LMFDB - Embedded newform 975.2.bb.a.874.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(724,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("975.724");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bb (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			874.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	975.874
Dual form			975.2.bb.a.724.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.633975 + 0.366025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.732051 + 1.26795i) q^{4} +(-0.366025 + 0.633975i) q^{6} +(-1.50000 - 0.866025i) q^{7} -2.53590i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.633975 + 0.366025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.732051 + 1.26795i) q^{4} +(-0.366025 + 0.633975i) q^{6} +(-1.50000 - 0.866025i) q^{7} -2.53590i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{11} +1.46410i q^{12} +(3.23205 - 1.59808i) q^{13} +1.26795 q^{14} +(-0.535898 - 0.928203i) q^{16} +(0.633975 + 0.366025i) q^{17} +0.732051i q^{18} +(-0.267949 + 0.464102i) q^{19} -1.73205 q^{21} +(-1.26795 - 0.732051i) q^{22} +(1.73205 - 1.00000i) q^{23} +(-1.26795 - 2.19615i) q^{24} +(-1.46410 + 2.19615i) q^{26} -1.00000i q^{27} +(2.19615 - 1.26795i) q^{28} +(-1.63397 - 2.83013i) q^{29} +4.46410 q^{31} +(5.07180 + 2.92820i) q^{32} +(1.73205 + 1.00000i) q^{33} -0.535898 q^{34} +(0.732051 + 1.26795i) q^{36} +(9.00000 - 5.19615i) q^{37} -0.392305i q^{38} +(2.00000 - 3.00000i) q^{39} +(5.36603 + 9.29423i) q^{41} +(1.09808 - 0.633975i) q^{42} +(7.96410 + 4.59808i) q^{43} -2.92820 q^{44} +(-0.732051 + 1.26795i) q^{46} -0.196152i q^{47} +(-0.928203 - 0.535898i) q^{48} +(-2.00000 - 3.46410i) q^{49} +0.732051 q^{51} +(-0.339746 + 5.26795i) q^{52} -9.46410i q^{53} +(0.366025 + 0.633975i) q^{54} +(-2.19615 + 3.80385i) q^{56} +0.535898i q^{57} +(2.07180 + 1.19615i) q^{58} +(-5.83013 + 10.0981i) q^{59} +(-2.69615 + 4.66987i) q^{61} +(-2.83013 + 1.63397i) q^{62} +(-1.50000 + 0.866025i) q^{63} -2.14359 q^{64} -1.46410 q^{66} +(7.96410 - 4.59808i) q^{67} +(-0.928203 + 0.535898i) q^{68} +(1.00000 - 1.73205i) q^{69} +(2.36603 - 4.09808i) q^{71} +(-2.19615 - 1.26795i) q^{72} +1.73205i q^{73} +(-3.80385 + 6.58846i) q^{74} +(-0.392305 - 0.679492i) q^{76} -3.46410i q^{77} +(-0.169873 + 2.63397i) q^{78} +11.0000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-6.80385 - 3.92820i) q^{82} +2.92820i q^{83} +(1.26795 - 2.19615i) q^{84} -6.73205 q^{86} +(-2.83013 - 1.63397i) q^{87} +(4.39230 - 2.53590i) q^{88} +(2.63397 + 4.56218i) q^{89} +(-6.23205 - 0.401924i) q^{91} +2.92820i q^{92} +(3.86603 - 2.23205i) q^{93} +(0.0717968 + 0.124356i) q^{94} +5.85641 q^{96} +(4.50000 + 2.59808i) q^{97} +(2.53590 + 1.46410i) q^{98} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{2} + 4 q^{4} + 2 q^{6} - 6 q^{7} + 2 q^{9}+O(q^{10}) $ 4 * q - 6 * q^2 + 4 * q^4 + 2 * q^6 - 6 * q^7 + 2 * q^9	$ 4 q - 6 q^{2} + 4 q^{4} + 2 q^{6} - 6 q^{7} + 2 q^{9} + 4 q^{11} + 6 q^{13} + 12 q^{14} - 16 q^{16} + 6 q^{17} - 8 q^{19} - 12 q^{22} - 12 q^{24} + 8 q^{26} - 12 q^{28} - 10 q^{29} + 4 q^{31} + 48 q^{32} - 16 q^{34} - 4 q^{36} + 36 q^{37} + 8 q^{39} + 18 q^{41} - 6 q^{42} + 18 q^{43} + 16 q^{44} + 4 q^{46} + 24 q^{48} - 8 q^{49} - 4 q^{51} - 36 q^{52} - 2 q^{54} + 12 q^{56} + 36 q^{58} - 6 q^{59} + 10 q^{61} + 6 q^{62} - 6 q^{63} - 64 q^{64} + 8 q^{66} + 18 q^{67} + 24 q^{68} + 4 q^{69} + 6 q^{71} + 12 q^{72} - 36 q^{74} + 40 q^{76} - 18 q^{78} + 44 q^{79} - 2 q^{81} - 48 q^{82} + 12 q^{84} - 20 q^{86} + 6 q^{87} - 24 q^{88} + 14 q^{89} - 18 q^{91} + 12 q^{93} + 28 q^{94} - 32 q^{96} + 18 q^{97} + 24 q^{98} + 8 q^{99}+O(q^{100}) $ 4 * q - 6 * q^2 + 4 * q^4 + 2 * q^6 - 6 * q^7 + 2 * q^9 + 4 * q^11 + 6 * q^13 + 12 * q^14 - 16 * q^16 + 6 * q^17 - 8 * q^19 - 12 * q^22 - 12 * q^24 + 8 * q^26 - 12 * q^28 - 10 * q^29 + 4 * q^31 + 48 * q^32 - 16 * q^34 - 4 * q^36 + 36 * q^37 + 8 * q^39 + 18 * q^41 - 6 * q^42 + 18 * q^43 + 16 * q^44 + 4 * q^46 + 24 * q^48 - 8 * q^49 - 4 * q^51 - 36 * q^52 - 2 * q^54 + 12 * q^56 + 36 * q^58 - 6 * q^59 + 10 * q^61 + 6 * q^62 - 6 * q^63 - 64 * q^64 + 8 * q^66 + 18 * q^67 + 24 * q^68 + 4 * q^69 + 6 * q^71 + 12 * q^72 - 36 * q^74 + 40 * q^76 - 18 * q^78 + 44 * q^79 - 2 * q^81 - 48 * q^82 + 12 * q^84 - 20 * q^86 + 6 * q^87 - 24 * q^88 + 14 * q^89 - 18 * q^91 + 12 * q^93 + 28 * q^94 - 32 * q^96 + 18 * q^97 + 24 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

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 $

$2$	−0.633975	+	0.366025i	−0.448288	+	0.258819i	−0.707107	−	0.707107i	$-0.750000\pi$
$2$	−0.633975	+	0.366025i	−0.448288	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−0.732051	+	1.26795i	−0.366025	+	0.633975i
$5$		0			0
$5$		0			0
$6$	−0.366025	+	0.633975i	−0.149429	+	0.258819i
$7$	−1.50000	−	0.866025i	−0.566947	−	0.327327i	0.188982	−	0.981981i	$-0.439481\pi$
$7$	−1.50000	−	0.866025i	−0.566947	−	0.327327i	−0.755929	+	0.654654i	$0.772814\pi$
$8$		−	2.53590i		−	0.896575i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$			1.46410i			0.422650i
$13$	3.23205	−	1.59808i	0.896410	−	0.443227i
$13$	3.23205	−	1.59808i	0.896410	−	0.443227i
$14$	1.26795			0.338874
$15$		0			0
$16$	−0.535898	−	0.928203i	−0.133975	−	0.232051i
$17$	0.633975	+	0.366025i	0.153761	+	0.0887742i	0.574907	−	0.818219i	$-0.305038\pi$
$17$	0.633975	+	0.366025i	0.153761	+	0.0887742i	−0.421145	+	0.906993i	$0.638372\pi$
$18$			0.732051i			0.172546i
$19$	−0.267949	+	0.464102i	−0.0614718	+	0.106472i	−0.895123	−	0.445818i	$-0.852913\pi$
$19$	−0.267949	+	0.464102i	−0.0614718	+	0.106472i	0.833652	+	0.552291i	$0.186246\pi$
$20$		0			0
$21$	−1.73205			−0.377964
$22$	−1.26795	−	0.732051i	−0.270328	−	0.156074i
$23$	1.73205	−	1.00000i	0.361158	−	0.208514i	−0.308431	−	0.951247i	$-0.599804\pi$
$23$	1.73205	−	1.00000i	0.361158	−	0.208514i	0.669588	+	0.742732i	$0.266471\pi$
$24$	−1.26795	−	2.19615i	−0.258819	−	0.448288i
$25$		0			0
$26$	−1.46410	+	2.19615i	−0.287134	+	0.430701i
$27$		−	1.00000i		−	0.192450i
$28$	2.19615	−	1.26795i	0.415034	−	0.239620i
$29$	−1.63397	−	2.83013i	−0.303421	−	0.525541i	0.673487	−	0.739199i	$-0.264796\pi$
$29$	−1.63397	−	2.83013i	−0.303421	−	0.525541i	−0.976909	+	0.213658i	$0.931462\pi$
$30$		0			0
$31$	4.46410			0.801776			0.400888	−	0.916127i	$-0.368702\pi$
$31$	4.46410			0.801776			0.400888	+	0.916127i	$0.368702\pi$
$32$	5.07180	+	2.92820i	0.896575	+	0.517638i
$33$	1.73205	+	1.00000i	0.301511	+	0.174078i
$34$	−0.535898			−0.0919058
$35$		0			0
$36$	0.732051	+	1.26795i	0.122008	+	0.211325i
$37$	9.00000	−	5.19615i	1.47959	−	0.854242i	0.479858	−	0.877346i	$-0.340688\pi$
$37$	9.00000	−	5.19615i	1.47959	−	0.854242i	0.999733	+	0.0231041i	$0.00735491\pi$
$38$		−	0.392305i		−	0.0636402i
$39$	2.00000	−	3.00000i	0.320256	−	0.480384i
$40$		0			0
$41$	5.36603	+	9.29423i	0.838032	+	1.45151i	0.891537	+	0.452947i	$0.149627\pi$
$41$	5.36603	+	9.29423i	0.838032	+	1.45151i	−0.0535050	+	0.998568i	$0.517039\pi$
$42$	1.09808	−	0.633975i	0.169437	−	0.0978244i
$43$	7.96410	+	4.59808i	1.21451	+	0.701200i	0.963739	−	0.266845i	$-0.0859813\pi$
$43$	7.96410	+	4.59808i	1.21451	+	0.701200i	0.250775	+	0.968045i	$0.419315\pi$
$44$	−2.92820			−0.441443
$45$		0			0
$46$	−0.732051	+	1.26795i	−0.107935	+	0.186949i
$47$		−	0.196152i		−	0.0286118i	−0.999898	−	0.0143059i	$-0.995446\pi$
$47$		−	0.196152i		−	0.0286118i	0.999898	−	0.0143059i	$-0.00455386\pi$
$48$	−0.928203	−	0.535898i	−0.133975	−	0.0773503i
$49$	−2.00000	−	3.46410i	−0.285714	−	0.494872i
$50$		0			0
$51$	0.732051			0.102508
$52$	−0.339746	+	5.26795i	−0.0471143	+	0.730533i
$53$		−	9.46410i		−	1.29999i	−0.759937	−	0.649997i	$-0.774770\pi$
$53$		−	9.46410i		−	1.29999i	0.759937	−	0.649997i	$-0.225230\pi$
$54$	0.366025	+	0.633975i	0.0498097	+	0.0862730i
$55$		0			0
$56$	−2.19615	+	3.80385i	−0.293473	+	0.508311i
$57$			0.535898i			0.0709815i
$58$	2.07180	+	1.19615i	0.272040	+	0.157063i
$59$	−5.83013	+	10.0981i	−0.759018	+	1.31466i	0.184334	+	0.982864i	$0.440987\pi$
$59$	−5.83013	+	10.0981i	−0.759018	+	1.31466i	−0.943352	+	0.331794i	$0.892346\pi$
$60$		0			0
