LMFDB - Embedded newform 1512.2.j.a.323.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(323,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1512.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.j (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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.56070144.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 $ x^8 - 4x^7 + 16x^6 - 34x^5 + 63x^4 - 74x^3 + 70x^2 - 38*x + 13
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.1
Root			$0.500000 - 0.564882i$ of defining polynomial
Character	$\chi$	$=$	1512.323
Dual form			1512.2.j.a.323.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 - 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} -3.12976 q^{5} -1.00000i q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(-1.36603 - 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} -3.12976 q^{5} -1.00000i q^{7} +(-2.00000 - 2.00000i) q^{8} +(4.27534 + 1.14557i) q^{10} +0.397714i q^{11} +6.55068i q^{13} +(-0.366025 + 1.36603i) q^{14} +(2.00000 + 3.46410i) q^{16} -2.00000i q^{17} -0.527479 q^{19} +(-5.42091 - 3.12976i) q^{20} +(0.145573 - 0.543288i) q^{22} +8.21634 q^{23} +4.79543 q^{25} +(2.39771 - 8.94839i) q^{26} +(1.00000 - 1.73205i) q^{28} -4.73205 q^{29} -7.55068i q^{31} +(-1.46410 - 5.46410i) q^{32} +(-0.732051 + 2.73205i) q^{34} +3.12976i q^{35} -3.35452i q^{37} +(0.720550 + 0.193071i) q^{38} +(6.25953 + 6.25953i) q^{40} +7.48429i q^{41} +1.62247 q^{43} +(-0.397714 + 0.688861i) q^{44} +(-11.2237 - 3.00739i) q^{46} -10.4557 q^{47} -1.00000 q^{49} +(-6.55068 - 1.75525i) q^{50} +(-6.55068 + 11.3461i) q^{52} +0.795428 q^{53} -1.24475i q^{55} +(-2.00000 + 2.00000i) q^{56} +(6.46410 + 1.73205i) q^{58} +2.47252i q^{59} -11.4641i q^{61} +(-2.76374 + 10.3144i) q^{62} +8.00000i q^{64} -20.5021i q^{65} -6.55068 q^{67} +(2.00000 - 3.46410i) q^{68} +(1.14557 - 4.27534i) q^{70} -2.21634 q^{71} -5.75525 q^{73} +(-1.22784 + 4.58237i) q^{74} +(-0.913620 - 0.527479i) q^{76} +0.397714 q^{77} -10.2911i q^{79} +(-6.25953 - 10.8418i) q^{80} +(2.73944 - 10.2237i) q^{82} -8.36930i q^{83} +6.25953i q^{85} +(-2.21634 - 0.593866i) q^{86} +(0.795428 - 0.795428i) q^{88} -5.31114i q^{89} +6.55068 q^{91} +(14.2311 + 8.21634i) q^{92} +(14.2827 + 3.82705i) q^{94} +1.65089 q^{95} -19.1014 q^{97} +(1.36603 + 0.366025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 8 q^{5} - 16 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 - 8 * q^5 - 16 * q^8	$ 8 q - 4 q^{2} - 8 q^{5} - 16 q^{8} + 4 q^{10} + 4 q^{14} + 16 q^{16} + 16 q^{19} - 12 q^{22} + 16 q^{23} + 32 q^{25} + 16 q^{26} + 8 q^{28} - 24 q^{29} + 16 q^{32} + 8 q^{34} - 20 q^{38} + 16 q^{40} + 8 q^{43} + 4 q^{46} - 8 q^{47} - 8 q^{49} + 8 q^{50} + 8 q^{52} - 16 q^{56} + 24 q^{58} - 12 q^{62} + 8 q^{67} + 16 q^{68} - 4 q^{70} + 32 q^{71} + 8 q^{73} + 28 q^{74} + 24 q^{76} - 16 q^{80} - 36 q^{82} + 32 q^{86} - 8 q^{91} - 24 q^{92} + 40 q^{94} + 112 q^{95} - 32 q^{97} + 4 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 - 8 * q^5 - 16 * q^8 + 4 * q^10 + 4 * q^14 + 16 * q^16 + 16 * q^19 - 12 * q^22 + 16 * q^23 + 32 * q^25 + 16 * q^26 + 8 * q^28 - 24 * q^29 + 16 * q^32 + 8 * q^34 - 20 * q^38 + 16 * q^40 + 8 * q^43 + 4 * q^46 - 8 * q^47 - 8 * q^49 + 8 * q^50 + 8 * q^52 - 16 * q^56 + 24 * q^58 - 12 * q^62 + 8 * q^67 + 16 * q^68 - 4 * q^70 + 32 * q^71 + 8 * q^73 + 28 * q^74 + 24 * q^76 - 16 * q^80 - 36 * q^82 + 32 * q^86 - 8 * q^91 - 24 * q^92 + 40 * q^94 + 112 * q^95 - 32 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$	−1.36603	−	0.366025i	−0.965926	−	0.258819i
$2$	−1.36603	−	0.366025i	−0.965926	−	0.258819i
$3$		0			0
$3$		0			0
$4$	1.73205	+	1.00000i	0.866025	+	0.500000i
$5$	−3.12976			−1.39967			−0.699837	−	0.714303i	$-0.746744\pi$
$5$	−3.12976			−1.39967			−0.699837	+	0.714303i	$0.746744\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$		0			0
$10$	4.27534	+	1.14557i	1.35198	+	0.362262i
$11$			0.397714i			0.119915i	0.998201	+	0.0599577i	$0.0190966\pi$
$11$			0.397714i			0.119915i	−0.998201	+	0.0599577i	$0.980903\pi$
$12$		0			0
$13$			6.55068i			1.81683i	0.418069	+	0.908415i	$0.362707\pi$
$13$			6.55068i			1.81683i	−0.418069	+	0.908415i	$0.637293\pi$
$14$	−0.366025	+	1.36603i	−0.0978244	+	0.365086i
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$		−	2.00000i		−	0.485071i	−0.970143	−	0.242536i	$-0.922021\pi$
$17$		−	2.00000i		−	0.485071i	0.970143	−	0.242536i	$-0.0779791\pi$
$18$		0			0
$19$	−0.527479			−0.121012			−0.0605060	−	0.998168i	$-0.519271\pi$
$19$	−0.527479			−0.121012			−0.0605060	+	0.998168i	$0.519271\pi$
$20$	−5.42091	−	3.12976i	−1.21215	−	0.699837i
$21$		0			0
$22$	0.145573	−	0.543288i	0.0310364	−	0.115829i
$23$	8.21634			1.71323			0.856613	−	0.515960i	$-0.172565\pi$
$23$	8.21634			1.71323			0.856613	+	0.515960i	$0.172565\pi$
$24$		0			0
$25$	4.79543			0.959086
$26$	2.39771	−	8.94839i	0.470230	−	1.75492i
$27$		0			0
$28$	1.00000	−	1.73205i	0.188982	−	0.327327i
$29$	−4.73205			−0.878720			−0.439360	−	0.898311i	$-0.644795\pi$
$29$	−4.73205			−0.878720			−0.439360	+	0.898311i	$0.644795\pi$
$30$		0			0
$31$		−	7.55068i		−	1.35614i	−0.734997	−	0.678071i	$-0.762816\pi$
$31$		−	7.55068i		−	1.35614i	0.734997	−	0.678071i	$-0.237184\pi$
$32$	−1.46410	−	5.46410i	−0.258819	−	0.965926i
$33$		0			0
$34$	−0.732051	+	2.73205i	−0.125546	+	0.468543i
$35$			3.12976i			0.529027i
$36$		0			0
$37$		−	3.35452i		−	0.551480i	−0.961232	−	0.275740i	$-0.911077\pi$
$37$		−	3.35452i		−	0.551480i	0.961232	−	0.275740i	$-0.0889229\pi$
$38$	0.720550	+	0.193071i	0.116889	+	0.0313202i
$39$		0			0
$40$	6.25953	+	6.25953i	0.989719	+	0.989719i
$41$			7.48429i			1.16885i	0.811448	+	0.584425i	$0.198680\pi$
$41$			7.48429i			1.16885i	−0.811448	+	0.584425i	$0.801320\pi$
$42$		0			0
$43$	1.62247			0.247425			0.123712	−	0.992318i	$-0.460520\pi$
$43$	1.62247			0.247425			0.123712	+	0.992318i	$0.460520\pi$
$44$	−0.397714	+	0.688861i	−0.0599577	+	0.103850i
$45$		0			0
$46$	−11.2237	−	3.00739i	−1.65485	−	0.443415i
$47$	−10.4557			−1.52512			−0.762559	−	0.646919i	$-0.776057\pi$
$47$	−10.4557			−1.52512			−0.762559	+	0.646919i	$0.776057\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	−6.55068	−	1.75525i	−0.926406	−	0.248230i
$51$		0			0
$52$	−6.55068	+	11.3461i	−0.908415	+	1.57342i
$53$	0.795428			0.109260			0.0546302	−	0.998507i	$-0.482602\pi$
$53$	0.795428			0.109260			0.0546302	+	0.998507i	$0.482602\pi$
$54$		0			0
$55$		−	1.24475i		−	0.167842i
$56$	−2.00000	+	2.00000i	−0.267261	+	0.267261i
$57$		0			0
$58$	6.46410	+	1.73205i	0.848778	+	0.227429i
$59$			2.47252i			0.321895i	0.986963	+	0.160947i	$0.0514550\pi$
$59$			2.47252i			0.321895i	−0.986963	+	0.160947i	$0.948545\pi$
$60$		0			0
