LMFDB - Embedded newform 722.2.i.b.7.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [722,2,Mod(7,722)] 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("722.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(722, base_ring=CyclotomicField(114)) chi = DirichletCharacter(H, H._module([50])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.i (of order $57$, degree $36$, minimal)

Newform invariants

comment:select newform

sage:traces = [612] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$612$
Relative dimension:	$17$ over $\Q(\zeta_{57})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{57}]$

Embedding invariants

Embedding label			7.5
Character	$\chi$	$=$	722.7
Dual form			722.2.i.b.619.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.191711 - 0.981451i) q^{2} +(-2.00265 + 0.221654i) q^{3} +(-0.926494 + 0.376309i) q^{4} +(0.168453 - 0.163874i) q^{5} +(0.601472 + 1.92301i) q^{6} +(0.945236 - 0.735707i) q^{7} +(0.546948 + 0.837166i) q^{8} +(1.03410 - 0.231747i) q^{9} +(-0.193129 - 0.133913i) q^{10} +(-0.292583 + 0.317830i) q^{11} +(1.77204 - 0.958978i) q^{12} +(-1.73826 - 2.36498i) q^{13} +(-0.903273 - 0.786661i) q^{14} +(-0.301030 + 0.365521i) q^{15} +(0.716783 - 0.697297i) q^{16} +(-3.40718 - 1.38388i) q^{17} +(-0.425695 - 0.970488i) q^{18} +(1.97727 + 3.88464i) q^{19} +(-0.0944038 + 0.215219i) q^{20} +(-1.72991 + 1.68288i) q^{21} +(0.368025 + 0.226224i) q^{22} +(-3.42219 - 0.378768i) q^{23} +(-1.28091 - 1.55532i) q^{24} +(-0.136250 + 4.94289i) q^{25} +(-1.98788 + 2.15941i) q^{26} +(3.69756 - 1.26937i) q^{27} +(-0.598902 + 1.03733i) q^{28} +(0.760360 + 5.48332i) q^{29} +(0.416452 + 0.225373i) q^{30} +(0.0409025 - 0.0140419i) q^{31} +(-0.821778 - 0.569808i) q^{32} +(0.515493 - 0.701354i) q^{33} +(-0.705016 + 3.60929i) q^{34} +(0.0386650 - 0.278832i) q^{35} +(-0.870876 + 0.603852i) q^{36} +(-7.05612 + 7.66499i) q^{37} +(3.43352 - 2.68532i) q^{38} +(4.00533 + 4.35095i) q^{39} +(0.229325 + 0.0513930i) q^{40} +(1.70566 + 4.55561i) q^{41} +(1.98331 + 1.37519i) q^{42} +(10.7434 - 7.44927i) q^{43} +(0.151474 - 0.404569i) q^{44} +(0.136220 - 0.208500i) q^{45} +(0.284328 + 3.43133i) q^{46} +(2.28000 + 7.28955i) q^{47} +(-1.28091 + 1.55532i) q^{48} +(-1.36619 + 5.39497i) q^{49} +(4.87733 - 0.813882i) q^{50} +(7.13014 + 2.01621i) q^{51} +(2.50045 + 1.53702i) q^{52} +(2.10742 + 6.73781i) q^{53} +(-1.95469 - 3.38562i) q^{54} +(0.00279745 + 0.101486i) q^{55} +(1.13290 + 0.388927i) q^{56} +(-4.82082 - 7.34131i) q^{57} +(5.23584 - 1.79747i) q^{58} +(-1.16518 - 3.11206i) q^{59} +(0.141354 - 0.451934i) q^{60} +(1.29884 + 2.56658i) q^{61} +(-0.0216228 - 0.0374519i) q^{62} +(0.806969 - 0.979848i) q^{63} +(-0.401695 + 0.915773i) q^{64} +(-0.680375 - 0.113535i) q^{65} +(-0.787170 - 0.371475i) q^{66} +(-13.8138 + 0.762126i) q^{67} +3.67750 q^{68} +6.93741 q^{69} +(-0.281073 + 0.0155072i) q^{70} +(-3.28151 + 6.48444i) q^{71} +(0.759608 + 0.738958i) q^{72} +(13.1367 + 5.33566i) q^{73} +(8.87555 + 5.45578i) q^{74} +(-0.822748 - 9.92909i) q^{75} +(-3.29375 - 2.85503i) q^{76} +(-0.0427304 + 0.515679i) q^{77} +(3.50238 - 4.76516i) q^{78} +(2.45712 - 1.70373i) q^{79} +(0.00647564 - 0.234924i) q^{80} +(-9.99873 + 4.71852i) q^{81} +(4.14412 - 2.54738i) q^{82} +(-0.00837813 + 0.0330845i) q^{83} +(0.969466 - 2.21016i) q^{84} +(-0.800733 + 0.325230i) q^{85} +(-9.37072 - 9.11597i) q^{86} +(-2.73813 - 10.8126i) q^{87} +(-0.426104 - 0.0711041i) q^{88} +(-14.7146 + 5.97656i) q^{89} +(-0.230748 - 0.0937216i) q^{90} +(-3.38300 - 0.956621i) q^{91} +(3.31317 - 0.936876i) q^{92} +(-0.0788011 + 0.0371871i) q^{93} +(6.71724 - 3.63519i) q^{94} +(0.969669 + 0.330358i) q^{95} +(1.77204 + 0.958978i) q^{96} +(-7.56906 - 0.417597i) q^{97} +(5.55681 + 0.306578i) q^{98} +(-0.228903 + 0.396472i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 612 q + 17 q^{2} - 19 q^{3} + 17 q^{4} + q^{5} - 2 q^{7} - 34 q^{8} + 4 q^{9} + q^{10} - 28 q^{11} + 4 q^{13} - 18 q^{14} - 52 q^{15} + 17 q^{16} + 18 q^{17} - 46 q^{18} - 12 q^{19} - 2 q^{20} - 65 q^{21}+ \cdots - 116 q^{99}+O(q^{100}) $ 612 * q + 17 * q^2 - 19 * q^3 + 17 * q^4 + q^5 - 2 * q^7 - 34 * q^8 + 4 * q^9 + q^10 - 28 * q^11 + 4 * q^13 - 18 * q^14 - 52 * q^15 + 17 * q^16 + 18 * q^17 - 46 * q^18 - 12 * q^19 - 2 * q^20 - 65 * q^21 + 33 * q^22 + 39 * q^23 + 20 * q^25 - 8 * q^26 + 158 * q^27 - 37 * q^28 - 42 * q^29 - 29 * q^30 + 12 * q^31 + 17 * q^32 + 60 * q^33 - q^34 - 14 * q^35 + 23 * q^36 - 6 * q^37 + 76 * q^38 - 108 * q^39 + q^40 + 8 * q^41 + 11 * q^42 + 7 * q^43 - 5 * q^44 - 101 * q^45 - 21 * q^46 + 105 * q^47 - 62 * q^49 - 78 * q^50 - 3 * q^51 + 4 * q^52 + 146 * q^53 - 79 * q^54 + 4 * q^55 - 21 * q^56 - 28 * q^57 + 8 * q^58 - 4 * q^59 - 14 * q^60 - 93 * q^61 - 6 * q^62 - 95 * q^63 - 34 * q^64 - 76 * q^65 - 16 * q^66 - 6 * q^67 + 78 * q^68 + 38 * q^69 + 81 * q^70 - 151 * q^71 + 23 * q^72 + 7 * q^73 - 35 * q^74 - 12 * q^75 - 7 * q^76 + 78 * q^77 - 3 * q^78 - 10 * q^79 + q^80 + 58 * q^81 - 30 * q^82 + 67 * q^83 - 22 * q^84 - 6 * q^85 - 12 * q^86 - 109 * q^87 + 10 * q^88 - 25 * q^89 - 73 * q^90 + 37 * q^91 + q^92 + 56 * q^93 - 39 * q^94 - 29 * q^95 - 153 * q^97 + 164 * q^98 - 116 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{25}{57}\right)$

Coefficient data

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

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

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

$2$	−0.191711	−	0.981451i	−0.135560	−	0.693991i
$2$	−0.191711	−	0.981451i	−0.135560	−	0.693991i
$3$	−2.00265	+	0.221654i	−1.15623	+	0.127972i	−0.667601	−	0.744519i	$-0.732679\pi$
$3$	−2.00265	+	0.221654i	−1.15623	+	0.127972i	−0.488631	+	0.872491i	$0.662503\pi$
$4$	−0.926494	+	0.376309i	−0.463247	+	0.188155i
$5$	0.168453	−	0.163874i	0.0753347	−	0.0732867i	−0.658666	−	0.752435i	$-0.728879\pi$
$5$	0.168453	−	0.163874i	0.0753347	−	0.0732867i	0.734001	+	0.679149i	$0.237651\pi$
$6$	0.601472	+	1.92301i	0.245550	+	0.785067i
$7$	0.945236	−	0.735707i	0.357266	−	0.278071i	−0.419637	−	0.907692i	$-0.637842\pi$
$7$	0.945236	−	0.735707i	0.357266	−	0.278071i	0.776902	+	0.629621i	$0.216790\pi$
$8$	0.546948	+	0.837166i	0.193375	+	0.295983i
$9$	1.03410	−	0.231747i	0.344699	−	0.0772489i
$10$	−0.193129	−	0.133913i	−0.0610727	−	0.0423469i
$11$	−0.292583	+	0.317830i	−0.0882170	+	0.0958292i	−0.778271	−	0.627929i	$-0.783903\pi$
$11$	−0.292583	+	0.317830i	−0.0882170	+	0.0958292i	0.690054	+	0.723758i	$0.257587\pi$
$12$	1.77204	−	0.958978i	0.511543	−	0.276833i
$13$	−1.73826	−	2.36498i	−0.482106	−	0.655929i	0.494948	−	0.868923i	$-0.335187\pi$
$13$	−1.73826	−	2.36498i	−0.482106	−	0.655929i	−0.977053	+	0.212994i	$0.931678\pi$
$14$	−0.903273	−	0.786661i	−0.241410	−	0.210244i
$15$	−0.301030	+	0.365521i	−0.0777257	+	0.0943771i
$16$	0.716783	−	0.697297i	0.179196	−	0.174324i
$17$	−3.40718	−	1.38388i	−0.826363	−	0.335640i	−0.0763650	−	0.997080i	$-0.524331\pi$
$17$	−3.40718	−	1.38388i	−0.826363	−	0.335640i	−0.749998	+	0.661440i	$0.769945\pi$
$18$	−0.425695	−	0.970488i	−0.100337	−	0.228746i
$19$	1.97727	+	3.88464i	0.453616	+	0.891197i
$19$	1.97727	+	3.88464i	0.453616	+	0.891197i
$20$	−0.0944038	+	0.215219i	−0.0211093	+	0.0481244i
$21$	−1.72991	+	1.68288i	−0.377497	+	0.367235i
$22$	0.368025	+	0.226224i	0.0784633	+	0.0482312i
$23$	−3.42219	−	0.378768i	−0.713576	−	0.0789786i	−0.254112	−	0.967175i	$-0.581783\pi$
$23$	−3.42219	−	0.378768i	−0.713576	−	0.0789786i	−0.459464	+	0.888196i	$0.651959\pi$
$24$	−1.28091	−	1.55532i	−0.261464	−	0.317478i
$25$	−0.136250	+	4.94289i	−0.0272500	+	0.988578i
$26$	−1.98788	+	2.15941i	−0.389854	+	0.423495i
$27$	3.69756	−	1.26937i	0.711596	−	0.244291i
$28$	−0.598902	+	1.03733i	−0.113182	+	0.196037i
$29$	0.760360	+	5.48332i	0.141195	+	1.01823i	0.920267	+	0.391291i	$0.127972\pi$
$29$	0.760360	+	5.48332i	0.141195	+	1.01823i	−0.779072	+	0.626935i	$0.784309\pi$
$30$	0.416452	+	0.225373i	0.0760334	+	0.0411472i
$31$	0.0409025	−	0.0140419i	0.00734631	−	0.00252199i	−0.321024	−	0.947071i	$-0.604027\pi$
$31$	0.0409025	−	0.0140419i	0.00734631	−	0.00252199i	0.328370	+	0.944549i	$0.393501\pi$
$32$	−0.821778	−	0.569808i	−0.145271	−	0.100729i
$33$	0.515493	−	0.701354i	0.0897359	−	0.122090i
$34$	−0.705016	+	3.60929i	−0.120909	+	0.618988i
$35$	0.0386650	−	0.278832i	0.00653559	−	0.0471312i
$36$	−0.870876	+	0.603852i	−0.145146	+	0.100642i
$37$	−7.05612	+	7.66499i	−1.16002	+	1.26012i	−0.200120	+	0.979771i	$0.564133\pi$
$37$	−7.05612	+	7.66499i	−1.16002	+	1.26012i	−0.959899	+	0.280345i	$0.909551\pi$
$38$	3.43352	−	2.68532i	0.556991	−	0.435616i
$39$	4.00533	+	4.35095i	0.641367	+	0.696710i
$40$	0.229325	+	0.0513930i	0.0362595	+	0.00812594i
$41$	1.70566	+	4.55561i	0.266379	+	0.711468i	0.999508	+	0.0313772i	$0.00998930\pi$
$41$	1.70566	+	4.55561i	0.266379	+	0.711468i	−0.733128	+	0.680090i	$0.761941\pi$
$42$	1.98331	+	1.37519i	0.306031	+	0.212197i
$43$	10.7434	−	7.44927i	1.63835	−	1.13600i	0.773839	−	0.633382i	$-0.218334\pi$
$43$	10.7434	−	7.44927i	1.63835	−	1.13600i	0.864507	−	0.502621i	$-0.167631\pi$
$44$	0.151474	−	0.404569i	0.0228355	−	0.0609910i
$45$	0.136220	−	0.208500i	0.0203065	−	0.0310814i
$46$	0.284328	+	3.43133i	0.0419219	+	0.505922i
$47$	2.28000	+	7.28955i	0.332572	+	1.06329i	0.958903	+	0.283734i	$0.0915732\pi$
$47$	2.28000	+	7.28955i	0.332572	+	1.06329i	−0.626332	+	0.779557i	$0.715444\pi$
$48$	−1.28091	+	1.55532i	−0.184883	+	0.224491i
$49$	−1.36619	+	5.39497i	−0.195170	+	0.770710i
$50$	4.87733	−	0.813882i	0.689758	−	0.115100i
$51$	7.13014	+	2.01621i	0.998419	+	0.282326i
$52$	2.50045	+	1.53702i	0.346750	+	0.213147i
$53$	2.10742	+	6.73781i	0.289477	+	0.925510i	0.979452	+	0.201677i	$0.0646390\pi$
$53$	2.10742	+	6.73781i	0.289477	+	0.925510i	−0.689975	+	0.723833i	$0.742379\pi$
$54$	−1.95469	−	3.38562i	−0.266000	−	0.460725i
$55$	0.00279745	+	0.101486i	0.000377208	+	0.0136844i
$56$	1.13290	+	0.388927i	0.151391	+	0.0519725i
$57$	−4.82082	−	7.34131i	−0.638534	−	0.972380i
