LMFDB - Embedded newform 135.5.h.a.89.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,5,Mod(44,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("135.44");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	135.h (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:	$13.9549450163$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.14
Character	$\chi$	$=$	135.89
Dual form			135.5.h.a.44.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.02189 - 1.76997i) q^{2} +(5.91148 + 10.2390i) q^{4} +(-15.4498 + 19.6546i) q^{5} +(-2.09732 - 1.21089i) q^{7} +56.8640 q^{8} +(19.0000 + 47.4305i) q^{10} +(-117.697 - 67.9523i) q^{11} +(-136.503 + 78.8098i) q^{13} +(-4.28647 + 2.47479i) q^{14} +(-36.4748 + 63.1763i) q^{16} -258.165 q^{17} -363.338 q^{19} +(-292.574 - 42.0027i) q^{20} +(-240.547 + 138.880i) q^{22} +(392.923 + 680.562i) q^{23} +(-147.606 - 607.320i) q^{25} +322.140i q^{26} -28.6326i q^{28} +(629.935 + 363.693i) q^{29} +(-463.170 - 802.234i) q^{31} +(529.459 + 917.050i) q^{32} +(-263.817 + 456.944i) q^{34} +(56.2028 - 22.5140i) q^{35} +1997.88i q^{37} +(-371.292 + 643.096i) q^{38} +(-878.539 + 1117.64i) q^{40} +(-1250.71 + 722.098i) q^{41} +(542.092 + 312.977i) q^{43} -1606.79i q^{44} +1606.10 q^{46} +(-188.637 + 326.730i) q^{47} +(-1197.57 - 2074.25i) q^{49} +(-1225.77 - 359.356i) q^{50} +(-1613.86 - 931.765i) q^{52} +694.739 q^{53} +(3153.97 - 1263.43i) q^{55} +(-119.262 - 68.8560i) q^{56} +(1287.45 - 743.309i) q^{58} +(2222.20 - 1282.99i) q^{59} +(-2577.00 + 4463.50i) q^{61} -1893.24 q^{62} +997.001 q^{64} +(559.965 - 3900.50i) q^{65} +(5671.56 - 3274.48i) q^{67} +(-1526.14 - 2643.35i) q^{68} +(17.5841 - 122.484i) q^{70} +3331.47i q^{71} -1735.66i q^{73} +(3536.18 + 2041.61i) q^{74} +(-2147.86 - 3720.21i) q^{76} +(164.565 + 285.036i) q^{77} +(-3695.54 + 6400.86i) q^{79} +(-678.175 - 1692.96i) q^{80} +2951.62i q^{82} +(5465.06 - 9465.75i) q^{83} +(3988.60 - 5074.13i) q^{85} +(1107.92 - 639.657i) q^{86} +(-6692.72 - 3864.04i) q^{88} -2325.29i q^{89} +381.719 q^{91} +(-4645.51 + 8046.26i) q^{92} +(385.534 + 667.764i) q^{94} +(5613.50 - 7141.26i) q^{95} +(14265.5 + 8236.22i) q^{97} -4895.13 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 162 q^{4} - 6 q^{5} + 28 q^{10} - 228 q^{11} - 282 q^{14} - 1058 q^{16} - 8 q^{19} + 2196 q^{20} - 148 q^{25} - 2370 q^{29} - 1112 q^{31} - 436 q^{34} - 850 q^{40} - 1830 q^{41} - 5668 q^{46} + 5396 q^{49}+ \cdots - 58746 q^{95}+O(q^{100}) $ 44 * q - 162 * q^4 - 6 * q^5 + 28 * q^10 - 228 * q^11 - 282 * q^14 - 1058 * q^16 - 8 * q^19 + 2196 * q^20 - 148 * q^25 - 2370 * q^29 - 1112 * q^31 - 436 * q^34 - 850 * q^40 - 1830 * q^41 - 5668 * q^46 + 5396 * q^49 - 13524 * q^50 - 3072 * q^55 + 8250 * q^56 + 27348 * q^59 + 2782 * q^61 + 8348 * q^64 + 24906 * q^65 + 4782 * q^70 - 64728 * q^74 - 1776 * q^76 + 7900 * q^79 + 6766 * q^85 - 9192 * q^86 + 1560 * q^91 - 18826 * q^94 - 58746 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.02189	−	1.76997i	0.255473	−	0.442492i	−0.709551	−	0.704654i	$-0.751102\pi$
$2$	1.02189	−	1.76997i	0.255473	−	0.442492i	0.965024	+	0.262162i	$0.0844356\pi$
$3$		0			0
$3$		0			0
$4$	5.91148	+	10.2390i	0.369467	+	0.639936i
$5$	−15.4498	+	19.6546i	−0.617993	+	0.786184i
$5$	−15.4498	+	19.6546i	−0.617993	+	0.786184i
$6$		0			0
$7$	−2.09732	−	1.21089i	−0.0428025	−	0.0247120i	0.478446	−	0.878117i	$-0.341200\pi$
$7$	−2.09732	−	1.21089i	−0.0428025	−	0.0247120i	−0.521249	+	0.853405i	$0.674534\pi$
$8$	56.8640			0.888501
$9$		0			0
$10$	19.0000	+	47.4305i	0.190000	+	0.474305i
$11$	−117.697	−	67.9523i	−0.972701	−	0.561589i	−0.0726425	−	0.997358i	$-0.523143\pi$
$11$	−117.697	−	67.9523i	−0.972701	−	0.561589i	−0.900059	+	0.435769i	$0.856477\pi$
$12$		0			0
$13$	−136.503	+	78.8098i	−0.807707	+	0.466330i	−0.846159	−	0.532930i	$-0.821091\pi$
$13$	−136.503	+	78.8098i	−0.807707	+	0.466330i	0.0384518	+	0.999260i	$0.487757\pi$
$14$	−4.28647	+	2.47479i	−0.0218697	+	0.0126265i
$15$		0			0
$16$	−36.4748	+	63.1763i	−0.142480	+	0.246782i
$17$	−258.165			−0.893305			−0.446652	−	0.894708i	$-0.647384\pi$
$17$	−258.165			−0.893305			−0.446652	+	0.894708i	$0.647384\pi$
$18$		0			0
$19$	−363.338			−1.00648			−0.503238	−	0.864148i	$-0.667858\pi$
$19$	−363.338			−1.00648			−0.503238	+	0.864148i	$0.667858\pi$
$20$	−292.574	−	42.0027i	−0.731436	−	0.105007i
$21$		0			0
$22$	−240.547	+	138.880i	−0.496997	+	0.286941i
$23$	392.923	+	680.562i	0.742765	+	1.28651i	0.951232	+	0.308477i	$0.0998194\pi$
$23$	392.923	+	680.562i	0.742765	+	1.28651i	−0.208467	+	0.978029i	$0.566847\pi$
$24$		0			0
$25$	−147.606	−	607.320i	−0.236170	−	0.971712i
$26$			322.140i			0.476538i
$27$		0			0
$28$		−	28.6326i		−	0.0365211i
$29$	629.935	+	363.693i	0.749031	+	0.432453i	0.825344	−	0.564631i	$-0.190981\pi$
$29$	629.935	+	363.693i	0.749031	+	0.432453i	−0.0763129	+	0.997084i	$0.524315\pi$
$30$		0			0
$31$	−463.170	−	802.234i	−0.481967	−	0.834790i	0.517819	−	0.855490i	$-0.326744\pi$
$31$	−463.170	−	802.234i	−0.481967	−	0.834790i	−0.999786	+	0.0206996i	$0.993411\pi$
$32$	529.459	+	917.050i	0.517050	+	0.895556i
$33$		0			0
$34$	−263.817	+	456.944i	−0.228215	+	0.395280i
$35$	56.2028	−	22.5140i	0.0458798	−	0.0183788i
$36$		0			0
$37$			1997.88i			1.45937i	0.683783	+	0.729685i	$0.260333\pi$
$37$			1997.88i			1.45937i	−0.683783	+	0.729685i	$0.739667\pi$
$38$	−371.292	+	643.096i	−0.257127	+	0.445357i
$39$		0			0
$40$	−878.539	+	1117.64i	−0.549087	+	0.698525i
$41$	−1250.71	+	722.098i	−0.744027	+	0.429564i	−0.823532	−	0.567270i	$-0.808000\pi$
$41$	−1250.71	+	722.098i	−0.744027	+	0.429564i	0.0795044	+	0.996835i	$0.474666\pi$
$42$		0			0
$43$	542.092	+	312.977i	0.293181	+	0.169268i	0.639376	−	0.768895i	$-0.279193\pi$
$43$	542.092	+	312.977i	0.293181	+	0.169268i	−0.346194	+	0.938163i	$0.612526\pi$
$44$		−	1606.79i		−	0.829956i
$45$		0			0
$46$	1606.10			0.759025
$47$	−188.637	+	326.730i	−0.0853950	+	0.147908i	−0.905559	−	0.424219i	$-0.860549\pi$
$47$	−188.637	+	326.730i	−0.0853950	+	0.147908i	0.820164	+	0.572128i	$0.193882\pi$
$48$		0			0
$49$	−1197.57	−	2074.25i	−0.498779	−	0.863910i
$50$	−1225.77	−	359.356i	−0.490309	−	0.143742i
$51$		0			0
$52$	−1613.86	−	931.765i	−0.596843	−	0.344588i
$53$	694.739			0.247326			0.123663	−	0.992324i	$-0.460536\pi$
$53$	694.739			0.247326			0.123663	+	0.992324i	$0.460536\pi$
$54$		0			0
$55$	3153.97	−	1263.43i	1.04263	−	0.417664i
$56$	−119.262	−	68.8560i	−0.0380300	−	0.0219566i
$57$		0			0
$58$	1287.45	−	743.309i	0.382714	−	0.220960i
$59$	2222.20	−	1282.99i	0.638381	−	0.368569i	−0.145610	−	0.989342i	$-0.546514\pi$
$59$	2222.20	−	1282.99i	0.638381	−	0.368569i	0.783991	+	0.620773i	$0.213181\pi$
$60$		0			0
$61$	−2577.00	+	4463.50i	−0.692556	+	1.19954i	0.278441	+	0.960453i	$0.410182\pi$
$61$	−2577.00	+	4463.50i	−0.692556	+	1.19954i	−0.970998	+	0.239089i	$0.923151\pi$
$62$	−1893.24			−0.492517
$63$		0			0
$64$	997.001			0.243408
$65$	559.965	−	3900.50i	0.132536	−	0.923195i
$66$		0			0
$67$	5671.56	−	3274.48i	1.26344	−	0.729445i	0.289698	−	0.957118i	$-0.406445\pi$
$67$	5671.56	−	3274.48i	1.26344	−	0.729445i	0.973738	+	0.227673i	$0.0731117\pi$
$68$	−1526.14	−	2643.35i	−0.330047	−	0.571658i
$69$		0			0
$70$	17.5841	−	122.484i	0.00358858	−	0.0249967i
$71$			3331.47i			0.660875i	0.943828	+	0.330438i	$0.107196\pi$
$71$			3331.47i			0.660875i	−0.943828	+	0.330438i	$0.892804\pi$
