LMFDB - Embedded newform 405.4.e.w.136.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,4,Mod(136,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("405.136");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	405.e (of order $3$, 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:	$23.8957735523$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 2 x^{10} + 32 x^{9} + 583 x^{8} - 624 x^{7} + 594 x^{6} + 9450 x^{5} + 90513 x^{4} + \cdots + 746496 $ x^12 - 2x^11 + 2x^10 + 32x^9 + 583x^8 - 624x^7 + 594x^6 + 9450x^5 + 90513x^4 - 20304x^3 + 10368x^2 + 124416*x + 746496
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			136.4
Root			$3.41462 - 3.41462i$ of defining polynomial
Character	$\chi$	$=$	405.136
Dual form			405.4.e.w.271.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0745751 - 0.129168i) q^{2} +(3.98888 + 6.90894i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(-10.0712 + 17.4439i) q^{7} +2.38308 q^{8} +O(q^{10})$	\(q+(0.0745751 - 0.129168i) q^{2} +(3.98888 + 6.90894i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(-10.0712 + 17.4439i) q^{7} +2.38308 q^{8} -0.745751 q^{10} +(4.94688 - 8.56825i) q^{11} +(5.91394 + 10.2432i) q^{13} +(1.50212 + 2.60176i) q^{14} +(-31.7333 + 54.9637i) q^{16} -6.09177 q^{17} -62.6618 q^{19} +(19.9444 - 34.5447i) q^{20} +(-0.737829 - 1.27796i) q^{22} +(-6.03804 - 10.4582i) q^{23} +(-12.5000 + 21.6506i) q^{25} +1.76413 q^{26} -160.691 q^{28} +(-70.2925 + 121.750i) q^{29} +(-89.0513 - 154.241i) q^{31} +(14.2654 + 24.7083i) q^{32} +(-0.454294 + 0.786861i) q^{34} +100.712 q^{35} -216.112 q^{37} +(-4.67301 + 8.09389i) q^{38} +(-5.95771 - 10.3191i) q^{40} +(-205.885 - 356.603i) q^{41} +(24.4588 - 42.3639i) q^{43} +78.9300 q^{44} -1.80115 q^{46} +(-307.710 + 532.969i) q^{47} +(-31.3590 - 54.3153i) q^{49} +(1.86438 + 3.22920i) q^{50} +(-47.1800 + 81.7181i) q^{52} +705.120 q^{53} -49.4688 q^{55} +(-24.0006 + 41.5702i) q^{56} +(10.4841 + 18.1590i) q^{58} +(-247.270 - 428.284i) q^{59} +(-333.101 + 576.948i) q^{61} -26.5640 q^{62} -503.477 q^{64} +(29.5697 - 51.2162i) q^{65} +(-138.909 - 240.598i) q^{67} +(-24.2993 - 42.0877i) q^{68} +(7.51062 - 13.0088i) q^{70} -239.308 q^{71} -919.015 q^{73} +(-16.1166 + 27.9147i) q^{74} +(-249.950 - 432.926i) q^{76} +(99.6423 + 172.586i) q^{77} +(-258.111 + 447.062i) q^{79} +317.333 q^{80} -61.4155 q^{82} +(326.081 - 564.788i) q^{83} +(15.2294 + 26.3781i) q^{85} +(-3.64803 - 6.31858i) q^{86} +(11.7888 - 20.4189i) q^{88} -543.003 q^{89} -238.242 q^{91} +(48.1700 - 83.4329i) q^{92} +(45.8949 + 79.4924i) q^{94} +(156.654 + 271.333i) q^{95} +(-566.695 + 981.545i) q^{97} -9.35439 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 34 q^{4} - 30 q^{5} - 40 q^{7} + 132 q^{8}+O(q^{10}) $ 12 * q - 4 * q^2 - 34 * q^4 - 30 * q^5 - 40 * q^7 + 132 * q^8	$ 12 q - 4 q^{2} - 34 q^{4} - 30 q^{5} - 40 q^{7} + 132 q^{8} + 40 q^{10} - 88 q^{11} - 20 q^{13} - 180 q^{14} - 58 q^{16} + 248 q^{17} - 92 q^{19} - 170 q^{20} + 74 q^{22} - 210 q^{23} - 150 q^{25} + 8 q^{26} + 704 q^{28} - 296 q^{29} + 104 q^{31} - 722 q^{32} + 428 q^{34} + 400 q^{35} - 408 q^{37} + 20 q^{38} - 330 q^{40} - 344 q^{41} - 512 q^{43} + 1432 q^{44} - 372 q^{46} - 238 q^{47} - 68 q^{49} - 100 q^{50} + 468 q^{52} + 1700 q^{53} + 880 q^{55} - 2316 q^{56} - 890 q^{58} - 1840 q^{59} + 364 q^{61} + 2076 q^{62} - 1980 q^{64} - 100 q^{65} - 88 q^{67} - 236 q^{68} - 900 q^{70} + 2728 q^{71} + 1672 q^{73} - 1316 q^{74} + 2106 q^{76} - 840 q^{77} + 680 q^{79} + 580 q^{80} + 3484 q^{82} - 2148 q^{83} - 620 q^{85} - 2872 q^{86} - 1296 q^{88} + 6000 q^{89} - 6116 q^{91} - 1002 q^{92} + 3662 q^{94} + 230 q^{95} + 612 q^{97} + 3964 q^{98}+O(q^{100}) $ 12 * q - 4 * q^2 - 34 * q^4 - 30 * q^5 - 40 * q^7 + 132 * q^8 + 40 * q^10 - 88 * q^11 - 20 * q^13 - 180 * q^14 - 58 * q^16 + 248 * q^17 - 92 * q^19 - 170 * q^20 + 74 * q^22 - 210 * q^23 - 150 * q^25 + 8 * q^26 + 704 * q^28 - 296 * q^29 + 104 * q^31 - 722 * q^32 + 428 * q^34 + 400 * q^35 - 408 * q^37 + 20 * q^38 - 330 * q^40 - 344 * q^41 - 512 * q^43 + 1432 * q^44 - 372 * q^46 - 238 * q^47 - 68 * q^49 - 100 * q^50 + 468 * q^52 + 1700 * q^53 + 880 * q^55 - 2316 * q^56 - 890 * q^58 - 1840 * q^59 + 364 * q^61 + 2076 * q^62 - 1980 * q^64 - 100 * q^65 - 88 * q^67 - 236 * q^68 - 900 * q^70 + 2728 * q^71 + 1672 * q^73 - 1316 * q^74 + 2106 * q^76 - 840 * q^77 + 680 * q^79 + 580 * q^80 + 3484 * q^82 - 2148 * q^83 - 620 * q^85 - 2872 * q^86 - 1296 * q^88 + 6000 * q^89 - 6116 * q^91 - 1002 * q^92 + 3662 * q^94 + 230 * q^95 + 612 * q^97 + 3964 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.0745751	−	0.129168i	0.0263663	−	0.0456677i	−0.852541	−	0.522660i	$-0.824940\pi$
$2$	0.0745751	−	0.129168i	0.0263663	−	0.0456677i	0.878907	+	0.476992i	$0.158273\pi$
$3$		0			0
$3$		0			0
$4$	3.98888	+	6.90894i	0.498610	+	0.863617i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$6$		0			0
$7$	−10.0712	+	17.4439i	−0.543795	+	0.941880i	0.454887	+	0.890549i	$0.349680\pi$
$7$	−10.0712	+	17.4439i	−0.543795	+	0.941880i	−0.998682	+	0.0513310i	$0.983654\pi$
$8$	2.38308			0.105318
$9$		0			0
$10$	−0.745751			−0.0235827
$11$	4.94688	−	8.56825i	0.135595	−	0.234857i	−0.790230	−	0.612811i	$-0.790039\pi$
$11$	4.94688	−	8.56825i	0.135595	−	0.234857i	0.925824	+	0.377954i	$0.123372\pi$
$12$		0			0
$13$	5.91394	+	10.2432i	0.126172	+	0.218536i	0.922190	−	0.386736i	$-0.126398\pi$
$13$	5.91394	+	10.2432i	0.126172	+	0.218536i	−0.796019	+	0.605272i	$0.793064\pi$
$14$	1.50212	+	2.60176i	0.0286757	+	0.0496677i
$15$		0			0
$16$	−31.7333	+	54.9637i	−0.495833	+	0.858808i
$17$	−6.09177			−0.0869101			−0.0434550	−	0.999055i	$-0.513837\pi$
$17$	−6.09177			−0.0869101			−0.0434550	+	0.999055i	$0.513837\pi$
$18$		0			0
$19$	−62.6618			−0.756610			−0.378305	−	0.925681i	$-0.623493\pi$
$19$	−62.6618			−0.756610			−0.378305	+	0.925681i	$0.623493\pi$
$20$	19.9444	−	34.5447i	0.222985	−	0.386221i
$21$		0			0
$22$	−0.737829	−	1.27796i	−0.00715025	−	0.0123846i
$23$	−6.03804	−	10.4582i	−0.0547399	−	0.0948123i	0.837357	−	0.546656i	$-0.184100\pi$
$23$	−6.03804	−	10.4582i	−0.0547399	−	0.0948123i	−0.892097	+	0.451844i	$0.850766\pi$
$24$		0			0
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	1.76413			0.0133067
$27$		0			0
$28$	−160.691			−1.08457
$29$	−70.2925	+	121.750i	−0.450103	+	0.779601i	−0.998392	−	0.0566879i	$-0.981946\pi$
$29$	−70.2925	+	121.750i	−0.450103	+	0.779601i	0.548289	+	0.836289i	$0.315279\pi$
$30$		0			0
$31$	−89.0513	−	154.241i	−0.515938	−	0.893631i	−0.999829	−	0.0185027i	$-0.994110\pi$
$31$	−89.0513	−	154.241i	−0.515938	−	0.893631i	0.483891	−	0.875129i	$-0.339223\pi$
$32$	14.2654	+	24.7083i	0.0788058	+	0.136496i
$33$		0			0
$34$	−0.454294	+	0.786861i	−0.00229149	+	0.00396899i
$35$	100.712			0.486385
$36$		0			0
$37$	−216.112			−0.960231			−0.480116	−	0.877205i	$-0.659405\pi$
$37$	−216.112			−0.960231			−0.480116	+	0.877205i	$0.659405\pi$
$38$	−4.67301	+	8.09389i	−0.0199490	+	0.0345527i
$39$		0			0
$40$	−5.95771	−	10.3191i	−0.0235499	−	0.0407897i
$41$	−205.885	−	356.603i	−0.784239	−	1.35834i	−0.929453	−	0.368942i	$-0.879720\pi$
$41$	−205.885	−	356.603i	−0.784239	−	1.35834i	0.145213	−	0.989400i	$-0.453613\pi$
$42$		0			0
$43$	24.4588	−	42.3639i	0.0867425	−	0.150242i	−0.819390	−	0.573237i	$-0.805688\pi$
$43$	24.4588	−	42.3639i	0.0867425	−	0.150242i	0.906132	+	0.422994i	$0.139021\pi$
$44$	78.9300			0.270435
$45$		0			0
$46$	−1.80115			−0.00577315
$47$	−307.710	+	532.969i	−0.954980	+	1.65407i	−0.220566	+	0.975372i	$0.570790\pi$
