LMFDB - Embedded newform 670.2.e.e.431.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(171,670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(670, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("670.171");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.34997693543$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{193})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 49x^{2} + 48x + 2304 $ x^4 - x^3 + 49x^2 + 48x + 2304
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			431.2
Root			$3.72311 - 6.44862i$ of defining polynomial
Character	$\chi$	$=$	670.431
Dual form			670.2.e.e.171.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.00000 - 1.73205i) q^{7} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.00000 - 1.73205i) q^{7} +1.00000 q^{8} -2.00000 q^{9} +(0.500000 - 0.866025i) q^{10} +(-0.500000 - 0.866025i) q^{12} +(-1.00000 + 1.73205i) q^{13} +2.00000 q^{14} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.72311 - 6.44862i) q^{17} +(1.00000 - 1.73205i) q^{18} +(2.72311 - 4.71657i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-1.00000 - 1.73205i) q^{21} +1.00000 q^{24} +1.00000 q^{25} +(-1.00000 - 1.73205i) q^{26} -5.00000 q^{27} +(-1.00000 + 1.73205i) q^{28} +(-3.00000 - 5.19615i) q^{29} +(0.500000 - 0.866025i) q^{30} +(-3.22311 - 5.58259i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.72311 + 6.44862i) q^{34} +(1.00000 + 1.73205i) q^{35} +(1.00000 + 1.73205i) q^{36} +(4.22311 - 7.31464i) q^{37} +(2.72311 + 4.71657i) q^{38} +(-1.00000 + 1.73205i) q^{39} -1.00000 q^{40} +(2.22311 + 3.85054i) q^{41} +2.00000 q^{42} -11.4462 q^{43} +2.00000 q^{45} +(-0.500000 + 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(3.72311 - 6.44862i) q^{51} +2.00000 q^{52} -4.44622 q^{53} +(2.50000 - 4.33013i) q^{54} +(-1.00000 - 1.73205i) q^{56} +(2.72311 - 4.71657i) q^{57} +6.00000 q^{58} +13.4462 q^{59} +(0.500000 + 0.866025i) q^{60} +(-4.00000 + 6.92820i) q^{61} +6.44622 q^{62} +(2.00000 + 3.46410i) q^{63} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +(-7.22311 + 3.85054i) q^{67} -7.44622 q^{68} -2.00000 q^{70} +(2.22311 + 3.85054i) q^{71} -2.00000 q^{72} +(-7.72311 + 13.3768i) q^{73} +(4.22311 + 7.31464i) q^{74} +1.00000 q^{75} -5.44622 q^{76} +(-1.00000 - 1.73205i) q^{78} +(-4.00000 - 6.92820i) q^{79} +(0.500000 - 0.866025i) q^{80} +1.00000 q^{81} -4.44622 q^{82} +(5.22311 - 9.04669i) q^{83} +(-1.00000 + 1.73205i) q^{84} +(-3.72311 + 6.44862i) q^{85} +(5.72311 - 9.91272i) q^{86} +(-3.00000 - 5.19615i) q^{87} +11.8924 q^{89} +(-1.00000 + 1.73205i) q^{90} +4.00000 q^{91} +(-3.22311 - 5.58259i) q^{93} +(-2.72311 + 4.71657i) q^{95} +(-0.500000 - 0.866025i) q^{96} +(-4.72311 + 8.18067i) q^{97} +(1.50000 + 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 8 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 4 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8 - 8 * q^9	$ 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 8 q^{9} + 2 q^{10} - 2 q^{12} - 4 q^{13} + 8 q^{14} - 4 q^{15} - 2 q^{16} + q^{17} + 4 q^{18} - 3 q^{19} + 2 q^{20} - 4 q^{21} + 4 q^{24} + 4 q^{25} - 4 q^{26} - 20 q^{27} - 4 q^{28} - 12 q^{29} + 2 q^{30} + q^{31} - 2 q^{32} + q^{34} + 4 q^{35} + 4 q^{36} + 3 q^{37} - 3 q^{38} - 4 q^{39} - 4 q^{40} - 5 q^{41} + 8 q^{42} - 18 q^{43} + 8 q^{45} - 2 q^{48} + 6 q^{49} - 2 q^{50} + q^{51} + 8 q^{52} + 10 q^{53} + 10 q^{54} - 4 q^{56} - 3 q^{57} + 24 q^{58} + 26 q^{59} + 2 q^{60} - 16 q^{61} - 2 q^{62} + 8 q^{63} + 4 q^{64} + 4 q^{65} - 15 q^{67} - 2 q^{68} - 8 q^{70} - 5 q^{71} - 8 q^{72} - 17 q^{73} + 3 q^{74} + 4 q^{75} + 6 q^{76} - 4 q^{78} - 16 q^{79} + 2 q^{80} + 4 q^{81} + 10 q^{82} + 7 q^{83} - 4 q^{84} - q^{85} + 9 q^{86} - 12 q^{87} - 8 q^{89} - 4 q^{90} + 16 q^{91} + q^{93} + 3 q^{95} - 2 q^{96} - 5 q^{97} + 6 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 4 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8 - 8 * q^9 + 2 * q^10 - 2 * q^12 - 4 * q^13 + 8 * q^14 - 4 * q^15 - 2 * q^16 + q^17 + 4 * q^18 - 3 * q^19 + 2 * q^20 - 4 * q^21 + 4 * q^24 + 4 * q^25 - 4 * q^26 - 20 * q^27 - 4 * q^28 - 12 * q^29 + 2 * q^30 + q^31 - 2 * q^32 + q^34 + 4 * q^35 + 4 * q^36 + 3 * q^37 - 3 * q^38 - 4 * q^39 - 4 * q^40 - 5 * q^41 + 8 * q^42 - 18 * q^43 + 8 * q^45 - 2 * q^48 + 6 * q^49 - 2 * q^50 + q^51 + 8 * q^52 + 10 * q^53 + 10 * q^54 - 4 * q^56 - 3 * q^57 + 24 * q^58 + 26 * q^59 + 2 * q^60 - 16 * q^61 - 2 * q^62 + 8 * q^63 + 4 * q^64 + 4 * q^65 - 15 * q^67 - 2 * q^68 - 8 * q^70 - 5 * q^71 - 8 * q^72 - 17 * q^73 + 3 * q^74 + 4 * q^75 + 6 * q^76 - 4 * q^78 - 16 * q^79 + 2 * q^80 + 4 * q^81 + 10 * q^82 + 7 * q^83 - 4 * q^84 - q^85 + 9 * q^86 - 12 * q^87 - 8 * q^89 - 4 * q^90 + 16 * q^91 + q^93 + 3 * q^95 - 2 * q^96 - 5 * q^97 + 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/670\mathbb{Z}\right)^\times$.

$n$	$471$	$537$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.00000			0.577350			0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000			0.577350			0.288675	+	0.957427i	$0.406785\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	0.612801	−	0.790237i	$-0.290043\pi$
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	−0.990766	+	0.135583i	$0.956709\pi$
$8$	1.00000			0.353553
$9$	−2.00000			−0.666667
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$	2.00000			0.534522
$15$	−1.00000			−0.258199
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.72311	−	6.44862i	0.902987	−	1.56402i	0.0793903	−	0.996844i	$-0.474703\pi$
$17$	3.72311	−	6.44862i	0.902987	−	1.56402i	0.823597	−	0.567176i	$-0.191964\pi$
$18$	1.00000	−	1.73205i	0.235702	−	0.408248i
$19$	2.72311	−	4.71657i	0.624725	−	1.08205i	−0.363870	−	0.931450i	$-0.618545\pi$
$19$	2.72311	−	4.71657i	0.624725	−	1.08205i	0.988594	−	0.150605i	$-0.0481221\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	−1.00000	−	1.73205i	−0.218218	−	0.377964i
$22$		0			0
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	1.00000			0.204124
$25$	1.00000			0.200000
$26$	−1.00000	−	1.73205i	−0.196116	−	0.339683i
$27$	−5.00000			−0.962250
$28$	−1.00000	+	1.73205i	−0.188982	+	0.327327i
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$	−3.22311	−	5.58259i	−0.578888	−	1.00266i	−0.995607	−	0.0936280i	$-0.970154\pi$
$31$	−3.22311	−	5.58259i	−0.578888	−	1.00266i	0.416719	−	0.909035i	$-0.363180\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	3.72311	+	6.44862i	0.638508	+	1.10593i
$35$	1.00000	+	1.73205i	0.169031	+	0.292770i
$36$	1.00000	+	1.73205i	0.166667	+	0.288675i
$37$	4.22311	−	7.31464i	0.694275	−	1.20252i	−0.276149	−	0.961115i	$-0.589058\pi$
$37$	4.22311	−	7.31464i	0.694275	−	1.20252i	0.970424	−	0.241405i	$-0.0776083\pi$
$38$	2.72311	+	4.71657i	0.441747	+	0.765128i
$39$	−1.00000	+	1.73205i	−0.160128	+	0.277350i
$40$	−1.00000			−0.158114
$41$	2.22311	+	3.85054i	0.347192	+	0.601354i	0.985749	−	0.168220i	$-0.0538020\pi$
$41$	2.22311	+	3.85054i	0.347192	+	0.601354i	−0.638558	+	0.769574i	$0.720469\pi$
$42$	2.00000			0.308607
$43$	−11.4462			−1.74553			−0.872766	−	0.488138i	$-0.837676\pi$
$43$	−11.4462			−1.74553			−0.872766	+	0.488138i	$0.837676\pi$
$44$		0			0
$45$	2.00000			0.298142
$46$		0			0
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	3.72311	−	6.44862i	0.521340	−	0.902987i
$52$	2.00000			0.277350
$53$	−4.44622			−0.610736			−0.305368	−	0.952234i	$-0.598779\pi$
$53$	−4.44622			−0.610736			−0.305368	+	0.952234i	$0.598779\pi$
$54$	2.50000	−	4.33013i	0.340207	−	0.589256i
$55$		0			0
$56$	−1.00000	−	1.73205i	−0.133631	−	0.231455i
$57$	2.72311	−	4.71657i	0.360685	−	0.624725i
$58$	6.00000			0.787839
$59$	13.4462			1.75055			0.875274	−	0.483626i	$-0.160681\pi$
$59$	13.4462			1.75055			0.875274	+	0.483626i	$0.160681\pi$
$60$	0.500000	+	0.866025i	0.0645497	+	0.111803i
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$	6.44622			0.818671
$63$	2.00000	+	3.46410i	0.251976	+	0.436436i
$64$	1.00000			0.125000
