LMFDB - Embedded newform 275.3.bk.c.82.15

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			82.15
Character	$\chi$	$=$	275.82
Dual form			275.3.bk.c.218.15

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

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

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 $

$2$	1.54871	−	3.03951i	0.774355	−	1.51976i	−0.0780945	−	0.996946i	$-0.524884\pi$
$2$	1.54871	−	3.03951i	0.774355	−	1.51976i	0.852449	−	0.522810i	$-0.175116\pi$
$3$	−2.39044	+	0.378609i	−0.796814	+	0.126203i	−0.541550	−	0.840669i	$-0.682162\pi$
$3$	−2.39044	+	0.378609i	−0.796814	+	0.126203i	−0.255264	+	0.966871i	$0.582162\pi$
$4$	−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	−0.00510261	−	0.999987i	$-0.501624\pi$
$7$	−2.23278	−	0.353637i	−0.318968	−	0.0505196i	−0.313866	+	0.949467i	$0.601624\pi$
$8$	−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	−0.0879203	−	0.996128i	$-0.528022\pi$
$13$	−12.2913	−	6.26272i	−0.945483	−	0.481747i	−0.857562	+	0.514380i	$0.828022\pi$
$14$	−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	−0.346269	−	0.938135i	$-0.612552\pi$
$17$	3.55582	−	1.81178i	0.209166	−	0.106575i	0.555435	+	0.831560i	$0.312552\pi$
$18$	−1.67696	+	10.5879i	−0.0931646	+	0.588218i
$19$	−21.1737	+	29.1430i	−1.11440	+	1.53384i	−0.299638	+	0.954053i	$0.596866\pi$
$19$	−21.1737	+	29.1430i	−1.11440	+	1.53384i	−0.814765	+	0.579792i	$0.803134\pi$
$20$		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	−0.0829138	−	0.996557i	$-0.526423\pi$
$23$	21.0138	−	21.0138i	0.913643	−	0.913643i	0.996557	+	0.0829138i	$0.0264226\pi$
$24$	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	0.945265	−	0.326302i	$-0.105803\pi$
$29$	9.94209	+	13.6841i	0.342831	+	0.471866i	−0.602435	+	0.798168i	$0.705803\pi$
$30$		0			0
$31$	−6.10743	−	18.7967i	−0.197014	−	0.606346i	−0.999947	−	0.0102774i	$-0.996729\pi$
$31$	−6.10743	−	18.7967i	−0.197014	−	0.606346i	0.802933	−	0.596069i	$-0.203271\pi$
$32$	−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	−0.271371	−	0.962475i	$-0.587477\pi$
$37$	−30.5946	−	4.84571i	−0.826881	−	0.130965i	−0.555510	+	0.831510i	$0.687477\pi$
$38$	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	0.254354	−	0.967111i	$-0.418137\pi$
$41$	−24.0598	−	17.4804i	−0.586823	−	0.426352i	−0.841178	+	0.540759i	$0.818137\pi$
$42$	8.47332	−	16.6298i	0.201746	−	0.395948i
$43$	−57.6762	+	57.6762i	−1.34131	+	1.34131i	−0.446546	+	0.894761i	$0.647346\pi$
$43$	−57.6762	+	57.6762i	−1.34131	+	1.34131i	−0.894761	+	0.446546i	$0.852654\pi$
$44$	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	−0.932693	−	0.360672i	$-0.882547\pi$
$47$	−7.38384	−	46.6198i	−0.157103	−	0.991910i	0.775590	−	0.631238i	$-0.217453\pi$
$48$	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	0.0113601	−	0.999935i	$-0.496384\pi$
$53$	−41.9192	−	21.3589i	−0.790927	−	0.402998i	−0.802288	+	0.596938i	$0.796384\pi$
$54$		−	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	0.673801	−	0.738913i	$-0.264661\pi$
$59$	−13.9926	−	19.2592i	−0.237163	−	0.326427i	−0.910964	+	0.412486i	$0.864661\pi$
$60$		0			0
$61$	14.5657	−	44.8286i	0.238782	−	0.734896i	−0.757815	−	0.652469i	$-0.773733\pi$
$61$	14.5657	−	44.8286i	0.238782	−	0.734896i	0.996597	−	0.0824262i	$-0.0262669\pi$
$62$	−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	0.870978	−	0.491322i	$-0.163486\pi$
$67$	25.4370	+	25.4370i	0.379656	+	0.379656i	−0.491322	+	0.870978i	$0.663486\pi$
$68$	−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	−0.980922	−	0.194400i	$-0.937724\pi$
$71$	−5.18827	+	15.9679i	−0.0730743	+	0.224899i	0.907848	+	0.419299i	$0.137724\pi$
$72$	34.7401	−	17.7010i	0.482502	−	0.245847i
$73$	9.30355	−	58.7403i	0.127446	−	0.804661i	−0.838307	−	0.545198i	$-0.816454\pi$
$73$	9.30355	−	58.7403i	0.127446	−	0.804661i	0.965753	−	0.259463i	$-0.0835456\pi$
