LMFDB - Embedded newform 670.2.e.e.431.1

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			431.1
Root			$-3.22311 + 5.58259i$ of defining polynomial
Character	$\chi$	$=$	670.431
Dual form			670.2.e.e.171.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.00000 - 1.73205i) q^{7} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$	\(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} +(-3.22311 + 5.58259i) q^{17} +(1.00000 - 1.73205i) q^{18} +(-4.22311 + 7.31464i) 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} +(3.72311 + 6.44862i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.22311 - 5.58259i) q^{34} +(1.00000 + 1.73205i) q^{35} +(1.00000 + 1.73205i) q^{36} +(-2.72311 + 4.71657i) q^{37} +(-4.22311 - 7.31464i) q^{38} +(-1.00000 + 1.73205i) q^{39} -1.00000 q^{40} +(-4.72311 - 8.18067i) q^{41} +2.00000 q^{42} +2.44622 q^{43} +2.00000 q^{45} +(-0.500000 + 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-3.22311 + 5.58259i) q^{51} +2.00000 q^{52} +9.44622 q^{53} +(2.50000 - 4.33013i) q^{54} +(-1.00000 - 1.73205i) q^{56} +(-4.22311 + 7.31464i) q^{57} +6.00000 q^{58} -0.446222 q^{59} +(0.500000 + 0.866025i) q^{60} +(-4.00000 + 6.92820i) q^{61} -7.44622 q^{62} +(2.00000 + 3.46410i) q^{63} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +(-0.276889 - 8.18067i) q^{67} +6.44622 q^{68} -2.00000 q^{70} +(-4.72311 - 8.18067i) q^{71} -2.00000 q^{72} +(-0.776889 + 1.34561i) q^{73} +(-2.72311 - 4.71657i) q^{74} +1.00000 q^{75} +8.44622 q^{76} +(-1.00000 - 1.73205i) q^{78} +(-4.00000 - 6.92820i) q^{79} +(0.500000 - 0.866025i) q^{80} +1.00000 q^{81} +9.44622 q^{82} +(-1.72311 + 2.98452i) q^{83} +(-1.00000 + 1.73205i) q^{84} +(3.22311 - 5.58259i) q^{85} +(-1.22311 + 2.11849i) q^{86} +(-3.00000 - 5.19615i) q^{87} -15.8924 q^{89} +(-1.00000 + 1.73205i) q^{90} +4.00000 q^{91} +(3.72311 + 6.44862i) q^{93} +(4.22311 - 7.31464i) q^{95} +(-0.500000 - 0.866025i) q^{96} +(2.22311 - 3.85054i) 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
$17$	−3.22311	+	5.58259i	−0.781719	+	1.35398i	0.149220	+	0.988804i	$0.452324\pi$
$17$	−3.22311	+	5.58259i	−0.781719	+	1.35398i	−0.930939	+	0.365173i	$0.881010\pi$
$18$	1.00000	−	1.73205i	0.235702	−	0.408248i
$19$	−4.22311	+	7.31464i	−0.968848	+	1.67809i	−0.269948	+	0.962875i	$0.587006\pi$
$19$	−4.22311	+	7.31464i	−0.968848	+	1.67809i	−0.698900	+	0.715219i	$0.746327\pi$
$20$	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
$31$	3.72311	+	6.44862i	0.668690	+	1.15821i	0.978271	+	0.207332i	$0.0664782\pi$
$31$	3.72311	+	6.44862i	0.668690	+	1.15821i	−0.309580	+	0.950873i	$0.600188\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−3.22311	−	5.58259i	−0.552759	−	0.957407i
$35$	1.00000	+	1.73205i	0.169031	+	0.292770i
$36$	1.00000	+	1.73205i	0.166667	+	0.288675i
$37$	−2.72311	+	4.71657i	−0.447677	+	0.775399i	−0.998234	−	0.0593984i	$-0.981082\pi$
$37$	−2.72311	+	4.71657i	−0.447677	+	0.775399i	0.550558	+	0.834797i	$0.314415\pi$
$38$	−4.22311	−	7.31464i	−0.685079	−	1.18659i
$39$	−1.00000	+	1.73205i	−0.160128	+	0.277350i
$40$	−1.00000			−0.158114
$41$	−4.72311	−	8.18067i	−0.737626	−	1.27761i	−0.953562	−	0.301198i	$-0.902613\pi$
$41$	−4.72311	−	8.18067i	−0.737626	−	1.27761i	0.215936	−	0.976408i	$-0.430720\pi$
$42$	2.00000			0.308607
$43$	2.44622			0.373045			0.186523	−	0.982451i	$-0.440278\pi$
$43$	2.44622			0.373045			0.186523	+	0.982451i	$0.440278\pi$
$44$		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
$51$	−3.22311	+	5.58259i	−0.451326	+	0.781719i
$52$	2.00000			0.277350
$53$	9.44622			1.29754			0.648769	−	0.760985i	$-0.275284\pi$
$53$	9.44622			1.29754			0.648769	+	0.760985i	$0.275284\pi$
$54$	2.50000	−	4.33013i	0.340207	−	0.589256i
$55$		0			0
$56$	−1.00000	−	1.73205i	−0.133631	−	0.231455i
$57$	−4.22311	+	7.31464i	−0.559365	+	0.968848i
$58$	6.00000			0.787839
$59$	−0.446222			−0.0580932			−0.0290466	−	0.999578i	$-0.509247\pi$
$59$	−0.446222			−0.0580932			−0.0290466	+	0.999578i	$0.509247\pi$
$60$	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	$0.995517\pi$
$62$	−7.44622			−0.945671
$63$	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
$67$	−0.276889	−	8.18067i	−0.0338274	−	0.999428i
$67$	−0.276889	−	8.18067i	−0.0338274	−	0.999428i
$68$	6.44622			0.781719
$69$		0			0
$70$	−2.00000			−0.239046
$71$	−4.72311	−	8.18067i	−0.560530	−	0.970867i	−0.997450	−	0.0713663i	$-0.977264\pi$
$71$	−4.72311	−	8.18067i	−0.560530	−	0.970867i	0.436920	−	0.899500i	$-0.356069\pi$
$72$	−2.00000			−0.235702
$73$	−0.776889	+	1.34561i	−0.0909280	+	0.157492i	−0.907902	−	0.419183i	$-0.862317\pi$
$73$	−0.776889	+	1.34561i	−0.0909280	+	0.157492i	0.816974	+	0.576675i	$0.195650\pi$
$74$	−2.72311	−	4.71657i	−0.316555	−	0.548290i
$75$	1.00000			0.115470
$76$	8.44622			0.968848
$77$		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
$82$	9.44622			1.04316
$83$	−1.72311	+	2.98452i	−0.189136	+	0.327593i	−0.944962	−	0.327179i	$-0.893902\pi$
$83$	−1.72311	+	2.98452i	−0.189136	+	0.327593i	0.755826	+	0.654772i	$0.227235\pi$
$84$	−1.00000	+	1.73205i	−0.109109	+	0.188982i
$85$	3.22311	−	5.58259i	0.349595	−	0.605517i
$86$	−1.22311	+	2.11849i	−0.131891	+	0.228443i
$87$	−3.00000	−	5.19615i	−0.321634	−	0.557086i
$88$		0			0
$89$	−15.8924			−1.68460			−0.842298	−	0.539012i	$-0.818798\pi$
$89$	−15.8924			−1.68460			−0.842298	+	0.539012i	$0.818798\pi$
$90$	−1.00000	+	1.73205i	−0.105409	+	0.182574i
$91$	4.00000			0.419314
$92$		0			0
$93$	3.72311	+	6.44862i	0.386069	+	0.668690i
$94$		0			0
$95$	4.22311	−	7.31464i	0.433282	−	0.750467i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	2.22311	−	3.85054i	0.225723	−	0.390963i	−0.730813	−	0.682577i	$-0.760859\pi$
$97$	2.22311	−	3.85054i	0.225723	−	0.390963i	0.956536	+	0.291614i	$0.0941923\pi$
$98$	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	$0.929823\pi$
$102$	−3.22311	−	5.58259i	−0.319136	−	0.552759i
$103$	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
$106$	−4.72311	+	8.18067i	−0.458749	+	0.794577i
$107$	−3.44622			−0.333159			−0.166579	−	0.986028i	$-0.553272\pi$
$107$	−3.44622			−0.333159			−0.166579	+	0.986028i	$0.553272\pi$
$108$	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
$111$	−2.72311	+	4.71657i	−0.258466	+	0.447677i
$112$	2.00000			0.188982
$113$	9.22311	+	15.9749i	0.867637	+	1.50279i	0.864404	+	0.502797i	$0.167696\pi$
$113$	9.22311	+	15.9749i	0.867637	+	1.50279i	0.00323284	+	0.999995i	$0.498971\pi$
$114$	−4.22311	−	7.31464i	−0.395531	−	0.685079i
$115$		0			0
$116$	−3.00000	+	5.19615i	−0.278543	+	0.482451i
$117$	2.00000	−	3.46410i	0.184900	−	0.320256i
$118$	0.223111	−	0.386440i	0.0205390	−	0.0355746i
