LMFDB - Embedded newform 275.3.bk.c.82.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(82,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 8])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.82"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.bk (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [128] 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:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			82.10
Character	$\chi$	$=$	275.82
Dual form			275.3.bk.c.218.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.319362 - 0.626784i) q^{2} +(-4.31726 + 0.683787i) q^{3} +(2.06028 + 2.83573i) q^{4} +(-0.950184 + 2.92437i) q^{6} +(-13.0084 - 2.06033i) q^{7} +(5.21454 - 0.825902i) q^{8} +(9.61169 - 3.12303i) q^{9} +(-0.213753 - 10.9979i) q^{11} +(-10.8338 - 10.8338i) q^{12} +(13.4978 + 6.87747i) q^{13} +(-5.44577 + 7.49547i) q^{14} +(-3.18494 + 9.80223i) q^{16} +(14.5897 - 7.43382i) q^{17} +(1.11215 - 7.02183i) q^{18} +(8.09319 - 11.1393i) q^{19} +57.5696 q^{21} +(-6.96158 - 3.37834i) q^{22} +(18.1828 - 18.1828i) q^{23} +(-21.9478 + 7.13127i) q^{24} +(8.62138 - 6.26380i) q^{26} +(-4.30879 + 2.19544i) q^{27} +(-20.9584 - 41.1331i) q^{28} +(-13.8997 - 19.1313i) q^{29} +(-7.50428 - 23.0958i) q^{31} +(20.0595 + 20.0595i) q^{32} +(8.44307 + 47.3348i) q^{33} -11.5187i q^{34} +(28.6588 + 20.8218i) q^{36} +(-40.3915 - 6.39739i) q^{37} +(-4.39728 - 8.63015i) q^{38} +(-62.9763 - 20.4622i) q^{39} +(6.47957 + 4.70768i) q^{41} +(18.3855 - 36.0837i) q^{42} +(2.02807 - 2.02807i) q^{43} +(30.7467 - 23.2649i) q^{44} +(-5.58978 - 17.2036i) q^{46} +(-12.9511 - 81.7699i) q^{47} +(7.04758 - 44.4966i) q^{48} +(118.372 + 38.4614i) q^{49} +(-57.9044 + 42.0700i) q^{51} +(8.30656 + 52.4456i) q^{52} +(31.8036 + 16.2048i) q^{53} +3.40182i q^{54} -69.5345 q^{56} +(-27.3235 + 53.6254i) q^{57} +(-16.4302 + 2.60229i) q^{58} +(-2.35343 - 3.23921i) q^{59} +(4.51999 - 13.9111i) q^{61} +(-16.8727 - 2.67237i) q^{62} +(-131.467 + 20.8224i) q^{63} +(-20.2297 + 6.57303i) q^{64} +(32.3651 + 9.82496i) q^{66} +(-9.03804 - 9.03804i) q^{67} +(51.1391 + 26.0566i) q^{68} +(-66.0667 + 90.9330i) q^{69} +(-13.6089 + 41.8839i) q^{71} +(47.5413 - 24.2235i) q^{72} +(-2.96178 + 18.6999i) q^{73} +(-16.9093 + 23.2737i) q^{74} +48.2622 q^{76} +(-19.8788 + 143.506i) q^{77} +(-32.9376 + 32.9376i) q^{78} +(-15.7496 + 5.11737i) q^{79} +(-56.4848 + 41.0386i) q^{81} +(5.02003 - 2.55783i) q^{82} +(40.1359 + 78.7712i) q^{83} +(118.609 + 163.251i) q^{84} +(-0.623474 - 1.91885i) q^{86} +(73.0905 + 73.0905i) q^{87} +(-10.1978 - 57.1726i) q^{88} -127.945i q^{89} +(-161.415 - 117.275i) q^{91} +(89.0229 + 14.0998i) q^{92} +(48.1906 + 94.5794i) q^{93} +(-55.3881 - 17.9967i) q^{94} +(-100.319 - 72.8858i) q^{96} +(34.4715 - 67.6542i) q^{97} +(61.9105 - 61.9105i) q^{98} +(-36.4014 - 105.041i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 48 q^{6} + 32 q^{11} + 280 q^{16} - 8 q^{21} + 528 q^{26} - 16 q^{31} + 336 q^{36} - 604 q^{41} - 1152 q^{46} - 1024 q^{51} - 992 q^{56} - 320 q^{61} + 1624 q^{66} + 536 q^{71} + 1776 q^{76} + 3680 q^{81}+ \cdots - 6584 q^{96}+O(q^{100}) $ 128 * q - 48 * q^6 + 32 * q^11 + 280 * q^16 - 8 * q^21 + 528 * q^26 - 16 * q^31 + 336 * q^36 - 604 * q^41 - 1152 * q^46 - 1024 * q^51 - 992 * q^56 - 320 * q^61 + 1624 * q^66 + 536 * q^71 + 1776 * q^76 + 3680 * q^81 + 872 * q^86 - 448 * q^91 - 6584 * q^96

Character values

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

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.319362	−	0.626784i	0.159681	−	0.313392i	−0.797279	−	0.603611i	$-0.793728\pi$
$2$	0.319362	−	0.626784i	0.159681	−	0.313392i	0.956960	+	0.290219i	$0.0937281\pi$
$3$	−4.31726	+	0.683787i	−1.43909	+	0.227929i	−0.826707	−	0.562633i	$-0.809788\pi$
$3$	−4.31726	+	0.683787i	−1.43909	+	0.227929i	−0.612381	+	0.790562i	$0.709788\pi$
$4$	2.06028	+	2.83573i	0.515069	+	0.708931i
$5$		0			0
$5$		0			0
$6$	−0.950184	+	2.92437i	−0.158364	+	0.487394i
$7$	−13.0084	−	2.06033i	−1.85834	−	0.294333i	−0.876127	−	0.482081i	$-0.839881\pi$
$7$	−13.0084	−	2.06033i	−1.85834	−	0.294333i	−0.982217	+	0.187748i	$0.939881\pi$
$8$	5.21454	−	0.825902i	0.651818	−	0.103238i
$9$	9.61169	−	3.12303i	1.06797	−	0.347003i
$10$		0			0
$11$	−0.213753	−	10.9979i	−0.0194321	−	0.999811i
$11$	−0.213753	−	10.9979i	−0.0194321	−	0.999811i
$12$	−10.8338	−	10.8338i	−0.902816	−	0.902816i
$13$	13.4978	+	6.87747i	1.03829	+	0.529036i	0.888114	−	0.459623i	$-0.152015\pi$
$13$	13.4978	+	6.87747i	1.03829	+	0.529036i	0.150178	+	0.988659i	$0.452015\pi$
$14$	−5.44577	+	7.49547i	−0.388984	+	0.535390i
$15$		0			0
$16$	−3.18494	+	9.80223i	−0.199059	+	0.612640i
$17$	14.5897	−	7.43382i	0.858217	−	0.437283i	0.0312352	−	0.999512i	$-0.490056\pi$
$17$	14.5897	−	7.43382i	0.858217	−	0.437283i	0.826982	+	0.562229i	$0.190056\pi$
$18$	1.11215	−	7.02183i	0.0617860	−	0.390102i
$19$	8.09319	−	11.1393i	0.425957	−	0.586280i	−0.541062	−	0.840983i	$-0.681978\pi$
$19$	8.09319	−	11.1393i	0.425957	−	0.586280i	0.967019	+	0.254703i	$0.0819776\pi$
$20$		0			0
$21$	57.5696			2.74141
$22$	−6.96158	−	3.37834i	−0.316436	−	0.153561i
$23$	18.1828	−	18.1828i	0.790556	−	0.790556i	−0.191029	−	0.981584i	$-0.561182\pi$
$23$	18.1828	−	18.1828i	0.790556	−	0.790556i	0.981584	+	0.191029i	$0.0611824\pi$
$24$	−21.9478	+	7.13127i	−0.914492	+	0.297136i
$25$		0			0
$26$	8.62138	−	6.26380i	0.331591	−	0.240915i
$27$	−4.30879	+	2.19544i	−0.159585	+	0.0813125i
$28$	−20.9584	−	41.1331i	−0.748513	−	1.46904i
$29$	−13.8997	−	19.1313i	−0.479300	−	0.659700i	0.499070	−	0.866562i	$-0.333675\pi$
$29$	−13.8997	−	19.1313i	−0.479300	−	0.659700i	−0.978370	+	0.206861i	$0.933675\pi$
$30$		0			0
$31$	−7.50428	−	23.0958i	−0.242074	−	0.745026i	−0.996104	−	0.0881865i	$-0.971893\pi$
$31$	−7.50428	−	23.0958i	−0.242074	−	0.745026i	0.754030	−	0.656840i	$-0.228107\pi$
$32$	20.0595	+	20.0595i	0.626860	+	0.626860i
$33$	8.44307	+	47.3348i	0.255851	+	1.43439i
$34$		−	11.5187i		−	0.338784i
$35$		0			0
$36$	28.6588	+	20.8218i	0.796077	+	0.578384i
$37$	−40.3915	−	6.39739i	−1.09166	−	0.172902i	−0.415456	−	0.909613i	$-0.636378\pi$
$37$	−40.3915	−	6.39739i	−1.09166	−	0.172902i	−0.676208	+	0.736711i	$0.736378\pi$
$38$	−4.39728	−	8.63015i	−0.115718	−	0.227109i
$39$	−62.9763	−	20.4622i	−1.61478	−	0.524673i
$40$		0			0
$41$	6.47957	+	4.70768i	0.158038	+	0.114822i	0.663994	−	0.747738i	$-0.268860\pi$
$41$	6.47957	+	4.70768i	0.158038	+	0.114822i	−0.505956	+	0.862559i	$0.668860\pi$
$42$	18.3855	−	36.0837i	0.437751	−	0.859135i
$43$	2.02807	−	2.02807i	0.0471645	−	0.0471645i	−0.683131	−	0.730296i	$-0.739382\pi$
$43$	2.02807	−	2.02807i	0.0471645	−	0.0471645i	0.730296	+	0.683131i	$0.239382\pi$
$44$	30.7467	−	23.2649i	0.698789	−	0.528748i
$45$		0			0
$46$	−5.58978	−	17.2036i	−0.121517	−	0.373990i
$47$	−12.9511	−	81.7699i	−0.275555	−	1.73979i	−0.605554	−	0.795804i	$-0.707048\pi$
$47$	−12.9511	−	81.7699i	−0.275555	−	1.73979i	0.329999	−	0.943981i	$-0.392952\pi$
$48$	7.04758	−	44.4966i	0.146825	−	0.927013i
$49$	118.372	+	38.4614i	2.41575	+	0.784926i
$50$		0			0
$51$	−57.9044	+	42.0700i	−1.13538	+	0.824902i
$52$	8.30656	+	52.4456i	0.159742	+	1.00857i
$53$	31.8036	+	16.2048i	0.600068	+	0.305750i	0.727511	−	0.686096i	$-0.240677\pi$
$53$	31.8036	+	16.2048i	0.600068	+	0.305750i	−0.127443	+	0.991846i	$0.540677\pi$
$54$			3.40182i			0.0629966i
$55$		0			0
$56$	−69.5345			−1.24169
$57$	−27.3235	+	53.6254i	−0.479360	+	0.940796i
$58$	−16.4302	+	2.60229i	−0.283280	+	0.0448671i
$59$	−2.35343	−	3.23921i	−0.0398886	−	0.0549019i	0.788607	−	0.614898i	$-0.210803\pi$
$59$	−2.35343	−	3.23921i	−0.0398886	−	0.0549019i	−0.828495	+	0.559996i	$0.810803\pi$
$60$		0			0
$61$	4.51999	−	13.9111i	0.0740982	−	0.228051i	−0.907147	−	0.420813i	$-0.861745\pi$
$61$	4.51999	−	13.9111i	0.0740982	−	0.228051i	0.981245	+	0.192763i	$0.0617447\pi$
$62$	−16.8727	−	2.67237i	−0.272140	−	0.0431027i
$63$	−131.467	+	20.8224i	−2.08678	+	0.330514i
$64$	−20.2297	+	6.57303i	−0.316089	+	0.102704i
$65$		0			0
$66$	32.3651	+	9.82496i	0.490380	+	0.148863i
$67$	−9.03804	−	9.03804i	−0.134896	−	0.134896i	0.636435	−	0.771331i	$-0.280409\pi$
$67$	−9.03804	−	9.03804i	−0.134896	−	0.134896i	−0.771331	+	0.636435i	$0.780409\pi$
$68$	51.1391	+	26.0566i	0.752045	+	0.383186i
$69$	−66.0667	+	90.9330i	−0.957488	+	1.31787i
$70$		0			0
