LMFDB - Embedded newform 338.3.d.f.239.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [338,3,Mod(99,338)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(338, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("338.99");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	338.d (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.20983293538$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.612074651904.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 74x^{6} + 2067x^{4} - 25778x^{2} + 121801 $ x^8 - 74x^6 + 2067x^4 - 25778*x^2 + 121801
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.3
Root			$3.90972 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	338.239
Dual form			338.3.d.f.99.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +3.04369 q^{3} -2.00000i q^{4} +(-4.79174 + 4.79174i) q^{5} +(-3.04369 + 3.04369i) q^{6} +(-3.11407 - 3.11407i) q^{7} +(2.00000 + 2.00000i) q^{8} +0.264067 q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +3.04369 q^{3} -2.00000i q^{4} +(-4.79174 + 4.79174i) q^{5} +(-3.04369 + 3.04369i) q^{6} +(-3.11407 - 3.11407i) q^{7} +(2.00000 + 2.00000i) q^{8} +0.264067 q^{9} -9.58347i q^{10} +(-10.1578 - 10.1578i) q^{11} -6.08739i q^{12} +6.22814 q^{14} +(-14.5846 + 14.5846i) q^{15} -4.00000 q^{16} -24.2437i q^{17} +(-0.264067 + 0.264067i) q^{18} +(18.6375 - 18.6375i) q^{19} +(9.58347 + 9.58347i) q^{20} +(-9.47827 - 9.47827i) q^{21} +20.3155 q^{22} +6.28742i q^{23} +(6.08739 + 6.08739i) q^{24} -20.9215i q^{25} -26.5895 q^{27} +(-6.22814 + 6.22814i) q^{28} -22.2223 q^{29} -29.1692i q^{30} +(8.59518 - 8.59518i) q^{31} +(4.00000 - 4.00000i) q^{32} +(-30.9171 - 30.9171i) q^{33} +(24.2437 + 24.2437i) q^{34} +29.8436 q^{35} -0.528135i q^{36} +(-4.49432 - 4.49432i) q^{37} +37.2749i q^{38} -19.1669 q^{40} +(-51.5933 + 51.5933i) q^{41} +18.9565 q^{42} +31.1417i q^{43} +(-20.3155 + 20.3155i) q^{44} +(-1.26534 + 1.26534i) q^{45} +(-6.28742 - 6.28742i) q^{46} +(-7.65637 - 7.65637i) q^{47} -12.1748 q^{48} -29.6051i q^{49} +(20.9215 + 20.9215i) q^{50} -73.7905i q^{51} -33.7616 q^{53} +(26.5895 - 26.5895i) q^{54} +97.3466 q^{55} -12.4563i q^{56} +(56.7267 - 56.7267i) q^{57} +(22.2223 - 22.2223i) q^{58} +(-26.7083 - 26.7083i) q^{59} +(29.1692 + 29.1692i) q^{60} -23.0717 q^{61} +17.1904i q^{62} +(-0.822324 - 0.822324i) q^{63} +8.00000i q^{64} +61.8342 q^{66} +(76.0996 - 76.0996i) q^{67} -48.4875 q^{68} +19.1370i q^{69} +(-29.8436 + 29.8436i) q^{70} +(1.61682 - 1.61682i) q^{71} +(0.528135 + 0.528135i) q^{72} +(-38.1773 - 38.1773i) q^{73} +8.98865 q^{74} -63.6786i q^{75} +(-37.2749 - 37.2749i) q^{76} +63.2639i q^{77} -19.1299 q^{79} +(19.1669 - 19.1669i) q^{80} -83.3069 q^{81} -103.187i q^{82} +(-34.7720 + 34.7720i) q^{83} +(-18.9565 + 18.9565i) q^{84} +(116.170 + 116.170i) q^{85} +(-31.1417 - 31.1417i) q^{86} -67.6380 q^{87} -40.6310i q^{88} +(2.54160 + 2.54160i) q^{89} -2.53068i q^{90} +12.5748 q^{92} +(26.1611 - 26.1611i) q^{93} +15.3127 q^{94} +178.612i q^{95} +(12.1748 - 12.1748i) q^{96} +(-17.7967 + 17.7967i) q^{97} +(29.6051 + 29.6051i) q^{98} +(-2.68233 - 2.68233i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 6 q^{5} - 10 q^{7} + 16 q^{8} + 84 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 6 * q^5 - 10 * q^7 + 16 * q^8 + 84 * q^9	$ 8 q - 8 q^{2} - 6 q^{5} - 10 q^{7} + 16 q^{8} + 84 q^{9} - 42 q^{11} + 20 q^{14} - 60 q^{15} - 32 q^{16} - 84 q^{18} - 22 q^{19} + 12 q^{20} + 102 q^{21} + 84 q^{22} + 72 q^{27} - 20 q^{28} + 12 q^{29} - 32 q^{31} + 32 q^{32} - 54 q^{33} + 60 q^{34} + 156 q^{35} - 32 q^{37} - 24 q^{40} + 12 q^{41} - 204 q^{42} - 84 q^{44} + 102 q^{45} + 108 q^{46} - 60 q^{47} + 88 q^{50} - 132 q^{53} - 72 q^{54} + 324 q^{55} + 294 q^{57} - 12 q^{58} - 234 q^{59} + 120 q^{60} - 72 q^{61} + 156 q^{63} + 108 q^{66} + 14 q^{67} - 120 q^{68} - 156 q^{70} - 162 q^{71} + 168 q^{72} - 166 q^{73} + 64 q^{74} + 44 q^{76} - 96 q^{79} + 24 q^{80} + 24 q^{81} + 240 q^{83} + 204 q^{84} + 234 q^{85} - 132 q^{86} - 720 q^{87} - 210 q^{89} - 216 q^{92} + 444 q^{93} + 120 q^{94} - 146 q^{97} + 16 q^{98} - 252 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 - 6 * q^5 - 10 * q^7 + 16 * q^8 + 84 * q^9 - 42 * q^11 + 20 * q^14 - 60 * q^15 - 32 * q^16 - 84 * q^18 - 22 * q^19 + 12 * q^20 + 102 * q^21 + 84 * q^22 + 72 * q^27 - 20 * q^28 + 12 * q^29 - 32 * q^31 + 32 * q^32 - 54 * q^33 + 60 * q^34 + 156 * q^35 - 32 * q^37 - 24 * q^40 + 12 * q^41 - 204 * q^42 - 84 * q^44 + 102 * q^45 + 108 * q^46 - 60 * q^47 + 88 * q^50 - 132 * q^53 - 72 * q^54 + 324 * q^55 + 294 * q^57 - 12 * q^58 - 234 * q^59 + 120 * q^60 - 72 * q^61 + 156 * q^63 + 108 * q^66 + 14 * q^67 - 120 * q^68 - 156 * q^70 - 162 * q^71 + 168 * q^72 - 166 * q^73 + 64 * q^74 + 44 * q^76 - 96 * q^79 + 24 * q^80 + 24 * q^81 + 240 * q^83 + 204 * q^84 + 234 * q^85 - 132 * q^86 - 720 * q^87 - 210 * q^89 - 216 * q^92 + 444 * q^93 + 120 * q^94 - 146 * q^97 + 16 * q^98 - 252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$	3.04369			1.01456			0.507282	−	0.861780i	$-0.330650\pi$
$3$	3.04369			1.01456			0.507282	+	0.861780i	$0.330650\pi$
$4$		−	2.00000i		−	0.500000i
$5$	−4.79174	+	4.79174i	−0.958347	+	0.958347i	−0.999167	−	0.0408192i	$-0.987003\pi$
$5$	−4.79174	+	4.79174i	−0.958347	+	0.958347i	0.0408192	+	0.999167i	$0.487003\pi$
$6$	−3.04369	+	3.04369i	−0.507282	+	0.507282i
$7$	−3.11407	−	3.11407i	−0.444867	−	0.444867i	0.448777	−	0.893644i	$-0.351860\pi$
$7$	−3.11407	−	3.11407i	−0.444867	−	0.444867i	−0.893644	+	0.448777i	$0.851860\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	0.264067			0.0293408
$10$		−	9.58347i		−	0.958347i
$11$	−10.1578	−	10.1578i	−0.923433	−	0.923433i	0.0738374	−	0.997270i	$-0.476475\pi$
$11$	−10.1578	−	10.1578i	−0.923433	−	0.923433i	−0.997270	+	0.0738374i	$0.976475\pi$
$12$		−	6.08739i		−	0.507282i
$13$		0			0
$13$		0			0
$14$	6.22814			0.444867
$15$	−14.5846	+	14.5846i	−0.972305	+	0.972305i
$16$	−4.00000			−0.250000
$17$		−	24.2437i		−	1.42610i	−0.701112	−	0.713051i	$-0.747313\pi$
$17$		−	24.2437i		−	1.42610i	0.701112	−	0.713051i	$-0.252687\pi$
$18$	−0.264067	+	0.264067i	−0.0146704	+	0.0146704i
$19$	18.6375	−	18.6375i	0.980919	−	0.980919i	−0.0189027	−	0.999821i	$-0.506017\pi$
$19$	18.6375	−	18.6375i	0.980919	−	0.980919i	0.999821	+	0.0189027i	$0.00601729\pi$
$20$	9.58347	+	9.58347i	0.479174	+	0.479174i
$21$	−9.47827	−	9.47827i	−0.451346	−	0.451346i
$22$	20.3155			0.923433
$23$			6.28742i			0.273366i	0.990615	+	0.136683i	$0.0436442\pi$
$23$			6.28742i			0.273366i	−0.990615	+	0.136683i	$0.956356\pi$
$24$	6.08739	+	6.08739i	0.253641	+	0.253641i
$25$		−	20.9215i		−	0.836859i
$26$		0			0
$27$	−26.5895			−0.984796
$28$	−6.22814	+	6.22814i	−0.222433	+	0.222433i
$29$	−22.2223			−0.766288			−0.383144	−	0.923689i	$-0.625159\pi$
$29$	−22.2223			−0.766288			−0.383144	+	0.923689i	$0.625159\pi$
$30$		−	29.1692i		−	0.972305i
$31$	8.59518	−	8.59518i	0.277264	−	0.277264i	−0.554752	−	0.832016i	$-0.687187\pi$
$31$	8.59518	−	8.59518i	0.277264	−	0.277264i	0.832016	+	0.554752i	$0.187187\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	−30.9171	−	30.9171i	−0.936882	−	0.936882i
$34$	24.2437	+	24.2437i	0.713051	+	0.713051i
$35$	29.8436			0.852674
$36$		−	0.528135i		−	0.0146704i
$37$	−4.49432	−	4.49432i	−0.121468	−	0.121468i	0.643760	−	0.765228i	$-0.277374\pi$
$37$	−4.49432	−	4.49432i	−0.121468	−	0.121468i	−0.765228	+	0.643760i	$0.777374\pi$
$38$			37.2749i			0.980919i
$39$		0			0
$40$	−19.1669			−0.479174
$41$	−51.5933	+	51.5933i	−1.25837	+	1.25837i	−0.306504	+	0.951870i	$0.599159\pi$
$41$	−51.5933	+	51.5933i	−1.25837	+	1.25837i	−0.951870	+	0.306504i	$0.900841\pi$
$42$	18.9565			0.451346
$43$			31.1417i			0.724225i	0.932134	+	0.362113i	$0.117944\pi$
$43$			31.1417i			0.724225i	−0.932134	+	0.362113i	$0.882056\pi$
$44$	−20.3155	+	20.3155i	−0.461716	+	0.461716i
$45$	−1.26534	+	1.26534i	−0.0281187	+	0.0281187i
$46$	−6.28742	−	6.28742i	−0.136683	−	0.136683i
$47$	−7.65637	−	7.65637i	−0.162902	−	0.162902i	0.620949	−	0.783851i	$-0.286747\pi$
$47$	−7.65637	−	7.65637i	−0.162902	−	0.162902i	−0.783851	+	0.620949i	$0.786747\pi$
$48$	−12.1748			−0.253641
$49$		−	29.6051i		−	0.604187i
