LMFDB - Embedded newform 882.4.k.c.521.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,4,Mod(215,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("882.215");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	882.k (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:	$52.0396846251$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.721389578983833600000000.8
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 625x^{8} + 390625 $ x^16 - 625*x^8 + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{22}\cdot 3^{12} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.6
Root			$0.291865 + 2.21694i$ of defining polynomial
Character	$\chi$	$=$	882.521
Dual form			882.4.k.c.215.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73205 - 1.00000i) q^{2} +(2.00000 - 3.46410i) q^{4} +(-2.96425 - 5.13424i) q^{5} -8.00000i q^{8} +O(q^{10})$	\(q+(1.73205 - 1.00000i) q^{2} +(2.00000 - 3.46410i) q^{4} +(-2.96425 - 5.13424i) q^{5} -8.00000i q^{8} +(-10.2685 - 5.92851i) q^{10} +(0.261120 + 0.150758i) q^{11} +72.5806i q^{13} +(-8.00000 - 13.8564i) q^{16} +(22.1883 - 38.4312i) q^{17} +(73.1251 - 42.2188i) q^{19} -23.7140 q^{20} +0.603030 q^{22} +(54.7442 - 31.6066i) q^{23} +(44.9264 - 77.8148i) q^{25} +(72.5806 + 125.713i) q^{26} -183.037i q^{29} +(-43.5654 - 25.1525i) q^{31} +(-27.7128 - 16.0000i) q^{32} -88.7531i q^{34} +(-142.735 - 247.224i) q^{37} +(84.4376 - 146.250i) q^{38} +(-41.0739 + 23.7140i) q^{40} +216.129 q^{41} -14.2498 q^{43} +(1.04448 - 0.603030i) q^{44} +(63.2132 - 109.488i) q^{46} +(-211.813 - 366.871i) q^{47} -179.706i q^{50} +(251.426 + 145.161i) q^{52} +(-175.733 - 101.459i) q^{53} -1.78753i q^{55} +(-183.037 - 317.029i) q^{58} +(-367.218 + 636.041i) q^{59} +(-548.910 + 316.913i) q^{61} -100.610 q^{62} -64.0000 q^{64} +(372.646 - 215.147i) q^{65} +(-66.9848 + 116.021i) q^{67} +(-88.7531 - 153.725i) q^{68} -1048.82i q^{71} +(131.942 + 76.1768i) q^{73} +(-494.449 - 285.470i) q^{74} -337.750i q^{76} +(-409.838 - 709.860i) q^{79} +(-47.4280 + 82.1478i) q^{80} +(374.346 - 216.129i) q^{82} -583.173 q^{83} -263.087 q^{85} +(-24.6813 + 14.2498i) q^{86} +(1.20606 - 2.08896i) q^{88} +(656.015 + 1136.25i) q^{89} -252.853i q^{92} +(-733.742 - 423.626i) q^{94} +(-433.523 - 250.294i) q^{95} -409.633i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4}+O(q^{10}) $ 16 * q + 32 * q^4	$ 16 q + 32 q^{4} - 128 q^{16} + 960 q^{22} + 40 q^{25} + 160 q^{37} + 2080 q^{43} + 672 q^{46} - 960 q^{58} - 1024 q^{64} + 3680 q^{67} - 448 q^{79} + 13440 q^{85} + 1920 q^{88}+O(q^{100}) $ 16 * q + 32 * q^4 - 128 * q^16 + 960 * q^22 + 40 * q^25 + 160 * q^37 + 2080 * q^43 + 672 * q^46 - 960 * q^58 - 1024 * q^64 + 3680 * q^67 - 448 * q^79 + 13440 * q^85 + 1920 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$	−2.96425	−	5.13424i	−0.265131	−	0.459220i	0.702467	−	0.711716i	$-0.252082\pi$
$5$	−2.96425	−	5.13424i	−0.265131	−	0.459220i	−0.967598	+	0.252496i	$0.918748\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	8.00000i		−	0.353553i
$9$		0			0
$10$	−10.2685	−	5.92851i	−0.324718	−	0.187476i
$11$	0.261120	+	0.150758i	0.00715733	+	0.00413228i	0.503574	−	0.863952i	$-0.332018\pi$
$11$	0.261120	+	0.150758i	0.00715733	+	0.00413228i	−0.496417	+	0.868084i	$0.665351\pi$
$12$		0			0
$13$			72.5806i			1.54848i	0.632893	+	0.774240i	$0.281867\pi$
$13$			72.5806i			1.54848i	−0.632893	+	0.774240i	$0.718133\pi$
$14$		0			0
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	22.1883	−	38.4312i	0.316556	−	0.548290i	−0.663211	−	0.748432i	$-0.730807\pi$
$17$	22.1883	−	38.4312i	0.316556	−	0.548290i	0.979767	+	0.200142i	$0.0641403\pi$
$18$		0			0
$19$	73.1251	−	42.2188i	0.882950	−	0.509771i	0.0113199	−	0.999936i	$-0.496397\pi$
$19$	73.1251	−	42.2188i	0.882950	−	0.509771i	0.871630	+	0.490165i	$0.163063\pi$
$20$	−23.7140			−0.265131
$21$		0			0
$22$	0.603030			0.00584393
$23$	54.7442	−	31.6066i	0.496303	−	0.286541i	−0.230883	−	0.972982i	$-0.574161\pi$
$23$	54.7442	−	31.6066i	0.496303	−	0.286541i	0.727185	+	0.686441i	$0.240828\pi$
$24$		0			0
$25$	44.9264	−	77.8148i	0.359411	−	0.622519i
$26$	72.5806	+	125.713i	0.547470	+	0.948246i
$27$		0			0
$28$		0			0
$29$		−	183.037i		−	1.17204i	−0.810298	−	0.586018i	$-0.800695\pi$
$29$		−	183.037i		−	1.17204i	0.810298	−	0.586018i	$-0.199305\pi$
$30$		0			0
$31$	−43.5654	−	25.1525i	−0.252406	−	0.145727i	0.368459	−	0.929644i	$-0.379885\pi$
$31$	−43.5654	−	25.1525i	−0.252406	−	0.145727i	−0.620865	+	0.783917i	$0.713219\pi$
$32$	−27.7128	−	16.0000i	−0.153093	−	0.0883883i
$33$		0			0
$34$		−	88.7531i		−	0.447677i
$35$		0			0
$36$		0			0
$37$	−142.735	−	247.224i	−0.634203	−	1.09847i	−0.986683	−	0.162652i	$-0.947995\pi$
$37$	−142.735	−	247.224i	−0.634203	−	1.09847i	0.352481	−	0.935819i	$-0.385338\pi$
$38$	84.4376	−	146.250i	0.360463	−	0.624340i
$39$		0			0
$40$	−41.0739	+	23.7140i	−0.162359	+	0.0937379i
$41$	216.129			0.823259			0.411630	−	0.911351i	$-0.364960\pi$
$41$	216.129			0.823259			0.411630	+	0.911351i	$0.364960\pi$
$42$		0			0
$43$	−14.2498			−0.0505365			−0.0252683	−	0.999681i	$-0.508044\pi$
$43$	−14.2498			−0.0505365			−0.0252683	+	0.999681i	$0.508044\pi$
$44$	1.04448	−	0.603030i	0.00357866	−	0.00206614i
$45$		0			0
$46$	63.2132	−	109.488i	0.202615	−	0.350939i
$47$	−211.813	−	366.871i	−0.657365	−	1.13859i	−0.981295	−	0.192508i	$-0.938338\pi$
$47$	−211.813	−	366.871i	−0.657365	−	1.13859i	0.323931	−	0.946081i	$-0.394995\pi$
$48$		0			0
$49$		0			0
$50$		−	179.706i		−	0.508284i
$51$		0			0
$52$	251.426	+	145.161i	0.670511	+	0.387120i
$53$	−175.733	−	101.459i	−0.455448	−	0.262953i	0.254680	−	0.967025i	$-0.418030\pi$
$53$	−175.733	−	101.459i	−0.455448	−	0.262953i	−0.710128	+	0.704072i	$0.751363\pi$
$54$		0			0
$55$		−	1.78753i		−	0.00438238i
$56$		0			0
$57$		0			0
$58$	−183.037	−	317.029i	−0.414377	−	0.717722i
$59$	−367.218	+	636.041i	−0.810301	+	1.40348i	0.102352	+	0.994748i	$0.467363\pi$
$59$	−367.218	+	636.041i	−0.810301	+	1.40348i	−0.912653	+	0.408734i	$0.865970\pi$
$60$		0			0
$61$	−548.910	+	316.913i	−1.15214	+	0.665190i	−0.949409	−	0.314044i	$-0.898316\pi$
$61$	−548.910	+	316.913i	−1.15214	+	0.665190i	−0.202734	+	0.979234i	$0.564983\pi$
$62$	−100.610			−0.206089
$63$		0			0
$64$	−64.0000			−0.125000
$65$	372.646	−	215.147i	0.711093	−	0.410550i
$66$		0			0
$67$	−66.9848	+	116.021i	−0.122142	+	0.211556i	−0.920612	−	0.390478i	$-0.872310\pi$
$67$	−66.9848	+	116.021i	−0.122142	+	0.211556i	0.798470	+	0.602034i	$0.205643\pi$
$68$	−88.7531	−	153.725i	−0.158278	−	0.274145i
$69$		0			0
$70$		0			0
$71$		−	1048.82i		−	1.75312i	−0.481293	−	0.876560i	$-0.659833\pi$
$71$		−	1048.82i		−	1.75312i	0.481293	−	0.876560i	$-0.340167\pi$
$72$		0			0
$73$	131.942	+	76.1768i	0.211543	+	0.122135i	0.602028	−	0.798475i	$-0.294359\pi$
$73$	131.942	+	76.1768i	0.211543	+	0.122135i	−0.390485	+	0.920609i	$0.627693\pi$
