LMFDB - Embedded newform 912.3.be.j.145.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,3,Mod(145,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

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

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

chi := DirichletCharacter("912.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	912.be (of order $6$, degree $2$, 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:	$24.8502001097$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 154 x^{18} - 24 x^{17} + 16374 x^{16} - 4328 x^{15} + 911836 x^{14} - 590088 x^{13} + \cdots + 338560000 $ x^20 + 154x^18 - 24x^17 + 16374x^16 - 4328x^15 + 911836x^14 - 590088x^13 + 36808708x^12 - 29040960x^11 + 727387008x^10 - 1003792064x^9 + 10261479936x^8 - 7069668864x^7 + 36940887936x^6 + 52280031232x^5 + 60574204416x^4 + 32700144640x^3 + 13448832000x^2 + 2490624000x + 338560000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{18} $
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.6
Root			$-0.268097 + 0.464358i$ of defining polynomial
Character	$\chi$	$=$	912.145
Dual form			912.3.be.j.673.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 0.866025i) q^{3} +(0.268097 + 0.464358i) q^{5} -12.8244 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 - 0.866025i) q^{3} +(0.268097 + 0.464358i) q^{5} -12.8244 q^{7} +(1.50000 - 2.59808i) q^{9} +13.8366 q^{11} +(10.2446 + 5.91471i) q^{13} +(0.804291 + 0.464358i) q^{15} +(-1.04037 - 1.80198i) q^{17} +(-9.37555 + 16.5257i) q^{19} +(-19.2366 + 11.1062i) q^{21} +(2.59050 - 4.48687i) q^{23} +(12.3562 - 21.4016i) q^{25} -5.19615i q^{27} +(22.5857 + 13.0399i) q^{29} -10.4041i q^{31} +(20.7548 - 11.9828i) q^{33} +(-3.43818 - 5.95510i) q^{35} +70.6885i q^{37} +20.4891 q^{39} +(69.8595 - 40.3334i) q^{41} +(-25.7235 - 44.5543i) q^{43} +1.60858 q^{45} +(20.3280 - 35.2091i) q^{47} +115.465 q^{49} +(-3.12112 - 1.80198i) q^{51} +(80.9701 + 46.7481i) q^{53} +(3.70954 + 6.42512i) q^{55} +(0.248361 + 32.9080i) q^{57} +(39.5395 - 22.8282i) q^{59} +(21.4787 - 37.2022i) q^{61} +(-19.2366 + 33.3187i) q^{63} +6.34287i q^{65} +(106.322 + 61.3850i) q^{67} -8.97374i q^{69} +(-63.7244 + 36.7913i) q^{71} +(-10.5490 - 18.2714i) q^{73} -42.8033i q^{75} -177.445 q^{77} +(-7.69299 + 4.44155i) q^{79} +(-4.50000 - 7.79423i) q^{81} +23.8115 q^{83} +(0.557843 - 0.966212i) q^{85} +45.1714 q^{87} +(-106.405 - 61.4328i) q^{89} +(-131.380 - 75.8525i) q^{91} +(-9.01019 - 15.6061i) q^{93} +(-10.1874 + 0.0768855i) q^{95} +(54.7700 - 31.6215i) q^{97} +(20.7548 - 35.9484i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9}+O(q^{10}) $ 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9	$ 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9} + 8 q^{11} + 18 q^{13} + 8 q^{17} - 28 q^{19} - 30 q^{21} + 8 q^{23} - 58 q^{25} + 108 q^{29} + 12 q^{33} - 20 q^{35} + 36 q^{39} - 36 q^{41} + 2 q^{43} + 296 q^{49} + 24 q^{51} - 72 q^{53} - 216 q^{55} - 30 q^{57} - 72 q^{59} - 26 q^{61} - 30 q^{63} - 138 q^{67} + 204 q^{71} + 218 q^{73} - 8 q^{77} + 78 q^{79} - 90 q^{81} + 112 q^{83} + 224 q^{85} + 216 q^{87} - 432 q^{89} + 330 q^{91} - 126 q^{93} - 220 q^{95} + 132 q^{97} + 12 q^{99}+O(q^{100}) $ 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9 + 8 * q^11 + 18 * q^13 + 8 * q^17 - 28 * q^19 - 30 * q^21 + 8 * q^23 - 58 * q^25 + 108 * q^29 + 12 * q^33 - 20 * q^35 + 36 * q^39 - 36 * q^41 + 2 * q^43 + 296 * q^49 + 24 * q^51 - 72 * q^53 - 216 * q^55 - 30 * q^57 - 72 * q^59 - 26 * q^61 - 30 * q^63 - 138 * q^67 + 204 * q^71 + 218 * q^73 - 8 * q^77 + 78 * q^79 - 90 * q^81 + 112 * q^83 + 224 * q^85 + 216 * q^87 - 432 * q^89 + 330 * q^91 - 126 * q^93 - 220 * q^95 + 132 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$4$		0			0
$5$	0.268097	+	0.464358i	0.0536194	+	0.0928716i	0.891589	−	0.452845i	$-0.149591\pi$
$5$	0.268097	+	0.464358i	0.0536194	+	0.0928716i	−0.837970	+	0.545717i	$0.816258\pi$
$6$		0			0
$7$	−12.8244			−1.83206			−0.916028	−	0.401115i	$-0.868623\pi$
$7$	−12.8244			−1.83206			−0.916028	+	0.401115i	$0.868623\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	13.8366			1.25787			0.628935	−	0.777458i	$-0.283491\pi$
$11$	13.8366			1.25787			0.628935	+	0.777458i	$0.283491\pi$
$12$		0			0
$13$	10.2446	+	5.91471i	0.788044	+	0.454978i	0.839274	−	0.543709i	$-0.182981\pi$
$13$	10.2446	+	5.91471i	0.788044	+	0.454978i	−0.0512294	+	0.998687i	$0.516314\pi$
$14$		0			0
$15$	0.804291	+	0.464358i	0.0536194	+	0.0309572i
$16$		0			0
$17$	−1.04037	−	1.80198i	−0.0611985	−	0.105999i	0.833803	−	0.552062i	$-0.186159\pi$
$17$	−1.04037	−	1.80198i	−0.0611985	−	0.105999i	−0.895001	+	0.446063i	$0.852826\pi$
$18$		0			0
$19$	−9.37555	+	16.5257i	−0.493450	+	0.869774i
$19$	−9.37555	+	16.5257i	−0.493450	+	0.869774i
$20$		0			0
$21$	−19.2366	+	11.1062i	−0.916028	+	0.528869i
$22$		0			0
$23$	2.59050	−	4.48687i	0.112630	−	0.195081i	−0.804200	−	0.594359i	$-0.797406\pi$
$23$	2.59050	−	4.48687i	0.112630	−	0.195081i	0.916830	+	0.399278i	$0.130739\pi$
$24$		0			0
$25$	12.3562	−	21.4016i	0.494250	−	0.856066i
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	22.5857	+	13.0399i	0.778817	+	0.449650i	0.836011	−	0.548713i	$-0.184882\pi$
$29$	22.5857	+	13.0399i	0.778817	+	0.449650i	−0.0571940	+	0.998363i	$0.518215\pi$
$30$		0			0
$31$		−	10.4041i		−	0.335615i	−0.985820	−	0.167808i	$-0.946331\pi$
$31$		−	10.4041i		−	0.335615i	0.985820	−	0.167808i	$-0.0536687\pi$
$32$		0			0
$33$	20.7548	−	11.9828i	0.628935	−	0.363116i
$34$		0			0
$35$	−3.43818	−	5.95510i	−0.0982337	−	0.170146i
$36$		0			0
$37$			70.6885i			1.91050i	0.295799	+	0.955250i	$0.404414\pi$
$37$			70.6885i			1.91050i	−0.295799	+	0.955250i	$0.595586\pi$
$38$		0			0
$39$	20.4891			0.525363
$40$		0			0
$41$	69.8595	−	40.3334i	1.70389	−	0.983741i	0.762149	−	0.647402i	$-0.224144\pi$
$41$	69.8595	−	40.3334i	1.70389	−	0.983741i	0.941741	−	0.336339i	$-0.109189\pi$
$42$		0			0
$43$	−25.7235	−	44.5543i	−0.598220	−	1.03615i	−0.993084	−	0.117407i	$-0.962542\pi$
$43$	−25.7235	−	44.5543i	−0.598220	−	1.03615i	0.394864	−	0.918740i	$-0.370792\pi$
$44$		0			0
$45$	1.60858			0.0357463
$46$		0			0
$47$	20.3280	−	35.2091i	0.432511	−	0.749131i	−0.564578	−	0.825380i	$-0.690961\pi$
$47$	20.3280	−	35.2091i	0.432511	−	0.749131i	0.997089	+	0.0762489i	$0.0242944\pi$
$48$		0			0
$49$	115.465			2.35643
$50$		0			0
$51$	−3.12112	−	1.80198i	−0.0611985	−	0.0353330i
$52$		0			0
$53$	80.9701	+	46.7481i	1.52774	+	0.882039i	0.999456	+	0.0329695i	$0.0104964\pi$
$53$	80.9701	+	46.7481i	1.52774	+	0.882039i	0.528281	+	0.849070i	$0.322837\pi$
$54$		0			0
$55$	3.70954	+	6.42512i	0.0674462	+	0.116820i
$56$		0			0
$57$	0.248361	+	32.9080i	0.00435720	+	0.577334i
