LMFDB - Embedded newform 1183.2.e.a.508.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(170,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1183.170");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			508.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1183.508
Dual form			1183.2.e.a.170.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} -3.00000 q^{6} +(0.500000 + 2.59808i) q^{7} -3.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} -3.00000 q^{6} +(0.500000 + 2.59808i) q^{7} -3.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +(-1.50000 + 2.59808i) q^{10} +(1.50000 - 2.59808i) q^{11} +(-1.50000 - 2.59808i) q^{12} +(2.00000 - 1.73205i) q^{14} -9.00000 q^{15} +(0.500000 + 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +(-3.00000 + 5.19615i) q^{18} +(0.500000 + 0.866025i) q^{19} -3.00000 q^{20} +(7.50000 + 2.59808i) q^{21} -3.00000 q^{22} +(-4.50000 + 7.79423i) q^{24} +(-2.00000 + 3.46410i) q^{25} -9.00000 q^{27} +(2.50000 + 0.866025i) q^{28} +7.00000 q^{29} +(4.50000 + 7.79423i) q^{30} +(-1.50000 + 2.59808i) q^{31} +(-2.50000 + 4.33013i) q^{32} +(-4.50000 - 7.79423i) q^{33} -2.00000 q^{34} +(6.00000 - 5.19615i) q^{35} -6.00000 q^{36} +(-1.00000 - 1.73205i) q^{37} +(0.500000 - 0.866025i) q^{38} +(4.50000 + 7.79423i) q^{40} +3.00000 q^{41} +(-1.50000 - 7.79423i) q^{42} -7.00000 q^{43} +(-1.50000 - 2.59808i) q^{44} +(-9.00000 + 15.5885i) q^{45} +(-0.500000 - 0.866025i) q^{47} +3.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} +4.00000 q^{50} +(-3.00000 - 5.19615i) q^{51} +(-1.50000 + 2.59808i) q^{53} +(4.50000 + 7.79423i) q^{54} -9.00000 q^{55} +(-1.50000 - 7.79423i) q^{56} +3.00000 q^{57} +(-3.50000 - 6.06218i) q^{58} +(2.00000 - 3.46410i) q^{59} +(-4.50000 + 7.79423i) q^{60} +(6.50000 + 11.2583i) q^{61} +3.00000 q^{62} +(12.0000 - 10.3923i) q^{63} +7.00000 q^{64} +(-4.50000 + 7.79423i) q^{66} +(1.50000 - 2.59808i) q^{67} +(-1.00000 - 1.73205i) q^{68} +(-7.50000 - 2.59808i) q^{70} +13.0000 q^{71} +(9.00000 + 15.5885i) q^{72} +(6.50000 - 11.2583i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(6.00000 + 10.3923i) q^{75} +1.00000 q^{76} +(7.50000 + 2.59808i) q^{77} +(1.50000 + 2.59808i) q^{79} +(1.50000 - 2.59808i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-1.50000 - 2.59808i) q^{82} +(6.00000 - 5.19615i) q^{84} -6.00000 q^{85} +(3.50000 + 6.06218i) q^{86} +(10.5000 - 18.1865i) q^{87} +(-4.50000 + 7.79423i) q^{88} +(-3.00000 - 5.19615i) q^{89} +18.0000 q^{90} +(4.50000 + 7.79423i) q^{93} +(-0.500000 + 0.866025i) q^{94} +(1.50000 - 2.59808i) q^{95} +(7.50000 + 12.9904i) q^{96} -5.00000 q^{97} +(5.50000 + 4.33013i) q^{98} -18.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 3 q^{3} + q^{4} - 3 q^{5} - 6 q^{6} + q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q - q^2 + 3 * q^3 + q^4 - 3 * q^5 - 6 * q^6 + q^7 - 6 * q^8 - 6 * q^9	$ 2 q - q^{2} + 3 q^{3} + q^{4} - 3 q^{5} - 6 q^{6} + q^{7} - 6 q^{8} - 6 q^{9} - 3 q^{10} + 3 q^{11} - 3 q^{12} + 4 q^{14} - 18 q^{15} + q^{16} + 2 q^{17} - 6 q^{18} + q^{19} - 6 q^{20} + 15 q^{21} - 6 q^{22} - 9 q^{24} - 4 q^{25} - 18 q^{27} + 5 q^{28} + 14 q^{29} + 9 q^{30} - 3 q^{31} - 5 q^{32} - 9 q^{33} - 4 q^{34} + 12 q^{35} - 12 q^{36} - 2 q^{37} + q^{38} + 9 q^{40} + 6 q^{41} - 3 q^{42} - 14 q^{43} - 3 q^{44} - 18 q^{45} - q^{47} + 6 q^{48} - 13 q^{49} + 8 q^{50} - 6 q^{51} - 3 q^{53} + 9 q^{54} - 18 q^{55} - 3 q^{56} + 6 q^{57} - 7 q^{58} + 4 q^{59} - 9 q^{60} + 13 q^{61} + 6 q^{62} + 24 q^{63} + 14 q^{64} - 9 q^{66} + 3 q^{67} - 2 q^{68} - 15 q^{70} + 26 q^{71} + 18 q^{72} + 13 q^{73} - 2 q^{74} + 12 q^{75} + 2 q^{76} + 15 q^{77} + 3 q^{79} + 3 q^{80} - 9 q^{81} - 3 q^{82} + 12 q^{84} - 12 q^{85} + 7 q^{86} + 21 q^{87} - 9 q^{88} - 6 q^{89} + 36 q^{90} + 9 q^{93} - q^{94} + 3 q^{95} + 15 q^{96} - 10 q^{97} + 11 q^{98} - 36 q^{99}+O(q^{100}) $ 2 * q - q^2 + 3 * q^3 + q^4 - 3 * q^5 - 6 * q^6 + q^7 - 6 * q^8 - 6 * q^9 - 3 * q^10 + 3 * q^11 - 3 * q^12 + 4 * q^14 - 18 * q^15 + q^16 + 2 * q^17 - 6 * q^18 + q^19 - 6 * q^20 + 15 * q^21 - 6 * q^22 - 9 * q^24 - 4 * q^25 - 18 * q^27 + 5 * q^28 + 14 * q^29 + 9 * q^30 - 3 * q^31 - 5 * q^32 - 9 * q^33 - 4 * q^34 + 12 * q^35 - 12 * q^36 - 2 * q^37 + q^38 + 9 * q^40 + 6 * q^41 - 3 * q^42 - 14 * q^43 - 3 * q^44 - 18 * q^45 - q^47 + 6 * q^48 - 13 * q^49 + 8 * q^50 - 6 * q^51 - 3 * q^53 + 9 * q^54 - 18 * q^55 - 3 * q^56 + 6 * q^57 - 7 * q^58 + 4 * q^59 - 9 * q^60 + 13 * q^61 + 6 * q^62 + 24 * q^63 + 14 * q^64 - 9 * q^66 + 3 * q^67 - 2 * q^68 - 15 * q^70 + 26 * q^71 + 18 * q^72 + 13 * q^73 - 2 * q^74 + 12 * q^75 + 2 * q^76 + 15 * q^77 + 3 * q^79 + 3 * q^80 - 9 * q^81 - 3 * q^82 + 12 * q^84 - 12 * q^85 + 7 * q^86 + 21 * q^87 - 9 * q^88 - 6 * q^89 + 36 * q^90 + 9 * q^93 - q^94 + 3 * q^95 + 15 * q^96 - 10 * q^97 + 11 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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	0.633316	−	0.773893i	$-0.281693\pi$
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i	−0.986869	+	0.161521i	$0.948360\pi$
$3$	1.50000	−	2.59808i	0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$3$	1.50000	−	2.59808i	0.866025	−	1.50000i	0.866025	−	0.500000i	$-0.166667\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	−0.977672	−	0.210138i	$-0.932609\pi$
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	0.306851	−	0.951757i	$-0.400725\pi$
$6$	−3.00000			−1.22474
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$8$	−3.00000			−1.06066
$9$	−3.00000	−	5.19615i	−1.00000	−	1.73205i
$10$	−1.50000	+	2.59808i	−0.474342	+	0.821584i
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$	−1.50000	−	2.59808i	−0.433013	−	0.750000i
$13$		0			0
$13$		0			0
$14$	2.00000	−	1.73205i	0.534522	−	0.462910i
$15$	−9.00000			−2.32379
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	−0.718900	−	0.695113i	$-0.755354\pi$
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	0.961436	+	0.275029i	$0.0886875\pi$
$18$	−3.00000	+	5.19615i	−0.707107	+	1.22474i
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	−0.802955	+	0.596040i	$0.796740\pi$
$20$	−3.00000			−0.670820
$21$	7.50000	+	2.59808i	1.63663	+	0.566947i
$22$	−3.00000			−0.639602
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	−4.50000	+	7.79423i	−0.918559	+	1.59099i
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$		0			0
$27$	−9.00000			−1.73205
$28$	2.50000	+	0.866025i	0.472456	+	0.163663i
$29$	7.00000			1.29987			0.649934	−	0.759991i	$-0.274797\pi$
$29$	7.00000			1.29987			0.649934	+	0.759991i	$0.274797\pi$
$30$	4.50000	+	7.79423i	0.821584	+	1.42302i
$31$	−1.50000	+	2.59808i	−0.269408	+	0.466628i	−0.968709	−	0.248199i	$-0.920161\pi$
