LMFDB - Embedded newform 1183.2.e.c.170.1

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			170.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1183.170
Dual form			1183.2.e.c.508.1

$q$-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} +(-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} - 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}+ \cdots + 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

Character values

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

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

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	$-0.718307\pi$
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i	0.986869	+	0.161521i	$0.0516399\pi$
$3$	1.50000	+	2.59808i	0.866025	+	1.50000i	0.866025	+	0.500000i	$0.166667\pi$
$3$	1.50000	+	2.59808i	0.866025	+	1.50000i			1.00000i	$0.5\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	−0.306851	−	0.951757i	$-0.599275\pi$
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	0.977672	−	0.210138i	$-0.0673912\pi$
$6$	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	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$	−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	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$	3.00000	+	5.19615i	0.707107	+	1.22474i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	0.802955	+	0.596040i	$0.203260\pi$
$20$	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	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	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	$-0.0798387\pi$
$31$	1.50000	+	2.59808i	0.269408	+	0.466628i	−0.699301	+	0.714827i	$0.746505\pi$
$32$	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	$-0.780765\pi$
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	0.936442	+	0.350823i	$0.114098\pi$
$38$	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	$-0.575267\pi$
$41$	−3.00000			−0.468521			−0.234261	+	0.972174i	$0.575267\pi$
$42$	−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	$-0.810098\pi$
$47$	0.500000	−	0.866025i	0.0729325	−	0.126323i	0.900185	+	0.435507i	$0.143431\pi$
$48$	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	0.744423	−	0.667708i	$-0.232725\pi$
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	−0.950464	+	0.310835i	$0.899391\pi$
$54$	−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	$-0.250514\pi$
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	−0.966342	+	0.257260i	$0.917180\pi$
$60$	4.50000	+	7.79423i	0.580948	+	1.00623i
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	0.896258	−	0.443533i	$-0.146275\pi$
$62$	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	$-0.225330\pi$
$67$	−1.50000	−	2.59808i	−0.183254	−	0.317406i	−0.942987	+	0.332830i	$0.891996\pi$
$68$	−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	$-0.780447\pi$
$71$	−13.0000			−1.54282			−0.771408	+	0.636341i	$0.780447\pi$
$72$	−9.00000	+	15.5885i	−1.06066	+	1.83712i
$73$	−6.50000	−	11.2583i	−0.760767	−	1.31769i	−0.942455	−	0.334332i	$-0.891489\pi$
$73$	−6.50000	−	11.2583i	−0.760767	−	1.31769i	0.181688	−	0.983356i	$-0.441844\pi$
$74$	−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	−0.769222	−	0.638982i	$-0.779356\pi$
$79$	1.50000	−	2.59808i	0.168763	−	0.292306i	0.937985	+	0.346675i	$0.112689\pi$
$80$	−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	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$	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	$-0.418307\pi$
$97$	5.00000			0.507673			0.253837	+	0.967247i	$0.418307\pi$
$98$	−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	0.963182	−	0.268851i	$-0.0866439\pi$
$101$	2.50000	+	4.33013i	0.248759	+	0.430864i	−0.714423	+	0.699715i	$0.753311\pi$
$102$	3.00000	+	5.19615i	0.297044	+	0.514496i
$103$	−2.50000	+	4.33013i	−0.246332	+	0.426660i	−0.962505	−	0.271263i	$-0.912559\pi$
$103$	−2.50000	+	4.33013i	−0.246332	+	0.426660i	0.716173	+	0.697923i	$0.245892\pi$
$104$		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	−0.992003	−	0.126217i	$-0.959717\pi$
$107$	−4.00000	+	6.92820i	−0.386695	+	0.669775i	0.605308	+	0.795991i	$0.293050\pi$
$108$	−4.50000	−	7.79423i	−0.433013	−	0.750000i
$109$	3.50000	+	6.06218i	0.335239	+	0.580651i	0.983531	−	0.180741i	$-0.0578495\pi$