$58$		0			0
$59$	39.5395	−	22.8282i	0.670161	−	0.386918i	−0.125976	−	0.992033i	$-0.540206\pi$
$59$	39.5395	−	22.8282i	0.670161	−	0.386918i	0.796138	+	0.605115i	$0.206873\pi$
$60$		0			0
$61$	21.4787	−	37.2022i	0.352110	−	0.609872i	−0.634509	−	0.772915i	$-0.718798\pi$
$61$	21.4787	−	37.2022i	0.352110	−	0.609872i	0.986619	+	0.163043i	$0.0521310\pi$
$62$		0			0
$63$	−19.2366	+	33.3187i	−0.305343	+	0.528869i
$64$		0			0
$65$			6.34287i			0.0975825i
$66$		0			0
$67$	106.322	+	61.3850i	1.58690	+	0.916194i	0.993815	+	0.111051i	$0.0354218\pi$
$67$	106.322	+	61.3850i	1.58690	+	0.916194i	0.593081	+	0.805143i	$0.297912\pi$
$68$		0			0
$69$		−	8.97374i		−	0.130054i
$70$		0			0
$71$	−63.7244	+	36.7913i	−0.897526	+	0.518187i	−0.876397	−	0.481590i	$-0.840060\pi$
$71$	−63.7244	+	36.7913i	−0.897526	+	0.518187i	−0.0211295	+	0.999777i	$0.506726\pi$
$72$		0			0
$73$	−10.5490	−	18.2714i	−0.144507	−	0.250293i	0.784682	−	0.619899i	$-0.212826\pi$
$73$	−10.5490	−	18.2714i	−0.144507	−	0.250293i	−0.929189	+	0.369605i	$0.879493\pi$
$74$		0			0
$75$		−	42.8033i		−	0.570711i
$76$		0			0
$77$	−177.445			−2.30449
$78$		0			0
$79$	−7.69299	+	4.44155i	−0.0973797	+	0.0562222i	−0.547899	−	0.836545i	$-0.684572\pi$
$79$	−7.69299	+	4.44155i	−0.0973797	+	0.0562222i	0.450519	+	0.892767i	$0.351239\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	23.8115			0.286885			0.143443	−	0.989659i	$-0.454183\pi$
$83$	23.8115			0.286885			0.143443	+	0.989659i	$0.454183\pi$
$84$		0			0
$85$	0.557843	−	0.966212i	0.00656286	−	0.0113672i
$86$		0			0
$87$	45.1714			0.519211
$88$		0			0
$89$	−106.405	−	61.4328i	−1.19556	−	0.690256i	−0.235997	−	0.971754i	$-0.575836\pi$
$89$	−106.405	−	61.4328i	−1.19556	−	0.690256i	−0.959562	+	0.281497i	$0.909169\pi$
$90$		0			0
$91$	−131.380	−	75.8525i	−1.44374	−	0.833544i
$92$		0			0
$93$	−9.01019	−	15.6061i	−0.0968837	−	0.167808i
$94$		0			0
$95$	−10.1874	+	0.0768855i	−0.107236	+	0.000809321i
$96$		0			0
$97$	54.7700	−	31.6215i	0.564639	−	0.325994i	−0.190366	−	0.981713i	$-0.560968\pi$
$97$	54.7700	−	31.6215i	0.564639	−	0.325994i	0.755005	+	0.655719i	$0.227634\pi$
$98$		0			0
$99$	20.7548	−	35.9484i	0.209645	−	0.363116i
$100$		0			0
$101$	−43.2582	+	74.9254i	−0.428299	+	0.741835i	−0.996722	−	0.0809010i	$-0.974220\pi$
$101$	−43.2582	+	74.9254i	−0.428299	+	0.741835i	0.568423	+	0.822736i	$0.307554\pi$
$102$		0			0
$103$		−	13.4230i		−	0.130320i	−0.997875	−	0.0651600i	$-0.979244\pi$
$103$		−	13.4230i		−	0.130320i	0.997875	−	0.0651600i	$-0.0207558\pi$
$104$		0			0
$105$	−10.3145	−	5.95510i	−0.0982337	−	0.0567153i
$106$		0			0
$107$			94.6567i			0.884642i	0.896857	+	0.442321i	$0.145845\pi$
$107$			94.6567i			0.884642i	−0.896857	+	0.442321i	$0.854155\pi$
$108$		0			0
$109$	102.711	−	59.3002i	0.942303	−	0.544039i	0.0516212	−	0.998667i	$-0.483561\pi$
$109$	102.711	−	59.3002i	0.942303	−	0.544039i	0.890681	+	0.454628i	$0.150228\pi$
$110$		0			0
$111$	61.2180	+	106.033i	0.551514	+	0.955250i
$112$		0			0
$113$			71.8022i			0.635418i	0.948188	+	0.317709i	$0.102913\pi$
$113$			71.8022i			0.635418i	−0.948188	+	0.317709i	$0.897087\pi$
$114$		0			0
$115$	2.77802			0.0241567
$116$		0			0
$117$	30.7337	−	17.7441i	0.262681	−	0.151659i
$118$		0			0
$119$	13.3422	+	23.1093i	0.112119	+	0.194196i
$120$		0			0
$121$	70.4505			0.582235
$122$		0			0
$123$	69.8595	−	121.000i	0.567963	−	0.983741i
$124$		0			0
$125$	26.6556			0.213244
$126$		0			0
$127$	13.3446	+	7.70451i	0.105076	+	0.0606654i	0.551617	−	0.834098i	$-0.314011\pi$
$127$	13.3446	+	7.70451i	0.105076	+	0.0606654i	−0.446541	+	0.894763i	$0.647344\pi$
$128$		0			0
$129$	−77.1704	−	44.5543i	−0.598220	−	0.345382i
$130$		0			0
$131$	57.9392	+	100.354i	0.442284	+	0.766058i	0.997859	−	0.0654087i	$-0.0208351\pi$
$131$	57.9392	+	100.354i	0.442284	+	0.766058i	−0.555575	+	0.831467i	$0.687502\pi$
$132$		0			0
$133$	120.236	−	211.932i	0.904027	−	1.59347i
$134$		0			0
$135$	2.41287	−	1.39307i	0.0178731	−	0.0103191i
$136$		0			0
$137$	−98.9620	+	171.407i	−0.722350	+	1.25115i	0.237705	+	0.971337i	$0.423605\pi$
$137$	−98.9620	+	171.407i	−0.722350	+	1.25115i	−0.960055	+	0.279810i	$0.909729\pi$
$138$		0			0
$139$	97.3714	−	168.652i	0.700514	−	1.21333i	−0.267773	−	0.963482i	$-0.586288\pi$
$139$	97.3714	−	168.652i	0.700514	−	1.21333i	0.968286	−	0.249843i	$-0.0803791\pi$
$140$		0			0
$141$		−	70.4183i		−	0.499421i
$142$		0			0
$143$	141.750	+	81.8392i	0.991257	+	0.572302i
$144$		0			0
$145$			13.9838i			0.0964399i
$146$		0			0
$147$	173.197	−	99.9955i	1.17821	−	0.680241i
$148$		0			0
$149$	−136.777	−	236.905i	−0.917966	−	1.58996i	−0.802500	−	0.596653i	$-0.796497\pi$
$149$	−136.777	−	236.905i	−0.917966	−	1.58996i	−0.115467	−	0.993311i	$-0.536836\pi$
$150$		0			0
$151$			105.016i			0.695471i	0.937593	+	0.347736i	$0.113049\pi$
$151$			105.016i			0.695471i	−0.937593	+	0.347736i	$0.886951\pi$
$152$		0			0
$153$	−6.24225			−0.0407990
$154$		0			0
$155$	4.83121	−	2.78930i	0.0311691	−	0.0179955i
$156$		0			0
$157$	69.7499	+	120.810i	0.444267	+	0.769493i	0.998001	−	0.0632010i	$-0.0201309\pi$
$157$	69.7499	+	120.810i	0.444267	+	0.769493i	−0.553734	+	0.832694i	$0.686798\pi$
$158$		0			0
$159$	161.940			1.01849
$160$		0			0
$161$	−33.2215	+	57.5413i	−0.206345	+	0.357400i
$162$		0			0
$163$	165.511			1.01541			0.507703	−	0.861532i	$-0.330495\pi$
$163$	165.511			1.01541			0.507703	+	0.861532i	$0.330495\pi$
$164$		0			0
$165$	11.1286	+	6.42512i	0.0674462	+	0.0389401i
$166$		0			0
$167$	−95.0483	−	54.8761i	−0.569151	−	0.328600i	0.187659	−	0.982234i	$-0.439910\pi$
$167$	−95.0483	−	54.8761i	−0.569151	−	0.328600i	−0.756810	+	0.653635i	$0.773243\pi$
$168$		0			0
$169$	−14.5325	−	25.1710i	−0.0859909	−	0.148941i
$170$		0			0
$171$	28.8717	+	49.1470i	0.168841	+	0.287409i
$172$		0			0
$173$	−129.070	+	74.5188i	−0.746071	+	0.430745i	−0.824273	−	0.566193i	$-0.808416\pi$
$173$	−129.070	+	74.5188i	−0.746071	+	0.430745i	0.0782012	+	0.996938i	$0.475082\pi$
$174$		0			0
$175$	−158.461	+	274.463i	−0.905493	+	1.56836i
$176$		0			0
$177$	39.5395	−	68.4845i	0.223387	−	0.386918i
$178$		0			0
$179$			103.787i			0.579814i	0.957055	+	0.289907i	$0.0936244\pi$
$179$			103.787i			0.579814i	−0.957055	+	0.289907i	$0.906376\pi$
$180$		0			0
$181$	34.5225	+	19.9316i	0.190732	+	0.110119i	0.592325	−	0.805699i	$-0.298210\pi$
$181$	34.5225	+	19.9316i	0.190732	+	0.110119i	−0.401593	+	0.915818i	$0.631543\pi$
$182$		0			0
$183$		−	74.4044i		−	0.406581i
$184$		0			0
$185$	−32.8248	+	18.9514i	−0.177431	+	0.102440i
$186$		0			0
$187$	−14.3952	−	24.9332i	−0.0769797	−	0.133333i
$188$		0			0
$189$			66.6375i			0.352579i
$190$		0			0
$191$	−30.1343			−0.157771			−0.0788855	−	0.996884i	$-0.525136\pi$
