LMFDB - Embedded newform 1950.2.i.y.601.2

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			601.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1950.601
Dual form			1950.2.i.y.451.2

$q$-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	−0.788526	−	0.615002i	$-0.789155\pi$
$7$	0.366025	−	0.633975i	0.138345	−	0.239620i	0.926870	+	0.375382i	$0.122489\pi$
$8$	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	−0.677049	−	0.735938i	$-0.736742\pi$
$17$	1.23205	−	2.13397i	0.298816	−	0.517565i	0.975865	+	0.218373i	$0.0700749\pi$
$18$	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	0.997494	−	0.0707462i	$-0.0225381\pi$
$23$	2.09808	+	3.63397i	0.437479	+	0.757736i	−0.560015	+	0.828482i	$0.689205\pi$
$24$	−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	0.999893	−	0.0146085i	$-0.00465020\pi$
$37$	2.96410	+	5.13397i	0.487295	+	0.844020i	−0.512598	+	0.858629i	$0.671317\pi$
$38$	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	$-0.661751\pi$
$43$	3.36603	−	5.83013i	0.513314	−	0.889086i	0.999881	−	0.0154426i	$-0.00491573\pi$
$44$	−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	$-0.748850\pi$
$47$	−9.66025			−1.40909			−0.704546	+	0.709658i	$0.748850\pi$
$48$	−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	$-0.405305\pi$
$53$	4.26795			0.586248			0.293124	+	0.956074i	$0.405305\pi$
$54$	−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	$0.0342426\pi$
$67$	4.83013	+	8.36603i	0.590094	+	1.02207i	−0.404125	+	0.914704i	$0.632424\pi$
$68$	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	$-0.234406\pi$
$73$	12.6603			1.48177			0.740885	+	0.671632i	$0.234406\pi$
$74$	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	$-0.340915\pi$
$83$	8.73205			0.958467			0.479234	+	0.877687i	$0.340915\pi$
$84$	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	$-0.663839\pi$
$97$	5.00000	−	8.66025i	0.507673	−	0.879316i	0.999961	−	0.00888289i	$-0.00282755\pi$
$98$	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	$-0.284175\pi$
$103$	12.7321			1.25453			0.627263	+	0.778807i	$0.284175\pi$
$104$	−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	0.728700	−	0.684833i	$-0.240125\pi$
$107$	−2.36603	−	4.09808i	−0.228732	−	0.396176i	−0.957433	+	0.288657i	$0.906791\pi$
$108$	−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	−0.996262	−	0.0863794i	$-0.972470\pi$
$113$	−4.50000	+	7.79423i	−0.423324	+	0.733219i	0.572938	+	0.819599i	$0.305804\pi$
$114$	−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	0.763542	−	0.645758i	$-0.223458\pi$
$127$	−2.00000	−	3.46410i	−0.177471	−	0.307389i	−0.941014	+	0.338368i	$0.890125\pi$
$128$	−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	−0.999966	−	0.00830645i	$-0.997356\pi$
$137$	−5.76795	+	9.99038i	−0.492789	+	0.853536i	0.507176	+	0.861842i	$0.330689\pi$
$138$	−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	$-0.650219\pi$
$157$	−11.3923			−0.909205			−0.454602	+	0.890694i	$0.650219\pi$
$158$	−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	−0.709192	−	0.705016i	$-0.750940\pi$
$163$	3.26795	−	5.66025i	0.255966	−	0.443345i	0.965157	+	0.261670i	$0.0842733\pi$
$164$	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	$-0.986556\pi$
$167$	−6.92820	−	12.0000i	−0.536120	−	0.928588i	0.462988	−	0.886365i	$-0.346777\pi$
$168$	−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	$0.500074\pi$
$173$	−11.3923	+	19.7321i	−0.866141	+	1.50020i	−0.865910	+	0.500200i	$0.833260\pi$
$174$	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	0.720923	−	0.693016i	$-0.243718\pi$
$193$	−3.33013	−	5.76795i	−0.239708	−	0.415186i	−0.960630	+	0.277830i	$0.910385\pi$
$194$	−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	$0.0527901\pi$