$61$		−	11.4641i		−	1.46783i	−0.679243	−	0.733914i	$-0.737692\pi$
$61$		−	11.4641i		−	1.46783i	0.679243	−	0.733914i	$-0.262308\pi$
$62$	−2.76374	+	10.3144i	−0.350995	+	1.30993i
$63$		0			0
$64$			8.00000i			1.00000i
$65$		−	20.5021i		−	2.54297i
$66$		0			0
$67$	−6.55068			−0.800293			−0.400146	−	0.916451i	$-0.631041\pi$
$67$	−6.55068			−0.800293			−0.400146	+	0.916451i	$0.631041\pi$
$68$	2.00000	−	3.46410i	0.242536	−	0.420084i
$69$		0			0
$70$	1.14557	−	4.27534i	0.136922	−	0.511001i
$71$	−2.21634			−0.263031			−0.131516	−	0.991314i	$-0.541984\pi$
$71$	−2.21634			−0.263031			−0.131516	+	0.991314i	$0.541984\pi$
$72$		0			0
$73$	−5.75525			−0.673601			−0.336800	−	0.941576i	$-0.609345\pi$
$73$	−5.75525			−0.673601			−0.336800	+	0.941576i	$0.609345\pi$
$74$	−1.22784	+	4.58237i	−0.142734	+	0.532689i
$75$		0			0
$76$	−0.913620	−	0.527479i	−0.104799	−	0.0605060i
$77$	0.397714			0.0453237
$78$		0			0
$79$		−	10.2911i		−	1.15784i	−0.815383	−	0.578922i	$-0.803473\pi$
$79$		−	10.2911i		−	1.15784i	0.815383	−	0.578922i	$-0.196527\pi$
$80$	−6.25953	−	10.8418i	−0.699837	−	1.21215i
$81$		0			0
$82$	2.73944	−	10.2237i	0.302521	−	1.12902i
$83$		−	8.36930i		−	0.918650i	−0.888268	−	0.459325i	$-0.848091\pi$
$83$		−	8.36930i		−	0.918650i	0.888268	−	0.459325i	$-0.151909\pi$
$84$		0			0
$85$			6.25953i			0.678941i
$86$	−2.21634	−	0.593866i	−0.238994	−	0.0640383i
$87$		0			0
$88$	0.795428	−	0.795428i	0.0847929	−	0.0847929i
$89$		−	5.31114i		−	0.562980i	−0.959564	−	0.281490i	$-0.909171\pi$
$89$		−	5.31114i		−	0.562980i	0.959564	−	0.281490i	$-0.0908286\pi$
$90$		0			0
$91$	6.55068			0.686697
$92$	14.2311	+	8.21634i	1.48370	+	0.856613i
$93$		0			0
$94$	14.2827	+	3.82705i	1.47315	+	0.394730i
$95$	1.65089			0.169377
$96$		0			0
$97$	−19.1014			−1.93945			−0.969724	−	0.244202i	$-0.921474\pi$
$97$	−19.1014			−1.93945			−0.969724	+	0.244202i	$0.921474\pi$
$98$	1.36603	+	0.366025i	0.137989	+	0.0369741i
$99$		0			0
$100$	8.30593	+	4.79543i	0.830593	+	0.479543i
$101$	−2.00000			−0.199007			−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	−2.00000			−0.199007			−0.0995037	+	0.995037i	$0.531726\pi$
$102$		0			0
$103$		−	17.0148i		−	1.67652i	−0.545274	−	0.838258i	$-0.683574\pi$
$103$		−	17.0148i		−	1.67652i	0.545274	−	0.838258i	$-0.316426\pi$
$104$	13.1014	−	13.1014i	1.28469	−	1.28469i
$105$		0			0
$106$	−1.08658	−	0.291147i	−0.105537	−	0.0282787i
$107$			1.91362i			0.184997i	0.995713	+	0.0924983i	$0.0294853\pi$
$107$			1.91362i			0.184997i	−0.995713	+	0.0924983i	$0.970515\pi$
$108$		0			0
$109$			7.07816i			0.677964i	0.940793	+	0.338982i	$0.110083\pi$
$109$			7.07816i			0.677964i	−0.940793	+	0.338982i	$0.889917\pi$
$110$	−0.455611	+	1.70036i	−0.0434408	+	0.162123i
$111$		0			0
$112$	3.46410	−	2.00000i	0.327327	−	0.188982i
$113$		−	9.98316i		−	0.939137i	−0.882896	−	0.469568i	$-0.844410\pi$
$113$		−	9.98316i		−	0.939137i	0.882896	−	0.469568i	$-0.155590\pi$
$114$		0			0
$115$	−25.7152			−2.39796
$116$	−8.19615	−	4.73205i	−0.760994	−	0.439360i
$117$		0			0
$118$	0.905006	−	3.37753i	0.0833125	−	0.310927i
$119$	−2.00000			−0.183340
$120$		0			0
$121$	10.8418			0.985620
$122$	−4.19615	+	15.6603i	−0.379902	+	1.41781i
$123$		0			0
$124$	7.55068	−	13.0782i	0.678071	−	1.17445i
$125$	0.640262			0.0572668
$126$		0			0
$127$			7.75525i			0.688167i	0.938939	+	0.344084i	$0.111810\pi$
$127$			7.75525i			0.688167i	−0.938939	+	0.344084i	$0.888190\pi$
$128$	2.92820	−	10.9282i	0.258819	−	0.965926i
$129$		0			0
$130$	−7.50428	+	28.0064i	−0.658169	+	2.45632i
$131$			14.9052i			1.30227i	0.758960	+	0.651137i	$0.225708\pi$
$131$			14.9052i			1.30227i	−0.758960	+	0.651137i	$0.774292\pi$
$132$		0			0
$133$			0.527479i			0.0457382i
$134$	8.94839	+	2.39771i	0.773023	+	0.207131i
$135$		0			0
$136$	−4.00000	+	4.00000i	−0.342997	+	0.342997i
$137$		−	22.4557i		−	1.91852i	−0.282527	−	0.959259i	$-0.591173\pi$
$137$		−	22.4557i		−	1.91852i	0.282527	−	0.959259i	$-0.408827\pi$
$138$		0			0
$139$	3.05496			0.259118			0.129559	−	0.991572i	$-0.458644\pi$
$139$	3.05496			0.259118			0.129559	+	0.991572i	$0.458644\pi$
$140$	−3.12976	+	5.42091i	−0.264513	+	0.458151i
$141$		0			0
$142$	3.02758	+	0.811237i	0.254069	+	0.0680775i
$143$	−2.60530			−0.217866
$144$		0			0
$145$	14.8102			1.22992
$146$	7.86182	+	2.10657i	0.650648	+	0.174341i
$147$		0			0
$148$	3.35452	−	5.81021i	0.275740	−	0.477596i
$149$	7.01458			0.574657			0.287329	−	0.957832i	$-0.407233\pi$
$149$	7.01458			0.574657			0.287329	+	0.957832i	$0.407233\pi$
$150$		0			0
$151$		−	9.81001i		−	0.798327i	−0.916880	−	0.399164i	$-0.869301\pi$
$151$		−	9.81001i		−	0.798327i	0.916880	−	0.399164i	$-0.130699\pi$
$152$	1.05496	+	1.05496i	0.0855684	+	0.0855684i
$153$		0			0
$154$	−0.543288	−	0.145573i	−0.0437794	−	0.0117306i
$155$			23.6318i			1.89816i
$156$		0			0
$157$		−	10.8966i		−	0.869642i	−0.900517	−	0.434821i	$-0.856812\pi$
$157$		−	10.8966i		−	0.869642i	0.900517	−	0.434821i	$-0.143188\pi$
$158$	−3.76682	+	14.0580i	−0.299672	+	1.11839i
$159$		0			0
$160$	4.58229	+	17.1014i	0.362262	+	1.35198i
$161$		−	8.21634i		−	0.647538i
$162$		0			0
$163$	−10.0148			−0.784418			−0.392209	−	0.919876i	$-0.628289\pi$
$163$	−10.0148			−0.784418			−0.392209	+	0.919876i	$0.628289\pi$
$164$	−7.48429	+	12.9632i	−0.584425	+	1.01225i
$165$		0			0
$166$	−3.06338	+	11.4327i	−0.237764	+	0.887348i
$167$	−14.5655			−1.12711			−0.563554	−	0.826079i	$-0.690566\pi$
$167$	−14.5655			−1.12711			−0.563554	+	0.826079i	$0.690566\pi$
$168$		0			0
$169$	−29.9114			−2.30087
$170$	2.29115	−	8.55068i	0.175723	−	0.655807i
$171$		0			0
$172$	2.81021	+	1.62247i	0.214276	+	0.123712i
$173$	−14.3175			−1.08854			−0.544270	−	0.838910i	$-0.683193\pi$
$173$	−14.3175			−1.08854			−0.544270	+	0.838910i	$0.683193\pi$
$174$		0			0
$175$		−	4.79543i		−	0.362500i
$176$	−1.37772	+	0.795428i	−0.103850	+	0.0599577i
$177$		0			0
$178$	−1.94401	+	7.25515i	−0.145710	+	0.543797i
$179$		−	19.8104i		−	1.48070i	−0.672222	−	0.740349i	$-0.734660\pi$
$179$		−	19.8104i		−	1.48070i	0.672222	−	0.740349i	$-0.265340\pi$
$180$		0			0
$181$		−	20.1732i		−	1.49946i	−0.661745	−	0.749729i	$-0.730184\pi$
$181$		−	20.1732i		−	1.49946i	0.661745	−	0.749729i	$-0.269816\pi$
$182$	−8.94839	−	2.39771i	−0.663299	−	0.177730i
$183$		0			0
$184$	−16.4327	−	16.4327i	−1.21143	−	1.21143i
$185$			10.4989i			0.771892i
$186$		0			0
$187$	0.795428			0.0581675
$188$	−18.1098	−	10.4557i	−1.32079	−	0.762559i
$189$		0			0
$190$	−2.25515	−	0.604266i	−0.163606	−	0.0438381i
$191$	6.43549			0.465656			0.232828	−	0.972518i	$-0.425202\pi$
$191$	6.43549			0.465656			0.232828	+	0.972518i	$0.425202\pi$
$192$		0			0
$193$	−9.98316			−0.718604			−0.359302	−	0.933221i	$-0.616985\pi$
$193$	−9.98316			−0.718604			−0.359302	+	0.933221i	$0.616985\pi$
$194$	26.0929	+	6.99158i	1.87336	+	0.501966i