$47$	−307.710	+	532.969i	−0.954980	+	1.65407i	−0.734414	+	0.678702i	$0.762543\pi$
$48$		0			0
$49$	−31.3590	−	54.3153i	−0.0914255	−	0.158354i
$50$	1.86438	+	3.22920i	0.00527325	+	0.00913354i
$51$		0			0
$52$	−47.1800	+	81.7181i	−0.125821	+	0.217928i
$53$	705.120			1.82746			0.913732	−	0.406316i	$-0.133187\pi$
$53$	705.120			1.82746			0.913732	+	0.406316i	$0.133187\pi$
$54$		0			0
$55$	−49.4688			−0.121280
$56$	−24.0006	+	41.5702i	−0.0572716	+	0.0991974i
$57$		0			0
$58$	10.4841	+	18.1590i	0.0237351	+	0.0411103i
$59$	−247.270	−	428.284i	−0.545624	−	0.945049i	−0.998567	−	0.0535095i	$-0.982959\pi$
$59$	−247.270	−	428.284i	−0.545624	−	0.945049i	0.452943	−	0.891539i	$-0.350374\pi$
$60$		0			0
$61$	−333.101	+	576.948i	−0.699167	+	1.21099i	0.269588	+	0.962976i	$0.413112\pi$
$61$	−333.101	+	576.948i	−0.699167	+	1.21099i	−0.968755	+	0.248018i	$0.920221\pi$
$62$	−26.5640			−0.0544135
$63$		0			0
$64$	−503.477			−0.983354
$65$	29.5697	−	51.2162i	0.0564257	−	0.0977322i
$66$		0			0
$67$	−138.909	−	240.598i	−0.253290	−	0.438712i	0.711139	−	0.703051i	$-0.248179\pi$
$67$	−138.909	−	240.598i	−0.253290	−	0.438712i	−0.964430	+	0.264339i	$0.914846\pi$
$68$	−24.2993	−	42.0877i	−0.0433342	−	0.0750570i
$69$		0			0
$70$	7.51062	−	13.0088i	0.0128242	−	0.0222121i
$71$	−239.308			−0.400009			−0.200005	−	0.979795i	$-0.564096\pi$
$71$	−239.308			−0.400009			−0.200005	+	0.979795i	$0.564096\pi$
$72$		0			0
$73$	−919.015			−1.47346			−0.736730	−	0.676187i	$-0.763631\pi$
$73$	−919.015			−1.47346			−0.736730	+	0.676187i	$0.763631\pi$
$74$	−16.1166	+	27.9147i	−0.0253177	+	0.0438516i
$75$		0			0
$76$	−249.950	−	432.926i	−0.377253	−	0.653422i
$77$	99.6423	+	172.586i	0.147471	+	0.255428i
$78$		0			0
$79$	−258.111	+	447.062i	−0.367592	+	0.636688i	−0.989189	−	0.146649i	$-0.953151\pi$
$79$	−258.111	+	447.062i	−0.367592	+	0.636688i	0.621596	+	0.783338i	$0.286484\pi$
$80$	317.333			0.443486
$81$		0			0
$82$	−61.4155			−0.0827099
$83$	326.081	−	564.788i	0.431229	−	0.746910i	−0.565751	−	0.824576i	$-0.691414\pi$
$83$	326.081	−	564.788i	0.431229	−	0.746910i	0.996979	+	0.0776662i	$0.0247469\pi$
$84$		0			0
$85$	15.2294	+	26.3781i	0.0194337	+	0.0336601i
$86$	−3.64803	−	6.31858i	−0.00457415	−	0.00792267i
$87$		0			0
$88$	11.7888	−	20.4189i	0.0142806	−	0.0247348i
$89$	−543.003			−0.646721			−0.323361	−	0.946276i	$-0.604813\pi$
$89$	−543.003			−0.646721			−0.323361	+	0.946276i	$0.604813\pi$
$90$		0			0
$91$	−238.242			−0.274446
$92$	48.1700	−	83.4329i	0.0545877	−	0.0945487i
$93$		0			0
$94$	45.8949	+	79.4924i	0.0503585	+	0.0872235i
$95$	156.654	+	271.333i	0.169183	+	0.293034i
$96$		0			0
$97$	−566.695	+	981.545i	−0.593188	+	1.02743i	0.400612	+	0.916248i	$0.368797\pi$
$97$	−566.695	+	981.545i	−0.593188	+	1.02743i	−0.993800	+	0.111183i	$0.964536\pi$
$98$	−9.35439			−0.00964220
$99$		0			0
$100$	−199.444			−0.199444
$101$	−599.618	+	1038.57i	−0.590735	+	1.02318i	0.403399	+	0.915024i	$0.367829\pi$
$101$	−599.618	+	1038.57i	−0.590735	+	1.02318i	−0.994134	+	0.108158i	$0.965505\pi$
$102$		0			0
$103$	622.967	+	1079.01i	0.595949	+	1.03221i	0.993412	+	0.114596i	$0.0365574\pi$
$103$	622.967	+	1079.01i	0.595949	+	1.03221i	−0.397463	+	0.917618i	$0.630109\pi$
$104$	14.0934	+	24.4105i	0.0132882	+	0.0230159i
$105$		0			0
$106$	52.5844	−	91.0788i	0.0481834	−	0.0834562i
$107$	1159.14			1.04728			0.523638	−	0.851941i	$-0.324574\pi$
$107$	1159.14			1.04728			0.523638	+	0.851941i	$0.324574\pi$
$108$		0			0
$109$	−118.618			−0.104234			−0.0521171	−	0.998641i	$-0.516597\pi$
$109$	−118.618			−0.104234			−0.0521171	+	0.998641i	$0.516597\pi$
$110$	−3.68914	+	6.38978i	−0.00319769	+	0.00553856i
$111$		0			0
$112$	−639.186	−	1107.10i	−0.539263	−	0.934030i
$113$	−191.641	−	331.932i	−0.159541	−	0.276333i	0.775162	−	0.631762i	$-0.217668\pi$
$113$	−191.641	−	331.932i	−0.159541	−	0.276333i	−0.934703	+	0.355429i	$0.884335\pi$
$114$		0			0
$115$	−30.1902	+	52.2910i	−0.0244804	+	0.0424014i
$116$	−1121.55			−0.897702
$117$		0			0
$118$	−73.7608			−0.0575443
$119$	61.3516	−	106.264i	0.0472612	−	0.0818589i
$120$		0			0
$121$	616.557	+	1067.91i	0.463228	+	0.802335i
$122$	49.6821	+	86.0519i	0.0368689	+	0.0638588i
$123$		0			0
$124$	710.429	−	1230.50i	0.514504	−	0.891146i
$125$	125.000			0.0894427
$126$		0			0
$127$	2570.69			1.79616			0.898079	−	0.439834i	$-0.144963\pi$
$127$	2570.69			1.79616			0.898079	+	0.439834i	$0.144963\pi$
$128$	−151.670	+	262.700i	−0.104733	+	0.181403i
$129$		0			0
$130$	−4.41033	−	7.63891i	−0.00297547	−	0.00515367i
$131$	329.029	+	569.894i	0.219446	+	0.380091i	0.954639	−	0.297767i	$-0.0962418\pi$
$131$	329.029	+	569.894i	0.219446	+	0.380091i	−0.735193	+	0.677858i	$0.762908\pi$
$132$		0			0
$133$	631.081	−	1093.06i	0.411441	−	0.712636i
$134$	−41.4367			−0.0267133
$135$		0			0
$136$	−14.5172			−0.00915323
$137$	313.367	−	542.767i	0.195421	−	0.338480i	−0.751617	−	0.659600i	$-0.770726\pi$
$137$	313.367	−	542.767i	0.195421	−	0.338480i	0.947039	+	0.321120i	$0.104059\pi$
$138$		0			0
$139$	486.872	+	843.288i	0.297093	+	0.514581i	0.975470	−	0.220134i	$-0.0706494\pi$
$139$	486.872	+	843.288i	0.297093	+	0.514581i	−0.678376	+	0.734715i	$0.737316\pi$
$140$	401.729	+	695.814i	0.242516	+	0.420050i
$141$		0			0
$142$	−17.8464	+	30.9109i	−0.0105468	+	0.0182675i
$143$	117.022			0.0684329
$144$		0			0
$145$	702.925			0.402584
$146$	−68.5357	+	118.707i	−0.0388497	+	0.0672896i
$147$		0			0
$148$	−862.043	−	1493.10i	−0.478780	−	0.829272i
$149$	−1487.92	−	2577.16i	−0.818089	−	1.41697i	−0.907088	−	0.420940i	$-0.861700\pi$
$149$	−1487.92	−	2577.16i	−0.818089	−	1.41697i	0.0889994	−	0.996032i	$-0.471633\pi$
$150$		0			0
$151$	1038.22	−	1798.24i	0.559529	−	0.969133i	−0.438007	−	0.898972i	$-0.644315\pi$
$151$	1038.22	−	1798.24i	0.559529	−	0.969133i	0.997536	−	0.0701611i	$-0.0223513\pi$
$152$	−149.328			−0.0796850
$153$		0			0
$154$	29.7233			0.0155531
$155$	−445.256	+	771.207i	−0.230735	+	0.399644i
$156$		0			0
$157$	−176.175	−	305.144i	−0.0895559	−	0.155115i	0.817768	−	0.575549i	$-0.195211\pi$
$157$	−176.175	−	305.144i	−0.0895559	−	0.155115i	−0.907324	+	0.420433i	$0.861878\pi$
$158$	38.4973	+	66.6793i	0.0193841	+	0.0335742i
$159$		0			0
$160$	71.3268	−	123.542i	0.0352430	−	0.0610427i
$161$	243.242			0.119069
$162$		0			0
$163$	2772.05			1.33205			0.666023	−	0.745931i	$-0.267995\pi$
$163$	2772.05			1.33205			0.666023	+	0.745931i	$0.267995\pi$
$164$	1642.50	−	2844.89i	0.782058	−	1.35456i
$165$		0			0
$166$	−48.6350	−	84.2382i	−0.0227398	−	0.0393865i
$167$	1917.72	+	3321.59i	0.888608	+	1.53912i	0.841521	+	0.540224i	$0.181661\pi$
$167$	1917.72	+	3321.59i	0.888608	+	1.53912i	0.0470874	+	0.998891i	$0.485006\pi$
$168$		0			0
$169$	1028.55	−	1781.50i	0.468161	−	0.810879i
$170$	4.54294			0.00204958
$171$		0			0
$172$	390.252			0.173003
$173$	567.727	−	983.332i	0.249500	−	0.432146i	−0.713887	−	0.700261i	$-0.753067\pi$
$173$	567.727	−	983.332i	0.249500	−	0.432146i	0.963387	+	0.268114i	$0.0864005\pi$
$174$		0			0
$175$	−251.781	−	436.097i	−0.108759	−	0.188376i
$176$	313.962	+	543.798i	0.134465	+	0.232900i
$177$		0			0
$178$	−40.4945	+	70.1385i	−0.0170516	+	0.0295343i
$179$	−3192.57			−1.33309			−0.666546	−	0.745464i	$-0.732228\pi$
$179$	−3192.57			−1.33309			−0.666546	+	0.745464i	$0.732228\pi$
$180$		0			0
$181$	990.641			0.406816			0.203408	−	0.979094i	$-0.434798\pi$
$181$	990.641			0.406816			0.203408	+	0.979094i	$0.434798\pi$
$182$	−17.7670	+	30.7733i	−0.00723612	+	0.0125333i
$183$		0			0
$184$	−14.3892	−	24.9228i	−0.00576513	−	0.00998549i
$185$	540.279	+	935.791i	0.214714	+	0.371896i
