LMFDB - Embedded newform 122.2.i.b.83.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [122,2,Mod(15,122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(122, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([14]))

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

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

chi := DirichletCharacter("122.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 122 = 2 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	122.i (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.974174904660$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			83.1
Character	$\chi$	$=$	122.83
Dual form			122.2.i.b.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.669131 + 0.743145i) q^{2} +(-0.932026 + 2.86848i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(3.28831 - 1.46405i) q^{5} +(-2.75534 + 1.22676i) q^{6} +(-3.72534 - 0.791845i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-4.93246 - 3.58364i) q^{9} +O(q^{10})$	\(q+(0.669131 + 0.743145i) q^{2} +(-0.932026 + 2.86848i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(3.28831 - 1.46405i) q^{5} +(-2.75534 + 1.22676i) q^{6} +(-3.72534 - 0.791845i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-4.93246 - 3.58364i) q^{9} +(3.28831 + 1.46405i) q^{10} +4.43910 q^{11} +(-2.75534 - 1.22676i) q^{12} +(-0.163238 + 0.282737i) q^{13} +(-1.90428 - 3.29831i) q^{14} +(1.13481 + 10.7970i) q^{15} +(-0.978148 - 0.207912i) q^{16} +(-0.0213446 + 0.203080i) q^{17} +(-0.637295 - 6.06345i) q^{18} +(3.08788 - 0.656349i) q^{19} +(1.11231 + 3.42333i) q^{20} +(5.74350 - 9.94803i) q^{21} +(2.97034 + 3.29889i) q^{22} +(-2.54540 - 1.84934i) q^{23} +(-0.932026 - 2.86848i) q^{24} +(5.32390 - 5.91279i) q^{25} +(-0.319343 + 0.0678784i) q^{26} +(7.55655 - 5.49016i) q^{27} +(1.17691 - 3.62216i) q^{28} +(-0.272899 - 0.472674i) q^{29} +(-7.26439 + 8.06793i) q^{30} +(-0.699790 + 0.777196i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.13735 + 12.7335i) q^{33} +(-0.165200 + 0.120025i) q^{34} +(-13.4094 + 2.85025i) q^{35} +(4.07959 - 4.53084i) q^{36} +(-1.01962 - 3.13807i) q^{37} +(2.55396 + 1.85556i) q^{38} +(-0.658884 - 0.731765i) q^{39} +(-1.79975 + 3.11726i) q^{40} +(2.18965 + 6.73906i) q^{41} +(11.2360 - 2.38828i) q^{42} +(0.197298 + 1.87717i) q^{43} +(-0.464012 + 4.41478i) q^{44} +(-21.4661 - 4.56276i) q^{45} +(-0.328876 - 3.12905i) q^{46} +(-6.47952 - 11.2229i) q^{47} +(1.50805 - 2.61202i) q^{48} +(6.85629 + 3.05262i) q^{49} +7.95644 q^{50} +(-0.562638 - 0.250503i) q^{51} +(-0.264125 - 0.191898i) q^{52} +(-7.44366 + 5.40814i) q^{53} +(9.13630 + 1.94198i) q^{54} +(14.5971 - 6.49907i) q^{55} +(3.47929 - 1.54908i) q^{56} +(-0.995259 + 9.46926i) q^{57} +(0.168661 - 0.519084i) q^{58} +(-1.49280 - 1.65792i) q^{59} -10.8565 q^{60} +(5.91561 - 5.09956i) q^{61} -1.04582 q^{62} +(15.5374 + 17.2560i) q^{63} +(0.309017 - 0.951057i) q^{64} +(-0.122837 + 1.16872i) q^{65} +(-12.2312 + 5.44570i) q^{66} +(-4.85984 + 2.16374i) q^{67} +(-0.199737 - 0.0424553i) q^{68} +(7.67717 - 5.57779i) q^{69} +(-11.0908 - 8.05791i) q^{70} +(-14.2097 - 6.32655i) q^{71} +6.09685 q^{72} +(-7.98755 - 3.55629i) q^{73} +(1.64978 - 2.85751i) q^{74} +(11.9987 + 20.7824i) q^{75} +(0.329982 + 3.13957i) q^{76} +(-16.5371 - 3.51508i) q^{77} +(0.102928 - 0.979293i) q^{78} +(0.454176 + 4.32119i) q^{79} +(-3.52085 + 0.748379i) q^{80} +(3.05341 + 9.39743i) q^{81} +(-3.54293 + 6.13654i) q^{82} +(8.91976 + 9.90640i) q^{83} +(9.29318 + 6.75189i) q^{84} +(0.227132 + 0.699041i) q^{85} +(-1.26299 + 1.40269i) q^{86} +(1.61021 - 0.342260i) q^{87} +(-3.59131 + 2.60924i) q^{88} +(2.31475 - 7.12405i) q^{89} +(-10.9728 - 19.0055i) q^{90} +(0.832002 - 0.924032i) q^{91} +(2.10528 - 2.33815i) q^{92} +(-1.57715 - 2.73170i) q^{93} +(4.00457 - 12.3248i) q^{94} +(9.19299 - 6.67909i) q^{95} +(2.95019 - 0.627082i) q^{96} +(-3.07019 + 3.40979i) q^{97} +(2.31922 + 7.13782i) q^{98} +(-21.8957 - 15.9081i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 12 q^{5} - q^{6} - 4 q^{7} - 6 q^{8} - 19 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 12 * q^5 - q^6 - 4 * q^7 - 6 * q^8 - 19 * q^9	\( 24 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 12 q^{5} - q^{6} - 4 q^{7} - 6 q^{8} - 19 q^{9} - 12 q^{10} + 6 q^{11} - q^{12} + 5 q^{13} - 4 q^{14} - 9 q^{15} + 3 q^{16} + 16 q^{17} + 17 q^{18} - 2 q^{19} - q^{20} + 10 q^{21} + 7 q^{22} + q^{23} - 3 q^{24} + 11 q^{25} - 9 q^{27} - 7 q^{28} + 2 q^{29} - 4 q^{30} + 14 q^{31} - 12 q^{32} + 7 q^{33} - 17 q^{34} + 9 q^{35} + 2 q^{36} - 38 q^{37} + 4 q^{38} - 40 q^{39} - 7 q^{40} - 10 q^{41} + 15 q^{42} - 5 q^{43} + 2 q^{44} - 96 q^{45} - 8 q^{46} + 3 q^{47} - q^{48} + 19 q^{49} + 38 q^{50} + 102 q^{51} + 20 q^{52} - 37 q^{53} + 17 q^{54} + 33 q^{55} + 6 q^{56} - 71 q^{57} + q^{58} - 17 q^{59} - 22 q^{60} + 70 q^{61} + 72 q^{62} + 146 q^{63} - 6 q^{64} + 2 q^{65} - 86 q^{66} - 4 q^{67} + q^{68} - 2 q^{69} - 28 q^{70} - 76 q^{71} + 46 q^{72} + 84 q^{73} + 19 q^{74} + 9 q^{75} - 2 q^{76} - 10 q^{77} - 5 q^{78} - 56 q^{79} - 7 q^{80} + 59 q^{81} - 20 q^{82} - 9 q^{83} + 25 q^{84} - 37 q^{85} - 65 q^{86} - 25 q^{87} - 4 q^{88} - 45 q^{89} - 31 q^{90} + 2 q^{91} + 7 q^{92} - 47 q^{93} + 24 q^{94} - 39 q^{95} + 9 q^{96} + 6 q^{97} + 7 q^{98} - 24 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 12 * q^5 - q^6 - 4 * q^7 - 6 * q^8 - 19 * q^9 - 12 * q^10 + 6 * q^11 - q^12 + 5 * q^13 - 4 * q^14 - 9 * q^15 + 3 * q^16 + 16 * q^17 + 17 * q^18 - 2 * q^19 - q^20 + 10 * q^21 + 7 * q^22 + q^23 - 3 * q^24 + 11 * q^25 - 9 * q^27 - 7 * q^28 + 2 * q^29 - 4 * q^30 + 14 * q^31 - 12 * q^32 + 7 * q^33 - 17 * q^34 + 9 * q^35 + 2 * q^36 - 38 * q^37 + 4 * q^38 - 40 * q^39 - 7 * q^40 - 10 * q^41 + 15 * q^42 - 5 * q^43 + 2 * q^44 - 96 * q^45 - 8 * q^46 + 3 * q^47 - q^48 + 19 * q^49 + 38 * q^50 + 102 * q^51 + 20 * q^52 - 37 * q^53 + 17 * q^54 + 33 * q^55 + 6 * q^56 - 71 * q^57 + q^58 - 17 * q^59 - 22 * q^60 + 70 * q^61 + 72 * q^62 + 146 * q^63 - 6 * q^64 + 2 * q^65 - 86 * q^66 - 4 * q^67 + q^68 - 2 * q^69 - 28 * q^70 - 76 * q^71 + 46 * q^72 + 84 * q^73 + 19 * q^74 + 9 * q^75 - 2 * q^76 - 10 * q^77 - 5 * q^78 - 56 * q^79 - 7 * q^80 + 59 * q^81 - 20 * q^82 - 9 * q^83 + 25 * q^84 - 37 * q^85 - 65 * q^86 - 25 * q^87 - 4 * q^88 - 45 * q^89 - 31 * q^90 + 2 * q^91 + 7 * q^92 - 47 * q^93 + 24 * q^94 - 39 * q^95 + 9 * q^96 + 6 * q^97 + 7 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/122\mathbb{Z}\right)^\times$.

$n$	$63$
$\chi(n)$	$e\left(\frac{4}{15}\right)$

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 $

$2$	0.669131	+	0.743145i	0.473147	+	0.525483i
$2$	0.669131	+	0.743145i	0.473147	+	0.525483i
$3$	−0.932026	+	2.86848i	−0.538105	+	1.65612i	0.198737	+	0.980053i	$0.436316\pi$
$3$	−0.932026	+	2.86848i	−0.538105	+	1.65612i	−0.736842	+	0.676065i	$0.763684\pi$
$4$	−0.104528	+	0.994522i	−0.0522642	+	0.497261i
$5$	3.28831	−	1.46405i	1.47058	−	0.654743i	0.493913	−	0.869511i	$-0.335566\pi$
$5$	3.28831	−	1.46405i	1.47058	−	0.654743i	0.976665	+	0.214768i	$0.0688996\pi$
$6$	−2.75534	+	1.22676i	−1.12486	+	0.500822i
$7$	−3.72534	−	0.791845i	−1.40804	−	0.299289i	−0.559683	−	0.828707i	$-0.689077\pi$
$7$	−3.72534	−	0.791845i	−1.40804	−	0.299289i	−0.848361	+	0.529417i	$0.822411\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	−4.93246	−	3.58364i	−1.64415	−	1.19455i
$10$	3.28831	+	1.46405i	1.03986	+	0.462974i
$11$	4.43910			1.33844			0.669219	−	0.743065i	$-0.266629\pi$
$11$	4.43910			1.33844			0.669219	+	0.743065i	$0.266629\pi$
$12$	−2.75534	−	1.22676i	−0.795399	−	0.354134i
$13$	−0.163238	+	0.282737i	−0.0452742	+	0.0784172i	−0.887774	−	0.460279i	$-0.847749\pi$
$13$	−0.163238	+	0.282737i	−0.0452742	+	0.0784172i	0.842500	+	0.538696i	$0.181083\pi$
$14$	−1.90428	−	3.29831i	−0.508941	−	0.881511i
$15$	1.13481	+	10.7970i	0.293007	+	2.78777i
$16$	−0.978148	−	0.207912i	−0.244537	−	0.0519779i
$17$	−0.0213446	+	0.203080i	−0.00517683	+	0.0492542i	−0.996805	−	0.0798693i	$-0.974550\pi$
$17$	−0.0213446	+	0.203080i	−0.00517683	+	0.0492542i	0.991629	+	0.129124i	$0.0412164\pi$
$18$	−0.637295	−	6.06345i	−0.150212	−	1.42917i
$19$	3.08788	−	0.656349i	0.708408	−	0.150577i	0.160403	−	0.987052i	$-0.448721\pi$
$19$	3.08788	−	0.656349i	0.708408	−	0.150577i	0.548005	+	0.836475i	$0.315387\pi$
$20$	1.11231	+	3.42333i	0.248720	+	0.765481i
$21$	5.74350	−	9.94803i	1.25333	−	2.17084i
$22$	2.97034	+	3.29889i	0.633278	+	0.703326i
$23$	−2.54540	−	1.84934i	−0.530752	−	0.385614i	0.289887	−	0.957061i	$-0.406382\pi$
$23$	−2.54540	−	1.84934i	−0.530752	−	0.385614i	−0.820639	+	0.571447i	$0.806382\pi$
$24$	−0.932026	−	2.86848i	−0.190249	−	0.585526i
$25$	5.32390	−	5.91279i	1.06478	−	1.18256i
$26$	−0.319343	+	0.0678784i	−0.0626283	+	0.0133120i
$27$	7.55655	−	5.49016i	1.45426	−	1.05658i
$28$	1.17691	−	3.62216i	0.222415	−	0.684524i
$29$	−0.272899	−	0.472674i	−0.0506760	−	0.0877734i	0.839575	−	0.543244i	$-0.182804\pi$
$29$	−0.272899	−	0.472674i	−0.0506760	−	0.0877734i	−0.890251	+	0.455471i	$0.849471\pi$
$30$	−7.26439	+	8.06793i	−1.32629	+	1.47299i
$31$	−0.699790	+	0.777196i	−0.125686	+	0.139589i	−0.802703	−	0.596379i	$-0.796606\pi$
$31$	−0.699790	+	0.777196i	−0.125686	+	0.139589i	0.677017	+	0.735967i	$0.263272\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−4.13735	+	12.7335i	−0.720221	+	2.21661i
$34$	−0.165200	+	0.120025i	−0.0283316	+	0.0205841i
$35$	−13.4094	+	2.85025i	−2.26660	+	0.481780i
$36$	4.07959	−	4.53084i	0.679932	−	0.755141i
$37$	−1.01962	−	3.13807i	−0.167625	−	0.515896i	0.831595	−	0.555382i	$-0.187428\pi$
$37$	−1.01962	−	3.13807i	−0.167625	−	0.515896i	−0.999220	+	0.0394859i	$0.987428\pi$
$38$	2.55396	+	1.85556i	0.414307	+	0.301011i
$39$	−0.658884	−	0.731765i	−0.105506	−	0.117176i
$40$	−1.79975	+	3.11726i	−0.284566	+	0.492883i
$41$	2.18965	+	6.73906i	0.341967	+	1.05246i	0.963188	+	0.268830i	$0.0866368\pi$
$41$	2.18965	+	6.73906i	0.341967	+	1.05246i	−0.621221	+	0.783635i	$0.713363\pi$
$42$	11.2360	−	2.38828i	1.73375	−	0.368520i