$74$	−494.449	−	285.470i	−0.776737	−	0.448449i
$75$		0			0
$76$		−	337.750i		−	0.509771i
$77$		0			0
$78$		0			0
$79$	−409.838	−	709.860i	−0.583675	−	1.01096i	−0.995039	−	0.0994839i	$-0.968281\pi$
$79$	−409.838	−	709.860i	−0.583675	−	1.01096i	0.411364	−	0.911471i	$-0.365053\pi$
$80$	−47.4280	+	82.1478i	−0.0662827	+	0.114805i
$81$		0			0
$82$	374.346	−	216.129i	0.504141	−	0.291066i
$83$	−583.173			−0.771223			−0.385611	−	0.922661i	$-0.626009\pi$
$83$	−583.173			−0.771223			−0.385611	+	0.922661i	$0.626009\pi$
$84$		0			0
$85$	−263.087			−0.335715
$86$	−24.6813	+	14.2498i	−0.0309472	+	0.0178674i
$87$		0			0
$88$	1.20606	−	2.08896i	0.00146098	−	0.00253050i
$89$	656.015	+	1136.25i	0.781320	+	1.35329i	0.931173	+	0.364577i	$0.118786\pi$
$89$	656.015	+	1136.25i	0.781320	+	1.35329i	−0.149854	+	0.988708i	$0.547880\pi$
$90$		0			0
$91$		0			0
$92$		−	252.853i		−	0.286541i
$93$		0			0
$94$	−733.742	−	423.626i	−0.805104	−	0.464827i
$95$	−433.523	−	250.294i	−0.468194	−	0.270312i
$96$		0			0
$97$		−	409.633i		−	0.428783i	−0.976748	−	0.214391i	$-0.931223\pi$
$97$		−	409.633i		−	0.428783i	0.976748	−	0.214391i	$-0.0687768\pi$
$98$		0			0
$99$		0			0
$100$	−179.706	−	311.259i	−0.179706	−	0.311259i
$101$	912.379	−	1580.29i	0.898863	−	1.55688i	0.0699124	−	0.997553i	$-0.477728\pi$
$101$	912.379	−	1580.29i	0.898863	−	1.55688i	0.828950	−	0.559322i	$-0.188939\pi$
$102$		0			0
$103$	1072.30	−	619.093i	1.02579	−	0.592243i	0.110018	−	0.993930i	$-0.464909\pi$
$103$	1072.30	−	619.093i	1.02579	−	0.592243i	0.915777	+	0.401687i	$0.131576\pi$
$104$	580.645			0.547470
$105$		0			0
$106$	−405.838			−0.371872
$107$	1440.22	−	831.510i	1.30123	−	0.751263i	0.320611	−	0.947211i	$-0.396112\pi$
$107$	1440.22	−	831.510i	1.30123	−	0.751263i	0.980614	+	0.195948i	$0.0627784\pi$
$108$		0			0
$109$	−692.426	+	1199.32i	−0.608463	+	1.05389i	0.383031	+	0.923735i	$0.374880\pi$
$109$	−692.426	+	1199.32i	−0.608463	+	1.05389i	−0.991494	+	0.130153i	$0.958453\pi$
$110$	−1.78753	−	3.09610i	−0.00154941	−	0.00268365i
$111$		0			0
$112$		0			0
$113$		−	1244.76i		−	1.03626i	−0.855303	−	0.518128i	$-0.826629\pi$
$113$		−	1244.76i		−	1.03626i	0.855303	−	0.518128i	$-0.173371\pi$
$114$		0			0
$115$	−324.552	−	187.380i	−0.263170	−	0.151941i
$116$	−634.057	−	366.073i	−0.507506	−	0.293009i
$117$		0			0
$118$			1468.87i			1.14594i
$119$		0			0
$120$		0			0
$121$	−665.455	−	1152.60i	−0.499966	−	0.865966i
$122$	−633.827	+	1097.82i	−0.470360	+	0.814688i
$123$		0			0
$124$	−174.262	+	100.610i	−0.126203	+	0.0728633i
$125$	−1273.76			−0.911426
$126$		0			0
$127$	−1503.09			−1.05022			−0.525108	−	0.851036i	$-0.675975\pi$
$127$	−1503.09			−1.05022			−0.525108	+	0.851036i	$0.675975\pi$
$128$	−110.851	+	64.0000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	430.294	−	745.292i	0.290302	−	0.502819i
$131$	−623.234	−	1079.47i	−0.415665	−	0.719954i	0.579833	−	0.814736i	$-0.303118\pi$
$131$	−623.234	−	1079.47i	−0.415665	−	0.719954i	−0.995498	+	0.0947820i	$0.969785\pi$
$132$		0			0
$133$		0			0
$134$			267.939i			0.172735i
$135$		0			0
$136$	−307.450	−	177.506i	−0.193850	−	0.111919i
$137$	1216.39	+	702.282i	0.758562	+	0.437956i	0.828779	−	0.559576i	$-0.189036\pi$
$137$	1216.39	+	702.282i	0.758562	+	0.437956i	−0.0702170	+	0.997532i	$0.522369\pi$
$138$		0			0
$139$			1205.14i			0.735387i	0.929947	+	0.367694i	$0.119852\pi$
$139$			1205.14i			0.735387i	−0.929947	+	0.367694i	$0.880148\pi$
$140$		0			0
$141$		0			0
$142$	−1048.82	−	1816.60i	−0.619821	−	1.07356i
$143$	−10.9421	+	18.9522i	−0.00639876	+	0.0110830i
$144$		0			0
$145$	−939.753	+	542.567i	−0.538222	+	0.310743i
$146$	304.707			0.172724
$147$		0			0
$148$	−1141.88			−0.634203
$149$	1936.73	−	1118.17i	1.06485	−	0.614794i	0.138083	−	0.990421i	$-0.455906\pi$
$149$	1936.73	−	1118.17i	1.06485	−	0.614794i	0.926771	+	0.375627i	$0.122572\pi$
$150$		0			0
$151$	−803.198	+	1391.18i	−0.432870	+	0.749752i	−0.997119	−	0.0758521i	$-0.975832\pi$
$151$	−803.198	+	1391.18i	−0.432870	+	0.749752i	0.564249	+	0.825604i	$0.309166\pi$
$152$	−337.750	−	585.001i	−0.180231	−	0.312170i
$153$		0			0
$154$		0			0
$155$			298.234i			0.154547i
$156$		0			0
$157$	1203.60	+	694.899i	0.611833	+	0.353242i	0.773683	−	0.633573i	$-0.218413\pi$
$157$	1203.60	+	694.899i	0.611833	+	0.353242i	−0.161849	+	0.986815i	$0.551746\pi$
$158$	−1419.72	−	819.675i	−0.714853	−	0.412721i
$159$		0			0
$160$			189.712i			0.0937379i
$161$		0			0
$162$		0			0
$163$	−870.071	−	1507.01i	−0.418094	−	0.724159i	0.577654	−	0.816282i	$-0.303968\pi$
$163$	−870.071	−	1507.01i	−0.418094	−	0.724159i	−0.995748	+	0.0921223i	$0.970635\pi$
$164$	432.257	−	748.692i	0.205815	−	0.356482i
$165$		0			0
$166$	−1010.08	+	583.173i	−0.472276	+	0.272668i
$167$	4077.15			1.88922			0.944609	−	0.328197i	$-0.106441\pi$
$167$	4077.15			1.88922			0.944609	+	0.328197i	$0.106441\pi$
$168$		0			0
$169$	−3070.94			−1.39779
$170$	−455.679	+	263.087i	−0.205582	+	0.118693i
$171$		0			0
$172$	−28.4996	+	49.3627i	−0.0126341	+	0.0218830i
$173$	574.978	+	995.891i	0.252686	+	0.437666i	0.964265	−	0.264941i	$-0.0853526\pi$
$173$	574.978	+	995.891i	0.252686	+	0.437666i	−0.711578	+	0.702607i	$0.752019\pi$
$174$		0			0
$175$		0			0
$176$		−	4.82424i		−	0.00206614i
$177$		0			0
$178$	2272.50	+	1312.03i	0.956917	+	0.552476i
$179$	3171.07	+	1830.82i	1.32412	+	0.764479i	0.984383	−	0.176042i	$-0.0563296\pi$
$179$	3171.07	+	1830.82i	1.32412	+	0.764479i	0.339734	+	0.940522i	$0.389663\pi$
$180$		0			0
$181$		−	4309.63i		−	1.76979i	−0.465790	−	0.884895i	$-0.654230\pi$
$181$		−	4309.63i		−	1.76979i	0.465790	−	0.884895i	$-0.345770\pi$
$182$		0			0
$183$		0			0
$184$	−252.853	−	437.954i	−0.101307	−	0.175470i
$185$	−846.206	+	1465.67i	−0.336293	+	0.582477i
$186$		0			0
$187$	11.5876	−	6.69010i	0.00453138	−	0.00261620i
$188$	−1694.51			−0.657365
$189$		0			0
$190$	−1001.18			−0.382279
$191$	3650.29	−	2107.49i	1.38286	−	0.798392i	0.390359	−	0.920663i	$-0.372351\pi$
$191$	3650.29	−	2107.49i	1.38286	−	0.798392i	0.992497	+	0.122270i	$0.0390175\pi$
$192$		0			0
$193$	−723.632	+	1253.37i	−0.269887	+	0.467458i	−0.968832	−	0.247717i	$-0.920320\pi$
$193$	−723.632	+	1253.37i	−0.269887	+	0.467458i	0.698945	+	0.715175i	$0.253653\pi$
$194$	−409.633	−	709.505i	−0.151598	−	0.262575i
$195$		0			0
$196$		0			0
$197$			524.696i			0.189762i	0.995489	+	0.0948808i	$0.0302470\pi$
$197$			524.696i			0.189762i	−0.995489	+	0.0948808i	$0.969753\pi$
$198$		0			0
$199$	−209.409	−	120.902i	−0.0745961	−	0.0430681i	0.462238	−	0.886756i	$-0.347047\pi$
$199$	−209.409	−	120.902i	−0.0745961	−	0.0430681i	−0.536834	+	0.843688i	$0.680380\pi$
$200$	−622.519	−	359.411i	−0.220094	−	0.127071i
$201$		0			0
$202$		−	3649.52i		−	1.27118i
$203$		0			0
$204$		0			0
$205$	−640.660	−	1109.66i	−0.218271	−	0.378057i
$206$	1238.19	−	2144.60i	0.418779	−	0.725346i