$71$	−13.6089	+	41.8839i	−0.191675	+	0.589914i	0.808325	+	0.588737i	$0.200375\pi$
$71$	−13.6089	+	41.8839i	−0.191675	+	0.589914i	−0.999999	+	0.00117716i	$0.999625\pi$
$72$	47.5413	−	24.2235i	0.660295	−	0.336437i
$73$	−2.96178	+	18.6999i	−0.0405723	+	0.256163i	−0.999635	−	0.0270318i	$-0.991394\pi$
$73$	−2.96178	+	18.6999i	−0.0405723	+	0.256163i	0.959062	+	0.283195i	$0.0913945\pi$
$74$	−16.9093	+	23.2737i	−0.228504	+	0.314509i
$75$		0			0
$76$	48.2622			0.635029
$77$	−19.8788	+	143.506i	−0.258166	+	1.86371i
$78$	−32.9376	+	32.9376i	−0.422278	+	0.422278i
$79$	−15.7496	+	5.11737i	−0.199363	+	0.0647768i	−0.406996	−	0.913430i	$-0.633424\pi$
$79$	−15.7496	+	5.11737i	−0.199363	+	0.0647768i	0.207634	+	0.978207i	$0.433424\pi$
$80$		0			0
$81$	−56.4848	+	41.0386i	−0.697343	+	0.506649i
$82$	5.02003	−	2.55783i	0.0612199	−	0.0311931i
$83$	40.1359	+	78.7712i	0.483565	+	0.949051i	0.995917	+	0.0902748i	$0.0287745\pi$
$83$	40.1359	+	78.7712i	0.483565	+	0.949051i	−0.512351	+	0.858776i	$0.671225\pi$
$84$	118.609	+	163.251i	1.41201	+	1.94347i
$85$		0			0
$86$	−0.623474	−	1.91885i	−0.00724969	−	0.0223123i
$87$	73.0905	+	73.0905i	0.840120	+	0.840120i
$88$	−10.1978	−	57.1726i	−0.115884	−	0.649688i
$89$		−	127.945i		−	1.43759i	−0.695224	−	0.718793i	$-0.744695\pi$
$89$		−	127.945i		−	1.43759i	0.695224	−	0.718793i	$-0.255305\pi$
$90$		0			0
$91$	−161.415	−	117.275i	−1.77379	−	1.28873i
$92$	89.0229	+	14.0998i	0.967640	+	0.153259i
$93$	48.1906	+	94.5794i	0.518178	+	1.01698i
$94$	−55.3881	−	17.9967i	−0.589236	−	0.191454i
$95$		0			0
$96$	−100.319	−	72.8858i	−1.04499	−	0.759227i
$97$	34.4715	−	67.6542i	0.355377	−	0.697466i	−0.642237	−	0.766506i	$-0.721994\pi$
$97$	34.4715	−	67.6542i	0.355377	−	0.697466i	0.997614	+	0.0690401i	$0.0219937\pi$
$98$	61.9105	−	61.9105i	0.631740	−	0.631740i
$99$	−36.4014	−	105.041i	−0.367690	−	1.06102i
$100$		0			0
$101$	2.71127	+	8.34445i	0.0268443	+	0.0826183i	0.963581	−	0.267416i	$-0.0861699\pi$
$101$	2.71127	+	8.34445i	0.0268443	+	0.0826183i	−0.936737	+	0.350034i	$0.886170\pi$
$102$	7.87631	+	49.7291i	0.0772188	+	0.487540i
$103$	12.7256	−	80.3463i	0.123550	−	0.780061i	−0.845642	−	0.533751i	$-0.820782\pi$
$103$	12.7256	−	80.3463i	0.123550	−	0.780061i	0.969191	−	0.246310i	$-0.0792181\pi$
$104$	76.0650	+	24.7150i	0.731394	+	0.237644i
$105$		0			0
$106$	20.3138	−	14.7588i	0.191639	−	0.139234i
$107$	9.20763	+	58.1347i	0.0860526	+	0.543315i	0.992621	+	0.121256i	$0.0386923\pi$
$107$	9.20763	+	58.1347i	0.0860526	+	0.543315i	−0.906569	+	0.422058i	$0.861308\pi$
$108$	−15.1030	−	7.69534i	−0.139842	−	0.0712531i
$109$		−	188.047i		−	1.72520i	−0.505885	−	0.862601i	$-0.668834\pi$
$109$		−	188.047i		−	1.72520i	0.505885	−	0.862601i	$-0.331166\pi$
$110$		0			0
$111$	178.755			1.61041
$112$	61.6268	−	120.949i	0.550239	−	1.07991i
$113$	−152.384	+	24.1353i	−1.34853	+	0.213587i	−0.788577	−	0.614936i	$-0.789182\pi$
$113$	−152.384	+	24.1353i	−1.34853	+	0.213587i	−0.559956	+	0.828523i	$0.689182\pi$
$114$	24.8854	+	34.2518i	0.218293	+	0.300455i
$115$		0			0
$116$	25.6139	−	78.8315i	0.220810	−	0.679582i
$117$	151.215	+	23.9501i	1.29244	+	0.204702i
$118$	−2.78188	+	0.440607i	−0.0235753	+	0.00373395i
$119$	−205.105	+	66.6426i	−1.72357	+	0.560022i
$120$		0			0
$121$	−120.909	+	4.70168i	−0.999245	+	0.0388568i
$122$	−7.27574	−	7.27574i	−0.0596372	−	0.0596372i
$123$	−31.1931	−	15.8937i	−0.253602	−	0.129217i
$124$	50.0325	−	68.8638i	0.403488	−	0.555353i
$125$		0			0
$126$	−28.9346	+	89.0514i	−0.229639	+	0.706757i
$127$	142.858	−	72.7897i	1.12486	−	0.573147i	0.210320	−	0.977633i	$-0.432549\pi$
$127$	142.858	−	72.7897i	1.12486	−	0.573147i	0.914544	+	0.404486i	$0.132549\pi$
$128$	−20.0920	+	126.856i	−0.156968	+	0.991059i
$129$	−7.36896	+	10.1425i	−0.0571237	+	0.0786241i
$130$		0			0
$131$	101.790			0.777022			0.388511	−	0.921444i	$-0.372990\pi$
$131$	101.790			0.777022			0.388511	+	0.921444i	$0.372990\pi$
$132$	−116.833	+	121.465i	−0.885102	+	0.920189i
$133$	−128.230	+	128.230i	−0.964136	+	0.964136i
$134$	−8.55130	+	2.77849i	−0.0638157	+	0.0207350i
$135$		0			0
$136$	69.9389	−	50.8136i	0.514257	−	0.373629i
$137$	−66.1876	+	33.7243i	−0.483121	+	0.246163i	−0.678548	−	0.734556i	$-0.737391\pi$
$137$	−66.1876	+	33.7243i	−0.483121	+	0.246163i	0.195427	+	0.980718i	$0.437391\pi$
$138$	35.8961	+	70.4501i	0.260117	+	0.510508i
$139$	16.4112	+	22.5880i	0.118066	+	0.162504i	0.863959	−	0.503561i	$-0.167977\pi$
$139$	16.4112	+	22.5880i	0.118066	+	0.162504i	−0.745893	+	0.666065i	$0.767977\pi$
$140$		0			0
$141$	111.827	+	344.167i	0.793096	+	2.44090i
$142$	21.9060	+	21.9060i	0.154267	+	0.154267i
$143$	72.7527	−	149.918i	0.508760	−	1.04838i
$144$			104.163i			0.723352i
$145$		0			0
$146$	10.7749	+	7.82845i	0.0738009	+	0.0536195i
$147$	−537.342	−	85.1067i	−3.65539	−	0.578957i
$148$	−65.0765	−	127.720i	−0.439706	−	0.862971i
$149$	156.113	+	50.7242i	1.04774	+	0.340431i	0.781780	−	0.623554i	$-0.214312\pi$
$149$	156.113	+	50.7242i	1.04774	+	0.340431i	0.265958	+	0.963985i	$0.414312\pi$
$150$		0			0
$151$	−78.3338	−	56.9128i	−0.518767	−	0.376906i	0.297372	−	0.954762i	$-0.403890\pi$
$151$	−78.3338	−	56.9128i	−0.518767	−	0.376906i	−0.816139	+	0.577855i	$0.803890\pi$
$152$	33.0023	−	64.7706i	0.217120	−	0.426122i
$153$	117.016	−	117.016i	0.764808	−	0.764808i
$154$	83.5986	+	58.2900i	0.542848	+	0.378507i
$155$		0			0
$156$	−71.7232	−	220.741i	−0.459764	−	1.41501i
$157$	−30.5273	−	192.742i	−0.194441	−	1.22765i	−0.871006	−	0.491272i	$-0.836532\pi$
$157$	−30.5273	−	192.742i	−0.194441	−	1.22765i	0.676565	−	0.736383i	$-0.263468\pi$
$158$	−1.82236	+	11.5059i	−0.0115339	+	0.0728222i
$159$	−148.385	−	48.2133i	−0.933241	−	0.303228i
$160$		0			0
$161$	−273.991	+	199.066i	−1.70181	+	1.23644i
$162$	7.68322	+	48.5099i	0.0474273	+	0.299444i
$163$	−67.2428	−	34.2619i	−0.412532	−	0.210196i	0.235392	−	0.971901i	$-0.424363\pi$
$163$	−67.2428	−	34.2619i	−0.412532	−	0.210196i	−0.647924	+	0.761705i	$0.724363\pi$
$164$			28.0734i			0.171179i
$165$		0			0
$166$	62.1904			0.374641
$167$	−41.2215	+	80.9018i	−0.246836	+	0.484442i	−0.980868	−	0.194672i	$-0.937636\pi$
$167$	−41.2215	+	80.9018i	−0.246836	+	0.484442i	0.734033	+	0.679114i	$0.237636\pi$
$168$	300.199	−	47.5468i	1.78690	−	0.283017i
$169$	35.5553	+	48.9377i	0.210386	+	0.289572i
$170$		0			0
$171$	43.0008	−	132.343i	0.251467	−	0.773935i
$172$	9.92945	+	1.57267i	0.0577294	+	0.00914344i
$173$	110.029	−	17.4269i	0.636005	−	0.100733i	0.169898	−	0.985462i	$-0.445656\pi$
$173$	110.029	−	17.4269i	0.636005	−	0.100733i	0.466107	+	0.884728i	$0.345656\pi$
$174$	69.1542	−	22.4696i	0.397438	−	0.129135i
$175$		0			0
$176$	108.485	+	32.9325i	0.616392	+	0.187116i
$177$	12.3753	+	12.3753i	0.0699169	+	0.0699169i
$178$	−80.1939	−	40.8609i	−0.450528	−	0.229555i
$179$	−64.2046	+	88.3700i	−0.358685	+	0.493687i	−0.949782	−	0.312913i	$-0.898695\pi$
$179$	−64.2046	+	88.3700i	−0.358685	+	0.493687i	0.591097	+	0.806601i	$0.298695\pi$
$180$		0			0
$181$	27.7256	−	85.3307i	0.153180	−	0.471440i	−0.844792	−	0.535095i	$-0.820276\pi$
$181$	27.7256	−	85.3307i	0.153180	−	0.471440i	0.997972	+	0.0636550i	$0.0202757\pi$
$182$	−125.056	+	63.7191i	−0.687120	+	0.350105i
$183$	−10.0018	+	63.1486i	−0.0546544	+	0.345074i
$184$	79.7976	−	109.832i	0.433683	−	0.596913i
$185$		0			0
$186$	74.6711			0.401457
$187$	−84.8751	−	158.867i	−0.453878	−	0.849558i
$188$	205.194	−	205.194i	1.09146	−	1.09146i
$189$	60.5738	−	19.6816i	0.320496	−	0.104136i
$190$		0			0
$191$	272.747	−	198.163i	1.42800	−	1.03750i	0.437611	−	0.899164i	$-0.355825\pi$
$191$	272.747	−	198.163i	1.42800	−	1.03750i	0.990385	−	0.138336i	$-0.0441755\pi$
$192$	82.8424	−	42.2103i	0.431471	−	0.219845i
$193$	−11.8565	−	23.2697i	−0.0614328	−	0.120569i	0.858248	−	0.513235i	$-0.171553\pi$
$193$	−11.8565	−	23.2697i	−0.0614328	−	0.120569i	−0.919681	+	0.392666i	$0.871553\pi$
$194$	−31.3956	−	43.2124i	−0.161833	−	0.222744i
$195$		0			0
$196$	134.813	+	414.911i	0.687821	+	2.11689i
$197$	−232.768	−	232.768i	−1.18157	−	1.18157i	−0.979339	−	0.202227i	$-0.935182\pi$
$197$	−232.768	−	232.768i	−1.18157	−	1.18157i	−0.202227	−	0.979339i	$-0.564818\pi$
$198$	−77.4633	−	10.7304i	−0.391229	−	0.0541939i
$199$			177.068i			0.889787i	0.895583	+	0.444894i	$0.146758\pi$
$199$			177.068i			0.889787i	−0.895583	+	0.444894i	$0.853242\pi$
$200$		0			0
$201$	45.1997	+	32.8395i	0.224874	+	0.163381i
$202$	6.09604	+	0.965518i	0.0301784	+	0.00477979i
