LMFDB - Embedded newform 1500.2.m.a.901.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1500,2,Mod(301,1500)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1500, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("1500.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.m (of order $5$, degree $4$, not 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:	$11.9775603032$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.26265625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 $ x^8 - 3x^7 + 2x^6 + x^4 + 8x^2 - 24x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			901.1
Root			$-0.0272949 - 1.41395i$ of defining polynomial
Character	$\chi$	$=$	1500.901
Dual form			1500.2.m.a.601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{3} -4.32440 q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{3} -4.32440 q^{7} +(0.309017 - 0.951057i) q^{9} +(0.180557 + 0.555698i) q^{11} +(-0.298591 + 0.918969i) q^{13} +(-1.88048 - 1.36625i) q^{17} +(4.35169 + 3.16169i) q^{19} +(3.49851 - 2.54182i) q^{21} +(0.419687 + 1.29166i) q^{23} +(0.309017 + 0.951057i) q^{27} +(0.571459 - 0.415189i) q^{29} +(-6.86707 - 4.98922i) q^{31} +(-0.472705 - 0.343440i) q^{33} +(1.89090 - 5.81960i) q^{37} +(-0.298591 - 0.918969i) q^{39} +(3.41820 - 10.5201i) q^{41} +7.03076 q^{43} +(7.33723 - 5.33081i) q^{47} +11.7004 q^{49} +2.32440 q^{51} +(7.20487 - 5.23465i) q^{53} -5.37899 q^{57} +(-2.25351 + 6.93558i) q^{59} +(-1.48752 - 4.57810i) q^{61} +(-1.33631 + 4.11275i) q^{63} +(-0.304195 - 0.221011i) q^{67} +(-1.09875 - 0.798291i) q^{69} +(-8.54359 + 6.20729i) q^{71} +(-0.0659364 - 0.202931i) q^{73} +(-0.780801 - 2.40306i) q^{77} +(5.68410 - 4.12974i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(13.0343 + 9.46998i) q^{83} +(-0.218278 + 0.671790i) q^{87} +(-4.33233 - 13.3335i) q^{89} +(1.29123 - 3.97399i) q^{91} +8.48817 q^{93} +(12.7436 - 9.25880i) q^{97} +0.584296 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} - 8 q^{7} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 - 8 * q^7 - 2 * q^9	$ 8 q - 2 q^{3} - 8 q^{7} - 2 q^{9} + 8 q^{11} - 3 q^{17} + 5 q^{19} + 7 q^{21} + 7 q^{23} - 2 q^{27} - 3 q^{29} - 3 q^{31} - 7 q^{33} + q^{37} + 10 q^{41} + 12 q^{43} + 33 q^{47} - 8 q^{49} - 8 q^{51} + 19 q^{53} - 10 q^{57} - 38 q^{59} + 46 q^{61} - 3 q^{63} + 8 q^{67} + 2 q^{69} - 25 q^{71} + 26 q^{73} - 23 q^{77} - 16 q^{79} - 2 q^{81} - 8 q^{83} - 3 q^{87} - 30 q^{89} + 25 q^{91} + 22 q^{93} + 14 q^{97} - 2 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 - 8 * q^7 - 2 * q^9 + 8 * q^11 - 3 * q^17 + 5 * q^19 + 7 * q^21 + 7 * q^23 - 2 * q^27 - 3 * q^29 - 3 * q^31 - 7 * q^33 + q^37 + 10 * q^41 + 12 * q^43 + 33 * q^47 - 8 * q^49 - 8 * q^51 + 19 * q^53 - 10 * q^57 - 38 * q^59 + 46 * q^61 - 3 * q^63 + 8 * q^67 + 2 * q^69 - 25 * q^71 + 26 * q^73 - 23 * q^77 - 16 * q^79 - 2 * q^81 - 8 * q^83 - 3 * q^87 - 30 * q^89 + 25 * q^91 + 22 * q^93 + 14 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times$.

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−4.32440			−1.63447			−0.817234	−	0.576306i	$-0.804494\pi$
$7$	−4.32440			−1.63447			−0.817234	+	0.576306i	$0.804494\pi$
$8$		0			0
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$		0			0
$11$	0.180557	+	0.555698i	0.0544401	+	0.167549i	0.974580	−	0.224041i	$-0.0719250\pi$
$11$	0.180557	+	0.555698i	0.0544401	+	0.167549i	−0.920140	+	0.391590i	$0.871925\pi$
$12$		0			0
$13$	−0.298591	+	0.918969i	−0.0828143	+	0.254876i	−0.983887	−	0.178792i	$-0.942781\pi$
$13$	−0.298591	+	0.918969i	−0.0828143	+	0.254876i	0.901073	+	0.433668i	$0.142781\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.88048	−	1.36625i	−0.456082	−	0.331363i	0.335910	−	0.941894i	$-0.390956\pi$
$17$	−1.88048	−	1.36625i	−0.456082	−	0.331363i	−0.791993	+	0.610531i	$0.790956\pi$
$18$		0			0
$19$	4.35169	+	3.16169i	0.998346	+	0.725341i	0.961733	−	0.273988i	$-0.0883430\pi$
$19$	4.35169	+	3.16169i	0.998346	+	0.725341i	0.0366134	+	0.999330i	$0.488343\pi$
$20$		0			0
$21$	3.49851	−	2.54182i	0.763437	−	0.554670i
$22$		0			0
$23$	0.419687	+	1.29166i	0.0875107	+	0.269330i	0.985230	−	0.171238i	$-0.0547768\pi$
$23$	0.419687	+	1.29166i	0.0875107	+	0.269330i	−0.897719	+	0.440569i	$0.854777\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$		0			0
$29$	0.571459	−	0.415189i	0.106117	−	0.0770987i	−0.533461	−	0.845825i	$-0.679109\pi$
$29$	0.571459	−	0.415189i	0.106117	−	0.0770987i	0.639578	+	0.768726i	$0.279109\pi$
$30$		0			0
$31$	−6.86707	−	4.98922i	−1.23336	−	0.896090i	−0.236225	−	0.971698i	$-0.575910\pi$
$31$	−6.86707	−	4.98922i	−1.23336	−	0.896090i	−0.997138	+	0.0756084i	$0.975910\pi$
$32$		0			0
$33$	−0.472705	−	0.343440i	−0.0822874	−	0.0597853i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.89090	−	5.81960i	0.310862	−	0.956736i	−0.666562	−	0.745450i	$-0.732235\pi$
$37$	1.89090	−	5.81960i	0.310862	−	0.956736i	0.977424	−	0.211286i	$-0.0677652\pi$
$38$		0			0
$39$	−0.298591	−	0.918969i	−0.0478129	−	0.147153i
$40$		0			0
$41$	3.41820	−	10.5201i	0.533833	−	1.64297i	−0.212325	−	0.977199i	$-0.568104\pi$
$41$	3.41820	−	10.5201i	0.533833	−	1.64297i	0.746158	−	0.665769i	$-0.231896\pi$
$42$		0			0
$43$	7.03076			1.07218			0.536090	−	0.844161i	$-0.319901\pi$
$43$	7.03076			1.07218			0.536090	+	0.844161i	$0.319901\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	7.33723	−	5.33081i	1.07025	−	0.777579i	0.0942890	−	0.995545i	$-0.469942\pi$
$47$	7.33723	−	5.33081i	1.07025	−	0.777579i	0.975956	+	0.217966i	$0.0699422\pi$
$48$		0			0
$49$	11.7004			1.67149
$50$		0			0
$51$	2.32440			0.325481
$52$		0			0
$53$	7.20487	−	5.23465i	0.989665	−	0.719034i	0.0298175	−	0.999555i	$-0.490507\pi$
$53$	7.20487	−	5.23465i	0.989665	−	0.719034i	0.959848	+	0.280521i	$0.0905074\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−5.37899			−0.712464
$58$		0			0
$59$	−2.25351	+	6.93558i	−0.293382	+	0.902936i	0.690379	+	0.723448i	$0.257444\pi$
$59$	−2.25351	+	6.93558i	−0.293382	+	0.902936i	−0.983760	+	0.179487i	$0.942556\pi$
$60$		0			0
$61$	−1.48752	−	4.57810i	−0.190457	−	0.586166i	0.809543	−	0.587061i	$-0.199715\pi$
$61$	−1.48752	−	4.57810i	−0.190457	−	0.586166i	−1.00000		0.000895115i	$0.999715\pi$
$62$		0			0
$63$	−1.33631	+	4.11275i	−0.168359	+	0.518157i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−0.304195	−	0.221011i	−0.0371634	−	0.0270008i	0.569049	−	0.822304i	$-0.307312\pi$
$67$	−0.304195	−	0.221011i	−0.0371634	−	0.0270008i	−0.606212	+	0.795303i	$0.707312\pi$
