LMFDB - Embedded newform 975.2.bc.h.751.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(751,975)]

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, 0, 5]))

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

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

chi := DirichletCharacter("975.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bc (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.78541419707$
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			751.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	975.751
Dual form			975.2.bc.h.901.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.633975 - 0.366025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.732051 + 1.26795i) q^{4} +(0.633975 + 0.366025i) q^{6} +(3.86603 + 2.23205i) q^{7} +2.53590i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.633975 - 0.366025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.732051 + 1.26795i) q^{4} +(0.633975 + 0.366025i) q^{6} +(3.86603 + 2.23205i) q^{7} +2.53590i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-3.00000 + 1.73205i) q^{11} -1.46410 q^{12} +(-0.866025 + 3.50000i) q^{13} +3.26795 q^{14} +(-0.535898 - 0.928203i) q^{16} +(3.36603 - 5.83013i) q^{17} +0.732051i q^{18} +(-4.73205 - 2.73205i) q^{19} +4.46410i q^{21} +(-1.26795 + 2.19615i) q^{22} +(0.267949 + 0.464102i) q^{23} +(-2.19615 + 1.26795i) q^{24} +(0.732051 + 2.53590i) q^{26} -1.00000 q^{27} +(-5.66025 + 3.26795i) q^{28} +(1.36603 + 2.36603i) q^{29} +3.19615i q^{31} +(-5.07180 - 2.92820i) q^{32} +(-3.00000 - 1.73205i) q^{33} -4.92820i q^{34} +(-0.732051 - 1.26795i) q^{36} +(-3.46410 + 2.00000i) q^{37} -4.00000 q^{38} +(-3.46410 + 1.00000i) q^{39} +(4.56218 - 2.63397i) q^{41} +(1.63397 + 2.83013i) q^{42} +(0.133975 - 0.232051i) q^{43} -5.07180i q^{44} +(0.339746 + 0.196152i) q^{46} +0.196152i q^{47} +(0.535898 - 0.928203i) q^{48} +(6.46410 + 11.1962i) q^{49} +6.73205 q^{51} +(-3.80385 - 3.66025i) q^{52} +6.92820 q^{53} +(-0.633975 + 0.366025i) q^{54} +(-5.66025 + 9.80385i) q^{56} -5.46410i q^{57} +(1.73205 + 1.00000i) q^{58} +(6.29423 + 3.63397i) q^{59} +(-2.23205 + 3.86603i) q^{61} +(1.16987 + 2.02628i) q^{62} +(-3.86603 + 2.23205i) q^{63} -2.14359 q^{64} -2.53590 q^{66} +(10.7942 - 6.23205i) q^{67} +(4.92820 + 8.53590i) q^{68} +(-0.267949 + 0.464102i) q^{69} +(-11.0263 - 6.36603i) q^{71} +(-2.19615 - 1.26795i) q^{72} +15.3923i q^{73} +(-1.46410 + 2.53590i) q^{74} +(6.92820 - 4.00000i) q^{76} -15.4641 q^{77} +(-1.83013 + 1.90192i) q^{78} +1.92820 q^{79} +(-0.500000 - 0.866025i) q^{81} +(1.92820 - 3.33975i) q^{82} -2.53590i q^{83} +(-5.66025 - 3.26795i) q^{84} -0.196152i q^{86} +(-1.36603 + 2.36603i) q^{87} +(-4.39230 - 7.60770i) q^{88} +(-1.09808 + 0.633975i) q^{89} +(-11.1603 + 11.5981i) q^{91} -0.784610 q^{92} +(-2.76795 + 1.59808i) q^{93} +(0.0717968 + 0.124356i) q^{94} -5.85641i q^{96} +(14.2583 + 8.23205i) q^{97} +(8.19615 + 4.73205i) q^{98} -3.46410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{2} + 2 q^{3} + 4 q^{4} + 6 q^{6} + 12 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q + 6 * q^2 + 2 * q^3 + 4 * q^4 + 6 * q^6 + 12 * q^7 - 2 * q^9	$ 4 q + 6 q^{2} + 2 q^{3} + 4 q^{4} + 6 q^{6} + 12 q^{7} - 2 q^{9} - 12 q^{11} + 8 q^{12} + 20 q^{14} - 16 q^{16} + 10 q^{17} - 12 q^{19} - 12 q^{22} + 8 q^{23} + 12 q^{24} - 4 q^{26} - 4 q^{27} + 12 q^{28} + 2 q^{29} - 48 q^{32} - 12 q^{33} + 4 q^{36} - 16 q^{38} - 6 q^{41} + 10 q^{42} + 4 q^{43} + 36 q^{46} + 16 q^{48} + 12 q^{49} + 20 q^{51} - 36 q^{52} - 6 q^{54} + 12 q^{56} - 6 q^{59} - 2 q^{61} + 22 q^{62} - 12 q^{63} - 64 q^{64} - 24 q^{66} + 12 q^{67} - 8 q^{68} - 8 q^{69} - 6 q^{71} + 12 q^{72} + 8 q^{74} - 48 q^{77} + 10 q^{78} - 20 q^{79} - 2 q^{81} - 20 q^{82} + 12 q^{84} - 2 q^{87} + 24 q^{88} + 6 q^{89} - 10 q^{91} + 80 q^{92} - 18 q^{93} + 28 q^{94} + 12 q^{97} + 12 q^{98}+O(q^{100}) $ 4 * q + 6 * q^2 + 2 * q^3 + 4 * q^4 + 6 * q^6 + 12 * q^7 - 2 * q^9 - 12 * q^11 + 8 * q^12 + 20 * q^14 - 16 * q^16 + 10 * q^17 - 12 * q^19 - 12 * q^22 + 8 * q^23 + 12 * q^24 - 4 * q^26 - 4 * q^27 + 12 * q^28 + 2 * q^29 - 48 * q^32 - 12 * q^33 + 4 * q^36 - 16 * q^38 - 6 * q^41 + 10 * q^42 + 4 * q^43 + 36 * q^46 + 16 * q^48 + 12 * q^49 + 20 * q^51 - 36 * q^52 - 6 * q^54 + 12 * q^56 - 6 * q^59 - 2 * q^61 + 22 * q^62 - 12 * q^63 - 64 * q^64 - 24 * q^66 + 12 * q^67 - 8 * q^68 - 8 * q^69 - 6 * q^71 + 12 * q^72 + 8 * q^74 - 48 * q^77 + 10 * q^78 - 20 * q^79 - 2 * q^81 - 20 * q^82 + 12 * q^84 - 2 * q^87 + 24 * q^88 + 6 * q^89 - 10 * q^91 + 80 * q^92 - 18 * q^93 + 28 * q^94 + 12 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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	−0.258819	−	0.965926i	$-0.583333\pi$
$2$	0.633975	−	0.366025i	0.448288	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.732051	+	1.26795i	−0.366025	+	0.633975i
$5$		0			0
$5$		0			0
$6$	0.633975	+	0.366025i	0.258819	+	0.149429i
$7$	3.86603	+	2.23205i	1.46122	+	0.843636i	0.999068	−	0.0431647i	$-0.0137440\pi$
$7$	3.86603	+	2.23205i	1.46122	+	0.843636i	0.462152	+	0.886801i	$0.347077\pi$
$8$			2.53590i			0.896575i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−3.00000	+	1.73205i	−0.904534	+	0.522233i	−0.878668	−	0.477432i	$-0.841568\pi$
$11$	−3.00000	+	1.73205i	−0.904534	+	0.522233i	−0.0258656	+	0.999665i	$0.508234\pi$
$12$	−1.46410			−0.422650
$13$	−0.866025	+	3.50000i	−0.240192	+	0.970725i
$13$	−0.866025	+	3.50000i	−0.240192	+	0.970725i
$14$	3.26795			0.873396
$15$		0			0
$16$	−0.535898	−	0.928203i	−0.133975	−	0.232051i
$17$	3.36603	−	5.83013i	0.816381	−	1.41401i	−0.0919509	−	0.995764i	$-0.529310\pi$
$17$	3.36603	−	5.83013i	0.816381	−	1.41401i	0.908332	−	0.418250i	$-0.137356\pi$
$18$			0.732051i			0.172546i
$19$	−4.73205	−	2.73205i	−1.08561	−	0.626775i	−0.153203	−	0.988195i	$-0.548959\pi$
$19$	−4.73205	−	2.73205i	−1.08561	−	0.626775i	−0.932403	+	0.361419i	$0.882292\pi$
$20$		0			0
$21$			4.46410i			0.974147i
$22$	−1.26795	+	2.19615i	−0.270328	+	0.468221i
$23$	0.267949	+	0.464102i	0.0558713	+	0.0967719i	0.892608	−	0.450833i	$-0.148873\pi$
$23$	0.267949	+	0.464102i	0.0558713	+	0.0967719i	−0.836737	+	0.547605i	$0.815540\pi$
$24$	−2.19615	+	1.26795i	−0.448288	+	0.258819i
$25$		0			0
$26$	0.732051	+	2.53590i	0.143567	+	0.497331i
$27$	−1.00000			−0.192450
$28$	−5.66025	+	3.26795i	−1.06969	+	0.617584i
$29$	1.36603	+	2.36603i	0.253665	+	0.439360i	0.964532	−	0.263966i	$-0.0850307\pi$
$29$	1.36603	+	2.36603i	0.253665	+	0.439360i	−0.710867	+	0.703326i	$0.751697\pi$
$30$		0			0
$31$			3.19615i			0.574046i	0.957924	+	0.287023i	$0.0926656\pi$
$31$			3.19615i			0.574046i	−0.957924	+	0.287023i	$0.907334\pi$
$32$	−5.07180	−	2.92820i	−0.896575	−	0.517638i
$33$	−3.00000	−	1.73205i	−0.522233	−	0.301511i
$34$		−	4.92820i		−	0.845180i
$35$		0			0
$36$	−0.732051	−	1.26795i	−0.122008	−	0.211325i
$37$	−3.46410	+	2.00000i	−0.569495	+	0.328798i	−0.756948	−	0.653476i	$-0.773310\pi$
$37$	−3.46410	+	2.00000i	−0.569495	+	0.328798i	0.187453	+	0.982274i	$0.439977\pi$
$38$	−4.00000			−0.648886
$39$	−3.46410	+	1.00000i	−0.554700	+	0.160128i
$40$		0			0
$41$	4.56218	−	2.63397i	0.712492	−	0.411358i	−0.0994908	−	0.995038i	$-0.531721\pi$
$41$	4.56218	−	2.63397i	0.712492	−	0.411358i	0.811983	+	0.583681i	$0.198388\pi$
$42$	1.63397	+	2.83013i	0.252128	+	0.436698i
$43$	0.133975	−	0.232051i	0.0204309	−	0.0353874i	−0.855629	−	0.517589i	$-0.826830\pi$
$43$	0.133975	−	0.232051i	0.0204309	−	0.0353874i	0.876060	+	0.482202i	$0.160163\pi$
$44$		−	5.07180i		−	0.764602i
$45$		0			0
$46$	0.339746	+	0.196152i	0.0500928	+	0.0289211i
$47$			0.196152i			0.0286118i	0.999898	+	0.0143059i	$0.00455386\pi$
$47$			0.196152i			0.0286118i	−0.999898	+	0.0143059i	$0.995446\pi$
$48$	0.535898	−	0.928203i	0.0773503	−	0.133975i
$49$	6.46410	+	11.1962i	0.923443	+	1.59945i
$50$		0			0
$51$	6.73205			0.942676
$52$	−3.80385	−	3.66025i	−0.527499	−	0.507586i
$53$	6.92820			0.951662			0.475831	−	0.879537i	$-0.342147\pi$
$53$	6.92820			0.951662			0.475831	+	0.879537i	$0.342147\pi$
$54$	−0.633975	+	0.366025i	−0.0862730	+	0.0498097i
$55$		0			0
$56$	−5.66025	+	9.80385i	−0.756383	+	1.31009i
$57$		−	5.46410i		−	0.723738i