$195$		0			0
$196$	−1.73205	−	1.00000i	−0.123718	−	0.0714286i
$197$	−23.6373			−1.68408			−0.842042	−	0.539412i	$-0.818647\pi$
$197$	−23.6373			−1.68408			−0.842042	+	0.539412i	$0.818647\pi$
$198$		0			0
$199$			21.6202i			1.53262i	0.642473	+	0.766308i	$0.277908\pi$
$199$			21.6202i			1.53262i	−0.642473	+	0.766308i	$0.722092\pi$
$200$	−9.59086	−	9.59086i	−0.678176	−	0.678176i
$201$		0			0
$202$	2.73205	+	0.732051i	0.192226	+	0.0515069i
$203$			4.73205i			0.332125i
$204$		0			0
$205$		−	23.4241i		−	1.63601i
$206$	−6.22784	+	23.2426i	−0.433914	+	1.61939i
$207$		0			0
$208$	−22.6922	+	13.1014i	−1.57342	+	0.908415i
$209$		−	0.209786i		−	0.0145112i
$210$		0			0
$211$	2.51906			0.173419			0.0867096	−	0.996234i	$-0.472365\pi$
$211$	2.51906			0.173419			0.0867096	+	0.996234i	$0.472365\pi$
$212$	1.37772	+	0.795428i	0.0946223	+	0.0546302i
$213$		0			0
$214$	0.700434	−	2.61405i	0.0478807	−	0.178693i
$215$	−5.07796			−0.346314
$216$		0			0
$217$	−7.55068			−0.512573
$218$	2.59078	−	9.66894i	0.175470	−	0.654863i
$219$		0			0
$220$	1.24475	−	2.15597i	0.0839211	−	0.145356i
$221$	13.1014			0.881292
$222$		0			0
$223$			0.882003i			0.0590633i	0.999564	+	0.0295316i	$0.00940158\pi$
$223$			0.882003i			0.0590633i	−0.999564	+	0.0295316i	$0.990598\pi$
$224$	−5.46410	+	1.46410i	−0.365086	+	0.0978244i
$225$		0			0
$226$	−3.65409	+	13.6373i	−0.243066	+	0.907136i
$227$			8.47868i			0.562750i	0.959598	+	0.281375i	$0.0907905\pi$
$227$			8.47868i			0.562750i	−0.959598	+	0.281375i	$0.909210\pi$
$228$		0			0
$229$		−	13.4641i		−	0.889733i	−0.895597	−	0.444866i	$-0.853251\pi$
$229$		−	13.4641i		−	0.889733i	0.895597	−	0.444866i	$-0.146749\pi$
$230$	35.1276	+	9.41242i	2.31625	+	0.620637i
$231$		0			0
$232$	9.46410	+	9.46410i	0.621349	+	0.621349i
$233$		−	17.4641i		−	1.14411i	−0.820215	−	0.572056i	$-0.806146\pi$
$233$		−	17.4641i		−	1.14411i	0.820215	−	0.572056i	$-0.193854\pi$
$234$		0			0
$235$	32.7238			2.13467
$236$	−2.47252	+	4.28253i	−0.160947	+	0.278769i
$237$		0			0
$238$	2.73205	+	0.732051i	0.177093	+	0.0474518i
$239$	27.6836			1.79071			0.895353	−	0.445357i	$-0.146923\pi$
$239$	27.6836			1.79071			0.895353	+	0.445357i	$0.146923\pi$
$240$		0			0
$241$	21.9116			1.41145			0.705724	−	0.708487i	$-0.250622\pi$
$241$	21.9116			1.41145			0.705724	+	0.708487i	$0.250622\pi$
$242$	−14.8102	−	3.96838i	−0.952036	−	0.255097i
$243$		0			0
$244$	11.4641	−	19.8564i	0.733914	−	1.27118i
$245$	3.12976			0.199953
$246$		0			0
$247$		−	3.45534i		−	0.219858i
$248$	−15.1014	+	15.1014i	−0.958937	+	0.958937i
$249$		0			0
$250$	−0.874614	−	0.234352i	−0.0553154	−	0.0148217i
$251$			15.9136i			1.00446i	0.864734	+	0.502229i	$0.167487\pi$
$251$			15.9136i			1.00446i	−0.864734	+	0.502229i	$0.832513\pi$
$252$		0			0
$253$			3.26775i			0.205442i
$254$	2.83862	−	10.5939i	0.178111	−	0.664718i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$			3.70344i			0.231014i	0.993307	+	0.115507i	$0.0368493\pi$
$257$			3.70344i			0.231014i	−0.993307	+	0.115507i	$0.963151\pi$
$258$		0			0
$259$	−3.35452			−0.208440
$260$	20.5021	−	35.5106i	1.27148	−	2.20228i
$261$		0			0
$262$	5.45568	−	20.3609i	0.337053	−	1.25790i
$263$	22.1995			1.36888			0.684440	−	0.729069i	$-0.260047\pi$
$263$	22.1995			1.36888			0.684440	+	0.729069i	$0.260047\pi$
$264$		0			0
$265$	−2.48950			−0.152929
$266$	0.193071	−	0.720550i	0.0118379	−	0.0441797i
$267$		0			0
$268$	−11.3461	−	6.55068i	−0.693074	−	0.400146i
$269$	−16.2480			−0.990655			−0.495328	−	0.868706i	$-0.664952\pi$
$269$	−16.2480			−0.990655			−0.495328	+	0.868706i	$0.664952\pi$
$270$		0			0
$271$			18.3755i			1.11623i	0.829764	+	0.558115i	$0.188475\pi$
$271$			18.3755i			1.11623i	−0.829764	+	0.558115i	$0.811525\pi$
$272$	6.92820	−	4.00000i	0.420084	−	0.242536i
$273$		0			0
$274$	−8.21935	+	30.6750i	−0.496549	+	1.85315i
$275$			1.90721i			0.115009i
$276$		0			0
$277$		−	31.7764i		−	1.90926i	−0.297798	−	0.954629i	$-0.596252\pi$
$277$		−	31.7764i		−	1.90926i	0.297798	−	0.954629i	$-0.403748\pi$
$278$	−4.17315	−	1.11819i	−0.250289	−	0.0670647i
$279$		0			0
$280$	6.25953	−	6.25953i	0.374078	−	0.374078i
$281$		−	4.86483i		−	0.290211i	−0.989416	−	0.145106i	$-0.953648\pi$
$281$		−	4.86483i		−	0.290211i	0.989416	−	0.145106i	$-0.0463522\pi$
$282$		0			0
$283$	−24.7386			−1.47056			−0.735279	−	0.677765i	$-0.762949\pi$
$283$	−24.7386			−1.47056			−0.735279	+	0.677765i	$0.762949\pi$
$284$	−3.83881	−	2.21634i	−0.227792	−	0.131516i
$285$		0			0
$286$	3.55890	+	0.953605i	0.210442	+	0.0563878i
$287$	7.48429			0.441784
$288$		0			0
$289$	13.0000			0.764706
$290$	−20.2311	−	5.42091i	−1.18801	−	0.318327i
$291$		0			0
$292$	−9.96838	−	5.75525i	−0.583355	−	0.336800i
$293$	15.9428			0.931388			0.465694	−	0.884946i	$-0.345805\pi$
$293$	15.9428			0.931388			0.465694	+	0.884946i	$0.345805\pi$
$294$		0			0
$295$		−	7.73841i		−	0.450548i
$296$	−6.70905	+	6.70905i	−0.389956	+	0.389956i
$297$		0			0
$298$	−9.58210	−	2.56752i	−0.555076	−	0.148732i
$299$			53.8226i			3.11264i
$300$		0			0
$301$		−	1.62247i		−	0.0935178i
$302$	−3.59071	+	13.4007i	−0.206622	+	0.771125i
$303$		0			0
$304$	−1.05496	−	1.82724i	−0.0605060	−	0.104799i
$305$			35.8799i			2.05448i
$306$		0			0
$307$	−5.64567			−0.322215			−0.161108	−	0.986937i	$-0.551507\pi$
$307$	−5.64567			−0.322215			−0.161108	+	0.986937i	$0.551507\pi$
$308$	0.688861	+	0.397714i	0.0392515	+	0.0226619i
$309$		0			0
$310$	8.64985	−	32.2817i	0.491279	−	1.83348i
$311$	19.0084			1.07787			0.538934	−	0.842348i	$-0.318827\pi$
$311$	19.0084			1.07787			0.538934	+	0.842348i	$0.318827\pi$
$312$		0			0
$313$	2.24475			0.126881			0.0634404	−	0.997986i	$-0.479793\pi$
$313$	2.24475			0.126881			0.0634404	+	0.997986i	$0.479793\pi$
$314$	−3.98843	+	14.8850i	−0.225080	+	0.840010i
$315$		0			0
$316$	10.2911	−	17.8248i	0.578922	−	1.00272i
$317$	24.4852			1.37523			0.687614	−	0.726076i	$-0.258658\pi$
$317$	24.4852			1.37523			0.687614	+	0.726076i	$0.258658\pi$
$318$		0			0
$319$		−	1.88200i		−	0.105372i
$320$		−	25.0381i		−	1.39967i
$321$		0			0
$322$	−3.00739	+	11.2237i	−0.167595	+	0.625474i
$323$			1.05496i			0.0586994i
$324$		0			0
$325$			31.4133i			1.74250i
$326$	13.6804	+	3.66566i	0.757690	+	0.203022i
$327$		0			0
$328$	14.9686	−	14.9686i	0.826501	−	0.826501i
$329$			10.4557i			0.576440i
$330$		0			0
$331$	4.34591			0.238873			0.119436	−	0.992842i	$-0.461891\pi$
$331$	4.34591			0.238873			0.119436	+	0.992842i	$0.461891\pi$
$332$	8.36930	−	14.4961i	0.459325	−	0.795574i
$333$		0			0
$334$	19.8968	+	5.33133i	1.08870	+	0.291717i
$335$	20.5021			1.12015
$336$		0			0
$337$	−27.5655			−1.50159			−0.750793	−	0.660538i	$-0.770328\pi$
$337$	−27.5655			−1.50159			−0.750793	+	0.660538i	$0.770328\pi$
$338$	40.8597	+	10.9483i	2.22247	+	0.595510i
