LMFDB - Embedded newform 475.2.l.f.176.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(101,475)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("475.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.l (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			176.1
Character	$\chi$	$=$	475.176
Dual form			475.2.l.f.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.22798 + 0.810919i) q^{2} +(-0.396806 + 2.25040i) q^{3} +(2.77422 - 2.32785i) q^{4} +(-0.940815 - 5.33563i) q^{6} +(0.818386 + 1.41749i) q^{7} +(-1.92225 + 3.32944i) q^{8} +(-2.08777 - 0.759885i) q^{9} +O(q^{10})$	\(q+(-2.22798 + 0.810919i) q^{2} +(-0.396806 + 2.25040i) q^{3} +(2.77422 - 2.32785i) q^{4} +(-0.940815 - 5.33563i) q^{6} +(0.818386 + 1.41749i) q^{7} +(-1.92225 + 3.32944i) q^{8} +(-2.08777 - 0.759885i) q^{9} +(-1.36374 + 2.36206i) q^{11} +(4.13776 + 7.16682i) q^{12} +(-1.07650 - 6.10515i) q^{13} +(-2.97282 - 2.49449i) q^{14} +(0.325107 - 1.84377i) q^{16} +(-2.93608 + 1.06864i) q^{17} +5.26771 q^{18} +(-3.46824 + 2.64032i) q^{19} +(-3.51465 + 1.27923i) q^{21} +(1.12294 - 6.36852i) q^{22} +(-5.59139 + 4.69173i) q^{23} +(-6.72981 - 5.64698i) q^{24} +(7.34921 + 12.7292i) q^{26} +(-0.889189 + 1.54012i) q^{27} +(5.57008 + 2.02734i) q^{28} +(-2.09149 - 0.761241i) q^{29} +(-2.21333 - 3.83360i) q^{31} +(-0.564364 - 3.20067i) q^{32} +(-4.77445 - 4.00624i) q^{33} +(5.67494 - 4.76184i) q^{34} +(-7.56083 + 2.75192i) q^{36} +2.04016 q^{37} +(5.58609 - 8.69505i) q^{38} +14.1662 q^{39} +(0.681538 - 3.86519i) q^{41} +(6.79323 - 5.70020i) q^{42} +(-0.362229 - 0.303946i) q^{43} +(1.71522 + 9.72747i) q^{44} +(8.65289 - 14.9872i) q^{46} +(2.16280 + 0.787194i) q^{47} +(4.02022 + 1.46324i) q^{48} +(2.16049 - 3.74208i) q^{49} +(-1.23982 - 7.03139i) q^{51} +(-17.1983 - 14.4311i) q^{52} +(4.87501 - 4.09062i) q^{53} +(0.732183 - 4.15242i) q^{54} -6.29258 q^{56} +(-4.56556 - 8.85263i) q^{57} +5.27711 q^{58} +(-11.5263 + 4.19524i) q^{59} +(-3.66993 + 3.07944i) q^{61} +(8.03999 + 6.74636i) q^{62} +(-0.631473 - 3.58126i) q^{63} +(5.72509 + 9.91615i) q^{64} +(13.8861 + 5.05414i) q^{66} +(-0.630496 - 0.229482i) q^{67} +(-5.65769 + 9.79940i) q^{68} +(-8.33957 - 14.4446i) q^{69} +(2.01848 + 1.69370i) q^{71} +(6.54321 - 5.49040i) q^{72} +(1.13097 - 6.41403i) q^{73} +(-4.54543 + 1.65440i) q^{74} +(-3.47540 + 15.3984i) q^{76} -4.46426 q^{77} +(-31.5620 + 11.4876i) q^{78} +(0.715459 - 4.05757i) q^{79} +(-8.21894 - 6.89651i) q^{81} +(1.61590 + 9.16425i) q^{82} +(3.21198 + 5.56331i) q^{83} +(-6.77258 + 11.7304i) q^{84} +(1.05351 + 0.383448i) q^{86} +(2.54302 - 4.40463i) q^{87} +(-5.24290 - 9.08097i) q^{88} +(3.00487 + 17.0415i) q^{89} +(7.77297 - 6.52229i) q^{91} +(-4.59011 + 26.0318i) q^{92} +(9.50539 - 3.45968i) q^{93} -5.45702 q^{94} +7.42673 q^{96} +(-0.122107 + 0.0444434i) q^{97} +(-1.77901 + 10.0893i) q^{98} +(4.64207 - 3.89516i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9}+O(q^{10}) $ 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9	$ 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 42 q^{16} - 12 q^{19} - 54 q^{21} - 24 q^{24} + 12 q^{26} - 42 q^{31} + 36 q^{34} + 18 q^{36} + 48 q^{39} + 6 q^{41} + 6 q^{44} - 6 q^{46} - 12 q^{49} + 108 q^{51} - 24 q^{54} + 36 q^{56} + 36 q^{59} + 48 q^{61} + 180 q^{66} - 66 q^{69} - 24 q^{71} - 84 q^{74} + 66 q^{76} - 48 q^{79} - 78 q^{81} + 54 q^{84} - 42 q^{86} + 12 q^{89} - 30 q^{91} + 72 q^{94} - 240 q^{96} + 36 q^{99}+O(q^{100}) $ 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9 - 12 * q^11 - 6 * q^14 - 42 * q^16 - 12 * q^19 - 54 * q^21 - 24 * q^24 + 12 * q^26 - 42 * q^31 + 36 * q^34 + 18 * q^36 + 48 * q^39 + 6 * q^41 + 6 * q^44 - 6 * q^46 - 12 * q^49 + 108 * q^51 - 24 * q^54 + 36 * q^56 + 36 * q^59 + 48 * q^61 + 180 * q^66 - 66 * q^69 - 24 * q^71 - 84 * q^74 + 66 * q^76 - 48 * q^79 - 78 * q^81 + 54 * q^84 - 42 * q^86 + 12 * q^89 - 30 * q^91 + 72 * q^94 - 240 * q^96 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−2.22798	+	0.810919i	−1.57542	+	0.573406i	−0.974202	−	0.225678i	$-0.927540\pi$
$2$	−2.22798	+	0.810919i	−1.57542	+	0.573406i	−0.601219	+	0.799084i	$0.705318\pi$
$3$	−0.396806	+	2.25040i	−0.229096	+	1.29927i	0.625601	+	0.780143i	$0.284854\pi$
$3$	−0.396806	+	2.25040i	−0.229096	+	1.29927i	−0.854698	+	0.519126i	$0.826257\pi$
$4$	2.77422	−	2.32785i	1.38711	−	1.16392i
$5$		0			0
$5$		0			0
$6$	−0.940815	−	5.33563i	−0.384086	−	2.17826i
$7$	0.818386	+	1.41749i	0.309321	+	0.535759i	0.978214	−	0.207599i	$-0.0665650\pi$
$7$	0.818386	+	1.41749i	0.309321	+	0.535759i	−0.668893	+	0.743359i	$0.733232\pi$
$8$	−1.92225	+	3.32944i	−0.679619	+	1.17713i
$9$	−2.08777	−	0.759885i	−0.695923	−	0.253295i
$10$		0			0
$11$	−1.36374	+	2.36206i	−0.411183	+	0.712189i	−0.995019	−	0.0996818i	$-0.968218\pi$
$11$	−1.36374	+	2.36206i	−0.411183	+	0.712189i	0.583837	+	0.811871i	$0.301551\pi$
$12$	4.13776	+	7.16682i	1.19447	+	2.06888i
$13$	−1.07650	−	6.10515i	−0.298568	−	1.69326i	−0.652336	−	0.757930i	$-0.726211\pi$
$13$	−1.07650	−	6.10515i	−0.298568	−	1.69326i	0.353768	−	0.935333i	$-0.384900\pi$
$14$	−2.97282	−	2.49449i	−0.794518	−	0.666680i
$15$		0			0
$16$	0.325107	−	1.84377i	0.0812767	−	0.460943i
$17$	−2.93608	+	1.06864i	−0.712103	+	0.259184i	−0.672570	−	0.740034i	$-0.734809\pi$
$17$	−2.93608	+	1.06864i	−0.712103	+	0.259184i	−0.0395336	+	0.999218i	$0.512587\pi$
$18$	5.26771			1.24161
$19$	−3.46824	+	2.64032i	−0.795669	+	0.605732i
$19$	−3.46824	+	2.64032i	−0.795669	+	0.605732i
$20$		0			0
$21$	−3.51465	+	1.27923i	−0.766960	+	0.279151i
$22$	1.12294	−	6.36852i	0.239412	−	1.35777i
$23$	−5.59139	+	4.69173i	−1.16588	+	0.978293i	−0.999969	−	0.00784655i	$-0.997502\pi$
$23$	−5.59139	+	4.69173i	−1.16588	+	0.978293i	−0.165915	+	0.986140i	$0.553058\pi$
$24$	−6.72981	−	5.64698i	−1.37372	−	1.15268i
$25$		0			0
$26$	7.34921	+	12.7292i	1.44130	+	2.49640i
$27$	−0.889189	+	1.54012i	−0.171124	+	0.296396i
$28$	5.57008	+	2.02734i	1.05265	+	0.383132i
$29$	−2.09149	−	0.761241i	−0.388381	−	0.141359i	0.140447	−	0.990088i	$-0.455146\pi$
$29$	−2.09149	−	0.761241i	−0.388381	−	0.141359i	−0.528828	+	0.848729i	$0.677368\pi$
$30$		0			0
$31$	−2.21333	−	3.83360i	−0.397526	−	0.688535i	0.595894	−	0.803063i	$-0.296798\pi$
$31$	−2.21333	−	3.83360i	−0.397526	−	0.688535i	−0.993420	+	0.114528i	$0.963464\pi$
$32$	−0.564364	−	3.20067i	−0.0997665	−	0.565804i
$33$	−4.77445	−	4.00624i	−0.831125	−	0.697397i
$34$	5.67494	−	4.76184i	0.973244	−	0.816649i
$35$		0			0
$36$	−7.56083	+	2.75192i	−1.26014	+	0.458653i
$37$	2.04016			0.335400			0.167700	−	0.985838i	$-0.446366\pi$
$37$	2.04016			0.335400			0.167700	+	0.985838i	$0.446366\pi$
$38$	5.58609	−	8.69505i	0.906183	−	1.41052i
$39$	14.1662			2.26841
$40$		0			0
$41$	0.681538	−	3.86519i	0.106438	−	0.603642i	−0.884198	−	0.467113i	$-0.845294\pi$
$41$	0.681538	−	3.86519i	0.106438	−	0.603642i	0.990636	−	0.136529i	$-0.0435947\pi$
$42$	6.79323	−	5.70020i	1.04822	−	0.879559i
$43$	−0.362229	−	0.303946i	−0.0552394	−	0.0463513i	0.614750	−	0.788722i	$-0.289257\pi$
$43$	−0.362229	−	0.303946i	−0.0552394	−	0.0463513i	−0.669989	+	0.742371i	$0.733701\pi$
$44$	1.71522	+	9.72747i	0.258579	+	1.46647i
$45$		0			0
$46$	8.65289	−	14.9872i	1.27580	−	2.20975i
$47$	2.16280	+	0.787194i	0.315477	+	0.114824i	0.494905	−	0.868947i	$-0.335203\pi$
$47$	2.16280	+	0.787194i	0.315477	+	0.114824i	−0.179429	+	0.983771i	$0.557425\pi$
$48$	4.02022	+	1.46324i	0.580269	+	0.211201i
$49$	2.16049	−	3.74208i	0.308641	−	0.534582i
$50$		0			0
$51$	−1.23982	−	7.03139i	−0.173610	−	0.984592i
$52$	−17.1983	−	14.4311i	−2.38498	−	2.00123i
$53$	4.87501	−	4.09062i	0.669634	−	0.561890i	−0.243323	−	0.969945i	$-0.578238\pi$
$53$	4.87501	−	4.09062i	0.669634	−	0.561890i	0.912957	+	0.408056i	$0.133793\pi$
$54$	0.732183	−	4.15242i	0.0996375	−	0.565073i
