58465	+	0.263354i
$899$	−4.05578	−	11.1432i	−0.135268	−	0.371645i
$900$	8.72059	−	14.4401i	0.290686	−	0.481337i
$901$	−3.62905	+	2.09523i	−0.120901	+	0.0698022i
$902$	−10.5486	−	9.02979i	−0.351229	−	0.300659i
$903$	3.72700	+	3.12733i	0.124027	+	0.104071i
$904$	9.16798	−	4.93798i	0.304922	−	0.164235i
$905$	35.9931	−	62.3418i	1.19645	−	2.07231i
$906$	−10.5859	+	3.73533i	−0.351693	+	0.124098i
$907$	−3.86208	+	0.680989i	−0.128238	+	0.0226119i	−0.237399	−	0.971412i	$-0.576295\pi$
$907$	−3.86208	+	0.680989i	−0.128238	+	0.0226119i	0.109161	+	0.994024i	$0.465184\pi$
$908$	−54.6239	−	10.7449i	−1.81276	−	0.356581i
$909$	−1.91713	+	5.26728i	−0.0635873	+	0.174705i
$910$	−0.265136	−	0.322371i	−0.00878919	−	0.0106865i
$911$	−24.5914			−0.814750			−0.407375	−	0.913261i	$-0.633556\pi$
$911$	−24.5914			−0.814750			−0.407375	+	0.913261i	$0.633556\pi$
$912$	17.3554	−	1.66997i	0.574696	−	0.0552982i
$913$	15.1416			0.501115
$914$	8.19772	+	9.96736i	0.271156	+	0.329691i
$915$	12.4534	−	34.2154i	0.411696	−	1.13113i
$916$	−48.1760	−	9.47652i	−1.59178	−	0.313113i
$917$	−9.05935	+	1.59741i	−0.299166	+	0.0527510i
$918$	0.581562	−	0.205209i	0.0191944	−	0.00677291i
$919$	−8.52050	+	14.7579i	−0.281065	+	0.486820i	−0.971647	−	0.236435i	$-0.924021\pi$
$919$	−8.52050	+	14.7579i	−0.281065	+	0.486820i	0.690582	+	0.723254i	$0.257354\pi$
$920$	41.5217	+	77.0901i	1.36893	+	2.54159i
$921$	10.7018	+	8.97990i	0.352637	+	0.295898i
$922$	−11.7829	−	10.0864i	−0.388050	−	0.332179i
$923$	−0.680604	+	0.392947i	−0.0224023	+	0.0129340i
$924$	2.87882	−	4.76694i	0.0947062	−	0.156821i
$925$	−27.1962	−	74.7208i	−0.894204	−	2.45681i
$926$	44.5962	−	7.41149i	1.46552	−	0.243557i
$927$	−2.08011	+	11.7969i	−0.0683199	+	0.387461i
$928$	14.8213	+	6.23666i	0.486532	+	0.204728i
$929$	−16.4499	+	13.8031i	−0.539705	+	0.452866i	−0.871437	−	0.490507i	$-0.836811\pi$
$929$	−16.4499	+	13.8031i	−0.539705	+	0.452866i	0.331732	+	0.943374i	$0.392367\pi$
$930$	0.212927	−	21.6230i	0.00698214	−	0.709047i
$931$	−4.72873	+	21.7846i	−0.154978	+	0.713961i
$932$	43.9243	+	0.865148i	1.43879	+	0.0283389i
$933$	21.5019	+	25.6250i	0.703942	+	0.838925i
$934$	16.0794	+	6.03238i	0.526134	+	0.197386i
$935$	−0.562750	+	3.19152i	−0.0184039	+	0.104374i
$936$	0.0239625	+	0.164108i	0.000783240	+	0.00536403i
$937$	31.6434	−	11.5173i	1.03375	−	0.376252i	0.231239	−	0.972897i	$-0.425722\pi$
$937$	31.6434	−	11.5173i	1.03375	−	0.376252i	0.802506	+	0.596644i	$0.203500\pi$
$938$	−7.73322	+	13.0948i	−0.252499	+	0.427562i
