LMFDB - Embedded newform 275.3.f.c.232.4

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			232.4
Character	$\chi$	$=$	275.232
Dual form			275.3.f.c.243.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.02070 - 1.02070i) q^{2} +(0.314710 - 0.314710i) q^{3} -1.91636i q^{4} -0.642447 q^{6} +(6.75035 + 6.75035i) q^{7} +(-6.03880 + 6.03880i) q^{8} +8.80192i q^{9} -3.31662 q^{11} +(-0.603097 - 0.603097i) q^{12} +(-16.4951 + 16.4951i) q^{13} -13.7801i q^{14} +4.66213 q^{16} +(17.2945 + 17.2945i) q^{17} +(8.98408 - 8.98408i) q^{18} -28.5631i q^{19} +4.24881 q^{21} +(3.38527 + 3.38527i) q^{22} +(-5.89670 + 5.89670i) q^{23} +3.80095i q^{24} +33.6731 q^{26} +(5.60244 + 5.60244i) q^{27} +(12.9361 - 12.9361i) q^{28} +43.9338i q^{29} +36.3584 q^{31} +(19.3966 + 19.3966i) q^{32} +(-1.04378 + 1.04378i) q^{33} -35.3049i q^{34} +16.8676 q^{36} +(-21.6303 - 21.6303i) q^{37} +(-29.1542 + 29.1542i) q^{38} +10.3824i q^{39} -34.5897 q^{41} +(-4.33674 - 4.33674i) q^{42} +(-6.04730 + 6.04730i) q^{43} +6.35584i q^{44} +12.0375 q^{46} +(12.0604 + 12.0604i) q^{47} +(1.46722 - 1.46722i) q^{48} +42.1345i q^{49} +10.8855 q^{51} +(31.6106 + 31.6106i) q^{52} +(40.1140 - 40.1140i) q^{53} -11.4368i q^{54} -81.5281 q^{56} +(-8.98910 - 8.98910i) q^{57} +(44.8431 - 44.8431i) q^{58} +15.3852i q^{59} +116.136 q^{61} +(-37.1108 - 37.1108i) q^{62} +(-59.4160 + 59.4160i) q^{63} -58.2446i q^{64} +2.13075 q^{66} +(-39.2934 - 39.2934i) q^{67} +(33.1425 - 33.1425i) q^{68} +3.71150i q^{69} -53.8611 q^{71} +(-53.1530 - 53.1530i) q^{72} +(20.3789 - 20.3789i) q^{73} +44.1559i q^{74} -54.7372 q^{76} +(-22.3884 - 22.3884i) q^{77} +(10.5973 - 10.5973i) q^{78} -0.0339654i q^{79} -75.6909 q^{81} +(35.3056 + 35.3056i) q^{82} +(-10.5848 + 10.5848i) q^{83} -8.14224i q^{84} +12.3449 q^{86} +(13.8264 + 13.8264i) q^{87} +(20.0284 - 20.0284i) q^{88} +89.4830i q^{89} -222.696 q^{91} +(11.3002 + 11.3002i) q^{92} +(11.4423 - 11.4423i) q^{93} -24.6200i q^{94} +12.2086 q^{96} +(-23.9332 - 23.9332i) q^{97} +(43.0065 - 43.0065i) q^{98} -29.1926i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	0.404285	−	0.914633i	$-0.367520\pi$
$2$	−1.02070	−	1.02070i	−0.510348	−	0.510348i	−0.914633	+	0.404285i	$0.867520\pi$
$3$	0.314710	−	0.314710i	0.104903	−	0.104903i	−0.652707	−	0.757610i	$-0.726367\pi$
$3$	0.314710	−	0.314710i	0.104903	−	0.104903i	0.757610	+	0.652707i	$0.226367\pi$
$4$		−	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	$-0.0111590\pi$
$7$	6.75035	+	6.75035i	0.964336	+	0.964336i	−0.0350498	+	0.999386i	$0.511159\pi$
$8$	−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	$0.604415\pi$
$13$	−16.4951	+	16.4951i	−1.26886	+	1.26886i	−0.946679	+	0.322178i	$0.895585\pi$
$14$		−	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	$0.00556347\pi$
$17$	17.2945	+	17.2945i	1.01732	+	1.01732i	0.0174773	+	0.999847i	$0.494437\pi$
$18$	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	−0.823579	−	0.567201i	$-0.808026\pi$
$23$	−5.89670	+	5.89670i	−0.256378	+	0.256378i	0.567201	+	0.823579i	$0.308026\pi$
$24$			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	0.351562	−	0.936165i	$-0.385651\pi$
$37$	−21.6303	−	21.6303i	−0.584602	−	0.584602i	−0.936165	+	0.351562i	$0.885651\pi$
$38$	−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	$-0.781706\pi$
$43$	−6.04730	+	6.04730i	−0.140635	+	0.140635i	0.633284	+	0.773919i	$0.281706\pi$
$44$			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	$-0.191922\pi$