$339$		0			0
$340$	−6.25953	+	10.8418i	−0.339471	+	0.587980i
$341$	3.00301			0.162622
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−3.24495	−	3.24495i	−0.174956	−	0.174956i
$345$		0			0
$346$	19.5581	+	5.24057i	1.05145	+	0.281735i
$347$			20.8364i			1.11856i	0.828980	+	0.559279i	$0.188922\pi$
$347$			20.8364i			1.11856i	−0.828980	+	0.559279i	$0.811078\pi$
$348$		0			0
$349$			4.88181i			0.261317i	0.991427	+	0.130659i	$0.0417092\pi$
$349$			4.88181i			0.261317i	−0.991427	+	0.130659i	$0.958291\pi$
$350$	−1.75525	+	6.55068i	−0.0938220	+	0.350148i
$351$		0			0
$352$	2.17315	−	0.582294i	0.115829	−	0.0310364i
$353$		−	7.44391i		−	0.396200i	−0.980182	−	0.198100i	$-0.936523\pi$
$353$		−	7.44391i		−	0.396200i	0.980182	−	0.198100i	$-0.0634770\pi$
$354$		0			0
$355$	6.93662			0.368158
$356$	5.31114	−	9.19916i	0.281490	−	0.487555i
$357$		0			0
$358$	−7.25111	+	27.0615i	−0.383233	+	1.43025i
$359$	22.3923			1.18182			0.590910	−	0.806737i	$-0.298769\pi$
$359$	22.3923			1.18182			0.590910	+	0.806737i	$0.298769\pi$
$360$		0			0
$361$	−18.7218			−0.985356
$362$	−7.38389	+	27.5570i	−0.388088	+	1.44837i
$363$		0			0
$364$	11.3461	+	6.55068i	0.594697	+	0.343349i
$365$	18.0126			0.942821
$366$		0			0
$367$			35.2575i			1.84042i	0.391419	+	0.920212i	$0.371984\pi$
$367$			35.2575i			1.84042i	−0.391419	+	0.920212i	$0.628016\pi$
$368$	16.4327	+	28.4622i	0.856613	+	1.48370i
$369$		0			0
$370$	3.84285	−	14.3417i	0.199780	−	0.745591i
$371$		−	0.795428i		−	0.0412966i
$372$		0			0
$373$			11.2681i			0.583442i	0.956503	+	0.291721i	$0.0942279\pi$
$373$			11.2681i			0.583442i	−0.956503	+	0.291721i	$0.905772\pi$
$374$	−1.08658	−	0.291147i	−0.0561855	−	0.0150548i
$375$		0			0
$376$	20.9114	+	20.9114i	1.07842	+	1.07842i
$377$		−	30.9981i		−	1.59649i
$378$		0			0
$379$	−5.47888			−0.281431			−0.140716	−	0.990050i	$-0.544940\pi$
$379$	−5.47888			−0.281431			−0.140716	+	0.990050i	$0.544940\pi$
$380$	2.85942	+	1.65089i	0.146685	+	0.0846886i
$381$		0			0
$382$	−8.79105	−	2.35555i	−0.449789	−	0.120521i
$383$	−31.6668			−1.61810			−0.809049	−	0.587741i	$-0.800017\pi$
$383$	−31.6668			−1.61810			−0.809049	+	0.587741i	$0.800017\pi$
$384$		0			0
$385$	−1.24475			−0.0634384
$386$	13.6373	+	3.65409i	0.694118	+	0.185988i
$387$		0			0
$388$	−33.0845	−	19.1014i	−1.67961	−	0.969724i
$389$	−25.1014			−1.27269			−0.636345	−	0.771405i	$-0.719554\pi$
$389$	−25.1014			−1.27269			−0.636345	+	0.771405i	$0.719554\pi$
$390$		0			0
$391$		−	16.4327i		−	0.831036i
$392$	2.00000	+	2.00000i	0.101015	+	0.101015i
$393$		0			0
$394$	32.2891	+	8.65183i	1.62670	+	0.435873i
$395$			32.2089i			1.62060i
$396$		0			0
$397$			4.04640i			0.203083i	0.994831	+	0.101541i	$0.0323774\pi$
$397$			4.04640i			0.203083i	−0.994831	+	0.101541i	$0.967623\pi$
$398$	7.91355	−	29.5338i	0.396670	−	1.48039i
$399$		0			0
$400$	9.59086	+	16.6119i	0.479543	+	0.830593i
$401$		−	5.87339i		−	0.293303i	−0.989188	−	0.146652i	$-0.953150\pi$
$401$		−	5.87339i		−	0.293303i	0.989188	−	0.146652i	$-0.0468496\pi$
$402$		0			0
$403$	49.4620			2.46388
$404$	−3.46410	−	2.00000i	−0.172345	−	0.0995037i
$405$		0			0
$406$	1.73205	−	6.46410i	0.0859602	−	0.320808i
$407$	1.33414			0.0661309
$408$		0			0
$409$	25.1101			1.24162			0.620808	−	0.783963i	$-0.286805\pi$
$409$	25.1101			1.24162			0.620808	+	0.783963i	$0.286805\pi$
$410$	−8.57380	+	31.9979i	−0.423430	+	1.58026i
$411$		0			0
$412$	17.0148	−	29.4705i	0.838258	−	1.45191i
$413$	2.47252			0.121665
$414$		0			0
$415$			26.1939i			1.28581i
$416$	35.7936	−	9.59086i	1.75492	−	0.470230i
$417$		0			0
$418$	−0.0767869	+	0.286573i	−0.00375577	+	0.0140167i
$419$		−	12.3059i		−	0.601184i	−0.953753	−	0.300592i	$-0.902816\pi$
$419$		−	12.3059i		−	0.601184i	0.953753	−	0.300592i	$-0.0971842\pi$
$420$		0			0
$421$			22.4095i			1.09217i	0.837729	+	0.546086i	$0.183883\pi$
$421$			22.4095i			1.09217i	−0.837729	+	0.546086i	$0.816117\pi$
$422$	−3.44110	−	0.922040i	−0.167510	−	0.0448842i
$423$		0			0
$424$	−1.59086	−	1.59086i	−0.0772588	−	0.0772588i
$425$		−	9.59086i		−	0.465225i
$426$		0			0
$427$	−11.4641			−0.554787
$428$	−1.91362	+	3.31449i	−0.0924983	+	0.160212i
$429$		0			0
$430$	6.93662	+	1.85866i	0.334514	+	0.0896327i
$431$	−21.4041			−1.03100			−0.515499	−	0.856890i	$-0.672393\pi$
$431$	−21.4041			−1.03100			−0.515499	+	0.856890i	$0.672393\pi$
$432$		0			0
$433$	19.3925			0.931944			0.465972	−	0.884799i	$-0.345705\pi$
$433$	19.3925			0.931944			0.465972	+	0.884799i	$0.345705\pi$
$434$	10.3144	+	2.76374i	0.495108	+	0.132664i
$435$		0			0
$436$	−7.07816	+	12.2597i	−0.338982	+	0.587134i
$437$	−4.33395			−0.207321
$438$		0			0
$439$		−	18.3755i		−	0.877013i	−0.898728	−	0.438507i	$-0.855508\pi$
$439$		−	18.3755i		−	0.877013i	0.898728	−	0.438507i	$-0.144492\pi$
$440$	−2.48950	+	2.48950i	−0.118682	+	0.118682i
$441$		0			0
$442$	−17.8968	−	4.79543i	−0.851263	−	0.228095i
$443$			8.58770i			0.408014i	0.978969	+	0.204007i	$0.0653965\pi$
$443$			8.58770i			0.408014i	−0.978969	+	0.204007i	$0.934603\pi$
$444$		0			0
$445$			16.6226i			0.787988i
$446$	0.322836	−	1.20484i	0.0152867	−	0.0570508i
$447$		0			0
$448$	8.00000			0.377964
$449$		−	7.78687i		−	0.367485i	−0.982974	−	0.183742i	$-0.941179\pi$
$449$		−	7.78687i		−	0.367485i	0.982974	−	0.183742i	$-0.0588212\pi$
$450$		0			0
$451$	−2.97661			−0.140163
$452$	9.98316	−	17.2913i	0.469568	−	0.813316i
$453$		0			0
$454$	3.10341	−	11.5821i	0.145650	−	0.543575i
$455$	−20.5021			−0.961152
$456$		0			0
$457$	10.3205			0.482773			0.241387	−	0.970429i	$-0.422398\pi$
$457$	10.3205			0.482773			0.241387	+	0.970429i	$0.422398\pi$
$458$	−4.92820	+	18.3923i	−0.230280	+	0.859416i
$459$		0			0
$460$	−44.5401	−	25.7152i	−2.07669	−	1.19898i
$461$	22.2016			1.03403			0.517015	−	0.855976i	$-0.327043\pi$
$461$	22.2016			1.03403			0.517015	+	0.855976i	$0.327043\pi$
$462$		0			0
$463$			27.9028i			1.29675i	0.761320	+	0.648377i	$0.224552\pi$
$463$			27.9028i			1.29675i	−0.761320	+	0.648377i	$0.775448\pi$
$464$	−9.46410	−	16.3923i	−0.439360	−	0.760994i
$465$		0			0
$466$	−6.39230	+	23.8564i	−0.296118	+	1.10513i
$467$		−	21.9602i		−	1.01619i	−0.861300	−	0.508097i	$-0.830349\pi$
$467$		−	21.9602i		−	1.01619i	0.861300	−	0.508097i	$-0.169651\pi$
$468$		0			0
$469$			6.55068i			0.302482i
$470$	−44.7016	−	11.9778i	−2.06193	−	0.552492i
$471$		0			0
$472$	4.94504	−	4.94504i	0.227614	−	0.227614i
$473$			0.645280i			0.0296700i
$474$		0			0
$475$	−2.52949			−0.116061
$476$	−3.46410	−	2.00000i	−0.158777	−	0.0916698i
$477$		0			0
$478$	−37.8166	−	10.1329i	−1.72969	−	0.463469i
$479$	6.13278			0.280214			0.140107	−	0.990136i	$-0.455255\pi$
$479$	6.13278			0.280214			0.140107	+	0.990136i	$0.455255\pi$
$480$		0			0
$481$	21.9744			1.00195
$482$	−29.9317	−	8.02019i	−1.36335	−	0.365310i
