LMFDB - Embedded newform 275.3.f.c.232.9

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			232.9
Character	$\chi$	$=$	275.232
Dual form			275.3.f.c.243.9

$q$-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 $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

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

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	0.914633	−	0.404285i	$-0.132480\pi$
$2$	1.02070	+	1.02070i	0.510348	+	0.510348i	−0.404285	+	0.914633i	$0.632480\pi$
$3$	−0.314710	+	0.314710i	−0.104903	+	0.104903i	−0.757610	−	0.652707i	$-0.773633\pi$
$3$	−0.314710	+	0.314710i	−0.104903	+	0.104903i	0.652707	+	0.757610i	$0.273633\pi$
$4$		−	1.91636i		−	0.479090i
$5$		0			0
$5$		0			0
$6$	−0.642447			−0.107074
$7$	−6.75035	−	6.75035i	−0.964336	−	0.964336i	0.0350498	−	0.999386i	$-0.488841\pi$
$7$	−6.75035	−	6.75035i	−0.964336	−	0.964336i	−0.999386	+	0.0350498i	$0.988841\pi$
$8$	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	0.322178	−	0.946679i	$-0.395585\pi$
$13$	16.4951	−	16.4951i	1.26886	−	1.26886i	0.946679	−	0.322178i	$-0.104415\pi$
$14$		−	13.7801i		−	0.984294i
$15$		0			0
$16$	4.66213			0.291383
$17$	−17.2945	−	17.2945i	−1.01732	−	1.01732i	−0.999847	−	0.0174773i	$-0.994437\pi$
$17$	−17.2945	−	17.2945i	−1.01732	−	1.01732i	−0.0174773	−	0.999847i	$-0.505563\pi$
$18$	−8.98408	+	8.98408i	−0.499116	+	0.499116i
$19$		−	28.5631i		−	1.50332i	−0.659550	−	0.751661i	$-0.729253\pi$
$19$		−	28.5631i		−	1.50332i	0.659550	−	0.751661i	$-0.270747\pi$
$20$		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	−0.567201	−	0.823579i	$-0.691974\pi$
$23$	5.89670	−	5.89670i	0.256378	−	0.256378i	0.823579	+	0.567201i	$0.191974\pi$
$24$			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	$0.273569\pi$
$29$			43.9338i			1.51496i	−0.652859	+	0.757479i	$0.726431\pi$
$30$		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	0.936165	−	0.351562i	$-0.114349\pi$
$37$	21.6303	+	21.6303i	0.584602	+	0.584602i	−0.351562	+	0.936165i	$0.614349\pi$
$38$	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	−0.633284	−	0.773919i	$-0.718294\pi$
$43$	6.04730	−	6.04730i	0.140635	−	0.140635i	0.773919	+	0.633284i	$0.218294\pi$
$44$			6.35584i			0.144451i
$45$		0			0
$46$	12.0375			0.261684
$47$	−12.0604	−	12.0604i	−0.256604	−	0.256604i	0.567068	−	0.823671i	$-0.308078\pi$
$47$	−12.0604	−	12.0604i	−0.256604	−	0.256604i	−0.823671	+	0.567068i	$0.808078\pi$
$48$	−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	−0.975751	−	0.218882i	$-0.929759\pi$
$53$	−40.1140	+	40.1140i	−0.756869	+	0.756869i	0.218882	+	0.975751i	$0.429759\pi$
$54$		−	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	$0.0416207\pi$
$59$			15.3852i			0.260766i	−0.991464	+	0.130383i	$0.958379\pi$
$60$		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	0.936673	−	0.350205i	$-0.113888\pi$
$67$	39.2934	+	39.2934i	0.586469	+	0.586469i	−0.350205	+	0.936673i	$0.613888\pi$
$68$	−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	−0.832775	−	0.553611i	$-0.813249\pi$
$73$	−20.3789	+	20.3789i	−0.279164	+	0.279164i	0.553611	+	0.832775i	$0.313249\pi$
$74$			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	$-0.999932\pi$
$79$		−	0.0339654i		−	0.000429942i	1.00000		0.000214971i	$-6.84274e-5\pi$
$80$		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	−0.640462	−	0.767990i	$-0.721257\pi$
