LMFDB - Embedded newform 315.2.bz.b.262.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(73,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("315.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bz (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$4$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			262.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	315.262
Dual form			315.2.bz.b.208.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.133975 - 0.500000i) q^{2} +(1.50000 + 0.866025i) q^{4} +(1.86603 + 1.23205i) q^{5} +(-0.866025 - 2.50000i) q^{7} +(1.36603 - 1.36603i) q^{8} +O(q^{10})$	\(q+(0.133975 - 0.500000i) q^{2} +(1.50000 + 0.866025i) q^{4} +(1.86603 + 1.23205i) q^{5} +(-0.866025 - 2.50000i) q^{7} +(1.36603 - 1.36603i) q^{8} +(0.866025 - 0.767949i) q^{10} +(-1.36603 + 2.36603i) q^{11} +(2.00000 + 2.00000i) q^{13} +(-1.36603 + 0.0980762i) q^{14} +(1.23205 + 2.13397i) q^{16} +(-1.00000 - 3.73205i) q^{17} +(-0.366025 - 0.633975i) q^{19} +(1.73205 + 3.46410i) q^{20} +(1.00000 + 1.00000i) q^{22} +(0.133975 + 0.0358984i) q^{23} +(1.96410 + 4.59808i) q^{25} +(1.26795 - 0.732051i) q^{26} +(0.866025 - 4.50000i) q^{28} +3.00000i q^{29} +(-6.46410 - 3.73205i) q^{31} +(4.96410 - 1.33013i) q^{32} -2.00000 q^{34} +(1.46410 - 5.73205i) q^{35} +(1.26795 - 4.73205i) q^{37} +(-0.366025 + 0.0980762i) q^{38} +(4.23205 - 0.866025i) q^{40} -6.46410i q^{41} +(2.83013 - 2.83013i) q^{43} +(-4.09808 + 2.36603i) q^{44} +(0.0358984 - 0.0621778i) q^{46} +(-8.83013 - 2.36603i) q^{47} +(-5.50000 + 4.33013i) q^{49} +(2.56218 - 0.366025i) q^{50} +(1.26795 + 4.73205i) q^{52} +(1.83013 + 6.83013i) q^{53} +(-5.46410 + 2.73205i) q^{55} +(-4.59808 - 2.23205i) q^{56} +(1.50000 + 0.401924i) q^{58} +(-4.09808 + 7.09808i) q^{59} +(1.33013 - 0.767949i) q^{61} +(-2.73205 + 2.73205i) q^{62} +2.26795i q^{64} +(1.26795 + 6.19615i) q^{65} +(-10.6962 + 2.86603i) q^{67} +(1.73205 - 6.46410i) q^{68} +(-2.66987 - 1.50000i) q^{70} -1.26795 q^{71} +(-12.9282 + 3.46410i) q^{73} +(-2.19615 - 1.26795i) q^{74} -1.26795i q^{76} +(7.09808 + 1.36603i) q^{77} +(-2.83013 + 1.63397i) q^{79} +(-0.330127 + 5.50000i) q^{80} +(-3.23205 - 0.866025i) q^{82} +(-2.09808 - 2.09808i) q^{83} +(2.73205 - 8.19615i) q^{85} +(-1.03590 - 1.79423i) q^{86} +(1.36603 + 5.09808i) q^{88} +(-0.330127 - 0.571797i) q^{89} +(3.26795 - 6.73205i) q^{91} +(0.169873 + 0.169873i) q^{92} +(-2.36603 + 4.09808i) q^{94} +(0.0980762 - 1.63397i) q^{95} +(5.92820 - 5.92820i) q^{97} +(1.42820 + 3.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 6 q^{4} + 4 q^{5} + 2 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 + 6 * q^4 + 4 * q^5 + 2 * q^8	$ 4 q + 4 q^{2} + 6 q^{4} + 4 q^{5} + 2 q^{8} - 2 q^{11} + 8 q^{13} - 2 q^{14} - 2 q^{16} - 4 q^{17} + 2 q^{19} + 4 q^{22} + 4 q^{23} - 6 q^{25} + 12 q^{26} - 12 q^{31} + 6 q^{32} - 8 q^{34} - 8 q^{35} + 12 q^{37} + 2 q^{38} + 10 q^{40} - 6 q^{43} - 6 q^{44} + 14 q^{46} - 18 q^{47} - 22 q^{49} - 14 q^{50} + 12 q^{52} - 10 q^{53} - 8 q^{55} - 8 q^{56} + 6 q^{58} - 6 q^{59} - 12 q^{61} - 4 q^{62} + 12 q^{65} - 22 q^{67} - 28 q^{70} - 12 q^{71} - 24 q^{73} + 12 q^{74} + 18 q^{77} + 6 q^{79} + 16 q^{80} - 6 q^{82} + 2 q^{83} + 4 q^{85} - 18 q^{86} + 2 q^{88} + 16 q^{89} + 20 q^{91} + 18 q^{92} - 6 q^{94} - 10 q^{95} - 4 q^{97} - 22 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 6 * q^4 + 4 * q^5 + 2 * q^8 - 2 * q^11 + 8 * q^13 - 2 * q^14 - 2 * q^16 - 4 * q^17 + 2 * q^19 + 4 * q^22 + 4 * q^23 - 6 * q^25 + 12 * q^26 - 12 * q^31 + 6 * q^32 - 8 * q^34 - 8 * q^35 + 12 * q^37 + 2 * q^38 + 10 * q^40 - 6 * q^43 - 6 * q^44 + 14 * q^46 - 18 * q^47 - 22 * q^49 - 14 * q^50 + 12 * q^52 - 10 * q^53 - 8 * q^55 - 8 * q^56 + 6 * q^58 - 6 * q^59 - 12 * q^61 - 4 * q^62 + 12 * q^65 - 22 * q^67 - 28 * q^70 - 12 * q^71 - 24 * q^73 + 12 * q^74 + 18 * q^77 + 6 * q^79 + 16 * q^80 - 6 * q^82 + 2 * q^83 + 4 * q^85 - 18 * q^86 + 2 * q^88 + 16 * q^89 + 20 * q^91 + 18 * q^92 - 6 * q^94 - 10 * q^95 - 4 * q^97 - 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	0.133975	−	0.500000i	0.0947343	−	0.353553i	−0.902245	−	0.431224i	$-0.858082\pi$
$2$	0.133975	−	0.500000i	0.0947343	−	0.353553i	0.996979	+	0.0776710i	$0.0247484\pi$
$3$		0			0
$3$		0			0
$4$	1.50000	+	0.866025i	0.750000	+	0.433013i
$5$	1.86603	+	1.23205i	0.834512	+	0.550990i
$5$	1.86603	+	1.23205i	0.834512	+	0.550990i
$6$		0			0
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$8$	1.36603	−	1.36603i	0.482963	−	0.482963i
$9$		0			0
$10$	0.866025	−	0.767949i	0.273861	−	0.242847i
$11$	−1.36603	+	2.36603i	−0.411872	+	0.713384i	−0.995094	−	0.0989291i	$-0.968458\pi$
$11$	−1.36603	+	2.36603i	−0.411872	+	0.713384i	0.583222	+	0.812313i	$0.301792\pi$
$12$		0			0
$13$	2.00000	+	2.00000i	0.554700	+	0.554700i	0.927794	−	0.373094i	$-0.121703\pi$
$13$	2.00000	+	2.00000i	0.554700	+	0.554700i	−0.373094	+	0.927794i	$0.621703\pi$
$14$	−1.36603	+	0.0980762i	−0.365086	+	0.0262120i
$15$		0			0
$16$	1.23205	+	2.13397i	0.308013	+	0.533494i
$17$	−1.00000	−	3.73205i	−0.242536	−	0.905155i	−0.974606	−	0.223926i	$-0.928112\pi$
$17$	−1.00000	−	3.73205i	−0.242536	−	0.905155i	0.732070	−	0.681229i	$-0.238554\pi$
$18$		0			0
$19$	−0.366025	−	0.633975i	−0.0839720	−	0.145444i	0.820981	−	0.570956i	$-0.193427\pi$
$19$	−0.366025	−	0.633975i	−0.0839720	−	0.145444i	−0.904953	+	0.425512i	$0.860094\pi$
$20$	1.73205	+	3.46410i	0.387298	+	0.774597i
$21$		0			0
$22$	1.00000	+	1.00000i	0.213201	+	0.213201i
$23$	0.133975	+	0.0358984i	0.0279356	+	0.00748533i	0.272760	−	0.962082i	$-0.412064\pi$
$23$	0.133975	+	0.0358984i	0.0279356	+	0.00748533i	−0.244824	+	0.969567i	$0.578730\pi$
$24$		0			0
$25$	1.96410	+	4.59808i	0.392820	+	0.919615i
$26$	1.26795	−	0.732051i	0.248665	−	0.143567i
$27$		0			0
$28$	0.866025	−	4.50000i	0.163663	−	0.850420i
$29$			3.00000i			0.557086i	0.960424	+	0.278543i	$0.0898515\pi$
$29$			3.00000i			0.557086i	−0.960424	+	0.278543i	$0.910149\pi$
$30$		0			0
$31$	−6.46410	−	3.73205i	−1.16099	−	0.670296i	−0.209447	−	0.977820i	$-0.567166\pi$
$31$	−6.46410	−	3.73205i	−1.16099	−	0.670296i	−0.951540	+	0.307524i	$0.900500\pi$
$32$	4.96410	−	1.33013i	0.877537	−	0.235135i
$33$		0			0
$34$	−2.00000			−0.342997
$35$	1.46410	−	5.73205i	0.247478	−	0.968893i
$36$		0			0
$37$	1.26795	−	4.73205i	0.208450	−	0.777944i	−0.779921	−	0.625878i	$-0.784741\pi$
$37$	1.26795	−	4.73205i	0.208450	−	0.777944i	0.988370	−	0.152066i	$-0.0485927\pi$
$38$	−0.366025	+	0.0980762i	−0.0593772	+	0.0159101i
$39$		0			0
$40$	4.23205	−	0.866025i	0.669146	−	0.136931i
$41$		−	6.46410i		−	1.00952i	−0.863259	−	0.504762i	$-0.831580\pi$
$41$		−	6.46410i		−	1.00952i	0.863259	−	0.504762i	$-0.168420\pi$
$42$		0			0
$43$	2.83013	−	2.83013i	0.431590	−	0.431590i	−0.457579	−	0.889169i	$-0.651283\pi$
$43$	2.83013	−	2.83013i	0.431590	−	0.431590i	0.889169	+	0.457579i	$0.151283\pi$
$44$	−4.09808	+	2.36603i	−0.617808	+	0.356692i
$45$		0			0
$46$	0.0358984	−	0.0621778i	0.00529293	−	0.00916762i
$47$	−8.83013	−	2.36603i	−1.28801	−	0.345120i	−0.451103	−	0.892472i	$-0.648969\pi$
$47$	−8.83013	−	2.36603i	−1.28801	−	0.345120i	−0.836903	+	0.547351i	$0.815636\pi$
$48$		0			0
$49$	−5.50000	+	4.33013i	−0.785714	+	0.618590i
$50$	2.56218	−	0.366025i	0.362347	−	0.0517638i
$51$		0			0
$52$	1.26795	+	4.73205i	0.175833	+	0.656217i
$53$	1.83013	+	6.83013i	0.251387	+	0.938190i	0.970065	+	0.242846i	$0.0780811\pi$
$53$	1.83013	+	6.83013i	0.251387	+	0.938190i	−0.718677	+	0.695344i	$0.755252\pi$
$54$		0			0
$55$	−5.46410	+	2.73205i	−0.736779	+	0.368390i
$56$	−4.59808	−	2.23205i	−0.614444	−	0.298270i
$57$		0			0
$58$	1.50000	+	0.401924i	0.196960	+	0.0527752i
$59$	−4.09808	+	7.09808i	−0.533524	+	0.924091i	0.465709	+	0.884938i	$0.345799\pi$
$59$	−4.09808	+	7.09808i	−0.533524	+	0.924091i	−0.999233	+	0.0391530i	$0.987534\pi$
$60$		0			0
$61$	1.33013	−	0.767949i	0.170305	−	0.0983258i	−0.412424	−	0.910992i	$-0.635318\pi$
$61$	1.33013	−	0.767949i	0.170305	−	0.0983258i	0.582730	+	0.812666i	$0.301985\pi$
$62$	−2.73205	+	2.73205i	−0.346971	+	0.346971i
