LMFDB - Embedded newform 930.2.e.b.929.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(929,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("930.929");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.e (of order $2$, degree $1$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			929.10
Character	$\chi$	$=$	930.929
Dual form			930.2.e.b.929.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.02858 + 1.39357i) q^{3} +1.00000 q^{4} +(-0.467590 - 2.18663i) q^{5} +(-1.02858 + 1.39357i) q^{6} +1.43029i q^{7} +1.00000 q^{8} +(-0.884063 - 2.86678i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.02858 + 1.39357i) q^{3} +1.00000 q^{4} +(-0.467590 - 2.18663i) q^{5} +(-1.02858 + 1.39357i) q^{6} +1.43029i q^{7} +1.00000 q^{8} +(-0.884063 - 2.86678i) q^{9} +(-0.467590 - 2.18663i) q^{10} -6.14209 q^{11} +(-1.02858 + 1.39357i) q^{12} -2.15469 q^{13} +1.43029i q^{14} +(3.52817 + 1.59750i) q^{15} +1.00000 q^{16} -0.937186i q^{17} +(-0.884063 - 2.86678i) q^{18} -5.64155 q^{19} +(-0.467590 - 2.18663i) q^{20} +(-1.99320 - 1.47116i) q^{21} -6.14209 q^{22} -0.266117i q^{23} +(-1.02858 + 1.39357i) q^{24} +(-4.56272 + 2.04489i) q^{25} -2.15469 q^{26} +(4.90438 + 1.71670i) q^{27} +1.43029i q^{28} +3.72847 q^{29} +(3.52817 + 1.59750i) q^{30} +(-3.50356 + 4.32724i) q^{31} +1.00000 q^{32} +(6.31761 - 8.55943i) q^{33} -0.937186i q^{34} +(3.12752 - 0.668789i) q^{35} +(-0.884063 - 2.86678i) q^{36} -7.85409 q^{37} -5.64155 q^{38} +(2.21626 - 3.00271i) q^{39} +(-0.467590 - 2.18663i) q^{40} -3.31985i q^{41} +(-1.99320 - 1.47116i) q^{42} -0.581900 q^{43} -6.14209 q^{44} +(-5.85522 + 3.27360i) q^{45} -0.266117i q^{46} -4.74525 q^{47} +(-1.02858 + 1.39357i) q^{48} +4.95427 q^{49} +(-4.56272 + 2.04489i) q^{50} +(1.30603 + 0.963966i) q^{51} -2.15469 q^{52} -6.07885i q^{53} +(4.90438 + 1.71670i) q^{54} +(2.87198 + 13.4305i) q^{55} +1.43029i q^{56} +(5.80276 - 7.86188i) q^{57} +3.72847 q^{58} -5.39747i q^{59} +(3.52817 + 1.59750i) q^{60} -9.71998i q^{61} +(-3.50356 + 4.32724i) q^{62} +(4.10032 - 1.26447i) q^{63} +1.00000 q^{64} +(1.00751 + 4.71151i) q^{65} +(6.31761 - 8.55943i) q^{66} +9.90260i q^{67} -0.937186i q^{68} +(0.370852 + 0.273721i) q^{69} +(3.12752 - 0.668789i) q^{70} +1.07592i q^{71} +(-0.884063 - 2.86678i) q^{72} +3.14657 q^{73} -7.85409 q^{74} +(1.84340 - 8.46179i) q^{75} -5.64155 q^{76} -8.78497i q^{77} +(2.21626 - 3.00271i) q^{78} -2.07491i q^{79} +(-0.467590 - 2.18663i) q^{80} +(-7.43686 + 5.06883i) q^{81} -3.31985i q^{82} -8.35010i q^{83} +(-1.99320 - 1.47116i) q^{84} +(-2.04928 + 0.438218i) q^{85} -0.581900 q^{86} +(-3.83502 + 5.19588i) q^{87} -6.14209 q^{88} -6.18921 q^{89} +(-5.85522 + 3.27360i) q^{90} -3.08183i q^{91} -0.266117i q^{92} +(-2.42663 - 9.33335i) q^{93} -4.74525 q^{94} +(2.63793 + 12.3360i) q^{95} +(-1.02858 + 1.39357i) q^{96} +10.6856i q^{97} +4.95427 q^{98} +(5.43000 + 17.6080i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{2} + 32 q^{4} - 2 q^{5} + 32 q^{8} + 4 q^{9}+O(q^{10}) $ 32 * q + 32 * q^2 + 32 * q^4 - 2 * q^5 + 32 * q^8 + 4 * q^9	$ 32 q + 32 q^{2} + 32 q^{4} - 2 q^{5} + 32 q^{8} + 4 q^{9} - 2 q^{10} + 32 q^{16} + 4 q^{18} + 8 q^{19} - 2 q^{20} + 10 q^{25} - 12 q^{31} + 32 q^{32} + 8 q^{33} - 16 q^{35} + 4 q^{36} + 8 q^{38} - 4 q^{39} - 2 q^{40} - 42 q^{45} + 4 q^{47} - 36 q^{49} + 10 q^{50} - 4 q^{51} - 12 q^{62} + 24 q^{63} + 32 q^{64} + 8 q^{66} - 8 q^{69} - 16 q^{70} + 4 q^{72} + 8 q^{76} - 4 q^{78} - 2 q^{80} + 24 q^{81} + 4 q^{87} - 42 q^{90} - 24 q^{93} + 4 q^{94} + 26 q^{95} - 36 q^{98}+O(q^{100}) $ 32 * q + 32 * q^2 + 32 * q^4 - 2 * q^5 + 32 * q^8 + 4 * q^9 - 2 * q^10 + 32 * q^16 + 4 * q^18 + 8 * q^19 - 2 * q^20 + 10 * q^25 - 12 * q^31 + 32 * q^32 + 8 * q^33 - 16 * q^35 + 4 * q^36 + 8 * q^38 - 4 * q^39 - 2 * q^40 - 42 * q^45 + 4 * q^47 - 36 * q^49 + 10 * q^50 - 4 * q^51 - 12 * q^62 + 24 * q^63 + 32 * q^64 + 8 * q^66 - 8 * q^69 - 16 * q^70 + 4 * q^72 + 8 * q^76 - 4 * q^78 - 2 * q^80 + 24 * q^81 + 4 * q^87 - 42 * q^90 - 24 * q^93 + 4 * q^94 + 26 * q^95 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.02858	+	1.39357i	−0.593849	+	0.804577i
$3$	−1.02858	+	1.39357i	−0.593849	+	0.804577i
$4$	1.00000			0.500000
$5$	−0.467590	−	2.18663i	−0.209113	−	0.977892i
$5$	−0.467590	−	2.18663i	−0.209113	−	0.977892i
$6$	−1.02858	+	1.39357i	−0.419914	+	0.568922i
$7$			1.43029i			0.540598i	0.962776	+	0.270299i	$0.0871226\pi$
$7$			1.43029i			0.540598i	−0.962776	+	0.270299i	$0.912877\pi$
$8$	1.00000			0.353553
$9$	−0.884063	−	2.86678i	−0.294688	−	0.955594i
$10$	−0.467590	−	2.18663i	−0.147865	−	0.691474i
$11$	−6.14209			−1.85191			−0.925956	−	0.377632i	$-0.876738\pi$
$11$	−6.14209			−1.85191			−0.925956	+	0.377632i	$0.876738\pi$
$12$	−1.02858	+	1.39357i	−0.296924	+	0.402288i
$13$	−2.15469			−0.597603			−0.298802	−	0.954315i	$-0.596587\pi$
$13$	−2.15469			−0.597603			−0.298802	+	0.954315i	$0.596587\pi$
$14$			1.43029i			0.382261i
$15$	3.52817	+	1.59750i	0.910970	+	0.412472i
$16$	1.00000			0.250000
$17$		−	0.937186i		−	0.227301i	−0.993521	−	0.113650i	$-0.963746\pi$
$17$		−	0.937186i		−	0.227301i	0.993521	−	0.113650i	$-0.0362544\pi$
$18$	−0.884063	−	2.86678i	−0.208376	−	0.675707i
$19$	−5.64155			−1.29426			−0.647130	−	0.762380i	$-0.724031\pi$
$19$	−5.64155			−1.29426			−0.647130	+	0.762380i	$0.724031\pi$
$20$	−0.467590	−	2.18663i	−0.104556	−	0.488946i
$21$	−1.99320	−	1.47116i	−0.434953	−	0.321034i
$22$	−6.14209			−1.30950
$23$		−	0.266117i		−	0.0554892i	−0.999615	−	0.0277446i	$-0.991167\pi$
$23$		−	0.266117i		−	0.0554892i	0.999615	−	0.0277446i	$-0.00883252\pi$
$24$	−1.02858	+	1.39357i	−0.209957	+	0.284461i
$25$	−4.56272	+	2.04489i	−0.912544	+	0.408979i
$26$	−2.15469			−0.422569
$27$	4.90438	+	1.71670i	0.943848	+	0.330379i
$28$			1.43029i			0.270299i
$29$	3.72847			0.692360			0.346180	−	0.938168i	$-0.387479\pi$
$29$	3.72847			0.692360			0.346180	+	0.938168i	$0.387479\pi$
$30$	3.52817	+	1.59750i	0.644153	+	0.291662i
$31$	−3.50356	+	4.32724i	−0.629258	+	0.777196i
$31$	−3.50356	+	4.32724i	−0.629258	+	0.777196i
$32$	1.00000			0.176777
$33$	6.31761	−	8.55943i	1.09975	−	1.49000i
$34$		−	0.937186i		−	0.160726i
$35$	3.12752	−	0.668789i	0.528647	−	0.113046i
$36$	−0.884063	−	2.86678i	−0.147344	−	0.477797i
$37$	−7.85409			−1.29120			−0.645602	−	0.763674i	$-0.723393\pi$
$37$	−7.85409			−1.29120			−0.645602	+	0.763674i	$0.723393\pi$
$38$	−5.64155			−0.915180
$39$	2.21626	−	3.00271i	0.354886	−	0.480818i
$40$	−0.467590	−	2.18663i	−0.0739324	−	0.345737i
$41$		−	3.31985i		−	0.518473i	−0.965814	−	0.259236i	$-0.916529\pi$
$41$		−	3.31985i		−	0.518473i	0.965814	−	0.259236i	$-0.0834709\pi$
$42$	−1.99320	−	1.47116i	−0.307558	−	0.227005i
$43$	−0.581900			−0.0887389			−0.0443694	−	0.999015i	$-0.514128\pi$
$43$	−0.581900			−0.0887389			−0.0443694	+	0.999015i	$0.514128\pi$
$44$	−6.14209			−0.925956
$45$	−5.85522	+	3.27360i	−0.872844	+	0.487999i
$46$		−	0.266117i		−	0.0392368i
$47$	−4.74525			−0.692166			−0.346083	−	0.938204i	$-0.612488\pi$
$47$	−4.74525			−0.692166			−0.346083	+	0.938204i	$0.612488\pi$
$48$	−1.02858	+	1.39357i	−0.148462	+	0.201144i
$49$	4.95427			0.707753
$50$	−4.56272	+	2.04489i	−0.645266	+	0.289192i
$51$	1.30603	+	0.963966i	0.182881	+	0.134982i
$52$	−2.15469			−0.298802
$53$		−	6.07885i		−	0.834995i	−0.908678	−	0.417497i	$-0.862907\pi$
$53$		−	6.07885i		−	0.834995i	0.908678	−	0.417497i	$-0.137093\pi$
$54$	4.90438	+	1.71670i	0.667402	+	0.233613i
$55$	2.87198	+	13.4305i	0.387258	+	1.81097i
$56$			1.43029i			0.191130i
$57$	5.80276	−	7.86188i	0.768594	−	1.04133i
$58$	3.72847			0.489573
$59$		−	5.39747i		−	0.702690i	−0.936246	−	0.351345i	$-0.885724\pi$
$59$		−	5.39747i		−	0.702690i	0.936246	−	0.351345i	$-0.114276\pi$
$60$	3.52817	+	1.59750i	0.455485	+	0.206236i
$61$		−	9.71998i		−	1.24452i	−0.782812	−	0.622258i	$-0.786216\pi$
$61$		−	9.71998i		−	1.24452i	0.782812	−	0.622258i	$-0.213784\pi$
$62$	−3.50356	+	4.32724i	−0.444953	+	0.549561i