$83$	10.5848	−	10.5848i	0.127528	−	0.127528i	0.767990	+	0.640462i	$0.221257\pi$
$84$		−	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	$0.167665\pi$
$89$			89.4830i			1.00543i	−0.864453	+	0.502713i	$0.832335\pi$
$90$		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	0.819629	−	0.572895i	$-0.194180\pi$
$97$	23.9332	+	23.9332i	0.246734	+	0.246734i	−0.572895	+	0.819629i	$0.694180\pi$
$98$	−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	−0.324601	−	0.945851i	$-0.605230\pi$
$103$	63.9888	−	63.9888i	0.621250	−	0.621250i	0.945851	+	0.324601i	$0.105230\pi$
$104$		−	199.222i		−	1.91560i
$105$		0			0
$106$	−81.8885			−0.772533
$107$	42.1620	+	42.1620i	0.394037	+	0.394037i	0.876124	−	0.482087i	$-0.160121\pi$
$107$	42.1620	+	42.1620i	0.394037	+	0.394037i	−0.482087	+	0.876124i	$0.660121\pi$
$108$	−10.7363	+	10.7363i	−0.0994101	+	0.0994101i
$109$		−	71.8370i		−	0.659055i	−0.944146	−	0.329527i	$-0.893111\pi$
$109$		−	71.8370i		−	0.659055i	0.944146	−	0.329527i	$-0.106889\pi$
$110$		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	0.199302	−	0.979938i	$-0.436132\pi$
$113$	133.254	−	133.254i	1.17924	−	1.17924i	0.979938	−	0.199302i	$-0.0638676\pi$
$114$			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	0.0929536	−	0.995670i	$-0.470369\pi$
$127$	−114.645	−	114.645i	−0.902717	−	0.902717i	−0.995670	+	0.0929536i	$0.970369\pi$
$128$	−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	0.580584	−	0.814200i	$-0.302824\pi$
$137$	−32.0054	−	32.0054i	−0.233616	−	0.233616i	−0.814200	+	0.580584i	$0.802824\pi$
$138$	−3.78831	+	3.78831i	−0.0274516	+	0.0274516i
$139$			26.8398i			0.193092i	0.995329	+	0.0965460i	$0.0307795\pi$
$139$			26.8398i			0.193092i	−0.995329	+	0.0965460i	$0.969221\pi$
$140$		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	$0.149521\pi$
$149$			134.889i			0.905298i	−0.891689	+	0.452649i	$0.850479\pi$
$150$		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	0.929616	−	0.368530i	$-0.120139\pi$
$157$	88.0904	+	88.0904i	0.561085	+	0.561085i	−0.368530	+	0.929616i	$0.620139\pi$
$158$	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	−0.811019	−	0.585020i	$-0.801087\pi$
$163$	−36.8377	+	36.8377i	−0.225998	+	0.225998i	0.585020	+	0.811019i	$0.301087\pi$
$164$			66.2863i			0.404185i
$165$		0			0
$166$	21.6077			0.130167
$167$	11.6573	+	11.6573i	0.0698042	+	0.0698042i	0.741147	−	0.671343i	$-0.234282\pi$
$167$	11.6573	+	11.6573i	0.0698042	+	0.0698042i	−0.671343	+	0.741147i	$0.734282\pi$
$168$	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	−0.511933	−	0.859025i	$-0.671070\pi$
$173$	60.0469	−	60.0469i	0.347092	−	0.347092i	0.859025	+	0.511933i	$0.171070\pi$
$174$		−	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	$-0.826935\pi$
$179$		−	185.195i		−	1.03461i	0.855801	−	0.517305i	$-0.173065\pi$
$180$		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	−0.836940	−	0.547295i	$-0.815658\pi$
$193$	−55.9014	+	55.9014i	−0.289645	+	0.289645i	0.547295	+	0.836940i	$0.315658\pi$
$194$			48.8571i			0.251841i
$195$		0			0
$196$	80.7448			0.411963
$197$	−80.7047	−	80.7047i	−0.409669	−	0.409669i	0.471954	−	0.881623i	$-0.343549\pi$
$197$	−80.7047	−	80.7047i	−0.409669	−	0.409669i	−0.881623	+	0.471954i	$0.843549\pi$
$198$	29.7968	−	29.7968i	0.150489	−	0.150489i
$199$			110.887i			0.557221i	0.960404	+	0.278610i	$0.0898738\pi$
