LMFDB - Embedded newform 74.3.d.c.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,3,Mod(31,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("74.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	74.d (of order $4$, 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:	$2.01635395627$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	74.31
Dual form			74.3.d.c.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.00000i) q^{2} -3.00000i q^{3} +2.00000i q^{4} +(3.00000 - 3.00000i) q^{5} +(3.00000 - 3.00000i) q^{6} +3.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} +6.00000 q^{10} -3.00000i q^{11} +6.00000 q^{12} +(-11.0000 + 11.0000i) q^{13} +(3.00000 + 3.00000i) q^{14} +(-9.00000 - 9.00000i) q^{15} -4.00000 q^{16} +(-12.0000 + 12.0000i) q^{17} +(-4.00000 + 4.00000i) q^{19} +(6.00000 + 6.00000i) q^{20} -9.00000i q^{21} +(3.00000 - 3.00000i) q^{22} +(-3.00000 + 3.00000i) q^{23} +(6.00000 + 6.00000i) q^{24} +7.00000i q^{25} -22.0000 q^{26} -27.0000i q^{27} +6.00000i q^{28} +(9.00000 + 9.00000i) q^{29} -18.0000i q^{30} +(-32.0000 - 32.0000i) q^{31} +(-4.00000 - 4.00000i) q^{32} -9.00000 q^{33} -24.0000 q^{34} +(9.00000 - 9.00000i) q^{35} +(35.0000 + 12.0000i) q^{37} -8.00000 q^{38} +(33.0000 + 33.0000i) q^{39} +12.0000i q^{40} +39.0000i q^{41} +(9.00000 - 9.00000i) q^{42} +(-7.00000 + 7.00000i) q^{43} +6.00000 q^{44} -6.00000 q^{46} +75.0000 q^{47} +12.0000i q^{48} -40.0000 q^{49} +(-7.00000 + 7.00000i) q^{50} +(36.0000 + 36.0000i) q^{51} +(-22.0000 - 22.0000i) q^{52} +39.0000 q^{53} +(27.0000 - 27.0000i) q^{54} +(-9.00000 - 9.00000i) q^{55} +(-6.00000 + 6.00000i) q^{56} +(12.0000 + 12.0000i) q^{57} +18.0000i q^{58} +(72.0000 - 72.0000i) q^{59} +(18.0000 - 18.0000i) q^{60} +(-80.0000 - 80.0000i) q^{61} -64.0000i q^{62} -8.00000i q^{64} +66.0000i q^{65} +(-9.00000 - 9.00000i) q^{66} -26.0000i q^{67} +(-24.0000 - 24.0000i) q^{68} +(9.00000 + 9.00000i) q^{69} +18.0000 q^{70} -51.0000 q^{71} +25.0000i q^{73} +(23.0000 + 47.0000i) q^{74} +21.0000 q^{75} +(-8.00000 - 8.00000i) q^{76} -9.00000i q^{77} +66.0000i q^{78} +(-28.0000 + 28.0000i) q^{79} +(-12.0000 + 12.0000i) q^{80} -81.0000 q^{81} +(-39.0000 + 39.0000i) q^{82} +27.0000 q^{83} +18.0000 q^{84} +72.0000i q^{85} -14.0000 q^{86} +(27.0000 - 27.0000i) q^{87} +(6.00000 + 6.00000i) q^{88} +(-60.0000 - 60.0000i) q^{89} +(-33.0000 + 33.0000i) q^{91} +(-6.00000 - 6.00000i) q^{92} +(-96.0000 + 96.0000i) q^{93} +(75.0000 + 75.0000i) q^{94} +24.0000i q^{95} +(-12.0000 + 12.0000i) q^{96} +(-32.0000 + 32.0000i) q^{97} +(-40.0000 - 40.0000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 6 q^{5} + 6 q^{6} + 6 q^{7} - 4 q^{8} + 12 q^{10} + 12 q^{12} - 22 q^{13} + 6 q^{14} - 18 q^{15} - 8 q^{16} - 24 q^{17} - 8 q^{19} + 12 q^{20} + 6 q^{22} - 6 q^{23} + 12 q^{24} - 44 q^{26}+ \cdots - 80 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 + 6 * q^5 + 6 * q^6 + 6 * q^7 - 4 * q^8 + 12 * q^10 + 12 * q^12 - 22 * q^13 + 6 * q^14 - 18 * q^15 - 8 * q^16 - 24 * q^17 - 8 * q^19 + 12 * q^20 + 6 * q^22 - 6 * q^23 + 12 * q^24 - 44 * q^26 + 18 * q^29 - 64 * q^31 - 8 * q^32 - 18 * q^33 - 48 * q^34 + 18 * q^35 + 70 * q^37 - 16 * q^38 + 66 * q^39 + 18 * q^42 - 14 * q^43 + 12 * q^44 - 12 * q^46 + 150 * q^47 - 80 * q^49 - 14 * q^50 + 72 * q^51 - 44 * q^52 + 78 * q^53 + 54 * q^54 - 18 * q^55 - 12 * q^56 + 24 * q^57 + 144 * q^59 + 36 * q^60 - 160 * q^61 - 18 * q^66 - 48 * q^68 + 18 * q^69 + 36 * q^70 - 102 * q^71 + 46 * q^74 + 42 * q^75 - 16 * q^76 - 56 * q^79 - 24 * q^80 - 162 * q^81 - 78 * q^82 + 54 * q^83 + 36 * q^84 - 28 * q^86 + 54 * q^87 + 12 * q^88 - 120 * q^89 - 66 * q^91 - 12 * q^92 - 192 * q^93 + 150 * q^94 - 24 * q^96 - 64 * q^97 - 80 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$		−	3.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$3$		−	3.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$4$			2.00000i			0.500000i
$5$	3.00000	−	3.00000i	0.600000	−	0.600000i	−0.340312	−	0.940312i	$-0.610533\pi$
$5$	3.00000	−	3.00000i	0.600000	−	0.600000i	0.940312	+	0.340312i	$0.110533\pi$
$6$	3.00000	−	3.00000i	0.500000	−	0.500000i
$7$	3.00000			0.428571			0.214286	−	0.976771i	$-0.431258\pi$
$7$	3.00000			0.428571			0.214286	+	0.976771i	$0.431258\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		0			0
$10$	6.00000			0.600000
$11$		−	3.00000i		−	0.272727i	−0.990659	−	0.136364i	$-0.956458\pi$
$11$		−	3.00000i		−	0.272727i	0.990659	−	0.136364i	$-0.0435416\pi$
$12$	6.00000			0.500000
$13$	−11.0000	+	11.0000i	−0.846154	+	0.846154i	−0.989651	−	0.143497i	$-0.954165\pi$
$13$	−11.0000	+	11.0000i	−0.846154	+	0.846154i	0.143497	+	0.989651i	$0.454165\pi$
$14$	3.00000	+	3.00000i	0.214286	+	0.214286i
$15$	−9.00000	−	9.00000i	−0.600000	−	0.600000i
$16$	−4.00000			−0.250000
$17$	−12.0000	+	12.0000i	−0.705882	+	0.705882i	−0.965667	−	0.259784i	$-0.916349\pi$
$17$	−12.0000	+	12.0000i	−0.705882	+	0.705882i	0.259784	+	0.965667i	$0.416349\pi$
$18$		0			0
$19$	−4.00000	+	4.00000i	−0.210526	+	0.210526i	−0.804491	−	0.593965i	$-0.797562\pi$
$19$	−4.00000	+	4.00000i	−0.210526	+	0.210526i	0.593965	+	0.804491i	$0.297562\pi$
$20$	6.00000	+	6.00000i	0.300000	+	0.300000i
$21$		−	9.00000i		−	0.428571i
$22$	3.00000	−	3.00000i	0.136364	−	0.136364i
$23$	−3.00000	+	3.00000i	−0.130435	+	0.130435i	−0.769310	−	0.638875i	$-0.779400\pi$
$23$	−3.00000	+	3.00000i	−0.130435	+	0.130435i	0.638875	+	0.769310i	$0.279400\pi$
$24$	6.00000	+	6.00000i	0.250000	+	0.250000i
$25$			7.00000i			0.280000i
$26$	−22.0000			−0.846154
$27$		−	27.0000i		−	1.00000i
$28$			6.00000i			0.214286i
$29$	9.00000	+	9.00000i	0.310345	+	0.310345i	0.845043	−	0.534698i	$-0.179575\pi$
$29$	9.00000	+	9.00000i	0.310345	+	0.310345i	−0.534698	+	0.845043i	$0.679575\pi$
$30$		−	18.0000i		−	0.600000i
$31$	−32.0000	−	32.0000i	−1.03226	−	1.03226i	−0.999462	−	0.0327960i	$-0.989559\pi$
$31$	−32.0000	−	32.0000i	−1.03226	−	1.03226i	−0.0327960	−	0.999462i	$-0.510441\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	−9.00000			−0.272727
$34$	−24.0000			−0.705882
$35$	9.00000	−	9.00000i	0.257143	−	0.257143i
$36$		0			0
$37$	35.0000	+	12.0000i	0.945946	+	0.324324i
$37$	35.0000	+	12.0000i	0.945946	+	0.324324i
$38$	−8.00000			−0.210526
$39$	33.0000	+	33.0000i	0.846154	+	0.846154i
$40$			12.0000i			0.300000i
$41$			39.0000i			0.951220i	0.879656	+	0.475610i	$0.157773\pi$
$41$			39.0000i			0.951220i	−0.879656	+	0.475610i	$0.842227\pi$
$42$	9.00000	−	9.00000i	0.214286	−	0.214286i
$43$	−7.00000	+	7.00000i	−0.162791	+	0.162791i	−0.783802	−	0.621011i	$-0.786722\pi$
$43$	−7.00000	+	7.00000i	−0.162791	+	0.162791i	0.621011	+	0.783802i	$0.286722\pi$
$44$	6.00000			0.136364
$45$		0			0
$46$	−6.00000			−0.130435
$47$	75.0000			1.59574			0.797872	−	0.602826i	$-0.205959\pi$
$47$	75.0000			1.59574			0.797872	+	0.602826i	$0.205959\pi$
$48$			12.0000i			0.250000i
$49$	−40.0000			−0.816327
$50$	−7.00000	+	7.00000i	−0.140000	+	0.140000i
$51$	36.0000	+	36.0000i	0.705882	+	0.705882i
$52$	−22.0000	−	22.0000i	−0.423077	−	0.423077i
$53$	39.0000			0.735849			0.367925	−	0.929856i	$-0.380068\pi$
$53$	39.0000			0.735849			0.367925	+	0.929856i	$0.380068\pi$
$54$	27.0000	−	27.0000i	0.500000	−	0.500000i
$55$	−9.00000	−	9.00000i	−0.163636	−	0.163636i
$56$	−6.00000	+	6.00000i	−0.107143	+	0.107143i
$57$	12.0000	+	12.0000i	0.210526	+	0.210526i
$58$			18.0000i			0.310345i
$59$	72.0000	−	72.0000i	1.22034	−	1.22034i	0.252828	−	0.967511i	$-0.418639\pi$
$59$	72.0000	−	72.0000i	1.22034	−	1.22034i	0.967511	−	0.252828i	$-0.0813606\pi$
$60$	18.0000	−	18.0000i	0.300000	−	0.300000i
$61$	−80.0000	−	80.0000i	−1.31148	−	1.31148i	−0.920328	−	0.391147i	$-0.872078\pi$
$61$	−80.0000	−	80.0000i	−1.31148	−	1.31148i	−0.391147	−	0.920328i	$-0.627922\pi$
$62$		−	64.0000i		−	1.03226i
$63$		0			0
$64$		−	8.00000i		−	0.125000i
$65$			66.0000i			1.01538i