$63$	4.10032	−	1.26447i	0.516592	−	0.159308i
$64$	1.00000			0.125000
$65$	1.00751	+	4.71151i	0.124966	+	0.584391i
$66$	6.31761	−	8.55943i	0.777644	−	1.05359i
$67$			9.90260i			1.20980i	0.796303	+	0.604898i	$0.206786\pi$
$67$			9.90260i			1.20980i	−0.796303	+	0.604898i	$0.793214\pi$
$68$		−	0.937186i		−	0.113650i
$69$	0.370852	+	0.273721i	0.0446453	+	0.0329522i
$70$	3.12752	−	0.668789i	0.373810	−	0.0799355i
$71$			1.07592i			0.127688i	0.997960	+	0.0638442i	$0.0203361\pi$
$71$			1.07592i			0.127688i	−0.997960	+	0.0638442i	$0.979664\pi$
$72$	−0.884063	−	2.86678i	−0.104188	−	0.337853i
$73$	3.14657			0.368279			0.184139	−	0.982900i	$-0.441050\pi$
$73$	3.14657			0.368279			0.184139	+	0.982900i	$0.441050\pi$
$74$	−7.85409			−0.913019
$75$	1.84340	−	8.46179i	0.212858	−	0.977083i
$76$	−5.64155			−0.647130
$77$		−	8.78497i		−	1.00114i
$78$	2.21626	−	3.00271i	0.250942	−	0.339990i
$79$		−	2.07491i		−	0.233446i	−0.993165	−	0.116723i	$-0.962761\pi$
$79$		−	2.07491i		−	0.233446i	0.993165	−	0.116723i	$-0.0372389\pi$
$80$	−0.467590	−	2.18663i	−0.0522781	−	0.244473i
$81$	−7.43686	+	5.06883i	−0.826318	+	0.563203i
$82$		−	3.31985i		−	0.366616i
$83$		−	8.35010i		−	0.916543i	−0.888812	−	0.458272i	$-0.848469\pi$
$83$		−	8.35010i		−	0.916543i	0.888812	−	0.458272i	$-0.151531\pi$
$84$	−1.99320	−	1.47116i	−0.217476	−	0.160517i
$85$	−2.04928	+	0.438218i	−0.222276	+	0.0475315i
$86$	−0.581900			−0.0627479
$87$	−3.83502	+	5.19588i	−0.411157	+	0.557057i
$88$	−6.14209			−0.654749
$89$	−6.18921			−0.656055			−0.328027	−	0.944668i	$-0.606384\pi$
$89$	−6.18921			−0.656055			−0.328027	+	0.944668i	$0.606384\pi$
$90$	−5.85522	+	3.27360i	−0.617194	+	0.345068i
$91$		−	3.08183i		−	0.323063i
$92$		−	0.266117i		−	0.0277446i
$93$	−2.42663	−	9.33335i	−0.251630	−	0.967824i
$94$	−4.74525			−0.489435
$95$	2.63793	+	12.3360i	0.270646	+	1.26565i
$96$	−1.02858	+	1.39357i	−0.104979	+	0.142230i
$97$			10.6856i			1.08495i	0.840071	+	0.542477i	$0.182513\pi$
$97$			10.6856i			1.08495i	−0.840071	+	0.542477i	$0.817487\pi$
$98$	4.95427			0.500457
$99$	5.43000	+	17.6080i	0.545735	+	1.76967i
$100$	−4.56272	+	2.04489i	−0.456272	+	0.204489i
$101$		−	12.6932i		−	1.26302i	−0.775368	−	0.631510i	$-0.782436\pi$
$101$		−	12.6932i		−	1.26302i	0.775368	−	0.631510i	$-0.217564\pi$
$102$	1.30603	+	0.963966i	0.129316	+	0.0954469i
$103$			14.3190i			1.41089i	0.708763	+	0.705447i	$0.249254\pi$
$103$			14.3190i			1.41089i	−0.708763	+	0.705447i	$0.750746\pi$
$104$	−2.15469			−0.211285
$105$	−2.28489	+	5.04631i	−0.222982	+	0.492469i
$106$		−	6.07885i		−	0.590430i
$107$	1.96466			0.189931			0.0949656	−	0.995481i	$-0.469726\pi$
$107$	1.96466			0.189931			0.0949656	+	0.995481i	$0.469726\pi$
$108$	4.90438	+	1.71670i	0.471924	+	0.165190i
$109$	−10.8671			−1.04088			−0.520439	−	0.853899i	$-0.674232\pi$
$109$	−10.8671			−1.04088			−0.520439	+	0.853899i	$0.674232\pi$
$110$	2.87198	+	13.4305i	0.273833	+	1.28055i
$111$	8.07852	−	10.9452i	0.766780	−	1.03887i
$112$			1.43029i			0.135150i
$113$	18.5351			1.74364			0.871818	−	0.489829i	$-0.162941\pi$
$113$	18.5351			1.74364			0.871818	+	0.489829i	$0.162941\pi$
$114$	5.80276	−	7.86188i	0.543478	−	0.736333i
$115$	−0.581900	+	0.124434i	−0.0542624	+	0.0116035i
$116$	3.72847			0.346180
$117$	1.90488	+	6.17702i	0.176106	+	0.571066i
$118$		−	5.39747i		−	0.496877i
$119$	1.34045			0.122878
$120$	3.52817	+	1.59750i	0.322077	+	0.145831i
$121$	26.7253			2.42957
$122$		−	9.71998i		−	0.880006i
$123$	4.62643	+	3.41471i	0.417151	+	0.307894i
$124$	−3.50356	+	4.32724i	−0.314629	+	0.388598i
$125$	6.60491	+	9.02082i	0.590761	+	0.806846i
$126$	4.10032	−	1.26447i	0.365286	−	0.112648i
$127$	−0.722563			−0.0641171			−0.0320585	−	0.999486i	$-0.510206\pi$
$127$	−0.722563			−0.0641171			−0.0320585	+	0.999486i	$0.510206\pi$
$128$	1.00000			0.0883883
$129$	0.598528	−	0.810917i	0.0526975	−	0.0713973i
$130$	1.00751	+	4.71151i	0.0883646	+	0.413227i
$131$		−	3.37246i		−	0.294654i	−0.989088	−	0.147327i	$-0.952933\pi$
$131$		−	3.37246i		−	0.294654i	0.989088	−	0.147327i	$-0.0470669\pi$
$132$	6.31761	−	8.55943i	0.549877	−	0.745002i
$133$		−	8.06904i		−	0.699675i
$134$			9.90260i			0.855454i
$135$	1.46055	−	11.5268i	0.125704	−	0.992068i
$136$		−	0.937186i		−	0.0803630i
$137$			18.7748i			1.60404i	0.597295	+	0.802021i	$0.296242\pi$
$137$			18.7748i			1.60404i	−0.597295	+	0.802021i	$0.703758\pi$
$138$	0.370852	+	0.273721i	0.0315690	+	0.0233007i
$139$			3.94403i			0.334528i	0.985912	+	0.167264i	$0.0534932\pi$
$139$			3.94403i			0.334528i	−0.985912	+	0.167264i	$0.946507\pi$
$140$	3.12752	−	0.668789i	0.264323	−	0.0565230i
$141$	4.88085	−	6.61283i	0.411042	−	0.556901i
$142$			1.07592i			0.0902894i
$143$	13.2343			1.10671
$144$	−0.884063	−	2.86678i	−0.0736719	−	0.238898i
$145$	−1.74340	−	8.15280i	−0.144781	−	0.677053i
$146$	3.14657			0.260412
$147$	−5.09585	+	6.90412i	−0.420298	+	0.569442i
$148$	−7.85409			−0.645602
$149$			10.5144i			0.861371i	0.902502	+	0.430686i	$0.141728\pi$
$149$			10.5144i			0.861371i	−0.902502	+	0.430686i	$0.858272\pi$
$150$	1.84340	−	8.46179i	0.150513	−	0.690902i
$151$		−	8.58926i		−	0.698984i	−0.936939	−	0.349492i	$-0.886354\pi$
$151$		−	8.58926i		−	0.698984i	0.936939	−	0.349492i	$-0.113646\pi$
$152$	−5.64155			−0.457590
$153$	−2.68671	+	0.828531i	−0.217207	+	0.0669828i
$154$		−	8.78497i		−	0.707913i
$155$	11.1003	+	5.63763i	0.891599	+	0.452825i
$156$	2.21626	−	3.00271i	0.177443	−	0.240409i
$157$			9.01331i			0.719341i	0.933079	+	0.359670i	$0.117111\pi$
$157$			9.01331i			0.719341i	−0.933079	+	0.359670i	$0.882889\pi$
$158$		−	2.07491i		−	0.165071i
$159$	8.47129	+	6.25256i	0.671817	+	0.495860i
$160$	−0.467590	−	2.18663i	−0.0369662	−	0.172868i
$161$	0.380624			0.0299974
$162$	−7.43686	+	5.06883i	−0.584295	+	0.398245i
$163$			14.2442i			1.11570i	0.829943	+	0.557848i	$0.188373\pi$
$163$			14.2442i			1.11570i	−0.829943	+	0.557848i	$0.811627\pi$
$164$		−	3.31985i		−	0.259236i
$165$	−21.6704	−	9.81199i	−1.68704	−	0.763862i
$166$		−	8.35010i		−	0.648094i
$167$		−	10.1611i		−	0.786288i	−0.919477	−	0.393144i	$-0.871387\pi$
$167$		−	10.1611i		−	0.786288i	0.919477	−	0.393144i	$-0.128613\pi$
$168$	−1.99320	−	1.47116i	−0.153779	−	0.113503i
$169$	−8.35731			−0.642870
$170$	−2.04928	+	0.438218i	−0.157173	+	0.0336098i
$171$	4.98748	+	16.1731i	0.381402	+	1.23679i
$172$	−0.581900			−0.0443694
$173$	−15.9489			−1.21258			−0.606288	−	0.795245i	$-0.707342\pi$
$173$	−15.9489			−1.21258			−0.606288	+	0.795245i	$0.707342\pi$
$174$	−3.83502	+	5.19588i	−0.290732	+	0.393899i
$175$	−2.92479	−	6.52601i	−0.221093	−	0.493320i
$176$	−6.14209			−0.462978
$177$	7.52174	+	5.55170i	0.565368	+	0.417292i
$178$	−6.18921			−0.463901
$179$	1.03414			0.0772953			0.0386477	−	0.999253i	$-0.487695\pi$
$179$	1.03414			0.0772953			0.0386477	+	0.999253i	$0.487695\pi$
$180$	−5.85522	+	3.27360i	−0.436422	+	0.244000i
$181$			1.53891i			0.114386i	0.998363	+	0.0571930i	$0.0182150\pi$
$181$			1.53891i			0.114386i	−0.998363	+	0.0571930i	$0.981785\pi$
$182$		−	3.08183i		−	0.228440i
$183$	13.5455	+	9.99774i	1.00131	+	0.739054i
$184$		−	0.266117i		−	0.0196184i
$185$	3.67249	+	17.1740i	0.270007	+	1.26266i
$186$	−2.42663	−	9.33335i	−0.177929	−	0.684355i
$187$			5.75628i			0.420941i
$188$	−4.74525			−0.346083
$189$	−2.45538	+	7.01468i	−0.178602	+	0.510243i
$190$	2.63793	+	12.3360i	0.191376	+	0.894947i
$191$		−	1.04692i		−	0.0757527i	−0.999282	−	0.0378764i	$-0.987941\pi$
$191$		−	1.04692i		−	0.0757527i	0.999282	−	0.0378764i	$-0.0120593\pi$
$192$	−1.02858	+	1.39357i	−0.0742311	+	0.100572i
$193$		−	21.9599i		−	1.58071i	−0.612649	−	0.790355i	$-0.709896\pi$
$193$		−	21.9599i		−	1.58071i	0.612649	−	0.790355i	$-0.290104\pi$
$194$			10.6856i			0.767178i
$195$	−7.60212	−	3.44211i	−0.544399	−	0.246495i
$196$	4.95427			0.353877
$197$			23.2946i			1.65967i	0.558009	+	0.829835i	$0.311565\pi$
$197$			23.2946i			1.65967i	−0.558009	+	0.829835i	$0.688435\pi$
$198$	5.43000	+	17.6080i	0.385893	+	1.25135i