$109$	3.50000	+	6.06218i	0.335239	+	0.580651i	−0.648292	+	0.761392i	$0.724516\pi$
$110$	−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	−0.954327	−	0.298764i	$-0.903426\pi$
$131$	−2.50000	+	4.33013i	−0.218426	+	0.378325i	0.735901	+	0.677089i	$0.236759\pi$
$132$	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	$-0.0261741\pi$
$137$	5.00000	+	8.66025i	0.427179	+	0.739895i	−0.569442	+	0.822031i	$0.692841\pi$
$138$		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	−0.376061	−	0.926595i	$-0.622722\pi$
$149$	7.50000	−	12.9904i	0.614424	−	1.06421i	0.990485	−	0.137619i	$-0.0439449\pi$
$150$	−6.00000	−	10.3923i	−0.489898	−	0.848528i
$151$	−10.5000	−	18.1865i	−0.854478	−	1.48000i	−0.877129	−	0.480256i	$-0.840544\pi$
$151$	−10.5000	−	18.1865i	−0.854478	−	1.48000i	0.0226507	−	0.999743i	$-0.492789\pi$
$152$	−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	−0.943777	−	0.330584i	$-0.892754\pi$
$157$	−9.50000	−	16.4545i	−0.758183	−	1.31321i	0.185594	−	0.982627i	$-0.440579\pi$
$158$	−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	$-0.845802\pi$
$163$	−0.500000	+	0.866025i	−0.0391630	+	0.0678323i	0.845780	+	0.533533i	$0.179136\pi$
$164$	−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	$-0.332235\pi$
$167$	13.0000			1.00597			0.502985	+	0.864295i	$0.332235\pi$
$168$	−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	0.237816	+	0.971310i	$0.423569\pi$
$173$	−9.50000	+	16.4545i	−0.722272	+	1.25101i	−0.960087	+	0.279701i	$0.909765\pi$
$174$	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	−0.986447	−	0.164079i	$-0.947535\pi$
$179$	−8.50000	−	14.7224i	−0.635320	−	1.10041i	0.351127	−	0.936328i	$-0.385798\pi$
$180$	−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	−0.375339	−	0.926887i	$-0.622474\pi$
$191$	8.50000	−	14.7224i	0.615038	−	1.06528i	0.990378	−	0.138390i	$-0.0441928\pi$
$192$	10.5000	+	18.1865i	0.757772	+	1.31250i
$193$	3.50000	+	6.06218i	0.251936	+	0.436365i	0.964059	−	0.265689i	$-0.0855996\pi$
$193$	3.50000	+	6.06218i	0.251936	+	0.436365i	−0.712123	+	0.702055i	$0.752266\pi$
$194$	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	$-0.488658\pi$
$197$	1.00000			0.0712470			0.0356235	+	0.999365i	$0.488658\pi$
$198$	9.00000	−	15.5885i	0.639602	−	1.10782i
$199$	10.0000	+	17.3205i	0.708881	+	1.22782i	0.965272	+	0.261245i	$0.0841331\pi$
$199$	10.0000	+	17.3205i	0.708881	+	1.22782i	−0.256391	+	0.966573i	$0.582534\pi$
$200$	−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	$-0.402565\pi$
$223$	9.00000			0.602685			0.301342	+	0.953516i	$0.402565\pi$
$224$	−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	$-0.209046\pi$
$227$	−2.00000	−	3.46410i	−0.132745	−	0.229920i	−0.924734	+	0.380615i	$0.875712\pi$
$228$	−1.50000	−	2.59808i	−0.0993399	−	0.172062i
$229$	−6.50000	+	11.2583i	−0.429532	+	0.743971i	−0.996832	−	0.0795401i	$-0.974655\pi$
$229$	−6.50000	+	11.2583i	−0.429532	+	0.743971i	0.567300	+	0.823511i	$0.307988\pi$
$230$		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	−0.284645	−	0.958633i	$-0.591876\pi$
$233$	10.5000	−	18.1865i	0.687878	−	1.19144i	0.972523	−	0.232806i	$-0.0747909\pi$
$234$		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	$-0.458705\pi$
$239$	4.00000			0.258738			0.129369	+	0.991596i	$0.458705\pi$
$240$	4.50000	−	7.79423i	0.290474	−	0.503115i
$241$	−13.0000	−	22.5167i	−0.837404	−	1.45043i	−0.892058	−	0.451920i	$-0.850739\pi$
$241$	−13.0000	−	22.5167i	−0.837404	−	1.45043i	0.0546547	−	0.998505i	$-0.482594\pi$
$242$	−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	−0.833150	−	0.553047i	$-0.813465\pi$
$257$	1.00000	−	1.73205i	0.0623783	−	0.108042i	0.895528	+	0.445005i	$0.146798\pi$
$258$	−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	0.896093	+	0.443866i	$0.146393\pi$
$263$	13.5000	+	23.3827i	0.832446	+	1.44184i	−0.0636476	+	0.997972i	$0.520273\pi$
$264$	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	−0.998361	−	0.0572259i	$-0.981774\pi$
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	0.449622	−	0.893219i	$-0.351559\pi$
$270$	13.5000	+	23.3827i	0.821584	+	1.42302i
$271$	−8.00000	+	13.8564i	−0.485965	+	0.841717i	−0.999870	−	0.0161307i	$-0.994865\pi$