$65$	1.00000	−	1.73205i	0.124035	−	0.214834i
$66$		0			0
$67$	−7.22311	+	3.85054i	−0.882443	+	0.470418i
$67$	−7.22311	+	3.85054i	−0.882443	+	0.470418i
$68$	−7.44622			−0.902987
$69$		0			0
$70$	−2.00000			−0.239046
$71$	2.22311	+	3.85054i	0.263835	+	0.456975i	0.967258	−	0.253796i	$-0.0816793\pi$
$71$	2.22311	+	3.85054i	0.263835	+	0.456975i	−0.703423	+	0.710772i	$0.748346\pi$
$72$	−2.00000			−0.235702
$73$	−7.72311	+	13.3768i	−0.903922	+	1.56564i	−0.0815637	+	0.996668i	$0.525991\pi$
$73$	−7.72311	+	13.3768i	−0.903922	+	1.56564i	−0.822358	+	0.568970i	$0.807342\pi$
$74$	4.22311	+	7.31464i	0.490927	+	0.850310i
$75$	1.00000			0.115470
$76$	−5.44622			−0.624725
$77$		0			0
$78$	−1.00000	−	1.73205i	−0.113228	−	0.196116i
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	1.00000			0.111111
$82$	−4.44622			−0.491003
$83$	5.22311	−	9.04669i	0.573311	−	0.993004i	−0.422912	−	0.906171i	$-0.638992\pi$
$83$	5.22311	−	9.04669i	0.573311	−	0.993004i	0.996223	−	0.0868329i	$-0.0276746\pi$
$84$	−1.00000	+	1.73205i	−0.109109	+	0.188982i
$85$	−3.72311	+	6.44862i	−0.403828	+	0.699451i
$86$	5.72311	−	9.91272i	0.617139	−	1.06892i
$87$	−3.00000	−	5.19615i	−0.321634	−	0.557086i
$88$		0			0
$89$	11.8924			1.26060			0.630298	−	0.776353i	$-0.282933\pi$
$89$	11.8924			1.26060			0.630298	+	0.776353i	$0.282933\pi$
$90$	−1.00000	+	1.73205i	−0.105409	+	0.182574i
$91$	4.00000			0.419314
$92$		0			0
$93$	−3.22311	−	5.58259i	−0.334221	−	0.578888i
$94$		0			0
$95$	−2.72311	+	4.71657i	−0.279385	+	0.483910i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	−4.72311	+	8.18067i	−0.479559	+	0.830621i	−0.999725	−	0.0234442i	$-0.992537\pi$
$97$	−4.72311	+	8.18067i	−0.479559	+	0.830621i	0.520166	+	0.854065i	$0.325870\pi$
$98$	1.50000	+	2.59808i	0.151523	+	0.262445i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$	3.72311	+	6.44862i	0.368643	+	0.638508i
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	0.947576	−	0.319531i	$-0.103525\pi$
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	−0.750510	+	0.660859i	$0.770192\pi$
$104$	−1.00000	+	1.73205i	−0.0980581	+	0.169842i
$105$	1.00000	+	1.73205i	0.0975900	+	0.169031i
$106$	2.22311	−	3.85054i	0.215928	−	0.373998i
$107$	10.4462			1.00987			0.504937	−	0.863156i	$-0.331516\pi$
$107$	10.4462			1.00987			0.504937	+	0.863156i	$0.331516\pi$
$108$	2.50000	+	4.33013i	0.240563	+	0.416667i
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$		0			0
$111$	4.22311	−	7.31464i	0.400840	−	0.694275i
$112$	2.00000			0.188982
$113$	2.27689	+	3.94369i	0.214192	+	0.370991i	0.953022	−	0.302900i	$-0.0979549\pi$
$113$	2.27689	+	3.94369i	0.214192	+	0.370991i	−0.738831	+	0.673891i	$0.764622\pi$
$114$	2.72311	+	4.71657i	0.255043	+	0.441747i
$115$		0			0
$116$	−3.00000	+	5.19615i	−0.278543	+	0.482451i
$117$	2.00000	−	3.46410i	0.184900	−	0.320256i
$118$	−6.72311	+	11.6448i	−0.618913	+	1.07199i
$119$	−14.8924			−1.36519
$120$	−1.00000			−0.0912871
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	−4.00000	−	6.92820i	−0.362143	−	0.627250i
$123$	2.22311	+	3.85054i	0.200451	+	0.347192i
$124$	−3.22311	+	5.58259i	−0.289444	+	0.501332i
$125$	−1.00000			−0.0894427
$126$	−4.00000			−0.356348
$127$	5.00000	+	8.66025i	0.443678	+	0.768473i	0.997959	−	0.0638564i	$-0.0203400\pi$
$127$	5.00000	+	8.66025i	0.443678	+	0.768473i	−0.554281	+	0.832330i	$0.687007\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−11.4462			−1.00778
$130$	1.00000	+	1.73205i	0.0877058	+	0.151911i
$131$	8.89244			0.776936			0.388468	−	0.921462i	$-0.373004\pi$
$131$	8.89244			0.776936			0.388468	+	0.921462i	$0.373004\pi$
$132$		0			0
$133$	−10.8924			−0.944495
$134$	0.276889	−	8.18067i	0.0239196	−	0.706702i
$135$	5.00000			0.430331
$136$	3.72311	−	6.44862i	0.319254	−	0.552964i
$137$	−7.44622			−0.636174			−0.318087	−	0.948062i	$-0.603040\pi$
$137$	−7.44622			−0.636174			−0.318087	+	0.948062i	$0.603040\pi$
$138$		0			0
$139$	−8.55378			−0.725522			−0.362761	−	0.931882i	$-0.618166\pi$
$139$	−8.55378			−0.725522			−0.362761	+	0.931882i	$0.618166\pi$
$140$	1.00000	−	1.73205i	0.0845154	−	0.146385i
$141$		0			0
$142$	−4.44622			−0.373119
$143$		0			0
$144$	1.00000	−	1.73205i	0.0833333	−	0.144338i
$145$	3.00000	+	5.19615i	0.249136	+	0.431517i
$146$	−7.72311	−	13.3768i	−0.639169	−	1.10707i
$147$	1.50000	−	2.59808i	0.123718	−	0.214286i
$148$	−8.44622			−0.694275
$149$	−12.0000			−0.983078			−0.491539	−	0.870855i	$-0.663566\pi$
$149$	−12.0000			−0.983078			−0.491539	+	0.870855i	$0.663566\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	−9.22311	+	15.9749i	−0.750566	+	1.30002i	0.196982	+	0.980407i	$0.436886\pi$
$151$	−9.22311	+	15.9749i	−0.750566	+	1.30002i	−0.947549	+	0.319612i	$0.896448\pi$
$152$	2.72311	−	4.71657i	0.220873	−	0.382564i
$153$	−7.44622	+	12.8972i	−0.601991	+	1.04268i
$154$		0			0
$155$	3.22311	+	5.58259i	0.258887	+	0.448405i
$156$	2.00000			0.160128
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	0.438948	+	0.898513i	$0.355351\pi$
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$	8.00000			0.636446
$159$	−4.44622			−0.352608
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$		0			0
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	−9.94622	−	17.2274i	−0.779048	−	1.34935i	−0.932491	−	0.361194i	$-0.882369\pi$
$163$	−9.94622	−	17.2274i	−0.779048	−	1.34935i	0.153443	−	0.988158i	$-0.450964\pi$
$164$	2.22311	−	3.85054i	0.173596	−	0.300677i
$165$		0			0
$166$	5.22311	+	9.04669i	0.405392	+	0.702160i
$167$	−4.44622	−	7.70108i	−0.344059	−	0.595928i	0.641123	−	0.767438i	$-0.278469\pi$
$167$	−4.44622	−	7.70108i	−0.344059	−	0.595928i	−0.985182	+	0.171510i	$0.945135\pi$
$168$	−1.00000	−	1.73205i	−0.0771517	−	0.133631i
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	−3.72311	−	6.44862i	−0.285550	−	0.494586i
$171$	−5.44622	+	9.43313i	−0.416483	+	0.721370i
$172$	5.72311	+	9.91272i	0.436383	+	0.755838i
$173$	−12.6693	+	21.9439i	−0.963232	+	1.66837i	−0.248938	+	0.968519i	$0.580082\pi$
$173$	−12.6693	+	21.9439i	−0.963232	+	1.66837i	−0.714293	+	0.699847i	$0.753252\pi$
$174$	6.00000			0.454859
$175$	−1.00000	−	1.73205i	−0.0755929	−	0.130931i
$176$		0			0
$177$	13.4462			1.01068
$178$	−5.94622	+	10.2992i	−0.445688	+	0.771955i
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$	−1.00000	−	1.73205i	−0.0745356	−	0.129099i
$181$	−2.44622	−	4.23698i	−0.181826	−	0.314932i	0.760676	−	0.649131i	$-0.224868\pi$
$181$	−2.44622	−	4.23698i	−0.181826	−	0.314932i	−0.942502	+	0.334199i	$0.891534\pi$
$182$	−2.00000	+	3.46410i	−0.148250	+	0.256776i
$183$	−4.00000	+	6.92820i	−0.295689	+	0.512148i
$184$		0			0
$185$	−4.22311	+	7.31464i	−0.310489	+	0.537783i
$186$	6.44622			0.472660
$187$		0			0
$188$		0			0
$189$	5.00000	+	8.66025i	0.363696	+	0.629941i
$190$	−2.72311	−	4.71657i	−0.197555	−	0.342176i
$191$	5.22311	−	9.04669i	0.377931	−	0.654596i	−0.612830	−	0.790215i	$-0.709969\pi$
$191$	5.22311	−	9.04669i	0.377931	−	0.654596i	0.990761	+	0.135619i	$0.0433023\pi$
$192$	1.00000			0.0721688
$193$	−6.89244			−0.496129			−0.248064	−	0.968744i	$-0.579794\pi$
$193$	−6.89244			−0.496129			−0.248064	+	0.968744i	$0.579794\pi$
$194$	−4.72311	−	8.18067i	−0.339100	−	0.587338i
$195$	1.00000	−	1.73205i	0.0716115	−	0.124035i
$196$	−3.00000			−0.214286
$197$	−10.4462	−	18.0934i	−0.744263	−	1.28910i	−0.950539	−	0.310607i	$-0.899468\pi$
$197$	−10.4462	−	18.0934i	−0.744263	−	1.28910i	0.206276	−	0.978494i	$-0.433866\pi$
$198$		0			0
$199$	4.22311	−	7.31464i	0.299368	−	0.518521i	−0.676623	−	0.736329i	$-0.736557\pi$
$199$	4.22311	−	7.31464i	0.299368	−	0.518521i	0.975992	+	0.217808i	$0.0698907\pi$
$200$	1.00000			0.0707107
$201$	−7.22311	+	3.85054i	−0.509479	+	0.271596i
$202$	6.00000			0.422159
$203$	−6.00000	+	10.3923i	−0.421117	+	0.729397i
$204$	−7.44622			−0.521340
$205$	−2.22311	−	3.85054i	−0.155269	−	0.268933i
$206$	−4.00000			−0.278693
$207$		0			0
$208$	−1.00000	−	1.73205i	−0.0693375	−	0.120096i
$209$		0			0
$210$	−2.00000			−0.138013