$50$	20.9215	+	20.9215i	0.418430	+	0.418430i
$51$		−	73.7905i		−	1.44687i
$52$		0			0
$53$	−33.7616			−0.637010			−0.318505	−	0.947921i	$-0.603181\pi$
$53$	−33.7616			−0.637010			−0.318505	+	0.947921i	$0.603181\pi$
$54$	26.5895	−	26.5895i	0.492398	−	0.492398i
$55$	97.3466			1.76994
$56$		−	12.4563i		−	0.222433i
$57$	56.7267	−	56.7267i	0.995205	−	0.995205i
$58$	22.2223	−	22.2223i	0.383144	−	0.383144i
$59$	−26.7083	−	26.7083i	−0.452683	−	0.452683i	0.443561	−	0.896244i	$-0.353715\pi$
$59$	−26.7083	−	26.7083i	−0.452683	−	0.452683i	−0.896244	+	0.443561i	$0.853715\pi$
$60$	29.1692	+	29.1692i	0.486153	+	0.486153i
$61$	−23.0717			−0.378225			−0.189113	−	0.981955i	$-0.560561\pi$
$61$	−23.0717			−0.378225			−0.189113	+	0.981955i	$0.560561\pi$
$62$			17.1904i			0.277264i
$63$	−0.822324	−	0.822324i	−0.0130528	−	0.0130528i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	61.8342			0.936882
$67$	76.0996	−	76.0996i	1.13581	−	1.13581i	0.146622	−	0.989193i	$-0.453160\pi$
$67$	76.0996	−	76.0996i	1.13581	−	1.13581i	0.989193	−	0.146622i	$-0.0468401\pi$
$68$	−48.4875			−0.713051
$69$			19.1370i			0.277348i
$70$	−29.8436	+	29.8436i	−0.426337	+	0.426337i
$71$	1.61682	−	1.61682i	0.0227721	−	0.0227721i	−0.695629	−	0.718401i	$-0.744874\pi$
$71$	1.61682	−	1.61682i	0.0227721	−	0.0227721i	0.718401	+	0.695629i	$0.244874\pi$
$72$	0.528135	+	0.528135i	0.00733521	+	0.00733521i
$73$	−38.1773	−	38.1773i	−0.522977	−	0.522977i	0.395492	−	0.918469i	$-0.370574\pi$
$73$	−38.1773	−	38.1773i	−0.522977	−	0.522977i	−0.918469	+	0.395492i	$0.870574\pi$
$74$	8.98865			0.121468
$75$		−	63.6786i		−	0.849047i
$76$	−37.2749	−	37.2749i	−0.490459	−	0.490459i
$77$			63.2639i			0.821610i
$78$		0			0
$79$	−19.1299			−0.242150			−0.121075	−	0.992643i	$-0.538634\pi$
$79$	−19.1299			−0.242150			−0.121075	+	0.992643i	$0.538634\pi$
$80$	19.1669	−	19.1669i	0.239587	−	0.239587i
$81$	−83.3069			−1.02848
$82$		−	103.187i		−	1.25837i
$83$	−34.7720	+	34.7720i	−0.418940	+	0.418940i	−0.884838	−	0.465898i	$-0.845731\pi$
$83$	−34.7720	+	34.7720i	−0.418940	+	0.418940i	0.465898	+	0.884838i	$0.345731\pi$
$84$	−18.9565	+	18.9565i	−0.225673	+	0.225673i
$85$	116.170	+	116.170i	1.36670	+	1.36670i
$86$	−31.1417	−	31.1417i	−0.362113	−	0.362113i
$87$	−67.6380			−0.777448
$88$		−	40.6310i		−	0.461716i
$89$	2.54160	+	2.54160i	0.0285573	+	0.0285573i	0.721241	−	0.692684i	$-0.243572\pi$
$89$	2.54160	+	2.54160i	0.0285573	+	0.0285573i	−0.692684	+	0.721241i	$0.743572\pi$
$90$		−	2.53068i		−	0.0281187i
$91$		0			0
$92$	12.5748			0.136683
$93$	26.1611	−	26.1611i	0.281302	−	0.281302i
$94$	15.3127			0.162902
$95$			178.612i			1.88012i
$96$	12.1748	−	12.1748i	0.126821	−	0.126821i
$97$	−17.7967	+	17.7967i	−0.183471	+	0.183471i	−0.792866	−	0.609395i	$-0.791412\pi$
$97$	−17.7967	+	17.7967i	−0.183471	+	0.183471i	0.609395	+	0.792866i	$0.291412\pi$
$98$	29.6051	+	29.6051i	0.302093	+	0.302093i
$99$	−2.68233	−	2.68233i	−0.0270943	−	0.0270943i
$100$	−41.8430			−0.418430
$101$			151.812i			1.50309i	0.659682	+	0.751545i	$0.270691\pi$
$101$			151.812i			1.50309i	−0.659682	+	0.751545i	$0.729309\pi$
$102$	73.7905	+	73.7905i	0.723436	+	0.723436i
$103$			17.3672i			0.168614i	0.996440	+	0.0843069i	$0.0268676\pi$
$103$			17.3672i			0.168614i	−0.996440	+	0.0843069i	$0.973132\pi$
$104$		0			0
$105$	90.8347			0.865093
$106$	33.7616	−	33.7616i	0.318505	−	0.318505i
$107$	53.1927			0.497128			0.248564	−	0.968615i	$-0.420041\pi$
$107$	53.1927			0.497128			0.248564	+	0.968615i	$0.420041\pi$
$108$			53.1790i			0.492398i
$109$	−53.3779	+	53.3779i	−0.489705	+	0.489705i	−0.908213	−	0.418508i	$-0.862553\pi$
$109$	−53.3779	+	53.3779i	−0.489705	+	0.489705i	0.418508	+	0.908213i	$0.362553\pi$
$110$	−97.3466	+	97.3466i	−0.884969	+	0.884969i
$111$	−13.6793	−	13.6793i	−0.123237	−	0.123237i
$112$	12.4563	+	12.4563i	0.111217	+	0.111217i
$113$	36.2266			0.320590			0.160295	−	0.987069i	$-0.448756\pi$
$113$	36.2266			0.320590			0.160295	+	0.987069i	$0.448756\pi$
$114$			113.453i			0.995205i
$115$	−30.1277	−	30.1277i	−0.261980	−	0.261980i
$116$			44.4447i			0.383144i
$117$		0			0
$118$	53.4166			0.452683
$119$	−75.4966	+	75.4966i	−0.634426	+	0.634426i
$120$	−58.3383			−0.486153
$121$			85.3603i			0.705457i
$122$	23.0717	−	23.0717i	0.189113	−	0.189113i
$123$	−157.034	+	157.034i	−1.27670	+	1.27670i
$124$	−17.1904	−	17.1904i	−0.138632	−	0.138632i
$125$	−19.5432	−	19.5432i	−0.156346	−	0.156346i
$126$	1.64465			0.0130528
$127$			133.085i			1.04791i	0.851745	+	0.523957i	$0.175545\pi$
$127$			133.085i			1.04791i	−0.851745	+	0.523957i	$0.824455\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$			94.7857i			0.734773i
$130$		0			0
$131$	38.2739			0.292167			0.146083	−	0.989272i	$-0.453333\pi$
$131$	38.2739			0.292167			0.146083	+	0.989272i	$0.453333\pi$
$132$	−61.8342	+	61.8342i	−0.468441	+	0.468441i
$133$	−116.077			−0.872757
$134$			152.199i			1.13581i
$135$	127.410	−	127.410i	0.943777	−	0.943777i
$136$	48.4875	−	48.4875i	0.356525	−	0.356525i
$137$	−5.68174	−	5.68174i	−0.0414725	−	0.0414725i	0.686066	−	0.727539i	$-0.259336\pi$
$137$	−5.68174	−	5.68174i	−0.0414725	−	0.0414725i	−0.727539	+	0.686066i	$0.759336\pi$
$138$	−19.1370	−	19.1370i	−0.138674	−	0.138674i
$139$	−243.961			−1.75512			−0.877558	−	0.479470i	$-0.840829\pi$
$139$	−243.961			−1.75512			−0.877558	+	0.479470i	$0.840829\pi$
$140$		−	59.6872i		−	0.426337i
$141$	−23.3036	−	23.3036i	−0.165274	−	0.165274i
$142$			3.23364i			0.0227721i
$143$		0			0
$144$	−1.05627			−0.00733521
$145$	106.484	−	106.484i	0.734370	−	0.734370i
$146$	76.3546			0.522977
$147$		−	90.1090i		−	0.612986i
$148$	−8.98865	+	8.98865i	−0.0607341	+	0.0607341i
$149$	133.736	−	133.736i	0.897559	−	0.897559i	−0.0976609	−	0.995220i	$-0.531136\pi$
$149$	133.736	−	133.736i	0.897559	−	0.897559i	0.995220	+	0.0976609i	$0.0311361\pi$
$150$	63.6786	+	63.6786i	0.424524	+	0.424524i
$151$	70.5995	+	70.5995i	0.467546	+	0.467546i	0.901119	−	0.433573i	$-0.142747\pi$
$151$	70.5995	+	70.5995i	0.467546	+	0.467546i	−0.433573	+	0.901119i	$0.642747\pi$
$152$	74.5498			0.490459
$153$		−	6.40198i		−	0.0418430i
$154$	−63.2639	−	63.2639i	−0.410805	−	0.410805i
$155$			82.3717i			0.531430i
$156$		0			0
$157$	176.794			1.12608			0.563038	−	0.826431i	$-0.309632\pi$
$157$	176.794			1.12608			0.563038	+	0.826431i	$0.309632\pi$
$158$	19.1299	−	19.1299i	0.121075	−	0.121075i
$159$	−102.760			−0.646288
$160$			38.3339i			0.239587i
$161$	19.5795	−	19.5795i	0.121612	−	0.121612i
$162$	83.3069	−	83.3069i	0.514240	−	0.514240i
$163$	−85.7350	−	85.7350i	−0.525981	−	0.525981i	0.393390	−	0.919372i	$-0.371302\pi$
$163$	−85.7350	−	85.7350i	−0.525981	−	0.525981i	−0.919372	+	0.393390i	$0.871302\pi$
$164$	103.187	+	103.187i	0.629187	+	0.629187i
$165$	296.293			1.79572
$166$		−	69.5441i		−	0.418940i
$167$	209.805	+	209.805i	1.25632	+	1.25632i	0.952839	+	0.303477i	$0.0981476\pi$
$167$	209.805	+	209.805i	1.25632	+	1.25632i	0.303477	+	0.952839i	$0.401852\pi$
$168$		−	37.9131i		−	0.225673i
$169$		0			0
$170$	−232.339			−1.36670
$171$	4.92154	−	4.92154i	0.0287810	−	0.0287810i
$172$	62.2834			0.362113
$173$		−	278.490i		−	1.60977i	−0.593432	−	0.804884i	$-0.702228\pi$
$173$		−	278.490i		−	1.60977i	0.593432	−	0.804884i	$-0.297772\pi$
$174$	67.6380	−	67.6380i	0.388724	−	0.388724i
$175$	−65.1509	+	65.1509i	−0.372291	+	0.372291i
$176$	40.6310	+	40.6310i	0.230858	+	0.230858i
$177$	−81.2919	−	81.2919i	−0.459276	−	0.459276i
$178$	−5.08321			−0.0285573
$179$		−	78.7547i		−	0.439971i	−0.975503	−	0.219985i	$-0.929399\pi$
$179$		−	78.7547i		−	0.439971i	0.975503	−	0.219985i	$-0.0706009\pi$
$180$	2.53068	+	2.53068i	0.0140593	+	0.0140593i
$181$		−	200.758i		−	1.10916i	−0.832130	−	0.554581i	$-0.812879\pi$
$181$		−	200.758i		−	1.10916i	0.832130	−	0.554581i	$-0.187121\pi$
$182$		0			0
$183$	−70.2233			−0.383734
$184$	−12.5748	+	12.5748i	−0.0683415	+	0.0683415i
$185$	43.0712			0.232818
$186$			52.3222i			0.281302i
$187$	−246.262	+	246.262i	−1.31691	+	1.31691i
$188$	−15.3127	+	15.3127i	−0.0814508	+	0.0814508i
$189$	82.8015	+	82.8015i	0.438103	+	0.438103i
$190$	−178.612	−	178.612i	−0.940061	−	0.940061i
$191$	40.5301			0.212199			0.106100	−	0.994356i	$-0.466164\pi$