$61$	−2.69615	+	4.66987i	−0.345207	+	0.597916i	−0.985391	−	0.170305i	$-0.945525\pi$
$61$	−2.69615	+	4.66987i	−0.345207	+	0.597916i	0.640184	+	0.768221i	$0.278858\pi$
$62$	−2.83013	+	1.63397i	−0.359426	+	0.207515i
$63$	−1.50000	+	0.866025i	−0.188982	+	0.109109i
$64$	−2.14359			−0.267949
$65$		0			0
$66$	−1.46410			−0.180218
$67$	7.96410	−	4.59808i	0.972970	−	0.561744i	0.0728295	−	0.997344i	$-0.476797\pi$
$67$	7.96410	−	4.59808i	0.972970	−	0.561744i	0.900140	+	0.435600i	$0.143464\pi$
$68$	−0.928203	+	0.535898i	−0.112561	+	0.0649872i
$69$	1.00000	−	1.73205i	0.120386	−	0.208514i
$70$		0			0
$71$	2.36603	−	4.09808i	0.280796	−	0.486352i	−0.690785	−	0.723060i	$-0.742735\pi$
$71$	2.36603	−	4.09808i	0.280796	−	0.486352i	0.971581	+	0.236708i	$0.0760684\pi$
$72$	−2.19615	−	1.26795i	−0.258819	−	0.149429i
$73$			1.73205i			0.202721i	0.994850	+	0.101361i	$0.0323196\pi$
$73$			1.73205i			0.202721i	−0.994850	+	0.101361i	$0.967680\pi$
$74$	−3.80385	+	6.58846i	−0.442188	+	0.765893i
$75$		0			0
$76$	−0.392305	−	0.679492i	−0.0450005	−	0.0779431i
$77$		−	3.46410i		−	0.394771i
$78$	−0.169873	+	2.63397i	−0.0192343	+	0.298239i
$79$	11.0000			1.23760			0.618798	−	0.785550i	$-0.287620\pi$
$79$	11.0000			1.23760			0.618798	+	0.785550i	$0.287620\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−6.80385	−	3.92820i	−0.751359	−	0.433797i
$83$			2.92820i			0.321412i	0.987002	+	0.160706i	$0.0513771\pi$
$83$			2.92820i			0.321412i	−0.987002	+	0.160706i	$0.948623\pi$
$84$	1.26795	−	2.19615i	0.138345	−	0.239620i
$85$		0			0
$86$	−6.73205			−0.725936
$87$	−2.83013	−	1.63397i	−0.303421	−	0.175180i
$88$	4.39230	−	2.53590i	0.468221	−	0.270328i
$89$	2.63397	+	4.56218i	0.279201	+	0.483590i	0.971186	−	0.238321i	$-0.0765972\pi$
$89$	2.63397	+	4.56218i	0.279201	+	0.483590i	−0.691986	+	0.721911i	$0.743264\pi$
$90$		0			0
$91$	−6.23205	−	0.401924i	−0.653296	−	0.0421331i
$92$			2.92820i			0.305286i
$93$	3.86603	−	2.23205i	0.400888	−	0.231453i
$94$	0.0717968	+	0.124356i	0.00740527	+	0.0128263i
$95$		0			0
$96$	5.85641			0.597717
$97$	4.50000	+	2.59808i	0.456906	+	0.263795i	0.710742	−	0.703452i	$-0.248359\pi$
$97$	4.50000	+	2.59808i	0.456906	+	0.263795i	−0.253837	+	0.967247i	$0.581693\pi$
$98$	2.53590	+	1.46410i	0.256164	+	0.147897i
$99$	2.00000			0.201008
$100$		0			0
$101$	−5.19615	−	9.00000i	−0.517036	−	0.895533i	−0.999804	−	0.0197851i	$-0.993702\pi$
$101$	−5.19615	−	9.00000i	−0.517036	−	0.895533i	0.482768	−	0.875748i	$-0.339632\pi$
$102$	−0.464102	+	0.267949i	−0.0459529	+	0.0265309i
$103$			5.73205i			0.564796i	0.959297	+	0.282398i	$0.0911298\pi$
$103$			5.73205i			0.564796i	−0.959297	+	0.282398i	$0.908870\pi$
$104$	−4.05256	−	8.19615i	−0.397386	−	0.803699i
$105$		0			0
$106$	3.46410	+	6.00000i	0.336463	+	0.582772i
$107$	−7.09808	+	4.09808i	−0.686197	+	0.396176i	−0.802186	−	0.597075i	$-0.796330\pi$
$107$	−7.09808	+	4.09808i	−0.686197	+	0.396176i	0.115989	+	0.993251i	$0.462996\pi$
$108$	1.26795	+	0.732051i	0.122008	+	0.0704416i
$109$	15.3923			1.47432			0.737158	−	0.675721i	$-0.236167\pi$
$109$	15.3923			1.47432			0.737158	+	0.675721i	$0.236167\pi$
$110$		0			0
$111$	5.19615	−	9.00000i	0.493197	−	0.854242i
$112$			1.85641i			0.175414i
$113$	−15.9282	−	9.19615i	−1.49840	−	0.865101i	−0.498401	−	0.866947i	$-0.666079\pi$
$113$	−15.9282	−	9.19615i	−1.49840	−	0.865101i	−0.999998	+	0.00184536i	$0.999413\pi$
$114$	−0.196152	−	0.339746i	−0.0183714	−	0.0318201i
$115$		0			0
$116$	4.78461			0.444240
$117$	0.232051	−	3.59808i	0.0214531	−	0.332642i
$118$		−	8.53590i		−	0.785793i
$119$	−0.633975	−	1.09808i	−0.0581164	−	0.100660i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$		−	3.94744i		−	0.357385i
$123$	9.29423	+	5.36603i	0.838032	+	0.483838i
$124$	−3.26795	+	5.66025i	−0.293471	+	0.508306i
$125$		0			0
$126$	0.633975	−	1.09808i	0.0564789	−	0.0978244i
$127$	0.571797	−	0.330127i	0.0507388	−	0.0292940i	−0.474416	−	0.880301i	$-0.657341\pi$
$127$	0.571797	−	0.330127i	0.0507388	−	0.0292940i	0.525155	+	0.851007i	$0.324007\pi$
$128$	−8.78461	+	5.07180i	−0.776457	+	0.448288i
$129$	9.19615			0.809676
$130$		0			0
$131$	−2.19615			−0.191879			−0.0959394	−	0.995387i	$-0.530585\pi$
$131$	−2.19615			−0.191879			−0.0959394	+	0.995387i	$0.530585\pi$
$132$	−2.53590	+	1.46410i	−0.220722	+	0.127434i
$133$	0.803848	−	0.464102i	0.0697024	−	0.0402427i
$134$	−3.36603	+	5.83013i	−0.290780	+	0.503646i
$135$		0			0
$136$	0.928203	−	1.60770i	0.0795928	−	0.137859i
$137$	−10.0981	−	5.83013i	−0.862737	−	0.498101i	0.00219097	−	0.999998i	$-0.499303\pi$
$137$	−10.0981	−	5.83013i	−0.862737	−	0.498101i	−0.864928	+	0.501896i	$0.832636\pi$
$138$			1.46410i			0.124633i
$139$	9.96410	−	17.2583i	0.845144	−	1.46383i	−0.0403520	−	0.999186i	$-0.512848\pi$
$139$	9.96410	−	17.2583i	0.845144	−	1.46383i	0.885496	−	0.464647i	$-0.153819\pi$
$140$		0			0
$141$	−0.0980762	−	0.169873i	−0.00825951	−	0.0143059i
$142$			3.46410i			0.290701i
$143$	6.00000	+	4.00000i	0.501745	+	0.334497i
$144$	−1.07180			−0.0893164
$145$		0			0
$146$	−0.633975	−	1.09808i	−0.0524681	−	0.0908774i
$147$	−3.46410	−	2.00000i	−0.285714	−	0.164957i
$148$			15.2154i			1.25070i
$149$	−2.92820	+	5.07180i	−0.239888	+	0.415498i	−0.960682	−	0.277651i	$-0.910444\pi$
$149$	−2.92820	+	5.07180i	−0.239888	+	0.415498i	0.720794	+	0.693149i	$0.243777\pi$
$150$		0			0
$151$	−0.928203			−0.0755361			−0.0377681	−	0.999287i	$-0.512025\pi$
$151$	−0.928203			−0.0755361			−0.0377681	+	0.999287i	$0.512025\pi$
$152$	1.17691	+	0.679492i	0.0954604	+	0.0551141i
$153$	0.633975	−	0.366025i	0.0512538	−	0.0295914i
$154$	1.26795	+	2.19615i	0.102174	+	0.176971i
$155$		0			0
$156$	2.33975	+	4.73205i	0.187330	+	0.378867i
$157$			3.73205i			0.297850i	0.988848	+	0.148925i	$0.0475813\pi$
$157$			3.73205i			0.297850i	−0.988848	+	0.148925i	$0.952419\pi$
$158$	−6.97372	+	4.02628i	−0.554799	+	0.320314i
$159$	−4.73205	−	8.19615i	−0.375276	−	0.649997i
$160$		0			0
$161$	−3.46410			−0.273009
$162$	0.633975	+	0.366025i	0.0498097	+	0.0287577i
$163$	−18.3564	−	10.5981i	−1.43778	−	0.830105i	−0.440089	−	0.897954i	$-0.645053\pi$
$163$	−18.3564	−	10.5981i	−1.43778	−	0.830105i	−0.997696	+	0.0678487i	$0.978386\pi$
$164$	−15.7128			−1.22696
$165$		0			0
$166$	−1.07180	−	1.85641i	−0.0831876	−	0.144085i
$167$	18.9282	−	10.9282i	1.46471	−	0.845650i	0.465485	−	0.885056i	$-0.345880\pi$
$167$	18.9282	−	10.9282i	1.46471	−	0.845650i	0.999223	+	0.0394060i	$0.0125466\pi$
$168$			4.39230i			0.338874i
$169$	7.89230	−	10.3301i	0.607100	−	0.794625i
$170$		0			0
$171$	0.267949	+	0.464102i	0.0204906	+	0.0354907i
$172$	−11.6603	+	6.73205i	−0.889086	+	0.513314i
$173$	−10.5622	−	6.09808i	−0.803028	−	0.463628i	0.0415012	−	0.999138i	$-0.486786\pi$
$173$	−10.5622	−	6.09808i	−0.803028	−	0.463628i	−0.844529	+	0.535510i	$0.820119\pi$
$174$	2.39230			0.181360
$175$		0			0
$176$	1.07180	−	1.85641i	0.0807897	−	0.139932i
$177$			11.6603i			0.876438i
$178$	−3.33975	−	1.92820i	−0.250325	−	0.144525i
$179$	8.83013	+	15.2942i	0.659995	+	1.14314i	0.980616	+	0.195937i	$0.0627748\pi$
$179$	8.83013	+	15.2942i	0.659995	+	1.14314i	−0.320622	+	0.947207i	$0.603892\pi$
$180$		0			0
$181$	8.39230			0.623795			0.311898	−	0.950116i	$-0.399035\pi$
$181$	8.39230			0.623795			0.311898	+	0.950116i	$0.399035\pi$
$182$	4.09808	−	2.02628i	0.303770	−	0.150198i
$183$			5.39230i			0.398611i
$184$	−2.53590	−	4.39230i	−0.186949	−	0.323805i
$185$		0			0
$186$	−1.63397	+	2.83013i	−0.119809	+	0.207515i
$187$			1.46410i			0.107066i
$188$	0.248711	+	0.143594i	0.0181391	+	0.0104726i
$189$	−0.866025	+	1.50000i	−0.0629941	+	0.109109i
$190$		0			0
$191$	−11.2942	+	19.5622i	−0.817222	+	1.41547i	0.0904999	+	0.995896i	$0.471154\pi$
$191$	−11.2942	+	19.5622i	−0.817222	+	1.41547i	−0.907722	+	0.419573i	$0.862180\pi$
$192$	−1.85641	+	1.07180i	−0.133975	+	0.0773503i
$193$	−16.6244	+	9.59808i	−1.19665	+	0.690885i	−0.959806	−	0.280664i	$-0.909445\pi$
$193$	−16.6244	+	9.59808i	−1.19665	+	0.690885i	−0.236841	+	0.971548i	$0.576112\pi$
$194$	−3.80385			−0.273100
$195$		0			0
$196$	5.85641			0.418315
$197$	−14.1962	+	8.19615i	−1.01143	+	0.583952i	−0.911611	−	0.411054i	$-0.865161\pi$