$58$	5.23584	−	1.79747i	0.687499	−	0.236019i
$59$	−1.16518	−	3.11206i	−0.151694	−	0.405156i	0.838492	−	0.544914i	$-0.183438\pi$
$59$	−1.16518	−	3.11206i	−0.151694	−	0.405156i	−0.990186	+	0.139758i	$0.955368\pi$
$60$	0.141354	−	0.451934i	0.0182487	−	0.0583444i
$61$	1.29884	+	2.56658i	0.166300	+	0.328617i	0.960145	−	0.279503i	$-0.0901697\pi$
$61$	1.29884	+	2.56658i	0.166300	+	0.328617i	−0.793845	+	0.608120i	$0.791924\pi$
$62$	−0.0216228	−	0.0374519i	−0.00274610	−	0.00475639i
$63$	0.806969	−	0.979848i	0.101668	−	0.123449i
$64$	−0.401695	+	0.915773i	−0.0502119	+	0.114472i
$65$	−0.680375	−	0.113535i	−0.0843901	−	0.0140822i
$66$	−0.787170	−	0.371475i	−0.0968940	−	0.0457254i
$67$	−13.8138	+	0.762126i	−1.68762	+	0.0931085i	−0.873260	−	0.487254i	$-0.837999\pi$
$67$	−13.8138	+	0.762126i	−1.68762	+	0.0931085i	−0.814358	+	0.580363i	$0.802911\pi$
$68$	3.67750			0.445962
$69$	6.93741			0.835167
$70$	−0.281073	+	0.0155072i	−0.0335946	+	0.00185347i
$71$	−3.28151	+	6.48444i	−0.389443	+	0.769561i	−0.999744	−	0.0226084i	$-0.992803\pi$
$71$	−3.28151	+	6.48444i	−0.389443	+	0.769561i	0.610301	+	0.792170i	$0.291049\pi$
$72$	0.759608	+	0.738958i	0.0895207	+	0.0870870i
$73$	13.1367	+	5.33566i	1.53753	+	0.624492i	0.978793	−	0.204852i	$-0.0656713\pi$
$73$	13.1367	+	5.33566i	1.53753	+	0.624492i	0.558739	+	0.829344i	$0.311285\pi$
$74$	8.87555	+	5.45578i	1.03176	+	0.634222i
$75$	−0.822748	−	9.92909i	−0.0950028	−	1.14651i
$76$	−3.29375	−	2.85503i	−0.377819	−	0.327494i
$77$	−0.0427304	+	0.515679i	−0.00486958	+	0.0587671i
$78$	3.50238	−	4.76516i	0.396567	−	0.539548i
$79$	2.45712	−	1.70373i	0.276448	−	0.191684i	−0.423466	−	0.905912i	$-0.639187\pi$
$79$	2.45712	−	1.70373i	0.276448	−	0.191684i	0.699914	+	0.714227i	$0.253222\pi$
$80$	0.00647564	−	0.234924i	0.000723998	−	0.0262653i
$81$	−9.99873	+	4.71852i	−1.11097	+	0.524280i
$82$	4.14412	−	2.54738i	0.457642	−	0.281311i
$83$	−0.00837813	+	0.0330845i	−0.000919620	+	0.00363150i	−0.969858	−	0.243669i	$-0.921649\pi$
$83$	−0.00837813	+	0.0330845i	−0.000919620	+	0.00363150i	0.968939	+	0.247301i	$0.0795436\pi$
$84$	0.969466	−	2.21016i	0.105777	−	0.241148i
$85$	−0.800733	+	0.325230i	−0.0868517	+	0.0352761i
$86$	−9.37072	−	9.11597i	−1.01047	−	0.983001i
$87$	−2.73813	−	10.8126i	−0.293559	−	1.15924i
$88$	−0.426104	−	0.0711041i	−0.0454228	−	0.00757973i
$89$	−14.7146	+	5.97656i	−1.55975	+	0.633514i	−0.983032	−	0.183433i	$-0.941279\pi$
$89$	−14.7146	+	5.97656i	−1.55975	+	0.633514i	−0.576713	+	0.816947i	$0.695665\pi$
$90$	−0.230748	−	0.0937216i	−0.0243229	−	0.00987913i
$91$	−3.38300	−	0.956621i	−0.354635	−	0.100281i
$92$	3.31317	−	0.936876i	0.345422	−	0.0976761i
$93$	−0.0788011	+	0.0371871i	−0.00817129	+	0.00385613i
$94$	6.71724	−	3.63519i	0.692831	−	0.374941i
$95$	0.969669	+	0.330358i	0.0994860	+	0.0338940i
$96$	1.77204	+	0.958978i	0.180858	+	0.0978752i
$97$	−7.56906	−	0.417597i	−0.768522	−	0.0424005i	−0.333416	−	0.942780i	$-0.608201\pi$
$97$	−7.56906	−	0.417597i	−0.768522	−	0.0424005i	−0.435106	+	0.900379i	$0.643289\pi$
$98$	5.55681	+	0.306578i	0.561323	+	0.0309690i
$99$	−0.228903	+	0.396472i	−0.0230056	+	0.0398469i
$100$	−1.73382	−	4.63083i	−0.173382	−	0.463083i
$101$	6.92801	−	1.55260i	0.689362	−	0.154490i	0.140097	−	0.990138i	$-0.455259\pi$
$101$	6.92801	−	1.55260i	0.689362	−	0.154490i	0.549265	+	0.835648i	$0.314908\pi$
$102$	0.611890	−	7.38442i	0.0605862	−	0.731166i
$103$	0.363762	+	0.283127i	0.0358426	+	0.0278974i	0.631976	−	0.774988i	$-0.282244\pi$
$103$	0.363762	+	0.283127i	0.0358426	+	0.0278974i	−0.596133	+	0.802886i	$0.703297\pi$
$104$	1.02915	−	2.74873i	0.100916	−	0.269536i
$105$	−0.0156285	+	0.566974i	−0.00152519	+	0.0553310i
$106$	6.20882	−	3.36004i	0.603054	−	0.326356i
$107$	−12.9949	−	4.46114i	−1.25626	−	0.431275i	−0.385375	−	0.922760i	$-0.625928\pi$
$107$	−12.9949	−	4.46114i	−1.25626	−	0.431275i	−0.870886	+	0.491485i	$0.836454\pi$
$108$	−2.94809	+	2.56749i	−0.283680	+	0.247057i
$109$	1.73167	−	5.53646i	0.165864	−	0.530297i	−0.833902	−	0.551912i	$-0.813898\pi$
$109$	1.73167	−	5.53646i	0.165864	−	0.530297i	0.999766	+	0.0216151i	$0.00688083\pi$
$110$	0.0990675	−	0.0222015i	0.00944571	−	0.00211683i
$111$	12.4320	−	16.9143i	1.17999	−	1.60544i
$112$	0.164523	−	1.18645i	0.0155459	−	0.112109i
$113$	−1.01622	−	0.790958i	−0.0955983	−	0.0744071i	0.565286	−	0.824895i	$-0.308766\pi$
$113$	−1.01622	−	0.790958i	−0.0955983	−	0.0744071i	−0.660884	+	0.750488i	$0.729819\pi$
$114$	−6.28094	+	6.13881i	−0.588264	+	0.574953i
$115$	−0.638550	+	0.497004i	−0.0595451	+	0.0463458i
$116$	−2.76789	−	4.79413i	−0.256992	−	0.445124i
$117$	−2.34560	−	2.04279i	−0.216851	−	0.188856i
$118$	−2.83096	+	1.74019i	−0.260611	+	0.160197i
$119$	−4.23872	+	1.19860i	−0.388563	+	0.109875i
$120$	−0.470650	−	0.0520915i	−0.0429643	−	0.00475529i
$121$	0.892962	+	10.7764i	0.0811783	+	0.979677i
$122$	2.26997	−	1.76679i	0.205514	−	0.159958i
$123$	−4.42561	−	8.74525i	−0.399044	−	0.788532i
$124$	−0.0326119	+	0.0284017i	−0.00292863	+	0.00255055i
$125$	1.58291	+	1.71950i	0.141580	+	0.153797i
$126$	−1.11638	−	0.604153i	−0.0994548	−	0.0538223i
$127$	9.65018	−	16.7146i	0.856315	−	1.48318i	−0.0191049	−	0.999817i	$-0.506082\pi$
$127$	9.65018	−	16.7146i	0.856315	−	1.48318i	0.875420	−	0.483363i	$-0.160585\pi$
$128$	0.975796	+	0.218681i	0.0862490	+	0.0193289i
$129$	−19.8640	+	17.2996i	−1.74893	+	1.52315i
$130$	0.0190065	+	0.689521i	0.00166698	+	0.0604750i
$131$	−11.2873	−	9.83008i	−0.986172	−	0.858858i	0.00381829	−	0.999993i	$-0.498785\pi$
$131$	−11.2873	−	9.83008i	−0.986172	−	0.858858i	−0.989990	+	0.141135i	$0.954925\pi$
$132$	−0.213675	+	0.843785i	−0.0185981	+	0.0734421i
$133$	4.72694	+	2.21721i	0.409878	+	0.192257i
$134$	3.39623	+	13.4114i	0.293390	+	1.15857i
$135$	0.414849	−	0.819764i	0.0357045	−	0.0705541i
$136$	−0.705016	−	3.60929i	−0.0604546	−	0.309494i
$137$	−11.1074	+	0.612813i	−0.948970	+	0.0523561i	−0.522955	−	0.852360i	$-0.675171\pi$
$137$	−11.1074	+	0.612813i	−0.948970	+	0.0523561i	−0.426015	+	0.904716i	$0.640083\pi$
$138$	−1.32998	−	6.80874i	−0.113215	−	0.579598i
$139$	19.9111	+	9.39625i	1.68883	+	0.796980i	0.997204	+	0.0747274i	$0.0238087\pi$
$139$	19.9111	+	9.39625i	1.68883	+	0.796980i	0.691630	+	0.722252i	$0.256893\pi$
$140$	0.0691042	+	0.272886i	0.00584037	+	0.0230631i
$141$	−6.18179	−	14.0931i	−0.520601	−	1.18685i
$142$	6.99326	+	1.97751i	0.586862	+	0.165949i
$143$	1.26025	+	0.139484i	0.105387	+	0.0116642i
$144$	0.579627	−	0.887185i	0.0483022	−	0.0739320i
$145$	1.02666	+	0.799080i	0.0852594	+	0.0663600i
$146$	2.71825	−	13.9159i	0.224964	−	1.15169i
$147$	1.54019	−	11.1071i	0.127033	−	0.916095i
$148$	3.65305	−	9.75685i	0.300279	−	0.802008i
$149$	−9.14574	−	11.1051i	−0.749248	−	0.909761i	0.249026	−	0.968497i	$-0.419890\pi$
$149$	−9.14574	−	11.1051i	−0.749248	−	0.909761i	−0.998274	+	0.0587355i	$0.981293\pi$
$150$	−9.58719	+	2.71100i	−0.782791	+	0.221352i
$151$	−16.9064	+	2.82118i	−1.37582	+	0.229584i	−0.805869	−	0.592093i	$-0.798302\pi$
$151$	−16.9064	+	2.82118i	−1.37582	+	0.229584i	−0.569953	+	0.821677i	$0.693039\pi$
$152$	−2.17063	+	3.78000i	−0.176061	+	0.306598i
$153$	−3.84407	−	0.641461i	−0.310774	−	0.0518591i
$154$	0.514306	−	0.0569234i	0.0414440	−	0.00458702i
$155$	0.00458908	−	0.00906826i	0.000368603	−	0.000728380i
$156$	−5.34822	−	2.52389i	−0.428200	−	0.202073i
$157$	−0.193557	+	0.0214229i	−0.0154475	+	0.00170973i	−0.117729	−	0.993046i	$-0.537561\pi$
$157$	−0.193557	+	0.0214229i	−0.0154475	+	0.00170973i	0.102281	+	0.994756i	$0.467386\pi$
$158$	−2.14318	−	2.08492i	−0.170502	−	0.165867i
$159$	−5.71390	−	13.0264i	−0.453142	−	1.03306i
$160$	−0.231808	+	0.0386819i	−0.0183260	+	0.00305808i
$161$	−3.51344	+	2.15970i	−0.276898	+	0.170209i
$162$	6.54786	+	8.90868i	0.514448	+	0.699932i
$163$	9.15659	+	3.14346i	0.717199	+	0.246215i	0.659057	−	0.752093i	$-0.270956\pi$
$163$	9.15659	+	3.14346i	0.717199	+	0.246215i	0.0581429	+	0.998308i	$0.481482\pi$
$164$	−3.29460	−	3.57889i	−0.257265	−	0.279465i
$165$	−0.0280971	−	0.202622i	−0.00218736	−	0.0157741i
$166$	0.0340770	+	0.00188008i	0.00264489	+	0.000145923i
$167$	2.83657	+	20.4559i	0.219500	+	1.58292i	0.705337	+	0.708872i	$0.250796\pi$
$167$	2.83657	+	20.4559i	0.219500	+	1.58292i	−0.485837	+	0.874050i	$0.661485\pi$
$168$	−2.35502	−	0.527773i	−0.181694	−	0.0407185i
$169$	1.30908	−	4.18536i	0.100698	−	0.321951i
$170$	0.472706	+	0.723531i	0.0362549	+	0.0554923i
$171$	2.94494	+	3.55887i	0.225205	+	0.272153i
$172$	−7.15042	+	10.9445i	−0.545214	+	0.834513i
$173$	−10.0632	−	12.2191i	−0.765094	−	0.929002i	0.233971	−	0.972244i	$-0.424828\pi$
$173$	−10.0632	−	12.2191i	−0.765094	−	0.929002i	−0.999065	+	0.0432414i	$0.986232\pi$
$174$	−10.0872	+	4.76024i	−0.764705	+	0.360873i
$175$	3.50773	+	4.77244i	0.265160	+	0.360763i
$176$	0.0119034	+	0.431832i	0.000897249	+	0.0325505i
$177$	3.02326	+	5.97412i	0.227242	+	0.449042i
$178$	8.68665	+	13.2959i	0.651092	+	0.996570i
$179$	0.662136	−	7.99079i	0.0494904	−	0.597260i	−0.926044	−	0.377415i	$-0.876813\pi$
$179$	0.662136	−	7.99079i	0.0494904	−	0.597260i	0.975535	−	0.219845i	$-0.0705552\pi$
$180$	−0.0477464	+	0.244435i	−0.00355881	+	0.0182191i
$181$	0.232773	−	1.19167i	0.0173019	−	0.0885759i	−0.971801	−	0.235803i	$-0.924228\pi$
$181$	0.232773	−	1.19167i	0.0173019	−	0.0885759i	0.989103	+	0.147227i	$0.0470349\pi$
$182$	−0.290320	+	3.50364i	−0.0215200	+	0.259707i
$183$	−3.17002	−	4.85207i	−0.234335	−	0.358676i
$184$	−1.55467	−	3.07211i	−0.114612	−	0.226479i
$185$	0.0674651	+	2.44751i	0.00496014	+	0.179944i
$186$	0.0516044	+	0.0702103i	0.00378382	+	0.00514807i
$187$	1.43672	−	0.678004i	0.105063	−	0.0495806i
$188$	−4.85553	−	5.89574i	−0.354126	−	0.429991i
$189$	2.56118	−	3.92018i	0.186298	−	0.285151i
$190$	0.138334	−	1.01502i	0.0100358	−	0.0736370i
$191$	7.09771	+	10.8638i	0.513572	+	0.786081i	0.995952	−	0.0898813i	$-0.0286488\pi$
$191$	7.09771	+	10.8638i	0.513572	+	0.786081i	−0.482380	+	0.875962i	$0.660228\pi$
$192$	0.601472	−	1.92301i	0.0434075	−	0.138781i
