LMFDB - Embedded newform 225.2.q.a.106.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			106.9
Character	$\chi$	$=$	225.106
Dual form			225.2.q.a.121.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16617 - 0.247876i) q^{2} +(-1.18208 + 1.26597i) q^{3} +(-0.528590 - 0.235343i) q^{4} +(0.918757 + 2.03860i) q^{5} +(1.69231 - 1.18332i) q^{6} +(0.157578 - 0.272934i) q^{7} +(2.48714 + 1.80701i) q^{8} +(-0.205352 - 2.99296i) q^{9} +O(q^{10})$	\(q+(-1.16617 - 0.247876i) q^{2} +(-1.18208 + 1.26597i) q^{3} +(-0.528590 - 0.235343i) q^{4} +(0.918757 + 2.03860i) q^{5} +(1.69231 - 1.18332i) q^{6} +(0.157578 - 0.272934i) q^{7} +(2.48714 + 1.80701i) q^{8} +(-0.205352 - 2.99296i) q^{9} +(-0.566103 - 2.60508i) q^{10} +(-2.82788 - 0.601085i) q^{11} +(0.922776 - 0.390983i) q^{12} +(-6.38538 + 1.35725i) q^{13} +(-0.251417 + 0.279226i) q^{14} +(-3.66685 - 1.24668i) q^{15} +(-1.67816 - 1.86379i) q^{16} +(0.794350 + 0.577129i) q^{17} +(-0.502410 + 3.54119i) q^{18} +(-5.88399 - 4.27497i) q^{19} +(-0.00587474 - 1.29381i) q^{20} +(0.159255 + 0.522120i) q^{21} +(3.14879 + 1.40193i) q^{22} +(-0.876336 + 0.973270i) q^{23} +(-5.22763 + 1.01260i) q^{24} +(-3.31177 + 3.74595i) q^{25} +7.78284 q^{26} +(4.03174 + 3.27797i) q^{27} +(-0.147528 + 0.107185i) q^{28} +(0.450873 + 4.28977i) q^{29} +(3.96713 + 2.36276i) q^{30} +(0.905916 - 8.61921i) q^{31} +(-1.57924 - 2.73533i) q^{32} +(4.10375 - 2.86948i) q^{33} +(-0.783287 - 0.869928i) q^{34} +(0.701179 + 0.0704794i) q^{35} +(-0.595827 + 1.63038i) q^{36} +(0.00738727 - 0.0227357i) q^{37} +(5.80205 + 6.44383i) q^{38} +(5.82981 - 9.68807i) q^{39} +(-1.39870 + 6.73048i) q^{40} +(-4.48136 + 0.952542i) q^{41} +(-0.0562962 - 0.648355i) q^{42} +(-1.34599 + 2.33132i) q^{43} +(1.35333 + 0.983252i) q^{44} +(5.91278 - 3.16844i) q^{45} +(1.26320 - 0.917772i) q^{46} +(0.544941 + 5.18477i) q^{47} +(4.34323 + 0.0786545i) q^{48} +(3.45034 + 5.97616i) q^{49} +(4.79061 - 3.54749i) q^{50} +(-1.66962 + 0.323407i) q^{51} +(3.69467 + 0.785326i) q^{52} +(-3.44104 + 2.50006i) q^{53} +(-3.88915 - 4.82203i) q^{54} +(-1.37277 - 6.31717i) q^{55} +(0.885114 - 0.394078i) q^{56} +(12.3674 - 2.39557i) q^{57} +(0.537539 - 5.11434i) q^{58} +(-5.06713 + 1.07705i) q^{59} +(1.64486 + 1.52195i) q^{60} +(7.24968 + 1.54097i) q^{61} +(-3.19295 + 9.82688i) q^{62} +(-0.849240 - 0.415579i) q^{63} +(2.71365 + 8.35176i) q^{64} +(-8.63350 - 11.7702i) q^{65} +(-5.49693 + 2.32907i) q^{66} +(0.260529 - 2.47877i) q^{67} +(-0.284062 - 0.492010i) q^{68} +(-0.196226 - 2.25990i) q^{69} +(-0.800221 - 0.255996i) q^{70} +(9.63629 - 7.00118i) q^{71} +(4.89758 - 7.81499i) q^{72} +(-0.283594 - 0.872814i) q^{73} +(-0.0142504 + 0.0246825i) q^{74} +(-0.827464 - 8.62063i) q^{75} +(2.10413 + 3.64447i) q^{76} +(-0.609670 + 0.677108i) q^{77} +(-9.19997 + 9.85283i) q^{78} +(1.18974 + 11.3196i) q^{79} +(2.25770 - 5.13348i) q^{80} +(-8.91566 + 1.22922i) q^{81} +5.46212 q^{82} +(-9.08283 + 4.04394i) q^{83} +(0.0386972 - 0.313467i) q^{84} +(-0.446720 + 2.14960i) q^{85} +(2.14753 - 2.38507i) q^{86} +(-5.96368 - 4.50007i) q^{87} +(-5.94717 - 6.60500i) q^{88} +(3.78718 + 11.6557i) q^{89} +(-7.68067 + 2.22928i) q^{90} +(-0.635757 + 1.95666i) q^{91} +(0.692276 - 0.308221i) q^{92} +(9.84078 + 11.3355i) q^{93} +(0.649689 - 6.18138i) q^{94} +(3.30899 - 15.9228i) q^{95} +(5.32964 + 1.23412i) q^{96} +(0.772754 + 7.35226i) q^{97} +(-2.54232 - 7.82445i) q^{98} +(-1.21831 + 8.58719i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−1.16617	−	0.247876i	−0.824604	−	0.175275i	−0.223763	−	0.974644i	$-0.571834\pi$
$2$	−1.16617	−	0.247876i	−0.824604	−	0.175275i	−0.600841	+	0.799369i	$0.705168\pi$
$3$	−1.18208	+	1.26597i	−0.682477	+	0.730907i
$3$	−1.18208	+	1.26597i	−0.682477	+	0.730907i
$4$	−0.528590	−	0.235343i	−0.264295	−	0.117672i
$5$	0.918757	+	2.03860i	0.410881	+	0.911689i
$5$	0.918757	+	2.03860i	0.410881	+	0.911689i
$6$	1.69231	−	1.18332i	0.690883	−	0.483088i
$7$	0.157578	−	0.272934i	0.0595591	−	0.103159i	−0.834708	−	0.550692i	$-0.814364\pi$
$7$	0.157578	−	0.272934i	0.0595591	−	0.103159i	0.894268	+	0.447533i	$0.147697\pi$
$8$	2.48714	+	1.80701i	0.879336	+	0.638875i
$9$	−0.205352	−	2.99296i	−0.0684508	−	0.997654i
$10$	−0.566103	−	2.60508i	−0.179017	−	0.823800i
$11$	−2.82788	−	0.601085i	−0.852639	−	0.181234i	−0.239195	−	0.970972i	$-0.576883\pi$
$11$	−2.82788	−	0.601085i	−0.852639	−	0.181234i	−0.613445	+	0.789738i	$0.710217\pi$
$12$	0.922776	−	0.390983i	0.266382	−	0.112867i
$13$	−6.38538	+	1.35725i	−1.77098	+	0.376434i	−0.973819	−	0.227326i	$-0.927002\pi$
$13$	−6.38538	+	1.35725i	−1.77098	+	0.376434i	−0.797166	+	0.603761i	$0.793668\pi$
$14$	−0.251417	+	0.279226i	−0.0671939	+	0.0746264i
$15$	−3.66685	−	1.24668i	−0.946777	−	0.321891i
$16$	−1.67816	−	1.86379i	−0.419541	−	0.465948i
$17$	0.794350	+	0.577129i	0.192658	+	0.139974i	0.679933	−	0.733274i	$-0.262009\pi$
$17$	0.794350	+	0.577129i	0.192658	+	0.139974i	−0.487275	+	0.873249i	$0.662009\pi$
$18$	−0.502410	+	3.54119i	−0.118419	+	0.834668i
$19$	−5.88399	−	4.27497i	−1.34988	−	0.980746i	−0.999017	−	0.0443190i	$-0.985888\pi$
$19$	−5.88399	−	4.27497i	−1.34988	−	0.980746i	−0.350863	−	0.936427i	$-0.614112\pi$
$20$	−0.00587474	−	1.29381i	−0.00131363	−	0.289304i
$21$	0.159255	+	0.522120i	0.0347522	+	0.113936i
$22$	3.14879	+	1.40193i	0.671324	+	0.298893i
$23$	−0.876336	+	0.973270i	−0.182729	+	0.202941i	−0.827549	−	0.561393i	$-0.810266\pi$
$23$	−0.876336	+	0.973270i	−0.182729	+	0.202941i	0.644820	+	0.764334i	$0.276932\pi$
$24$	−5.22763	+	1.01260i	−1.06709	+	0.206696i
$25$	−3.31177	+	3.74595i	−0.662354	+	0.749191i
$26$	7.78284			1.52634
$27$	4.03174	+	3.27797i	0.775909	+	0.630845i
$28$	−0.147528	+	0.107185i	−0.0278801	+	0.0202561i
$29$	0.450873	+	4.28977i	0.0837249	+	0.796589i	0.953145	+	0.302515i	$0.0978263\pi$
$29$	0.450873	+	4.28977i	0.0837249	+	0.796589i	−0.869420	+	0.494074i	$0.835507\pi$
$30$	3.96713	+	2.36276i	0.724296	+	0.431379i
$31$	0.905916	−	8.61921i	0.162707	−	1.54806i	−0.543110	−	0.839662i	$-0.682753\pi$
$31$	0.905916	−	8.61921i	0.162707	−	1.54806i	0.705817	−	0.708394i	$-0.250580\pi$
$32$	−1.57924	−	2.73533i	−0.279173	−	0.483542i
$33$	4.10375	−	2.86948i	0.714372	−	0.499512i
$34$	−0.783287	−	0.869928i	−0.134333	−	0.149191i
$35$	0.701179	+	0.0704794i	0.118521	+	0.0119132i
$36$	−0.595827	+	1.63038i	−0.0993045	+	0.271730i
$37$	0.00738727	−	0.0227357i	0.00121446	−	0.00373772i	−0.950447	−	0.310885i	$-0.899375\pi$
$37$	0.00738727	−	0.0227357i	0.00121446	−	0.00373772i	0.951662	+	0.307148i	$0.0993745\pi$
$38$	5.80205	+	6.44383i	0.941217	+	1.04533i
$39$	5.82981	−	9.68807i	0.933517	−	1.55133i
$40$	−1.39870	+	6.73048i	−0.221153	+	1.06418i
$41$	−4.48136	+	0.952542i	−0.699871	+	0.148762i	−0.544087	−	0.839029i	$-0.683124\pi$
$41$	−4.48136	+	0.952542i	−0.699871	+	0.148762i	−0.155784	+	0.987791i	$0.549790\pi$
$42$	−0.0562962	−	0.648355i	−0.00868669	−	0.100043i
$43$	−1.34599	+	2.33132i	−0.205261	+	0.355523i	−0.950216	−	0.311592i	$-0.899138\pi$
$43$	−1.34599	+	2.33132i	−0.205261	+	0.355523i	0.744955	+	0.667115i	$0.232471\pi$
$44$	1.35333	+	0.983252i	0.204022	+	0.148231i
$45$	5.91278	−	3.16844i	0.881426	−	0.472323i
$46$	1.26320	−	0.917772i	0.186249	−	0.135318i
$47$	0.544941	+	5.18477i	0.0794878	+	0.756276i	0.959573	+	0.281460i	$0.0908187\pi$
$47$	0.544941	+	5.18477i	0.0794878	+	0.756276i	−0.880085	+	0.474816i	$0.842515\pi$
$48$	4.34323	+	0.0786545i	0.626892	+	0.0113528i
$49$	3.45034	+	5.97616i	0.492905	+	0.853737i
$50$	4.79061	−	3.54749i	0.677494	−	0.501691i
$51$	−1.66962	+	0.323407i	−0.233793	+	0.0452860i
$52$	3.69467	+	0.785326i	0.512358	+	0.108905i
$53$	−3.44104	+	2.50006i	−0.472663	+	0.343410i	−0.798478	−	0.602024i	$-0.794361\pi$
$53$	−3.44104	+	2.50006i	−0.472663	+	0.343410i	0.325815	+	0.945433i	$0.394361\pi$
$54$	−3.88915	−	4.82203i	−0.529246	−	0.656195i
$55$	−1.37277	−	6.31717i	−0.185104	−	0.851808i
$56$	0.885114	−	0.394078i	0.118278	−	0.0526609i
$57$	12.3674	−	2.39557i	1.63810	−	0.317301i
$58$	0.537539	−	5.11434i	0.0705823	−	0.671546i
$59$	−5.06713	+	1.07705i	−0.659684	+	0.140220i	−0.525576	−	0.850747i	$-0.676150\pi$
$59$	−5.06713	+	1.07705i	−0.659684	+	0.140220i	−0.134108	+	0.990967i	$0.542817\pi$
$60$	1.64486	+	1.52195i	0.212351	+	0.196483i
$61$	7.24968	+	1.54097i	0.928226	+	0.197301i	0.647131	−	0.762379i	$-0.275969\pi$
$61$	7.24968	+	1.54097i	0.928226	+	0.197301i	0.281096	+	0.959680i	$0.409302\pi$
$62$	−3.19295	+	9.82688i	−0.405505	+	1.24801i
$63$	−0.849240	−	0.415579i	−0.106994	−	0.0523580i
$64$	2.71365	+	8.35176i	0.339207	+	1.04397i
$65$	−8.63350	−	11.7702i	−1.07085	−	1.45992i
$66$	−5.49693	+	2.32907i	−0.676626	+	0.286688i
$67$	0.260529	−	2.47877i	0.0318287	−	0.302830i	−0.967014	−	0.254725i	$-0.918015\pi$
$67$	0.260529	−	2.47877i	0.0318287	−	0.302830i	0.998842	−	0.0481052i	$-0.0153183\pi$
$68$	−0.284062	−	0.492010i	−0.0344476	−	0.0596649i
$69$	−0.196226	−	2.25990i	−0.0236228	−	0.272060i
$70$	−0.800221	−	0.255996i	−0.0956447	−	0.0305974i
$71$	9.63629	−	7.00118i	1.14362	−	0.830887i	0.155999	−	0.987757i	$-0.450140\pi$
$71$	9.63629	−	7.00118i	1.14362	−	0.830887i	0.987619	+	0.156870i	$0.0501405\pi$
$72$	4.89758	−	7.81499i	0.577185	−	0.921005i
$73$	−0.283594	−	0.872814i	−0.0331922	−	0.102155i	0.933088	−	0.359649i	$-0.117103\pi$
$73$	−0.283594	−	0.872814i	−0.0331922	−	0.102155i	−0.966280	+	0.257493i	$0.917103\pi$
$74$	−0.0142504	+	0.0246825i	−0.00165658	+	0.00286928i
$75$	−0.827464	−	8.62063i	−0.0955474	−	0.995425i
$76$	2.10413	+	3.64447i	0.241361	+	0.418049i
