LMFDB - Embedded newform 336.2.bq.b.37.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(37,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 0, 4]))

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

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

chi := DirichletCharacter("336.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bq (of order $12$, degree $4$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$30$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.8
Character	$\chi$	$=$	336.37
Dual form			336.2.bq.b.109.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.978024 + 1.02150i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.0869382 - 1.99811i) q^{4} +(0.298815 - 0.0800672i) q^{5} +(1.20908 - 0.733565i) q^{6} +(-2.15167 + 1.53959i) q^{7} +(2.12610 + 1.86539i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.978024 + 1.02150i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.0869382 - 1.99811i) q^{4} +(0.298815 - 0.0800672i) q^{5} +(1.20908 - 0.733565i) q^{6} +(-2.15167 + 1.53959i) q^{7} +(2.12610 + 1.86539i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-0.210459 + 0.383548i) q^{10} +(1.29734 - 4.84172i) q^{11} +(-0.433173 + 1.95253i) q^{12} +(-4.35505 + 4.35505i) q^{13} +(0.531685 - 3.70369i) q^{14} -0.309356 q^{15} +(-3.98488 + 0.347424i) q^{16} +(-1.39725 - 2.42010i) q^{17} +(-1.35775 + 0.395636i) q^{18} +(-1.71139 - 6.38701i) q^{19} +(-0.185962 - 0.590104i) q^{20} +(2.47682 - 0.930237i) q^{21} +(3.67701 + 6.06055i) q^{22} +(-5.30544 - 3.06309i) q^{23} +(-1.57086 - 2.35211i) q^{24} +(-4.24725 + 2.45215i) q^{25} +(-0.189355 - 8.70805i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(3.26333 + 4.16541i) q^{28} +(2.26783 - 2.26783i) q^{29} +(0.302558 - 0.316008i) q^{30} +(-1.55467 - 2.69277i) q^{31} +(3.54242 - 4.41036i) q^{32} +(-2.50626 + 4.34097i) q^{33} +(3.83869 + 0.939626i) q^{34} +(-0.519679 + 0.632330i) q^{35} +(0.923764 - 1.77388i) q^{36} +(2.56322 - 0.686814i) q^{37} +(8.19813 + 4.49845i) q^{38} +(5.33383 - 3.07949i) q^{39} +(0.784668 + 0.387176i) q^{40} +1.09493i q^{41} +(-1.47215 + 3.43988i) q^{42} +(-3.86349 - 3.86349i) q^{43} +(-9.78708 - 2.17129i) q^{44} +(0.298815 + 0.0800672i) q^{45} +(8.31780 - 2.42374i) q^{46} +(-2.83426 + 4.90908i) q^{47} +(3.93902 + 0.695778i) q^{48} +(2.25933 - 6.62536i) q^{49} +(1.64903 - 6.73684i) q^{50} +(0.723269 + 2.69928i) q^{51} +(9.08050 + 8.32326i) q^{52} +(2.53409 - 9.45734i) q^{53} +(1.41388 - 0.0307446i) q^{54} -1.55065i q^{55} +(-7.44660 - 0.740372i) q^{56} +6.61232i q^{57} +(0.0986038 + 4.53459i) q^{58} +(-3.84475 + 14.3488i) q^{59} +(0.0268948 + 0.618127i) q^{60} +(1.47687 + 5.51176i) q^{61} +(4.27117 + 1.04549i) q^{62} +(-2.63319 + 0.257491i) q^{63} +(1.04063 + 7.93203i) q^{64} +(-0.952658 + 1.65005i) q^{65} +(-1.98313 - 6.80573i) q^{66} +(-0.999507 - 0.267817i) q^{67} +(-4.71416 + 3.00225i) q^{68} +(4.33187 + 4.33187i) q^{69} +(-0.137669 - 1.14929i) q^{70} -2.98981i q^{71} +(0.908564 + 2.67853i) q^{72} +(-9.78190 + 5.64758i) q^{73} +(-1.80531 + 3.29006i) q^{74} +(4.73719 - 1.26933i) q^{75} +(-12.6132 + 3.97483i) q^{76} +(4.66283 + 12.4151i) q^{77} +(-2.07091 + 8.46034i) q^{78} +(-7.66553 + 13.2771i) q^{79} +(-1.16293 + 0.422874i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-1.11847 - 1.07086i) q^{82} +(8.57101 - 8.57101i) q^{83} +(-2.07405 - 4.86809i) q^{84} +(-0.611289 - 0.611289i) q^{85} +(7.72516 - 0.167982i) q^{86} +(-2.77751 + 1.60360i) q^{87} +(11.7900 - 7.87396i) q^{88} +(-0.966296 - 0.557891i) q^{89} +(-0.374037 + 0.226933i) q^{90} +(2.66562 - 16.0756i) q^{91} +(-5.65915 + 10.8671i) q^{92} +(0.804756 + 3.00339i) q^{93} +(-2.24267 - 7.69640i) q^{94} +(-1.02278 - 1.77151i) q^{95} +(-4.56320 + 3.34324i) q^{96} +9.49689 q^{97} +(4.55815 + 8.78768i) q^{98} +(3.54439 - 3.54439i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8}+O(q^{10}) $ 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8	$ 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8} - 8 q^{10} + 4 q^{11} + 8 q^{13} + 32 q^{14} + 8 q^{15} + 12 q^{16} - 16 q^{17} - 4 q^{18} - 8 q^{19} - 64 q^{20} + 12 q^{21} + 24 q^{22} - 8 q^{24} - 8 q^{26} - 8 q^{28} - 64 q^{29} - 52 q^{31} - 4 q^{33} + 32 q^{34} - 8 q^{35} + 24 q^{37} - 40 q^{38} - 60 q^{40} + 24 q^{42} - 32 q^{43} - 12 q^{44} - 8 q^{45} + 4 q^{46} - 8 q^{47} + 32 q^{48} + 20 q^{49} - 16 q^{50} - 8 q^{51} - 16 q^{52} + 4 q^{54} - 104 q^{56} + 4 q^{58} + 52 q^{59} - 16 q^{60} + 4 q^{61} - 144 q^{62} + 8 q^{63} - 64 q^{64} + 24 q^{65} + 24 q^{66} + 12 q^{68} + 24 q^{69} - 48 q^{70} + 4 q^{72} + 16 q^{74} + 16 q^{75} - 8 q^{76} + 8 q^{77} - 56 q^{78} + 28 q^{79} + 68 q^{80} + 60 q^{81} + 28 q^{82} + 8 q^{83} + 24 q^{84} - 80 q^{85} + 36 q^{86} + 40 q^{88} + 8 q^{90} + 36 q^{91} - 184 q^{92} + 4 q^{93} + 60 q^{94} - 16 q^{95} + 36 q^{96} + 24 q^{97} + 124 q^{98} - 8 q^{99}+O(q^{100}) $ 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8 - 8 * q^10 + 4 * q^11 + 8 * q^13 + 32 * q^14 + 8 * q^15 + 12 * q^16 - 16 * q^17 - 4 * q^18 - 8 * q^19 - 64 * q^20 + 12 * q^21 + 24 * q^22 - 8 * q^24 - 8 * q^26 - 8 * q^28 - 64 * q^29 - 52 * q^31 - 4 * q^33 + 32 * q^34 - 8 * q^35 + 24 * q^37 - 40 * q^38 - 60 * q^40 + 24 * q^42 - 32 * q^43 - 12 * q^44 - 8 * q^45 + 4 * q^46 - 8 * q^47 + 32 * q^48 + 20 * q^49 - 16 * q^50 - 8 * q^51 - 16 * q^52 + 4 * q^54 - 104 * q^56 + 4 * q^58 + 52 * q^59 - 16 * q^60 + 4 * q^61 - 144 * q^62 + 8 * q^63 - 64 * q^64 + 24 * q^65 + 24 * q^66 + 12 * q^68 + 24 * q^69 - 48 * q^70 + 4 * q^72 + 16 * q^74 + 16 * q^75 - 8 * q^76 + 8 * q^77 - 56 * q^78 + 28 * q^79 + 68 * q^80 + 60 * q^81 + 28 * q^82 + 8 * q^83 + 24 * q^84 - 80 * q^85 + 36 * q^86 + 40 * q^88 + 8 * q^90 + 36 * q^91 - 184 * q^92 + 4 * q^93 + 60 * q^94 - 16 * q^95 + 36 * q^96 + 24 * q^97 + 124 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.978024	+	1.02150i	−0.691567	+	0.722312i
$2$	−0.978024	+	1.02150i	−0.691567	+	0.722312i
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$4$	−0.0869382	−	1.99811i	−0.0434691	−	0.999055i
$5$	0.298815	−	0.0800672i	0.133634	−	0.0358071i	−0.191382	−	0.981516i	$-0.561297\pi$
$5$	0.298815	−	0.0800672i	0.133634	−	0.0358071i	0.325016	+	0.945708i	$0.394630\pi$
$6$	1.20908	−	0.733565i	0.493606	−	0.299477i
$7$	−2.15167	+	1.53959i	−0.813253	+	0.581910i
$7$	−2.15167	+	1.53959i	−0.813253	+	0.581910i
$8$	2.12610	+	1.86539i	0.751691	+	0.659515i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$	−0.210459	+	0.383548i	−0.0665531	+	0.121289i
$11$	1.29734	−	4.84172i	0.391161	−	1.45983i	−0.437060	−	0.899433i	$-0.643980\pi$
$11$	1.29734	−	4.84172i	0.391161	−	1.45983i	0.828221	−	0.560402i	$-0.189353\pi$
$12$	−0.433173	+	1.95253i	−0.125046	+	0.563646i
$13$	−4.35505	+	4.35505i	−1.20787	+	1.20787i	−0.236161	+	0.971714i	$0.575889\pi$
$13$	−4.35505	+	4.35505i	−1.20787	+	1.20787i	−0.971714	+	0.236161i	$0.924111\pi$
$14$	0.531685	−	3.70369i	0.142099	−	0.989852i
$15$	−0.309356			−0.0798754
$16$	−3.98488	+	0.347424i	−0.996221	+	0.0868560i
$17$	−1.39725	−	2.42010i	−0.338882	−	0.586961i	0.645340	−	0.763895i	$-0.276716\pi$
$17$	−1.39725	−	2.42010i	−0.338882	−	0.586961i	−0.984223	+	0.176934i	$0.943382\pi$
$18$	−1.35775	+	0.395636i	−0.320024	+	0.0932523i
$19$	−1.71139	−	6.38701i	−0.392621	−	1.46528i	−0.825795	−	0.563970i	$-0.809273\pi$
$19$	−1.71139	−	6.38701i	−0.392621	−	1.46528i	0.433175	−	0.901310i	$-0.357393\pi$
$20$	−0.185962	−	0.590104i	−0.0415823	−	0.131951i
$21$	2.47682	−	0.930237i	0.540487	−	0.202994i
$22$	3.67701	+	6.06055i	0.783941	+	1.29211i
$23$	−5.30544	−	3.06309i	−1.10626	−	0.638699i	−0.168402	−	0.985718i	$-0.553861\pi$
$23$	−5.30544	−	3.06309i	−1.10626	−	0.638699i	−0.937858	+	0.347019i	$0.887194\pi$
$24$	−1.57086	−	2.35211i	−0.320650	−	0.480122i
$25$	−4.24725	+	2.45215i	−0.849449	+	0.490430i
$26$	−0.189355	−	8.70805i	−0.0371356	−	1.70779i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	3.26333	+	4.16541i	0.616711	+	0.787189i
$29$	2.26783	−	2.26783i	0.421126	−	0.421126i	−0.464466	−	0.885591i	$-0.653754\pi$
$29$	2.26783	−	2.26783i	0.421126	−	0.421126i	0.885591	+	0.464466i	$0.153754\pi$
$30$	0.302558	−	0.316008i	0.0552392	−	0.0576949i
$31$	−1.55467	−	2.69277i	−0.279227	−	0.483635i	0.691966	−	0.721930i	$-0.256745\pi$
$31$	−1.55467	−	2.69277i	−0.279227	−	0.483635i	−0.971193	+	0.238295i	$0.923411\pi$
$32$	3.54242	−	4.41036i	0.626217	−	0.779649i
$33$	−2.50626	+	4.34097i	−0.436284	+	0.755666i
$34$	3.83869	+	0.939626i	0.658329	+	0.161145i
$35$	−0.519679	+	0.632330i	−0.0878418	+	0.106883i
$36$	0.923764	−	1.77388i	0.153961	−	0.295647i
$37$	2.56322	−	0.686814i	0.421391	−	0.112911i	−0.0418911	−	0.999122i	$-0.513338\pi$
$37$	2.56322	−	0.686814i	0.421391	−	0.112911i	0.463282	+	0.886211i	$0.346672\pi$
$38$	8.19813	+	4.49845i	1.32991	+	0.729745i
$39$	5.33383	−	3.07949i	0.854097	−	0.493113i
$40$	0.784668	+	0.387176i	0.124067	+	0.0612178i
$41$			1.09493i			0.170999i	0.996338	+	0.0854993i	$0.0272485\pi$
$41$			1.09493i			0.170999i	−0.996338	+	0.0854993i	$0.972751\pi$
$42$	−1.47215	+	3.43988i	−0.227158	+	0.530785i
$43$	−3.86349	−	3.86349i	−0.589177	−	0.589177i	0.348231	−	0.937409i	$-0.386782\pi$
$43$	−3.86349	−	3.86349i	−0.589177	−	0.589177i	−0.937409	+	0.348231i	$0.886782\pi$
$44$	−9.78708	−	2.17129i	−1.47546	−	0.327334i
$45$	0.298815	+	0.0800672i	0.0445447	+	0.0119357i
$46$	8.31780	−	2.42374i	1.22639	−	0.357361i
$47$	−2.83426	+	4.90908i	−0.413419	+	0.716063i	−0.995261	−	0.0972390i	$-0.968999\pi$
$47$	−2.83426	+	4.90908i	−0.413419	+	0.716063i	0.581842	+	0.813302i	$0.302332\pi$
$48$	3.93902	+	0.695778i	0.568549	+	0.100427i
$49$	2.25933	−	6.62536i	0.322761	−	0.946480i
$50$	1.64903	−	6.73684i	0.233208	−	0.952733i
$51$	0.723269	+	2.69928i	0.101278	+	0.377974i
$52$	9.08050	+	8.32326i	1.25924	+	1.15423i