$119$	12.8924			1.18185
$120$	−1.00000			−0.0912871
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	−4.00000	−	6.92820i	−0.362143	−	0.627250i
$123$	−4.72311	−	8.18067i	−0.425869	−	0.737626i
$124$	3.72311	−	6.44862i	0.334345	−	0.579103i
$125$	−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
$129$	2.44622			0.215378
$130$	1.00000	+	1.73205i	0.0877058	+	0.151911i
$131$	−18.8924			−1.65064			−0.825320	−	0.564665i	$-0.809005\pi$
$131$	−18.8924			−1.65064			−0.825320	+	0.564665i	$0.809005\pi$
$132$		0			0
$133$	16.8924			1.46476
$134$	7.22311	+	3.85054i	0.623982	+	0.332636i
$135$	5.00000			0.430331
$136$	−3.22311	+	5.58259i	−0.276379	+	0.478703i
$137$	6.44622			0.550738			0.275369	−	0.961339i	$-0.411200\pi$
$137$	6.44622			0.550738			0.275369	+	0.961339i	$0.411200\pi$
$138$		0			0
$139$	−22.4462			−1.90386			−0.951932	−	0.306310i	$-0.900906\pi$
$139$	−22.4462			−1.90386			−0.951932	+	0.306310i	$0.900906\pi$
$140$	1.00000	−	1.73205i	0.0845154	−	0.146385i
$141$		0			0
$142$	9.44622			0.792709
$143$		0			0
$144$	1.00000	−	1.73205i	0.0833333	−	0.144338i
$145$	3.00000	+	5.19615i	0.249136	+	0.431517i
$146$	−0.776889	−	1.34561i	−0.0642958	−	0.111364i
$147$	1.50000	−	2.59808i	0.123718	−	0.214286i
$148$	5.44622			0.447677
$149$	−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
$151$	−2.27689	+	3.94369i	−0.185291	+	0.320933i	−0.943674	−	0.330876i	$-0.892656\pi$
$151$	−2.27689	+	3.94369i	−0.185291	+	0.320933i	0.758384	+	0.651808i	$0.225989\pi$
$152$	−4.22311	+	7.31464i	−0.342540	+	0.593296i
$153$	6.44622	−	11.1652i	0.521146	−	0.902652i
$154$		0			0
$155$	−3.72311	−	6.44862i	−0.299047	−	0.517965i
$156$	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
$159$	9.44622			0.749134
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$		0			0
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	3.94622	+	6.83506i	0.309092	+	0.535363i	0.978164	−	0.207835i	$-0.0666416\pi$
$163$	3.94622	+	6.83506i	0.309092	+	0.535363i	−0.669072	+	0.743198i	$0.733308\pi$
$164$	−4.72311	+	8.18067i	−0.368813	+	0.638803i
$165$		0			0
$166$	−1.72311	−	2.98452i	−0.133739	−	0.231643i
$167$	9.44622	+	16.3613i	0.730971	+	1.26608i	0.956469	+	0.291835i	$0.0942657\pi$
$167$	9.44622	+	16.3613i	0.730971	+	1.26608i	−0.225498	+	0.974244i	$0.572401\pi$
$168$	−1.00000	−	1.73205i	−0.0771517	−	0.133631i
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	3.22311	+	5.58259i	0.247201	+	0.428165i
$171$	8.44622	−	14.6293i	0.645899	−	1.11873i
$172$	−1.22311	−	2.11849i	−0.0932613	−	0.161533i
$173$	8.16933	−	14.1497i	0.621103	−	1.07578i	−0.368178	−	0.929755i	$-0.620018\pi$
$173$	8.16933	−	14.1497i	0.621103	−	1.07578i	0.989281	−	0.146026i	$-0.0466484\pi$
$174$	6.00000			0.454859
$175$	−1.00000	−	1.73205i	−0.0755929	−	0.130931i
$176$		0			0
$177$	−0.446222			−0.0335401
$178$	7.94622	−	13.7633i	0.595595	−	1.03160i
$179$	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
$181$	11.4462	+	19.8254i	0.850791	+	1.47361i	0.880496	+	0.474054i	$0.157210\pi$
$181$	11.4462	+	19.8254i	0.850791	+	1.47361i	−0.0297045	+	0.999559i	$0.509457\pi$
$182$	−2.00000	+	3.46410i	−0.148250	+	0.256776i
$183$	−4.00000	+	6.92820i	−0.295689	+	0.512148i
$184$		0			0
$185$	2.72311	−	4.71657i	0.200207	−	0.346769i
$186$	−7.44622			−0.545983
$187$		0			0
$188$		0			0
$189$	5.00000	+	8.66025i	0.363696	+	0.629941i
$190$	4.22311	+	7.31464i	0.306377	+	0.530660i
$191$	−1.72311	+	2.98452i	−0.124680	+	0.215952i	−0.921608	−	0.388123i	$-0.873124\pi$
$191$	−1.72311	+	2.98452i	−0.124680	+	0.215952i	0.796928	+	0.604074i	$0.206457\pi$
$192$	1.00000			0.0721688
$193$	20.8924			1.50387			0.751936	−	0.659237i	$-0.229120\pi$
$193$	20.8924			1.50387			0.751936	+	0.659237i	$0.229120\pi$
$194$	2.22311	+	3.85054i	0.159610	+	0.276453i
$195$	1.00000	−	1.73205i	0.0716115	−	0.124035i
$196$	−3.00000			−0.214286
$197$	3.44622	+	5.96903i	0.245533	+	0.425276i	0.962281	−	0.272056i	$-0.0877036\pi$
$197$	3.44622	+	5.96903i	0.245533	+	0.425276i	−0.716748	+	0.697332i	$0.754370\pi$
$198$		0			0
$199$	−2.72311	+	4.71657i	−0.193036	+	0.334349i	−0.946255	−	0.323422i	$-0.895167\pi$
$199$	−2.72311	+	4.71657i	−0.193036	+	0.334349i	0.753219	+	0.657770i	$0.228500\pi$
$200$	1.00000			0.0707107
$201$	−0.276889	−	8.18067i	−0.0195302	−	0.577020i
$202$	6.00000			0.422159
$203$	−6.00000	+	10.3923i	−0.421117	+	0.729397i
$204$	6.44622			0.451326
$205$	4.72311	+	8.18067i	0.329876	+	0.571363i
$206$	−4.00000			−0.278693
$207$		0			0
$208$	−1.00000	−	1.73205i	−0.0693375	−	0.120096i
$209$		0			0
$210$	−2.00000			−0.138013
$211$	4.77689	−	8.27381i	0.328855	−	0.569593i	−0.653430	−	0.756987i	$-0.726671\pi$
$211$	4.77689	−	8.27381i	0.328855	−	0.569593i	0.982285	+	0.187394i	$0.0600041\pi$
$212$	−4.72311	−	8.18067i	−0.324385	−	0.561851i
$213$	−4.72311	−	8.18067i	−0.323622	−	0.560530i
$214$	1.72311	−	2.98452i	0.117789	−	0.204017i
$215$	−2.44622			−0.166831
$216$	−5.00000			−0.340207
$217$	7.44622	−	12.8972i	0.505482	−	0.875521i
$218$	−7.00000	+	12.1244i	−0.474100	+	0.821165i
$219$	−0.776889	+	1.34561i	−0.0524973	+	0.0909280i
$220$		0			0
$221$	−6.44622	−	11.1652i	−0.433620	−	0.751052i
$222$	−2.72311	−	4.71657i	−0.182763	−	0.316555i
$223$	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
$226$	−18.4462			−1.22702
$227$	−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	$0.929878\pi$
$228$	8.44622			0.559365
$229$	−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
$233$	−9.66933	−	16.7478i	−0.633459	−	1.09718i	−0.986839	−	0.161704i	$-0.948301\pi$
$233$	−9.66933	−	16.7478i	−0.633459	−	1.09718i	0.353380	−	0.935480i	$-0.385032\pi$
$234$	2.00000	+	3.46410i	0.130744	+	0.226455i
$235$		0			0
$236$	0.223111	+	0.386440i	0.0145233	+	0.0251551i
$237$	−4.00000	−	6.92820i	−0.259828	−	0.450035i
$238$	−6.44622	+	11.1652i	−0.417847	+	0.723731i
$239$	6.44622	+	11.1652i	0.416971	+	0.722216i	0.995633	−	0.0933519i	$-0.0297582\pi$
$239$	6.44622	+	11.1652i	0.416971	+	0.722216i	−0.578662	+	0.815568i	$0.696425\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	17.4462			1.12381			0.561905	−	0.827202i	$-0.310069\pi$
$241$	17.4462			1.12381			0.561905	+	0.827202i	$0.310069\pi$
$242$	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
$246$	9.44622			0.602269
$247$	−8.44622	−	14.6293i	−0.537420	−	0.930839i
$248$	3.72311	+	6.44862i	0.236418	+	0.409488i
$249$	−1.72311	+	2.98452i	−0.109198	+	0.189136i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	2.77689	−	4.80971i	0.175276	−	0.303586i	−0.764981	−	0.644053i	$-0.777252\pi$
$251$	2.77689	−	4.80971i	0.175276	−	0.303586i	0.940257	+	0.340467i	$0.110585\pi$
$252$	2.00000	−	3.46410i	0.125988	−	0.218218i