$43$	0.197298	+	1.87717i	0.0300877	+	0.286265i	0.999212	+	0.0396925i	$0.0126378\pi$
$43$	0.197298	+	1.87717i	0.0300877	+	0.286265i	−0.969124	+	0.246573i	$0.920696\pi$
$44$	−0.464012	+	4.41478i	−0.0699525	+	0.665553i
$45$	−21.4661	−	4.56276i	−3.19998	−	0.680176i
$46$	−0.328876	−	3.12905i	−0.0484902	−	0.461353i
$47$	−6.47952	−	11.2229i	−0.945136	−	1.63702i	−0.755480	−	0.655172i	$-0.772596\pi$
$47$	−6.47952	−	11.2229i	−0.945136	−	1.63702i	−0.189656	−	0.981851i	$-0.560737\pi$
$48$	1.50805	−	2.61202i	0.217668	−	0.377012i
$49$	6.85629	+	3.05262i	0.979471	+	0.436088i
$50$	7.95644			1.12521
$51$	−0.562638	−	0.250503i	−0.0787851	−	0.0350774i
$52$	−0.264125	−	0.191898i	−0.0366276	−	0.0266115i
$53$	−7.44366	+	5.40814i	−1.02247	+	0.742865i	−0.966787	−	0.255584i	$-0.917732\pi$
$53$	−7.44366	+	5.40814i	−1.02247	+	0.742865i	−0.0556786	+	0.998449i	$0.517732\pi$
$54$	9.13630	+	1.94198i	1.24329	+	0.264270i
$55$	14.5971	−	6.49907i	1.96828	−	0.876334i
$56$	3.47929	−	1.54908i	0.464940	−	0.207005i
$57$	−0.995259	+	9.46926i	−0.131825	+	1.25423i
$58$	0.168661	−	0.519084i	0.0221462	−	0.0681591i
$59$	−1.49280	−	1.65792i	−0.194346	−	0.215843i	0.638094	−	0.769959i	$-0.279723\pi$
$59$	−1.49280	−	1.65792i	−0.194346	−	0.215843i	−0.832440	+	0.554115i	$0.813057\pi$
$60$	−10.8565			−1.40156
$61$	5.91561	−	5.09956i	0.757416	−	0.652932i
$61$	5.91561	−	5.09956i	0.757416	−	0.652932i
$62$	−1.04582			−0.132819
$63$	15.5374	+	17.2560i	1.95753	+	2.17405i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−0.122837	+	1.16872i	−0.0152361	+	0.144962i
$66$	−12.2312	+	5.44570i	−1.50556	+	0.670319i
$67$	−4.85984	+	2.16374i	−0.593723	+	0.264343i	−0.681524	−	0.731795i	$-0.738683\pi$
$67$	−4.85984	+	2.16374i	−0.593723	+	0.264343i	0.0878010	+	0.996138i	$0.472016\pi$
$68$	−0.199737	−	0.0424553i	−0.0242216	−	0.00514847i
$69$	7.67717	−	5.57779i	0.924223	−	0.671487i
$70$	−11.0908	−	8.05791i	−1.32560	−	0.963105i
$71$	−14.2097	−	6.32655i	−1.68638	−	0.750823i	−0.999716	−	0.0238441i	$-0.992409\pi$
$71$	−14.2097	−	6.32655i	−1.68638	−	0.750823i	−0.686660	−	0.726979i	$-0.740924\pi$
$72$	6.09685			0.718521
$73$	−7.98755	−	3.55629i	−0.934873	−	0.416232i	−0.117976	−	0.993016i	$-0.537641\pi$
$73$	−7.98755	−	3.55629i	−0.934873	−	0.416232i	−0.816896	+	0.576784i	$0.804307\pi$
$74$	1.64978	−	2.85751i	0.191783	−	0.332179i
$75$	11.9987	+	20.7824i	1.38549	+	2.39974i
$76$	0.329982	+	3.13957i	0.0378516	+	0.360134i
$77$	−16.5371	−	3.51508i	−1.88458	−	0.400580i
$78$	0.102928	−	0.979293i	0.0116543	−	0.110883i
$79$	0.454176	+	4.32119i	0.0510987	+	0.486172i	0.989906	+	0.141728i	$0.0452659\pi$
$79$	0.454176	+	4.32119i	0.0510987	+	0.486172i	−0.938807	+	0.344444i	$0.888067\pi$
$80$	−3.52085	+	0.748379i	−0.393643	+	0.0836713i
$81$	3.05341	+	9.39743i	0.339268	+	1.04416i
$82$	−3.54293	+	6.13654i	−0.391252	+	0.677668i
$83$	8.91976	+	9.90640i	0.979071	+	1.08737i	0.996163	+	0.0875146i	$0.0278925\pi$
$83$	8.91976	+	9.90640i	0.979071	+	1.08737i	−0.0170922	+	0.999854i	$0.505441\pi$
$84$	9.29318	+	6.75189i	1.01397	+	0.736692i
$85$	0.227132	+	0.699041i	0.0246359	+	0.0758216i
$86$	−1.26299	+	1.40269i	−0.136192	+	0.151256i
$87$	1.61021	−	0.342260i	0.172632	−	0.0366941i
$88$	−3.59131	+	2.60924i	−0.382835	+	0.278146i
$89$	2.31475	−	7.12405i	0.245363	−	0.755148i	−0.750214	−	0.661195i	$-0.770050\pi$
$89$	2.31475	−	7.12405i	0.245363	−	0.755148i	0.995577	−	0.0939532i	$-0.0299504\pi$
$90$	−10.9728	−	19.0055i	−1.15664	−	2.00335i
$91$	0.832002	−	0.924032i	0.0872175	−	0.0968649i
$92$	2.10528	−	2.33815i	0.219490	−	0.243768i
$93$	−1.57715	−	2.73170i	−0.163543	−	0.283264i
$94$	4.00457	−	12.3248i	0.413039	−	1.27120i
$95$	9.19299	−	6.67909i	0.943180	−	0.685261i
$96$	2.95019	−	0.627082i	0.301102	−	0.0640013i
$97$	−3.07019	+	3.40979i	−0.311730	+	0.346211i	−0.878567	−	0.477618i	$-0.841500\pi$
$97$	−3.07019	+	3.40979i	−0.311730	+	0.346211i	0.566837	+	0.823830i	$0.308167\pi$
$98$	2.31922	+	7.13782i	0.234276	+	0.721029i
$99$	−21.8957	−	15.9081i	−2.20060	−	1.59883i
$100$	5.32390	+	5.91279i	0.532390	+	0.591279i
$101$	−2.12285	+	3.67688i	−0.211231	+	0.365863i	−0.952100	−	0.305786i	$-0.901081\pi$
$101$	−2.12285	+	3.67688i	−0.211231	+	0.365863i	0.740869	+	0.671650i	$0.234414\pi$
$102$	−0.190319	−	0.585741i	−0.0188444	−	0.0579970i
$103$	14.7482	−	3.13482i	1.45318	−	0.308883i	0.587395	−	0.809300i	$-0.300153\pi$
$103$	14.7482	−	3.13482i	1.45318	−	0.308883i	0.865784	+	0.500417i	$0.166820\pi$
$104$	−0.0341261	−	0.324689i	−0.00334634	−	0.0318383i
$105$	4.32199	−	41.1210i	0.421783	−	4.01300i
$106$	−8.99981	−	1.91297i	−0.874139	−	0.185804i
$107$	0.663604	+	6.31377i	0.0641530	+	0.610375i	0.978615	+	0.205703i	$0.0659479\pi$
$107$	0.663604	+	6.31377i	0.0641530	+	0.610375i	−0.914462	+	0.404673i	$0.867385\pi$
$108$	4.67020	+	8.08903i	0.449391	+	0.778367i
$109$	−4.97195	+	8.61167i	−0.476227	+	0.824849i	−0.999629	−	0.0272369i	$-0.991329\pi$
$109$	−4.97195	+	8.61167i	−0.476227	+	0.824849i	0.523402	+	0.852086i	$0.324663\pi$
$110$	14.5971	+	6.49907i	1.39178	+	0.619662i
$111$	9.95182			0.944585
$112$	3.47929	+	1.54908i	0.328762	+	0.146374i
$113$	14.6590	+	10.6504i	1.37901	+	1.00191i	0.996972	+	0.0777587i	$0.0247764\pi$
$113$	14.6590	+	10.6504i	1.37901	+	1.00191i	0.382034	+	0.924148i	$0.375224\pi$
$114$	−7.70299	+	5.59655i	−0.721451	+	0.524165i
$115$	−11.0776	−	2.35461i	−1.03299	−	0.219569i
$116$	0.498611	−	0.221996i	0.0462948	−	0.0206118i
$117$	1.81840	−	0.809602i	0.168111	−	0.0748477i
$118$	0.233198	−	2.21874i	0.0214677	−	0.204251i
$119$	0.240324	−	0.739641i	0.0220304	−	0.0678028i
$120$	−7.26439	−	8.06793i	−0.663145	−	0.736497i
$121$	8.70560			0.791418
$122$	7.74803	+	0.983882i	0.701474	+	0.0890765i
$123$	−21.3717			−1.92702
$124$	−0.699790	−	0.777196i	−0.0628430	−	0.0697943i
$125$	3.28847	−	10.1209i	0.294130	−	0.905239i
$126$	−2.42718	+	23.0930i	−0.216230	+	2.05729i
$127$	0.248826	−	0.110784i	0.0220797	−	0.00983053i	−0.395667	−	0.918394i	$-0.629487\pi$
$127$	0.248826	−	0.110784i	0.0220797	−	0.00983053i	0.417747	+	0.908563i	$0.362820\pi$
$128$	0.913545	−	0.406737i	0.0807468	−	0.0359508i
$129$	−5.56851	−	1.18362i	−0.490280	−	0.104212i
$130$	−0.950721	+	0.690739i	−0.0833837	+	0.0605818i
$131$	2.06428	+	1.49979i	0.180357	+	0.131037i	0.674301	−	0.738457i	$-0.264445\pi$
$131$	2.06428	+	1.49979i	0.180357	+	0.131037i	−0.493944	+	0.869494i	$0.664445\pi$
$132$	−12.2312	−	5.44570i	−1.06459	−	0.473987i
$133$	−12.0231			−1.04254
$134$	−4.85984	−	2.16374i	−0.419826	−	0.186919i
$135$	16.8104	−	29.1165i	1.44681	−	2.50595i
$136$	−0.102099	−	0.176841i	−0.00875496	−	0.0151640i
$137$	0.298368	+	2.83879i	0.0254913	+	0.242534i	0.999847	+	0.0175184i	$0.00557658\pi$
$137$	0.298368	+	2.83879i	0.0254913	+	0.242534i	−0.974355	+	0.225015i	$0.927757\pi$
$138$	9.28214	+	1.97298i	0.790148	+	0.167951i
$139$	1.55014	−	14.7486i	0.131482	−	1.25096i	−0.707465	−	0.706749i	$-0.750161\pi$
$139$	1.55014	−	14.7486i	0.131482	−	1.25096i	0.838946	−	0.544214i	$-0.183172\pi$
$140$	−1.43297	−	13.6338i	−0.121108	−	1.15227i
$141$	38.2316	−	8.12639i	3.21969	−	0.684365i
$142$	−4.80657	−	14.7931i	−0.403359	−	1.24141i
$143$	−0.724632	+	1.25510i	−0.0605968	+	0.104957i
$144$	4.07959	+	4.53084i	0.339966	+	0.377570i
$145$	−1.58940	−	1.15476i	−0.131992	−	0.0958979i
$146$	−2.70188	−	8.31553i	−0.223609	−	0.688198i
$147$	−15.1466	+	16.8220i	−1.24927	+	1.38746i
$148$	3.22746	−	0.686018i	0.265296	−	0.0563904i
$149$	−14.3333	+	10.4138i	−1.17423	+	0.853129i	−0.991509	−	0.130036i	$-0.958491\pi$
$149$	−14.3333	+	10.4138i	−1.17423	+	0.853129i	−0.182722	+	0.983165i	$0.558491\pi$
$150$	−7.41561	+	22.8229i	−0.605482	+	1.86348i
$151$	7.11141	+	12.3173i	0.578718	+	1.00237i	0.995627	+	0.0934211i	$0.0297803\pi$
$151$	7.11141	+	12.3173i	0.578718	+	1.00237i	−0.416908	+	0.908949i	$0.636886\pi$
$152$	−2.11236	+	2.34601i	−0.171335	+	0.190286i
$153$	0.833048	−	0.925193i	0.0673479	−	0.0747974i
$154$	−8.45329	−	14.6415i	−0.681186	−	1.17985i
$155$	−1.16327	+	3.58019i	−0.0934365	+	0.287568i
$156$	0.796628	−	0.578784i	0.0637813	−	0.0463398i
$157$	6.36740	−	1.35343i	0.508174	−	0.108016i	0.0533122	−	0.998578i	$-0.483022\pi$
$157$	6.36740	−	1.35343i	0.508174	−	0.108016i	0.454861	+	0.890562i	$0.349689\pi$
$158$	−2.90737	+	3.22896i	−0.231298	+	0.256882i
$159$	−8.57545	−	26.3925i	−0.680077	−	2.09306i
$160$	−2.91206	−	2.11574i	−0.230219	−	0.167264i
$161$	8.01807	+	8.90497i	0.631913	+	0.701810i
$162$	−4.94052	+	8.55723i	−0.388164	+	0.672320i
$163$	−3.39068	−	10.4354i	−0.265578	−	0.817366i	−0.991560	−	0.129652i	$-0.958614\pi$
$163$	−3.39068	−	10.4354i	−0.265578	−	0.817366i	0.725981	−	0.687715i	$-0.241386\pi$
$164$	−6.93103	+	1.47324i	−0.541222	+	0.115040i
$165$	5.03753	+	47.9289i	0.392171	+	3.73126i
$166$	−1.39340	+	13.2573i	−0.108149	+	1.02897i
$167$	3.04173	+	0.646541i	0.235376	+	0.0500308i	0.324090	−	0.946026i	$-0.394942\pi$
$167$	3.04173	+	0.646541i	0.235376	+	0.0500308i	−0.0887131	+	0.996057i	$0.528275\pi$
$168$	1.20072	+	11.4241i	0.0926374	+	0.881386i
$169$	6.44671	+	11.1660i	0.495900	+	0.858925i
$170$	−0.367508	+	0.636542i	−0.0281865	+	0.0488205i
$171$	−17.5830	−	7.82844i	−1.34460	−	0.598655i
$172$	−1.88751			−0.143921
$173$	13.6174	+	6.06286i	1.03531	+	0.460951i	0.852792	−	0.522251i	$-0.174908\pi$
$173$	13.6174	+	6.06286i	1.03531	+	0.460951i	0.182521	+	0.983202i	$0.441574\pi$
$174$	1.33179	+	0.967600i	0.100962	+	0.0733535i
$175$	−24.5153	+	17.8114i	−1.85318	+	1.34642i
$176$	−4.34209	−	0.922941i	−0.327298	−	0.0695693i
$177$	6.14705	−	2.73684i	0.462041	−	0.205714i
$178$	6.84307	−	3.04673i	0.512910	−	0.228362i
$179$	0.835860	−	7.95268i	0.0624751	−	0.594411i	−0.917837	−	0.396957i	$-0.870066\pi$
$179$	0.835860	−	7.95268i	0.0624751	−	0.594411i	0.980312	−	0.197454i	$-0.0632673\pi$
$180$	6.78158	−	20.8716i	0.505469	−	1.55567i
$181$	−0.771028	−	0.856314i	−0.0573101	−	0.0636493i	0.713808	−	0.700341i	$-0.246969\pi$
$181$	−0.771028	−	0.856314i	−0.0573101	−	0.0636493i	−0.771118	+	0.636692i	$0.780302\pi$
$182$	1.24341			0.0921675
$183$	9.11450	+	21.7217i	0.673763	+	1.60572i
