LMFDB - Embedded newform 1950.2.i.bh.601.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(451,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("1950.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.i (of order $3$, degree $2$, 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:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			601.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1950.601
Dual form			1950.2.i.bh.451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-0.366025 + 0.633975i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-0.366025 + 0.633975i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.36603 + 2.36603i) q^{11} -1.00000 q^{12} +(3.23205 + 1.59808i) q^{13} -0.732051 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.23205 + 2.13397i) q^{17} -1.00000 q^{18} +(-2.36603 + 4.09808i) q^{19} -0.732051 q^{21} +(-1.36603 + 2.36603i) q^{22} +(-2.09808 - 3.63397i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(0.232051 + 3.59808i) q^{26} -1.00000 q^{27} +(-0.366025 - 0.633975i) q^{28} +(-0.232051 - 0.401924i) q^{29} +4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.36603 + 2.36603i) q^{33} -2.46410 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-2.96410 - 5.13397i) q^{37} -4.73205 q^{38} +(0.232051 + 3.59808i) q^{39} +(-0.598076 - 1.03590i) q^{41} +(-0.366025 - 0.633975i) q^{42} +(-3.36603 + 5.83013i) q^{43} -2.73205 q^{44} +(2.09808 - 3.63397i) q^{46} +9.66025 q^{47} +(0.500000 - 0.866025i) q^{48} +(3.23205 + 5.59808i) q^{49} -2.46410 q^{51} +(-3.00000 + 2.00000i) q^{52} -4.26795 q^{53} +(-0.500000 - 0.866025i) q^{54} +(0.366025 - 0.633975i) q^{56} -4.73205 q^{57} +(0.232051 - 0.401924i) q^{58} +(-4.19615 + 7.26795i) q^{59} +(-7.06218 + 12.2321i) q^{61} +(2.00000 + 3.46410i) q^{62} +(-0.366025 - 0.633975i) q^{63} +1.00000 q^{64} -2.73205 q^{66} +(-4.83013 - 8.36603i) q^{67} +(-1.23205 - 2.13397i) q^{68} +(2.09808 - 3.63397i) q^{69} +(-2.36603 + 4.09808i) q^{71} +(0.500000 - 0.866025i) q^{72} -12.6603 q^{73} +(2.96410 - 5.13397i) q^{74} +(-2.36603 - 4.09808i) q^{76} -2.00000 q^{77} +(-3.00000 + 2.00000i) q^{78} +12.0000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(0.598076 - 1.03590i) q^{82} -8.73205 q^{83} +(0.366025 - 0.633975i) q^{84} -6.73205 q^{86} +(0.232051 - 0.401924i) q^{87} +(-1.36603 - 2.36603i) q^{88} +(-4.46410 - 7.73205i) q^{89} +(-2.19615 + 1.46410i) q^{91} +4.19615 q^{92} +(2.00000 + 3.46410i) q^{93} +(4.83013 + 8.36603i) q^{94} +1.00000 q^{96} +(-5.00000 + 8.66025i) q^{97} +(-3.23205 + 5.59808i) q^{98} -2.73205 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{6} + 2 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^6 + 2 * q^7 - 4 * q^8 - 2 * q^9	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{6} + 2 q^{7} - 4 q^{8} - 2 q^{9} + 2 q^{11} - 4 q^{12} + 6 q^{13} + 4 q^{14} - 2 q^{16} + 2 q^{17} - 4 q^{18} - 6 q^{19} + 4 q^{21} - 2 q^{22} + 2 q^{23} - 2 q^{24} - 6 q^{26} - 4 q^{27} + 2 q^{28} + 6 q^{29} + 16 q^{31} + 2 q^{32} - 2 q^{33} + 4 q^{34} - 2 q^{36} + 2 q^{37} - 12 q^{38} - 6 q^{39} + 8 q^{41} + 2 q^{42} - 10 q^{43} - 4 q^{44} - 2 q^{46} + 4 q^{47} + 2 q^{48} + 6 q^{49} + 4 q^{51} - 12 q^{52} - 24 q^{53} - 2 q^{54} - 2 q^{56} - 12 q^{57} - 6 q^{58} + 4 q^{59} - 4 q^{61} + 8 q^{62} + 2 q^{63} + 4 q^{64} - 4 q^{66} - 2 q^{67} + 2 q^{68} - 2 q^{69} - 6 q^{71} + 2 q^{72} - 16 q^{73} - 2 q^{74} - 6 q^{76} - 8 q^{77} - 12 q^{78} + 48 q^{79} - 2 q^{81} - 8 q^{82} - 28 q^{83} - 2 q^{84} - 20 q^{86} - 6 q^{87} - 2 q^{88} - 4 q^{89} + 12 q^{91} - 4 q^{92} + 8 q^{93} + 2 q^{94} + 4 q^{96} - 20 q^{97} - 6 q^{98} - 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^6 + 2 * q^7 - 4 * q^8 - 2 * q^9 + 2 * q^11 - 4 * q^12 + 6 * q^13 + 4 * q^14 - 2 * q^16 + 2 * q^17 - 4 * q^18 - 6 * q^19 + 4 * q^21 - 2 * q^22 + 2 * q^23 - 2 * q^24 - 6 * q^26 - 4 * q^27 + 2 * q^28 + 6 * q^29 + 16 * q^31 + 2 * q^32 - 2 * q^33 + 4 * q^34 - 2 * q^36 + 2 * q^37 - 12 * q^38 - 6 * q^39 + 8 * q^41 + 2 * q^42 - 10 * q^43 - 4 * q^44 - 2 * q^46 + 4 * q^47 + 2 * q^48 + 6 * q^49 + 4 * q^51 - 12 * q^52 - 24 * q^53 - 2 * q^54 - 2 * q^56 - 12 * q^57 - 6 * q^58 + 4 * q^59 - 4 * q^61 + 8 * q^62 + 2 * q^63 + 4 * q^64 - 4 * q^66 - 2 * q^67 + 2 * q^68 - 2 * q^69 - 6 * q^71 + 2 * q^72 - 16 * q^73 - 2 * q^74 - 6 * q^76 - 8 * q^77 - 12 * q^78 + 48 * q^79 - 2 * q^81 - 8 * q^82 - 28 * q^83 - 2 * q^84 - 20 * q^86 - 6 * q^87 - 2 * q^88 - 4 * q^89 + 12 * q^91 - 4 * q^92 + 8 * q^93 + 2 * q^94 + 4 * q^96 - 20 * q^97 - 6 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−0.366025	+	0.633975i	−0.138345	+	0.239620i	−0.926870	−	0.375382i	$-0.877511\pi$
$7$	−0.366025	+	0.633975i	−0.138345	+	0.239620i	0.788526	+	0.615002i	$0.210845\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	1.36603	+	2.36603i	0.411872	+	0.713384i	0.995094	−	0.0989291i	$-0.0315417\pi$
$11$	1.36603	+	2.36603i	0.411872	+	0.713384i	−0.583222	+	0.812313i	$0.698208\pi$
$12$	−1.00000			−0.288675
$13$	3.23205	+	1.59808i	0.896410	+	0.443227i
$13$	3.23205	+	1.59808i	0.896410	+	0.443227i
$14$	−0.732051			−0.195649
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.23205	+	2.13397i	−0.298816	+	0.517565i	−0.975865	−	0.218373i	$-0.929925\pi$
$17$	−1.23205	+	2.13397i	−0.298816	+	0.517565i	0.677049	+	0.735938i	$0.263258\pi$
$18$	−1.00000			−0.235702
$19$	−2.36603	+	4.09808i	−0.542803	+	0.940163i	0.455938	+	0.890011i	$0.349304\pi$
$19$	−2.36603	+	4.09808i	−0.542803	+	0.940163i	−0.998742	+	0.0501517i	$0.984030\pi$
$20$		0			0
$21$	−0.732051			−0.159747
$22$	−1.36603	+	2.36603i	−0.291238	+	0.504438i
$23$	−2.09808	−	3.63397i	−0.437479	−	0.757736i	0.560015	−	0.828482i	$-0.310795\pi$
$23$	−2.09808	−	3.63397i	−0.437479	−	0.757736i	−0.997494	+	0.0707462i	$0.977462\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$		0			0
$26$	0.232051	+	3.59808i	0.0455089	+	0.705641i
$27$	−1.00000			−0.192450
$28$	−0.366025	−	0.633975i	−0.0691723	−	0.119810i
$29$	−0.232051	−	0.401924i	−0.0430908	−	0.0746354i	0.843676	−	0.536853i	$-0.180387\pi$
$29$	−0.232051	−	0.401924i	−0.0430908	−	0.0746354i	−0.886766	+	0.462218i	$0.847054\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−1.36603	+	2.36603i	−0.237795	+	0.411872i
$34$	−2.46410			−0.422590
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−2.96410	−	5.13397i	−0.487295	−	0.844020i	0.512598	−	0.858629i	$-0.328683\pi$
$37$	−2.96410	−	5.13397i	−0.487295	−	0.844020i	−0.999893	+	0.0146085i	$0.995350\pi$
$38$	−4.73205			−0.767640
$39$	0.232051	+	3.59808i	0.0371579	+	0.576153i
$40$		0			0
$41$	−0.598076	−	1.03590i	−0.0934038	−	0.161780i	0.815538	−	0.578704i	$-0.196441\pi$
$41$	−0.598076	−	1.03590i	−0.0934038	−	0.161780i	−0.908941	+	0.416924i	$0.863108\pi$
$42$	−0.366025	−	0.633975i	−0.0564789	−	0.0978244i
$43$	−3.36603	+	5.83013i	−0.513314	+	0.889086i	0.486567	+	0.873643i	$0.338249\pi$
$43$	−3.36603	+	5.83013i	−0.513314	+	0.889086i	−0.999881	+	0.0154426i	$0.995084\pi$
$44$	−2.73205			−0.411872
$45$		0			0
$46$	2.09808	−	3.63397i	0.309344	−	0.535800i
$47$	9.66025			1.40909			0.704546	−	0.709658i	$-0.251150\pi$
$47$	9.66025			1.40909			0.704546	+	0.709658i	$0.251150\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	3.23205	+	5.59808i	0.461722	+	0.799725i
$50$		0			0
$51$	−2.46410			−0.345043
$52$	−3.00000	+	2.00000i	−0.416025	+	0.277350i
$53$	−4.26795			−0.586248			−0.293124	−	0.956074i	$-0.594695\pi$
$53$	−4.26795			−0.586248			−0.293124	+	0.956074i	$0.594695\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$		0			0
$56$	0.366025	−	0.633975i	0.0489122	−	0.0847184i
$57$	−4.73205			−0.626775
$58$	0.232051	−	0.401924i	0.0304698	−	0.0527752i
$59$	−4.19615	+	7.26795i	−0.546293	+	0.946206i	0.452232	+	0.891900i	$0.350628\pi$
$59$	−4.19615	+	7.26795i	−0.546293	+	0.946206i	−0.998524	+	0.0543060i	$0.982705\pi$
$60$		0			0
$61$	−7.06218	+	12.2321i	−0.904219	+	1.56615i	−0.0822573	+	0.996611i	$0.526213\pi$
$61$	−7.06218	+	12.2321i	−0.904219	+	1.56615i	−0.821962	+	0.569542i	$0.807120\pi$