$193$	4.67771	+	1.04830i	0.336709	+	0.0754583i	0.383756	−	0.923434i	$-0.374630\pi$
$193$	4.67771	+	1.04830i	0.336709	+	0.0754583i	−0.0470472	+	0.998893i	$0.514981\pi$
$194$	1.04122	+	7.50872i	0.0747551	+	0.539095i
$195$	1.38772	+	0.0765627i	0.0993767	+	0.00548277i
$196$	−0.764409	−	5.51252i	−0.0546006	−	0.393751i
$197$	−11.0645	−	12.0193i	−0.788314	−	0.856337i	0.204142	−	0.978941i	$-0.434560\pi$
$197$	−11.0645	−	12.0193i	−0.788314	−	0.856337i	−0.992456	+	0.122604i	$0.960875\pi$
$198$	0.433001	+	0.148649i	0.0307720	+	0.0105641i
$199$	9.46300	+	12.8749i	0.670814	+	0.912675i	0.999495	−	0.0317656i	$-0.0101130\pi$
$199$	9.46300	+	12.8749i	0.670814	+	0.912675i	−0.328681	+	0.944441i	$0.606604\pi$
$200$	−4.21254	+	2.58944i	−0.297872	+	0.183101i
$201$	27.4952	−	4.58814i	1.93936	−	0.323622i
$202$	−2.85198	−	6.50185i	−0.200664	−	0.457469i
$203$	4.75283	+	4.62363i	0.333584	+	0.324515i
$204$	−7.36475	+	0.815131i	−0.515636	+	0.0570706i
$205$	1.03387	+	0.487896i	0.0722087	+	0.0340761i
$206$	0.208139	−	0.411293i	0.0145017	−	0.0286562i
$207$	−3.62666	+	0.401398i	−0.252070	+	0.0278991i
$208$	−2.89505	−	0.483098i	−0.200736	−	0.0334968i
$209$	−1.81317	−	0.508143i	−0.125419	−	0.0351490i
$210$	0.559454	−	0.0933563i	0.0386060	−	0.00644220i
$211$	11.1196	−	3.14434i	0.765508	−	0.216465i	0.133102	−	0.991102i	$-0.457506\pi$
$211$	11.1196	−	3.14434i	0.765508	−	0.216465i	0.632406	+	0.774637i	$0.282068\pi$
$212$	−4.48802	−	5.44950i	−0.308238	−	0.374273i
$213$	5.13442	−	13.7134i	0.351805	−	0.939629i
$214$	−1.88714	+	13.6091i	−0.129002	+	0.930298i
$215$	0.589012	−	3.01541i	0.0401703	−	0.205649i
$216$	3.08505	+	2.40119i	0.209911	+	0.163380i
$217$	0.0283319	−	0.0433651i	0.00192329	−	0.00294382i
$218$	−5.76575	−	0.638153i	−0.390506	−	0.0432212i
$219$	−27.4909	−	7.77368i	−1.85766	−	0.525296i
$220$	−0.0407820	−	0.0929737i	−0.00274952	−	0.00626828i
$221$	2.64971	+	10.4635i	0.178239	+	0.703849i
$222$	−18.9839	−	8.95874i	−1.27412	−	0.601271i
$223$	1.10040	+	5.63345i	0.0736884	+	0.377243i	1.00000		0.000484877i	$0.000154341\pi$
$223$	1.10040	+	5.63345i	0.0736884	+	0.377243i	−0.926311	+	0.376759i	$0.877039\pi$
$224$	−1.19599	+	0.0659844i	−0.0799102	+	0.00440877i
$225$	1.00460	+	5.14301i	0.0669735	+	0.342867i
$226$	−0.581467	+	1.14901i	−0.0386786	+	0.0764310i
$227$	−2.82140	−	11.1415i	−0.187263	−	0.739484i	−0.989750	−	0.142814i	$-0.954385\pi$
$227$	−2.82140	−	11.1415i	−0.187263	−	0.739484i	0.802487	−	0.596670i	$-0.203510\pi$
$228$	7.22907	+	4.98756i	0.478757	+	0.330309i
$229$	−5.16325	+	20.3892i	−0.341197	+	1.34736i	0.526463	+	0.850198i	$0.323518\pi$
$229$	−5.16325	+	20.3892i	−0.341197	+	1.34736i	−0.867660	+	0.497158i	$0.834377\pi$
$230$	0.610202	+	0.531425i	0.0402355	+	0.0350411i
$231$	−0.0287280	−	1.04220i	−0.00189016	−	0.0685716i
$232$	−4.17457	+	3.63564i	−0.274074	+	0.238691i
$233$	−9.46243	−	2.12058i	−0.619904	−	0.138924i	−0.102596	−	0.994723i	$-0.532715\pi$
$233$	−9.46243	−	2.12058i	−0.619904	−	0.138924i	−0.517308	+	0.855799i	$0.673066\pi$
$234$	−1.55522	+	2.69372i	−0.101668	+	0.176094i
$235$	1.57864	+	0.854318i	0.102979	+	0.0557296i
$236$	2.25063	+	2.44484i	0.146504	+	0.159146i
$237$	−4.54312	+	3.95661i	−0.295107	+	0.257009i
$238$	1.98897	+	3.93031i	0.128926	+	0.254764i
$239$	2.92962	−	2.28022i	0.189502	−	0.147495i	−0.515018	−	0.857179i	$-0.672215\pi$
$239$	2.92962	−	2.28022i	0.189502	−	0.147495i	0.704520	+	0.709684i	$0.251162\pi$
$240$	0.0391033	+	0.471907i	0.00252411	+	0.0304614i
$241$	0.295812	+	0.0327405i	0.0190549	+	0.00210900i	0.119531	−	0.992831i	$-0.461861\pi$
$241$	0.295812	+	0.0327405i	0.0190549	+	0.00210900i	−0.100476	+	0.994940i	$0.532036\pi$
$242$	10.4054	−	2.94236i	0.668882	−	0.189142i
$243$	8.98668	−	5.52409i	0.576496	−	0.354371i
$244$	−2.16920	−	1.88916i	−0.138869	−	0.120941i
$245$	0.653956	+	1.13268i	0.0417797	+	0.0723646i
$246$	−7.73460	+	6.02008i	−0.493140	+	0.383826i
$247$	5.75011	−	11.4287i	0.365871	−	0.727191i
$248$	0.0341269	+	0.0265621i	0.00216706	+	0.00168669i
$249$	0.00944519	−	0.0681138i	0.000598565	−	0.00431654i
$250$	1.38414	−	1.88320i	0.0875410	−	0.119104i
$251$	−0.174823	+	0.0391788i	−0.0110348	+	0.00247295i	−0.224195	−	0.974544i	$-0.571975\pi$
$251$	−0.174823	+	0.0391788i	−0.0110348	+	0.00247295i	0.213160	+	0.977017i	$0.431624\pi$
$252$	−0.378926	+	1.21149i	−0.0238701	+	0.0763169i
$253$	1.12166	−	0.976852i	0.0705180	−	0.0614142i
$254$	−18.2546	−	6.26682i	−1.14540	−	0.393215i
$255$	1.53150	−	0.828807i	0.0959064	−	0.0519019i
$256$	0.0275543	−	0.999620i	0.00172215	−	0.0624763i
$257$	−3.82618	+	10.2193i	−0.238671	+	0.637461i	−0.999940	−	0.0109751i	$-0.996506\pi$
$257$	−3.82618	+	10.2193i	−0.238671	+	0.637461i	0.761269	+	0.648436i	$0.224577\pi$
$258$	20.7869	+	16.1791i	1.29413	+	1.00727i
$259$	−1.03051	+	12.4365i	−0.0640331	+	0.772764i
$260$	0.673088	−	0.150842i	0.0417431	−	0.00935485i
$261$	2.05703	+	5.49407i	0.127327	+	0.340074i
$262$	−7.48386	+	12.9624i	−0.462354	+	0.800821i
$263$	20.0316	+	1.10517i	1.23520	+	0.0681479i	0.660886	−	0.750487i	$-0.270181\pi$
$263$	20.0316	+	1.10517i	1.23520	+	0.0681479i	0.574315	+	0.818635i	$0.305269\pi$
$264$	0.869098	+	0.0479495i	0.0534893	+	0.00295109i
$265$	1.45916	+	0.789655i	0.0896352	+	0.0485081i
$266$	1.26988	−	5.06433i	0.0778613	−	0.310514i
$267$	28.1435	−	15.2305i	1.72236	−	0.932092i
$268$	12.5116	−	5.90435i	0.764265	−	0.360666i
$269$	−9.98886	+	2.82458i	−0.609032	+	0.172218i	−0.562635	−	0.826705i	$-0.690212\pi$
$269$	−9.98886	+	2.82458i	−0.609032	+	0.172218i	−0.0463966	+	0.998923i	$0.514774\pi$
$270$	−0.884090	−	0.249997i	−0.0538040	−	0.0152143i
$271$	−20.4312	−	8.29842i	−1.24110	−	0.504093i	−0.341122	−	0.940019i	$-0.610807\pi$
$271$	−20.4312	−	8.29842i	−1.24110	−	0.504093i	−0.899982	+	0.435926i	$0.856421\pi$
$272$	−3.40718	+	1.38388i	−0.206591	+	0.0839099i
$273$	6.98701	+	1.16593i	0.422873	+	0.0705650i
$274$	2.73086	+	10.7839i	0.164977	+	0.651479i
$275$	−1.53113	−	1.48951i	−0.0923308	−	0.0898207i
$276$	−6.42747	+	2.61061i	−0.386888	+	0.157140i
$277$	4.99469	−	11.3868i	0.300102	−	0.684164i	−0.699432	−	0.714700i	$-0.746563\pi$
$277$	4.99469	−	11.3868i	0.300102	−	0.684164i	0.999534	+	0.0305356i	$0.00972131\pi$
$278$	5.40481	−	21.3431i	0.324159	−	1.28007i
$279$	0.0390430	−	0.0239997i	0.00233745	−	0.00143682i
$280$	0.254577	−	0.120138i	0.0152139	−	0.00717960i
$281$	−0.741144	+	26.8873i	−0.0442129	+	1.60396i	0.574607	+	0.818430i	$0.305155\pi$
$281$	−0.741144	+	26.8873i	−0.0442129	+	1.60396i	−0.618819	+	0.785533i	$0.712389\pi$
$282$	−12.6465	+	8.76892i	−0.753091	+	0.522182i
$283$	11.0773	−	15.0713i	0.658480	−	0.895894i	−0.340537	−	0.940231i	$-0.610609\pi$
$283$	11.0773	−	15.0713i	0.658480	−	0.895894i	0.999017	+	0.0443373i	$0.0141176\pi$
$284$	0.600144	−	7.24266i	0.0356120	−	0.429773i
$285$	−2.01514	−	0.446661i	−0.119366	−	0.0264579i
$286$	−0.104706	−	1.26361i	−0.00619138	−	0.0747189i
$287$	4.96385	+	3.05127i	0.293007	+	0.180111i
$288$	−0.981849	−	0.398793i	−0.0578560	−	0.0234991i
$289$	−2.49154	−	2.42380i	−0.146561	−	0.142577i
$290$	0.587437	−	1.16081i	0.0344955	−	0.0681650i
$291$	15.2508	−	0.841408i	0.894015	−	0.0493242i
$292$	−14.1789			−0.829758
$293$	4.20770			0.245817			0.122908	−	0.992418i	$-0.460778\pi$
$293$	4.20770			0.245817			0.122908	+	0.992418i	$0.460778\pi$
$294$	−11.1963	+	0.617718i	−0.652983	+	0.0360261i
$295$	−0.706266	−	0.333295i	−0.0411204	−	0.0194052i
$296$	−10.2762	−	1.71480i	−0.597292	−	0.0996705i
$297$	−0.678397	+	1.54659i	−0.0393646	+	0.0897423i
$298$	−9.14574	+	11.1051i	−0.529798	+	0.643298i
$299$	5.05287	+	8.75183i	0.292215	+	0.506131i
$300$	4.49868	+	8.88964i	0.259732	+	0.513243i
$301$	4.67452	−	14.9453i	0.269435	−	0.861432i
$302$	6.00998	+	16.0519i	0.345836	+	0.923686i
$303$	−13.5302	+	4.64494i	−0.777292	+	0.266845i
$304$	4.12602	+	1.40570i	0.236643	+	0.0806223i
$305$	0.639390	+	0.219503i	0.0366114	+	0.0125687i
$306$	0.107385	+	3.89574i	0.00613881	+	0.222705i
$307$	2.98541	+	5.17088i	0.170386	+	0.295118i	0.938555	−	0.345130i	$-0.112165\pi$
$307$	2.98541	+	5.17088i	0.170386	+	0.295118i	−0.768169	+	0.640248i	$0.778832\pi$
$308$	−0.154465	−	0.493853i	−0.00880148	−	0.0281399i
$309$	−0.791245	−	0.486377i	−0.0450124	−	0.0276690i
$310$	−0.00977983	−	0.00276547i	−0.000555457	−	0.000157068i
$311$	8.51485	−	1.42088i	0.482833	−	0.0805705i	0.0818279	−	0.996646i	$-0.473924\pi$
$311$	8.51485	−	1.42088i	0.482833	−	0.0805705i	0.401005	+	0.916076i	$0.368661\pi$
$312$	−1.45176	+	5.73287i	−0.0821898	+	0.324560i
$313$	0.168574	−	0.204688i	0.00952836	−	0.0115696i	−0.767131	−	0.641491i	$-0.778316\pi$
$313$	0.168574	−	0.204688i	0.00952836	−	0.0115696i	0.776659	+	0.629921i	$0.216913\pi$
$314$	0.0581324	+	0.185860i	0.00328060	+	0.0104887i
$315$	−0.0246350	−	0.297300i	−0.00138802	−	0.0167510i
$316$	−1.63538	+	2.50313i	−0.0919972	+	0.140812i
$317$	8.14297	−	21.7489i	0.457355	−	1.22154i	−0.481262	−	0.876577i	$-0.659821\pi$
$317$	8.14297	−	21.7489i	0.457355	−	1.22154i	0.938616	−	0.344963i	$-0.112108\pi$
$318$	−11.6893	+	8.10521i	−0.655506	+	0.454518i
$319$	−1.96523	−	1.36266i	−0.110032	−	0.0762942i
$320$	0.0824045	+	0.220093i	0.00460655	+	0.0123036i
$321$	27.0130	+	6.05376i	1.50772	+	0.337888i
$322$	2.79321	+	3.03423i	0.155659	+	0.169091i
$323$	−1.36105	−	15.9720i	−0.0757308	−	0.888704i
$324$	7.48815	−	8.13429i	0.416008	−	0.451905i
$325$	11.9267	−	8.26979i	0.661574	−	0.458725i
$326$	1.32974	−	9.58938i	0.0736474	−	0.531107i
$327$	−2.24076	+	11.4714i	−0.123914	+	0.634372i
$328$	−2.88090	+	3.91961i	−0.159071	+	0.216424i
$329$	7.51811	+	5.21294i	0.414487	+	0.287399i
$330$	−0.193477	+	0.0664206i	−0.0106505	+	0.00365634i
$331$	−19.9542	−	10.7987i	−1.09678	−	0.593550i	−0.176303	−	0.984336i	$-0.556414\pi$
$331$	−19.9542	−	10.7987i	−1.09678	−	0.593550i	−0.920481	+	0.390786i	$0.872203\pi$
$332$	−0.00468772	−	0.0338054i	−0.000257272	−	0.00185531i
$333$	−5.52038	+	9.56158i	−0.302515	+	0.523971i
$334$	19.5326	−	6.70556i	1.06878	−	0.366912i
$335$	−2.20208	+	2.39210i	−0.120313	+	0.130694i
$336$	−0.0665006	+	2.41252i	−0.00362791	+	0.131614i