$211$	11.7231	−	20.3050i	0.807052	−	1.39786i	−0.107845	−	0.994168i	$-0.534395\pi$
$211$	11.7231	−	20.3050i	0.807052	−	1.39786i	0.914897	−	0.403688i	$-0.132272\pi$
$212$	2.22311	+	3.85054i	0.152684	+	0.264456i
$213$	2.22311	+	3.85054i	0.152325	+	0.263835i
$214$	−5.22311	+	9.04669i	−0.357045	+	0.618419i
$215$	11.4462			0.780626
$216$	−5.00000			−0.340207
$217$	−6.44622	+	11.1652i	−0.437598	+	0.757942i
$218$	−7.00000	+	12.1244i	−0.474100	+	0.821165i
$219$	−7.72311	+	13.3768i	−0.521879	+	0.903922i
$220$		0			0
$221$	7.44622	+	12.8972i	0.500887	+	0.867562i
$222$	4.22311	+	7.31464i	0.283437	+	0.490927i
$223$	2.00000			0.133930			0.0669650	−	0.997755i	$-0.478668\pi$
$223$	2.00000			0.133930			0.0669650	+	0.997755i	$0.478668\pi$
$224$	−1.00000	+	1.73205i	−0.0668153	+	0.115728i
$225$	−2.00000			−0.133333
$226$	−4.55378			−0.302913
$227$	−4.50000	−	7.79423i	−0.298675	−	0.517321i	0.677158	−	0.735838i	$-0.263211\pi$
$227$	−4.50000	−	7.79423i	−0.298675	−	0.517321i	−0.975833	+	0.218517i	$0.929878\pi$
$228$	−5.44622			−0.360685
$229$	−4.00000	+	6.92820i	−0.264327	+	0.457829i	−0.967387	−	0.253302i	$-0.918483\pi$
$229$	−4.00000	+	6.92820i	−0.264327	+	0.457829i	0.703060	+	0.711131i	$0.251817\pi$
$230$		0			0
$231$		0			0
$232$	−3.00000	−	5.19615i	−0.196960	−	0.341144i
$233$	11.1693	+	19.3459i	0.731727	+	1.26739i	0.956144	+	0.292896i	$0.0946189\pi$
$233$	11.1693	+	19.3459i	0.731727	+	1.26739i	−0.224417	+	0.974493i	$0.572048\pi$
$234$	2.00000	+	3.46410i	0.130744	+	0.226455i
$235$		0			0
$236$	−6.72311	−	11.6448i	−0.437637	−	0.758010i
$237$	−4.00000	−	6.92820i	−0.259828	−	0.450035i
$238$	7.44622	−	12.8972i	0.482667	−	0.836004i
$239$	−7.44622	−	12.8972i	−0.481656	−	0.834253i	0.518122	−	0.855307i	$-0.326631\pi$
$239$	−7.44622	−	12.8972i	−0.481656	−	0.834253i	−0.999778	+	0.0210538i	$0.993298\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	3.55378			0.228919			0.114459	−	0.993428i	$-0.463486\pi$
$241$	3.55378			0.228919			0.114459	+	0.993428i	$0.463486\pi$
$242$	5.50000	+	9.52628i	0.353553	+	0.612372i
$243$	16.0000			1.02640
$244$	8.00000			0.512148
$245$	−1.50000	+	2.59808i	−0.0958315	+	0.165985i
$246$	−4.44622			−0.283481
$247$	5.44622	+	9.43313i	0.346535	+	0.600216i
$248$	−3.22311	−	5.58259i	−0.204668	−	0.354495i
$249$	5.22311	−	9.04669i	0.331001	−	0.573311i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	9.72311	−	16.8409i	0.613717	−	1.06299i	−0.376891	−	0.926258i	$-0.623007\pi$
$251$	9.72311	−	16.8409i	0.613717	−	1.06299i	0.990608	−	0.136732i	$-0.0436599\pi$
$252$	2.00000	−	3.46410i	0.125988	−	0.218218i
$253$		0			0
$254$	−10.0000			−0.627456
$255$	−3.72311	+	6.44862i	−0.233150	+	0.403828i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	−0.997374	−	0.0724199i	$-0.976928\pi$
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	0.435970	−	0.899961i	$-0.356405\pi$
$258$	5.72311	−	9.91272i	0.356305	−	0.617139i
$259$	−16.8924			−1.04965
$260$	−2.00000			−0.124035
$261$	6.00000	+	10.3923i	0.371391	+	0.643268i
$262$	−4.44622	+	7.70108i	−0.274689	+	0.475774i
$263$	20.8924			1.28828			0.644142	−	0.764906i	$-0.277215\pi$
$263$	20.8924			1.28828			0.644142	+	0.764906i	$0.277215\pi$
$264$		0			0
$265$	4.44622			0.273129
$266$	5.44622	−	9.43313i	0.333929	−	0.578383i
$267$	11.8924			0.727806
$268$	6.94622	+	4.33013i	0.424308	+	0.264505i
$269$		0			0			−	1.00000i	$-0.5\pi$
$269$		0			0				1.00000i	$0.5\pi$
$270$	−2.50000	+	4.33013i	−0.152145	+	0.263523i
$271$	−11.5538			−0.701842			−0.350921	−	0.936405i	$-0.614131\pi$
$271$	−11.5538			−0.701842			−0.350921	+	0.936405i	$0.614131\pi$
$272$	3.72311	+	6.44862i	0.225747	+	0.391005i
$273$	4.00000			0.242091
$274$	3.72311	−	6.44862i	0.224921	−	0.389575i
$275$		0			0
$276$		0			0
$277$	18.4462			1.10833			0.554163	−	0.832408i	$-0.313038\pi$
$277$	18.4462			1.10833			0.554163	+	0.832408i	$0.313038\pi$
$278$	4.27689	−	7.40779i	0.256511	−	0.444290i
$279$	6.44622	+	11.1652i	0.385925	+	0.668442i
$280$	1.00000	+	1.73205i	0.0597614	+	0.103510i
$281$	8.94622	−	15.4953i	0.533687	−	0.924373i	−0.465539	−	0.885027i	$-0.654139\pi$
$281$	8.94622	−	15.4953i	0.533687	−	0.924373i	0.999226	−	0.0393453i	$-0.0125272\pi$
$282$		0			0
$283$	18.3387			1.09012			0.545060	−	0.838397i	$-0.316507\pi$
$283$	18.3387			1.09012			0.545060	+	0.838397i	$0.316507\pi$
$284$	2.22311	−	3.85054i	0.131917	−	0.228488i
$285$	−2.72311	+	4.71657i	−0.161303	+	0.279385i
$286$		0			0
$287$	4.44622	−	7.70108i	0.262452	−	0.454581i
$288$	1.00000	+	1.73205i	0.0589256	+	0.102062i
$289$	−19.2231	−	33.2954i	−1.13077	−	1.95855i
$290$	−6.00000			−0.352332
$291$	−4.72311	+	8.18067i	−0.276874	+	0.479559i
$292$	15.4462			0.903922
$293$	16.4462			0.960799			0.480399	−	0.877050i	$-0.340492\pi$
$293$	16.4462			0.960799			0.480399	+	0.877050i	$0.340492\pi$
$294$	1.50000	+	2.59808i	0.0874818	+	0.151523i
$295$	−13.4462			−0.782869
$296$	4.22311	−	7.31464i	0.245463	−	0.425155i
$297$		0			0
$298$	6.00000	−	10.3923i	0.347571	−	0.602010i
$299$		0			0
$300$	−0.500000	−	0.866025i	−0.0288675	−	0.0500000i
$301$	11.4462	+	19.8254i	0.659749	+	1.14272i
$302$	−9.22311	−	15.9749i	−0.530730	−	0.919252i
$303$	−3.00000	−	5.19615i	−0.172345	−	0.298511i
$304$	2.72311	+	4.71657i	0.156181	+	0.270514i
$305$	4.00000	−	6.92820i	0.229039	−	0.396708i
$306$	−7.44622	−	12.8972i	−0.425672	−	0.737286i
$307$	4.94622	−	8.56711i	0.282296	−	0.488951i	−0.689654	−	0.724139i	$-0.742237\pi$
$307$	4.94622	−	8.56711i	0.282296	−	0.488951i	0.971950	+	0.235188i	$0.0755707\pi$
$308$		0			0
$309$	2.00000	+	3.46410i	0.113776	+	0.197066i
$310$	−6.44622			−0.366121
$311$	19.3387			1.09660			0.548298	−	0.836283i	$-0.315276\pi$
$311$	19.3387			1.09660			0.548298	+	0.836283i	$0.315276\pi$
$312$	−1.00000	+	1.73205i	−0.0566139	+	0.0980581i
$313$	33.4462			1.89049			0.945246	−	0.326358i	$-0.105822\pi$
$313$	33.4462			1.89049			0.945246	+	0.326358i	$0.105822\pi$
$314$	−7.00000	−	12.1244i	−0.395033	−	0.684217i
$315$	−2.00000	−	3.46410i	−0.112687	−	0.195180i
$316$	−4.00000	+	6.92820i	−0.225018	+	0.389742i
$317$	−9.77689	+	16.9341i	−0.549125	+	0.951112i	0.449210	+	0.893426i	$0.351706\pi$
$317$	−9.77689	+	16.9341i	−0.549125	+	0.951112i	−0.998335	+	0.0576858i	$0.981628\pi$
$318$	2.22311	−	3.85054i	0.124666	−	0.215928i
$319$		0			0
$320$	−1.00000			−0.0559017
$321$	10.4462			0.583051
$322$		0			0
$323$	−20.2769	−	35.1206i	−1.12824	−	1.95416i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−1.00000	+	1.73205i	−0.0554700	+	0.0960769i
$326$	19.8924			1.10174
$327$	14.0000			0.774202
$328$	2.22311	+	3.85054i	0.122751	+	0.212611i
$329$		0			0
$330$		0			0
$331$	−3.27689	−	5.67574i	−0.180114	−	0.311967i	0.761805	−	0.647806i	$-0.224313\pi$
$331$	−3.27689	−	5.67574i	−0.180114	−	0.311967i	−0.941919	+	0.335839i	$0.890980\pi$
$332$	−10.4462			−0.573311
$333$	−8.44622	+	14.6293i	−0.462850	+	0.801680i
$334$	8.89244			0.486573
$335$	7.22311	−	3.85054i	0.394641	−	0.210378i
$336$	2.00000			0.109109
$337$	−11.4462	+	19.8254i	−0.623515	+	1.07996i	0.365310	+	0.930886i	$0.380963\pi$
$337$	−11.4462	+	19.8254i	−0.623515	+	1.07996i	−0.988826	+	0.149075i	$0.952371\pi$
$338$	−9.00000			−0.489535
$339$	2.27689	+	3.94369i	0.123664	+	0.214192i
$340$	7.44622			0.403828
$341$		0			0
$342$	−5.44622	−	9.43313i	−0.294498	−	0.510085i
$343$	−20.0000			−1.07990
$344$	−11.4462			−0.617139
$345$		0			0
$346$	−12.6693	−	21.9439i	−0.681108	−	1.17971i
$347$	−9.72311	−	16.8409i	−0.521964	−	0.904068i	−0.999674	−	0.0255503i	$-0.991866\pi$
$347$	−9.72311	−	16.8409i	−0.521964	−	0.904068i	0.477710	−	0.878518i	$-0.341467\pi$
$348$	−3.00000	+	5.19615i	−0.160817	+	0.278543i
$349$	8.00000			0.428230			0.214115	−	0.976808i	$-0.431313\pi$
$349$	8.00000			0.428230			0.214115	+	0.976808i	$0.431313\pi$
$350$	2.00000			0.106904
$351$	5.00000	−	8.66025i	0.266880	−	0.462250i
$352$		0			0
$353$	7.44622	−	12.8972i	0.396322	−	0.686451i	−0.596947	−	0.802281i	$-0.703620\pi$
$353$	7.44622	−	12.8972i	0.396322	−	0.686451i	0.993269	+	0.115830i	$0.0369529\pi$