$483$		0			0
$484$	18.7786	+	10.8418i	0.853572	+	0.492810i
$485$	59.7827			2.71459
$486$		0			0
$487$		−	19.7848i		−	0.896535i	−0.893899	−	0.448268i	$-0.852041\pi$
$487$		−	19.7848i		−	0.896535i	0.893899	−	0.448268i	$-0.147959\pi$
$488$	−22.9282	+	22.9282i	−1.03791	+	1.03791i
$489$		0			0
$490$	−4.27534	−	1.14557i	−0.193140	−	0.0517517i
$491$		−	28.3809i		−	1.28081i	−0.768037	−	0.640405i	$-0.778766\pi$
$491$		−	28.3809i		−	1.28081i	0.768037	−	0.640405i	$-0.221234\pi$
$492$		0			0
$493$			9.46410i			0.426242i
$494$	−1.26474	+	4.72009i	−0.0569035	+	0.212367i
$495$		0			0
$496$	26.1563	−	15.1014i	1.17445	−	0.678071i
$497$			2.21634i			0.0994164i
$498$		0			0
$499$	10.7407			0.480818			0.240409	−	0.970672i	$-0.422718\pi$
$499$	10.7407			0.480818			0.240409	+	0.970672i	$0.422718\pi$
$500$	1.10897	+	0.640262i	0.0495945	+	0.0286334i
$501$		0			0
$502$	5.82479	−	21.7384i	0.259973	−	0.970233i
$503$	−14.7321			−0.656870			−0.328435	−	0.944527i	$-0.606521\pi$
$503$	−14.7321			−0.656870			−0.328435	+	0.944527i	$0.606521\pi$
$504$		0			0
$505$	6.25953			0.278545
$506$	1.19608	−	4.46383i	0.0531723	−	0.198442i
$507$		0			0
$508$	−7.75525	+	13.4325i	−0.344084	+	0.595970i
$509$	−23.2913			−1.03237			−0.516185	−	0.856477i	$-0.672648\pi$
$509$	−23.2913			−1.03237			−0.516185	+	0.856477i	$0.672648\pi$
$510$		0			0
$511$			5.75525i			0.254597i
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$		0			0
$514$	1.35555	−	5.05900i	0.0597909	−	0.223143i
$515$			53.2523i			2.34657i
$516$		0			0
$517$		−	4.15837i		−	0.182885i
$518$	4.58237	+	1.22784i	0.201338	+	0.0539482i
$519$		0			0
$520$	−41.0042	+	41.0042i	−1.79815	+	1.79815i
$521$			1.91027i			0.0836905i	0.999124	+	0.0418453i	$0.0133237\pi$
$521$			1.91027i			0.0836905i	−0.999124	+	0.0418453i	$0.986676\pi$
$522$		0			0
$523$	25.5885			1.11891			0.559453	−	0.828862i	$-0.311011\pi$
$523$	25.5885			1.11891			0.559453	+	0.828862i	$0.311011\pi$
$524$	−14.9052	+	25.8166i	−0.651137	+	1.12780i
$525$		0			0
$526$	−30.3251	−	8.12558i	−1.32224	−	0.354292i
$527$	−15.1014			−0.657825
$528$		0			0
$529$	44.5082			1.93514
$530$	3.40072	+	0.911221i	0.147718	+	0.0395809i
$531$		0			0
$532$	−0.527479	+	0.913620i	−0.0228691	+	0.0396105i
$533$	−49.0272			−2.12360
$534$		0			0
$535$		−	5.98918i		−	0.258935i
$536$	13.1014	+	13.1014i	0.565892	+	0.565892i
$537$		0			0
$538$	22.1951	+	5.94717i	0.956900	+	0.256400i
$539$		−	0.397714i		−	0.0171308i
$540$		0			0
$541$			7.91959i			0.340490i	0.985402	+	0.170245i	$0.0544559\pi$
$541$			7.91959i			0.340490i	−0.985402	+	0.170245i	$0.945544\pi$
$542$	6.72589	−	25.1014i	0.288902	−	1.07820i
$543$		0			0
$544$	−10.9282	+	2.92820i	−0.468543	+	0.125546i
$545$		−	22.1530i		−	0.948929i
$546$		0			0
$547$	−7.65409			−0.327265			−0.163633	−	0.986521i	$-0.552321\pi$
$547$	−7.65409			−0.327265			−0.163633	+	0.986521i	$0.552321\pi$
$548$	22.4557	−	38.8944i	0.959259	−	1.66149i
$549$		0			0
$550$	0.698087	−	2.60530i	0.0297665	−	0.111090i
$551$	2.49606			0.106336
$552$		0			0
$553$	−10.2911			−0.437624
$554$	−11.6310	+	43.4073i	−0.494152	+	1.84420i
$555$		0			0
$556$	5.29134	+	3.05496i	0.224403	+	0.129559i
$557$	−27.6373			−1.17103			−0.585514	−	0.810662i	$-0.699107\pi$
$557$	−27.6373			−1.17103			−0.585514	+	0.810662i	$0.699107\pi$
$558$		0			0
$559$			10.6283i			0.449529i
$560$	−10.8418	+	6.25953i	−0.458151	+	0.264513i
$561$		0			0
$562$	−1.78065	+	6.64548i	−0.0751122	+	0.280322i
$563$		−	33.9198i		−	1.42955i	−0.699355	−	0.714774i	$-0.746529\pi$
$563$		−	33.9198i		−	1.42955i	0.699355	−	0.714774i	$-0.253471\pi$
$564$		0			0
$565$			31.2449i			1.31448i
$566$	33.7936	+	9.05496i	1.42045	+	0.380608i
$567$		0			0
$568$	4.43268	+	4.43268i	0.185991	+	0.185991i
$569$		−	18.7382i		−	0.785547i	−0.919635	−	0.392773i	$-0.871516\pi$
$569$		−	18.7382i		−	0.785547i	0.919635	−	0.392773i	$-0.128484\pi$
$570$		0			0
$571$	15.2449			0.637981			0.318991	−	0.947758i	$-0.396656\pi$
$571$	15.2449			0.637981			0.318991	+	0.947758i	$0.396656\pi$
$572$	−4.51251	−	2.60530i	−0.188677	−	0.108933i
$573$		0			0
$574$	−10.2237	−	2.73944i	−0.426730	−	0.114342i
$575$	39.4009			1.64313
$576$		0			0
$577$	1.49366			0.0621818			0.0310909	−	0.999517i	$-0.490102\pi$
$577$	1.49366			0.0621818			0.0310909	+	0.999517i	$0.490102\pi$
$578$	−17.7583	−	4.75833i	−0.738649	−	0.197920i
$579$		0			0
$580$	25.6520	+	14.8102i	1.06514	+	0.614960i
$581$	−8.36930			−0.347217
$582$		0			0
$583$			0.316353i			0.0131020i
$584$	11.5105	+	11.5105i	0.476308	+	0.476308i
$585$		0			0
$586$	−21.7783	−	5.83546i	−0.899651	−	0.241061i
$587$			16.2195i			0.669452i	0.942315	+	0.334726i	$0.108644\pi$
$587$			16.2195i			0.669452i	−0.942315	+	0.334726i	$0.891356\pi$
$588$		0			0
$589$			3.98282i			0.164109i
$590$	−2.83245	+	10.5709i	−0.116610	+	0.435196i
$591$		0			0
$592$	11.6204	−	6.70905i	0.477596	−	0.275740i
$593$			21.3871i			0.878263i	0.898423	+	0.439131i	$0.144714\pi$
$593$			21.3871i			0.878263i	−0.898423	+	0.439131i	$0.855286\pi$
$594$		0			0
$595$	6.25953			0.256616
$596$	12.1496	+	7.01458i	0.497668	+	0.287329i
$597$		0			0
$598$	19.7004	−	73.5230i	0.805611	−	3.00658i
$599$	11.7672			0.480795			0.240398	−	0.970674i	$-0.422722\pi$
$599$	11.7672			0.480795			0.240398	+	0.970674i	$0.422722\pi$
$600$		0			0
$601$	−15.7552			−0.642670			−0.321335	−	0.946966i	$-0.604132\pi$
$601$	−15.7552			−0.642670			−0.321335	+	0.946966i	$0.604132\pi$
$602$	−0.593866	+	2.21634i	−0.0242042	+	0.0903313i
$603$		0			0
$604$	9.81001	−	16.9914i	0.399164	−	0.691372i
$605$	−33.9324			−1.37955
$606$		0			0
$607$			1.95400i			0.0793102i	0.999213	+	0.0396551i	$0.0126259\pi$
$607$			1.95400i			0.0793102i	−0.999213	+	0.0396551i	$0.987374\pi$
$608$	0.772283	+	2.88220i	0.0313202	+	0.116889i
$609$		0			0
$610$	13.1330	−	49.0129i	0.531738	−	1.98447i
$611$		−	68.4918i		−	2.77088i
$612$		0			0
$613$		−	3.47046i		−	0.140171i	−0.997541	−	0.0700853i	$-0.977673\pi$
$613$		−	3.47046i		−	0.140171i	0.997541	−	0.0700853i	$-0.0223271\pi$
$614$	7.71213	+	2.06646i	0.311236	+	0.0833955i
$615$		0			0
$616$	−0.795428	−	0.795428i	−0.0320487	−	0.0320487i
$617$			24.9456i			1.00427i	0.864789	+	0.502136i	$0.167452\pi$
$617$			24.9456i			1.00427i	−0.864789	+	0.502136i	$0.832548\pi$
$618$		0			0
$619$	−37.3233			−1.50015			−0.750075	−	0.661353i	$-0.769983\pi$
$619$	−37.3233			−1.50015			−0.750075	+	0.661353i	$0.769983\pi$
$620$	−23.6318	+	40.9316i	−0.949078	+	1.64385i
$621$		0			0
$622$	−25.9660	−	6.95756i	−1.04114	−	0.278973i
$623$	−5.31114			−0.212786
$624$		0			0
$625$	−25.9810			−1.03924
$626$	−3.06639	−	0.821636i	−0.122557	−	0.0328392i
$627$		0			0
$628$	10.8966	−	18.8734i	0.434821	−	0.753132i
$629$	−6.70905			−0.267507
$630$		0			0
$631$		−	9.51886i		−	0.378940i	−0.981887	−	0.189470i	$-0.939323\pi$