$62$	2.00000	+	3.46410i	0.254000	+	0.439941i
$63$	−0.366025	−	0.633975i	−0.0461149	−	0.0798733i
$64$	1.00000			0.125000
$65$		0			0
$66$	−2.73205			−0.336292
$67$	−4.83013	−	8.36603i	−0.590094	−	1.02207i	−0.994219	−	0.107369i	$-0.965757\pi$
$67$	−4.83013	−	8.36603i	−0.590094	−	1.02207i	0.404125	−	0.914704i	$-0.367576\pi$
$68$	−1.23205	−	2.13397i	−0.149408	−	0.258782i
$69$	2.09808	−	3.63397i	0.252579	−	0.437479i
$70$		0			0
$71$	−2.36603	+	4.09808i	−0.280796	+	0.486352i	−0.971581	−	0.236708i	$-0.923932\pi$
$71$	−2.36603	+	4.09808i	−0.280796	+	0.486352i	0.690785	+	0.723060i	$0.257265\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−12.6603			−1.48177			−0.740885	−	0.671632i	$-0.765594\pi$
$73$	−12.6603			−1.48177			−0.740885	+	0.671632i	$0.765594\pi$
$74$	2.96410	−	5.13397i	0.344570	−	0.596812i
$75$		0			0
$76$	−2.36603	−	4.09808i	−0.271402	−	0.470082i
$77$	−2.00000			−0.227921
$78$	−3.00000	+	2.00000i	−0.339683	+	0.226455i
$79$	12.0000			1.35011			0.675053	−	0.737769i	$-0.264121\pi$
$79$	12.0000			1.35011			0.675053	+	0.737769i	$0.264121\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.598076	−	1.03590i	0.0660465	−	0.114396i
$83$	−8.73205			−0.958467			−0.479234	−	0.877687i	$-0.659085\pi$
$83$	−8.73205			−0.958467			−0.479234	+	0.877687i	$0.659085\pi$
$84$	0.366025	−	0.633975i	0.0399366	−	0.0691723i
$85$		0			0
$86$	−6.73205			−0.725936
$87$	0.232051	−	0.401924i	0.0248785	−	0.0430908i
$88$	−1.36603	−	2.36603i	−0.145619	−	0.252219i
$89$	−4.46410	−	7.73205i	−0.473194	−	0.819596i	0.526335	−	0.850277i	$-0.323566\pi$
$89$	−4.46410	−	7.73205i	−0.473194	−	0.819596i	−0.999529	+	0.0306813i	$0.990232\pi$
$90$		0			0
$91$	−2.19615	+	1.46410i	−0.230219	+	0.153480i
$92$	4.19615			0.437479
$93$	2.00000	+	3.46410i	0.207390	+	0.359211i
$94$	4.83013	+	8.36603i	0.498190	+	0.862890i
$95$		0			0
$96$	1.00000			0.102062
$97$	−5.00000	+	8.66025i	−0.507673	+	0.879316i	0.492287	+	0.870433i	$0.336161\pi$
$97$	−5.00000	+	8.66025i	−0.507673	+	0.879316i	−0.999961	+	0.00888289i	$0.997172\pi$
$98$	−3.23205	+	5.59808i	−0.326486	+	0.565491i
$99$	−2.73205			−0.274581
$100$		0			0
$101$	−0.0358984	−	0.0621778i	−0.00357202	−	0.00618692i	0.864234	−	0.503090i	$-0.167804\pi$
$101$	−0.0358984	−	0.0621778i	−0.00357202	−	0.00618692i	−0.867806	+	0.496903i	$0.834470\pi$
$102$	−1.23205	−	2.13397i	−0.121991	−	0.211295i
$103$	−12.7321			−1.25453			−0.627263	−	0.778807i	$-0.715825\pi$
$103$	−12.7321			−1.25453			−0.627263	+	0.778807i	$0.715825\pi$
$104$	−3.23205	−	1.59808i	−0.316929	−	0.156704i
$105$		0			0
$106$	−2.13397	−	3.69615i	−0.207270	−	0.359002i
$107$	2.36603	+	4.09808i	0.228732	+	0.396176i	0.957433	−	0.288657i	$-0.0932086\pi$
$107$	2.36603	+	4.09808i	0.228732	+	0.396176i	−0.728700	+	0.684833i	$0.759875\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$		0			0
$111$	2.96410	−	5.13397i	0.281340	−	0.487295i
$112$	0.732051			0.0691723
$113$	4.50000	−	7.79423i	0.423324	−	0.733219i	−0.572938	−	0.819599i	$-0.694196\pi$
$113$	4.50000	−	7.79423i	0.423324	−	0.733219i	0.996262	+	0.0863794i	$0.0275297\pi$
$114$	−2.36603	−	4.09808i	−0.221599	−	0.383820i
$115$		0			0
$116$	0.464102			0.0430908
$117$	−3.00000	+	2.00000i	−0.277350	+	0.184900i
$118$	−8.39230			−0.772574
$119$	−0.901924	−	1.56218i	−0.0826792	−	0.143205i
$120$		0			0
$121$	1.76795	−	3.06218i	0.160723	−	0.278380i
$122$	−14.1244			−1.27876
$123$	0.598076	−	1.03590i	0.0539267	−	0.0934038i
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$		0			0
$126$	0.366025	−	0.633975i	0.0326081	−	0.0564789i
$127$	2.00000	+	3.46410i	0.177471	+	0.307389i	0.941014	−	0.338368i	$-0.109875\pi$
$127$	2.00000	+	3.46410i	0.177471	+	0.307389i	−0.763542	+	0.645758i	$0.776542\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−6.73205			−0.592724
$130$		0			0
$131$	13.8564			1.21064			0.605320	−	0.795982i	$-0.293045\pi$
$131$	13.8564			1.21064			0.605320	+	0.795982i	$0.293045\pi$
$132$	−1.36603	−	2.36603i	−0.118897	−	0.205936i
$133$	−1.73205	−	3.00000i	−0.150188	−	0.260133i
$134$	4.83013	−	8.36603i	0.417259	−	0.722715i
$135$		0			0
$136$	1.23205	−	2.13397i	0.105647	−	0.182987i
$137$	5.76795	−	9.99038i	0.492789	−	0.853536i	−0.507176	−	0.861842i	$-0.669311\pi$
$137$	5.76795	−	9.99038i	0.492789	−	0.853536i	0.999966	+	0.00830645i	$0.00264405\pi$
$138$	4.19615			0.357200
$139$	7.46410	−	12.9282i	0.633097	−	1.09656i	−0.353818	−	0.935314i	$-0.615117\pi$
$139$	7.46410	−	12.9282i	0.633097	−	1.09656i	0.986915	−	0.161242i	$-0.0515498\pi$
$140$		0			0
$141$	4.83013	+	8.36603i	0.406770	+	0.704546i
$142$	−4.73205			−0.397105
$143$	0.633975	+	9.83013i	0.0530156	+	0.822037i
$144$	1.00000			0.0833333
$145$		0			0
$146$	−6.33013	−	10.9641i	−0.523885	−	0.907396i
$147$	−3.23205	+	5.59808i	−0.266575	+	0.461722i
$148$	5.92820			0.487295
$149$	−3.03590	+	5.25833i	−0.248710	+	0.430779i	−0.963168	−	0.268899i	$-0.913340\pi$
$149$	−3.03590	+	5.25833i	−0.248710	+	0.430779i	0.714458	+	0.699679i	$0.246673\pi$
$150$		0			0
$151$	19.1244			1.55632			0.778159	−	0.628067i	$-0.216154\pi$
$151$	19.1244			1.55632			0.778159	+	0.628067i	$0.216154\pi$
$152$	2.36603	−	4.09808i	0.191910	−	0.332398i
$153$	−1.23205	−	2.13397i	−0.0996054	−	0.172522i
$154$	−1.00000	−	1.73205i	−0.0805823	−	0.139573i
$155$		0			0
$156$	−3.23205	−	1.59808i	−0.258771	−	0.127948i
$157$	11.3923			0.909205			0.454602	−	0.890694i	$-0.349781\pi$
$157$	11.3923			0.909205			0.454602	+	0.890694i	$0.349781\pi$
$158$	6.00000	+	10.3923i	0.477334	+	0.826767i
$159$	−2.13397	−	3.69615i	−0.169235	−	0.293124i
$160$		0			0
$161$	3.07180			0.242092
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	−3.26795	+	5.66025i	−0.255966	+	0.443345i	−0.965157	−	0.261670i	$-0.915727\pi$
$163$	−3.26795	+	5.66025i	−0.255966	+	0.443345i	0.709192	+	0.705016i	$0.249060\pi$
$164$	1.19615			0.0934038
$165$		0			0
$166$	−4.36603	−	7.56218i	−0.338869	−	0.586939i
$167$	6.92820	+	12.0000i	0.536120	+	0.928588i	0.999108	+	0.0422232i	$0.0134441\pi$
$167$	6.92820	+	12.0000i	0.536120	+	0.928588i	−0.462988	+	0.886365i	$0.653223\pi$
$168$	0.732051			0.0564789
$169$	7.89230	+	10.3301i	0.607100	+	0.794625i
$170$		0			0
$171$	−2.36603	−	4.09808i	−0.180934	−	0.313388i
$172$	−3.36603	−	5.83013i	−0.256657	−	0.444543i
$173$	11.3923	−	19.7321i	0.866141	−	1.50020i	0.000231036	−	1.00000i	$-0.499926\pi$
$173$	11.3923	−	19.7321i	0.866141	−	1.50020i	0.865910	−	0.500200i	$-0.166740\pi$
$174$	0.464102			0.0351835
$175$		0			0
$176$	1.36603	−	2.36603i	0.102968	−	0.178346i
$177$	−8.39230			−0.630804
$178$	4.46410	−	7.73205i	0.334599	−	0.579542i
$179$	−3.90192	−	6.75833i	−0.291643	−	0.505141i	0.682555	−	0.730834i	$-0.260869\pi$
$179$	−3.90192	−	6.75833i	−0.291643	−	0.505141i	−0.974199	+	0.225693i	$0.927535\pi$
$180$		0			0
$181$	8.12436			0.603879			0.301939	−	0.953327i	$-0.402366\pi$
$181$	8.12436			0.603879			0.301939	+	0.953327i	$0.402366\pi$
$182$	−2.36603	−	1.16987i	−0.175381	−	0.0867168i
$183$	−14.1244			−1.04410
$184$	2.09808	+	3.63397i	0.154672	+	0.267900i
$185$		0			0
$186$	−2.00000	+	3.46410i	−0.146647	+	0.254000i
$187$	−6.73205			−0.492296
$188$	−4.83013	+	8.36603i	−0.352273	+	0.610155i
$189$	0.366025	−	0.633975i	0.0266244	−	0.0461149i
$190$		0			0
$191$	1.26795	−	2.19615i	0.0917456	−	0.158908i	−0.816500	−	0.577345i	$-0.804089\pi$
$191$	1.26795	−	2.19615i	0.0917456	−	0.158908i	0.908246	+	0.418437i	$0.137422\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	3.33013	+	5.76795i	0.239708	+	0.415186i	0.960630	−	0.277830i	$-0.0896150\pi$
$193$	3.33013	+	5.76795i	0.239708	+	0.415186i	−0.720923	+	0.693016i	$0.756282\pi$
$194$	−10.0000			−0.717958
$195$		0			0
$196$	−6.46410			−0.461722
$197$	−8.92820	−	15.4641i	−0.636108	−	1.10177i	−0.986279	−	0.165086i	$-0.947210\pi$
$197$	−8.92820	−	15.4641i	−0.636108	−	1.10177i	0.350171	−	0.936686i	$-0.386123\pi$
$198$	−1.36603	−	2.36603i	−0.0970792	−	0.168146i
$199$	−5.02628	+	8.70577i	−0.356304	+	0.617136i	−0.987340	−	0.158617i	$-0.949296\pi$