$47$	12.0604	+	12.0604i	0.256604	+	0.256604i	−0.567068	+	0.823671i	$0.691922\pi$
$48$	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	$-0.570241\pi$
$53$	40.1140	−	40.1140i	0.756869	−	0.756869i	0.975751	+	0.218882i	$0.0702411\pi$
$54$		−	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	0.350205	−	0.936673i	$-0.386112\pi$
$67$	−39.2934	−	39.2934i	−0.586469	−	0.586469i	−0.936673	+	0.350205i	$0.886112\pi$
$68$	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	$-0.686751\pi$
$73$	20.3789	−	20.3789i	0.279164	−	0.279164i	0.832775	+	0.553611i	$0.186751\pi$
$74$			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	−0.767990	−	0.640462i	$-0.778743\pi$
$83$	−10.5848	+	10.5848i	−0.127528	+	0.127528i	0.640462	+	0.767990i	$0.278743\pi$
$84$		−	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	0.572895	−	0.819629i	$-0.305820\pi$
$97$	−23.9332	−	23.9332i	−0.246734	−	0.246734i	−0.819629	+	0.572895i	$0.805820\pi$
$98$	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	$-0.894770\pi$
$103$	−63.9888	+	63.9888i	−0.621250	+	0.621250i	0.324601	+	0.945851i	$0.394770\pi$
$104$		−	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	$-0.339879\pi$
$107$	−42.1620	−	42.1620i	−0.394037	−	0.394037i	−0.876124	+	0.482087i	$0.839879\pi$
$108$	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	$0.563868\pi$
$113$	−133.254	+	133.254i	−1.17924	+	1.17924i	−0.979938	+	0.199302i	$0.936132\pi$
$114$			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	$-0.0296308\pi$
$127$	114.645	+	114.645i	0.902717	+	0.902717i	−0.0929536	+	0.995670i	$0.529631\pi$
$128$	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	$-0.197176\pi$
$137$	32.0054	+	32.0054i	0.233616	+	0.233616i	−0.580584	+	0.814200i	$0.697176\pi$
$138$	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	0.368530	−	0.929616i	$-0.379861\pi$
$157$	−88.0904	−	88.0904i	−0.561085	−	0.561085i	−0.929616	+	0.368530i	$0.879861\pi$
$158$	−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	$-0.698913\pi$
$163$	36.8377	−	36.8377i	0.225998	−	0.225998i	0.811019	+	0.585020i	$0.198913\pi$
$164$			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	$-0.265718\pi$
$167$	−11.6573	−	11.6573i	−0.0698042	−	0.0698042i	−0.741147	+	0.671343i	$0.765718\pi$
$168$	−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	$-0.828930\pi$
$173$	−60.0469	+	60.0469i	−0.347092	+	0.347092i	0.511933	+	0.859025i	$0.328930\pi$
$174$		−	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	−0.547295	−	0.836940i	$-0.684342\pi$
$193$	55.9014	−	55.9014i	0.289645	−	0.289645i	0.836940	+	0.547295i	$0.184342\pi$
$194$			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	$-0.156451\pi$
$197$	80.7047	+	80.7047i	0.409669	+	0.409669i	−0.471954	+	0.881623i	$0.656451\pi$
$198$	−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	−0.471161	−	0.882047i	$-0.656165\pi$
$223$	91.6277	−	91.6277i	0.410887	−	0.410887i	0.882047	+	0.471161i	$0.156165\pi$
$224$			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	$-0.324458\pi$
$227$	−74.4106	−	74.4106i	−0.327800	−	0.327800i	−0.851749	+	0.523949i	$0.824458\pi$
$228$	−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	−0.777756	−	0.628566i	$-0.783642\pi$
$233$	−34.7612	+	34.7612i	−0.149189	+	0.149189i	0.628566	+	0.777756i	$0.283642\pi$
$234$			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	0.199893	−	0.979818i	$-0.435941\pi$
$257$	−200.441	−	200.441i	−0.779925	−	0.779925i	−0.979818	+	0.199893i	$0.935941\pi$