$354$	−6.72311	+	11.6448i	−0.357329	+	0.618913i
$355$	−2.22311	−	3.85054i	−0.117990	−	0.204366i
$356$	−5.94622	−	10.2992i	−0.315149	−	0.545854i
$357$	−14.8924			−0.788192
$358$	−6.00000	+	10.3923i	−0.317110	+	0.549250i
$359$	13.3387			0.703988			0.351994	−	0.936002i	$-0.385504\pi$
$359$	13.3387			0.703988			0.351994	+	0.936002i	$0.385504\pi$
$360$	2.00000			0.105409
$361$	−5.33067	−	9.23299i	−0.280561	−	0.485947i
$362$	4.89244			0.257141
$363$	5.50000	−	9.52628i	0.288675	−	0.500000i
$364$	−2.00000	−	3.46410i	−0.104828	−	0.181568i
$365$	7.72311	−	13.3768i	0.404246	−	0.700175i
$366$	−4.00000	−	6.92820i	−0.209083	−	0.362143i
$367$	−9.89244	−	17.1342i	−0.516381	−	0.894399i	−0.999819	−	0.0190200i	$-0.993945\pi$
$367$	−9.89244	−	17.1342i	−0.516381	−	0.894399i	0.483438	−	0.875379i	$-0.339388\pi$
$368$		0			0
$369$	−4.44622	−	7.70108i	−0.231461	−	0.400902i
$370$	−4.22311	−	7.31464i	−0.219549	−	0.380270i
$371$	4.44622	+	7.70108i	0.230836	+	0.399820i
$372$	−3.22311	+	5.58259i	−0.167111	+	0.289444i
$373$	5.77689	+	10.0059i	0.299116	+	0.518084i	0.975934	−	0.218066i	$-0.0699749\pi$
$373$	5.77689	+	10.0059i	0.299116	+	0.518084i	−0.676818	+	0.736150i	$0.736642\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	12.0000			0.618031
$378$	−10.0000			−0.514344
$379$	10.8924	−	18.8663i	0.559507	−	0.969095i	−0.438030	−	0.898960i	$-0.644324\pi$
$379$	10.8924	−	18.8663i	0.559507	−	0.969095i	0.997538	−	0.0701348i	$-0.0223429\pi$
$380$	5.44622			0.279385
$381$	5.00000	+	8.66025i	0.256158	+	0.443678i
$382$	5.22311	+	9.04669i	0.267238	+	0.462869i
$383$	3.00000	−	5.19615i	0.153293	−	0.265511i	−0.779143	−	0.626846i	$-0.784346\pi$
$383$	3.00000	−	5.19615i	0.153293	−	0.265511i	0.932436	+	0.361335i	$0.117679\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$		0			0
$386$	3.44622	−	5.96903i	0.175408	−	0.303816i
$387$	22.8924			1.16369
$388$	9.44622			0.479559
$389$	−4.44622	+	7.70108i	−0.225432	+	0.390460i	−0.956449	−	0.291899i	$-0.905713\pi$
$389$	−4.44622	+	7.70108i	−0.225432	+	0.390460i	0.731017	+	0.682360i	$0.239046\pi$
$390$	1.00000	+	1.73205i	0.0506370	+	0.0877058i
$391$		0			0
$392$	1.50000	−	2.59808i	0.0757614	−	0.131223i
$393$	8.89244			0.448564
$394$	20.8924			1.05255
$395$	4.00000	+	6.92820i	0.201262	+	0.348596i
$396$		0			0
$397$	−35.3387			−1.77360			−0.886798	−	0.462156i	$-0.847076\pi$
$397$	−35.3387			−1.77360			−0.886798	+	0.462156i	$0.847076\pi$
$398$	4.22311	+	7.31464i	0.211685	+	0.366650i
$399$	−10.8924			−0.545304
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	18.0000			0.898877			0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000			0.898877			0.449439	+	0.893311i	$0.351624\pi$
$402$	0.276889	−	8.18067i	0.0138100	−	0.408015i
$403$	12.8924			0.642218
$404$	−3.00000	+	5.19615i	−0.149256	+	0.258518i
$405$	−1.00000			−0.0496904
$406$	−6.00000	−	10.3923i	−0.297775	−	0.515761i
$407$		0			0
$408$	3.72311	−	6.44862i	0.184321	−	0.319254i
$409$	−6.22311	−	10.7787i	−0.307713	−	0.532975i	0.670149	−	0.742227i	$-0.266230\pi$
$409$	−6.22311	−	10.7787i	−0.307713	−	0.532975i	−0.977862	+	0.209252i	$0.932897\pi$
$410$	4.44622			0.219583
$411$	−7.44622			−0.367295
$412$	2.00000	−	3.46410i	0.0985329	−	0.170664i
$413$	−13.4462	−	23.2895i	−0.661645	−	1.14600i
$414$		0			0
$415$	−5.22311	+	9.04669i	−0.256392	+	0.444085i
$416$	2.00000			0.0980581
$417$	−8.55378			−0.418880
$418$		0			0
$419$	−9.72311	+	16.8409i	−0.475005	+	0.822733i	−0.999590	−	0.0286251i	$-0.990887\pi$
$419$	−9.72311	+	16.8409i	−0.475005	+	0.822733i	0.524585	+	0.851358i	$0.324220\pi$
$420$	1.00000	−	1.73205i	0.0487950	−	0.0845154i
$421$	−14.4462	+	25.0216i	−0.704066	+	1.21948i	0.262962	+	0.964806i	$0.415301\pi$
$421$	−14.4462	+	25.0216i	−0.704066	+	1.21948i	−0.967028	+	0.254671i	$0.918033\pi$
$422$	11.7231	+	20.3050i	0.570672	+	0.988433i
$423$		0			0
$424$	−4.44622			−0.215928
$425$	3.72311	−	6.44862i	0.180597	−	0.312804i
$426$	−4.44622			−0.215420
$427$	16.0000			0.774294
$428$	−5.22311	−	9.04669i	−0.252469	−	0.437288i
$429$		0			0
$430$	−5.72311	+	9.91272i	−0.275993	+	0.478034i
$431$	12.6693	+	21.9439i	0.610260	+	1.05700i	0.991196	+	0.132400i	$0.0422685\pi$
$431$	12.6693	+	21.9439i	0.610260	+	1.05700i	−0.380936	+	0.924601i	$0.624398\pi$
$432$	2.50000	−	4.33013i	0.120281	−	0.208333i
$433$	10.1693	+	17.6138i	0.488707	+	0.846465i	0.999916	−	0.0129914i	$-0.00413540\pi$
$433$	10.1693	+	17.6138i	0.488707	+	0.846465i	−0.511209	+	0.859457i	$0.670802\pi$
$434$	−6.44622	−	11.1652i	−0.309429	−	0.535946i
$435$	3.00000	+	5.19615i	0.143839	+	0.249136i
$436$	−7.00000	−	12.1244i	−0.335239	−	0.580651i
$437$		0			0
$438$	−7.72311	−	13.3768i	−0.369025	−	0.639169i
$439$	8.77689	−	15.2020i	0.418898	−	0.725553i	−0.576931	−	0.816793i	$-0.695750\pi$
$439$	8.77689	−	15.2020i	0.418898	−	0.725553i	0.995829	+	0.0912403i	$0.0290831\pi$
$440$		0			0
$441$	−3.00000	+	5.19615i	−0.142857	+	0.247436i
$442$	−14.8924			−0.708361
$443$	−2.94622	−	5.10301i	−0.139979	−	0.242451i	0.787509	−	0.616303i	$-0.211370\pi$
$443$	−2.94622	−	5.10301i	−0.139979	−	0.242451i	−0.927489	+	0.373852i	$0.878037\pi$
$444$	−8.44622			−0.400840
$445$	−11.8924			−0.563756
$446$	−1.00000	+	1.73205i	−0.0473514	+	0.0820150i
$447$	−12.0000			−0.567581
$448$	−1.00000	−	1.73205i	−0.0472456	−	0.0818317i
$449$	12.6693	+	21.9439i	0.597903	+	1.03560i	0.993130	+	0.117015i	$0.0373325\pi$
$449$	12.6693	+	21.9439i	0.597903	+	1.03560i	−0.395227	+	0.918583i	$0.629334\pi$
$450$	1.00000	−	1.73205i	0.0471405	−	0.0816497i
$451$		0			0
$452$	2.27689	−	3.94369i	0.107096	−	0.185495i
$453$	−9.22311	+	15.9749i	−0.433340	+	0.750566i
$454$	9.00000			0.422391
$455$	−4.00000			−0.187523
$456$	2.72311	−	4.71657i	0.127521	−	0.220873i
$457$	−6.27689	−	10.8719i	−0.293620	−	0.508566i	0.681043	−	0.732244i	$-0.261527\pi$
$457$	−6.27689	−	10.8719i	−0.293620	−	0.508566i	−0.974663	+	0.223678i	$0.928194\pi$
$458$	−4.00000	−	6.92820i	−0.186908	−	0.323734i
$459$	−18.6156	+	32.2431i	−0.868900	+	1.50498i
$460$		0			0
$461$	9.10756			0.424181			0.212091	−	0.977250i	$-0.431973\pi$
$461$	9.10756			0.424181			0.212091	+	0.977250i	$0.431973\pi$
$462$		0			0
$463$	13.8924	−	24.0624i	0.645637	−	1.11828i	−0.338517	−	0.940960i	$-0.609925\pi$
$463$	13.8924	−	24.0624i	0.645637	−	1.11828i	0.984154	−	0.177315i	$-0.0567412\pi$
$464$	6.00000			0.278543
$465$	3.22311	+	5.58259i	0.149468	+	0.258887i
$466$	−22.3387			−1.03482
$467$	−5.22311	+	9.04669i	−0.241697	+	0.418631i	−0.961198	−	0.275860i	$-0.911037\pi$
$467$	−5.22311	+	9.04669i	−0.241697	+	0.418631i	0.719501	+	0.694491i	$0.244371\pi$
$468$	−4.00000			−0.184900
$469$	13.8924	+	8.66025i	0.641493	+	0.399893i
$470$		0			0
$471$	−7.00000	+	12.1244i	−0.322543	+	0.558661i
$472$	13.4462			0.618913
$473$		0			0
$474$	8.00000			0.367452
$475$	2.72311	−	4.71657i	0.124945	−	0.216411i
$476$	7.44622	+	12.8972i	0.341297	+	0.591144i
$477$	8.89244			0.407157
$478$	14.8924			0.681165
$479$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$479$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$480$	0.500000	+	0.866025i	0.0228218	+	0.0395285i
$481$	8.44622	+	14.6293i	0.385115	+	0.667038i
$482$	−1.77689	+	3.07766i	−0.0809351	+	0.140184i
$483$		0			0
$484$	−11.0000			−0.500000
$485$	4.72311	−	8.18067i	0.214465	−	0.371465i
$486$	−8.00000	+	13.8564i	−0.362887	+	0.628539i
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	−0.625859	−	0.779936i	$-0.715252\pi$
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	0.988374	+	0.152042i	$0.0485850\pi$
$488$	−4.00000	+	6.92820i	−0.181071	+	0.313625i
$489$	−9.94622	−	17.2274i	−0.449784	−	0.779048i
$490$	−1.50000	−	2.59808i	−0.0677631	−	0.117369i
$491$	−4.33867			−0.195801			−0.0979006	−	0.995196i	$-0.531213\pi$
$491$	−4.33867			−0.195801			−0.0979006	+	0.995196i	$0.531213\pi$
$492$	2.22311	−	3.85054i	0.100226	−	0.173596i
$493$	−44.6773			−2.01217
$494$	−10.8924			−0.490074
$495$		0			0
$496$	6.44622			0.289444