$74$	−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	0.716819	−	0.697259i	$-0.245597\pi$
$79$	134.820	−	43.8055i	1.70658	−	0.554500i	0.989758	+	0.142759i	$0.0455973\pi$
$80$		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	0.663209	−	0.748435i	$-0.269194\pi$
$83$	−27.5653	−	54.0999i	−0.332112	−	0.651806i	−0.995321	+	0.0966282i	$0.969194\pi$
$84$	−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	$0.394549\pi$
$89$			168.321i			1.89125i	−0.325257	+	0.945626i	$0.605451\pi$
$90$		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	−0.982491	−	0.186308i	$-0.940348\pi$
$97$	−24.6643	+	48.4063i	−0.254271	+	0.499034i	0.728221	+	0.685343i	$0.240348\pi$
$98$	−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	−0.994753	−	0.102304i	$-0.967378\pi$
$101$	−25.2615	−	77.7469i	−0.250114	−	0.769772i	0.744639	−	0.667467i	$-0.232622\pi$
$102$	5.15434	+	32.5432i	0.0505327	+	0.319051i
$103$	19.4219	−	122.625i	0.188563	−	1.19054i	−0.693871	−	0.720100i	$-0.744096\pi$
$103$	19.4219	−	122.625i	0.188563	−	1.19054i	0.882433	−	0.470438i	$-0.155904\pi$
$104$	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	0.975784	+	0.218735i	$0.0701931\pi$
$107$	12.3426	+	77.9279i	0.115351	+	0.728299i	−0.860433	+	0.509563i	$0.829807\pi$
$108$	−199.975	−	101.892i	−1.85162	−	0.943448i
$109$			9.65784i			0.0886040i	0.999018	+	0.0443020i	$0.0141064\pi$
$109$			9.65784i			0.0886040i	−0.999018	+	0.0443020i	$0.985894\pi$
$110$		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	−0.628340	−	0.777939i	$-0.716265\pi$
$113$	−111.365	+	17.6385i	−0.985531	+	0.156093i	−0.357191	+	0.934032i	$0.616265\pi$
$114$	−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	0.241304	−	0.970450i	$-0.422425\pi$
$127$	148.368	−	75.5971i	1.16825	−	0.595252i	0.926945	+	0.375197i	$0.122425\pi$
$128$	−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	−0.720880	−	0.693059i	$-0.756262\pi$
$137$	−79.9952	+	40.7596i	−0.583907	+	0.297515i	0.136974	+	0.990575i	$0.456262\pi$
$138$	111.390	+	218.616i	0.807176	+	1.58417i
$139$	27.4367	+	37.7633i	0.197386	+	0.271679i	0.896224	−	0.443601i	$-0.146299\pi$
$139$	27.4367	+	37.7633i	0.197386	+	0.271679i	−0.698838	+	0.715280i	$0.746299\pi$
$140$		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	0.786612	−	0.617448i	$-0.211833\pi$
$149$	157.950	+	51.3210i	1.06007	+	0.344437i	0.273455	+	0.961885i	$0.411833\pi$
$150$		0			0
$151$	173.632	+	126.151i	1.14988	+	0.835435i	0.988465	−	0.151452i	$-0.0483949\pi$
$151$	173.632	+	126.151i	1.14988	+	0.835435i	0.161413	+	0.986887i	$0.448395\pi$
$152$	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	0.975489	−	0.220050i	$-0.0706221\pi$
$157$	−3.18010	−	20.0784i	−0.0202554	−	0.127888i	−0.995744	+	0.0921624i	$0.970622\pi$
$158$	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	0.955889	−	0.293729i	$-0.0948962\pi$
$163$	208.659	+	106.317i	1.28011	+	0.652251i	0.324226	+	0.945980i	$0.394896\pi$
$164$			227.125i			1.38491i
$165$		0			0
$166$	−207.128			−1.24776
$167$	−85.1951	+	167.205i	−0.510151	+	1.00123i	0.481999	+	0.876172i	$0.339911\pi$
$167$	−85.1951	+	167.205i	−0.510151	+	1.00123i	−0.992150	+	0.125055i	$0.960089\pi$
$168$	−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	−0.552173	−	0.833730i	$-0.686201\pi$
$173$	−141.805	+	22.4597i	−0.819684	+	0.129825i	−0.267511	+	0.963555i	$0.586201\pi$
$174$	−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	−0.443979	−	0.896037i	$-0.646434\pi$
$179$	97.6266	−	134.372i	0.545400	−	0.750679i	0.989379	+	0.145358i	$0.0464335\pi$
$180$		0			0
$181$	95.3179	−	293.358i	0.526618	−	1.62076i	−0.234475	−	0.972122i	$-0.575337\pi$
$181$	95.3179	−	293.358i	0.526618	−	1.62076i	0.761093	−	0.648643i	$-0.224663\pi$
$182$	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	−0.921024	−	0.389505i	$-0.872646\pi$