$337$	−0.0277973	−	0.0337523i	−0.00151421	−	0.00183861i	0.771159	−	0.636643i	$-0.219677\pi$
$337$	−0.0277973	−	0.0337523i	−0.00151421	−	0.00183861i	−0.772673	+	0.634804i	$0.781081\pi$
$338$	−4.35869	−	0.482420i	−0.237082	−	0.0262402i
$339$	2.21046	+	1.35877i	0.120056	+	0.0737980i
$340$	0.619487	−	0.602647i	0.0335964	−	0.0326831i
$341$	−0.00750445	+	0.0171084i	−0.000406389	+	0.000926474i
$342$	2.92828	−	3.57259i	0.158343	−	0.193183i
$343$	6.04581	+	13.7831i	0.326443	+	0.744215i
$344$	12.1123	+	4.91961i	0.653054	+	0.265247i
$345$	1.16863	−	1.13686i	0.0629170	−	0.0612066i
$346$	−10.0632	+	12.2191i	−0.541003	+	0.656904i
$347$	−19.5450	−	17.0217i	−1.04923	−	0.913773i	−0.0528325	−	0.998603i	$-0.516825\pi$
$347$	−19.5450	−	17.0217i	−1.04923	−	0.913773i	−0.996395	+	0.0848300i	$0.972965\pi$
$348$	6.60576	+	8.98746i	0.354106	+	0.481779i
$349$	31.8525	−	17.2377i	1.70503	−	0.922714i	0.735571	−	0.677448i	$-0.236914\pi$
$349$	31.8525	−	17.2377i	1.70503	−	0.922714i	0.969456	−	0.245266i	$-0.0788753\pi$
$350$	4.01145	−	4.35760i	0.214421	−	0.232923i
$351$	−9.42936	−	6.53817i	−0.503302	−	0.348982i
$352$	0.421540	−	0.0944693i	0.0224681	−	0.00503523i
$353$	3.36621	+	5.15236i	0.179165	+	0.274233i	0.915444	−	0.402446i	$-0.131840\pi$
$353$	3.36621	+	5.15236i	0.179165	+	0.274233i	−0.736279	+	0.676678i	$0.763419\pi$
$354$	5.28372	−	4.11248i	0.280826	−	0.218576i
$355$	0.509850	+	1.63008i	0.0270600	+	0.0865157i
$356$	11.3840	−	11.0745i	0.603349	−	0.586947i
$357$	8.22301	−	3.33990i	0.435208	−	0.176766i
$358$	−7.96951	+	0.882066i	−0.421202	+	0.0466186i
$359$	−5.93712	−	30.3948i	−0.313349	−	1.60417i	−0.722275	−	0.691606i	$-0.756904\pi$
$359$	−5.93712	−	30.3948i	−0.313349	−	1.60417i	0.408926	−	0.912568i	$-0.365904\pi$
$360$	0.249055			0.0131263
$361$	−11.1808	+	15.3619i	−0.588464	+	0.808523i
$362$	−1.21419			−0.0638163
$363$	−4.17693	−	21.3835i	−0.219232	−	1.12235i
$364$	3.49431	−	0.386751i	0.183152	−	0.0202712i
$365$	3.08730	−	1.25395i	0.161596	−	0.0656348i
$366$	−4.15435	+	4.04141i	−0.217151	+	0.211248i
$367$	7.32991	+	23.4350i	0.382618	+	1.22330i	0.923958	+	0.382494i	$0.124935\pi$
$367$	7.32991	+	23.4350i	0.382618	+	1.22330i	−0.541340	+	0.840804i	$0.682083\pi$
$368$	−2.71708	+	2.11479i	−0.141638	+	0.110241i
$369$	2.81957	+	4.31567i	0.146781	+	0.224665i
$370$	2.38918	−	0.535427i	0.124207	−	0.0278355i
$371$	6.94907	+	4.81838i	0.360778	+	0.250158i
$372$	0.0590149	−	0.0641073i	0.00305978	−	0.00332381i
$373$	0.744968	−	0.403157i	0.0385730	−	0.0208747i	−0.456546	−	0.889700i	$-0.650914\pi$
$373$	0.744968	−	0.403157i	0.0385730	−	0.0208747i	0.495119	+	0.868825i	$0.335124\pi$
$374$	−0.940863	−	1.28009i	−0.0486508	−	0.0661919i
$375$	−3.55115	−	3.09270i	−0.183381	−	0.159706i
$376$	−4.85553	+	5.89574i	−0.250405	+	0.304050i
$377$	11.6463	−	11.3297i	0.599813	−	0.583507i
$378$	−4.33847	−	1.76213i	−0.223147	−	0.0906344i
$379$	12.5601	+	28.6342i	0.645170	+	1.47084i	0.868295	+	0.496049i	$0.165216\pi$
$379$	12.5601	+	28.6342i	0.645170	+	1.47084i	−0.223125	+	0.974790i	$0.571626\pi$
$380$	−1.02271	+	0.0588211i	−0.0524639	+	0.00301746i
$381$	−15.6211	+	35.6125i	−0.800293	+	1.82449i
$382$	9.30164	−	9.04877i	0.475913	−	0.462975i
$383$	26.4150	+	16.2372i	1.34974	+	0.829684i	0.994464	−	0.105077i	$-0.0335087\pi$
$383$	26.4150	+	16.2372i	1.34974	+	0.829684i	0.355279	+	0.934760i	$0.384386\pi$
$384$	−2.00265	−	0.221654i	−0.102197	−	0.0113112i
$385$	0.0773084	+	0.0938703i	0.00394000	+	0.00478408i
$386$	0.132088	−	4.79192i	0.00672312	−	0.243902i
$387$	9.38333	−	10.1930i	0.476981	−	0.518140i
$388$	7.16983	−	2.46141i	0.363993	−	0.124959i
$389$	−10.5078	+	18.2001i	−0.532768	+	0.922781i	0.466500	+	0.884521i	$0.345515\pi$
$389$	−10.5078	+	18.2001i	−0.532768	+	0.922781i	−0.999268	+	0.0382597i	$0.987819\pi$
$390$	−0.190898	−	1.37666i	−0.00966651	−	0.0697098i
$391$	11.1359	+	6.02642i	0.563164	+	0.304769i
$392$	−5.26372	+	1.80704i	−0.265858	+	0.0912692i
$393$	24.7833	+	17.1844i	1.25015	+	0.866837i
$394$	−9.67514	+	13.1635i	−0.487427	+	0.663168i
$395$	0.134713	−	0.689657i	0.00677816	−	0.0347004i
$396$	0.0628813	−	0.453467i	0.00315990	−	0.0227876i
$397$	−3.01604	+	2.09128i	−0.151371	+	0.104958i	−0.643072	−	0.765806i	$-0.722340\pi$
$397$	−3.01604	+	2.09128i	−0.151371	+	0.104958i	0.491701	+	0.870764i	$0.336375\pi$
$398$	10.8219	−	11.7557i	0.542453	−	0.589261i
$399$	−9.95787	−	3.39256i	−0.498517	−	0.169840i
$400$	3.34900	+	3.63798i	0.167450	+	0.181899i
$401$	3.92128	+	0.878780i	0.195820	+	0.0438842i	0.315487	−	0.948930i	$-0.397832\pi$
$401$	3.92128	+	0.878780i	0.195820	+	0.0438842i	−0.119668	+	0.992814i	$0.538183\pi$
$402$	−9.77416	−	26.1056i	−0.487491	−	1.30203i
$403$	−0.104308	−	0.0723255i	−0.00519595	−	0.00360279i
$404$	−5.83450	+	4.04555i	−0.290277	+	0.201274i
$405$	−0.911079	+	2.43338i	−0.0452719	+	0.120916i
$406$	3.62670	−	5.55107i	0.179990	−	0.275495i
$407$	−0.371661	−	4.48529i	−0.0184226	−	0.222327i
$408$	2.21191	+	7.07188i	0.109506	+	0.350110i
$409$	5.81705	−	7.06325i	0.287635	−	0.349255i	−0.608087	−	0.793870i	$-0.708063\pi$
$409$	5.81705	−	7.06325i	0.287635	−	0.349255i	0.895722	+	0.444615i	$0.146659\pi$
$410$	0.280642	−	1.10823i	0.0138599	−	0.0547316i
$411$	22.1085	−	3.68925i	1.09053	−	0.181977i
$412$	−0.443567	−	0.125429i	−0.0218530	−	0.00617943i
$413$	−3.39094	−	2.08440i	−0.166857	−	0.102567i
$414$	1.08922	+	3.48243i	0.0535323	+	0.171152i
$415$	0.00401037	+	0.00694616i	0.000196861	+	0.000340974i
$416$	0.0808742	+	2.93396i	0.00396518	+	0.143849i
$417$	−41.9576	−	14.4041i	−2.05467	−	0.705371i
$418$	−0.151115	+	1.87695i	−0.00739127	+	0.0918047i
$419$	−13.0380	+	4.47596i	−0.636949	+	0.218665i	−0.624213	−	0.781254i	$-0.714580\pi$
$419$	−13.0380	+	4.47596i	−0.636949	+	0.218665i	−0.0127356	+	0.999919i	$0.504054\pi$
$420$	−0.198878	−	0.531179i	−0.00970425	−	0.0259189i
$421$	0.236621	−	0.756520i	0.0115322	−	0.0368705i	−0.948461	−	0.316894i	$-0.897360\pi$
$421$	0.236621	−	0.756520i	0.0115322	−	0.0368705i	0.959993	+	0.280024i	$0.0903424\pi$
$422$	−5.21777	−	10.3106i	−0.253997	−	0.501912i
$423$	4.04707	+	7.00972i	0.196775	+	0.340824i
$424$	−4.48802	+	5.44950i	−0.217957	+	0.264651i
$425$	7.30458	−	16.6528i	0.354324	−	0.807778i
$426$	−14.4434	−	2.41018i	−0.699785	−	0.116773i
$427$	3.11596	+	1.47046i	0.150792	+	0.0711605i
$428$	13.7184	−	0.756867i	0.663106	−	0.0365846i
$429$	−2.55475			−0.123345
$430$	−3.07240			−0.148164
$431$	−31.7526	+	1.75184i	−1.52947	+	0.0843831i	−0.800154	−	0.599795i	$-0.795249\pi$
$431$	−31.7526	+	1.75184i	−1.52947	+	0.0843831i	−0.729315	+	0.684178i	$0.760161\pi$
$432$	1.76522	−	3.48816i	0.0849290	−	0.167824i
$433$	−4.50968	−	4.38708i	−0.216721	−	0.210830i	0.580922	−	0.813959i	$-0.302692\pi$
$433$	−4.50968	−	4.38708i	−0.216721	−	0.210830i	−0.797643	+	0.603129i	$0.793920\pi$
$434$	−0.0479923	−	0.0194928i	−0.00230370	−	0.000935684i
$435$	−2.23316	−	1.37272i	−0.107072	−	0.0658168i
$436$	0.479039	+	5.78115i	0.0229418	+	0.276867i
$437$	−5.29521	−	14.0429i	−0.253304	−	0.671763i
$438$	−2.35920	+	28.4713i	−0.112727	+	1.36041i
$439$	−21.3697	+	29.0745i	−1.01992	+	1.38765i	−0.100245	+	0.994963i	$0.531963\pi$
$439$	−21.3697	+	29.0745i	−1.01992	+	1.38765i	−0.919673	+	0.392686i	$0.871546\pi$
$440$	−0.0834308	+	0.0578496i	−0.00397741	+	0.00275787i
$441$	−0.162509	+	5.89553i	−0.00773853	+	0.280740i
$442$	9.76141	−	4.60652i	0.464303	−	0.219110i
$443$	12.4773	−	7.66975i	0.592813	−	0.364401i	−0.194548	−	0.980893i	$-0.562324\pi$
$443$	12.4773	−	7.66975i	0.592813	−	0.364401i	0.787361	+	0.616492i	$0.211447\pi$
$444$	−5.15314	+	20.3493i	−0.244557	+	0.965735i
$445$	−1.49932	+	3.41811i	−0.0710748	+	0.162034i
$446$	5.31800	−	2.15998i	0.251814	−	0.102278i
$447$	20.7772	+	20.2124i	0.982728	+	0.956013i
$448$	0.294044	+	1.16115i	0.0138923	+	0.0548593i
$449$	−27.4862	−	4.58663i	−1.29715	−	0.216457i	−0.524569	−	0.851368i	$-0.675773\pi$
$449$	−27.4862	−	4.58663i	−1.29715	−	0.216457i	−0.772585	+	0.634911i	$0.781037\pi$
$450$	4.85502	−	1.97194i	0.228868	−	0.0929580i
$451$	−1.94696	−	0.790785i	−0.0916785	−	0.0372366i
$452$	1.23917	+	0.350404i	0.0582857	+	0.0164816i
$453$	33.2323	−	9.39720i	1.56139	−	0.441519i
$454$	−10.3939	+	4.90500i	−0.487810	+	0.230203i
$455$	−0.726643	+	0.393240i	−0.0340656	+	0.0184354i
$456$	3.50916	−	8.05115i	0.164331	−	0.377030i
$457$	−0.521443	−	0.282191i	−0.0243921	−	0.0132003i	0.463706	−	0.885989i	$-0.346520\pi$
$457$	−0.521443	−	0.282191i	−0.0243921	−	0.0132003i	−0.488098	+	0.872789i	$0.662309\pi$
$458$	21.0009	+	1.15865i	0.981306	+	0.0541401i
$459$	−14.3549	−	0.791982i	−0.670030	−	0.0369666i
$460$	0.404586	−	0.700763i	0.0188639	−	0.0326733i
$461$	12.9612	+	34.6179i	0.603664	+	1.61232i	0.778449	+	0.627708i	$0.216007\pi$
$461$	12.9612	+	34.6179i	0.603664	+	1.61232i	−0.174785	+	0.984607i	$0.555923\pi$
$462$	−1.01736	+	0.227995i	−0.0473318	+	0.0106073i
$463$	1.24983	−	15.0832i	0.0580846	−	0.700977i	−0.903877	−	0.427792i	$-0.859291\pi$
$463$	1.24983	−	15.0832i	0.0580846	−	0.700977i	0.961962	−	0.273185i	$-0.0880770\pi$
$464$	4.36851	+	3.40015i	0.202803	+	0.157848i
$465$	−0.00718031	+	0.0191778i	−0.000332979	+	0.000889347i
$466$	−0.267198	+	9.69345i	−0.0123777	+	0.449041i
$467$	−17.9948	+	9.73832i	−0.832702	+	0.450636i	−0.835586	−	0.549360i	$-0.814872\pi$
$467$	−17.9948	+	9.73832i	−0.832702	+	0.450636i	0.00288361	+	0.999996i	$0.499082\pi$
$468$	2.94191	+	1.00996i	0.135990	+	0.0466854i
$469$	−12.4966	+	10.8833i	−0.577037	+	0.502542i
$470$	0.535829	−	1.71314i	0.0247160	−	0.0790214i
$471$	0.382879	−	0.0858052i	0.0176421	−	0.00395369i
$472$	1.96802	−	2.67759i	0.0905855	−	0.123246i
$473$	−0.775719	+	5.59408i	−0.0356676	+	0.257216i
$474$	4.75418	+	3.70033i	0.218367	+	0.169962i
$475$	−19.4707	+	9.24414i	−0.893379	+	0.424150i
$476$	3.47611	−	2.70556i	0.159327	−	0.124009i
$477$	3.74075	+	6.47916i	0.171277	+	0.296660i
$478$	−2.79956	−	2.43814i	−0.128049	−	0.111518i
$479$	−17.4665	+	10.7366i	−0.798063	+	0.490568i	−0.861708	−	0.507405i	$-0.830605\pi$