$72$		0			0
$73$		−	1735.66i		−	0.325701i	−0.986651	−	0.162850i	$-0.947931\pi$
$73$		−	1735.66i		−	0.325701i	0.986651	−	0.162850i	$-0.0520688\pi$
$74$	3536.18	+	2041.61i	0.645759	+	0.372829i
$75$		0			0
$76$	−2147.86	−	3720.21i	−0.371860	−	0.644081i
$77$	164.565	+	285.036i	0.0277560	+	0.0480748i
$78$		0			0
$79$	−3695.54	+	6400.86i	−0.592139	+	1.02561i	0.401805	+	0.915725i	$0.368383\pi$
$79$	−3695.54	+	6400.86i	−0.592139	+	1.02561i	−0.993944	+	0.109889i	$0.964950\pi$
$80$	−678.175	−	1692.96i	−0.105965	−	0.264525i
$81$		0			0
$82$			2951.62i			0.438968i
$83$	5465.06	−	9465.75i	0.793302	−	1.37404i	−0.130610	−	0.991434i	$-0.541694\pi$
$83$	5465.06	−	9465.75i	0.793302	−	1.37404i	0.923912	−	0.382605i	$-0.124973\pi$
$84$		0			0
$85$	3988.60	−	5074.13i	0.552056	−	0.702302i
$86$	1107.92	−	639.657i	0.149800	−	0.0864868i
$87$		0			0
$88$	−6692.72	−	3864.04i	−0.864245	−	0.498972i
$89$		−	2325.29i		−	0.293560i	−0.989169	−	0.146780i	$-0.953109\pi$
$89$		−	2325.29i		−	0.293560i	0.989169	−	0.146780i	$-0.0468909\pi$
$90$		0			0
$91$	381.719			0.0460958
$92$	−4645.51	+	8046.26i	−0.548855	+	0.950645i
$93$		0			0
$94$	385.534	+	667.764i	0.0436321	+	0.0755731i
$95$	5613.50	−	7141.26i	0.621995	−	0.791275i
$96$		0			0
$97$	14265.5	+	8236.22i	1.51616	+	0.875355i	0.999820	+	0.0189715i	$0.00603918\pi$
$97$	14265.5	+	8236.22i	1.51616	+	0.875355i	0.516340	+	0.856384i	$0.327294\pi$
$98$	−4895.13			−0.509697
$99$		0			0
$100$	5345.77	−	5101.50i	0.534577	−	0.510150i
$101$	−2850.51	−	1645.74i	−0.279434	−	0.161332i	0.353733	−	0.935346i	$-0.384912\pi$
$101$	−2850.51	−	1645.74i	−0.279434	−	0.161332i	−0.633167	+	0.774015i	$0.718245\pi$
$102$		0			0
$103$	−1997.64	+	1153.34i	−0.188297	+	0.108713i	−0.591185	−	0.806536i	$-0.701340\pi$
$103$	−1997.64	+	1153.34i	−0.188297	+	0.108713i	0.402888	+	0.915249i	$0.368006\pi$
$104$	−7762.08	+	4481.44i	−0.717648	+	0.414334i
$105$		0			0
$106$	709.948	−	1229.67i	0.0631851	−	0.109440i
$107$	3623.64			0.316503			0.158251	−	0.987399i	$-0.449414\pi$
$107$	3623.64			0.316503			0.158251	+	0.987399i	$0.449414\pi$
$108$		0			0
$109$	17380.4			1.46288			0.731438	−	0.681908i	$-0.238850\pi$
$109$	17380.4			1.46288			0.731438	+	0.681908i	$0.238850\pi$
$110$	986.777	−	6873.51i	0.0815518	−	0.568059i
$111$		0			0
$112$	152.999	−	88.3340i	0.0121970	−	0.00704193i
$113$	−5120.93	−	8869.71i	−0.401044	−	0.694628i	0.592808	−	0.805343i	$-0.298019\pi$
$113$	−5120.93	−	8869.71i	−0.401044	−	0.694628i	−0.993852	+	0.110715i	$0.964686\pi$
$114$		0			0
$115$	−19446.8	−	2791.82i	−1.47045	−	0.211102i
$116$			8599.86i			0.639109i
$117$		0			0
$118$		−	5244.30i		−	0.376638i
$119$	541.455	+	312.609i	0.0382357	+	0.0220754i
$120$		0			0
$121$	1914.53	+	3316.06i	0.130765	+	0.226492i
$122$	5266.83	+	9122.41i	0.353858	+	0.612901i
$123$		0			0
$124$	5476.04	−	9484.78i	0.356142	−	0.616856i
$125$	14217.1	+	6481.84i	0.909895	+	0.414838i
$126$		0			0
$127$			27661.2i			1.71500i	0.514484	+	0.857500i	$0.327983\pi$
$127$			27661.2i			1.71500i	−0.514484	+	0.857500i	$0.672017\pi$
$128$	−7452.52	+	12908.1i	−0.454866	+	0.787850i
$129$		0			0
$130$	−6331.53	−	4977.00i	−0.374647	−	0.294497i
$131$	11192.2	−	6461.79i	0.652185	−	0.376539i	−0.137108	−	0.990556i	$-0.543781\pi$
$131$	11192.2	−	6461.79i	0.652185	−	0.376539i	0.789293	+	0.614017i	$0.210447\pi$
$132$		0			0
$133$	762.036	+	439.962i	0.0430797	+	0.0248721i
$134$		−	13384.6i		−	0.745413i
$135$		0			0
$136$	−14680.3			−0.793702
$137$	−17968.9	+	31123.0i	−0.957369	+	1.65821i	−0.228519	+	0.973539i	$0.573388\pi$
$137$	−17968.9	+	31123.0i	−0.957369	+	1.65821i	−0.728850	+	0.684673i	$0.759945\pi$
$138$		0			0
$139$	−9010.90	−	15607.3i	−0.466379	−	0.807792i	0.532884	−	0.846188i	$-0.321108\pi$
$139$	−9010.90	−	15607.3i	−0.466379	−	0.807792i	−0.999263	+	0.0383967i	$0.987775\pi$
$140$	562.762	+	442.368i	0.0287123	+	0.0225698i
$141$		0			0
$142$	5896.59	+	3404.40i	0.292432	+	0.168836i
$143$	21421.2			1.04754
$144$		0			0
$145$	−16880.6	+	6762.12i	−0.802883	+	0.321623i
$146$	−3072.06	−	1773.65i	−0.144120	−	0.0832077i
$147$		0			0
$148$	−20456.2	+	11810.4i	−0.933904	+	0.539190i
$149$	−30500.0	+	17609.2i	−1.37381	+	0.793172i	−0.991406	−	0.130822i	$-0.958238\pi$
$149$	−30500.0	+	17609.2i	−1.37381	+	0.793172i	−0.382408	+	0.923994i	$0.624905\pi$
$150$		0			0
$151$	−5908.59	+	10234.0i	−0.259137	+	0.448839i	−0.966011	−	0.258501i	$-0.916771\pi$
$151$	−5908.59	+	10234.0i	−0.259137	+	0.448839i	0.706874	+	0.707340i	$0.250105\pi$
$152$	−20660.9			−0.894255
$153$		0			0
$154$	672.671			0.0283636
$155$	22923.5	+	3290.95i	0.954151	+	0.136980i
$156$		0			0
$157$	−4657.79	+	2689.18i	−0.188965	+	0.109099i	−0.591498	−	0.806307i	$-0.701463\pi$
$157$	−4657.79	+	2689.18i	−0.188965	+	0.109099i	0.402533	+	0.915405i	$0.368130\pi$
$158$	7552.87	+	13082.0i	0.302550	+	0.524033i
$159$		0			0
$160$	−26204.3	−	3761.95i	−1.02360	−	0.146951i
$161$		−	1903.14i		−	0.0734209i
$162$		0			0
$163$		−	12593.5i		−	0.473991i	−0.971511	−	0.236995i	$-0.923837\pi$
$163$		−	12593.5i		−	0.473991i	0.971511	−	0.236995i	$-0.0761626\pi$
$164$	−14787.1	−	8537.33i	−0.549788	−	0.317420i
$165$		0			0
$166$	−11169.4	−	19345.9i	−0.405334	−	0.702059i
$167$	17707.1	+	30669.5i	0.634912	+	1.09970i	0.986534	+	0.163558i	$0.0522971\pi$
$167$	17707.1	+	30669.5i	0.634912	+	1.09970i	−0.351622	+	0.936142i	$0.614370\pi$
$168$		0			0
$169$	−1858.54	+	3219.09i	−0.0650727	+	0.112709i
$170$	−4905.13	−	12244.9i	−0.169728	−	0.423699i
$171$		0			0
$172$			7400.63i			0.250156i
$173$	10598.2	−	18356.6i	0.354112	−	0.613340i	−0.632854	−	0.774271i	$-0.718117\pi$
$173$	10598.2	−	18356.6i	0.354112	−	0.613340i	0.986966	+	0.160932i	$0.0514499\pi$
$174$		0			0
$175$	−425.819	+	1452.48i	−0.0139043	+	0.0474279i
$176$	8585.95	−	4957.10i	0.277181	−	0.160030i
$177$		0			0
$178$	−4115.68	−	2376.19i	−0.129898	−	0.0749965i
$179$			16660.9i			0.519986i	0.965611	+	0.259993i	$0.0837202\pi$
$179$			16660.9i			0.519986i	−0.965611	+	0.259993i	$0.916280\pi$
$180$		0			0
$181$	45130.9			1.37758			0.688791	−	0.724960i	$-0.258142\pi$
$181$	45130.9			1.37758			0.688791	+	0.724960i	$0.258142\pi$
$182$	390.076	−	675.631i	0.0117762	−	0.0203970i
$183$		0			0
$184$	22343.2	+	38699.5i	0.659947	+	1.14306i
$185$	−39267.5	−	30866.8i	−1.14733	−	0.901880i
$186$		0			0
$187$	30385.2	+	17542.9i	0.868919	+	0.501670i
$188$	−4460.51			−0.126203
$189$		0			0
$190$	−6903.40	−	17233.3i	−0.191230	−	0.477377i
$191$	−30912.8	−	17847.5i	−0.847367	−	0.489228i	0.0123943	−	0.999923i	$-0.496055\pi$
$191$	−30912.8	−	17847.5i	−0.847367	−	0.489228i	−0.859762	+	0.510695i	$0.829388\pi$
$192$		0			0
$193$	21060.2	−	12159.1i	0.565390	−	0.326428i	−0.189916	−	0.981800i	$-0.560822\pi$
$193$	21060.2	−	12159.1i	0.565390	−	0.326428i	0.755306	+	0.655372i	$0.227488\pi$
$194$	29155.7	−	16833.0i	0.774675	−	0.447259i
$195$		0			0
$196$	14158.8	−	24523.7i	0.368565	−	0.638373i
$197$	−13918.9			−0.358652			−0.179326	−	0.983790i	$-0.557392\pi$
$197$	−13918.9			−0.358652			−0.179326	+	0.983790i	$0.557392\pi$
$198$		0			0
$199$	−41162.0			−1.03942			−0.519709	−	0.854343i	$-0.673960\pi$
$199$	−41162.0			−1.03942			−0.519709	+	0.854343i	$0.673960\pi$
$200$	−8393.49	−	34534.7i	−0.209837	−	0.863366i
$201$		0			0
$202$	−5825.82	+	3363.54i	−0.142776	+	0.0824316i
$203$	−880.784	−	1525.56i	−0.0213736	−	0.0370201i