$191$	−159.522	+	115.900i	−0.835196	+	0.606805i	0.0858287	+	0.996310i	$0.472646\pi$
$192$	171.133	−	87.1964i	0.891315	−	0.454148i
$193$	−61.3806	−	120.466i	−0.318034	−	0.624177i	0.675545	−	0.737319i	$-0.263908\pi$
$193$	−61.3806	−	120.466i	−0.318034	−	0.624177i	−0.993579	+	0.113142i	$0.963908\pi$
$194$	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	0.842367	−	0.538904i	$-0.181161\pi$
$197$	59.7822	+	59.7822i	0.303463	+	0.303463i	−0.538904	+	0.842367i	$0.681161\pi$
$198$	−95.2759	−	69.4793i	−0.481192	−	0.350906i
$199$		−	245.076i		−	1.23154i	−0.787927	−	0.615769i	$-0.788845\pi$
$199$		−	245.076i		−	1.23154i	0.787927	−	0.615769i	$-0.211155\pi$
$200$		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	0.877263	+	0.480009i	$0.159367\pi$
$211$	94.8835	+	292.021i	0.449685	+	1.38399i	−0.427578	+	0.903978i	$0.640633\pi$
$212$	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	−0.648476	−	0.761235i	$-0.724593\pi$
$223$	−229.685	+	36.3786i	−1.02998	+	0.163133i	−0.381503	+	0.924368i	$0.624593\pi$
$224$	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	−0.311901	−	0.950115i	$-0.600966\pi$
$227$	−204.785	−	32.4348i	−0.902138	−	0.142885i	−0.590237	+	0.807230i	$0.700966\pi$
$228$	−657.636	+	104.159i	−2.88437	+	0.456839i
$229$	8.32217	−	2.70404i	0.0363413	−	0.0118080i	−0.290790	−	0.956787i	$-0.593918\pi$
$229$	8.32217	−	2.70404i	0.0363413	−	0.0118080i	0.327131	+	0.944979i	$0.393918\pi$
$230$		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	0.252870	−	0.967500i	$-0.418626\pi$
$233$	−88.8247	−	45.2584i	−0.381222	−	0.194242i	−0.634091	+	0.773258i	$0.718626\pi$
$234$	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	−0.735813	−	0.677185i	$-0.763200\pi$
$239$	32.4101	−	44.6086i	0.135607	−	0.186647i	0.871420	+	0.490538i	$0.163200\pi$
$240$		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	0.806655	+	0.591023i	$0.201276\pi$
$251$	125.864	+	387.371i	0.501452	+	1.54331i	−0.305203	+	0.952287i	$0.598724\pi$
$252$	−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	0.144953	−	0.989439i	$-0.453697\pi$
$257$	−5.89609	−	0.933850i	−0.0229420	−	0.00363366i	−0.167895	+	0.985805i	$0.553697\pi$
$258$	−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	−0.452804	−	0.891610i	$-0.649576\pi$
$263$	115.406	−	115.406i	0.438806	−	0.438806i	0.891610	+	0.452804i	$0.149576\pi$
$264$	−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	−0.550229	−	0.835014i	$-0.685459\pi$
$269$	−399.783	−	129.897i	−1.48618	−	0.482890i	−0.935953	+	0.352124i	$0.885459\pi$
$270$		0			0
$271$	−235.240	+	170.912i	−0.868043	+	0.630670i	−0.930061	−	0.367405i	$-0.880246\pi$
$271$	−235.240	+	170.912i	−0.868043	+	0.630670i	0.0620182	+	0.998075i	$0.480246\pi$
$272$	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	0.418501	+	0.908216i	$0.362556\pi$
$277$	−155.743	+	305.663i	−0.562250	+	1.10348i	−0.980751	+	0.195262i	$0.937444\pi$
$278$	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	−0.989772	−	0.142657i	$-0.954435\pi$
$281$	−29.5550	+	90.9610i	−0.105178	+	0.323705i	0.884594	+	0.466362i	$0.154435\pi$
$282$	384.903	+	60.9626i	1.36490	+	0.216180i
$283$	48.4877	−	7.67970i	0.171335	−	0.0271368i	−0.0701775	−	0.997535i	$-0.522357\pi$
$283$	48.4877	−	7.67970i	0.171335	−	0.0271368i	0.241512	+	0.970398i	$0.422357\pi$
$284$	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	−0.488361	−	0.872642i	$-0.662405\pi$
$293$	72.0074	−	454.637i	0.245759	−	1.55166i	0.734120	−	0.679020i	$-0.237595\pi$
$294$	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	0.373691	−	0.927553i	$-0.378092\pi$
$307$	−170.036	−	170.036i	−0.553862	−	0.553862i	−0.927553	+	0.373691i	$0.878092\pi$
$308$	−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	0.272778	−	0.962077i	$-0.412058\pi$
$311$	−173.513	−	126.064i	−0.557919	−	0.405352i	−0.830697	+	0.556725i	$0.812058\pi$