$258$	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	$-0.777302\pi$
$263$	−31.8630	+	31.8630i	−0.121152	+	0.121152i	0.643931	+	0.765083i	$0.277302\pi$
$264$		−	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	0.378263	−	0.925698i	$-0.376522\pi$
$277$	−151.640	−	151.640i	−0.547436	−	0.547436i	−0.925698	+	0.378263i	$0.876522\pi$
$278$	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	$-0.745448\pi$
$283$	5.72303	−	5.72303i	0.0202227	−	0.0202227i	0.717146	+	0.696923i	$0.245448\pi$
$284$			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	$-0.369170\pi$
$293$	385.663	−	385.663i	1.31626	−	1.31626i	0.916716	−	0.399540i	$-0.130830\pi$
$294$		−	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	$-0.177084\pi$
$307$	98.5870	+	98.5870i	0.321130	+	0.321130i	−0.528070	+	0.849201i	$0.677084\pi$
$308$	−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	$-0.521978\pi$
$313$	290.660	−	290.660i	0.928625	−	0.928625i	0.997617	+	0.0689921i	$0.0219783\pi$
$314$			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	$-0.272151\pi$
$317$	−31.1725	−	31.1725i	−0.0983359	−	0.0983359i	−0.754563	+	0.656227i	$0.772151\pi$
$318$	−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	$-0.985149\pi$
$337$	−352.350	−	352.350i	−1.04555	−	1.04555i	−0.0466376	−	0.998912i	$-0.514851\pi$
$338$	−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	$0.171134\pi$
$347$	475.747	+	475.747i	1.37103	+	1.37103i	0.512105	+	0.858923i	$0.328866\pi$
$348$	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	−0.391741	−	0.920075i	$-0.628127\pi$
$353$	186.502	−	186.502i	0.528334	−	0.528334i	0.920075	+	0.391741i	$0.128127\pi$
$354$		−	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	0.990900	−	0.134603i	$-0.0429758\pi$
$367$	314.261	+	314.261i	0.856297	+	0.856297i	−0.134603	+	0.990900i	$0.542976\pi$
$368$	−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	$-0.772802\pi$
$373$	−37.7552	+	37.7552i	−0.101220	+	0.101220i	0.654683	+	0.755903i	$0.272802\pi$
$374$			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	−0.854646	−	0.519211i	$-0.826226\pi$
$383$	−128.471	+	128.471i	−0.335435	+	0.335435i	0.519211	+	0.854646i	$0.326226\pi$
$384$		−	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	0.773219	−	0.634139i	$-0.218645\pi$
$397$	55.2146	+	55.2146i	0.139080	+	0.139080i	−0.634139	+	0.773219i	$0.718645\pi$
$398$	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	−0.619445	−	0.785040i	$-0.712642\pi$
$433$	71.7028	−	71.7028i	0.165595	−	0.165595i	0.785040	+	0.619445i	$0.212642\pi$
$434$		−	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	−0.348344	−	0.937367i	$-0.613256\pi$
$443$	260.937	−	260.937i	0.589022	−	0.589022i	0.937367	+	0.348344i	$0.113256\pi$
$444$			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	0.893161	−	0.449738i	$-0.148483\pi$
$457$	202.644	+	202.644i	0.443423	+	0.443423i	−0.449738	+	0.893161i	$0.648483\pi$
$458$	−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	$-0.516368\pi$
$463$	438.590	−	438.590i	0.947279	−	0.947279i	0.998678	+	0.0513990i	$0.0163680\pi$
$464$			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	$-0.431191\pi$
$467$	−355.965	−	355.965i	−0.762238	−	0.762238i	−0.976726	+	0.214489i	$0.931191\pi$
$468$	−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	0.981273	−	0.192625i	$-0.0617000\pi$
$487$	384.072	+	384.072i	0.788648	+	0.788648i	−0.192625	+	0.981273i	$0.561700\pi$