$497$	4.44622	−	7.70108i	0.199440	−	0.345441i
$498$	5.22311	+	9.04669i	0.234053	+	0.405392i
$499$	−6.27689	+	10.8719i	−0.280992	+	0.486693i	−0.971629	−	0.236509i	$-0.923997\pi$
$499$	−6.27689	+	10.8719i	−0.280992	+	0.486693i	0.690637	+	0.723201i	$0.257330\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	−4.44622	−	7.70108i	−0.198643	−	0.344059i
$502$	9.72311	+	16.8409i	0.433964	+	0.751647i
$503$	1.44622	+	2.50493i	0.0644839	+	0.111689i	0.896465	−	0.443115i	$-0.146127\pi$
$503$	1.44622	+	2.50493i	0.0644839	+	0.111689i	−0.831981	+	0.554804i	$0.812793\pi$
$504$	2.00000	+	3.46410i	0.0890871	+	0.154303i
$505$	3.00000	+	5.19615i	0.133498	+	0.231226i
$506$		0			0
$507$	4.50000	+	7.79423i	0.199852	+	0.346154i
$508$	5.00000	−	8.66025i	0.221839	−	0.384237i
$509$	18.0000			0.797836			0.398918	−	0.916987i	$-0.369386\pi$
$509$	18.0000			0.797836			0.398918	+	0.916987i	$0.369386\pi$
$510$	−3.72311	−	6.44862i	−0.164862	−	0.285550i
$511$	30.8924			1.36660
$512$	1.00000			0.0441942
$513$	−13.6156	+	23.5828i	−0.601141	+	1.04121i
$514$	18.0000			0.793946
$515$	−2.00000	−	3.46410i	−0.0881305	−	0.152647i
$516$	5.72311	+	9.91272i	0.251946	+	0.436383i
$517$		0			0
$518$	8.44622	−	14.6293i	0.371106	−	0.642774i
$519$	−12.6693	+	21.9439i	−0.556122	+	0.963232i
$520$	1.00000	−	1.73205i	0.0438529	−	0.0759555i
$521$	28.3387			1.24154			0.620770	−	0.783993i	$-0.286820\pi$
$521$	28.3387			1.24154			0.620770	+	0.783993i	$0.286820\pi$
$522$	−12.0000			−0.525226
$523$	18.3924	−	31.8566i	0.804245	−	1.39299i	−0.112554	−	0.993646i	$-0.535903\pi$
$523$	18.3924	−	31.8566i	0.804245	−	1.39299i	0.916799	−	0.399348i	$-0.130764\pi$
$524$	−4.44622	−	7.70108i	−0.194234	−	0.336423i
$525$	−1.00000	−	1.73205i	−0.0436436	−	0.0755929i
$526$	−10.4462	+	18.0934i	−0.455477	+	0.788909i
$527$	−48.0000			−2.09091
$528$		0			0
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	−2.22311	+	3.85054i	−0.0965658	+	0.167257i
$531$	−26.8924			−1.16703
$532$	5.44622	+	9.43313i	0.236124	+	0.408978i
$533$	−8.89244			−0.385175
$534$	−5.94622	+	10.2992i	−0.257318	+	0.445688i
$535$	−10.4462			−0.451630
$536$	−7.22311	+	3.85054i	−0.311991	+	0.166318i
$537$	12.0000			0.517838
$538$		0			0
$539$		0			0
$540$	−2.50000	−	4.33013i	−0.107583	−	0.186339i
$541$	−42.6773			−1.83484			−0.917421	−	0.397918i	$-0.869733\pi$
$541$	−42.6773			−1.83484			−0.917421	+	0.397918i	$0.869733\pi$
$542$	5.77689	−	10.0059i	0.248139	−	0.429789i
$543$	−2.44622	−	4.23698i	−0.104977	−	0.181826i
$544$	−7.44622			−0.319254
$545$	−14.0000			−0.599694
$546$	−2.00000	+	3.46410i	−0.0855921	+	0.148250i
$547$	2.77689	+	4.80971i	0.118731	+	0.205648i	0.919265	−	0.393639i	$-0.128784\pi$
$547$	2.77689	+	4.80971i	0.118731	+	0.205648i	−0.800534	+	0.599287i	$0.795451\pi$
$548$	3.72311	+	6.44862i	0.159043	+	0.275471i
$549$	8.00000	−	13.8564i	0.341432	−	0.591377i
$550$		0			0
$551$	−32.6773			−1.39210
$552$		0			0
$553$	−8.00000	+	13.8564i	−0.340195	+	0.589234i
$554$	−9.22311	+	15.9749i	−0.391852	+	0.678708i
$555$	−4.22311	+	7.31464i	−0.179261	+	0.310489i
$556$	4.27689	+	7.40779i	0.181380	+	0.314160i
$557$	−9.66933	−	16.7478i	−0.409703	−	0.709626i	0.585153	−	0.810923i	$-0.301034\pi$
$557$	−9.66933	−	16.7478i	−0.409703	−	0.709626i	−0.994856	+	0.101297i	$0.967701\pi$
$558$	−12.8924			−0.545781
$559$	11.4462	−	19.8254i	0.484124	−	0.838527i
$560$	−2.00000			−0.0845154
$561$		0			0
$562$	8.94622	+	15.4953i	0.377374	+	0.653630i
$563$	−0.107556			−0.00453295			−0.00226647	−	0.999997i	$-0.500721\pi$
$563$	−0.107556			−0.00453295			−0.00226647	+	0.999997i	$0.500721\pi$
$564$		0			0
$565$	−2.27689	−	3.94369i	−0.0957894	−	0.165912i
$566$	−9.16933	+	15.8818i	−0.385416	+	0.667560i
$567$	−1.00000	−	1.73205i	−0.0419961	−	0.0727393i
$568$	2.22311	+	3.85054i	0.0932797	+	0.161565i
$569$	7.50000	+	12.9904i	0.314416	+	0.544585i	0.979313	−	0.202350i	$-0.0648579\pi$
$569$	7.50000	+	12.9904i	0.314416	+	0.544585i	−0.664897	+	0.746935i	$0.731525\pi$
$570$	−2.72311	−	4.71657i	−0.114059	−	0.197555i
$571$	20.7231	+	35.8935i	0.867235	+	1.50210i	0.864811	+	0.502098i	$0.167438\pi$
$571$	20.7231	+	35.8935i	0.867235	+	1.50210i	0.00242469	+	0.999997i	$0.499228\pi$
$572$		0			0
$573$	5.22311	−	9.04669i	0.218199	−	0.377931i
$574$	4.44622	+	7.70108i	0.185582	+	0.321437i
$575$		0			0
$576$	−2.00000			−0.0833333
$577$	−1.72311	−	2.98452i	−0.0717340	−	0.124247i	0.827927	−	0.560835i	$-0.189520\pi$
$577$	−1.72311	−	2.98452i	−0.0717340	−	0.124247i	−0.899661	+	0.436588i	$0.856187\pi$
$578$	38.4462			1.59915
$579$	−6.89244			−0.286440
$580$	3.00000	−	5.19615i	0.124568	−	0.215758i
$581$	−20.8924			−0.866765
$582$	−4.72311	−	8.18067i	−0.195779	−	0.339100i
$583$		0			0
$584$	−7.72311	+	13.3768i	−0.319585	+	0.553537i
$585$	−2.00000	+	3.46410i	−0.0826898	+	0.143223i
$586$	−8.22311	+	14.2428i	−0.339694	+	0.588367i
$587$	4.50000	−	7.79423i	0.185735	−	0.321702i	−0.758089	−	0.652151i	$-0.773867\pi$
$587$	4.50000	−	7.79423i	0.185735	−	0.321702i	0.943824	+	0.330449i	$0.107200\pi$
$588$	−3.00000			−0.123718
$589$	−35.1076			−1.44658
$590$	6.72311	−	11.6448i	0.276786	−	0.479408i
$591$	−10.4462	−	18.0934i	−0.429700	−	0.744263i
$592$	4.22311	+	7.31464i	0.173569	+	0.300630i
$593$	−0.830667	+	1.43876i	−0.0341114	+	0.0590827i	−0.882577	−	0.470168i	$-0.844193\pi$
$593$	−0.830667	+	1.43876i	−0.0341114	+	0.0590827i	0.848466	+	0.529250i	$0.177527\pi$
$594$		0			0
$595$	14.8924			0.610531
$596$	6.00000	+	10.3923i	0.245770	+	0.425685i
$597$	4.22311	−	7.31464i	0.172840	−	0.299368i
$598$		0			0
$599$	13.4462	+	23.2895i	0.549398	+	0.951585i	0.998316	+	0.0580119i	$0.0184761\pi$
$599$	13.4462	+	23.2895i	0.549398	+	0.951585i	−0.448918	+	0.893573i	$0.648191\pi$
$600$	1.00000			0.0408248
$601$	−4.72311	+	8.18067i	−0.192660	+	0.333696i	−0.946131	−	0.323785i	$-0.895045\pi$
$601$	−4.72311	+	8.18067i	−0.192660	+	0.333696i	0.753471	+	0.657481i	$0.228378\pi$
$602$	−22.8924			−0.933026
$603$	14.4462	−	7.70108i	0.588296	−	0.313612i
$604$	18.4462			0.750566
$605$	−5.50000	+	9.52628i	−0.223607	+	0.387298i
$606$	6.00000			0.243733
$607$	−14.4462	−	25.0216i	−0.586354	−	1.01560i	−0.994705	−	0.102770i	$-0.967229\pi$
$607$	−14.4462	−	25.0216i	−0.586354	−	1.01560i	0.408351	−	0.912825i	$-0.366104\pi$
$608$	−5.44622			−0.220873
$609$	−6.00000	+	10.3923i	−0.243132	+	0.421117i
$610$	4.00000	+	6.92820i	0.161955	+	0.280515i
$611$		0			0
$612$	14.8924			0.601991
$613$	4.22311	−	7.31464i	0.170570	−	0.295436i	−0.768049	−	0.640391i	$-0.778772\pi$
$613$	4.22311	−	7.31464i	0.170570	−	0.295436i	0.938619	+	0.344955i	$0.112106\pi$
$614$	4.94622	+	8.56711i	0.199613	+	0.345740i
$615$	−2.22311	−	3.85054i	−0.0896445	−	0.155269i
$616$		0			0
$617$	6.00000			0.241551			0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000			0.241551			0.120775	+	0.992680i	$0.461462\pi$
$618$	−4.00000			−0.160904
$619$	−6.16933	+	10.6856i	−0.247966	+	0.429490i	−0.962961	−	0.269639i	$-0.913096\pi$
$619$	−6.16933	+	10.6856i	−0.247966	+	0.429490i	0.714995	+	0.699130i	$0.246429\pi$
$620$	3.22311	−	5.58259i	0.129443	−	0.224202i
$621$		0			0
$622$	−9.66933	+	16.7478i	−0.387705	+	0.671525i
$623$	−11.8924	−	20.5983i	−0.476461	−	0.825254i
$624$	−1.00000	−	1.73205i	−0.0400320	−	0.0693375i
$625$	1.00000			0.0400000
$626$	−16.7231	+	28.9653i	−0.668390	+	1.15769i
$627$		0			0
$628$	14.0000			0.558661
$629$	−31.4462	−	54.4665i	−1.25384	−	2.17172i
$630$	4.00000			0.159364
$631$	15.4462	−	26.7536i	0.614904	−	1.06505i	−0.375497	−	0.926824i	$-0.622528\pi$
$631$	15.4462	−	26.7536i	0.614904	−	1.06505i	0.990401	−	0.138222i	$-0.0441387\pi$
$632$	−4.00000	−	6.92820i	−0.159111	−	0.275589i
$633$	11.7231	−	20.3050i	0.465952	−	0.807052i
$634$	−9.77689	−	16.9341i	−0.388290	−	0.672538i
$635$	−5.00000	−	8.66025i	−0.198419	−	0.343672i
$636$	2.22311	+	3.85054i	0.0881521	+	0.152684i
$637$	3.00000	+	5.19615i	0.118864	+	0.205879i
$638$		0			0
$639$	−4.44622	−	7.70108i	−0.175890	−	0.304650i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	15.6156	+	27.0469i	0.616777	+	1.06829i	0.990070	+	0.140576i	$0.0448954\pi$