$271$	−8.00000	+	13.8564i	−0.485965	+	0.841717i	0.513905	+	0.857847i	$0.328199\pi$
$272$	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	−0.980373	−	0.197153i	$-0.936830\pi$
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	0.319447	−	0.947604i	$-0.396503\pi$
$278$	−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	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$	1.50000	−	2.59808i	0.0893237	−	0.154713i
$283$	−0.500000	−	0.866025i	−0.0297219	−	0.0514799i	0.850782	−	0.525519i	$-0.176129\pi$
$283$	−0.500000	−	0.866025i	−0.0297219	−	0.0514799i	−0.880504	+	0.474039i	$0.842796\pi$
$284$	−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	$-0.604124\pi$
$293$	−11.0000			−0.642627			−0.321313	+	0.946973i	$0.604124\pi$
$294$	−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	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$	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	0.964942	−	0.262463i	$-0.0845347\pi$
$311$	4.50000	+	7.79423i	0.255172	+	0.441970i	−0.709771	+	0.704433i	$0.751201\pi$
$312$		0			0
$313$	−9.50000	+	16.4545i	−0.536972	+	0.930062i	0.462093	+	0.886831i	$0.347098\pi$
$313$	−9.50000	+	16.4545i	−0.536972	+	0.930062i	−0.999065	+	0.0432311i	$0.986235\pi$
$314$	−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	$-0.914667\pi$
$317$	−4.50000	+	7.79423i	−0.252745	+	0.437767i	0.711535	+	0.702650i	$0.248000\pi$
$318$	−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	0.124574	+	0.992210i	$0.460243\pi$
$331$	−14.5000	+	25.1147i	−0.796992	+	1.38043i	−0.921567	+	0.388221i	$0.873090\pi$
$332$		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	0.953189	−	0.302374i	$-0.0977791\pi$
$347$	4.00000	+	6.92820i	0.214731	+	0.371925i	−0.738458	+	0.674299i	$0.764446\pi$
$348$	−10.5000	+	18.1865i	−0.562859	+	0.974901i
$349$	−23.0000			−1.23116			−0.615581	−	0.788074i	$-0.711079\pi$
$349$	−23.0000			−1.23116			−0.615581	+	0.788074i	$0.711079\pi$
$350$	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	−0.979202	−	0.202889i	$-0.934967\pi$
$353$	−12.5000	−	21.6506i	−0.665308	−	1.15235i	0.313894	−	0.949458i	$-0.398366\pi$
$354$	−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	$-0.685252\pi$
$359$	8.50000	−	14.7224i	0.448613	−	0.777020i	0.998296	+	0.0583530i	$0.0185849\pi$
$360$	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	0.913493	+	0.406855i	$0.133375\pi$
$367$	15.5000	+	26.8468i	0.809093	+	1.40139i	−0.104399	+	0.994535i	$0.533292\pi$
$368$		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	−0.725689	−	0.688023i	$-0.758479\pi$
$373$	4.50000	−	7.79423i	0.233001	−	0.403570i	0.958690	+	0.284453i	$0.0918121\pi$
$374$	−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	$-0.178078\pi$
$379$	33.0000			1.69510			0.847548	+	0.530719i	$0.178078\pi$
$380$	−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	0.462563	+	0.886586i	$0.346930\pi$
$383$	−10.5000	+	18.1865i	−0.536525	+	0.929288i	−0.999088	+	0.0427020i	$0.986403\pi$
$384$	−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	0.892735	+	0.450582i	$0.148784\pi$
$389$	16.5000	+	28.5788i	0.836583	+	1.44900i	−0.0561516	+	0.998422i	$0.517883\pi$
$390$		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	$-0.841322\pi$
$397$	−0.500000	+	0.866025i	−0.0250943	+	0.0434646i	0.853206	+	0.521575i	$0.174655\pi$
$398$	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	$-0.849236\pi$
$401$	−1.00000	+	1.73205i	−0.0499376	+	0.0864945i	0.839976	+	0.542623i	$0.182569\pi$
$402$	−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	$-0.0541630\pi$
$409$	7.00000	+	12.1244i	0.346128	+	0.599511i	−0.639430	+	0.768849i	$0.720830\pi$
$410$	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	$-0.644537\pi$
$421$	−18.0000			−0.877266			−0.438633	+	0.898666i	$0.644537\pi$
$422$	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	$-0.0971186\pi$
$431$	4.50000	+	7.79423i	0.216757	+	0.375435i	−0.737057	+	0.675830i	$0.763785\pi$
$432$	−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	−0.609503	−	0.792784i	$-0.708631\pi$
$439$	8.00000	−	13.8564i	0.381819	−	0.661330i	0.991322	+	0.131453i	$0.0419644\pi$
$440$	−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	−0.705278	−	0.708931i	$-0.749178\pi$
$443$	5.50000	−	9.52628i	0.261313	−	0.452607i	0.966591	+	0.256323i	$0.0825112\pi$