$77$	−0.609670	+	0.677108i	−0.0694784	+	0.0771636i
$78$	−9.19997	+	9.85283i	−1.04169	+	1.11561i
$79$	1.18974	+	11.3196i	0.133857	+	1.27356i	0.830856	+	0.556488i	$0.187851\pi$
$79$	1.18974	+	11.3196i	0.133857	+	1.27356i	−0.696999	+	0.717072i	$0.745482\pi$
$80$	2.25770	−	5.13348i	0.252418	−	0.573940i
$81$	−8.91566	+	1.22922i	−0.990629	+	0.136581i
$82$	5.46212			0.603191
$83$	−9.08283	+	4.04394i	−0.996970	+	0.443880i	−0.839333	−	0.543617i	$-0.817054\pi$
$83$	−9.08283	+	4.04394i	−0.996970	+	0.443880i	−0.157637	+	0.987497i	$0.550388\pi$
$84$	0.0386972	−	0.313467i	0.00422221	−	0.0342021i
$85$	−0.446720	+	2.14960i	−0.0484536	+	0.233157i
$86$	2.14753	−	2.38507i	0.231574	−	0.257189i
$87$	−5.96368	−	4.50007i	−0.639373	−	0.482459i
$88$	−5.94717	−	6.60500i	−0.633971	−	0.704096i
$89$	3.78718	+	11.6557i	0.401440	+	1.23551i	0.923831	+	0.382800i	$0.125040\pi$
$89$	3.78718	+	11.6557i	0.401440	+	1.23551i	−0.522391	+	0.852706i	$0.674960\pi$
$90$	−7.68067	+	2.22928i	−0.809614	+	0.234987i
$91$	−0.635757	+	1.95666i	−0.0666455	+	0.205114i
$92$	0.692276	−	0.308221i	0.0721747	−	0.0321343i
$93$	9.84078	+	11.3355i	1.02044	+	1.17544i
$94$	0.649689	−	6.18138i	0.0670103	−	0.637561i
$95$	3.30899	−	15.9228i	0.339496	−	1.63364i
$96$	5.32964	+	1.23412i	0.543954	+	0.125957i
$97$	0.772754	+	7.35226i	0.0784612	+	0.746509i	0.961052	+	0.276367i	$0.0891306\pi$
$97$	0.772754	+	7.35226i	0.0784612	+	0.746509i	−0.882591	+	0.470142i	$0.844203\pi$
$98$	−2.54232	−	7.82445i	−0.256813	−	0.790389i
$99$	−1.21831	+	8.58719i	−0.122445	+	0.863045i
$100$	2.63216	−	1.20067i	0.263216	−	0.120067i
$101$	−5.77262	+	9.99848i	−0.574397	+	0.994885i	0.421709	+	0.906731i	$0.361430\pi$
$101$	−5.77262	+	9.99848i	−0.574397	+	0.994885i	−0.996107	+	0.0881544i	$0.971903\pi$
$102$	2.02721	+	0.0367122i	0.200724	+	0.00363505i
$103$	−14.9529	−	6.65745i	−1.47335	−	0.655978i	−0.496139	−	0.868243i	$-0.665249\pi$
$103$	−14.9529	−	6.65745i	−1.47335	−	0.655978i	−0.977212	+	0.212265i	$0.931916\pi$
$104$	−18.3339	−	8.16277i	−1.79779	−	0.800426i
$105$	−0.918078	+	0.804358i	−0.0895952	+	0.0784973i
$106$	4.63253	−	2.06253i	0.449951	−	0.200331i
$107$	−10.1611			−0.982314			−0.491157	−	0.871071i	$-0.663426\pi$
$107$	−10.1611			−0.982314			−0.491157	+	0.871071i	$0.663426\pi$
$108$	−1.35969	−	2.68154i	−0.130836	−	0.258032i
$109$	3.42411	−	10.5383i	0.327970	−	1.00939i	−0.642112	−	0.766611i	$-0.721942\pi$
$109$	3.42411	−	10.5383i	0.327970	−	1.00939i	0.970082	−	0.242777i	$-0.0780584\pi$
$110$	0.0349956	+	7.70715i	0.00333670	+	0.734848i
$111$	0.0200503	+	0.0362276i	0.00190309	+	0.00343857i
$112$	−0.773134	+	0.164335i	−0.0730543	+	0.0155282i
$113$	14.3476	−	3.04967i	1.34970	−	0.286888i	0.524349	−	0.851503i	$-0.324309\pi$
$113$	14.3476	−	3.04967i	1.34970	−	0.286888i	0.825355	+	0.564615i	$0.190975\pi$
$114$	−15.0162	−	0.271938i	−1.40640	−	0.0254694i
$115$	−2.78925	−	0.892300i	−0.260099	−	0.0832074i
$116$	0.771242	−	2.37364i	0.0716080	−	0.220387i
$117$	5.37346	+	18.8325i	0.496777	+	1.74106i
$118$	6.17609			0.568555
$119$	0.282690	−	0.125862i	0.0259142	−	0.0115377i
$120$	−6.86720	−	9.72671i	−0.626887	−	0.887923i
$121$	−2.41337	−	1.07450i	−0.219397	−	0.0976820i
$122$	−8.07236	−	3.59405i	−0.730837	−	0.325390i
$123$	4.09146	−	6.79925i	0.368914	−	0.613067i
$124$	−2.50733	+	4.34283i	−0.225165	+	0.389998i
$125$	−10.6792	−	3.30976i	−0.955178	−	0.296034i
$126$	0.887343	+	0.695141i	0.0790508	+	0.0619281i
$127$	4.75644	+	14.6388i	0.422066	+	1.29899i	0.905776	+	0.423757i	$0.139289\pi$
$127$	4.75644	+	14.6388i	0.422066	+	1.29899i	−0.483710	+	0.875228i	$0.660711\pi$
$128$	−0.434062	−	4.12983i	−0.0383660	−	0.365029i
$129$	−1.36031	−	4.45980i	−0.119768	−	0.392663i
$130$	7.15054	+	15.8661i	0.627144	+	1.39155i
$131$	−0.348937	+	3.31991i	−0.0304868	+	0.290062i	0.968647	+	0.248442i	$0.0799186\pi$
$131$	−0.348937	+	3.31991i	−0.0304868	+	0.290062i	−0.999134	+	0.0416200i	$0.986748\pi$
$132$	−2.84452	+	0.550987i	−0.247583	+	0.0479572i
$133$	−2.09398	+	0.932298i	−0.181571	+	0.0808405i
$134$	−0.918249	+	2.82608i	−0.0793247	+	0.244136i
$135$	−2.97827	+	11.2308i	−0.256329	+	0.966590i
$136$	0.932779	+	2.87080i	0.0799851	+	0.246169i
$137$	−5.65113	−	6.27621i	−0.482808	−	0.536213i	0.451693	−	0.892174i	$-0.350820\pi$
$137$	−5.65113	−	6.27621i	−0.482808	−	0.536213i	−0.934501	+	0.355961i	$0.884154\pi$
$138$	−0.331344	+	2.68406i	−0.0282059	+	0.228482i
$139$	−0.957106	+	1.06297i	−0.0811807	+	0.0901603i	−0.782367	−	0.622818i	$-0.785988\pi$
$139$	−0.957106	+	1.06297i	−0.0811807	+	0.0901603i	0.701186	+	0.712978i	$0.252654\pi$
$140$	−0.354049	−	0.202273i	−0.0299226	−	0.0170952i
$141$	−7.20792	−	5.43896i	−0.607016	−	0.458043i
$142$	−12.9729	+	5.77593i	−1.08867	+	0.484705i
$143$	18.8729			1.57823
$144$	−5.23364	+	5.40542i	−0.436137	+	0.450452i
$145$	−8.33087	+	4.86040i	−0.691841	+	0.403634i
$146$	0.114368	+	1.08814i	0.00946519	+	0.0900553i
$147$	−11.6442	−	2.69631i	−0.960399	−	0.222388i
$148$	−0.00925554	+	0.0102793i	−0.000760800	+	0.000844954i
$149$	10.3534	+	17.9326i	0.848181	+	1.46909i	0.882830	+	0.469693i	$0.155635\pi$
$149$	10.3534	+	17.9326i	0.848181	+	1.46909i	−0.0346486	+	0.999400i	$0.511031\pi$
$150$	−1.17189	+	10.2582i	−0.0956844	+	0.837578i
$151$	10.6562	−	18.4570i	0.867186	−	1.50201i	0.00232675	−	0.999997i	$-0.499259\pi$
$151$	10.6562	−	18.4570i	0.867186	−	1.50201i	0.864860	−	0.502014i	$-0.167407\pi$
$152$	−6.90938	−	21.2649i	−0.560425	−	1.72481i
$153$	1.56420	−	2.49597i	0.126458	−	0.201788i
$154$	0.878816	−	0.638497i	0.0708170	−	0.0514516i
$155$	18.4034	−	6.07216i	1.47820	−	0.487728i
$156$	−5.36161	+	3.74901i	−0.429272	+	0.300161i
$157$	−6.98186	−	12.0929i	−0.557213	−	0.965122i	−0.997728	−	0.0673760i	$-0.978537\pi$
$157$	−6.98186	−	12.0929i	−0.557213	−	0.965122i	0.440514	−	0.897746i	$-0.354796\pi$
$158$	1.41843	−	13.4955i	0.112845	−	1.07364i
$159$	0.902600	−	7.31153i	0.0715808	−	0.579842i
$160$	4.12530	−	5.73254i	0.326133	−	0.453197i
$161$	0.127547	+	0.392548i	0.0100521	+	0.0309371i
$162$	10.7018	+	0.776501i	0.840816	+	0.0610077i
$163$	−0.190245	+	0.585515i	−0.0149012	+	0.0458611i	−0.958231	−	0.285997i	$-0.907675\pi$
$163$	−0.190245	+	0.585515i	−0.0149012	+	0.0458611i	0.943329	+	0.331858i	$0.107675\pi$
$164$	2.59298	+	0.551154i	0.202477	+	0.0430379i
$165$	9.62007	+	5.72956i	0.748921	+	0.446045i
$166$	11.5945	−	2.46448i	0.899907	−	0.191281i
$167$	0.564465	−	5.37053i	0.0436796	−	0.415584i	−0.950732	−	0.310013i	$-0.899666\pi$
$167$	0.564465	−	5.37053i	0.0436796	−	0.415584i	0.994412	−	0.105571i	$-0.0336669\pi$
$168$	−0.547389	+	1.58636i	−0.0422320	+	0.122390i
$169$	27.0548	−	12.0456i	2.08114	−	0.926582i
$170$	1.05378	−	2.39606i	0.0808216	−	0.183769i
$171$	−11.5865	+	18.4885i	−0.886045	+	1.41385i
$172$	1.26014	−	0.915544i	0.0960846	−	0.0698096i
$173$	0.355757	+	0.0756186i	0.0270477	+	0.00574917i	0.221416	−	0.975180i	$-0.428932\pi$
$173$	0.355757	+	0.0756186i	0.0270477	+	0.00574917i	−0.194368	+	0.980929i	$0.562266\pi$
$174$	5.83918	+	6.72609i	0.442667	+	0.509903i
$175$	0.500534	+	1.49418i	0.0378368	+	0.112949i
$176$	3.62536	+	6.27931i	0.273272	+	0.473321i
$177$	4.62626	−	7.68799i	0.347731	−	0.577865i
$178$	−1.52730	−	14.5313i	−0.114476	−	1.08917i
$179$	12.2855	−	8.92591i	0.918259	−	0.667154i	−0.0248313	−	0.999692i	$-0.507905\pi$
$179$	12.2855	−	8.92591i	0.918259	−	0.667154i	0.943090	+	0.332538i	$0.107905\pi$
$180$	−3.87111	+	0.283269i	−0.288535	+	0.0211136i
$181$	0.0462635	+	0.0336124i	0.00343874	+	0.00249839i	0.589503	−	0.807766i	$-0.299324\pi$
$181$	0.0462635	+	0.0336124i	0.00343874	+	0.00249839i	−0.586065	+	0.810264i	$0.699324\pi$
$182$	1.22641	−	2.12420i	0.0909074	−	0.157456i
$183$	−10.5205	+	7.35631i	−0.777701	+	0.543794i
$184$	−3.93828	+	0.837107i	−0.290334	+	0.0617124i
$185$	0.0531361	−	0.00582888i	0.00390664	−	0.000428548i
$186$	−8.66619	−	15.6584i	−0.635436	−	1.14813i
$187$	−1.89943	−	2.10953i	−0.138900	−	0.154264i
$188$	0.932151	−	2.86887i	0.0679841	−	0.209234i
$189$	1.52998	−	0.583862i	0.111290	−	0.0424697i
$190$	−7.80571	+	17.7484i	−0.566286	+	1.28760i
$191$	1.60360	+	1.78098i	0.116033	+	0.128867i	0.798363	−	0.602177i	$-0.205700\pi$
$191$	1.60360	+	1.78098i	0.116033	+	0.128867i	−0.682330	+	0.731044i	$0.739033\pi$
$192$	−13.7808	−	6.43709i	−0.994546	−	0.464557i
$193$	2.94773	+	5.10562i	0.212182	+	0.367511i	0.952397	−	0.304860i	$-0.0986095\pi$
$193$	2.94773	+	5.10562i	0.212182	+	0.367511i	−0.740215	+	0.672370i	$0.765276\pi$
$194$	0.921292	−	8.76550i	0.0661449	−	0.629326i
$195$	25.1063	+	2.98367i	1.79790	+	0.213665i
$196$	−0.417364	−	3.97095i	−0.0298117	−	0.283640i
$197$	−12.8434	+	9.33130i	−0.915057	+	0.664828i	−0.942289	−	0.334801i	$-0.891331\pi$
$197$	−12.8434	+	9.33130i	−0.915057	+	0.664828i	0.0272318	+	0.999629i	$0.491331\pi$
$198$	3.54932	−	9.71210i	0.252239	−	0.690209i
$199$	4.61006			0.326798			0.163399	−	0.986560i	$-0.447754\pi$
$199$	4.61006			0.326798			0.163399	+	0.986560i	$0.447754\pi$
$200$	−15.0058	+	3.33229i	−1.06107	+	0.235629i
$201$	2.83008	+	3.25994i	0.199618	+	0.229938i
$202$	9.21022	−	10.2290i	0.648029	−	0.719709i
$203$	1.24187	+	0.552916i	0.0871622	+	0.0388071i
$204$	0.958654	+	0.221984i	0.0671192	+	0.0155420i
$205$	−6.05913	−	8.26054i	−0.423188	−	0.576941i
$206$	15.7873	+	11.4702i	1.09995	+	0.799164i
$207$	3.09292	+	2.42298i	0.214973	+	0.168409i
$208$	13.2453	+	9.62331i	0.918400	+	0.667256i
$209$	14.0696	+	15.6259i	0.973217	+	1.08087i
$210$	1.27001	−	0.710445i	0.0876392	−	0.0490254i
