LMFDB - Embedded newform 684.2.cc.a.535.115

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(211,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 6, 1]))

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

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

chi := DirichletCharacter("684.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.cc (of order $18$, degree $6$, 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:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$696$
Relative dimension:	$116$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			535.115
Character	$\chi$	$=$	684.535
Dual form			684.2.cc.a.583.115

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41382 - 0.0331660i) q^{2} +(-1.71007 - 0.275074i) q^{3} +(1.99780 - 0.0937818i) q^{4} +(-0.487566 - 0.409117i) q^{5} +(-2.42686 - 0.332190i) q^{6} +(-1.01671 - 0.586999i) q^{7} +(2.82143 - 0.198850i) q^{8} +(2.84867 + 0.940789i) q^{9} +O(q^{10})$	\(q+(1.41382 - 0.0331660i) q^{2} +(-1.71007 - 0.275074i) q^{3} +(1.99780 - 0.0937818i) q^{4} +(-0.487566 - 0.409117i) q^{5} +(-2.42686 - 0.332190i) q^{6} +(-1.01671 - 0.586999i) q^{7} +(2.82143 - 0.198850i) q^{8} +(2.84867 + 0.940789i) q^{9} +(-0.702902 - 0.562248i) q^{10} -3.53898i q^{11} +(-3.44217 - 0.389169i) q^{12} +(-3.69058 - 4.39826i) q^{13} +(-1.45692 - 0.796193i) q^{14} +(0.721234 + 0.833734i) q^{15} +(3.98241 - 0.374715i) q^{16} +(0.0453581 + 0.0380600i) q^{17} +(4.05872 + 1.23563i) q^{18} +(3.92348 + 1.89902i) q^{19} +(-1.01243 - 0.771608i) q^{20} +(1.57718 + 1.28348i) q^{21} +(-0.117374 - 5.00350i) q^{22} +(-0.329637 + 0.905671i) q^{23} +(-4.87953 - 0.436053i) q^{24} +(-0.797897 - 4.52510i) q^{25} +(-5.36370 - 6.09597i) q^{26} +(-4.61263 - 2.39241i) q^{27} +(-2.08624 - 1.07736i) q^{28} +(3.19840 - 8.78753i) q^{29} +(1.04735 + 1.15483i) q^{30} +1.69013 q^{31} +(5.61800 - 0.661861i) q^{32} +(-0.973481 + 6.05190i) q^{33} +(0.0653907 + 0.0523058i) q^{34} +(0.255563 + 0.702155i) q^{35} +(5.77930 + 1.61236i) q^{36} +7.20123i q^{37} +(5.61010 + 2.55476i) q^{38} +(5.10130 + 8.53651i) q^{39} +(-1.45699 - 1.05734i) q^{40} +(4.10791 + 0.724336i) q^{41} +(2.27242 + 1.76231i) q^{42} +(-4.34014 - 11.9244i) q^{43} +(-0.331892 - 7.07018i) q^{44} +(-1.00402 - 1.62413i) q^{45} +(-0.436012 + 1.29139i) q^{46} +(-2.98026 + 8.18820i) q^{47} +(-6.91327 - 0.454668i) q^{48} +(-2.81086 - 4.86856i) q^{49} +(-1.27817 - 6.37123i) q^{50} +(-0.0670962 - 0.0775620i) q^{51} +(-7.78551 - 8.44073i) q^{52} +(3.85847 - 0.680353i) q^{53} +(-6.60080 - 3.22946i) q^{54} +(-1.44786 + 1.72549i) q^{55} +(-2.98531 - 1.45400i) q^{56} +(-6.18705 - 4.32670i) q^{57} +(4.23053 - 12.5301i) q^{58} +(6.13510 - 2.23299i) q^{59} +(1.51907 + 1.59799i) q^{60} +(-7.36100 + 6.17661i) q^{61} +(2.38955 - 0.0560548i) q^{62} +(-2.34403 - 2.62868i) q^{63} +(7.92092 - 1.12208i) q^{64} +3.65432i q^{65} +(-1.17561 + 8.58862i) q^{66} +(1.22266 + 6.93404i) q^{67} +(0.0941858 + 0.0717825i) q^{68} +(0.812829 - 1.45809i) q^{69} +(0.384609 + 0.984247i) q^{70} +(-1.72865 + 9.80369i) q^{71} +(8.22439 + 2.08791i) q^{72} +(-9.78246 + 3.56052i) q^{73} +(0.238836 + 10.1813i) q^{74} +(0.119723 + 7.95770i) q^{75} +(8.01643 + 3.42592i) q^{76} +(-2.07738 + 3.59813i) q^{77} +(7.49546 + 11.8999i) q^{78} +(3.96955 + 3.33085i) q^{79} +(-2.09499 - 1.44657i) q^{80} +(7.22983 + 5.35999i) q^{81} +(5.83189 + 0.887841i) q^{82} +(8.82113 + 5.09288i) q^{83} +(3.27126 + 2.41622i) q^{84} +(-0.00654411 - 0.0371135i) q^{85} +(-6.53168 - 16.7151i) q^{86} +(-7.88670 + 14.1475i) q^{87} +(-0.703727 - 9.98499i) q^{88} +(1.40092 - 3.84898i) q^{89} +(-1.47338 - 2.26294i) q^{90} +(1.17048 + 6.63813i) q^{91} +(-0.573614 + 1.84026i) q^{92} +(-2.89024 - 0.464910i) q^{93} +(-3.94200 + 11.6755i) q^{94} +(-1.13604 - 2.53106i) q^{95} +(-9.78923 - 0.413535i) q^{96} +(-7.75312 - 1.36708i) q^{97} +(-4.13554 - 6.79006i) q^{98} +(3.32944 - 10.0814i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 696 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 6 q^{6} - 18 q^{8}+O(q^{10}) $ 696 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 6 * q^6 - 18 * q^8	$ 696 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 6 q^{6} - 18 q^{8} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 15 q^{14} - 3 q^{16} - 24 q^{17} - 6 q^{20} - 30 q^{21} + 21 q^{22} + 24 q^{24} - 6 q^{25} - 30 q^{26} - 6 q^{29} - 21 q^{30} - 3 q^{32} + 36 q^{33} + 33 q^{34} + 54 q^{36} - 3 q^{38} - 33 q^{40} + 54 q^{41} - 87 q^{42} - 33 q^{44} - 6 q^{45} - 18 q^{46} + 6 q^{48} + 282 q^{49} - 3 q^{52} - 24 q^{53} - 51 q^{54} - 63 q^{56} - 12 q^{57} - 6 q^{58} - 27 q^{60} - 6 q^{61} - 18 q^{62} - 24 q^{64} - 30 q^{66} + 3 q^{68} - 18 q^{69} - 45 q^{70} + 12 q^{72} - 60 q^{73} + 3 q^{74} - 3 q^{76} + 72 q^{77} - 81 q^{78} - 12 q^{80} - 72 q^{81} - 12 q^{82} - 9 q^{84} - 6 q^{85} - 57 q^{86} - 9 q^{88} - 24 q^{89} + 39 q^{90} + 81 q^{92} - 48 q^{93} + 15 q^{96} + 30 q^{97} - 63 q^{98}+O(q^{100}) $ 696 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 6 * q^6 - 18 * q^8 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 15 * q^14 - 3 * q^16 - 24 * q^17 - 6 * q^20 - 30 * q^21 + 21 * q^22 + 24 * q^24 - 6 * q^25 - 30 * q^26 - 6 * q^29 - 21 * q^30 - 3 * q^32 + 36 * q^33 + 33 * q^34 + 54 * q^36 - 3 * q^38 - 33 * q^40 + 54 * q^41 - 87 * q^42 - 33 * q^44 - 6 * q^45 - 18 * q^46 + 6 * q^48 + 282 * q^49 - 3 * q^52 - 24 * q^53 - 51 * q^54 - 63 * q^56 - 12 * q^57 - 6 * q^58 - 27 * q^60 - 6 * q^61 - 18 * q^62 - 24 * q^64 - 30 * q^66 + 3 * q^68 - 18 * q^69 - 45 * q^70 + 12 * q^72 - 60 * q^73 + 3 * q^74 - 3 * q^76 + 72 * q^77 - 81 * q^78 - 12 * q^80 - 72 * q^81 - 12 * q^82 - 9 * q^84 - 6 * q^85 - 57 * q^86 - 9 * q^88 - 24 * q^89 + 39 * q^90 + 81 * q^92 - 48 * q^93 + 15 * q^96 + 30 * q^97 - 63 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.41382	−	0.0331660i	0.999725	−	0.0234519i
$2$	1.41382	−	0.0331660i	0.999725	−	0.0234519i
$3$	−1.71007	−	0.275074i	−0.987309	−	0.158814i
$3$	−1.71007	−	0.275074i	−0.987309	−	0.158814i
$4$	1.99780	−	0.0937818i	0.998900	−	0.0468909i
$5$	−0.487566	−	0.409117i	−0.218046	−	0.182962i	0.527221	−	0.849728i	$-0.323234\pi$
$5$	−0.487566	−	0.409117i	−0.218046	−	0.182962i	−0.745268	+	0.666765i	$0.767678\pi$
$6$	−2.42686	−	0.332190i	−0.990761	−	0.135616i
$7$	−1.01671	−	0.586999i	−0.384281	−	0.221865i	0.295398	−	0.955374i	$-0.404548\pi$
$7$	−1.01671	−	0.586999i	−0.384281	−	0.221865i	−0.679679	+	0.733509i	$0.737881\pi$
$8$	2.82143	−	0.198850i	0.997526	−	0.0703041i
$9$	2.84867	+	0.940789i	0.949556	+	0.313596i
$10$	−0.702902	−	0.562248i	−0.222277	−	0.177799i
$11$		−	3.53898i		−	1.06704i	−0.845786	−	0.533522i	$-0.820868\pi$
$11$		−	3.53898i		−	1.06704i	0.845786	−	0.533522i	$-0.179132\pi$
$12$	−3.44217	−	0.389169i	−0.993669	−	0.112343i
$13$	−3.69058	−	4.39826i	−1.02358	−	1.21986i	−0.975268	−	0.221026i	$-0.929060\pi$
$13$	−3.69058	−	4.39826i	−1.02358	−	1.21986i	−0.0483142	−	0.998832i	$-0.515385\pi$
$14$	−1.45692	−	0.796193i	−0.389378	−	0.212792i
$15$	0.721234	+	0.833734i	0.186222	+	0.215269i
$16$	3.98241	−	0.374715i	0.995602	−	0.0936786i
$17$	0.0453581	+	0.0380600i	0.0110010	+	0.00923090i	0.648272	−	0.761409i	$-0.275492\pi$
$17$	0.0453581	+	0.0380600i	0.0110010	+	0.00923090i	−0.637271	+	0.770640i	$0.719937\pi$
$18$	4.05872	+	1.23563i	0.956650	+	0.291241i
$19$	3.92348	+	1.89902i	0.900109	+	0.435666i
$19$	3.92348	+	1.89902i	0.900109	+	0.435666i
$20$	−1.01243	−	0.771608i	−0.226386	−	0.172537i
$21$	1.57718	+	1.28348i	0.344169	+	0.280078i
$22$	−0.117374	−	5.00350i	−0.0250242	−	1.06675i
$23$	−0.329637	+	0.905671i	−0.0687342	+	0.188846i	−0.969304	−	0.245866i	$-0.920928\pi$
$23$	−0.329637	+	0.905671i	−0.0687342	+	0.188846i	0.900570	+	0.434712i	$0.143150\pi$
$24$	−4.87953	−	0.436053i	−0.996031	−	0.0890090i
$25$	−0.797897	−	4.52510i	−0.159579	−	0.905019i
$26$	−5.36370	−	6.09597i	−1.05191	−	1.19552i
$27$	−4.61263	−	2.39241i	−0.887702	−	0.460419i
$28$	−2.08624	−	1.07736i	−0.394262	−	0.203601i
$29$	3.19840	−	8.78753i	0.593928	−	1.63180i	−0.169220	−	0.985578i	$-0.554125\pi$
$29$	3.19840	−	8.78753i	0.593928	−	1.63180i	0.763147	−	0.646225i	$-0.223653\pi$
$30$	1.04735	+	1.15483i	0.191219	+	0.210843i
$31$	1.69013			0.303556			0.151778	−	0.988415i	$-0.451500\pi$
$31$	1.69013			0.303556			0.151778	+	0.988415i	$0.451500\pi$
$32$	5.61800	−	0.661861i	0.993132	−	0.117002i
$33$	−0.973481	+	6.05190i	−0.169461	+	1.05350i
$34$	0.0653907	+	0.0523058i	0.0112144	+	0.00897037i
$35$	0.255563	+	0.702155i	0.0431981	+	0.118686i
$36$	5.77930	+	1.61236i	0.963217	+	0.268726i
$37$			7.20123i			1.18387i	0.805984	+	0.591937i	$0.201637\pi$
$37$			7.20123i			1.18387i	−0.805984	+	0.591937i	$0.798363\pi$
$38$	5.61010	+	2.55476i	0.910078	+	0.414436i
$39$	5.10130	+	8.53651i	0.816861	+	1.36694i
$40$	−1.45699	−	1.05734i	−0.230370	−	0.167180i
$41$	4.10791	+	0.724336i	0.641548	+	0.113122i	0.484952	−	0.874541i	$-0.338837\pi$
$41$	4.10791	+	0.724336i	0.641548	+	0.113122i	0.156596	+	0.987663i	$0.449948\pi$
$42$	2.27242	+	1.76231i	0.350642	+	0.271930i
$43$	−4.34014	−	11.9244i	−0.661865	−	1.81846i	−0.568258	−	0.822850i	$-0.692383\pi$
$43$	−4.34014	−	11.9244i	−0.661865	−	1.81846i	−0.0936067	−	0.995609i	$-0.529840\pi$
$44$	−0.331892	−	7.07018i	−0.0500346	−	1.06587i
$45$	−1.00402	−	1.62413i	−0.149671	−	0.242112i
$46$	−0.436012	+	1.29139i	−0.0642865	+	0.190406i
$47$	−2.98026	+	8.18820i	−0.434716	+	1.19437i	0.508170	+	0.861257i	$0.330322\pi$
$47$	−2.98026	+	8.18820i	−0.434716	+	1.19437i	−0.942886	+	0.333115i	$0.891900\pi$
$48$	−6.91327	−	0.454668i	−0.997844	−	0.0656257i
$49$	−2.81086	−	4.86856i	−0.401552	−	0.695509i
$50$	−1.27817	−	6.37123i	−0.180760	−	0.901028i
$51$	−0.0670962	−	0.0775620i	−0.00939535	−	0.0108609i
$52$	−7.78551	−	8.44073i	−1.07966	−	1.17052i
$53$	3.85847	−	0.680353i	0.530002	−	0.0934536i	0.0977576	−	0.995210i	$-0.468833\pi$
$53$	3.85847	−	0.680353i	0.530002	−	0.0934536i	0.432244	+	0.901757i	$0.357722\pi$