$66$	−9.00000	−	9.00000i	−0.136364	−	0.136364i
$67$		−	26.0000i		−	0.388060i	−0.980996	−	0.194030i	$-0.937844\pi$
$67$		−	26.0000i		−	0.388060i	0.980996	−	0.194030i	$-0.0621559\pi$
$68$	−24.0000	−	24.0000i	−0.352941	−	0.352941i
$69$	9.00000	+	9.00000i	0.130435	+	0.130435i
$70$	18.0000			0.257143
$71$	−51.0000			−0.718310			−0.359155	−	0.933278i	$-0.616935\pi$
$71$	−51.0000			−0.718310			−0.359155	+	0.933278i	$0.616935\pi$
$72$		0			0
$73$			25.0000i			0.342466i	0.985231	+	0.171233i	$0.0547750\pi$
$73$			25.0000i			0.342466i	−0.985231	+	0.171233i	$0.945225\pi$
$74$	23.0000	+	47.0000i	0.310811	+	0.635135i
$75$	21.0000			0.280000
$76$	−8.00000	−	8.00000i	−0.105263	−	0.105263i
$77$		−	9.00000i		−	0.116883i
$78$			66.0000i			0.846154i
$79$	−28.0000	+	28.0000i	−0.354430	+	0.354430i	−0.861755	−	0.507325i	$-0.830635\pi$
$79$	−28.0000	+	28.0000i	−0.354430	+	0.354430i	0.507325	+	0.861755i	$0.330635\pi$
$80$	−12.0000	+	12.0000i	−0.150000	+	0.150000i
$81$	−81.0000			−1.00000
$82$	−39.0000	+	39.0000i	−0.475610	+	0.475610i
$83$	27.0000			0.325301			0.162651	−	0.986684i	$-0.447996\pi$
$83$	27.0000			0.325301			0.162651	+	0.986684i	$0.447996\pi$
$84$	18.0000			0.214286
$85$			72.0000i			0.847059i
$86$	−14.0000			−0.162791
$87$	27.0000	−	27.0000i	0.310345	−	0.310345i
$88$	6.00000	+	6.00000i	0.0681818	+	0.0681818i
$89$	−60.0000	−	60.0000i	−0.674157	−	0.674157i	0.284514	−	0.958672i	$-0.408168\pi$
$89$	−60.0000	−	60.0000i	−0.674157	−	0.674157i	−0.958672	+	0.284514i	$0.908168\pi$
$90$		0			0
$91$	−33.0000	+	33.0000i	−0.362637	+	0.362637i
$92$	−6.00000	−	6.00000i	−0.0652174	−	0.0652174i
$93$	−96.0000	+	96.0000i	−1.03226	+	1.03226i
$94$	75.0000	+	75.0000i	0.797872	+	0.797872i
$95$			24.0000i			0.252632i
$96$	−12.0000	+	12.0000i	−0.125000	+	0.125000i
$97$	−32.0000	+	32.0000i	−0.329897	+	0.329897i	−0.852547	−	0.522650i	$-0.824943\pi$
$97$	−32.0000	+	32.0000i	−0.329897	+	0.329897i	0.522650	+	0.852547i	$0.324943\pi$
$98$	−40.0000	−	40.0000i	−0.408163	−	0.408163i
$99$		0			0
$100$	−14.0000			−0.140000
$101$		−	183.000i		−	1.81188i	−0.423405	−	0.905941i	$-0.639165\pi$
$101$		−	183.000i		−	1.81188i	0.423405	−	0.905941i	$-0.360835\pi$
$102$			72.0000i			0.705882i
$103$	−119.000	−	119.000i	−1.15534	−	1.15534i	−0.985466	−	0.169874i	$-0.945664\pi$
$103$	−119.000	−	119.000i	−1.15534	−	1.15534i	−0.169874	−	0.985466i	$-0.554336\pi$
$104$		−	44.0000i		−	0.423077i
$105$	−27.0000	−	27.0000i	−0.257143	−	0.257143i
$106$	39.0000	+	39.0000i	0.367925	+	0.367925i
$107$	−24.0000			−0.224299			−0.112150	−	0.993691i	$-0.535774\pi$
$107$	−24.0000			−0.224299			−0.112150	+	0.993691i	$0.535774\pi$
$108$	54.0000			0.500000
$109$	28.0000	−	28.0000i	0.256881	−	0.256881i	−0.566903	−	0.823784i	$-0.691859\pi$
$109$	28.0000	−	28.0000i	0.256881	−	0.256881i	0.823784	+	0.566903i	$0.191859\pi$
$110$		−	18.0000i		−	0.163636i
$111$	36.0000	−	105.000i	0.324324	−	0.945946i
$112$	−12.0000			−0.107143
$113$	63.0000	+	63.0000i	0.557522	+	0.557522i	0.928601	−	0.371079i	$-0.121012\pi$
$113$	63.0000	+	63.0000i	0.557522	+	0.557522i	−0.371079	+	0.928601i	$0.621012\pi$
$114$			24.0000i			0.210526i
$115$			18.0000i			0.156522i
$116$	−18.0000	+	18.0000i	−0.155172	+	0.155172i
$117$		0			0
$118$	144.000			1.22034
$119$	−36.0000	+	36.0000i	−0.302521	+	0.302521i
$120$	36.0000			0.300000
$121$	112.000			0.925620
$122$		−	160.000i		−	1.31148i
$123$	117.000			0.951220
$124$	64.0000	−	64.0000i	0.516129	−	0.516129i
$125$	96.0000	+	96.0000i	0.768000	+	0.768000i
$126$		0			0
$127$	−155.000			−1.22047			−0.610236	−	0.792220i	$-0.708925\pi$
$127$	−155.000			−1.22047			−0.610236	+	0.792220i	$0.708925\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$	21.0000	+	21.0000i	0.162791	+	0.162791i
$130$	−66.0000	+	66.0000i	−0.507692	+	0.507692i
$131$	84.0000	+	84.0000i	0.641221	+	0.641221i	0.950856	−	0.309634i	$-0.100207\pi$
$131$	84.0000	+	84.0000i	0.641221	+	0.641221i	−0.309634	+	0.950856i	$0.600207\pi$
$132$		−	18.0000i		−	0.136364i
$133$	−12.0000	+	12.0000i	−0.0902256	+	0.0902256i
$134$	26.0000	−	26.0000i	0.194030	−	0.194030i
$135$	−81.0000	−	81.0000i	−0.600000	−	0.600000i
$136$		−	48.0000i		−	0.352941i
$137$	216.000			1.57664			0.788321	−	0.615264i	$-0.210951\pi$
$137$	216.000			1.57664			0.788321	+	0.615264i	$0.210951\pi$
$138$			18.0000i			0.130435i
$139$			208.000i			1.49640i	0.663472	+	0.748201i	$0.269082\pi$
$139$			208.000i			1.49640i	−0.663472	+	0.748201i	$0.730918\pi$
$140$	18.0000	+	18.0000i	0.128571	+	0.128571i
$141$		−	225.000i		−	1.59574i
$142$	−51.0000	−	51.0000i	−0.359155	−	0.359155i
$143$	33.0000	+	33.0000i	0.230769	+	0.230769i
$144$		0			0
$145$	54.0000			0.372414
$146$	−25.0000	+	25.0000i	−0.171233	+	0.171233i
$147$			120.000i			0.816327i
$148$	−24.0000	+	70.0000i	−0.162162	+	0.472973i
$149$	57.0000			0.382550			0.191275	−	0.981536i	$-0.438738\pi$
$149$	57.0000			0.382550			0.191275	+	0.981536i	$0.438738\pi$
$150$	21.0000	+	21.0000i	0.140000	+	0.140000i
$151$		−	240.000i		−	1.58940i	−0.607000	−	0.794702i	$-0.707627\pi$
$151$		−	240.000i		−	1.58940i	0.607000	−	0.794702i	$-0.292373\pi$
$152$		−	16.0000i		−	0.105263i
$153$		0			0
$154$	9.00000	−	9.00000i	0.0584416	−	0.0584416i
$155$	−192.000			−1.23871
$156$	−66.0000	+	66.0000i	−0.423077	+	0.423077i
$157$	63.0000			0.401274			0.200637	−	0.979666i	$-0.435699\pi$
$157$	63.0000			0.401274			0.200637	+	0.979666i	$0.435699\pi$
$158$	−56.0000			−0.354430
$159$		−	117.000i		−	0.735849i
$160$	−24.0000			−0.150000
$161$	−9.00000	+	9.00000i	−0.0559006	+	0.0559006i
$162$	−81.0000	−	81.0000i	−0.500000	−	0.500000i
$163$	137.000	+	137.000i	0.840491	+	0.840491i	0.988923	−	0.148432i	$-0.0474226\pi$
$163$	137.000	+	137.000i	0.840491	+	0.840491i	−0.148432	+	0.988923i	$0.547423\pi$
$164$	−78.0000			−0.475610
$165$	−27.0000	+	27.0000i	−0.163636	+	0.163636i
$166$	27.0000	+	27.0000i	0.162651	+	0.162651i
$167$	−132.000	+	132.000i	−0.790419	+	0.790419i	−0.981562	−	0.191143i	$-0.938781\pi$
$167$	−132.000	+	132.000i	−0.790419	+	0.790419i	0.191143	+	0.981562i	$0.438781\pi$
$168$	18.0000	+	18.0000i	0.107143	+	0.107143i
$169$		−	73.0000i		−	0.431953i
$170$	−72.0000	+	72.0000i	−0.423529	+	0.423529i
$171$		0			0
$172$	−14.0000	−	14.0000i	−0.0813953	−	0.0813953i
$173$			87.0000i			0.502890i	0.967872	+	0.251445i	$0.0809058\pi$
$173$			87.0000i			0.502890i	−0.967872	+	0.251445i	$0.919094\pi$
$174$	54.0000			0.310345
$175$			21.0000i			0.120000i
$176$			12.0000i			0.0681818i
$177$	−216.000	−	216.000i	−1.22034	−	1.22034i
$178$		−	120.000i		−	0.674157i
$179$	51.0000	+	51.0000i	0.284916	+	0.284916i	0.835066	−	0.550150i	$-0.185429\pi$
$179$	51.0000	+	51.0000i	0.284916	+	0.284916i	−0.550150	+	0.835066i	$0.685429\pi$
$180$		0			0
$181$	255.000			1.40884			0.704420	−	0.709784i	$-0.251207\pi$
$181$	255.000			1.40884			0.704420	+	0.709784i	$0.251207\pi$
$182$	−66.0000			−0.362637
$183$	−240.000	+	240.000i	−1.31148	+	1.31148i
$184$		−	12.0000i		−	0.0652174i
$185$	141.000	−	69.0000i	0.762162	−	0.372973i
$186$	−192.000			−1.03226
$187$	36.0000	+	36.0000i	0.192513	+	0.192513i
$188$			150.000i			0.797872i
$189$		−	81.0000i		−	0.428571i
$190$	−24.0000	+	24.0000i	−0.126316	+	0.126316i
$191$	−24.0000	+	24.0000i	−0.125654	+	0.125654i	−0.767137	−	0.641483i	$-0.778320\pi$
$191$	−24.0000	+	24.0000i	−0.125654	+	0.125654i	0.641483	+	0.767137i	$0.278320\pi$
$192$	−24.0000			−0.125000
$193$	−163.000	+	163.000i	−0.844560	+	0.844560i	−0.989448	−	0.144888i	$-0.953718\pi$
$193$	−163.000	+	163.000i	−0.844560	+	0.844560i	0.144888	+	0.989448i	$0.453718\pi$
$194$	−64.0000			−0.329897
$195$	198.000			1.01538
$196$		−	80.0000i		−	0.408163i
$197$	−225.000			−1.14213			−0.571066	−	0.820904i	$-0.693470\pi$
$197$	−225.000			−1.14213			−0.571066	+	0.820904i	$0.693470\pi$
$198$		0			0
$199$	−101.000	−	101.000i	−0.507538	−	0.507538i	0.406232	−	0.913770i	$-0.366842\pi$