$641$	15.6156	+	27.0469i	0.616777	+	1.06829i	−0.373293	+	0.927714i	$0.621771\pi$
$642$	−5.22311	+	9.04669i	−0.206140	+	0.357045i
$643$	10.7849			0.425314			0.212657	−	0.977127i	$-0.431788\pi$
$643$	10.7849			0.425314			0.212657	+	0.977127i	$0.431788\pi$
$644$		0			0
$645$	11.4462			0.450695
$646$	40.5538			1.59557
$647$	−3.00000	+	5.19615i	−0.117942	+	0.204282i	−0.918952	−	0.394369i	$-0.870963\pi$
$647$	−3.00000	+	5.19615i	−0.117942	+	0.204282i	0.801010	+	0.598651i	$0.204296\pi$
$648$	1.00000			0.0392837
$649$		0			0
$650$	−1.00000	−	1.73205i	−0.0392232	−	0.0679366i
$651$	−6.44622	+	11.1652i	−0.252647	+	0.437598i
$652$	−9.94622	+	17.2274i	−0.389524	+	0.674676i
$653$	−8.22311	+	14.2428i	−0.321795	+	0.557366i	−0.980859	−	0.194722i	$-0.937620\pi$
$653$	−8.22311	+	14.2428i	−0.321795	+	0.557366i	0.659063	+	0.752087i	$0.270953\pi$
$654$	−7.00000	+	12.1244i	−0.273722	+	0.474100i
$655$	−8.89244			−0.347457
$656$	−4.44622			−0.173596
$657$	15.4462	−	26.7536i	0.602615	−	1.04376i
$658$		0			0
$659$	−17.1693	−	29.7382i	−0.668822	−	1.15843i	−0.978234	−	0.207506i	$-0.933465\pi$
$659$	−17.1693	−	29.7382i	−0.668822	−	1.15843i	0.309412	−	0.950928i	$-0.399868\pi$
$660$		0			0
$661$	−45.7849			−1.78083			−0.890413	−	0.455154i	$-0.849584\pi$
$661$	−45.7849			−1.78083			−0.890413	+	0.455154i	$0.849584\pi$
$662$	6.55378			0.254720
$663$	7.44622	+	12.8972i	0.289187	+	0.500887i
$664$	5.22311	−	9.04669i	0.202696	−	0.351080i
$665$	10.8924			0.422391
$666$	−8.44622	−	14.6293i	−0.327284	−	0.566873i
$667$		0			0
$668$	−4.44622	+	7.70108i	−0.172029	+	0.297964i
$669$	2.00000			0.0773245
$670$	−0.276889	+	8.18067i	−0.0106972	+	0.316047i
$671$		0			0
$672$	−1.00000	+	1.73205i	−0.0385758	+	0.0668153i
$673$	27.2311			1.04968			0.524841	−	0.851200i	$-0.324125\pi$
$673$	27.2311			1.04968			0.524841	+	0.851200i	$0.324125\pi$
$674$	−11.4462	−	19.8254i	−0.440892	−	0.763647i
$675$	−5.00000			−0.192450
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	18.6693	+	32.3362i	0.717521	+	1.24278i	0.961979	+	0.273123i	$0.0880565\pi$
$677$	18.6693	+	32.3362i	0.717521	+	1.24278i	−0.244458	+	0.969660i	$0.578610\pi$
$678$	−4.55378			−0.174887
$679$	18.8924			0.725025
$680$	−3.72311	+	6.44862i	−0.142775	+	0.247293i
$681$	−4.50000	−	7.79423i	−0.172440	−	0.298675i
$682$		0			0
$683$	−17.9462	+	31.0838i	−0.686693	+	1.18939i	0.286208	+	0.958167i	$0.407605\pi$
$683$	−17.9462	+	31.0838i	−0.686693	+	1.18939i	−0.972902	+	0.231220i	$0.925728\pi$
$684$	10.8924			0.416483
$685$	7.44622			0.284506
$686$	10.0000	−	17.3205i	0.381802	−	0.661300i
$687$	−4.00000	+	6.92820i	−0.152610	+	0.264327i
$688$	5.72311	−	9.91272i	0.218192	−	0.377919i
$689$	4.44622	−	7.70108i	0.169388	−	0.293388i
$690$		0			0
$691$	24.4462	+	42.3421i	0.929978	+	1.61077i	0.783353	+	0.621577i	$0.213508\pi$
$691$	24.4462	+	42.3421i	0.929978	+	1.61077i	0.146625	+	0.989192i	$0.453159\pi$
$692$	25.3387			0.963232
$693$		0			0
$694$	19.4462			0.738168
$695$	8.55378			0.324463
$696$	−3.00000	−	5.19615i	−0.113715	−	0.196960i
$697$	33.1076			1.25404
$698$	−4.00000	+	6.92820i	−0.151402	+	0.262236i
$699$	11.1693	+	19.3459i	0.422463	+	0.731727i
$700$	−1.00000	+	1.73205i	−0.0377964	+	0.0654654i
$701$	−1.44622	−	2.50493i	−0.0546231	−	0.0946099i	0.837421	−	0.546558i	$-0.184062\pi$
$701$	−1.44622	−	2.50493i	−0.0546231	−	0.0946099i	−0.892044	+	0.451949i	$0.850729\pi$
$702$	5.00000	+	8.66025i	0.188713	+	0.326860i
$703$	−23.0000	−	39.8372i	−0.867461	−	1.50249i
$704$		0			0
$705$		0			0
$706$	7.44622	+	12.8972i	0.280242	+	0.485394i
$707$	−6.00000	+	10.3923i	−0.225653	+	0.390843i
$708$	−6.72311	−	11.6448i	−0.252670	−	0.437637i
$709$	10.8924	−	18.8663i	0.409074	−	0.708538i	−0.585712	−	0.810519i	$-0.699185\pi$
$709$	10.8924	−	18.8663i	0.409074	−	0.708538i	0.994786	+	0.101982i	$0.0325183\pi$
$710$	4.44622			0.166864
$711$	8.00000	+	13.8564i	0.300023	+	0.519656i
$712$	11.8924			0.445688
$713$		0			0
$714$	7.44622	−	12.8972i	0.278668	−	0.482667i
$715$		0			0
$716$	−6.00000	−	10.3923i	−0.224231	−	0.388379i
$717$	−7.44622	−	12.8972i	−0.278084	−	0.481656i
$718$	−6.66933	+	11.5516i	−0.248897	+	0.431103i
$719$	−17.1156	+	29.6450i	−0.638302	+	1.10557i	0.347503	+	0.937679i	$0.387030\pi$
$719$	−17.1156	+	29.6450i	−0.638302	+	1.10557i	−0.985805	+	0.167893i	$0.946304\pi$
$720$	−1.00000	+	1.73205i	−0.0372678	+	0.0645497i
$721$	4.00000	−	6.92820i	0.148968	−	0.258020i
$722$	10.6613			0.396774
$723$	3.55378			0.132166
$724$	−2.44622	+	4.23698i	−0.0909131	+	0.157466i
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$	5.50000	+	9.52628i	0.204124	+	0.353553i
$727$	−15.8924	+	27.5265i	−0.589418	+	1.02090i	0.404891	+	0.914365i	$0.367310\pi$
$727$	−15.8924	+	27.5265i	−0.589418	+	1.02090i	−0.994309	+	0.106537i	$0.966024\pi$
$728$	4.00000			0.148250
$729$	13.0000			0.481481
$730$	7.72311	+	13.3768i	0.285845	+	0.495098i
$731$	−42.6156	+	73.8123i	−1.57619	+	2.73005i
$732$	8.00000			0.295689
$733$	−21.2231	−	36.7595i	−0.783893	−	1.35774i	−0.929658	−	0.368424i	$-0.879897\pi$
$733$	−21.2231	−	36.7595i	−0.783893	−	1.35774i	0.145764	−	0.989319i	$-0.453436\pi$
$734$	19.7849			0.730274
$735$	−1.50000	+	2.59808i	−0.0553283	+	0.0958315i
$736$		0			0
$737$		0			0
$738$	8.89244			0.327335
$739$	−3.27689	+	5.67574i	−0.120542	+	0.208785i	−0.919982	−	0.391961i	$-0.871797\pi$
$739$	−3.27689	+	5.67574i	−0.120542	+	0.208785i	0.799439	+	0.600747i	$0.205130\pi$
$740$	8.44622			0.310489
$741$	5.44622	+	9.43313i	0.200072	+	0.346535i
$742$	−8.89244			−0.326452
$743$	13.4462	−	23.2895i	0.493294	−	0.854410i	−0.506676	−	0.862136i	$-0.669126\pi$
$743$	13.4462	−	23.2895i	0.493294	−	0.854410i	0.999970	+	0.00772614i	$0.00245933\pi$
$744$	−3.22311	−	5.58259i	−0.118165	−	0.204668i
$745$	12.0000			0.439646
$746$	−11.5538			−0.423014
$747$	−10.4462	+	18.0934i	−0.382207	+	0.662002i
$748$		0			0
$749$	−10.4462	−	18.0934i	−0.381697	−	0.661118i
$750$	0.500000	−	0.866025i	0.0182574	−	0.0316228i
$751$	3.55378			0.129679			0.0648396	−	0.997896i	$-0.479346\pi$
$751$	3.55378			0.129679			0.0648396	+	0.997896i	$0.479346\pi$
$752$		0			0
$753$	9.72311	−	16.8409i	0.354330	−	0.613717i
$754$	−6.00000	+	10.3923i	−0.218507	+	0.378465i
$755$	9.22311	−	15.9749i	0.335663	−	0.581386i
$756$	5.00000	−	8.66025i	0.181848	−	0.314970i
$757$	4.22311	+	7.31464i	0.153492	+	0.265855i	0.932509	−	0.361147i	$-0.117615\pi$
$757$	4.22311	+	7.31464i	0.153492	+	0.265855i	−0.779017	+	0.627003i	$0.784282\pi$
$758$	10.8924	+	18.8663i	0.395631	+	0.685254i
$759$		0			0
$760$	−2.72311	+	4.71657i	−0.0987776	+	0.171088i
$761$	−19.5538			−0.708824			−0.354412	−	0.935089i	$-0.615319\pi$
$761$	−19.5538			−0.708824			−0.354412	+	0.935089i	$0.615319\pi$
$762$	−10.0000			−0.362262
$763$	−14.0000	−	24.2487i	−0.506834	−	0.877862i
$764$	−10.4462			−0.377931
$765$	7.44622	−	12.8972i	0.269219	−	0.466301i
$766$	3.00000	+	5.19615i	0.108394	+	0.187745i
$767$	−13.4462	+	23.2895i	−0.485515	+	0.840937i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	−18.1693	−	31.4702i	−0.655203	−	1.13484i	−0.981843	−	0.189696i	$-0.939250\pi$
$769$	−18.1693	−	31.4702i	−0.655203	−	1.13484i	0.326640	−	0.945149i	$-0.394084\pi$
$770$		0			0
$771$	−9.00000	−	15.5885i	−0.324127	−	0.561405i
$772$	3.44622	+	5.96903i	0.124032	+	0.214830i
$773$	−0.669333	−	1.15932i	−0.0240742	−	0.0416978i	0.853737	−	0.520704i	$-0.174330\pi$
$773$	−0.669333	−	1.15932i	−0.0240742	−	0.0416978i	−0.877812	+	0.479006i	$0.840997\pi$
$774$	−11.4462	+	19.8254i	−0.411426	+	0.712611i
$775$	−3.22311	−	5.58259i	−0.115778	−	0.200533i
$776$	−4.72311	+	8.18067i	−0.169550	+	0.293669i
$777$	−16.8924			−0.606013
$778$	−4.44622	−	7.70108i	−0.159405	−	0.276097i
$779$	24.2151			0.867596
$780$	−2.00000			−0.0716115
$781$		0			0
$782$		0			0
$783$	15.0000	+	25.9808i	0.536056	+	0.928477i
$784$	1.50000	+	2.59808i	0.0535714	+	0.0927884i
$785$	7.00000	−	12.1244i	0.249841	−	0.432737i