$444$	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	$-0.615161\pi$
$449$	−15.0000			−0.707894			−0.353947	+	0.935266i	$0.615161\pi$
$450$	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	$-0.971655\pi$
$457$	−9.00000	+	15.5885i	−0.421002	+	0.729197i	0.575036	+	0.818128i	$0.304988\pi$
$458$	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	$-0.803294\pi$
$461$	−35.0000			−1.63011			−0.815056	+	0.579382i	$0.803294\pi$
$462$	22.5000	−	7.79423i	1.04679	−	0.362620i
$463$	8.00000			0.371792			0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000			0.371792			0.185896	+	0.982569i	$0.440481\pi$
$464$	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	−0.773611	−	0.633661i	$-0.781552\pi$
$467$	3.50000	−	6.06218i	0.161961	−	0.280524i	0.935572	+	0.353137i	$0.114885\pi$
$468$		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	−0.919880	−	0.392200i	$-0.871714\pi$
$479$	−17.5000	−	30.3109i	−0.799595	−	1.38494i	0.120284	−	0.992739i	$-0.461619\pi$
$480$	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	$-0.0485850\pi$
$487$	8.00000	+	13.8564i	0.362515	+	0.627894i	−0.625859	+	0.779936i	$0.715252\pi$
$488$	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	0.276683	+	0.960961i	$0.410765\pi$
$499$	−15.5000	+	26.8468i	−0.693875	+	1.20183i	−0.970558	+	0.240866i	$0.922569\pi$
$500$	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	0.192599	+	0.981278i	$0.438308\pi$
$509$	−17.0000	+	29.4449i	−0.753512	+	1.30512i	−0.946111	+	0.323843i	$0.895025\pi$
$510$	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	0.989933	−	0.141537i	$-0.0452044\pi$
$521$	8.50000	+	14.7224i	0.372392	+	0.645001i	−0.617541	+	0.786539i	$0.711871\pi$
$522$	21.0000	+	36.3731i	0.919145	+	1.59201i
$523$	−2.00000	+	3.46410i	−0.0874539	+	0.151475i	−0.906434	−	0.422347i	$-0.861206\pi$
$523$	−2.00000	+	3.46410i	−0.0874539	+	0.151475i	0.818980	+	0.573822i	$0.194540\pi$
$524$	−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	0.127222	+	0.991874i	$0.459394\pi$
$541$	−18.5000	+	32.0429i	−0.795377	+	1.37763i	−0.922599	+	0.385759i	$0.873939\pi$
$542$	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	$-0.146422\pi$
$557$	1.50000	+	2.59808i	0.0635570	+	0.110084i	−0.832496	+	0.554031i	$0.813089\pi$
$558$	−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	0.820798	−	0.571218i	$-0.193529\pi$
$563$	−2.00000	−	3.46410i	−0.0842900	−	0.145994i	−0.905088	+	0.425223i	$0.860196\pi$
$564$	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	−0.951592	−	0.307364i	$-0.900553\pi$
$569$	−5.00000	+	8.66025i	−0.209611	+	0.363057i	0.741981	+	0.670421i	$0.233886\pi$
$570$	4.50000	+	7.79423i	0.188484	+	0.326464i
$571$	−21.5000	−	37.2391i	−0.899747	−	1.55841i	−0.827817	−	0.560998i	$-0.810418\pi$
$571$	−21.5000	−	37.2391i	−0.899747	−	1.55841i	−0.0719297	−	0.997410i	$-0.522916\pi$
$572$		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	$-0.173293\pi$
$577$	−0.500000	−	0.866025i	−0.0208153	−	0.0360531i	−0.876245	+	0.481865i	$0.839960\pi$
$578$	−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	$-0.261533\pi$
$587$	33.0000			1.36206			0.681028	+	0.732257i	$0.261533\pi$
$588$	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	−0.443573	−	0.896238i	$-0.646289\pi$
$593$	13.5000	−	23.3827i	0.554379	−	0.960212i	0.997952	−	0.0639736i	$-0.0203773\pi$
$594$	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	0.999923	+	0.0124417i	$0.00396043\pi$
$599$	12.5000	+	21.6506i	0.510736	+	0.884621i	−0.489186	+	0.872179i	$0.662706\pi$
$600$	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	−0.955789	−	0.294052i	$-0.904996\pi$
$607$	−5.50000	+	9.52628i	−0.223238	+	0.386660i	0.732551	+	0.680712i	$0.238329\pi$
$608$	−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	−0.999984	−	0.00563283i	$-0.998207\pi$
$613$	−12.5000	−	21.6506i	−0.504870	−	0.874461i	0.495114	−	0.868828i	$-0.335126\pi$
$614$	−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	$-0.268745\pi$
$617$	33.0000			1.32853			0.664265	+	0.747497i	$0.268745\pi$
$618$	−7.50000	+	12.9904i	−0.301694	+	0.522550i
$619$	5.50000	+	9.52628i	0.221064	+	0.382893i	0.955131	−	0.296183i	$-0.0957138\pi$
$619$	5.50000	+	9.52628i	0.221064	+	0.382893i	−0.734068	+	0.679076i	$0.762380\pi$