$184$	3.14628			0.231947
$185$	−7.94714	−	8.82619i	−0.584285	−	0.648914i
$186$	0.974731	−	2.99991i	0.0714708	−	0.219964i
$187$	−0.0947508	+	0.901493i	−0.00692886	+	0.0659237i
$188$	11.8387	−	5.27092i	0.863424	−	0.384421i
$189$	−32.4980	+	14.4691i	−2.36388	+	1.05247i
$190$	11.1148	+	2.36253i	0.806355	+	0.171396i
$191$	−16.5461	+	12.0215i	−1.19724	+	0.869843i	−0.994010	−	0.109289i	$-0.965143\pi$
$191$	−16.5461	+	12.0215i	−1.19724	+	0.869843i	−0.203226	+	0.979132i	$0.565143\pi$
$192$	2.44008	+	1.77282i	0.176097	+	0.127942i
$193$	2.09150	+	0.931196i	0.150549	+	0.0670289i	0.480628	−	0.876924i	$-0.340409\pi$
$193$	2.09150	+	0.931196i	0.150549	+	0.0670289i	−0.330079	+	0.943953i	$0.607075\pi$
$194$	−4.58832			−0.329422
$195$	−3.23796	−	1.44163i	−0.231875	−	0.103237i
$196$	−3.75257	+	6.49965i	−0.268041	+	0.464261i
$197$	−0.442765	−	0.766892i	−0.0315457	−	0.0546388i	0.849822	−	0.527071i	$-0.176710\pi$
$197$	−0.442765	−	0.766892i	−0.0315457	−	0.0546388i	−0.881367	+	0.472432i	$0.843376\pi$
$198$	−2.82901	−	26.9163i	−0.201049	−	1.91286i
$199$	16.8316	+	3.57767i	1.19316	+	0.253615i	0.761345	−	0.648346i	$-0.224539\pi$
$199$	16.8316	+	3.57767i	1.19316	+	0.253615i	0.431817	+	0.901961i	$0.357872\pi$
$200$	−0.831674	+	7.91285i	−0.0588083	+	0.559523i
$201$	−1.67715	−	15.9570i	−0.118297	−	1.12552i
$202$	−4.15292	+	0.882730i	−0.292198	+	0.0621087i
$203$	0.642355	+	1.97696i	0.0450845	+	0.138756i
$204$	0.307942	−	0.533371i	0.0215603	−	0.0373435i
$205$	17.0666	+	18.9544i	1.19198	+	1.32383i
$206$	12.1981	+	8.86242i	0.849880	+	0.617474i
$207$	5.92770	+	18.2436i	0.412003	+	1.26802i
$208$	0.218456	−	0.242620i	0.0151472	−	0.0168226i
$209$	13.7074	−	2.91360i	0.948161	−	0.201538i
$210$	33.4508	−	24.3035i	2.30833	−	1.67710i
$211$	−8.67623	+	26.7027i	−0.597296	+	1.83829i	−0.0543485	+	0.998522i	$0.517308\pi$
$211$	−8.67623	+	26.7027i	−0.597296	+	1.83829i	−0.542948	+	0.839767i	$0.682692\pi$
$212$	−4.60044	−	7.96819i	−0.315959	−	0.547257i
$213$	31.3913	−	34.8636i	2.15090	−	2.38882i
$214$	−4.24801	+	4.71789i	−0.290388	+	0.322509i
$215$	3.39705	+	5.88386i	0.231677	+	0.401276i
$216$	−2.88635	+	8.88326i	−0.196391	+	0.604429i
$217$	3.22237	−	2.34119i	0.218749	−	0.158930i
$218$	−9.72661	+	2.06745i	−0.658769	+	0.140026i
$219$	17.6457	−	19.5976i	1.19239	−	1.32428i
$220$	4.93765	+	15.1965i	0.332896	+	1.02455i
$221$	−0.0539341	−	0.0391854i	−0.00362800	−	0.00263590i
$222$	6.65907	+	7.39564i	0.446927	+	0.496363i
$223$	1.24278	−	2.15255i	0.0832224	−	0.144145i	−0.821410	−	0.570338i	$-0.806812\pi$
$223$	1.24278	−	2.15255i	0.0832224	−	0.144145i	0.904632	+	0.426193i	$0.140145\pi$
$224$	1.17691	+	3.62216i	0.0786356	+	0.242016i
$225$	−47.4492	+	10.0856i	−3.16328	+	0.672376i
$226$	1.89401	+	18.0203i	0.125988	+	1.19869i
$227$	1.13835	−	10.8306i	0.0755547	−	0.718855i	−0.889523	−	0.456891i	$-0.848963\pi$
$227$	1.13835	−	10.8306i	0.0755547	−	0.718855i	0.965078	−	0.261964i	$-0.0843703\pi$
$228$	−9.31335	−	1.97961i	−0.616792	−	0.131103i
$229$	−2.19431	−	20.8775i	−0.145004	−	1.37962i	−0.788906	−	0.614514i	$-0.789352\pi$
$229$	−2.19431	−	20.8775i	−0.145004	−	1.37962i	0.643902	−	0.765108i	$-0.277314\pi$
$230$	−5.66253	−	9.80780i	−0.373376	−	0.646707i
$231$	25.4960	−	44.1603i	1.67751	−	2.90553i
$232$	0.498611	+	0.221996i	0.0327354	+	0.0145747i
$233$	−18.4505			−1.20873			−0.604366	−	0.796707i	$-0.706573\pi$
$233$	−18.4505			−1.20873			−0.604366	+	0.796707i	$0.706573\pi$
$234$	1.81840	+	0.809602i	0.118872	+	0.0529253i
$235$	−37.7375	−	27.4179i	−2.46173	−	1.78855i
$236$	1.80488	−	1.31132i	0.117488	−	0.0853599i
$237$	−12.8186	−	2.72467i	−0.832655	−	0.176986i
$238$	0.710468	−	0.316321i	0.0460528	−	0.0205040i
$239$	0.00895844	−	0.00398856i	0.000579473	−	0.000257998i	−0.406447	−	0.913674i	$-0.633232\pi$
$239$	0.00895844	−	0.00398856i	0.000579473	−	0.000257998i	0.407026	+	0.913416i	$0.366566\pi$
$240$	1.13481	−	10.7970i	0.0732516	−	0.696943i
$241$	−2.47194	+	7.60786i	−0.159232	+	0.490066i	−0.998565	−	0.0535519i	$-0.982946\pi$
$241$	−2.47194	+	7.60786i	−0.159232	+	0.490066i	0.839333	+	0.543617i	$0.182946\pi$
$242$	5.82518	+	6.46952i	0.374457	+	0.415877i
$243$	−1.78097			−0.114249
$244$	4.45328	+	6.41625i	0.285092	+	0.410759i
$245$	27.0148			1.72591
$246$	−14.3004	−	15.8823i	−0.911763	−	1.01262i
$247$	−0.318486	+	0.980201i	−0.0202648	+	0.0623687i
$248$	0.109318	−	1.04009i	0.00694170	−	0.0660459i
$249$	−36.7298	+	16.3531i	−2.32765	+	1.03634i
$250$	9.72170	−	4.32838i	0.614854	−	0.273751i
$251$	−25.2545	−	5.36800i	−1.59405	−	0.338825i	−0.676498	−	0.736445i	$-0.736503\pi$
$251$	−25.2545	−	5.36800i	−1.59405	−	0.338825i	−0.917551	+	0.397619i	$0.869837\pi$
$252$	−18.7856	+	13.6485i	−1.18338	+	0.859776i
$253$	−11.2993	−	8.20940i	−0.710379	−	0.516121i
$254$	0.248826	+	0.110784i	0.0156127	+	0.00695123i
$255$	−2.21688			−0.138826
$256$	0.913545	+	0.406737i	0.0570966	+	0.0254210i
$257$	−5.10093	+	8.83507i	−0.318187	+	0.551117i	−0.980110	−	0.198456i	$-0.936407\pi$
$257$	−5.10093	+	8.83507i	−0.318187	+	0.551117i	0.661923	+	0.749572i	$0.269741\pi$
$258$	−2.84646	−	4.93020i	−0.177213	−	0.306941i
$259$	1.31357	+	12.4978i	0.0816211	+	0.776573i
$260$	−1.14948	−	0.244329i	−0.0712875	−	0.0151526i
$261$	−0.347834	+	3.30942i	−0.0215304	+	0.204848i
$262$	0.266714	+	2.53762i	0.0164777	+	0.156774i
$263$	21.8419	−	4.64264i	1.34683	−	0.286277i	0.522622	−	0.852565i	$-0.324954\pi$
$263$	21.8419	−	4.64264i	1.34683	−	0.286277i	0.824208	+	0.566287i	$0.191621\pi$
$264$	−4.13735	−	12.7335i	−0.254637	−	0.783691i
$265$	−16.5593	+	28.6815i	−1.01723	+	1.76189i
$266$	−8.04504	−	8.93492i	−0.493273	−	0.547835i
$267$	18.2778	+	13.2796i	1.11858	+	0.812699i
$268$	−1.64389	−	5.05939i	−0.100417	−	0.309051i
$269$	8.09855	−	8.99435i	0.493778	−	0.548395i	−0.443821	−	0.896116i	$-0.646377\pi$
$269$	8.09855	−	8.99435i	0.493778	−	0.548395i	0.937598	+	0.347720i	$0.113044\pi$
$270$	32.8862	−	6.99017i	2.00139	−	0.425408i
$271$	−21.9620	+	15.9563i	−1.33409	+	0.969277i	−0.334456	+	0.942411i	$0.608552\pi$
$271$	−21.9620	+	15.9563i	−1.33409	+	0.969277i	−0.999639	+	0.0268651i	$0.991448\pi$
$272$	0.0631009	−	0.194205i	0.00382606	−	0.0117754i
$273$	1.87512	+	3.24780i	0.113487	+	0.196566i
$274$	−1.90998	+	2.12125i	−0.115386	+	0.128149i
$275$	23.6333	−	26.2474i	1.42514	−	1.58278i
$276$	4.74475	+	8.21815i	0.285601	+	0.494675i
$277$	2.03671	−	6.26835i	0.122374	−	0.376628i	−0.871040	−	0.491213i	$-0.836554\pi$
$277$	2.03671	−	6.26835i	0.122374	−	0.376628i	0.993413	+	0.114585i	$0.0365537\pi$
$278$	11.9976	−	8.71678i	0.719570	−	0.522798i
$279$	6.23688	−	1.32569i	0.373392	−	0.0793669i
$280$	9.17307	−	10.1877i	0.548196	−	0.608833i
$281$	−5.34501	−	16.4503i	−0.318857	−	0.981340i	−0.974138	−	0.225955i	$-0.927450\pi$
$281$	−5.34501	−	16.4503i	−0.318857	−	0.981340i	0.655281	−	0.755385i	$-0.272550\pi$
$282$	31.6210	+	22.9740i	1.88301	+	1.36808i
$283$	−5.52892	−	6.14048i	−0.328660	−	0.365014i	0.556056	−	0.831145i	$-0.312314\pi$
$283$	−5.52892	−	6.14048i	−0.328660	−	0.365014i	−0.884716	+	0.466131i	$0.845647\pi$
$284$	7.77720	−	13.4705i	0.461492	−	0.799328i
$285$	10.5908	+	32.5950i	0.627342	+	1.93076i
$286$	−1.41759	+	0.301319i	−0.0838241	+	0.0178174i
$287$	−2.82091	−	26.8391i	−0.166513	−	1.58426i
$288$	−0.637295	+	6.06345i	−0.0375529	+	0.357292i
$289$	16.5877	+	3.52583i	0.975748	+	0.207402i
$290$	−0.205357	−	1.95384i	−0.0120590	−	0.114733i
$291$	−6.91942	−	11.9848i	−0.405623	−	0.702560i
$292$	4.37173	−	7.57206i	0.255836	−	0.443122i
$293$	−6.97021	−	3.10334i	−0.407204	−	0.181299i	0.192905	−	0.981218i	$-0.438209\pi$
$293$	−6.97021	−	3.10334i	−0.407204	−	0.181299i	−0.600108	+	0.799919i	$0.704876\pi$
$294$	−22.6363			−1.32017
$295$	−7.33608	−	3.26623i	−0.427123	−	0.190167i
$296$	2.66941	+	1.93944i	0.155156	+	0.112727i
$297$	33.5443	−	24.3713i	1.94644	−	1.41417i
$298$	−17.3298	−	3.68356i	−1.00389	−	0.213383i
$299$	0.938384	−	0.417796i	0.0542682	−	0.0241617i
$300$	−21.9227	+	9.76063i	−1.26571	+	0.563530i
$301$	0.751423	−	7.14931i	0.0433113	−	0.412079i
$302$	−4.39509	+	13.5267i	−0.252909	+	0.778375i
$303$	−8.56851	−	9.51630i	−0.492248	−	0.546697i
$304$	−3.15687			−0.181059
$305$	11.9864	−	25.4297i	0.686337	−	1.45610i
$306$	1.24497			0.0711702
$307$	15.5176	+	17.2340i	0.885634	+	0.983596i	0.999952	−	0.00984822i	$-0.00313484\pi$
$307$	15.5176	+	17.2340i	0.885634	+	0.983596i	−0.114318	+	0.993444i	$0.536468\pi$
$308$	5.22442	−	16.0791i	0.297689	−	0.916193i
$309$	−4.75350	+	45.2266i	−0.270417	+	2.57285i
$310$	−3.43898	+	1.53113i	−0.195321	+	0.0869626i
$311$	−7.73003	+	3.44163i	−0.438330	+	0.195157i	−0.614023	−	0.789288i	$-0.710450\pi$
$311$	−7.73003	+	3.44163i	−0.438330	+	0.195157i	0.175693	+	0.984445i	$0.443783\pi$
$312$	0.963169	+	0.204728i	0.0545287	+	0.0115904i
$313$	19.6856	−	14.3025i	1.11270	−	0.808423i	0.129612	−	0.991565i	$-0.458627\pi$
$313$	19.6856	−	14.3025i	1.11270	−	0.808423i	0.983086	+	0.183142i	$0.0586268\pi$
$314$	5.26642	+	3.82628i	0.297201	+	0.215929i
$315$	76.3554	+	33.9956i	4.30214	+	1.91544i
$316$	−4.34499			−0.244425
$317$	14.0475	+	6.25433i	0.788984	+	0.351278i	0.761351	−	0.648340i	$-0.224536\pi$
$317$	14.0475	+	6.25433i	0.788984	+	0.351278i	0.0276330	+	0.999618i	$0.491203\pi$
$318$	13.8754	−	24.0328i	0.778092	−	1.34769i
$319$	−1.21142	−	2.09825i	−0.0678267	−	0.117479i
$320$	−0.376251	−	3.57979i	−0.0210331	−	0.200116i
$321$	−18.7294	−	3.98106i	−1.04537	−	0.222201i
$322$	−1.25255	+	11.9172i	−0.0698017	+	0.664118i
$323$	0.0673820	+	0.641097i	0.00374924	+	0.0356716i
$324$	−9.66512	+	2.05438i	−0.536951	+	0.114132i
$325$	0.802701	+	2.47046i	0.0445258	+	0.137036i
$326$	5.48623	−	9.50243i	0.303854	−	0.526291i
$327$	−20.0684	−	22.2883i	−1.10979	−	1.23254i
$328$	−5.73259	−	4.16497i	−0.316529	−	0.229972i
$329$	15.2516	+	46.9397i	0.840850	+	2.58787i
$330$	−32.2474	+	35.8143i	−1.77516	+	1.97151i
$331$	12.0475	−	2.56078i	0.662193	−	0.140753i	0.135458	−	0.990783i	$-0.456749\pi$
$331$	12.0475	−	2.56078i	0.662193	−	0.140753i	0.526735	+	0.850030i	$0.323416\pi$