$203$	141.396	+	277.506i	0.696533	+	1.36702i
$204$	−238.598	−	77.5252i	−1.16960	−	0.380025i
$205$		0			0
$206$	−46.2957	−	33.6358i	−0.224736	−	0.163280i
$207$	117.982	−	231.553i	0.569961	−	1.11861i
$208$	−110.404	+	110.404i	−0.530790	+	0.530790i
$209$	−124.239	−	86.6272i	−0.594446	−	0.414484i
$210$		0			0
$211$	59.0985	+	181.886i	0.280088	+	0.862021i	0.987828	+	0.155549i	$0.0497145\pi$
$211$	59.0985	+	181.886i	0.280088	+	0.862021i	−0.707741	+	0.706472i	$0.750285\pi$
$212$	19.5720	+	123.573i	0.0923207	+	0.582890i
$213$	30.1136	−	190.130i	0.141378	−	0.892627i
$214$	39.3784	+	12.7948i	0.184011	+	0.0597889i
$215$		0			0
$216$	−20.6551	+	15.0068i	−0.0956257	+	0.0694761i
$217$	50.0338	+	315.901i	0.230571	+	1.45576i
$218$	−117.865	−	60.0551i	−0.540664	−	0.275482i
$219$		−	82.7578i		−	0.377889i
$220$		0			0
$221$	248.055			1.12242
$222$	57.0877	−	112.041i	0.257152	−	0.504689i
$223$	−89.9452	+	14.2459i	−0.403342	+	0.0638830i	−0.354810	−	0.934939i	$-0.615454\pi$
$223$	−89.9452	+	14.2459i	−0.403342	+	0.0638830i	−0.0485320	+	0.998822i	$0.515454\pi$
$224$	−219.613	−	302.272i	−0.980416	−	1.34943i
$225$		0			0
$226$	−33.5382	+	103.220i	−0.148399	+	0.456725i
$227$	186.341	+	29.5135i	0.820886	+	0.130016i	0.552730	−	0.833360i	$-0.313586\pi$
$227$	186.341	+	29.5135i	0.820886	+	0.130016i	0.268155	+	0.963376i	$0.413586\pi$
$228$	−208.361	+	33.0011i	−0.913863	+	0.144742i
$229$	399.540	−	129.818i	1.74471	−	0.566892i	0.749272	−	0.662262i	$-0.230403\pi$
$229$	399.540	−	129.818i	1.74471	−	0.566892i	0.995442	+	0.0953700i	$0.0304034\pi$
$230$		0			0
$231$	−12.3057	−	633.146i	−0.0532712	−	2.74089i
$232$	−88.2812	−	88.2812i	−0.380522	−	0.380522i
$233$	66.4024	+	33.8337i	0.284989	+	0.145209i	0.590642	−	0.806934i	$-0.298875\pi$
$233$	66.4024	+	33.8337i	0.284989	+	0.145209i	−0.305653	+	0.952143i	$0.598875\pi$
$234$	63.3040	−	87.1305i	0.270530	−	0.372353i
$235$		0			0
$236$	4.33681	−	13.3473i	0.0183763	−	0.0565565i
$237$	64.4962	−	32.8624i	0.272136	−	0.138660i
$238$	−23.7322	+	149.839i	−0.0997153	+	0.629577i
$239$	−223.524	+	307.655i	−0.935249	+	1.28726i	0.0225279	+	0.999746i	$0.492829\pi$
$239$	−223.524	+	307.655i	−0.935249	+	1.28726i	−0.957777	+	0.287513i	$0.907171\pi$
$240$		0			0
$241$	200.573			0.832252			0.416126	−	0.909307i	$-0.363388\pi$
$241$	200.573			0.832252			0.416126	+	0.909307i	$0.363388\pi$
$242$	−35.6667	+	77.2851i	−0.147383	+	0.319360i
$243$	246.573	−	246.573i	1.01471	−	1.01471i
$244$	48.7605	−	15.8432i	0.199838	−	0.0649313i
$245$		0			0
$246$	−19.9238	+	14.4755i	−0.0809909	+	0.0588434i
$247$	185.851	−	94.6956i	0.752431	−	0.383383i
$248$	−58.2063	−	114.236i	−0.234703	−	0.460630i
$249$	−227.140	−	312.632i	−0.912210	−	1.25555i
$250$		0			0
$251$	−130.177	−	400.643i	−0.518633	−	1.59619i	−0.776574	−	0.630026i	$-0.783044\pi$
$251$	−130.177	−	400.643i	−0.518633	−	1.59619i	0.257941	−	0.966161i	$-0.416956\pi$
$252$	−329.905	−	329.905i	−1.30915	−	1.30915i
$253$	−203.859	−	196.086i	−0.805768	−	0.775044i
$254$		−	112.787i		−	0.444044i
$255$		0			0
$256$	4.26078	+	3.09564i	0.0166437	+	0.0120923i
$257$	285.808	+	45.2675i	1.11209	+	0.176138i	0.685335	−	0.728228i	$-0.259656\pi$
$257$	285.808	+	45.2675i	1.11209	+	0.176138i	0.426758	+	0.904366i	$0.359656\pi$
$258$	4.00379	+	7.85788i	0.0155186	+	0.0304569i
$259$	512.249	+	166.440i	1.97780	+	0.642625i
$260$		0			0
$261$	−193.347	−	140.475i	−0.740794	−	0.538219i
$262$	32.5078	−	63.8002i	0.124076	−	0.243512i
$263$	−223.157	+	223.157i	−0.848508	+	0.848508i	−0.989947	−	0.141439i	$-0.954827\pi$
$263$	−223.157	+	223.157i	−0.848508	+	0.848508i	0.141439	+	0.989947i	$0.454827\pi$
$264$	83.1206	+	239.856i	0.314851	+	0.908545i
$265$		0			0
$266$	39.4207	+	121.324i	0.148198	+	0.456107i
$267$	87.4873	+	552.373i	0.327668	+	2.06881i
$268$	7.00855	−	44.2502i	0.0261513	−	0.165113i
$269$	−6.81385	−	2.21395i	−0.0253303	−	0.00823031i	0.296324	−	0.955087i	$-0.404239\pi$
$269$	−6.81385	−	2.21395i	−0.0253303	−	0.00823031i	−0.321655	+	0.946857i	$0.604239\pi$
$270$		0			0
$271$	6.58911	−	4.78727i	0.0243141	−	0.0176652i	−0.575562	−	0.817758i	$-0.695217\pi$
$271$	6.58911	−	4.78727i	0.0243141	−	0.0176652i	0.599876	+	0.800093i	$0.295217\pi$
$272$	26.4008	+	166.688i	0.0970616	+	0.612823i
$273$	777.062	+	395.933i	2.84638	+	1.45030i
$274$			52.2556i			0.190714i
$275$		0			0
$276$	−393.977			−1.42745
$277$	−49.1219	+	96.4071i	−0.177335	+	0.348040i	−0.962515	−	0.271228i	$-0.912570\pi$
$277$	−49.1219	+	96.4071i	−0.177335	+	0.348040i	0.785180	+	0.619268i	$0.212570\pi$
$278$	19.3989	−	3.07249i	0.0697803	−	0.0110521i
$279$	−144.258	−	198.554i	−0.517053	−	0.711662i
$280$		0			0
$281$	−149.234	+	459.294i	−0.531081	+	1.63450i	0.220888	+	0.975299i	$0.429104\pi$
$281$	−149.234	+	459.294i	−0.531081	+	1.63450i	−0.751969	+	0.659199i	$0.770896\pi$
$282$	251.431	+	39.8228i	0.891600	+	0.141216i
$283$	−345.559	+	54.7312i	−1.22106	+	0.193396i	−0.733497	−	0.679693i	$-0.762113\pi$
$283$	−345.559	+	54.7312i	−1.22106	+	0.193396i	−0.487560	+	0.873089i	$0.662113\pi$
$284$	−146.809	+	47.7013i	−0.516935	+	0.167962i
$285$		0			0
$286$	−70.7316	−	93.4783i	−0.247313	−	0.326847i
$287$	−74.5895	−	74.5895i	−0.259894	−	0.259894i
$288$	255.452	+	130.160i	0.886988	+	0.451943i
$289$	−12.2725	+	16.8917i	−0.0424656	+	0.0584488i
$290$		0			0
$291$	−102.562	+	315.652i	−0.352445	+	1.08472i
$292$	−59.1300	+	30.1282i	−0.202500	+	0.103179i
$293$	6.72234	−	42.4432i	0.0229431	−	0.144857i	−0.973558	−	0.228442i	$-0.926637\pi$
$293$	6.72234	−	42.4432i	0.0229431	−	0.144857i	0.996501	+	0.0835846i	$0.0266369\pi$
$294$	−224.950	+	309.617i	−0.765137	+	1.05312i
$295$		0			0
$296$	−215.907			−0.729415
$297$	25.0663	+	46.9185i	0.0843982	+	0.157975i
$298$	81.6497	−	81.6497i	0.273992	−	0.273992i
$299$	370.479	−	120.376i	1.23906	−	0.402595i
$300$		0			0
$301$	−30.5605	+	22.2035i	−0.101530	+	0.0737658i
$302$	−60.6889	+	30.9225i	−0.200957	+	0.102392i
$303$	−17.4111	−	34.1712i	−0.0574624	−	0.112776i
$304$	83.4139	+	114.809i	0.274388	+	0.377662i
$305$		0			0
$306$	−35.9731	−	110.714i	−0.117559	−	0.361810i
$307$	−193.007	−	193.007i	−0.628687	−	0.628687i	0.319051	−	0.947738i	$-0.396636\pi$
$307$	−193.007	−	193.007i	−0.628687	−	0.628687i	−0.947738	+	0.319051i	$0.896636\pi$
$308$	−447.899	+	239.291i	−1.45422	+	0.776918i
$309$			355.578i			1.15074i
$310$		0			0
$311$	411.736	+	299.144i	1.32391	+	0.961877i	0.999875	+	0.0158323i	$0.00503980\pi$
$311$	411.736	+	299.144i	1.32391	+	0.961877i	0.324036	+	0.946045i	$0.394960\pi$
$312$	−345.292	−	54.6889i	−1.10671	−	0.175285i
$313$	80.7764	+	158.533i	0.258072	+	0.506494i	0.983295	−	0.182020i	$-0.0582635\pi$
$313$	80.7764	+	158.533i	0.258072	+	0.506494i	−0.725223	+	0.688514i	$0.758263\pi$
$314$	−130.557	−	42.4204i	−0.415785	−	0.135097i
$315$		0			0
$316$	−46.9601	−	34.1185i	−0.148608	−	0.107970i
$317$	156.348	−	306.850i	0.493211	−	0.967982i	−0.501489	−	0.865164i	$-0.667214\pi$
$317$	156.348	−	306.850i	0.493211	−	0.967982i	0.994700	−	0.102818i	$-0.0327859\pi$
$318$	−77.6079	+	77.6079i	−0.244050	+	0.244050i
$319$	−207.434	+	156.957i	−0.650262	+	0.492029i
$320$		0			0
$321$	−79.5035	−	244.687i	−0.247674	−	0.762264i
$322$	37.2691	+	235.308i	0.115742	+	0.730769i
$323$	35.2694	−	222.682i	0.109193	−	0.689419i
$324$	−232.748	−	75.6246i	−0.718359	−	0.233409i
$325$		0			0
$326$	−42.9496	+	31.2047i	−0.131747	+	0.0957200i
$327$	128.584	+	811.849i	0.393224	+	2.48272i
$328$	37.6761	+	19.1969i	0.114866	+	0.0585272i
$329$			1090.38i			3.31423i
$330$		0			0
$331$	−371.190			−1.12142			−0.560709	−	0.828013i	$-0.689471\pi$
$331$	−371.190			−1.12142			−0.560709	+	0.828013i	$0.689471\pi$
$332$	−140.682	+	276.105i	−0.423742	+	0.831641i
$333$	−408.210	+	64.6542i	−1.22586	+	0.194157i
$334$	37.5433	+	51.6740i	0.112405	+	0.154712i
$335$		0			0
$336$	−183.355	+	564.310i	−0.545701	+	1.67949i
$337$	507.358	+	80.3577i	1.50551	+	0.238450i	0.854035	−	0.520216i	$-0.174149\pi$
$337$	507.358	+	80.3577i	1.50551	+	0.238450i	0.651480	+	0.758666i	$0.274149\pi$
$338$	42.0283	−	6.65663i	0.124344	−	0.0196942i
$339$	641.379	−	208.397i	1.89197	−	0.614740i
$340$		0			0
$341$	−252.402	+	87.4683i	−0.740181	+	0.256505i
$342$	−69.2176	−	69.2176i	−0.202391	−	0.202391i
$343$	−885.569	−	451.220i	−2.58184	−	1.31551i
$344$	8.90049	−	12.2505i	0.0258735	−	0.0356118i
$345$		0			0
$346$	24.2162	−	74.5297i	0.0699890	−	0.215404i