$199$	−101.000	−	101.000i	−0.507538	−	0.507538i	−0.913770	+	0.406232i	$0.866842\pi$
$200$	−14.0000	−	14.0000i	−0.0700000	−	0.0700000i
$201$	−78.0000			−0.388060
$202$	183.000	−	183.000i	0.905941	−	0.905941i
$203$	27.0000	+	27.0000i	0.133005	+	0.133005i
$204$	−72.0000	+	72.0000i	−0.352941	+	0.352941i
$205$	117.000	+	117.000i	0.570732	+	0.570732i
$206$		−	238.000i		−	1.15534i
$207$		0			0
$208$	44.0000	−	44.0000i	0.211538	−	0.211538i
$209$	12.0000	+	12.0000i	0.0574163	+	0.0574163i
$210$		−	54.0000i		−	0.257143i
$211$	163.000			0.772512			0.386256	−	0.922392i	$-0.373768\pi$
$211$	163.000			0.772512			0.386256	+	0.922392i	$0.373768\pi$
$212$			78.0000i			0.367925i
$213$			153.000i			0.718310i
$214$	−24.0000	−	24.0000i	−0.112150	−	0.112150i
$215$			42.0000i			0.195349i
$216$	54.0000	+	54.0000i	0.250000	+	0.250000i
$217$	−96.0000	−	96.0000i	−0.442396	−	0.442396i
$218$	56.0000			0.256881
$219$	75.0000			0.342466
$220$	18.0000	−	18.0000i	0.0818182	−	0.0818182i
$221$		−	264.000i		−	1.19457i
$222$	141.000	−	69.0000i	0.635135	−	0.310811i
$223$	275.000			1.23318			0.616592	−	0.787283i	$-0.288513\pi$
$223$	275.000			1.23318			0.616592	+	0.787283i	$0.288513\pi$
$224$	−12.0000	−	12.0000i	−0.0535714	−	0.0535714i
$225$		0			0
$226$			126.000i			0.557522i
$227$	−216.000	+	216.000i	−0.951542	+	0.951542i	−0.998879	−	0.0473371i	$-0.984926\pi$
$227$	−216.000	+	216.000i	−0.951542	+	0.951542i	0.0473371	+	0.998879i	$0.484926\pi$
$228$	−24.0000	+	24.0000i	−0.105263	+	0.105263i
$229$	−359.000			−1.56769			−0.783843	−	0.620959i	$-0.786743\pi$
$229$	−359.000			−1.56769			−0.783843	+	0.620959i	$0.786743\pi$
$230$	−18.0000	+	18.0000i	−0.0782609	+	0.0782609i
$231$	−27.0000			−0.116883
$232$	−36.0000			−0.155172
$233$		−	168.000i		−	0.721030i	−0.932753	−	0.360515i	$-0.882601\pi$
$233$		−	168.000i		−	0.721030i	0.932753	−	0.360515i	$-0.117399\pi$
$234$		0			0
$235$	225.000	−	225.000i	0.957447	−	0.957447i
$236$	144.000	+	144.000i	0.610169	+	0.610169i
$237$	84.0000	+	84.0000i	0.354430	+	0.354430i
$238$	−72.0000			−0.302521
$239$	−195.000	+	195.000i	−0.815900	+	0.815900i	−0.985511	−	0.169611i	$-0.945749\pi$
$239$	−195.000	+	195.000i	−0.815900	+	0.815900i	0.169611	+	0.985511i	$0.445749\pi$
$240$	36.0000	+	36.0000i	0.150000	+	0.150000i
$241$	329.000	−	329.000i	1.36515	−	1.36515i	0.497925	−	0.867220i	$-0.334095\pi$
$241$	329.000	−	329.000i	1.36515	−	1.36515i	0.867220	−	0.497925i	$-0.165905\pi$
$242$	112.000	+	112.000i	0.462810	+	0.462810i
$243$		0			0
$244$	160.000	−	160.000i	0.655738	−	0.655738i
$245$	−120.000	+	120.000i	−0.489796	+	0.489796i
$246$	117.000	+	117.000i	0.475610	+	0.475610i
$247$		−	88.0000i		−	0.356275i
$248$	128.000			0.516129
$249$		−	81.0000i		−	0.325301i
$250$			192.000i			0.768000i
$251$	−177.000	−	177.000i	−0.705179	−	0.705179i	0.260338	−	0.965517i	$-0.416166\pi$
$251$	−177.000	−	177.000i	−0.705179	−	0.705179i	−0.965517	+	0.260338i	$0.916166\pi$
$252$		0			0
$253$	9.00000	+	9.00000i	0.0355731	+	0.0355731i
$254$	−155.000	−	155.000i	−0.610236	−	0.610236i
$255$	216.000			0.847059
$256$	16.0000			0.0625000
$257$	72.0000	−	72.0000i	0.280156	−	0.280156i	−0.553015	−	0.833171i	$-0.686523\pi$
$257$	72.0000	−	72.0000i	0.280156	−	0.280156i	0.833171	+	0.553015i	$0.186523\pi$
$258$			42.0000i			0.162791i
$259$	105.000	+	36.0000i	0.405405	+	0.138996i
$260$	−132.000			−0.507692
$261$		0			0
$262$			168.000i			0.641221i
$263$			45.0000i			0.171103i	0.996334	+	0.0855513i	$0.0272652\pi$
$263$			45.0000i			0.171103i	−0.996334	+	0.0855513i	$0.972735\pi$
$264$	18.0000	−	18.0000i	0.0681818	−	0.0681818i
$265$	117.000	−	117.000i	0.441509	−	0.441509i
$266$	−24.0000			−0.0902256
$267$	−180.000	+	180.000i	−0.674157	+	0.674157i
$268$	52.0000			0.194030
$269$	−312.000			−1.15985			−0.579926	−	0.814669i	$-0.696918\pi$
$269$	−312.000			−1.15985			−0.579926	+	0.814669i	$0.696918\pi$
$270$		−	162.000i		−	0.600000i
$271$	−219.000			−0.808118			−0.404059	−	0.914733i	$-0.632401\pi$
$271$	−219.000			−0.808118			−0.404059	+	0.914733i	$0.632401\pi$
$272$	48.0000	−	48.0000i	0.176471	−	0.176471i
$273$	99.0000	+	99.0000i	0.362637	+	0.362637i
$274$	216.000	+	216.000i	0.788321	+	0.788321i
$275$	21.0000			0.0763636
$276$	−18.0000	+	18.0000i	−0.0652174	+	0.0652174i
$277$	56.0000	+	56.0000i	0.202166	+	0.202166i	0.800927	−	0.598761i	$-0.204340\pi$
$277$	56.0000	+	56.0000i	0.202166	+	0.202166i	−0.598761	+	0.800927i	$0.704340\pi$
$278$	−208.000	+	208.000i	−0.748201	+	0.748201i
$279$		0			0
$280$			36.0000i			0.128571i
$281$	240.000	−	240.000i	0.854093	−	0.854093i	−0.136542	−	0.990634i	$-0.543599\pi$
$281$	240.000	−	240.000i	0.854093	−	0.854093i	0.990634	+	0.136542i	$0.0435988\pi$
$282$	225.000	−	225.000i	0.797872	−	0.797872i
$283$	176.000	+	176.000i	0.621908	+	0.621908i	0.946019	−	0.324111i	$-0.105065\pi$
$283$	176.000	+	176.000i	0.621908	+	0.621908i	−0.324111	+	0.946019i	$0.605065\pi$
$284$		−	102.000i		−	0.359155i
$285$	72.0000			0.252632
$286$			66.0000i			0.230769i
$287$			117.000i			0.407666i
$288$		0			0
$289$			1.00000i			0.00346021i
$290$	54.0000	+	54.0000i	0.186207	+	0.186207i
$291$	96.0000	+	96.0000i	0.329897	+	0.329897i
$292$	−50.0000			−0.171233
$293$	504.000			1.72014			0.860068	−	0.510179i	$-0.170421\pi$
$293$	504.000			1.72014			0.860068	+	0.510179i	$0.170421\pi$
$294$	−120.000	+	120.000i	−0.408163	+	0.408163i
$295$		−	432.000i		−	1.46441i
$296$	−94.0000	+	46.0000i	−0.317568	+	0.155405i
$297$	−81.0000			−0.272727
$298$	57.0000	+	57.0000i	0.191275	+	0.191275i
$299$		−	66.0000i		−	0.220736i
$300$			42.0000i			0.140000i
$301$	−21.0000	+	21.0000i	−0.0697674	+	0.0697674i
$302$	240.000	−	240.000i	0.794702	−	0.794702i
$303$	−549.000			−1.81188
$304$	16.0000	−	16.0000i	0.0526316	−	0.0526316i
$305$	−480.000			−1.57377
$306$		0			0
$307$		−	315.000i		−	1.02606i	−0.858371	−	0.513029i	$-0.828523\pi$
$307$		−	315.000i		−	1.02606i	0.858371	−	0.513029i	$-0.171477\pi$
$308$	18.0000			0.0584416
$309$	−357.000	+	357.000i	−1.15534	+	1.15534i
$310$	−192.000	−	192.000i	−0.619355	−	0.619355i
$311$	−84.0000	−	84.0000i	−0.270096	−	0.270096i	0.559043	−	0.829139i	$-0.311169\pi$
$311$	−84.0000	−	84.0000i	−0.270096	−	0.270096i	−0.829139	+	0.559043i	$0.811169\pi$
$312$	−132.000			−0.423077
$313$	−221.000	+	221.000i	−0.706070	+	0.706070i	−0.965706	−	0.259636i	$-0.916397\pi$
$313$	−221.000	+	221.000i	−0.706070	+	0.706070i	0.259636	+	0.965706i	$0.416397\pi$
$314$	63.0000	+	63.0000i	0.200637	+	0.200637i
$315$		0			0
$316$	−56.0000	−	56.0000i	−0.177215	−	0.177215i
$317$		−	240.000i		−	0.757098i	−0.925581	−	0.378549i	$-0.876423\pi$
$317$		−	240.000i		−	0.757098i	0.925581	−	0.378549i	$-0.123577\pi$
$318$	117.000	−	117.000i	0.367925	−	0.367925i
$319$	27.0000	−	27.0000i	0.0846395	−	0.0846395i
$320$	−24.0000	−	24.0000i	−0.0750000	−	0.0750000i
$321$			72.0000i			0.224299i
$322$	−18.0000			−0.0559006
$323$		−	96.0000i		−	0.297214i
$324$		−	162.000i		−	0.500000i
$325$	−77.0000	−	77.0000i	−0.236923	−	0.236923i
$326$			274.000i			0.840491i
$327$	−84.0000	−	84.0000i	−0.256881	−	0.256881i
$328$	−78.0000	−	78.0000i	−0.237805	−	0.237805i
$329$	225.000			0.683891
$330$	−54.0000			−0.163636
$331$	−221.000	+	221.000i	−0.667674	+	0.667674i	−0.957177	−	0.289503i	$-0.906510\pi$
$331$	−221.000	+	221.000i	−0.667674	+	0.667674i	0.289503	+	0.957177i	$0.406510\pi$
$332$			54.0000i			0.162651i
$333$		0			0
$334$	−264.000			−0.790419
$335$	−78.0000	−	78.0000i	−0.232836	−	0.232836i
$336$			36.0000i			0.107143i
$337$			393.000i			1.16617i	0.812410	+	0.583086i	$0.198155\pi$
$337$			393.000i			1.16617i	−0.812410	+	0.583086i	$0.801845\pi$
$338$	73.0000	−	73.0000i	0.215976	−	0.215976i
$339$	189.000	−	189.000i	0.557522	−	0.557522i
$340$	−144.000			−0.423529
$341$	−96.0000	+	96.0000i	−0.281525	+	0.281525i
$342$		0			0
$343$	−267.000			−0.778426
$344$		−	28.0000i		−	0.0813953i
$345$	54.0000			0.156522
