LMFDB - Embedded newform 275.3.f.c.243.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(232,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.232"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			243.9
Character	$\chi$	$=$	275.243
Dual form			275.3.f.c.232.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.02070 - 1.02070i) q^{2} +(-0.314710 - 0.314710i) q^{3} +1.91636i q^{4} -0.642447 q^{6} +(-6.75035 + 6.75035i) q^{7} +(6.03880 + 6.03880i) q^{8} -8.80192i q^{9} -3.31662 q^{11} +(0.603097 - 0.603097i) q^{12} +(16.4951 + 16.4951i) q^{13} +13.7801i q^{14} +4.66213 q^{16} +(-17.2945 + 17.2945i) q^{17} +(-8.98408 - 8.98408i) q^{18} +28.5631i q^{19} +4.24881 q^{21} +(-3.38527 + 3.38527i) q^{22} +(5.89670 + 5.89670i) q^{23} -3.80095i q^{24} +33.6731 q^{26} +(-5.60244 + 5.60244i) q^{27} +(-12.9361 - 12.9361i) q^{28} -43.9338i q^{29} +36.3584 q^{31} +(-19.3966 + 19.3966i) q^{32} +(1.04378 + 1.04378i) q^{33} +35.3049i q^{34} +16.8676 q^{36} +(21.6303 - 21.6303i) q^{37} +(29.1542 + 29.1542i) q^{38} -10.3824i q^{39} -34.5897 q^{41} +(4.33674 - 4.33674i) q^{42} +(6.04730 + 6.04730i) q^{43} -6.35584i q^{44} +12.0375 q^{46} +(-12.0604 + 12.0604i) q^{47} +(-1.46722 - 1.46722i) q^{48} -42.1345i q^{49} +10.8855 q^{51} +(-31.6106 + 31.6106i) q^{52} +(-40.1140 - 40.1140i) q^{53} +11.4368i q^{54} -81.5281 q^{56} +(8.98910 - 8.98910i) q^{57} +(-44.8431 - 44.8431i) q^{58} -15.3852i q^{59} +116.136 q^{61} +(37.1108 - 37.1108i) q^{62} +(59.4160 + 59.4160i) q^{63} +58.2446i q^{64} +2.13075 q^{66} +(39.2934 - 39.2934i) q^{67} +(-33.1425 - 33.1425i) q^{68} -3.71150i q^{69} -53.8611 q^{71} +(53.1530 - 53.1530i) q^{72} +(-20.3789 - 20.3789i) q^{73} -44.1559i q^{74} -54.7372 q^{76} +(22.3884 - 22.3884i) q^{77} +(-10.5973 - 10.5973i) q^{78} +0.0339654i q^{79} -75.6909 q^{81} +(-35.3056 + 35.3056i) q^{82} +(10.5848 + 10.5848i) q^{83} +8.14224i q^{84} +12.3449 q^{86} +(-13.8264 + 13.8264i) q^{87} +(-20.0284 - 20.0284i) q^{88} -89.4830i q^{89} -222.696 q^{91} +(-11.3002 + 11.3002i) q^{92} +(-11.4423 - 11.4423i) q^{93} +24.6200i q^{94} +12.2086 q^{96} +(23.9332 - 23.9332i) q^{97} +(-43.0065 - 43.0065i) q^{98} +29.1926i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{6} - 128 q^{16} - 88 q^{21} + 96 q^{26} + 360 q^{31} + 176 q^{36} - 152 q^{41} + 56 q^{46} - 512 q^{51} - 1048 q^{56} + 784 q^{61} - 440 q^{66} + 728 q^{71} + 1704 q^{76} - 568 q^{81} - 328 q^{86}+ \cdots + 1568 q^{96}+O(q^{100}) $ 24 * q - 8 * q^6 - 128 * q^16 - 88 * q^21 + 96 * q^26 + 360 * q^31 + 176 * q^36 - 152 * q^41 + 56 * q^46 - 512 * q^51 - 1048 * q^56 + 784 * q^61 - 440 * q^66 + 728 * q^71 + 1704 * q^76 - 568 * q^81 - 328 * q^86 - 968 * q^91 + 1568 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.02070	−	1.02070i	0.510348	−	0.510348i	−0.404285	−	0.914633i	$-0.632480\pi$
$2$	1.02070	−	1.02070i	0.510348	−	0.510348i	0.914633	+	0.404285i	$0.132480\pi$
$3$	−0.314710	−	0.314710i	−0.104903	−	0.104903i	0.652707	−	0.757610i	$-0.273633\pi$
$3$	−0.314710	−	0.314710i	−0.104903	−	0.104903i	−0.757610	+	0.652707i	$0.773633\pi$
$4$			1.91636i			0.479090i
$5$		0			0
$5$		0			0
$6$	−0.642447			−0.107074
$7$	−6.75035	+	6.75035i	−0.964336	+	0.964336i	−0.999386	−	0.0350498i	$-0.988841\pi$
$7$	−6.75035	+	6.75035i	−0.964336	+	0.964336i	0.0350498	+	0.999386i	$0.488841\pi$
$8$	6.03880	+	6.03880i	0.754851	+	0.754851i
$9$		−	8.80192i		−	0.977991i
$10$		0			0
$11$	−3.31662			−0.301511
$11$	−3.31662			−0.301511
$12$	0.603097	−	0.603097i	0.0502581	−	0.0502581i
$13$	16.4951	+	16.4951i	1.26886	+	1.26886i	0.946679	+	0.322178i	$0.104415\pi$
$13$	16.4951	+	16.4951i	1.26886	+	1.26886i	0.322178	+	0.946679i	$0.395585\pi$
$14$			13.7801i			0.984294i
$15$		0			0
$16$	4.66213			0.291383
$17$	−17.2945	+	17.2945i	−1.01732	+	1.01732i	−0.0174773	+	0.999847i	$0.505563\pi$
$17$	−17.2945	+	17.2945i	−1.01732	+	1.01732i	−0.999847	+	0.0174773i	$0.994437\pi$
$18$	−8.98408	−	8.98408i	−0.499116	−	0.499116i
$19$			28.5631i			1.50332i	0.659550	+	0.751661i	$0.270747\pi$
$19$			28.5631i			1.50332i	−0.659550	+	0.751661i	$0.729253\pi$
$20$		0			0
$21$	4.24881			0.202324
$22$	−3.38527	+	3.38527i	−0.153876	+	0.153876i
$23$	5.89670	+	5.89670i	0.256378	+	0.256378i	0.823579	−	0.567201i	$-0.191974\pi$
$23$	5.89670	+	5.89670i	0.256378	+	0.256378i	−0.567201	+	0.823579i	$0.691974\pi$
$24$		−	3.80095i		−	0.158373i
$25$		0			0
$26$	33.6731			1.29512
$27$	−5.60244	+	5.60244i	−0.207498	+	0.207498i
$28$	−12.9361	−	12.9361i	−0.462003	−	0.462003i
$29$		−	43.9338i		−	1.51496i	−0.652859	−	0.757479i	$-0.726431\pi$
$29$		−	43.9338i		−	1.51496i	0.652859	−	0.757479i	$-0.273569\pi$
$30$		0			0
$31$	36.3584			1.17285			0.586425	−	0.810003i	$-0.300535\pi$
$31$	36.3584			1.17285			0.586425	+	0.810003i	$0.300535\pi$
$32$	−19.3966	+	19.3966i	−0.606144	+	0.606144i
$33$	1.04378	+	1.04378i	0.0316296	+	0.0316296i
$34$			35.3049i			1.03838i
$35$		0			0
$36$	16.8676			0.468545
$37$	21.6303	−	21.6303i	0.584602	−	0.584602i	−0.351562	−	0.936165i	$-0.614349\pi$
$37$	21.6303	−	21.6303i	0.584602	−	0.584602i	0.936165	+	0.351562i	$0.114349\pi$
$38$	29.1542	+	29.1542i	0.767217	+	0.767217i
$39$		−	10.3824i		−	0.266215i
$40$		0			0
$41$	−34.5897			−0.843651			−0.421826	−	0.906677i	$-0.638611\pi$
$41$	−34.5897			−0.843651			−0.421826	+	0.906677i	$0.638611\pi$
$42$	4.33674	−	4.33674i	0.103256	−	0.103256i
$43$	6.04730	+	6.04730i	0.140635	+	0.140635i	0.773919	−	0.633284i	$-0.218294\pi$
$43$	6.04730	+	6.04730i	0.140635	+	0.140635i	−0.633284	+	0.773919i	$0.718294\pi$
$44$		−	6.35584i		−	0.144451i
$45$		0			0
$46$	12.0375			0.261684
$47$	−12.0604	+	12.0604i	−0.256604	+	0.256604i	−0.823671	−	0.567068i	$-0.808078\pi$
$47$	−12.0604	+	12.0604i	−0.256604	+	0.256604i	0.567068	+	0.823671i	$0.308078\pi$
$48$	−1.46722	−	1.46722i	−0.0305671	−	0.0305671i
$49$		−	42.1345i		−	0.859887i
$50$		0			0
$51$	10.8855			0.213442
$52$	−31.6106	+	31.6106i	−0.607896	+	0.607896i
$53$	−40.1140	−	40.1140i	−0.756869	−	0.756869i	0.218882	−	0.975751i	$-0.429759\pi$
$53$	−40.1140	−	40.1140i	−0.756869	−	0.756869i	−0.975751	+	0.218882i	$0.929759\pi$
$54$			11.4368i			0.211792i
$55$		0			0
$56$	−81.5281			−1.45586
$57$	8.98910	−	8.98910i	0.157703	−	0.157703i
$58$	−44.8431	−	44.8431i	−0.773156	−	0.773156i
$59$		−	15.3852i		−	0.260766i	−0.991464	−	0.130383i	$-0.958379\pi$
$59$		−	15.3852i		−	0.260766i	0.991464	−	0.130383i	$-0.0416207\pi$
$60$		0			0
$61$	116.136			1.90387			0.951936	−	0.306297i	$-0.0990902\pi$
$61$	116.136			1.90387			0.951936	+	0.306297i	$0.0990902\pi$
$62$	37.1108	−	37.1108i	0.598562	−	0.598562i
$63$	59.4160	+	59.4160i	0.943111	+	0.943111i
$64$			58.2446i			0.910072i
$65$		0			0
$66$	2.13075			0.0322842
$67$	39.2934	−	39.2934i	0.586469	−	0.586469i	−0.350205	−	0.936673i	$-0.613888\pi$
$67$	39.2934	−	39.2934i	0.586469	−	0.586469i	0.936673	+	0.350205i	$0.113888\pi$
$68$	−33.1425	−	33.1425i	−0.487390	−	0.487390i
$69$		−	3.71150i		−	0.0537899i
$70$		0			0
$71$	−53.8611			−0.758608			−0.379304	−	0.925272i	$-0.623836\pi$
$71$	−53.8611			−0.758608			−0.379304	+	0.925272i	$0.623836\pi$
$72$	53.1530	−	53.1530i	0.738237	−	0.738237i
$73$	−20.3789	−	20.3789i	−0.279164	−	0.279164i	0.553611	−	0.832775i	$-0.313249\pi$