$199$	−5.02628	+	8.70577i	−0.356304	+	0.617136i	0.631037	+	0.775753i	$0.282630\pi$
$200$		0			0
$201$	4.83013	−	8.36603i	0.340691	−	0.590094i
$202$	0.0358984	−	0.0621778i	0.00252580	−	0.00437482i
$203$	0.339746			0.0238455
$204$	1.23205	−	2.13397i	0.0862608	−	0.149408i
$205$		0			0
$206$	−6.36603	−	11.0263i	−0.443542	−	0.768237i
$207$	4.19615			0.291653
$208$	−0.232051	−	3.59808i	−0.0160898	−	0.249482i
$209$	−12.9282			−0.894263
$210$		0			0
$211$	7.26795	+	12.5885i	0.500346	+	0.866625i	1.00000		0.000399869i	$0.000127282\pi$
$211$	7.26795	+	12.5885i	0.500346	+	0.866625i	−0.499654	+	0.866225i	$0.666539\pi$
$212$	2.13397	−	3.69615i	0.146562	−	0.253853i
$213$	−4.73205			−0.324235
$214$	−2.36603	+	4.09808i	−0.161738	+	0.280139i
$215$		0			0
$216$	1.00000			0.0680414
$217$	−1.46410	+	2.53590i	−0.0993897	+	0.172148i
$218$	5.00000	+	8.66025i	0.338643	+	0.586546i
$219$	−6.33013	−	10.9641i	−0.427750	−	0.740885i
$220$		0			0
$221$	−7.39230	+	4.92820i	−0.497260	+	0.331507i
$222$	5.92820			0.397875
$223$	10.1962	+	17.6603i	0.682785	+	1.18262i	0.974127	+	0.225999i	$0.0725647\pi$
$223$	10.1962	+	17.6603i	0.682785	+	1.18262i	−0.291343	+	0.956619i	$0.594102\pi$
$224$	0.366025	+	0.633975i	0.0244561	+	0.0423592i
$225$		0			0
$226$	9.00000			0.598671
$227$	3.09808	−	5.36603i	0.205627	−	0.356156i	−0.744706	−	0.667393i	$-0.767410\pi$
$227$	3.09808	−	5.36603i	0.205627	−	0.356156i	0.950332	+	0.311237i	$0.100743\pi$
$228$	2.36603	−	4.09808i	0.156694	−	0.271402i
$229$	−12.7846			−0.844831			−0.422415	−	0.906402i	$-0.638818\pi$
$229$	−12.7846			−0.844831			−0.422415	+	0.906402i	$0.638818\pi$
$230$		0			0
$231$	−1.00000	−	1.73205i	−0.0657952	−	0.113961i
$232$	0.232051	+	0.401924i	0.0152349	+	0.0263876i
$233$	8.39230			0.549798			0.274899	−	0.961473i	$-0.411356\pi$
$233$	8.39230			0.549798			0.274899	+	0.961473i	$0.411356\pi$
$234$	−3.23205	−	1.59808i	−0.211286	−	0.104470i
$235$		0			0
$236$	−4.19615	−	7.26795i	−0.273146	−	0.473103i
$237$	6.00000	+	10.3923i	0.389742	+	0.675053i
$238$	0.901924	−	1.56218i	0.0584630	−	0.101261i
$239$	26.5885			1.71986			0.859932	−	0.510408i	$-0.170506\pi$
$239$	26.5885			1.71986			0.859932	+	0.510408i	$0.170506\pi$
$240$		0			0
$241$	−5.69615	+	9.86603i	−0.366921	+	0.635527i	−0.989083	−	0.147363i	$-0.952922\pi$
$241$	−5.69615	+	9.86603i	−0.366921	+	0.635527i	0.622161	+	0.782889i	$0.286255\pi$
$242$	3.53590			0.227296
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−7.06218	−	12.2321i	−0.452110	−	0.783077i
$245$		0			0
$246$	1.19615			0.0762639
$247$	−14.1962	+	9.46410i	−0.903280	+	0.602186i
$248$	−4.00000			−0.254000
$249$	−4.36603	−	7.56218i	−0.276686	−	0.479234i
$250$		0			0
$251$	7.26795	−	12.5885i	0.458749	−	0.794576i	−0.540146	−	0.841571i	$-0.681631\pi$
$251$	7.26795	−	12.5885i	0.458749	−	0.794576i	0.998895	+	0.0469948i	$0.0149644\pi$
$252$	0.732051			0.0461149
$253$	5.73205	−	9.92820i	0.360371	−	0.624181i
$254$	−2.00000	+	3.46410i	−0.125491	+	0.217357i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.50000	−	2.59808i	−0.0935674	−	0.162064i	0.815442	−	0.578838i	$-0.196494\pi$
$257$	−1.50000	−	2.59808i	−0.0935674	−	0.162064i	−0.909010	+	0.416775i	$0.863160\pi$
$258$	−3.36603	−	5.83013i	−0.209560	−	0.362968i
$259$	4.33975			0.269659
$260$		0			0
$261$	0.464102			0.0287272
$262$	6.92820	+	12.0000i	0.428026	+	0.741362i
$263$	3.56218	+	6.16987i	0.219653	+	0.380451i	0.954702	−	0.297564i	$-0.0961741\pi$
$263$	3.56218	+	6.16987i	0.219653	+	0.380451i	−0.735049	+	0.678014i	$0.762841\pi$
$264$	1.36603	−	2.36603i	0.0840731	−	0.145619i
$265$		0			0
$266$	1.73205	−	3.00000i	0.106199	−	0.183942i
$267$	4.46410	−	7.73205i	0.273199	−	0.473194i
$268$	9.66025			0.590094
$269$	8.19615	−	14.1962i	0.499728	−	0.865555i	−0.500272	−	0.865868i	$-0.666767\pi$
$269$	8.19615	−	14.1962i	0.499728	−	0.865555i	1.00000		0.000313781i	$9.98796e-5\pi$
$270$		0			0
$271$	10.9282	+	18.9282i	0.663841	+	1.14981i	0.979598	+	0.200966i	$0.0644082\pi$
$271$	10.9282	+	18.9282i	0.663841	+	1.14981i	−0.315757	+	0.948840i	$0.602258\pi$
$272$	2.46410			0.149408
$273$	−2.36603	−	1.16987i	−0.143198	−	0.0708039i
$274$	11.5359			0.696909
$275$		0			0
$276$	2.09808	+	3.63397i	0.126289	+	0.218740i
$277$	−11.1603	+	19.3301i	−0.670555	+	1.16143i	0.307192	+	0.951647i	$0.400610\pi$
$277$	−11.1603	+	19.3301i	−0.670555	+	1.16143i	−0.977747	+	0.209787i	$0.932723\pi$
$278$	14.9282			0.895334
$279$	−2.00000	+	3.46410i	−0.119737	+	0.207390i
$280$		0			0
$281$	−1.73205			−0.103325			−0.0516627	−	0.998665i	$-0.516452\pi$
$281$	−1.73205			−0.103325			−0.0516627	+	0.998665i	$0.516452\pi$
$282$	−4.83013	+	8.36603i	−0.287630	+	0.498190i
$283$	−4.83013	−	8.36603i	−0.287121	−	0.497309i	0.686000	−	0.727601i	$-0.259365\pi$
$283$	−4.83013	−	8.36603i	−0.287121	−	0.497309i	−0.973121	+	0.230293i	$0.926032\pi$
$284$	−2.36603	−	4.09808i	−0.140398	−	0.243176i
$285$		0			0
$286$	−8.19615	+	5.46410i	−0.484649	+	0.323099i
$287$	0.875644			0.0516877
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	5.46410	+	9.46410i	0.321418	+	0.556712i
$290$		0			0
$291$	−10.0000			−0.586210
$292$	6.33013	−	10.9641i	0.370443	−	0.641626i
$293$	5.13397	−	8.89230i	0.299930	−	0.519494i	−0.676190	−	0.736728i	$-0.736370\pi$
$293$	5.13397	−	8.89230i	0.299930	−	0.519494i	0.976120	+	0.217234i	$0.0697033\pi$
$294$	−6.46410			−0.376994
$295$		0			0
$296$	2.96410	+	5.13397i	0.172285	+	0.298406i
$297$	−1.36603	−	2.36603i	−0.0792648	−	0.137291i
$298$	−6.07180			−0.351730
$299$	−0.973721	−	15.0981i	−0.0563117	−	0.873144i
$300$		0			0
$301$	−2.46410	−	4.26795i	−0.142028	−	0.246001i
$302$	9.56218	+	16.5622i	0.550242	+	0.953046i
$303$	0.0358984	−	0.0621778i	0.00206231	−	0.00357202i
$304$	4.73205			0.271402
$305$		0			0
$306$	1.23205	−	2.13397i	0.0704317	−	0.121991i
$307$	22.7321			1.29739			0.648693	−	0.761050i	$-0.275316\pi$
$307$	22.7321			1.29739			0.648693	+	0.761050i	$0.275316\pi$
$308$	1.00000	−	1.73205i	0.0569803	−	0.0986928i
$309$	−6.36603	−	11.0263i	−0.362151	−	0.627263i
$310$		0			0
$311$	−21.1244			−1.19785			−0.598926	−	0.800804i	$-0.704406\pi$
$311$	−21.1244			−1.19785			−0.598926	+	0.800804i	$0.704406\pi$
$312$	−0.232051	−	3.59808i	−0.0131373	−	0.203701i
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$	5.69615	+	9.86603i	0.321452	+	0.556772i
$315$		0			0
$316$	−6.00000	+	10.3923i	−0.337526	+	0.584613i
$317$	−26.2679			−1.47536			−0.737678	−	0.675153i	$-0.764077\pi$
$317$	−26.2679			−1.47536			−0.737678	+	0.675153i	$0.764077\pi$
$318$	2.13397	−	3.69615i	0.119667	−	0.207270i
$319$	0.633975	−	1.09808i	0.0354958	−	0.0614805i
$320$		0			0
$321$	−2.36603	+	4.09808i	−0.132059	+	0.228732i
$322$	1.53590	+	2.66025i	0.0855923	+	0.148250i
$323$	−5.83013	−	10.0981i	−0.324397	−	0.561872i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−6.53590			−0.361990
$327$	5.00000	+	8.66025i	0.276501	+	0.478913i
$328$	0.598076	+	1.03590i	0.0330232	+	0.0571979i
$329$	−3.53590	+	6.12436i	−0.194940	+	0.337647i
$330$		0			0
$331$	−6.39230	+	11.0718i	−0.351353	+	0.608561i	−0.986487	−	0.163841i	$-0.947612\pi$
$331$	−6.39230	+	11.0718i	−0.351353	+	0.608561i	0.635134	+	0.772402i	$0.280945\pi$
$332$	4.36603	−	7.56218i	0.239617	−	0.415028i
$333$	5.92820			0.324864
$334$	−6.92820	+	12.0000i	−0.379094	+	0.656611i
$335$		0			0
$336$	0.366025	+	0.633975i	0.0199683	+	0.0345861i
$337$	27.0526			1.47365			0.736823	−	0.676085i	$-0.236325\pi$
$337$	27.0526			1.47365			0.736823	+	0.676085i	$0.236325\pi$
$338$	−5.00000	+	12.0000i	−0.271964	+	0.652714i
$339$	9.00000			0.488813
$340$		0			0
$341$	5.46410	+	9.46410i	0.295898	+	0.512510i
$342$	2.36603	−	4.09808i	0.127940	−	0.221599i
$343$	−9.85641			−0.532196
$344$	3.36603	−	5.83013i	0.181484	−	0.314339i
$345$		0			0
$346$	22.7846			1.22491
$347$	5.83013	−	10.0981i	0.312978	−	0.542093i	−0.666028	−	0.745927i	$-0.732007\pi$
$347$	5.83013	−	10.0981i	0.312978	−	0.542093i	0.979006	+	0.203834i	$0.0653402\pi$
$348$	0.232051	+	0.401924i	0.0124392	+	0.0215454i