$204$		0			0
$205$	5130.70	−	35738.5i	0.122087	−	0.850410i
$206$			4714.34i			0.111093i
$207$		0			0
$208$		−	11498.3i		−	0.265771i
$209$	42763.7	+	24689.6i	0.979001	+	0.565226i
$210$		0			0
$211$	24325.2	+	42132.5i	0.546377	+	0.946352i	0.998519	+	0.0544061i	$0.0173266\pi$
$211$	24325.2	+	42132.5i	0.546377	+	0.946352i	−0.452142	+	0.891946i	$0.649340\pi$
$212$	4106.94	+	7113.42i	0.0913790	+	0.158273i
$213$		0			0
$214$	3702.96	−	6413.72i	0.0808577	−	0.140050i
$215$	−14526.7	+	5819.16i	−0.314260	+	0.125888i
$216$		0			0
$217$			2243.39i			0.0476415i
$218$	17760.9	−	30762.8i	0.373725	−	0.647310i
$219$		0			0
$220$	31580.9	+	24824.7i	0.652498	+	0.512907i
$221$	35240.2	−	20345.9i	0.721529	−	0.416575i
$222$		0			0
$223$	24767.9	+	14299.7i	0.498057	+	0.287553i	0.727911	−	0.685672i	$-0.240491\pi$
$223$	24767.9	+	14299.7i	0.498057	+	0.287553i	−0.229854	+	0.973225i	$0.573825\pi$
$224$		−	2564.46i		−	0.0511094i
$225$		0			0
$226$	−20932.1			−0.409823
$227$	−4539.31	+	7862.32i	−0.0880923	+	0.152580i	−0.906705	−	0.421766i	$-0.861410\pi$
$227$	−4539.31	+	7862.32i	−0.0880923	+	0.152580i	0.818612	+	0.574346i	$0.194744\pi$
$228$		0			0
$229$	−11598.2	−	20088.6i	−0.221166	−	0.383071i	0.733996	−	0.679154i	$-0.237653\pi$
$229$	−11598.2	−	20088.6i	−0.221166	−	0.383071i	−0.955162	+	0.296082i	$0.904320\pi$
$230$	−24813.9	+	31567.2i	−0.469072	+	0.596733i
$231$		0			0
$232$	35820.6	+	20681.1i	0.665514	+	0.384235i
$233$	−18159.1			−0.334490			−0.167245	−	0.985915i	$-0.553487\pi$
$233$	−18159.1			−0.334490			−0.167245	+	0.985915i	$0.553487\pi$
$234$		0			0
$235$	−3507.33	−	8755.51i	−0.0635097	−	0.158542i
$236$	26273.0	+	15168.7i	0.471722	+	0.272349i
$237$		0			0
$238$	1106.62	−	638.905i	0.0195363	−	0.0112793i
$239$	28454.7	−	16428.3i	0.498147	−	0.287605i	−0.229801	−	0.973238i	$-0.573807\pi$
$239$	28454.7	−	16428.3i	0.498147	−	0.287605i	0.727948	+	0.685632i	$0.240474\pi$
$240$		0			0
$241$	17841.6	−	30902.5i	0.307185	−	0.532060i	−0.670561	−	0.741855i	$-0.733946\pi$
$241$	17841.6	−	30902.5i	0.307185	−	0.532060i	0.977745	+	0.209795i	$0.0672797\pi$
$242$	7825.76			0.133627
$243$		0			0
$244$	−60935.6			−1.02351
$245$	59270.7	+	8509.04i	0.987434	+	0.141758i
$246$		0			0
$247$	49596.5	−	28634.6i	0.812938	−	0.469350i
$248$	−26337.7	−	45618.2i	−0.428228	−	0.741712i
$249$		0			0
$250$	26001.0	−	18540.1i	0.416016	−	0.296641i
$251$		−	7904.26i		−	0.125462i	−0.998030	−	0.0627312i	$-0.980019\pi$
$251$		−	7904.26i		−	0.125462i	0.998030	−	0.0627312i	$-0.0199811\pi$
$252$		0			0
$253$		−	106800.i		−	1.66852i
$254$	48959.5	+	28266.8i	0.758873	+	0.438136i
$255$		0			0
$256$	23207.3	+	40196.3i	0.354116	+	0.613346i
$257$	−37848.7	−	65555.8i	−0.573039	−	0.992533i	−0.996252	−	0.0865023i	$-0.972431\pi$
$257$	−37848.7	−	65555.8i	−0.573039	−	0.992533i	0.423213	−	0.906030i	$-0.360902\pi$
$258$		0			0
$259$	2419.21	−	4190.19i	0.0360640	−	0.0624646i
$260$	43247.4	−	17324.2i	0.639754	−	0.256276i
$261$		0			0
$262$		−	26413.0i		−	0.384782i
$263$	−9619.50	+	16661.5i	−0.139072	+	0.240881i	−0.927146	−	0.374701i	$-0.877745\pi$
$263$	−9619.50	+	16661.5i	−0.139072	+	0.240881i	0.788073	+	0.615581i	$0.211079\pi$
$264$		0			0
$265$	−10733.6	+	13654.8i	−0.152846	+	0.194444i
$266$	1557.44	−	899.186i	0.0220114	−	0.0127083i
$267$		0			0
$268$	67054.7	+	38714.0i	0.933597	+	0.539012i
$269$		−	44799.5i		−	0.619111i	−0.950881	−	0.309556i	$-0.899820\pi$
$269$		−	44799.5i		−	0.619111i	0.950881	−	0.309556i	$-0.100180\pi$
$270$		0			0
$271$	−18271.5			−0.248792			−0.124396	−	0.992233i	$-0.539699\pi$
$271$	−18271.5			−0.248792			−0.124396	+	0.992233i	$0.539699\pi$
$272$	9416.53	−	16309.9i	0.127278	−	0.220452i
$273$		0			0
$274$	36724.4	+	63608.6i	0.489163	+	0.847256i
$275$	−23896.0	+	81509.8i	−0.315980	+	1.07782i
$276$		0			0
$277$	−100122.	−	57805.4i	−1.30488	−	0.753371i	−0.323641	−	0.946180i	$-0.604907\pi$
$277$	−100122.	−	57805.4i	−1.30488	−	0.753371i	−0.981236	+	0.192809i	$0.938240\pi$
$278$	−36832.6			−0.476588
$279$		0			0
$280$	3195.92	−	1280.24i	0.0407642	−	0.0163295i
$281$	−104701.	−	60449.1i	−1.32598	−	0.765557i	−0.341308	−	0.939952i	$-0.610870\pi$
$281$	−104701.	−	60449.1i	−1.32598	−	0.765557i	−0.984676	+	0.174395i	$0.944203\pi$
$282$		0			0
$283$	−123681.	+	71407.4i	−1.54430	+	0.891600i	−0.545737	+	0.837957i	$0.683750\pi$
$283$	−123681.	+	71407.4i	−1.54430	+	0.891600i	−0.998560	+	0.0536438i	$0.982916\pi$
$284$	−34110.9	+	19693.9i	−0.422918	+	0.244172i
$285$		0			0
$286$	21890.1	−	37914.8i	0.267619	−	0.463529i
$287$	3497.52			0.0424616
$288$		0			0
$289$	−16871.8			−0.202006
$290$	−5281.41	+	36788.3i	−0.0627992	+	0.437435i
$291$		0			0
$292$	17771.4	−	10260.3i	0.208428	−	0.120336i
$293$	24499.4	+	42434.3i	0.285378	+	0.494290i	0.972701	−	0.232063i	$-0.0745475\pi$
$293$	24499.4	+	42434.3i	0.285378	+	0.494290i	−0.687323	+	0.726352i	$0.741214\pi$
$294$		0			0
$295$	−9115.99	+	63498.5i	−0.104751	+	0.729658i
$296$			113607.i			1.29665i
$297$		0			0
$298$			71978.7i			0.810535i
$299$	−107270.	−	61932.3i	−1.19987	−	0.692747i
$300$		0			0
$301$	−757.961	−	1312.83i	−0.00836592	−	0.0144902i
$302$	12075.9	+	20916.0i	0.132405	+	0.229332i
$303$		0			0
$304$	13252.7	−	22954.3i	0.143403	−	0.248381i
$305$	−47914.1	−	119610.i	−0.515066	−	1.28579i
$306$		0			0
$307$			116431.i			1.23536i	0.786430	+	0.617680i	$0.211927\pi$
$307$			116431.i			1.23536i	−0.786430	+	0.617680i	$0.788073\pi$
$308$	−1945.65	+	3369.96i	−0.0205099	+	0.0355242i
$309$		0			0
$310$	29250.1	−	37210.8i	0.304372	−	0.387209i
$311$	33284.3	−	19216.7i	0.344127	−	0.198682i	−0.317968	−	0.948101i	$-0.603001\pi$
$311$	33284.3	−	19216.7i	0.344127	−	0.198682i	0.662096	+	0.749419i	$0.269667\pi$
$312$		0			0
$313$	−67083.4	−	38730.6i	−0.684741	−	0.395335i	0.116898	−	0.993144i	$-0.462705\pi$
$313$	−67083.4	−	38730.6i	−0.684741	−	0.395335i	−0.801639	+	0.597809i	$0.796038\pi$
$314$			10992.2i			0.111487i
$315$		0			0
$316$	−87384.4			−0.875104
$317$	−2741.17	+	4747.85i	−0.0272783	+	0.0472475i	−0.879342	−	0.476190i	$-0.842017\pi$
$317$	−2741.17	+	4747.85i	−0.0272783	+	0.0472475i	0.852064	+	0.523438i	$0.175351\pi$
$318$		0			0
$319$	−49427.6	−	85611.0i	−0.485722	−	0.841295i
$320$	−15403.5	+	19595.7i	−0.150425	+	0.191364i
$321$		0			0
$322$	−3368.50	−	1944.80i	−0.0324881	−	0.0187570i
$323$	93801.2			0.899090
$324$		0			0
$325$	68011.4	+	71267.9i	0.643895	+	0.674725i
$326$	−22290.0	−	12869.1i	−0.209737	−	0.121092i
$327$		0			0
$328$	−71120.4	+	41061.4i	−0.661069	+	0.381668i
$329$	791.267	−	456.838i	0.00731023	−	0.00422056i
$330$		0			0
$331$	−33569.2	+	58143.6i	−0.306397	+	0.530696i	−0.977571	−	0.210604i	$-0.932457\pi$
$331$	−33569.2	+	58143.6i	−0.306397	+	0.530696i	0.671174	+	0.741300i	$0.265790\pi$
$332$	129226.			1.17240
$333$		0			0
$334$	72378.7			0.648811
$335$	−23266.1	+	162062.i	−0.207316	+	1.44408i
$336$		0			0
$337$	−80579.2	+	46522.4i	−0.709517	+	0.409640i	−0.810882	−	0.585209i	$-0.801012\pi$
$337$	−80579.2	+	46522.4i	−0.709517	+	0.409640i	0.101365	+	0.994849i	$0.467679\pi$
$338$	3798.45	+	6579.11i	0.0332486	+	0.0575882i
$339$		0			0
$340$	75532.5	+	10843.6i	0.653395	+	0.0938030i
$341$			125894.i			1.08267i
$342$		0			0
$343$			11615.2i			0.0987273i
$344$	30825.5	+	17797.1i	0.260492	+	0.150395i
$345$		0			0
$346$	−21660.4	−	37517.0i	−0.180932	−	0.313383i
