LMFDB - Embedded newform 936.2.g.e.469.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [936,2,Mod(469,936)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(936, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("936.469");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.g (of order $2$, degree $1$, 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:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} - 4 x^{13} + 9 x^{12} - 10 x^{11} + 2 x^{10} - 8 x^{9} + 28 x^{8} + \cdots + 256 $ x^16 - 2x^15 + 2x^14 - 4x^13 + 9x^12 - 10x^11 + 2x^10 - 8x^9 + 28x^8 - 16x^7 + 8x^6 - 80x^5 + 144x^4 - 128x^3 + 128x^2 - 256*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			469.12
Root			$-1.32561 + 0.492712i$ of defining polynomial
Character	$\chi$	$=$	936.469
Dual form			936.2.g.e.469.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.492712 + 1.32561i) q^{2} +(-1.51447 + 1.30629i) q^{4} +4.33571i q^{5} -2.30442 q^{7} +(-2.47782 - 1.36397i) q^{8} +(-5.74745 + 2.13626i) q^{10} -0.582255i q^{11} +1.00000i q^{13} +(-1.13542 - 3.05476i) q^{14} +(0.587238 - 3.95666i) q^{16} -3.40894 q^{17} -0.0627418i q^{19} +(-5.66368 - 6.56631i) q^{20} +(0.771842 - 0.286884i) q^{22} +6.65973 q^{23} -13.7984 q^{25} +(-1.32561 + 0.492712i) q^{26} +(3.48998 - 3.01023i) q^{28} +2.41805i q^{29} +5.63600 q^{31} +(5.53432 - 1.17105i) q^{32} +(-1.67963 - 4.51892i) q^{34} -9.99131i q^{35} -9.27328i q^{37} +(0.0831710 - 0.0309136i) q^{38} +(5.91378 - 10.7431i) q^{40} -4.75376 q^{41} +7.86434i q^{43} +(0.760592 + 0.881808i) q^{44} +(3.28133 + 8.82819i) q^{46} +0.0312900 q^{47} -1.68964 q^{49} +(-6.79864 - 18.2913i) q^{50} +(-1.30629 - 1.51447i) q^{52} +13.1656i q^{53} +2.52449 q^{55} +(5.70994 + 3.14316i) q^{56} +(-3.20539 + 1.19140i) q^{58} +4.75759i q^{59} -3.29149i q^{61} +(2.77693 + 7.47113i) q^{62} +(4.27917 + 6.75934i) q^{64} -4.33571 q^{65} -11.8777i q^{67} +(5.16274 - 4.45305i) q^{68} +(13.2446 - 4.92284i) q^{70} -13.6251 q^{71} +0.437175 q^{73} +(12.2927 - 4.56905i) q^{74} +(0.0819587 + 0.0950206i) q^{76} +1.34176i q^{77} -6.54503 q^{79} +(17.1549 + 2.54610i) q^{80} +(-2.34224 - 6.30162i) q^{82} +6.62844i q^{83} -14.7802i q^{85} +(-10.4250 + 3.87485i) q^{86} +(-0.794179 + 1.44272i) q^{88} -8.23880 q^{89} -2.30442i q^{91} +(-10.0860 + 8.69951i) q^{92} +(0.0154170 + 0.0414783i) q^{94} +0.272031 q^{95} -0.664432 q^{97} +(-0.832504 - 2.23980i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 4 q^{7} + 4 q^{8} - 8 q^{10} - 12 q^{14} - 12 q^{16} - 16 q^{17} - 24 q^{20} + 16 q^{22} + 8 q^{23} - 32 q^{25} + 2 q^{26} + 32 q^{28} - 4 q^{31} + 28 q^{32} - 32 q^{34} - 12 q^{38} - 12 q^{40}+ \cdots + 46 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 + 4 * q^7 + 4 * q^8 - 8 * q^10 - 12 * q^14 - 12 * q^16 - 16 * q^17 - 24 * q^20 + 16 * q^22 + 8 * q^23 - 32 * q^25 + 2 * q^26 + 32 * q^28 - 4 * q^31 + 28 * q^32 - 32 * q^34 - 12 * q^38 - 12 * q^40 + 36 * q^41 - 16 * q^44 + 44 * q^46 - 24 * q^47 + 48 * q^49 + 34 * q^50 + 24 * q^55 + 64 * q^56 - 28 * q^58 - 52 * q^62 - 48 * q^64 - 4 * q^65 - 32 * q^68 + 84 * q^70 - 32 * q^73 + 60 * q^74 + 64 * q^76 + 68 * q^80 - 32 * q^82 - 56 * q^86 - 36 * q^88 + 60 * q^89 - 32 * q^92 + 24 * q^95 + 40 * q^97 + 46 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$1$	$1$	$-1$	$1$

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 $

$2$	0.492712	+	1.32561i	0.348400	+	0.937346i
$2$	0.492712	+	1.32561i	0.348400	+	0.937346i
$3$		0			0
$3$		0			0
$4$	−1.51447	+	1.30629i	−0.757235	+	0.653143i
$5$			4.33571i			1.93899i	0.245112	+	0.969495i	$0.421175\pi$
$5$			4.33571i			1.93899i	−0.245112	+	0.969495i	$0.578825\pi$
$6$		0			0
$7$	−2.30442			−0.870990			−0.435495	−	0.900191i	$-0.643427\pi$
$7$	−2.30442			−0.870990			−0.435495	+	0.900191i	$0.643427\pi$
$8$	−2.47782	−	1.36397i	−0.876041	−	0.482236i
$9$		0			0
$10$	−5.74745	+	2.13626i	−1.81750	+	0.675544i
$11$		−	0.582255i		−	0.175557i	−0.996140	−	0.0877783i	$-0.972023\pi$
$11$		−	0.582255i		−	0.175557i	0.996140	−	0.0877783i	$-0.0279767\pi$
$12$		0			0
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	−1.13542	−	3.05476i	−0.303453	−	0.816419i
$15$		0			0
$16$	0.587238	−	3.95666i	0.146810	−	0.989165i
$17$	−3.40894			−0.826790			−0.413395	−	0.910552i	$-0.635657\pi$
$17$	−3.40894			−0.826790			−0.413395	+	0.910552i	$0.635657\pi$
$18$		0			0
$19$		−	0.0627418i		−	0.0143940i	−0.999974	−	0.00719698i	$-0.997709\pi$
$19$		−	0.0627418i		−	0.0143940i	0.999974	−	0.00719698i	$-0.00229089\pi$
$20$	−5.66368	−	6.56631i	−1.26644	−	1.46827i
$21$		0			0
$22$	0.771842	−	0.286884i	0.164557	−	0.0611639i
$23$	6.65973			1.38865			0.694325	−	0.719662i	$-0.255703\pi$
$23$	6.65973			1.38865			0.694325	+	0.719662i	$0.255703\pi$
$24$		0			0
$25$	−13.7984			−2.75968
$26$	−1.32561	+	0.492712i	−0.259973	+	0.0966288i
$27$		0			0
$28$	3.48998	−	3.01023i	0.659544	−	0.568881i
$29$			2.41805i			0.449021i	0.974472	+	0.224510i	$0.0720783\pi$
$29$			2.41805i			0.449021i	−0.974472	+	0.224510i	$0.927922\pi$
$30$		0			0
$31$	5.63600			1.01226			0.506128	−	0.862458i	$-0.331076\pi$
$31$	5.63600			1.01226			0.506128	+	0.862458i	$0.331076\pi$
$32$	5.53432	−	1.17105i	0.978338	−	0.207014i
$33$		0			0
$34$	−1.67963	−	4.51892i	−0.288054	−	0.774988i
$35$		−	9.99131i		−	1.68884i
$36$		0			0
$37$		−	9.27328i		−	1.52452i	−0.647272	−	0.762259i	$-0.724090\pi$
$37$		−	9.27328i		−	1.52452i	0.647272	−	0.762259i	$-0.275910\pi$
$38$	0.0831710	−	0.0309136i	0.0134921	−	0.00501486i
$39$		0			0
$40$	5.91378	−	10.7431i	0.935051	−	1.69863i
$41$	−4.75376			−0.742413			−0.371207	−	0.928550i	$-0.621056\pi$
$41$	−4.75376			−0.742413			−0.371207	+	0.928550i	$0.621056\pi$
$42$		0			0
$43$			7.86434i			1.19930i	0.800262	+	0.599650i	$0.204694\pi$
$43$			7.86434i			1.19930i	−0.800262	+	0.599650i	$0.795306\pi$
$44$	0.760592	+	0.881808i	0.114664	+	0.132938i
$45$		0			0
$46$	3.28133	+	8.82819i	0.483806	+	1.30165i
$47$	0.0312900			0.00456412			0.00228206	−	0.999997i	$-0.499274\pi$
$47$	0.0312900			0.00456412			0.00228206	+	0.999997i	$0.499274\pi$
$48$		0			0
$49$	−1.68964			−0.241377
$50$	−6.79864	−	18.2913i	−0.961473	−	2.58678i
$51$		0			0
$52$	−1.30629	−	1.51447i	−0.181149	−	0.210019i
$53$			13.1656i			1.80843i	0.427078	+	0.904215i	$0.359543\pi$
$53$			13.1656i			1.80843i	−0.427078	+	0.904215i	$0.640457\pi$
$54$		0			0
$55$	2.52449			0.340402
$56$	5.70994	+	3.14316i	0.763023	+	0.420023i
$57$		0			0
$58$	−3.20539	+	1.19140i	−0.420888	+	0.156439i
$59$			4.75759i			0.619385i	0.950837	+	0.309693i	$0.100226\pi$
$59$			4.75759i			0.619385i	−0.950837	+	0.309693i	$0.899774\pi$
$60$		0			0
$61$		−	3.29149i		−	0.421432i	−0.977547	−	0.210716i	$-0.932420\pi$
$61$		−	3.29149i		−	0.421432i	0.977547	−	0.210716i	$-0.0675795\pi$
