LMFDB - Embedded newform 936.2.g.d.469.5

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:	$8$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			469.5
Root			$0.951057 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	936.469
Dual form			936.2.g.d.469.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.221232 - 1.39680i) q^{2} +(-1.90211 + 0.618034i) q^{4} -2.52015i q^{5} +2.79360 q^{7} +(1.28408 + 2.52015i) q^{8} +(-3.52015 + 0.557537i) q^{10} -5.31375i q^{11} -1.00000i q^{13} +(-0.618034 - 3.90211i) q^{14} +(3.23607 - 2.35114i) q^{16} +4.35114 q^{17} +6.02967i q^{19} +(1.55754 + 4.79360i) q^{20} +(-7.42226 + 1.17557i) q^{22} -0.568158 q^{23} -1.35114 q^{25} +(-1.39680 + 0.221232i) q^{26} +(-5.31375 + 1.72654i) q^{28} -2.68915i q^{29} +1.90868 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-0.962611 - 6.07768i) q^{34} -7.04029i q^{35} -9.60845i q^{37} +(8.42226 - 1.33395i) q^{38} +(6.35114 - 3.23607i) q^{40} -11.2093 q^{41} -9.48746i q^{43} +(3.28408 + 10.1074i) q^{44} +(0.125695 + 0.793604i) q^{46} -3.95669 q^{47} +0.804226 q^{49} +(0.298915 + 1.88728i) q^{50} +(0.618034 + 1.90211i) q^{52} +8.05934i q^{53} -13.3914 q^{55} +(3.58721 + 7.04029i) q^{56} +(-3.75621 + 0.594926i) q^{58} +6.19868i q^{59} -7.23607i q^{61} +(-0.422260 - 2.66605i) q^{62} +(-4.70228 + 6.47214i) q^{64} -2.52015 q^{65} +10.0297i q^{67} +(-8.27636 + 2.68915i) q^{68} +(-9.83390 + 1.55754i) q^{70} +1.63052 q^{71} -5.17442 q^{73} +(-13.4211 + 2.12569i) q^{74} +(-3.72654 - 11.4691i) q^{76} -14.8445i q^{77} +9.17442 q^{79} +(-5.92522 - 8.15537i) q^{80} +(2.47985 + 15.6572i) q^{82} +4.61147i q^{83} -10.9655i q^{85} +(-13.2521 + 2.09893i) q^{86} +(13.3914 - 6.82328i) q^{88} -11.4182 q^{89} -2.79360i q^{91} +(1.08070 - 0.351141i) q^{92} +(0.875345 + 5.52671i) q^{94} +15.1957 q^{95} -10.2514 q^{97} +(-0.177920 - 1.12334i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 4 q^{7} + 4 q^{8} - 4 q^{10} + 4 q^{14} + 8 q^{16} + 16 q^{17} + 12 q^{20} - 20 q^{22} + 8 q^{23} + 8 q^{25} - 2 q^{26} - 4 q^{31} - 32 q^{32} + 16 q^{34} + 28 q^{38} + 32 q^{40} - 36 q^{41}+ \cdots + 6 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 4 * q^7 + 4 * q^8 - 4 * q^10 + 4 * q^14 + 8 * q^16 + 16 * q^17 + 12 * q^20 - 20 * q^22 + 8 * q^23 + 8 * q^25 - 2 * q^26 - 4 * q^31 - 32 * q^32 + 16 * q^34 + 28 * q^38 + 32 * q^40 - 36 * q^41 + 20 * q^44 - 12 * q^46 - 24 * q^47 - 24 * q^49 - 22 * q^50 - 4 * q^52 - 40 * q^55 - 8 * q^56 + 12 * q^58 + 36 * q^62 + 4 * q^65 - 12 * q^70 - 16 * q^71 + 32 * q^73 - 4 * q^74 - 24 * q^76 + 44 * q^82 - 8 * q^86 + 40 * q^88 - 60 * q^89 + 40 * q^92 - 44 * q^94 + 24 * q^95 - 56 * q^97 + 6 * 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 $

$2$	−0.221232	−	1.39680i	−0.156434	−	0.987688i
$2$	−0.221232	−	1.39680i	−0.156434	−	0.987688i
$3$		0			0
$3$		0			0
$4$	−1.90211	+	0.618034i	−0.951057	+	0.309017i
$5$		−	2.52015i		−	1.12704i	−0.826101	−	0.563522i	$-0.809446\pi$
$5$		−	2.52015i		−	1.12704i	0.826101	−	0.563522i	$-0.190554\pi$
$6$		0			0
$7$	2.79360			1.05588			0.527942	−	0.849281i	$-0.322964\pi$
$7$	2.79360			1.05588			0.527942	+	0.849281i	$0.322964\pi$
$8$	1.28408	+	2.52015i	0.453990	+	0.891007i
$9$		0			0
$10$	−3.52015	+	0.557537i	−1.11317	+	0.176309i
$11$		−	5.31375i		−	1.60216i	−0.598560	−	0.801078i	$-0.704260\pi$
$11$		−	5.31375i		−	1.60216i	0.598560	−	0.801078i	$-0.295740\pi$
$12$		0			0
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−0.618034	−	3.90211i	−0.165177	−	1.04288i
$15$		0			0
$16$	3.23607	−	2.35114i	0.809017	−	0.587785i
$17$	4.35114			1.05531			0.527653	−	0.849460i	$-0.323072\pi$
$17$	4.35114			1.05531			0.527653	+	0.849460i	$0.323072\pi$
$18$		0			0
$19$			6.02967i			1.38330i	0.722232	+	0.691651i	$0.243116\pi$
$19$			6.02967i			1.38330i	−0.722232	+	0.691651i	$0.756884\pi$
$20$	1.55754	+	4.79360i	0.348276	+	1.07188i
$21$		0			0
$22$	−7.42226	+	1.17557i	−1.58243	+	0.250632i
$23$	−0.568158			−0.118469			−0.0592346	−	0.998244i	$-0.518866\pi$
$23$	−0.568158			−0.118469			−0.0592346	+	0.998244i	$0.518866\pi$
$24$		0			0
$25$	−1.35114			−0.270228
$26$	−1.39680	+	0.221232i	−0.273935	+	0.0433871i
$27$		0			0
$28$	−5.31375	+	1.72654i	−1.00420	+	0.326286i
$29$		−	2.68915i		−	0.499363i	−0.968328	−	0.249682i	$-0.919674\pi$
$29$		−	2.68915i		−	0.499363i	0.968328	−	0.249682i	$-0.0803260\pi$
$30$		0			0
$31$	1.90868			0.342809			0.171404	−	0.985201i	$-0.445170\pi$
$31$	1.90868			0.342809			0.171404	+	0.985201i	$0.445170\pi$
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$		0			0
$34$	−0.962611	−	6.07768i	−0.165086	−	1.04231i
$35$		−	7.04029i		−	1.19003i
$36$		0			0
$37$		−	9.60845i		−	1.57962i	−0.613352	−	0.789810i	$-0.710179\pi$
$37$		−	9.60845i		−	1.57962i	0.613352	−	0.789810i	$-0.289821\pi$
$38$	8.42226	−	1.33395i	1.36627	−	0.216396i
$39$		0			0
$40$	6.35114	−	3.23607i	1.00420	−	0.511667i
$41$	−11.2093			−1.75060			−0.875299	−	0.483582i	$-0.839336\pi$
$41$	−11.2093			−1.75060			−0.875299	+	0.483582i	$0.839336\pi$
$42$		0			0
$43$		−	9.48746i		−	1.44682i	−0.690417	−	0.723412i	$-0.742573\pi$
$43$		−	9.48746i		−	1.44682i	0.690417	−	0.723412i	$-0.257427\pi$
$44$	3.28408	+	10.1074i	0.495094	+	1.52374i
$45$		0			0
$46$	0.125695	+	0.793604i	0.0185327	+	0.117011i
$47$	−3.95669			−0.577142			−0.288571	−	0.957458i	$-0.593180\pi$
$47$	−3.95669			−0.577142			−0.288571	+	0.957458i	$0.593180\pi$
$48$		0			0
$49$	0.804226			0.114889
$50$	0.298915	+	1.88728i	0.0422730	+	0.266901i
$51$		0			0
$52$	0.618034	+	1.90211i	0.0857059	+	0.263776i
$53$			8.05934i			1.10704i	0.832837	+	0.553518i	$0.186715\pi$
$53$			8.05934i			1.10704i	−0.832837	+	0.553518i	$0.813285\pi$
$54$		0			0
$55$	−13.3914			−1.80570
$56$	3.58721	+	7.04029i	0.479361	+	0.940799i
$57$		0			0
$58$	−3.75621	+	0.594926i	−0.493215	+	0.0781176i
$59$			6.19868i			0.806999i	0.914980	+	0.403500i	$0.132206\pi$
$59$			6.19868i			0.806999i	−0.914980	+	0.403500i	$0.867794\pi$
$60$		0			0
$61$		−	7.23607i		−	0.926484i	−0.886232	−	0.463242i	$-0.846686\pi$
$61$		−	7.23607i		−	0.926484i	0.886232	−	0.463242i	$-0.153314\pi$
$62$	−0.422260	−	2.66605i	−0.0536271	−	0.338588i
$63$		0			0
$64$	−4.70228	+	6.47214i	−0.587785	+	0.809017i
$65$	−2.52015			−0.312586
$66$		0			0
$67$			10.0297i			1.22532i	0.790347	+	0.612660i	$0.209900\pi$
$67$			10.0297i			1.22532i	−0.790347	+	0.612660i	$0.790100\pi$
$68$	−8.27636	+	2.68915i	−1.00366	+	0.326108i
$69$		0			0
$70$	−9.83390	+	1.55754i	−1.17538	+	0.186161i
$71$	1.63052			0.193507			0.0967536	−	0.995308i	$-0.469154\pi$
$71$	1.63052			0.193507			0.0967536	+	0.995308i	$0.469154\pi$
$72$		0			0
