LMFDB - Embedded newform 275.3.bk.c.218.15

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			218.15
Character	$\chi$	$=$	275.218
Dual form			275.3.bk.c.82.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.54871 + 3.03951i) q^{2} +(-2.39044 - 0.378609i) q^{3} +(-4.48900 + 6.17857i) q^{4} +(-2.55131 - 7.85213i) q^{6} +(-2.23278 + 0.353637i) q^{7} +(-12.2547 - 1.94095i) q^{8} +(-2.98864 - 0.971069i) q^{9} +(-5.01119 - 9.79224i) q^{11} +(13.0699 - 13.0699i) q^{12} +(-12.2913 + 6.26272i) q^{13} +(-4.53281 - 6.23888i) q^{14} +(-3.63939 - 11.2009i) q^{16} +(3.55582 + 1.81178i) q^{17} +(-1.67696 - 10.5879i) q^{18} +(-21.1737 - 29.1430i) q^{19} +5.47122 q^{21} +(22.0028 - 30.3969i) q^{22} +(21.0138 + 21.0138i) q^{23} +(28.5593 + 9.27947i) q^{24} +(-38.0712 - 27.6604i) q^{26} +(26.1846 + 13.3417i) q^{27} +(7.83796 - 15.3829i) q^{28} +(9.94209 - 13.6841i) q^{29} +(-6.10743 + 18.7967i) q^{31} +(-6.68470 + 6.68470i) q^{32} +(8.27153 + 25.3051i) q^{33} +13.6139i q^{34} +(19.4158 - 14.1064i) q^{36} +(-30.5946 + 4.84571i) q^{37} +(55.7888 - 109.492i) q^{38} +(31.7527 - 10.3171i) q^{39} +(-24.0598 + 17.4804i) q^{41} +(8.47332 + 16.6298i) q^{42} +(-57.6762 - 57.6762i) q^{43} +(82.9973 + 12.9953i) q^{44} +(-31.3274 + 96.4159i) q^{46} +(-7.38384 + 46.6198i) q^{47} +(4.45899 + 28.1530i) q^{48} +(-41.7415 + 13.5626i) q^{49} +(-7.81403 - 5.67722i) q^{51} +(16.4808 - 104.056i) q^{52} +(-41.9192 + 21.3589i) q^{53} +100.251i q^{54} +28.0484 q^{56} +(39.5806 + 77.6813i) q^{57} +(56.9904 + 9.02639i) q^{58} +(-13.9926 + 19.2592i) q^{59} +(14.5657 + 44.8286i) q^{61} +(-66.5915 + 10.5471i) q^{62} +(7.01639 + 1.11129i) q^{63} +(-75.4744 - 24.5231i) q^{64} +(-64.1048 + 64.3316i) q^{66} +(25.4370 - 25.4370i) q^{67} +(-27.1563 + 13.8368i) q^{68} +(-42.2762 - 58.1882i) q^{69} +(-5.18827 - 15.9679i) q^{71} +(34.7401 + 17.7010i) q^{72} +(9.30355 + 58.7403i) q^{73} +(-62.1107 - 85.4881i) q^{74} +275.111 q^{76} +(14.6518 + 20.0918i) q^{77} +(80.5345 + 80.5345i) q^{78} +(134.820 + 43.8055i) q^{79} +(-34.6607 - 25.1825i) q^{81} +(-90.3936 - 46.0578i) q^{82} +(-27.5653 + 54.0999i) q^{83} +(-24.5603 + 33.8043i) q^{84} +(85.9839 - 264.631i) q^{86} +(-28.9469 + 28.9469i) q^{87} +(42.4043 + 129.727i) q^{88} -168.321i q^{89} +(25.2290 - 18.3299i) q^{91} +(-224.166 + 35.5044i) q^{92} +(21.7161 - 42.6202i) q^{93} +(-153.137 + 49.7572i) q^{94} +(18.5103 - 13.4485i) q^{96} +(-24.6643 - 48.4063i) q^{97} +(-105.869 - 105.869i) q^{98} +(5.46772 + 34.1317i) 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 $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.54871	+	3.03951i	0.774355	+	1.51976i	0.852449	+	0.522810i	$0.175116\pi$
$2$	1.54871	+	3.03951i	0.774355	+	1.51976i	−0.0780945	+	0.996946i	$0.524884\pi$
$3$	−2.39044	−	0.378609i	−0.796814	−	0.126203i	−0.255264	−	0.966871i	$-0.582162\pi$
$3$	−2.39044	−	0.378609i	−0.796814	−	0.126203i	−0.541550	+	0.840669i	$0.682162\pi$
$4$	−4.48900	+	6.17857i	−1.12225	+	1.54464i
$5$		0			0
$5$		0			0
$6$	−2.55131	−	7.85213i	−0.425219	−	1.30869i
$7$	−2.23278	+	0.353637i	−0.318968	+	0.0505196i	−0.313866	−	0.949467i	$-0.601624\pi$
$7$	−2.23278	+	0.353637i	−0.318968	+	0.0505196i	−0.00510261	+	0.999987i	$0.501624\pi$
$8$	−12.2547	−	1.94095i	−1.53184	−	0.242619i
$9$	−2.98864	−	0.971069i	−0.332072	−	0.107897i
$10$		0			0
$11$	−5.01119	−	9.79224i	−0.455563	−	0.890204i
$11$	−5.01119	−	9.79224i	−0.455563	−	0.890204i
$12$	13.0699	−	13.0699i	1.08916	−	1.08916i
$13$	−12.2913	+	6.26272i	−0.945483	+	0.481747i	−0.857562	−	0.514380i	$-0.828022\pi$
$13$	−12.2913	+	6.26272i	−0.945483	+	0.481747i	−0.0879203	+	0.996128i	$0.528022\pi$
$14$	−4.53281	−	6.23888i	−0.323772	−	0.445634i
$15$		0			0
$16$	−3.63939	−	11.2009i	−0.227462	−	0.700055i
$17$	3.55582	+	1.81178i	0.209166	+	0.106575i	0.555435	−	0.831560i	$-0.312552\pi$
$17$	3.55582	+	1.81178i	0.209166	+	0.106575i	−0.346269	+	0.938135i	$0.612552\pi$
$18$	−1.67696	−	10.5879i	−0.0931646	−	0.588218i
$19$	−21.1737	−	29.1430i	−1.11440	−	1.53384i	−0.814765	−	0.579792i	$-0.803134\pi$
$19$	−21.1737	−	29.1430i	−1.11440	−	1.53384i	−0.299638	−	0.954053i	$-0.596866\pi$
$20$		0			0
$21$	5.47122			0.260534
$22$	22.0028	−	30.3969i	1.00013	−	1.38168i
$23$	21.0138	+	21.0138i	0.913643	+	0.913643i	0.996557	−	0.0829138i	$-0.0264226\pi$
$23$	21.0138	+	21.0138i	0.913643	+	0.913643i	−0.0829138	+	0.996557i	$0.526423\pi$
$24$	28.5593	+	9.27947i	1.18997	+	0.386645i
$25$		0			0
$26$	−38.0712	−	27.6604i	−1.46428	−	1.06386i
$27$	26.1846	+	13.3417i	0.969798	+	0.494137i
$28$	7.83796	−	15.3829i	0.279927	−	0.549388i
$29$	9.94209	−	13.6841i	0.342831	−	0.471866i	−0.602435	−	0.798168i	$-0.705803\pi$
$29$	9.94209	−	13.6841i	0.342831	−	0.471866i	0.945265	+	0.326302i	$0.105803\pi$
$30$		0			0
$31$	−6.10743	+	18.7967i	−0.197014	+	0.606346i	0.802933	+	0.596069i	$0.203271\pi$
$31$	−6.10743	+	18.7967i	−0.197014	+	0.606346i	−0.999947	+	0.0102774i	$0.996729\pi$
$32$	−6.68470	+	6.68470i	−0.208897	+	0.208897i
$33$	8.27153	+	25.3051i	0.250652	+	0.766820i
$34$			13.6139i			0.400408i
$35$		0			0
$36$	19.4158	−	14.1064i	0.539329	−	0.391845i
$37$	−30.5946	+	4.84571i	−0.826881	+	0.130965i	−0.555510	−	0.831510i	$-0.687477\pi$
$37$	−30.5946	+	4.84571i	−0.826881	+	0.130965i	−0.271371	+	0.962475i	$0.587477\pi$
$38$	55.7888	−	109.492i	1.46813	−	2.88136i
$39$	31.7527	−	10.3171i	0.814171	−	0.264540i
$40$		0			0
$41$	−24.0598	+	17.4804i	−0.586823	+	0.426352i	−0.841178	−	0.540759i	$-0.818137\pi$
$41$	−24.0598	+	17.4804i	−0.586823	+	0.426352i	0.254354	+	0.967111i	$0.418137\pi$
$42$	8.47332	+	16.6298i	0.201746	+	0.395948i
$43$	−57.6762	−	57.6762i	−1.34131	−	1.34131i	−0.894761	−	0.446546i	$-0.852654\pi$
$43$	−57.6762	−	57.6762i	−1.34131	−	1.34131i	−0.446546	−	0.894761i	$-0.647346\pi$
$44$	82.9973	+	12.9953i	1.88630	+	0.295348i
$45$		0			0
$46$	−31.3274	+	96.4159i	−0.681031	+	2.09600i
$47$	−7.38384	+	46.6198i	−0.157103	+	0.991910i	0.775590	+	0.631238i	$0.217453\pi$
$47$	−7.38384	+	46.6198i	−0.157103	+	0.991910i	−0.932693	+	0.360672i	$0.882547\pi$
$48$	4.45899	+	28.1530i	0.0928957	+	0.586520i
$49$	−41.7415	+	13.5626i	−0.851868	+	0.276789i
$50$		0			0
$51$	−7.81403	−	5.67722i	−0.153216	−	0.111318i
$52$	16.4808	−	104.056i	0.316939	−	2.00107i
$53$	−41.9192	+	21.3589i	−0.790927	+	0.402998i	−0.802288	−	0.596938i	$-0.796384\pi$
$53$	−41.9192	+	21.3589i	−0.790927	+	0.402998i	0.0113601	+	0.999935i	$0.496384\pi$
$54$			100.251i			1.85649i
$55$		0			0
$56$	28.0484			0.500865
$57$	39.5806	+	77.6813i	0.694396	+	1.36283i
$58$	56.9904	+	9.02639i	0.982593	+	0.155627i
$59$	−13.9926	+	19.2592i	−0.237163	+	0.326427i	−0.910964	−	0.412486i	$-0.864661\pi$
$59$	−13.9926	+	19.2592i	−0.237163	+	0.326427i	0.673801	+	0.738913i	$0.264661\pi$
$60$		0			0
$61$	14.5657	+	44.8286i	0.238782	+	0.734896i	0.996597	+	0.0824262i	$0.0262669\pi$
$61$	14.5657	+	44.8286i	0.238782	+	0.734896i	−0.757815	+	0.652469i	$0.773733\pi$
$62$	−66.5915	+	10.5471i	−1.07406	+	0.170114i
$63$	7.01639	+	1.11129i	0.111371	+	0.0176395i
$64$	−75.4744	−	24.5231i	−1.17929	−	0.383174i
$65$		0			0
$66$	−64.1048	+	64.3316i	−0.971286	+	0.974721i
$67$	25.4370	−	25.4370i	0.379656	−	0.379656i	−0.491322	−	0.870978i	$-0.663486\pi$
$67$	25.4370	−	25.4370i	0.379656	−	0.379656i	0.870978	+	0.491322i	$0.163486\pi$
$68$	−27.1563	+	13.8368i	−0.399357	+	0.203483i
$69$	−42.2762	−	58.1882i	−0.612699	−	0.843308i
$70$		0			0
$71$	−5.18827	−	15.9679i	−0.0730743	−	0.224899i	0.907848	−	0.419299i	$-0.137724\pi$
$71$	−5.18827	−	15.9679i	−0.0730743	−	0.224899i	−0.980922	+	0.194400i	$0.937724\pi$
$72$	34.7401	+	17.7010i	0.482502	+	0.245847i
$73$	9.30355	+	58.7403i	0.127446	+	0.804661i	0.965753	+	0.259463i	$0.0835456\pi$
$73$	9.30355	+	58.7403i	0.127446	+	0.804661i	−0.838307	+	0.545198i	$0.816454\pi$
$74$	−62.1107	−	85.4881i	−0.839334	−	1.15524i
$75$		0			0
$76$	275.111			3.61988
$77$	14.6518	+	20.0918i	0.190283	+	0.260932i
$78$	80.5345	+	80.5345i	1.03249	+	1.03249i
$79$	134.820	+	43.8055i	1.70658	+	0.554500i	0.989758	−	0.142759i	$-0.0455973\pi$
$79$	134.820	+	43.8055i	1.70658	+	0.554500i	0.716819	+	0.697259i	$0.245597\pi$
$80$		0			0
$81$	−34.6607	−	25.1825i	−0.427910	−	0.310895i