$312$	−409.145	−	64.8021i	−1.31136	−	0.207699i
$313$	72.2129	+	141.726i	0.230712	+	0.452798i	0.977119	−	0.212691i	$-0.0682229\pi$
$313$	72.2129	+	141.726i	0.230712	+	0.452798i	−0.746407	+	0.665489i	$0.768223\pi$
$314$	−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	−0.910445	−	0.413629i	$-0.864261\pi$
$317$	−12.8910	+	25.3001i	−0.0406657	+	0.0798109i	0.869780	+	0.493440i	$0.164261\pi$
$318$	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	−0.416353	−	0.909203i	$-0.636692\pi$
$337$	−368.438	−	58.3548i	−1.09329	−	0.173160i	−0.676934	+	0.736043i	$0.736692\pi$
$338$	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	0.774203	−	0.632937i	$-0.218151\pi$
$347$	604.240	−	307.876i	1.74133	−	0.887250i	0.967122	−	0.254313i	$-0.0818492\pi$
$348$	−48.9080	+	308.793i	−0.140540	+	0.887336i
$349$	24.7765	−	34.1019i	0.0709927	−	0.0977131i	−0.772044	−	0.635569i	$-0.780766\pi$
$349$	24.7765	−	34.1019i	0.0709927	−	0.0977131i	0.843037	+	0.537856i	$0.180766\pi$
$350$		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	−0.987154	−	0.159772i	$-0.948924\pi$
$353$	−292.066	+	292.066i	−0.827382	+	0.827382i	0.159772	+	0.987154i	$0.448924\pi$
$354$	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	0.670526	−	0.741886i	$-0.266068\pi$
$359$	−86.9687	−	119.702i	−0.242253	−	0.333432i	−0.912779	+	0.408453i	$0.866068\pi$
$360$		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	−0.338740	−	0.940880i	$-0.610001\pi$
$367$	−349.255	−	55.3166i	−0.951649	−	0.150726i	−0.612909	+	0.790154i	$0.710001\pi$
$368$	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	−0.611100	−	0.791554i	$-0.709273\pi$
$373$	67.3093	−	67.3093i	0.180454	−	0.180454i	0.791554	+	0.611100i	$0.209273\pi$
$374$	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	−0.470212	−	0.882553i	$-0.655823\pi$
$379$	−518.993	−	168.631i	−1.36937	−	0.444937i	−0.899162	+	0.437617i	$0.855823\pi$
$380$		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	0.801090	−	0.598544i	$-0.204254\pi$
$383$	301.699	+	153.723i	0.787726	+	0.401366i	−0.0133638	+	0.999911i	$0.504254\pi$
$384$		−	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	−0.982309	−	0.187265i	$-0.940038\pi$
$389$	−333.318	−	458.773i	−0.856859	−	1.17937i	0.125450	−	0.992100i	$-0.459962\pi$
$390$		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	0.0814297	−	0.996679i	$-0.474051\pi$
$397$	−363.354	−	363.354i	−0.915249	−	0.915249i	−0.996679	+	0.0814297i	$0.974051\pi$
$398$	−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	−0.998559	−	0.0536695i	$-0.982908\pi$
$401$	−63.8238	+	196.429i	−0.159162	+	0.489849i	0.839397	+	0.543519i	$0.182908\pi$
$402$	−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	0.110696	−	0.993854i	$-0.464692\pi$
$409$	320.829	−	104.244i	0.784423	−	0.254875i	0.673728	+	0.738980i	$0.264692\pi$
$410$		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	$0.214746\pi$
$419$			523.431i			1.24924i	−0.780930	+	0.624619i	$0.785254\pi$
$420$		0			0
$421$	−264.208	−	191.959i	−0.627574	−	0.455959i	0.227985	−	0.973665i	$-0.426786\pi$
$421$	−264.208	−	191.959i	−0.627574	−	0.455959i	−0.855559	+	0.517706i	$0.826786\pi$
$422$	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	0.969388	+	0.245534i	$0.0789632\pi$
$431$	141.996	+	437.020i	0.329458	+	1.01397i	−0.639930	+	0.768433i	$0.721037\pi$
$432$	54.1431	+	341.846i	0.125331	+	0.791310i
$433$	−45.7255	+	288.700i	−0.105602	+	0.666743i	0.876926	+	0.480626i	$0.159590\pi$
$433$	−45.7255	+	288.700i	−0.105602	+	0.666743i	−0.982528	+	0.186117i	$0.940410\pi$
$434$	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	$0.105786\pi$
$439$			286.451i			0.652507i	−0.945282	+	0.326253i	$0.894214\pi$
$440$		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	−0.490017	−	0.871713i	$-0.663009\pi$