$31$	−1.50000	+	2.59808i	−0.269408	+	0.466628i	0.699301	+	0.714827i	$0.253495\pi$
$32$	−2.50000	+	4.33013i	−0.441942	+	0.765466i
$33$	−4.50000	−	7.79423i	−0.783349	−	1.35680i
$34$	−2.00000			−0.342997
$35$	6.00000	−	5.19615i	1.01419	−	0.878310i
$36$	−6.00000			−1.00000
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$	0.500000	−	0.866025i	0.0811107	−	0.140488i
$39$		0			0
$40$	4.50000	+	7.79423i	0.711512	+	1.23238i
$41$	3.00000			0.468521			0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000			0.468521			0.234261	+	0.972174i	$0.424733\pi$
$42$	−1.50000	−	7.79423i	−0.231455	−	1.20268i
$43$	−7.00000			−1.06749			−0.533745	−	0.845645i	$-0.679216\pi$
$43$	−7.00000			−1.06749			−0.533745	+	0.845645i	$0.679216\pi$
$44$	−1.50000	−	2.59808i	−0.226134	−	0.391675i
$45$	−9.00000	+	15.5885i	−1.34164	+	2.32379i
$46$		0			0
$47$	−0.500000	−	0.866025i	−0.0729325	−	0.126323i	0.827253	−	0.561830i	$-0.189902\pi$
$47$	−0.500000	−	0.866025i	−0.0729325	−	0.126323i	−0.900185	+	0.435507i	$0.856569\pi$
$48$	3.00000			0.433013
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	4.00000			0.565685
$51$	−3.00000	−	5.19615i	−0.420084	−	0.727607i
$52$		0			0
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	−0.950464	−	0.310835i	$-0.899391\pi$
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	0.744423	+	0.667708i	$0.232725\pi$
$54$	4.50000	+	7.79423i	0.612372	+	1.06066i
$55$	−9.00000			−1.21356
$56$	−1.50000	−	7.79423i	−0.200446	−	1.04155i
$57$	3.00000			0.397360
$58$	−3.50000	−	6.06218i	−0.459573	−	0.796003i
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$	−4.50000	+	7.79423i	−0.580948	+	1.00623i
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	0.896258	+	0.443533i	$0.146275\pi$
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	3.00000			0.381000
$63$	12.0000	−	10.3923i	1.51186	−	1.30931i
$64$	7.00000			0.875000
$65$		0			0
$66$	−4.50000	+	7.79423i	−0.553912	+	0.959403i
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	−0.759733	−	0.650236i	$-0.774670\pi$
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	0.942987	+	0.332830i	$0.108004\pi$
$68$	−1.00000	−	1.73205i	−0.121268	−	0.210042i
$69$		0			0
$70$	−7.50000	−	2.59808i	−0.896421	−	0.310530i
$71$	13.0000			1.54282			0.771408	−	0.636341i	$-0.219553\pi$
$71$	13.0000			1.54282			0.771408	+	0.636341i	$0.219553\pi$
$72$	9.00000	+	15.5885i	1.06066	+	1.83712i
$73$	6.50000	−	11.2583i	0.760767	−	1.31769i	−0.181688	−	0.983356i	$-0.558156\pi$
$73$	6.50000	−	11.2583i	0.760767	−	1.31769i	0.942455	−	0.334332i	$-0.108511\pi$
$74$	−1.00000	+	1.73205i	−0.116248	+	0.201347i
$75$	6.00000	+	10.3923i	0.692820	+	1.20000i
$76$	1.00000			0.114708
$77$	7.50000	+	2.59808i	0.854704	+	0.296078i
$78$		0			0
$79$	1.50000	+	2.59808i	0.168763	+	0.292306i	0.937985	−	0.346675i	$-0.112689\pi$
$79$	1.50000	+	2.59808i	0.168763	+	0.292306i	−0.769222	+	0.638982i	$0.779356\pi$
$80$	1.50000	−	2.59808i	0.167705	−	0.290474i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−1.50000	−	2.59808i	−0.165647	−	0.286910i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$	6.00000	−	5.19615i	0.654654	−	0.566947i
$85$	−6.00000			−0.650791
$86$	3.50000	+	6.06218i	0.377415	+	0.653701i
$87$	10.5000	−	18.1865i	1.12572	−	1.94980i
$88$	−4.50000	+	7.79423i	−0.479702	+	0.830868i
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$	18.0000			1.89737
$91$		0			0
$92$		0			0
$93$	4.50000	+	7.79423i	0.466628	+	0.808224i
$94$	−0.500000	+	0.866025i	−0.0515711	+	0.0893237i
$95$	1.50000	−	2.59808i	0.153897	−	0.266557i
$96$	7.50000	+	12.9904i	0.765466	+	1.32583i
$97$	−5.00000			−0.507673			−0.253837	−	0.967247i	$-0.581693\pi$
$97$	−5.00000			−0.507673			−0.253837	+	0.967247i	$0.581693\pi$
$98$	5.50000	+	4.33013i	0.555584	+	0.437409i
$99$	−18.0000			−1.80907
$100$	2.00000	+	3.46410i	0.200000	+	0.346410i
$101$	2.50000	−	4.33013i	0.248759	−	0.430864i	−0.714423	−	0.699715i	$-0.753311\pi$
$101$	2.50000	−	4.33013i	0.248759	−	0.430864i	0.963182	+	0.268851i	$0.0866439\pi$
$102$	−3.00000	+	5.19615i	−0.297044	+	0.514496i
$103$	−2.50000	−	4.33013i	−0.246332	−	0.426660i	0.716173	−	0.697923i	$-0.245892\pi$
$103$	−2.50000	−	4.33013i	−0.246332	−	0.426660i	−0.962505	+	0.271263i	$0.912559\pi$
$104$		0			0
$105$	−4.50000	−	23.3827i	−0.439155	−	2.28192i
$106$	3.00000			0.291386
$107$	−4.00000	−	6.92820i	−0.386695	−	0.669775i	0.605308	−	0.795991i	$-0.293050\pi$
$107$	−4.00000	−	6.92820i	−0.386695	−	0.669775i	−0.992003	+	0.126217i	$0.959717\pi$
$108$	−4.50000	+	7.79423i	−0.433013	+	0.750000i
$109$	−3.50000	+	6.06218i	−0.335239	+	0.580651i	−0.983531	−	0.180741i	$-0.942150\pi$
$109$	−3.50000	+	6.06218i	−0.335239	+	0.580651i	0.648292	+	0.761392i	$0.275484\pi$
$110$	4.50000	+	7.79423i	0.429058	+	0.743151i
$111$	−6.00000			−0.569495
$112$	−2.00000	+	1.73205i	−0.188982	+	0.163663i
$113$	15.0000			1.41108			0.705541	−	0.708669i	$-0.250704\pi$
$113$	15.0000			1.41108			0.705541	+	0.708669i	$0.250704\pi$
$114$	−1.50000	−	2.59808i	−0.140488	−	0.243332i
$115$		0			0
$116$	3.50000	−	6.06218i	0.324967	−	0.562859i
$117$		0			0
$118$	−4.00000			−0.368230
$119$	5.00000	+	1.73205i	0.458349	+	0.158777i
$120$	27.0000			2.46475
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	6.50000	−	11.2583i	0.588482	−	1.01928i
$123$	4.50000	−	7.79423i	0.405751	−	0.702782i
$124$	1.50000	+	2.59808i	0.134704	+	0.233314i
$125$	−3.00000			−0.268328
$126$	−15.0000	−	5.19615i	−1.33631	−	0.462910i
$127$	11.0000			0.976092			0.488046	−	0.872818i	$-0.337710\pi$
$127$	11.0000			0.976092			0.488046	+	0.872818i	$0.337710\pi$
$128$	1.50000	+	2.59808i	0.132583	+	0.229640i
$129$	−10.5000	+	18.1865i	−0.924473	+	1.60123i
$130$		0			0
$131$	−2.50000	−	4.33013i	−0.218426	−	0.378325i	0.735901	−	0.677089i	$-0.236759\pi$
$131$	−2.50000	−	4.33013i	−0.218426	−	0.378325i	−0.954327	+	0.298764i	$0.903426\pi$
$132$	−9.00000			−0.783349
$133$	−2.00000	+	1.73205i	−0.173422	+	0.150188i
$134$	−3.00000			−0.259161
$135$	13.5000	+	23.3827i	1.16190	+	2.01246i
$136$	−3.00000	+	5.19615i	−0.257248	+	0.445566i
$137$	−5.00000	+	8.66025i	−0.427179	+	0.739895i	−0.996621	−	0.0821359i	$-0.973826\pi$
$137$	−5.00000	+	8.66025i	−0.427179	+	0.739895i	0.569442	+	0.822031i	$0.307159\pi$
$138$		0			0
$139$	−15.0000			−1.27228			−0.636142	−	0.771572i	$-0.719471\pi$
$139$	−15.0000			−1.27228			−0.636142	+	0.771572i	$0.719471\pi$
$140$	−1.50000	−	7.79423i	−0.126773	−	0.658733i
$141$	−3.00000			−0.252646
$142$	−6.50000	−	11.2583i	−0.545468	−	0.944778i
$143$		0			0
$144$	3.00000	−	5.19615i	0.250000	−	0.433013i
$145$	−10.5000	−	18.1865i	−0.871978	−	1.51031i
$146$	−13.0000			−1.07589
$147$	−3.00000	+	20.7846i	−0.247436	+	1.71429i