$62$	2.77693	+	7.47113i	0.352670	+	0.948834i
$63$		0			0
$64$	4.27917	+	6.75934i	0.534896	+	0.844918i
$65$	−4.33571			−0.537779
$66$		0			0
$67$		−	11.8777i		−	1.45109i	−0.688175	−	0.725545i	$-0.741588\pi$
$67$		−	11.8777i		−	1.45109i	0.688175	−	0.725545i	$-0.258412\pi$
$68$	5.16274	−	4.45305i	0.626074	−	0.540012i
$69$		0			0
$70$	13.2446	−	4.92284i	1.58303	−	0.588392i
$71$	−13.6251			−1.61700			−0.808500	−	0.588496i	$-0.799720\pi$
$71$	−13.6251			−1.61700			−0.808500	+	0.588496i	$0.799720\pi$
$72$		0			0
$73$	0.437175			0.0511675			0.0255837	−	0.999673i	$-0.491856\pi$
$73$	0.437175			0.0511675			0.0255837	+	0.999673i	$0.491856\pi$
$74$	12.2927	−	4.56905i	1.42900	−	0.531142i
$75$		0			0
$76$	0.0819587	+	0.0950206i	0.00940131	+	0.0108996i
$77$			1.34176i			0.152908i
$78$		0			0
$79$	−6.54503			−0.736373			−0.368187	−	0.929752i	$-0.620021\pi$
$79$	−6.54503			−0.736373			−0.368187	+	0.929752i	$0.620021\pi$
$80$	17.1549	+	2.54610i	1.91798	+	0.284662i
$81$		0			0
$82$	−2.34224	−	6.30162i	−0.258657	−	0.695898i
$83$			6.62844i			0.727566i	0.931484	+	0.363783i	$0.118515\pi$
$83$			6.62844i			0.727566i	−0.931484	+	0.363783i	$0.881485\pi$
$84$		0			0
$85$		−	14.7802i		−	1.60314i
$86$	−10.4250	+	3.87485i	−1.12416	+	0.417836i
$87$		0			0
$88$	−0.794179	+	1.44272i	−0.0846598	+	0.153795i
$89$	−8.23880			−0.873311			−0.436655	−	0.899629i	$-0.643837\pi$
$89$	−8.23880			−0.873311			−0.436655	+	0.899629i	$0.643837\pi$
$90$		0			0
$91$		−	2.30442i		−	0.241569i
$92$	−10.0860	+	8.69951i	−1.05153	+	0.906986i
$93$		0			0
$94$	0.0154170	+	0.0414783i	0.00159014	+	0.00427816i
$95$	0.272031			0.0279097
$96$		0			0
$97$	−0.664432			−0.0674629			−0.0337314	−	0.999431i	$-0.510739\pi$
$97$	−0.664432			−0.0674629			−0.0337314	+	0.999431i	$0.510739\pi$
$98$	−0.832504	−	2.23980i	−0.0840956	−	0.226253i
$99$		0			0
$100$	20.8973	−	18.0246i	2.08973	−	1.80246i
$101$			11.3867i			1.13302i	0.824055	+	0.566510i	$0.191707\pi$
$101$			11.3867i			1.13302i	−0.824055	+	0.566510i	$0.808293\pi$
$102$		0			0
$103$	−14.9131			−1.46943			−0.734716	−	0.678375i	$-0.762685\pi$
$103$	−14.9131			−1.46943			−0.734716	+	0.678375i	$0.762685\pi$
$104$	1.36397	−	2.47782i	0.133748	−	0.242970i
$105$		0			0
$106$	−17.4524	+	6.48683i	−1.69512	+	0.630057i
$107$		−	7.39073i		−	0.714489i	−0.934011	−	0.357244i	$-0.883716\pi$
$107$		−	7.39073i		−	0.714489i	0.934011	−	0.357244i	$-0.116284\pi$
$108$		0			0
$109$			17.4880i			1.67505i	0.546399	+	0.837525i	$0.315998\pi$
$109$			17.4880i			1.67505i	−0.546399	+	0.837525i	$0.684002\pi$
$110$	1.24385	+	3.34649i	0.118596	+	0.319075i
$111$		0			0
$112$	−1.35324	+	9.11781i	−0.127870	+	0.861552i
$113$	−10.4662			−0.984576			−0.492288	−	0.870432i	$-0.663839\pi$
$113$	−10.4662			−0.984576			−0.492288	+	0.870432i	$0.663839\pi$
$114$		0			0
$115$			28.8747i			2.69258i
$116$	−3.15866	−	3.66207i	−0.293275	−	0.340014i
$117$		0			0
$118$	−6.30669	+	2.34412i	−0.580578	+	0.215794i
$119$	7.85564			0.720126
$120$		0			0
$121$	10.6610			0.969180
$122$	4.36322	−	1.62176i	0.395028	−	0.146827i
$123$		0			0
$124$	−8.53556	+	7.36223i	−0.766516	+	0.661148i
$125$		−	38.1473i		−	3.41200i
$126$		0			0
$127$	20.9445			1.85852			0.929262	−	0.369420i	$-0.120444\pi$
$127$	20.9445			1.85852			0.929262	+	0.369420i	$0.120444\pi$
$128$	−6.85183	+	9.00291i	−0.605622	+	0.795752i
$129$		0			0
$130$	−2.13626	−	5.74745i	−0.187362	−	0.504085i
$131$			3.39073i			0.296249i	0.988969	+	0.148125i	$0.0473237\pi$
$131$			3.39073i			0.296249i	−0.988969	+	0.148125i	$0.952676\pi$
$132$		0			0
$133$			0.144584i			0.0125370i
$134$	15.7451	−	5.85228i	1.36017	−	0.505560i
$135$		0			0
$136$	8.44674	+	4.64969i	0.724302	+	0.398708i
$137$	5.78852			0.494546			0.247273	−	0.968946i	$-0.420466\pi$
$137$	5.78852			0.494546			0.247273	+	0.968946i	$0.420466\pi$
$138$		0			0
$139$			18.0874i			1.53415i	0.641558	+	0.767075i	$0.278289\pi$
$139$			18.0874i			1.53415i	−0.641558	+	0.767075i	$0.721711\pi$
$140$	13.0515	+	15.1315i	1.10305	+	1.27885i
$141$		0			0
$142$	−6.71324	−	18.0615i	−0.563363	−	1.51569i
$143$	0.582255			0.0486906
$144$		0			0
$145$	−10.4840			−0.870647
$146$	0.215401	+	0.579522i	0.0178267	+	0.0479616i
$147$		0			0
$148$	12.1135	+	14.0441i	0.995727	+	1.15442i
$149$		−	9.21251i		−	0.754719i	−0.926067	−	0.377359i	$-0.876832\pi$
$149$		−	9.21251i		−	0.754719i	0.926067	−	0.377359i	$-0.123168\pi$
$150$		0			0
$151$	−2.49249			−0.202836			−0.101418	−	0.994844i	$-0.532338\pi$
$151$	−2.49249			−0.202836			−0.101418	+	0.994844i	$0.532338\pi$
$152$	−0.0855780	+	0.155463i	−0.00694129	+	0.0126097i
$153$		0			0
$154$	−1.77865	+	0.661102i	−0.143328	+	0.0532732i
$155$			24.4361i			1.96275i
$156$		0			0
$157$			4.18956i			0.334363i	0.985926	+	0.167182i	$0.0534666\pi$
$157$			4.18956i			0.334363i	−0.985926	+	0.167182i	$0.946533\pi$
$158$	−3.22481	−	8.67614i	−0.256552	−	0.690237i
$159$		0			0
$160$	5.07732	+	23.9952i	0.401397	+	1.89699i
$161$	−15.3468			−1.20950
$162$		0			0
$163$		−	10.8387i		−	0.848949i	−0.905440	−	0.424475i	$-0.860459\pi$
$163$		−	10.8387i		−	0.848949i	0.905440	−	0.424475i	$-0.139541\pi$
$164$	7.19943	−	6.20977i	0.562181	−	0.484902i
$165$		0			0
$166$	−8.78671	+	3.26591i	−0.681981	+	0.253484i
$167$	13.5345			1.04733			0.523667	−	0.851923i	$-0.324564\pi$
$167$	13.5345			1.04733			0.523667	+	0.851923i	$0.324564\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	19.5927	−	7.28238i	1.50269	−	0.558533i
$171$		0			0
$172$	−10.2731	−	11.9103i	−0.783314	−	0.908152i
$173$			11.3922i			0.866134i	0.901362	+	0.433067i	$0.142569\pi$
$173$			11.3922i			0.866134i	−0.901362	+	0.433067i	$0.857431\pi$
$174$		0			0
$175$	31.7974			2.40365
$176$	−2.30379	−	0.341923i	−0.173654	−	0.0257734i
$177$		0			0
$178$	−4.05935	−	10.9214i	−0.304261	−	0.818594i
$179$			9.99131i			0.746786i	0.927673	+	0.373393i	$0.121806\pi$
$179$			9.99131i			0.746786i	−0.927673	+	0.373393i	$0.878194\pi$
$180$		0			0
$181$			24.2251i			1.80064i	0.435229	+	0.900320i	$0.356668\pi$
$181$			24.2251i			1.80064i	−0.435229	+	0.900320i	$0.643332\pi$
$182$	3.05476	−	1.13542i	0.226434	−	0.0841627i
$183$		0			0
$184$	−16.5016	−	9.08368i	−1.21651	−	0.669657i
$185$	40.2063			2.95602
$186$		0			0
$187$			1.98487i			0.145148i
$188$	−0.0473878	+	0.0408737i	−0.00345611	+	0.00298102i
$189$		0			0
$190$	0.134033	+	0.360606i	0.00972375	+	0.0261611i
$191$	14.2745			1.03287			0.516434	−	0.856327i	$-0.327259\pi$
$191$	14.2745			1.03287			0.516434	+	0.856327i	$0.327259\pi$
$192$		0			0
$193$	4.98894			0.359112			0.179556	−	0.983748i	$-0.442534\pi$
$193$	4.98894			0.359112			0.179556	+	0.983748i	$0.442534\pi$
$194$	−0.327374	−	0.880776i	−0.0235041	−	0.0632361i
$195$		0			0
$196$	2.55890	−	2.20715i	0.182779	−	0.157653i