$55$		0			0
$56$	−6.29258			−0.840881
$57$	−4.56556	−	8.85263i	−0.604724	−	1.17256i
$58$	5.27711			0.692919
$59$	−11.5263	+	4.19524i	−1.50060	+	0.546174i	−0.956216	−	0.292661i	$-0.905459\pi$
$59$	−11.5263	+	4.19524i	−1.50060	+	0.546174i	−0.544385	+	0.838835i	$0.683237\pi$
$60$		0			0
$61$	−3.66993	+	3.07944i	−0.469887	+	0.394282i	−0.846753	−	0.531986i	$-0.821446\pi$
$61$	−3.66993	+	3.07944i	−0.469887	+	0.394282i	0.376867	+	0.926268i	$0.377002\pi$
$62$	8.03999	+	6.74636i	1.02108	+	0.856788i
$63$	−0.631473	−	3.58126i	−0.0795581	−	0.451197i
$64$	5.72509	+	9.91615i	0.715637	+	1.23952i
$65$		0			0
$66$	13.8861	+	5.05414i	1.70926	+	0.622121i
$67$	−0.630496	−	0.229482i	−0.0770274	−	0.0280357i	0.303219	−	0.952921i	$-0.401939\pi$
$67$	−0.630496	−	0.229482i	−0.0770274	−	0.0280357i	−0.380246	+	0.924885i	$0.624161\pi$
$68$	−5.65769	+	9.79940i	−0.686095	+	1.18835i
$69$	−8.33957	−	14.4446i	−1.00397	−	1.73892i
$70$		0			0
$71$	2.01848	+	1.69370i	0.239549	+	0.201006i	0.754657	−	0.656120i	$-0.227803\pi$
$71$	2.01848	+	1.69370i	0.239549	+	0.201006i	−0.515107	+	0.857126i	$0.672248\pi$
$72$	6.54321	−	5.49040i	0.771124	−	0.647050i
$73$	1.13097	−	6.41403i	0.132370	−	0.750706i	−0.844286	−	0.535893i	$-0.819975\pi$
$73$	1.13097	−	6.41403i	0.132370	−	0.750706i	0.976655	−	0.214812i	$-0.0689140\pi$
$74$	−4.54543	+	1.65440i	−0.528395	+	0.192320i
$75$		0			0
$76$	−3.47540	+	15.3984i	−0.398656	+	1.76632i
$77$	−4.46426			−0.508750
$78$	−31.5620	+	11.4876i	−3.57369	+	1.30072i
$79$	0.715459	−	4.05757i	0.0804954	−	0.456512i	−0.917743	−	0.397176i	$-0.869990\pi$
$79$	0.715459	−	4.05757i	0.0804954	−	0.456512i	0.998238	−	0.0593365i	$-0.0188985\pi$
$80$		0			0
$81$	−8.21894	−	6.89651i	−0.913216	−	0.766279i
$82$	1.61590	+	9.16425i	0.178447	+	1.01202i
$83$	3.21198	+	5.56331i	0.352560	+	0.610653i	0.986697	−	0.162568i	$-0.0519777\pi$
$83$	3.21198	+	5.56331i	0.352560	+	0.610653i	−0.634137	+	0.773221i	$0.718644\pi$
$84$	−6.77258	+	11.7304i	−0.738949	+	1.27990i
$85$		0			0
$86$	1.05351	+	0.383448i	0.113603	+	0.0413483i
$87$	2.54302	−	4.40463i	0.272640	−	0.472226i
$88$	−5.24290	−	9.08097i	−0.558895	−	0.968034i
$89$	3.00487	+	17.0415i	0.318516	+	1.80639i	0.551791	+	0.833982i	$0.313944\pi$
$89$	3.00487	+	17.0415i	0.318516	+	1.80639i	−0.233276	+	0.972411i	$0.574944\pi$
$90$		0			0
$91$	7.77297	−	6.52229i	0.814828	−	0.683722i
$92$	−4.59011	+	26.0318i	−0.478552	+	2.71400i
$93$	9.50539	−	3.45968i	0.985664	−	0.358752i
$94$	−5.45702			−0.562849
$95$		0			0
$96$	7.42673			0.757988
$97$	−0.122107	+	0.0444434i	−0.0123981	+	0.00451254i	−0.348212	−	0.937416i	$-0.613211\pi$
$97$	−0.122107	+	0.0444434i	−0.0123981	+	0.00451254i	0.335814	+	0.941928i	$0.390989\pi$
$98$	−1.77901	+	10.0893i	−0.179707	+	1.01917i
$99$	4.64207	−	3.89516i	0.466546	−	0.391478i
$100$		0			0
$101$	0.648657	+	3.67872i	0.0645438	+	0.366046i	0.999923	+	0.0123999i	$0.00394711\pi$
$101$	0.648657	+	3.67872i	0.0645438	+	0.366046i	−0.935379	+	0.353646i	$0.884942\pi$
$102$	8.46419	+	14.6604i	0.838080	+	1.45160i
$103$	−3.29977	+	5.71537i	−0.325136	+	0.563152i	−0.981540	−	0.191258i	$-0.938743\pi$
$103$	−3.29977	+	5.71537i	−0.325136	+	0.563152i	0.656404	+	0.754410i	$0.272077\pi$
$104$	22.3960	+	8.15148i	2.19611	+	0.799319i
$105$		0			0
$106$	−7.54427	+	13.0671i	−0.732764	+	1.26918i
$107$	−5.89764	−	10.2150i	−0.570146	−	0.987522i	−0.996550	−	0.0829897i	$-0.973553\pi$
$107$	−5.89764	−	10.2150i	−0.570146	−	0.987522i	0.426404	−	0.904533i	$-0.359780\pi$
$108$	1.11836	+	6.34253i	0.107614	+	0.610310i
$109$	5.54468	+	4.65254i	0.531084	+	0.445632i	0.868475	−	0.495732i	$-0.165100\pi$
$109$	5.54468	+	4.65254i	0.531084	+	0.445632i	−0.337392	+	0.941364i	$0.609545\pi$
$110$		0			0
$111$	−0.809547	+	4.59117i	−0.0768388	+	0.435774i
$112$	2.87958	−	1.04808i	0.272095	−	0.0990345i
$113$	−13.2879			−1.25002			−0.625010	−	0.780616i	$-0.714905\pi$
$113$	−13.2879			−1.25002			−0.625010	+	0.780616i	$0.714905\pi$
$114$	17.3508	+	16.0212i	1.62505	+	1.50052i
$115$		0			0
$116$	−7.57432	+	2.75683i	−0.703258	+	0.255965i
$117$	−2.39173	+	13.5642i	−0.221115	+	1.25401i
$118$	22.2785	−	18.6939i	2.05090	−	1.72091i
$119$	−3.91763	−	3.28728i	−0.359129	−	0.301345i
$120$		0			0
$121$	1.78043	+	3.08380i	0.161858	+	0.280345i
$122$	5.67937	−	9.83695i	0.514186	−	0.890596i
$123$	8.42779	+	3.06747i	0.759909	+	0.276584i
$124$	−15.0643	−	5.48296i	−1.35282	−	0.492384i
$125$		0			0
$126$	4.31102	+	7.46691i	0.384057	+	0.665205i
$127$	1.50964	+	8.56161i	0.133959	+	0.759720i	0.975579	+	0.219650i	$0.0704914\pi$
$127$	1.50964	+	8.56161i	0.133959	+	0.759720i	−0.841620	+	0.540071i	$0.818397\pi$
$128$	−15.8172	−	13.2722i	−1.39806	−	1.17311i
$129$	0.827735	−	0.694552i	0.0728780	−	0.0611519i
$130$		0			0
$131$	−9.90994	+	3.60692i	−0.865835	+	0.315138i	−0.736479	−	0.676460i	$-0.763513\pi$
$131$	−9.90994	+	3.60692i	−0.865835	+	0.315138i	−0.129356	+	0.991598i	$0.541291\pi$
$132$	−22.5713			−1.96458
$133$	−6.58098	−	2.75538i	−0.570643	−	0.238922i
$134$	1.59083			0.137426
$135$		0			0
$136$	2.08589	−	11.8297i	0.178864	−	1.01439i
$137$	−0.304287	+	0.255327i	−0.0259970	+	0.0218141i	−0.655694	−	0.755027i	$-0.727624\pi$
$137$	−0.304287	+	0.255327i	−0.0259970	+	0.0218141i	0.629697	+	0.776841i	$0.283179\pi$
$138$	30.2938	+	25.4195i	2.57878	+	2.16385i
$139$	−1.30330	−	7.39141i	−0.110545	−	0.626931i	−0.988860	−	0.148849i	$-0.952443\pi$
$139$	−1.30330	−	7.39141i	−0.110545	−	0.626931i	0.878315	−	0.478082i	$-0.158668\pi$
$140$		0			0
$141$	−2.62971	+	4.55480i	−0.221462	+	0.383583i
$142$	−5.87059	−	2.13672i	−0.492649	−	0.179310i
$143$	15.8888	+	5.78306i	1.32869	+	0.483604i
$144$	−2.07980	+	3.60232i	−0.173317	+	0.300194i
$145$		0			0
$146$	2.68149	+	15.2075i	0.221922	+	1.25858i
$147$	7.56387	+	6.34684i	0.623858	+	0.523479i
$148$	5.65985	−	4.74918i	0.465237	−	0.390380i
$149$	−0.640034	+	3.62981i	−0.0524336	+	0.297366i	−0.999736	−	0.0229749i	$-0.992686\pi$
$149$	−0.640034	+	3.62981i	−0.0524336	+	0.297366i	0.947302	+	0.320341i	$0.103797\pi$
$150$		0			0
$151$	−4.49051			−0.365433			−0.182716	−	0.983166i	$-0.558489\pi$
$151$	−4.49051			−0.365433			−0.182716	+	0.983166i	$0.558489\pi$
$152$	−2.12396	−	16.6227i	−0.172276	−	1.34828i
$153$	6.94189			0.561219
$154$	9.94629	−	3.62015i	0.801495	−	0.291720i
$155$		0			0
$156$	39.3002	−	32.9768i	3.14653	−	2.64025i
$157$	15.5240	+	13.0262i	1.23895	+	1.03960i	0.997605	+	0.0691635i	$0.0220330\pi$
$157$	15.5240	+	13.0262i	1.23895	+	1.03960i	0.241345	+	0.970439i	$0.422411\pi$
$158$	1.69633	+	9.62037i	0.134953	+	0.765355i
$159$	7.27109	+	12.5939i	0.576635	+	0.998761i
$160$		0			0
$161$	−11.2264	−	4.08607i	−0.884762	−	0.322027i
$162$	23.9042	+	8.70040i	1.87809	+	0.683568i
$163$	−7.82949	+	13.5611i	−0.613253	+	1.06219i	0.377436	+	0.926036i	$0.376806\pi$
$163$	−7.82949	+	13.5611i	−0.613253	+	1.06219i	−0.990688	+	0.136149i	$0.956527\pi$
$164$	−7.10685	−	12.3094i	−0.554952	−	0.961205i
$165$		0			0
$166$	−11.6676	−	9.79030i	−0.905583	−	0.759875i
$167$	4.63128	−	3.88610i	0.358379	−	0.300716i	−0.445765	−	0.895150i	$-0.647068\pi$
$167$	4.63128	−	3.88610i	0.358379	−	0.300716i	0.804144	+	0.594434i	$0.202624\pi$
$168$	2.49693	−	14.1608i	0.192643	−	1.09253i
$169$	−23.8980	+	8.69815i	−1.83831	+	0.669088i
$170$		0			0
$171$	9.24723	−	2.87692i	0.707153	−	0.220003i
$172$	−1.71244			−0.130573
$173$	−1.54147	+	0.561050i	−0.117196	+	0.0426558i	−0.399952	−	0.916536i	$-0.630973\pi$
$173$	−1.54147	+	0.561050i	−0.117196	+	0.0426558i	0.282757	+	0.959192i	$0.408751\pi$
$174$	−2.09399	+	11.8756i	−0.158745	+	0.900288i
$175$		0			0
$176$	3.91175	+	3.28235i	0.294859	+	0.247416i
$177$	−4.86726	−	27.6036i	−0.365845	−	2.07481i
$178$	−20.5141	−	35.5314i	−1.53759	−	2.66319i
$179$	7.09424	−	12.2876i	0.530248	−	0.918417i	−0.469129	−	0.883130i	$-0.655432\pi$