$148$	−2.00000			−0.164399
$149$	−7.50000	−	12.9904i	−0.614424	−	1.06421i	−0.990485	−	0.137619i	$-0.956055\pi$
$149$	−7.50000	−	12.9904i	−0.614424	−	1.06421i	0.376061	−	0.926595i	$-0.377278\pi$
$150$	6.00000	−	10.3923i	0.489898	−	0.848528i
$151$	10.5000	−	18.1865i	0.854478	−	1.48000i	−0.0226507	−	0.999743i	$-0.507211\pi$
$151$	10.5000	−	18.1865i	0.854478	−	1.48000i	0.877129	−	0.480256i	$-0.159456\pi$
$152$	−1.50000	−	2.59808i	−0.121666	−	0.210732i
$153$	−12.0000			−0.970143
$154$	−1.50000	−	7.79423i	−0.120873	−	0.628077i
$155$	9.00000			0.722897
$156$		0			0
$157$	−9.50000	+	16.4545i	−0.758183	+	1.31321i	0.185594	+	0.982627i	$0.440579\pi$
$157$	−9.50000	+	16.4545i	−0.758183	+	1.31321i	−0.943777	+	0.330584i	$0.892754\pi$
$158$	1.50000	−	2.59808i	0.119334	−	0.206692i
$159$	4.50000	+	7.79423i	0.356873	+	0.618123i
$160$	15.0000			1.18585
$161$		0			0
$162$	9.00000			0.707107
$163$	0.500000	+	0.866025i	0.0391630	+	0.0678323i	0.884943	−	0.465700i	$-0.154198\pi$
$163$	0.500000	+	0.866025i	0.0391630	+	0.0678323i	−0.845780	+	0.533533i	$0.820864\pi$
$164$	1.50000	−	2.59808i	0.117130	−	0.202876i
$165$	−13.5000	+	23.3827i	−1.05097	+	1.82034i
$166$		0			0
$167$	−13.0000			−1.00597			−0.502985	−	0.864295i	$-0.667765\pi$
$167$	−13.0000			−1.00597			−0.502985	+	0.864295i	$0.667765\pi$
$168$	−22.5000	−	7.79423i	−1.73591	−	0.601338i
$169$		0			0
$170$	3.00000	+	5.19615i	0.230089	+	0.398527i
$171$	3.00000	−	5.19615i	0.229416	−	0.397360i
$172$	−3.50000	+	6.06218i	−0.266872	+	0.462237i
$173$	−9.50000	−	16.4545i	−0.722272	−	1.25101i	−0.960087	−	0.279701i	$-0.909765\pi$
$173$	−9.50000	−	16.4545i	−0.722272	−	1.25101i	0.237816	−	0.971310i	$-0.423569\pi$
$174$	−21.0000			−1.59201
$175$	−10.0000	−	3.46410i	−0.755929	−	0.261861i
$176$	3.00000			0.226134
$177$	−6.00000	−	10.3923i	−0.450988	−	0.781133i
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	−8.50000	+	14.7224i	−0.635320	+	1.10041i	0.351127	+	0.936328i	$0.385798\pi$
$179$	−8.50000	+	14.7224i	−0.635320	+	1.10041i	−0.986447	+	0.164079i	$0.947535\pi$
$180$	9.00000	+	15.5885i	0.670820	+	1.16190i
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$		0			0
$183$	39.0000			2.88296
$184$		0			0
$185$	−3.00000	+	5.19615i	−0.220564	+	0.382029i
$186$	4.50000	−	7.79423i	0.329956	−	0.571501i
$187$	−3.00000	−	5.19615i	−0.219382	−	0.379980i
$188$	−1.00000			−0.0729325
$189$	−4.50000	−	23.3827i	−0.327327	−	1.70084i
$190$	−3.00000			−0.217643
$191$	8.50000	+	14.7224i	0.615038	+	1.06528i	0.990378	+	0.138390i	$0.0441928\pi$
$191$	8.50000	+	14.7224i	0.615038	+	1.06528i	−0.375339	+	0.926887i	$0.622474\pi$
$192$	10.5000	−	18.1865i	0.757772	−	1.31250i
$193$	−3.50000	+	6.06218i	−0.251936	+	0.436365i	−0.964059	−	0.265689i	$-0.914400\pi$
$193$	−3.50000	+	6.06218i	−0.251936	+	0.436365i	0.712123	+	0.702055i	$0.247734\pi$
$194$	2.50000	+	4.33013i	0.179490	+	0.310885i
$195$		0			0
$196$	−1.00000	+	6.92820i	−0.0714286	+	0.494872i
$197$	−1.00000			−0.0712470			−0.0356235	−	0.999365i	$-0.511342\pi$
$197$	−1.00000			−0.0712470			−0.0356235	+	0.999365i	$0.511342\pi$
$198$	9.00000	+	15.5885i	0.639602	+	1.10782i
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	−0.256391	−	0.966573i	$-0.582534\pi$
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	0.965272	−	0.261245i	$-0.0841331\pi$
$200$	6.00000	−	10.3923i	0.424264	−	0.734847i
$201$	−4.50000	−	7.79423i	−0.317406	−	0.549762i
$202$	−5.00000			−0.351799
$203$	3.50000	+	18.1865i	0.245652	+	1.27644i
$204$	−6.00000			−0.420084
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$	−2.50000	+	4.33013i	−0.174183	+	0.301694i
$207$		0			0
$208$		0			0
$209$	3.00000			0.207514
$210$	−18.0000	+	15.5885i	−1.24212	+	1.07571i
$211$	7.00000			0.481900			0.240950	−	0.970538i	$-0.422541\pi$
$211$	7.00000			0.481900			0.240950	+	0.970538i	$0.422541\pi$
$212$	1.50000	+	2.59808i	0.103020	+	0.178437i
$213$	19.5000	−	33.7750i	1.33612	−	2.31422i
$214$	−4.00000	+	6.92820i	−0.273434	+	0.473602i
$215$	10.5000	+	18.1865i	0.716094	+	1.24031i
$216$	27.0000			1.83712
$217$	−7.50000	−	2.59808i	−0.509133	−	0.176369i
$218$	7.00000			0.474100
$219$	−19.5000	−	33.7750i	−1.31769	−	2.28230i
$220$	−4.50000	+	7.79423i	−0.303390	+	0.525487i
$221$		0			0
$222$	3.00000	+	5.19615i	0.201347	+	0.348743i
$223$	−9.00000			−0.602685			−0.301342	−	0.953516i	$-0.597435\pi$
$223$	−9.00000			−0.602685			−0.301342	+	0.953516i	$0.597435\pi$
$224$	−12.5000	−	4.33013i	−0.835191	−	0.289319i
$225$	24.0000			1.60000
$226$	−7.50000	−	12.9904i	−0.498893	−	0.864107i
$227$	2.00000	−	3.46410i	0.132745	−	0.229920i	−0.791989	−	0.610535i	$-0.790954\pi$
$227$	2.00000	−	3.46410i	0.132745	−	0.229920i	0.924734	+	0.380615i	$0.124288\pi$
$228$	1.50000	−	2.59808i	0.0993399	−	0.172062i
$229$	6.50000	+	11.2583i	0.429532	+	0.743971i	0.996832	−	0.0795401i	$-0.0253452\pi$
$229$	6.50000	+	11.2583i	0.429532	+	0.743971i	−0.567300	+	0.823511i	$0.692012\pi$
$230$		0			0
$231$	18.0000	−	15.5885i	1.18431	−	1.02565i
$232$	−21.0000			−1.37872
$233$	10.5000	+	18.1865i	0.687878	+	1.19144i	0.972523	+	0.232806i	$0.0747909\pi$
$233$	10.5000	+	18.1865i	0.687878	+	1.19144i	−0.284645	+	0.958633i	$0.591876\pi$
$234$		0			0
$235$	−1.50000	+	2.59808i	−0.0978492	+	0.169480i
$236$	−2.00000	−	3.46410i	−0.130189	−	0.225494i
$237$	9.00000			0.584613
$238$	−1.00000	−	5.19615i	−0.0648204	−	0.336817i
$239$	−4.00000			−0.258738			−0.129369	−	0.991596i	$-0.541295\pi$
$239$	−4.00000			−0.258738			−0.129369	+	0.991596i	$0.541295\pi$
$240$	−4.50000	−	7.79423i	−0.290474	−	0.503115i
$241$	13.0000	−	22.5167i	0.837404	−	1.45043i	−0.0546547	−	0.998505i	$-0.517406\pi$
$241$	13.0000	−	22.5167i	0.837404	−	1.45043i	0.892058	−	0.451920i	$-0.149261\pi$
$242$	1.00000	−	1.73205i	0.0642824	−	0.111340i
$243$		0			0
$244$	13.0000			0.832240
$245$	16.5000	+	12.9904i	1.05415	+	0.829925i
$246$	−9.00000			−0.573819
$247$		0			0
$248$	4.50000	−	7.79423i	0.285750	−	0.494934i
$249$		0			0
$250$	1.50000	+	2.59808i	0.0948683	+	0.164317i
$251$	−23.0000			−1.45175			−0.725874	−	0.687828i	$-0.758564\pi$
$251$	−23.0000			−1.45175			−0.725874	+	0.687828i	$0.758564\pi$
$252$	−3.00000	−	15.5885i	−0.188982	−	0.981981i
$253$		0			0
$254$	−5.50000	−	9.52628i	−0.345101	−	0.597732i
$255$	−9.00000	+	15.5885i	−0.563602	+	0.976187i
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	1.00000	+	1.73205i	0.0623783	+	0.108042i	0.895528	−	0.445005i	$-0.146798\pi$
$257$	1.00000	+	1.73205i	0.0623783	+	0.108042i	−0.833150	+	0.553047i	$0.813465\pi$
$258$	21.0000			1.30740
$259$	4.00000	−	3.46410i	0.248548	−	0.215249i
$260$		0			0
$261$	−21.0000	−	36.3731i	−1.29987	−	2.25144i
$262$	−2.50000	+	4.33013i	−0.154451	+	0.267516i