$631$		−	9.51886i		−	0.378940i	0.981887	−	0.189470i	$-0.0606770\pi$
$632$	−20.5823	+	20.5823i	−0.818720	+	0.818720i
$633$		0			0
$634$	−33.4475	−	8.96222i	−1.32837	−	0.355935i
$635$		−	24.2721i		−	0.963209i
$636$		0			0
$637$		−	6.55068i		−	0.259547i
$638$	−0.688861	+	2.57086i	−0.0272723	+	0.101781i
$639$		0			0
$640$	−9.16459	+	34.2027i	−0.362262	+	1.35198i
$641$		−	41.9263i		−	1.65599i	−0.560735	−	0.827995i	$-0.689481\pi$
$641$		−	41.9263i		−	1.65599i	0.560735	−	0.827995i	$-0.310519\pi$
$642$		0			0
$643$	2.79303			0.110146			0.0550732	−	0.998482i	$-0.482461\pi$
$643$	2.79303			0.110146			0.0550732	+	0.998482i	$0.482461\pi$
$644$	8.21634	−	14.2311i	0.323769	−	0.560785i
$645$		0			0
$646$	0.386141	−	1.44110i	0.0151925	−	0.0566993i
$647$	−30.2089			−1.18763			−0.593817	−	0.804600i	$-0.702380\pi$
$647$	−30.2089			−1.18763			−0.593817	+	0.804600i	$0.702380\pi$
$648$		0			0
$649$	−0.983356			−0.0386001
$650$	11.4981	−	42.9114i	0.450991	−	1.68312i
$651$		0			0
$652$	−17.3461	−	10.0148i	−0.679326	−	0.392209i
$653$	−36.8020			−1.44017			−0.720086	−	0.693884i	$-0.755898\pi$
$653$	−36.8020			−1.44017			−0.720086	+	0.693884i	$0.755898\pi$
$654$		0			0
$655$		−	46.6498i		−	1.82276i
$656$	−25.9263	+	14.9686i	−1.01225	+	0.584425i
$657$		0			0
$658$	3.82705	−	14.2827i	0.149194	−	0.556799i
$659$		−	27.5858i		−	1.07459i	−0.843394	−	0.537296i	$-0.819446\pi$
$659$		−	27.5858i		−	1.07459i	0.843394	−	0.537296i	$-0.180554\pi$
$660$		0			0
$661$		−	43.9007i		−	1.70754i	−0.520650	−	0.853770i	$-0.674310\pi$
$661$		−	43.9007i		−	1.70754i	0.520650	−	0.853770i	$-0.325690\pi$
$662$	−5.93662	−	1.59071i	−0.230733	−	0.0618248i
$663$		0			0
$664$	−16.7386	+	16.7386i	−0.649584	+	0.649584i
$665$		−	1.65089i		−	0.0640186i
$666$		0			0
$667$	−38.8801			−1.50544
$668$	−25.2281	−	14.5655i	−0.976105	−	0.563554i
$669$		0			0
$670$	−28.0064	−	7.50428i	−1.08198	−	0.289916i
$671$	4.55943			0.176015
$672$		0			0
$673$	−1.78085			−0.0686465			−0.0343233	−	0.999411i	$-0.510928\pi$
$673$	−1.78085			−0.0686465			−0.0343233	+	0.999411i	$0.510928\pi$
$674$	37.6551	+	10.0897i	1.45042	+	0.388639i
$675$		0			0
$676$	−51.8080	−	29.9114i	−1.99262	−	1.15044i
$677$	45.7356			1.75776			0.878881	−	0.477041i	$-0.158291\pi$
$677$	45.7356			1.75776			0.878881	+	0.477041i	$0.158291\pi$
$678$		0			0
$679$			19.1014i			0.733043i
$680$	12.5191	−	12.5191i	0.480084	−	0.480084i
$681$		0			0
$682$	−4.10219	−	1.09918i	−0.157081	−	0.0420897i
$683$			23.5159i			0.899811i	0.893076	+	0.449906i	$0.148542\pi$
$683$			23.5159i			0.899811i	−0.893076	+	0.449906i	$0.851458\pi$
$684$		0			0
$685$			70.2810i			2.68530i
$686$	0.366025	−	1.36603i	0.0139749	−	0.0521551i
$687$		0			0
$688$	3.24495	+	5.62041i	0.123712	+	0.214276i
$689$			5.21059i			0.198508i
$690$		0			0
$691$	−31.3501			−1.19261			−0.596306	−	0.802757i	$-0.703366\pi$
$691$	−31.3501			−1.19261			−0.596306	+	0.802757i	$0.703366\pi$
$692$	−24.7986	−	14.3175i	−0.942703	−	0.544270i
$693$		0			0
$694$	7.62666	−	28.4631i	0.289504	−	1.08044i
$695$	−9.56130			−0.362681
$696$		0			0
$697$	14.9686			0.566975
$698$	1.78687	−	6.66867i	0.0676339	−	0.252413i
$699$		0			0
$700$	4.79543	−	8.30593i	0.181250	−	0.313934i
$701$	−1.40072			−0.0529046			−0.0264523	−	0.999650i	$-0.508421\pi$
$701$	−1.40072			−0.0529046			−0.0264523	+	0.999650i	$0.508421\pi$
$702$		0			0
$703$			1.76944i			0.0667357i
$704$	−3.18171			−0.119915
$705$		0			0
$706$	−2.72466	+	10.1686i	−0.102544	+	0.382699i
$707$			2.00000i			0.0752177i
$708$		0			0
$709$			39.4709i			1.48236i	0.671307	+	0.741179i	$0.265733\pi$
$709$			39.4709i			1.48236i	−0.671307	+	0.741179i	$0.734267\pi$
$710$	−9.47560	−	2.53898i	−0.355613	−	0.0952862i
$711$		0			0
$712$	−10.6223	+	10.6223i	−0.398087	+	0.398087i
$713$		−	62.0389i		−	2.32338i
$714$		0			0
$715$	8.15396			0.304941
$716$	19.8104	−	34.3126i	0.740349	−	1.28232i
$717$		0			0
$718$	−30.5885	−	8.19615i	−1.14155	−	0.305878i
$719$	−12.0694			−0.450113			−0.225056	−	0.974346i	$-0.572257\pi$
$719$	−12.0694			−0.450113			−0.225056	+	0.974346i	$0.572257\pi$
$720$		0			0
$721$	−17.0148			−0.633663
$722$	25.5744	+	6.85264i	0.951781	+	0.255029i
$723$		0			0
$724$	20.1732	−	34.9409i	0.749729	−	1.29857i
$725$	−22.6922			−0.842768
$726$		0			0
$727$		−	2.39230i		−	0.0887257i	−0.999015	−	0.0443628i	$-0.985874\pi$
$727$		−	2.39230i		−	0.0887257i	0.999015	−	0.0443628i	$-0.0141258\pi$
$728$	−13.1014	−	13.1014i	−0.485568	−	0.485568i
$729$		0			0
$730$	−24.6056	−	6.59306i	−0.910695	−	0.244020i
$731$		−	3.24495i		−	0.120019i
$732$		0			0
$733$		−	14.5802i		−	0.538533i	−0.963066	−	0.269267i	$-0.913219\pi$
$733$		−	14.5802i		−	0.538533i	0.963066	−	0.269267i	$-0.0867813\pi$
$734$	12.9051	−	48.1626i	0.476337	−	1.77771i
$735$		0			0
$736$	−12.0296	−	44.8949i	−0.443415	−	1.65485i
$737$		−	2.60530i		−	0.0959673i
$738$		0			0
$739$	30.3459			1.11629			0.558146	−	0.829743i	$-0.311513\pi$
$739$	30.3459			1.11629			0.558146	+	0.829743i	$0.311513\pi$
$740$	−10.4989	+	18.1846i	−0.385946	+	0.668478i
$741$		0			0
$742$	−0.291147	+	1.08658i	−0.0106883	+	0.0398894i
$743$	16.6659			0.611411			0.305706	−	0.952126i	$-0.401108\pi$
$743$	16.6659			0.611411			0.305706	+	0.952126i	$0.401108\pi$
$744$		0			0
$745$	−21.9540			−0.804332
$746$	4.12443	−	15.3926i	0.151006	−	0.563562i
$747$		0			0
$748$	1.37772	+	0.795428i	0.0503745	+	0.0290837i
$749$	1.91362			0.0699222
$750$		0			0
$751$		−	2.10155i		−	0.0766866i	−0.999265	−	0.0383433i	$-0.987792\pi$
$751$		−	2.10155i		−	0.0766866i	0.999265	−	0.0383433i	$-0.0122080\pi$
$752$	−20.9114	−	36.2195i	−0.762559	−	1.32079i
$753$		0			0
$754$	−11.3461	+	42.3442i	−0.413201	+	1.54209i
$755$			30.7030i			1.11740i
$756$		0			0
$757$			39.2408i			1.42623i	0.701046	+	0.713116i	$0.252717\pi$
$757$			39.2408i			1.42623i	−0.701046	+	0.713116i	$0.747283\pi$
$758$	7.48429	+	2.00541i	0.271842	+	0.0728397i
$759$		0			0
$760$	−3.30177	−	3.30177i	−0.119768	−	0.119768i
$761$			22.7618i			0.825113i	0.910932	+	0.412556i	$0.135364\pi$
$761$			22.7618i			0.825113i	−0.910932	+	0.412556i	$0.864636\pi$
$762$		0			0
$763$	7.07816			0.256246
$764$	11.1466	+	6.43549i	0.403270	+	0.232828i
$765$		0			0
$766$	43.2577	+	11.5909i	1.56296	+	0.418795i
$767$	−16.1967			−0.584828
$768$		0			0
$769$	−52.9030			−1.90773			−0.953865	−	0.300234i	$-0.902935\pi$
$769$	−52.9030			−1.90773			−0.953865	+	0.300234i	$0.902935\pi$
$770$	1.70036	+	0.455611i	0.0612768	+	0.0164191i
$771$		0			0
$772$	−17.2913	−	9.98316i	−0.622329	−	0.359302i
$773$	−6.27110			−0.225556			−0.112778	−	0.993620i	$-0.535975\pi$
$773$	−6.27110			−0.225556			−0.112778	+	0.993620i	$0.535975\pi$
$774$		0			0
$775$		−	36.2087i		−	1.30066i
$776$	38.2027	+	38.2027i	1.37140	+	1.37140i
$777$		0			0