$63$		0			0
$64$			2.26795i			0.283494i
$65$	1.26795	+	6.19615i	0.157270	+	0.768538i
$66$		0			0
$67$	−10.6962	+	2.86603i	−1.30674	+	0.350141i	−0.843996	−	0.536350i	$-0.819803\pi$
$67$	−10.6962	+	2.86603i	−1.30674	+	0.350141i	−0.462747	+	0.886490i	$0.653136\pi$
$68$	1.73205	−	6.46410i	0.210042	−	0.783887i
$69$		0			0
$70$	−2.66987	−	1.50000i	−0.319111	−	0.179284i
$71$	−1.26795			−0.150478			−0.0752389	−	0.997166i	$-0.523972\pi$
$71$	−1.26795			−0.150478			−0.0752389	+	0.997166i	$0.523972\pi$
$72$		0			0
$73$	−12.9282	+	3.46410i	−1.51313	+	0.405442i	−0.917474	−	0.397796i	$-0.869775\pi$
$73$	−12.9282	+	3.46410i	−1.51313	+	0.405442i	−0.595658	+	0.803238i	$0.703109\pi$
$74$	−2.19615	−	1.26795i	−0.255298	−	0.147396i
$75$		0			0
$76$		−	1.26795i		−	0.145444i
$77$	7.09808	+	1.36603i	0.808901	+	0.155673i
$78$		0			0
$79$	−2.83013	+	1.63397i	−0.318414	+	0.183837i	−0.650686	−	0.759347i	$-0.725518\pi$
$79$	−2.83013	+	1.63397i	−0.318414	+	0.183837i	0.332271	+	0.943184i	$0.392185\pi$
$80$	−0.330127	+	5.50000i	−0.0369093	+	0.614919i
$81$		0			0
$82$	−3.23205	−	0.866025i	−0.356920	−	0.0956365i
$83$	−2.09808	−	2.09808i	−0.230294	−	0.230294i	0.582522	−	0.812815i	$-0.302066\pi$
$83$	−2.09808	−	2.09808i	−0.230294	−	0.230294i	−0.812815	+	0.582522i	$0.802066\pi$
$84$		0			0
$85$	2.73205	−	8.19615i	0.296333	−	0.888998i
$86$	−1.03590	−	1.79423i	−0.111704	−	0.193477i
$87$		0			0
$88$	1.36603	+	5.09808i	0.145619	+	0.543457i
$89$	−0.330127	−	0.571797i	−0.0349934	−	0.0606103i	0.847998	−	0.529999i	$-0.177808\pi$
$89$	−0.330127	−	0.571797i	−0.0349934	−	0.0606103i	−0.882992	+	0.469389i	$0.844474\pi$
$90$		0			0
$91$	3.26795	−	6.73205i	0.342574	−	0.705711i
$92$	0.169873	+	0.169873i	0.0177105	+	0.0177105i
$93$		0			0
$94$	−2.36603	+	4.09808i	−0.244037	+	0.422684i
$95$	0.0980762	−	1.63397i	0.0100624	−	0.167642i
$96$		0			0
$97$	5.92820	−	5.92820i	0.601918	−	0.601918i	−0.338903	−	0.940821i	$-0.610056\pi$
$97$	5.92820	−	5.92820i	0.601918	−	0.601918i	0.940821	+	0.338903i	$0.110056\pi$
$98$	1.42820	+	3.33013i	0.144270	+	0.336394i
$99$		0			0
$100$	−1.03590	+	8.59808i	−0.103590	+	0.859808i
$101$	−7.16025	−	4.13397i	−0.712472	−	0.411346i	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	−7.16025	−	4.13397i	−0.712472	−	0.411346i	−0.811976	+	0.583691i	$0.801608\pi$
$102$		0			0
$103$	1.23205	−	4.59808i	0.121398	−	0.453062i	−0.878288	−	0.478132i	$-0.841314\pi$
$103$	1.23205	−	4.59808i	0.121398	−	0.453062i	0.999686	+	0.0250698i	$0.00798081\pi$
$104$	5.46410			0.535799
$105$		0			0
$106$	3.66025			0.355515
$107$	3.40192	−	12.6962i	0.328876	−	1.22738i	−0.581481	−	0.813560i	$-0.697526\pi$
$107$	3.40192	−	12.6962i	0.328876	−	1.22738i	0.910357	−	0.413823i	$-0.135807\pi$
$108$		0			0
$109$	8.76795	+	5.06218i	0.839817	+	0.484869i	0.857202	−	0.514980i	$-0.172201\pi$
$109$	8.76795	+	5.06218i	0.839817	+	0.484869i	−0.0173849	+	0.999849i	$0.505534\pi$
$110$	0.633975	+	3.09808i	0.0604471	+	0.295390i
$111$		0			0
$112$	4.26795	−	4.92820i	0.403283	−	0.465671i
$113$	7.73205	−	7.73205i	0.727370	−	0.727370i	−0.242725	−	0.970095i	$-0.578041\pi$
$113$	7.73205	−	7.73205i	0.727370	−	0.727370i	0.970095	+	0.242725i	$0.0780413\pi$
$114$		0			0
$115$	0.205771	+	0.232051i	0.0191883	+	0.0216388i
$116$	−2.59808	+	4.50000i	−0.241225	+	0.417815i
$117$		0			0
$118$	3.00000	+	3.00000i	0.276172	+	0.276172i
$119$	−8.46410	+	5.73205i	−0.775903	+	0.525456i
$120$		0			0
$121$	1.76795	+	3.06218i	0.160723	+	0.278380i
$122$	−0.205771	−	0.767949i	−0.0186297	−	0.0695269i
$123$		0			0
$124$	−6.46410	−	11.1962i	−0.580493	−	1.00544i
$125$	−2.00000	+	11.0000i	−0.178885	+	0.983870i
$126$		0			0
$127$	0.464102	+	0.464102i	0.0411824	+	0.0411824i	0.727398	−	0.686216i	$-0.240729\pi$
$127$	0.464102	+	0.464102i	0.0411824	+	0.0411824i	−0.686216	+	0.727398i	$0.740729\pi$
$128$	11.0622	+	2.96410i	0.977768	+	0.261992i
$129$		0			0
$130$	3.26795	+	0.196152i	0.286618	+	0.0172037i
$131$	13.3923	−	7.73205i	1.17009	−	0.675552i	0.216390	−	0.976307i	$-0.430572\pi$
$131$	13.3923	−	7.73205i	1.17009	−	0.675552i	0.953702	+	0.300755i	$0.0972385\pi$
$132$		0			0
$133$	−1.26795	+	1.46410i	−0.109945	+	0.126954i
$134$			5.73205i			0.495174i
$135$		0			0
$136$	−6.46410	−	3.73205i	−0.554292	−	0.320021i
$137$	−13.1962	+	3.53590i	−1.12742	+	0.302092i	−0.773884	−	0.633327i	$-0.781689\pi$
$137$	−13.1962	+	3.53590i	−1.12742	+	0.302092i	−0.353539	+	0.935420i	$0.615022\pi$
$138$		0			0
$139$	5.66025			0.480096			0.240048	−	0.970761i	$-0.422837\pi$
$139$	5.66025			0.480096			0.240048	+	0.970761i	$0.422837\pi$
$140$	7.16025	−	7.33013i	0.605152	−	0.619509i
$141$		0			0
$142$	−0.169873	+	0.633975i	−0.0142554	+	0.0532020i
$143$	−7.46410	+	2.00000i	−0.624180	+	0.167248i
$144$		0			0
$145$	−3.69615	+	5.59808i	−0.306949	+	0.464895i
$146$			6.92820i			0.573382i
$147$		0			0
$148$	6.00000	−	6.00000i	0.493197	−	0.493197i
$149$	0.696152	−	0.401924i	0.0570310	−	0.0329269i	−0.471213	−	0.882019i	$-0.656184\pi$
$149$	0.696152	−	0.401924i	0.0570310	−	0.0329269i	0.528244	+	0.849092i	$0.322850\pi$
$150$		0			0
$151$	−6.92820	+	12.0000i	−0.563809	+	0.976546i	0.433350	+	0.901226i	$0.357331\pi$
$151$	−6.92820	+	12.0000i	−0.563809	+	0.976546i	−0.997159	+	0.0753205i	$0.976002\pi$
$152$	−1.36603	−	0.366025i	−0.110799	−	0.0296886i
$153$		0			0
$154$	1.63397	−	3.36603i	0.131669	−	0.271242i
$155$	−7.46410	−	14.9282i	−0.599531	−	1.19906i
$156$		0			0
$157$	−1.24167	−	4.63397i	−0.0990960	−	0.369831i	0.898513	−	0.438948i	$-0.144649\pi$
$157$	−1.24167	−	4.63397i	−0.0990960	−	0.369831i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$	0.437822	+	1.63397i	0.0348313	+	0.129992i
$159$		0			0
$160$	10.9019	+	3.63397i	0.861873	+	0.287291i
$161$	−0.0262794	−	0.366025i	−0.00207111	−	0.0288468i
$162$		0			0
$163$	13.5622	+	3.63397i	1.06227	+	0.284635i	0.747314	−	0.664471i	$-0.231343\pi$
$163$	13.5622	+	3.63397i	1.06227	+	0.284635i	0.314958	+	0.949106i	$0.398010\pi$
$164$	5.59808	−	9.69615i	0.437136	−	0.757142i
$165$		0			0
$166$	−1.33013	+	0.767949i	−0.103238	+	0.0596044i
$167$	11.7583	−	11.7583i	0.909887	−	0.909887i	−0.0863757	−	0.996263i	$-0.527529\pi$
$167$	11.7583	−	11.7583i	0.909887	−	0.909887i	0.996263	+	0.0863757i	$0.0275285\pi$
$168$		0			0
$169$		−	5.00000i		−	0.384615i
$170$	−3.73205	−	2.46410i	−0.286235	−	0.188988i
$171$		0			0
$172$	6.69615	−	1.79423i	0.510577	−	0.136809i
$173$	−5.33975	+	19.9282i	−0.405973	+	1.51511i	0.396280	+	0.918130i	$0.370301\pi$
$173$	−5.33975	+	19.9282i	−0.405973	+	1.51511i	−0.802253	+	0.596984i	$0.796366\pi$
$174$		0			0
$175$	9.79423	−	8.89230i	0.740374	−	0.672195i
$176$	−6.73205			−0.507447
$177$		0			0
$178$	−0.330127	+	0.0884573i	−0.0247441	+	0.00663015i
$179$	6.80385	+	3.92820i	0.508543	+	0.293608i	0.732235	−	0.681052i	$-0.238477\pi$
$179$	6.80385	+	3.92820i	0.508543	+	0.293608i	−0.223691	+	0.974660i	$0.571811\pi$
$180$		0			0
$181$			1.19615i			0.0889093i	0.999011	+	0.0444547i	$0.0141550\pi$
$181$			1.19615i			0.0889093i	−0.999011	+	0.0444547i	$0.985845\pi$
$182$	−2.92820	−	2.53590i	−0.217053	−	0.187973i
$183$		0			0
$184$	0.232051	−	0.133975i	0.0171070	−	0.00987674i
$185$	8.19615	−	7.26795i	0.602593	−	0.534350i
$186$		0			0
$187$	10.1962	+	2.73205i	0.745617	+	0.199787i
$188$	−11.1962	−	11.1962i	−0.816563	−	0.816563i
$189$		0			0
$190$	−0.803848	−	0.267949i	−0.0583172	−	0.0194391i
$191$	6.63397	+	11.4904i	0.480018	+	0.831415i	0.999737	−	0.0229220i	$-0.00729695\pi$
$191$	6.63397	+	11.4904i	0.480018	+	0.831415i	−0.519720	+	0.854337i	$0.673964\pi$
$192$		0			0
$193$	2.09808	+	7.83013i	0.151023	+	0.563625i	0.999413	+	0.0342537i	$0.0109054\pi$
$193$	2.09808	+	7.83013i	0.151023	+	0.563625i	−0.848390	+	0.529371i	$0.822428\pi$
$194$	−2.16987	−	3.75833i	−0.155788	−	0.269832i
$195$		0			0
$196$	−12.0000	+	1.73205i	−0.857143	+	0.123718i
$197$	10.1244	+	10.1244i	0.721330	+	0.721330i	0.968876	−	0.247546i	$-0.0796240\pi$
$197$	10.1244	+	10.1244i	0.721330	+	0.721330i	−0.247546	+	0.968876i	$0.579624\pi$
$198$		0			0