$253$		0			0
$254$	−10.0000			−0.627456
$255$	3.22311	−	5.58259i	0.201839	−	0.349595i
$256$	−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	$-0.356405\pi$
$258$	−1.22311	+	2.11849i	−0.0761476	+	0.131891i
$259$	10.8924			0.676824
$260$	−2.00000			−0.124035
$261$	6.00000	+	10.3923i	0.371391	+	0.643268i
$262$	9.44622	−	16.3613i	0.583590	−	1.01081i
$263$	−6.89244			−0.425006			−0.212503	−	0.977160i	$-0.568162\pi$
$263$	−6.89244			−0.425006			−0.212503	+	0.977160i	$0.568162\pi$
$264$		0			0
$265$	−9.44622			−0.580277
$266$	−8.44622	+	14.6293i	−0.517871	+	0.896979i
$267$	−15.8924			−0.972602
$268$	−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
$271$	−25.4462			−1.54575			−0.772874	−	0.634560i	$-0.781182\pi$
$271$	−25.4462			−1.54575			−0.772874	+	0.634560i	$0.781182\pi$
$272$	−3.22311	−	5.58259i	−0.195430	−	0.338494i
$273$	4.00000			0.242091
$274$	−3.22311	+	5.58259i	−0.194715	+	0.337257i
$275$		0			0
$276$		0			0
$277$	4.55378			0.273610			0.136805	−	0.990598i	$-0.456317\pi$
$277$	4.55378			0.273610			0.136805	+	0.990598i	$0.456317\pi$
$278$	11.2231	−	19.4390i	0.673117	−	1.16587i
$279$	−7.44622	−	12.8972i	−0.445794	−	0.772137i
$280$	1.00000	+	1.73205i	0.0597614	+	0.103510i
$281$	−4.94622	+	8.56711i	−0.295067	+	0.511071i	−0.975000	−	0.222203i	$-0.928675\pi$
$281$	−4.94622	+	8.56711i	−0.295067	+	0.511071i	0.679934	+	0.733274i	$0.262009\pi$
$282$		0			0
$283$	−23.3387			−1.38734			−0.693670	−	0.720293i	$-0.744007\pi$
$283$	−23.3387			−1.38734			−0.693670	+	0.720293i	$0.744007\pi$
$284$	−4.72311	+	8.18067i	−0.280265	+	0.485433i
$285$	4.22311	−	7.31464i	0.250156	−	0.433282i
$286$		0			0
$287$	−9.44622	+	16.3613i	−0.557593	+	0.965779i
$288$	1.00000	+	1.73205i	0.0589256	+	0.102062i
$289$	−12.2769	−	21.2642i	−0.722170	−	1.25084i
$290$	−6.00000			−0.352332
$291$	2.22311	−	3.85054i	0.130321	−	0.225723i
$292$	1.55378			0.0909280
$293$	2.55378			0.149193			0.0745967	−	0.997214i	$-0.476233\pi$
$293$	2.55378			0.149193			0.0745967	+	0.997214i	$0.476233\pi$
$294$	1.50000	+	2.59808i	0.0874818	+	0.151523i
$295$	0.446222			0.0259800
$296$	−2.72311	+	4.71657i	−0.158278	+	0.274145i
$297$		0			0
$298$	6.00000	−	10.3923i	0.347571	−	0.602010i
$299$		0			0
$300$	−0.500000	−	0.866025i	−0.0288675	−	0.0500000i
$301$	−2.44622	−	4.23698i	−0.140998	−	0.244216i
$302$	−2.27689	−	3.94369i	−0.131020	−	0.226934i
$303$	−3.00000	−	5.19615i	−0.172345	−	0.298511i
$304$	−4.22311	−	7.31464i	−0.242212	−	0.419524i
$305$	4.00000	−	6.92820i	0.229039	−	0.396708i
$306$	6.44622	+	11.1652i	0.368506	+	0.638271i
$307$	−8.94622	+	15.4953i	−0.510588	+	0.884364i	0.489337	+	0.872095i	$0.337239\pi$
$307$	−8.94622	+	15.4953i	−0.510588	+	0.884364i	−0.999925	+	0.0122693i	$0.996094\pi$
$308$		0			0
$309$	2.00000	+	3.46410i	0.113776	+	0.197066i
$310$	7.44622			0.422917
$311$	−22.3387			−1.26671			−0.633355	−	0.773862i	$-0.718323\pi$
$311$	−22.3387			−1.26671			−0.633355	+	0.773862i	$0.718323\pi$
$312$	−1.00000	+	1.73205i	−0.0566139	+	0.0980581i
$313$	19.5538			1.10524			0.552622	−	0.833432i	$-0.313627\pi$
$313$	19.5538			1.10524			0.552622	+	0.833432i	$0.313627\pi$
$314$	−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
$317$	−16.7231	+	28.9653i	−0.939263	+	1.62685i	−0.172415	+	0.985024i	$0.555157\pi$
$317$	−16.7231	+	28.9653i	−0.939263	+	1.62685i	−0.766849	+	0.641828i	$0.778176\pi$
$318$	−4.72311	+	8.18067i	−0.264859	+	0.458749i
$319$		0			0
$320$	−1.00000			−0.0559017
$321$	−3.44622			−0.192349
$322$		0			0
$323$	−27.2231	−	47.1518i	−1.51473	−	2.62360i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−1.00000	+	1.73205i	−0.0554700	+	0.0960769i
$326$	−7.89244			−0.437122
$327$	14.0000			0.774202
$328$	−4.72311	−	8.18067i	−0.260790	−	0.451702i
$329$		0			0
$330$		0			0
$331$	−10.2231	−	17.7069i	−0.561913	−	0.973262i	−0.997330	−	0.0730328i	$-0.976732\pi$
$331$	−10.2231	−	17.7069i	−0.561913	−	0.973262i	0.435417	−	0.900229i	$-0.356601\pi$
$332$	3.44622			0.189136
$333$	5.44622	−	9.43313i	0.298451	−	0.516933i
$334$	−18.8924			−1.03375
$335$	0.276889	+	8.18067i	0.0151281	+	0.446958i
$336$	2.00000			0.109109
$337$	2.44622	−	4.23698i	0.133254	−	0.230803i	−0.791675	−	0.610942i	$-0.790791\pi$
$337$	2.44622	−	4.23698i	0.133254	−	0.230803i	0.924929	+	0.380139i	$0.124124\pi$
$338$	−9.00000			−0.489535
$339$	9.22311	+	15.9749i	0.500931	+	0.867637i
$340$	−6.44622			−0.349595
$341$		0			0
$342$	8.44622	+	14.6293i	0.456719	+	0.791061i
$343$	−20.0000			−1.07990
$344$	2.44622			0.131891
$345$		0			0
$346$	8.16933	+	14.1497i	0.439186	+	0.760693i
$347$	−2.77689	−	4.80971i	−0.149071	−	0.258199i	0.781813	−	0.623513i	$-0.214295\pi$
$347$	−2.77689	−	4.80971i	−0.149071	−	0.258199i	−0.930884	+	0.365314i	$0.880962\pi$
$348$	−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
$353$	−6.44622	+	11.1652i	−0.343098	+	0.594263i	−0.985006	−	0.172518i	$-0.944810\pi$
$353$	−6.44622	+	11.1652i	−0.343098	+	0.594263i	0.641909	+	0.766781i	$0.278143\pi$
$354$	0.223111	−	0.386440i	0.0118582	−	0.0205390i
$355$	4.72311	+	8.18067i	0.250677	+	0.434185i
$356$	7.94622	+	13.7633i	0.421149	+	0.729451i
$357$	12.8924			0.682340
$358$	−6.00000	+	10.3923i	−0.317110	+	0.549250i
$359$	−28.3387			−1.49566			−0.747829	−	0.663892i	$-0.768904\pi$
$359$	−28.3387			−1.49566			−0.747829	+	0.663892i	$0.768904\pi$
$360$	2.00000			0.105409
$361$	−26.1693	−	45.3266i	−1.37733	−	2.38561i
$362$	−22.8924			−1.20320
$363$	5.50000	−	9.52628i	0.288675	−	0.500000i
$364$	−2.00000	−	3.46410i	−0.104828	−	0.181568i
$365$	0.776889	−	1.34561i	0.0406642	−	0.0704325i
$366$	−4.00000	−	6.92820i	−0.209083	−	0.362143i
$367$	17.8924	+	30.9906i	0.933978	+	1.61770i	0.776446	+	0.630183i	$0.217020\pi$
$367$	17.8924	+	30.9906i	0.933978	+	1.61770i	0.157532	+	0.987514i	$0.449646\pi$
$368$		0			0
$369$	9.44622	+	16.3613i	0.491751	+	0.851737i
$370$	2.72311	+	4.71657i	0.141568	+	0.245203i
$371$	−9.44622	−	16.3613i	−0.490423	−	0.849438i
$372$	3.72311	−	6.44862i	0.193034	−	0.334345i
$373$	12.7231	+	22.0371i	0.658778	+	1.14104i	0.980932	+	0.194349i	$0.0622596\pi$
$373$	12.7231	+	22.0371i	0.658778	+	1.14104i	−0.322155	+	0.946687i	$0.604407\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	12.0000			0.618031
$378$	−10.0000			−0.514344
$379$	−16.8924	+	29.2586i	−0.867707	+	1.50291i	−0.00337217	+	0.999994i	$0.501073\pi$
$379$	−16.8924	+	29.2586i	−0.867707	+	1.50291i	−0.864334	+	0.502918i	$0.832260\pi$
$380$	−8.44622			−0.433282
$381$	5.00000	+	8.66025i	0.256158	+	0.443678i
$382$	−1.72311	−	2.98452i	−0.0881620	−	0.152701i
$383$	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
$386$	−10.4462	+	18.0934i	−0.531699	+	0.920929i