$263$	13.5000	−	23.3827i	0.832446	−	1.44184i	−0.0636476	−	0.997972i	$-0.520273\pi$
$263$	13.5000	−	23.3827i	0.832446	−	1.44184i	0.896093	−	0.443866i	$-0.146393\pi$
$264$	13.5000	+	23.3827i	0.830868	+	1.43910i
$265$	9.00000			0.552866
$266$	2.50000	+	0.866025i	0.153285	+	0.0530994i
$267$	−18.0000			−1.10158
$268$	−1.50000	−	2.59808i	−0.0916271	−	0.158703i
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	0.449622	+	0.893219i	$0.351559\pi$
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	−0.998361	+	0.0572259i	$0.981774\pi$
$270$	13.5000	−	23.3827i	0.821584	−	1.42302i
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	0.999870	−	0.0161307i	$-0.00513477\pi$
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	−0.513905	+	0.857847i	$0.671801\pi$
$272$	2.00000			0.121268
$273$		0			0
$274$	10.0000			0.604122
$275$	6.00000	+	10.3923i	0.361814	+	0.626680i
$276$		0			0
$277$	−11.0000	+	19.0526i	−0.660926	+	1.14476i	0.319447	+	0.947604i	$0.396503\pi$
$277$	−11.0000	+	19.0526i	−0.660926	+	1.14476i	−0.980373	+	0.197153i	$0.936830\pi$
$278$	7.50000	+	12.9904i	0.449820	+	0.779111i
$279$	18.0000			1.07763
$280$	−18.0000	+	15.5885i	−1.07571	+	0.931589i
$281$	−18.0000			−1.07379			−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000			−1.07379			−0.536895	+	0.843649i	$0.680403\pi$
$282$	1.50000	+	2.59808i	0.0893237	+	0.154713i
$283$	−0.500000	+	0.866025i	−0.0297219	+	0.0514799i	−0.880504	−	0.474039i	$-0.842796\pi$
$283$	−0.500000	+	0.866025i	−0.0297219	+	0.0514799i	0.850782	+	0.525519i	$0.176129\pi$
$284$	6.50000	−	11.2583i	0.385704	−	0.668059i
$285$	−4.50000	−	7.79423i	−0.266557	−	0.461690i
$286$		0			0
$287$	1.50000	+	7.79423i	0.0885422	+	0.460079i
$288$	30.0000			1.76777
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	−10.5000	+	18.1865i	−0.616581	+	1.06795i
$291$	−7.50000	+	12.9904i	−0.439658	+	0.761510i
$292$	−6.50000	−	11.2583i	−0.380384	−	0.658844i
$293$	11.0000			0.642627			0.321313	−	0.946973i	$-0.395876\pi$
$293$	11.0000			0.642627			0.321313	+	0.946973i	$0.395876\pi$
$294$	19.5000	−	7.79423i	1.13726	−	0.454569i
$295$	−12.0000			−0.698667
$296$	3.00000	+	5.19615i	0.174371	+	0.302020i
$297$	−13.5000	+	23.3827i	−0.783349	+	1.35680i
$298$	−7.50000	+	12.9904i	−0.434463	+	0.752513i
$299$		0			0
$300$	12.0000			0.692820
$301$	−3.50000	−	18.1865i	−0.201737	−	1.04825i
$302$	−21.0000			−1.20841
$303$	−7.50000	−	12.9904i	−0.430864	−	0.746278i
$304$	−0.500000	+	0.866025i	−0.0286770	+	0.0496700i
$305$	19.5000	−	33.7750i	1.11657	−	1.93395i
$306$	6.00000	+	10.3923i	0.342997	+	0.594089i
$307$	12.0000			0.684876			0.342438	−	0.939540i	$-0.388747\pi$
$307$	12.0000			0.684876			0.342438	+	0.939540i	$0.388747\pi$
$308$	6.00000	−	5.19615i	0.341882	−	0.296078i
$309$	−15.0000			−0.853320
$310$	−4.50000	−	7.79423i	−0.255583	−	0.442682i
$311$	4.50000	−	7.79423i	0.255172	−	0.441970i	−0.709771	−	0.704433i	$-0.751201\pi$
$311$	4.50000	−	7.79423i	0.255172	−	0.441970i	0.964942	+	0.262463i	$0.0845347\pi$
$312$		0			0
$313$	−9.50000	−	16.4545i	−0.536972	−	0.930062i	−0.999065	−	0.0432311i	$-0.986235\pi$
$313$	−9.50000	−	16.4545i	−0.536972	−	0.930062i	0.462093	−	0.886831i	$-0.347098\pi$
$314$	19.0000			1.07223
$315$	−45.0000	−	15.5885i	−2.53546	−	0.878310i
$316$	3.00000			0.168763
$317$	4.50000	+	7.79423i	0.252745	+	0.437767i	0.964281	−	0.264883i	$-0.0853332\pi$
$317$	4.50000	+	7.79423i	0.252745	+	0.437767i	−0.711535	+	0.702650i	$0.752000\pi$
$318$	4.50000	−	7.79423i	0.252347	−	0.437079i
$319$	10.5000	−	18.1865i	0.587887	−	1.01825i
$320$	−10.5000	−	18.1865i	−0.586968	−	1.01666i
$321$	−24.0000			−1.33955
$322$		0			0
$323$	2.00000			0.111283
$324$	4.50000	+	7.79423i	0.250000	+	0.433013i
$325$		0			0
$326$	0.500000	−	0.866025i	0.0276924	−	0.0479647i
$327$	10.5000	+	18.1865i	0.580651	+	1.00572i
$328$	−9.00000			−0.496942
$329$	2.00000	−	1.73205i	0.110264	−	0.0954911i
$330$	27.0000			1.48630
$331$	14.5000	+	25.1147i	0.796992	+	1.38043i	0.921567	+	0.388221i	$0.126910\pi$
$331$	14.5000	+	25.1147i	0.796992	+	1.38043i	−0.124574	+	0.992210i	$0.539757\pi$
$332$		0			0
$333$	−6.00000	+	10.3923i	−0.328798	+	0.569495i
$334$	6.50000	+	11.2583i	0.355664	+	0.616028i
$335$	−9.00000			−0.491723
$336$	1.50000	+	7.79423i	0.0818317	+	0.425210i
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$		0			0
$339$	22.5000	−	38.9711i	1.22203	−	2.11662i
$340$	−3.00000	+	5.19615i	−0.162698	+	0.281801i
$341$	4.50000	+	7.79423i	0.243689	+	0.422081i
$342$	−6.00000			−0.324443
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	21.0000			1.13224
$345$		0			0
$346$	−9.50000	+	16.4545i	−0.510723	+	0.884598i
$347$	4.00000	−	6.92820i	0.214731	−	0.371925i	−0.738458	−	0.674299i	$-0.764446\pi$
$347$	4.00000	−	6.92820i	0.214731	−	0.371925i	0.953189	+	0.302374i	$0.0977791\pi$
$348$	−10.5000	−	18.1865i	−0.562859	−	0.974901i
$349$	23.0000			1.23116			0.615581	−	0.788074i	$-0.288921\pi$
$349$	23.0000			1.23116			0.615581	+	0.788074i	$0.288921\pi$
$350$	2.00000	+	10.3923i	0.106904	+	0.555492i
$351$		0			0
$352$	7.50000	+	12.9904i	0.399751	+	0.692390i
$353$	12.5000	−	21.6506i	0.665308	−	1.15235i	−0.313894	−	0.949458i	$-0.601634\pi$
$353$	12.5000	−	21.6506i	0.665308	−	1.15235i	0.979202	−	0.202889i	$-0.0650330\pi$
$354$	−6.00000	+	10.3923i	−0.318896	+	0.552345i
$355$	−19.5000	−	33.7750i	−1.03495	−	1.79259i
$356$	−6.00000			−0.317999
$357$	12.0000	−	10.3923i	0.635107	−	0.550019i
$358$	17.0000			0.898478
$359$	−8.50000	−	14.7224i	−0.448613	−	0.777020i	0.549683	−	0.835373i	$-0.314748\pi$
$359$	−8.50000	−	14.7224i	−0.448613	−	0.777020i	−0.998296	+	0.0583530i	$0.981415\pi$
$360$	27.0000	−	46.7654i	1.42302	−	2.46475i
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	11.0000	+	19.0526i	0.578147	+	1.00138i
$363$	6.00000			0.314918
$364$		0			0
$365$	−39.0000			−2.04135
$366$	−19.5000	−	33.7750i	−1.01928	−	1.76545i
$367$	15.5000	−	26.8468i	0.809093	−	1.40139i	−0.104399	−	0.994535i	$-0.533292\pi$
$367$	15.5000	−	26.8468i	0.809093	−	1.40139i	0.913493	−	0.406855i	$-0.133375\pi$
$368$		0			0
$369$	−9.00000	−	15.5885i	−0.468521	−	0.811503i
$370$	6.00000			0.311925
$371$	−7.50000	−	2.59808i	−0.389381	−	0.134885i
$372$	9.00000			0.466628
$373$	4.50000	+	7.79423i	0.233001	+	0.403570i	0.958690	−	0.284453i	$-0.0918121\pi$
$373$	4.50000	+	7.79423i	0.233001	+	0.403570i	−0.725689	+	0.688023i	$0.758479\pi$
$374$	−3.00000	+	5.19615i	−0.155126	+	0.268687i
$375$	−4.50000	+	7.79423i	−0.232379	+	0.402492i
$376$	1.50000	+	2.59808i	0.0773566	+	0.133986i
$377$		0			0
$378$	−18.0000	+	15.5885i	−0.925820	+	0.801784i
$379$	−33.0000			−1.69510			−0.847548	−	0.530719i	$-0.821922\pi$
$379$	−33.0000			−1.69510			−0.847548	+	0.530719i	$0.821922\pi$