$786$	−4.44622	+	7.70108i	−0.158591	+	0.274689i
$787$	1.22311	−	2.11849i	0.0435992	−	0.0755160i	−0.843402	−	0.537283i	$-0.819451\pi$
$787$	1.22311	−	2.11849i	0.0435992	−	0.0755160i	0.887002	+	0.461767i	$0.152784\pi$
$788$	−10.4462	+	18.0934i	−0.372131	+	0.644550i
$789$	20.8924			0.743791
$790$	−8.00000			−0.284627
$791$	4.55378	−	7.88737i	0.161914	−	0.280443i
$792$		0			0
$793$	−8.00000	−	13.8564i	−0.284088	−	0.492055i
$794$	17.6693	−	30.6042i	0.627061	−	1.08610i
$795$	4.44622			0.157691
$796$	−8.44622			−0.299368
$797$	6.77689	+	11.7379i	0.240050	+	0.415778i	0.960728	−	0.277491i	$-0.0895029\pi$
$797$	6.77689	+	11.7379i	0.240050	+	0.415778i	−0.720678	+	0.693269i	$0.756170\pi$
$798$	5.44622	−	9.43313i	0.192794	−	0.333929i
$799$		0			0
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−23.7849			−0.840398
$802$	−9.00000	+	15.5885i	−0.317801	+	0.550448i
$803$		0			0
$804$	6.94622	+	4.33013i	0.244974	+	0.152712i
$805$		0			0
$806$	−6.44622	+	11.1652i	−0.227058	+	0.393277i
$807$		0			0
$808$	−3.00000	−	5.19615i	−0.105540	−	0.182800i
$809$	35.7849			1.25813			0.629065	−	0.777353i	$-0.283438\pi$
$809$	35.7849			1.25813			0.629065	+	0.777353i	$0.283438\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	−2.44622	−	4.23698i	−0.0858985	−	0.148781i	0.819875	−	0.572542i	$-0.194043\pi$
$811$	−2.44622	−	4.23698i	−0.0858985	−	0.148781i	−0.905774	+	0.423762i	$0.860709\pi$
$812$	12.0000			0.421117
$813$	−11.5538			−0.405209
$814$		0			0
$815$	9.94622	+	17.2274i	0.348401	+	0.603448i
$816$	3.72311	+	6.44862i	0.130335	+	0.225747i
$817$	−31.1693	+	53.9869i	−1.09048	+	1.88876i
$818$	12.4462			0.435172
$819$	−8.00000			−0.279543
$820$	−2.22311	+	3.85054i	−0.0776344	+	0.134467i
$821$	22.3387	−	38.6917i	0.779625	−	1.35035i	−0.152533	−	0.988298i	$-0.548743\pi$
$821$	22.3387	−	38.6917i	0.779625	−	1.35035i	0.932158	−	0.362051i	$-0.117924\pi$
$822$	3.72311	−	6.44862i	0.129858	−	0.224921i
$823$	−8.44622	+	14.6293i	−0.294417	+	0.509945i	−0.974849	−	0.222866i	$-0.928459\pi$
$823$	−8.44622	+	14.6293i	−0.294417	+	0.509945i	0.680432	+	0.732811i	$0.261792\pi$
$824$	2.00000	+	3.46410i	0.0696733	+	0.120678i
$825$		0			0
$826$	26.8924			0.935708
$827$	−8.89244	+	15.4022i	−0.309221	+	0.535586i	−0.978192	−	0.207702i	$-0.933401\pi$
$827$	−8.89244	+	15.4022i	−0.309221	+	0.535586i	0.668972	+	0.743288i	$0.266735\pi$
$828$		0			0
$829$	19.7849			0.687158			0.343579	−	0.939124i	$-0.388361\pi$
$829$	19.7849			0.687158			0.343579	+	0.939124i	$0.388361\pi$
$830$	−5.22311	−	9.04669i	−0.181297	−	0.314015i
$831$	18.4462			0.639892
$832$	−1.00000	+	1.73205i	−0.0346688	+	0.0600481i
$833$	−11.1693	−	19.3459i	−0.386994	−	0.670294i
$834$	4.27689	−	7.40779i	0.148097	−	0.256511i
$835$	4.44622	+	7.70108i	0.153868	+	0.266507i
$836$		0			0
$837$	16.1156	+	27.9130i	0.557035	+	0.964813i
$838$	−9.72311	−	16.8409i	−0.335879	−	0.581760i
$839$	15.7769	+	27.3264i	0.544679	+	0.943411i	0.998627	+	0.0523832i	$0.0166817\pi$
$839$	15.7769	+	27.3264i	0.544679	+	0.943411i	−0.453948	+	0.891028i	$0.649985\pi$
$840$	1.00000	+	1.73205i	0.0345033	+	0.0597614i
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	−14.4462	−	25.0216i	−0.497850	−	0.862301i
$843$	8.94622	−	15.4953i	0.308124	−	0.533687i
$844$	−23.4462			−0.807052
$845$	−4.50000	−	7.79423i	−0.154805	−	0.268130i
$846$		0			0
$847$	−22.0000			−0.755929
$848$	2.22311	−	3.85054i	0.0763419	−	0.132228i
$849$	18.3387			0.629381
$850$	3.72311	+	6.44862i	0.127702	+	0.221186i
$851$		0			0
$852$	2.22311	−	3.85054i	0.0761625	−	0.131917i
$853$	−1.77689	+	3.07766i	−0.0608395	+	0.105377i	−0.894841	−	0.446385i	$-0.852711\pi$
$853$	−1.77689	+	3.07766i	−0.0608395	+	0.105377i	0.834001	+	0.551762i	$0.186044\pi$
$854$	−8.00000	+	13.8564i	−0.273754	+	0.474156i
$855$	5.44622	−	9.43313i	0.186257	−	0.322606i
$856$	10.4462			0.357045
$857$	−18.0000			−0.614868			−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000			−0.614868			−0.307434	+	0.951569i	$0.599470\pi$
$858$		0			0
$859$	−22.7231	−	39.3576i	−0.775303	−	1.34286i	−0.934624	−	0.355637i	$-0.884264\pi$
$859$	−22.7231	−	39.3576i	−0.775303	−	1.34286i	0.159322	−	0.987227i	$-0.449069\pi$
$860$	−5.72311	−	9.91272i	−0.195156	−	0.338021i
$861$	4.44622	−	7.70108i	0.151527	−	0.262452i
$862$	−25.3387			−0.863038
$863$	5.78489			0.196920			0.0984599	−	0.995141i	$-0.468608\pi$
$863$	5.78489			0.196920			0.0984599	+	0.995141i	$0.468608\pi$
$864$	2.50000	+	4.33013i	0.0850517	+	0.147314i
$865$	12.6693	−	21.9439i	0.430770	−	0.746116i
$866$	−20.3387			−0.691136
$867$	−19.2231	−	33.2954i	−0.652851	−	1.13077i
$868$	12.8924			0.437598
$869$		0			0
$870$	−6.00000			−0.203419
$871$	0.553778	−	16.3613i	0.0187641	−	0.554383i
$872$	14.0000			0.474100
$873$	9.44622	−	16.3613i	0.319706	−	0.553747i
$874$		0			0
$875$	1.00000	+	1.73205i	0.0338062	+	0.0585540i
$876$	15.4462			0.521879
$877$	9.55378	−	16.5476i	0.322608	−	0.558774i	−0.658417	−	0.752653i	$-0.728774\pi$
$877$	9.55378	−	16.5476i	0.322608	−	0.558774i	0.981025	+	0.193879i	$0.0621071\pi$
$878$	8.77689	+	15.2020i	0.296206	+	0.513043i
$879$	16.4462			0.554717
$880$		0			0
$881$	9.77689	−	16.9341i	0.329392	−	0.570523i	−0.653000	−	0.757358i	$-0.726490\pi$
$881$	9.77689	−	16.9341i	0.329392	−	0.570523i	0.982391	+	0.186835i	$0.0598230\pi$
$882$	−3.00000	−	5.19615i	−0.101015	−	0.174964i
$883$	2.00000	+	3.46410i	0.0673054	+	0.116576i	0.897714	−	0.440578i	$-0.145226\pi$
$883$	2.00000	+	3.46410i	0.0673054	+	0.116576i	−0.830409	+	0.557154i	$0.811893\pi$
$884$	7.44622	−	12.8972i	0.250444	−	0.433781i
$885$	−13.4462			−0.451990
$886$	5.89244			0.197961
$887$	28.4462	−	49.2703i	0.955131	−	1.65433i	0.221062	−	0.975260i	$-0.429048\pi$
$887$	28.4462	−	49.2703i	0.955131	−	1.65433i	0.734069	−	0.679075i	$-0.237619\pi$
$888$	4.22311	−	7.31464i	0.141718	−	0.245463i
$889$	10.0000	−	17.3205i	0.335389	−	0.580911i
$890$	5.94622	−	10.2992i	0.199318	−	0.345229i
$891$		0			0
$892$	−1.00000	−	1.73205i	−0.0334825	−	0.0579934i
$893$		0			0
$894$	6.00000	−	10.3923i	0.200670	−	0.347571i
$895$	−12.0000			−0.401116
$896$	2.00000			0.0668153
$897$		0			0
$898$	−25.3387			−0.845562
$899$	−19.3387	+	33.4956i	−0.644981	+	1.11714i
$900$	1.00000	+	1.73205i	0.0333333	+	0.0577350i
$901$	−16.5538	+	28.6720i	−0.551486	+	0.955202i
$902$		0			0
$903$	11.4462	+	19.8254i	0.380906	+	0.659749i
$904$	2.27689	+	3.94369i	0.0757282	+	0.131165i
$905$	2.44622	+	4.23698i	0.0813152	+	0.140842i
$906$	−9.22311	−	15.9749i	−0.306417	−	0.530730i
$907$	11.6693	+	20.2119i	0.387474	+	0.671124i	0.992109	−	0.125378i	$-0.0400144\pi$
$907$	11.6693	+	20.2119i	0.387474	+	0.671124i	−0.604635	+	0.796503i	$0.706681\pi$
$908$	−4.50000	+	7.79423i	−0.149338	+	0.258661i
$909$	6.00000	+	10.3923i	0.199007	+	0.344691i
$910$	2.00000	−	3.46410i	0.0662994	−	0.114834i
$911$	−49.3387			−1.63466			−0.817331	−	0.576168i	$-0.804547\pi$
$911$	−49.3387			−1.63466			−0.817331	+	0.576168i	$0.804547\pi$
$912$	2.72311	+	4.71657i	0.0901712	+	0.156181i
$913$		0			0
$914$	12.5538			0.415242
$915$	4.00000	−	6.92820i	0.132236	−	0.229039i
$916$	8.00000			0.264327
$917$	−8.89244	−	15.4022i	−0.293654	−	0.508624i
$918$	−18.6156	−	32.2431i	−0.614405	−	1.06418i
$919$	−13.7769	+	23.8623i	−0.454458	+	0.787144i	−0.998657	−	0.0518123i	$-0.983500\pi$
$919$	−13.7769	+	23.8623i	−0.454458	+	0.787144i	0.544199	+	0.838956i	$0.316834\pi$
$920$		0			0
$921$	4.94622	−	8.56711i	0.162984	−	0.282296i
$922$	−4.55378	+	7.88737i	−0.149971	+	0.259757i
$923$	−8.89244			−0.292698
$924$		0			0
$925$	4.22311	−	7.31464i	0.138855	−	0.240504i
$926$	13.8924	+	24.0624i	0.456534	+	0.790740i
$927$	−4.00000	−	6.92820i	−0.131377	−	0.227552i
$928$	−3.00000	+	5.19615i	−0.0984798	+	0.170572i
$929$	−7.66133			−0.251360			−0.125680	−	0.992071i	$-0.540111\pi$
$929$	−7.66133			−0.251360			−0.125680	+	0.992071i	$0.540111\pi$
$930$	−6.44622			−0.211380
$931$	−8.16933	−	14.1497i	−0.267739	−	0.463738i
$932$	11.1693	−	19.3459i	0.365864	−	0.633694i
$933$	19.3387			0.633120