$191$	−30.1343			−0.157771			−0.0788855	+	0.996884i	$0.525136\pi$
$192$		0			0
$193$	37.3548	−	21.5668i	0.193548	−	0.111745i	−0.400094	−	0.916474i	$-0.631023\pi$
$193$	37.3548	−	21.5668i	0.193548	−	0.111745i	0.593642	+	0.804729i	$0.297689\pi$
$194$		0			0
$195$	5.49308	+	9.51430i	0.0281697	+	0.0487913i
$196$		0			0
$197$	−22.9822			−0.116661			−0.0583305	−	0.998297i	$-0.518578\pi$
$197$	−22.9822			−0.116661			−0.0583305	+	0.998297i	$0.518578\pi$
$198$		0			0
$199$	135.388	−	234.500i	0.680344	−	1.17839i	−0.294532	−	0.955642i	$-0.595164\pi$
$199$	135.388	−	234.500i	0.680344	−	1.17839i	0.974876	−	0.222748i	$-0.0715029\pi$
$200$		0			0
$201$	212.644			1.05793
$202$		0			0
$203$	−289.648	−	167.228i	−1.42684	−	0.823784i
$204$		0			0
$205$	37.4583	+	21.6265i	0.182723	+	0.105495i
$206$		0			0
$207$	−7.77149	−	13.4606i	−0.0375434	−	0.0650271i
$208$		0			0
$209$	−129.725	+	228.659i	−0.620696	+	1.09406i
$210$		0			0
$211$	−186.337	+	107.582i	−0.883112	+	0.509865i	−0.871683	−	0.490070i	$-0.836971\pi$
$211$	−186.337	+	107.582i	−0.883112	+	0.509865i	−0.0114290	+	0.999935i	$0.503638\pi$
$212$		0			0
$213$	−63.7244	+	110.374i	−0.299175	+	0.518187i
$214$		0			0
$215$	13.7928	−	23.8898i	0.0641524	−	0.111115i
$216$		0			0
$217$			133.426i			0.614865i
$218$		0			0
$219$	−31.6470	−	18.2714i	−0.144507	−	0.0834312i
$220$		0			0
$221$		−	24.6140i		−	0.111376i
$222$		0			0
$223$	−147.129	+	84.9452i	−0.659773	+	0.380920i	−0.792190	−	0.610274i	$-0.791059\pi$
$223$	−147.129	+	84.9452i	−0.659773	+	0.380920i	0.132418	+	0.991194i	$0.457726\pi$
$224$		0			0
$225$	−37.0687	−	64.2049i	−0.164750	−	0.285355i
$226$		0			0
$227$			344.308i			1.51678i	0.651804	+	0.758388i	$0.274013\pi$
$227$			344.308i			1.51678i	−0.651804	+	0.758388i	$0.725987\pi$
$228$		0			0
$229$	−377.658			−1.64916			−0.824580	−	0.565745i	$-0.808589\pi$
$229$	−377.658			−1.64916			−0.824580	+	0.565745i	$0.808589\pi$
$230$		0			0
$231$	−266.168	+	153.672i	−1.15224	+	0.665248i
$232$		0			0
$233$	−176.634	−	305.939i	−0.758086	−	1.31304i	−0.943826	−	0.330444i	$-0.892802\pi$
$233$	−176.634	−	305.939i	−0.758086	−	1.31304i	0.185740	−	0.982599i	$-0.440532\pi$
$234$		0			0
$235$	21.7995			0.0927640
$236$		0			0
$237$	−7.69299	+	13.3247i	−0.0324599	+	0.0562222i
$238$		0			0
$239$	22.2427			0.0930657			0.0465328	−	0.998917i	$-0.485183\pi$
$239$	22.2427			0.0930657			0.0465328	+	0.998917i	$0.485183\pi$
$240$		0			0
$241$	−215.305	−	124.306i	−0.893381	−	0.515794i	−0.0183344	−	0.999832i	$-0.505836\pi$
$241$	−215.305	−	124.306i	−0.893381	−	0.515794i	−0.875047	+	0.484038i	$0.839170\pi$
$242$		0			0
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	30.9558	+	53.6170i	0.126350	+	0.218845i
$246$		0			0
$247$	−193.793	+	113.845i	−0.784588	+	0.460912i
$248$		0			0
$249$	35.7172	−	20.6213i	0.143443	−	0.0828166i
$250$		0			0
$251$	56.2275	−	97.3889i	0.224014	−	0.388004i	−0.732009	−	0.681295i	$-0.761417\pi$
$251$	56.2275	−	97.3889i	0.224014	−	0.388004i	0.956023	+	0.293291i	$0.0947505\pi$
$252$		0			0
$253$	35.8436	−	62.0829i	0.141674	−	0.245387i
$254$		0			0
$255$		−	1.93242i		−	0.00757814i
$256$		0			0
$257$	329.222	+	190.077i	1.28102	+	0.739598i	0.977035	−	0.213079i	$-0.0683491\pi$
$257$	329.222	+	190.077i	1.28102	+	0.739598i	0.303986	+	0.952676i	$0.401682\pi$
$258$		0			0
$259$		−	906.537i		−	3.50014i
$260$		0			0
$261$	67.7571	−	39.1196i	0.259606	−	0.149883i
$262$		0			0
$263$	−63.7916	−	110.490i	−0.242553	−	0.420115i	0.718887	−	0.695126i	$-0.244652\pi$
$263$	−63.7916	−	110.490i	−0.242553	−	0.420115i	−0.961441	+	0.275012i	$0.911318\pi$
$264$		0			0
$265$			50.1321i			0.189178i
$266$		0			0
$267$	−212.810			−0.797039
$268$		0			0
$269$	163.353	−	94.3121i	0.607262	−	0.350603i	−0.164631	−	0.986355i	$-0.552643\pi$
$269$	163.353	−	94.3121i	0.607262	−	0.350603i	0.771893	+	0.635752i	$0.219310\pi$
$270$		0			0
$271$	182.818	+	316.650i	0.674606	+	1.16845i	0.976584	+	0.215136i	$0.0690196\pi$
$271$	182.818	+	316.650i	0.674606	+	1.16845i	−0.301978	+	0.953315i	$0.597647\pi$
$272$		0			0
$273$	−262.761			−0.962494
$274$		0			0
$275$	170.968	−	296.125i	0.621702	−	1.07682i
$276$		0			0
$277$	−299.281			−1.08044			−0.540219	−	0.841525i	$-0.681658\pi$
$277$	−299.281			−1.08044			−0.540219	+	0.841525i	$0.681658\pi$
$278$		0			0
$279$	−27.0306	−	15.6061i	−0.0968837	−	0.0559359i
$280$		0			0
$281$	4.01944	+	2.32063i	0.0143041	+	0.00825846i	0.507135	−	0.861867i	$-0.330705\pi$
$281$	4.01944	+	2.32063i	0.0143041	+	0.00825846i	−0.492831	+	0.870125i	$0.664038\pi$
$282$		0			0
$283$	147.964	+	256.280i	0.522839	+	0.905584i	0.999647	+	0.0265766i	$0.00846059\pi$
$283$	147.964	+	256.280i	0.522839	+	0.905584i	−0.476807	+	0.879008i	$0.658206\pi$
$284$		0			0
$285$	−15.2145	+	8.93788i	−0.0533843	+	0.0313610i
$286$		0			0
$287$	−895.905	+	517.251i	−3.12162	+	1.80227i
$288$		0			0
$289$	142.335	−	246.532i	0.492509	−	0.853051i
$290$		0			0
$291$	54.7700	−	94.8644i	0.188213	−	0.325994i
$292$		0			0
$293$			182.004i			0.621175i	0.950545	+	0.310588i	$0.100526\pi$
$293$			182.004i			0.621175i	−0.950545	+	0.310588i	$0.899474\pi$
$294$		0			0
$295$	21.2009	+	12.2403i	0.0718673	+	0.0414926i
$296$		0			0
$297$		−	71.8969i		−	0.242077i
$298$		0			0
$299$	53.0770	−	30.6440i	0.177515	−	0.102488i
$300$		0			0
$301$	329.887	+	571.382i	1.09597	+	1.89828i
$302$		0			0
$303$			149.851i			0.494557i
$304$		0			0
$305$	23.0335			0.0755197
$306$		0			0
$307$	−90.0676	+	52.0006i	−0.293380	+	0.169383i	−0.639465	−	0.768820i	$-0.720844\pi$
$307$	−90.0676	+	52.0006i	−0.293380	+	0.169383i	0.346085	+	0.938203i	$0.387511\pi$
$308$		0			0
$309$	−11.6246	−	20.1344i	−0.0376201	−	0.0651600i
$310$		0			0
$311$	−60.1035			−0.193259			−0.0966295	−	0.995320i	$-0.530806\pi$
$311$	−60.1035			−0.193259			−0.0966295	+	0.995320i	$0.530806\pi$
$312$		0			0
$313$	124.286	−	215.270i	0.397080	−	0.687763i	−0.596284	−	0.802773i	$-0.703357\pi$
$313$	124.286	−	215.270i	0.397080	−	0.687763i	0.993364	+	0.115011i	$0.0366902\pi$
$314$		0			0
$315$	−20.6291			−0.0654892
$316$		0			0
$317$	−394.756	−	227.913i	−1.24529	−	0.718968i	−0.275123	−	0.961409i	$-0.588718\pi$
$317$	−394.756	−	227.913i	−1.24529	−	0.718968i	−0.970166	+	0.242441i	$0.922052\pi$
$318$		0			0
$319$	312.508	+	180.427i	0.979650	+	0.565601i
$320$		0			0
$321$	81.9751	+	141.985i	0.255374	+	0.442321i
$322$		0			0
$323$	39.5331	−	0.298361i	0.122394	−	0.000923718i
$324$		0			0
$325$	253.169	−	146.167i	0.778982	−	0.449745i
$326$		0			0
$327$	102.711	−	177.901i	0.314101	−	0.544039i
$328$		0			0
$329$	−260.694	+	451.536i	−0.792384	+	1.37245i
$330$		0			0
$331$		−	394.152i		−	1.19079i	−0.803433	−	0.595396i	$-0.796995\pi$