$346$	−87.0000	+	87.0000i	−0.251445	+	0.251445i
$347$	243.000	+	243.000i	0.700288	+	0.700288i	0.964472	−	0.264184i	$-0.0851026\pi$
$347$	243.000	+	243.000i	0.700288	+	0.700288i	−0.264184	+	0.964472i	$0.585103\pi$
$348$	54.0000	+	54.0000i	0.155172	+	0.155172i
$349$	−48.0000			−0.137536			−0.0687679	−	0.997633i	$-0.521907\pi$
$349$	−48.0000			−0.137536			−0.0687679	+	0.997633i	$0.521907\pi$
$350$	−21.0000	+	21.0000i	−0.0600000	+	0.0600000i
$351$	297.000	+	297.000i	0.846154	+	0.846154i
$352$	−12.0000	+	12.0000i	−0.0340909	+	0.0340909i
$353$	252.000	+	252.000i	0.713881	+	0.713881i	0.967345	−	0.253464i	$-0.0815699\pi$
$353$	252.000	+	252.000i	0.713881	+	0.713881i	−0.253464	+	0.967345i	$0.581570\pi$
$354$		−	432.000i		−	1.22034i
$355$	−153.000	+	153.000i	−0.430986	+	0.430986i
$356$	120.000	−	120.000i	0.337079	−	0.337079i
$357$	108.000	+	108.000i	0.302521	+	0.302521i
$358$			102.000i			0.284916i
$359$	−285.000			−0.793872			−0.396936	−	0.917846i	$-0.629926\pi$
$359$	−285.000			−0.793872			−0.396936	+	0.917846i	$0.629926\pi$
$360$		0			0
$361$			329.000i			0.911357i
$362$	255.000	+	255.000i	0.704420	+	0.704420i
$363$		−	336.000i		−	0.925620i
$364$	−66.0000	−	66.0000i	−0.181319	−	0.181319i
$365$	75.0000	+	75.0000i	0.205479	+	0.205479i
$366$	−480.000			−1.31148
$367$	464.000			1.26431			0.632153	−	0.774844i	$-0.282172\pi$
$367$	464.000			1.26431			0.632153	+	0.774844i	$0.282172\pi$
$368$	12.0000	−	12.0000i	0.0326087	−	0.0326087i
$369$		0			0
$370$	210.000	+	72.0000i	0.567568	+	0.194595i
$371$	117.000			0.315364
$372$	−192.000	−	192.000i	−0.516129	−	0.516129i
$373$			233.000i			0.624665i	0.949973	+	0.312332i	$0.101110\pi$
$373$			233.000i			0.624665i	−0.949973	+	0.312332i	$0.898890\pi$
$374$			72.0000i			0.192513i
$375$	288.000	−	288.000i	0.768000	−	0.768000i
$376$	−150.000	+	150.000i	−0.398936	+	0.398936i
$377$	−198.000			−0.525199
$378$	81.0000	−	81.0000i	0.214286	−	0.214286i
$379$	−237.000			−0.625330			−0.312665	−	0.949863i	$-0.601222\pi$
$379$	−237.000			−0.625330			−0.312665	+	0.949863i	$0.601222\pi$
$380$	−48.0000			−0.126316
$381$			465.000i			1.22047i
$382$	−48.0000			−0.125654
$383$	264.000	−	264.000i	0.689295	−	0.689295i	−0.272781	−	0.962076i	$-0.587943\pi$
$383$	264.000	−	264.000i	0.689295	−	0.689295i	0.962076	+	0.272781i	$0.0879435\pi$
$384$	−24.0000	−	24.0000i	−0.0625000	−	0.0625000i
$385$	−27.0000	−	27.0000i	−0.0701299	−	0.0701299i
$386$	−326.000			−0.844560
$387$		0			0
$388$	−64.0000	−	64.0000i	−0.164948	−	0.164948i
$389$	336.000	−	336.000i	0.863753	−	0.863753i	−0.128019	−	0.991772i	$-0.540862\pi$
$389$	336.000	−	336.000i	0.863753	−	0.863753i	0.991772	+	0.128019i	$0.0408617\pi$
$390$	198.000	+	198.000i	0.507692	+	0.507692i
$391$		−	72.0000i		−	0.184143i
$392$	80.0000	−	80.0000i	0.204082	−	0.204082i
$393$	252.000	−	252.000i	0.641221	−	0.641221i
$394$	−225.000	−	225.000i	−0.571066	−	0.571066i
$395$			168.000i			0.425316i
$396$		0			0
$397$		−	65.0000i		−	0.163728i	−0.996644	−	0.0818640i	$-0.973913\pi$
$397$		−	65.0000i		−	0.163728i	0.996644	−	0.0818640i	$-0.0260873\pi$
$398$		−	202.000i		−	0.507538i
$399$	36.0000	+	36.0000i	0.0902256	+	0.0902256i
$400$		−	28.0000i		−	0.0700000i
$401$	−189.000	−	189.000i	−0.471322	−	0.471322i	0.431020	−	0.902342i	$-0.358154\pi$
$401$	−189.000	−	189.000i	−0.471322	−	0.471322i	−0.902342	+	0.431020i	$0.858154\pi$
$402$	−78.0000	−	78.0000i	−0.194030	−	0.194030i
$403$	704.000			1.74690
$404$	366.000			0.905941
$405$	−243.000	+	243.000i	−0.600000	+	0.600000i
$406$			54.0000i			0.133005i
$407$	36.0000	−	105.000i	0.0884521	−	0.257985i
$408$	−144.000			−0.352941
$409$	88.0000	+	88.0000i	0.215159	+	0.215159i	0.806455	−	0.591296i	$-0.201383\pi$
$409$	88.0000	+	88.0000i	0.215159	+	0.215159i	−0.591296	+	0.806455i	$0.701383\pi$
$410$			234.000i			0.570732i
$411$		−	648.000i		−	1.57664i
$412$	238.000	−	238.000i	0.577670	−	0.577670i
$413$	216.000	−	216.000i	0.523002	−	0.523002i
$414$		0			0
$415$	81.0000	−	81.0000i	0.195181	−	0.195181i
$416$	88.0000			0.211538
$417$	624.000			1.49640
$418$			24.0000i			0.0574163i
$419$	429.000			1.02387			0.511933	−	0.859025i	$-0.328930\pi$
$419$	429.000			1.02387			0.511933	+	0.859025i	$0.328930\pi$
$420$	54.0000	−	54.0000i	0.128571	−	0.128571i
$421$	28.0000	+	28.0000i	0.0665083	+	0.0665083i	0.739579	−	0.673070i	$-0.235025\pi$
$421$	28.0000	+	28.0000i	0.0665083	+	0.0665083i	−0.673070	+	0.739579i	$0.735025\pi$
$422$	163.000	+	163.000i	0.386256	+	0.386256i
$423$		0			0
$424$	−78.0000	+	78.0000i	−0.183962	+	0.183962i
$425$	−84.0000	−	84.0000i	−0.197647	−	0.197647i
$426$	−153.000	+	153.000i	−0.359155	+	0.359155i
$427$	−240.000	−	240.000i	−0.562061	−	0.562061i
$428$		−	48.0000i		−	0.112150i
$429$	99.0000	−	99.0000i	0.230769	−	0.230769i
$430$	−42.0000	+	42.0000i	−0.0976744	+	0.0976744i
$431$	9.00000	+	9.00000i	0.0208817	+	0.0208817i	0.717471	−	0.696589i	$-0.245300\pi$
$431$	9.00000	+	9.00000i	0.0208817	+	0.0208817i	−0.696589	+	0.717471i	$0.745300\pi$
$432$			108.000i			0.250000i
$433$	−423.000			−0.976905			−0.488453	−	0.872590i	$-0.662438\pi$
$433$	−423.000			−0.976905			−0.488453	+	0.872590i	$0.662438\pi$
$434$		−	192.000i		−	0.442396i
$435$		−	162.000i		−	0.372414i
$436$	56.0000	+	56.0000i	0.128440	+	0.128440i
$437$		−	24.0000i		−	0.0549199i
$438$	75.0000	+	75.0000i	0.171233	+	0.171233i
$439$	344.000	+	344.000i	0.783599	+	0.783599i	0.980436	−	0.196837i	$-0.0630670\pi$
$439$	344.000	+	344.000i	0.783599	+	0.783599i	−0.196837	+	0.980436i	$0.563067\pi$
$440$	36.0000			0.0818182
$441$		0			0
$442$	264.000	−	264.000i	0.597285	−	0.597285i
$443$		−	675.000i		−	1.52370i	−0.647752	−	0.761851i	$-0.724291\pi$
$443$		−	675.000i		−	1.52370i	0.647752	−	0.761851i	$-0.275709\pi$
$444$	210.000	+	72.0000i	0.472973	+	0.162162i
$445$	−360.000			−0.808989
$446$	275.000	+	275.000i	0.616592	+	0.616592i
$447$		−	171.000i		−	0.382550i
$448$		−	24.0000i		−	0.0535714i
$449$	−396.000	+	396.000i	−0.881960	+	0.881960i	−0.993734	−	0.111774i	$-0.964347\pi$
$449$	−396.000	+	396.000i	−0.881960	+	0.881960i	0.111774	+	0.993734i	$0.464347\pi$
$450$		0			0
$451$	117.000			0.259424
$452$	−126.000	+	126.000i	−0.278761	+	0.278761i
$453$	−720.000			−1.58940
$454$	−432.000			−0.951542
$455$			198.000i			0.435165i
$456$	−48.0000			−0.105263
$457$	−493.000	+	493.000i	−1.07877	+	1.07877i	−0.0821551	+	0.996620i	$0.526180\pi$
$457$	−493.000	+	493.000i	−1.07877	+	1.07877i	−0.996620	+	0.0821551i	$0.973820\pi$
$458$	−359.000	−	359.000i	−0.783843	−	0.783843i
$459$	324.000	+	324.000i	0.705882	+	0.705882i
$460$	−36.0000			−0.0782609
$461$	285.000	−	285.000i	0.618221	−	0.618221i	−0.326854	−	0.945075i	$-0.605988\pi$
$461$	285.000	−	285.000i	0.618221	−	0.618221i	0.945075	+	0.326854i	$0.105988\pi$
$462$	−27.0000	−	27.0000i	−0.0584416	−	0.0584416i
$463$	43.0000	−	43.0000i	0.0928726	−	0.0928726i	−0.659144	−	0.752017i	$-0.729081\pi$
$463$	43.0000	−	43.0000i	0.0928726	−	0.0928726i	0.752017	+	0.659144i	$0.229081\pi$
$464$	−36.0000	−	36.0000i	−0.0775862	−	0.0775862i
$465$			576.000i			1.23871i
$466$	168.000	−	168.000i	0.360515	−	0.360515i
$467$	−507.000	+	507.000i	−1.08565	+	1.08565i	−0.0896827	+	0.995970i	$0.528585\pi$
$467$	−507.000	+	507.000i	−1.08565	+	1.08565i	−0.995970	+	0.0896827i	$0.971415\pi$
$468$		0			0
$469$		−	78.0000i		−	0.166311i
$470$	450.000			0.957447
$471$		−	189.000i		−	0.401274i
$472$			288.000i			0.610169i
$473$	21.0000	+	21.0000i	0.0443975	+	0.0443975i
$474$			168.000i			0.354430i
$475$	−28.0000	−	28.0000i	−0.0589474	−	0.0589474i
$476$	−72.0000	−	72.0000i	−0.151261	−	0.151261i
$477$		0			0
$478$	−390.000			−0.815900
$479$	−501.000	+	501.000i	−1.04593	+	1.04593i	−0.0470358	+	0.998893i	$0.514977\pi$
$479$	−501.000	+	501.000i	−1.04593	+	1.04593i	−0.998893	+	0.0470358i	$0.985023\pi$
$480$			72.0000i			0.150000i
$481$	−517.000	+	253.000i	−1.07484	+	0.525988i
$482$	658.000			1.36515