$332$	−10.7845	+	7.83540i	−0.591876	+	0.430023i
$333$	−6.21648	+	19.1324i	−0.340661	+	1.04845i
$334$	1.55484	+	2.69307i	0.0850773	+	0.147358i
$335$	−12.8128	+	14.2301i	−0.700040	+	0.777473i
$336$	−7.68630	+	8.53650i	−0.419322	+	0.465705i
$337$	−7.94201	−	13.7560i	−0.432629	−	0.749336i	0.564470	−	0.825454i	$-0.309081\pi$
$337$	−7.94201	−	13.7560i	−0.432629	−	0.749336i	−0.997099	+	0.0761182i	$0.975747\pi$
$338$	−3.98428	+	12.2624i	−0.216716	+	0.666985i
$339$	−44.2131	+	32.1227i	−2.40133	+	1.74467i
$340$	−0.718953	+	0.152818i	−0.0389907	+	0.00828773i
$341$	−3.10644	+	3.45005i	−0.168223	+	0.186831i
$342$	−5.94763	−	18.3049i	−0.321611	−	0.989817i
$343$	−1.55646	−	1.13083i	−0.0840409	−	0.0610593i
$344$	−1.26299	−	1.40269i	−0.0680958	−	0.0756281i
$345$	17.0788	−	29.5813i	0.919490	−	1.59260i
$346$	4.60624	+	14.1766i	0.247633	+	0.762136i
$347$	8.48855	−	1.80430i	0.455689	−	0.0968597i	0.0256521	−	0.999671i	$-0.491834\pi$
$347$	8.48855	−	1.80430i	0.455689	−	0.0968597i	0.430037	+	0.902811i	$0.358500\pi$
$348$	0.172073	+	1.63716i	0.00922406	+	0.0877610i
$349$	0.284224	−	2.70421i	0.0152142	−	0.144753i	−0.984278	−	0.176628i	$-0.943481\pi$
$349$	0.284224	−	2.70421i	0.0152142	−	0.144753i	0.999492	+	0.0318748i	$0.0101478\pi$
$350$	−29.6404	−	6.30026i	−1.58435	−	0.336763i
$351$	0.318752	+	3.03272i	0.0170137	+	0.161875i
$352$	−2.21955	−	3.84437i	−0.118302	−	0.204906i
$353$	−5.44940	+	9.43864i	−0.290042	+	0.502368i	−0.973819	−	0.227323i	$-0.927003\pi$
$353$	−5.44940	+	9.43864i	−0.290042	+	0.502368i	0.683777	+	0.729691i	$0.260336\pi$
$354$	6.14705	+	2.73684i	0.326712	+	0.145462i
$355$	−55.9882			−2.97154
$356$	6.84307	+	3.04673i	0.362682	+	0.161476i
$357$	1.89766	+	1.37873i	0.100435	+	0.0729700i
$358$	6.46929	−	4.70022i	0.341913	−	0.248414i
$359$	−5.50957	−	1.17110i	−0.290784	−	0.0618081i	0.0602100	−	0.998186i	$-0.480823\pi$
$359$	−5.50957	−	1.17110i	−0.290784	−	0.0618081i	−0.350994	+	0.936378i	$0.614156\pi$
$360$	20.0483	−	8.92610i	1.05664	−	0.470447i
$361$	−8.25315	+	3.67454i	−0.434376	+	0.193397i
$362$	0.120446	−	1.14597i	0.00633052	−	0.0602309i
$363$	−8.11384	+	24.9718i	−0.425866	+	1.31068i
$364$	0.832002	+	0.924032i	0.0436088	+	0.0484324i
$365$	−31.4722			−1.64733
$366$	−10.0436	+	21.3081i	−0.524988	+	1.11379i
$367$	16.4522			0.858799			0.429400	−	0.903115i	$-0.358725\pi$
$367$	16.4522			0.858799			0.429400	+	0.903115i	$0.358725\pi$
$368$	2.10528	+	2.33815i	0.109745	+	0.121884i
$369$	13.3500	−	41.0871i	0.694973	−	2.13891i
$370$	1.24146	−	11.8117i	0.0645407	−	0.614063i
$371$	32.0125	−	14.2529i	1.66201	−	0.739974i
$372$	2.88159	−	1.28297i	0.149404	−	0.0665188i
$373$	2.75649	+	0.585909i	0.142725	+	0.0303372i	0.278720	−	0.960372i	$-0.410090\pi$
$373$	2.75649	+	0.585909i	0.142725	+	0.0303372i	−0.135995	+	0.990710i	$0.543423\pi$
$374$	−0.733341	+	0.532803i	−0.0379201	+	0.0275506i
$375$	25.9666	+	18.8658i	1.34091	+	0.974228i
$376$	11.8387	+	5.27092i	0.610533	+	0.271827i
$377$	0.178190			0.00917727
$378$	−32.4980	−	14.4691i	−1.67152	−	0.744208i
$379$	17.3507	−	30.0524i	0.891247	−	1.54369i	0.0528662	−	0.998602i	$-0.483164\pi$
$379$	17.3507	−	30.0524i	0.891247	−	1.54369i	0.838381	−	0.545084i	$-0.183502\pi$
$380$	5.68158	+	9.84078i	0.291459	+	0.504821i
$381$	0.0858708	+	0.817006i	0.00439929	+	0.0418565i
$382$	−20.0052	−	4.25224i	−1.02356	−	0.217564i
$383$	1.43610	−	13.6636i	0.0733812	−	0.698176i	−0.894551	−	0.446965i	$-0.852505\pi$
$383$	1.43610	−	13.6636i	0.0733812	−	0.698176i	0.967932	−	0.251210i	$-0.0808286\pi$
$384$	0.315268	+	2.99958i	0.0160885	+	0.153071i
$385$	−59.5255	+	12.6525i	−3.03370	+	0.644833i
$386$	0.707473	+	2.17738i	0.0360094	+	0.110826i
$387$	5.75393	−	9.96609i	0.292489	−	0.506605i
$388$	−3.07019	−	3.40979i	−0.155865	−	0.173106i
$389$	−10.4873	−	7.61949i	−0.531729	−	0.386323i	0.289275	−	0.957246i	$-0.406586\pi$
$389$	−10.4873	−	7.61949i	−0.531729	−	0.386323i	−0.821004	+	0.570923i	$0.806586\pi$
$390$	−1.09528	−	3.37091i	−0.0554614	−	0.170693i
$391$	0.429895	−	0.477447i	0.0217407	−	0.0241455i
$392$	−7.34114	+	1.56041i	−0.370784	+	0.0788125i
$393$	−6.22608	+	4.52351i	−0.314064	+	0.228181i
$394$	0.273644	−	0.842190i	0.0137860	−	0.0424289i
$395$	7.81992	+	13.5445i	0.393463	+	0.681497i
$396$	18.1097	−	20.1129i	0.910047	−	1.01071i
$397$	11.8003	−	13.1056i	0.592242	−	0.657752i	−0.370291	−	0.928916i	$-0.620742\pi$
$397$	11.8003	−	13.1056i	0.592242	−	0.657752i	0.962533	+	0.271164i	$0.0874086\pi$
$398$	8.60383	+	14.9023i	0.431271	+	0.746983i
$399$	11.2059	−	34.4881i	0.560995	−	1.72656i
$400$	−6.43690	+	4.67668i	−0.321845	+	0.233834i
$401$	−37.0746	+	7.88046i	−1.85142	+	0.393531i	−0.992870	−	0.119200i	$-0.961967\pi$
$401$	−37.0746	+	7.88046i	−1.85142	+	0.393531i	−0.858549	+	0.512731i	$0.828634\pi$
$402$	10.7361	−	11.9237i	0.535470	−	0.594699i
$403$	−0.105510	−	0.324725i	−0.00525581	−	0.0161757i
$404$	−3.43484	−	2.49556i	−0.170890	−	0.124159i
$405$	23.7989	+	26.4313i	1.18258	+	1.31338i
$406$	−1.03935	+	1.80021i	−0.0515822	+	0.0893429i
$407$	−4.52620	−	13.9302i	−0.224356	−	0.690495i
$408$	0.602425	−	0.128049i	0.0298245	−	0.00633939i
$409$	−3.08674	−	29.3684i	−0.152630	−	1.45217i	−0.755926	−	0.654657i	$-0.772813\pi$
$409$	−3.08674	−	29.3684i	−0.152630	−	1.45217i	0.603296	−	0.797517i	$-0.293854\pi$
$410$	−2.66606	+	25.3659i	−0.131668	+	1.25273i
$411$	−8.42109	−	1.78996i	−0.415382	−	0.0882921i
$412$	1.57604	+	14.9951i	0.0776461	+	0.738753i
$413$	4.24837	+	7.35839i	0.209049	+	0.362083i
$414$	−9.59122	+	16.6125i	−0.471383	+	0.816459i
$415$	43.8344	+	19.5163i	2.15175	+	0.958020i
$416$	0.326477			0.0160069
$417$	40.8614	+	18.1927i	2.00099	+	0.890899i
$418$	11.3373	+	8.23701i	0.554524	+	0.402885i
$419$	20.1143	−	14.6139i	0.982650	−	0.713937i	0.0243508	−	0.999703i	$-0.492248\pi$
$419$	20.1143	−	14.6139i	0.982650	−	0.713937i	0.958299	+	0.285766i	$0.0922481\pi$
$420$	40.4440	+	8.59663i	1.97346	+	0.419473i
$421$	4.42481	−	1.97005i	0.215652	−	0.0960144i	−0.296068	−	0.955167i	$-0.595675\pi$
$421$	4.42481	−	1.97005i	0.215652	−	0.0960144i	0.511720	+	0.859153i	$0.329009\pi$
$422$	−25.6495	+	11.4199i	−1.24860	+	0.555911i
$423$	−8.25873	+	78.5766i	−0.401553	+	3.82052i
$424$	2.84323	−	8.75055i	0.138079	−	0.424964i
$425$	1.08713	+	1.20738i	0.0527337	+	0.0585668i
$426$	46.9136			2.27297
$427$	−26.0757	+	14.3133i	−1.26189	+	0.692671i
$428$	−6.34855			−0.306869
$429$	−2.92485	−	3.24838i	−0.141213	−	0.156833i
$430$	−2.09949	+	6.46157i	−0.101246	+	0.311604i
$431$	2.24064	−	21.3182i	0.107928	−	1.02686i	−0.797777	−	0.602953i	$-0.793991\pi$
$431$	2.24064	−	21.3182i	0.107928	−	1.02686i	0.905704	−	0.423910i	$-0.139343\pi$
$432$	−8.53289	+	3.79909i	−0.410539	+	0.182784i
$433$	16.8568	−	7.50511i	0.810084	−	0.360673i	0.0404688	−	0.999181i	$-0.487115\pi$
$433$	16.8568	−	7.50511i	0.810084	−	0.360673i	0.769615	+	0.638508i	$0.220448\pi$
$434$	3.89603	+	0.828127i	0.187016	+	0.0397514i
$435$	4.79377	−	3.48288i	0.229844	−	0.166991i
$436$	−8.04479	−	5.84488i	−0.385275	−	0.279919i
$437$	−9.07370	−	4.03987i	−0.434054	−	0.193253i
$438$	26.3712			1.26006
$439$	20.6926	+	9.21295i	0.987605	+	0.439710i	0.835999	−	0.548731i	$-0.184889\pi$
$439$	20.6926	+	9.21295i	0.987605	+	0.439710i	0.151606	+	0.988441i	$0.451555\pi$
$440$	−7.98928	+	13.8378i	−0.380874	+	0.659693i
$441$	−22.8789	−	39.6274i	−1.08947	−	1.88702i
$442$	−0.00696852	−	0.0663010i	−0.000331459	−	0.00315362i
$443$	−7.74153	−	1.64551i	−0.367811	−	0.0781806i	0.0202984	−	0.999794i	$-0.493538\pi$
$443$	−7.74153	−	1.64551i	−0.367811	−	0.0781806i	−0.388109	+	0.921613i	$0.626872\pi$
$444$	−1.04025	+	9.89730i	−0.0493680	+	0.469705i
$445$	−2.81837	−	26.8150i	−0.133604	−	1.27115i
$446$	2.43124	−	0.516775i	0.115122	−	0.0244700i
$447$	−16.5127	−	50.8207i	−0.781022	−	2.40374i
$448$	−1.90428	+	3.29831i	−0.0899688	+	0.155831i
$449$	−16.6219	−	18.4605i	−0.784435	−	0.871203i	0.209875	−	0.977728i	$-0.432694\pi$
$449$	−16.6219	−	18.4605i	−0.784435	−	0.871203i	−0.994310	+	0.106525i	$0.966028\pi$
$450$	−39.2448	−	28.5130i	−1.85002	−	1.34412i
$451$	9.72009	+	29.9154i	0.457701	+	1.40866i
$452$	−12.1244	+	13.4655i	−0.570282	+	0.633362i
$453$	−41.9600	+	8.91888i	−1.97145	+	0.419045i
$454$	8.81044	−	6.40116i	0.413494	−	0.300421i
$455$	1.38305	−	4.25660i	0.0648385	−	0.199552i
$456$	−4.76071	−	8.24579i	−0.222941	−	0.386144i
$457$	16.4643	−	18.2855i	0.770170	−	0.855360i	−0.222660	−	0.974896i	$-0.571474\pi$
$457$	16.4643	−	18.2855i	0.770170	−	0.855360i	0.992830	+	0.119536i	$0.0381407\pi$
$458$	14.0467	−	15.6004i	0.656359	−	0.728961i
$459$	0.953651	+	1.65177i	0.0445126	+	0.0770981i
$460$	3.49964	−	10.7708i	0.163172	−	0.502190i
$461$	16.8135	−	12.2158i	0.783085	−	0.568944i	−0.122818	−	0.992429i	$-0.539193\pi$
$461$	16.8135	−	12.2158i	0.783085	−	0.568944i	0.905903	+	0.423485i	$0.139193\pi$
$462$	49.8776	−	10.6018i	2.32052	−	0.493241i
$463$	−18.7441	+	20.8175i	−0.871114	+	0.967470i	−0.999706	−	0.0242277i	$-0.992287\pi$
$463$	−18.7441	+	20.8175i	−0.871114	+	0.967470i	0.128593	+	0.991697i	$0.458954\pi$
$464$	0.168661	+	0.519084i	0.00782988	+	0.0240979i
$465$	−9.18551	−	6.67366i	−0.425968	−	0.309484i
$466$	−12.3458	−	13.7114i	−0.571907	−	0.635167i
$467$	−18.3118	+	31.7170i	−0.847370	+	1.46769i	0.0361762	+	0.999345i	$0.488482\pi$
$467$	−18.3118	+	31.7170i	−0.847370	+	1.46769i	−0.883547	+	0.468343i	$0.844851\pi$
$468$	0.615093	+	1.89306i	0.0284327	+	0.0875068i
$469$	19.8179	−	4.21242i	0.915104	−	0.194511i
$470$	−4.87585	−	46.3906i	−0.224906	−	2.13984i
$471$	−2.05229	+	19.5262i	−0.0945643	+	0.899719i
$472$	2.18220	+	0.463842i	0.100444	+	0.0213501i
$473$	0.875827	+	8.33293i	0.0402706	+	0.383149i
$474$	−6.55247	−	11.3492i	−0.300965	−	0.521286i
$475$	12.5587	−	21.7523i	0.576233	−	0.998065i
$476$	0.710468	+	0.316321i	0.0325643	+	0.0144985i
$477$	56.0963			2.56848
$478$	0.00895844	+	0.00398856i	0.000409750	+	0.000182432i
$479$	18.8625	+	13.7044i	0.861851	+	0.626172i	0.928388	−	0.371612i	$-0.121195\pi$
$479$	18.8625	+	13.7044i	0.861851	+	0.626172i	−0.0665366	+	0.997784i	$0.521195\pi$