$68$		0			0
$69$	−1.09875	−	0.798291i	−0.132274	−	0.0961030i
$70$		0			0
$71$	−8.54359	+	6.20729i	−1.01394	+	0.736669i	−0.965031	−	0.262134i	$-0.915574\pi$
$71$	−8.54359	+	6.20729i	−1.01394	+	0.736669i	−0.0489067	+	0.998803i	$0.515574\pi$
$72$		0			0
$73$	−0.0659364	−	0.202931i	−0.00771727	−	0.0237513i	0.947124	−	0.320869i	$-0.103975\pi$
$73$	−0.0659364	−	0.202931i	−0.00771727	−	0.0237513i	−0.954841	+	0.297117i	$0.903975\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.780801	−	2.40306i	−0.0889806	−	0.273854i
$78$		0			0
$79$	5.68410	−	4.12974i	0.639511	−	0.464632i	−0.220171	−	0.975461i	$-0.570661\pi$
$79$	5.68410	−	4.12974i	0.639511	−	0.464632i	0.859682	+	0.510829i	$0.170661\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		0			0
$83$	13.0343	+	9.46998i	1.43070	+	1.03946i	0.989886	+	0.141867i	$0.0453105\pi$
$83$	13.0343	+	9.46998i	1.43070	+	1.03946i	0.440815	+	0.897598i	$0.354690\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−0.218278	+	0.671790i	−0.0234018	+	0.0720235i
$88$		0			0
$89$	−4.33233	−	13.3335i	−0.459226	−	1.41335i	−0.866101	−	0.499869i	$-0.833382\pi$
$89$	−4.33233	−	13.3335i	−0.459226	−	1.41335i	0.406875	−	0.913484i	$-0.366618\pi$
$90$		0			0
$91$	1.29123	−	3.97399i	0.135357	−	0.416587i
$92$		0			0
$93$	8.48817			0.880182
$94$		0			0
$95$		0			0
$96$		0			0
$97$	12.7436	−	9.25880i	1.29392	−	0.940089i	0.294044	−	0.955792i	$-0.404999\pi$
$97$	12.7436	−	9.25880i	1.29392	−	0.940089i	0.999877	+	0.0157030i	$0.00499863\pi$
$98$		0			0
$99$	0.584296			0.0587239
$100$		0			0
$101$	7.14178			0.710634			0.355317	−	0.934746i	$-0.384373\pi$
$101$	7.14178			0.710634			0.355317	+	0.934746i	$0.384373\pi$
$102$		0			0
$103$	1.07238	−	0.779130i	0.105665	−	0.0767699i	−0.533698	−	0.845675i	$-0.679198\pi$
$103$	1.07238	−	0.779130i	0.105665	−	0.0767699i	0.639363	+	0.768905i	$0.279198\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−17.6796			−1.70915			−0.854573	−	0.519331i	$-0.826181\pi$
$107$	−17.6796			−1.70915			−0.854573	+	0.519331i	$0.826181\pi$
$108$		0			0
$109$	1.09385	−	3.36653i	0.104772	−	0.322455i	−0.884905	−	0.465772i	$-0.845777\pi$
$109$	1.09385	−	3.36653i	0.104772	−	0.322455i	0.989677	+	0.143317i	$0.0457768\pi$
$110$		0			0
$111$	1.89090	+	5.81960i	0.179476	+	0.552372i
$112$		0			0
$113$	−5.40414	+	16.6322i	−0.508379	+	1.56463i	0.286636	+	0.958039i	$0.407463\pi$
$113$	−5.40414	+	16.6322i	−0.508379	+	1.56463i	−0.795015	+	0.606590i	$0.792537\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.781722	+	0.567954i	0.0722702	+	0.0525074i
$118$		0			0
$119$	8.13192	+	5.90819i	0.745452	+	0.541603i
$120$		0			0
$121$	8.62299	−	6.26497i	0.783908	−	0.569542i
$122$		0			0
$123$	3.41820	+	10.5201i	0.308208	+	0.948568i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−5.40966	−	16.6492i	−0.480030	−	1.47738i	−0.839052	−	0.544051i	$-0.816890\pi$
$127$	−5.40966	−	16.6492i	−0.480030	−	1.47738i	0.359022	−	0.933329i	$-0.383110\pi$
$128$		0			0
$129$	−5.68800	+	4.13258i	−0.500801	+	0.363853i
$130$		0			0
$131$	15.2629	+	11.0892i	1.33353	+	0.968865i	0.999656	+	0.0262465i	$0.00835549\pi$
$131$	15.2629	+	11.0892i	1.33353	+	0.968865i	0.333872	+	0.942618i	$0.391645\pi$
$132$		0			0
$133$	−18.8184	−	13.6724i	−1.63177	−	1.18555i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.09472	+	12.6023i	−0.349836	+	1.07668i	0.609108	+	0.793087i	$0.291528\pi$
$137$	−4.09472	+	12.6023i	−0.349836	+	1.07668i	−0.958944	+	0.283596i	$0.908472\pi$
$138$		0			0
$139$	−5.22318	−	16.0753i	−0.443024	−	1.36349i	−0.884636	−	0.466283i	$-0.845593\pi$
$139$	−5.22318	−	16.0753i	−0.443024	−	1.36349i	0.441611	−	0.897206i	$-0.354407\pi$
$140$		0			0
$141$	−2.80257	+	8.62543i	−0.236019	+	0.726393i
$142$		0			0
$143$	−0.564582			−0.0472128
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−9.46582	+	6.87732i	−0.780728	+	0.567232i
$148$		0			0
$149$	12.1625			0.996388			0.498194	−	0.867066i	$-0.333997\pi$
$149$	12.1625			0.996388			0.498194	+	0.867066i	$0.333997\pi$
$150$		0			0
$151$	−9.84446			−0.801131			−0.400565	−	0.916268i	$-0.631186\pi$
$151$	−9.84446			−0.801131			−0.400565	+	0.916268i	$0.631186\pi$
$152$		0			0
$153$	−1.88048	+	1.36625i	−0.152027	+	0.110454i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	18.4804			1.47489			0.737447	−	0.675405i	$-0.236031\pi$
$157$	18.4804			1.47489			0.737447	+	0.675405i	$0.236031\pi$
$158$		0			0
$159$	−2.75202	+	8.46984i	−0.218249	+	0.671702i
$160$		0			0
$161$	−1.81489	−	5.58566i	−0.143033	−	0.440212i
$162$		0			0
$163$	4.49212	−	13.8253i	0.351850	−	1.08288i	−0.605964	−	0.795492i	$-0.707212\pi$
$163$	4.49212	−	13.8253i	0.351850	−	1.08288i	0.957814	−	0.287390i	$-0.0927876\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.63490	−	2.64091i	−0.281277	−	0.204360i	0.438197	−	0.898879i	$-0.355617\pi$
$167$	−3.63490	−	2.64091i	−0.281277	−	0.204360i	−0.719474	+	0.694519i	$0.755617\pi$
$168$		0			0
$169$	9.76187	+	7.09242i	0.750913	+	0.545570i
$170$		0			0
$171$	4.35169	−	3.16169i	0.332782	−	0.241780i
$172$		0			0
$173$	−0.617465	−	1.90036i	−0.0469450	−	0.144482i	0.924836	−	0.380365i	$-0.124202\pi$
$173$	−0.617465	−	1.90036i	−0.0469450	−	0.144482i	−0.971781	+	0.235883i	$0.924202\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−2.25351	−	6.93558i	−0.169384	−	0.521310i
$178$		0			0
$179$	−11.3095	+	8.21683i	−0.845312	+	0.614155i	−0.923849	−	0.382756i	$-0.874975\pi$
$179$	−11.3095	+	8.21683i	−0.845312	+	0.614155i	0.0785376	+	0.996911i	$0.474975\pi$
$180$		0			0
$181$	−10.9524	−	7.95740i	−0.814087	−	0.591469i	0.100926	−	0.994894i	$-0.467820\pi$
$181$	−10.9524	−	7.95740i	−0.814087	−	0.591469i	−0.915013	+	0.403425i	$0.867820\pi$
$182$		0			0
$183$	3.89437	+	2.82942i	0.287880	+	0.209157i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.419687	−	1.29166i	0.0306905	−	0.0944557i
$188$		0			0
$189$	−1.33631	−	4.11275i	−0.0972024	−	0.299158i
$190$		0			0
$191$	0.786594	−	2.42089i	0.0569160	−	0.175169i	−0.918557	−	0.395288i	$-0.870645\pi$
$191$	0.786594	−	2.42089i	0.0569160	−	0.175169i	0.975473	+	0.220119i	$0.0706446\pi$
$192$		0			0
$193$	−5.60541			−0.403486			−0.201743	−	0.979438i	$-0.564661\pi$
$193$	−5.60541			−0.403486			−0.201743	+	0.979438i	$0.564661\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−6.35580	+	4.61776i	−0.452832	+	0.329002i	−0.790713	−	0.612187i	$-0.790290\pi$
$197$	−6.35580	+	4.61776i	−0.452832	+	0.329002i	0.337881	+	0.941189i	$0.390290\pi$
$198$		0			0