$939$	−29.3676	+	16.9554i	−0.958374	+	0.553318i
$940$	−23.0594	+	26.4070i	−0.752114	+	0.861303i
$941$	−11.0964	+	13.2242i	−0.361732	+	0.431096i	−0.915960	−	0.401269i	$-0.868569\pi$
$941$	−11.0964	+	13.2242i	−0.361732	+	0.431096i	0.554228	+	0.832365i	$0.313014\pi$
$942$	−21.3073	+	12.0236i	−0.694229	+	0.391750i
$943$	−20.4504	+	35.4212i	−0.665957	+	1.15347i
$944$	1.59378	+	4.98100i	0.0518733	+	0.162118i
$945$	0.874057	+	4.95702i	0.0284331	+	0.161252i
$946$	9.98643	+	1.86245i	0.324687	+	0.0605534i
$947$	−20.1580	+	55.3836i	−0.655047	+	1.79973i	−0.0568409	+	0.998383i	$0.518103\pi$
$947$	−20.1580	+	55.3836i	−0.655047	+	1.79973i	−0.598206	+	0.801343i	$0.704119\pi$
$948$	7.53076	+	9.34244i	0.244588	+	0.303428i
$949$		−	0.273297i		−	0.00887159i
$950$	−15.3653	−	49.6717i	−0.498515	−	1.61156i
$951$	−9.90920			−0.321328
$952$	−1.04996	−	1.32913i	−0.0340295	−	0.0430773i
$953$	24.1958	+	8.80655i	0.783779	+	0.285272i	0.702747	−	0.711439i	$-0.251956\pi$
$953$	24.1958	+	8.80655i	0.783779	+	0.285272i	0.0810313	+	0.996712i	$0.474179\pi$
$954$	−2.49152	+	13.3595i	−0.0806659	+	0.432530i
$955$	23.8921	−	4.21282i	0.773131	−	0.136324i
$956$	21.9354	−	7.49804i	0.709442	−	0.242504i
$957$	4.99130	+	2.88173i	0.161346	+	0.0931530i
$958$	28.6387	−	16.1607i	0.925274	−	0.522127i
$959$	−10.1510	−	8.51766i	−0.327791	−	0.275050i
$960$	21.3102	+	20.1416i	0.687785	+	0.650067i
$961$	6.79852	+	11.7754i	0.219307	+	0.379851i
$962$	0.673145	+	0.397529i	0.0217031	+	0.0128169i
$963$	4.08083	+	11.2120i	0.131503	+	0.361301i
$964$	−1.20278	−	7.70579i	−0.0387391	−	0.248187i
$965$	−55.5644	−	9.79751i	−1.78868	−	0.315393i
$966$	−15.3579	−	5.76172i	−0.494134	−	0.185380i
$967$	2.22404	−	1.86619i	0.0715202	−	0.0600126i	−0.606327	−	0.795216i	$-0.707358\pi$
$967$	2.22404	−	1.86619i	0.0715202	−	0.0600126i	0.677847	+	0.735203i	$0.262913\pi$
$968$	−0.575521	+	19.4766i	−0.0184979	+	0.626003i
$969$	0.719651	−	1.75932i	0.0231185	−	0.0565174i
$970$	40.0920	+	0.394795i	1.28728	+	0.0126761i
$971$	25.2809	+	30.1286i	0.811304	+	0.966874i	0.999885	−	0.0151836i	$-0.00483329\pi$
$971$	25.2809	+	30.1286i	0.811304	+	0.966874i	−0.188581	+	0.982058i	$0.560389\pi$
$972$	0.720917	−	1.86555i	0.0231234	−	0.0598376i
$973$	28.5591	+	5.03575i	0.915564	+	0.161439i
$974$	1.68487	−	0.280011i	0.0539868	−	0.00897214i
$975$	0.464743	−	0.169152i	0.0148837	−	0.00541721i
$976$	33.6034	+	21.2077i	1.07562	+	0.678841i
$977$	15.3343	+	26.5598i	0.490587	+	0.849722i	0.999941	−	0.0108350i	$-0.00344896\pi$
$977$	15.3343	+	26.5598i	0.490587	+	0.849722i	−0.509354	+	0.860557i	$0.670116\pi$