$331$		−	394.152i		−	1.19079i	0.803433	−	0.595396i	$-0.203005\pi$
$332$		0			0
$333$	183.654	+	106.033i	0.551514	+	0.318417i
$334$		0			0
$335$			65.8286i			0.196503i
$336$		0			0
$337$	−169.999	+	98.1492i	−0.504449	+	0.291244i	−0.730549	−	0.682860i	$-0.760736\pi$
$337$	−169.999	+	98.1492i	−0.504449	+	0.291244i	0.226100	+	0.974104i	$0.427402\pi$
$338$		0			0
$339$	62.1825	+	107.703i	0.183429	+	0.317709i
$340$		0			0
$341$		−	143.957i		−	0.422160i
$342$		0			0
$343$	−852.371			−2.48505
$344$		0			0
$345$	4.16703	−	2.40583i	0.0120783	−	0.00697343i
$346$		0			0
$347$	−45.1449	−	78.1932i	−0.130100	−	0.225341i	0.793615	−	0.608421i	$-0.208197\pi$
$347$	−45.1449	−	78.1932i	−0.130100	−	0.225341i	−0.923715	+	0.383080i	$0.874863\pi$
$348$		0			0
$349$	118.693			0.340094			0.170047	−	0.985436i	$-0.445608\pi$
$349$	118.693			0.340094			0.170047	+	0.985436i	$0.445608\pi$
$350$		0			0
$351$	30.7337	−	53.2324i	0.0875605	−	0.151659i
$352$		0			0
$353$	299.812			0.849326			0.424663	−	0.905351i	$-0.360393\pi$
$353$	299.812			0.849326			0.424663	+	0.905351i	$0.360393\pi$
$354$		0			0
$355$	−34.1686	−	19.7273i	−0.0962497	−	0.0555698i
$356$		0			0
$357$	40.0265	+	23.1093i	0.112119	+	0.0647320i
$358$		0			0
$359$	−170.443	−	295.215i	−0.474770	−	0.822326i	0.524812	−	0.851218i	$-0.324135\pi$
$359$	−170.443	−	295.215i	−0.474770	−	0.822326i	−0.999583	+	0.0288918i	$0.990802\pi$
$360$		0			0
$361$	−185.198	−	309.875i	−0.513014	−	0.858380i
$362$		0			0
$363$	105.676	−	61.0119i	0.291118	−	0.168077i
$364$		0			0
$365$	5.65632	−	9.79703i	0.0154968	−	0.0268412i
$366$		0			0
$367$	18.0119	−	31.1975i	0.0490786	−	0.0850067i	−0.840442	−	0.541901i	$-0.817705\pi$
$367$	18.0119	−	31.1975i	0.0490786	−	0.0850067i	0.889521	+	0.456894i	$0.151038\pi$
$368$		0			0
$369$		−	242.000i		−	0.655827i
$370$		0			0
$371$	−1038.39	−	599.515i	−2.79890	−	1.61594i
$372$		0			0
$373$			417.570i			1.11949i	0.828664	+	0.559746i	$0.189101\pi$
$373$			417.570i			1.11949i	−0.828664	+	0.559746i	$0.810899\pi$
$374$		0			0
$375$	39.9833	−	23.0844i	0.106622	−	0.0615584i
$376$		0			0
$377$	154.254	+	267.175i	0.409161	+	0.708688i
$378$		0			0
$379$		−	244.018i		−	0.643846i	−0.946766	−	0.321923i	$-0.895671\pi$
$379$		−	244.018i		−	0.643846i	0.946766	−	0.321923i	$-0.104329\pi$
$380$		0			0
$381$	26.6892			0.0700504
$382$		0			0
$383$	−308.319	+	178.008i	−0.805009	+	0.464772i	−0.845220	−	0.534419i	$-0.820531\pi$
$383$	−308.319	+	178.008i	−0.805009	+	0.464772i	0.0402103	+	0.999191i	$0.487197\pi$
$384$		0			0
$385$	−47.5726	−	82.3982i	−0.123565	−	0.214021i
$386$		0			0
$387$	−154.341			−0.398813
$388$		0			0
$389$	209.770	−	363.332i	0.539254	−	0.934015i	−0.459690	−	0.888079i	$-0.652040\pi$
$389$	209.770	−	363.332i	0.539254	−	0.934015i	0.998944	−	0.0459361i	$-0.0146271\pi$
$390$		0			0
$391$	−10.7803			−0.0275712
$392$		0			0
$393$	173.817	+	100.354i	0.442284	+	0.255353i
$394$		0			0
$395$	−4.12494	−	2.38154i	−0.0104429	−	0.00602920i
$396$		0			0
$397$	65.9465	+	114.223i	0.166112	+	0.287714i	0.937050	−	0.349196i	$-0.113545\pi$
$397$	65.9465	+	114.223i	0.166112	+	0.287714i	−0.770938	+	0.636911i	$0.780212\pi$
$398$		0			0
$399$	−3.18507	−	422.025i	−0.00798264	−	1.05771i
$400$		0			0
$401$	−597.793	+	345.136i	−1.49075	+	0.860688i	−0.999944	−	0.0105785i	$-0.996633\pi$
$401$	−597.793	+	345.136i	−1.49075	+	0.860688i	−0.490811	+	0.871266i	$0.663299\pi$
$402$		0			0
$403$	61.5370	−	106.585i	0.152697	−	0.264480i
$404$		0			0
$405$	2.41287	−	4.17922i	0.00595771	−	0.0103191i
$406$		0			0
$407$			978.086i			2.40316i
$408$		0			0
$409$	−255.340	−	147.421i	−0.624303	−	0.360441i	0.154239	−	0.988033i	$-0.450707\pi$
$409$	−255.340	−	147.421i	−0.624303	−	0.360441i	−0.778542	+	0.627592i	$0.784041\pi$
$410$		0			0
$411$			342.814i			0.834098i
$412$		0			0
$413$	−507.070	+	292.757i	−1.22777	+	0.708855i
$414$		0			0
$415$	6.38379	+	11.0570i	0.0153826	+	0.0266435i
$416$		0			0
$417$		−	337.304i		−	0.808884i
$418$		0			0
$419$	546.214			1.30361			0.651806	−	0.758385i	$-0.274011\pi$
$419$	546.214			1.30361			0.651806	+	0.758385i	$0.274011\pi$
$420$		0			0
$421$	−89.8755	+	51.8897i	−0.213481	+	0.123253i	−0.602928	−	0.797796i	$-0.705999\pi$
$421$	−89.8755	+	51.8897i	−0.213481	+	0.123253i	0.389447	+	0.921049i	$0.372666\pi$
$422$		0			0
$423$	−60.9840	−	105.627i	−0.144170	−	0.249710i
$424$		0			0
$425$	−51.4205			−0.120989
$426$		0			0
$427$	−275.451	+	477.095i	−0.645084	+	1.11732i
$428$		0			0
$429$	283.499			0.660838
$430$		0			0
$431$	486.075	+	280.636i	1.12779	+	0.651127i	0.943377	−	0.331723i	$-0.107630\pi$
$431$	486.075	+	280.636i	1.12779	+	0.651127i	0.184408	+	0.982850i	$0.440963\pi$
$432$		0			0
$433$	168.998	+	97.5709i	0.390295	+	0.225337i	0.682288	−	0.731084i	$-0.260985\pi$
$433$	168.998	+	97.5709i	0.390295	+	0.225337i	−0.291993	+	0.956420i	$0.594318\pi$
$434$		0			0
$435$	12.1103	+	20.9757i	0.0278398	+	0.0482200i
$436$		0			0
$437$	49.8614	+	84.8766i	0.114099	+	0.194226i
$438$		0			0
$439$	413.806	−	238.911i	0.942611	−	0.544217i	0.0518333	−	0.998656i	$-0.483494\pi$
$439$	413.806	−	238.911i	0.942611	−	0.544217i	0.890778	+	0.454439i	$0.150160\pi$
$440$		0			0
$441$	173.197	−	299.986i	0.392738	−	0.680241i
$442$		0			0
$443$	30.4953	−	52.8194i	0.0688381	−	0.119231i	−0.829552	−	0.558429i	$-0.811404\pi$
$443$	30.4953	−	52.8194i	0.0688381	−	0.119231i	0.898390	+	0.439198i	$0.144737\pi$
$444$		0			0
$445$		−	65.8799i		−	0.148045i
$446$		0			0
$447$	−410.331	−	236.905i	−0.917966	−	0.529988i
$448$		0			0
$449$			627.678i			1.39795i	0.715148	+	0.698973i	$0.246359\pi$
$449$			627.678i			1.39795i	−0.715148	+	0.698973i	$0.753641\pi$
$450$		0			0
$451$	966.615	−	558.075i	2.14327	−	1.23742i
$452$		0			0
$453$	90.9466	+	157.524i	0.200765	+	0.347736i
$454$		0			0
$455$		−	81.3433i		−	0.178777i
$456$		0			0
$457$	−496.025			−1.08539			−0.542697	−	0.839929i	$-0.682597\pi$
$457$	−496.025			−1.08539			−0.542697	+	0.839929i	$0.682597\pi$
$458$		0			0
$459$	−9.36337	+	5.40595i	−0.0203995	+	0.0117777i
$460$		0			0
$461$	−280.481	−	485.807i	−0.608418	−	1.05381i	−0.991501	−	0.130097i	$-0.958471\pi$
$461$	−280.481	−	485.807i	−0.608418	−	1.05381i	0.383083	−	0.923714i	$-0.374862\pi$
$462$		0			0
$463$	647.655			1.39882			0.699411	−	0.714719i	$-0.253446\pi$
$463$	647.655			1.39882			0.699411	+	0.714719i	$0.253446\pi$
$464$		0			0
$465$	4.83121	−	8.36790i	0.0103897	−	0.0179955i
$466$		0			0
$467$	−844.539			−1.80844			−0.904218	−	0.427072i	$-0.859545\pi$
$467$	−844.539			−1.80844			−0.904218	+	0.427072i	$0.859545\pi$
$468$		0			0
$469$	−1363.51	−	787.225i	−2.90728	−	1.67852i
$470$		0			0
$471$	209.250	+	120.810i	0.444267	+	0.256498i
$472$		0			0
$473$	−355.924	−	616.479i	−0.752482	−	1.30334i