$199$	16.9970			1.20489			0.602443	−	0.798162i	$-0.294194\pi$
$199$	16.9970			1.20489			0.602443	+	0.798162i	$0.294194\pi$
$200$		0			0
$201$	0.376006			0.0265214
$202$		0			0
$203$	−2.47122	+	1.79544i	−0.173445	+	0.126015i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.35813			0.0943969
$208$		0			0
$209$	−0.971215	+	2.98909i	−0.0671804	+	0.206760i
$210$		0			0
$211$	−4.00341	−	12.3212i	−0.275606	−	0.848229i	−0.989058	−	0.147525i	$-0.952869\pi$
$211$	−4.00341	−	12.3212i	−0.275606	−	0.848229i	0.713452	−	0.700704i	$-0.247131\pi$
$212$		0			0
$213$	3.26336	−	10.0436i	0.223602	−	0.688176i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	29.6959	+	21.5754i	2.01589	+	1.46463i
$218$		0			0
$219$	0.172624	+	0.125419i	0.0116648	+	0.00847500i
$220$		0			0
$221$	1.81703	−	1.32015i	0.122227	−	0.0888030i
$222$		0			0
$223$	−5.86518	−	18.0512i	−0.392761	−	1.20880i	−0.930691	−	0.365806i	$-0.880793\pi$
$223$	−5.86518	−	18.0512i	−0.392761	−	1.20880i	0.537930	−	0.842990i	$-0.319207\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.119005	+	0.366260i	0.00789865	+	0.0243095i	0.954928	−	0.296837i	$-0.0959318\pi$
$227$	0.119005	+	0.366260i	0.00789865	+	0.0243095i	−0.947030	+	0.321147i	$0.895932\pi$
$228$		0			0
$229$	−8.30740	+	6.03568i	−0.548968	+	0.398849i	−0.827405	−	0.561606i	$-0.810184\pi$
$229$	−8.30740	+	6.03568i	−0.548968	+	0.398849i	0.278437	+	0.960455i	$0.410184\pi$
$230$		0			0
$231$	2.04416	+	1.48517i	0.134496	+	0.0977172i
$232$		0			0
$233$	−17.5055	−	12.7185i	−1.14682	−	0.833217i	−0.158769	−	0.987316i	$-0.550753\pi$
$233$	−17.5055	−	12.7185i	−1.14682	−	0.833217i	−0.988055	+	0.154099i	$0.950753\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−2.17113	+	6.68206i	−0.141030	+	0.434047i
$238$		0			0
$239$	−2.38438	−	7.33836i	−0.154233	−	0.474679i	0.843850	−	0.536579i	$-0.180284\pi$
$239$	−2.38438	−	7.33836i	−0.154233	−	0.474679i	−0.998082	+	0.0619006i	$0.980284\pi$
$240$		0			0
$241$	−7.82629	+	24.0868i	−0.504136	+	1.55157i	0.298083	+	0.954540i	$0.403653\pi$
$241$	−7.82629	+	24.0868i	−0.504136	+	1.55157i	−0.802219	+	0.597030i	$0.796347\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−4.20487	+	3.05502i	−0.267550	+	0.194386i
$248$		0			0
$249$	−16.1113			−1.02101
$250$		0			0
$251$	−2.39913			−0.151432			−0.0757160	−	0.997129i	$-0.524124\pi$
$251$	−2.39913			−0.151432			−0.0757160	+	0.997129i	$0.524124\pi$
$252$		0			0
$253$	−0.641997	+	0.466438i	−0.0403620	+	0.0293247i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	14.3086			0.892548			0.446274	−	0.894896i	$-0.352751\pi$
$257$	14.3086			0.892548			0.446274	+	0.894896i	$0.352751\pi$
$258$		0			0
$259$	−8.17701	+	25.1662i	−0.508095	+	1.56375i
$260$		0			0
$261$	−0.218278	−	0.671790i	−0.0135111	−	0.0415828i
$262$		0			0
$263$	−4.04210	+	12.4403i	−0.249247	+	0.767103i	0.745662	+	0.666324i	$0.232133\pi$
$263$	−4.04210	+	12.4403i	−0.249247	+	0.767103i	−0.994909	+	0.100779i	$0.967867\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	11.3422	+	8.24058i	0.694131	+	0.504315i
$268$		0			0
$269$	−24.8165	−	18.0302i	−1.51309	−	1.09932i	−0.964783	−	0.263046i	$-0.915273\pi$
$269$	−24.8165	−	18.0302i	−1.51309	−	1.09932i	−0.548306	−	0.836278i	$-0.684727\pi$
$270$		0			0
$271$	−11.5174	+	8.36785i	−0.699629	+	0.508310i	−0.879811	−	0.475323i	$-0.842331\pi$
$271$	−11.5174	+	8.36785i	−0.699629	+	0.508310i	0.180182	+	0.983633i	$0.442331\pi$
$272$		0			0
$273$	1.29123	+	3.97399i	0.0781486	+	0.240517i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−6.22072	−	19.1454i	−0.373767	−	1.15034i	−0.944307	−	0.329066i	$-0.893266\pi$
$277$	−6.22072	−	19.1454i	−0.373767	−	1.15034i	0.570540	−	0.821270i	$-0.306734\pi$
$278$		0			0
$279$	−6.86707	+	4.98922i	−0.411121	+	0.298697i
$280$		0			0
$281$	7.94172	+	5.77000i	0.473763	+	0.344209i	0.798906	−	0.601456i	$-0.205412\pi$
$281$	7.94172	+	5.77000i	0.473763	+	0.344209i	−0.325143	+	0.945665i	$0.605412\pi$
$282$		0			0
$283$	5.29540	+	3.84733i	0.314779	+	0.228700i	0.733944	−	0.679210i	$-0.237677\pi$
$283$	5.29540	+	3.84733i	0.314779	+	0.228700i	−0.419166	+	0.907910i	$0.637677\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−14.7816	+	45.4932i	−0.872532	+	2.68538i
$288$		0			0
$289$	−3.58373	−	11.0296i	−0.210807	−	0.648799i
$290$		0			0
$291$	−4.86764	+	14.9811i	−0.285346	+	0.878205i
$292$		0			0
$293$	−0.869428			−0.0507925			−0.0253963	−	0.999677i	$-0.508085\pi$
$293$	−0.869428			−0.0507925			−0.0253963	+	0.999677i	$0.508085\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−0.472705	+	0.343440i	−0.0274291	+	0.0199284i
$298$		0			0
$299$	−1.31231			−0.0758930
$300$		0			0
$301$	−30.4038			−1.75244
$302$		0			0
$303$	−5.77782	+	4.19783i	−0.331927	+	0.241159i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−21.7261			−1.23997			−0.619986	−	0.784613i	$-0.712862\pi$
$307$	−21.7261			−1.23997			−0.619986	+	0.784613i	$0.712862\pi$
$308$		0			0
$309$	−0.409613	+	1.26066i	−0.0233021	+	0.0717163i
$310$		0			0
$311$	5.86610	+	18.0540i	0.332636	+	1.02375i	0.967875	+	0.251432i	$0.0809016\pi$
$311$	5.86610	+	18.0540i	0.332636	+	1.02375i	−0.635239	+	0.772316i	$0.719098\pi$
$312$		0			0
$313$	1.87947	−	5.78443i	0.106234	−	0.326955i	−0.883784	−	0.467895i	$-0.845012\pi$
$313$	1.87947	−	5.78443i	0.106234	−	0.326955i	0.990018	+	0.140940i	$0.0450125\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.60038	+	1.16274i	0.0898860	+	0.0653060i	0.631821	−	0.775115i	$-0.282308\pi$
$317$	1.60038	+	1.16274i	0.0898860	+	0.0653060i	−0.541935	+	0.840421i	$0.682308\pi$
$318$		0			0
$319$	0.333901	+	0.242593i	0.0186949	+	0.0135826i
$320$		0			0
$321$	14.3031	−	10.3918i	0.798319	−	0.580013i
$322$		0			0
$323$	−3.86361	−	11.8910i	−0.214977	−	0.661631i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	1.09385	+	3.36653i	0.0604901	+	0.186169i
$328$		0			0
$329$	−31.7291	+	23.0525i	−1.74928	+	1.27093i
$330$		0			0
$331$	10.6230	+	7.71805i	0.583892	+	0.424223i	0.840125	−	0.542393i	$-0.182481\pi$
$331$	10.6230	+	7.71805i	0.583892	+	0.424223i	−0.256233	+	0.966615i	$0.582481\pi$
$332$		0			0
$333$	−4.95044	−	3.59671i	−0.271283	−	0.197098i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−3.55245	+	10.9333i	−0.193514	+	0.595576i	0.806476	+	0.591266i	$0.201372\pi$
$337$	−3.55245	+	10.9333i	−0.193514	+	0.595576i	−0.999991	+	0.00430942i	$0.998628\pi$
$338$		0			0
$339$	−5.40414	−	16.6322i	−0.293513	−	0.903339i
$340$		0			0
$341$	1.53260	−	4.71686i	0.0829949	−	0.255432i
$342$		0			0
$343$	−20.3264			−1.09752