$73$	−20.3789	−	20.3789i	−0.279164	−	0.279164i	−0.832775	+	0.553611i	$0.813249\pi$
$74$		−	44.1559i		−	0.596701i
$75$		0			0
$76$	−54.7372			−0.720226
$77$	22.3884	−	22.3884i	0.290758	−	0.290758i
$78$	−10.5973	−	10.5973i	−0.135862	−	0.135862i
$79$			0.0339654i			0.000429942i	1.00000		0.000214971i	$6.84274e-5\pi$
$79$			0.0339654i			0.000429942i	−1.00000		0.000214971i	$0.999932\pi$
$80$		0			0
$81$	−75.6909			−0.934456
$82$	−35.3056	+	35.3056i	−0.430556	+	0.430556i
$83$	10.5848	+	10.5848i	0.127528	+	0.127528i	0.767990	−	0.640462i	$-0.221257\pi$
$83$	10.5848	+	10.5848i	0.127528	+	0.127528i	−0.640462	+	0.767990i	$0.721257\pi$
$84$			8.14224i			0.0969314i
$85$		0			0
$86$	12.3449			0.143546
$87$	−13.8264	+	13.8264i	−0.158924	+	0.158924i
$88$	−20.0284	−	20.0284i	−0.227596	−	0.227596i
$89$		−	89.4830i		−	1.00543i	−0.864453	−	0.502713i	$-0.832335\pi$
$89$		−	89.4830i		−	1.00543i	0.864453	−	0.502713i	$-0.167665\pi$
$90$		0			0
$91$	−222.696			−2.44721
$92$	−11.3002	+	11.3002i	−0.122828	+	0.122828i
$93$	−11.4423	−	11.4423i	−0.123036	−	0.123036i
$94$			24.6200i			0.261914i
$95$		0			0
$96$	12.2086			0.127173
$97$	23.9332	−	23.9332i	0.246734	−	0.246734i	−0.572895	−	0.819629i	$-0.694180\pi$
$97$	23.9332	−	23.9332i	0.246734	−	0.246734i	0.819629	+	0.572895i	$0.194180\pi$
$98$	−43.0065	−	43.0065i	−0.438842	−	0.438842i
$99$			29.1926i			0.294875i
$100$		0			0
$101$	−54.3047			−0.537670			−0.268835	−	0.963186i	$-0.586639\pi$
$101$	−54.3047			−0.537670			−0.268835	+	0.963186i	$0.586639\pi$
$102$	11.1108	−	11.1108i	0.108929	−	0.108929i
$103$	63.9888	+	63.9888i	0.621250	+	0.621250i	0.945851	−	0.324601i	$-0.105230\pi$
$103$	63.9888	+	63.9888i	0.621250	+	0.621250i	−0.324601	+	0.945851i	$0.605230\pi$
$104$			199.222i			1.91560i
$105$		0			0
$106$	−81.8885			−0.772533
$107$	42.1620	−	42.1620i	0.394037	−	0.394037i	−0.482087	−	0.876124i	$-0.660121\pi$
$107$	42.1620	−	42.1620i	0.394037	−	0.394037i	0.876124	+	0.482087i	$0.160121\pi$
$108$	−10.7363	−	10.7363i	−0.0994101	−	0.0994101i
$109$			71.8370i			0.659055i	0.944146	+	0.329527i	$0.106889\pi$
$109$			71.8370i			0.659055i	−0.944146	+	0.329527i	$0.893111\pi$
$110$		0			0
$111$	−13.6145			−0.122654
$112$	−31.4710	+	31.4710i	−0.280991	+	0.280991i
$113$	133.254	+	133.254i	1.17924	+	1.17924i	0.979938	+	0.199302i	$0.0638676\pi$
$113$	133.254	+	133.254i	1.17924	+	1.17924i	0.199302	+	0.979938i	$0.436132\pi$
$114$		−	18.3503i		−	0.160967i
$115$		0			0
$116$	84.1929			0.725801
$117$	145.189	−	145.189i	1.24093	−	1.24093i
$118$	−15.7036	−	15.7036i	−0.133082	−	0.133082i
$119$		−	233.488i		−	1.96208i
$120$		0			0
$121$	11.0000			0.0909091
$122$	118.540	−	118.540i	0.971637	−	0.971637i
$123$	10.8857	+	10.8857i	0.0885019	+	0.0885019i
$124$			69.6757i			0.561901i
$125$		0			0
$126$	121.291			0.962630
$127$	−114.645	+	114.645i	−0.902717	+	0.902717i	−0.995670	−	0.0929536i	$-0.970369\pi$
$127$	−114.645	+	114.645i	−0.902717	+	0.902717i	0.0929536	+	0.995670i	$0.470369\pi$
$128$	−18.1364	−	18.1364i	−0.141690	−	0.141690i
$129$		−	3.80629i		−	0.0295061i
$130$		0			0
$131$	246.196			1.87936			0.939679	−	0.342059i	$-0.111124\pi$
$131$	246.196			1.87936			0.939679	+	0.342059i	$0.111124\pi$
$132$	−2.00025	+	2.00025i	−0.0151534	+	0.0151534i
$133$	−192.811	−	192.811i	−1.44971	−	1.44971i
$134$		−	80.2133i		−	0.598606i
$135$		0			0
$136$	−208.876			−1.53586
$137$	−32.0054	+	32.0054i	−0.233616	+	0.233616i	−0.814200	−	0.580584i	$-0.802824\pi$
$137$	−32.0054	+	32.0054i	−0.233616	+	0.233616i	0.580584	+	0.814200i	$0.302824\pi$
$138$	−3.78831	−	3.78831i	−0.0274516	−	0.0274516i
$139$		−	26.8398i		−	0.193092i	−0.995329	−	0.0965460i	$-0.969221\pi$
$139$		−	26.8398i		−	0.193092i	0.995329	−	0.0965460i	$-0.0307795\pi$
$140$		0			0
$141$	7.59104			0.0538372
$142$	−54.9759	+	54.9759i	−0.387154	+	0.387154i
$143$	−54.7082	−	54.7082i	−0.382575	−	0.382575i
$144$		−	41.0357i		−	0.284970i
$145$		0			0
$146$	−41.6014			−0.284941
$147$	−13.2601	+	13.2601i	−0.0902050	+	0.0902050i
$148$	41.4514	+	41.4514i	0.280077	+	0.280077i
$149$		−	134.889i		−	0.905298i	−0.891689	−	0.452649i	$-0.850479\pi$
$149$		−	134.889i		−	0.905298i	0.891689	−	0.452649i	$-0.149521\pi$
$150$		0			0
$151$	197.235			1.30619			0.653096	−	0.757275i	$-0.273470\pi$
$151$	197.235			1.30619			0.653096	+	0.757275i	$0.273470\pi$
$152$	−172.487	+	172.487i	−1.13478	+	1.13478i
$153$	152.225	+	152.225i	0.994934	+	0.994934i
$154$		−	45.7035i		−	0.296776i
$155$		0			0
$156$	19.8964			0.127541
$157$	88.0904	−	88.0904i	0.561085	−	0.561085i	−0.368530	−	0.929616i	$-0.620139\pi$
$157$	88.0904	−	88.0904i	0.561085	−	0.561085i	0.929616	+	0.368530i	$0.120139\pi$
$158$	0.0346684	+	0.0346684i	0.000219420	+	0.000219420i
$159$			25.2486i			0.158796i
$160$		0			0
$161$	−79.6096			−0.494469
$162$	−77.2575	+	77.2575i	−0.476898	+	0.476898i
$163$	−36.8377	−	36.8377i	−0.225998	−	0.225998i	0.585020	−	0.811019i	$-0.301087\pi$
$163$	−36.8377	−	36.8377i	−0.225998	−	0.225998i	−0.811019	+	0.585020i	$0.801087\pi$
$164$		−	66.2863i		−	0.404185i
$165$		0			0
$166$	21.6077			0.130167
$167$	11.6573	−	11.6573i	0.0698042	−	0.0698042i	−0.671343	−	0.741147i	$-0.734282\pi$
$167$	11.6573	−	11.6573i	0.0698042	−	0.0698042i	0.741147	+	0.671343i	$0.234282\pi$
$168$	25.6577	+	25.6577i	0.152724	+	0.152724i
$169$			375.180i			2.22000i
$170$		0			0
$171$	251.410			1.47023
$172$	−11.5888	+	11.5888i	−0.0673767	+	0.0673767i
$173$	60.0469	+	60.0469i	0.347092	+	0.347092i	0.859025	−	0.511933i	$-0.171070\pi$
$173$	60.0469	+	60.0469i	0.347092	+	0.347092i	−0.511933	+	0.859025i	$0.671070\pi$
$174$			28.2251i			0.162213i
$175$		0			0
$176$	−15.4625			−0.0878554
$177$	−4.84188	+	4.84188i	−0.0273553	+	0.0273553i
$178$	−91.3349	−	91.3349i	−0.513118	−	0.513118i
$179$			185.195i			1.03461i	0.855801	+	0.517305i	$0.173065\pi$
$179$			185.195i			1.03461i	−0.855801	+	0.517305i	$0.826935\pi$
$180$		0			0
$181$	76.9684			0.425240			0.212620	−	0.977135i	$-0.431800\pi$
$181$	76.9684			0.425240			0.212620	+	0.977135i	$0.431800\pi$
$182$	−227.305	+	227.305i	−1.24893	+	1.24893i
$183$	−36.5492	−	36.5492i	−0.199723	−	0.199723i
$184$			71.2180i			0.387054i
$185$		0			0
$186$	−23.3583			−0.125582
$187$	57.3594	−	57.3594i	0.306735	−	0.306735i
$188$	−23.1120	−	23.1120i	−0.122936	−	0.122936i
$189$		−	75.6369i		−	0.400195i
$190$		0			0
$191$	132.807			0.695327			0.347663	−	0.937619i	$-0.386975\pi$
$191$	132.807			0.695327			0.347663	+	0.937619i	$0.386975\pi$
$192$	18.3302	−	18.3302i	0.0954696	−	0.0954696i
$193$	−55.9014	−	55.9014i	−0.289645	−	0.289645i	0.547295	−	0.836940i	$-0.315658\pi$
$193$	−55.9014	−	55.9014i	−0.289645	−	0.289645i	−0.836940	+	0.547295i	$0.815658\pi$
$194$		−	48.8571i		−	0.251841i
$195$		0			0
$196$	80.7448			0.411963
$197$	−80.7047	+	80.7047i	−0.409669	+	0.409669i	−0.881623	−	0.471954i	$-0.843549\pi$
$197$	−80.7047	+	80.7047i	−0.409669	+	0.409669i	0.471954	+	0.881623i	$0.343549\pi$
$198$	29.7968	+	29.7968i	0.150489	+	0.150489i
$199$		−	110.887i		−	0.557221i	−0.960404	−	0.278610i	$-0.910126\pi$
$199$		−	110.887i		−	0.557221i	0.960404	−	0.278610i	$-0.0898738\pi$
$200$		0			0
$201$	−24.7321			−0.123045
$202$	−55.4286	+	55.4286i	−0.274399	+	0.274399i
$203$	296.569	+	296.569i	1.46093	+	1.46093i