$199$			5.07538i			0.359784i	0.983686	+	0.179892i	$0.0575748\pi$
$199$			5.07538i			0.359784i	−0.983686	+	0.179892i	$0.942425\pi$
$200$	−4.56272	+	2.04489i	−0.322633	+	0.144596i
$201$	−13.7999	−	10.1856i	−0.973373	−	0.718435i
$202$		−	12.6932i		−	0.893089i
$203$			5.33280i			0.374289i
$204$	1.30603	+	0.963966i	0.0914405	+	0.0674912i
$205$	−7.25928	+	1.55233i	−0.507010	+	0.108419i
$206$			14.3190i			0.997652i
$207$	−0.762899	+	0.235264i	−0.0530251	+	0.0163520i
$208$	−2.15469			−0.149401
$209$	34.6509			2.39685
$210$	−2.28489	+	5.04631i	−0.157672	+	0.348228i
$211$	18.6497			1.28390			0.641950	−	0.766747i	$-0.278126\pi$
$211$	18.6497			1.28390			0.641950	+	0.766747i	$0.278126\pi$
$212$		−	6.07885i		−	0.417497i
$213$	−1.49937	−	1.10667i	−0.102735	−	0.0758276i
$214$	1.96466			0.134302
$215$	0.272090	+	1.27240i	0.0185564	+	0.0867770i
$216$	4.90438	+	1.71670i	0.333701	+	0.116807i
$217$	−6.18921	−	5.01111i	−0.420151	−	0.340176i
$218$	−10.8671			−0.736013
$219$	−3.23649	+	4.38497i	−0.218702	+	0.296309i
$220$	2.87198	+	13.4305i	0.193629	+	0.905484i
$221$			2.01934i			0.135836i
$222$	8.07852	−	10.9452i	0.542195	−	0.734594i
$223$	−7.26279			−0.486352			−0.243176	−	0.969982i	$-0.578189\pi$
$223$	−7.26279			−0.486352			−0.243176	+	0.969982i	$0.578189\pi$
$224$			1.43029i			0.0955652i
$225$	9.89599	+	11.2725i	0.659733	+	0.751500i
$226$	18.5351			1.23294
$227$	−16.5730			−1.09999			−0.549993	−	0.835169i	$-0.685370\pi$
$227$	−16.5730			−1.09999			−0.549993	+	0.835169i	$0.685370\pi$
$228$	5.80276	−	7.86188i	0.384297	−	0.520666i
$229$		−	19.1781i		−	1.26732i	−0.773610	−	0.633662i	$-0.781551\pi$
$229$		−	19.1781i		−	1.26732i	0.773610	−	0.633662i	$-0.218449\pi$
$230$	−0.581900	+	0.124434i	−0.0383693	+	0.00820491i
$231$	12.2425	+	9.03601i	0.805494	+	0.594526i
$232$	3.72847			0.244786
$233$	−19.6843			−1.28956			−0.644781	−	0.764367i	$-0.723052\pi$
$233$	−19.6843			−1.28956			−0.644781	+	0.764367i	$0.723052\pi$
$234$	1.90488	+	6.17702i	0.124526	+	0.403805i
$235$	2.21883	+	10.3761i	0.144741	+	0.676863i
$236$		−	5.39747i		−	0.351345i
$237$	2.89153	+	2.13420i	0.187825	+	0.138631i
$238$	1.34045			0.0868882
$239$	2.93174			0.189639			0.0948194	−	0.995494i	$-0.469773\pi$
$239$	2.93174			0.189639			0.0948194	+	0.995494i	$0.469773\pi$
$240$	3.52817	+	1.59750i	0.227743	+	0.103118i
$241$			26.2006i			1.68773i	0.536558	+	0.843863i	$0.319724\pi$
$241$			26.2006i			1.68773i	−0.536558	+	0.843863i	$0.680276\pi$
$242$	26.7253			1.71797
$243$	0.585621	−	15.5775i	0.0375676	−	0.999294i
$244$		−	9.71998i		−	0.622258i
$245$	−2.31657	−	10.8332i	−0.148000	−	0.692106i
$246$	4.62643	+	3.41471i	0.294970	+	0.217714i
$247$	12.1558			0.773454
$248$	−3.50356	+	4.32724i	−0.222476	+	0.274780i
$249$	11.6364	+	8.58872i	0.737429	+	0.544288i
$250$	6.60491	+	9.02082i	0.417731	+	0.570527i
$251$	−16.0306			−1.01184			−0.505922	−	0.862579i	$-0.668848\pi$
$251$	−16.0306			−1.01184			−0.505922	+	0.862579i	$0.668848\pi$
$252$	4.10032	−	1.26447i	0.258296	−	0.0796539i
$253$			1.63452i			0.102761i
$254$	−0.722563			−0.0453376
$255$	1.49715	−	3.30655i	0.0937554	−	0.207064i
$256$	1.00000			0.0625000
$257$	−18.9905			−1.18459			−0.592296	−	0.805720i	$-0.701779\pi$
$257$	−18.9905			−1.18459			−0.592296	+	0.805720i	$0.701779\pi$
$258$	0.598528	−	0.810917i	0.0372627	−	0.0504855i
$259$		−	11.2336i		−	0.698023i
$260$	1.00751	+	4.71151i	0.0624832	+	0.292196i
$261$	−3.29621	−	10.6887i	−0.204030	−	0.661615i
$262$		−	3.37246i		−	0.208352i
$263$		−	21.8884i		−	1.34969i	−0.737957	−	0.674847i	$-0.764209\pi$
$263$		−	21.8884i		−	1.34969i	0.737957	−	0.674847i	$-0.235791\pi$
$264$	6.31761	−	8.55943i	0.388822	−	0.526796i
$265$	−13.2922	+	2.84241i	−0.816534	+	0.174608i
$266$		−	8.06904i		−	0.494745i
$267$	6.36607	−	8.62508i	0.389597	−	0.527847i
$268$			9.90260i			0.604898i
$269$	21.2950			1.29838			0.649191	−	0.760626i	$-0.275108\pi$
$269$	21.2950			1.29838			0.649191	+	0.760626i	$0.275108\pi$
$270$	1.46055	−	11.5268i	0.0888864	−	0.701498i
$271$		−	11.2154i		−	0.681285i	−0.940193	−	0.340642i	$-0.889355\pi$
$271$		−	11.2154i		−	0.681285i	0.940193	−	0.340642i	$-0.110645\pi$
$272$		−	0.937186i		−	0.0568252i
$273$	4.29474	+	3.16989i	0.259929	+	0.191851i
$274$			18.7748i			1.13423i
$275$	28.0247	−	12.5599i	1.68995	−	0.757392i
$276$	0.370852	+	0.273721i	0.0223227	+	0.0164761i
$277$	−11.5071			−0.691397			−0.345698	−	0.938346i	$-0.612358\pi$
$277$	−11.5071			−0.691397			−0.345698	+	0.938346i	$0.612358\pi$
$278$			3.94403i			0.236547i
$279$	15.5026	+	6.21839i	0.928118	+	0.372285i
$280$	3.12752	−	0.668789i	0.186905	−	0.0399678i
$281$		−	23.5749i		−	1.40636i	−0.711013	−	0.703179i	$-0.751763\pi$
$281$		−	23.5749i		−	1.40636i	0.711013	−	0.703179i	$-0.248237\pi$
$282$	4.88085	−	6.61283i	0.290650	−	0.393788i
$283$		−	16.0120i		−	0.951817i	−0.879495	−	0.475908i	$-0.842119\pi$
$283$		−	16.0120i		−	0.951817i	0.879495	−	0.475908i	$-0.157881\pi$
$284$			1.07592i			0.0638442i
$285$	−19.9044	−	9.01237i	−1.17903	−	0.533847i
$286$	13.2343			0.782561
$287$	4.74834			0.280286
$288$	−0.884063	−	2.86678i	−0.0520939	−	0.168927i
$289$	16.1217			0.948334
$290$	−1.74340	−	8.15280i	−0.102376	−	0.478749i
$291$	−14.8910	−	10.9909i	−0.872929	−	0.644298i
$292$	3.14657			0.184139
$293$	−12.2492			−0.715608			−0.357804	−	0.933797i	$-0.616474\pi$
$293$	−12.2492			−0.715608			−0.357804	+	0.933797i	$0.616474\pi$
$294$	−5.09585	+	6.90412i	−0.297196	+	0.402656i
$295$	−11.8023	+	2.52380i	−0.687155	+	0.146941i
$296$	−7.85409			−0.456510
$297$	−30.1232	−	10.5441i	−1.74792	−	0.611833i
$298$			10.5144i			0.609081i
$299$			0.573399i			0.0331605i
$300$	1.84340	−	8.46179i	0.106429	−	0.488542i
$301$		−	0.832285i		−	0.0479721i
$302$		−	8.58926i		−	0.494256i
$303$	17.6888	+	13.0559i	1.01620	+	0.750042i
$304$	−5.64155			−0.323565
$305$	−21.2540	+	4.54496i	−1.21700	+	0.260244i
$306$	−2.68671	+	0.828531i	−0.153589	+	0.0473640i
$307$		−	28.8870i		−	1.64867i	−0.566102	−	0.824335i	$-0.691549\pi$
$307$		−	28.8870i		−	1.64867i	0.566102	−	0.824335i	$-0.308451\pi$
$308$		−	8.78497i		−	0.500570i
$309$	−19.9545	−	14.7282i	−1.13517	−	0.837857i
$310$	11.1003	+	5.63763i	0.630456	+	0.320196i
$311$		−	8.54298i		−	0.484428i	−0.970223	−	0.242214i	$-0.922126\pi$
$311$		−	8.54298i		−	0.484428i	0.970223	−	0.242214i	$-0.0778736\pi$
$312$	2.21626	−	3.00271i	0.125471	−	0.169995i
$313$	−31.8575			−1.80069			−0.900347	−	0.435172i	$-0.856688\pi$
$313$	−31.8575			−1.80069			−0.900347	+	0.435172i	$0.856688\pi$
$314$			9.01331i			0.508651i
$315$	−4.68219	−	8.37465i	−0.263812	−	0.471858i
$316$		−	2.07491i		−	0.116723i
$317$	7.46567			0.419314			0.209657	−	0.977775i	$-0.432765\pi$
$317$	7.46567			0.419314			0.209657	+	0.977775i	$0.432765\pi$
$318$	8.47129	+	6.25256i	0.475047	+	0.350626i
$319$	−22.9006			−1.28219
$320$	−0.467590	−	2.18663i	−0.0261391	−	0.122236i
$321$	−2.02081	+	2.73789i	−0.112790	+	0.152814i
$322$	0.380624			0.0212114
$323$			5.28718i			0.294186i
$324$	−7.43686	+	5.06883i	−0.413159	+	0.281602i
$325$	9.83124	−	4.40611i	0.545339	−	0.244407i
$326$			14.2442i			0.788916i
$327$	11.1776	−	15.1440i	0.618124	−	0.837467i
$328$		−	3.31985i		−	0.183308i
$329$		−	6.78708i		−	0.374184i
$330$	−21.6704	−	9.81199i	−1.19291	−	0.540132i
$331$		−	34.6148i		−	1.90260i	−0.308261	−	0.951302i	$-0.599747\pi$
$331$		−	34.6148i		−	1.90260i	0.308261	−	0.951302i	$-0.400253\pi$
$332$		−	8.35010i		−	0.458272i
$333$	6.94351	+	22.5159i	0.380502	+	1.23387i
$334$		−	10.1611i		−	0.555989i
$335$	21.6533	−	4.63035i	1.18305	−	0.252983i
$336$	−1.99320	−	1.47116i	−0.108738	−	0.0802584i
$337$	24.5024			1.33473			0.667364	−	0.744732i	$-0.267423\pi$
$337$	24.5024			1.33473			0.667364	+	0.744732i	$0.267423\pi$
$338$	−8.35731			−0.454578
$339$	−19.0648	+	25.8299i	−1.03546	+	1.40289i
$340$	−2.04928	+	0.438218i	−0.111138	+	0.0237657i
$341$	21.5192	−	26.5783i	1.16533	−	1.43930i
$342$	4.98748	+	16.1731i	0.269692	+	0.874540i
$343$			17.0981i			0.923209i
$344$	−0.581900			−0.0313739