$73$	−5.17442			−0.605620			−0.302810	−	0.953051i	$-0.597925\pi$
$73$	−5.17442			−0.605620			−0.302810	+	0.953051i	$0.597925\pi$
$74$	−13.4211	+	2.12569i	−1.56017	+	0.247107i
$75$		0			0
$76$	−3.72654	−	11.4691i	−0.427464	−	1.31560i
$77$		−	14.8445i		−	1.69169i
$78$		0			0
$79$	9.17442			1.03220			0.516101	−	0.856528i	$-0.327383\pi$
$79$	9.17442			1.03220			0.516101	+	0.856528i	$0.327383\pi$
$80$	−5.92522	−	8.15537i	−0.662460	−	0.911798i
$81$		0			0
$82$	2.47985	+	15.6572i	0.273854	+	1.72905i
$83$			4.61147i			0.506175i	0.967443	+	0.253087i	$0.0814460\pi$
$83$			4.61147i			0.506175i	−0.967443	+	0.253087i	$0.918554\pi$
$84$		0			0
$85$		−	10.9655i		−	1.18938i
$86$	−13.2521	+	2.09893i	−1.42901	+	0.226333i
$87$		0			0
$88$	13.3914	−	6.82328i	1.42753	−	0.727364i
$89$	−11.4182			−1.21033			−0.605164	−	0.796101i	$-0.706892\pi$
$89$	−11.4182			−1.21033			−0.605164	+	0.796101i	$0.706892\pi$
$90$		0			0
$91$		−	2.79360i		−	0.292849i
$92$	1.08070	−	0.351141i	0.112671	−	0.0366090i
$93$		0			0
$94$	0.875345	+	5.52671i	0.0902850	+	0.570037i
$95$	15.1957			1.55904
$96$		0			0
$97$	−10.2514			−1.04087			−0.520435	−	0.853901i	$-0.674230\pi$
$97$	−10.2514			−1.04087			−0.520435	+	0.853901i	$0.674230\pi$
$98$	−0.177920	−	1.12334i	−0.0179727	−	0.113475i
$99$		0			0
$100$	2.57002	−	0.835051i	0.257002	−	0.0835051i
$101$			3.01905i			0.300407i	0.988655	+	0.150203i	$0.0479929\pi$
$101$			3.01905i			0.300407i	−0.988655	+	0.150203i	$0.952007\pi$
$102$		0			0
$103$	12.9193			1.27298			0.636488	−	0.771286i	$-0.280386\pi$
$103$	12.9193			1.27298			0.636488	+	0.771286i	$0.280386\pi$
$104$	2.52015	−	1.28408i	0.247121	−	0.125914i
$105$		0			0
$106$	11.2573	−	1.78298i	1.09341	−	0.173179i
$107$		−	10.9537i		−	1.05893i	−0.848331	−	0.529466i	$-0.822392\pi$
$107$		−	10.9537i		−	1.05893i	0.848331	−	0.529466i	$-0.177608\pi$
$108$		0			0
$109$			5.45309i			0.522311i	0.965297	+	0.261155i	$0.0841035\pi$
$109$			5.45309i			0.522311i	−0.965297	+	0.261155i	$0.915896\pi$
$110$	2.96261	+	18.7052i	0.282474	+	1.78347i
$111$		0			0
$112$	9.04029	−	6.56816i	0.854227	−	0.620633i
$113$	13.6334			1.28252			0.641262	−	0.767322i	$-0.278411\pi$
$113$	13.6334			1.28252			0.641262	+	0.767322i	$0.278411\pi$
$114$		0			0
$115$			1.43184i			0.133520i
$116$	1.66199	+	5.11507i	0.154312	+	0.474923i
$117$		0			0
$118$	8.65833	−	1.37134i	0.797064	−	0.126242i
$119$	12.1554			1.11428
$120$		0			0
$121$	−17.2360			−1.56691
$122$	−10.1074	+	1.60085i	−0.915077	+	0.144934i
$123$		0			0
$124$	−3.63052	+	1.17963i	−0.326030	+	0.105934i
$125$		−	9.19566i		−	0.822485i
$126$		0			0
$127$	19.4377			1.72481			0.862406	−	0.506217i	$-0.168956\pi$
$127$	19.4377			1.72481			0.862406	+	0.506217i	$0.168956\pi$
$128$	10.0806	+	5.13632i	0.891007	+	0.453990i
$129$		0			0
$130$	0.557537	+	3.52015i	0.0488992	+	0.308737i
$131$		−	12.7235i		−	1.11166i	−0.831296	−	0.555830i	$-0.812401\pi$
$131$		−	12.7235i		−	1.11166i	0.831296	−	0.555830i	$-0.187599\pi$
$132$		0			0
$133$			16.8445i			1.46061i
$134$	14.0095	−	2.21888i	1.21023	−	0.191682i
$135$		0			0
$136$	5.58721	+	10.9655i	0.479099	+	0.940285i
$137$	9.23054			0.788619			0.394309	−	0.918978i	$-0.370984\pi$
$137$	9.23054			0.788619			0.394309	+	0.918978i	$0.370984\pi$
$138$		0			0
$139$			11.7507i			0.996681i	0.866982	+	0.498340i	$0.166057\pi$
$139$			11.7507i			0.996681i	−0.866982	+	0.498340i	$0.833943\pi$
$140$	4.35114	+	13.3914i	0.367739	+	1.13178i
$141$		0			0
$142$	−0.360723	−	2.27751i	−0.0302712	−	0.191125i
$143$	−5.31375			−0.444358
$144$		0			0
$145$	−6.77706			−0.562804
$146$	1.14475	+	7.22764i	0.0947398	+	0.598164i
$147$		0			0
$148$	5.93835	+	18.2764i	0.488129	+	1.50231i
$149$			17.6079i			1.44250i	0.692675	+	0.721249i	$0.256432\pi$
$149$			17.6079i			1.44250i	−0.692675	+	0.721249i	$0.743568\pi$
$150$		0			0
$151$	−11.6250			−0.946029			−0.473014	−	0.881055i	$-0.656834\pi$
$151$	−11.6250			−0.946029			−0.473014	+	0.881055i	$0.656834\pi$
$152$	−15.1957	+	7.74258i	−1.23253	+	0.628006i
$153$		0			0
$154$	−20.7349	+	3.28408i	−1.67086	+	0.264639i
$155$		−	4.81015i		−	0.386360i
$156$		0			0
$157$		−	13.4781i		−	1.07567i	−0.843051	−	0.537833i	$-0.819243\pi$
$157$		−	13.4781i		−	1.07567i	0.843051	−	0.537833i	$-0.180757\pi$
$158$	−2.02967	−	12.8148i	−0.161472	−	1.01949i
$159$		0			0
$160$	−10.0806	+	10.0806i	−0.796940	+	0.796940i
$161$	−1.58721			−0.125090
$162$		0			0
$163$		−	9.79349i		−	0.767085i	−0.923523	−	0.383543i	$-0.874704\pi$
$163$		−	9.79349i		−	0.767085i	0.923523	−	0.383543i	$-0.125296\pi$
$164$	21.3214	−	6.92773i	1.66492	−	0.540965i
$165$		0			0
$166$	6.44131	−	1.02020i	0.499943	−	0.0791831i
$167$	16.6054			1.28497			0.642484	−	0.766299i	$-0.277904\pi$
$167$	16.6054			1.28497			0.642484	+	0.766299i	$0.277904\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	−15.3167	+	2.42592i	−1.17473	+	0.186060i
$171$		0			0
$172$	5.86357	+	18.0462i	0.447093	+	1.37601i
$173$			16.1979i			1.23150i	0.787942	+	0.615750i	$0.211147\pi$
$173$			16.1979i			1.23150i	−0.787942	+	0.615750i	$0.788853\pi$
$174$		0			0
$175$	−3.77455			−0.285329
$176$	−12.4934	−	17.1957i	−0.941724	−	1.29617i
$177$		0			0
$178$	2.52607	+	15.9490i	0.189337	+	1.19543i
$179$			1.22795i			0.0917816i	0.998946	+	0.0458908i	$0.0146126\pi$
$179$			1.22795i			0.0917816i	−0.998946	+	0.0458908i	$0.985387\pi$
$180$		0			0
$181$		−	7.00592i		−	0.520746i	−0.965508	−	0.260373i	$-0.916154\pi$
$181$		−	7.00592i		−	0.520746i	0.965508	−	0.260373i	$-0.0838455\pi$
$182$	−3.90211	+	0.618034i	−0.289244	+	0.0458117i
$183$		0			0
$184$	−0.729560	−	1.43184i	−0.0537839	−	0.105557i
$185$	−24.2147			−1.78030
$186$		0			0
$187$		−	23.1209i		−	1.69077i
$188$	7.52607	−	2.44537i	0.548895	−	0.178347i
$189$		0			0
$190$	−3.36176	−	21.2253i	−0.243888	−	1.53985i
$191$	14.3701			1.03978			0.519891	−	0.854232i	$-0.325972\pi$
$191$	14.3701			1.03978			0.519891	+	0.854232i	$0.325972\pi$
$192$		0			0
$193$	−3.67383			−0.264448			−0.132224	−	0.991220i	$-0.542212\pi$
$193$	−3.67383			−0.264448			−0.132224	+	0.991220i	$0.542212\pi$
$194$	2.26793	+	14.3192i	0.162828	+	1.02806i
$195$		0			0
$196$	−1.52973	+	0.497039i	−0.109266	+	0.0355028i
$197$		−	6.88442i		−	0.490494i	−0.969461	−	0.245247i	$-0.921131\pi$
$197$		−	6.88442i		−	0.490494i	0.969461	−	0.245247i	$-0.0788691\pi$
$198$		0			0
$199$	15.3952			1.09133			0.545667	−	0.838002i	$-0.316276\pi$
$199$	15.3952			1.09133			0.545667	+	0.838002i	$0.316276\pi$
$200$	−1.73497	−	3.40507i	−0.122681	−	0.240775i
$201$		0			0
$202$	4.21702	−	0.667910i	0.296708	−	0.0469940i
$203$		−	7.51243i		−	0.527269i
$204$		0			0
$205$			28.2491i			1.97300i