$204$			20.8606i			0.102258i
$205$		0			0
$206$	130.626			0.634108
$207$	51.9022	−	51.9022i	0.250735	−	0.250735i
$208$	76.9025	+	76.9025i	0.369724	+	0.369724i
$209$		−	94.7331i		−	0.453268i
$210$		0			0
$211$	302.264			1.43253			0.716266	−	0.697827i	$-0.245850\pi$
$211$	302.264			1.43253			0.716266	+	0.697827i	$0.245850\pi$
$212$	76.8729	−	76.8729i	0.362608	−	0.362608i
$213$	16.9506	+	16.9506i	0.0795805	+	0.0795805i
$214$		−	86.0691i		−	0.402192i
$215$		0			0
$216$	−67.6641			−0.313260
$217$	−245.432	+	245.432i	−1.13102	+	1.13102i
$218$	73.3237	+	73.3237i	0.336347	+	0.336347i
$219$			12.8269i			0.0585704i
$220$		0			0
$221$	−570.551			−2.58168
$222$	−13.8963	+	13.8963i	−0.0625960	+	0.0625960i
$223$	−91.6277	−	91.6277i	−0.410887	−	0.410887i	0.471161	−	0.882047i	$-0.343835\pi$
$223$	−91.6277	−	91.6277i	−0.410887	−	0.410887i	−0.882047	+	0.471161i	$0.843835\pi$
$224$		−	261.868i		−	1.16905i
$225$		0			0
$226$	272.024			1.20365
$227$	74.4106	−	74.4106i	0.327800	−	0.327800i	−0.523949	−	0.851749i	$-0.675542\pi$
$227$	74.4106	−	74.4106i	0.327800	−	0.327800i	0.851749	+	0.523949i	$0.175542\pi$
$228$	17.2263	+	17.2263i	0.0755541	+	0.0755541i
$229$			248.036i			1.08313i	0.840660	+	0.541563i	$0.182167\pi$
$229$			248.036i			1.08313i	−0.840660	+	0.541563i	$0.817833\pi$
$230$		0			0
$231$	−14.0917			−0.0610030
$232$	265.308	−	265.308i	1.14357	−	1.14357i
$233$	34.7612	+	34.7612i	0.149189	+	0.149189i	0.777756	−	0.628566i	$-0.216358\pi$
$233$	34.7612	+	34.7612i	0.149189	+	0.149189i	−0.628566	+	0.777756i	$0.716358\pi$
$234$		−	296.387i		−	1.26661i
$235$		0			0
$236$	29.4836			0.124930
$237$	0.0106893	−	0.0106893i	4.51024e−5	−	4.51024e-5i
$238$	−238.320	−	238.320i	−1.00135	−	1.00135i
$239$			288.165i			1.20571i	0.797851	+	0.602855i	$0.205970\pi$
$239$			288.165i			1.20571i	−0.797851	+	0.602855i	$0.794030\pi$
$240$		0			0
$241$	47.2232			0.195947			0.0979735	−	0.995189i	$-0.468764\pi$
$241$	47.2232			0.195947			0.0979735	+	0.995189i	$0.468764\pi$
$242$	11.2277	−	11.2277i	0.0463953	−	0.0463953i
$243$	74.2427	+	74.2427i	0.305525	+	0.305525i
$244$			222.559i			0.912125i
$245$		0			0
$246$	22.2220			0.0903335
$247$	−471.152	+	471.152i	−1.90750	+	1.90750i
$248$	219.561	+	219.561i	0.885327	+	0.885327i
$249$		−	6.66229i		−	0.0267562i
$250$		0			0
$251$	243.921			0.971795			0.485897	−	0.874016i	$-0.338493\pi$
$251$	243.921			0.971795			0.485897	+	0.874016i	$0.338493\pi$
$252$	−113.862	+	113.862i	−0.451835	+	0.451835i
$253$	−19.5571	−	19.5571i	−0.0773009	−	0.0773009i
$254$			234.035i			0.921400i
$255$		0			0
$256$	−270.002			−1.05469
$257$	200.441	−	200.441i	0.779925	−	0.779925i	−0.199893	−	0.979818i	$-0.564059\pi$
$257$	200.441	−	200.441i	0.779925	−	0.779925i	0.979818	+	0.199893i	$0.0640593\pi$
$258$	−3.88507	−	3.88507i	−0.0150584	−	0.0150584i
$259$			292.024i			1.12751i
$260$		0			0
$261$	−386.702			−1.48162
$262$	251.291	−	251.291i	0.959126	−	0.959126i
$263$	31.8630	+	31.8630i	0.121152	+	0.121152i	0.765083	−	0.643931i	$-0.222698\pi$
$263$	31.8630	+	31.8630i	0.121152	+	0.121152i	−0.643931	+	0.765083i	$0.722698\pi$
$264$			12.6063i			0.0477512i
$265$		0			0
$266$	−393.603			−1.47971
$267$	−28.1612	+	28.1612i	−0.105473	+	0.105473i
$268$	75.3003	+	75.3003i	0.280971	+	0.280971i
$269$		−	140.105i		−	0.520838i	−0.965496	−	0.260419i	$-0.916139\pi$
$269$		−	140.105i		−	0.520838i	0.965496	−	0.260419i	$-0.0838607\pi$
$270$		0			0
$271$	−418.468			−1.54416			−0.772081	−	0.635524i	$-0.780784\pi$
$271$	−418.468			−1.54416			−0.772081	+	0.635524i	$0.780784\pi$
$272$	−80.6293	+	80.6293i	−0.296431	+	0.296431i
$273$	70.0847	+	70.0847i	0.256720	+	0.256720i
$274$			65.3357i			0.238451i
$275$		0			0
$276$	7.11257			0.0257702
$277$	151.640	−	151.640i	0.547436	−	0.547436i	−0.378263	−	0.925698i	$-0.623478\pi$
$277$	151.640	−	151.640i	0.547436	−	0.547436i	0.925698	+	0.378263i	$0.123478\pi$
$278$	−27.3953	−	27.3953i	−0.0985441	−	0.0985441i
$279$		−	320.023i		−	1.14704i
$280$		0			0
$281$	158.386			0.563651			0.281825	−	0.959466i	$-0.409060\pi$
$281$	158.386			0.563651			0.281825	+	0.959466i	$0.409060\pi$
$282$	7.74815	−	7.74815i	0.0274757	−	0.0274757i
$283$	−5.72303	−	5.72303i	−0.0202227	−	0.0202227i	0.696923	−	0.717146i	$-0.254552\pi$
$283$	−5.72303	−	5.72303i	−0.0202227	−	0.0202227i	−0.717146	+	0.696923i	$0.754552\pi$
$284$		−	103.217i		−	0.363441i
$285$		0			0
$286$	−111.681			−0.390493
$287$	233.493	−	233.493i	0.813563	−	0.813563i
$288$	170.727	+	170.727i	0.592803	+	0.592803i
$289$		−	309.201i		−	1.06990i
$290$		0			0
$291$	−15.0640			−0.0517665
$292$	39.0534	−	39.0534i	0.133744	−	0.133744i
$293$	−385.663	−	385.663i	−1.31626	−	1.31626i	−0.916716	−	0.399540i	$-0.869170\pi$
$293$	−385.663	−	385.663i	−1.31626	−	1.31626i	−0.399540	−	0.916716i	$-0.630830\pi$
$294$			27.0691i			0.0920719i
$295$		0			0
$296$	261.242			0.882575
$297$	18.5812	−	18.5812i	0.0625630	−	0.0625630i
$298$	−137.681	−	137.681i	−0.462017	−	0.462017i
$299$			194.534i			0.650615i
$300$		0			0
$301$	−81.6428			−0.271239
$302$	201.317	−	201.317i	0.666612	−	0.666612i
$303$	17.0902	+	17.0902i	0.0564034	+	0.0564034i
$304$			133.165i			0.438043i
$305$		0			0
$306$	310.751			1.01553
$307$	−98.5870	+	98.5870i	−0.321130	+	0.321130i	−0.849201	−	0.528070i	$-0.822916\pi$
$307$	−98.5870	+	98.5870i	−0.321130	+	0.321130i	0.528070	+	0.849201i	$0.322916\pi$
$308$	42.9042	+	42.9042i	0.139299	+	0.139299i
$309$		−	40.2758i		−	0.130342i
$310$		0			0
$311$	156.521			0.503282			0.251641	−	0.967821i	$-0.419030\pi$
$311$	156.521			0.503282			0.251641	+	0.967821i	$0.419030\pi$
$312$	62.6971	−	62.6971i	0.200952	−	0.200952i
$313$	−290.660	−	290.660i	−0.928625	−	0.928625i	0.0689921	−	0.997617i	$-0.478022\pi$
$313$	−290.660	−	290.660i	−0.928625	−	0.928625i	−0.997617	+	0.0689921i	$0.978022\pi$
$314$		−	179.827i		−	0.572698i
$315$		0			0
$316$	−0.0650900			−0.000205981
$317$	31.1725	−	31.1725i	0.0983359	−	0.0983359i	−0.656227	−	0.754563i	$-0.727849\pi$
$317$	31.1725	−	31.1725i	0.0983359	−	0.0983359i	0.754563	+	0.656227i	$0.227849\pi$
$318$	25.7711	+	25.7711i	0.0810413	+	0.0810413i
$319$			145.712i			0.456777i
$320$		0			0
$321$	−26.5376			−0.0826716
$322$	−81.2572	+	81.2572i	−0.252351	+	0.252351i
$323$	−493.985	−	493.985i	−1.52937	−	1.52937i
$324$		−	145.051i		−	0.447688i
$325$		0			0
$326$	−75.2002			−0.230676
$327$	22.6078	−	22.6078i	0.0691371	−	0.0691371i
$328$	−208.880	−	208.880i	−0.636831	−	0.636831i
$329$		−	162.824i		−	0.494904i
$330$		0			0
$331$	−504.338			−1.52368			−0.761841	−	0.647765i	$-0.775704\pi$
$331$	−504.338			−1.52368			−0.761841	+	0.647765i	$0.775704\pi$
$332$	−20.2843	+	20.2843i	−0.0610972	+	0.0610972i
$333$	−190.388	−	190.388i	−0.571736	−	0.571736i
$334$		−	23.7971i		−	0.0712489i
$335$		0			0
$336$	19.8085			0.0589539
$337$	352.350	−	352.350i	1.04555	−	1.04555i	0.0466376	−	0.998912i	$-0.485149\pi$
$337$	352.350	−	352.350i	1.04555	−	1.04555i	0.998912	−	0.0466376i	$-0.0148506\pi$
$338$	382.944	+	382.944i	1.13297	+	1.13297i
$339$		−	83.8729i		−	0.247413i
$340$		0			0
$341$	−120.587			−0.353628
$342$	256.613	−	256.613i	0.750331	−	0.750331i
$343$	−46.3448	−	46.3448i	−0.135116	−	0.135116i
$344$			73.0369i			0.212317i
$345$		0			0