$488$	−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	−0.854723	−	0.519085i	$-0.826273\pi$
$503$	−168.826	+	168.826i	−0.335637	+	0.335637i	0.519085	+	0.854723i	$0.326273\pi$
$504$		−	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	−0.998559	−	0.0536681i	$-0.982909\pi$
$523$	−494.178	+	494.178i	−0.944891	+	0.944891i	0.0536681	+	0.998559i	$0.482909\pi$
$524$		−	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	$-0.337911\pi$
$547$	−210.940	−	210.940i	−0.385630	−	0.385630i	−0.873126	+	0.487495i	$0.837911\pi$
$548$	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	$-9.96569e-5\pi$
$557$	556.826	+	556.826i	0.999687	+	0.999687i	−0.000313081		1.00000i	$0.500100\pi$
$558$	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	$-0.987500\pi$
$563$	−540.463	+	540.463i	−0.959969	+	0.959969i	0.0392598	+	0.999229i	$0.487500\pi$
$564$		−	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	0.538037	−	0.842922i	$-0.319166\pi$
$577$	−175.919	−	175.919i	−0.304885	−	0.304885i	−0.842922	+	0.538037i	$0.819166\pi$
$578$	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	$-0.172272\pi$
$587$	200.703	+	200.703i	0.341913	+	0.341913i	−0.515173	+	0.857086i	$0.672272\pi$
$588$	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	$-0.567360\pi$
$593$	455.216	−	455.216i	0.767650	−	0.767650i	0.977692	+	0.210043i	$0.0673603\pi$
$594$			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	0.0314218	−	0.999506i	$-0.489996\pi$
$607$	−587.627	−	587.627i	−0.968084	−	0.968084i	−0.999506	+	0.0314218i	$0.989996\pi$
$608$	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	$-0.608337\pi$
$613$	373.206	−	373.206i	0.608819	−	0.608819i	0.942637	+	0.333818i	$0.108337\pi$
$614$		−	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	$-0.276186\pi$
$617$	−71.7013	−	71.7013i	−0.116210	−	0.116210i	−0.762820	+	0.646611i	$0.776186\pi$
$618$	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	−0.888895	−	0.458112i	$-0.848526\pi$
$643$	−276.993	+	276.993i	−0.430783	+	0.430783i	0.458112	+	0.888895i	$0.348526\pi$
$644$			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	$-0.974965\pi$
$647$	−695.834	−	695.834i	−1.07548	−	1.07548i	−0.0785682	−	0.996909i	$-0.525035\pi$
$648$	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	$-0.559513\pi$
$653$	520.242	−	520.242i	0.796695	−	0.796695i	0.982573	+	0.185878i	$0.0595128\pi$
$654$			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	$0.594527\pi$
$673$	−840.475	+	840.475i	−1.24885	+	1.24885i	−0.956229	+	0.292619i	$0.905473\pi$
$674$			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	$-0.377397\pi$
$677$	−373.040	−	373.040i	−0.551019	−	0.551019i	−0.926735	+	0.375716i	$0.877397\pi$
$678$	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	$-0.590054\pi$
$683$	465.186	−	465.186i	0.681093	−	0.681093i	0.960246	+	0.279154i	$0.0900538\pi$
$684$		−	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	$0.187473\pi$
$727$	1008.36	+	1008.36i	1.38702	+	1.38702i	0.555499	+	0.831517i	$0.312527\pi$
$728$	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	$-0.773041\pi$
$733$	−74.9699	+	74.9699i	−0.102278	+	0.102278i	0.654116	+	0.756394i	$0.273041\pi$
$734$		−	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	$-0.404717\pi$
$743$	929.063	−	929.063i	1.25042	−	1.25042i	0.955531	−	0.294891i	$-0.0952833\pi$
$744$			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	$-0.345711\pi$