$347$	−403.252	+	205.467i	−1.16211	+	0.592124i	−0.925227	−	0.379414i	$-0.876126\pi$
$347$	−403.252	+	205.467i	−1.16211	+	0.592124i	−0.236882	+	0.971538i	$0.576126\pi$
$348$	−56.6780	+	357.851i	−0.162868	+	1.02831i
$349$	244.753	−	336.873i	0.701298	−	0.965254i	−0.298643	−	0.954365i	$-0.596534\pi$
$349$	244.753	−	336.873i	0.701298	−	0.965254i	0.999941	−	0.0108886i	$-0.00346603\pi$
$350$		0			0
$351$	−73.2582			−0.208713
$352$	216.325	−	224.901i	0.614561	−	0.638923i
$353$	−37.2917	+	37.2917i	−0.105642	+	0.105642i	−0.757952	−	0.652310i	$-0.773800\pi$
$353$	−37.2917	+	37.2917i	−0.105642	+	0.105642i	0.652310	+	0.757952i	$0.273800\pi$
$354$	11.7088	−	3.80443i	0.0330758	−	0.0107470i
$355$		0			0
$356$	362.817	−	263.602i	1.01915	−	0.740456i
$357$	839.922	−	427.962i	2.35272	−	1.19877i
$358$	34.8844	+	68.4644i	0.0974424	+	0.191241i
$359$	30.7953	+	42.3861i	0.0857808	+	0.118067i	0.849751	−	0.527185i	$-0.176752\pi$
$359$	30.7953	+	42.3861i	0.0857808	+	0.118067i	−0.763970	+	0.645252i	$0.776752\pi$
$360$		0			0
$361$	52.9704	+	163.026i	0.146733	+	0.451596i
$362$	−44.6294	−	44.6294i	−0.123286	−	0.123286i
$363$	518.779	−	102.974i	1.42914	−	0.283675i
$364$		−	699.347i		−	1.92128i
$365$		0			0
$366$	36.3863	+	26.4362i	0.0994162	+	0.0722301i
$367$	−400.357	−	63.4104i	−1.09089	−	0.172780i	−0.415029	−	0.909808i	$-0.636229\pi$
$367$	−400.357	−	63.4104i	−1.09089	−	0.172780i	−0.675862	+	0.737028i	$0.736229\pi$
$368$	120.321	+	236.143i	0.326959	+	0.641692i
$369$	76.9819	+	25.0129i	0.208623	+	0.0677857i
$370$		0			0
$371$	−380.327	−	276.324i	−1.02514	−	0.744809i
$372$	−168.915	+	331.515i	−0.454073	+	0.891169i
$373$	302.827	−	302.827i	0.811869	−	0.811869i	−0.173045	−	0.984914i	$-0.555361\pi$
$373$	302.827	−	302.827i	0.811869	−	0.811869i	0.984914	+	0.173045i	$0.0553606\pi$
$374$	−126.681	+	2.46215i	−0.338720	+	0.00658328i
$375$		0			0
$376$	−135.068	−	415.696i	−0.359223	−	1.10558i
$377$	−56.0404	−	353.825i	−0.148648	−	0.938529i
$378$	7.00887	−	44.2522i	0.0185420	−	0.117069i
$379$	−687.228	−	223.294i	−1.81327	−	0.589166i	−0.999973	−	0.00731228i	$-0.997672\pi$
$379$	−687.228	−	223.294i	−1.81327	−	0.589166i	−0.813293	−	0.581854i	$-0.802328\pi$
$380$		0			0
$381$	−566.982	+	411.936i	−1.48814	+	1.08120i
$382$	−37.0999	−	234.239i	−0.0971200	−	0.613192i
$383$	158.162	+	80.5874i	0.412955	+	0.210411i	0.648110	−	0.761547i	$-0.275560\pi$
$383$	158.162	+	80.5874i	0.412955	+	0.210411i	−0.235155	+	0.971958i	$0.575560\pi$
$384$		−	561.408i		−	1.46200i
$385$		0			0
$386$	−18.3716			−0.0475949
$387$	13.1595	−	25.8270i	0.0340039	−	0.0667363i
$388$	262.870	−	41.6344i	0.677499	−	0.107305i
$389$	−125.468	−	172.692i	−0.322540	−	0.443938i	0.616701	−	0.787198i	$-0.288469\pi$
$389$	−125.468	−	172.692i	−0.322540	−	0.443938i	−0.939240	+	0.343260i	$0.888469\pi$
$390$		0			0
$391$	130.114	−	400.449i	0.332771	−	1.02417i
$392$	649.021	+	102.795i	1.65566	+	0.262232i
$393$	−439.454	+	69.6026i	−1.11820	+	0.177106i
$394$	−220.233	+	71.5580i	−0.558967	+	0.181619i
$395$		0			0
$396$	222.871	−	319.638i	0.562806	−	0.807166i
$397$	233.012	+	233.012i	0.586931	+	0.586931i	0.936799	−	0.349868i	$-0.113773\pi$
$397$	233.012	+	233.012i	0.586931	+	0.586931i	−0.349868	+	0.936799i	$0.613773\pi$
$398$	110.983	+	56.5487i	0.278852	+	0.142082i
$399$	465.921	−	641.285i	1.16772	−	1.60723i
$400$		0			0
$401$	68.5200	−	210.883i	0.170873	−	0.525893i	−0.828548	−	0.559918i	$-0.810833\pi$
$401$	68.5200	−	210.883i	0.170873	−	0.525893i	0.999421	+	0.0340253i	$0.0108327\pi$
$402$	35.0183	−	17.8427i	0.0871103	−	0.0443849i
$403$	57.5495	−	363.353i	0.142803	−	0.901621i
$404$	−18.0766	+	24.8803i	−0.0447440	+	0.0615849i
$405$		0			0
$406$	219.093			0.539637
$407$	−61.7242	+	445.591i	−0.151657	+	1.09482i
$408$	−267.199	+	267.199i	−0.654900	+	0.654900i
$409$	−626.680	+	203.621i	−1.53222	+	0.497850i	−0.949218	−	0.314618i	$-0.898123\pi$
$409$	−626.680	+	203.621i	−1.53222	+	0.497850i	−0.583006	+	0.812468i	$0.698123\pi$
$410$		0			0
$411$	262.689	−	190.855i	0.639146	−	0.464367i
$412$	254.058	−	129.449i	0.616646	−	0.314197i
$413$	23.9405	+	46.9858i	0.0579673	+	0.113767i
$414$	−107.454	−	147.898i	−0.259552	−	0.357242i
$415$		0			0
$416$	132.801	+	408.718i	0.319232	+	0.982496i
$417$	−86.2968	−	86.2968i	−0.206947	−	0.206947i
$418$	−93.9738	+	50.2057i	−0.224818	+	0.120109i
$419$			154.214i			0.368052i	0.982921	+	0.184026i	$0.0589131\pi$
$419$			154.214i			0.368052i	−0.982921	+	0.184026i	$0.941087\pi$
$420$		0			0
$421$	39.6777	+	28.8275i	0.0942463	+	0.0684740i	0.633910	−	0.773406i	$-0.281449\pi$
$421$	39.6777	+	28.8275i	0.0942463	+	0.0684740i	−0.539664	+	0.841880i	$0.681449\pi$
$422$	132.877	+	21.0457i	0.314875	+	0.0498713i
$423$	−379.852	−	745.501i	−0.897995	−	1.76241i
$424$	179.225	+	58.2337i	0.422700	+	0.137344i
$425$		0			0
$426$	−109.553	−	79.5949i	−0.257167	−	0.186842i
$427$	−87.4593	+	171.649i	−0.204823	+	0.401987i
$428$	−145.884	+	145.884i	−0.340850	+	0.340850i
$429$	−211.581	+	696.982i	−0.493195	+	1.62467i
$430$		0			0
$431$	255.703	+	786.973i	0.593279	+	1.82592i	0.563114	+	0.826379i	$0.309603\pi$
$431$	255.703	+	786.973i	0.593279	+	1.82592i	0.0301645	+	0.999545i	$0.490397\pi$
$432$	−7.79696	−	49.2281i	−0.0180485	−	0.113954i
$433$	−46.0859	+	290.975i	−0.106434	+	0.671998i	0.875563	+	0.483103i	$0.160490\pi$
$433$	−46.0859	+	290.975i	−0.106434	+	0.671998i	−0.981997	+	0.188895i	$0.939510\pi$
$434$	213.980	+	69.5265i	0.493043	+	0.160199i
$435$		0			0
$436$	533.250	−	387.429i	1.22305	−	0.888598i
$437$	−55.3871	−	349.700i	−0.126744	−	0.800230i
$438$	−51.8712	−	26.4297i	−0.118427	−	0.0603418i
$439$		−	29.9375i		−	0.0681948i	−0.999419	−	0.0340974i	$-0.989144\pi$
$439$		−	29.9375i		−	0.0681948i	0.999419	−	0.0340974i	$-0.0108557\pi$
$440$		0			0
$441$	1257.87			2.85231
$442$	79.2193	−	155.477i	0.179229	−	0.351757i
$443$	418.383	−	66.2654i	0.944431	−	0.149583i	0.334819	−	0.942283i	$-0.391325\pi$
$443$	418.383	−	66.2654i	0.944431	−	0.149583i	0.609613	+	0.792699i	$0.291325\pi$
$444$	368.285	+	506.901i	0.829472	+	1.14167i
$445$		0			0
$446$	−19.7960	+	60.9258i	−0.0443856	+	0.136605i
$447$	−708.665	−	112.242i	−1.58538	−	0.251100i
$448$	276.699	−	43.8248i	0.617631	−	0.0978231i
$449$	40.8177	−	13.2625i	0.0909081	−	0.0295378i	−0.263210	−	0.964739i	$-0.584781\pi$
$449$	40.8177	−	13.2625i	0.0909081	−	0.0295378i	0.354118	+	0.935201i	$0.384781\pi$
$450$		0			0
$451$	50.3897	−	72.2681i	0.111729	−	0.160240i
$452$	−382.394	−	382.394i	−0.846005	−	0.846005i
$453$	377.104	+	192.144i	0.832459	+	0.424159i
$454$	78.0089	−	107.370i	0.171826	−	0.236498i
$455$		0			0
$456$	−98.1902	+	302.198i	−0.215329	+	0.662716i
$457$	74.0125	−	37.7112i	0.161953	−	0.0825191i	−0.371135	−	0.928579i	$-0.621031\pi$
$457$	74.0125	−	37.7112i	0.161953	−	0.0825191i	0.533088	+	0.846060i	$0.321031\pi$
$458$	46.2299	−	291.884i	0.100939	−	0.637301i
$459$	−46.5434	+	64.0615i	−0.101402	+	0.139568i
$460$		0			0
$461$	−130.682			−0.283475			−0.141738	−	0.989904i	$-0.545269\pi$
$461$	−130.682			−0.283475			−0.141738	+	0.989904i	$0.545269\pi$
$462$	−400.775	−	194.490i	−0.867479	−	0.420974i
$463$	−199.934	+	199.934i	−0.431823	+	0.431823i	−0.889248	−	0.457425i	$-0.848772\pi$
$463$	−199.934	+	199.934i	−0.431823	+	0.431823i	0.457425	+	0.889248i	$0.348772\pi$
$464$	231.799	−	75.3161i	0.499567	−	0.162319i
$465$		0			0
$466$	42.4129	−	30.8147i	0.0910147	−	0.0661261i
$467$	−420.327	+	214.167i	−0.900057	+	0.458602i	−0.841856	−	0.539703i	$-0.818537\pi$
$467$	−420.327	+	214.167i	−0.900057	+	0.458602i	−0.0582017	+	0.998305i	$0.518537\pi$
$468$	243.629	+	478.149i	0.520575	+	1.02169i
$469$	98.9491	+	136.192i	0.210979	+	0.290388i
$470$		0			0
$471$	263.589	+	811.243i	0.559636	+	1.72238i
$472$	−14.9473	−	14.9473i	−0.0316680	−	0.0316680i
$473$	−22.7381	−	21.8711i	−0.0480721	−	0.0462391i
$474$		−	50.9202i		−	0.107427i
$475$		0			0
$476$	−611.552	−	444.319i	−1.28477	−	0.933443i
$477$	356.295	+	56.4315i	0.746949	+	0.118305i
$478$	121.448	+	238.355i	0.254075	+	0.498650i
$479$	31.1473	+	10.1204i	0.0650256	+	0.0211281i	0.341349	−	0.939937i	$-0.389116\pi$
$479$	31.1473	+	10.1204i	0.0650256	+	0.0211281i	−0.276324	+	0.961065i	$0.589116\pi$
$480$		0			0
$481$	−501.199	−	364.142i	−1.04199	−	0.757053i
$482$	64.0553	−	125.716i	0.132895	−	0.260821i
$483$	1046.77	−	1046.77i	2.16723	−	2.16723i
$484$	−262.438	−	333.177i	−0.542227	−	0.688382i