$344$		0			0
$345$		0			0
$346$		0			0
$347$	24.0905	−	17.5028i	1.29325	−	0.939599i	0.293381	−	0.955995i	$-0.405219\pi$
$347$	24.0905	−	17.5028i	1.29325	−	0.939599i	0.999866	+	0.0163966i	$0.00521942\pi$
$348$		0			0
$349$	10.0870			0.539946			0.269973	−	0.962868i	$-0.412985\pi$
$349$	10.0870			0.539946			0.269973	+	0.962868i	$0.412985\pi$
$350$		0			0
$351$	−0.966262			−0.0515752
$352$		0			0
$353$	−11.5382	+	8.38300i	−0.614117	+	0.446182i	−0.850862	−	0.525390i	$-0.823919\pi$
$353$	−11.5382	+	8.38300i	−0.614117	+	0.446182i	0.236745	+	0.971572i	$0.423919\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−10.0516			−0.531988
$358$		0			0
$359$	−2.04232	+	6.28562i	−0.107790	+	0.331742i	−0.990375	−	0.138410i	$-0.955801\pi$
$359$	−2.04232	+	6.28562i	−0.107790	+	0.331742i	0.882585	+	0.470152i	$0.155801\pi$
$360$		0			0
$361$	3.06962	+	9.44731i	0.161559	+	0.497227i
$362$		0			0
$363$	−3.29369	+	10.1369i	−0.172874	+	0.532051i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	7.72012	+	5.60900i	0.402987	+	0.292787i	0.770757	−	0.637130i	$-0.219878\pi$
$367$	7.72012	+	5.60900i	0.402987	+	0.292787i	−0.367770	+	0.929917i	$0.619878\pi$
$368$		0			0
$369$	−8.94895	−	6.50180i	−0.465864	−	0.338470i
$370$		0			0
$371$	−31.1567	+	22.6367i	−1.61758	+	1.17524i
$372$		0			0
$373$	0.402767	+	1.23959i	0.0208545	+	0.0641835i	0.960942	−	0.276749i	$-0.0892571\pi$
$373$	0.402767	+	1.23959i	0.0208545	+	0.0641835i	−0.940088	+	0.340933i	$0.889257\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.210914	+	0.649125i	0.0108626	+	0.0334317i
$378$		0			0
$379$	−19.6474	+	14.2747i	−1.00922	+	0.733240i	−0.964045	−	0.265739i	$-0.914384\pi$
$379$	−19.6474	+	14.2747i	−1.00922	+	0.733240i	−0.0451733	+	0.998979i	$0.514384\pi$
$380$		0			0
$381$	14.1627	+	10.2898i	0.725576	+	0.527162i
$382$		0			0
$383$	9.81489	+	7.13094i	0.501518	+	0.364374i	0.809596	−	0.586987i	$-0.199686\pi$
$383$	9.81489	+	7.13094i	0.501518	+	0.364374i	−0.308079	+	0.951361i	$0.599686\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.17262	−	6.68665i	0.110441	−	0.339901i
$388$		0			0
$389$	−9.04178	−	27.8278i	−0.458437	−	1.41092i	−0.867053	−	0.498217i	$-0.833988\pi$
$389$	−9.04178	−	27.8278i	−0.458437	−	1.41092i	0.408616	−	0.912706i	$-0.366012\pi$
$390$		0			0
$391$	0.975518	−	3.00234i	0.0493341	−	0.151835i
$392$		0			0
$393$	−18.8660			−0.951664
$394$		0			0
$395$		0			0
$396$		0			0
$397$	5.09179	−	3.69940i	0.255550	−	0.185668i	−0.452633	−	0.891697i	$-0.649515\pi$
$397$	5.09179	−	3.69940i	0.255550	−	0.185668i	0.708183	+	0.706029i	$0.249515\pi$
$398$		0			0
$399$	23.2609			1.16450
$400$		0			0
$401$	30.3064			1.51343			0.756714	−	0.653747i	$-0.226804\pi$
$401$	30.3064			1.51343			0.756714	+	0.653747i	$0.226804\pi$
$402$		0			0
$403$	6.63539	−	4.82089i	0.330532	−	0.240146i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.57536			0.177224
$408$		0			0
$409$	5.70942	−	17.5718i	0.282313	−	0.868870i	−0.704878	−	0.709328i	$-0.748998\pi$
$409$	5.70942	−	17.5718i	0.282313	−	0.868870i	0.987191	−	0.159541i	$-0.0510015\pi$
$410$		0			0
$411$	−4.09472	−	12.6023i	−0.201978	−	0.621623i
$412$		0			0
$413$	9.74505	−	29.9922i	0.479523	−	1.47582i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	13.6745	+	9.93508i	0.669641	+	0.486523i
$418$		0			0
$419$	18.1586	+	13.1930i	0.887108	+	0.644522i	0.935122	−	0.354325i	$-0.115289\pi$
$419$	18.1586	+	13.1930i	0.887108	+	0.644522i	−0.0480143	+	0.998847i	$0.515289\pi$
$420$		0			0
$421$	5.05679	−	3.67397i	0.246453	−	0.179058i	−0.457700	−	0.889106i	$-0.651327\pi$
$421$	5.05679	−	3.67397i	0.246453	−	0.179058i	0.704153	+	0.710048i	$0.251327\pi$
$422$		0			0
$423$	−2.80257	−	8.62543i	−0.136266	−	0.419383i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	6.43260	+	19.7975i	0.311296	+	0.958069i
$428$		0			0
$429$	0.456757	−	0.331853i	0.0220524	−	0.0160220i
$430$		0			0
$431$	−27.9850	−	20.3323i	−1.34799	−	0.979373i	−0.999109	−	0.0422061i	$-0.986561\pi$
$431$	−27.9850	−	20.3323i	−1.34799	−	0.979373i	−0.348882	−	0.937167i	$-0.613439\pi$
$432$		0			0
$433$	−3.18056	−	2.31081i	−0.152848	−	0.111050i	0.508733	−	0.860924i	$-0.330114\pi$
$433$	−3.18056	−	2.31081i	−0.152848	−	0.111050i	−0.661581	+	0.749874i	$0.730114\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.25749	+	6.94784i	−0.107990	+	0.332360i
$438$		0			0
$439$	1.54170	+	4.74487i	0.0735815	+	0.226460i	0.981083	−	0.193589i	$-0.0620128\pi$
$439$	1.54170	+	4.74487i	0.0735815	+	0.226460i	−0.907501	+	0.420049i	$0.862013\pi$
$440$		0			0
$441$	3.61562	−	11.1277i	0.172173	−	0.529893i
$442$		0			0
$443$	−9.92754			−0.471672			−0.235836	−	0.971793i	$-0.575783\pi$
$443$	−9.92754			−0.471672			−0.235836	+	0.971793i	$0.575783\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−9.83964	+	7.14892i	−0.465399	+	0.338132i
$448$		0			0
$449$	9.87365			0.465966			0.232983	−	0.972481i	$-0.425151\pi$
$449$	9.87365			0.465966			0.232983	+	0.972481i	$0.425151\pi$
$450$		0			0
$451$	6.46320			0.304340
$452$		0			0
$453$	7.96433	−	5.78643i	0.374197	−	0.271870i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−12.6424			−0.591387			−0.295693	−	0.955283i	$-0.595551\pi$
$457$	−12.6424			−0.591387			−0.295693	+	0.955283i	$0.595551\pi$
$458$		0			0
$459$	0.718278	−	2.21063i	0.0335263	−	0.103183i
$460$		0			0
$461$	12.2911	+	37.8280i	0.572452	+	1.76183i	0.644697	+	0.764438i	$0.276984\pi$
$461$	12.2911	+	37.8280i	0.572452	+	1.76183i	−0.0722451	+	0.997387i	$0.523016\pi$
$462$		0			0
$463$	−1.36545	+	4.20242i	−0.0634578	+	0.195303i	−0.977759	−	0.209732i	$-0.932741\pi$
$463$	−1.36545	+	4.20242i	−0.0634578	+	0.195303i	0.914301	+	0.405035i	$0.132741\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−9.12137	−	6.62706i	−0.422086	−	0.306664i	0.356390	−	0.934337i	$-0.384007\pi$
$467$	−9.12137	−	6.62706i	−0.422086	−	0.306664i	−0.778477	+	0.627673i	$0.784007\pi$
$468$		0			0
$469$	1.31546	+	0.955738i	0.0607423	+	0.0441319i
$470$		0			0
$471$	−14.9509	+	10.8625i	−0.688902	+	0.500517i
$472$		0			0
$473$	1.26945	+	3.90698i	0.0583696	+	0.179643i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−2.75202	−	8.46984i	−0.126006	−	0.387807i
$478$		0			0
$479$	4.49728	−	3.26747i	0.205486	−	0.149294i	−0.480283	−	0.877114i	$-0.659466\pi$
$479$	4.49728	−	3.26747i	0.205486	−	0.149294i	0.685769	+	0.727819i	$0.259466\pi$
$480$		0			0
$481$	4.78343	+	3.47536i	0.218105	+	0.158463i
$482$		0			0