$179$	7.09424	−	12.2876i	0.530248	−	0.918417i	0.999377	−	0.0352872i	$-0.0112346\pi$
$180$		0			0
$181$	−21.5620	−	7.84794i	−1.60269	−	0.583333i	−0.622718	−	0.782446i	$-0.713972\pi$
$181$	−21.5620	−	7.84794i	−1.60269	−	0.583333i	−0.979976	+	0.199113i	$0.936194\pi$
$182$	−12.0290	+	20.8348i	−0.891647	+	1.54438i
$183$	−5.47372	−	9.48076i	−0.404629	−	0.700838i
$184$	−4.87277	−	27.6349i	−0.359226	−	2.03727i
$185$		0			0
$186$	−18.3723	+	15.4162i	−1.34712	+	1.13037i
$187$	1.47983	−	8.39256i	0.108216	−	0.613724i
$188$	7.83255	−	2.85082i	0.571248	−	0.207917i
$189$	−2.91080			−0.211729
$190$		0			0
$191$	10.2099			0.738762			0.369381	−	0.929278i	$-0.379570\pi$
$191$	10.2099			0.738762			0.369381	+	0.929278i	$0.379570\pi$
$192$	−24.5871	+	8.94896i	−1.77442	+	0.645835i
$193$	−2.05447	+	11.6515i	−0.147884	+	0.838693i	0.817122	+	0.576465i	$0.195568\pi$
$193$	−2.05447	+	11.6515i	−0.147884	+	0.838693i	−0.965006	+	0.262228i	$0.915543\pi$
$194$	0.236012	−	0.198038i	0.0169447	−	0.0142183i
$195$		0			0
$196$	−2.71731	−	15.4106i	−0.194094	−	1.10076i
$197$	−1.36337	−	2.36143i	−0.0971363	−	0.168245i	0.813362	−	0.581758i	$-0.197635\pi$
$197$	−1.36337	−	2.36143i	−0.0971363	−	0.168245i	−0.910498	+	0.413513i	$0.864302\pi$
$198$	−7.18379	+	12.4427i	−0.510529	+	0.884263i
$199$	−4.20830	−	1.53170i	−0.298319	−	0.108579i	0.188525	−	0.982068i	$-0.439629\pi$
$199$	−4.20830	−	1.53170i	−0.298319	−	0.108579i	−0.486843	+	0.873489i	$0.661852\pi$
$200$		0			0
$201$	0.766611	−	1.32781i	0.0540726	−	0.0936564i
$202$	−4.42834	−	7.67010i	−0.311577	−	0.539666i
$203$	−0.632600	−	3.58765i	−0.0443998	−	0.251804i
$204$	−19.8076	−	16.6205i	−1.38681	−	1.16367i
$205$		0			0
$206$	2.71712	−	15.4096i	0.189311	−	1.07364i
$207$	15.2387	−	5.54643i	1.05916	−	0.385504i
$208$	−11.6065			−0.804764
$209$	−1.50684	−	11.7929i	−0.104230	−	0.815733i
$210$		0			0
$211$	6.89756	−	2.51051i	0.474847	−	0.172830i	−0.0934995	−	0.995619i	$-0.529805\pi$
$211$	6.89756	−	2.51051i	0.474847	−	0.172830i	0.568347	+	0.822789i	$0.307583\pi$
$212$	4.00202	−	22.6966i	0.274860	−	1.55881i
$213$	−4.61246	+	3.87031i	−0.316041	+	0.265189i
$214$	21.4234	+	17.9763i	1.46447	+	1.22884i
$215$		0			0
$216$	−3.41849	−	5.92100i	−0.232599	−	0.402873i
$217$	3.62272	−	6.27473i	0.245926	−	0.425956i
$218$	−16.1263	−	5.86948i	−1.09221	−	0.397532i
$219$	13.9854	+	5.09026i	0.945044	+	0.343968i
$220$		0			0
$221$	9.68493	+	16.7748i	0.651479	+	1.12839i
$222$	−1.91941	−	10.8855i	−0.128822	−	0.730588i
$223$	12.7019	+	10.6581i	0.850580	+	0.713721i	0.959917	−	0.280284i	$-0.0904285\pi$
$223$	12.7019	+	10.6581i	0.850580	+	0.713721i	−0.109338	+	0.994005i	$0.534873\pi$
$224$	4.07504	−	3.41936i	0.272275	−	0.228466i
$225$		0			0
$226$	29.6052	−	10.7754i	1.96931	−	0.716770i
$227$	−11.7828			−0.782052			−0.391026	−	0.920380i	$-0.627880\pi$
$227$	−11.7828			−0.782052			−0.391026	+	0.920380i	$0.627880\pi$
$228$	−33.2735	−	13.9312i	−2.20359	−	0.922617i
$229$	−7.82331			−0.516979			−0.258490	−	0.966014i	$-0.583225\pi$
$229$	−7.82331			−0.516979			−0.258490	+	0.966014i	$0.583225\pi$
$230$		0			0
$231$	1.77145	−	10.0464i	0.116553	−	0.661003i
$232$	6.55488	−	5.50020i	0.430349	−	0.361106i
$233$	5.14763	+	4.31937i	0.337232	+	0.282971i	0.795639	−	0.605771i	$-0.207135\pi$
$233$	5.14763	+	4.31937i	0.337232	+	0.282971i	−0.458407	+	0.888742i	$0.651580\pi$
$234$	−5.67071	−	32.1602i	−0.370706	−	2.10238i
$235$		0			0
$236$	−22.2107	+	38.4701i	−1.44580	+	2.50419i
$237$	8.84726	+	3.22014i	0.574691	+	0.209170i
$238$	11.3941	+	4.14713i	0.738572	+	0.268818i
$239$	7.98728	−	13.8344i	0.516654	−	0.894871i	−0.483159	−	0.875533i	$-0.660511\pi$
$239$	7.98728	−	13.8344i	0.516654	−	0.894871i	0.999813	−	0.0193382i	$-0.00615593\pi$
$240$		0			0
$241$	1.81557	+	10.2966i	0.116951	+	0.663261i	0.985766	+	0.168124i	$0.0537710\pi$
$241$	1.81557	+	10.2966i	0.116951	+	0.663261i	−0.868815	+	0.495137i	$0.835118\pi$
$242$	−6.46748	−	5.42686i	−0.415746	−	0.348852i
$243$	14.6943	−	12.3300i	0.942639	−	0.790968i
$244$	−3.01274	+	17.0861i	−0.192871	+	1.09383i
$245$		0			0
$246$	−21.2644			−1.35577
$247$	19.8531	+	18.3318i	1.26322	+	1.16642i
$248$	17.0183			1.08066
$249$	−13.7942	+	5.02068i	−0.874172	+	0.318173i
$250$		0			0
$251$	−9.08999	+	7.62741i	−0.573755	+	0.481438i	−0.882890	−	0.469581i	$-0.844405\pi$
$251$	−9.08999	+	7.62741i	−0.573755	+	0.481438i	0.309135	+	0.951018i	$0.399961\pi$
$252$	−10.0885	−	8.46525i	−0.635515	−	0.533260i
$253$	−3.45698	−	19.6055i	−0.217339	−	1.23259i
$254$	−10.3062	−	17.8509i	−0.646670	−	1.12007i
$255$		0			0
$256$	24.4839	+	8.91141i	1.53024	+	0.556963i
$257$	3.58614	+	1.30525i	0.223697	+	0.0814191i	0.451437	−	0.892303i	$-0.350911\pi$
$257$	3.58614	+	1.30525i	0.223697	+	0.0814191i	−0.227740	+	0.973722i	$0.573134\pi$
$258$	−1.28095	+	2.21868i	−0.0797486	+	0.138129i
$259$	1.66963	+	2.89189i	0.103746	+	0.179693i
$260$		0			0
$261$	3.78810	+	3.17859i	0.234477	+	0.196750i
$262$	19.1542	−	16.0723i	1.18335	−	0.992951i
$263$	−0.368060	+	2.08737i	−0.0226956	+	0.128713i	−0.994050	−	0.108921i	$-0.965261\pi$
$263$	−0.368060	+	2.08737i	−0.0226956	+	0.128713i	0.971355	+	0.237633i	$0.0763717\pi$
$264$	22.5162	−	8.19524i	1.38578	−	0.504382i
$265$		0			0
$266$	16.8967	+	0.802292i	1.03600	+	0.0491917i
$267$	−39.5425			−2.41996
$268$	−2.28334	+	0.831067i	−0.139477	+	0.0507655i
$269$	−0.682137	+	3.86859i	−0.0415906	+	0.235872i	−0.998516	−	0.0544625i	$-0.982655\pi$
$269$	−0.682137	+	3.86859i	−0.0415906	+	0.235872i	0.956925	+	0.290335i	$0.0937666\pi$
$270$		0			0
$271$	14.5057	+	12.1717i	0.881159	+	0.739380i	0.966417	−	0.256979i	$-0.0827271\pi$
$271$	14.5057	+	12.1717i	0.881159	+	0.739380i	−0.0852584	+	0.996359i	$0.527172\pi$
$272$	1.01580	+	5.76088i	0.0615918	+	0.349305i
$273$	11.5934	+	20.0804i	0.701665	+	1.21532i
$274$	0.470897	−	0.815617i	0.0284479	−	0.0492732i
$275$		0			0
$276$	−56.7606	−	20.6592i	−3.41659	−	1.24354i
$277$	−7.51370	+	13.0141i	−0.451454	+	0.781942i	−0.998477	−	0.0551762i	$-0.982428\pi$
$277$	−7.51370	+	13.0141i	−0.451454	+	0.781942i	0.547022	+	0.837118i	$0.315761\pi$
$278$	8.89757	+	15.4110i	0.533641	+	0.924293i
$279$	1.70782	+	9.68554i	0.102245	+	0.579858i
$280$		0			0
$281$	21.0532	−	17.6657i	1.25593	−	1.05385i	0.259826	−	0.965655i	$-0.416335\pi$
$281$	21.0532	−	17.6657i	1.25593	−	1.05385i	0.996103	−	0.0881948i	$-0.0281098\pi$
$282$	2.16538	−	12.2805i	0.128947	−	0.731292i
$283$	−19.1093	+	6.95521i	−1.13593	+	0.413444i	−0.840442	−	0.541902i	$-0.817704\pi$
$283$	−19.1093	+	6.95521i	−1.13593	+	0.413444i	−0.295488	+	0.955347i	$0.595482\pi$
$284$	9.54240			0.566237
$285$		0			0
$286$	−40.0896			−2.37055
$287$	6.03662	−	2.19715i	0.356330	−	0.129694i
$288$	−1.25388	+	7.11111i	−0.0738856	+	0.419026i
$289$	−5.54421	+	4.65214i	−0.326130	+	0.273656i
$290$		0			0
$291$	−0.0515625	−	0.292425i	−0.00302265	−	0.0171423i
$292$	−11.7934	−	20.4267i	−0.690154	−	1.19538i
$293$	−2.29329	+	3.97210i	−0.133976	+	0.232053i	−0.925206	−	0.379466i	$-0.876108\pi$
$293$	−2.29329	+	3.97210i	−0.133976	+	0.232053i	0.791230	+	0.611519i	$0.209441\pi$
$294$	−21.9989	−	8.00696i	−1.28300	−	0.466975i
$295$		0			0
$296$	−3.92169	+	6.79257i	−0.227944	+	0.394810i
$297$	−2.42524	−	4.20064i	−0.140727	−	0.243746i
$298$	−1.51750	−	8.60617i	−0.0879064	−	0.498542i
$299$	34.6628	+	29.0856i	2.00460	+	1.68206i
$300$		0			0
$301$	0.134396	−	0.762200i	0.00774648	−	0.0439325i
$302$	10.0048	−	3.64144i	0.575710	−	0.209541i
$303$	−8.53597			−0.490379
$304$	3.74061	+	7.25303i	0.214538	+	0.415990i
$305$		0			0
$306$	−15.4664	+	5.62931i	−0.884156	+	0.321806i
$307$	−4.22361	+	23.9533i	−0.241054	+	1.36709i	0.588426	+	0.808551i	$0.299748\pi$
$307$	−4.22361	+	23.9533i	−0.241054	+	1.36709i	−0.829480	+	0.558536i	$0.811363\pi$
$308$	−12.3849	+	10.3921i	−0.705692	+	0.592146i
$309$	−11.5525	−	9.69369i	−0.657198	−	0.551455i