$620$	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	$-0.665792\pi$
$631$	−25.0000			−0.995234			−0.497617	+	0.867397i	$0.665792\pi$
$632$	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	0.987200	−	0.159489i	$-0.0509845\pi$
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	−0.631721	+	0.775196i	$0.717651\pi$
$642$	−12.0000	+	20.7846i	−0.473602	+	0.820303i
$643$	19.0000			0.749287			0.374643	−	0.927169i	$-0.377765\pi$
$643$	19.0000			0.749287			0.374643	+	0.927169i	$0.377765\pi$
$644$		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	0.763908	−	0.645325i	$-0.223278\pi$
$647$	−4.50000	−	7.79423i	−0.176913	−	0.306423i	−0.940822	+	0.338902i	$0.889945\pi$
$648$	−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	−0.986634	−	0.162951i	$-0.947899\pi$
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	0.634437	+	0.772975i	$0.281232\pi$
$654$	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	$-0.222669\pi$
$661$	−4.50000	−	7.79423i	−0.175030	−	0.303160i	−0.940172	+	0.340701i	$0.889335\pi$
$662$	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	−0.925412	−	0.378962i	$-0.876281\pi$
$677$	−3.50000	+	6.06218i	−0.134516	+	0.232988i	0.790897	+	0.611950i	$0.209615\pi$
$678$	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	$-0.0929302\pi$
$683$	6.00000	+	10.3923i	0.229584	+	0.397650i	−0.728101	+	0.685470i	$0.759597\pi$
$684$	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	$-0.857575\pi$
$691$	−2.00000	+	3.46410i	−0.0760836	+	0.131781i	0.825473	+	0.564441i	$0.190908\pi$
$692$	−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	$-0.767108\pi$
$709$	5.50000	−	9.52628i	0.206557	−	0.357767i	0.950628	+	0.310334i	$0.100441\pi$
$710$	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	−0.769832	−	0.638247i	$-0.779660\pi$
$719$	4.50000	−	7.79423i	0.167822	−	0.290676i	0.937654	+	0.347571i	$0.112993\pi$
$720$	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	$-0.886487\pi$
$733$	−4.50000	+	7.79423i	−0.166211	+	0.287886i	0.770873	+	0.636988i	$0.219820\pi$
$734$	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	$-0.160812\pi$
$739$	0.500000	+	0.866025i	0.0183928	+	0.0318573i	−0.856683	+	0.515844i	$0.827478\pi$
$740$	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	$-0.885054\pi$
$743$	−51.0000			−1.87101			−0.935504	+	0.353315i	$0.885054\pi$
$744$	−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	0.489053	+	0.872254i	$0.337342\pi$
$751$	−14.0000	+	24.2487i	−0.510867	+	0.884848i	−0.999921	+	0.0125942i	$0.995991\pi$
$752$	−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	$-0.885491\pi$
$761$	−4.50000	+	7.79423i	−0.163125	+	0.282541i	0.772863	+	0.634573i	$0.218824\pi$
$762$	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	$-0.611300\pi$
$769$	−19.0000			−0.685158			−0.342579	+	0.939489i	$0.611300\pi$
$770$	−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	$-0.201080\pi$
$773$	−3.00000	−	5.19615i	−0.107903	−	0.186893i	−0.914920	+	0.403634i	$0.867747\pi$
$774$	−21.0000	−	36.3731i	−0.754829	−	1.30740i
$775$	6.00000	−	10.3923i	0.215526	−	0.373303i
$776$	15.0000			0.538469
$777$	−3.00000	+	15.5885i	−0.107624	+	0.559233i
$778$	33.0000			1.18311
$779$	1.50000	−	2.59808i	0.0537431	−	0.0930857i
$780$		0			0
$781$	19.5000	+	33.7750i	0.697765	+	1.20856i
$782$		0			0
$783$	−63.0000			−2.25144
$784$	−5.50000	+	4.33013i	−0.196429	+	0.154647i
$785$	−57.0000			−2.03442
$786$	−7.50000	+	12.9904i	−0.267516	+	0.463352i
$787$	−10.0000	−	17.3205i	−0.356462	−	0.617409i	0.630905	−	0.775860i	$-0.282684\pi$
$787$	−10.0000	−	17.3205i	−0.356462	−	0.617409i	−0.987367	+	0.158450i	$0.949350\pi$
$788$	0.500000	+	0.866025i	0.0178118	+	0.0308509i
$789$	−40.5000	+	70.1481i	−1.44184	+	2.49734i
$790$	−9.00000			−0.320206
$791$	−7.50000	+	38.9711i	−0.266669	+	1.38565i
$792$	54.0000			1.91881
$793$		0			0
$794$	0.500000	+	0.866025i	0.0177443	+	0.0307341i
$795$	−13.5000	−	23.3827i	−0.478796	−	0.829298i
$796$	−10.0000	+	17.3205i	−0.354441	+	0.613909i
$797$	3.00000			0.106265			0.0531327	−	0.998587i	$-0.483079\pi$
$797$	3.00000			0.106265			0.0531327	+	0.998587i	$0.483079\pi$
$798$	−6.00000	−	5.19615i	−0.212398	−	0.183942i
$799$	2.00000			0.0707549
$800$	10.0000	−	17.3205i	0.353553	−	0.612372i
$801$	18.0000	+	31.1769i	0.635999	+	1.10158i