$443$	−304.198	+	48.1802i	−0.686676	+	0.108759i	−0.196660	+	0.980472i	$0.563009\pi$
$444$	−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	0.00461218	−	0.999989i	$-0.498532\pi$
$449$	267.659	−	86.9677i	0.596123	−	0.193692i	0.591510	+	0.806297i	$0.298532\pi$
$450$		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	−0.478217	−	0.878242i	$-0.658717\pi$
$457$	−22.2989	+	11.3619i	−0.0487941	+	0.0248618i	0.429423	+	0.903103i	$0.358717\pi$
$458$	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	−0.433804	−	0.901007i	$-0.642829\pi$
$463$	216.315	−	216.315i	0.467203	−	0.467203i	0.901007	+	0.433804i	$0.142829\pi$
$464$	−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	−0.277496	−	0.960727i	$-0.589504\pi$
$467$	157.211	−	80.1031i	0.336641	−	0.171527i	0.614137	+	0.789200i	$0.289504\pi$
$468$	−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	−0.348573	−	0.937282i	$-0.613334\pi$
$479$	−565.936	−	183.884i	−1.18149	−	0.383891i	−0.832922	+	0.553391i	$0.813334\pi$
$480$		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	−0.941949	−	0.335755i	$-0.891008\pi$
$487$	−72.9801	−	460.778i	−0.149856	−	0.946156i	0.792093	−	0.610401i	$-0.208992\pi$
$488$	−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	−0.679031	−	0.734109i	$-0.737600\pi$
$491$	−93.6260	+	68.0233i	−0.190684	+	0.138540i	0.488347	+	0.872649i	$0.337600\pi$
$492$	−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	0.927118	−	0.374770i	$-0.122278\pi$
$499$	141.813	+	195.189i	0.284195	+	0.391161i	−0.642923	+	0.765931i	$0.722278\pi$
$500$		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	0.284342	−	0.958723i	$-0.408225\pi$
$503$	428.067	−	67.7992i	0.851028	−	0.134790i	0.566687	+	0.823933i	$0.308225\pi$
$504$	−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	−0.937081	−	0.349112i	$-0.886483\pi$
$509$	−160.580	+	221.019i	−0.315481	+	0.434223i	0.621600	+	0.783335i	$0.286483\pi$
$510$		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	−0.124094	−	0.992270i	$-0.539602\pi$
$521$	407.039	−	295.731i	0.781264	−	0.567622i	0.905358	+	0.424649i	$0.139602\pi$
$522$	−161.559	+	82.3183i	−0.309500	+	0.157698i
$523$	−20.4357	−	40.1074i	−0.0390741	−	0.0766871i	0.870644	−	0.491913i	$-0.163702\pi$
$523$	−20.4357	−	40.1074i	−0.0390741	−	0.0766871i	−0.909718	+	0.415226i	$0.863702\pi$
$524$	−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	0.941282	+	0.337622i	$0.109623\pi$
$541$	204.616	+	629.743i	0.378218	+	1.16404i	−0.563064	+	0.826414i	$0.690377\pi$
$542$	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	−0.989222	−	0.146424i	$-0.953224\pi$
$547$	−51.2339	−	323.478i	−0.0936635	−	0.591368i	0.895558	−	0.444944i	$-0.146776\pi$
$548$	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	−0.640782	−	0.767723i	$-0.721390\pi$
$557$	−828.504	−	131.222i	−1.48744	−	0.235587i	−0.846659	+	0.532136i	$0.821390\pi$
$558$	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	−0.307343	−	0.951599i	$-0.599440\pi$
$563$	−708.172	−	360.832i	−1.25785	−	0.640909i	−0.950511	+	0.310690i	$0.899440\pi$
$564$	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	0.00652189	−	0.999979i	$-0.497924\pi$
$569$	543.704	−	748.344i	0.955543	−	1.31519i	0.949021	−	0.315213i	$-0.102076\pi$
$570$		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	−0.624393	−	0.781110i	$-0.714654\pi$
$577$	−207.415	+	105.683i	−0.359471	+	0.183159i	0.264922	+	0.964270i	$0.414654\pi$
$578$	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	0.230703	−	0.973024i	$-0.425897\pi$
$587$	87.7179	+	13.8932i	0.149434	+	0.0236681i	−0.0812691	+	0.996692i	$0.525897\pi$
$588$	−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	−0.427839	−	0.903855i	$-0.640725\pi$
$593$	282.278	−	282.278i	0.476016	−	0.476016i	0.903855	+	0.427839i	$0.140725\pi$