$53$	2.53409	−	9.45734i	0.348084	−	1.29907i	−0.540885	−	0.841097i	$-0.681910\pi$
$53$	2.53409	−	9.45734i	0.348084	−	1.29907i	0.888968	−	0.457969i	$-0.151423\pi$
$54$	1.41388	−	0.0307446i	0.192405	−	0.00418380i
$55$		−	1.55065i		−	0.209090i
$56$	−7.44660	−	0.740372i	−0.995094	−	0.0989364i
$57$			6.61232i			0.875823i
$58$	0.0986038	+	4.53459i	0.0129473	+	0.595421i
$59$	−3.84475	+	14.3488i	−0.500544	+	1.86806i	−0.00409201	+	0.999992i	$0.501303\pi$
$59$	−3.84475	+	14.3488i	−0.500544	+	1.86806i	−0.496452	+	0.868064i	$0.665364\pi$
$60$	0.0268948	+	0.618127i	0.00347211	+	0.0797999i
$61$	1.47687	+	5.51176i	0.189094	+	0.705708i	0.993717	+	0.111922i	$0.0357007\pi$
$61$	1.47687	+	5.51176i	0.189094	+	0.705708i	−0.804623	+	0.593786i	$0.797633\pi$
$62$	4.27117	+	1.04549i	0.542439	+	0.132777i
$63$	−2.63319	+	0.257491i	−0.331751	+	0.0324408i
$64$	1.04063	+	7.93203i	0.130079	+	0.991504i
$65$	−0.952658	+	1.65005i	−0.118163	+	0.204664i
$66$	−1.98313	−	6.80573i	−0.244107	−	0.837727i
$67$	−0.999507	−	0.267817i	−0.122109	−	0.0327191i	0.197247	−	0.980354i	$-0.436800\pi$
$67$	−0.999507	−	0.267817i	−0.122109	−	0.0327191i	−0.319356	+	0.947635i	$0.603467\pi$
$68$	−4.71416	+	3.00225i	−0.571676	+	0.364077i
$69$	4.33187	+	4.33187i	0.521496	+	0.521496i
$70$	−0.137669	−	1.14929i	−0.0164546	−	0.137366i
$71$		−	2.98981i		−	0.354825i	−0.984137	−	0.177413i	$-0.943227\pi$
$71$		−	2.98981i		−	0.354825i	0.984137	−	0.177413i	$-0.0567727\pi$
$72$	0.908564	+	2.67853i	0.107075	+	0.315668i
$73$	−9.78190	+	5.64758i	−1.14489	+	0.661000i	−0.947636	−	0.319354i	$-0.896534\pi$
$73$	−9.78190	+	5.64758i	−1.14489	+	0.661000i	−0.197249	+	0.980353i	$0.563201\pi$
$74$	−1.80531	+	3.29006i	−0.209863	+	0.382462i
$75$	4.73719	−	1.26933i	0.547003	−	0.146569i
$76$	−12.6132	+	3.97483i	−1.44683	+	0.455944i
$77$	4.66283	+	12.4151i	0.531379	+	1.41484i
$78$	−2.07091	+	8.46034i	−0.234484	+	0.957945i
$79$	−7.66553	+	13.2771i	−0.862440	+	1.49379i	0.00712745	+	0.999975i	$0.497731\pi$
$79$	−7.66553	+	13.2771i	−0.862440	+	1.49379i	−0.869567	+	0.493815i	$0.835602\pi$
$80$	−1.16293	+	0.422874i	−0.130019	+	0.0472788i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−1.11847	−	1.07086i	−0.123514	−	0.118257i
$83$	8.57101	−	8.57101i	0.940791	−	0.940791i	−0.0575517	−	0.998343i	$-0.518329\pi$
$83$	8.57101	−	8.57101i	0.940791	−	0.940791i	0.998343	+	0.0575517i	$0.0183294\pi$
$84$	−2.07405	−	4.86809i	−0.226297	−	0.531153i
$85$	−0.611289	−	0.611289i	−0.0663036	−	0.0663036i
$86$	7.72516	−	0.167982i	0.833026	−	0.0181140i
$87$	−2.77751	+	1.60360i	−0.297781	+	0.171924i
$88$	11.7900	−	7.87396i	1.25682	−	0.839367i
$89$	−0.966296	−	0.557891i	−0.102427	−	0.0591364i	0.447911	−	0.894078i	$-0.352168\pi$
$89$	−0.966296	−	0.557891i	−0.102427	−	0.0591364i	−0.550339	+	0.834942i	$0.685501\pi$
$90$	−0.374037	+	0.226933i	−0.0394270	+	0.0239208i
$91$	2.66562	−	16.0756i	0.279433	−	1.68518i
$92$	−5.65915	+	10.8671i	−0.590008	+	1.13298i
$93$	0.804756	+	3.00339i	0.0834493	+	0.311437i
$94$	−2.24267	−	7.69640i	−0.231314	−	0.793823i
$95$	−1.02278	−	1.77151i	−0.104935	−	0.181753i
$96$	−4.56320	+	3.34324i	−0.465729	+	0.341218i
$97$	9.49689			0.964263			0.482132	−	0.876099i	$-0.339863\pi$
$97$	9.49689			0.964263			0.482132	+	0.876099i	$0.339863\pi$
$98$	4.55815	+	8.78768i	0.460443	+	0.887689i
$99$	3.54439	−	3.54439i	0.356224	−	0.356224i
$100$	5.26891	+	8.27328i	0.526891	+	0.827328i
$101$	0.222933	−	0.831998i	0.0221827	−	0.0827869i	−0.953947	−	0.299975i	$-0.903022\pi$
$101$	0.222933	−	0.831998i	0.0221827	−	0.0827869i	0.976130	+	0.217188i	$0.0696884\pi$
$102$	−3.46469	−	1.90113i	−0.343056	−	0.188240i
$103$	−7.83942	−	4.52609i	−0.772441	−	0.445969i	0.0613036	−	0.998119i	$-0.480474\pi$
$103$	−7.83942	−	4.52609i	−0.772441	−	0.445969i	−0.833745	+	0.552150i	$0.813808\pi$
$104$	−17.3832	+	1.13541i	−1.70456	+	0.111337i
$105$	0.665631	−	0.476281i	0.0649589	−	0.0464803i
$106$	7.18231	+	11.8381i	0.697607	+	1.14982i
$107$	14.3540	−	3.84615i	1.38766	−	0.371822i	0.513761	−	0.857933i	$-0.328252\pi$
$107$	14.3540	−	3.84615i	1.38766	−	0.371822i	0.873897	+	0.486111i	$0.161585\pi$
$108$	−1.35140	+	1.47435i	−0.130039	+	0.141870i
$109$	12.0824	+	3.23746i	1.15728	+	0.310092i	0.785879	−	0.618380i	$-0.212211\pi$
$109$	12.0824	+	3.23746i	1.15728	+	0.310092i	0.371401	+	0.928473i	$0.378877\pi$
$110$	1.58400	+	1.51658i	0.151028	+	0.144600i
$111$	−2.65364			−0.251873
$112$	8.03925	−	6.88262i	0.759637	−	0.650347i
$113$	−11.1439			−1.04833			−0.524163	−	0.851618i	$-0.675622\pi$
$113$	−11.1439			−1.04833			−0.524163	+	0.851618i	$0.675622\pi$
$114$	−6.75450	−	6.46700i	−0.632617	−	0.605690i
$115$	−1.83060	−	0.490507i	−0.170704	−	0.0457400i
$116$	−4.72854	−	4.33421i	−0.439034	−	0.402422i
$117$	−5.94912	+	1.59406i	−0.549996	+	0.147371i
$118$	−10.8971	−	17.9609i	−1.00316	−	1.65344i
$119$	6.73238	+	3.05607i	0.617156	+	0.280149i
$120$	−0.657723	−	0.577070i	−0.0600416	−	0.0526790i
$121$	−12.2329	−	7.06268i	−1.11208	−	0.642062i
$122$	−7.07469	−	3.88200i	−0.640512	−	0.351460i
$123$	0.283388	−	1.05762i	0.0255522	−	0.0953621i
$124$	−5.24528	+	3.34050i	−0.471040	+	0.299986i
$125$	−2.16654	+	2.16654i	−0.193781	+	0.193781i
$126$	2.31230	−	2.94165i	0.205996	−	0.262063i
$127$	16.7177			1.48345			0.741727	−	0.670702i	$-0.234007\pi$
$127$	16.7177			1.48345			0.741727	+	0.670702i	$0.234007\pi$
$128$	−9.12036	−	6.69471i	−0.806133	−	0.591734i
$129$	2.73190	+	4.73180i	0.240531	+	0.416611i
$130$	−0.753812	−	2.58693i	−0.0661136	−	0.226889i
$131$	−0.0308362	−	0.115082i	−0.00269417	−	0.0100548i	0.964566	−	0.263843i	$-0.0849901\pi$
$131$	−0.0308362	−	0.115082i	−0.00269417	−	0.0100548i	−0.967260	+	0.253788i	$0.918323\pi$
$132$	8.89162	+	4.63039i	0.773916	+	0.403023i
$133$	13.5157	+	11.1079i	1.17196	+	0.963173i
$134$	1.25112	−	0.759068i	0.108080	−	0.0655735i
$135$	−0.267910	−	0.154678i	−0.0230580	−	0.0133126i
$136$	1.54375	−	7.75180i	0.132375	−	0.664712i
$137$	−1.58295	+	0.913917i	−0.135241	+	0.0780812i	−0.566094	−	0.824341i	$-0.691546\pi$
$137$	−1.58295	+	0.913917i	−0.135241	+	0.0780812i	0.430853	+	0.902422i	$0.358213\pi$
$138$	−8.66169	+	0.188347i	−0.737332	+	0.0160332i
$139$	1.45200	+	1.45200i	0.123157	+	0.123157i	0.765999	−	0.642842i	$-0.222245\pi$
$139$	1.45200	+	1.45200i	0.123157	+	0.123157i	−0.642842	+	0.765999i	$0.722245\pi$
$140$	1.30864	+	0.983402i	0.110601	+	0.0831127i
$141$	4.00825	−	4.00825i	0.337555	−	0.337555i
$142$	3.05410	+	2.92410i	0.256294	+	0.245385i
$143$	15.4360	+	26.7359i	1.29082	+	2.23577i
$144$	−3.62472	−	1.69156i	−0.302060	−	0.140964i
$145$	0.496083	−	0.859241i	0.0411974	−	0.0713561i
$146$	3.79791	−	15.5157i	0.314317	−	1.28409i
$147$	−3.89711	+	5.81485i	−0.321429	+	0.479601i
$148$	−1.59517	−	5.06189i	−0.131122	−	0.416085i
$149$	15.5075	−	4.15524i	1.27043	−	0.340410i	0.440233	−	0.897884i	$-0.354896\pi$
$149$	15.5075	−	4.15524i	1.27043	−	0.340410i	0.830195	+	0.557473i	$0.188229\pi$
$150$	−3.33646	+	6.08049i	−0.272421	+	0.496470i
$151$	2.21971	−	1.28155i	0.180638	−	0.104291i	−0.406955	−	0.913448i	$-0.633409\pi$
$151$	2.21971	−	1.28155i	0.180638	−	0.104291i	0.587592	+	0.809157i	$0.300076\pi$
$152$	8.27567	−	16.7719i	0.671245	−	1.36038i
$153$		−	2.79450i		−	0.225922i
$154$	−17.2425	−	7.37920i	−1.38944	−	0.594633i
$155$	−0.680161	−	0.680161i	−0.0546318	−	0.0546318i
$156$	−6.61687	−	10.3899i	−0.529774	−	0.831854i
$157$	−10.1461	−	2.71864i	−0.809746	−	0.216971i	−0.169888	−	0.985463i	$-0.554340\pi$
$157$	−10.1461	−	2.71864i	−0.809746	−	0.216971i	−0.639859	+	0.768493i	$0.721007\pi$
$158$	−6.06552	−	20.8157i	−0.482547	−	1.65601i
$159$	−4.89548	+	8.47922i	−0.388237	+	0.672446i
$160$	0.705402	−	1.60151i	0.0557669	−	0.126611i
$161$	16.1314	−	1.57744i	1.27133	−	0.124320i
$162$	−1.37366	−	0.336242i	−0.107925	−	0.0264177i
$163$	−2.79881	−	10.4453i	−0.219219	−	0.818138i	−0.984638	−	0.174606i	$-0.944135\pi$
$163$	−2.79881	−	10.4453i	−0.219219	−	0.818138i	0.765419	−	0.643532i	$-0.222532\pi$
$164$	2.18778	−	0.0951908i	0.170837	−	0.00743316i
$165$	−0.401339	+	1.49782i	−0.0312442	+	0.116605i
$166$	0.372662	+	17.1380i	0.0289242	+	1.33016i
$167$			6.23970i			0.482842i	0.970420	+	0.241421i	$0.0776135\pi$
$167$			6.23970i			0.482842i	−0.970420	+	0.241421i	$0.922387\pi$
$168$	7.00124	+	2.64247i	0.540157	+	0.203871i
$169$		−	24.9330i		−	1.91792i
$170$	1.22229	−	0.0265785i	0.0937454	−	0.00203848i
$171$	1.71139	−	6.38701i	0.130874	−	0.488427i
$172$	−7.38380	+	8.05557i	−0.563010	+	0.614232i
$173$	−3.58623	−	13.3840i	−0.272656	−	1.01757i	−0.957396	−	0.288779i	$-0.906751\pi$
$173$	−3.58623	−	13.3840i	−0.272656	−	1.01757i	0.684740	−	0.728788i	$-0.259916\pi$
$174$	1.07839	−	4.40560i	0.0817529	−	0.333988i
$175$	5.36335	−	11.8152i	0.405431	−	0.893147i
$176$	−3.48760	+	19.7444i	−0.262888	+	1.48829i
$177$	7.42749	−	12.8648i	0.558284	−	0.966977i
$178$	1.51495	−	0.441444i	0.113550	−	0.0330876i
$179$	−12.1198	−	3.24748i	−0.905875	−	0.242728i	−0.224337	−	0.974512i	$-0.572022\pi$
$179$	−12.1198	−	3.24748i	−0.905875	−	0.242728i	−0.681538	+	0.731783i	$0.738688\pi$
$180$	0.134005	−	0.604026i	0.00998812	−	0.0450214i
$181$	−3.73434	−	3.73434i	−0.277571	−	0.277571i	0.554567	−	0.832139i	$-0.312884\pi$
$181$	−3.73434	−	3.73434i	−0.277571	−	0.277571i	−0.832139	+	0.554567i	$0.812884\pi$
$182$	13.8143	+	18.4453i	1.02398	+	1.36726i
$183$		−	5.70619i		−	0.421814i
$184$	−5.56603	−	16.4092i	−0.410333	−	1.20970i
$185$	0.710938	−	0.410460i	0.0522692	−	0.0301776i
$186$	−3.85504	−	2.11533i	−0.282665	−	0.155103i
$187$	−13.5302	+	3.62540i	−0.989424	+	0.265115i
$188$	10.0553	+	5.23637i	0.733357	+	0.381902i
$189$	2.61011	+	0.432803i	0.189858	+	0.0314818i
$190$	2.80990	+	0.687803i	0.203852	+	0.0498985i
$191$	−3.63621	+	6.29810i	−0.263107	+	0.455715i	−0.967066	−	0.254526i	$-0.918081\pi$
$191$	−3.63621	+	6.29810i	−0.263107	+	0.455715i	0.703959	+	0.710241i	$0.251414\pi$