$480$	8.78306	−	6.38127i	0.400890	−	0.291264i
$481$	1.05369	+	0.223969i	0.0480442	+	0.0102121i
$482$	−7.30780	+	3.25364i	−0.332861	+	0.148199i
$483$	−33.0168	+	14.7000i	−1.50232	+	0.668874i
$484$	−0.909983	+	8.65791i	−0.0413629	+	0.393541i
$485$	−5.10363	+	15.7074i	−0.231744	+	0.713234i
$486$	−1.19170	−	1.32352i	−0.0540568	−	0.0600361i
$487$	−19.8006			−0.897249			−0.448625	−	0.893720i	$-0.648086\pi$
$487$	−19.8006			−0.897249			−0.448625	+	0.893720i	$0.648086\pi$
$488$	−1.78838	+	7.60274i	−0.0809562	+	0.344160i
$489$	33.0940			1.49656
$490$	18.0764	+	20.0759i	0.816611	+	0.906938i
$491$	0.245891	−	0.756773i	0.0110969	−	0.0341527i	−0.945355	−	0.326044i	$-0.894284\pi$
$491$	0.245891	−	0.756773i	0.0110969	−	0.0341527i	0.956452	+	0.291891i	$0.0942844\pi$
$492$	2.23395	−	21.2546i	0.100714	−	0.958232i
$493$	0.101816	−	0.0453313i	0.00458555	−	0.00204162i
$494$	−0.941540	+	0.419201i	−0.0423619	+	0.0188607i
$495$	−95.2901	−	20.2545i	−4.28297	−	0.910373i
$496$	0.846086	−	0.614718i	0.0379904	−	0.0276016i
$497$	47.9261	+	34.8203i	2.14978	+	1.56191i
$498$	−36.7298	−	16.3531i	−1.64590	−	0.732802i
$499$	7.19901			0.322272			0.161136	−	0.986932i	$-0.448484\pi$
$499$	7.19901			0.322272			0.161136	+	0.986932i	$0.448484\pi$
$500$	9.72170	+	4.32838i	0.434768	+	0.193571i
$501$	−4.68956	+	8.12256i	−0.209514	+	0.362889i
$502$	−12.9093	−	22.3596i	−0.576172	−	0.997959i
$503$	−1.97275	−	18.7694i	−0.0879604	−	0.836888i	−0.946188	−	0.323618i	$-0.895101\pi$
$503$	−1.97275	−	18.7694i	−0.0879604	−	0.836888i	0.858227	−	0.513270i	$-0.171566\pi$
$504$	−22.7128	−	4.82776i	−1.01171	−	0.215045i
$505$	−1.59745	+	15.1987i	−0.0710854	+	0.676333i
$506$	−1.45991	−	13.8902i	−0.0649011	−	0.617493i
$507$	−38.0380	+	8.08523i	−1.68933	+	0.359078i
$508$	0.0841681	+	0.259043i	0.00373436	+	0.0114932i
$509$	−11.0784	+	19.1884i	−0.491043	+	0.850512i	−0.999947	−	0.0103115i	$-0.996718\pi$
$509$	−11.0784	+	19.1884i	−0.491043	+	0.850512i	0.508903	+	0.860824i	$0.330051\pi$
$510$	−1.48338	−	1.64746i	−0.0656852	−	0.0729508i
$511$	26.9403	+	19.5733i	1.19177	+	0.865871i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	19.7303	−	21.9127i	0.871112	−	0.967468i
$514$	−9.97892	+	2.12109i	−0.440152	+	0.0935571i
$515$	43.9070	−	31.9003i	1.93477	−	1.40570i
$516$	1.75921	−	5.41428i	0.0774447	−	0.238350i
$517$	−28.7632	−	49.8194i	−1.26501	−	2.19105i
$518$	−8.40870	+	9.33881i	−0.369457	+	0.410324i
$519$	−30.0830	+	33.4105i	−1.32050	+	1.46656i
$520$	−0.587578	−	1.01771i	−0.0257670	−	0.0446297i
$521$	−5.92361	+	18.2310i	−0.259518	+	0.798714i	0.733388	+	0.679811i	$0.237938\pi$
$521$	−5.92361	+	18.2310i	−0.259518	+	0.798714i	−0.992906	+	0.118904i	$0.962062\pi$
$522$	−2.69212	+	1.95594i	−0.117831	+	0.0856092i
$523$	−1.39452	+	0.296415i	−0.0609782	+	0.0129613i	−0.238300	−	0.971192i	$-0.576590\pi$
$523$	−1.39452	+	0.296415i	−0.0609782	+	0.0129613i	0.177322	+	0.984153i	$0.443257\pi$
$524$	−1.70735	+	1.89620i	−0.0745859	+	0.0828360i
$525$	−28.2428	−	86.9224i	−1.23262	−	3.79361i
$526$	18.0652	+	13.1252i	0.787682	+	0.572284i
$527$	−0.142896	−	0.158703i	−0.00622467	−	0.00691319i
$528$	6.69438	−	11.5950i	0.291336	−	0.504608i
$529$	−4.04840	−	12.4597i	−0.176017	−	0.541726i
$530$	−32.3949	+	6.88574i	−1.40714	+	0.299097i
$531$	1.42178	+	13.5273i	0.0616998	+	0.587035i
$532$	1.25676	−	11.9573i	0.0544874	−	0.518413i
$533$	−2.26282	−	0.480977i	−0.0980136	−	0.0208334i
$534$	2.36157	+	22.4688i	0.102195	+	0.972322i
$535$	11.4258	+	19.7901i	0.493981	+	0.855601i
$536$	2.65988	−	4.60704i	0.114889	−	0.198994i
$537$	22.0331	+	9.80975i	0.950797	+	0.423322i
$538$	12.1031			0.521802
$539$	30.4358	+	13.5509i	1.31096	+	0.583678i
$540$	27.1998	+	19.7618i	1.17049	+	0.850414i
$541$	24.6354	−	17.8987i	1.05916	−	0.769524i	0.0852267	−	0.996362i	$-0.472839\pi$
$541$	24.6354	−	17.8987i	1.05916	−	0.769524i	0.973933	+	0.226837i	$0.0728385\pi$
$542$	−26.5533	−	5.64407i	−1.14056	−	0.242434i
$543$	3.17494	−	1.41357i	0.136250	−	0.0606622i
$544$	0.186545	−	0.0830552i	0.00799805	−	0.00356096i
$545$	−3.74140	+	35.5971i	−0.160264	+	1.52481i
$546$	−1.15889	+	3.56669i	−0.0495958	+	0.152640i
$547$	−5.84885	−	6.49581i	−0.250079	−	0.277741i	0.605015	−	0.796214i	$-0.293167\pi$
$547$	−5.84885	−	6.49581i	−0.250079	−	0.277741i	−0.855094	+	0.518474i	$0.826500\pi$
$548$	−2.85442			−0.121935
$549$	−47.4535	+	3.95396i	−2.02527	+	0.168751i
$550$	35.3194			1.50603
$551$	−1.15292	−	1.28045i	−0.0491160	−	0.0545488i
$552$	−2.93242	+	9.02506i	−0.124812	+	0.384132i
$553$	1.72976	−	16.4575i	0.0735567	−	0.699845i
$554$	6.02111	−	2.68077i	0.255813	−	0.113895i
$555$	32.7247	−	14.5700i	1.38909	−	0.618461i
$556$	14.5058	+	3.08330i	0.615183	+	0.130761i
$557$	−35.4664	+	25.7679i	−1.50276	+	1.09182i	−0.533494	+	0.845804i	$0.679121\pi$
$557$	−35.4664	+	25.7679i	−1.50276	+	1.09182i	−0.969266	+	0.246015i	$0.920879\pi$
$558$	5.15846	+	3.74784i	0.218375	+	0.158659i
$559$	−0.562952	−	0.250642i	−0.0238103	−	0.0106010i
$560$	13.7089			0.579309
$561$	−2.49761	−	1.11201i	−0.105449	−	0.0469489i
$562$	8.64841	−	14.9795i	0.364811	−	0.631872i
$563$	22.8523	+	39.5814i	0.963111	+	1.66816i	0.714607	+	0.699526i	$0.246605\pi$
$563$	22.8523	+	39.5814i	0.963111	+	1.66816i	0.248503	+	0.968631i	$0.420061\pi$
$564$	4.08557	+	38.8716i	0.172034	+	1.63679i
$565$	63.7962	+	13.5603i	2.68393	+	0.570487i
$566$	0.863702	−	8.21757i	0.0363041	−	0.345410i
$567$	−3.93367	−	37.4264i	−0.165199	−	1.57176i
$568$	15.2145	−	3.23394i	0.638386	−	0.135693i
$569$	12.2630	+	37.7415i	0.514090	+	1.58221i	0.784932	+	0.619582i	$0.212698\pi$
$569$	12.2630	+	37.7415i	0.514090	+	1.58221i	−0.270842	+	0.962624i	$0.587302\pi$
$570$	−17.1362	+	29.6808i	−0.717756	+	1.24319i
$571$	4.85497	+	5.39199i	0.203174	+	0.225648i	0.836118	−	0.548550i	$-0.184820\pi$
$571$	4.85497	+	5.39199i	0.203174	+	0.225648i	−0.632943	+	0.774198i	$0.718153\pi$
$572$	−1.17248	−	0.851856i	−0.0490238	−	0.0356179i
$573$	−19.0619	−	58.6666i	−0.796323	−	2.45083i
$574$	18.0578	−	20.0552i	0.753719	−	0.837089i
$575$	−24.4862	+	5.20470i	−1.02114	+	0.217051i
$576$	−4.93246	+	3.58364i	−0.205519	+	0.149318i
$577$	−10.4591	+	32.1897i	−0.435417	+	1.34007i	0.457242	+	0.889342i	$0.348837\pi$
$577$	−10.4591	+	32.1897i	−0.435417	+	1.34007i	−0.892659	+	0.450733i	$0.851163\pi$
$578$	8.47915	+	14.6863i	0.352686	+	0.610870i
$579$	−4.62045	+	5.13153i	−0.192019	+	0.213259i
$580$	1.31457	−	1.45998i	0.0545847	−	0.0606225i
$581$	−25.3848	−	43.9677i	−1.05314	−	1.82409i
$582$	4.27643	−	13.1615i	0.177264	−	0.545562i
$583$	−33.0431	+	24.0073i	−1.36851	+	0.994279i
$584$	8.55240	−	1.81787i	0.353901	−	0.0752240i
$585$	4.79415	−	5.32445i	0.198214	−	0.220139i
$586$	−2.35775	−	7.25641i	−0.0973978	−	0.299760i
$587$	−9.22837	−	6.70481i	−0.380896	−	0.276737i	0.380819	−	0.924650i	$-0.375642\pi$
$587$	−9.22837	−	6.70481i	−0.380896	−	0.276737i	−0.761715	+	0.647913i	$0.775642\pi$
$588$	−15.1466	−	16.8220i	−0.624636	−	0.693729i
$589$	−1.65076	+	2.85919i	−0.0680183	+	0.117811i
$590$	−2.48151	−	7.63731i	−0.102162	−	0.314423i
$591$	2.61248	−	0.555300i	0.107463	−	0.0228420i
$592$	0.344899	+	3.28149i	0.0141752	+	0.134868i
$593$	−1.63952	+	15.5990i	−0.0673271	+	0.640575i	0.907872	+	0.419247i	$0.137706\pi$
$593$	−1.63952	+	15.5990i	−0.0673271	+	0.640575i	−0.975199	+	0.221328i	$0.928961\pi$
$594$	40.5569	+	8.62064i	1.66407	+	0.353709i
$595$	−0.292612	−	2.78402i	−0.0119959	−	0.114134i
$596$	−8.85848	−	15.3433i	−0.362857	−	0.628487i
$597$	−25.9500	+	44.9467i	−1.06206	+	1.83955i
$598$	0.938384	+	0.417796i	0.0383734	+	0.0170849i
$599$	1.45331			0.0593808			0.0296904	−	0.999559i	$-0.490548\pi$
$599$	1.45331			0.0593808			0.0296904	+	0.999559i	$0.490548\pi$
$600$	−21.9227	−	9.76063i	−0.894991	−	0.398476i
$601$	−5.10897	−	3.71188i	−0.208399	−	0.151411i	0.478690	−	0.877984i	$-0.341112\pi$
$601$	−5.10897	−	3.71188i	−0.208399	−	0.151411i	−0.687089	+	0.726573i	$0.741112\pi$
$602$	5.81577	−	4.22541i	0.237033	−	0.172215i
$603$	31.7250	+	6.74335i	1.29194	+	0.274611i
$604$	−12.9932	+	5.78494i	−0.528686	+	0.235386i
$605$	28.6267	−	12.7454i	1.16384	−	0.518176i
$606$	1.33853	−	12.7353i	0.0543742	−	0.517336i
$607$	12.5471	−	38.6159i	0.509270	−	1.56737i	−0.284201	−	0.958765i	$-0.591728\pi$
$607$	12.5471	−	38.6159i	0.509270	−	1.56737i	0.793471	−	0.608608i	$-0.208272\pi$
$608$	−2.11236	−	2.34601i	−0.0856673	−	0.0951432i
$609$	−6.26958			−0.254056
$610$	26.9184	−	8.10820i	1.08989	−	0.328291i
$611$	4.23083			0.171161
$612$	0.833048	+	0.925193i	0.0336740	+	0.0373987i
$613$	−1.90079	+	5.85004i	−0.0767724	+	0.236281i	−0.982076	−	0.188483i	$-0.939643\pi$
$613$	−1.90079	+	5.85004i	−0.0767724	+	0.236281i	0.905304	+	0.424764i	$0.139643\pi$
$614$	−2.42408	+	23.0636i	−0.0978279	+	0.930771i
$615$	−70.2768	+	31.2892i	−2.83383	+	1.26170i
$616$	15.4449	−	6.87653i	0.622294	−	0.277063i
$617$	19.8942	+	4.22865i	0.800911	+	0.170239i	0.590145	−	0.807297i	$-0.299071\pi$
$617$	19.8942	+	4.22865i	0.800911	+	0.170239i	0.210767	+	0.977536i	$0.432404\pi$
$618$	−36.7906	+	26.7299i	−1.47993	+	1.07524i
$619$	−13.8357	−	10.0523i	−0.556106	−	0.404034i	0.273926	−	0.961751i	$-0.411678\pi$
$619$	−13.8357	−	10.0523i	−0.556106	−	0.404034i	−0.830032	+	0.557716i	$0.811678\pi$
$620$	−3.43898	−	1.53113i	−0.138113	−	0.0614918i
$621$	−29.3876			−1.17928
$622$	−7.73003	−	3.44163i	−0.309946	−	0.137997i
$623$	−14.2643	+	24.7066i	−0.571489	+	0.989848i
$624$	0.492343	+	0.852764i	0.0197095	+	0.0341379i
$625$	0.154416	+	1.46917i	0.00617662	+	0.0587666i
$626$	23.8011	+	5.05907i	0.951282	+	0.202201i
$627$	−4.41805	+	42.0350i	−0.176440	+	1.67872i
$628$	0.680444	+	6.47399i	0.0271527	+	0.258340i
$629$	0.659044	−	0.140084i	0.0262778	−	0.00558552i
$630$	25.8281	+	79.4906i	1.02901	+	3.16698i
$631$	11.9439	−	20.6874i	0.475477	−	0.823551i	−0.524128	−	0.851639i	$-0.675609\pi$
$631$	11.9439	−	20.6874i	0.475477	−	0.823551i	0.999605	+	0.0280886i	$0.00894207\pi$
$632$	−2.90737	−	3.22896i	−0.115649	−	0.128441i
$633$	−68.5097	−	49.7752i	−2.72301	−	1.97839i
$634$	4.75171	+	14.6243i	0.188715	+	0.580804i