$346$	122.579			0.354276
$347$	−475.747	+	475.747i	−1.37103	+	1.37103i	−0.512105	+	0.858923i	$0.671134\pi$
$347$	−475.747	+	475.747i	−1.37103	+	1.37103i	−0.858923	+	0.512105i	$0.828866\pi$
$348$	−26.4964	−	26.4964i	−0.0761390	−	0.0761390i
$349$		−	131.927i		−	0.378014i	−0.981976	−	0.189007i	$-0.939473\pi$
$349$		−	131.927i		−	0.378014i	0.981976	−	0.189007i	$-0.0605270\pi$
$350$		0			0
$351$	−184.826			−0.526570
$352$	64.3312	−	64.3312i	0.182759	−	0.182759i
$353$	−186.502	−	186.502i	−0.528334	−	0.528334i	0.391741	−	0.920075i	$-0.371873\pi$
$353$	−186.502	−	186.502i	−0.528334	−	0.528334i	−0.920075	+	0.391741i	$0.871873\pi$
$354$			9.88418i			0.0279214i
$355$		0			0
$356$	171.482			0.481690
$357$	−73.4811	+	73.4811i	−0.205829	+	0.205829i
$358$	189.028	+	189.028i	0.528011	+	0.528011i
$359$		−	426.565i		−	1.18820i	−0.804390	−	0.594101i	$-0.797508\pi$
$359$		−	426.565i		−	1.18820i	0.804390	−	0.594101i	$-0.202492\pi$
$360$		0			0
$361$	−454.851			−1.25997
$362$	78.5613	−	78.5613i	0.217020	−	0.217020i
$363$	−3.46181	−	3.46181i	−0.00953667	−	0.00953667i
$364$		−	426.765i		−	1.17243i
$365$		0			0
$366$	−74.6113			−0.203856
$367$	−314.261	+	314.261i	−0.856297	+	0.856297i	−0.990900	−	0.134603i	$-0.957024\pi$
$367$	−314.261	+	314.261i	−0.856297	+	0.856297i	0.134603	+	0.990900i	$0.457024\pi$
$368$	27.4912	+	27.4912i	0.0747043	+	0.0747043i
$369$			304.456i			0.825083i
$370$		0			0
$371$	541.568			1.45975
$372$	21.9276	−	21.9276i	0.0589453	−	0.0589453i
$373$	37.7552	+	37.7552i	0.101220	+	0.101220i	0.755903	−	0.654683i	$-0.227198\pi$
$373$	37.7552	+	37.7552i	0.101220	+	0.101220i	−0.654683	+	0.755903i	$0.727198\pi$
$374$		−	117.093i		−	0.313083i
$375$		0			0
$376$	−145.660			−0.387395
$377$	724.694	−	724.694i	1.92227	−	1.92227i
$378$	−77.2023	−	77.2023i	−0.204239	−	0.204239i
$379$			362.907i			0.957539i	0.877941	+	0.478770i	$0.158917\pi$
$379$			362.907i			0.957539i	−0.877941	+	0.478770i	$0.841083\pi$
$380$		0			0
$381$	72.1599			0.189396
$382$	135.556	−	135.556i	0.354859	−	0.354859i
$383$	128.471	+	128.471i	0.335435	+	0.335435i	0.854646	−	0.519211i	$-0.173774\pi$
$383$	128.471	+	128.471i	0.335435	+	0.335435i	−0.519211	+	0.854646i	$0.673774\pi$
$384$			11.4154i			0.0297276i
$385$		0			0
$386$	−114.117			−0.295639
$387$	53.2278	−	53.2278i	0.137540	−	0.137540i
$388$	45.8646	+	45.8646i	0.118208	+	0.118208i
$389$			471.776i			1.21279i	0.795163	+	0.606396i	$0.207385\pi$
$389$			471.776i			1.21279i	−0.795163	+	0.606396i	$0.792615\pi$
$390$		0			0
$391$	−203.961			−0.521640
$392$	254.442	−	254.442i	0.649086	−	0.649086i
$393$	−77.4803	−	77.4803i	−0.197151	−	0.197151i
$394$			164.750i			0.418147i
$395$		0			0
$396$	−55.9436			−0.141272
$397$	−55.2146	+	55.2146i	−0.139080	+	0.139080i	−0.773219	−	0.634139i	$-0.781355\pi$
$397$	−55.2146	+	55.2146i	−0.139080	+	0.139080i	0.634139	+	0.773219i	$0.281355\pi$
$398$	−113.182	−	113.182i	−0.284376	−	0.284376i
$399$			121.359i			0.304158i
$400$		0			0
$401$	537.053			1.33928			0.669642	−	0.742684i	$-0.266447\pi$
$401$	537.053			1.33928			0.669642	+	0.742684i	$0.266447\pi$
$402$	−25.2439	+	25.2439i	−0.0627958	+	0.0627958i
$403$	599.736	+	599.736i	1.48818	+	1.48818i
$404$		−	104.067i		−	0.257592i
$405$		0			0
$406$	605.413			1.49116
$407$	−71.7396	+	71.7396i	−0.176264	+	0.176264i
$408$	65.7355	+	65.7355i	0.161116	+	0.161116i
$409$		−	184.546i		−	0.451213i	−0.974218	−	0.225607i	$-0.927564\pi$
$409$		−	184.546i		−	0.451213i	0.974218	−	0.225607i	$-0.0724364\pi$
$410$		0			0
$411$	20.1449			0.0490143
$412$	−122.625	+	122.625i	−0.297635	+	0.297635i
$413$	103.856	+	103.856i	0.251466	+	0.251466i
$414$		−	105.953i		−	0.255925i
$415$		0			0
$416$	−639.899			−1.53822
$417$	−8.44675	+	8.44675i	−0.0202560	+	0.0202560i
$418$	−96.6937	−	96.6937i	−0.231325	−	0.231325i
$419$			230.898i			0.551070i	0.961291	+	0.275535i	$0.0888549\pi$
$419$			230.898i			0.551070i	−0.961291	+	0.275535i	$0.911145\pi$
$420$		0			0
$421$	309.379			0.734867			0.367433	−	0.930050i	$-0.380237\pi$
$421$	309.379			0.734867			0.367433	+	0.930050i	$0.380237\pi$
$422$	308.520	−	308.520i	0.731090	−	0.731090i
$423$	106.154	+	106.154i	0.250956	+	0.250956i
$424$		−	484.482i		−	1.14265i
$425$		0			0
$426$	34.6029			0.0812275
$427$	−783.960	+	783.960i	−1.83597	+	1.83597i
$428$	80.7975	+	80.7975i	0.188779	+	0.188779i
$429$			34.4344i			0.0802668i
$430$		0			0
$431$	362.971			0.842161			0.421080	−	0.907023i	$-0.361651\pi$
$431$	362.971			0.842161			0.421080	+	0.907023i	$0.361651\pi$
$432$	−26.1193	+	26.1193i	−0.0604614	+	0.0604614i
$433$	−71.7028	−	71.7028i	−0.165595	−	0.165595i	0.619445	−	0.785040i	$-0.287358\pi$
$433$	−71.7028	−	71.7028i	−0.165595	−	0.165595i	−0.785040	+	0.619445i	$0.787358\pi$
$434$			501.022i			1.15443i
$435$		0			0
$436$	−137.665			−0.315746
$437$	−168.428	+	168.428i	−0.385419	+	0.385419i
$438$	13.0924	+	13.0924i	0.0298913	+	0.0298913i
$439$			162.771i			0.370777i	0.982665	+	0.185388i	$0.0593543\pi$
$439$			162.771i			0.370777i	−0.982665	+	0.185388i	$0.940646\pi$
$440$		0			0
$441$	−370.864			−0.840961
$442$	−582.359	+	582.359i	−1.31755	+	1.31755i
$443$	−260.937	−	260.937i	−0.589022	−	0.589022i	0.348344	−	0.937367i	$-0.386744\pi$
$443$	−260.937	−	260.937i	−0.589022	−	0.589022i	−0.937367	+	0.348344i	$0.886744\pi$
$444$		−	26.0903i		−	0.0587620i
$445$		0			0
$446$	−187.048			−0.419390
$447$	−42.4510	+	42.4510i	−0.0949688	+	0.0949688i
$448$	−393.171	−	393.171i	−0.877615	−	0.877615i
$449$		−	375.138i		−	0.835496i	−0.908563	−	0.417748i	$-0.862820\pi$
$449$		−	375.138i		−	0.835496i	0.908563	−	0.417748i	$-0.137180\pi$
$450$		0			0
$451$	114.721			0.254370
$452$	−255.363	+	255.363i	−0.564962	+	0.564962i
$453$	−62.0718	−	62.0718i	−0.137024	−	0.137024i
$454$		−	151.901i		−	0.334584i
$455$		0			0
$456$	108.567			0.238085
$457$	−202.644	+	202.644i	−0.443423	+	0.443423i	−0.893161	−	0.449738i	$-0.851517\pi$
$457$	−202.644	+	202.644i	−0.443423	+	0.443423i	0.449738	+	0.893161i	$0.351517\pi$
$458$	253.169	+	253.169i	0.552771	+	0.552771i
$459$		−	193.783i		−	0.422185i
$460$		0			0
$461$	−234.312			−0.508268			−0.254134	−	0.967169i	$-0.581791\pi$
$461$	−234.312			−0.508268			−0.254134	+	0.967169i	$0.581791\pi$
$462$	−14.3833	+	14.3833i	−0.0311328	+	0.0311328i
$463$	−438.590	−	438.590i	−0.947279	−	0.947279i	0.0513990	−	0.998678i	$-0.483632\pi$
$463$	−438.590	−	438.590i	−0.947279	−	0.947279i	−0.998678	+	0.0513990i	$0.983632\pi$
$464$		−	204.825i		−	0.441434i
$465$		0			0
$466$	70.9611			0.152277
$467$	355.965	−	355.965i	0.762238	−	0.762238i	−0.214489	−	0.976726i	$-0.568809\pi$
$467$	355.965	−	355.965i	0.762238	−	0.762238i	0.976726	+	0.214489i	$0.0688085\pi$
$468$	278.234	+	278.234i	0.594517	+	0.594517i
$469$			530.489i			1.13111i
$470$		0			0
$471$	−55.4459			−0.117719
$472$	92.9083	−	92.9083i	0.196840	−	0.196840i
$473$	−20.0566	−	20.0566i	−0.0424030	−	0.0424030i
$474$		−	0.0218210i		−	4.60358e-5i
$475$		0			0
$476$	447.447			0.940015
$477$	−353.080	+	353.080i	−0.740211	+	0.740211i
$478$	294.128	+	294.128i	0.615331	+	0.615331i
$479$			497.329i			1.03827i	0.854694	+	0.519133i	$0.173745\pi$
$479$			497.329i			1.03827i	−0.854694	+	0.519133i	$0.826255\pi$
$480$		0			0
$481$	713.590			1.48355