$380$	−1.50000	−	2.59808i	−0.0769484	−	0.133278i
$381$	16.5000	−	28.5788i	0.845321	−	1.46414i
$382$	8.50000	−	14.7224i	0.434898	−	0.753265i
$383$	10.5000	+	18.1865i	0.536525	+	0.929288i	0.999088	+	0.0427020i	$0.0135966\pi$
$383$	10.5000	+	18.1865i	0.536525	+	0.929288i	−0.462563	+	0.886586i	$0.653070\pi$
$384$	9.00000			0.459279
$385$	−4.50000	−	23.3827i	−0.229341	−	1.19169i
$386$	7.00000			0.356291
$387$	21.0000	+	36.3731i	1.06749	+	1.84895i
$388$	−2.50000	+	4.33013i	−0.126918	+	0.219829i
$389$	16.5000	−	28.5788i	0.836583	−	1.44900i	−0.0561516	−	0.998422i	$-0.517883\pi$
$389$	16.5000	−	28.5788i	0.836583	−	1.44900i	0.892735	−	0.450582i	$-0.148784\pi$
$390$		0			0
$391$		0			0
$392$	19.5000	−	7.79423i	0.984899	−	0.393668i
$393$	−15.0000			−0.756650
$394$	0.500000	+	0.866025i	0.0251896	+	0.0436297i
$395$	4.50000	−	7.79423i	0.226420	−	0.392170i
$396$	−9.00000	+	15.5885i	−0.452267	+	0.783349i
$397$	0.500000	+	0.866025i	0.0250943	+	0.0434646i	0.878300	−	0.478110i	$-0.158678\pi$
$397$	0.500000	+	0.866025i	0.0250943	+	0.0434646i	−0.853206	+	0.521575i	$0.825345\pi$
$398$	−20.0000			−1.00251
$399$	1.50000	+	7.79423i	0.0750939	+	0.390199i
$400$	−4.00000			−0.200000
$401$	1.00000	+	1.73205i	0.0499376	+	0.0864945i	0.889914	−	0.456129i	$-0.150764\pi$
$401$	1.00000	+	1.73205i	0.0499376	+	0.0864945i	−0.839976	+	0.542623i	$0.817431\pi$
$402$	−4.50000	+	7.79423i	−0.224440	+	0.388741i
$403$		0			0
$404$	−2.50000	−	4.33013i	−0.124380	−	0.215432i
$405$	27.0000			1.34164
$406$	14.0000	−	12.1244i	0.694808	−	0.601722i
$407$	−6.00000			−0.297409
$408$	9.00000	+	15.5885i	0.445566	+	0.771744i
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	−0.985558	−	0.169338i	$-0.945837\pi$
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	0.639430	+	0.768849i	$0.279170\pi$
$410$	−4.50000	+	7.79423i	−0.222239	+	0.384930i
$411$	15.0000	+	25.9808i	0.739895	+	1.28154i
$412$	−5.00000			−0.246332
$413$	10.0000	+	3.46410i	0.492068	+	0.170457i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−22.5000	+	38.9711i	−1.10183	+	1.90843i
$418$	−1.50000	−	2.59808i	−0.0733674	−	0.127076i
$419$	−25.0000			−1.22133			−0.610665	−	0.791889i	$-0.709098\pi$
$419$	−25.0000			−1.22133			−0.610665	+	0.791889i	$0.709098\pi$
$420$	−22.5000	−	7.79423i	−1.09789	−	0.380319i
$421$	18.0000			0.877266			0.438633	−	0.898666i	$-0.355463\pi$
$421$	18.0000			0.877266			0.438633	+	0.898666i	$0.355463\pi$
$422$	−3.50000	−	6.06218i	−0.170377	−	0.295102i
$423$	−3.00000	+	5.19615i	−0.145865	+	0.252646i
$424$	4.50000	−	7.79423i	0.218539	−	0.378521i
$425$	4.00000	+	6.92820i	0.194029	+	0.336067i
$426$	−39.0000			−1.88956
$427$	−26.0000	+	22.5167i	−1.25823	+	1.08966i
$428$	−8.00000			−0.386695
$429$		0			0
$430$	10.5000	−	18.1865i	0.506355	−	0.877033i
$431$	−4.50000	+	7.79423i	−0.216757	+	0.375435i	−0.953815	−	0.300395i	$-0.902881\pi$
$431$	−4.50000	+	7.79423i	−0.216757	+	0.375435i	0.737057	+	0.675830i	$0.236215\pi$
$432$	−4.50000	−	7.79423i	−0.216506	−	0.375000i
$433$	27.0000			1.29754			0.648769	−	0.760986i	$-0.275284\pi$
$433$	27.0000			1.29754			0.648769	+	0.760986i	$0.275284\pi$
$434$	1.50000	+	7.79423i	0.0720023	+	0.374135i
$435$	−63.0000			−3.02062
$436$	3.50000	+	6.06218i	0.167620	+	0.290326i
$437$		0			0
$438$	−19.5000	+	33.7750i	−0.931746	+	1.61383i
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	0.991322	−	0.131453i	$-0.0419644\pi$
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	−0.609503	+	0.792784i	$0.708631\pi$
$440$	27.0000			1.28717
$441$	33.0000	+	25.9808i	1.57143	+	1.23718i
$442$		0			0
$443$	5.50000	+	9.52628i	0.261313	+	0.452607i	0.966591	−	0.256323i	$-0.0825112\pi$
$443$	5.50000	+	9.52628i	0.261313	+	0.452607i	−0.705278	+	0.708931i	$0.749178\pi$
$444$	−3.00000	+	5.19615i	−0.142374	+	0.246598i
$445$	−9.00000	+	15.5885i	−0.426641	+	0.738964i
$446$	4.50000	+	7.79423i	0.213081	+	0.369067i
$447$	−45.0000			−2.12843
$448$	3.50000	+	18.1865i	0.165359	+	0.859233i
$449$	15.0000			0.707894			0.353947	−	0.935266i	$-0.384839\pi$
$449$	15.0000			0.707894			0.353947	+	0.935266i	$0.384839\pi$
$450$	−12.0000	−	20.7846i	−0.565685	−	0.979796i
$451$	4.50000	−	7.79423i	0.211897	−	0.367016i
$452$	7.50000	−	12.9904i	0.352770	−	0.611016i
$453$	−31.5000	−	54.5596i	−1.48000	−	2.56343i
$454$	−4.00000			−0.187729
$455$		0			0
$456$	−9.00000			−0.421464
$457$	9.00000	+	15.5885i	0.421002	+	0.729197i	0.996038	−	0.0889312i	$-0.0283451\pi$
$457$	9.00000	+	15.5885i	0.421002	+	0.729197i	−0.575036	+	0.818128i	$0.695012\pi$
$458$	6.50000	−	11.2583i	0.303725	−	0.526067i
$459$	−9.00000	+	15.5885i	−0.420084	+	0.727607i
$460$		0			0
$461$	35.0000			1.63011			0.815056	−	0.579382i	$-0.196706\pi$
$461$	35.0000			1.63011			0.815056	+	0.579382i	$0.196706\pi$
$462$	−22.5000	−	7.79423i	−1.04679	−	0.362620i
$463$	−8.00000			−0.371792			−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000			−0.371792			−0.185896	+	0.982569i	$0.559519\pi$
$464$	3.50000	+	6.06218i	0.162483	+	0.281430i
$465$	13.5000	−	23.3827i	0.626048	−	1.08435i
$466$	10.5000	−	18.1865i	0.486403	−	0.842475i
$467$	3.50000	+	6.06218i	0.161961	+	0.280524i	0.935572	−	0.353137i	$-0.114885\pi$
$467$	3.50000	+	6.06218i	0.161961	+	0.280524i	−0.773611	+	0.633661i	$0.781552\pi$
$468$		0			0
$469$	7.50000	+	2.59808i	0.346318	+	0.119968i
$470$	3.00000			0.138380
$471$	28.5000	+	49.3634i	1.31321	+	2.27455i
$472$	−6.00000	+	10.3923i	−0.276172	+	0.478345i
$473$	−10.5000	+	18.1865i	−0.482791	+	0.836218i
$474$	−4.50000	−	7.79423i	−0.206692	−	0.358001i
$475$	−4.00000			−0.183533
$476$	4.00000	−	3.46410i	0.183340	−	0.158777i
$477$	18.0000			0.824163
$478$	2.00000	+	3.46410i	0.0914779	+	0.158444i
$479$	17.5000	−	30.3109i	0.799595	−	1.38494i	−0.120284	−	0.992739i	$-0.538381\pi$
$479$	17.5000	−	30.3109i	0.799595	−	1.38494i	0.919880	−	0.392200i	$-0.128286\pi$
$480$	22.5000	−	38.9711i	1.02698	−	1.77878i
$481$		0			0
$482$	−26.0000			−1.18427
$483$		0			0
$484$	2.00000			0.0909091
$485$	7.50000	+	12.9904i	0.340557	+	0.589863i
$486$		0			0
$487$	−8.00000	+	13.8564i	−0.362515	+	0.627894i	−0.988374	−	0.152042i	$-0.951415\pi$
$487$	−8.00000	+	13.8564i	−0.362515	+	0.627894i	0.625859	+	0.779936i	$0.284748\pi$
$488$	−19.5000	−	33.7750i	−0.882724	−	1.52892i
$489$	3.00000			0.135665
$490$	3.00000	−	20.7846i	0.135526	−	0.938953i
$491$	15.0000			0.676941			0.338470	−	0.940977i	$-0.390091\pi$
$491$	15.0000			0.676941			0.338470	+	0.940977i	$0.390091\pi$
$492$	−4.50000	−	7.79423i	−0.202876	−	0.351391i
$493$	7.00000	−	12.1244i	0.315264	−	0.546054i
$494$		0			0
$495$	27.0000	+	46.7654i	1.21356	+	2.10195i
$496$	−3.00000			−0.134704
$497$	6.50000	+	33.7750i	0.291565	+	1.51502i