$349$	16.4641	+	28.5167i	0.881303	+	1.52646i	0.849893	+	0.526955i	$0.176666\pi$
$349$	16.4641	+	28.5167i	0.881303	+	1.52646i	0.0314101	+	0.999507i	$0.490000\pi$
$350$		0			0
$351$	−3.23205	−	1.59808i	−0.172514	−	0.0852990i
$352$	2.73205			0.145619
$353$	11.6244	+	20.1340i	0.618702	+	1.07162i	0.989723	+	0.142999i	$0.0456745\pi$
$353$	11.6244	+	20.1340i	0.618702	+	1.07162i	−0.371021	+	0.928625i	$0.620992\pi$
$354$	−4.19615	−	7.26795i	−0.223023	−	0.386287i
$355$		0			0
$356$	8.92820			0.473194
$357$	0.901924	−	1.56218i	0.0477349	−	0.0826792i
$358$	3.90192	−	6.75833i	0.206223	−	0.357189i
$359$	33.1244			1.74824			0.874118	−	0.485713i	$-0.161440\pi$
$359$	33.1244			1.74824			0.874118	+	0.485713i	$0.161440\pi$
$360$		0			0
$361$	−1.69615	−	2.93782i	−0.0892712	−	0.154622i
$362$	4.06218	+	7.03590i	0.213503	+	0.369799i
$363$	3.53590			0.185587
$364$	−0.169873	−	2.63397i	−0.00890376	−	0.138058i
$365$		0			0
$366$	−7.06218	−	12.2321i	−0.369146	−	0.639380i
$367$	−9.49038	−	16.4378i	−0.495394	−	0.858047i	0.504592	−	0.863358i	$-0.331643\pi$
$367$	−9.49038	−	16.4378i	−0.495394	−	0.858047i	−0.999986	+	0.00531057i	$0.998310\pi$
$368$	−2.09808	+	3.63397i	−0.109370	+	0.189434i
$369$	1.19615			0.0622692
$370$		0			0
$371$	1.56218	−	2.70577i	0.0811042	−	0.140477i
$372$	−4.00000			−0.207390
$373$	15.2321	−	26.3827i	0.788686	−	1.36604i	−0.138087	−	0.990420i	$-0.544095\pi$
$373$	15.2321	−	26.3827i	0.788686	−	1.36604i	0.926772	−	0.375624i	$-0.122571\pi$
$374$	−3.36603	−	5.83013i	−0.174053	−	0.301469i
$375$		0			0
$376$	−9.66025			−0.498190
$377$	−0.107695	−	1.66987i	−0.00554658	−	0.0860028i
$378$	0.732051			0.0376526
$379$	11.1244	+	19.2679i	0.571420	+	0.989728i	0.996421	+	0.0845351i	$0.0269405\pi$
$379$	11.1244	+	19.2679i	0.571420	+	0.989728i	−0.425001	+	0.905193i	$0.639726\pi$
$380$		0			0
$381$	−2.00000	+	3.46410i	−0.102463	+	0.177471i
$382$	2.53590			0.129748
$383$	6.53590	−	11.3205i	0.333969	−	0.578451i	−0.649317	−	0.760518i	$-0.724945\pi$
$383$	6.53590	−	11.3205i	0.333969	−	0.578451i	0.983286	+	0.182067i	$0.0582786\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$		0			0
$386$	−3.33013	+	5.76795i	−0.169499	+	0.293581i
$387$	−3.36603	−	5.83013i	−0.171105	−	0.296362i
$388$	−5.00000	−	8.66025i	−0.253837	−	0.439658i
$389$	−37.9282			−1.92304			−0.961518	−	0.274742i	$-0.911408\pi$
$389$	−37.9282			−1.92304			−0.961518	+	0.274742i	$0.911408\pi$
$390$		0			0
$391$	10.3397			0.522903
$392$	−3.23205	−	5.59808i	−0.163243	−	0.282746i
$393$	6.92820	+	12.0000i	0.349482	+	0.605320i
$394$	8.92820	−	15.4641i	0.449796	−	0.779070i
$395$		0			0
$396$	1.36603	−	2.36603i	0.0686454	−	0.118897i
$397$	7.66025	−	13.2679i	0.384457	−	0.665899i	−0.607237	−	0.794521i	$-0.707722\pi$
$397$	7.66025	−	13.2679i	0.384457	−	0.665899i	0.991694	+	0.128622i	$0.0410553\pi$
$398$	−10.0526			−0.503889
$399$	1.73205	−	3.00000i	0.0867110	−	0.150188i
$400$		0			0
$401$	−14.5263	−	25.1603i	−0.725408	−	1.25644i	−0.958806	−	0.284062i	$-0.908318\pi$
$401$	−14.5263	−	25.1603i	−0.725408	−	1.25644i	0.233398	−	0.972381i	$-0.425015\pi$
$402$	9.66025			0.481810
$403$	12.9282	+	6.39230i	0.644000	+	0.318423i
$404$	0.0717968			0.00357202
$405$		0			0
$406$	0.169873	+	0.294229i	0.00843065	+	0.0146023i
$407$	8.09808	−	14.0263i	0.401407	−	0.695257i
$408$	2.46410			0.121991
$409$	−14.9641	+	25.9186i	−0.739927	+	1.28159i	0.212600	+	0.977139i	$0.431807\pi$
$409$	−14.9641	+	25.9186i	−0.739927	+	1.28159i	−0.952528	+	0.304452i	$0.901527\pi$
$410$		0			0
$411$	11.5359			0.569024
$412$	6.36603	−	11.0263i	0.313632	−	0.543226i
$413$	−3.07180	−	5.32051i	−0.151153	−	0.261805i
$414$	2.09808	+	3.63397i	0.103115	+	0.178600i
$415$		0			0
$416$	3.00000	−	2.00000i	0.147087	−	0.0980581i
$417$	14.9282			0.731037
$418$	−6.46410	−	11.1962i	−0.316170	−	0.547622i
$419$	6.73205	+	11.6603i	0.328882	+	0.569641i	0.982290	−	0.187365i	$-0.0599948\pi$
$419$	6.73205	+	11.6603i	0.328882	+	0.569641i	−0.653408	+	0.757006i	$0.726661\pi$
$420$		0			0
$421$	−21.0526			−1.02604			−0.513019	−	0.858377i	$-0.671473\pi$
$421$	−21.0526			−1.02604			−0.513019	+	0.858377i	$0.671473\pi$
$422$	−7.26795	+	12.5885i	−0.353798	+	0.612797i
$423$	−4.83013	+	8.36603i	−0.234849	+	0.406770i
$424$	4.26795			0.207270
$425$		0			0
$426$	−2.36603	−	4.09808i	−0.114634	−	0.198552i
$427$	−5.16987	−	8.95448i	−0.250188	−	0.433338i
$428$	−4.73205			−0.228732
$429$	−8.19615	+	5.46410i	−0.395714	+	0.263809i
$430$		0			0
$431$	9.09808	+	15.7583i	0.438239	+	0.759052i	0.997554	−	0.0699032i	$-0.0222691\pi$
$431$	9.09808	+	15.7583i	0.438239	+	0.759052i	−0.559315	+	0.828955i	$0.688936\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−12.5981	+	21.8205i	−0.605425	+	1.04863i	0.386559	+	0.922265i	$0.373663\pi$
$433$	−12.5981	+	21.8205i	−0.605425	+	1.04863i	−0.991984	+	0.126362i	$0.959670\pi$
$434$	−2.92820			−0.140558
$435$		0			0
$436$	−5.00000	+	8.66025i	−0.239457	+	0.414751i
$437$	19.8564			0.949861
$438$	6.33013	−	10.9641i	0.302465	−	0.523885i
$439$	−10.0981	−	17.4904i	−0.481955	−	0.834770i	0.517831	−	0.855483i	$-0.326740\pi$
$439$	−10.0981	−	17.4904i	−0.481955	−	0.834770i	−0.999785	+	0.0207128i	$0.993406\pi$
$440$		0			0
$441$	−6.46410			−0.307814
$442$	−7.96410	−	3.93782i	−0.378814	−	0.187303i
$443$	34.6410			1.64584			0.822922	−	0.568154i	$-0.192342\pi$
$443$	34.6410			1.64584			0.822922	+	0.568154i	$0.192342\pi$
$444$	2.96410	+	5.13397i	0.140670	+	0.243648i
$445$		0			0
$446$	−10.1962	+	17.6603i	−0.482802	+	0.836237i
$447$	−6.07180			−0.287186
$448$	−0.366025	+	0.633975i	−0.0172931	+	0.0299525i
$449$	−9.92820	+	17.1962i	−0.468541	+	0.811537i	−0.999353	−	0.0359526i	$-0.988553\pi$
$449$	−9.92820	+	17.1962i	−0.468541	+	0.811537i	0.530813	+	0.847489i	$0.321887\pi$
$450$		0			0
$451$	1.63397	−	2.83013i	0.0769409	−	0.133265i
$452$	4.50000	+	7.79423i	0.211662	+	0.366610i
$453$	9.56218	+	16.5622i	0.449270	+	0.778159i
$454$	6.19615			0.290800
$455$		0			0
$456$	4.73205			0.221599
$457$	−9.59808	−	16.6244i	−0.448979	−	0.777655i	0.549341	−	0.835598i	$-0.314879\pi$
$457$	−9.59808	−	16.6244i	−0.448979	−	0.777655i	−0.998320	+	0.0579439i	$0.981546\pi$
$458$	−6.39230	−	11.0718i	−0.298693	−	0.517351i
$459$	1.23205	−	2.13397i	0.0575072	−	0.0996054i
$460$		0			0
$461$	−19.9641	+	34.5788i	−0.929821	+	1.61050i	−0.146202	+	0.989255i	$0.546705\pi$
$461$	−19.9641	+	34.5788i	−0.929821	+	1.61050i	−0.783618	+	0.621242i	$0.786628\pi$
$462$	1.00000	−	1.73205i	0.0465242	−	0.0805823i
$463$	23.6603			1.09959			0.549793	−	0.835301i	$-0.314707\pi$
$463$	23.6603			1.09959			0.549793	+	0.835301i	$0.314707\pi$
$464$	−0.232051	+	0.401924i	−0.0107727	+	0.0186588i
$465$		0			0
$466$	4.19615	+	7.26795i	0.194383	+	0.336681i
$467$	−16.0526			−0.742824			−0.371412	−	0.928468i	$-0.621126\pi$
$467$	−16.0526			−0.742824			−0.371412	+	0.928468i	$0.621126\pi$
$468$	−0.232051	−	3.59808i	−0.0107266	−	0.166321i
$469$	7.07180			0.326545
$470$		0			0
$471$	5.69615	+	9.86603i	0.262465	+	0.454602i
$472$	4.19615	−	7.26795i	0.193144	−	0.334534i
$473$	−18.3923			−0.845679
$474$	−6.00000	+	10.3923i	−0.275589	+	0.477334i
$475$		0			0
$476$	1.80385			0.0826792
$477$	2.13397	−	3.69615i	0.0977080	−	0.169235i
$478$	13.2942	+	23.0263i	0.608064	+	1.05320i
$479$	8.00000	+	13.8564i	0.365529	+	0.633115i	0.988861	−	0.148842i	$-0.0475547\pi$
$479$	8.00000	+	13.8564i	0.365529	+	0.633115i	−0.623332	+	0.781958i	$0.714221\pi$
$480$		0			0
$481$	−1.37564	−	21.3301i	−0.0627240	−	0.972570i
$482$	−11.3923			−0.518905
$483$	1.53590	+	2.66025i	0.0698858	+	0.121046i
$484$	1.76795	+	3.06218i	0.0803613	+	0.139190i
$485$		0			0
$486$	1.00000			0.0453609
$487$	−10.2224	+	17.7058i	−0.463223	+	0.802325i	−0.999119	−	0.0419584i	$-0.986640\pi$
$487$	−10.2224	+	17.7058i	−0.463223	+	0.802325i	0.535897	+	0.844284i	$0.319974\pi$
$488$	7.06218	−	12.2321i	0.319690	−	0.553719i
$489$	−6.53590			−0.295564
$490$		0			0
$491$	−16.0981	−	27.8827i	−0.726496	−	1.25833i	−0.958355	−	0.285579i	$-0.907814\pi$
$491$	−16.0981	−	27.8827i	−0.726496	−	1.25833i	0.231859	−	0.972749i	$-0.425519\pi$