$211$	0.0990841	−	0.110044i	0.00682123	−	0.00757575i	−0.739725	−	0.672910i	$-0.765044\pi$
$211$	0.0990841	−	0.110044i	0.00682123	−	0.00757575i	0.746546	+	0.665334i	$0.231711\pi$
$212$	2.40727	−	0.511681i	0.165332	−	0.0351424i
$213$	−2.52764	+	20.4752i	−0.173191	+	1.40294i
$214$	11.8496	+	2.51870i	0.810020	+	0.172175i
$215$	−5.98927	−	0.602015i	−0.408465	−	0.0410571i
$216$	4.10418	+	15.4382i	0.279254	+	1.05043i
$217$	−2.20972	−	1.60546i	−0.150006	−	0.108986i
$218$	−6.60528	+	11.4407i	−0.447366	+	0.774861i
$219$	1.44019	+	0.672718i	0.0973188	+	0.0454581i
$220$	−0.761075	+	3.66227i	−0.0513117	+	0.246910i
$221$	−5.85553	−	2.60705i	−0.393886	−	0.175369i
$222$	−0.0144020	−	0.0472173i	−0.000966600	−	0.00316902i
$223$	1.61074	+	0.342372i	0.107863	+	0.0229270i	0.261527	−	0.965196i	$-0.415774\pi$
$223$	1.61074	+	0.342372i	0.107863	+	0.0229270i	−0.153664	+	0.988123i	$0.549107\pi$
$224$	−0.995419			−0.0665092
$225$	11.8916	+	9.14277i	0.792772	+	0.609518i
$226$	−17.4876			−1.16326
$227$	3.58225	+	0.761432i	0.237763	+	0.0505380i	0.325252	−	0.945627i	$-0.394551\pi$
$227$	3.58225	+	0.761432i	0.237763	+	0.0505380i	−0.0874891	+	0.996165i	$0.527884\pi$
$228$	−7.10104	−	1.64430i	−0.470278	−	0.108896i
$229$	−0.773433	−	0.344355i	−0.0511099	−	0.0227556i	0.381023	−	0.924566i	$-0.375572\pi$
$229$	−0.773433	−	0.344355i	−0.0511099	−	0.0227556i	−0.432132	+	0.901810i	$0.642239\pi$
$230$	3.03155	+	1.73196i	0.199894	+	0.114202i
$231$	−0.136515	−	1.57222i	−0.00898202	−	0.103445i
$232$	−6.63027	+	11.4840i	−0.435299	+	0.753960i
$233$	9.04329	+	6.57033i	0.592445	+	0.430437i	0.843189	−	0.537617i	$-0.180675\pi$
$233$	9.04329	+	6.57033i	0.592445	+	0.430437i	−0.250744	+	0.968053i	$0.580675\pi$
$234$	−1.59822	−	23.2938i	−0.104479	−	1.52276i
$235$	−10.0690	+	5.87446i	−0.656829	+	0.383207i
$236$	2.93191	+	0.623197i	0.190851	+	0.0405667i
$237$	−15.7367	−	11.8746i	−1.02221	−	0.771338i
$238$	−0.360862	+	0.0767036i	−0.0233912	+	0.00497196i
$239$	−10.9299	+	12.1389i	−0.706996	+	0.785199i	−0.984473	−	0.175533i	$-0.943835\pi$
$239$	−10.9299	+	12.1389i	−0.706996	+	0.785199i	0.277477	+	0.960732i	$0.410502\pi$
$240$	3.83003	+	8.92638i	0.247227	+	0.576195i
$241$	1.40222	+	1.55732i	0.0903247	+	0.100316i	0.786613	−	0.617447i	$-0.211833\pi$
$241$	1.40222	+	1.55732i	0.0903247	+	0.100316i	−0.696288	+	0.717763i	$0.745166\pi$
$242$	2.54805	+	1.85127i	0.163795	+	0.119004i
$243$	8.98290	−	12.7400i	0.576254	−	0.817271i
$244$	−3.46945	−	2.52070i	−0.222109	−	0.161372i
$245$	−9.01297	+	12.5245i	−0.575818	+	0.800161i
$246$	−6.45669	+	6.91488i	−0.411664	+	0.440876i
$247$	43.3737	+	19.3112i	2.75980	+	1.22874i
$248$	17.8282	−	19.8002i	1.13209	−	1.25731i
$249$	5.61718	−	16.2789i	0.355974	−	1.03163i
$250$	11.6333	+	6.50685i	0.735756	+	0.411529i
$251$	−15.8673			−1.00154			−0.500769	−	0.865581i	$-0.666949\pi$
$251$	−15.8673			−1.00154			−0.500769	+	0.865581i	$0.666949\pi$
$252$	0.351096	+	0.419534i	0.0221170	+	0.0264282i
$253$	3.06320	−	2.22554i	0.192582	−	0.139919i
$254$	−1.91818	−	18.2503i	−0.120358	−	1.14513i
$255$	−2.19327	−	3.10654i	−0.137348	−	0.194539i
$256$	1.31835	−	12.5433i	0.0823968	−	0.783953i
$257$	−1.09760	−	1.90109i	−0.0684661	−	0.118587i	0.829760	−	0.558120i	$-0.188477\pi$
$257$	−1.09760	−	1.90109i	−0.0684661	−	0.118587i	−0.898226	+	0.439533i	$0.855144\pi$
$258$	0.480865	+	5.53805i	0.0299374	+	0.344784i
$259$	−0.00504127	−	0.00559889i	−0.000313249	−	0.000347898i
$260$	1.79354	+	8.25347i	0.111230	+	0.511858i
$261$	12.7465	−	2.23036i	0.788990	−	0.138056i
$262$	1.22985	−	3.78508i	0.0759801	−	0.233843i
$263$	−19.8482	−	22.0437i	−1.22389	−	1.35927i	−0.912546	−	0.408973i	$-0.865887\pi$
$263$	−19.8482	−	22.0437i	−1.22389	−	1.35927i	−0.311346	−	0.950297i	$-0.600780\pi$
$264$	15.3918	+	0.278740i	0.947299	+	0.0171553i
$265$	−8.25810	−	4.71795i	−0.507291	−	0.289821i
$266$	2.67302	−	0.568167i	0.163893	−	0.0348366i
$267$	−19.2326	−	8.98362i	−1.17701	−	0.549788i
$268$	−0.721076	+	1.24894i	−0.0440467	+	0.0762912i
$269$	−20.4742	−	14.8754i	−1.24833	−	0.906968i	−0.250210	−	0.968192i	$-0.580500\pi$
$269$	−20.4742	−	14.8754i	−1.24833	−	0.906968i	−0.998124	+	0.0612238i	$0.980500\pi$
$270$	6.25699	−	12.3587i	0.380789	−	0.752126i
$271$	−15.2201	+	11.0580i	−0.924555	+	0.671728i	−0.944654	−	0.328070i	$-0.893602\pi$
$271$	−15.2201	+	11.0580i	−0.924555	+	0.671728i	0.0200987	+	0.999798i	$0.493602\pi$
$272$	−0.257402	−	2.44902i	−0.0156073	−	0.148494i
$273$	−1.72555	−	3.11779i	−0.104435	−	0.188697i
$274$	5.03443	+	8.71989i	0.304141	+	0.526788i
$275$	11.6169	−	8.60247i	0.700528	−	0.518748i
$276$	−0.428130	+	1.24074i	−0.0257704	+	0.0746839i
$277$	−22.1401	−	4.70603i	−1.33027	−	0.282758i	−0.512692	−	0.858573i	$-0.671352\pi$
$277$	−22.1401	−	4.70603i	−1.33027	−	0.282758i	−0.817580	+	0.575814i	$0.804685\pi$
$278$	1.37963	−	1.00236i	0.0827447	−	0.0601176i
$279$	−25.9830	−	0.941397i	−1.55556	−	0.0563599i
$280$	1.61657	+	1.44233i	0.0966087	+	0.0861958i
$281$	−0.856636	+	0.381399i	−0.0511026	+	0.0227523i	−0.432129	−	0.901812i	$-0.642237\pi$
$281$	−0.856636	+	0.381399i	−0.0511026	+	0.0227523i	0.381026	+	0.924564i	$0.375571\pi$
$282$	7.05744	+	8.12940i	0.420265	+	0.484099i
$283$	−1.21199	+	11.5313i	−0.0720454	+	0.685466i	0.897577	+	0.440858i	$0.145326\pi$
$283$	−1.21199	+	11.5313i	−0.0720454	+	0.685466i	−0.969622	+	0.244608i	$0.921341\pi$
$284$	−6.74133	+	1.43291i	−0.400024	+	0.0850278i
$285$	16.2462	+	23.0111i	0.962342	+	1.36306i
$286$	−22.0090	−	4.67815i	−1.30142	−	0.276625i
$287$	−0.446185	+	1.37322i	−0.0263375	+	0.0810583i
$288$	−7.86244	+	5.28832i	−0.463299	+	0.311617i
$289$	−4.95538	−	15.2511i	−0.291493	−	0.897122i
$290$	10.9200	−	3.60301i	0.641242	−	0.211576i
$291$	−10.2212	−	7.71271i	−0.599177	−	0.452127i
$292$	−0.0555058	+	0.528103i	−0.00324823	+	0.0309049i
$293$	11.8547	+	20.5330i	0.692561	+	1.19955i	0.970996	+	0.239096i	$0.0768509\pi$
$293$	11.8547	+	20.5330i	0.692561	+	1.19955i	−0.278435	+	0.960455i	$0.589816\pi$
$294$	12.9107	+	6.03067i	0.752970	+	0.351716i
$295$	−6.85114	−	9.34030i	−0.398889	−	0.543813i
$296$	0.0594568	−	0.0431979i	0.00345586	−	0.00251083i
$297$	−9.43096	−	11.6931i	−0.547240	−	0.678504i
$298$	−7.62869	−	23.4787i	−0.441918	−	1.36008i
$299$	4.27476	−	7.40411i	0.247216	−	0.428190i
$300$	−1.59142	+	4.75152i	−0.0918807	+	0.274329i
$301$	0.424198	+	0.734732i	0.0244504	+	0.0423493i
$302$	−17.0019	+	18.8825i	−0.978350	+	1.08657i
$303$	−5.83403	−	19.1270i	−0.335156	−	1.09882i
$304$	1.90666	+	18.1406i	0.109354	+	1.04044i
$305$	3.51928	+	16.1950i	0.201513	+	0.927321i
$306$	−2.44281	+	2.52299i	−0.139646	+	0.144230i
$307$	−12.6269			−0.720652			−0.360326	−	0.932826i	$-0.617335\pi$
$307$	−12.6269			−0.720652			−0.360326	+	0.932826i	$0.617335\pi$
$308$	0.481619	−	0.214430i	0.0274428	−	0.0122183i
$309$	26.1037	−	11.0602i	1.48499	−	0.629193i
$310$	−22.9666	+	2.51937i	−1.30442	+	0.143091i
$311$	−9.47726	+	10.5256i	−0.537406	+	0.596850i	−0.949296	−	0.314384i	$-0.898202\pi$
$311$	−9.47726	+	10.5256i	−0.537406	+	0.596850i	0.411890	+	0.911234i	$0.364869\pi$
$312$	32.0060	−	13.5610i	1.81198	−	0.767742i
$313$	1.87423	+	2.08155i	0.105938	+	0.117656i	0.793782	−	0.608203i	$-0.208109\pi$
$313$	1.87423	+	2.08155i	0.105938	+	0.117656i	−0.687844	+	0.725859i	$0.741443\pi$
$314$	5.14446	+	15.8330i	0.290319	+	0.893509i
$315$	0.0669536	−	2.11308i	0.00377241	−	0.119058i
$316$	2.03512	−	6.26345i	0.114484	−	0.352347i
$317$	27.2462	−	12.1308i	1.53030	−	0.681332i	0.542929	−	0.839778i	$-0.317315\pi$
$317$	27.2462	−	12.1308i	1.53030	−	0.681332i	0.987368	+	0.158446i	$0.0506485\pi$
$318$	−2.86494	+	8.30272i	−0.160658	+	0.465594i
$319$	1.30350	−	12.4020i	0.0729820	−	0.694377i
$320$	−14.5327	+	13.2053i	−0.812403	+	0.738198i
$321$	12.0113	−	12.8637i	0.670407	−	0.717980i
$322$	−0.0514372	−	0.489392i	−0.00286648	−	0.0272728i
$323$	−2.20674	−	6.79164i	−0.122786	−	0.377897i
$324$	5.00202	+	1.44849i	0.277890	+	0.0804715i
$325$	16.0627	−	28.4142i	0.890998	−	1.57614i
$326$	0.366993	−	0.635650i	0.0203259	−	0.0352054i
$327$	9.29360	+	16.7920i	0.513937	+	0.928600i
$328$	−12.8670	−	5.72877i	−0.710462	−	0.316318i
$329$	1.50097	+	0.668275i	0.0827512	+	0.0368432i
$330$	−9.79838	−	9.06620i	−0.539383	−	0.499078i
$331$	−18.6133	+	8.28716i	−1.02308	+	0.455504i	−0.848531	−	0.529145i	$-0.822513\pi$
$331$	−18.6133	+	8.28716i	−1.02308	+	0.455504i	−0.174547	+	0.984649i	$0.555846\pi$
$332$	5.75281			0.315726
$333$	−0.0695641	−	0.0174410i	−0.00381209	−	0.000955762i
$334$	−1.98949	+	6.12301i	−0.108860	+	0.335036i
$335$	5.29259	−	1.74627i	0.289165	−	0.0954091i
$336$	0.705868	−	1.17302i	0.0385082	−	0.0639936i
$337$	−25.9922	+	5.52480i	−1.41588	+	0.300955i	−0.851412	−	0.524498i	$-0.824253\pi$
$337$	−25.9922	+	5.52480i	−1.41588	+	0.300955i	−0.564471	+	0.825453i	$0.690920\pi$
$338$	−34.5362	+	7.34089i	−1.87852	+	0.399292i
$339$	−13.0992	+	21.7685i	−0.711453	+	1.18230i
$340$	0.742026	−	1.03113i	0.0402420	−	0.0559206i
$341$	−7.74271	+	23.8296i	−0.419291	+	1.29045i
$342$	18.0947	−	18.6886i	0.978448	−	1.01056i
$343$	4.38089			0.236546
$344$	−7.56039	+	3.36610i	−0.407629	+	0.181488i
$345$	4.42675	−	2.47633i	0.238328	−	0.133321i
$346$	−0.396128	−	0.176368i	−0.0212960	−	0.00948158i
$347$	18.7081	+	8.32938i	1.00430	+	0.447144i	0.841931	−	0.539585i	$-0.181419\pi$
$347$	18.7081	+	8.32938i	1.00430	+	0.447144i	0.162372	+	0.986730i	$0.448086\pi$
$348$	2.09328	+	3.78221i	0.112211	+	0.202748i
$349$	2.88806	−	5.00227i	0.154594	−	0.267766i	−0.778317	−	0.627872i	$-0.783926\pi$