$54$	−6.60080	−	3.22946i	−0.898255	−	0.439474i
$55$	−1.44786	+	1.72549i	−0.195229	+	0.232665i
$56$	−2.98531	−	1.45400i	−0.398928	−	0.194299i
$57$	−6.18705	−	4.32670i	−0.819495	−	0.573086i
$58$	4.23053	−	12.5301i	0.555495	−	1.64528i
$59$	6.13510	−	2.23299i	0.798721	−	0.290711i	0.0897648	−	0.995963i	$-0.471388\pi$
$59$	6.13510	−	2.23299i	0.798721	−	0.290711i	0.708957	+	0.705252i	$0.249166\pi$
$60$	1.51907	+	1.59799i	0.196111	+	0.206300i
$61$	−7.36100	+	6.17661i	−0.942480	+	0.790834i	−0.978015	−	0.208534i	$-0.933131\pi$
$61$	−7.36100	+	6.17661i	−0.942480	+	0.790834i	0.0355353	+	0.999368i	$0.488686\pi$
$62$	2.38955	−	0.0560548i	0.303473	−	0.00711897i
$63$	−2.34403	−	2.62868i	−0.295321	−	0.331182i
$64$	7.92092	−	1.12208i	0.990115	−	0.140260i
$65$			3.65432i			0.453262i
$66$	−1.17561	+	8.58862i	−0.144708	+	1.05719i
$67$	1.22266	+	6.93404i	0.149372	+	0.847128i	0.963753	+	0.266798i	$0.0859656\pi$
$67$	1.22266	+	6.93404i	0.149372	+	0.847128i	−0.814381	+	0.580331i	$0.802923\pi$
$68$	0.0941858	+	0.0717825i	0.0114217	+	0.00870490i
$69$	0.812829	−	1.45809i	0.0978531	−	0.175533i
$70$	0.384609	+	0.984247i	0.0459696	+	0.117640i
$71$	−1.72865	+	9.80369i	−0.205154	+	1.16348i	0.692044	+	0.721855i	$0.256710\pi$
$71$	−1.72865	+	9.80369i	−0.205154	+	1.16348i	−0.897198	+	0.441629i	$0.854401\pi$
$72$	8.22439	+	2.08791i	0.969254	+	0.246063i
$73$	−9.78246	+	3.56052i	−1.14495	+	0.416728i	−0.843699	−	0.536817i	$-0.819627\pi$
$73$	−9.78246	+	3.56052i	−1.14495	+	0.416728i	−0.301252	+	0.953545i	$0.597404\pi$
$74$	0.238836	+	10.1813i	0.0277641	+	1.18355i
$75$	0.119723	+	7.95770i	0.0138245	+	0.918877i
$76$	8.01643	+	3.42592i	0.919547	+	0.392979i
$77$	−2.07738	+	3.59813i	−0.236739	+	0.410045i
$78$	7.49546	+	11.8999i	0.848694	+	1.34740i
$79$	3.96955	+	3.33085i	0.446609	+	0.374749i	0.838176	−	0.545400i	$-0.183622\pi$
$79$	3.96955	+	3.33085i	0.446609	+	0.374749i	−0.391567	+	0.920150i	$0.628067\pi$
$80$	−2.09499	−	1.44657i	−0.234227	−	0.161732i
$81$	7.22983	+	5.35999i	0.803315	+	0.595555i
$82$	5.83189	+	0.887841i	0.644025	+	0.0980456i
$83$	8.82113	+	5.09288i	0.968245	+	0.559017i	0.898701	−	0.438562i	$-0.144512\pi$
$83$	8.82113	+	5.09288i	0.968245	+	0.559017i	0.0695444	+	0.997579i	$0.477845\pi$
$84$	3.27126	+	2.41622i	0.356923	+	0.263632i
$85$	−0.00654411	−	0.0371135i	−0.000709809	−	0.00402553i
$86$	−6.53168	−	16.7151i	−0.704329	−	1.80244i
$87$	−7.88670	+	14.1475i	−0.845543	+	1.51677i
$88$	−0.703727	−	9.98499i	−0.0750175	−	1.06440i
$89$	1.40092	−	3.84898i	0.148497	−	0.407992i	−0.843035	−	0.537859i	$-0.819233\pi$
$89$	1.40092	−	3.84898i	0.148497	−	0.407992i	0.991531	+	0.129868i	$0.0414553\pi$
$90$	−1.47338	−	2.26294i	−0.155308	−	0.238535i
$91$	1.17048	+	6.63813i	0.122700	+	0.695865i
$92$	−0.573614	+	1.84026i	−0.0598034	+	0.191861i
$93$	−2.89024	−	0.464910i	−0.299704	−	0.0482089i
$94$	−3.94200	+	11.6755i	−0.406586	+	1.20424i
$95$	−1.13604	−	2.53106i	−0.116555	−	0.259681i
$96$	−9.78923	−	0.413535i	−0.999109	−	0.0422063i
$97$	−7.75312	−	1.36708i	−0.787210	−	0.138806i	−0.234430	−	0.972133i	$-0.575322\pi$
$97$	−7.75312	−	1.36708i	−0.787210	−	0.138806i	−0.552781	+	0.833327i	$0.686433\pi$
$98$	−4.13554	−	6.79006i	−0.417753	−	0.685900i
$99$	3.32944	−	10.0814i	0.334621	−	1.01322i
$100$	−2.01841	−	8.96541i	−0.201841	−	0.896541i
$101$	1.84826	+	10.4820i	0.183908	+	1.04300i	0.927350	+	0.374195i	$0.122081\pi$
$101$	1.84826	+	10.4820i	0.183908	+	1.04300i	−0.743442	+	0.668801i	$0.766808\pi$
$102$	−0.0974347	−	0.107434i	−0.00964747	−	0.0106375i
$103$	8.17352	+	14.1570i	0.805361	+	1.39493i	0.916047	+	0.401071i	$0.131362\pi$
$103$	8.17352	+	14.1570i	0.805361	+	1.39493i	−0.110686	+	0.993855i	$0.535305\pi$
$104$	−11.2873	−	11.6755i	−1.10681	−	1.14488i
$105$	−0.243887	−	1.27103i	−0.0238009	−	0.124040i
$106$	5.43264	−	1.08987i	0.527664	−	0.105857i
$107$	−0.993137	−	1.72016i	−0.0960102	−	0.166295i	0.814020	−	0.580837i	$-0.197275\pi$
$107$	−0.993137	−	1.72016i	−0.0960102	−	0.166295i	−0.910030	+	0.414543i	$0.863941\pi$
$108$	−9.43948	−	4.34697i	−0.908315	−	0.418288i
$109$	10.9465	+	1.93016i	1.04848	+	0.184876i	0.671240	−	0.741240i	$-0.265762\pi$
$109$	10.9465	+	1.93016i	1.04848	+	0.184876i	0.377241	+	0.926115i	$0.376873\pi$
$110$	−1.98979	+	2.48756i	−0.189719	+	0.237179i
$111$	1.98087	−	12.3146i	0.188016	−	1.16885i
$112$	−4.26892	−	1.95669i	−0.403375	−	0.184890i
$113$	17.0254	+	9.82963i	1.60162	+	0.924694i	0.991164	+	0.132641i	$0.0423458\pi$
$113$	17.0254	+	9.82963i	1.60162	+	0.924694i	0.610453	+	0.792053i	$0.290987\pi$
$114$	−8.89091	−	5.91200i	−0.832710	−	0.553710i
$115$	0.531245	−	0.306715i	0.0495389	−	0.0286013i
$116$	5.56565	−	17.8557i	0.516758	−	1.65786i
$117$	−6.37540	−	16.0012i	−0.589406	−	1.47932i
$118$	8.59989	−	3.36054i	0.791684	−	0.309362i
$119$	−0.0237750	−	0.0653212i	−0.00217945	−	0.00598798i
$120$	2.20070	+	2.20890i	0.200895	+	0.201644i
$121$	−1.52440			−0.138582
$122$	−10.2023	+	8.97678i	−0.923674	+	0.812720i
$123$	−6.82557	−	2.36864i	−0.615441	−	0.213573i
$124$	3.37654	−	0.158503i	0.303222	−	0.0142340i
$125$	−3.05345	+	5.28872i	−0.273108	+	0.473038i
$126$	−3.40124	−	3.63875i	−0.303006	−	0.324165i
$127$	−1.90144	−	0.692068i	−0.168726	−	0.0614111i	0.256276	−	0.966604i	$-0.417504\pi$
$127$	−1.90144	−	0.692068i	−0.168726	−	0.0614111i	−0.425002	+	0.905192i	$0.639727\pi$
$128$	11.1616	−	1.84913i	0.986553	−	0.163442i
$129$	4.14184	+	21.5855i	0.364669	+	1.90049i
$130$	0.121199	+	5.16657i	0.0106299	+	0.453138i
$131$	0.964518	+	2.64999i	0.0842704	+	0.231531i	0.974670	−	0.223649i	$-0.0717970\pi$
$131$	0.964518	+	2.64999i	0.0842704	+	0.231531i	−0.890399	+	0.455180i	$0.849575\pi$
$132$	−1.37726	+	12.1818i	−0.119875	+	1.06029i
$133$	−2.87433	−	4.23384i	−0.249236	−	0.367120i
$134$	1.95860	+	9.76297i	0.169197	+	0.843392i
$135$	1.27019	+	3.05356i	0.109321	+	0.262809i
$136$	0.135543	+	0.0983640i	0.0116227	+	0.00843465i
$137$	−1.85063	+	1.55287i	−0.158110	+	0.132670i	−0.718411	−	0.695619i	$-0.755130\pi$
$137$	−1.85063	+	1.55287i	−0.158110	+	0.132670i	0.560300	+	0.828289i	$0.310686\pi$
$138$	1.10084	−	2.08844i	0.0937096	−	0.177779i
$139$	−12.5530	−	14.9601i	−1.06473	−	1.26890i	−0.961667	−	0.274220i	$-0.911580\pi$
$139$	−12.5530	−	14.9601i	−1.06473	−	1.26890i	−0.103062	−	0.994675i	$-0.532864\pi$
$140$	0.576414	+	1.37880i	0.0487159	+	0.116530i
$141$	7.34881	−	13.1826i	0.618882	−	1.11018i
$142$	−2.11887	+	13.9180i	−0.177811	+	1.16798i
$143$	−15.5654	+	13.0609i	−1.30164	+	1.09221i
$144$	11.6971	+	2.67917i	0.974758	+	0.223264i
$145$	−5.15455	+	2.97598i	−0.428062	+	0.247142i
$146$	−13.7126	+	5.35840i	−1.13486	+	0.443464i
$147$	3.46756	+	9.09877i	0.285999	+	0.750454i
$148$	0.675344	+	14.3866i	0.0555129	+	1.18257i
$149$	0.807198	−	4.57785i	0.0661282	−	0.375032i	−0.933726	−	0.357987i	$-0.883463\pi$
$149$	0.807198	−	4.57785i	0.0661282	−	0.375032i	0.999855	−	0.0170447i	$-0.00542575\pi$
$150$	0.433193	+	11.2468i	0.0353701	+	0.918300i
$151$	−6.32564	−	10.9563i	−0.514773	−	0.891613i	−0.999853	−	0.0171432i	$-0.994543\pi$
$151$	−6.32564	−	10.9563i	−0.514773	−	0.891613i	0.485080	−	0.874470i	$-0.338790\pi$
$152$	11.4474	+	4.57777i	0.928510	+	0.371306i
$153$	0.0934038	+	0.151093i	0.00755125	+	0.0122151i
$154$	−2.81771	+	5.15602i	−0.227058	+	0.415484i
$155$	−0.824050	−	0.691460i	−0.0661893	−	0.0555394i
$156$	10.9919	+	16.5758i	0.880060	+	1.32713i
$157$	−12.0800	−	10.1363i	−0.964091	−	0.808969i	0.0175226	−	0.999846i	$-0.494422\pi$
$157$	−12.0800	−	10.1363i	−0.964091	−	0.808969i	−0.981614	+	0.190878i	$0.938867\pi$
$158$	5.72272	+	4.57758i	0.455275	+	0.364173i
$159$	−6.78540	+	0.102086i	−0.538117	+	0.00809596i
$160$	−3.00993	−	1.97572i	−0.237956	−	0.156194i
$161$	0.866775	−	0.727310i	0.0683114	−	0.0573201i
$162$	10.3995	+	7.33831i	0.817061	+	0.576552i
$163$	7.08490	+	4.09047i	0.554932	+	0.320390i	0.751109	−	0.660178i	$-0.229519\pi$
$163$	7.08490	+	4.09047i	0.554932	+	0.320390i	−0.196177	+	0.980569i	$0.562853\pi$
$164$	8.27472	+	1.06183i	0.646147	+	0.0829150i
$165$	2.95057	−	2.55244i	0.229702	−	0.198707i
$166$	12.6404	+	6.90788i	0.981089	+	0.536156i
$167$	−4.87303	−	1.77364i	−0.377086	−	0.137248i	0.146522	−	0.989207i	$-0.453192\pi$
$167$	−4.87303	−	1.77364i	−0.377086	−	0.137248i	−0.523608	+	0.851959i	$0.675414\pi$
$168$	4.70512	+	3.30762i	0.363008	+	0.255189i
$169$	−3.46690	+	19.6617i	−0.266684	+	1.51244i
$170$	−0.0104831	−	0.0522549i	−0.000804020	−	0.00400777i
$171$	9.39012	+	9.10086i	0.718081	+	0.695960i
$172$	−9.78903	−	23.4156i	−0.746406	−	1.78542i
$173$	8.29974	+	1.46347i	0.631017	+	0.111265i	0.480004	−	0.877266i	$-0.340635\pi$
$173$	8.29974	+	1.46347i	0.631017	+	0.111265i	0.151013	+	0.988532i	$0.451746\pi$
$174$	−10.6812	+	20.2636i	−0.809739	+	1.53618i
$175$	−1.84500	+	5.06908i	−0.139469	+	0.383187i
$176$	−1.32611	−	14.0937i	−0.0999592	−	1.06235i
$177$	−11.1057	+	2.13097i	−0.834753	+	0.160173i
$178$	1.85299	−	5.48825i	0.138888	−	0.411362i
$179$	5.59470	−	9.69031i	0.418168	−	0.724287i	−0.577588	−	0.816329i	$-0.696006\pi$
$179$	5.59470	−	9.69031i	0.418168	−	0.724287i	0.995755	+	0.0920413i	$0.0293392\pi$
$180$	−2.15815	−	3.15054i	−0.160859	−	0.234827i
$181$	2.27725	+	2.71392i	0.169267	+	0.201724i	0.844009	−	0.536329i	$-0.180190\pi$
$181$	2.27725	+	2.71392i	0.169267	+	0.201724i	−0.674742	+	0.738054i	$0.735745\pi$
$182$	1.87502	+	9.34633i	0.138985	+	0.692796i
$183$	14.2868	−	8.53762i	1.05611	−	0.631119i
$184$	−0.749956	+	2.62084i	−0.0552875	+	0.193211i
$185$	2.94614	−	3.51107i	0.216605	−	0.258139i
$186$	−4.10171	−	0.561444i	−0.300752	−	0.0411670i
$187$	0.134694	−	0.160522i	0.00984977	−	0.0117385i
$188$	−5.18606	+	16.6379i	−0.378233	+	1.21344i
$189$	3.28538	+	5.14000i	0.238976	+	0.373880i
$190$	−1.69010	−	3.54080i	−0.122613	−	0.256876i
$191$	17.4564	−	10.0784i	1.26310	−	0.729251i	0.289427	−	0.957200i	$-0.406535\pi$
$191$	17.4564	−	10.0784i	1.26310	−	0.729251i	0.973673	+	0.227949i	$0.0732020\pi$
$192$	−13.8540	−	0.259997i	−0.999824	−	0.0187637i