$197$	8.92820	+	15.4641i	0.636108	+	1.10177i	−0.350171	+	0.936686i	$0.613877\pi$
$198$	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	$-0.927435\pi$
$223$	−10.1962	−	17.6603i	−0.682785	−	1.18262i	0.291343	−	0.956619i	$-0.405898\pi$
$224$	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	−0.950332	−	0.311237i	$-0.899257\pi$
$227$	−3.09808	+	5.36603i	−0.205627	+	0.356156i	0.744706	+	0.667393i	$0.232590\pi$
$228$	−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	$-0.588644\pi$
$233$	−8.39230			−0.549798			−0.274899	+	0.961473i	$0.588644\pi$
$234$	−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	0.909010	−	0.416775i	$-0.136840\pi$
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	−0.815442	+	0.578838i	$0.803506\pi$
$258$	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	0.735049	−	0.678014i	$-0.237159\pi$
$263$	−3.56218	−	6.16987i	−0.219653	−	0.380451i	−0.954702	+	0.297564i	$0.903826\pi$
$264$	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	$-0.599390\pi$
$277$	11.1603	−	19.3301i	0.670555	−	1.16143i	0.977747	−	0.209787i	$-0.0672772\pi$
$278$	−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	0.973121	−	0.230293i	$-0.0739684\pi$
$283$	4.83013	+	8.36603i	0.287121	+	0.497309i	−0.686000	+	0.727601i	$0.740635\pi$
$284$	−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	−0.976120	−	0.217234i	$-0.930297\pi$
$293$	−5.13397	+	8.89230i	−0.299930	+	0.519494i	0.676190	+	0.736728i	$0.263630\pi$
$294$	−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	$-0.724684\pi$
$307$	−22.7321			−1.29739			−0.648693	+	0.761050i	$0.724684\pi$
$308$	−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	$-0.629485\pi$
$313$	−14.0000			−0.791327			−0.395663	+	0.918396i	$0.629485\pi$
$314$	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	$-0.235923\pi$
$317$	26.2679			1.47536			0.737678	+	0.675153i	$0.235923\pi$
$318$	−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	$-0.763675\pi$
$337$	−27.0526			−1.47365			−0.736823	+	0.676085i	$0.763675\pi$
$338$	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	−0.979006	−	0.203834i	$-0.934660\pi$
$347$	−5.83013	+	10.0981i	−0.312978	+	0.542093i	0.666028	+	0.745927i	$0.267993\pi$
$348$	−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	$-0.954325\pi$
$353$	−11.6244	−	20.1340i	−0.618702	−	1.07162i	0.371021	−	0.928625i	$-0.379008\pi$
$354$	−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	0.999986	−	0.00531057i	$-0.00169042\pi$
$367$	9.49038	+	16.4378i	0.495394	+	0.858047i	−0.504592	+	0.863358i	$0.668357\pi$
$368$	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	$0.455905\pi$
$373$	−15.2321	+	26.3827i	−0.788686	+	1.36604i	−0.926772	+	0.375624i	$0.877429\pi$
$374$	−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	−0.983286	−	0.182067i	$-0.941721\pi$
$383$	−6.53590	+	11.3205i	−0.333969	+	0.578451i	0.649317	+	0.760518i	$0.275055\pi$
$384$	−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	−0.991694	−	0.128622i	$-0.958945\pi$
$397$	−7.66025	+	13.2679i	−0.384457	+	0.665899i	0.607237	+	0.794521i	$0.292278\pi$
$398$	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	$-0.626337\pi$
$433$	12.5981	−	21.8205i	0.605425	−	1.04863i	0.991984	−	0.126362i	$-0.0403301\pi$
$434$	−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	$-0.807658\pi$
$443$	−34.6410			−1.64584			−0.822922	+	0.568154i	$0.807658\pi$
$444$	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	0.998320	−	0.0579439i	$-0.0184544\pi$
$457$	9.59808	+	16.6244i	0.448979	+	0.777655i	−0.549341	+	0.835598i	$0.685121\pi$
$458$	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	$-0.685293\pi$
$463$	−23.6603			−1.09959			−0.549793	+	0.835301i	$0.685293\pi$