$479$	−17.4665	+	10.7366i	−0.798063	+	0.490568i	0.0636445	+	0.997973i	$0.479728\pi$
$480$	0.455657	−	0.128848i	0.0207978	−	0.00588106i
$481$	30.3929	+	3.36389i	1.38580	+	0.153380i
$482$	−0.0245771	−	0.296602i	−0.00111946	−	0.0135098i
$483$	6.55750	−	5.10390i	0.298376	−	0.232236i
$484$	−4.88260	−	9.64828i	−0.221936	−	0.438558i
$485$	−1.34347	+	1.17003i	−0.0610037	+	0.0531282i
$486$	−7.14447	−	7.76096i	−0.324080	−	0.352044i
$487$	0.865742	+	0.468516i	0.0392305	+	0.0212305i	0.495444	−	0.868640i	$-0.335005\pi$
$487$	0.865742	+	0.468516i	0.0392305	+	0.0212305i	−0.456214	+	0.889870i	$0.650795\pi$
$488$	−1.43826	+	2.49113i	−0.0651068	+	0.112768i
$489$	−19.0342	−	4.26567i	−0.860757	−	0.192900i
$490$	0.986305	−	0.858973i	0.0445567	−	0.0388045i
$491$	0.283917	+	10.3000i	0.0128130	+	0.464832i	0.978633	+	0.205617i	$0.0659200\pi$
$491$	0.283917	+	10.3000i	0.0128130	+	0.464832i	−0.965820	+	0.259215i	$0.916536\pi$
$492$	7.39122	+	6.43702i	0.333222	+	0.290203i
$493$	4.99755	−	19.7349i	0.225079	−	0.888815i
$494$	−12.3191	−	3.45245i	−0.554262	−	0.155333i
$495$	0.0264119	+	0.104298i	0.00118713	+	0.00468786i
$496$	0.0195269	−	0.0385862i	0.000876783	−	0.00173257i
$497$	1.66885	+	8.54356i	0.0748579	+	0.383231i
$498$	−0.0686611	+	0.00378814i	−0.00307678	+	0.000169751i
$499$	6.14087	+	31.4378i	0.274903	+	1.40735i	0.821621	+	0.570034i	$0.193070\pi$
$499$	6.14087	+	31.4378i	0.274903	+	1.40735i	−0.546718	+	0.837317i	$0.684123\pi$
$500$	−2.11362	−	0.997442i	−0.0945240	−	0.0446070i
$501$	−10.2148	−	40.3372i	−0.456363	−	1.80213i
$502$	0.0719676	+	0.164070i	0.00321207	+	0.00732279i
$503$	−22.3914	−	6.33167i	−0.998381	−	0.282315i	−0.266565	−	0.963817i	$-0.585889\pi$
$503$	−22.3914	−	6.33167i	−0.998381	−	0.282315i	−0.731817	+	0.681502i	$0.761327\pi$
$504$	1.26167	+	0.139641i	0.0561991	+	0.00622011i
$505$	0.912615	−	1.39686i	0.0406108	−	0.0621595i
$506$	−1.17377	−	0.913579i	−0.0521803	−	0.0406136i
$507$	−1.69393	+	8.67199i	−0.0752302	+	0.385136i
$508$	−2.65097	+	19.1174i	−0.117618	+	0.848199i
$509$	2.19977	−	5.87532i	0.0975031	−	0.260419i	−0.878664	−	0.477441i	$-0.841564\pi$
$509$	2.19977	−	5.87532i	0.0975031	−	0.260419i	0.976167	+	0.217022i	$0.0696344\pi$
$510$	−1.10704	−	1.34420i	−0.0490205	−	0.0595223i
$511$	16.3427	−	4.62129i	0.722961	−	0.204434i
$512$	−0.986361	+	0.164595i	−0.0435914	+	0.00727412i
$513$	12.2421	+	11.8538i	0.540503	+	0.523357i
$514$	10.7632	+	1.79607i	0.474746	+	0.0792212i
$515$	0.107674	−	0.0119174i	0.00474469	−	0.000525143i
$516$	11.8939	−	23.5030i	0.523600	−	1.03466i
$517$	−2.98392	−	1.40815i	−0.131233	−	0.0619302i
$518$	12.4033	−	1.37280i	0.544972	−	0.0603175i
$519$	22.8616	+	22.2401i	1.00351	+	0.976232i
$520$	−0.277083	−	0.631685i	−0.0121509	−	0.0277012i
$521$	−16.0536	+	2.67888i	−0.703323	+	0.117364i	−0.505440	−	0.862862i	$-0.668670\pi$
$521$	−16.0536	+	2.67888i	−0.703323	+	0.117364i	−0.197883	+	0.980226i	$0.563407\pi$
$522$	4.99781	−	3.07214i	0.218748	−	0.134464i
$523$	7.81907	+	10.6382i	0.341904	+	0.465177i	0.942418	−	0.334437i	$-0.108546\pi$
$523$	7.81907	+	10.6382i	0.341904	+	0.465177i	−0.600514	+	0.799614i	$0.705037\pi$
$524$	14.1567	+	4.86001i	0.618439	+	0.212311i
$525$	−8.08259	−	8.78004i	−0.352753	−	0.383192i
$526$	−2.75559	−	19.8719i	−0.120150	−	0.866456i
$527$	−0.158795	−	0.00876094i	−0.00691720	−	0.000381632i
$528$	−0.119555	−	0.862170i	−0.00520298	−	0.0375211i
$529$	−10.8754	−	2.43723i	−0.472843	−	0.105967i
$530$	0.495273	−	1.58348i	0.0215133	−	0.0687818i
$531$	−1.92612	−	2.94815i	−0.0835866	−	0.127939i
$532$	−5.21384	−	0.275440i	−0.226049	−	0.0119419i
$533$	7.80908	−	11.9527i	0.338249	−	0.517729i
$534$	−20.3434	−	24.7016i	−0.880346	−	1.06894i
$535$	−2.92010	+	1.37803i	−0.126247	+	0.0595773i
$536$	−8.19343	−	11.1476i	−0.353902	−	0.481502i
$537$	0.445159	+	16.1495i	0.0192100	+	0.696904i
$538$	4.68716	+	9.26208i	0.202078	+	0.399317i
$539$	−1.31496	−	2.01269i	−0.0566392	−	0.0866927i
$540$	−0.0758703	+	0.915619i	−0.00326494	+	0.0394019i
$541$	0.133851	−	0.685243i	0.00575471	−	0.0294609i	−0.978464	−	0.206419i	$-0.933819\pi$
$541$	0.133851	−	0.685243i	0.00575471	−	0.0294609i	0.984218	+	0.176959i	$0.0566259\pi$
$542$	−4.22762	+	21.6431i	−0.181592	+	0.929650i
$543$	−0.202026	+	2.43809i	−0.00866976	+	0.104628i
$544$	2.01140	+	3.07868i	0.0862381	+	0.131997i
$545$	−0.615577	−	1.21641i	−0.0263684	−	0.0521054i
$546$	−0.195185	−	7.08093i	−0.00835313	−	0.303036i
$547$	−0.627530	−	0.853785i	−0.0268312	−	0.0365052i	0.792143	−	0.610336i	$-0.208966\pi$
$547$	−0.627530	−	0.853785i	−0.0268312	−	0.0365052i	−0.818974	+	0.573831i	$0.805457\pi$
$548$	10.0603	−	4.74759i	0.429757	−	0.202807i
$549$	1.93792	+	2.35309i	0.0827086	+	0.100427i
$550$	−1.16835	+	1.78829i	−0.0498184	+	0.0762528i
$551$	−19.7973	+	13.7957i	−0.843392	+	0.587717i
$552$	3.79441	+	5.80777i	0.161501	+	0.247195i
$553$	1.06911	−	3.41815i	0.0454633	−	0.145354i
$554$	−12.1331	−	2.71909i	−0.515485	−	0.115523i
$555$	−0.677608	−	4.88656i	−0.0287629	−	0.207423i
$556$	−21.9834	−	1.21286i	−0.932303	−	0.0514366i
$557$	4.42260	+	31.8935i	0.187392	+	1.35137i	0.817977	+	0.575251i	$0.195096\pi$
$557$	4.42260	+	31.8935i	0.187392	+	1.35137i	−0.630585	+	0.776120i	$0.717185\pi$
$558$	−0.0310395	−	0.0337179i	−0.00131401	−	0.00142739i
$559$	−36.2921	−	12.4591i	−1.53499	−	0.526964i
$560$	−0.166714	−	0.226823i	−0.00704497	−	0.00958502i
$561$	−2.72697	+	1.67626i	−0.115133	+	0.0707718i
$562$	26.5307	−	4.42719i	1.11913	−	0.186750i
$563$	−11.4197	−	26.0343i	−0.481284	−	1.09722i	−0.973902	−	0.226971i	$-0.927118\pi$
$563$	−11.4197	−	26.0343i	−0.481284	−	1.09722i	0.492618	−	0.870246i	$-0.336040\pi$
$564$	11.0307	+	10.7309i	0.464478	+	0.451852i
$565$	−0.300804	+	0.0332930i	−0.0126549	+	0.00140065i
$566$	−16.9154	−	7.98255i	−0.711006	−	0.335532i
$567$	−5.97972	+	11.8163i	−0.251125	+	0.496236i
$568$	−7.22337	+	0.799482i	−0.303086	+	0.0335455i
$569$	−26.6509	−	4.44724i	−1.11726	−	0.186438i	−0.422978	−	0.906140i	$-0.639015\pi$
$569$	−26.6509	−	4.44724i	−1.11726	−	0.186438i	−0.694283	+	0.719702i	$0.744279\pi$
$570$	−0.0520534	+	2.06339i	−0.00218028	+	0.0864258i
$571$	18.9354	−	3.15976i	0.792423	−	0.132232i	0.245480	−	0.969402i	$-0.421054\pi$
$571$	18.9354	−	3.15976i	0.792423	−	0.132232i	0.546943	+	0.837170i	$0.315791\pi$
$572$	−1.22010	+	0.345011i	−0.0510149	+	0.0144256i
$573$	−16.6223	−	20.1833i	−0.694404	−	0.843169i
$574$	2.04305	−	5.45674i	0.0852752	−	0.227760i
$575$	2.33848	−	16.8639i	0.0975214	−	0.703274i
$576$	−0.203165	+	1.04009i	−0.00846520	+	0.0433371i
$577$	−13.4318	−	10.4544i	−0.559173	−	0.435222i	0.294785	−	0.955564i	$-0.404752\pi$
$577$	−13.4318	−	10.4544i	−0.559173	−	0.435222i	−0.853958	+	0.520342i	$0.825805\pi$
$578$	−1.90119	+	2.90999i	−0.0790792	+	0.121040i
$579$	−9.60019	−	1.06255i	−0.398970	−	0.0441580i
$580$	−1.25189	−	0.354002i	−0.0519821	−	0.0146991i
$581$	0.0164212	+	0.0374365i	0.000681265	+	0.00155313i
$582$	−3.74953	−	14.8066i	−0.155423	−	0.613752i
$583$	−2.75807	−	1.30157i	−0.114228	−	0.0539053i
$584$	2.71825	+	13.9159i	0.112482	+	0.575845i
$585$	−0.729885	+	0.0402689i	−0.0301770	+	0.00166491i
$586$	−0.806661	−	4.12965i	−0.0333229	−	0.170594i
$587$	−4.33324	+	8.56271i	−0.178852	+	0.353421i	−0.964006	−	0.265879i	$-0.914338\pi$
$587$	−4.33324	+	8.56271i	−0.178852	+	0.353421i	0.785155	+	0.619300i	$0.212583\pi$
$588$	2.75271	+	10.8702i	0.113520	+	0.448280i
$589$	0.135423	+	0.131127i	0.00558000	+	0.00540299i
$590$	−0.191714	+	0.757062i	−0.00789274	+	0.0311677i
$591$	24.8225	+	21.6179i	1.02106	+	0.889242i
$592$	0.287069	+	10.4143i	0.0117985	+	0.428027i
$593$	31.2228	−	27.1920i	1.28217	−	1.11664i	0.295248	−	0.955421i	$-0.404598\pi$
$593$	31.2228	−	27.1920i	1.28217	−	1.11664i	0.986919	−	0.161219i	$-0.0515425\pi$
$594$	1.64796	+	0.369316i	0.0676166	+	0.0151532i
$595$	−0.517608	+	0.896524i	−0.0212199	+	0.0367539i
$596$	12.6524	+	6.84714i	0.518263	+	0.280470i
$597$	−21.8048	−	23.6864i	−0.892413	−	0.969419i
$598$	7.62080	−	6.63696i	0.311638	−	0.271406i
$599$	−3.73471	−	7.37998i	−0.152596	−	0.301538i	0.803126	−	0.595809i	$-0.203169\pi$
$599$	−3.73471	−	7.37998i	−0.152596	−	0.301538i	−0.955722	+	0.294272i	$0.904923\pi$
$600$	7.86230	−	6.11948i	0.320977	−	0.249827i
$601$	1.87980	+	22.6858i	0.0766787	+	0.925374i	0.921007	+	0.389547i	$0.127368\pi$
$601$	1.87980	+	22.6858i	0.0766787	+	0.925374i	−0.844328	+	0.535827i	$0.820000\pi$
$602$	−15.5642	−	1.72265i	−0.634351	−	0.0702099i
$603$	−14.1081	+	3.98940i	−0.574528	+	0.162461i
$604$	14.6020	−	8.97583i	0.594148	−	0.365222i
$605$	1.91640	+	1.66900i	0.0779128	+	0.0678544i
$606$	7.15268	+	12.3888i	0.290558	+	0.503260i
$607$	33.9611	−	26.4330i	1.37844	−	1.07288i	0.390071	−	0.920785i	$-0.372450\pi$
$607$	33.9611	−	26.4330i	1.37844	−	1.07288i	0.988366	−	0.152096i	$-0.0486022\pi$
$608$	0.588623	−	4.31897i	0.0238718	−	0.175157i
$609$	−10.5431	−	8.20604i	−0.427229	−	0.332525i
$610$	0.0928536	−	0.669612i	0.00375953	−	0.0271118i
$611$	13.2765	−	18.0633i	0.537108	−	0.730762i
$612$	3.80289	−	0.852248i	0.153723	−	0.0344501i
$613$	−12.0202	+	38.4306i	−0.485490	+	1.55220i	0.312737	+	0.949840i	$0.398754\pi$
$613$	−12.0202	+	38.4306i	−0.485490	+	1.55220i	−0.798227	+	0.602357i	$0.794228\pi$
$614$	4.50263	−	3.92135i	0.181712	−	0.158253i
$615$	−2.17863	−	0.747924i	−0.0878508	−	0.0301592i
$616$	−0.455081	+	0.246277i	−0.0183357	+	0.00992279i
$617$	0.354312	−	12.8538i	0.0142641	−	0.517474i	−0.958423	−	0.285352i	$-0.907889\pi$
$617$	0.354312	−	12.8538i	0.0142641	−	0.517474i	0.972687	−	0.232122i	$-0.0745667\pi$
$618$	−0.325665	+	0.869813i	−0.0131002	+	0.0349890i
$619$	−26.4132	−	20.5582i	−1.06164	−	0.826304i	−0.0763266	−	0.997083i	$-0.524319\pi$
$619$	−26.4132	−	20.5582i	−1.06164	−	0.826304i	−0.985309	+	0.170778i	$0.945372\pi$
$620$	−0.000839280		0.0101286i	−3.37063e−5		0.000406775i
$621$	−13.1346	+	2.94352i	−0.527071	+	0.118119i
$622$	−3.02691	−	8.08451i	−0.121368	−	0.324159i
$623$	−9.51179	+	16.4749i	−0.381082	+	0.660053i
$624$	5.90486	+	0.325780i	0.236383	+	0.0130416i