$193$	−14.2639	−	2.51511i	−1.02674	−	0.181041i	−0.365180	−	0.930937i	$-0.618993\pi$
$193$	−14.2639	−	2.51511i	−1.02674	−	0.181041i	−0.661556	+	0.749895i	$0.730104\pi$
$194$	−11.0069	−	1.67568i	−0.790249	−	0.120307i
$195$	1.00521	−	6.24914i	0.0719843	−	0.447510i
$196$	−6.07213	−	9.46280i	−0.433723	−	0.675914i
$197$	4.46222	+	7.72879i	0.317920	+	0.550654i	0.980054	−	0.198732i	$-0.0636823\pi$
$197$	4.46222	+	7.72879i	0.317920	+	0.550654i	−0.662134	+	0.749386i	$0.730349\pi$
$198$	4.37288	−	14.3637i	0.310767	−	1.02079i
$199$	−2.14596	−	2.55745i	−0.152123	−	0.181293i	0.684601	−	0.728918i	$-0.259976\pi$
$199$	−2.14596	−	2.55745i	−0.152123	−	0.181293i	−0.836724	+	0.547625i	$0.815532\pi$
$200$	−3.15102	−	12.6086i	−0.222811	−	0.891561i
$201$	−0.183459	−	12.1940i	−0.0129402	−	0.860099i
$202$	2.96075	+	14.7584i	0.208318	+	1.03840i
$203$	−8.41012	+	7.05693i	−0.590275	+	0.495299i
$204$	−0.141319	−	0.148661i	−0.00989429	−	0.0104083i
$205$	−1.70654	−	2.03378i	−0.119190	−	0.142045i
$206$	12.0255	+	19.7444i	0.837853	+	1.37566i
$207$	−1.79107	+	2.26984i	−0.124488	+	0.157765i
$208$	−16.3455	−	16.1328i	−1.13336	−	1.11861i
$209$	6.72061	−	13.8851i	0.464874	−	0.960455i
$210$	−0.386968	−	1.78893i	−0.0267033	−	0.123448i
$211$	−16.0564	+	5.84406i	−1.10537	+	0.402322i	−0.829293	−	0.558814i	$-0.811257\pi$
$211$	−16.0564	+	5.84406i	−1.10537	+	0.402322i	−0.276077	+	0.961136i	$0.589035\pi$
$212$	7.64465	−	1.72106i	0.525037	−	0.118203i
$213$	5.65285	−	16.2895i	0.387327	−	1.11614i
$214$	−1.46117	−	2.39907i	−0.0998837	−	0.163997i
$215$	−2.76238	+	7.58957i	−0.188393	+	0.517605i
$216$	−13.4899	−	5.83279i	−0.917875	−	0.396871i
$217$	−1.71838	−	0.992104i	−0.116651	−	0.0673484i
$218$	15.5404	+	2.36585i	1.05253	+	0.160236i
$219$	17.7081	−	3.39784i	1.19660	−	0.229605i
$220$	−2.73071	+	3.58296i	−0.184104	+	0.241563i
$221$		−	0.339960i		−	0.0228682i
$222$	2.39217	−	17.4764i	0.160552	−	1.17294i
$223$	15.7860	−	5.74564i	1.05711	−	0.384756i	0.245768	−	0.969329i	$-0.420960\pi$
$223$	15.7860	−	5.74564i	1.05711	−	0.384756i	0.811342	+	0.584572i	$0.198738\pi$
$224$	−6.10040	−	2.62484i	−0.407600	−	0.175379i
$225$	1.98422	−	13.6412i	0.132281	−	0.909410i
$226$	24.3970	+	13.3327i	1.62286	+	0.886879i
$227$	−4.24031	−	7.34442i	−0.281439	−	0.487467i	0.690300	−	0.723523i	$-0.257478\pi$
$227$	−4.24031	−	7.34442i	−0.281439	−	0.487467i	−0.971739	+	0.236056i	$0.924145\pi$
$228$	−12.7663	−	8.06366i	−0.845466	−	0.534029i
$229$	0.149213	−	0.258445i	0.00986027	−	0.0170785i	−0.861053	−	0.508515i	$-0.830195\pi$
$229$	0.149213	−	0.258445i	0.00986027	−	0.0170785i	0.870913	+	0.491436i	$0.163528\pi$
$230$	0.740915	−	0.451260i	0.0488545	−	0.0297552i
$231$	4.54221	−	5.58161i	0.298855	−	0.367243i
$232$	7.27665	−	25.4294i	0.477736	−	1.66952i
$233$	0.355753	−	2.01758i	0.0233062	−	0.132176i	−0.970935	−	0.239345i	$-0.923067\pi$
$233$	0.355753	−	2.01758i	0.0233062	−	0.132176i	0.994241	+	0.107169i	$0.0341785\pi$
$234$	−9.54439	−	22.4115i	−0.623937	−	1.46509i
$235$	4.80300	−	2.77302i	0.313313	−	0.180892i
$236$	12.0473	−	5.03643i	0.784211	−	0.327844i
$237$	−5.87197	−	6.78789i	−0.381426	−	0.440921i
$238$	−0.0357801	−	0.0915642i	−0.00231928	−	0.00593523i
$239$	−10.7195	+	6.18891i	−0.693388	+	0.400328i	−0.804880	−	0.593438i	$-0.797770\pi$
$239$	−10.7195	+	6.18891i	−0.693388	+	0.400328i	0.111492	+	0.993765i	$0.464437\pi$
$240$	3.18466	+	3.05001i	0.205569	+	0.196877i
$241$	−24.9882	+	4.40609i	−1.60963	+	0.283821i	−0.904891	−	0.425644i	$-0.860047\pi$
$241$	−24.9882	+	4.40609i	−1.60963	+	0.283821i	−0.704740	+	0.709466i	$0.748936\pi$
$242$	−2.15523	+	0.0505582i	−0.138544	+	0.00325000i
$243$	−10.8891	−	11.1547i	−0.698537	−	0.715574i
$244$	−14.1266	+	13.0300i	−0.904360	+	0.834158i
$245$	−0.621326	+	3.52372i	−0.0396951	+	0.225122i
$246$	−9.72871	−	3.12247i	−0.620280	−	0.199081i
$247$	−6.12753	−	24.2650i	−0.389885	−	1.54394i
$248$	4.76858	−	0.336082i	0.302805	−	0.0213413i
$249$	−13.6838	−	11.1356i	−0.867177	−	0.705693i
$250$	−4.14163	+	7.57860i	−0.261940	+	0.479313i
$251$	29.1660	−	5.14276i	1.84094	−	0.324608i	0.858737	−	0.512416i	$-0.171250\pi$
$251$	29.1660	−	5.14276i	1.84094	−	0.324608i	0.982206	+	0.187809i	$0.0601385\pi$
$252$	−4.92943	−	5.03174i	−0.310525	−	0.316970i
$253$	3.20516	+	1.16658i	0.201506	+	0.0733423i
$254$	−2.71126	−	0.915400i	−0.170119	−	0.0574373i
$255$	0.000981937		0.0652668i	6.14913e−5		0.00408716i
$256$	15.7192	−	2.98453i	0.982449	−	0.186533i
$257$	11.4207	−	2.01378i	0.712406	−	0.125616i	0.194312	−	0.980940i	$-0.437753\pi$
$257$	11.4207	−	2.01378i	0.712406	−	0.125616i	0.518094	+	0.855323i	$0.326642\pi$
$258$	6.57174	+	30.3807i	0.409139	+	1.89142i
$259$	4.22711	−	7.32157i	0.262660	−	0.454940i
$260$	0.342709	+	7.30060i	0.0212539	+	0.452764i
$261$	17.3784	−	22.0237i	1.07570	−	1.36324i
$262$	1.45155	+	3.71464i	0.0896770	+	0.229491i
$263$	−6.65017	+	7.92536i	−0.410067	+	0.488699i	−0.931062	−	0.364861i	$-0.881117\pi$
$263$	−6.65017	+	7.92536i	−0.410067	+	0.488699i	0.520995	+	0.853560i	$0.325561\pi$
$264$	−1.54318	+	17.2686i	−0.0949764	+	1.06281i
$265$	−2.15960	−	1.24685i	−0.132663	−	0.0765932i
$266$	−4.20422	−	5.89058i	−0.257777	−	0.361174i
$267$	−3.45442	+	6.19667i	−0.211407	+	0.379230i
$268$	3.09292	+	13.7382i	0.188930	+	0.839192i
$269$	4.69883	+	12.9099i	0.286493	+	0.787132i	0.996550	+	0.0829889i	$0.0264466\pi$
$269$	4.69883	+	12.9099i	0.286493	+	0.787132i	−0.710058	+	0.704143i	$0.751331\pi$
$270$	1.89710	+	4.27507i	0.115454	+	0.260173i
$271$	0.478173	+	0.0843148i	0.0290470	+	0.00512176i	0.188153	−	0.982140i	$-0.439750\pi$
$271$	0.478173	+	0.0843148i	0.0290470	+	0.00512176i	−0.159106	+	0.987262i	$0.550861\pi$
$272$	0.194896	+	0.134574i	0.0118173	+	0.00815975i
$273$	−0.175629	−	11.6736i	−0.0106296	−	0.706520i
$274$	−2.56497	+	2.25686i	−0.154955	+	0.136342i
$275$	−16.0142	+	2.82374i	−0.965695	+	0.170278i
$276$	1.48713	−	2.98919i	0.0895146	−	0.179928i
$277$	21.8041			1.31008			0.655041	−	0.755593i	$-0.272651\pi$
$277$	21.8041			1.31008			0.655041	+	0.755593i	$0.272651\pi$
$278$	−18.2439	−	20.7346i	−1.09419	−	1.24358i
$279$	4.81462	+	1.59006i	0.288244	+	0.0951942i
$280$	0.860677	+	1.93026i	0.0514353	+	0.115355i
$281$	14.9015	+	17.7589i	0.888950	+	1.05941i	0.997862	+	0.0653583i	$0.0208190\pi$
$281$	14.9015	+	17.7589i	0.888950	+	1.05941i	−0.108912	+	0.994051i	$0.534737\pi$
$282$	9.95272	−	18.8816i	0.592676	−	1.12438i
$283$	−5.14754	−	14.1428i	−0.305990	−	0.840699i	−0.993428	−	0.114457i	$-0.963487\pi$
$283$	−5.14754	−	14.1428i	−0.305990	−	0.840699i	0.687439	−	0.726242i	$-0.258735\pi$
$284$	−2.53410	+	19.7479i	−0.150371	+	1.17182i
$285$	1.24647	+	4.64078i	0.0738346	+	0.274896i
$286$	−21.5735	+	18.9821i	−1.27567	+	1.12243i
$287$	−3.75138	−	3.14778i	−0.221437	−	0.185808i
$288$	16.6265	+	3.39993i	0.979726	+	0.200343i
$289$	−2.95141	−	16.7383i	−0.173612	−	0.984605i
$290$	−7.18893	+	4.37847i	−0.422149	+	0.257113i
$291$	12.8823	+	4.47049i	0.755175	+	0.262065i
$292$	−19.2095	+	8.03063i	−1.12415	+	0.469957i
$293$	18.8958	−	10.9095i	1.10391	−	0.637341i	0.166663	−	0.986014i	$-0.446701\pi$
$293$	18.8958	−	10.9095i	1.10391	−	0.637341i	0.937245	+	0.348673i	$0.113368\pi$
$294$	5.20429	+	12.7491i	0.303520	+	0.743540i
$295$	−3.90482	−	1.42124i	−0.227347	−	0.0827477i
$296$	1.43196	+	20.3177i	0.0832312	+	1.18095i
$297$	−8.46669	+	16.3240i	−0.491287	+	0.947216i
$298$	0.989408	−	6.49904i	0.0573148	−	0.376480i
$299$	5.19993	−	1.89262i	0.300720	−	0.109453i
$300$	0.985471	+	15.8867i	0.0568962	+	0.917218i
$301$	−2.58696	+	14.6714i	−0.149110	+	0.845644i
$302$	−9.30672	−	15.2805i	−0.535541	−	0.879295i
$303$	−0.277329	−	18.4333i	−0.0159321	−	1.05897i
$304$	16.3365	+	6.09250i	0.936963	+	0.349429i
$305$	6.11593			0.350197
$306$	0.137068	+	0.210521i	0.00783564	+	0.0120347i
$307$	5.46543	−	1.98926i	0.311929	−	0.113533i	−0.181312	−	0.983426i	$-0.558034\pi$
$307$	5.46543	−	1.98926i	0.311929	−	0.113533i	0.493241	+	0.869893i	$0.335812\pi$
$308$	−3.81275	+	7.38316i	−0.217252	+	0.420694i
$309$	−10.0831	−	26.4577i	−0.573606	−	1.50513i
$310$	−1.18800	−	0.950273i	−0.0674736	−	0.0539719i
$311$		−	25.9275i		−	1.47021i	−0.677953	−	0.735106i	$-0.737133\pi$
$311$		−	25.9275i		−	1.47021i	0.677953	−	0.735106i	$-0.262867\pi$
$312$	16.0904	+	23.0707i	0.910941	+	1.30612i
$313$	17.3974	+	6.33215i	0.983361	+	0.357914i	0.783146	−	0.621838i	$-0.213614\pi$
$313$	17.3974	+	6.33215i	0.983361	+	0.357914i	0.200215	+	0.979752i	$0.435836\pi$
$314$	−17.4152	−	13.9304i	−0.982798	−	0.786136i
$315$	0.0674359	+	2.24064i	0.00379958	+	0.126246i
$316$	8.24274	+	6.28209i	0.463690	+	0.353395i
$317$	−21.6157	+	3.81142i	−1.21406	+	0.214071i	−0.743766	−	0.668440i	$-0.766962\pi$
$317$	−21.6157	+	3.81142i	−1.21406	+	0.214071i	−0.470291	+	0.882511i	$0.655851\pi$
$318$	−9.58997	+	0.369376i	−0.537779	+	0.0207136i
$319$	−31.0989	−	11.3191i	−1.74120	−	0.633747i
$320$	−4.32103	−	2.69349i	−0.241553	−	0.150571i
$321$	1.22516	+	3.21478i	0.0683818	+	0.179432i
$322$	1.20135	−	1.05704i	0.0669484	−	0.0589063i
$323$	0.105685	+	0.235464i	0.00588047	+	0.0131016i
$324$	14.9464	+	10.0302i	0.830357	+	0.557232i
$325$	−16.9578	+	20.2096i	−0.940652	+	1.12103i
$326$	10.1525	+	5.54823i	0.562293	+	0.307288i
$327$	−18.1883	−	6.31179i	−1.00581	−	0.349043i
$328$	11.7342	+	1.22680i	0.647914	+	0.0677389i
$329$	7.83654	−	6.57563i	0.432042	−	0.362526i
$330$	4.08693	−	3.70656i	0.224978	−	0.204039i
$331$	10.7206			0.589256			0.294628	−	0.955612i	$-0.404804\pi$
$331$	10.7206			0.589256			0.294628	+	0.955612i	$0.404804\pi$
$332$	18.1005	+	9.34730i	0.993393	+	0.513000i
$333$	−6.77484	+	20.5139i	−0.371259	+	1.12416i
$334$	−6.94843	−	2.34599i	−0.380201	−	0.128367i
$335$	2.24071	−	3.88102i	0.122423	−	0.212043i
$336$	6.76191	+	4.52035i	0.368893	+	0.246605i
$337$	−1.18953	+	1.41762i	−0.0647977	+	0.0772229i	−0.797470	−	0.603359i	$-0.793829\pi$
$337$	−1.18953	+	1.41762i	−0.0647977	+	0.0772229i	0.732672	+	0.680582i	$0.238273\pi$