$349$	2.88806	−	5.00227i	0.154594	−	0.267766i	0.932911	+	0.360106i	$0.117260\pi$
$350$	−0.213335	−	1.86653i	−0.0114032	−	0.0997701i
$351$	−30.1932	−	15.4589i	−1.61159	−	0.825138i
$352$	2.82175	+	8.68445i	0.150400	+	0.462883i
$353$	−1.44559	−	13.7539i	−0.0769411	−	0.732045i	−0.963187	−	0.268831i	$-0.913363\pi$
$353$	−1.44559	−	13.7539i	−0.0769411	−	0.732045i	0.886246	−	0.463214i	$-0.153304\pi$
$354$	−7.30066	+	7.81874i	−0.388026	+	0.415561i
$355$	23.1260	+	13.2122i	1.22740	+	0.701229i
$356$	0.741236	−	7.05239i	0.0392854	−	0.373776i
$357$	−0.174827	+	0.506657i	−0.00925281	+	0.0268151i
$358$	−16.5394	+	7.36382i	−0.874135	+	0.389190i
$359$	0.158269	−	0.487102i	0.00835313	−	0.0257083i	−0.946793	−	0.321843i	$-0.895698\pi$
$359$	0.158269	−	0.487102i	0.00835313	−	0.0257083i	0.955146	+	0.296135i	$0.0956977\pi$
$360$	20.4313	+	2.80413i	1.07682	+	0.147791i
$361$	10.4747	+	32.2377i	0.551299	+	1.69672i
$362$	−0.0456192	−	0.0506652i	−0.00239769	−	0.00266291i
$363$	4.21310	−	1.78510i	0.221130	−	0.0936934i
$364$	0.796542	−	0.884650i	0.0417501	−	0.0463682i
$365$	1.51876	−	1.38004i	0.0794957	−	0.0722345i
$366$	14.0922	−	5.97089i	0.736609	−	0.312103i
$367$	−17.8610	+	7.95224i	−0.932337	+	0.415103i	−0.815964	−	0.578102i	$-0.803793\pi$
$367$	−17.8610	+	7.95224i	−0.932337	+	0.415103i	−0.116373	+	0.993206i	$0.537127\pi$
$368$	3.28461			0.171222
$369$	3.77118	+	13.2169i	0.196320	+	0.688046i
$370$	−0.0634103	−	0.00637373i	−0.00329655	−	0.000331354i
$371$	0.140118	+	1.33313i	0.00727455	+	0.0692127i
$372$	−2.53400	−	8.30780i	−0.131382	−	0.430739i
$373$	16.5937	−	18.4292i	0.859191	−	0.954228i	−0.140165	−	0.990128i	$-0.544763\pi$
$373$	16.5937	−	18.4292i	0.859191	−	0.954228i	0.999355	+	0.0359001i	$0.0114298\pi$
$374$	1.69214	+	2.93088i	0.0874987	+	0.151552i
$375$	16.8138	−	9.60713i	0.868260	−	0.496110i
$376$	−8.01359	+	13.8800i	−0.413270	+	0.715804i
$377$	−8.70129	−	26.7798i	−0.448139	−	1.37923i
$378$	−1.92894	+	0.301634i	−0.0992140	+	0.0155144i
$379$	15.1691	−	11.0210i	0.779184	−	0.566110i	−0.125550	−	0.992087i	$-0.540070\pi$
$379$	15.1691	−	11.0210i	0.779184	−	0.566110i	0.904734	+	0.425977i	$0.140070\pi$
$380$	−5.49642	+	7.63786i	−0.281960	+	0.391814i
$381$	−24.1548	−	11.2828i	−1.23749	−	0.578036i
$382$	−1.42861	−	2.47442i	−0.0730938	−	0.126602i
$383$	−0.573056	+	5.45227i	−0.0292818	+	0.278598i	0.970077	+	0.242797i	$0.0780649\pi$
$383$	−0.573056	+	5.45227i	−0.0292818	+	0.278598i	−0.999359	+	0.0358009i	$0.988602\pi$
$384$	5.74133	+	4.33229i	0.292986	+	0.221081i
$385$	−1.94049	−	0.620776i	−0.0988965	−	0.0316377i
$386$	−2.17198	−	6.68468i	−0.110551	−	0.340241i
$387$	7.25396	+	3.54975i	0.368740	+	0.180444i
$388$	1.32184	−	4.06819i	0.0671061	−	0.206531i
$389$	1.53381	+	0.326022i	0.0777673	+	0.0165300i	0.246631	−	0.969109i	$-0.420676\pi$
$389$	1.53381	+	0.326022i	0.0777673	+	0.0165300i	−0.168864	+	0.985639i	$0.554010\pi$
$390$	−28.5385	−	9.70270i	−1.44510	−	0.491316i
$391$	−1.25782	+	0.267358i	−0.0636107	+	0.0135209i
$392$	−2.21753	+	21.0983i	−0.112002	+	1.06563i
$393$	−3.79043	−	4.36616i	−0.191202	−	0.220244i
$394$	17.2906	−	7.69827i	0.871087	−	0.387833i
$395$	−21.9831	+	12.8254i	−1.10609	+	0.645317i
$396$	2.66493	−	4.25238i	0.133918	−	0.213690i
$397$	7.83333	−	5.69125i	0.393143	−	0.285635i	−0.373599	−	0.927590i	$-0.621876\pi$
$397$	7.83333	−	5.69125i	0.393143	−	0.285635i	0.766742	+	0.641955i	$0.221876\pi$
$398$	−5.37609	−	1.14272i	−0.269479	−	0.0572796i
$399$	1.29500	−	3.75296i	0.0648309	−	0.187883i
$400$	12.5394	−	0.113877i	0.626969	−	0.00569383i
$401$	−0.505309	−	0.875221i	−0.0252339	−	0.0437064i	0.853133	−	0.521694i	$-0.174700\pi$
$401$	−0.505309	−	0.875221i	−0.0252339	−	0.0437064i	−0.878367	+	0.477988i	$0.841366\pi$
$402$	−2.49228	−	4.50314i	−0.124304	−	0.224596i
$403$	5.91384	+	56.2665i	0.294590	+	2.80283i
$404$	5.40443	−	3.92655i	0.268880	−	0.195353i
$405$	−10.6972	−	17.0461i	−0.531549	−	0.847027i
$406$	−1.31117	−	0.952622i	−0.0650724	−	0.0472779i
$407$	−0.0345565	+	0.0598535i	−0.00171290	+	0.00296683i
$408$	−4.73696	−	2.21266i	−0.234515	−	0.109543i
$409$	−7.84185	+	1.66684i	−0.387754	+	0.0824197i	−0.397664	−	0.917531i	$-0.630179\pi$
$409$	−7.84185	+	1.66684i	−0.387754	+	0.0824197i	0.00990955	+	0.999951i	$0.496846\pi$
$410$	5.01836	+	11.1351i	0.247839	+	0.549922i
$411$	14.6256	+	0.264865i	0.721427	+	0.0130648i
$412$	6.33716	+	7.03812i	0.312209	+	0.346744i
$413$	−0.504507	+	1.55271i	−0.0248251	+	0.0764040i
$414$	−3.00626	−	3.59226i	−0.147750	−	0.176550i
$415$	−16.5889	−	14.8009i	−0.814316	−	0.726546i
$416$	13.7966	+	15.3227i	0.676434	+	0.751256i
$417$	−0.214311	−	2.46819i	−0.0104949	−	0.120868i
$418$	−12.5342	−	21.7099i	−0.613070	−	1.06187i
$419$	−2.61646	+	24.8939i	−0.127822	+	1.21615i	0.723058	+	0.690788i	$0.242736\pi$
$419$	−2.61646	+	24.8939i	−0.127822	+	1.21615i	−0.850880	+	0.525360i	$0.823931\pi$
$420$	0.674587	−	0.209112i	0.0329165	−	0.0102036i
$421$	−3.44840	−	32.8093i	−0.168065	−	1.59903i	−0.675515	−	0.737346i	$-0.736079\pi$
$421$	−3.44840	−	32.8093i	−0.168065	−	1.59903i	0.507450	−	0.861681i	$-0.330588\pi$
$422$	−0.142826	+	0.103769i	−0.00695265	+	0.00505140i
$423$	15.4059	−	2.69569i	0.749061	−	0.131069i
$424$	−13.0760			−0.635026
$425$	−4.79260	+	1.06428i	−0.232475	+	0.0516250i
$426$	8.02298	−	23.2510i	0.388714	−	1.12651i
$427$	1.56298	−	1.73586i	0.0756377	−	0.0840042i
$428$	5.37108	+	2.39136i	0.259621	+	0.115591i
$429$	−22.3094	+	23.8925i	−1.07711	+	1.15354i
$430$	6.83526	+	2.18665i	0.329625	+	0.105449i
$431$	4.71468	+	3.42542i	0.227098	+	0.164997i	0.695516	−	0.718511i	$-0.255176\pi$
$431$	4.71468	+	3.42542i	0.227098	+	0.164997i	−0.468418	+	0.883507i	$0.655176\pi$
$432$	−0.656483	−	13.0153i	−0.0315851	−	0.626198i
$433$	−1.68629	−	1.22516i	−0.0810381	−	0.0588776i	0.546529	−	0.837440i	$-0.315949\pi$
$433$	−1.68629	−	1.22516i	−0.0810381	−	0.0588776i	−0.627567	+	0.778563i	$0.715949\pi$
$434$	2.17895	+	2.41997i	0.104593	+	0.116162i
$435$	3.69468	−	16.2920i	0.177146	−	0.781143i
$436$	−4.29007	+	4.76461i	−0.205457	+	0.228183i
$437$	9.31706	−	1.98040i	0.445695	−	0.0947355i
$438$	−1.51275	−	1.14149i	−0.0722818	−	0.0545425i
$439$	−22.2890	−	4.73767i	−1.06380	−	0.226117i	−0.357413	−	0.933946i	$-0.616341\pi$
$439$	−22.2890	−	4.73767i	−1.06380	−	0.226117i	−0.706383	+	0.707830i	$0.749674\pi$
$440$	8.00095	−	18.1923i	0.381430	−	0.867284i
$441$	17.1779	−	11.5540i	0.817995	−	0.550188i
$442$	6.18230	+	4.49170i	0.294062	+	0.213648i
$443$	4.50211	−	7.79787i	0.213901	−	0.370488i	−0.739031	−	0.673672i	$-0.764716\pi$
$443$	4.50211	−	7.79787i	0.213901	−	0.370488i	0.952932	+	0.303184i	$0.0980495\pi$
$444$	−0.00207246	−	0.0238682i	−9.83547e−5	−	0.00113274i
$445$	−20.2819	+	18.4293i	−0.961453	+	0.873634i
$446$	−1.79352	−	0.798526i	−0.0849256	−	0.0378113i
$447$	−34.9406	−	8.09076i	−1.65263	−	0.382680i
$448$	2.70709	+	0.575410i	0.127898	+	0.0271856i
$449$	−2.14345			−0.101156			−0.0505779	−	0.998720i	$-0.516106\pi$
$449$	−2.14345			−0.101156			−0.0505779	+	0.998720i	$0.516106\pi$
$450$	−11.6013	−	13.6096i	−0.546890	−	0.641564i
$451$	13.2453			0.623698
$452$	−8.30169	−	1.76458i	−0.390479	−	0.0829988i
$453$	10.7695	+	35.3081i	0.505996	+	1.65892i
$454$	−3.98876	−	1.77591i	−0.187202	−	0.0833477i
$455$	−4.57295	+	0.501640i	−0.214383	+	0.0235173i
$456$	35.0882	+	16.3898i	1.64315	+	0.767525i
$457$	9.78295	−	16.9446i	0.457627	−	0.792634i	−0.541208	−	0.840889i	$-0.682033\pi$
$457$	9.78295	−	16.9446i	0.457627	−	0.792634i	0.998835	+	0.0482552i	$0.0153661\pi$
$458$	0.816594	+	0.593290i	0.0381569	+	0.0277226i
$459$	1.31080	+	4.93068i	0.0611831	+	0.230145i
$460$	1.26437	+	1.12809i	0.0589516	+	0.0525976i
$461$	3.73066	+	0.792976i	0.173754	+	0.0369326i	0.293967	−	0.955816i	$-0.405024\pi$
$461$	3.73066	+	0.792976i	0.173754	+	0.0369326i	−0.120213	+	0.992748i	$0.538358\pi$
$462$	−0.230517	+	1.86731i	−0.0107246	+	0.0868752i
$463$	−8.85242	+	1.88164i	−0.411407	+	0.0874473i	−0.408966	−	0.912550i	$-0.634110\pi$
$463$	−8.85242	+	1.88164i	−0.411407	+	0.0874473i	−0.00244131	+	0.999997i	$0.500777\pi$
$464$	7.23859	−	8.03927i	0.336043	−	0.373214i
$465$	−14.0673	+	30.4760i	−0.652353	+	1.41329i
$466$	−8.91735	−	9.90372i	−0.413088	−	0.458781i
$467$	24.8972	+	18.0889i	1.15211	+	0.837053i	0.988759	−	0.149515i	$-0.0477713\pi$
$467$	24.8972	+	18.0889i	1.15211	+	0.837053i	0.163346	+	0.986569i	$0.447771\pi$
$468$	1.59174	−	11.2193i	0.0735783	−	0.518611i
$469$	−0.635487	−	0.461708i	−0.0293441	−	0.0213197i
$470$	13.1983	−	4.35473i	0.608790	−	0.200869i
$471$	23.5624	+	5.45606i	1.08570	+	0.251402i
$472$	−14.5489	−	6.47759i	−0.669667	−	0.298155i
$473$	5.20763	−	5.78365i	0.239447	−	0.265933i
$474$	15.4082	+	17.7485i	0.707721	+	0.815216i
$475$	35.5003	−	7.88343i	1.62886	−	0.361717i
$476$	−0.179048			−0.00820666
$477$	8.18921	+	9.78551i	0.374958	+	0.448048i
$478$	15.7550	−	11.4467i	0.720617	−	0.523559i
$479$	−1.28729	−	12.2478i	−0.0588179	−	0.559615i	−0.983758	−	0.179501i	$-0.942552\pi$
$479$	−1.28729	−	12.2478i	−0.0588179	−	0.559615i	0.924940	−	0.380113i	$-0.124115\pi$
$480$	2.38077	+	11.9989i	0.108667	+	0.547670i
$481$	−0.0163124	+	0.155202i	−0.000743782	+	0.00707662i
$482$	−1.24920	−	2.16367i	−0.0568993	−	0.0985524i
$483$	−0.647725	−	0.302555i	−0.0294725	−	0.0137667i
$484$	1.02281	+	1.13594i	0.0464912	+	0.0516338i
$485$	−14.2783	+	8.33027i	−0.648346	+	0.378258i
$486$	−13.6335	+	12.6303i	−0.618428	+	0.572922i
$487$	1.53444	−	4.72251i	0.0695320	−	0.213997i	−0.910252	−	0.414054i	$-0.864113\pi$