$310$		0			0
$311$	−11.0103	−	19.0703i	−0.624334	−	1.08138i	−0.988669	−	0.150111i	$-0.952037\pi$
$311$	−11.0103	−	19.0703i	−0.624334	−	1.08138i	0.364335	−	0.931268i	$-0.381296\pi$
$312$	−27.2310	+	47.1654i	−1.54165	+	2.67022i
$313$	27.7037	+	10.0833i	1.56591	+	0.569943i	0.972080	−	0.234649i	$-0.0753942\pi$
$313$	27.7037	+	10.0833i	1.56591	+	0.569943i	0.593827	+	0.804593i	$0.297616\pi$
$314$	−45.1504	−	16.4334i	−2.54798	−	0.927390i
$315$		0			0
$316$	−7.46057	−	12.9221i	−0.419690	−	0.726924i
$317$	1.39668	+	7.92095i	0.0784452	+	0.444885i	0.998580	+	0.0532818i	$0.0169682\pi$
$317$	1.39668	+	7.92095i	0.0784452	+	0.444885i	−0.920134	+	0.391603i	$0.871921\pi$
$318$	−26.4125	−	22.1627i	−1.48114	−	1.24282i
$319$	4.65035	−	3.90211i	0.260370	−	0.218476i
$320$		0			0
$321$	25.3281	−	9.21867i	1.41368	−	0.514536i
$322$	28.3256			1.57853
$323$	7.36145	−	11.4585i	0.409602	−	0.637568i
$324$	−38.8552			−2.15862
$325$		0			0
$326$	6.44702	−	36.5629i	0.357068	−	2.02503i
$327$	−12.6702	+	10.6316i	−0.700666	+	0.587928i
$328$	11.5588	+	9.69901i	0.638230	+	0.535538i
$329$	0.654167	+	3.70997i	0.0360654	+	0.204537i
$330$		0			0
$331$	−9.10916	+	15.7775i	−0.500685	+	0.867212i	0.499315	+	0.866421i	$0.333585\pi$
$331$	−9.10916	+	15.7775i	−0.500685	+	0.867212i	−1.00000		0.000790925i	$0.999748\pi$
$332$	21.8613	+	7.95686i	1.19979	+	0.436689i
$333$	−4.25937	−	1.55028i	−0.233412	−	0.0849551i
$334$	−7.16709	+	12.4138i	−0.392166	+	0.679251i
$335$		0			0
$336$	1.21597	+	6.89610i	0.0663365	+	0.376213i
$337$	−7.35654	−	6.17287i	−0.400736	−	0.336258i	0.420042	−	0.907505i	$-0.362015\pi$
$337$	−7.35654	−	6.17287i	−0.400736	−	0.336258i	−0.820778	+	0.571247i	$0.806460\pi$
$338$	46.1907	−	38.7586i	2.51244	−	2.10819i
$339$	5.27272	−	29.9031i	0.286375	−	1.62411i
$340$		0			0
$341$	12.0736			0.653823
$342$	−18.2697	+	13.9085i	−0.987912	+	0.752084i
$343$	18.5299			1.00052
$344$	1.70826	−	0.621757i	0.0921035	−	0.0335229i
$345$		0			0
$346$	2.97940	−	2.50002i	0.160174	−	0.134402i
$347$	−0.970021	−	0.813944i	−0.0520734	−	0.0436948i	0.616379	−	0.787449i	$-0.288599\pi$
$347$	−0.970021	−	0.813944i	−0.0520734	−	0.0436948i	−0.668453	+	0.743754i	$0.733043\pi$
$348$	−3.19843	−	18.1392i	−0.171454	−	0.972363i
$349$	−13.3074	−	23.0491i	−0.712330	−	1.23379i	−0.963980	−	0.265974i	$-0.914307\pi$
$349$	−13.3074	−	23.0491i	−0.712330	−	1.23379i	0.251650	−	0.967818i	$-0.419027\pi$
$350$		0			0
$351$	10.3599	+	3.77068i	0.552969	+	0.201264i
$352$	8.32983	+	3.03181i	0.443982	+	0.161596i
$353$	−13.4371	+	23.2738i	−0.715187	+	1.23874i	0.247701	+	0.968837i	$0.420325\pi$
$353$	−13.4371	+	23.2738i	−0.715187	+	1.23874i	−0.962888	+	0.269903i	$0.913008\pi$
$354$	33.2284	+	57.5533i	1.76607	+	3.05892i
$355$		0			0
$356$	48.0062	+	40.2820i	2.54432	+	2.13494i
$357$	8.95225	−	7.51183i	0.473803	−	0.397568i
$358$	−5.84160	+	33.1294i	−0.308738	+	1.75094i
$359$	19.7868	−	7.20180i	1.04431	−	0.380097i	0.237795	−	0.971315i	$-0.423575\pi$
$359$	19.7868	−	7.20180i	1.04431	−	0.380097i	0.806511	+	0.591219i	$0.201353\pi$
$360$		0			0
$361$	5.05739	−	18.3146i	0.266178	−	0.963924i
$362$	54.4039			2.85940
$363$	−7.64627	+	2.78302i	−0.401325	+	0.146070i
$364$	6.38103	−	36.1886i	0.334457	−	1.89680i
$365$		0			0
$366$	19.8835	+	16.6842i	1.03933	+	0.872098i
$367$	1.91320	+	10.8503i	0.0998682	+	0.566381i	0.993146	+	0.116877i	$0.0372882\pi$
$367$	1.91320	+	10.8503i	0.0998682	+	0.566381i	−0.893278	+	0.449504i	$0.851601\pi$
$368$	6.83268	+	11.8346i	0.356178	+	0.616919i
$369$	−4.36000	+	7.55174i	−0.226972	+	0.393128i
$370$		0			0
$371$	9.78803	+	3.56255i	0.508169	+	0.184959i
$372$	18.3165	−	31.7251i	0.949665	−	1.64487i
$373$	2.41654	+	4.18558i	0.125124	+	0.216721i	0.921781	−	0.387710i	$-0.126734\pi$
$373$	2.41654	+	4.18558i	0.125124	+	0.216721i	−0.796657	+	0.604431i	$0.793401\pi$
$374$	3.50864	+	19.8985i	0.181427	+	1.02893i
$375$		0			0
$376$	−6.77836	+	5.68772i	−0.349567	+	0.293322i
$377$	−2.39599	+	13.5884i	−0.123400	+	0.699836i
$378$	6.48520	−	2.36042i	0.333563	−	0.121407i
$379$	2.03721			0.104644			0.0523221	−	0.998630i	$-0.483338\pi$
$379$	2.03721			0.104644			0.0523221	+	0.998630i	$0.483338\pi$
$380$		0			0
$381$	−19.8661			−1.01777
$382$	−22.7475	+	8.27940i	−1.16386	+	0.423611i
$383$	6.00483	−	34.0551i	0.306833	−	1.74013i	−0.307918	−	0.951413i	$-0.599632\pi$
$383$	6.00483	−	34.0551i	0.306833	−	1.74013i	0.614751	−	0.788721i	$-0.289257\pi$
$384$	36.1442	−	30.3286i	1.84448	−	1.54770i
$385$		0			0
$386$	−4.87109	−	27.6253i	−0.247932	−	1.40609i
$387$	0.525286	+	0.909821i	0.0267018	+	0.0462488i
$388$	−0.235295	+	0.407543i	−0.0119453	+	0.0206899i
$389$	4.25700	+	1.54942i	0.215839	+	0.0785588i	0.447676	−	0.894196i	$-0.352252\pi$
$389$	4.25700	+	1.54942i	0.215839	+	0.0785588i	−0.231838	+	0.972754i	$0.574474\pi$
$390$		0			0
$391$	11.4029	−	19.7505i	0.576672	−	0.998825i
$392$	8.30601	+	14.3864i	0.419517	+	0.726624i
$393$	−4.18469	−	23.7326i	−0.211090	−	1.19715i
$394$	4.95250	+	4.15564i	0.249503	+	0.209358i
$395$		0			0
$396$	3.81079	−	21.6121i	0.191500	−	1.08605i
$397$	−23.6190	+	8.59660i	−1.18540	+	0.431451i	−0.858107	−	0.513471i	$-0.828359\pi$
$397$	−23.6190	+	8.59660i	−1.18540	+	0.431451i	−0.327295	+	0.944922i	$0.606137\pi$
$398$	10.6181			0.532237
$399$	8.81208	−	13.7165i	0.441156	−	0.686683i
$400$		0			0
$401$	−27.1680	+	9.88834i	−1.35671	+	0.493800i	−0.915034	−	0.403377i	$-0.867836\pi$
$401$	−27.1680	+	9.88834i	−1.35671	+	0.493800i	−0.441671	+	0.897177i	$0.645614\pi$
$402$	−0.631249	+	3.57999i	−0.0314839	+	0.178554i
$403$	−21.0220	+	17.6396i	−1.04718	+	0.878690i
$404$	10.3630	+	8.69560i	0.515579	+	0.432622i
$405$		0			0
$406$	4.31872	+	7.48024i	0.214334	+	0.371238i
$407$	−2.78224	+	4.81898i	−0.137910	+	0.238868i
$408$	25.7938	+	9.38819i	1.27699	+	0.464785i
$409$	21.5769	+	7.85333i	1.06691	+	0.388322i	0.815019	−	0.579434i	$-0.196726\pi$
$409$	21.5769	+	7.85333i	1.06691	+	0.388322i	0.251888	+	0.967756i	$0.418949\pi$
$410$		0			0
$411$	−0.453845	−	0.786083i	−0.0223865	−	0.0387746i
$412$	4.15022	+	23.5371i	0.204467	+	1.15959i
$413$	−15.3797	−	12.9051i	−0.756785	−	0.635018i
$414$	−29.4538	+	24.7147i	−1.44758	+	1.21466i
$415$		0			0
$416$	−18.9330	+	6.89106i	−0.928268	+	0.337862i
$417$	17.1508			0.839877
$418$	12.9203	+	25.0525i	0.631953	+	1.22536i
$419$	8.98058			0.438730			0.219365	−	0.975643i	$-0.429601\pi$
$419$	8.98058			0.438730			0.219365	+	0.975643i	$0.429601\pi$
$420$		0			0
$421$	−5.91109	+	33.5235i	−0.288089	+	1.63383i	0.405949	+	0.913896i	$0.366941\pi$
$421$	−5.91109	+	33.5235i	−0.288089	+	1.63383i	−0.694038	+	0.719938i	$0.744170\pi$
$422$	−13.3318	+	11.1867i	−0.648983	+	0.544561i
$423$	−3.91724	−	3.28696i	−0.190463	−	0.159817i
$424$	4.24846	+	24.0942i	0.206324	+	1.17012i
$425$		0			0
$426$	7.13796	−	12.3633i	0.345835	−	0.599005i
$427$	−7.36848	−	2.68191i	−0.356586	−	0.129787i
$428$	−40.1404	−	14.6099i	−1.94026	−	0.706196i
$429$	−19.3190	+	33.4615i	−0.932729	+	1.61553i
$430$		0			0
$431$	6.59394	+	37.3961i	0.317619	+	1.80131i	0.557144	+	0.830416i	$0.311897\pi$
$431$	6.59394	+	37.3961i	0.317619	+	1.80131i	−0.239525	+	0.970890i	$0.576992\pi$
$432$	2.55055	+	2.14016i	0.122713	+	0.102969i
$433$	−28.3283	+	23.7703i	−1.36137	+	1.14233i	−0.385814	+	0.922576i	$0.626079\pi$
$433$	−28.3283	+	23.7703i	−1.36137	+	1.14233i	−0.975556	+	0.219749i	$0.929476\pi$
$434$	−2.98305	+	16.9177i	−0.143191	+	0.812076i
$435$		0			0
$436$	26.2126			1.25535
$437$	7.00459	−	31.0351i	0.335075	−	1.48461i
$438$	−35.2869			−1.68607
$439$	−20.8452	+	7.58705i	−0.994889	+	0.362110i	−0.787611	−	0.616172i	$-0.788682\pi$
$439$	−20.8452	+	7.58705i	−0.994889	+	0.362110i	−0.207277	+	0.978282i	$0.566460\pi$
$440$		0			0
$441$	−7.35415	+	6.17086i	−0.350198	+	0.293851i
$442$	−35.1808	−	29.5202i	−1.67338	−	1.40413i