$199$			110.887i			0.557221i	−0.960404	+	0.278610i	$0.910126\pi$
$200$		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	−0.882047	−	0.471161i	$-0.843835\pi$
$223$	−91.6277	+	91.6277i	−0.410887	+	0.410887i	0.471161	+	0.882047i	$0.343835\pi$
$224$			261.868i			1.16905i
$225$		0			0
$226$	272.024			1.20365
$227$	74.4106	+	74.4106i	0.327800	+	0.327800i	0.851749	−	0.523949i	$-0.175542\pi$
$227$	74.4106	+	74.4106i	0.327800	+	0.327800i	−0.523949	+	0.851749i	$0.675542\pi$
$228$	17.2263	−	17.2263i	0.0755541	−	0.0755541i
$229$		−	248.036i		−	1.08313i	−0.840660	−	0.541563i	$-0.817833\pi$
$229$		−	248.036i		−	1.08313i	0.840660	−	0.541563i	$-0.182167\pi$
$230$		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	−0.628566	−	0.777756i	$-0.716358\pi$
$233$	34.7612	−	34.7612i	0.149189	−	0.149189i	0.777756	+	0.628566i	$0.216358\pi$
$234$			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	$-0.794030\pi$
$239$		−	288.165i		−	1.20571i	0.797851	−	0.602855i	$-0.205970\pi$
$240$		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	0.979818	−	0.199893i	$-0.0640593\pi$
$257$	200.441	+	200.441i	0.779925	+	0.779925i	−0.199893	+	0.979818i	$0.564059\pi$
$258$	−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	−0.643931	−	0.765083i	$-0.722698\pi$
$263$	31.8630	−	31.8630i	0.121152	−	0.121152i	0.765083	+	0.643931i	$0.222698\pi$
$264$		−	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	$0.0838607\pi$
$269$			140.105i			0.520838i	−0.965496	+	0.260419i	$0.916139\pi$
$270$		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	0.925698	−	0.378263i	$-0.123478\pi$
$277$	151.640	+	151.640i	0.547436	+	0.547436i	−0.378263	+	0.925698i	$0.623478\pi$
$278$	−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	−0.717146	−	0.696923i	$-0.754552\pi$
$283$	−5.72303	+	5.72303i	−0.0202227	+	0.0202227i	0.696923	+	0.717146i	$0.254552\pi$
$284$			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	−0.399540	+	0.916716i	$0.630830\pi$
$293$	−385.663	+	385.663i	−1.31626	+	1.31626i	−0.916716	+	0.399540i	$0.869170\pi$
$294$		−	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	0.528070	−	0.849201i	$-0.322916\pi$
$307$	−98.5870	−	98.5870i	−0.321130	−	0.321130i	−0.849201	+	0.528070i	$0.822916\pi$
$308$	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	−0.997617	−	0.0689921i	$-0.978022\pi$
$313$	−290.660	+	290.660i	−0.928625	+	0.928625i	0.0689921	+	0.997617i	$0.478022\pi$
$314$			179.827i			0.572698i
$315$		0			0
$316$	−0.0650900			−0.000205981
$317$	31.1725	+	31.1725i	0.0983359	+	0.0983359i	0.754563	−	0.656227i	$-0.227849\pi$
$317$	31.1725	+	31.1725i	0.0983359	+	0.0983359i	−0.656227	+	0.754563i	$0.727849\pi$
$318$	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	0.998912	+	0.0466376i	$0.0148506\pi$
$337$	352.350	+	352.350i	1.04555	+	1.04555i	0.0466376	+	0.998912i	$0.485149\pi$
$338$	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	−0.858923	−	0.512105i	$-0.828866\pi$
$347$	−475.747	−	475.747i	−1.37103	−	1.37103i	−0.512105	−	0.858923i	$-0.671134\pi$
$348$	−26.4964	+	26.4964i	−0.0761390	+	0.0761390i
$349$			131.927i			0.378014i	0.981976	+	0.189007i	$0.0605270\pi$
$349$			131.927i			0.378014i	−0.981976	+	0.189007i	$0.939473\pi$
$350$		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	−0.920075	−	0.391741i	$-0.871873\pi$
$353$	−186.502	+	186.502i	−0.528334	+	0.528334i	0.391741	+	0.920075i	$0.371873\pi$