$58$	1.73205	+	1.00000i	0.227429	+	0.131306i
$59$	6.29423	+	3.63397i	0.819439	+	0.473103i	0.850223	−	0.526423i	$-0.176467\pi$
$59$	6.29423	+	3.63397i	0.819439	+	0.473103i	−0.0307841	+	0.999526i	$0.509800\pi$
$60$		0			0
$61$	−2.23205	+	3.86603i	−0.285785	+	0.494994i	−0.972799	−	0.231650i	$-0.925588\pi$
$61$	−2.23205	+	3.86603i	−0.285785	+	0.494994i	0.687014	+	0.726644i	$0.258921\pi$
$62$	1.16987	+	2.02628i	0.148574	+	0.257338i
$63$	−3.86603	+	2.23205i	−0.487073	+	0.281212i
$64$	−2.14359			−0.267949
$65$		0			0
$66$	−2.53590			−0.312148
$67$	10.7942	−	6.23205i	1.31872	−	0.761366i	0.335201	−	0.942146i	$-0.391196\pi$
$67$	10.7942	−	6.23205i	1.31872	−	0.761366i	0.983524	+	0.180780i	$0.0578623\pi$
$68$	4.92820	+	8.53590i	0.597632	+	1.03513i
$69$	−0.267949	+	0.464102i	−0.0322573	+	0.0558713i
$70$		0			0
$71$	−11.0263	−	6.36603i	−1.30858	−	0.755508i	−0.326720	−	0.945121i	$-0.605943\pi$
$71$	−11.0263	−	6.36603i	−1.30858	−	0.755508i	−0.981859	+	0.189613i	$0.939277\pi$
$72$	−2.19615	−	1.26795i	−0.258819	−	0.149429i
$73$			15.3923i			1.80153i	0.434304	+	0.900767i	$0.356994\pi$
$73$			15.3923i			1.80153i	−0.434304	+	0.900767i	$0.643006\pi$
$74$	−1.46410	+	2.53590i	−0.170198	+	0.294792i
$75$		0			0
$76$	6.92820	−	4.00000i	0.794719	−	0.458831i
$77$	−15.4641			−1.76230
$78$	−1.83013	+	1.90192i	−0.207221	+	0.215350i
$79$	1.92820			0.216940			0.108470	−	0.994100i	$-0.465405\pi$
$79$	1.92820			0.216940			0.108470	+	0.994100i	$0.465405\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.92820	−	3.33975i	0.212934	−	0.368813i
$83$		−	2.53590i		−	0.278351i	−0.990268	−	0.139176i	$-0.955555\pi$
$83$		−	2.53590i		−	0.278351i	0.990268	−	0.139176i	$-0.0444452\pi$
$84$	−5.66025	−	3.26795i	−0.617584	−	0.356562i
$85$		0			0
$86$		−	0.196152i		−	0.0211517i
$87$	−1.36603	+	2.36603i	−0.146453	+	0.253665i
$88$	−4.39230	−	7.60770i	−0.468221	−	0.810983i
$89$	−1.09808	+	0.633975i	−0.116396	+	0.0672012i	−0.557068	−	0.830467i	$-0.688074\pi$
$89$	−1.09808	+	0.633975i	−0.116396	+	0.0672012i	0.440672	+	0.897668i	$0.354740\pi$
$90$		0			0
$91$	−11.1603	+	11.5981i	−1.16991	+	1.21581i
$92$	−0.784610			−0.0818012
$93$	−2.76795	+	1.59808i	−0.287023	+	0.165713i
$94$	0.0717968	+	0.124356i	0.00740527	+	0.0128263i
$95$		0			0
$96$		−	5.85641i		−	0.597717i
$97$	14.2583	+	8.23205i	1.44771	+	0.835838i	0.998345	−	0.0575081i	$-0.0183155\pi$
$97$	14.2583	+	8.23205i	1.44771	+	0.835838i	0.449369	+	0.893346i	$0.351649\pi$
$98$	8.19615	+	4.73205i	0.827936	+	0.478009i
$99$		−	3.46410i		−	0.348155i
$100$		0			0
$101$	−2.46410	−	4.26795i	−0.245187	−	0.424677i	0.716997	−	0.697076i	$-0.245516\pi$
$101$	−2.46410	−	4.26795i	−0.245187	−	0.424677i	−0.962184	+	0.272399i	$0.912183\pi$
$102$	4.26795	−	2.46410i	0.422590	−	0.243982i
$103$	−3.19615			−0.314926			−0.157463	−	0.987525i	$-0.550332\pi$
$103$	−3.19615			−0.314926			−0.157463	+	0.987525i	$0.550332\pi$
$104$	−8.87564	−	2.19615i	−0.870329	−	0.215350i
$105$		0			0
$106$	4.39230	−	2.53590i	0.426618	−	0.246308i
$107$	8.56218	+	14.8301i	0.827737	+	1.43368i	0.899809	+	0.436283i	$0.143705\pi$
$107$	8.56218	+	14.8301i	0.827737	+	1.43368i	−0.0720725	+	0.997399i	$0.522961\pi$
$108$	0.732051	−	1.26795i	0.0704416	−	0.122008i
$109$			8.26795i			0.791926i	0.918266	+	0.395963i	$0.129589\pi$
$109$			8.26795i			0.791926i	−0.918266	+	0.395963i	$0.870411\pi$
$110$		0			0
$111$	−3.46410	−	2.00000i	−0.328798	−	0.189832i
$112$		−	4.78461i		−	0.452103i
$113$	9.73205	−	16.8564i	0.915514	−	1.58572i	0.109368	−	0.994001i	$-0.465117\pi$
$113$	9.73205	−	16.8564i	0.915514	−	1.58572i	0.806147	−	0.591716i	$-0.201549\pi$
$114$	−2.00000	−	3.46410i	−0.187317	−	0.324443i
$115$		0			0
$116$	−4.00000			−0.371391
$117$	−2.59808	−	2.50000i	−0.240192	−	0.231125i
$118$	5.32051			0.489792
$119$	26.0263	−	15.0263i	2.38583	−	1.37746i
$120$		0			0
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$			3.26795i			0.295866i
$123$	4.56218	+	2.63397i	0.411358	+	0.237497i
$124$	−4.05256	−	2.33975i	−0.363931	−	0.210115i
$125$		0			0
$126$	−1.63397	+	2.83013i	−0.145566	+	0.252128i
$127$	−7.33013	−	12.6962i	−0.650444	−	1.12660i	−0.983015	−	0.183523i	$-0.941250\pi$
$127$	−7.33013	−	12.6962i	−0.650444	−	1.12660i	0.332572	−	0.943078i	$-0.392084\pi$
$128$	8.78461	−	5.07180i	0.776457	−	0.448288i
$129$	0.267949			0.0235916
$130$		0			0
$131$	1.26795			0.110781			0.0553906	−	0.998465i	$-0.482360\pi$
$131$	1.26795			0.110781			0.0553906	+	0.998465i	$0.482360\pi$
$132$	4.39230	−	2.53590i	0.382301	−	0.220722i
$133$	−12.1962	−	21.1244i	−1.05754	−	1.83171i
$134$	4.56218	−	7.90192i	0.394112	−	0.682622i
$135$		0			0
$136$	14.7846	+	8.53590i	1.26777	+	0.731947i
$137$	7.90192	+	4.56218i	0.675107	+	0.389773i	0.798009	−	0.602646i	$-0.205887\pi$
$137$	7.90192	+	4.56218i	0.675107	+	0.389773i	−0.122902	+	0.992419i	$0.539220\pi$
$138$			0.392305i			0.0333952i
$139$	8.96410	−	15.5263i	0.760325	−	1.31692i	−0.182358	−	0.983232i	$-0.558373\pi$
$139$	8.96410	−	15.5263i	0.760325	−	1.31692i	0.942683	−	0.333690i	$-0.108294\pi$
$140$		0			0
$141$	−0.169873	+	0.0980762i	−0.0143059	+	0.00825951i
$142$	−9.32051			−0.782160
$143$	−3.46410	−	12.0000i	−0.289683	−	1.00349i
$144$	1.07180			0.0893164
$145$		0			0
$146$	5.63397	+	9.75833i	0.466271	+	0.807605i
$147$	−6.46410	+	11.1962i	−0.533150	+	0.923443i
$148$		−	5.85641i		−	0.481394i
$149$	−3.46410	−	2.00000i	−0.283790	−	0.163846i	0.351348	−	0.936245i	$-0.385723\pi$
$149$	−3.46410	−	2.00000i	−0.283790	−	0.163846i	−0.635138	+	0.772399i	$0.719057\pi$
$150$		0			0
$151$		−	17.8564i		−	1.45313i	−0.687096	−	0.726567i	$-0.741115\pi$
$151$		−	17.8564i		−	1.45313i	0.687096	−	0.726567i	$-0.258885\pi$
$152$	6.92820	−	12.0000i	0.561951	−	0.973329i
$153$	3.36603	+	5.83013i	0.272127	+	0.471338i
$154$	−9.80385	+	5.66025i	−0.790017	+	0.456116i
$155$		0			0
$156$	1.26795	−	5.12436i	0.101517	−	0.410277i
$157$	−9.73205			−0.776702			−0.388351	−	0.921511i	$-0.626955\pi$
$157$	−9.73205			−0.776702			−0.388351	+	0.921511i	$0.626955\pi$
$158$	1.22243	−	0.705771i	0.0972515	−	0.0561482i
$159$	3.46410	+	6.00000i	0.274721	+	0.475831i
$160$		0			0
$161$			2.39230i			0.188540i
$162$	−0.633975	−	0.366025i	−0.0498097	−	0.0287577i
$163$	−4.79423	−	2.76795i	−0.375513	−	0.216803i	0.300351	−	0.953829i	$-0.402896\pi$
$163$	−4.79423	−	2.76795i	−0.375513	−	0.216803i	−0.675864	+	0.737026i	$0.736229\pi$
$164$			7.71281i			0.602270i
$165$		0			0
$166$	−0.928203	−	1.60770i	−0.0720425	−	0.124781i
$167$	15.1244	−	8.73205i	1.17036	−	0.675706i	0.216593	−	0.976262i	$-0.430505\pi$
$167$	15.1244	−	8.73205i	1.17036	−	0.675706i	0.953764	+	0.300556i	$0.0971721\pi$
$168$	−11.3205			−0.873396
$169$	−11.5000	−	6.06218i	−0.884615	−	0.466321i
$170$		0			0
$171$	4.73205	−	2.73205i	0.361869	−	0.208925i
$172$	0.196152	+	0.339746i	0.0149565	+	0.0259054i
$173$	−1.63397	+	2.83013i	−0.124229	+	0.215171i	−0.921431	−	0.388542i	$-0.872979\pi$
$173$	−1.63397	+	2.83013i	−0.124229	+	0.215171i	0.797202	+	0.603712i	$0.206312\pi$
$174$			2.00000i			0.151620i
$175$		0			0
$176$	3.21539	+	1.85641i	0.242369	+	0.139932i
$177$			7.26795i			0.546293i
$178$	−0.464102	+	0.803848i	−0.0347859	+	0.0602509i
$179$	4.56218	+	7.90192i	0.340993	+	0.590618i	0.984617	−	0.174724i	$-0.0559034\pi$
$179$	4.56218	+	7.90192i	0.340993	+	0.590618i	−0.643624	+	0.765342i	$0.722570\pi$
$180$		0			0
$181$	14.5359			1.08044			0.540222	−	0.841522i	$-0.318340\pi$
$181$	14.5359			1.08044			0.540222	+	0.841522i	$0.318340\pi$
$182$	−2.83013	+	11.4378i	−0.209783	+	0.847828i
$183$	−4.46410			−0.329996
$184$	−1.17691	+	0.679492i	−0.0867633	+	0.0500928i
$185$		0			0
$186$	−1.16987	+	2.02628i	−0.0857792	+	0.148574i
$187$			23.3205i			1.70536i
$188$	−0.248711	−	0.143594i	−0.0181391	−	0.0104726i
$189$	−3.86603	−	2.23205i	−0.281212	−	0.162358i
$190$		0			0
$191$	13.7583	−	23.8301i	0.995518	−	1.72429i	0.415855	−	0.909431i	$-0.363482\pi$
$191$	13.7583	−	23.8301i	0.995518	−	1.72429i	0.579662	−	0.814857i	$-0.303184\pi$
$192$	−1.07180	−	1.85641i	−0.0773503	−	0.133975i
$193$	−5.25833	+	3.03590i	−0.378503	+	0.218529i	−0.677167	−	0.735830i	$-0.736792\pi$
$193$	−5.25833	+	3.03590i	−0.378503	+	0.218529i	0.298664	+	0.954358i	$0.403459\pi$