$474$		0			0
$475$	237.831	+	404.848i	0.500696	+	0.852312i
$476$		0			0
$477$	242.910	−	140.244i	0.509246	−	0.294013i
$478$		0			0
$479$	−342.254	+	592.802i	−0.714518	+	1.23758i	0.248627	+	0.968599i	$0.420021\pi$
$479$	−342.254	+	592.802i	−0.714518	+	1.23758i	−0.963145	+	0.268982i	$0.913313\pi$
$480$		0			0
$481$	−418.102	+	724.174i	−0.869235	+	1.50556i
$482$		0			0
$483$			115.083i			0.238266i
$484$		0			0
$485$	29.3674	+	16.9552i	0.0605512	+	0.0349593i
$486$		0			0
$487$		−	61.0672i		−	0.125395i	−0.998033	−	0.0626974i	$-0.980030\pi$
$487$		−	61.0672i		−	0.125395i	0.998033	−	0.0626974i	$-0.0199703\pi$
$488$		0			0
$489$	248.267	−	143.337i	0.507703	−	0.293123i
$490$		0			0
$491$	−39.2347	−	67.9565i	−0.0799077	−	0.138404i	0.823302	−	0.567603i	$-0.192129\pi$
$491$	−39.2347	−	67.9565i	−0.0799077	−	0.138404i	−0.903210	+	0.429199i	$0.858796\pi$
$492$		0			0
$493$		−	54.2653i		−	0.110072i
$494$		0			0
$495$	22.2573			0.0449642
$496$		0			0
$497$	817.226	−	471.826i	1.64432	−	0.949347i
$498$		0			0
$499$	259.674	+	449.768i	0.520388	+	0.901339i	0.999719	+	0.0237047i	$0.00754614\pi$
$499$	259.674	+	449.768i	0.520388	+	0.901339i	−0.479331	+	0.877634i	$0.659121\pi$
$500$		0			0
$501$	−190.097			−0.379434
$502$		0			0
$503$	217.835	−	377.301i	0.433072	−	0.750102i	−0.564064	−	0.825731i	$-0.690763\pi$
$503$	217.835	−	377.301i	0.433072	−	0.750102i	0.997136	+	0.0756288i	$0.0240964\pi$
$504$		0			0
$505$	−46.3896			−0.0918605
$506$		0			0
$507$	−43.5974	−	25.1710i	−0.0859909	−	0.0496469i
$508$		0			0
$509$	563.611	+	325.401i	1.10729	+	0.639295i	0.938126	−	0.346293i	$-0.112560\pi$
$509$	563.611	+	325.401i	1.10729	+	0.639295i	0.169165	+	0.985588i	$0.445893\pi$
$510$		0			0
$511$	135.285	+	234.320i	0.264745	+	0.458551i
$512$		0			0
$513$	85.8701	+	48.7168i	0.167388	+	0.0949645i
$514$		0			0
$515$	6.23306	−	3.59866i	0.0121030	−	0.00698768i
$516$		0			0
$517$	281.270	−	487.174i	0.544042	−	0.942309i
$518$		0			0
$519$	−129.070	+	223.556i	−0.248690	+	0.430745i
$520$		0			0
$521$			155.270i			0.298024i	0.988835	+	0.149012i	$0.0476093\pi$
$521$			155.270i			0.298024i	−0.988835	+	0.149012i	$0.952391\pi$
$522$		0			0
$523$	348.284	+	201.082i	0.665936	+	0.384478i	0.794535	−	0.607218i	$-0.207715\pi$
$523$	348.284	+	201.082i	0.665936	+	0.384478i	−0.128599	+	0.991697i	$0.541048\pi$
$524$		0			0
$525$			548.926i			1.04557i
$526$		0			0
$527$	−18.7479	+	10.8241i	−0.0355748	+	0.0205391i
$528$		0			0
$529$	251.079	+	434.881i	0.474629	+	0.822081i
$530$		0			0
$531$		−	136.969i		−	0.257945i
$532$		0			0
$533$	954.241			1.79032
$534$		0			0
$535$	−43.9546	+	25.3772i	−0.0821581	+	0.0474340i
$536$		0			0
$537$	89.8819	+	155.680i	0.167378	+	0.289907i
$538$		0			0
$539$	1597.64			2.96408
$540$		0			0
$541$	−133.340	+	230.952i	−0.246470	+	0.426899i	−0.962544	−	0.271126i	$-0.912604\pi$
$541$	−133.340	+	230.952i	−0.246470	+	0.426899i	0.716074	+	0.698025i	$0.245937\pi$
$542$		0			0
$543$	69.0450			0.127155
$544$		0			0
$545$	55.0730	+	31.7964i	0.101051	+	0.0583421i
$546$		0			0
$547$	76.2531	+	44.0247i	0.139402	+	0.0804840i	0.568079	−	0.822974i	$-0.307687\pi$
$547$	76.2531	+	44.0247i	0.139402	+	0.0804840i	−0.428677	+	0.903458i	$0.641020\pi$
$548$		0			0
$549$	−64.4361	−	111.607i	−0.117370	−	0.203291i
$550$		0			0
$551$	−427.246	+	250.989i	−0.775401	+	0.455515i
$552$		0			0
$553$	98.6579	−	56.9602i	0.178405	−	0.103002i
$554$		0			0
$555$	−32.8248	+	56.8542i	−0.0591437	+	0.102440i
$556$		0			0
$557$	327.943	−	568.014i	0.588767	−	1.01977i	−0.405627	−	0.914039i	$-0.632947\pi$
$557$	327.943	−	568.014i	0.588767	−	1.01977i	0.994394	−	0.105736i	$-0.0337198\pi$
$558$		0			0
$559$		−	608.587i		−	1.08871i
$560$		0			0
$561$	−43.1856	−	24.9332i	−0.0769797	−	0.0444443i
$562$		0			0
$563$		−	959.403i		−	1.70409i	−0.523468	−	0.852046i	$-0.675362\pi$
$563$		−	959.403i		−	1.70409i	0.523468	−	0.852046i	$-0.324638\pi$
$564$		0			0
$565$	−33.3419	+	19.2500i	−0.0590122	+	0.0340707i
$566$		0			0
$567$	57.7097	+	99.9562i	0.101781	+	0.176290i
$568$		0			0
$569$		−	601.848i		−	1.05773i	−0.848706	−	0.528865i	$-0.822618\pi$
$569$		−	601.848i		−	1.05773i	0.848706	−	0.528865i	$-0.177382\pi$
$570$		0			0
$571$	549.040			0.961541			0.480771	−	0.876846i	$-0.340357\pi$
$571$	549.040			0.961541			0.480771	+	0.876846i	$0.340357\pi$
$572$		0			0
$573$	−45.2014	+	26.0971i	−0.0788855	+	0.0455446i
$574$		0			0
$575$	−64.0176	−	110.882i	−0.111335	−	0.192838i
$576$		0			0
$577$	392.155			0.679644			0.339822	−	0.940490i	$-0.389633\pi$
$577$	392.155			0.679644			0.339822	+	0.940490i	$0.389633\pi$
$578$		0			0
$579$	37.3548	−	64.7003i	0.0645160	−	0.111745i
$580$		0			0
$581$	−305.367			−0.525589
$582$		0			0
$583$	1120.35	+	646.833i	1.92169	+	1.10949i
$584$		0			0
$585$	16.4792	+	9.51430i	0.0281697	+	0.0162638i
$586$		0			0
$587$	352.178	+	609.990i	0.599962	+	1.03916i	0.992826	+	0.119568i	$0.0381510\pi$
$587$	352.178	+	609.990i	0.599962	+	1.03916i	−0.392864	+	0.919597i	$0.628516\pi$
$588$		0			0
$589$	171.935	+	97.5439i	0.291909	+	0.165609i
$590$		0			0
$591$	−34.4734	+	19.9032i	−0.0583305	+	0.0336772i
$592$		0			0
$593$	−124.231	+	215.175i	−0.209496	+	0.362858i	−0.951556	−	0.307476i	$-0.900516\pi$
$593$	−124.231	+	215.175i	−0.209496	+	0.362858i	0.742060	+	0.670334i	$0.233849\pi$
$594$		0			0
$595$	−7.15399	+	12.3911i	−0.0120235	+	0.0208253i
$596$		0			0
$597$		−	468.999i		−	0.785593i
$598$		0			0
$599$	421.593	+	243.407i	0.703829	+	0.406356i	0.808772	−	0.588123i	$-0.200133\pi$
$599$	421.593	+	243.407i	0.703829	+	0.406356i	−0.104943	+	0.994478i	$0.533466\pi$
$600$		0			0
$601$		−	425.895i		−	0.708644i	−0.935123	−	0.354322i	$-0.884712\pi$
$601$		−	425.895i		−	0.708644i	0.935123	−	0.354322i	$-0.115288\pi$
$602$		0			0
$603$	318.966	−	184.155i	0.528965	−	0.305398i
$604$		0			0
$605$	18.8876	+	32.7142i	0.0312191	+	0.0540731i
$606$		0			0
$607$		−	577.825i		−	0.951935i	−0.879463	−	0.475968i	$-0.842098\pi$
$607$		−	577.825i		−	0.951935i	0.879463	−	0.475968i	$-0.157902\pi$
$608$		0			0
$609$	−579.295			−0.951224
$610$		0			0
$611$	416.504	−	240.468i	0.681675	−	0.393565i
$612$		0			0
$613$	−177.356	−	307.189i	−0.289324	−	0.501124i	0.684325	−	0.729178i	$-0.260097\pi$
$613$	−177.356	−	307.189i	−0.289324	−	0.501124i	−0.973649	+	0.228054i	$0.926764\pi$
$614$		0			0
$615$	74.9165			0.121815
$616$		0			0
$617$	−452.501	+	783.756i	−0.733390	+	1.27027i	0.222037	+	0.975038i	$0.428730\pi$
$617$	−452.501	+	783.756i	−0.733390	+	1.27027i	−0.955426	+	0.295230i	$0.904604\pi$
$618$		0			0
$619$	−416.283			−0.672509			−0.336255	−	0.941771i	$-0.609160\pi$
$619$	−416.283			−0.672509			−0.336255	+	0.941771i	$0.609160\pi$
$620$		0			0
$621$	−23.3145	−	13.4606i	−0.0375434	−	0.0216757i