$482$	48.2006	−	48.2006i	0.100001	−	0.100001i
$483$	25.0539	+	25.0539i	0.0518715	+	0.0518715i
$484$			21.0799i			0.0435536i
$485$		0			0
$486$	151.558			0.311849
$487$	−384.072	+	384.072i	−0.788648	+	0.788648i	−0.981273	−	0.192625i	$-0.938300\pi$
$487$	−384.072	+	384.072i	−0.788648	+	0.788648i	0.192625	+	0.981273i	$0.438300\pi$
$488$	701.324	+	701.324i	1.43714	+	1.43714i
$489$			23.1864i			0.0474160i
$490$		0			0
$491$	−579.880			−1.18102			−0.590509	−	0.807031i	$-0.701073\pi$
$491$	−579.880			−1.18102			−0.590509	+	0.807031i	$0.701073\pi$
$492$	−20.8610	+	20.8610i	−0.0424003	+	0.0424003i
$493$	759.814	+	759.814i	1.54120	+	1.54120i
$494$			961.807i			1.94698i
$495$		0			0
$496$	169.507			0.341749
$497$	363.582	−	363.582i	0.731553	−	0.731553i
$498$	−6.80017	−	6.80017i	−0.0136550	−	0.0136550i
$499$		−	488.110i		−	0.978175i	−0.872235	−	0.489088i	$-0.837330\pi$
$499$		−	488.110i		−	0.978175i	0.872235	−	0.489088i	$-0.162670\pi$
$500$		0			0
$501$	−7.33734			−0.0146454
$502$	248.969	−	248.969i	0.495954	−	0.495954i
$503$	168.826	+	168.826i	0.335637	+	0.335637i	0.854723	−	0.519085i	$-0.173727\pi$
$503$	168.826	+	168.826i	0.335637	+	0.335637i	−0.519085	+	0.854723i	$0.673727\pi$
$504$			717.603i			1.42382i
$505$		0			0
$506$	−39.9238			−0.0789008
$507$	118.073	−	118.073i	0.232885	−	0.232885i
$508$	−219.701	−	219.701i	−0.432482	−	0.432482i
$509$			290.669i			0.571058i	0.958370	+	0.285529i	$0.0921693\pi$
$509$			290.669i			0.571058i	−0.958370	+	0.285529i	$0.907831\pi$
$510$		0			0
$511$	275.130			0.538415
$512$	−203.044	+	203.044i	−0.396571	+	0.396571i
$513$	−160.023	−	160.023i	−0.311936	−	0.311936i
$514$		−	409.178i		−	0.796067i
$515$		0			0
$516$	7.29422			0.0141361
$517$	39.9997	−	39.9997i	0.0773689	−	0.0773689i
$518$	298.068	+	298.068i	0.575421	+	0.575421i
$519$		−	37.7948i		−	0.0728223i
$520$		0			0
$521$	−742.193			−1.42456			−0.712278	−	0.701898i	$-0.752336\pi$
$521$	−742.193			−1.42456			−0.712278	+	0.701898i	$0.752336\pi$
$522$	−394.705	+	394.705i	−0.756140	+	0.756140i
$523$	494.178	+	494.178i	0.944891	+	0.944891i	0.998559	−	0.0536681i	$-0.0170913\pi$
$523$	494.178	+	494.178i	0.944891	+	0.944891i	−0.0536681	+	0.998559i	$0.517091\pi$
$524$			471.799i			0.900381i
$525$		0			0
$526$	65.0450			0.123660
$527$	−628.800	+	628.800i	−1.19317	+	1.19317i
$528$	4.86622	+	4.86622i	0.00921632	+	0.00921632i
$529$		−	459.458i		−	0.868540i
$530$		0			0
$531$	−135.419			−0.255027
$532$	369.495	−	369.495i	0.694539	−	0.694539i
$533$	−570.562	−	570.562i	−1.07047	−	1.07047i
$534$			57.4880i			0.107656i
$535$		0			0
$536$	474.570			0.885393
$537$	58.2828	−	58.2828i	0.108534	−	0.108534i
$538$	−143.005	−	143.005i	−0.265809	−	0.265809i
$539$			139.744i			0.259266i
$540$		0			0
$541$	−391.118			−0.722955			−0.361477	−	0.932381i	$-0.617728\pi$
$541$	−391.118			−0.722955			−0.361477	+	0.932381i	$0.617728\pi$
$542$	−427.129	+	427.129i	−0.788060	+	0.788060i
$543$	−24.2227	−	24.2227i	−0.0446091	−	0.0446091i
$544$		−	670.910i		−	1.23329i
$545$		0			0
$546$	143.070			0.262034
$547$	210.940	−	210.940i	0.385630	−	0.385630i	−0.487495	−	0.873126i	$-0.662089\pi$
$547$	210.940	−	210.940i	0.385630	−	0.385630i	0.873126	+	0.487495i	$0.162089\pi$
$548$	−61.3339	−	61.3339i	−0.111923	−	0.111923i
$549$		−	1022.22i		−	1.86197i
$550$		0			0
$551$	1254.89			2.27747
$552$	22.4130	−	22.4130i	0.0406033	−	0.0406033i
$553$	−0.229279	−	0.229279i	−0.000414609	−	0.000414609i
$554$		−	309.556i		−	0.558766i
$555$		0			0
$556$	51.4347			0.0925084
$557$	−556.826	+	556.826i	−0.999687	+	0.999687i	−1.00000		0.000313081i	$-0.999900\pi$
$557$	−556.826	+	556.826i	−0.999687	+	0.999687i	0.000313081		1.00000i	$0.499900\pi$
$558$	−326.646	−	326.646i	−0.585388	−	0.585388i
$559$			199.502i			0.356891i
$560$		0			0
$561$	−36.1032			−0.0643550
$562$	161.664	−	161.664i	0.287658	−	0.287658i
$563$	540.463	+	540.463i	0.959969	+	0.959969i	0.999229	−	0.0392598i	$-0.0125000\pi$
$563$	540.463	+	540.463i	0.959969	+	0.959969i	−0.0392598	+	0.999229i	$0.512500\pi$
$564$			14.5472i			0.0257928i
$565$		0			0
$566$	−11.6829			−0.0206413
$567$	510.940	−	510.940i	0.901129	−	0.901129i
$568$	−325.257	−	325.257i	−0.572635	−	0.572635i
$569$		−	115.520i		−	0.203022i	−0.994834	−	0.101511i	$-0.967632\pi$
$569$		−	115.520i		−	0.203022i	0.994834	−	0.101511i	$-0.0323678\pi$
$570$		0			0
$571$	445.704			0.780567			0.390284	−	0.920695i	$-0.372377\pi$
$571$	445.704			0.780567			0.390284	+	0.920695i	$0.372377\pi$
$572$	104.841	−	104.841i	0.183288	−	0.183288i
$573$	−41.7958	−	41.7958i	−0.0729421	−	0.0729421i
$574$		−	476.650i		−	0.830401i
$575$		0			0
$576$	512.664			0.890042
$577$	175.919	−	175.919i	0.304885	−	0.304885i	−0.538037	−	0.842922i	$-0.680834\pi$
$577$	175.919	−	175.919i	0.304885	−	0.304885i	0.842922	+	0.538037i	$0.180834\pi$
$578$	−315.600	−	315.600i	−0.546021	−	0.546021i
$579$			35.1855i			0.0607694i
$580$		0			0
$581$	−142.902			−0.245959
$582$	−15.3758	+	15.3758i	−0.0264189	+	0.0264189i
$583$	133.043	+	133.043i	0.228205	+	0.228205i
$584$		−	246.129i		−	0.421454i
$585$		0			0
$586$	−787.289			−1.34350
$587$	−200.703	+	200.703i	−0.341913	+	0.341913i	−0.857086	−	0.515173i	$-0.827728\pi$
$587$	−200.703	+	200.703i	−0.341913	+	0.341913i	0.515173	+	0.857086i	$0.327728\pi$
$588$	−25.4112	−	25.4112i	−0.0432163	−	0.0432163i
$589$			1038.51i			1.76317i
$590$		0			0
$591$	50.7972			0.0859512
$592$	100.843	−	100.843i	0.170343	−	0.170343i
$593$	−455.216	−	455.216i	−0.767650	−	0.767650i	0.210043	−	0.977692i	$-0.432640\pi$
$593$	−455.216	−	455.216i	−0.767650	−	0.767650i	−0.977692	+	0.210043i	$0.932640\pi$
$594$		−	37.9315i		−	0.0638578i
$595$		0			0
$596$	258.496			0.433719
$597$	−34.8972	+	34.8972i	−0.0584543	+	0.0584543i
$598$	198.560	+	198.560i	0.332040	+	0.332040i
$599$		−	816.330i		−	1.36282i	−0.731901	−	0.681411i	$-0.761367\pi$
$599$		−	816.330i		−	1.36282i	0.731901	−	0.681411i	$-0.238633\pi$
$600$		0			0
$601$	322.902			0.537274			0.268637	−	0.963241i	$-0.413427\pi$
$601$	322.902			0.537274			0.268637	+	0.963241i	$0.413427\pi$
$602$	−83.3325	+	83.3325i	−0.138426	+	0.138426i
$603$	−345.857	−	345.857i	−0.573561	−	0.573561i
$604$			377.973i			0.625783i
$605$		0			0
$606$	34.8879			0.0575708
$607$	587.627	−	587.627i	0.968084	−	0.968084i	−0.0314218	−	0.999506i	$-0.510004\pi$
$607$	587.627	−	587.627i	0.968084	−	0.968084i	0.999506	+	0.0314218i	$0.0100035\pi$
$608$	−554.027	−	554.027i	−0.911229	−	0.911229i
$609$		−	186.666i		−	0.306513i
$610$		0			0
$611$	−397.875			−0.651187
$612$	−291.717	+	291.717i	−0.476663	+	0.476663i
$613$	−373.206	−	373.206i	−0.608819	−	0.608819i	0.333818	−	0.942637i	$-0.391663\pi$
$613$	−373.206	−	373.206i	−0.608819	−	0.608819i	−0.942637	+	0.333818i	$0.891663\pi$
$614$			201.255i			0.327776i
$615$		0			0
$616$	270.398			0.438958
$617$	71.7013	−	71.7013i	0.116210	−	0.116210i	−0.646611	−	0.762820i	$-0.723814\pi$
$617$	71.7013	−	71.7013i	0.116210	−	0.116210i	0.762820	+	0.646611i	$0.223814\pi$
$618$	−41.1094	−	41.1094i	−0.0665200	−	0.0665200i
$619$		−	45.4335i		−	0.0733983i	−0.999326	−	0.0366991i	$-0.988316\pi$
$619$		−	45.4335i		−	0.0733983i	0.999326	−	0.0366991i	$-0.0116843\pi$
$620$		0			0
$621$	−66.0718			−0.106396