$485$		0			0
$486$	−75.8019	−	233.294i	−0.155971	−	0.480029i
$487$	28.7971	+	181.818i	0.0591317	+	0.373343i	0.999453	+	0.0330563i	$0.0105241\pi$
$487$	28.7971	+	181.818i	0.0591317	+	0.373343i	−0.940322	+	0.340287i	$0.889476\pi$
$488$	12.0805	−	76.2731i	0.0247551	−	0.156297i
$489$	313.733	+	101.938i	0.641580	+	0.208462i
$490$		0			0
$491$	−59.1038	+	42.9414i	−0.120374	+	0.0874571i	−0.646344	−	0.763047i	$-0.723703\pi$
$491$	−59.1038	+	42.9414i	−0.120374	+	0.0874571i	0.525969	+	0.850504i	$0.323703\pi$
$492$	−19.1962	−	121.200i	−0.0390168	−	0.246342i
$493$	−345.011	−	175.792i	−0.699820	−	0.356576i
$494$		−	146.730i		−	0.297025i
$495$		0			0
$496$	250.291			0.504619
$497$	263.325	−	516.804i	0.529829	−	1.03985i
$498$	−268.492	+	42.5250i	−0.539141	+	0.0853916i
$499$	347.130	+	477.783i	0.695651	+	0.957481i	0.999988	+	0.00491681i	$0.00156508\pi$
$499$	347.130	+	477.783i	0.695651	+	0.957481i	−0.304337	+	0.952564i	$0.598435\pi$
$500$		0			0
$501$	122.645	−	377.461i	0.244800	−	0.753416i
$502$	−292.690	−	46.3575i	−0.583048	−	0.0923457i
$503$	218.725	−	34.6426i	0.434840	−	0.0688719i	0.0648228	−	0.997897i	$-0.479352\pi$
$503$	218.725	−	34.6426i	0.434840	−	0.0688719i	0.370017	+	0.929025i	$0.379352\pi$
$504$	−668.344	+	217.158i	−1.32608	+	0.430870i
$505$		0			0
$506$	−188.009	+	65.1532i	−0.371558	+	0.128761i
$507$	−186.965	−	186.965i	−0.368766	−	0.368766i
$508$	500.738	+	255.139i	0.985704	+	0.502241i
$509$	135.399	−	186.360i	0.266009	−	0.366130i	−0.655028	−	0.755605i	$-0.727343\pi$
$509$	135.399	−	186.360i	0.266009	−	0.366130i	0.921037	+	0.389474i	$0.127343\pi$
$510$		0			0
$511$	77.0560	−	237.154i	0.150795	−	0.464098i
$512$	−454.451	+	231.554i	−0.887600	+	0.452255i
$513$	−10.4162	+	65.7651i	−0.0203044	+	0.128197i
$514$	119.649	−	164.683i	0.232781	−	0.320395i
$515$		0			0
$516$	−43.9434			−0.0851617
$517$	−896.531	+	159.914i	−1.73410	+	0.309311i
$518$	267.915	−	267.915i	0.517210	−	0.517210i
$519$	−463.107	+	150.473i	−0.892307	+	0.289928i
$520$		0			0
$521$	360.809	−	262.143i	0.692531	−	0.503153i	−0.184960	−	0.982746i	$-0.559216\pi$
$521$	360.809	−	262.143i	0.692531	−	0.503153i	0.877491	+	0.479593i	$0.159216\pi$
$522$	−149.795	+	76.3245i	−0.286964	+	0.146216i
$523$	1.31625	+	2.58329i	0.00251673	+	0.00493937i	0.892261	−	0.451519i	$-0.149118\pi$
$523$	1.31625	+	2.58329i	0.00251673	+	0.00493937i	−0.889745	+	0.456458i	$0.849118\pi$
$524$	209.715	+	288.648i	0.400220	+	0.550855i
$525$		0			0
$526$	68.6034	+	211.140i	0.130425	+	0.401406i
$527$	−281.175	−	281.175i	−0.533539	−	0.533539i
$528$	−490.877	−	67.9974i	−0.929691	−	0.128783i
$529$		−	132.227i		−	0.249956i
$530$		0			0
$531$	−32.7366	−	23.7845i	−0.0616508	−	0.0447919i
$532$	−627.815	−	99.4361i	−1.18010	−	0.186910i
$533$	55.0830	+	108.106i	0.103345	+	0.202826i
$534$	374.159	+	121.571i	0.700671	+	0.227662i
$535$		0			0
$536$	−54.5938	−	39.6647i	−0.101854	−	0.0740013i
$537$	216.762	−	425.419i	0.403653	−	0.792214i
$538$	−3.56375	+	3.56375i	−0.00662408	+	0.00662408i
$539$	397.693	−	1310.07i	0.737835	−	2.43055i
$540$		0			0
$541$	182.354	+	561.227i	0.337068	+	1.03739i	0.965695	+	0.259680i	$0.0836172\pi$
$541$	182.354	+	561.227i	0.337068	+	1.03739i	−0.628627	+	0.777707i	$0.716383\pi$
$542$	−0.896269	−	5.65882i	−0.00165363	−	0.0104406i
$543$	−61.3508	+	387.353i	−0.112985	+	0.713358i
$544$	441.781	+	143.543i	0.812098	+	0.263867i
$545$		0			0
$546$	496.329	−	360.604i	0.909027	−	0.660447i
$547$	−31.5603	−	199.264i	−0.0576971	−	0.364285i	−0.999597	−	0.0283912i	$-0.990962\pi$
$547$	−31.5603	−	199.264i	−0.0576971	−	0.364285i	0.941900	−	0.335894i	$-0.109038\pi$
$548$	−231.998	−	118.209i	−0.423353	−	0.215709i
$549$		−	147.825i		−	0.269263i
$550$		0			0
$551$	−325.603			−0.590930
$552$	−269.406	+	528.738i	−0.488054	+	0.957860i
$553$	215.421	−	34.1194i	0.389550	−	0.0616987i
$554$	44.7387	+	61.5776i	0.0807558	+	0.111151i
$555$		0			0
$556$	−30.2420	+	93.0752i	−0.0543920	+	0.167401i
$557$	−50.4026	−	7.98299i	−0.0904894	−	0.0143321i	0.111026	−	0.993818i	$-0.464586\pi$
$557$	−50.4026	−	7.98299i	−0.0904894	−	0.0143321i	−0.201515	+	0.979485i	$0.564586\pi$
$558$	−170.521	+	27.0078i	−0.305593	+	0.0484011i
$559$	41.3226	−	13.4265i	0.0739223	−	0.0240188i
$560$		0			0
$561$	475.060	+	627.835i	0.846809	+	1.11914i
$562$	240.218	+	240.218i	0.427435	+	0.427435i
$563$	−391.463	−	199.460i	−0.695317	−	0.354281i	0.0703471	−	0.997523i	$-0.477589\pi$
$563$	−391.463	−	199.460i	−0.695317	−	0.354281i	−0.765664	+	0.643241i	$0.777589\pi$
$564$	−745.569	+	1026.19i	−1.32193	+	1.81948i
$565$		0			0
$566$	−76.0539	+	234.070i	−0.134371	+	0.413551i
$567$	819.330	−	417.470i	1.44503	−	0.736278i
$568$	−36.3722	+	229.645i	−0.0640356	+	0.404305i
$569$	202.911	−	279.283i	0.356609	−	0.490831i	−0.592591	−	0.805504i	$-0.701895\pi$
$569$	202.911	−	279.283i	0.356609	−	0.490831i	0.949200	+	0.314673i	$0.101895\pi$
$570$		0			0
$571$	−326.598			−0.571975			−0.285987	−	0.958233i	$-0.592322\pi$
$571$	−326.598			−0.571975			−0.285987	+	0.958233i	$0.592322\pi$
$572$	575.017	−	102.565i	1.00527	−	0.179310i
$573$	−1042.02	+	1042.02i	−1.81854	+	1.81854i
$574$	−70.5725	+	22.9304i	−0.122949	+	0.0399484i
$575$		0			0
$576$	−173.914	+	126.356i	−0.301934	+	0.219368i
$577$	−24.0532	+	12.2557i	−0.0416867	+	0.0212404i	−0.474710	−	0.880142i	$-0.657447\pi$
$577$	−24.0532	+	12.2557i	−0.0416867	+	0.0212404i	0.433023	+	0.901383i	$0.357447\pi$
$578$	6.66806	+	13.0868i	0.0115364	+	0.0226415i
$579$	67.0993	+	92.3543i	0.115888	+	0.159507i
$580$		0			0
$581$	−359.810	−	1107.38i	−0.619294	−	1.90599i
$582$	165.091	+	165.091i	0.283662	+	0.283662i
$583$	171.421	−	353.238i	0.294032	−	0.605896i
$584$			99.9577i			0.171160i
$585$		0			0
$586$	−24.4558	−	17.7682i	−0.0417335	−	0.0303212i
$587$	607.382	+	96.1998i	1.03472	+	0.163884i	0.650617	−	0.759406i	$-0.274510\pi$
$587$	607.382	+	96.1998i	1.03472	+	0.163884i	0.384105	+	0.923290i	$0.374510\pi$
$588$	−865.734	−	1699.10i	−1.47234	−	2.88962i
$589$	−318.005	−	103.326i	−0.539907	−	0.175426i
$590$		0			0
$591$	1164.09	+	845.759i	1.96969	+	1.43106i
$592$	191.353	−	375.552i	0.323232	−	0.634378i
$593$	76.0314	−	76.0314i	0.128215	−	0.128215i	−0.640087	−	0.768302i	$-0.721102\pi$
$593$	76.0314	−	76.0314i	0.128215	−	0.128215i	0.768302	+	0.640087i	$0.221102\pi$
$594$	37.4129	−	0.727149i	0.0629847	−	0.00122416i
$595$		0			0
$596$	177.796	+	547.199i	0.298315	+	0.918120i
$597$	−121.077	−	764.448i	−0.202808	−	1.28048i
$598$	42.8673	−	270.654i	0.0716845	−	0.452598i
$599$	117.889	+	38.3046i	0.196810	+	0.0639475i	0.405763	−	0.913978i	$-0.367006\pi$
$599$	117.889	+	38.3046i	0.196810	+	0.0639475i	−0.208953	+	0.977926i	$0.567006\pi$
$600$		0			0
$601$	−621.369	+	451.451i	−1.03389	+	0.751167i	−0.969084	−	0.246731i	$-0.920644\pi$
$601$	−621.369	+	451.451i	−1.03389	+	0.751167i	−0.0648083	+	0.997898i	$0.520644\pi$
$602$	4.15693	+	26.2458i	0.00690519	+	0.0435977i
$603$	−115.097	−	58.6448i	−0.190874	−	0.0972551i
$604$		−	339.389i		−	0.561903i
$605$		0			0
$606$	−26.9784			−0.0445189
$607$	−541.208	+	1062.18i	−0.891612	+	1.74989i	−0.277382	+	0.960760i	$0.589467\pi$
$607$	−541.208	+	1062.18i	−0.891612	+	1.74989i	−0.614230	+	0.789127i	$0.710533\pi$
$608$	385.795	−	61.1039i	0.634531	−	0.100500i
$609$	−800.200	−	1101.38i	−1.31396	−	1.80851i
$610$		0			0
$611$	387.559	−	1192.79i	0.634303	−	1.95219i
$612$	572.909	+	90.7398i	0.936125	+	0.148268i
$613$	797.332	−	126.285i	1.30071	−	0.206011i	0.532617	−	0.846356i	$-0.321208\pi$
$613$	797.332	−	126.285i	1.30071	−	0.206011i	0.768088	+	0.640345i	$0.221208\pi$
$614$	−182.613	+	59.3345i	−0.297415	+	0.0966360i
$615$		0			0
$616$	14.8632	+	764.735i	0.0241286	+	1.24145i
$617$	−235.936	−	235.936i	−0.382392	−	0.382392i	0.489571	−	0.871963i	$-0.337153\pi$
$617$	−235.936	−	235.936i	−0.382392	−	0.382392i	−0.871963	+	0.489571i	$0.837153\pi$
$618$	222.870	+	113.558i	0.360631	+	0.183751i
$619$	−176.392	+	242.783i	−0.284963	+	0.392218i	−0.927370	−	0.374146i	$-0.877936\pi$
$619$	−176.392	+	242.783i	−0.284963	+	0.392218i	0.642407	+	0.766364i	$0.277936\pi$
$620$		0			0
$621$	−38.4266	+	118.265i	−0.0618786	+	0.190443i
$622$	318.991	−	162.534i	0.512848	−	0.261309i
$623$	−263.609	+	1664.36i	−0.423129	+	2.67153i
$624$	401.151	−	552.137i	0.642871	−	0.884835i
$625$		0			0
$626$	125.163			0.199940
$627$	595.608	+	289.039i	0.949934	+	0.460987i