$82$	−90.3936	−	46.0578i	−1.10236	−	0.561681i
$83$	−27.5653	+	54.0999i	−0.332112	+	0.651806i	−0.995321	−	0.0966282i	$-0.969194\pi$
$83$	−27.5653	+	54.0999i	−0.332112	+	0.651806i	0.663209	+	0.748435i	$0.269194\pi$
$84$	−24.5603	+	33.8043i	−0.292384	+	0.402432i
$85$		0			0
$86$	85.9839	−	264.631i	0.999812	−	3.07711i
$87$	−28.9469	+	28.9469i	−0.332723	+	0.332723i
$88$	42.4043	+	129.727i	0.481867	+	1.47418i
$89$		−	168.321i		−	1.89125i	−0.325257	−	0.945626i	$-0.605451\pi$
$89$		−	168.321i		−	1.89125i	0.325257	−	0.945626i	$-0.394549\pi$
$90$		0			0
$91$	25.2290	−	18.3299i	0.277241	−	0.201428i
$92$	−224.166	+	35.5044i	−2.43659	+	0.385918i
$93$	21.7161	−	42.6202i	0.233506	−	0.458281i
$94$	−153.137	+	49.7572i	−1.62911	+	0.529331i
$95$		0			0
$96$	18.5103	−	13.4485i	0.192815	−	0.140088i
$97$	−24.6643	−	48.4063i	−0.254271	−	0.499034i	0.728221	−	0.685343i	$-0.240348\pi$
$97$	−24.6643	−	48.4063i	−0.254271	−	0.499034i	−0.982491	+	0.186308i	$0.940348\pi$
$98$	−105.869	−	105.869i	−1.08030	−	1.08030i
$99$	5.46772	+	34.1317i	0.0552295	+	0.344765i
$100$		0			0
$101$	−25.2615	+	77.7469i	−0.250114	+	0.769772i	0.744639	+	0.667467i	$0.232622\pi$
$101$	−25.2615	+	77.7469i	−0.250114	+	0.769772i	−0.994753	+	0.102304i	$0.967378\pi$
$102$	5.15434	−	32.5432i	0.0505327	−	0.319051i
$103$	19.4219	+	122.625i	0.188563	+	1.19054i	0.882433	+	0.470438i	$0.155904\pi$
$103$	19.4219	+	122.625i	0.188563	+	1.19054i	−0.693871	+	0.720100i	$0.744096\pi$
$104$	162.781	−	52.8909i	1.56521	−	0.508566i
$105$		0			0
$106$	−129.841	−	94.3351i	−1.22492	−	0.889954i
$107$	12.3426	−	77.9279i	0.115351	−	0.728299i	−0.860433	−	0.509563i	$-0.829807\pi$
$107$	12.3426	−	77.9279i	0.115351	−	0.728299i	0.975784	−	0.218735i	$-0.0701931\pi$
$108$	−199.975	+	101.892i	−1.85162	+	0.943448i
$109$		−	9.65784i		−	0.0886040i	−0.999018	−	0.0443020i	$-0.985894\pi$
$109$		−	9.65784i		−	0.0886040i	0.999018	−	0.0443020i	$-0.0141064\pi$
$110$		0			0
$111$	74.9692			0.675398
$112$	12.0870	+	23.7221i	0.107920	+	0.211804i
$113$	−111.365	−	17.6385i	−0.985531	−	0.156093i	−0.357191	−	0.934032i	$-0.616265\pi$
$113$	−111.365	−	17.6385i	−0.985531	−	0.156093i	−0.628340	+	0.777939i	$0.716265\pi$
$114$	−174.814	+	240.611i	−1.53346	+	2.11063i
$115$		0			0
$116$	39.9183	+	122.856i	0.344123	+	1.05910i
$117$	42.8158	−	6.78135i	0.365947	−	0.0579603i
$118$	−80.2091	−	12.7039i	−0.679738	−	0.107660i
$119$	−8.58008	−	2.78784i	−0.0721015	−	0.0234272i
$120$		0			0
$121$	−70.7759	+	98.1416i	−0.584925	+	0.811087i
$122$	−113.699	+	113.699i	−0.931960	+	0.931960i
$123$	64.1317	−	32.6767i	0.521396	−	0.265664i
$124$	−88.7208	−	122.114i	−0.715490	−	0.984788i
$125$		0			0
$126$	7.48857	+	23.0475i	0.0594331	+	0.182916i
$127$	148.368	+	75.5971i	1.16825	+	0.595252i	0.926945	−	0.375197i	$-0.122425\pi$
$127$	148.368	+	75.5971i	1.16825	+	0.595252i	0.241304	+	0.970450i	$0.422425\pi$
$128$	−36.4341	−	230.036i	−0.284641	−	1.79716i
$129$	116.035	+	159.708i	0.899495	+	1.23805i
$130$		0			0
$131$	16.7516			0.127875			0.0639373	−	0.997954i	$-0.479634\pi$
$131$	16.7516			0.127875			0.0639373	+	0.997954i	$0.479634\pi$
$132$	−193.480	−	62.4881i	−1.46576	−	0.473394i
$133$	57.5822	+	57.5822i	0.432949	+	0.432949i
$134$	116.710	+	37.9215i	0.870973	+	0.282996i
$135$		0			0
$136$	−40.0589	−	29.1045i	−0.294551	−	0.214004i
$137$	−79.9952	−	40.7596i	−0.583907	−	0.297515i	0.136974	−	0.990575i	$-0.456262\pi$
$137$	−79.9952	−	40.7596i	−0.583907	−	0.297515i	−0.720880	+	0.693059i	$0.756262\pi$
$138$	111.390	−	218.616i	0.807176	−	1.58417i
$139$	27.4367	−	37.7633i	0.197386	−	0.271679i	−0.698838	−	0.715280i	$-0.746299\pi$
$139$	27.4367	−	37.7633i	0.197386	−	0.271679i	0.896224	+	0.443601i	$0.146299\pi$
$140$		0			0
$141$	35.3013	−	108.646i	0.250364	−	0.770540i
$142$	40.4994	−	40.4994i	0.285207	−	0.285207i
$143$	122.920	+	88.9754i	0.859580	+	0.622206i
$144$			37.0096i			0.257011i
$145$		0			0
$146$	−164.133	+	119.250i	−1.12420	+	0.816780i
$147$	104.916	−	16.6170i	0.713712	−	0.113041i
$148$	107.399	−	210.783i	0.725672	−	1.42421i
$149$	157.950	−	51.3210i	1.06007	−	0.344437i	0.273455	−	0.961885i	$-0.411833\pi$
$149$	157.950	−	51.3210i	1.06007	−	0.344437i	0.786612	+	0.617448i	$0.211833\pi$
$150$		0			0
$151$	173.632	−	126.151i	1.14988	−	0.835435i	0.161413	−	0.986887i	$-0.448395\pi$
$151$	173.632	−	126.151i	1.14988	−	0.835435i	0.988465	+	0.151452i	$0.0483949\pi$
$152$	202.912	+	398.236i	1.33494	+	2.61998i
$153$	−8.86772	−	8.86772i	−0.0579589	−	0.0579589i
$154$	−38.3778	+	75.6506i	−0.249207	+	0.491238i
$155$		0			0
$156$	−78.7929	+	242.500i	−0.505083	+	1.55448i
$157$	−3.18010	+	20.0784i	−0.0202554	+	0.127888i	−0.995744	−	0.0921624i	$-0.970622\pi$
$157$	−3.18010	+	20.0784i	−0.0202554	+	0.127888i	0.975489	+	0.220050i	$0.0706221\pi$
$158$	75.6488	+	477.628i	0.478790	+	3.02296i
$159$	108.292	−	35.1862i	0.681081	−	0.221297i
$160$		0			0
$161$	−54.3504	−	39.4879i	−0.337580	−	0.245266i
$162$	22.8631	−	144.352i	0.141130	−	0.891062i
$163$	208.659	−	106.317i	1.28011	−	0.652251i	0.324226	−	0.945980i	$-0.394896\pi$
$163$	208.659	−	106.317i	1.28011	−	0.652251i	0.955889	+	0.293729i	$0.0948962\pi$
$164$		−	227.125i		−	1.38491i
$165$		0			0
$166$	−207.128			−1.24776
$167$	−85.1951	−	167.205i	−0.510151	−	1.00123i	−0.992150	−	0.125055i	$-0.960089\pi$
$167$	−85.1951	−	167.205i	−0.510151	−	1.00123i	0.481999	−	0.876172i	$-0.339911\pi$
$168$	−67.0481	−	10.6194i	−0.399096	−	0.0632106i
$169$	12.5181	−	17.2297i	0.0740715	−	0.101951i
$170$		0			0
$171$	34.9806	+	107.659i	0.204565	+	0.629586i
$172$	615.265	−	97.4484i	3.57712	−	0.566560i
$173$	−141.805	−	22.4597i	−0.819684	−	0.129825i	−0.267511	−	0.963555i	$-0.586201\pi$
$173$	−141.805	−	22.4597i	−0.819684	−	0.129825i	−0.552173	+	0.833730i	$0.686201\pi$
$174$	−132.815	−	43.1541i	−0.763303	−	0.248012i
$175$		0			0
$176$	−91.4441	+	91.7675i	−0.519569	+	0.521406i
$177$	40.7402	−	40.7402i	0.230171	−	0.230171i
$178$	511.615	−	260.681i	2.87424	−	1.46450i
$179$	97.6266	+	134.372i	0.545400	+	0.750679i	0.989379	−	0.145358i	$-0.0464335\pi$
$179$	97.6266	+	134.372i	0.545400	+	0.750679i	−0.443979	+	0.896037i	$0.646434\pi$
$180$		0			0
$181$	95.3179	+	293.358i	0.526618	+	1.62076i	0.761093	+	0.648643i	$0.224663\pi$
$181$	95.3179	+	293.358i	0.526618	+	1.62076i	−0.234475	+	0.972122i	$0.575337\pi$
$182$	94.7864	+	48.2961i	0.520804	+	0.265363i
$183$	−17.8460	−	112.675i	−0.0975189	−	0.615710i
$184$	−216.731	−	298.304i	−1.17788	−	1.62122i
$185$		0			0
$186$	163.176			0.877292
$187$	−0.0774976	−	43.8986i	−0.000414426	−	0.234752i
$188$	−254.898	−	254.898i	−1.35584	−	1.35584i
$189$	−63.1825	−	20.5292i	−0.334299	−	0.108620i
$190$		0			0
$191$	−159.522	−	115.900i	−0.835196	−	0.606805i	0.0858287	−	0.996310i	$-0.472646\pi$
$191$	−159.522	−	115.900i	−0.835196	−	0.606805i	−0.921024	+	0.389505i	$0.872646\pi$
$192$	171.133	+	87.1964i	0.891315	+	0.454148i
$193$	−61.3806	+	120.466i	−0.318034	+	0.624177i	−0.993579	−	0.113142i	$-0.963908\pi$
$193$	−61.3806	+	120.466i	−0.318034	+	0.624177i	0.675545	+	0.737319i	$0.263908\pi$
$194$	108.934	−	149.935i	0.561515	−	0.772859i
$195$		0			0
$196$	103.580	−	318.786i	0.528468	−	1.62646i
$197$	59.7822	−	59.7822i	0.303463	−	0.303463i	−0.538904	−	0.842367i	$-0.681161\pi$
$197$	59.7822	−	59.7822i	0.303463	−	0.303463i	0.842367	+	0.538904i	$0.181161\pi$
$198$	−95.2759	+	69.4793i	−0.481192	+	0.350906i
$199$			245.076i			1.23154i	0.787927	+	0.615769i	$0.211155\pi$
$199$			245.076i			1.23154i	−0.787927	+	0.615769i	$0.788845\pi$
$200$		0			0
$201$	−70.4362	+	51.1749i	−0.350429	+	0.254602i
$202$	−275.435	+	43.6247i	−1.36354	+	0.215964i
$203$	−17.3593	+	34.0695i	−0.0855136	+	0.167830i
$204$	70.1543	−	22.7945i	0.343893	−	0.111738i
$205$		0			0
$206$	−342.642	+	248.944i	−1.66331	+	1.20847i
$207$	−42.3969	−	83.2086i	−0.204816	−	0.401974i
$208$	114.881	+	114.881i	0.552311	+	0.552311i
$209$	−179.270	+	353.379i	−0.857753	+	1.69081i
$210$		0			0
$211$	94.8835	−	292.021i	0.449685	−	1.38399i	−0.427578	−	0.903978i	$-0.640633\pi$
$211$	94.8835	−	292.021i	0.449685	−	1.38399i	0.877263	−	0.480009i	$-0.159367\pi$
$212$	56.2075	−	354.880i	0.265130	−	1.67396i