$347$	25688.7	+	44494.1i	0.213345	+	0.369525i	0.952759	−	0.303726i	$-0.0982307\pi$
$347$	25688.7	+	44494.1i	0.213345	+	0.369525i	−0.739414	+	0.673251i	$0.764897\pi$
$348$		0			0
$349$	−5628.71	+	9749.21i	−0.0462123	+	0.0800421i	−0.888206	−	0.459445i	$-0.848048\pi$
$349$	−5628.71	+	9749.21i	−0.0462123	+	0.0800421i	0.841994	+	0.539487i	$0.181382\pi$
$350$	2135.70	+	2237.96i	0.0174343	+	0.0182691i
$351$		0			0
$352$		−	143912.i		−	1.16148i
$353$	−78993.2	+	136820.i	−0.633929	+	1.09800i	0.352812	+	0.935694i	$0.385225\pi$
$353$	−78993.2	+	136820.i	−0.633929	+	1.09800i	−0.986741	+	0.162302i	$0.948108\pi$
$354$		0			0
$355$	−65478.8	−	51470.6i	−0.519570	−	0.408416i
$356$	23808.6	−	13745.9i	0.187860	−	0.108461i
$357$		0			0
$358$	29489.2	+	17025.6i	0.230089	+	0.132842i
$359$			101263.i			0.785710i	0.919600	+	0.392855i	$0.128513\pi$
$359$			101263.i			0.785710i	−0.919600	+	0.392855i	$0.871487\pi$
$360$		0			0
$361$	1693.47			0.0129946
$362$	46118.9	−	79880.2i	0.351934	−	0.609568i
$363$		0			0
$364$	2256.53	+	3908.42i	0.0170309	+	0.0294984i
$365$	34113.7	+	26815.6i	0.256061	+	0.201281i
$366$		0			0
$367$	−170900.	−	98669.4i	−1.26885	−	0.732572i	−0.294082	−	0.955780i	$-0.595014\pi$
$367$	−170900.	−	98669.4i	−1.26885	−	0.732572i	−0.974771	+	0.223208i	$0.928347\pi$
$368$	−57327.2			−0.423316
$369$		0			0
$370$	−94760.3	+	37959.6i	−0.692187	+	0.277280i
$371$	−1457.09	−	841.252i	−0.0105862	−	0.00611193i
$372$		0			0
$373$	207774.	−	119959.i	1.49339	−	0.862212i	0.493423	−	0.869789i	$-0.335745\pi$
$373$	207774.	−	119959.i	1.49339	−	0.862212i	0.999971	+	0.00757777i	$0.00241210\pi$
$374$	62100.7	−	35853.9i	0.443970	−	0.256326i
$375$		0			0
$376$	−10726.7	+	18579.2i	−0.0758735	+	0.131417i
$377$	−114650.			−0.806663
$378$		0			0
$379$	201753.			1.40456			0.702282	−	0.711898i	$-0.252164\pi$
$379$	201753.			1.40456			0.702282	+	0.711898i	$0.252164\pi$
$380$	106303.	+	15261.2i	0.736173	+	0.105687i
$381$		0			0
$382$	−63179.0	+	36476.4i	−0.432958	+	0.249969i
$383$	30536.6	+	52891.0i	0.208173	+	0.360565i	0.951139	−	0.308763i	$-0.0999151\pi$
$383$	30536.6	+	52891.0i	0.208173	+	0.360565i	−0.742966	+	0.669329i	$0.766582\pi$
$384$		0			0
$385$	−8144.76	−	1169.28i	−0.0549487	−	0.00788856i
$386$		−	49701.1i		−	0.333574i
$387$		0			0
$388$			194753.i			1.29366i
$389$	−49647.1	−	28663.8i	−0.328091	−	0.189424i	0.326902	−	0.945058i	$-0.393995\pi$
$389$	−49647.1	−	28663.8i	−0.328091	−	0.189424i	−0.654993	+	0.755635i	$0.727329\pi$
$390$		0			0
$391$	−101439.	−	175697.i	−0.663516	−	1.14924i
$392$	−68098.5	−	117950.i	−0.443165	−	0.767584i
$393$		0			0
$394$	−14223.6	+	24636.0i	−0.0916258	+	0.158701i
$395$	−68710.9	−	171526.i	−0.440384	−	1.09935i
$396$		0			0
$397$		−	258112.i		−	1.63767i	−0.574029	−	0.818835i	$-0.694620\pi$
$397$		−	258112.i		−	1.63767i	0.574029	−	0.818835i	$-0.305380\pi$
$398$	−42063.1	+	72855.4i	−0.265543	+	0.459934i
$399$		0			0
$400$	43752.1	+	12826.7i	0.273451	+	0.0801667i
$401$	159961.	−	92353.5i	0.994776	−	0.574334i	0.0880773	−	0.996114i	$-0.471928\pi$
$401$	159961.	−	92353.5i	0.994776	−	0.574334i	0.906698	+	0.421780i	$0.138594\pi$
$402$		0			0
$403$	126448.	+	73004.6i	0.778576	+	0.449511i
$404$		−	38915.1i		−	0.238427i
$405$		0			0
$406$	−3600.26			−0.0218415
$407$	135760.	−	235144.i	0.819566	−	1.41953i
$408$		0			0
$409$	25843.5	+	44762.2i	0.154491	+	0.267587i	0.932874	−	0.360204i	$-0.117293\pi$
$409$	25843.5	+	44762.2i	0.154491	+	0.267587i	−0.778382	+	0.627790i	$0.783959\pi$
$410$	−58012.9	−	45602.0i	−0.345109	−	0.271279i
$411$		0			0
$412$	−23618.0	−	13635.9i	−0.139139	−	0.0803320i
$413$	−6214.23			−0.0364324
$414$		0			0
$415$	101611.	+	253658.i	0.589993	+	1.47283i
$416$	−144545.	−	83453.1i	−0.835250	−	0.482232i
$417$		0			0
$418$	87399.7	−	50460.2i	0.500216	−	0.288800i
$419$	−293177.	+	169266.i	−1.66994	+	0.964142i	−0.702278	+	0.711903i	$0.747833\pi$
$419$	−293177.	+	169266.i	−1.66994	+	0.964142i	−0.967665	+	0.252239i	$0.918833\pi$
$420$		0			0
$421$	−112147.	+	194245.i	−0.632740	+	1.09594i	0.354249	+	0.935151i	$0.384736\pi$
$421$	−112147.	+	194245.i	−0.632740	+	1.09594i	−0.986989	+	0.160787i	$0.948597\pi$
$422$	99430.9			0.558337
$423$		0			0
$424$	39505.7			0.219749
$425$	38106.8	+	156789.i	0.210972	+	0.868035i
$426$		0			0
$427$	10809.6	−	6240.93i	0.0592862	−	0.0342289i
$428$	21421.1	+	37102.4i	0.116937	+	0.202541i
$429$		0			0
$430$	−4544.93	+	31658.3i	−0.0245805	+	0.171218i
$431$			334739.i			1.80199i	0.433833	+	0.900993i	$0.357161\pi$
$431$			334739.i			1.80199i	−0.433833	+	0.900993i	$0.642839\pi$
$432$		0			0
$433$		−	79690.3i		−	0.425040i	−0.977157	−	0.212520i	$-0.931833\pi$
$433$		−	79690.3i		−	0.425040i	0.977157	−	0.212520i	$-0.0681671\pi$
$434$	3970.72	+	2292.50i	0.0210809	+	0.0121711i
$435$		0			0
$436$	102744.	+	177958.i	0.540485	+	0.936147i
$437$	−142764.	−	247274.i	−0.747575	−	1.29484i
$438$		0			0
$439$	25448.4	−	44077.8i	0.132048	−	0.228713i	−0.792418	−	0.609978i	$-0.791178\pi$
$439$	25448.4	−	44077.8i	0.132048	−	0.228713i	0.924466	+	0.381265i	$0.124511\pi$
$440$	179347.	−	71843.9i	0.926381	−	0.371095i
$441$		0			0
$442$		−	83165.3i		−	0.425694i
$443$	145297.	−	251662.i	0.740372	−	1.28236i	−0.211955	−	0.977280i	$-0.567983\pi$
$443$	145297.	−	251662.i	0.740372	−	1.28236i	0.952326	−	0.305082i	$-0.0986838\pi$
$444$		0			0
$445$	45702.6	+	35925.3i	0.230792	+	0.181418i
$446$	50620.1	−	29225.6i	0.254480	−	0.146924i
$447$		0			0
$448$	−2091.03	−	1207.26i	−0.0104185	−	0.00601511i
$449$		−	361637.i		−	1.79382i	−0.442210	−	0.896912i	$-0.645805\pi$
$449$		−	361637.i		−	1.79382i	0.442210	−	0.896912i	$-0.354195\pi$
$450$		0			0
$451$	196273.			0.964955
$452$	60544.5	−	104866.i	0.296345	−	0.513285i
$453$		0			0
$454$	9277.36	+	16068.9i	0.0450104	+	0.0779602i
$455$	−5897.50	+	7502.54i	−0.0284869	+	0.0362398i
$456$		0			0
$457$	−63960.2	−	36927.5i	−0.306251	−	0.176814i	0.338997	−	0.940788i	$-0.389912\pi$
$457$	−63960.2	−	36927.5i	−0.306251	−	0.176814i	−0.645248	+	0.763973i	$0.723246\pi$
$458$	−47408.3			−0.226008
$459$		0			0
$460$	−86373.7	−	215619.i	−0.408193	−	1.01899i
$461$	−5305.41	−	3063.08i	−0.0249642	−	0.0144131i	0.487466	−	0.873142i	$-0.337921\pi$
$461$	−5305.41	−	3063.08i	−0.0249642	−	0.0144131i	−0.512430	+	0.858729i	$0.671255\pi$
$462$		0			0
$463$	207709.	−	119921.i	0.968933	−	0.559414i	0.0700222	−	0.997545i	$-0.477693\pi$
$463$	207709.	−	119921.i	0.968933	−	0.559414i	0.898911	+	0.438132i	$0.144360\pi$
$464$	−45953.6	+	26531.3i	−0.213444	+	0.123232i
$465$		0			0
$466$	−18556.6	+	32141.0i	−0.0854530	+	0.148009i
$467$	55135.6			0.252812			0.126406	−	0.991979i	$-0.459656\pi$
$467$	55135.6			0.252812			0.126406	+	0.991979i	$0.459656\pi$
$468$		0			0
$469$	−15860.1			−0.0721042
$470$	−19081.1	−	2739.32i	−0.0863787	−	0.0124007i
$471$		0			0
$472$	126364.	−	72956.0i	0.567202	−	0.327474i
$473$	−42535.0	−	73672.8i	−0.190118	−	0.329295i
$474$		0			0
$475$	53631.0	+	220662.i	0.237700	+	0.978005i
$476$			7391.93i			0.0326245i
$477$		0			0
$478$		−	67151.7i		−	0.293901i
$479$	315795.	+	182324.i	1.37637	+	0.794645i	0.991720	−	0.128419i	$-0.0409904\pi$
$479$	315795.	+	182324.i	1.37637	+	0.794645i	0.384646	+	0.923064i	$0.374324\pi$
$480$		0			0
$481$	−157452.	−	272715.i	−0.680548	−	1.17874i
$482$	−36464.3	−	63158.0i	−0.156955	−	0.271853i
$483$		0			0
$484$	−22635.4	+	39205.7i	−0.0966268	+	0.167363i