$628$	483.668	−	483.668i	0.770172	−	0.770172i
$629$	−636.857	+	206.927i	−1.01249	+	0.328978i
$630$		0			0
$631$	−13.7479	+	9.98844i	−0.0217875	+	0.0158295i	−0.598626	−	0.801029i	$-0.704286\pi$
$631$	−13.7479	+	9.98844i	−0.0217875	+	0.0158295i	0.576838	+	0.816858i	$0.304286\pi$
$632$	−77.9007	+	39.6924i	−0.123261	+	0.0628044i
$633$	−379.515	−	744.841i	−0.599550	−	1.17668i
$634$	−142.397	−	195.993i	−0.224601	−	0.309137i
$635$		0			0
$636$	−168.995	−	520.113i	−0.265715	−	0.817787i
$637$	1333.24	+	1333.24i	2.09300	+	2.09300i
$638$	32.1318	+	180.142i	0.0503634	+	0.282355i
$639$			445.076i			0.696520i
$640$		0			0
$641$	−365.294	−	265.402i	−0.569882	−	0.414043i	0.265181	−	0.964199i	$-0.414568\pi$
$641$	−365.294	−	265.402i	−0.569882	−	0.414043i	−0.835062	+	0.550156i	$0.814568\pi$
$642$	−178.756	−	28.3122i	−0.278436	−	0.0441000i
$643$	527.892	+	1036.05i	0.820983	+	1.61127i	0.791077	+	0.611716i	$0.209521\pi$
$643$	527.892	+	1036.05i	0.820983	+	1.61127i	0.0299052	+	0.999553i	$0.490479\pi$
$644$	−1129.00	−	366.833i	−1.75310	−	0.569616i
$645$		0			0
$646$	−128.310	−	93.2227i	−0.198622	−	0.144308i
$647$	−29.5178	+	57.9320i	−0.0456226	+	0.0895395i	−0.912692	−	0.408647i	$-0.866001\pi$
$647$	−29.5178	+	57.9320i	−0.0456226	+	0.0895395i	0.867070	+	0.498187i	$0.166001\pi$
$648$	−260.648	+	260.648i	−0.402235	+	0.402235i
$649$	−35.1216	+	26.5752i	−0.0541164	+	0.0409479i
$650$		0			0
$651$	−432.018	−	1329.62i	−0.663623	−	2.04242i
$652$	−41.3813	−	261.271i	−0.0634682	−	0.400722i
$653$	129.098	−	815.090i	0.197699	−	1.24822i	−0.666665	−	0.745358i	$-0.732279\pi$
$653$	129.098	−	815.090i	0.197699	−	1.24822i	0.864364	−	0.502866i	$-0.167721\pi$
$654$	549.918	+	178.679i	0.840854	+	0.273210i
$655$		0			0
$656$	−66.7828	+	48.5206i	−0.101803	+	0.0739643i
$657$	29.9327	+	188.988i	0.0455597	+	0.287653i
$658$	683.432	+	348.226i	1.03865	+	0.529219i
$659$		−	162.422i		−	0.246467i	−0.992378	−	0.123234i	$-0.960674\pi$
$659$		−	162.422i		−	0.246467i	0.992378	−	0.123234i	$-0.0393264\pi$
$660$		0			0
$661$	−665.501			−1.00681			−0.503405	−	0.864051i	$-0.667920\pi$
$661$	−665.501			−1.00681			−0.503405	+	0.864051i	$0.667920\pi$
$662$	−118.544	+	232.656i	−0.179069	+	0.351443i
$663$	−1070.92	+	169.617i	−1.61526	+	0.255832i
$664$	274.348	+	377.607i	0.413174	+	0.568686i
$665$		0			0
$666$	−89.8428	+	276.508i	−0.134899	+	0.415177i
$667$	−600.596	−	95.1250i	−0.900443	−	0.142616i
$668$	−314.343	+	49.7871i	−0.470574	+	0.0745315i
$669$	378.576	−	123.007i	0.565883	−	0.183867i
$670$		0			0
$671$	−153.959	−	46.7370i	−0.229448	−	0.0696527i
$672$	1154.82	+	1154.82i	1.71848	+	1.71848i
$673$	476.355	+	242.715i	0.707808	+	0.360646i	0.770546	−	0.637384i	$-0.219983\pi$
$673$	476.355	+	242.715i	0.707808	+	0.360646i	−0.0627386	+	0.998030i	$0.519983\pi$
$674$	212.398	−	292.341i	0.315130	−	0.433740i
$675$		0			0
$676$	−65.5201	+	201.650i	−0.0969232	+	0.298299i
$677$	434.836	−	221.560i	0.642298	−	0.327267i	−0.102326	−	0.994751i	$-0.532629\pi$
$677$	434.836	−	221.560i	0.642298	−	0.327267i	0.744624	+	0.667484i	$0.232629\pi$
$678$	74.2126	−	468.560i	0.109458	−	0.691092i
$679$	−587.809	+	809.050i	−0.865699	+	1.19153i
$680$		0			0
$681$	−824.665			−1.21096
$682$	−25.7839	+	186.135i	−0.0378063	+	0.272926i
$683$	586.916	−	586.916i	0.859321	−	0.859321i	−0.131937	−	0.991258i	$-0.542120\pi$
$683$	586.916	−	586.916i	0.859321	−	0.859321i	0.991258	+	0.131937i	$0.0421197\pi$
$684$	463.882	−	150.724i	0.678190	−	0.220357i
$685$		0			0
$686$	−565.635	+	410.958i	−0.824541	+	0.599064i
$687$	−1636.15	+	833.660i	−2.38159	+	1.21348i
$688$	13.4204	+	26.3389i	0.0195063	+	0.0382834i
$689$	317.831	+	437.457i	0.461294	+	0.634916i
$690$		0			0
$691$	−210.321	−	647.301i	−0.304372	−	0.936759i	−0.979911	−	0.199435i	$-0.936089\pi$
$691$	−210.321	−	647.301i	−0.304372	−	0.936759i	0.675539	−	0.737324i	$-0.263911\pi$
$692$	276.107	+	276.107i	0.398999	+	0.398999i
$693$	257.104	+	1441.42i	0.371002	+	2.07997i
$694$			318.370i			0.458747i
$695$		0			0
$696$	441.499	+	320.768i	0.634337	+	0.460873i
$697$	129.531	+	20.5157i	0.185841	+	0.0294343i
$698$	−132.982	−	260.992i	−0.190519	−	0.373914i
$699$	−309.812	−	100.664i	−0.443222	−	0.144011i
$700$		0			0
$701$	306.948	+	223.011i	0.437872	+	0.318133i	0.784789	−	0.619763i	$-0.212771\pi$
$701$	306.948	+	223.011i	0.437872	+	0.318133i	−0.346917	+	0.937896i	$0.612771\pi$
$702$	−23.3959	+	45.9171i	−0.0333275	+	0.0654089i
$703$	−398.159	+	398.159i	−0.566371	+	0.566371i
$704$	76.6138	+	221.080i	0.108826	+	0.314033i
$705$		0			0
$706$	11.4643	+	35.2834i	0.0162383	+	0.0499765i
$707$	−18.0771	−	114.134i	−0.0255687	−	0.161434i
$708$	−9.59643	+	60.5895i	−0.0135543	+	0.0855783i
$709$	496.742	+	161.401i	0.700623	+	0.227646i	0.637602	−	0.770366i	$-0.279926\pi$
$709$	496.742	+	161.401i	0.700623	+	0.227646i	0.0630213	+	0.998012i	$0.479926\pi$
$710$		0			0
$711$	−135.399	+	98.3732i	−0.190435	+	0.138359i
$712$	−105.670	−	667.175i	−0.148413	−	0.937044i
$713$	−556.395	−	283.497i	−0.780357	−	0.397612i
$714$		−	663.124i		−	0.928745i
$715$		0			0
$716$	−382.872			−0.534738
$717$	754.643	−	1481.07i	1.05250	−	2.06565i
$718$	36.4018	−	5.76547i	0.0506988	−	0.00802991i
$719$	661.760	+	910.834i	0.920389	+	1.26681i	0.963492	+	0.267736i	$0.0862755\pi$
$719$	661.760	+	910.834i	0.920389	+	1.26681i	−0.0431034	+	0.999071i	$0.513724\pi$
$720$		0			0
$721$	−331.080	+	1018.96i	−0.459195	+	1.41326i
$722$	119.099	+	18.8634i	0.164957	+	0.0261266i
$723$	−865.925	+	137.149i	−1.19768	+	0.189694i
$724$	299.097	−	97.1824i	0.413117	−	0.134230i
$725$		0			0
$726$	101.136	−	358.049i	0.139306	−	0.493180i
$727$	−417.576	−	417.576i	−0.574382	−	0.574382i	0.358968	−	0.933350i	$-0.383129\pi$
$727$	−417.576	−	417.576i	−0.574382	−	0.574382i	−0.933350	+	0.358968i	$0.883129\pi$
$728$	−938.563	−	478.222i	−1.28923	−	0.656898i
$729$	−526.571	+	724.763i	−0.722320	+	0.994188i
$730$		0			0
$731$	14.5126	−	44.6653i	0.0198531	−	0.0611017i
$732$	−199.679	+	101.741i	−0.272785	+	0.138991i
$733$	88.4052	−	558.168i	0.120607	−	0.761485i	−0.851049	−	0.525086i	$-0.824033\pi$
$733$	88.4052	−	558.168i	0.120607	−	0.761485i	0.971656	−	0.236398i	$-0.0759670\pi$
$734$	−167.604	+	230.686i	−0.228343	+	0.314287i
$735$		0			0
$736$	729.476			0.991136
$737$	−97.4677	+	101.332i	−0.132249	+	0.137492i
$738$	40.2628	−	40.2628i	0.0545566	−	0.0545566i
$739$	−50.0728	+	16.2696i	−0.0677575	+	0.0220157i	−0.342700	−	0.939445i	$-0.611341\pi$
$739$	−50.0728	+	16.2696i	−0.0677575	+	0.0220157i	0.274942	+	0.961461i	$0.411341\pi$
$740$		0			0
$741$	−737.614	+	535.908i	−0.995431	+	0.723223i
$742$	−294.658	+	150.136i	−0.397113	+	0.202339i
$743$	−83.3096	−	163.504i	−0.112126	−	0.220060i	0.828124	−	0.560545i	$-0.189408\pi$
$743$	−83.3096	−	163.504i	−0.112126	−	0.220060i	−0.940250	+	0.340486i	$0.889408\pi$
$744$	329.405	+	453.387i	0.442749	+	0.609392i
$745$		0			0
$746$	−93.0955	−	286.519i	−0.124793	−	0.384073i
$747$	631.779	+	631.779i	0.845755	+	0.845755i
$748$	275.638	−	567.993i	0.368500	−	0.759349i
$749$		−	775.210i		−	1.03499i
$750$		0			0
$751$	−733.343	−	532.805i	−0.976488	−	0.709460i	−0.0195674	−	0.999809i	$-0.506229\pi$
$751$	−733.343	−	532.805i	−0.976488	−	0.709460i	−0.956921	+	0.290348i	$0.906229\pi$
$752$	842.776	+	133.483i	1.12071	+	0.177504i
$753$	835.962	+	1640.67i	1.11018	+	2.17884i
$754$	−239.669	−	77.8732i	−0.317864	−	0.103280i
$755$		0			0
$756$	180.610	+	131.221i	0.238903	+	0.173573i
$757$	−323.576	+	635.055i	−0.427446	+	0.838910i	0.572375	+	0.819992i	$0.306022\pi$
$757$	−323.576	+	635.055i	−0.427446	+	0.838910i	−0.999821	+	0.0189178i	$0.993978\pi$
$758$	−359.432	+	359.432i	−0.474184	+	0.474184i
$759$	1014.20	+	707.159i	1.33623	+	0.931699i
$760$		0			0
$761$	291.455	+	897.006i	0.382989	+	1.17872i	0.937928	+	0.346829i	$0.112741\pi$
$761$	291.455	+	897.006i	0.382989	+	1.17872i	−0.554939	+	0.831891i	$0.687259\pi$
$762$	77.1224	+	486.932i	0.101211	+	0.639018i
$763$	−387.439	+	2446.19i	−0.507783	+	3.20602i
$764$	1123.87	+	365.167i	1.47103	+	0.477968i
$765$		0			0
$766$	101.022	−	73.3966i	0.131882	−	0.0958180i
$767$	−9.48847	−	59.9079i	−0.0123709	−	0.0781067i
$768$	−20.5117	−	10.4512i	−0.0267079	−	0.0136084i
$769$			220.165i			0.286301i	0.989701	+	0.143150i	$0.0457232\pi$
$769$			220.165i			0.286301i	−0.989701	+	0.143150i	$0.954277\pi$
$770$		0			0
$771$	−1264.86			−1.64055
$772$	41.5589	−	81.5639i	0.0538328	−	0.105653i