$345$	0.425122	−	0.938906i	0.0228878	−	0.0505490i
$346$	−15.9489			−0.857420
$347$			20.1749i			1.08304i	0.840687	+	0.541522i	$0.182152\pi$
$347$			20.1749i			1.08304i	−0.840687	+	0.541522i	$0.817848\pi$
$348$	−3.83502	+	5.19588i	−0.205579	+	0.278529i
$349$	−16.0548			−0.859395			−0.429697	−	0.902973i	$-0.641380\pi$
$349$	−16.0548			−0.859395			−0.429697	+	0.902973i	$0.641380\pi$
$350$	−2.92479	−	6.52601i	−0.156337	−	0.348830i
$351$	−10.5674	−	3.69896i	−0.564047	−	0.197436i
$352$	−6.14209			−0.327375
$353$		−	32.4059i		−	1.72479i	−0.506233	−	0.862397i	$-0.668962\pi$
$353$		−	32.4059i		−	1.72479i	0.506233	−	0.862397i	$-0.331038\pi$
$354$	7.52174	+	5.55170i	0.399776	+	0.295070i
$355$	2.35265	−	0.503090i	0.124865	−	0.0267013i
$356$	−6.18921			−0.328027
$357$	−1.37875	+	1.86800i	−0.0729712	+	0.0988652i
$358$	1.03414			0.0546560
$359$			13.4229i			0.708434i	0.935163	+	0.354217i	$0.115253\pi$
$359$			13.4229i			0.708434i	−0.935163	+	0.354217i	$0.884747\pi$
$360$	−5.85522	+	3.27360i	−0.308597	+	0.172534i
$361$	12.8271			0.675109
$362$			1.53891i			0.0808831i
$363$	−27.4890	+	37.2436i	−1.44280	+	1.95478i
$364$		−	3.08183i		−	0.161532i
$365$	−1.47131	−	6.88040i	−0.0770117	−	0.360137i
$366$	13.5455	+	9.99774i	0.708032	+	0.522590i
$367$	31.8055			1.66023			0.830116	−	0.557590i	$-0.188274\pi$
$367$	31.8055			1.66023			0.830116	+	0.557590i	$0.188274\pi$
$368$		−	0.266117i		−	0.0138723i
$369$	−9.51727	+	2.93495i	−0.495449	+	0.152788i
$370$	3.67249	+	17.1740i	0.190924	+	0.892834i
$371$	8.69451			0.451397
$372$	−2.42663	−	9.33335i	−0.125815	−	0.483912i
$373$		−	23.7216i		−	1.22826i	−0.789206	−	0.614128i	$-0.789508\pi$
$373$		−	23.7216i		−	1.22826i	0.789206	−	0.614128i	$-0.210492\pi$
$374$			5.75628i			0.297650i
$375$	−19.3648	−	0.0742023i	−0.999993	−	0.00383179i
$376$	−4.74525			−0.244718
$377$	−8.03371			−0.413757
$378$	−2.45538	+	7.01468i	−0.126291	+	0.360796i
$379$	−6.39563			−0.328521			−0.164261	−	0.986417i	$-0.552524\pi$
$379$	−6.39563			−0.328521			−0.164261	+	0.986417i	$0.552524\pi$
$380$	2.63793	+	12.3360i	0.135323	+	0.632823i
$381$	0.743211	−	1.00694i	0.0380758	−	0.0515871i
$382$		−	1.04692i		−	0.0535653i
$383$			8.99421i			0.459583i	0.973240	+	0.229791i	$0.0738044\pi$
$383$			8.99421i			0.459583i	−0.973240	+	0.229791i	$0.926196\pi$
$384$	−1.02858	+	1.39357i	−0.0524893	+	0.0711152i
$385$	−19.2095	+	4.10776i	−0.979007	+	0.209351i
$386$		−	21.9599i		−	1.11773i
$387$	0.514436	+	1.66818i	0.0261503	+	0.0847983i
$388$			10.6856i			0.542477i
$389$	18.6693			0.946569			0.473285	−	0.880910i	$-0.343068\pi$
$389$	18.6693			0.946569			0.473285	+	0.880910i	$0.343068\pi$
$390$	−7.60212	−	3.44211i	−0.384948	−	0.174298i
$391$	−0.249401			−0.0126127
$392$	4.95427			0.250229
$393$	4.69976	+	3.46884i	0.237071	+	0.174980i
$394$			23.2946i			1.17356i
$395$	−4.53707	+	0.970207i	−0.228285	+	0.0488164i
$396$	5.43000	+	17.6080i	0.272868	+	0.884837i
$397$		−	1.03561i		−	0.0519759i	−0.999662	−	0.0259879i	$-0.991727\pi$
$397$		−	1.03561i		−	0.0519759i	0.999662	−	0.0259879i	$-0.00827315\pi$
$398$			5.07538i			0.254406i
$399$	11.2448	+	8.29962i	0.562942	+	0.415501i
$400$	−4.56272	+	2.04489i	−0.228136	+	0.102245i
$401$	−23.1541			−1.15626			−0.578130	−	0.815945i	$-0.696217\pi$
$401$	−23.1541			−1.15626			−0.578130	+	0.815945i	$0.696217\pi$
$402$	−13.7999	−	10.1856i	−0.688279	−	0.508010i
$403$	7.54909	−	9.32387i	0.376047	−	0.464455i
$404$		−	12.6932i		−	0.631510i
$405$	14.5611	+	13.8916i	0.723545	+	0.690277i
$406$			5.33280i			0.264662i
$407$	48.2405			2.39119
$408$	1.30603	+	0.963966i	0.0646582	+	0.0477235i
$409$			23.5176i			1.16287i	0.813593	+	0.581435i	$0.197509\pi$
$409$			23.5176i			1.16287i	−0.813593	+	0.581435i	$0.802491\pi$
$410$	−7.25928	+	1.55233i	−0.358510	+	0.0766639i
$411$	−26.1640	−	19.3113i	−1.29058	−	0.952558i
$412$			14.3190i			0.705447i
$413$	7.71994			0.379873
$414$	−0.762899	+	0.235264i	−0.0374944	+	0.0115626i
$415$	−18.2586	+	3.90442i	−0.896280	+	0.191661i
$416$	−2.15469			−0.105642
$417$	−5.49627	−	4.05673i	−0.269153	−	0.198659i
$418$	34.6509			1.69483
$419$		−	29.4500i		−	1.43873i	−0.694633	−	0.719364i	$-0.744433\pi$
$419$		−	29.4500i		−	1.43873i	0.694633	−	0.719364i	$-0.255567\pi$
$420$	−2.28489	+	5.04631i	−0.111491	+	0.246234i
$421$	−25.1408			−1.22529			−0.612644	−	0.790359i	$-0.709894\pi$
$421$	−25.1408			−1.22529			−0.612644	+	0.790359i	$0.709894\pi$
$422$	18.6497			0.907854
$423$	4.19510	+	13.6036i	0.203973	+	0.661429i
$424$		−	6.07885i		−	0.295215i
$425$	1.91644	+	4.27611i	0.0929612	+	0.207422i
$426$	−1.49937	−	1.10667i	−0.0726447	−	0.0536182i
$427$	13.9024			0.672783
$428$	1.96466			0.0949656
$429$	−13.6125	+	18.4429i	−0.657217	+	0.890432i
$430$	0.272090	+	1.27240i	0.0131214	+	0.0613606i
$431$			38.4053i			1.84992i	0.380068	+	0.924959i	$0.375901\pi$
$431$			38.4053i			1.84992i	−0.380068	+	0.924959i	$0.624099\pi$
$432$	4.90438	+	1.71670i	0.235962	+	0.0825948i
$433$	−25.1896			−1.21054			−0.605268	−	0.796022i	$-0.706934\pi$
$433$	−25.1896			−1.21054			−0.605268	+	0.796022i	$0.706934\pi$
$434$	−6.18921	−	5.01111i	−0.297092	−	0.240541i
$435$	13.1547	+	5.95623i	0.630720	+	0.285580i
$436$	−10.8671			−0.520439
$437$			1.50131i			0.0718175i
$438$	−3.23649	+	4.38497i	−0.154646	+	0.209522i
$439$	−0.444962			−0.0212369			−0.0106184	−	0.999944i	$-0.503380\pi$
$439$	−0.444962			−0.0212369			−0.0106184	+	0.999944i	$0.503380\pi$
$440$	2.87198	+	13.4305i	0.136916	+	0.640274i
$441$	−4.37989	−	14.2028i	−0.208566	−	0.676325i
$442$			2.01934i			0.0960504i
$443$	−22.7564			−1.08119			−0.540596	−	0.841283i	$-0.681801\pi$
$443$	−22.7564			−1.08119			−0.540596	+	0.841283i	$0.681801\pi$
$444$	8.07852	−	10.9452i	0.383390	−	0.519436i
$445$	2.89401	+	13.5335i	0.137189	+	0.641551i
$446$	−7.26279			−0.343903
$447$	−14.6525	−	10.8148i	−0.693039	−	0.511524i
$448$			1.43029i			0.0675748i
$449$	−27.0215			−1.27522			−0.637612	−	0.770358i	$-0.720078\pi$
$449$	−27.0215			−1.27522			−0.637612	+	0.770358i	$0.720078\pi$
$450$	9.89599	+	11.2725i	0.466502	+	0.531391i
$451$			20.3908i			0.960166i
$452$	18.5351			0.871818
$453$	11.9697	+	8.83470i	0.562386	+	0.415091i
$454$	−16.5730			−0.777808
$455$	−6.73883	+	1.44103i	−0.315921	+	0.0675566i
$456$	5.80276	−	7.86188i	0.271739	−	0.368166i
$457$	4.77341			0.223291			0.111645	−	0.993748i	$-0.464388\pi$
$457$	4.77341			0.223291			0.111645	+	0.993748i	$0.464388\pi$
$458$		−	19.1781i		−	0.896133i
$459$	1.60887	−	4.59631i	0.0750954	−	0.214538i
$460$	−0.581900	+	0.124434i	−0.0271312	+	0.00580175i
$461$	23.4023			1.08995			0.544976	−	0.838451i	$-0.316539\pi$
$461$	23.4023			1.08995			0.544976	+	0.838451i	$0.316539\pi$
$462$	12.2425	+	9.03601i	0.569570	+	0.420393i
$463$	32.0488			1.48943			0.744717	−	0.667380i	$-0.232584\pi$
$463$	32.0488			1.48943			0.744717	+	0.667380i	$0.232584\pi$
$464$	3.72847			0.173090
$465$	−19.2739	+	9.67033i	−0.893808	+	0.448451i
$466$	−19.6843			−0.911858
$467$	−16.2069			−0.749965			−0.374983	−	0.927032i	$-0.622351\pi$
$467$	−16.2069			−0.749965			−0.374983	+	0.927032i	$0.622351\pi$
$468$	1.90488	+	6.17702i	0.0880532	+	0.285533i
$469$	−14.1636			−0.654013
$470$	2.21883	+	10.3761i	0.102347	+	0.478614i
$471$	−12.5607	−	9.27088i	−0.578765	−	0.427180i
$472$		−	5.39747i		−	0.248439i
$473$	3.57408			0.164337
$474$	2.89153	+	2.13420i	0.132812	+	0.0980272i
$475$	25.7408	−	11.5364i	1.18107	−	0.529325i
$476$	1.34045			0.0614392
$477$	−17.4267	+	5.37409i	−0.797915	+	0.246063i
$478$	2.93174			0.134095
$479$		−	31.7707i		−	1.45164i	−0.687886	−	0.725819i	$-0.741461\pi$
$479$		−	31.7707i		−	1.45164i	0.687886	−	0.725819i	$-0.258539\pi$
$480$	3.52817	+	1.59750i	0.161038	+	0.0729155i
$481$	16.9231			0.771628
$482$			26.2006i			1.19340i
$483$	−0.391501	+	0.530426i	−0.0178139	+	0.0241352i
$484$	26.7253			1.21479
$485$	23.3654	−	4.99646i	1.06097	−	0.226877i
$486$	0.585621	−	15.5775i	0.0265643	−	0.706608i
$487$	−36.9394			−1.67389			−0.836943	−	0.547290i	$-0.815659\pi$