$483$	27.0000	+	27.0000i	0.0559006	+	0.0559006i
$484$			224.000i			0.462810i
$485$			192.000i			0.395876i
$486$		0			0
$487$	−308.000	+	308.000i	−0.632444	+	0.632444i	−0.948680	−	0.316237i	$-0.897581\pi$
$487$	−308.000	+	308.000i	−0.632444	+	0.632444i	0.316237	+	0.948680i	$0.397581\pi$
$488$	320.000			0.655738
$489$	411.000	−	411.000i	0.840491	−	0.840491i
$490$	−240.000			−0.489796
$491$	−696.000			−1.41752			−0.708758	−	0.705452i	$-0.750744\pi$
$491$	−696.000			−1.41752			−0.708758	+	0.705452i	$0.750744\pi$
$492$			234.000i			0.475610i
$493$	−216.000			−0.438134
$494$	88.0000	−	88.0000i	0.178138	−	0.178138i
$495$		0			0
$496$	128.000	+	128.000i	0.258065	+	0.258065i
$497$	−153.000			−0.307847
$498$	81.0000	−	81.0000i	0.162651	−	0.162651i
$499$	112.000	+	112.000i	0.224449	+	0.224449i	0.810369	−	0.585920i	$-0.199267\pi$
$499$	112.000	+	112.000i	0.224449	+	0.224449i	−0.585920	+	0.810369i	$0.699267\pi$
$500$	−192.000	+	192.000i	−0.384000	+	0.384000i
$501$	396.000	+	396.000i	0.790419	+	0.790419i
$502$		−	354.000i		−	0.705179i
$503$	60.0000	−	60.0000i	0.119284	−	0.119284i	−0.644945	−	0.764229i	$-0.723120\pi$
$503$	60.0000	−	60.0000i	0.119284	−	0.119284i	0.764229	+	0.644945i	$0.223120\pi$
$504$		0			0
$505$	−549.000	−	549.000i	−1.08713	−	1.08713i
$506$			18.0000i			0.0355731i
$507$	−219.000			−0.431953
$508$		−	310.000i		−	0.610236i
$509$		−	921.000i		−	1.80943i	−0.426017	−	0.904715i	$-0.640084\pi$
$509$		−	921.000i		−	1.80943i	0.426017	−	0.904715i	$-0.359916\pi$
$510$	216.000	+	216.000i	0.423529	+	0.423529i
$511$			75.0000i			0.146771i
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	108.000	+	108.000i	0.210526	+	0.210526i
$514$	144.000			0.280156
$515$	−714.000			−1.38641
$516$	−42.0000	+	42.0000i	−0.0813953	+	0.0813953i
$517$		−	225.000i		−	0.435203i
$518$	69.0000	+	141.000i	0.133205	+	0.272201i
$519$	261.000			0.502890
$520$	−132.000	−	132.000i	−0.253846	−	0.253846i
$521$		−	513.000i		−	0.984645i	−0.870413	−	0.492322i	$-0.836148\pi$
$521$		−	513.000i		−	0.984645i	0.870413	−	0.492322i	$-0.163852\pi$
$522$		0			0
$523$	−151.000	+	151.000i	−0.288719	+	0.288719i	−0.836574	−	0.547855i	$-0.815445\pi$
$523$	−151.000	+	151.000i	−0.288719	+	0.288719i	0.547855	+	0.836574i	$0.315445\pi$
$524$	−168.000	+	168.000i	−0.320611	+	0.320611i
$525$	63.0000			0.120000
$526$	−45.0000	+	45.0000i	−0.0855513	+	0.0855513i
$527$	768.000			1.45731
$528$	36.0000			0.0681818
$529$			511.000i			0.965974i
$530$	234.000			0.441509
$531$		0			0
$532$	−24.0000	−	24.0000i	−0.0451128	−	0.0451128i
$533$	−429.000	−	429.000i	−0.804878	−	0.804878i
$534$	−360.000			−0.674157
$535$	−72.0000	+	72.0000i	−0.134579	+	0.134579i
$536$	52.0000	+	52.0000i	0.0970149	+	0.0970149i
$537$	153.000	−	153.000i	0.284916	−	0.284916i
$538$	−312.000	−	312.000i	−0.579926	−	0.579926i
$539$			120.000i			0.222635i
$540$	162.000	−	162.000i	0.300000	−	0.300000i
$541$	112.000	−	112.000i	0.207024	−	0.207024i	−0.595977	−	0.803001i	$-0.703235\pi$
$541$	112.000	−	112.000i	0.207024	−	0.207024i	0.803001	+	0.595977i	$0.203235\pi$
$542$	−219.000	−	219.000i	−0.404059	−	0.404059i
$543$		−	765.000i		−	1.40884i
$544$	96.0000			0.176471
$545$		−	168.000i		−	0.308257i
$546$			198.000i			0.362637i
$547$	−392.000	−	392.000i	−0.716636	−	0.716636i	0.251279	−	0.967915i	$-0.419149\pi$
$547$	−392.000	−	392.000i	−0.716636	−	0.716636i	−0.967915	+	0.251279i	$0.919149\pi$
$548$			432.000i			0.788321i
$549$		0			0
$550$	21.0000	+	21.0000i	0.0381818	+	0.0381818i
$551$	−72.0000			−0.130672
$552$	−36.0000			−0.0652174
$553$	−84.0000	+	84.0000i	−0.151899	+	0.151899i
$554$			112.000i			0.202166i
$555$	−207.000	−	423.000i	−0.372973	−	0.762162i
$556$	−416.000			−0.748201
$557$	129.000	+	129.000i	0.231598	+	0.231598i	0.813359	−	0.581762i	$-0.197636\pi$
$557$	129.000	+	129.000i	0.231598	+	0.231598i	−0.581762	+	0.813359i	$0.697636\pi$
$558$		0			0
$559$		−	154.000i		−	0.275492i
$560$	−36.0000	+	36.0000i	−0.0642857	+	0.0642857i
$561$	108.000	−	108.000i	0.192513	−	0.192513i
$562$	480.000			0.854093
$563$	303.000	−	303.000i	0.538188	−	0.538188i	−0.384808	−	0.922997i	$-0.625732\pi$
$563$	303.000	−	303.000i	0.538188	−	0.538188i	0.922997	+	0.384808i	$0.125732\pi$
$564$	450.000			0.797872
$565$	378.000			0.669027
$566$			352.000i			0.621908i
$567$	−243.000			−0.428571
$568$	102.000	−	102.000i	0.179577	−	0.179577i
$569$	312.000	+	312.000i	0.548330	+	0.548330i	0.925958	−	0.377627i	$-0.123260\pi$
$569$	312.000	+	312.000i	0.548330	+	0.548330i	−0.377627	+	0.925958i	$0.623260\pi$
$570$	72.0000	+	72.0000i	0.126316	+	0.126316i
$571$	1083.00			1.89667			0.948336	−	0.317267i	$-0.102765\pi$
$571$	1083.00			1.89667			0.948336	+	0.317267i	$0.102765\pi$
$572$	−66.0000	+	66.0000i	−0.115385	+	0.115385i
$573$	72.0000	+	72.0000i	0.125654	+	0.125654i
$574$	−117.000	+	117.000i	−0.203833	+	0.203833i
$575$	−21.0000	−	21.0000i	−0.0365217	−	0.0365217i
$576$		0			0
$577$	−196.000	+	196.000i	−0.339688	+	0.339688i	−0.856250	−	0.516562i	$-0.827212\pi$
$577$	−196.000	+	196.000i	−0.339688	+	0.339688i	0.516562	+	0.856250i	$0.327212\pi$
$578$	−1.00000	+	1.00000i	−0.00173010	+	0.00173010i
$579$	489.000	+	489.000i	0.844560	+	0.844560i
$580$			108.000i			0.186207i
$581$	81.0000			0.139415
$582$			192.000i			0.329897i
$583$		−	117.000i		−	0.200686i
$584$	−50.0000	−	50.0000i	−0.0856164	−	0.0856164i
$585$		0			0
$586$	504.000	+	504.000i	0.860068	+	0.860068i
$587$	612.000	+	612.000i	1.04259	+	1.04259i	0.999052	+	0.0435377i	$0.0138628\pi$
$587$	612.000	+	612.000i	1.04259	+	1.04259i	0.0435377	+	0.999052i	$0.486137\pi$
$588$	−240.000			−0.408163
$589$	256.000			0.434635
$590$	432.000	−	432.000i	0.732203	−	0.732203i
$591$			675.000i			1.14213i
$592$	−140.000	−	48.0000i	−0.236486	−	0.0810811i
$593$	−57.0000			−0.0961214			−0.0480607	−	0.998844i	$-0.515304\pi$
$593$	−57.0000			−0.0961214			−0.0480607	+	0.998844i	$0.515304\pi$
$594$	−81.0000	−	81.0000i	−0.136364	−	0.136364i
$595$			216.000i			0.363025i
$596$			114.000i			0.191275i
$597$	−303.000	+	303.000i	−0.507538	+	0.507538i
$598$	66.0000	−	66.0000i	0.110368	−	0.110368i
$599$	795.000			1.32721			0.663606	−	0.748082i	$-0.269025\pi$
$599$	795.000			1.32721			0.663606	+	0.748082i	$0.269025\pi$
$600$	−42.0000	+	42.0000i	−0.0700000	+	0.0700000i
$601$	558.000			0.928453			0.464226	−	0.885717i	$-0.346332\pi$
$601$	558.000			0.928453			0.464226	+	0.885717i	$0.346332\pi$
$602$	−42.0000			−0.0697674
$603$		0			0
$604$	480.000			0.794702
$605$	336.000	−	336.000i	0.555372	−	0.555372i
$606$	−549.000	−	549.000i	−0.905941	−	0.905941i
$607$	−668.000	−	668.000i	−1.10049	−	1.10049i	−0.994351	−	0.106143i	$-0.966150\pi$
$607$	−668.000	−	668.000i	−1.10049	−	1.10049i	−0.106143	−	0.994351i	$-0.533850\pi$
$608$	32.0000			0.0526316
$609$	81.0000	−	81.0000i	0.133005	−	0.133005i
$610$	−480.000	−	480.000i	−0.786885	−	0.786885i
$611$	−825.000	+	825.000i	−1.35025	+	1.35025i
$612$		0			0
$613$			183.000i			0.298532i	0.988797	+	0.149266i	$0.0476910\pi$
$613$			183.000i			0.298532i	−0.988797	+	0.149266i	$0.952309\pi$
$614$	315.000	−	315.000i	0.513029	−	0.513029i
$615$	351.000	−	351.000i	0.570732	−	0.570732i
$616$	18.0000	+	18.0000i	0.0292208	+	0.0292208i
$617$			297.000i			0.481361i	0.970604	+	0.240681i	$0.0773707\pi$
$617$			297.000i			0.481361i	−0.970604	+	0.240681i	$0.922629\pi$
$618$	−714.000			−1.15534
$619$			165.000i			0.266559i	0.991078	+	0.133279i	$0.0425508\pi$
$619$			165.000i			0.266559i	−0.991078	+	0.133279i	$0.957449\pi$
$620$		−	384.000i		−	0.619355i
$621$	81.0000	+	81.0000i	0.130435	+	0.130435i
$622$		−	168.000i		−	0.270096i
$623$	−180.000	−	180.000i	−0.288925	−	0.288925i
$624$	−132.000	−	132.000i	−0.211538	−	0.211538i
$625$	401.000			0.641600
$626$	−442.000			−0.706070
$627$	36.0000	−	36.0000i	0.0574163	−	0.0574163i
$628$			126.000i			0.200637i
$629$	−564.000	+	276.000i	−0.896661	+	0.438792i