$622$	159.760	−	159.760i	0.256849	−	0.256849i
$623$	604.042	+	604.042i	0.969569	+	0.969569i
$624$		−	48.4040i		−	0.0775705i
$625$		0			0
$626$	−593.350			−0.947844
$627$	−29.8135	+	29.8135i	−0.0475494	+	0.0475494i
$628$	168.813	+	168.813i	0.268810	+	0.268810i
$629$			748.171i			1.18946i
$630$		0			0
$631$	536.778			0.850678			0.425339	−	0.905034i	$-0.360155\pi$
$631$	536.778			0.850678			0.425339	+	0.905034i	$0.360155\pi$
$632$	−0.205111	+	0.205111i	−0.000324542	+	0.000324542i
$633$	−95.1256	−	95.1256i	−0.150277	−	0.150277i
$634$		−	63.6353i		−	0.100371i
$635$		0			0
$636$	−48.3854			−0.0760776
$637$	695.014	−	695.014i	1.09107	−	1.09107i
$638$	148.728	+	148.728i	0.233115	+	0.233115i
$639$			474.081i			0.741911i
$640$		0			0
$641$	241.341			0.376508			0.188254	−	0.982120i	$-0.439717\pi$
$641$	241.341			0.376508			0.188254	+	0.982120i	$0.439717\pi$
$642$	−27.0868	+	27.0868i	−0.0421913	+	0.0421913i
$643$	276.993	+	276.993i	0.430783	+	0.430783i	0.888895	−	0.458112i	$-0.151474\pi$
$643$	276.993	+	276.993i	0.430783	+	0.430783i	−0.458112	+	0.888895i	$0.651474\pi$
$644$		−	152.560i		−	0.236895i
$645$		0			0
$646$	−1008.42			−1.56102
$647$	695.834	−	695.834i	1.07548	−	1.07548i	0.0785682	−	0.996909i	$-0.474965\pi$
$647$	695.834	−	695.834i	1.07548	−	1.07548i	0.996909	−	0.0785682i	$-0.0250348\pi$
$648$	−457.083	−	457.083i	−0.705375	−	0.705375i
$649$			51.0270i			0.0786240i
$650$		0			0
$651$	154.480			0.237296
$652$	70.5943	−	70.5943i	0.108273	−	0.108273i
$653$	−520.242	−	520.242i	−0.796695	−	0.796695i	0.185878	−	0.982573i	$-0.440487\pi$
$653$	−520.242	−	520.242i	−0.796695	−	0.796695i	−0.982573	+	0.185878i	$0.940487\pi$
$654$		−	46.1514i		−	0.0705679i
$655$		0			0
$656$	−161.262			−0.245826
$657$	−179.374	+	179.374i	−0.273019	+	0.273019i
$658$	−166.193	−	166.193i	−0.252573	−	0.252573i
$659$		−	702.435i		−	1.06591i	−0.846143	−	0.532955i	$-0.821081\pi$
$659$		−	702.435i		−	1.06591i	0.846143	−	0.532955i	$-0.178919\pi$
$660$		0			0
$661$	−101.789			−0.153993			−0.0769966	−	0.997031i	$-0.524533\pi$
$661$	−101.789			−0.153993			−0.0769966	+	0.997031i	$0.524533\pi$
$662$	−514.776	+	514.776i	−0.777608	+	0.777608i
$663$	179.558	+	179.558i	0.270827	+	0.270827i
$664$			127.839i			0.192529i
$665$		0			0
$666$	−388.657			−0.583568
$667$	259.064	−	259.064i	0.388402	−	0.388402i
$668$	22.3396	+	22.3396i	0.0334425	+	0.0334425i
$669$			57.6723i			0.0862068i
$670$		0			0
$671$	−385.180			−0.574039
$672$	−82.4124	+	82.4124i	−0.122637	+	0.122637i
$673$	840.475	+	840.475i	1.24885	+	1.24885i	0.956229	+	0.292619i	$0.0945267\pi$
$673$	840.475	+	840.475i	1.24885	+	1.24885i	0.292619	+	0.956229i	$0.405473\pi$
$674$		−	719.285i		−	1.06719i
$675$		0			0
$676$	−718.979			−1.06358
$677$	373.040	−	373.040i	0.551019	−	0.551019i	−0.375716	−	0.926735i	$-0.622603\pi$
$677$	373.040	−	373.040i	0.551019	−	0.551019i	0.926735	+	0.375716i	$0.122603\pi$
$678$	−85.6087	−	85.6087i	−0.126267	−	0.126267i
$679$			323.115i			0.475869i
$680$		0			0
$681$	−46.8355			−0.0687747
$682$	−123.083	+	123.083i	−0.180473	+	0.180473i
$683$	−465.186	−	465.186i	−0.681093	−	0.681093i	0.279154	−	0.960246i	$-0.409946\pi$
$683$	−465.186	−	465.186i	−0.681093	−	0.681093i	−0.960246	+	0.279154i	$0.909946\pi$
$684$			481.792i			0.704374i
$685$		0			0
$686$	−94.6078			−0.137912
$687$	78.0593	−	78.0593i	0.113623	−	0.113623i
$688$	28.1933	+	28.1933i	0.0409787	+	0.0409787i
$689$		−	1323.37i		−	1.92072i
$690$		0			0
$691$	370.066			0.535551			0.267775	−	0.963481i	$-0.413712\pi$
$691$	370.066			0.535551			0.267775	+	0.963481i	$0.413712\pi$
$692$	−115.071	+	115.071i	−0.166288	+	0.166288i
$693$	−197.061	−	197.061i	−0.284359	−	0.284359i
$694$			971.186i			1.39940i
$695$		0			0
$696$	−166.990			−0.239928
$697$	598.212	−	598.212i	0.858267	−	0.858267i
$698$	−134.657	−	134.657i	−0.192919	−	0.192919i
$699$		−	21.8794i		−	0.0313010i
$700$		0			0
$701$	−757.792			−1.08102			−0.540508	−	0.841339i	$-0.681768\pi$
$701$	−757.792			−1.08102			−0.540508	+	0.841339i	$0.681768\pi$
$702$	−188.651	+	188.651i	−0.268734	+	0.268734i
$703$	617.828	+	617.828i	0.878845	+	0.878845i
$704$		−	193.175i		−	0.274397i
$705$		0			0
$706$	−380.724			−0.539269
$707$	366.576	−	366.576i	0.518495	−	0.518495i
$708$	−9.27878	−	9.27878i	−0.0131056	−	0.0131056i
$709$		−	498.939i		−	0.703723i	−0.936052	−	0.351861i	$-0.885549\pi$
$709$		−	498.939i		−	0.703723i	0.936052	−	0.351861i	$-0.114451\pi$
$710$		0			0
$711$	0.298961			0.000420479
$712$	540.370	−	540.370i	0.758947	−	0.758947i
$713$	214.394	+	214.394i	0.300693	+	0.300693i
$714$			150.004i			0.210089i
$715$		0			0
$716$	−354.900			−0.495671
$717$	90.6883	−	90.6883i	0.126483	−	0.126483i
$718$	−435.393	−	435.393i	−0.606397	−	0.606397i
$719$			1161.66i			1.61566i	0.589416	+	0.807830i	$0.299358\pi$
$719$			1161.66i			1.61566i	−0.589416	+	0.807830i	$0.700642\pi$
$720$		0			0
$721$	−863.893			−1.19819
$722$	−464.264	+	464.264i	−0.643026	+	0.643026i
$723$	−14.8616	−	14.8616i	−0.0205555	−	0.0205555i
$724$			147.499i			0.203728i
$725$		0			0
$726$	−7.06691			−0.00973404
$727$	−1008.36	+	1008.36i	−1.38702	+	1.38702i	−0.555499	+	0.831517i	$0.687473\pi$
$727$	−1008.36	+	1008.36i	−1.38702	+	1.38702i	−0.831517	+	0.555499i	$0.812527\pi$
$728$	−1344.82	−	1344.82i	−1.84728	−	1.84728i
$729$			634.489i			0.870355i
$730$		0			0
$731$	−209.170			−0.286143
$732$	70.0414	−	70.0414i	0.0956850	−	0.0956850i
$733$	74.9699	+	74.9699i	0.102278	+	0.102278i	0.756394	−	0.654116i	$-0.226959\pi$
$733$	74.9699	+	74.9699i	0.102278	+	0.102278i	−0.654116	+	0.756394i	$0.726959\pi$
$734$			641.530i			0.874019i
$735$		0			0
$736$	−228.752			−0.310804
$737$	−130.321	+	130.321i	−0.176827	+	0.176827i
$738$	310.757	+	310.757i	0.421080	+	0.421080i
$739$		−	1094.78i		−	1.48144i	−0.671815	−	0.740719i	$-0.734485\pi$
$739$		−	1094.78i		−	1.48144i	0.671815	−	0.740719i	$-0.265515\pi$
$740$		0			0
$741$	296.553			0.400206
$742$	552.776	−	552.776i	0.744981	−	0.744981i
$743$	−929.063	−	929.063i	−1.25042	−	1.25042i	−0.955531	−	0.294891i	$-0.904717\pi$
$743$	−929.063	−	929.063i	−1.25042	−	1.25042i	−0.294891	−	0.955531i	$-0.595283\pi$
$744$		−	138.196i		−	0.185747i
$745$		0			0
$746$	77.0732			0.103315
$747$	93.1665	−	93.1665i	0.124721	−	0.124721i
$748$	109.921	+	109.921i	0.146954	+	0.146954i
$749$			569.216i			0.759968i
$750$		0			0
$751$	1375.81			1.83198			0.915988	−	0.401205i	$-0.131409\pi$
$751$	1375.81			1.83198			0.915988	+	0.401205i	$0.131409\pi$
$752$	−56.2271	+	56.2271i	−0.0747700	+	0.0747700i
$753$	−76.7642	−	76.7642i	−0.101945	−	0.101945i
$754$		−	1479.39i		−	1.96205i
$755$		0			0
$756$	144.947			0.191729
$757$	317.073	−	317.073i	0.418854	−	0.418854i	−0.465954	−	0.884809i	$-0.654289\pi$
$757$	317.073	−	317.073i	0.418854	−	0.418854i	0.884809	+	0.465954i	$0.154289\pi$
$758$	370.418	+	370.418i	0.488678	+	0.488678i
$759$			12.3097i			0.0162183i
$760$		0			0
$761$	−683.671			−0.898385			−0.449192	−	0.893435i	$-0.648288\pi$
$761$	−683.671			−0.898385			−0.449192	+	0.893435i	$0.648288\pi$
$762$	73.6533	−	73.6533i	0.0966579	−	0.0966579i
$763$	−484.925	−	484.925i	−0.635550	−	0.635550i
$764$			254.507i			0.333124i
$765$		0			0
$766$	262.261			0.342377
$767$	253.781	−	253.781i	0.330875	−	0.330875i