$206$	−2.85816	−	18.0457i	−0.199137	−	1.25730i
$207$		0			0
$208$	−2.35114	−	3.23607i	−0.163022	−	0.224381i
$209$	32.0402			2.21627
$210$		0			0
$211$			1.57035i			0.108107i	0.998538	+	0.0540537i	$0.0172142\pi$
$211$			1.57035i			0.108107i	−0.998538	+	0.0540537i	$0.982786\pi$
$212$	−4.98095	−	15.3298i	−0.342093	−	1.05285i
$213$		0			0
$214$	−15.3001	+	2.42330i	−1.04589	+	0.165653i
$215$	−23.9098			−1.63063
$216$		0			0
$217$	5.33209			0.361966
$218$	7.61688	−	1.20640i	0.515880	−	0.0817074i
$219$		0			0
$220$	25.4720	−	8.27636i	1.71732	−	0.557992i
$221$		−	4.35114i		−	0.292689i
$222$		0			0
$223$	27.6571			1.85205			0.926027	−	0.377457i	$-0.123202\pi$
$223$	27.6571			1.85205			0.926027	+	0.377457i	$0.123202\pi$
$224$	−11.1744	−	11.1744i	−0.746622	−	0.746622i
$225$		0			0
$226$	−3.01615	−	19.0432i	−0.200631	−	1.26673i
$227$			22.9434i			1.52281i	0.648276	+	0.761405i	$0.275490\pi$
$227$			22.9434i			1.52281i	−0.648276	+	0.761405i	$0.724510\pi$
$228$		0			0
$229$			23.5064i			1.55335i	0.629904	+	0.776673i	$0.283094\pi$
$229$			23.5064i			1.55335i	−0.629904	+	0.776673i	$0.716906\pi$
$230$	2.00000	−	0.316769i	0.131876	−	0.0208871i
$231$		0			0
$232$	6.77706	−	3.45309i	0.444936	−	0.226706i
$233$	−3.47433			−0.227611			−0.113805	−	0.993503i	$-0.536304\pi$
$233$	−3.47433			−0.227611			−0.113805	+	0.993503i	$0.536304\pi$
$234$		0			0
$235$			9.97144i			0.650465i
$236$	−3.83099	−	11.7906i	−0.249376	−	0.767502i
$237$		0			0
$238$	−2.68915	−	16.9786i	−0.174312	−	1.10056i
$239$	11.5820			0.749177			0.374589	−	0.927191i	$-0.377784\pi$
$239$	11.5820			0.749177			0.374589	+	0.927191i	$0.377784\pi$
$240$		0			0
$241$	10.0058			0.644531			0.322265	−	0.946649i	$-0.395556\pi$
$241$	10.0058			0.644531			0.322265	+	0.946649i	$0.395556\pi$
$242$	3.81314	+	24.0752i	0.245118	+	1.54761i
$243$		0			0
$244$	4.47214	+	13.7638i	0.286299	+	0.881138i
$245$		−	2.02677i		−	0.129485i
$246$		0			0
$247$	6.02967			0.383659
$248$	2.45089	+	4.81015i	0.155632	+	0.305445i
$249$		0			0
$250$	−12.8445	+	2.03437i	−0.812359	+	0.128665i
$251$			11.3723i			0.717811i	0.933374	+	0.358906i	$0.116850\pi$
$251$			11.3723i			0.717811i	−0.933374	+	0.358906i	$0.883150\pi$
$252$		0			0
$253$			3.01905i			0.189806i
$254$	−4.30023	−	27.1506i	−0.269820	−	1.70358i
$255$		0			0
$256$	4.94427	−	15.2169i	0.309017	−	0.951057i
$257$	−11.3510			−0.708058			−0.354029	−	0.935235i	$-0.615189\pi$
$257$	−11.3510			−0.708058			−0.354029	+	0.935235i	$0.615189\pi$
$258$		0			0
$259$		−	26.8422i		−	1.66789i
$260$	4.79360	−	1.55754i	0.297287	−	0.0965943i
$261$		0			0
$262$	−17.7722	+	2.81485i	−1.09797	+	0.173902i
$263$	−3.88712			−0.239690			−0.119845	−	0.992793i	$-0.538240\pi$
$263$	−3.88712			−0.239690			−0.119845	+	0.992793i	$0.538240\pi$
$264$		0			0
$265$	20.3107			1.24768
$266$	23.5285	−	3.72654i	1.44262	−	0.228489i
$267$		0			0
$268$	−6.19868	−	19.0776i	−0.378645	−	1.16535i
$269$		−	25.2300i		−	1.53830i	−0.639067	−	0.769151i	$-0.720679\pi$
$269$		−	25.2300i		−	1.53830i	0.639067	−	0.769151i	$-0.279321\pi$
$270$		0			0
$271$	−2.90649			−0.176556			−0.0882782	−	0.996096i	$-0.528136\pi$
$271$	−2.90649			−0.176556			−0.0882782	+	0.996096i	$0.528136\pi$
$272$	14.0806	−	10.2301i	0.853761	−	0.620294i
$273$		0			0
$274$	−2.04209	−	12.8932i	−0.123367	−	0.778909i
$275$			7.17963i			0.432948i
$276$		0			0
$277$			4.26825i			0.256454i	0.991745	+	0.128227i	$0.0409286\pi$
$277$			4.26825i			0.256454i	−0.991745	+	0.128227i	$0.959071\pi$
$278$	16.4134	−	2.59963i	0.984410	−	0.155915i
$279$		0			0
$280$	17.7426	−	9.04029i	1.06032	−	0.540261i
$281$	18.9900			1.13285			0.566424	−	0.824114i	$-0.308327\pi$
$281$	18.9900			1.13285			0.566424	+	0.824114i	$0.308327\pi$
$282$		0			0
$283$			13.1957i			0.784401i	0.919880	+	0.392200i	$0.128286\pi$
$283$			13.1957i			0.784401i	−0.919880	+	0.392200i	$0.871714\pi$
$284$	−3.10143	+	1.00772i	−0.184036	+	0.0597970i
$285$		0			0
$286$	1.17557	+	7.42226i	0.0695129	+	0.438887i
$287$	−31.3144			−1.84843
$288$		0			0
$289$	1.93243			0.113672
$290$	1.49930	+	9.46621i	0.0880420	+	0.555875i
$291$		0			0
$292$	9.84233	−	3.19797i	0.575979	−	0.187147i
$293$		−	12.0980i		−	0.706770i	−0.935478	−	0.353385i	$-0.885031\pi$
$293$		−	12.0980i		−	0.706770i	0.935478	−	0.353385i	$-0.114969\pi$
$294$		0			0
$295$	15.6216			0.909524
$296$	24.2147	−	12.3380i	1.40745	−	0.717132i
$297$		0			0
$298$	24.5948	−	3.89544i	1.42474	−	0.225657i
$299$			0.568158i			0.0328574i
$300$		0			0
$301$		−	26.5042i		−	1.52768i
$302$	2.57182	+	16.2378i	0.147991	+	0.934382i
$303$		0			0
$304$	14.1766	+	19.5124i	0.813084	+	1.11911i
$305$	−18.2360			−1.04419
$306$		0			0
$307$			24.7863i			1.41463i	0.706900	+	0.707314i	$0.250093\pi$
$307$			24.7863i			1.41463i	−0.706900	+	0.707314i	$0.749907\pi$
$308$	9.17442	+	28.2360i	0.522761	+	1.60889i
$309$		0			0
$310$	−6.71883	+	1.06416i	−0.381604	+	0.0604401i
$311$	6.72956			0.381598			0.190799	−	0.981629i	$-0.438892\pi$
$311$	6.72956			0.381598			0.190799	+	0.981629i	$0.438892\pi$
$312$		0			0
$313$	11.4956			0.649768			0.324884	−	0.945754i	$-0.394675\pi$
$313$	11.4956			0.649768			0.324884	+	0.945754i	$0.394675\pi$
$314$	−18.8262	+	2.98177i	−1.06242	+	0.168271i
$315$		0			0
$316$	−17.4508	+	5.67010i	−0.981683	+	0.318968i
$317$			2.86756i			0.161058i	0.996752	+	0.0805291i	$0.0256610\pi$
$317$			2.86756i			0.161058i	−0.996752	+	0.0805291i	$0.974339\pi$
$318$		0			0
$319$	−14.2895			−0.800058
$320$	16.3107	+	11.8504i	0.911798	+	0.662460i
$321$		0			0
$322$	0.351141	+	2.21702i	0.0195683	+	0.123550i
$323$			26.2360i			1.45981i
$324$		0			0
$325$			1.35114i			0.0749478i
$326$	−13.6796	+	2.16663i	−0.757641	+	0.119999i
$327$		0			0
$328$	−14.3936	−	28.2491i	−0.794755	−	1.55979i
$329$	−11.0534			−0.609395
$330$		0			0
$331$			1.44967i			0.0796811i	0.999206	+	0.0398405i	$0.0126850\pi$
$331$			1.44967i			0.0796811i	−0.999206	+	0.0398405i	$0.987315\pi$
$332$	−2.85004	−	8.77154i	−0.156417	−	0.481401i
$333$		0			0
$334$	−3.67365	−	23.1945i	−0.201013	−	1.26915i
$335$	25.2762			1.38099
$336$		0			0
$337$	−22.6774			−1.23532			−0.617660	−	0.786446i	$-0.711919\pi$
$337$	−22.6774			−1.23532			−0.617660	+	0.786446i	$0.711919\pi$
$338$	0.221232	+	1.39680i	0.0120334	+	0.0759760i
$339$		0			0
$340$	6.77706	+	20.8576i	0.367538	+	1.13116i
$341$		−	10.1422i		−	0.549233i
$342$		0			0
$343$	−17.3085			−0.934573
$344$	23.9098	−	12.1826i	1.28913	−	0.656844i
$345$		0			0
$346$	22.6252	−	3.58348i	1.21634	−	0.192649i
$347$			33.7652i			1.81261i	0.422621	+	0.906307i	$0.361110\pi$
$347$			33.7652i			1.81261i	−0.422621	+	0.906307i	$0.638890\pi$
$348$		0			0