$197$		−	10.9989i		−	0.783637i	−0.920042	−	0.391819i	$-0.871846\pi$
$197$		−	10.9989i		−	0.783637i	0.920042	−	0.391819i	$-0.128154\pi$
$198$		0			0
$199$	9.13566			0.647609			0.323805	−	0.946124i	$-0.395038\pi$
$199$	9.13566			0.647609			0.323805	+	0.946124i	$0.395038\pi$
$200$	34.1899	+	18.8206i	2.41759	+	1.33082i
$201$		0			0
$202$	−15.0943	+	5.61037i	−1.06203	+	0.394744i
$203$		−	5.57221i		−	0.391093i
$204$		0			0
$205$		−	20.6110i		−	1.43953i
$206$	−7.34787	−	19.7689i	−0.511950	−	1.37737i
$207$		0			0
$208$	3.95666	+	0.587238i	0.274345	+	0.0407176i
$209$	−0.0365318			−0.00252696
$210$		0			0
$211$			1.06551i			0.0733526i	0.999327	+	0.0366763i	$0.0116770\pi$
$211$			1.06551i			0.0733526i	−0.999327	+	0.0366763i	$0.988323\pi$
$212$	−17.1980	−	19.9389i	−1.18116	−	1.36941i
$213$		0			0
$214$	9.79721	−	3.64150i	0.669723	−	0.248928i
$215$	−34.0975			−2.32543
$216$		0			0
$217$	−12.9877			−0.881665
$218$	−23.1823	+	8.61657i	−1.57010	+	0.583587i
$219$		0			0
$220$	−3.82327	+	3.29771i	−0.257765	+	0.222331i
$221$		−	3.40894i		−	0.229310i
$222$		0			0
$223$	8.91055			0.596695			0.298347	−	0.954457i	$-0.403565\pi$
$223$	8.91055			0.596695			0.298347	+	0.954457i	$0.403565\pi$
$224$	−12.7534	+	2.69858i	−0.852123	+	0.180307i
$225$		0			0
$226$	−5.15682	−	13.8741i	−0.343026	−	0.922888i
$227$			17.1895i			1.14091i	0.821330	+	0.570454i	$0.193233\pi$
$227$			17.1895i			1.14091i	−0.821330	+	0.570454i	$0.806767\pi$
$228$		0			0
$229$			10.3375i			0.683122i	0.939860	+	0.341561i	$0.110956\pi$
$229$			10.3375i			0.683122i	−0.939860	+	0.341561i	$0.889044\pi$
$230$	−38.2765	+	14.2269i	−2.52388	+	0.938094i
$231$		0			0
$232$	3.29815	−	5.99149i	0.216534	−	0.393361i
$233$	−0.475100			−0.0311248			−0.0155624	−	0.999879i	$-0.504954\pi$
$233$	−0.475100			−0.0311248			−0.0155624	+	0.999879i	$0.504954\pi$
$234$		0			0
$235$			0.135664i			0.00884977i
$236$	−6.21477	−	7.20522i	−0.404547	−	0.469020i
$237$		0			0
$238$	3.87057	+	10.4135i	0.250892	+	0.675007i
$239$	−8.74191			−0.565467			−0.282734	−	0.959198i	$-0.591241\pi$
$239$	−8.74191			−0.565467			−0.282734	+	0.959198i	$0.591241\pi$
$240$		0			0
$241$	11.6534			0.750660			0.375330	−	0.926891i	$-0.377529\pi$
$241$	11.6534			0.750660			0.375330	+	0.926891i	$0.377529\pi$
$242$	5.25279	+	14.1323i	0.337662	+	0.908457i
$243$		0			0
$244$	4.29962	+	4.98486i	0.275255	+	0.319123i
$245$		−	7.32578i		−	0.468027i
$246$		0			0
$247$	0.0627418			0.00399217
$248$	−13.9650	−	7.68734i	−0.886778	−	0.488147i
$249$		0			0
$250$	50.5684	−	18.7957i	3.19823	−	1.18874i
$251$		−	5.41847i		−	0.342011i	−0.985270	−	0.171005i	$-0.945298\pi$
$251$		−	5.41847i		−	0.342011i	0.985270	−	0.171005i	$-0.0547015\pi$
$252$		0			0
$253$		−	3.87767i		−	0.243787i
$254$	10.3196	+	27.7642i	0.647510	+	1.74208i
$255$		0			0
$256$	−15.3103	−	4.64700i	−0.956894	−	0.290438i
$257$	−1.09367			−0.0682212			−0.0341106	−	0.999418i	$-0.510860\pi$
$257$	−1.09367			−0.0682212			−0.0341106	+	0.999418i	$0.510860\pi$
$258$		0			0
$259$			21.3695i			1.32784i
$260$	6.56631	−	5.66368i	0.407225	−	0.351246i
$261$		0			0
$262$	−4.49478	+	1.67065i	−0.277688	+	0.103213i
$263$	−8.89318			−0.548377			−0.274189	−	0.961676i	$-0.588409\pi$
$263$	−8.89318			−0.548377			−0.274189	+	0.961676i	$0.588409\pi$
$264$		0			0
$265$	−57.0821			−3.50653
$266$	−0.191661	+	0.0712381i	−0.0117515	+	0.00436789i
$267$		0			0
$268$	15.5156	+	17.9884i	0.947769	+	1.09882i
$269$			15.6451i			0.953901i	0.878930	+	0.476951i	$0.158258\pi$
$269$			15.6451i			0.953901i	−0.878930	+	0.476951i	$0.841742\pi$
$270$		0			0
$271$	17.2508			1.04791			0.523956	−	0.851746i	$-0.324456\pi$
$271$	17.2508			1.04791			0.523956	+	0.851746i	$0.324456\pi$
$272$	−2.00186	+	13.4880i	−0.121381	+	0.817831i
$273$		0			0
$274$	2.85207	+	7.67330i	0.172300	+	0.463561i
$275$			8.03420i			0.484480i
$276$		0			0
$277$			5.22709i			0.314065i	0.987593	+	0.157033i	$0.0501928\pi$
$277$			5.22709i			0.314065i	−0.987593	+	0.157033i	$0.949807\pi$
$278$	−23.9767	+	8.91186i	−1.43803	+	0.534498i
$279$		0			0
$280$	−13.6279	+	24.7567i	−0.814420	+	1.47949i
$281$	−23.5272			−1.40351			−0.701757	−	0.712416i	$-0.747601\pi$
$281$	−23.5272			−1.40351			−0.701757	+	0.712416i	$0.747601\pi$
$282$		0			0
$283$		−	6.22302i		−	0.369920i	−0.982746	−	0.184960i	$-0.940784\pi$
$283$		−	6.22302i		−	0.369920i	0.982746	−	0.184960i	$-0.0592156\pi$
$284$	20.6348	−	17.7983i	1.22445	−	1.05613i
$285$		0			0
$286$	0.286884	+	0.771842i	0.0169638	+	0.0456400i
$287$	10.9547			0.646634
$288$		0			0
$289$	−5.37912			−0.316419
$290$	−5.16558	−	13.8976i	−0.303333	−	0.816097i
$291$		0			0
$292$	−0.662088	+	0.571075i	−0.0387458	+	0.0334197i
$293$			13.3240i			0.778396i	0.921154	+	0.389198i	$0.127248\pi$
$293$			13.3240i			0.778396i	−0.921154	+	0.389198i	$0.872752\pi$
$294$		0			0
$295$	−20.6275			−1.20098
$296$	−12.6485	+	22.9775i	−0.735178	+	1.33554i
$297$		0			0
$298$	12.2122	−	4.53912i	0.707432	−	0.262944i
$299$			6.65973i			0.385142i
$300$		0			0
$301$		−	18.1228i		−	1.04458i
$302$	−1.22808	−	3.30406i	−0.0706679	−	0.190127i
$303$		0			0
$304$	−0.248248	−	0.0368444i	−0.0142380	−	0.00211317i
$305$	14.2710			0.817152
$306$		0			0
$307$		−	28.7588i		−	1.64135i	−0.571396	−	0.820675i	$-0.693598\pi$
$307$		−	28.7588i		−	1.64135i	0.571396	−	0.820675i	$-0.306402\pi$
$308$	−1.75272	−	2.03206i	−0.0998708	−	0.115787i
$309$		0			0
$310$	−32.3927	+	12.0400i	−1.83978	+	0.683824i
$311$	−21.9394			−1.24407			−0.622034	−	0.782990i	$-0.713694\pi$
$311$	−21.9394			−1.24407			−0.622034	+	0.782990i	$0.713694\pi$
$312$		0			0
$313$	−2.60950			−0.147498			−0.0737488	−	0.997277i	$-0.523496\pi$
$313$	−2.60950			−0.147498			−0.0737488	+	0.997277i	$0.523496\pi$
$314$	−5.55371	+	2.06425i	−0.313414	+	0.116492i
$315$		0			0
$316$	9.91225	−	8.54967i	0.557608	−	0.480957i
$317$		−	16.0656i		−	0.902334i	−0.892439	−	0.451167i	$-0.851008\pi$
$317$		−	16.0656i		−	0.902334i	0.892439	−	0.451167i	$-0.148992\pi$
$318$		0			0
$319$	1.40792			0.0788286
$320$	−29.3066	+	18.5533i	−1.63829	+	1.03716i
$321$		0			0
$322$	−7.56157	−	20.3439i	−0.421390	−	1.13372i
$323$			0.213883i			0.0119008i
$324$		0			0
$325$		−	13.7984i		−	0.765398i
$326$	14.3678	−	5.34034i	0.795759	−	0.295774i
$327$		0			0
$328$	11.7790	+	6.48399i	0.650385	+	0.358019i
$329$	−0.0721054			−0.00397530
$330$		0			0
$331$		−	4.12863i		−	0.226930i	−0.993542	−	0.113465i	$-0.963805\pi$
$331$		−	4.12863i		−	0.226930i	0.993542	−	0.113465i	$-0.0361950\pi$
$332$	−8.65864	−	10.0386i	−0.475204	−	0.550938i
$333$		0			0
$334$	6.66863	+	17.9415i	0.364891	+	0.981715i
$335$	51.4982			2.81365
$336$		0			0
$337$	6.01639			0.327734			0.163867	−	0.986482i	$-0.447603\pi$
$337$	6.01639			0.327734			0.163867	+	0.986482i	$0.447603\pi$