$186$		0			0
$187$	−30.1353	+	52.1958i	−0.0117845	+	0.0204114i
$188$	−4909.66			−1.90465
$189$		0			0
$190$	46.7301			0.0178429
$191$	1641.86	−	2843.79i	0.621994	−	1.07733i	−0.367120	−	0.930174i	$-0.619656\pi$
$191$	1641.86	−	2843.79i	0.621994	−	1.07733i	0.989114	−	0.147152i	$-0.0470105\pi$
$192$		0			0
$193$	1184.00	+	2050.76i	0.441588	+	0.764853i	0.997808	−	0.0661824i	$-0.0210819\pi$
$193$	1184.00	+	2050.76i	0.441588	+	0.764853i	−0.556219	+	0.831035i	$0.687749\pi$
$194$	84.5227	+	146.398i	0.0312803	+	0.0541790i
$195$		0			0
$196$	250.174	−	433.314i	0.0911713	−	0.157913i
$197$	3754.00			1.35767			0.678836	−	0.734290i	$-0.262485\pi$
$197$	3754.00			1.35767			0.678836	+	0.734290i	$0.262485\pi$
$198$		0			0
$199$	1905.82			0.678894			0.339447	−	0.940625i	$-0.389760\pi$
$199$	1905.82			0.678894			0.339447	+	0.940625i	$0.389760\pi$
$200$	−29.7886	+	51.5953i	−0.0105318	+	0.0182417i
$201$		0			0
$202$	89.4331	+	154.903i	0.0311509	+	0.0539550i
$203$	−1415.86	−	2452.34i	−0.489527	−	0.847886i
$204$		0			0
$205$	−1029.42	+	1783.01i	−0.350722	+	0.607469i
$206$	185.831			0.0628518
$207$		0			0
$208$	−750.676			−0.250240
$209$	−309.981	+	536.902i	−0.102592	+	0.177695i
$210$		0			0
$211$	1844.59	+	3194.93i	0.601834	+	1.04241i	0.992543	+	0.121893i	$0.0388966\pi$
$211$	1844.59	+	3194.93i	0.601834	+	1.04241i	−0.390709	+	0.920514i	$0.627770\pi$
$212$	2812.64	+	4871.63i	0.911192	+	1.57823i
$213$		0			0
$214$	86.4431	−	149.724i	0.0276128	−	0.0478267i
$215$	−244.588			−0.0775849
$216$		0			0
$217$	3587.42			1.12226
$218$	−8.84593	+	15.3216i	−0.00274826	+	0.00476013i
$219$		0			0
$220$	−197.325	−	341.777i	−0.0604712	−	0.104739i
$221$	−36.0264	−	62.3995i	−0.0109656	−	0.0189930i
$222$		0			0
$223$	−84.8583	+	146.979i	−0.0254822	+	0.0441365i	−0.878485	−	0.477769i	$-0.841445\pi$
$223$	−84.8583	+	146.979i	−0.0254822	+	0.0441365i	0.853003	+	0.521906i	$0.174779\pi$
$224$	−574.679			−0.171417
$225$		0			0
$226$	−57.1667			−0.0168260
$227$	−1803.73	+	3124.15i	−0.527391	+	0.913468i	0.472099	+	0.881545i	$0.343496\pi$
$227$	−1803.73	+	3124.15i	−0.527391	+	0.913468i	−0.999490	+	0.0319228i	$0.989837\pi$
$228$		0			0
$229$	3046.95	+	5277.47i	0.879250	+	1.52290i	0.852166	+	0.523272i	$0.175289\pi$
$229$	3046.95	+	5277.47i	0.879250	+	1.52290i	0.0270836	+	0.999633i	$0.491378\pi$
$230$	4.50287	+	7.79921i	0.00129092	+	0.00223593i
$231$		0			0
$232$	−167.513	+	290.141i	−0.0474041	+	0.0821064i
$233$	−3930.28			−1.10507			−0.552534	−	0.833490i	$-0.686339\pi$
$233$	−3930.28			−1.10507			−0.552534	+	0.833490i	$0.686339\pi$
$234$		0			0
$235$	3077.10			0.854160
$236$	1972.66	−	3416.75i	0.544107	−	0.942421i
$237$		0			0
$238$	−9.15059	−	15.8493i	−0.00249221	−	0.00431663i
$239$	−1831.12	−	3171.59i	−0.495587	−	0.858382i	0.504400	−	0.863470i	$-0.331714\pi$
$239$	−1831.12	−	3171.59i	−0.495587	−	0.858382i	−0.999987	+	0.00508843i	$0.998380\pi$
$240$		0			0
$241$	−111.414	+	192.976i	−0.0297794	+	0.0515795i	−0.880531	−	0.473989i	$-0.842814\pi$
$241$	−111.414	+	192.976i	−0.0297794	+	0.0515795i	0.850752	+	0.525568i	$0.176147\pi$
$242$	183.919			0.0488544
$243$		0			0
$244$	−5314.80			−1.39445
$245$	−156.795	+	271.577i	−0.0408867	+	0.0708179i
$246$		0			0
$247$	−370.578	−	641.860i	−0.0954629	−	0.165347i
$248$	−212.217	−	367.570i	−0.0543378	−	0.0941159i
$249$		0			0
$250$	9.32189	−	16.1460i	0.00235827	−	0.00408465i
$251$	4748.92			1.19422			0.597110	−	0.802159i	$-0.296316\pi$
$251$	4748.92			1.19422			0.597110	+	0.802159i	$0.296316\pi$
$252$		0			0
$253$	−119.478			−0.0296898
$254$	191.710	−	332.051i	0.0473580	−	0.0820264i
$255$		0			0
$256$	−1991.29	−	3449.01i	−0.486154	−	0.842044i
$257$	2826.07	+	4894.90i	0.685936	+	1.18808i	0.973142	+	0.230208i	$0.0739405\pi$
$257$	2826.07	+	4894.90i	0.685936	+	1.18808i	−0.287205	+	0.957869i	$0.592726\pi$
$258$		0			0
$259$	2176.51	−	3769.82i	0.522169	−	0.904423i
$260$	471.800			0.112538
$261$		0			0
$262$	98.1494			0.0231438
$263$	−1644.93	+	2849.11i	−0.385669	+	0.667998i	−0.991862	−	0.127320i	$-0.959363\pi$
$263$	−1644.93	+	2849.11i	−0.385669	+	0.667998i	0.606193	+	0.795318i	$0.292696\pi$
$264$		0			0
$265$	−1762.80	−	3053.26i	−0.408634	−	0.707774i
$266$	−94.1258	−	163.031i	−0.0216963	−	0.0375791i
$267$		0			0
$268$	1108.18	−	1919.43i	0.252586	−	0.437492i
$269$	−5452.66			−1.23589			−0.617945	−	0.786221i	$-0.712035\pi$
$269$	−5452.66			−1.23589			−0.617945	+	0.786221i	$0.712035\pi$
$270$		0			0
$271$	−238.923			−0.0535555			−0.0267778	−	0.999641i	$-0.508525\pi$
$271$	−238.923			−0.0535555			−0.0267778	+	0.999641i	$0.508525\pi$
$272$	193.312	−	334.826i	0.0430929	−	0.0746390i
$273$		0			0
$274$	−46.7387	−	80.9539i	−0.0103051	−	0.0178489i
$275$	123.672	+	214.206i	0.0271189	+	0.0469714i
$276$		0			0
$277$	−1878.87	+	3254.30i	−0.407547	+	0.705892i	−0.994614	−	0.103646i	$-0.966949\pi$
$277$	−1878.87	+	3254.30i	−0.407547	+	0.705892i	0.587067	+	0.809538i	$0.300282\pi$
$278$	145.234			0.0313330
$279$		0			0
$280$	240.006			0.0512253
$281$	236.491	−	409.615i	0.0502060	−	0.0869593i	−0.839830	−	0.542849i	$-0.817346\pi$
$281$	236.491	−	409.615i	0.0502060	−	0.0869593i	0.890036	+	0.455890i	$0.150679\pi$
$282$		0			0
$283$	−1176.94	−	2038.52i	−0.247215	−	0.428190i	0.715537	−	0.698575i	$-0.246182\pi$
$283$	−1176.94	−	2038.52i	−0.247215	−	0.428190i	−0.962752	+	0.270385i	$0.912849\pi$
$284$	−954.571	−	1653.37i	−0.199449	−	0.345455i
$285$		0			0
$286$	8.72695	−	15.1155i	0.00180432	−	0.00312517i
$287$	8294.05			1.70586
$288$		0			0
$289$	−4875.89			−0.992447
$290$	52.4207	−	90.7952i	0.0106146	−	0.0183851i
$291$		0			0
$292$	−3665.84	−	6349.42i	−0.734682	−	1.27251i
$293$	−2071.53	−	3587.99i	−0.413038	−	0.715402i	0.582183	−	0.813058i	$-0.302199\pi$
$293$	−2071.53	−	3587.99i	−0.413038	−	0.715402i	−0.995220	+	0.0976560i	$0.968866\pi$
$294$		0			0
$295$	−1236.35	+	2141.42i	−0.244011	+	0.422639i
$296$	−515.013			−0.101130
$297$		0			0
$298$	−443.847			−0.0862798
$299$	71.4172	−	123.698i	0.0138133	−	0.0239253i
$300$		0			0
$301$	492.660	+	853.311i	0.0943403	+	0.163402i
$302$	−154.850	−	268.208i	−0.0295054	−	0.0511048i
$303$		0			0
$304$	1988.47	−	3444.12i	0.375152	−	0.649783i
$305$	3331.01			0.625354
$306$		0			0
$307$	224.413			0.0417196			0.0208598	−	0.999782i	$-0.493360\pi$
$307$	224.413			0.0417196			0.0208598	+	0.999782i	$0.493360\pi$
$308$	−794.922	+	1376.85i	−0.147061	+	0.254718i
$309$		0			0
$310$	66.4101	+	115.026i	0.0121672	+	0.0210742i
$311$	−3038.06	−	5262.08i	−0.553931	−	0.959437i	−0.997986	−	0.0634374i	$-0.979794\pi$
$311$	−3038.06	−	5262.08i	−0.553931	−	0.959437i	0.444055	−	0.896000i	$-0.353540\pi$
$312$		0			0
$313$	−1728.17	+	2993.27i	−0.312082	+	0.540542i	−0.978813	−	0.204757i	$-0.934360\pi$
$313$	−1728.17	+	2993.27i	−0.312082	+	0.540542i	0.666731	+	0.745299i	$0.267693\pi$
$314$	−52.5530			−0.00944502
$315$		0			0
$316$	−4118.30			−0.733140
$317$	−3816.02	+	6609.54i	−0.676117	+	1.17107i	0.300025	+	0.953931i	$0.403005\pi$
$317$	−3816.02	+	6609.54i	−0.676117	+	1.17107i	−0.976141	+	0.217137i	$0.930328\pi$
$318$		0			0
$319$	695.457	+	1204.57i	0.122063	+	0.211419i
$320$	1258.69	+	2180.12i	0.219885	+	0.380851i
$321$		0			0
$322$	18.1398	−	31.4190i	0.00313941	−	0.00543762i
$323$	381.721			0.0657571
$324$		0			0
$325$	−295.697			−0.0504687
$326$	206.726	−	358.059i	0.0351211	−	0.0608315i
$327$		0			0
$328$	−490.641	−	849.815i	−0.0825949	−	0.143058i
$329$	−6198.02	−	10735.3i	−1.03863	−	1.79895i
$330$		0			0
$331$	−595.190	+	1030.90i	−0.0988357	+	0.171188i	−0.911203	−	0.411958i	$-0.864845\pi$