$194$	12.0526			0.865323
$195$		0			0
$196$	−18.9282			−1.35201
$197$	2.53590	−	1.46410i	0.180675	−	0.104313i	−0.406935	−	0.913457i	$-0.633402\pi$
$197$	2.53590	−	1.46410i	0.180675	−	0.104313i	0.587610	+	0.809144i	$0.300069\pi$
$198$	−1.26795	−	2.19615i	−0.0901092	−	0.156074i
$199$	−7.50000	+	12.9904i	−0.531661	+	0.920864i	0.467656	+	0.883911i	$0.345099\pi$
$199$	−7.50000	+	12.9904i	−0.531661	+	0.920864i	−0.999317	+	0.0369532i	$0.988235\pi$
$200$		0			0
$201$	10.7942	+	6.23205i	0.761366	+	0.439575i
$202$	−3.12436	−	1.80385i	−0.219829	−	0.126918i
$203$			12.1962i			0.856002i
$204$	−4.92820	+	8.53590i	−0.345043	+	0.597632i
$205$		0			0
$206$	−2.02628	+	1.16987i	−0.141178	+	0.0815089i
$207$	−0.535898			−0.0372475
$208$	3.71281	−	1.07180i	0.257437	−	0.0743157i
$209$	18.9282			1.30929
$210$		0			0
$211$	−5.76795	−	9.99038i	−0.397082	−	0.687766i	0.596283	−	0.802775i	$-0.296644\pi$
$211$	−5.76795	−	9.99038i	−0.397082	−	0.687766i	−0.993365	+	0.115008i	$0.963310\pi$
$212$	−5.07180	+	8.78461i	−0.348332	+	0.603329i
$213$		−	12.7321i		−	0.872386i
$214$	10.8564	+	6.26795i	0.742129	+	0.428468i
$215$		0			0
$216$		−	2.53590i		−	0.172546i
$217$	−7.13397	+	12.3564i	−0.484286	+	0.838808i
$218$	3.02628	+	5.24167i	0.204966	+	0.355011i
$219$	−13.3301	+	7.69615i	−0.900767	+	0.520058i
$220$		0			0
$221$	17.4904	+	16.8301i	1.17653	+	1.13212i
$222$	−2.92820			−0.196528
$223$	10.2679	−	5.92820i	0.687593	−	0.396982i	−0.115117	−	0.993352i	$-0.536724\pi$
$223$	10.2679	−	5.92820i	0.687593	−	0.396982i	0.802710	+	0.596370i	$0.203391\pi$
$224$	−13.0718	−	22.6410i	−0.873396	−	1.51277i
$225$		0			0
$226$		−	14.2487i		−	0.947810i
$227$	−10.0981	−	5.83013i	−0.670233	−	0.386959i	0.125932	−	0.992039i	$-0.459808\pi$
$227$	−10.0981	−	5.83013i	−0.670233	−	0.386959i	−0.796165	+	0.605080i	$0.793141\pi$
$228$	6.92820	+	4.00000i	0.458831	+	0.264906i
$229$			18.3923i			1.21540i	0.794168	+	0.607699i	$0.207907\pi$
$229$			18.3923i			1.21540i	−0.794168	+	0.607699i	$0.792093\pi$
$230$		0			0
$231$	−7.73205	−	13.3923i	−0.508732	−	0.881149i
$232$	−6.00000	+	3.46410i	−0.393919	+	0.227429i
$233$	23.8564			1.56289			0.781443	−	0.623977i	$-0.214484\pi$
$233$	23.8564			1.56289			0.781443	+	0.623977i	$0.214484\pi$
$234$	−2.56218	−	0.633975i	−0.167495	−	0.0414442i
$235$		0			0
$236$	−9.21539	+	5.32051i	−0.599871	+	0.346336i
$237$	0.964102	+	1.66987i	0.0626251	+	0.108470i
$238$	11.0000	−	19.0526i	0.713024	−	1.23499i
$239$			5.46410i			0.353443i	0.984261	+	0.176722i	$0.0565492\pi$
$239$			5.46410i			0.353443i	−0.984261	+	0.176722i	$0.943451\pi$
$240$		0			0
$241$	1.39230	+	0.803848i	0.0896862	+	0.0517804i	0.544172	−	0.838973i	$-0.316844\pi$
$241$	1.39230	+	0.803848i	0.0896862	+	0.0517804i	−0.454486	+	0.890754i	$0.650177\pi$
$242$		−	0.732051i		−	0.0470580i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−3.26795	−	5.66025i	−0.209209	−	0.362361i
$245$		0			0
$246$	3.85641			0.245875
$247$	13.6603	−	14.1962i	0.869181	−	0.903280i
$248$	−8.10512			−0.514675
$249$	2.19615	−	1.26795i	0.139176	−	0.0803530i
$250$		0			0
$251$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$251$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$252$		−	6.53590i		−	0.411723i
$253$	−1.60770	−	0.928203i	−0.101075	−	0.0583556i
$254$	−9.29423	−	5.36603i	−0.583172	−	0.336694i
$255$		0			0
$256$	5.85641	−	10.1436i	0.366025	−	0.633975i
$257$	−5.36603	−	9.29423i	−0.334723	−	0.579758i	0.648708	−	0.761037i	$-0.275310\pi$
$257$	−5.36603	−	9.29423i	−0.334723	−	0.579758i	−0.983432	+	0.181279i	$0.941976\pi$
$258$	0.169873	−	0.0980762i	0.0105758	−	0.00610596i
$259$	−17.8564			−1.10954
$260$		0			0
$261$	−2.73205			−0.169110
$262$	0.803848	−	0.464102i	0.0496619	−	0.0286723i
$263$	−3.16987	−	5.49038i	−0.195463	−	0.338551i	0.751589	−	0.659631i	$-0.229288\pi$
$263$	−3.16987	−	5.49038i	−0.195463	−	0.338551i	−0.947052	+	0.321080i	$0.895954\pi$
$264$	4.39230	−	7.60770i	0.270328	−	0.468221i
$265$		0			0
$266$	−15.4641	−	8.92820i	−0.948165	−	0.547423i
$267$	−1.09808	−	0.633975i	−0.0672012	−	0.0387986i
$268$			18.2487i			1.11472i
$269$	−7.83013	+	13.5622i	−0.477411	+	0.826901i	−0.999665	−	0.0258897i	$-0.991758\pi$
$269$	−7.83013	+	13.5622i	−0.477411	+	0.826901i	0.522254	+	0.852790i	$0.325091\pi$
$270$		0			0
$271$	−3.23205	+	1.86603i	−0.196333	+	0.113353i	−0.594944	−	0.803767i	$-0.702826\pi$
$271$	−3.23205	+	1.86603i	−0.196333	+	0.113353i	0.398611	+	0.917120i	$0.369492\pi$
$272$	−7.21539			−0.437497
$273$	−15.6244	−	3.86603i	−0.945629	−	0.233983i
$274$	6.67949			0.403523
$275$		0			0
$276$	−0.392305	−	0.679492i	−0.0236140	−	0.0409006i
$277$	−10.1244	+	17.5359i	−0.608314	+	1.05363i	0.383205	+	0.923663i	$0.374820\pi$
$277$	−10.1244	+	17.5359i	−0.608314	+	1.05363i	−0.991518	+	0.129967i	$0.958513\pi$
$278$		−	13.1244i		−	0.787147i
$279$	−2.76795	−	1.59808i	−0.165713	−	0.0956743i
$280$		0			0
$281$		−	21.1244i		−	1.26017i	−0.776525	−	0.630087i	$-0.783019\pi$
$281$		−	21.1244i		−	1.26017i	0.776525	−	0.630087i	$-0.216981\pi$
$282$	−0.0717968	+	0.124356i	−0.00427544	+	0.00740527i
$283$	0.133975	+	0.232051i	0.00796396	+	0.0137940i	0.869980	−	0.493087i	$-0.164132\pi$
$283$	0.133975	+	0.232051i	0.00796396	+	0.0137940i	−0.862016	+	0.506881i	$0.830798\pi$
$284$	16.1436	−	9.32051i	0.957946	−	0.553070i
$285$		0			0
$286$	−6.58846	−	6.33975i	−0.389584	−	0.374877i
$287$	23.5167			1.38814
$288$	5.07180	−	2.92820i	0.298858	−	0.172546i
$289$	−14.1603	−	24.5263i	−0.832956	−	1.44272i
$290$		0			0
$291$			16.4641i			0.965143i
$292$	−19.5167	−	11.2679i	−1.14213	−	0.659407i
$293$	−21.2942	−	12.2942i	−1.24402	−	0.718237i	−0.274112	−	0.961698i	$-0.588384\pi$
$293$	−21.2942	−	12.2942i	−1.24402	−	0.718237i	−0.969911	+	0.243461i	$0.921717\pi$
$294$			9.46410i			0.551958i
$295$		0			0
$296$	−5.07180	−	8.78461i	−0.294792	−	0.510595i
$297$	3.00000	−	1.73205i	0.174078	−	0.100504i
$298$	−2.92820			−0.169626
$299$	−1.85641	+	0.535898i	−0.107359	+	0.0309918i
$300$		0			0
$301$	1.03590	−	0.598076i	0.0597082	−	0.0344725i
$302$	−6.53590	−	11.3205i	−0.376099	−	0.651422i
$303$	2.46410	−	4.26795i	0.141559	−	0.245187i
$304$			5.85641i			0.335888i
$305$		0			0
$306$	4.26795	+	2.46410i	0.243982	+	0.140863i
$307$			12.0718i			0.688974i	0.938791	+	0.344487i	$0.111947\pi$
$307$			12.0718i			0.688974i	−0.938791	+	0.344487i	$0.888053\pi$
$308$	11.3205	−	19.6077i	0.645046	−	1.11725i
$309$	−1.59808	−	2.76795i	−0.0909114	−	0.157463i
$310$		0			0
$311$	−10.1962			−0.578171			−0.289085	−	0.957303i	$-0.593351\pi$
$311$	−10.1962			−0.578171			−0.289085	+	0.957303i	$0.593351\pi$
$312$	−2.53590	−	8.78461i	−0.143567	−	0.497331i
$313$	10.8038			0.610670			0.305335	−	0.952245i	$-0.401232\pi$
$313$	10.8038			0.610670			0.305335	+	0.952245i	$0.401232\pi$
$314$	−6.16987	+	3.56218i	−0.348186	+	0.201025i
$315$		0			0
$316$	−1.41154	+	2.44486i	−0.0794055	+	0.137534i
$317$			17.4641i			0.980882i	0.871474	+	0.490441i	$0.163164\pi$
$317$			17.4641i			0.980882i	−0.871474	+	0.490441i	$0.836836\pi$
$318$	4.39230	+	2.53590i	0.246308	+	0.142206i
$319$	−8.19615	−	4.73205i	−0.458896	−	0.264944i
$320$		0			0
$321$	−8.56218	+	14.8301i	−0.477894	+	0.827737i
$322$	0.875644	+	1.51666i	0.0487978	+	0.0845202i
$323$	−31.8564	+	18.3923i	−1.77254	+	1.02338i
$324$	1.46410			0.0813390
$325$		0			0
$326$	−4.05256			−0.224450
$327$	−7.16025	+	4.13397i	−0.395963	+	0.228609i
$328$	6.67949	+	11.5692i	0.368813	+	0.638803i
$329$	−0.437822	+	0.758330i	−0.0241379	+	0.0418081i
$330$		0			0
$331$	7.03590	+	4.06218i	0.386728	+	0.223277i	0.680741	−	0.732524i	$-0.261658\pi$
$331$	7.03590	+	4.06218i	0.386728	+	0.223277i	−0.294013	+	0.955801i	$0.594991\pi$
$332$	3.21539	+	1.85641i	0.176467	+	0.101884i
$333$		−	4.00000i		−	0.219199i
$334$	6.39230	−	11.0718i	0.349771	−	0.605822i
$335$		0			0
$336$	4.14359	−	2.39230i	0.226052	−	0.130511i
$337$	31.0526			1.69154			0.845770	−	0.533547i	$-0.179141\pi$
$337$	31.0526			1.69154			0.845770	+	0.533547i	$0.179141\pi$
$338$	−9.50962	+	0.366025i	−0.517255	+	0.0199092i
$339$	19.4641			1.05714
$340$		0			0
$341$	−5.53590	−	9.58846i	−0.299786	−	0.519244i
$342$	2.00000	−	3.46410i	0.108148	−	0.187317i
$343$			26.4641i			1.42893i