$443$	−1.71023	−	9.69917i	−0.0812553	−	0.460822i	−0.998102	−	0.0615822i	$-0.980385\pi$
$443$	−1.71023	−	9.69917i	−0.0812553	−	0.460822i	0.916847	−	0.399239i	$-0.130726\pi$
$444$	8.44168	+	14.6214i	0.400625	+	0.693902i
$445$		0			0
$446$	−36.9424	−	13.4459i	−1.74927	−	0.636683i
$447$	−7.91456	−	2.88066i	−0.374346	−	0.136251i
$448$	−9.37067	+	16.2305i	−0.442723	+	0.766818i
$449$	18.6520	+	32.3061i	0.880240	+	1.52462i	0.851073	+	0.525047i	$0.175952\pi$
$449$	18.6520	+	32.3061i	0.880240	+	1.52462i	0.0291671	+	0.999575i	$0.490715\pi$
$450$		0			0
$451$	8.20040	+	6.88095i	0.386142	+	0.324011i
$452$	−36.8636	+	30.9322i	−1.73392	+	1.45493i
$453$	1.78186	−	10.1054i	0.0837192	−	0.474795i
$454$	26.2519	−	9.55490i	1.23206	−	0.448434i
$455$		0			0
$456$	38.2504	+	1.81622i	1.79124	+	0.0850521i
$457$	14.0343			0.656498			0.328249	−	0.944591i	$-0.393542\pi$
$457$	14.0343			0.656498			0.328249	+	0.944591i	$0.393542\pi$
$458$	17.4302	−	6.34407i	0.814460	−	0.296439i
$459$	0.964885	−	5.47214i	0.0450370	−	0.255417i
$460$		0			0
$461$	−7.76457	−	6.51525i	−0.361632	−	0.303445i	0.443809	−	0.896122i	$-0.353627\pi$
$461$	−7.76457	−	6.51525i	−0.361632	−	0.303445i	−0.805441	+	0.592676i	$0.798071\pi$
$462$	4.20004	+	23.8196i	0.195404	+	1.10819i
$463$	0.361065	+	0.625383i	0.0167801	+	0.0290640i	0.874294	−	0.485398i	$-0.161325\pi$
$463$	0.361065	+	0.625383i	0.0167801	+	0.0290640i	−0.857513	+	0.514462i	$0.827992\pi$
$464$	−2.08351	+	3.60875i	−0.0967247	+	0.167532i
$465$		0			0
$466$	−14.9715	−	5.44917i	−0.693540	−	0.252428i
$467$	17.5086	−	30.3258i	0.810201	−	1.40331i	−0.102522	−	0.994731i	$-0.532691\pi$
$467$	17.5086	−	30.3258i	0.810201	−	1.40331i	0.912723	−	0.408579i	$-0.133976\pi$
$468$	24.9401	+	43.1976i	1.15286	+	1.99681i
$469$	−0.190702	−	1.08152i	−0.00880580	−	0.0499402i
$470$		0			0
$471$	−35.4742	+	29.7664i	−1.63456	+	1.37156i
$472$	8.18872	−	46.4406i	0.376917	−	2.13760i
$473$	1.21193	−	0.441105i	0.0557244	−	0.0202820i
$474$	−22.3228			−1.02532
$475$		0			0
$476$	−18.5207			−0.848895
$477$	−13.2863	+	4.83581i	−0.608337	+	0.221417i
$478$	−6.57695	+	37.2997i	−0.300823	+	1.70605i
$479$	−20.6527	+	17.3296i	−0.943645	+	0.791812i	−0.978216	−	0.207590i	$-0.933438\pi$
$479$	−20.6527	+	17.3296i	−0.943645	+	0.791812i	0.0345713	+	0.999402i	$0.488993\pi$
$480$		0			0
$481$	−2.19623	−	12.4555i	−0.100140	−	0.567920i
$482$	−12.3947	−	21.4683i	−0.564565	−	0.977855i
$483$	13.6500	−	23.6425i	0.621096	−	1.07577i
$484$	12.1179	+	4.41057i	0.550816	+	0.200480i
$485$		0			0
$486$	−22.7400	+	39.3868i	−1.03151	+	1.78662i
$487$	−1.53379	−	2.65660i	−0.0695026	−	0.120382i	0.829180	−	0.558982i	$-0.188808\pi$
$487$	−1.53379	−	2.65660i	−0.0695026	−	0.120382i	−0.898682	+	0.438600i	$0.855475\pi$
$488$	−3.19827	−	18.1383i	−0.144779	−	0.821081i
$489$	−27.4110	−	23.0006i	−1.23957	−	1.04012i
$490$		0			0
$491$	0.216866	−	1.22991i	0.00978703	−	0.0555050i	−0.979523	−	0.201332i	$-0.935473\pi$
$491$	0.216866	−	1.22991i	0.00978703	−	0.0555050i	0.989310	+	0.145827i	$0.0465842\pi$
$492$	30.5212	−	11.1088i	1.37600	−	0.500823i
$493$	6.95428			0.313205
$494$	−59.0980	−	24.7436i	−2.65895	−	1.11327i
$495$		0			0
$496$	−7.78785	+	2.83455i	−0.349685	+	0.127275i
$497$	−0.748908	+	4.24727i	−0.0335931	+	0.190516i
$498$	26.6619	−	22.3720i	1.19475	−	1.00251i
$499$	14.9931	+	12.5807i	0.671181	+	0.563188i	0.913415	−	0.407030i	$-0.133436\pi$
$499$	14.9931	+	12.5807i	0.671181	+	0.563188i	−0.242233	+	0.970218i	$0.577880\pi$
$500$		0			0
$501$	6.90757	+	11.9643i	0.308607	+	0.534524i
$502$	14.0671	−	24.3650i	0.627846	−	1.08746i
$503$	4.80990	+	1.75066i	0.214463	+	0.0780581i	0.447017	−	0.894525i	$-0.352486\pi$
$503$	4.80990	+	1.75066i	0.214463	+	0.0780581i	−0.232555	+	0.972583i	$0.574708\pi$
$504$	13.1374	+	4.78164i	0.585188	+	0.212991i
$505$		0			0
$506$	23.6006	+	40.8774i	1.04917	+	1.81722i
$507$	−10.0915	−	57.2315i	−0.448177	−	2.54174i
$508$	24.1182	+	20.2376i	1.07007	+	0.897898i
$509$	−12.1303	+	10.1785i	−0.537664	+	0.451154i	−0.870738	−	0.491747i	$-0.836359\pi$
$509$	−12.1303	+	10.1785i	−0.537664	+	0.451154i	0.333074	+	0.942901i	$0.391914\pi$
$510$		0			0
$511$	10.0174	−	3.64603i	0.443143	−	0.161291i
$512$	−20.4803			−0.905108
$513$	−0.982494	−	7.68925i	−0.0433782	−	0.339489i
$514$	−9.04830			−0.399103
$515$		0			0
$516$	0.679509	−	3.85368i	0.0299137	−	0.169649i
$517$	−4.80890	+	4.03514i	−0.211495	+	0.177465i
$518$	−6.06501	−	5.08914i	−0.266481	−	0.223604i
$519$	−0.650921	−	3.69156i	−0.0285723	−	0.162041i
$520$		0			0
$521$	14.9866	−	25.9576i	0.656575	−	1.13722i	−0.324921	−	0.945741i	$-0.605338\pi$
$521$	14.9866	−	25.9576i	0.656575	−	1.13722i	0.981496	−	0.191481i	$-0.0613289\pi$
$522$	−11.0174	−	4.01000i	−0.482218	−	0.175513i
$523$	−28.5446	−	10.3894i	−1.24817	−	0.454296i	−0.368386	−	0.929673i	$-0.620090\pi$
$523$	−28.5446	−	10.3894i	−1.24817	−	0.454296i	−0.879782	+	0.475377i	$0.842312\pi$
$524$	−19.0960	+	33.0752i	−0.834213	+	1.44490i
$525$		0			0
$526$	−0.872659	−	4.94909i	−0.0380497	−	0.215791i
$527$	10.5953	+	8.89048i	0.461537	+	0.387275i
$528$	−8.93880	+	7.50054i	−0.389011	+	0.326419i
$529$	5.25736	−	29.8160i	0.228581	−	1.29635i
$530$		0			0
$531$	27.2522			1.18265
$532$	−24.6712	+	7.67550i	−1.06963	+	0.332775i
$533$	−24.3313			−1.05390
$534$	88.0999	−	32.0658i	3.81246	−	1.38762i
$535$		0			0
$536$	1.97602	−	1.65808i	0.0853510	−	0.0716180i
$537$	24.8369	+	20.8407i	1.07179	+	0.899341i
$538$	−1.61732	−	9.17230i	−0.0697278	−	0.395446i
$539$	5.89268	+	10.2064i	0.253816	+	0.439622i
$540$		0			0
$541$	22.4204	+	8.16035i	0.963927	+	0.350841i	0.775571	−	0.631260i	$-0.217462\pi$
$541$	22.4204	+	8.16035i	0.963927	+	0.350841i	0.188356	+	0.982101i	$0.439684\pi$
$542$	−42.1887	−	15.3554i	−1.81216	−	0.659573i
$543$	26.2170	−	45.4091i	1.12508	−	1.94869i
$544$	5.07740	+	8.79431i	0.217692	+	0.377053i
$545$		0			0
$546$	−42.1135	−	35.3374i	−1.80229	−	1.51230i
$547$	−10.5256	+	8.83204i	−0.450043	+	0.377631i	−0.839452	−	0.543434i	$-0.817124\pi$
$547$	−10.5256	+	8.83204i	−0.450043	+	0.377631i	0.389409	+	0.921065i	$0.372679\pi$
$548$	−0.249797	+	1.41667i	−0.0106708	+	0.0605171i
$549$	10.0020	−	3.64043i	0.426874	−	0.155370i
$550$		0			0
$551$	9.26373	−	2.88205i	0.394648	−	0.122779i
$552$	64.1230			2.72926
$553$	6.33707	−	2.30650i	0.269480	−	0.0980826i
$554$	6.18699	−	35.0882i	0.262860	−	1.49075i
$555$		0			0
$556$	−20.8217	−	17.4715i	−0.883038	−	0.740957i
$557$	−4.69396	−	26.6208i	−0.198889	−	1.12796i	−0.906770	−	0.421626i	$-0.861460\pi$
$557$	−4.69396	−	26.6208i	−0.198889	−	1.12796i	0.707881	−	0.706332i	$-0.249651\pi$
$558$	−11.6592	−	20.1943i	−0.493573	−	0.854893i
$559$	−1.46570	+	2.53866i	−0.0619923	+	0.107374i
$560$		0			0
$561$	18.2994	+	6.66044i	0.772601	+	0.281204i
$562$	−32.5807	+	56.4314i	−1.37433	+	2.38042i
$563$	−19.0839	−	33.0543i	−0.804290	−	1.39307i	−0.916769	−	0.399417i	$-0.869213\pi$
$563$	−19.0839	−	33.0543i	−0.804290	−	1.39307i	0.112479	−	0.993654i	$-0.464121\pi$
$564$	3.30747	+	18.7576i	0.139270	+	0.789838i
$565$		0			0
$566$	36.9350	−	30.9922i	1.55250	−	1.30270i
$567$	3.04944	−	17.2942i	0.128065	−	0.726290i
$568$	−9.51911	+	3.46467i	−0.399413	+	0.145374i
$569$	2.28061			0.0956082			0.0478041	−	0.998857i	$-0.484778\pi$
$569$	2.28061			0.0956082			0.0478041	+	0.998857i	$0.484778\pi$
$570$		0			0
$571$	−14.4656			−0.605367			−0.302683	−	0.953091i	$-0.597883\pi$
$571$	−14.4656			−0.605367			−0.302683	+	0.953091i	$0.597883\pi$
$572$	57.5412	−	20.9433i	2.40592	−	0.875683i
$573$	−4.05135	+	22.9764i	−0.169248	+	0.959851i
$574$	−11.6678	+	9.79042i	−0.487003	+	0.408644i
$575$		0			0
$576$	−4.41753	−	25.0530i	−0.184064	−	1.04388i
$577$	−4.08915	−	7.08262i	−0.170234	−	0.294853i	0.768268	−	0.640128i	$-0.221119\pi$
$577$	−4.08915	−	7.08262i	−0.170234	−	0.294853i	−0.938501	+	0.345275i	$0.887786\pi$