$635$	0.656023	−	0.728587i	0.0260335	−	0.0289131i
$636$	27.1443	−	5.76970i	1.07634	−	0.228784i
$637$	−1.98230	+	1.44023i	−0.0785416	+	0.0570638i
$638$	0.748701	−	2.30427i	0.0296414	−	0.0912268i
$639$	47.4164	+	82.1277i	1.87577	+	3.24892i
$640$	2.40854	−	2.67495i	0.0952059	−	0.105737i
$641$	−5.69802	+	6.32829i	−0.225058	+	0.249952i	−0.845090	−	0.534624i	$-0.820453\pi$
$641$	−5.69802	+	6.32829i	−0.225058	+	0.249952i	0.620032	+	0.784577i	$0.287120\pi$
$642$	−9.57393	−	16.5825i	−0.377853	−	0.654460i
$643$	8.82323	−	27.1551i	0.347954	−	1.07089i	−0.612029	−	0.790835i	$-0.709646\pi$
$643$	8.82323	−	27.1551i	0.347954	−	1.07089i	0.959983	−	0.280058i	$-0.0903536\pi$
$644$	−9.69431	+	7.04333i	−0.382009	+	0.277546i
$645$	−20.0439	+	4.26046i	−0.789227	+	0.167755i
$646$	−0.431341	+	0.479052i	−0.0169709	+	0.0188481i
$647$	7.84268	+	24.1373i	0.308328	+	0.948935i	0.978415	+	0.206652i	$0.0662568\pi$
$647$	7.84268	+	24.1373i	0.308328	+	0.948935i	−0.670087	+	0.742283i	$0.733743\pi$
$648$	−7.99393	−	5.80793i	−0.314031	−	0.228157i
$649$	−6.62669	−	7.35969i	−0.260120	−	0.288893i
$650$	−1.29880	+	2.24958i	−0.0509430	+	0.0882359i
$651$	3.71233	+	11.4254i	0.145498	+	0.447795i
$652$	10.7327	−	2.28130i	0.420325	−	0.0893428i
$653$	−4.75991	−	45.2875i	−0.186270	−	1.77224i	−0.544651	−	0.838663i	$-0.683338\pi$
$653$	−4.75991	−	45.2875i	−0.186270	−	1.77224i	0.358381	−	0.933575i	$-0.383329\pi$
$654$	3.13500	−	29.8275i	0.122588	−	1.16635i
$655$	8.98377	+	1.90956i	0.351025	+	0.0746127i
$656$	−0.740675	−	7.04705i	−0.0289185	−	0.275141i
$657$	26.6538	+	46.1658i	1.03986	+	1.80110i
$658$	−24.6777	+	42.7430i	−0.962036	+	1.66629i
$659$	−0.0390679	−	0.0173942i	−0.00152187	−	0.000677580i	0.405976	−	0.913884i	$-0.366932\pi$
$659$	−0.0390679	−	0.0173942i	−0.00152187	−	0.000677580i	−0.407497	+	0.913206i	$0.633598\pi$
$660$	−48.1929			−1.87591
$661$	−18.3437	−	8.16715i	−0.713488	−	0.317665i	0.0176983	−	0.999843i	$-0.494366\pi$
$661$	−18.3437	−	8.16715i	−0.713488	−	0.317665i	−0.731186	+	0.682178i	$0.761033\pi$
$662$	9.96442	+	7.23957i	0.387278	+	0.281374i
$663$	0.162671	−	0.118187i	0.00631760	−	0.00459001i
$664$	−13.0391	−	2.77154i	−0.506014	−	0.107557i
$665$	−39.5358	+	17.6025i	−1.53313	+	0.682594i
$666$	−18.3778	+	8.18231i	−0.712124	+	0.317058i
$667$	−0.179500	+	1.70783i	−0.00695026	+	0.0661273i
$668$	−0.960947	+	2.95749i	−0.0371801	+	0.114429i
$669$	5.01625	+	5.57111i	0.193939	+	0.215392i
$670$	−19.1485			−0.739770
$671$	26.2600	−	22.6375i	1.01376	−	0.873910i
$672$	−11.4870			−0.443121
$673$	4.06337	+	4.51282i	0.156631	+	0.173957i	0.816353	−	0.577553i	$-0.195992\pi$
$673$	4.06337	+	4.51282i	0.156631	+	0.173957i	−0.659722	+	0.751510i	$0.729326\pi$
$674$	4.90843	−	15.1066i	0.189066	−	0.581885i
$675$	7.76818	−	73.9093i	0.298997	−	2.84477i
$676$	−11.7787	+	5.24422i	−0.453028	+	0.201701i
$677$	5.97586	−	2.66062i	0.229671	−	0.102256i	−0.288675	−	0.957427i	$-0.593215\pi$
$677$	5.97586	−	2.66062i	0.229671	−	0.102256i	0.518346	+	0.855171i	$0.326548\pi$
$678$	−53.4562	−	11.3625i	−2.05297	−	0.436373i
$679$	14.1375	−	10.2715i	0.542547	−	0.394184i
$680$	−0.594640	−	0.432031i	−0.0228034	−	0.0165676i
$681$	30.0065	+	13.3598i	1.14985	+	0.511947i
$682$	−4.64250			−0.177770
$683$	−12.5767	−	5.59950i	−0.481234	−	0.214259i	0.151758	−	0.988418i	$-0.451507\pi$
$683$	−12.5767	−	5.59950i	−0.481234	−	0.214259i	−0.632992	+	0.774159i	$0.718173\pi$
$684$	9.62347	−	16.6683i	0.367963	−	0.637330i
$685$	5.13726	+	8.89799i	0.196284	+	0.339975i
$686$	−0.201101	−	1.91335i	−0.00767808	−	0.0730520i
$687$	61.9318	+	13.1640i	2.36284	+	0.502238i
$688$	0.197298	−	1.87717i	0.00752193	−	0.0715664i
$689$	−0.313990	−	2.98742i	−0.0119621	−	0.113812i
$690$	33.4111	−	7.10175i	1.27194	−	0.270359i
$691$	6.37914	+	19.6330i	0.242674	+	0.746874i	0.996010	+	0.0892383i	$0.0284433\pi$
$691$	6.37914	+	19.6330i	0.242674	+	0.746874i	−0.753336	+	0.657635i	$0.771557\pi$
$692$	−7.45306	+	12.9091i	−0.283323	+	0.490729i
$693$	68.9719	+	76.6011i	2.62003	+	2.90983i
$694$	7.02080	+	5.10091i	0.266506	+	0.193628i
$695$	−16.4954	−	50.7676i	−0.625706	−	1.92573i
$696$	−1.10151	+	1.22335i	−0.0417526	+	0.0463709i
$697$	−1.41531	+	0.300833i	−0.0536086	+	0.0113949i
$698$	2.19980	−	1.59825i	0.0832638	−	0.0604947i
$699$	17.1963	−	52.9248i	0.650425	−	2.00180i
$700$	−15.1513	−	26.2428i	−0.572665	−	0.991885i
$701$	18.5497	−	20.6016i	0.700614	−	0.778111i	−0.282860	−	0.959161i	$-0.591283\pi$
$701$	18.5497	−	20.6016i	0.700614	−	0.778111i	0.983474	+	0.181050i	$0.0579497\pi$
$702$	−2.04047	+	2.26617i	−0.0770124	+	0.0855310i
$703$	−5.20814	−	9.02077i	−0.196429	−	0.340225i
$704$	1.37176	−	4.22183i	0.0517000	−	0.159116i
$705$	113.820	−	82.6952i	4.28671	−	3.11448i
$706$	−10.6606	+	2.26599i	−0.401218	+	0.0852816i
$707$	10.8198	−	12.0167i	0.406922	−	0.451933i
$708$	2.07931	+	6.39945i	0.0781452	+	0.240506i
$709$	0.153219	+	0.111320i	0.00575426	+	0.00418071i	0.590659	−	0.806922i	$-0.298868\pi$
$709$	0.153219	+	0.111320i	0.00575426	+	0.00418071i	−0.584904	+	0.811102i	$0.698868\pi$
$710$	−37.4634	−	41.6073i	−1.40598	−	1.56149i
$711$	13.2454	−	22.9417i	0.496741	−	0.860381i
$712$	2.31475	+	7.12405i	0.0867488	+	0.266985i
$713$	3.21854	−	0.684123i	0.120535	−	0.0256206i
$714$	0.245185	+	2.33278i	0.00917583	+	0.0873022i
$715$	−0.545287	+	5.18806i	−0.0203926	+	0.194022i
$716$	7.82174	+	1.66256i	0.292312	+	0.0621329i
$717$	0.00309159	+	0.0294146i	0.000115458	+	0.00109851i
$718$	−2.81633	−	4.87803i	−0.105105	−	0.182046i
$719$	−5.10679	+	8.84522i	−0.190451	+	0.329871i	−0.945400	−	0.325913i	$-0.894328\pi$
$719$	−5.10679	+	8.84522i	−0.190451	+	0.329871i	0.754949	+	0.655784i	$0.227662\pi$
$720$	20.0483	+	8.92610i	0.747158	+	0.332656i
$721$	−57.4242			−2.13859
$722$	−8.25315	−	3.67454i	−0.307151	−	0.136752i
$723$	−19.5191	−	14.1815i	−0.725923	−	0.527414i
$724$	0.932217	−	0.677295i	0.0346456	−	0.0251715i
$725$	−4.24771	−	0.902878i	−0.157756	−	0.0335321i
$726$	−23.9869	+	10.6797i	−0.890238	+	0.396359i
$727$	−16.4875	+	7.34070i	−0.611487	+	0.272251i	−0.689024	−	0.724738i	$-0.741961\pi$
$727$	−16.4875	+	7.34070i	−0.611487	+	0.272251i	0.0775380	+	0.996989i	$0.475294\pi$
$728$	−0.129972	+	1.23660i	−0.00481707	+	0.0458313i
$729$	−7.50032	+	23.0836i	−0.277790	+	0.854948i
$730$	−21.0590	−	23.3884i	−0.779428	−	0.865642i
$731$	−0.385427			−0.0142555
$732$	−22.5555	+	6.79403i	−0.833674	+	0.251114i
$733$	−42.1644			−1.55738			−0.778688	−	0.627411i	$-0.784115\pi$
$733$	−42.1644			−1.55738			−0.778688	+	0.627411i	$0.784115\pi$
$734$	11.0087	+	12.2264i	0.406338	+	0.451284i
$735$	−25.1785	+	77.4915i	−0.928723	+	2.85832i
$736$	−0.328876	+	3.12905i	−0.0121225	+	0.115338i
$737$	−21.5733	+	9.60505i	−0.794662	+	0.353807i
$738$	39.4665	−	17.5716i	1.45278	−	0.646821i
$739$	24.2322	+	5.15072i	0.891396	+	0.189472i	0.630772	−	0.775968i	$-0.282738\pi$
$739$	24.2322	+	5.15072i	0.891396	+	0.189472i	0.260624	+	0.965440i	$0.416072\pi$
$740$	9.60854	−	6.98101i	0.353217	−	0.256627i
$741$	−2.51485	−	1.82714i	−0.0923853	−	0.0671218i
$742$	32.0125	+	14.2529i	1.17522	+	0.523241i
$743$	21.3633			0.783743			0.391871	−	0.920020i	$-0.371828\pi$
$743$	21.3633			0.783743			0.391871	+	0.920020i	$0.371828\pi$
$744$	2.88159	+	1.28297i	0.105644	+	0.0470359i
$745$	−31.8861	+	55.2284i	−1.16822	+	2.02341i
$746$	1.40903	+	2.44052i	0.0515884	+	0.0893537i
$747$	−8.49537	−	80.8281i	−0.310830	−	2.95735i
$748$	−0.886651	−	0.188463i	−0.0324192	−	0.00689091i
$749$	2.52738	−	24.0464i	0.0923484	−	0.878636i
$750$	3.35500	+	31.9207i	0.122507	+	1.16558i
$751$	35.7817	−	7.60563i	1.30569	−	0.277533i	0.498020	−	0.867165i	$-0.334060\pi$
$751$	35.7817	−	7.60563i	1.30569	−	0.277533i	0.807672	+	0.589632i	$0.200727\pi$
$752$	4.00457	+	12.3248i	0.146031	+	0.449439i
$753$	38.9358	−	67.4388i	1.41890	−	2.45761i
$754$	0.119233	+	0.132421i	0.00434219	+	0.00482250i
$755$	41.4177	+	30.0917i	1.50735	+	1.09515i
$756$	−10.9928	−	33.8324i	−0.399805	−	1.23047i
$757$	−2.67007	+	2.96541i	−0.0970453	+	0.107780i	−0.789711	−	0.613479i	$-0.789769\pi$
$757$	−2.67007	+	2.96541i	−0.0970453	+	0.107780i	0.692666	+	0.721259i	$0.256436\pi$
$758$	33.9432	−	7.21484i	1.23287	−	0.262055i
$759$	34.0797	−	24.7604i	1.23702	−	0.898744i
$760$	−3.51141	+	10.8070i	−0.127372	+	0.392011i
$761$	5.78738	+	10.0240i	0.209792	+	0.363371i	0.951649	−	0.307187i	$-0.0993879\pi$
$761$	5.78738	+	10.0240i	0.209792	+	0.363371i	−0.741857	+	0.670559i	$0.766055\pi$
$762$	−0.549695	+	0.610498i	−0.0199133	+	0.0221160i
$763$	25.3413	−	28.1444i	0.917417	−	1.01889i
$764$	−10.2261	−	17.7121i	−0.369966	−	0.640800i
$765$	1.38479	−	4.26195i	0.0500672	−	0.154091i
$766$	11.1149	−	8.07548i	0.401599	−	0.291779i
$767$	0.712440	−	0.151434i	0.0257247	−	0.00546795i
$768$	−2.01816	+	2.24140i	−0.0728242	+	0.0808795i
$769$	15.7340	+	48.4243i	0.567383	+	1.74623i	0.660763	+	0.750595i	$0.270233\pi$
$769$	15.7340	+	48.4243i	0.567383	+	1.74623i	−0.0933794	+	0.995631i	$0.529767\pi$
$770$	−49.2330	−	35.7699i	−1.77423	−	1.28906i
$771$	−20.5890	−	22.8664i	−0.741496	−	0.823514i
$772$	−1.14472	+	1.98271i	−0.0411992	+	0.0713592i
$773$	9.13815	+	28.1243i	0.328676	+	1.01156i	0.969754	+	0.244086i	$0.0784878\pi$
$773$	9.13815	+	28.1243i	0.328676	+	1.01156i	−0.641077	+	0.767476i	$0.721512\pi$
$774$	11.2564	−	2.39262i	0.404602	−	0.0860009i
$775$	0.869782	+	8.27542i	0.0312435	+	0.297262i
$776$	0.479610	−	4.56319i	0.0172170	−	0.163809i
$777$	−37.0739	−	7.88029i	−1.33002	−	0.282704i
$778$	−1.35501	−	12.8920i	−0.0485794	−	0.462202i
$779$	11.1846	+	19.3722i	0.400729	+	0.694083i
$780$	1.77219	−	3.06953i	0.0634547	−	0.109907i
$781$	−63.0781	−	28.0842i	−2.25711	−	1.00493i
$782$	0.642468			0.0229746
$783$	−4.65723	−	2.07353i	−0.166436	−	0.0741020i
$784$	−6.07179	−	4.41142i	−0.216850	−	0.157551i
$785$	18.9565	−	13.7727i	0.676586	−	0.491569i
$786$	−7.52768	−	1.60006i	−0.268504	−	0.0570722i
$787$	12.7878	−	5.69350i	0.455836	−	0.202951i	−0.165957	−	0.986133i	$-0.553071\pi$
$787$	12.7878	−	5.69350i	0.455836	−	0.202951i	0.621793	+	0.783182i	$0.286405\pi$