$487$	1.53444	−	4.72251i	0.0695320	−	0.213997i	0.979784	+	0.200056i	$0.0641125\pi$
$488$	15.2464	+	16.9329i	0.690173	+	0.766514i
$489$	−0.516357	−	0.932972i	−0.0233505	−	0.0421905i
$490$	13.6152	−	12.3715i	0.615070	−	0.558889i
$491$	18.6448	−	3.96308i	0.841430	−	0.178852i	0.233018	−	0.972472i	$-0.425140\pi$
$491$	18.6448	−	3.96308i	0.841430	−	0.178852i	0.608412	+	0.793621i	$0.291807\pi$
$492$	−3.76286	+	2.63112i	−0.169643	+	0.118620i
$493$	−2.11760	+	3.66778i	−0.0953718	+	0.165189i
$494$	−45.7942	−	33.2714i	−2.06038	−	1.49695i
$495$	−18.6252	+	5.40589i	−0.837139	+	0.242976i
$496$	−17.5847	+	12.7760i	−0.789576	+	0.573660i
$497$	−0.392386	−	3.73331i	−0.0176009	−	0.167462i
$498$	−10.5857	+	17.5915i	−0.474357	+	0.788293i
$499$	−2.50922	−	4.34610i	−0.112328	−	0.194558i	0.804380	−	0.594115i	$-0.202497\pi$
$499$	−2.50922	−	4.34610i	−0.112328	−	0.194558i	−0.916709	+	0.399557i	$0.869164\pi$
$500$	4.86600	+	4.26279i	0.217614	+	0.190638i
$501$	6.13167	+	7.06301i	0.273943	+	0.315552i
$502$	18.5039	+	3.93313i	0.825871	+	0.175544i
$503$	−5.48055	+	3.98186i	−0.244366	+	0.177542i	−0.703226	−	0.710966i	$-0.748258\pi$
$503$	−5.48055	+	3.98186i	−0.244366	+	0.177542i	0.458860	+	0.888508i	$0.348258\pi$
$504$	−1.36122	−	2.56819i	−0.0606337	−	0.114396i
$505$	−25.6865	−	2.58190i	−1.14304	−	0.114893i
$506$	−4.12386	+	1.83606i	−0.183328	+	0.0816228i
$507$	−16.7317	+	48.4894i	−0.743083	+	2.15349i
$508$	0.930943	−	8.85733i	0.0413039	−	0.392981i
$509$	9.72702	−	2.06754i	0.431143	−	0.0916422i	0.0127717	−	0.999918i	$-0.495935\pi$
$509$	9.72702	−	2.06754i	0.431143	−	0.0916422i	0.418371	+	0.908276i	$0.362601\pi$
$510$	1.78767	+	4.16641i	0.0791596	+	0.184492i
$511$	−0.282909	−	0.0601341i	−0.0125152	−	0.00266018i
$512$	−7.21302	+	22.1994i	−0.318774	+	0.981084i
$513$	−9.70953	−	36.5231i	−0.428686	−	1.61253i
$514$	0.808743	+	2.48906i	0.0356721	+	0.109788i
$515$	−0.166186	−	36.5995i	−0.00732303	−	1.61277i
$516$	−0.330540	+	2.67755i	−0.0145512	+	0.117872i
$517$	1.57546	−	14.9895i	0.0692886	−	0.659237i
$518$	0.00449112	+	0.00777885i	0.000197329	+	0.000341783i
$519$	−0.516266	+	0.360990i	−0.0226616	+	0.0158457i
$520$	−0.203763	−	44.8750i	−0.00893558	−	1.96790i
$521$	15.4969	−	11.2591i	0.678930	−	0.493272i	−0.194072	−	0.980987i	$-0.562170\pi$
$521$	15.4969	−	11.2591i	0.678930	−	0.493272i	0.873003	+	0.487715i	$0.162170\pi$
$522$	−15.4174	−	0.558592i	−0.674802	−	0.0244489i
$523$	0.0808887	+	0.248950i	0.00353702	+	0.0108858i	0.952809	−	0.303569i	$-0.0981783\pi$
$523$	0.0808887	+	0.248950i	0.00353702	+	0.0108858i	−0.949272	+	0.314455i	$0.898178\pi$
$524$	0.965764	−	1.67275i	0.0421896	−	0.0730745i
$525$	−2.48325	−	1.13258i	−0.108378	−	0.0494300i
$526$	17.6822	+	30.6265i	0.770980	+	1.33538i
$527$	5.69401	−	6.32384i	0.248035	−	0.275471i
$528$	−12.2349	−	2.83308i	−0.532455	−	0.123294i
$529$	2.22487	+	21.1682i	0.0967333	+	0.920356i
$530$	8.46084	+	7.54890i	0.367516	+	0.327903i
$531$	4.26412	+	14.9446i	0.185047	+	0.648539i
$532$	1.32626			0.0575009
$533$	27.3223	−	12.1647i	1.18346	−	0.526911i
$534$	20.2015	+	15.2437i	0.874206	+	0.659659i
$535$	−9.33561	−	20.7145i	−0.403614	−	0.895565i
$536$	5.12714	−	5.69427i	0.221459	−	0.245955i
$537$	−3.22253	+	26.1042i	−0.139063	+	1.12648i
$538$	20.1891	+	22.4222i	0.870412	+	0.966691i
$539$	−6.16497	−	18.9738i	−0.265544	−	0.817261i
$540$	4.21737	−	5.23555i	0.181487	−	0.225302i
$541$	6.23922	−	19.2023i	0.268245	−	0.825573i	−0.722683	−	0.691180i	$-0.757091\pi$
$541$	6.23922	−	19.2023i	0.268245	−	0.825573i	0.990928	−	0.134394i	$-0.0429087\pi$
$542$	20.4902	−	9.12282i	0.880129	−	0.391859i
$543$	−0.0972395	+	0.0188354i	−0.00417295	+	0.000808305i
$544$	0.324166	−	3.08423i	0.0138985	−	0.132235i
$545$	24.6293	−	2.70177i	1.05500	−	0.115731i
$546$	1.23945	+	4.06358i	0.0530437	+	0.173905i
$547$	0.785409	+	7.47267i	0.0335817	+	0.319508i	0.998398	+	0.0565830i	$0.0180206\pi$
$547$	0.785409	+	7.47267i	0.0335817	+	0.319508i	−0.964816	+	0.262925i	$0.915313\pi$
$548$	1.51006	+	4.64750i	0.0645067	+	0.198531i
$549$	3.12332	−	22.0145i	0.133300	−	0.939554i
$550$	−15.6796	+	7.15234i	−0.668582	+	0.304977i
$551$	15.6857	−	27.1684i	0.668233	−	1.15741i
$552$	3.59563	−	5.97527i	0.153040	−	0.254324i
$553$	3.27699	+	1.45901i	0.139352	+	0.0620435i
$554$	24.6526	+	10.9760i	1.04739	+	0.466327i
$555$	−0.0554321	+	0.0741588i	−0.00235296	+	0.00314787i
$556$	0.756081	−	0.336629i	0.0320650	−	0.0142762i
$557$	17.2753			0.731980			0.365990	−	0.930619i	$-0.380730\pi$
$557$	17.2753			0.731980			0.365990	+	0.930619i	$0.380730\pi$
$558$	30.0672	+	7.53840i	1.27284	+	0.319126i
$559$	5.43045	−	16.7132i	0.229684	−	0.706894i
$560$	−1.04534	−	1.42513i	−0.0441735	−	0.0602226i
$561$	4.91587	+	0.0890249i	0.207548	+	0.00375863i
$562$	1.09352	−	0.232435i	0.0461273	−	0.00980467i
$563$	−2.64361	+	0.561918i	−0.111415	+	0.0236820i	−0.263282	−	0.964719i	$-0.584805\pi$
$563$	−2.64361	+	0.561918i	−0.111415	+	0.0236820i	0.151867	+	0.988401i	$0.451472\pi$
$564$	2.53001	+	4.57132i	0.106533	+	0.192487i
$565$	19.3990	+	26.4470i	0.816120	+	1.11263i
$566$	4.27172	−	13.1470i	0.179554	−	0.552610i
$567$	−1.06942	+	2.62709i	−0.0449114	+	0.110327i
$568$	36.6180			1.53646
$569$	−39.0521	+	17.3871i	−1.63715	+	0.728906i	−0.999154	−	0.0411349i	$-0.986903\pi$
$569$	−39.0521	+	17.3871i	−1.63715	+	0.728906i	−0.637995	+	0.770040i	$0.720236\pi$
$570$	−13.2419	−	30.8619i	−0.554640	−	1.29266i
$571$	27.6907	+	12.3287i	1.15882	+	0.515941i	0.893872	−	0.448322i	$-0.147978\pi$
$571$	27.6907	+	12.3287i	1.15882	+	0.515941i	0.264949	+	0.964262i	$0.414645\pi$
$572$	−9.97604	−	4.44162i	−0.417119	−	0.185714i
$573$	−4.15026	−	0.0751599i	−0.173380	−	0.00313985i
$574$	0.860713	−	1.49080i	0.0359255	−	0.0622247i
$575$	−0.743598	−	6.50596i	−0.0310102	−	0.271317i
$576$	24.4393	−	9.83692i	1.01830	−	0.409872i
$577$	11.8163	+	36.3667i	0.491917	+	1.51396i	0.821707	+	0.569910i	$0.193022\pi$
$577$	11.8163	+	36.3667i	0.491917	+	1.51396i	−0.329790	+	0.944054i	$0.606978\pi$
$578$	1.99841	+	19.0136i	0.0831229	+	0.790862i
$579$	−9.94803	−	2.30354i	−0.413426	−	0.0957319i
$580$	5.54748	−	0.608543i	0.230346	−	0.0252684i
$581$	−0.327531	+	3.11625i	−0.0135883	+	0.129284i
$582$	10.0078	+	11.5279i	0.414837	+	0.477847i
$583$	11.2336	−	5.00152i	0.465248	−	0.207142i
$584$	0.871846	−	2.68327i	0.0360773	−	0.111034i
$585$	−33.4550	+	28.2568i	−1.38319	+	1.16827i
$586$	−8.73494	−	26.8834i	−0.360837	−	1.11054i
$587$	12.5219	+	13.9069i	0.516832	+	0.574000i	0.943905	−	0.330217i	$-0.107122\pi$
$587$	12.5219	+	13.9069i	0.516832	+	0.574000i	−0.427073	+	0.904217i	$0.640455\pi$
$588$	5.52046	+	4.16563i	0.227660	+	0.171788i
$589$	−42.1773	+	46.8426i	−1.73789	+	1.93012i
$590$	5.67432	+	12.5906i	0.233608	+	0.518346i
$591$	3.36889	−	27.2898i	0.138578	−	1.12255i
$592$	−0.0547716	+	0.0243859i	−0.00225110	+	0.00100225i
$593$	−42.4830			−1.74457			−0.872284	−	0.489000i	$-0.837362\pi$
$593$	−42.4830			−1.74457			−0.872284	+	0.489000i	$0.837362\pi$
$594$	8.09962	+	15.9738i	0.332331	+	0.655415i
$595$	0.516306	+	0.460656i	0.0211665	+	0.0188851i
$596$	−1.25238	−	11.9156i	−0.0512994	−	0.488081i
$597$	−5.44948	+	5.83619i	−0.223032	+	0.238859i
$598$	−6.82039	+	7.57481i	−0.278906	+	0.309757i
$599$	−22.9566	−	39.7621i	−0.937983	−	1.62463i	−0.769226	−	0.638977i	$-0.779358\pi$
$599$	−22.9566	−	39.7621i	−0.937983	−	1.62463i	−0.168757	−	0.985658i	$-0.553975\pi$
$600$	13.5196	−	22.9359i	0.551934	−	0.936356i
$601$	13.8303	−	23.9548i	0.564150	−	0.977136i	−0.432978	−	0.901404i	$-0.642537\pi$
$601$	13.8303	−	23.9548i	0.564150	−	0.977136i	0.997128	−	0.0757320i	$-0.0241293\pi$
$602$	−0.312563	−	0.961968i	−0.0127391	−	0.0392069i
$603$	−7.47237	−	0.270733i	−0.304299	−	0.0110251i
$604$	−9.97648	+	7.24834i	−0.405937	+	0.294931i
$605$	−0.0268222	−	5.90710i	−0.00109048	−	0.240158i
$606$	2.06232	+	23.7514i	0.0837758	+	0.964834i
$607$	−7.77177	−	13.4611i	−0.315446	−	0.546369i	0.664086	−	0.747656i	$-0.268821\pi$
$607$	−7.77177	−	13.4611i	−0.315446	−	0.546369i	−0.979532	+	0.201287i	$0.935488\pi$
$608$	−2.40120	+	22.8459i	−0.0973814	+	0.926523i
$609$	−2.16797	+	0.918575i	−0.0878506	+	0.0372225i
$610$	−0.0897161	−	19.7584i	−0.00363250	−	0.799993i
$611$	−10.5167	−	32.3671i	−0.425460	−	1.30943i
$612$	−1.41423	+	0.951222i	−0.0571670	+	0.0384509i
$613$	−12.9646	+	39.9011i	−0.523637	+	1.61159i	0.243359	+	0.969936i	$0.421751\pi$
$613$	−12.9646	+	39.9011i	−0.523637	+	1.61159i	−0.766996	+	0.641652i	$0.778249\pi$
$614$	14.7250	+	3.12990i	0.594253	+	0.126312i
$615$	17.6200	+	2.09399i	0.710507	+	0.0844377i
$616$	−2.73988	+	0.582379i	−0.110393	+	0.0234647i
$617$	0.968484	−	9.21451i	0.0389897	−	0.370962i	−0.957578	−	0.288176i	$-0.906951\pi$
$617$	0.968484	−	9.21451i	0.0389897	−	0.370962i	0.996567	−	0.0827867i	$-0.0263820\pi$
$618$	−33.1828	+	6.42755i	−1.33481	+	0.258554i
$619$	9.46155	−	4.21255i	0.380292	−	0.169317i	−0.207683	−	0.978196i	$-0.566592\pi$
$619$	9.46155	−	4.21255i	0.380292	−	0.169317i	0.587975	+	0.808879i	$0.299926\pi$
$620$	−11.1569	−	1.12144i	−0.448073	−	0.0450383i
$621$	−6.72351	+	1.05137i	−0.269805	+	0.0421901i
$622$	13.6611	−	9.92537i	0.547760	−	0.397971i
$623$	3.77802	+	0.803044i	0.151363	+	0.0321733i
$624$	−27.8399	+	5.39263i	−1.11449	+	0.215878i
$625$	−3.06433	−	24.8115i	−0.122573	−	0.992459i
$626$	−1.66970	−	2.89201i	−0.0667347	−	0.115588i
$627$	−36.4134	−	0.659435i	−1.45421	−	0.0263353i
$628$	0.844549	+	8.03534i	0.0337012	+	0.320645i
$629$	0.0189895	−	0.0137967i	0.000757161	−	0.000550110i