$331$	−595.190	+	1030.90i	−0.0988357	+	0.171188i	0.812367	+	0.583146i	$0.198178\pi$
$332$	5202.78			0.860059
$333$		0			0
$334$	572.056			0.0937172
$335$	−694.546	+	1202.99i	−0.113275	+	0.196198i
$336$		0			0
$337$	−347.609	−	602.076i	−0.0561883	−	0.0973209i	0.836563	−	0.547871i	$-0.184561\pi$
$337$	−347.609	−	602.076i	−0.0561883	−	0.0973209i	−0.892751	+	0.450550i	$0.851228\pi$
$338$	−153.408	−	265.711i	−0.0246873	−	0.0427597i
$339$		0			0
$340$	−121.497	+	210.438i	−0.0193796	+	0.0335665i
$341$	−1762.11			−0.279834
$342$		0			0
$343$	−5645.57			−0.888723
$344$	58.2873	−	100.957i	0.00913559	−	0.0158233i
$345$		0			0
$346$	−84.6765	−	146.664i	−0.0131568	−	0.0227882i
$347$	5116.21	+	8861.54i	0.791506	+	1.37093i	0.925034	+	0.379884i	$0.124036\pi$
$347$	5116.21	+	8861.54i	0.791506	+	1.37093i	−0.133528	+	0.991045i	$0.542631\pi$
$348$		0			0
$349$	−3998.80	+	6926.12i	−0.613326	+	1.06231i	0.377350	+	0.926071i	$0.376835\pi$
$349$	−3998.80	+	6926.12i	−0.613326	+	1.06231i	−0.990676	+	0.136241i	$0.956498\pi$
$350$	−75.1062			−0.0114703
$351$		0			0
$352$	282.276			0.0427426
$353$	2718.35	−	4708.32i	0.409867	−	0.709911i	−0.585007	−	0.811028i	$-0.698908\pi$
$353$	2718.35	−	4708.32i	0.409867	−	0.709911i	0.994875	+	0.101117i	$0.0322416\pi$
$354$		0			0
$355$	598.271	+	1036.24i	0.0894448	+	0.154923i
$356$	−2165.97	−	3751.57i	−0.322461	−	0.558520i
$357$		0			0
$358$	−238.086	+	412.377i	−0.0351487	+	0.0608793i
$359$	4767.51			0.700890			0.350445	−	0.936583i	$-0.386030\pi$
$359$	4767.51			0.700890			0.350445	+	0.936583i	$0.386030\pi$
$360$		0			0
$361$	−2932.50			−0.427541
$362$	73.8771	−	127.959i	0.0107262	−	0.0185784i
$363$		0			0
$364$	−950.320	−	1646.00i	−0.136841	−	0.237016i
$365$	2297.54	+	3979.45i	0.329476	+	0.570669i
$366$		0			0
$367$	−6360.69	+	11017.0i	−0.904701	+	1.56699i	−0.0833840	+	0.996517i	$0.526573\pi$
$367$	−6360.69	+	11017.0i	−0.904701	+	1.56699i	−0.821317	+	0.570471i	$0.806761\pi$
$368$	766.428			0.108567
$369$		0			0
$370$	161.166			0.0226449
$371$	−7101.42	+	12300.0i	−0.993766	+	1.72125i
$372$		0			0
$373$	4653.06	+	8059.34i	0.645915	+	1.11876i	0.984089	+	0.177675i	$0.0568574\pi$
$373$	4653.06	+	8059.34i	0.645915	+	1.11876i	−0.338174	+	0.941084i	$0.609809\pi$
$374$	4.49468	+	7.78502i	0.000621429	+	0.00107635i
$375$		0			0
$376$	−733.298	+	1270.11i	−0.100577	+	0.174204i
$377$	−1662.82			−0.227161
$378$		0			0
$379$	−11623.8			−1.57539			−0.787694	−	0.616067i	$-0.788725\pi$
$379$	−11623.8			−1.57539			−0.787694	+	0.616067i	$0.788725\pi$
$380$	−1249.75	+	2164.63i	−0.168713	+	0.292219i
$381$		0			0
$382$	−244.884	−	424.151i	−0.0327993	−	0.0568101i
$383$	−5821.46	−	10083.1i	−0.776664	−	1.34522i	−0.933854	−	0.357654i	$-0.883577\pi$
$383$	−5821.46	−	10083.1i	−0.776664	−	1.34522i	0.157190	−	0.987568i	$-0.449757\pi$
$384$		0			0
$385$	498.212	−	862.928i	0.0659512	−	0.114231i
$386$	353.189			0.0465721
$387$		0			0
$388$	−9041.91			−1.18308
$389$	3489.65	−	6044.26i	0.454839	−	0.787805i	−0.543840	−	0.839189i	$-0.683030\pi$
$389$	3489.65	−	6044.26i	0.454839	−	0.787805i	0.998679	+	0.0513843i	$0.0163633\pi$
$390$		0			0
$391$	36.7824	+	63.7089i	0.00475745	+	0.00824015i
$392$	−74.7310	−	129.438i	−0.00962880	−	0.0166776i
$393$		0			0
$394$	279.955	−	484.896i	0.0357967	−	0.0620018i
$395$	2581.11			0.328785
$396$		0			0
$397$	2884.53			0.364661			0.182330	−	0.983237i	$-0.441636\pi$
$397$	2884.53			0.364661			0.182330	+	0.983237i	$0.441636\pi$
$398$	142.127	−	246.170i	0.0178999	−	0.0310035i
$399$		0			0
$400$	−793.332	−	1374.09i	−0.0991666	−	0.171762i
$401$	5497.18	+	9521.40i	0.684579	+	1.18573i	0.973569	+	0.228393i	$0.0733472\pi$
$401$	5497.18	+	9521.40i	0.684579	+	1.18573i	−0.288990	+	0.957332i	$0.593319\pi$
$402$		0			0
$403$	1053.29	−	1824.35i	0.130194	−	0.225502i
$404$	−9567.21			−1.17818
$405$		0			0
$406$	−422.352			−0.0516280
$407$	−1069.08	+	1851.70i	−0.130202	+	0.225517i
$408$		0			0
$409$	1423.27	+	2465.17i	0.172069	+	0.298031i	0.939143	−	0.343527i	$-0.111622\pi$
$409$	1423.27	+	2465.17i	0.172069	+	0.298031i	−0.767074	+	0.641558i	$0.778288\pi$
$410$	153.539	+	265.937i	0.0184945	+	0.0320334i
$411$		0			0
$412$	−4969.88	+	8608.08i	−0.594292	+	1.02934i
$413$	9961.25			1.18683
$414$		0			0
$415$	−3260.81			−0.385703
$416$	−168.729	+	292.247i	−0.0198861	+	0.0344438i
$417$		0			0
$418$	46.2337	+	80.0790i	0.00540996	+	0.00937032i
$419$	−4152.56	−	7192.44i	−0.484167	−	0.838601i	0.515668	−	0.856788i	$-0.327544\pi$
$419$	−4152.56	−	7192.44i	−0.484167	−	0.838601i	−0.999835	+	0.0181874i	$0.994210\pi$
$420$		0			0
$421$	−1785.74	+	3092.99i	−0.206726	+	0.358060i	−0.950681	−	0.310170i	$-0.899614\pi$
$421$	−1785.74	+	3092.99i	−0.206726	+	0.358060i	0.743955	+	0.668229i	$0.232947\pi$
$422$	550.243			0.0634725
$423$		0			0
$424$	1680.36			0.192466
$425$	76.1471	−	131.891i	0.00869101	−	0.0150533i
$426$		0			0
$427$	−6709.47	−	11621.1i	−0.760407	−	1.31706i
$428$	4623.68	+	8008.44i	0.522182	+	0.904445i
$429$		0			0
$430$	−18.2402	+	31.5929i	−0.00204562	+	0.00354313i
$431$	−13408.7			−1.49854			−0.749272	−	0.662262i	$-0.769597\pi$
$431$	−13408.7			−1.49854			−0.749272	+	0.662262i	$0.769597\pi$
$432$		0			0
$433$	−1698.17			−0.188473			−0.0942364	−	0.995550i	$-0.530041\pi$
$433$	−1698.17			−0.188473			−0.0942364	+	0.995550i	$0.530041\pi$
$434$	267.532	−	463.379i	0.0295898	−	0.0512510i
$435$		0			0
$436$	−473.152	−	819.523i	−0.0519721	−	0.0900184i
$437$	378.354	+	655.329i	0.0414168	+	0.0717360i
$438$		0			0
$439$	5365.08	−	9292.59i	0.583283	−	1.01028i	−0.411804	−	0.911272i	$-0.635101\pi$
$439$	5365.08	−	9292.59i	0.583283	−	1.01028i	0.995087	−	0.0990034i	$-0.0315655\pi$
$440$	−117.888			−0.0127730
$441$		0			0
$442$	−10.7467			−0.00115649
$443$	4219.76	−	7308.84i	0.452566	−	0.783868i	−0.545978	−	0.837799i	$-0.683842\pi$
$443$	4219.76	−	7308.84i	0.452566	−	0.783868i	0.998545	+	0.0539314i	$0.0171752\pi$
$444$		0			0
$445$	1357.51	+	2351.27i	0.144611	+	0.250474i
$446$	12.6566	+	21.9219i	0.00134374	+	0.00232743i
$447$		0			0
$448$	5070.63	−	8782.59i	0.534743	−	0.926202i
$449$	−3860.69			−0.405784			−0.202892	−	0.979201i	$-0.565034\pi$
$449$	−3860.69			−0.405784			−0.202892	+	0.979201i	$0.565034\pi$
$450$		0			0
$451$	−4073.95			−0.425355
$452$	1528.87	−	2648.08i	0.159097	−	0.275564i
$453$		0			0
$454$	269.027	+	465.968i	0.0278107	+	0.0481695i
$455$	595.606	+	1031.62i	0.0613680	+	0.106293i
$456$		0			0
$457$	1736.43	−	3007.59i	0.177739	−	0.307854i	−0.763366	−	0.645966i	$-0.776455\pi$
$457$	1736.43	−	3007.59i	0.177739	−	0.307854i	0.941106	+	0.338112i	$0.109788\pi$
$458$	908.906			0.0927301
$459$		0			0
$460$	−481.700			−0.0488247
$461$	−3420.95	+	5925.27i	−0.345618	+	0.598627i	−0.985466	−	0.169874i	$-0.945664\pi$
$461$	−3420.95	+	5925.27i	−0.345618	+	0.598627i	0.639848	+	0.768501i	$0.278997\pi$
$462$		0			0
$463$	−3090.27	−	5352.50i	−0.310188	−	0.537261i	0.668215	−	0.743968i	$-0.267059\pi$
$463$	−3090.27	−	5352.50i	−0.310188	−	0.537261i	−0.978403	+	0.206707i	$0.933725\pi$
$464$	−4461.22	−	7727.06i	−0.446351	−	0.773103i
$465$		0			0
$466$	−293.101	+	507.665i	−0.0291365	+	0.0504660i
$467$	10977.3			1.08772			0.543861	−	0.839175i	$-0.316962\pi$
$467$	10977.3			1.08772			0.543861	+	0.839175i	$0.316962\pi$
$468$		0			0
$469$	5595.94			0.550952
$470$	229.475	−	397.462i	0.0225210	−	0.0390075i
$471$		0			0
$472$	−589.266	−	1020.64i	−0.0574643	−	0.0995311i
$473$	−241.990	−	419.138i	−0.0235237	−	0.0407442i
$474$		0			0
$475$	783.272	−	1356.67i	0.0756610	−	0.131049i
$476$	978.895			0.0942596
$477$		0			0