$483$	4.75145	+	3.45213i	0.216198	+	0.157077i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	5.14021	−	15.8199i	0.232925	−	0.716870i	−0.764465	−	0.644665i	$-0.776997\pi$
$487$	5.14021	−	15.8199i	0.232925	−	0.716870i	0.997390	−	0.0722042i	$-0.0230033\pi$
$488$		0			0
$489$	4.49212	+	13.8253i	0.203141	+	0.625202i
$490$		0			0
$491$	0.327326	−	1.00741i	0.0147720	−	0.0454636i	−0.943399	−	0.331661i	$-0.892391\pi$
$491$	0.327326	−	1.00741i	0.0147720	−	0.0454636i	0.958171	+	0.286197i	$0.0923912\pi$
$492$		0			0
$493$	−1.64187			−0.0739459
$494$		0			0
$495$		0			0
$496$		0			0
$497$	36.9459	−	26.8428i	1.65725	−	1.20406i
$498$		0			0
$499$	24.9700			1.11781			0.558906	−	0.829231i	$-0.311221\pi$
$499$	24.9700			1.11781			0.558906	+	0.829231i	$0.311221\pi$
$500$		0			0
$501$	4.49299			0.200732
$502$		0			0
$503$	10.1502	−	7.37458i	0.452576	−	0.328816i	−0.338036	−	0.941133i	$-0.609762\pi$
$503$	10.1502	−	7.37458i	0.452576	−	0.328816i	0.790612	+	0.612317i	$0.209762\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−12.0663			−0.535885
$508$		0			0
$509$	−4.76735	+	14.6724i	−0.211309	+	0.650342i	0.788086	+	0.615565i	$0.211072\pi$
$509$	−4.76735	+	14.6724i	−0.211309	+	0.650342i	−0.999395	+	0.0347770i	$0.988928\pi$
$510$		0			0
$511$	0.285135	+	0.877556i	0.0126136	+	0.0388208i
$512$		0			0
$513$	−1.66220	+	5.11572i	−0.0733878	+	0.225865i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	4.28711	+	3.11477i	0.188547	+	0.136987i
$518$		0			0
$519$	1.61654	+	1.17449i	0.0709584	+	0.0515543i
$520$		0			0
$521$	15.6466	−	11.3679i	0.685490	−	0.498037i	−0.189685	−	0.981845i	$-0.560747\pi$
$521$	15.6466	−	11.3679i	0.685490	−	0.498037i	0.875174	+	0.483808i	$0.160747\pi$
$522$		0			0
$523$	−2.14779	−	6.61022i	−0.0939163	−	0.289045i	0.893053	−	0.449951i	$-0.148558\pi$
$523$	−2.14779	−	6.61022i	−0.0939163	−	0.289045i	−0.986970	+	0.160906i	$0.948558\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.09686	+	18.7642i	0.265583	+	0.817382i
$528$		0			0
$529$	17.1151	−	12.4349i	0.744136	−	0.540647i
$530$		0			0
$531$	5.89976	+	4.28642i	0.256028	+	0.186015i
$532$		0			0
$533$	8.64703	+	6.28244i	0.374545	+	0.272123i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	4.31984	−	13.2951i	0.186415	−	0.573727i
$538$		0			0
$539$	2.11259	+	6.50189i	0.0909958	+	0.280056i
$540$		0			0
$541$	1.75145	−	5.39040i	0.0753006	−	0.231751i	−0.906321	−	0.422590i	$-0.861121\pi$
$541$	1.75145	−	5.39040i	0.0753006	−	0.231751i	0.981621	+	0.190839i	$0.0611209\pi$
$542$		0			0
$543$	13.5379			0.580968
$544$		0			0
$545$		0			0
$546$		0			0
$547$	10.0315	−	7.28835i	0.428918	−	0.311627i	−0.352298	−	0.935888i	$-0.614600\pi$
$547$	10.0315	−	7.28835i	0.428918	−	0.311627i	0.781216	+	0.624261i	$0.214600\pi$
$548$		0			0
$549$	−4.81370			−0.205444
$550$		0			0
$551$	3.79951			0.161865
$552$		0			0
$553$	−24.5803	+	17.8586i	−1.04526	+	0.759427i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−24.8970			−1.05492			−0.527461	−	0.849579i	$-0.676856\pi$
$557$	−24.8970			−1.05492			−0.527461	+	0.849579i	$0.676856\pi$
$558$		0			0
$559$	−2.09932	+	6.46105i	−0.0887919	+	0.273273i
$560$		0			0
$561$	0.419687	+	1.29166i	0.0177192	+	0.0545340i
$562$		0			0
$563$	7.73423	−	23.8035i	0.325959	−	1.00320i	−0.645047	−	0.764143i	$-0.723162\pi$
$563$	7.73423	−	23.8035i	0.325959	−	1.00320i	0.971006	−	0.239055i	$-0.0768377\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	3.49851	+	2.54182i	0.146924	+	0.106746i
$568$		0			0
$569$	−1.69282	−	1.22991i	−0.0709669	−	0.0515605i	0.551736	−	0.834019i	$-0.313966\pi$
$569$	−1.69282	−	1.22991i	−0.0709669	−	0.0515605i	−0.622703	+	0.782458i	$0.713966\pi$
$570$		0			0
$571$	9.32956	−	6.77832i	0.390430	−	0.283664i	−0.375202	−	0.926943i	$-0.622427\pi$
$571$	9.32956	−	6.77832i	0.390430	−	0.283664i	0.765632	+	0.643279i	$0.222427\pi$
$572$		0			0
$573$	0.786594	+	2.42089i	0.0328604	+	0.101134i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	1.80625	+	5.55908i	0.0751954	+	0.231427i	0.981589	−	0.191007i	$-0.0611755\pi$
$577$	1.80625	+	5.55908i	0.0751954	+	0.231427i	−0.906393	+	0.422435i	$0.861175\pi$
$578$		0			0
$579$	4.53487	−	3.29478i	0.188463	−	0.136926i
$580$		0			0
$581$	−56.3655	−	40.9519i	−2.33843	−	1.69897i
$582$		0			0
$583$	4.20978	+	3.05858i	0.174351	+	0.126673i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	2.84381	−	8.75234i	0.117377	−	0.361248i	−0.875059	−	0.484017i	$-0.839177\pi$
$587$	2.84381	−	8.75234i	0.117377	−	0.361248i	0.992435	+	0.122769i	$0.0391774\pi$
$588$		0			0
$589$	−14.1090	−	43.4231i	−0.581352	−	1.78922i
$590$		0			0
$591$	2.42770	−	7.47170i	0.0998623	−	0.307345i
$592$		0			0
$593$	14.9033			0.612004			0.306002	−	0.952031i	$-0.401009\pi$
$593$	14.9033			0.612004			0.306002	+	0.952031i	$0.401009\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−13.7509	+	9.99060i	−0.562786	+	0.408888i
$598$		0			0
$599$	−7.52244			−0.307359			−0.153679	−	0.988121i	$-0.549112\pi$
$599$	−7.52244			−0.307359			−0.153679	+	0.988121i	$0.549112\pi$
$600$		0			0
$601$	18.6618			0.761232			0.380616	−	0.924733i	$-0.375712\pi$
$601$	18.6618			0.761232			0.380616	+	0.924733i	$0.375712\pi$
$602$		0			0
$603$	−0.304195	+	0.221011i	−0.0123878	+	0.00900025i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−0.810016			−0.0328776			−0.0164388	−	0.999865i	$-0.505233\pi$
$607$	−0.810016			−0.0328776			−0.0164388	+	0.999865i	$0.505233\pi$
$608$		0			0
$609$	0.943920	−	2.90509i	0.0382496	−	0.117720i
$610$		0			0
$611$	2.70802	+	8.33443i	0.109555	+	0.337175i
$612$		0			0
$613$	−1.54232	+	4.74678i	−0.0622938	+	0.191721i	−0.977360	−	0.211583i	$-0.932138\pi$
$613$	−1.54232	+	4.74678i	−0.0622938	+	0.191721i	0.915066	+	0.403304i	$0.132138\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−34.4722	−	25.0455i	−1.38780	−	1.00829i	−0.996103	−	0.0881990i	$-0.971889\pi$
$617$	−34.4722	−	25.0455i	−1.38780	−	1.00829i	−0.391695	−	0.920095i	$-0.628111\pi$
$618$		0			0
$619$	−29.9038	−	21.7264i	−1.20193	−	0.873257i	−0.207461	−	0.978243i	$-0.566520\pi$
$619$	−29.9038	−	21.7264i	−1.20193	−	0.873257i	−0.994474	+	0.104987i	$0.966520\pi$
$620$		0			0
$621$	−1.09875	+	0.798291i	−0.0440915	+	0.0320343i
$622$		0			0
$623$	18.7347	+	57.6595i	0.750590	+	2.31008i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−0.971215	−	2.98909i	−0.0387866	−	0.119373i
$628$		0			0
$629$	−11.5068	+	8.36018i	−0.458806	+	0.333342i
$630$		0			0
$631$	26.8891	+	19.5361i	1.07044	+	0.777719i	0.975991	−	0.217811i	$-0.0698915\pi$
$631$	26.8891	+	19.5361i	1.07044	+	0.777719i	0.0944476	+	0.995530i	$0.469892\pi$