$344$	0.588457	+	0.339746i	0.0317275	+	0.0183179i
$345$		0			0
$346$			2.39230i			0.128611i
$347$	3.26795	−	5.66025i	0.175433	−	0.303858i	−0.764878	−	0.644175i	$-0.777201\pi$
$347$	3.26795	−	5.66025i	0.175433	−	0.303858i	0.940311	+	0.340317i	$0.110534\pi$
$348$	−2.00000	−	3.46410i	−0.107211	−	0.185695i
$349$	25.9641	−	14.9904i	1.38983	−	0.802417i	0.396531	−	0.918021i	$-0.370214\pi$
$349$	25.9641	−	14.9904i	1.38983	−	0.802417i	0.993295	+	0.115605i	$0.0368805\pi$
$350$		0			0
$351$	0.866025	−	3.50000i	0.0462250	−	0.186816i
$352$	20.2872			1.08131
$353$	31.9808	−	18.4641i	1.70216	−	0.982745i	0.758599	−	0.651558i	$-0.225884\pi$
$353$	31.9808	−	18.4641i	1.70216	−	0.982745i	0.943565	−	0.331187i	$-0.107449\pi$
$354$	2.66025	+	4.60770i	0.141391	+	0.244896i
$355$		0			0
$356$		−	1.85641i		−	0.0983893i
$357$	26.0263	+	15.0263i	1.37746	+	0.795275i
$358$	5.78461	+	3.33975i	0.305726	+	0.176511i
$359$			33.6603i			1.77652i	0.459341	+	0.888260i	$0.348086\pi$
$359$			33.6603i			1.77652i	−0.459341	+	0.888260i	$0.651914\pi$
$360$		0			0
$361$	5.42820	+	9.40192i	0.285695	+	0.494838i
$362$	9.21539	−	5.32051i	0.484350	−	0.279640i
$363$	1.00000			0.0524864
$364$	−6.53590	−	22.6410i	−0.342574	−	1.18671i
$365$		0			0
$366$	−2.83013	+	1.63397i	−0.147933	+	0.0854092i
$367$	−9.06218	−	15.6962i	−0.473042	−	0.819332i	0.526482	−	0.850186i	$-0.323511\pi$
$367$	−9.06218	−	15.6962i	−0.473042	−	0.819332i	−0.999524	+	0.0308537i	$0.990177\pi$
$368$	0.287187	−	0.497423i	0.0149707	−	0.0259299i
$369$			5.26795i			0.274238i
$370$		0			0
$371$	26.7846	+	15.4641i	1.39059	+	0.802856i
$372$		−	4.67949i		−	0.242620i
$373$	−0.937822	+	1.62436i	−0.0485586	+	0.0841059i	−0.889283	−	0.457357i	$-0.848796\pi$
$373$	−0.937822	+	1.62436i	−0.0485586	+	0.0841059i	0.840724	+	0.541463i	$0.182129\pi$
$374$	8.53590	+	14.7846i	0.441381	+	0.764494i
$375$		0			0
$376$	−0.497423			−0.0256526
$377$	−9.46410	+	2.73205i	−0.487426	+	0.140708i
$378$	−3.26795			−0.168085
$379$	−17.0885	+	9.86603i	−0.877775	+	0.506784i	−0.869924	−	0.493185i	$-0.835832\pi$
$379$	−17.0885	+	9.86603i	−0.877775	+	0.506784i	−0.00785092	+	0.999969i	$0.502499\pi$
$380$		0			0
$381$	7.33013	−	12.6962i	0.375534	−	0.650444i
$382$		−	20.1436i		−	1.03064i
$383$	−7.22243	−	4.16987i	−0.369049	−	0.213071i	0.303994	−	0.952674i	$-0.401680\pi$
$383$	−7.22243	−	4.16987i	−0.369049	−	0.213071i	−0.673043	+	0.739603i	$0.735013\pi$
$384$	8.78461	+	5.07180i	0.448288	+	0.258819i
$385$		0			0
$386$	−2.22243	+	3.84936i	−0.113119	+	0.195928i
$387$	0.133975	+	0.232051i	0.00681031	+	0.0117958i
$388$	−20.8756	+	12.0526i	−1.05980	+	0.611876i
$389$	−17.4641			−0.885465			−0.442733	−	0.896654i	$-0.645991\pi$
$389$	−17.4641			−0.885465			−0.442733	+	0.896654i	$0.645991\pi$
$390$		0			0
$391$	3.60770			0.182449
$392$	−28.3923	+	16.3923i	−1.43403	+	0.827936i
$393$	0.633975	+	1.09808i	0.0319798	+	0.0553906i
$394$	1.07180	−	1.85641i	0.0539963	−	0.0935244i
$395$		0			0
$396$	4.39230	+	2.53590i	0.220722	+	0.127434i
$397$	−21.0622	−	12.1603i	−1.05708	−	0.610306i	−0.132457	−	0.991189i	$-0.542287\pi$
$397$	−21.0622	−	12.1603i	−1.05708	−	0.610306i	−0.924623	+	0.380883i	$0.875620\pi$
$398$			10.9808i			0.550416i
$399$	12.1962	−	21.1244i	0.610571	−	1.05754i
$400$		0			0
$401$	−13.2679	+	7.66025i	−0.662570	+	0.382535i	−0.793255	−	0.608889i	$-0.791615\pi$
$401$	−13.2679	+	7.66025i	−0.662570	+	0.382535i	0.130686	+	0.991424i	$0.458282\pi$
$402$	9.12436			0.455081
$403$	−11.1865	−	2.76795i	−0.557241	−	0.137881i
$404$	7.21539			0.358979
$405$		0			0
$406$	4.46410	+	7.73205i	0.221550	+	0.383735i
$407$	6.92820	−	12.0000i	0.343418	−	0.594818i
$408$			17.0718i			0.845180i
$409$	2.30385	+	1.33013i	0.113918	+	0.0657705i	0.555876	−	0.831265i	$-0.312383\pi$
$409$	2.30385	+	1.33013i	0.113918	+	0.0657705i	−0.441958	+	0.897036i	$0.645716\pi$
$410$		0			0
$411$			9.12436i			0.450071i
$412$	2.33975	−	4.05256i	0.115271	−	0.199655i
$413$	16.2224	+	28.0981i	0.798254	+	1.38262i
$414$	−0.339746	+	0.196152i	−0.0166976	+	0.00964037i
$415$		0			0
$416$	14.6410	−	15.2154i	0.717835	−	0.745996i
$417$	17.9282			0.877948
$418$	12.0000	−	6.92820i	0.586939	−	0.338869i
$419$	−10.2224	−	17.7058i	−0.499398	−	0.864984i	0.500601	−	0.865678i	$-0.333112\pi$
$419$	−10.2224	−	17.7058i	−0.499398	−	0.864984i	−1.00000		0.000694440i	$0.999779\pi$
$420$		0			0
$421$			23.5885i			1.14963i	0.818283	+	0.574816i	$0.194926\pi$
$421$			23.5885i			1.14963i	−0.818283	+	0.574816i	$0.805074\pi$
$422$	−7.31347	−	4.22243i	−0.356014	−	0.205545i
$423$	−0.169873	−	0.0980762i	−0.00825951	−	0.00476863i
$424$			17.5692i			0.853237i
$425$		0			0
$426$	−4.66025	−	8.07180i	−0.225790	−	0.391080i
$427$	−17.2583	+	9.96410i	−0.835189	+	0.482197i
$428$	−25.0718			−1.21189
$429$	8.66025	−	9.00000i	0.418121	−	0.434524i
$430$		0			0
$431$	−20.1962	+	11.6603i	−0.972814	+	0.561655i	−0.900093	−	0.435698i	$-0.856502\pi$
$431$	−20.1962	+	11.6603i	−0.972814	+	0.561655i	−0.0727213	+	0.997352i	$0.523168\pi$
$432$	0.535898	+	0.928203i	0.0257834	+	0.0446582i
$433$	−2.40192	+	4.16025i	−0.115429	+	0.199929i	−0.917951	−	0.396693i	$-0.870158\pi$
$433$	−2.40192	+	4.16025i	−0.115429	+	0.199929i	0.802522	+	0.596622i	$0.203491\pi$
$434$			10.4449i			0.501370i
$435$		0			0
$436$	−10.4833	−	6.05256i	−0.502061	−	0.289865i
$437$		−	2.92820i		−	0.140075i
$438$	−5.63397	+	9.75833i	−0.269202	+	0.466271i
$439$	7.69615	+	13.3301i	0.367317	+	0.636212i	0.989145	−	0.146942i	$-0.0469430\pi$
$439$	7.69615	+	13.3301i	0.367317	+	0.636212i	−0.621828	+	0.783154i	$0.713610\pi$
$440$		0			0
$441$	−12.9282			−0.615629
$442$	17.2487	+	4.26795i	0.820438	+	0.203006i
$443$	−3.12436			−0.148443			−0.0742213	−	0.997242i	$-0.523647\pi$
$443$	−3.12436			−0.148443			−0.0742213	+	0.997242i	$0.523647\pi$
$444$	5.07180	−	2.92820i	0.240697	−	0.138966i
$445$		0			0
$446$	4.33975	−	7.51666i	0.205493	−	0.355924i
$447$		−	4.00000i		−	0.189194i
$448$	−8.28719	−	4.78461i	−0.391533	−	0.226052i
$449$	9.58846	+	5.53590i	0.452507	+	0.261255i	0.708889	−	0.705321i	$-0.249197\pi$
$449$	9.58846	+	5.53590i	0.452507	+	0.261255i	−0.256381	+	0.966576i	$0.582530\pi$
$450$		0			0
$451$	−9.12436	+	15.8038i	−0.429649	+	0.744174i
$452$	14.2487	+	24.6795i	0.670203	+	1.16083i
$453$	15.4641	−	8.92820i	0.726567	−	0.419484i
$454$	−8.53590			−0.400610
$455$		0			0
$456$	13.8564			0.648886
$457$	4.66987	−	2.69615i	0.218447	−	0.126121i	−0.386784	−	0.922170i	$-0.626414\pi$
$457$	4.66987	−	2.69615i	0.218447	−	0.126121i	0.605231	+	0.796050i	$0.293081\pi$
$458$	6.73205	+	11.6603i	0.314568	+	0.544848i
$459$	−3.36603	+	5.83013i	−0.157113	+	0.272127i
$460$		0			0
$461$	9.97372	+	5.75833i	0.464522	+	0.268192i	0.713944	−	0.700203i	$-0.246907\pi$
$461$	9.97372	+	5.75833i	0.464522	+	0.268192i	−0.249421	+	0.968395i	$0.580240\pi$
$462$	−9.80385	−	5.66025i	−0.456116	−	0.263339i
$463$		−	1.78461i		−	0.0829378i	−0.999140	−	0.0414689i	$-0.986796\pi$
$463$		−	1.78461i		−	0.0829378i	0.999140	−	0.0414689i	$-0.0132038\pi$
$464$	1.46410	−	2.53590i	0.0679692	−	0.117726i
$465$		0			0
$466$	15.1244	−	8.73205i	0.700622	−	0.404504i
$467$	−23.6603			−1.09487			−0.547433	−	0.836850i	$-0.684395\pi$
$467$	−23.6603			−1.09487			−0.547433	+	0.836850i	$0.684395\pi$
$468$	5.07180	−	1.46410i	0.234444	−	0.0676781i
$469$	55.6410			2.56926
$470$		0			0
$471$	−4.86603	−	8.42820i	−0.224215	−	0.388351i
$472$	−9.21539	+	15.9615i	−0.424173	+	0.734689i
$473$			0.928203i			0.0426788i
$474$	1.22243	+	0.705771i	0.0561482	+	0.0324172i
$475$		0			0
$476$			44.0000i			2.01674i
$477$	−3.46410	+	6.00000i	−0.158610	+	0.274721i
$478$	2.00000	+	3.46410i	0.0914779	+	0.158444i
$479$	−31.0981	+	17.9545i	−1.42091	+	0.820361i	−0.996376	−	0.0850522i	$-0.972894\pi$
$479$	−31.0981	+	17.9545i	−1.42091	+	0.820361i	−0.424531	+	0.905413i	$0.639561\pi$
$480$		0			0
$481$	−4.00000	−	13.8564i	−0.182384	−	0.631798i
$482$	1.17691			0.0536070
$483$	−2.07180	+	1.19615i	−0.0942700	+	0.0544268i
$484$	0.732051	+	1.26795i	0.0332750	+	0.0576341i
$485$		0			0
$486$		−	0.732051i		−	0.0332065i
$487$	−18.0000	−	10.3923i	−0.815658	−	0.470920i	0.0332590	−	0.999447i	$-0.489411\pi$
$487$	−18.0000	−	10.3923i	−0.815658	−	0.470920i	−0.848917	+	0.528526i	$0.822745\pi$