$625$	−24.1379	−	1.33172i	−0.965515	−	0.0532689i
$626$	−0.233209	−	0.126206i	−0.00932089	−	0.00504422i
$627$	3.74377	+	0.615740i	0.149512	+	0.0245903i
$628$	0.171268	−	0.0926855i	0.00683433	−	0.00369855i
$629$	34.6489	−	16.3512i	1.38154	−	0.651965i
$630$	−0.287063	+	0.0811736i	−0.0114369	+	0.00323403i
$631$	−1.32834	−	0.375619i	−0.0528803	−	0.0149531i	0.245561	−	0.969381i	$-0.421028\pi$
$631$	−1.32834	−	0.375619i	−0.0528803	−	0.0149531i	−0.298441	+	0.954428i	$0.596467\pi$
$632$	2.77022	+	1.12517i	0.110193	+	0.0447567i
$633$	−21.5718	+	8.76172i	−0.857403	+	0.348247i
$634$	−22.9066	−	3.82243i	−0.909736	−	0.151808i
$635$	−1.11348	−	4.39705i	−0.0441872	−	0.174491i
$636$	10.1958	+	9.91867i	0.404291	+	0.393301i
$637$	15.1338	−	6.14682i	0.599623	−	0.243546i
$638$	−0.960628	+	2.19001i	−0.0380316	+	0.0867034i
$639$	−1.89065	+	7.46602i	−0.0747931	+	0.295351i
$640$	0.200212	−	0.123070i	0.00791409	−	0.00486477i
$641$	2.52556	−	1.19184i	0.0997536	−	0.0470748i	−0.376250	−	0.926518i	$-0.622787\pi$
$641$	2.52556	−	1.19184i	0.0997536	−	0.0470748i	0.476004	+	0.879443i	$0.342085\pi$
$642$	0.762789	−	27.6725i	0.0301049	−	1.09215i
$643$	16.3495	−	11.3365i	0.644761	−	0.447067i	−0.201751	−	0.979437i	$-0.564663\pi$
$643$	16.3495	−	11.3365i	0.644761	−	0.447067i	0.846512	+	0.532369i	$0.178698\pi$
$644$	2.44247	−	3.32309i	0.0962466	−	0.130948i
$645$	−0.511209	+	6.16938i	−0.0201289	+	0.242919i
$646$	−15.4148	+	4.39780i	−0.606486	+	0.173029i
$647$	0.308391	+	3.72173i	0.0121241	+	0.146316i	0.999958	−	0.00919842i	$-0.00292799\pi$
$647$	0.308391	+	3.72173i	0.0121241	+	0.146316i	−0.987834	+	0.155515i	$0.950296\pi$
$648$	−9.41897	−	5.78982i	−0.370012	−	0.227446i
$649$	1.33002	+	0.540207i	0.0522078	+	0.0212050i
$650$	−10.4029	−	10.1201i	−0.408034	−	0.396942i
$651$	−0.0471268	+	0.0931252i	−0.00184705	+	0.00364986i
$652$	−9.66644	+	0.533312i	−0.378567	+	0.0208861i
$653$	22.7638			0.890815			0.445408	−	0.895328i	$-0.353059\pi$
$653$	22.7638			0.890815			0.445408	+	0.895328i	$0.353059\pi$
$654$	11.6882			0.457046
$655$	−3.51227	+	0.193777i	−0.137236	+	0.00757151i
$656$	4.39920	+	2.07603i	0.171760	+	0.0810555i
$657$	14.8211	+	2.47321i	0.578227	+	0.0964890i
$658$	3.67495	−	8.37804i	0.143264	−	0.326610i
$659$	1.15271	−	1.39965i	0.0449030	−	0.0545227i	−0.748984	−	0.662589i	$-0.769458\pi$
$659$	1.15271	−	1.39965i	0.0449030	−	0.0545227i	0.793887	+	0.608066i	$0.208054\pi$
$660$	0.102280	+	0.177154i	0.00398125	+	0.00689573i
$661$	12.3061	+	24.3174i	0.478651	+	0.945839i	0.995939	+	0.0900282i	$0.0286957\pi$
$661$	12.3061	+	24.3174i	0.478651	+	0.945839i	−0.517289	+	0.855811i	$0.673059\pi$
$662$	−6.77295	+	21.6543i	−0.263238	+	0.841620i
$663$	−7.62571	−	20.3674i	−0.296158	−	0.791003i
$664$	−0.0322796	+	0.0110816i	−0.00125269	+	0.000430050i
$665$	1.15961	−	0.401126i	0.0449679	−	0.0155550i
$666$	10.4425	+	3.58493i	0.404640	+	0.138913i
$667$	−0.525191	−	19.0530i	−0.0203355	−	0.737733i
$668$	−10.3258	−	17.8848i	−0.399517	−	0.691984i
$669$	−3.45240	−	11.0379i	−0.133477	−	0.426751i
$670$	2.76989	+	1.70265i	0.107010	+	0.0657789i
$671$	−1.19575	−	0.338127i	−0.0461615	−	0.0130532i
$672$	2.38052	−	0.397238i	0.0918305	−	0.0153238i
$673$	5.54164	−	21.8834i	0.213614	−	0.843544i	−0.766030	−	0.642805i	$-0.777771\pi$
$673$	5.54164	−	21.8834i	0.213614	−	0.843544i	0.979645	−	0.200740i	$-0.0643346\pi$
$674$	−0.0277973	+	0.0337523i	−0.00107071	+	0.00130009i
$675$	5.77058	+	18.4496i	0.222110	+	0.710125i
$676$	0.362136	+	4.37033i	0.0139283	+	0.168090i
$677$	8.02812	−	12.2880i	0.308546	−	0.472265i	−0.648902	−	0.760872i	$-0.724771\pi$
$677$	8.02812	−	12.2880i	0.308546	−	0.472265i	0.957447	+	0.288608i	$0.0931923\pi$
$678$	0.909793	−	2.42995i	0.0349404	−	0.0933217i
$679$	−7.46178	+	5.17388i	−0.286357	+	0.198555i
$680$	−0.710231	−	0.492463i	−0.0272361	−	0.0188851i
$681$	8.11982	+	21.6871i	0.311152	+	0.831051i
$682$	0.0182298	+	0.00408539i	0.000698054	+	0.000156438i
$683$	−0.681618	−	0.740434i	−0.0260814	−	0.0283319i	0.722547	−	0.691322i	$-0.242971\pi$
$683$	−0.681618	−	0.740434i	−0.0260814	−	0.0283319i	−0.748628	+	0.662990i	$0.769287\pi$
$684$	−4.06770	−	2.18906i	−0.155533	−	0.0837009i
$685$	−1.77066	+	1.92345i	−0.0676534	+	0.0734911i
$686$	12.3684	−	8.57603i	0.472226	−	0.327434i
$687$	5.82085	−	41.9769i	0.222079	−	1.60152i
$688$	2.50629	−	12.8308i	0.0955515	−	0.489170i
$689$	12.2716	−	16.6961i	0.467510	−	0.636070i
$690$	−1.33981	−	0.929007i	−0.0510059	−	0.0353667i
$691$	4.08012	−	1.40071i	0.155215	−	0.0532854i	−0.245997	−	0.969271i	$-0.579115\pi$
$691$	4.08012	−	1.40071i	0.155215	−	0.0532854i	0.401212	+	0.915985i	$0.368589\pi$
$692$	13.9217	+	7.53405i	0.529224	+	0.286402i
$693$	0.0753195	+	0.543165i	0.00286115	+	0.0206331i
$694$	−12.9590	+	22.4457i	−0.491917	+	0.852026i
$695$	4.89389	−	1.68007i	0.185636	−	0.0637288i
$696$	7.55436	−	8.20623i	0.286347	−	0.311056i
$697$	0.492920	−	17.8822i	0.0186707	−	0.677338i
$698$	−23.0245	−	27.9571i	−0.871488	−	1.05819i
$699$	19.4200	+	2.14940i	0.734532	+	0.0812979i
$700$	−5.04581	−	3.10165i	−0.190714	−	0.117231i
$701$	21.9557	−	21.3589i	0.829257	−	0.806714i	−0.154165	−	0.988045i	$-0.549269\pi$
$701$	21.9557	−	21.3589i	0.829257	−	0.806714i	0.983422	+	0.181331i	$0.0580407\pi$
$702$	−4.60919	+	10.5079i	−0.173963	+	0.396595i
$703$	−43.7276	−	12.2547i	−1.64922	−	0.462196i
$704$	−0.173531	−	0.395610i	−0.00654018	−	0.0149101i
$705$	−3.35083	−	1.36099i	−0.126200	−	0.0512579i
$706$	4.41146	−	4.29153i	0.166027	−	0.161514i
$707$	5.40634	−	6.56456i	0.203326	−	0.246886i
$708$	−5.04915	−	4.39730i	−0.189758	−	0.165261i
$709$	−20.2697	−	27.5779i	−0.761245	−	1.03571i	−0.997942	−	0.0641271i	$-0.979574\pi$
$709$	−20.2697	−	27.5779i	−0.761245	−	1.03571i	0.236697	−	0.971583i	$-0.423935\pi$
$710$	1.50210	−	0.812897i	0.0563729	−	0.0305075i
$711$	2.14607	−	2.33125i	0.0804838	−	0.0874287i
$712$	−13.0515	−	9.04971i	−0.489126	−	0.339152i
$713$	−0.145295	+	0.0325613i	−0.00544134	+	0.00121943i
$714$	−4.85439	−	7.43019i	−0.181671	−	0.278068i
$715$	0.235151	−	0.183025i	0.00879413	−	0.00684475i
$716$	2.39354	+	7.65259i	0.0894510	+	0.285991i
$717$	−5.36160	+	5.21584i	−0.200233	+	0.194789i
$718$	−28.6928	+	11.6540i	−1.07080	+	0.434923i
$719$	30.1349	−	3.33533i	1.12384	−	0.124387i	0.471180	−	0.882037i	$-0.343828\pi$
$719$	30.1349	−	3.33533i	1.12384	−	0.124387i	0.652661	+	0.757650i	$0.273653\pi$
$720$	−0.0477464	−	0.244435i	−0.00177940	−	0.00910956i
$721$	0.552140			0.0205628
$722$	17.2205	+	8.02838i	0.640880	+	0.298786i
$723$	−0.599666			−0.0223018
$724$	0.232773	+	1.19167i	0.00865093	+	0.0442879i
$725$	−27.2070	+	3.01127i	−1.01044	+	0.111836i
$726$	−20.1862	+	8.19891i	−0.749178	+	0.304290i
$727$	−18.0538	+	17.5630i	−0.669577	+	0.651375i	−0.951352	−	0.308106i	$-0.900305\pi$
$727$	−18.0538	+	17.5630i	−0.669577	+	0.651375i	0.281775	+	0.959481i	$0.409077\pi$
$728$	−1.04947	−	3.35536i	−0.0388961	−	0.124358i
$729$	9.40187	−	7.31777i	0.348217	−	0.271028i
$730$	−1.82256	−	2.78963i	−0.0674559	−	0.103249i
$731$	−46.9134	+	10.5135i	−1.73516	+	0.388858i
$732$	4.76288	+	3.30251i	0.176041	+	0.122064i
$733$	−21.9937	+	23.8915i	−0.812355	+	0.882453i	−0.994913	−	0.100743i	$-0.967878\pi$
$733$	−21.9937	+	23.8915i	−0.812355	+	0.882453i	0.182558	+	0.983195i	$0.441562\pi$
$734$	21.5951	−	11.6867i	0.797090	−	0.431364i
$735$	−1.56071	−	2.12342i	−0.0575676	−	0.0783236i
$736$	2.59646	+	2.26126i	0.0957066	+	0.0833510i
$737$	3.79944	−	4.61340i	0.139954	−	0.169937i
$738$	3.69508	−	3.59463i	0.136018	−	0.132320i
$739$	−19.5181	−	7.92756i	−0.717984	−	0.291620i	−0.0120796	−	0.999927i	$-0.503845\pi$
$739$	−19.5181	−	7.92756i	−0.717984	−	0.291620i	−0.705904	+	0.708307i	$0.749459\pi$
$740$	−0.983527	−	2.24222i	−0.0361552	−	0.0824255i
$741$	−8.98225	+	24.1623i	−0.329971	+	0.887623i
$742$	3.39679	−	7.74391i	0.124700	−	0.284288i
$743$	−10.3942	+	10.1116i	−0.381325	+	0.370958i	−0.862838	−	0.505480i	$-0.831315\pi$
$743$	−10.3942	+	10.1116i	−0.381325	+	0.370958i	0.481513	+	0.876439i	$0.340087\pi$
$744$	−0.0742320	−	0.0456302i	−0.00272148	−	0.00167288i
$745$	−3.36046	−	0.371936i	−0.123118	−	0.0136267i
$746$	−0.538497	−	0.653861i	−0.0197158	−	0.0239395i
$747$	−0.000996583		0.0361542i	−3.64631e−5		0.00132281i
$748$	−1.07597	+	1.16882i	−0.0393415	+	0.0427362i
$749$	−15.5653	+	5.34358i	−0.568744	+	0.195250i
$750$	−2.35454	+	4.07819i	−0.0859758	+	0.148914i
$751$	1.21111	+	8.73389i	0.0441940	+	0.318704i	0.999717	+	0.0237877i	$0.00757257\pi$
$751$	1.21111	+	8.73389i	0.0441940	+	0.318704i	−0.955523	+	0.294917i	$0.904708\pi$
$752$	6.71724	+	3.63519i	0.244953	+	0.132562i
$753$	0.341426	−	0.117212i	0.0124423	−	0.00427143i
$754$	−13.3522	−	9.25822i	−0.486259	−	0.337165i
$755$	−2.38562	+	3.24576i	−0.0868217	+	0.118125i
$756$	−0.897718	+	4.59582i	−0.0326497	+	0.167148i
$757$	1.39766	−	10.0792i	0.0507987	−	0.366334i	−0.948040	−	0.318152i	$-0.896938\pi$
$757$	1.39766	−	10.0792i	0.0507987	−	0.366334i	0.998839	−	0.0481823i	$-0.0153428\pi$
$758$	25.6951	−	17.8166i	0.933290	−	0.647129i
$759$	−2.02977	+	2.20491i	−0.0736759	+	0.0800333i
$760$	0.253794	+	0.992463i	0.00920609	+	0.0360004i
$761$	−28.3491	−	30.7954i	−1.02765	−	1.11633i	−0.993141	−	0.116927i	$-0.962696\pi$
$761$	−28.3491	−	30.7954i	−1.02765	−	1.11633i	−0.0345144	−	0.999404i	$-0.510988\pi$
$762$	37.9467	+	8.50406i	1.37466	+	0.308069i
$763$	−2.43638	−	6.50727i	−0.0882027	−	0.235579i
$764$	−10.6642	−	7.39436i	−0.385815	−	0.267518i
$765$	−0.752665	+	0.521886i	−0.0272127	+	0.0188688i
$766$	10.8720	−	29.0379i	0.392822	−	1.04918i
$767$	−5.33460	+	8.16521i	−0.192621	+	0.294829i
$768$	0.166388	+	2.00800i	0.00600399	+	0.0724574i
$769$	−7.20662	−	23.0408i	−0.259877	−	0.830874i	−0.989183	−	0.146686i	$-0.953139\pi$
$769$	−7.20662	−	23.0408i	−0.259877	−	0.830874i	0.729306	−	0.684188i	$-0.239843\pi$
$770$	0.0773084	−	0.0938703i	0.00278600	−	0.00338285i
$771$	5.39737	−	21.3137i	0.194382	−	0.767596i
$772$	−4.72836	+	0.789024i	−0.170177	+	0.0283976i
$773$	3.67765	+	1.03994i	0.132276	+	0.0374041i	0.337598	−	0.941290i	$-0.390386\pi$