$207$		0			0
$208$	1005.71	−	580.645i	0.335256	−	0.193560i
$209$	25.4592			0.00842608
$210$		0			0
$211$	−425.807			−0.138928			−0.0694640	−	0.997584i	$-0.522129\pi$
$211$	−425.807			−0.138928			−0.0694640	+	0.997584i	$0.522129\pi$
$212$	−702.931	+	405.838i	−0.227724	+	0.131477i
$213$		0			0
$214$	1663.02	−	2880.44i	0.531223	−	0.920105i
$215$	42.2400	+	73.1618i	0.0133988	+	0.0232074i
$216$		0			0
$217$		0			0
$218$			2769.71i			0.860496i
$219$		0			0
$220$	−6.19220	−	3.57507i	−0.00189763	−	0.00109560i
$221$	2789.36	+	1610.44i	0.849016	+	0.490180i
$222$		0			0
$223$			5867.25i			1.76189i	0.473223	+	0.880943i	$0.343090\pi$
$223$			5867.25i			1.76189i	−0.473223	+	0.880943i	$0.656910\pi$
$224$		0			0
$225$		0			0
$226$	−1244.76	−	2155.98i	−0.366372	−	0.634574i
$227$	−1919.79	+	3325.17i	−0.561325	+	0.972244i	0.436056	+	0.899920i	$0.356375\pi$
$227$	−1919.79	+	3325.17i	−0.561325	+	0.972244i	−0.997381	+	0.0723245i	$0.976958\pi$
$228$		0			0
$229$	2080.46	−	1201.15i	0.600352	−	0.346614i	−0.168828	−	0.985646i	$-0.553998\pi$
$229$	2080.46	−	1201.15i	0.600352	−	0.346614i	0.769180	+	0.639032i	$0.220665\pi$
$230$	−749.520			−0.214878
$231$		0			0
$232$	−1464.29			−0.414377
$233$	1881.39	−	1086.22i	0.528987	−	0.305411i	−0.211617	−	0.977353i	$-0.567873\pi$
$233$	1881.39	−	1086.22i	0.528987	−	0.305411i	0.740604	+	0.671942i	$0.234540\pi$
$234$		0			0
$235$	−1255.74	+	2175.00i	−0.348575	+	0.603750i
$236$	1468.87	+	2544.16i	0.405150	+	0.701741i
$237$		0			0
$238$		0			0
$239$		−	1130.57i		−	0.305985i	−0.988227	−	0.152992i	$-0.951109\pi$
$239$		−	1130.57i		−	0.305985i	0.988227	−	0.152992i	$-0.0488910\pi$
$240$		0			0
$241$	−4083.87	−	2357.82i	−1.09156	−	0.630210i	−0.157566	−	0.987509i	$-0.550365\pi$
$241$	−4083.87	−	2357.82i	−1.09156	−	0.630210i	−0.933990	+	0.357298i	$0.883698\pi$
$242$	−2305.20	−	1330.91i	−0.612331	−	0.353529i
$243$		0			0
$244$			2535.31i			0.665190i
$245$		0			0
$246$		0			0
$247$	3064.26	+	5307.46i	0.789370	+	1.36723i
$248$	−201.220	+	348.524i	−0.0515222	+	0.0892390i
$249$		0			0
$250$	−2206.21	+	1273.76i	−0.558132	+	0.322238i
$251$	−3318.30			−0.834460			−0.417230	−	0.908801i	$-0.636999\pi$
$251$	−3318.30			−0.834460			−0.417230	+	0.908801i	$0.636999\pi$
$252$		0			0
$253$	19.0597			0.00473627
$254$	−2603.42	+	1503.09i	−0.643123	+	0.371307i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−2543.28	−	4405.10i	−0.617298	−	1.06919i	−0.989977	−	0.141232i	$-0.954894\pi$
$257$	−2543.28	−	4405.10i	−0.617298	−	1.06919i	0.372678	−	0.927961i	$-0.378440\pi$
$258$		0			0
$259$		0			0
$260$		−	1721.18i		−	0.410550i
$261$		0			0
$262$	−2158.94	−	1246.47i	−0.509084	−	0.293920i
$263$	2190.68	+	1264.79i	0.513624	+	0.296541i	0.734322	−	0.678801i	$-0.237500\pi$
$263$	2190.68	+	1264.79i	0.513624	+	0.296541i	−0.220698	+	0.975342i	$0.570834\pi$
$264$		0			0
$265$			1203.01i			0.278868i
$266$		0			0
$267$		0			0
$268$	267.939	+	464.085i	0.0610709	+	0.105778i
$269$	2141.24	−	3708.73i	0.485329	−	0.840614i	−0.514529	−	0.857473i	$-0.672033\pi$
$269$	2141.24	−	3708.73i	0.485329	−	0.840614i	0.999858	+	0.0168589i	$0.00536661\pi$
$270$		0			0
$271$	−672.205	+	388.098i	−0.150677	+	0.0869936i	−0.573443	−	0.819245i	$-0.694393\pi$
$271$	−672.205	+	388.098i	−0.150677	+	0.0869936i	0.422766	+	0.906239i	$0.361059\pi$
$272$	−710.025			−0.158278
$273$		0			0
$274$	2809.13			0.619364
$275$	23.4624	−	13.5460i	0.00514485	−	0.00297038i
$276$		0			0
$277$	−1450.81	+	2512.87i	−0.314695	+	0.545068i	−0.979373	−	0.202062i	$-0.935236\pi$
$277$	−1450.81	+	2512.87i	−0.314695	+	0.545068i	0.664677	+	0.747130i	$0.268569\pi$
$278$	1205.14	+	2087.37i	0.259999	+	0.450331i
$279$		0			0
$280$		0			0
$281$			4406.68i			0.935518i	0.883856	+	0.467759i	$0.154939\pi$
$281$			4406.68i			0.935518i	−0.883856	+	0.467759i	$0.845061\pi$
$282$		0			0
$283$	−54.4018	−	31.4089i	−0.0114270	−	0.00659740i	0.494276	−	0.869305i	$-0.335433\pi$
$283$	−54.4018	−	31.4089i	−0.0114270	−	0.00659740i	−0.505703	+	0.862708i	$0.668767\pi$
$284$	−3633.20	−	2097.63i	−0.759123	−	0.438280i
$285$		0			0
$286$			43.7683i			0.00904921i
$287$		0			0
$288$		0			0
$289$	1471.86	+	2549.34i	0.299585	+	0.518897i
$290$	−1085.13	+	1879.51i	−0.219728	+	0.380581i
$291$		0			0
$292$	527.768	−	304.707i	0.105772	−	0.0610673i
$293$	−3299.73			−0.657927			−0.328963	−	0.944343i	$-0.606699\pi$
$293$	−3299.73			−0.657927			−0.328963	+	0.944343i	$0.606699\pi$
$294$		0			0
$295$	4354.11			0.859343
$296$	−1977.80	+	1141.88i	−0.388368	+	0.224225i
$297$		0			0
$298$	2236.35	−	3873.47i	0.434725	−	0.752966i
$299$	2294.03	+	3973.37i	0.443702	+	0.768514i
$300$		0			0
$301$		0			0
$302$			3212.79i			0.612170i
$303$		0			0
$304$	−1170.00	−	675.501i	−0.220737	−	0.127443i
$305$	3254.22	+	1878.82i	0.610937	+	0.352725i
$306$		0			0
$307$		−	5596.99i		−	1.04051i	−0.854011	−	0.520255i	$-0.825837\pi$
$307$		−	5596.99i		−	1.04051i	0.854011	−	0.520255i	$-0.174163\pi$
$308$		0			0
$309$		0			0
$310$	298.234	+	516.556i	0.0546405	+	0.0946400i
$311$	2908.98	−	5038.50i	0.530395	−	0.918672i	−0.468976	−	0.883211i	$-0.655377\pi$
$311$	2908.98	−	5038.50i	0.530395	−	0.918672i	0.999371	−	0.0354606i	$-0.0112898\pi$
$312$		0			0
$313$	978.372	−	564.863i	0.176680	−	0.102006i	−0.409052	−	0.912511i	$-0.634140\pi$
$313$	978.372	−	564.863i	0.176680	−	0.102006i	0.585732	+	0.810505i	$0.300807\pi$
$314$	2779.60			0.499560
$315$		0			0
$316$	−3278.70			−0.583675
$317$	−7043.02	+	4066.29i	−1.24787	+	0.720459i	−0.970685	−	0.240357i	$-0.922735\pi$
$317$	−7043.02	+	4066.29i	−1.24787	+	0.720459i	−0.277187	+	0.960816i	$0.589402\pi$
$318$		0			0
$319$	27.5942	−	47.7945i	0.00484319	−	0.00838864i
$320$	189.712	+	328.591i	0.0331414	+	0.0574025i
$321$		0			0
$322$		0			0
$323$		−	3747.05i		−	0.645484i
$324$		0			0
$325$	5647.84	+	3260.78i	0.963957	+	0.556541i
$326$	−3014.02	−	1740.14i	−0.512058	−	0.295637i
$327$		0			0
$328$		−	1729.03i		−	0.291066i
$329$		0			0
$330$		0			0
$331$	3871.50	+	6705.64i	0.642891	+	1.11352i	0.984784	+	0.173782i	$0.0555987\pi$
$331$	3871.50	+	6705.64i	0.642891	+	1.11352i	−0.341893	+	0.939739i	$0.611068\pi$
$332$	−1166.35	+	2020.17i	−0.192806	+	0.333949i
$333$		0			0
$334$	7061.83	−	4077.15i	1.15691	−	0.667940i
$335$	794.240			0.129534
$336$		0			0
$337$	10498.7			1.69703			0.848517	−	0.529169i	$-0.177496\pi$
$337$	10498.7			1.69703			0.848517	+	0.529169i	$0.177496\pi$
$338$	−5319.02	+	3070.94i	−0.855967	+	0.494193i
$339$		0			0
$340$	−526.173	+	911.359i	−0.0839287	+	0.145369i
$341$	−7.58387	−	13.1356i	−0.00120437	−	0.00208603i
$342$		0			0
$343$		0			0
$344$			113.998i			0.0178674i
$345$		0			0
$346$	1991.78	+	1149.96i	0.309476	+	0.178676i
$347$	−2915.58	−	1683.31i	−0.451057	−	0.260418i	0.257220	−	0.966353i	$-0.417194\pi$
$347$	−2915.58	−	1683.31i	−0.451057	−	0.260418i	−0.708276	+	0.705935i	$0.750527\pi$