$387$	−4.89244			−0.248697
$388$	−4.44622			−0.225723
$389$	9.44622	−	16.3613i	0.478942	−	0.829553i	−0.520766	−	0.853699i	$-0.674354\pi$
$389$	9.44622	−	16.3613i	0.478942	−	0.829553i	0.999708	+	0.0241468i	$0.00768691\pi$
$390$	1.00000	+	1.73205i	0.0506370	+	0.0877058i
$391$		0			0
$392$	1.50000	−	2.59808i	0.0757614	−	0.131223i
$393$	−18.8924			−0.952998
$394$	−6.89244			−0.347236
$395$	4.00000	+	6.92820i	0.201262	+	0.348596i
$396$		0			0
$397$	6.33867			0.318129			0.159064	−	0.987268i	$-0.449152\pi$
$397$	6.33867			0.318129			0.159064	+	0.987268i	$0.449152\pi$
$398$	−2.72311	−	4.71657i	−0.136497	−	0.236420i
$399$	16.8924			0.845680
$400$	−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	$0.351624\pi$
$402$	7.22311	+	3.85054i	0.360256	+	0.192048i
$403$	−14.8924			−0.741845
$404$	−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
$408$	−3.22311	+	5.58259i	−0.159568	+	0.276379i
$409$	0.723111	+	1.25246i	0.0357555	+	0.0619304i	0.883349	−	0.468715i	$-0.155283\pi$
$409$	0.723111	+	1.25246i	0.0357555	+	0.0619304i	−0.847594	+	0.530645i	$0.821950\pi$
$410$	−9.44622			−0.466516
$411$	6.44622			0.317969
$412$	2.00000	−	3.46410i	0.0985329	−	0.170664i
$413$	0.446222	+	0.772879i	0.0219571	+	0.0380309i
$414$		0			0
$415$	1.72311	−	2.98452i	0.0845842	−	0.146504i
$416$	2.00000			0.0980581
$417$	−22.4462			−1.09920
$418$		0			0
$419$	−2.77689	+	4.80971i	−0.135660	+	0.234970i	−0.925849	−	0.377893i	$-0.876649\pi$
$419$	−2.77689	+	4.80971i	−0.135660	+	0.234970i	0.790189	+	0.612863i	$0.209982\pi$
$420$	1.00000	−	1.73205i	0.0487950	−	0.0845154i
$421$	−0.553778	+	0.959172i	−0.0269895	+	0.0467472i	−0.879205	−	0.476444i	$-0.841925\pi$
$421$	−0.553778	+	0.959172i	−0.0269895	+	0.0467472i	0.852215	+	0.523191i	$0.175259\pi$
$422$	4.77689	+	8.27381i	0.232535	+	0.402763i
$423$		0			0
$424$	9.44622			0.458749
$425$	−3.22311	+	5.58259i	−0.156344	+	0.270795i
$426$	9.44622			0.457671
$427$	16.0000			0.774294
$428$	1.72311	+	2.98452i	0.0832897	+	0.144262i
$429$		0			0
$430$	1.22311	−	2.11849i	0.0589836	−	0.102163i
$431$	−8.16933	−	14.1497i	−0.393503	−	0.681567i	0.599406	−	0.800445i	$-0.295404\pi$
$431$	−8.16933	−	14.1497i	−0.393503	−	0.681567i	−0.992909	+	0.118878i	$0.962070\pi$
$432$	2.50000	−	4.33013i	0.120281	−	0.208333i
$433$	−10.6693	−	18.4798i	−0.512735	−	0.888084i	−0.999891	−	0.0147686i	$-0.995299\pi$
$433$	−10.6693	−	18.4798i	−0.512735	−	0.888084i	0.487156	−	0.873315i	$-0.338034\pi$
$434$	7.44622	+	12.8972i	0.357430	+	0.619087i
$435$	3.00000	+	5.19615i	0.143839	+	0.249136i
$436$	−7.00000	−	12.1244i	−0.335239	−	0.580651i
$437$		0			0
$438$	−0.776889	−	1.34561i	−0.0371212	−	0.0642958i
$439$	15.7231	−	27.2332i	0.750423	−	1.29977i	−0.197195	−	0.980364i	$-0.563183\pi$
$439$	15.7231	−	27.2332i	0.750423	−	1.29977i	0.947618	−	0.319407i	$-0.103484\pi$
$440$		0			0
$441$	−3.00000	+	5.19615i	−0.142857	+	0.247436i
$442$	12.8924			0.613231
$443$	10.9462	+	18.9594i	0.520071	+	0.900789i	0.999728	+	0.0233328i	$0.00742775\pi$
$443$	10.9462	+	18.9594i	0.520071	+	0.900789i	−0.479657	+	0.877456i	$0.659239\pi$
$444$	5.44622			0.258466
$445$	15.8924			0.753374
$446$	−1.00000	+	1.73205i	−0.0473514	+	0.0820150i
$447$	−12.0000			−0.567581
$448$	−1.00000	−	1.73205i	−0.0472456	−	0.0818317i
$449$	−8.16933	−	14.1497i	−0.385535	−	0.667766i	0.606309	−	0.795229i	$-0.292650\pi$
$449$	−8.16933	−	14.1497i	−0.385535	−	0.667766i	−0.991843	+	0.127464i	$0.959316\pi$
$450$	1.00000	−	1.73205i	0.0471405	−	0.0816497i
$451$		0			0
$452$	9.22311	−	15.9749i	0.433819	−	0.751396i
$453$	−2.27689	+	3.94369i	−0.106978	+	0.185291i
$454$	9.00000			0.422391
$455$	−4.00000			−0.187523
$456$	−4.22311	+	7.31464i	−0.197765	+	0.342540i
$457$	−13.2231	−	22.9031i	−0.618551	−	1.07136i	−0.989750	−	0.142809i	$-0.954387\pi$
$457$	−13.2231	−	22.9031i	−0.618551	−	1.07136i	0.371199	−	0.928553i	$-0.378947\pi$
$458$	−4.00000	−	6.92820i	−0.186908	−	0.323734i
$459$	16.1156	−	27.9130i	0.752210	−	1.30287i
$460$		0			0
$461$	36.8924			1.71825			0.859126	−	0.511764i	$-0.171008\pi$
$461$	36.8924			1.71825			0.859126	+	0.511764i	$0.171008\pi$
$462$		0			0
$463$	−13.8924	+	24.0624i	−0.645637	+	1.11828i	0.338517	+	0.940960i	$0.390075\pi$
$463$	−13.8924	+	24.0624i	−0.645637	+	1.11828i	−0.984154	+	0.177315i	$0.943259\pi$
$464$	6.00000			0.278543
$465$	−3.72311	−	6.44862i	−0.172655	−	0.299047i
$466$	19.3387			0.895846
$467$	1.72311	−	2.98452i	0.0797361	−	0.138107i	−0.823400	−	0.567461i	$-0.807926\pi$
$467$	1.72311	−	2.98452i	0.0797361	−	0.138107i	0.903136	+	0.429355i	$0.141259\pi$
$468$	−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
$472$	−0.446222			−0.0205390
$473$		0			0
$474$	8.00000			0.367452
$475$	−4.22311	+	7.31464i	−0.193770	+	0.335619i
$476$	−6.44622	−	11.1652i	−0.295462	−	0.511755i
$477$	−18.8924			−0.865026
$478$	−12.8924			−0.589687
$479$		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
$481$	−5.44622	−	9.43313i	−0.248326	−	0.430114i
$482$	−8.72311	+	15.1089i	−0.397327	+	0.688190i
$483$		0			0
$484$	−11.0000			−0.500000
$485$	−2.22311	+	3.85054i	−0.100946	+	0.174844i
$486$	−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
$489$	3.94622	+	6.83506i	0.178454	+	0.309092i
$490$	−1.50000	−	2.59808i	−0.0677631	−	0.117369i
$491$	37.3387			1.68507			0.842535	−	0.538641i	$-0.181062\pi$
$491$	37.3387			1.68507			0.842535	+	0.538641i	$0.181062\pi$
$492$	−4.72311	+	8.18067i	−0.212934	+	0.368813i
$493$	38.6773			1.74194
$494$	16.8924			0.760027
$495$		0			0
$496$	−7.44622			−0.334345
$497$	−9.44622	+	16.3613i	−0.423721	+	0.733906i
$498$	−1.72311	−	2.98452i	−0.0772145	−	0.133739i
$499$	−13.2231	+	22.9031i	−0.591948	+	1.02528i	0.402022	+	0.915630i	$0.368307\pi$
$499$	−13.2231	+	22.9031i	−0.591948	+	1.02528i	−0.993970	+	0.109654i	$0.965026\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	9.44622	+	16.3613i	0.422026	+	0.730971i
$502$	2.77689	+	4.80971i	0.123939	+	0.214668i
$503$	−12.4462	−	21.5575i	−0.554950	−	0.961201i	−0.997907	−	0.0646585i	$-0.979404\pi$
$503$	−12.4462	−	21.5575i	−0.554950	−	0.961201i	0.442958	−	0.896542i	$-0.353929\pi$
$504$	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	$0.369386\pi$
$510$	3.22311	+	5.58259i	0.142722	+	0.247201i
$511$	3.10756			0.137470
$512$	1.00000			0.0441942
$513$	21.1156	−	36.5732i	0.932275	−	1.61475i
$514$	18.0000			0.793946
$515$	−2.00000	−	3.46410i	−0.0881305	−	0.152647i
$516$	−1.22311	−	2.11849i	−0.0538445	−	0.0932613i
$517$		0			0
$518$	−5.44622	+	9.43313i	−0.239293	+	0.414468i
$519$	8.16933	−	14.1497i	0.358594	−	0.621103i
$520$	1.00000	−	1.73205i	0.0438529	−	0.0759555i
$521$	−13.3387			−0.584378			−0.292189	−	0.956361i	$-0.594384\pi$