$630$		0			0
$631$	380.000	+	380.000i	0.602219	+	0.602219i	0.940901	−	0.338682i	$-0.109981\pi$
$631$	380.000	+	380.000i	0.602219	+	0.602219i	−0.338682	+	0.940901i	$0.609981\pi$
$632$		−	112.000i		−	0.177215i
$633$		−	489.000i		−	0.772512i
$634$	240.000	−	240.000i	0.378549	−	0.378549i
$635$	−465.000	+	465.000i	−0.732283	+	0.732283i
$636$	234.000			0.367925
$637$	440.000	−	440.000i	0.690738	−	0.690738i
$638$	54.0000			0.0846395
$639$		0			0
$640$		−	48.0000i		−	0.0750000i
$641$	−111.000			−0.173167			−0.0865835	−	0.996245i	$-0.527595\pi$
$641$	−111.000			−0.173167			−0.0865835	+	0.996245i	$0.527595\pi$
$642$	−72.0000	+	72.0000i	−0.112150	+	0.112150i
$643$	−643.000	−	643.000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$643$	−643.000	−	643.000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$644$	−18.0000	−	18.0000i	−0.0279503	−	0.0279503i
$645$	126.000			0.195349
$646$	96.0000	−	96.0000i	0.148607	−	0.148607i
$647$	300.000	+	300.000i	0.463679	+	0.463679i	0.899859	−	0.436181i	$-0.143669\pi$
$647$	300.000	+	300.000i	0.463679	+	0.463679i	−0.436181	+	0.899859i	$0.643669\pi$
$648$	162.000	−	162.000i	0.250000	−	0.250000i
$649$	−216.000	−	216.000i	−0.332820	−	0.332820i
$650$		−	154.000i		−	0.236923i
$651$	−288.000	+	288.000i	−0.442396	+	0.442396i
$652$	−274.000	+	274.000i	−0.420245	+	0.420245i
$653$	408.000	+	408.000i	0.624809	+	0.624809i	0.946757	−	0.321949i	$-0.104338\pi$
$653$	408.000	+	408.000i	0.624809	+	0.624809i	−0.321949	+	0.946757i	$0.604338\pi$
$654$		−	168.000i		−	0.256881i
$655$	504.000			0.769466
$656$		−	156.000i		−	0.237805i
$657$		0			0
$658$	225.000	+	225.000i	0.341945	+	0.341945i
$659$		−	843.000i		−	1.27921i	−0.768703	−	0.639605i	$-0.779098\pi$
$659$		−	843.000i		−	1.27921i	0.768703	−	0.639605i	$-0.220902\pi$
$660$	−54.0000	−	54.0000i	−0.0818182	−	0.0818182i
$661$	172.000	+	172.000i	0.260212	+	0.260212i	0.825140	−	0.564928i	$-0.191096\pi$
$661$	172.000	+	172.000i	0.260212	+	0.260212i	−0.564928	+	0.825140i	$0.691096\pi$
$662$	−442.000			−0.667674
$663$	−792.000			−1.19457
$664$	−54.0000	+	54.0000i	−0.0813253	+	0.0813253i
$665$			72.0000i			0.108271i
$666$		0			0
$667$	−54.0000			−0.0809595
$668$	−264.000	−	264.000i	−0.395210	−	0.395210i
$669$		−	825.000i		−	1.23318i
$670$		−	156.000i		−	0.232836i
$671$	−240.000	+	240.000i	−0.357675	+	0.357675i
$672$	−36.0000	+	36.0000i	−0.0535714	+	0.0535714i
$673$	561.000			0.833581			0.416790	−	0.909003i	$-0.363155\pi$
$673$	561.000			0.833581			0.416790	+	0.909003i	$0.363155\pi$
$674$	−393.000	+	393.000i	−0.583086	+	0.583086i
$675$	189.000			0.280000
$676$	146.000			0.215976
$677$			201.000i			0.296898i	0.988920	+	0.148449i	$0.0474281\pi$
$677$			201.000i			0.296898i	−0.988920	+	0.148449i	$0.952572\pi$
$678$	378.000			0.557522
$679$	−96.0000	+	96.0000i	−0.141384	+	0.141384i
$680$	−144.000	−	144.000i	−0.211765	−	0.211765i
$681$	648.000	+	648.000i	0.951542	+	0.951542i
$682$	−192.000			−0.281525
$683$	−729.000	+	729.000i	−1.06735	+	1.06735i	−0.0697881	+	0.997562i	$0.522232\pi$
$683$	−729.000	+	729.000i	−1.06735	+	1.06735i	−0.997562	+	0.0697881i	$0.977768\pi$
$684$		0			0
$685$	648.000	−	648.000i	0.945985	−	0.945985i
$686$	−267.000	−	267.000i	−0.389213	−	0.389213i
$687$			1077.00i			1.56769i
$688$	28.0000	−	28.0000i	0.0406977	−	0.0406977i
$689$	−429.000	+	429.000i	−0.622642	+	0.622642i
$690$	54.0000	+	54.0000i	0.0782609	+	0.0782609i
$691$			328.000i			0.474674i	0.971427	+	0.237337i	$0.0762746\pi$
$691$			328.000i			0.474674i	−0.971427	+	0.237337i	$0.923725\pi$
$692$	−174.000			−0.251445
$693$		0			0
$694$			486.000i			0.700288i
$695$	624.000	+	624.000i	0.897842	+	0.897842i
$696$			108.000i			0.155172i
$697$	−468.000	−	468.000i	−0.671449	−	0.671449i
$698$	−48.0000	−	48.0000i	−0.0687679	−	0.0687679i
$699$	−504.000			−0.721030
$700$	−42.0000			−0.0600000
$701$	816.000	−	816.000i	1.16405	−	1.16405i	0.180471	−	0.983580i	$-0.442238\pi$
$701$	816.000	−	816.000i	1.16405	−	1.16405i	0.983580	−	0.180471i	$-0.0577622\pi$
$702$			594.000i			0.846154i
$703$	−188.000	+	92.0000i	−0.267425	+	0.130868i
$704$	−24.0000			−0.0340909
$705$	−675.000	−	675.000i	−0.957447	−	0.957447i
$706$			504.000i			0.713881i
$707$		−	549.000i		−	0.776521i
$708$	432.000	−	432.000i	0.610169	−	0.610169i
$709$	−532.000	+	532.000i	−0.750353	+	0.750353i	−0.974545	−	0.224192i	$-0.928026\pi$
$709$	−532.000	+	532.000i	−0.750353	+	0.750353i	0.224192	+	0.974545i	$0.428026\pi$
$710$	−306.000			−0.430986
$711$		0			0
$712$	240.000			0.337079
$713$	192.000			0.269285
$714$			216.000i			0.302521i
$715$	198.000			0.276923
$716$	−102.000	+	102.000i	−0.142458	+	0.142458i
$717$	585.000	+	585.000i	0.815900	+	0.815900i
$718$	−285.000	−	285.000i	−0.396936	−	0.396936i
$719$	267.000			0.371349			0.185675	−	0.982611i	$-0.440553\pi$
$719$	267.000			0.371349			0.185675	+	0.982611i	$0.440553\pi$
$720$		0			0
$721$	−357.000	−	357.000i	−0.495146	−	0.495146i
$722$	−329.000	+	329.000i	−0.455679	+	0.455679i
$723$	−987.000	−	987.000i	−1.36515	−	1.36515i
$724$			510.000i			0.704420i
$725$	−63.0000	+	63.0000i	−0.0868966	+	0.0868966i
$726$	336.000	−	336.000i	0.462810	−	0.462810i
$727$	−164.000	−	164.000i	−0.225585	−	0.225585i	0.585261	−	0.810845i	$-0.300992\pi$
$727$	−164.000	−	164.000i	−0.225585	−	0.225585i	−0.810845	+	0.585261i	$0.800992\pi$
$728$		−	132.000i		−	0.181319i
$729$	−729.000			−1.00000
$730$			150.000i			0.205479i
$731$		−	168.000i		−	0.229822i
$732$	−480.000	−	480.000i	−0.655738	−	0.655738i
$733$		−	585.000i		−	0.798090i	−0.916931	−	0.399045i	$-0.869342\pi$
$733$		−	585.000i		−	0.798090i	0.916931	−	0.399045i	$-0.130658\pi$
$734$	464.000	+	464.000i	0.632153	+	0.632153i
$735$	360.000	+	360.000i	0.489796	+	0.489796i
$736$	24.0000			0.0326087
$737$	−78.0000			−0.105834
$738$		0			0
$739$			387.000i			0.523681i	0.965111	+	0.261840i	$0.0843294\pi$
$739$			387.000i			0.523681i	−0.965111	+	0.261840i	$0.915671\pi$
$740$	138.000	+	282.000i	0.186486	+	0.381081i
$741$	−264.000			−0.356275
$742$	117.000	+	117.000i	0.157682	+	0.157682i
$743$		−	555.000i		−	0.746972i	−0.927636	−	0.373486i	$-0.878162\pi$
$743$		−	555.000i		−	0.746972i	0.927636	−	0.373486i	$-0.121838\pi$
$744$		−	384.000i		−	0.516129i
$745$	171.000	−	171.000i	0.229530	−	0.229530i
$746$	−233.000	+	233.000i	−0.312332	+	0.312332i
$747$		0			0
$748$	−72.0000	+	72.0000i	−0.0962567	+	0.0962567i
$749$	−72.0000			−0.0961282
$750$	576.000			0.768000
$751$		−	269.000i		−	0.358189i	−0.983832	−	0.179095i	$-0.942683\pi$
$751$		−	269.000i		−	0.358189i	0.983832	−	0.179095i	$-0.0573168\pi$
$752$	−300.000			−0.398936
$753$	−531.000	+	531.000i	−0.705179	+	0.705179i
$754$	−198.000	−	198.000i	−0.262599	−	0.262599i
$755$	−720.000	−	720.000i	−0.953642	−	0.953642i
$756$	162.000			0.214286
$757$	263.000	−	263.000i	0.347424	−	0.347424i	−0.511725	−	0.859149i	$-0.670993\pi$
$757$	263.000	−	263.000i	0.347424	−	0.347424i	0.859149	+	0.511725i	$0.170993\pi$
$758$	−237.000	−	237.000i	−0.312665	−	0.312665i
$759$	27.0000	−	27.0000i	0.0355731	−	0.0355731i
$760$	−48.0000	−	48.0000i	−0.0631579	−	0.0631579i
$761$		−	183.000i		−	0.240473i	−0.992745	−	0.120237i	$-0.961635\pi$
$761$		−	183.000i		−	0.240473i	0.992745	−	0.120237i	$-0.0383653\pi$
$762$	−465.000	+	465.000i	−0.610236	+	0.610236i
$763$	84.0000	−	84.0000i	0.110092	−	0.110092i
$764$	−48.0000	−	48.0000i	−0.0628272	−	0.0628272i
$765$		0			0
$766$	528.000			0.689295
$767$			1584.00i			2.06519i
$768$		−	48.0000i		−	0.0625000i
$769$	863.000	+	863.000i	1.12224	+	1.12224i	0.991405	+	0.130832i	$0.0417649\pi$
$769$	863.000	+	863.000i	1.12224	+	1.12224i	0.130832	+	0.991405i	$0.458235\pi$
$770$		−	54.0000i		−	0.0701299i
$771$	−216.000	−	216.000i	−0.280156	−	0.280156i
$772$	−326.000	−	326.000i	−0.422280	−	0.422280i
$773$	−855.000			−1.10608			−0.553040	−	0.833155i	$-0.686532\pi$