$349$		−	6.34741i		−	0.339769i	−0.985464	−	0.169885i	$-0.945661\pi$
$349$		−	6.34741i		−	0.339769i	0.985464	−	0.169885i	$-0.0543395\pi$
$350$	0.835051	+	5.27230i	0.0446354	+	0.281817i
$351$		0			0
$352$	−21.2550	+	21.2550i	−1.13290	+	1.13290i
$353$	−32.1856			−1.71307			−0.856534	−	0.516090i	$-0.827387\pi$
$353$	−32.1856			−1.71307			−0.856534	+	0.516090i	$0.827387\pi$
$354$		0			0
$355$		−	4.10915i		−	0.218091i
$356$	21.7187	−	7.05684i	1.15109	−	0.374012i
$357$		0			0
$358$	1.71521	−	0.271662i	0.0906516	−	0.0143578i
$359$	−22.9222			−1.20979			−0.604894	−	0.796306i	$-0.706784\pi$
$359$	−22.9222			−1.20979			−0.604894	+	0.796306i	$0.706784\pi$
$360$		0			0
$361$	−17.3570			−0.913524
$362$	−9.78589	+	1.54993i	−0.514335	+	0.0814626i
$363$		0			0
$364$	1.72654	+	5.31375i	0.0904954	+	0.278516i
$365$			13.0403i			0.682560i
$366$		0			0
$367$	−9.68093			−0.505340			−0.252670	−	0.967552i	$-0.581309\pi$
$367$	−9.68093			−0.505340			−0.252670	+	0.967552i	$0.581309\pi$
$368$	−1.83860	+	1.33582i	−0.0958436	+	0.0696344i
$369$		0			0
$370$	5.35706	+	33.8232i	0.278500	+	1.75838i
$371$			22.5146i			1.16890i
$372$		0			0
$373$			23.2975i			1.20630i	0.797628	+	0.603149i	$0.206088\pi$
$373$			23.2975i			1.20630i	−0.797628	+	0.603149i	$0.793912\pi$
$374$	−32.2953	+	5.11507i	−1.66995	+	0.264494i
$375$		0			0
$376$	−5.08070	−	9.97144i	−0.262017	−	0.514238i
$377$	−2.68915			−0.138498
$378$		0			0
$379$		−	9.48276i		−	0.487097i	−0.969889	−	0.243548i	$-0.921689\pi$
$379$		−	9.48276i		−	0.487097i	0.969889	−	0.243548i	$-0.0783114\pi$
$380$	−28.9039	+	9.39144i	−1.48274	+	0.481770i
$381$		0			0
$382$	−3.17912	−	20.0722i	−0.162658	−	1.02698i
$383$	5.68406			0.290442			0.145221	−	0.989399i	$-0.453611\pi$
$383$	5.68406			0.290442			0.145221	+	0.989399i	$0.453611\pi$
$384$		0			0
$385$	−37.4104			−1.90661
$386$	0.812768	+	5.13162i	0.0413688	+	0.261192i
$387$		0			0
$388$	19.4993	−	6.33571i	0.989927	−	0.321647i
$389$			1.79842i			0.0911834i	0.998960	+	0.0455917i	$0.0145173\pi$
$389$			1.79842i			0.0911834i	−0.998960	+	0.0455917i	$0.985483\pi$
$390$		0			0
$391$	−2.47214			−0.125021
$392$	1.03269	+	2.02677i	0.0521587	+	0.102367i
$393$		0			0
$394$	−9.61617	+	1.52305i	−0.484456	+	0.0767302i
$395$		−	23.1209i		−	1.16334i
$396$		0			0
$397$		−	4.61064i		−	0.231402i	−0.993284	−	0.115701i	$-0.963089\pi$
$397$		−	4.61064i		−	0.231402i	0.993284	−	0.115701i	$-0.0369114\pi$
$398$	−3.40590	−	21.5040i	−0.170722	−	1.07790i
$399$		0			0
$400$	−4.37238	+	3.17672i	−0.218619	+	0.158836i
$401$	19.4701			0.972290			0.486145	−	0.873878i	$-0.338403\pi$
$401$	19.4701			0.972290			0.486145	+	0.873878i	$0.338403\pi$
$402$		0			0
$403$		−	1.90868i		−	0.0950780i
$404$	−1.86588	−	5.74258i	−0.0928308	−	0.285704i
$405$		0			0
$406$	−10.4934	+	1.66199i	−0.520778	+	0.0824831i
$407$	−51.0569			−2.53080
$408$		0			0
$409$	34.5696			1.70936			0.854678	−	0.519159i	$-0.173755\pi$
$409$	34.5696			1.70936			0.854678	+	0.519159i	$0.173755\pi$
$410$	39.4584	−	6.24959i	1.94871	−	0.308645i
$411$		0			0
$412$	−24.5740	+	7.98457i	−1.21067	+	0.393371i
$413$			17.3167i			0.852097i
$414$		0			0
$415$	11.6216			0.570481
$416$	−4.00000	+	4.00000i	−0.196116	+	0.196116i
$417$		0			0
$418$	−7.08831	−	44.7538i	−0.346700	−	2.18898i
$419$			5.72235i			0.279555i	0.990183	+	0.139778i	$0.0446388\pi$
$419$			5.72235i			0.279555i	−0.990183	+	0.139778i	$0.955361\pi$
$420$		0			0
$421$		−	30.8897i		−	1.50547i	−0.658322	−	0.752736i	$-0.728734\pi$
$421$		−	30.8897i		−	1.50547i	0.658322	−	0.752736i	$-0.271266\pi$
$422$	2.19347	−	0.347411i	0.106776	−	0.0169117i
$423$		0			0
$424$	−20.3107	+	10.3488i	−0.986376	+	0.502584i
$425$	−5.87901			−0.285174
$426$		0			0
$427$		−	20.2147i		−	0.978258i
$428$	6.76974	+	20.8351i	0.327228	+	1.00710i
$429$		0			0
$430$	5.28960	+	33.3972i	0.255087	+	1.61056i
$431$	−16.3709			−0.788559			−0.394279	−	0.918991i	$-0.629006\pi$
$431$	−16.3709			−0.788559			−0.394279	+	0.918991i	$0.629006\pi$
$432$		0			0
$433$	−9.17672			−0.441005			−0.220503	−	0.975386i	$-0.570770\pi$
$433$	−9.17672			−0.441005			−0.220503	+	0.975386i	$0.570770\pi$
$434$	−1.17963	−	7.44788i	−0.0566239	−	0.357509i
$435$		0			0
$436$	−3.37019	−	10.3724i	−0.161403	−	0.496747i
$437$		−	3.42581i		−	0.163879i
$438$		0			0
$439$	−19.1494			−0.913953			−0.456977	−	0.889479i	$-0.651068\pi$
$439$	−19.1494			−0.913953			−0.456977	+	0.889479i	$0.651068\pi$
$440$	−17.1957	−	33.7484i	−0.819771	−	1.60889i
$441$		0			0
$442$	−6.07768	+	0.962611i	−0.289086	+	0.0457867i
$443$		−	5.89817i		−	0.280230i	−0.990135	−	0.140115i	$-0.955253\pi$
$443$		−	5.89817i		−	0.280230i	0.990135	−	0.140115i	$-0.0447473\pi$
$444$		0			0
$445$			28.7756i			1.36409i
$446$	−6.11862	−	38.6314i	−0.289725	−	1.82925i
$447$		0			0
$448$	−13.1363	+	18.0806i	−0.620633	+	0.854227i
$449$	21.8310			1.03027			0.515134	−	0.857110i	$-0.327742\pi$
$449$	21.8310			1.03027			0.515134	+	0.857110i	$0.327742\pi$
$450$		0			0
$451$			59.5634i			2.80473i
$452$	−25.9323	+	8.42592i	−1.21975	+	0.396322i
$453$		0			0
$454$	32.0475	−	5.07582i	1.50406	−	0.238220i
$455$	−7.04029			−0.330054
$456$		0			0
$457$	6.84244			0.320076			0.160038	−	0.987111i	$-0.448838\pi$
$457$	6.84244			0.320076			0.160038	+	0.987111i	$0.448838\pi$
$458$	32.8338	−	5.20036i	1.53422	−	0.242997i
$459$		0			0
$460$	−0.884927	−	2.72353i	−0.0412599	−	0.126985i
$461$		−	22.2688i		−	1.03716i	−0.855029	−	0.518580i	$-0.826461\pi$
$461$		−	22.2688i		−	1.03716i	0.855029	−	0.518580i	$-0.173539\pi$
$462$		0			0
$463$	26.4021			1.22701			0.613504	−	0.789692i	$-0.289760\pi$
$463$	26.4021			1.22701			0.613504	+	0.789692i	$0.289760\pi$
$464$	−6.32258	−	8.70228i	−0.293518	−	0.403993i
$465$		0			0
$466$	0.768632	+	4.85295i	0.0356062	+	0.224809i
$467$		−	11.3035i		−	0.523065i	−0.965195	−	0.261532i	$-0.915772\pi$
$467$		−	11.3035i		−	0.523065i	0.965195	−	0.261532i	$-0.0842278\pi$
$468$		0			0
$469$			28.0189i			1.29379i
$470$	13.9281	−	2.20600i	0.642457	−	0.101755i
$471$		0			0
$472$	−15.6216	+	7.95959i	−0.719042	+	0.366370i
$473$	−50.4140			−2.31804
$474$		0			0
$475$		−	8.14694i		−	0.373807i
$476$	−23.1209	+	7.51243i	−1.05974	+	0.344332i
$477$		0			0
$478$	−2.56231	−	16.1778i	−0.117197	−	0.739954i
$479$	40.4023			1.84603			0.923015	−	0.384764i	$-0.125717\pi$
$479$	40.4023			1.84603			0.923015	+	0.384764i	$0.125717\pi$
$480$		0			0
$481$	−9.60845			−0.438108
$482$	−2.21360	−	13.9761i	−0.100827	−	0.636596i
$483$		0			0
$484$	32.7847	−	10.6524i	1.49022	−	0.484200i
$485$			25.8350i			1.17311i
$486$		0			0
$487$	−36.4018			−1.64952			−0.824762	−	0.565480i	$-0.808691\pi$