$498$		0			0
$499$	15.5000	+	26.8468i	0.693875	+	1.20183i	0.970558	+	0.240866i	$0.0774314\pi$
$499$	15.5000	+	26.8468i	0.693875	+	1.20183i	−0.276683	+	0.960961i	$0.589235\pi$
$500$	−1.50000	+	2.59808i	−0.0670820	+	0.116190i
$501$	−19.5000	+	33.7750i	−0.871196	+	1.50896i
$502$	11.5000	+	19.9186i	0.513270	+	0.889010i
$503$	−31.0000			−1.38222			−0.691111	−	0.722749i	$-0.742878\pi$
$503$	−31.0000			−1.38222			−0.691111	+	0.722749i	$0.742878\pi$
$504$	−36.0000	+	31.1769i	−1.60357	+	1.38873i
$505$	−15.0000			−0.667491
$506$		0			0
$507$		0			0
$508$	5.50000	−	9.52628i	0.244023	−	0.422660i
$509$	17.0000	+	29.4449i	0.753512	+	1.30512i	0.946111	+	0.323843i	$0.104975\pi$
$509$	17.0000	+	29.4449i	0.753512	+	1.30512i	−0.192599	+	0.981278i	$0.561692\pi$
$510$	18.0000			0.797053
$511$	32.5000	+	11.2583i	1.43772	+	0.498039i
$512$	−11.0000			−0.486136
$513$	−4.50000	−	7.79423i	−0.198680	−	0.344124i
$514$	1.00000	−	1.73205i	0.0441081	−	0.0763975i
$515$	−7.50000	+	12.9904i	−0.330489	+	0.572425i
$516$	10.5000	+	18.1865i	0.462237	+	0.800617i
$517$	−3.00000			−0.131940
$518$	−5.00000	−	1.73205i	−0.219687	−	0.0761019i
$519$	−57.0000			−2.50202
$520$		0			0
$521$	8.50000	−	14.7224i	0.372392	−	0.645001i	−0.617541	−	0.786539i	$-0.711871\pi$
$521$	8.50000	−	14.7224i	0.372392	−	0.645001i	0.989933	+	0.141537i	$0.0452044\pi$
$522$	−21.0000	+	36.3731i	−0.919145	+	1.59201i
$523$	−2.00000	−	3.46410i	−0.0874539	−	0.151475i	0.818980	−	0.573822i	$-0.194540\pi$
$523$	−2.00000	−	3.46410i	−0.0874539	−	0.151475i	−0.906434	+	0.422347i	$0.861206\pi$
$524$	−5.00000			−0.218426
$525$	−24.0000	+	20.7846i	−1.04745	+	0.907115i
$526$	−27.0000			−1.17726
$527$	3.00000	+	5.19615i	0.130682	+	0.226348i
$528$	4.50000	−	7.79423i	0.195837	−	0.339200i
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$	−4.50000	−	7.79423i	−0.195468	−	0.338560i
$531$	−24.0000			−1.04151
$532$	0.500000	+	2.59808i	0.0216777	+	0.112641i
$533$		0			0
$534$	9.00000	+	15.5885i	0.389468	+	0.674579i
$535$	−12.0000	+	20.7846i	−0.518805	+	0.898597i
$536$	−4.50000	+	7.79423i	−0.194370	+	0.336659i
$537$	25.5000	+	44.1673i	1.10041	+	1.90596i
$538$	18.0000			0.776035
$539$	−3.00000	+	20.7846i	−0.129219	+	0.895257i
$540$	27.0000			1.16190
$541$	18.5000	+	32.0429i	0.795377	+	1.37763i	0.922599	+	0.385759i	$0.126061\pi$
$541$	18.5000	+	32.0429i	0.795377	+	1.37763i	−0.127222	+	0.991874i	$0.540606\pi$
$542$	8.00000	−	13.8564i	0.343629	−	0.595184i
$543$	−33.0000	+	57.1577i	−1.41617	+	2.45287i
$544$	5.00000	+	8.66025i	0.214373	+	0.371305i
$545$	21.0000			0.899541
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$	5.00000	+	8.66025i	0.213589	+	0.369948i
$549$	39.0000	−	67.5500i	1.66448	−	2.88296i
$550$	6.00000	−	10.3923i	0.255841	−	0.443129i
$551$	3.50000	+	6.06218i	0.149105	+	0.258257i
$552$		0			0
$553$	−6.00000	+	5.19615i	−0.255146	+	0.220963i
$554$	22.0000			0.934690
$555$	9.00000	+	15.5885i	0.382029	+	0.661693i
$556$	−7.50000	+	12.9904i	−0.318071	+	0.550915i
$557$	−1.50000	+	2.59808i	−0.0635570	+	0.110084i	−0.896053	−	0.443947i	$-0.853578\pi$
$557$	−1.50000	+	2.59808i	−0.0635570	+	0.110084i	0.832496	+	0.554031i	$0.186911\pi$
$558$	−9.00000	−	15.5885i	−0.381000	−	0.659912i
$559$		0			0
$560$	7.50000	+	2.59808i	0.316933	+	0.109789i
$561$	−18.0000			−0.759961
$562$	9.00000	+	15.5885i	0.379642	+	0.657559i
$563$	−2.00000	+	3.46410i	−0.0842900	+	0.145994i	−0.905088	−	0.425223i	$-0.860196\pi$
$563$	−2.00000	+	3.46410i	−0.0842900	+	0.145994i	0.820798	+	0.571218i	$0.193529\pi$
$564$	−1.50000	+	2.59808i	−0.0631614	+	0.109399i
$565$	−22.5000	−	38.9711i	−0.946582	−	1.63953i
$566$	1.00000			0.0420331
$567$	−22.5000	−	7.79423i	−0.944911	−	0.327327i
$568$	−39.0000			−1.63640
$569$	−5.00000	−	8.66025i	−0.209611	−	0.363057i	0.741981	−	0.670421i	$-0.233886\pi$
$569$	−5.00000	−	8.66025i	−0.209611	−	0.363057i	−0.951592	+	0.307364i	$0.900553\pi$
$570$	−4.50000	+	7.79423i	−0.188484	+	0.326464i
$571$	−21.5000	+	37.2391i	−0.899747	+	1.55841i	−0.0719297	+	0.997410i	$0.522916\pi$
$571$	−21.5000	+	37.2391i	−0.899747	+	1.55841i	−0.827817	+	0.560998i	$0.810418\pi$
$572$		0			0
$573$	51.0000			2.13056
$574$	6.00000	−	5.19615i	0.250435	−	0.216883i
$575$		0			0
$576$	−21.0000	−	36.3731i	−0.875000	−	1.51554i
$577$	0.500000	−	0.866025i	0.0208153	−	0.0360531i	−0.855430	−	0.517918i	$-0.826707\pi$
$577$	0.500000	−	0.866025i	0.0208153	−	0.0360531i	0.876245	+	0.481865i	$0.160040\pi$
$578$	6.50000	−	11.2583i	0.270364	−	0.468285i
$579$	10.5000	+	18.1865i	0.436365	+	0.755807i
$580$	−21.0000			−0.871978
$581$		0			0
$582$	15.0000			0.621770
$583$	4.50000	+	7.79423i	0.186371	+	0.322804i
$584$	−19.5000	+	33.7750i	−0.806916	+	1.39762i
$585$		0			0
$586$	−5.50000	−	9.52628i	−0.227203	−	0.393527i
$587$	−33.0000			−1.36206			−0.681028	−	0.732257i	$-0.738467\pi$
$587$	−33.0000			−1.36206			−0.681028	+	0.732257i	$0.738467\pi$
$588$	16.5000	+	12.9904i	0.680449	+	0.535714i
$589$	−3.00000			−0.123613
$590$	6.00000	+	10.3923i	0.247016	+	0.427844i
$591$	−1.50000	+	2.59808i	−0.0617018	+	0.106871i
$592$	1.00000	−	1.73205i	0.0410997	−	0.0711868i
$593$	−13.5000	−	23.3827i	−0.554379	−	0.960212i	−0.997952	−	0.0639736i	$-0.979623\pi$
$593$	−13.5000	−	23.3827i	−0.554379	−	0.960212i	0.443573	−	0.896238i	$-0.353711\pi$
$594$	27.0000			1.10782
$595$	−3.00000	−	15.5885i	−0.122988	−	0.639064i
$596$	−15.0000			−0.614424
$597$	−30.0000	−	51.9615i	−1.22782	−	2.12664i
$598$		0			0
$599$	12.5000	−	21.6506i	0.510736	−	0.884621i	−0.489186	−	0.872179i	$-0.662706\pi$
$599$	12.5000	−	21.6506i	0.510736	−	0.884621i	0.999923	−	0.0124417i	$-0.00396043\pi$
$600$	−18.0000	−	31.1769i	−0.734847	−	1.27279i
$601$	35.0000			1.42768			0.713840	−	0.700309i	$-0.246954\pi$
$601$	35.0000			1.42768			0.713840	+	0.700309i	$0.246954\pi$
$602$	−14.0000	+	12.1244i	−0.570597	+	0.494152i
$603$	−18.0000			−0.733017
$604$	−10.5000	−	18.1865i	−0.427239	−	0.740000i
$605$	3.00000	−	5.19615i	0.121967	−	0.211254i
$606$	−7.50000	+	12.9904i	−0.304667	+	0.527698i
$607$	−5.50000	−	9.52628i	−0.223238	−	0.386660i	0.732551	−	0.680712i	$-0.238329\pi$
$607$	−5.50000	−	9.52628i	−0.223238	−	0.386660i	−0.955789	+	0.294052i	$0.904996\pi$
$608$	−5.00000			−0.202777
$609$	52.5000	+	18.1865i	2.12741	+	0.736956i
$610$	−39.0000			−1.57906
$611$		0			0
$612$	−6.00000	+	10.3923i	−0.242536	+	0.420084i
$613$	12.5000	−	21.6506i	0.504870	−	0.874461i	−0.495114	−	0.868828i	$-0.664874\pi$
$613$	12.5000	−	21.6506i	0.504870	−	0.874461i	0.999984	−	0.00563283i	$-0.00179300\pi$
$614$	−6.00000	−	10.3923i	−0.242140	−	0.419399i
$615$	−27.0000			−1.08875
$616$	−22.5000	−	7.79423i	−0.906551	−	0.314038i
$617$	−33.0000			−1.32853			−0.664265	−	0.747497i	$-0.731255\pi$