$630$	−0.601861	+	2.44760i	−0.0239787	+	0.0975148i
$631$	29.6450	+	21.5383i	1.18015	+	0.857428i	0.992188	−	0.124749i	$-0.0398126\pi$
$631$	29.6450	+	21.5383i	1.18015	+	0.857428i	0.187960	+	0.982177i	$0.439813\pi$
$632$	−17.4957	+	30.3034i	−0.695941	+	1.20541i
$633$	0.0221865	+	0.255519i	0.000881835	+	0.0101560i
$634$	−34.7805	+	7.39282i	−1.38131	+	0.293606i
$635$	−25.4727	+	23.1460i	−1.01085	+	0.918521i
$636$	−2.19783	+	3.65238i	−0.0871495	+	0.144826i
$637$	−30.1429	−	33.4770i	−1.19430	−	1.32641i
$638$	−4.59425	+	14.1397i	−0.181888	+	0.559794i
$639$	−22.9331	−	27.4034i	−0.907220	−	1.08406i
$640$	8.02026	−	4.67918i	0.317029	−	0.184961i
$641$	−17.6253	−	19.5749i	−0.696157	−	0.773161i	0.286603	−	0.958050i	$-0.407474\pi$
$641$	−17.6253	−	19.5749i	−0.696157	−	0.773161i	−0.982759	+	0.184889i	$0.940807\pi$
$642$	−17.1958	+	12.0239i	−0.678664	+	0.474544i
$643$	24.3415	+	42.1606i	0.959934	+	1.66265i	0.722651	+	0.691213i	$0.242923\pi$
$643$	24.3415	+	42.1606i	0.959934	+	1.66265i	0.237282	+	0.971441i	$0.423743\pi$
$644$	0.0249638	−	0.237514i	0.000983711	−	0.00935938i
$645$	7.84195	−	6.87059i	0.308777	−	0.270529i
$646$	0.889937	+	8.46718i	0.0350141	+	0.333137i
$647$	10.6167	−	7.71348i	0.417386	−	0.303248i	−0.359199	−	0.933261i	$-0.616950\pi$
$647$	10.6167	−	7.71348i	0.417386	−	0.303248i	0.776585	+	0.630012i	$0.216950\pi$
$648$	−24.3957	−	13.0535i	−0.958354	−	0.512788i
$649$	14.9767			0.587885
$650$	−25.7750	+	29.1542i	−1.01098	+	1.14352i
$651$	4.64454	−	0.899653i	0.182034	−	0.0352602i
$652$	0.238359	−	0.264724i	0.00933485	−	0.0103674i
$653$	−44.1587	−	19.6607i	−1.72806	−	0.769383i	−0.996119	−	0.0880168i	$-0.971947\pi$
$653$	−44.1587	−	19.6607i	−1.72806	−	0.769383i	−0.731943	−	0.681366i	$-0.761386\pi$
$654$	−6.67554	−	21.8859i	−0.261034	−	0.855807i
$655$	−7.08856	+	2.33885i	−0.276973	+	0.0913864i
$656$	9.29580	+	6.75379i	0.362940	+	0.263691i
$657$	−2.55406	+	1.02802i	−0.0996435	+	0.0401070i
$658$	−1.58473	−	1.15137i	−0.0617792	−	0.0448853i
$659$	20.0735	+	22.2938i	0.781951	+	0.868444i	0.994064	−	0.108801i	$-0.0347011\pi$
$659$	20.0735	+	22.2938i	0.781951	+	0.868444i	−0.212113	+	0.977245i	$0.568034\pi$
$660$	−3.73666	−	5.29261i	−0.145449	−	0.206014i
$661$	8.02224	−	8.90960i	0.312029	−	0.346543i	−0.566648	−	0.823960i	$-0.691760\pi$
$661$	8.02224	−	8.90960i	0.312029	−	0.346543i	0.878677	+	0.477417i	$0.158427\pi$
$662$	23.7604	−	5.05042i	0.923473	−	0.196290i
$663$	10.2222	−	4.33116i	0.396996	−	0.168208i
$664$	−29.8977	−	6.35495i	−1.16026	−	0.246620i
$665$	−3.82444	−	3.41222i	−0.148305	−	0.132320i
$666$	0.0768001	+	0.0375824i	0.00297594	+	0.00145629i
$667$	−4.57022	−	3.32046i	−0.176959	−	0.128569i
$668$	−1.56229	+	2.70596i	−0.0604468	+	0.104697i
$669$	−2.33746	+	1.63443i	−0.0903714	+	0.0631906i
$670$	−6.60489	+	0.724539i	−0.255169	+	0.0279914i
$671$	−19.5750	−	8.71535i	−0.755685	−	0.336452i
$672$	1.17667	−	1.26017i	0.0453910	−	0.0486121i
$673$	25.3929	+	5.39742i	0.978824	+	0.208055i	0.669427	−	0.742878i	$-0.266540\pi$
$673$	25.3929	+	5.39742i	0.978824	+	0.208055i	0.309397	+	0.950933i	$0.399873\pi$
$674$	31.6806			1.22029
$675$	−25.6313	+	4.24684i	−0.986550	+	0.163461i
$676$	−17.1357			−0.659067
$677$	−38.4473	−	8.17223i	−1.47765	−	0.314084i	−0.602572	−	0.798065i	$-0.705857\pi$
$677$	−38.4473	−	8.17223i	−1.47765	−	0.314084i	−0.875079	+	0.483980i	$0.839191\pi$
$678$	20.6718	−	22.1387i	0.793895	−	0.850232i
$679$	2.12845	+	0.947647i	0.0816824	+	0.0363674i
$680$	−4.99541	+	4.53913i	−0.191565	+	0.174068i
$681$	−5.19848	+	3.63494i	−0.199206	+	0.139291i
$682$	14.9361	−	25.8700i	0.571932	−	0.990615i
$683$	−26.3578	−	19.1501i	−1.00855	−	0.732757i	−0.0446482	−	0.999003i	$-0.514217\pi$
$683$	−26.3578	−	19.1501i	−1.00855	−	0.732757i	−0.963905	+	0.266246i	$0.914217\pi$
$684$	10.4757	−	7.04600i	0.400547	−	0.269410i
$685$	7.60267	−	17.2867i	0.290483	−	0.660491i
$686$	−5.10885	−	1.08592i	−0.195057	−	0.0414606i
$687$	1.35021	−	0.572086i	0.0515135	−	0.0218264i
$688$	6.60389	−	1.40370i	0.251771	−	0.0535156i
$689$	18.5791	−	20.6342i	0.707807	−	0.786100i
$690$	−5.77615	+	1.79052i	−0.219894	+	0.0681640i
$691$	22.3344	+	24.8048i	0.849639	+	0.943620i	0.998979	−	0.0451661i	$-0.0143817\pi$
$691$	22.3344	+	24.8048i	0.849639	+	0.943620i	−0.149340	+	0.988786i	$0.547715\pi$
$692$	−0.170254	−	0.123696i	−0.00647207	−	0.00470223i
$693$	2.15176	+	1.68568i	0.0817384	+	0.0640335i
$694$	−19.7521	−	14.3507i	−0.749779	−	0.544746i
$695$	−3.04632	−	0.974541i	−0.115554	−	0.0369664i
$696$	−6.70080	−	21.9687i	−0.253993	−	0.832723i
$697$	−4.10951	−	1.82967i	−0.155659	−	0.0693037i
$698$	−4.60791	+	5.11760i	−0.174412	+	0.193704i
$699$	−19.0078	+	3.68183i	−0.718940	+	0.139260i
$700$	0.0870675	−	0.907604i	0.00329084	−	0.0343042i
$701$	−47.0156			−1.77575			−0.887877	−	0.460081i	$-0.847820\pi$
$701$	−47.0156			−1.77575			−0.887877	+	0.460081i	$0.847820\pi$
$702$	31.3784	+	25.5119i	1.18430	+	0.962884i
$703$	−0.140661	+	0.102196i	−0.00530513	+	0.00385441i
$704$	−2.65377	−	25.2490i	−0.100018	−	0.951606i
$705$	4.46553	−	19.6911i	0.168181	−	0.741611i
$706$	−1.72346	+	16.3976i	−0.0648633	+	0.617133i
$707$	1.81928	+	3.15109i	0.0684211	+	0.118509i
$708$	−4.25472	+	2.97504i	−0.159902	+	0.111809i
$709$	−1.96106	−	2.17797i	−0.0736490	−	0.0817955i	0.705194	−	0.709014i	$-0.250860\pi$
$709$	−1.96106	−	2.17797i	−0.0736490	−	0.0817955i	−0.778843	+	0.627219i	$0.784193\pi$
$710$	−23.6938	−	21.1400i	−0.889212	−	0.793369i
$711$	33.6350	−	5.88537i	1.26141	−	0.220719i
$712$	−11.6428	+	35.8329i	−0.436333	+	1.34289i
$713$	7.59494	+	8.43503i	0.284433	+	0.315894i
$714$	0.329465	−	0.547510i	0.0123299	−	0.0204901i
$715$	17.3396	+	38.4743i	0.648465	+	1.43886i
$716$	−8.59463	+	1.82684i	−0.321196	+	0.0682724i
$717$	−2.44738	−	28.1861i	−0.0913990	−	1.05263i
$718$	−0.305309	+	0.528811i	−0.0113940	+	0.0197351i
$719$	13.9385	+	10.1269i	0.519820	+	0.377671i	0.816536	−	0.577295i	$-0.195892\pi$
$719$	13.9385	+	10.1269i	0.519820	+	0.377671i	−0.296716	+	0.954966i	$0.595892\pi$
$720$	−15.8279	−	5.70303i	−0.589872	−	0.212540i
$721$	−4.17330	+	3.03208i	−0.155422	+	0.112920i
$722$	−4.22424	−	40.1910i	−0.157210	−	1.49575i
$723$	−3.62906	−	0.0657210i	−0.134966	−	0.00244419i
$724$	−0.0165440	−	0.0286550i	−0.000614851	−	0.00106495i
$725$	−17.5624	−	12.5178i	−0.652253	−	0.464899i
$726$	−5.35565	+	1.03740i	−0.198767	+	0.0385014i
$727$	0.169906	+	0.0361146i	0.00630145	+	0.00133942i	0.211061	−	0.977473i	$-0.432308\pi$
$727$	0.169906	+	0.0361146i	0.00630145	+	0.00133942i	−0.204760	+	0.978812i	$0.565641\pi$
$728$	−5.11692	+	3.71766i	−0.189646	+	0.137786i
$729$	5.50988	+	26.4318i	0.204070	+	0.978956i
$730$	−2.11321	+	1.23289i	−0.0782134	+	0.0456313i
$731$	−2.41466	+	1.07508i	−0.0893094	+	0.0397631i
$732$	7.29232	−	1.41253i	0.269532	−	0.0522087i
$733$	5.54047	−	52.7141i	0.204642	−	1.94704i	−0.100988	−	0.994888i	$-0.532200\pi$
$733$	5.54047	−	52.7141i	0.204642	−	1.94704i	0.305630	−	0.952150i	$-0.401133\pi$
$734$	22.8001	−	4.84631i	0.841566	−	0.178880i
$735$	−5.20152	−	26.2152i	−0.191861	−	0.966960i
$736$	4.04616	+	0.860038i	0.149144	+	0.0317014i
$737$	−2.22670	+	6.85308i	−0.0820216	+	0.252436i
$738$	−1.12166	−	16.3479i	−0.0412889	−	0.601776i
$739$	−1.32714	−	4.08451i	−0.0488195	−	0.150251i	0.923675	−	0.383177i	$-0.125170\pi$
$739$	−1.32714	−	4.08451i	−0.0488195	−	0.150251i	−0.972494	+	0.232926i	$0.925170\pi$
$740$	−0.0294590	−	0.00942414i	−0.00108293	−	0.000346438i
$741$	−75.7188	+	32.0823i	−2.78160	+	1.17857i
$742$	0.167051	−	1.58938i	0.00613264	−	0.0583481i
$743$	−15.1680	−	26.2718i	−0.556461	−	0.963820i	−0.997788	−	0.0664731i	$-0.978825\pi$
$743$	−15.1680	−	26.2718i	−0.556461	−	0.963820i	0.441327	−	0.897346i	$-0.354508\pi$
$744$	3.99201	+	45.9754i	0.146354	+	1.68554i
$745$	−27.0451	+	37.5820i	−0.990855	+	1.37690i
$746$	−23.9192	+	17.3783i	−0.875745	+	0.636266i
$747$	13.9685	+	26.3542i	0.511082	+	0.964248i
$748$	0.507554	+	1.56209i	0.0185580	+	0.0571157i
$749$	−1.60118	+	2.77332i	−0.0585057	+	0.101335i
$750$	−21.9890	+	7.03578i	−0.802926	+	0.256910i
$751$	13.8299	+	23.9541i	0.504661	+	0.874099i	0.999985	+	0.00539081i	$0.00171596\pi$
$751$	13.8299	+	23.9541i	0.504661	+	0.874099i	−0.495324	+	0.868708i	$0.664951\pi$
$752$	8.74882	−	9.71655i	0.319037	−	0.354326i
$753$	18.7565	−	20.0875i	0.683526	−	0.732031i
$754$	3.50907	+	33.3866i	0.127793	+	1.21587i
$755$	47.4169	+	4.76614i	1.72568	+	0.173457i
$756$	−0.946142	−	0.0514480i	−0.0344109	−	0.00187115i
$757$	31.2908			1.13729			0.568643	−	0.822585i	$-0.307469\pi$
$757$	31.2908			1.13729			0.568643	+	0.822585i	$0.307469\pi$
$758$	−20.4215	+	9.09225i	−0.741743	+	0.330245i
$759$	−0.803491	+	6.50869i	−0.0291649	+	0.236250i
$760$	37.0026	−	33.6227i	1.34222	−	1.21962i
$761$	−12.3374	+	13.7021i	−0.447230	+	0.496699i	−0.924034	−	0.382311i	$-0.875128\pi$
$761$	−12.3374	+	13.7021i	−0.447230	+	0.496699i	0.476804	+	0.879010i	$0.341795\pi$
$762$	25.3718	+	19.1450i	0.919122	+	0.693552i
$763$	−2.33670	−	2.59517i	−0.0845942	−	0.0939514i
$764$	−0.428507	−	1.31881i	−0.0155028	−	0.0477128i
$765$	6.52541	+	0.895591i	0.235927	+	0.0323802i
$766$	2.01977	−	6.21620i	0.0729771	−	0.224601i
$767$	30.8937	−	13.7548i	1.11551	−	0.496656i
$768$	14.3210	+	16.4962i	0.516763	+	0.595255i
$769$	1.71866	−	16.3520i	0.0619765	−	0.589667i	−0.918826	−	0.394663i	$-0.870861\pi$
$769$	1.71866	−	16.3520i	0.0619765	−	0.589667i	0.980802	−	0.195004i	$-0.0624719\pi$
$770$	2.10906	+	1.20493i	0.0760052	+	0.0434227i
$771$	3.70417	+	0.857729i	0.133403	+	0.0308904i