$487$	−36.4018			−1.64952			−0.824762	+	0.565480i	$0.808691\pi$
$488$	18.2360	−	9.29168i	0.825503	−	0.420615i
$489$		0			0
$490$	−2.83099	+	0.448385i	−0.127891	+	0.0202560i
$491$			3.76382i			0.169859i	0.996387	+	0.0849294i	$0.0270665\pi$
$491$			3.76382i			0.169859i	−0.996387	+	0.0849294i	$0.972934\pi$
$492$		0			0
$493$		−	11.7009i		−	0.526981i
$494$	−1.33395	−	8.42226i	−0.0600175	−	0.378935i
$495$		0			0
$496$	6.17661	−	4.48757i	0.277338	−	0.201498i
$497$	4.55503			0.204321
$498$		0			0
$499$			16.9348i			0.758107i	0.925375	+	0.379053i	$0.123750\pi$
$499$			16.9348i			0.758107i	−0.925375	+	0.379053i	$0.876250\pi$
$500$	5.68323	+	17.4912i	0.254162	+	0.782230i
$501$		0			0
$502$	15.8848	−	2.51591i	0.708974	−	0.112290i
$503$	12.9809			0.578792			0.289396	−	0.957209i	$-0.406546\pi$
$503$	12.9809			0.578792			0.289396	+	0.957209i	$0.406546\pi$
$504$		0			0
$505$	7.60845			0.338572
$506$	4.21702	−	0.667910i	0.187469	−	0.0296922i
$507$		0			0
$508$	−36.9726	+	12.0131i	−1.64039	+	0.532996i
$509$			13.4857i			0.597741i	0.954294	+	0.298871i	$0.0966099\pi$
$509$			13.4857i			0.597741i	−0.954294	+	0.298871i	$0.903390\pi$
$510$		0			0
$511$	−14.4553			−0.639464
$512$	−22.3488	−	3.53971i	−0.987688	−	0.156434i
$513$		0			0
$514$	2.51121	+	15.8551i	0.110765	+	0.699340i
$515$		−	32.5585i		−	1.43470i
$516$		0			0
$517$			21.0249i			0.924672i
$518$	−37.4933	+	5.93835i	−1.64736	+	0.260916i
$519$		0			0
$520$	−3.23607	−	6.35114i	−0.141911	−	0.278516i
$521$	35.4175			1.55167			0.775834	−	0.630937i	$-0.217330\pi$
$521$	35.4175			1.55167			0.775834	+	0.630937i	$0.217330\pi$
$522$		0			0
$523$			4.72122i			0.206445i	0.994658	+	0.103222i	$0.0329153\pi$
$523$			4.72122i			0.206445i	−0.994658	+	0.103222i	$0.967085\pi$
$524$	7.86357	+	24.2016i	0.343522	+	1.05725i
$525$		0			0
$526$	0.859954	+	5.42954i	0.0374958	+	0.236739i
$527$	8.30493			0.361768
$528$		0			0
$529$	−22.6772			−0.985965
$530$	−4.49338	−	28.3701i	−0.195180	−	1.23232i
$531$		0			0
$532$	−10.4105	−	32.0402i	−0.451352	−	1.38912i
$533$			11.2093i			0.485529i
$534$		0			0
$535$	−27.6049			−1.19346
$536$	−25.2762	+	12.8789i	−1.09177	+	0.556283i
$537$		0			0
$538$	−35.2414	+	5.58168i	−1.51936	+	0.240643i
$539$		−	4.27346i		−	0.184071i
$540$		0			0
$541$		−	26.4200i		−	1.13589i	−0.823068	−	0.567943i	$-0.807739\pi$
$541$		−	26.4200i		−	1.13589i	0.823068	−	0.567943i	$-0.192261\pi$
$542$	0.643007	+	4.05979i	0.0276195	+	0.174383i
$543$		0			0
$544$	−17.4046	−	17.4046i	−0.746215	−	0.746215i
$545$	13.7426			0.588667
$546$		0			0
$547$		−	26.9939i		−	1.15417i	−0.816683	−	0.577087i	$-0.804189\pi$
$547$		−	26.9939i		−	1.15417i	0.816683	−	0.577087i	$-0.195811\pi$
$548$	−17.5575	+	5.70479i	−0.750021	+	0.243697i
$549$		0			0
$550$	10.0285	−	1.58836i	0.427618	−	0.0677280i
$551$	16.2147			0.690770
$552$		0			0
$553$	25.6297			1.08989
$554$	5.96190	−	0.944272i	0.253297	−	0.0401183i
$555$		0			0
$556$	−7.26233	−	22.3511i	−0.307991	−	0.947900i
$557$			24.7636i			1.04927i	0.851329	+	0.524633i	$0.175797\pi$
$557$			24.7636i			1.04927i	−0.851329	+	0.524633i	$0.824203\pi$
$558$		0			0
$559$	−9.48746			−0.401277
$560$	−16.5527	−	22.7829i	−0.699480	−	0.962752i
$561$		0			0
$562$	−4.20119	−	26.5252i	−0.177216	−	1.11890i
$563$			19.7426i			0.832050i	0.909353	+	0.416025i	$0.136577\pi$
$563$			19.7426i			0.832050i	−0.909353	+	0.416025i	$0.863423\pi$
$564$		0			0
$565$		−	34.3582i		−	1.44546i
$566$	18.4317	−	2.91930i	0.774743	−	0.122707i
$567$		0			0
$568$	2.09372	+	4.10915i	0.0878504	+	0.172416i
$569$	−2.17684			−0.0912577			−0.0456289	−	0.998958i	$-0.514529\pi$
$569$	−2.17684			−0.0912577			−0.0456289	+	0.998958i	$0.514529\pi$
$570$		0			0
$571$		−	4.05934i		−	0.169878i	−0.996386	−	0.0849391i	$-0.972930\pi$
$571$		−	4.05934i		−	0.169878i	0.996386	−	0.0849391i	$-0.0270696\pi$
$572$	10.1074	−	3.28408i	0.422610	−	0.137314i
$573$		0			0
$574$	6.92773	+	43.7400i	0.289158	+	1.82567i
$575$	0.767662			0.0320137
$576$		0			0
$577$	−27.5489			−1.14687			−0.573437	−	0.819249i	$-0.694390\pi$
$577$	−27.5489			−1.14687			−0.573437	+	0.819249i	$0.694390\pi$
$578$	−0.427514	−	2.69922i	−0.0177823	−	0.112273i
$579$		0			0
$580$	12.8907	−	4.18845i	0.535259	−	0.173916i
$581$			12.8826i			0.534461i
$582$		0			0
$583$	42.8254			1.77365
$584$	−6.64436	−	13.0403i	−0.274946	−	0.539611i
$585$		0			0
$586$	−16.8985	+	2.67645i	−0.698069	+	0.110563i
$587$			14.3268i			0.591329i	0.955292	+	0.295664i	$0.0955410\pi$
$587$			14.3268i			0.591329i	−0.955292	+	0.295664i	$0.904459\pi$
$588$		0			0
$589$			11.5087i			0.474208i
$590$	−3.45599	−	21.8203i	−0.142281	−	0.898326i
$591$		0			0
$592$	−22.5908	−	31.0936i	−0.928477	−	1.27794i
$593$	−27.6050			−1.13360			−0.566801	−	0.823855i	$-0.691819\pi$
$593$	−27.6050			−1.13360			−0.566801	+	0.823855i	$0.691819\pi$
$594$		0			0
$595$		−	30.6333i		−	1.25584i
$596$	−10.8823	−	33.4923i	−0.445757	−	1.37190i
$597$		0			0
$598$	0.793604	−	0.125695i	0.0324529	−	0.00514003i
$599$	18.5204			0.756724			0.378362	−	0.925658i	$-0.376487\pi$
$599$	18.5204			0.756724			0.378362	+	0.925658i	$0.376487\pi$
$600$		0			0
$601$	35.1640			1.43437			0.717185	−	0.696883i	$-0.245430\pi$
$601$	35.1640			1.43437			0.717185	+	0.696883i	$0.245430\pi$
$602$	−37.0211	+	5.86357i	−1.50887	+	0.238981i
$603$		0			0
$604$	22.1121	−	7.18464i	0.899727	−	0.292339i
$605$			43.4371i			1.76597i
$606$		0			0
$607$	−35.5432			−1.44265			−0.721327	−	0.692594i	$-0.756468\pi$
$607$	−35.5432			−1.44265			−0.721327	+	0.692594i	$0.756468\pi$
$608$	24.1187	−	24.1187i	0.978142	−	0.978142i
$609$		0			0
$610$	4.03437	+	25.4720i	0.163347	+	1.03133i
$611$			3.95669i			0.160070i
$612$		0			0
$613$		−	37.3356i		−	1.50797i	−0.656891	−	0.753985i	$-0.728129\pi$
$613$		−	37.3356i		−	1.50797i	0.656891	−	0.753985i	$-0.271871\pi$
$614$	34.6215	−	5.48351i	1.39721	−	0.221297i
$615$		0			0
$616$	37.4104	−	19.0615i	1.50731	−	0.768011i
$617$	−20.1630			−0.811731			−0.405865	−	0.913933i	$-0.633030\pi$
$617$	−20.1630			−0.811731			−0.405865	+	0.913933i	$0.633030\pi$
$618$		0			0
$619$			15.1066i			0.607187i	0.952802	+	0.303594i	$0.0981865\pi$
$619$			15.1066i			0.607187i	−0.952802	+	0.303594i	$0.901813\pi$
$620$	2.97283	+	9.14945i	0.119392	+	0.367451i
$621$		0			0
$622$	−1.48879	−	9.39986i	−0.0596951	−	0.376900i
$623$	−31.8979			−1.27796
$624$		0			0
$625$	−29.9301			−1.19720
$626$	−2.54319	−	16.0570i	−0.101646	−	0.641768i
$627$		0			0
$628$	8.32990	+	25.6368i	0.332399	+	1.02302i
$629$		−	41.8077i		−	1.66698i
$630$		0			0
$631$	0.390213			0.0155341			0.00776706	−	0.999970i	$-0.497528\pi$
$631$	0.390213			0.0155341			0.00776706	+	0.999970i	$0.497528\pi$