$768$	84.9723	+	84.9723i	0.110641	+	0.110641i
$769$		−	635.630i		−	0.826567i	−0.910603	−	0.413283i	$-0.864382\pi$
$769$		−	635.630i		−	0.826567i	0.910603	−	0.413283i	$-0.135618\pi$
$770$		0			0
$771$	−126.161			−0.163634
$772$	107.127	−	107.127i	0.138766	−	0.138766i
$773$	966.787	+	966.787i	1.25069	+	1.25069i	0.955409	+	0.295286i	$0.0954148\pi$
$773$	966.787	+	966.787i	1.25069	+	1.25069i	0.295286	+	0.955409i	$0.404585\pi$
$774$		−	108.659i		−	0.140386i
$775$		0			0
$776$	289.056			0.372495
$777$	91.9029	−	91.9029i	0.118279	−	0.118279i
$778$	481.540	+	481.540i	0.618946	+	0.618946i
$779$		−	987.989i		−	1.26828i
$780$		0			0
$781$	178.637			0.228729
$782$	−208.182	+	208.182i	−0.266218	+	0.266218i
$783$	246.137	+	246.137i	0.314351	+	0.314351i
$784$		−	196.436i		−	0.250557i
$785$		0			0
$786$	−158.168			−0.201231
$787$	−68.3007	+	68.3007i	−0.0867861	+	0.0867861i	−0.749167	−	0.662381i	$-0.769546\pi$
$787$	−68.3007	+	68.3007i	−0.0867861	+	0.0867861i	0.662381	+	0.749167i	$0.269546\pi$
$788$	−154.659	−	154.659i	−0.196268	−	0.196268i
$789$		−	20.0552i		−	0.0254186i
$790$		0			0
$791$	−1799.02			−2.27437
$792$	−176.289	+	176.289i	−0.222587	+	0.222587i
$793$	1915.68	+	1915.68i	2.41574	+	2.41574i
$794$			112.715i			0.141958i
$795$		0			0
$796$	212.499			0.266959
$797$	342.399	−	342.399i	0.429610	−	0.429610i	−0.458886	−	0.888495i	$-0.651751\pi$
$797$	342.399	−	342.399i	0.429610	−	0.429610i	0.888495	+	0.458886i	$0.151751\pi$
$798$	123.871	+	123.871i	0.155227	+	0.155227i
$799$		−	417.157i		−	0.522098i
$800$		0			0
$801$	−787.622			−0.983298
$802$	548.168	−	548.168i	0.683501	−	0.683501i
$803$	67.5893	+	67.5893i	0.0841710	+	0.0841710i
$804$		−	47.3955i		−	0.0589496i
$805$		0			0
$806$	1224.30			1.51898
$807$	−44.0926	+	44.0926i	−0.0546376	+	0.0546376i
$808$	−327.936	−	327.936i	−0.405861	−	0.405861i
$809$		−	13.7222i		−	0.0169619i	−0.999964	−	0.00848096i	$-0.997300\pi$
$809$		−	13.7222i		−	0.0169619i	0.999964	−	0.00848096i	$-0.00269961\pi$
$810$		0			0
$811$	−1099.42			−1.35564			−0.677819	−	0.735229i	$-0.737075\pi$
$811$	−1099.42			−1.35564			−0.677819	+	0.735229i	$0.737075\pi$
$812$	−568.332	+	568.332i	−0.699916	+	0.699916i
$813$	131.696	+	131.696i	0.161988	+	0.161988i
$814$			146.449i			0.179912i
$815$		0			0
$816$	50.7497			0.0621933
$817$	−172.730	+	172.730i	−0.211419	+	0.211419i
$818$	−188.366	−	188.366i	−0.230276	−	0.230276i
$819$			1960.15i			2.39335i
$820$		0			0
$821$	1490.61			1.81560			0.907801	−	0.419401i	$-0.137760\pi$
$821$	1490.61			1.81560			0.907801	+	0.419401i	$0.137760\pi$
$822$	20.5618	−	20.5618i	0.0250143	−	0.0250143i
$823$	−715.153	−	715.153i	−0.868959	−	0.868959i	0.123398	−	0.992357i	$-0.460621\pi$
$823$	−715.153	−	715.153i	−0.868959	−	0.868959i	−0.992357	+	0.123398i	$0.960621\pi$
$824$			772.831i			0.937902i
$825$		0			0
$826$	212.010			0.256671
$827$	50.7044	−	50.7044i	0.0613112	−	0.0613112i	−0.675786	−	0.737098i	$-0.736196\pi$
$827$	50.7044	−	50.7044i	0.0613112	−	0.0613112i	0.737098	+	0.675786i	$0.236196\pi$
$828$	99.4633	+	99.4633i	0.120125	+	0.120125i
$829$			581.423i			0.701355i	0.936496	+	0.350677i	$0.114049\pi$
$829$			581.423i			0.701355i	−0.936496	+	0.350677i	$0.885951\pi$
$830$		0			0
$831$	−95.4451			−0.114856
$832$	−960.753	+	960.753i	−1.15475	+	1.15475i
$833$	728.695	+	728.695i	0.874784	+	0.874784i
$834$			17.2431i			0.0206752i
$835$		0			0
$836$	181.543			0.217156
$837$	−203.696	+	203.696i	−0.243364	+	0.243364i
$838$	235.677	+	235.677i	0.281237	+	0.281237i
$839$			154.873i			0.184592i	0.995732	+	0.0922961i	$0.0294206\pi$
$839$			154.873i			0.184592i	−0.995732	+	0.0922961i	$0.970579\pi$
$840$		0			0
$841$	−1089.18			−1.29510
$842$	315.782	−	315.782i	0.375038	−	0.375038i
$843$	−49.8456	−	49.8456i	−0.0591289	−	0.0591289i
$844$			579.247i			0.686312i
$845$		0			0
$846$	216.703			0.256150
$847$	−74.2539	+	74.2539i	−0.0876669	+	0.0876669i
$848$	−187.017	−	187.017i	−0.220539	−	0.220539i
$849$			3.60219i			0.00424286i
$850$		0			0
$851$	255.095			0.299759
$852$	−32.4835	+	32.4835i	−0.0381262	+	0.0381262i
$853$	−683.375	−	683.375i	−0.801143	−	0.801143i	0.182131	−	0.983274i	$-0.441700\pi$
$853$	−683.375	−	683.375i	−0.801143	−	0.801143i	−0.983274	+	0.182131i	$0.941700\pi$
$854$			1600.37i			1.87397i
$855$		0			0
$856$	509.216			0.594878
$857$	26.2520	−	26.2520i	0.0306324	−	0.0306324i	−0.691625	−	0.722257i	$-0.743105\pi$
$857$	26.2520	−	26.2520i	0.0306324	−	0.0306324i	0.722257	+	0.691625i	$0.243105\pi$
$858$	35.1471	+	35.1471i	0.0409640	+	0.0409640i
$859$		−	1173.28i		−	1.36587i	−0.730481	−	0.682933i	$-0.760704\pi$
$859$		−	1173.28i		−	1.36587i	0.730481	−	0.682933i	$-0.239296\pi$
$860$		0			0
$861$	−146.965			−0.170691
$862$	370.483	−	370.483i	0.429795	−	0.429795i
$863$	−310.953	−	310.953i	−0.360316	−	0.360316i	0.503613	−	0.863929i	$-0.332004\pi$
$863$	−310.953	−	310.953i	−0.360316	−	0.360316i	−0.863929	+	0.503613i	$0.832004\pi$
$864$		−	217.337i		−	0.251547i
$865$		0			0
$866$	−146.374			−0.169023
$867$	−97.3086	+	97.3086i	−0.112236	+	0.112236i
$868$	−470.335	−	470.335i	−0.541861	−	0.541861i
$869$		−	0.112651i		−	0.000129632i
$870$		0			0
$871$	1296.30			1.48829
$872$	−433.809	+	433.809i	−0.497488	+	0.497488i
$873$	−210.658	−	210.658i	−0.241304	−	0.241304i
$874$			343.828i			0.393395i
$875$		0			0
$876$	−24.5810			−0.0280605
$877$	381.058	−	381.058i	0.434502	−	0.434502i	−0.455654	−	0.890157i	$-0.650595\pi$
$877$	381.058	−	381.058i	0.434502	−	0.434502i	0.890157	+	0.455654i	$0.150595\pi$
$878$	166.140	+	166.140i	0.189225	+	0.189225i
$879$			242.744i			0.276159i
$880$		0			0
$881$	1023.66			1.16193			0.580967	−	0.813927i	$-0.302674\pi$
$881$	1023.66			1.16193			0.580967	+	0.813927i	$0.302674\pi$
$882$	−378.539	+	378.539i	−0.429183	+	0.429183i
$883$	517.278	+	517.278i	0.585819	+	0.585819i	0.936496	−	0.350677i	$-0.114049\pi$
$883$	517.278	+	517.278i	0.585819	+	0.585819i	−0.350677	+	0.936496i	$0.614049\pi$
$884$		−	1093.38i		−	1.23686i
$885$		0			0
$886$	−532.674			−0.601213
$887$	−356.870	+	356.870i	−0.402334	+	0.402334i	−0.879055	−	0.476721i	$-0.841825\pi$
$887$	−356.870	+	356.870i	−0.402334	+	0.402334i	0.476721	+	0.879055i	$0.341825\pi$
$888$	−82.2156	−	82.2156i	−0.0925851	−	0.0925851i
$889$		−	1547.79i		−	1.74104i
$890$		0			0
$891$	251.038			0.281749
$892$	175.592	−	175.592i	0.196852	−	0.196852i
$893$	−344.482	−	344.482i	−0.385758	−	0.385758i
$894$			86.6592i			0.0969343i
$895$		0			0
$896$	244.854			0.273274
$897$	61.2217	−	61.2217i	0.0682517	−	0.0682517i
$898$	−382.902	−	382.902i	−0.426394	−	0.426394i
$899$		−	1597.36i		−	1.77682i
$900$		0			0
$901$	1387.51			1.53996
$902$	117.095	−	117.095i	0.129817	−	0.129817i
$903$	25.6938	+	25.6938i	0.0284538	+	0.0284538i
$904$			1609.39i			1.78030i
$905$		0			0
$906$	−126.713			−0.139860
$907$	−1013.93	+	1013.93i	−1.11789	+	1.11789i	−0.125840	+	0.992050i	$0.540163\pi$
$907$	−1013.93	+	1013.93i	−1.11789	+	1.11789i	−0.992050	+	0.125840i	$0.959837\pi$
$908$	142.597	+	142.597i	0.157046	+	0.157046i
$909$			477.985i			0.525837i
$910$		0			0
$911$	875.724			0.961278			0.480639	−	0.876919i	$-0.340405\pi$
$911$	875.724			0.961278			0.480639	+	0.876919i	$0.340405\pi$
$912$	41.9084	−	41.9084i	0.0459521	−	0.0459521i