$338$	−4.24948	+	27.9132i	−0.231141	+	1.51828i
$339$	−26.4108	−	21.4926i	−1.43444	−	1.16732i
$340$	−0.0165544	−	0.0735316i	−0.000897788	−	0.00398781i
$341$		−	5.98134i		−	0.323908i
$342$	13.5778	+	12.5556i	0.734205	+	0.678928i
$343$			14.8179i			0.800091i
$344$	−14.6166	−	32.7809i	−0.788073	−	1.76743i
$345$	−0.992835	+	0.378371i	−0.0534524	+	0.0203708i
$346$	11.7829	+	1.79382i	0.633453	+	0.0964362i
$347$	12.2413	−	14.5886i	0.657145	−	0.783155i	−0.329828	−	0.944041i	$-0.606991\pi$
$347$	12.2413	−	14.5886i	0.657145	−	0.783155i	0.986973	+	0.160886i	$0.0514352\pi$
$348$	−14.4293	+	29.0035i	−0.773490	+	1.55475i
$349$	−8.17381	+	14.1574i	−0.437534	+	0.757831i	−0.997499	−	0.0706855i	$-0.977481\pi$
$349$	−8.17381	+	14.1574i	−0.437534	+	0.757831i	0.559965	+	0.828516i	$0.310815\pi$
$350$	−2.44038	+	7.22799i	−0.130444	+	0.386352i
$351$	6.50085	+	29.1169i	0.346990	+	1.55415i
$352$	−2.34232	−	19.8820i	−0.124846	−	1.05971i
$353$	21.1641			1.12645			0.563225	−	0.826304i	$-0.309561\pi$
$353$	21.1641			1.12645			0.563225	+	0.826304i	$0.309561\pi$
$354$	−15.6308	+	3.38114i	−0.830767	+	0.179706i
$355$	4.85368	−	4.07273i	0.257607	−	0.216158i
$356$	2.43779	−	7.82088i	0.129202	−	0.414506i
$357$	0.0226887	+	0.118244i	0.00120081	+	0.00625811i
$358$	7.58854	−	13.8859i	0.401067	−	0.733895i
$359$	−17.2464	+	20.5534i	−0.910230	+	1.08477i	0.0858499	+	0.996308i	$0.472639\pi$
$359$	−17.2464	+	20.5534i	−0.910230	+	1.08477i	−0.996080	+	0.0884614i	$0.971805\pi$
$360$	−3.15574	−	4.38273i	−0.166322	−	0.230990i
$361$	11.7874	+	14.9016i	0.620391	+	0.784293i
$362$	3.30964	+	3.76148i	0.173951	+	0.197699i
$363$	2.60683	+	0.419322i	0.136823	+	0.0220087i
$364$	2.96092	+	13.1519i	0.155195	+	0.689346i
$365$	6.22626	+	2.26618i	0.325898	+	0.118617i
$366$	19.9159	−	12.5445i	1.04102	−	0.655713i
$367$	−1.24671	+	0.219829i	−0.0650779	+	0.0114750i	−0.206092	−	0.978533i	$-0.566075\pi$
$367$	−1.24671	+	0.219829i	−0.0650779	+	0.0114750i	0.141014	+	0.990008i	$0.454964\pi$
$368$	−0.973383	+	3.73027i	−0.0507411	+	0.194454i
$369$	11.0206	+	5.92807i	0.573711	+	0.308603i
$370$	4.04888	−	5.06175i	0.210491	−	0.263148i
$371$	−4.32232	−	1.57320i	−0.224404	−	0.0816763i
$372$	−5.81772	−	0.657746i	−0.301635	−	0.0341025i
$373$			12.5003i			0.647241i	0.946187	+	0.323621i	$0.104900\pi$
$373$			12.5003i			0.647241i	−0.946187	+	0.323621i	$0.895100\pi$
$374$	0.185109	−	0.231417i	0.00957177	−	0.0119663i
$375$	6.67639	−	8.20416i	0.344767	−	0.423661i
$376$	−6.78037	+	23.6951i	−0.349671	+	1.22198i
$377$	−50.4538	+	18.3637i	−2.59850	+	0.945777i
$378$	4.81542	+	7.15810i	0.247679	+	0.368173i
$379$	16.2044			0.832367			0.416183	−	0.909281i	$-0.363367\pi$
$379$	16.2044			0.832367			0.416183	+	0.909281i	$0.363367\pi$
$380$	−2.50694	−	4.95001i	−0.128603	−	0.253930i
$381$	3.06123	+	1.70652i	0.156831	+	0.0874277i
$382$	24.3460	−	14.8281i	1.24565	−	0.758672i
$383$	1.58090	−	8.96570i	0.0807800	−	0.458126i	−0.917408	−	0.397949i	$-0.869722\pi$
$383$	1.58090	−	8.96570i	0.0807800	−	0.458126i	0.998188	−	0.0601774i	$-0.0191666\pi$
$384$	−19.5957	+	0.0918904i	−0.999989	+	0.00468926i
$385$	2.48491	−	0.904434i	0.126643	−	0.0460942i
$386$	−20.2500	−	3.08285i	−1.03070	−	0.156913i
$387$	−1.14524	−	38.0519i	−0.0582158	−	1.93429i
$388$	−15.6174	−	2.00406i	−0.792853	−	0.101741i
$389$	−24.2817	−	8.83783i	−1.23113	−	0.448096i	−0.357148	−	0.934048i	$-0.616251\pi$
$389$	−24.2817	−	8.83783i	−1.23113	−	0.448096i	−0.873985	+	0.485952i	$0.838473\pi$
$390$	1.21393	−	8.86852i	0.0614696	−	0.449075i
$391$	−0.0494216	+	0.0285336i	−0.00249936	+	0.00144300i
$392$	−8.89877	−	13.1774i	−0.449456	−	0.665557i
$393$	−0.920450	−	4.79698i	−0.0464305	−	0.241976i
$394$	6.56513	+	10.7792i	0.330746	+	0.543046i
$395$	−0.572713	−	3.24802i	−0.0288163	−	0.163425i
$396$	5.70610	−	20.4528i	0.286742	−	1.02779i
$397$	−12.2783	−	10.3027i	−0.616228	−	0.517077i	0.280387	−	0.959887i	$-0.409537\pi$
$397$	−12.2783	−	10.3027i	−0.616228	−	0.517077i	−0.896615	+	0.442810i	$0.853982\pi$
$398$	−3.11882	−	3.54461i	−0.156333	−	0.177675i
$399$	3.75068	+	8.03081i	0.187769	+	0.402043i
$400$	−4.87317	−	17.7218i	−0.243659	−	0.886090i
$401$	5.86688	+	16.1191i	0.292978	+	0.804951i	0.995627	+	0.0934144i	$0.0297781\pi$
$401$	5.86688	+	16.1191i	0.292978	+	0.804951i	−0.702649	+	0.711536i	$0.748000\pi$
$402$	−0.663805	−	17.2341i	−0.0331076	−	0.859559i
$403$	−6.23756	−	7.43363i	−0.310715	−	0.370295i
$404$	4.67546	+	20.7676i	0.232613	+	1.03322i
$405$	−1.33216	−	5.57120i	−0.0661955	−	0.276835i
$406$	−11.6564	+	10.2562i	−0.578497	+	0.509006i
$407$	25.4850			1.26325
$408$	−0.204730	−	0.205494i	−0.0101357	−	0.0101734i
$409$	16.8464	−	2.97047i	0.833000	−	0.146880i	0.259146	−	0.965838i	$-0.416559\pi$
$409$	16.8464	−	2.97047i	0.833000	−	0.146880i	0.573854	+	0.818958i	$0.305448\pi$
$410$	−2.48020	−	2.81880i	−0.122488	−	0.139211i
$411$	3.59186	−	2.14645i	0.177173	−	0.105876i
$412$	17.6567	+	27.5162i	0.869885	+	1.35563i
$413$	−7.54839	−	1.33098i	−0.371432	−	0.0654935i
$414$	−2.45698	+	3.26856i	−0.120754	+	0.160641i
$415$	−2.21730	−	6.09199i	−0.108843	−	0.299044i
$416$	−23.6447	−	22.2668i	−1.15928	−	1.09172i
$417$	17.3513	+	29.0357i	0.849698	+	1.42188i
$418$	9.04124	−	19.8540i	0.442222	−	0.971093i
$419$	−13.8202	−	7.97907i	−0.675159	−	0.389803i	0.122870	−	0.992423i	$-0.460790\pi$
$419$	−13.8202	−	7.97907i	−0.675159	−	0.389803i	−0.798028	+	0.602620i	$0.794124\pi$
$420$	−0.606436	−	2.51639i	−0.0295911	−	0.122787i
$421$	17.9937	−	21.4440i	0.876959	−	1.04512i	−0.121660	−	0.992572i	$-0.538822\pi$
$421$	17.9937	−	21.4440i	0.876959	−	1.04512i	0.998618	−	0.0525471i	$-0.0167340\pi$
$422$	−22.5072	+	8.79501i	−1.09563	+	0.428134i
$423$	−16.1932	+	20.5217i	−0.787338	+	0.997798i
$424$	10.7511	−	2.68682i	0.522120	−	0.130484i
$425$	0.136034	−	0.235618i	0.00659862	−	0.0114291i
$426$	7.45189	−	23.2179i	0.361045	−	1.12491i
$427$	11.1097	−	1.95894i	0.537635	−	0.0947996i
$428$	−2.14541	−	3.34341i	−0.103702	−	0.161610i
$429$	30.2105	−	18.0534i	1.45858	−	0.871626i
$430$	−3.65380	+	10.8219i	−0.176202	+	0.521880i
$431$	0.811453	+	0.295345i	0.0390863	+	0.0142263i	0.361489	−	0.932376i	$-0.382268\pi$
$431$	0.811453	+	0.295345i	0.0390863	+	0.0142263i	−0.322403	+	0.946603i	$0.604491\pi$
$432$	−19.2659	−	7.79913i	−0.926929	−	0.375236i
$433$	30.5612	−	5.38876i	1.46868	−	0.258967i	0.618633	−	0.785680i	$-0.287687\pi$
$433$	30.5612	−	5.38876i	1.46868	−	0.258967i	0.850043	+	0.526713i	$0.176576\pi$
$434$	−2.46239	−	1.34567i	−0.118198	−	0.0645942i
$435$	9.63325	−	3.67125i	0.461879	−	0.176023i
$436$	22.0499	+	2.82949i	1.05600	+	0.135508i
$437$	−3.01322	+	2.92740i	−0.144142	+	0.140036i
$438$	24.9234	−	5.39126i	1.19089	−	0.257604i
$439$	−0.790674	+	4.48413i	−0.0377368	+	0.214016i	−0.997845	−	0.0656120i	$-0.979100\pi$
$439$	−0.790674	+	4.48413i	−0.0377368	+	0.214016i	0.960108	+	0.279628i	$0.0902111\pi$
$440$	−3.74191	+	5.15625i	−0.178389	+	0.245814i
$441$	−3.42693	−	16.5133i	−0.163187	−	0.786350i
$442$	−0.0112751	−	0.480644i	−0.000536303	−	0.0228619i
$443$	−12.4370	+	2.19298i	−0.590901	+	0.104192i	−0.461100	−	0.887348i	$-0.652545\pi$
$443$	−12.4370	+	2.19298i	−0.590901	+	0.104192i	−0.129801	+	0.991540i	$0.541434\pi$
$444$	2.80249	−	24.7879i	0.133000	−	1.17638i
$445$	−2.25772	+	1.30350i	−0.107026	+	0.0617917i
$446$	22.1281	−	8.64688i	1.04780	−	0.409442i
$447$	−2.63961	+	7.60639i	−0.124849	+	0.359770i
$448$	−8.71195	−	3.50874i	−0.411601	−	0.165772i
$449$	−16.4354	+	9.48899i	−0.775635	+	0.447813i	−0.834881	−	0.550430i	$-0.814464\pi$
$449$	−16.4354	+	9.48899i	−0.775635	+	0.447813i	0.0592463	+	0.998243i	$0.481130\pi$
$450$	2.35292	−	19.3520i	0.110917	−	0.912262i
$451$	2.56341	−	14.5378i	0.120706	−	0.684560i
$452$	34.9352	+	18.0410i	1.64321	+	0.848576i
$453$	7.80348	+	20.4761i	0.366639	+	0.962050i
$454$	−6.23863	−	10.2431i	−0.292794	−	0.480732i
$455$	2.14508	−	3.71539i	0.100563	−	0.174180i
$456$	−18.3167	−	10.9772i	−0.857758	−	0.514054i
$457$	−1.44824	−	2.50842i	−0.0677456	−	0.117339i	0.830163	−	0.557521i	$-0.188247\pi$
$457$	−1.44824	−	2.50842i	−0.0677456	−	0.117339i	−0.897909	+	0.440182i	$0.854914\pi$
$458$	0.202389	−	0.370344i	0.00945704	−	0.0173050i
$459$	−0.118165	−	0.284072i	−0.00551549	−	0.0132593i
$460$	1.03256	−	0.662576i	0.0481432	−	0.0308927i
$461$	−12.9511	+	4.71380i	−0.603192	+	0.219544i	−0.625522	−	0.780207i	$-0.715114\pi$
$461$	−12.9511	+	4.71380i	−0.603192	+	0.219544i	0.0223300	+	0.999751i	$0.492892\pi$
$462$	6.23677	−	8.04207i	0.290161	−	0.374151i
$463$			38.4671i			1.78772i	0.448350	+	0.893858i	$0.352012\pi$
$463$			38.4671i			1.78772i	−0.448350	+	0.893858i	$0.647988\pi$
$464$	9.44452	−	36.1940i	0.438451	−	1.68027i
$465$	1.21898	+	1.40912i	0.0565288	+	0.0653463i
$466$	0.436057	−	2.86430i	0.0202000	−	0.132686i
$467$	−18.6543	−	10.7701i	−0.863218	−	0.498379i	0.00187029	−	0.999998i	$-0.499405\pi$
$467$	−18.6543	−	10.7701i	−0.863218	−	0.498379i	−0.865089	+	0.501619i	$0.832738\pi$
$468$	−14.2374	−	31.3694i	−0.658124	−	1.45005i
$469$	2.82718	−	7.76763i	0.130547	−	0.358676i
$470$	6.69864	−	4.07985i	0.308985	−	0.188190i
$471$	17.8694	+	20.6567i	0.823380	+	0.951813i
$472$	16.8657	−	7.52019i	0.776307	−	0.346145i
$473$	−42.2004	+	15.3597i	−1.94038	+	0.706239i
$474$	−8.52707	−	9.40214i	−0.391661	−	0.431855i
$475$	5.46272	−	19.2694i	0.250647	−	0.884139i
$476$	−0.0536236	−	0.128269i	−0.00245783	−	0.00587920i
$477$	11.6316	+	1.69191i	0.532573	+	0.0774672i
$478$	−14.9503	+	9.10556i	−0.683809	+	0.416479i
$479$	7.88746	+	9.39991i	0.360387	+	0.429493i	0.915522	−	0.402268i	$-0.131778\pi$
$479$	7.88746	+	9.39991i	0.360387	+	0.429493i	−0.555135	+	0.831760i	$0.687333\pi$
$480$	4.60371	+	4.20656i	0.210130	+	0.192002i
$481$	31.6729	−	26.5767i	1.44416	−	1.21179i
$482$	−35.1828	+	7.05820i	−1.60253	+	0.321492i
$483$	−1.68231	+	1.00532i	−0.0765477	+	0.0457438i
$484$	−3.04544	+	0.142961i	−0.138429	+	0.00649822i
$485$	3.22086	+	3.83848i	0.146252	+	0.174296i
$486$	−15.7653	−	15.4096i	−0.715126	−	0.698995i