$632$	11.7807	+	23.1209i	0.468610	+	0.919699i
$633$		0			0
$634$	4.00541	−	0.634395i	0.159075	−	0.0251950i
$635$		−	48.9857i		−	1.94394i
$636$		0			0
$637$		−	0.804226i		−	0.0318646i
$638$	3.16129	+	19.9596i	0.125157	+	0.790208i
$639$		0			0
$640$	12.9443	−	25.4046i	0.511667	−	1.00420i
$641$	36.5386			1.44319			0.721593	−	0.692317i	$-0.243410\pi$
$641$	36.5386			1.44319			0.721593	+	0.692317i	$0.243410\pi$
$642$		0			0
$643$			29.1064i			1.14785i	0.818910	+	0.573923i	$0.194579\pi$
$643$			29.1064i			1.14785i	−0.818910	+	0.573923i	$0.805421\pi$
$644$	3.01905	−	0.980949i	0.118967	−	0.0386548i
$645$		0			0
$646$	36.6464	−	5.80423i	1.44183	−	0.228364i
$647$	15.1906			0.597206			0.298603	−	0.954377i	$-0.403479\pi$
$647$	15.1906			0.597206			0.298603	+	0.954377i	$0.403479\pi$
$648$		0			0
$649$	32.9382			1.29294
$650$	1.88728	−	0.298915i	0.0740251	−	0.0117244i
$651$		0			0
$652$	6.05271	+	18.6283i	0.237042	+	0.729542i
$653$			15.9205i			0.623016i	0.950243	+	0.311508i	$0.100834\pi$
$653$			15.9205i			0.623016i	−0.950243	+	0.311508i	$0.899166\pi$
$654$		0			0
$655$	−32.0652			−1.25289
$656$	−36.2741	+	26.3546i	−1.41626	+	1.02898i
$657$		0			0
$658$	2.44537	+	15.4394i	0.0953304	+	0.601892i
$659$			7.56597i			0.294728i	0.989082	+	0.147364i	$0.0470789\pi$
$659$			7.56597i			0.294728i	−0.989082	+	0.147364i	$0.952921\pi$
$660$		0			0
$661$			32.0806i			1.24779i	0.781508	+	0.623895i	$0.214451\pi$
$661$			32.0806i			1.24779i	−0.781508	+	0.623895i	$0.785549\pi$
$662$	2.02490	−	0.320713i	0.0787001	−	0.0124649i
$663$		0			0
$664$	−11.6216	+	5.92149i	−0.451005	+	0.229798i
$665$	42.4507			1.64617
$666$		0			0
$667$			1.52786i			0.0591591i
$668$	−31.5854	+	10.2627i	−1.22208	+	0.397077i
$669$		0			0
$670$	−5.59191	−	35.3059i	−0.216034	−	1.36399i
$671$	−38.4507			−1.48437
$672$		0			0
$673$	19.0592			0.734679			0.367340	−	0.930087i	$-0.380269\pi$
$673$	19.0592			0.734679			0.367340	+	0.930087i	$0.380269\pi$
$674$	5.01697	+	31.6759i	0.193247	+	1.22011i
$675$		0			0
$676$	1.90211	−	0.618034i	0.0731582	−	0.0237705i
$677$		−	4.40095i		−	0.169142i	−0.996417	−	0.0845711i	$-0.973048\pi$
$677$		−	4.40095i		−	0.169142i	0.996417	−	0.0845711i	$-0.0269520\pi$
$678$		0			0
$679$	−28.6383			−1.09904
$680$	27.6347	−	14.0806i	1.05974	−	0.539966i
$681$		0			0
$682$	−14.1667	+	2.24379i	−0.542471	+	0.0859190i
$683$		−	33.8071i		−	1.29359i	−0.762662	−	0.646797i	$-0.776108\pi$
$683$		−	33.8071i		−	1.29359i	0.762662	−	0.646797i	$-0.223892\pi$
$684$		0			0
$685$		−	23.2623i		−	0.888808i
$686$	3.82920	+	24.1766i	0.146199	+	0.923067i
$687$		0			0
$688$	−22.3063	−	30.7021i	−0.850422	−	1.17050i
$689$	8.05934			0.307037
$690$		0			0
$691$			12.4856i			0.474974i	0.971391	+	0.237487i	$0.0763237\pi$
$691$			12.4856i			0.474974i	−0.971391	+	0.237487i	$0.923676\pi$
$692$	−10.0108	−	30.8101i	−0.380554	−	1.17123i
$693$		0			0
$694$	47.1634	−	7.46994i	1.79030	−	0.283555i
$695$	29.6135			1.12330
$696$		0			0
$697$	−48.7732			−1.84742
$698$	−8.86608	+	1.40425i	−0.335586	+	0.0531516i
$699$		0			0
$700$	7.17963	−	2.33280i	0.271364	−	0.0881716i
$701$			34.2016i			1.29178i	0.763432	+	0.645888i	$0.223513\pi$
$701$			34.2016i			1.29178i	−0.763432	+	0.645888i	$0.776487\pi$
$702$		0			0
$703$	57.9358			2.18509
$704$	34.3913	+	24.9868i	1.29617	+	0.941724i
$705$		0			0
$706$	7.12048	+	44.9570i	0.267983	+	1.69198i
$707$			8.43403i			0.317195i
$708$		0			0
$709$		−	41.6463i		−	1.56406i	−0.623240	−	0.782030i	$-0.714184\pi$
$709$		−	41.6463i		−	1.56406i	0.623240	−	0.782030i	$-0.285816\pi$
$710$	−5.73967	+	0.909075i	−0.215406	+	0.0341170i
$711$		0			0
$712$	−14.6619	−	28.7756i	−0.549477	−	1.07841i
$713$	−1.08443			−0.0406122
$714$		0			0
$715$			13.3914i			0.500811i
$716$	−0.758917	−	2.33571i	−0.0283621	−	0.0872895i
$717$		0			0
$718$	5.07112	+	32.0178i	0.189252	+	1.19489i
$719$	−33.0401			−1.23219			−0.616093	−	0.787673i	$-0.711286\pi$
$719$	−33.0401			−1.23219			−0.616093	+	0.787673i	$0.711286\pi$
$720$		0			0
$721$	36.0914			1.34411
$722$	3.83991	+	24.2442i	0.142907	+	0.902277i
$723$		0			0
$724$	4.32990	+	13.3261i	0.160919	+	0.495259i
$725$			3.63342i			0.134942i
$726$		0			0
$727$	−7.80551			−0.289490			−0.144745	−	0.989469i	$-0.546236\pi$
$727$	−7.80551			−0.289490			−0.144745	+	0.989469i	$0.546236\pi$
$728$	7.04029	−	3.58721i	0.260931	−	0.132951i
$729$		0			0
$730$	18.2147	−	2.88493i	0.674157	−	0.106776i
$731$		−	41.2813i		−	1.52684i
$732$		0			0
$733$			29.3035i			1.08235i	0.840910	+	0.541175i	$0.182020\pi$
$733$			29.3035i			1.08235i	−0.840910	+	0.541175i	$0.817980\pi$
$734$	2.14173	+	13.5223i	0.0790526	+	0.499119i
$735$		0			0
$736$	2.27263	+	2.27263i	0.0837703	+	0.0837703i
$737$	53.2952			1.96315
$738$		0			0
$739$		−	42.2408i		−	1.55385i	−0.629591	−	0.776926i	$-0.716778\pi$
$739$		−	42.2408i		−	1.55385i	0.629591	−	0.776926i	$-0.283222\pi$
$740$	46.0591	−	14.9655i	1.69317	−	0.550143i
$741$		0			0
$742$	31.4485	−	4.98095i	1.15451	−	0.182856i
$743$	−19.3835			−0.711112			−0.355556	−	0.934655i	$-0.615709\pi$
$743$	−19.3835			−0.711112			−0.355556	+	0.934655i	$0.615709\pi$
$744$		0			0
$745$	44.3746			1.62576
$746$	32.5420	−	5.15414i	1.19145	−	0.188707i
$747$		0			0
$748$	14.2895	+	43.9785i	0.522476	+	1.60801i
$749$		−	30.6002i		−	1.11811i
$750$		0			0
$751$	9.06886			0.330927			0.165464	−	0.986216i	$-0.447088\pi$
$751$	9.06886			0.330927			0.165464	+	0.986216i	$0.447088\pi$
$752$	−12.8041	+	9.30273i	−0.466918	+	0.339236i
$753$		0			0
$754$	0.594926	+	3.75621i	0.0216659	+	0.136793i
$755$			29.2967i			1.06622i
$756$		0			0
$757$			6.34174i			0.230495i	0.993337	+	0.115247i	$0.0367660\pi$
$757$			6.34174i			0.230495i	−0.993337	+	0.115247i	$0.963234\pi$
$758$	−13.2455	+	2.09789i	−0.481100	+	0.0761987i
$759$		0			0
$760$	19.5124	+	38.2953i	0.707790	+	1.38912i
$761$	−19.1133			−0.692856			−0.346428	−	0.938077i	$-0.612605\pi$
$761$	−19.1133			−0.692856			−0.346428	+	0.938077i	$0.612605\pi$
$762$		0			0
$763$			15.2338i			0.551499i
$764$	−27.3335	+	8.88120i	−0.988892	+	0.321310i
$765$		0			0
$766$	−1.25749	−	7.93950i	−0.0454351	−	0.286866i
$767$	6.19868			0.223821
$768$		0			0
$769$	−5.22795			−0.188525			−0.0942624	−	0.995547i	$-0.530049\pi$
$769$	−5.22795			−0.188525			−0.0942624	+	0.995547i	$0.530049\pi$
$770$	8.27636	+	52.2549i	0.298259	+	1.88314i
$771$		0			0
$772$	6.98804	−	2.27055i	0.251505	−	0.0817190i
$773$			32.5414i			1.17043i	0.810877	+	0.585216i	$0.198990\pi$
$773$			32.5414i			1.17043i	−0.810877	+	0.585216i	$0.801010\pi$
$774$		0			0
$775$	−2.57889			−0.0926366
$776$	−13.1636	−	25.8350i	−0.472545	−	0.927423i