$488$	−9.80385	−	5.66025i	−0.443799	−	0.256228i
$489$		−	5.53590i		−	0.250342i
$490$		0			0
$491$	3.56218	+	6.16987i	0.160759	+	0.278442i	0.935141	−	0.354276i	$-0.115273\pi$
$491$	3.56218	+	6.16987i	0.160759	+	0.278442i	−0.774382	+	0.632718i	$0.781939\pi$
$492$	−6.67949	+	3.85641i	−0.301135	+	0.173860i
$493$	18.3923			0.828348
$494$	3.46410	−	14.0000i	0.155857	−	0.629890i
$495$		0			0
$496$	2.96668	−	1.71281i	0.133208	−	0.0769076i
$497$	−28.4186	−	49.2224i	−1.27475	−	2.20793i
$498$	0.928203	−	1.60770i	0.0415938	−	0.0720425i
$499$			0.392305i			0.0175620i	0.999961	+	0.00878099i	$0.00279511\pi$
$499$			0.392305i			0.0175620i	−0.999961	+	0.00878099i	$0.997205\pi$
$500$		0			0
$501$	15.1244	+	8.73205i	0.675706	+	0.390119i
$502$		0			0
$503$	−15.3923	+	26.6603i	−0.686309	+	1.18872i	0.286715	+	0.958016i	$0.407437\pi$
$503$	−15.3923	+	26.6603i	−0.686309	+	1.18872i	−0.973024	+	0.230706i	$0.925896\pi$
$504$	−5.66025	−	9.80385i	−0.252128	−	0.436698i
$505$		0			0
$506$	−1.35898			−0.0604142
$507$	−0.500000	−	12.9904i	−0.0222058	−	0.576923i
$508$	21.4641			0.952316
$509$	11.1962	−	6.46410i	0.496261	−	0.286516i	−0.230907	−	0.972976i	$-0.574169\pi$
$509$	11.1962	−	6.46410i	0.496261	−	0.286516i	0.727168	+	0.686459i	$0.240836\pi$
$510$		0			0
$511$	−34.3564	+	59.5070i	−1.51984	+	2.63244i
$512$			11.7128i			0.517638i
$513$	4.73205	+	2.73205i	0.208925	+	0.120623i
$514$	−6.80385	−	3.92820i	−0.300105	−	0.173266i
$515$		0			0
$516$	−0.196152	+	0.339746i	−0.00863513	+	0.0149565i
$517$	−0.339746	−	0.588457i	−0.0149420	−	0.0258803i
$518$	−11.3205	+	6.53590i	−0.497395	+	0.287171i
$519$	−3.26795			−0.143447
$520$		0			0
$521$	−12.7321			−0.557801			−0.278901	−	0.960320i	$-0.589970\pi$
$521$	−12.7321			−0.557801			−0.278901	+	0.960320i	$0.589970\pi$
$522$	−1.73205	+	1.00000i	−0.0758098	+	0.0437688i
$523$	−18.7321	−	32.4449i	−0.819095	−	1.41871i	−0.906350	−	0.422529i	$-0.861143\pi$
$523$	−18.7321	−	32.4449i	−0.819095	−	1.41871i	0.0872541	−	0.996186i	$-0.472191\pi$
$524$	−0.928203	+	1.60770i	−0.0405487	+	0.0702325i
$525$		0			0
$526$	−4.01924	−	2.32051i	−0.175247	−	0.101179i
$527$	18.6340	+	10.7583i	0.811709	+	0.468640i
$528$			3.71281i			0.161579i
$529$	11.3564	−	19.6699i	0.493757	−	0.855212i
$530$		0			0
$531$	−6.29423	+	3.63397i	−0.273146	+	0.157701i
$532$	35.7128			1.54835
$533$	5.26795	+	18.2487i	0.228180	+	0.790439i
$534$	−0.928203			−0.0401673
$535$		0			0
$536$	15.8038	+	27.3731i	0.682622	+	1.18234i
$537$	−4.56218	+	7.90192i	−0.196873	+	0.340993i
$538$			11.4641i			0.494253i
$539$	−38.7846	−	22.3923i	−1.67057	−	0.964505i
$540$		0			0
$541$		−	17.5885i		−	0.756187i	−0.925767	−	0.378093i	$-0.876580\pi$
$541$		−	17.5885i		−	0.756187i	0.925767	−	0.378093i	$-0.123420\pi$
$542$	−1.36603	+	2.36603i	−0.0586758	+	0.101629i
$543$	7.26795	+	12.5885i	0.311898	+	0.540222i
$544$	−34.1436	+	19.7128i	−1.46389	+	0.845180i
$545$		0			0
$546$	−11.3205	+	3.26795i	−0.484473	+	0.139855i
$547$	24.6603			1.05440			0.527198	−	0.849742i	$-0.323243\pi$
$547$	24.6603			1.05440			0.527198	+	0.849742i	$0.323243\pi$
$548$	−11.5692	+	6.67949i	−0.494213	+	0.285334i
$549$	−2.23205	−	3.86603i	−0.0952616	−	0.164998i
$550$		0			0
$551$		−	14.9282i		−	0.635963i
$552$	−1.17691	−	0.679492i	−0.0500928	−	0.0289211i
$553$	7.45448	+	4.30385i	0.316997	+	0.183018i
$554$			14.8231i			0.629773i
$555$		0			0
$556$	13.1244	+	22.7321i	0.556597	+	0.964054i
$557$	18.5885	−	10.7321i	0.787618	−	0.454732i	−0.0515052	−	0.998673i	$-0.516402\pi$
$557$	18.5885	−	10.7321i	0.787618	−	0.454732i	0.839123	+	0.543941i	$0.183069\pi$
$558$	−2.33975			−0.0990493
$559$	0.696152	+	0.669873i	0.0294441	+	0.0283326i
$560$		0			0
$561$	−20.1962	+	11.6603i	−0.852682	+	0.492296i
$562$	−7.73205	−	13.3923i	−0.326157	−	0.564920i
$563$	1.73205	−	3.00000i	0.0729972	−	0.126435i	−0.827216	−	0.561884i	$-0.810077\pi$
$563$	1.73205	−	3.00000i	0.0729972	−	0.126435i	0.900214	+	0.435449i	$0.143410\pi$
$564$		−	0.287187i		−	0.0120928i
$565$		0			0
$566$	0.169873	+	0.0980762i	0.00714029	+	0.00412245i
$567$		−	4.46410i		−	0.187475i
$568$	16.1436	−	27.9615i	0.677370	−	1.17324i
$569$	−22.0981	−	38.2750i	−0.926400	−	1.60457i	−0.789295	−	0.614015i	$-0.789554\pi$
$569$	−22.0981	−	38.2750i	−0.926400	−	1.60457i	−0.137105	−	0.990557i	$-0.543780\pi$
$570$		0			0
$571$	3.85641			0.161386			0.0806928	−	0.996739i	$-0.474287\pi$
$571$	3.85641			0.161386			0.0806928	+	0.996739i	$0.474287\pi$
$572$	17.7513	+	4.39230i	0.742219	+	0.183651i
$573$	27.5167			1.14952
$574$	14.9090	−	8.60770i	0.622288	−	0.359278i
$575$		0			0
$576$	1.07180	−	1.85641i	0.0446582	−	0.0773503i
$577$			11.7128i			0.487611i	0.969824	+	0.243805i	$0.0783958\pi$
$577$			11.7128i			0.487611i	−0.969824	+	0.243805i	$0.921604\pi$
$578$	−17.9545	−	10.3660i	−0.746808	−	0.431170i
$579$	−5.25833	−	3.03590i	−0.218529	−	0.126168i
$580$		0			0
$581$	5.66025	−	9.80385i	0.234827	−	0.406732i
$582$	6.02628	+	10.4378i	0.249797	+	0.432662i
$583$	−20.7846	+	12.0000i	−0.860811	+	0.496989i
$584$	−39.0333			−1.61521
$585$		0			0
$586$	−18.0000			−0.743573
$587$	22.2224	−	12.8301i	0.917218	−	0.529556i	0.0344715	−	0.999406i	$-0.489025\pi$
$587$	22.2224	−	12.8301i	0.917218	−	0.529556i	0.882746	+	0.469850i	$0.155692\pi$
$588$	−9.46410	−	16.3923i	−0.390293	−	0.676007i
$589$	8.73205	−	15.1244i	0.359798	−	0.623188i
$590$		0			0
$591$	2.53590	+	1.46410i	0.104313	+	0.0602251i
$592$	3.71281	+	2.14359i	0.152596	+	0.0881012i
$593$			21.3205i			0.875528i	0.899090	+	0.437764i	$0.144230\pi$
$593$			21.3205i			0.875528i	−0.899090	+	0.437764i	$0.855770\pi$
$594$	1.26795	−	2.19615i	0.0520246	−	0.0901092i
$595$		0			0
$596$	5.07180	−	2.92820i	0.207749	−	0.119944i
$597$	−15.0000			−0.613909
$598$	−0.980762	+	1.01924i	−0.0401063	+	0.0416797i
$599$	−23.1244			−0.944836			−0.472418	−	0.881375i	$-0.656619\pi$
$599$	−23.1244			−0.944836			−0.472418	+	0.881375i	$0.656619\pi$
$600$		0			0
$601$	11.1244	+	19.2679i	0.453772	+	0.785956i	0.998617	−	0.0525809i	$-0.0167447\pi$
$601$	11.1244	+	19.2679i	0.453772	+	0.785956i	−0.544845	+	0.838537i	$0.683411\pi$
$602$	0.437822	−	0.758330i	0.0178443	−	0.0309072i
$603$			12.4641i			0.507577i
$604$	22.6410	+	13.0718i	0.921250	+	0.531884i
$605$		0			0
$606$		−	3.60770i		−	0.146553i
$607$	8.80385	−	15.2487i	0.357337	−	0.618926i	−0.630178	−	0.776451i	$-0.717018\pi$
$607$	8.80385	−	15.2487i	0.357337	−	0.618926i	0.987515	+	0.157525i	$0.0503514\pi$
$608$	16.0000	+	27.7128i	0.648886	+	1.12390i
$609$	−10.5622	+	6.09808i	−0.428001	+	0.247107i
$610$		0			0
$611$	−0.686533	−	0.169873i	−0.0277742	−	0.00687233i
$612$	−9.85641			−0.398422
$613$	1.91858	−	1.10770i	0.0774909	−	0.0447394i	−0.460754	−	0.887528i	$-0.652421\pi$
$613$	1.91858	−	1.10770i	0.0774909	−	0.0447394i	0.538245	+	0.842789i	$0.319088\pi$
$614$	4.41858	+	7.65321i	0.178320	+	0.308859i
$615$		0			0
$616$		−	39.2154i		−	1.58003i
$617$	21.3397	+	12.3205i	0.859106	+	0.496005i	0.863713	−	0.503984i	$-0.168133\pi$
$617$	21.3397	+	12.3205i	0.859106	+	0.496005i	−0.00460693	+	0.999989i	$0.501466\pi$
$618$	−2.02628	−	1.16987i	−0.0815089	−	0.0470592i
$619$			11.5885i			0.465779i	0.972503	+	0.232890i	$0.0748181\pi$
$619$			11.5885i			0.465779i	−0.972503	+	0.232890i	$0.925182\pi$
$620$		0			0
$621$	−0.267949	−	0.464102i	−0.0107524	−	0.0186238i
$622$	−6.46410	+	3.73205i	−0.259187	+	0.149642i
$623$	−5.66025			−0.226773
$624$	2.78461	+	2.67949i	0.111474	+	0.107266i
$625$		0			0
$626$	6.84936	−	3.95448i	0.273756	−	0.158053i
$627$	9.46410	+	16.3923i	0.377960	+	0.654646i
$628$	7.12436	−	12.3397i	0.284293	−	0.492409i
$629$			26.9282i			1.07370i
$630$		0			0
$631$	−9.01666	−	5.20577i	−0.358948	−	0.207238i	0.309671	−	0.950844i	$-0.399781\pi$
$631$	−9.01666	−	5.20577i	−0.358948	−	0.207238i	−0.668619	+	0.743605i	$0.733114\pi$
$632$			4.88973i			0.194503i
$633$	5.76795	−	9.99038i	0.229255	−	0.397082i
$634$	6.39230	+	11.0718i	0.253871	+	0.439717i
$635$		0			0
$636$	−10.1436			−0.402220
$637$	−44.7846	+	12.9282i	−1.77443	+	0.512234i
$638$	−6.92820			−0.274290
$639$	11.0263	−	6.36603i	0.436193	−	0.251836i
$640$		0			0
$641$	19.3923	−	33.5885i	0.765950	−	1.32666i	−0.173793	−	0.984782i	$-0.555602\pi$