$487$	−36.9394			−1.67389			−0.836943	+	0.547290i	$0.815659\pi$
$488$		−	9.71998i		−	0.440003i
$489$	−19.8503	−	14.6513i	−0.897663	−	0.662554i
$490$	−2.31657	−	10.8332i	−0.104652	−	0.489393i
$491$	−17.2323			−0.777681			−0.388840	−	0.921305i	$-0.627124\pi$
$491$	−17.2323			−0.777681			−0.388840	+	0.921305i	$0.627124\pi$
$492$	4.62643	+	3.41471i	0.208576	+	0.153947i
$493$		−	3.49427i		−	0.157374i
$494$	12.1558			0.546915
$495$	35.9633	−	20.1068i	1.61643	−	0.903731i
$496$	−3.50356	+	4.32724i	−0.157315	+	0.194299i
$497$	−1.53888			−0.0690282
$498$	11.6364	+	8.58872i	0.521441	+	0.384870i
$499$		−	16.0253i		−	0.717392i	−0.933454	−	0.358696i	$-0.883221\pi$
$499$		−	16.0253i		−	0.717392i	0.933454	−	0.358696i	$-0.116779\pi$
$500$	6.60491	+	9.02082i	0.295381	+	0.403423i
$501$	14.1601	+	10.4514i	0.632629	+	0.466936i
$502$	−16.0306			−0.715482
$503$	−26.5562			−1.18408			−0.592042	−	0.805907i	$-0.701678\pi$
$503$	−26.5562			−1.18408			−0.592042	+	0.805907i	$0.701678\pi$
$504$	4.10032	−	1.26447i	0.182643	−	0.0563238i
$505$	−27.7553	+	5.93520i	−1.23510	+	0.264113i
$506$			1.63452i			0.0726631i
$507$	8.59613	−	11.6465i	0.381768	−	0.517238i
$508$	−0.722563			−0.0320585
$509$	−38.8908			−1.72380			−0.861901	−	0.507076i	$-0.830726\pi$
$509$	−38.8908			−1.72380			−0.861901	+	0.507076i	$0.830726\pi$
$510$	1.49715	−	3.30655i	0.0662950	−	0.146417i
$511$			4.50051i			0.199091i
$512$	1.00000			0.0441942
$513$	−27.6683	−	9.68484i	−1.22159	−	0.427596i
$514$	−18.9905			−0.837634
$515$	31.3104	−	6.69542i	1.37970	−	0.295036i
$516$	0.598528	−	0.810917i	0.0263487	−	0.0356986i
$517$	29.1458			1.28183
$518$		−	11.2336i		−	0.493577i
$519$	16.4047	−	22.2259i	0.720086	−	0.975610i
$520$	1.00751	+	4.71151i	0.0441823	+	0.206614i
$521$			7.52553i			0.329700i	0.986319	+	0.164850i	$0.0527139\pi$
$521$			7.52553i			0.329700i	−0.986319	+	0.164850i	$0.947286\pi$
$522$	−3.29621	−	10.6887i	−0.144271	−	0.467833i
$523$	16.6320			0.727268			0.363634	−	0.931542i	$-0.381536\pi$
$523$	16.6320			0.727268			0.363634	+	0.931542i	$0.381536\pi$
$524$		−	3.37246i		−	0.147327i
$525$	12.1028	+	2.63660i	0.528210	+	0.115071i
$526$		−	21.8884i		−	0.954378i
$527$	4.05543	+	3.28349i	0.176657	+	0.143031i
$528$	6.31761	−	8.55943i	0.274939	−	0.372501i
$529$	22.9292			0.996921
$530$	−13.2922	+	2.84241i	−0.577377	+	0.123466i
$531$	−15.4734	+	4.77170i	−0.671486	+	0.207074i
$532$		−	8.06904i		−	0.349837i
$533$			7.15324i			0.309841i
$534$	6.36607	−	8.62508i	0.275487	−	0.373244i
$535$	−0.918657	−	4.29600i	−0.0397170	−	0.185732i
$536$			9.90260i			0.427727i
$537$	−1.06369	+	1.44115i	−0.0459017	+	0.0621900i
$538$	21.2950			0.918094
$539$	−30.4296			−1.31070
$540$	1.46055	−	11.5268i	0.0628522	−	0.496034i
$541$	39.8624			1.71382			0.856909	−	0.515467i	$-0.172382\pi$
$541$	39.8624			1.71382			0.856909	+	0.515467i	$0.172382\pi$
$542$		−	11.2154i		−	0.481741i
$543$	−2.14457	−	1.58288i	−0.0920323	−	0.0679280i
$544$		−	0.937186i		−	0.0401815i
$545$	5.08134	+	23.7623i	0.217661	+	1.01787i
$546$	4.29474	+	3.16989i	0.183798	+	0.135659i
$547$			37.8837i			1.61979i	0.586576	+	0.809894i	$0.300476\pi$
$547$			37.8837i			1.61979i	−0.586576	+	0.809894i	$0.699524\pi$
$548$			18.7748i			0.802021i
$549$	−27.8650	+	8.59308i	−1.18925	+	0.366744i
$550$	28.0247	−	12.5599i	1.19498	−	0.535557i
$551$	−21.0344			−0.896094
$552$	0.370852	+	0.273721i	0.0157845	+	0.0116504i
$553$	2.96772			0.126200
$554$	−11.5071			−0.488891
$555$	−27.7106	−	12.5469i	−1.17625	−	0.532586i
$556$			3.94403i			0.167264i
$557$			46.5143i			1.97087i	0.170040	+	0.985437i	$0.445610\pi$
$557$			46.5143i			1.97087i	−0.170040	+	0.985437i	$0.554390\pi$
$558$	15.5026	+	6.21839i	0.656279	+	0.263245i
$559$	1.25381			0.0530307
$560$	3.12752	−	0.668789i	0.132162	−	0.0282615i
$561$	−8.02177	−	5.92077i	−0.338679	−	0.249975i
$562$		−	23.5749i		−	0.994446i
$563$	−34.5665			−1.45681			−0.728403	−	0.685149i	$-0.759737\pi$
$563$	−34.5665			−1.45681			−0.728403	+	0.685149i	$0.759737\pi$
$564$	4.88085	−	6.61283i	0.205521	−	0.278450i
$565$	−8.66683	−	40.5295i	−0.364616	−	1.70509i
$566$		−	16.0120i		−	0.673036i
$567$	−7.24989	−	10.6369i	−0.304467	−	0.446706i
$568$			1.07592i			0.0451447i
$569$	1.58064			0.0662640			0.0331320	−	0.999451i	$-0.489452\pi$
$569$	1.58064			0.0662640			0.0331320	+	0.999451i	$0.489452\pi$
$570$	−19.9044	−	9.01237i	−0.833702	−	0.377486i
$571$			42.0954i			1.76164i	0.473455	+	0.880818i	$0.343007\pi$
$571$			42.0954i			1.76164i	−0.473455	+	0.880818i	$0.656993\pi$
$572$	13.2343			0.553354
$573$	1.45896	+	1.07684i	0.0609489	+	0.0449856i
$574$	4.74834			0.198192
$575$	0.544181	+	1.21422i	0.0226939	+	0.0506363i
$576$	−0.884063	−	2.86678i	−0.0368360	−	0.119449i
$577$		−	18.4249i		−	0.767037i	−0.923533	−	0.383519i	$-0.874712\pi$
$577$		−	18.4249i		−	0.767037i	0.923533	−	0.383519i	$-0.125288\pi$
$578$	16.1217			0.670574
$579$	30.6027	+	22.5875i	1.27180	+	0.938703i
$580$	−1.74340	−	8.15280i	−0.0723906	−	0.338527i
$581$	11.9431			0.495482
$582$	−14.8910	−	10.9909i	−0.617254	−	0.455588i
$583$			37.3369i			1.54634i
$584$	3.14657			0.130206
$585$	12.6162	−	7.05359i	0.521615	−	0.291630i
$586$	−12.2492			−0.506011
$587$			14.3651i			0.592912i	0.955047	+	0.296456i	$0.0958047\pi$
$587$			14.3651i			0.592912i	−0.955047	+	0.296456i	$0.904195\pi$
$588$	−5.09585	+	6.90412i	−0.210149	+	0.284721i
$589$	19.7655	−	24.4124i	0.814424	−	1.00589i
$590$	−11.8023	+	2.52380i	−0.485892	+	0.103903i
$591$	−32.4626	−	23.9602i	−1.33533	−	0.985593i
$592$	−7.85409			−0.322801
$593$	14.0337			0.576295			0.288148	−	0.957586i	$-0.406961\pi$
$593$	14.0337			0.576295			0.288148	+	0.957586i	$0.406961\pi$
$594$	−30.1232	−	10.5441i	−1.23597	−	0.432631i
$595$	−0.626779	−	2.93106i	−0.0256954	−	0.120162i
$596$			10.5144i			0.430686i
$597$	−7.07288	−	5.22041i	−0.289474	−	0.213657i
$598$			0.573399i			0.0234480i
$599$		−	23.7354i		−	0.969800i	−0.874569	−	0.484900i	$-0.838856\pi$
$599$		−	23.7354i		−	0.969800i	0.874569	−	0.484900i	$-0.161144\pi$
$600$	1.84340	−	8.46179i	0.0752567	−	0.345451i
$601$			41.9092i			1.70951i	0.519029	+	0.854756i	$0.326293\pi$
$601$			41.9092i			1.70951i	−0.519029	+	0.854756i	$0.673707\pi$
$602$		−	0.832285i		−	0.0339214i
$603$	28.3886	−	8.75452i	1.15607	−	0.356512i
$604$		−	8.58926i		−	0.349492i
$605$	−12.4965	−	58.4385i	−0.508055	−	2.37586i
$606$	17.6888	+	13.0559i	0.718559	+	0.530360i
$607$		−	27.8920i		−	1.13210i	−0.824370	−	0.566051i	$-0.808470\pi$
$607$		−	27.8920i		−	1.13210i	0.824370	−	0.566051i	$-0.191530\pi$
$608$	−5.64155			−0.228795
$609$	−7.43161	−	5.48519i	−0.301144	−	0.222271i
$610$	−21.2540	+	4.54496i	−0.860550	+	0.184020i
$611$	10.2245			0.413641
$612$	−2.68671	+	0.828531i	−0.108604	+	0.0334914i
$613$	1.56857			0.0633540			0.0316770	−	0.999498i	$-0.489915\pi$
$613$	1.56857			0.0633540			0.0316770	+	0.999498i	$0.489915\pi$
$614$		−	28.8870i		−	1.16579i
$615$	5.30345	−	11.7130i	0.213856	−	0.472313i
$616$		−	8.78497i		−	0.353957i
$617$	−46.7418			−1.88175			−0.940877	−	0.338749i	$-0.889996\pi$
$617$	−46.7418			−1.88175			−0.940877	+	0.338749i	$0.889996\pi$
$618$	−19.9545	−	14.7282i	−0.802688	−	0.592455i
$619$		−	29.9363i		−	1.20324i	−0.798782	−	0.601621i	$-0.794522\pi$
$619$		−	29.9363i		−	1.20324i	0.798782	−	0.601621i	$-0.205478\pi$
$620$	11.1003	+	5.63763i	0.445800	+	0.226413i
$621$	0.456843	−	1.30514i	0.0183325	−	0.0523734i
$622$		−	8.54298i		−	0.342542i
$623$		−	8.85236i		−	0.354662i
$624$	2.21626	−	3.00271i	0.0887215	−	0.120204i
$625$	16.6368	−	18.6606i	0.665473	−	0.746422i
$626$	−31.8575			−1.27328
$627$	−35.6411	+	48.2884i	−1.42337	+	1.92845i
$628$			9.01331i			0.359670i
$629$			7.36074i			0.293492i
$630$	−4.68219	−	8.37465i	−0.186543	−	0.333654i
$631$			30.7486i			1.22408i	0.790826	+	0.612041i	$0.209651\pi$
$631$			30.7486i			1.22408i	−0.790826	+	0.612041i	$0.790349\pi$
$632$		−	2.07491i		−	0.0825355i
$633$	−19.1827	+	25.9897i	−0.762442	+	1.03300i
$634$	7.46567			0.296500