$191$	40.5301			0.212199			0.106100	+	0.994356i	$0.466164\pi$
$192$			24.3495i			0.126821i
$193$	−102.596	−	102.596i	−0.531588	−	0.531588i	0.389457	−	0.921045i	$-0.372663\pi$
$193$	−102.596	−	102.596i	−0.531588	−	0.531588i	−0.921045	+	0.389457i	$0.872663\pi$
$194$		−	35.5934i		−	0.183471i
$195$		0			0
$196$	−59.2103			−0.302093
$197$	109.482	−	109.482i	0.555745	−	0.555745i	−0.372348	−	0.928093i	$-0.621447\pi$
$197$	109.482	−	109.482i	0.555745	−	0.555745i	0.928093	+	0.372348i	$0.121447\pi$
$198$	5.36467			0.0270943
$199$		−	260.350i		−	1.30829i	−0.756368	−	0.654147i	$-0.773028\pi$
$199$		−	260.350i		−	1.30829i	0.756368	−	0.654147i	$-0.226972\pi$
$200$	41.8430	−	41.8430i	0.209215	−	0.209215i
$201$	231.624	−	231.624i	1.15236	−	1.15236i
$202$	−151.812	−	151.812i	−0.751545	−	0.751545i
$203$	69.2019	+	69.2019i	0.340896	+	0.340896i
$204$	−147.581			−0.723436
$205$		−	494.443i		−	2.41192i
$206$	−17.3672	−	17.3672i	−0.0843069	−	0.0843069i
$207$			1.66030i			0.00802079i
$208$		0			0
$209$	−378.630			−1.81162
$210$	−90.8347	+	90.8347i	−0.432546	+	0.432546i
$211$	416.406			1.97349			0.986744	−	0.162283i	$-0.0518858\pi$
$211$	416.406			1.97349			0.986744	+	0.162283i	$0.0518858\pi$
$212$			67.5231i			0.318505i
$213$	4.92110	−	4.92110i	0.0231037	−	0.0231037i
$214$	−53.1927	+	53.1927i	−0.248564	+	0.248564i
$215$	−149.223	−	149.223i	−0.694059	−	0.694059i
$216$	−53.1790	−	53.1790i	−0.246199	−	0.246199i
$217$	−53.5320			−0.246691
$218$		−	106.756i		−	0.489705i
$219$	−116.200	−	116.200i	−0.530594	−	0.530594i
$220$		−	194.693i		−	0.884969i
$221$		0			0
$222$	27.3587			0.123237
$223$	−144.463	+	144.463i	−0.647817	+	0.647817i	−0.952465	−	0.304648i	$-0.901461\pi$
$223$	−144.463	+	144.463i	−0.647817	+	0.647817i	0.304648	+	0.952465i	$0.401461\pi$
$224$	−24.9126			−0.111217
$225$		−	5.52468i		−	0.0245541i
$226$	−36.2266	+	36.2266i	−0.160295	+	0.160295i
$227$	−78.6605	+	78.6605i	−0.346522	+	0.346522i	−0.858812	−	0.512290i	$-0.828797\pi$
$227$	−78.6605	+	78.6605i	−0.346522	+	0.346522i	0.512290	+	0.858812i	$0.328797\pi$
$228$	−113.453	−	113.453i	−0.497603	−	0.497603i
$229$	212.309	+	212.309i	0.927114	+	0.927114i	0.997519	−	0.0704045i	$-0.0224290\pi$
$229$	212.309	+	212.309i	0.927114	+	0.927114i	−0.0704045	+	0.997519i	$0.522429\pi$
$230$	60.2553			0.261980
$231$			192.556i			0.833576i
$232$	−44.4447	−	44.4447i	−0.191572	−	0.191572i
$233$		−	46.5826i		−	0.199925i	−0.994991	−	0.0999627i	$-0.968128\pi$
$233$		−	46.5826i		−	0.199925i	0.994991	−	0.0999627i	$-0.0318723\pi$
$234$		0			0
$235$	73.3746			0.312233
$236$	−53.4166	+	53.4166i	−0.226342	+	0.226342i
$237$	−58.2255			−0.245677
$238$		−	150.993i		−	0.634426i
$239$	−138.309	+	138.309i	−0.578698	+	0.578698i	−0.934544	−	0.355847i	$-0.884192\pi$
$239$	−138.309	+	138.309i	−0.578698	+	0.578698i	0.355847	+	0.934544i	$0.384192\pi$
$240$	58.3383	−	58.3383i	0.243076	−	0.243076i
$241$	158.998	+	158.998i	0.659741	+	0.659741i	0.955319	−	0.295578i	$-0.0955121\pi$
$241$	158.998	+	158.998i	0.659741	+	0.659741i	−0.295578	+	0.955319i	$0.595512\pi$
$242$	−85.3603	−	85.3603i	−0.352728	−	0.352728i
$243$	−14.2551			−0.0586629
$244$			46.1435i			0.189113i
$245$	141.860	+	141.860i	0.579021	+	0.579021i
$246$		−	314.068i		−	1.27670i
$247$		0			0
$248$	34.3807			0.138632
$249$	−105.835	+	105.835i	−0.425042	+	0.425042i
$250$	39.0864			0.156346
$251$			3.49014i			0.0139049i	0.999976	+	0.00695247i	$0.00221306\pi$
$251$			3.49014i			0.0139049i	−0.999976	+	0.00695247i	$0.997787\pi$
$252$	−1.64465	+	1.64465i	−0.00652638	+	0.00652638i
$253$	63.8661	−	63.8661i	0.252435	−	0.252435i
$254$	−133.085	−	133.085i	−0.523957	−	0.523957i
$255$	353.584	+	353.584i	1.38661	+	1.38661i
$256$	16.0000			0.0625000
$257$			185.413i			0.721452i	0.932672	+	0.360726i	$0.117471\pi$
$257$			185.413i			0.721452i	−0.932672	+	0.360726i	$0.882529\pi$
$258$	−94.7857	−	94.7857i	−0.367387	−	0.367387i
$259$			27.9913i			0.108074i
$260$		0			0
$261$	−5.86820			−0.0224835
$262$	−38.2739	+	38.2739i	−0.146083	+	0.146083i
$263$	−187.352			−0.712363			−0.356182	−	0.934417i	$-0.615922\pi$
$263$	−187.352			−0.712363			−0.356182	+	0.934417i	$0.615922\pi$
$264$		−	123.668i		−	0.468441i
$265$	161.776	−	161.776i	0.610477	−	0.610477i
$266$	116.077	−	116.077i	0.436378	−	0.436378i
$267$	7.73586	+	7.73586i	0.0289733	+	0.0289733i
$268$	−152.199	−	152.199i	−0.567907	−	0.567907i
$269$	344.012			1.27885			0.639427	−	0.768852i	$-0.279172\pi$
$269$	344.012			1.27885			0.639427	+	0.768852i	$0.279172\pi$
$270$			254.820i			0.943777i
$271$	17.1517	+	17.1517i	0.0632903	+	0.0632903i	0.738043	−	0.674753i	$-0.235750\pi$
$271$	17.1517	+	17.1517i	0.0632903	+	0.0632903i	−0.674753	+	0.738043i	$0.735750\pi$
$272$			96.9749i			0.356525i
$273$		0			0
$274$	11.3635			0.0414725
$275$	−212.515	+	212.515i	−0.772783	+	0.772783i
$276$	38.2740			0.138674
$277$		−	494.891i		−	1.78661i	−0.449450	−	0.893306i	$-0.648380\pi$
$277$		−	494.891i		−	1.78661i	0.449450	−	0.893306i	$-0.351620\pi$
$278$	243.961	−	243.961i	0.877558	−	0.877558i
$279$	2.26971	−	2.26971i	0.00813515	−	0.00813515i
$280$	59.6872	+	59.6872i	0.213169	+	0.213169i
$281$	−145.653	−	145.653i	−0.518337	−	0.518337i	0.398731	−	0.917068i	$-0.369451\pi$
$281$	−145.653	−	145.653i	−0.518337	−	0.518337i	−0.917068	+	0.398731i	$0.869451\pi$
$282$	46.6073			0.165274
$283$		−	430.214i		−	1.52019i	−0.649811	−	0.760096i	$-0.725152\pi$
$283$		−	430.214i		−	1.52019i	0.649811	−	0.760096i	$-0.274848\pi$
$284$	−3.23364	−	3.23364i	−0.0113860	−	0.0113860i
$285$			543.639i			1.90750i
$286$		0			0
$287$	321.330			1.11962
$288$	1.05627	−	1.05627i	0.00366760	−	0.00366760i
$289$	−298.758			−1.03377
$290$			212.967i			0.734370i
$291$	−54.1677	+	54.1677i	−0.186143	+	0.186143i
$292$	−76.3546	+	76.3546i	−0.261488	+	0.261488i
$293$	−67.0896	−	67.0896i	−0.228975	−	0.228975i	0.583290	−	0.812264i	$-0.301765\pi$
$293$	−67.0896	−	67.0896i	−0.228975	−	0.228975i	−0.812264	+	0.583290i	$0.801765\pi$
$294$	90.1090	+	90.1090i	0.306493	+	0.306493i
$295$	255.958			0.867656
$296$		−	17.9773i		−	0.0607341i
$297$	270.090	+	270.090i	0.909393	+	0.909393i
$298$			267.473i			0.897559i
$299$		0			0
$300$	−127.357			−0.424524
$301$	96.9774	−	96.9774i	0.322184	−	0.322184i
$302$	−141.199			−0.467546
$303$			462.069i			1.52498i
$304$	−74.5498	+	74.5498i	−0.245230	+	0.245230i
$305$	110.554	−	110.554i	0.362471	−	0.362471i
$306$	6.40198	+	6.40198i	0.0209215	+	0.0209215i
$307$	−210.306	−	210.306i	−0.685035	−	0.685035i	0.276095	−	0.961130i	$-0.410959\pi$
$307$	−210.306	−	210.306i	−0.685035	−	0.685035i	−0.961130	+	0.276095i	$0.910959\pi$
$308$	126.528			0.410805
$309$			52.8605i			0.171069i
$310$	−82.3717	−	82.3717i	−0.265715	−	0.265715i
$311$		−	246.623i		−	0.793001i	−0.918035	−	0.396500i	$-0.870225\pi$
$311$		−	246.623i		−	0.793001i	0.918035	−	0.396500i	$-0.129775\pi$
$312$		0			0
$313$	−118.526			−0.378679			−0.189339	−	0.981912i	$-0.560635\pi$
$313$	−118.526			−0.378679			−0.189339	+	0.981912i	$0.560635\pi$
$314$	−176.794	+	176.794i	−0.563038	+	0.563038i
$315$	7.88072			0.0250182
$316$			38.2597i			0.121075i
$317$	284.814	−	284.814i	0.898466	−	0.898466i	−0.0968348	−	0.995300i	$-0.530872\pi$
$317$	284.814	−	284.814i	0.898466	−	0.898466i	0.995300	+	0.0968348i	$0.0308718\pi$
$318$	102.760	−	102.760i	0.323144	−	0.323144i
$319$	225.729	+	225.729i	0.707615	+	0.707615i
$320$	−38.3339	−	38.3339i	−0.119793	−	0.119793i
$321$	161.902			0.504369
$322$			39.1589i			0.121612i
$323$	−451.841	−	451.841i	−1.39889	−	1.39889i
$324$			166.614i			0.514240i
$325$		0			0
$326$	171.470			0.525981
$327$	−162.466	+	162.466i	−0.496838	+	0.496838i
$328$	−206.373			−0.629187
$329$			47.6849i			0.144939i
$330$	−296.293	+	296.293i	−0.897858	+	0.897858i
$331$	−317.064	+	317.064i	−0.957898	+	0.957898i	−0.999149	−	0.0412510i	$-0.986866\pi$
$331$	−317.064	+	317.064i	−0.957898	+	0.957898i	0.0412510	+	0.999149i	$0.486866\pi$
$332$	69.5441	+	69.5441i	0.209470	+	0.209470i
$333$	−1.18680	−	1.18680i	−0.00356398	−	0.00356398i
$334$	−419.609			−1.25632
$335$			729.298i			2.17701i
$336$	37.9131	+	37.9131i	0.112837	+	0.112837i
$337$		−	474.455i		−	1.40788i	−0.710260	−	0.703939i	$-0.751423\pi$
$337$		−	474.455i		−	1.40788i	0.710260	−	0.703939i	$-0.248577\pi$