$521$	−13.3387			−0.584378			−0.292189	+	0.956361i	$0.594384\pi$
$522$	−12.0000			−0.525226
$523$	−9.39244	+	16.2682i	−0.410703	+	0.711358i	−0.994967	−	0.100205i	$-0.968050\pi$
$523$	−9.39244	+	16.2682i	−0.410703	+	0.711358i	0.584264	+	0.811564i	$0.301383\pi$
$524$	9.44622	+	16.3613i	0.412660	+	0.714748i
$525$	−1.00000	−	1.73205i	−0.0436436	−	0.0755929i
$526$	3.44622	−	5.96903i	0.150262	−	0.260262i
$527$	−48.0000			−2.09091
$528$		0			0
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	4.72311	−	8.18067i	0.205159	−	0.355346i
$531$	0.892444			0.0387288
$532$	−8.44622	−	14.6293i	−0.366190	−	0.634260i
$533$	18.8924			0.818323
$534$	7.94622	−	13.7633i	0.343867	−	0.595595i
$535$	3.44622			0.148993
$536$	−0.276889	−	8.18067i	−0.0119598	−	0.353351i
$537$	12.0000			0.517838
$538$		0			0
$539$		0			0
$540$	−2.50000	−	4.33013i	−0.107583	−	0.186339i
$541$	40.6773			1.74886			0.874428	−	0.485156i	$-0.161237\pi$
$541$	40.6773			1.74886			0.874428	+	0.485156i	$0.161237\pi$
$542$	12.7231	−	22.0371i	0.546504	−	0.946573i
$543$	11.4462	+	19.8254i	0.491204	+	0.850791i
$544$	6.44622			0.276379
$545$	−14.0000			−0.599694
$546$	−2.00000	+	3.46410i	−0.0855921	+	0.148250i
$547$	9.72311	+	16.8409i	0.415730	+	0.720066i	0.995505	−	0.0947111i	$-0.0301927\pi$
$547$	9.72311	+	16.8409i	0.415730	+	0.720066i	−0.579775	+	0.814777i	$0.696859\pi$
$548$	−3.22311	−	5.58259i	−0.137684	−	0.238477i
$549$	8.00000	−	13.8564i	0.341432	−	0.591377i
$550$		0			0
$551$	50.6773			2.15893
$552$		0			0
$553$	−8.00000	+	13.8564i	−0.340195	+	0.589234i
$554$	−2.27689	+	3.94369i	−0.0967357	+	0.167551i
$555$	2.72311	−	4.71657i	0.115590	−	0.200207i
$556$	11.2231	+	19.4390i	0.475966	+	0.824397i
$557$	11.1693	+	19.3459i	0.473260	+	0.819710i	0.999532	−	0.0306064i	$-0.00974384\pi$
$557$	11.1693	+	19.3459i	0.473260	+	0.819710i	−0.526272	+	0.850316i	$0.676411\pi$
$558$	14.8924			0.630447
$559$	−2.44622	+	4.23698i	−0.103464	+	0.179205i
$560$	−2.00000			−0.0845154
$561$		0			0
$562$	−4.94622	−	8.56711i	−0.208644	−	0.361382i
$563$	−27.8924			−1.17553			−0.587763	−	0.809033i	$-0.699991\pi$
$563$	−27.8924			−1.17553			−0.587763	+	0.809033i	$0.699991\pi$
$564$		0			0
$565$	−9.22311	−	15.9749i	−0.388019	−	0.672069i
$566$	11.6693	−	20.2119i	0.490499	−	0.849569i
$567$	−1.00000	−	1.73205i	−0.0419961	−	0.0727393i
$568$	−4.72311	−	8.18067i	−0.198177	−	0.343253i
$569$	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	$0.731525\pi$
$570$	4.22311	+	7.31464i	0.176887	+	0.306377i
$571$	13.7769	+	23.8623i	0.576545	+	0.998605i	0.995872	+	0.0907697i	$0.0289327\pi$
$571$	13.7769	+	23.8623i	0.576545	+	0.998605i	−0.419327	+	0.907835i	$0.637734\pi$
$572$		0			0
$573$	−1.72311	+	2.98452i	−0.0719840	+	0.124680i
$574$	−9.44622	−	16.3613i	−0.394278	−	0.682909i
$575$		0			0
$576$	−2.00000			−0.0833333
$577$	5.22311	+	9.04669i	0.217441	+	0.376619i	0.954025	−	0.299727i	$-0.0968957\pi$
$577$	5.22311	+	9.04669i	0.217441	+	0.376619i	−0.736584	+	0.676346i	$0.763562\pi$
$578$	24.5538			1.02130
$579$	20.8924			0.868260
$580$	3.00000	−	5.19615i	0.124568	−	0.215758i
$581$	6.89244			0.285947
$582$	2.22311	+	3.85054i	0.0921509	+	0.159610i
$583$		0			0
$584$	−0.776889	+	1.34561i	−0.0321479	+	0.0556818i
$585$	−2.00000	+	3.46410i	−0.0826898	+	0.143223i
$586$	−1.27689	+	2.21164i	−0.0527478	+	0.0913619i
$587$	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
$589$	−62.8924			−2.59144
$590$	−0.223111	+	0.386440i	−0.00918533	+	0.0159095i
$591$	3.44622	+	5.96903i	0.141759	+	0.245533i
$592$	−2.72311	−	4.71657i	−0.111919	−	0.193850i
$593$	−21.6693	+	37.5324i	−0.889853	+	1.54127i	−0.0498044	+	0.998759i	$0.515860\pi$
$593$	−21.6693	+	37.5324i	−0.889853	+	1.54127i	−0.840048	+	0.542511i	$0.817474\pi$
$594$		0			0
$595$	−12.8924			−0.528539
$596$	6.00000	+	10.3923i	0.245770	+	0.425685i
$597$	−2.72311	+	4.71657i	−0.111450	+	0.193036i
$598$		0			0
$599$	−0.446222	−	0.772879i	−0.0182321	−	0.0315790i	0.856765	−	0.515706i	$-0.172470\pi$
$599$	−0.446222	−	0.772879i	−0.0182321	−	0.0315790i	−0.874998	+	0.484127i	$0.839137\pi$
$600$	1.00000			0.0408248
$601$	2.22311	−	3.85054i	0.0906826	−	0.157067i	−0.817116	−	0.576473i	$-0.804428\pi$
$601$	2.22311	−	3.85054i	0.0906826	−	0.157067i	0.907799	+	0.419406i	$0.137762\pi$
$602$	4.89244			0.199401
$603$	0.553778	+	16.3613i	0.0225516	+	0.666285i
$604$	4.55378			0.185291
$605$	−5.50000	+	9.52628i	−0.223607	+	0.387298i
$606$	6.00000			0.243733
$607$	−0.553778	−	0.959172i	−0.0224772	−	0.0389316i	0.854568	−	0.519339i	$-0.173822\pi$
$607$	−0.553778	−	0.959172i	−0.0224772	−	0.0389316i	−0.877045	+	0.480408i	$0.840489\pi$
$608$	8.44622			0.342540
$609$	−6.00000	+	10.3923i	−0.243132	+	0.421117i
$610$	4.00000	+	6.92820i	0.161955	+	0.280515i
$611$		0			0
$612$	−12.8924			−0.521146
$613$	−2.72311	+	4.71657i	−0.109985	+	0.190500i	−0.915764	−	0.401716i	$-0.868414\pi$
$613$	−2.72311	+	4.71657i	−0.109985	+	0.190500i	0.805779	+	0.592217i	$0.201747\pi$
$614$	−8.94622	−	15.4953i	−0.361040	−	0.625340i
$615$	4.72311	+	8.18067i	0.190454	+	0.329876i
$616$		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
$619$	14.6693	−	25.4080i	0.589610	−	1.02123i	−0.404673	−	0.914461i	$-0.632615\pi$
$619$	14.6693	−	25.4080i	0.589610	−	1.02123i	0.994283	−	0.106774i	$-0.0340520\pi$
$620$	−3.72311	+	6.44862i	−0.149524	+	0.258983i
$621$		0			0
$622$	11.1693	−	19.3459i	0.447849	−	0.775698i
$623$	15.8924	+	27.5265i	0.636717	+	1.10283i
$624$	−1.00000	−	1.73205i	−0.0400320	−	0.0693375i
$625$	1.00000			0.0400000
$626$	−9.77689	+	16.9341i	−0.390763	+	0.676821i
$627$		0			0
$628$	14.0000			0.558661
$629$	−17.5538	−	30.4040i	−0.699915	−	1.21229i
$630$	4.00000			0.159364
$631$	1.55378	−	2.69122i	0.0618549	−	0.107136i	−0.833440	−	0.552611i	$-0.813632\pi$
$631$	1.55378	−	2.69122i	0.0618549	−	0.107136i	0.895295	+	0.445475i	$0.146965\pi$
$632$	−4.00000	−	6.92820i	−0.159111	−	0.275589i
$633$	4.77689	−	8.27381i	0.189864	−	0.328855i
$634$	−16.7231	−	28.9653i	−0.664160	−	1.15036i
$635$	−5.00000	−	8.66025i	−0.198419	−	0.343672i
$636$	−4.72311	−	8.18067i	−0.187284	−	0.324385i
$637$	3.00000	+	5.19615i	0.118864	+	0.205879i
$638$		0			0
$639$	9.44622	+	16.3613i	0.373687	+	0.647244i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−19.1156	−	33.1091i	−0.755019	−	1.30773i	−0.945365	−	0.326014i	$-0.894294\pi$
$641$	−19.1156	−	33.1091i	−0.755019	−	1.30773i	0.190346	−	0.981717i	$-0.439039\pi$
$642$	1.72311	−	2.98452i	0.0680058	−	0.117789i
$643$	−44.7849			−1.76614			−0.883072	−	0.469238i	$-0.844529\pi$
$643$	−44.7849			−1.76614			−0.883072	+	0.469238i	$0.844529\pi$
$644$		0			0
$645$	−2.44622			−0.0963199
$646$	54.4462			2.14216