$197$	−14.1962	+	8.19615i	−1.01143	+	0.583952i	−0.0998228	+	0.995005i	$0.531828\pi$
$198$	−1.26795	+	0.732051i	−0.0901092	+	0.0520246i
$199$	−12.4282	+	21.5263i	−0.881012	+	1.52596i	−0.0307946	+	0.999526i	$0.509804\pi$
$199$	−12.4282	+	21.5263i	−0.881012	+	1.52596i	−0.850217	+	0.526432i	$0.823530\pi$
$200$		0			0
$201$	4.59808	−	7.96410i	0.324323	−	0.561744i
$202$	6.58846	+	3.80385i	0.463562	+	0.267638i
$203$			5.66025i			0.397272i
$204$	−0.535898	+	0.928203i	−0.0375204	+	0.0649872i
$205$		0			0
$206$	−2.09808	−	3.63397i	−0.146180	−	0.253191i
$207$		−	2.00000i		−	0.139010i
$208$	−3.21539	−	2.14359i	−0.222947	−	0.148631i
$209$	−1.07180			−0.0741377
$210$		0			0
$211$	−11.1603	−	19.3301i	−0.768304	−	1.33074i	−0.938482	−	0.345328i	$-0.887768\pi$
$211$	−11.1603	−	19.3301i	−0.768304	−	1.33074i	0.170179	−	0.985413i	$-0.445566\pi$
$212$	12.0000	+	6.92820i	0.824163	+	0.475831i
$213$		−	4.73205i		−	0.324235i
$214$	3.00000	−	5.19615i	0.205076	−	0.355202i
$215$		0			0
$216$	−2.53590			−0.172546
$217$	−6.69615	−	3.86603i	−0.454564	−	0.262443i
$218$	−9.75833	+	5.63397i	−0.660918	+	0.381581i
$219$	0.866025	+	1.50000i	0.0585206	+	0.101361i
$220$		0			0
$221$	2.63397	+	0.169873i	0.177180	+	0.0114269i
$222$			7.60770i			0.510595i
$223$	1.60770	−	0.928203i	0.107659	−	0.0621571i	−0.445204	−	0.895429i	$-0.646869\pi$
$223$	1.60770	−	0.928203i	0.107659	−	0.0621571i	0.552863	+	0.833272i	$0.313535\pi$
$224$	−5.07180	−	8.78461i	−0.338874	−	0.586946i
$225$		0			0
$226$	13.4641			0.895619
$227$	−4.09808	−	2.36603i	−0.271999	−	0.157039i	0.357797	−	0.933799i	$-0.383528\pi$
$227$	−4.09808	−	2.36603i	−0.271999	−	0.157039i	−0.629796	+	0.776761i	$0.716861\pi$
$228$	−0.679492	−	0.392305i	−0.0450005	−	0.0259810i
$229$	−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
$231$	−1.73205	−	3.00000i	−0.113961	−	0.197386i
$232$	−7.17691	+	4.14359i	−0.471188	+	0.272040i
$233$		−	28.2487i		−	1.85063i	−0.379194	−	0.925317i	$-0.623799\pi$
$233$		−	28.2487i		−	1.85063i	0.379194	−	0.925317i	$-0.376201\pi$
$234$	1.16987	+	2.36603i	0.0764770	+	0.154672i
$235$		0			0
$236$	−8.53590	−	14.7846i	−0.555640	−	0.962396i
$237$	9.52628	−	5.50000i	0.618798	−	0.357263i
$238$	0.803848	+	0.464102i	0.0521057	+	0.0300832i
$239$	13.8564			0.896296			0.448148	−	0.893959i	$-0.352084\pi$
$239$	13.8564			0.896296			0.448148	+	0.893959i	$0.352084\pi$
$240$		0			0
$241$	−2.00000	+	3.46410i	−0.128831	+	0.223142i	−0.923224	−	0.384262i	$-0.874456\pi$
$241$	−2.00000	+	3.46410i	−0.128831	+	0.223142i	0.794393	+	0.607404i	$0.207789\pi$
$242$			5.12436i			0.329406i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−3.94744	−	6.83717i	−0.252709	−	0.437705i
$245$		0			0
$246$	−7.85641			−0.500906
$247$	−0.124356	+	1.92820i	−0.00791256	+	0.122689i
$248$		−	11.3205i		−	0.718853i
$249$	1.46410	+	2.53590i	0.0927837	+	0.160706i
$250$		0			0
$251$	3.26795	−	5.66025i	0.206271	−	0.357272i	−0.744266	−	0.667883i	$-0.767200\pi$
$251$	3.26795	−	5.66025i	0.206271	−	0.357272i	0.950537	+	0.310611i	$0.100534\pi$
$252$		−	2.53590i		−	0.159747i
$253$	3.46410	+	2.00000i	0.217786	+	0.125739i
$254$	−0.241670	+	0.418584i	−0.0151637	+	0.0262643i
$255$		0			0
$256$	5.85641	−	10.1436i	0.366025	−	0.633975i
$257$	1.90192	−	1.09808i	0.118639	−	0.0684961i	−0.439506	−	0.898239i	$-0.644847\pi$
$257$	1.90192	−	1.09808i	0.118639	−	0.0684961i	0.558145	+	0.829743i	$0.311513\pi$
$258$	−5.83013	+	3.36603i	−0.362968	+	0.209560i
$259$	−18.0000			−1.11847
$260$		0			0
$261$	−3.26795			−0.202281
$262$	1.39230	−	0.803848i	0.0860169	−	0.0496619i
$263$	2.49038	−	1.43782i	0.153563	−	0.0886599i	−0.421249	−	0.906945i	$-0.638408\pi$
$263$	2.49038	−	1.43782i	0.153563	−	0.0886599i	0.574813	+	0.818285i	$0.305075\pi$
$264$	2.53590	−	4.39230i	0.156074	−	0.270328i
$265$		0			0
$266$	−0.339746	+	0.588457i	−0.0208312	+	0.0360806i
$267$	4.56218	+	2.63397i	0.279201	+	0.161197i
$268$			13.4641i			0.822451i
$269$	−14.2942	+	24.7583i	−0.871535	+	1.50954i	−0.0111254	+	0.999938i	$0.503541\pi$
$269$	−14.2942	+	24.7583i	−0.871535	+	1.50954i	−0.860409	+	0.509604i	$0.829792\pi$
$270$		0			0
$271$	−11.2321	−	19.4545i	−0.682298	−	1.18178i	−0.974278	−	0.225351i	$-0.927647\pi$
$271$	−11.2321	−	19.4545i	−0.682298	−	1.18178i	0.291979	−	0.956425i	$-0.405686\pi$
$272$		−	0.784610i		−	0.0475740i
$273$	−5.59808	+	2.76795i	−0.338811	+	0.167524i
$274$	8.53590			0.515672
$275$		0			0
$276$	1.46410	+	2.53590i	0.0881286	+	0.152643i
$277$	−22.8564	−	13.1962i	−1.37331	−	0.792880i	−0.381965	−	0.924177i	$-0.624753\pi$
$277$	−22.8564	−	13.1962i	−1.37331	−	0.792880i	−0.991343	+	0.131297i	$0.958086\pi$
$278$			14.5885i			0.874958i
$279$	2.23205	−	3.86603i	0.133629	−	0.231453i
$280$		0			0
$281$	−11.2679			−0.672189			−0.336095	−	0.941828i	$-0.609106\pi$
$281$	−11.2679			−0.672189			−0.336095	+	0.941828i	$0.609106\pi$
$282$	0.124356	+	0.0717968i	0.00740527	+	0.00427544i
$283$	13.9641	−	8.06218i	0.830080	−	0.479247i	−0.0238003	−	0.999717i	$-0.507577\pi$
$283$	13.9641	−	8.06218i	0.830080	−	0.479247i	0.853880	+	0.520470i	$0.174243\pi$
$284$	3.46410	+	6.00000i	0.205557	+	0.356034i
$285$		0			0
$286$	−5.26795	−	0.339746i	−0.311500	−	0.0200896i
$287$		−	18.5885i		−	1.09724i
$288$	5.07180	−	2.92820i	0.298858	−	0.172546i
$289$	−8.23205	−	14.2583i	−0.484238	−	0.838725i
$290$		0			0
$291$	5.19615			0.304604
$292$	−2.19615	−	1.26795i	−0.128520	−	0.0742011i
$293$	−7.09808	−	4.09808i	−0.414674	−	0.239412i	0.278122	−	0.960546i	$-0.410288\pi$
$293$	−7.09808	−	4.09808i	−0.414674	−	0.239412i	−0.692796	+	0.721134i	$0.743621\pi$
$294$	2.92820			0.170776
$295$		0			0
$296$	−13.1769	−	22.8231i	−0.765893	−	1.32656i
$297$	1.73205	−	1.00000i	0.100504	−	0.0580259i
$298$		−	4.28719i		−	0.248350i
$299$	4.00000	−	6.00000i	0.231326	−	0.346989i
$300$		0			0
$301$	−7.96410	−	13.7942i	−0.459043	−	0.795086i
$302$	0.588457	−	0.339746i	0.0338619	−	0.0195502i
$303$	−9.00000	−	5.19615i	−0.517036	−	0.298511i
$304$	0.574374			0.0329426
$305$		0			0
$306$	−0.267949	+	0.464102i	−0.0153176	+	0.0265309i
$307$			6.66025i			0.380121i	0.981772	+	0.190060i	$0.0608684\pi$
$307$			6.66025i			0.380121i	−0.981772	+	0.190060i	$0.939132\pi$
$308$	4.39230	+	2.53590i	0.250275	+	0.144496i
$309$	2.86603	+	4.96410i	0.163042	+	0.282398i
$310$		0			0
$311$	12.5885			0.713826			0.356913	−	0.934138i	$-0.383829\pi$
$311$	12.5885			0.713826			0.356913	+	0.934138i	$0.383829\pi$
$312$	−7.60770	−	5.07180i	−0.430701	−	0.287134i
$313$			19.1962i			1.08503i	0.840046	+	0.542515i	$0.182528\pi$
$313$			19.1962i			1.08503i	−0.840046	+	0.542515i	$0.817472\pi$
$314$	−1.36603	−	2.36603i	−0.0770893	−	0.133523i
$315$		0			0
$316$	−8.05256	+	13.9474i	−0.452992	+	0.784605i
$317$			28.3923i			1.59467i	0.603537	+	0.797335i	$0.293758\pi$
$317$			28.3923i			1.59467i	−0.603537	+	0.797335i	$0.706242\pi$
$318$	6.00000	+	3.46410i	0.336463	+	0.194257i
$319$	3.26795	−	5.66025i	0.182970	−	0.316913i
$320$		0			0
$321$	−4.09808	+	7.09808i	−0.228732	+	0.396176i
$322$	2.19615	−	1.26795i	0.122387	−	0.0706600i
$323$	−0.339746	+	0.196152i	−0.0189040	+	0.0109142i
$324$	1.46410			0.0813390
$325$		0			0
$326$	15.5167			0.859388
$327$	13.3301	−	7.69615i	0.737158	−	0.425598i
$328$	23.5692	−	13.6077i	1.30139	−	0.751359i
$329$	−0.169873	+	0.294229i	−0.00936540	+	0.0162213i
$330$		0			0
$331$	−11.9641	+	20.7224i	−0.657606	+	1.13901i	0.323627	+	0.946185i	$0.395098\pi$
$331$	−11.9641	+	20.7224i	−0.657606	+	1.13901i	−0.981234	+	0.192823i	$0.938236\pi$
$332$	−3.71281	−	2.14359i	−0.203767	−	0.117645i
$333$		−	10.3923i		−	0.569495i
$334$	−8.00000	+	13.8564i	−0.437741	+	0.758189i
$335$		0			0
$336$	0.928203	+	1.60770i	0.0506376	+	0.0877070i
$337$		−	25.5885i		−	1.39389i	−0.717124	−	0.696946i	$-0.754542\pi$
$337$		−	25.5885i		−	1.39389i	0.717124	−	0.696946i	$-0.245458\pi$
$338$	−1.22243	+	9.43782i	−0.0664915	+	0.513350i
$339$	−18.3923			−0.998933
$340$		0			0
$341$	4.46410	+	7.73205i	0.241745	+	0.418714i
$342$	−0.339746	−	0.196152i	−0.0183714	−	0.0106067i
$343$			19.0526i			1.02874i
$344$	11.6603	−	20.1962i	0.628679	−	1.08890i
$345$		0			0
$346$	8.92820			0.479983
$347$	−1.26795	−	0.732051i	−0.0680671	−	0.0392985i	0.465580	−	0.885006i	$-0.345846\pi$