$338$		0			0
$339$	110.263			0.325259
$340$	232.339	−	232.339i	0.683350	−	0.683350i
$341$	−174.616			−0.512069
$342$			9.84309i			0.0287810i
$343$	−244.782	+	244.782i	−0.713650	+	0.713650i
$344$	−62.2834	+	62.2834i	−0.181056	+	0.181056i
$345$	−91.6994	−	91.6994i	−0.265795	−	0.265795i
$346$	278.490	+	278.490i	0.804884	+	0.804884i
$347$	−533.636			−1.53785			−0.768927	−	0.639336i	$-0.779209\pi$
$347$	−533.636			−1.53785			−0.768927	+	0.639336i	$0.779209\pi$
$348$			135.276i			0.388724i
$349$	191.046	+	191.046i	0.547409	+	0.547409i	0.925690	−	0.378282i	$-0.123485\pi$
$349$	191.046	+	191.046i	0.547409	+	0.547409i	−0.378282	+	0.925690i	$0.623485\pi$
$350$		−	130.302i		−	0.372291i
$351$		0			0
$352$	−81.2621			−0.230858
$353$	249.596	−	249.596i	0.707072	−	0.707072i	−0.258846	−	0.965919i	$-0.583342\pi$
$353$	249.596	−	249.596i	0.707072	−	0.707072i	0.965919	+	0.258846i	$0.0833423\pi$
$354$	162.584			0.459276
$355$			15.4947i			0.0436471i
$356$	5.08321	−	5.08321i	0.0142787	−	0.0142787i
$357$	−229.789	+	229.789i	−0.643666	+	0.643666i
$358$	78.7547	+	78.7547i	0.219985	+	0.219985i
$359$	−116.092	−	116.092i	−0.323375	−	0.323375i	0.526685	−	0.850060i	$-0.323435\pi$
$359$	−116.092	−	116.092i	−0.323375	−	0.323375i	−0.850060	+	0.526685i	$0.823435\pi$
$360$	−5.06137			−0.0140593
$361$		−	333.709i		−	0.924403i
$362$	200.758	+	200.758i	0.554581	+	0.554581i
$363$			259.810i			0.715731i
$364$		0			0
$365$	365.871			1.00239
$366$	70.2233	−	70.2233i	0.191867	−	0.191867i
$367$	686.325			1.87009			0.935047	−	0.354523i	$-0.115357\pi$
$367$	686.325			1.87009			0.935047	+	0.354523i	$0.115357\pi$
$368$		−	25.1497i		−	0.0683415i
$369$	−13.6241	+	13.6241i	−0.0369217	+	0.0369217i
$370$	−43.0712	+	43.0712i	−0.116409	+	0.116409i
$371$	105.136	+	105.136i	0.283385	+	0.283385i
$372$	−52.3222	−	52.3222i	−0.140651	−	0.140651i
$373$	−617.271			−1.65488			−0.827441	−	0.561552i	$-0.810204\pi$
$373$	−617.271			−1.65488			−0.827441	+	0.561552i	$0.810204\pi$
$374$		−	492.524i		−	1.31691i
$375$	−59.4835	−	59.4835i	−0.158623	−	0.158623i
$376$		−	30.6255i		−	0.0814508i
$377$		0			0
$378$	−165.603			−0.438103
$379$	379.482	−	379.482i	1.00127	−	1.00127i	0.00127208	−	0.999999i	$-0.499595\pi$
$379$	379.482	−	379.482i	1.00127	−	1.00127i	0.999999	−	0.00127208i	$-0.000404916\pi$
$380$	357.223			0.940061
$381$			405.070i			1.06318i
$382$	−40.5301	+	40.5301i	−0.106100	+	0.106100i
$383$	−185.253	+	185.253i	−0.483690	+	0.483690i	−0.906308	−	0.422618i	$-0.861111\pi$
$383$	−185.253	+	185.253i	−0.483690	+	0.483690i	0.422618	+	0.906308i	$0.361111\pi$
$384$	−24.3495	−	24.3495i	−0.0634103	−	0.0634103i
$385$	−303.144	−	303.144i	−0.787387	−	0.787387i
$386$	205.193			0.531588
$387$			8.22350i			0.0212494i
$388$	35.5934	+	35.5934i	0.0917356	+	0.0917356i
$389$			184.591i			0.474527i	0.971445	+	0.237264i	$0.0762505\pi$
$389$			184.591i			0.474527i	−0.971445	+	0.237264i	$0.923749\pi$
$390$		0			0
$391$	152.431			0.389848
$392$	59.2103	−	59.2103i	0.151047	−	0.151047i
$393$	116.494			0.296422
$394$			218.963i			0.555745i
$395$	91.6653	−	91.6653i	0.232064	−	0.232064i
$396$	−5.36467	+	5.36467i	−0.0135471	+	0.0135471i
$397$	−179.508	−	179.508i	−0.452162	−	0.452162i	0.443910	−	0.896072i	$-0.353591\pi$
$397$	−179.508	−	179.508i	−0.452162	−	0.452162i	−0.896072	+	0.443910i	$0.853591\pi$
$398$	260.350	+	260.350i	0.654147	+	0.654147i
$399$	−353.302			−0.885468
$400$			83.6859i			0.209215i
$401$	−191.654	−	191.654i	−0.477941	−	0.477941i	0.426532	−	0.904473i	$-0.359735\pi$
$401$	−191.654	−	191.654i	−0.477941	−	0.477941i	−0.904473	+	0.426532i	$0.859735\pi$
$402$			463.248i			1.15236i
$403$		0			0
$404$	303.624			0.751545
$405$	399.185	−	399.185i	0.985641	−	0.985641i
$406$	−138.404			−0.340896
$407$			91.3046i			0.224336i
$408$	147.581	−	147.581i	0.361718	−	0.361718i
$409$	111.635	−	111.635i	0.272946	−	0.272946i	−0.557339	−	0.830285i	$-0.688178\pi$
$409$	111.635	−	111.635i	0.272946	−	0.272946i	0.830285	+	0.557339i	$0.188178\pi$
$410$	494.443	+	494.443i	1.20596	+	1.20596i
$411$	−17.2935	−	17.2935i	−0.0420766	−	0.0420766i
$412$	34.7344			0.0843069
$413$			166.343i			0.402768i
$414$	−1.66030	−	1.66030i	−0.00401039	−	0.00401039i
$415$		−	333.237i		−	0.802980i
$416$		0			0
$417$	−742.543			−1.78068
$418$	378.630	−	378.630i	0.905812	−	0.905812i
$419$	−652.476			−1.55722			−0.778611	−	0.627507i	$-0.784075\pi$
$419$	−652.476			−1.55722			−0.778611	+	0.627507i	$0.784075\pi$
$420$		−	181.669i		−	0.432546i
$421$	−294.576	+	294.576i	−0.699704	+	0.699704i	−0.964347	−	0.264642i	$-0.914746\pi$
$421$	−294.576	+	294.576i	−0.699704	+	0.699704i	0.264642	+	0.964347i	$0.414746\pi$
$422$	−416.406	+	416.406i	−0.986744	+	0.986744i
$423$	−2.02180	−	2.02180i	−0.00477966	−	0.00477966i
$424$	−67.5231	−	67.5231i	−0.159253	−	0.159253i
$425$	−507.215			−1.19345
$426$			9.84219i			0.0231037i
$427$	71.8470	+	71.8470i	0.168260	+	0.168260i
$428$		−	106.385i		−	0.248564i
$429$		0			0
$430$	298.445			0.694059
$431$	−49.9398	+	49.9398i	−0.115870	+	0.115870i	−0.762664	−	0.646795i	$-0.776109\pi$
$431$	−49.9398	+	49.9398i	−0.115870	+	0.115870i	0.646795	+	0.762664i	$0.276109\pi$
$432$	106.358			0.246199
$433$			466.918i			1.07833i	0.842199	+	0.539167i	$0.181261\pi$
$433$			466.918i			1.07833i	−0.842199	+	0.539167i	$0.818739\pi$
$434$	53.5320	−	53.5320i	0.123346	−	0.123346i
$435$	324.103	−	324.103i	0.745066	−	0.745066i
$436$	106.756	+	106.756i	0.244853	+	0.244853i
$437$	117.182	+	117.182i	0.268150	+	0.268150i
$438$	232.400			0.530594
$439$		−	119.600i		−	0.272438i	−0.990679	−	0.136219i	$-0.956505\pi$
$439$		−	119.600i		−	0.272438i	0.990679	−	0.136219i	$-0.0434951\pi$
$440$	194.693	+	194.693i	0.442485	+	0.442485i
$441$		−	7.81775i		−	0.0177273i
$442$		0			0
$443$	−56.7213			−0.128039			−0.0640195	−	0.997949i	$-0.520392\pi$
$443$	−56.7213			−0.128039			−0.0640195	+	0.997949i	$0.520392\pi$
$444$	−27.3587	+	27.3587i	−0.0616187	+	0.0616187i
$445$	−24.3574			−0.0547357
$446$		−	288.926i		−	0.647817i
$447$	407.052	−	407.052i	0.910631	−	0.910631i
$448$	24.9126	−	24.9126i	0.0556084	−	0.0556084i
$449$	−130.674	−	130.674i	−0.291033	−	0.291033i	0.546455	−	0.837488i	$-0.315977\pi$
$449$	−130.674	−	130.674i	−0.291033	−	0.291033i	−0.837488	+	0.546455i	$0.815977\pi$
$450$	5.52468	+	5.52468i	0.0122771	+	0.0122771i
$451$	1048.14			2.32405
$452$		−	72.4533i		−	0.160295i
$453$	214.883	+	214.883i	0.474356	+	0.474356i
$454$		−	157.321i		−	0.346522i
$455$		0			0
$456$	226.907			0.497603
$457$	−209.389	+	209.389i	−0.458182	+	0.458182i	−0.898058	−	0.439876i	$-0.855022\pi$
$457$	−209.389	+	209.389i	−0.458182	+	0.458182i	0.439876	+	0.898058i	$0.355022\pi$
$458$	−424.618			−0.927114
$459$			644.629i			1.40442i
$460$	−60.2553	+	60.2553i	−0.130990	+	0.130990i
$461$	436.453	−	436.453i	0.946752	−	0.946752i	−0.0519000	−	0.998652i	$-0.516528\pi$
$461$	436.453	−	436.453i	0.946752	−	0.946752i	0.998652	+	0.0519000i	$0.0165277\pi$
$462$	−192.556	−	192.556i	−0.416788	−	0.416788i
$463$	−198.699	−	198.699i	−0.429156	−	0.429156i	0.459185	−	0.888341i	$-0.348142\pi$
$463$	−198.699	−	198.699i	−0.429156	−	0.429156i	−0.888341	+	0.459185i	$0.848142\pi$
$464$	88.8894			0.191572
$465$			250.714i			0.539170i
$466$	46.5826	+	46.5826i	0.0999627	+	0.0999627i
$467$			522.015i			1.11781i	0.829233	+	0.558903i	$0.188777\pi$
$467$			522.015i			1.11781i	−0.829233	+	0.558903i	$0.811223\pi$
$468$		0			0
$469$	−473.959			−1.01057
$470$	−73.3746	+	73.3746i	−0.156116	+	0.156116i
$471$	538.107			1.14248
$472$		−	106.833i		−	0.226342i
$473$	316.330	−	316.330i	0.668773	−	0.668773i
$474$	58.2255	−	58.2255i	0.122839	−	0.122839i
$475$	−389.923	−	389.923i	−0.820891	−	0.820891i
$476$	150.993	+	150.993i	0.317213	+	0.317213i
$477$	−8.91532			−0.0186904
$478$		−	276.617i		−	0.578698i
$479$	240.091	+	240.091i	0.501234	+	0.501234i	0.911821	−	0.410587i	$-0.134676\pi$
$479$	240.091	+	240.091i	0.501234	+	0.501234i	−0.410587	+	0.911821i	$0.634676\pi$
$480$			116.677i			0.243076i
$481$		0			0
$482$	−317.995			−0.659741
$483$	59.5939	−	59.5939i	0.123383	−	0.123383i
$484$	170.721			0.352728
$485$		−	170.554i		−	0.351658i
$486$	14.2551	−	14.2551i	0.0293314	−	0.0293314i