$199$	5.53590	−	9.58846i	0.392429	−	0.679708i	−0.600340	−	0.799745i	$-0.704968\pi$
$199$	5.53590	−	9.58846i	0.392429	−	0.679708i	0.992769	+	0.120037i	$0.0383014\pi$
$200$	8.96410	+	3.59808i	0.633858	+	0.254422i
$201$		0			0
$202$	−3.02628	+	3.02628i	−0.212928	+	0.212928i
$203$	7.50000	−	2.59808i	0.526397	−	0.182349i
$204$		0			0
$205$	7.96410	−	12.0622i	0.556237	−	0.842459i
$206$	−2.13397	−	1.23205i	−0.148681	−	0.0858410i
$207$		0			0
$208$	−1.80385	+	6.73205i	−0.125074	+	0.466784i
$209$	2.00000			0.138343
$210$		0			0
$211$	−0.196152			−0.0135037			−0.00675184	−	0.999977i	$-0.502149\pi$
$211$	−0.196152			−0.0135037			−0.00675184	+	0.999977i	$0.502149\pi$
$212$	−3.16987	+	11.8301i	−0.217708	+	0.812496i
$213$		0			0
$214$	−5.89230	−	3.40192i	−0.402790	−	0.232551i
$215$	8.76795	−	1.79423i	0.597969	−	0.122365i
$216$		0			0
$217$	−3.73205	+	19.3923i	−0.253348	+	1.31644i
$218$	3.70577	−	3.70577i	0.250987	−	0.250987i
$219$		0			0
$220$	−10.5622	−	0.633975i	−0.712102	−	0.0427426i
$221$	5.46410	−	9.46410i	0.367555	−	0.636624i
$222$		0			0
$223$	−18.1244	−	18.1244i	−1.21370	−	1.21370i	−0.969802	−	0.243895i	$-0.921575\pi$
$223$	−18.1244	−	18.1244i	−1.21370	−	1.21370i	−0.243895	−	0.969802i	$-0.578425\pi$
$224$	−7.62436	−	11.2583i	−0.509424	−	0.752229i
$225$		0			0
$226$	−2.83013	−	4.90192i	−0.188257	−	0.326071i
$227$	5.09808	+	19.0263i	0.338371	+	1.26282i	0.900168	+	0.435543i	$0.143444\pi$
$227$	5.09808	+	19.0263i	0.338371	+	1.26282i	−0.561797	+	0.827275i	$0.689890\pi$
$228$		0			0
$229$	9.19615	+	15.9282i	0.607699	+	1.05257i	0.991619	+	0.129199i	$0.0412406\pi$
$229$	9.19615	+	15.9282i	0.607699	+	1.05257i	−0.383920	+	0.923366i	$0.625426\pi$
$230$	0.143594	−	0.0717968i	0.00946828	−	0.00473414i
$231$		0			0
$232$	4.09808	+	4.09808i	0.269052	+	0.269052i
$233$	−6.46410	−	1.73205i	−0.423477	−	0.113470i	0.0407854	−	0.999168i	$-0.487014\pi$
$233$	−6.46410	−	1.73205i	−0.423477	−	0.113470i	−0.464263	+	0.885698i	$0.653681\pi$
$234$		0			0
$235$	−13.5622	−	15.2942i	−0.884699	−	0.997685i
$236$	−12.2942	+	7.09808i	−0.800286	+	0.462045i
$237$		0			0
$238$	1.73205	+	5.00000i	0.112272	+	0.324102i
$239$		−	2.39230i		−	0.154745i	−0.997002	−	0.0773727i	$-0.975347\pi$
$239$		−	2.39230i		−	0.154745i	0.997002	−	0.0773727i	$-0.0246531\pi$
$240$		0			0
$241$	21.4641	+	12.3923i	1.38262	+	0.798259i	0.992470	−	0.122491i	$-0.0390882\pi$
$241$	21.4641	+	12.3923i	1.38262	+	0.798259i	0.390155	+	0.920749i	$0.372422\pi$
$242$	1.76795	−	0.473721i	0.113648	−	0.0304519i
$243$		0			0
$244$	2.66025			0.170305
$245$	−15.5981	+	1.30385i	−0.996525	+	0.0832998i
$246$		0			0
$247$	0.535898	−	2.00000i	0.0340984	−	0.127257i
$248$	−13.9282	+	3.73205i	−0.884442	+	0.236985i
$249$		0			0
$250$	5.23205	+	2.47372i	0.330904	+	0.156452i
$251$			21.8564i			1.37956i	0.724017	+	0.689782i	$0.242294\pi$
$251$			21.8564i			1.37956i	−0.724017	+	0.689782i	$0.757706\pi$
$252$		0			0
$253$	−0.267949	+	0.267949i	−0.0168458	+	0.0168458i
$254$	0.294229	−	0.169873i	0.0184615	−	0.0106588i
$255$		0			0
$256$	0.696152	−	1.20577i	0.0435095	−	0.0753607i
$257$	2.73205	+	0.732051i	0.170421	+	0.0456641i	0.343020	−	0.939328i	$-0.388550\pi$
$257$	2.73205	+	0.732051i	0.170421	+	0.0456641i	−0.172600	+	0.984992i	$0.555217\pi$
$258$		0			0
$259$	−12.9282	+	0.928203i	−0.803319	+	0.0576757i
$260$	−3.46410	+	10.3923i	−0.214834	+	0.644503i
$261$		0			0
$262$	−2.07180	−	7.73205i	−0.127996	−	0.477688i
$263$	−4.06218	−	15.1603i	−0.250485	−	0.934821i	−0.970547	−	0.240912i	$-0.922553\pi$
$263$	−4.06218	−	15.1603i	−0.250485	−	0.934821i	0.720062	−	0.693909i	$-0.244113\pi$
$264$		0			0
$265$	−5.00000	+	15.0000i	−0.307148	+	0.921443i
$266$	0.562178	+	0.830127i	0.0344693	+	0.0508984i
$267$		0			0
$268$	−18.5263	−	4.96410i	−1.13167	−	0.303231i
$269$	11.4282	−	19.7942i	0.696790	−	1.20688i	−0.272784	−	0.962075i	$-0.587944\pi$
$269$	11.4282	−	19.7942i	0.696790	−	1.20688i	0.969574	−	0.244800i	$-0.0787223\pi$
$270$		0			0
$271$	18.4186	−	10.6340i	1.11885	−	0.645968i	0.177742	−	0.984077i	$-0.443121\pi$
$271$	18.4186	−	10.6340i	1.11885	−	0.645968i	0.941107	+	0.338109i	$0.109787\pi$
$272$	6.73205	−	6.73205i	0.408191	−	0.408191i
$273$		0			0
$274$			7.07180i			0.427223i
$275$	−13.5622	−	1.63397i	−0.817830	−	0.0985324i
$276$		0			0
$277$	5.19615	−	1.39230i	0.312207	−	0.0836555i	−0.0993135	−	0.995056i	$-0.531665\pi$
$277$	5.19615	−	1.39230i	0.312207	−	0.0836555i	0.411520	+	0.911401i	$0.364998\pi$
$278$	0.758330	−	2.83013i	0.0454816	−	0.169740i
$279$		0			0
$280$	−5.83013	−	9.83013i	−0.348417	−	0.587462i
$281$	0.928203			0.0553720			0.0276860	−	0.999617i	$-0.491186\pi$
$281$	0.928203			0.0553720			0.0276860	+	0.999617i	$0.491186\pi$
$282$		0			0
$283$	−1.90192	+	0.509619i	−0.113058	+	0.0302937i	−0.314904	−	0.949123i	$-0.601972\pi$
$283$	−1.90192	+	0.509619i	−0.113058	+	0.0302937i	0.201847	+	0.979417i	$0.435306\pi$
$284$	−1.90192	−	1.09808i	−0.112858	−	0.0651588i
$285$		0			0
$286$			4.00000i			0.236525i
$287$	−16.1603	+	5.59808i	−0.953910	+	0.330444i
$288$		0			0
$289$	1.79423	−	1.03590i	0.105543	−	0.0609352i
$290$	2.30385	+	2.59808i	0.135287	+	0.152564i
$291$		0			0
$292$	−22.3923	−	6.00000i	−1.31041	−	0.351123i
$293$	−2.39230	−	2.39230i	−0.139760	−	0.139760i	0.633765	−	0.773525i	$-0.281508\pi$
$293$	−2.39230	−	2.39230i	−0.139760	−	0.139760i	−0.773525	+	0.633765i	$0.781508\pi$
$294$		0			0
$295$	−16.3923	+	8.19615i	−0.954397	+	0.477198i
$296$	−4.73205	−	8.19615i	−0.275045	−	0.476392i
$297$		0			0
$298$	−0.107695	−	0.401924i	−0.00623861	−	0.0232828i
$299$	0.196152	+	0.339746i	0.0113438	+	0.0196480i
$300$		0			0
$301$	−9.52628	−	4.62436i	−0.549086	−	0.266543i
$302$	5.07180	+	5.07180i	0.291849	+	0.291849i
$303$		0			0
$304$	0.901924	−	1.56218i	0.0517289	−	0.0895970i
$305$	3.42820	+	0.205771i	0.196298	+	0.0117824i
$306$		0			0
$307$	−6.29423	+	6.29423i	−0.359231	+	0.359231i	−0.863529	−	0.504299i	$-0.831751\pi$
$307$	−6.29423	+	6.29423i	−0.359231	+	0.359231i	0.504299	+	0.863529i	$0.331751\pi$
$308$	9.46410	+	8.19615i	0.539267	+	0.467019i
$309$		0			0
$310$	−8.46410	+	1.73205i	−0.480729	+	0.0983739i
$311$	13.2224	+	7.63397i	0.749775	+	0.432883i	0.825613	−	0.564237i	$-0.190830\pi$
$311$	13.2224	+	7.63397i	0.749775	+	0.432883i	−0.0758374	+	0.997120i	$0.524163\pi$
$312$		0			0
$313$	−1.39230	+	5.19615i	−0.0786977	+	0.293704i	−0.994046	−	0.108958i	$-0.965248\pi$
$313$	−1.39230	+	5.19615i	−0.0786977	+	0.293704i	0.915349	+	0.402662i	$0.131915\pi$
$314$	−2.48334			−0.140143
$315$		0			0
$316$	−5.66025			−0.318414
$317$	2.46410	−	9.19615i	0.138398	−	0.516507i	−0.861563	−	0.507651i	$-0.830514\pi$
$317$	2.46410	−	9.19615i	0.138398	−	0.516507i	0.999961	−	0.00885679i	$-0.00281924\pi$
$318$		0			0
$319$	−7.09808	−	4.09808i	−0.397416	−	0.229448i
$320$	−2.79423	+	4.23205i	−0.156202	+	0.236579i
$321$		0			0
$322$	−0.186533	−	0.0358984i	−0.0103951	−	0.00200054i
$323$	−2.00000	+	2.00000i	−0.111283	+	0.111283i
$324$		0			0
$325$	−5.26795	+	13.1244i	−0.292213	+	0.728008i
$326$	3.63397	−	6.29423i	0.201267	−	0.348605i
$327$		0			0
$328$	−8.83013	−	8.83013i	−0.487562	−	0.487562i
$329$	1.73205	+	24.1244i	0.0954911	+	1.33002i
$330$		0			0
$331$	0.928203	+	1.60770i	0.0510187	+	0.0883669i	0.890407	−	0.455165i	$-0.150420\pi$
$331$	0.928203	+	1.60770i	0.0510187	+	0.0883669i	−0.839388	+	0.543532i	$0.817087\pi$
$332$	−1.33013	−	4.96410i	−0.0730002	−	0.272440i
$333$		0			0
$334$	−4.30385	−	7.45448i	−0.235496	−	0.407891i
$335$	−23.4904	−	7.83013i	−1.28342	−	0.427806i
$336$		0			0
$337$	9.53590	+	9.53590i	0.519453	+	0.519453i	0.917406	−	0.397953i	$-0.130279\pi$
$337$	9.53590	+	9.53590i	0.519453	+	0.519453i	−0.397953	+	0.917406i	$0.630279\pi$
$338$	−2.50000	−	0.669873i	−0.135982	−	0.0364363i
$339$		0			0
$340$	11.1962	−	9.92820i	0.607197	−	0.538432i
$341$	17.6603	−	10.1962i	0.956356	−	0.552153i
$342$		0			0
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$		−	7.73205i		−	0.416884i
$345$		0			0
$346$	9.24871	+	5.33975i	0.497214	+	0.287067i
$347$	−29.0885	+	7.79423i	−1.56155	+	0.418416i	−0.933154	−	0.359477i	$-0.882955\pi$