$617$	−33.0000			−1.32853			−0.664265	+	0.747497i	$0.731255\pi$
$618$	7.50000	+	12.9904i	0.301694	+	0.522550i
$619$	−5.50000	+	9.52628i	−0.221064	+	0.382893i	−0.955131	−	0.296183i	$-0.904286\pi$
$619$	−5.50000	+	9.52628i	−0.221064	+	0.382893i	0.734068	+	0.679076i	$0.237620\pi$
$620$	4.50000	−	7.79423i	0.180724	−	0.313024i
$621$		0			0
$622$	−9.00000			−0.360867
$623$	12.0000	−	10.3923i	0.480770	−	0.416359i
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	−9.50000	+	16.4545i	−0.379696	+	0.657653i
$627$	4.50000	−	7.79423i	0.179713	−	0.311272i
$628$	9.50000	+	16.4545i	0.379091	+	0.656605i
$629$	−4.00000			−0.159490
$630$	9.00000	+	46.7654i	0.358569	+	1.86318i
$631$	25.0000			0.995234			0.497617	−	0.867397i	$-0.334208\pi$
$631$	25.0000			0.995234			0.497617	+	0.867397i	$0.334208\pi$
$632$	−4.50000	−	7.79423i	−0.179000	−	0.310038i
$633$	10.5000	−	18.1865i	0.417338	−	0.722850i
$634$	4.50000	−	7.79423i	0.178718	−	0.309548i
$635$	−16.5000	−	28.5788i	−0.654783	−	1.13412i
$636$	9.00000			0.356873
$637$		0			0
$638$	−21.0000			−0.831398
$639$	−39.0000	−	67.5500i	−1.54282	−	2.67224i
$640$	4.50000	−	7.79423i	0.177878	−	0.308094i
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	−0.631721	−	0.775196i	$-0.717651\pi$
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	0.987200	+	0.159489i	$0.0509845\pi$
$642$	12.0000	+	20.7846i	0.473602	+	0.820303i
$643$	−19.0000			−0.749287			−0.374643	−	0.927169i	$-0.622235\pi$
$643$	−19.0000			−0.749287			−0.374643	+	0.927169i	$0.622235\pi$
$644$		0			0
$645$	63.0000			2.48062
$646$	−1.00000	−	1.73205i	−0.0393445	−	0.0681466i
$647$	−4.50000	+	7.79423i	−0.176913	+	0.306423i	−0.940822	−	0.338902i	$-0.889945\pi$
$647$	−4.50000	+	7.79423i	−0.176913	+	0.306423i	0.763908	+	0.645325i	$0.223278\pi$
$648$	13.5000	−	23.3827i	0.530330	−	0.918559i
$649$	−6.00000	−	10.3923i	−0.235521	−	0.407934i
$650$		0			0
$651$	−18.0000	+	15.5885i	−0.705476	+	0.610960i
$652$	1.00000			0.0391630
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	0.634437	−	0.772975i	$-0.281232\pi$
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	−0.986634	+	0.162951i	$0.947899\pi$
$654$	10.5000	−	18.1865i	0.410582	−	0.711150i
$655$	−7.50000	+	12.9904i	−0.293049	+	0.507576i
$656$	1.50000	+	2.59808i	0.0585652	+	0.101438i
$657$	−78.0000			−3.04307
$658$	−2.50000	−	0.866025i	−0.0974601	−	0.0337612i
$659$	29.0000			1.12968			0.564840	−	0.825201i	$-0.308938\pi$
$659$	29.0000			1.12968			0.564840	+	0.825201i	$0.308938\pi$
$660$	13.5000	+	23.3827i	0.525487	+	0.910170i
$661$	4.50000	−	7.79423i	0.175030	−	0.303160i	−0.765142	−	0.643862i	$-0.777331\pi$
$661$	4.50000	−	7.79423i	0.175030	−	0.303160i	0.940172	+	0.340701i	$0.110665\pi$
$662$	14.5000	−	25.1147i	0.563559	−	0.976112i
$663$		0			0
$664$		0			0
$665$	7.50000	+	2.59808i	0.290838	+	0.100749i
$666$	12.0000			0.464991
$667$		0			0
$668$	−6.50000	+	11.2583i	−0.251493	+	0.435598i
$669$	−13.5000	+	23.3827i	−0.521940	+	0.904027i
$670$	4.50000	+	7.79423i	0.173850	+	0.301117i
$671$	39.0000			1.50558
$672$	−30.0000	+	25.9808i	−1.15728	+	1.00223i
$673$	−41.0000			−1.58043			−0.790217	−	0.612827i	$-0.790032\pi$
$673$	−41.0000			−1.58043			−0.790217	+	0.612827i	$0.790032\pi$
$674$	−7.00000	−	12.1244i	−0.269630	−	0.467013i
$675$	18.0000	−	31.1769i	0.692820	−	1.20000i
$676$		0			0
$677$	−3.50000	−	6.06218i	−0.134516	−	0.232988i	0.790897	−	0.611950i	$-0.209615\pi$
$677$	−3.50000	−	6.06218i	−0.134516	−	0.232988i	−0.925412	+	0.378962i	$0.876281\pi$
$678$	−45.0000			−1.72821
$679$	−2.50000	−	12.9904i	−0.0959412	−	0.498525i
$680$	18.0000			0.690268
$681$	−6.00000	−	10.3923i	−0.229920	−	0.398234i
$682$	4.50000	−	7.79423i	0.172314	−	0.298456i
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	−0.957685	−	0.287819i	$-0.907070\pi$
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	0.728101	+	0.685470i	$0.240403\pi$
$684$	−3.00000	−	5.19615i	−0.114708	−	0.198680i
$685$	30.0000			1.14624
$686$	−8.50000	+	16.4545i	−0.324532	+	0.628235i
$687$	39.0000			1.48794
$688$	−3.50000	−	6.06218i	−0.133436	−	0.231118i
$689$		0			0
$690$		0			0
$691$	2.00000	+	3.46410i	0.0760836	+	0.131781i	0.901557	−	0.432660i	$-0.142425\pi$
$691$	2.00000	+	3.46410i	0.0760836	+	0.131781i	−0.825473	+	0.564441i	$0.809092\pi$
$692$	−19.0000			−0.722272
$693$	−9.00000	−	46.7654i	−0.341882	−	1.77647i
$694$	−8.00000			−0.303676
$695$	22.5000	+	38.9711i	0.853474	+	1.47826i
$696$	−31.5000	+	54.5596i	−1.19400	+	2.06808i
$697$	3.00000	−	5.19615i	0.113633	−	0.196818i
$698$	−11.5000	−	19.9186i	−0.435281	−	0.753930i
$699$	63.0000			2.38288
$700$	−8.00000	+	6.92820i	−0.302372	+	0.261861i
$701$	42.0000			1.58632			0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000			1.58632			0.793159	+	0.609015i	$0.208435\pi$
$702$		0			0
$703$	1.00000	−	1.73205i	0.0377157	−	0.0653255i
$704$	10.5000	−	18.1865i	0.395734	−	0.685431i
$705$	4.50000	+	7.79423i	0.169480	+	0.293548i
$706$	−25.0000			−0.940887
$707$	12.5000	+	4.33013i	0.470111	+	0.162851i
$708$	−12.0000			−0.450988
$709$	−5.50000	−	9.52628i	−0.206557	−	0.357767i	0.744071	−	0.668101i	$-0.232892\pi$
$709$	−5.50000	−	9.52628i	−0.206557	−	0.357767i	−0.950628	+	0.310334i	$0.899559\pi$
$710$	−19.5000	+	33.7750i	−0.731822	+	1.26755i
$711$	9.00000	−	15.5885i	0.337526	−	0.584613i
$712$	9.00000	+	15.5885i	0.337289	+	0.584202i
$713$		0			0
$714$	−15.0000	−	5.19615i	−0.561361	−	0.194461i
$715$		0			0
$716$	8.50000	+	14.7224i	0.317660	+	0.550203i
$717$	−6.00000	+	10.3923i	−0.224074	+	0.388108i
$718$	−8.50000	+	14.7224i	−0.317217	+	0.549436i
$719$	4.50000	+	7.79423i	0.167822	+	0.290676i	0.937654	−	0.347571i	$-0.112993\pi$
$719$	4.50000	+	7.79423i	0.167822	+	0.290676i	−0.769832	+	0.638247i	$0.779660\pi$
$720$	−18.0000			−0.670820
$721$	10.0000	−	8.66025i	0.372419	−	0.322525i
$722$	−18.0000			−0.669891
$723$	−39.0000	−	67.5500i	−1.45043	−	2.51221i
$724$	−11.0000	+	19.0526i	−0.408812	+	0.708083i
$725$	−14.0000	+	24.2487i	−0.519947	+	0.900575i
$726$	−3.00000	−	5.19615i	−0.111340	−	0.192847i
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	19.5000	+	33.7750i	0.721727	+	1.25007i
$731$	−7.00000	+	12.1244i	−0.258904	+	0.448435i
$732$	19.5000	−	33.7750i	0.720741	−	1.24836i
$733$	4.50000	+	7.79423i	0.166211	+	0.287886i	0.937085	−	0.349102i	$-0.113513\pi$
$733$	4.50000	+	7.79423i	0.166211	+	0.287886i	−0.770873	+	0.636988i	$0.780180\pi$
$734$	−31.0000			−1.14423
$735$	58.5000	−	23.3827i	2.15781	−	0.862483i
$736$		0			0
$737$	−4.50000	−	7.79423i	−0.165760	−	0.287104i
$738$	−9.00000	+	15.5885i	−0.331295	+	0.573819i
$739$	−0.500000	+	0.866025i	−0.0183928	+	0.0318573i	−0.875075	−	0.483987i	$-0.839188\pi$