$788$	0.808972	−	0.360178i	0.0288185	−	0.0128308i
$789$	−7.03990	+	66.9801i	−0.250627	+	2.38456i
$790$	−4.83297	+	14.8744i	−0.171949	+	0.529206i
$791$	−46.1764	−	51.2841i	−1.64184	−	1.82345i
$792$	27.0645			0.961696
$793$	0.476182	+	2.50501i	0.0169097	+	0.0889555i
$794$	17.6353			0.625855
$795$	−66.8387	−	74.2319i	−2.37053	−	2.63274i
$796$	−5.31746	+	16.3655i	−0.188472	+	0.580058i
$797$	0.981613	−	9.33943i	0.0347705	−	0.330819i	−0.963285	−	0.268482i	$-0.913478\pi$
$797$	0.981613	−	9.33943i	0.0347705	−	0.330819i	0.998055	−	0.0623372i	$-0.0198554\pi$
$798$	33.1278	−	14.7495i	1.17271	−	0.522125i
$799$	2.41744	−	1.07632i	0.0855231	−	0.0380773i
$800$	−7.78257	−	1.65424i	−0.275156	−	0.0584861i
$801$	−36.9474	+	26.8439i	−1.30547	+	0.948482i
$802$	−30.6641	−	22.2788i	−1.08279	−	0.786691i
$803$	−35.4575	−	15.7867i	−1.25127	−	0.557101i
$804$	16.0449			0.565860
$805$	39.4033	+	17.5435i	1.38878	+	0.618326i
$806$	0.170718	−	0.295692i	0.00601329	−	0.0104153i
$807$	18.2521	+	31.6135i	0.642503	+	1.11285i
$808$	−0.443796	−	4.22244i	−0.0156127	−	0.148545i
$809$	−39.2657	−	8.34618i	−1.38051	−	0.293436i	−0.542942	−	0.839770i	$-0.682690\pi$
$809$	−39.2657	−	8.34618i	−1.38051	−	0.293436i	−0.837567	+	0.546334i	$0.816023\pi$
$810$	−3.71775	+	35.3720i	−0.130628	+	1.24285i
$811$	−1.07831	−	10.2594i	−0.0378645	−	0.360257i	−0.997006	−	0.0773287i	$-0.975361\pi$
$811$	−1.07831	−	10.2594i	−0.0378645	−	0.360257i	0.959141	−	0.282928i	$-0.0913058\pi$
$812$	−2.03328	+	0.432187i	−0.0713541	+	0.0151668i
$813$	−25.3012	−	77.8692i	−0.887353	−	2.73099i
$814$	7.32355	−	12.6848i	0.256690	−	0.444601i
$815$	−26.4276	−	29.3508i	−0.925719	−	1.02812i
$816$	0.498261	+	0.362008i	0.0174426	+	0.0126728i
$817$	1.84131	+	5.66697i	0.0644193	+	0.198262i
$818$	19.7595	−	21.9452i	0.690876	−	0.767296i
$819$	−7.41521	+	1.57615i	−0.259109	+	0.0550752i
$820$	−20.6345	+	14.9918i	−0.720588	+	0.523537i
$821$	−15.5626	+	47.8967i	−0.543138	+	1.67161i	0.182239	+	0.983254i	$0.441665\pi$
$821$	−15.5626	+	47.8967i	−0.543138	+	1.67161i	−0.725377	+	0.688352i	$0.758335\pi$
$822$	−4.30461	−	7.45580i	−0.150141	−	0.260051i
$823$	22.3505	−	24.8227i	0.779088	−	0.865265i	−0.214685	−	0.976683i	$-0.568873\pi$
$823$	22.3505	−	24.8227i	0.779088	−	0.865265i	0.993774	+	0.111418i	$0.0355393\pi$
$824$	−10.0889	+	11.2049i	−0.351464	+	0.390340i
$825$	53.2634	+	92.2550i	1.85439	+	3.21191i
$826$	−2.62564	+	8.08088i	−0.0913576	+	0.281170i
$827$	−20.6306	+	14.9890i	−0.717395	+	0.521218i	−0.885551	−	0.464543i	$-0.846219\pi$
$827$	−20.6306	+	14.9890i	−0.717395	+	0.521218i	0.168156	+	0.985760i	$0.446219\pi$
$828$	−18.7632	+	3.98825i	−0.652068	+	0.138601i
$829$	−11.2130	+	12.4533i	−0.389443	+	0.432520i	−0.905704	−	0.423911i	$-0.860657\pi$
$829$	−11.2130	+	12.4533i	−0.389443	+	0.432520i	0.516261	+	0.856431i	$0.327324\pi$
$830$	14.8275	+	45.6343i	0.514670	+	1.58399i
$831$	16.0824	+	11.6845i	0.557891	+	0.405331i
$832$	0.218456	+	0.242620i	0.00757359	+	0.00841132i
$833$	−0.766271	+	1.32722i	−0.0265497	+	0.0459855i
$834$	13.8218	+	42.5392i	0.478611	+	1.47301i
$835$	10.9487	−	2.32723i	0.378897	−	0.0805370i
$836$	1.46482	+	13.9369i	0.0506620	+	0.482017i
$837$	−1.02107	+	9.71488i	−0.0352935	+	0.335795i
$838$	24.3194	+	5.16925i	0.840099	+	0.178569i
$839$	2.56357	+	24.3907i	0.0885041	+	0.842061i	0.945256	+	0.326331i	$0.105812\pi$
$839$	2.56357	+	24.3907i	0.0885041	+	0.842061i	−0.856751	+	0.515730i	$0.827521\pi$
$840$	20.6738	+	35.8080i	0.713313	+	1.23549i
$841$	14.3511	−	24.8568i	0.494864	−	0.857129i
$842$	4.42481	+	1.97005i	0.152489	+	0.0678924i
$843$	52.1689			1.79679
$844$	−25.6495	−	11.4199i	−0.882892	−	0.393089i
$845$	37.5464	+	27.2791i	1.29164	+	0.938428i
$846$	−63.9199	+	46.4405i	−2.19761	+	1.59666i
$847$	−32.4313	−	6.89348i	−1.11435	−	0.236863i
$848$	8.40541	−	3.74233i	0.288643	−	0.128512i
$849$	22.7670	−	10.1365i	0.781360	−	0.347884i
$850$	−0.169827	+	1.61580i	−0.00582502	+	0.0554213i
$851$	−3.20802	+	9.87327i	−0.109970	+	0.338451i
$852$	31.3913	+	34.8636i	1.07545	+	1.19441i
$853$	−19.4841			−0.667124			−0.333562	−	0.942728i	$-0.608251\pi$
$853$	−19.4841			−0.667124			−0.333562	+	0.942728i	$0.608251\pi$
$854$	−28.0849	−	9.80053i	−0.961047	−	0.335367i
$855$	−69.2795			−2.36931
$856$	−4.24801	−	4.71789i	−0.145194	−	0.161254i
$857$	14.4527	−	44.4809i	0.493696	−	1.51944i	−0.325283	−	0.945617i	$-0.605460\pi$
$857$	14.4527	−	44.4809i	0.493696	−	1.51944i	0.818979	−	0.573823i	$-0.194540\pi$
$858$	0.456907	−	4.34718i	0.0155985	−	0.148410i
$859$	−47.7151	+	21.2441i	−1.62802	+	0.724840i	−0.998634	−	0.0522553i	$-0.983359\pi$
$859$	−47.7151	+	21.2441i	−1.62802	+	0.724840i	−0.629383	+	0.777095i	$0.716692\pi$
$860$	−6.20671	+	2.76341i	−0.211647	+	0.0942314i
$861$	79.6167	+	16.9231i	2.71333	+	0.576736i
$862$	17.3418	−	12.5996i	0.590665	−	0.429143i
$863$	−41.4632	−	30.1248i	−1.41142	−	1.02546i	−0.993114	−	0.117155i	$-0.962623\pi$
$863$	−41.4632	−	30.1248i	−1.41142	−	1.02546i	−0.418310	−	0.908304i	$-0.637377\pi$
$864$	−8.53289	−	3.79909i	−0.290295	−	0.129248i
$865$	53.6546			1.82431
$866$	16.8568	+	7.50511i	0.572816	+	0.255034i
$867$	−25.5740	+	44.2954i	−0.868537	+	1.50435i
$868$	1.99154	+	3.44944i	0.0675971	+	0.117082i
$869$	2.01613	+	19.1822i	0.0683925	+	0.650712i
$870$	5.79595	+	1.23197i	0.196501	+	0.0417676i
$871$	0.181543	−	1.72726i	0.00615134	−	0.0585261i
$872$	−1.03942	−	9.88943i	−0.0351992	−	0.334898i
$873$	27.3630	−	5.81619i	0.926098	−	0.196848i
$874$	−3.06928	−	9.44627i	−0.103820	−	0.319525i
$875$	−20.2648	+	35.0997i	−0.685076	+	1.18659i
$876$	17.6457	+	19.5976i	0.596195	+	0.662141i
$877$	6.66146	+	4.83983i	0.224941	+	0.163429i	0.694548	−	0.719446i	$-0.255604\pi$
$877$	6.66146	+	4.83983i	0.224941	+	0.163429i	−0.469607	+	0.882876i	$0.655604\pi$
$878$	6.99951	+	21.5423i	0.236222	+	0.727017i
$879$	15.3983	−	17.1015i	0.519371	−	0.576820i
$880$	−15.6294	+	3.32213i	−0.526867	+	0.111989i
$881$	20.2468	−	14.7102i	0.682133	−	0.495599i	−0.191931	−	0.981408i	$-0.561475\pi$
$881$	20.2468	−	14.7102i	0.682133	−	0.495599i	0.874065	+	0.485809i	$0.161475\pi$
$882$	14.1399	−	43.5182i	0.476116	−	1.46534i
$883$	−3.42884	−	5.93893i	−0.115390	−	0.199861i	0.802546	−	0.596591i	$-0.203478\pi$
$883$	−3.42884	−	5.93893i	−0.115390	−	0.199861i	−0.917935	+	0.396730i	$0.870145\pi$
$884$	0.0446084	−	0.0495427i	0.00150034	−	0.00166630i
$885$	16.2065	−	17.9992i	0.544777	−	0.605036i
$886$	−3.95724	−	6.85414i	−0.132946	−	0.230269i
$887$	−0.412736	+	1.27027i	−0.0138583	+	0.0426515i	−0.957747	−	0.287614i	$-0.907138\pi$
$887$	−0.412736	+	1.27027i	−0.0138583	+	0.0426515i	0.943888	+	0.330265i	$0.107138\pi$
$888$	−8.05119	+	5.84953i	−0.270180	+	0.196297i
$889$	−1.01468	+	0.215678i	−0.0340314	+	0.00723360i
$890$	18.0416	−	20.0372i	0.604755	−	0.671649i
$891$	13.5544	+	41.7161i	0.454089	+	1.39754i
$892$	2.01085	+	1.46097i	0.0673283	+	0.0489169i
$893$	−27.3741	−	30.4020i	−0.916040	−	1.01737i
$894$	26.7180	−	46.2770i	0.893585	−	1.54773i
$895$	−8.89456	−	27.3746i	−0.297312	−	0.915033i
$896$	−3.72534	+	0.791845i	−0.124455	+	0.0264537i
$897$	0.323840	+	3.08113i	0.0108127	+	0.102876i
$898$	2.59659	−	24.7049i	0.0866494	−	0.824414i
$899$	0.558333	+	0.118677i	0.0186214	+	0.00395811i
$900$	−5.07060	−	48.2435i	−0.169020	−	1.60812i
$901$	−0.939404	−	1.62710i	−0.0312961	−	0.0542064i
$902$	−15.7274	+	27.2407i	−0.523666	+	0.907017i
$903$	19.8073	+	8.81878i	0.659146	+	0.293471i
$904$	−18.1196			−0.602648
$905$	−3.78907	−	1.68700i	−0.125953	−	0.0560778i
$906$	−34.7048	−	25.2145i	−1.15299	−	0.837695i
$907$	−11.4060	+	8.28693i	−0.378729	+	0.275163i	−0.760821	−	0.648961i	$-0.775204\pi$
$907$	−11.4060	+	8.28693i	−0.378729	+	0.275163i	0.382092	+	0.924124i	$0.375204\pi$
$908$	10.6523	+	2.26422i	0.353510	+	0.0751408i
$909$	23.6475	−	10.5285i	0.784337	−	0.349209i
$910$	4.08871	−	1.82041i	0.135540	−	0.0603461i
$911$	1.15313	−	10.9713i	0.0382050	−	0.363497i	−0.958671	−	0.284516i	$-0.908167\pi$
$911$	1.15313	−	10.9713i	0.0382050	−	0.363497i	0.996876	−	0.0789801i	$-0.0251664\pi$
$912$	2.94228	−	9.05541i	0.0974286	−	0.299854i
$913$	39.5957	+	43.9755i	1.31043	+	1.45538i
$914$	24.6056			0.813880
$915$	61.7730	+	58.0838i	2.04215	+	1.92019i
$916$	20.9925			0.693611
$917$	−6.50255	−	7.22181i	−0.214733	−	0.238485i
$918$	−0.589389	+	1.81395i	−0.0194527	+	0.0598693i
$919$	−0.362116	+	3.44530i	−0.0119451	+	0.113650i	−0.998870	−	0.0475327i	$-0.984864\pi$
$919$	−0.362116	+	3.44530i	−0.0119451	+	0.113650i	0.986925	+	0.161183i	$0.0515308\pi$
$920$	10.3460	−	4.60632i	0.341096	−	0.151866i
$921$	−63.8981	+	28.4493i	−2.10552	+	0.937436i
$922$	20.3285	+	4.32096i	0.669485	+	0.142303i
$923$	4.10831	−	2.98486i	0.135227	−	0.0982480i
$924$	41.2533	+	29.9723i	1.35714	+	0.986016i
$925$	−23.9831	−	10.6780i	−0.788560	−	0.351090i
$926$	−28.0127			−0.920553
$927$	−83.9787	−	37.3897i	−2.75822	−	1.22804i
$928$	−0.272899	+	0.472674i	−0.00895834	+	0.0155163i
$929$	−12.7824	−	22.1398i	−0.419378	−	0.726384i	0.576499	−	0.817098i	$-0.304418\pi$
$929$	−12.7824	−	22.1398i	−0.419378	−	0.726384i	−0.995877	+	0.0907139i	$0.971085\pi$
$930$	−1.18681	−	11.2917i	−0.0389169	−	0.370270i
$931$	23.1750	+	4.92600i	0.759530	+	0.161443i
$932$	1.92860	−	18.3494i	0.0631734	−	0.601055i
$933$	−2.66766	−	25.3811i	−0.0873354	−	0.830941i
$934$	−35.8233	+	7.61449i	−1.17218	+	0.249154i
$935$	1.00826	+	3.10311i	0.0329737	+	0.101483i
$936$	−0.995241	+	1.72381i	−0.0325305	+	0.0563444i
$937$	−14.7500	−	16.3816i	−0.481862	−	0.535162i	0.452369	−	0.891831i	$-0.350579\pi$
$937$	−14.7500	−	16.3816i	−0.481862	−	0.535162i	−0.934231	+	0.356669i	$0.883913\pi$
$938$	16.3912	+	11.9089i	0.535191	+	0.388839i
$939$	22.6788	+	69.7982i	0.740095	+	2.27778i
$940$	31.2124	−	34.6649i	1.01804	−	1.13064i
$941$	28.1005	−	5.97294i	0.916049	−	0.194712i	0.274315	−	0.961640i	$-0.411549\pi$
$941$	28.1005	−	5.97294i	0.916049	−	0.194712i	0.641734	+	0.766928i	$0.278216\pi$
$942$	−15.8840	+	11.5404i	−0.517530	+	0.376007i
$943$	6.88928	−	21.2030i	0.224346	−	0.690465i
$944$	1.11548	+	1.93207i	0.0363057	+	0.0628834i