$934$	−5.22311	−	9.04669i	−0.170905	−	0.296017i
$935$		0			0
$936$	2.00000	−	3.46410i	0.0653720	−	0.113228i
$937$	22.8924			0.747864			0.373932	−	0.927456i	$-0.378009\pi$
$937$	22.8924			0.747864			0.373932	+	0.927456i	$0.378009\pi$
$938$	−14.4462	+	7.70108i	−0.471686	+	0.251449i
$939$	33.4462			1.09148
$940$		0			0
$941$	−29.7849			−0.970960			−0.485480	−	0.874248i	$-0.661355\pi$
$941$	−29.7849			−0.970960			−0.485480	+	0.874248i	$0.661355\pi$
$942$	−7.00000	−	12.1244i	−0.228072	−	0.395033i
$943$		0			0
$944$	−6.72311	+	11.6448i	−0.218819	+	0.379005i
$945$	−5.00000	−	8.66025i	−0.162650	−	0.281718i
$946$		0			0
$947$	1.66133			0.0539861			0.0269931	−	0.999636i	$-0.491407\pi$
$947$	1.66133			0.0539861			0.0269931	+	0.999636i	$0.491407\pi$
$948$	−4.00000	+	6.92820i	−0.129914	+	0.225018i
$949$	−15.4462	−	26.7536i	−0.501406	−	0.868460i
$950$	2.72311	+	4.71657i	0.0883494	+	0.153026i
$951$	−9.77689	+	16.9341i	−0.317037	+	0.549125i
$952$	−14.8924			−0.482667
$953$	13.4462			0.435566			0.217783	−	0.975997i	$-0.430118\pi$
$953$	13.4462			0.435566			0.217783	+	0.975997i	$0.430118\pi$
$954$	−4.44622	+	7.70108i	−0.143952	+	0.249332i
$955$	−5.22311	+	9.04669i	−0.169016	+	0.292744i
$956$	−7.44622	+	12.8972i	−0.240828	+	0.417126i
$957$		0			0
$958$		0			0
$959$	7.44622	+	12.8972i	0.240451	+	0.416473i
$960$	−1.00000			−0.0322749
$961$	−5.27689	+	9.13984i	−0.170222	+	0.294834i
$962$	−16.8924			−0.544634
$963$	−20.8924			−0.673250
$964$	−1.77689	−	3.07766i	−0.0572297	−	0.0991248i
$965$	6.89244			0.221876
$966$		0			0
$967$	11.0000	+	19.0526i	0.353736	+	0.612689i	0.986901	−	0.161328i	$-0.0515777\pi$
$967$	11.0000	+	19.0526i	0.353736	+	0.612689i	−0.633165	+	0.774017i	$0.718244\pi$
$968$	5.50000	−	9.52628i	0.176777	−	0.306186i
$969$	−20.2769	−	35.1206i	−0.651388	−	1.12824i
$970$	4.72311	+	8.18067i	0.151650	+	0.262665i
$971$	0.830667	+	1.43876i	0.0266574	+	0.0461719i	0.879046	−	0.476736i	$-0.158180\pi$
$971$	0.830667	+	1.43876i	0.0266574	+	0.0461719i	−0.852389	+	0.522908i	$0.824847\pi$
$972$	−8.00000	−	13.8564i	−0.256600	−	0.444444i
$973$	8.55378	+	14.8156i	0.274222	+	0.474966i
$974$	8.00000	+	13.8564i	0.256337	+	0.443988i
$975$	−1.00000	+	1.73205i	−0.0320256	+	0.0554700i
$976$	−4.00000	−	6.92820i	−0.128037	−	0.221766i
$977$	−13.4462	+	23.2895i	−0.430183	+	0.745098i	−0.996889	−	0.0788217i	$-0.974884\pi$
$977$	−13.4462	+	23.2895i	−0.430183	+	0.745098i	0.566706	+	0.823920i	$0.308218\pi$
$978$	19.8924			0.636090
$979$		0			0
$980$	3.00000			0.0958315
$981$	−28.0000			−0.893971
$982$	2.16933	−	3.75739i	0.0692262	−	0.119903i
$983$	56.8924			1.81459			0.907294	−	0.420498i	$-0.138145\pi$
$983$	56.8924			1.81459			0.907294	+	0.420498i	$0.138145\pi$
$984$	2.22311	+	3.85054i	0.0708702	+	0.122751i
$985$	10.4462	+	18.0934i	0.332844	+	0.576503i
$986$	22.3387	−	38.6917i	0.711408	−	1.23219i
$987$		0			0
$988$	5.44622	−	9.43313i	0.173267	−	0.300108i
$989$		0			0
$990$		0			0
$991$	45.3387			1.44023			0.720115	−	0.693855i	$-0.244089\pi$
$991$	45.3387			1.44023			0.720115	+	0.693855i	$0.244089\pi$
$992$	−3.22311	+	5.58259i	−0.102334	+	0.177247i
$993$	−3.27689	−	5.67574i	−0.103989	−	0.180114i
$994$	4.44622	+	7.70108i	0.141026	+	0.244264i
$995$	−4.22311	+	7.31464i	−0.133882	+	0.231890i
$996$	−10.4462			−0.331001
$997$	33.5538			1.06266			0.531329	−	0.847165i	$-0.321693\pi$
$997$	33.5538			1.06266			0.531329	+	0.847165i	$0.321693\pi$
$998$	−6.27689	−	10.8719i	−0.198691	−	0.344144i
$999$	−21.1156	+	36.5732i	−0.668067	+	1.15713i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.e.e.431.2	yes	4
67.37	even	3	inner	670.2.e.e.171.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.e.e.171.2	✓	4	67.37	even	3	inner
670.2.e.e.431.2	yes	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.00000 - 1.73205i) q^{7} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.00000 - 1.73205i) q^{7} +1.00000 q^{8} -2.00000 q^{9} +(0.500000 - 0.866025i) q^{10} +(-0.500000 - 0.866025i) q^{12} +(-1.00000 + 1.73205i) q^{13} +2.00000 q^{14} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.72311 - 6.44862i) q^{17} +(1.00000 - 1.73205i) q^{18} +(2.72311 - 4.71657i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-1.00000 - 1.73205i) q^{21} +1.00000 q^{24} +1.00000 q^{25} +(-1.00000 - 1.73205i) q^{26} -5.00000 q^{27} +(-1.00000 + 1.73205i) q^{28} +(-3.00000 - 5.19615i) q^{29} +(0.500000 - 0.866025i) q^{30} +(-3.22311 - 5.58259i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.72311 + 6.44862i) q^{34} +(1.00000 + 1.73205i) q^{35} +(1.00000 + 1.73205i) q^{36} +(4.22311 - 7.31464i) q^{37} +(2.72311 + 4.71657i) q^{38} +(-1.00000 + 1.73205i) q^{39} -1.00000 q^{40} +(2.22311 + 3.85054i) q^{41} +2.00000 q^{42} -11.4462 q^{43} +2.00000 q^{45} +(-0.500000 + 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(3.72311 - 6.44862i) q^{51} +2.00000 q^{52} -4.44622 q^{53} +(2.50000 - 4.33013i) q^{54} +(-1.00000 - 1.73205i) q^{56} +(2.72311 - 4.71657i) q^{57} +6.00000 q^{58} +13.4462 q^{59} +(0.500000 + 0.866025i) q^{60} +(-4.00000 + 6.92820i) q^{61} +6.44622 q^{62} +(2.00000 + 3.46410i) q^{63} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +(-7.22311 + 3.85054i) q^{67} -7.44622 q^{68} -2.00000 q^{70} +(2.22311 + 3.85054i) q^{71} -2.00000 q^{72} +(-7.72311 + 13.3768i) q^{73} +(4.22311 + 7.31464i) q^{74} +1.00000 q^{75} -5.44622 q^{76} +(-1.00000 - 1.73205i) q^{78} +(-4.00000 - 6.92820i) q^{79} +(0.500000 - 0.866025i) q^{80} +1.00000 q^{81} -4.44622 q^{82} +(5.22311 - 9.04669i) q^{83} +(-1.00000 + 1.73205i) q^{84} +(-3.72311 + 6.44862i) q^{85} +(5.72311 - 9.91272i) q^{86} +(-3.00000 - 5.19615i) q^{87} +11.8924 q^{89} +(-1.00000 + 1.73205i) q^{90} +4.00000 q^{91} +(-3.22311 - 5.58259i) q^{93} +(-2.72311 + 4.71657i) q^{95} +(-0.500000 - 0.866025i) q^{96} +(-4.72311 + 8.18067i) q^{97} +(1.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 8 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 4 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8 - 8 * q^9	\( 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 8 q^{9} + 2 q^{10} - 2 q^{12} - 4 q^{13} + 8 q^{14} - 4 q^{15} - 2 q^{16} + q^{17} + 4 q^{18} - 3 q^{19} + 2 q^{20} - 4 q^{21} + 4 q^{24} + 4 q^{25} - 4 q^{26} - 20 q^{27} - 4 q^{28} - 12 q^{29} + 2 q^{30} + q^{31} - 2 q^{32} + q^{34} + 4 q^{35} + 4 q^{36} + 3 q^{37} - 3 q^{38} - 4 q^{39} - 4 q^{40} - 5 q^{41} + 8 q^{42} - 18 q^{43} + 8 q^{45} - 2 q^{48} + 6 q^{49} - 2 q^{50} + q^{51} + 8 q^{52} + 10 q^{53} + 10 q^{54} - 4 q^{56} - 3 q^{57} + 24 q^{58} + 26 q^{59} + 2 q^{60} - 16 q^{61} - 2 q^{62} + 8 q^{63} + 4 q^{64} + 4 q^{65} - 15 q^{67} - 2 q^{68} - 8 q^{70} - 5 q^{71} - 8 q^{72} - 17 q^{73} + 3 q^{74} + 4 q^{75} + 6 q^{76} - 4 q^{78} - 16 q^{79} + 2 q^{80} + 4 q^{81} + 10 q^{82} + 7 q^{83} - 4 q^{84} - q^{85} + 9 q^{86} - 12 q^{87} - 8 q^{89} - 4 q^{90} + 16 q^{91} + q^{93} + 3 q^{95} - 2 q^{96} - 5 q^{97} + 6 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 4 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8 - 8 * q^9 + 2 * q^10 - 2 * q^12 - 4 * q^13 + 8 * q^14 - 4 * q^15 - 2 * q^16 + q^17 + 4 * q^18 - 3 * q^19 + 2 * q^20 - 4 * q^21 + 4 * q^24 + 4 * q^25 - 4 * q^26 - 20 * q^27 - 4 * q^28 - 12 * q^29 + 2 * q^30 + q^31 - 2 * q^32 + q^34 + 4 * q^35 + 4 * q^36 + 3 * q^37 - 3 * q^38 - 4 * q^39 - 4 * q^40 - 5 * q^41 + 8 * q^42 - 18 * q^43 + 8 * q^45 - 2 * q^48 + 6 * q^49 - 2 * q^50 + q^51 + 8 * q^52 + 10 * q^53 + 10 * q^54 - 4 * q^56 - 3 * q^57 + 24 * q^58 + 26 * q^59 + 2 * q^60 - 16 * q^61 - 2 * q^62 + 8 * q^63 + 4 * q^64 + 4 * q^65 - 15 * q^67 - 2 * q^68 - 8 * q^70 - 5 * q^71 - 8 * q^72 - 17 * q^73 + 3 * q^74 + 4 * q^75 + 6 * q^76 - 4 * q^78 - 16 * q^79 + 2 * q^80 + 4 * q^81 + 10 * q^82 + 7 * q^83 - 4 * q^84 - q^85 + 9 * q^86 - 12 * q^87 - 8 * q^89 - 4 * q^90 + 16 * q^91 + q^93 + 3 * q^95 - 2 * q^96 - 5 * q^97 + 6 * q^98

Introduction

L-functions

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