$594$	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	−0.486997	−	0.873404i	$-0.661908\pi$
$599$	−835.221	−	271.380i	−1.39436	−	0.453055i	−0.907363	+	0.420349i	$0.861908\pi$
$600$		0			0
$601$	−352.495	+	256.103i	−0.586515	+	0.426128i	−0.841067	−	0.540931i	$-0.818072\pi$
$601$	−352.495	+	256.103i	−0.586515	+	0.426128i	0.254552	+	0.967059i	$0.418072\pi$
$602$	−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	−0.795685	−	0.605711i	$-0.792889\pi$
$607$	98.3567	−	193.036i	0.162037	−	0.318016i	0.957722	+	0.287695i	$0.0928888\pi$
$608$	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	0.821779	−	0.569806i	$-0.192982\pi$
$613$	1090.78	−	172.763i	1.77942	−	0.281832i	0.957638	+	0.287974i	$0.0929816\pi$
$614$	−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	0.998197	+	0.0600293i	$0.0191194\pi$
$617$	652.925	+	652.925i	1.05823	+	1.05823i	0.0600293	+	0.998197i	$0.480881\pi$
$618$	913.319	+	465.359i	1.47786	+	0.753008i
$619$	−325.696	+	448.282i	−0.526165	+	0.724203i	−0.986540	−	0.163521i	$-0.947715\pi$
$619$	−325.696	+	448.282i	−0.526165	+	0.724203i	0.460375	+	0.887724i	$0.347715\pi$
$620$		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	−0.277852	−	0.960624i	$-0.589623\pi$
$631$	346.983	−	252.098i	0.549894	−	0.399522i	0.827747	+	0.561102i	$0.189623\pi$
$632$	−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	0.546852	−	0.837229i	$-0.315826\pi$
$641$	−51.5449	−	37.4495i	−0.0804132	−	0.0584236i	−0.627266	+	0.778805i	$0.715826\pi$
$642$	−643.390	−	101.903i	−1.00217	−	0.158727i
$643$	−30.5733	−	60.0035i	−0.0475479	−	0.0933180i	0.866010	−	0.500027i	$-0.166676\pi$
$643$	−30.5733	−	60.0035i	−0.0475479	−	0.0933180i	−0.913558	+	0.406709i	$0.866676\pi$
$644$	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	−0.668685	−	0.743546i	$-0.733142\pi$
$647$	210.857	−	413.830i	0.325900	−	0.639614i	0.994584	+	0.103932i	$0.0331424\pi$
$648$	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	−0.834724	−	0.550669i	$-0.814373\pi$
$653$	84.4407	−	533.137i	0.129312	−	0.816443i	0.964035	−	0.265774i	$-0.0856274\pi$
$654$	−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	$0.274574\pi$
$659$			1001.07i			1.51907i	−0.650465	+	0.759536i	$0.725426\pi$
$660$		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	0.258593	−	0.965986i	$-0.416741\pi$
$673$	−249.622	−	127.189i	−0.370910	−	0.188988i	−0.629502	+	0.776999i	$0.716741\pi$
$674$	−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	−0.740652	−	0.671889i	$-0.765483\pi$
$677$	−428.152	+	218.154i	−0.632426	+	0.322237i	0.108226	+	0.994126i	$0.465483\pi$
$678$	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	−0.985200	−	0.171406i	$-0.945169\pi$
$683$	−555.821	+	555.821i	−0.813794	+	0.813794i	0.171406	+	0.985200i	$0.445169\pi$
$684$	−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	1.00000		6.96426e-5i	$2.21679e-5\pi$
$691$	131.998	+	406.247i	0.191024	+	0.587911i	−0.808976	+	0.587842i	$0.799978\pi$
$692$	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	0.697595	−	0.716493i	$-0.254254\pi$
$701$	162.449	+	118.026i	0.231738	+	0.168368i	−0.465856	+	0.884860i	$0.654254\pi$
$702$	−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	−0.161687	−	0.986842i	$-0.551694\pi$
$709$	−618.635	−	201.007i	−0.872546	−	0.283507i	−0.710859	+	0.703335i	$0.751694\pi$
$710$		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	0.748551	−	0.663077i	$-0.230750\pi$
$719$	−81.5254	−	112.210i	−0.113387	−	0.156064i	−0.861939	+	0.507013i	$0.830750\pi$
$720$		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	0.359840	−	0.933014i	$-0.382831\pi$
$727$	−416.697	−	416.697i	−0.573173	−	0.573173i	−0.933014	+	0.359840i	$0.882831\pi$
$728$	−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	0.822099	+	0.569345i	$0.192803\pi$
$733$	−99.4688	+	628.021i	−0.135701	+	0.856782i	−0.957800	+	0.287437i	$0.907197\pi$