$777$		0			0
$778$	2.51203	−	0.397867i	0.0900607	−	0.0142642i
$779$		−	67.5884i		−	2.42161i
$780$		0			0
$781$		−	8.66418i		−	0.310029i
$782$	0.546915	+	3.45309i	0.0195576	+	0.123482i
$783$		0			0
$784$	2.60253	−	1.89085i	0.0929475	−	0.0675303i
$785$	−33.9667			−1.21232
$786$		0			0
$787$			8.62409i			0.307416i	0.988116	+	0.153708i	$0.0491214\pi$
$787$			8.62409i			0.307416i	−0.988116	+	0.153708i	$0.950879\pi$
$788$	4.25480	+	13.0949i	0.151571	+	0.466488i
$789$		0			0
$790$	−32.2953	+	5.11507i	−1.14902	+	0.181986i
$791$	38.0864			1.35420
$792$		0			0
$793$	−7.23607			−0.256960
$794$	−6.44016	+	1.02002i	−0.228553	+	0.0361992i
$795$		0			0
$796$	−29.2833	+	9.51474i	−1.03792	+	0.337241i
$797$		−	27.6486i		−	0.979365i	−0.871901	−	0.489682i	$-0.837113\pi$
$797$		−	27.6486i		−	0.979365i	0.871901	−	0.489682i	$-0.162887\pi$
$798$		0			0
$799$	−17.2161			−0.609062
$800$	5.40456	+	5.40456i	0.191080	+	0.191080i
$801$		0			0
$802$	−4.30740	−	27.1959i	−0.152100	−	0.960319i
$803$			27.4956i			0.970298i
$804$		0			0
$805$			4.00000i			0.140981i
$806$	−2.66605	+	0.422260i	−0.0939074	+	0.0148735i
$807$		0			0
$808$	−7.60845	+	3.87670i	−0.267664	+	0.136382i
$809$	24.4163			0.858431			0.429216	−	0.903202i	$-0.358790\pi$
$809$	24.4163			0.858431			0.429216	+	0.903202i	$0.358790\pi$
$810$		0			0
$811$		−	9.54312i		−	0.335104i	−0.985863	−	0.167552i	$-0.946414\pi$
$811$		−	9.54312i		−	0.335104i	0.985863	−	0.167552i	$-0.0535863\pi$
$812$	4.64294	+	14.2895i	0.162935	+	0.501463i
$813$		0			0
$814$	11.2954	+	71.3164i	0.395904	+	2.49964i
$815$	−24.6810			−0.864539
$816$		0			0
$817$	57.2063			2.00139
$818$	−7.64789	−	48.2869i	−0.267402	−	1.68831i
$819$		0			0
$820$	−17.4589	−	53.7330i	−0.609691	−	1.87644i
$821$		−	2.26876i		−	0.0791802i	−0.999216	−	0.0395901i	$-0.987395\pi$
$821$		−	2.26876i		−	0.0791802i	0.999216	−	0.0395901i	$-0.0126052\pi$
$822$		0			0
$823$	−14.4047			−0.502115			−0.251058	−	0.967972i	$-0.580778\pi$
$823$	−14.4047			−0.502115			−0.251058	+	0.967972i	$0.580778\pi$
$824$	16.5894	+	32.5585i	0.577919	+	1.13423i
$825$		0			0
$826$	24.1879	−	3.83099i	0.841606	−	0.133297i
$827$		−	15.2993i		−	0.532010i	−0.963972	−	0.266005i	$-0.914296\pi$
$827$		−	15.2993i		−	0.532010i	0.963972	−	0.266005i	$-0.0857038\pi$
$828$		0			0
$829$		−	21.5350i		−	0.747940i	−0.927441	−	0.373970i	$-0.877996\pi$
$829$		−	21.5350i		−	0.747940i	0.927441	−	0.373970i	$-0.122004\pi$
$830$	−2.57106	−	16.2331i	−0.0892429	−	0.563457i
$831$		0			0
$832$	6.47214	+	4.70228i	0.224381	+	0.163022i
$833$	3.49930			0.121244
$834$		0			0
$835$		−	41.8481i		−	1.44821i
$836$	−60.9440	+	19.8019i	−2.10779	+	0.684864i
$837$		0			0
$838$	7.99300	−	1.26597i	0.276113	−	0.0437321i
$839$	−47.6245			−1.64418			−0.822090	−	0.569358i	$-0.807192\pi$
$839$	−47.6245			−1.64418			−0.822090	+	0.569358i	$0.807192\pi$
$840$		0			0
$841$	21.7685			0.750636
$842$	−43.1468	+	6.83379i	−1.48694	+	0.235508i
$843$		0			0
$844$	−0.970530	−	2.98698i	−0.0334070	−	0.102816i
$845$			2.52015i			0.0866957i
$846$		0			0
$847$	−48.1504			−1.65447
$848$	18.9487	+	26.0806i	0.650700	+	0.895611i
$849$		0			0
$850$	1.30062	+	8.21181i	0.0446110	+	0.281663i
$851$			5.45912i			0.187136i
$852$		0			0
$853$		−	15.3358i		−	0.525088i	−0.964920	−	0.262544i	$-0.915438\pi$
$853$		−	15.3358i		−	0.525088i	0.964920	−	0.262544i	$-0.0845616\pi$
$854$	−28.2360	+	4.47214i	−0.966214	+	0.153033i
$855$		0			0
$856$	27.6049	−	14.0654i	0.943515	−	0.480745i
$857$	−15.0828			−0.515218			−0.257609	−	0.966249i	$-0.582935\pi$
$857$	−15.0828			−0.515218			−0.257609	+	0.966249i	$0.582935\pi$
$858$		0			0
$859$			15.0249i			0.512642i	0.966592	+	0.256321i	$0.0825104\pi$
$859$			15.0249i			0.512642i	−0.966592	+	0.256321i	$0.917490\pi$
$860$	45.4791	−	14.7771i	1.55083	−	0.503894i
$861$		0			0
$862$	3.62176	+	22.8669i	0.123358	+	0.778850i
$863$	1.32919			0.0452460			0.0226230	−	0.999744i	$-0.492798\pi$
$863$	1.32919			0.0452460			0.0226230	+	0.999744i	$0.492798\pi$
$864$		0			0
$865$	40.8210			1.38795
$866$	2.03018	+	12.8181i	0.0689884	+	0.435576i
$867$		0			0
$868$	−10.1422	+	3.29541i	−0.344250	+	0.111854i
$869$		−	48.7506i		−	1.65375i
$870$		0			0
$871$	10.0297			0.339842
$872$	−13.7426	+	7.00219i	−0.465382	+	0.237124i
$873$		0			0
$874$	−4.78518	+	0.757897i	−0.161861	+	0.0256363i
$875$		−	25.6890i		−	0.868448i
$876$		0			0
$877$			44.4244i			1.50011i	0.661378	+	0.750053i	$0.269972\pi$
$877$			44.4244i			1.50011i	−0.661378	+	0.750053i	$0.730028\pi$
$878$	4.23647	+	26.7480i	0.142974	+	0.902701i
$879$		0			0
$880$	−43.3356	+	31.4852i	−1.46084	+	1.06136i
$881$	36.5136			1.23017			0.615087	−	0.788459i	$-0.289121\pi$
$881$	36.5136			1.23017			0.615087	+	0.788459i	$0.289121\pi$
$882$		0			0
$883$			6.77808i			0.228101i	0.993475	+	0.114050i	$0.0363825\pi$
$883$			6.77808i			0.228101i	−0.993475	+	0.114050i	$0.963617\pi$
$884$	2.68915	+	8.27636i	0.0904460	+	0.278364i
$885$		0			0
$886$	−8.23858	+	1.30486i	−0.276780	+	0.0438377i
$887$	48.6502			1.63351			0.816756	−	0.576983i	$-0.195770\pi$
$887$	48.6502			1.63351			0.816756	+	0.576983i	$0.195770\pi$
$888$		0			0
$889$	54.3011			1.82120
$890$	40.1938	−	6.36607i	1.34730	−	0.213391i
$891$		0			0
$892$	−52.6069	+	17.0930i	−1.76141	+	0.572316i
$893$		−	23.8575i		−	0.798362i
$894$		0			0
$895$	3.09462			0.103442
$896$	28.1612	+	14.3488i	0.940799	+	0.479361i
$897$		0			0
$898$	−4.82971	−	30.4936i	−0.161169	−	1.01758i
$899$		−	5.13273i		−	0.171186i
$900$		0			0
$901$			35.0673i			1.16826i
$902$	83.1983	−	13.1773i	2.77020	−	0.438757i
$903$		0			0
$904$	17.5064	+	34.3582i	0.582254	+	1.14274i
$905$	−17.6560			−0.586904
$906$		0			0
$907$		−	36.5196i		−	1.21261i	−0.795230	−	0.606307i	$-0.792650\pi$
$907$		−	36.5196i		−	1.21261i	0.795230	−	0.606307i	$-0.207350\pi$
$908$	−14.1798	−	43.6410i	−0.470574	−	1.44828i
$909$		0			0
$910$	1.55754	+	9.83390i	0.0516318	+	0.325991i
$911$	23.9142			0.792312			0.396156	−	0.918183i	$-0.370344\pi$
$911$	23.9142			0.792312			0.396156	+	0.918183i	$0.370344\pi$
$912$		0			0
$913$	24.5042			0.810971
$914$	−1.51377	−	9.55754i	−0.0500709	−	0.316135i
$915$		0			0
$916$	−14.5278	−	44.7118i	−0.480010	−	1.47732i
$917$		−	35.5445i		−	1.17378i
$918$		0			0
$919$	18.4982			0.610198			0.305099	−	0.952321i	$-0.401310\pi$
$919$	18.4982			0.610198			0.305099	+	0.952321i	$0.401310\pi$
$920$	−3.60845	+	1.83860i	−0.118967	+	0.0606168i
$921$		0			0
$922$	−31.1051	+	4.92656i	−1.02439	+	0.162247i
$923$		−	1.63052i		−	0.0536692i
$924$		0			0
$925$			12.9824i			0.426858i
$926$	−5.84097	−	36.8785i	−0.191946	−	1.21190i
$927$		0			0