$802$	1.00000	+	1.73205i	0.0353112	+	0.0611608i
$803$	−19.5000	+	33.7750i	−0.688140	+	1.19189i
$804$	9.00000			0.317406
$805$		0			0
$806$		0			0
$807$	27.0000	−	46.7654i	0.950445	−	1.64622i
$808$	7.50000	+	12.9904i	0.263849	+	0.457000i
$809$	−5.50000	−	9.52628i	−0.193370	−	0.334926i	0.752995	−	0.658026i	$-0.228608\pi$
$809$	−5.50000	−	9.52628i	−0.193370	−	0.334926i	−0.946365	+	0.323100i	$0.895275\pi$
$810$	−13.5000	+	23.3827i	−0.474342	+	0.821584i
$811$	4.00000			0.140459			0.0702295	−	0.997531i	$-0.477627\pi$
$811$	4.00000			0.140459			0.0702295	+	0.997531i	$0.477627\pi$
$812$	−17.5000	+	6.06218i	−0.614130	+	0.212741i
$813$	−48.0000			−1.68343
$814$	−3.00000	+	5.19615i	−0.105150	+	0.182125i
$815$	1.50000	+	2.59808i	0.0525427	+	0.0910066i
$816$	3.00000	+	5.19615i	0.105021	+	0.181902i
$817$	3.50000	−	6.06218i	0.122449	−	0.212089i
$818$	14.0000			0.489499
$819$		0			0
$820$	−9.00000			−0.314294
$821$	−27.0000	+	46.7654i	−0.942306	+	1.63212i	−0.181250	+	0.983437i	$0.558014\pi$
$821$	−27.0000	+	46.7654i	−0.942306	+	1.63212i	−0.761056	+	0.648686i	$0.775319\pi$
$822$	15.0000	+	25.9808i	0.523185	+	0.906183i
$823$	−20.0000	−	34.6410i	−0.697156	−	1.20751i	−0.969448	−	0.245295i	$-0.921115\pi$
$823$	−20.0000	−	34.6410i	−0.697156	−	1.20751i	0.272292	−	0.962215i	$-0.412218\pi$
$824$	−7.50000	+	12.9904i	−0.261275	+	0.452541i
$825$	−36.0000			−1.25336
$826$	2.00000	−	10.3923i	0.0695889	−	0.361595i
$827$	−4.00000			−0.139094			−0.0695468	−	0.997579i	$-0.522155\pi$
$827$	−4.00000			−0.139094			−0.0695468	+	0.997579i	$0.522155\pi$
$828$		0			0
$829$	−5.50000	−	9.52628i	−0.191023	−	0.330861i	0.754567	−	0.656223i	$-0.227847\pi$
$829$	−5.50000	−	9.52628i	−0.191023	−	0.330861i	−0.945589	+	0.325362i	$0.894514\pi$
$830$		0			0
$831$	33.0000	−	57.1577i	1.14476	−	1.98278i
$832$		0			0
$833$	−2.00000	−	13.8564i	−0.0692959	−	0.480096i
$834$	−45.0000			−1.55822
$835$	19.5000	−	33.7750i	0.674825	−	1.16883i
$836$	1.50000	+	2.59808i	0.0518786	+	0.0898563i
$837$	−13.5000	−	23.3827i	−0.466628	−	0.808224i
$838$	−12.5000	+	21.6506i	−0.431805	+	0.747909i
$839$	−37.0000			−1.27738			−0.638691	−	0.769463i	$-0.720524\pi$
$839$	−37.0000			−1.27738			−0.638691	+	0.769463i	$0.720524\pi$
$840$	−13.5000	+	70.1481i	−0.465794	+	2.42034i
$841$	20.0000			0.689655
$842$	−9.00000	+	15.5885i	−0.310160	+	0.537214i
$843$	27.0000	+	46.7654i	0.929929	+	1.61068i
$844$	3.50000	+	6.06218i	0.120475	+	0.208669i
$845$		0			0
$846$	6.00000			0.206284
$847$	4.00000	+	3.46410i	0.137442	+	0.119028i
$848$	−3.00000			−0.103020
$849$	1.50000	−	2.59808i	0.0514799	−	0.0891657i
$850$	−4.00000	−	6.92820i	−0.137199	−	0.237635i
$851$		0			0
$852$	19.5000	−	33.7750i	0.668059	−	1.15711i
$853$	6.00000			0.205436			0.102718	−	0.994711i	$-0.467246\pi$
$853$	6.00000			0.205436			0.102718	+	0.994711i	$0.467246\pi$
$854$	32.5000	−	11.2583i	1.11213	−	0.385252i
$855$	−18.0000			−0.615587
$856$	−12.0000	+	20.7846i	−0.410152	+	0.710403i
$857$	16.5000	+	28.5788i	0.563629	+	0.976235i	0.997176	+	0.0751033i	$0.0239287\pi$
$857$	16.5000	+	28.5788i	0.563629	+	0.976235i	−0.433546	+	0.901131i	$0.642738\pi$
$858$		0			0
$859$	−12.5000	+	21.6506i	−0.426494	+	0.738710i	−0.996559	−	0.0828900i	$-0.973585\pi$
$859$	−12.5000	+	21.6506i	−0.426494	+	0.738710i	0.570064	+	0.821600i	$0.306918\pi$
$860$	−21.0000			−0.716094
$861$	22.5000	−	7.79423i	0.766798	−	0.265627i
$862$	9.00000			0.306541
$863$	18.5000	−	32.0429i	0.629747	−	1.09075i	−0.357855	−	0.933777i	$-0.616492\pi$
$863$	18.5000	−	32.0429i	0.629747	−	1.09075i	0.987602	−	0.156977i	$-0.0501749\pi$
$864$	−22.5000	−	38.9711i	−0.765466	−	1.32583i
$865$	28.5000	+	49.3634i	0.969029	+	1.67841i
$866$	13.5000	−	23.3827i	0.458749	−	0.794576i
$867$	39.0000			1.32451
$868$	−6.00000	−	5.19615i	−0.203653	−	0.176369i
$869$	−9.00000			−0.305304
$870$	31.5000	−	54.5596i	1.06795	−	1.84974i
$871$		0			0
$872$	10.5000	+	18.1865i	0.355575	+	0.615874i
$873$	−15.0000	+	25.9808i	−0.507673	+	0.879316i
$874$		0			0
$875$	−1.50000	+	7.79423i	−0.0507093	+	0.263493i
$876$	39.0000			1.31769
$877$	−22.5000	+	38.9711i	−0.759771	+	1.31596i	0.183196	+	0.983076i	$0.441356\pi$
$877$	−22.5000	+	38.9711i	−0.759771	+	1.31596i	−0.942967	+	0.332886i	$0.891978\pi$
$878$	−8.00000	−	13.8564i	−0.269987	−	0.467631i