$347$	−1.26795	−	0.732051i	−0.0680671	−	0.0392985i	−0.533647	+	0.845707i	$0.679179\pi$
$348$	4.14359	−	2.39230i	0.222120	−	0.128241i
$349$	15.4282	+	26.7224i	0.825853	+	1.43042i	0.901266	+	0.433267i	$0.142639\pi$
$349$	15.4282	+	26.7224i	0.825853	+	1.43042i	−0.0754130	+	0.997152i	$0.524028\pi$
$350$		0			0
$351$	−1.59808	−	3.23205i	−0.0852990	−	0.172514i
$352$			11.7128i			0.624295i
$353$	−8.32051	+	4.80385i	−0.442856	+	0.255683i	−0.704808	−	0.709398i	$-0.748967\pi$
$353$	−8.32051	+	4.80385i	−0.442856	+	0.255683i	0.261952	+	0.965081i	$0.415634\pi$
$354$	−4.26795	−	7.39230i	−0.226839	−	0.392897i
$355$		0			0
$356$	−7.71281			−0.408778
$357$	−1.09808	−	0.633975i	−0.0581164	−	0.0335535i
$358$	−11.1962	−	6.46410i	−0.591735	−	0.341638i
$359$	−0.196152			−0.0103525			−0.00517626	−	0.999987i	$-0.501648\pi$
$359$	−0.196152			−0.0103525			−0.00517626	+	0.999987i	$0.501648\pi$
$360$		0			0
$361$	9.35641	+	16.2058i	0.492442	+	0.852935i
$362$	−5.32051	+	3.07180i	−0.279640	+	0.161450i
$363$		−	7.00000i		−	0.367405i
$364$	5.07180	−	7.60770i	0.265834	−	0.398752i
$365$		0			0
$366$	−1.97372	−	3.41858i	−0.103168	−	0.178692i
$367$	−13.0359	+	7.52628i	−0.680468	+	0.392869i	−0.800031	−	0.599958i	$-0.795184\pi$
$367$	−13.0359	+	7.52628i	−0.680468	+	0.392869i	0.119563	+	0.992827i	$0.461851\pi$
$368$	−1.85641	−	1.07180i	−0.0967719	−	0.0558713i
$369$	10.7321			0.558688
$370$		0			0
$371$	−8.19615	+	14.1962i	−0.425523	+	0.737028i
$372$			6.53590i			0.338871i
$373$	−6.35641	−	3.66987i	−0.329122	−	0.190019i	0.326329	−	0.945256i	$-0.394188\pi$
$373$	−6.35641	−	3.66987i	−0.329122	−	0.190019i	−0.655451	+	0.755237i	$0.727522\pi$
$374$	−0.535898	−	0.928203i	−0.0277106	−	0.0479962i
$375$		0			0
$376$	−0.497423			−0.0256526
$377$	−9.80385	−	6.53590i	−0.504924	−	0.336616i
$378$		−	1.26795i		−	0.0652163i
$379$	3.23205	+	5.59808i	0.166019	+	0.287554i	0.937017	−	0.349284i	$-0.113575\pi$
$379$	3.23205	+	5.59808i	0.166019	+	0.287554i	−0.770997	+	0.636838i	$0.780242\pi$
$380$		0			0
$381$	0.330127	−	0.571797i	0.0169129	−	0.0292940i
$382$		−	16.5359i		−	0.846050i
$383$	16.6865	+	9.63397i	0.852642	+	0.492273i	0.861541	−	0.507687i	$-0.169499\pi$
$383$	16.6865	+	9.63397i	0.852642	+	0.492273i	−0.00889939	+	0.999960i	$0.502833\pi$
$384$	−5.07180	+	8.78461i	−0.258819	+	0.448288i
$385$		0			0
$386$	7.02628	−	12.1699i	0.357628	−	0.619430i
$387$	7.96410	−	4.59808i	0.404838	−	0.233733i
$388$	−6.58846	+	3.80385i	−0.334478	+	0.193111i
$389$	14.5359			0.736999			0.368500	−	0.929628i	$-0.379872\pi$
$389$	14.5359			0.736999			0.368500	+	0.929628i	$0.379872\pi$
$390$		0			0
$391$	1.46410			0.0740428
$392$	−8.78461	+	5.07180i	−0.443690	+	0.256164i
$393$	−1.90192	+	1.09808i	−0.0959394	+	0.0553906i
$394$	6.00000	−	10.3923i	0.302276	−	0.523557i
$395$		0			0
$396$	−1.46410	+	2.53590i	−0.0735739	+	0.127434i
$397$	8.42820	+	4.86603i	0.422999	+	0.244219i	0.696360	−	0.717693i	$-0.254802\pi$
$397$	8.42820	+	4.86603i	0.422999	+	0.244219i	−0.273360	+	0.961912i	$0.588135\pi$
$398$		−	18.1962i		−	0.912091i
$399$	0.464102	−	0.803848i	0.0232341	−	0.0402427i
$400$		0			0
$401$	15.1244	+	26.1962i	0.755274	+	1.30817i	0.945238	+	0.326382i	$0.105830\pi$
$401$	15.1244	+	26.1962i	0.755274	+	1.30817i	−0.189964	+	0.981791i	$0.560837\pi$
$402$			6.73205i			0.335764i
$403$	14.4282	−	7.13397i	0.718720	−	0.355369i
$404$	15.2154			0.756994
$405$		0			0
$406$	−2.07180	−	3.58846i	−0.102822	−	0.178092i
$407$	18.0000	+	10.3923i	0.892227	+	0.515127i
$408$		−	1.85641i		−	0.0919058i
$409$	3.16025	−	5.47372i	0.156265	−	0.270658i	−0.777254	−	0.629187i	$-0.783388\pi$
$409$	3.16025	−	5.47372i	0.156265	−	0.270658i	0.933519	+	0.358529i	$0.116721\pi$
$410$		0			0
$411$	−11.6603			−0.575158
$412$	−7.26795	−	4.19615i	−0.358066	−	0.206730i
$413$	17.4904	−	10.0981i	0.860645	−	0.496894i
$414$	0.732051	+	1.26795i	0.0359783	+	0.0623163i
$415$		0			0
$416$	21.0718	+	1.35898i	1.03313	+	0.0666297i
$417$		−	19.9282i		−	0.975888i
$418$	0.679492	−	0.392305i	0.0332350	−	0.0191883i
$419$	−19.9545	−	34.5622i	−0.974840	−	1.68847i	−0.680461	−	0.732784i	$-0.738220\pi$
$419$	−19.9545	−	34.5622i	−0.974840	−	1.68847i	−0.294379	−	0.955689i	$-0.595113\pi$
$420$		0			0
$421$	12.8564			0.626583			0.313291	−	0.949657i	$-0.398568\pi$
$421$	12.8564			0.626583			0.313291	+	0.949657i	$0.398568\pi$
$422$	14.1506	+	8.16987i	0.688842	+	0.397703i
$423$	−0.169873	−	0.0980762i	−0.00825951	−	0.00476863i
$424$	−24.0000			−1.16554
$425$		0			0
$426$	1.73205	+	3.00000i	0.0839181	+	0.145350i
$427$	8.08846	−	4.66987i	0.391428	−	0.225991i
$428$		−	12.0000i		−	0.580042i
$429$	7.19615	+	0.464102i	0.347434	+	0.0224070i
$430$		0			0
$431$	10.5359	+	18.2487i	0.507496	+	0.879009i	0.999962	+	0.00867780i	$0.00276226\pi$
$431$	10.5359	+	18.2487i	0.507496	+	0.879009i	−0.492466	+	0.870332i	$0.663904\pi$
$432$	−0.928203	+	0.535898i	−0.0446582	+	0.0257834i
$433$	−16.5000	−	9.52628i	−0.792939	−	0.457804i	0.0480569	−	0.998845i	$-0.484697\pi$
$433$	−16.5000	−	9.52628i	−0.792939	−	0.457804i	−0.840996	+	0.541041i	$0.818030\pi$
$434$	5.66025			0.271701
$435$		0			0
$436$	−11.2679	+	19.5167i	−0.539637	+	0.934679i
$437$			1.07180i			0.0512710i
$438$	−1.09808	−	0.633975i	−0.0524681	−	0.0302925i
$439$	−9.69615	−	16.7942i	−0.462772	−	0.801545i	0.536326	−	0.844011i	$-0.319812\pi$
$439$	−9.69615	−	16.7942i	−0.462772	−	0.801545i	−0.999098	+	0.0424662i	$0.986479\pi$
$440$		0			0
$441$	−4.00000			−0.190476
$442$	−1.73205	+	0.856406i	−0.0823853	+	0.0407351i
$443$			29.1244i			1.38374i	0.722022	+	0.691870i	$0.243213\pi$
$443$			29.1244i			1.38374i	−0.722022	+	0.691870i	$0.756787\pi$
$444$	7.60770	+	13.1769i	0.361045	+	0.625349i
$445$		0			0
$446$	−0.679492	+	1.17691i	−0.0321749	+	0.0557285i
$447$			5.85641i			0.276999i
$448$	3.21539	+	1.85641i	0.151913	+	0.0877070i
$449$	7.73205	−	13.3923i	0.364898	−	0.632022i	−0.623862	−	0.781535i	$-0.714437\pi$
$449$	7.73205	−	13.3923i	0.364898	−	0.632022i	0.988760	+	0.149513i	$0.0477705\pi$
$450$		0			0
$451$	−10.7321	+	18.5885i	−0.505353	+	0.875296i
$452$	23.3205	−	13.4641i	1.09690	−	0.633298i
$453$	−0.803848	+	0.464102i	−0.0377681	+	0.0218054i
$454$	3.46410			0.162578
$455$		0			0
$456$	1.35898			0.0636402
$457$	12.5718	−	7.25833i	0.588084	−	0.339530i	−0.176256	−	0.984344i	$-0.556399\pi$
$457$	12.5718	−	7.25833i	0.588084	−	0.339530i	0.764339	+	0.644814i	$0.223065\pi$
$458$	8.10512	−	4.67949i	0.378727	−	0.218658i
$459$	0.366025	−	0.633975i	0.0170846	−	0.0295914i
$460$		0			0
$461$	5.02628	−	8.70577i	0.234097	−	0.405468i	−0.724913	−	0.688841i	$-0.758120\pi$
$461$	5.02628	−	8.70577i	0.234097	−	0.405468i	0.959010	+	0.283373i	$0.0914533\pi$
$462$	2.19615	+	1.26795i	0.102174	+	0.0589903i
$463$		−	1.33975i		−	0.0622633i	−0.999515	−	0.0311316i	$-0.990089\pi$
$463$		−	1.33975i		−	0.0622633i	0.999515	−	0.0311316i	$-0.00991111\pi$
$464$	−1.75129	+	3.03332i	−0.0813015	+	0.140818i
$465$		0			0
$466$	10.3397	+	17.9090i	0.478979	+	0.829617i
$467$		−	10.3397i		−	0.478466i	−0.970962	−	0.239233i	$-0.923104\pi$
$467$		−	10.3397i		−	0.478466i	0.970962	−	0.239233i	$-0.0768960\pi$
$468$	4.39230	+	2.92820i	0.203034	+	0.135356i
$469$	−15.9282			−0.735496
$470$		0			0
$471$	1.86603	+	3.23205i	0.0859819	+	0.148925i
$472$	25.6077	+	14.7846i	1.17869	+	0.680517i
$473$			18.3923i			0.845679i
$474$	−4.02628	+	6.97372i	−0.184933	+	0.320314i
$475$		0			0
$476$	1.85641			0.0850883
$477$	−8.19615	−	4.73205i	−0.375276	−	0.216666i
$478$	−8.78461	+	5.07180i	−0.401799	+	0.231979i
$479$	19.4186	+	33.6340i	0.887258	+	1.53678i	0.843104	+	0.537751i	$0.180726\pi$
$479$	19.4186	+	33.6340i	0.887258	+	1.53678i	0.0441539	+	0.999025i	$0.485941\pi$
$480$		0			0
$481$	20.7846	−	31.1769i	0.947697	−	1.42154i
$482$		−	2.92820i		−	0.133376i
$483$	−3.00000	+	1.73205i	−0.136505	+	0.0788110i
$484$	5.12436	+	8.87564i	0.232925	+	0.403438i
$485$		0			0
$486$	0.732051			0.0332065
$487$	4.85641	+	2.80385i	0.220065	+	0.127054i	0.605980	−	0.795480i	$-0.292781\pi$
$487$	4.85641	+	2.80385i	0.220065	+	0.127054i	−0.385915	+	0.922534i	$0.626114\pi$
$488$	11.8423	+	6.83717i	0.536077	+	0.309504i