$578$	8.57989	−	14.8608i	0.356876	−	0.618128i
$579$	−25.4053	−	9.24678i	−1.05581	−	0.384283i
$580$		0			0
$581$	−5.25728	+	9.10587i	−0.218109	+	0.377775i
$582$	0.352014	+	0.609705i	0.0145914	+	0.0252731i
$583$	3.01407	+	17.0936i	0.124830	+	0.707945i
$584$	19.1811	+	16.0949i	0.793721	+	0.666011i
$585$		0			0
$586$	1.88836	−	10.7094i	0.0780076	−	0.442403i
$587$	−32.3587	+	11.7776i	−1.33559	+	0.486114i	−0.908420	−	0.418058i	$-0.862711\pi$
$587$	−32.3587	+	11.7776i	−1.33559	+	0.486114i	−0.427168	+	0.904172i	$0.640489\pi$
$588$	35.7584			1.47465
$589$	17.7983	+	7.45194i	0.733366	+	0.307052i
$590$		0			0
$591$	5.85516	−	2.13110i	0.240849	−	0.0876619i
$592$	0.663268	−	3.76158i	0.0272602	−	0.154600i
$593$	−2.03093	+	1.70415i	−0.0834003	+	0.0699812i	−0.683535	−	0.729918i	$-0.739558\pi$
$593$	−2.03093	+	1.70415i	−0.0834003	+	0.0699812i	0.600134	+	0.799899i	$0.295114\pi$
$594$	8.80977	+	7.39228i	0.361469	+	0.303309i
$595$		0			0
$596$	6.67406	+	11.5598i	0.273380	+	0.473508i
$597$	5.11681	−	8.86258i	0.209417	−	0.362721i
$598$	−100.814	−	36.6934i	−4.12260	−	1.50050i
$599$	2.30660	+	0.839535i	0.0942453	+	0.0343025i	0.388712	−	0.921359i	$-0.372920\pi$
$599$	2.30660	+	0.839535i	0.0942453	+	0.0343025i	−0.294467	+	0.955662i	$0.595142\pi$
$600$		0			0
$601$	−7.48153	−	12.9584i	−0.305178	−	0.528584i	0.672123	−	0.740440i	$-0.265383\pi$
$601$	−7.48153	−	12.9584i	−0.305178	−	0.528584i	−0.977301	+	0.211856i	$0.932049\pi$
$602$	0.318649	+	1.80715i	0.0129872	+	0.0736540i
$603$	1.14195	+	0.958210i	0.0465038	+	0.0390213i
$604$	−12.4577	+	10.4532i	−0.506896	+	0.425336i
$605$		0			0
$606$	19.0180	−	6.92198i	0.772553	−	0.281186i
$607$	43.0431			1.74706			0.873532	−	0.486767i	$-0.161824\pi$
$607$	43.0431			1.74706			0.873532	+	0.486767i	$0.161824\pi$
$608$	10.4082	+	9.61059i	0.422106	+	0.389761i
$609$	8.32467			0.337333
$610$		0			0
$611$	2.47768	−	14.0516i	0.100236	−	0.568468i
$612$	19.2584	−	16.1597i	0.778473	−	0.653217i
$613$	30.0229	+	25.1922i	1.21261	+	1.01750i	0.999178	+	0.0405478i	$0.0129103\pi$
$613$	30.0229	+	25.1922i	1.21261	+	1.01750i	0.213437	+	0.976957i	$0.431534\pi$
$614$	−10.0141	−	56.7925i	−0.404134	−	2.29196i
$615$		0			0
$616$	8.58143	−	14.8635i	0.345756	−	0.598866i
$617$	26.2201	+	9.54332i	1.05558	+	0.384200i	0.810766	−	0.585370i	$-0.199051\pi$
$617$	26.2201	+	9.54332i	1.05558	+	0.384200i	0.244814	+	0.969570i	$0.421273\pi$
$618$	33.5995	+	12.2292i	1.35157	+	0.491932i
$619$	12.4298	−	21.5291i	0.499597	−	0.865327i	−0.500403	−	0.865792i	$-0.666815\pi$
$619$	12.4298	−	21.5291i	0.499597	−	0.865327i	1.00000		0.000465813i	$0.000148273\pi$
$620$		0			0
$621$	−2.25403	−	12.7832i	−0.0904511	−	0.512974i
$622$	39.9951	+	33.5599i	1.60366	+	1.34563i
$623$	−21.6969	+	18.2059i	−0.869268	+	0.729403i
$624$	4.60552	−	26.1192i	0.184368	−	1.04561i
$625$		0			0
$626$	−69.9001			−2.79377
$627$	27.1367	+	1.28851i	1.08374	+	0.0514582i
$628$	73.3901			2.92858
$629$	−5.99005	+	2.18020i	−0.238839	+	0.0869303i
$630$		0			0
$631$	33.9105	−	28.4543i	1.34995	−	1.13275i	0.371007	−	0.928630i	$-0.379012\pi$
$631$	33.9105	−	28.4543i	1.34995	−	1.13275i	0.978947	−	0.204116i	$-0.0654320\pi$
$632$	12.1341	+	10.1817i	0.482670	+	0.405008i
$633$	2.91265	+	16.5184i	0.115767	+	0.656549i
$634$	−9.53501	−	16.5151i	−0.378684	−	0.655900i
$635$		0			0
$636$	49.4883	+	18.0123i	1.96234	+	0.714233i
$637$	−25.1717	−	9.16175i	−0.997339	−	0.363002i
$638$	−7.19661	+	12.4649i	−0.284916	+	0.493490i
$639$	−2.92709	−	5.06988i	−0.115794	−	0.200561i
$640$		0			0
$641$	15.5815	+	13.0744i	0.615432	+	0.516409i	0.896364	−	0.443319i	$-0.146199\pi$
$641$	15.5815	+	13.0744i	0.615432	+	0.516409i	−0.280932	+	0.959728i	$0.590644\pi$
$642$	−48.9549	+	41.0780i	−1.93210	+	1.62122i
$643$	5.27382	−	29.9093i	0.207979	−	1.17951i	−0.684703	−	0.728822i	$-0.740068\pi$
$643$	5.27382	−	29.9093i	0.207979	−	1.17951i	0.892682	−	0.450686i	$-0.148821\pi$
$644$	−40.6562	+	14.7977i	−1.60208	+	0.583109i
$645$		0			0
$646$	−7.10926	+	31.4989i	−0.279710	+	1.23931i
$647$	−48.5913			−1.91032			−0.955161	−	0.296087i	$-0.904318\pi$
$647$	−48.5913			−1.91032			−0.955161	+	0.296087i	$0.904318\pi$
$648$	38.7604	−	14.1076i	1.52265	−	0.554200i
$649$	5.80948	−	32.9472i	0.228042	−	1.29329i
$650$		0			0
$651$	12.6831	+	10.6424i	0.497091	+	0.417109i
$652$	9.84739	+	55.8473i	0.385653	+	2.18715i
$653$	9.97774	+	17.2820i	0.390459	+	0.676295i	0.992510	−	0.122163i	$-0.0389829\pi$
$653$	9.97774	+	17.2820i	0.390459	+	0.676295i	−0.602051	+	0.798458i	$0.705650\pi$
$654$	19.6077	−	33.9615i	0.766721	−	1.32800i
$655$		0			0
$656$	−6.90496	−	2.51320i	−0.269594	−	0.0981240i
$657$	−7.23513	+	12.5316i	−0.282269	+	0.488905i
$658$	−4.46595	−	7.73526i	−0.174101	−	0.301552i
$659$	−2.95696	−	16.7698i	−0.115187	−	0.653257i	−0.986658	−	0.162810i	$-0.947944\pi$
$659$	−2.95696	−	16.7698i	−0.115187	−	0.653257i	0.871471	−	0.490448i	$-0.163167\pi$
$660$		0			0
$661$	−21.0919	+	17.6982i	−0.820379	+	0.688380i	−0.953061	−	0.302779i	$-0.902086\pi$
$661$	−21.0919	+	17.6982i	−0.820379	+	0.688380i	0.132682	+	0.991159i	$0.457641\pi$
$662$	7.50074	−	42.5388i	0.291525	−	1.65332i
$663$	−41.5930	+	15.1386i	−1.61534	+	0.587935i
$664$	−24.6969			−0.958427
$665$		0			0
$666$	10.7470			0.416436
$667$	15.2659	−	5.55633i	0.591098	−	0.215142i
$668$	3.80193	−	21.5618i	0.147101	−	0.834253i
$669$	−29.0252	+	24.3551i	−1.12218	+	0.941621i
$670$		0			0
$671$	−2.26901	−	12.8682i	−0.0875940	−	0.496770i
$672$	6.07793	+	10.5273i	0.234461	+	0.406099i
$673$	18.6280	−	32.2647i	0.718057	−	1.24371i	−0.243711	−	0.969848i	$-0.578365\pi$
$673$	18.6280	−	32.2647i	0.718057	−	1.24371i	0.961768	−	0.273864i	$-0.0883017\pi$
$674$	21.3959	+	7.78748i	0.824140	+	0.299962i
$675$		0			0
$676$	−46.0503	+	79.7615i	−1.77117	+	3.06775i
$677$	−11.3940	−	19.7350i	−0.437907	−	0.758478i	0.559621	−	0.828749i	$-0.310947\pi$
$677$	−11.3940	−	19.7350i	−0.437907	−	0.758478i	−0.997528	+	0.0702711i	$0.977614\pi$
$678$	12.5015	+	70.8993i	0.480116	+	2.72287i
$679$	−0.162929	−	0.136713i	−0.00625263	−	0.00524658i
$680$		0			0
$681$	4.67549	−	26.5160i	0.179165	−	1.01610i
$682$	−26.8998	+	9.79072i	−1.03005	+	0.374906i
$683$	−4.61408			−0.176553			−0.0882764	−	0.996096i	$-0.528136\pi$
$683$	−4.61408			−0.176553			−0.0882764	+	0.996096i	$0.528136\pi$
$684$	18.9568	−	29.5074i	0.724833	−	1.12824i
$685$		0			0
$686$	−41.2842	+	15.0262i	−1.57624	+	0.573704i
$687$	3.10434	−	17.6056i	0.118438	−	0.671695i
$688$	−0.678170	+	0.569052i	−0.0258550	+	0.0216949i
$689$	−30.2218	−	25.3591i	−1.15136	−	0.966104i
$690$		0			0
$691$	−17.8800	−	30.9690i	−0.680186	−	1.17812i	−0.974924	−	0.222538i	$-0.928566\pi$
$691$	−17.8800	−	30.9690i	−0.680186	−	1.17812i	0.294738	−	0.955578i	$-0.404768\pi$
$692$	−2.97035	+	5.14479i	−0.112916	+	0.195576i
$693$	9.32034	+	3.39233i	0.354050	+	0.128864i
$694$	2.82123	+	1.02684i	0.107092	+	0.0389785i
$695$		0			0
$696$	9.77663	+	16.9336i	0.370582	+	0.641867i
$697$	2.12947	+	12.0768i	0.0806594	+	0.457442i
$698$	48.3397	+	40.5618i	1.82968	+	1.53529i
$699$	−11.7629	+	9.87026i	−0.444915	+	0.373328i
$700$		0			0
$701$	−30.8939	+	11.2444i	−1.16685	+	0.424697i	−0.851538	−	0.524293i	$-0.824330\pi$
$701$	−30.8939	+	11.2444i	−1.16685	+	0.424697i	−0.315307	+	0.948990i	$0.602108\pi$
$702$	−26.1393			−0.986565
$703$	−7.07575	+	5.38667i	−0.266867	+	0.203162i
$704$	−31.2301			−1.17703
$705$		0			0
$706$	11.0645	−	62.7500i	0.416419	−	2.36163i
$707$	−4.68368	+	3.93007i	−0.176148	+	0.147806i
$708$	−77.7598	−	65.2482i	−2.92239	−	2.45218i
$709$	7.71396	+	43.7480i	0.289704	+	1.64299i	0.687983	+	0.725727i	$0.258496\pi$
$709$	7.71396	+	43.7480i	0.289704	+	1.64299i	−0.398279	+	0.917264i	$0.630392\pi$
$710$		0			0
$711$	−4.57700	+	7.92760i	−0.171651	+	0.297308i
$712$	−62.5147	−	22.7535i	−2.34284	−	0.852723i