$928$	−10.7566	+	10.7566i	−0.353103	+	0.353103i
$929$	−31.5521			−1.03519			−0.517595	−	0.855625i	$-0.673173\pi$
$929$	−31.5521			−1.03519			−0.517595	+	0.855625i	$0.673173\pi$
$930$		0			0
$931$			4.84922i			0.158927i
$932$	6.60856	−	2.14725i	0.216471	−	0.0703356i
$933$		0			0
$934$	−15.7888	+	2.50070i	−0.516625	+	0.0818254i
$935$	−58.2680			−1.90557
$936$		0			0
$937$	−5.54201			−0.181050			−0.0905248	−	0.995894i	$-0.528854\pi$
$937$	−5.54201			−0.181050			−0.0905248	+	0.995894i	$0.528854\pi$
$938$	39.1369	−	6.19868i	1.27787	−	0.202394i
$939$		0			0
$940$	−6.16269	−	18.9668i	−0.201005	−	0.618629i
$941$			9.62480i			0.313760i	0.987618	+	0.156880i	$0.0501435\pi$
$941$			9.62480i			0.313760i	−0.987618	+	0.156880i	$0.949856\pi$
$942$		0			0
$943$	6.36865			0.207392
$944$	14.5740	+	20.0593i	0.474342	+	0.652876i
$945$		0			0
$946$	11.1532	+	70.4184i	0.362621	+	2.28950i
$947$			31.1231i			1.01137i	0.862719	+	0.505683i	$0.168759\pi$
$947$			31.1231i			1.01137i	−0.862719	+	0.505683i	$0.831241\pi$
$948$		0			0
$949$			5.17442i			0.167969i
$950$	−11.3797	+	1.80236i	−0.369205	+	0.0584763i
$951$		0			0
$952$	15.6085	+	30.6333i	0.505873	+	0.992831i
$953$	17.0359			0.551847			0.275924	−	0.961180i	$-0.411016\pi$
$953$	17.0359			0.551847			0.275924	+	0.961180i	$0.411016\pi$
$954$		0			0
$955$		−	36.2147i		−	1.17188i
$956$	−22.0303	+	7.15807i	−0.712510	+	0.231509i
$957$		0			0
$958$	−8.93828	−	56.4341i	−0.288783	−	1.82330i
$959$	25.7865			0.832689
$960$		0			0
$961$	−27.3570			−0.882482
$962$	2.12569	+	13.4211i	0.0685351	+	0.432714i
$963$		0			0
$964$	−19.0322	+	6.18393i	−0.612985	+	0.199171i
$965$			9.25860i			0.298045i
$966$		0			0
$967$	7.56565			0.243295			0.121647	−	0.992573i	$-0.461182\pi$
$967$	7.56565			0.243295			0.121647	+	0.992573i	$0.461182\pi$
$968$	−22.1323	−	43.4371i	−0.711360	−	1.39612i
$969$		0			0
$970$	36.0864	−	5.71552i	1.15866	−	0.183514i
$971$		−	25.0676i		−	0.804457i	−0.915539	−	0.402228i	$-0.868236\pi$
$971$		−	25.0676i		−	0.804457i	0.915539	−	0.402228i	$-0.131764\pi$
$972$		0			0
$973$			32.8268i			1.05238i
$974$	8.05324	+	50.8462i	0.258042	+	1.62922i
$975$		0			0
$976$	−17.0130	−	23.4164i	−0.544573	−	0.749541i
$977$	37.9292			1.21346			0.606732	−	0.794907i	$-0.292480\pi$
$977$	37.9292			1.21346			0.606732	+	0.794907i	$0.292480\pi$
$978$		0			0
$979$			60.6735i			1.93913i
$980$	1.25261	+	3.85514i	0.0400132	+	0.123148i
$981$		0			0
$982$	5.25731	−	0.832676i	0.167768	−	0.0265718i
$983$	10.3543			0.330250			0.165125	−	0.986273i	$-0.447197\pi$
$983$	10.3543			0.330250			0.165125	+	0.986273i	$0.447197\pi$
$984$		0			0
$985$	−17.3497			−0.552809
$986$	−16.3438	+	2.58861i	−0.520493	+	0.0824380i
$987$		0			0
$988$	−11.4691	+	3.72654i	−0.364881	+	0.118557i
$989$			5.39038i			0.171404i
$990$		0			0
$991$	−45.2348			−1.43693			−0.718466	−	0.695562i	$-0.755155\pi$
$991$	−45.2348			−1.43693			−0.718466	+	0.695562i	$0.755155\pi$
$992$	−7.63471	−	7.63471i	−0.242402	−	0.242402i
$993$		0			0
$994$	−1.00772	−	6.36247i	−0.0319628	−	0.201805i
$995$		−	38.7981i		−	1.22998i
$996$		0			0
$997$		−	24.7402i		−	0.783529i	−0.920066	−	0.391764i	$-0.871865\pi$
$997$		−	24.7402i		−	0.783529i	0.920066	−	0.391764i	$-0.128135\pi$
$998$	23.6546	−	3.74652i	0.748773	−	0.118594i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.g.d.469.5		8
3.2	odd	2		312.2.g.a.157.4	yes	8
4.3	odd	2		3744.2.g.d.1873.2		8
8.3	odd	2		3744.2.g.d.1873.7		8
8.5	even	2	inner	936.2.g.d.469.6		8
12.11	even	2		1248.2.g.a.625.8		8
24.5	odd	2		312.2.g.a.157.3	✓	8
24.11	even	2		1248.2.g.a.625.1		8
48.5	odd	4		9984.2.a.y.1.1		4
48.11	even	4		9984.2.a.bh.1.1		4
48.29	odd	4		9984.2.a.bb.1.4		4
48.35	even	4		9984.2.a.s.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.g.a.157.3	✓	8	24.5	odd	2
312.2.g.a.157.4	yes	8	3.2	odd	2
936.2.g.d.469.5		8	1.1	even	1	trivial
936.2.g.d.469.6		8	8.5	even	2	inner
1248.2.g.a.625.1		8	24.11	even	2
1248.2.g.a.625.8		8	12.11	even	2
3744.2.g.d.1873.2		8	4.3	odd	2
3744.2.g.d.1873.7		8	8.3	odd	2
9984.2.a.s.1.4		4	48.35	even	4
9984.2.a.y.1.1		4	48.5	odd	4
9984.2.a.bb.1.4		4	48.29	odd	4
9984.2.a.bh.1.1		4	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)

\(f(q)\)	\(=\)	\(q+(-0.221232 - 1.39680i) q^{2} +(-1.90211 + 0.618034i) q^{4} -2.52015i q^{5} +2.79360 q^{7} +(1.28408 + 2.52015i) q^{8} +(-3.52015 + 0.557537i) q^{10} -5.31375i q^{11} -1.00000i q^{13} +(-0.618034 - 3.90211i) q^{14} +(3.23607 - 2.35114i) q^{16} +4.35114 q^{17} +6.02967i q^{19} +(1.55754 + 4.79360i) q^{20} +(-7.42226 + 1.17557i) q^{22} -0.568158 q^{23} -1.35114 q^{25} +(-1.39680 + 0.221232i) q^{26} +(-5.31375 + 1.72654i) q^{28} -2.68915i q^{29} +1.90868 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-0.962611 - 6.07768i) q^{34} -7.04029i q^{35} -9.60845i q^{37} +(8.42226 - 1.33395i) q^{38} +(6.35114 - 3.23607i) q^{40} -11.2093 q^{41} -9.48746i q^{43} +(3.28408 + 10.1074i) q^{44} +(0.125695 + 0.793604i) q^{46} -3.95669 q^{47} +0.804226 q^{49} +(0.298915 + 1.88728i) q^{50} +(0.618034 + 1.90211i) q^{52} +8.05934i q^{53} -13.3914 q^{55} +(3.58721 + 7.04029i) q^{56} +(-3.75621 + 0.594926i) q^{58} +6.19868i q^{59} -7.23607i q^{61} +(-0.422260 - 2.66605i) q^{62} +(-4.70228 + 6.47214i) q^{64} -2.52015 q^{65} +10.0297i q^{67} +(-8.27636 + 2.68915i) q^{68} +(-9.83390 + 1.55754i) q^{70} +1.63052 q^{71} -5.17442 q^{73} +(-13.4211 + 2.12569i) q^{74} +(-3.72654 - 11.4691i) q^{76} -14.8445i q^{77} +9.17442 q^{79} +(-5.92522 - 8.15537i) q^{80} +(2.47985 + 15.6572i) q^{82} +4.61147i q^{83} -10.9655i q^{85} +(-13.2521 + 2.09893i) q^{86} +(13.3914 - 6.82328i) q^{88} -11.4182 q^{89} -2.79360i q^{91} +(1.08070 - 0.351141i) q^{92} +(0.875345 + 5.52671i) q^{94} +15.1957 q^{95} -10.2514 q^{97} +(-0.177920 - 1.12334i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 4 q^{7} + 4 q^{8} - 4 q^{10} + 4 q^{14} + 8 q^{16} + 16 q^{17} + 12 q^{20} - 20 q^{22} + 8 q^{23} + 8 q^{25} - 2 q^{26} - 4 q^{31} - 32 q^{32} + 16 q^{34} + 28 q^{38} + 32 q^{40} - 36 q^{41}+ \cdots + 6 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 4 * q^7 + 4 * q^8 - 4 * q^10 + 4 * q^14 + 8 * q^16 + 16 * q^17 + 12 * q^20 - 20 * q^22 + 8 * q^23 + 8 * q^25 - 2 * q^26 - 4 * q^31 - 32 * q^32 + 16 * q^34 + 28 * q^38 + 32 * q^40 - 36 * q^41 + 20 * q^44 - 12 * q^46 - 24 * q^47 - 24 * q^49 - 22 * q^50 - 4 * q^52 - 40 * q^55 - 8 * q^56 + 12 * q^58 + 36 * q^62 + 4 * q^65 - 12 * q^70 - 16 * q^71 + 32 * q^73 - 4 * q^74 - 24 * q^76 + 44 * q^82 - 8 * q^86 + 40 * q^88 - 60 * q^89 + 40 * q^92 - 44 * q^94 + 24 * q^95 - 56 * q^97 + 6 * q^98

Introduction

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