$487$	152.582	−	152.582i	0.313310	−	0.313310i	−0.532880	−	0.846191i	$-0.678890\pi$
$487$	152.582	−	152.582i	0.313310	−	0.313310i	0.846191	+	0.532880i	$0.178890\pi$
$488$	−46.1435	−	46.1435i	−0.0945563	−	0.0945563i
$489$	−260.951	−	260.951i	−0.533642	−	0.533642i
$490$	−283.720			−0.579021
$491$			555.234i			1.13082i	0.824809	+	0.565412i	$0.191283\pi$
$491$			555.234i			1.13082i	−0.824809	+	0.565412i	$0.808717\pi$
$492$	314.068	+	314.068i	0.638350	+	0.638350i
$493$			538.753i			1.09280i
$494$		0			0
$495$	25.7061			0.0519315
$496$	−34.3807	+	34.3807i	−0.0693160	+	0.0693160i
$497$	−10.0698			−0.0202611
$498$		−	211.671i		−	0.425042i
$499$	401.619	−	401.619i	0.804847	−	0.804847i	−0.179002	−	0.983849i	$-0.557287\pi$
$499$	401.619	−	401.619i	0.804847	−	0.804847i	0.983849	+	0.179002i	$0.0572868\pi$
$500$	−39.0864	+	39.0864i	−0.0781728	+	0.0781728i
$501$	638.581	+	638.581i	1.27461	+	1.27461i
$502$	−3.49014	−	3.49014i	−0.00695247	−	0.00695247i
$503$	−393.667			−0.782637			−0.391319	−	0.920255i	$-0.627981\pi$
$503$	−393.667			−0.782637			−0.391319	+	0.920255i	$0.627981\pi$
$504$		−	3.28930i		−	0.00652638i
$505$	−727.443	−	727.443i	−1.44048	−	1.44048i
$506$			127.732i			0.252435i
$507$		0			0
$508$	266.170			0.523957
$509$	−308.986	+	308.986i	−0.607045	+	0.607045i	−0.942173	−	0.335127i	$-0.891221\pi$
$509$	−308.986	+	308.986i	−0.607045	+	0.607045i	0.335127	+	0.942173i	$0.391221\pi$
$510$	−707.169			−1.38661
$511$			237.774i			0.465310i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−495.561	+	495.561i	−0.966005	+	0.966005i
$514$	−185.413	−	185.413i	−0.360726	−	0.360726i
$515$	−83.2191	−	83.2191i	−0.161591	−	0.161591i
$516$	189.571			0.367387
$517$			155.543i			0.300857i
$518$	−27.9913	−	27.9913i	−0.0540372	−	0.0540372i
$519$		−	847.638i		−	1.63321i
$520$		0			0
$521$	947.876			1.81934			0.909669	−	0.415333i	$-0.136335\pi$
$521$	947.876			1.81934			0.909669	+	0.415333i	$0.136335\pi$
$522$	5.86820	−	5.86820i	0.0112418	−	0.0112418i
$523$	−136.693			−0.261364			−0.130682	−	0.991424i	$-0.541717\pi$
$523$	−136.693			−0.261364			−0.130682	+	0.991424i	$0.541717\pi$
$524$		−	76.5477i		−	0.146083i
$525$	−198.299	+	198.299i	−0.377713	+	0.377713i
$526$	187.352	−	187.352i	0.356182	−	0.356182i
$527$	−208.379	−	208.379i	−0.395406	−	0.395406i
$528$	123.668	+	123.668i	0.234221	+	0.234221i
$529$	489.468			0.925271
$530$			323.553i			0.610477i
$531$	−7.05280	−	7.05280i	−0.0132821	−	0.0132821i
$532$			232.153i			0.436378i
$533$		0			0
$534$	−15.4717			−0.0289733
$535$	−254.886	+	254.886i	−0.476422	+	0.476422i
$536$	304.398			0.567907
$537$		−	239.705i		−	0.446378i
$538$	−344.012	+	344.012i	−0.639427	+	0.639427i
$539$	−300.722	+	300.722i	−0.557926	+	0.557926i
$540$	−254.820	−	254.820i	−0.471888	−	0.471888i
$541$	394.763	+	394.763i	0.729691	+	0.729691i	0.970558	−	0.240867i	$-0.0774318\pi$
$541$	394.763	+	394.763i	0.729691	+	0.729691i	−0.240867	+	0.970558i	$0.577432\pi$
$542$	−34.3034			−0.0632903
$543$		−	611.047i		−	1.12532i
$544$	−96.9749	−	96.9749i	−0.178263	−	0.178263i
$545$		−	511.545i		−	0.938616i
$546$		0			0
$547$	−716.303			−1.30951			−0.654756	−	0.755840i	$-0.727229\pi$
$547$	−716.303			−1.30951			−0.654756	+	0.755840i	$0.727229\pi$
$548$	−11.3635	+	11.3635i	−0.0207363	+	0.0207363i
$549$	−6.09249			−0.0110974
$550$		−	425.031i		−	0.772783i
$551$	−414.168	+	414.168i	−0.751666	+	0.751666i
$552$	−38.2740	+	38.2740i	−0.0693369	+	0.0693369i
$553$	59.5717	+	59.5717i	0.107725	+	0.107725i
$554$	494.891	+	494.891i	0.893306	+	0.893306i
$555$	131.096			0.236208
$556$			487.922i			0.877558i
$557$	−42.6249	−	42.6249i	−0.0765259	−	0.0765259i	0.667808	−	0.744334i	$-0.267233\pi$
$557$	−42.6249	−	42.6249i	−0.0765259	−	0.0765259i	−0.744334	+	0.667808i	$0.767233\pi$
$558$			4.53941i			0.00813515i
$559$		0			0
$560$	−119.374			−0.213169
$561$	−749.546	+	749.546i	−1.33609	+	1.33609i
$562$	291.305			0.518337
$563$		−	269.269i		−	0.478276i	−0.970986	−	0.239138i	$-0.923135\pi$
$563$		−	269.269i		−	0.478276i	0.970986	−	0.239138i	$-0.0768648\pi$
$564$	−46.6073	+	46.6073i	−0.0826370	+	0.0826370i
$565$	−173.588	+	173.588i	−0.307236	+	0.307236i
$566$	430.214	+	430.214i	0.760096	+	0.760096i
$567$	259.423	+	259.423i	0.457537	+	0.457537i
$568$	6.46727			0.0113860
$569$		−	268.979i		−	0.472723i	−0.971665	−	0.236361i	$-0.924045\pi$
$569$		−	268.979i		−	0.472723i	0.971665	−	0.236361i	$-0.0759549\pi$
$570$	−543.639	−	543.639i	−0.953752	−	0.953752i
$571$		−	328.719i		−	0.575689i	−0.957677	−	0.287845i	$-0.907061\pi$
$571$		−	328.719i		−	0.575689i	0.957677	−	0.287845i	$-0.0929387\pi$
$572$		0			0
$573$	123.361			0.215290
$574$	−321.330	+	321.330i	−0.559809	+	0.559809i
$575$	131.542			0.228769
$576$			2.11254i			0.00366760i
$577$	18.1490	−	18.1490i	0.0314540	−	0.0314540i	−0.691205	−	0.722659i	$-0.742920\pi$
$577$	18.1490	−	18.1490i	0.0314540	−	0.0314540i	0.722659	+	0.691205i	$0.242920\pi$
$578$	298.758	−	298.758i	0.516883	−	0.516883i
$579$	−312.272	−	312.272i	−0.539330	−	0.539330i
$580$	−212.967	−	212.967i	−0.367185	−	0.367185i
$581$	216.565			0.372745
$582$		−	108.335i		−	0.186143i
$583$	342.942	+	342.942i	0.588236	+	0.588236i
$584$		−	152.709i		−	0.261488i
$585$		0			0
$586$	134.179			0.228975
$587$	82.3521	−	82.3521i	0.140293	−	0.140293i	−0.633472	−	0.773765i	$-0.718371\pi$
$587$	82.3521	−	82.3521i	0.140293	−	0.140293i	0.773765	+	0.633472i	$0.218371\pi$
$588$	−180.218			−0.306493
$589$		−	320.385i		−	0.543947i
$590$	−255.958	+	255.958i	−0.433828	+	0.433828i
$591$	333.229	−	333.229i	0.563839	−	0.563839i
$592$	17.9773	+	17.9773i	0.0303671	+	0.0303671i
$593$	−215.404	−	215.404i	−0.363244	−	0.363244i	0.501762	−	0.865006i	$-0.332685\pi$
$593$	−215.404	−	215.404i	−0.363244	−	0.363244i	−0.865006	+	0.501762i	$0.832685\pi$
$594$	−540.180			−0.909393
$595$		−	723.520i		−	1.21600i
$596$	−267.473	−	267.473i	−0.448779	−	0.448779i
$597$		−	792.427i		−	1.32735i
$598$		0			0
$599$	−657.704			−1.09800			−0.549002	−	0.835821i	$-0.684992\pi$
$599$	−657.704			−1.09800			−0.549002	+	0.835821i	$0.684992\pi$
$600$	127.357	−	127.357i	0.212262	−	0.212262i
$601$	299.134			0.497726			0.248863	−	0.968539i	$-0.419943\pi$
$601$	299.134			0.497726			0.248863	+	0.968539i	$0.419943\pi$
$602$			193.955i			0.322184i
$603$	20.0954	−	20.0954i	0.0333257	−	0.0333257i
$604$	141.199	−	141.199i	0.233773	−	0.233773i
$605$	−409.024	−	409.024i	−0.676073	−	0.676073i
$606$	−462.069	−	462.069i	−0.762490	−	0.762490i
$607$	−711.961			−1.17292			−0.586459	−	0.809979i	$-0.699478\pi$
$607$	−711.961			−1.17292			−0.586459	+	0.809979i	$0.699478\pi$
$608$		−	149.100i		−	0.245230i
$609$	210.629	+	210.629i	0.345861	+	0.345861i
$610$			221.107i			0.362471i
$611$		0			0
$612$	−12.8040			−0.0209215
$613$	−516.745	+	516.745i	−0.842978	+	0.842978i	−0.989245	−	0.146267i	$-0.953274\pi$
$613$	−516.745	+	516.745i	−0.842978	+	0.842978i	0.146267	+	0.989245i	$0.453274\pi$
$614$	420.611			0.685035
$615$		−	1504.93i		−	2.44704i
$616$	−126.528	+	126.528i	−0.205402	+	0.205402i
$617$	247.979	−	247.979i	0.401911	−	0.401911i	−0.476995	−	0.878906i	$-0.658274\pi$
$617$	247.979	−	247.979i	0.401911	−	0.401911i	0.878906	+	0.476995i	$0.158274\pi$
$618$	−52.8605	−	52.8605i	−0.0855347	−	0.0855347i
$619$	−283.795	−	283.795i	−0.458474	−	0.458474i	0.439680	−	0.898154i	$-0.355092\pi$
$619$	−283.795	−	283.795i	−0.458474	−	0.458474i	−0.898154	+	0.439680i	$0.855092\pi$
$620$	164.743			0.265715
$621$		−	167.179i		−	0.269210i
$622$	246.623	+	246.623i	0.396500	+	0.396500i
$623$		−	15.8295i		−	0.0254084i
$624$		0			0
$625$	710.329			1.13653
$626$	118.526	−	118.526i	0.189339	−	0.189339i
$627$	−1152.43			−1.83801
$628$		−	353.588i		−	0.563038i
$629$	−108.959	+	108.959i	−0.173226	+	0.173226i
$630$	−7.88072	+	7.88072i	−0.0125091	+	0.0125091i
$631$	816.497	+	816.497i	1.29397	+	1.29397i	0.932308	+	0.361664i	$0.117791\pi$
$631$	816.497	+	816.497i	1.29397	+	1.29397i	0.361664	+	0.932308i	$0.382209\pi$
$632$	−38.2597	−	38.2597i	−0.0605376	−	0.0605376i
$633$	1267.41			2.00223
$634$			569.627i			0.898466i
$635$	−637.708	−	637.708i	−1.00427	−	1.00427i
$636$			205.520i			0.323144i
$637$		0			0
$638$	−451.459			−0.707615
$639$	0.426949	−	0.426949i	0.000668151	−	0.000668151i