$492$	0.598076	+	1.03590i	0.0269634	+	0.0467019i
$493$	1.14359			0.0515049
$494$	−15.2942	−	7.56218i	−0.688120	−	0.340238i
$495$		0			0
$496$	−2.00000	−	3.46410i	−0.0898027	−	0.155543i
$497$	−1.73205	−	3.00000i	−0.0776931	−	0.134568i
$498$	4.36603	−	7.56218i	0.195646	−	0.338869i
$499$	19.6077			0.877761			0.438880	−	0.898545i	$-0.355375\pi$
$499$	19.6077			0.877761			0.438880	+	0.898545i	$0.355375\pi$
$500$		0			0
$501$	−6.92820	+	12.0000i	−0.309529	+	0.536120i
$502$	14.5359			0.648769
$503$	16.0981	−	27.8827i	0.717778	−	1.24323i	−0.244101	−	0.969750i	$-0.578493\pi$
$503$	16.0981	−	27.8827i	0.717778	−	1.24323i	0.961878	−	0.273478i	$-0.0881739\pi$
$504$	0.366025	+	0.633975i	0.0163041	+	0.0282395i
$505$		0			0
$506$	11.4641			0.509641
$507$	−5.00000	+	12.0000i	−0.222058	+	0.532939i
$508$	−4.00000			−0.177471
$509$	−12.3564	−	21.4019i	−0.547688	−	0.948624i	−0.998432	−	0.0559705i	$-0.982175\pi$
$509$	−12.3564	−	21.4019i	−0.547688	−	0.948624i	0.450744	−	0.892653i	$-0.351159\pi$
$510$		0			0
$511$	4.63397	−	8.02628i	0.204995	−	0.355062i
$512$	−1.00000			−0.0441942
$513$	2.36603	−	4.09808i	0.104463	−	0.180934i
$514$	1.50000	−	2.59808i	0.0661622	−	0.114596i
$515$		0			0
$516$	3.36603	−	5.83013i	0.148181	−	0.256657i
$517$	13.1962	+	22.8564i	0.580366	+	1.00522i
$518$	2.16987	+	3.75833i	0.0953387	+	0.165132i
$519$	22.7846			1.00013
$520$		0			0
$521$	39.4449			1.72811			0.864055	−	0.503397i	$-0.167917\pi$
$521$	39.4449			1.72811			0.864055	+	0.503397i	$0.167917\pi$
$522$	0.232051	+	0.401924i	0.0101566	+	0.0175917i
$523$	11.2224	+	19.4378i	0.490723	+	0.849957i	0.999943	−	0.0106796i	$-0.00339949\pi$
$523$	11.2224	+	19.4378i	0.490723	+	0.849957i	−0.509220	+	0.860636i	$0.670066\pi$
$524$	−6.92820	+	12.0000i	−0.302660	+	0.524222i
$525$		0			0
$526$	−3.56218	+	6.16987i	−0.155318	+	0.269019i
$527$	−4.92820	+	8.53590i	−0.214676	+	0.371830i
$528$	2.73205			0.118897
$529$	2.69615	−	4.66987i	0.117224	−	0.203038i
$530$		0			0
$531$	−4.19615	−	7.26795i	−0.182098	−	0.315402i
$532$	3.46410			0.150188
$533$	−0.277568	−	4.30385i	−0.0120228	−	0.186420i
$534$	8.92820			0.386361
$535$		0			0
$536$	4.83013	+	8.36603i	0.208630	+	0.361357i
$537$	3.90192	−	6.75833i	0.168380	−	0.291643i
$538$	16.3923			0.706722
$539$	−8.83013	+	15.2942i	−0.380340	+	0.658769i
$540$		0			0
$541$	9.19615			0.395373			0.197687	−	0.980265i	$-0.436657\pi$
$541$	9.19615			0.395373			0.197687	+	0.980265i	$0.436657\pi$
$542$	−10.9282	+	18.9282i	−0.469407	+	0.813036i
$543$	4.06218	+	7.03590i	0.174325	+	0.301939i
$544$	1.23205	+	2.13397i	0.0528237	+	0.0914934i
$545$		0			0
$546$	−0.169873	−	2.63397i	−0.00726989	−	0.112724i
$547$	−36.1962			−1.54764			−0.773818	−	0.633408i	$-0.781655\pi$
$547$	−36.1962			−1.54764			−0.773818	+	0.633408i	$0.781655\pi$
$548$	5.76795	+	9.99038i	0.246395	+	0.426768i
$549$	−7.06218	−	12.2321i	−0.301406	−	0.522051i
$550$		0			0
$551$	2.19615			0.0935592
$552$	−2.09808	+	3.63397i	−0.0893001	+	0.154672i
$553$	−4.39230	+	7.60770i	−0.186780	+	0.323512i
$554$	−22.3205			−0.948308
$555$		0			0
$556$	7.46410	+	12.9282i	0.316548	+	0.548278i
$557$	1.33013	+	2.30385i	0.0563593	+	0.0976172i	0.892829	−	0.450397i	$-0.148717\pi$
$557$	1.33013	+	2.30385i	0.0563593	+	0.0976172i	−0.836469	+	0.548014i	$0.815384\pi$
$558$	−4.00000			−0.169334
$559$	−20.1962	+	13.4641i	−0.854206	+	0.569471i
$560$		0			0
$561$	−3.36603	−	5.83013i	−0.142114	−	0.246148i
$562$	−0.866025	−	1.50000i	−0.0365311	−	0.0632737i
$563$	4.00000	−	6.92820i	0.168580	−	0.291989i	−0.769341	−	0.638838i	$-0.779415\pi$
$563$	4.00000	−	6.92820i	0.168580	−	0.291989i	0.937921	+	0.346850i	$0.112749\pi$
$564$	−9.66025			−0.406770
$565$		0			0
$566$	4.83013	−	8.36603i	0.203025	−	0.351650i
$567$	0.732051			0.0307432
$568$	2.36603	−	4.09808i	0.0992762	−	0.171951i
$569$	−22.9282	−	39.7128i	−0.961200	−	1.66485i	−0.719494	−	0.694498i	$-0.755626\pi$
$569$	−22.9282	−	39.7128i	−0.961200	−	1.66485i	−0.241706	−	0.970350i	$-0.577707\pi$
$570$		0			0
$571$	−8.33975			−0.349008			−0.174504	−	0.984657i	$-0.555832\pi$
$571$	−8.33975			−0.349008			−0.174504	+	0.984657i	$0.555832\pi$
$572$	−8.83013	−	4.36603i	−0.369206	−	0.182553i
$573$	2.53590			0.105939
$574$	0.437822	+	0.758330i	0.0182743	+	0.0316521i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	27.9808			1.16485			0.582427	−	0.812883i	$-0.302103\pi$
$577$	27.9808			1.16485			0.582427	+	0.812883i	$0.302103\pi$
$578$	−5.46410	+	9.46410i	−0.227277	+	0.393655i
$579$	−3.33013	+	5.76795i	−0.138395	+	0.239708i
$580$		0			0
$581$	3.19615	−	5.53590i	0.132599	−	0.229668i
$582$	−5.00000	−	8.66025i	−0.207257	−	0.358979i
$583$	−5.83013	−	10.0981i	−0.241459	−	0.418220i
$584$	12.6603			0.523885
$585$		0			0
$586$	10.2679			0.424165
$587$	18.9282	+	32.7846i	0.781251	+	1.35317i	0.931214	+	0.364474i	$0.118751\pi$
$587$	18.9282	+	32.7846i	0.781251	+	1.35317i	−0.149963	+	0.988692i	$0.547915\pi$
$588$	−3.23205	−	5.59808i	−0.133288	−	0.230861i
$589$	−9.46410	+	16.3923i	−0.389962	+	0.675433i
$590$		0			0
$591$	8.92820	−	15.4641i	0.367257	−	0.636108i
$592$	−2.96410	+	5.13397i	−0.121824	+	0.211005i
$593$	1.39230			0.0571751			0.0285876	−	0.999591i	$-0.490899\pi$
$593$	1.39230			0.0571751			0.0285876	+	0.999591i	$0.490899\pi$
$594$	1.36603	−	2.36603i	0.0560487	−	0.0970792i
$595$		0			0
$596$	−3.03590	−	5.25833i	−0.124355	−	0.215390i
$597$	−10.0526			−0.411424
$598$	12.5885	−	8.39230i	0.514780	−	0.343187i
$599$	−32.7846			−1.33954			−0.669771	−	0.742567i	$-0.733608\pi$
$599$	−32.7846			−1.33954			−0.669771	+	0.742567i	$0.733608\pi$
$600$		0			0
$601$	−8.50000	−	14.7224i	−0.346722	−	0.600541i	0.638943	−	0.769254i	$-0.279372\pi$
$601$	−8.50000	−	14.7224i	−0.346722	−	0.600541i	−0.985665	+	0.168714i	$0.946039\pi$
$602$	2.46410	−	4.26795i	0.100429	−	0.173949i
$603$	9.66025			0.393396
$604$	−9.56218	+	16.5622i	−0.389079	+	0.673905i
$605$		0			0
$606$	0.0717968			0.00291654
$607$	13.8038	−	23.9090i	0.560281	−	0.970435i	−0.437191	−	0.899369i	$-0.644027\pi$
$607$	13.8038	−	23.9090i	0.560281	−	0.970435i	0.997472	−	0.0710661i	$-0.0226401\pi$
$608$	2.36603	+	4.09808i	0.0959550	+	0.166199i
$609$	0.169873	+	0.294229i	0.00688360	+	0.0119227i
$610$		0			0
$611$	31.2224	+	15.4378i	1.26312	+	0.624547i
$612$	2.46410			0.0996054
$613$	−9.89230	−	17.1340i	−0.399546	−	0.692035i	0.594123	−	0.804374i	$-0.297499\pi$
$613$	−9.89230	−	17.1340i	−0.399546	−	0.692035i	−0.993670	+	0.112339i	$0.964166\pi$
$614$	11.3660	+	19.6865i	0.458695	+	0.794484i
$615$		0			0
$616$	2.00000			0.0805823
$617$	11.3564	−	19.6699i	0.457192	−	0.791879i	−0.541620	−	0.840624i	$-0.682189\pi$
$617$	11.3564	−	19.6699i	0.457192	−	0.791879i	0.998811	+	0.0487445i	$0.0155220\pi$
$618$	6.36603	−	11.0263i	0.256079	−	0.443542i
$619$	40.1051			1.61196			0.805980	−	0.591942i	$-0.201639\pi$
$619$	40.1051			1.61196			0.805980	+	0.591942i	$0.201639\pi$
$620$		0			0
$621$	2.09808	+	3.63397i	0.0841929	+	0.145826i
$622$	−10.5622	−	18.2942i	−0.423505	−	0.733532i
$623$	6.53590			0.261855
$624$	3.00000	−	2.00000i	0.120096	−	0.0800641i
$625$		0			0
$626$	7.00000	+	12.1244i	0.279776	+	0.484587i
$627$	−6.46410	−	11.1962i	−0.258151	−	0.447131i
$628$	−5.69615	+	9.86603i	−0.227301	+	0.393697i
$629$	14.6077			0.582447
$630$		0			0
$631$	8.92820	−	15.4641i	0.355426	−	0.615616i	−0.631765	−	0.775160i	$-0.717669\pi$
$631$	8.92820	−	15.4641i	0.355426	−	0.615616i	0.987191	+	0.159544i	$0.0510024\pi$
$632$	−12.0000			−0.477334
$633$	−7.26795	+	12.5885i	−0.288875	+	0.500346i
$634$	−13.1340	−	22.7487i	−0.521617	−	0.903467i
$635$		0			0
$636$	4.26795			0.169235
$637$	1.50000	+	23.2583i	0.0594322	+	0.921529i
$638$	1.26795			0.0501986
$639$	−2.36603	−	4.09808i	−0.0935985	−	0.162117i
$640$		0			0
$641$	14.5263	−	25.1603i	0.573754	−	0.993770i	−0.422422	−	0.906399i	$-0.638820\pi$
$641$	14.5263	−	25.1603i	0.573754	−	0.993770i	0.996176	−	0.0873711i	$-0.0278466\pi$
$642$	−4.73205			−0.186759