$632$		0			0
$633$	10.4811	+	7.61494i	0.416585	+	0.302667i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−3.49364	+	10.7523i	−0.138423	+	0.426022i
$638$		0			0
$639$	3.26336	+	10.0436i	0.129097	+	0.397319i
$640$		0			0
$641$	−8.41649	+	25.9033i	−0.332431	+	1.02312i	0.635542	+	0.772066i	$0.280777\pi$
$641$	−8.41649	+	25.9033i	−0.332431	+	1.02312i	−0.967974	+	0.251052i	$0.919223\pi$
$642$		0			0
$643$	12.8557			0.506978			0.253489	−	0.967338i	$-0.418422\pi$
$643$	12.8557			0.506978			0.253489	+	0.967338i	$0.418422\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	25.7597	−	18.7155i	1.01272	−	0.735784i	0.0479418	−	0.998850i	$-0.484734\pi$
$647$	25.7597	−	18.7155i	1.01272	−	0.735784i	0.964778	+	0.263066i	$0.0847338\pi$
$648$		0			0
$649$	−4.26098			−0.167258
$650$		0			0
$651$	−36.7062			−1.43863
$652$		0			0
$653$	−11.7323	+	8.52402i	−0.459121	+	0.333571i	−0.793186	−	0.608979i	$-0.791579\pi$
$653$	−11.7323	+	8.52402i	−0.459121	+	0.333571i	0.334066	+	0.942550i	$0.391579\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−0.213375			−0.00832454
$658$		0			0
$659$	10.2713	−	31.6118i	0.400113	−	1.23142i	−0.524795	−	0.851229i	$-0.675858\pi$
$659$	10.2713	−	31.6118i	0.400113	−	1.23142i	0.924908	−	0.380192i	$-0.124142\pi$
$660$		0			0
$661$	−9.84316	−	30.2941i	−0.382854	−	1.17830i	−0.938025	−	0.346568i	$-0.887347\pi$
$661$	−9.84316	−	30.2941i	−0.382854	−	1.17830i	0.555170	−	0.831737i	$-0.312653\pi$
$662$		0			0
$663$	−0.694044	+	2.13605i	−0.0269545	+	0.0829573i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.776118	+	0.563883i	0.0300514	+	0.0218336i
$668$		0			0
$669$	15.3552	+	11.1562i	0.593668	+	0.431325i
$670$		0			0
$671$	2.27546	−	1.65322i	0.0878432	−	0.0638218i
$672$		0			0
$673$	8.09358	+	24.9095i	0.311985	+	0.960190i	0.976978	+	0.213341i	$0.0684344\pi$
$673$	8.09358	+	24.9095i	0.311985	+	0.960190i	−0.664993	+	0.746849i	$0.731566\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	4.58711	+	14.1177i	0.176297	+	0.542586i	0.999690	−	0.0248849i	$-0.00792192\pi$
$677$	4.58711	+	14.1177i	0.176297	+	0.542586i	−0.823393	+	0.567471i	$0.807922\pi$
$678$		0			0
$679$	−55.1086	+	40.0387i	−2.11487	+	1.53655i
$680$		0			0
$681$	−0.311560	−	0.226361i	−0.0119390	−	0.00867418i
$682$		0			0
$683$	−4.55174	−	3.30703i	−0.174168	−	0.126540i	0.497286	−	0.867586i	$-0.334330\pi$
$683$	−4.55174	−	3.30703i	−0.174168	−	0.126540i	−0.671454	+	0.741046i	$0.734330\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	3.17314	−	9.76593i	0.121063	−	0.372593i
$688$		0			0
$689$	2.65917	+	8.18408i	0.101306	+	0.311788i
$690$		0			0
$691$	10.6330	−	32.7249i	0.404497	−	1.24492i	−0.516817	−	0.856096i	$-0.672883\pi$
$691$	10.6330	−	32.7249i	0.404497	−	1.24492i	0.921314	−	0.388819i	$-0.127117\pi$
$692$		0			0
$693$	−2.52673			−0.0959824
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−20.8009	+	15.1128i	−0.787891	+	0.572436i
$698$		0			0
$699$	21.6380			0.818425
$700$		0			0
$701$	8.86294			0.334749			0.167374	−	0.985893i	$-0.446471\pi$
$701$	8.86294			0.334749			0.167374	+	0.985893i	$0.446471\pi$
$702$		0			0
$703$	26.6284	−	19.3466i	1.00431	−	0.729673i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−30.8839			−1.16151
$708$		0			0
$709$	0.474877	−	1.46152i	0.0178344	−	0.0548885i	−0.941743	−	0.336333i	$-0.890813\pi$
$709$	0.474877	−	1.46152i	0.0178344	−	0.0548885i	0.959578	+	0.281444i	$0.0908134\pi$
$710$		0			0
$711$	−2.17113	−	6.68206i	−0.0814239	−	0.250597i
$712$		0			0
$713$	3.56237	−	10.9638i	0.133412	−	0.410599i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	6.24238	+	4.53535i	0.233126	+	0.169376i
$718$		0			0
$719$	15.4808	+	11.2474i	0.577335	+	0.419459i	0.837762	−	0.546035i	$-0.183863\pi$
$719$	15.4808	+	11.2474i	0.577335	+	0.419459i	−0.260427	+	0.965493i	$0.583863\pi$
$720$		0			0
$721$	−4.63740	+	3.36926i	−0.172706	+	0.125478i
$722$		0			0
$723$	−7.82629	−	24.0868i	−0.291063	−	0.895799i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−14.4649	−	44.5184i	−0.536474	−	1.65110i	−0.740443	−	0.672119i	$-0.765384\pi$
$727$	−14.4649	−	44.5184i	−0.536474	−	1.65110i	0.203970	−	0.978977i	$-0.434616\pi$
$728$		0			0
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$		0			0
$731$	−13.2212	−	9.60574i	−0.489003	−	0.355281i
$732$		0			0
$733$	41.2634	+	29.9796i	1.52410	+	1.10732i	0.959409	+	0.282019i	$0.0910042\pi$
$733$	41.2634	+	29.9796i	1.52410	+	1.10732i	0.564690	+	0.825303i	$0.308996\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.0678906	−	0.208946i	0.00250078	−	0.00769662i
$738$		0			0
$739$	4.08075	+	12.5592i	0.150113	+	0.461999i	0.997633	−	0.0687637i	$-0.0219054\pi$
$739$	4.08075	+	12.5592i	0.150113	+	0.461999i	−0.847520	+	0.530763i	$0.821905\pi$
$740$		0			0
$741$	1.60612	−	4.94312i	0.0590022	−	0.181590i
$742$		0			0
$743$	−10.6063			−0.389107			−0.194553	−	0.980892i	$-0.562326\pi$
$743$	−10.6063			−0.389107			−0.194553	+	0.980892i	$0.562326\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	13.0343	−	9.46998i	0.476900	−	0.346488i
$748$		0			0
$749$	76.4534			2.79355
$750$		0			0
$751$	28.2581			1.03115			0.515577	−	0.856843i	$-0.327578\pi$
$751$	28.2581			1.03115			0.515577	+	0.856843i	$0.327578\pi$
$752$		0			0
$753$	1.94094	−	1.41018i	0.0707318	−	0.0513897i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−27.7474			−1.00849			−0.504247	−	0.863559i	$-0.668230\pi$
$757$	−27.7474			−1.00849			−0.504247	+	0.863559i	$0.668230\pi$
$758$		0			0
$759$	0.245221	−	0.754713i	0.00890096	−	0.0273943i
$760$		0			0
$761$	−4.97988	−	15.3265i	−0.180521	−	0.555585i	0.819322	−	0.573334i	$-0.194350\pi$
$761$	−4.97988	−	15.3265i	−0.180521	−	0.555585i	−0.999842	+	0.0177487i	$0.994350\pi$
$762$		0			0
$763$	−4.73024	+	14.5582i	−0.171246	+	0.527042i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−5.70071	−	4.14181i	−0.205841	−	0.149552i
$768$		0			0
$769$	28.1081	+	20.4217i	1.01360	+	0.736426i	0.964962	−	0.262390i	$-0.0845108\pi$
$769$	28.1081	+	20.4217i	1.01360	+	0.736426i	0.0486417	+	0.998816i	$0.484511\pi$
$770$		0			0
$771$	−11.5759	+	8.41040i	−0.416897	+	0.302893i
$772$		0			0
$773$	−7.25215	−	22.3198i	−0.260842	−	0.802788i	−0.992622	−	0.121248i	$-0.961310\pi$
$773$	−7.25215	−	22.3198i	−0.260842	−	0.802788i	0.731781	−	0.681540i	$-0.238690\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−8.17701	−	25.1662i	−0.293349	−	0.902834i
$778$		0			0
$779$	48.1363	−	34.9731i	1.72466	−	1.25304i
$780$		0			0