$347$	−29.0885	+	7.79423i	−1.56155	+	0.418416i	−0.628396	+	0.777893i	$0.716288\pi$
$348$		0			0
$349$	−6.26795			−0.335516			−0.167758	−	0.985828i	$-0.553653\pi$
$349$	−6.26795			−0.335516			−0.167758	+	0.985828i	$0.553653\pi$
$350$	−3.13397	−	6.08846i	−0.167518	−	0.325442i
$351$		0			0
$352$	−3.63397	+	13.5622i	−0.193691	+	0.722867i
$353$	−13.5622	+	3.63397i	−0.721842	+	0.193417i	−0.600993	−	0.799254i	$-0.705228\pi$
$353$	−13.5622	+	3.63397i	−0.721842	+	0.193417i	−0.120849	+	0.992671i	$0.538562\pi$
$354$		0			0
$355$	−2.36603	−	1.56218i	−0.125576	−	0.0829118i
$356$		−	1.14359i		−	0.0606103i
$357$		0			0
$358$	2.87564	−	2.87564i	0.151983	−	0.151983i
$359$	29.6603	−	17.1244i	1.56541	−	0.903789i	0.568715	−	0.822535i	$-0.307441\pi$
$359$	29.6603	−	17.1244i	1.56541	−	0.903789i	0.996693	−	0.0812542i	$-0.0258926\pi$
$360$		0			0
$361$	9.23205	−	15.9904i	0.485897	−	0.841599i
$362$	0.598076	+	0.160254i	0.0314342	+	0.00842277i
$363$		0			0
$364$	10.7321	−	7.26795i	0.562512	−	0.380944i
$365$	−28.3923	−	9.46410i	−1.48612	−	0.495374i
$366$		0			0
$367$	0.133975	+	0.500000i	0.00699342	+	0.0260998i	0.969334	−	0.245746i	$-0.0790328\pi$
$367$	0.133975	+	0.500000i	0.00699342	+	0.0260998i	−0.962341	+	0.271845i	$0.912366\pi$
$368$	0.0884573	+	0.330127i	0.00461115	+	0.0172091i
$369$		0			0
$370$	−2.53590	−	5.07180i	−0.131835	−	0.263670i
$371$	15.4904	−	10.4904i	0.804221	−	0.544633i
$372$		0			0
$373$	−7.73205	−	2.07180i	−0.400350	−	0.107274i	0.0530251	−	0.998593i	$-0.483114\pi$
$373$	−7.73205	−	2.07180i	−0.400350	−	0.107274i	−0.453376	+	0.891320i	$0.649780\pi$
$374$	2.73205	−	4.73205i	0.141271	−	0.244689i
$375$		0			0
$376$	−15.2942	+	8.83013i	−0.788740	+	0.455379i
$377$	−6.00000	+	6.00000i	−0.309016	+	0.309016i
$378$		0			0
$379$			2.33975i			0.120185i	0.998193	+	0.0600923i	$0.0191395\pi$
$379$			2.33975i			0.120185i	−0.998193	+	0.0600923i	$0.980860\pi$
$380$	1.56218	−	2.36603i	0.0801380	−	0.121375i
$381$		0			0
$382$	6.63397	−	1.77757i	0.339424	−	0.0909483i
$383$	−8.18653	+	30.5526i	−0.418312	+	1.56116i	0.359795	+	0.933031i	$0.382847\pi$
$383$	−8.18653	+	30.5526i	−0.418312	+	1.56116i	−0.778107	+	0.628131i	$0.783820\pi$
$384$		0			0
$385$	11.5622	+	11.2942i	0.589263	+	0.575607i
$386$	4.19615			0.213579
$387$		0			0
$388$	14.0263	−	3.75833i	0.712076	−	0.190800i
$389$	−4.26795	−	2.46410i	−0.216394	−	0.124935i	0.387886	−	0.921707i	$-0.373206\pi$
$389$	−4.26795	−	2.46410i	−0.216394	−	0.124935i	−0.604279	+	0.796773i	$0.706539\pi$
$390$		0			0
$391$		−	0.535898i		−	0.0271015i
$392$	−1.59808	+	13.4282i	−0.0807150	+	0.678227i
$393$		0			0
$394$	6.41858	−	3.70577i	0.323364	−	0.186694i
$395$	−7.29423	−	0.437822i	−0.367012	−	0.0220292i
$396$		0			0
$397$	−3.63397	−	0.973721i	−0.182384	−	0.0488696i	0.166471	−	0.986046i	$-0.446763\pi$
$397$	−3.63397	−	0.973721i	−0.182384	−	0.0488696i	−0.348855	+	0.937177i	$0.613429\pi$
$398$	−4.05256	−	4.05256i	−0.203136	−	0.203136i
$399$		0			0
$400$	−7.39230	+	9.85641i	−0.369615	+	0.492820i
$401$	5.50000	+	9.52628i	0.274657	+	0.475720i	0.970049	−	0.242911i	$-0.0781024\pi$
$401$	5.50000	+	9.52628i	0.274657	+	0.475720i	−0.695392	+	0.718631i	$0.744769\pi$
$402$		0			0
$403$	−5.46410	−	20.3923i	−0.272186	−	1.01581i
$404$	−7.16025	−	12.4019i	−0.356236	−	0.617019i
$405$		0			0
$406$	−0.294229	−	4.09808i	−0.0146023	−	0.203384i
$407$	9.46410	+	9.46410i	0.469118	+	0.469118i
$408$		0			0
$409$	10.4282	−	18.0622i	0.515641	−	0.893117i	−0.484194	−	0.874961i	$-0.660887\pi$
$409$	10.4282	−	18.0622i	0.515641	−	0.893117i	0.999835	−	0.0181564i	$-0.00577967\pi$
$410$	−4.96410	−	5.59808i	−0.245160	−	0.276469i
$411$		0			0
$412$	5.83013	−	5.83013i	0.287230	−	0.287230i
$413$	21.2942	+	4.09808i	1.04782	+	0.201653i
$414$		0			0
$415$	−1.33013	−	6.50000i	−0.0652934	−	0.319072i
$416$	12.5885	+	7.26795i	0.617200	+	0.356341i
$417$		0			0
$418$	0.267949	−	1.00000i	0.0131058	−	0.0489116i
$419$	23.8564			1.16546			0.582731	−	0.812665i	$-0.301984\pi$
$419$	23.8564			1.16546			0.582731	+	0.812665i	$0.301984\pi$
$420$		0			0
$421$	−17.3397			−0.845088			−0.422544	−	0.906343i	$-0.638863\pi$
$421$	−17.3397			−0.845088			−0.422544	+	0.906343i	$0.638863\pi$
$422$	−0.0262794	+	0.0980762i	−0.00127926	+	0.00477428i
$423$		0			0
$424$	11.8301	+	6.83013i	0.574522	+	0.331700i
$425$	15.1962	−	11.9282i	0.737122	−	0.578603i
$426$		0			0
$427$	−3.07180	−	2.66025i	−0.148655	−	0.128739i
$428$	16.0981	−	16.0981i	0.778130	−	0.778130i
$429$		0			0
$430$	0.277568	−	4.62436i	0.0133855	−	0.223006i
$431$	3.09808	−	5.36603i	0.149229	−	0.258472i	−0.781714	−	0.623637i	$-0.785654\pi$
$431$	3.09808	−	5.36603i	0.149229	−	0.258472i	0.930943	+	0.365165i	$0.118987\pi$
$432$		0			0
$433$	17.5359	+	17.5359i	0.842721	+	0.842721i	0.989212	−	0.146491i	$-0.0467978\pi$
$433$	17.5359	+	17.5359i	0.842721	+	0.842721i	−0.146491	+	0.989212i	$0.546798\pi$
$434$	9.19615	+	4.46410i	0.441429	+	0.214284i
$435$		0			0
$436$	8.76795	+	15.1865i	0.419909	+	0.727303i
$437$	−0.0262794	−	0.0980762i	−0.00125712	−	0.00469162i
$438$		0			0
$439$	−1.66025	−	2.87564i	−0.0792396	−	0.137247i	0.823682	−	0.567051i	$-0.191916\pi$
$439$	−1.66025	−	2.87564i	−0.0792396	−	0.137247i	−0.902922	+	0.429804i	$0.858583\pi$
$440$	−3.73205	+	11.1962i	−0.177919	+	0.533756i
$441$		0			0
$442$	−4.00000	−	4.00000i	−0.190261	−	0.190261i
$443$	−13.0622	−	3.50000i	−0.620603	−	0.166290i	−0.0652010	−	0.997872i	$-0.520769\pi$
$443$	−13.0622	−	3.50000i	−0.620603	−	0.166290i	−0.555402	+	0.831582i	$0.687436\pi$
$444$		0			0
$445$	0.0884573	−	1.47372i	0.00419328	−	0.0698611i
$446$	−11.4904	+	6.63397i	−0.544085	+	0.314128i
$447$		0			0
$448$	5.66987	−	1.96410i	0.267876	−	0.0927951i
$449$			33.0526i			1.55985i	0.625875	+	0.779923i	$0.284742\pi$
$449$			33.0526i			1.55985i	−0.625875	+	0.779923i	$0.715258\pi$
$450$		0			0
$451$	15.2942	+	8.83013i	0.720177	+	0.415794i
$452$	18.2942	−	4.90192i	0.860488	−	0.230567i
$453$		0			0
$454$	10.1962			0.478529
$455$	14.3923	−	8.53590i	0.674722	−	0.400169i
$456$		0			0
$457$	3.14359	−	11.7321i	0.147051	−	0.548802i	−0.852604	−	0.522557i	$-0.824978\pi$
$457$	3.14359	−	11.7321i	0.147051	−	0.548802i	0.999656	−	0.0262453i	$-0.00835510\pi$
$458$	9.19615	−	2.46410i	0.429708	−	0.115140i
$459$		0			0
$460$	0.107695	+	0.526279i	0.00502131	+	0.0245379i
$461$		−	5.60770i		−	0.261176i	−0.991437	−	0.130588i	$-0.958313\pi$
$461$		−	5.60770i		−	0.261176i	0.991437	−	0.130588i	$-0.0416866\pi$
$462$		0			0
$463$	−4.75833	+	4.75833i	−0.221138	+	0.221138i	−0.808978	−	0.587839i	$-0.799979\pi$
$463$	−4.75833	+	4.75833i	−0.221138	+	0.221138i	0.587839	+	0.808978i	$0.299979\pi$
$464$	−6.40192	+	3.69615i	−0.297202	+	0.171590i
$465$		0			0
$466$	−1.73205	+	3.00000i	−0.0802357	+	0.138972i
$467$	−13.5981	−	3.64359i	−0.629244	−	0.168605i	−0.0699173	−	0.997553i	$-0.522274\pi$
$467$	−13.5981	−	3.64359i	−0.629244	−	0.168605i	−0.559327	+	0.828947i	$0.688940\pi$
$468$		0			0
$469$	16.4282	+	24.2583i	0.758584	+	1.12015i
$470$	−9.46410	+	4.73205i	−0.436546	+	0.218273i
$471$		0			0
$472$	4.09808	+	15.2942i	0.188629	+	0.703974i
$473$	2.83013	+	10.5622i	0.130129	+	0.485649i
$474$		0			0
$475$	2.19615	−	2.92820i	0.100766	−	0.134355i
$476$	−17.6603	+	1.26795i	−0.809456	+	0.0581164i
$477$		0			0
$478$	−1.19615	−	0.320508i	−0.0547107	−	0.0146597i
$479$	6.53590	−	11.3205i	0.298633	−	0.517247i	−0.677191	−	0.735808i	$-0.736803\pi$
$479$	6.53590	−	11.3205i	0.298633	−	0.517247i	0.975823	+	0.218560i	$0.0701361\pi$
$480$		0			0
$481$	12.0000	−	6.92820i	0.547153	−	0.315899i
$482$	9.07180	−	9.07180i	0.413209	−	0.413209i
$483$		0			0
$484$			6.12436i			0.278380i
$485$	18.3660	−	3.75833i	0.833958	−	0.170657i
$486$		0			0
$487$	−27.2224	+	7.29423i	−1.23357	+	0.330533i	−0.815967	−	0.578098i	$-0.803795\pi$
$487$	−27.2224	+	7.29423i	−1.23357	+	0.330533i	−0.417599	+	0.908631i	$0.637128\pi$
$488$	0.767949	−	2.86603i	0.0347634	−	0.129739i
$489$		0			0
$490$	−1.43782	+	7.97372i	−0.0649542	+	0.360216i
$491$	−37.7128			−1.70196			−0.850978	−	0.525202i	$-0.823990\pi$