$879$	−16.5000	−	28.5788i	−0.556531	−	0.963940i
$880$	−4.50000	+	7.79423i	−0.151695	+	0.262743i
$881$	15.0000			0.505363			0.252681	−	0.967550i	$-0.418688\pi$
$881$	15.0000			0.505363			0.252681	+	0.967550i	$0.418688\pi$
$882$	−6.00000	−	41.5692i	−0.202031	−	1.39971i
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$		0			0
$885$	−18.0000	−	31.1769i	−0.605063	−	1.04800i
$886$	−5.50000	−	9.52628i	−0.184776	−	0.320042i
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	−0.994077	−	0.108678i	$-0.965338\pi$
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	0.591156	+	0.806557i	$0.298672\pi$
$888$	18.0000			0.604040
$889$	−5.50000	+	28.5788i	−0.184464	+	0.958503i
$890$	−18.0000			−0.603361
$891$	−13.5000	+	23.3827i	−0.452267	+	0.783349i
$892$	4.50000	+	7.79423i	0.150671	+	0.260970i
$893$	0.500000	+	0.866025i	0.0167319	+	0.0289804i
$894$	22.5000	−	38.9711i	0.752513	−	1.30339i
$895$	−51.0000			−1.70474
$896$	−6.00000	−	5.19615i	−0.200446	−	0.173591i
$897$		0			0
$898$	−7.50000	+	12.9904i	−0.250278	+	0.433495i
$899$	10.5000	+	18.1865i	0.350195	+	0.606555i
$900$	12.0000	+	20.7846i	0.400000	+	0.692820i
$901$	3.00000	−	5.19615i	0.0999445	−	0.173109i
$902$	9.00000			0.299667
$903$	52.5000	−	18.1865i	1.74709	−	0.605210i
$904$	45.0000			1.49668
$905$	−33.0000	+	57.1577i	−1.09696	+	1.89999i
$906$	−31.5000	−	54.5596i	−1.04652	−	1.81262i
$907$	23.5000	+	40.7032i	0.780305	+	1.35153i	0.931764	+	0.363064i	$0.118269\pi$
$907$	23.5000	+	40.7032i	0.780305	+	1.35153i	−0.151460	+	0.988463i	$0.548397\pi$
$908$	2.00000	−	3.46410i	0.0663723	−	0.114960i
$909$	−30.0000			−0.995037
$910$		0			0
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$	−1.50000	+	2.59808i	−0.0496700	+	0.0860309i
$913$		0			0
$914$	9.00000	+	15.5885i	0.297694	+	0.515620i
$915$	58.5000	−	101.325i	1.93395	−	3.34970i
$916$	−13.0000			−0.429532
$917$	−10.0000	−	8.66025i	−0.330229	−	0.285987i
$918$	−18.0000			−0.594089
$919$	12.5000	−	21.6506i	0.412337	−	0.714189i	−0.582808	−	0.812610i	$-0.698046\pi$
$919$	12.5000	−	21.6506i	0.412337	−	0.714189i	0.995145	+	0.0984214i	$0.0313793\pi$
$920$		0			0
$921$	−18.0000	−	31.1769i	−0.593120	−	1.02731i
$922$	−17.5000	+	30.3109i	−0.576332	+	0.998236i
$923$		0			0
$924$	−4.50000	+	23.3827i	−0.148039	+	0.769234i
$925$	−8.00000			−0.263038
$926$	4.00000	−	6.92820i	0.131448	−	0.227675i
$927$	−15.0000	−	25.9808i	−0.492665	−	0.853320i
$928$	17.5000	+	30.3109i	0.574466	+	0.995004i
$929$	−6.50000	+	11.2583i	−0.213258	+	0.369374i	−0.952732	−	0.303811i	$-0.901741\pi$
$929$	−6.50000	+	11.2583i	−0.213258	+	0.369374i	0.739474	+	0.673185i	$0.235074\pi$
$930$	27.0000			0.885365
$931$	5.50000	−	4.33013i	0.180255	−	0.141914i
$932$	21.0000			0.687878
$933$	−13.5000	+	23.3827i	−0.441970	+	0.765515i
$934$	−3.50000	−	6.06218i	−0.114523	−	0.198361i
$935$	−9.00000	−	15.5885i	−0.294331	−	0.509797i
$936$		0			0
$937$	22.0000			0.718709			0.359354	−	0.933201i	$-0.382997\pi$
$937$	22.0000			0.718709			0.359354	+	0.933201i	$0.382997\pi$
$938$	1.50000	−	7.79423i	0.0489767	−	0.254491i
$939$	−57.0000			−1.86012
$940$	1.50000	−	2.59808i	0.0489246	−	0.0847399i
$941$	−8.50000	−	14.7224i	−0.277092	−	0.479938i	0.693569	−	0.720390i	$-0.256037\pi$
$941$	−8.50000	−	14.7224i	−0.277092	−	0.479938i	−0.970661	+	0.240453i	$0.922704\pi$
$942$	−28.5000	−	49.3634i	−0.928580	−	1.60835i
$943$		0			0
$944$	−4.00000			−0.130189
$945$	−54.0000	−	46.7654i	−1.75662	−	1.52128i
$946$	21.0000			0.682769
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	−0.946892	−	0.321552i	$-0.895796\pi$
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	0.751918	+	0.659256i	$0.229129\pi$
$948$	4.50000	+	7.79423i	0.146153	+	0.253145i
$949$		0			0
$950$	2.00000	−	3.46410i	0.0648886	−	0.112390i
$951$	−27.0000			−0.875535
$952$	−15.0000	+	5.19615i	−0.486153	+	0.168408i
$953$	−33.0000			−1.06897			−0.534487	−	0.845176i	$-0.679495\pi$
$953$	−33.0000			−1.06897			−0.534487	+	0.845176i	$0.679495\pi$
$954$	9.00000	−	15.5885i	0.291386	−	0.504695i
$955$	−25.5000	−	44.1673i	−0.825161	−	1.42922i
$956$	2.00000	+	3.46410i	0.0646846	+	0.112037i
$957$	31.5000	−	54.5596i	1.01825	−	1.76366i
$958$	−35.0000			−1.13080
$959$	−25.0000	+	8.66025i	−0.807292	+	0.279654i
$960$	63.0000			2.03332