$485$	−382280.	+	153136.i	−1.62517	+	0.651017i
$486$		0			0
$487$			119653.i			0.504505i	0.967661	+	0.252253i	$0.0811714\pi$
$487$			119653.i			0.504505i	−0.967661	+	0.252253i	$0.918829\pi$
$488$	−146539.	+	253813.i	−0.615337	+	1.06579i
$489$		0			0
$490$	75628.9	−	96211.8i	0.314989	−	0.400716i
$491$	91852.2	−	53030.9i	0.381001	−	0.219971i	−0.297253	−	0.954799i	$-0.596070\pi$
$491$	91852.2	−	53030.9i	0.381001	−	0.219971i	0.678254	+	0.734828i	$0.262737\pi$
$492$		0			0
$493$	−162627.	−	93892.9i	−0.669113	−	0.386312i
$494$		−	117046.i		−	0.479624i
$495$		0			0
$496$	67576.2			0.274682
$497$	4034.04	−	6987.17i	0.0163316	−	0.0282871i
$498$		0			0
$499$	−95907.1	−	166116.i	−0.385167	−	0.667129i	0.606625	−	0.794988i	$-0.292523\pi$
$499$	−95907.1	−	166116.i	−0.385167	−	0.667129i	−0.991792	+	0.127859i	$0.959190\pi$
$500$	17676.8	+	183886.i	0.0707071	+	0.735544i
$501$		0			0
$502$	−13990.3	−	8077.29i	−0.0555161	−	0.0320522i
$503$	155699.			0.615391			0.307696	−	0.951485i	$-0.400442\pi$
$503$	155699.			0.615391			0.307696	+	0.951485i	$0.400442\pi$
$504$		0			0
$505$	76386.3	−	30599.2i	0.299525	−	0.119985i
$506$	−189032.	−	109138.i	−0.738304	−	0.426260i
$507$		0			0
$508$	−283223.	+	163519.i	−1.09749	+	0.633637i
$509$	253416.	−	146310.i	0.978132	−	0.564725i	0.0764267	−	0.997075i	$-0.475649\pi$
$509$	253416.	−	146310.i	0.978132	−	0.564725i	0.901706	+	0.432350i	$0.142316\pi$
$510$		0			0
$511$	−2101.69	+	3640.24i	−0.00804873	+	0.0139408i
$512$	−143619.			−0.547864
$513$		0			0
$514$	−154709.			−0.585583
$515$	8194.78	−	57081.7i	0.0308975	−	0.215220i
$516$		0			0
$517$	44404.1	−	25636.7i	0.166128	−	0.0959138i
$518$	−4944.33	−	8563.83i	−0.0184267	−	0.0319160i
$519$		0			0
$520$	31841.9	−	221798.i	0.117758	−	0.820259i
$521$		−	28599.3i		−	0.105361i	−0.998611	−	0.0526805i	$-0.983224\pi$
$521$		−	28599.3i		−	0.105361i	0.998611	−	0.0526805i	$-0.0167765\pi$
$522$		0			0
$523$			255598.i			0.934444i	0.884140	+	0.467222i	$0.154745\pi$
$523$			255598.i			0.934444i	−0.884140	+	0.467222i	$0.845255\pi$
$524$	132324.	+	76397.5i	0.481923	+	0.278238i
$525$		0			0
$526$	19660.2	+	34052.4i	0.0710584	+	0.123077i
$527$	119574.	+	207109.i	0.430543	+	0.745722i
$528$		0			0
$529$	−168856.	+	292467.i	−0.603400	+	1.04512i
$530$	13200.0	+	32951.8i	0.0469919	+	0.117308i
$531$		0			0
$532$			10403.3i			0.0367577i
$533$	113817.	−	197136.i	0.400638	−	0.693925i
$534$		0			0
$535$	−55984.5	+	71221.1i	−0.195596	+	0.248829i
$536$	322508.	−	186200.i	1.12256	−	0.648112i
$537$		0			0
$538$	−79293.6	−	45780.2i	−0.273952	−	0.158166i
$539$			325510.i			1.12043i
$540$		0			0
$541$	222986.			0.761874			0.380937	−	0.924601i	$-0.375601\pi$
$541$	222986.			0.761874			0.380937	+	0.924601i	$0.375601\pi$
$542$	−18671.5	+	32339.9i	−0.0635595	+	0.110088i
$543$		0			0
$544$	−136688.	−	236750.i	−0.461883	−	0.800005i
$545$	−268524.	+	341605.i	−0.904046	+	1.15009i
$546$		0			0
$547$	92696.0	+	53518.0i	0.309803	+	0.178865i	0.646838	−	0.762627i	$-0.276091\pi$
$547$	92696.0	+	53518.0i	0.309803	+	0.178865i	−0.337035	+	0.941492i	$0.609424\pi$
$548$	−424890.			−1.41487
$549$		0			0
$550$	119851.	+	125589.i	0.396200	+	0.415171i
$551$	−228879.	−	132143.i	−0.753882	−	0.435254i
$552$		0			0
$553$	15501.5	−	8949.77i	0.0506900	−	0.0292659i
$554$	−204627.	+	118142.i	−0.666721	+	0.384931i
$555$		0			0
$556$	106536.	−	184525.i	0.344624	−	0.596906i
$557$	165757.			0.534272			0.267136	−	0.963659i	$-0.413923\pi$
$557$	165757.			0.534272			0.267136	+	0.963659i	$0.413923\pi$
$558$		0			0
$559$	−98662.6			−0.315740
$560$	−627.637	+	4371.88i	−0.00200139	+	0.0139409i
$561$		0			0
$562$	−213986.	+	123545.i	−0.677505	+	0.391158i
$563$	198623.	+	344026.i	0.626634	+	1.08536i	0.988223	+	0.153024i	$0.0489011\pi$
$563$	198623.	+	344026.i	0.626634	+	1.08536i	−0.361589	+	0.932338i	$0.617766\pi$
$564$		0			0
$565$	253448.	+	36385.6i	0.793947	+	0.113981i
$566$			291882.i			0.911118i
$567$		0			0
$568$			189441.i			0.587188i
$569$	39485.1	+	22796.7i	0.121957	+	0.0704122i	0.559738	−	0.828670i	$-0.310902\pi$
$569$	39485.1	+	22796.7i	0.121957	+	0.0704122i	−0.437780	+	0.899082i	$0.644235\pi$
$570$		0			0
$571$	137353.	+	237902.i	0.421275	+	0.729669i	0.996064	−	0.0886320i	$-0.0282495\pi$
$571$	137353.	+	237902.i	0.421275	+	0.729669i	−0.574790	+	0.818301i	$0.694916\pi$
$572$	126631.	+	219331.i	0.387033	+	0.670361i
$573$		0			0
$574$	3574.08	−	6190.49i	0.0108478	−	0.0187889i
$575$	355321.	−	339085.i	1.07469	−	1.02559i
$576$		0			0
$577$			85338.7i			0.256327i	0.991753	+	0.128164i	$0.0409082\pi$
$577$			85338.7i			0.256327i	−0.991753	+	0.128164i	$0.959092\pi$
$578$	−17241.1	+	29862.5i	−0.0516071	+	0.0893861i
$579$		0			0
$580$	−169027.	−	132866.i	−0.502457	−	0.394965i
$581$	−22924.0	+	13235.2i	−0.0679106	+	0.0392082i
$582$		0			0
$583$	−81768.6	−	47209.1i	−0.240574	−	0.138896i
$584$		−	98696.7i		−	0.289385i
$585$		0			0
$586$	100143.			0.291625
$587$	−183601.	+	318006.i	−0.532843	+	0.922910i	0.466422	+	0.884562i	$0.345543\pi$
$587$	−183601.	+	318006.i	−0.532843	+	0.922910i	−0.999264	+	0.0383480i	$0.987790\pi$
$588$		0			0
$589$	168287.	+	291482.i	0.485088	+	0.840197i
$590$	103075.	+	81023.5i	0.296106	+	0.232759i
$591$		0			0
$592$	−126218.	−	72872.3i	−0.360147	−	0.207931i
$593$	203932.			0.579930			0.289965	−	0.957037i	$-0.406356\pi$
$593$	203932.			0.579930			0.289965	+	0.957037i	$0.406356\pi$
$594$		0			0
$595$	−14509.6	+	5812.33i	−0.0409847	+	0.0164178i
$596$	−360601.	−	208193.i	−1.01516	−	0.586102i
$597$		0			0
$598$	−219236.	+	126576.i	−0.613070	+	0.353956i
$599$	−150018.	+	86613.1i	−0.418110	+	0.241396i	−0.694268	−	0.719716i	$-0.744272\pi$
$599$	−150018.	+	86613.1i	−0.418110	+	0.241396i	0.276158	+	0.961112i	$0.410939\pi$
$600$		0			0
$601$	194986.	−	337727.i	0.539828	−	0.935010i	−0.459085	−	0.888393i	$-0.651823\pi$
$601$	194986.	−	337727.i	0.539828	−	0.935010i	0.998913	−	0.0466173i	$-0.0148441\pi$
$602$	−3098.21			−0.00854906
$603$		0			0
$604$	−139714.			−0.382971
$605$	−94755.0	−	13603.3i	−0.258876	−	0.0371648i
$606$		0			0
$607$	−162922.	+	94063.2i	−0.442184	+	0.255295i	−0.704524	−	0.709681i	$-0.748839\pi$
$607$	−162922.	+	94063.2i	−0.442184	+	0.255295i	0.262340	+	0.964976i	$0.415506\pi$
$608$	−192373.	−	333199.i	−0.520398	−	0.901356i
$609$		0			0
$610$	−260669.	−	37422.2i	−0.700535	−	0.100570i
$611$		−	59465.9i		−	0.159289i
$612$		0			0
$613$		−	105068.i		−	0.279608i	−0.990179	−	0.139804i	$-0.955353\pi$
$613$		−	105068.i		−	0.279608i	0.990179	−	0.139804i	$-0.0446472\pi$
$614$	206080.	+	118980.i	0.546636	+	0.315601i
$615$		0			0
$616$	9357.85	+	16208.3i	0.0246612	+	0.0427145i
$617$	40749.7	+	70580.5i	0.107042	+	0.185402i	0.914571	−	0.404426i	$-0.132529\pi$
$617$	40749.7	+	70580.5i	0.107042	+	0.185402i	−0.807529	+	0.589828i	$0.799195\pi$
$618$		0			0
$619$	−61533.5	+	106579.i	−0.160594	+	0.278158i	−0.935082	−	0.354431i	$-0.884674\pi$
$619$	−61533.5	+	106579.i	−0.160594	+	0.278158i	0.774488	+	0.632589i	$0.218008\pi$
$620$	101816.	+	254167.i	0.264869	+	0.661205i
$621$		0			0
$622$		−	78549.5i		−	0.203031i
$623$	−2815.67	+	4876.88i	−0.00725446	+	0.0125651i
$624$		0			0
$625$	−347050.	+	179289.i	−0.888447	+	0.458979i
$626$	−137104.	+	79156.9i	−0.349865	+	0.201995i
$627$		0			0
$628$	−55068.9	−	31794.0i	−0.139633	−	0.0806170i
$629$		−	515782.i		−	1.30366i
$630$		0			0