$354$		−	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	$0.202492\pi$
$359$			426.565i			1.18820i	−0.804390	+	0.594101i	$0.797508\pi$
$360$		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	0.134603	−	0.990900i	$-0.457024\pi$
$367$	−314.261	−	314.261i	−0.856297	−	0.856297i	−0.990900	+	0.134603i	$0.957024\pi$
$368$	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	−0.654683	−	0.755903i	$-0.727198\pi$
$373$	37.7552	−	37.7552i	0.101220	−	0.101220i	0.755903	+	0.654683i	$0.227198\pi$
$374$			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	$-0.841083\pi$
$379$		−	362.907i		−	0.957539i	0.877941	−	0.478770i	$-0.158917\pi$
$380$		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	−0.519211	−	0.854646i	$-0.673774\pi$
$383$	128.471	−	128.471i	0.335435	−	0.335435i	0.854646	+	0.519211i	$0.173774\pi$
$384$		−	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	$-0.792615\pi$
$389$		−	471.776i		−	1.21279i	0.795163	−	0.606396i	$-0.207385\pi$
$390$		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	0.634139	−	0.773219i	$-0.281355\pi$
$397$	−55.2146	−	55.2146i	−0.139080	−	0.139080i	−0.773219	+	0.634139i	$0.781355\pi$
$398$	−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	$0.0724364\pi$
$409$			184.546i			0.451213i	−0.974218	+	0.225607i	$0.927564\pi$
$410$		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	$-0.911145\pi$
$419$		−	230.898i		−	0.551070i	0.961291	−	0.275535i	$-0.0888549\pi$
$420$		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	−0.785040	−	0.619445i	$-0.787358\pi$
$433$	−71.7028	+	71.7028i	−0.165595	+	0.165595i	0.619445	+	0.785040i	$0.287358\pi$
$434$		−	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	$-0.940646\pi$
$439$		−	162.771i		−	0.370777i	0.982665	−	0.185388i	$-0.0593543\pi$
$440$		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	−0.937367	−	0.348344i	$-0.886744\pi$
$443$	−260.937	+	260.937i	−0.589022	+	0.589022i	0.348344	+	0.937367i	$0.386744\pi$
$444$			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	$0.137180\pi$
$449$			375.138i			0.835496i	−0.908563	+	0.417748i	$0.862820\pi$
$450$		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	0.449738	−	0.893161i	$-0.351517\pi$
$457$	−202.644	−	202.644i	−0.443423	−	0.443423i	−0.893161	+	0.449738i	$0.851517\pi$
$458$	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	−0.998678	−	0.0513990i	$-0.983632\pi$
$463$	−438.590	+	438.590i	−0.947279	+	0.947279i	0.0513990	+	0.998678i	$0.483632\pi$
$464$			204.825i			0.441434i
$465$		0			0
$466$	70.9611			0.152277
$467$	355.965	+	355.965i	0.762238	+	0.762238i	0.976726	−	0.214489i	$-0.0688085\pi$
$467$	355.965	+	355.965i	0.762238	+	0.762238i	−0.214489	+	0.976726i	$0.568809\pi$
$468$	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	$-0.826255\pi$
$479$		−	497.329i		−	1.03827i	0.854694	−	0.519133i	$-0.173745\pi$
$480$		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	0.192625	−	0.981273i	$-0.438300\pi$
$487$	−384.072	−	384.072i	−0.788648	−	0.788648i	−0.981273	+	0.192625i	$0.938300\pi$
$488$	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	$0.162670\pi$
$499$			488.110i			0.978175i	−0.872235	+	0.489088i	$0.837330\pi$
$500$		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	−0.519085	−	0.854723i	$-0.673727\pi$
$503$	168.826	−	168.826i	0.335637	−	0.335637i	0.854723	+	0.519085i	$0.173727\pi$