$478$	−546.223			−0.0522671
$479$	−2642.83	+	4577.51i	−0.252096	+	0.436643i	−0.964103	−	0.265530i	$-0.914453\pi$
$479$	−2642.83	+	4577.51i	−0.252096	+	0.436643i	0.712007	+	0.702172i	$0.247786\pi$
$480$		0			0
$481$	−1278.07	−	2213.69i	−0.121154	−	0.209845i
$482$	16.6175	+	28.7823i	0.00157034	+	0.00271992i
$483$		0			0
$484$	−4918.74	+	8519.50i	−0.461940	+	0.800104i
$485$	5666.95			0.530563
$486$		0			0
$487$	15418.1			1.43462			0.717312	−	0.696752i	$-0.245372\pi$
$487$	15418.1			1.43462			0.717312	+	0.696752i	$0.245372\pi$
$488$	−793.808	+	1374.92i	−0.0736352	+	0.127540i
$489$		0			0
$490$	23.3860	+	40.5057i	0.00215606	+	0.00373441i
$491$	−6891.19	−	11935.9i	−0.633392	−	1.09707i	−0.986853	−	0.161617i	$-0.948329\pi$
$491$	−6891.19	−	11935.9i	−0.633392	−	1.09707i	0.353462	−	0.935449i	$-0.385004\pi$
$492$		0			0
$493$	428.205	−	741.674i	0.0391185	−	0.0677552i
$494$	−110.544			−0.0100680
$495$		0			0
$496$	11303.6			1.02328
$497$	2410.13	−	4174.46i	0.217523	−	0.376761i
$498$		0			0
$499$	1151.32	+	1994.14i	0.103287	+	0.178898i	0.913037	−	0.407877i	$-0.133731\pi$
$499$	1151.32	+	1994.14i	0.103287	+	0.178898i	−0.809750	+	0.586775i	$0.800397\pi$
$500$	498.610	+	863.617i	0.0445970	+	0.0772443i
$501$		0			0
$502$	354.151	−	613.408i	0.0314871	−	0.0545373i
$503$	830.769			0.0736425			0.0368213	−	0.999322i	$-0.488277\pi$
$503$	830.769			0.0736425			0.0368213	+	0.999322i	$0.488277\pi$
$504$		0			0
$505$	5996.18			0.528369
$506$	−8.91008	+	15.4327i	−0.000782809	+	0.00135586i
$507$		0			0
$508$	10254.2	+	17760.8i	0.895582	+	1.55119i
$509$	6932.15	+	12006.8i	0.603658	+	1.04557i	0.992262	+	0.124162i	$0.0396242\pi$
$509$	6932.15	+	12006.8i	0.603658	+	1.04557i	−0.388604	+	0.921405i	$0.627042\pi$
$510$		0			0
$511$	9255.61	−	16031.2i	0.801260	−	1.38782i
$512$	−3020.72			−0.260739
$513$		0			0
$514$	843.019			0.0723423
$515$	3114.84	−	5395.05i	0.266517	−	0.461620i
$516$		0			0
$517$	3044.41	+	5273.07i	0.258980	+	0.448567i
$518$	−324.627	−	562.270i	−0.0275353	−	0.0476925i
$519$		0			0
$520$	70.4671	−	122.053i	0.00594267	−	0.0102930i
$521$	−2262.83			−0.190281			−0.0951403	−	0.995464i	$-0.530330\pi$
$521$	−2262.83			−0.190281			−0.0951403	+	0.995464i	$0.530330\pi$
$522$		0			0
$523$	8379.47			0.700590			0.350295	−	0.936639i	$-0.386081\pi$
$523$	8379.47			0.700590			0.350295	+	0.936639i	$0.386081\pi$
$524$	−2624.91	+	4546.48i	−0.218835	+	0.379034i
$525$		0			0
$526$	245.342	+	424.945i	0.0203373	+	0.0352252i
$527$	542.480	+	939.603i	0.0448402	+	0.0776656i
$528$		0			0
$529$	6010.58	−	10410.6i	0.494007	−	0.855645i
$530$	−525.844			−0.0430966
$531$		0			0
$532$	10069.2			0.820593
$533$	2435.18	−	4217.86i	0.197898	−	0.342769i
$534$		0			0
$535$	−2897.86	−	5019.23i	−0.234178	−	0.405608i
$536$	−331.032	−	573.365i	−0.0266762	−	0.0462045i
$537$		0			0
$538$	−406.633	+	704.308i	−0.0325858	+	0.0564403i
$539$	−620.517			−0.0495873
$540$		0			0
$541$	11880.6			0.944155			0.472078	−	0.881557i	$-0.343504\pi$
$541$	11880.6			0.944155			0.472078	+	0.881557i	$0.343504\pi$
$542$	−17.8177	+	30.8612i	−0.00141206	+	0.00244576i
$543$		0			0
$544$	−86.9013	−	150.518i	−0.00684901	−	0.0118628i
$545$	296.544	+	513.630i	0.0233075	+	0.0403697i
$546$		0			0
$547$	4334.23	−	7507.11i	0.338791	−	0.586803i	−0.645415	−	0.763832i	$-0.723316\pi$
$547$	4334.23	−	7507.11i	0.338791	−	0.586803i	0.984206	+	0.177030i	$0.0566488\pi$
$548$	4999.93			0.389756
$549$		0			0
$550$	36.8914			0.00286010
$551$	4404.65	−	7629.08i	0.340553	−	0.589854i
$552$		0			0
$553$	−5198.99	−	9004.92i	−0.399790	−	0.692456i
$554$	280.234	+	485.380i	0.0214910	+	0.0372235i
$555$		0			0
$556$	−3884.15	+	6727.54i	−0.296267	+	0.513150i
$557$	−19918.2			−1.51519			−0.757594	−	0.652726i	$-0.773625\pi$
$557$	−19918.2			−1.51519			−0.757594	+	0.652726i	$0.773625\pi$
$558$		0			0
$559$	578.591			0.0437778
$560$	−3195.93	+	5535.51i	−0.241166	+	0.417711i
$561$		0			0
$562$	−35.2727	−	61.0941i	−0.00264749	−	0.00458558i
$563$	7241.12	+	12542.0i	0.542055	+	0.938866i	0.998786	+	0.0492616i	$0.0156868\pi$
$563$	7241.12	+	12542.0i	0.542055	+	0.938866i	−0.456731	+	0.889605i	$0.650980\pi$
$564$		0			0
$565$	−958.207	+	1659.66i	−0.0713488	+	0.123580i
$566$	−351.082			−0.0260726
$567$		0			0
$568$	−570.292			−0.0421284
$569$	8316.59	−	14404.8i	0.612741	−	1.06130i	−0.378035	−	0.925791i	$-0.623400\pi$
$569$	8316.59	−	14404.8i	0.612741	−	1.06130i	0.990776	−	0.135508i	$-0.0432665\pi$
$570$		0			0
$571$	−415.181	−	719.114i	−0.0304287	−	0.0527040i	0.850410	−	0.526120i	$-0.176354\pi$
$571$	−415.181	−	719.114i	−0.0304287	−	0.0527040i	−0.880839	+	0.473416i	$0.843021\pi$
$572$	466.788	+	808.500i	0.0341213	+	0.0590998i
$573$		0			0
$574$	618.529	−	1071.32i	0.0449772	−	0.0779028i
$575$	301.902			0.0218960
$576$		0			0
$577$	−21152.6			−1.52616			−0.763080	−	0.646305i	$-0.776314\pi$
$577$	−21152.6			−1.52616			−0.763080	+	0.646305i	$0.776314\pi$
$578$	−363.620	+	629.808i	−0.0261671	+	0.0453228i
$579$		0			0
$580$	2803.88	+	4856.46i	0.200732	+	0.347679i
$581$	6568.06	+	11376.2i	0.469000	+	0.812332i
$582$		0			0
$583$	3488.15	−	6041.65i	0.247795	−	0.429193i
$584$	−2190.09			−0.155183
$585$		0			0
$586$	−617.938			−0.0435610
$587$	−8527.26	+	14769.7i	−0.599587	+	1.03852i	0.393294	+	0.919413i	$0.371335\pi$
$587$	−8527.26	+	14769.7i	−0.599587	+	1.03852i	−0.992882	+	0.119103i	$0.961998\pi$
$588$		0			0
$589$	5580.11	+	9665.04i	0.390364	+	0.676131i
$590$	184.402	+	319.393i	0.0128673	+	0.0222868i
$591$		0			0
$592$	6857.94	−	11878.3i	0.476114	−	0.824654i
$593$	−24693.4			−1.71001			−0.855006	−	0.518619i	$-0.826446\pi$
$593$	−24693.4			−1.71001			−0.855006	+	0.518619i	$0.826446\pi$
$594$		0			0
$595$	−613.516			−0.0422717
$596$	11870.3	−	20559.9i	0.815814	−	1.41303i
$597$		0			0
$598$	−10.6519	−	18.4496i	−0.000728409	−	0.00126164i
$599$	7320.59	+	12679.6i	0.499351	+	0.864901i	1.00000		0.000749436i	$-0.000238553\pi$
$599$	7320.59	+	12679.6i	0.499351	+	0.864901i	−0.500649	+	0.865650i	$0.666905\pi$
$600$		0			0
$601$	−6561.87	+	11365.5i	−0.445365	+	0.771394i	−0.998078	−	0.0619774i	$-0.980259\pi$
$601$	−6561.87	+	11365.5i	−0.445365	+	0.771394i	0.552713	+	0.833372i	$0.313593\pi$
$602$	146.961			0.00994961
$603$		0			0
$604$	16565.3			1.11595
$605$	3082.78	−	5339.54i	0.207162	−	0.358815i
$606$		0			0
$607$	5292.76	+	9167.33i	0.353915	+	0.612999i	0.986932	−	0.161139i	$-0.0515168\pi$
$607$	5292.76	+	9167.33i	0.353915	+	0.612999i	−0.633016	+	0.774138i	$0.718183\pi$
$608$	−893.893	−	1548.27i	−0.0596253	−	0.103274i
$609$		0			0
$610$	248.410	−	430.259i	0.0164883	−	0.0285585i
$611$	−7279.11			−0.481966
$612$		0			0
$613$	17835.2			1.17513			0.587566	−	0.809176i	$-0.300086\pi$
$613$	17835.2			1.17513			0.587566	+	0.809176i	$0.300086\pi$
$614$	16.7356	−	28.9869i	0.00109999	−	0.00190524i
$615$		0			0
$616$	237.456	+	411.286i	0.0155315	+	0.0269013i
$617$	9389.81	+	16263.6i	0.612674	+	1.06118i	0.990788	+	0.135423i	$0.0432393\pi$
$617$	9389.81	+	16263.6i	0.612674	+	1.06118i	−0.378114	+	0.925759i	$0.623427\pi$
$618$		0			0
$619$	−1645.15	+	2849.48i	−0.106824	+	0.185024i	−0.914482	−	0.404627i	$-0.867401\pi$
$619$	−1645.15	+	2849.48i	−0.106824	+	0.185024i	0.807658	+	0.589651i	$0.200735\pi$
$620$	−7104.29			−0.460186
$621$		0			0
$622$	−906.255			−0.0584204
$623$	5468.70	−	9472.07i	0.351684	−	0.609134i
$624$		0			0
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	257.756	+	446.447i	0.0164569	+	0.0285041i
$627$		0			0
$628$	1405.48	−	2434.36i	0.0893069	−	0.154684i
$629$	1316.50			0.0834538
$630$		0			0