$643$	16.3923	−	28.3923i	0.646449	−	1.11968i	−0.337515	−	0.941320i	$-0.609586\pi$
$643$	16.3923	−	28.3923i	0.646449	−	1.11968i	0.983965	−	0.178363i	$-0.0570802\pi$
$644$	−1.53590	+	2.66025i	−0.0605229	+	0.104829i
$645$		0			0
$646$	5.83013	−	10.0981i	0.229383	−	0.397303i
$647$	5.66025	+	9.80385i	0.222528	+	0.385429i	0.955575	−	0.294749i	$-0.0952359\pi$
$647$	5.66025	+	9.80385i	0.222528	+	0.385429i	−0.733047	+	0.680178i	$0.761903\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−22.9282			−0.900011
$650$		0			0
$651$	−2.92820			−0.114765
$652$	−3.26795	−	5.66025i	−0.127983	−	0.221673i
$653$	−18.3205	−	31.7321i	−0.716937	−	1.24177i	−0.962208	−	0.272317i	$-0.912210\pi$
$653$	−18.3205	−	31.7321i	−0.716937	−	1.24177i	0.245271	−	0.969455i	$-0.421123\pi$
$654$	−5.00000	+	8.66025i	−0.195515	+	0.338643i
$655$		0			0
$656$	−0.598076	+	1.03590i	−0.0233510	+	0.0404450i
$657$	6.33013	−	10.9641i	0.246962	−	0.427750i
$658$	−7.07180			−0.275687
$659$	17.2679	−	29.9090i	0.672664	−	1.16509i	−0.304482	−	0.952518i	$-0.598483\pi$
$659$	17.2679	−	29.9090i	0.672664	−	1.16509i	0.977146	−	0.212570i	$-0.0681833\pi$
$660$		0			0
$661$	−3.25833	−	5.64359i	−0.126734	−	0.219510i	0.795675	−	0.605724i	$-0.207116\pi$
$661$	−3.25833	−	5.64359i	−0.126734	−	0.219510i	−0.922410	+	0.386213i	$0.873783\pi$
$662$	−12.7846			−0.496888
$663$	−7.96410	−	3.93782i	−0.309300	−	0.152932i
$664$	8.73205			0.338869
$665$		0			0
$666$	2.96410	+	5.13397i	0.114857	+	0.198937i
$667$	−0.973721	+	1.68653i	−0.0377026	+	0.0653028i
$668$	−13.8564			−0.536120
$669$	−10.1962	+	17.6603i	−0.394206	+	0.682785i
$670$		0			0
$671$	−38.5885			−1.48969
$672$	−0.366025	+	0.633975i	−0.0141197	+	0.0244561i
$673$	6.86603	+	11.8923i	0.264666	+	0.458415i	0.967476	−	0.252963i	$-0.0814050\pi$
$673$	6.86603	+	11.8923i	0.264666	+	0.458415i	−0.702810	+	0.711377i	$0.748072\pi$
$674$	13.5263	+	23.4282i	0.521013	+	0.902421i
$675$		0			0
$676$	−12.8923	+	1.66987i	−0.495858	+	0.0642259i
$677$	−20.6410			−0.793299			−0.396649	−	0.917970i	$-0.629827\pi$
$677$	−20.6410			−0.793299			−0.396649	+	0.917970i	$0.629827\pi$
$678$	4.50000	+	7.79423i	0.172821	+	0.299336i
$679$	−3.66025	−	6.33975i	−0.140468	−	0.243297i
$680$		0			0
$681$	6.19615			0.237437
$682$	−5.46410	+	9.46410i	−0.209231	+	0.362399i
$683$	−6.53590	+	11.3205i	−0.250089	+	0.433167i	−0.963550	−	0.267528i	$-0.913793\pi$
$683$	−6.53590	+	11.3205i	−0.250089	+	0.433167i	0.713461	+	0.700695i	$0.247127\pi$
$684$	4.73205			0.180934
$685$		0			0
$686$	−4.92820	−	8.53590i	−0.188160	−	0.325902i
$687$	−6.39230	−	11.0718i	−0.243882	−	0.422415i
$688$	6.73205			0.256657
$689$	−13.7942	−	6.82051i	−0.525518	−	0.259841i
$690$		0			0
$691$	−4.70577	−	8.15064i	−0.179016	−	0.310065i	0.762528	−	0.646955i	$-0.223958\pi$
$691$	−4.70577	−	8.15064i	−0.179016	−	0.310065i	−0.941544	+	0.336891i	$0.890625\pi$
$692$	11.3923	+	19.7321i	0.433070	+	0.750100i
$693$	1.00000	−	1.73205i	0.0379869	−	0.0657952i
$694$	11.6603			0.442617
$695$		0			0
$696$	−0.232051	+	0.401924i	−0.00879586	+	0.0152349i
$697$	2.94744			0.111642
$698$	−16.4641	+	28.5167i	−0.623175	+	1.07937i
$699$	4.19615	+	7.26795i	0.158713	+	0.274899i
$700$		0			0
$701$	−6.53590			−0.246857			−0.123429	−	0.992353i	$-0.539389\pi$
$701$	−6.53590			−0.246857			−0.123429	+	0.992353i	$0.539389\pi$
$702$	−0.232051	−	3.59808i	−0.00875819	−	0.135801i
$703$	28.0526			1.05802
$704$	1.36603	+	2.36603i	0.0514840	+	0.0891729i
$705$		0			0
$706$	−11.6244	+	20.1340i	−0.437488	+	0.757752i
$707$	0.0525589			0.00197668
$708$	4.19615	−	7.26795i	0.157701	−	0.273146i
$709$	0.526279	−	0.911543i	0.0197648	−	0.0342337i	−0.855974	−	0.517019i	$-0.827042\pi$
$709$	0.526279	−	0.911543i	0.0197648	−	0.0342337i	0.875739	+	0.482785i	$0.160375\pi$
$710$		0			0
$711$	−6.00000	+	10.3923i	−0.225018	+	0.389742i
$712$	4.46410	+	7.73205i	0.167299	+	0.289771i
$713$	−8.39230	−	14.5359i	−0.314294	−	0.544374i
$714$	1.80385			0.0675073
$715$		0			0
$716$	7.80385			0.291643
$717$	13.2942	+	23.0263i	0.496482	+	0.859932i
$718$	16.5622	+	28.6865i	0.618095	+	1.07057i
$719$	5.80385	−	10.0526i	0.216447	−	0.374897i	−0.737272	−	0.675596i	$-0.763886\pi$
$719$	5.80385	−	10.0526i	0.216447	−	0.374897i	0.953719	+	0.300699i	$0.0972198\pi$
$720$		0			0
$721$	4.66025	−	8.07180i	0.173557	−	0.300609i
$722$	1.69615	−	2.93782i	0.0631243	−	0.109334i
$723$	−11.3923			−0.423684
$724$	−4.06218	+	7.03590i	−0.150970	+	0.261487i
$725$		0			0
$726$	1.76795	+	3.06218i	0.0656147	+	0.113648i
$727$	16.7321			0.620557			0.310279	−	0.950646i	$-0.399578\pi$
$727$	16.7321			0.620557			0.310279	+	0.950646i	$0.399578\pi$
$728$	2.19615	−	1.46410i	0.0813948	−	0.0542632i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−8.29423	−	14.3660i	−0.306773	−	0.531347i
$732$	7.06218	−	12.2321i	0.261026	−	0.452110i
$733$	−24.6077			−0.908906			−0.454453	−	0.890771i	$-0.650165\pi$
$733$	−24.6077			−0.908906			−0.454453	+	0.890771i	$0.650165\pi$
$734$	9.49038	−	16.4378i	0.350296	−	0.606731i
$735$		0			0
$736$	−4.19615			−0.154672
$737$	13.1962	−	22.8564i	0.486087	−	0.841927i
$738$	0.598076	+	1.03590i	0.0220155	+	0.0381319i
$739$	−14.9282	−	25.8564i	−0.549143	−	0.951143i	−0.998334	−	0.0577074i	$-0.981621\pi$
$739$	−14.9282	−	25.8564i	−0.549143	−	0.951143i	0.449191	−	0.893436i	$-0.351712\pi$
$740$		0			0
$741$	−15.2942	−	7.56218i	−0.561848	−	0.277804i
$742$	3.12436			0.114699
$743$	−7.26795	−	12.5885i	−0.266635	−	0.461826i	0.701356	−	0.712812i	$-0.252579\pi$
$743$	−7.26795	−	12.5885i	−0.266635	−	0.461826i	−0.967991	+	0.250986i	$0.919245\pi$
$744$	−2.00000	−	3.46410i	−0.0733236	−	0.127000i
$745$		0			0
$746$	30.4641			1.11537
$747$	4.36603	−	7.56218i	0.159745	−	0.276686i
$748$	3.36603	−	5.83013i	0.123074	−	0.213171i
$749$	−3.46410			−0.126576
$750$		0			0
$751$	1.02628	+	1.77757i	0.0374495	+	0.0648644i	0.884143	−	0.467217i	$-0.154743\pi$
$751$	1.02628	+	1.77757i	0.0374495	+	0.0648644i	−0.846693	+	0.532081i	$0.821410\pi$
$752$	−4.83013	−	8.36603i	−0.176137	−	0.305078i
$753$	14.5359			0.529718
$754$	1.39230	−	0.928203i	0.0507048	−	0.0338032i
$755$		0			0
$756$	0.366025	+	0.633975i	0.0133122	+	0.0230574i
$757$	18.0526	+	31.2679i	0.656131	+	1.13645i	0.981609	+	0.190903i	$0.0611416\pi$
$757$	18.0526	+	31.2679i	0.656131	+	1.13645i	−0.325477	+	0.945550i	$0.605525\pi$
$758$	−11.1244	+	19.2679i	−0.404055	+	0.699843i
$759$	11.4641			0.416121
$760$		0			0
$761$	−18.4641	+	31.9808i	−0.669323	+	1.15930i	0.308771	+	0.951137i	$0.400082\pi$
$761$	−18.4641	+	31.9808i	−0.669323	+	1.15930i	−0.978094	+	0.208165i	$0.933251\pi$
$762$	−4.00000			−0.144905
$763$	−3.66025	+	6.33975i	−0.132510	+	0.229514i
$764$	1.26795	+	2.19615i	0.0458728	+	0.0794540i
$765$		0			0
$766$	13.0718			0.472303
$767$	−25.1769	+	16.7846i	−0.909086	+	0.606057i
$768$	−1.00000			−0.0360844
$769$	−19.2679	−	33.3731i	−0.694820	−	1.20346i	−0.970241	−	0.242140i	$-0.922151\pi$
$769$	−19.2679	−	33.3731i	−0.694820	−	1.20346i	0.275421	−	0.961324i	$-0.411183\pi$
$770$		0			0
$771$	1.50000	−	2.59808i	0.0540212	−	0.0935674i
$772$	−6.66025			−0.239708
$773$	−14.3205	+	24.8038i	−0.515073	+	0.892132i	0.484774	+	0.874639i	$0.338902\pi$
$773$	−14.3205	+	24.8038i	−0.515073	+	0.892132i	−0.999847	+	0.0174930i	$0.994432\pi$
$774$	3.36603	−	5.83013i	0.120989	−	0.209560i
$775$		0			0
$776$	5.00000	−	8.66025i	0.179490	−	0.310885i
$777$	2.16987	+	3.75833i	0.0778438	+	0.134829i
$778$	−18.9641	−	32.8468i	−0.679896	−	1.17761i
$779$	5.66025			0.202800
$780$		0			0
$781$	−12.9282			−0.462607
$782$	5.16987	+	8.95448i	0.184874	+	0.320212i
$783$	0.232051	+	0.401924i	0.00829282	+	0.0143636i
$784$	3.23205	−	5.59808i	0.115430	−	0.199931i
$785$		0			0
$786$	−6.92820	+	12.0000i	−0.247121	+	0.428026i
$787$	7.66025	−	13.2679i	0.273059	−	0.472951i	−0.696585	−	0.717474i	$-0.745298\pi$
$787$	7.66025	−	13.2679i	0.273059	−	0.472951i	0.969643	+	0.244523i	$0.0786314\pi$
$788$	17.8564			0.636108
$789$	−3.56218	+	6.16987i	−0.126817	+	0.219653i
$790$		0			0
$791$	3.29423	+	5.70577i	0.117129	+	0.202874i
$792$	2.73205			0.0970792