$640$	76.6678			0.119793
$641$			260.009i			0.405630i	0.979217	+	0.202815i	$0.0650091\pi$
$641$			260.009i			0.405630i	−0.979217	+	0.202815i	$0.934991\pi$
$642$	−161.902	+	161.902i	−0.252184	+	0.252184i
$643$	8.72268	−	8.72268i	0.0135656	−	0.0135656i	−0.700291	−	0.713857i	$-0.746947\pi$
$643$	8.72268	−	8.72268i	0.0135656	−	0.0135656i	0.713857	+	0.700291i	$0.246947\pi$
$644$	−39.1589	−	39.1589i	−0.0608058	−	0.0608058i
$645$	−454.188	−	454.188i	−0.704168	−	0.704168i
$646$	903.683			1.39889
$647$		−	950.162i		−	1.46857i	−0.678844	−	0.734283i	$-0.737519\pi$
$647$		−	950.162i		−	1.46857i	0.678844	−	0.734283i	$-0.262481\pi$
$648$	−166.614	−	166.614i	−0.257120	−	0.257120i
$649$			542.593i			0.836045i
$650$		0			0
$651$	−162.935			−0.250284
$652$	−171.470	+	171.470i	−0.262991	+	0.262991i
$653$	565.768			0.866414			0.433207	−	0.901295i	$-0.357382\pi$
$653$	565.768			0.866414			0.433207	+	0.901295i	$0.357382\pi$
$654$		−	324.932i		−	0.496838i
$655$	−183.398	+	183.398i	−0.279997	+	0.279997i
$656$	206.373	−	206.373i	0.314593	−	0.314593i
$657$	−10.0814	−	10.0814i	−0.0153446	−	0.0153446i
$658$	−47.6849	−	47.6849i	−0.0724695	−	0.0724695i
$659$	380.347			0.577158			0.288579	−	0.957456i	$-0.406817\pi$
$659$	380.347			0.577158			0.288579	+	0.957456i	$0.406817\pi$
$660$		−	592.587i		−	0.897858i
$661$	−702.933	−	702.933i	−1.06344	−	1.06344i	−0.997847	−	0.0655919i	$-0.979106\pi$
$661$	−702.933	−	702.933i	−1.06344	−	1.06344i	−0.0655919	−	0.997847i	$-0.520894\pi$
$662$		−	634.128i		−	0.957898i
$663$		0			0
$664$	−139.088			−0.209470
$665$	556.209	−	556.209i	0.836404	−	0.836404i
$666$	2.37361			0.00356398
$667$		−	139.721i		−	0.209477i
$668$	419.609	−	419.609i	0.628158	−	0.628158i
$669$	−439.702	+	439.702i	−0.657252	+	0.657252i
$670$	−729.298	−	729.298i	−1.08850	−	1.08850i
$671$	234.357	+	234.357i	0.349266	+	0.349266i
$672$	−75.8262			−0.112837
$673$			633.506i			0.941316i	0.882316	+	0.470658i	$0.155983\pi$
$673$			633.506i			0.941316i	−0.882316	+	0.470658i	$0.844017\pi$
$674$	474.455	+	474.455i	0.703939	+	0.703939i
$675$			556.292i			0.824136i
$676$		0			0
$677$	−221.745			−0.327540			−0.163770	−	0.986499i	$-0.552366\pi$
$677$	−221.745			−0.327540			−0.163770	+	0.986499i	$0.552366\pi$
$678$	−110.263	+	110.263i	−0.162629	+	0.162629i
$679$	110.840			0.163240
$680$			464.678i			0.683350i
$681$	−239.418	+	239.418i	−0.351569	+	0.351569i
$682$	174.616	−	174.616i	0.256035	−	0.256035i
$683$	−472.664	−	472.664i	−0.692040	−	0.692040i	0.270640	−	0.962681i	$-0.412765\pi$
$683$	−472.664	−	472.664i	−0.692040	−	0.692040i	−0.962681	+	0.270640i	$0.912765\pi$
$684$	−9.84309	−	9.84309i	−0.0143905	−	0.0143905i
$685$	54.4508			0.0794902
$686$		−	489.564i		−	0.713650i
$687$	646.204	+	646.204i	0.940617	+	0.940617i
$688$		−	124.567i		−	0.181056i
$689$		0			0
$690$	183.399			0.265795
$691$	401.253	−	401.253i	0.580684	−	0.580684i	−0.354407	−	0.935091i	$-0.615317\pi$
$691$	401.253	−	401.253i	0.580684	−	0.580684i	0.935091	+	0.354407i	$0.115317\pi$
$692$	−556.980			−0.804884
$693$			16.7059i			0.0241067i
$694$	533.636	−	533.636i	0.768927	−	0.768927i
$695$	1169.00	−	1169.00i	1.68201	−	1.68201i
$696$	−135.276	−	135.276i	−0.194362	−	0.194362i
$697$	1250.81	+	1250.81i	1.79457	+	1.79457i
$698$	−382.091			−0.547409
$699$		−	141.783i		−	0.202837i
$700$	130.302	+	130.302i	0.186146	+	0.186146i
$701$		−	597.453i		−	0.852287i	−0.904656	−	0.426143i	$-0.859872\pi$
$701$		−	597.453i		−	0.852287i	0.904656	−	0.426143i	$-0.140128\pi$
$702$		0			0
$703$	−167.526			−0.238301
$704$	81.2621	−	81.2621i	0.115429	−	0.115429i
$705$	223.330			0.316780
$706$			499.193i			0.707072i
$707$	472.753	−	472.753i	0.668675	−	0.668675i
$708$	−162.584	+	162.584i	−0.229638	+	0.229638i
$709$	28.0397	+	28.0397i	0.0395482	+	0.0395482i	0.726604	−	0.687056i	$-0.241097\pi$
$709$	28.0397	+	28.0397i	0.0395482	+	0.0395482i	−0.687056	+	0.726604i	$0.741097\pi$
$710$	−15.4947	−	15.4947i	−0.0218236	−	0.0218236i
$711$	−5.05157			−0.00710489
$712$			10.1664i			0.0142787i
$713$	54.0415	+	54.0415i	0.0757946	+	0.0757946i
$714$		−	459.577i		−	0.643666i
$715$		0			0
$716$	−157.509			−0.219985
$717$	−420.969	+	420.969i	−0.587126	+	0.587126i
$718$	232.183			0.323375
$719$		−	998.560i		−	1.38882i	−0.719581	−	0.694409i	$-0.755666\pi$
$719$		−	998.560i		−	1.38882i	0.719581	−	0.694409i	$-0.244334\pi$
$720$	5.06137	−	5.06137i	0.00702967	−	0.00702967i
$721$	54.0827	−	54.0827i	0.0750107	−	0.0750107i
$722$	333.709	+	333.709i	0.462201	+	0.462201i
$723$	483.940	+	483.940i	0.669350	+	0.669350i
$724$	−401.517			−0.554581
$725$			464.924i			0.641275i
$726$	−259.810	−	259.810i	−0.357866	−	0.357866i
$727$			685.178i			0.942473i	0.882007	+	0.471237i	$0.156192\pi$
$727$			685.178i			0.942473i	−0.882007	+	0.471237i	$0.843808\pi$
$728$		0			0
$729$	706.374			0.968963
$730$	−365.871	+	365.871i	−0.501194	+	0.501194i
$731$	754.991			1.03282
$732$			140.447i			0.191867i
$733$	−176.253	+	176.253i	−0.240454	+	0.240454i	−0.817038	−	0.576584i	$-0.804385\pi$
$733$	−176.253	+	176.253i	−0.240454	+	0.240454i	0.576584	+	0.817038i	$0.304385\pi$
$734$	−686.325	+	686.325i	−0.935047	+	0.935047i
$735$	431.779	+	431.779i	0.587454	+	0.587454i
$736$	25.1497	+	25.1497i	0.0341708	+	0.0341708i
$737$	−1546.00			−2.09770
$738$		−	27.2482i		−	0.0369217i
$739$	979.260	+	979.260i	1.32511	+	1.32511i	0.909575	+	0.415539i	$0.136407\pi$
$739$	979.260	+	979.260i	1.32511	+	1.32511i	0.415539	+	0.909575i	$0.363593\pi$
$740$		−	86.1425i		−	0.116409i
$741$		0			0
$742$	−210.272			−0.283385
$743$	412.390	−	412.390i	0.555033	−	0.555033i	−0.372856	−	0.927889i	$-0.621621\pi$
$743$	412.390	−	412.390i	0.555033	−	0.555033i	0.927889	+	0.372856i	$0.121621\pi$
$744$	104.644			0.140651
$745$			1281.66i			1.72035i
$746$	617.271	−	617.271i	0.827441	−	0.827441i
$747$	−9.18216	+	9.18216i	−0.0122920	+	0.0122920i
$748$	492.524	+	492.524i	0.658455	+	0.658455i
$749$	−165.646	−	165.646i	−0.221156	−	0.221156i
$750$	118.967			0.158623
$751$			1168.92i			1.55649i	0.627962	+	0.778244i	$0.283889\pi$
$751$			1168.92i			1.55649i	−0.627962	+	0.778244i	$0.716111\pi$
$752$	30.6255	+	30.6255i	0.0407254	+	0.0407254i
$753$			10.6229i			0.0141075i
$754$		0			0
$755$	−676.588			−0.896143
$756$	165.603	−	165.603i	0.219052	−	0.219052i
$757$	−1122.69			−1.48307			−0.741537	−	0.670912i	$-0.765903\pi$
$757$	−1122.69			−1.48307			−0.741537	+	0.670912i	$0.765903\pi$
$758$			758.964i			1.00127i
$759$	194.389	−	194.389i	0.256112	−	0.256112i
$760$	−357.223	+	357.223i	−0.470030	+	0.470030i
$761$	−672.687	−	672.687i	−0.883951	−	0.883951i	0.109982	−	0.993934i	$-0.464921\pi$
$761$	−672.687	−	672.687i	−0.883951	−	0.883951i	−0.993934	+	0.109982i	$0.964921\pi$
$762$	−405.070	−	405.070i	−0.531588	−	0.531588i
$763$	332.445			0.435707
$764$		−	81.0601i		−	0.106100i
$765$	30.6766	+	30.6766i	0.0401001	+	0.0401001i
$766$		−	370.506i		−	0.483690i
$767$		0			0
$768$	48.6991			0.0634103
$769$	145.921	−	145.921i	0.189755	−	0.189755i	−0.605835	−	0.795590i	$-0.707161\pi$
$769$	145.921	−	145.921i	0.189755	−	0.189755i	0.795590	+	0.605835i	$0.207161\pi$
$770$	606.288			0.787387
$771$			564.340i			0.731959i
$772$	−205.193	+	205.193i	−0.265794	+	0.265794i
$773$	−316.008	+	316.008i	−0.408808	+	0.408808i	−0.881323	−	0.472515i	$-0.843346\pi$
$773$	−316.008	+	316.008i	−0.408808	+	0.408808i	0.472515	+	0.881323i	$0.343346\pi$
$774$	−8.22350	−	8.22350i	−0.0106247	−	0.0106247i
$775$	−179.824	−	179.824i	−0.232031	−	0.232031i
$776$	−71.1868			−0.0917356
$777$			85.1969i			0.109648i
$778$	−184.591	−	184.591i	−0.237264	−	0.237264i
$779$			1923.14i			2.46872i
$780$		0			0
$781$	−32.8465			−0.0420570
$782$	−152.431	+	152.431i	−0.194924	+	0.194924i
$783$	590.881			0.754637
$784$			118.421i			0.151047i
$785$	−847.151	+	847.151i	−1.07917	+	1.07917i
$786$	−116.494	+	116.494i	−0.148211	+	0.148211i
$787$	−474.398	−	474.398i	−0.602793	−	0.602793i	0.338260	−	0.941053i	$-0.390162\pi$
$787$	−474.398	−	474.398i	−0.602793	−	0.602793i	−0.941053	+	0.338260i	$0.890162\pi$
$788$	−218.963	−	218.963i	−0.277872	−	0.277872i
$789$	−570.240			−0.722738
$790$			183.331i			0.232064i
$791$	−112.812	−	112.812i	−0.142620	−	0.142620i
$792$		−	10.7293i		−	0.0135471i