$192$	1.04779	−	7.93109i	0.0756177	−	0.572377i
$193$	5.25450	+	9.10106i	0.378227	+	0.655109i	0.990804	−	0.135302i	$-0.0432005\pi$
$193$	5.25450	+	9.10106i	0.378227	+	0.655109i	−0.612577	+	0.790411i	$0.709867\pi$
$194$	−9.28819	+	9.70110i	−0.666853	+	0.696499i
$195$	1.34726	−	1.34726i	0.0964795	−	0.0964795i
$196$	−13.4346	−	3.93839i	−0.959616	−	0.281313i
$197$	−5.29116	−	5.29116i	−0.376980	−	0.376980i	0.493032	−	0.870011i	$-0.335889\pi$
$197$	−5.29116	−	5.29116i	−0.376980	−	0.376980i	−0.870011	+	0.493032i	$0.835889\pi$
$198$	0.154108	+	7.08710i	0.0109520	+	0.503658i
$199$	−5.58478	+	3.22437i	−0.395894	+	0.228570i	−0.684711	−	0.728815i	$-0.740072\pi$
$199$	−5.58478	+	3.22437i	−0.395894	+	0.228570i	0.288817	+	0.957384i	$0.406738\pi$
$200$	−13.6043	−	2.70926i	−0.961970	−	0.191573i
$201$	0.896134	+	0.517383i	0.0632084	+	0.0364934i
$202$	0.631855	+	1.04144i	0.0444571	+	0.0732755i
$203$	−1.38808	+	8.37114i	−0.0974245	+	0.587539i
$204$	5.33057	−	1.67984i	0.373214	−	0.117612i
$205$	0.0876677	+	0.327180i	0.00612297	+	0.0228513i
$206$	12.2906	−	3.58137i	0.856324	−	0.249526i
$207$	−3.06309	−	5.30544i	−0.212900	−	0.368753i
$208$	15.8413	−	18.8674i	1.09840	−	1.30822i
$209$	−33.1444			−2.29264
$210$	−0.164480	+	1.14576i	−0.0113502	+	0.0790648i
$211$	−0.454333	+	0.454333i	−0.0312776	+	0.0312776i	−0.722573	−	0.691295i	$-0.757041\pi$
$211$	−0.454333	+	0.454333i	−0.0312776	+	0.0312776i	0.691295	+	0.722573i	$0.257041\pi$
$212$	−19.1171	−	4.24118i	−1.31297	−	0.291285i
$213$	−0.773819	+	2.88793i	−0.0530212	+	0.197878i
$214$	−10.1097	+	18.4243i	−0.691088	+	1.25946i
$215$	−1.46381	−	0.845131i	−0.0998310	−	0.0576374i
$216$	−0.184351	−	2.82241i	−0.0125435	−	0.192041i
$217$	7.49088	+	3.40038i	0.508514	+	0.230833i
$218$	−15.1239	+	9.17586i	−1.02432	+	0.621468i
$219$	10.9103	−	2.92340i	0.737249	−	0.197545i
$220$	−3.09837	+	0.134811i	−0.208892	+	0.00908895i
$221$	16.6248	+	4.45460i	1.11830	+	0.299648i
$222$	2.59533	−	2.71071i	0.174187	−	0.181931i
$223$	−1.97010			−0.131927			−0.0659637	−	0.997822i	$-0.521012\pi$
$223$	−1.97010			−0.131927			−0.0659637	+	0.997822i	$0.521012\pi$
$224$	−0.831951	+	14.9435i	−0.0555871	+	0.998454i
$225$	−4.90430			−0.326953
$226$	10.8990	−	11.3835i	0.724988	−	0.757218i
$227$	−13.1484	−	3.52310i	−0.872689	−	0.233836i	−0.205439	−	0.978670i	$-0.565862\pi$
$227$	−13.1484	−	3.52310i	−0.872689	−	0.233836i	−0.667250	+	0.744834i	$0.732529\pi$
$228$	13.2121	−	0.574863i	0.874995	−	0.0380712i
$229$	−21.7687	+	5.83291i	−1.43852	+	0.385450i	−0.892015	−	0.452007i	$-0.850708\pi$
$229$	−21.7687	+	5.83291i	−1.43852	+	0.385450i	−0.546504	+	0.837457i	$0.684042\pi$
$230$	2.29142	−	1.39023i	0.151092	−	0.0916693i
$231$	−1.29068	−	13.1989i	−0.0849204	−	0.868426i
$232$	9.05203	−	0.591250i	0.594295	−	0.0388175i
$233$	4.91761	+	2.83919i	0.322164	+	0.186001i	0.652357	−	0.757912i	$-0.273780\pi$
$233$	4.91761	+	2.83919i	0.322164	+	0.186001i	−0.330193	+	0.943913i	$0.607114\pi$
$234$	4.19004	−	7.63607i	0.273911	−	0.499186i
$235$	−0.453862	+	1.69384i	−0.0296067	+	0.110494i
$236$	29.0047	+	6.43478i	1.88805	+	0.418868i
$237$	10.8407	−	10.8407i	0.704179	−	0.704179i
$238$	−9.70621	+	3.88824i	−0.629160	+	0.252037i
$239$	−5.02284			−0.324900			−0.162450	−	0.986717i	$-0.551940\pi$
$239$	−5.02284			−0.324900			−0.162450	+	0.986717i	$0.551940\pi$
$240$	1.23275	−	0.107478i	0.0795735	−	0.00693766i
$241$	−1.39526	−	2.41666i	−0.0898767	−	0.155671i	0.817582	−	0.575812i	$-0.195314\pi$
$241$	−1.39526	−	2.41666i	−0.0898767	−	0.155671i	−0.907459	+	0.420141i	$0.861981\pi$
$242$	19.1786	−	5.58850i	1.23285	−	0.359242i
$243$	−0.258819	−	0.965926i	−0.0166032	−	0.0619642i
$244$	10.8847	−	3.43013i	0.696821	−	0.219592i
$245$	0.144647	−	2.16066i	0.00924114	−	0.138039i
$246$	0.803199	+	1.32386i	0.0512101	+	0.0844060i
$247$	35.2690	+	20.3626i	2.24411	+	1.29564i
$248$	1.71768	−	8.62516i	0.109072	−	0.547698i
$249$	−10.4973	+	6.06062i	−0.665240	+	0.384076i
$250$	−0.0941999	−	4.33206i	−0.00595772	−	0.273984i
$251$	13.6781	+	13.6781i	0.863354	+	0.863354i	0.991726	−	0.128372i	$-0.0409753\pi$
$251$	13.6781	+	13.6781i	0.863354	+	0.863354i	−0.128372	+	0.991726i	$0.540975\pi$
$252$	0.743420	+	5.23902i	0.0468310	+	0.330027i
$253$	−21.7136	+	21.7136i	−1.36512	+	1.36512i
$254$	−16.3503	+	17.0772i	−1.02591	+	1.07152i
$255$	0.432247	+	0.748674i	0.0270684	+	0.0468838i
$256$	15.7586	−	2.76889i	0.984912	−	0.173056i
$257$	1.94162	−	3.36298i	0.121115	−	0.209777i	−0.799093	−	0.601208i	$-0.794686\pi$
$257$	1.94162	−	3.36298i	0.121115	−	0.209777i	0.920208	+	0.391431i	$0.128020\pi$
$258$	−7.50541	−	1.83716i	−0.467267	−	0.114377i
$259$	−4.45779	+	5.42410i	−0.276993	+	0.337037i
$260$	3.37981	+	1.76006i	0.209607	+	0.109154i
$261$	3.09791	−	0.830084i	0.191756	−	0.0513809i
$262$	0.147715	+	0.0810539i	0.00912589	+	0.00500753i
$263$	−10.5476	+	6.08968i	−0.650395	+	0.375506i	−0.788608	−	0.614897i	$-0.789198\pi$
$263$	−10.5476	+	6.08968i	−0.650395	+	0.375506i	0.138212	+	0.990403i	$0.455864\pi$
$264$	−13.4262	+	4.55419i	−0.826324	+	0.280291i
$265$		−	3.02889i		−	0.186063i
$266$	−24.5654	+	2.94259i	−1.50620	+	0.180422i
$267$	0.788978	+	0.788978i	0.0482847	+	0.0482847i
$268$	−0.448233	+	2.02041i	−0.0273802	+	0.123416i
$269$	3.38515	+	0.907049i	0.206396	+	0.0553038i	0.360536	−	0.932745i	$-0.382594\pi$
$269$	3.38515	+	0.907049i	0.206396	+	0.0553038i	−0.154139	+	0.988049i	$0.549260\pi$
$270$	0.420027	−	0.122392i	0.0255620	−	0.00744856i
$271$	2.40652	−	4.16822i	0.146186	−	0.253201i	−0.783629	−	0.621229i	$-0.786634\pi$
$271$	2.40652	−	4.16822i	0.146186	−	0.253201i	0.929815	+	0.368028i	$0.119967\pi$
$272$	6.40867	+	9.15839i	0.388583	+	0.555309i
$273$	−6.73547	+	14.8379i	−0.407649	+	0.898033i
$274$	0.614594	−	2.51082i	0.0371290	−	0.151684i
$275$	6.36252	+	23.7453i	0.383674	+	1.43189i
$276$	8.27895	−	9.03216i	0.498334	−	0.543672i
$277$	−3.55277	+	13.2591i	−0.213465	+	0.796663i	0.773236	+	0.634119i	$0.218637\pi$
$277$	−3.55277	+	13.2591i	−0.213465	+	0.796663i	−0.986701	+	0.162545i	$0.948030\pi$
$278$	−2.90331	+	0.0631320i	−0.174129	+	0.00378641i
$279$		−	3.10934i		−	0.186151i
$280$	−2.28443	+	0.374994i	−0.136521	+	0.0224102i
$281$		−	21.7584i		−	1.29800i	−0.760790	−	0.648998i	$-0.775188\pi$
$281$		−	21.7584i		−	1.29800i	0.760790	−	0.648998i	$-0.224812\pi$
$282$	0.174276	+	8.01460i	0.0103780	+	0.477262i
$283$	4.19022	−	15.6381i	0.249083	−	0.929589i	−0.722205	−	0.691679i	$-0.756871\pi$
$283$	4.19022	−	15.6381i	0.249083	−	0.929589i	0.971287	−	0.237910i	$-0.0764622\pi$
$284$	−5.97397	+	0.259929i	−0.354490	+	0.0154239i
$285$	0.529430	+	1.97586i	0.0313607	+	0.117040i
$286$	−42.4076	−	10.3805i	−2.50762	−	0.613809i
$287$	−1.68574	−	2.35591i	−0.0995059	−	0.139065i
$288$	5.27300	−	2.04828i	0.310715	−	0.120696i
$289$	4.59540	−	7.95946i	0.270318	−	0.468204i
$290$	0.392536	+	1.34711i	0.0230505	+	0.0791049i
$291$	−9.17329	−	2.45798i	−0.537748	−	0.144089i
$292$	12.1349	+	19.0543i	0.710142	+	1.11507i
$293$	−9.49030	−	9.49030i	−0.554429	−	0.554429i	0.373287	−	0.927716i	$-0.378231\pi$
$293$	−9.49030	−	9.49030i	−0.554429	−	0.554429i	−0.927716	+	0.373287i	$0.878231\pi$
$294$	−2.12842	−	9.66798i	−0.124132	−	0.563848i
$295$			4.59548i			0.267559i
$296$	6.73085	+	3.32118i	0.391223	+	0.193040i
$297$	−4.34097	+	2.50626i	−0.251889	+	0.145428i
$298$	−10.9222	+	19.9049i	−0.632704	+	1.15306i
$299$	36.4454	−	9.76552i	2.10769	−	0.564755i
$300$	−2.94809	−	9.35507i	−0.170208	−	0.540115i
$301$	14.2611	+	2.36475i	0.821999	+	0.136302i
$302$	−0.861823	+	3.52083i	−0.0495923	+	0.202601i
$303$	−0.430674	+	0.745949i	−0.0247416	+	0.0428537i
$304$	9.03870	+	24.8569i	0.518405	+	1.42564i
$305$	0.882622	+	1.52875i	0.0505388	+	0.0875357i
$306$	2.85459	+	2.73308i	0.163186	+	0.156240i
$307$	−0.280221	+	0.280221i	−0.0159931	+	0.0159931i	−0.715058	−	0.699065i	$-0.753600\pi$
$307$	−0.280221	+	0.280221i	−0.0159931	+	0.0159931i	0.699065	+	0.715058i	$0.253600\pi$
$308$	24.4014	−	10.3962i	1.39040	−	0.592378i
$309$	6.40086	+	6.40086i	0.364132	+	0.364132i
$310$	1.36000	−	0.0295729i	0.0772428	−	0.00167963i
$311$	−13.2379	+	7.64288i	−0.750650	+	0.433388i	−0.825929	−	0.563774i	$-0.809349\pi$
$311$	−13.2379	+	7.64288i	−0.750650	+	0.433388i	0.0752786	+	0.997163i	$0.476015\pi$
$312$	17.0847	+	3.40237i	0.967232	+	0.192621i
$313$	−0.329401	−	0.190180i	−0.0186189	−	0.0107496i	0.490662	−	0.871350i	$-0.336755\pi$
$313$	−0.329401	−	0.190180i	−0.0186189	−	0.0107496i	−0.509281	+	0.860601i	$0.670088\pi$
$314$	12.7002	−	7.70537i	0.716715	−	0.434839i
$315$	−0.766220	+	0.287774i	−0.0431716	+	0.0162143i
$316$	27.1955	+	14.1623i	1.52987	+	0.796691i
$317$	−3.60188	−	13.4424i	−0.202302	−	0.755001i	−0.990255	−	0.139266i	$-0.955526\pi$
$317$	−3.60188	−	13.4424i	−0.202302	−	0.755001i	0.787953	−	0.615735i	$-0.211141\pi$
$318$	−3.87366	−	13.2936i	−0.217224	−	0.745470i
$319$	−8.03807	−	13.9223i	−0.450045	−	0.779502i
$320$	0.946051	+	2.28689i	0.0528859	+	0.127841i
$321$	−14.8604			−0.829427
$322$	−14.1656	+	18.0211i	−0.789416	+	1.00428i
$323$	−13.0660	+	13.0660i	−0.727010	+	0.727010i
$324$	1.68694	−	1.07435i	0.0937191	−	0.0596859i
$325$	7.81775	−	29.1762i	0.433651	−	1.61841i
$326$	13.4072	+	7.35675i	0.742556	+	0.407453i
$327$	−10.8327	−	6.25429i	−0.599052	−	0.345863i
$328$	−2.04246	+	2.32792i	−0.112776	+	0.128538i
$329$	−1.45959	−	14.9263i	−0.0804699	−	0.822913i
$330$	−1.13751	−	1.87487i	−0.0626176	−	0.103208i
$331$	−29.0623	+	7.78722i	−1.59741	+	0.428024i	−0.944258	−	0.329205i	$-0.893219\pi$
$331$	−29.0623	+	7.78722i	−1.59741	+	0.428024i	−0.653149	+	0.757229i	$0.726553\pi$
$332$	−17.8710	−	16.3807i	−0.980797	−	0.899006i
$333$	2.56322	+	0.686814i	0.140464	+	0.0376372i
$334$	−6.37387	−	6.10257i	−0.348763	−	0.333918i
$335$	−0.320111			−0.0174895
$336$	−9.54667	+	4.56740i	−0.520814	+	0.249172i
$337$	29.3313			1.59778			0.798889	−	0.601478i	$-0.205421\pi$