$504$		−	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	$-0.907831\pi$
$509$		−	290.669i		−	0.571058i	0.958370	−	0.285529i	$-0.0921693\pi$
$510$		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	−0.0536681	−	0.998559i	$-0.517091\pi$
$523$	494.178	−	494.178i	0.944891	−	0.944891i	0.998559	+	0.0536681i	$0.0170913\pi$
$524$		−	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	0.873126	−	0.487495i	$-0.162089\pi$
$547$	210.940	+	210.940i	0.385630	+	0.385630i	−0.487495	+	0.873126i	$0.662089\pi$
$548$	−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	0.000313081	−	1.00000i	$-0.499900\pi$
$557$	−556.826	−	556.826i	−0.999687	−	0.999687i	−1.00000		0.000313081i	$0.999900\pi$
$558$	−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	−0.0392598	−	0.999229i	$-0.512500\pi$
$563$	540.463	−	540.463i	0.959969	−	0.959969i	0.999229	+	0.0392598i	$0.0125000\pi$
$564$		−	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	$0.0323678\pi$
$569$			115.520i			0.203022i	−0.994834	+	0.101511i	$0.967632\pi$
$570$		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	0.842922	−	0.538037i	$-0.180834\pi$
$577$	175.919	+	175.919i	0.304885	+	0.304885i	−0.538037	+	0.842922i	$0.680834\pi$
$578$	−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	0.515173	−	0.857086i	$-0.327728\pi$
$587$	−200.703	−	200.703i	−0.341913	−	0.341913i	−0.857086	+	0.515173i	$0.827728\pi$
$588$	−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	−0.977692	−	0.210043i	$-0.932640\pi$
$593$	−455.216	+	455.216i	−0.767650	+	0.767650i	0.210043	+	0.977692i	$0.432640\pi$
$594$			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	$0.238633\pi$
$599$			816.330i			1.36282i	−0.731901	+	0.681411i	$0.761367\pi$
$600$		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	0.999506	−	0.0314218i	$-0.0100035\pi$
$607$	587.627	+	587.627i	0.968084	+	0.968084i	−0.0314218	+	0.999506i	$0.510004\pi$
$608$	−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	−0.942637	−	0.333818i	$-0.891663\pi$
$613$	−373.206	+	373.206i	−0.608819	+	0.608819i	0.333818	+	0.942637i	$0.391663\pi$
$614$		−	201.255i		−	0.327776i
$615$		0			0
$616$	270.398			0.438958
$617$	71.7013	+	71.7013i	0.116210	+	0.116210i	0.762820	−	0.646611i	$-0.223814\pi$
$617$	71.7013	+	71.7013i	0.116210	+	0.116210i	−0.646611	+	0.762820i	$0.723814\pi$
$618$	−41.1094	+	41.1094i	−0.0665200	+	0.0665200i
$619$			45.4335i			0.0733983i	0.999326	+	0.0366991i	$0.0116843\pi$
$619$			45.4335i			0.0733983i	−0.999326	+	0.0366991i	$0.988316\pi$
$620$		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	−0.458112	−	0.888895i	$-0.651474\pi$
$643$	276.993	−	276.993i	0.430783	−	0.430783i	0.888895	+	0.458112i	$0.151474\pi$
$644$			152.560i			0.236895i
$645$		0			0
$646$	−1008.42			−1.56102
$647$	695.834	+	695.834i	1.07548	+	1.07548i	0.996909	+	0.0785682i	$0.0250348\pi$
$647$	695.834	+	695.834i	1.07548	+	1.07548i	0.0785682	+	0.996909i	$0.474965\pi$
$648$	−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	−0.982573	−	0.185878i	$-0.940487\pi$
$653$	−520.242	+	520.242i	−0.796695	+	0.796695i	0.185878	+	0.982573i	$0.440487\pi$
$654$			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	$0.178919\pi$
$659$			702.435i			1.06591i	−0.846143	+	0.532955i	$0.821081\pi$
$660$		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	0.292619	−	0.956229i	$-0.405473\pi$