$622$		0			0
$623$	1364.58	+	787.838i	2.19033	+	1.26459i
$624$		0			0
$625$	−301.760	−	522.664i	−0.482816	−	0.836262i
$626$		0			0
$627$	3.43646	+	455.334i	0.00548079	+	0.726211i
$628$		0			0
$629$	127.379	−	73.5425i	0.202511	−	0.116920i
$630$		0			0
$631$	166.325	−	288.084i	0.263590	−	0.456551i	−0.703603	−	0.710593i	$-0.748427\pi$
$631$	166.325	−	288.084i	0.263590	−	0.456551i	0.967193	+	0.254042i	$0.0817601\pi$
$632$		0			0
$633$	−186.337	+	322.745i	−0.294371	+	0.509865i
$634$		0			0
$635$			8.26223i			0.0130114i
$636$		0			0
$637$	1182.89	+	682.941i	1.85697	+	1.07212i
$638$		0			0
$639$			220.748i			0.345458i
$640$		0			0
$641$	84.1170	−	48.5650i	0.131228	−	0.0757644i	−0.432949	−	0.901418i	$-0.642527\pi$
$641$	84.1170	−	48.5650i	0.131228	−	0.0757644i	0.564177	+	0.825654i	$0.309194\pi$
$642$		0			0
$643$	73.7693	+	127.772i	0.114727	+	0.198713i	0.917671	−	0.397342i	$-0.130067\pi$
$643$	73.7693	+	127.772i	0.114727	+	0.198713i	−0.802944	+	0.596055i	$0.796734\pi$
$644$		0			0
$645$		−	47.7795i		−	0.0740768i
$646$		0			0
$647$	−28.8356			−0.0445681			−0.0222841	−	0.999752i	$-0.507094\pi$
$647$	−28.8356			−0.0445681			−0.0222841	+	0.999752i	$0.507094\pi$
$648$		0			0
$649$	547.091	−	315.863i	0.842975	−	0.486692i
$650$		0			0
$651$	115.550	+	200.139i	0.177496	+	0.307433i
$652$		0			0
$653$	−110.512			−0.169237			−0.0846187	−	0.996413i	$-0.526967\pi$
$653$	−110.512			−0.169237			−0.0846187	+	0.996413i	$0.526967\pi$
$654$		0			0
$655$	−31.0666	+	53.8090i	−0.0474300	+	0.0821512i
$656$		0			0
$657$	−63.2941			−0.0963380
$658$		0			0
$659$	−805.767	−	465.210i	−1.22271	−	0.705933i	−0.257216	−	0.966354i	$-0.582805\pi$
$659$	−805.767	−	465.210i	−1.22271	−	0.705933i	−0.965495	+	0.260421i	$0.916139\pi$
$660$		0			0
$661$	756.773	+	436.923i	1.14489	+	0.661003i	0.947637	−	0.319349i	$-0.103464\pi$
$661$	756.773	+	436.923i	1.14489	+	0.661003i	0.197254	+	0.980352i	$0.436798\pi$
$662$		0			0
$663$	−21.3164	−	36.9211i	−0.0321514	−	0.0556879i
$664$		0			0
$665$	130.647	−	0.986009i	0.196462	−	0.00148272i
$666$		0			0
$667$	117.016	−	67.5594i	0.175437	−	0.101288i
$668$		0			0
$669$	−147.129	+	254.835i	−0.219924	+	0.380920i
$670$		0			0
$671$	297.191	−	514.750i	0.442908	−	0.767139i
$672$		0			0
$673$		−	582.726i		−	0.865863i	−0.901427	−	0.432932i	$-0.857479\pi$
$673$		−	582.726i		−	0.865863i	0.901427	−	0.432932i	$-0.142521\pi$
$674$		0			0
$675$	−111.206	−	64.2049i	−0.164750	−	0.0951184i
$676$		0			0
$677$		−	1182.04i		−	1.74599i	−0.487726	−	0.872997i	$-0.662173\pi$
$677$		−	1182.04i		−	1.74599i	0.487726	−	0.872997i	$-0.337827\pi$
$678$		0			0
$679$	−702.391	+	405.526i	−1.03445	+	0.597240i
$680$		0			0
$681$	298.179	+	516.462i	0.437855	+	0.758388i
$682$		0			0
$683$		−	560.851i		−	0.821159i	−0.911825	−	0.410579i	$-0.865326\pi$
$683$		−	560.851i		−	0.821159i	0.911825	−	0.410579i	$-0.134674\pi$
$684$		0			0
$685$	−106.126			−0.154928
$686$		0			0
$687$	−566.487	+	327.061i	−0.824580	+	0.476072i
$688$		0			0
$689$	553.003	+	957.828i	0.802616	+	1.39017i
$690$		0			0
$691$	−975.733			−1.41206			−0.706030	−	0.708182i	$-0.749515\pi$
$691$	−975.733			−1.41206			−0.706030	+	0.708182i	$0.749515\pi$
$692$		0			0
$693$	−266.168	+	461.017i	−0.384081	+	0.665248i
$694$		0			0
$695$	104.420			0.150245
$696$		0			0
$697$	−145.360	−	83.9237i	−0.208551	−	0.120407i
$698$		0			0
$699$	−529.902	−	305.939i	−0.758086	−	0.437681i
$700$		0			0
$701$	−442.139	−	765.807i	−0.630726	−	1.09245i	−0.987404	−	0.158222i	$-0.949424\pi$
$701$	−442.139	−	765.807i	−0.630726	−	1.09245i	0.356677	−	0.934228i	$-0.383910\pi$
$702$		0			0
$703$	−1168.18	−	662.744i	−1.66170	−	0.942736i
$704$		0			0
$705$	32.6993	−	18.8789i	0.0463820	−	0.0267786i
$706$		0			0
$707$	554.760	−	960.872i	0.784667	−	1.35908i
$708$		0			0
$709$	−555.769	+	962.621i	−0.783878	+	1.35772i	0.145789	+	0.989316i	$0.453428\pi$
$709$	−555.769	+	962.621i	−0.783878	+	1.35772i	−0.929667	+	0.368401i	$0.879905\pi$
$710$		0			0
$711$			26.6493i			0.0374815i
$712$		0			0
$713$	−46.6817	−	26.9517i	−0.0654722	−	0.0378004i
$714$		0			0
$715$			87.7635i			0.122746i
$716$		0			0
$717$	33.3640	−	19.2627i	0.0465328	−	0.0268657i
$718$		0			0
$719$	−367.495	−	636.520i	−0.511119	−	0.885285i	−0.999917	−	0.0128874i	$-0.995898\pi$
$719$	−367.495	−	636.520i	−0.511119	−	0.885285i	0.488798	−	0.872397i	$-0.337436\pi$
$720$		0			0
$721$			172.141i			0.238753i
$722$		0			0
$723$	−430.610			−0.595588
$724$		0			0
$725$	558.149	−	322.247i	0.769860	−	0.444479i
$726$		0			0
$727$	161.224	+	279.249i	0.221767	+	0.384111i	0.955344	−	0.295494i	$-0.0954843\pi$
$727$	161.224	+	279.249i	0.221767	+	0.384111i	−0.733578	+	0.679605i	$0.762151\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−53.5241	+	92.7064i	−0.0732203	+	0.126821i
$732$		0			0
$733$	247.225			0.337279			0.168639	−	0.985678i	$-0.446063\pi$
$733$	247.225			0.337279			0.168639	+	0.985678i	$0.446063\pi$
$734$		0			0
$735$	92.8674	+	53.6170i	0.126350	+	0.0729483i
$736$		0			0
$737$	1471.13	+	849.358i	1.99611	+	1.15245i
$738$		0			0
$739$	300.818	+	521.032i	0.407061	+	0.705051i	0.994559	−	0.104175i	$-0.0332203\pi$
$739$	300.818	+	521.032i	0.407061	+	0.705051i	−0.587498	+	0.809226i	$0.699887\pi$
$740$		0			0
$741$	−192.097	+	338.598i	−0.259240	+	0.456947i
$742$		0			0
$743$	447.584	−	258.412i	0.602400	−	0.347796i	−0.167585	−	0.985858i	$-0.553597\pi$
$743$	447.584	−	258.412i	0.602400	−	0.347796i	0.769985	+	0.638062i	$0.220263\pi$
$744$		0			0
$745$	73.3390	−	127.027i	0.0984417	−	0.170506i
$746$		0			0
$747$	35.7172	−	61.8640i	0.0478142	−	0.0828166i
$748$		0			0
$749$		−	1213.91i		−	1.62071i
$750$		0			0
$751$	−871.327	−	503.061i	−1.16022	−	0.669854i	−0.208865	−	0.977945i	$-0.566977\pi$
$751$	−871.327	−	503.061i	−1.16022	−	0.669854i	−0.951357	+	0.308090i	$0.900310\pi$
$752$		0			0
$753$		−	194.778i		−	0.258669i
$754$		0			0
$755$	−48.7651	+	28.1545i	−0.0645895	+	0.0372908i
$756$		0			0
$757$	−3.12796	−	5.41779i	−0.00413205	−	0.00715692i	0.863952	−	0.503574i	$-0.167982\pi$
$757$	−3.12796	−	5.41779i	−0.00413205	−	0.00715692i	−0.868084	+	0.496417i	$0.834649\pi$
$758$		0			0
$759$		−	124.166i		−	0.163591i
$760$		0			0
$761$	636.960			0.837004			0.418502	−	0.908216i	$-0.362555\pi$
$761$	636.960			0.837004			0.418502	+	0.908216i	$0.362555\pi$
$762$		0			0
$763$	−1317.21	+	760.489i	−1.72635	+	0.996709i
$764$		0			0
$765$	−1.67353	−	2.89864i	−0.00218762	−	0.00378907i
$766$		0			0
$767$	540.087			0.704156
$768$		0			0
$769$	−504.684	+	874.139i	−0.656287	+	1.13672i	0.325283	+	0.945617i	$0.394540\pi$
$769$	−504.684	+	874.139i	−0.656287	+	1.13672i	−0.981570	+	0.191105i	$0.938793\pi$
$770$		0			0
$771$	658.445			0.854014