$338$	−0.492712	−	1.32561i	−0.0268000	−	0.0721035i
$339$		0			0
$340$	19.3071	+	22.3842i	1.04708	+	1.21395i
$341$		−	3.28159i		−	0.177708i
$342$		0			0
$343$	20.0246			1.08123
$344$	10.7267	−	19.4864i	0.578346	−	1.05064i
$345$		0			0
$346$	−15.1016	+	5.61308i	−0.811867	+	0.301761i
$347$			1.60019i			0.0859029i	0.999077	+	0.0429514i	$0.0136761\pi$
$347$			1.60019i			0.0859029i	−0.999077	+	0.0429514i	$0.986324\pi$
$348$		0			0
$349$			0.755303i			0.0404305i	0.999796	+	0.0202152i	$0.00643515\pi$
$349$			0.755303i			0.0404305i	−0.999796	+	0.0202152i	$0.993565\pi$
$350$	15.6669	+	42.1508i	0.837433	+	2.25306i
$351$		0			0
$352$	−0.681848	−	3.22239i	−0.0363426	−	0.171754i
$353$	−23.2960			−1.23992			−0.619962	−	0.784632i	$-0.712852\pi$
$353$	−23.2960			−1.23992			−0.619962	+	0.784632i	$0.712852\pi$
$354$		0			0
$355$		−	59.0745i		−	3.13535i
$356$	12.4774	−	10.7622i	0.661301	−	0.570396i
$357$		0			0
$358$	−13.2446	+	4.92284i	−0.699997	+	0.260180i
$359$	32.9111			1.73698			0.868491	−	0.495706i	$-0.165090\pi$
$359$	32.9111			1.73698			0.868491	+	0.495706i	$0.165090\pi$
$360$		0			0
$361$	18.9961			0.999793
$362$	−32.1130	+	11.9360i	−1.68782	+	0.627343i
$363$		0			0
$364$	3.01023	+	3.48998i	0.157779	+	0.182925i
$365$			1.89547i			0.0992132i
$366$		0			0
$367$	2.51714			0.131394			0.0656969	−	0.997840i	$-0.479073\pi$
$367$	2.51714			0.131394			0.0656969	+	0.997840i	$0.479073\pi$
$368$	3.91085	−	26.3503i	0.203867	−	1.37360i
$369$		0			0
$370$	19.8101	+	53.2977i	1.02988	+	2.77082i
$371$		−	30.3390i		−	1.57512i
$372$		0			0
$373$			25.9826i			1.34533i	0.739947	+	0.672665i	$0.234850\pi$
$373$			25.9826i			1.34533i	−0.739947	+	0.672665i	$0.765150\pi$
$374$	−2.63116	+	0.977972i	−0.136054	+	0.0505697i
$375$		0			0
$376$	−0.0775309	−	0.0426786i	−0.00399835	−	0.00220098i
$377$	−2.41805			−0.124536
$378$		0			0
$379$		−	25.5104i		−	1.31038i	−0.755464	−	0.655190i	$-0.772589\pi$
$379$		−	25.5104i		−	1.31038i	0.755464	−	0.655190i	$-0.227411\pi$
$380$	−0.411982	+	0.355349i	−0.0211342	+	0.0182290i
$381$		0			0
$382$	7.03323	+	18.9224i	0.359851	+	0.968155i
$383$	25.1320			1.28419			0.642093	−	0.766627i	$-0.278066\pi$
$383$	25.1320			1.28419			0.642093	+	0.766627i	$0.278066\pi$
$384$		0			0
$385$	−5.81750			−0.296487
$386$	2.45811	+	6.61338i	0.125115	+	0.336612i
$387$		0			0
$388$	1.00626	−	0.867938i	0.0510852	−	0.0440629i
$389$		−	21.2888i		−	1.07938i	−0.841862	−	0.539692i	$-0.818541\pi$
$389$		−	21.2888i		−	1.07938i	0.841862	−	0.539692i	$-0.181459\pi$
$390$		0			0
$391$	−22.7026			−1.14812
$392$	4.18661	+	2.30461i	0.211456	+	0.116401i
$393$		0			0
$394$	14.5802	−	5.41928i	0.734539	−	0.273019i
$395$		−	28.3774i		−	1.42782i
$396$		0			0
$397$			12.1291i			0.608741i	0.952554	+	0.304371i	$0.0984461\pi$
$397$			12.1291i			0.608741i	−0.952554	+	0.304371i	$0.901554\pi$
$398$	4.50125	+	12.1103i	0.225627	+	0.607034i
$399$		0			0
$400$	−8.10295	+	54.5956i	−0.405147	+	2.72978i
$401$	−10.4114			−0.519919			−0.259959	−	0.965620i	$-0.583709\pi$
$401$	−10.4114			−0.519919			−0.259959	+	0.965620i	$0.583709\pi$
$402$		0			0
$403$			5.63600i			0.280749i
$404$	−14.8743	−	17.2448i	−0.740024	−	0.857962i
$405$		0			0
$406$	7.38656	−	2.74550i	0.366589	−	0.136257i
$407$	−5.39942			−0.267639
$408$		0			0
$409$	−2.94848			−0.145793			−0.0728965	−	0.997340i	$-0.523224\pi$
$409$	−2.94848			−0.145793			−0.0728965	+	0.997340i	$0.523224\pi$
$410$	27.3220	−	10.1553i	1.34934	−	0.501533i
$411$		0			0
$412$	22.5854	−	19.4808i	1.11271	−	0.959749i
$413$		−	10.9635i		−	0.539478i
$414$		0			0
$415$	−28.7390			−1.41074
$416$	1.17105	+	5.53432i	0.0574153	+	0.271342i
$417$		0			0
$418$	−0.0179996	−	0.0484268i	−0.000880391	−	0.00236863i
$419$		−	26.3514i		−	1.28735i	−0.765299	−	0.643675i	$-0.777409\pi$
$419$		−	26.3514i		−	1.28735i	0.765299	−	0.643675i	$-0.222591\pi$
$420$		0			0
$421$		−	4.54054i		−	0.221292i	−0.993860	−	0.110646i	$-0.964708\pi$
$421$		−	4.54054i		−	0.221292i	0.993860	−	0.110646i	$-0.0352920\pi$
$422$	−1.41244	+	0.524988i	−0.0687567	+	0.0255560i
$423$		0			0
$424$	17.9574	−	32.6219i	0.872090	−	1.58426i
$425$	47.0380			2.28168
$426$		0			0
$427$			7.58498i			0.367063i
$428$	9.65440	+	11.1930i	0.466663	+	0.541036i
$429$		0			0
$430$	−16.8002	−	45.1999i	−0.810180	−	2.17973i
$431$	−15.3547			−0.739608			−0.369804	−	0.929110i	$-0.620575\pi$
$431$	−15.3547			−0.739608			−0.369804	+	0.929110i	$0.620575\pi$
$432$		0			0
$433$	27.9869			1.34497			0.672483	−	0.740113i	$-0.265228\pi$
$433$	27.9869			1.34497			0.672483	+	0.740113i	$0.265228\pi$
$434$	−6.39921	−	17.2166i	−0.307172	−	0.826425i
$435$		0			0
$436$	−22.8444	−	26.4851i	−1.09405	−	1.26841i
$437$		−	0.417844i		−	0.0199882i
$438$		0			0
$439$	−6.64728			−0.317257			−0.158629	−	0.987338i	$-0.550707\pi$
$439$	−6.64728			−0.317257			−0.158629	+	0.987338i	$0.550707\pi$
$440$	−6.25523	−	3.44333i	−0.298207	−	0.164154i
$441$		0			0
$442$	4.51892	−	1.67963i	0.214943	−	0.0798917i
$443$			32.6534i			1.55141i	0.631096	+	0.775705i	$0.282605\pi$
$443$			32.6534i			1.55141i	−0.631096	+	0.775705i	$0.717395\pi$
$444$		0			0
$445$		−	35.7211i		−	1.69334i
$446$	4.39033	+	11.8119i	0.207888	+	0.559309i
$447$		0			0
$448$	−9.86102	−	15.5764i	−0.465889	−	0.735915i
$449$	21.1274			0.997063			0.498531	−	0.866872i	$-0.333873\pi$
$449$	21.1274			0.997063			0.498531	+	0.866872i	$0.333873\pi$
$450$		0			0
$451$			2.76790i			0.130336i
$452$	15.8507	−	13.6718i	0.745555	−	0.643069i
$453$		0			0
$454$	−22.7865	+	8.46948i	−1.06943	+	0.397492i
$455$	9.99131			0.468400
$456$		0			0
$457$	18.2163			0.852121			0.426060	−	0.904695i	$-0.359901\pi$
$457$	18.2163			0.852121			0.426060	+	0.904695i	$0.359901\pi$
$458$	−13.7035	+	5.09342i	−0.640322	+	0.238000i
$459$		0			0
$460$	−37.7186	−	43.7298i	−1.75864	−	2.03891i
$461$			20.4992i			0.954741i	0.878702	+	0.477371i	$0.158410\pi$
$461$			20.4992i			0.954741i	−0.878702	+	0.477371i	$0.841590\pi$
$462$		0			0
$463$	−5.45645			−0.253583			−0.126791	−	0.991929i	$-0.540468\pi$
$463$	−5.45645			−0.253583			−0.126791	+	0.991929i	$0.540468\pi$
$464$	9.56740	+	1.41997i	0.444156	+	0.0659205i
$465$		0			0
$466$	−0.234087	−	0.629796i	−0.0108439	−	0.0291747i
$467$		−	33.7488i		−	1.56171i	−0.624714	−	0.780853i	$-0.714785\pi$
$467$		−	33.7488i		−	1.56171i	0.624714	−	0.780853i	$-0.285215\pi$
$468$		0			0
$469$			27.3712i			1.26388i
$470$	−0.179838	+	0.0668435i	−0.00829530	+	0.00308326i
$471$		0			0
$472$	6.48921	−	11.7884i	0.298690	−	0.542607i
$473$	4.57905			0.210545
$474$		0			0
$475$			0.865737i			0.0397227i
$476$	−11.8971	+	10.2617i	−0.545304	+	0.470345i
$477$		0			0
$478$	−4.30724	−	11.5883i	−0.197009	−	0.530038i
$479$	7.19006			0.328522			0.164261	−	0.986417i	$-0.447476\pi$