$713$	30.3618	+	11.0508i	1.13706	+	0.413855i
$714$	−13.8540	+	23.9958i	−0.518471	+	0.898019i
$715$		0			0
$716$	−8.92264	−	50.6028i	−0.333455	−	1.89112i
$717$	27.9635	+	23.4641i	1.04431	+	0.876284i
$718$	−38.2445	+	32.0910i	−1.42727	+	1.19762i
$719$	−3.48789	+	19.7808i	−0.130076	+	0.737699i	0.848086	+	0.529858i	$0.177755\pi$
$719$	−3.48789	+	19.7808i	−0.130076	+	0.737699i	−0.978163	+	0.207841i	$0.933356\pi$
$720$		0			0
$721$	−10.8019			−0.402285
$722$	3.58385	+	44.9056i	0.133377	+	1.67121i
$723$	−23.8919			−0.888548
$724$	−78.0868	+	28.4213i	−2.90207	+	1.05627i
$725$		0			0
$726$	14.7790	−	12.4010i	0.548498	−	0.460245i
$727$	−0.559054	−	0.469102i	−0.0207342	−	0.0173980i	0.632362	−	0.774673i	$-0.282086\pi$
$727$	−0.559054	−	0.469102i	−0.0207342	−	0.0173980i	−0.653096	+	0.757275i	$0.726530\pi$
$728$	6.77397	+	38.4171i	0.251060	+	1.42383i
$729$	5.82299	+	10.0857i	0.215666	+	0.373545i
$730$		0			0
$731$	1.38834	+	0.505315i	0.0513497	+	0.0186898i
$732$	−37.2551	−	13.5597i	−1.37699	−	0.501183i
$733$	14.7474	−	25.5432i	0.544707	−	0.943461i	−0.453918	−	0.891043i	$-0.649974\pi$
$733$	14.7474	−	25.5432i	0.544707	−	0.943461i	0.998625	−	0.0524171i	$-0.0166925\pi$
$734$	−13.0613	−	22.6228i	−0.482101	−	0.835023i
$735$		0			0
$736$	18.1723	+	15.2483i	0.669838	+	0.562061i
$737$	1.40188	−	1.17632i	0.0516390	−	0.0433303i
$738$	3.59015	−	20.3607i	0.132155	−	0.749489i
$739$	38.0572	−	13.8517i	1.39996	−	0.509542i	0.471790	−	0.881711i	$-0.343608\pi$
$739$	38.0572	−	13.8517i	1.39996	−	0.509542i	0.928165	+	0.372169i	$0.121386\pi$
$740$		0			0
$741$	−49.1318	+	37.4033i	−1.80490	+	1.37405i
$742$	−24.6965			−0.906637
$743$	18.2617	−	6.64673i	0.669958	−	0.243845i	0.0154284	−	0.999881i	$-0.495089\pi$
$743$	18.2617	−	6.64673i	0.669958	−	0.243845i	0.654530	+	0.756036i	$0.272867\pi$
$744$	−6.75297	+	38.2980i	−0.247576	+	1.40407i
$745$		0			0
$746$	−8.77818	−	7.36576i	−0.321392	−	0.269680i
$747$	−2.47839	−	14.0556i	−0.0906795	−	0.514269i
$748$	−15.4312	−	26.7277i	−0.564221	−	0.977260i
$749$	9.65309	−	16.7196i	0.352716	−	0.610923i
$750$		0			0
$751$	−5.32221	−	1.93713i	−0.194210	−	0.0706868i	0.243084	−	0.970005i	$-0.421841\pi$
$751$	−5.32221	−	1.93713i	−0.194210	−	0.0706868i	−0.437294	+	0.899318i	$0.644063\pi$
$752$	2.15455	−	3.73178i	0.0785682	−	0.136084i
$753$	−13.5578	−	23.4827i	−0.494072	−	0.855758i
$754$	−5.68082	−	32.2176i	−0.206883	−	1.17329i
$755$		0			0
$756$	−8.07520	+	6.77590i	−0.293692	+	0.246437i
$757$	−2.18425	+	12.3875i	−0.0793879	+	0.450231i	0.919039	+	0.394166i	$0.128967\pi$
$757$	−2.18425	+	12.3875i	−0.0793879	+	0.450231i	−0.998427	+	0.0560650i	$0.982145\pi$
$758$	−4.53886	+	1.65201i	−0.164859	+	0.0600037i
$759$	45.4920			1.65126
$760$		0			0
$761$	50.0335			1.81371			0.906857	−	0.421439i	$-0.138475\pi$
$761$	50.0335			1.81371			0.906857	+	0.421439i	$0.138475\pi$
$762$	44.2613	−	16.1098i	1.60342	−	0.583596i
$763$	−2.05722	+	11.6671i	−0.0744764	+	0.422377i
$764$	28.3245	−	23.7671i	1.02475	−	0.859864i
$765$		0			0
$766$	14.2373	+	80.7436i	0.514413	+	2.91738i
$767$	38.0207	+	65.8538i	1.37285	+	2.37784i
$768$	−29.7696	+	51.5625i	−1.07422	+	1.86060i
$769$	29.8303	+	10.8573i	1.07571	+	0.391525i	0.818308	−	0.574780i	$-0.194912\pi$
$769$	29.8303	+	10.8573i	1.07571	+	0.391525i	0.257399	+	0.966305i	$0.417135\pi$
$770$		0			0
$771$	−4.36033	+	7.55231i	−0.157033	+	0.271990i
$772$	21.4234	+	37.1064i	0.771044	+	1.33549i
$773$	−1.98608	−	11.2636i	−0.0714342	−	0.405124i	−0.999468	−	0.0326266i	$-0.989613\pi$
$773$	−1.98608	−	11.2636i	−0.0714342	−	0.405124i	0.928033	−	0.372497i	$-0.121498\pi$
$774$	−1.90812	−	1.60110i	−0.0685859	−	0.0575504i
$775$		0			0
$776$	0.0867493	−	0.491980i	0.00311412	−	0.0176610i
$777$	−7.17044	+	2.60983i	−0.257238	+	0.0936270i
$778$	−10.7410			−0.385083
$779$	7.84162	+	15.2049i	0.280955	+	0.544772i
$780$		0			0
$781$	−6.75332	+	2.45801i	−0.241653	+	0.0879544i
$782$	−9.38951	+	53.2506i	−0.335768	+	1.90424i
$783$	3.03213	−	2.54426i	0.108360	−	0.0909246i
$784$	−6.19714	−	5.20002i	−0.221327	−	0.185715i
$785$		0			0
$786$	28.5686	+	49.4823i	1.01901	+	1.76497i
$787$	3.32012	−	5.75062i	0.118350	−	0.204987i	−0.800764	−	0.598980i	$-0.795573\pi$
$787$	3.32012	−	5.75062i	0.118350	−	0.204987i	0.919114	+	0.393992i	$0.128906\pi$
$788$	−9.27935	−	3.37741i	−0.330563	−	0.120315i
$789$	−4.55138	−	1.65657i	−0.162033	−	0.0589753i
$790$		0			0
$791$	−10.8746	−	18.8354i	−0.386657	−	0.669710i
$792$	4.04546	+	22.9430i	0.143749	+	0.815242i
$793$	22.7511	+	19.0905i	0.807916	+	0.677922i
$794$	45.6515	−	38.3061i	1.62011	−	1.35943i
$795$		0			0
$796$	−15.2403	+	5.54703i	−0.540179	+	0.196609i
$797$	0.186468			0.00660502			0.00330251	−	0.999995i	$-0.498949\pi$
$797$	0.186468			0.00660502			0.00330251	+	0.999995i	$0.498949\pi$
$798$	−8.51019	+	37.7060i	−0.301258	+	1.33478i
$799$	−7.19137			−0.254412
$800$		0			0
$801$	6.67609	−	37.8620i	0.235888	−	1.33779i
$802$	52.5112	−	44.0621i	1.85423	−	1.55589i
$803$	13.6080	+	11.4185i	0.480217	+	0.402950i
$804$	−0.964190	−	5.46819i	−0.0340044	−	0.192848i
$805$		0			0
$806$	32.5324	−	56.3478i	1.14591	−	1.98477i
$807$	−8.43520	−	3.07016i	−0.296933	−	0.108075i
$808$	−13.4949	−	4.91176i	−0.474750	−	0.172795i
$809$	−0.609985	+	1.05652i	−0.0214459	+	0.0371454i	−0.876549	−	0.481312i	$-0.840160\pi$
$809$	−0.609985	+	1.05652i	−0.0214459	+	0.0371454i	0.855103	+	0.518458i	$0.173494\pi$
$810$		0			0
$811$	−3.31560	−	18.8037i	−0.116427	−	0.660288i	−0.986034	−	0.166544i	$-0.946739\pi$
$811$	−3.31560	−	18.8037i	−0.116427	−	0.660288i	0.869608	−	0.493744i	$-0.164372\pi$
$812$	−10.1065	−	8.48035i	−0.354668	−	0.297602i
$813$	−33.1472	+	27.8138i	−1.16252	+	0.975473i
$814$	2.29098	−	12.9928i	0.0802987	−	0.455396i
$815$		0			0
$816$	−13.3674			−0.467951
$817$	2.05881	+	0.0977570i	0.0720287	+	0.00342008i
$818$	−54.4413			−1.90349
$819$	−21.1844	+	7.71047i	−0.740241	+	0.269426i
$820$		0			0
$821$	−7.64305	+	6.41328i	−0.266744	+	0.223825i	−0.766343	−	0.642432i	$-0.777925\pi$
$821$	−7.64305	+	6.41328i	−0.266744	+	0.223825i	0.499598	+	0.866257i	$0.333481\pi$
$822$	1.64861	+	1.38335i	0.0575019	+	0.0482498i
$823$	4.89822	+	27.7792i	0.170741	+	0.968322i	0.942945	+	0.332948i	$0.108043\pi$
$823$	4.89822	+	27.7792i	0.170741	+	0.968322i	−0.772204	+	0.635375i	$0.780846\pi$
$824$	−12.6860	−	21.9727i	−0.441937	−	0.765457i
$825$		0			0
$826$	44.7307	+	16.2806i	1.55638	+	0.566476i
$827$	8.31907	+	3.02789i	0.289283	+	0.105290i	0.482585	−	0.875849i	$-0.339698\pi$
$827$	8.31907	+	3.02789i	0.289283	+	0.105290i	−0.193303	+	0.981139i	$0.561920\pi$
$828$	29.3643	−	50.8604i	1.02048	−	1.76752i
$829$	−22.8446	−	39.5680i	−0.793425	−	1.37425i	−0.923834	−	0.382793i	$-0.874962\pi$
$829$	−22.8446	−	39.5680i	−0.793425	−	1.37425i	0.130409	−	0.991460i	$-0.458371\pi$
$830$		0			0
$831$	−26.3055	−	22.0729i	−0.912526	−	0.765701i
$832$	54.3765	−	45.6273i	1.88517	−	1.58184i
$833$	−2.34441	+	13.2958i	−0.0812290	+	0.460673i
$834$	−38.2116	+	13.9079i	−1.32316	+	0.481591i
$835$		0			0
$836$	−31.6325	−	29.2085i	−1.09403	−	1.01020i
$837$	7.87227			0.272105
$838$	−20.0086	+	7.28252i	−0.691184	+	0.251570i
$839$	0.0317008	−	0.179784i	0.00109443	−	0.00620684i	−0.984256	−	0.176751i	$-0.943441\pi$
$839$	0.0317008	−	0.179784i	0.00109443	−	0.00620684i	0.985350	+	0.170544i	$0.0545525\pi$
$840$		0			0
$841$	−18.4204	−	15.4566i	−0.635187	−	0.532985i
$842$	−14.0150	−	79.4831i	−0.482989	−	2.73917i
$843$	31.4010	+	54.3880i	1.08151	+	1.87322i
$844$	13.2913	−	23.0212i	0.457505	−	0.792422i
$845$		0			0
$846$	11.3930	+	4.14671i	0.391699	+	0.142567i
$847$	−2.91416	+	5.04748i	−0.100132	+	0.173433i
$848$	−5.95727	−	10.3183i	−0.204573	−	0.354332i
$849$	−8.06933	−	45.7634i	−0.276939	−	1.57060i
$850$		0			0
$851$	−11.4073	+	9.57186i	−0.391037	+	0.328119i
$852$	−3.78648	+	21.4742i	−0.129723	+	0.735695i