$772$		0			0
$773$	546.616	+	315.589i	0.707136	+	0.408265i	0.810000	−	0.586430i	$-0.199467\pi$
$773$	546.616	+	315.589i	0.707136	+	0.408265i	−0.102864	+	0.994695i	$0.532801\pi$
$774$		0			0
$775$	−222.664	−	128.555i	−0.287309	−	0.165878i
$776$		0			0
$777$	−785.084	−	1359.80i	−1.01040	−	1.75007i
$778$		0			0
$779$	11.5669	+	1532.63i	0.0148484	+	1.96743i
$780$		0			0
$781$	−881.726	+	509.065i	−1.12897	+	0.651812i
$782$		0			0
$783$	67.7571	−	117.359i	0.0865352	−	0.149883i
$784$		0			0
$785$	−37.3995	+	64.7778i	−0.0476427	+	0.0825195i
$786$		0			0
$787$		−	228.970i		−	0.290940i	−0.989363	−	0.145470i	$-0.953531\pi$
$787$		−	228.970i		−	0.290940i	0.989363	−	0.145470i	$-0.0464695\pi$
$788$		0			0
$789$	−191.375	−	110.490i	−0.242553	−	0.140038i
$790$		0			0
$791$		−	920.819i		−	1.16412i
$792$		0			0
$793$	440.080	−	254.080i	0.554956	−	0.320404i
$794$		0			0
$795$	43.4157	+	75.1982i	0.0546109	+	0.0945889i
$796$		0			0
$797$			868.165i			1.08929i	0.838666	+	0.544646i	$0.183336\pi$
$797$			868.165i			1.08929i	−0.838666	+	0.544646i	$0.816664\pi$
$798$		0			0
$799$	−84.5950			−0.105876
$800$		0			0
$801$	−319.214	+	184.298i	−0.398520	+	0.230085i
$802$		0			0
$803$	−145.962	−	252.814i	−0.181771	−	0.314836i
$804$		0			0
$805$	−35.6264			−0.0442564
$806$		0			0
$807$	163.353	−	282.936i	0.202421	−	0.350603i
$808$		0			0
$809$	−1237.44			−1.52959			−0.764794	−	0.644275i	$-0.777159\pi$
$809$	−1237.44			−1.52959			−0.764794	+	0.644275i	$0.777159\pi$
$810$		0			0
$811$	−59.5034	−	34.3543i	−0.0733704	−	0.0423604i	0.462866	−	0.886428i	$-0.346821\pi$
$811$	−59.5034	−	34.3543i	−0.0733704	−	0.0423604i	−0.536236	+	0.844068i	$0.680154\pi$
$812$		0			0
$813$	548.454	+	316.650i	0.674606	+	0.389484i
$814$		0			0
$815$	44.3731	+	76.8565i	0.0544455	+	0.0943024i
$816$		0			0
$817$	977.463	−	7.37703i	1.19641	−	0.00902941i
$818$		0			0
$819$	−394.141	+	227.557i	−0.481247	+	0.277848i
$820$		0			0
$821$	311.989	−	540.381i	0.380011	−	0.658199i	−0.611052	−	0.791590i	$-0.709253\pi$
$821$	311.989	−	540.381i	0.380011	−	0.658199i	0.991063	+	0.133392i	$0.0425868\pi$
$822$		0			0
$823$	−29.5232	+	51.1357i	−0.0358727	+	0.0621333i	−0.883404	−	0.468612i	$-0.844754\pi$
$823$	−29.5232	+	51.1357i	−0.0358727	+	0.0621333i	0.847532	+	0.530745i	$0.178088\pi$
$824$		0			0
$825$		−	592.251i		−	0.717879i
$826$		0			0
$827$	372.722	+	215.191i	0.450692	+	0.260207i	0.708122	−	0.706090i	$-0.249543\pi$
$827$	372.722	+	215.191i	0.450692	+	0.260207i	−0.257431	+	0.966297i	$0.582876\pi$
$828$		0			0
$829$			18.2254i			0.0219848i	0.999940	+	0.0109924i	$0.00349906\pi$
$829$			18.2254i			0.0219848i	−0.999940	+	0.0109924i	$0.996501\pi$
$830$		0			0
$831$	−448.922	+	259.185i	−0.540219	+	0.311895i
$832$		0			0
$833$	−120.127	−	208.066i	−0.144210	−	0.249779i
$834$		0			0
$835$		−	58.8485i		−	0.0704773i
$836$		0			0
$837$	−54.0611			−0.0645892
$838$		0			0
$839$	−484.320	+	279.622i	−0.577259	+	0.333281i	−0.760043	−	0.649872i	$-0.774822\pi$
$839$	−484.320	+	279.622i	−0.577259	+	0.333281i	0.182784	+	0.983153i	$0.441489\pi$
$840$		0			0
$841$	−80.4245	−	139.299i	−0.0956296	−	0.165635i
$842$		0			0
$843$	8.03889			0.00953605
$844$		0			0
$845$	7.79223	−	13.4965i	0.00922157	−	0.0159722i
$846$		0			0
$847$	−903.484			−1.06669
$848$		0			0
$849$	443.891	+	256.280i	0.522839	+	0.301861i
$850$		0			0
$851$	317.170	+	183.118i	0.372703	+	0.215180i
$852$		0			0
$853$	−427.509	−	740.467i	−0.501183	−	0.868074i	−0.999999	−	0.00136643i	$-0.999565\pi$
$853$	−427.509	−	740.467i	−0.501183	−	0.868074i	0.498816	−	0.866708i	$-0.333768\pi$
$854$		0			0
$855$	−15.0813	+	26.5830i	−0.0176390	+	0.0310912i
$856$		0			0
$857$	995.618	−	574.820i	1.16175	−	0.670735i	0.210025	−	0.977696i	$-0.432645\pi$
$857$	995.618	−	574.820i	1.16175	−	0.670735i	0.951722	+	0.306961i	$0.0993120\pi$
$858$		0			0
$859$	676.013	−	1170.89i	0.786977	−	1.36308i	−0.140834	−	0.990033i	$-0.544978\pi$
$859$	676.013	−	1170.89i	0.786977	−	1.36308i	0.927811	−	0.373051i	$-0.121688\pi$
$860$		0			0
$861$	−895.905	+	1551.75i	−1.04054	+	1.80227i
$862$		0			0
$863$		−	228.033i		−	0.264233i	−0.991234	−	0.132116i	$-0.957823\pi$
$863$		−	228.033i		−	0.264233i	0.991234	−	0.132116i	$-0.0421772\pi$
$864$		0			0
$865$	−69.2068	−	39.9566i	−0.0800078	−	0.0461926i
$866$		0			0
$867$		−	493.064i		−	0.568701i
$868$		0			0
$869$	−106.445	+	61.4558i	−0.122491	+	0.0707202i
$870$		0			0
$871$	726.149	+	1257.73i	0.833696	+	1.44400i
$872$		0			0
$873$		−	189.729i		−	0.217330i
$874$		0			0
$875$	−341.841			−0.390676
$876$		0			0
$877$	−62.8915	+	36.3104i	−0.0717121	+	0.0414030i	−0.535427	−	0.844581i	$-0.679849\pi$
$877$	−62.8915	+	36.3104i	−0.0717121	+	0.0414030i	0.463715	+	0.885984i	$0.346516\pi$
$878$		0			0
$879$	157.620	+	273.007i	0.179318	+	0.310588i
$880$		0			0
$881$	1128.26			1.28066			0.640331	−	0.768099i	$-0.278797\pi$
$881$	1128.26			1.28066			0.640331	+	0.768099i	$0.278797\pi$
$882$		0			0
$883$	−26.6671	+	46.1888i	−0.0302006	+	0.0523089i	−0.880731	−	0.473617i	$-0.842948\pi$
$883$	−26.6671	+	46.1888i	−0.0302006	+	0.0523089i	0.850530	+	0.525926i	$0.176281\pi$
$884$		0			0
$885$	42.4017			0.0479116
$886$		0			0
$887$	362.407	+	209.236i	0.408576	+	0.235892i	0.690178	−	0.723640i	$-0.257532\pi$
$887$	362.407	+	209.236i	0.408576	+	0.235892i	−0.281602	+	0.959531i	$0.590866\pi$
$888$		0			0
$889$	−171.136	−	98.8056i	−0.192504	−	0.111142i
$890$		0			0
$891$	−62.2645	−	107.845i	−0.0698816	−	0.121039i
$892$		0			0
$893$	391.270	+	666.040i	0.438152	+	0.745845i
$894$		0			0
$895$	−48.1942	+	27.8249i	−0.0538482	+	0.0310893i
$896$		0			0
$897$	53.0770	−	91.9321i	0.0591717	−	0.102488i
$898$		0			0
$899$	135.668	−	234.983i	0.150909	−	0.261383i
$900$		0			0
$901$		−	194.542i		−	0.215918i
$902$		0			0
$903$	989.662	+	571.382i	1.09597	+	0.632759i
$904$		0			0
$905$			21.3744i			0.0236181i
$906$		0			0
$907$	−378.596	+	218.583i	−0.417416	+	0.240995i	−0.693971	−	0.720003i	$-0.744141\pi$
$907$	−378.596	+	218.583i	−0.417416	+	0.240995i	0.276555	+	0.960998i	$0.410807\pi$
$908$		0			0
$909$	129.775	+	224.776i	0.142766	+	0.247278i
$910$		0			0
$911$		−	1450.78i		−	1.59252i	−0.604957	−	0.796258i	$-0.706810\pi$
$911$		−	1450.78i		−	1.59252i	0.604957	−	0.796258i	$-0.293190\pi$
$912$		0			0
$913$	329.469			0.360864
$914$		0			0
$915$	34.5503	−	19.9476i	0.0377599	−	0.0218007i
$916$		0			0
$917$	−743.034	−	1286.97i	−0.810288	−	1.40346i
$918$		0			0
$919$	1032.12			1.12309			0.561545	−	0.827446i	$-0.310207\pi$
$919$	1032.12			1.12309			0.561545	+	0.827446i	$0.310207\pi$
$920$		0			0
$921$	−90.0676	+	156.002i	−0.0977933	+	0.169383i
$922$		0			0
$923$	−870.439			−0.943054
$924$		0			0
$925$	1512.85	+	873.445i	1.63551	+	0.944265i