$487$	10.5558	+	18.2831i	0.478328	+	0.828488i	0.999691	−	0.0248464i	$-0.00790967\pi$
$487$	10.5558	+	18.2831i	0.478328	+	0.828488i	−0.521363	+	0.853335i	$0.674576\pi$
$488$	−19.5403	+	18.8906i	−0.884549	+	0.855138i
$489$	−10.9905	−	8.94385i	−0.497007	−	0.404455i
$490$	−0.761579	+	5.00252i	−0.0344046	+	0.225991i
$491$	−14.1926	−	2.50255i	−0.640505	−	0.112938i	−0.156042	−	0.987750i	$-0.549874\pi$
$491$	−14.1926	−	2.50255i	−0.640505	−	0.112938i	−0.484462	+	0.874812i	$0.660985\pi$
$492$	−13.8583	−	4.09196i	−0.624778	−	0.184480i
$493$	0.479526	−	0.276855i	0.0215968	−	0.0124689i
$494$	−9.46802	−	34.1032i	−0.425986	−	1.53438i
$495$	−5.74778	+	3.55322i	−0.258344	+	0.159705i
$496$	6.73079	−	0.633316i	0.302221	−	0.0284367i
$497$	7.51230	−	8.95281i	0.336973	−	0.401588i
$498$	−19.7159	−	15.2900i	−0.883489	−	0.685162i
$499$	−11.5927	+	13.8157i	−0.518962	+	0.618475i	−0.960335	−	0.278849i	$-0.910047\pi$
$499$	−11.5927	+	13.8157i	−0.518962	+	0.618475i	0.441373	+	0.897324i	$0.354492\pi$
$500$	−5.60419	+	10.8522i	−0.250627	+	0.485324i
$501$	7.84533	+	4.37348i	0.350503	+	0.195393i
$502$	41.0651	−	8.23827i	1.83282	−	0.367692i
$503$	−24.8427	−	29.6064i	−1.10768	−	1.32008i	−0.942645	−	0.333797i	$-0.891670\pi$
$503$	−24.8427	−	29.6064i	−1.10768	−	1.32008i	−0.165037	−	0.986287i	$-0.552774\pi$
$504$	−7.13624	−	6.95051i	−0.317873	−	0.309601i
$505$	3.38720	−	5.86681i	0.150729	−	0.261070i
$506$	4.57022	+	1.54304i	0.203171	+	0.0685965i
$507$	11.3371	−	32.6693i	0.503496	−	1.45089i
$508$	−3.86360	−	1.20429i	−0.171420	−	0.0534319i
$509$	1.70614	−	4.68759i	0.0756234	−	0.207774i	−0.896121	−	0.443810i	$-0.853626\pi$
$509$	1.70614	−	4.68759i	0.0756234	−	0.207774i	0.971744	+	0.236037i	$0.0758486\pi$
$510$	0.00355292	+	0.0922432i	0.000157326	+	0.00408460i
$511$	12.0360	+	2.12227i	0.532440	+	0.0938835i
$512$	22.1252	−	4.74095i	0.977804	−	0.209522i
$513$	−13.5544	−	18.1461i	−0.598439	−	0.801168i
$514$	16.0801	−	3.22592i	0.709264	−	0.142289i
$515$	1.80671	−	10.2464i	0.0796133	−	0.451509i
$516$	10.2989	+	42.7350i	0.453383	+	1.88130i
$517$	28.9779	+	10.5471i	1.27445	+	0.463861i
$518$	5.73357	−	10.4916i	0.251919	−	0.460975i
$519$	−13.7906	−	4.78567i	−0.605338	−	0.210068i
$520$	0.726662	+	10.3104i	0.0318662	+	0.452141i
$521$	23.1720	+	13.3784i	1.01518	+	0.586117i	0.912705	−	0.408619i	$-0.133989\pi$
$521$	23.1720	+	13.3784i	1.01518	+	0.586117i	0.102478	+	0.994735i	$0.467323\pi$
$522$	23.8396	−	31.7141i	1.04343	−	1.38809i
$523$	−5.28348	+	4.43337i	−0.231030	+	0.193858i	−0.750953	−	0.660356i	$-0.770405\pi$
$523$	−5.28348	+	4.43337i	−0.231030	+	0.193858i	0.519922	+	0.854214i	$0.325961\pi$
$524$	2.17544	+	5.20370i	0.0950344	+	0.227325i
$525$	4.54944	−	8.16097i	0.198554	−	0.356174i
$526$	−9.13932	+	11.4256i	−0.398493	+	0.498181i
$527$	0.0766611	+	0.0643263i	0.00333941	+	0.00280210i
$528$	−1.60906	+	24.4659i	−0.0700254	+	1.06474i
$529$	16.9074	+	14.1870i	0.735106	+	0.616827i
$530$	−3.09465	−	1.69120i	−0.134423	−	0.0734610i
$531$	19.5776	−	0.589223i	0.849597	−	0.0255701i
$532$	−6.13939	−	8.18880i	−0.266176	−	0.355030i
$533$	−11.9748	−	20.7409i	−0.518684	−	0.898387i
$534$	−4.67842	+	8.87558i	−0.202455	+	0.384084i
$535$	−0.219528	+	1.24500i	−0.00949101	+	0.0538262i
$536$	4.82848	+	19.3208i	0.208559	+	0.834531i
$537$	−12.2329	+	15.0321i	−0.527887	+	0.648684i
$538$	7.07149	+	18.0965i	0.304874	+	0.780197i
$539$	−17.2297	+	9.94760i	−0.742138	+	0.428473i
$540$	2.82395	+	5.98128i	0.121524	+	0.257394i
$541$	−8.84265	+	7.41987i	−0.380175	+	0.319005i	−0.812771	−	0.582583i	$-0.802042\pi$
$541$	−8.84265	+	7.41987i	−0.380175	+	0.319005i	0.432596	+	0.901588i	$0.357598\pi$
$542$	0.678850	+	0.103347i	0.0291591	+	0.00443915i
$543$	−3.14773	−	5.26740i	−0.135082	−	0.226046i
$544$	0.280012	+	0.183800i	0.0120054	+	0.00788037i
$545$	−4.54747	−	5.41946i	−0.194792	−	0.232144i
$546$	−0.635477	−	16.4986i	−0.0271959	−	0.706076i
$547$	−8.76441	+	7.35421i	−0.374739	+	0.314443i	−0.810633	−	0.585555i	$-0.800877\pi$
$547$	−8.76441	+	7.35421i	−0.374739	+	0.314443i	0.435894	+	0.899998i	$0.356432\pi$
$548$	−3.55156	+	3.27587i	−0.151715	+	0.139938i
$549$	−26.7800	+	10.6700i	−1.14294	+	0.455384i
$550$	−22.5477	+	4.52340i	−0.961436	+	0.192879i
$551$	29.2366	−	28.4039i	1.24552	−	1.21005i
$552$	2.00340	−	4.27552i	0.0852703	−	0.181978i
$553$	−2.08068	−	5.71663i	−0.0884797	−	0.243096i
$554$	30.8272	−	0.723155i	1.30972	−	0.0307239i
$555$	−6.00391	+	5.19377i	−0.254852	+	0.220463i
$556$	−26.4813	−	28.7100i	−1.12306	−	1.21757i
$557$	0.157325	+	0.0572615i	0.00666606	+	0.00242625i	0.345351	−	0.938474i	$-0.387760\pi$
$557$	0.157325	+	0.0572615i	0.00666606	+	0.00242625i	−0.338685	+	0.940900i	$0.609982\pi$
$558$	6.85976	+	2.08838i	0.290397	+	0.0884081i
$559$	−36.4291	+	63.0971i	−1.54079	+	2.66872i
$560$	1.28087	+	2.70050i	0.0541264	+	0.114117i
$561$	−0.274491	+	0.237452i	−0.0115890	+	0.0100252i
$562$	21.6571	+	24.6138i	0.913551	+	1.03827i
$563$	9.41665			0.396865			0.198432	−	0.980115i	$-0.436415\pi$
$563$	9.41665			0.396865			0.198432	+	0.980115i	$0.436415\pi$
$564$	13.4452	−	27.0254i	0.566144	−	1.13797i
$565$	−4.27955	−	11.7580i	−0.180042	−	0.494662i
$566$	−7.74678	−	19.8246i	−0.325621	−	0.833292i
$567$	−4.20434	−	9.69347i	−0.176566	−	0.407088i
$568$	−2.92781	+	28.0041i	−0.122848	+	1.17503i
$569$	−8.32704	+	4.80762i	−0.349088	+	0.201546i	−0.664283	−	0.747481i	$-0.731263\pi$
$569$	−8.32704	+	4.80762i	−0.349088	+	0.201546i	0.315196	+	0.949027i	$0.397930\pi$
$570$	1.91621	+	6.51991i	0.0802611	+	0.273089i
$571$	−0.818882	−	0.472782i	−0.0342691	−	0.0197853i	0.482768	−	0.875749i	$-0.339632\pi$
$571$	−0.818882	−	0.472782i	−0.0342691	−	0.0197853i	−0.517037	+	0.855963i	$0.672965\pi$
$572$	−29.8716	+	27.5528i	−1.24899	+	1.15204i
$573$	−32.6239	+	12.4330i	−1.36288	+	0.519398i
$574$	−5.40819	−	4.32599i	−0.225734	−	0.180563i
$575$	4.36127	+	0.769009i	0.181877	+	0.0320699i
$576$	23.6197	+	4.25547i	0.984155	+	0.177311i
$577$	−16.2338	−	28.1178i	−0.675823	−	1.17056i	−0.976228	−	0.216748i	$-0.930455\pi$
$577$	−16.2338	−	28.1178i	−0.675823	−	1.17056i	0.300405	−	0.953812i	$-0.402878\pi$
$578$	−4.72792	−	23.5671i	−0.196655	−	0.980262i
$579$	23.7004	+	8.22462i	0.984954	+	0.341804i
$580$	−10.0187	+	6.42882i	−0.416003	+	0.266942i
$581$	−5.97904	−	10.3560i	−0.248052	−	0.429639i
$582$	18.3616	+	5.89323i	0.761113	+	0.244282i
$583$	−2.40776	−	13.6551i	−0.0997191	−	0.565535i
$584$	−26.8925	+	11.9910i	−1.11282	+	0.496191i
$585$	−3.43794	+	10.4099i	−0.142142	+	0.430398i
$586$	26.3536	−	16.0509i	1.08866	−	0.663055i
$587$	−9.19622	−	1.62154i	−0.379569	−	0.0669282i	−0.0193912	−	0.999812i	$-0.506173\pi$
$587$	−9.19622	−	1.62154i	−0.379569	−	0.0669282i	−0.360178	+	0.932884i	$0.617284\pi$
$588$	7.78079	+	17.8523i	0.320874	+	0.736217i
$589$	6.63119	+	3.20959i	0.273234	+	0.132249i
$590$	−5.56787	−	1.87987i	−0.229225	−	0.0773932i
$591$	−5.50472	−	14.4442i	−0.226434	−	0.594155i
$592$	2.69840	+	28.6782i	0.110904	+	1.17867i
$593$	−4.69293	−	26.6149i	−0.192715	−	1.09294i	−0.915635	−	0.402011i	$-0.868311\pi$
$593$	−4.69293	−	26.6149i	−0.192715	−	1.09294i	0.722919	−	0.690932i	$-0.242800\pi$
$594$	−11.4290	+	23.3601i	−0.468938	+	0.958477i
$595$	−0.0151321	+	0.0415751i	−0.000620356	+	0.00170441i
$596$	1.18330	−	9.22132i	0.0484699	−	0.377720i
$597$	2.96624	+	4.96371i	0.121400	+	0.203151i
$598$	7.28902	−	2.84829i	0.298070	−	0.116475i
$599$	5.75481	+	32.6372i	0.235135	+	1.33352i	0.842329	+	0.538964i	$0.181184\pi$
$599$	5.75481	+	32.6372i	0.235135	+	1.33352i	−0.607193	+	0.794554i	$0.707705\pi$
$600$	1.92018	+	22.4283i	0.0783911	+	0.915631i
$601$	10.6831	+	6.16788i	0.435772	+	0.251593i	0.701803	−	0.712371i	$-0.252379\pi$
$601$	10.6831	+	6.16788i	0.435772	+	0.251593i	−0.266030	+	0.963965i	$0.585712\pi$
$602$	−3.17092	+	20.8286i	−0.129237	+	0.848908i
$603$	−3.04052	+	20.9031i	−0.123820	+	0.851239i
$604$	−13.6649	−	21.2953i	−0.556015	−	0.866494i
$605$	0.743245	+	0.623656i	0.0302172	+	0.0253552i
$606$	−1.00345	−	26.0523i	−0.0407625	−	1.05830i
$607$	−7.94843	+	13.7671i	−0.322617	+	0.558789i	−0.981027	−	0.193871i	$-0.937896\pi$
$607$	−7.94843	+	13.7671i	−0.322617	+	0.558789i	0.658410	+	0.752659i	$0.271229\pi$
$608$	23.2990	+	8.07191i	0.944900	+	0.327359i
$609$	16.3231	−	9.75443i	0.661444	−	0.395269i
$610$	8.64685	−	0.202841i	0.350101	−	0.00821279i
$611$	47.0127	−	17.1112i	1.90193	−	0.692247i
$612$	0.200772	+	0.293093i	0.00811572	+	0.0118476i
$613$	−1.23616	+	7.01061i	−0.0499280	+	0.283156i	−0.999542	−	0.0302665i	$-0.990364\pi$
$613$	−1.23616	+	7.01061i	−0.0499280	+	0.283156i	0.949614	+	0.313422i	$0.101476\pi$
$614$	7.66119	−	2.99372i	0.309180	−	0.120817i
$615$	2.35886	+	3.94732i	0.0951186	+	0.159171i
$616$	−5.14569	+	10.5649i	−0.207326	+	0.425674i
$617$	1.12574	+	6.38441i	0.0453208	+	0.257027i	0.999047	−	0.0436499i	$-0.0138986\pi$
$617$	1.12574	+	6.38441i	0.0453208	+	0.257027i	−0.953726	+	0.300677i	$0.902787\pi$
$618$	−15.1332	−	37.0721i	−0.608747	−	1.49126i
$619$			14.7887i			0.594410i	0.954814	+	0.297205i	$0.0960544\pi$
$619$			14.7887i			0.594410i	−0.954814	+	0.297205i	$0.903946\pi$
$620$	−1.71113	−	1.30412i	−0.0687208	−	0.0523746i
$621$	3.68723	−	3.38890i	0.147964	−	0.135992i
$622$	−0.859910	−	36.6569i	−0.0344792	−	1.46981i
$623$	−3.68368	+	3.09097i	−0.147583	+	0.123837i
$624$	23.5142	+	32.0843i	0.941322	+	1.28440i
$625$	−17.9365	+	6.52836i	−0.717461	+	0.261134i
$626$	24.8069	+	8.37554i	0.991484	+	0.334754i
$627$	−15.3121	+	21.8959i	−0.611508	+	0.874437i
$628$	−25.0841	−	19.1175i	−1.00096	−	0.762872i
$629$	−0.274079	+	0.326634i	−0.0109282	+	0.0130238i
$630$	0.169656	+	3.16563i	0.00675924	+	0.126122i
$631$	35.5646	−	6.27100i	1.41581	−	0.249645i	0.587184	−	0.809454i	$-0.300237\pi$
$631$	35.5646	−	6.27100i	1.41581	−	0.249645i	0.828622	+	0.559809i	$0.189126\pi$
$632$	11.8621	+	8.60840i	0.471850	+	0.342424i
$633$	29.0651	−	5.57705i	1.15524	−	0.221668i
$634$	−30.4343	+	6.10559i	−1.20870	+	0.242484i
$635$	0.643942	+	1.11534i	0.0255541	+	0.0442609i