$491$	−37.7128			−1.70196			−0.850978	+	0.525202i	$0.823990\pi$
$492$		0			0
$493$	11.1962	−	3.00000i	0.504249	−	0.135113i
$494$	−0.928203	−	0.535898i	−0.0417618	−	0.0241112i
$495$		0			0
$496$		−	18.3923i		−	0.825839i
$497$	1.09808	+	3.16987i	0.0492554	+	0.142188i
$498$		0			0
$499$	9.97372	−	5.75833i	0.446485	−	0.257778i	−0.259860	−	0.965646i	$-0.583676\pi$
$499$	9.97372	−	5.75833i	0.446485	−	0.257778i	0.706345	+	0.707868i	$0.250343\pi$
$500$	−12.5263	+	14.7679i	−0.560192	+	0.660443i
$501$		0			0
$502$	10.9282	+	2.92820i	0.487750	+	0.130692i
$503$	−17.6340	−	17.6340i	−0.786260	−	0.786260i	0.194619	−	0.980879i	$-0.437653\pi$
$503$	−17.6340	−	17.6340i	−0.786260	−	0.786260i	−0.980879	+	0.194619i	$0.937653\pi$
$504$		0			0
$505$	−8.26795	−	16.5359i	−0.367919	−	0.735838i
$506$	0.0980762	+	0.169873i	0.00436002	+	0.00755178i
$507$		0			0
$508$	0.294229	+	1.09808i	0.0130543	+	0.0487193i
$509$	−19.4545	−	33.6962i	−0.862305	−	1.49356i	−0.869699	−	0.493583i	$-0.835687\pi$
$509$	−19.4545	−	33.6962i	−0.862305	−	1.49356i	0.00739389	−	0.999973i	$-0.497646\pi$
$510$		0			0
$511$	19.8564	+	29.3205i	0.878396	+	1.29706i
$512$	15.6865	+	15.6865i	0.693253	+	0.693253i
$513$		0			0
$514$	0.732051	−	1.26795i	0.0322894	−	0.0559268i
$515$	7.96410	−	7.06218i	0.350940	−	0.311197i
$516$		0			0
$517$	17.6603	−	17.6603i	0.776697	−	0.776697i
$518$	−1.26795	+	6.58846i	−0.0557105	+	0.289480i
$519$		0			0
$520$	10.1962	+	6.73205i	0.447131	+	0.295220i
$521$	20.6603	+	11.9282i	0.905142	+	0.522584i	0.878865	−	0.477071i	$-0.158301\pi$
$521$	20.6603	+	11.9282i	0.905142	+	0.522584i	0.0262772	+	0.999655i	$0.491635\pi$
$522$		0			0
$523$	−11.4904	+	42.8827i	−0.502439	+	1.87513i	−0.0188717	+	0.999822i	$0.506007\pi$
$523$	−11.4904	+	42.8827i	−0.502439	+	1.87513i	−0.483568	+	0.875307i	$0.660659\pi$
$524$	26.7846			1.17009
$525$		0			0
$526$	−8.12436			−0.354239
$527$	−7.46410	+	27.8564i	−0.325141	+	1.21344i
$528$		0			0
$529$	−19.9019	−	11.4904i	−0.865301	−	0.499582i
$530$	6.83013	+	4.50962i	0.296682	+	0.195885i
$531$		0			0
$532$	−3.16987	+	1.09808i	−0.137431	+	0.0476076i
$533$	12.9282	−	12.9282i	0.559983	−	0.559983i
$534$		0			0
$535$	21.9904	−	19.5000i	0.950727	−	0.843059i
$536$	−10.6962	+	18.5263i	−0.462003	+	0.800213i
$537$		0			0
$538$	−8.36603	−	8.36603i	−0.360685	−	0.360685i
$539$	−2.73205	−	18.9282i	−0.117678	−	0.815295i
$540$		0			0
$541$	−18.3564	−	31.7942i	−0.789204	−	1.36694i	−0.926455	−	0.376404i	$-0.877160\pi$
$541$	−18.3564	−	31.7942i	−0.789204	−	1.36694i	0.137252	−	0.990536i	$-0.456173\pi$
$542$	−2.84936	−	10.6340i	−0.122391	−	0.456768i
$543$		0			0
$544$	−9.92820	−	17.1962i	−0.425668	−	0.737279i
$545$	10.1244	+	20.2487i	0.433680	+	0.867359i
$546$		0			0
$547$	−16.7583	−	16.7583i	−0.716534	−	0.716534i	0.251359	−	0.967894i	$-0.419122\pi$
$547$	−16.7583	−	16.7583i	−0.716534	−	0.716534i	−0.967894	+	0.251359i	$0.919122\pi$
$548$	−22.8564	−	6.12436i	−0.976377	−	0.261620i
$549$		0			0
$550$	−2.63397	+	6.56218i	−0.112313	+	0.279812i
$551$	1.90192	−	1.09808i	0.0810247	−	0.0467796i
$552$		0			0
$553$	6.53590	+	5.66025i	0.277935	+	0.240698i
$554$		−	2.78461i		−	0.118307i
$555$		0			0
$556$	8.49038	+	4.90192i	0.360072	+	0.207888i
$557$	31.2224	−	8.36603i	1.32294	−	0.354480i	0.472860	−	0.881138i	$-0.343222\pi$
$557$	31.2224	−	8.36603i	1.32294	−	0.354480i	0.850077	+	0.526658i	$0.176555\pi$
$558$		0			0
$559$	11.3205			0.478806
$560$	14.0359	−	3.93782i	0.593125	−	0.166403i
$561$		0			0
$562$	0.124356	−	0.464102i	0.00524563	−	0.0195769i
$563$	23.7224	−	6.35641i	0.999781	−	0.267891i	0.278427	−	0.960457i	$-0.410187\pi$
$563$	23.7224	−	6.35641i	0.999781	−	0.267891i	0.721354	+	0.692567i	$0.243520\pi$
$564$		0			0
$565$	23.9545	−	4.90192i	1.00777	−	0.206225i
$566$			1.01924i			0.0428418i
$567$		0			0
$568$	−1.73205	+	1.73205i	−0.0726752	+	0.0726752i
$569$	−25.0526	+	14.4641i	−1.05026	+	0.606367i	−0.922722	−	0.385467i	$-0.874040\pi$
$569$	−25.0526	+	14.4641i	−1.05026	+	0.606367i	−0.127536	+	0.991834i	$0.540707\pi$
$570$		0			0
$571$	9.02628	−	15.6340i	0.377738	−	0.654261i	−0.612995	−	0.790087i	$-0.710035\pi$
$571$	9.02628	−	15.6340i	0.377738	−	0.654261i	0.990733	+	0.135826i	$0.0433687\pi$
$572$	−12.9282	−	3.46410i	−0.540555	−	0.144841i
$573$		0			0
$574$	0.633975	+	8.83013i	0.0264616	+	0.368562i
$575$	0.0980762	+	0.686533i	0.00409006	+	0.0286304i
$576$		0			0
$577$	1.50962	+	5.63397i	0.0628463	+	0.234545i	0.990204	−	0.139632i	$-0.0445919\pi$
$577$	1.50962	+	5.63397i	0.0628463	+	0.234545i	−0.927357	+	0.374177i	$0.877925\pi$
$578$	−0.277568	−	1.03590i	−0.0115453	−	0.0430877i
$579$		0			0
$580$	−10.3923	+	5.19615i	−0.431517	+	0.215758i
$581$	−3.42820	+	7.06218i	−0.142226	+	0.292989i
$582$		0			0
$583$	−18.6603	−	5.00000i	−0.772829	−	0.207079i
$584$	−12.9282	+	22.3923i	−0.534973	+	0.926600i
$585$		0			0
$586$	−1.51666	+	0.875644i	−0.0626527	+	0.0361725i
$587$	15.7846	−	15.7846i	0.651501	−	0.651501i	−0.301854	−	0.953354i	$-0.597605\pi$
$587$	15.7846	−	15.7846i	0.651501	−	0.651501i	0.953354	+	0.301854i	$0.0976054\pi$
$588$		0			0
$589$			5.46410i			0.225144i
$590$	1.90192	+	9.29423i	0.0783010	+	0.382637i
$591$		0			0
$592$	11.6603	−	3.12436i	0.479233	−	0.128410i
$593$	−5.56218	+	20.7583i	−0.228411	+	0.852442i	0.752598	+	0.658481i	$0.228801\pi$
$593$	−5.56218	+	20.7583i	−0.228411	+	0.852442i	−0.981009	+	0.193962i	$0.937866\pi$
$594$		0			0
$595$	−22.8564	+	0.267949i	−0.937021	+	0.0109848i
$596$	1.39230			0.0570310
$597$		0			0
$598$	0.196152	−	0.0525589i	0.00802127	−	0.00214929i
$599$	−15.3397	−	8.85641i	−0.626765	−	0.361863i	0.152733	−	0.988267i	$-0.451193\pi$
$599$	−15.3397	−	8.85641i	−0.626765	−	0.361863i	−0.779498	+	0.626405i	$0.784526\pi$
$600$		0			0
$601$			41.1769i			1.67964i	0.542864	+	0.839821i	$0.317340\pi$
$601$			41.1769i			1.67964i	−0.542864	+	0.839821i	$0.682660\pi$
$602$	−3.58846	+	4.14359i	−0.146255	+	0.168880i
$603$		0			0
$604$	−20.7846	+	12.0000i	−0.845714	+	0.488273i
$605$	−0.473721	+	7.89230i	−0.0192595	+	0.320868i
$606$		0			0
$607$	12.6962	+	3.40192i	0.515321	+	0.138080i	0.507101	−	0.861886i	$-0.330717\pi$
$607$	12.6962	+	3.40192i	0.515321	+	0.138080i	0.00821951	+	0.999966i	$0.497384\pi$
$608$	−2.66025	−	2.66025i	−0.107888	−	0.107888i
$609$		0			0
$610$	0.562178	−	1.68653i	0.0227619	−	0.0682857i
$611$	−12.9282	−	22.3923i	−0.523019	−	0.905896i
$612$		0			0
$613$	−6.53590	−	24.3923i	−0.263982	−	0.985196i	−0.962870	−	0.269965i	$-0.912988\pi$
$613$	−6.53590	−	24.3923i	−0.263982	−	0.985196i	0.698888	−	0.715231i	$-0.253679\pi$
$614$	2.30385	+	3.99038i	0.0929757	+	0.161039i
$615$		0			0
$616$	11.5622	−	7.83013i	0.465853	−	0.315485i
$617$	−33.9090	−	33.9090i	−1.36512	−	1.36512i	−0.867249	−	0.497874i	$-0.834114\pi$
$617$	−33.9090	−	33.9090i	−1.36512	−	1.36512i	−0.497874	−	0.867249i	$-0.665886\pi$
$618$		0			0
$619$	−5.09808	+	8.83013i	−0.204909	+	0.354913i	−0.950104	−	0.311934i	$-0.899023\pi$
$619$	−5.09808	+	8.83013i	−0.204909	+	0.354913i	0.745195	+	0.666847i	$0.232357\pi$
$620$	1.73205	−	28.8564i	0.0695608	−	1.15890i
$621$		0			0
$622$	5.58846	−	5.58846i	0.224077	−	0.224077i
$623$	−1.14359	+	1.32051i	−0.0458171	+	0.0529050i
$624$		0			0
$625$	−17.2846	+	18.0622i	−0.691384	+	0.722487i
$626$	2.41154	+	1.39230i	0.0963846	+	0.0556477i
$627$		0			0
$628$	2.15064	−	8.02628i	0.0858197	−	0.320283i
$629$	−18.9282			−0.754717
$630$		0			0
$631$	−4.58846			−0.182664			−0.0913318	−	0.995821i	$-0.529112\pi$
$631$	−4.58846			−0.182664			−0.0913318	+	0.995821i	$0.529112\pi$
$632$	−1.63397	+	6.09808i	−0.0649960	+	0.242568i
$633$		0			0
$634$	−4.26795	−	2.46410i	−0.169502	−	0.0978620i
$635$	0.294229	+	1.43782i	0.0116761	+	0.0570582i
$636$		0			0
$637$	−19.6603	−	2.33975i	−0.778968	−	0.0927041i
$638$	−3.00000	+	3.00000i	−0.118771	+	0.118771i
$639$		0			0
$640$	16.9904	+	19.1603i	0.671604	+	0.757376i
$641$	5.33013	−	9.23205i	0.210527	−	0.364644i	−0.741352	−	0.671116i	$-0.765815\pi$
$641$	5.33013	−	9.23205i	0.210527	−	0.364644i	0.951880	+	0.306472i	$0.0991486\pi$
$642$		0			0