$781$	−4.99199	−	3.62689i	−0.178627	−	0.129780i
$782$		0			0
$783$	0.571459	+	0.415189i	0.0204223	+	0.0148377i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	7.91755	−	24.3677i	0.282230	−	0.868615i	−0.704985	−	0.709222i	$-0.749046\pi$
$787$	7.91755	−	24.3677i	0.282230	−	0.868615i	0.987215	−	0.159393i	$-0.0509536\pi$
$788$		0			0
$789$	−4.04210	−	12.4403i	−0.143903	−	0.442887i
$790$		0			0
$791$	23.3696	−	71.9244i	0.830929	−	2.55734i
$792$		0			0
$793$	4.65129			0.165172
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.55577	+	1.13034i	−0.0551083	+	0.0400386i	−0.614998	−	0.788528i	$-0.710843\pi$
$797$	−1.55577	+	1.13034i	−0.0551083	+	0.0400386i	0.559890	+	0.828567i	$0.310843\pi$
$798$		0			0
$799$	−21.0807			−0.745781
$800$		0			0
$801$	−14.0197			−0.495362
$802$		0			0
$803$	0.100863	−	0.0732815i	0.00355939	−	0.00258605i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	30.6749			1.07981
$808$		0			0
$809$	−14.0321	+	43.1862i	−0.493341	+	1.51835i	0.326185	+	0.945306i	$0.394237\pi$
$809$	−14.0321	+	43.1862i	−0.493341	+	1.51835i	−0.819526	+	0.573041i	$0.805763\pi$
$810$		0			0
$811$	−7.39190	−	22.7499i	−0.259565	−	0.798858i	−0.992896	−	0.118987i	$-0.962035\pi$
$811$	−7.39190	−	22.7499i	−0.259565	−	0.798858i	0.733331	−	0.679872i	$-0.237965\pi$
$812$		0			0
$813$	4.39924	−	13.5395i	0.154288	−	0.474850i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	30.5957	+	22.2291i	1.07041	+	0.777697i
$818$		0			0
$819$	−3.38048	−	2.45606i	−0.118123	−	0.0858217i
$820$		0			0
$821$	25.5538	−	18.5659i	0.891834	−	0.647955i	−0.0445216	−	0.999008i	$-0.514176\pi$
$821$	25.5538	−	18.5659i	0.891834	−	0.647955i	0.936356	+	0.351053i	$0.114176\pi$
$822$		0			0
$823$	−2.63669	−	8.11491i	−0.0919094	−	0.282868i	0.894527	−	0.447015i	$-0.147513\pi$
$823$	−2.63669	−	8.11491i	−0.0919094	−	0.282868i	−0.986436	+	0.164147i	$0.947513\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−5.49842	−	16.9224i	−0.191199	−	0.588450i	−1.00000		0.000367397i	$-0.999883\pi$
$827$	−5.49842	−	16.9224i	−0.191199	−	0.588450i	0.808801	−	0.588082i	$-0.200117\pi$
$828$		0			0
$829$	37.2323	−	27.0508i	1.29313	−	0.939515i	0.293267	−	0.956030i	$-0.405257\pi$
$829$	37.2323	−	27.0508i	1.29313	−	0.939515i	0.999864	+	0.0165158i	$0.00525737\pi$
$830$		0			0
$831$	16.2861	+	11.8325i	0.564957	+	0.410465i
$832$		0			0
$833$	−22.0023	−	15.9856i	−0.762335	−	0.553869i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	2.62299	−	8.07273i	0.0906637	−	0.279034i
$838$		0			0
$839$	0.312751	+	0.962548i	0.0107974	+	0.0332308i	0.956310	−	0.292354i	$-0.0944387\pi$
$839$	0.312751	+	0.962548i	0.0107974	+	0.0332308i	−0.945513	+	0.325585i	$0.894439\pi$
$840$		0			0
$841$	−8.80731	+	27.1061i	−0.303700	+	0.934694i
$842$		0			0
$843$	−9.81651			−0.338099
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−37.2892	+	27.0922i	−1.28127	+	0.930899i
$848$		0			0
$849$	−6.54547			−0.224640
$850$		0			0
$851$	8.31054			0.284882
$852$		0			0
$853$	−7.93916	+	5.76813i	−0.271832	+	0.197497i	−0.715347	−	0.698770i	$-0.753731\pi$
$853$	−7.93916	+	5.76813i	−0.271832	+	0.197497i	0.443515	+	0.896267i	$0.353731\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	57.3424			1.95878			0.979390	−	0.201979i	$-0.0647372\pi$
$857$	57.3424			1.95878			0.979390	+	0.201979i	$0.0647372\pi$
$858$		0			0
$859$	3.31727	−	10.2095i	0.113184	−	0.348344i	−0.878380	−	0.477963i	$-0.841375\pi$
$859$	3.31727	−	10.2095i	0.113184	−	0.348344i	0.991564	+	0.129619i	$0.0413754\pi$
$860$		0			0
$861$	−14.7816	−	45.4932i	−0.503757	−	1.55040i
$862$		0			0
$863$	−2.97661	+	9.16105i	−0.101325	+	0.311846i	−0.988850	−	0.148913i	$-0.952423\pi$
$863$	−2.97661	+	9.16105i	−0.101325	+	0.311846i	0.887525	+	0.460759i	$0.152423\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	9.38232	+	6.81665i	0.318640	+	0.231506i
$868$		0			0
$869$	3.32120	+	2.41299i	0.112664	+	0.0818551i
$870$		0			0
$871$	0.293932	−	0.213554i	0.00995951	−	0.00723601i
$872$		0			0
$873$	−4.86764	−	14.9811i	−0.164745	−	0.507032i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.217491	+	0.669370i	0.00734416	+	0.0226030i	0.954661	−	0.297694i	$-0.0962174\pi$
$877$	0.217491	+	0.669370i	0.00734416	+	0.0226030i	−0.947317	+	0.320297i	$0.896217\pi$
$878$		0			0
$879$	0.703382	−	0.511037i	0.0237245	−	0.0172369i
$880$		0			0
$881$	−8.03076	−	5.83469i	−0.270563	−	0.196576i	0.444228	−	0.895914i	$-0.353478\pi$
$881$	−8.03076	−	5.83469i	−0.270563	−	0.196576i	−0.714791	+	0.699338i	$0.753478\pi$
$882$		0			0
$883$	13.6241	+	9.89850i	0.458488	+	0.333111i	0.792938	−	0.609302i	$-0.208550\pi$
$883$	13.6241	+	9.89850i	0.458488	+	0.333111i	−0.334450	+	0.942414i	$0.608550\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−14.3358	+	44.1212i	−0.481351	+	1.48144i	0.355847	+	0.934544i	$0.384192\pi$
$887$	−14.3358	+	44.1212i	−0.481351	+	1.48144i	−0.837198	+	0.546901i	$0.815808\pi$
$888$		0			0
$889$	23.3935	+	71.9979i	0.784594	+	2.41473i
$890$		0			0
$891$	0.180557	−	0.555698i	0.00604890	−	0.0186166i
$892$		0			0
$893$	48.7837			1.63249
$894$		0			0
$895$		0			0
$896$		0			0
$897$	1.06168	−	0.771358i	0.0354486	−	0.0257549i
$898$		0			0
$899$	−5.99572			−0.199968
$900$		0			0
$901$	−20.7004			−0.689630
$902$		0			0
$903$	24.5972	−	17.8709i	0.818543	−	0.594706i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−28.5101			−0.946662			−0.473331	−	0.880885i	$-0.656949\pi$
$907$	−28.5101			−0.946662			−0.473331	+	0.880885i	$0.656949\pi$
$908$		0			0
$909$	2.20693	−	6.79224i	0.0731993	−	0.225284i
$910$		0			0
$911$	−2.00884	−	6.18256i	−0.0665557	−	0.204837i	0.912248	−	0.409639i	$-0.134345\pi$
$911$	−2.00884	−	6.18256i	−0.0665557	−	0.204837i	−0.978804	+	0.204801i	$0.934345\pi$
$912$		0			0
$913$	−2.90901	+	8.95301i	−0.0962742	+	0.296301i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−66.0029	−	47.9539i	−2.17961	−	1.58358i
$918$		0			0
$919$	−13.6130	−	9.89041i	−0.449051	−	0.326255i	0.340170	−	0.940364i	$-0.389515\pi$
$919$	−13.6130	−	9.89041i	−0.449051	−	0.326255i	−0.789221	+	0.614109i	$0.789515\pi$
$920$		0			0
$921$	17.5768	−	12.7703i	0.579174	−	0.420795i
$922$		0			0
$923$	−3.15326	−	9.70474i	−0.103791	−	0.319436i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−0.409613	−	1.26066i	−0.0134534	−	0.0414054i
$928$		0			0
$929$	25.5979	−	18.5979i	0.839839	−	0.610179i	−0.0824866	−	0.996592i	$-0.526286\pi$
$929$	25.5979	−	18.5979i	0.839839	−	0.610179i	0.922326	+	0.386413i	$0.126286\pi$
$930$		0			0