$978$	3.72645	−	4.35323i	0.119159	−	0.139201i
$979$	−20.1206	+	23.9788i	−0.643057	+	0.766366i
$980$	−32.8298	+	18.1018i	−1.04871	+	0.578242i
$981$	−6.27800	−	3.62460i	−0.200441	−	0.115725i
$982$	17.3713	−	6.12959i	0.554339	−	0.195603i
$983$	0.466892	+	2.64787i	0.0148915	+	0.0844540i	0.991348	−	0.131261i	$-0.0419027\pi$
$983$	0.466892	+	2.64787i	0.0148915	+	0.0844540i	−0.976456	+	0.215715i	$0.930792\pi$
$984$	−2.77582	+	13.4127i	−0.0884898	+	0.427581i
$985$	−68.6809	−	24.9978i	−2.18836	−	0.796496i
$986$	1.35393	−	1.11355i	0.0431178	−	0.0354625i
$987$		−	6.56757i		−	0.209048i
$988$	0.426877	+	0.281211i	0.0135808	+	0.00894651i
$989$		−	29.9228i		−	0.951490i
$990$	6.67602	+	8.11717i	0.212178	+	0.257981i
$991$	13.9247	+	5.06819i	0.442334	+	0.160996i	0.553579	−	0.832797i	$-0.313262\pi$
$991$	13.9247	+	5.06819i	0.442334	+	0.160996i	−0.111245	+	0.993793i	$0.535484\pi$
$992$	23.0103	+	5.23664i	0.730576	+	0.166264i
$993$	−3.78074	−	21.4416i	−0.119978	−	0.680429i
$994$	−8.66144	−	24.5465i	−0.274724	−	0.778568i
$995$	−49.9641	−	28.8468i	−1.58397	−	0.914504i
$996$	−7.21178	−	13.0794i	−0.228514	−	0.414437i
$997$	1.02010	−	1.21571i	0.0323070	−	0.0385020i	−0.749649	−	0.661836i	$-0.769778\pi$
$997$	1.02010	−	1.21571i	0.0323070	−	0.0385020i	0.781956	+	0.623334i	$0.214222\pi$
$998$	−22.5119	−	19.2706i	−0.712602	−	0.610001i
$999$	−4.71373	−	8.16442i	−0.149136	−	0.258311i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bk.a.253.12	✓	240
8.5	even	2	inner	456.2.bk.a.253.29	yes	240
19.16	even	9	inner	456.2.bk.a.301.29	yes	240
152.149	even	18	inner	456.2.bk.a.301.12	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bk.a.253.12	✓	240	1.1	even	1	trivial
456.2.bk.a.253.29	yes	240	8.5	even	2	inner
456.2.bk.a.301.12	yes	240	152.149	even	18	inner
456.2.bk.a.301.29	yes	240	19.16	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bk (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.898327 - 1.09225i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(-0.386016 + 1.96239i) q^{4} +(3.60963 - 0.636475i) q^{5} +(1.33362 - 0.470580i) q^{6} +(-0.686638 + 1.18929i) q^{7} +(2.49019 - 1.34125i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(-3.93782 - 3.37085i) q^{10} +(1.75591 - 1.01378i) q^{11} +(-1.71202 - 1.03391i) q^{12} +(-0.0200547 - 0.0551000i) q^{13} +(1.91583 - 0.318394i) q^{14} +(-0.636475 + 3.60963i) q^{15} +(-3.70198 - 1.51503i) q^{16} +(-0.334054 + 0.280304i) q^{17} +(-0.0139254 + 1.41415i) q^{18} +(3.22669 + 