$773$	−1243.99	+	197.028i	−1.60930	+	0.254887i	−0.895367	−	0.445330i	$-0.853086\pi$
$773$	−1243.99	+	197.028i	−1.60930	+	0.254887i	−0.713930	+	0.700217i	$0.753086\pi$
$774$	−11.9853	−	16.4963i	−0.0154848	−	0.0213131i
$775$		0			0
$776$	123.877	−	381.256i	0.159636	−	0.491309i
$777$	−2325.32	−	368.295i	−2.99269	−	0.473996i
$778$	−148.310	+	23.4900i	−0.190630	+	0.0301928i
$779$	104.881	−	34.0778i	0.134635	−	0.0437456i
$780$		0			0
$781$	463.545	+	140.717i	0.593528	+	0.180175i
$782$	−209.441	−	209.441i	−0.267828	−	0.267828i
$783$	101.893	+	51.9168i	0.130131	+	0.0663050i
$784$	−754.015	+	1037.81i	−0.961753	+	1.32374i
$785$		0			0
$786$	−96.7191	+	297.671i	−0.123052	+	0.378716i
$787$	862.761	−	439.599i	1.09627	−	0.558575i	0.190214	−	0.981743i	$-0.439082\pi$
$787$	862.761	−	439.599i	1.09627	−	0.558575i	0.906052	+	0.423167i	$0.139082\pi$
$788$	180.500	−	1139.63i	0.229061	−	1.44624i
$789$	810.837	−	1116.02i	1.02768	−	1.41448i
$790$		0			0
$791$	2032.00			2.56890
$792$	−276.570	−	517.677i	−0.349205	−	0.653633i
$793$	156.683	−	156.683i	0.197583	−	0.197583i
$794$	220.463	−	71.6328i	0.277661	−	0.0902176i
$795$		0			0
$796$	−502.115	+	364.808i	−0.630798	+	0.458302i
$797$	−44.2726	+	22.5580i	−0.0555490	+	0.0283036i	−0.481544	−	0.876422i	$-0.659924\pi$
$797$	−44.2726	+	22.5580i	−0.0555490	+	0.0283036i	0.425995	+	0.904725i	$0.359924\pi$
$798$	−253.150	−	496.834i	−0.317230	−	0.622599i
$799$	−796.815	−	1096.72i	−0.997266	−	1.37262i
$800$		0			0
$801$	−399.576	−	1229.77i	−0.498847	−	1.53529i
$802$	−110.295	−	110.295i	−0.137525	−	0.137525i
$803$	206.294	+	28.5762i	0.256903	+	0.0355869i
$804$			195.832i			0.243573i
$805$		0			0
$806$	−209.365	−	152.112i	−0.259758	−	0.188725i
$807$	30.9310	+	4.89900i	0.0383284	+	0.00607063i
$808$	21.0297	+	41.2732i	0.0260269	+	0.0510807i
$809$	−599.027	−	194.636i	−0.740454	−	0.240588i	−0.0855854	−	0.996331i	$-0.527276\pi$
$809$	−599.027	−	194.636i	−0.740454	−	0.240588i	−0.654869	+	0.755743i	$0.727276\pi$
$810$		0			0
$811$	542.416	+	394.089i	0.668824	+	0.485929i	0.869631	−	0.493702i	$-0.164356\pi$
$811$	542.416	+	394.089i	0.668824	+	0.485929i	−0.200807	+	0.979631i	$0.564356\pi$
$812$	−495.615	+	972.700i	−0.610363	+	1.19791i
$813$	−25.1734	+	25.1734i	−0.0309636	+	0.0309636i
$814$	259.576	+	180.993i	0.318890	+	0.222350i
$815$		0			0
$816$	−227.958	−	701.583i	−0.279360	−	0.859783i
$817$	−6.17778	−	39.0049i	−0.00756154	−	0.0477417i
$818$	−72.5118	+	457.821i	−0.0886452	+	0.559684i
$819$	−1917.72	−	623.106i	−2.34154	−	0.760814i
$820$		0			0
$821$	199.936	−	145.262i	0.243528	−	0.176933i	−0.459326	−	0.888268i	$-0.651909\pi$
$821$	199.936	−	145.262i	0.243528	−	0.176933i	0.702854	+	0.711335i	$0.251909\pi$
$822$	−35.7317	−	225.601i	−0.0434692	−	0.274454i
$823$	666.072	+	339.381i	0.809322	+	0.412370i	0.809130	−	0.587630i	$-0.199939\pi$
$823$	666.072	+	339.381i	0.809322	+	0.412370i	0.000192247		1.00000i	$0.499939\pi$
$824$		−	429.479i		−	0.521212i
$825$		0			0
$826$	37.0956			0.0449100
$827$	450.337	−	883.836i	0.544543	−	1.06873i	−0.440714	−	0.897647i	$-0.645275\pi$
$827$	450.337	−	883.836i	0.544543	−	1.06873i	0.985257	−	0.171078i	$-0.0547251\pi$
$828$	899.695	−	142.498i	1.08659	−	0.172099i
$829$	−240.484	−	330.998i	−0.290090	−	0.399274i	0.638954	−	0.769245i	$-0.279368\pi$
$829$	−240.484	−	330.998i	−0.290090	−	0.399274i	−0.929043	+	0.369971i	$0.879368\pi$
$830$		0			0
$831$	146.150	−	449.804i	0.175873	−	0.541280i
$832$	−318.262	−	50.4078i	−0.382527	−	0.0605863i
$833$	2012.92	−	318.816i	2.41648	−	0.382732i
$834$	−81.6493	+	26.5295i	−0.0979009	+	0.0318099i
$835$		0			0
$836$	−10.3162	−	530.784i	−0.0123399	−	0.634910i
$837$	83.0398	+	83.0398i	0.0992112	+	0.0992112i
$838$	96.6587	+	49.2501i	0.115345	+	0.0587710i
$839$	880.069	−	1211.31i	1.04895	−	1.44376i	0.159234	−	0.987241i	$-0.449098\pi$
$839$	880.069	−	1211.31i	1.04895	−	1.44376i	0.889716	−	0.456515i	$-0.150902\pi$
$840$		0			0
$841$	87.0783	−	267.999i	0.103541	−	0.318667i
$842$	30.7402	−	15.6629i	0.0365085	−	0.0186020i
$843$	330.222	−	2084.94i	0.391722	−	2.47324i
$844$	−394.021	+	542.323i	−0.466849	+	0.642563i
$845$		0			0
$846$	−588.578			−0.695719
$847$	1582.52	+	187.950i	1.86838	+	0.221901i
$848$	−260.135	+	260.135i	−0.306763	+	0.306763i
$849$	1454.45	−	472.578i	1.71313	−	0.556629i
$850$		0			0
$851$	−850.753	+	618.108i	−0.999710	+	0.726332i
$852$	601.197	−	306.325i	0.705631	−	0.359537i
$853$	−325.133	−	638.110i	−0.381164	−	0.748077i	0.618113	−	0.786089i	$-0.287897\pi$
$853$	−325.133	−	638.110i	−0.381164	−	0.748077i	−0.999277	+	0.0380123i	$0.987897\pi$
$854$	79.6553	+	109.636i	0.0932732	+	0.128380i
$855$		0			0
$856$	96.0271	+	295.541i	0.112181	+	0.345258i
$857$	626.565	+	626.565i	0.731114	+	0.731114i	0.970841	−	0.239726i	$-0.0770577\pi$
$857$	626.565	+	626.565i	0.731114	+	0.731114i	−0.239726	+	0.970841i	$0.577058\pi$
$858$	369.286	+	355.205i	0.430404	+	0.413992i
$859$		−	842.626i		−	0.980938i	−0.871459	−	0.490469i	$-0.836825\pi$
$859$		−	842.626i		−	0.980938i	0.871459	−	0.490469i	$-0.163175\pi$
$860$		0			0
$861$	373.026	+	271.019i	0.433247	+	0.314773i
$862$	574.924	+	91.0590i	0.666965	+	0.105637i
$863$	−450.407	−	883.974i	−0.521909	−	1.02430i	−0.990059	−	0.140655i	$-0.955079\pi$
$863$	−450.407	−	883.974i	−0.521909	−	1.02430i	0.468150	−	0.883649i	$-0.344921\pi$
$864$	−130.472	−	42.3928i	−0.151009	−	0.0490658i
$865$		0			0
$866$	167.660	+	121.812i	0.193603	+	0.140661i
$867$	41.4335	−	81.3178i	0.0477895	−	0.0937922i
$868$	−792.725	+	792.725i	−0.913278	+	0.913278i
$869$	59.6470	+	172.120i	0.0686386	+	0.198066i
$870$		0			0
$871$	−59.8348	−	184.153i	−0.0686966	−	0.211427i
$872$	−155.308	−	980.579i	−0.178106	−	1.12452i
$873$	120.044	−	757.927i	0.137507	−	0.868186i
$874$	−236.875	−	76.9653i	−0.271024	−	0.0880610i
$875$		0			0
$876$	234.678	−	170.504i	0.267898	−	0.194639i
$877$	93.2731	+	588.903i	0.106355	+	0.671497i	0.982048	+	0.188630i	$0.0604047\pi$
$877$	93.2731	+	588.903i	0.106355	+	0.671497i	−0.875693	+	0.482867i	$0.839595\pi$
$878$	−18.7644	−	9.56092i	−0.0213717	−	0.0108894i
$879$			187.835i			0.213692i
$880$		0			0
$881$	1087.40			1.23428			0.617138	−	0.786855i	$-0.288292\pi$
$881$	1087.40			1.23428			0.617138	+	0.786855i	$0.288292\pi$
$882$	401.716	−	788.413i	0.455461	−	0.893892i
$883$	283.520	−	44.9052i	0.321088	−	0.0508553i	0.00618976	−	0.999981i	$-0.498030\pi$
$883$	283.520	−	44.9052i	0.321088	−	0.0508553i	0.314898	+	0.949126i	$0.398030\pi$
$884$	511.061	+	703.415i	0.578123	+	0.795718i
$885$		0			0
$886$	92.0817	−	283.398i	0.103930	−	0.319863i
$887$	−588.141	−	93.1524i	−0.663068	−	0.105020i	−0.184176	−	0.982893i	$-0.558962\pi$
$887$	−588.141	−	93.1524i	−0.663068	−	0.105020i	−0.478892	+	0.877874i	$0.658962\pi$
$888$	932.127	−	147.634i	1.04969	−	0.166255i
$889$	−2008.32	+	652.543i	−2.25908	+	0.734020i
$890$		0			0
$891$	463.413	+	612.443i	0.520105	+	0.687366i
$892$	−225.709	−	225.709i	−0.253037	−	0.253037i
$893$	−1015.68	−	517.513i	−1.13738	−	0.579522i
$894$	−296.672	+	408.334i	−0.331848	+	0.456750i
$895$		0			0
$896$	522.729	−	1608.79i	0.583402	−	1.79553i
$897$	−1517.14	+	773.024i	−1.69135	+	0.861788i
$898$	4.72293	−	29.8194i	0.00525939	−	0.0332065i
$899$	−337.546	+	464.592i	−0.375468	+	0.516787i
$900$		0			0
$901$	584.468			0.648688
$902$	−29.2039	−	54.6631i	−0.0323768	−	0.0606021i
$903$	116.755	−	116.755i	0.129297	−	0.129297i
$904$	−774.680	+	251.709i	−0.856947	+	0.278439i
$905$		0			0
$906$	240.866	−	174.999i	0.265856	−	0.193156i
$907$	−29.1369	+	14.8460i	−0.0321245	+	0.0163682i	−0.469979	−	0.882678i	$-0.655739\pi$
$907$	−29.1369	+	14.8460i	−0.0321245	+	0.0163682i	0.437854	+	0.899046i	$0.355739\pi$
$908$	300.222	+	589.218i	0.330641	+	0.648919i
$909$	52.1199	+	71.7369i	0.0573376	+	0.0789184i
$910$		0			0
$911$	236.993	+	729.389i	0.260146	+	0.800646i	0.992772	+	0.120015i	$0.0382943\pi$
$911$	236.993	+	729.389i	0.260146	+	0.800646i	−0.732626	+	0.680631i	$0.761706\pi$
$912$	−438.625	−	438.625i	−0.480948	−	0.480948i
$913$	857.740	−	458.249i	0.939475	−	0.501916i
$914$		−	58.4333i		−	0.0639314i
$915$		0			0
$916$	1191.29	+	865.523i	1.30054	+	0.944894i
$917$	−1324.12	−	209.721i	−1.44397	−	0.228703i
$918$	25.2885	+	49.6315i	0.0275474	+	0.0540648i
$919$	−441.604	−	143.486i	−0.480526	−	0.156132i	0.0587304	−	0.998274i	$-0.481295\pi$