$348$		0			0
$349$			1047.69i			0.160692i	0.996767	+	0.0803461i	$0.0256026\pi$
$349$			1047.69i			0.160692i	−0.996767	+	0.0803461i	$0.974397\pi$
$350$		0			0
$351$		0			0
$352$	−4.82424	−	8.35583i	−0.000730492	−	0.00126525i
$353$	−2721.84	+	4714.36i	−0.410393	+	0.710822i	−0.994933	−	0.100543i	$-0.967942\pi$
$353$	−2721.84	+	4714.36i	−0.410393	+	0.710822i	0.584539	+	0.811365i	$0.301275\pi$
$354$		0			0
$355$	−5384.87	+	3108.95i	−0.805068	+	0.464806i
$356$	5248.12			0.781320
$357$		0			0
$358$	7323.27			1.08114
$359$	967.163	−	558.392i	0.142186	−	0.0820913i	−0.427219	−	0.904148i	$-0.640507\pi$
$359$	967.163	−	558.392i	0.142186	−	0.0820913i	0.569406	+	0.822057i	$0.307173\pi$
$360$		0			0
$361$	135.353	−	234.438i	0.0197336	−	0.0341796i
$362$	−4309.63	−	7464.49i	−0.625715	−	1.08377i
$363$		0			0
$364$		0			0
$365$		−	903.229i		−	0.129527i
$366$		0			0
$367$	6627.58	+	3826.44i	0.942662	+	0.544246i	0.890794	−	0.454408i	$-0.150149\pi$
$367$	6627.58	+	3826.44i	0.942662	+	0.544246i	0.0518681	+	0.998654i	$0.483482\pi$
$368$	−875.908	−	505.706i	−0.124076	−	0.0716351i
$369$		0			0
$370$			3384.82i			0.475591i
$371$		0			0
$372$		0			0
$373$	5746.03	+	9952.41i	0.797635	+	1.38154i	0.921152	+	0.389202i	$0.127249\pi$
$373$	5746.03	+	9952.41i	0.797635	+	1.38154i	−0.123517	+	0.992342i	$0.539417\pi$
$374$	13.3802	−	23.1752i	0.00184993	−	0.00320417i
$375$		0			0
$376$	−2934.97	+	1694.51i	−0.402552	+	0.232413i
$377$	13284.9			1.81487
$378$		0			0
$379$	8186.54			1.10954			0.554768	−	0.832005i	$-0.312807\pi$
$379$	8186.54			1.10954			0.554768	+	0.832005i	$0.312807\pi$
$380$	−1734.09	+	1001.18i	−0.234097	+	0.135156i
$381$		0			0
$382$	4214.99	−	7300.57i	0.564549	−	0.977827i
$383$	1035.00	+	1792.68i	0.138084	+	0.239169i	0.926771	−	0.375626i	$-0.122572\pi$
$383$	1035.00	+	1792.68i	0.138084	+	0.239169i	−0.788687	+	0.614795i	$0.789239\pi$
$384$		0			0
$385$		0			0
$386$			2894.53i			0.381678i
$387$		0			0
$388$	−1419.01	−	819.266i	−0.185668	−	0.107196i
$389$	555.443	+	320.685i	0.0723961	+	0.0417979i	0.535761	−	0.844370i	$-0.320025\pi$
$389$	555.443	+	320.685i	0.0723961	+	0.0417979i	−0.463365	+	0.886168i	$0.653358\pi$
$390$		0			0
$391$		−	2805.18i		−	0.362824i
$392$		0			0
$393$		0			0
$394$	524.696	+	908.800i	0.0670909	+	0.116205i
$395$	−2429.73	+	4208.41i	−0.309501	+	0.536071i
$396$		0			0
$397$	−9090.01	+	5248.12i	−1.14915	+	0.663465i	−0.948681	−	0.316234i	$-0.897581\pi$
$397$	−9090.01	+	5248.12i	−1.14915	+	0.663465i	−0.200474	+	0.979699i	$0.564248\pi$
$398$	−483.610			−0.0609074
$399$		0			0
$400$	−1437.65			−0.179706
$401$	−7675.03	+	4431.18i	−0.955792	+	0.551827i	−0.894875	−	0.446316i	$-0.852736\pi$
$401$	−7675.03	+	4431.18i	−0.955792	+	0.551827i	−0.0609169	+	0.998143i	$0.519402\pi$
$402$		0			0
$403$	1825.58	−	3162.00i	0.225655	−	0.390845i
$404$	−3649.52	−	6321.15i	−0.449431	−	0.778438i
$405$		0			0
$406$		0			0
$407$		−	86.0736i		−	0.0104828i
$408$		0			0
$409$	−7704.71	−	4448.32i	−0.931475	−	0.537787i	−0.0441973	−	0.999023i	$-0.514073\pi$
$409$	−7704.71	−	4448.32i	−0.931475	−	0.537787i	−0.887278	+	0.461235i	$0.847406\pi$
$410$	−2219.31	−	1281.32i	−0.267327	−	0.154341i
$411$		0			0
$412$		−	4952.74i		−	0.592243i
$413$		0			0
$414$		0			0
$415$	1728.67	+	2994.15i	0.204475	+	0.354161i
$416$	1161.29	−	2011.41i	0.136868	−	0.237061i
$417$		0			0
$418$	44.0967	−	25.4592i	0.00515990	−	0.00297907i
$419$	−14741.9			−1.71883			−0.859415	−	0.511279i	$-0.829172\pi$
$419$	−14741.9			−1.71883			−0.859415	+	0.511279i	$0.829172\pi$
$420$		0			0
$421$	841.087			0.0973683			0.0486841	−	0.998814i	$-0.484497\pi$
$421$	841.087			0.0973683			0.0486841	+	0.998814i	$0.484497\pi$
$422$	−737.520	+	425.807i	−0.0850756	+	0.0491184i
$423$		0			0
$424$	−811.675	+	1405.86i	−0.0929680	+	0.161025i
$425$	−1993.68	−	3453.15i	−0.227547	−	0.394123i
$426$		0			0
$427$		0			0
$428$		−	6652.08i		−	0.751263i
$429$		0			0
$430$	146.324	+	84.4799i	0.0164101	+	0.00947438i
$431$	6674.95	+	3853.78i	0.745988	+	0.430697i	0.824243	−	0.566237i	$-0.191601\pi$
$431$	6674.95	+	3853.78i	0.745988	+	0.430697i	−0.0782543	+	0.996933i	$0.524935\pi$
$432$		0			0
$433$			9675.58i			1.07385i	0.843629	+	0.536927i	$0.180415\pi$
$433$			9675.58i			1.07385i	−0.843629	+	0.536927i	$0.819585\pi$
$434$		0			0
$435$		0			0
$436$	2769.71	+	4797.27i	0.304231	+	0.526944i
$437$	2668.79	−	4622.47i	0.292140	−	0.506002i
$438$		0			0
$439$	5580.80	−	3222.08i	0.606736	−	0.350299i	−0.164951	−	0.986302i	$-0.552747\pi$
$439$	5580.80	−	3222.08i	0.606736	−	0.350299i	0.771687	+	0.636003i	$0.219413\pi$
$440$	−14.3003			−0.00154941
$441$		0			0
$442$	6441.75			0.693219
$443$	236.321	−	136.440i	0.0253452	−	0.0146331i	−0.487274	−	0.873249i	$-0.662009\pi$
$443$	236.321	−	136.440i	0.0253452	−	0.0146331i	0.512619	+	0.858616i	$0.328675\pi$
$444$		0			0
$445$	3889.19	−	6736.27i	0.414304	−	0.717595i
$446$	5867.25	+	10162.4i	0.622920	+	1.07893i
$447$		0			0
$448$		0			0
$449$			599.676i			0.0630299i	0.999503	+	0.0315150i	$0.0100332\pi$
$449$			599.676i			0.0630299i	−0.999503	+	0.0315150i	$0.989967\pi$
$450$		0			0
$451$	56.4355	+	32.5830i	0.00589234	+	0.00340194i
$452$	−4311.96	−	2489.51i	−0.448712	−	0.259064i
$453$		0			0
$454$			7679.16i			0.793834i
$455$		0			0
$456$		0			0
$457$	−472.564	−	818.504i	−0.0483711	−	0.0837812i	0.840826	−	0.541305i	$-0.182070\pi$
$457$	−472.564	−	818.504i	−0.0483711	−	0.0837812i	−0.889197	+	0.457524i	$0.848736\pi$
$458$	2402.31	−	4160.92i	0.245093	−	0.424513i
$459$		0			0
$460$	−1298.21	+	749.520i	−0.131585	+	0.0759707i
$461$	−1164.43			−0.117641			−0.0588207	−	0.998269i	$-0.518734\pi$
$461$	−1164.43			−0.117641			−0.0588207	+	0.998269i	$0.518734\pi$
$462$		0			0
$463$	17312.8			1.73778			0.868892	−	0.495002i	$-0.164833\pi$
$463$	17312.8			1.73778			0.868892	+	0.495002i	$0.164833\pi$
$464$	−2536.23	+	1464.29i	−0.253753	+	0.146504i
$465$		0			0
$466$	2172.44	−	3762.78i	0.215958	−	0.374050i
$467$	596.907	+	1033.87i	0.0591468	+	0.102445i	0.894083	−	0.447902i	$-0.147829\pi$
$467$	596.907	+	1033.87i	0.0591468	+	0.102445i	−0.834936	+	0.550347i	$0.814495\pi$
$468$		0			0
$469$		0			0
$470$			5022.94i			0.492960i
$471$		0			0
$472$	5088.33	+	2937.75i	0.496206	+	0.286485i
$473$	−3.72090	−	2.14826i	−0.000361707	−	0.000208831i
$474$		0			0
$475$		−	7586.95i		−	0.732870i
$476$		0			0
$477$		0			0
$478$	−1130.57	−	1958.20i	−0.108182	−	0.187377i
$479$	6842.36	−	11851.3i	0.652684	−	1.13048i	−0.329785	−	0.944056i	$-0.606976\pi$
$479$	6842.36	−	11851.3i	0.652684	−	1.13048i	0.982469	−	0.186426i	$-0.0596903\pi$
$480$		0			0
$481$	17943.7	−	10359.8i	1.70096	−	0.982050i
$482$	−9431.29			−0.891252
$483$		0			0
$484$	−5323.64			−0.499966
$485$	−2103.15	+	1214.26i	−0.196906	+	0.113684i
$486$		0			0
$487$	3965.64	−	6868.69i	0.368994	−	0.639117i	−0.620414	−	0.784274i	$-0.713036\pi$