$479$	7.19006			0.328522			0.164261	+	0.986417i	$0.447476\pi$
$480$		0			0
$481$	9.27328			0.422825
$482$	5.74176	+	15.4478i	0.261530	+	0.703628i
$483$		0			0
$484$	−16.1457	+	13.9263i	−0.733897	+	0.633013i
$485$		−	2.88079i		−	0.130810i
$486$		0			0
$487$	−9.72505			−0.440684			−0.220342	−	0.975423i	$-0.570717\pi$
$487$	−9.72505			−0.440684			−0.220342	+	0.975423i	$0.570717\pi$
$488$	−4.48949	+	8.15571i	−0.203230	+	0.369192i
$489$		0			0
$490$	9.71111	−	3.60950i	0.438703	−	0.163061i
$491$			7.93742i			0.358211i	0.983830	+	0.179105i	$0.0573203\pi$
$491$			7.93742i			0.358211i	−0.983830	+	0.179105i	$0.942680\pi$
$492$		0			0
$493$		−	8.24300i		−	0.371246i
$494$	0.0309136	+	0.0831710i	0.00139087	+	0.00374204i
$495$		0			0
$496$	3.30968	−	22.2997i	0.148609	−	1.00129i
$497$	31.3980			1.40839
$498$		0			0
$499$		−	10.1702i		−	0.455282i	−0.973745	−	0.227641i	$-0.926899\pi$
$499$		−	10.1702i		−	0.455282i	0.973745	−	0.227641i	$-0.0731013\pi$
$500$	49.8313	+	57.7730i	2.22852	+	2.58369i
$501$		0			0
$502$	7.18276	−	2.66974i	0.320582	−	0.119156i
$503$	22.4670			1.00176			0.500878	−	0.865518i	$-0.333011\pi$
$503$	22.4670			1.00176			0.500878	+	0.865518i	$0.333011\pi$
$504$		0			0
$505$	−49.3695			−2.19691
$506$	5.14026	−	1.91057i	0.228513	−	0.0849353i
$507$		0			0
$508$	−31.7198	+	27.3595i	−1.40734	+	1.21388i
$509$			2.95818i			0.131119i	0.997849	+	0.0655595i	$0.0208832\pi$
$509$			2.95818i			0.131119i	−0.997849	+	0.0655595i	$0.979117\pi$
$510$		0			0
$511$	−1.00744			−0.0445663
$512$	−1.38347	−	22.5851i	−0.0611412	−	0.998129i
$513$		0			0
$514$	−0.538864	−	1.44978i	−0.0237683	−	0.0639469i
$515$		−	64.6589i		−	2.84921i
$516$		0			0
$517$		−	0.0182188i		−	0.000801261i
$518$	−28.3276	+	10.5290i	−1.24464	+	0.462619i
$519$		0			0
$520$	10.7431	+	5.91378i	0.471117	+	0.259337i
$521$	38.3759			1.68128			0.840640	−	0.541594i	$-0.182179\pi$
$521$	38.3759			1.68128			0.840640	+	0.541594i	$0.182179\pi$
$522$		0			0
$523$			20.7001i			0.905153i	0.891726	+	0.452576i	$0.149495\pi$
$523$			20.7001i			0.905153i	−0.891726	+	0.452576i	$0.850505\pi$
$524$	−4.42926	−	5.13516i	−0.193493	−	0.224330i
$525$		0			0
$526$	−4.38178	−	11.7889i	−0.191055	−	0.514019i
$527$	−19.2128			−0.836923
$528$		0			0
$529$	21.3520			0.928349
$530$	−28.1250	−	75.6685i	−1.22167	−	3.28683i
$531$		0			0
$532$	−0.188868	−	0.218968i	−0.00818845	−	0.00949345i
$533$		−	4.75376i		−	0.205908i
$534$		0			0
$535$	32.0441			1.38539
$536$	−16.2008	+	29.4307i	−0.699768	+	1.27121i
$537$		0			0
$538$	−20.7393	+	7.70855i	−0.894135	+	0.332339i
$539$			0.983800i			0.0423753i
$540$		0			0
$541$			0.180587i			0.00776404i	0.999992	+	0.00388202i	$0.00123569\pi$
$541$			0.180587i			0.00776404i	−0.999992	+	0.00388202i	$0.998764\pi$
$542$	8.49967	+	22.8678i	0.365092	+	0.982255i
$543$		0			0
$544$	−18.8662	+	3.99203i	−0.808880	+	0.171157i
$545$	−75.8231			−3.24791
$546$		0			0
$547$		−	11.6587i		−	0.498489i	−0.968441	−	0.249244i	$-0.919818\pi$
$547$		−	11.6587i		−	0.498489i	0.968441	−	0.249244i	$-0.0801822\pi$
$548$	−8.76653	+	7.56145i	−0.374488	+	0.323009i
$549$		0			0
$550$	−10.6502	+	3.95854i	−0.454126	+	0.168793i
$551$	0.151713			0.00646319
$552$		0			0
$553$	15.0825			0.641374
$554$	−6.92907	+	2.57545i	−0.294388	+	0.109420i
$555$		0			0
$556$	−23.6272	−	27.3928i	−1.00202	−	1.16171i
$557$			13.1212i			0.555961i	0.960587	+	0.277981i	$0.0896651\pi$
$557$			13.1212i			0.555961i	−0.960587	+	0.277981i	$0.910335\pi$
$558$		0			0
$559$	−7.86434			−0.332626
$560$	−39.5322	−	5.86728i	−1.67054	−	0.247938i
$561$		0			0
$562$	−11.5921	−	31.1878i	−0.488984	−	1.31558i
$563$		−	22.1529i		−	0.933633i	−0.884354	−	0.466817i	$-0.845401\pi$
$563$		−	22.1529i		−	0.933633i	0.884354	−	0.466817i	$-0.154599\pi$
$564$		0			0
$565$		−	45.3784i		−	1.90908i
$566$	8.24929	−	3.06616i	0.346743	−	0.128880i
$567$		0			0
$568$	33.7605	+	18.5842i	1.41656	+	0.779776i
$569$	−32.0592			−1.34399			−0.671997	−	0.740554i	$-0.734563\pi$
$569$	−32.0592			−1.34399			−0.671997	+	0.740554i	$0.734563\pi$
$570$		0			0
$571$			19.0642i			0.797812i	0.916992	+	0.398906i	$0.130610\pi$
$571$			19.0642i			0.797812i	−0.916992	+	0.398906i	$0.869390\pi$
$572$	−0.881808	+	0.760592i	−0.0368703	+	0.0318019i
$573$		0			0
$574$	5.39750	+	14.5216i	0.225287	+	0.606120i
$575$	−91.8937			−3.83223
$576$		0			0
$577$	6.36039			0.264786			0.132393	−	0.991197i	$-0.457734\pi$
$577$	6.36039			0.264786			0.132393	+	0.991197i	$0.457734\pi$
$578$	−2.65035	−	7.13060i	−0.110240	−	0.296594i
$579$		0			0
$580$	15.8777	−	13.6951i	0.659284	−	0.568656i
$581$		−	15.2747i		−	0.633703i
$582$		0			0
$583$	7.66572			0.317482
$584$	−1.08324	−	0.596294i	−0.0448248	−	0.0246748i
$585$		0			0
$586$	−17.6624	+	6.56489i	−0.729627	+	0.271193i
$587$		−	16.8490i		−	0.695432i	−0.937600	−	0.347716i	$-0.886957\pi$
$587$		−	16.8490i		−	0.695432i	0.937600	−	0.347716i	$-0.113043\pi$
$588$		0			0
$589$		−	0.353613i		−	0.0145704i
$590$	−10.1634	−	27.3440i	−0.418422	−	1.12574i
$591$		0			0
$592$	−36.6912	−	5.44562i	−1.50800	−	0.223814i
$593$	30.9202			1.26974			0.634871	−	0.772618i	$-0.281053\pi$
$593$	30.9202			1.26974			0.634871	+	0.772618i	$0.281053\pi$
$594$		0			0
$595$			34.0598i			1.39632i
$596$	12.0342	+	13.9521i	0.492939	+	0.571499i
$597$		0			0
$598$	−8.82819	+	3.28133i	−0.361012	+	0.134184i
$599$	0.158853			0.00649057			0.00324528	−	0.999995i	$-0.498967\pi$
$599$	0.158853			0.00649057			0.00324528	+	0.999995i	$0.498967\pi$
$600$		0			0
$601$	−6.96910			−0.284276			−0.142138	−	0.989847i	$-0.545398\pi$
$601$	−6.96910			−0.284276			−0.142138	+	0.989847i	$0.545398\pi$
$602$	24.0237	−	8.92930i	0.979131	−	0.363931i
$603$		0			0
$604$	3.77480	−	3.25590i	0.153594	−	0.132481i
$605$			46.2229i			1.87923i
$606$		0			0
$607$	43.8942			1.78161			0.890805	−	0.454385i	$-0.150141\pi$
$607$	43.8942			1.78161			0.890805	+	0.454385i	$0.150141\pi$
$608$	−0.0734736	−	0.347233i	−0.00297975	−	0.0140822i
$609$		0			0
$610$	7.03147	+	18.9177i	0.284696	+	0.765954i
$611$			0.0312900i			0.00126586i
$612$		0			0
$613$		−	0.317515i		−	0.0128243i	−0.999979	−	0.00641216i	$-0.997959\pi$
$613$		−	0.317515i		−	0.0128243i	0.999979	−	0.00641216i	$-0.00204107\pi$
$614$	38.1228	−	14.1698i	1.53851	−	0.571846i
$615$		0			0
$616$	1.83012	−	3.32464i	0.0737378	−	0.133954i
$617$	−2.54233			−0.102350			−0.0511752	−	0.998690i	$-0.516297\pi$
$617$	−2.54233			−0.102350			−0.0511752	+	0.998690i	$0.516297\pi$
$618$		0			0
$619$			36.6748i			1.47409i	0.675846	+	0.737043i	$0.263778\pi$
$619$			36.6748i			1.47409i	−0.675846	+	0.737043i	$0.736222\pi$
$620$	−31.9205	−	37.0077i	−1.28196	−	1.48627i
$621$		0			0
$622$	−10.8098	−	29.0830i	−0.433433	−	1.16612i
$623$	18.9857			0.760645
$624$		0			0
$625$	96.4039			3.85616