$919$	−441.604	−	143.486i	−0.480526	−	0.156132i	−0.539257	+	0.842141i	$0.681295\pi$
$920$		0			0
$921$	965.238	+	701.286i	1.04803	+	0.761440i
$922$	−41.7349	+	81.9093i	−0.0452656	+	0.0888388i
$923$	−471.746	+	471.746i	−0.511101	+	0.511101i
$924$	1770.07	−	1339.35i	1.91566	−	1.44951i
$925$		0			0
$926$	61.4640	+	189.167i	0.0663759	+	0.204284i
$927$	−128.609	−	812.006i	−0.138737	−	0.875951i
$928$	104.943	−	662.587i	0.113086	−	0.713994i
$929$	−1166.82	−	379.121i	−1.25599	−	0.408096i	−0.395927	−	0.918282i	$-0.629577\pi$
$929$	−1166.82	−	379.121i	−1.25599	−	0.408096i	−0.860064	+	0.510186i	$0.829577\pi$
$930$		0			0
$931$	1386.44	−	1007.31i	1.48919	−	1.08196i
$932$	40.8641	+	258.006i	0.0438456	+	0.276830i
$933$	−1982.12	−	1009.94i	−2.12446	−	1.08247i
$934$			331.851i			0.355301i
$935$		0			0
$936$	808.299			0.863567
$937$	−630.977	+	1238.36i	−0.673401	+	1.32162i	0.260978	+	0.965345i	$0.415955\pi$
$937$	−630.977	+	1238.36i	−0.673401	+	1.32162i	−0.934379	+	0.356280i	$0.884045\pi$
$938$	116.963	−	18.5252i	0.124694	−	0.0197497i
$939$	−457.136	−	629.193i	−0.486833	−	0.670067i
$940$		0			0
$941$	−452.206	+	1391.75i	−0.480559	+	1.47901i	0.357753	+	0.933816i	$0.383543\pi$
$941$	−452.206	+	1391.75i	−0.480559	+	1.47901i	−0.838311	+	0.545192i	$0.816457\pi$
$942$	592.654	+	93.8672i	0.629144	+	0.0996467i
$943$	203.415	−	32.2178i	0.215711	−	0.0341652i
$944$	39.2470	−	12.7521i	0.0415752	−	0.0135086i
$945$		0			0
$946$	−20.9701	+	7.26707i	−0.0221672	+	0.00768190i
$947$	760.281	+	760.281i	0.802831	+	0.802831i	0.983537	−	0.180706i	$-0.0578383\pi$
$947$	760.281	+	760.281i	0.802831	+	0.802831i	−0.180706	+	0.983537i	$0.557838\pi$
$948$	226.069	+	115.188i	0.238469	+	0.121506i
$949$	−168.586	+	232.038i	−0.177646	+	0.244508i
$950$		0			0
$951$	−465.175	+	1431.66i	−0.489143	+	1.50543i
$952$	−1014.49	+	516.907i	−1.06564	+	0.542969i
$953$	−226.751	+	1431.65i	−0.237934	+	1.50225i	0.522389	+	0.852708i	$0.325041\pi$
$953$	−226.751	+	1431.65i	−0.237934	+	1.50225i	−0.760322	+	0.649546i	$0.774959\pi$
$954$	149.157	−	205.298i	0.156349	−	0.215197i
$955$		0			0
$956$	−1332.95			−1.39430
$957$	788.220	−	819.467i	0.823636	−	0.856287i
$958$	16.2905	−	16.2905i	0.0170047	−	0.0170047i
$959$	930.479	−	302.331i	0.970259	−	0.315256i
$960$		0			0
$961$	300.363	−	218.227i	0.312553	−	0.227083i
$962$	−388.303	+	197.850i	−0.403641	+	0.205665i
$963$	270.057	+	530.017i	0.280433	+	0.550381i
$964$	413.235	+	568.769i	0.428667	+	0.590009i
$965$		0			0
$966$	−321.801	−	990.401i	−0.333127	−	1.02526i
$967$	−915.159	−	915.159i	−0.946390	−	0.946390i	0.0522446	−	0.998634i	$-0.483362\pi$
$967$	−915.159	−	915.159i	−0.946390	−	0.946390i	−0.998634	+	0.0522446i	$0.983362\pi$
$968$	−626.600	+	124.376i	−0.647314	+	0.128487i
$969$			985.496i			1.01702i
$970$		0			0
$971$	1380.55	+	1003.03i	1.42178	+	1.03298i	0.991475	+	0.130299i	$0.0415937\pi$
$971$	1380.55	+	1003.03i	1.42178	+	1.03298i	0.430304	+	0.902684i	$0.358406\pi$
$972$	1207.22	+	191.205i	1.24200	+	0.196713i
$973$	−166.944	−	327.647i	−0.171577	−	0.336739i
$974$	123.157	+	40.0162i	0.126445	+	0.0410844i
$975$		0			0
$976$	121.964	+	88.6120i	0.124963	+	0.0907910i
$977$	−624.597	+	1225.84i	−0.639301	+	1.25470i	0.313063	+	0.949732i	$0.398645\pi$
$977$	−624.597	+	1225.84i	−0.639301	+	1.25470i	−0.952363	+	0.304966i	$0.901355\pi$
$978$	164.087	−	164.087i	0.167778	−	0.167778i
$979$	−1407.13	+	27.3487i	−1.43731	+	0.0279353i
$980$		0			0
$981$	−587.276	−	1807.45i	−0.598651	−	1.84246i
$982$	8.03946	+	50.7592i	0.00818682	+	0.0516896i
$983$	−3.59295	+	22.6850i	−0.00365508	+	0.0230773i	−0.989448	−	0.144885i	$-0.953719\pi$
$983$	−3.59295	+	22.6850i	−0.00365508	+	0.0230773i	0.985793	+	0.167962i	$0.0537187\pi$
$984$	−175.784	−	57.1157i	−0.178642	−	0.0580444i
$985$		0			0
$986$	−220.367	+	160.106i	−0.223496	+	0.162379i
$987$	−745.588	−	4707.46i	−0.755409	−	4.76946i
$988$	651.434	+	331.922i	0.659346	+	0.335954i
$989$		−	73.7521i		−	0.0745723i
$990$		0			0
$991$	−1037.25			−1.04667			−0.523337	−	0.852126i	$-0.675313\pi$
$991$	−1037.25			−1.04667			−0.523337	+	0.852126i	$0.675313\pi$
$992$	312.759	−	613.823i	0.315281	−	0.618774i
$993$	1602.52	−	253.815i	1.61382	−	0.255604i
$994$	−239.828	−	330.095i	−0.241276	−	0.332088i
$995$		0			0
$996$	418.566	−	1288.21i	0.420247	−	1.29339i
$997$	−27.9529	−	4.42730i	−0.0280370	−	0.00444063i	0.142400	−	0.989809i	$-0.454518\pi$
$997$	−27.9529	−	4.42730i	−0.0280370	−	0.00444063i	−0.170437	+	0.985369i	$0.554518\pi$
$998$	410.327	−	64.9894i	0.411149	−	0.0651196i
$999$	188.084	−	61.1121i	0.188272	−	0.0611733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.bk.c.82.10	yes	128
5.2	odd	4	inner	275.3.bk.c.93.10	yes	128
5.3	odd	4	inner	275.3.bk.c.93.7	yes	128
5.4	even	2	inner	275.3.bk.c.82.7	✓	128
11.9	even	5	inner	275.3.bk.c.207.7	yes	128
55.9	even	10	inner	275.3.bk.c.207.10	yes	128
55.42	odd	20	inner	275.3.bk.c.218.7	yes	128
55.53	odd	20	inner	275.3.bk.c.218.10	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.bk.c.82.7	✓	128	5.4	even	2	inner
275.3.bk.c.82.10	yes	128	1.1	even	1	trivial
275.3.bk.c.93.7	yes	128	5.3	odd	4	inner
275.3.bk.c.93.10	yes	128	5.2	odd	4	inner
275.3.bk.c.207.7	yes	128	11.9	even	5	inner
275.3.bk.c.207.10	yes	128	55.9	even	10	inner
275.3.bk.c.218.7	yes	128	55.42	odd	20	inner
275.3.bk.c.218.10	yes	128	55.53	odd	20	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.bk (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.319362 - 0.626784i) q^{2} +(-4.31726 + 0.683787i) q^{3} +(2.06028 + 2.83573i) q^{4} +(-0.950184 + 2.92437i) q^{6} +(-13.0084 - 2.06033i) q^{7} +(5.21454 - 0.825902i) q^{8} +(9.61169 - 3.12303i) q^{9} +(-0.213753 - 10.9979i) q^{11} +(-10.8338 - 10.8338i) q^{12} +(13.4978 + 6.87747i) q^{13} +(-5.44577 + 7.49547i) q^{14} +(-3.18494 + 9.80223i) q^{16} +(14.5897 - 7.43382i) q^{17} +(1.11215 - 7.02183i) q^{18} +(8.09319 - 11.1393i) q^{19} +57.5696 q^{21} +(-6.96158 - 3.37834i) q^{22} +(18.1828 - 18.1828i) q^{23} +(-21.9478 + 7.13127i) q^{24} +(8.62138 - 6.26380i) q^{26} +(-4.30879 + 2.19544i) q^{27} +(-20.9584 - 41.1331i) q^{28} +(-13.8997 - 19.1313i) q^{29} +(-7.50428 - 23.0958i) q^{31} +(20.0595 + 20.0595i) q^{32} +(8.44307 + 47.3348i) q^{33} -11.5187i q^{34} +(28.6588 + 20.8218i) q^{36} +(-40.3915 - 6.39739i) q^{37} +(-4.39728 - 8.63015i) q^{38} +(-62.9763 - 20.4622i) q^{39} +(6.47957 + 4.70768i) q^{41} +(18.3855 - 36.0837i) q^{42} +(2.02807 - 2.02807i) q^{43} +(30.7467 - 23.2649i) q^{44} +(-5.58978 - 17.2036i) q^{46} +(-12.9511 - 81.7699i) q^{47} +(7.04758 - 44.4966i) q^{48} +(118.372 + 38.4614i) q^{49} +(-57.9044 + 42.0700i) q^{51} +(8.30656 + 52.4456i) q^{52} +(31.8036 + 16.2048i) q^{53} +3.40182i q^{54} -69.5345 q^{56} +(-27.3235 + 53.6254i) q^{57} +(-16.4302 + 2.60229i) q^{58} +(-2.35343 - 3.23921i) q^{59} +(4.51999 - 13.9111i) q^{61} +(-16.8727 - 2.67237i) q^{62} +(-131.467 + 20.8224i) q^{63} +(-20.2297 + 6.57303i) q^{64} +(32.3651 + 9.82496i) q^{66} +(-9.03804 - 9.03804i) q^{67} +(51.1391 + 26.0566i) q^{68} +(-66.0667 + 90.9330i) q^{69} +(-13.6089 + 41.8839i) q^{71} +(47.5413 - 24.2235i) q^{72} +(-2.96178 + 18.6999i) q^{73} +(-16.9093 + 23.2737i) q^{74} +48.2622 q^{76} +(-19.8788 + 143.506i) q^{77} +(-32.9376 + 32.9376i) q^{78} +(-15.7496 + 5.11737i) q^{79} +(-56.4848 + 41.0386i) q^{81} +(5.02003 - 2.55783i) q^{82} +(40.1359 + 78.7712i) q^{83} +(118.609 + 163.251i) q^{84} +(-0.623474 - 1.91885i) q^{86} +(73.0905 + 73.0905i) q^{87} +(-10.1978 - 57.1726i) q^{88} -127.945i q^{89} +(-161.415 - 117.275i) q^{91} +(89.0229 + 14.0998i) q^{92} +(48.1906 + 94.5794i) q^{93} +(-55.3881 - 17.9967i) q^{94} +(-100.319 - 72.8858i) q^{96} +(34.4715 - 67.6542i) q^{97} +(61.9105 - 61.9105i) q^{98} +(-36.4014 - 105.041i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 48 q^{6} + 32 q^{11} + 280 q^{16} - 8 q^{21} + 528 q^{26} - 16 q^{31} + 336 q^{36} - 604 q^{41} - 1152 q^{46} - 1024 q^{51} - 992 q^{56} - 320 q^{61} + 1624 q^{66} + 536 q^{71} + 1776 q^{76} + 3680 q^{81}+ \cdots - 6584 q^{96}+O(q^{100}) \) 128 * q - 48 * q^6 + 32 * q^11 + 280 * q^16 - 8 * q^21 + 528 * q^26 - 16 * q^31 + 336 * q^36 - 604 * q^41 - 1152 * q^46 - 1024 * q^51 - 992 * q^56 - 320 * q^61 + 1624 * q^66 + 536 * q^71 + 1776 * q^76 + 3680 * q^81 + 872 * q^86 - 448 * q^91 - 6584 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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