$635$	0.337863	+	1.57998i	0.0134077	+	0.0626996i
$636$	8.47129	+	6.25256i	0.335909	+	0.247930i
$637$	−10.6749			−0.422956
$638$	−22.9006			−0.906645
$639$	3.08443	−	0.951183i	0.122018	−	0.0376282i
$640$	−0.467590	−	2.18663i	−0.0184831	−	0.0864342i
$641$	18.5868			0.734134			0.367067	−	0.930195i	$-0.380362\pi$
$641$	18.5868			0.734134			0.367067	+	0.930195i	$0.380362\pi$
$642$	−2.02081	+	2.73789i	−0.0797549	+	0.108056i
$643$	−12.1089			−0.477527			−0.238763	−	0.971078i	$-0.576742\pi$
$643$	−12.1089			−0.477527			−0.238763	+	0.971078i	$0.576742\pi$
$644$	0.380624			0.0149987
$645$	−2.05304	−	0.929584i	−0.0808385	−	0.0366023i
$646$			5.28718i			0.208021i
$647$		−	36.0790i		−	1.41841i	−0.705001	−	0.709206i	$-0.749054\pi$
$647$		−	36.0790i		−	1.41841i	0.705001	−	0.709206i	$-0.250946\pi$
$648$	−7.43686	+	5.06883i	−0.292148	+	0.199122i
$649$			33.1518i			1.30132i
$650$	9.83124	−	4.40611i	0.385613	−	0.172822i
$651$	13.3494	−	3.47078i	0.523204	−	0.136031i
$652$			14.2442i			0.557848i
$653$	18.9900			0.743136			0.371568	−	0.928406i	$-0.378820\pi$
$653$	18.9900			0.743136			0.371568	+	0.928406i	$0.378820\pi$
$654$	11.1776	−	15.1440i	0.437080	−	0.592179i
$655$	−7.37434	+	1.57693i	−0.288139	+	0.0616158i
$656$		−	3.31985i		−	0.129618i
$657$	−2.78177	−	9.02054i	−0.108527	−	0.351925i
$658$		−	6.78708i		−	0.264588i
$659$			42.3138i			1.64831i	0.566362	+	0.824157i	$0.308350\pi$
$659$			42.3138i			1.64831i	−0.566362	+	0.824157i	$0.691650\pi$
$660$	−21.6704	−	9.81199i	−0.843518	−	0.381931i
$661$	−8.71066			−0.338805			−0.169403	−	0.985547i	$-0.554184\pi$
$661$	−8.71066			−0.338805			−0.169403	+	0.985547i	$0.554184\pi$
$662$		−	34.6148i		−	1.34534i
$663$	−2.81409	−	2.07705i	−0.109290	−	0.0806659i
$664$		−	8.35010i		−	0.324047i
$665$	−17.6440	+	3.77300i	−0.684206	+	0.146311i
$666$	6.94351	+	22.5159i	0.269055	+	0.872475i
$667$		−	0.992210i		−	0.0384185i
$668$		−	10.1611i		−	0.393144i
$669$	7.47033	−	10.1212i	0.288820	−	0.391308i
$670$	21.6533	−	4.63035i	0.836542	−	0.178886i
$671$			59.7010i			2.30473i
$672$	−1.99320	−	1.47116i	−0.0768895	−	0.0567513i
$673$	19.9893			0.770533			0.385266	−	0.922805i	$-0.374110\pi$
$673$	19.9893			0.770533			0.385266	+	0.922805i	$0.374110\pi$
$674$	24.5024			0.943795
$675$	−25.8878	+	2.19612i	−0.996421	+	0.0845286i
$676$	−8.35731			−0.321435
$677$			19.5949i			0.753092i	0.926398	+	0.376546i	$0.122888\pi$
$677$			19.5949i			0.753092i	−0.926398	+	0.376546i	$0.877112\pi$
$678$	−19.0648	+	25.8299i	−0.732178	+	0.991993i
$679$	−15.2834			−0.586524
$680$	−2.04928	+	0.438218i	−0.0785863	+	0.0168049i
$681$	17.0466	−	23.0956i	0.653226	−	0.885024i
$682$	21.5192	−	26.5783i	0.824013	−	1.01774i
$683$	−18.6472			−0.713516			−0.356758	−	0.934197i	$-0.616118\pi$
$683$	−18.6472			−0.713516			−0.356758	+	0.934197i	$0.616118\pi$
$684$	4.98748	+	16.1731i	0.190701	+	0.618393i
$685$	41.0537	−	8.77892i	1.56858	−	0.335425i
$686$			17.0981i			0.652807i
$687$	26.7260	+	19.7261i	1.01966	+	0.752599i
$688$	−0.581900			−0.0221847
$689$			13.0980i			0.498996i
$690$	0.425122	−	0.938906i	0.0161841	−	0.0357436i
$691$	12.0491			0.458371			0.229186	−	0.973383i	$-0.426394\pi$
$691$	12.0491			0.458371			0.229186	+	0.973383i	$0.426394\pi$
$692$	−15.9489			−0.606288
$693$	−25.1846	+	7.76647i	−0.956683	+	0.295024i
$694$			20.1749i			0.765827i
$695$	8.62414	−	1.84419i	0.327132	−	0.0699540i
$696$	−3.83502	+	5.19588i	−0.145366	+	0.196949i
$697$	−3.11131			−0.117849
$698$	−16.0548			−0.607684
$699$	20.2468	−	27.4314i	0.765805	−	1.03755i
$700$	−2.92479	−	6.52601i	−0.110547	−	0.246660i
$701$		−	19.5578i		−	0.738689i	−0.929293	−	0.369344i	$-0.879582\pi$
$701$		−	19.5578i		−	0.738689i	0.929293	−	0.369344i	$-0.120418\pi$
$702$	−10.5674	−	3.69896i	−0.398841	−	0.139608i
$703$	44.3092			1.67115
$704$	−6.14209			−0.231489
$705$	−16.7421	−	7.58053i	−0.630542	−	0.285499i
$706$		−	32.4059i		−	1.21961i
$707$	18.1549			0.682786
$708$	7.52174	+	5.55170i	0.282684	+	0.208646i
$709$			12.5711i			0.472118i	0.971739	+	0.236059i	$0.0758558\pi$
$709$			12.5711i			0.472118i	−0.971739	+	0.236059i	$0.924144\pi$
$710$	2.35265	−	0.503090i	0.0882932	−	0.0188806i
$711$	−5.94832	+	1.83435i	−0.223079	+	0.0687936i
$712$	−6.18921			−0.231950
$713$	1.15155	+	0.932358i	0.0431260	+	0.0349171i
$714$	−1.37875	+	1.86800i	−0.0515984	+	0.0699082i
$715$	−6.18823	−	28.9386i	−0.231427	−	1.08224i
$716$	1.03414			0.0386477
$717$	−3.01552	+	4.08558i	−0.112617	+	0.152579i
$718$			13.4229i			0.500939i
$719$	−29.9896			−1.11842			−0.559212	−	0.829025i	$-0.688896\pi$
$719$	−29.9896			−1.11842			−0.559212	+	0.829025i	$0.688896\pi$
$720$	−5.85522	+	3.27360i	−0.218211	+	0.122000i
$721$	−20.4803			−0.762727
$722$	12.8271			0.477374
$723$	−36.5123	−	26.9493i	−1.35791	−	1.00225i
$724$			1.53891i			0.0571930i
$725$	−17.0120	+	7.62433i	−0.631809	+	0.283161i
$726$	−27.4890	+	37.2436i	−1.02021	+	1.38224i
$727$		−	7.68466i		−	0.285008i	−0.989794	−	0.142504i	$-0.954485\pi$
$727$		−	7.68466i		−	0.285008i	0.989794	−	0.142504i	$-0.0455154\pi$
$728$		−	3.08183i		−	0.114220i
$729$	21.1059	+	16.8387i	0.781699	+	0.623655i
$730$	−1.47131	−	6.88040i	−0.0544555	−	0.254655i
$731$			0.545348i			0.0201704i
$732$	13.5455	+	9.99774i	0.500654	+	0.369527i
$733$		−	36.7050i		−	1.35573i	−0.735187	−	0.677865i	$-0.762906\pi$
$733$		−	36.7050i		−	1.35573i	0.735187	−	0.677865i	$-0.237094\pi$
$734$	31.8055			1.17396
$735$	17.4795	+	7.91445i	0.644742	+	0.291929i
$736$		−	0.266117i		−	0.00980920i
$737$		−	60.8227i		−	2.24043i
$738$	−9.51727	+	2.93495i	−0.350336	+	0.108037i
$739$			2.40715i			0.0885485i	0.999019	+	0.0442742i	$0.0140975\pi$
$739$			2.40715i			0.0885485i	−0.999019	+	0.0442742i	$0.985902\pi$
$740$	3.67249	+	17.1740i	0.135003	+	0.631329i
$741$	−12.5031	+	16.9399i	−0.459315	+	0.622303i
$742$	8.69451			0.319186
$743$		−	18.2769i		−	0.670516i	−0.942126	−	0.335258i	$-0.891177\pi$
$743$		−	18.2769i		−	0.670516i	0.942126	−	0.335258i	$-0.108823\pi$
$744$	−2.42663	−	9.33335i	−0.0889645	−	0.342177i
$745$	22.9911	−	4.91641i	0.842328	−	0.180123i
$746$		−	23.7216i		−	0.868508i
$747$	−23.9379	+	7.38202i	−0.875843	+	0.270094i
$748$			5.75628i			0.210471i
$749$			2.81004i			0.102677i
$750$	−19.3648	−	0.0742023i	−0.707102	−	0.00270949i
$751$	−3.72662			−0.135986			−0.0679932	−	0.997686i	$-0.521660\pi$
$751$	−3.72662			−0.135986			−0.0679932	+	0.997686i	$0.521660\pi$
$752$	−4.74525			−0.173041
$753$	16.4887	−	22.3398i	0.600883	−	0.814107i
$754$	−8.03371			−0.292570
$755$	−18.7815	+	4.01625i	−0.683530	+	0.146166i
$756$	−2.45538	+	7.01468i	−0.0893012	+	0.255121i
$757$	−29.0108			−1.05442			−0.527208	−	0.849736i	$-0.676761\pi$
$757$	−29.0108			−1.05442			−0.527208	+	0.849736i	$0.676761\pi$
$758$	−6.39563			−0.232300
$759$	−2.27781	−	1.68122i	−0.0826792	−	0.0610245i
$760$	2.63793	+	12.3360i	0.0956878	+	0.447473i
$761$	23.8506			0.864583			0.432291	−	0.901734i	$-0.357705\pi$
$761$	23.8506			0.864583			0.432291	+	0.901734i	$0.357705\pi$
$762$	0.743211	−	1.00694i	0.0269237	−	0.0364776i
$763$		−	15.5431i		−	0.562697i
$764$		−	1.04692i		−	0.0378764i
$765$	3.06797	+	5.48742i	0.110923	+	0.198398i
$766$			8.99421i			0.324974i
$767$			11.6299i			0.419930i
$768$	−1.02858	+	1.39357i	−0.0371155	+	0.0502861i
$769$	−3.98799			−0.143811			−0.0719054	−	0.997411i	$-0.522908\pi$
$769$	−3.98799			−0.143811			−0.0719054	+	0.997411i	$0.522908\pi$
$770$	−19.2095	+	4.10776i	−0.692262	+	0.148033i
$771$	19.5331	−	26.4645i	0.703469	−	0.953096i
$772$		−	21.9599i		−	0.790355i
$773$		−	33.0339i		−	1.18815i	−0.804411	−	0.594074i	$-0.797519\pi$
$773$		−	33.0339i		−	1.18815i	0.804411	−	0.594074i	$-0.202481\pi$
$774$	0.514436	+	1.66818i	0.0184910	+	0.0599615i
$775$	7.13702	−	26.9084i	0.256369	−	0.966579i
$776$			10.6856i			0.383589i
$777$	15.6548	+	11.5546i	0.561613	+	0.414520i
$778$	18.6693			0.669326
$779$			18.7291i			0.671039i
$780$	−7.60212	−	3.44211i	−0.272199	−	0.123247i
$781$		−	6.60841i		−	0.236468i
$782$	−0.249401			−0.00891856