$641$	19.3923	−	33.5885i	0.765950	−	1.32666i	0.939743	−	0.341882i	$-0.111064\pi$
$642$			12.5359i			0.494752i
$643$	3.27757	+	1.89230i	0.129255	+	0.0746252i	0.563233	−	0.826298i	$-0.309557\pi$
$643$	3.27757	+	1.89230i	0.129255	+	0.0746252i	−0.433978	+	0.900923i	$0.642891\pi$
$644$	−3.03332	−	1.75129i	−0.119530	−	0.0690104i
$645$		0			0
$646$	−13.4641	+	23.3205i	−0.529738	+	0.917533i
$647$	−1.00000	−	1.73205i	−0.0393141	−	0.0680939i	0.845699	−	0.533660i	$-0.179184\pi$
$647$	−1.00000	−	1.73205i	−0.0393141	−	0.0680939i	−0.885013	+	0.465566i	$0.845851\pi$
$648$	2.19615	−	1.26795i	0.0862730	−	0.0498097i
$649$	−25.1769			−0.988280
$650$		0			0
$651$	−14.2679			−0.559205
$652$	7.01924	−	4.05256i	0.274895	−	0.158710i
$653$	−0.241670	−	0.418584i	−0.00945727	−	0.0163805i	0.861258	−	0.508168i	$-0.169677\pi$
$653$	−0.241670	−	0.418584i	−0.00945727	−	0.0163805i	−0.870715	+	0.491787i	$0.836344\pi$
$654$	−3.02628	+	5.24167i	−0.118337	+	0.204966i
$655$		0			0
$656$	−4.88973	−	2.82309i	−0.190912	−	0.110223i
$657$	−13.3301	−	7.69615i	−0.520058	−	0.300256i
$658$			0.641016i			0.0249894i
$659$	18.5885	−	32.1962i	0.724103	−	1.25418i	−0.235238	−	0.971938i	$-0.575587\pi$
$659$	18.5885	−	32.1962i	0.724103	−	1.25418i	0.959342	−	0.282246i	$-0.0910796\pi$
$660$		0			0
$661$	18.2321	−	10.5263i	0.709145	−	0.409425i	−0.101600	−	0.994825i	$-0.532396\pi$
$661$	18.2321	−	10.5263i	0.709145	−	0.409425i	0.810744	+	0.585401i	$0.199063\pi$
$662$	5.94744			0.231154
$663$	−5.83013	+	23.5622i	−0.226423	+	0.915079i
$664$	6.43078			0.249563
$665$		0			0
$666$	−1.46410	−	2.53590i	−0.0567328	−	0.0982641i
$667$	−0.732051	+	1.26795i	−0.0283451	+	0.0490952i
$668$			25.5692i			0.989303i
$669$	10.2679	+	5.92820i	0.396982	+	0.229198i
$670$		0			0
$671$		−	15.4641i		−	0.596985i
$672$	13.0718	−	22.6410i	0.504256	−	0.873396i
$673$	9.33013	+	16.1603i	0.359650	+	0.622932i	0.987902	−	0.155078i	$-0.0495628\pi$
$673$	9.33013	+	16.1603i	0.359650	+	0.622932i	−0.628252	+	0.778010i	$0.716229\pi$
$674$	19.6865	−	11.3660i	0.758297	−	0.437803i
$675$		0			0
$676$	16.1051	−	10.1436i	0.619428	−	0.390138i
$677$	−32.7846			−1.26001			−0.630007	−	0.776589i	$-0.716948\pi$
$677$	−32.7846			−1.26001			−0.630007	+	0.776589i	$0.716948\pi$
$678$	12.3397	−	7.12436i	0.473905	−	0.273609i
$679$	36.7487	+	63.6506i	1.41029	+	2.44269i
$680$		0			0
$681$		−	11.6603i		−	0.446822i
$682$	−7.01924	−	4.05256i	−0.268781	−	0.155180i
$683$	−35.7391	−	20.6340i	−1.36752	−	0.789537i	−0.376908	−	0.926251i	$-0.623013\pi$
$683$	−35.7391	−	20.6340i	−1.36752	−	0.789537i	−0.990611	+	0.136714i	$0.956346\pi$
$684$			8.00000i			0.305888i
$685$		0			0
$686$	9.68653	+	16.7776i	0.369834	+	0.640571i
$687$	−15.9282	+	9.19615i	−0.607699	+	0.350855i
$688$	−0.287187			−0.0109489
$689$	−6.00000	+	24.2487i	−0.228582	+	0.923802i
$690$		0			0
$691$	−37.7487	+	21.7942i	−1.43603	+	0.829092i	−0.997571	−	0.0696602i	$-0.977808\pi$
$691$	−37.7487	+	21.7942i	−1.43603	+	0.829092i	−0.438458	+	0.898752i	$0.644475\pi$
$692$	−2.39230	−	4.14359i	−0.0909418	−	0.157516i
$693$	7.73205	−	13.3923i	0.293716	−	0.508732i
$694$		−	4.78461i		−	0.181621i
$695$		0			0
$696$	−6.00000	−	3.46410i	−0.227429	−	0.131306i
$697$		−	35.4641i		−	1.34330i
$698$	10.9737	−	19.0070i	0.415361	−	0.719427i
$699$	11.9282	+	20.6603i	0.451166	+	0.781443i
$700$		0			0
$701$	8.78461			0.331790			0.165895	−	0.986143i	$-0.446949\pi$
$701$	8.78461			0.331790			0.165895	+	0.986143i	$0.446949\pi$
$702$	−0.732051	−	2.53590i	−0.0276295	−	0.0957113i
$703$	21.8564			0.824330
$704$	6.43078	−	3.71281i	0.242369	−	0.139932i
$705$		0			0
$706$	13.5167	−	23.4115i	0.508706	−	0.881105i
$707$		−	22.0000i		−	0.827395i
$708$	−9.21539	−	5.32051i	−0.346336	−	0.199957i
$709$	−26.5526	−	15.3301i	−0.997202	−	0.575735i	−0.0897830	−	0.995961i	$-0.528617\pi$
$709$	−26.5526	−	15.3301i	−0.997202	−	0.575735i	−0.907419	+	0.420226i	$0.861951\pi$
$710$		0			0
$711$	−0.964102	+	1.66987i	−0.0361566	+	0.0626251i
$712$	−1.60770	−	2.78461i	−0.0602509	−	0.104358i
$713$	−1.48334	+	0.856406i	−0.0555515	+	0.0320727i
$714$	22.0000			0.823329
$715$		0			0
$716$	−13.3590			−0.499249
$717$	−4.73205	+	2.73205i	−0.176722	+	0.102030i
$718$	12.3205	+	21.3397i	0.459797	+	0.796392i
$719$	17.3660	−	30.0788i	0.647643	−	1.12175i	−0.336041	−	0.941847i	$-0.609088\pi$
$719$	17.3660	−	30.0788i	0.647643	−	1.12175i	0.983684	−	0.179904i	$-0.0575787\pi$
$720$		0			0
$721$	−12.3564	−	7.13397i	−0.460177	−	0.265683i
$722$	6.88269	+	3.97372i	0.256147	+	0.147887i
$723$			1.60770i			0.0597908i
$724$	−10.6410	+	18.4308i	−0.395470	+	0.684975i
$725$		0			0
$726$	0.633975	−	0.366025i	0.0235290	−	0.0135845i
$727$	−6.26795			−0.232465			−0.116233	−	0.993222i	$-0.537082\pi$
$727$	−6.26795			−0.232465			−0.116233	+	0.993222i	$0.537082\pi$
$728$	−29.4115	−	28.3013i	−1.09006	−	1.04891i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−0.901924	−	1.56218i	−0.0333589	−	0.0577792i
$732$	3.26795	−	5.66025i	0.120787	−	0.209209i
$733$			2.32051i			0.0857099i	0.999081	+	0.0428550i	$0.0136453\pi$
$733$			2.32051i			0.0857099i	−0.999081	+	0.0428550i	$0.986355\pi$
$734$	−11.4904	−	6.63397i	−0.424118	−	0.244864i
$735$		0			0
$736$		−	3.13844i		−	0.115684i
$737$	−21.5885	+	37.3923i	−0.795221	+	1.37736i
$738$	1.92820	+	3.33975i	0.0709781	+	0.122938i
$739$	9.00000	−	5.19615i	0.331070	−	0.191144i	−0.325246	−	0.945629i	$-0.605447\pi$
$739$	9.00000	−	5.19615i	0.331070	−	0.191144i	0.656316	+	0.754486i	$0.272114\pi$
$740$		0			0
$741$	19.1244	+	4.73205i	0.702551	+	0.173836i
$742$	22.6410			0.831178
$743$	−34.5622	+	19.9545i	−1.26796	+	0.732059i	−0.974602	−	0.223943i	$-0.928107\pi$
$743$	−34.5622	+	19.9545i	−1.26796	+	0.732059i	−0.293361	+	0.956002i	$0.594774\pi$
$744$	−4.05256	−	7.01924i	−0.148574	−	0.257338i
$745$		0			0
$746$			1.37307i			0.0502716i
$747$	2.19615	+	1.26795i	0.0803530	+	0.0463918i
$748$	−29.5692	−	17.0718i	−1.08116	−	0.624207i
$749$			76.4449i			2.79323i
$750$		0			0
$751$	−10.6603	−	18.4641i	−0.388998	−	0.673765i	0.603317	−	0.797502i	$-0.293845\pi$
$751$	−10.6603	−	18.4641i	−0.388998	−	0.673765i	−0.992315	+	0.123737i	$0.960512\pi$
$752$	0.182069	−	0.105118i	0.00663938	−	0.00383325i
$753$		0			0
$754$	−5.00000	+	5.19615i	−0.182089	+	0.189233i
$755$		0			0
$756$	5.66025	−	3.26795i	0.205861	−	0.118854i
$757$	13.4641	+	23.3205i	0.489361	+	0.847598i	0.999925	−	0.0122415i	$-0.00389668\pi$
$757$	13.4641	+	23.3205i	0.489361	+	0.847598i	−0.510564	+	0.859840i	$0.670563\pi$
$758$	−7.22243	+	12.5096i	−0.262331	+	0.454370i
$759$		−	1.85641i		−	0.0673833i
$760$		0			0
$761$	−5.07180	−	2.92820i	−0.183852	−	0.106147i	0.405249	−	0.914206i	$-0.367185\pi$
$761$	−5.07180	−	2.92820i	−0.183852	−	0.106147i	−0.589101	+	0.808059i	$0.700518\pi$
$762$		−	10.7321i		−	0.388781i
$763$	−18.4545	+	31.9641i	−0.668097	+	1.15718i
$764$	20.1436	+	34.8897i	0.728770	+	1.26227i
$765$		0			0
$766$	−6.10512			−0.220587
$767$	−18.1699	+	18.8827i	−0.656076	+	0.681814i
$768$	11.7128			0.422650
$769$	43.6410	−	25.1962i	1.57374	−	0.908596i	0.578030	−	0.816015i	$-0.303822\pi$
$769$	43.6410	−	25.1962i	1.57374	−	0.908596i	0.995705	−	0.0925811i	$-0.0295117\pi$
$770$		0			0
$771$	5.36603	−	9.29423i	0.193253	−	0.334723i
$772$		−	8.88973i		−	0.319948i
$773$	−6.80385	−	3.92820i	−0.244717	−	0.141288i	0.372626	−	0.927982i	$-0.378458\pi$
$773$	−6.80385	−	3.92820i	−0.244717	−	0.141288i	−0.617343	+	0.786694i	$0.711791\pi$
$774$	0.169873	+	0.0980762i	0.00610596	+	0.00352528i
$775$		0			0
$776$	−20.8756	+	36.1577i	−0.749392	+	1.29798i
$777$	−8.92820	−	15.4641i	−0.320298	−	0.554772i
$778$	−11.0718	+	6.39230i	−0.396943	+	0.229175i
$779$	−28.7846			−1.03132
$780$		0			0
$781$	44.1051			1.57821
$782$	2.28719	−	1.32051i	0.0817896	−	0.0472213i
$783$	−1.36603	−	2.36603i	−0.0488178	−	0.0845548i
$784$	6.92820	−	12.0000i	0.247436	−	0.428571i
$785$		0			0
$786$	0.803848	+	0.464102i	0.0286723	+	0.0165540i
$787$	18.6506	+	10.7679i	0.664823	+	0.383836i	0.794112	−	0.607771i	$-0.207936\pi$
$787$	18.6506	+	10.7679i	0.664823	+	0.383836i	−0.129289	+	0.991607i	$0.541269\pi$
$788$			4.28719i			0.152725i
$789$	3.16987	−	5.49038i	0.112850	−	0.195463i