$213$	6.35669	+	40.1346i	0.0298436	+	0.188425i
$214$	255.978	−	83.1723i	1.19616	−	0.388656i
$215$		0			0
$216$	−294.988	−	214.321i	−1.36569	−	0.992229i
$217$	6.98931	−	44.1288i	0.0322088	−	0.203358i
$218$	29.3551	−	14.9572i	0.134656	−	0.0686109i
$219$		−	143.938i		−	0.657249i
$220$		0			0
$221$	−55.0523			−0.249105
$222$	116.105	+	227.870i	0.522998	+	1.02644i
$223$	−229.685	−	36.3786i	−1.02998	−	0.163133i	−0.381503	−	0.924368i	$-0.624593\pi$
$223$	−229.685	−	36.3786i	−1.02998	−	0.163133i	−0.648476	+	0.761235i	$0.724593\pi$
$224$	12.5615	−	17.2894i	0.0560781	−	0.0771849i
$225$		0			0
$226$	−118.860	−	365.812i	−0.525927	−	1.61864i
$227$	−204.785	+	32.4348i	−0.902138	+	0.142885i	−0.590237	−	0.807230i	$-0.700966\pi$
$227$	−204.785	+	32.4348i	−0.902138	+	0.142885i	−0.311901	+	0.950115i	$0.600966\pi$
$228$	−657.636	−	104.159i	−2.88437	−	0.456839i
$229$	8.32217	+	2.70404i	0.0363413	+	0.0118080i	0.327131	−	0.944979i	$-0.393918\pi$
$229$	8.32217	+	2.70404i	0.0363413	+	0.0118080i	−0.290790	+	0.956787i	$0.593918\pi$
$230$		0			0
$231$	−27.4173	−	53.5755i	−0.118690	−	0.231928i
$232$	−148.397	+	148.397i	−0.639644	+	0.639644i
$233$	−88.8247	+	45.2584i	−0.381222	+	0.194242i	−0.634091	−	0.773258i	$-0.718626\pi$
$233$	−88.8247	+	45.2584i	−0.381222	+	0.194242i	0.252870	+	0.967500i	$0.418626\pi$
$234$	86.9212	+	119.637i	0.371458	+	0.511268i
$235$		0			0
$236$	−56.1815	−	172.909i	−0.238057	−	0.732665i
$237$	−305.693	−	155.758i	−1.28984	−	0.657208i
$238$	−4.81438	−	30.3968i	−0.0202285	−	0.127718i
$239$	32.4101	+	44.6086i	0.135607	+	0.186647i	0.871420	−	0.490538i	$-0.163200\pi$
$239$	32.4101	+	44.6086i	0.135607	+	0.186647i	−0.735813	+	0.677185i	$0.763200\pi$
$240$		0			0
$241$	225.159			0.934271			0.467135	−	0.884186i	$-0.345286\pi$
$241$	225.159			0.934271			0.467135	+	0.884186i	$0.345286\pi$
$242$	−407.914	−	63.1317i	−1.68559	−	0.260875i
$243$	−113.702	−	113.702i	−0.467907	−	0.467907i
$244$	−342.362	−	111.240i	−1.40312	−	0.455903i
$245$		0			0
$246$	198.643	+	144.322i	0.807490	+	0.586676i
$247$	442.766	+	225.600i	1.79257	+	0.913362i
$248$	111.328	−	218.494i	0.448904	−	0.881024i
$249$	86.3759	−	118.886i	0.346891	−	0.477455i
$250$		0			0
$251$	125.864	−	387.371i	0.501452	−	1.54331i	−0.305203	−	0.952287i	$-0.598724\pi$
$251$	125.864	−	387.371i	0.501452	−	1.54331i	0.806655	−	0.591023i	$-0.201276\pi$
$252$	−38.3627	+	38.3627i	−0.152233	+	0.152233i
$253$	100.468	−	311.076i	0.397107	−	1.22955i
$254$			568.043i			2.23639i
$255$		0			0
$256$	385.962	−	280.417i	1.50766	−	1.09538i
$257$	−5.89609	+	0.933850i	−0.0229420	+	0.00363366i	−0.167895	−	0.985805i	$-0.553697\pi$
$257$	−5.89609	+	0.933850i	−0.0229420	+	0.00363366i	0.144953	+	0.989439i	$0.453697\pi$
$258$	−305.731	+	600.031i	−1.18500	+	2.32570i
$259$	66.5973	−	21.6388i	0.257133	−	0.0835474i
$260$		0			0
$261$	−43.0016	+	31.2425i	−0.164757	+	0.119703i
$262$	25.9433	+	50.9166i	0.0990203	+	0.194338i
$263$	115.406	+	115.406i	0.438806	+	0.438806i	0.891610	−	0.452804i	$-0.149576\pi$
$263$	115.406	+	115.406i	0.438806	+	0.438806i	−0.452804	+	0.891610i	$0.649576\pi$
$264$	−52.2491	−	326.160i	−0.197913	−	1.23546i
$265$		0			0
$266$	−85.8437	+	264.200i	−0.322721	+	0.993232i
$267$	−63.7279	+	402.362i	−0.238681	+	1.50698i
$268$	42.9777	+	271.351i	0.160365	+	1.01250i
$269$	−399.783	+	129.897i	−1.48618	+	0.482890i	−0.935953	−	0.352124i	$-0.885459\pi$
$269$	−399.783	+	129.897i	−1.48618	+	0.482890i	−0.550229	+	0.835014i	$0.685459\pi$
$270$		0			0
$271$	−235.240	−	170.912i	−0.868043	−	0.630670i	0.0620182	−	0.998075i	$-0.480246\pi$
$271$	−235.240	−	170.912i	−0.868043	−	0.630670i	−0.930061	+	0.367405i	$0.880246\pi$
$272$	7.35254	−	46.4221i	0.0270314	−	0.170670i
$273$	−67.2482	+	34.2647i	−0.246331	+	0.125512i
$274$		−	306.271i		−	1.11778i
$275$		0			0
$276$	549.298			1.99021
$277$	−155.743	−	305.663i	−0.562250	−	1.10348i	−0.980751	−	0.195262i	$-0.937444\pi$
$277$	−155.743	−	305.663i	−0.562250	−	1.10348i	0.418501	−	0.908216i	$-0.362556\pi$
$278$	157.273	+	24.9097i	0.565732	+	0.0896031i
$279$	36.5059	−	50.2460i	0.130845	−	0.180093i
$280$		0			0
$281$	−29.5550	−	90.9610i	−0.105178	−	0.323705i	0.884594	−	0.466362i	$-0.154435\pi$
$281$	−29.5550	−	90.9610i	−0.105178	−	0.323705i	−0.989772	+	0.142657i	$0.954435\pi$
$282$	384.903	−	60.9626i	1.36490	−	0.216180i
$283$	48.4877	+	7.67970i	0.171335	+	0.0271368i	0.241512	−	0.970398i	$-0.422357\pi$
$283$	48.4877	+	7.67970i	0.171335	+	0.0271368i	−0.0701775	+	0.997535i	$0.522357\pi$
$284$	121.949	+	39.6235i	0.429397	+	0.139520i
$285$		0			0
$286$	−80.0748	+	511.414i	−0.279982	+	1.78816i
$287$	47.5384	−	47.5384i	0.165639	−	0.165639i
$288$	26.4695	−	13.4869i	0.0919079	−	0.0468294i
$289$	−160.509	−	220.921i	−0.555393	−	0.764433i
$290$		0			0
$291$	40.6314	+	125.051i	0.139627	+	0.429727i
$292$	−404.695	−	206.202i	−1.38594	−	0.706172i
$293$	72.0074	+	454.637i	0.245759	+	1.55166i	0.734120	+	0.679020i	$0.237595\pi$
$293$	72.0074	+	454.637i	0.245759	+	1.55166i	−0.488361	+	0.872642i	$0.662405\pi$
$294$	212.991	+	293.157i	0.724460	+	0.997134i
$295$		0			0
$296$	384.333			1.29842
$297$	−0.570681	−	323.263i	−0.00192148	−	1.08843i
$298$	400.609	+	400.609i	1.34433	+	1.34433i
$299$	−389.890	−	126.683i	−1.30398	−	0.423688i
$300$		0			0
$301$	149.175	+	108.382i	0.495597	+	0.360072i
$302$	652.341	+	332.385i	2.16007	+	1.10061i
$303$	89.8218	−	176.285i	0.296442	−	0.581799i
$304$	−249.369	+	343.227i	−0.820292	+	1.12903i
$305$		0			0
$306$	13.2200	−	40.6871i	0.0432027	−	0.132964i
$307$	−170.036	+	170.036i	−0.553862	+	0.553862i	−0.927553	−	0.373691i	$-0.878092\pi$
$307$	−170.036	+	170.036i	−0.553862	+	0.553862i	0.373691	+	0.927553i	$0.378092\pi$
$308$	−189.910	+	0.335263i	−0.616592	+	0.00108852i
$309$		−	300.482i		−	0.972434i
$310$		0			0
$311$	−173.513	+	126.064i	−0.557919	+	0.405352i	−0.830697	−	0.556725i	$-0.812058\pi$
$311$	−173.513	+	126.064i	−0.557919	+	0.405352i	0.272778	+	0.962077i	$0.412058\pi$
$312$	−409.145	+	64.8021i	−1.31136	+	0.207699i
$313$	72.2129	−	141.726i	0.230712	−	0.452798i	−0.746407	−	0.665489i	$-0.768223\pi$
$313$	72.2129	−	141.726i	0.230712	−	0.452798i	0.977119	+	0.212691i	$0.0682229\pi$
$314$	−65.9536	+	21.4296i	−0.210043	+	0.0682472i
$315$		0			0
$316$	−875.860	+	636.350i	−2.77171	+	2.01376i
$317$	−12.8910	−	25.3001i	−0.0406657	−	0.0798109i	0.869780	−	0.493440i	$-0.164261\pi$
$317$	−12.8910	−	25.3001i	−0.0406657	−	0.0798109i	−0.910445	+	0.413629i	$0.864261\pi$
$318$	274.662	+	274.662i	0.863716	+	0.863716i
$319$	−183.820	−	28.7816i	−0.576237	−	0.0902245i
$320$		0			0
$321$	−59.0084	+	181.609i	−0.183827	+	0.565761i
$322$	35.8509	−	226.354i	0.111338	−	0.702963i
$323$	−22.4889	−	141.990i	−0.0696252	−	0.439596i
$324$	311.184	−	101.110i	0.960444	−	0.312067i
$325$		0			0
$326$	646.303	+	469.567i	1.98253	+	1.44039i
$327$	−3.65654	+	23.0865i	−0.0111821	+	0.0706009i
$328$	328.774	−	167.519i	1.00236	−	0.510727i
$329$		−	106.703i		−	0.324325i
$330$		0			0
$331$	151.309			0.457126			0.228563	−	0.973529i	$-0.426597\pi$
$331$	151.309			0.457126			0.228563	+	0.973529i	$0.426597\pi$
$332$	−210.520	−	413.169i	−0.634096	−	1.24448i
$333$	96.1419	+	15.2274i	0.288714	+	0.0457279i
$334$	376.279	−	517.903i	1.12658	−	1.55061i
$335$		0			0
$336$	−19.9119	−	61.2825i	−0.0592616	−	0.182388i
$337$	−368.438	+	58.3548i	−1.09329	+	0.173160i	−0.676934	−	0.736043i	$-0.736692\pi$
$337$	−368.438	+	58.3548i	−1.09329	+	0.173160i	−0.416353	+	0.909203i	$0.636692\pi$
$338$	71.7567	+	11.3651i	0.212298	+	0.0336247i
$339$	259.533	+	84.3275i	0.765585	+	0.248754i
$340$		0			0
$341$	214.668	−	34.3886i	0.629524	−	0.100846i
$342$	−273.057	+	273.057i	−0.798412	+	0.798412i
$343$	187.100	−	95.3323i	0.545481	−	0.277937i
$344$	594.857	+	818.751i	1.72924	+	2.38009i
$345$		0			0
$346$	−151.348	−	465.803i	−0.437423	−	1.34625i
$347$	604.240	+	307.876i	1.74133	+	0.887250i	0.967122	+	0.254313i	$0.0818492\pi$
$347$	604.240	+	307.876i	1.74133	+	0.887250i	0.774203	+	0.632937i	$0.218151\pi$
$348$	−48.9080	−	308.793i	−0.140540	−	0.887336i
$349$	24.7765	+	34.1019i	0.0709927	+	0.0977131i	0.843037	−	0.537856i	$-0.180766\pi$
$349$	24.7765	+	34.1019i	0.0709927	+	0.0977131i	−0.772044	+	0.635569i	$0.780766\pi$