$631$	−760006.			−1.90879			−0.954396	−	0.298545i	$-0.903499\pi$
$631$	−760006.			−1.90879			−0.954396	+	0.298545i	$0.903499\pi$
$632$	−210143.	+	363979.i	−0.526116	+	0.911259i
$633$		0			0
$634$	5602.36	+	9703.57i	0.0139377	+	0.0241409i
$635$	−543670.	−	427361.i	−1.34831	−	1.05986i
$636$		0			0
$637$	326942.	+	188760.i	0.805734	+	0.465191i
$638$	−202038.			−0.496355
$639$		0			0
$640$	−138564.	−	345905.i	−0.338292	−	0.844494i
$641$	209786.	+	121120.i	0.510577	+	0.294782i	0.733071	−	0.680152i	$-0.238086\pi$
$641$	209786.	+	121120.i	0.510577	+	0.294782i	−0.222494	+	0.974934i	$0.571420\pi$
$642$		0			0
$643$	335283.	−	193576.i	0.810941	−	0.468197i	−0.0363415	−	0.999339i	$-0.511570\pi$
$643$	335283.	−	193576.i	0.810941	−	0.468197i	0.847283	+	0.531142i	$0.178237\pi$
$644$	19486.2	−	11250.4i	0.0469847	−	0.0271266i
$645$		0			0
$646$	95854.5	−	166025.i	0.229693	−	0.397840i
$647$	−174684.			−0.417297			−0.208649	−	0.977991i	$-0.566907\pi$
$647$	−174684.			−0.417297			−0.208649	+	0.977991i	$0.566907\pi$
$648$		0			0
$649$	−348729.			−0.827939
$650$	195642.	−	47549.9i	0.463058	−	0.112544i
$651$		0			0
$652$	128944.	−	74446.0i	0.303324	−	0.175124i
$653$	−149972.	−	259759.i	−0.351709	−	0.609178i	0.634840	−	0.772644i	$-0.281066\pi$
$653$	−149972.	−	259759.i	−0.351709	−	0.609178i	−0.986549	+	0.163466i	$0.947733\pi$
$654$		0			0
$655$	−45912.8	+	319811.i	−0.107017	+	0.745436i
$656$		−	105354.i		−	0.244817i
$657$		0			0
$658$		−	1867.35i		−	0.00431295i
$659$	−206766.	−	119376.i	−0.476111	−	0.274883i	0.242683	−	0.970106i	$-0.421972\pi$
$659$	−206766.	−	119376.i	−0.476111	−	0.274883i	−0.718794	+	0.695223i	$0.755306\pi$
$660$		0			0
$661$	174605.	+	302425.i	0.399627	+	0.692174i	0.993680	−	0.112252i	$-0.0358063\pi$
$661$	174605.	+	302425.i	0.399627	+	0.692174i	−0.594053	+	0.804426i	$0.702473\pi$
$662$	68608.1	+	118833.i	0.156552	+	0.271157i
$663$		0			0
$664$	310765.	−	538261.i	0.704849	−	1.22083i
$665$	−20420.6	+	8180.19i	−0.0461769	+	0.0184978i
$666$		0			0
$667$			571613.i			1.28484i
$668$	−209350.	+	362605.i	−0.469159	+	0.812607i
$669$		0			0
$670$	263070.	+	206790.i	0.586032	+	0.460660i
$671$	606610.	−	350226.i	1.34730	−	0.777864i
$672$		0			0
$673$	−154058.	−	88945.3i	−0.340137	−	0.196378i	0.320196	−	0.947351i	$-0.396251\pi$
$673$	−154058.	−	88945.3i	−0.340137	−	0.196378i	−0.660332	+	0.750973i	$0.729585\pi$
$674$			190163.i			0.418607i
$675$		0			0
$676$	−43946.9			−0.0961690
$677$	23441.0	−	40601.0i	0.0511444	−	0.0885848i	−0.839320	−	0.543638i	$-0.817046\pi$
$677$	23441.0	−	40601.0i	0.0511444	−	0.0885848i	0.890464	+	0.455053i	$0.150380\pi$
$678$		0			0
$679$	−19946.3	−	34548.0i	−0.0432636	−	0.0749347i
$680$	226808.	−	288536.i	0.490502	−	0.623996i
$681$		0			0
$682$	222828.	+	128650.i	0.479072	+	0.276592i
$683$	880813.			1.88817			0.944087	−	0.329696i	$-0.106946\pi$
$683$	880813.			1.88817			0.944087	+	0.329696i	$0.106946\pi$
$684$		0			0
$685$	−334094.	−	834015.i	−0.712013	−	1.77743i
$686$	20558.5	+	11869.4i	0.0436860	+	0.0252221i
$687$		0			0
$688$	−39545.5	+	22831.6i	−0.0835449	+	0.0482346i
$689$	−94833.7	+	54752.2i	−0.199767	+	0.115336i
$690$		0			0
$691$	43555.7	−	75440.8i	0.0912198	−	0.157997i	−0.816805	−	0.576914i	$-0.804257\pi$
$691$	43555.7	−	75440.8i	0.0912198	−	0.157997i	0.908025	+	0.418917i	$0.137590\pi$
$692$	250605.			0.523331
$693$		0			0
$694$	105004.			0.218016
$695$	445973.	+	64024.9i	0.923292	+	0.132550i
$696$		0			0
$697$	322890.	−	186420.i	0.664643	−	0.383732i
$698$	11503.9	+	19925.3i	0.0236120	+	0.0408971i
$699$		0			0
$700$	−17389.1	+	4226.35i	−0.0354880	+	0.00862520i
$701$			595389.i			1.21162i	0.795611	+	0.605808i	$0.207150\pi$
$701$			595389.i			1.21162i	−0.795611	+	0.605808i	$0.792850\pi$
$702$		0			0
$703$		−	725905.i		−	1.46882i
$704$	−117344.	−	67748.5i	−0.236764	−	0.136696i
$705$		0			0
$706$	161445.	+	279631.i	0.323903	+	0.561016i
$707$	3985.62	+	6903.30i	0.00797365	+	0.0138108i
$708$		0			0
$709$	323680.	−	560629.i	0.643906	−	1.11528i	−0.340647	−	0.940191i	$-0.610646\pi$
$709$	323680.	−	560629.i	0.643906	−	1.11528i	0.984553	−	0.175087i	$-0.0560207\pi$
$710$	−158013.	+	63297.8i	−0.313456	+	0.125566i
$711$		0			0
$712$		−	132225.i		−	0.260828i
$713$	363980.	−	630432.i	0.715976	−	1.24011i
$714$		0			0
$715$	−330954.	+	421025.i	−0.647374	+	0.823562i
$716$	−170590.	+	98490.4i	−0.332758	+	0.192118i
$717$		0			0
$718$	179232.	+	103480.i	0.347670	+	0.200727i
$719$			234792.i			0.454178i	0.973874	+	0.227089i	$0.0729209\pi$
$719$			234792.i			0.454178i	−0.973874	+	0.227089i	$0.927079\pi$
$720$		0			0
$721$	5586.26			0.0107461
$722$	1730.54	−	2997.39i	0.00331977	−	0.00575001i
$723$		0			0
$724$	266791.	+	462095.i	0.508971	+	0.881564i
$725$	127896.	−	436255.i	0.243321	−	0.829974i
$726$		0			0
$727$	772639.	+	446083.i	1.46187	+	0.844009i	0.999098	−	0.0424699i	$-0.0135227\pi$
$727$	772639.	+	446083.i	1.46187	+	0.844009i	0.462769	+	0.886479i	$0.346856\pi$
$728$	21706.1			0.0409562
$729$		0			0
$730$	82323.2	−	32977.5i	0.154482	−	0.0618830i
$731$	−139949.	−	80799.8i	−0.261900	−	0.151208i
$732$		0			0
$733$	354772.	−	204828.i	0.660300	−	0.381224i	−0.132092	−	0.991238i	$-0.542169\pi$
$733$	354772.	−	204828.i	0.660300	−	0.381224i	0.792391	+	0.610013i	$0.208836\pi$
$734$	−349283.	+	201659.i	−0.648314	+	0.374304i
$735$		0			0
$736$	−416073.	+	720659.i	−0.768093	+	1.33038i
$737$	−890033.			−1.63859
$738$		0			0
$739$	635453.			1.16357			0.581787	−	0.813341i	$-0.302354\pi$
$739$	635453.			1.16357			0.581787	+	0.813341i	$0.302354\pi$
$740$	83916.2	−	584528.i	0.153244	−	1.06744i
$741$		0			0
$742$	−2977.98	+	1719.34i	−0.00540896	+	0.00312286i
$743$	−22811.7	−	39511.0i	−0.0413219	−	0.0715716i	0.844625	−	0.535359i	$-0.179824\pi$
$743$	−22811.7	−	39511.0i	−0.0413219	−	0.0715716i	−0.885947	+	0.463787i	$0.846490\pi$
$744$		0			0
$745$	125118.	−	871525.i	0.225428	−	1.57024i
$746$		−	490338.i		−	0.881086i
$747$		0			0
$748$			414818.i			0.741404i
$749$	−7599.93	−	4387.82i	−0.0135471	−	0.00782142i
$750$		0			0
$751$	−134221.	−	232478.i	−0.237981	−	0.412195i	0.722154	−	0.691732i	$-0.243152\pi$
$751$	−134221.	−	232478.i	−0.237981	−	0.412195i	−0.960135	+	0.279538i	$0.909819\pi$
$752$	−13761.0	−	23834.8i	−0.0243341	−	0.0421479i
$753$		0			0
$754$	−117160.	+	202927.i	−0.206080	+	0.356942i
$755$	−109858.	−	274244.i	−0.192725	−	0.481108i
$756$		0			0
$757$			453292.i			0.791018i	0.918462	+	0.395509i	$0.129432\pi$
$757$			453292.i			0.791018i	−0.918462	+	0.395509i	$0.870568\pi$
$758$	206170.	−	357096.i	0.358828	−	0.621508i
$759$		0			0
$760$	319207.	−	406081.i	0.552643	−	0.703049i
$761$	−20609.8	+	11899.1i	−0.0355881	+	0.0205468i	−0.517689	−	0.855569i	$-0.673207\pi$
$761$	−20609.8	+	11899.1i	−0.0355881	+	0.0205468i	0.482100	+	0.876116i	$0.339874\pi$
$762$		0			0
$763$	−36452.3	−	21045.8i	−0.0626147	−	0.0361506i
$764$		−	422021.i		−	0.723015i
$765$		0			0
$766$	124820.			0.212730
$767$	−202224.	+	350263.i	−0.343750	+	0.595392i
$768$		0			0
$769$	424556.	+	735352.i	0.717930	+	1.24349i	0.961818	+	0.273688i	$0.0882437\pi$
$769$	424556.	+	735352.i	0.717930	+	1.24349i	−0.243888	+	0.969803i	$0.578423\pi$
$770$	−10392.6	+	13221.1i	−0.0175285	+	0.0222990i
$771$		0			0
$772$	248994.	+	143757.i	0.417786	+	0.241209i
$773$	−367992.			−0.615857			−0.307928	−	0.951410i	$-0.599636\pi$
$773$	−367992.			−0.615857			−0.307928	+	0.951410i	$0.599636\pi$