$337$	29.3313			1.59778			0.798889	+	0.601478i	$0.205421\pi$
$338$	25.4692	+	24.3851i	1.38534	+	1.32637i
$339$	10.7641	+	2.88424i	0.584628	+	0.156651i
$340$	−1.16828	+	1.27457i	−0.0633588	+	0.0691231i
$341$	−15.0546	+	4.03385i	−0.815250	+	0.218445i
$342$	4.85056	+	7.99484i	0.262288	+	0.432311i
$343$	5.33902	+	17.7340i	0.288280	+	0.957546i
$344$	−1.00726	−	15.4211i	−0.0543077	−	0.831451i
$345$	1.64127	+	0.947587i	0.0883629	+	0.0510164i
$346$	17.1792	+	9.42652i	0.923561	+	0.506773i
$347$	−3.82977	+	14.2929i	−0.205593	+	0.767284i	0.783675	+	0.621171i	$0.213343\pi$
$347$	−3.82977	+	14.2929i	−0.205593	+	0.767284i	−0.989268	+	0.146112i	$0.953324\pi$
$348$	3.44564	+	5.41036i	0.184706	+	0.290026i
$349$	−4.18328	+	4.18328i	−0.223926	+	0.223926i	−0.810149	−	0.586223i	$-0.800614\pi$
$349$	−4.18328	+	4.18328i	−0.223926	+	0.223926i	0.586223	+	0.810149i	$0.300614\pi$
$350$	6.82380	+	17.0343i	0.364748	+	0.910519i
$351$	6.15898			0.328742
$352$	−16.7580	−	22.8731i	−0.893206	−	1.21914i
$353$	−6.01340	−	10.4155i	−0.320061	−	0.554362i	0.660439	−	0.750879i	$-0.270370\pi$
$353$	−6.01340	−	10.4155i	−0.320061	−	0.554362i	−0.980500	+	0.196517i	$0.937037\pi$
$354$	5.87716	+	20.1693i	0.312368	+	1.07199i
$355$	−0.239386	−	0.893400i	−0.0127053	−	0.0474167i
$356$	−1.03072	+	1.97927i	−0.0546281	+	0.104901i
$357$	−5.71201	−	4.69440i	−0.302311	−	0.248454i
$358$	15.1708	−	9.20428i	0.801799	−	0.486461i
$359$	0.235975	+	0.136240i	0.0124543	+	0.00719050i	0.506214	−	0.862408i	$-0.331045\pi$
$359$	0.235975	+	0.136240i	0.0124543	+	0.00719050i	−0.493760	+	0.869598i	$0.664378\pi$
$360$	0.485955	+	0.727638i	0.0256121	+	0.0383499i
$361$	−21.4105	+	12.3614i	−1.12687	+	0.650598i
$362$	7.46691	−	0.162367i	0.392452	−	0.00853381i
$363$	9.98813	+	9.98813i	0.524241	+	0.524241i
$364$	−32.3526	−	3.92863i	−1.69574	−	0.205916i
$365$	−2.47079	+	2.47079i	−0.129327	+	0.129327i
$366$	5.82889	+	5.58079i	0.304681	+	0.291713i
$367$	9.76776	+	16.9183i	0.509873	+	0.883126i	0.999935	+	0.0114381i	$0.00364096\pi$
$367$	9.76776	+	16.9183i	0.509873	+	0.883126i	−0.490062	+	0.871688i	$0.663026\pi$
$368$	22.2057	+	10.3628i	1.15755	+	0.540200i
$369$	−0.547463	+	0.948233i	−0.0284998	+	0.0493631i
$370$	−0.276028	+	1.12767i	−0.0143500	+	0.0586245i
$371$	9.10792	+	24.2505i	0.472859	+	1.25902i
$372$	5.93114	−	1.86910i	0.307515	−	0.0969083i
$373$	3.21240	−	0.860761i	0.166332	−	0.0445685i	−0.174692	−	0.984623i	$-0.555893\pi$
$373$	3.21240	−	0.860761i	0.166332	−	0.0445685i	0.341024	+	0.940055i	$0.389226\pi$
$374$	9.52947	−	17.3668i	0.492757	−	0.898018i
$375$	2.65346	−	1.53198i	0.137024	−	0.0791110i
$376$	−15.1833	+	5.15021i	−0.783018	+	0.265602i
$377$			19.7531i			1.01733i
$378$	−2.99486	+	2.24295i	−0.154039	+	0.115365i
$379$	−18.6843	−	18.6843i	−0.959748	−	0.959748i	0.0394724	−	0.999221i	$-0.487432\pi$
$379$	−18.6843	−	18.6843i	−0.959748	−	0.959748i	−0.999221	+	0.0394724i	$0.987432\pi$
$380$	−3.45075	+	2.19764i	−0.177019	+	0.112736i
$381$	−16.1480	−	4.32685i	−0.827289	−	0.221671i
$382$	−2.87723	−	9.87410i	−0.147212	−	0.505203i
$383$	5.07802	−	8.79539i	0.259475	−	0.449423i	−0.706627	−	0.707587i	$-0.749784\pi$
$383$	5.07802	−	8.79539i	0.259475	−	0.449423i	0.966101	+	0.258163i	$0.0831172\pi$
$384$	7.07687	+	8.82711i	0.361140	+	0.450457i
$385$	2.38737	+	3.33649i	0.121672	+	0.170043i
$386$	−14.4358	−	3.53357i	−0.734762	−	0.179854i
$387$	−1.41414	−	5.27763i	−0.0718846	−	0.268277i
$388$	−0.825642	−	18.9758i	−0.0419156	−	0.963352i
$389$	5.10214	−	19.0414i	0.258689	−	0.965439i	−0.707313	−	0.706901i	$-0.750093\pi$
$389$	5.10214	−	19.0414i	0.258689	−	0.965439i	0.966001	−	0.258538i	$-0.0832407\pi$
$390$	0.0585781	+	2.69389i	0.00296622	+	0.136410i
$391$			17.1196i			0.865776i
$392$	17.1625	−	9.87167i	0.866835	−	0.498595i
$393$			0.119142i			0.00600991i
$394$	10.5798	−	0.230056i	0.533004	−	0.0115901i
$395$	−1.22752	+	4.58115i	−0.0617630	+	0.230503i
$396$	−7.39022	−	6.77393i	−0.371372	−	0.340403i
$397$	−0.294326	−	1.09844i	−0.0147718	−	0.0551292i	0.958147	−	0.286278i	$-0.0924182\pi$
$397$	−0.294326	−	1.09844i	−0.0147718	−	0.0551292i	−0.972918	+	0.231149i	$0.925751\pi$
$398$	2.16834	−	8.85838i	0.108689	−	0.444031i
$399$	−10.1803	−	14.2275i	−0.509650	−	0.712265i
$400$	16.0729	−	11.2471i	0.803643	−	0.562356i
$401$	4.23857	−	7.34141i	0.211664	−	0.366613i	−0.740572	−	0.671978i	$-0.765445\pi$
$401$	4.23857	−	7.34141i	0.211664	−	0.366613i	0.952235	+	0.305365i	$0.0987785\pi$
$402$	−1.40495	+	0.409391i	−0.0700725	+	0.0204185i
$403$	18.4978	+	4.95647i	0.921442	+	0.246900i
$404$	−1.68180	−	0.373113i	−0.0836729	−	0.0185630i
$405$	0.218748	+	0.218748i	0.0108697	+	0.0108697i
$406$	−7.19357	−	9.60511i	−0.357011	−	0.476694i
$407$		−	13.3014i		−	0.659328i
$408$	−3.49746	+	7.08812i	−0.173150	+	0.350914i
$409$	24.9755	−	14.4196i	1.23496	−	0.713004i	0.266900	−	0.963724i	$-0.414001\pi$
$409$	24.9755	−	14.4196i	1.23496	−	0.713004i	0.968060	+	0.250720i	$0.0806675\pi$
$410$	−0.419957	−	0.230437i	−0.0207402	−	0.0113805i
$411$	1.76555	−	0.473078i	0.0870882	−	0.0233352i
$412$	−8.36208	+	16.0575i	−0.411970	+	0.791097i
$413$	−13.8187	−	36.7932i	−0.679972	−	1.81047i
$414$	8.41530	+	2.05988i	0.413589	+	0.101238i
$415$	1.87489	−	3.24740i	0.0920347	−	0.159409i
$416$	3.77994	+	34.6348i	0.185327	+	1.69811i
$417$	−1.02672	−	1.77833i	−0.0502786	−	0.0870851i
$418$	32.4160	−	33.8571i	1.58552	−	1.65600i
$419$	23.8569	−	23.8569i	1.16549	−	1.16549i	0.182232	−	0.983255i	$-0.441668\pi$
$419$	23.8569	−	23.8569i	1.16549	−	1.16549i	0.983255	−	0.182232i	$-0.0583323\pi$
$420$	−1.00953	−	1.28860i	−0.0492601	−	0.0628770i
$421$	−19.1624	−	19.1624i	−0.933918	−	0.933918i	0.0640302	−	0.997948i	$-0.479605\pi$
$421$	−19.1624	−	19.1624i	−0.933918	−	0.933918i	−0.997948	+	0.0640302i	$0.979605\pi$
$422$	−0.0197541	−	0.908452i	−0.000961616	−	0.0442227i
$423$	−4.90908	+	2.83426i	−0.238688	+	0.137806i
$424$	23.0294	−	15.3802i	1.11841	−	0.746930i
$425$	11.8689	+	6.85252i	0.575727	+	0.332396i
$426$	−2.19322	−	3.61493i	−0.106262	−	0.175144i
$427$	−11.6636	−	9.58568i	−0.564440	−	0.463884i
$428$	−8.93295	−	28.3466i	−0.431791	−	1.37018i
$429$	−7.99026	−	29.8201i	−0.385773	−	1.43973i
$430$	2.29494	−	0.668728i	0.110672	−	0.0322489i
$431$	−16.4450	−	28.4837i	−0.792130	−	1.37201i	−0.924646	−	0.380828i	$-0.875639\pi$
$431$	−16.4450	−	28.4837i	−0.792130	−	1.37201i	0.132516	−	0.991181i	$-0.457695\pi$
$432$	3.06340	+	2.57207i	0.147388	+	0.123749i
$433$	−5.07148			−0.243720			−0.121860	−	0.992547i	$-0.538886\pi$
$433$	−5.07148			−0.243720			−0.121860	+	0.992547i	$0.538886\pi$
$434$	−10.7998	+	4.32631i	−0.518405	+	0.207669i
$435$	−0.701567	+	0.701567i	−0.0336376	+	0.0336376i
$436$	5.41838	−	24.4233i	0.259493	−	1.16967i
$437$	−10.4843	+	39.1280i	−0.501533	+	1.87175i
$438$	−7.68426	+	14.0041i	−0.367168	+	0.669140i
$439$	25.8714	+	14.9369i	1.23478	+	0.712898i	0.968022	−	0.250866i	$-0.0807155\pi$
$439$	25.8714	+	14.9369i	1.23478	+	0.712898i	0.266754	+	0.963765i	$0.414049\pi$
$440$	2.89257	−	3.29685i	0.137898	−	0.157171i
$441$	5.26932	−	4.60807i	0.250920	−	0.219432i
$442$	−20.8098	+	12.6256i	−0.989822	+	0.600537i
$443$	−26.7421	+	7.16552i	−1.27056	+	0.340444i	−0.830244	−	0.557401i	$-0.811799\pi$
$443$	−26.7421	+	7.16552i	−1.27056	+	0.340444i	−0.440312	+	0.897845i	$0.645132\pi$
$444$	0.230703	+	5.30227i	0.0109487	+	0.251635i
$445$	−0.333413	−	0.0893376i	−0.0158053	−	0.00423501i
$446$	1.92680	−	2.01246i	0.0912367	−	0.0952928i
$447$	−16.0546			−0.759356
$448$	−14.4512	−	15.4649i	−0.682753	−	0.730649i
$449$	−13.7176			−0.647374			−0.323687	−	0.946164i	$-0.604922\pi$
$449$	−13.7176			−0.647374			−0.323687	+	0.946164i	$0.604922\pi$
$450$	4.79652	−	5.00976i	0.226110	−	0.236162i
$451$	5.30133	+	1.42049i	0.249630	+	0.0668881i
$452$	0.968827	+	22.2666i	0.0455698	+	1.04734i
$453$	−2.47577	+	0.663380i	−0.116322	+	0.0311683i
$454$	16.4583	−	9.98544i	0.772426	−	0.468640i
$455$	−0.490602	−	5.01706i	−0.0229998	−	0.235204i
$456$	−12.3346	+	14.0585i	−0.577619	+	0.658348i
$457$	18.4149	+	10.6319i	0.861415	+	0.497338i	0.864486	−	0.502657i	$-0.167644\pi$
$457$	18.4149	+	10.6319i	0.861415	+	0.497338i	−0.00307105	+	0.999995i	$0.500978\pi$
$458$	15.3320	−	27.9416i	0.716417	−	1.30562i
$459$	−0.723269	+	2.69928i	−0.0337593	+	0.125991i
$460$	−0.820938	+	3.70038i	−0.0382764	+	0.172531i
$461$	−11.2879	+	11.2879i	−0.525731	+	0.525731i	−0.919297	−	0.393566i	$-0.871241\pi$
$461$	−11.2879	+	11.2879i	−0.525731	+	0.525731i	0.393566	+	0.919297i	$0.371241\pi$
$462$	14.7451	+	11.5904i	0.686002	+	0.539236i
$463$	−14.0330			−0.652168			−0.326084	−	0.945341i	$-0.605729\pi$
$463$	−14.0330			−0.652168			−0.326084	+	0.945341i	$0.605729\pi$
$464$	−8.24914	+	9.82494i	−0.382957	+	0.456111i
$465$	0.480946	+	0.833023i	0.0223033	+	0.0386305i
$466$	−7.70978	+	2.24657i	−0.357149	+	0.104070i
$467$	−6.48692	−	24.2095i	−0.300179	−	1.12028i	−0.937017	−	0.349285i	$-0.886425\pi$
$467$	−6.48692	−	24.2095i	−0.300179	−	1.12028i	0.636838	−	0.770998i	$-0.280242\pi$
$468$	3.70231	+	11.7484i	0.171139	+	0.543070i
$469$	2.56293	−	0.962578i	0.118345	−	0.0444477i
$470$	−1.28637	−	2.12024i	−0.0593359	−	0.0977992i
$471$	9.09674	+	5.25200i	0.419155	+	0.242000i
$472$	−34.9405	+	23.3351i	−1.60827	+	1.07408i
$473$	−23.7182	+	13.6937i	−1.09056	+	0.629638i
$474$	0.471347	+	21.6763i	0.0216497	+	0.995624i
$475$	22.9306	+	22.9306i	1.05213	+	1.05213i
$476$	5.52105	−	13.7177i	0.253057	−	0.628750i
$477$	6.92326	−	6.92326i	0.316994	−	0.316994i
$478$	4.91245	−	5.13084i	0.224690	−	0.234679i
$479$	−12.3183	−	21.3358i	−0.562836	−	0.974860i	−0.997247	−	0.0741455i	$-0.976377\pi$
$479$	−12.3183	−	21.3358i	−0.562836	−	0.974860i	0.434412	−	0.900714i	$-0.356956\pi$
$480$	−1.09587	+	1.36437i	−0.0500193	+	0.0622748i
$481$	−8.17187	+	14.1541i	−0.372605	+	0.645371i
$482$	3.83323	+	0.938291i	0.174599	+	0.0427380i