$487$	3965.64	−	6868.69i	0.368994	−	0.639117i	0.989409	+	0.145157i	$0.0463688\pi$
$488$	2535.31	+	4391.28i	0.235180	+	0.407344i
$489$		0			0
$490$		0			0
$491$		−	486.246i		−	0.0446924i	−0.999750	−	0.0223462i	$-0.992886\pi$
$491$		−	486.246i		−	0.0446924i	0.999750	−	0.0223462i	$-0.00711361\pi$
$492$		0			0
$493$	−7034.32	−	4061.26i	−0.642616	−	0.371015i
$494$	10614.9	+	6128.53i	0.966777	+	0.558169i
$495$		0			0
$496$			804.881i			0.0728633i
$497$		0			0
$498$		0			0
$499$	9466.43	+	16396.3i	0.849249	+	1.47094i	0.881879	+	0.471476i	$0.156279\pi$
$499$	9466.43	+	16396.3i	0.849249	+	1.47094i	−0.0326295	+	0.999468i	$0.510388\pi$
$500$	−2547.51	+	4412.42i	−0.227856	+	0.394659i
$501$		0			0
$502$	−5747.47	+	3318.30i	−0.511000	+	0.295026i
$503$	1543.07			0.136784			0.0683918	−	0.997659i	$-0.478213\pi$
$503$	1543.07			0.136784			0.0683918	+	0.997659i	$0.478213\pi$
$504$		0			0
$505$	−10818.1			−0.953265
$506$	33.0124	−	19.0597i	0.00290036	−	0.00167452i
$507$		0			0
$508$	−3006.17	+	5206.84i	−0.262554	+	0.454757i
$509$	7390.31	+	12800.4i	0.643556	+	1.11467i	0.984633	+	0.174636i	$0.0558748\pi$
$509$	7390.31	+	12800.4i	0.643556	+	1.11467i	−0.341077	+	0.940035i	$0.610792\pi$
$510$		0			0
$511$		0			0
$512$			512.000i			0.0441942i
$513$		0			0
$514$	−8810.20	−	5086.57i	−0.756033	−	0.436496i
$515$	−6357.14	−	3670.29i	−0.543940	−	0.314044i
$516$		0			0
$517$		−	127.730i		−	0.0108657i
$518$		0			0
$519$		0			0
$520$	−1721.18	−	2981.17i	−0.145151	−	0.251409i
$521$	−10937.3	+	18943.9i	−0.919712	+	1.59299i	−0.119861	+	0.992791i	$0.538245\pi$
$521$	−10937.3	+	18943.9i	−0.919712	+	1.59299i	−0.799852	+	0.600198i	$0.795089\pi$
$522$		0			0
$523$	8466.50	−	4888.14i	0.707866	−	0.408687i	−0.102404	−	0.994743i	$-0.532653\pi$
$523$	8466.50	−	4888.14i	0.707866	−	0.408687i	0.810271	+	0.586056i	$0.199320\pi$
$524$	−4985.87			−0.415665
$525$		0			0
$526$	5059.16			0.419372
$527$	−1933.28	+	1116.18i	−0.159801	+	0.0922612i
$528$		0			0
$529$	−4085.55	+	7076.37i	−0.335789	+	0.581604i
$530$	1203.01	+	2083.67i	0.0985948	+	0.170771i
$531$		0			0
$532$		0			0
$533$			15686.7i			1.27480i
$534$		0			0
$535$	−8538.34	−	4929.61i	−0.689990	−	0.398366i
$536$	928.169	+	535.879i	0.0747963	+	0.0431837i
$537$		0			0
$538$		−	8564.94i		−	0.686358i
$539$		0			0
$540$		0			0
$541$	−10668.3	−	18478.1i	−0.847814	−	1.46846i	−0.883155	−	0.469082i	$-0.844585\pi$
$541$	−10668.3	−	18478.1i	−0.847814	−	1.46846i	0.0353408	−	0.999375i	$-0.488748\pi$
$542$	−776.195	+	1344.41i	−0.0615137	+	0.106545i
$543$		0			0
$544$	−1229.80	+	710.025i	−0.0969250	+	0.0559597i
$545$	8210.11			0.645289
$546$		0			0
$547$	−8314.27			−0.649895			−0.324948	−	0.945732i	$-0.605347\pi$
$547$	−8314.27			−0.649895			−0.324948	+	0.945732i	$0.605347\pi$
$548$	4865.55	−	2809.13i	0.379281	−	0.218978i
$549$		0			0
$550$	27.0920	−	46.9247i	0.00210038	−	0.00363796i
$551$	−7727.58	−	13384.6i	−0.597470	−	1.03485i
$552$		0			0
$553$		0			0
$554$			5803.23i			0.445046i
$555$		0			0
$556$	4174.73	+	2410.28i	0.318432	+	0.183847i
$557$	10646.6	+	6146.84i	0.809897	+	0.467594i	0.846920	−	0.531720i	$-0.178454\pi$
$557$	10646.6	+	6146.84i	0.809897	+	0.467594i	−0.0370231	+	0.999314i	$0.511788\pi$
$558$		0			0
$559$		−	1034.26i		−	0.0782548i
$560$		0			0
$561$		0			0
$562$	4406.68	+	7632.60i	0.330756	+	0.572886i
$563$	2396.12	−	4150.19i	0.179368	−	0.310675i	−0.762296	−	0.647228i	$-0.775928\pi$
$563$	2396.12	−	4150.19i	0.179368	−	0.310675i	0.941664	+	0.336554i	$0.109261\pi$
$564$		0			0
$565$	−6390.87	+	3689.77i	−0.475869	+	0.274743i
$566$	−125.636			−0.00933014
$567$		0			0
$568$	−8390.52			−0.619821
$569$	−14058.7	+	8116.79i	−1.03580	+	0.598020i	−0.918641	−	0.395093i	$-0.870712\pi$
$569$	−14058.7	+	8116.79i	−1.03580	+	0.598020i	−0.117160	+	0.993113i	$0.537379\pi$
$570$		0			0
$571$	−797.890	+	1381.99i	−0.0584775	+	0.101286i	−0.893782	−	0.448501i	$-0.851958\pi$
$571$	−797.890	+	1381.99i	−0.0584775	+	0.101286i	0.835305	+	0.549787i	$0.185291\pi$
$572$	43.7683	+	75.8089i	0.00319938	+	0.00554148i
$573$		0			0
$574$		0			0
$575$		−	5679.88i		−	0.411944i
$576$		0			0
$577$	11171.0	+	6449.56i	0.805985	+	0.465336i	0.845560	−	0.533881i	$-0.179267\pi$
$577$	11171.0	+	6449.56i	0.805985	+	0.465336i	−0.0395747	+	0.999217i	$0.512600\pi$
$578$	5098.68	+	2943.72i	0.366915	+	0.211839i
$579$		0			0
$580$			4340.53i			0.310743i
$581$		0			0
$582$		0			0
$583$	−30.5916	−	52.9861i	−0.00217320	−	0.00376408i
$584$	609.415	−	1055.54i	0.0431811	−	0.0747918i
$585$		0			0
$586$	−5715.31	+	3299.73i	−0.402896	+	0.232612i
$587$	13092.3			0.920575			0.460287	−	0.887770i	$-0.347746\pi$
$587$	13092.3			0.920575			0.460287	+	0.887770i	$0.347746\pi$
$588$		0			0
$589$	−4247.64			−0.297149
$590$	7541.54	−	4354.11i	0.526238	−	0.303824i
$591$		0			0
$592$	−2283.76	+	3955.59i	−0.158551	+	0.274618i
$593$	−9802.47	−	16978.4i	−0.678818	−	1.17575i	−0.975337	−	0.220721i	$-0.929159\pi$
$593$	−9802.47	−	16978.4i	−0.678818	−	1.17575i	0.296519	−	0.955027i	$-0.404174\pi$
$594$		0			0
$595$		0			0
$596$		−	8945.38i		−	0.614794i
$597$		0			0
$598$	7946.74	+	4588.05i	0.543422	+	0.313745i
$599$	−10173.0	−	5873.41i	−0.693922	−	0.400636i	0.111158	−	0.993803i	$-0.464544\pi$
$599$	−10173.0	−	5873.41i	−0.693922	−	0.400636i	−0.805080	+	0.593167i	$0.797878\pi$
$600$		0			0
$601$			8546.19i			0.580044i	0.957020	+	0.290022i	$0.0936626\pi$
$601$			8546.19i			0.580044i	−0.957020	+	0.290022i	$0.906337\pi$
$602$		0			0
$603$		0			0
$604$	3212.79	+	5564.72i	0.216435	+	0.374876i
$605$	−3945.15	+	6833.20i	−0.265113	+	0.459189i
$606$		0			0
$607$	−25690.8	+	14832.6i	−1.71788	+	0.991821i	−0.795124	+	0.606447i	$0.792594\pi$
$607$	−25690.8	+	14832.6i	−1.71788	+	0.991821i	−0.922760	+	0.385374i	$0.874072\pi$
$608$	−2702.00			−0.180231
$609$		0			0
$610$	7515.29			0.498828
$611$	26627.7	−	15373.5i	1.76308	−	1.01792i
$612$		0			0
$613$	−2944.56	+	5100.13i	−0.194013	+	0.336040i	−0.946576	−	0.322480i	$-0.895484\pi$
$613$	−2944.56	+	5100.13i	−0.194013	+	0.336040i	0.752564	+	0.658519i	$0.228817\pi$
$614$	−5596.99	−	9694.26i	−0.367876	−	0.637180i
$615$		0			0
$616$		0			0
$617$			20676.7i			1.34913i	0.738214	+	0.674566i	$0.235669\pi$
$617$			20676.7i			1.34913i	−0.738214	+	0.674566i	$0.764331\pi$
$618$		0			0
$619$	8937.57	+	5160.11i	0.580341	+	0.335060i	0.761269	−	0.648436i	$-0.224577\pi$
$619$	8937.57	+	5160.11i	0.580341	+	0.335060i	−0.180928	+	0.983496i	$0.557910\pi$
$620$	1033.11	+	596.468i	0.0669206	+	0.0386366i
$621$		0			0
$622$		−	11635.9i		−	0.750092i
$623$		0			0
$624$		0			0
$625$	−1840.06	−	3187.09i	−0.117764	−	0.203974i
$626$	1129.73	−	1956.74i	0.0721293	−	0.124932i
$627$		0			0
$628$	4814.40	−	2779.60i	0.305917	−	0.176621i
$629$	−12668.2			−0.803042
$630$		0			0
$631$	−12520.8			−0.789928			−0.394964	−	0.918696i	$-0.629243\pi$