2.93061i) q^{19} +(-0.144359 + 7.32921i) q^{20} +(-0.882725 - 1.05199i) q^{21} +(-2.68468 - 1.00719i) q^{22} +(-1.46664 + 8.31776i) q^{23} +(0.408665 + 2.79875i) q^{24} +(7.92587 - 2.88478i) q^{25} +(-0.0421672 + 0.0714026i) q^{26} +(0.866025 - 0.500000i) q^{27} +(-2.06881 - 1.80654i) q^{28} +(1.82717 - 2.17753i) q^{29} +(4.51438 - 2.54744i) q^{30} +(2.08584 - 3.61278i) q^{31} +(1.67080 + 5.40448i) q^{32} +(0.352081 + 1.99675i) q^{33} +(0.606252 + 0.113065i) q^{34} +(-1.72156 + 4.72993i) q^{35} +(1.55711 - 1.25516i) q^{36} -9.42746i q^{37} +(0.302341 - 6.15700i) q^{38} +0.0586362 q^{39} +(8.13500 - 6.42635i) q^{40} +(4.55055 + 1.65626i) q^{41} +(-0.356060 + 1.90919i) q^{42} +(-3.48899 + 0.615202i) q^{43} +(1.31162 + 3.83712i) q^{44} +(-3.17426 - 1.83266i) q^{45} +(10.4026 - 5.87013i) q^{46} +(3.66354 + 3.07407i) q^{47} +(2.68982 - 2.96056i) q^{48} +(2.55706 + 4.42895i) q^{49} +(-10.2709 - 6.06554i) q^{50} +(-0.149147 - 0.409778i) q^{51} +(0.115869 - 0.0180859i) q^{52} +(9.46348 + 1.66867i) q^{53} +(-1.32410 - 0.496752i) q^{54} +(5.69295 - 4.77695i) q^{55} +(-0.114726 + 3.88252i) q^{56} +(-3.85747 + 2.02976i) q^{57} +(-4.01980 - 0.0395839i) q^{58} +(-0.840408 - 1.00156i) q^{59} +(-6.83783 - 2.64239i) q^{60} +(-9.78309 - 1.72502i) q^{61} +(-5.81983 + 0.967205i) q^{62} +(1.29046 - 0.469688i) q^{63} +(4.40211 - 6.67993i) q^{64} +(-0.107460 - 0.186126i) q^{65} +(1.86466 - 2.17829i) q^{66} +(-5.03340 + 5.99857i) q^{67} +(-0.421118 - 0.763747i) q^{68} +(-7.31451 - 4.22303i) q^{69} +(6.71279 - 2.36866i) q^{70} +(-2.32739 - 13.1993i) q^{71} +(-2.76973 - 0.573209i) q^{72} +(4.37981 + 1.59412i) q^{73} +(-10.2971 + 8.46895i) q^{74} +8.43453i q^{75} +(-6.99657 + 5.20077i) q^{76} +2.78439i q^{77} +(-0.0526745 - 0.0640453i) q^{78} +(-5.63803 - 2.05207i) q^{79} +(-14.3271 - 3.11248i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-2.27883 - 6.45819i) q^{82} +(6.46743 + 3.73397i) q^{83} +(2.40517 - 1.32617i) q^{84} +(-1.02740 + 1.22441i) q^{85} +(3.80621 + 3.25819i) q^{86} +(1.42128 + 2.46174i) q^{87} +(3.01283 - 4.87961i) q^{88} +(-14.5073 + 5.28024i) q^{89} +(0.849803 + 5.11340i) q^{90} +(0.0793003 + 0.0139828i) q^{91} +(-15.7566 - 6.08892i) q^{92} +(2.68151 + 3.19570i) q^{93} +(0.0665969 - 6.76302i) q^{94} +(13.5124 + 8.52473i) q^{95} +(-5.65000 - 0.278400i) q^{96} +(-5.92525 + 4.97188i) q^{97} +(2.54044 - 6.77159i) q^{98} +(-1.99675 - 0.352081i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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