$673$	840.475	−	840.475i	1.24885	−	1.24885i	0.956229	−	0.292619i	$-0.0945267\pi$
$674$			719.285i			1.06719i
$675$		0			0
$676$	−718.979			−1.06358
$677$	373.040	+	373.040i	0.551019	+	0.551019i	0.926735	−	0.375716i	$-0.122603\pi$
$677$	373.040	+	373.040i	0.551019	+	0.551019i	−0.375716	+	0.926735i	$0.622603\pi$
$678$	−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	−0.960246	−	0.279154i	$-0.909946\pi$
$683$	−465.186	+	465.186i	−0.681093	+	0.681093i	0.279154	+	0.960246i	$0.409946\pi$
$684$		−	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	$0.114451\pi$
$709$			498.939i			0.703723i	−0.936052	+	0.351861i	$0.885549\pi$
$710$		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	$-0.700642\pi$
$719$		−	1161.66i		−	1.61566i	0.589416	−	0.807830i	$-0.299358\pi$
$720$		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	−0.831517	−	0.555499i	$-0.812527\pi$
$727$	−1008.36	−	1008.36i	−1.38702	−	1.38702i	−0.555499	−	0.831517i	$-0.687473\pi$
$728$	−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	−0.654116	−	0.756394i	$-0.726959\pi$
$733$	74.9699	−	74.9699i	0.102278	−	0.102278i	0.756394	+	0.654116i	$0.226959\pi$
$734$		−	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	$0.265515\pi$
$739$			1094.78i			1.48144i	−0.671815	+	0.740719i	$0.734485\pi$
$740$		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	−0.294891	+	0.955531i	$0.595283\pi$
$743$	−929.063	+	929.063i	−1.25042	+	1.25042i	−0.955531	+	0.294891i	$0.904717\pi$
$744$			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	0.884809	−	0.465954i	$-0.154289\pi$
$757$	317.073	+	317.073i	0.418854	+	0.418854i	−0.465954	+	0.884809i	$0.654289\pi$
$758$	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	$0.135618\pi$
$769$			635.630i			0.826567i	−0.910603	+	0.413283i	$0.864382\pi$
$770$		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	0.295286	−	0.955409i	$-0.404585\pi$
$773$	966.787	−	966.787i	1.25069	−	1.25069i	0.955409	−	0.295286i	$-0.0954148\pi$
$774$			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	0.662381	−	0.749167i	$-0.269546\pi$
$787$	−68.3007	−	68.3007i	−0.0867861	−	0.0867861i	−0.749167	+	0.662381i	$0.769546\pi$
$788$	−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	0.888495	−	0.458886i	$-0.151751\pi$
$797$	342.399	+	342.399i	0.429610	+	0.429610i	−0.458886	+	0.888495i	$0.651751\pi$
$798$	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	$0.00269961\pi$
$809$			13.7222i			0.0169619i	−0.999964	+	0.00848096i	$0.997300\pi$
$810$		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	−0.992357	−	0.123398i	$-0.960621\pi$
$823$	−715.153	+	715.153i	−0.868959	+	0.868959i	0.123398	+	0.992357i	$0.460621\pi$
$824$		−	772.831i		−	0.937902i
$825$		0			0
$826$	212.010			0.256671
$827$	50.7044	+	50.7044i	0.0613112	+	0.0613112i	0.737098	−	0.675786i	$-0.236196\pi$
$827$	50.7044	+	50.7044i	0.0613112	+	0.0613112i	−0.675786	+	0.737098i	$0.736196\pi$
$828$	99.4633	−	99.4633i	0.120125	−	0.120125i
$829$		−	581.423i		−	0.701355i	−0.936496	−	0.350677i	$-0.885951\pi$
$829$		−	581.423i		−	0.701355i	0.936496	−	0.350677i	$-0.114049\pi$
$830$		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	$-0.970579\pi$
$839$		−	154.873i		−	0.184592i	0.995732	−	0.0922961i	$-0.0294206\pi$
$840$		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	−0.983274	−	0.182131i	$-0.941700\pi$