$631$	−12520.8			−0.789928			−0.394964	+	0.918696i	$0.629243\pi$
$632$	−5678.88	+	3278.70i	−0.357427	+	0.206360i
$633$		0			0
$634$	−8132.57	+	14086.0i	−0.509441	+	0.882378i
$635$	4455.53	+	7717.20i	0.278445	+	0.482280i
$636$		0			0
$637$		0			0
$638$		−	110.377i		−	0.00684930i
$639$		0			0
$640$	657.182	+	379.424i	0.0405897	+	0.0234345i
$641$	−16685.0	−	9633.09i	−1.02811	−	0.593579i	−0.111667	−	0.993746i	$-0.535619\pi$
$641$	−16685.0	−	9633.09i	−1.02811	−	0.593579i	−0.916442	+	0.400167i	$0.868952\pi$
$642$		0			0
$643$		−	7084.07i		−	0.434477i	−0.976119	−	0.217238i	$-0.930295\pi$
$643$		−	7084.07i		−	0.434477i	0.976119	−	0.217238i	$-0.0697049\pi$
$644$		0			0
$645$		0			0
$646$	−3747.05	−	6490.08i	−0.228213	−	0.395277i
$647$	−1807.41	+	3130.52i	−0.109825	+	0.190222i	−0.915699	−	0.401865i	$-0.868362\pi$
$647$	−1807.41	+	3130.52i	−0.109825	+	0.190222i	0.805875	+	0.592086i	$0.201696\pi$
$648$		0			0
$649$	−191.776	+	110.722i	−0.0115992	+	0.00669679i
$650$	13043.1			0.787068
$651$		0			0
$652$	−6960.57			−0.418094
$653$	−9513.09	+	5492.39i	−0.570101	+	0.329148i	−0.757190	−	0.653195i	$-0.773428\pi$
$653$	−9513.09	+	5492.39i	−0.570101	+	0.329148i	0.187089	+	0.982343i	$0.440095\pi$
$654$		0			0
$655$	−3694.84	+	6399.66i	−0.220411	+	0.381764i
$656$	−1729.03	−	2994.77i	−0.102907	−	0.178241i
$657$		0			0
$658$		0			0
$659$		−	8581.81i		−	0.507283i	−0.967298	−	0.253642i	$-0.918372\pi$
$659$		−	8581.81i		−	0.507283i	0.967298	−	0.253642i	$-0.0816284\pi$
$660$		0			0
$661$	11784.8	+	6803.96i	0.693458	+	0.400368i	0.804906	−	0.593402i	$-0.202216\pi$
$661$	11784.8	+	6803.96i	0.693458	+	0.400368i	−0.111448	+	0.993770i	$0.535549\pi$
$662$	13411.3	+	7743.01i	0.787378	+	0.454593i
$663$		0			0
$664$			4665.38i			0.272668i
$665$		0			0
$666$		0			0
$667$	−5785.16	−	10020.2i	−0.335836	−	0.581685i
$668$	8154.30	−	14123.7i	0.472305	−	0.818056i
$669$		0			0
$670$	1375.66	−	794.240i	0.0793232	−	0.0457973i
$671$	−191.108			−0.0109950
$672$		0			0
$673$	−21092.1			−1.20809			−0.604043	−	0.796951i	$-0.706445\pi$
$673$	−21092.1			−1.20809			−0.604043	+	0.796951i	$0.706445\pi$
$674$	18184.3	−	10498.7i	1.03922	−	0.599992i
$675$		0			0
$676$	−6141.88	+	10638.0i	−0.349447	+	0.605260i
$677$	8037.22	+	13920.9i	0.456271	+	0.790285i	0.998760	−	0.0497780i	$-0.0158514\pi$
$677$	8037.22	+	13920.9i	0.456271	+	0.790285i	−0.542489	+	0.840063i	$0.682518\pi$
$678$		0			0
$679$		0			0
$680$			2104.69i			0.118693i
$681$		0			0
$682$	−26.2713	−	15.1677i	−0.00147504	−	0.000851617i
$683$	13172.5	+	7605.13i	0.737966	+	0.426065i	0.821329	−	0.570455i	$-0.193233\pi$
$683$	13172.5	+	7605.13i	0.737966	+	0.426065i	−0.0833636	+	0.996519i	$0.526566\pi$
$684$		0			0
$685$		−	8326.97i		−	0.464463i
$686$		0			0
$687$		0			0
$688$	113.998	+	197.451i	0.00631707	+	0.0109415i
$689$	7363.98	−	12754.8i	0.407178	−	0.705252i
$690$		0			0
$691$	12910.4	−	7453.83i	0.710760	−	0.410358i	−0.100582	−	0.994929i	$-0.532071\pi$
$691$	12910.4	−	7453.83i	0.710760	−	0.410358i	0.811342	+	0.584571i	$0.198737\pi$
$692$	4599.82			0.252686
$693$		0			0
$694$	−6733.25			−0.368286
$695$	6187.49	−	3572.35i	0.337705	−	0.194974i
$696$		0			0
$697$	4795.52	−	8306.09i	0.260607	−	0.451385i
$698$	1047.69	+	1814.65i	0.0568133	+	0.0984035i
$699$		0			0
$700$		0			0
$701$			2306.38i			0.124266i	0.998068	+	0.0621331i	$0.0197903\pi$
$701$			2306.38i			0.124266i	−0.998068	+	0.0621331i	$0.980210\pi$
$702$		0			0
$703$	−20875.0	−	12052.2i	−1.11994	−	0.646597i
$704$	−16.7117	−	9.64849i	−0.000894666	−	0.000516536i
$705$		0			0
$706$			10887.4i			0.580384i
$707$		0			0
$708$		0			0
$709$	−13208.3	−	22877.5i	−0.699645	−	1.21182i	−0.968590	−	0.248665i	$-0.920008\pi$
$709$	−13208.3	−	22877.5i	−0.699645	−	1.21182i	0.268945	−	0.963156i	$-0.413325\pi$
$710$	−6217.91	+	10769.7i	−0.328668	+	0.569269i
$711$		0			0
$712$	9090.01	−	5248.12i	0.478459	−	0.276238i
$713$	−3179.94			−0.167026
$714$		0			0
$715$	129.740			0.00678603
$716$	12684.3	−	7323.27i	0.662058	−	0.382240i
$717$		0			0
$718$	1116.78	−	1934.33i	0.0580473	−	0.100541i
$719$	8803.21	+	15247.6i	0.456613	+	0.790876i	0.998779	−	0.0493947i	$-0.0157292\pi$
$719$	8803.21	+	15247.6i	0.456613	+	0.790876i	−0.542167	+	0.840271i	$0.682396\pi$
$720$		0			0
$721$		0			0
$722$		−	541.411i		−	0.0279075i
$723$		0			0
$724$	−14929.0	−	8619.26i	−0.766342	−	0.442448i
$725$	−14243.0	−	8223.18i	−0.729614	−	0.421243i
$726$		0			0
$727$			5209.41i			0.265758i	0.991132	+	0.132879i	$0.0424222\pi$
$727$			5209.41i			0.265758i	−0.991132	+	0.132879i	$0.957578\pi$
$728$		0			0
$729$		0			0
$730$	−903.229	−	1564.44i	−0.0457945	−	0.0793185i
$731$	−316.178	+	547.636i	−0.0159976	+	0.0277087i
$732$		0			0
$733$	1735.56	−	1002.03i	0.0874550	−	0.0504922i	−0.455635	−	0.890167i	$-0.650588\pi$
$733$	1735.56	−	1002.03i	0.0874550	−	0.0504922i	0.543090	+	0.839675i	$0.317254\pi$
$734$	15305.7			0.769680
$735$		0			0
$736$	−2022.82			−0.101307
$737$	−34.9821	+	20.1969i	−0.00174842	+	0.00100945i
$738$		0			0
$739$	−1847.19	+	3199.42i	−0.0919485	+	0.159259i	−0.908331	−	0.418252i	$-0.862643\pi$
$739$	−1847.19	+	3199.42i	−0.0919485	+	0.159259i	0.816382	+	0.577512i	$0.195976\pi$
$740$	3384.82	+	5862.69i	0.168147	+	0.291239i
$741$		0			0
$742$		0			0
$743$		−	15503.5i		−	0.765502i	−0.923851	−	0.382751i	$-0.874977\pi$
$743$		−	15503.5i		−	0.765502i	0.923851	−	0.382751i	$-0.125023\pi$
$744$		0			0
$745$	−11481.9	−	6629.10i	−0.564652	−	0.326002i
$746$	19904.8	+	11492.1i	0.976900	+	0.564013i
$747$		0			0
$748$		−	53.5208i		−	0.00261620i
$749$		0			0
$750$		0			0
$751$	−6996.78	−	12118.8i	−0.339968	−	0.588843i	0.644458	−	0.764640i	$-0.277083\pi$
$751$	−6996.78	−	12118.8i	−0.339968	−	0.588843i	−0.984426	+	0.175797i	$0.943750\pi$
$752$	−3389.01	+	5869.94i	−0.164341	+	0.284647i
$753$		0			0
$754$	23010.1	−	13284.9i	1.11138	−	0.641655i
$755$	9523.53			0.459069
$756$		0			0
$757$	−21959.1			−1.05431			−0.527157	−	0.849768i	$-0.676742\pi$
$757$	−21959.1			−1.05431			−0.527157	+	0.849768i	$0.676742\pi$
$758$	14179.5	−	8186.54i	0.679449	−	0.392280i
$759$		0			0
$760$	−2002.35	+	3468.18i	−0.0955698	+	0.165532i
$761$	−10181.0	−	17634.1i	−0.484970	−	0.839992i	0.514881	−	0.857262i	$-0.327836\pi$
$761$	−10181.0	−	17634.1i	−0.484970	−	0.839992i	−0.999851	+	0.0172695i	$0.994503\pi$
$762$		0			0
$763$		0			0
$764$		−	16860.0i		−	0.798392i
$765$		0			0
$766$	3585.36	+	2070.01i	0.169118	+	0.0976402i
$767$	−46164.2	−	26652.9i	−2.17326	−	1.25473i
$768$		0			0
$769$			11078.4i			0.519501i	0.965676	+	0.259750i	$0.0836403\pi$
$769$			11078.4i			0.519501i	−0.965676	+	0.259750i	$0.916360\pi$
$770$		0			0
$771$		0			0
$772$	2894.53	+	5013.47i	0.134944	+	0.233729i
$773$	16013.7	−	27736.5i	0.745112	−	1.29057i	−0.205031	−	0.978756i	$-0.565729\pi$
$773$	16013.7	−	27736.5i	0.745112	−	1.29057i	0.950142	−	0.311816i	$-0.100937\pi$
$774$		0			0