$772$	−0.356567	−	3.39251i	−0.0128331	−	0.122099i
$773$	11.8001	+	36.3171i	0.424421	+	1.30623i	0.903547	+	0.428489i	$0.140954\pi$
$773$	11.8001	+	36.3171i	0.424421	+	1.30623i	−0.479126	+	0.877746i	$0.659046\pi$
$774$	−7.57943	−	5.93769i	−0.272437	−	0.213426i
$775$	29.2870	+	31.9384i	1.05202	+	1.14726i
$776$	−11.3637	+	19.6825i	−0.407932	+	0.706559i
$777$	0.0130472		0.000236281i	0.000468067		8.47653e-6i
$778$	−1.70787	−	0.760391i	−0.0612299	−	0.0272613i
$779$	30.4404	+	13.5529i	1.09064	+	0.485584i
$780$	−12.5687	−	7.48574i	−0.450033	−	0.268032i
$781$	−31.4586	+	14.0063i	−1.12568	+	0.501184i
$782$	1.53310			0.0548235
$783$	−12.2439	+	18.7732i	−0.437561	+	0.670898i
$784$	5.34808	−	16.4597i	0.191003	−	0.587846i
$785$	18.2380	−	25.3437i	0.650943	−	0.904555i
$786$	3.33801	+	6.03123i	0.119063	+	0.215127i
$787$	12.3966	−	2.63498i	0.441891	−	0.0939267i	0.0184071	−	0.999831i	$-0.494140\pi$
$787$	12.3966	−	2.63498i	0.441891	−	0.0939267i	0.423483	+	0.905904i	$0.360807\pi$
$788$	8.98497	−	1.90982i	0.320076	−	0.0680344i
$789$	51.3688	+	0.930272i	1.82878	+	0.0331186i
$790$	28.8151	−	9.50746i	1.02520	−	0.338260i
$791$	1.42851	−	4.39650i	0.0507919	−	0.156321i
$792$	−18.5473	+	19.1560i	−0.659049	+	0.680680i
$793$	−48.3834			−1.71814
$794$	−10.5457	+	4.69524i	−0.374252	+	0.166628i
$795$	15.7345	−	4.87748i	0.558047	−	0.172986i
$796$	−2.43683	−	1.08495i	−0.0863712	−	0.0384549i
$797$	19.2212	+	8.55785i	0.680851	+	0.303134i	0.717867	−	0.696180i	$-0.245119\pi$
$797$	19.2212	+	8.55785i	0.680851	+	0.303134i	−0.0370159	+	0.999315i	$0.511785\pi$
$798$	−2.44045	+	4.05558i	−0.0863910	+	0.143566i
$799$	−2.55941	+	4.43302i	−0.0905452	+	0.156829i
$800$	15.4765	+	3.14302i	0.547177	+	0.111122i
$801$	34.1075	−	13.7284i	1.20513	−	0.485070i
$802$	0.372328	+	1.14591i	0.0131473	+	0.0404634i
$803$	0.277337	+	2.63868i	0.00978699	+	0.0931170i
$804$	−0.728746	−	2.38921i	−0.0257009	−	0.0842610i
$805$	−0.683064	+	0.620673i	−0.0240749	+	0.0218758i
$806$	7.05060	−	67.0819i	0.248347	−	2.36286i
$807$	43.0340	−	8.33574i	1.51487	−	0.293432i
$808$	−32.4247	+	14.4364i	−1.14070	+	0.507871i
$809$	−11.6292	+	35.7910i	−0.408861	+	1.25834i	0.508767	+	0.860904i	$0.330102\pi$
$809$	−11.6292	+	35.7910i	−0.408861	+	1.25834i	−0.917628	+	0.397441i	$0.869898\pi$
$810$	8.24941	+	22.5302i	0.289855	+	0.791629i
$811$	8.42021	+	25.9147i	0.295673	+	0.909989i	0.982994	+	0.183636i	$0.0587866\pi$
$811$	8.42021	+	25.9147i	0.295673	+	0.909989i	−0.687321	+	0.726354i	$0.741213\pi$
$812$	−0.526315	−	0.584532i	−0.0184700	−	0.0205131i
$813$	3.99230	−	32.3397i	0.140016	−	1.13420i
$814$	0.0551348	−	0.0612334i	0.00193247	−	0.00214623i
$815$	−1.36842	+	0.150112i	−0.0479336	+	0.00525819i
$816$	3.40465	+	2.56908i	0.119187	+	0.0899359i
$817$	17.8861	−	7.96342i	0.625756	−	0.278605i
$818$	9.55806			0.334190
$819$	5.98676	+	1.50099i	0.209194	+	0.0524490i
$820$	1.25873	+	5.79242i	0.0439568	+	0.202280i
$821$	2.10819	+	20.0581i	0.0735763	+	0.700032i	0.967682	+	0.252175i	$0.0811459\pi$
$821$	2.10819	+	20.0581i	0.0735763	+	0.700032i	−0.894105	+	0.447857i	$0.852187\pi$
$822$	−16.9902	−	3.93421i	−0.592602	−	0.137221i
$823$	−32.2377	+	35.8036i	−1.12374	+	1.24804i	−0.158301	+	0.987391i	$0.550602\pi$
$823$	−32.2377	+	35.8036i	−1.12374	+	1.24804i	−0.965435	+	0.260645i	$0.916065\pi$
$824$	−25.1598	−	43.5780i	−0.876483	−	1.51811i
$825$	−2.84176	+	24.8755i	−0.0989375	+	0.866055i
$826$	0.973219	−	1.68566i	0.0338626	−	0.0586518i
$827$	−6.10623	−	18.7930i	−0.212334	−	0.653498i	−0.999332	−	0.0365422i	$-0.988366\pi$
$827$	−6.10623	−	18.7930i	−0.212334	−	0.653498i	0.786998	−	0.616956i	$-0.211634\pi$
$828$	−1.06465	−	2.00866i	−0.0369993	−	0.0698058i
$829$	21.1194	−	15.3441i	0.733507	−	0.532924i	−0.157164	−	0.987573i	$-0.550235\pi$
$829$	21.1194	−	15.3441i	0.733507	−	0.532924i	0.890671	+	0.454648i	$0.150235\pi$
$830$	15.6766	+	21.3723i	0.544143	+	0.741842i
$831$	32.1292	−	22.4658i	1.11455	−	0.779330i
$832$	−28.6631	−	49.6460i	−0.993716	−	1.72117i
$833$	−0.708240	+	6.73845i	−0.0245390	+	0.233473i
$834$	−0.361883	+	2.93144i	−0.0125310	+	0.101508i
$835$	11.4670	−	3.78349i	0.396830	−	0.130933i
$836$	−3.75961	−	11.5709i	−0.130029	−	0.400188i
$837$	31.9059	−	31.7809i	1.10283	−	1.09851i
$838$	9.22184	−	28.3819i	0.318563	−	0.980436i
$839$	2.91824	+	0.620290i	0.100749	+	0.0214148i	0.258010	−	0.966142i	$-0.416933\pi$
$839$	2.91824	+	0.620290i	0.100749	+	0.0214148i	−0.157261	+	0.987557i	$0.550267\pi$
$840$	−3.73687	+	0.341572i	−0.128934	+	0.0117854i
$841$	10.1675	−	2.16116i	0.350603	−	0.0745229i
$842$	−4.11124	+	39.1159i	−0.141683	+	1.34802i
$843$	0.529777	−	1.53532i	0.0182465	−	0.0528792i
$844$	−0.0782730	+	0.0348494i	−0.00269427	+	0.00119957i
$845$	49.4129	+	44.0869i	1.69985	+	1.51664i
$846$	−18.6341	−	0.675135i	−0.640652	−	0.0232116i
$847$	−0.673564	+	0.489373i	−0.0231439	+	0.0168150i
$848$	10.4342	+	2.21786i	0.358313	+	0.0761617i
$849$	−13.1656	−	15.1653i	−0.451843	−	0.520473i
$850$	5.85278	−	0.0531521i	0.200749	−	0.00182310i
$851$	0.0156542	+	0.0271139i	0.000536620	+	0.000929453i
$852$	6.15480	−	10.2281i	0.210860	−	0.350410i
$853$	−2.84812	−	27.0980i	−0.0975177	−	0.927819i	−0.928453	−	0.371450i	$-0.878861\pi$
$853$	−2.84812	−	27.0980i	−0.0975177	−	0.927819i	0.830935	−	0.556369i	$-0.187806\pi$
$854$	−2.25297	+	1.63688i	−0.0770950	+	0.0560128i
$855$	−48.3358	−	6.63392i	−1.65305	−	0.226875i
$856$	−25.2722	−	18.3613i	−0.863784	−	0.627576i
$857$	−25.6908	+	44.4978i	−0.877582	+	1.52002i	−0.0235962	+	0.999722i	$0.507512\pi$
$857$	−25.6908	+	44.4978i	−0.877582	+	1.52002i	−0.853986	+	0.520296i	$0.825822\pi$
$858$	31.9389	−	22.3327i	1.09037	−	0.762426i
$859$	−47.3418	+	10.0628i	−1.61528	+	0.343339i	−0.924931	−	0.380135i	$-0.875877\pi$
$859$	−47.3418	+	10.0628i	−1.61528	+	0.343339i	−0.690351	+	0.723474i	$0.742544\pi$
$860$	3.02419	+	1.72775i	0.103124	+	0.0589159i
$861$	−1.21102	−	2.18811i	−0.0412714	−	0.0745707i
$862$	−4.64902	−	5.16326i	−0.158346	−	0.175861i
$863$	0.728582	−	2.24234i	0.0248012	−	0.0763303i	−0.937890	−	0.346933i	$-0.887223\pi$
$863$	0.728582	−	2.24234i	0.0248012	−	0.0763303i	0.962691	+	0.270603i	$0.0872230\pi$
$864$	2.59922	−	16.2048i	0.0884271	−	0.551300i
$865$	0.172699	+	0.794722i	0.00587193	+	0.0270214i
$866$	1.66281	+	1.84674i	0.0565045	+	0.0627547i
$867$	25.1651	+	11.7547i	0.854650	+	0.399211i
$868$	0.790204	+	1.36867i	0.0268213	+	0.0464558i
$869$	3.43962	−	32.7258i	0.116681	−	1.11015i
$870$	−8.34702	+	18.0834i	−0.282990	+	0.613084i
$871$	1.70074	+	16.1815i	0.0576275	+	0.548289i
$872$	27.5591	−	20.0229i	0.933269	−	0.678060i
$873$	21.8464	−	3.82263i	0.739387	−	0.129376i
$874$	−11.3561			−0.384127
$875$	−2.58616	+	2.39317i	−0.0874281	+	0.0809040i
$876$	−0.602949	−	0.694531i	−0.0203718	−	0.0234660i
$877$	18.3361	−	20.3643i	0.619165	−	0.687652i	−0.349241	−	0.937033i	$-0.613560\pi$
$877$	18.3361	−	20.3643i	0.619165	−	0.687652i	0.968405	+	0.249381i	$0.0802271\pi$
$878$	24.8183	+	11.0498i	0.837578	+	0.372914i
$879$	−40.0074	−	9.26402i	−1.34942	−	0.312468i
$880$	−9.47017	+	13.1598i	−0.319239	+	0.443617i
$881$	−34.8348	−	25.3090i	−1.17362	−	0.852682i	−0.182179	−	0.983265i	$-0.558315\pi$
$881$	−34.8348	−	25.3090i	−1.17362	−	0.852682i	−0.991437	+	0.130584i	$0.958315\pi$
$882$	−22.8962	+	9.21584i	−0.770956	+	0.310313i
$883$	11.2465	+	8.17107i	0.378475	+	0.274979i	0.760717	−	0.649084i	$-0.224848\pi$
$883$	11.2465	+	8.17107i	0.378475	+	0.274979i	−0.382241	+	0.924063i	$0.624848\pi$
$884$	2.48162	+	2.75612i	0.0834660	+	0.0926984i
$885$	19.9231	+	2.36770i	0.669709	+	0.0795893i
$886$	−7.18311	+	7.97765i	−0.241321	+	0.268014i
$887$	5.62735	−	1.19613i	0.188948	−	0.0401621i	−0.112466	−	0.993656i	$-0.535875\pi$
$887$	5.62735	−	1.19613i	0.188948	−	0.0401621i	0.301414	+	0.953493i	$0.402541\pi$
$888$	−0.0155958	+	0.126334i	−0.000523361	+	0.00423949i
$889$	4.74494	+	1.00857i	0.159140	+	0.0338263i
$890$	28.2202	−	16.4643i	0.945944	−	0.551883i
$891$	25.9513	+	1.88297i	0.869402	+	0.0630818i
$892$	−0.770844	−	0.560051i	−0.0258098	−	0.0187519i
$893$	18.9583	−	32.8368i	0.634416	−	1.09884i
$894$	38.7411	+	18.0961i	1.29569	+	0.605225i
$895$	29.4837	+	16.8444i	0.985532	+	0.563046i
$896$	−1.19557	−	0.532301i	−0.0399411	−	0.0177829i
$897$	4.32023	+	14.1640i	0.144248	+	0.472922i
$898$	2.49962	+	0.531311i	0.0834134	+	0.0177301i
$899$	37.3829			1.24679
$900$	−4.13408	−	7.63139i	−0.137803	−	0.254380i
$901$	−4.17624			−0.139131
$902$	−15.4463	−	3.28320i	−0.514304	−	0.109319i
$903$	−1.43159	−	0.331495i	−0.0476402	−	0.0110314i
$904$	41.1951	+	18.3413i	1.37013	+	0.610021i
$905$	−0.0260173	+	0.125194i	−0.000864844	+	0.00416160i
$906$	−3.80700	−	43.8446i	−0.126479	−	1.45664i
$907$	−9.88602	+	17.1231i	−0.328260	+	0.568563i	−0.982167	−	0.188012i	$-0.939796\pi$
$907$	−9.88602	+	17.1231i	−0.328260	+	0.568563i	0.653907	+	0.756575i	$0.273129\pi$
$908$	−1.71435	−	1.24555i	−0.0568926	−	0.0413349i
$909$	31.1105	+	15.2240i	1.03187	+	0.504949i
$910$	5.45716	+	0.548530i	0.180903	+	0.0181836i
$911$	20.7570	+	4.41203i	0.687709	+	0.146177i	0.538496	−	0.842628i	$-0.318993\pi$
$911$	20.7570	+	4.41203i	0.687709	+	0.146177i	0.149213	+	0.988805i	$0.452326\pi$
$912$	−25.2193	−	19.0300i	−0.835095	−	0.630146i
$913$	28.1160	−	5.97623i	0.930502	−	0.197784i
$914$	−15.6087	+	17.3352i	−0.516290	+	0.573398i
$915$	−24.6624	−	14.6885i	−0.815314	−	0.485587i
$916$	0.327787	+	0.364045i	0.0108304	+	0.0120284i
$917$	0.851132	+	0.618383i	0.0281068	+	0.0204208i
$918$	−0.306415	−	6.07491i	−0.0101132	−	0.200502i