$774$		0			0
$775$	−418846.	+	399707.i	−0.697350	+	0.665485i
$776$	811197.	+	468345.i	1.34711	+	0.777754i
$777$		0			0
$778$	−101468.	+	58582.5i	−0.167637	+	0.0967851i
$779$	454430.	−	262366.i	0.748846	−	0.432346i
$780$		0			0
$781$	226381.	−	392104.i	0.371140	−	0.642834i
$782$	−414638.			−0.678040
$783$		0			0
$784$	174724.			0.284264
$785$	19107.3	−	133094.i	0.0310071	−	0.215983i
$786$		0			0
$787$	−9633.41	+	5561.85i	−0.0155536	+	0.00897987i	−0.507757	−	0.861501i	$-0.669525\pi$
$787$	−9633.41	+	5561.85i	−0.0155536	+	0.00897987i	0.492203	+	0.870480i	$0.336192\pi$
$788$	−82281.5	−	142516.i	−0.132510	−	0.229515i
$789$		0			0
$790$	−373811.	−	53665.2i	−0.598960	−	0.0859881i
$791$			24803.5i			0.0396424i
$792$		0			0
$793$		−	812372.i		−	1.29184i
$794$	−456849.	−	263762.i	−0.724655	−	0.418380i
$795$		0			0
$796$	−243328.	−	421457.i	−0.384031	−	0.665162i
$797$	−131296.	−	227411.i	−0.206697	−	0.358009i	0.743975	−	0.668207i	$-0.232938\pi$
$797$	−131296.	−	227411.i	−0.206697	−	0.358009i	−0.950672	+	0.310198i	$0.899605\pi$
$798$		0			0
$799$	48699.6	−	84350.2i	0.0762837	−	0.132127i
$800$	478791.	−	456913.i	0.748111	−	0.713927i
$801$		0			0
$802$		−	377501.i		−	0.586906i
$803$	−117942.	+	204282.i	−0.182910	+	0.316810i
$804$		0			0
$805$	37405.5	+	29403.2i	0.0577223	+	0.0453736i
$806$	258431.	−	149205.i	0.397810	−	0.229675i
$807$		0			0
$808$	−162092.	−	93583.6i	−0.248278	−	0.143343i
$809$			1.09146e6i			1.66767i	0.552012	+	0.833836i	$0.313860\pi$
$809$			1.09146e6i			1.66767i	−0.552012	+	0.833836i	$0.686140\pi$
$810$		0			0
$811$	−380079.			−0.577873			−0.288936	−	0.957348i	$-0.593302\pi$
$811$	−380079.			−0.577873			−0.288936	+	0.957348i	$0.593302\pi$
$812$	10413.5	−	18036.7i	0.0157937	−	0.0273555i
$813$		0			0
$814$	−277464.	−	480583.i	−0.418754	−	0.725303i
$815$	247519.	+	194567.i	0.372644	+	0.292923i
$816$		0			0
$817$	−196963.	−	113716.i	−0.295080	−	0.170365i
$818$	105637.			0.157873
$819$		0			0
$820$	396256.	−	158734.i	0.589316	−	0.236071i
$821$	−468285.	−	270364.i	−0.694743	−	0.401110i	0.110644	−	0.993860i	$-0.464709\pi$
$821$	−468285.	−	270364.i	−0.694743	−	0.401110i	−0.805386	+	0.592750i	$0.798042\pi$
$822$		0			0
$823$	41821.1	−	24145.4i	0.0617441	−	0.0356480i	−0.468810	−	0.883299i	$-0.655317\pi$
$823$	41821.1	−	24145.4i	0.0617441	−	0.0356480i	0.530554	+	0.847651i	$0.321984\pi$
$824$	−113594.	+	65583.5i	−0.167302	+	0.0965917i
$825$		0			0
$826$	−6350.27	+	10999.0i	−0.00930748	+	0.0161210i
$827$	433990.			0.634554			0.317277	−	0.948333i	$-0.397232\pi$
$827$	433990.			0.634554			0.317277	+	0.948333i	$0.397232\pi$
$828$		0			0
$829$	−126257.			−0.183716			−0.0918578	−	0.995772i	$-0.529281\pi$
$829$	−126257.			−0.183716			−0.0918578	+	0.995772i	$0.529281\pi$
$830$	552801.	+	79361.5i	0.802441	+	0.115200i
$831$		0			0
$832$	−136093.	+	78573.4i	−0.196603	+	0.113509i
$833$	309170.	+	535498.i	0.445561	+	0.771735i
$834$		0			0
$835$	−876368.	−	125813.i	−1.25694	−	0.180449i
$836$			583809.i			0.835331i
$837$		0			0
$838$			691884.i			0.985247i
$839$	−130170.	−	75153.9i	−0.184922	−	0.106765i	0.404681	−	0.914458i	$-0.367382\pi$
$839$	−130170.	−	75153.9i	−0.184922	−	0.106765i	−0.589603	+	0.807693i	$0.700716\pi$
$840$		0			0
$841$	−89095.3	−	154318.i	−0.125969	−	0.218184i
$842$	229205.	+	396994.i	0.323295	+	0.559964i
$843$		0			0
$844$	−287596.	+	498131.i	−0.403737	+	0.699292i
$845$	−34555.7	−	86263.2i	−0.0483957	−	0.120813i
$846$		0			0
$847$		−	9273.13i		−	0.0129259i
$848$	−25340.5	+	43891.1i	−0.0352390	+	0.0610358i
$849$		0			0
$850$	316452.	+	92773.2i	0.437996	+	0.128406i
$851$	−1.35968e6	+	785011.i	−1.87749	+	1.08397i
$852$		0			0
$853$	247353.	+	142809.i	0.339953	+	0.196272i	0.660251	−	0.751045i	$-0.270450\pi$
$853$	247353.	+	142809.i	0.339953	+	0.196272i	−0.320298	+	0.947317i	$0.603783\pi$
$854$		−	25510.2i		−	0.0349782i
$855$		0			0
$856$	206055.			0.281213
$857$	−604631.	+	1.04725e6i	−0.823244	+	1.42590i	0.0800099	+	0.996794i	$0.474505\pi$
$857$	−604631.	+	1.04725e6i	−0.823244	+	1.42590i	−0.903254	+	0.429106i	$0.858829\pi$
$858$		0			0
$859$	−322885.	−	559253.i	−0.437584	−	0.757918i	0.559919	−	0.828548i	$-0.310832\pi$
$859$	−322885.	−	559253.i	−0.437584	−	0.757918i	−0.997503	+	0.0706299i	$0.977499\pi$
$860$	−145456.	−	114338.i	−0.196669	−	0.154595i
$861$		0			0
$862$	592477.	+	342067.i	0.797364	+	0.460358i
$863$	−753393.			−1.01158			−0.505790	−	0.862657i	$-0.668799\pi$
$863$	−753393.			−1.01158			−0.505790	+	0.862657i	$0.668799\pi$
$864$		0			0
$865$	197052.	+	491910.i	0.263359	+	0.657437i
$866$	−141049.	−	81434.8i	−0.188077	−	0.108586i
$867$		0			0
$868$	−22970.0	+	13261.7i	−0.0304875	+	0.0176020i
$869$	869906.	−	502241.i	1.15195	−	0.665077i
$870$		0			0
$871$	−516122.	+	893949.i	−0.680324	+	1.17836i
$872$	988321.			1.29977
$873$		0			0
$874$	−583556.			−0.763940
$875$	−21969.1	−	30809.8i	−0.0286943	−	0.0402414i
$876$		0			0
$877$	−765073.	+	441715.i	−0.994726	+	0.574306i	−0.906684	−	0.421811i	$-0.861395\pi$
$877$	−765073.	+	441715.i	−0.994726	+	0.574306i	−0.0880427	+	0.996117i	$0.528061\pi$
$878$	−52010.9	−	90085.5i	−0.0674691	−	0.116860i
$879$		0			0
$880$	−35221.5	+	245340.i	−0.0454824	+	0.316813i
$881$		−	404743.i		−	0.521468i	−0.965411	−	0.260734i	$-0.916035\pi$
$881$		−	404743.i		−	0.521468i	0.965411	−	0.260734i	$-0.0839646\pi$
$882$		0			0
$883$		−	27686.5i		−	0.0355096i	−0.999842	−	0.0177548i	$-0.994348\pi$
$883$		−	27686.5i		−	0.0355096i	0.999842	−	0.0177548i	$-0.00565183\pi$
$884$	416643.	+	240549.i	0.533163	+	0.307822i
$885$		0			0
$886$	−296956.	−	514342.i	−0.378289	−	0.655216i
$887$	636301.	+	1.10210e6i	0.808752	+	1.40080i	0.913729	+	0.406324i	$0.133190\pi$
$887$	636301.	+	1.10210e6i	0.808752	+	1.40080i	−0.104978	+	0.994475i	$0.533477\pi$
$888$		0			0
$889$	33494.7	−	58014.5i	0.0423811	−	0.0734062i
$890$	110290.	−	44180.4i	0.139237	−	0.0557763i
$891$		0			0
$892$			338131.i			0.424967i
$893$	68539.1	−	118713.i	0.0859480	−	0.148866i
$894$		0			0
$895$	−327463.	−	257407.i	−0.408804	−	0.321347i
$896$	31260.6	−	18048.3i	0.0389387	−	0.0224813i
$897$		0			0
$898$	−640085.	−	369553.i	−0.793752	−	0.458273i
$899$		−	673807.i		−	0.833712i
$900$		0			0
$901$	−179357.			−0.220938
$902$	200569.	−	347396.i	0.246520	−	0.426985i
$903$		0			0
$904$	−291197.	−	504367.i	−0.356328	−	0.617177i
$905$	−697265.	+	887030.i	−0.851335	+	1.08303i
$906$		0			0
$907$	−479947.	−	277097.i	−0.583416	−	0.336836i	0.179074	−	0.983836i	$-0.442690\pi$
$907$	−479947.	−	277097.i	−0.583416	−	0.336836i	−0.762490	+	0.647000i	$0.776023\pi$
$908$	−107336.			−0.130189
$909$		0			0
$910$	7252.65	+	18105.1i	0.00875818	+	0.0218635i
$911$	771670.	+	445524.i	0.929811	+	0.536827i	0.886752	−	0.462246i	$-0.152956\pi$
$911$	771670.	+	445524.i	0.929811	+	0.536827i	0.0430595	+	0.999073i	$0.486289\pi$
$912$		0			0
$913$	−1.28644e6	+	742726.i	−1.54329	+	0.891019i
$914$	−130721.	+	75471.6i	−0.156478	+	0.0903424i
$915$		0			0
$916$	137125.	−	237507.i	0.163427	−	0.283065i
$917$	−31298.1			−0.0372202
$918$		0			0
$919$	242131.			0.286695			0.143347	−	0.989672i	$-0.454213\pi$
$919$	242131.			0.286695			0.143347	+	0.989672i	$0.454213\pi$
$920$	−1.10582e6	−	158754.i	−1.30650	−	0.187564i
$921$		0			0
$922$	−10843.1	+	6260.27i	−0.0127553	+	0.00736430i
$923$	−262553.	−	454754.i	−0.308186	−	0.533794i