$483$	−15.9900	−	2.65143i	−0.727572	−	0.120644i
$484$	−13.0485	+	25.0567i	−0.593113	+	1.13894i
$485$	2.83781	−	0.760390i	0.128858	−	0.0345275i
$486$	1.23983	+	0.680314i	0.0562397	+	0.0308597i
$487$	7.04268	−	4.06609i	0.319134	−	0.184252i	−0.331872	−	0.943324i	$-0.607680\pi$
$487$	7.04268	−	4.06609i	0.319134	−	0.184252i	0.651007	+	0.759072i	$0.274347\pi$
$488$	−7.14160	+	14.4735i	−0.323285	+	0.655185i
$489$			10.8138i			0.489015i
$490$	2.06565	+	2.26093i	0.0933165	+	0.102138i
$491$	2.74823	+	2.74823i	0.124026	+	0.124026i	0.766395	−	0.642369i	$-0.222048\pi$
$491$	2.74823	+	2.74823i	0.124026	+	0.124026i	−0.642369	+	0.766395i	$0.722048\pi$
$492$	−2.13787	−	0.474292i	−0.0963827	−	0.0213827i
$493$	−8.65711	−	2.31966i	−0.389897	−	0.104472i
$494$	−55.2943	+	16.1123i	−2.48781	+	0.724927i
$495$	0.775326	−	1.34290i	0.0348483	−	0.0603591i
$496$	7.13071	+	10.1902i	0.320178	+	0.457555i
$497$	4.60308	+	6.43307i	0.206476	+	0.288563i
$498$	4.07567	−	16.6505i	0.182635	−	0.746125i
$499$	10.5666	+	39.4352i	0.473028	+	1.76536i	0.628796	+	0.777570i	$0.283548\pi$
$499$	10.5666	+	39.4352i	0.473028	+	1.76536i	−0.155768	+	0.987794i	$0.549785\pi$
$500$	4.51734	+	4.14063i	0.202022	+	0.185175i
$501$	1.61495	−	6.02708i	0.0721507	−	0.269270i
$502$	−27.3497	+	0.594715i	−1.22068	+	0.0265434i
$503$		−	13.8605i		−	0.618009i	−0.951061	−	0.309004i	$-0.900004\pi$
$503$		−	13.8605i		−	0.618009i	0.951061	−	0.309004i	$-0.0999958\pi$
$504$	−6.07876	−	4.36448i	−0.270769	−	0.194409i
$505$		−	0.266463i		−	0.0118575i
$506$	−0.944093	−	43.4169i	−0.0419700	−	1.93012i
$507$	−6.45314	+	24.0834i	−0.286594	+	1.06958i
$508$	−1.45340	−	33.4037i	−0.0644844	−	1.48205i
$509$	−6.00160	−	22.3983i	−0.266016	−	0.992786i	−0.961625	−	0.274366i	$-0.911532\pi$
$509$	−6.00160	−	22.3983i	−0.266016	−	0.992786i	0.695609	−	0.718420i	$-0.255135\pi$
$510$	−1.18752	−	0.290679i	−0.0525843	−	0.0128715i
$511$	12.3524	−	27.2118i	0.546439	−	1.20378i
$512$	−12.5839	+	18.8055i	−0.556133	+	0.831093i
$513$	−3.30616	+	5.72643i	−0.145970	+	0.252828i
$514$	1.53635	+	5.27245i	0.0677654	+	0.232558i
$515$	−2.70493	−	0.724783i	−0.119193	−	0.0319378i
$516$	9.21714	−	5.87002i	0.405762	−	0.258413i
$517$	20.0914	+	20.0914i	0.883619	+	0.883619i
$518$	−1.18092	−	9.85855i	−0.0518865	−	0.433160i
$519$			13.8561i			0.608217i
$520$	−5.10344	+	1.73110i	−0.223801	+	0.0759138i
$521$	6.98928	−	4.03526i	0.306206	−	0.176788i	−0.339022	−	0.940779i	$-0.610096\pi$
$521$	6.98928	−	4.03526i	0.306206	−	0.176788i	0.645227	+	0.763991i	$0.276763\pi$
$522$	−2.18190	+	3.97637i	−0.0954992	+	0.174041i
$523$	5.90765	−	1.58295i	0.258323	−	0.0692176i	−0.127333	−	0.991860i	$-0.540642\pi$
$523$	5.90765	−	1.58295i	0.258323	−	0.0692176i	0.385656	+	0.922642i	$0.373975\pi$
$524$	−0.227266	+	0.0716191i	−0.00992816	+	0.00312870i
$525$	−8.23860	+	10.0245i	−0.359562	+	0.437505i
$526$	4.09521	−	16.7303i	0.178560	−	0.729476i
$527$	−4.34451	+	7.52492i	−0.189250	+	0.327791i
$528$	8.47900	−	18.1690i	0.369001	−	0.790704i
$529$	7.26510	+	12.5835i	0.315874	+	0.547110i
$530$	3.09402	+	2.96233i	0.134396	+	0.128675i
$531$	−10.5041	+	10.5041i	−0.455837	+	0.455837i
$532$	21.0197	−	27.9716i	0.911319	−	1.21272i
$533$	−4.76846	−	4.76846i	−0.206545	−	0.206545i
$534$	−1.57758	+	0.0343042i	−0.0682687	+	0.00148449i
$535$	3.98125	−	2.29858i	0.172125	−	0.0993762i
$536$	−1.62547	−	2.43388i	−0.0702097	−	0.105128i
$537$	10.8663	+	6.27366i	0.468915	+	0.270728i
$538$	−4.23732	+	2.57083i	−0.182684	+	0.110836i
$539$	−29.1471	−	19.5344i	−1.25545	−	0.841404i
$540$	−0.285772	+	0.548761i	−0.0122977	+	0.0236149i
$541$	3.66370	+	13.6731i	0.157515	+	0.587853i	0.998877	+	0.0473814i	$0.0150876\pi$
$541$	3.66370	+	13.6731i	0.157515	+	0.587853i	−0.841362	+	0.540472i	$0.818246\pi$
$542$	1.90421	+	6.53489i	0.0817930	+	0.280698i
$543$	2.64058	+	4.57361i	0.113318	+	0.196273i
$544$	−15.6232	−	2.41065i	−0.669838	−	0.103356i
$545$	3.86960			0.165756
$546$	−8.56955	−	21.3922i	−0.366743	−	0.915500i
$547$	−4.15884	+	4.15884i	−0.177819	+	0.177819i	−0.790405	−	0.612585i	$-0.790130\pi$
$547$	−4.15884	+	4.15884i	−0.177819	+	0.177819i	0.612585	+	0.790405i	$0.290130\pi$
$548$	1.96372	+	3.08345i	0.0838861	+	0.131719i
$549$	−1.47687	+	5.51176i	−0.0630313	+	0.235236i
$550$	−30.4786	−	16.7241i	−1.29961	−	0.713118i
$551$	−18.3658	−	10.6035i	−0.782409	−	0.451724i
$552$	1.12937	+	17.2906i	0.0480692	+	0.735938i
$553$	−3.94761	−	40.3696i	−0.167869	−	1.71669i
$554$	−10.0695	−	16.5969i	−0.427814	−	0.705135i
$555$	−0.792948	+	0.212470i	−0.0336588	+	0.00901884i
$556$	2.77502	−	3.02749i	0.117687	−	0.128394i
$557$	29.8331	+	7.99376i	1.26407	+	0.338707i	0.827756	−	0.561088i	$-0.189617\pi$
$557$	29.8331	+	7.99376i	1.26407	+	0.338707i	0.436314	+	0.899794i	$0.356284\pi$
$558$	3.17620	+	3.04101i	0.134459	+	0.128736i
$559$	33.6515			1.42331
$560$	1.85117	−	2.70031i	0.0782264	−	0.114109i
$561$	14.0075			0.591396
$562$	22.2263	+	21.2802i	0.937558	+	0.897652i
$563$	20.9574	+	5.61553i	0.883251	+	0.236666i	0.671809	−	0.740724i	$-0.265518\pi$
$563$	20.9574	+	5.61553i	0.883251	+	0.236666i	0.211442	+	0.977391i	$0.432184\pi$
$564$	−8.35739	−	7.66045i	−0.351909	−	0.322563i
$565$	−3.32995	+	0.892258i	−0.140092	+	0.0375376i
$566$	11.8762	+	19.5748i	0.499196	+	0.822789i
$567$	−2.40916	−	1.09360i	−0.101175	−	0.0459270i
$568$	5.57716	−	6.35664i	0.234013	−	0.266719i
$569$	24.8836	+	14.3666i	1.04317	+	0.602277i	0.920731	−	0.390198i	$-0.127594\pi$
$569$	24.8836	+	14.3666i	1.04317	+	0.602277i	0.122444	+	0.992475i	$0.460927\pi$
$570$	−2.53614	−	1.39162i	−0.106227	−	0.0582887i
$571$	−9.69480	+	36.1815i	−0.405715	+	1.51415i	0.397019	+	0.917811i	$0.370045\pi$
$571$	−9.69480	+	36.1815i	−0.405715	+	1.51415i	−0.802733	+	0.596338i	$0.796622\pi$
$572$	52.0793	−	33.1672i	2.17755	−	1.38679i
$573$	5.14238	−	5.14238i	0.214826	−	0.214826i
$574$	4.05526	+	0.582155i	0.169263	+	0.0242987i
$575$	30.0447			1.25295
$576$	−3.06480	+	7.38965i	−0.127700	+	0.307902i
$577$	−13.8585	−	24.0036i	−0.576937	−	0.999284i	−0.995828	−	0.0912476i	$-0.970915\pi$
$577$	−13.8585	−	24.0036i	−0.576937	−	0.999284i	0.418891	−	0.908036i	$-0.362419\pi$
$578$	3.63621	+	12.4788i	0.151246	+	0.519048i
$579$	−2.71993	−	10.1509i	−0.113036	−	0.421858i
$580$	−1.75999	−	0.916527i	−0.0730794	−	0.0380567i
$581$	−5.24611	+	31.6378i	−0.217645	+	1.31256i
$582$	11.4825	−	6.96659i	0.475966	−	0.288774i
$583$	−42.5023	−	24.5387i	−1.76026	−	1.01629i
$584$	−31.3323	−	6.23973i	−1.29654	−	0.258202i
$585$	−1.65005	+	0.952658i	−0.0682213	+	0.0393876i
$586$	18.9761	−	0.412632i	0.783896	−	0.0170457i
$587$	−16.0127	−	16.0127i	−0.660915	−	0.660915i	0.294680	−	0.955596i	$-0.404787\pi$
$587$	−16.0127	−	16.0127i	−0.660915	−	0.660915i	−0.955596	+	0.294680i	$0.904787\pi$
$588$	11.9575	+	7.28133i	0.493120	+	0.300277i
$589$	−14.5381	+	14.5381i	−0.599030	+	0.599030i
$590$	−4.69430	−	4.49449i	−0.193261	−	0.185035i
$591$	3.74142	+	6.48033i	0.153901	+	0.266565i
$592$	−9.97553	+	3.62740i	−0.409992	+	0.149085i
$593$	1.80051	−	3.11858i	0.0739381	−	0.128065i	−0.826686	−	0.562664i	$-0.809777\pi$
$593$	1.80051	−	3.11858i	0.0739381	−	0.128065i	0.900624	+	0.434599i	$0.143110\pi$
$594$	1.68542	−	6.88550i	0.0691536	−	0.282515i
$595$	2.25643	+	0.374156i	0.0925044	+	0.0153389i
$596$	−9.65081	−	30.6245i	−0.395313	−	1.25443i
$597$	6.22901	−	1.66906i	0.254936	−	0.0683100i
$598$	−25.6690	+	46.7800i	−1.04968	+	1.91298i
$599$	3.78182	−	2.18343i	0.154521	−	0.0892127i	−0.420746	−	0.907179i	$-0.638232\pi$
$599$	3.78182	−	2.18343i	0.154521	−	0.0892127i	0.575267	+	0.817966i	$0.304898\pi$
$600$	12.4395	+	6.13799i	0.507842	+	0.250583i
$601$			5.04350i			0.205729i	0.994695	+	0.102864i	$0.0328008\pi$
$601$			5.04350i			0.205729i	−0.994695	+	0.102864i	$0.967199\pi$
$602$	−16.3633	+	12.2550i	−0.666920	+	0.499477i
$603$	−0.731690	−	0.731690i	−0.0297967	−	0.0297967i
$604$	−2.75366	−	4.32381i	−0.112045	−	0.175933i
$605$	−4.22087	−	1.13098i	−0.171603	−	0.0459808i
$606$	−0.340780	−	1.16949i	−0.0138432	−	0.0475073i
$607$	0.897292	−	1.55415i	0.0364199	−	0.0630812i	−0.847241	−	0.531209i	$-0.821738\pi$
$607$	0.897292	−	1.55415i	0.0364199	−	0.0630812i	0.883661	+	0.468128i	$0.155071\pi$
$608$	−34.2315	−	15.0776i	−1.38827	−	0.611476i
$609$	3.50740	−	7.72664i	0.142127	−	0.313099i
$610$	−2.42484	−	0.593549i	−0.0981791	−	0.0240321i
$611$	−9.03596	−	33.7227i	−0.365556	−	1.36427i
$612$	−5.58371	+	0.242948i	−0.225708	+	0.00982060i
$613$	0.140782	−	0.525404i	0.00568611	−	0.0212209i	−0.963024	−	0.269414i	$-0.913170\pi$
$613$	0.140782	−	0.525404i	0.00568611	−	0.0212209i	0.968711	+	0.248193i	$0.0798367\pi$
$614$	−0.0121838	−	0.560310i	−0.000491700	−	0.0226123i
$615$		−	0.338722i		−	0.0136586i
$616$	−13.2454	+	35.0939i	−0.533673	+	1.41397i
$617$		−	2.44879i		−	0.0985844i	−0.998784	−	0.0492922i	$-0.984303\pi$
$617$		−	2.44879i		−	0.0985844i	0.998784	−	0.0492922i	$-0.0156966\pi$
$618$	−12.7987	+	0.278305i	−0.514839	+	0.0111951i
$619$	11.0093	−	41.0872i	0.442500	−	1.65143i	−0.279954	−	0.960013i	$-0.590319\pi$
$619$	11.0093	−	41.0872i	0.442500	−	1.65143i	0.722454	−	0.691419i	$-0.243014\pi$
$620$	−1.29990	+	1.41817i	−0.0522054	+	0.0569550i
$621$	1.58557	+	5.91744i	0.0636269	+	0.237459i
$622$	5.13971	−	20.9974i	0.206084	−	0.841921i
$623$	2.93807	−	0.287304i	0.117711	−	0.0115106i
$624$	−20.1848	+	14.1245i	−0.808039	+	0.565433i
$625$	11.7868	−	20.4154i	0.471473	−	0.816615i
$626$	0.516432	−	0.150484i	0.0206408	−	0.00601455i
$627$	32.0150	+	8.57839i	1.27856	+	0.342588i
$628$	−4.55005	+	20.5094i	−0.181567	+	0.818412i
$629$	−5.24362	−	5.24362i	−0.209077	−	0.209077i
$630$	0.455419	−	1.06415i	0.0181443	−	0.0423966i
$631$		−	40.4557i		−	1.61052i	−0.592924	−	0.805259i	$-0.702027\pi$
$631$		−	40.4557i		−	1.61052i	0.592924	−	0.805259i	$-0.297973\pi$
$632$	−41.0647	+	13.9292i	−1.63347	+	0.554076i
$633$	0.556442	−	0.321262i	0.0221166	−	0.0127690i