$647$	−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
$651$	7.44622	−	12.8972i	0.291840	−	0.505482i
$652$	3.94622	−	6.83506i	0.154546	−	0.267681i
$653$	−1.27689	+	2.21164i	−0.0499685	+	0.0865480i	−0.889928	−	0.456101i	$-0.849245\pi$
$653$	−1.27689	+	2.21164i	−0.0499685	+	0.0865480i	0.839959	+	0.542649i	$0.182579\pi$
$654$	−7.00000	+	12.1244i	−0.273722	+	0.474100i
$655$	18.8924			0.738189
$656$	9.44622			0.368813
$657$	1.55378	−	2.69122i	0.0606187	−	0.104995i
$658$		0			0
$659$	3.66933	+	6.35547i	0.142937	+	0.247574i	0.928601	−	0.371079i	$-0.121012\pi$
$659$	3.66933	+	6.35547i	0.142937	+	0.247574i	−0.785664	+	0.618653i	$0.787679\pi$
$660$		0			0
$661$	9.78489			0.380588			0.190294	−	0.981727i	$-0.439056\pi$
$661$	9.78489			0.380588			0.190294	+	0.981727i	$0.439056\pi$
$662$	20.4462			0.794665
$663$	−6.44622	−	11.1652i	−0.250351	−	0.433620i
$664$	−1.72311	+	2.98452i	−0.0668697	+	0.115822i
$665$	−16.8924			−0.655061
$666$	5.44622	+	9.43313i	0.211037	+	0.365526i
$667$		0			0
$668$	9.44622	−	16.3613i	0.365485	−	0.633039i
$669$	2.00000			0.0773245
$670$	−7.22311	−	3.85054i	−0.279053	−	0.148759i
$671$		0			0
$672$	−1.00000	+	1.73205i	−0.0385758	+	0.0668153i
$673$	−42.2311			−1.62789			−0.813945	−	0.580942i	$-0.802684\pi$
$673$	−42.2311			−1.62789			−0.813945	+	0.580942i	$0.802684\pi$
$674$	2.44622	+	4.23698i	0.0942250	+	0.163202i
$675$	−5.00000			−0.192450
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	−2.16933	−	3.75739i	−0.0833742	−	0.144408i	0.821323	−	0.570463i	$-0.193236\pi$
$677$	−2.16933	−	3.75739i	−0.0833742	−	0.144408i	−0.904697	+	0.426055i	$0.859903\pi$
$678$	−18.4462			−0.708423
$679$	−8.89244			−0.341261
$680$	3.22311	−	5.58259i	0.123601	−	0.214083i
$681$	−4.50000	−	7.79423i	−0.172440	−	0.298675i
$682$		0			0
$683$	−4.05378	+	7.02135i	−0.155114	+	0.268664i	−0.933100	−	0.359616i	$-0.882908\pi$
$683$	−4.05378	+	7.02135i	−0.155114	+	0.268664i	0.777987	+	0.628281i	$0.216241\pi$
$684$	−16.8924			−0.645899
$685$	−6.44622			−0.246297
$686$	10.0000	−	17.3205i	0.381802	−	0.661300i
$687$	−4.00000	+	6.92820i	−0.152610	+	0.264327i
$688$	−1.22311	+	2.11849i	−0.0466307	+	0.0807667i
$689$	−9.44622	+	16.3613i	−0.359872	+	0.623317i
$690$		0			0
$691$	10.5538	+	18.2797i	0.401485	+	0.695392i	0.993905	−	0.110237i	$-0.0351610\pi$
$691$	10.5538	+	18.2797i	0.401485	+	0.695392i	−0.592421	+	0.805629i	$0.701828\pi$
$692$	−16.3387			−0.621103
$693$		0			0
$694$	5.55378			0.210819
$695$	22.4462			0.851434
$696$	−3.00000	−	5.19615i	−0.113715	−	0.196960i
$697$	60.8924			2.30647
$698$	−4.00000	+	6.92820i	−0.151402	+	0.262236i
$699$	−9.66933	−	16.7478i	−0.365728	−	0.633459i
$700$	−1.00000	+	1.73205i	−0.0377964	+	0.0654654i
$701$	12.4462	+	21.5575i	0.470087	+	0.814215i	0.999415	−	0.0342024i	$-0.0108891\pi$
$701$	12.4462	+	21.5575i	0.470087	+	0.814215i	−0.529328	+	0.848418i	$0.677556\pi$
$702$	5.00000	+	8.66025i	0.188713	+	0.326860i
$703$	−23.0000	−	39.8372i	−0.867461	−	1.50249i
$704$		0			0
$705$		0			0
$706$	−6.44622	−	11.1652i	−0.242607	−	0.420207i
$707$	−6.00000	+	10.3923i	−0.225653	+	0.390843i
$708$	0.223111	+	0.386440i	0.00838502	+	0.0145233i
$709$	−16.8924	+	29.2586i	−0.634409	+	1.09883i	0.352231	+	0.935913i	$0.385423\pi$
$709$	−16.8924	+	29.2586i	−0.634409	+	1.09883i	−0.986640	+	0.162916i	$0.947910\pi$
$710$	−9.44622			−0.354510
$711$	8.00000	+	13.8564i	0.300023	+	0.519656i
$712$	−15.8924			−0.595595
$713$		0			0
$714$	−6.44622	+	11.1652i	−0.241244	+	0.417847i
$715$		0			0
$716$	−6.00000	−	10.3923i	−0.224231	−	0.388379i
$717$	6.44622	+	11.1652i	0.240739	+	0.416971i
$718$	14.1693	−	24.5420i	0.528795	−	0.915899i
$719$	17.6156	−	30.5110i	0.656949	−	1.13787i	−0.324452	−	0.945902i	$-0.605180\pi$
$719$	17.6156	−	30.5110i	0.656949	−	1.13787i	0.981401	−	0.191967i	$-0.0614868\pi$
$720$	−1.00000	+	1.73205i	−0.0372678	+	0.0645497i
$721$	4.00000	−	6.92820i	0.148968	−	0.258020i
$722$	52.3387			1.94784
$723$	17.4462			0.648832
$724$	11.4462	−	19.8254i	0.425395	−	0.736807i
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$	5.50000	+	9.52628i	0.204124	+	0.353553i
$727$	11.8924	−	20.5983i	0.441066	−	0.763949i	−0.556703	−	0.830712i	$-0.687934\pi$
$727$	11.8924	−	20.5983i	0.441066	−	0.763949i	0.997769	+	0.0667626i	$0.0212670\pi$
$728$	4.00000			0.148250
$729$	13.0000			0.481481
$730$	0.776889	+	1.34561i	0.0287540	+	0.0498033i
$731$	−7.88445	+	13.6563i	−0.291617	+	0.505095i
$732$	8.00000			0.295689
$733$	−14.2769	−	24.7283i	−0.527329	−	0.913360i	−0.999493	−	0.0318496i	$-0.989860\pi$
$733$	−14.2769	−	24.7283i	−0.527329	−	0.913360i	0.472164	−	0.881511i	$-0.343473\pi$
$734$	−35.7849			−1.32084
$735$	−1.50000	+	2.59808i	−0.0553283	+	0.0958315i
$736$		0			0
$737$		0			0
$738$	−18.8924			−0.695440
$739$	−10.2231	+	17.7069i	−0.376063	+	0.651361i	−0.990486	−	0.137617i	$-0.956056\pi$
$739$	−10.2231	+	17.7069i	−0.376063	+	0.651361i	0.614422	+	0.788977i	$0.289389\pi$
$740$	−5.44622			−0.200207
$741$	−8.44622	−	14.6293i	−0.310280	−	0.537420i
$742$	18.8924			0.693563
$743$	−0.446222	+	0.772879i	−0.0163703	+	0.0283542i	−0.874095	−	0.485756i	$-0.838544\pi$
$743$	−0.446222	+	0.772879i	−0.0163703	+	0.0283542i	0.857724	+	0.514110i	$0.171878\pi$
$744$	3.72311	+	6.44862i	0.136496	+	0.236418i
$745$	12.0000			0.439646
$746$	−25.4462			−0.931652
$747$	3.44622	−	5.96903i	0.126091	−	0.218395i
$748$		0			0
$749$	3.44622	+	5.96903i	0.125922	+	0.218104i
$750$	0.500000	−	0.866025i	0.0182574	−	0.0316228i
$751$	17.4462			0.636622			0.318311	−	0.947986i	$-0.396884\pi$
$751$	17.4462			0.636622			0.318311	+	0.947986i	$0.396884\pi$
$752$		0			0
$753$	2.77689	−	4.80971i	0.101195	−	0.175276i
$754$	−6.00000	+	10.3923i	−0.218507	+	0.378465i
$755$	2.27689	−	3.94369i	0.0828645	−	0.143525i
$756$	5.00000	−	8.66025i	0.181848	−	0.314970i
$757$	−2.72311	−	4.71657i	−0.0989732	−	0.171427i	0.812287	−	0.583258i	$-0.198222\pi$
$757$	−2.72311	−	4.71657i	−0.0989732	−	0.171427i	−0.911260	+	0.411832i	$0.864889\pi$
$758$	−16.8924	−	29.2586i	−0.613561	−	1.06272i
$759$		0			0
$760$	4.22311	−	7.31464i	0.153188	−	0.265330i
$761$	−33.4462			−1.21242			−0.606212	−	0.795303i	$-0.707312\pi$
$761$	−33.4462			−1.21242			−0.606212	+	0.795303i	$0.707312\pi$
$762$	−10.0000			−0.362262
$763$	−14.0000	−	24.2487i	−0.506834	−	0.877862i
$764$	3.44622			0.124680
$765$	−6.44622	+	11.1652i	−0.233064	+	0.403678i
$766$	3.00000	+	5.19615i	0.108394	+	0.187745i
$767$	0.446222	−	0.772879i	0.0161121	−	0.0279070i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	2.66933	+	4.62342i	0.0962586	+	0.166725i	0.910133	−	0.414316i	$-0.135979\pi$
$769$	2.66933	+	4.62342i	0.0962586	+	0.166725i	−0.813875	+	0.581041i	$0.802646\pi$