$643$	−17.5359	−	17.5359i	−0.691548	−	0.691548i	0.271024	−	0.962573i	$-0.412638\pi$
$643$	−17.5359	−	17.5359i	−0.691548	−	0.691548i	−0.962573	+	0.271024i	$0.912638\pi$
$644$	0.277568	−	0.571797i	0.0109377	−	0.0225319i
$645$		0			0
$646$	0.732051	+	1.26795i	0.0288022	+	0.0498868i
$647$	−10.5981	−	39.5526i	−0.416653	−	1.55497i	−0.781501	−	0.623904i	$-0.785546\pi$
$647$	−10.5981	−	39.5526i	−0.416653	−	1.55497i	0.364847	−	0.931067i	$-0.381121\pi$
$648$		0			0
$649$	−11.1962	−	19.3923i	−0.439487	−	0.761215i
$650$	5.85641	+	4.39230i	0.229707	+	0.172280i
$651$		0			0
$652$	17.1962	+	17.1962i	0.673453	+	0.673453i
$653$	−19.6603	−	5.26795i	−0.769365	−	0.206151i	−0.147274	−	0.989096i	$-0.547050\pi$
$653$	−19.6603	−	5.26795i	−0.769365	−	0.206151i	−0.622091	+	0.782945i	$0.713717\pi$
$654$		0			0
$655$	34.5167	+	2.07180i	1.34868	+	0.0809518i
$656$	13.7942	−	7.96410i	0.538574	−	0.310946i
$657$		0			0
$658$	12.2942	+	2.36603i	0.479279	+	0.0922373i
$659$			27.6603i			1.07749i	0.842469	+	0.538745i	$0.181101\pi$
$659$			27.6603i			1.07749i	−0.842469	+	0.538745i	$0.818899\pi$
$660$		0			0
$661$	−41.7224	−	24.0885i	−1.62281	−	0.936932i	−0.986163	−	0.165781i	$-0.946985\pi$
$661$	−41.7224	−	24.0885i	−1.62281	−	0.936932i	−0.636652	−	0.771151i	$-0.719681\pi$
$662$	0.928203	−	0.248711i	0.0360756	−	0.00966644i
$663$		0			0
$664$	−5.73205			−0.222447
$665$	−4.16987	+	1.16987i	−0.161701	+	0.0453657i
$666$		0			0
$667$	−0.107695	+	0.401924i	−0.00416997	+	0.0155626i
$668$	27.8205	−	7.45448i	1.07641	−	0.288423i
$669$		0			0
$670$	−7.06218	+	10.6962i	−0.272836	+	0.413228i
$671$			4.19615i			0.161991i
$672$		0			0
$673$	4.39230	−	4.39230i	0.169311	−	0.169311i	−0.617366	−	0.786676i	$-0.711800\pi$
$673$	4.39230	−	4.39230i	0.169311	−	0.169311i	0.786676	+	0.617366i	$0.211800\pi$
$674$	6.04552	−	3.49038i	0.232865	−	0.134444i
$675$		0			0
$676$	4.33013	−	7.50000i	0.166543	−	0.288462i
$677$	25.8564	+	6.92820i	0.993742	+	0.266272i	0.718822	−	0.695194i	$-0.244682\pi$
$677$	25.8564	+	6.92820i	0.993742	+	0.266272i	0.274921	+	0.961467i	$0.411348\pi$
$678$		0			0
$679$	−19.9545	−	9.68653i	−0.765783	−	0.371735i
$680$	−7.46410	−	14.9282i	−0.286235	−	0.572470i
$681$		0			0
$682$	−2.73205	−	10.1962i	−0.104616	−	0.390431i
$683$	4.57180	+	17.0622i	0.174935	+	0.652866i	0.996563	+	0.0828417i	$0.0263996\pi$
$683$	4.57180	+	17.0622i	0.174935	+	0.652866i	−0.821628	+	0.570024i	$0.806934\pi$
$684$		0			0
$685$	−28.9808	−	9.66025i	−1.10730	−	0.369099i
$686$	7.08846	−	6.45448i	0.270639	−	0.246433i
$687$		0			0
$688$	9.52628	+	2.55256i	0.363186	+	0.0973154i
$689$	−10.0000	+	17.3205i	−0.380970	+	0.659859i
$690$		0			0
$691$	−44.0263	+	25.4186i	−1.67484	+	0.966969i	−0.709971	+	0.704231i	$0.751292\pi$
$691$	−44.0263	+	25.4186i	−1.67484	+	0.966969i	−0.964867	+	0.262738i	$0.915375\pi$
$692$	−25.2679	+	25.2679i	−0.960543	+	0.960543i
$693$		0			0
$694$			15.5885i			0.591730i
$695$	10.5622	+	6.97372i	0.400646	+	0.264528i
$696$		0			0
$697$	−24.1244	+	6.46410i	−0.913775	+	0.244845i
$698$	−0.839746	+	3.13397i	−0.0317849	+	0.118623i
$699$		0			0
$700$	22.3923	−	4.85641i	0.846350	−	0.183555i
$701$	20.2679			0.765510			0.382755	−	0.923850i	$-0.374975\pi$
$701$	20.2679			0.765510			0.382755	+	0.923850i	$0.374975\pi$
$702$		0			0
$703$	−3.46410	+	0.928203i	−0.130651	+	0.0350078i
$704$	−5.36603	−	3.09808i	−0.202240	−	0.116763i
$705$		0			0
$706$			7.26795i			0.273533i
$707$	−4.13397	+	21.4808i	−0.155474	+	0.807867i
$708$		0			0
$709$	−18.9904	+	10.9641i	−0.713199	+	0.411765i	−0.812244	−	0.583317i	$-0.801754\pi$
$709$	−18.9904	+	10.9641i	−0.713199	+	0.411765i	0.0990456	+	0.995083i	$0.468421\pi$
$710$	−1.09808	+	0.973721i	−0.0412101	+	0.0365431i
$711$		0			0
$712$	−1.23205	−	0.330127i	−0.0461731	−	0.0123720i
$713$	−0.732051	−	0.732051i	−0.0274155	−	0.0274155i
$714$		0			0
$715$	−16.3923	−	5.46410i	−0.613037	−	0.204346i
$716$	6.80385	+	11.7846i	0.254272	+	0.440412i
$717$		0			0
$718$	−4.58846	−	17.1244i	−0.171240	−	0.639075i
$719$	19.2942	+	33.4186i	0.719553	+	1.24630i	0.961177	+	0.275933i	$0.0889867\pi$
$719$	19.2942	+	33.4186i	0.719553	+	1.24630i	−0.241624	+	0.970370i	$0.577680\pi$
$720$		0			0
$721$	−12.5622	+	0.901924i	−0.467840	+	0.0335894i
$722$	−6.75833	−	6.75833i	−0.251519	−	0.251519i
$723$		0			0
$724$	−1.03590	+	1.79423i	−0.0384989	+	0.0666820i
$725$	−13.7942	+	5.89230i	−0.512305	+	0.218835i
$726$		0			0
$727$	10.0981	−	10.0981i	0.374517	−	0.374517i	−0.494602	−	0.869119i	$-0.664686\pi$
$727$	10.0981	−	10.0981i	0.374517	−	0.374517i	0.869119	+	0.494602i	$0.164686\pi$
$728$	−4.73205	−	13.6603i	−0.175381	−	0.506283i
$729$		0			0
$730$	−8.53590	+	12.9282i	−0.315928	+	0.478494i
$731$	−13.3923	−	7.73205i	−0.495332	−	0.285980i
$732$		0			0
$733$	−1.16987	+	4.36603i	−0.0432102	+	0.161263i	−0.984160	−	0.177284i	$-0.943269\pi$
$733$	−1.16987	+	4.36603i	−0.0432102	+	0.161263i	0.940949	+	0.338547i	$0.109935\pi$
$734$	0.267949			0.00989019
$735$		0			0
$736$	0.712813			0.0262746
$737$	7.83013	−	29.2224i	0.288426	−	1.07642i
$738$		0			0
$739$	19.5622	+	11.2942i	0.719606	+	0.415465i	0.814608	−	0.580012i	$-0.196952\pi$
$739$	19.5622	+	11.2942i	0.719606	+	0.415465i	−0.0950014	+	0.995477i	$0.530286\pi$
$740$	18.5885	−	3.80385i	0.683325	−	0.139832i
$741$		0			0
$742$	−3.16987	−	9.15064i	−0.116370	−	0.335930i
$743$	6.16987	−	6.16987i	0.226351	−	0.226351i	−0.584816	−	0.811166i	$-0.698833\pi$
$743$	6.16987	−	6.16987i	0.226351	−	0.226351i	0.811166	+	0.584816i	$0.198833\pi$
$744$		0			0
$745$	1.79423	+	0.107695i	0.0657355	+	0.00394565i
$746$	−2.07180	+	3.58846i	−0.0758539	+	0.131383i
$747$		0			0
$748$	12.9282	+	12.9282i	0.472702	+	0.472702i
$749$	−34.6865	+	2.49038i	−1.26742	+	0.0909965i
$750$		0			0
$751$	3.19615	+	5.53590i	0.116629	+	0.202008i	0.918430	−	0.395584i	$-0.129458\pi$
$751$	3.19615	+	5.53590i	0.116629	+	0.202008i	−0.801801	+	0.597592i	$0.796124\pi$
$752$	−5.83013	−	21.7583i	−0.212603	−	0.793445i
$753$		0			0
$754$	2.19615	+	3.80385i	0.0799792	+	0.138528i
$755$	−27.7128	+	13.8564i	−1.00857	+	0.504286i
$756$		0			0
$757$	12.7321	+	12.7321i	0.462754	+	0.462754i	0.899557	−	0.436803i	$-0.143889\pi$
$757$	12.7321	+	12.7321i	0.462754	+	0.462754i	−0.436803	+	0.899557i	$0.643889\pi$
$758$	1.16987	+	0.313467i	0.0424917	+	0.0113856i
$759$		0			0
$760$	−2.09808	−	2.36603i	−0.0761052	−	0.0858248i
$761$	−24.9282	+	14.3923i	−0.903647	+	0.521721i	−0.878382	−	0.477960i	$-0.841376\pi$
$761$	−24.9282	+	14.3923i	−0.903647	+	0.521721i	−0.0252651	+	0.999681i	$0.508043\pi$
$762$		0			0
$763$	5.06218	−	26.3038i	0.183263	−	0.952263i
$764$			22.9808i			0.831415i
$765$		0			0
$766$	14.1795	+	8.18653i	0.512326	+	0.295791i
$767$	−22.3923	+	6.00000i	−0.808539	+	0.216647i
$768$		0			0
$769$	−15.1769			−0.547294			−0.273647	−	0.961830i	$-0.588230\pi$
$769$	−15.1769			−0.547294			−0.273647	+	0.961830i	$0.588230\pi$
$770$	7.19615	−	4.26795i	0.259331	−	0.153806i
$771$		0			0
$772$	−3.63397	+	13.5622i	−0.130790	+	0.488113i
$773$	−15.1962	+	4.07180i	−0.546568	+	0.146452i	−0.521528	−	0.853234i	$-0.674638\pi$
$773$	−15.1962	+	4.07180i	−0.546568	+	0.146452i	−0.0250395	+	0.999686i	$0.507971\pi$
$774$		0			0
$775$	4.46410	−	37.0526i	0.160355	−	1.33097i
$776$		−	16.1962i		−	0.581408i
$777$		0			0
$778$	−1.80385	+	1.80385i	−0.0646711	+	0.0646711i
$779$	−4.09808	+	2.36603i	−0.146829	+	0.0847717i
$780$		0			0
$781$	1.73205	−	3.00000i	0.0619777	−	0.107348i
$782$	−0.267949	−	0.0717968i	−0.00958184	−	0.00256745i
$783$		0			0
$784$	−16.0167	−	6.40192i	−0.572024	−	0.228640i
$785$	3.39230	−	10.1769i	0.121077	−	0.363230i
$786$		0			0
$787$	8.35641	+	31.1865i	0.297874	+	1.11168i	0.938908	+	0.344168i	$0.111839\pi$
$787$	8.35641	+	31.1865i	0.297874	+	1.11168i	−0.641034	+	0.767512i	$0.721494\pi$
$788$	6.41858	+	23.9545i	0.228653	+	0.853343i
$789$		0			0
$790$	−1.19615	+	3.58846i	−0.0425572	+	0.127672i
$791$	−26.0263	−	12.6340i	−0.925388	−	0.449212i
$792$		0			0
$793$	4.19615	+	1.12436i	0.149010	+	0.0399270i
$794$	−0.973721	+	1.68653i	−0.0345560	+	0.0598528i
$795$		0			0