$626$	−1.28573	−	3.45917i	−0.0513882	−	0.138256i
$627$		0			0
$628$	−5.47276	−	6.34496i	−0.218387	−	0.253191i
$629$			31.6121i			1.26046i
$630$		0			0
$631$	−32.5523			−1.29589			−0.647943	−	0.761689i	$-0.724370\pi$
$631$	−32.5523			−1.29589			−0.647943	+	0.761689i	$0.724370\pi$
$632$	16.2174	+	8.92722i	0.645093	+	0.355106i
$633$		0			0
$634$	21.2967	−	7.91572i	0.845800	−	0.314373i
$635$			90.8094i			3.60366i
$636$		0			0
$637$		−	1.68964i		−	0.0669458i
$638$	0.693701	+	1.86635i	0.0274639	+	0.0738897i
$639$		0			0
$640$	−39.0340	−	29.7076i	−1.54296	−	1.17430i
$641$	−17.0435			−0.673178			−0.336589	−	0.941652i	$-0.609273\pi$
$641$	−17.0435			−0.673178			−0.336589	+	0.941652i	$0.609273\pi$
$642$		0			0
$643$		−	11.2883i		−	0.445168i	−0.974914	−	0.222584i	$-0.928551\pi$
$643$		−	11.2883i		−	0.445168i	0.974914	−	0.222584i	$-0.0714492\pi$
$644$	23.2423	−	20.0473i	0.915876	−	0.789976i
$645$		0			0
$646$	−0.283525	+	0.105383i	−0.0111552	+	0.00414623i
$647$	−22.0458			−0.866711			−0.433355	−	0.901223i	$-0.642670\pi$
$647$	−22.0458			−0.866711			−0.433355	+	0.901223i	$0.642670\pi$
$648$		0			0
$649$	2.77013			0.108737
$650$	18.2913	−	6.79864i	0.717442	−	0.266665i
$651$		0			0
$652$	14.1584	+	16.4148i	0.554485	+	0.642854i
$653$		−	28.8324i		−	1.12830i	−0.825673	−	0.564149i	$-0.809204\pi$
$653$		−	28.8324i		−	1.12830i	0.825673	−	0.564149i	$-0.190796\pi$
$654$		0			0
$655$	−14.7012			−0.574425
$656$	−2.79159	+	18.8090i	−0.108993	+	0.734369i
$657$		0			0
$658$	−0.0355272	−	0.0955834i	−0.00138499	−	0.00372623i
$659$			44.5007i			1.73350i	0.498742	+	0.866750i	$0.333795\pi$
$659$			44.5007i			1.73350i	−0.498742	+	0.866750i	$0.666205\pi$
$660$		0			0
$661$			11.2482i			0.437503i	0.975781	+	0.218752i	$0.0701984\pi$
$661$			11.2482i			0.437503i	−0.975781	+	0.218752i	$0.929802\pi$
$662$	5.47295	−	2.03423i	0.212712	−	0.0790625i
$663$		0			0
$664$	9.04100	−	16.4241i	0.350859	−	0.637378i
$665$	−0.626873			−0.0243091
$666$		0			0
$667$			16.1036i			0.623533i
$668$	−20.4977	+	17.6800i	−0.793078	+	0.684059i
$669$		0			0
$670$	25.3738	+	68.2664i	0.980275	+	2.63736i
$671$	−1.91649			−0.0739852
$672$		0			0
$673$	−45.9571			−1.77152			−0.885758	−	0.464147i	$-0.846361\pi$
$673$	−45.9571			−1.77152			−0.885758	+	0.464147i	$0.846361\pi$
$674$	2.96435	+	7.97538i	0.114182	+	0.307200i
$675$		0			0
$676$	1.51447	−	1.30629i	0.0582488	−	0.0502417i
$677$		−	42.4795i		−	1.63262i	−0.577613	−	0.816310i	$-0.696016\pi$
$677$		−	42.4795i		−	1.63262i	0.577613	−	0.816310i	$-0.303984\pi$
$678$		0			0
$679$	1.53113			0.0587595
$680$	−20.1597	+	36.6226i	−0.773091	+	1.40441i
$681$		0			0
$682$	4.35011	−	1.61688i	0.166574	−	0.0619136i
$683$			11.8075i			0.451800i	0.974150	+	0.225900i	$0.0725323\pi$
$683$			11.8075i			0.451800i	−0.974150	+	0.225900i	$0.927468\pi$
$684$		0			0
$685$			25.0973i			0.958920i
$686$	9.86636	+	26.5448i	0.376699	+	1.01348i
$687$		0			0
$688$	31.1165	+	4.61824i	1.18631	+	0.176069i
$689$	−13.1656			−0.501568
$690$		0			0
$691$			23.5462i			0.895739i	0.894099	+	0.447870i	$0.147817\pi$
$691$			23.5462i			0.895739i	−0.894099	+	0.447870i	$0.852183\pi$
$692$	−14.8815	−	17.2532i	−0.565709	−	0.655867i
$693$		0			0
$694$	−2.12123	+	0.788434i	−0.0805207	+	0.0299286i
$695$	−78.4216			−2.97470
$696$		0			0
$697$	16.2053			0.613820
$698$	−1.00124	+	0.372147i	−0.0378973	+	0.0140860i
$699$		0			0
$700$	−48.1561	+	41.5364i	−1.82013	+	1.56993i
$701$			5.15813i			0.194820i	0.995244	+	0.0974099i	$0.0310558\pi$
$701$			5.15813i			0.194820i	−0.995244	+	0.0974099i	$0.968944\pi$
$702$		0			0
$703$	−0.581822			−0.0219438
$704$	3.93566	−	2.49157i	0.148331	−	0.0939046i
$705$		0			0
$706$	−11.4782	−	30.8814i	−0.431989	−	1.16224i
$707$		−	26.2398i		−	0.986849i
$708$		0			0
$709$			20.1043i			0.755032i	0.926003	+	0.377516i	$0.123222\pi$
$709$			20.1043i			0.755032i	−0.926003	+	0.377516i	$0.876778\pi$
$710$	78.3096	−	29.1067i	2.93891	−	1.09235i
$711$		0			0
$712$	20.4142	+	11.2375i	0.765056	+	0.421142i
$713$	37.5343			1.40567
$714$		0			0
$715$			2.52449i			0.0944107i
$716$	−13.0515	−	15.1315i	−0.487758	−	0.565492i
$717$		0			0
$718$	16.2157	+	43.6272i	0.605164	+	1.62815i
$719$	10.5580			0.393745			0.196873	−	0.980429i	$-0.436921\pi$
$719$	10.5580			0.393745			0.196873	+	0.980429i	$0.436921\pi$
$720$		0			0
$721$	34.3661			1.27986
$722$	9.35959	+	25.1813i	0.348328	+	0.937152i
$723$		0			0
$724$	−31.6449	−	36.6882i	−1.17607	−	1.36351i
$725$		−	33.3652i		−	1.23915i
$726$		0			0
$727$	−51.2972			−1.90251			−0.951255	−	0.308407i	$-0.900204\pi$
$727$	−51.2972			−1.90251			−0.951255	+	0.308407i	$0.900204\pi$
$728$	−3.14316	+	5.70994i	−0.116493	+	0.211624i
$729$		0			0
$730$	−2.51264	+	0.933918i	−0.0929971	+	0.0345659i
$731$		−	26.8091i		−	0.991569i
$732$		0			0
$733$		−	22.1820i		−	0.819313i	−0.912240	−	0.409656i	$-0.865649\pi$
$733$		−	22.1820i		−	0.819313i	0.912240	−	0.409656i	$-0.134351\pi$
$734$	1.24023	+	3.33674i	0.0457776	+	0.123161i
$735$		0			0
$736$	36.8571	−	7.79885i	1.35857	−	0.287469i
$737$	−6.91585			−0.254748
$738$		0			0
$739$		−	19.5216i		−	0.718115i	−0.933315	−	0.359057i	$-0.883098\pi$
$739$		−	19.5216i		−	0.718115i	0.933315	−	0.359057i	$-0.116902\pi$
$740$	−60.8912	+	52.5208i	−2.23840	+	1.93070i
$741$		0			0
$742$	40.2176	−	14.9484i	1.47644	−	0.548773i
$743$	49.0478			1.79939			0.899695	−	0.436518i	$-0.143789\pi$
$743$	49.0478			1.79939			0.899695	+	0.436518i	$0.143789\pi$
$744$		0			0
$745$	39.9428			1.46339
$746$	−34.4428	+	12.8020i	−1.26104	+	0.468713i
$747$		0			0
$748$	−2.59281	−	3.00603i	−0.0948026	−	0.109911i
$749$			17.0314i			0.622313i
$750$		0			0
$751$	−16.3556			−0.596825			−0.298412	−	0.954437i	$-0.596457\pi$
$751$	−16.3556			−0.596825			−0.298412	+	0.954437i	$0.596457\pi$
$752$	0.0183747	−	0.123804i	0.000670056	−	0.00451466i
$753$		0			0
$754$	−1.19140	−	3.20539i	−0.0433883	−	0.116733i
$755$		−	10.8067i		−	0.393296i
$756$		0			0
$757$		−	9.50390i		−	0.345425i	−0.984972	−	0.172713i	$-0.944747\pi$
$757$		−	9.50390i		−	0.345425i	0.984972	−	0.172713i	$-0.0552532\pi$
$758$	33.8167	−	12.5693i	1.22828	−	0.456536i
$759$		0			0
$760$	−0.674042	−	0.371042i	−0.0244501	−	0.0134591i
$761$	−21.2994			−0.772102			−0.386051	−	0.922477i	$-0.626161\pi$
$761$	−21.2994			−0.772102			−0.386051	+	0.922477i	$0.626161\pi$
$762$		0			0
$763$		−	40.2998i		−	1.45895i
$764$	−21.6183	+	18.6466i	−0.782124	+	0.674610i
$765$		0			0
$766$	12.3828	+	33.3152i	0.447410	+	1.20373i
$767$	−4.75759			−0.171787
$768$		0			0
$769$	−28.7969			−1.03844			−0.519222	−	0.854639i	$-0.673778\pi$
$769$	−28.7969			−1.03844			−0.519222	+	0.854639i	$0.673778\pi$
$770$	−2.86635	−	7.71172i	−0.103296	−	0.277911i
$771$		0			0
$772$	−7.55560	+	6.51698i	−0.271932	+	0.234551i