$793$		0			0
$794$	359.016			0.452162
$795$	492.398	−	492.398i	0.619368	−	0.619368i
$796$	−520.701			−0.654147
$797$		−	239.289i		−	0.300237i	−0.988668	−	0.150118i	$-0.952035\pi$
$797$		−	239.289i		−	0.300237i	0.988668	−	0.150118i	$-0.0479655\pi$
$798$	353.302	−	353.302i	0.442734	−	0.442734i
$799$	−185.619	+	185.619i	−0.232314	+	0.232314i
$800$	−83.6859	−	83.6859i	−0.104607	−	0.104607i
$801$	0.671155	+	0.671155i	0.000837896	+	0.000837896i
$802$	383.309			0.477941
$803$			775.592i			0.965868i
$804$	−463.248	−	463.248i	−0.576179	−	0.576179i
$805$			187.639i			0.233092i
$806$		0			0
$807$	1047.07			1.29748
$808$	−303.624	+	303.624i	−0.375772	+	0.375772i
$809$	468.093			0.578606			0.289303	−	0.957238i	$-0.406576\pi$
$809$	468.093			0.578606			0.289303	+	0.957238i	$0.406576\pi$
$810$			798.369i			0.985641i
$811$	680.928	−	680.928i	0.839615	−	0.839615i	−0.149193	−	0.988808i	$-0.547668\pi$
$811$	680.928	−	680.928i	0.839615	−	0.839615i	0.988808	+	0.149193i	$0.0476675\pi$
$812$	138.404	−	138.404i	0.170448	−	0.170448i
$813$	52.2044	+	52.2044i	0.0642121	+	0.0642121i
$814$	−91.3046	−	91.3046i	−0.112168	−	0.112168i
$815$	821.639			1.00815
$816$			295.162i			0.361718i
$817$	580.402	+	580.402i	0.710406	+	0.710406i
$818$			223.270i			0.272946i
$819$		0			0
$820$	−988.886			−1.20596
$821$	891.115	−	891.115i	1.08540	−	1.08540i	0.0894064	−	0.995995i	$-0.471503\pi$
$821$	891.115	−	891.115i	1.08540	−	1.08540i	0.995995	−	0.0894064i	$-0.0284970\pi$
$822$	34.5869			0.0420766
$823$			576.431i			0.700402i	0.936675	+	0.350201i	$0.113887\pi$
$823$			576.431i			0.700402i	−0.936675	+	0.350201i	$0.886113\pi$
$824$	−34.7344	+	34.7344i	−0.0421534	+	0.0421534i
$825$	−646.832	+	646.832i	−0.784038	+	0.784038i
$826$	−166.343	−	166.343i	−0.201384	−	0.201384i
$827$	−434.651	−	434.651i	−0.525575	−	0.525575i	0.393675	−	0.919250i	$-0.371204\pi$
$827$	−434.651	−	434.651i	−0.525575	−	0.525575i	−0.919250	+	0.393675i	$0.871204\pi$
$828$	3.32061			0.00401039
$829$			126.254i			0.152297i	0.997096	+	0.0761486i	$0.0242624\pi$
$829$			126.254i			0.152297i	−0.997096	+	0.0761486i	$0.975738\pi$
$830$	333.237	+	333.237i	0.401490	+	0.401490i
$831$		−	1506.30i		−	1.81263i
$832$		0			0
$833$	−717.739			−0.861632
$834$	742.543	−	742.543i	0.890340	−	0.890340i
$835$	−2010.66			−2.40797
$836$			757.259i			0.905812i
$837$	−228.542	+	228.542i	−0.273048	+	0.273048i
$838$	652.476	−	652.476i	0.778611	−	0.778611i
$839$	900.412	+	900.412i	1.07320	+	1.07320i	0.997100	+	0.0760962i	$0.0242456\pi$
$839$	900.412	+	900.412i	1.07320	+	1.07320i	0.0760962	+	0.997100i	$0.475754\pi$
$840$	181.669	+	181.669i	0.216273	+	0.216273i
$841$	−347.167			−0.412803
$842$		−	589.151i		−	0.699704i
$843$	−443.322	−	443.322i	−0.525886	−	0.525886i
$844$		−	832.812i		−	0.986744i
$845$		0			0
$846$	4.04360			0.00477966
$847$	265.818	−	265.818i	0.313834	−	0.313834i
$848$	135.046			0.159253
$849$		−	1309.44i		−	1.54233i
$850$	507.215	−	507.215i	0.596723	−	0.596723i
$851$	28.2577	−	28.2577i	0.0332053	−	0.0332053i
$852$	−9.84219	−	9.84219i	−0.0115519	−	0.0115519i
$853$	−162.871	−	162.871i	−0.190939	−	0.190939i	0.605163	−	0.796102i	$-0.293108\pi$
$853$	−162.871	−	162.871i	−0.190939	−	0.190939i	−0.796102	+	0.605163i	$0.793108\pi$
$854$	−143.694			−0.168260
$855$			47.1655i			0.0551643i
$856$	106.385	+	106.385i	0.124282	+	0.124282i
$857$			1077.67i			1.25750i	0.777609	+	0.628748i	$0.216432\pi$
$857$			1077.67i			1.25750i	−0.777609	+	0.628748i	$0.783568\pi$
$858$		0			0
$859$	654.044			0.761402			0.380701	−	0.924698i	$-0.375683\pi$
$859$	654.044			0.761402			0.380701	+	0.924698i	$0.375683\pi$
$860$	−298.445	+	298.445i	−0.347030	+	0.347030i
$861$	978.030			1.13592
$862$		−	99.8796i		−	0.115870i
$863$	−916.358	+	916.358i	−1.06183	+	1.06183i	−0.0638705	+	0.997958i	$0.520344\pi$
$863$	−916.358	+	916.358i	−1.06183	+	1.06183i	−0.997958	+	0.0638705i	$0.979656\pi$
$864$	−106.358	+	106.358i	−0.123100	+	0.123100i
$865$	1334.45	+	1334.45i	1.54272	+	1.54272i
$866$	−466.918	−	466.918i	−0.539167	−	0.539167i
$867$	−909.329			−1.04882
$868$			107.064i			0.123346i
$869$	194.317	+	194.317i	0.223610	+	0.223610i
$870$			648.207i			0.745066i
$871$		0			0
$872$	−213.512			−0.244853
$873$	−4.69953	+	4.69953i	−0.00538319	+	0.00538319i
$874$	−234.363			−0.268150
$875$			121.718i			0.139106i
$876$	−232.400	+	232.400i	−0.265297	+	0.265297i
$877$	−648.782	+	648.782i	−0.739774	+	0.739774i	−0.972534	−	0.232760i	$-0.925224\pi$
$877$	−648.782	+	648.782i	−0.739774	+	0.739774i	0.232760	+	0.972534i	$0.425224\pi$
$878$	119.600	+	119.600i	0.136219	+	0.136219i
$879$	−204.200	−	204.200i	−0.232309	−	0.232309i
$880$	−389.387			−0.442485
$881$		−	966.844i		−	1.09744i	−0.836007	−	0.548719i	$-0.815116\pi$
$881$		−	966.844i		−	1.09744i	0.836007	−	0.548719i	$-0.184884\pi$
$882$	7.81775	+	7.81775i	0.00886367	+	0.00886367i
$883$			1129.48i			1.27914i	0.768731	+	0.639572i	$0.220888\pi$
$883$			1129.48i			1.27914i	−0.768731	+	0.639572i	$0.779112\pi$
$884$		0			0
$885$	779.059			0.880293
$886$	56.7213	−	56.7213i	0.0640195	−	0.0640195i
$887$	−1654.95			−1.86579			−0.932894	−	0.360151i	$-0.882725\pi$
$887$	−1654.95			−1.86579			−0.932894	+	0.360151i	$0.882725\pi$
$888$		−	54.7174i		−	0.0616187i
$889$	414.436	−	414.436i	0.466182	−	0.466182i
$890$	24.3574	−	24.3574i	0.0273679	−	0.0273679i
$891$	846.211	+	846.211i	0.949732	+	0.949732i
$892$	288.926	+	288.926i	0.323909	+	0.323909i
$893$	−285.391			−0.319586
$894$			814.104i			0.910631i
$895$	377.372	+	377.372i	0.421645	+	0.421645i
$896$			49.8251i			0.0556084i
$897$		0			0
$898$	261.348			0.291033
$899$	−191.005	+	191.005i	−0.212464	+	0.212464i
$900$	−11.0494			−0.0122771
$901$			818.506i			0.908442i
$902$	−1048.14	+	1048.14i	−1.16202	+	1.16202i
$903$	295.169	−	295.169i	0.326876	−	0.326876i
$904$	72.4533	+	72.4533i	0.0801474	+	0.0801474i
$905$	961.981	+	961.981i	1.06296	+	1.06296i
$906$	−429.766			−0.474356
$907$		−	446.186i		−	0.491936i	−0.969278	−	0.245968i	$-0.920894\pi$
$907$		−	446.186i		−	0.491936i	0.969278	−	0.245968i	$-0.0791058\pi$
$908$	157.321	+	157.321i	0.173261	+	0.173261i
$909$			40.0886i			0.0441019i
$910$		0			0
$911$	1639.85			1.80005			0.900025	−	0.435838i	$-0.143548\pi$
$911$	1639.85			1.80005			0.900025	+	0.435838i	$0.143548\pi$
$912$	−226.907	+	226.907i	−0.248801	+	0.248801i
$913$	706.412			0.773726
$914$		−	418.779i		−	0.458182i
$915$	336.491	−	336.491i	0.367750	−	0.367750i
$916$	424.618	−	424.618i	0.463557	−	0.463557i
$917$	−119.187	−	119.187i	−0.129975	−	0.129975i
$918$	−644.629	−	644.629i	−0.702210	−	0.702210i
$919$	1190.62			1.29556			0.647782	−	0.761826i	$-0.275697\pi$
$919$	1190.62			1.29556			0.647782	+	0.761826i	$0.275697\pi$
$920$		−	120.511i		−	0.130990i
$921$	−640.106	−	640.106i	−0.695012	−	0.695012i
$922$			872.906i			0.946752i
$923$		0			0
$924$	385.112			0.416788
$925$	−94.0279	+	94.0279i	−0.101652	+	0.101652i
$926$	397.399			0.429156
$927$			4.58611i			0.00494727i
$928$	−88.8894	+	88.8894i	−0.0957860	+	0.0957860i
$929$	−563.775	+	563.775i	−0.606863	+	0.606863i	−0.942125	−	0.335262i	$-0.891175\pi$
$929$	−563.775	+	563.775i	−0.606863	+	0.606863i	0.335262	+	0.942125i	$0.391175\pi$
$930$	−250.714	−	250.714i	−0.269585	−	0.269585i
$931$	−551.765	−	551.765i	−0.592658	−	0.592658i
$932$	−93.1652			−0.0999627
$933$		−	750.646i		−	0.804550i
$934$	−522.015	−	522.015i	−0.558903	−	0.558903i
$935$		−	2360.05i		−	2.52411i
$936$		0			0
$937$	406.611			0.433950			0.216975	−	0.976177i	$-0.430381\pi$
$937$	406.611			0.433950			0.216975	+	0.976177i	$0.430381\pi$
$938$	473.959	−	473.959i	0.505286	−	0.505286i
$939$	−360.758			−0.384194
$940$		−	146.749i		−	0.156116i
$941$	67.4219	−	67.4219i	0.0716492	−	0.0716492i	−0.670374	−	0.742023i	$-0.733866\pi$
$941$	67.4219	−	67.4219i	0.0716492	−	0.0716492i	0.742023	+	0.670374i	$0.233866\pi$
$942$	−538.107	+	538.107i	−0.571239	+	0.571239i
$943$	−324.389	−	324.389i	−0.343997	−	0.343997i
$944$	106.833	+	106.833i	0.113171	+	0.113171i
$945$	−793.526			−0.839710
$946$			632.660i			0.668773i
$947$	−1163.65	−	1163.65i	−1.22877	−	1.22877i	−0.964428	−	0.264344i	$-0.914845\pi$
$947$	−1163.65	−	1163.65i	−1.22877	−	1.22877i	−0.264344	−	0.964428i	$-0.585155\pi$