$489$	−21.1962			−0.958523
$490$		0			0
$491$	9.49038	+	16.4378i	0.428295	+	0.741829i	0.996722	−	0.0809052i	$-0.0257811\pi$
$491$	9.49038	+	16.4378i	0.428295	+	0.741829i	−0.568427	+	0.822734i	$0.692448\pi$
$492$	−13.6077	+	7.85641i	−0.613482	+	0.354194i
$493$		−	2.39230i		−	0.107744i
$494$	−0.626933	−	1.26795i	−0.0282071	−	0.0570477i
$495$		0			0
$496$	−2.39230	−	4.14359i	−0.107418	−	0.186053i
$497$	−7.09808	+	4.09808i	−0.318392	+	0.183824i
$498$	−1.85641	−	1.07180i	−0.0831876	−	0.0480284i
$499$	25.3205			1.13350			0.566751	−	0.823889i	$-0.308200\pi$
$499$	25.3205			1.13350			0.566751	+	0.823889i	$0.308200\pi$
$500$		0			0
$501$	10.9282	−	18.9282i	0.488236	−	0.845650i
$502$			4.78461i			0.213548i
$503$	11.1962	+	6.46410i	0.499212	+	0.288220i	0.728388	−	0.685165i	$-0.240270\pi$
$503$	11.1962	+	6.46410i	0.499212	+	0.288220i	−0.229176	+	0.973385i	$0.573603\pi$
$504$	2.19615	+	3.80385i	0.0978244	+	0.169437i
$505$		0			0
$506$	−2.92820			−0.130175
$507$	1.66987	−	12.8923i	0.0741617	−	0.572567i
$508$			0.966679i			0.0428894i
$509$	−9.00000	−	15.5885i	−0.398918	−	0.690946i	0.594675	−	0.803966i	$-0.297281\pi$
$509$	−9.00000	−	15.5885i	−0.398918	−	0.690946i	−0.993593	+	0.113020i	$0.963948\pi$
$510$		0			0
$511$	1.50000	−	2.59808i	0.0663561	−	0.114932i
$512$		−	11.7128i		−	0.517638i
$513$	0.464102	+	0.267949i	0.0204906	+	0.0118302i
$514$	−0.803848	+	1.39230i	−0.0354562	+	0.0614119i
$515$		0			0
$516$	−6.73205	+	11.6603i	−0.296362	+	0.513314i
$517$	0.339746	−	0.196152i	0.0149420	−	0.00862677i
$518$	11.4115	−	6.58846i	0.501394	−	0.289480i
$519$	−12.1962			−0.535352
$520$		0			0
$521$	23.8038			1.04287			0.521433	−	0.853292i	$-0.325398\pi$
$521$	23.8038			1.04287			0.521433	+	0.853292i	$0.325398\pi$
$522$	2.07180	−	1.19615i	0.0906801	−	0.0523542i
$523$	25.2679	−	14.5885i	1.10489	−	0.637909i	0.167389	−	0.985891i	$-0.446466\pi$
$523$	25.2679	−	14.5885i	1.10489	−	0.637909i	0.937501	+	0.347982i	$0.113133\pi$
$524$	1.60770	−	2.78461i	0.0702325	−	0.121646i
$525$		0			0
$526$	−1.05256	+	1.82309i	−0.0458937	+	0.0794903i
$527$	2.83013	+	1.63397i	0.123282	+	0.0711771i
$528$		−	2.14359i		−	0.0932879i
$529$	−9.50000	+	16.4545i	−0.413043	+	0.715412i
$530$		0			0
$531$	5.83013	+	10.0981i	0.253006	+	0.438219i
$532$			1.35898i			0.0589194i
$533$	32.1962	+	21.4641i	1.39457	+	0.929713i
$534$	−3.85641			−0.166883
$535$		0			0
$536$	−11.6603	−	20.1962i	−0.503646	−	0.872341i
$537$	15.2942	+	8.83013i	0.659995	+	0.381048i
$538$		−	20.9282i		−	0.902279i
$539$	4.00000	−	6.92820i	0.172292	−	0.298419i
$540$		0			0
$541$	11.2487			0.483620			0.241810	−	0.970324i	$-0.422259\pi$
$541$	11.2487			0.483620			0.241810	+	0.970324i	$0.422259\pi$
$542$	14.2417	+	8.22243i	0.611732	+	0.353184i
$543$	7.26795	−	4.19615i	0.311898	−	0.180074i
$544$	2.14359	+	3.71281i	0.0919058	+	0.159186i
$545$		0			0
$546$	2.53590	−	3.80385i	0.108526	−	0.162790i
$547$			31.9808i			1.36740i	0.729764	+	0.683699i	$0.239630\pi$
$547$			31.9808i			1.36740i	−0.729764	+	0.683699i	$0.760370\pi$
$548$	14.7846	−	8.53590i	0.631567	−	0.364636i
$549$	2.69615	+	4.66987i	0.115069	+	0.199305i
$550$		0			0
$551$	1.75129			0.0746074
$552$	−4.39230	−	2.53590i	−0.186949	−	0.107935i
$553$	−16.5000	−	9.52628i	−0.701651	−	0.405099i
$554$	19.3205			0.820850
$555$		0			0
$556$	14.5885	+	25.2679i	0.618688	+	1.07160i
$557$	−8.19615	+	4.73205i	−0.347282	+	0.200503i	−0.663488	−	0.748187i	$-0.730924\pi$
$557$	−8.19615	+	4.73205i	−0.347282	+	0.200503i	0.316205	+	0.948691i	$0.397591\pi$
$558$			3.26795i			0.138343i
$559$	33.0885	+	2.13397i	1.39949	+	0.0902575i
$560$		0			0
$561$	0.732051	+	1.26795i	0.0309072	+	0.0535329i
$562$	7.14359	−	4.12436i	0.301334	−	0.173975i
$563$	30.1244	+	17.3923i	1.26959	+	0.732998i	0.974910	−	0.222598i	$-0.0714537\pi$
$563$	30.1244	+	17.3923i	1.26959	+	0.732998i	0.294680	+	0.955596i	$0.404787\pi$
$564$	0.287187			0.0120928
$565$		0			0
$566$	−5.90192	+	10.2224i	−0.248076	+	0.429681i
$567$			1.73205i			0.0727393i
$568$	−10.3923	−	6.00000i	−0.436051	−	0.251754i
$569$	−9.49038	−	16.4378i	−0.397857	−	0.689109i	0.595604	−	0.803278i	$-0.296913\pi$
$569$	−9.49038	−	16.4378i	−0.397857	−	0.689109i	−0.993461	+	0.114169i	$0.963579\pi$
$570$		0			0
$571$	−42.7846			−1.79048			−0.895240	−	0.445584i	$-0.852996\pi$
$571$	−42.7846			−1.79048			−0.895240	+	0.445584i	$0.852996\pi$
$572$	−9.46410	+	4.67949i	−0.395714	+	0.195659i
$573$			22.5885i			0.943646i
$574$	6.80385	+	11.7846i	0.283987	+	0.491880i
$575$		0			0
$576$	−1.07180	+	1.85641i	−0.0446582	+	0.0773503i
$577$			8.53590i			0.355354i	0.984089	+	0.177677i	$0.0568582\pi$
$577$			8.53590i			0.355354i	−0.984089	+	0.177677i	$0.943142\pi$
$578$	10.4378	+	6.02628i	0.434156	+	0.250660i
$579$	−9.59808	+	16.6244i	−0.398882	+	0.690885i
$580$		0			0
$581$	2.53590	−	4.39230i	0.105207	−	0.182224i
$582$	−3.29423	+	1.90192i	−0.136550	+	0.0788373i
$583$	16.3923	−	9.46410i	0.678900	−	0.391963i
$584$	4.39230			0.181755
$585$		0			0
$586$	6.00000			0.247858
$587$	−25.0981	+	14.4904i	−1.03591	+	0.598082i	−0.918672	−	0.395022i	$-0.870737\pi$
$587$	−25.0981	+	14.4904i	−1.03591	+	0.598082i	−0.117237	+	0.993104i	$0.537404\pi$
$588$	5.07180	−	2.92820i	0.209157	−	0.120757i
$589$	−1.19615	+	2.07180i	−0.0492866	+	0.0853669i
$590$		0			0
$591$	−8.19615	+	14.1962i	−0.337145	+	0.583952i
$592$	−9.64617	−	5.56922i	−0.396455	−	0.228894i
$593$		−	15.4641i		−	0.635035i	−0.948252	−	0.317517i	$-0.897151\pi$
$593$		−	15.4641i		−	0.635035i	0.948252	−	0.317517i	$-0.102849\pi$
$594$	−0.732051	+	1.26795i	−0.0300364	+	0.0520246i
$595$		0			0
$596$	−4.28719	−	7.42563i	−0.175610	−	0.304165i
$597$			24.8564i			1.01730i
$598$	−0.339746	+	5.26795i	−0.0138932	+	0.215422i
$599$	18.9808			0.775533			0.387766	−	0.921758i	$-0.373247\pi$
$599$	18.9808			0.775533			0.387766	+	0.921758i	$0.373247\pi$
$600$		0			0
$601$	5.26795	+	9.12436i	0.214884	+	0.372190i	0.953237	−	0.302225i	$-0.0977293\pi$
$601$	5.26795	+	9.12436i	0.214884	+	0.372190i	−0.738353	+	0.674415i	$0.764396\pi$
$602$	10.0981	+	5.83013i	0.411567	+	0.237618i
$603$		−	9.19615i		−	0.374496i
$604$	0.679492	−	1.17691i	0.0276481	−	0.0478880i
$605$		0			0
$606$	7.60770			0.309041
$607$	15.9282	+	9.19615i	0.646506	+	0.373260i	0.787116	−	0.616805i	$-0.211573\pi$
$607$	15.9282	+	9.19615i	0.646506	+	0.373260i	−0.140610	+	0.990065i	$0.544906\pi$
$608$	−2.71797	+	1.56922i	−0.110228	+	0.0636402i
$609$	2.83013	+	4.90192i	0.114683	+	0.198636i
$610$		0			0
$611$	−0.313467	−	0.633975i	−0.0126815	−	0.0256479i
$612$			1.07180i			0.0433248i
$613$	24.4808	−	14.1340i	0.988769	−	0.570866i	0.0838627	−	0.996477i	$-0.473274\pi$
$613$	24.4808	−	14.1340i	0.988769	−	0.570866i	0.904906	+	0.425611i	$0.139941\pi$
$614$	−2.43782	−	4.22243i	−0.0983825	−	0.170403i
$615$		0			0
$616$	−8.78461			−0.353942
$617$	−29.5359	−	17.0526i	−1.18907	−	0.686510i	−0.230975	−	0.972960i	$-0.574192\pi$
$617$	−29.5359	−	17.0526i	−1.18907	−	0.686510i	−0.958095	+	0.286449i	$0.907525\pi$
$618$	−3.63397	−	2.09808i	−0.146180	−	0.0843970i
$619$	−31.9282			−1.28330			−0.641651	−	0.766996i	$-0.721750\pi$
$619$	−31.9282			−1.28330			−0.641651	+	0.766996i	$0.721750\pi$
$620$		0			0
$621$	−1.00000	−	1.73205i	−0.0401286	−	0.0695048i
$622$	−7.98076	+	4.60770i	−0.319999	+	0.184752i
$623$		−	9.12436i		−	0.365560i
$624$	−3.85641	−	0.248711i	−0.154380	−	0.00995642i
$625$		0			0
$626$	−7.02628	−	12.1699i	−0.280827	−	0.486406i
$627$	−0.928203	+	0.535898i	−0.0370689	+	0.0214017i
$628$	−4.73205	−	2.73205i	−0.188829	−	0.109021i
$629$	7.60770			0.303339
$630$		0			0
$631$	−12.6962	+	21.9904i	−0.505426	+	0.875423i	0.494554	+	0.869147i	$0.335331\pi$
$631$	−12.6962	+	21.9904i	−0.505426	+	0.875423i	−0.999980	+	0.00627660i	$0.998002\pi$
$632$		−	27.8949i		−	1.10960i
$633$	−19.3301	−	11.1603i	−0.768304	−	0.443580i
$634$	−10.3923	−	18.0000i	−0.412731	−	0.714871i
$635$		0			0
$636$	13.8564			0.549442
$637$	−12.0000	−	8.00000i	−0.475457	−	0.316972i
$638$			4.78461i			0.189425i
$639$	−2.36603	−	4.09808i	−0.0935985	−	0.162117i
$640$		0			0
$641$	1.73205	−	3.00000i	0.0684119	−	0.118493i	−0.829790	−	0.558075i	$-0.811540\pi$