$790$		0			0
$791$	75.2487	−	43.4449i	2.67554	−	1.54472i
$792$	8.78461			0.312148
$793$	−11.5981	−	11.1603i	−0.411860	−	0.396312i
$794$	−17.8038			−0.631835
$795$		0			0
$796$	−10.9808	−	19.0192i	−0.389203	−	0.674119i
$797$	15.2224	−	26.3660i	0.539206	−	0.933933i	−0.459741	−	0.888053i	$-0.652058\pi$
$797$	15.2224	−	26.3660i	0.539206	−	0.933933i	0.998947	−	0.0458794i	$-0.0146090\pi$
$798$		−	17.8564i		−	0.632110i
$799$	1.14359	+	0.660254i	0.0404574	+	0.0233581i
$800$		0			0
$801$		−	1.26795i		−	0.0448008i
$802$	−5.60770	+	9.71281i	−0.198015	+	0.342971i
$803$	−26.6603	−	46.1769i	−0.940820	−	1.62955i
$804$	−15.8038	+	9.12436i	−0.557359	+	0.321791i
$805$		0			0
$806$	−8.10512	+	2.33975i	−0.285491	+	0.0824140i
$807$	−15.6603			−0.551267
$808$	10.8231	−	6.24871i	0.380755	−	0.219829i
$809$	−18.0000	−	31.1769i	−0.632846	−	1.09612i	−0.986967	−	0.160922i	$-0.948553\pi$
$809$	−18.0000	−	31.1769i	−0.632846	−	1.09612i	0.354121	−	0.935200i	$-0.384780\pi$
$810$		0			0
$811$		−	0.947441i		−	0.0332692i	−0.999862	−	0.0166346i	$-0.994705\pi$
$811$		−	0.947441i		−	0.0332692i	0.999862	−	0.0166346i	$-0.00529520\pi$
$812$	−15.4641	−	8.92820i	−0.542684	−	0.313319i
$813$	−3.23205	−	1.86603i	−0.113353	−	0.0654444i
$814$		−	10.1436i		−	0.355533i
$815$		0			0
$816$	−3.60770	−	6.24871i	−0.126295	−	0.218749i
$817$	−1.26795	+	0.732051i	−0.0443599	+	0.0256112i
$818$	1.94744			0.0680907
$819$	−4.46410	−	15.4641i	−0.155988	−	0.540359i
$820$		0			0
$821$	−0.803848	+	0.464102i	−0.0280545	+	0.0161973i	−0.513962	−	0.857813i	$-0.671823\pi$
$821$	−0.803848	+	0.464102i	−0.0280545	+	0.0161973i	0.485907	+	0.874010i	$0.338489\pi$
$822$	3.33975	+	5.78461i	0.116487	+	0.201761i
$823$	6.58846	−	11.4115i	0.229659	−	0.397781i	−0.728048	−	0.685526i	$-0.759572\pi$
$823$	6.58846	−	11.4115i	0.229659	−	0.397781i	0.957707	+	0.287745i	$0.0929055\pi$
$824$		−	8.10512i		−	0.282355i
$825$		0			0
$826$	20.5692	+	11.8756i	0.715695	+	0.413207i
$827$		−	2.58846i		−	0.0900095i	−0.998987	−	0.0450047i	$-0.985670\pi$
$827$		−	2.58846i		−	0.0900095i	0.998987	−	0.0450047i	$-0.0143303\pi$
$828$	0.392305	−	0.679492i	0.0136335	−	0.0236140i
$829$	−19.0885	−	33.0622i	−0.662970	−	1.14830i	−0.979832	−	0.199825i	$-0.935963\pi$
$829$	−19.0885	−	33.0622i	−0.662970	−	1.14830i	0.316862	−	0.948472i	$-0.397371\pi$
$830$		0			0
$831$	−20.2487			−0.702420
$832$	1.85641	−	7.50258i	0.0643593	−	0.260105i
$833$	87.0333			3.01553
$834$	11.3660	−	6.56218i	0.393573	−	0.227230i
$835$		0			0
$836$	−13.8564	+	24.0000i	−0.479234	+	0.830057i
$837$		−	3.19615i		−	0.110475i
$838$	−12.9615	−	7.48334i	−0.447748	−	0.258508i
$839$	−17.7846	−	10.2679i	−0.613993	−	0.354489i	0.160534	−	0.987030i	$-0.448678\pi$
$839$	−17.7846	−	10.2679i	−0.613993	−	0.354489i	−0.774527	+	0.632541i	$0.782012\pi$
$840$		0			0
$841$	10.7679	−	18.6506i	0.371309	−	0.643125i
$842$	8.63397	+	14.9545i	0.297546	+	0.515366i
$843$	18.2942	−	10.5622i	0.630087	−	0.363781i
$844$	16.8897			0.581368
$845$		0			0
$846$	−0.143594			−0.00493685
$847$	3.86603	−	2.23205i	0.132838	−	0.0766942i
$848$	−3.71281	−	6.43078i	−0.127499	−	0.220834i
$849$	−0.133975	+	0.232051i	−0.00459800	+	0.00796396i
$850$		0			0
$851$	−1.85641	−	1.07180i	−0.0636368	−	0.0367407i
$852$	16.1436	+	9.32051i	0.553070	+	0.319315i
$853$		−	16.6077i		−	0.568637i	−0.958730	−	0.284318i	$-0.908233\pi$
$853$		−	16.6077i		−	0.568637i	0.958730	−	0.284318i	$-0.0917673\pi$
$854$	−7.29423	+	12.6340i	−0.249603	+	0.432326i
$855$		0			0
$856$	−37.6077	+	21.7128i	−1.28540	+	0.742129i
$857$	−17.1244			−0.584957			−0.292478	−	0.956272i	$-0.594480\pi$
$857$	−17.1244			−0.584957			−0.292478	+	0.956272i	$0.594480\pi$
$858$	2.19615	−	8.87564i	0.0749754	−	0.303010i
$859$	7.78461			0.265607			0.132804	−	0.991142i	$-0.457602\pi$
$859$	7.78461			0.265607			0.132804	+	0.991142i	$0.457602\pi$
$860$		0			0
$861$	11.7583	+	20.3660i	0.400723	+	0.694072i
$862$	−8.53590	+	14.7846i	−0.290734	+	0.503566i
$863$		−	34.3923i		−	1.17073i	−0.810771	−	0.585364i	$-0.800952\pi$
$863$		−	34.3923i		−	1.17073i	0.810771	−	0.585364i	$-0.199048\pi$
$864$	5.07180	+	2.92820i	0.172546	+	0.0996195i
$865$		0			0
$866$			3.51666i			0.119501i
$867$	14.1603	−	24.5263i	0.480907	−	0.832956i
$868$	−10.4449	−	18.0910i	−0.354522	−	0.614050i
$869$	−5.78461	+	3.33975i	−0.196229	+	0.113293i
$870$		0			0
$871$	12.4641	+	43.1769i	0.422330	+	1.46299i
$872$	−20.9667			−0.710021
$873$	−14.2583	+	8.23205i	−0.482571	+	0.278613i
$874$	−1.07180	−	1.85641i	−0.0362541	−	0.0627939i
$875$		0			0
$876$		−	22.5359i		−	0.761417i
$877$	16.1436	+	9.32051i	0.545130	+	0.314731i	0.747156	−	0.664649i	$-0.231419\pi$
$877$	16.1436	+	9.32051i	0.545130	+	0.314731i	−0.202025	+	0.979380i	$0.564752\pi$
$878$	9.75833	+	5.63397i	0.329328	+	0.190137i
$879$		−	24.5885i		−	0.829348i
$880$		0			0
$881$	−12.5885	−	21.8038i	−0.424116	−	0.734590i	0.572222	−	0.820099i	$-0.306082\pi$
$881$	−12.5885	−	21.8038i	−0.424116	−	0.734590i	−0.996337	+	0.0855088i	$0.972748\pi$
$882$	−8.19615	+	4.73205i	−0.275979	+	0.159336i
$883$	−0.660254			−0.0222193			−0.0111097	−	0.999938i	$-0.503536\pi$
$883$	−0.660254			−0.0222193			−0.0111097	+	0.999938i	$0.503536\pi$
$884$	−34.1436	+	9.85641i	−1.14837	+	0.331507i
$885$		0			0
$886$	−1.98076	+	1.14359i	−0.0665450	+	0.0384198i
$887$	−1.49038	−	2.58142i	−0.0500421	−	0.0866755i	0.839919	−	0.542711i	$-0.182602\pi$
$887$	−1.49038	−	2.58142i	−0.0500421	−	0.0866755i	−0.889961	+	0.456036i	$0.849269\pi$
$888$	5.07180	−	8.78461i	0.170198	−	0.294792i
$889$		−	65.4449i		−	2.19495i
$890$		0			0
$891$	3.00000	+	1.73205i	0.100504	+	0.0580259i
$892$			17.3590i			0.581222i
$893$	0.535898	−	0.928203i	0.0179332	−	0.0310611i
$894$	−1.46410	−	2.53590i	−0.0489669	−	0.0848131i
$895$		0			0
$896$	45.2820			1.51277
$897$	−1.39230	−	1.33975i	−0.0464877	−	0.0447328i
$898$	8.10512			0.270471
$899$	−7.56218	+	4.36603i	−0.252213	+	0.145615i
$900$		0			0
$901$	23.3205	−	40.3923i	0.776919	−	1.34566i
$902$			13.3590i			0.444806i
$903$	1.03590	+	0.598076i	0.0344725	+	0.0199027i
$904$	42.7461	+	24.6795i	1.42172	+	0.820828i
$905$		0			0
$906$	6.53590	−	11.3205i	0.217141	−	0.376099i
$907$	12.2679	+	21.2487i	0.407351	+	0.705552i	0.994592	−	0.103860i	$-0.0331194\pi$
$907$	12.2679	+	21.2487i	0.407351	+	0.705552i	−0.587241	+	0.809412i	$0.699786\pi$
$908$	14.7846	−	8.53590i	0.490645	−	0.283274i
$909$	4.92820			0.163458
$910$		0			0
$911$	−7.71281			−0.255537			−0.127768	−	0.991804i	$-0.540781\pi$
$911$	−7.71281			−0.255537			−0.127768	+	0.991804i	$0.540781\pi$
$912$	−5.07180	+	2.92820i	−0.167944	+	0.0969625i
$913$	4.39230	+	7.60770i	0.145364	+	0.251778i
$914$	1.97372	−	3.41858i	0.0652849	−	0.113077i
$915$		0			0
$916$	−23.3205	−	13.4641i	−0.770531	−	0.444866i
$917$	4.90192	+	2.83013i	0.161876	+	0.0934590i
$918$			4.92820i			0.162655i
$919$	9.53590	−	16.5167i	0.314560	−	0.544834i	−0.664784	−	0.747036i	$-0.731476\pi$
$919$	9.53590	−	16.5167i	0.314560	−	0.544834i	0.979344	+	0.202202i	$0.0648096\pi$
$920$		0			0
$921$	−10.4545	+	6.03590i	−0.344487	+	0.198890i
$922$	8.43078			0.277653
$923$	31.8301	−	33.0788i	1.04770	−	1.08880i
$924$	22.6410			0.744835
$925$		0			0
$926$	−0.653212	−	1.13140i	−0.0214659	−	0.0371800i
$927$	1.59808	−	2.76795i	0.0524877	−	0.0909114i
$928$		−	16.0000i		−	0.525226i
$929$	−13.2679	−	7.66025i	−0.435307	−	0.251325i	0.266298	−	0.963891i	$-0.414200\pi$
$929$	−13.2679	−	7.66025i	−0.435307	−	0.251325i	−0.701605	+	0.712566i	$0.747533\pi$
$930$		0			0
$931$		−	70.6410i		−	2.31517i
$932$	−17.4641	+	30.2487i	−0.572056	+	0.990829i
$933$	−5.09808	−	8.83013i	−0.166904	−	0.289085i
$934$	−15.0000	+	8.66025i	−0.490815	+	0.283372i
$935$		0			0
$936$	6.33975	−	6.58846i	0.207221	−	0.215350i
$937$	−32.2487			−1.05352			−0.526760	−	0.850014i	$-0.676593\pi$
$937$	−32.2487			−1.05352			−0.526760	+	0.850014i	$0.676593\pi$
$938$	35.2750	−	20.3660i	1.15177	−	0.664974i
$939$	5.40192	+	9.35641i	0.176285	+	0.305335i
$940$		0			0
$941$		−	9.41154i		−	0.306808i	−0.988164	−	0.153404i	$-0.950976\pi$
$941$		−	9.41154i		−	0.306808i	0.988164	−	0.153404i	$-0.0490235\pi$
$942$	−6.16987	−	3.56218i	−0.201025	−	0.116062i
$943$	2.44486	+	1.41154i	0.0796157	+	0.0459662i