$636$	−13.5463	+	0.840294i	−0.537145	+	0.0333198i
$637$	−11.0395	+	30.3307i	−0.437400	+	1.20175i
$638$	−44.3438	−	14.9718i	−1.75559	−	0.592738i
$639$	−14.1476	+	26.3012i	−0.559669	+	1.04046i
$640$	−6.19852	−	3.66481i	−0.245018	−	0.144864i
$641$	−2.05591	−	5.64857i	−0.0812036	−	0.223105i	0.892446	−	0.451154i	$-0.148988\pi$
$641$	−2.05591	−	5.64857i	−0.0812036	−	0.223105i	−0.973650	+	0.228049i	$0.926765\pi$
$642$	1.83878	+	4.50451i	0.0725710	+	0.177779i
$643$	−20.9497	−	3.69399i	−0.826174	−	0.145677i	−0.255454	−	0.966821i	$-0.582225\pi$
$643$	−20.9497	−	3.69399i	−0.826174	−	0.145677i	−0.570720	+	0.821144i	$0.693336\pi$
$644$	1.66343	−	1.53431i	0.0655485	−	0.0604602i
$645$	6.81155	−	12.2188i	0.268204	−	0.481116i
$646$	0.157229	+	0.329399i	0.00618611	+	0.0129600i
$647$			43.5207i			1.71098i	0.517822	+	0.855488i	$0.326743\pi$
$647$			43.5207i			1.71098i	−0.517822	+	0.855488i	$0.673257\pi$
$648$	21.4643	+	13.6852i	0.843197	+	0.537605i
$649$	−7.90252	−	21.7120i	−0.310201	−	0.852270i
$650$	−23.3052	+	29.1352i	−0.914103	+	1.14278i
$651$	2.66564	+	2.16925i	0.104475	+	0.0850195i
$652$	14.5378	+	7.50751i	0.569345	+	0.294017i
$653$	−12.1660			−0.476094			−0.238047	−	0.971254i	$-0.576507\pi$
$653$	−12.1660			−0.476094			−0.238047	+	0.971254i	$0.576507\pi$
$654$	−25.9244	−	8.32052i	−1.01372	−	0.325358i
$655$	0.613889	−	1.68665i	0.0239866	−	0.0659027i
$656$	16.6308	+	1.34531i	0.649324	+	0.0525254i
$657$	−31.2167	+	0.939521i	−1.21788	+	0.0366542i
$658$	10.8614	−	9.55670i	0.423421	−	0.372559i
$659$	3.19817	+	18.1377i	0.124583	+	0.706546i	0.981555	+	0.191182i	$0.0612321\pi$
$659$	3.19817	+	18.1377i	0.124583	+	0.706546i	−0.856971	+	0.515364i	$0.827657\pi$
$660$	5.65528	−	5.37597i	0.220131	−	0.209259i
$661$	−0.720439	+	1.97939i	−0.0280218	+	0.0769894i	−0.952915	−	0.303238i	$-0.901932\pi$
$661$	−0.720439	+	1.97939i	−0.0280218	+	0.0769894i	0.924893	+	0.380228i	$0.124154\pi$
$662$	15.1570	−	0.355558i	0.589094	−	0.0138192i
$663$	−0.0935140	+	0.581355i	−0.00363178	+	0.0225780i
$664$	25.9009	+	12.6151i	1.00515	+	0.489562i
$665$	−0.330709	+	3.24021i	−0.0128243	+	0.125650i
$666$	−8.89807	+	29.2278i	−0.344793	+	1.13255i
$667$	6.90430	+	5.79340i	0.267336	+	0.224321i
$668$	−9.90167	−	3.08637i	−0.383107	−	0.119415i
$669$	−28.5756	+	5.48312i	−1.10480	+	0.211990i
$670$	3.03925	−	5.56139i	0.117416	−	0.214855i
$671$	21.8589	+	26.0505i	0.843855	+	1.00567i
$672$	9.71008	+	6.16671i	0.374575	+	0.237886i
$673$		−	14.1986i		−	0.547315i	−0.961827	−	0.273658i	$-0.911766\pi$
$673$		−	14.1986i		−	0.547315i	0.961827	−	0.273658i	$-0.0882335\pi$
$674$	−1.63477	+	2.04372i	−0.0629688	+	0.0787212i
$675$	−7.14547	+	22.7815i	−0.275029	+	0.876860i
$676$	−5.08225	+	39.6054i	−0.195471	+	1.52328i
$677$	6.57345	+	3.79519i	0.252638	+	0.145861i	0.620972	−	0.783833i	$-0.286738\pi$
$677$	6.57345	+	3.79519i	0.252638	+	0.145861i	−0.368333	+	0.929694i	$0.620071\pi$
$678$	−38.0530	−	29.5108i	−1.46142	−	1.13336i
$679$	7.08022	+	5.94101i	0.271714	+	0.227995i
$680$	−0.0258438	−	0.103412i	−0.000991063	−	0.00396566i
$681$	5.23096	+	13.7259i	0.200451	+	0.525976i
$682$	−0.198377	−	8.45657i	−0.00759625	−	0.323819i
$683$	7.42489			0.284106			0.142053	−	0.989859i	$-0.454630\pi$
$683$	7.42489			0.284106			0.142053	+	0.989859i	$0.454630\pi$
$684$	19.6131	+	17.3011i	0.749925	+	0.661523i
$685$	1.53761			0.0587490
$686$	0.491450	+	20.9499i	0.0187636	+	0.799870i
$687$	−0.326256	+	0.400913i	−0.0124474	+	0.0152958i
$688$	−21.7525	−	45.8617i	−0.829305	−	1.74846i
$689$	−17.2324	−	14.4597i	−0.656500	−	0.550869i
$690$	−1.39115	+	0.567879i	−0.0529600	+	0.0216188i
$691$	43.6833	+	25.2206i	1.66179	+	0.959436i	0.971859	+	0.235562i	$0.0756930\pi$
$691$	43.6833	+	25.2206i	1.66179	+	0.959436i	0.689932	+	0.723874i	$0.257640\pi$
$692$	16.7185	+	2.14535i	0.635541	+	0.0815540i
$693$	−9.30284	+	8.29549i	−0.353386	+	0.315120i
$694$	16.8231	−	21.0317i	0.638598	−	0.798351i
$695$			12.4296i			0.471483i
$696$	−19.4385	+	41.4844i	−0.736815	+	1.57246i
$697$	0.158759	+	0.189202i	0.00601342	+	0.00716652i
$698$	−11.0868	+	20.2872i	−0.419641	+	0.767883i
$699$	−1.16334	+	3.35233i	−0.0440017	+	0.126797i
$700$	−3.21054	+	10.3000i	−0.121347	+	0.389305i
$701$	−31.5128	−	26.4424i	−1.19022	−	0.998715i	−0.999855	−	0.0170021i	$-0.994588\pi$
$701$	−31.5128	−	26.4424i	−1.19022	−	0.998715i	−0.190367	−	0.981713i	$-0.560968\pi$
$702$	10.1568	+	40.9506i	0.383342	+	1.54558i
$703$	−13.6753	+	28.2539i	−0.515773	+	1.06562i
$704$	−3.97103	−	28.0320i	−0.149664	−	1.05650i
$705$	−8.97625	+	3.42087i	−0.338065	+	0.128837i
$706$	29.9223	−	0.701927i	1.12614	−	0.0264174i
$707$	4.27377	−	11.7421i	0.160731	−	0.441606i
$708$	−21.9871	+	5.29876i	−0.826324	+	0.199139i
$709$	0.542698	+	3.07779i	0.0203814	+	0.115589i	0.993301	−	0.115554i	$-0.0368645\pi$
$709$	0.542698	+	3.07779i	0.0203814	+	0.115589i	−0.972920	+	0.231143i	$0.925753\pi$
$710$	6.72718	−	5.91910i	0.252467	−	0.222140i
$711$	8.17430	+	13.2230i	0.306560	+	0.495901i
$712$	3.18721	−	11.1382i	0.119446	−	0.417422i
$713$	−0.557130	+	1.53070i	−0.0208647	+	0.0573252i
$714$	0.0359995	+	0.166423i	0.00134725	+	0.00622823i
$715$	12.9326			0.483651
$716$	10.2683	−	19.8840i	0.383745	−	0.743099i
$717$	20.0335	−	7.63481i	0.748165	−	0.285127i
$718$	−23.7017	+	29.6310i	−0.884539	+	1.10582i
$719$	12.9548	+	35.5931i	0.483134	+	1.32740i	0.906792	+	0.421578i	$0.138523\pi$
$719$	12.9548	+	35.5931i	0.483134	+	1.32740i	−0.423658	+	0.905822i	$0.639254\pi$
$720$	−4.60701	−	6.09175i	−0.171693	−	0.227026i
$721$		−	19.1914i		−	0.714725i
$722$	17.1596	+	20.6773i	0.638614	+	0.769528i
$723$	43.9435	−	0.661129i	1.63428	−	0.0245877i
$724$	4.80401	+	5.20831i	0.178540	+	0.193565i
$725$	−42.3164	−	7.46152i	−1.57159	−	0.277114i
$726$	3.69950	+	0.506389i	0.137301	+	0.0187939i
$727$	1.06771	+	2.93350i	0.0395991	+	0.108797i	0.957916	−	0.287048i	$-0.0926739\pi$
$727$	1.06771	+	2.93350i	0.0395991	+	0.108797i	−0.918317	+	0.395845i	$0.870452\pi$
$728$	4.62242	+	18.4963i	0.171318	+	0.685517i
$729$	15.5528	+	22.0706i	0.576029	+	0.817430i
$730$	8.87801	+	2.99747i	0.328590	+	0.110941i
$731$	0.256983	−	0.706055i	0.00950487	−	0.0261144i
$732$	27.7416	−	18.3963i	1.02536	−	0.679947i
$733$	17.1766	+	29.7508i	0.634433	+	1.09887i	0.986635	+	0.162946i	$0.0520996\pi$
$733$	17.1766	+	29.7508i	0.634433	+	1.09887i	−0.352202	+	0.935924i	$0.614567\pi$
$734$	−1.75534	+	0.352148i	−0.0647909	+	0.0129980i
$735$	2.03179	−	5.85489i	0.0749438	−	0.215961i
$736$	−1.25247	+	5.30624i	−0.0461668	+	0.195591i
$737$	24.5395	−	4.32697i	0.903923	−	0.159386i
$738$	15.7779	+	8.01575i	0.580791	+	0.295064i
$739$	−7.66185	+	9.13103i	−0.281846	+	0.335891i	−0.888331	−	0.459204i	$-0.848135\pi$
$739$	−7.66185	+	9.13103i	−0.281846	+	0.335891i	0.606485	+	0.795095i	$0.292579\pi$
$740$	5.55653	−	7.29072i	0.204262	−	0.268012i
$741$	3.80383	+	43.1803i	0.139737	+	1.58627i
$742$	−6.16318	−	2.08087i	−0.226257	−	0.0763911i
$743$	−17.1971	+	6.25924i	−0.630901	+	0.229629i	−0.637623	−	0.770348i	$-0.720082\pi$
$743$	−17.1971	+	6.25924i	−0.630901	+	0.229629i	0.00672256	+	0.999977i	$0.497860\pi$
$744$	−8.24705	−	0.736986i	−0.302351	−	0.0270192i
$745$	−2.26644	+	1.90177i	−0.0830358	+	0.0696753i
$746$	0.414585	+	17.6732i	0.0151790	+	0.647063i
$747$	20.3372	+	22.8068i	0.744098	+	0.834456i
$748$	0.254037	−	0.333322i	0.00928851	−	0.0121875i
$749$			2.33188i			0.0852051i
$750$	9.16714	−	11.8207i	0.334737	−	0.431630i
$751$	−3.72152	−	21.1058i	−0.135800	−	0.770162i	−0.974299	−	0.225258i	$-0.927677\pi$
$751$	−3.72152	−	21.1058i	−0.135800	−	0.770162i	0.838499	−	0.544904i	$-0.183434\pi$
$752$	−8.80039	+	33.7255i	−0.320917	+	1.22984i
$753$	−51.2905	+	0.771665i	−1.86913	+	0.0281210i
$754$	−70.7237	+	27.6364i	−2.57561	+	1.00646i
$755$	−1.39825	+	7.92985i	−0.0508874	+	0.288597i
$756$	7.04557	+	9.96059i	0.256245	+	0.362263i
$757$	−13.2676	+	4.82901i	−0.482219	+	0.175513i	−0.571680	−	0.820477i	$-0.693708\pi$
$757$	−13.2676	+	4.82901i	−0.482219	+	0.175513i	0.0894603	+	0.995990i	$0.471486\pi$
$758$	22.9102	−	0.537437i	0.832138	−	0.0195206i
$759$	−5.16014	−	2.87659i	−0.187301	−	0.104414i
$760$	−3.70855	−	6.91531i	−0.134523	−	0.250844i
$761$	−3.99067	+	6.91204i	−0.144662	+	0.250561i	−0.929247	−	0.369460i	$-0.879543\pi$
$761$	−3.99067	+	6.91204i	−0.144662	+	0.250561i	0.784585	+	0.620021i	$0.212876\pi$
$762$	4.38464	+	2.31119i	0.158839	+	0.0837257i
$763$	−9.99640	−	8.38798i	−0.361894	−	0.303665i
$764$	33.9292	−	21.7718i	1.22752	−	0.787677i
$765$	0.0162740	−	0.111881i	0.000588387	−	0.00404506i
$766$	1.93775	−	12.7284i	0.0700138	−	0.459894i
$767$	−32.4633	−	18.7427i	−1.17218	−	0.676760i
$768$	−27.7018	+	0.779828i	−0.999604	+	0.0281396i
$769$	1.38889	+	7.87679i	0.0500847	+	0.284044i	0.999556	−	0.0298109i	$-0.00949050\pi$
$769$	1.38889	+	7.87679i	0.0500847	+	0.284044i	−0.949471	+	0.313855i	$0.898379\pi$
$770$	3.48323	−	1.36113i	0.125527	−	0.0490516i
$771$	−20.0842	+	0.302166i	−0.723314	+	0.0108822i
$772$	−28.7323	−	3.68699i	−1.03410	−	0.132698i
$773$	3.38806	−	9.30861i	0.121860	−	0.334807i	−0.863731	−	0.503953i	$-0.831879\pi$
$773$	3.38806	−	9.30861i	0.121860	−	0.334807i	0.985591	+	0.169145i	$0.0541008\pi$
$774$	−2.88120	−	53.7608i	−0.103563	−	1.93239i
$775$	−1.34855	−	7.64800i	−0.0484413	−	0.274724i
$776$	−22.1467	−	2.31542i	−0.795021	−	0.0831188i
$777$	−9.24262	+	11.3576i	−0.331577	+	0.407453i
$778$	−34.6232	−	11.6898i	−1.24130	−	0.419100i
$779$	14.7418	+	10.6429i	0.528180	+	0.381323i
$780$	1.42215	−	12.5788i	0.0509210	−	0.450393i
$781$	34.6951	+	6.11768i	1.24149	+	0.218908i
$782$	−0.0689271	+	0.0419806i	−0.00246483	+	0.00150122i
$783$	−35.7764	+	32.8818i	−1.27854	+	1.17510i
$784$	−13.0183	−	18.3353i	−0.464941	−	0.654833i
$785$	1.74287	+	9.88428i	0.0622055	+	0.352785i
$786$	−1.46045	−	6.75156i	−0.0520926	−	0.240820i
$787$	−11.3975	−	19.7411i	−0.406279	−	0.703695i	0.588191	−	0.808722i	$-0.299840\pi$
$787$	−11.3975	−	19.7411i	−0.406279	−	0.703695i	−0.994469	+	0.105027i	$0.966507\pi$