$634$	17.2542	+	9.46766i	0.685251	+	0.376009i
$635$	4.99549	−	1.33854i	0.198240	−	0.0531183i
$636$	17.3680	+	9.04454i	0.688687	+	0.358639i
$637$	19.0143	+	38.6933i	0.753375	+	1.53309i
$638$	22.0831	+	5.40547i	0.874280	+	0.214005i
$639$	1.49490	−	2.58925i	0.0591375	−	0.102429i
$640$	−3.26133	−	1.27024i	−0.128915	−	0.0502105i
$641$	16.9953	+	29.4368i	0.671276	+	1.16268i	0.977543	+	0.210738i	$0.0675866\pi$
$641$	16.9953	+	29.4368i	0.671276	+	1.16268i	−0.306267	+	0.951946i	$0.599080\pi$
$642$	14.5338	−	15.1800i	0.573604	−	0.599105i
$643$	24.8887	−	24.8887i	0.981516	−	0.981516i	−0.0183162	−	0.999832i	$-0.505831\pi$
$643$	24.8887	−	24.8887i	0.981516	−	0.981516i	0.999832	+	0.0183162i	$0.00583056\pi$
$644$	−4.55433	−	32.0952i	−0.179466	−	1.26473i
$645$	1.19520	+	1.19520i	0.0470608	+	0.0470608i
$646$	−0.568100	−	26.1258i	−0.0223516	−	1.02791i
$647$	32.8200	−	18.9486i	1.29029	−	0.744947i	0.311582	−	0.950219i	$-0.399141\pi$
$647$	32.8200	−	18.9486i	1.29029	−	0.744947i	0.978705	+	0.205272i	$0.0658079\pi$
$648$	−0.552425	+	2.77396i	−0.0217013	+	0.108971i
$649$	64.4850	+	37.2304i	2.53126	+	1.46142i
$650$	22.1577	+	36.5209i	0.869096	+	1.43247i
$651$	−6.35555	−	5.22330i	−0.249094	−	0.204717i
$652$	−20.6275	+	6.50041i	−0.807835	+	0.254576i
$653$	−8.86346	−	33.0789i	−0.346854	−	1.29448i	−0.890432	−	0.455117i	$-0.849597\pi$
$653$	−8.86346	−	33.0789i	−0.346854	−	1.29448i	0.543578	−	0.839359i	$-0.317069\pi$
$654$	16.9835	−	4.94884i	0.664106	−	0.193515i
$655$	−0.0184286	−	0.0319193i	−0.000720066	−	0.00124719i
$656$	−0.380403	−	4.36315i	−0.0148523	−	0.170352i
$657$	−11.2952			−0.440666
$658$	16.6748	+	13.1073i	0.650050	+	0.510975i
$659$	0.0184256	−	0.0184256i	0.000717758	−	0.000717758i	−0.706748	−	0.707466i	$-0.749838\pi$
$659$	0.0184256	−	0.0184256i	0.000717758	−	0.000717758i	0.707466	+	0.706748i	$0.249838\pi$
$660$	3.02769	+	0.671701i	0.117853	+	0.0261459i
$661$	−4.83067	+	18.0283i	−0.187891	+	0.701219i	0.806102	+	0.591777i	$0.201573\pi$
$661$	−4.83067	+	18.0283i	−0.187891	+	0.701219i	−0.993993	+	0.109443i	$0.965093\pi$
$662$	20.4689	−	37.3033i	0.795548	−	1.44983i
$663$	−14.9054	−	8.60562i	−0.578876	−	0.334214i
$664$	34.2111	−	2.23456i	1.32765	−	0.0867179i
$665$	4.92807	+	2.23703i	0.191102	+	0.0867482i
$666$	−3.20848	+	1.94662i	−0.124326	+	0.0754300i
$667$	−18.9784	+	5.08525i	−0.734847	+	0.196902i
$668$	12.4676	−	0.542468i	0.482386	−	0.0209887i
$669$	1.90297	+	0.509899i	0.0735730	+	0.0197138i
$670$	0.313076	−	0.326995i	0.0120952	−	0.0126329i
$671$	28.6024			1.10418
$672$	4.67126	−	14.2190i	0.180198	−	0.548509i
$673$	−12.3067			−0.474389			−0.237194	−	0.971462i	$-0.576228\pi$
$673$	−12.3067			−0.474389			−0.237194	+	0.971462i	$0.576228\pi$
$674$	−28.6867	+	29.9620i	−1.10497	+	1.15409i
$675$	4.73719	+	1.26933i	0.182334	+	0.0488564i
$676$	−49.8189	+	2.16763i	−1.91611	+	0.0833704i
$677$	30.8158	−	8.25706i	1.18435	−	0.317344i	0.387697	−	0.921787i	$-0.373271\pi$
$677$	30.8158	−	8.25706i	1.18435	−	0.317344i	0.796649	+	0.604442i	$0.206604\pi$
$678$	−13.4739	+	8.17475i	−0.517460	+	0.313949i
$679$	−20.4341	+	14.6213i	−0.784190	+	0.561114i
$680$	−0.159370	−	2.43996i	−0.00611157	−	0.0935681i
$681$	11.7885	+	6.80610i	0.451737	+	0.260810i
$682$	10.6031	−	19.3235i	0.406014	−	0.739934i
$683$	−4.64921	+	17.3511i	−0.177897	+	0.663920i	0.818143	+	0.575015i	$0.195004\pi$
$683$	−4.64921	+	17.3511i	−0.177897	+	0.663920i	−0.996040	+	0.0889057i	$0.971663\pi$
$684$	−12.9107	−	2.86428i	−0.493654	−	0.109518i
$685$	−0.399834	+	0.399834i	−0.0152769	+	0.0152769i
$686$	−23.3370	−	11.8905i	−0.891012	−	0.453980i
$687$	22.5367			0.859827
$688$	16.7378	+	14.0533i	0.638124	+	0.535777i
$689$	30.1512	+	52.2233i	1.14867	+	1.98955i
$690$	−2.57316	+	0.749799i	−0.0979586	+	0.0285443i
$691$	2.21094	+	8.25134i	0.0841081	+	0.313896i	0.995144	−	0.0984318i	$-0.0313826\pi$
$691$	2.21094	+	8.25134i	0.0841081	+	0.313896i	−0.911036	+	0.412327i	$0.864716\pi$
$692$	−26.4309	+	8.32926i	−1.00475	+	0.316631i
$693$	−2.16943	+	13.0832i	−0.0824100	+	0.496991i
$694$	−10.8546	−	17.8909i	−0.412037	−	0.679131i
$695$	0.550137	+	0.317622i	0.0208679	+	0.0120481i
$696$	−8.89662	−	1.77174i	−0.337226	−	0.0671574i
$697$	2.64983	−	1.52988i	0.100370	−	0.0579484i
$698$	−0.181886	−	8.36459i	−0.00688451	−	0.316604i
$699$	−4.01521	−	4.01521i	−0.151869	−	0.151869i
$700$	−24.0744	−	9.68937i	−0.909926	−	0.366224i
$701$	4.46461	−	4.46461i	0.168626	−	0.168626i	−0.617749	−	0.786375i	$-0.711955\pi$
$701$	4.46461	−	4.46461i	0.168626	−	0.168626i	0.786375	+	0.617749i	$0.211955\pi$
$702$	−6.02363	+	6.29142i	−0.227347	+	0.237454i
$703$	−8.77336	−	15.1959i	−0.330894	−	0.573125i
$704$	39.7547	+	5.25206i	1.49831	+	0.197945i
$705$	0.876795	−	1.51865i	0.0330220	−	0.0571958i
$706$	16.5207	+	4.04392i	0.621766	+	0.152195i
$707$	0.801258	+	2.13341i	0.0301344	+	0.0802350i
$708$	−26.3510	−	13.7225i	−0.990331	−	0.515723i
$709$	−22.1566	+	5.93684i	−0.832108	+	0.222963i	−0.649633	−	0.760248i	$-0.725077\pi$
$709$	−22.1566	+	5.93684i	−0.832108	+	0.222963i	−0.182475	+	0.983211i	$0.558411\pi$
$710$	1.14674	+	0.629233i	0.0430362	+	0.0236147i
$711$	−13.2771	+	7.66553i	−0.497930	+	0.287480i
$712$	−1.01376	−	2.98866i	−0.0379923	−	0.112005i
$713$			19.0484i			0.713368i
$714$	10.3818	−	1.24360i	0.388530	−	0.0465405i
$715$	6.75318	+	6.75318i	0.252555	+	0.252555i
$716$	−5.43516	+	24.4990i	−0.203121	+	0.915570i
$717$	4.85169	+	1.30001i	0.181190	+	0.0485496i
$718$	−0.369960	+	0.107803i	−0.0138068	+	0.00402318i
$719$	−22.9207	+	39.6999i	−0.854799	+	1.48056i	0.0220320	+	0.999757i	$0.492986\pi$
$719$	−22.9207	+	39.6999i	−0.854799	+	1.48056i	−0.876831	+	0.480798i	$0.840347\pi$
$720$	−1.21856	−	0.215243i	−0.0454130	−	0.00802164i
$721$	23.8361	−	2.33085i	0.887704	−	0.0868056i
$722$	8.31281	−	33.9606i	0.309371	−	1.26388i
$723$	0.722241	+	2.69544i	0.0268604	+	0.100244i
$724$	−7.13696	+	7.78628i	−0.265243	+	0.289375i
$725$	−4.07098	+	15.1931i	−0.151192	+	0.564258i
$726$	−19.9715	+	0.434278i	−0.741214	+	0.0161176i
$727$			28.2755i			1.04868i	0.851509	+	0.524339i	$0.175688\pi$
$727$			28.2755i			1.04868i	−0.851509	+	0.524339i	$0.824312\pi$
$728$	35.6547	−	29.2060i	1.32145	−	1.08245i
$729$			1.00000i			0.0370370i
$730$	−0.107428	−	4.94042i	−0.00397611	−	0.182853i
$731$	−3.95180	+	14.7483i	−0.146163	+	0.545486i
$732$	−11.4016	+	0.496086i	−0.421415	+	0.0183359i
$733$	−8.22520	−	30.6969i	−0.303805	−	1.13381i	−0.933969	−	0.357353i	$-0.883679\pi$
$733$	−8.22520	−	30.6969i	−0.303805	−	1.13381i	0.630165	−	0.776462i	$-0.282987\pi$
$734$	−26.8352	−	6.56866i	−0.990504	−	0.242454i
$735$	−0.698937	+	2.04960i	−0.0257807	+	0.0756005i
$736$	−32.3034	+	12.5481i	−1.19072	+	0.462530i
$737$	−2.59339	+	4.49189i	−0.0955289	+	0.165461i
$738$	−0.433192	−	1.48663i	−0.0159460	−	0.0547236i
$739$	1.93900	+	0.519553i	0.0713272	+	0.0191121i	0.294306	−	0.955711i	$-0.404911\pi$
$739$	1.93900	+	0.519553i	0.0713272	+	0.0191121i	−0.222979	+	0.974823i	$0.571578\pi$
$740$	−0.881952	−	1.38485i	−0.0324212	−	0.0509080i
$741$	−28.7970	−	28.7970i	−1.05788	−	1.05788i
$742$	−33.6797	−	14.4138i	−1.23642	−	0.529147i
$743$			26.1742i			0.960238i	0.877204	+	0.480119i	$0.159406\pi$
$743$			26.1742i			0.960238i	−0.877204	+	0.480119i	$0.840594\pi$
$744$	−3.89150	+	7.88670i	−0.142669	+	0.289140i
$745$	4.30119	−	2.48329i	0.157583	−	0.0909808i
$746$	−2.26254	+	4.12333i	−0.0828374	+	0.150966i
$747$	11.7082	−	3.13721i	0.428381	−	0.114784i
$748$	8.42023	+	26.7196i	0.307874	+	0.976964i
$749$	−24.9636	+	30.3750i	−0.912150	+	1.10988i
$750$	−1.03023	+	4.20883i	−0.0376187	+	0.153685i
$751$	−21.9945	+	38.0955i	−0.802589	+	1.39013i	0.115318	+	0.993329i	$0.463211\pi$
$751$	−21.9945	+	38.0955i	−0.802589	+	1.39013i	−0.917907	+	0.396796i	$0.870122\pi$
$752$	9.58866	−	20.5468i	0.349662	−	0.749265i
$753$	−9.67187	−	16.7522i	−0.352463	−	0.610483i
$754$	−20.1778	−	19.3190i	−0.734833	−	0.703555i
$755$	0.560673	−	0.560673i	0.0204050	−	0.0204050i
$756$	0.637870	−	5.25292i	0.0231991	−	0.191047i
$757$	34.2769	+	34.2769i	1.24581	+	1.24581i	0.957551	+	0.288263i	$0.0930776\pi$
$757$	34.2769	+	34.2769i	1.24581	+	1.24581i	0.288263	+	0.957551i	$0.406922\pi$
$758$	37.3598	−	0.812382i	1.35697	−	0.0295070i
$759$	26.5936	−	15.3538i	0.965287	−	0.557308i
$760$	1.13002	−	5.67429i	0.0409900	−	0.205828i
$761$	30.0774	+	17.3652i	1.09031	+	0.629488i	0.933658	−	0.358166i	$-0.116598\pi$
$761$	30.0774	+	17.3652i	1.09031	+	0.629488i	0.156648	+	0.987654i	$0.449931\pi$
$762$	20.2131	−	12.2635i	0.732242	−	0.444260i
$763$	−30.9816	+	11.6359i	−1.12161	+	0.421250i
$764$	12.9004	+	6.71800i	0.466721	+	0.243049i
$765$	−0.223747	−	0.835037i	−0.00808961	−	0.0301908i
$766$	4.01809	+	13.7893i	0.145180	+	0.498228i
$767$	−45.7457	−	79.2340i	−1.65178	−	2.86097i
$768$	−15.9383	−	1.40408i	−0.575123	−	0.0506655i
$769$	23.3081			0.840511			0.420255	−	0.907406i	$-0.361941\pi$
$769$	23.3081			0.840511			0.420255	+	0.907406i	$0.361941\pi$
$770$	−5.74314	−	0.824458i	−0.206968	−	0.0297114i
$771$	−2.74586	+	2.74586i	−0.0988899	+	0.0988899i
$772$	17.7281	−	11.2903i	0.638048	−	0.406347i
$773$	2.79578	−	10.4340i	0.100557	−	0.375284i	−0.897246	−	0.441531i	$-0.854436\pi$
$773$	2.79578	−	10.4340i	0.100557	−	0.375284i	0.997803	+	0.0662464i	$0.0211024\pi$
$774$	6.77418	+	3.71710i	0.243493	+	0.133609i
$775$	13.2061	+	7.62456i	0.474378	+	0.273882i
$776$	20.1914	+	17.7154i	0.724828	+	0.635946i
$777$	5.70975	−	4.08552i	0.204836	−	0.146567i
$778$	14.4609	+	23.8348i	0.518448	+	0.854520i
$779$	6.99330	−	1.87385i	0.250561	−	0.0671376i
$780$	−2.80911	−	2.57485i	−0.100582	−	0.0921944i
$781$	−14.4758	−	3.87879i	−0.517986	−	0.138794i
$782$	−17.4877	−	16.7434i	−0.625360	−	0.598742i
$783$	−3.20720			−0.114616
$784$	−6.70135	+	27.1862i	−0.239334	+	0.970937i
$785$	−3.24948			−0.115979
$786$	−0.121704	−	0.116524i	−0.00434103	−	0.00415626i