$773$	3.67765	+	1.03994i	0.132276	+	0.0374041i	−0.205322	+	0.978694i	$0.565824\pi$
$774$	−11.8028	−	7.25517i	−0.424244	−	0.260782i
$775$	0.0638344	+	0.204090i	0.00229300	+	0.00733113i
$776$	−3.79029	−	6.56497i	−0.136063	−	0.235669i
$777$	−0.692823	−	25.1343i	−0.0248549	−	0.901689i
$778$	19.8770	+	6.82377i	0.712624	+	0.244644i
$779$	−14.3244	+	15.6335i	−0.513224	+	0.560130i
$780$	−1.31453	+	0.451277i	−0.0470676	+	0.0161583i
$781$	−1.10083	−	2.94019i	−0.0393909	−	0.105208i
$782$	3.77978	−	12.0846i	0.135165	−	0.432146i
$783$	9.77185	+	19.3097i	0.349217	+	0.690073i
$784$	2.78263	+	4.81966i	0.0993797	+	0.172131i
$785$	−0.0290947	+	0.0353277i	−0.00103843	+	0.00126090i
$786$	12.1144	−	27.6181i	0.432106	−	0.985103i
$787$	1.24779	+	0.208220i	0.0444790	+	0.00742223i	0.186792	−	0.982399i	$-0.440191\pi$
$787$	1.24779	+	0.208220i	0.0444790	+	0.00742223i	−0.142313	+	0.989822i	$0.545454\pi$
$788$	14.7742	+	6.97210i	0.526308	+	0.248371i
$789$	−40.3613	+	2.22679i	−1.43690	+	0.0792759i
$790$	−0.702691			−0.0250006
$791$	−1.54249			−0.0548445
$792$	−0.457111	+	0.0252195i	−0.0162427	+	0.000896136i
$793$	3.81220	−	7.53312i	0.135375	−	0.267509i
$794$	2.63069	+	2.55918i	0.0933599	+	0.0908219i
$795$	−3.09721	−	1.25798i	−0.109847	−	0.0446159i
$796$	−13.6123	−	8.36748i	−0.482477	−	0.296577i
$797$	2.84631	+	34.3499i	0.100822	+	1.21674i	0.839758	+	0.542960i	$0.182697\pi$
$797$	2.84631	+	34.3499i	0.100822	+	1.21674i	−0.738937	+	0.673775i	$0.764672\pi$
$798$	−1.42060	+	10.4236i	−0.0502888	+	0.368990i
$799$	2.31949	−	27.9921i	0.0820576	−	0.990288i
$800$	2.92847	−	3.98432i	0.103537	−	0.140867i
$801$	−13.8313	+	9.59040i	−0.488704	+	0.338860i
$802$	0.110728	−	4.01702i	0.00390996	−	0.141846i
$803$	−5.53939	+	2.61410i	−0.195481	+	0.0922497i
$804$	−23.7476	+	14.5976i	−0.837513	+	0.514817i
$805$	−0.237932	+	0.939572i	−0.00838600	+	0.0331156i
$806$	−0.0509870	+	0.116239i	−0.00179594	+	0.00409433i
$807$	19.3781	−	7.87072i	0.682143	−	0.277062i
$808$	5.08905	+	4.95070i	0.179032	+	0.174165i
$809$	3.95586	+	15.6213i	0.139081	+	0.549217i	0.999232	+	0.0391787i	$0.0124742\pi$
$809$	3.95586	+	15.6213i	0.139081	+	0.549217i	−0.860152	+	0.510039i	$0.829631\pi$
$810$	2.56291	+	0.427674i	0.0900515	+	0.0150269i
$811$	43.7232	−	17.7588i	1.53533	−	0.623597i	0.556973	−	0.830530i	$-0.311962\pi$
$811$	43.7232	−	17.7588i	1.53533	−	0.623597i	0.978355	+	0.206934i	$0.0663485\pi$
$812$	−6.14339	−	2.49523i	−0.215591	−	0.0875653i
$813$	42.7559	+	12.0902i	1.49951	+	0.424022i
$814$	−4.33084	+	1.22464i	−0.151796	+	0.0429238i
$815$	2.05759	−	0.971001i	0.0720743	−	0.0340127i
$816$	6.51666	−	3.52664i	0.228129	−	0.123457i
$817$	50.1802	+	27.0048i	1.75558	+	0.944779i
$818$	−8.04743	−	4.35505i	−0.281372	−	0.152271i
$819$	−3.72004	−	0.205241i	−0.129989	−	0.00717169i
$820$	−1.14148	−	0.0629770i	−0.0398621	−	0.00219925i
$821$	−8.64643	+	14.9761i	−0.301762	+	0.522668i	−0.976535	−	0.215358i	$-0.930908\pi$
$821$	−8.64643	+	14.9761i	−0.301762	+	0.522668i	0.674773	+	0.738026i	$0.264242\pi$
$822$	−7.85924	−	20.9911i	−0.274123	−	0.732149i
$823$	24.8843	−	5.57671i	0.867413	−	0.194392i	0.237813	−	0.971311i	$-0.423569\pi$
$823$	24.8843	−	5.57671i	0.867413	−	0.194392i	0.629600	+	0.776919i	$0.283219\pi$
$824$	−0.0380658	+	0.459386i	−0.00132608	+	0.0160035i
$825$	3.39648	+	2.64359i	0.118250	+	0.0920379i
$826$	−1.39566	+	3.72765i	−0.0485613	+	0.129701i
$827$	0.451264	−	16.3710i	0.0156920	−	0.569276i	−0.950393	−	0.311052i	$-0.899319\pi$
$827$	0.451264	−	16.3710i	0.0156920	−	0.569276i	0.966085	−	0.258224i	$-0.0831374\pi$
$828$	3.20903	−	1.73664i	0.111521	−	0.0603523i
$829$	23.9130	+	8.20933i	0.830531	+	0.285122i	0.706995	−	0.707218i	$-0.250050\pi$
$829$	23.9130	+	8.20933i	0.830531	+	0.285122i	0.123536	+	0.992340i	$0.460577\pi$
$830$	0.00604849	−	0.00526763i	0.000209946	−	0.000182842i
$831$	−7.47872	+	23.9108i	−0.259434	+	0.829457i
$832$	2.86404	−	0.641846i	0.0992927	−	0.0222520i
$833$	12.1208	−	16.4910i	0.419962	−	0.571379i
$834$	−6.09318	+	43.9408i	−0.210989	+	1.52155i
$835$	3.83001	+	2.98102i	0.132543	+	0.103162i
$836$	1.87111	−	0.211520i	0.0647136	−	0.00731557i
$837$	0.133415	−	0.103841i	0.00461150	−	0.00358928i
$838$	6.89246	+	11.9381i	0.238096	+	0.412394i
$839$	29.3305	+	25.5440i	1.01260	+	0.881876i	0.993022	−	0.117932i	$-0.0376264\pi$
$839$	29.3305	+	25.5440i	1.01260	+	0.881876i	0.0195810	+	0.999808i	$0.493767\pi$
$840$	−0.483200	+	0.297022i	−0.0166720	+	0.0102482i
$841$	−1.58284	+	0.447584i	−0.0545806	+	0.0154339i
$842$	−0.787851	−	0.0871993i	−0.0271511	−	0.00300509i
$843$	−4.47542	−	54.0102i	−0.154141	−	1.86021i
$844$	−9.11904	+	7.09763i	−0.313890	+	0.244311i
$845$	−0.465353	−	0.919563i	−0.0160086	−	0.0316339i
$846$	6.10384	−	5.31584i	0.209854	−	0.182762i
$847$	8.77237	+	9.52933i	0.301422	+	0.327432i
$848$	6.20882	+	3.36004i	0.213212	+	0.115384i
$849$	−18.8435	+	32.6378i	−0.646706	+	1.12013i
$850$	−17.7443	−	3.97658i	−0.608623	−	0.136396i
$851$	27.0506	−	23.5584i	0.927284	−	0.807573i
$852$	0.403481	+	14.6375i	0.0138230	+	0.501474i
$853$	−29.2019	−	25.4320i	−0.999856	−	0.870775i	−0.00823597	−	0.999966i	$-0.502622\pi$
$853$	−29.2019	−	25.4320i	−0.999856	−	0.870775i	−0.991620	+	0.129191i	$0.958762\pi$
$854$	0.845820	−	3.34007i	0.0289434	−	0.114295i
$855$	1.07929	+	0.116904i	0.0369110	+	0.00399805i
$856$	−3.37280	−	13.3189i	−0.115280	−	0.455230i
$857$	−5.67912	+	11.2222i	−0.193995	+	0.383344i	−0.968421	−	0.249320i	$-0.919793\pi$
$857$	−5.67912	+	11.2222i	−0.193995	+	0.383344i	0.774426	+	0.632664i	$0.218039\pi$
$858$	0.489773	+	2.50736i	0.0167206	+	0.0856000i
$859$	−22.0053	+	1.21406i	−0.750809	+	0.0414233i	−0.426451	−	0.904511i	$-0.640236\pi$
$859$	−22.0053	+	1.21406i	−0.750809	+	0.0414233i	−0.324359	+	0.945934i	$0.605149\pi$
$860$	0.589012	+	3.01541i	0.0200851	+	0.102825i
$861$	−10.6172	−	5.01037i	−0.361833	−	0.170753i
$862$	7.80665	+	30.8278i	0.265896	+	1.05000i
$863$	0.777670	+	1.77291i	0.0264722	+	0.0603505i	0.928512	−	0.371302i	$-0.121089\pi$
$863$	0.777670	+	1.77291i	0.0264722	+	0.0603505i	−0.902040	+	0.431653i	$0.857931\pi$
$864$	−3.76187	−	1.06376i	−0.127981	−	0.0361897i
$865$	−3.69758	−	0.409249i	−0.125722	−	0.0139149i
$866$	−3.44116	+	5.26708i	−0.116935	+	0.178983i
$867$	5.52693	+	4.30178i	0.187704	+	0.146096i
$868$	−0.00993059	+	0.0508391i	−0.000337066	+	0.00172559i
$869$	−0.177415	+	1.27943i	−0.00601840	+	0.0434016i
$870$	−0.919136	+	2.45490i	−0.0311616	+	0.0832290i
$871$	25.8143	+	31.3445i	0.874683	+	1.06207i
$872$	5.58208	−	1.57846i	0.189033	−	0.0534534i
$873$	−7.92392	+	1.32227i	−0.268184	+	0.0447520i
$874$	−12.7673	+	7.88917i	−0.431860	+	0.266855i
$875$	2.76127	+	0.460775i	0.0933481	+	0.0155770i
$876$	28.3954	−	3.14281i	0.959393	−	0.106186i
$877$	1.20603	−	2.38317i	0.0407246	−	0.0804740i	−0.870984	−	0.491311i	$-0.836518\pi$
$877$	1.20603	−	2.38317i	0.0407246	−	0.0804740i	0.911709	+	0.410837i	$0.134763\pi$
$878$	32.6320	+	15.3994i	1.10128	+	0.519704i
$879$	−8.42656	+	0.932652i	−0.284221	+	0.0314576i
$880$	0.0727712	+	0.0707929i	0.00245312	+	0.00238643i
$881$	22.5379	+	51.3812i	0.759321	+	1.73108i	0.678798	+	0.734325i	$0.262501\pi$
$881$	22.5379	+	51.3812i	0.759321	+	1.73108i	0.0805232	+	0.996753i	$0.474341\pi$
$882$	5.81733	−	0.970741i	0.195880	−	0.0326866i
$883$	4.96165	−	3.04991i	0.166973	−	0.102638i	−0.437666	−	0.899138i	$-0.644195\pi$
$883$	4.96165	−	3.04991i	0.166973	−	0.102638i	0.604639	+	0.796500i	$0.293318\pi$
$884$	−6.39244	−	8.69723i	−0.215001	−	0.292519i
$885$	1.48828	+	0.510927i	0.0500280	+	0.0171746i
$886$	−9.91952	−	10.7755i	−0.333253	−	0.362009i
$887$	2.84889	+	20.5447i	0.0956565	+	0.689825i	0.976359	+	0.216155i	$0.0693516\pi$
$887$	2.84889	+	20.5447i	0.0956565	+	0.689825i	−0.880703	+	0.473670i	$0.842929\pi$
$888$	20.9598	+	1.15638i	0.703363	+	0.0388056i
$889$	−3.17535	−	22.8990i	−0.106498	−	0.768006i
$890$	3.64215	+	0.816225i	0.122085	+	0.0273599i
$891$	1.42577	−	4.55845i	0.0477652	−	0.152714i
$892$	−3.13943	−	4.80526i	−0.105116	−	0.160892i
$893$	−23.8091	+	23.2704i	−0.796741	+	0.778713i
$894$	15.8543	−	24.2667i	0.530246	−	0.811601i
$895$	−1.19794	−	1.45458i	−0.0400429	−	0.0486214i
$896$	1.08324	−	0.511195i	0.0361886	−	0.0170778i
$897$	−12.0590	−	16.4069i	−0.402639	−	0.547810i
$898$	0.767836	+	27.8557i	0.0256230	+	0.929556i
$899$	0.108097	+	0.213605i	0.00360522	+	0.00712411i
$900$	−2.86612	−	4.38692i	−0.0955373	−	0.146231i
$901$	2.14393	−	25.8734i	0.0714246	−	0.861967i
$902$	−0.402865	+	2.06244i	−0.0134139	+	0.0686719i
$903$	−6.04877	+	30.9663i	−0.201290	+	1.03050i
$904$	0.106342	−	1.28336i	0.00353689	−	0.0426840i
$905$	−0.156072	−	0.238886i	−0.00518800	−	0.00794083i
$906$	−15.5939	−	30.8143i	−0.518072	−	1.02374i
$907$	−0.364173	−	13.2115i	−0.0120922	−	0.438681i	−0.981305	−	0.192458i	$-0.938354\pi$
$907$	−0.364173	−	13.2115i	−0.0120922	−	0.438681i	0.969213	−	0.246223i	$-0.0791896\pi$
$908$	6.80664	+	9.26077i	0.225886	+	0.307329i
$909$	6.80442	−	3.21108i	0.225688	−	0.106505i
$910$	0.525251	+	0.637777i	0.0174119	+	0.0211421i
$911$	23.6545	−	36.2059i	0.783709	−	1.19956i	−0.192195	−	0.981357i	$-0.561561\pi$
$911$	23.6545	−	36.2059i	0.783709	−	1.19956i	0.975904	−	0.218199i	$-0.0700183\pi$
$912$	−8.57456	−	1.90058i	−0.283932	−	0.0629344i
$913$	−0.00806393	−	0.0123428i	−0.000266877	−	0.000408486i
$914$	−0.176991	+	0.565870i	−0.00585433	+	0.0187173i
$915$	−1.32913	−	0.297865i	−0.0439397	−	0.00984711i
$916$	−2.88893	−	20.8334i	−0.0954529	−	0.688357i
$917$	−17.9012	−	0.987636i	−0.591149	−	0.0326146i
$918$	1.97470	+	14.2405i	0.0651747	+	0.470006i
$919$	37.8976	+	41.1678i	1.25013	+	1.35800i	0.908345	+	0.418222i	$0.137347\pi$
$919$	37.8976	+	41.1678i	1.25013	+	1.35800i	0.341783	+	0.939779i	$0.388969\pi$
$920$	−0.765329	−	0.262738i	−0.0252321	−	0.00866220i
$921$	−7.12488	−	9.69375i	−0.234773	−	0.319420i
$922$	31.4910	−	19.3574i	1.03710	−	0.637503i
$923$	21.0397	−	3.51091i	0.692530	−	0.115563i
$924$	0.418805	+	0.954779i	0.0137777	+	0.0314099i