$783$	18.2859	+	6.40067i	0.653483	+	0.228741i
$784$	4.95427			0.176938
$785$	19.7088	−	4.21453i	0.703437	−	0.150423i
$786$	4.69976	+	3.46884i	0.167635	+	0.123729i
$787$	−3.70275			−0.131989			−0.0659944	−	0.997820i	$-0.521022\pi$
$787$	−3.70275			−0.131989			−0.0659944	+	0.997820i	$0.521022\pi$
$788$			23.2946i			0.829835i
$789$	30.5029	+	22.5138i	1.08593	+	0.801514i
$790$	−4.53707	+	0.970207i	−0.161422	+	0.0345184i
$791$			26.5106i			0.942607i
$792$	5.43000	+	17.6080i	0.192947	+	0.625674i
$793$			20.9435i			0.743727i
$794$		−	1.03561i		−	0.0367525i
$795$	9.71096	−	21.4472i	0.344412	−	0.760655i
$796$			5.07538i			0.179892i
$797$			17.0487i			0.603897i	0.953324	+	0.301949i	$0.0976371\pi$
$797$			17.0487i			0.603897i	−0.953324	+	0.301949i	$0.902363\pi$
$798$	11.2448	+	8.29962i	0.398060	+	0.293804i
$799$			4.44718i			0.157330i
$800$	−4.56272	+	2.04489i	−0.161316	+	0.0722979i
$801$	5.47165	+	17.7431i	0.193331	+	0.626922i
$802$	−23.1541			−0.817599
$803$	−19.3266			−0.682019
$804$	−13.7999	−	10.1856i	−0.486687	−	0.359218i
$805$	−0.177976	−	0.832285i	−0.00627283	−	0.0293342i
$806$	7.54909	−	9.32387i	0.265905	−	0.328419i
$807$	−21.9036	+	29.6761i	−0.771042	+	1.04465i
$808$		−	12.6932i		−	0.446545i
$809$	12.2057			0.429131			0.214565	−	0.976710i	$-0.431167\pi$
$809$	12.2057			0.429131			0.214565	+	0.976710i	$0.431167\pi$
$810$	14.5611	+	13.8916i	0.511624	+	0.488099i
$811$	−8.81711			−0.309611			−0.154805	−	0.987945i	$-0.549475\pi$
$811$	−8.81711			−0.309611			−0.154805	+	0.987945i	$0.549475\pi$
$812$			5.33280i			0.187144i
$813$	15.6294	+	11.5359i	0.548146	+	0.404580i
$814$	48.2405			1.69083
$815$	31.1469	−	6.66047i	1.09103	−	0.233306i
$816$	1.30603	+	0.963966i	0.0457203	+	0.0337456i
$817$	3.28282			0.114851
$818$			23.5176i			0.822274i
$819$	−8.83493	+	2.72453i	−0.308717	+	0.0952028i
$820$	−7.25928	+	1.55233i	−0.253505	+	0.0542096i
$821$	46.0522			1.60723			0.803617	−	0.595147i	$-0.202906\pi$
$821$	46.0522			1.60723			0.803617	+	0.595147i	$0.202906\pi$
$822$	−26.1640	−	19.3113i	−0.912575	−	0.673561i
$823$	49.1211			1.71225			0.856127	−	0.516765i	$-0.172864\pi$
$823$	49.1211			1.71225			0.856127	+	0.516765i	$0.172864\pi$
$824$			14.3190i			0.498826i
$825$	−11.3224	+	51.9731i	−0.394194	+	1.80947i
$826$	7.71994			0.268611
$827$		−	4.36099i		−	0.151646i	−0.997121	−	0.0758232i	$-0.975842\pi$
$827$		−	4.36099i		−	0.151646i	0.997121	−	0.0758232i	$-0.0241585\pi$
$828$	−0.762899	+	0.235264i	−0.0265126	+	0.00817600i
$829$		−	54.4132i		−	1.88985i	−0.327288	−	0.944925i	$-0.606135\pi$
$829$		−	54.4132i		−	1.88985i	0.327288	−	0.944925i	$-0.393865\pi$
$830$	−18.2586	+	3.90442i	−0.633766	+	0.135525i
$831$	11.8360	−	16.0360i	0.410585	−	0.556282i
$832$	−2.15469			−0.0747004
$833$		−	4.64307i		−	0.160873i
$834$	−5.49627	−	4.05673i	−0.190320	−	0.140473i
$835$	−22.2185	+	4.75122i	−0.768904	+	0.164423i
$836$	34.6509			1.19843
$837$	−24.6114	+	15.2079i	−0.850694	+	0.525661i
$838$		−	29.4500i		−	1.01733i
$839$			13.8190i			0.477084i	0.971132	+	0.238542i	$0.0766695\pi$
$839$			13.8190i			0.477084i	−0.971132	+	0.238542i	$0.923330\pi$
$840$	−2.28489	+	5.04631i	−0.0788360	+	0.174114i
$841$	−15.0985			−0.520637
$842$	−25.1408			−0.866409
$843$	32.8532	+	24.2485i	1.13152	+	0.835164i
$844$	18.6497			0.641950
$845$	3.90779	+	18.2744i	0.134432	+	0.628657i
$846$	4.19510	+	13.6036i	0.144231	+	0.467701i
$847$			38.2249i			1.31342i
$848$		−	6.07885i		−	0.208749i
$849$	22.3139	+	16.4696i	0.765810	+	0.565235i
$850$	1.91644	+	4.27611i	0.0657335	+	0.146670i
$851$			2.09011i			0.0716479i
$852$	−1.49937	−	1.10667i	−0.0513676	−	0.0379138i
$853$		−	3.77301i		−	0.129185i	−0.997912	−	0.0645927i	$-0.979425\pi$
$853$		−	3.77301i		−	0.129185i	0.997912	−	0.0645927i	$-0.0205748\pi$
$854$	13.9024			0.475730
$855$	33.0325	−	18.4682i	1.12969	−	0.631598i
$856$	1.96466			0.0671508
$857$	13.7021			0.468056			0.234028	−	0.972230i	$-0.424809\pi$
$857$	13.7021			0.468056			0.234028	+	0.972230i	$0.424809\pi$
$858$	−13.6125	+	18.4429i	−0.464723	+	0.629630i
$859$		−	8.73138i		−	0.297911i	−0.988844	−	0.148955i	$-0.952409\pi$
$859$		−	8.73138i		−	0.297911i	0.988844	−	0.148955i	$-0.0475911\pi$
$860$	0.272090	+	1.27240i	0.00927821	+	0.0433885i
$861$	−4.88403	+	6.61713i	−0.166447	+	0.225511i
$862$			38.4053i			1.30809i
$863$		−	51.8139i		−	1.76377i	−0.471468	−	0.881883i	$-0.656276\pi$
$863$		−	51.8139i		−	1.76377i	0.471468	−	0.881883i	$-0.343724\pi$
$864$	4.90438	+	1.71670i	0.166850	+	0.0584033i
$865$	7.45756	+	34.8745i	0.253565	+	1.18577i
$866$	−25.1896			−0.855978
$867$	−16.5824	+	22.4667i	−0.563167	+	0.763008i
$868$	−6.18921	−	5.01111i	−0.210075	−	0.170088i
$869$			12.7443i			0.432321i
$870$	13.1547	+	5.95623i	0.445986	+	0.201935i
$871$		−	21.3370i		−	0.722978i
$872$	−10.8671			−0.368006
$873$	30.6331	−	9.44671i	1.03677	−	0.319723i
$874$			1.50131i			0.0507826i
$875$	−12.9024	+	9.44693i	−0.436180	+	0.319365i
$876$	−3.23649	+	4.38497i	−0.109351	+	0.148154i
$877$			3.05904i			0.103296i	0.998665	+	0.0516482i	$0.0164474\pi$
$877$			3.05904i			0.103296i	−0.998665	+	0.0516482i	$0.983553\pi$
$878$	−0.444962			−0.0150167
$879$	12.5993	−	17.0701i	0.424963	−	0.575761i
$880$	2.87198	+	13.4305i	0.0968145	+	0.452742i
$881$	−27.5213			−0.927215			−0.463607	−	0.886041i	$-0.653445\pi$
$881$	−27.5213			−0.927215			−0.463607	+	0.886041i	$0.653445\pi$
$882$	−4.37989	−	14.2028i	−0.147479	−	0.478234i
$883$	−31.9348			−1.07469			−0.537346	−	0.843362i	$-0.680573\pi$
$883$	−31.9348			−1.07469			−0.537346	+	0.843362i	$0.680573\pi$
$884$			2.01934i			0.0679179i
$885$	8.62245	−	19.0432i	0.289840	−	0.640130i
$886$	−22.7564			−0.764518
$887$	9.83965			0.330383			0.165191	−	0.986262i	$-0.447176\pi$
$887$	9.83965			0.330383			0.165191	+	0.986262i	$0.447176\pi$
$888$	8.07852	−	10.9452i	0.271098	−	0.367297i
$889$		−	1.03347i		−	0.0346616i
$890$	2.89401	+	13.5335i	0.0970075	+	0.453645i
$891$	45.6779	−	31.1332i	1.53027	−	1.04300i
$892$	−7.26279			−0.243176
$893$	26.7706			0.895842
$894$	−14.6525	−	10.8148i	−0.490053	−	0.361702i
$895$	−0.483554	−	2.26129i	−0.0161634	−	0.0755864i
$896$			1.43029i			0.0477826i
$897$	−0.799071	−	0.589785i	−0.0266802	−	0.0196923i
$898$	−27.0215			−0.901719
$899$	−13.0629	+	16.1340i	−0.435674	+	0.538100i
$900$	9.89599	+	11.2725i	0.329866	+	0.375750i
$901$	−5.69701			−0.189795
$902$			20.3908i			0.678940i
$903$	1.15985	+	0.856068i	0.0385972	+	0.0284882i
$904$	18.5351			0.616469
$905$	3.36502	−	0.719577i	0.111857	−	0.0239195i
$906$	11.9697	+	8.83470i	0.397667	+	0.293513i
$907$		−	12.4039i		−	0.411866i	−0.978566	−	0.205933i	$-0.933977\pi$
$907$		−	12.4039i		−	0.411866i	0.978566	−	0.205933i	$-0.0660229\pi$
$908$	−16.5730			−0.549993
$909$	−36.3886	+	11.2216i	−1.20693	+	0.372196i
$910$	−6.73883	+	1.44103i	−0.223390	+	0.0477697i
$911$	8.44554			0.279813			0.139907	−	0.990165i	$-0.455320\pi$
$911$	8.44554			0.279813			0.139907	+	0.990165i	$0.455320\pi$
$912$	5.80276	−	7.86188i	0.192149	−	0.260333i
$913$			51.2871i			1.69736i
$914$	4.77341			0.157890
$915$	15.5277	−	34.2938i	0.513328	−	1.13372i
$916$		−	19.1781i		−	0.633662i
$917$	4.82360			0.159289
$918$	1.60887	−	4.59631i	0.0531005	−	0.151701i
$919$	27.6348			0.911589			0.455795	−	0.890085i	$-0.349355\pi$
$919$	27.6348			0.911589			0.455795	+	0.890085i	$0.349355\pi$
$920$	−0.581900	+	0.124434i	−0.0191847	+	0.00410245i
$921$	40.2561	+	29.7125i	1.32648	+	0.979061i
$922$	23.4023			0.770713
$923$		−	2.31828i		−	0.0763070i
$924$	12.2425	+	9.03601i	0.402747	+	0.297263i
$925$	35.8360	−	16.0608i	1.17828	−	0.528075i
$926$	32.0488			1.05319
$927$	41.0495	−	12.6589i	1.34824	−	0.415773i
$928$	3.72847			0.122393
$929$	36.4188			1.19486			0.597431	−	0.801920i	$-0.296188\pi$
$929$	36.4188			1.19486			0.597431	+	0.801920i	$0.296188\pi$
$930$	−19.2739	+	9.67033i	−0.632017	+	0.317102i
$931$	−27.9498			−0.916017
$932$	−19.6843			−0.644781
$933$	11.9052	+	8.78711i	0.389760	+	0.287677i
$934$	−16.2069			−0.530306