$350$		0			0
$351$	−405.397			−1.15498
$352$	98.9565	+	31.9599i	0.281126	+	0.0907951i
$353$	−292.066	−	292.066i	−0.827382	−	0.827382i	0.159772	−	0.987154i	$-0.448924\pi$
$353$	−292.066	−	292.066i	−0.827382	−	0.827382i	−0.987154	+	0.159772i	$0.948924\pi$
$354$	186.925	+	60.7357i	0.528038	+	0.171570i
$355$		0			0
$356$	1039.99	+	755.594i	2.92131	+	2.12246i
$357$	19.4547	+	9.91265i	0.0544949	+	0.0277665i
$358$	−257.229	+	504.840i	−0.718516	+	1.41017i
$359$	−86.9687	+	119.702i	−0.242253	+	0.333432i	−0.912779	−	0.408453i	$-0.866068\pi$
$359$	−86.9687	+	119.702i	−0.242253	+	0.333432i	0.670526	+	0.741886i	$0.266068\pi$
$360$		0			0
$361$	−289.438	+	890.798i	−0.801767	+	2.46759i
$362$	−744.047	+	744.047i	−2.05538	+	2.05538i
$363$	206.343	−	207.805i	0.568438	−	0.572466i
$364$			238.162i			0.654291i
$365$		0			0
$366$	314.839	−	228.744i	0.860215	−	0.624983i
$367$	−349.255	+	55.3166i	−0.951649	+	0.150726i	−0.612909	−	0.790154i	$-0.710001\pi$
$367$	−349.255	+	55.3166i	−0.951649	+	0.150726i	−0.338740	+	0.940880i	$0.610001\pi$
$368$	158.896	−	311.850i	0.431782	−	0.847419i
$369$	88.8808	−	28.8791i	0.240869	−	0.0782632i
$370$		0			0
$371$	86.0429	−	62.5138i	0.231922	−	0.168501i
$372$	165.848	+	325.496i	0.445829	+	0.874989i
$373$	67.3093	+	67.3093i	0.180454	+	0.180454i	0.791554	−	0.611100i	$-0.209273\pi$
$373$	67.3093	+	67.3093i	0.180454	+	0.180454i	−0.611100	+	0.791554i	$0.709273\pi$
$374$	133.310	−	68.2218i	0.356445	−	0.182411i
$375$		0			0
$376$	180.974	−	556.979i	0.481313	−	1.48133i
$377$	−36.5012	+	230.460i	−0.0968202	+	0.611299i
$378$	−35.4524	−	223.838i	−0.0937894	−	0.592163i
$379$	−518.993	+	168.631i	−1.36937	+	0.444937i	−0.899162	−	0.437617i	$-0.855823\pi$
$379$	−518.993	+	168.631i	−1.36937	+	0.444937i	−0.470212	+	0.882553i	$0.655823\pi$
$380$		0			0
$381$	−326.042	−	236.884i	−0.855754	−	0.621742i
$382$	105.225	−	664.365i	0.275458	−	1.73918i
$383$	301.699	−	153.723i	0.787726	−	0.401366i	−0.0133638	−	0.999911i	$-0.504254\pi$
$383$	301.699	−	153.723i	0.787726	−	0.401366i	0.801090	+	0.598544i	$0.204254\pi$
$384$			563.681i			1.46792i
$385$		0			0
$386$	−461.219			−1.19487
$387$	116.366	+	228.381i	0.300687	+	0.590132i
$388$	409.800	+	64.9059i	1.05619	+	0.167283i
$389$	−333.318	+	458.773i	−0.856859	+	1.17937i	0.125450	+	0.992100i	$0.459962\pi$
$389$	−333.318	+	458.773i	−0.856859	+	1.17937i	−0.982309	+	0.187265i	$0.940038\pi$
$390$		0			0
$391$	36.6489	+	112.794i	0.0937312	+	0.288475i
$392$	537.854	−	85.1877i	1.37208	−	0.217316i
$393$	−40.0437	−	6.34229i	−0.101892	−	0.0161382i
$394$	274.294	+	89.1236i	0.696178	+	0.226202i
$395$		0			0
$396$	−235.430	−	119.435i	−0.594520	−	0.301602i
$397$	−363.354	+	363.354i	−0.915249	+	0.915249i	−0.996679	−	0.0814297i	$-0.974051\pi$
$397$	−363.354	+	363.354i	−0.915249	+	0.915249i	0.0814297	+	0.996679i	$0.474051\pi$
$398$	−744.912	+	379.551i	−1.87164	+	0.953647i
$399$	−115.846	−	159.448i	−0.290340	−	0.399619i
$400$		0			0
$401$	−63.8238	−	196.429i	−0.159162	−	0.489849i	0.839397	−	0.543519i	$-0.182908\pi$
$401$	−63.8238	−	196.429i	−0.159162	−	0.489849i	−0.998559	+	0.0536695i	$0.982908\pi$
$402$	−264.632	−	134.837i	−0.658289	−	0.335415i
$403$	−42.6505	−	269.285i	−0.105833	−	0.668201i
$404$	−366.966	−	505.086i	−0.908332	−	1.25021i
$405$		0			0
$406$	−130.439			−0.321279
$407$	200.766	+	275.307i	0.493282	+	0.676430i
$408$	84.7393	+	84.7393i	0.207694	+	0.207694i
$409$	320.829	+	104.244i	0.784423	+	0.254875i	0.673728	−	0.738980i	$-0.264692\pi$
$409$	320.829	+	104.244i	0.784423	+	0.254875i	0.110696	+	0.993854i	$0.464692\pi$
$410$		0			0
$411$	175.792	+	127.720i	0.427717	+	0.310755i
$412$	−844.835	−	430.465i	−2.05057	−	1.04482i
$413$	24.4317	−	47.9498i	0.0591566	−	0.116101i
$414$	187.253	−	257.732i	0.452302	−	0.622540i
$415$		0			0
$416$	40.2991	−	124.028i	0.0968728	−	0.298144i
$417$	−79.8832	+	79.8832i	−0.191567	+	0.191567i
$418$	−1351.74	+	2.38632i	−3.23382	+	0.00570891i
$419$		−	523.431i		−	1.24924i	−0.780930	−	0.624619i	$-0.785254\pi$
$419$		−	523.431i		−	1.24924i	0.780930	−	0.624619i	$-0.214746\pi$
$420$		0			0
$421$	−264.208	+	191.959i	−0.627574	+	0.455959i	−0.855559	−	0.517706i	$-0.826786\pi$
$421$	−264.208	+	191.959i	−0.627574	+	0.455959i	0.227985	+	0.973665i	$0.426786\pi$
$422$	1034.55	−	163.857i	2.45154	−	0.388286i
$423$	67.3387	−	132.160i	0.159193	−	0.312434i
$424$	555.163	−	180.383i	1.30935	−	0.425433i
$425$		0			0
$426$	−112.145	+	81.4780i	−0.263251	+	0.191263i
$427$	−48.3751	−	94.9415i	−0.113291	−	0.222345i
$428$	426.078	+	426.078i	0.995509	+	0.995509i
$429$	−260.146	−	259.229i	−0.606401	−	0.604264i
$430$		0			0
$431$	141.996	−	437.020i	0.329458	−	1.01397i	−0.639930	−	0.768433i	$-0.721037\pi$
$431$	141.996	−	437.020i	0.329458	−	1.01397i	0.969388	−	0.245534i	$-0.0789632\pi$
$432$	54.1431	−	341.846i	0.125331	−	0.791310i
$433$	−45.7255	−	288.700i	−0.105602	−	0.666743i	−0.982528	−	0.186117i	$-0.940410\pi$
$433$	−45.7255	−	288.700i	−0.105602	−	0.666743i	0.876926	−	0.480626i	$-0.159590\pi$
$434$	144.954	−	47.0985i	0.333996	−	0.108522i
$435$		0			0
$436$	59.6717	+	43.3540i	0.136862	+	0.0994358i
$437$	167.467	−	1057.34i	0.383219	−	2.41955i
$438$	437.500	−	222.917i	0.998859	−	0.508944i
$439$		−	286.451i		−	0.652507i	−0.945282	−	0.326253i	$-0.894214\pi$
$439$		−	286.451i		−	0.652507i	0.945282	−	0.326253i	$-0.105786\pi$
$440$		0			0
$441$	137.921			0.312746
$442$	−85.2599	−	167.332i	−0.192896	−	0.378579i
$443$	−304.198	−	48.1802i	−0.686676	−	0.108759i	−0.196660	−	0.980472i	$-0.563009\pi$
$443$	−304.198	−	48.1802i	−0.686676	−	0.108759i	−0.490017	+	0.871713i	$0.663009\pi$
$444$	−336.536	+	463.203i	−0.757965	+	1.04325i
$445$		0			0
$446$	−245.142	−	754.471i	−0.549647	−	1.69164i
$447$	−397.001	+	62.8787i	−0.888145	+	0.140668i
$448$	177.190	+	28.0641i	0.395513	+	0.0626432i
$449$	267.659	+	86.9677i	0.596123	+	0.193692i	0.591510	−	0.806297i	$-0.298532\pi$
$449$	267.659	+	86.9677i	0.596123	+	0.193692i	0.00461218	+	0.999989i	$0.498532\pi$
$450$		0			0
$451$	291.741	+	148.001i	0.646875	+	0.328162i
$452$	608.898	−	608.898i	1.34712	−	1.34712i
$453$	−462.818	+	235.817i	−1.02167	+	0.520568i
$454$	−415.739	−	572.215i	−0.915724	−	1.26039i
$455$		0			0
$456$	−334.272	−	1028.78i	−0.733053	−	2.25611i
$457$	−22.2989	−	11.3619i	−0.0487941	−	0.0248618i	0.429423	−	0.903103i	$-0.358717\pi$
$457$	−22.2989	−	11.3619i	−0.0487941	−	0.0248618i	−0.478217	+	0.878242i	$0.658717\pi$
$458$	4.66966	+	29.4831i	0.0101958	+	0.0643736i
$459$	68.9354	+	94.8814i	0.150186	+	0.206713i
$460$		0			0
$461$	−786.245			−1.70552			−0.852761	−	0.522302i	$-0.825073\pi$
$461$	−786.245			−1.70552			−0.852761	+	0.522302i	$0.825073\pi$
$462$	120.382	−	166.308i	0.260567	−	0.359974i
$463$	216.315	+	216.315i	0.467203	+	0.467203i	0.901007	−	0.433804i	$-0.142829\pi$
$463$	216.315	+	216.315i	0.467203	+	0.467203i	−0.433804	+	0.901007i	$0.642829\pi$
$464$	−189.457	−	61.5584i	−0.408313	−	0.132669i
$465$		0			0
$466$	−275.127	−	199.892i	−0.590402	−	0.428952i
$467$	157.211	+	80.1031i	0.336641	+	0.171527i	0.614137	−	0.789200i	$-0.289504\pi$
$467$	157.211	+	80.1031i	0.336641	+	0.171527i	−0.277496	+	0.960727i	$0.589504\pi$
$468$	−150.301	+	294.982i	−0.321155	+	0.630303i
$469$	−47.7997	+	65.7906i	−0.101918	+	0.140278i
$470$		0			0
$471$	15.2037	−	46.7922i	0.0322796	−	0.0993465i
$472$	208.857	−	208.857i	0.442493	−	0.442493i
$473$	−275.753	+	853.805i	−0.582987	+	1.80509i
$474$		−	1170.38i		−	2.46916i
$475$		0			0
$476$	55.7408	−	40.4981i	0.117102	−	0.0850799i
$477$	146.022	−	23.1277i	0.306127	−	0.0484857i
$478$	−85.3948	+	167.597i	−0.178650	+	0.350621i
$479$	−565.936	+	183.884i	−1.18149	+	0.383891i	−0.832922	−	0.553391i	$-0.813334\pi$
$479$	−565.936	+	183.884i	−1.18149	+	0.383891i	−0.348573	+	0.937282i	$0.613334\pi$
$480$		0			0
$481$	345.699	−	251.165i	0.718709	−	0.522173i
$482$	348.706	+	684.374i	0.723457	+	1.41986i
$483$	114.971	+	114.971i	0.238035	+	0.238035i
$484$	−288.662	−	877.851i	−0.596409	−	1.81374i
$485$		0			0
$486$	169.507	−	521.688i	0.348779	−	1.07343i
$487$	−72.9801	+	460.778i	−0.149856	+	0.946156i	0.792093	+	0.610401i	$0.208992\pi$