$793$	−42.3731	+	28.2487i	−1.50471	+	1.00314i
$794$	15.3205			0.543704
$795$		0			0
$796$	−5.02628	−	8.70577i	−0.178152	−	0.308568i
$797$	−7.46410	+	12.9282i	−0.264392	+	0.457940i	−0.967404	−	0.253237i	$-0.918505\pi$
$797$	−7.46410	+	12.9282i	−0.264392	+	0.457940i	0.703012	+	0.711178i	$0.251838\pi$
$798$	3.46410			0.122628
$799$	−11.9019	+	20.6147i	−0.421060	+	0.729297i
$800$		0			0
$801$	8.92820			0.315463
$802$	14.5263	−	25.1603i	0.512941	−	0.888439i
$803$	−17.2942	−	29.9545i	−0.610300	−	1.05707i
$804$	4.83013	+	8.36603i	0.170345	+	0.295047i
$805$		0			0
$806$	0.928203	+	14.3923i	0.0326946	+	0.506947i
$807$	16.3923			0.577036
$808$	0.0358984	+	0.0621778i	0.00126290	+	0.00218741i
$809$	24.9904	+	43.2846i	0.878615	+	1.52181i	0.852861	+	0.522138i	$0.174865\pi$
$809$	24.9904	+	43.2846i	0.878615	+	1.52181i	0.0257537	+	0.999668i	$0.491801\pi$
$810$		0			0
$811$	−6.14359			−0.215731			−0.107865	−	0.994166i	$-0.534402\pi$
$811$	−6.14359			−0.215731			−0.107865	+	0.994166i	$0.534402\pi$
$812$	−0.169873	+	0.294229i	−0.00596137	+	0.0103254i
$813$	−10.9282	+	18.9282i	−0.383269	+	0.663841i
$814$	16.1962			0.567675
$815$		0			0
$816$	1.23205	+	2.13397i	0.0431304	+	0.0747041i
$817$	−15.9282	−	27.5885i	−0.557257	−	0.965198i
$818$	−29.9282			−1.04642
$819$	−0.169873	−	2.63397i	−0.00593584	−	0.0920385i
$820$		0			0
$821$	19.1244	+	33.1244i	0.667445	+	1.15605i	0.978616	+	0.205694i	$0.0659452\pi$
$821$	19.1244	+	33.1244i	0.667445	+	1.15605i	−0.311172	+	0.950354i	$0.600721\pi$
$822$	5.76795	+	9.99038i	0.201180	+	0.348455i
$823$	−9.80385	+	16.9808i	−0.341741	+	0.591912i	−0.984756	−	0.173941i	$-0.944350\pi$
$823$	−9.80385	+	16.9808i	−0.341741	+	0.591912i	0.643015	+	0.765853i	$0.277683\pi$
$824$	12.7321			0.443542
$825$		0			0
$826$	3.07180	−	5.32051i	0.106881	−	0.185124i
$827$	−7.21539			−0.250904			−0.125452	−	0.992100i	$-0.540038\pi$
$827$	−7.21539			−0.250904			−0.125452	+	0.992100i	$0.540038\pi$
$828$	−2.09808	+	3.63397i	−0.0729132	+	0.126289i
$829$	−21.0622	−	36.4808i	−0.731520	−	1.26703i	−0.956234	−	0.292604i	$-0.905478\pi$
$829$	−21.0622	−	36.4808i	−0.731520	−	1.26703i	0.224714	−	0.974425i	$-0.427855\pi$
$830$		0			0
$831$	−22.3205			−0.774290
$832$	3.23205	+	1.59808i	0.112051	+	0.0554033i
$833$	−15.9282			−0.551880
$834$	7.46410	+	12.9282i	0.258461	+	0.447667i
$835$		0			0
$836$	6.46410	−	11.1962i	0.223566	−	0.387227i
$837$	−4.00000			−0.138260
$838$	−6.73205	+	11.6603i	−0.232555	+	0.402797i
$839$	14.0526	−	24.3397i	0.485148	−	0.840301i	−0.514706	−	0.857367i	$-0.672099\pi$
$839$	14.0526	−	24.3397i	0.485148	−	0.840301i	0.999854	+	0.0170653i	$0.00543232\pi$
$840$		0			0
$841$	14.3923	−	24.9282i	0.496286	−	0.859593i
$842$	−10.5263	−	18.2321i	−0.362760	−	0.628318i
$843$	−0.866025	−	1.50000i	−0.0298275	−	0.0516627i
$844$	−14.5359			−0.500346
$845$		0			0
$846$	−9.66025			−0.332126
$847$	1.29423	+	2.24167i	0.0444702	+	0.0770247i
$848$	2.13397	+	3.69615i	0.0732810	+	0.126926i
$849$	4.83013	−	8.36603i	0.165770	−	0.287121i
$850$		0			0
$851$	−12.4378	+	21.5429i	−0.426363	+	0.738482i
$852$	2.36603	−	4.09808i	0.0810587	−	0.140398i
$853$	25.9282			0.887765			0.443882	−	0.896085i	$-0.353601\pi$
$853$	25.9282			0.887765			0.443882	+	0.896085i	$0.353601\pi$
$854$	5.16987	−	8.95448i	0.176909	−	0.306416i
$855$		0			0
$856$	−2.36603	−	4.09808i	−0.0808691	−	0.140069i
$857$	9.92820			0.339141			0.169570	−	0.985518i	$-0.445762\pi$
$857$	9.92820			0.339141			0.169570	+	0.985518i	$0.445762\pi$
$858$	−8.83013	−	4.36603i	−0.301456	−	0.149054i
$859$	42.3013			1.44330			0.721650	−	0.692258i	$-0.243384\pi$
$859$	42.3013			1.44330			0.721650	+	0.692258i	$0.243384\pi$
$860$		0			0
$861$	0.437822	+	0.758330i	0.0149209	+	0.0258438i
$862$	−9.09808	+	15.7583i	−0.309882	+	0.536731i
$863$	3.12436			0.106354			0.0531772	−	0.998585i	$-0.483065\pi$
$863$	3.12436			0.106354			0.0531772	+	0.998585i	$0.483065\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$		0			0
$866$	−25.1962			−0.856200
$867$	−5.46410	+	9.46410i	−0.185571	+	0.321418i
$868$	−1.46410	−	2.53590i	−0.0496948	−	0.0860740i
$869$	16.3923	+	28.3923i	0.556071	+	0.963143i
$870$		0			0
$871$	−2.24167	−	34.7583i	−0.0759561	−	1.17774i
$872$	−10.0000			−0.338643
$873$	−5.00000	−	8.66025i	−0.169224	−	0.293105i
$874$	9.92820	+	17.1962i	0.335826	+	0.581669i
$875$		0			0
$876$	12.6603			0.427750
$877$	−8.23205	+	14.2583i	−0.277977	+	0.481470i	−0.970882	−	0.239559i	$-0.922997\pi$
$877$	−8.23205	+	14.2583i	−0.277977	+	0.481470i	0.692905	+	0.721029i	$0.256330\pi$
$878$	10.0981	−	17.4904i	0.340794	−	0.590272i
$879$	10.2679			0.346329
$880$		0			0
$881$	−21.0622	−	36.4808i	−0.709603	−	1.22907i	−0.965005	−	0.262233i	$-0.915541\pi$
$881$	−21.0622	−	36.4808i	−0.709603	−	1.22907i	0.255402	−	0.966835i	$-0.417792\pi$
$882$	−3.23205	−	5.59808i	−0.108829	−	0.188497i
$883$	−30.2487			−1.01795			−0.508975	−	0.860781i	$-0.669975\pi$
$883$	−30.2487			−1.01795			−0.508975	+	0.860781i	$0.669975\pi$
$884$	−0.571797	−	8.86603i	−0.0192316	−	0.298197i
$885$		0			0
$886$	17.3205	+	30.0000i	0.581894	+	1.00787i
$887$	21.4641	+	37.1769i	0.720694	+	1.24828i	0.960722	+	0.277513i	$0.0895100\pi$
$887$	21.4641	+	37.1769i	0.720694	+	1.24828i	−0.240028	+	0.970766i	$0.577157\pi$
$888$	−2.96410	+	5.13397i	−0.0994687	+	0.172285i
$889$	−2.92820			−0.0982088
$890$		0			0
$891$	1.36603	−	2.36603i	0.0457636	−	0.0792648i
$892$	−20.3923			−0.682785
$893$	−22.8564	+	39.5885i	−0.764860	+	1.32478i
$894$	−3.03590	−	5.25833i	−0.101536	−	0.175865i
$895$		0			0
$896$	−0.732051			−0.0244561
$897$	12.5885	−	8.39230i	0.420316	−	0.280211i
$898$	−19.8564			−0.662617
$899$	−0.928203	−	1.60770i	−0.0309573	−	0.0536196i
$900$		0			0
$901$	5.25833	−	9.10770i	0.175180	−	0.303421i
$902$	3.26795			0.108811
$903$	2.46410	−	4.26795i	0.0820002	−	0.142028i
$904$	−4.50000	+	7.79423i	−0.149668	+	0.259232i
$905$		0			0
$906$	−9.56218	+	16.5622i	−0.317682	+	0.550242i
$907$	−3.46410	−	6.00000i	−0.115024	−	0.199227i	0.802766	−	0.596295i	$-0.203361\pi$
$907$	−3.46410	−	6.00000i	−0.115024	−	0.199227i	−0.917789	+	0.397068i	$0.870028\pi$
$908$	3.09808	+	5.36603i	0.102813	+	0.178078i
$909$	0.0717968			0.00238135
$910$		0			0
$911$	−32.1051			−1.06369			−0.531845	−	0.846842i	$-0.678501\pi$
$911$	−32.1051			−1.06369			−0.531845	+	0.846842i	$0.678501\pi$
$912$	2.36603	+	4.09808i	0.0783469	+	0.135701i
$913$	−11.9282	−	20.6603i	−0.394766	−	0.683755i
$914$	9.59808	−	16.6244i	0.317476	−	0.549885i
$915$		0			0
$916$	6.39230	−	11.0718i	0.211208	−	0.365822i
$917$	−5.07180	+	8.78461i	−0.167485	+	0.290093i
$918$	2.46410			0.0813275
$919$	25.2679	−	43.7654i	0.833513	−	1.44369i	−0.0617229	−	0.998093i	$-0.519659\pi$
$919$	25.2679	−	43.7654i	0.833513	−	1.44369i	0.895236	−	0.445593i	$-0.147007\pi$
$920$		0			0
$921$	11.3660	+	19.6865i	0.374523	+	0.648693i
$922$	−39.9282			−1.31497
$923$	−14.1962	+	9.46410i	−0.467272	+	0.311515i
$924$	2.00000			0.0657952
$925$		0			0
$926$	11.8301	+	20.4904i	0.388762	+	0.673356i
$927$	6.36603	−	11.0263i	0.209088	−	0.362151i
$928$	−0.464102			−0.0152349
$929$	−4.20577	+	7.28461i	−0.137987	+	0.239000i	−0.926734	−	0.375717i	$-0.877397\pi$
$929$	−4.20577	+	7.28461i	−0.137987	+	0.239000i	0.788748	+	0.614717i	$0.210730\pi$
$930$		0			0
$931$	−30.5885			−1.00250
$932$	−4.19615	+	7.26795i	−0.137450	+	0.238070i
$933$	−10.5622	−	18.2942i	−0.345790	−	0.598926i
$934$	−8.02628	−	13.9019i	−0.262628	−	0.454885i
$935$		0			0
$936$	3.00000	−	2.00000i	0.0980581	−	0.0653720i
$937$	−21.0526			−0.687757			−0.343879	−	0.939014i	$-0.611741\pi$
$937$	−21.0526			−0.687757			−0.343879	+	0.939014i	$0.611741\pi$
$938$	3.53590	+	6.12436i	0.115451	+	0.199967i
$939$	7.00000	+	12.1244i	0.228436	+	0.395663i
$940$		0			0
$941$	−8.39230			−0.273581			−0.136791	−	0.990600i	$-0.543679\pi$
$941$	−8.39230			−0.273581			−0.136791	+	0.990600i	$0.543679\pi$
$942$	−5.69615	+	9.86603i	−0.185591	+	0.321452i
$943$	−2.50962	+	4.34679i	−0.0817244	+	0.141551i
$944$	8.39230			0.273146