$944$		−	7.78976i		−	0.253535i
$945$		0			0
$946$	0.339746	+	0.588457i	0.0110461	+	0.0191324i
$947$	4.68653	−	2.70577i	0.152292	−	0.0879258i	−0.421918	−	0.906634i	$-0.638643\pi$
$947$	4.68653	−	2.70577i	0.152292	−	0.0879258i	0.574209	+	0.818708i	$0.305310\pi$
$948$	−2.82309			−0.0916896
$949$	−53.8731	−	13.3301i	−1.74879	−	0.432714i
$950$		0			0
$951$	−15.1244	+	8.73205i	−0.490441	+	0.283156i
$952$	38.1051	+	66.0000i	1.23499	+	2.13907i
$953$	−12.1244	+	21.0000i	−0.392746	+	0.680257i	−0.992811	−	0.119695i	$-0.961808\pi$
$953$	−12.1244	+	21.0000i	−0.392746	+	0.680257i	0.600064	+	0.799952i	$0.295142\pi$
$954$			5.07180i			0.164205i
$955$		0			0
$956$	−6.92820	−	4.00000i	−0.224074	−	0.129369i
$957$		−	9.46410i		−	0.305931i
$958$	−13.1436	+	22.7654i	−0.424650	+	0.735516i
$959$	20.3660	+	35.2750i	0.657653	+	1.13909i
$960$		0			0
$961$	20.7846			0.670471
$962$	−7.60770	−	7.32051i	−0.245282	−	0.236023i
$963$	−17.1244			−0.551825
$964$	−2.03848	+	1.17691i	−0.0656549	+	0.0379059i
$965$		0			0
$966$	−0.875644	+	1.51666i	−0.0281734	+	0.0487978i
$967$		−	16.2487i		−	0.522523i	−0.965268	−	0.261262i	$-0.915861\pi$
$967$		−	16.2487i		−	0.522523i	0.965268	−	0.261262i	$-0.0841385\pi$
$968$	2.19615	+	1.26795i	0.0705870	+	0.0407534i
$969$	−31.8564	−	18.3923i	−1.02338	−	0.590846i
$970$		0			0
$971$	−30.5885	+	52.9808i	−0.981630	+	1.70023i	−0.325584	+	0.945513i	$0.605561\pi$
$971$	−30.5885	+	52.9808i	−0.981630	+	1.70023i	−0.656047	+	0.754720i	$0.727773\pi$
$972$	0.732051	+	1.26795i	0.0234805	+	0.0406695i
$973$	69.3109	−	40.0167i	2.22201	−	1.28288i
$974$	−15.2154			−0.487533
$975$		0			0
$976$	4.78461			0.153152
$977$	12.9282	−	7.46410i	0.413610	−	0.238798i	−0.278730	−	0.960370i	$-0.589913\pi$
$977$	12.9282	−	7.46410i	0.413610	−	0.238798i	0.692340	+	0.721572i	$0.256580\pi$
$978$	−2.02628	−	3.50962i	−0.0647933	−	0.112225i
$979$	2.19615	−	3.80385i	0.0701893	−	0.121571i
$980$		0			0
$981$	−7.16025	−	4.13397i	−0.228609	−	0.131988i
$982$	4.51666	+	2.60770i	0.144132	+	0.0832149i
$983$		−	3.85641i		−	0.123000i	−0.998107	−	0.0615001i	$-0.980412\pi$
$983$		−	3.85641i		−	0.123000i	0.998107	−	0.0615001i	$-0.0195885\pi$
$984$	−6.67949	+	11.5692i	−0.212934	+	0.368813i
$985$		0			0
$986$	11.6603	−	6.73205i	0.371338	−	0.214392i
$987$	−0.875644			−0.0278721
$988$	8.00000	+	27.7128i	0.254514	+	0.881662i
$989$	0.143594			0.00456601
$990$		0			0
$991$	−7.53590	−	13.0526i	−0.239386	−	0.414628i	0.721152	−	0.692776i	$-0.243613\pi$
$991$	−7.53590	−	13.0526i	−0.239386	−	0.414628i	−0.960538	+	0.278148i	$0.910279\pi$
$992$	9.35898	−	16.2102i	0.297148	−	0.514675i
$993$			8.12436i			0.257819i
$994$	−36.0333	−	20.8038i	−1.14291	−	0.659858i
$995$		0			0
$996$			3.71281i			0.117645i
$997$	−13.2058	+	22.8731i	−0.418231	+	0.724397i	−0.995762	−	0.0919717i	$-0.970683\pi$
$997$	−13.2058	+	22.8731i	−0.418231	+	0.724397i	0.577531	+	0.816369i	$0.304016\pi$
$998$	0.143594	+	0.248711i	0.00454537	+	0.00787282i
$999$	3.46410	−	2.00000i	0.109599	−	0.0632772i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bc.h.751.1		4
5.2	odd	4		975.2.w.a.49.2		4
5.3	odd	4		975.2.w.f.49.1		4
5.4	even	2		195.2.bb.a.166.2	yes	4
13.4	even	6	inner	975.2.bc.h.901.1		4
15.14	odd	2		585.2.bu.a.361.1		4
65.4	even	6		195.2.bb.a.121.2	✓	4
65.17	odd	12		975.2.w.f.199.1		4
65.24	odd	12		2535.2.a.n.1.2		2
65.43	odd	12		975.2.w.a.199.2		4
65.54	odd	12		2535.2.a.s.1.1		2
195.89	even	12		7605.2.a.bk.1.1		2
195.119	even	12		7605.2.a.y.1.2		2
195.134	odd	6		585.2.bu.a.316.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bb.a.121.2	✓	4	65.4	even	6
195.2.bb.a.166.2	yes	4	5.4	even	2
585.2.bu.a.316.1		4	195.134	odd	6
585.2.bu.a.361.1		4	15.14	odd	2
975.2.w.a.49.2		4	5.2	odd	4
975.2.w.a.199.2		4	65.43	odd	12
975.2.w.f.49.1		4	5.3	odd	4
975.2.w.f.199.1		4	65.17	odd	12
975.2.bc.h.751.1		4	1.1	even	1	trivial
975.2.bc.h.901.1		4	13.4	even	6	inner
2535.2.a.n.1.2		2	65.24	odd	12
2535.2.a.s.1.1		2	65.54	odd	12
7605.2.a.y.1.2		2	195.119	even	12
7605.2.a.bk.1.1		2	195.89	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.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.633975 - 0.366025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.732051 + 1.26795i) q^{4} +(0.633975 + 0.366025i) q^{6} +(3.86603 + 2.23205i) q^{7} +2.53590i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.633975 - 0.366025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.732051 + 1.26795i) q^{4} +(0.633975 + 0.366025i) q^{6} +(3.86603 + 2.23205i) q^{7} +2.53590i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-3.00000 + 1.73205i) q^{11} -1.46410 q^{12} +(-0.866025 + 3.50000i) q^{13} +3.26795 q^{14} +(-0.535898 - 0.928203i) q^{16} +(3.36603 - 5.83013i) q^{17} +0.732051i q^{18} +(-4.73205 - 2.73205i) q^{19} +4.46410i q^{21} +(-1.26795 + 2.19615i) q^{22} +(0.267949 + 0.464102i) q^{23} +(-2.19615 + 1.26795i) q^{24} +(0.732051 + 2.53590i) q^{26} -1.00000 q^{27} +(-5.66025 + 3.26795i) q^{28} +(1.36603 + 2.36603i) q^{29} +3.19615i q^{31} +(-5.07180 - 2.92820i) q^{32} +(-3.00000 - 1.73205i) q^{33} -4.92820i q^{34} +(-0.732051 - 1.26795i) q^{36} +(-3.46410 + 2.00000i) q^{37} -4.00000 q^{38} +(-3.46410 + 1.00000i) q^{39} +(4.56218 - 2.63397i) q^{41} +(1.63397 + 2.83013i) q^{42} +(0.133975 - 0.232051i) q^{43} -5.07180i q^{44} +(0.339746 + 0.196152i) q^{46} +0.196152i q^{47} +(0.535898 - 0.928203i) q^{48} +(6.46410 + 11.1962i) q^{49} +6.73205 q^{51} +(-3.80385 - 3.66025i) q^{52} +6.92820 q^{53} +(-0.633975 + 0.366025i) q^{54} +(-5.66025 + 9.80385i) q^{56} -5.46410i q^{57} +(1.73205 + 1.00000i) q^{58} +(6.29423 + 3.63397i) q^{59} +(-2.23205 + 3.86603i) q^{61} +(1.16987 + 2.02628i) q^{62} +(-3.86603 + 2.23205i) q^{63} -2.14359 q^{64} -2.53590 q^{66} +(10.7942 - 6.23205i) q^{67} +(4.92820 + 8.53590i) q^{68} +(-0.267949 + 0.464102i) q^{69} +(-11.0263 - 6.36603i) q^{71} +(-2.19615 - 1.26795i) q^{72} +15.3923i q^{73} +(-1.46410 + 2.53590i) q^{74} +(6.92820 - 4.00000i) q^{76} -15.4641 q^{77} +(-1.83013 + 1.90192i) q^{78} +1.92820 q^{79} +(-0.500000 - 0.866025i) q^{81} +(1.92820 - 3.33975i) q^{82} -2.53590i q^{83} +(-5.66025 - 3.26795i) q^{84} -0.196152i q^{86} +(-1.36603 + 2.36603i) q^{87} +(-4.39230 - 7.60770i) q^{88} +(-1.09808 + 0.633975i) q^{89} +(-11.1603 + 11.5981i) q^{91} -0.784610 q^{92} +(-2.76795 + 1.59808i) q^{93} +(0.0717968 + 0.124356i) q^{94} -5.85641i q^{96} +(14.2583 + 8.23205i) q^{97} +(8.19615 + 4.73205i) q^{98} -3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{2} + 2 q^{3} + 4 q^{4} + 6 q^{6} + 12 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q + 6 * q^2 + 2 * q^3 + 4 * q^4 + 6 * q^6 + 12 * q^7 - 2 * q^9	\( 4 q + 6 q^{2} + 2 q^{3} + 4 q^{4} + 6 q^{6} + 12 q^{7} - 2 q^{9} - 12 q^{11} + 8 q^{12} + 20 q^{14} - 16 q^{16} + 10 q^{17} - 12 q^{19} - 12 q^{22} + 8 q^{23} + 12 q^{24} - 4 q^{26} - 4 q^{27} + 12 q^{28} + 2 q^{29} - 48 q^{32} - 12 q^{33} + 4 q^{36} - 16 q^{38} - 6 q^{41} + 10 q^{42} + 4 q^{43} + 36 q^{46} + 16 q^{48} + 12 q^{49} + 20 q^{51} - 36 q^{52} - 6 q^{54} + 12 q^{56} - 6 q^{59} - 2 q^{61} + 22 q^{62} - 12 q^{63} - 64 q^{64} - 24 q^{66} + 12 q^{67} - 8 q^{68} - 8 q^{69} - 6 q^{71} + 12 q^{72} + 8 q^{74} - 48 q^{77} + 10 q^{78} - 20 q^{79} - 2 q^{81} - 20 q^{82} + 12 q^{84} - 2 q^{87} + 24 q^{88} + 6 q^{89} - 10 q^{91} + 80 q^{92} - 18 q^{93} + 28 q^{94} + 12 q^{97} + 12 q^{98}+O(q^{100}) \) 4 * q + 6 * q^2 + 2 * q^3 + 4 * q^4 + 6 * q^6 + 12 * q^7 - 2 * q^9 - 12 * q^11 + 8 * q^12 + 20 * q^14 - 16 * q^16 + 10 * q^17 - 12 * q^19 - 12 * q^22 + 8 * q^23 + 12 * q^24 - 4 * q^26 - 4 * q^27 + 12 * q^28 + 2 * q^29 - 48 * q^32 - 12 * q^33 + 4 * q^36 - 16 * q^38 - 6 * q^41 + 10 * q^42 + 4 * q^43 + 36 * q^46 + 16 * q^48 + 12 * q^49 + 20 * q^51 - 36 * q^52 - 6 * q^54 + 12 * q^56 - 6 * q^59 - 2 * q^61 + 22 * q^62 - 12 * q^63 - 64 * q^64 - 24 * q^66 + 12 * q^67 - 8 * q^68 - 8 * q^69 - 6 * q^71 + 12 * q^72 + 8 * q^74 - 48 * q^77 + 10 * q^78 - 20 * q^79 - 2 * q^81 - 20 * q^82 + 12 * q^84 - 2 * q^87 + 24 * q^88 + 6 * q^89 - 10 * q^91 + 80 * q^92 - 18 * q^93 + 28 * q^94 + 12 * q^97 + 12 * q^98

Introduction

L-functions

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