$487$	−72.9801	+	460.778i	−0.149856	+	0.946156i	−0.941949	+	0.335755i	$0.891008\pi$
$488$	−91.4880	−	577.633i	−0.187475	−	1.18367i
$489$	−539.039	+	175.144i	−1.10233	+	0.358168i
$490$		0			0
$491$	−93.6260	−	68.0233i	−0.190684	−	0.138540i	0.488347	−	0.872649i	$-0.337600\pi$
$491$	−93.6260	−	68.0233i	−0.190684	−	0.138540i	−0.679031	+	0.734109i	$0.737600\pi$
$492$	−85.9913	+	542.928i	−0.174779	+	1.10351i
$493$	60.1449	−	30.6454i	0.121998	−	0.0621610i
$494$			1695.18i			3.43154i
$495$		0			0
$496$	232.767			0.469289
$497$	17.2311	+	33.8179i	0.0346702	+	0.0680441i
$498$	495.127	+	78.4205i	0.994232	+	0.157471i
$499$	141.813	−	195.189i	0.284195	−	0.391161i	−0.642923	−	0.765931i	$-0.722278\pi$
$499$	141.813	−	195.189i	0.284195	−	0.391161i	0.927118	+	0.374770i	$0.122278\pi$
$500$		0			0
$501$	140.349	+	431.949i	0.280137	+	0.862174i
$502$	1372.35	−	217.358i	2.73376	−	0.432984i
$503$	428.067	+	67.7992i	0.851028	+	0.134790i	0.566687	−	0.823933i	$-0.308225\pi$
$503$	428.067	+	67.7992i	0.851028	+	0.134790i	0.284342	+	0.958723i	$0.408225\pi$
$504$	−83.8268	−	27.2370i	−0.166323	−	0.0540416i
$505$		0			0
$506$	1101.12	−	176.393i	2.17612	−	0.348602i
$507$	−36.4471	+	36.4471i	−0.0718877	+	0.0718877i
$508$	−1133.10	+	577.345i	−2.23052	+	1.13651i
$509$	−160.580	−	221.019i	−0.315481	−	0.434223i	0.621600	−	0.783335i	$-0.286483\pi$
$509$	−160.580	−	221.019i	−0.315481	−	0.434223i	−0.937081	+	0.349112i	$0.886483\pi$
$510$		0			0
$511$	−41.5455	−	127.864i	−0.0813024	−	0.250223i
$512$	620.001	+	315.906i	1.21094	+	0.617005i
$513$	−165.605	−	1045.59i	−0.322817	−	2.03819i
$514$	−11.9698	−	16.4750i	−0.0232875	−	0.0320525i
$515$		0			0
$516$	−1507.65			−2.92180
$517$	493.514	−	161.316i	0.954572	−	0.312023i
$518$	168.911	+	168.911i	0.326084	+	0.326084i
$519$	330.474	+	107.377i	0.636751	+	0.206893i
$520$		0			0
$521$	407.039	+	295.731i	0.781264	+	0.567622i	0.905358	−	0.424649i	$-0.139602\pi$
$521$	407.039	+	295.731i	0.781264	+	0.567622i	−0.124094	+	0.992270i	$0.539602\pi$
$522$	−161.559	−	82.3183i	−0.309500	−	0.157698i
$523$	−20.4357	+	40.1074i	−0.0390741	+	0.0766871i	−0.909718	−	0.415226i	$-0.863702\pi$
$523$	−20.4357	+	40.1074i	−0.0390741	+	0.0766871i	0.870644	+	0.491913i	$0.163702\pi$
$524$	−75.1978	+	103.501i	−0.143507	+	0.197521i
$525$		0			0
$526$	−172.048	+	529.508i	−0.327087	+	1.00667i
$527$	−55.7725	+	55.7725i	−0.105830	+	0.105830i
$528$	253.336	−	184.743i	0.479803	−	0.349893i
$529$			354.158i			0.669487i
$530$		0			0
$531$	60.5210	−	43.9711i	0.113975	−	0.0828080i
$532$	−614.262	+	97.2895i	−1.15463	+	0.182875i
$533$	186.250	−	365.536i	0.349437	−	0.685809i
$534$	−1321.68	+	429.440i	−2.47506	+	0.804195i
$535$		0			0
$536$	−361.094	+	262.350i	−0.673683	+	0.489460i
$537$	−182.496	−	358.169i	−0.339844	−	0.666982i
$538$	−1013.97	−	1013.97i	−1.88471	−	1.88471i
$539$	341.983	+	340.778i	0.634478	+	0.632241i
$540$		0			0
$541$	204.616	−	629.743i	0.378218	−	1.16404i	−0.563064	−	0.826414i	$-0.690377\pi$
$541$	204.616	−	629.743i	0.378218	−	1.16404i	0.941282	−	0.337622i	$-0.109623\pi$
$542$	155.170	−	979.706i	0.286292	−	1.80758i
$543$	−116.784	−	737.344i	−0.215072	−	1.35791i
$544$	−35.8808	+	11.6584i	−0.0659574	+	0.0214308i
$545$		0			0
$546$	−208.296	−	151.336i	−0.381494	−	0.277172i
$547$	−51.2339	+	323.478i	−0.0936635	+	0.591368i	0.895558	+	0.444944i	$0.146776\pi$
$547$	−51.2339	+	323.478i	−0.0936635	+	0.591368i	−0.989222	+	0.146424i	$0.953224\pi$
$548$	610.934	−	311.287i	1.11484	−	0.568041i
$549$		−	148.121i		−	0.269802i
$550$		0			0
$551$	−609.307			−1.10582
$552$	405.142	+	795.135i	0.733952	+	1.44046i
$553$	−316.514	−	50.1308i	−0.572357	−	0.0906525i
$554$	687.867	−	946.767i	1.24164	−	1.70897i
$555$		0			0
$556$	110.160	+	339.039i	0.198130	+	0.609782i
$557$	−828.504	+	131.222i	−1.48744	+	0.235587i	−0.846659	−	0.532136i	$-0.821390\pi$
$557$	−828.504	+	131.222i	−1.48744	+	0.235587i	−0.640782	+	0.767723i	$0.721390\pi$
$558$	209.260	+	33.1436i	0.375018	+	0.0593971i
$559$	1070.12	+	347.704i	1.91435	+	0.622011i
$560$		0			0
$561$	−16.4352	+	104.966i	−0.0292962	+	0.187106i
$562$	230.705	−	230.705i	0.410507	−	0.410507i
$563$	−708.172	+	360.832i	−1.25785	+	0.640909i	−0.950511	−	0.310690i	$-0.899440\pi$
$563$	−708.172	+	360.832i	−1.25785	+	0.640909i	−0.307343	+	0.951599i	$0.599440\pi$
$564$	512.811	+	705.824i	0.909240	+	1.25146i
$565$		0			0
$566$	51.7509	+	159.273i	0.0914326	+	0.281401i
$567$	86.2952	+	43.9696i	0.152196	+	0.0775478i
$568$	32.5878	+	205.752i	0.0573730	+	0.362239i
$569$	543.704	+	748.344i	0.955543	+	1.31519i	0.949021	+	0.315213i	$0.102076\pi$
$569$	543.704	+	748.344i	0.955543	+	1.31519i	0.00652189	+	0.999979i	$0.497924\pi$
$570$		0			0
$571$	290.179			0.508194			0.254097	−	0.967179i	$-0.418222\pi$
$571$	290.179			0.508194			0.254097	+	0.967179i	$0.418222\pi$
$572$	−1101.53	+	360.059i	−1.92575	+	0.629475i
$573$	337.448	+	337.448i	0.588915	+	0.588915i
$574$	218.117	+	70.8704i	0.379994	+	0.123468i
$575$		0			0
$576$	201.753	+	146.582i	0.350265	+	0.254482i
$577$	−207.415	−	105.683i	−0.359471	−	0.183159i	0.264922	−	0.964270i	$-0.414654\pi$
$577$	−207.415	−	105.683i	−0.359471	−	0.183159i	−0.624393	+	0.781110i	$0.714654\pi$
$578$	422.912	−	830.011i	0.731681	−	1.43600i
$579$	192.336	−	264.728i	0.332187	−	0.457216i
$580$		0			0
$581$	42.4154	−	130.541i	0.0730042	−	0.224684i
$582$	−317.167	+	317.167i	−0.544960	+	0.544960i
$583$	419.216	+	303.449i	0.719067	+	0.520496i
$584$		−	737.902i		−	1.26353i
$585$		0			0
$586$	−1270.36	+	922.968i	−2.16784	+	1.57503i
$587$	87.7179	−	13.8932i	0.149434	−	0.0236681i	−0.0812691	−	0.996692i	$-0.525897\pi$
$587$	87.7179	−	13.8932i	0.149434	−	0.0236681i	0.230703	+	0.973024i	$0.425897\pi$
$588$	−368.296	+	722.822i	−0.626354	+	1.22929i
$589$	677.111	−	220.007i	1.14959	−	0.373526i
$590$		0			0
$591$	−165.540	+	120.272i	−0.280102	+	0.203506i
$592$	165.622	+	325.051i	0.279767	+	0.549073i
$593$	282.278	+	282.278i	0.476016	+	0.476016i	0.903855	−	0.427839i	$-0.140725\pi$
$593$	282.278	+	282.278i	0.476016	+	0.476016i	−0.427839	+	0.903855i	$0.640725\pi$
$594$	981.679	−	502.375i	1.65266	−	0.845750i
$595$		0			0
$596$	−391.946	+	1206.29i	−0.657627	+	2.02397i
$597$	92.7879	−	585.840i	0.155424	−	0.981306i
$598$	−218.772	−	1381.27i	−0.365839	−	2.30981i
$599$	−835.221	+	271.380i	−1.39436	+	0.453055i	−0.907363	−	0.420349i	$-0.861908\pi$
$599$	−835.221	+	271.380i	−1.39436	+	0.453055i	−0.486997	+	0.873404i	$0.661908\pi$
$600$		0			0
$601$	−352.495	−	256.103i	−0.586515	−	0.426128i	0.254552	−	0.967059i	$-0.418072\pi$
$601$	−352.495	−	256.103i	−0.586515	−	0.426128i	−0.841067	+	0.540931i	$0.818072\pi$
$602$	−98.3995	+	621.270i	−0.163454	+	1.03201i
$603$	−100.723	+	51.3210i	−0.167037	+	0.0851094i
$604$			1639.09i			2.71372i
$605$		0			0
$606$	674.929			1.11374
$607$	98.3567	+	193.036i	0.162037	+	0.318016i	0.957722	−	0.287695i	$-0.0928888\pi$
$607$	98.3567	+	193.036i	0.162037	+	0.318016i	−0.795685	+	0.605711i	$0.792889\pi$
$608$	336.352	+	53.2729i	0.553211	+	0.0876199i
$609$	54.3953	−	74.8687i	0.0893191	−	0.122937i
$610$		0			0
$611$	−201.209	−	619.259i	−0.329312	−	1.01352i
$612$	94.5970	−	14.9827i	0.154570	−	0.0244815i
$613$	1090.78	+	172.763i	1.77942	+	0.281832i	0.957638	−	0.287974i	$-0.0929816\pi$
$613$	1090.78	+	172.763i	1.77942	+	0.281832i	0.821779	+	0.569806i	$0.192982\pi$
$614$	−780.161	−	253.490i	−1.27062	−	0.412850i
$615$		0			0
$616$	−140.556	−	274.657i	−0.228175	−	0.445872i
$617$	652.925	−	652.925i	1.05823	−	1.05823i	0.0600293	−	0.998197i	$-0.480881\pi$
$617$	652.925	−	652.925i	1.05823	−	1.05823i	0.998197	−	0.0600293i	$-0.0191194\pi$
$618$	913.319	−	465.359i	1.47786	−	0.753008i
$619$	−325.696	−	448.282i	−0.526165	−	0.724203i	0.460375	−	0.887724i	$-0.347715\pi$
$619$	−325.696	−	448.282i	−0.526165	−	0.724203i	−0.986540	+	0.163521i	$0.947715\pi$
$620$		0			0
$621$	269.877	+	830.596i	0.434585	+	1.33751i
$622$	−651.895	−	332.157i	−1.04806	−	0.534015i
$623$	59.5247	+	375.824i	0.0955453	+	0.603250i
$624$	−231.121	−	318.110i	−0.370386	−	0.509792i
$625$		0			0
$626$	542.614			0.866795
$627$	562.328	−	776.858i	0.896855	−	1.23901i
$628$	−109.780	−	109.780i	−0.174809	−	0.174809i