$778$	34.2891	+	9.18773i	1.22932	+	0.329396i
$779$		−	3.94780i		−	0.141445i
$780$		0			0
$781$		−	0.881470i		−	0.0315415i
$782$	−6.01478	+	22.4475i	−0.215088	+	0.802719i
$783$		0			0
$784$	−2.00000	−	3.46410i	−0.0714286	−	0.123718i
$785$			34.1038i			1.21722i
$786$		0			0
$787$	−20.5651			−0.733065			−0.366533	−	0.930405i	$-0.619455\pi$
$787$	−20.5651			−0.733065			−0.366533	+	0.930405i	$0.619455\pi$
$788$	−40.9409	−	23.6373i	−1.45846	−	0.842042i
$789$		0			0
$790$	11.7893	−	43.9981i	0.419443	−	1.56538i
$791$	−9.98316			−0.354960
$792$		0			0
$793$	75.0976			2.66679
$794$	1.48108	−	5.52748i	0.0525617	−	0.196163i
$795$		0			0
$796$	−21.6202	+	37.4473i	−0.766308	+	1.32728i
$797$	16.6802			0.590845			0.295422	−	0.955367i	$-0.404540\pi$
$797$	16.6802			0.590845			0.295422	+	0.955367i	$0.404540\pi$
$798$		0			0
$799$			20.9114i			0.739791i
$800$	−7.02099	−	26.2027i	−0.248230	−	0.926406i
$801$		0			0
$802$	−2.14981	+	8.02320i	−0.0759124	+	0.283309i
$803$		−	2.28894i		−	0.0807751i
$804$		0			0
$805$			25.7152i			0.906342i
$806$	−67.5664	−	18.1044i	−2.37993	−	0.637699i
$807$		0			0
$808$	4.00000	+	4.00000i	0.140720	+	0.140720i
$809$			54.5485i			1.91782i	0.283707	+	0.958911i	$0.408436\pi$
$809$			54.5485i			1.91782i	−0.283707	+	0.958911i	$0.591564\pi$
$810$		0			0
$811$	−9.77845			−0.343368			−0.171684	−	0.985152i	$-0.554921\pi$
$811$	−9.77845			−0.343368			−0.171684	+	0.985152i	$0.554921\pi$
$812$	−4.73205	+	8.19615i	−0.166062	+	0.287629i
$813$		0			0
$814$	−1.82247	−	0.488330i	−0.0638776	−	0.0171159i
$815$	31.3439			1.09793
$816$		0			0
$817$	−0.855821			−0.0299414
$818$	−34.3010	−	9.19094i	−1.19931	−	0.321354i
$819$		0			0
$820$	23.4241	−	40.5717i	0.818004	−	1.41682i
$821$	−28.5488			−0.996359			−0.498179	−	0.867074i	$-0.665998\pi$
$821$	−28.5488			−0.996359			−0.498179	+	0.867074i	$0.665998\pi$
$822$		0			0
$823$			33.5912i			1.17092i	0.810702	+	0.585459i	$0.199086\pi$
$823$			33.5912i			1.17092i	−0.810702	+	0.585459i	$0.800914\pi$
$824$	−34.0296	+	34.0296i	−1.18548	+	1.18548i
$825$		0			0
$826$	−3.37753	−	0.905006i	−0.117519	−	0.0314892i
$827$		−	25.9650i		−	0.902893i	−0.892298	−	0.451446i	$-0.850908\pi$
$827$		−	25.9650i		−	0.902893i	0.892298	−	0.451446i	$-0.149092\pi$
$828$		0			0
$829$			23.7613i			0.825263i	0.910898	+	0.412631i	$0.135390\pi$
$829$			23.7613i			0.825263i	−0.910898	+	0.412631i	$0.864610\pi$
$830$	9.58765	−	35.7816i	0.332792	−	1.24200i
$831$		0			0
$832$	−52.4054			−1.81683
$833$			2.00000i			0.0692959i
$834$		0			0
$835$	45.5864			1.57758
$836$	0.209786	−	0.363360i	0.00725559	−	0.0125671i
$837$		0			0
$838$	−4.50428	+	16.8102i	−0.155598	+	0.580699i
$839$	−2.77243			−0.0957148			−0.0478574	−	0.998854i	$-0.515239\pi$
$839$	−2.77243			−0.0957148			−0.0478574	+	0.998854i	$0.515239\pi$
$840$		0			0
$841$	−6.60770			−0.227852
$842$	8.20244	−	30.6119i	0.282675	−	1.05496i
$843$		0			0
$844$	4.36314	+	2.51906i	0.150185	+	0.0867096i
$845$	93.6155			3.22047
$846$		0			0
$847$		−	10.8418i		−	0.372529i
$848$	1.59086	+	2.75544i	0.0546302	+	0.0946223i
$849$		0			0
$850$	−3.51050	+	13.1014i	−0.120409	+	0.449373i
$851$		−	27.5619i		−	0.944810i
$852$		0			0
$853$		−	0.236670i		−	0.00810344i	−0.999992	−	0.00405172i	$-0.998710\pi$
$853$		−	0.236670i		−	0.00810344i	0.999992	−	0.00405172i	$-0.00128971\pi$
$854$	15.6603	+	4.19615i	0.535883	+	0.143589i
$855$		0			0
$856$	3.82724	−	3.82724i	0.130812	−	0.130812i
$857$		−	21.2139i		−	0.724654i	−0.932051	−	0.362327i	$-0.881982\pi$
$857$		−	21.2139i		−	0.724654i	0.932051	−	0.362327i	$-0.118018\pi$
$858$		0			0
$859$	12.6199			0.430585			0.215292	−	0.976550i	$-0.430930\pi$
$859$	12.6199			0.430585			0.215292	+	0.976550i	$0.430930\pi$
$860$	−8.79529	−	5.07796i	−0.299917	−	0.173157i
$861$		0			0
$862$	29.2385	+	7.83443i	0.995868	+	0.266842i
$863$	−25.8396			−0.879589			−0.439795	−	0.898098i	$-0.644949\pi$
$863$	−25.8396			−0.879589			−0.439795	+	0.898098i	$0.644949\pi$
$864$		0			0
$865$	44.8104			1.52360
$866$	−26.4906	−	7.09815i	−0.900189	−	0.241205i
$867$		0			0
$868$	−13.0782	−	7.55068i	−0.443902	−	0.256287i
$869$	4.09293			0.138843
$870$		0			0
$871$		−	42.9114i		−	1.45400i
$872$	14.1563	−	14.1563i	0.479393	−	0.479393i
$873$		0			0
$874$	5.92028	+	1.58633i	0.200256	+	0.0536586i
$875$		−	0.640262i		−	0.0216448i
$876$		0			0
$877$		−	55.0972i		−	1.86050i	−0.366925	−	0.930251i	$-0.619589\pi$
$877$		−	55.0972i		−	1.86050i	0.366925	−	0.930251i	$-0.380411\pi$
$878$	−6.72589	+	25.1014i	−0.226988	+	0.847130i
$879$		0			0
$880$	4.31195	−	2.48950i	0.145356	−	0.0839211i
$881$			33.7034i			1.13550i	0.823202	+	0.567749i	$0.192186\pi$
$881$			33.7034i			1.13550i	−0.823202	+	0.567749i	$0.807814\pi$
$882$		0			0
$883$	19.8396			0.667655			0.333827	−	0.942634i	$-0.391660\pi$
$883$	19.8396			0.667655			0.333827	+	0.942634i	$0.391660\pi$
$884$	22.6922	+	13.1014i	0.763222	+	0.440646i
$885$		0			0
$886$	3.14332	−	11.7310i	0.105602	−	0.394111i
$887$	−17.5967			−0.590840			−0.295420	−	0.955367i	$-0.595460\pi$
$887$	−17.5967			−0.590840			−0.295420	+	0.955367i	$0.595460\pi$
$888$		0			0
$889$	7.75525			0.260103
$890$	6.08430	−	22.7069i	0.203946	−	0.761138i
$891$		0			0
$892$	−0.882003	+	1.52767i	−0.0295316	+	0.0511503i
$893$	5.51515			0.184558
$894$		0			0
$895$			62.0019i			2.07249i
$896$	−10.9282	−	2.92820i	−0.365086	−	0.0978244i
$897$		0			0
$898$	−2.85019	+	10.6371i	−0.0951121	+	0.354963i
$899$			35.7302i			1.19167i
$900$		0			0
$901$		−	1.59086i		−	0.0529991i
$902$	4.06612	+	1.08951i	0.135387	+	0.0362768i
$903$		0			0
$904$	−19.9663	+	19.9663i	−0.664070	+	0.664070i
$905$			63.1372i			2.09875i
$906$		0			0
$907$	−10.8190			−0.359238			−0.179619	−	0.983736i	$-0.557486\pi$
$907$	−10.8190			−0.359238			−0.179619	+	0.983736i	$0.557486\pi$
$908$	−8.47868	+	14.6855i	−0.281375	+	0.487356i
$909$		0			0
$910$	28.0064	+	7.50428i	0.928402	+	0.248765i
$911$	33.4364			1.10780			0.553899	−	0.832584i	$-0.313139\pi$
$911$	33.4364			1.10780			0.553899	+	0.832584i	$0.313139\pi$
$912$		0			0
$913$	3.32859			0.110160
$914$	−14.0981	−	3.77757i	−0.466323	−	0.124951i
$915$		0			0
$916$	13.4641	−	23.3205i	0.444866	−	0.770531i
$917$	14.9052			0.492213
$918$		0			0
$919$			3.70049i			0.122068i	0.998136	+	0.0610339i	$0.0194398\pi$
$919$			3.70049i			0.122068i	−0.998136	+	0.0610339i	$0.980560\pi$
$920$	51.4304	+	51.4304i	1.69561	+	1.69561i
$921$		0			0
$922$	−30.3279	−	8.12634i	−0.998796	−	0.267627i
$923$		−	14.5185i		−	0.477883i
$924$		0			0
$925$		−	16.0864i		−	0.528917i
$926$	10.2131	−	38.1159i	0.335624	−	1.25257i
$927$		0			0
$928$	6.92820	+	25.8564i	0.227429	+	0.848778i
$929$		−	17.0318i		−	0.558796i	−0.960175	−	0.279398i	$-0.909865\pi$
$929$		−	17.0318i		−	0.558796i	0.960175	−	0.279398i	$-0.0901348\pi$
$930$		0			0
$931$	0.527479			0.0172874