$464$	−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	$-0.378874\pi$
$467$	16.0526			0.742824			0.371412	+	0.928468i	$0.378874\pi$
$468$	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	−0.535897	−	0.844284i	$-0.680026\pi$
$487$	10.2224	−	17.7058i	0.463223	−	0.802325i	0.999119	+	0.0419584i	$0.0133597\pi$
$488$	−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	$0.421507\pi$
$503$	−16.0981	+	27.8827i	−0.717778	+	1.24323i	−0.961878	+	0.273478i	$0.911826\pi$
$504$	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	0.509220	−	0.860636i	$-0.329934\pi$
$523$	−11.2224	−	19.4378i	−0.490723	−	0.849957i	−0.999943	+	0.0106796i	$0.996601\pi$
$524$	−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	$-0.218345\pi$
$547$	36.1962			1.54764			0.773818	+	0.633408i	$0.218345\pi$
$548$	−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	0.836469	−	0.548014i	$-0.184616\pi$
$557$	−1.33013	−	2.30385i	−0.0563593	−	0.0976172i	−0.892829	+	0.450397i	$0.851283\pi$
$558$	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	−0.937921	−	0.346850i	$-0.887251\pi$
$563$	−4.00000	+	6.92820i	−0.168580	+	0.291989i	0.769341	+	0.638838i	$0.220585\pi$
$564$	−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	$-0.697897\pi$
$577$	−27.9808			−1.16485			−0.582427	+	0.812883i	$0.697897\pi$
$578$	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	$-0.881249\pi$
$587$	−18.9282	−	32.7846i	−0.781251	−	1.35317i	0.149963	−	0.988692i	$-0.452085\pi$
$588$	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	$-0.509101\pi$
$593$	−1.39230			−0.0571751			−0.0285876	+	0.999591i	$0.509101\pi$
$594$	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	$0.355973\pi$
$607$	−13.8038	+	23.9090i	−0.560281	+	0.970435i	−0.997472	+	0.0710661i	$0.977360\pi$
$608$	−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	0.993670	−	0.112339i	$-0.0358343\pi$
$613$	9.89230	+	17.1340i	0.399546	+	0.692035i	−0.594123	+	0.804374i	$0.702501\pi$
$614$	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	−0.998811	−	0.0487445i	$-0.984478\pi$
$617$	−11.3564	+	19.6699i	−0.457192	+	0.791879i	0.541620	+	0.840624i	$0.317811\pi$
$618$	−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	$0.390414\pi$
$643$	−16.3923	+	28.3923i	−0.646449	+	1.11968i	−0.983965	+	0.178363i	$0.942920\pi$
$644$	−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	0.733047	−	0.680178i	$-0.238097\pi$
$647$	−5.66025	−	9.80385i	−0.222528	−	0.385429i	−0.955575	+	0.294749i	$0.904764\pi$
$648$	−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	$0.0877898\pi$
$653$	18.3205	+	31.7321i	0.716937	+	1.24177i	−0.245271	+	0.969455i	$0.578877\pi$
$654$	−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	0.702810	−	0.711377i	$-0.251928\pi$
$673$	−6.86603	−	11.8923i	−0.264666	−	0.458415i	−0.967476	+	0.252963i	$0.918595\pi$
$674$	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	$-0.370173\pi$
$677$	20.6410			0.793299			0.396649	+	0.917970i	$0.370173\pi$
$678$	−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	−0.713461	−	0.700695i	$-0.752873\pi$
$683$	6.53590	−	11.3205i	0.250089	−	0.433167i	0.963550	+	0.267528i	$0.0862067\pi$
$684$	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	$-0.600422\pi$
$727$	−16.7321			−0.620557			−0.310279	+	0.950646i	$0.600422\pi$
$728$	−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	$-0.349835\pi$
$733$	24.6077			0.908906			0.454453	+	0.890771i	$0.349835\pi$
$734$	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	0.967991	−	0.250986i	$-0.0807548\pi$
$743$	7.26795	+	12.5885i	0.266635	+	0.461826i	−0.701356	+	0.712812i	$0.747421\pi$
$744$	−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	$-0.938858\pi$
$757$	−18.0526	−	31.2679i	−0.656131	−	1.13645i	0.325477	−	0.945550i	$-0.394475\pi$