$773$			14.0271i			0.504518i	0.967660	+	0.252259i	$0.0811735\pi$
$773$			14.0271i			0.504518i	−0.967660	+	0.252259i	$0.918826\pi$
$774$		0			0
$775$	−77.7679			−2.79350
$776$	1.64634	+	0.906266i	0.0591003	+	0.0325330i
$777$		0			0
$778$	28.2206	−	10.4892i	1.01176	−	0.376058i
$779$			0.298260i			0.0106863i
$780$		0			0
$781$			7.93328i			0.283875i
$782$	−11.1859	−	30.0948i	−0.400006	−	1.07619i
$783$		0			0
$784$	−0.992219	+	6.68532i	−0.0354364	+	0.238761i
$785$	−18.1647			−0.648327
$786$		0			0
$787$			6.25929i			0.223119i	0.993758	+	0.111560i	$0.0355846\pi$
$787$			6.25929i			0.223119i	−0.993758	+	0.111560i	$0.964415\pi$
$788$	14.3677	+	16.6575i	0.511827	+	0.593398i
$789$		0			0
$790$	37.6172	−	13.9819i	1.33836	−	0.497452i
$791$	24.1185			0.857556
$792$		0			0
$793$	3.29149			0.116884
$794$	−16.0784	+	5.97615i	−0.570601	+	0.212085i
$795$		0			0
$796$	−13.8357	+	11.9338i	−0.490393	+	0.422981i
$797$		−	17.5042i		−	0.620031i	−0.950732	−	0.310015i	$-0.899666\pi$
$797$		−	17.5042i		−	0.620031i	0.950732	−	0.310015i	$-0.100334\pi$
$798$		0			0
$799$	−0.106666			−0.00377356
$800$	−76.3647	+	16.1586i	−2.69990	+	0.571292i
$801$		0			0
$802$	−5.12980	−	13.8014i	−0.181140	−	0.487344i
$803$		−	0.254548i		−	0.00898279i
$804$		0			0
$805$		−	66.5395i		−	2.34521i
$806$	−7.47113	+	2.77693i	−0.263159	+	0.0978131i
$807$		0			0
$808$	15.5311	−	28.2142i	0.546383	−	0.992572i
$809$	28.5503			1.00377			0.501887	−	0.864933i	$-0.332639\pi$
$809$	28.5503			1.00377			0.501887	+	0.864933i	$0.332639\pi$
$810$		0			0
$811$		−	17.7550i		−	0.623462i	−0.950170	−	0.311731i	$-0.899091\pi$
$811$		−	17.7550i		−	0.623462i	0.950170	−	0.311731i	$-0.100909\pi$
$812$	7.27890	+	8.43895i	0.255439	+	0.296149i
$813$		0			0
$814$	−2.66036	−	7.15751i	−0.0932455	−	0.250870i
$815$	46.9933			1.64610
$816$		0			0
$817$	0.493423			0.0172627
$818$	−1.45275	−	3.90853i	−0.0507943	−	0.136658i
$819$		0			0
$820$	26.9238	+	31.2147i	0.940219	+	1.09006i
$821$			47.7170i			1.66534i	0.553773	+	0.832668i	$0.313188\pi$
$821$			47.7170i			1.66534i	−0.553773	+	0.832668i	$0.686812\pi$
$822$		0			0
$823$	11.6508			0.406122			0.203061	−	0.979166i	$-0.434911\pi$
$823$	11.6508			0.406122			0.203061	+	0.979166i	$0.434911\pi$
$824$	36.9520	+	20.3410i	1.28728	+	0.708613i
$825$		0			0
$826$	14.5333	−	5.40184i	0.505678	−	0.187954i
$827$			45.4863i			1.58171i	0.612001	+	0.790857i	$0.290365\pi$
$827$			45.4863i			1.58171i	−0.612001	+	0.790857i	$0.709635\pi$
$828$		0			0
$829$			35.2812i			1.22537i	0.790328	+	0.612684i	$0.209910\pi$
$829$			35.2812i			1.22537i	−0.790328	+	0.612684i	$0.790090\pi$
$830$	−14.1601	−	38.0967i	−0.491503	−	1.32235i
$831$		0			0
$832$	−6.75934	+	4.27917i	−0.234338	+	0.148354i
$833$	5.75987			0.199568
$834$		0			0
$835$			58.6819i			2.03077i
$836$	0.0553263	−	0.0477209i	0.00191350	−	0.00165046i
$837$		0			0
$838$	34.9316	−	12.9836i	1.20669	−	0.448513i
$839$	−21.3143			−0.735853			−0.367926	−	0.929855i	$-0.619932\pi$
$839$	−21.3143			−0.735853			−0.367926	+	0.929855i	$0.619932\pi$
$840$		0			0
$841$	23.1530			0.798380
$842$	6.01897	−	2.23718i	0.207428	−	0.0770983i
$843$		0			0
$844$	−1.39186	−	1.61368i	−0.0479097	−	0.0555451i
$845$		−	4.33571i		−	0.149153i
$846$		0			0
$847$	−24.5674			−0.844146
$848$	52.0917	+	7.73132i	1.78884	+	0.265495i
$849$		0			0
$850$	23.1762	+	62.3539i	0.794936	+	2.13872i
$851$		−	61.7575i		−	2.11702i
$852$		0			0
$853$		−	9.99152i		−	0.342103i	−0.985262	−	0.171052i	$-0.945284\pi$
$853$		−	9.99152i		−	0.342103i	0.985262	−	0.171052i	$-0.0547165\pi$
$854$	−10.0547	+	3.73721i	−0.344065	+	0.127885i
$855$		0			0
$856$	−10.0807	+	18.3129i	−0.344552	+	0.625922i
$857$	49.7277			1.69867			0.849333	−	0.527857i	$-0.177004\pi$
$857$	49.7277			1.69867			0.849333	+	0.527857i	$0.177004\pi$
$858$		0			0
$859$		−	16.8742i		−	0.575741i	−0.957669	−	0.287870i	$-0.907053\pi$
$859$		−	16.8742i		−	0.575741i	0.957669	−	0.287870i	$-0.0929472\pi$
$860$	51.6396	−	44.5411i	1.76090	−	1.51884i
$861$		0			0
$862$	−7.56542	−	20.3542i	−0.257679	−	0.693268i
$863$	−36.9205			−1.25679			−0.628394	−	0.777895i	$-0.716287\pi$
$863$	−36.9205			−1.25679			−0.628394	+	0.777895i	$0.716287\pi$
$864$		0			0
$865$	−49.3934			−1.67942
$866$	13.7895	+	37.0997i	0.468586	+	1.26070i
$867$		0			0
$868$	19.6695	−	16.9657i	0.667627	−	0.575853i
$869$			3.81088i			0.129275i
$870$		0			0
$871$	11.8777			0.402460
$872$	23.8532	−	43.3322i	0.807770	−	1.46741i
$873$		0			0
$874$	0.553897	−	0.205877i	0.0187358	−	0.00696388i
$875$			87.9076i			2.97182i
$876$		0			0
$877$		−	4.90899i		−	0.165765i	−0.996559	−	0.0828824i	$-0.973587\pi$
$877$		−	4.90899i		−	0.165765i	0.996559	−	0.0828824i	$-0.0264126\pi$
$878$	−3.27519	−	8.81168i	−0.110532	−	0.297380i
$879$		0			0
$880$	1.48248	−	9.98856i	0.0499743	−	0.336714i
$881$	7.76972			0.261769			0.130884	−	0.991398i	$-0.458218\pi$
$881$	7.76972			0.261769			0.130884	+	0.991398i	$0.458218\pi$
$882$		0			0
$883$		−	15.6142i		−	0.525459i	−0.964869	−	0.262730i	$-0.915377\pi$
$883$		−	15.6142i		−	0.525459i	0.964869	−	0.262730i	$-0.0846227\pi$
$884$	4.45305	+	5.16274i	0.149772	+	0.173642i
$885$		0			0
$886$	−43.2856	+	16.0887i	−1.45421	+	0.540511i
$887$	2.11858			0.0711349			0.0355674	−	0.999367i	$-0.488676\pi$
$887$	2.11858			0.0711349			0.0355674	+	0.999367i	$0.488676\pi$
$888$		0			0
$889$	−48.2650			−1.61876
$890$	47.3521	−	17.6002i	1.58725	−	0.589960i
$891$		0			0
$892$	−13.4948	+	11.6397i	−0.451838	+	0.389727i
$893$		−	0.00196319i		−	6.56957e-5i
$894$		0			0
$895$	−43.3195			−1.44801
$896$	15.7895	−	20.7465i	0.527491	−	0.693092i
$897$		0			0
$898$	10.4097	+	28.0066i	0.347377	+	0.934593i
$899$			13.6281i			0.454524i
$900$		0			0
$901$		−	44.8807i		−	1.49519i
$902$	−3.66916	+	1.36378i	−0.122170	+	0.0454089i
$903$		0			0
$904$	25.9333	+	14.2756i	0.862529	+	0.474798i
$905$	−105.033			−3.49142
$906$		0			0
$907$		−	28.8005i		−	0.956305i	−0.878277	−	0.478153i	$-0.841307\pi$
$907$		−	28.8005i		−	0.956305i	0.878277	−	0.478153i	$-0.158693\pi$
$908$	−22.4544	−	26.0330i	−0.745175	−	0.863935i
$909$		0			0
$910$	4.92284	+	13.2446i	0.163191	+	0.439053i
$911$	−4.72015			−0.156386			−0.0781929	−	0.996938i	$-0.524915\pi$
$911$	−4.72015			−0.156386			−0.0781929	+	0.996938i	$0.524915\pi$
$912$		0			0
$913$	3.85945			0.127729
$914$	8.97537	+	24.1476i	0.296879	+	0.798732i
$915$		0			0
$916$	−13.5037	−	15.6559i	−0.446176	−	0.517284i
$917$		−	7.81367i		−	0.258030i
$918$		0			0
$919$	43.7254			1.44237			0.721185	−	0.692743i	$-0.243598\pi$
$919$	43.7254			1.44237			0.721185	+	0.692743i	$0.243598\pi$
$920$	39.3842	−	71.5462i	1.29846	−	2.35881i
$921$		0			0
$922$	−27.1738	+	10.1002i	−0.894923	+	0.332632i
$923$		−	13.6251i		−	0.448475i
$924$		0			0
$925$			127.956i			4.20718i