$948$			116.451i			0.122839i
$949$		0			0
$950$	779.846			0.820891
$951$	866.885	−	866.885i	0.911551	−	0.911551i
$952$	−301.987			−0.317213
$953$		−	932.332i		−	0.978312i	−0.872196	−	0.489156i	$-0.837305\pi$
$953$		−	932.332i		−	0.978312i	0.872196	−	0.489156i	$-0.162695\pi$
$954$	8.91532	−	8.91532i	0.00934520	−	0.00934520i
$955$	−194.209	+	194.209i	−0.203361	+	0.203361i
$956$	276.617	+	276.617i	0.289349	+	0.289349i
$957$	687.051	+	687.051i	0.717921	+	0.717921i
$958$	−480.182			−0.501234
$959$			35.3866i			0.0368995i
$960$	−116.677	−	116.677i	−0.121538	−	0.121538i
$961$			813.246i			0.846249i
$962$		0			0
$963$	14.0465			0.0145862
$964$	317.995	−	317.995i	0.329871	−	0.329871i
$965$	983.231			1.01889
$966$			119.188i			0.123383i
$967$	540.669	−	540.669i	0.559120	−	0.559120i	−0.369937	−	0.929057i	$-0.620621\pi$
$967$	540.669	−	540.669i	0.559120	−	0.559120i	0.929057	+	0.369937i	$0.120621\pi$
$968$	−170.721	+	170.721i	−0.176364	+	0.176364i
$969$	−1375.27	−	1375.27i	−1.41926	−	1.41926i
$970$	170.554	+	170.554i	0.175829	+	0.175829i
$971$	1696.76			1.74743			0.873716	−	0.486436i	$-0.161703\pi$
$971$	1696.76			1.74743			0.873716	+	0.486436i	$0.161703\pi$
$972$			28.5102i			0.0293314i
$973$	759.712	+	759.712i	0.780794	+	0.780794i
$974$			305.164i			0.313310i
$975$		0			0
$976$	92.2869			0.0945563
$977$	−201.781	+	201.781i	−0.206531	+	0.206531i	−0.802791	−	0.596260i	$-0.796653\pi$
$977$	−201.781	+	201.781i	−0.206531	+	0.206531i	0.596260	+	0.802791i	$0.296653\pi$
$978$	521.902			0.533642
$979$		−	51.6340i		−	0.0527416i
$980$	283.720	−	283.720i	0.289510	−	0.289510i
$981$	−14.0954	+	14.0954i	−0.0143684	+	0.0143684i
$982$	−555.234	−	555.234i	−0.565412	−	0.565412i
$983$	41.0192	+	41.0192i	0.0417286	+	0.0417286i	0.727663	−	0.685935i	$-0.240606\pi$
$983$	41.0192	+	41.0192i	0.0417286	+	0.0417286i	−0.685935	+	0.727663i	$0.740606\pi$
$984$	−628.137			−0.638350
$985$			1049.21i			1.06519i
$986$	−538.753	−	538.753i	−0.546402	−	0.546402i
$987$			145.138i			0.147050i
$988$		0			0
$989$	−195.801			−0.197979
$990$	−25.7061	+	25.7061i	−0.0259657	+	0.0259657i
$991$	376.148			0.379564			0.189782	−	0.981826i	$-0.439222\pi$
$991$	376.148			0.379564			0.189782	+	0.981826i	$0.439222\pi$
$992$		−	68.7614i		−	0.0693160i
$993$	−965.046	+	965.046i	−0.971849	+	0.971849i
$994$	10.0698	−	10.0698i	0.0101305	−	0.0101305i
$995$	1247.53	+	1247.53i	1.25380	+	1.25380i
$996$	211.671	+	211.671i	0.212521	+	0.212521i
$997$	−1445.10			−1.44945			−0.724724	−	0.689040i	$-0.758033\pi$
$997$	−1445.10			−1.44945			−0.724724	+	0.689040i	$0.758033\pi$
$998$			803.237i			0.804847i
$999$	119.502	+	119.502i	0.119621	+	0.119621i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.3.d.f.239.3		8
13.2	odd	12		338.3.f.h.319.1		8
13.3	even	3		338.3.f.i.19.1		8
13.4	even	6		338.3.f.h.249.1		8
13.5	odd	4		338.3.d.g.99.3		8
13.6	odd	12		26.3.f.b.11.1	✓	8
13.7	odd	12		338.3.f.i.89.1		8
13.8	odd	4	inner	338.3.d.f.99.3		8
13.9	even	3		338.3.f.j.249.1		8
13.10	even	6		26.3.f.b.19.1	yes	8
13.11	odd	12		338.3.f.j.319.1		8
13.12	even	2		338.3.d.g.239.3		8
39.23	odd	6		234.3.bb.f.19.1		8
39.32	even	12		234.3.bb.f.37.1		8
52.19	even	12		208.3.bd.f.193.2		8
52.23	odd	6		208.3.bd.f.97.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.3.f.b.11.1	✓	8	13.6	odd	12
26.3.f.b.19.1	yes	8	13.10	even	6
208.3.bd.f.97.2		8	52.23	odd	6
208.3.bd.f.193.2		8	52.19	even	12
234.3.bb.f.19.1		8	39.23	odd	6
234.3.bb.f.37.1		8	39.32	even	12
338.3.d.f.99.3		8	13.8	odd	4	inner
338.3.d.f.239.3		8	1.1	even	1	trivial
338.3.d.g.99.3		8	13.5	odd	4
338.3.d.g.239.3		8	13.12	even	2
338.3.f.h.249.1		8	13.4	even	6
338.3.f.h.319.1		8	13.2	odd	12
338.3.f.i.19.1		8	13.3	even	3
338.3.f.i.89.1		8	13.7	odd	12
338.3.f.j.249.1		8	13.9	even	3
338.3.f.j.319.1		8	13.11	odd	12

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:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	338.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +3.04369 q^{3} -2.00000i q^{4} +(-4.79174 + 4.79174i) q^{5} +(-3.04369 + 3.04369i) q^{6} +(-3.11407 - 3.11407i) q^{7} +(2.00000 + 2.00000i) q^{8} +0.264067 q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +3.04369 q^{3} -2.00000i q^{4} +(-4.79174 + 4.79174i) q^{5} +(-3.04369 + 3.04369i) q^{6} +(-3.11407 - 3.11407i) q^{7} +(2.00000 + 2.00000i) q^{8} +0.264067 q^{9} -9.58347i q^{10} +(-10.1578 - 10.1578i) q^{11} -6.08739i q^{12} +6.22814 q^{14} +(-14.5846 + 14.5846i) q^{15} -4.00000 q^{16} -24.2437i q^{17} +(-0.264067 + 0.264067i) q^{18} +(18.6375 - 18.6375i) q^{19} +(9.58347 + 9.58347i) q^{20} +(-9.47827 - 9.47827i) q^{21} +20.3155 q^{22} +6.28742i q^{23} +(6.08739 + 6.08739i) q^{24} -20.9215i q^{25} -26.5895 q^{27} +(-6.22814 + 6.22814i) q^{28} -22.2223 q^{29} -29.1692i q^{30} +(8.59518 - 8.59518i) q^{31} +(4.00000 - 4.00000i) q^{32} +(-30.9171 - 30.9171i) q^{33} +(24.2437 + 24.2437i) q^{34} +29.8436 q^{35} -0.528135i q^{36} +(-4.49432 - 4.49432i) q^{37} +37.2749i q^{38} -19.1669 q^{40} +(-51.5933 + 51.5933i) q^{41} +18.9565 q^{42} +31.1417i q^{43} +(-20.3155 + 20.3155i) q^{44} +(-1.26534 + 1.26534i) q^{45} +(-6.28742 - 6.28742i) q^{46} +(-7.65637 - 7.65637i) q^{47} -12.1748 q^{48} -29.6051i q^{49} +(20.9215 + 20.9215i) q^{50} -73.7905i q^{51} -33.7616 q^{53} +(26.5895 - 26.5895i) q^{54} +97.3466 q^{55} -12.4563i q^{56} +(56.7267 - 56.7267i) q^{57} +(22.2223 - 22.2223i) q^{58} +(-26.7083 - 26.7083i) q^{59} +(29.1692 + 29.1692i) q^{60} -23.0717 q^{61} +17.1904i q^{62} +(-0.822324 - 0.822324i) q^{63} +8.00000i q^{64} +61.8342 q^{66} +(76.0996 - 76.0996i) q^{67} -48.4875 q^{68} +19.1370i q^{69} +(-29.8436 + 29.8436i) q^{70} +(1.61682 - 1.61682i) q^{71} +(0.528135 + 0.528135i) q^{72} +(-38.1773 - 38.1773i) q^{73} +8.98865 q^{74} -63.6786i q^{75} +(-37.2749 - 37.2749i) q^{76} +63.2639i q^{77} -19.1299 q^{79} +(19.1669 - 19.1669i) q^{80} -83.3069 q^{81} -103.187i q^{82} +(-34.7720 + 34.7720i) q^{83} +(-18.9565 + 18.9565i) q^{84} +(116.170 + 116.170i) q^{85} +(-31.1417 - 31.1417i) q^{86} -67.6380 q^{87} -40.6310i q^{88} +(2.54160 + 2.54160i) q^{89} -2.53068i q^{90} +12.5748 q^{92} +(26.1611 - 26.1611i) q^{93} +15.3127 q^{94} +178.612i q^{95} +(12.1748 - 12.1748i) q^{96} +(-17.7967 + 17.7967i) q^{97} +(29.6051 + 29.6051i) q^{98} +(-2.68233 - 2.68233i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 6 q^{5} - 10 q^{7} + 16 q^{8} + 84 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 6 * q^5 - 10 * q^7 + 16 * q^8 + 84 * q^9	\( 8 q - 8 q^{2} - 6 q^{5} - 10 q^{7} + 16 q^{8} + 84 q^{9} - 42 q^{11} + 20 q^{14} - 60 q^{15} - 32 q^{16} - 84 q^{18} - 22 q^{19} + 12 q^{20} + 102 q^{21} + 84 q^{22} + 72 q^{27} - 20 q^{28} + 12 q^{29} - 32 q^{31} + 32 q^{32} - 54 q^{33} + 60 q^{34} + 156 q^{35} - 32 q^{37} - 24 q^{40} + 12 q^{41} - 204 q^{42} - 84 q^{44} + 102 q^{45} + 108 q^{46} - 60 q^{47} + 88 q^{50} - 132 q^{53} - 72 q^{54} + 324 q^{55} + 294 q^{57} - 12 q^{58} - 234 q^{59} + 120 q^{60} - 72 q^{61} + 156 q^{63} + 108 q^{66} + 14 q^{67} - 120 q^{68} - 156 q^{70} - 162 q^{71} + 168 q^{72} - 166 q^{73} + 64 q^{74} + 44 q^{76} - 96 q^{79} + 24 q^{80} + 24 q^{81} + 240 q^{83} + 204 q^{84} + 234 q^{85} - 132 q^{86} - 720 q^{87} - 210 q^{89} - 216 q^{92} + 444 q^{93} + 120 q^{94} - 146 q^{97} + 16 q^{98} - 252 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 6 * q^5 - 10 * q^7 + 16 * q^8 + 84 * q^9 - 42 * q^11 + 20 * q^14 - 60 * q^15 - 32 * q^16 - 84 * q^18 - 22 * q^19 + 12 * q^20 + 102 * q^21 + 84 * q^22 + 72 * q^27 - 20 * q^28 + 12 * q^29 - 32 * q^31 + 32 * q^32 - 54 * q^33 + 60 * q^34 + 156 * q^35 - 32 * q^37 - 24 * q^40 + 12 * q^41 - 204 * q^42 - 84 * q^44 + 102 * q^45 + 108 * q^46 - 60 * q^47 + 88 * q^50 - 132 * q^53 - 72 * q^54 + 324 * q^55 + 294 * q^57 - 12 * q^58 - 234 * q^59 + 120 * q^60 - 72 * q^61 + 156 * q^63 + 108 * q^66 + 14 * q^67 - 120 * q^68 - 156 * q^70 - 162 * q^71 + 168 * q^72 - 166 * q^73 + 64 * q^74 + 44 * q^76 - 96 * q^79 + 24 * q^80 + 24 * q^81 + 240 * q^83 + 204 * q^84 + 234 * q^85 - 132 * q^86 - 720 * q^87 - 210 * q^89 - 216 * q^92 + 444 * q^93 + 120 * q^94 - 146 * q^97 + 16 * q^98 - 252 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more