$641$	1.73205	−	3.00000i	0.0684119	−	0.118493i	0.898202	+	0.439582i	$0.144873\pi$
$642$		−	6.00000i		−	0.236801i
$643$	−11.7679	−	6.79423i	−0.464083	−	0.267938i	0.249677	−	0.968329i	$-0.419676\pi$
$643$	−11.7679	−	6.79423i	−0.464083	−	0.267938i	−0.713759	+	0.700391i	$0.753009\pi$
$644$	2.53590	−	4.39230i	0.0999284	−	0.173081i
$645$		0			0
$646$	0.143594	−	0.248711i	0.00564961	−	0.00978542i
$647$	3.58846	−	2.07180i	0.141077	−	0.0814507i	−0.427800	−	0.903873i	$-0.640711\pi$
$647$	3.58846	−	2.07180i	0.141077	−	0.0814507i	0.568877	+	0.822423i	$0.307378\pi$
$648$	−2.19615	+	1.26795i	−0.0862730	+	0.0498097i
$649$	−23.3205			−0.915410
$650$		0			0
$651$	−7.73205			−0.303043
$652$	26.8756	−	15.5167i	1.05253	−	0.607679i
$653$	11.7058	−	6.75833i	0.458082	−	0.264474i	−0.253155	−	0.967426i	$-0.581468\pi$
$653$	11.7058	−	6.75833i	0.458082	−	0.264474i	0.711238	+	0.702952i	$0.248135\pi$
$654$	−5.63397	+	9.75833i	−0.220306	+	0.381581i
$655$		0			0
$656$	5.75129	−	9.96152i	0.224550	−	0.388932i
$657$	1.50000	+	0.866025i	0.0585206	+	0.0337869i
$658$		−	0.248711i		−	0.00969578i
$659$	−9.12436	+	15.8038i	−0.355434	+	0.615630i	−0.987192	−	0.159535i	$-0.949000\pi$
$659$	−9.12436	+	15.8038i	−0.355434	+	0.615630i	0.631758	+	0.775166i	$0.282334\pi$
$660$		0			0
$661$	−18.0885	−	31.3301i	−0.703559	−	1.21860i	−0.967209	−	0.253982i	$-0.918260\pi$
$661$	−18.0885	−	31.3301i	−0.703559	−	1.21860i	0.263649	−	0.964619i	$-0.415074\pi$
$662$		−	17.5167i		−	0.680804i
$663$	2.36603	−	1.16987i	0.0918888	−	0.0454341i
$664$	7.42563			0.288170
$665$		0			0
$666$	3.80385	+	6.58846i	0.147396	+	0.255298i
$667$	−5.66025	−	3.26795i	−0.219166	−	0.126535i
$668$			32.0000i			1.23812i
$669$	0.928203	−	1.60770i	0.0358864	−	0.0621571i
$670$		0			0
$671$	−10.7846			−0.416335
$672$	−8.78461	−	5.07180i	−0.338874	−	0.195649i
$673$	−11.2128	+	6.47372i	−0.432222	+	0.249544i	−0.700293	−	0.713856i	$-0.746947\pi$
$673$	−11.2128	+	6.47372i	−0.432222	+	0.249544i	0.268071	+	0.963399i	$0.413614\pi$
$674$	9.36603	+	16.2224i	0.360766	+	0.624865i
$675$		0			0
$676$	7.32051	+	17.5692i	0.281558	+	0.675739i
$677$		−	50.9282i		−	1.95733i	−0.205463	−	0.978665i	$-0.565870\pi$
$677$		−	50.9282i		−	1.95733i	0.205463	−	0.978665i	$-0.434130\pi$
$678$	11.6603	−	6.73205i	0.447809	−	0.258543i
$679$	−4.50000	−	7.79423i	−0.172694	−	0.299115i
$680$		0			0
$681$	−4.73205			−0.181333
$682$	−5.66025	−	3.26795i	−0.216742	−	0.125136i
$683$	−14.3660	−	8.29423i	−0.549701	−	0.317370i	0.199301	−	0.979938i	$-0.436133\pi$
$683$	−14.3660	−	8.29423i	−0.549701	−	0.317370i	−0.749001	+	0.662569i	$0.769466\pi$
$684$	−0.784610			−0.0300003
$685$		0			0
$686$	−6.97372	−	12.0788i	−0.266258	−	0.461172i
$687$	−11.0718	+	6.39230i	−0.422415	+	0.243882i
$688$		−	9.85641i		−	0.375772i
$689$	−15.1244	−	30.5885i	−0.576192	−	1.16533i
$690$		0			0
$691$	13.9641	+	24.1865i	0.531219	+	0.920099i	0.999336	+	0.0364324i	$0.0115994\pi$
$691$	13.9641	+	24.1865i	0.531219	+	0.920099i	−0.468117	+	0.883667i	$0.655067\pi$
$692$	15.4641	−	8.92820i	0.587857	−	0.339399i
$693$	−3.00000	−	1.73205i	−0.113961	−	0.0657952i
$694$	1.07180			0.0406848
$695$		0			0
$696$	−4.14359	+	7.17691i	−0.157063	+	0.272040i
$697$			7.85641i			0.297583i
$698$	−19.5622	−	11.2942i	−0.740439	−	0.427493i
$699$	−14.1244	−	24.4641i	−0.534232	−	0.925317i
$700$		0			0
$701$	−37.4641			−1.41500			−0.707500	−	0.706714i	$-0.750177\pi$
$701$	−37.4641			−1.41500			−0.707500	+	0.706714i	$0.750177\pi$
$702$	2.19615	+	1.46410i	0.0828884	+	0.0552590i
$703$			5.56922i			0.210047i
$704$	−2.14359	−	3.71281i	−0.0807897	−	0.139932i
$705$		0			0
$706$	3.51666	−	6.09103i	0.132351	−	0.229239i
$707$			18.0000i			0.676960i
$708$	−14.7846	−	8.53590i	−0.555640	−	0.320799i
$709$	−18.6244	+	32.2583i	−0.699452	+	1.21149i	0.269204	+	0.963083i	$0.413239\pi$
$709$	−18.6244	+	32.2583i	−0.699452	+	1.21149i	−0.968657	+	0.248404i	$0.920094\pi$
$710$		0			0
$711$	5.50000	−	9.52628i	0.206266	−	0.357263i
$712$	11.5692	−	6.67949i	0.433575	−	0.250325i
$713$	7.73205	−	4.46410i	0.289568	−	0.167182i
$714$	0.928203			0.0347371
$715$		0			0
$716$	−25.8564			−0.966299
$717$	12.0000	−	6.92820i	0.448148	−	0.258738i
$718$	0.124356	−	0.0717968i	0.00464091	−	0.00267943i
$719$	11.8301	−	20.4904i	0.441189	−	0.764162i	−0.556589	−	0.830788i	$-0.687890\pi$
$719$	11.8301	−	20.4904i	0.441189	−	0.764162i	0.997778	+	0.0666259i	$0.0212234\pi$
$720$		0			0
$721$	4.96410	−	8.59808i	0.184873	−	0.320209i
$722$	−11.8634	−	6.84936i	−0.441512	−	0.254907i
$723$			4.00000i			0.148762i
$724$	−6.14359	+	10.6410i	−0.228325	+	0.395470i
$725$		0			0
$726$	2.56218	+	4.43782i	0.0950913	+	0.164703i
$727$			2.66025i			0.0986634i	0.998782	+	0.0493317i	$0.0157091\pi$
$727$			2.66025i			0.0986634i	−0.998782	+	0.0493317i	$0.984291\pi$
$728$	−1.01924	+	15.8038i	−0.0377755	+	0.585730i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	3.36603	+	5.83013i	0.124497	+	0.215635i
$732$	−6.83717	−	3.94744i	−0.252709	−	0.145902i
$733$			13.9808i			0.516391i	0.966093	+	0.258196i	$0.0831279\pi$
$733$			13.9808i			0.516391i	−0.966093	+	0.258196i	$0.916872\pi$
$734$	5.50962	−	9.54294i	0.203364	−	0.352236i
$735$		0			0
$736$	11.7128			0.431740
$737$	15.9282	+	9.19615i	0.586723	+	0.338745i
$738$	−6.80385	+	3.92820i	−0.250453	+	0.144599i
$739$	0.535898	+	0.928203i	0.0197133	+	0.0341445i	0.875714	−	0.482831i	$-0.160391\pi$
$739$	0.535898	+	0.928203i	0.0197133	+	0.0341445i	−0.856000	+	0.516975i	$0.827058\pi$
$740$		0			0
$741$	0.856406	+	1.73205i	0.0314609	+	0.0636285i
$742$		−	12.0000i		−	0.440534i
$743$	−31.0981	+	17.9545i	−1.14088	+	0.658686i	−0.946648	−	0.322270i	$-0.895554\pi$
$743$	−31.0981	+	17.9545i	−1.14088	+	0.658686i	−0.194230	+	0.980956i	$0.562221\pi$
$744$	−5.66025	−	9.80385i	−0.207515	−	0.359426i
$745$		0			0
$746$	5.37307			0.196722
$747$	2.53590	+	1.46410i	0.0927837	+	0.0535687i
$748$	−1.85641	−	1.07180i	−0.0678769	−	0.0391888i
$749$	14.1962			0.518716
$750$		0			0
$751$	−5.19615	−	9.00000i	−0.189610	−	0.328415i	0.755510	−	0.655137i	$-0.227389\pi$
$751$	−5.19615	−	9.00000i	−0.189610	−	0.328415i	−0.945120	+	0.326722i	$0.894056\pi$
$752$	−0.182069	+	0.105118i	−0.00663938	+	0.00383325i
$753$		−	6.53590i		−	0.238181i
$754$	8.60770	+	0.555136i	0.313474	+	0.0202169i
$755$		0			0
$756$	−1.26795	−	2.19615i	−0.0461149	−	0.0798733i
$757$	16.3923	−	9.46410i	0.595788	−	0.343979i	−0.171595	−	0.985168i	$-0.554892\pi$
$757$	16.3923	−	9.46410i	0.595788	−	0.343979i	0.767383	+	0.641189i	$0.221559\pi$
$758$	−4.09808	−	2.36603i	−0.148849	−	0.0859379i
$759$	4.00000			0.145191
$760$		0			0
$761$	12.5359	−	21.7128i	0.454426	−	0.787089i	−0.544229	−	0.838937i	$-0.683178\pi$
$761$	12.5359	−	21.7128i	0.454426	−	0.787089i	0.998655	+	0.0518478i	$0.0165111\pi$
$762$			0.483340i			0.0175095i
$763$	−23.0885	−	13.3301i	−0.835858	−	0.482583i
$764$	−16.5359	−	28.6410i	−0.598248	−	1.03620i
$765$		0			0
$766$	−14.1051			−0.509639
$767$	−2.70577	+	41.9545i	−0.0976997	+	1.51489i
$768$		−	11.7128i		−	0.422650i
$769$	−4.39230	−	7.60770i	−0.158391	−	0.274341i	0.775898	−	0.630859i	$-0.217297\pi$
$769$	−4.39230	−	7.60770i	−0.158391	−	0.274341i	−0.934288	+	0.356518i	$0.883964\pi$
$770$		0			0
$771$	1.09808	−	1.90192i	0.0395462	−	0.0684961i
$772$		−	28.1051i		−	1.01153i
$773$	−19.3923	−	11.1962i	−0.697493	−	0.402698i	0.108920	−	0.994050i	$-0.465261\pi$
$773$	−19.3923	−	11.1962i	−0.697493	−	0.402698i	−0.806413	+	0.591353i	$0.798594\pi$
$774$	−3.36603	+	5.83013i	−0.120989	+	0.209560i
$775$		0			0
$776$	6.58846	−	11.4115i	0.236512	−	0.409651i
$777$	−15.5885	+	9.00000i	−0.559233	+	0.322873i
$778$	−9.21539	+	5.32051i	−0.330388	+	0.190749i
$779$	−5.75129			−0.206061
$780$		0			0
$781$	9.46410			0.338652
$782$	−0.928203	+	0.535898i	−0.0331925	+	0.0191637i
$783$	−2.83013	+	1.63397i	−0.101140	+	0.0583935i
$784$	−2.14359	+	3.71281i	−0.0765569	+	0.132600i
$785$		0			0
$786$	0.803848	−	1.39230i	0.0286723	−	0.0496619i
$787$	38.2128	+	22.0622i	1.36214	+	0.786432i	0.989908	−	0.141708i	$-0.0452595\pi$
$787$	38.2128	+	22.0622i	1.36214	+	0.786432i	0.372231	+	0.928140i	$0.378593\pi$
$788$		−	24.0000i		−	0.854965i
$789$	1.43782	−	2.49038i	0.0511878	−	0.0886599i