$932$	17.4641	−	30.2487i	0.572056	−	0.990829i
$933$		0			0
$934$	−8.03798	+	29.9981i	−0.263011	+	0.981569i
$935$	−2.48950			−0.0814155
$936$		0			0
$937$	−11.6077			−0.379207			−0.189603	−	0.981861i	$-0.560720\pi$
$937$	−11.6077			−0.379207			−0.189603	+	0.981861i	$0.560720\pi$
$938$	2.39771	−	8.94839i	0.0782881	−	0.292175i
$939$		0			0
$940$	56.6793	+	32.7238i	1.84868	+	1.06733i
$941$	−50.5834			−1.64897			−0.824486	−	0.565882i	$-0.808536\pi$
$941$	−50.5834			−1.64897			−0.824486	+	0.565882i	$0.808536\pi$
$942$		0			0
$943$			61.4935i			2.00250i
$944$	−8.56506	+	4.94504i	−0.278769	+	0.160947i
$945$		0			0
$946$	0.236189	−	0.881470i	0.00767917	−	0.0286590i
$947$			42.8764i			1.39330i	0.717413	+	0.696648i	$0.245326\pi$
$947$			42.8764i			1.39330i	−0.717413	+	0.696648i	$0.754674\pi$
$948$		0			0
$949$		−	37.7008i		−	1.22382i
$950$	3.45534	+	0.925857i	0.112106	+	0.0300388i
$951$		0			0
$952$	4.00000	+	4.00000i	0.129641	+	0.129641i
$953$		−	11.4074i		−	0.369523i	−0.982783	−	0.184761i	$-0.940849\pi$
$953$		−	11.4074i		−	0.369523i	0.982783	−	0.184761i	$-0.0591512\pi$
$954$		0			0
$955$	−20.1416			−0.651766
$956$	47.9495	+	27.6836i	1.55080	+	0.895353i
$957$		0			0
$958$	−8.37753	−	2.24475i	−0.270666	−	0.0725246i
$959$	−22.4557			−0.725132
$960$		0			0
$961$	−26.0127			−0.839120
$962$	−30.0176	−	8.04319i	−0.967806	−	0.259323i
$963$		0			0
$964$	37.9519	+	21.9116i	1.22235	+	0.705724i
$965$	31.2449			1.00581
$966$		0			0
$967$		−	24.7090i		−	0.794589i	−0.917691	−	0.397295i	$-0.869949\pi$
$967$		−	24.7090i		−	0.794589i	0.917691	−	0.397295i	$-0.130051\pi$
$968$	−21.6836	−	21.6836i	−0.696939	−	0.696939i
$969$		0			0
$970$	−81.6647	−	21.8820i	−2.62210	−	0.702589i
$971$		−	28.3585i		−	0.910067i	−0.890474	−	0.455034i	$-0.849627\pi$
$971$		−	28.3585i		−	0.910067i	0.890474	−	0.455034i	$-0.150373\pi$
$972$		0			0
$973$		−	3.05496i		−	0.0979375i
$974$	−7.24174	+	27.0265i	−0.232040	+	0.865986i
$975$		0			0
$976$	39.7128	−	22.9282i	1.27118	−	0.733914i
$977$		−	23.4704i		−	0.750885i	−0.926846	−	0.375442i	$-0.877491\pi$
$977$		−	23.4704i		−	0.750885i	0.926846	−	0.375442i	$-0.122509\pi$
$978$		0			0
$979$	2.11231			0.0675099
$980$	5.42091	+	3.12976i	0.173165	+	0.0999767i
$981$		0			0
$982$	−10.3881	+	38.7690i	−0.331498	+	1.23717i
$983$	−26.2425			−0.837007			−0.418504	−	0.908215i	$-0.637445\pi$
$983$	−26.2425			−0.837007			−0.418504	+	0.908215i	$0.637445\pi$
$984$		0			0
$985$	73.9790			2.35717
$986$	3.46410	−	12.9282i	0.110319	−	0.411718i
$987$		0			0
$988$	3.45534	−	5.98483i	0.109929	−	0.190403i
$989$	13.3308			0.423895
$990$		0			0
$991$			44.2579i			1.40590i	0.711241	+	0.702949i	$0.248134\pi$
$991$			44.2579i			1.40590i	−0.711241	+	0.702949i	$0.751866\pi$
$992$	−41.2577	+	11.0550i	−1.30993	+	0.350995i
$993$		0			0
$994$	0.811237	−	3.02758i	0.0257309	−	0.0960289i
$995$		−	67.6662i		−	2.14516i
$996$		0			0
$997$		−	28.1271i		−	0.890796i	−0.895333	−	0.445398i	$-0.853062\pi$
$997$		−	28.1271i		−	0.890796i	0.895333	−	0.445398i	$-0.146938\pi$
$998$	−14.6720	−	3.93136i	−0.464435	−	0.124445i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.j.a.323.1	✓	8
3.2	odd	2		1512.2.j.b.323.8	yes	8
4.3	odd	2		6048.2.j.a.5615.4		8
8.3	odd	2		1512.2.j.b.323.6	yes	8
8.5	even	2		6048.2.j.b.5615.5		8
12.11	even	2		6048.2.j.b.5615.6		8
24.5	odd	2		6048.2.j.a.5615.3		8
24.11	even	2	inner	1512.2.j.a.323.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.j.a.323.1	✓	8	1.1	even	1	trivial
1512.2.j.a.323.3	yes	8	24.11	even	2	inner
1512.2.j.b.323.6	yes	8	8.3	odd	2
1512.2.j.b.323.8	yes	8	3.2	odd	2
6048.2.j.a.5615.3		8	24.5	odd	2
6048.2.j.a.5615.4		8	4.3	odd	2
6048.2.j.b.5615.5		8	8.5	even	2
6048.2.j.b.5615.6		8	12.11	even	2

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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 - 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} -3.12976 q^{5} -1.00000i q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(-1.36603 - 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} -3.12976 q^{5} -1.00000i q^{7} +(-2.00000 - 2.00000i) q^{8} +(4.27534 + 1.14557i) q^{10} +0.397714i q^{11} +6.55068i q^{13} +(-0.366025 + 1.36603i) q^{14} +(2.00000 + 3.46410i) q^{16} -2.00000i q^{17} -0.527479 q^{19} +(-5.42091 - 3.12976i) q^{20} +(0.145573 - 0.543288i) q^{22} +8.21634 q^{23} +4.79543 q^{25} +(2.39771 - 8.94839i) q^{26} +(1.00000 - 1.73205i) q^{28} -4.73205 q^{29} -7.55068i q^{31} +(-1.46410 - 5.46410i) q^{32} +(-0.732051 + 2.73205i) q^{34} +3.12976i q^{35} -3.35452i q^{37} +(0.720550 + 0.193071i) q^{38} +(6.25953 + 6.25953i) q^{40} +7.48429i q^{41} +1.62247 q^{43} +(-0.397714 + 0.688861i) q^{44} +(-11.2237 - 3.00739i) q^{46} -10.4557 q^{47} -1.00000 q^{49} +(-6.55068 - 1.75525i) q^{50} +(-6.55068 + 11.3461i) q^{52} +0.795428 q^{53} -1.24475i q^{55} +(-2.00000 + 2.00000i) q^{56} +(6.46410 + 1.73205i) q^{58} +2.47252i q^{59} -11.4641i q^{61} +(-2.76374 + 10.3144i) q^{62} +8.00000i q^{64} -20.5021i q^{65} -6.55068 q^{67} +(2.00000 - 3.46410i) q^{68} +(1.14557 - 4.27534i) q^{70} -2.21634 q^{71} -5.75525 q^{73} +(-1.22784 + 4.58237i) q^{74} +(-0.913620 - 0.527479i) q^{76} +0.397714 q^{77} -10.2911i q^{79} +(-6.25953 - 10.8418i) q^{80} +(2.73944 - 10.2237i) q^{82} -8.36930i q^{83} +6.25953i q^{85} +(-2.21634 - 0.593866i) q^{86} +(0.795428 - 0.795428i) q^{88} -5.31114i q^{89} +6.55068 q^{91} +(14.2311 + 8.21634i) q^{92} +(14.2827 + 3.82705i) q^{94} +1.65089 q^{95} -19.1014 q^{97} +(1.36603 + 0.366025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 8 q^{5} - 16 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 - 8 * q^5 - 16 * q^8	\( 8 q - 4 q^{2} - 8 q^{5} - 16 q^{8} + 4 q^{10} + 4 q^{14} + 16 q^{16} + 16 q^{19} - 12 q^{22} + 16 q^{23} + 32 q^{25} + 16 q^{26} + 8 q^{28} - 24 q^{29} + 16 q^{32} + 8 q^{34} - 20 q^{38} + 16 q^{40} + 8 q^{43} + 4 q^{46} - 8 q^{47} - 8 q^{49} + 8 q^{50} + 8 q^{52} - 16 q^{56} + 24 q^{58} - 12 q^{62} + 8 q^{67} + 16 q^{68} - 4 q^{70} + 32 q^{71} + 8 q^{73} + 28 q^{74} + 24 q^{76} - 16 q^{80} - 36 q^{82} + 32 q^{86} - 8 q^{91} - 24 q^{92} + 40 q^{94} + 112 q^{95} - 32 q^{97} + 4 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 - 8 * q^5 - 16 * q^8 + 4 * q^10 + 4 * q^14 + 16 * q^16 + 16 * q^19 - 12 * q^22 + 16 * q^23 + 32 * q^25 + 16 * q^26 + 8 * q^28 - 24 * q^29 + 16 * q^32 + 8 * q^34 - 20 * q^38 + 16 * q^40 + 8 * q^43 + 4 * q^46 - 8 * q^47 - 8 * q^49 + 8 * q^50 + 8 * q^52 - 16 * q^56 + 24 * q^58 - 12 * q^62 + 8 * q^67 + 16 * q^68 - 4 * q^70 + 32 * q^71 + 8 * q^73 + 28 * q^74 + 24 * q^76 - 16 * q^80 - 36 * q^82 + 32 * q^86 - 8 * q^91 - 24 * q^92 + 40 * q^94 + 112 * q^95 - 32 * q^97 + 4 * q^98

Introduction

L-functions

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