$734$	−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	0.148217	−	0.988955i	$-0.452646\pi$
$739$	627.722	−	203.959i	0.849421	−	0.275994i	0.701203	+	0.712961i	$0.252646\pi$
$740$		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	0.788152	−	0.615481i	$-0.211038\pi$
$743$	−128.574	−	252.340i	−0.173047	−	0.339623i	−0.961198	+	0.275858i	$0.911038\pi$
$744$	−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	0.732220	−	0.681068i	$-0.238484\pi$
$751$	233.376	+	169.558i	0.310754	+	0.225776i	−0.421466	+	0.906844i	$0.638484\pi$
$752$	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	−0.837500	−	0.546438i	$-0.815983\pi$
$757$	73.3139	−	143.887i	0.0968480	−	0.190075i	0.934348	+	0.356363i	$0.115983\pi$
$758$	−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	−0.997237	−	0.0742887i	$-0.976331\pi$
$761$	−178.166	−	548.339i	−0.234121	−	0.720551i	0.763116	−	0.646262i	$-0.223669\pi$
$762$	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	$-0.995072\pi$
$769$		−	23.8117i		−	0.0309646i	0.999880	−	0.0154823i	$-0.00492836\pi$
$770$		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	−0.922577	−	0.385813i	$-0.873921\pi$
$773$	−1299.24	+	205.779i	−1.68078	+	0.266209i	−0.758200	+	0.652022i	$0.773921\pi$
$774$	−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	−0.490941	−	0.871193i	$-0.663347\pi$
$787$	−58.7876	+	29.9538i	−0.0746984	+	0.0380607i	0.416242	+	0.909254i	$0.363347\pi$
$788$	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	0.285700	−	0.958319i	$-0.407774\pi$
$797$	979.455	−	499.057i	1.22893	−	0.626169i	0.943227	+	0.332150i	$0.107774\pi$
$798$	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	0.148011	−	0.988986i	$-0.452713\pi$
$809$	−253.667	−	82.4213i	−0.313556	−	0.101881i	−0.461567	+	0.887105i	$0.652713\pi$
$810$		0			0
$811$	338.287	+	245.780i	0.417123	+	0.303057i	0.776479	−	0.630143i	$-0.217004\pi$
$811$	338.287	+	245.780i	0.417123	+	0.303057i	−0.359356	+	0.933200i	$0.617004\pi$
$812$	−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	−0.453667	−	0.891171i	$-0.649884\pi$
$821$	208.285	−	151.328i	0.253697	−	0.184321i	0.707363	+	0.706850i	$0.249884\pi$
$822$	−115.957	−	732.123i	−0.141067	−	0.890661i
$823$	−1112.28	−	566.734i	−1.35149	−	0.688619i	−0.379843	−	0.925051i	$-0.624022\pi$
$823$	−1112.28	−	566.734i	−1.35149	−	0.688619i	−0.971648	+	0.236432i	$0.924022\pi$
$824$			1540.43i			1.86946i
$825$		0			0
$826$	183.582			0.222254
$827$	−638.541	+	1253.21i	−0.772117	+	1.51536i	0.0827808	+	0.996568i	$0.473620\pi$
$827$	−638.541	+	1253.21i	−0.772117	+	1.51536i	−0.854898	+	0.518797i	$0.826380\pi$
$828$	704.430	−	111.571i	0.850760	−	0.134747i
$829$	−12.8668	−	17.7097i	−0.0155209	−	0.0213627i	0.801186	−	0.598415i	$-0.204203\pi$
$829$	−12.8668	−	17.7097i	−0.0155209	−	0.0213627i	−0.816707	+	0.577053i	$0.804203\pi$
$830$		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	−0.648852	−	0.760915i	$-0.724751\pi$
$839$	230.999	−	317.943i	0.275327	−	0.378955i	0.924179	+	0.381959i	$0.124751\pi$
$840$		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	0.887308	−	0.461178i	$-0.152573\pi$
$853$	−6.26065	−	12.2872i	−0.00733957	−	0.0144047i	−0.894647	+	0.446773i	$0.852573\pi$
$854$	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	0.646074	−	0.763275i	$-0.276410\pi$
$857$	−100.441	−	100.441i	−0.117201	−	0.117201i	−0.763275	+	0.646074i	$0.776410\pi$
$858$	385.040	+	1192.19i	0.448764	+	1.38950i
$859$			57.6453i			0.0671075i	0.999437	+	0.0335537i	$0.0106825\pi$
$859$			57.6453i			0.0671075i	−0.999437	+	0.0335537i	$0.989318\pi$
$860$		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	0.905295	−	0.424784i	$-0.139650\pi$
$863$	25.4744	+	49.9964i	0.0295185	+	0.0579332i	−0.875776	+	0.482717i	$0.839650\pi$
$864$	−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	0.950784	+	0.309854i	$0.100280\pi$