$925$	−36.9258	−	35.9220i	−1.21411	−	1.18111i
$926$	−15.0431	+	1.66497i	−0.494346	+	0.0547142i
$927$	0.441779	+	0.208481i	0.0145099	+	0.00684740i
$928$	2.49959	−	4.93933i	0.0820531	−	0.162141i
$929$	45.5915	−	5.04607i	1.49581	−	0.165556i	0.675451	−	0.737405i	$-0.263949\pi$
$929$	45.5915	−	5.04607i	1.49581	−	0.165556i	0.820359	+	0.571849i	$0.193774\pi$
$930$	0.0201986	+	0.00337055i	0.000662338	+	0.000110525i
$931$	−23.6588	+	5.36014i	−0.775387	+	0.175672i
$932$	9.56488	−	1.59610i	0.313308	−	0.0522819i
$933$	−16.7373	+	4.73287i	−0.547956	+	0.154947i
$934$	13.0075	+	15.7941i	0.425618	+	0.516800i
$935$	0.130913	−	0.349653i	0.00428131	−	0.0114349i
$936$	0.427230	−	3.08096i	0.0139645	−	0.100704i
$937$	10.0825	−	51.6170i	0.329382	−	1.68625i	−0.337688	−	0.941258i	$-0.609645\pi$
$937$	10.0825	−	51.6170i	0.329382	−	1.68625i	0.667070	−	0.744995i	$-0.267548\pi$
$938$	13.0771	+	10.1783i	0.426983	+	0.332334i
$939$	−0.292225	+	0.447284i	−0.00953641	+	0.0145966i
$940$	−1.78409	−	0.197463i	−0.0581906	−	0.00644053i
$941$	52.8719	+	14.9508i	1.72358	+	0.487381i	0.982847	−	0.184424i	$-0.0590420\pi$
$941$	52.8719	+	14.9508i	1.72358	+	0.487381i	0.740728	+	0.671805i	$0.234481\pi$
$942$	−0.157616	−	0.359327i	−0.00513539	−	0.0117075i
$943$	−4.11157	−	16.2362i	−0.133891	−	0.528725i
$944$	−3.00522	−	1.41820i	−0.0978114	−	0.0461583i
$945$	−0.210976	−	1.08008i	−0.00686304	−	0.0351350i
$946$	5.63903	−	0.311114i	0.183341	−	0.0101152i
$947$	9.43932	+	48.3241i	0.306737	+	1.57032i	0.742240	+	0.670134i	$0.233763\pi$
$947$	9.43932	+	48.3241i	0.306737	+	1.57032i	−0.435504	+	0.900187i	$0.643430\pi$
$948$	2.72026	−	5.37539i	0.0883501	−	0.174585i
$949$	−10.2162	−	40.3428i	−0.331631	−	1.30958i
$950$	12.8054	+	17.3374i	0.415463	+	0.562499i
$951$	−11.4868	+	45.3604i	−0.372485	+	1.47091i
$952$	−3.32178	−	2.89294i	−0.107660	−	0.0937609i
$953$	1.27836	+	46.3764i	0.0414100	+	1.50228i	0.680274	+	0.732958i	$0.261861\pi$
$953$	1.27836	+	46.3764i	0.0414100	+	1.50228i	−0.638864	+	0.769320i	$0.720595\pi$
$954$	5.64184	−	4.91349i	0.182661	−	0.159080i
$955$	2.97594	+	0.666923i	0.0962990	+	0.0215811i
$956$	−1.85621	+	3.21505i	−0.0600342	+	0.103982i
$957$	4.23771	+	2.29333i	0.136986	+	0.0741329i
$958$	13.8860	+	15.0842i	0.448635	+	0.487347i
$959$	−10.0483	+	8.75105i	−0.324476	+	0.282586i
$960$	−0.213812	−	0.422504i	−0.00690075	−	0.0136363i
$961$	−24.4619	+	19.0394i	−0.789093	+	0.614176i
$962$	−2.52516	−	30.4741i	−0.0814143	−	0.982524i
$963$	−14.4718	−	1.60174i	−0.466348	−	0.0516153i
$964$	−0.286389	+	0.0809830i	−0.00922396	+	0.00260829i
$965$	0.959766	−	0.589966i	0.0308960	−	0.0189917i
$966$	−6.26638	−	5.45739i	−0.201617	−	0.175589i
$967$	−23.7454	−	41.1282i	−0.763599	−	1.32259i	−0.940984	−	0.338451i	$-0.890097\pi$
$967$	−23.7454	−	41.1282i	−0.763599	−	1.32259i	0.177385	−	0.984142i	$-0.443236\pi$
$968$	−8.53328	+	6.64172i	−0.274270	+	0.213473i
$969$	6.26595	+	31.6846i	0.201291	+	1.01786i
$970$	1.40588	+	1.09424i	0.0451401	+	0.0351340i
$971$	1.79514	−	12.9456i	0.0576088	−	0.415444i	−0.939692	−	0.342022i	$-0.888888\pi$
$971$	1.79514	−	12.9456i	0.0576088	−	0.415444i	0.997301	−	0.0734229i	$-0.0233923\pi$
$972$	−6.24734	+	8.49981i	−0.200383	+	0.272632i
$973$	25.7335	−	5.76702i	0.824979	−	0.184882i
$974$	0.293854	−	0.939503i	0.00941569	−	0.0301036i
$975$	−22.0520	+	19.2051i	−0.706229	+	0.615056i
$976$	2.72065	+	0.934002i	0.0870860	+	0.0298967i
$977$	−43.9888	+	23.8055i	−1.40733	+	0.761606i	−0.989171	−	0.146770i	$-0.953112\pi$
$977$	−43.9888	+	23.8055i	−1.40733	+	0.761606i	−0.418155	+	0.908376i	$0.637323\pi$
$978$	−0.537485	+	19.4989i	−0.0171869	+	0.623507i
$979$	2.40571	−	6.42537i	0.0768869	−	0.205356i
$980$	−1.03213	−	0.803336i	−0.0329700	−	0.0256616i
$981$	0.507660	−	6.12655i	0.0162084	−	0.195606i
$982$	10.0545	−	2.25327i	0.320852	−	0.0719047i
$983$	6.17234	+	16.4856i	0.196867	+	0.525809i	0.997285	−	0.0736331i	$-0.0234594\pi$
$983$	6.17234	+	16.4856i	0.196867	+	0.525809i	−0.800418	+	0.599442i	$0.795389\pi$
$984$	4.90065	−	8.48817i	0.156227	−	0.270593i
$985$	−3.83350	−	0.211500i	−0.122146	−	0.00673896i
$986$	−20.3269	−	1.12147i	−0.647341	−	0.0357148i
$987$	−16.2116	−	8.77329i	−0.516022	−	0.279257i
$988$	−1.02671	+	12.7525i	−0.0326640	+	0.405709i
$989$	−39.5873	+	21.4236i	−1.25880	+	0.681231i
$990$	0.0973003	−	0.0459171i	0.00309241	−	0.00145934i
$991$	−46.6138	+	13.1811i	−1.48073	+	0.418712i	−0.914179	−	0.405311i	$-0.867163\pi$
$991$	−46.6138	+	13.1811i	−1.48073	+	0.418712i	−0.566556	+	0.824023i	$0.691724\pi$
$992$	−0.0416139	−	0.0117673i	−0.00132124	−	0.000373612i
$993$	42.3550	+	17.2031i	1.34409	+	0.545924i
$994$	8.06515	−	3.27578i	0.255811	−	0.103901i
$995$	3.70393	+	0.618077i	0.117423	+	0.0195944i
$996$	0.0168809	+	0.0666613i	0.000534893	+	0.00211225i
$997$	16.8962	+	16.4369i	0.535109	+	0.520562i	0.914452	−	0.404694i	$-0.132622\pi$
$997$	16.8962	+	16.4369i	0.535109	+	0.520562i	−0.379343	+	0.925256i	$0.623850\pi$
$998$	29.6774	−	12.0539i	0.939423	−	0.381561i
$999$	−16.3607	+	37.2986i	−0.517629	+	1.18008i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.i.b.7.5	✓	612
361.258	even	57	inner	722.2.i.b.619.5	yes	612

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.i.b.7.5	✓	612	1.1	even	1	trivial
722.2.i.b.619.5	yes	612	361.258	even	57	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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.i (of order \(57\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.191711 - 0.981451i) q^{2} +(-2.00265 + 0.221654i) q^{3} +(-0.926494 + 0.376309i) q^{4} +(0.168453 - 0.163874i) q^{5} +(0.601472 + 1.92301i) q^{6} +(0.945236 - 0.735707i) q^{7} +(0.546948 + 0.837166i) q^{8} +(1.03410 - 0.231747i) q^{9} +(-0.193129 - 0.133913i) q^{10} +(-0.292583 + 0.317830i) q^{11} +(1.77204 - 0.958978i) q^{12} +(-1.73826 - 2.36498i) q^{13} +(-0.903273 - 0.786661i) q^{14} +(-0.301030 + 0.365521i) q^{15} +(0.716783 - 0.697297i) q^{16} +(-3.40718 - 1.38388i) q^{17} +(-0.425695 - 0.970488i) q^{18} +(1.97727 + 3.88464i) q^{19} +(-0.0944038 + 0.215219i) q^{20} +(-1.72991 + 1.68288i) q^{21} +(0.368025 + 0.226224i) q^{22} +(-3.42219 - 0.378768i) q^{23} +(-1.28091 - 1.55532i) q^{24} +(-0.136250 + 4.94289i) q^{25} +(-1.98788 + 2.15941i) q^{26} +(3.69756 - 1.26937i) q^{27} +(-0.598902 + 1.03733i) q^{28} +(0.760360 + 5.48332i) q^{29} +(0.416452 + 0.225373i) q^{30} +(0.0409025 - 0.0140419i) q^{31} +(-0.821778 - 0.569808i) q^{32} +(0.515493 - 0.701354i) q^{33} +(-0.705016 + 3.60929i) q^{34} +(0.0386650 - 0.278832i) q^{35} +(-0.870876 + 0.603852i) q^{36} +(-7.05612 + 7.66499i) q^{37} +(3.43352 - 2.68532i) q^{38} +(4.00533 + 4.35095i) q^{39} +(0.229325 + 0.0513930i) q^{40} +(1.70566 + 4.55561i) q^{41} +(1.98331 + 1.37519i) q^{42} +(10.7434 - 7.44927i) q^{43} +(0.151474 - 0.404569i) q^{44} +(0.136220 - 0.208500i) q^{45} +(0.284328 + 3.43133i) q^{46} +(2.28000 + 7.28955i) q^{47} +(-1.28091 + 1.55532i) q^{48} +(-1.36619 + 5.39497i) q^{49} +(4.87733 - 0.813882i) q^{50} +(7.13014 + 2.01621i) q^{51} +(2.50045 + 1.53702i) q^{52} +(2.10742 + 6.73781i) q^{53} +(-1.95469 - 3.38562i) q^{54} +(0.00279745 + 0.101486i) q^{55} +(1.13290 + 0.388927i) q^{56} +(-4.82082 - 7.34131i) q^{57} +(5.23584 - 1.79747i) q^{58} +(-1.16518 - 3.11206i) q^{59} +(0.141354 - 0.451934i) q^{60} +(1.29884 + 2.56658i) q^{61} +(-0.0216228 - 0.0374519i) q^{62} +(0.806969 - 0.979848i) q^{63} +(-0.401695 + 0.915773i) q^{64} +(-0.680375 - 0.113535i) q^{65} +(-0.787170 - 0.371475i) q^{66} +(-13.8138 + 0.762126i) q^{67} +3.67750 q^{68} +6.93741 q^{69} +(-0.281073 + 0.0155072i) q^{70} +(-3.28151 + 6.48444i) q^{71} +(0.759608 + 0.738958i) q^{72} +(13.1367 + 5.33566i) q^{73} +(8.87555 + 5.45578i) q^{74} +(-0.822748 - 9.92909i) q^{75} +(-3.29375 - 2.85503i) q^{76} +(-0.0427304 + 0.515679i) q^{77} +(3.50238 - 4.76516i) q^{78} +(2.45712 - 1.70373i) q^{79} +(0.00647564 - 0.234924i) q^{80} +(-9.99873 + 4.71852i) q^{81} +(4.14412 - 2.54738i) q^{82} +(-0.00837813 + 0.0330845i) q^{83} +(0.969466 - 2.21016i) q^{84} +(-0.800733 + 0.325230i) q^{85} +(-9.37072 - 9.11597i) q^{86} +(-2.73813 - 10.8126i) q^{87} +(-0.426104 - 0.0711041i) q^{88} +(-14.7146 + 5.97656i) q^{89} +(-0.230748 - 0.0937216i) q^{90} +(-3.38300 - 0.956621i) q^{91} +(3.31317 - 0.936876i) q^{92} +(-0.0788011 + 0.0371871i) q^{93} +(6.71724 - 3.63519i) q^{94} +(0.969669 + 0.330358i) q^{95} +(1.77204 + 0.958978i) q^{96} +(-7.56906 - 0.417597i) q^{97} +(5.55681 + 0.306578i) q^{98} +(-0.228903 + 0.396472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 612 q + 17 q^{2} - 19 q^{3} + 17 q^{4} + q^{5} - 2 q^{7} - 34 q^{8} + 4 q^{9} + q^{10} - 28 q^{11} + 4 q^{13} - 18 q^{14} - 52 q^{15} + 17 q^{16} + 18 q^{17} - 46 q^{18} - 12 q^{19} - 2 q^{20} - 65 q^{21}+ \cdots - 116 q^{99}+O(q^{100}) \) 612 * q + 17 * q^2 - 19 * q^3 + 17 * q^4 + q^5 - 2 * q^7 - 34 * q^8 + 4 * q^9 + q^10 - 28 * q^11 + 4 * q^13 - 18 * q^14 - 52 * q^15 + 17 * q^16 + 18 * q^17 - 46 * q^18 - 12 * q^19 - 2 * q^20 - 65 * q^21 + 33 * q^22 + 39 * q^23 + 20 * q^25 - 8 * q^26 + 158 * q^27 - 37 * q^28 - 42 * q^29 - 29 * q^30 + 12 * q^31 + 17 * q^32 + 60 * q^33 - q^34 - 14 * q^35 + 23 * q^36 - 6 * q^37 + 76 * q^38 - 108 * q^39 + q^40 + 8 * q^41 + 11 * q^42 + 7 * q^43 - 5 * q^44 - 101 * q^45 - 21 * q^46 + 105 * q^47 - 62 * q^49 - 78 * q^50 - 3 * q^51 + 4 * q^52 + 146 * q^53 - 79 * q^54 + 4 * q^55 - 21 * q^56 - 28 * q^57 + 8 * q^58 - 4 * q^59 - 14 * q^60 - 93 * q^61 - 6 * q^62 - 95 * q^63 - 34 * q^64 - 76 * q^65 - 16 * q^66 - 6 * q^67 + 78 * q^68 + 38 * q^69 + 81 * q^70 - 151 * q^71 + 23 * q^72 + 7 * q^73 - 35 * q^74 - 12 * q^75 - 7 * q^76 + 78 * q^77 - 3 * q^78 - 10 * q^79 + q^80 + 58 * q^81 - 30 * q^82 + 67 * q^83 - 22 * q^84 - 6 * q^85 - 12 * q^86 - 109 * q^87 + 10 * q^88 - 25 * q^89 - 73 * q^90 + 37 * q^91 + q^92 + 56 * q^93 - 39 * q^94 - 29 * q^95 - 153 * q^97 + 164 * q^98 - 116 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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