$770$		0			0
$771$	−9.00000	−	15.5885i	−0.324127	−	0.561405i
$772$	−10.4462	−	18.0934i	−0.375968	−	0.651195i
$773$	20.1693	+	34.9343i	0.725440	+	1.25650i	0.958792	+	0.284107i	$0.0916972\pi$
$773$	20.1693	+	34.9343i	0.725440	+	1.25650i	−0.233352	+	0.972392i	$0.574969\pi$
$774$	2.44622	−	4.23698i	0.0879276	−	0.152295i
$775$	3.72311	+	6.44862i	0.133738	+	0.231641i
$776$	2.22311	−	3.85054i	0.0798050	−	0.138226i
$777$	10.8924			0.390764
$778$	9.44622	+	16.3613i	0.338663	+	0.586582i
$779$	79.7849			2.85859
$780$	−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
$786$	9.44622	−	16.3613i	0.336936	−	0.583590i
$787$	−5.72311	+	9.91272i	−0.204007	+	0.353350i	−0.949816	−	0.312810i	$-0.898730\pi$
$787$	−5.72311	+	9.91272i	−0.204007	+	0.353350i	0.745809	+	0.666160i	$0.232063\pi$
$788$	3.44622	−	5.96903i	0.122767	−	0.212638i
$789$	−6.89244			−0.245378
$790$	−8.00000			−0.284627
$791$	18.4462	−	31.9498i	0.655872	−	1.13600i
$792$		0			0
$793$	−8.00000	−	13.8564i	−0.284088	−	0.492055i
$794$	−3.16933	+	5.48945i	−0.112475	+	0.194813i
$795$	−9.44622			−0.335023
$796$	5.44622			0.193036
$797$	13.7231	+	23.7691i	0.486098	+	0.841946i	0.999872	−	0.0159795i	$-0.00508664\pi$
$797$	13.7231	+	23.7691i	0.486098	+	0.841946i	−0.513775	+	0.857925i	$0.671753\pi$
$798$	−8.44622	+	14.6293i	−0.298993	+	0.517871i
$799$		0			0
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	31.7849			1.12306
$802$	−9.00000	+	15.5885i	−0.317801	+	0.550448i
$803$		0			0
$804$	−6.94622	+	4.33013i	−0.244974	+	0.152712i
$805$		0			0
$806$	7.44622	−	12.8972i	0.262282	−	0.454286i
$807$		0			0
$808$	−3.00000	−	5.19615i	−0.105540	−	0.182800i
$809$	−19.7849			−0.695600			−0.347800	−	0.937569i	$-0.613071\pi$
$809$	−19.7849			−0.695600			−0.347800	+	0.937569i	$0.613071\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	11.4462	+	19.8254i	0.401931	+	0.696165i	0.993959	−	0.109752i	$-0.0350058\pi$
$811$	11.4462	+	19.8254i	0.401931	+	0.696165i	−0.592028	+	0.805918i	$0.701672\pi$
$812$	12.0000			0.421117
$813$	−25.4462			−0.892438
$814$		0			0
$815$	−3.94622	−	6.83506i	−0.138230	−	0.239422i
$816$	−3.22311	−	5.58259i	−0.112831	−	0.195430i
$817$	−10.3307	+	17.8932i	−0.361424	+	0.626005i
$818$	−1.44622			−0.0505660
$819$	−8.00000			−0.279543
$820$	4.72311	−	8.18067i	0.164938	−	0.285681i
$821$	−19.3387	+	33.4956i	−0.674924	+	1.16900i	0.301567	+	0.953445i	$0.402490\pi$
$821$	−19.3387	+	33.4956i	−0.674924	+	1.16900i	−0.976491	+	0.215558i	$0.930843\pi$
$822$	−3.22311	+	5.58259i	−0.112419	+	0.194715i
$823$	5.44622	−	9.43313i	0.189843	−	0.328818i	−0.755355	−	0.655316i	$-0.772535\pi$
$823$	5.44622	−	9.43313i	0.189843	−	0.328818i	0.945198	+	0.326498i	$0.105869\pi$
$824$	2.00000	+	3.46410i	0.0696733	+	0.120678i
$825$		0			0
$826$	−0.892444			−0.0310521
$827$	18.8924	−	32.7227i	0.656955	−	1.13788i	−0.324445	−	0.945904i	$-0.605178\pi$
$827$	18.8924	−	32.7227i	0.656955	−	1.13788i	0.981400	−	0.191974i	$-0.0614890\pi$
$828$		0			0
$829$	−35.7849			−1.24286			−0.621430	−	0.783469i	$-0.713448\pi$
$829$	−35.7849			−1.24286			−0.621430	+	0.783469i	$0.713448\pi$
$830$	1.72311	+	2.98452i	0.0598101	+	0.103594i
$831$	4.55378			0.157969
$832$	−1.00000	+	1.73205i	−0.0346688	+	0.0600481i
$833$	9.66933	+	16.7478i	0.335023	+	0.580276i
$834$	11.2231	−	19.4390i	0.388625	−	0.673117i
$835$	−9.44622	−	16.3613i	−0.326900	−	0.566207i
$836$		0			0
$837$	−18.6156	−	32.2431i	−0.643448	−	1.11448i
$838$	−2.77689	−	4.80971i	−0.0959260	−	0.166149i
$839$	22.7231	+	39.3576i	0.784489	+	1.35877i	0.929304	+	0.369316i	$0.120408\pi$
$839$	22.7231	+	39.3576i	0.784489	+	1.35877i	−0.144815	+	0.989459i	$0.546259\pi$
$840$	1.00000	+	1.73205i	0.0345033	+	0.0597614i
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	−0.553778	−	0.959172i	−0.0190845	−	0.0330552i
$843$	−4.94622	+	8.56711i	−0.170357	+	0.295067i
$844$	−9.55378			−0.328855
$845$	−4.50000	−	7.79423i	−0.154805	−	0.268130i
$846$		0			0
$847$	−22.0000			−0.755929
$848$	−4.72311	+	8.18067i	−0.162192	+	0.280925i
$849$	−23.3387			−0.800981
$850$	−3.22311	−	5.58259i	−0.110552	−	0.191481i
$851$		0			0
$852$	−4.72311	+	8.18067i	−0.161811	+	0.280265i
$853$	−8.72311	+	15.1089i	−0.298674	+	0.517318i	−0.975833	−	0.218519i	$-0.929878\pi$
$853$	−8.72311	+	15.1089i	−0.298674	+	0.517318i	0.677159	+	0.735837i	$0.263211\pi$
$854$	−8.00000	+	13.8564i	−0.273754	+	0.474156i
$855$	−8.44622	+	14.6293i	−0.288855	+	0.500311i
$856$	−3.44622			−0.117789
$857$	−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
$859$	−15.7769	−	27.3264i	−0.538301	−	0.932364i	−0.998996	−	0.0448054i	$-0.985733\pi$
$859$	−15.7769	−	27.3264i	−0.538301	−	0.932364i	0.460695	−	0.887558i	$-0.347600\pi$
$860$	1.22311	+	2.11849i	0.0417077	+	0.0722399i
$861$	−9.44622	+	16.3613i	−0.321926	+	0.557593i
$862$	16.3387			0.556497
$863$	−49.7849			−1.69470			−0.847349	−	0.531037i	$-0.821803\pi$
$863$	−49.7849			−1.69470			−0.847349	+	0.531037i	$0.821803\pi$
$864$	2.50000	+	4.33013i	0.0850517	+	0.147314i
$865$	−8.16933	+	14.1497i	−0.277766	+	0.481104i
$866$	21.3387			0.725117
$867$	−12.2769	−	21.2642i	−0.416945	−	0.722170i
$868$	−14.8924			−0.505482
$869$		0			0
$870$	−6.00000			−0.203419
$871$	14.4462	+	7.70108i	0.489492	+	0.260941i
$872$	14.0000			0.474100
$873$	−4.44622	+	7.70108i	−0.150482	+	0.260642i
$874$		0			0
$875$	1.00000	+	1.73205i	0.0338062	+	0.0585540i
$876$	1.55378			0.0524973
$877$	23.4462	−	40.6100i	0.791723	−	1.37130i	−0.133177	−	0.991092i	$-0.542518\pi$
$877$	23.4462	−	40.6100i	0.791723	−	1.37130i	0.924900	−	0.380212i	$-0.124149\pi$
$878$	15.7231	+	27.2332i	0.530629	+	0.919077i
$879$	2.55378			0.0861368
$880$		0			0
$881$	16.7231	−	28.9653i	0.563416	−	0.975865i	−0.433779	−	0.901019i	$-0.642820\pi$
$881$	16.7231	−	28.9653i	0.563416	−	0.975865i	0.997195	−	0.0748458i	$-0.0238465\pi$
$882$	−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	$0.811893\pi$
$884$	−6.44622	+	11.1652i	−0.216810	+	0.375526i
$885$	0.446222			0.0149996
$886$	−21.8924			−0.735491
$887$	14.5538	−	25.2079i	0.488668	−	0.846398i	−0.511247	−	0.859434i	$-0.670816\pi$
$887$	14.5538	−	25.2079i	0.488668	−	0.846398i	0.999915	+	0.0130360i	$0.00414959\pi$
$888$	−2.72311	+	4.71657i	−0.0913816	+	0.158278i
$889$	10.0000	−	17.3205i	0.335389	−	0.580911i
$890$	−7.94622	+	13.7633i	−0.266358	+	0.461346i
$891$		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
$898$	16.3387			0.545228
$899$	22.3387	−	38.6917i	0.745036	−	1.29044i
$900$	1.00000	+	1.73205i	0.0333333	+	0.0577350i
$901$	−30.4462	+	52.7344i	−1.01431	+	1.75684i
$902$		0			0
$903$	−2.44622	−	4.23698i	−0.0814052	−	0.140998i
$904$	9.22311	+	15.9749i	0.306756	+	0.531317i