$787$	−20.3756	−	5.45962i	−0.726311	−	0.194614i	−0.123325	−	0.992366i	$-0.539356\pi$
$787$	−20.3756	−	5.45962i	−0.726311	−	0.194614i	−0.602986	+	0.797752i	$0.706022\pi$
$788$	−10.1123	+	11.0323i	−0.360236	+	0.393010i
$789$	11.7644	−	3.15225i	0.418822	−	0.112223i
$790$	−3.47912	−	5.73439i	−0.123782	−	0.204020i
$791$	23.9779	−	17.1570i	0.852554	−	0.610031i
$792$	14.1474	−	0.924063i	0.502706	−	0.0328352i
$793$	−30.4359	−	17.5721i	−1.08081	−	0.624005i
$794$	1.40992	+	0.773646i	0.0500362	+	0.0274557i
$795$	−0.783935	+	2.92569i	−0.0278033	+	0.103763i
$796$	6.92818	+	10.8787i	0.245563	+	0.385584i
$797$	−4.20910	+	4.20910i	−0.149094	+	0.149094i	−0.777713	−	0.628619i	$-0.783620\pi$
$797$	−4.20910	+	4.20910i	−0.149094	+	0.149094i	0.628619	+	0.777713i	$0.283620\pi$
$798$	24.4900	+	3.51567i	0.866935	+	0.124453i
$799$	15.8406			0.560402
$800$	−4.23066	+	27.4184i	−0.149576	+	0.969388i
$801$	−0.557891	−	0.966296i	−0.0197121	−	0.0341424i
$802$	3.35386	+	11.5098i	0.118429	+	0.406425i
$803$	14.6536	+	54.6881i	0.517115	+	1.92990i
$804$	0.955880	−	1.83555i	0.0337113	−	0.0647350i
$805$	4.69401	−	1.76296i	0.165442	−	0.0621362i
$806$	−23.1544	+	14.0480i	−0.815577	+	0.494821i
$807$	−3.03505	−	1.75228i	−0.106839	−	0.0616833i
$808$	2.02598	−	1.35306i	0.0712738	−	0.0476003i
$809$	24.8935	−	14.3723i	0.875210	−	0.505303i	0.00613399	−	0.999981i	$-0.498047\pi$
$809$	24.8935	−	14.3723i	0.875210	−	0.505303i	0.869076	+	0.494678i	$0.164714\pi$
$810$	−0.437392	+	0.00951101i	−0.0153684	+	0.000334183i
$811$	−0.876235	−	0.876235i	−0.0307688	−	0.0307688i	0.691555	−	0.722324i	$-0.256926\pi$
$811$	−0.876235	−	0.876235i	−0.0307688	−	0.0307688i	−0.722324	+	0.691555i	$0.756926\pi$
$812$	16.8471	+	2.04577i	0.591219	+	0.0717926i
$813$	−3.40334	+	3.40334i	−0.119360	+	0.119360i
$814$	13.5875	+	13.0091i	0.476241	+	0.455970i
$815$	−1.67265	−	2.89711i	−0.0585904	−	0.101482i
$816$	−3.81993	−	10.5050i	−0.133724	−	0.367749i
$817$	−18.0642	+	31.2881i	−0.631987	+	1.09463i
$818$	−9.69696	+	39.6153i	−0.339046	+	1.38512i
$819$	10.3463	−	12.5891i	0.361529	−	0.439898i
$820$	0.646120	−	0.203614i	0.0225635	−	0.00711051i
$821$	−6.88250	+	1.84416i	−0.240201	+	0.0643616i	−0.376911	−	0.926249i	$-0.623014\pi$
$821$	−6.88250	+	1.84416i	−0.240201	+	0.0643616i	0.136710	+	0.990611i	$0.456347\pi$
$822$	−1.24350	+	2.26620i	−0.0433721	+	0.0790427i
$823$	3.45331	−	1.99377i	0.120375	−	0.0694985i	−0.438604	−	0.898681i	$-0.644527\pi$
$823$	3.45331	−	1.99377i	0.120375	−	0.0694985i	0.558978	+	0.829182i	$0.311193\pi$
$824$	−8.22449	−	24.2465i	−0.286514	−	0.844668i
$825$		−	24.5829i		−	0.855867i
$826$	51.0993	+	21.8688i	1.77797	+	0.760913i
$827$	−33.6810	−	33.6810i	−1.17120	−	1.17120i	−0.981923	−	0.189280i	$-0.939385\pi$
$827$	−33.6810	−	33.6810i	−1.17120	−	1.17120i	−0.189280	−	0.981923i	$-0.560615\pi$
$828$	−10.3345	+	6.58164i	−0.359150	+	0.228728i
$829$	−2.09918	−	0.562475i	−0.0729077	−	0.0195356i	0.222181	−	0.975005i	$-0.428682\pi$
$829$	−2.09918	−	0.562475i	−0.0729077	−	0.0195356i	−0.295089	+	0.955470i	$0.595349\pi$
$830$	1.48355	+	5.09124i	0.0514947	+	0.176720i
$831$	6.86343	−	11.8878i	0.238090	−	0.412383i
$832$	−39.0764	−	30.0124i	−1.35473	−	1.04049i
$833$	−19.1909	+	3.78946i	−0.664926	+	0.131297i
$834$	2.82072	+	0.690452i	0.0976737	+	0.0239084i
$835$	0.499595	+	1.86451i	0.0172892	+	0.0645242i
$836$	2.88151	+	66.2261i	0.0996591	+	2.29048i
$837$	−0.804756	+	3.00339i	−0.0278164	+	0.103812i
$838$	1.03728	+	47.7026i	0.0358324	+	1.64786i
$839$		−	56.0274i		−	1.93428i	−0.254244	−	0.967140i	$-0.581826\pi$
$839$		−	56.0274i		−	1.93428i	0.254244	−	0.967140i	$-0.418174\pi$
$840$	2.30365	+	0.229039i	0.0794835	+	0.00790258i
$841$			18.7139i			0.645306i
$842$	38.3157	−	0.833169i	1.32045	−	0.0287129i
$843$	−5.63148	+	21.0170i	−0.193959	+	0.723863i
$844$	0.947307	+	0.868309i	0.0326076	+	0.0298884i
$845$	−1.99632	−	7.45036i	−0.0686754	−	0.256300i
$846$	1.90599	−	7.78661i	0.0655294	−	0.267709i
$847$	37.1948	−	3.63715i	1.27803	−	0.124974i
$848$	−6.81233	+	38.5668i	−0.233937	+	1.32439i
$849$	−8.09488	+	14.0207i	−0.277816	+	0.481191i
$850$	−18.6080	+	5.42221i	−0.638248	+	0.185980i
$851$	−15.7028	−	4.20755i	−0.538285	−	0.144233i
$852$	5.83768	+	1.29510i	0.199996	+	0.0443695i
$853$	−27.7591	−	27.7591i	−0.950454	−	0.950454i	0.0483754	−	0.998829i	$-0.484596\pi$
$853$	−27.7591	−	27.7591i	−0.950454	−	0.950454i	−0.998829	+	0.0483754i	$0.984596\pi$
$854$	21.1991	−	2.53935i	0.725417	−	0.0868949i
$855$		−	2.04556i		−	0.0699567i
$856$	37.6928	+	18.5986i	1.28831	+	0.635687i
$857$	−17.5619	+	10.1394i	−0.599903	+	0.346354i	−0.769003	−	0.639245i	$-0.779247\pi$
$857$	−17.5619	+	10.1394i	−0.599903	+	0.346354i	0.169100	+	0.985599i	$0.445914\pi$
$858$	38.2760	+	21.0027i	1.30672	+	0.717019i
$859$	−39.3375	+	10.5404i	−1.34218	+	0.359635i	−0.857242	−	0.514914i	$-0.827824\pi$
$859$	−39.3375	+	10.5404i	−1.34218	+	0.359635i	−0.484936	+	0.874550i	$0.661157\pi$
$860$	−1.56140	+	2.99833i	−0.0532434	+	0.102242i
$861$	1.01854	+	2.71194i	0.0347118	+	0.0924226i
$862$	45.1798	+	11.0590i	1.53883	+	0.376672i
$863$	−4.62151	+	8.00469i	−0.157318	+	0.272483i	−0.933901	−	0.357533i	$-0.883618\pi$
$863$	−4.62151	+	8.00469i	−0.157318	+	0.272483i	0.776583	+	0.630015i	$0.216951\pi$
$864$	−5.62346	+	0.613729i	−0.191314	+	0.0208795i
$865$	−2.14324	−	3.71220i	−0.0728723	−	0.126219i
$866$	4.96003	−	5.18054i	0.168549	−	0.176042i
$867$	−6.49887	+	6.49887i	−0.220713	+	0.220713i
$868$	6.14309	−	15.2632i	0.208510	−	0.518068i
$869$	54.3392	+	54.3392i	1.84333	+	1.84333i
$870$	−0.0305037	−	1.40280i	−0.00103417	−	0.0475595i
$871$	5.51927	−	3.18655i	0.187013	−	0.107972i
$872$	19.6492	+	29.4215i	0.665406	+	0.996338i
$873$	8.22455	+	4.74844i	0.278359	+	0.160711i
$874$	−29.7155	−	48.9779i	−1.00514	−	1.65670i
$875$	1.32609	−	7.99726i	0.0448300	−	0.270357i
$876$	−6.78980	−	21.5458i	−0.229406	−	0.727965i
$877$	−4.54825	−	16.9743i	−0.153583	−	0.573181i	−0.999222	−	0.0394260i	$-0.987447\pi$
$877$	−4.54825	−	16.9743i	−0.153583	−	0.573181i	0.845639	−	0.533755i	$-0.179220\pi$
$878$	−40.5609	+	11.8191i	−1.36887	+	0.398876i
$879$	6.71065	+	11.6232i	0.226345	+	0.392040i
$880$	0.538734	+	6.17917i	0.0181607	+	0.208300i
$881$	−25.0174			−0.842857			−0.421429	−	0.906862i	$-0.638471\pi$
$881$	−25.0174			−0.842857			−0.421429	+	0.906862i	$0.638471\pi$
$882$	−0.446362	+	9.88943i	−0.0150298	+	0.332994i
$883$	12.6688	−	12.6688i	0.426339	−	0.426339i	−0.461040	−	0.887379i	$-0.652524\pi$
$883$	12.6688	−	12.6688i	0.426339	−	0.426339i	0.887379	+	0.461040i	$0.152524\pi$
$884$	7.45544	−	33.6054i	0.250754	−	1.13027i
$885$	1.18940	−	4.43889i	0.0399811	−	0.149212i
$886$	18.8348	−	34.3252i	0.632768	−	1.15318i
$887$	24.4147	+	14.0958i	0.819764	+	0.473291i	0.850335	−	0.526242i	$-0.176399\pi$
$887$	24.4147	+	14.0958i	0.819764	+	0.473291i	−0.0305712	+	0.999533i	$0.509733\pi$
$888$	−5.64192	−	4.95008i	−0.189330	−	0.166114i
$889$	−35.9708	+	25.7384i	−1.20642	+	0.863237i
$890$	0.417344	−	0.253208i	0.0139894	−	0.00848754i
$891$	4.84172	−	1.29734i	0.162204	−	0.0434624i
$892$	0.171277	+	3.93647i	0.00573477	+	0.131803i
$893$	36.2049	+	9.70106i	1.21155	+	0.324634i
$894$	15.7018	−	16.3998i	0.525146	−	0.548492i
$895$	−3.88159			−0.129747
$896$	29.9311	+	0.363169i	0.999926	+	0.0121326i
$897$	−37.7311			−1.25980
$898$	13.4161	−	14.0126i	0.447703	−	0.467606i
$899$	−9.63246	−	2.58101i	−0.321261	−	0.0860815i
$900$	0.426371	+	9.79933i	0.0142124	+	0.326644i
$901$	−26.4285	+	7.08149i	−0.880461	+	0.235919i
$902$	−6.63586	+	4.02605i	−0.220950	+	0.134053i
$903$	−13.1632	−	5.97523i	−0.438043	−	0.198843i
$904$	−23.6930	−	20.7877i	−0.788017	−	0.691387i
$905$	−1.41487	−	0.816878i	−0.0470320	−	0.0271540i
$906$	1.74371	−	3.17781i	0.0579310	−	0.105576i
$907$	−1.46419	+	5.46442i	−0.0486175	+	0.181443i	−0.985965	−	0.166953i	$-0.946607\pi$
$907$	−1.46419	+	5.46442i	−0.0486175	+	0.181443i	0.937347	+	0.348397i	$0.113274\pi$
$908$	−5.89644	+	26.5782i	−0.195680	+	0.882028i
$909$	0.609065	−	0.609065i	0.0202014	−	0.0202014i
$910$	5.60477	+	4.40566i	0.185796	+	0.146046i
$911$	6.72518			0.222815			0.111407	−	0.993775i	$-0.464464\pi$
$911$	6.72518			0.222815			0.111407	+	0.993775i	$0.464464\pi$
$912$	−2.29728	−	26.3493i	−0.0760704	−	0.872513i
$913$	−30.3790	−	52.6179i	−1.00540	−	1.74140i
$914$	−28.8708	+	8.41270i	−0.954960	+	0.278267i
$915$	−0.456879	−	1.70509i	−0.0151039	−	0.0563687i
$916$	13.5473	+	42.9892i	0.447617	+	1.42040i
$917$	0.243529	+	0.200143i	0.00804202	+	0.00660932i
$918$	−2.04994	−	3.37878i	−0.0676583	−	0.111516i
$919$	−39.5945	−	22.8599i	−1.30610	−	0.754079i	−0.324659	−	0.945831i	$-0.605250\pi$
$919$	−39.5945	−	22.8599i	−1.30610	−	0.754079i	−0.981443	+	0.191752i	$0.938583\pi$
$920$	−2.97705	−	4.45765i	−0.0981504	−	0.146964i
$921$	0.343200	−	0.198146i	0.0113088	−	0.00652915i
$922$	−0.490792	−	22.5705i	−0.0161634	−	0.743320i
$923$	13.0208	+	13.0208i	0.428584	+	0.428584i
$924$	−26.2607	+	3.72641i	−0.863913	+	0.122590i
$925$	−9.20247	+	9.20247i	−0.302575	+	0.302575i
$926$	13.7246	−	14.3347i	0.451018	−	0.471069i
$927$	−4.52609	−	7.83942i	−0.148656	−	0.257480i
$928$	−1.96835	−	18.0356i	−0.0646143	−	0.592046i
$929$	21.0705	−	36.4951i	0.691299	−	1.19737i	−0.280113	−	0.959967i	$-0.590372\pi$
$929$	21.0705	−	36.4951i	0.691299	−	1.19737i	0.971412	−	0.237399i	$-0.0762947\pi$
$930$	−1.32131	−	0.323429i	−0.0433276	−	0.0106056i
$931$	−46.1828	−	3.09174i	−1.51358	−	0.101328i
$932$	5.24548	−	10.0728i	0.171821	−	0.329944i
$933$	14.7649	−	3.95625i	0.483382	−	0.129522i
$934$	31.0745	+	17.0511i	1.01679	+	0.557928i
$935$	−3.75274	+	2.16665i	−0.122728	+	0.0708569i
$936$	−15.6220	−	7.70829i	−0.510620	−	0.251953i
$937$		−	24.6206i		−	0.804320i	−0.915569	−	0.402160i	$-0.868260\pi$
$937$		−	24.6206i		−	0.804320i	0.915569	−	0.402160i	$-0.131740\pi$