$790$		0			0
$791$	15.9282	+	27.5885i	0.566342	+	0.980933i
$792$		−	5.07180i		−	0.180218i
$793$	−1.25129	+	19.4019i	−0.0444346	+	0.688983i
$794$	−7.12436			−0.252834
$795$		0			0
$796$	−18.1962	−	31.5167i	−0.644946	−	1.11708i
$797$	−6.63397	−	3.83013i	−0.234987	−	0.135670i	0.377883	−	0.925853i	$-0.376652\pi$
$797$	−6.63397	−	3.83013i	−0.234987	−	0.135670i	−0.612871	+	0.790183i	$0.709985\pi$
$798$			0.679492i			0.0240538i
$799$	0.0717968	−	0.124356i	0.00253999	−	0.00439939i
$800$		0			0
$801$	5.26795			0.186134
$802$	−19.1769	−	11.0718i	−0.677160	−	0.390959i
$803$	−3.00000	+	1.73205i	−0.105868	+	0.0611227i
$804$	6.73205	+	11.6603i	0.237421	+	0.411225i
$805$		0			0
$806$	−6.53590	+	9.80385i	−0.230217	+	0.345326i
$807$			28.5885i			1.00636i
$808$	−22.8231	+	13.1769i	−0.802913	+	0.463562i
$809$	−22.0526	−	38.1962i	−0.775327	−	1.34291i	−0.934611	−	0.355672i	$-0.884252\pi$
$809$	−22.0526	−	38.1962i	−0.775327	−	1.34291i	0.159284	−	0.987233i	$-0.449081\pi$
$810$		0			0
$811$	−17.6410			−0.619460			−0.309730	−	0.950825i	$-0.600239\pi$
$811$	−17.6410			−0.619460			−0.309730	+	0.950825i	$0.600239\pi$
$812$	−7.17691	−	4.14359i	−0.251860	−	0.145412i
$813$	−19.4545	−	11.2321i	−0.682298	−	0.393925i
$814$	−15.2154			−0.533299
$815$		0			0
$816$	−0.392305	−	0.679492i	−0.0137334	−	0.0237870i
$817$	−4.26795	+	2.46410i	−0.149317	+	0.0862080i
$818$			4.62693i			0.161777i
$819$	−3.46410	+	5.19615i	−0.121046	+	0.181568i
$820$		0			0
$821$	−17.0000	−	29.4449i	−0.593304	−	1.02763i	−0.993784	−	0.111327i	$-0.964490\pi$
$821$	−17.0000	−	29.4449i	−0.593304	−	1.02763i	0.400480	−	0.916306i	$-0.368843\pi$
$822$	7.39230	−	4.26795i	0.257836	−	0.148862i
$823$	10.9808	+	6.33975i	0.382765	+	0.220990i	0.679021	−	0.734119i	$-0.262405\pi$
$823$	10.9808	+	6.33975i	0.382765	+	0.220990i	−0.296255	+	0.955109i	$0.595738\pi$
$824$	14.5359			0.506382
$825$		0			0
$826$	−7.39230	+	12.8038i	−0.257211	+	0.445503i
$827$		−	11.6603i		−	0.405467i	−0.979234	−	0.202733i	$-0.935018\pi$
$827$		−	11.6603i		−	0.405467i	0.979234	−	0.202733i	$-0.0649825\pi$
$828$	2.53590	+	1.46410i	0.0881286	+	0.0508810i
$829$	23.1603	+	40.1147i	0.804389	+	1.39324i	0.916703	+	0.399570i	$0.130840\pi$
$829$	23.1603	+	40.1147i	0.804389	+	1.39324i	−0.112314	+	0.993673i	$0.535826\pi$
$830$		0			0
$831$	−26.3923			−0.915539
$832$	−6.92820	+	3.42563i	−0.240192	+	0.118762i
$833$		−	2.92820i		−	0.101456i
$834$	7.29423	+	12.6340i	0.252578	+	0.437479i
$835$		0			0
$836$	0.784610	−	1.35898i	0.0271363	−	0.0470014i
$837$		−	4.46410i		−	0.154302i
$838$	25.3013	+	14.6077i	0.874018	+	0.504614i
$839$	19.1962	−	33.2487i	0.662725	−	1.14787i	−0.317172	−	0.948368i	$-0.602733\pi$
$839$	19.1962	−	33.2487i	0.662725	−	1.14787i	0.979897	−	0.199505i	$-0.0639334\pi$
$840$		0			0
$841$	9.16025	−	15.8660i	0.315871	−	0.547104i
$842$	−8.15064	+	4.70577i	−0.280889	+	0.162172i
$843$	−9.75833	+	5.63397i	−0.336095	+	0.194044i
$844$	32.6795			1.12487
$845$		0			0
$846$	0.143594			0.00493685
$847$	−10.5000	+	6.06218i	−0.360784	+	0.208299i
$848$	−8.78461	+	5.07180i	−0.301665	+	0.174166i
$849$	8.06218	−	13.9641i	0.276693	−	0.479247i
$850$		0			0
$851$	10.3923	−	18.0000i	0.356244	−	0.617032i
$852$	6.00000	+	3.46410i	0.205557	+	0.118678i
$853$		−	32.6603i		−	1.11827i	−0.829078	−	0.559133i	$-0.811134\pi$
$853$		−	32.6603i		−	1.11827i	0.829078	−	0.559133i	$-0.188866\pi$
$854$	−3.41858	+	5.92116i	−0.116982	+	0.202618i
$855$		0			0
$856$	10.3923	+	18.0000i	0.355202	+	0.615227i
$857$			47.8038i			1.63295i	0.577382	+	0.816474i	$0.304074\pi$
$857$			47.8038i			1.63295i	−0.577382	+	0.816474i	$0.695926\pi$
$858$	−4.73205	+	2.33975i	−0.161550	+	0.0798776i
$859$	−11.9282			−0.406985			−0.203493	−	0.979077i	$-0.565229\pi$
$859$	−11.9282			−0.406985			−0.203493	+	0.979077i	$0.565229\pi$
$860$		0			0
$861$	−9.29423	−	16.0981i	−0.316746	−	0.548621i
$862$	−13.3590	−	7.71281i	−0.455009	−	0.262699i
$863$			47.9615i			1.63263i	0.577607	+	0.816315i	$0.303986\pi$
$863$			47.9615i			1.63263i	−0.577607	+	0.816315i	$0.696014\pi$
$864$	2.92820	−	5.07180i	0.0996195	−	0.172546i
$865$		0			0
$866$	13.9474			0.473953
$867$	−14.2583	−	8.23205i	−0.484238	−	0.279575i
$868$	9.80385	−	5.66025i	0.332764	−	0.192122i
$869$	11.0000	+	19.0526i	0.373149	+	0.646314i
$870$		0			0
$871$	18.3923	−	27.5885i	0.623199	−	0.934799i
$872$		−	39.0333i		−	1.32184i
$873$	4.50000	−	2.59808i	0.152302	−	0.0879316i
$874$	−0.392305	−	0.679492i	−0.0132699	−	0.0229842i
$875$		0			0
$876$	−2.53590			−0.0856801
$877$	4.85641	+	2.80385i	0.163989	+	0.0946792i	0.579749	−	0.814795i	$-0.303151\pi$
$877$	4.85641	+	2.80385i	0.163989	+	0.0946792i	−0.415759	+	0.909475i	$0.636484\pi$
$878$	12.2942	+	7.09808i	0.414910	+	0.239548i
$879$	−8.19615			−0.276449
$880$		0			0
$881$	7.80385	+	13.5167i	0.262918	+	0.455388i	0.967016	−	0.254715i	$-0.0819817\pi$
$881$	7.80385	+	13.5167i	0.262918	+	0.455388i	−0.704098	+	0.710103i	$0.748648\pi$
$882$	2.53590	−	1.46410i	0.0853881	−	0.0492989i
$883$			31.7321i			1.06787i	0.845526	+	0.533934i	$0.179287\pi$
$883$			31.7321i			1.06787i	−0.845526	+	0.533934i	$0.820713\pi$
$884$	−2.14359	+	3.21539i	−0.0720969	+	0.108145i
$885$		0			0
$886$	−10.6603	−	18.4641i	−0.358138	−	0.620314i
$887$	−32.2750	+	18.6340i	−1.08369	+	0.625668i	−0.931889	−	0.362744i	$-0.881840\pi$
$887$	−32.2750	+	18.6340i	−1.08369	+	0.625668i	−0.151799	+	0.988411i	$0.548507\pi$
$888$	−22.8231	−	13.1769i	−0.765893	−	0.442188i
$889$	−1.14359			−0.0383549
$890$		0			0
$891$	1.00000	−	1.73205i	0.0335013	−	0.0580259i
$892$			2.71797i			0.0910043i
$893$	0.0910347	+	0.0525589i	0.00304636	+	0.00175882i
$894$	−2.14359	−	3.71281i	−0.0716925	−	0.124175i
$895$		0			0
$896$	17.5692			0.586946
$897$	0.464102	−	7.19615i	0.0154959	−	0.240273i
$898$			11.3205i			0.377770i
$899$	−7.29423	−	12.6340i	−0.243276	−	0.421367i
$900$		0			0
$901$	3.46410	−	6.00000i	0.115406	−	0.199889i
$902$		−	15.7128i		−	0.523179i
$903$	−13.7942	−	7.96410i	−0.459043	−	0.265029i
$904$	−23.3205	+	40.3923i	−0.775629	+	1.34343i
$905$		0			0
$906$	0.339746	−	0.588457i	0.0112873	−	0.0195502i
$907$	−48.7128	+	28.1244i	−1.61748	+	0.933854i	−0.629914	+	0.776665i	$0.716910\pi$
$907$	−48.7128	+	28.1244i	−1.61748	+	0.933854i	−0.987569	+	0.157189i	$0.949757\pi$
$908$	6.00000	−	3.46410i	0.199117	−	0.114960i
$909$	−10.3923			−0.344691
$910$		0			0
$911$	−43.0333			−1.42576			−0.712879	−	0.701287i	$-0.752609\pi$
$911$	−43.0333			−1.42576			−0.712879	+	0.701287i	$0.752609\pi$
$912$	0.497423	−	0.287187i	0.0164713	−	0.00950971i
$913$	−5.07180	+	2.92820i	−0.167852	+	0.0969094i
$914$	−5.31347	+	9.20319i	−0.175754	+	0.304415i
$915$		0			0
$916$	9.35898	−	16.2102i	0.309230	−	0.535601i
$917$	3.29423	+	1.90192i	0.108785	+	0.0628071i
$918$			0.535898i			0.0176873i
$919$	1.92820	−	3.33975i	0.0636056	−	0.110168i	−0.832469	−	0.554072i	$-0.813073\pi$
$919$	1.92820	−	3.33975i	0.0636056	−	0.110168i	0.896075	+	0.443904i	$0.146407\pi$
$920$		0			0
$921$	3.33013	+	5.76795i	0.109731	+	0.190060i
$922$			7.35898i			0.242355i
$923$	1.09808	−	17.0263i	0.0361436	−	0.560427i
$924$	5.07180			0.166850
$925$		0			0
$926$	0.490381	+	0.849365i	0.0161149	+	0.0279119i
$927$	4.96410	+	2.86603i	0.163042	+	0.0941326i
$928$		−	19.1384i		−	0.628250i
$929$	−20.5359	+	35.5692i	−0.673761	+	1.16699i	0.303068	+	0.952969i	$0.401989\pi$
$929$	−20.5359	+	35.5692i	−0.673761	+	1.16699i	−0.976829	+	0.214019i	$0.931344\pi$
$930$		0			0
$931$	2.14359			0.0702534
$932$	35.8179	+	20.6795i	1.17326	+	0.677379i
$933$	10.9019	−	6.29423i	0.356913	−	0.206064i
$934$	3.78461	+	6.55514i	0.123836	+	0.214491i
$935$		0			0
$936$	−9.12436	−	0.588457i	−0.298239	−	0.0192343i
$937$			12.5359i			0.409530i	0.978811	+	0.204765i	$0.0656430\pi$
$937$			12.5359i			0.409530i	−0.978811	+	0.204765i	$0.934357\pi$
$938$	10.0981	−	5.83013i	0.329714	−	0.190360i
$939$	9.59808	+	16.6244i	0.313221	+	0.542515i
$940$		0			0
$941$	41.5167			1.35340			0.676702	−	0.736257i	$-0.263408\pi$
$941$	41.5167			1.35340			0.676702	+	0.736257i	$0.263408\pi$
$942$	−2.36603	−	1.36603i	−0.0770893	−	0.0445075i
$943$	18.5885	+	10.7321i	0.605323	+	0.349484i