$788$	9.63944	+	15.0221i	0.343391	+	0.535140i
$789$	13.5523	−	11.7236i	0.482475	−	0.417372i
$790$	−0.917439	−	4.57313i	−0.0326410	−	0.162705i
$791$	−11.5400	−	19.9878i	−0.410314	−	0.710685i
$792$	7.38908	−	29.1060i	0.262560	−	1.03424i
$793$	54.3327	+	9.58032i	1.92941	+	0.340207i
$794$	−17.7010	−	14.1590i	−0.628185	−	0.502483i
$795$	3.35009	+	2.72624i	0.118816	+	0.0966899i
$796$	−4.52703	−	4.90802i	−0.160456	−	0.173960i
$797$	20.5411	+	11.8594i	0.727603	+	0.420082i	0.817545	−	0.575865i	$-0.195335\pi$
$797$	20.5411	+	11.8594i	0.727603	+	0.420082i	−0.0899414	+	0.995947i	$0.528668\pi$
$798$	5.56915	+	11.2298i	0.197146	+	0.397529i
$799$	−0.446822	+	0.257973i	−0.0158074	+	0.00912642i
$800$	−7.47757	−	24.8939i	−0.264372	−	0.880132i
$801$	7.61183	−	9.64652i	0.268951	−	0.340843i
$802$	8.82935	+	22.5950i	0.311775	+	0.797859i
$803$	12.6006	+	34.6200i	0.444667	+	1.22171i
$804$	−1.51009	−	24.3440i	−0.0532568	−	0.858547i
$805$	−0.720165			−0.0253825
$806$	−9.06535	−	10.3030i	−0.319313	−	0.362907i
$807$	−4.48414	−	23.3694i	−0.157849	−	0.822641i
$808$	7.29906	+	29.2066i	0.256780	+	1.02749i
$809$	24.9680	−	43.2458i	0.877827	−	1.52044i	0.0241060	−	0.999709i	$-0.492326\pi$
$809$	24.9680	−	43.2458i	0.877827	−	1.52044i	0.853721	−	0.520731i	$-0.174341\pi$
$810$	−2.06821	−	7.83251i	−0.0726696	−	0.275206i
$811$	−4.96639	−	1.80762i	−0.174394	−	0.0634741i	0.253348	−	0.967375i	$-0.418468\pi$
$811$	−4.96639	−	1.80762i	−0.174394	−	0.0634741i	−0.427741	+	0.903901i	$0.640691\pi$
$812$	−16.1399	+	14.8870i	−0.566400	+	0.522433i
$813$	−0.794516	−	0.275717i	−0.0278649	−	0.00966982i
$814$	36.0313	−	0.845236i	1.26290	−	0.0296255i
$815$	−1.78088	−	4.89292i	−0.0623815	−	0.171392i
$816$	−0.296268	−	0.283742i	−0.0103715	−	0.00993295i
$817$	5.61631	−	55.0273i	0.196490	−	1.92516i
$818$	23.7193	−	4.75845i	0.829326	−	0.166375i
$819$	−2.91077	+	20.0110i	−0.101710	+	0.699241i
$820$	−3.60006	−	3.90304i	−0.125720	−	0.136300i
$821$	−16.4154	+	13.7742i	−0.572903	+	0.480722i	−0.882608	−	0.470110i	$-0.844214\pi$
$821$	−16.4154	+	13.7742i	−0.572903	+	0.480722i	0.309705	+	0.950833i	$0.399770\pi$
$822$	5.00707	−	3.15383i	0.174642	−	0.110002i
$823$	19.2250	+	22.9115i	0.670143	+	0.798645i	0.988803	−	0.149224i	$-0.0476775\pi$
$823$	19.2250	+	22.9115i	0.670143	+	0.798645i	−0.318661	+	0.947869i	$0.603233\pi$
$824$	25.8761	+	38.3175i	0.901437	+	1.33485i
$825$	28.1622	−	0.423699i	0.980481	−	0.0147513i
$826$	−10.7162	−	1.63143i	−0.372866	−	0.0567647i
$827$	−16.7348	+	14.0422i	−0.581927	+	0.488295i	−0.885579	−	0.464488i	$-0.846238\pi$
$827$	−16.7348	+	14.0422i	−0.581927	+	0.488295i	0.303652	+	0.952783i	$0.401794\pi$
$828$	−3.36534	+	4.70265i	−0.116954	+	0.163429i
$829$	−28.7429	+	16.5947i	−0.998283	+	0.576359i	−0.907740	−	0.419534i	$-0.862194\pi$
$829$	−28.7429	+	16.5947i	−0.998283	+	0.576359i	−0.0905429	+	0.995893i	$0.528860\pi$
$830$	−3.33692	−	8.53947i	−0.115826	−	0.296409i
$831$	−37.2865	−	5.99774i	−1.29346	−	0.208059i
$832$	−34.1680	−	30.6971i	−1.18456	−	1.06423i
$833$	0.0578018	−	0.327810i	0.00200271	−	0.0113579i
$834$	25.4947	+	40.4759i	0.882811	+	1.40157i
$835$	1.65030	+	2.85840i	0.0571109	+	0.0989190i
$836$	12.1243	−	28.3700i	0.419326	−	0.981197i
$837$	−7.79595	−	4.04348i	−0.269467	−	0.139763i
$838$	−19.8039	−	10.8226i	−0.684115	−	0.373862i
$839$	−22.0799	−	18.5272i	−0.762282	−	0.639630i	0.176438	−	0.984312i	$-0.443543\pi$
$839$	−22.0799	−	18.5272i	−0.762282	−	0.639630i	−0.938720	+	0.344681i	$0.887987\pi$
$840$	−0.940853	−	3.53763i	−0.0324625	−	0.122060i
$841$	−44.7756	−	37.5712i	−1.54399	−	1.29556i
$842$	24.7287	−	30.9149i	0.852208	−	1.06540i
$843$	−20.5976	−	34.4680i	−0.709419	−	1.18714i
$844$	−31.5295	+	13.1811i	−1.08529	+	0.453711i
$845$	9.73429	−	8.16804i	0.334870	−	0.280989i
$846$	−22.2137	+	29.5511i	−0.763721	+	1.01599i
$847$	1.54987	+	0.894820i	0.0532543	+	0.0307464i
$848$	15.1111	−	4.15527i	0.518916	−	0.142692i
$849$	4.91235	+	25.6010i	0.168591	+	0.878625i
$850$	0.184514	−	0.337634i	0.00632877	−	0.0115807i
$851$	−6.52195	−	2.37379i	−0.223569	−	0.0813726i
$852$	9.76562	−	33.0732i	0.334564	−	1.13307i
$853$	6.66668	−	37.8086i	0.228263	−	1.29454i	−0.628086	−	0.778144i	$-0.716161\pi$
$853$	6.66668	−	37.8086i	0.228263	−	1.29454i	0.856349	−	0.516398i	$-0.172727\pi$
$854$	15.6422	−	3.13806i	0.535264	−	0.107382i
$855$	−0.854995	−	8.27892i	−0.0292402	−	0.283133i
$856$	−3.14412	−	4.65584i	−0.107464	−	0.159133i
$857$	−12.0319	−	2.12155i	−0.411002	−	0.0724707i	−0.0356754	−	0.999363i	$-0.511358\pi$
$857$	−12.0319	−	2.12155i	−0.411002	−	0.0724707i	−0.375326	+	0.926893i	$0.622469\pi$
$858$	42.1137	−	26.5263i	1.43774	−	0.905593i
$859$	9.66594	−	26.5570i	0.329798	−	0.906112i	−0.658365	−	0.752699i	$-0.728751\pi$
$859$	9.66594	−	26.5570i	0.329798	−	0.906112i	0.988162	−	0.153412i	$-0.0490263\pi$
$860$	−4.80692	+	15.4215i	−0.163915	+	0.525869i
$861$	5.54925	+	6.41483i	0.189118	+	0.218617i
$862$	1.15705	+	0.390653i	0.0394092	+	0.0133057i
$863$	4.59136	−	7.95247i	0.156292	−	0.270705i	−0.777237	−	0.629208i	$-0.783379\pi$
$863$	4.59136	−	7.95247i	0.156292	−	0.270705i	0.933529	+	0.358503i	$0.116713\pi$
$864$	−27.4972	−	10.3876i	−0.935474	−	0.353394i
$865$	−3.44794	−	4.10910i	−0.117234	−	0.139713i
$866$	43.0294	−	8.63235i	1.46220	−	0.293339i
$867$	0.442856	+	29.4355i	0.0150402	+	0.999681i
$868$	−3.52601	−	1.82087i	−0.119681	−	0.0618045i
$869$	11.7878	−	14.0482i	0.399874	−	0.476551i
$870$	13.4980	−	5.51000i	0.457624	−	0.186807i
$871$	25.9854	−	30.9682i	0.880482	−	1.04932i
$872$	31.2685	+	3.26910i	1.05888	+	0.110706i
$873$	−20.7999	−	11.1884i	−0.703971	−	0.378671i
$874$	−4.16307	+	4.23876i	−0.140818	+	0.143378i
$875$	6.20895	−	3.58474i	0.209901	−	0.121186i
$876$	35.0586	−	8.44891i	1.18452	−	0.285462i
$877$	−17.7646	−	3.13237i	−0.599867	−	0.105773i	−0.134535	−	0.990909i	$-0.542954\pi$
$877$	−17.7646	−	3.13237i	−0.599867	−	0.105773i	−0.465332	+	0.885136i	$0.654065\pi$
$878$	−0.969153	+	6.36600i	−0.0327073	+	0.214842i
$879$	−35.3141	+	13.4583i	−1.19112	+	0.453937i
$880$	−5.11939	+	7.41413i	−0.172575	+	0.249930i
$881$	16.4338	+	28.4641i	0.553667	+	0.958980i	0.998006	+	0.0631211i	$0.0201054\pi$
$881$	16.4338	+	28.4641i	0.553667	+	0.958980i	−0.444338	+	0.895859i	$0.646561\pi$
$882$	−5.39276	−	23.2333i	−0.181584	−	0.782307i
$883$	5.68955	+	6.78054i	0.191469	+	0.228183i	0.853235	−	0.521527i	$-0.174637\pi$
$883$	5.68955	+	6.78054i	0.191469	+	0.228183i	−0.661766	+	0.749710i	$0.730193\pi$
$884$	−0.0318821	−	0.679172i	−0.00107231	−	0.0228430i
$885$	6.28656	+	3.50453i	0.211320	+	0.117803i
$886$	−17.5111	+	3.51298i	−0.588295	+	0.118021i
$887$	8.61017	−	7.22479i	0.289101	−	0.242585i	−0.486690	−	0.873575i	$-0.661796\pi$
$887$	8.61017	−	7.22479i	0.289101	−	0.242585i	0.775791	+	0.630990i	$0.217351\pi$
$888$	3.14012	−	35.1386i	0.105375	−	1.17918i
$889$	1.52698	+	1.81978i	0.0512131	+	0.0610334i
$890$	−3.14879	+	1.91780i	−0.105548	+	0.0642846i
$891$	18.9689	−	25.5862i	0.635483	−	0.857171i
$892$	30.9985	−	12.9591i	1.03791	−	0.433902i
$893$	−27.2426	+	26.4667i	−0.911638	+	0.885674i
$894$	−3.47967	+	10.8417i	−0.116378	+	0.362599i
$895$	−6.69225	+	2.43578i	−0.223697	+	0.0814191i
$896$	−12.4335	−	4.67180i	−0.415376	−	0.156074i
$897$	−9.41285	+	1.80615i	−0.314286	+	0.0603055i
$898$	−22.9221	+	13.9609i	−0.764919	+	0.465880i
$899$	5.40571	−	14.8521i	0.180290	−	0.495344i
$900$	2.68478	−	27.4384i	0.0894927	−	0.914613i
$901$	0.200907	+	0.115994i	0.00669319	+	0.00386431i
$902$	3.14205	−	20.6390i	0.104619	−	0.687202i
$903$	8.45959	−	24.3775i	0.281517	−	0.811231i
$904$	49.9906	+	24.3481i	1.66266	+	0.809806i
$905$		−	2.25488i		−	0.0749547i
$906$	11.7119	+	28.6908i	0.389100	+	0.953187i
$907$	53.4715	−	19.4620i	1.77549	−	0.646226i	0.775605	−	0.631218i	$-0.217445\pi$
$907$	53.4715	−	19.4620i	1.77549	−	0.646226i	0.999887	−	0.0150081i	$-0.00477741\pi$
$908$	−9.16006	−	14.2750i	−0.303987	−	0.473733i
$909$	−4.59626	+	31.5985i	−0.152448	+	1.04806i
$910$	2.90954	−	5.32405i	0.0964505	−	0.176491i
$911$	18.9310	+	32.7895i	0.627212	+	1.08636i	0.988109	+	0.153757i	$0.0491374\pi$
$911$	18.9310	+	32.7895i	0.627212	+	1.08636i	−0.360897	+	0.932606i	$0.617529\pi$
$912$	−26.2607	−	14.9123i	−0.869577	−	0.493797i
$913$	18.0236	−	31.2178i	0.596495	−	1.03316i
$914$	−2.13075	−	3.49843i	−0.0704788	−	0.115718i
$915$	−10.4587	−	1.68233i	−0.345753	−	0.0556161i
$916$	0.273860	−	0.530314i	0.00904860	−	0.0175221i
$917$	0.574905	−	3.26045i	0.0189850	−	0.107670i
$918$	−0.176487	−	0.397709i	−0.00582493	−	0.0131263i
$919$	−4.85921	+	2.80547i	−0.160290	+	0.0925438i	−0.578000	−	0.816037i	$-0.696166\pi$
$919$	−4.85921	+	2.80547i	−0.160290	+	0.0925438i	0.417709	+	0.908581i	$0.362833\pi$
$920$	1.43788	−	0.971011i	0.0474055	−	0.0320133i
$921$	−9.89346	+	1.89837i	−0.326001	+	0.0625533i
$922$	−18.1542	+	7.09403i	−0.597877	+	0.233629i
$923$	49.4989	−	28.5782i	1.62928	−	0.940663i
$924$	8.55097	−	11.5769i	0.281306	−	0.380853i
$925$	32.5862	−	5.74583i	1.07143	−	0.188922i
$926$	1.27580	+	54.3857i	0.0419254	+	1.78722i
$927$	9.96495	+	48.0181i	0.327292	+	1.57712i
$928$	12.1525	−	51.4852i	0.398925	−	1.69009i
$929$	7.95681	−	45.1253i	0.261054	−	1.48051i	−0.518986	−	0.854783i	$-0.673690\pi$
$929$	7.95681	−	45.1253i	0.261054	−	1.48051i	0.780040	−	0.625730i	$-0.215199\pi$
$930$	1.77016	+	1.95182i	0.0580458	+	0.0640026i
$931$	−1.78287	−	24.4396i	−0.0584313	−	0.800976i
$932$	0.521511	−	4.06408i	0.0170827	−	0.133123i
$933$	−7.13196	+	44.3377i	−0.233490	+	1.45155i
$934$	−26.7311	−	14.6083i	−0.874669	−	0.477998i
$935$	−0.131344	+	0.0231595i	−0.00429541	+	0.000757397i
$936$	−21.1696	−	43.8786i	−0.691949	−	1.43422i
$937$	−29.3648	−	10.6879i	−0.959307	−	0.349159i	−0.185545	−	0.982636i	$-0.559405\pi$
$937$	−29.3648	−	10.6879i	−0.959307	−	0.349159i	−0.773762	+	0.633477i	$0.781627\pi$
$938$	3.73952	−	11.0758i	0.122100	−	0.361639i
$939$	−28.0090	−	15.6140i	−0.914039	−	0.509543i
$940$	9.33538	−	5.99037i	0.304487	−	0.195384i