$758$	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	$-0.661098\pi$
$773$	14.3205	−	24.8038i	0.515073	−	0.892132i	0.999847	−	0.0174930i	$-0.00556848\pi$
$774$	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	−0.969643	−	0.244523i	$-0.921369\pi$
$787$	−7.66025	+	13.2679i	−0.273059	+	0.472951i	0.696585	+	0.717474i	$0.254702\pi$
$788$	−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	−0.703012	−	0.711178i	$-0.748162\pi$
$797$	7.46410	−	12.9282i	0.264392	−	0.457940i	0.967404	+	0.253237i	$0.0814954\pi$
$798$	−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	−0.643015	−	0.765853i	$-0.722317\pi$
$823$	9.80385	−	16.9808i	0.341741	−	0.591912i	0.984756	+	0.173941i	$0.0556502\pi$
$824$	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	$-0.459962\pi$
$827$	7.21539			0.250904			0.125452	+	0.992100i	$0.459962\pi$
$828$	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	$-0.646399\pi$
$853$	−25.9282			−0.887765			−0.443882	+	0.896085i	$0.646399\pi$
$854$	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	$-0.554238\pi$
$857$	−9.92820			−0.339141			−0.169570	+	0.985518i	$0.554238\pi$
$858$	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	$-0.516935\pi$
$863$	−3.12436			−0.106354			−0.0531772	+	0.998585i	$0.516935\pi$
$864$	−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	−0.692905	−	0.721029i	$-0.743670\pi$
$877$	8.23205	−	14.2583i	0.277977	−	0.481470i	0.970882	+	0.239559i	$0.0770029\pi$
$878$	−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	$-0.330025\pi$
$883$	30.2487			1.01795			0.508975	+	0.860781i	$0.330025\pi$
$884$	−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	$-0.910490\pi$
$887$	−21.4641	−	37.1769i	−0.720694	−	1.24828i	0.240028	−	0.970766i	$-0.422843\pi$
$888$	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	0.917789	−	0.397068i	$-0.129972\pi$
$907$	3.46410	+	6.00000i	0.115024	+	0.199227i	−0.802766	+	0.596295i	$0.796639\pi$
$908$	−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	$-0.388259\pi$
$937$	21.0526			0.687757			0.343879	+	0.939014i	$0.388259\pi$
$938$	−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	0.998403	−	0.0564979i	$-0.0179934\pi$
$947$	13.8564	+	24.0000i	0.450273	+	0.779895i	−0.548130	+	0.836393i	$0.684660\pi$
$948$	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	−0.973065	−	0.230531i	$-0.925954\pi$
$953$	−8.85641	+	15.3397i	−0.286887	+	0.496903i	0.686178	+	0.727434i	$0.259287\pi$
$954$	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	$-0.424633\pi$
$967$	14.5885			0.469133			0.234567	+	0.972100i	$0.424633\pi$
$968$	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	0.997367	−	0.0725173i	$-0.0231033\pi$
$977$	13.6244	+	23.5981i	0.435882	+	0.754969i	−0.561485	+	0.827487i	$0.689770\pi$
$978$	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	$-0.376557\pi$
$983$	23.7128			0.756321			0.378161	+	0.925740i	$0.376557\pi$
$984$	−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	−0.849156	−	0.528143i	$-0.822889\pi$
$997$	1.03590	−	1.79423i	0.0328072	−	0.0568238i	0.881963	+	0.471319i	$0.156222\pi$
$998$	−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.y.601.2		4
5.2	odd	4		390.2.y.c.289.2	yes	4
5.3	odd	4		390.2.y.b.289.1	yes	4
5.4	even	2		1950.2.i.bh.601.1		4
13.9	even	3	inner	1950.2.i.y.451.2		4
15.2	even	4		1170.2.bp.e.289.1		4
15.8	even	4		1170.2.bp.d.289.2		4
65.9	even	6		1950.2.i.bh.451.1		4
65.22	odd	12		390.2.y.b.139.1	✓	4
65.48	odd	12		390.2.y.c.139.2	yes	4
195.113	even	12		1170.2.bp.e.919.1		4
195.152	even	12		1170.2.bp.d.919.2		4

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

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

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