$629$	−117.568	−	38.2002i	−0.186913	−	0.0607317i
$630$		0			0
$631$	346.983	+	252.098i	0.549894	+	0.399522i	0.827747	−	0.561102i	$-0.189623\pi$
$631$	346.983	+	252.098i	0.549894	+	0.399522i	−0.277852	+	0.960624i	$0.589623\pi$
$632$	−1567.15	−	798.502i	−2.47967	−	1.26345i
$633$	−337.375	+	662.136i	−0.532978	+	1.04603i
$634$	56.9354	−	78.3649i	0.0898035	−	0.123604i
$635$		0			0
$636$	−268.722	+	827.040i	−0.422518	+	1.30038i
$637$	428.118	−	428.118i	0.672084	−	0.672084i
$638$	−197.201	−	603.297i	−0.309093	−	0.945606i
$639$			52.7604i			0.0825672i
$640$		0			0
$641$	−51.5449	+	37.4495i	−0.0804132	+	0.0584236i	−0.627266	−	0.778805i	$-0.715826\pi$
$641$	−51.5449	+	37.4495i	−0.0804132	+	0.0584236i	0.546852	+	0.837229i	$0.315826\pi$
$642$	−643.390	+	101.903i	−1.00217	+	0.158727i
$643$	−30.5733	+	60.0035i	−0.0475479	+	0.0933180i	−0.913558	−	0.406709i	$-0.866676\pi$
$643$	−30.5733	+	60.0035i	−0.0475479	+	0.0933180i	0.866010	+	0.500027i	$0.166676\pi$
$644$	487.958	−	158.547i	0.757698	−	0.246191i
$645$		0			0
$646$	396.750	−	288.256i	0.614164	−	0.446216i
$647$	210.857	+	413.830i	0.325900	+	0.639614i	0.994584	−	0.103932i	$-0.0331424\pi$
$647$	210.857	+	413.830i	0.325900	+	0.639614i	−0.668685	+	0.743546i	$0.733142\pi$
$648$	375.879	+	375.879i	0.580060	+	0.580060i
$649$	258.710	+	40.5077i	0.398629	+	0.0624155i
$650$		0			0
$651$	−33.4151	+	102.841i	−0.0513288	+	0.157974i
$652$	−279.781	+	1766.47i	−0.429112	+	2.70931i
$653$	84.4407	+	533.137i	0.129312	+	0.816443i	0.964035	+	0.265774i	$0.0856274\pi$
$653$	84.4407	+	533.137i	0.129312	+	0.816443i	−0.834724	+	0.550669i	$0.814373\pi$
$654$	−75.8346	+	24.6402i	−0.115955	+	0.0376761i
$655$		0			0
$656$	283.359	+	205.872i	0.431950	+	0.313830i
$657$	29.2359	−	184.588i	0.0444991	−	0.280956i
$658$	324.325	−	165.252i	0.492895	−	0.251142i
$659$		−	1001.07i		−	1.51907i	−0.650465	−	0.759536i	$-0.725426\pi$
$659$		−	1001.07i		−	1.51907i	0.650465	−	0.759536i	$-0.274574\pi$
$660$		0			0
$661$	1225.83			1.85451			0.927254	−	0.374432i	$-0.122162\pi$
$661$	1225.83			1.85451			0.927254	+	0.374432i	$0.122162\pi$
$662$	234.333	+	459.905i	0.353978	+	0.694721i
$663$	131.599	+	20.8433i	0.198490	+	0.0314378i
$664$	442.810	−	609.475i	0.666882	−	0.917885i
$665$		0			0
$666$	102.612	+	315.807i	0.154072	+	0.474185i
$667$	496.476	−	78.6340i	0.744341	−	0.117892i
$668$	1415.53	+	224.198i	2.11905	+	0.335625i
$669$	535.276	+	173.922i	0.800113	+	0.259973i
$670$		0			0
$671$	365.981	−	367.276i	0.545427	−	0.547356i
$672$	−36.5734	+	36.5734i	−0.0544248	+	0.0544248i
$673$	−249.622	+	127.189i	−0.370910	+	0.188988i	−0.629502	−	0.776999i	$-0.716741\pi$
$673$	−249.622	+	127.189i	−0.370910	+	0.188988i	0.258593	+	0.965986i	$0.416741\pi$
$674$	−747.973	−	1029.50i	−1.10975	−	1.52744i
$675$		0			0
$676$	50.2611	+	154.688i	0.0743508	+	0.228828i
$677$	−428.152	−	218.154i	−0.632426	−	0.322237i	0.108226	−	0.994126i	$-0.465483\pi$
$677$	−428.152	−	218.154i	−0.632426	−	0.322237i	−0.740652	+	0.671889i	$0.765483\pi$
$678$	145.627	+	919.454i	0.214789	+	1.35613i
$679$	72.1881	+	99.3584i	0.106315	+	0.146331i
$680$		0			0
$681$	501.807			0.736868
$682$	436.982	+	599.227i	0.640736	+	0.878632i
$683$	−555.821	−	555.821i	−0.813794	−	0.813794i	0.171406	−	0.985200i	$-0.445169\pi$
$683$	−555.821	−	555.821i	−0.813794	−	0.813794i	−0.985200	+	0.171406i	$0.945169\pi$
$684$	−822.209	−	267.152i	−1.20206	−	0.390573i
$685$		0			0
$686$	579.527	+	421.051i	0.844792	+	0.613777i
$687$	−18.8699	−	9.61469i	−0.0274671	−	0.0139952i
$688$	−436.118	+	855.930i	−0.633893	+	1.24408i
$689$	381.475	−	525.056i	0.553665	−	0.762055i
$690$		0			0
$691$	131.998	−	406.247i	0.191024	−	0.587911i	−0.808976	−	0.587842i	$-0.799978\pi$
$691$	131.998	−	406.247i	0.191024	−	0.587911i	1.00000		6.96426e-5i	$-2.21679e-5\pi$
$692$	775.333	−	775.333i	1.12042	−	1.12042i
$693$	−24.2785	−	74.2750i	−0.0350339	−	0.107179i
$694$			2313.40i			3.33344i
$695$		0			0
$696$	410.920	−	298.551i	0.590402	−	0.428952i
$697$	−117.223	+	18.5663i	−0.168182	+	0.0266374i
$698$	−65.2816	+	128.122i	−0.0935266	+	0.183556i
$699$	229.465	−	74.5578i	0.328277	−	0.106664i
$700$		0			0
$701$	162.449	−	118.026i	0.231738	−	0.168368i	−0.465856	−	0.884860i	$-0.654254\pi$
$701$	162.449	−	118.026i	0.231738	−	0.168368i	0.697595	+	0.716493i	$0.254254\pi$
$702$	−627.842	−	1232.21i	−0.894361	−	1.75528i
$703$	789.018	+	789.018i	1.12236	+	1.12236i
$704$	138.080	+	861.954i	0.196137	+	1.22437i
$705$		0			0
$706$	435.413	−	1340.06i	0.616732	−	1.89811i
$707$	28.9091	−	182.525i	0.0408899	−	0.258168i
$708$	68.8338	+	434.599i	0.0972229	+	0.613841i
$709$	−618.635	+	201.007i	−0.872546	+	0.283507i	−0.710859	−	0.703335i	$-0.751694\pi$
$709$	−618.635	+	201.007i	−0.872546	+	0.283507i	−0.161687	+	0.986842i	$0.551694\pi$
$710$		0			0
$711$	−360.389	−	261.838i	−0.506877	−	0.368268i
$712$	−326.704	+	2062.73i	−0.458854	+	2.89709i
$713$	−523.331	+	266.650i	−0.733984	+	0.373984i
$714$			74.4845i			0.104320i
$715$		0			0
$716$	−1268.47			−1.77161
$717$	−60.5852	−	118.905i	−0.0844981	−	0.165837i
$718$	−498.526	−	78.9587i	−0.694325	−	0.109970i
$719$	−81.5254	+	112.210i	−0.113387	+	0.156064i	−0.861939	−	0.507013i	$-0.830750\pi$
$719$	−81.5254	+	112.210i	−0.113387	+	0.156064i	0.748551	+	0.663077i	$0.230750\pi$
$720$		0			0
$721$	−86.7298	−	266.927i	−0.120291	−	0.370218i
$722$	−3155.85	+	499.837i	−4.37098	+	0.692295i
$723$	−538.230	−	85.2472i	−0.744440	−	0.117908i
$724$	−2240.42	−	727.956i	−3.09450	−	1.00546i
$725$		0			0
$726$	951.192	+	305.352i	1.31018	+	0.420595i
$727$	−416.697	+	416.697i	−0.573173	+	0.573173i	−0.933014	−	0.359840i	$-0.882831\pi$
$727$	−416.697	+	416.697i	−0.573173	+	0.573173i	0.359840	+	0.933014i	$0.382831\pi$
$728$	−344.751	+	175.659i	−0.473559	+	0.241290i
$729$	455.391	+	626.792i	0.624679	+	0.859797i
$730$		0			0
$731$	−100.590	−	309.583i	−0.137605	−	0.423506i
$732$	776.281	+	395.535i	1.06049	+	0.540348i
$733$	−99.4688	−	628.021i	−0.135701	−	0.856782i	−0.957800	−	0.287437i	$-0.907197\pi$
$733$	−99.4688	−	628.021i	−0.135701	−	0.856782i	0.822099	−	0.569345i	$-0.192803\pi$
$734$	−709.030	−	975.896i	−0.965981	−	1.32956i
$735$		0			0
$736$	−280.942			−0.381714
$737$	−376.554	−	121.615i	−0.510929	−	0.165014i
$738$	225.429	+	225.429i	0.305459	+	0.305459i
$739$	627.722	+	203.959i	0.849421	+	0.275994i	0.701203	−	0.712961i	$-0.252646\pi$
$739$	627.722	+	203.959i	0.849421	+	0.275994i	0.148217	+	0.988955i	$0.452646\pi$
$740$		0			0
$741$	−972.992	−	706.920i	−1.31308	−	0.954008i
$742$	323.267	+	164.713i	0.435670	+	0.221985i
$743$	−128.574	+	252.340i	−0.173047	+	0.339623i	−0.961198	−	0.275858i	$-0.911038\pi$
$743$	−128.574	+	252.340i	−0.173047	+	0.339623i	0.788152	+	0.615481i	$0.211038\pi$
$744$	−348.847	+	480.147i	−0.468881	+	0.645359i
$745$		0			0
$746$	−100.345	+	308.830i	−0.134511	+	0.413981i
$747$	134.918	−	134.918i	0.180613	−	0.180613i
$748$	271.579	+	196.582i	0.363073	+	0.262810i
$749$			178.361i			0.238132i
$750$		0			0
$751$	233.376	−	169.558i	0.310754	−	0.225776i	−0.421466	−	0.906844i	$-0.638484\pi$
$751$	233.376	−	169.558i	0.310754	−	0.225776i	0.732220	+	0.681068i	$0.238484\pi$
$752$	549.055	−	86.9618i	0.730127	−	0.115641i
$753$	−447.533	+	878.334i	−0.594334	+	1.16645i
$754$	−757.015	+	245.969i	−1.00400	+	0.326219i
$755$		0			0
$756$	410.467	−	298.222i	0.542946	−	0.394473i
$757$	73.3139	+	143.887i	0.0968480	+	0.190075i	0.934348	−	0.356363i	$-0.115983\pi$
$757$	73.3139	+	143.887i	0.0968480	+	0.190075i	−0.837500	+	0.546438i	$0.815983\pi$
$758$	−1316.32	−	1316.32i	−1.73658	−	1.73658i
$759$	−357.939	+	705.571i	−0.471593	+	0.929606i
$760$		0			0
$761$	−178.166	+	548.339i	−0.234121	+	0.720551i	0.763116	+	0.646262i	$0.223669\pi$
$761$	−178.166	+	548.339i	−0.234121	+	0.720551i	−0.997237	+	0.0742887i	$0.976331\pi$
$762$	215.066	−	1357.87i	0.282239	−	1.78199i
$763$	3.41537	+	21.5638i	0.00447624	+	0.0282619i
$764$	1432.19	−	465.347i	1.87460	−	0.609093i
$765$		0			0
$766$	934.488	+	678.945i	1.21996	+	0.886352i
$767$	51.3723	−	324.352i	0.0669782	−	0.422884i
$768$	−1028.79	+	524.193i	−1.33957	+	0.682543i
$769$			23.8117i			0.0309646i	0.999880	+	0.0154823i	$0.00492836\pi$