$631$	2094.43			0.132136			0.0660682	−	0.997815i	$-0.478955\pi$
$631$	2094.43			0.132136			0.0660682	+	0.997815i	$0.478955\pi$
$632$	−615.101	+	1065.39i	−0.0387142	+	0.0670550i
$633$		0			0
$634$	569.160	+	985.814i	0.0356533	+	0.0617534i
$635$	−6426.73	−	11131.4i	−0.401633	−	0.695649i
$636$		0			0
$637$	370.910	−	642.435i	0.0230706	−	0.0399595i
$638$	207.455			0.0128734
$639$		0			0
$640$	1516.70			0.0936762
$641$	2102.87	−	3642.27i	0.129576	−	0.224432i	−0.793936	−	0.608001i	$-0.791972\pi$
$641$	2102.87	−	3642.27i	0.129576	−	0.224432i	0.923512	+	0.383569i	$0.125305\pi$
$642$		0			0
$643$	−3517.09	−	6091.78i	−0.215709	−	0.373618i	0.737783	−	0.675038i	$-0.235873\pi$
$643$	−3517.09	−	6091.78i	−0.215709	−	0.373618i	−0.953492	+	0.301420i	$0.902539\pi$
$644$	970.261	+	1680.54i	0.0593690	+	0.102830i
$645$		0			0
$646$	28.4669	−	49.3061i	0.00173377	−	0.00300298i
$647$	−11051.7			−0.671543			−0.335772	−	0.941943i	$-0.608997\pi$
$647$	−11051.7			−0.671543			−0.335772	+	0.941943i	$0.608997\pi$
$648$		0			0
$649$	−4892.87			−0.295935
$650$	−22.0516	+	38.1946i	−0.00133067	+	0.00230479i
$651$		0			0
$652$	11057.4	+	19151.9i	0.664171	+	1.15038i
$653$	−1277.76	−	2213.14i	−0.0765734	−	0.132629i	0.825196	−	0.564846i	$-0.191065\pi$
$653$	−1277.76	−	2213.14i	−0.0765734	−	0.132629i	−0.901769	+	0.432217i	$0.857731\pi$
$654$		0			0
$655$	1645.14	−	2849.47i	0.0981390	−	0.169982i
$656$	26133.6			1.55541
$657$		0			0
$658$	−1848.87			−0.109539
$659$	−2333.59	+	4041.90i	−0.137942	+	0.238922i	−0.926717	−	0.375759i	$-0.877382\pi$
$659$	−2333.59	+	4041.90i	−0.137942	+	0.238922i	0.788775	+	0.614681i	$0.210715\pi$
$660$		0			0
$661$	2267.41	+	3927.28i	0.133422	+	0.231094i	0.924994	−	0.379982i	$-0.124070\pi$
$661$	2267.41	+	3927.28i	0.133422	+	0.231094i	−0.791571	+	0.611077i	$0.790737\pi$
$662$	88.7727	+	153.759i	0.00521186	+	0.00902720i
$663$		0			0
$664$	777.077	−	1345.94i	0.0454163	−	0.0786634i
$665$	−6310.81			−0.368004
$666$		0			0
$667$	1697.71			0.0985544
$668$	−15299.1	+	26498.8i	−0.886137	+	1.53484i
$669$		0			0
$670$	103.592	+	179.426i	0.00597328	+	0.0103460i
$671$	3295.62	+	5708.19i	0.189607	+	0.328409i
$672$		0			0
$673$	−13710.0	+	23746.4i	−0.785262	+	1.36011i	0.143581	+	0.989639i	$0.454138\pi$
$673$	−13710.0	+	23746.4i	−0.785262	+	1.36011i	−0.928842	+	0.370475i	$0.879195\pi$
$674$	−103.692			−0.00592590
$675$		0			0
$676$	16411.0			0.933719
$677$	13259.9	−	22966.9i	0.752764	−	1.30383i	−0.193715	−	0.981058i	$-0.562054\pi$
$677$	13259.9	−	22966.9i	0.752764	−	1.30383i	0.946478	−	0.322767i	$-0.104613\pi$
$678$		0			0
$679$	−11414.6	−	19770.7i	−0.645145	−	1.11742i
$680$	36.2930	+	62.8613i	0.00204673	+	0.00354503i
$681$		0			0
$682$	−131.409	+	227.607i	−0.00737818	+	0.0127794i
$683$	−4297.61			−0.240767			−0.120383	−	0.992727i	$-0.538412\pi$
$683$	−4297.61			−0.240767			−0.120383	+	0.992727i	$0.538412\pi$
$684$		0			0
$685$	−3133.67			−0.174790
$686$	−421.018	+	729.225i	−0.0234323	+	0.0405859i
$687$		0			0
$688$	1552.32	+	2688.69i	0.0860196	+	0.148990i
$689$	4170.04	+	7222.72i	0.230574	+	0.399367i
$690$		0			0
$691$	10950.6	−	18967.0i	0.602866	−	1.04419i	−0.389519	−	0.921019i	$-0.627359\pi$
$691$	10950.6	−	18967.0i	0.602866	−	1.04419i	0.992385	−	0.123176i	$-0.0393080\pi$
$692$	9058.37			0.497612
$693$		0			0
$694$	1526.17			0.0834763
$695$	2434.36	−	4216.44i	0.132864	−	0.230128i
$696$		0			0
$697$	1254.20	+	2172.34i	0.0681583	+	0.118054i
$698$	596.421	+	1033.03i	0.0323422	+	0.0560184i
$699$		0			0
$700$	2008.64	−	3479.07i	0.108457	−	0.187852i
$701$	11225.3			0.604814			0.302407	−	0.953179i	$-0.402210\pi$
$701$	11225.3			0.604814			0.302407	+	0.953179i	$0.402210\pi$
$702$		0			0
$703$	13541.9			0.726521
$704$	−2490.64	+	4313.92i	−0.133338	+	0.230948i
$705$		0			0
$706$	−405.442	−	702.247i	−0.0216133	−	0.0374354i
$707$	−12077.8	−	20919.3i	−0.642477	−	1.11280i
$708$		0			0
$709$	−5779.38	+	10010.2i	−0.306134	+	0.530240i	−0.977513	−	0.210874i	$-0.932369\pi$
$709$	−5779.38	+	10010.2i	−0.306134	+	0.530240i	0.671379	+	0.741114i	$0.265702\pi$
$710$	178.464			0.00943331
$711$		0			0
$712$	−1294.02			−0.0681117
$713$	−1075.39	+	1862.63i	−0.0564848	+	0.0978346i
$714$		0			0
$715$	−292.556	−	506.722i	−0.0153021	−	0.0265039i
$716$	−12734.8	−	22057.2i	−0.664693	−	1.15128i
$717$		0			0
$718$	355.538	−	615.809i	0.0184799	−	0.0320081i
$719$	17315.4			0.898128			0.449064	−	0.893500i	$-0.351757\pi$
$719$	17315.4			0.898128			0.449064	+	0.893500i	$0.351757\pi$
$720$		0			0
$721$	−25096.2			−1.29630
$722$	−218.691	+	378.785i	−0.0112727	+	0.0195248i
$723$		0			0
$724$	3951.54	+	6844.27i	0.202842	+	0.351333i
$725$	−1757.31	−	3043.75i	−0.0900206	−	0.155920i
$726$		0			0
$727$	15728.5	−	27242.5i	0.802390	−	1.38978i	−0.115649	−	0.993290i	$-0.536895\pi$
$727$	15728.5	−	27242.5i	0.802390	−	1.38978i	0.918039	−	0.396490i	$-0.129772\pi$
$728$	−567.752			−0.0289042
$729$		0			0
$730$	685.357			0.0347482
$731$	−148.997	+	258.071i	−0.00753880	+	0.0130576i
$732$		0			0
$733$	−8046.18	−	13936.4i	−0.405447	−	0.702254i	0.588927	−	0.808186i	$-0.299551\pi$
$733$	−8046.18	−	13936.4i	−0.405447	−	0.702254i	−0.994373	+	0.105932i	$0.966217\pi$
$734$	948.698	+	1643.19i	0.0477072	+	0.0826313i
$735$		0			0
$736$	172.270	−	298.380i	0.00862764	−	0.0149435i
$737$	−2748.67			−0.137379
$738$		0			0
$739$	13798.5			0.686857			0.343429	−	0.939179i	$-0.388412\pi$
$739$	13798.5			0.686857			0.343429	+	0.939179i	$0.388412\pi$
$740$	−4310.22	+	7465.51i	−0.214117	+	0.370862i
$741$		0			0
$742$	1059.18	+	1834.55i	0.0524038	+	0.0907661i
$743$	−9684.40	−	16773.9i	−0.478178	−	0.828228i	0.521509	−	0.853246i	$-0.325369\pi$
$743$	−9684.40	−	16773.9i	−0.478178	−	0.828228i	−0.999687	+	0.0250174i	$0.992036\pi$
$744$		0			0
$745$	−7439.61	+	12885.8i	−0.365861	+	0.633689i
$746$	1388.01			0.0681215
$747$		0			0
$748$	−480.824			−0.0235035
$749$	−11674.0	+	20219.9i	−0.569503	+	0.986408i
$750$		0			0
$751$	−1175.45	−	2035.94i	−0.0571141	−	0.0989246i	0.836055	−	0.548646i	$-0.184857\pi$
$751$	−1175.45	−	2035.94i	−0.0571141	−	0.0989246i	−0.893169	+	0.449722i	$0.851523\pi$
$752$	−19529.3	−	33825.7i	−0.947021	−	1.64029i
$753$		0			0
$754$	−124.005	+	214.783i	−0.00598939	+	0.0103739i
$755$	−10382.2			−0.500458
$756$		0			0
$757$	−32608.1			−1.56560			−0.782801	−	0.622272i	$-0.786210\pi$
$757$	−32608.1			−1.56560			−0.782801	+	0.622272i	$0.786210\pi$
$758$	−866.842	+	1501.41i	−0.0415371	+	0.0719444i
$759$		0			0
$760$	373.321	+	646.611i	0.0178181	+	0.0308619i
$761$	16488.6	+	28559.2i	0.785431	+	1.36041i	0.928741	+	0.370728i	$0.120892\pi$
$761$	16488.6	+	28559.2i	0.785431	+	1.36041i	−0.143310	+	0.989678i	$0.545775\pi$
$762$		0			0
$763$	1194.63	−	2069.15i	0.0566820	−	0.0981760i
$764$	26196.7			1.24053
$765$		0			0
$766$	−1736.54			−0.0819110
$767$	2924.68	−	5065.70i	0.137685	−	0.238477i
$768$		0			0
$769$	−13393.9	−	23198.9i	−0.628082	−	1.08787i	−0.987936	−	0.154862i	$-0.950507\pi$
$769$	−13393.9	−	23198.9i	−0.628082	−	1.08787i	0.359854	−	0.933009i	$-0.382827\pi$
$770$	−74.3083	−	128.706i	−0.00347777	−	0.00602368i
$771$		0			0
$772$	−9445.70	+	16360.4i	−0.440360	+	0.762726i
$773$	−1474.56			−0.0686108			−0.0343054	−	0.999411i	$-0.510922\pi$
$773$	−1474.56			−0.0686108			−0.0343054	+	0.999411i	$0.510922\pi$
$774$		0			0
$775$	4452.56			0.206375
$776$	−1350.48	+	2339.10i	−0.0624736	+	0.108207i
$777$		0			0
$778$	−520.483	−	901.502i	−0.0239848	−	0.0415430i
$779$	12901.1	+	22345.4i	0.593364	+	1.02774i
$780$		0			0
$781$	−1183.83	+	2050.45i	−0.0542391	+	0.0939450i
$782$	10.9722			0.000501745
$783$		0			0