$773$	−855.000			−1.10608			−0.553040	+	0.833155i	$0.686532\pi$
$774$		0			0
$775$	224.000	−	224.000i	0.289032	−	0.289032i
$776$		−	128.000i		−	0.164948i
$777$	108.000	−	315.000i	0.138996	−	0.405405i
$778$	672.000			0.863753
$779$	−156.000	−	156.000i	−0.200257	−	0.200257i
$780$			396.000i			0.507692i
$781$			153.000i			0.195903i
$782$	72.0000	−	72.0000i	0.0920716	−	0.0920716i
$783$	243.000	−	243.000i	0.310345	−	0.310345i
$784$	160.000			0.204082
$785$	189.000	−	189.000i	0.240764	−	0.240764i
$786$	504.000			0.641221
$787$	−19.0000			−0.0241423			−0.0120712	−	0.999927i	$-0.503842\pi$
$787$	−19.0000			−0.0241423			−0.0120712	+	0.999927i	$0.503842\pi$
$788$		−	450.000i		−	0.571066i
$789$	135.000			0.171103
$790$	−168.000	+	168.000i	−0.212658	+	0.212658i
$791$	189.000	+	189.000i	0.238938	+	0.238938i
$792$		0			0
$793$	1760.00			2.21942
$794$	65.0000	−	65.0000i	0.0818640	−	0.0818640i
$795$	−351.000	−	351.000i	−0.441509	−	0.441509i
$796$	202.000	−	202.000i	0.253769	−	0.253769i
$797$	−384.000	−	384.000i	−0.481807	−	0.481807i	0.423902	−	0.905708i	$-0.360660\pi$
$797$	−384.000	−	384.000i	−0.481807	−	0.481807i	−0.905708	+	0.423902i	$0.860660\pi$
$798$			72.0000i			0.0902256i
$799$	−900.000	+	900.000i	−1.12641	+	1.12641i
$800$	28.0000	−	28.0000i	0.0350000	−	0.0350000i
$801$		0			0
$802$		−	378.000i		−	0.471322i
$803$	75.0000			0.0933998
$804$		−	156.000i		−	0.194030i
$805$			54.0000i			0.0670807i
$806$	704.000	+	704.000i	0.873449	+	0.873449i
$807$			936.000i			1.15985i
$808$	366.000	+	366.000i	0.452970	+	0.452970i
$809$	−825.000	−	825.000i	−1.01978	−	1.01978i	−0.999800	−	0.0199771i	$-0.993641\pi$
$809$	−825.000	−	825.000i	−1.01978	−	1.01978i	−0.0199771	−	0.999800i	$-0.506359\pi$
$810$	−486.000			−0.600000
$811$	−531.000			−0.654747			−0.327374	−	0.944895i	$-0.606164\pi$
$811$	−531.000			−0.654747			−0.327374	+	0.944895i	$0.606164\pi$
$812$	−54.0000	+	54.0000i	−0.0665025	+	0.0665025i
$813$			657.000i			0.808118i
$814$	141.000	−	69.0000i	0.173219	−	0.0847666i
$815$	822.000			1.00859
$816$	−144.000	−	144.000i	−0.176471	−	0.176471i
$817$		−	56.0000i		−	0.0685435i
$818$			176.000i			0.215159i
$819$		0			0
$820$	−234.000	+	234.000i	−0.285366	+	0.285366i
$821$	63.0000			0.0767357			0.0383678	−	0.999264i	$-0.487784\pi$
$821$	63.0000			0.0767357			0.0383678	+	0.999264i	$0.487784\pi$
$822$	648.000	−	648.000i	0.788321	−	0.788321i
$823$	584.000			0.709599			0.354800	−	0.934942i	$-0.384549\pi$
$823$	584.000			0.709599			0.354800	+	0.934942i	$0.384549\pi$
$824$	476.000			0.577670
$825$		−	63.0000i		−	0.0763636i
$826$	432.000			0.523002
$827$	837.000	−	837.000i	1.01209	−	1.01209i	0.0121659	−	0.999926i	$-0.496127\pi$
$827$	837.000	−	837.000i	1.01209	−	1.01209i	0.999926	−	0.0121659i	$-0.00387262\pi$
$828$		0			0
$829$	−608.000	−	608.000i	−0.733414	−	0.733414i	0.237881	−	0.971294i	$-0.423547\pi$
$829$	−608.000	−	608.000i	−0.733414	−	0.733414i	−0.971294	+	0.237881i	$0.923547\pi$
$830$	162.000			0.195181
$831$	168.000	−	168.000i	0.202166	−	0.202166i
$832$	88.0000	+	88.0000i	0.105769	+	0.105769i
$833$	480.000	−	480.000i	0.576230	−	0.576230i
$834$	624.000	+	624.000i	0.748201	+	0.748201i
$835$			792.000i			0.948503i
$836$	−24.0000	+	24.0000i	−0.0287081	+	0.0287081i
$837$	−864.000	+	864.000i	−1.03226	+	1.03226i
$838$	429.000	+	429.000i	0.511933	+	0.511933i
$839$			1506.00i			1.79499i	0.441021	+	0.897497i	$0.354617\pi$
$839$			1506.00i			1.79499i	−0.441021	+	0.897497i	$0.645383\pi$
$840$	108.000			0.128571
$841$		−	679.000i		−	0.807372i
$842$			56.0000i			0.0665083i
$843$	−720.000	−	720.000i	−0.854093	−	0.854093i
$844$			326.000i			0.386256i
$845$	−219.000	−	219.000i	−0.259172	−	0.259172i
$846$		0			0
$847$	336.000			0.396694
$848$	−156.000			−0.183962
$849$	528.000	−	528.000i	0.621908	−	0.621908i
$850$		−	168.000i		−	0.197647i
$851$	−141.000	+	69.0000i	−0.165687	+	0.0810811i
$852$	−306.000			−0.359155
$853$	−121.000	−	121.000i	−0.141852	−	0.141852i	0.632615	−	0.774467i	$-0.281982\pi$
$853$	−121.000	−	121.000i	−0.141852	−	0.141852i	−0.774467	+	0.632615i	$0.781982\pi$
$854$		−	480.000i		−	0.562061i
$855$		0			0
$856$	48.0000	−	48.0000i	0.0560748	−	0.0560748i
$857$	900.000	−	900.000i	1.05018	−	1.05018i	0.0515021	−	0.998673i	$-0.483599\pi$
$857$	900.000	−	900.000i	1.05018	−	1.05018i	0.998673	−	0.0515021i	$-0.0164009\pi$
$858$	198.000			0.230769
$859$	556.000	−	556.000i	0.647264	−	0.647264i	−0.305067	−	0.952331i	$-0.598679\pi$
$859$	556.000	−	556.000i	0.647264	−	0.647264i	0.952331	+	0.305067i	$0.0986788\pi$
$860$	−84.0000			−0.0976744
$861$	351.000			0.407666
$862$			18.0000i			0.0208817i
$863$	−96.0000			−0.111240			−0.0556199	−	0.998452i	$-0.517714\pi$
$863$	−96.0000			−0.111240			−0.0556199	+	0.998452i	$0.517714\pi$
$864$	−108.000	+	108.000i	−0.125000	+	0.125000i
$865$	261.000	+	261.000i	0.301734	+	0.301734i
$866$	−423.000	−	423.000i	−0.488453	−	0.488453i
$867$	3.00000			0.00346021
$868$	192.000	−	192.000i	0.221198	−	0.221198i
$869$	84.0000	+	84.0000i	0.0966628	+	0.0966628i
$870$	162.000	−	162.000i	0.186207	−	0.186207i
$871$	286.000	+	286.000i	0.328358	+	0.328358i
$872$			112.000i			0.128440i
$873$		0			0
$874$	24.0000	−	24.0000i	0.0274600	−	0.0274600i
$875$	288.000	+	288.000i	0.329143	+	0.329143i
$876$			150.000i			0.171233i
$877$	336.000			0.383124			0.191562	−	0.981480i	$-0.438645\pi$
$877$	336.000			0.383124			0.191562	+	0.981480i	$0.438645\pi$
$878$			688.000i			0.783599i
$879$		−	1512.00i		−	1.72014i
$880$	36.0000	+	36.0000i	0.0409091	+	0.0409091i
$881$			1464.00i			1.66175i	0.556461	+	0.830874i	$0.312159\pi$
$881$			1464.00i			1.66175i	−0.556461	+	0.830874i	$0.687841\pi$
$882$		0			0
$883$	−1120.00	−	1120.00i	−1.26840	−	1.26840i	−0.946913	−	0.321490i	$-0.895816\pi$
$883$	−1120.00	−	1120.00i	−1.26840	−	1.26840i	−0.321490	−	0.946913i	$-0.604184\pi$
$884$	528.000			0.597285
$885$	−1296.00			−1.46441
$886$	675.000	−	675.000i	0.761851	−	0.761851i
$887$		−	237.000i		−	0.267193i	−0.991036	−	0.133596i	$-0.957347\pi$
$887$		−	237.000i		−	0.267193i	0.991036	−	0.133596i	$-0.0426526\pi$
$888$	138.000	+	282.000i	0.155405	+	0.317568i
$889$	−465.000			−0.523060
$890$	−360.000	−	360.000i	−0.404494	−	0.404494i
$891$			243.000i			0.272727i
$892$			550.000i			0.616592i
$893$	−300.000	+	300.000i	−0.335946	+	0.335946i
$894$	171.000	−	171.000i	0.191275	−	0.191275i
$895$	306.000			0.341899
$896$	24.0000	−	24.0000i	0.0267857	−	0.0267857i
$897$	−198.000			−0.220736
$898$	−792.000			−0.881960
$899$		−	576.000i		−	0.640712i
$900$		0			0
$901$	−468.000	+	468.000i	−0.519423	+	0.519423i
$902$	117.000	+	117.000i	0.129712	+	0.129712i
$903$	63.0000	+	63.0000i	0.0697674	+	0.0697674i
$904$	−252.000			−0.278761
$905$	765.000	−	765.000i	0.845304	−	0.845304i
$906$	−720.000	−	720.000i	−0.794702	−	0.794702i
$907$	464.000	−	464.000i	0.511577	−	0.511577i	−0.403433	−	0.915009i	$-0.632183\pi$
$907$	464.000	−	464.000i	0.511577	−	0.511577i	0.915009	+	0.403433i	$0.132183\pi$
$908$	−432.000	−	432.000i	−0.475771	−	0.475771i
$909$		0			0
$910$	−198.000	+	198.000i	−0.217582	+	0.217582i
$911$	273.000	−	273.000i	0.299671	−	0.299671i	−0.541214	−	0.840885i	$-0.682035\pi$
$911$	273.000	−	273.000i	0.299671	−	0.299671i	0.840885	+	0.541214i	$0.182035\pi$
$912$	−48.0000	−	48.0000i	−0.0526316	−	0.0526316i
$913$		−	81.0000i		−	0.0887185i
$914$	−986.000			−1.07877
$915$			1440.00i			1.57377i
$916$		−	718.000i		−	0.783843i
$917$	252.000	+	252.000i	0.274809	+	0.274809i
$918$			648.000i			0.705882i
$919$	721.000	+	721.000i	0.784548	+	0.784548i	0.980595	−	0.196046i	$-0.0628103\pi$
$919$	721.000	+	721.000i	0.784548	+	0.784548i	−0.196046	+	0.980595i	$0.562810\pi$
$920$	−36.0000	−	36.0000i	−0.0391304	−	0.0391304i
$921$	−945.000			−1.02606
$922$	570.000			0.618221
$923$	561.000	−	561.000i	0.607801	−	0.607801i
$924$		−	54.0000i		−	0.0584416i
$925$	−84.0000	+	245.000i	−0.0908108	+	0.264865i