$931$	50.9165	+	36.9930i	1.66872	+	1.21240i
$932$		0			0
$933$	−15.3576	−	11.1580i	−0.502787	−	0.365296i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	0.726513	−	2.23598i	0.0237341	−	0.0730462i	−0.938488	−	0.345312i	$-0.887773\pi$
$937$	0.726513	−	2.23598i	0.0237341	−	0.0730462i	0.962222	+	0.272266i	$0.0877731\pi$
$938$		0			0
$939$	1.87947	+	5.78443i	0.0613343	+	0.188768i
$940$		0			0
$941$	1.32816	−	4.08766i	0.0432968	−	0.133254i	−0.927071	−	0.374885i	$-0.877682\pi$
$941$	1.32816	−	4.08766i	0.0432968	−	0.133254i	0.970368	+	0.241631i	$0.0776823\pi$
$942$		0			0
$943$	15.0230			0.489217
$944$		0			0
$945$		0			0
$946$		0			0
$947$	22.5245	−	16.3650i	0.731948	−	0.531791i	−0.158231	−	0.987402i	$-0.550579\pi$
$947$	22.5245	−	16.3650i	0.731948	−	0.531791i	0.890179	+	0.455611i	$0.150579\pi$
$948$		0			0
$949$	0.206176			0.00669275
$950$		0			0
$951$	−1.97817			−0.0641467
$952$		0			0
$953$	−36.0991	+	26.2275i	−1.16936	+	0.849593i	−0.990933	−	0.134359i	$-0.957102\pi$
$953$	−36.0991	+	26.2275i	−1.16936	+	0.849593i	−0.178432	+	0.983952i	$0.557102\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−0.412724			−0.0133415
$958$		0			0
$959$	17.7072	−	54.4971i	0.571795	−	1.75980i
$960$		0			0
$961$	12.6848	+	39.0399i	0.409188	+	1.25935i
$962$		0			0
$963$	−5.46328	+	16.8143i	−0.176052	+	0.541832i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−44.6460	−	32.4372i	−1.43572	−	1.04311i	−0.988916	−	0.148479i	$-0.952562\pi$
$967$	−44.6460	−	32.4372i	−1.43572	−	1.04311i	−0.446804	−	0.894632i	$-0.647438\pi$
$968$		0			0
$969$	10.1151	+	7.34902i	0.324942	+	0.236084i
$970$		0			0
$971$	5.00915	−	3.63936i	0.160751	−	0.116793i	−0.504502	−	0.863411i	$-0.668324\pi$
$971$	5.00915	−	3.63936i	0.160751	−	0.116793i	0.665253	+	0.746618i	$0.268324\pi$
$972$		0			0
$973$	22.5871	+	69.5160i	0.724109	+	2.22858i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−7.46728	−	22.9819i	−0.238900	−	0.735257i	−0.996580	−	0.0826317i	$-0.973667\pi$
$977$	−7.46728	−	22.9819i	−0.238900	−	0.735257i	0.757681	−	0.652626i	$-0.226333\pi$
$978$		0			0
$979$	6.62719	−	4.81494i	0.211806	−	0.153886i
$980$		0			0
$981$	−2.86374	−	2.08063i	−0.0914321	−	0.0664293i
$982$		0			0
$983$	−7.70430	−	5.59750i	−0.245729	−	0.178533i	0.458103	−	0.888899i	$-0.348529\pi$
$983$	−7.70430	−	5.59750i	−0.245729	−	0.178533i	−0.703832	+	0.710367i	$0.748529\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	12.1194	−	37.2998i	0.385766	−	1.18727i
$988$		0			0
$989$	2.95072	+	9.08137i	0.0938273	+	0.288771i
$990$		0			0
$991$	−3.21741	+	9.90216i	−0.102204	+	0.314553i	−0.989064	−	0.147486i	$-0.952882\pi$
$991$	−3.21741	+	9.90216i	−0.102204	+	0.314553i	0.886860	+	0.462039i	$0.152882\pi$
$992$		0			0
$993$	−13.1307			−0.416691
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−46.7359	+	33.9556i	−1.48014	+	1.07539i	−0.502629	+	0.864502i	$0.667634\pi$
$997$	−46.7359	+	33.9556i	−1.48014	+	1.07539i	−0.977511	+	0.210883i	$0.932366\pi$
$998$		0			0
$999$	6.11909			0.193599

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1500.2.m.a.901.1		8
5.2	odd	4		1500.2.o.b.349.3		16
5.3	odd	4		1500.2.o.b.349.2		16
5.4	even	2		300.2.m.b.181.1	yes	8
15.14	odd	2		900.2.n.b.181.2		8
25.2	odd	20		7500.2.d.c.1249.1		8
25.3	odd	20		1500.2.o.b.649.4		16
25.4	even	10		300.2.m.b.121.1	✓	8
25.11	even	5		7500.2.a.f.1.1		4
25.14	even	10		7500.2.a.e.1.4		4
25.21	even	5	inner	1500.2.m.a.601.1		8
25.22	odd	20		1500.2.o.b.649.1		16
25.23	odd	20		7500.2.d.c.1249.8		8
75.29	odd	10		900.2.n.b.721.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.m.b.121.1	✓	8	25.4	even	10
300.2.m.b.181.1	yes	8	5.4	even	2
900.2.n.b.181.2		8	15.14	odd	2
900.2.n.b.721.2		8	75.29	odd	10
1500.2.m.a.601.1		8	25.21	even	5	inner
1500.2.m.a.901.1		8	1.1	even	1	trivial
1500.2.o.b.349.2		16	5.3	odd	4
1500.2.o.b.349.3		16	5.2	odd	4
1500.2.o.b.649.1		16	25.22	odd	20
1500.2.o.b.649.4		16	25.3	odd	20
7500.2.a.e.1.4		4	25.14	even	10
7500.2.a.f.1.1		4	25.11	even	5
7500.2.d.c.1249.1		8	25.2	odd	20
7500.2.d.c.1249.8		8	25.23	odd	20

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:	\( N \)	\(=\)	\( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1500.m (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{3} -4.32440 q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{3} -4.32440 q^{7} +(0.309017 - 0.951057i) q^{9} +(0.180557 + 0.555698i) q^{11} +(-0.298591 + 0.918969i) q^{13} +(-1.88048 - 1.36625i) q^{17} +(4.35169 + 3.16169i) q^{19} +(3.49851 - 2.54182i) q^{21} +(0.419687 + 1.29166i) q^{23} +(0.309017 + 0.951057i) q^{27} +(0.571459 - 0.415189i) q^{29} +(-6.86707 - 4.98922i) q^{31} +(-0.472705 - 0.343440i) q^{33} +(1.89090 - 5.81960i) q^{37} +(-0.298591 - 0.918969i) q^{39} +(3.41820 - 10.5201i) q^{41} +7.03076 q^{43} +(7.33723 - 5.33081i) q^{47} +11.7004 q^{49} +2.32440 q^{51} +(7.20487 - 5.23465i) q^{53} -5.37899 q^{57} +(-2.25351 + 6.93558i) q^{59} +(-1.48752 - 4.57810i) q^{61} +(-1.33631 + 4.11275i) q^{63} +(-0.304195 - 0.221011i) q^{67} +(-1.09875 - 0.798291i) q^{69} +(-8.54359 + 6.20729i) q^{71} +(-0.0659364 - 0.202931i) q^{73} +(-0.780801 - 2.40306i) q^{77} +(5.68410 - 4.12974i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(13.0343 + 9.46998i) q^{83} +(-0.218278 + 0.671790i) q^{87} +(-4.33233 - 13.3335i) q^{89} +(1.29123 - 3.97399i) q^{91} +8.48817 q^{93} +(12.7436 - 9.25880i) q^{97} +0.584296 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} - 8 q^{7} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 - 8 * q^7 - 2 * q^9	\( 8 q - 2 q^{3} - 8 q^{7} - 2 q^{9} + 8 q^{11} - 3 q^{17} + 5 q^{19} + 7 q^{21} + 7 q^{23} - 2 q^{27} - 3 q^{29} - 3 q^{31} - 7 q^{33} + q^{37} + 10 q^{41} + 12 q^{43} + 33 q^{47} - 8 q^{49} - 8 q^{51} + 19 q^{53} - 10 q^{57} - 38 q^{59} + 46 q^{61} - 3 q^{63} + 8 q^{67} + 2 q^{69} - 25 q^{71} + 26 q^{73} - 23 q^{77} - 16 q^{79} - 2 q^{81} - 8 q^{83} - 3 q^{87} - 30 q^{89} + 25 q^{91} + 22 q^{93} + 14 q^{97} - 2 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 - 8 * q^7 - 2 * q^9 + 8 * q^11 - 3 * q^17 + 5 * q^19 + 7 * q^21 + 7 * q^23 - 2 * q^27 - 3 * q^29 - 3 * q^31 - 7 * q^33 + q^37 + 10 * q^41 + 12 * q^43 + 33 * q^47 - 8 * q^49 - 8 * q^51 + 19 * q^53 - 10 * q^57 - 38 * q^59 + 46 * q^61 - 3 * q^63 + 8 * q^67 + 2 * q^69 - 25 * q^71 + 26 * q^73 - 23 * q^77 - 16 * q^79 - 2 * q^81 - 8 * q^83 - 3 * q^87 - 30 * q^89 + 25 * q^91 + 22 * q^93 + 14 * q^97 - 2 * q^99

Introduction

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