$945$		0			0
$946$	−9.19615	−	15.9282i	−0.298993	−	0.517871i
$947$	−13.8564	−	24.0000i	−0.450273	−	0.779895i	0.548130	−	0.836393i	$-0.315340\pi$
$947$	−13.8564	−	24.0000i	−0.450273	−	0.779895i	−0.998403	+	0.0564979i	$0.982007\pi$
$948$	−12.0000			−0.389742
$949$	−40.9186	−	20.2321i	−1.32827	−	0.656760i
$950$		0			0
$951$	−13.1340	−	22.7487i	−0.425898	−	0.737678i
$952$	0.901924	+	1.56218i	0.0292315	+	0.0506305i
$953$	8.85641	−	15.3397i	0.286887	−	0.496903i	−0.686178	−	0.727434i	$-0.740713\pi$
$953$	8.85641	−	15.3397i	0.286887	−	0.496903i	0.973065	+	0.230531i	$0.0740462\pi$
$954$	4.26795			0.138180
$955$		0			0
$956$	−13.2942	+	23.0263i	−0.429966	+	0.744723i
$957$	1.26795			0.0409870
$958$	−8.00000	+	13.8564i	−0.258468	+	0.447680i
$959$	4.22243	+	7.31347i	0.136349	+	0.236164i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	17.7846	−	11.8564i	0.573399	−	0.382266i
$963$	−4.73205			−0.152488
$964$	−5.69615	−	9.86603i	−0.183461	−	0.317763i
$965$		0			0
$966$	−1.53590	+	2.66025i	−0.0494167	+	0.0855923i
$967$	−14.5885			−0.469133			−0.234567	−	0.972100i	$-0.575367\pi$
$967$	−14.5885			−0.469133			−0.234567	+	0.972100i	$0.575367\pi$
$968$	−1.76795	+	3.06218i	−0.0568240	+	0.0984221i
$969$	5.83013	−	10.0981i	0.187291	−	0.324397i
$970$		0			0
$971$	20.5359	−	35.5692i	0.659028	−	1.14147i	−0.321839	−	0.946794i	$-0.604301\pi$
$971$	20.5359	−	35.5692i	0.659028	−	1.14147i	0.980868	−	0.194676i	$-0.0623656\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	5.46410	+	9.46410i	0.175171	+	0.303405i
$974$	−20.4449			−0.655096
$975$		0			0
$976$	14.1244			0.452110
$977$	−13.6244	−	23.5981i	−0.435882	−	0.754969i	0.561485	−	0.827487i	$-0.310230\pi$
$977$	−13.6244	−	23.5981i	−0.435882	−	0.754969i	−0.997367	+	0.0725173i	$0.976897\pi$
$978$	−3.26795	−	5.66025i	−0.104497	−	0.180995i
$979$	12.1962	−	21.1244i	0.389791	−	0.675137i
$980$		0			0
$981$	−5.00000	+	8.66025i	−0.159638	+	0.276501i
$982$	16.0981	−	27.8827i	0.513710	−	0.889772i
$983$	−23.7128			−0.756321			−0.378161	−	0.925740i	$-0.623443\pi$
$983$	−23.7128			−0.756321			−0.378161	+	0.925740i	$0.623443\pi$
$984$	−0.598076	+	1.03590i	−0.0190660	+	0.0330232i
$985$		0			0
$986$	0.571797	+	0.990381i	0.0182097	+	0.0315402i
$987$	−7.07180			−0.225098
$988$	−1.09808	−	17.0263i	−0.0349345	−	0.541678i
$989$	28.2487			0.898257
$990$		0			0
$991$	15.0263	+	26.0263i	0.477325	+	0.826752i	0.999662	−	0.0259873i	$-0.00827294\pi$
$991$	15.0263	+	26.0263i	0.477325	+	0.826752i	−0.522337	+	0.852739i	$0.674940\pi$
$992$	2.00000	−	3.46410i	0.0635001	−	0.109985i
$993$	−12.7846			−0.405707
$994$	1.73205	−	3.00000i	0.0549373	−	0.0951542i
$995$		0			0
$996$	8.73205			0.276686
$997$	−1.03590	+	1.79423i	−0.0328072	+	0.0568238i	−0.881963	−	0.471319i	$-0.843778\pi$
$997$	−1.03590	+	1.79423i	−0.0328072	+	0.0568238i	0.849156	+	0.528143i	$0.177111\pi$
$998$	9.80385	+	16.9808i	0.310335	+	0.537517i
$999$	2.96410	+	5.13397i	0.0937800	+	0.162432i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.i.bh.601.1		4
5.2	odd	4		390.2.y.b.289.1	yes	4
5.3	odd	4		390.2.y.c.289.2	yes	4
5.4	even	2		1950.2.i.y.601.2		4
13.9	even	3	inner	1950.2.i.bh.451.1		4
15.2	even	4		1170.2.bp.d.289.2		4
15.8	even	4		1170.2.bp.e.289.1		4
65.9	even	6		1950.2.i.y.451.2		4
65.22	odd	12		390.2.y.c.139.2	yes	4
65.48	odd	12		390.2.y.b.139.1	✓	4
195.113	even	12		1170.2.bp.d.919.2		4
195.152	even	12		1170.2.bp.e.919.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.y.b.139.1	✓	4	65.48	odd	12
390.2.y.b.289.1	yes	4	5.2	odd	4
390.2.y.c.139.2	yes	4	65.22	odd	12
390.2.y.c.289.2	yes	4	5.3	odd	4
1170.2.bp.d.289.2		4	15.2	even	4
1170.2.bp.d.919.2		4	195.113	even	12
1170.2.bp.e.289.1		4	15.8	even	4
1170.2.bp.e.919.1		4	195.152	even	12
1950.2.i.y.451.2		4	65.9	even	6
1950.2.i.y.601.2		4	5.4	even	2
1950.2.i.bh.451.1		4	13.9	even	3	inner
1950.2.i.bh.601.1		4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-0.366025 + 0.633975i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-0.366025 + 0.633975i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.36603 + 2.36603i) q^{11} -1.00000 q^{12} +(3.23205 + 1.59808i) q^{13} -0.732051 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.23205 + 2.13397i) q^{17} -1.00000 q^{18} +(-2.36603 + 4.09808i) q^{19} -0.732051 q^{21} +(-1.36603 + 2.36603i) q^{22} +(-2.09808 - 3.63397i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(0.232051 + 3.59808i) q^{26} -1.00000 q^{27} +(-0.366025 - 0.633975i) q^{28} +(-0.232051 - 0.401924i) q^{29} +4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.36603 + 2.36603i) q^{33} -2.46410 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-2.96410 - 5.13397i) q^{37} -4.73205 q^{38} +(0.232051 + 3.59808i) q^{39} +(-0.598076 - 1.03590i) q^{41} +(-0.366025 - 0.633975i) q^{42} +(-3.36603 + 5.83013i) q^{43} -2.73205 q^{44} +(2.09808 - 3.63397i) q^{46} +9.66025 q^{47} +(0.500000 - 0.866025i) q^{48} +(3.23205 + 5.59808i) q^{49} -2.46410 q^{51} +(-3.00000 + 2.00000i) q^{52} -4.26795 q^{53} +(-0.500000 - 0.866025i) q^{54} +(0.366025 - 0.633975i) q^{56} -4.73205 q^{57} +(0.232051 - 0.401924i) q^{58} +(-4.19615 + 7.26795i) q^{59} +(-7.06218 + 12.2321i) q^{61} +(2.00000 + 3.46410i) q^{62} +(-0.366025 - 0.633975i) q^{63} +1.00000 q^{64} -2.73205 q^{66} +(-4.83013 - 8.36603i) q^{67} +(-1.23205 - 2.13397i) q^{68} +(2.09808 - 3.63397i) q^{69} +(-2.36603 + 4.09808i) q^{71} +(0.500000 - 0.866025i) q^{72} -12.6603 q^{73} +(2.96410 - 5.13397i) q^{74} +(-2.36603 - 4.09808i) q^{76} -2.00000 q^{77} +(-3.00000 + 2.00000i) q^{78} +12.0000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(0.598076 - 1.03590i) q^{82} -8.73205 q^{83} +(0.366025 - 0.633975i) q^{84} -6.73205 q^{86} +(0.232051 - 0.401924i) q^{87} +(-1.36603 - 2.36603i) q^{88} +(-4.46410 - 7.73205i) q^{89} +(-2.19615 + 1.46410i) q^{91} +4.19615 q^{92} +(2.00000 + 3.46410i) q^{93} +(4.83013 + 8.36603i) q^{94} +1.00000 q^{96} +(-5.00000 + 8.66025i) q^{97} +(-3.23205 + 5.59808i) q^{98} -2.73205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{6} + 2 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^6 + 2 * q^7 - 4 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{6} + 2 q^{7} - 4 q^{8} - 2 q^{9} + 2 q^{11} - 4 q^{12} + 6 q^{13} + 4 q^{14} - 2 q^{16} + 2 q^{17} - 4 q^{18} - 6 q^{19} + 4 q^{21} - 2 q^{22} + 2 q^{23} - 2 q^{24} - 6 q^{26} - 4 q^{27} + 2 q^{28} + 6 q^{29} + 16 q^{31} + 2 q^{32} - 2 q^{33} + 4 q^{34} - 2 q^{36} + 2 q^{37} - 12 q^{38} - 6 q^{39} + 8 q^{41} + 2 q^{42} - 10 q^{43} - 4 q^{44} - 2 q^{46} + 4 q^{47} + 2 q^{48} + 6 q^{49} + 4 q^{51} - 12 q^{52} - 24 q^{53} - 2 q^{54} - 2 q^{56} - 12 q^{57} - 6 q^{58} + 4 q^{59} - 4 q^{61} + 8 q^{62} + 2 q^{63} + 4 q^{64} - 4 q^{66} - 2 q^{67} + 2 q^{68} - 2 q^{69} - 6 q^{71} + 2 q^{72} - 16 q^{73} - 2 q^{74} - 6 q^{76} - 8 q^{77} - 12 q^{78} + 48 q^{79} - 2 q^{81} - 8 q^{82} - 28 q^{83} - 2 q^{84} - 20 q^{86} - 6 q^{87} - 2 q^{88} - 4 q^{89} + 12 q^{91} - 4 q^{92} + 8 q^{93} + 2 q^{94} + 4 q^{96} - 20 q^{97} - 6 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^6 + 2 * q^7 - 4 * q^8 - 2 * q^9 + 2 * q^11 - 4 * q^12 + 6 * q^13 + 4 * q^14 - 2 * q^16 + 2 * q^17 - 4 * q^18 - 6 * q^19 + 4 * q^21 - 2 * q^22 + 2 * q^23 - 2 * q^24 - 6 * q^26 - 4 * q^27 + 2 * q^28 + 6 * q^29 + 16 * q^31 + 2 * q^32 - 2 * q^33 + 4 * q^34 - 2 * q^36 + 2 * q^37 - 12 * q^38 - 6 * q^39 + 8 * q^41 + 2 * q^42 - 10 * q^43 - 4 * q^44 - 2 * q^46 + 4 * q^47 + 2 * q^48 + 6 * q^49 + 4 * q^51 - 12 * q^52 - 24 * q^53 - 2 * q^54 - 2 * q^56 - 12 * q^57 - 6 * q^58 + 4 * q^59 - 4 * q^61 + 8 * q^62 + 2 * q^63 + 4 * q^64 - 4 * q^66 - 2 * q^67 + 2 * q^68 - 2 * q^69 - 6 * q^71 + 2 * q^72 - 16 * q^73 - 2 * q^74 - 6 * q^76 - 8 * q^77 - 12 * q^78 + 48 * q^79 - 2 * q^81 - 8 * q^82 - 28 * q^83 - 2 * q^84 - 20 * q^86 - 6 * q^87 - 2 * q^88 - 4 * q^89 + 12 * q^91 - 4 * q^92 + 8 * q^93 + 2 * q^94 + 4 * q^96 - 20 * q^97 - 6 * q^98 - 4 * q^99

Introduction

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