$941$	−25.7191	+	4.53497i	−0.838419	+	0.147836i	−0.576340	−	0.817210i	$-0.695519\pi$
$941$	−25.7191	+	4.53497i	−0.838419	+	0.147836i	−0.262080	+	0.965046i	$0.584408\pi$
$942$	25.9493	+	28.6124i	0.845475	+	0.932241i
$943$	−2.01013	+	3.48165i	−0.0654589	+	0.113378i
$944$	23.5957	−	11.1916i	0.767976	−	0.364256i
$945$	0.501020	−	3.85019i	0.0162982	−	0.125247i
$946$	−59.1545	+	23.1155i	−1.92328	+	0.751550i
$947$	−30.8140	+	36.7228i	−1.00132	+	1.19333i	−0.0202283	+	0.999795i	$0.506439\pi$
$947$	−30.8140	+	36.7228i	−1.00132	+	1.19333i	−0.981094	+	0.193534i	$0.938005\pi$
$948$	−12.3676	−	13.0102i	−0.401681	−	0.422551i
$949$	51.7630	+	29.8854i	1.68030	+	0.970121i
$950$	7.08425	−	27.4247i	0.229843	−	0.889774i
$951$	38.0127	−	0.571900i	1.23265	−	0.0185451i
$952$	−0.0800685	−	0.179571i	−0.00259504	−	0.00581994i
$953$	−18.0779	−	49.6687i	−0.585601	−	1.60893i	−0.778457	−	0.627698i	$-0.783997\pi$
$953$	−18.0779	−	49.6687i	−0.585601	−	1.60893i	0.192856	−	0.981227i	$-0.438225\pi$
$954$	16.5011	+	2.00629i	0.534244	+	0.0649560i
$955$	−12.6344	−	2.22779i	−0.408840	−	0.0720895i
$956$	−20.8350	+	13.3695i	−0.673853	+	0.432401i
$957$	50.0677	+	27.9109i	1.61846	+	0.902231i
$958$	11.4632	+	13.0282i	0.370361	+	0.420923i
$959$	2.79309	−	0.492497i	0.0901936	−	0.0159036i
$960$	6.64836	+	5.79465i	0.214575	+	0.187022i
$961$	−28.1435			−0.907854
$962$	43.8984	−	38.6252i	1.41534	−	1.24533i
$963$	−1.21081	−	5.83451i	−0.0390177	−	0.188015i
$964$	−49.5082	+	11.1459i	−1.59455	+	0.358986i
$965$	5.92561	+	7.06187i	0.190752	+	0.227330i
$966$	−2.34515	+	1.47715i	−0.0754538	+	0.0475264i
$967$	−20.9947	−	57.6825i	−0.675144	−	1.85494i	−0.488629	−	0.872491i	$-0.662503\pi$
$967$	−20.9947	−	57.6825i	−0.675144	−	1.85494i	−0.186515	−	0.982452i	$-0.559719\pi$
$968$	−4.30098	+	0.303127i	−0.138239	+	0.00974286i
$969$	−0.115959	−	0.431730i	−0.00372513	−	0.0138692i
$970$	4.68104	+	5.32011i	0.150299	+	0.170818i
$971$	−17.8265	−	14.9582i	−0.572079	−	0.480032i	0.310256	−	0.950653i	$-0.399585\pi$
$971$	−17.8265	−	14.9582i	−0.572079	−	0.480032i	−0.882335	+	0.470621i	$0.844030\pi$
$972$	−22.8004	−	21.2636i	−0.731323	−	0.682032i
$973$	3.98122	+	22.5786i	0.127632	+	0.723838i
$974$	15.5304	+	25.4991i	0.497626	+	0.817043i
$975$	34.5582	−	29.8951i	1.10675	−	0.957410i
$976$	−27.0001	+	27.3561i	−0.864251	+	0.875647i
$977$	11.6848	−	6.74622i	0.373830	−	0.215831i	−0.301301	−	0.953529i	$-0.597421\pi$
$977$	11.6848	−	6.74622i	0.373830	−	0.215831i	0.675130	+	0.737699i	$0.264087\pi$
$978$	−15.8353	−	12.2805i	−0.506356	−	0.392688i
$979$	−13.6215	−	4.95782i	−0.435345	−	0.158453i
$980$	−0.910825	+	7.09795i	−0.0290952	+	0.226736i
$981$	29.3670	+	15.7967i	0.937616	+	0.504350i
$982$	−20.1489	−	3.06745i	−0.642977	−	0.0978862i
$983$	−54.4290	+	19.8105i	−1.73602	+	0.631858i	−0.999029	−	0.0440490i	$-0.985974\pi$
$983$	−54.4290	+	19.8105i	−1.73602	+	0.631858i	−0.736987	+	0.675907i	$0.763752\pi$
$984$	−19.7289	−	5.32569i	−0.628933	−	0.169777i
$985$	0.986349	−	5.59387i	0.0314277	−	0.178235i
$986$	0.668784	−	0.407328i	0.0212984	−	0.0129720i
$987$	−15.2098	+	9.08916i	−0.484133	+	0.289311i
$988$	−14.5172	−	47.9019i	−0.461853	−	1.52396i
$989$	12.2303			0.388901
$990$	−8.00851	+	5.21426i	−0.254527	+	0.165720i
$991$	−11.8977	+	4.33043i	−0.377944	+	0.137561i	−0.524005	−	0.851715i	$-0.675563\pi$
$991$	−11.8977	+	4.33043i	−0.377944	+	0.137561i	0.146061	+	0.989276i	$0.453341\pi$
$992$	9.49515	−	1.11863i	0.301471	−	0.0355166i
$993$	−18.3329	−	2.94895i	−0.581777	−	0.0935820i
$994$	10.3241	−	12.9069i	0.327462	−	0.409381i
$995$			2.12487i			0.0673630i
$996$	−28.3819	−	20.9635i	−0.899314	−	0.664254i
$997$	−8.86172	−	3.22540i	−0.280653	−	0.102149i	0.197858	−	0.980231i	$-0.436601\pi$
$997$	−8.86172	−	3.22540i	−0.280653	−	0.102149i	−0.478512	+	0.878081i	$0.658824\pi$
$998$	−15.9319	+	19.9174i	−0.504315	+	0.630475i
$999$	17.2283	−	33.2166i	0.545078	−	1.05093i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.cc.a.535.115	yes	696
4.3	odd	2	inner	684.2.cc.a.535.106	yes	696
9.7	even	3		684.2.bt.a.79.39	✓	696
19.13	odd	18		684.2.bt.a.355.51	yes	696
36.7	odd	6		684.2.bt.a.79.51	yes	696
76.51	even	18		684.2.bt.a.355.39	yes	696
171.70	odd	18	inner	684.2.cc.a.583.106	yes	696
684.583	even	18	inner	684.2.cc.a.583.115	yes	696

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.bt.a.79.39	✓	696	9.7	even	3
684.2.bt.a.79.51	yes	696	36.7	odd	6
684.2.bt.a.355.39	yes	696	76.51	even	18
684.2.bt.a.355.51	yes	696	19.13	odd	18
684.2.cc.a.535.106	yes	696	4.3	odd	2	inner
684.2.cc.a.535.115	yes	696	1.1	even	1	trivial
684.2.cc.a.583.106	yes	696	171.70	odd	18	inner
684.2.cc.a.583.115	yes	696	684.583	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.cc (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41382 - 0.0331660i) q^{2} +(-1.71007 - 0.275074i) q^{3} +(1.99780 - 0.0937818i) q^{4} +(-0.487566 - 0.409117i) q^{5} +(-2.42686 - 0.332190i) q^{6} +(-1.01671 - 0.586999i) q^{7} +(2.82143 - 0.198850i) q^{8} +(2.84867 + 0.940789i) q^{9} +O(q^{10})\)	\(q+(1.41382 - 0.0331660i) q^{2} +(-1.71007 - 0.275074i) q^{3} +(1.99780 - 0.0937818i) q^{4} +(-0.487566 - 0.409117i) q^{5} +(-2.42686 - 0.332190i) q^{6} +(-1.01671 - 0.586999i) q^{7} +(2.82143 - 0.198850i) q^{8} +(2.84867 + 0.940789i) q^{9} +(-0.702902 - 0.562248i) q^{10} -3.53898i q^{11} +(-3.44217 - 0.389169i) q^{12} +(-3.69058 - 4.39826i) q^{13} +(-1.45692 - 0.796193i) q^{14} +(0.721234 + 0.833734i) q^{15} +(3.98241 - 0.374715i) q^{16} +(0.0453581 + 0.0380600i) q^{17} +(4.05872 + 1.23563i) q^{18} +(3.92348 + 1.89902i) q^{19} +(-1.01243 - 0.771608i) q^{20} +(1.57718 + 1.28348i) q^{21} +(-0.117374 - 5.00350i) q^{22} +(-0.329637 + 0.905671i) q^{23} +(-4.87953 - 0.436053i) q^{24} +(-0.797897 - 4.52510i) q^{25} +(-5.36370 - 6.09597i) q^{26} +(-4.61263 - 2.39241i) q^{27} +(-2.08624 - 1.07736i) q^{28} +(3.19840 - 8.78753i) q^{29} +(1.04735 + 1.15483i) q^{30} +1.69013 q^{31} +(5.61800 - 0.661861i) q^{32} +(-0.973481 + 6.05190i) q^{33} +(0.0653907 + 0.0523058i) q^{34} +(0.255563 + 0.702155i) q^{35} +(5.77930 + 1.61236i) q^{36} +7.20123i q^{37} +(5.61010 + 2.55476i) q^{38} +(5.10130 + 8.53651i) q^{39} +(-1.45699 - 1.05734i) q^{40} +(4.10791 + 0.724336i) q^{41} +(2.27242 + 1.76231i) q^{42} +(-4.34014 - 11.9244i) q^{43} +(-0.331892 - 7.07018i) q^{44} +(-1.00402 - 1.62413i) q^{45} +(-0.436012 + 1.29139i) q^{46} +(-2.98026 + 8.18820i) q^{47} +(-6.91327 - 0.454668i) q^{48} +(-2.81086 - 4.86856i) q^{49} +(-1.27817 - 6.37123i) q^{50} +(-0.0670962 - 0.0775620i) q^{51} +(-7.78551 - 8.44073i) q^{52} +(3.85847 - 0.680353i) q^{53} +(-6.60080 - 3.22946i) q^{54} +(-1.44786 + 1.72549i) q^{55} +(-2.98531 - 1.45400i) q^{56} +(-6.18705 - 4.32670i) q^{57} +(4.23053 - 12.5301i) q^{58} +(6.13510 - 2.23299i) q^{59} +(1.51907 + 1.59799i) q^{60} +(-7.36100 + 6.17661i) q^{61} +(2.38955 - 0.0560548i) q^{62} +(-2.34403 - 2.62868i) q^{63} +(7.92092 - 1.12208i) q^{64} +3.65432i q^{65} +(-1.17561 + 8.58862i) q^{66} +(1.22266 + 6.93404i) q^{67} +(0.0941858 + 0.0717825i) q^{68} +(0.812829 - 1.45809i) q^{69} +(0.384609 + 0.984247i) q^{70} +(-1.72865 + 9.80369i) q^{71} +(8.22439 + 2.08791i) q^{72} +(-9.78246 + 3.56052i) q^{73} +(0.238836 + 10.1813i) q^{74} +(0.119723 + 7.95770i) q^{75} +(8.01643 + 3.42592i) q^{76} +(-2.07738 + 3.59813i) q^{77} +(7.49546 + 11.8999i) q^{78} +(3.96955 + 3.33085i) q^{79} +(-2.09499 - 1.44657i) q^{80} +(7.22983 + 5.35999i) q^{81} +(5.83189 + 0.887841i) q^{82} +(8.82113 + 5.09288i) q^{83} +(3.27126 + 2.41622i) q^{84} +(-0.00654411 - 0.0371135i) q^{85} +(-6.53168 - 16.7151i) q^{86} +(-7.88670 + 14.1475i) q^{87} +(-0.703727 - 9.98499i) q^{88} +(1.40092 - 3.84898i) q^{89} +(-1.47338 - 2.26294i) q^{90} +(1.17048 + 6.63813i) q^{91} +(-0.573614 + 1.84026i) q^{92} +(-2.89024 - 0.464910i) q^{93} +(-3.94200 + 11.6755i) q^{94} +(-1.13604 - 2.53106i) q^{95} +(-9.78923 - 0.413535i) q^{96} +(-7.75312 - 1.36708i) q^{97} +(-4.13554 - 6.79006i) q^{98} +(3.32944 - 10.0814i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 696 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 6 q^{6} - 18 q^{8}+O(q^{10}) \) 696 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 6 * q^6 - 18 * q^8	\( 696 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 6 q^{6} - 18 q^{8} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 15 q^{14} - 3 q^{16} - 24 q^{17} - 6 q^{20} - 30 q^{21} + 21 q^{22} + 24 q^{24} - 6 q^{25} - 30 q^{26} - 6 q^{29} - 21 q^{30} - 3 q^{32} + 36 q^{33} + 33 q^{34} + 54 q^{36} - 3 q^{38} - 33 q^{40} + 54 q^{41} - 87 q^{42} - 33 q^{44} - 6 q^{45} - 18 q^{46} + 6 q^{48} + 282 q^{49} - 3 q^{52} - 24 q^{53} - 51 q^{54} - 63 q^{56} - 12 q^{57} - 6 q^{58} - 27 q^{60} - 6 q^{61} - 18 q^{62} - 24 q^{64} - 30 q^{66} + 3 q^{68} - 18 q^{69} - 45 q^{70} + 12 q^{72} - 60 q^{73} + 3 q^{74} - 3 q^{76} + 72 q^{77} - 81 q^{78} - 12 q^{80} - 72 q^{81} - 12 q^{82} - 9 q^{84} - 6 q^{85} - 57 q^{86} - 9 q^{88} - 24 q^{89} + 39 q^{90} + 81 q^{92} - 48 q^{93} + 15 q^{96} + 30 q^{97} - 63 q^{98}+O(q^{100}) \) 696 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 6 * q^6 - 18 * q^8 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 15 * q^14 - 3 * q^16 - 24 * q^17 - 6 * q^20 - 30 * q^21 + 21 * q^22 + 24 * q^24 - 6 * q^25 - 30 * q^26 - 6 * q^29 - 21 * q^30 - 3 * q^32 + 36 * q^33 + 33 * q^34 + 54 * q^36 - 3 * q^38 - 33 * q^40 + 54 * q^41 - 87 * q^42 - 33 * q^44 - 6 * q^45 - 18 * q^46 + 6 * q^48 + 282 * q^49 - 3 * q^52 - 24 * q^53 - 51 * q^54 - 63 * q^56 - 12 * q^57 - 6 * q^58 - 27 * q^60 - 6 * q^61 - 18 * q^62 - 24 * q^64 - 30 * q^66 + 3 * q^68 - 18 * q^69 - 45 * q^70 + 12 * q^72 - 60 * q^73 + 3 * q^74 - 3 * q^76 + 72 * q^77 - 81 * q^78 - 12 * q^80 - 72 * q^81 - 12 * q^82 - 9 * q^84 - 6 * q^85 - 57 * q^86 - 9 * q^88 - 24 * q^89 + 39 * q^90 + 81 * q^92 - 48 * q^93 + 15 * q^96 + 30 * q^97 - 63 * q^98

Introduction

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