$877$	124.784	+	787.853i	0.142285	+	0.898350i	−0.808500	+	0.588497i	$0.799720\pi$
$878$	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	0.428456	−	0.903563i	$-0.359058\pi$
$883$	984.685	−	155.959i	1.11516	−	0.176624i	0.686702	+	0.726939i	$0.259058\pi$
$884$	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	−0.566913	−	0.823778i	$-0.691862\pi$
$887$	−1206.89	−	191.152i	−1.36064	−	0.215504i	−0.793727	+	0.608274i	$0.791862\pi$
$888$	−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	−0.329223	−	0.944252i	$-0.606787\pi$
$907$	218.751	−	111.459i	0.241181	−	0.122888i	0.570404	+	0.821365i	$0.306787\pi$
$908$	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	0.957150	−	0.289592i	$-0.0935198\pi$
$911$	11.4615	+	35.2749i	0.0125813	+	0.0387211i	−0.944569	+	0.328314i	$0.893520\pi$
$912$	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	0.834469	−	0.551054i	$-0.185774\pi$
$919$	1089.63	+	354.042i	1.18567	+	0.385247i	0.351198	+	0.936301i	$0.385774\pi$
$920$		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	0.877790	−	0.479046i	$-0.159017\pi$
$929$	1213.61	+	394.326i	1.30636	+	0.424462i	0.428571	+	0.903508i	$0.359017\pi$
$930$		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	−0.605064	−	0.796177i	$-0.706853\pi$
$937$	369.838	−	725.847i	0.394704	−	0.774650i	0.999768	+	0.0215265i	$0.00685264\pi$
$938$	−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	−0.747820	−	0.663902i	$-0.768899\pi$
$941$	232.814	−	716.527i	0.247411	−	0.761452i	0.995231	−	0.0975506i	$-0.0311008\pi$
$942$	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	0.478493	−	0.878091i	$-0.341183\pi$
$947$	−378.420	−	378.420i	−0.399598	−	0.399598i	−0.878091	+	0.478493i	$0.841183\pi$
$948$	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	0.931953	+	0.362580i	$0.118104\pi$
$953$	−63.3081	+	399.711i	−0.0664303	+	0.419424i	−0.998383	+	0.0568446i	$0.981896\pi$
$954$	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	0.917339	−	0.398107i	$-0.130333\pi$
$967$	502.098	+	502.098i	0.519233	+	0.519233i	−0.398107	+	0.917339i	$0.630333\pi$
$968$	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	−0.0834887	−	0.996509i	$-0.526606\pi$
$971$	−1026.37	−	745.702i	−1.05702	−	0.767973i	−0.973536	+	0.228536i	$0.926606\pi$
$972$	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	−0.944781	−	0.327704i	$-0.893725\pi$
$977$	−121.475	+	238.408i	−0.124335	+	0.244020i	0.820446	+	0.571724i	$0.193725\pi$
$978$	−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	−0.904363	−	0.426763i	$-0.859654\pi$
$983$	86.1250	−	543.772i	0.0876144	−	0.553176i	0.991978	−	0.126412i	$-0.0403462\pi$
$984$	−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	0.308336	−	0.951277i	$-0.400228\pi$
$997$	306.698	+	48.5762i	0.307621	+	0.0487224i	−0.000715499		1.00000i	$0.500228\pi$
$998$	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.82.15	yes	128
5.2	odd	4	inner	275.3.bk.c.93.15	yes	128
5.3	odd	4	inner	275.3.bk.c.93.2	yes	128
5.4	even	2	inner	275.3.bk.c.82.2	✓	128
11.9	even	5	inner	275.3.bk.c.207.2	yes	128
55.9	even	10	inner	275.3.bk.c.207.15	yes	128
55.42	odd	20	inner	275.3.bk.c.218.2	yes	128
55.53	odd	20	inner	275.3.bk.c.218.15	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.bk.c.82.2	✓	128	5.4	even	2	inner
275.3.bk.c.82.15	yes	128	1.1	even	1	trivial
275.3.bk.c.93.2	yes	128	5.3	odd	4	inner
275.3.bk.c.93.15	yes	128	5.2	odd	4	inner
275.3.bk.c.207.2	yes	128	11.9	even	5	inner
275.3.bk.c.207.15	yes	128	55.9	even	10	inner
275.3.bk.c.218.2	yes	128	55.42	odd	20	inner
275.3.bk.c.218.15	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+(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

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Database

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