$935$	12.5869	−	2.69158i	0.411635	−	0.0880240i
$936$	1.90488	+	6.17702i	0.0622630	+	0.201902i
$937$			23.3601i			0.763142i	0.924340	+	0.381571i	$0.124617\pi$
$937$			23.3601i			0.763142i	−0.924340	+	0.381571i	$0.875383\pi$
$938$	−14.1636			−0.462457
$939$	32.7679	−	44.3957i	1.06934	−	1.44880i
$940$	2.21883	+	10.3761i	0.0723703	+	0.338432i
$941$	25.0131			0.815404			0.407702	−	0.913115i	$-0.366330\pi$
$941$	25.0131			0.815404			0.407702	+	0.913115i	$0.366330\pi$
$942$	−12.5607	−	9.27088i	−0.409249	−	0.302062i
$943$	−0.883467			−0.0287697
$944$		−	5.39747i		−	0.175673i
$945$	16.4866	+	2.08901i	0.536310	+	0.0679556i
$946$	3.57408			0.116203
$947$			47.4728i			1.54266i	0.636437	+	0.771329i	$0.280408\pi$
$947$			47.4728i			1.54266i	−0.636437	+	0.771329i	$0.719592\pi$
$948$	2.89153	+	2.13420i	0.0939125	+	0.0693157i
$949$	−6.77989			−0.220085
$950$	25.7408	−	11.5364i	0.835142	−	0.374289i
$951$	−7.67901	+	10.4039i	−0.249009	+	0.337370i
$952$	1.34045			0.0434441
$953$			4.33551i			0.140441i	0.997531	+	0.0702204i	$0.0223703\pi$
$953$			4.33551i			0.140441i	−0.997531	+	0.0702204i	$0.977630\pi$
$954$	−17.4267	+	5.37409i	−0.564211	+	0.173993i
$955$	−2.28924	+	0.489531i	−0.0740779	+	0.0158408i
$956$	2.93174			0.0948194
$957$	23.5551	−	31.9136i	0.761427	−	1.03162i
$958$		−	31.7707i		−	1.02646i
$959$	−26.8534			−0.867143
$960$	3.52817	+	1.59750i	0.113871	+	0.0515591i
$961$	−6.45009	−	30.3215i	−0.208067	−	0.978114i
$962$	16.9231			0.545623
$963$	−1.73689	−	5.63226i	−0.0559704	−	0.181497i
$964$			26.2006i			0.843863i
$965$	−48.0183	+	10.2682i	−1.54576	+	0.330546i
$966$	−0.391501	+	0.530426i	−0.0125963	+	0.0170662i
$967$	15.2927			0.491779			0.245889	−	0.969298i	$-0.420920\pi$
$967$	15.2927			0.491779			0.245889	+	0.969298i	$0.420920\pi$
$968$	26.7253			0.858984
$969$	−7.36804	−	5.43826i	−0.236696	−	0.174702i
$970$	23.3654	−	4.99646i	0.750217	−	0.160427i
$971$			20.9450i			0.672156i	0.941834	+	0.336078i	$0.109100\pi$
$971$			20.9450i			0.672156i	−0.941834	+	0.336078i	$0.890900\pi$
$972$	0.585621	−	15.5775i	0.0187838	−	0.499647i
$973$	−5.64110			−0.180845
$974$	−36.9394			−1.18362
$975$	−3.97197	+	18.2325i	−0.127205	+	0.583908i
$976$		−	9.71998i		−	0.311129i
$977$	33.0491			1.05734			0.528668	−	0.848829i	$-0.322692\pi$
$977$	33.0491			1.05734			0.528668	+	0.848829i	$0.322692\pi$
$978$	−19.8503	−	14.6513i	−0.634743	−	0.468497i
$979$	38.0147			1.21496
$980$	−2.31657	−	10.8332i	−0.0740000	−	0.346053i
$981$	9.60720	+	31.1536i	0.306734	+	0.994657i
$982$	−17.2323			−0.549903
$983$			44.8133i			1.42932i	0.699470	+	0.714662i	$0.253419\pi$
$983$			44.8133i			1.42932i	−0.699470	+	0.714662i	$0.746581\pi$
$984$	4.62643	+	3.41471i	0.147485	+	0.108857i
$985$	50.9367	−	10.8923i	1.62298	−	0.347058i
$986$		−	3.49427i		−	0.111280i
$987$	9.45825	+	6.98102i	0.301060	+	0.222208i
$988$	12.1558			0.386727
$989$			0.154853i			0.00492405i
$990$	35.9633	−	20.1068i	1.14299	−	0.639034i
$991$		−	3.08059i		−	0.0978581i	−0.998802	−	0.0489290i	$-0.984419\pi$
$991$		−	3.08059i		−	0.0978581i	0.998802	−	0.0489290i	$-0.0155808\pi$
$992$	−3.50356	+	4.32724i	−0.111238	+	0.137390i
$993$	48.2381	+	35.6040i	1.53079	+	1.12986i
$994$	−1.53888			−0.0488103
$995$	11.0980	−	2.37320i	0.351830	−	0.0752353i
$996$	11.6364	+	8.58872i	0.368715	+	0.272144i
$997$			43.4068i			1.37471i	0.726323	+	0.687353i	$0.241228\pi$
$997$			43.4068i			1.37471i	−0.726323	+	0.687353i	$0.758772\pi$
$998$		−	16.0253i		−	0.507273i
$999$	−38.5194	−	13.4831i	−1.21870	−	0.426587i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.e.b.929.10	yes	32
3.2	odd	2		930.2.e.a.929.9	✓	32
5.4	even	2		930.2.e.a.929.23	yes	32
15.14	odd	2	inner	930.2.e.b.929.24	yes	32
31.30	odd	2	inner	930.2.e.b.929.23	yes	32
93.92	even	2		930.2.e.a.929.24	yes	32
155.154	odd	2		930.2.e.a.929.10	yes	32
465.464	even	2	inner	930.2.e.b.929.9	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.e.a.929.9	✓	32	3.2	odd	2
930.2.e.a.929.10	yes	32	155.154	odd	2
930.2.e.a.929.23	yes	32	5.4	even	2
930.2.e.a.929.24	yes	32	93.92	even	2
930.2.e.b.929.9	yes	32	465.464	even	2	inner
930.2.e.b.929.10	yes	32	1.1	even	1	trivial
930.2.e.b.929.23	yes	32	31.30	odd	2	inner
930.2.e.b.929.24	yes	32	15.14	odd	2	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.02858 + 1.39357i) q^{3} +1.00000 q^{4} +(-0.467590 - 2.18663i) q^{5} +(-1.02858 + 1.39357i) q^{6} +1.43029i q^{7} +1.00000 q^{8} +(-0.884063 - 2.86678i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.02858 + 1.39357i) q^{3} +1.00000 q^{4} +(-0.467590 - 2.18663i) q^{5} +(-1.02858 + 1.39357i) q^{6} +1.43029i q^{7} +1.00000 q^{8} +(-0.884063 - 2.86678i) q^{9} +(-0.467590 - 2.18663i) q^{10} -6.14209 q^{11} +(-1.02858 + 1.39357i) q^{12} -2.15469 q^{13} +1.43029i q^{14} +(3.52817 + 1.59750i) q^{15} +1.00000 q^{16} -0.937186i q^{17} +(-0.884063 - 2.86678i) q^{18} -5.64155 q^{19} +(-0.467590 - 2.18663i) q^{20} +(-1.99320 - 1.47116i) q^{21} -6.14209 q^{22} -0.266117i q^{23} +(-1.02858 + 1.39357i) q^{24} +(-4.56272 + 2.04489i) q^{25} -2.15469 q^{26} +(4.90438 + 1.71670i) q^{27} +1.43029i q^{28} +3.72847 q^{29} +(3.52817 + 1.59750i) q^{30} +(-3.50356 + 4.32724i) q^{31} +1.00000 q^{32} +(6.31761 - 8.55943i) q^{33} -0.937186i q^{34} +(3.12752 - 0.668789i) q^{35} +(-0.884063 - 2.86678i) q^{36} -7.85409 q^{37} -5.64155 q^{38} +(2.21626 - 3.00271i) q^{39} +(-0.467590 - 2.18663i) q^{40} -3.31985i q^{41} +(-1.99320 - 1.47116i) q^{42} -0.581900 q^{43} -6.14209 q^{44} +(-5.85522 + 3.27360i) q^{45} -0.266117i q^{46} -4.74525 q^{47} +(-1.02858 + 1.39357i) q^{48} +4.95427 q^{49} +(-4.56272 + 2.04489i) q^{50} +(1.30603 + 0.963966i) q^{51} -2.15469 q^{52} -6.07885i q^{53} +(4.90438 + 1.71670i) q^{54} +(2.87198 + 13.4305i) q^{55} +1.43029i q^{56} +(5.80276 - 7.86188i) q^{57} +3.72847 q^{58} -5.39747i q^{59} +(3.52817 + 1.59750i) q^{60} -9.71998i q^{61} +(-3.50356 + 4.32724i) q^{62} +(4.10032 - 1.26447i) q^{63} +1.00000 q^{64} +(1.00751 + 4.71151i) q^{65} +(6.31761 - 8.55943i) q^{66} +9.90260i q^{67} -0.937186i q^{68} +(0.370852 + 0.273721i) q^{69} +(3.12752 - 0.668789i) q^{70} +1.07592i q^{71} +(-0.884063 - 2.86678i) q^{72} +3.14657 q^{73} -7.85409 q^{74} +(1.84340 - 8.46179i) q^{75} -5.64155 q^{76} -8.78497i q^{77} +(2.21626 - 3.00271i) q^{78} -2.07491i q^{79} +(-0.467590 - 2.18663i) q^{80} +(-7.43686 + 5.06883i) q^{81} -3.31985i q^{82} -8.35010i q^{83} +(-1.99320 - 1.47116i) q^{84} +(-2.04928 + 0.438218i) q^{85} -0.581900 q^{86} +(-3.83502 + 5.19588i) q^{87} -6.14209 q^{88} -6.18921 q^{89} +(-5.85522 + 3.27360i) q^{90} -3.08183i q^{91} -0.266117i q^{92} +(-2.42663 - 9.33335i) q^{93} -4.74525 q^{94} +(2.63793 + 12.3360i) q^{95} +(-1.02858 + 1.39357i) q^{96} +10.6856i q^{97} +4.95427 q^{98} +(5.43000 + 17.6080i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{2} + 32 q^{4} - 2 q^{5} + 32 q^{8} + 4 q^{9}+O(q^{10}) \) 32 * q + 32 * q^2 + 32 * q^4 - 2 * q^5 + 32 * q^8 + 4 * q^9	\( 32 q + 32 q^{2} + 32 q^{4} - 2 q^{5} + 32 q^{8} + 4 q^{9} - 2 q^{10} + 32 q^{16} + 4 q^{18} + 8 q^{19} - 2 q^{20} + 10 q^{25} - 12 q^{31} + 32 q^{32} + 8 q^{33} - 16 q^{35} + 4 q^{36} + 8 q^{38} - 4 q^{39} - 2 q^{40} - 42 q^{45} + 4 q^{47} - 36 q^{49} + 10 q^{50} - 4 q^{51} - 12 q^{62} + 24 q^{63} + 32 q^{64} + 8 q^{66} - 8 q^{69} - 16 q^{70} + 4 q^{72} + 8 q^{76} - 4 q^{78} - 2 q^{80} + 24 q^{81} + 4 q^{87} - 42 q^{90} - 24 q^{93} + 4 q^{94} + 26 q^{95} - 36 q^{98}+O(q^{100}) \) 32 * q + 32 * q^2 + 32 * q^4 - 2 * q^5 + 32 * q^8 + 4 * q^9 - 2 * q^10 + 32 * q^16 + 4 * q^18 + 8 * q^19 - 2 * q^20 + 10 * q^25 - 12 * q^31 + 32 * q^32 + 8 * q^33 - 16 * q^35 + 4 * q^36 + 8 * q^38 - 4 * q^39 - 2 * q^40 - 42 * q^45 + 4 * q^47 - 36 * q^49 + 10 * q^50 - 4 * q^51 - 12 * q^62 + 24 * q^63 + 32 * q^64 + 8 * q^66 - 8 * q^69 - 16 * q^70 + 4 * q^72 + 8 * q^76 - 4 * q^78 - 2 * q^80 + 24 * q^81 + 4 * q^87 - 42 * q^90 - 24 * q^93 + 4 * q^94 + 26 * q^95 - 36 * q^98

Introduction

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