$739$	−0.500000	+	0.866025i	−0.0183928	+	0.0318573i	0.856683	+	0.515844i	$0.172522\pi$
$740$	3.00000	+	5.19615i	0.110282	+	0.191014i
$741$		0			0
$742$	1.50000	+	7.79423i	0.0550667	+	0.286135i
$743$	51.0000			1.87101			0.935504	−	0.353315i	$-0.114946\pi$
$743$	51.0000			1.87101			0.935504	+	0.353315i	$0.114946\pi$
$744$	−13.5000	−	23.3827i	−0.494934	−	0.857251i
$745$	−22.5000	+	38.9711i	−0.824336	+	1.42779i
$746$	4.50000	−	7.79423i	0.164757	−	0.285367i
$747$		0			0
$748$	−6.00000			−0.219382
$749$	16.0000	−	13.8564i	0.584627	−	0.506302i
$750$	9.00000			0.328634
$751$	−14.0000	−	24.2487i	−0.510867	−	0.884848i	−0.999921	−	0.0125942i	$-0.995991\pi$
$751$	−14.0000	−	24.2487i	−0.510867	−	0.884848i	0.489053	−	0.872254i	$-0.337342\pi$
$752$	0.500000	−	0.866025i	0.0182331	−	0.0315807i
$753$	−34.5000	+	59.7558i	−1.25725	+	2.17762i
$754$		0			0
$755$	−63.0000			−2.29280
$756$	−22.5000	−	7.79423i	−0.818317	−	0.283473i
$757$	3.00000			0.109037			0.0545184	−	0.998513i	$-0.482638\pi$
$757$	3.00000			0.109037			0.0545184	+	0.998513i	$0.482638\pi$
$758$	16.5000	+	28.5788i	0.599307	+	1.03803i
$759$		0			0
$760$	−4.50000	+	7.79423i	−0.163232	+	0.282726i
$761$	4.50000	+	7.79423i	0.163125	+	0.282541i	0.935988	−	0.352032i	$-0.114509\pi$
$761$	4.50000	+	7.79423i	0.163125	+	0.282541i	−0.772863	+	0.634573i	$0.781176\pi$
$762$	−33.0000			−1.19546
$763$	−17.5000	−	6.06218i	−0.633543	−	0.219466i
$764$	17.0000			0.615038
$765$	18.0000	+	31.1769i	0.650791	+	1.12720i
$766$	10.5000	−	18.1865i	0.379380	−	0.657106i
$767$		0			0
$768$	−25.5000	−	44.1673i	−0.920152	−	1.59375i
$769$	19.0000			0.685158			0.342579	−	0.939489i	$-0.388700\pi$
$769$	19.0000			0.685158			0.342579	+	0.939489i	$0.388700\pi$
$770$	−18.0000	+	15.5885i	−0.648675	+	0.561769i
$771$	6.00000			0.216085
$772$	3.50000	+	6.06218i	0.125968	+	0.218183i
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	−0.807018	−	0.590527i	$-0.798920\pi$
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	0.914920

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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} -3.00000 q^{6} +(0.500000 + 2.59808i) q^{7} -3.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} -3.00000 q^{6} +(0.500000 + 2.59808i) q^{7} -3.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +(-1.50000 + 2.59808i) q^{10} +(1.50000 - 2.59808i) q^{11} +(-1.50000 - 2.59808i) q^{12} +(2.00000 - 1.73205i) q^{14} -9.00000 q^{15} +(0.500000 + 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +(-3.00000 + 5.19615i) q^{18} +(0.500000 + 0.866025i) q^{19} -3.00000 q^{20} +(7.50000 + 2.59808i) q^{21} -3.00000 q^{22} +(-4.50000 + 7.79423i) q^{24} +(-2.00000 + 3.46410i) q^{25} -9.00000 q^{27} +(2.50000 + 0.866025i) q^{28} +7.00000 q^{29} +(4.50000 + 7.79423i) q^{30} +(-1.50000 + 2.59808i) q^{31} +(-2.50000 + 4.33013i) q^{32} +(-4.50000 - 7.79423i) q^{33} -2.00000 q^{34} +(6.00000 - 5.19615i) q^{35} -6.00000 q^{36} +(-1.00000 - 1.73205i) q^{37} +(0.500000 - 0.866025i) q^{38} +(4.50000 + 7.79423i) q^{40} +3.00000 q^{41} +(-1.50000 - 7.79423i) q^{42} -7.00000 q^{43} +(-1.50000 - 2.59808i) q^{44} +(-9.00000 + 15.5885i) q^{45} +(-0.500000 - 0.866025i) q^{47} +3.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} +4.00000 q^{50} +(-3.00000 - 5.19615i) q^{51} +(-1.50000 + 2.59808i) q^{53} +(4.50000 + 7.79423i) q^{54} -9.00000 q^{55} +(-1.50000 - 7.79423i) q^{56} +3.00000 q^{57} +(-3.50000 - 6.06218i) q^{58} +(2.00000 - 3.46410i) q^{59} +(-4.50000 + 7.79423i) q^{60} +(6.50000 + 11.2583i) q^{61} +3.00000 q^{62} +(12.0000 - 10.3923i) q^{63} +7.00000 q^{64} +(-4.50000 + 7.79423i) q^{66} +(1.50000 - 2.59808i) q^{67} +(-1.00000 - 1.73205i) q^{68} +(-7.50000 - 2.59808i) q^{70} +13.0000 q^{71} +(9.00000 + 15.5885i) q^{72} +(6.50000 - 11.2583i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(6.00000 + 10.3923i) q^{75} +1.00000 q^{76} +(7.50000 + 2.59808i) q^{77} +(1.50000 + 2.59808i) q^{79} +(1.50000 - 2.59808i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-1.50000 - 2.59808i) q^{82} +(6.00000 - 5.19615i) q^{84} -6.00000 q^{85} +(3.50000 + 6.06218i) q^{86} +(10.5000 - 18.1865i) q^{87} +(-4.50000 + 7.79423i) q^{88} +(-3.00000 - 5.19615i) q^{89} +18.0000 q^{90} +(4.50000 + 7.79423i) q^{93} +(-0.500000 + 0.866025i) q^{94} +(1.50000 - 2.59808i) q^{95} +(7.50000 + 12.9904i) q^{96} -5.00000 q^{97} +(5.50000 + 4.33013i) q^{98} -18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 3 q^{3} + q^{4} - 3 q^{5} - 6 q^{6} + q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q - q^2 + 3 * q^3 + q^4 - 3 * q^5 - 6 * q^6 + q^7 - 6 * q^8 - 6 * q^9	\( 2 q - q^{2} + 3 q^{3} + q^{4} - 3 q^{5} - 6 q^{6} + q^{7} - 6 q^{8} - 6 q^{9} - 3 q^{10} + 3 q^{11} - 3 q^{12} + 4 q^{14} - 18 q^{15} + q^{16} + 2 q^{17} - 6 q^{18} + q^{19} - 6 q^{20} + 15 q^{21} - 6 q^{22} - 9 q^{24} - 4 q^{25} - 18 q^{27} + 5 q^{28} + 14 q^{29} + 9 q^{30} - 3 q^{31} - 5 q^{32} - 9 q^{33} - 4 q^{34} + 12 q^{35} - 12 q^{36} - 2 q^{37} + q^{38} + 9 q^{40} + 6 q^{41} - 3 q^{42} - 14 q^{43} - 3 q^{44} - 18 q^{45} - q^{47} + 6 q^{48} - 13 q^{49} + 8 q^{50} - 6 q^{51} - 3 q^{53} + 9 q^{54} - 18 q^{55} - 3 q^{56} + 6 q^{57} - 7 q^{58} + 4 q^{59} - 9 q^{60} + 13 q^{61} + 6 q^{62} + 24 q^{63} + 14 q^{64} - 9 q^{66} + 3 q^{67} - 2 q^{68} - 15 q^{70} + 26 q^{71} + 18 q^{72} + 13 q^{73} - 2 q^{74} + 12 q^{75} + 2 q^{76} + 15 q^{77} + 3 q^{79} + 3 q^{80} - 9 q^{81} - 3 q^{82} + 12 q^{84} - 12 q^{85} + 7 q^{86} + 21 q^{87} - 9 q^{88} - 6 q^{89} + 36 q^{90} + 9 q^{93} - q^{94} + 3 q^{95} + 15 q^{96} - 10 q^{97} + 11 q^{98} - 36 q^{99}+O(q^{100}) \) 2 * q - q^2 + 3 * q^3 + q^4 - 3 * q^5 - 6 * q^6 + q^7 - 6 * q^8 - 6 * q^9 - 3 * q^10 + 3 * q^11 - 3 * q^12 + 4 * q^14 - 18 * q^15 + q^16 + 2 * q^17 - 6 * q^18 + q^19 - 6 * q^20 + 15 * q^21 - 6 * q^22 - 9 * q^24 - 4 * q^25 - 18 * q^27 + 5 * q^28 + 14 * q^29 + 9 * q^30 - 3 * q^31 - 5 * q^32 - 9 * q^33 - 4 * q^34 + 12 * q^35 - 12 * q^36 - 2 * q^37 + q^38 + 9 * q^40 + 6 * q^41 - 3 * q^42 - 14 * q^43 - 3 * q^44 - 18 * q^45 - q^47 + 6 * q^48 - 13 * q^49 + 8 * q^50 - 6 * q^51 - 3 * q^53 + 9 * q^54 - 18 * q^55 - 3 * q^56 + 6 * q^57 - 7 * q^58 + 4 * q^59 - 9 * q^60 + 13 * q^61 + 6 * q^62 + 24 * q^63 + 14 * q^64 - 9 * q^66 + 3 * q^67 - 2 * q^68 - 15 * q^70 + 26 * q^71 + 18 * q^72 + 13 * q^73 - 2 * q^74 + 12 * q^75 + 2 * q^76 + 15 * q^77 + 3 * q^79 + 3 * q^80 - 9 * q^81 - 3 * q^82 + 12 * q^84 - 12 * q^85 + 7 * q^86 + 21 * q^87 - 9 * q^88 - 6 * q^89 + 36 * q^90 + 9 * q^93 - q^94 + 3 * q^95 + 15 * q^96 - 10 * q^97 + 11 * q^98 - 36 * q^99

Introduction

L-functions

Modular forms

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