$926$	86.0000			0.0928726
$927$		0			0
$928$		−	72.0000i		−	0.0775862i
$929$		−	414.000i		−	0.445640i	−0.974860	−	0.222820i	$-0.928474\pi$
$929$		−	414.000i		−	0.445640i	0.974860	−	0.222820i	$-0.0715263\pi$
$930$	−576.000	+	576.000i	−0.619355	+	0.619355i
$931$	160.000	−	160.000i	0.171858	−	0.171858i
$932$	336.000			0.360515
$933$	−252.000	+	252.000i	−0.270096	+	0.270096i
$934$	−1014.00			−1.08565
$935$	216.000			0.231016
$936$		0			0
$937$	−1159.00			−1.23693			−0.618463	−	0.785814i	$-0.712244\pi$
$937$	−1159.00			−1.23693			−0.618463	+	0.785814i	$0.712244\pi$
$938$	78.0000	−	78.0000i	0.0831557	−	0.0831557i
$939$	663.000	+	663.000i	0.706070	+	0.706070i
$940$	450.000	+	450.000i	0.478723	+	0.478723i
$941$	−240.000			−0.255048			−0.127524	−	0.991835i	$-0.540703\pi$
$941$	−240.000			−0.255048			−0.127524	+	0.991835i	$0.540703\pi$
$942$	189.000	−	189.000i	0.200637	−	0.200637i
$943$	−117.000	−	117.000i	−0.124072	−	0.124072i
$944$	−288.000	+	288.000i	−0.305085	+	0.305085i
$945$	−243.000	−	243.000i	−0.257143	−	0.257143i
$946$			42.0000i			0.0443975i
$947$	−540.000	+	540.000i	−0.570222	+	0.570222i	−0.932190	−	0.361969i	$-0.882105\pi$
$947$	−540.000	+	540.000i	−0.570222	+	0.570222i	0.361969	+	0.932190i	$0.382105\pi$
$948$	−168.000	+	168.000i	−0.177215	+	0.177215i
$949$	−275.000	−	275.000i	−0.289779	−	0.289779i
$950$		−	56.0000i		−	0.0589474i
$951$	−720.000			−0.757098
$952$		−	144.000i		−	0.151261i
$953$			255.000i			0.267576i	0.991010	+	0.133788i	$0.0427141\pi$
$953$			255.000i			0.267576i	−0.991010	+	0.133788i	$0.957286\pi$
$954$		0			0
$955$			144.000i			0.150785i
$956$	−390.000	−	390.000i	−0.407950	−	0.407950i
$957$	−81.0000	−	81.0000i	−0.0846395	−	0.0846395i
$958$	−1002.00			−1.04593
$959$	648.000			0.675704
$960$	−72.0000	+	72.0000i	−0.0750000	+	0.0750000i
$961$			1087.00i			1.13111i
$962$	−770.000	−	264.000i	−0.800416	−	0.274428i
$963$		0			0
$964$	658.000	+	658.000i	0.682573	+	0.682573i
$965$			978.000i			1.01347i
$966$			54.0000i			0.0559006i
$967$	1027.00	−	1027.00i	1.06205	−	1.06205i	0.0641044	−	0.997943i	$-0.479581\pi$
$967$	1027.00	−	1027.00i	1.06205	−	1.06205i	0.997943	−	0.0641044i	$-0.0204191\pi$
$968$	−224.000	+	224.000i	−0.231405	+	0.231405i
$969$	−288.000			−0.297214
$970$	−192.000	+	192.000i	−0.197938	+	0.197938i
$971$	−630.000			−0.648816			−0.324408	−	0.945917i	$-0.605165\pi$
$971$	−630.000			−0.648816			−0.324408	+	0.945917i	$0.605165\pi$
$972$		0			0
$973$			624.000i			0.641316i
$974$	−616.000			−0.632444
$975$	−231.000	+	231.000i	−0.236923	+	0.236923i
$976$	320.000	+	320.000i	0.327869	+	0.327869i
$977$	24.0000	+	24.0000i	0.0245650	+	0.0245650i	0.719283	−	0.694718i	$-0.244471\pi$
$977$	24.0000	+	24.0000i	0.0245650	+	0.0245650i	−0.694718	+	0.719283i	$0.744471\pi$
$978$	822.000			0.840491
$979$	−180.000	+	180.000i	−0.183861	+	0.183861i
$980$	−240.000	−	240.000i	−0.244898	−	0.244898i
$981$		0			0
$982$	−696.000	−	696.000i	−0.708758	−	0.708758i
$983$			675.000i			0.686673i	0.939212	+	0.343337i	$0.111557\pi$
$983$			675.000i			0.686673i	−0.939212	+	0.343337i	$0.888443\pi$
$984$	−234.000	+	234.000i	−0.237805	+	0.237805i
$985$	−675.000	+	675.000i	−0.685279	+	0.685279i
$986$	−216.000	−	216.000i	−0.219067	−	0.219067i
$987$		−	675.000i		−	0.683891i
$988$	176.000			0.178138
$989$		−	42.0000i		−	0.0424671i
$990$		0			0
$991$	−817.000	−	817.000i	−0.824420	−	0.824420i	0.162319	−	0.986738i	$-0.448103\pi$
$991$	−817.000	−	817.000i	−0.824420	−	0.824420i	−0.986738	+	0.162319i	$0.948103\pi$
$992$			256.000i			0.258065i
$993$	663.000	+	663.000i	0.667674	+	0.667674i
$994$	−153.000	−	153.000i	−0.153924	−	0.153924i
$995$	−606.000			−0.609045
$996$	162.000			0.162651
$997$	929.000	−	929.000i	0.931795	−	0.931795i	−0.0660227	−	0.997818i	$-0.521031\pi$
$997$	929.000	−	929.000i	0.931795	−	0.931795i	0.997818	+	0.0660227i	$0.0210310\pi$
$998$			224.000i			0.224449i
$999$	324.000	−	945.000i	0.324324	−	0.945946i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.3.d.c.31.1	✓	2
3.2	odd	2		666.3.i.b.253.1		2
4.3	odd	2		592.3.k.b.401.1		2
37.6	odd	4	inner	74.3.d.c.43.1	yes	2
111.80	even	4		666.3.i.b.487.1		2
148.43	even	4		592.3.k.b.561.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.3.d.c.31.1	✓	2	1.1	even	1	trivial
74.3.d.c.43.1	yes	2	37.6	odd	4	inner
592.3.k.b.401.1		2	4.3	odd	2
592.3.k.b.561.1		2	148.43	even	4
666.3.i.b.253.1		2	3.2	odd	2
666.3.i.b.487.1		2	111.80	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	74.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} -3.00000i q^{3} +2.00000i q^{4} +(3.00000 - 3.00000i) q^{5} +(3.00000 - 3.00000i) q^{6} +3.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} +6.00000 q^{10} -3.00000i q^{11} +6.00000 q^{12} +(-11.0000 + 11.0000i) q^{13} +(3.00000 + 3.00000i) q^{14} +(-9.00000 - 9.00000i) q^{15} -4.00000 q^{16} +(-12.0000 + 12.0000i) q^{17} +(-4.00000 + 4.00000i) q^{19} +(6.00000 + 6.00000i) q^{20} -9.00000i q^{21} +(3.00000 - 3.00000i) q^{22} +(-3.00000 + 3.00000i) q^{23} +(6.00000 + 6.00000i) q^{24} +7.00000i q^{25} -22.0000 q^{26} -27.0000i q^{27} +6.00000i q^{28} +(9.00000 + 9.00000i) q^{29} -18.0000i q^{30} +(-32.0000 - 32.0000i) q^{31} +(-4.00000 - 4.00000i) q^{32} -9.00000 q^{33} -24.0000 q^{34} +(9.00000 - 9.00000i) q^{35} +(35.0000 + 12.0000i) q^{37} -8.00000 q^{38} +(33.0000 + 33.0000i) q^{39} +12.0000i q^{40} +39.0000i q^{41} +(9.00000 - 9.00000i) q^{42} +(-7.00000 + 7.00000i) q^{43} +6.00000 q^{44} -6.00000 q^{46} +75.0000 q^{47} +12.0000i q^{48} -40.0000 q^{49} +(-7.00000 + 7.00000i) q^{50} +(36.0000 + 36.0000i) q^{51} +(-22.0000 - 22.0000i) q^{52} +39.0000 q^{53} +(27.0000 - 27.0000i) q^{54} +(-9.00000 - 9.00000i) q^{55} +(-6.00000 + 6.00000i) q^{56} +(12.0000 + 12.0000i) q^{57} +18.0000i q^{58} +(72.0000 - 72.0000i) q^{59} +(18.0000 - 18.0000i) q^{60} +(-80.0000 - 80.0000i) q^{61} -64.0000i q^{62} -8.00000i q^{64} +66.0000i q^{65} +(-9.00000 - 9.00000i) q^{66} -26.0000i q^{67} +(-24.0000 - 24.0000i) q^{68} +(9.00000 + 9.00000i) q^{69} +18.0000 q^{70} -51.0000 q^{71} +25.0000i q^{73} +(23.0000 + 47.0000i) q^{74} +21.0000 q^{75} +(-8.00000 - 8.00000i) q^{76} -9.00000i q^{77} +66.0000i q^{78} +(-28.0000 + 28.0000i) q^{79} +(-12.0000 + 12.0000i) q^{80} -81.0000 q^{81} +(-39.0000 + 39.0000i) q^{82} +27.0000 q^{83} +18.0000 q^{84} +72.0000i q^{85} -14.0000 q^{86} +(27.0000 - 27.0000i) q^{87} +(6.00000 + 6.00000i) q^{88} +(-60.0000 - 60.0000i) q^{89} +(-33.0000 + 33.0000i) q^{91} +(-6.00000 - 6.00000i) q^{92} +(-96.0000 + 96.0000i) q^{93} +(75.0000 + 75.0000i) q^{94} +24.0000i q^{95} +(-12.0000 + 12.0000i) q^{96} +(-32.0000 + 32.0000i) q^{97} +(-40.0000 - 40.0000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 6 q^{5} + 6 q^{6} + 6 q^{7} - 4 q^{8} + 12 q^{10} + 12 q^{12} - 22 q^{13} + 6 q^{14} - 18 q^{15} - 8 q^{16} - 24 q^{17} - 8 q^{19} + 12 q^{20} + 6 q^{22} - 6 q^{23} + 12 q^{24} - 44 q^{26}+ \cdots - 80 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 + 6 * q^5 + 6 * q^6 + 6 * q^7 - 4 * q^8 + 12 * q^10 + 12 * q^12 - 22 * q^13 + 6 * q^14 - 18 * q^15 - 8 * q^16 - 24 * q^17 - 8 * q^19 + 12 * q^20 + 6 * q^22 - 6 * q^23 + 12 * q^24 - 44 * q^26 + 18 * q^29 - 64 * q^31 - 8 * q^32 - 18 * q^33 - 48 * q^34 + 18 * q^35 + 70 * q^37 - 16 * q^38 + 66 * q^39 + 18 * q^42 - 14 * q^43 + 12 * q^44 - 12 * q^46 + 150 * q^47 - 80 * q^49 - 14 * q^50 + 72 * q^51 - 44 * q^52 + 78 * q^53 + 54 * q^54 - 18 * q^55 - 12 * q^56 + 24 * q^57 + 144 * q^59 + 36 * q^60 - 160 * q^61 - 18 * q^66 - 48 * q^68 + 18 * q^69 + 36 * q^70 - 102 * q^71 + 46 * q^74 + 42 * q^75 - 16 * q^76 - 56 * q^79 - 24 * q^80 - 162 * q^81 - 78 * q^82 + 54 * q^83 + 36 * q^84 - 28 * q^86 + 54 * q^87 + 12 * q^88 - 120 * q^89 - 66 * q^91 - 12 * q^92 - 192 * q^93 + 150 * q^94 - 24 * q^96 - 64 * q^97 - 80 * q^98

Introduction

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