$784$	3980.49			0.181327
$785$	−880.874	+	1525.72i	−0.0400506	+	0.0693697i
$786$		0			0
$787$	−8632.17	−	14951.4i	−0.390983	−	0.677202i	0.601596	−	0.798800i	$-0.294532\pi$
$787$	−8632.17	−	14951.4i	−0.390983	−	0.677202i	−0.992579	+	0.121598i	$0.961198\pi$
$788$	14974.2	+	25936.1i	0.676948	+	1.17251i
$789$		0			0
$790$	192.487	−	333.397i	0.00866882	−	0.0150148i
$791$	7720.25			0.347030
$792$		0			0
$793$	−7879.76			−0.352861
$794$	215.114	−	372.588i	0.00961475	−	0.0166532i
$795$		0			0
$796$	7602.07	+	13167.2i	0.338503	+	0.586304i
$797$	−21780.6	−	37725.2i	−0.968017	−	1.67665i	−0.701282	−	0.712884i	$-0.747388\pi$
$797$	−21780.6	−	37725.2i	−0.968017	−	1.67665i	−0.266735	−	0.963770i	$-0.585945\pi$
$798$		0			0
$799$	1874.50	−	3246.72i	0.0829974	−	0.143756i
$800$	−713.268			−0.0315223
$801$		0			0
$802$	1639.81			0.0721992
$803$	−4546.26	+	7874.36i	−0.199793	+	0.346052i
$804$		0			0
$805$	−608.104	−	1053.27i	−0.0266247	−	0.0461153i
$806$	−157.098	−	272.102i	−0.00686544	−	0.0118913i
$807$		0			0
$808$	−1428.94	+	2475.00i	−0.0622153	+	0.107760i
$809$	1854.39			0.0805896			0.0402948	−	0.999188i	$-0.487170\pi$
$809$	1854.39			0.0805896			0.0402948	+	0.999188i	$0.487170\pi$
$810$		0			0
$811$	−42771.0			−1.85190			−0.925952	−	0.377642i	$-0.876735\pi$
$811$	−42771.0			−1.85190			−0.925952	+	0.377642i	$0.876735\pi$
$812$	11295.4	−	19564.2i	0.488166	−	0.845528i
$813$		0			0
$814$	159.453	+	276.181i	0.00686590	+	0.0118921i
$815$	−6930.12	−	12003.3i	−0.297855	−	0.515899i
$816$		0			0
$817$	−1532.63	+	2654.59i	−0.0656303	+	0.113675i
$818$	424.561			0.0181472
$819$		0			0
$820$	−16425.0			−0.699494
$821$	−12908.4	+	22358.0i	−0.548727	+	0.950424i	0.449635	+	0.893213i	$0.351554\pi$
$821$	−12908.4	+	22358.0i	−0.548727	+	0.950424i	−0.998362	+	0.0572112i	$0.981779\pi$
$822$		0			0
$823$	−20675.3	−	35810.7i	−0.875694	−	1.51675i	−0.856022	−	0.516940i	$-0.827071\pi$
$823$	−20675.3	−	35810.7i	−0.875694	−	1.51675i	−0.0196723	−	0.999806i	$-0.506262\pi$
$824$	1484.58	+	2571.37i	0.0627645	+	0.108711i
$825$		0			0
$826$	742.861	−	1286.67i	0.0312923	−	0.0541998i
$827$	−14681.0			−0.617302			−0.308651	−	0.951175i	$-0.599878\pi$
$827$	−14681.0			−0.617302			−0.308651	+	0.951175i	$0.599878\pi$
$828$		0			0
$829$	−31867.1			−1.33509			−0.667546	−	0.744568i	$-0.732655\pi$
$829$	−31867.1			−1.33509			−0.667546	+	0.744568i	$0.732655\pi$
$830$	−243.175	+	421.191i	−0.0101695	+	0.0176142i
$831$		0			0
$832$	−2977.54	−	5157.24i	−0.124072	−	0.214898i
$833$	191.032	+	330.876i	0.00794580	+	0.0137625i
$834$		0			0
$835$	9588.60	−	16607.9i	0.397398	−	0.688313i
$836$	−4945.90			−0.204614
$837$		0			0
$838$	−1238.71			−0.0510627
$839$	762.080	−	1319.96i	0.0313587	−	0.0543148i	−0.849920	−	0.526911i	$-0.823350\pi$
$839$	762.080	−	1319.96i	0.0313587	−	0.0543148i	0.881279	+	0.472597i	$0.156683\pi$
$840$		0			0
$841$	2312.44	+	4005.27i	0.0948149	+	0.164224i
$842$	266.343	+	461.320i	0.0109012	+	0.0188814i
$843$		0			0
$844$	−14715.7	+	25488.4i	−0.600161	+	1.03951i
$845$	−10285.5			−0.418736
$846$		0			0
$847$	−24837.9			−1.00760
$848$	−22375.8	+	38756.0i	−0.906117	+	1.56944i
$849$		0			0
$850$	−11.3574	−	19.6715i	−0.000458299	−	0.000793797i
$851$	1304.89	+	2260.14i	0.0525630	+	0.0910418i
$852$		0			0
$853$	−21649.2	+	37497.6i	−0.868999	+	1.50515i	−0.00597785	+	0.999982i	$0.501903\pi$
$853$	−21649.2	+	37497.6i	−0.868999	+	1.50515i	−0.863021	+	0.505168i	$0.831431\pi$
$854$	−2001.44			−0.0801964
$855$		0			0
$856$	2762.33			0.110297
$857$	6686.02	−	11580.5i	0.266500	−	0.461591i	−0.701456	−	0.712713i	$-0.747466\pi$
$857$	6686.02	−	11580.5i	0.266500	−	0.461591i	0.967955	+	0.251122i	$0.0807995\pi$
$858$		0			0
$859$	−8170.81	−	14152.3i	−0.324545	−	0.562129i	0.656875	−	0.754000i	$-0.271878\pi$
$859$	−8170.81	−	14152.3i	−0.324545	−	0.562129i	−0.981420	+	0.191871i	$0.938545\pi$
$860$	−975.631	−	1689.84i	−0.0386846	−	0.0670036i
$861$		0			0
$862$	−999.952	+	1731.97i	−0.0395110	+	0.0684351i
$863$	48077.3			1.89637			0.948186	−	0.317715i	$-0.102916\pi$
$863$	48077.3			1.89637			0.948186	+	0.317715i	$0.102916\pi$
$864$		0			0
$865$	−5677.27			−0.223159
$866$	−126.641	+	219.349i	−0.00496932	+	0.00860712i
$867$		0			0
$868$	14309.8	+	24785.3i	0.559569	+	0.969201i
$869$	2553.69	+	4423.13i	0.0996871	+	0.172663i
$870$		0			0
$871$	1643.00	−	2845.76i	0.0639162	−	0.110706i
$872$	−282.676			−0.0109778
$873$		0			0
$874$	112.863			0.00436803
$875$	−1258.90	+	2180.48i	−0.0486385	+	0.0842443i
$876$		0			0
$877$	25442.9	+	44068.4i	0.979643	+	1.69679i	0.663675	+	0.748021i	$0.268996\pi$
$877$	25442.9	+	44068.4i	0.979643	+	1.69679i	0.315968	+	0.948770i	$0.397671\pi$
$878$	−800.202	−	1385.99i	−0.0307580	−	0.0532744i
$879$		0			0
$880$	1569.81	−	2718.99i	0.0601344	−	0.104156i
$881$	2826.26			0.108081			0.0540404	−	0.998539i	$-0.482790\pi$
$881$	2826.26			0.108081			0.0540404	+	0.998539i	$0.482790\pi$
$882$		0			0
$883$	−2235.30			−0.0851913			−0.0425956	−	0.999092i	$-0.513563\pi$
$883$	−2235.30			−0.0851913			−0.0425956	+	0.999092i	$0.513563\pi$
$884$	287.410	−	497.808i	0.0109351	−	0.0189402i
$885$		0			0
$886$	−629.378	−	1090.11i	−0.0238650	−	0.0413354i
$887$	−4026.66	−	6974.37i	−0.152426	−	0.264010i	0.779693	−	0.626162i	$-0.215375\pi$
$887$	−4026.66	−	6974.37i	−0.152426	−	0.264010i	−0.932119	+	0.362153i	$0.882042\pi$
$888$		0			0
$889$	−25890.0	+	44842.8i	−0.976741	+	1.69177i
$890$	404.945			0.0152514
$891$		0			0
$892$	−1353.96			−0.0508227
$893$	19281.6	−	33396.8i	0.722548	−	1.25149i
$894$		0			0
$895$	7981.41	+	13824.2i	0.298089	+	0.516304i
$896$	−3055.00	−	5291.41i	−0.113907	−	0.197292i
$897$		0			0
$898$	−287.911	+	498.677i	−0.0106990	+	0.0185312i
$899$	25038.5			0.928901
$900$		0			0
$901$	−4295.43			−0.158825
$902$	−303.815	+	526.224i	−0.0112150	+	0.0194250i
$903$		0			0
$904$	−456.697	−	791.023i	−0.0168026	−	0.0291029i
$905$	−2476.60	−	4289.60i	−0.0909669	−	0.157559i
$906$		0			0
$907$	10288.8	−	17820.6i	0.376662	−	0.652398i	−0.613912	−	0.789374i	$-0.710405\pi$
$907$	10288.8	−	17820.6i	0.376662	−	0.652398i	0.990574	+	0.136977i	$0.0437385\pi$
$908$	−28779.4			−1.05185
$909$		0			0
$910$	177.670			0.00647218
$911$	−21634.0	+	37471.1i	−0.786790	+	1.36276i	0.141134	+	0.989990i	$0.454925\pi$
$911$	−21634.0	+	37471.1i	−0.786790	+	1.36276i	−0.927924	+	0.372769i	$0.878408\pi$
$912$		0			0
$913$	−3226.17	−	5587.88i	−0.116945	−	0.202554i
$914$	−258.989	−	448.583i	−0.00937265	−	0.0162339i
$915$		0			0
$916$	−24307.8	+	42102.4i	−0.876805	+	1.51867i
$917$	−13254.9			−0.477333
$918$		0			0
$919$	39601.9			1.42149			0.710743	−	0.703452i	$-0.248359\pi$
$919$	39601.9			1.42149			0.710743	+	0.703452i	$0.248359\pi$
$920$	−71.9458	+	124.614i	−0.00257824	+	0.00446565i
$921$		0			0
$922$	510.236	+	883.754i	0.0182253	+	0.0315671i
$923$	−1415.26	−	2451.29i	−0.0504699	−	0.0874164i
$924$		0			0
$925$	2701.40	−	4678.96i	0.0960231	−	0.166317i
$926$	−921.827			−0.0327140
$927$		0			0
$928$	−4010.99			−0.141883
$929$	−4242.40	+	7348.05i	−0.149826	+	0.259507i	−0.931163	−	0.364603i	$-0.881205\pi$
$929$	−4242.40	+	7348.05i	−0.149826	+	0.259507i	0.781337	+	0.624110i	$0.214538\pi$
$930$		0			0
$931$	1965.01	+	3403.49i	0.0691735	+	0.119812i
$932$	−15677.4	−	27154.0i	−0.550998	−	0.954356i
$933$		0			0
$934$	818.629	−	1417.91i	0.0286792	−	0.0496738i
$935$	301.353			0.0105404
$936$		0			0
$937$	−31244.9			−1.08935			−0.544677	−	0.838646i	$-0.683348\pi$
$937$	−31244.9			−1.08935			−0.544677	+	0.838646i	$0.683348\pi$
$938$	417.318	−	722.816i	0.0145266	−	0.0251607i
$939$		0			0