$961$	11.0000	−	19.0526i	0.354839	−	0.614599i
$962$		0			0
$963$	−24.0000	−	41.5692i	−0.773389	−	1.33955i
$964$	13.0000	−	22.5167i	0.418702	−	0.725213i
$965$	21.0000			0.676014
$966$		0			0
$967$	8.00000			0.257263			0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000			0.257263			0.128631	+	0.991692i	$0.458942\pi$
$968$	3.00000	−	5.19615i	0.0964237	−	0.167011i
$969$	−3.00000	−	5.19615i	−0.0963739	−	0.166924i
$970$	−7.50000	−	12.9904i	−0.240810	−	0.417096i
$971$	0.500000	−	0.866025i	0.0160458	−	0.0277921i	−0.857891	−	0.513832i	$-0.828226\pi$
$971$	0.500000	−	0.866025i	0.0160458	−	0.0277921i	0.873937	+	0.486040i	$0.161559\pi$
$972$		0			0
$973$	7.50000	−	38.9711i	0.240439	−	1.24936i
$974$	16.0000			0.512673
$975$		0			0
$976$	−6.50000	−	11.2583i	−0.208060	−	0.360370i
$977$	−2.50000	−	4.33013i	−0.0799821	−	0.138533i	0.823260	−	0.567665i	$-0.192153\pi$
$977$	−2.50000	−	4.33013i	−0.0799821	−	0.138533i	−0.903242	+	0.429132i	$0.858820\pi$
$978$	−1.50000	+	2.59808i	−0.0479647	+	0.0830773i
$979$	−18.0000			−0.575282
$980$	−19.5000	−	7.79423i	−0.622905	−	0.248978i
$981$	−42.0000			−1.34096
$982$	7.50000	−	12.9904i	0.239335	−	0.414540i
$983$	23.5000	+	40.7032i	0.749534	+	1.29823i	0.948046	+	0.318132i	$0.103056\pi$
$983$	23.5000	+	40.7032i	0.749534	+	1.29823i	−0.198513	+	0.980098i	$0.563611\pi$
$984$	−13.5000	−	23.3827i	−0.430364	−	0.745413i
$985$	1.50000	−	2.59808i	0.0477940	−	0.0827816i
$986$	14.0000			0.445851
$987$	−1.50000	+	7.79423i	−0.0477455	+	0.248093i
$988$		0			0
$989$		0			0
$990$	−27.0000	−	46.7654i	−0.858116	−	1.48630i
$991$	−6.50000	−	11.2583i	−0.206479	−	0.357633i	0.744124	−	0.668042i	$-0.232867\pi$
$991$	−6.50000	−	11.2583i	−0.206479	−	0.357633i	−0.950603	+	0.310409i	$0.899534\pi$
$992$	−7.50000	+	12.9904i	−0.238125	+	0.412445i
$993$	−87.0000			−2.76086
$994$	−26.0000	−	22.5167i	−0.824670	−	0.714185i
$995$	60.0000			1.90213
$996$		0			0
$997$	−1.00000	−	1.73205i	−0.0316703	−	0.0548546i	0.849756	−	0.527176i	$-0.176749\pi$
$997$	−1.00000	−	1.73205i	−0.0316703	−	0.0548546i	−0.881426	+	0.472322i	$0.843416\pi$
$998$	15.5000	+	26.8468i	0.490644	+	0.849820i
$999$	−9.00000	+	15.5885i	−0.284747	+	0.493197i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.c.170.1		2
7.2	even	3		8281.2.a.c.1.1		1
7.4	even	3	inner	1183.2.e.c.508.1		2
7.5	odd	6		8281.2.a.g.1.1		1
13.4	even	6		91.2.h.a.16.1	yes	2
13.10	even	6		91.2.g.a.9.1	✓	2
13.12	even	2		1183.2.e.a.170.1		2
39.17	odd	6		819.2.s.a.289.1		2
39.23	odd	6		819.2.n.c.100.1		2
91.4	even	6		91.2.g.a.81.1	yes	2
91.10	odd	6		637.2.h.a.165.1		2
91.12	odd	6		8281.2.a.j.1.1		1
91.17	odd	6		637.2.g.a.263.1		2
91.23	even	6		637.2.f.b.295.1		2
91.25	even	6		1183.2.e.a.508.1		2
91.30	even	6		637.2.f.b.393.1		2
91.51	even	6		8281.2.a.i.1.1		1
91.62	odd	6		637.2.g.a.373.1		2
91.69	odd	6		637.2.h.a.471.1		2
91.75	odd	6		637.2.f.a.295.1		2
91.82	odd	6		637.2.f.a.393.1		2
91.88	even	6		91.2.h.a.74.1	yes	2
273.95	odd	6		819.2.n.c.172.1		2
273.179	odd	6		819.2.s.a.802.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.a.9.1	✓	2	13.10	even	6
91.2.g.a.81.1	yes	2	91.4	even	6
91.2.h.a.16.1	yes	2	13.4	even	6
91.2.h.a.74.1	yes	2	91.88	even	6
637.2.f.a.295.1		2	91.75	odd	6
637.2.f.a.393.1		2	91.82	odd	6
637.2.f.b.295.1		2	91.23	even	6
637.2.f.b.393.1		2	91.30	even	6
637.2.g.a.263.1		2	91.17	odd	6
637.2.g.a.373.1		2	91.62	odd	6
637.2.h.a.165.1		2	91.10	odd	6
637.2.h.a.471.1		2	91.69	odd	6
819.2.n.c.100.1		2	39.23	odd	6
819.2.n.c.172.1		2	273.95	odd	6
819.2.s.a.289.1		2	39.17	odd	6
819.2.s.a.802.1		2	273.179	odd	6
1183.2.e.a.170.1		2	13.12	even	2
1183.2.e.a.508.1		2	91.25	even	6
1183.2.e.c.170.1		2	1.1	even	1	trivial
1183.2.e.c.508.1		2	7.4	even	3	inner
8281.2.a.c.1.1		1	7.2	even	3
8281.2.a.g.1.1		1	7.5	odd	6
8281.2.a.i.1.1		1	91.51	even	6
8281.2.a.j.1.1		1	91.12	odd	6

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} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 3 q^{3} + q^{4} + 3 q^{5} + 6 q^{6} - q^{7} + 6 q^{8} - 6 q^{9} - 3 q^{10} - 3 q^{11} - 3 q^{12} + 4 q^{14} + 18 q^{15} + q^{16} + 2 q^{17} + 6 q^{18} - q^{19} + 6 q^{20} - 15 q^{21}+ \cdots + 36 q^{99}+O(q^{100}) \) 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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