$919$	−0.706640	−	0.513404i	−0.0233099	−	0.0169356i	0.576069	−	0.817401i	$-0.304586\pi$
$919$	−0.706640	−	0.513404i	−0.0233099	−	0.0169356i	−0.599379	+	0.800465i	$0.704586\pi$
$920$	−5.32485	−	7.25948i	−0.175555	−	0.239338i
$921$	14.9260	−	15.9852i	0.491829	−	0.526730i
$922$	−4.15401	−	1.84948i	−0.136805	−	0.0609095i
$923$	−52.0290	+	57.7840i	−1.71255	+	1.90198i
$924$	−0.297852	+	0.863189i	−0.00979860	+	0.0283968i
$925$	0.0607019	+	0.102968i	0.00199587	+	0.00338556i
$926$	10.7898			0.354575
$927$	−16.8549	+	46.1205i	−0.553587	+	1.51480i
$928$	11.0219	−	8.00787i	0.361811	−	0.262871i
$929$	−1.35255	−	12.8687i	−0.0443759	−	0.422208i	−0.994046	−	0.108958i	$-0.965249\pi$
$929$	−1.35255	−	12.8687i	−0.0443759	−	0.422208i	0.949671	−	0.313251i	$-0.101418\pi$
$930$	23.9590	−	32.0531i	0.785647	−	1.05106i
$931$	5.24615	−	49.9138i	0.171936	−	1.63586i
$932$	−3.23391	−	5.60129i	−0.105930	−	0.183476i
$933$	−2.12211	−	24.4400i	−0.0694747	−	0.800130i
$934$	−24.5505	−	27.2661i	−0.803316	−	0.892173i
$935$	2.55537	−	5.81031i	0.0835694	−	0.190017i
$936$	−20.6660	+	56.5489i	−0.675488	+	1.84836i
$937$	−0.517445	+	1.59253i	−0.0169042	+	0.0520257i	−0.959153	−	0.282889i	$-0.908707\pi$
$937$	−0.517445	+	1.59253i	−0.0169042	+	0.0520257i	0.942249	+	0.334914i	$0.108707\pi$
$938$	0.626637	+	0.695951i	0.0204604	+	0.0227236i
$939$	−4.85067	−	0.0878441i	−0.158296	−	0.00286668i
$940$	6.70489	−	0.735508i	0.218689	−	0.0239896i
$941$	9.83792	−	2.09111i	0.320707	−	0.0681684i	−0.0447453	−	0.998998i	$-0.514248\pi$
$941$	9.83792	−	2.09111i	0.320707	−	0.0681684i	0.365452	+	0.930830i	$0.380914\pi$
$942$	−26.1253	−	12.2032i	−0.851208	−	0.397603i
$943$	3.00010	−	5.19632i	0.0976966	−	0.169216i
$944$	10.5109	+	7.63660i	0.342100	+	0.248550i
$945$	2.59594	+	2.58260i	0.0844461	+	0.0840119i
$946$	−7.50659	+	5.45386i	−0.244060	+	0.177320i
$947$	4.26952	+	40.6218i	0.138741	+	1.32003i	0.813315	+	0.581823i	$0.197660\pi$
$947$	4.26952	+	40.6218i	0.138741	+	1.32003i	−0.674575	+	0.738207i	$0.735673\pi$
$948$	5.52365	+	9.98033i	0.179400	+	0.324146i
$949$	2.99549	+	5.18833i	0.0972376	+	0.168420i
$950$	−43.3534	+	0.393714i	−1.40657	+	0.0127738i
$951$	−16.8501	+	48.8324i	−0.546402	+	1.58350i
$952$	0.930524	+	0.197789i	0.0301585	+	0.00641038i
$953$	−28.0837	+	20.4040i	−0.909720	+	0.660951i	−0.940944	−	0.338562i	$-0.890060\pi$
$953$	−28.0837	+	20.4040i	−0.909720	+	0.660951i	0.0312237	+	0.999512i	$0.490060\pi$
$954$	−7.12439	−	13.4414i	−0.230661	−	0.435183i
$955$	−2.15739	+	4.90540i	−0.0698114	+	0.158735i
$956$	8.63424	−	3.84421i	0.279251	−	0.124331i
$957$	14.1597	+	16.3104i	0.457717	+	0.527239i
$958$	−1.53473	+	14.6020i	−0.0495850	+	0.471770i
$959$	−2.60349	+	0.553388i	−0.0840710	+	0.0178698i
$960$	0.461413	−	34.0077i	0.0148920	−	1.09759i
$961$	−43.1476	−	9.17130i	−1.39186	−	0.295848i
$962$	0.0574940	−	0.176948i	0.00185368	−	0.00570504i
$963$	2.08661	+	30.4119i	0.0672402	+	0.980010i
$964$	−0.374693	−	1.15319i	−0.0120680	−	0.0371416i
$965$	−7.70007	+	10.7001i	−0.247874	+	0.344448i
$966$	0.680358	+	0.513385i	0.0218902	+	0.0165179i
$967$	2.19986	−	20.9302i	0.0707426	−	0.673071i	−0.900480	−	0.434897i	$-0.856785\pi$
$967$	2.19986	−	20.9302i	0.0707426	−	0.673071i	0.971223	−	0.238174i	$-0.0765487\pi$
$968$	−4.06075	−	7.03343i	−0.130517	−	0.226063i
$969$	11.2066	+	5.23464i	0.360007	+	0.168161i
$970$	18.7158	−	6.17522i	0.600928	−	0.198274i
$971$	27.0192	−	19.6306i	0.867089	−	0.629977i	−0.0627155	−	0.998031i	$-0.519976\pi$
$971$	27.0192	−	19.6306i	0.867089	−	0.629977i	0.929804	+	0.368055i	$0.119976\pi$
$972$	−7.74655	+	4.62017i	−0.248471	+	0.148192i
$973$	0.139302	+	0.428728i	0.00446583	+	0.0137444i
$974$	−2.96001	+	5.12688i	−0.0948448	+	0.164276i
$975$	16.9841	+	53.9229i	0.543925	+	1.72691i
$976$	−9.29412	−	16.0979i	−0.297497	−	0.515281i
$977$	5.17890	−	5.75176i	0.165688	−	0.184015i	−0.654583	−	0.755990i	$-0.727156\pi$
$977$	5.17890	−	5.75176i	0.165688	−	0.184015i	0.820271	+	0.571975i	$0.193823\pi$
$978$	0.370897	+	1.21599i	0.0118600	+	0.0388832i
$979$	−3.70361	−	35.2375i	−0.118368	−	1.12620i
$980$	7.71173	−	4.49918i	0.246342	−	0.143721i
$981$	−32.2440	−	8.08416i	−1.02947	−	0.258107i
$982$	−22.7253			−0.725195
$983$	−43.9585	+	19.5716i	−1.40206	+	0.624236i	−0.961829	−	0.273650i	$-0.911769\pi$
$983$	−43.9585	+	19.5716i	−1.40206	+	0.624236i	−0.440228	+	0.897886i	$0.645102\pi$
$984$	22.4623	−	9.51735i	0.716073	−	0.303402i
$985$	−30.8228	−	17.6094i	−0.982095	−	0.561083i
$986$	3.37863	−	3.75234i	0.107597	−	0.119499i
$987$	−2.62029	+	1.11022i	−0.0834047	+	0.0353388i
$988$	−18.3822	−	20.4154i	−0.584814	−	0.649502i
$989$	−1.08947	−	3.35303i	−0.0346430	−	0.106620i
$990$	23.0600	−	1.68742i	0.732896	−	0.0536298i
$991$	−15.7450	+	48.4581i	−0.500157	+	1.53932i	0.308607	+	0.951190i	$0.400137\pi$
$991$	−15.7450	+	48.4581i	−0.500157	+	1.53932i	−0.808763	+	0.588134i	$0.799863\pi$
$992$	−25.0070	+	11.1339i	−0.793974	+	0.353500i
$993$	11.5112	−	33.3599i	0.365296	−	1.05865i
$994$	−0.467810	+	4.45092i	−0.0148380	+	0.141175i
$995$	4.23552	+	9.39806i	0.134275	+	0.297939i
$996$	−6.80031	+	7.28288i	−0.215476	+	0.230767i
$997$	−1.58042	−	15.0367i	−0.0500525	−	0.476218i	−0.990623	−	0.136620i	$-0.956376\pi$
$997$	−1.58042	−	15.0367i	−0.0500525	−	0.476218i	0.940571	−	0.339597i	$-0.110291\pi$
$998$	1.84887	+	5.69025i	0.0585251	+	0.180122i
$999$	0.104310	−	0.0674492i	0.00330024	−	0.00213400i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.106.9	yes	224
3.2	odd	2		675.2.r.a.181.20		224
9.4	even	3	inner	225.2.q.a.31.20	✓	224
9.5	odd	6		675.2.r.a.631.9		224
25.21	even	5	inner	225.2.q.a.196.20	yes	224
75.71	odd	10		675.2.r.a.46.9		224
225.121	even	15	inner	225.2.q.a.121.9	yes	224
225.221	odd	30		675.2.r.a.496.20		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.20	✓	224	9.4	even	3	inner
225.2.q.a.106.9	yes	224	1.1	even	1	trivial
225.2.q.a.121.9	yes	224	225.121	even	15	inner
225.2.q.a.196.20	yes	224	25.21	even	5	inner
675.2.r.a.46.9		224	75.71	odd	10
675.2.r.a.181.20		224	3.2	odd	2
675.2.r.a.496.20		224	225.221	odd	30
675.2.r.a.631.9		224	9.5	odd	6

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16617 - 0.247876i) q^{2} +(-1.18208 + 1.26597i) q^{3} +(-0.528590 - 0.235343i) q^{4} +(0.918757 + 2.03860i) q^{5} +(1.69231 - 1.18332i) q^{6} +(0.157578 - 0.272934i) q^{7} +(2.48714 + 1.80701i) q^{8} +(-0.205352 - 2.99296i) q^{9} +O(q^{10})\)	\(q+(-1.16617 - 0.247876i) q^{2} +(-1.18208 + 1.26597i) q^{3} +(-0.528590 - 0.235343i) q^{4} +(0.918757 + 2.03860i) q^{5} +(1.69231 - 1.18332i) q^{6} +(0.157578 - 0.272934i) q^{7} +(2.48714 + 1.80701i) q^{8} +(-0.205352 - 2.99296i) q^{9} +(-0.566103 - 2.60508i) q^{10} +(-2.82788 - 0.601085i) q^{11} +(0.922776 - 0.390983i) q^{12} +(-6.38538 + 1.35725i) q^{13} +(-0.251417 + 0.279226i) q^{14} +(-3.66685 - 1.24668i) q^{15} +(-1.67816 - 1.86379i) q^{16} +(0.794350 + 0.577129i) q^{17} +(-0.502410 + 3.54119i) q^{18} +(-5.88399 - 4.27497i) q^{19} +(-0.00587474 - 1.29381i) q^{20} +(0.159255 + 0.522120i) q^{21} +(3.14879 + 1.40193i) q^{22} +(-0.876336 + 0.973270i) q^{23} +(-5.22763 + 1.01260i) q^{24} +(-3.31177 + 3.74595i) q^{25} +7.78284 q^{26} +(4.03174 + 3.27797i) q^{27} +(-0.147528 + 0.107185i) q^{28} +(0.450873 + 4.28977i) q^{29} +(3.96713 + 2.36276i) q^{30} +(0.905916 - 8.61921i) q^{31} +(-1.57924 - 2.73533i) q^{32} +(4.10375 - 2.86948i) q^{33} +(-0.783287 - 0.869928i) q^{34} +(0.701179 + 0.0704794i) q^{35} +(-0.595827 + 1.63038i) q^{36} +(0.00738727 - 0.0227357i) q^{37} +(5.80205 + 6.44383i) q^{38} +(5.82981 - 9.68807i) q^{39} +(-1.39870 + 6.73048i) q^{40} +(-4.48136 + 0.952542i) q^{41} +(-0.0562962 - 0.648355i) q^{42} +(-1.34599 + 2.33132i) q^{43} +(1.35333 + 0.983252i) q^{44} +(5.91278 - 3.16844i) q^{45} +(1.26320 - 0.917772i) q^{46} +(0.544941 + 5.18477i) q^{47} +(4.34323 + 0.0786545i) q^{48} +(3.45034 + 5.97616i) q^{49} +(4.79061 - 3.54749i) q^{50} +(-1.66962 + 0.323407i) q^{51} +(3.69467 + 0.785326i) q^{52} +(-3.44104 + 2.50006i) q^{53} +(-3.88915 - 4.82203i) q^{54} +(-1.37277 - 6.31717i) q^{55} +(0.885114 - 0.394078i) q^{56} +(12.3674 - 2.39557i) q^{57} +(0.537539 - 5.11434i) q^{58} +(-5.06713 + 1.07705i) q^{59} +(1.64486 + 1.52195i) q^{60} +(7.24968 + 1.54097i) q^{61} +(-3.19295 + 9.82688i) q^{62} +(-0.849240 - 0.415579i) q^{63} +(2.71365 + 8.35176i) q^{64} +(-8.63350 - 11.7702i) q^{65} +(-5.49693 + 2.32907i) q^{66} +(0.260529 - 2.47877i) q^{67} +(-0.284062 - 0.492010i) q^{68} +(-0.196226 - 2.25990i) q^{69} +(-0.800221 - 0.255996i) q^{70} +(9.63629 - 7.00118i) q^{71} +(4.89758 - 7.81499i) q^{72} +(-0.283594 - 0.872814i) q^{73} +(-0.0142504 + 0.0246825i) q^{74} +(-0.827464 - 8.62063i) q^{75} +(2.10413 + 3.64447i) q^{76} +(-0.609670 + 0.677108i) q^{77} +(-9.19997 + 9.85283i) q^{78} +(1.18974 + 11.3196i) q^{79} +(2.25770 - 5.13348i) q^{80} +(-8.91566 + 1.22922i) q^{81} +5.46212 q^{82} +(-9.08283 + 4.04394i) q^{83} +(0.0386972 - 0.313467i) q^{84} +(-0.446720 + 2.14960i) q^{85} +(2.14753 - 2.38507i) q^{86} +(-5.96368 - 4.50007i) q^{87} +(-5.94717 - 6.60500i) q^{88} +(3.78718 + 11.6557i) q^{89} +(-7.68067 + 2.22928i) q^{90} +(-0.635757 + 1.95666i) q^{91} +(0.692276 - 0.308221i) q^{92} +(9.84078 + 11.3355i) q^{93} +(0.649689 - 6.18138i) q^{94} +(3.30899 - 15.9228i) q^{95} +(5.32964 + 1.23412i) q^{96} +(0.772754 + 7.35226i) q^{97} +(-2.54232 - 7.82445i) q^{98} +(-1.21831 + 8.58719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

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