$940$	12274.2	+	21259.5i	0.425892	+	0.737667i
$941$	9757.45	+	16900.4i	0.338027	+	0.585481i	0.984062	−	0.177828i	$-0.0569070\pi$
$941$	9757.45	+	16900.4i	0.338027	+	0.585481i	−0.646034	+	0.763308i	$0.723574\pi$
$942$		0			0
$943$	−2486.28	+	4306.37i	−0.0858584	+	0.148711i
$944$	31386.8			1.08215
$945$		0			0
$946$	−72.1855			−0.00248092
$947$	−14681.8	+	25429.7i	−0.503797	+	0.872601i	0.496194	+	0.868212i	$0.334731\pi$
$947$	−14681.8	+	25429.7i	−0.503797	+	0.872601i	−0.999990	+	0.00438958i	$0.998603\pi$
$948$		0			0
$949$	−5435.00	−	9413.70i	−0.185909	−	0.322004i
$950$	−116.825	−	202.347i	−0.00398980	−	0.00691054i
$951$		0			0
$952$	146.206	−	253.236i	0.00497748	−	0.00862125i
$953$	21469.5			0.729763			0.364881	−	0.931054i	$-0.381110\pi$
$953$	21469.5			0.729763			0.364881	+	0.931054i	$0.381110\pi$
$954$		0			0
$955$	−16418.6			−0.556328
$956$	14608.2	−	25302.2i	0.494209	−	0.855995i
$957$		0			0
$958$	394.178	+	682.736i	0.0132936	+	0.0230253i
$959$	6311.97	+	10932.7i	0.212538	+	0.368127i
$960$		0			0
$961$	−964.767	+	1671.03i	−0.0323845	+	0.0560916i
$962$	−381.249			−0.0127775
$963$		0			0
$964$	−1777.67			−0.0593932
$965$	5920.02	−	10253.8i	0.197484	−	0.342053i
$966$		0			0
$967$	−11194.7	−	19389.8i	−0.372283	−	0.644813i	0.617633	−	0.786466i	$-0.288092\pi$
$967$	−11194.7	−	19389.8i	−0.372283	−	0.644813i	−0.989916	+	0.141653i	$0.954758\pi$
$968$	1469.31	+	2544.91i	0.0487865	+	0.0845007i
$969$		0			0
$970$	422.613	−	731.988i	0.0139890	−	0.0242296i
$971$	−9483.42			−0.313427			−0.156713	−	0.987644i	$-0.550090\pi$
$971$	−9483.42			−0.313427			−0.156713	+	0.987644i	$0.550090\pi$
$972$		0			0
$973$	−19613.6			−0.646231
$974$	1149.81	−	1991.53i	0.0378257	−	0.0655160i
$975$		0			0
$976$	−21140.8	−	36616.9i	−0.693340	−	1.20090i
$977$	−23171.8	−	40134.8i	−0.758784	−	1.31425i	−0.943471	−	0.331455i	$-0.892460\pi$
$977$	−23171.8	−	40134.8i	−0.758784	−	1.31425i	0.184687	−	0.982797i	$-0.440873\pi$
$978$		0			0
$979$	−2686.17	+	4652.59i	−0.0876920	+	0.151887i
$980$	−2501.74			−0.0815461
$981$		0			0
$982$	−2055.65			−0.0668007
$983$	20565.2	−	35619.9i	0.667270	−	1.15575i	−0.311394	−	0.950281i	$-0.600796\pi$
$983$	20565.2	−	35619.9i	0.667270	−	1.15575i	0.978664	−	0.205465i	$-0.0658707\pi$
$984$		0			0
$985$	−9385.00	−	16255.3i	−0.303585	−	0.525824i
$986$	−63.8669	−	110.621i	−0.00206282	−	0.00357290i
$987$		0			0
$988$	2956.38	−	5120.60i	0.0951974	−	0.164887i
$989$	−590.732			−0.0189931
$990$		0			0
$991$	25380.8			0.813568			0.406784	−	0.913524i	$-0.366650\pi$
$991$	25380.8			0.813568			0.406784	+	0.913524i	$0.366650\pi$
$992$	2540.70	−	4400.62i	0.0813178	−	0.140847i
$993$		0			0
$994$	−359.471	−	622.622i	−0.0114705	−	0.0198676i
$995$	−4764.55	−	8252.44i	−0.151805	−	0.262934i
$996$		0			0
$997$	14175.5	−	24552.7i	0.450294	−	0.779932i	−0.548110	−	0.836406i	$-0.684653\pi$
$997$	14175.5	−	24552.7i	0.450294	−	0.779932i	0.998404	+	0.0564744i	$0.0179859\pi$
$998$	343.438			0.0108931
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.4.e.w.136.4		12
3.2	odd	2		405.4.e.x.136.3		12
9.2	odd	6		405.4.a.k.1.4	✓	6
9.4	even	3	inner	405.4.e.w.271.4		12
9.5	odd	6		405.4.e.x.271.3		12
9.7	even	3		405.4.a.l.1.3	yes	6
45.29	odd	6		2025.4.a.z.1.3		6
45.34	even	6		2025.4.a.y.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.4.a.k.1.4	✓	6	9.2	odd	6
405.4.a.l.1.3	yes	6	9.7	even	3
405.4.e.w.136.4		12	1.1	even	1	trivial
405.4.e.w.271.4		12	9.4	even	3	inner
405.4.e.x.136.3		12	3.2	odd	2
405.4.e.x.271.3		12	9.5	odd	6
2025.4.a.y.1.4		6	45.34	even	6
2025.4.a.z.1.3		6	45.29	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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	405.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0745751 - 0.129168i) q^{2} +(3.98888 + 6.90894i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(-10.0712 + 17.4439i) q^{7} +2.38308 q^{8} +O(q^{10})\)	\(q+(0.0745751 - 0.129168i) q^{2} +(3.98888 + 6.90894i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(-10.0712 + 17.4439i) q^{7} +2.38308 q^{8} -0.745751 q^{10} +(4.94688 - 8.56825i) q^{11} +(5.91394 + 10.2432i) q^{13} +(1.50212 + 2.60176i) q^{14} +(-31.7333 + 54.9637i) q^{16} -6.09177 q^{17} -62.6618 q^{19} +(19.9444 - 34.5447i) q^{20} +(-0.737829 - 1.27796i) q^{22} +(-6.03804 - 10.4582i) q^{23} +(-12.5000 + 21.6506i) q^{25} +1.76413 q^{26} -160.691 q^{28} +(-70.2925 + 121.750i) q^{29} +(-89.0513 - 154.241i) q^{31} +(14.2654 + 24.7083i) q^{32} +(-0.454294 + 0.786861i) q^{34} +100.712 q^{35} -216.112 q^{37} +(-4.67301 + 8.09389i) q^{38} +(-5.95771 - 10.3191i) q^{40} +(-205.885 - 356.603i) q^{41} +(24.4588 - 42.3639i) q^{43} +78.9300 q^{44} -1.80115 q^{46} +(-307.710 + 532.969i) q^{47} +(-31.3590 - 54.3153i) q^{49} +(1.86438 + 3.22920i) q^{50} +(-47.1800 + 81.7181i) q^{52} +705.120 q^{53} -49.4688 q^{55} +(-24.0006 + 41.5702i) q^{56} +(10.4841 + 18.1590i) q^{58} +(-247.270 - 428.284i) q^{59} +(-333.101 + 576.948i) q^{61} -26.5640 q^{62} -503.477 q^{64} +(29.5697 - 51.2162i) q^{65} +(-138.909 - 240.598i) q^{67} +(-24.2993 - 42.0877i) q^{68} +(7.51062 - 13.0088i) q^{70} -239.308 q^{71} -919.015 q^{73} +(-16.1166 + 27.9147i) q^{74} +(-249.950 - 432.926i) q^{76} +(99.6423 + 172.586i) q^{77} +(-258.111 + 447.062i) q^{79} +317.333 q^{80} -61.4155 q^{82} +(326.081 - 564.788i) q^{83} +(15.2294 + 26.3781i) q^{85} +(-3.64803 - 6.31858i) q^{86} +(11.7888 - 20.4189i) q^{88} -543.003 q^{89} -238.242 q^{91} +(48.1700 - 83.4329i) q^{92} +(45.8949 + 79.4924i) q^{94} +(156.654 + 271.333i) q^{95} +(-566.695 + 981.545i) q^{97} -9.35439 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 34 q^{4} - 30 q^{5} - 40 q^{7} + 132 q^{8}+O(q^{10}) \) 12 * q - 4 * q^2 - 34 * q^4 - 30 * q^5 - 40 * q^7 + 132 * q^8	\( 12 q - 4 q^{2} - 34 q^{4} - 30 q^{5} - 40 q^{7} + 132 q^{8} + 40 q^{10} - 88 q^{11} - 20 q^{13} - 180 q^{14} - 58 q^{16} + 248 q^{17} - 92 q^{19} - 170 q^{20} + 74 q^{22} - 210 q^{23} - 150 q^{25} + 8 q^{26} + 704 q^{28} - 296 q^{29} + 104 q^{31} - 722 q^{32} + 428 q^{34} + 400 q^{35} - 408 q^{37} + 20 q^{38} - 330 q^{40} - 344 q^{41} - 512 q^{43} + 1432 q^{44} - 372 q^{46} - 238 q^{47} - 68 q^{49} - 100 q^{50} + 468 q^{52} + 1700 q^{53} + 880 q^{55} - 2316 q^{56} - 890 q^{58} - 1840 q^{59} + 364 q^{61} + 2076 q^{62} - 1980 q^{64} - 100 q^{65} - 88 q^{67} - 236 q^{68} - 900 q^{70} + 2728 q^{71} + 1672 q^{73} - 1316 q^{74} + 2106 q^{76} - 840 q^{77} + 680 q^{79} + 580 q^{80} + 3484 q^{82} - 2148 q^{83} - 620 q^{85} - 2872 q^{86} - 1296 q^{88} + 6000 q^{89} - 6116 q^{91} - 1002 q^{92} + 3662 q^{94} + 230 q^{95} + 612 q^{97} + 3964 q^{98}+O(q^{100}) \) 12 * q - 4 * q^2 - 34 * q^4 - 30 * q^5 - 40 * q^7 + 132 * q^8 + 40 * q^10 - 88 * q^11 - 20 * q^13 - 180 * q^14 - 58 * q^16 + 248 * q^17 - 92 * q^19 - 170 * q^20 + 74 * q^22 - 210 * q^23 - 150 * q^25 + 8 * q^26 + 704 * q^28 - 296 * q^29 + 104 * q^31 - 722 * q^32 + 428 * q^34 + 400 * q^35 - 408 * q^37 + 20 * q^38 - 330 * q^40 - 344 * q^41 - 512 * q^43 + 1432 * q^44 - 372 * q^46 - 238 * q^47 - 68 * q^49 - 100 * q^50 + 468 * q^52 + 1700 * q^53 + 880 * q^55 - 2316 * q^56 - 890 * q^58 - 1840 * q^59 + 364 * q^61 + 2076 * q^62 - 1980 * q^64 - 100 * q^65 - 88 * q^67 - 236 * q^68 - 900 * q^70 + 2728 * q^71 + 1672 * q^73 - 1316 * q^74 + 2106 * q^76 - 840 * q^77 + 680 * q^79 + 580 * q^80 + 3484 * q^82 - 2148 * q^83 - 620 * q^85 - 2872 * q^86 - 1296 * q^88 + 6000 * q^89 - 6116 * q^91 - 1002 * q^92 + 3662 * q^94 + 230 * q^95 + 612 * q^97 + 3964 * q^98

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