$926$	−2.68846	−	7.23311i	−0.0883482	−	0.237695i
$927$		0			0
$928$	2.83165	+	13.3823i	0.0929534	+	0.439294i
$929$	−4.56638			−0.149818			−0.0749091	−	0.997190i	$-0.523867\pi$
$929$	−4.56638			−0.149818			−0.0749091	+	0.997190i	$0.523867\pi$
$930$		0			0
$931$			0.106011i			0.00347437i
$932$	0.719525	−	0.620616i	0.0235688	−	0.0203290i
$933$		0			0
$934$	44.7376	−	16.6284i	1.46386	−	0.544099i
$935$	−8.60585			−0.281441
$936$		0			0
$937$	−14.8258			−0.484338			−0.242169	−	0.970234i	$-0.577859\pi$
$937$	−14.8258			−0.484338			−0.242169	+	0.970234i	$0.577859\pi$
$938$	−36.2835	+	13.4861i	−1.18470	+	0.440337i
$939$		0			0
$940$	−0.177216	−	0.205460i	−0.00578016	−	0.00670136i
$941$			23.4674i			0.765015i	0.923952	+	0.382508i	$0.124939\pi$
$941$			23.4674i			0.765015i	−0.923952	+	0.382508i	$0.875061\pi$
$942$		0			0
$943$	−31.6588			−1.03095
$944$	18.8242	+	2.79384i	0.612674	+	0.0909317i
$945$		0			0
$946$	2.25615	+	6.07003i	0.0733539	+	0.197354i
$947$			6.85871i			0.222878i	0.993771	+	0.111439i	$0.0355460\pi$
$947$			6.85871i			0.222878i	−0.993771	+	0.111439i	$0.964454\pi$
$948$		0			0
$949$			0.437175i			0.0141913i
$950$	−1.14763	+	0.426559i	−0.0372340	+	0.0138394i
$951$		0			0
$952$	−19.4649	−	10.7149i	−0.630860	−	0.347271i
$953$	33.6118			1.08879			0.544396	−	0.838828i	$-0.316759\pi$
$953$	33.6118			1.08879			0.544396	+	0.838828i	$0.316759\pi$
$954$		0			0
$955$			61.8902i			2.00272i
$956$	13.2394	−	11.4194i	0.428191	−	0.369331i
$957$		0			0
$958$	3.54263	+	9.53120i	0.114457	+	0.307939i
$959$	−13.3392			−0.430745
$960$		0			0
$961$	0.764545			0.0246627
$962$	4.56905	+	12.2927i	0.147312	+	0.396333i
$963$		0			0
$964$	−17.6487	+	15.2226i	−0.568426	+	0.490288i
$965$			21.6306i			0.696314i
$966$		0			0
$967$	38.4327			1.23591			0.617956	−	0.786212i	$-0.287961\pi$
$967$	38.4327			1.23591			0.617956	+	0.786212i	$0.287961\pi$
$968$	−26.4160	−	14.5413i	−0.849041	−	0.467374i
$969$		0			0
$970$	3.81879	−	1.41940i	0.122614	−	0.0455741i
$971$		−	38.2120i		−	1.22628i	−0.789974	−	0.613141i	$-0.789906\pi$
$971$		−	38.2120i		−	1.22628i	0.789974	−	0.613141i	$-0.210094\pi$
$972$		0			0
$973$		−	41.6809i		−	1.33623i
$974$	−4.79165	−	12.8916i	−0.153534	−	0.413073i
$975$		0			0
$976$	−13.0233	−	1.93289i	−0.416866	−	0.0618702i
$977$	3.28633			0.105139			0.0525695	−	0.998617i	$-0.483259\pi$
$977$	3.28633			0.105139			0.0525695	+	0.998617i	$0.483259\pi$
$978$		0			0
$979$			4.79708i			0.153315i
$980$	9.56956	+	11.0947i	0.305688	+	0.354406i
$981$		0			0
$982$	−10.5219	+	3.91086i	−0.335767	+	0.124801i
$983$	13.0281			0.415530			0.207765	−	0.978179i	$-0.433381\pi$
$983$	13.0281			0.415530			0.207765	+	0.978179i	$0.433381\pi$
$984$		0			0
$985$	47.6880			1.51946
$986$	10.9270	−	4.06142i	0.347986	−	0.129342i
$987$		0			0
$988$	−0.0950206	+	0.0819587i	−0.00302301	+	0.00260745i
$989$			52.3744i			1.66541i
$990$		0			0
$991$	11.7140			0.372106			0.186053	−	0.982540i	$-0.440430\pi$
$991$	11.7140			0.372106			0.186053	+	0.982540i	$0.440430\pi$
$992$	31.1914	−	6.60002i	0.990329	−	0.209551i
$993$		0			0
$994$	15.4702	+	41.6214i	0.490683	+	1.32015i
$995$			39.6096i			1.25571i
$996$		0			0
$997$			61.2009i			1.93825i	0.246566	+	0.969126i	$0.420698\pi$
$997$			61.2009i			1.93825i	−0.246566	+	0.969126i	$0.579302\pi$
$998$	13.4817	−	5.01100i	0.426757	−	0.158620i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.g.e.469.12		16
3.2	odd	2		312.2.g.b.157.5	✓	16
4.3	odd	2		3744.2.g.e.1873.16		16
8.3	odd	2		3744.2.g.e.1873.1		16
8.5	even	2	inner	936.2.g.e.469.11		16
12.11	even	2		1248.2.g.b.625.9		16
24.5	odd	2		312.2.g.b.157.6	yes	16
24.11	even	2		1248.2.g.b.625.8		16
48.5	odd	4		9984.2.a.bt.1.8		8
48.11	even	4		9984.2.a.bv.1.8		8
48.29	odd	4		9984.2.a.bu.1.1		8
48.35	even	4		9984.2.a.bs.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.g.b.157.5	✓	16	3.2	odd	2
312.2.g.b.157.6	yes	16	24.5	odd	2
936.2.g.e.469.11		16	8.5	even	2	inner
936.2.g.e.469.12		16	1.1	even	1	trivial
1248.2.g.b.625.8		16	24.11	even	2
1248.2.g.b.625.9		16	12.11	even	2
3744.2.g.e.1873.1		16	8.3	odd	2
3744.2.g.e.1873.16		16	4.3	odd	2
9984.2.a.bs.1.1		8	48.35	even	4
9984.2.a.bt.1.8		8	48.5	odd	4
9984.2.a.bu.1.1		8	48.29	odd	4
9984.2.a.bv.1.8		8	48.11	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.492712 + 1.32561i) q^{2} +(-1.51447 + 1.30629i) q^{4} +4.33571i q^{5} -2.30442 q^{7} +(-2.47782 - 1.36397i) q^{8} +(-5.74745 + 2.13626i) q^{10} -0.582255i q^{11} +1.00000i q^{13} +(-1.13542 - 3.05476i) q^{14} +(0.587238 - 3.95666i) q^{16} -3.40894 q^{17} -0.0627418i q^{19} +(-5.66368 - 6.56631i) q^{20} +(0.771842 - 0.286884i) q^{22} +6.65973 q^{23} -13.7984 q^{25} +(-1.32561 + 0.492712i) q^{26} +(3.48998 - 3.01023i) q^{28} +2.41805i q^{29} +5.63600 q^{31} +(5.53432 - 1.17105i) q^{32} +(-1.67963 - 4.51892i) q^{34} -9.99131i q^{35} -9.27328i q^{37} +(0.0831710 - 0.0309136i) q^{38} +(5.91378 - 10.7431i) q^{40} -4.75376 q^{41} +7.86434i q^{43} +(0.760592 + 0.881808i) q^{44} +(3.28133 + 8.82819i) q^{46} +0.0312900 q^{47} -1.68964 q^{49} +(-6.79864 - 18.2913i) q^{50} +(-1.30629 - 1.51447i) q^{52} +13.1656i q^{53} +2.52449 q^{55} +(5.70994 + 3.14316i) q^{56} +(-3.20539 + 1.19140i) q^{58} +4.75759i q^{59} -3.29149i q^{61} +(2.77693 + 7.47113i) q^{62} +(4.27917 + 6.75934i) q^{64} -4.33571 q^{65} -11.8777i q^{67} +(5.16274 - 4.45305i) q^{68} +(13.2446 - 4.92284i) q^{70} -13.6251 q^{71} +0.437175 q^{73} +(12.2927 - 4.56905i) q^{74} +(0.0819587 + 0.0950206i) q^{76} +1.34176i q^{77} -6.54503 q^{79} +(17.1549 + 2.54610i) q^{80} +(-2.34224 - 6.30162i) q^{82} +6.62844i q^{83} -14.7802i q^{85} +(-10.4250 + 3.87485i) q^{86} +(-0.794179 + 1.44272i) q^{88} -8.23880 q^{89} -2.30442i q^{91} +(-10.0860 + 8.69951i) q^{92} +(0.0154170 + 0.0414783i) q^{94} +0.272031 q^{95} -0.664432 q^{97} +(-0.832504 - 2.23980i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 4 q^{7} + 4 q^{8} - 8 q^{10} - 12 q^{14} - 12 q^{16} - 16 q^{17} - 24 q^{20} + 16 q^{22} + 8 q^{23} - 32 q^{25} + 2 q^{26} + 32 q^{28} - 4 q^{31} + 28 q^{32} - 32 q^{34} - 12 q^{38} - 12 q^{40}+ \cdots + 46 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 + 4 * q^7 + 4 * q^8 - 8 * q^10 - 12 * q^14 - 12 * q^16 - 16 * q^17 - 24 * q^20 + 16 * q^22 + 8 * q^23 - 32 * q^25 + 2 * q^26 + 32 * q^28 - 4 * q^31 + 28 * q^32 - 32 * q^34 - 12 * q^38 - 12 * q^40 + 36 * q^41 - 16 * q^44 + 44 * q^46 - 24 * q^47 + 48 * q^49 + 34 * q^50 + 24 * q^55 + 64 * q^56 - 28 * q^58 - 52 * q^62 - 48 * q^64 - 4 * q^65 - 32 * q^68 + 84 * q^70 - 32 * q^73 + 60 * q^74 + 64 * q^76 + 68 * q^80 - 32 * q^82 - 56 * q^86 - 36 * q^88 + 60 * q^89 - 32 * q^92 + 24 * q^95 + 40 * q^97 + 46 * q^98

Introduction

L-functions

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