$775$	−3914.48	+	2260.02i	−0.181435	+	0.104752i
$776$	−3277.06			−0.151598
$777$		0			0
$778$	1282.74			0.0591112
$779$	15804.4	−	9124.69i	0.726897	−	0.419674i
$780$		0			0
$781$	158.117	−	273.866i	0.00724439	−	0.0125476i
$782$	−2805.18	−	4858.72i	−0.128278	−	0.222183i
$783$		0			0
$784$		0			0
$785$		−	8239.43i		−	0.374621i
$786$		0			0
$787$	15550.2	+	8977.93i	0.704327	+	0.406644i	0.808957	−	0.587868i	$-0.200032\pi$
$787$	15550.2	+	8977.93i	0.704327	+	0.406644i	−0.104630	+	0.994511i	$0.533366\pi$
$788$	1817.60	+	1049.39i	0.0821692	+	0.0474404i
$789$		0			0
$790$			9718.90i			0.437700i
$791$		0			0
$792$		0			0
$793$	−23001.7	−	39840.2i	−1.03003	−	1.78407i
$794$	−10496.2	+	18180.0i	−0.469140	+	0.812575i
$795$		0			0
$796$	−837.636	+	483.610i	−0.0372980	+	0.0215340i
$797$	−34542.4			−1.53520			−0.767601	−	0.640928i	$-0.778550\pi$
$797$	−34542.4			−1.53520			−0.767601	+	0.640928i	$0.778550\pi$
$798$		0			0
$799$	−18799.1			−0.832370
$800$	−2490.07	+	1437.65i	−0.110047	+	0.0635355i
$801$		0			0
$802$	−8862.36	+	15350.1i	−0.390201	+	0.675847i
$803$	22.9685	+	39.7826i	0.00100939	+	0.00174831i
$804$		0			0
$805$		0			0
$806$		−	7302.34i		−	0.319124i
$807$		0			0
$808$	−12642.3	−	7299.03i	−0.550439	−	0.317796i
$809$	29119.4	+	16812.1i	1.26549	+	0.730633i	0.974132	−	0.225979i	$-0.0725582\pi$
$809$	29119.4	+	16812.1i	1.26549	+	0.730633i	0.291362	+	0.956613i	$0.405892\pi$
$810$		0			0
$811$			27864.3i			1.20647i	0.797563	+	0.603235i	$0.206122\pi$
$811$			27864.3i			1.20647i	−0.797563	+	0.603235i	$0.793878\pi$
$812$		0			0
$813$		0			0
$814$	−86.0736	−	149.084i	−0.00370624	−	0.00641939i
$815$	−5158.22	+	8934.31i	−0.221699	+	0.383994i
$816$		0			0
$817$	−1042.02	+	601.609i	−0.0446212	+	0.0257621i
$818$	−17793.3			−0.760546
$819$		0			0
$820$	−5125.28			−0.218271
$821$	−22105.1	+	12762.4i	−0.939677	+	0.542523i	−0.889859	−	0.456235i	$-0.849197\pi$
$821$	−22105.1	+	12762.4i	−0.939677	+	0.542523i	−0.0498181	+	0.998758i	$0.515864\pi$
$822$		0			0
$823$	17378.7	−	30100.8i	0.736069	−	1.27491i	−0.218184	−	0.975908i	$-0.570013\pi$
$823$	17378.7	−	30100.8i	0.736069	−	1.27491i	0.954253	−	0.299001i	$-0.0966533\pi$
$824$	−4952.74	−	8578.40i	−0.209389	−	0.362673i
$825$		0			0
$826$		0			0
$827$		−	11443.1i		−	0.481155i	−0.970630	−	0.240577i	$-0.922663\pi$
$827$		−	11443.1i		−	0.481155i	0.970630	−	0.240577i	$-0.0773368\pi$
$828$		0			0
$829$	17909.6	+	10340.1i	0.750333	+	0.433205i	0.825814	−	0.563942i	$-0.190716\pi$
$829$	17909.6	+	10340.1i	0.750333	+	0.433205i	−0.0754813	+	0.997147i	$0.524049\pi$
$830$	5988.29	+	3457.34i	0.250430	+	0.144586i
$831$		0			0
$832$		−	4645.16i		−	0.193560i
$833$		0			0
$834$		0			0
$835$	−12085.7	−	20933.1i	−0.500890	−	0.867567i
$836$	50.9184	−	88.1933i	0.00210652	−	0.00364860i
$837$		0			0
$838$	−25533.7	+	14741.9i	−1.05256	+	0.607698i
$839$	−18946.5			−0.779626			−0.389813	−	0.920894i	$-0.627460\pi$
$839$	−18946.5			−0.779626			−0.389813	+	0.920894i	$0.627460\pi$
$840$		0			0
$841$	−9113.39			−0.373668
$842$	1456.80	−	841.087i	0.0596257	−	0.0344249i
$843$		0			0
$844$	−851.615	+	1475.04i	−0.0347320	+	0.0601575i
$845$	9103.04	+	15766.9i	0.370597	+	0.641892i
$846$		0			0
$847$		0			0
$848$			3246.70i			0.131477i
$849$		0			0
$850$	−6906.30	−	3987.36i	−0.278687	−	0.160900i
$851$	−15627.8	−	9022.74i	−0.629513	−	0.363450i
$852$		0			0
$853$		−	31070.4i		−	1.24716i	−0.781758	−	0.623582i	$-0.785677\pi$
$853$		−	31070.4i		−	1.24716i	0.781758	−	0.623582i	$-0.214323\pi$
$854$		0			0
$855$		0			0
$856$	−6652.08	−	11521.7i	−0.265612	−	0.460053i
$857$	−2273.62	+	3938.03i	−0.0906249	+	0.156967i	−0.907774	−	0.419459i	$-0.862220\pi$
$857$	−2273.62	+	3938.03i	−0.0906249	+	0.156967i	0.817149	+	0.576426i	$0.195553\pi$
$858$		0			0
$859$	−8093.86	+	4672.99i	−0.321489	+	0.185612i	−0.652056	−	0.758171i	$-0.726093\pi$
$859$	−8093.86	+	4672.99i	−0.321489	+	0.185612i	0.330567	+	0.943782i	$0.392760\pi$
$860$	337.920			0.0133988
$861$		0			0
$862$	15415.1			0.609097
$863$	40356.5	−	23299.8i	1.59183	−	0.919044i	0.598838	−	0.800870i	$-0.295629\pi$
$863$	40356.5	−	23299.8i	1.59183	−	0.919044i	0.992993	−	0.118174i	$-0.0377041\pi$
$864$		0			0
$865$	3408.76	−	5904.15i	0.133990	−	0.232077i
$866$	9675.58	+	16758.6i	0.379665	+	0.657598i
$867$		0			0
$868$		0			0
$869$		−	247.145i		−	0.00964765i
$870$		0			0
$871$	−8420.88	−	4861.80i	−0.327590	−	0.189134i
$872$	9594.54	+	5539.41i	0.372606	+	0.215124i
$873$		0			0
$874$		−	10675.1i		−	0.413149i
$875$		0			0
$876$		0			0
$877$	−14426.8	−	24987.9i	−0.555482	−	0.962122i	−0.997866	−	0.0652967i	$-0.979201\pi$
$877$	−14426.8	−	24987.9i	−0.555482	−	0.962122i	0.442384	−	0.896826i	$-0.354133\pi$
$878$	6444.15	−	11161.6i	0.247699	−	0.429027i
$879$		0			0
$880$	−24.7688	+	14.3003i	−0.000948814	+	0.000547798i
$881$	−5508.01			−0.210635			−0.105317	−	0.994439i	$-0.533586\pi$
$881$	−5508.01			−0.210635			−0.105317	+	0.994439i	$0.533586\pi$
$882$		0			0
$883$	23461.7			0.894168			0.447084	−	0.894492i	$-0.352463\pi$
$883$	23461.7			0.894168			0.447084	+	0.894492i	$0.352463\pi$
$884$	11157.4	−	6441.75i	0.424508	−	0.245090i
$885$		0			0
$886$	272.880	−	472.642i	0.0103472	−	0.0179218i
$887$	−15920.2	−	27574.5i	−0.602646	−	1.04381i	−0.992419	−	0.122902i	$-0.960780\pi$
$887$	−15920.2	−	27574.5i	−0.602646	−	1.04381i	0.389773	−	0.920911i	$-0.372553\pi$
$888$		0			0
$889$		0			0
$890$		−	15556.8i		−	0.585914i
$891$		0			0
$892$	20324.8	+	11734.5i	0.762919	+	0.440471i
$893$	−30977.7	−	17885.0i	−1.16084	−	0.670211i
$894$		0			0
$895$		−	21708.0i		−	0.810748i
$896$		0			0
$897$		0			0
$898$	599.676	+	1038.67i	0.0222844	+	0.0385978i
$899$	−4603.83	+	7974.07i	−0.170797	+	0.295829i
$900$		0			0
$901$	−7798.42	+	4502.42i	−0.288350	+	0.166479i
$902$	130.332			0.00481107
$903$		0			0
$904$	−9958.05			−0.366372
$905$	−22126.6	+	12774.8i	−0.812723	+	0.469226i
$906$		0			0
$907$	12707.9	−	22010.8i	0.465225	−	0.805794i	−0.533986	−	0.845493i	$-0.679307\pi$
$907$	12707.9	−	22010.8i	0.465225	−	0.805794i	0.999212	+	0.0396992i	$0.0126400\pi$
$908$	7679.16	+	13300.7i	0.280663	+	0.486122i
$909$		0			0
$910$		0			0
$911$		−	45216.6i		−	1.64445i	−0.569165	−	0.822224i	$-0.692733\pi$
$911$		−	45216.6i		−	1.64445i	0.569165	−	0.822224i	$-0.307267\pi$
$912$		0			0
$913$	−152.278	−	87.9177i	−0.00551989	−	0.00318691i
$914$	−1637.01	−	945.127i	−0.0592423	−	0.0342035i
$915$		0			0
$916$		−	9609.24i		−	0.346614i
$917$		0			0
$918$		0			0
$919$	12586.0	+	21799.6i	0.451767	+	0.782483i	0.998496	−	0.0548264i	$-0.0174605\pi$
$919$	12586.0	+	21799.6i	0.451767	+	0.782483i	−0.546729	+	0.837310i	$0.684127\pi$
$920$	−1499.04	+	2596.41i	−0.0537194	+	0.0930448i
$921$		0			0
$922$	−2016.84	+	1164.43i	−0.0720404	+	0.0415925i
$923$	76123.6			2.71467
$924$		0			0
$925$	−25650.3			−0.911758
$926$	29986.6	−	17312.8i	1.06417	−	0.614399i
$927$		0			0