$905$	−11.4462	−	19.8254i	−0.380485	−	0.659020i
$906$	−2.27689	−	3.94369i	−0.0756446	−	0.131020i
$907$	−9.16933	−	15.8818i	−0.304463	−	0.527345i	0.672679	−	0.739935i	$-0.265144\pi$
$907$	−9.16933	−	15.8818i	−0.304463	−	0.527345i	−0.977142	+	0.212590i	$0.931810\pi$
$908$	−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
$911$	−7.66133			−0.253831			−0.126916	−	0.991914i	$-0.540508\pi$
$911$	−7.66133			−0.253831			−0.126916	+	0.991914i	$0.540508\pi$
$912$	−4.22311	−	7.31464i	−0.139841	−	0.242212i
$913$		0			0
$914$	26.4462			0.874763
$915$	4.00000	−	6.92820i	0.132236	−	0.229039i
$916$	8.00000			0.264327
$917$	18.8924	+	32.7227i	0.623883	+	1.08060i
$918$	16.1156	+	27.9130i	0.531893	+	0.921265i
$919$	−20.7231	+	35.8935i	−0.683592	+	1.18402i	0.290285	+	0.956940i	$0.406250\pi$
$919$	−20.7231	+	35.8935i	−0.683592	+	1.18402i	−0.973877	+	0.227076i	$0.927083\pi$
$920$		0			0
$921$	−8.94622	+	15.4953i	−0.294788	+	0.510588i
$922$	−18.4462	+	31.9498i	−0.607494	+	1.05221i
$923$	18.8924			0.621852
$924$		0			0
$925$	−2.72311	+	4.71657i	−0.0895353	+	0.155080i
$926$	−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
$929$	−49.3387			−1.61875			−0.809375	−	0.587293i	$-0.800194\pi$
$929$	−49.3387			−1.61875			−0.809375	+	0.587293i	$0.800194\pi$
$930$	7.44622			0.244171
$931$	12.6693	+	21.9439i	0.415221	+	0.719183i
$932$	−9.66933	+	16.7478i	−0.316730	+	0.548592i
$933$	−22.3387			−0.731335
$934$	1.72311	+	2.98452i	0.0563819	+	0.0976563i
$935$		0			0
$936$	2.00000	−	3.46410i	0.0653720	−	0.113228i
$937$	−4.89244			−0.159829			−0.0799146	−	0.996802i	$-0.525465\pi$
$937$	−4.89244			−0.159829			−0.0799146	+	0.996802i	$0.525465\pi$
$938$	−0.553778	−	16.3613i	−0.0180815	−	0.534217i
$939$	19.5538			0.638113
$940$		0			0
$941$	25.7849			0.840563			0.420282	−	0.907394i	$-0.361931\pi$
$941$	25.7849			0.840563			0.420282	+	0.907394i	$0.361931\pi$
$942$	−7.00000	−	12.1244i	−0.228072	−	0.395033i
$943$		0			0
$944$	0.223111	−	0.386440i	0.00726164	−	0.0125775i
$945$	−5.00000	−	8.66025i	−0.162650	−	0.281718i
$946$		0			0
$947$	43.3387			1.40832			0.704159	−	0.710043i	$-0.251324\pi$
$947$	43.3387			1.40832			0.704159	+	0.710043i	$0.251324\pi$
$948$	−4.00000	+	6.92820i	−0.129914	+	0.225018i
$949$	−1.55378	−	2.69122i	−0.0504378	−	0.0873608i
$950$	−4.22311	−	7.31464i	−0.137016	−	0.237318i
$951$	−16.7231	+	28.9653i	−0.542284	+	0.939263i
$952$	12.8924			0.417847
$953$	−0.446222			−0.0144545			−0.00722727	−	0.999974i	$-0.502301\pi$
$953$	−0.446222			−0.0144545			−0.00722727	+	0.999974i	$0.502301\pi$
$954$	9.44622	−	16.3613i	0.305833	−	0.529718i
$955$	1.72311	−	2.98452i	0.0557586	−	0.0965767i
$956$	6.44622	−	11.1652i	0.208486	−	0.361108i
$957$		0			0
$958$		0			0
$959$	−6.44622	−	11.1652i	−0.208159	−	0.360543i
$960$	−1.00000			−0.0322749
$961$	−12.2231	+	21.1710i	−0.394294	+	0.682937i
$962$	10.8924			0.351186
$963$	6.89244			0.222106
$964$	−8.72311	−	15.1089i	−0.280952	−	0.486624i
$965$	−20.8924			−0.672552
$966$		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
$969$	−27.2231	−	47.1518i	−0.874532	−	1.51473i
$970$	−2.22311	−	3.85054i	−0.0713798	−	0.123633i
$971$	21.6693	+	37.5324i	0.695402	+	1.20447i	0.970045	+	0.242925i	$0.0781070\pi$
$971$	21.6693	+	37.5324i	0.695402	+	1.20447i	−0.274643	+	0.961546i	$0.588560\pi$
$972$	−8.00000	−	13.8564i	−0.256600	−	0.444444i
$973$	22.4462	+	38.8780i	0.719593	+	1.24637i
$974$	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
$977$	0.446222	−	0.772879i	0.0142759	−	0.0247266i	−0.858799	−	0.512312i	$-0.828789\pi$
$977$	0.446222	−	0.772879i	0.0142759	−	0.0247266i	0.873075	+	0.487586i	$0.162122\pi$
$978$	−7.89244			−0.252373
$979$		0			0
$980$	3.00000			0.0958315
$981$	−28.0000			−0.893971
$982$	−18.6693	+	32.3362i	−0.595762	+	1.03189i
$983$	29.1076			0.928387			0.464193	−	0.885734i	$-0.346344\pi$
$983$	29.1076			0.928387			0.464193	+	0.885734i	$0.346344\pi$
$984$	−4.72311	−	8.18067i	−0.150567	−	0.260790i
$985$	−3.44622	−	5.96903i	−0.109806	−	0.190189i
$986$	−19.3387	+	33.4956i	−0.615869	+	1.06672i
$987$		0			0
$988$	−8.44622	+	14.6293i	−0.268710	+	0.465420i
$989$		0			0
$990$		0			0
$991$	3.66133			0.116306			0.0581531	−	0.998308i	$-0.481479\pi$
$991$	3.66133			0.116306			0.0581531	+	0.998308i	$0.481479\pi$
$992$	3.72311	−	6.44862i	0.118209	−	0.204744i
$993$	−10.2231	−	17.7069i	−0.324421	−	0.561913i
$994$	−9.44622	−	16.3613i	−0.299616	−	0.518950i
$995$	2.72311	−	4.71657i	0.0863284	−	0.149525i
$996$	3.44622			0.109198
$997$	47.4462			1.50264			0.751318	−	0.659940i	$-0.229418\pi$
$997$	47.4462			1.50264			0.751318	+	0.659940i	$0.229418\pi$
$998$	−13.2231	−	22.9031i	−0.418570	−	0.724985i
$999$	13.6156	−	23.5828i	0.430777	−	0.746128i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.e.e.431.1	yes	4
67.37	even	3	inner	670.2.e.e.171.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.e.e.171.1	✓	4	67.37	even	3	inner
670.2.e.e.431.1	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} +(-3.22311 + 5.58259i) q^{17} +(1.00000 - 1.73205i) q^{18} +(-4.22311 + 7.31464i) 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} +(3.72311 + 6.44862i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.22311 - 5.58259i) q^{34} +(1.00000 + 1.73205i) q^{35} +(1.00000 + 1.73205i) q^{36} +(-2.72311 + 4.71657i) q^{37} +(-4.22311 - 7.31464i) q^{38} +(-1.00000 + 1.73205i) q^{39} -1.00000 q^{40} +(-4.72311 - 8.18067i) q^{41} +2.00000 q^{42} +2.44622 q^{43} +2.00000 q^{45} +(-0.500000 + 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-3.22311 + 5.58259i) q^{51} +2.00000 q^{52} +9.44622 q^{53} +(2.50000 - 4.33013i) q^{54} +(-1.00000 - 1.73205i) q^{56} +(-4.22311 + 7.31464i) q^{57} +6.00000 q^{58} -0.446222 q^{59} +(0.500000 + 0.866025i) q^{60} +(-4.00000 + 6.92820i) q^{61} -7.44622 q^{62} +(2.00000 + 3.46410i) q^{63} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +(-0.276889 - 8.18067i) q^{67} +6.44622 q^{68} -2.00000 q^{70} +(-4.72311 - 8.18067i) q^{71} -2.00000 q^{72} +(-0.776889 + 1.34561i) q^{73} +(-2.72311 - 4.71657i) q^{74} +1.00000 q^{75} +8.44622 q^{76} +(-1.00000 - 1.73205i) q^{78} +(-4.00000 - 6.92820i) q^{79} +(0.500000 - 0.866025i) q^{80} +1.00000 q^{81} +9.44622 q^{82} +(-1.72311 + 2.98452i) q^{83} +(-1.00000 + 1.73205i) q^{84} +(3.22311 - 5.58259i) q^{85} +(-1.22311 + 2.11849i) q^{86} +(-3.00000 - 5.19615i) q^{87} -15.8924 q^{89} +(-1.00000 + 1.73205i) q^{90} +4.00000 q^{91} +(3.72311 + 6.44862i) q^{93} +(4.22311 - 7.31464i) q^{95} +(-0.500000 - 0.866025i) q^{96} +(2.22311 - 3.85054i) 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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