$913$	−35.1058	−	35.1058i	−0.0384511	−	0.0384511i
$914$			413.676i			0.452600i
$915$		0			0
$916$	−475.325			−0.518914
$917$	−1661.91	+	1661.91i	−1.81233	+	1.81233i
$918$	−197.794	−	197.794i	−0.215461	−	0.215461i
$919$		−	941.570i		−	1.02456i	−0.858819	−	0.512280i	$-0.828801\pi$
$919$		−	941.570i		−	1.02456i	0.858819	−	0.512280i	$-0.171199\pi$
$920$		0			0
$921$	62.0526			0.0673753
$922$	−239.161	+	239.161i	−0.259394	+	0.259394i
$923$	−888.447	−	888.447i	−0.962565	−	0.962565i
$924$		−	27.0048i		−	0.0292259i
$925$		0			0
$926$	−895.335			−0.966884
$927$	563.224	−	563.224i	0.607577	−	0.607577i
$928$	852.166	+	852.166i	0.918283	+	0.918283i
$929$		−	466.840i		−	0.502519i	−0.967920	−	0.251259i	$-0.919155\pi$
$929$		−	466.840i		−	0.502519i	0.967920	−	0.251259i	$-0.0808447\pi$
$930$		0			0
$931$	1203.49			1.29269
$932$	−66.6148	+	66.6148i	−0.0714752	+	0.0714752i
$933$	−49.2586	−	49.2586i	−0.0527959	−	0.0527959i
$934$		−	726.664i		−	0.778013i
$935$		0			0
$936$	1753.53			1.87343
$937$	−704.534	+	704.534i	−0.751904	+	0.751904i	−0.974834	−	0.222930i	$-0.928438\pi$
$937$	−704.534	+	704.534i	−0.751904	+	0.751904i	0.222930	+	0.974834i	$0.428438\pi$
$938$	541.468	+	541.468i	0.577258	+	0.577258i
$939$			182.947i			0.194832i
$940$		0			0
$941$	786.311			0.835612			0.417806	−	0.908536i	$-0.362799\pi$
$941$	786.311			0.835612			0.417806	+	0.908536i	$0.362799\pi$
$942$	−56.5934	+	56.5934i	−0.0600779	+	0.0600779i
$943$	−203.965	−	203.965i	−0.216294	−	0.216294i
$944$		−	71.7279i		−	0.0759830i
$945$		0			0
$946$	−40.9434			−0.0432806
$947$	−1325.60	+	1325.60i	−1.39979	+	1.39979i	−0.599144	+	0.800641i	$0.704492\pi$
$947$	−1325.60	+	1325.60i	−1.39979	+	1.39979i	−0.800641	+	0.599144i	$0.795508\pi$
$948$	0.0204845	+	0.0204845i	2.16081e−5	+	2.16081e-5i
$949$		−	672.307i		−	0.708438i
$950$		0			0
$951$	−19.6206			−0.0206315
$952$	1409.99	−	1409.99i	1.48108	−	1.48108i
$953$	468.268	+	468.268i	0.491363	+	0.491363i	0.908735	−	0.417373i	$-0.137049\pi$
$953$	468.268	+	468.268i	0.491363	+	0.491363i	−0.417373	+	0.908735i	$0.637049\pi$
$954$			720.776i			0.755530i
$955$		0			0
$956$	−552.227			−0.577643
$957$	45.8570	−	45.8570i	0.0479175	−	0.0479175i
$958$	507.622	+	507.622i	0.529877	+	0.529877i
$959$		−	432.096i		−	0.450569i
$960$		0			0
$961$	360.930			0.375578
$962$	728.358	−	728.358i	0.757129	−	0.757129i
$963$	−371.106	−	371.106i	−0.385365	−	0.385365i
$964$			90.4966i			0.0938762i
$965$		0			0
$966$	51.1449			0.0529450
$967$	747.653	−	747.653i	0.773167	−	0.773167i	−0.205492	−	0.978659i	$-0.565879\pi$
$967$	747.653	−	747.653i	0.773167	−	0.773167i	0.978659	+	0.205492i	$0.0658794\pi$
$968$	66.4268	+	66.4268i	0.0686228	+	0.0686228i
$969$			310.924i			0.320871i
$970$		0			0
$971$	−1367.72			−1.40857			−0.704286	−	0.709917i	$-0.748733\pi$
$971$	−1367.72			−1.40857			−0.704286	+	0.709917i	$0.748733\pi$
$972$	−142.276	+	142.276i	−0.146374	+	0.146374i
$973$	181.178	+	181.178i	0.186206	+	0.186206i
$974$			784.041i			0.804970i
$975$		0			0
$976$	541.442			0.554756
$977$	479.474	−	479.474i	0.490761	−	0.490761i	−0.417785	−	0.908546i	$-0.637193\pi$
$977$	479.474	−	479.474i	0.490761	−	0.490761i	0.908546	+	0.417785i	$0.137193\pi$
$978$	23.6663	+	23.6663i	0.0241986	+	0.0241986i
$979$			296.781i			0.303148i
$980$		0			0
$981$	632.303			0.644549
$982$	−591.881	+	591.881i	−0.602730	+	0.602730i
$983$	1087.00	+	1087.00i	1.10580	+	1.10580i	0.993697	+	0.112102i	$0.0357584\pi$
$983$	1087.00	+	1087.00i	1.10580	+	1.10580i	0.112102	+	0.993697i	$0.464242\pi$
$984$			131.474i			0.133611i
$985$		0			0
$986$	1551.08			1.57310
$987$	−51.2422	+	51.2422i	−0.0519171	+	0.0519171i
$988$	−902.897	−	902.897i	−0.913864	−	0.913864i
$989$			71.3182i			0.0721114i
$990$		0			0
$991$	515.451			0.520132			0.260066	−	0.965591i	$-0.416256\pi$
$991$	515.451			0.520132			0.260066	+	0.965591i	$0.416256\pi$
$992$	−705.228	+	705.228i	−0.710916	+	0.710916i
$993$	158.720	+	158.720i	0.159839	+	0.159839i
$994$		−	742.213i		−	0.746693i
$995$		0			0
$996$	12.7673			0.0128186
$997$	−121.706	+	121.706i	−0.122072	+	0.122072i	−0.765504	−	0.643432i	$-0.777510\pi$
$997$	−121.706	+	121.706i	−0.122072	+	0.122072i	0.643432	+	0.765504i	$0.277510\pi$
$998$	−498.212	−	498.212i	−0.499210	−	0.499210i
$999$			242.365i			0.242608i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.f.c.243.9	yes	24
5.2	odd	4	inner	275.3.f.c.232.9	yes	24
5.3	odd	4	inner	275.3.f.c.232.4	✓	24
5.4	even	2	inner	275.3.f.c.243.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.f.c.232.4	✓	24	5.3	odd	4	inner
275.3.f.c.232.9	yes	24	5.2	odd	4	inner
275.3.f.c.243.4	yes	24	5.4	even	2	inner
275.3.f.c.243.9	yes	24	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.02070 - 1.02070i) q^{2} +(-0.314710 - 0.314710i) q^{3} +1.91636i q^{4} -0.642447 q^{6} +(-6.75035 + 6.75035i) q^{7} +(6.03880 + 6.03880i) q^{8} -8.80192i q^{9} -3.31662 q^{11} +(0.603097 - 0.603097i) q^{12} +(16.4951 + 16.4951i) q^{13} +13.7801i q^{14} +4.66213 q^{16} +(-17.2945 + 17.2945i) q^{17} +(-8.98408 - 8.98408i) q^{18} +28.5631i q^{19} +4.24881 q^{21} +(-3.38527 + 3.38527i) q^{22} +(5.89670 + 5.89670i) q^{23} -3.80095i q^{24} +33.6731 q^{26} +(-5.60244 + 5.60244i) q^{27} +(-12.9361 - 12.9361i) q^{28} -43.9338i q^{29} +36.3584 q^{31} +(-19.3966 + 19.3966i) q^{32} +(1.04378 + 1.04378i) q^{33} +35.3049i q^{34} +16.8676 q^{36} +(21.6303 - 21.6303i) q^{37} +(29.1542 + 29.1542i) q^{38} -10.3824i q^{39} -34.5897 q^{41} +(4.33674 - 4.33674i) q^{42} +(6.04730 + 6.04730i) q^{43} -6.35584i q^{44} +12.0375 q^{46} +(-12.0604 + 12.0604i) q^{47} +(-1.46722 - 1.46722i) q^{48} -42.1345i q^{49} +10.8855 q^{51} +(-31.6106 + 31.6106i) q^{52} +(-40.1140 - 40.1140i) q^{53} +11.4368i q^{54} -81.5281 q^{56} +(8.98910 - 8.98910i) q^{57} +(-44.8431 - 44.8431i) q^{58} -15.3852i q^{59} +116.136 q^{61} +(37.1108 - 37.1108i) q^{62} +(59.4160 + 59.4160i) q^{63} +58.2446i q^{64} +2.13075 q^{66} +(39.2934 - 39.2934i) q^{67} +(-33.1425 - 33.1425i) q^{68} -3.71150i q^{69} -53.8611 q^{71} +(53.1530 - 53.1530i) q^{72} +(-20.3789 - 20.3789i) q^{73} -44.1559i q^{74} -54.7372 q^{76} +(22.3884 - 22.3884i) q^{77} +(-10.5973 - 10.5973i) q^{78} +0.0339654i q^{79} -75.6909 q^{81} +(-35.3056 + 35.3056i) q^{82} +(10.5848 + 10.5848i) q^{83} +8.14224i q^{84} +12.3449 q^{86} +(-13.8264 + 13.8264i) q^{87} +(-20.0284 - 20.0284i) q^{88} -89.4830i q^{89} -222.696 q^{91} +(-11.3002 + 11.3002i) q^{92} +(-11.4423 - 11.4423i) q^{93} +24.6200i q^{94} +12.2086 q^{96} +(23.9332 - 23.9332i) q^{97} +(-43.0065 - 43.0065i) q^{98} +29.1926i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{6} - 128 q^{16} - 88 q^{21} + 96 q^{26} + 360 q^{31} + 176 q^{36} - 152 q^{41} + 56 q^{46} - 512 q^{51} - 1048 q^{56} + 784 q^{61} - 440 q^{66} + 728 q^{71} + 1704 q^{76} - 568 q^{81} - 328 q^{86}+ \cdots + 1568 q^{96}+O(q^{100}) \) 24 * q - 8 * q^6 - 128 * q^16 - 88 * q^21 + 96 * q^26 + 360 * q^31 + 176 * q^36 - 152 * q^41 + 56 * q^46 - 512 * q^51 - 1048 * q^56 + 784 * q^61 - 440 * q^66 + 728 * q^71 + 1704 * q^76 - 568 * q^81 - 328 * q^86 - 968 * q^91 + 1568 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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