$944$	12.4974			0.406756
$945$		0			0
$946$	−6.73205	−	11.6603i	−0.218878	−	0.379108i
$947$	10.6865	−	6.16987i	0.347266	−	0.200494i	−0.316215	−	0.948688i	$-0.602412\pi$
$947$	10.6865	−	6.16987i	0.347266	−	0.200494i	0.663480	+	0.748194i	$0.269079\pi$
$948$			16.1051i			0.523070i
$949$	2.76795	+	5.59808i	0.0898514	+	0.181721i
$950$		0			0
$951$	14.1962	+	24.5885i	0.460342	+	0.797335i
$952$	−2.78461	+	1.60770i	−0.0902497	+	0.0521057i
$953$	−16.8564	−	9.73205i	−0.546033	−	0.315252i	0.201488	−	0.979491i	$-0.435422\pi$
$953$	−16.8564	−	9.73205i	−0.546033	−	0.315252i	−0.747520	+	0.664239i	$0.768756\pi$
$954$	6.92820			0.224309
$955$		0			0
$956$	−10.1436	+	17.5692i	−0.328067	+	0.568229i
$957$		−	6.53590i		−	0.211276i
$958$	−24.6218	−	14.2154i	−0.795494	−	0.459278i
$959$	10.0981	+	17.4904i	0.326084	+	0.564794i
$960$		0			0
$961$	−11.0718			−0.357155
$962$	−1.76537	+	27.3731i	−0.0569179	+	0.882543i
$963$			8.19615i			0.264117i
$964$	−2.92820	−	5.07180i	−0.0943111	−	0.163352i
$965$		0			0
$966$	1.26795	−	2.19615i	0.0407956	−	0.0706600i
$967$		−	28.1051i		−	0.903800i	−0.892069	−	0.451900i	$-0.850746\pi$
$967$		−	28.1051i		−	0.903800i	0.892069	−	0.451900i	$-0.149254\pi$
$968$	−15.3731	−	8.87564i	−0.494109	−	0.285274i
$969$	−0.196152	+	0.339746i	−0.00630132	+	0.0109142i
$970$		0			0
$971$	3.80385	−	6.58846i	0.122071	−	0.211434i	−0.798513	−	0.601977i	$-0.794380\pi$
$971$	3.80385	−	6.58846i	0.122071	−	0.211434i	0.920584	+	0.390544i	$0.127713\pi$
$972$	1.26795	−	0.732051i	0.0406695	−	0.0234805i
$973$	−29.8923	+	17.2583i	−0.958303	+	0.553277i
$974$	−4.10512			−0.131536
$975$		0			0
$976$	5.77945			0.184996
$977$	−39.3731	+	22.7321i	−1.25966	+	0.727263i	−0.973008	−	0.230773i	$-0.925874\pi$
$977$	−39.3731	+	22.7321i	−1.25966	+	0.727263i	−0.286648	+	0.958036i	$0.592541\pi$
$978$	13.4378	−	7.75833i	0.429694	−	0.248084i
$979$	−5.26795	+	9.12436i	−0.168364	+	0.291616i
$980$		0			0
$981$	7.69615	−	13.3301i	0.245719	−	0.425598i
$982$	−12.0333	−	6.94744i	−0.383999	−	0.221702i
$983$			13.6077i			0.434018i	0.976170	+	0.217009i	$0.0696301\pi$
$983$			13.6077i			0.434018i	−0.976170	+	0.217009i	$0.930370\pi$
$984$	13.6077	−	23.5692i	0.433797	−	0.751359i
$985$		0			0
$986$	0.875644	+	1.51666i	0.0278862	+	0.0483003i
$987$			0.339746i			0.0108142i
$988$	−2.35383	−	1.56922i	−0.0748853	−	0.0499235i
$989$	18.3923			0.584841
$990$		0			0
$991$	−0.464102	−	0.803848i	−0.0147427	−	0.0255351i	0.858560	−	0.512713i	$-0.171360\pi$
$991$	−0.464102	−	0.803848i	−0.0147427	−	0.0255351i	−0.873303	+	0.487178i	$0.838026\pi$
$992$	22.6410	+	13.0718i	0.718853	+	0.415030i
$993$			23.9282i			0.759339i
$994$	3.00000	−	5.19615i	0.0951542	−	0.164812i
$995$		0			0
$996$	−4.28719			−0.135845
$997$	1.03590	+	0.598076i	0.0328072	+	0.0189413i	0.516314	−	0.856399i	$-0.327304\pi$
$997$	1.03590	+	0.598076i	0.0328072	+	0.0189413i	−0.483507	+	0.875341i	$0.660637\pi$
$998$	−16.0526	+	9.26795i	−0.508135	+	0.293372i
$999$	−5.19615	−	9.00000i	−0.164399	−	0.284747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bb.a.874.2		4
5.2	odd	4		195.2.i.c.16.1	✓	4
5.3	odd	4		975.2.i.j.601.2		4
5.4	even	2		975.2.bb.h.874.1		4
13.9	even	3		975.2.bb.h.724.1		4
15.2	even	4		585.2.j.c.406.2		4
65.9	even	6	inner	975.2.bb.a.724.2		4
65.22	odd	12		195.2.i.c.61.1	yes	4
65.42	odd	12		2535.2.a.o.1.2		2
65.48	odd	12		975.2.i.j.451.2		4
65.62	odd	12		2535.2.a.r.1.1		2
195.62	even	12		7605.2.a.z.1.2		2
195.107	even	12		7605.2.a.bj.1.1		2
195.152	even	12		585.2.j.c.451.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.c.16.1	✓	4	5.2	odd	4
195.2.i.c.61.1	yes	4	65.22	odd	12
585.2.j.c.406.2		4	15.2	even	4
585.2.j.c.451.2		4	195.152	even	12
975.2.i.j.451.2		4	65.48	odd	12
975.2.i.j.601.2		4	5.3	odd	4
975.2.bb.a.724.2		4	65.9	even	6	inner
975.2.bb.a.874.2		4	1.1	even	1	trivial
975.2.bb.h.724.1		4	13.9	even	3
975.2.bb.h.874.1		4	5.4	even	2
2535.2.a.o.1.2		2	65.42	odd	12
2535.2.a.r.1.1		2	65.62	odd	12
7605.2.a.z.1.2		2	195.62	even	12
7605.2.a.bj.1.1		2	195.107	even	12

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.633975 + 0.366025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.732051 + 1.26795i) q^{4} +(-0.366025 + 0.633975i) q^{6} +(-1.50000 - 0.866025i) q^{7} -2.53590i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.633975 + 0.366025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.732051 + 1.26795i) q^{4} +(-0.366025 + 0.633975i) q^{6} +(-1.50000 - 0.866025i) q^{7} -2.53590i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{11} +1.46410i q^{12} +(3.23205 - 1.59808i) q^{13} +1.26795 q^{14} +(-0.535898 - 0.928203i) q^{16} +(0.633975 + 0.366025i) q^{17} +0.732051i q^{18} +(-0.267949 + 0.464102i) q^{19} -1.73205 q^{21} +(-1.26795 - 0.732051i) q^{22} +(1.73205 - 1.00000i) q^{23} +(-1.26795 - 2.19615i) q^{24} +(-1.46410 + 2.19615i) q^{26} -1.00000i q^{27} +(2.19615 - 1.26795i) q^{28} +(-1.63397 - 2.83013i) q^{29} +4.46410 q^{31} +(5.07180 + 2.92820i) q^{32} +(1.73205 + 1.00000i) q^{33} -0.535898 q^{34} +(0.732051 + 1.26795i) q^{36} +(9.00000 - 5.19615i) q^{37} -0.392305i q^{38} +(2.00000 - 3.00000i) q^{39} +(5.36603 + 9.29423i) q^{41} +(1.09808 - 0.633975i) q^{42} +(7.96410 + 4.59808i) q^{43} -2.92820 q^{44} +(-0.732051 + 1.26795i) q^{46} -0.196152i q^{47} +(-0.928203 - 0.535898i) q^{48} +(-2.00000 - 3.46410i) q^{49} +0.732051 q^{51} +(-0.339746 + 5.26795i) q^{52} -9.46410i q^{53} +(0.366025 + 0.633975i) q^{54} +(-2.19615 + 3.80385i) q^{56} +0.535898i q^{57} +(2.07180 + 1.19615i) q^{58} +(-5.83013 + 10.0981i) q^{59} +(-2.69615 + 4.66987i) q^{61} +(-2.83013 + 1.63397i) q^{62} +(-1.50000 + 0.866025i) q^{63} -2.14359 q^{64} -1.46410 q^{66} +(7.96410 - 4.59808i) q^{67} +(-0.928203 + 0.535898i) q^{68} +(1.00000 - 1.73205i) q^{69} +(2.36603 - 4.09808i) q^{71} +(-2.19615 - 1.26795i) q^{72} +1.73205i q^{73} +(-3.80385 + 6.58846i) q^{74} +(-0.392305 - 0.679492i) q^{76} -3.46410i q^{77} +(-0.169873 + 2.63397i) q^{78} +11.0000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-6.80385 - 3.92820i) q^{82} +2.92820i q^{83} +(1.26795 - 2.19615i) q^{84} -6.73205 q^{86} +(-2.83013 - 1.63397i) q^{87} +(4.39230 - 2.53590i) q^{88} +(2.63397 + 4.56218i) q^{89} +(-6.23205 - 0.401924i) q^{91} +2.92820i q^{92} +(3.86603 - 2.23205i) q^{93} +(0.0717968 + 0.124356i) q^{94} +5.85641 q^{96} +(4.50000 + 2.59808i) q^{97} +(2.53590 + 1.46410i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{2} + 4 q^{4} + 2 q^{6} - 6 q^{7} + 2 q^{9}+O(q^{10}) \) 4 * q - 6 * q^2 + 4 * q^4 + 2 * q^6 - 6 * q^7 + 2 * q^9	\( 4 q - 6 q^{2} + 4 q^{4} + 2 q^{6} - 6 q^{7} + 2 q^{9} + 4 q^{11} + 6 q^{13} + 12 q^{14} - 16 q^{16} + 6 q^{17} - 8 q^{19} - 12 q^{22} - 12 q^{24} + 8 q^{26} - 12 q^{28} - 10 q^{29} + 4 q^{31} + 48 q^{32} - 16 q^{34} - 4 q^{36} + 36 q^{37} + 8 q^{39} + 18 q^{41} - 6 q^{42} + 18 q^{43} + 16 q^{44} + 4 q^{46} + 24 q^{48} - 8 q^{49} - 4 q^{51} - 36 q^{52} - 2 q^{54} + 12 q^{56} + 36 q^{58} - 6 q^{59} + 10 q^{61} + 6 q^{62} - 6 q^{63} - 64 q^{64} + 8 q^{66} + 18 q^{67} + 24 q^{68} + 4 q^{69} + 6 q^{71} + 12 q^{72} - 36 q^{74} + 40 q^{76} - 18 q^{78} + 44 q^{79} - 2 q^{81} - 48 q^{82} + 12 q^{84} - 20 q^{86} + 6 q^{87} - 24 q^{88} + 14 q^{89} - 18 q^{91} + 12 q^{93} + 28 q^{94} - 32 q^{96} + 18 q^{97} + 24 q^{98} + 8 q^{99}+O(q^{100}) \) 4 * q - 6 * q^2 + 4 * q^4 + 2 * q^6 - 6 * q^7 + 2 * q^9 + 4 * q^11 + 6 * q^13 + 12 * q^14 - 16 * q^16 + 6 * q^17 - 8 * q^19 - 12 * q^22 - 12 * q^24 + 8 * q^26 - 12 * q^28 - 10 * q^29 + 4 * q^31 + 48 * q^32 - 16 * q^34 - 4 * q^36 + 36 * q^37 + 8 * q^39 + 18 * q^41 - 6 * q^42 + 18 * q^43 + 16 * q^44 + 4 * q^46 + 24 * q^48 - 8 * q^49 - 4 * q^51 - 36 * q^52 - 2 * q^54 + 12 * q^56 + 36 * q^58 - 6 * q^59 + 10 * q^61 + 6 * q^62 - 6 * q^63 - 64 * q^64 + 8 * q^66 + 18 * q^67 + 24 * q^68 + 4 * q^69 + 6 * q^71 + 12 * q^72 - 36 * q^74 + 40 * q^76 - 18 * q^78 + 44 * q^79 - 2 * q^81 - 48 * q^82 + 12 * q^84 - 20 * q^86 + 6 * q^87 - 24 * q^88 + 14 * q^89 - 18 * q^91 + 12 * q^93 + 28 * q^94 - 32 * q^96 + 18 * q^97 + 24 * q^98 + 8 * q^99

Introduction

L-functions

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