$926$		0			0
$927$	−34.8739	−	20.1344i	−0.0376201	−	0.0217200i
$928$		0			0
$929$	182.887	+	316.770i	0.196865	+	0.340980i	0.947510	−	0.319725i	$-0.103591\pi$
$929$	182.887	+	316.770i	0.196865	+	0.340980i	−0.750645	+	0.660705i	$0.770257\pi$
$930$		0			0
$931$	−1082.55	+	1908.14i	−1.16278	+	2.04956i
$932$		0			0
$933$	−90.1553	+	52.0512i	−0.0966295	+	0.0557891i
$934$		0			0
$935$	7.71863	−	13.3691i	0.00825522	−	0.0142985i
$936$		0			0
$937$	11.7436	−	20.3405i	0.0125332	−	0.0217081i	−0.859691	−	0.510815i	$-0.829344\pi$
$937$	11.7436	−	20.3405i	0.0125332	−	0.0217081i	0.872224	+	0.489107i	$0.162677\pi$
$938$		0			0
$939$		−	430.540i		−	0.458509i
$940$		0			0
$941$	−623.052	−	359.720i	−0.662117	−	0.382274i	0.130966	−	0.991387i	$-0.458192\pi$
$941$	−623.052	−	359.720i	−0.662117	−	0.382274i	−0.793083	+	0.609113i	$0.791525\pi$
$942$		0			0
$943$		−	417.934i		−	0.443196i
$944$		0			0
$945$	−30.9436	+	17.8653i	−0.0327446	+	0.0189051i
$946$		0			0
$947$	271.004	+	469.393i	0.286171	+	0.495664i	0.972893	−	0.231257i	$-0.0742840\pi$
$947$	271.004	+	469.393i	0.286171	+	0.495664i	−0.686721	+	0.726921i	$0.740951\pi$
$948$		0			0
$949$		−	249.577i		−	0.262990i
$950$		0			0
$951$	−789.513			−0.830192
$952$		0			0
$953$	−144.494	+	83.4234i	−0.151620	+	0.0875376i	−0.573890	−	0.818932i	$-0.694566\pi$
$953$	−144.494	+	83.4234i	−0.151620	+	0.0875376i	0.422271	+	0.906470i	$0.361233\pi$
$954$		0			0
$955$	−8.07891	−	13.9931i	−0.00845960	−	0.0146525i
$956$		0			0
$957$	625.017			0.653100
$958$		0			0
$959$	1269.13	−	2198.19i	1.32339	−	2.29217i
$960$		0			0
$961$	852.755			0.887362
$962$		0			0
$963$	245.925	+	141.985i	0.255374	+	0.147440i
$964$		0			0
$965$	20.0294	+	11.5640i	0.0207559	+	0.0119834i
$966$		0			0
$967$	−921.600	−	1596.26i	−0.953051	−	1.65073i	−0.738767	−	0.673961i	$-0.764591\pi$
$967$	−921.600	−	1596.26i	−0.953051	−	1.65073i	−0.214284	−	0.976771i	$-0.568742\pi$
$968$		0			0
$969$	59.0413	−	34.6842i	0.0609301	−	0.0357938i
$970$		0			0
$971$	−1030.18	+	594.776i	−1.06095	+	0.612539i	−0.925695	−	0.378271i	$-0.876519\pi$
$971$	−1030.18	+	594.776i	−1.06095	+	0.612539i	−0.135255	+	0.990811i	$0.543185\pi$
$972$		0			0
$973$	−1248.73	+	2162.86i	−1.28338	+	2.22288i
$974$		0			0
$975$	253.169	−	438.502i	0.259661	−	0.449745i
$976$		0			0
$977$			991.089i			1.01442i	0.861822	+	0.507211i	$0.169323\pi$
$977$			991.089i			1.01442i	−0.861822	+	0.507211i	$0.830677\pi$
$978$		0			0
$979$	−1472.28	−	850.019i	−1.50386	−	0.868252i
$980$		0			0
$981$		−	355.801i		−	0.362692i
$982$		0			0
$983$	168.660	−	97.3758i	0.171577	−	0.0990598i	−0.411752	−	0.911296i	$-0.635083\pi$
$983$	168.660	−	97.3758i	0.171577	−	0.0990598i	0.583329	+	0.812236i	$0.301750\pi$
$984$		0			0
$985$	−6.16147	−	10.6720i	−0.00625530	−	0.0108345i
$986$		0			0
$987$			903.071i			0.914966i
$988$		0			0
$989$	−266.546			−0.269511
$990$		0			0
$991$	−1480.50	+	854.766i	−1.49394	+	0.862529i	−0.999976	−	0.00695077i	$-0.997787\pi$
$991$	−1480.50	+	854.766i	−1.49394	+	0.862529i	−0.493968	+	0.869480i	$0.664454\pi$
$992$		0			0
$993$	−341.346	−	591.228i	−0.343752	−	0.595396i
$994$		0			0
$995$	145.189			0.145919
$996$		0			0
$997$	42.8319	−	74.1870i	0.0429607	−	0.0744102i	−0.843745	−	0.536743i	$-0.819654\pi$
$997$	42.8319	−	74.1870i	0.0429607	−	0.0744102i	0.886706	+	0.462333i	$0.152988\pi$
$998$		0			0
$999$	367.308			0.367676

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.3.be.j.145.6		20
4.3	odd	2		456.3.w.a.145.6	✓	20
12.11	even	2		1368.3.bv.c.145.5		20
19.8	odd	6	inner	912.3.be.j.673.6		20
76.27	even	6		456.3.w.a.217.6	yes	20
228.179	odd	6		1368.3.bv.c.217.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.3.w.a.145.6	✓	20	4.3	odd	2
456.3.w.a.217.6	yes	20	76.27	even	6
912.3.be.j.145.6		20	1.1	even	1	trivial
912.3.be.j.673.6		20	19.8	odd	6	inner
1368.3.bv.c.145.5		20	12.11	even	2
1368.3.bv.c.217.5		20	228.179	odd	6

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	912.be (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{3} +(0.268097 + 0.464358i) q^{5} -12.8244 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 0.866025i) q^{3} +(0.268097 + 0.464358i) q^{5} -12.8244 q^{7} +(1.50000 - 2.59808i) q^{9} +13.8366 q^{11} +(10.2446 + 5.91471i) q^{13} +(0.804291 + 0.464358i) q^{15} +(-1.04037 - 1.80198i) q^{17} +(-9.37555 + 16.5257i) q^{19} +(-19.2366 + 11.1062i) q^{21} +(2.59050 - 4.48687i) q^{23} +(12.3562 - 21.4016i) q^{25} -5.19615i q^{27} +(22.5857 + 13.0399i) q^{29} -10.4041i q^{31} +(20.7548 - 11.9828i) q^{33} +(-3.43818 - 5.95510i) q^{35} +70.6885i q^{37} +20.4891 q^{39} +(69.8595 - 40.3334i) q^{41} +(-25.7235 - 44.5543i) q^{43} +1.60858 q^{45} +(20.3280 - 35.2091i) q^{47} +115.465 q^{49} +(-3.12112 - 1.80198i) q^{51} +(80.9701 + 46.7481i) q^{53} +(3.70954 + 6.42512i) q^{55} +(0.248361 + 32.9080i) q^{57} +(39.5395 - 22.8282i) q^{59} +(21.4787 - 37.2022i) q^{61} +(-19.2366 + 33.3187i) q^{63} +6.34287i q^{65} +(106.322 + 61.3850i) q^{67} -8.97374i q^{69} +(-63.7244 + 36.7913i) q^{71} +(-10.5490 - 18.2714i) q^{73} -42.8033i q^{75} -177.445 q^{77} +(-7.69299 + 4.44155i) q^{79} +(-4.50000 - 7.79423i) q^{81} +23.8115 q^{83} +(0.557843 - 0.966212i) q^{85} +45.1714 q^{87} +(-106.405 - 61.4328i) q^{89} +(-131.380 - 75.8525i) q^{91} +(-9.01019 - 15.6061i) q^{93} +(-10.1874 + 0.0768855i) q^{95} +(54.7700 - 31.6215i) q^{97} +(20.7548 - 35.9484i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9}+O(q^{10}) \) 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9	\( 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9} + 8 q^{11} + 18 q^{13} + 8 q^{17} - 28 q^{19} - 30 q^{21} + 8 q^{23} - 58 q^{25} + 108 q^{29} + 12 q^{33} - 20 q^{35} + 36 q^{39} - 36 q^{41} + 2 q^{43} + 296 q^{49} + 24 q^{51} - 72 q^{53} - 216 q^{55} - 30 q^{57} - 72 q^{59} - 26 q^{61} - 30 q^{63} - 138 q^{67} + 204 q^{71} + 218 q^{73} - 8 q^{77} + 78 q^{79} - 90 q^{81} + 112 q^{83} + 224 q^{85} + 216 q^{87} - 432 q^{89} + 330 q^{91} - 126 q^{93} - 220 q^{95} + 132 q^{97} + 12 q^{99}+O(q^{100}) \) 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9 + 8 * q^11 + 18 * q^13 + 8 * q^17 - 28 * q^19 - 30 * q^21 + 8 * q^23 - 58 * q^25 + 108 * q^29 + 12 * q^33 - 20 * q^35 + 36 * q^39 - 36 * q^41 + 2 * q^43 + 296 * q^49 + 24 * q^51 - 72 * q^53 - 216 * q^55 - 30 * q^57 - 72 * q^59 - 26 * q^61 - 30 * q^63 - 138 * q^67 + 204 * q^71 + 218 * q^73 - 8 * q^77 + 78 * q^79 - 90 * q^81 + 112 * q^83 + 224 * q^85 + 216 * q^87 - 432 * q^89 + 330 * q^91 - 126 * q^93 - 220 * q^95 + 132 * q^97 + 12 * q^99

Introduction

L-functions

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Database

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