$757$	−317.073	−	317.073i	−0.418854	−	0.418854i	−0.884809	+	0.465954i	$0.845711\pi$
$758$	−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	$0.595415\pi$
$773$	−966.787	+	966.787i	−1.25069	+	1.25069i	−0.955409	+	0.295286i	$0.904585\pi$
$774$			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	$-0.230454\pi$
$787$	68.3007	+	68.3007i	0.0867861	+	0.0867861i	−0.662381	+	0.749167i	$0.730454\pi$
$788$	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	$-0.348249\pi$
$797$	−342.399	−	342.399i	−0.429610	−	0.429610i	−0.888495	+	0.458886i	$0.848249\pi$
$798$	−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	−0.123398	−	0.992357i	$-0.539379\pi$
$823$	715.153	−	715.153i	0.868959	−	0.868959i	0.992357	+	0.123398i	$0.0393792\pi$
$824$		−	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	$-0.263804\pi$
$827$	−50.7044	−	50.7044i	−0.0613112	−	0.0613112i	−0.737098	+	0.675786i	$0.763804\pi$
$828$	−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	−0.182131	−	0.983274i	$-0.558300\pi$
$853$	683.375	−	683.375i	0.801143	−	0.801143i	0.983274	+	0.182131i	$0.0582995\pi$
$854$		−	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	$-0.256895\pi$
$857$	−26.2520	−	26.2520i	−0.0306324	−	0.0306324i	−0.722257	+	0.691625i	$0.756895\pi$
$858$	−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	−0.503613	−	0.863929i	$-0.667996\pi$
$863$	310.953	−	310.953i	0.360316	−	0.360316i	0.863929	+	0.503613i	$0.167996\pi$
$864$			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	$-0.349405\pi$
$877$	−381.058	−	381.058i	−0.434502	−	0.434502i	−0.890157	+	0.455654i	$0.849405\pi$
$878$	−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	$-0.885951\pi$
$883$	−517.278	+	517.278i	−0.585819	+	0.585819i	0.350677	+	0.936496i	$0.385951\pi$
$884$			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	$-0.158175\pi$
$887$	356.870	+	356.870i	0.402334	+	0.402334i	−0.476721	+	0.879055i	$0.658175\pi$
$888$	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	$0.0401627\pi$
$907$	1013.93	+	1013.93i	1.11789	+	1.11789i	0.125840	+	0.992050i	$0.459837\pi$
$908$	−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	0.974834	−	0.222930i	$-0.0715622\pi$
$937$	704.534	+	704.534i	0.751904	+	0.751904i	−0.222930	+	0.974834i	$0.571562\pi$
$938$	−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	$0.204492\pi$
$947$	1325.60	+	1325.60i	1.39979	+	1.39979i	0.599144	+	0.800641i	$0.295508\pi$
$948$	−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	$-0.862951\pi$
$953$	−468.268	+	468.268i	−0.491363	+	0.491363i	0.417373	+	0.908735i	$0.362951\pi$
$954$		−	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	$-0.434121\pi$
$967$	−747.653	−	747.653i	−0.773167	−	0.773167i	−0.978659	+	0.205492i	$0.934121\pi$
$968$	−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	$-0.362807\pi$
$977$	−479.474	−	479.474i	−0.490761	−	0.490761i	−0.908546	+	0.417785i	$0.862807\pi$
$978$	−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	$0.535758\pi$
$983$	−1087.00	+	1087.00i	−1.10580	+	1.10580i	−0.993697	+	0.112102i	$0.964242\pi$
$984$		−	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	$-0.222490\pi$
$997$	121.706	+	121.706i	0.122072	+	0.122072i	−0.643432	+	0.765504i	$0.722490\pi$
$998$	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.232.4	✓	24
5.2	odd	4	inner	275.3.f.c.243.9	yes	24
5.3	odd	4	inner	275.3.f.c.243.4	yes	24
5.4	even	2	inner	275.3.f.c.232.9	yes	24

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