$853$	−683.375	+	683.375i	−0.801143	+	0.801143i	0.182131	+	0.983274i	$0.441700\pi$
$854$		−	1600.37i		−	1.87397i
$855$		0			0
$856$	509.216			0.594878
$857$	26.2520	+	26.2520i	0.0306324	+	0.0306324i	0.722257	−	0.691625i	$-0.243105\pi$
$857$	26.2520	+	26.2520i	0.0306324	+	0.0306324i	−0.691625	+	0.722257i	$0.743105\pi$
$858$	35.1471	−	35.1471i	0.0409640	−	0.0409640i
$859$			1173.28i			1.36587i	0.730481	+	0.682933i	$0.239296\pi$
$859$			1173.28i			1.36587i	−0.730481	+	0.682933i	$0.760704\pi$
$860$		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	−0.863929	−	0.503613i	$-0.832004\pi$
$863$	−310.953	+	310.953i	−0.360316	+	0.360316i	0.503613	+	0.863929i	$0.332004\pi$
$864$			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	0.890157	−	0.455654i	$-0.150595\pi$
$877$	381.058	+	381.058i	0.434502	+	0.434502i	−0.455654	+	0.890157i	$0.650595\pi$
$878$	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	−0.350677	−	0.936496i	$-0.614049\pi$
$883$	517.278	−	517.278i	0.585819	−	0.585819i	0.936496	+	0.350677i	$0.114049\pi$
$884$			1093.38i			1.23686i
$885$		0			0
$886$	−532.674			−0.601213
$887$	−356.870	−	356.870i	−0.402334	−	0.402334i	0.476721	−	0.879055i	$-0.341825\pi$
$887$	−356.870	−	356.870i	−0.402334	−	0.402334i	−0.879055	+	0.476721i	$0.841825\pi$
$888$	−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	−0.992050	−	0.125840i	$-0.959837\pi$
$907$	−1013.93	−	1013.93i	−1.11789	−	1.11789i	−0.125840	−	0.992050i	$-0.540163\pi$
$908$	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	$0.171199\pi$
$919$			941.570i			1.02456i	−0.858819	+	0.512280i	$0.828801\pi$
$920$		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	$0.0808447\pi$
$929$			466.840i			0.502519i	−0.967920	+	0.251259i	$0.919155\pi$
$930$		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	0.222930	−	0.974834i	$-0.428438\pi$
$937$	−704.534	−	704.534i	−0.751904	−	0.751904i	−0.974834	+	0.222930i	$0.928438\pi$
$938$	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	−0.800641	−	0.599144i	$-0.795508\pi$
$947$	−1325.60	−	1325.60i	−1.39979	−	1.39979i	−0.599144	−	0.800641i	$-0.704492\pi$
$948$	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	−0.417373	−	0.908735i	$-0.637049\pi$
$953$	468.268	−	468.268i	0.491363	−	0.491363i	0.908735	+	0.417373i	$0.137049\pi$
$954$		−	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	0.978659	−	0.205492i	$-0.0658794\pi$
$967$	747.653	+	747.653i	0.773167	+	0.773167i	−0.205492	+	0.978659i	$0.565879\pi$
$968$	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	0.908546	−	0.417785i	$-0.137193\pi$
$977$	479.474	+	479.474i	0.490761	+	0.490761i	−0.417785	+	0.908546i	$0.637193\pi$
$978$	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	0.112102	−	0.993697i	$-0.464242\pi$
$983$	1087.00	−	1087.00i	1.10580	−	1.10580i	0.993697	−	0.112102i	$-0.0357584\pi$
$984$		−	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	0.643432	−	0.765504i	$-0.277510\pi$
$997$	−121.706	−	121.706i	−0.122072	−	0.122072i	−0.765504	+	0.643432i	$0.777510\pi$
$998$	−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.232.9	yes	24
5.2	odd	4	inner	275.3.f.c.243.4	yes	24
5.3	odd	4	inner	275.3.f.c.243.9	yes	24
5.4	even	2	inner	275.3.f.c.232.4	✓	24

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

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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