$938$	−1.52333	+	3.55947i	−0.0497386	+	0.116221i
$939$	0.268955	+	0.268955i	0.00877701	+	0.00877701i
$940$	3.42393	+	0.759608i	0.111676	+	0.0247757i
$941$	−17.7852	−	4.76552i	−0.579780	−	0.155352i	−0.0430018	−	0.999075i	$-0.513692\pi$
$941$	−17.7852	−	4.76552i	−0.579780	−	0.155352i	−0.536778	+	0.843723i	$0.680359\pi$
$942$	−14.2618	+	4.15576i	−0.464673	+	0.135402i
$943$	3.35386	−	5.80906i	0.109217	−	0.189169i
$944$	10.3358	−	58.5141i	0.336401	−	1.90447i
$945$	0.814594	−	0.0796563i	0.0264987	−	0.00259122i
$946$	9.20881	−	37.6210i	0.299404	−	1.22317i
$947$	−0.605257	−	2.25885i	−0.0196682	−	0.0734027i	0.955394	−	0.295334i	$-0.0954308\pi$
$947$	−0.605257	−	2.25885i	−0.0196682	−	0.0734027i	−0.975062	+	0.221931i	$0.928764\pi$
$948$	−22.6034	−	20.7184i	−0.734123	−	0.672903i
$949$	18.0052	−	67.1963i	0.584473	−	2.18128i
$950$	−45.8504	+	0.997008i	−1.48758	+	0.0323472i
$951$			13.9166i			0.451277i
$952$	8.61297	+	19.0560i	0.279148	+	0.617609i
$953$			41.5858i			1.34710i	0.739143	+	0.673548i	$0.235231\pi$
$953$			41.5858i			1.34710i	−0.739143	+	0.673548i	$0.764769\pi$
$954$	0.301019	+	13.8432i	0.00974584	+	0.448191i
$955$	−0.582283	+	2.17311i	−0.0188422	+	0.0703202i
$956$	0.436676	+	10.0362i	0.0141231	+	0.324593i
$957$	4.16081	+	15.5284i	0.134500	+	0.501961i
$958$	33.8422	+	8.28383i	1.09339	+	0.267638i
$959$	1.99892	−	4.40354i	0.0645486	−	0.142198i
$960$	−0.321925	−	2.45382i	−0.0103901	−	0.0791967i
$961$	10.6660	−	18.4741i	0.344065	−	0.595938i
$962$	−6.46617	−	22.1906i	−0.208478	−	0.715455i
$963$	14.3540	+	3.84615i	0.462553	+	0.123941i
$964$	−4.70746	+	2.99799i	−0.151617	+	0.0965586i
$965$	2.29882	+	2.29882i	0.0740016	+	0.0740016i
$966$	18.3471	−	13.7407i	0.590308	−	0.442100i
$967$			25.2014i			0.810423i	0.914223	+	0.405211i	$0.132802\pi$
$967$			25.2014i			0.810423i	−0.914223	+	0.405211i	$0.867198\pi$
$968$	−12.8338	−	37.8352i	−0.412493	−	1.21607i
$969$	16.0025	−	9.23904i	0.514074	−	0.296801i
$970$	−1.99871	+	3.64251i	−0.0641747	+	0.116954i
$971$	48.9180	−	13.1076i	1.56985	−	0.420641i	0.634088	−	0.773261i	$-0.281376\pi$
$971$	48.9180	−	13.1076i	1.56985	−	0.420641i	0.935767	+	0.352620i	$0.114709\pi$
$972$	−1.90752	+	0.601125i	−0.0611839	+	0.0192811i
$973$	−5.35970	−	0.888734i	−0.171824	−	0.0284915i
$974$	−2.73438	+	11.1709i	−0.0876153	+	0.357938i
$975$	−15.1027	+	26.1587i	−0.483675	+	0.837749i
$976$	−7.80007	−	21.4506i	−0.249674	−	0.686617i
$977$	−16.3946	−	28.3963i	−0.524510	−	0.908477i	−0.999593	−	0.0285363i	$-0.990915\pi$
$977$	−16.3946	−	28.3963i	−0.524510	−	0.908477i	0.475083	−	0.879941i	$-0.342418\pi$
$978$	−11.0463	−	10.5761i	−0.353221	−	0.338187i
$979$	−3.95477	+	3.95477i	−0.126395	+	0.126395i
$980$	−4.32980	−	0.101177i	−0.138310	−	0.00323197i
$981$	8.84490	+	8.84490i	0.282396	+	0.282396i
$982$	−5.49516	+	0.119491i	−0.175358	+	0.00381312i
$983$	−1.29233	+	0.746127i	−0.0412189	+	0.0237977i	−0.520468	−	0.853881i	$-0.674242\pi$
$983$	−1.29233	+	0.746127i	−0.0412189	+	0.0237977i	0.479249	+	0.877679i	$0.340909\pi$
$984$	2.57538	−	1.71997i	0.0821001	−	0.0548308i
$985$	−2.00473	−	1.15743i	−0.0638759	−	0.0368788i
$986$	10.8364	−	6.57458i	0.345101	−	0.209377i
$987$	−2.45335	+	14.7955i	−0.0780910	+	0.470945i
$988$	37.6204	−	72.2416i	1.19686	−	2.29831i
$989$	8.66327	+	32.3318i	0.275476	+	1.02809i
$990$	0.613494	+	2.10539i	0.0194981	+	0.0669137i
$991$	−23.2692	−	40.3035i	−0.739171	−	1.28028i	−0.952869	−	0.303382i	$-0.901884\pi$
$991$	−23.2692	−	40.3035i	−0.739171	−	1.28028i	0.213698	−	0.976900i	$-0.431449\pi$
$992$	−17.3834	−	2.68225i	−0.551922	−	0.0851614i
$993$	30.0875			0.954798
$994$	−11.0733	−	1.58964i	−0.351224	−	0.0504202i
$995$	−1.41065	+	1.41065i	−0.0447206	+	0.0447206i
$996$	13.0224	+	20.4479i	0.412631	+	0.647915i
$997$	1.41260	−	5.27188i	0.0447374	−	0.166962i	−0.939943	−	0.341332i	$-0.889122\pi$
$997$	1.41260	−	5.27188i	0.0447374	−	0.166962i	0.984680	+	0.174370i	$0.0557887\pi$
$998$	−50.6177	−	27.7748i	−1.60227	−	0.879195i
$999$	−2.29812	−	1.32682i	−0.0727094	−	0.0419788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bq.b.37.8	✓	120
7.4	even	3	inner	336.2.bq.b.277.11	yes	120
16.13	even	4	inner	336.2.bq.b.205.11	yes	120
112.109	even	12	inner	336.2.bq.b.109.8	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bq.b.37.8	✓	120	1.1	even	1	trivial
336.2.bq.b.109.8	yes	120	112.109	even	12	inner
336.2.bq.b.205.11	yes	120	16.13	even	4	inner
336.2.bq.b.277.11	yes	120	7.4	even	3	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bq (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.978024 + 1.02150i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.0869382 - 1.99811i) q^{4} +(0.298815 - 0.0800672i) q^{5} +(1.20908 - 0.733565i) q^{6} +(-2.15167 + 1.53959i) q^{7} +(2.12610 + 1.86539i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.978024 + 1.02150i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.0869382 - 1.99811i) q^{4} +(0.298815 - 0.0800672i) q^{5} +(1.20908 - 0.733565i) q^{6} +(-2.15167 + 1.53959i) q^{7} +(2.12610 + 1.86539i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-0.210459 + 0.383548i) q^{10} +(1.29734 - 4.84172i) q^{11} +(-0.433173 + 1.95253i) q^{12} +(-4.35505 + 4.35505i) q^{13} +(0.531685 - 3.70369i) q^{14} -0.309356 q^{15} +(-3.98488 + 0.347424i) q^{16} +(-1.39725 - 2.42010i) q^{17} +(-1.35775 + 0.395636i) q^{18} +(-1.71139 - 6.38701i) q^{19} +(-0.185962 - 0.590104i) q^{20} +(2.47682 - 0.930237i) q^{21} +(3.67701 + 6.06055i) q^{22} +(-5.30544 - 3.06309i) q^{23} +(-1.57086 - 2.35211i) q^{24} +(-4.24725 + 2.45215i) q^{25} +(-0.189355 - 8.70805i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(3.26333 + 4.16541i) q^{28} +(2.26783 - 2.26783i) q^{29} +(0.302558 - 0.316008i) q^{30} +(-1.55467 - 2.69277i) q^{31} +(3.54242 - 4.41036i) q^{32} +(-2.50626 + 4.34097i) q^{33} +(3.83869 + 0.939626i) q^{34} +(-0.519679 + 0.632330i) q^{35} +(0.923764 - 1.77388i) q^{36} +(2.56322 - 0.686814i) q^{37} +(8.19813 + 4.49845i) q^{38} +(5.33383 - 3.07949i) q^{39} +(0.784668 + 0.387176i) q^{40} +1.09493i q^{41} +(-1.47215 + 3.43988i) q^{42} +(-3.86349 - 3.86349i) q^{43} +(-9.78708 - 2.17129i) q^{44} +(0.298815 + 0.0800672i) q^{45} +(8.31780 - 2.42374i) q^{46} +(-2.83426 + 4.90908i) q^{47} +(3.93902 + 0.695778i) q^{48} +(2.25933 - 6.62536i) q^{49} +(1.64903 - 6.73684i) q^{50} +(0.723269 + 2.69928i) q^{51} +(9.08050 + 8.32326i) q^{52} +(2.53409 - 9.45734i) q^{53} +(1.41388 - 0.0307446i) q^{54} -1.55065i q^{55} +(-7.44660 - 0.740372i) q^{56} +6.61232i q^{57} +(0.0986038 + 4.53459i) q^{58} +(-3.84475 + 14.3488i) q^{59} +(0.0268948 + 0.618127i) q^{60} +(1.47687 + 5.51176i) q^{61} +(4.27117 + 1.04549i) q^{62} +(-2.63319 + 0.257491i) q^{63} +(1.04063 + 7.93203i) q^{64} +(-0.952658 + 1.65005i) q^{65} +(-1.98313 - 6.80573i) q^{66} +(-0.999507 - 0.267817i) q^{67} +(-4.71416 + 3.00225i) q^{68} +(4.33187 + 4.33187i) q^{69} +(-0.137669 - 1.14929i) q^{70} -2.98981i q^{71} +(0.908564 + 2.67853i) q^{72} +(-9.78190 + 5.64758i) q^{73} +(-1.80531 + 3.29006i) q^{74} +(4.73719 - 1.26933i) q^{75} +(-12.6132 + 3.97483i) q^{76} +(4.66283 + 12.4151i) q^{77} +(-2.07091 + 8.46034i) q^{78} +(-7.66553 + 13.2771i) q^{79} +(-1.16293 + 0.422874i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-1.11847 - 1.07086i) q^{82} +(8.57101 - 8.57101i) q^{83} +(-2.07405 - 4.86809i) q^{84} +(-0.611289 - 0.611289i) q^{85} +(7.72516 - 0.167982i) q^{86} +(-2.77751 + 1.60360i) q^{87} +(11.7900 - 7.87396i) q^{88} +(-0.966296 - 0.557891i) q^{89} +(-0.374037 + 0.226933i) q^{90} +(2.66562 - 16.0756i) q^{91} +(-5.65915 + 10.8671i) q^{92} +(0.804756 + 3.00339i) q^{93} +(-2.24267 - 7.69640i) q^{94} +(-1.02278 - 1.77151i) q^{95} +(-4.56320 + 3.34324i) q^{96} +9.49689 q^{97} +(4.55815 + 8.78768i) q^{98} +(3.54439 - 3.54439i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8}+O(q^{10}) \) 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8	\( 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8} - 8 q^{10} + 4 q^{11} + 8 q^{13} + 32 q^{14} + 8 q^{15} + 12 q^{16} - 16 q^{17} - 4 q^{18} - 8 q^{19} - 64 q^{20} + 12 q^{21} + 24 q^{22} - 8 q^{24} - 8 q^{26} - 8 q^{28} - 64 q^{29} - 52 q^{31} - 4 q^{33} + 32 q^{34} - 8 q^{35} + 24 q^{37} - 40 q^{38} - 60 q^{40} + 24 q^{42} - 32 q^{43} - 12 q^{44} - 8 q^{45} + 4 q^{46} - 8 q^{47} + 32 q^{48} + 20 q^{49} - 16 q^{50} - 8 q^{51} - 16 q^{52} + 4 q^{54} - 104 q^{56} + 4 q^{58} + 52 q^{59} - 16 q^{60} + 4 q^{61} - 144 q^{62} + 8 q^{63} - 64 q^{64} + 24 q^{65} + 24 q^{66} + 12 q^{68} + 24 q^{69} - 48 q^{70} + 4 q^{72} + 16 q^{74} + 16 q^{75} - 8 q^{76} + 8 q^{77} - 56 q^{78} + 28 q^{79} + 68 q^{80} + 60 q^{81} + 28 q^{82} + 8 q^{83} + 24 q^{84} - 80 q^{85} + 36 q^{86} + 40 q^{88} + 8 q^{90} + 36 q^{91} - 184 q^{92} + 4 q^{93} + 60 q^{94} - 16 q^{95} + 36 q^{96} + 24 q^{97} + 124 q^{98} - 8 q^{99}+O(q^{100}) \) 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8 - 8 * q^10 + 4 * q^11 + 8 * q^13 + 32 * q^14 + 8 * q^15 + 12 * q^16 - 16 * q^17 - 4 * q^18 - 8 * q^19 - 64 * q^20 + 12 * q^21 + 24 * q^22 - 8 * q^24 - 8 * q^26 - 8 * q^28 - 64 * q^29 - 52 * q^31 - 4 * q^33 + 32 * q^34 - 8 * q^35 + 24 * q^37 - 40 * q^38 - 60 * q^40 + 24 * q^42 - 32 * q^43 - 12 * q^44 - 8 * q^45 + 4 * q^46 - 8 * q^47 + 32 * q^48 + 20 * q^49 - 16 * q^50 - 8 * q^51 - 16 * q^52 + 4 * q^54 - 104 * q^56 + 4 * q^58 + 52 * q^59 - 16 * q^60 + 4 * q^61 - 144 * q^62 + 8 * q^63 - 64 * q^64 + 24 * q^65 + 24 * q^66 + 12 * q^68 + 24 * q^69 - 48 * q^70 + 4 * q^72 + 16 * q^74 + 16 * q^75 - 8 * q^76 + 8 * q^77 - 56 * q^78 + 28 * q^79 + 68 * q^80 + 60 * q^81 + 28 * q^82 + 8 * q^83 + 24 * q^84 - 80 * q^85 + 36 * q^86 + 40 * q^88 + 8 * q^90 + 36 * q^91 - 184 * q^92 + 4 * q^93 + 60 * q^94 - 16 * q^95 + 36 * q^96 + 24 * q^97 + 124 * q^98 - 8 * q^99

Introduction

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