$769$			23.8117i			0.0309646i	−0.999880	+	0.0154823i	$0.995072\pi$
$770$		0			0
$771$	14.4478			0.0187391
$772$	−468.772	−	920.016i	−0.607217	−	1.19173i
$773$	−1299.24	−	205.779i	−1.68078	−	0.266209i	−0.758200	−	0.652022i	$-0.773921\pi$
$773$	−1299.24	−	205.779i	−1.68078	−	0.266209i	−0.922577	+	0.385813i	$0.873921\pi$
$774$	−513.950	+	707.392i	−0.664018	+	0.913943i
$775$		0			0
$776$	208.299	+	641.077i	0.268426	+	0.826130i
$777$	−167.390	+	26.5119i	−0.215431	+	0.0341209i
$778$	−1910.66	−	302.619i	−2.45586	−	0.388970i
$779$	1018.87	+	331.050i	1.30792	+	0.424968i
$780$		0			0
$781$	−130.362	+	130.823i	−0.166916	+	0.167507i
$782$	−286.079	+	286.079i	−0.365830	+	0.365830i
$783$	442.898	−	225.668i	0.565643	−	0.288209i
$784$	303.827	+	418.182i	0.387535	+	0.533396i
$785$		0			0
$786$	−42.7385	−	131.536i	−0.0543747	−	0.167348i
$787$	−58.7876	−	29.9538i	−0.0746984	−	0.0380607i	0.416242	−	0.909254i	$-0.363347\pi$
$787$	−58.7876	−	29.9538i	−0.0746984	−	0.0380607i	−0.490941	+	0.871193i	$0.663347\pi$
$788$	101.007	+	637.731i	0.128181	+	0.809304i
$789$	−232.177	−	319.565i	−0.294268	−	0.405025i
$790$		0			0
$791$	254.891			0.322239
$792$	−0.757146	−	428.887i	−0.000955992	−	0.541524i
$793$	−459.780	−	459.780i	−0.579798	−	0.579798i
$794$	−1667.15	−	541.689i	−2.09968	−	0.682229i
$795$		0			0
$796$	−1514.22	−	1100.15i	−1.90229	−	1.38209i
$797$	979.455	+	499.057i	1.22893	+	0.626169i	0.943227	−	0.332150i	$-0.107774\pi$
$797$	979.455	+	499.057i	1.22893	+	0.626169i	0.285700	+	0.958319i	$0.407774\pi$
$798$	305.233	−	599.053i	0.382497	−	0.750693i
$799$	−110.720	+	152.394i	−0.138574	+	0.190730i
$800$		0			0
$801$	−163.452	+	503.053i	−0.204060	+	0.628031i
$802$	498.205	−	498.205i	0.621204	−	0.621204i
$803$	528.577	−	385.461i	0.658253	−	0.480027i
$804$		−	664.919i		−	0.827014i
$805$		0			0
$806$	752.442	−	546.681i	0.933550	−	0.678264i
$807$	1004.84	−	159.151i	1.24515	−	0.197213i
$808$	460.475	−	903.734i	0.569895	−	1.11848i
$809$	−253.667	+	82.4213i	−0.313556	+	0.101881i	−0.461567	−	0.887105i	$-0.652713\pi$
$809$	−253.667	+	82.4213i	−0.313556	+	0.101881i	0.148011	+	0.988986i	$0.452713\pi$
$810$		0			0
$811$	338.287	−	245.780i	0.417123	−	0.303057i	−0.359356	−	0.933200i	$-0.617004\pi$
$811$	338.287	−	245.780i	0.417123	−	0.303057i	0.776479	+	0.630143i	$0.217004\pi$
$812$	−132.575	−	260.193i	−0.163270	−	0.320435i
$813$	497.618	+	497.618i	0.612076	+	0.612076i
$814$	−525.871	+	1036.60i	−0.646033	+	1.27346i
$815$		0			0
$816$	−35.1516	+	108.186i	−0.0430780	+	0.132580i
$817$	−459.644	+	2902.08i	−0.562599	+	3.55211i
$818$	180.021	+	1136.61i	0.220074	+	1.38950i
$819$	−93.2000	+	30.2825i	−0.113797	+	0.0369750i
$820$		0			0
$821$	208.285	+	151.328i	0.253697	+	0.184321i	0.707363	−	0.706850i	$-0.249884\pi$
$821$	208.285	+	151.328i	0.253697	+	0.184321i	−0.453667	+	0.891171i	$0.649884\pi$
$822$	−115.957	+	732.123i	−0.141067	+	0.890661i
$823$	−1112.28	+	566.734i	−1.35149	+	0.688619i	−0.971648	−	0.236432i	$-0.924022\pi$
$823$	−1112.28	+	566.734i	−1.35149	+	0.688619i	−0.379843	+	0.925051i	$0.624022\pi$
$824$		−	1540.43i		−	1.86946i
$825$		0			0
$826$	183.582			0.222254
$827$	−638.541	−	1253.21i	−0.772117	−	1.51536i	−0.854898	−	0.518797i	$-0.826380\pi$
$827$	−638.541	−	1253.21i	−0.772117	−	1.51536i	0.0827808	−	0.996568i	$-0.473620\pi$
$828$	704.430	+	111.571i	0.850760	+	0.134747i
$829$	−12.8668	+	17.7097i	−0.0155209	+	0.0213627i	−0.816707	−	0.577053i	$-0.804203\pi$
$829$	−12.8668	+	17.7097i	−0.0155209	+	0.0213627i	0.801186	+	0.598415i	$0.204203\pi$
$830$		0			0
$831$	256.568	+	789.636i	0.308747	+	0.950224i
$832$	1081.26	−	171.254i	1.29959	−	0.205835i
$833$	−172.998	−	27.4002i	−0.207681	−	0.0328934i
$834$	−366.522	−	119.090i	−0.439475	−	0.142794i
$835$		0			0
$836$	−1378.63	−	2693.95i	−1.64908	−	3.22243i
$837$	−410.701	+	410.701i	−0.490682	+	0.490682i
$838$	1590.97	−	810.642i	1.89854	−	0.967353i
$839$	230.999	+	317.943i	0.275327	+	0.378955i	0.924179	−	0.381959i	$-0.124751\pi$
$839$	230.999	+	317.943i	0.275327	+	0.378955i	−0.648852	+	0.760915i	$0.724751\pi$
$840$		0			0
$841$	171.474	+	527.741i	0.203892	+	0.627517i
$842$	−992.643	−	505.777i	−1.17891	−	0.600685i
$843$	36.2109	+	228.627i	0.0429548	+	0.271206i
$844$	1378.34	+	1897.13i	1.63311	+	2.24778i
$845$		0			0
$846$	505.989			0.598096
$847$	123.321	−	244.157i	0.145597	−	0.288261i
$848$	391.798	+	391.798i	0.462026	+	0.462026i
$849$	−113.000	−	36.7158i	−0.133097	−	0.0432459i
$850$		0			0
$851$	−744.735	−	541.082i	−0.875129	−	0.635819i
$852$	−276.509	−	140.889i	−0.324542	−	0.165362i
$853$	−6.26065	+	12.2872i	−0.00733957	+	0.0144047i	−0.894647	−	0.446773i	$-0.852573\pi$
$853$	−6.26065	+	12.2872i	−0.00733957	+	0.0144047i	0.887308	+	0.461178i	$0.152573\pi$
$854$	213.657	−	294.073i	0.250184	−	0.344348i
$855$		0			0
$856$	−302.509	+	931.027i	−0.353398	+	1.08765i
$857$	−100.441	+	100.441i	−0.117201	+	0.117201i	−0.763275	−	0.646074i	$-0.776410\pi$
$857$	−100.441	+	100.441i	−0.117201	+	0.117201i	0.646074	+	0.763275i	$0.276410\pi$
$858$	385.040	−	1192.19i	0.448764	−	1.38950i
$859$		−	57.6453i		−	0.0671075i	−0.999437	−	0.0335537i	$-0.989318\pi$
$859$		−	57.6453i		−	0.0671075i	0.999437	−	0.0335537i	$-0.0106825\pi$
$860$		0			0
$861$	−131.636	+	95.6393i	−0.152888	+	0.111079i
$862$	1548.24	−	245.217i	1.79610	−	0.284474i
$863$	25.4744	−	49.9964i	0.0295185	−	0.0579332i	−0.875776	−	0.482717i	$-0.839650\pi$
$863$	25.4744	−	49.9964i	0.0295185	−	0.0579332i	0.905295	+	0.424784i	$0.139650\pi$
$864$	−264.221	+	85.8506i	−0.305811	+	0.0993642i
$865$		0			0
$866$	806.691	−	586.095i	0.931513	−	0.676784i
$867$	300.044	+	588.869i	0.346071	+	0.679203i
$868$	241.278	+	241.278i	0.277970	+	0.277970i
$869$	−246.652	−	1539.70i	−0.283834	−	1.77181i
$870$		0			0
$871$	−153.348	+	471.957i	−0.176060	+	0.541857i
$872$	−18.7454	+	118.354i	−0.0214970	+	0.135727i
$873$	26.7068	+	168.620i	0.0305920	+	0.193150i
$874$	3473.17	−	1128.50i	3.97388	−	1.29119i
$875$		0			0
$876$	889.329	+	646.135i	1.01522	+	0.737597i
$877$	124.784	−	787.853i	0.142285	−	0.898350i	−0.808500	−	0.588497i	$-0.799720\pi$
$877$	124.784	−	787.853i	0.142285	−	0.898350i	0.950784	−	0.309854i	$-0.100280\pi$
$878$	870.670	−	443.629i	0.991651	−	0.505272i
$879$		−	1114.05i		−	1.26740i
$880$		0			0
$881$	−1510.53			−1.71456			−0.857279	−	0.514852i	$-0.827847\pi$
$881$	−1510.53			−1.71456			−0.857279	+	0.514852i	$0.827847\pi$
$882$	213.599	+	419.212i	0.242176	+	0.475297i
$883$	984.685	+	155.959i	1.11516	+	0.176624i	0.686702	−	0.726939i	$-0.259058\pi$
$883$	984.685	+	155.959i	1.11516	+	0.176624i	0.428456	+	0.903563i	$0.359058\pi$
$884$	247.129	−	340.144i	0.279558	−	0.384779i
$885$		0			0
$886$	−324.669	−	999.230i	−0.366444	−	1.12780i
$887$	−1206.89	+	191.152i	−1.36064	+	0.215504i	−0.793727	−	0.608274i	$-0.791862\pi$
$887$	−1206.89	+	191.152i	−1.36064	+	0.215504i	−0.566913	+	0.823778i	$0.691862\pi$
$888$	−918.725	−	145.512i	−1.03460	−	0.163865i
$889$	−358.006	−	116.323i	−0.402706	−	0.130847i
$890$		0			0
$891$	−72.9015	+	465.600i	−0.0818199	+	0.522559i
$892$	1255.82	−	1255.82i	1.40787	−	1.40787i
$893$	1514.98	−	771.923i	1.69651	−	0.864416i
$894$	−805.959	−	1109.31i	−0.901520	−	1.24084i
$895$		0			0
$896$	162.699	+	500.735i	0.181583	+	0.558856i
$897$	884.045	+	450.443i	0.985557	+	0.502167i
$898$	150.187	+	948.241i	0.167246	+	1.05595i
$899$	196.496	+	270.453i	0.218572	+	0.300838i
$900$		0			0
$901$	−187.755			−0.208385
$902$	1.97009	+	1115.96i	0.00218413	+	1.23721i
$903$	−315.559	−	315.559i	−0.349456	−	0.349456i
$904$	1330.51	+	432.308i	1.47180	+	0.478217i
$905$		0			0
$906$	−1433.54	−	1041.53i	−1.58227	−	1.14959i
$907$	218.751	+	111.459i	0.241181	+	0.122888i	0.570404	−	0.821365i	$-0.306787\pi$
$907$	218.751	+	111.459i	0.241181	+	0.122888i	−0.329223	+	0.944252i	$0.606787\pi$
$908$	718.879	−	1410.88i	0.791717	−	1.55383i
$909$	150.995	−	207.827i	0.166111	−	0.228633i
$910$		0			0
$911$	11.4615	−	35.2749i	0.0125813	−	0.0387211i	−0.944569	−	0.328314i	$-0.893520\pi$
$911$	11.4615	−	35.2749i	0.0125813	−	0.0387211i	0.957150	+	0.289592i	$0.0935198\pi$
$912$	726.050	−	726.050i	0.796107	−	0.796107i
$913$	667.894	−	1.17908i	0.731538	−	0.00129144i