$924$		0			0
$925$	1.21335e6	−	294899.i	1.41809	−	0.344660i
$926$		−	490184.i		−	0.571660i
$927$		0			0
$928$			770242.i			0.894399i
$929$	−953051.	−	550244.i	−1.10429	−	0.637565i	−0.166949	−	0.985966i	$-0.553391\pi$
$929$	−953051.	−	550244.i	−1.10429	−	0.637565i	−0.937346	+	0.348401i	$0.886725\pi$
$930$		0			0
$931$	435122.	+	753653.i	0.502009	+	0.869505i
$932$	−107347.	−	185931.i	−0.123583	−	0.214052i
$933$		0			0
$934$	56342.5	−	97588.1i	0.0645866	−	0.111867i
$935$	−814245.	+	326174.i	−0.931391	+	0.373101i
$936$		0			0
$937$			580897.i			0.661637i	0.943694	+	0.330819i	$0.107325\pi$
$937$			580897.i			0.661637i	−0.943694	+	0.330819i	$0.892675\pi$
$938$	−16207.3	+	28071.9i	−0.0184207	+	0.0319055i
$939$		0			0
$940$	68914.0	−	87669.4i	0.0779923	−	0.0992185i
$941$	−721653.	+	416647.i	−0.814985	+	0.470532i	−0.848684	−	0.528900i	$-0.822604\pi$
$941$	−721653.	+	416647.i	−0.814985	+	0.470532i	0.0336993	+	0.999432i	$0.489271\pi$
$942$		0			0
$943$	−982865.	−	567457.i	−1.10528	−	0.638131i
$944$			187188.i			0.210055i
$945$		0			0
$946$	−173865.			−0.194280
$947$	−78904.6	+	136667.i	−0.0879837	+	0.152392i	−0.906659	−	0.421865i	$-0.861376\pi$
$947$	−78904.6	+	136667.i	−0.0879837	+	0.152392i	0.818675	+	0.574257i	$0.194709\pi$
$948$		0			0
$949$	136787.	+	236922.i	0.151884	+	0.263071i
$950$	445370.	+	130568.i	0.493485	+	0.144673i
$951$		0			0
$952$	30789.3	+	17776.2i	0.0339724	+	0.0196140i
$953$	904204.			0.995590			0.497795	−	0.867295i	$-0.334143\pi$
$953$	904204.			0.995590			0.497795	+	0.867295i	$0.334143\pi$
$954$		0			0
$955$	828383.	−	331838.i	0.908290	−	0.363847i
$956$	336418.	+	194231.i	0.368098	+	0.212522i
$957$		0			0
$958$	645415.	−	372631.i	0.703247	−	0.406020i
$959$	75373.0	−	43516.6i	0.0819556	−	0.0473171i
$960$		0			0
$961$	32708.0	−	56651.8i	0.0354166	−	0.0613433i
$962$	−643596.			−0.695446
$963$		0			0
$964$	421881.			0.453979
$965$	−86393.8	+	601786.i	−0.0927743	+	0.646230i
$966$		0			0
$967$	605117.	−	349365.i	0.647122	−	0.373616i	−0.140230	−	0.990119i	$-0.544784\pi$
$967$	605117.	−	349365.i	0.647122	−	0.373616i	0.787353	+	0.616503i	$0.211451\pi$
$968$	108868.	+	188565.i	0.116185	+	0.201238i
$969$		0			0
$970$	−119603.	+	833110.i	−0.127116	+	0.885439i
$971$		−	1.63052e6i		−	1.72937i	−0.502311	−	0.864687i	$-0.667517\pi$
$971$		−	1.63052e6i		−	1.72937i	0.502311	−	0.864687i	$-0.332483\pi$
$972$		0			0
$973$			43644.8i			0.0461006i
$974$	211782.	+	122272.i	0.223239	+	0.128887i
$975$		0			0
$976$	−187992.	−	325611.i	−0.197351	−	0.341821i
$977$	−260634.	−	451431.i	−0.273050	−	0.472936i	0.696592	−	0.717468i	$-0.254699\pi$
$977$	−260634.	−	451431.i	−0.273050	−	0.472936i	−0.969641	+	0.244532i	$0.921366\pi$
$978$		0			0
$979$	−158009.	+	273679.i	−0.164860	+	0.285546i
$980$	263254.	+	657173.i	0.274108	+	0.684270i
$981$		0			0
$982$		−	216767.i		−	0.224786i
$983$	−275182.	+	476630.i	−0.284783	+	0.493258i	−0.972556	−	0.232667i	$-0.925255\pi$
$983$	−275182.	+	476630.i	−0.284783	+	0.493258i	0.687774	+	0.725925i	$0.258588\pi$
$984$		0			0
$985$	215045.	−	273571.i	0.221644	−	0.281967i
$986$	−332374.	+	191896.i	−0.341880	+	0.197385i
$987$		0			0
$988$	586378.	+	338545.i	0.600708	+	0.346819i
$989$			491903.i			0.502906i
$990$		0			0
$991$	1.51931e6			1.54703			0.773516	−	0.633777i	$-0.218496\pi$
$991$	1.51931e6			1.54703			0.773516	+	0.633777i	$0.218496\pi$
$992$	490459.	−	849499.i	0.498401	−	0.863256i
$993$		0			0
$994$	−8244.70	−	14280.2i	−0.00834454	−	0.0144532i
$995$	635946.	−	809023.i	0.642353	−	0.817174i
$996$		0			0
$997$	−1.62802e6	−	939936.i	−1.63783	−	0.945601i	−0.981579	−	0.191057i	$-0.938808\pi$
$997$	−1.62802e6	−	939936.i	−1.63783	−	0.945601i	−0.656250	−	0.754544i	$-0.727858\pi$
$998$	−392026.			−0.393599
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.5.h.a.89.14		44
3.2	odd	2		45.5.h.a.29.9	yes	44
5.4	even	2	inner	135.5.h.a.89.9		44
9.2	odd	6		405.5.d.a.404.28		44
9.4	even	3		45.5.h.a.14.14	yes	44
9.5	odd	6	inner	135.5.h.a.44.9		44
9.7	even	3		405.5.d.a.404.18		44
15.14	odd	2		45.5.h.a.29.14	yes	44
45.4	even	6		45.5.h.a.14.9	✓	44
45.14	odd	6	inner	135.5.h.a.44.14		44
45.29	odd	6		405.5.d.a.404.17		44
45.34	even	6		405.5.d.a.404.27		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.h.a.14.9	✓	44	45.4	even	6
45.5.h.a.14.14	yes	44	9.4	even	3
45.5.h.a.29.9	yes	44	3.2	odd	2
45.5.h.a.29.14	yes	44	15.14	odd	2
135.5.h.a.44.9		44	9.5	odd	6	inner
135.5.h.a.44.14		44	45.14	odd	6	inner
135.5.h.a.89.9		44	5.4	even	2	inner
135.5.h.a.89.14		44	1.1	even	1	trivial
405.5.d.a.404.17		44	45.29	odd	6
405.5.d.a.404.18		44	9.7	even	3
405.5.d.a.404.27		44	45.34	even	6
405.5.d.a.404.28		44	9.2	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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	135.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.02189 - 1.76997i) q^{2} +(5.91148 + 10.2390i) q^{4} +(-15.4498 + 19.6546i) q^{5} +(-2.09732 - 1.21089i) q^{7} +56.8640 q^{8} +(19.0000 + 47.4305i) q^{10} +(-117.697 - 67.9523i) q^{11} +(-136.503 + 78.8098i) q^{13} +(-4.28647 + 2.47479i) q^{14} +(-36.4748 + 63.1763i) q^{16} -258.165 q^{17} -363.338 q^{19} +(-292.574 - 42.0027i) q^{20} +(-240.547 + 138.880i) q^{22} +(392.923 + 680.562i) q^{23} +(-147.606 - 607.320i) q^{25} +322.140i q^{26} -28.6326i q^{28} +(629.935 + 363.693i) q^{29} +(-463.170 - 802.234i) q^{31} +(529.459 + 917.050i) q^{32} +(-263.817 + 456.944i) q^{34} +(56.2028 - 22.5140i) q^{35} +1997.88i q^{37} +(-371.292 + 643.096i) q^{38} +(-878.539 + 1117.64i) q^{40} +(-1250.71 + 722.098i) q^{41} +(542.092 + 312.977i) q^{43} -1606.79i q^{44} +1606.10 q^{46} +(-188.637 + 326.730i) q^{47} +(-1197.57 - 2074.25i) q^{49} +(-1225.77 - 359.356i) q^{50} +(-1613.86 - 931.765i) q^{52} +694.739 q^{53} +(3153.97 - 1263.43i) q^{55} +(-119.262 - 68.8560i) q^{56} +(1287.45 - 743.309i) q^{58} +(2222.20 - 1282.99i) q^{59} +(-2577.00 + 4463.50i) q^{61} -1893.24 q^{62} +997.001 q^{64} +(559.965 - 3900.50i) q^{65} +(5671.56 - 3274.48i) q^{67} +(-1526.14 - 2643.35i) q^{68} +(17.5841 - 122.484i) q^{70} +3331.47i q^{71} -1735.66i q^{73} +(3536.18 + 2041.61i) q^{74} +(-2147.86 - 3720.21i) q^{76} +(164.565 + 285.036i) q^{77} +(-3695.54 + 6400.86i) q^{79} +(-678.175 - 1692.96i) q^{80} +2951.62i q^{82} +(5465.06 - 9465.75i) q^{83} +(3988.60 - 5074.13i) q^{85} +(1107.92 - 639.657i) q^{86} +(-6692.72 - 3864.04i) q^{88} -2325.29i q^{89} +381.719 q^{91} +(-4645.51 + 8046.26i) q^{92} +(385.534 + 667.764i) q^{94} +(5613.50 - 7141.26i) q^{95} +(14265.5 + 8236.22i) q^{97} -4895.13 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 162 q^{4} - 6 q^{5} + 28 q^{10} - 228 q^{11} - 282 q^{14} - 1058 q^{16} - 8 q^{19} + 2196 q^{20} - 148 q^{25} - 2370 q^{29} - 1112 q^{31} - 436 q^{34} - 850 q^{40} - 1830 q^{41} - 5668 q^{46} + 5396 q^{49}+ \cdots - 58746 q^{95}+O(q^{100}) \) 44 * q - 162 * q^4 - 6 * q^5 + 28 * q^10 - 228 * q^11 - 282 * q^14 - 1058 * q^16 - 8 * q^19 + 2196 * q^20 - 148 * q^25 - 2370 * q^29 - 1112 * q^31 - 436 * q^34 - 850 * q^40 - 1830 * q^41 - 5668 * q^46 + 5396 * q^49 - 13524 * q^50 - 3072 * q^55 + 8250 * q^56 + 27348 * q^59 + 2782 * q^61 + 8348 * q^64 + 24906 * q^65 + 4782 * q^70 - 64728 * q^74 - 1776 * q^76 + 7900 * q^79 + 6766 * q^85 - 9192 * q^86 + 1560 * q^91 - 18826 * q^94 - 58746 * q^95

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