$796$	16.6077	−	9.58846i	0.588644	−	0.339854i
$797$	22.5359	−	22.5359i	0.798262	−	0.798262i	−0.184559	−	0.982821i	$-0.559086\pi$
$797$	22.5359	−	22.5359i	0.798262	−	0.798262i	0.982821	+	0.184559i	$0.0590857\pi$
$798$		0			0
$799$			35.3205i			1.24955i
$800$	15.8660	+	20.2128i	0.560949	+	0.714631i
$801$		0			0
$802$	5.50000	−	1.47372i	0.194212	−	0.0520389i
$803$	9.46410	−	35.3205i	0.333981	−	1.24643i
$804$		0			0
$805$	0.401924	−	0.715390i	0.0141660	−	0.0252142i
$806$	−10.9282			−0.384930
$807$		0			0
$808$	−15.4282	+	4.13397i	−0.542762	+	0.145433i
$809$	−3.99038	−	2.30385i	−0.140294	−	0.0809990i	0.428210	−	0.903679i	$-0.359144\pi$
$809$	−3.99038	−	2.30385i	−0.140294	−	0.0809990i	−0.568504	+	0.822680i	$0.692478\pi$
$810$		0			0
$811$		−	42.9282i		−	1.50741i	−0.657211	−	0.753707i	$-0.728264\pi$
$811$		−	42.9282i		−	1.50741i	0.657211	−	0.753707i	$-0.271736\pi$
$812$	13.5000	+	2.59808i	0.473757	+	0.0911746i
$813$		0			0
$814$	6.00000	−	3.46410i	0.210300	−	0.121417i
$815$	20.8301	+	23.4904i	0.729648	+	0.822832i
$816$		0			0
$817$	−2.83013	−	0.758330i	−0.0990136	−	0.0265306i
$818$	−7.63397	−	7.63397i	−0.266916	−	0.266916i
$819$		0			0
$820$	22.3923	−	11.1962i	0.781973	−	0.390987i
$821$	−24.6603	−	42.7128i	−0.860649	−	1.49069i	−0.871304	−	0.490744i	$-0.836725\pi$
$821$	−24.6603	−	42.7128i	−0.860649	−	1.49069i	0.0106549	−	0.999943i	$-0.496608\pi$
$822$		0			0
$823$	14.3038	+	53.3827i	0.498601	+	1.86080i	0.508849	+	0.860856i	$0.330071\pi$
$823$	14.3038	+	53.3827i	0.498601	+	1.86080i	−0.0102479	+	0.999947i	$0.503262\pi$
$824$	−4.59808	−	7.96410i	−0.160182	−	0.277443i
$825$		0			0
$826$	4.90192	−	10.0981i	0.170560	−	0.351357i
$827$	33.2224	+	33.2224i	1.15526	+	1.15526i	0.985483	+	0.169774i	$0.0543038\pi$
$827$	33.2224	+	33.2224i	1.15526	+	1.15526i	0.169774	+	0.985483i	$0.445696\pi$
$828$		0			0
$829$	7.26795	−	12.5885i	0.252426	−	0.437215i	−0.711767	−	0.702416i	$-0.752105\pi$
$829$	7.26795	−	12.5885i	0.252426	−	0.437215i	0.964193	+	0.265200i	$0.0854381\pi$
$830$	−3.42820	−	0.205771i	−0.118995	−	0.00714243i
$831$		0			0
$832$	−4.53590	+	4.53590i	−0.157254	+	0.157254i
$833$	21.6603	+	16.1962i	0.750483	+	0.561163i
$834$		0			0
$835$	36.4282	−	7.45448i	1.26065	−	0.257973i
$836$	3.00000	+	1.73205i	0.103757	+	0.0599042i
$837$		0			0
$838$	3.19615	−	11.9282i	0.110409	−	0.412053i
$839$	6.87564			0.237374			0.118687	−	0.992932i	$-0.462132\pi$
$839$	6.87564			0.237374			0.118687	+	0.992932i	$0.462132\pi$
$840$		0			0
$841$	20.0000			0.689655
$842$	−2.32309	+	8.66987i	−0.0800588	+	0.298784i
$843$		0			0
$844$	−0.294229	−	0.169873i	−0.0101278	−	0.00584727i
$845$	6.16025	−	9.33013i	0.211919	−	0.320966i
$846$		0			0
$847$	6.12436	−	7.07180i	0.210435	−	0.242990i
$848$	−12.3205	+	12.3205i	−0.423088	+	0.423088i
$849$		0			0
$850$	−3.92820	−	9.19615i	−0.134736	−	0.315425i
$851$	0.339746	−	0.588457i	0.0116463	−	0.0201721i
$852$		0			0
$853$	18.1244	+	18.1244i	0.620566	+	0.620566i	0.945676	−	0.325110i	$-0.105401\pi$
$853$	18.1244	+	18.1244i	0.620566	+	0.620566i	−0.325110	+	0.945676i	$0.605401\pi$
$854$	−1.74167	+	1.17949i	−0.0595987	+	0.0403614i
$855$		0			0
$856$	−12.6962	−	21.9904i	−0.433946	−	0.751616i
$857$	2.97372	+	11.0981i	0.101580	+	0.379103i	0.997935	−	0.0642351i	$-0.0204608\pi$
$857$	2.97372	+	11.0981i	0.101580	+	0.379103i	−0.896354	+	0.443338i	$0.853794\pi$
$858$		0			0
$859$	17.4641	+	30.2487i	0.595867	+	1.03207i	0.993424	+	0.114495i	$0.0365250\pi$
$859$	17.4641	+	30.2487i	0.595867	+	1.03207i	−0.397556	+	0.917578i	$0.630142\pi$
$860$	14.7058	+	4.90192i	0.501463	+	0.167154i
$861$		0			0
$862$	−2.26795	−	2.26795i	−0.0772467	−	0.0772467i
$863$	49.9449	+	13.3827i	1.70014	+	0.455552i	0.972976	−	0.230908i	$-0.0741697\pi$
$863$	49.9449	+	13.3827i	1.70014	+	0.455552i	0.727167	+	0.686460i	$0.240836\pi$
$864$		0			0
$865$	−34.5167	+	30.6077i	−1.17360	+	1.04069i
$866$	11.1173	−	6.41858i	0.377782	−	0.218112i
$867$		0			0
$868$	−22.3923	+	25.8564i	−0.760044	+	0.877624i
$869$		−	8.92820i		−	0.302869i
$870$		0			0
$871$	−27.1244	−	15.6603i	−0.919074	−	0.530627i
$872$	18.8923	−	5.06218i	0.639774	−	0.171427i
$873$		0			0
$874$	−0.0525589			−0.00177783
$875$	29.2321	−	4.52628i	0.988224	−	0.153016i
$876$		0			0
$877$	10.4904	−	39.1506i	0.354235	−	1.32202i	−0.527209	−	0.849735i	$-0.676762\pi$
$877$	10.4904	−	39.1506i	0.354235	−	1.32202i	0.881444	−	0.472288i	$-0.156572\pi$
$878$	−1.66025	+	0.444864i	−0.0560309	+	0.0150134i
$879$		0			0
$880$	−12.5622	−	8.29423i	−0.423471	−	0.279598i
$881$			25.1436i			0.847109i	0.905871	+	0.423555i	$0.139218\pi$
$881$			25.1436i			0.847109i	−0.905871	+	0.423555i	$0.860782\pi$
$882$		0			0
$883$	8.07180	−	8.07180i	0.271638	−	0.271638i	−0.558122	−	0.829759i	$-0.688478\pi$
$883$	8.07180	−	8.07180i	0.271638	−	0.271638i	0.829759	+	0.558122i	$0.188478\pi$
$884$	16.3923	−	9.46410i	0.551333	−	0.318312i
$885$		0			0
$886$	−3.50000	+	6.06218i	−0.117585	+	0.203663i
$887$	−10.8923	−	2.91858i	−0.365728	−	0.0979965i	0.0712748	−	0.997457i	$-0.477293\pi$
$887$	−10.8923	−	2.91858i	−0.365728	−	0.0979965i	−0.437003	+	0.899460i	$0.643960\pi$
$888$		0			0
$889$	0.758330	−	1.56218i	0.0254336	−	0.0523938i
$890$	−0.725009	−	0.241670i	−0.0243024	−	0.00810079i
$891$		0			0
$892$	−11.4904	−	42.8827i	−0.384726	−	1.43582i
$893$	1.73205	+	6.46410i	0.0579609	+	0.216313i
$894$		0			0
$895$	7.85641	+	15.7128i	0.262611	+	0.525221i
$896$	−2.16987	−	30.2224i	−0.0724904	−	1.00966i
$897$		0			0
$898$	16.5263	+	4.42820i	0.551489	+	0.147771i
$899$	11.1962	−	19.3923i	0.373413	−	0.646770i
$900$		0			0
$901$	23.6603	−	13.6603i	0.788237	−	0.455089i
$902$	6.46410	−	6.46410i	0.215231	−	0.215231i
$903$		0			0
$904$		−	21.1244i		−	0.702586i
$905$	−1.47372	+	2.23205i	−0.0489881	+	0.0741959i
$906$		0			0
$907$	32.4545	−	8.69615i	1.07763	−	0.288751i	0.324007	−	0.946055i	$-0.394970\pi$
$907$	32.4545	−	8.69615i	1.07763	−	0.288751i	0.753626	+	0.657304i	$0.228303\pi$
$908$	−8.83013	+	32.9545i	−0.293038	+	1.09363i
$909$		0			0
$910$	−2.33975	−	8.33975i	−0.0775618	−	0.276460i
$911$	7.51666			0.249038			0.124519	−	0.992217i	$-0.460261\pi$
$911$	7.51666			0.249038			0.124519	+	0.992217i	$0.460261\pi$
$912$		0			0
$913$	7.83013	−	2.09808i	0.259139	−	0.0694362i
$914$	−5.44486	−	3.14359i	−0.180100	−	0.103981i
$915$		0			0
$916$			31.8564i			1.05257i
$917$	−30.9282	−	26.7846i	−1.02134	−	0.884506i
$918$		0			0
$919$	48.6673	−	28.0981i	1.60539	−	0.926870i	0.615002	−	0.788526i	$-0.289155\pi$
$919$	48.6673	−	28.0981i	1.60539	−	0.926870i	0.990384	−	0.138344i	$-0.0441780\pi$
$920$	0.598076	+	0.0358984i	0.0197180	+	0.00118353i
$921$		0			0
$922$	−2.80385	−	0.751289i	−0.0923398	−	0.0247424i
$923$	−2.53590	−	2.53590i	−0.0834701	−	0.0834701i
$924$		0			0
$925$	24.2487	−	3.46410i	0.797293	−	0.113899i
$926$	1.74167	+	3.01666i	0.0572348	+	0.0991336i
$927$		0			0
$928$	3.99038	+	14.8923i	0.130991	+	0.488864i
$929$	−18.1603	−	31.4545i	−0.595819	−	1.03199i	−0.993431	−	0.114435i	$-0.963494\pi$
$929$	−18.1603	−	31.4545i	−0.595819	−	1.03199i	0.397612	−	0.917554i	$-0.369839\pi$
$930$		0			0
$931$	4.75833	+	1.90192i	0.155948	+	0.0623330i
$932$	−8.19615	−	8.19615i	−0.268474	−	0.268474i
$933$		0			0
$934$	−3.64359	+	6.31089i	−0.119222	+	0.206499i
$935$	15.6603	+	17.6603i	0.512145	+	0.577552i
$936$		0			0
$937$	−17.0718	+	17.0718i	−0.557711	+	0.557711i	−0.928655	−	0.370944i	$-0.879034\pi$
$937$	−17.0718	+	17.0718i	−0.557711	+	0.557711i	0.370944	+	0.928655i	$0.379034\pi$
$938$	14.3301	−	4.96410i	0.467895	−	0.162084i
$939$		0			0
$940$	−7.09808	−	34.6865i	−0.231514	−	1.13135i
$941$	−35.1962	−	20.3205i	−1.14736	−	0.662430i	−0.199119	−	0.979975i	$-0.563808\pi$
$941$	−35.1962	−	20.3205i	−1.14736	−	0.662430i	−0.948243	+	0.317546i	$0.897141\pi$
$942$		0			0
$943$	0.232051	−	0.866025i	0.00755661	−	0.0282017i
$944$	−20.1962			−0.657329
$945$		0			0
$946$	5.66025			0.184031
$947$	−0.349365	+	1.30385i	−0.0113528	+	0.0423694i	−0.971370	−	0.237572i	$-0.923648\pi$
$947$	−0.349365	+	1.30385i	−0.0113528	+	0.0423694i	0.960017	+	0.279941i	$0.0903151\pi$