$945$	−85.6803	+	95.1576i	−2.78718	+	3.09548i
$946$	−5.60653	+	6.22669i	−0.182284	+	0.202447i
$947$	−16.7411	−	28.9964i	−0.544012	−	0.942256i	−0.998668	−	0.0515892i	$-0.983571\pi$
$947$	−16.7411	−	28.9964i	−0.544012	−	0.942256i	0.454657	−	0.890667i	$-0.349762\pi$
$948$	4.04965	−	12.4635i	0.131526	−	0.404797i
$949$	2.30937	−	1.67786i	0.0749654	−	0.0544655i
$950$	24.5685	−	5.22220i	0.797109	−	0.169431i
$951$	−31.0330	+	34.4657i	−1.00631	+	1.11763i
$952$	0.240324	+	0.739641i	0.00778894	+	0.0239719i
$953$	−19.0788	−	13.8615i	−0.618022	−	0.449019i	0.234208	−	0.972186i	$-0.424750\pi$
$953$	−19.0788	−	13.8615i	−0.618022	−	0.449019i	−0.852230	+	0.523167i	$0.824750\pi$
$954$	37.5358	+	41.6877i	1.21527	+	1.34969i
$955$	−36.8088	+	63.7547i	−1.19110	+	2.06305i
$956$	0.00303029	+	0.00932629i	9.80067e−5	+	0.000301634i
$957$	7.14786	−	1.51933i	0.231058	−	0.0491128i
$958$	2.43712	+	23.1877i	0.0787398	+	0.749159i
$959$	1.13635	−	10.8117i	0.0366948	−	0.349128i
$960$	10.6192	+	2.25719i	0.342734	+	0.0728504i
$961$	3.12606	+	29.7424i	0.100840	+	0.959433i
$962$	0.538616	+	0.932911i	0.0173657	+	0.0300782i
$963$	19.3531	−	33.5205i	0.623644	−	1.08018i
$964$	−7.30780	−	3.25364i	−0.235368	−	0.104793i
$965$	8.24082			0.265281
$966$	−33.0168	−	14.7000i	−1.06230	−	0.472965i
$967$	6.33951	+	4.60592i	0.203865	+	0.148117i	0.685034	−	0.728512i	$-0.259788\pi$
$967$	6.33951	+	4.60592i	0.203865	+	0.148117i	−0.481169	+	0.876628i	$0.659788\pi$
$968$	−7.04298	+	5.11702i	−0.226370	+	0.164467i
$969$	−1.90178	−	0.404235i	−0.0610939	−	0.0129859i
$970$	−15.0878	+	6.71754i	−0.484441	+	0.215687i
$971$	34.3367	−	15.2877i	1.10192	−	0.490606i	0.226519	−	0.974007i	$-0.427265\pi$
$971$	34.3367	−	15.2877i	1.10192	−	0.490606i	0.875399	+	0.483401i	$0.160599\pi$
$972$	0.186162	−	1.77122i	0.00597116	−	0.0568118i
$973$	−17.4534	+	53.7162i	−0.559532	+	1.72206i
$974$	−13.2492	−	14.7147i	−0.424531	−	0.471489i
$975$	−7.83460			−0.250908
$976$	−6.84660	+	3.75820i	−0.219154	+	0.120297i
$977$	−28.2247			−0.902987			−0.451493	−	0.892274i	$-0.649109\pi$
$977$	−28.2247			−0.902987			−0.451493	+	0.892274i	$0.649109\pi$
$978$	22.1442	+	24.5937i	0.708095	+	0.786419i
$979$	10.2754	−	31.6244i	0.328403	−	1.01072i
$980$	−2.82382	+	26.8668i	−0.0902036	+	0.858230i
$981$	55.3851	−	24.6590i	1.76831	−	0.787302i
$982$	0.726925	−	0.323648i	0.0231971	−	0.0103280i
$983$	15.1102	+	3.21177i	0.481940	+	0.102439i	0.442474	−	0.896782i	$-0.354101\pi$
$983$	15.1102	+	3.21177i	0.481940	+	0.102439i	0.0394659	+	0.999221i	$0.487434\pi$
$984$	17.2901	−	12.5620i	0.551187	−	0.400461i
$985$	−2.57872	−	1.87355i	−0.0821648	−	0.0596962i
$986$	0.101816	+	0.0453313i	0.00324247	+	0.00144364i
$987$	−148.861			−4.73828
$988$	−0.941540	−	0.419201i	−0.0299544	−	0.0133365i
$989$	2.96932	−	5.14301i	0.0944188	−	0.163538i
$990$	−48.7095	−	84.3673i	−1.54809	−	2.68137i
$991$	3.60604	+	34.3092i	0.114550	+	1.08987i	0.889213	+	0.457493i	$0.151253\pi$
$991$	3.60604	+	34.3092i	0.114550	+	1.08987i	−0.774663	+	0.632374i	$0.782081\pi$
$992$	1.02297	+	0.217438i	0.0324792	+	0.00690367i
$993$	−3.88306	+	36.9449i	−0.123225	+	1.17241i
$994$	6.19226	+	58.9154i	0.196406	+	1.86868i
$995$	60.5856	−	12.8779i	1.92069	−	0.408256i
$996$	−12.4243	−	38.2379i	−0.393678	−	1.21161i
$997$	2.32261	−	4.02288i	0.0735578	−	0.127406i	−0.826900	−	0.562348i	$-0.809898\pi$
$997$	2.32261	−	4.02288i	0.0735578	−	0.127406i	0.900458	+	0.434943i	$0.143231\pi$
$998$	4.81708	+	5.34991i	0.152482	+	0.169348i
$999$	−24.9333	−	18.1151i	−0.788856	−	0.573137i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	122.2.i.b.83.1	yes	24
4.3	odd	2		976.2.bw.b.449.3		24
61.5	even	30		7442.2.a.u.1.1		12
61.25	even	15	inner	122.2.i.b.25.1	✓	24
61.56	even	15		7442.2.a.w.1.1		12
244.147	odd	30		976.2.bw.b.513.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
122.2.i.b.25.1	✓	24	61.25	even	15	inner
122.2.i.b.83.1	yes	24	1.1	even	1	trivial
976.2.bw.b.449.3		24	4.3	odd	2
976.2.bw.b.513.3		24	244.147	odd	30
7442.2.a.u.1.1		12	61.5	even	30
7442.2.a.w.1.1		12	61.56	even	15

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 122 = 2 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	122.i (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.669131 + 0.743145i) q^{2} +(-0.932026 + 2.86848i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(3.28831 - 1.46405i) q^{5} +(-2.75534 + 1.22676i) q^{6} +(-3.72534 - 0.791845i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-4.93246 - 3.58364i) q^{9} +O(q^{10})\)	\(q+(0.669131 + 0.743145i) q^{2} +(-0.932026 + 2.86848i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(3.28831 - 1.46405i) q^{5} +(-2.75534 + 1.22676i) q^{6} +(-3.72534 - 0.791845i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-4.93246 - 3.58364i) q^{9} +(3.28831 + 1.46405i) q^{10} +4.43910 q^{11} +(-2.75534 - 1.22676i) q^{12} +(-0.163238 + 0.282737i) q^{13} +(-1.90428 - 3.29831i) q^{14} +(1.13481 + 10.7970i) q^{15} +(-0.978148 - 0.207912i) q^{16} +(-0.0213446 + 0.203080i) q^{17} +(-0.637295 - 6.06345i) q^{18} +(3.08788 - 0.656349i) q^{19} +(1.11231 + 3.42333i) q^{20} +(5.74350 - 9.94803i) q^{21} +(2.97034 + 3.29889i) q^{22} +(-2.54540 - 1.84934i) q^{23} +(-0.932026 - 2.86848i) q^{24} +(5.32390 - 5.91279i) q^{25} +(-0.319343 + 0.0678784i) q^{26} +(7.55655 - 5.49016i) q^{27} +(1.17691 - 3.62216i) q^{28} +(-0.272899 - 0.472674i) q^{29} +(-7.26439 + 8.06793i) q^{30} +(-0.699790 + 0.777196i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.13735 + 12.7335i) q^{33} +(-0.165200 + 0.120025i) q^{34} +(-13.4094 + 2.85025i) q^{35} +(4.07959 - 4.53084i) q^{36} +(-1.01962 - 3.13807i) q^{37} +(2.55396 + 1.85556i) q^{38} +(-0.658884 - 0.731765i) q^{39} +(-1.79975 + 3.11726i) q^{40} +(2.18965 + 6.73906i) q^{41} +(11.2360 - 2.38828i) q^{42} +(0.197298 + 1.87717i) q^{43} +(-0.464012 + 4.41478i) q^{44} +(-21.4661 - 4.56276i) q^{45} +(-0.328876 - 3.12905i) q^{46} +(-6.47952 - 11.2229i) q^{47} +(1.50805 - 2.61202i) q^{48} +(6.85629 + 3.05262i) q^{49} +7.95644 q^{50} +(-0.562638 - 0.250503i) q^{51} +(-0.264125 - 0.191898i) q^{52} +(-7.44366 + 5.40814i) q^{53} +(9.13630 + 1.94198i) q^{54} +(14.5971 - 6.49907i) q^{55} +(3.47929 - 1.54908i) q^{56} +(-0.995259 + 9.46926i) q^{57} +(0.168661 - 0.519084i) q^{58} +(-1.49280 - 1.65792i) q^{59} -10.8565 q^{60} +(5.91561 - 5.09956i) q^{61} -1.04582 q^{62} +(15.5374 + 17.2560i) q^{63} +(0.309017 - 0.951057i) q^{64} +(-0.122837 + 1.16872i) q^{65} +(-12.2312 + 5.44570i) q^{66} +(-4.85984 + 2.16374i) q^{67} +(-0.199737 - 0.0424553i) q^{68} +(7.67717 - 5.57779i) q^{69} +(-11.0908 - 8.05791i) q^{70} +(-14.2097 - 6.32655i) q^{71} +6.09685 q^{72} +(-7.98755 - 3.55629i) q^{73} +(1.64978 - 2.85751i) q^{74} +(11.9987 + 20.7824i) q^{75} +(0.329982 + 3.13957i) q^{76} +(-16.5371 - 3.51508i) q^{77} +(0.102928 - 0.979293i) q^{78} +(0.454176 + 4.32119i) q^{79} +(-3.52085 + 0.748379i) q^{80} +(3.05341 + 9.39743i) q^{81} +(-3.54293 + 6.13654i) q^{82} +(8.91976 + 9.90640i) q^{83} +(9.29318 + 6.75189i) q^{84} +(0.227132 + 0.699041i) q^{85} +(-1.26299 + 1.40269i) q^{86} +(1.61021 - 0.342260i) q^{87} +(-3.59131 + 2.60924i) q^{88} +(2.31475 - 7.12405i) q^{89} +(-10.9728 - 19.0055i) q^{90} +(0.832002 - 0.924032i) q^{91} +(2.10528 - 2.33815i) q^{92} +(-1.57715 - 2.73170i) q^{93} +(4.00457 - 12.3248i) q^{94} +(9.19299 - 6.67909i) q^{95} +(2.95019 - 0.627082i) q^{96} +(-3.07019 + 3.40979i) q^{97} +(2.31922 + 7.13782i) q^{98} +(-21.8957 - 15.9081i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 12 q^{5} - q^{6} - 4 q^{7} - 6 q^{8} - 19 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 12 * q^5 - q^6 - 4 * q^7 - 6 * q^8 - 19 * q^9	\( 24 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 12 q^{5} - q^{6} - 4 q^{7} - 6 q^{8} - 19 q^{9} - 12 q^{10} + 6 q^{11} - q^{12} + 5 q^{13} - 4 q^{14} - 9 q^{15} + 3 q^{16} + 16 q^{17} + 17 q^{18} - 2 q^{19} - q^{20} + 10 q^{21} + 7 q^{22} + q^{23} - 3 q^{24} + 11 q^{25} - 9 q^{27} - 7 q^{28} + 2 q^{29} - 4 q^{30} + 14 q^{31} - 12 q^{32} + 7 q^{33} - 17 q^{34} + 9 q^{35} + 2 q^{36} - 38 q^{37} + 4 q^{38} - 40 q^{39} - 7 q^{40} - 10 q^{41} + 15 q^{42} - 5 q^{43} + 2 q^{44} - 96 q^{45} - 8 q^{46} + 3 q^{47} - q^{48} + 19 q^{49} + 38 q^{50} + 102 q^{51} + 20 q^{52} - 37 q^{53} + 17 q^{54} + 33 q^{55} + 6 q^{56} - 71 q^{57} + q^{58} - 17 q^{59} - 22 q^{60} + 70 q^{61} + 72 q^{62} + 146 q^{63} - 6 q^{64} + 2 q^{65} - 86 q^{66} - 4 q^{67} + q^{68} - 2 q^{69} - 28 q^{70} - 76 q^{71} + 46 q^{72} + 84 q^{73} + 19 q^{74} + 9 q^{75} - 2 q^{76} - 10 q^{77} - 5 q^{78} - 56 q^{79} - 7 q^{80} + 59 q^{81} - 20 q^{82} - 9 q^{83} + 25 q^{84} - 37 q^{85} - 65 q^{86} - 25 q^{87} - 4 q^{88} - 45 q^{89} - 31 q^{90} + 2 q^{91} + 7 q^{92} - 47 q^{93} + 24 q^{94} - 39 q^{95} + 9 q^{96} + 6 q^{97} + 7 q^{98} - 24 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 12 * q^5 - q^6 - 4 * q^7 - 6 * q^8 - 19 * q^9 - 12 * q^10 + 6 * q^11 - q^12 + 5 * q^13 - 4 * q^14 - 9 * q^15 + 3 * q^16 + 16 * q^17 + 17 * q^18 - 2 * q^19 - q^20 + 10 * q^21 + 7 * q^22 + q^23 - 3 * q^24 + 11 * q^25 - 9 * q^27 - 7 * q^28 + 2 * q^29 - 4 * q^30 + 14 * q^31 - 12 * q^32 + 7 * q^33 - 17 * q^34 + 9 * q^35 + 2 * q^36 - 38 * q^37 + 4 * q^38 - 40 * q^39 - 7 * q^40 - 10 * q^41 + 15 * q^42 - 5 * q^43 + 2 * q^44 - 96 * q^45 - 8 * q^46 + 3 * q^47 - q^48 + 19 * q^49 + 38 * q^50 + 102 * q^51 + 20 * q^52 - 37 * q^53 + 17 * q^54 + 33 * q^55 + 6 * q^56 - 71 * q^57 + q^58 - 17 * q^59 - 22 * q^60 + 70 * q^61 + 72 * q^62 + 146 * q^63 - 6 * q^64 + 2 * q^65 - 86 * q^66 - 4 * q^67 + q^68 - 2 * q^69 - 28 * q^70 - 76 * q^71 + 46 * q^72 + 84 * q^73 + 19 * q^74 + 9 * q^75 - 2 * q^76 - 10 * q^77 - 5 * q^78 - 56 * q^79 - 7 * q^80 + 59 * q^81 - 20 * q^82 - 9 * q^83 + 25 * q^84 - 37 * q^85 - 65 * q^86 - 25 * q^87 - 4 * q^88 - 45 * q^89 - 31 * q^90 + 2 * q^91 + 7 * q^92 - 47 * q^93 + 24 * q^94 - 39 * q^95 + 9 * q^96 + 6 * q^97 + 7 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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