$928$	−2928.59	+	5072.46i	−0.103594	+	0.179431i
$929$	3130.74	+	5422.59i	0.110566	+	0.191506i	0.915999	−	0.401181i	$-0.131400\pi$
$929$	3130.74	+	5422.59i	0.110566	+	0.191506i	−0.805432	+	0.592688i	$0.798067\pi$
$930$		0			0
$931$		0			0
$932$		−	8689.77i		−	0.305411i
$933$		0			0
$934$	2067.75	+	1193.81i	0.0724397	+	0.0418231i
$935$	−68.6971	−	39.6623i	−0.00240282	−	0.00138727i
$936$		0			0
$937$		−	11786.7i		−	0.410946i	−0.978663	−	0.205473i	$-0.934127\pi$
$937$		−	11786.7i		−	0.410946i	0.978663	−	0.205473i	$-0.0658732\pi$
$938$		0			0
$939$		0			0
$940$	5022.94	+	8699.99i	0.174288	+	0.301875i
$941$	−13564.8	+	23495.0i	−0.469927	+	0.813937i	−0.999409	−	0.0343840i	$-0.989053\pi$
$941$	−13564.8	+	23495.0i	−0.469927	+	0.813937i	0.529482	+	0.848321i	$0.322386\pi$
$942$		0			0
$943$	11831.8	−	6831.09i	0.408586	−	0.235897i
$944$	11751.0			0.405150
$945$		0			0
$946$	−8.59305			−0.000295332
$947$	−22387.0	+	12925.1i	−0.768195	+	0.443517i	−0.832230	−	0.554430i	$-0.812936\pi$
$947$	−22387.0	+	12925.1i	−0.768195	+	0.443517i	0.0640356	+	0.997948i	$0.479603\pi$
$948$		0			0
$949$	−5528.96	+	9576.43i	−0.189123	+	0.327570i
$950$	−7586.95	−	13141.0i	−0.259109	−	0.448790i
$951$		0			0
$952$		0			0
$953$			832.068i			0.0282826i	0.999900	+	0.0141413i	$0.00450147\pi$
$953$			832.068i			0.0282826i	−0.999900	+	0.0141413i	$0.995499\pi$
$954$		0			0
$955$	−21640.8	−	12494.3i	−0.733276	−	0.423357i
$956$	−3916.40	−	2261.13i	−0.132495	−	0.0764962i
$957$		0			0
$958$		−	27369.5i		−	0.923034i
$959$		0			0
$960$		0			0
$961$	−13630.2	−	23608.2i	−0.457527	−	0.792461i
$962$	20719.6	−	35887.4i	0.694414	−	1.20276i
$963$		0			0
$964$	−16335.5	+	9431.29i	−0.545778	+	0.315105i
$965$	8580.12			0.286222
$966$		0			0
$967$	51021.0			1.69672			0.848358	−	0.529423i	$-0.177592\pi$
$967$	51021.0			1.69672			0.848358	+	0.529423i	$0.177592\pi$
$968$	−9220.81	+	5323.64i	−0.306165	+	0.176765i
$969$		0			0
$970$	−2428.51	+	4206.30i	−0.0803864	+	0.139233i
$971$	−7589.01	−	13144.5i	−0.250816	−	0.434427i	0.712934	−	0.701231i	$-0.247366\pi$
$971$	−7589.01	−	13144.5i	−0.250816	−	0.434427i	−0.963751	+	0.266804i	$0.914032\pi$
$972$		0			0
$973$		0			0
$974$		−	15862.6i		−	0.521837i
$975$		0			0
$976$	8782.56	+	5070.61i	0.288036	+	0.166298i
$977$	−34167.6	−	19726.7i	−1.11885	−	0.645969i	−0.177744	−	0.984077i	$-0.556880\pi$
$977$	−34167.6	−	19726.7i	−1.11885	−	0.645969i	−0.941108	+	0.338107i	$0.890213\pi$
$978$		0			0
$979$			395.597i			0.0129145i
$980$		0			0
$981$		0			0
$982$	−486.246	−	842.203i	−0.0158012	−	0.0273684i
$983$	−21831.6	+	37813.4i	−0.708361	+	1.22692i	0.257103	+	0.966384i	$0.417232\pi$
$983$	−21831.6	+	37813.4i	−0.708361	+	1.22692i	−0.965465	+	0.260534i	$0.916101\pi$
$984$		0			0
$985$	2693.91	−	1555.33i	0.0871423	−	0.0503117i
$986$	−16245.1			−0.524694
$987$		0			0
$988$	24514.1			0.789370
$989$	−780.094	+	450.387i	−0.0250814	+	0.0144808i
$990$		0			0
$991$	4278.28	−	7410.20i	0.137138	−	0.237531i	−0.789274	−	0.614041i	$-0.789543\pi$
$991$	4278.28	−	7410.20i	0.137138	−	0.237531i	0.926412	+	0.376511i	$0.122876\pi$
$992$	804.881	+	1394.09i	0.0257611	+	0.0446195i
$993$		0			0
$994$		0			0
$995$			1433.54i			0.0456747i
$996$		0			0
$997$	−689.352	−	397.998i	−0.0218977	−	0.0126426i	0.489011	−	0.872278i	$-0.337358\pi$
$997$	−689.352	−	397.998i	−0.0218977	−	0.0126426i	−0.510909	+	0.859635i	$0.670691\pi$
$998$	32792.7	+	18932.9i	1.04011	+	0.600510i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.4.k.c.521.6		16
3.2	odd	2	inner	882.4.k.c.521.3		16
7.2	even	3	inner	882.4.k.c.215.2		16
7.3	odd	6		126.4.d.a.125.6	yes	8
7.4	even	3		126.4.d.a.125.7	yes	8
7.5	odd	6	inner	882.4.k.c.215.3		16
7.6	odd	2	inner	882.4.k.c.521.7		16
21.2	odd	6	inner	882.4.k.c.215.7		16
21.5	even	6	inner	882.4.k.c.215.6		16
21.11	odd	6		126.4.d.a.125.2	✓	8
21.17	even	6		126.4.d.a.125.3	yes	8
21.20	even	2	inner	882.4.k.c.521.2		16
28.3	even	6		1008.4.k.c.881.4		8
28.11	odd	6		1008.4.k.c.881.5		8
84.11	even	6		1008.4.k.c.881.3		8
84.59	odd	6		1008.4.k.c.881.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.4.d.a.125.2	✓	8	21.11	odd	6
126.4.d.a.125.3	yes	8	21.17	even	6
126.4.d.a.125.6	yes	8	7.3	odd	6
126.4.d.a.125.7	yes	8	7.4	even	3
882.4.k.c.215.2		16	7.2	even	3	inner
882.4.k.c.215.3		16	7.5	odd	6	inner
882.4.k.c.215.6		16	21.5	even	6	inner
882.4.k.c.215.7		16	21.2	odd	6	inner
882.4.k.c.521.2		16	21.20	even	2	inner
882.4.k.c.521.3		16	3.2	odd	2	inner
882.4.k.c.521.6		16	1.1	even	1	trivial
882.4.k.c.521.7		16	7.6	odd	2	inner
1008.4.k.c.881.3		8	84.11	even	6
1008.4.k.c.881.4		8	28.3	even	6
1008.4.k.c.881.5		8	28.11	odd	6
1008.4.k.c.881.6		8	84.59	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	882.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 - 1.00000i) q^{2} +(2.00000 - 3.46410i) q^{4} +(-2.96425 - 5.13424i) q^{5} -8.00000i q^{8} +O(q^{10})\)	\(q+(1.73205 - 1.00000i) q^{2} +(2.00000 - 3.46410i) q^{4} +(-2.96425 - 5.13424i) q^{5} -8.00000i q^{8} +(-10.2685 - 5.92851i) q^{10} +(0.261120 + 0.150758i) q^{11} +72.5806i q^{13} +(-8.00000 - 13.8564i) q^{16} +(22.1883 - 38.4312i) q^{17} +(73.1251 - 42.2188i) q^{19} -23.7140 q^{20} +0.603030 q^{22} +(54.7442 - 31.6066i) q^{23} +(44.9264 - 77.8148i) q^{25} +(72.5806 + 125.713i) q^{26} -183.037i q^{29} +(-43.5654 - 25.1525i) q^{31} +(-27.7128 - 16.0000i) q^{32} -88.7531i q^{34} +(-142.735 - 247.224i) q^{37} +(84.4376 - 146.250i) q^{38} +(-41.0739 + 23.7140i) q^{40} +216.129 q^{41} -14.2498 q^{43} +(1.04448 - 0.603030i) q^{44} +(63.2132 - 109.488i) q^{46} +(-211.813 - 366.871i) q^{47} -179.706i q^{50} +(251.426 + 145.161i) q^{52} +(-175.733 - 101.459i) q^{53} -1.78753i q^{55} +(-183.037 - 317.029i) q^{58} +(-367.218 + 636.041i) q^{59} +(-548.910 + 316.913i) q^{61} -100.610 q^{62} -64.0000 q^{64} +(372.646 - 215.147i) q^{65} +(-66.9848 + 116.021i) q^{67} +(-88.7531 - 153.725i) q^{68} -1048.82i q^{71} +(131.942 + 76.1768i) q^{73} +(-494.449 - 285.470i) q^{74} -337.750i q^{76} +(-409.838 - 709.860i) q^{79} +(-47.4280 + 82.1478i) q^{80} +(374.346 - 216.129i) q^{82} -583.173 q^{83} -263.087 q^{85} +(-24.6813 + 14.2498i) q^{86} +(1.20606 - 2.08896i) q^{88} +(656.015 + 1136.25i) q^{89} -252.853i q^{92} +(-733.742 - 423.626i) q^{94} +(-433.523 - 250.294i) q^{95} -409.633i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4}+O(q^{10}) \) 16 * q + 32 * q^4	\( 16 q + 32 q^{4} - 128 q^{16} + 960 q^{22} + 40 q^{25} + 160 q^{37} + 2080 q^{43} + 672 q^{46} - 960 q^{58} - 1024 q^{64} + 3680 q^{67} - 448 q^{79} + 13440 q^{85} + 1920 q^{88}+O(q^{100}) \) 16 * q + 32 * q^4 - 128 * q^16 + 960 * q^22 + 40 * q^25 + 160 * q^37 + 2080 * q^43 + 672 * q^46 - 960 * q^58 - 1024 * q^64 + 3680 * q^67 - 448 * q^79 + 13440 * q^85 + 1920 * q^88

Introduction

L-functions

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