$948$		0			0
$949$	−32.7846	−	18.9282i	−1.06423	−	0.614435i
$950$	−1.16987	−	1.49038i	−0.0379557	−	0.0483543i
$951$		0			0
$952$	−3.73205	+	19.3923i	−0.120956	+	0.628508i
$953$	37.8564	−	37.8564i	1.22629	−	1.22629i	0.260932	−	0.965357i	$-0.415970\pi$
$953$	37.8564	−	37.8564i	1.22629	−	1.22629i	0.965357	−	0.260932i	$-0.0840299\pi$
$954$		0			0
$955$	−1.77757	+	29.6147i	−0.0575208	+	0.958310i
$956$	2.07180	−	3.58846i	0.0670067	−	0.116059i
$957$		0			0
$958$	−4.78461	−	4.78461i	−0.154584	−	0.154584i
$959$	20.2679	+	29.9282i	0.654486	+	0.966432i
$960$		0			0
$961$	12.3564	+	21.4019i	0.398594	+	0.690385i
$962$	−1.85641	−	6.92820i	−0.0598529	−	0.223374i
$963$		0			0
$964$	21.4641	+	37.1769i	0.691312	+	1.19739i
$965$	−5.73205	+	17.1962i	−0.184521	+	0.553564i
$966$		0			0
$967$	−13.5622	−	13.5622i	−0.436130	−	0.436130i	0.454577	−	0.890707i	$-0.349790\pi$
$967$	−13.5622	−	13.5622i	−0.436130	−	0.436130i	−0.890707	+	0.454577i	$0.849790\pi$
$968$	6.59808	+	1.76795i	0.212070	+	0.0568240i
$969$		0			0
$970$	0.581416	−	9.68653i	0.0186681	−	0.311016i
$971$	−29.0718	+	16.7846i	−0.932958	+	0.538644i	−0.887746	−	0.460334i	$-0.847730\pi$
$971$	−29.0718	+	16.7846i	−0.932958	+	0.538644i	−0.0452124	+	0.998977i	$0.514396\pi$
$972$		0			0
$973$	−4.90192	−	14.1506i	−0.157148	−	0.453649i
$974$			14.5885i			0.467444i
$975$		0			0
$976$	3.27757	+	1.89230i	0.104912	+	0.0605712i
$977$	−0.562178	+	0.150635i	−0.0179857	+	0.00481924i	−0.267801	−	0.963474i	$-0.586297\pi$
$977$	−0.562178	+	0.150635i	−0.0179857	+	0.00481924i	0.249815	+	0.968294i	$0.419630\pi$
$978$		0			0
$979$	1.80385			0.0576512
$980$	−24.5263	−	11.5526i	−0.783463	−	0.369033i
$981$		0			0
$982$	−5.05256	+	18.8564i	−0.161234	+	0.601732i
$983$	−54.1147	+	14.5000i	−1.72599	+	0.462478i	−0.979253	−	0.202639i	$-0.935048\pi$
$983$	−54.1147	+	14.5000i	−1.72599	+	0.462478i	−0.746739	+	0.665118i	$0.768381\pi$
$984$		0			0
$985$	6.41858	+	31.3660i	0.204513	+	0.999405i
$986$		−	6.00000i		−	0.191079i
$987$		0			0
$988$	2.53590	−	2.53590i	0.0806777	−	0.0806777i
$989$	0.480762	−	0.277568i	0.0152873	−	0.00882615i
$990$		0			0
$991$	−15.8564	+	27.4641i	−0.503695	+	0.872426i	0.496296	+	0.868154i	$0.334693\pi$
$991$	−15.8564	+	27.4641i	−0.503695	+	0.872426i	−0.999991	+	0.00427229i	$0.998640\pi$
$992$	−37.0526	−	9.92820i	−1.17642	−	0.315221i
$993$		0			0
$994$	1.73205	−	0.124356i	0.0549373	−	0.00394432i
$995$	22.1436	−	11.0718i	0.701999	−	0.351000i
$996$		0			0
$997$	−10.6865	−	39.8827i	−0.338446	−	1.26310i	−0.900085	−	0.435715i	$-0.856496\pi$
$997$	−10.6865	−	39.8827i	−0.338446	−	1.26310i	0.561639	−	0.827382i	$-0.310171\pi$
$998$	−1.54294	−	5.75833i	−0.0488409	−	0.182277i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bz.b.262.1		4
3.2	odd	2		35.2.k.a.17.1	✓	4
5.3	odd	4		315.2.bz.a.73.1		4
7.5	odd	6		315.2.bz.a.82.1		4
12.11	even	2		560.2.ci.a.17.1		4
15.2	even	4		175.2.o.a.143.1		4
15.8	even	4		35.2.k.b.3.1	yes	4
15.14	odd	2		175.2.o.b.157.1		4
21.2	odd	6		245.2.l.b.117.1		4
21.5	even	6		35.2.k.b.12.1	yes	4
21.11	odd	6		245.2.f.a.97.1		4
21.17	even	6		245.2.f.b.97.1		4
21.20	even	2		245.2.l.a.227.1		4
35.33	even	12	inner	315.2.bz.b.208.1		4
60.23	odd	4		560.2.ci.b.353.1		4
84.47	odd	6		560.2.ci.b.257.1		4
105.23	even	12		245.2.l.a.68.1		4
105.38	odd	12		245.2.f.a.48.1		4
105.47	odd	12		175.2.o.b.68.1		4
105.53	even	12		245.2.f.b.48.1		4
105.68	odd	12		35.2.k.a.33.1	yes	4
105.83	odd	4		245.2.l.b.178.1		4
105.89	even	6		175.2.o.a.82.1		4
420.383	even	12		560.2.ci.a.33.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.k.a.17.1	✓	4	3.2	odd	2
35.2.k.a.33.1	yes	4	105.68	odd	12
35.2.k.b.3.1	yes	4	15.8	even	4
35.2.k.b.12.1	yes	4	21.5	even	6
175.2.o.a.82.1		4	105.89	even	6
175.2.o.a.143.1		4	15.2	even	4
175.2.o.b.68.1		4	105.47	odd	12
175.2.o.b.157.1		4	15.14	odd	2
245.2.f.a.48.1		4	105.38	odd	12
245.2.f.a.97.1		4	21.11	odd	6
245.2.f.b.48.1		4	105.53	even	12
245.2.f.b.97.1		4	21.17	even	6
245.2.l.a.68.1		4	105.23	even	12
245.2.l.a.227.1		4	21.20	even	2
245.2.l.b.117.1		4	21.2	odd	6
245.2.l.b.178.1		4	105.83	odd	4
315.2.bz.a.73.1		4	5.3	odd	4
315.2.bz.a.82.1		4	7.5	odd	6
315.2.bz.b.208.1		4	35.33	even	12	inner
315.2.bz.b.262.1		4	1.1	even	1	trivial
560.2.ci.a.17.1		4	12.11	even	2
560.2.ci.a.33.1		4	420.383	even	12
560.2.ci.b.257.1		4	84.47	odd	6
560.2.ci.b.353.1		4	60.23	odd	4

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.133975 - 0.500000i) q^{2} +(1.50000 + 0.866025i) q^{4} +(1.86603 + 1.23205i) q^{5} +(-0.866025 - 2.50000i) q^{7} +(1.36603 - 1.36603i) q^{8} +O(q^{10})\)	\(q+(0.133975 - 0.500000i) q^{2} +(1.50000 + 0.866025i) q^{4} +(1.86603 + 1.23205i) q^{5} +(-0.866025 - 2.50000i) q^{7} +(1.36603 - 1.36603i) q^{8} +(0.866025 - 0.767949i) q^{10} +(-1.36603 + 2.36603i) q^{11} +(2.00000 + 2.00000i) q^{13} +(-1.36603 + 0.0980762i) q^{14} +(1.23205 + 2.13397i) q^{16} +(-1.00000 - 3.73205i) q^{17} +(-0.366025 - 0.633975i) q^{19} +(1.73205 + 3.46410i) q^{20} +(1.00000 + 1.00000i) q^{22} +(0.133975 + 0.0358984i) q^{23} +(1.96410 + 4.59808i) q^{25} +(1.26795 - 0.732051i) q^{26} +(0.866025 - 4.50000i) q^{28} +3.00000i q^{29} +(-6.46410 - 3.73205i) q^{31} +(4.96410 - 1.33013i) q^{32} -2.00000 q^{34} +(1.46410 - 5.73205i) q^{35} +(1.26795 - 4.73205i) q^{37} +(-0.366025 + 0.0980762i) q^{38} +(4.23205 - 0.866025i) q^{40} -6.46410i q^{41} +(2.83013 - 2.83013i) q^{43} +(-4.09808 + 2.36603i) q^{44} +(0.0358984 - 0.0621778i) q^{46} +(-8.83013 - 2.36603i) q^{47} +(-5.50000 + 4.33013i) q^{49} +(2.56218 - 0.366025i) q^{50} +(1.26795 + 4.73205i) q^{52} +(1.83013 + 6.83013i) q^{53} +(-5.46410 + 2.73205i) q^{55} +(-4.59808 - 2.23205i) q^{56} +(1.50000 + 0.401924i) q^{58} +(-4.09808 + 7.09808i) q^{59} +(1.33013 - 0.767949i) q^{61} +(-2.73205 + 2.73205i) q^{62} +2.26795i q^{64} +(1.26795 + 6.19615i) q^{65} +(-10.6962 + 2.86603i) q^{67} +(1.73205 - 6.46410i) q^{68} +(-2.66987 - 1.50000i) q^{70} -1.26795 q^{71} +(-12.9282 + 3.46410i) q^{73} +(-2.19615 - 1.26795i) q^{74} -1.26795i q^{76} +(7.09808 + 1.36603i) q^{77} +(-2.83013 + 1.63397i) q^{79} +(-0.330127 + 5.50000i) q^{80} +(-3.23205 - 0.866025i) q^{82} +(-2.09808 - 2.09808i) q^{83} +(2.73205 - 8.19615i) q^{85} +(-1.03590 - 1.79423i) q^{86} +(1.36603 + 5.09808i) q^{88} +(-0.330127 - 0.571797i) q^{89} +(3.26795 - 6.73205i) q^{91} +(0.169873 + 0.169873i) q^{92} +(-2.36603 + 4.09808i) q^{94} +(0.0980762 - 1.63397i) q^{95} +(5.92820 - 5.92820i) q^{97} +(1.42820 + 3.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 6 q^{4} + 4 q^{5} + 2 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 + 6 * q^4 + 4 * q^5 + 2 * q^8	\( 4 q + 4 q^{2} + 6 q^{4} + 4 q^{5} + 2 q^{8} - 2 q^{11} + 8 q^{13} - 2 q^{14} - 2 q^{16} - 4 q^{17} + 2 q^{19} + 4 q^{22} + 4 q^{23} - 6 q^{25} + 12 q^{26} - 12 q^{31} + 6 q^{32} - 8 q^{34} - 8 q^{35} + 12 q^{37} + 2 q^{38} + 10 q^{40} - 6 q^{43} - 6 q^{44} + 14 q^{46} - 18 q^{47} - 22 q^{49} - 14 q^{50} + 12 q^{52} - 10 q^{53} - 8 q^{55} - 8 q^{56} + 6 q^{58} - 6 q^{59} - 12 q^{61} - 4 q^{62} + 12 q^{65} - 22 q^{67} - 28 q^{70} - 12 q^{71} - 24 q^{73} + 12 q^{74} + 18 q^{77} + 6 q^{79} + 16 q^{80} - 6 q^{82} + 2 q^{83} + 4 q^{85} - 18 q^{86} + 2 q^{88} + 16 q^{89} + 20 q^{91} + 18 q^{92} - 6 q^{94} - 10 q^{95} - 4 q^{97} - 22 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 6 * q^4 + 4 * q^5 + 2 * q^8 - 2 * q^11 + 8 * q^13 - 2 * q^14 - 2 * q^16 - 4 * q^17 + 2 * q^19 + 4 * q^22 + 4 * q^23 - 6 * q^25 + 12 * q^26 - 12 * q^31 + 6 * q^32 - 8 * q^34 - 8 * q^35 + 12 * q^37 + 2 * q^38 + 10 * q^40 - 6 * q^43 - 6 * q^44 + 14 * q^46 - 18 * q^47 - 22 * q^49 - 14 * q^50 + 12 * q^52 - 10 * q^53 - 8 * q^55 - 8 * q^56 + 6 * q^58 - 6 * q^59 - 12 * q^61 - 4 * q^62 + 12 * q^65 - 22 * q^67 - 28 * q^70 - 12 * q^71 - 24 * q^73 + 12 * q^74 + 18 * q^77 + 6 * q^79 + 16 * q^80 - 6 * q^82 + 2 * q^83 + 4 * q^85 - 18 * q^86 + 2 * q^88 + 16 * q^89 + 20 * q^91 + 18 * q^92 - 6 * q^94 - 10 * q^95 - 4 * q^97 - 22 * q^98

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