$914$		−	85.3740i		−	0.0934070i
$915$		0			0
$916$	−54.0653	+	39.2807i	−0.0590232	+	0.0428829i
$917$	−37.4026	+	5.92399i	−0.0407880	+	0.00646018i
$918$	−181.632	+	356.474i	−0.197857	+	0.388315i
$919$	1089.63	−	354.042i	1.18567	−	0.385247i	0.351198	−	0.936301i	$-0.385774\pi$
$919$	1089.63	−	354.042i	1.18567	−	0.385247i	0.834469	+	0.551054i	$0.185774\pi$
$920$		0			0
$921$	470.837	−	342.083i	0.511224	−	0.371426i
$922$	−1217.67	−	2389.80i	−1.32068	−	2.59198i
$923$	163.773	+	163.773i	0.177435	+	0.177435i
$924$	454.096	+	71.1002i	0.491446	+	0.0769483i
$925$		0			0
$926$	−322.483	+	992.501i	−0.348254	+	1.07182i
$927$	61.0324	−	385.344i	0.0658386	−	0.415689i
$928$	25.0143	+	157.934i	0.0269550	+	0.170187i
$929$	1213.61	−	394.326i	1.30636	−	0.424462i	0.428571	−	0.903508i	$-0.359017\pi$
$929$	1213.61	−	394.326i	1.30636	−	0.424462i	0.877790	+	0.479046i	$0.159017\pi$
$930$		0			0
$931$	1279.08	+	929.304i	1.37388	+	0.998179i
$932$	119.101	−	751.975i	0.127791	−	0.806840i
$933$	462.501	−	235.656i	0.495714	−	0.252579i
$934$			601.902i			0.644435i
$935$		0			0
$936$	−537.857			−0.574633
$937$	369.838	+	725.847i	0.394704	+	0.774650i	0.999768	−	0.0215265i	$-0.00685264\pi$
$937$	369.838	+	725.847i	0.394704	+	0.774650i	−0.605064	+	0.796177i	$0.706853\pi$
$938$	−273.999	−	43.3972i	−0.292110	−	0.0462657i
$939$	−226.279	+	311.447i	−0.240979	+	0.331679i
$940$		0			0
$941$	232.814	+	716.527i	0.247411	+	0.761452i	0.995231	+	0.0975506i	$0.0311008\pi$
$941$	232.814	+	716.527i	0.247411	+	0.761452i	−0.747820	+	0.663902i	$0.768899\pi$
$942$	165.772	−	26.2556i	0.175978	−	0.0278722i
$943$	−872.917	−	138.256i	−0.925680	−	0.146613i
$944$	266.645	+	86.6381i	0.282463	+	0.0917777i
$945$		0			0
$946$	−3022.21	+	484.142i	−3.19473	+	0.511778i
$947$	−378.420	+	378.420i	−0.399598	+	0.399598i	−0.878091	−	0.478493i	$-0.841183\pi$
$947$	−378.420	+	378.420i	−0.399598	+	0.399598i	0.478493	+	0.878091i	$0.341183\pi$
$948$	2334.62	−	1189.55i	2.46268	−	1.25480i
$949$	−482.226	−	663.727i	−0.508141	−	0.699397i
$950$		0			0
$951$	21.2364	+	65.3590i	0.0223306	+	0.0687266i
$952$	99.7352	+	50.8176i	0.104764	+	0.0533799i
$953$	−63.3081	−	399.711i	−0.0664303	−	0.419424i	−0.998383	−	0.0568446i	$-0.981896\pi$
$953$	−63.3081	−	399.711i	−0.0664303	−	0.419424i	0.931953	−	0.362580i	$-0.118104\pi$
$954$	296.443	+	408.019i	0.310737	+	0.427693i
$955$		0			0
$956$	−421.107			−0.440488
$957$	428.513	+	138.397i	0.447767	+	0.144615i
$958$	−1435.39	−	1435.39i	−1.49832	−	1.49832i
$959$	193.026	+	62.7179i	0.201278	+	0.0653992i
$960$		0			0
$961$	461.449	+	335.262i	0.480176	+	0.348868i
$962$	1298.81	+	661.775i	1.35011	+	0.687916i
$963$	−112.561	+	220.913i	−0.116886	+	0.229401i
$964$	−1010.74	+	1391.16i	−1.04848	+	1.44311i
$965$		0			0
$966$	−171.399	+	527.512i	−0.177432	+	0.546079i
$967$	502.098	−	502.098i	0.519233	−	0.519233i	−0.398107	−	0.917339i	$-0.630333\pi$
$967$	502.098	−	502.098i	0.519233	−	0.519233i	0.917339	+	0.398107i	$0.130333\pi$
$968$	1057.83	−	1065.32i	1.09280	−	1.10054i
$969$			347.932i			0.359063i
$970$		0			0
$971$	−1026.37	+	745.702i	−1.05702	+	0.767973i	−0.973536	−	0.228536i	$-0.926606\pi$
$971$	−1026.37	+	745.702i	−1.05702	+	0.767973i	−0.0834887	+	0.996509i	$0.526606\pi$
$972$	1212.92	−	192.107i	1.24786	−	0.197641i
$973$	−47.9055	+	94.0198i	−0.0492348	+	0.0966288i
$974$	−1513.57	+	491.787i	−1.55397	+	0.504915i
$975$		0			0
$976$	449.110	−	326.298i	0.460154	−	0.334321i
$977$	−121.475	−	238.408i	−0.124335	−	0.244020i	0.820446	−	0.571724i	$-0.193725\pi$
$977$	−121.475	−	238.408i	−0.124335	−	0.244020i	−0.944781	+	0.327704i	$0.893725\pi$
$978$	−1367.17	−	1367.17i	−1.39792	−	1.39792i
$979$	−1648.24	+	843.490i	−1.68360	+	0.861584i
$980$		0			0
$981$	−9.37843	+	28.8638i	−0.00956007	+	0.0294229i
$982$	61.7581	−	389.926i	0.0628902	−	0.397073i
$983$	86.1250	+	543.772i	0.0876144	+	0.553176i	0.991978	+	0.126412i	$0.0403462\pi$
$983$	86.1250	+	543.772i	0.0876144	+	0.553176i	−0.904363	+	0.426763i	$0.859654\pi$
$984$	−849.338	+	275.967i	−0.863149	+	0.280454i
$985$		0			0
$986$	186.294	+	135.350i	0.188939	+	0.137272i
$987$	−40.3986	+	255.067i	−0.0409307	+	0.258426i
$988$	−3381.46	+	1722.94i	−3.42253	+	1.74387i
$989$		−	2423.99i		−	2.45095i
$990$		0			0
$991$	−1331.21			−1.34330			−0.671650	−	0.740869i	$-0.734414\pi$
$991$	−1331.21			−1.34330			−0.671650	+	0.740869i	$0.734414\pi$
$992$	−84.8242	−	166.477i	−0.0855082	−	0.167819i
$993$	−361.695	−	57.2868i	−0.364245	−	0.0576907i
$994$	−76.1041	+	104.748i	−0.0765635	+	0.105381i
$995$		0			0
$996$	346.806	+	1067.36i	0.348199	+	1.07165i
$997$	306.698	−	48.5762i	0.307621	−	0.0487224i	−0.000715499	−	1.00000i	$-0.500228\pi$
$997$	306.698	−	48.5762i	0.307621	−	0.0487224i	0.308336	+	0.951277i	$0.400228\pi$
$998$	812.909	+	128.752i	0.814538	+	0.129010i
$999$	−865.756	−	281.301i	−0.866622	−	0.281583i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.bk.c.218.15	yes	128
5.2	odd	4	inner	275.3.bk.c.207.2	yes	128
5.3	odd	4	inner	275.3.bk.c.207.15	yes	128
5.4	even	2	inner	275.3.bk.c.218.2	yes	128
11.5	even	5	inner	275.3.bk.c.93.2	yes	128
55.27	odd	20	inner	275.3.bk.c.82.15	yes	128
55.38	odd	20	inner	275.3.bk.c.82.2	✓	128
55.49	even	10	inner	275.3.bk.c.93.15	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.bk.c.82.2	✓	128	55.38	odd	20	inner
275.3.bk.c.82.15	yes	128	55.27	odd	20	inner
275.3.bk.c.93.2	yes	128	11.5	even	5	inner
275.3.bk.c.93.15	yes	128	55.49	even	10	inner
275.3.bk.c.207.2	yes	128	5.2	odd	4	inner
275.3.bk.c.207.15	yes	128	5.3	odd	4	inner
275.3.bk.c.218.2	yes	128	5.4	even	2	inner
275.3.bk.c.218.15	yes	128	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(1.54871 + 3.03951i) q^{2} +(-2.39044 - 0.378609i) q^{3} +(-4.48900 + 6.17857i) q^{4} +(-2.55131 - 7.85213i) q^{6} +(-2.23278 + 0.353637i) q^{7} +(-12.2547 - 1.94095i) q^{8} +(-2.98864 - 0.971069i) q^{9} +(-5.01119 - 9.79224i) q^{11} +(13.0699 - 13.0699i) q^{12} +(-12.2913 + 6.26272i) q^{13} +(-4.53281 - 6.23888i) q^{14} +(-3.63939 - 11.2009i) q^{16} +(3.55582 + 1.81178i) q^{17} +(-1.67696 - 10.5879i) q^{18} +(-21.1737 - 29.1430i) q^{19} +5.47122 q^{21} +(22.0028 - 30.3969i) q^{22} +(21.0138 + 21.0138i) q^{23} +(28.5593 + 9.27947i) q^{24} +(-38.0712 - 27.6604i) q^{26} +(26.1846 + 13.3417i) q^{27} +(7.83796 - 15.3829i) q^{28} +(9.94209 - 13.6841i) q^{29} +(-6.10743 + 18.7967i) q^{31} +(-6.68470 + 6.68470i) q^{32} +(8.27153 + 25.3051i) q^{33} +13.6139i q^{34} +(19.4158 - 14.1064i) q^{36} +(-30.5946 + 4.84571i) q^{37} +(55.7888 - 109.492i) q^{38} +(31.7527 - 10.3171i) q^{39} +(-24.0598 + 17.4804i) q^{41} +(8.47332 + 16.6298i) q^{42} +(-57.6762 - 57.6762i) q^{43} +(82.9973 + 12.9953i) q^{44} +(-31.3274 + 96.4159i) q^{46} +(-7.38384 + 46.6198i) q^{47} +(4.45899 + 28.1530i) q^{48} +(-41.7415 + 13.5626i) q^{49} +(-7.81403 - 5.67722i) q^{51} +(16.4808 - 104.056i) q^{52} +(-41.9192 + 21.3589i) q^{53} +100.251i q^{54} +28.0484 q^{56} +(39.5806 + 77.6813i) q^{57} +(56.9904 + 9.02639i) q^{58} +(-13.9926 + 19.2592i) q^{59} +(14.5657 + 44.8286i) q^{61} +(-66.5915 + 10.5471i) q^{62} +(7.01639 + 1.11129i) q^{63} +(-75.4744 - 24.5231i) q^{64} +(-64.1048 + 64.3316i) q^{66} +(25.4370 - 25.4370i) q^{67} +(-27.1563 + 13.8368i) q^{68} +(-42.2762 - 58.1882i) q^{69} +(-5.18827 - 15.9679i) q^{71} +(34.7401 + 17.7010i) q^{72} +(9.30355 + 58.7403i) q^{73} +(-62.1107 - 85.4881i) q^{74} +275.111 q^{76} +(14.6518 + 20.0918i) q^{77} +(80.5345 + 80.5345i) q^{78} +(134.820 + 43.8055i) q^{79} +(-34.6607 - 25.1825i) q^{81} +(-90.3936 - 46.0578i) q^{82} +(-27.5653 + 54.0999i) q^{83} +(-24.5603 + 33.8043i) q^{84} +(85.9839 - 264.631i) q^{86} +(-28.9469 + 28.9469i) q^{87} +(42.4043 + 129.727i) q^{88} -168.321i q^{89} +(25.2290 - 18.3299i) q^{91} +(-224.166 + 35.5044i) q^{92} +(21.7161 - 42.6202i) q^{93} +(-153.137 + 49.7572i) q^{94} +(18.5103 - 13.4485i) q^{96} +(-24.6643 - 48.4063i) q^{97} +(-105.869 - 105.869i) q^{98} +(5.46772 + 34.1317i) 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

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Database

Properties

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