$853$	46.2501	−	16.8337i	1.58357	−	0.576374i	0.607597	−	0.794246i	$-0.292134\pi$
$853$	46.2501	−	16.8337i	1.58357	−	0.576374i	0.975977	+	0.217872i	$0.0699115\pi$
$854$	18.5917			0.636193
$855$		0			0
$856$	45.3470			1.54993
$857$	−29.6660	+	10.7975i	−1.01337	+	0.368837i	−0.794727	−	0.606968i	$-0.792386\pi$
$857$	−29.6660	+	10.7975i	−1.01337	+	0.368837i	−0.218645	+	0.975805i	$0.570164\pi$
$858$	15.9078	−	90.2176i	0.543083	−	3.07998i
$859$	−8.18869	+	6.87112i	−0.279394	+	0.234440i	−0.771706	−	0.635979i	$-0.780596\pi$
$859$	−8.18869	+	6.87112i	−0.279394	+	0.234440i	0.492312	+	0.870419i	$0.336152\pi$
$860$		0			0
$861$	2.54910	+	14.4567i	0.0868730	+	0.492681i
$862$	−45.0164	−	77.9706i	−1.53326	−	2.65569i
$863$	−12.7913	+	22.1552i	−0.435420	+	0.754170i	−0.997330	−	0.0730285i	$-0.976734\pi$
$863$	−12.7913	+	22.1552i	−0.435420	+	0.754170i	0.561909	+	0.827199i	$0.310067\pi$
$864$	5.43124	+	1.97681i	0.184775	+	0.0672524i
$865$		0			0
$866$	43.8392	−	75.9316i	1.48971	−	2.58026i
$867$	−8.26921	−	14.3227i	−0.280837	−	0.486424i
$868$	−4.55640	−	25.8406i	−0.154654	−	0.877088i
$869$	8.60854	+	7.22342i	0.292025	+	0.245038i
$870$		0			0
$871$	−0.722290	+	4.09631i	−0.0244739	+	0.138798i
$872$	−26.1486	+	9.51731i	−0.885503	+	0.322297i
$873$	0.288703			0.00977113
$874$	9.56087	+	74.8258i	0.323401	+	2.53102i
$875$		0			0
$876$	50.6479	−	18.4343i	1.71123	−	0.622838i
$877$	−5.39963	+	30.6228i	−0.182332	+	1.03406i	0.747003	+	0.664821i	$0.231492\pi$
$877$	−5.39963	+	30.6228i	−0.182332	+	1.03406i	−0.929335	+	0.369237i	$0.879619\pi$
$878$	40.2903	−	33.8076i	1.35973	−	1.14095i
$879$	−8.02882	−	6.73698i	−0.270805	−	0.227233i
$880$		0			0
$881$	23.7233	+	41.0899i	0.799257	+	1.38435i	0.920101	+	0.391682i	$0.128107\pi$
$881$	23.7233	+	41.0899i	0.799257	+	1.38435i	−0.120844	+	0.992672i	$0.538560\pi$
$882$	11.3808	−	19.7122i	0.383213	−	0.663744i
$883$	−13.6568	−	4.97065i	−0.459586	−	0.167276i	0.101843	−	0.994801i	$-0.467526\pi$
$883$	−13.6568	−	4.97065i	−0.459586	−	0.167276i	−0.561429	+	0.827525i	$0.689748\pi$
$884$	65.9173	+	23.9919i	2.21704	+	0.806936i
$885$		0			0
$886$	11.6756	+	20.2227i	0.392249	+	0.679396i
$887$	−6.44703	−	36.5629i	−0.216470	−	1.22766i	−0.878337	−	0.478042i	$-0.841347\pi$
$887$	−6.44703	−	36.5629i	−0.216470	−	1.22766i	0.661867	−	0.749621i	$-0.269764\pi$
$888$	−13.7299	−	11.5207i	−0.460744	−	0.386610i
$889$	−10.9005	+	9.14660i	−0.365591	+	0.306767i
$890$		0			0
$891$	27.4985	−	10.0086i	0.921234	−	0.335302i
$892$	60.0483			2.01057
$893$	−9.57955	+	2.98031i	−0.320567	+	0.0997322i
$894$	19.9695			0.667879
$895$		0			0
$896$	5.86861	−	33.2825i	0.196056	−	1.11189i
$897$	−79.2086	+	66.4639i	−2.64470	+	2.21917i
$898$	−67.7539	−	56.8523i	−2.26098	−	1.89718i
$899$	1.71087	+	9.70283i	0.0570607	+	0.323607i
$900$		0			0
$901$	−9.94198	+	17.2200i	−0.331215	+	0.573682i
$902$	−23.8502	−	8.68077i	−0.794126	−	0.289038i
$903$	1.66192	+	0.604891i	0.0553054	+	0.0201295i
$904$	25.5427	−	44.2412i	0.849537	−	1.47144i
$905$		0			0
$906$	4.22474	+	23.9597i	0.140358	+	0.796007i
$907$	8.32358	+	6.98432i	0.276380	+	0.231910i	0.770432	−	0.637522i	$-0.220040\pi$
$907$	8.32358	+	6.98432i	0.276380	+	0.231910i	−0.494052	+	0.869432i	$0.664485\pi$
$908$	−32.6881	+	27.4286i	−1.08479	+	0.910250i
$909$	1.44116	−	8.17321i	0.0478002	−	0.271088i
$910$		0			0
$911$	−39.5522			−1.31042			−0.655211	−	0.755446i	$-0.727420\pi$
$911$	−39.5522			−1.31042			−0.655211	+	0.755446i	$0.727420\pi$
$912$	−17.8065	+	5.53981i	−0.589633	+	0.183441i
$913$	−17.5212			−0.579867
$914$	−31.2682	+	11.3807i	−1.03426	+	0.376440i
$915$		0			0
$916$	−21.7036	+	18.2115i	−0.717108	+	0.601725i
$917$	−13.2229	−	11.0953i	−0.436659	−	0.366400i
$918$	2.28771	+	12.9743i	0.0755058	+	0.428214i
$919$	−16.0782	−	27.8483i	−0.530372	−	0.918631i	−0.999372	−	0.0354331i	$-0.988719\pi$
$919$	−16.0782	−	27.8483i	−0.530372	−	0.918631i	0.469000	−	0.883198i	$-0.344614\pi$
$920$		0			0
$921$	−52.2286	−	19.0096i	−1.72099	−	0.626389i
$922$	22.5827	+	8.21942i	0.743720	+	0.270692i
$923$	8.16742	−	14.1464i	0.268834	−	0.465634i
$924$	−18.4721	−	31.9945i	−0.607686	−	1.05254i
$925$		0			0
$926$	−1.31158	−	1.10055i	−0.0431012	−	0.0361662i
$927$	11.2322	−	9.42491i	0.368913	−	0.309555i
$928$	−1.25612	+	7.12380i	−0.0412341	+	0.233850i
$929$	10.2742	−	3.73950i	0.337085	−	0.122689i	−0.167931	−	0.985799i	$-0.553709\pi$
$929$	10.2742	−	3.73950i	0.337085	−	0.122689i	0.505016	+	0.863110i	$0.331486\pi$
$930$		0			0
$931$	2.38720	+	18.6828i	0.0782372	+	0.612304i
$932$	24.3355			0.797136
$933$	47.2848	−	17.2103i	1.54803	−	0.563439i
$934$	−14.4171	+	81.7633i	−0.471741	+	2.67538i
$935$		0			0
$936$	−40.5635	−	34.0368i	−1.32586	−	1.11253i
$937$	−7.81940	−	44.3460i	−0.255449	−	1.44872i	−0.794918	−	0.606716i	$-0.792486\pi$
$937$	−7.81940	−	44.3460i	−0.255449	−	1.44872i	0.539470	−	0.842005i	$-0.318625\pi$
$938$	1.30191	+	2.25497i	0.0425088	+	0.0736275i
$939$	−33.6845	+	58.3433i	−1.09925	+	1.90396i
$940$		0			0
$941$	40.0794	+	14.5877i	1.30655	+	0.475545i	0.899125	−	0.437693i	$-0.144204\pi$
$941$	40.0794	+	14.5877i	1.30655	+	0.475545i	0.407426	+	0.913238i	$0.366427\pi$
$942$	54.8977	−	95.0855i	1.78866	−	3.09805i
$943$	14.3237	+	24.8094i	0.466444	+	0.807905i
$944$	3.98778	+	22.6158i	0.129791	+	0.736083i
$945$		0			0
$946$	−2.34245	+	1.96555i	−0.0761596	+	0.0639055i
$947$	−4.29139	+	24.3377i	−0.139452	+	0.790869i	0.832204	+	0.554469i	$0.187079\pi$
$947$	−4.29139	+	24.3377i	−0.139452	+	0.790869i	−0.971656	+	0.236400i	$0.924032\pi$
$948$	32.0403	−	11.6617i	1.04062	−	0.378754i
$949$	−40.3761			−1.31066
$950$		0			0
$951$	−18.3795			−0.595996
$952$	18.4755	−	6.72453i	0.598794	−	0.217943i
$953$	2.69451	−	15.2813i	0.0872836	−	0.495010i	−0.909557	−	0.415580i	$-0.863579\pi$
$953$	2.69451	−	15.2813i	0.0872836	−	0.495010i	0.996840	−	0.0794303i	$-0.0253101\pi$
$954$	25.6801	−	21.5482i	0.831426	−	0.697649i
$955$		0			0
$956$	−10.0458	−	56.9728i	−0.324906	−	1.84263i
$957$	6.93602	+	12.0135i	0.224210	+	0.388342i
$958$	31.9608	−	55.3578i	1.03261	−	1.78853i
$959$	−0.610947	−	0.222367i	−0.0197285	−	0.00718059i
$960$		0			0
$961$	5.70235	−	9.87675i	0.183947	−	0.318605i
$962$	14.9935	+	25.9695i	0.483411	+	0.837292i
$963$	4.55067	+	25.8081i	0.146643	+	0.831655i
$964$	29.0057	+	24.3387i	0.934210	+	0.783895i
$965$		0			0
$966$	−11.2398	+	63.7440i	−0.361634	+	2.05093i
$967$	15.0830	−	5.48978i	0.485038	−	0.176539i	−0.0879145	−	0.996128i	$-0.528020\pi$
$967$	15.0830	−	5.48978i	0.485038	−	0.176539i	0.572952	+	0.819589i	$0.305798\pi$
$968$	−13.6898			−0.440006
$969$	22.8652	+	21.1130i	0.734535	+	0.678248i
$970$		0			0
$971$	5.42132	−	1.97320i	0.173978	−	0.0633230i	−0.253562	−	0.967319i	$-0.581602\pi$
$971$	5.42132	−	1.97320i	0.173978	−	0.0633230i	0.427541	+	0.903996i	$0.359380\pi$
$972$	12.0629	−	68.4122i	0.386918	−	2.19432i
$973$	9.41061	−	7.89644i	0.301690	−	0.253148i
$974$	5.57154	+	4.67507i	0.178524	+	0.149799i
$975$		0			0
$976$	4.48466	+	7.76766i	0.143551	+	0.248637i
$977$	23.3862	−	40.5060i	0.748190	−	1.29590i	−0.200499	−	0.979694i	$-0.564256\pi$
$977$	23.3862	−	40.5060i	0.748190	−	1.29590i	0.948689	−	0.316209i	$-0.102410\pi$
$978$	79.7229	+	29.0168i	2.54926	+	0.927854i
$979$	−44.3509	−	16.1424i	−1.41746	−	0.515914i
$980$		0			0
$981$	−8.04061	−	13.9267i	−0.256717	−	0.444647i
$982$	0.514183	+	2.91607i	0.0164082	+	0.0930557i
$983$	25.7421	+	21.6002i	0.821046	+	0.688939i	0.953217	−	0.302288i	$-0.0977503\pi$
$983$	25.7421	+	21.6002i	0.821046	+	0.688939i	−0.132171	+	0.991227i	$0.542195\pi$
$984$	−26.4133	+	22.1634i	−0.842025	+	0.706543i
$985$		0			0
$986$	−15.4940	+	5.63936i	−0.493430	+	0.179594i
$987$	−8.60848			−0.274011
$988$	97.7507	+	4.64142i	3.10986	+	0.147663i
$989$	3.45139			0.109748
$990$		0			0
$991$	−7.91905	+	44.9112i	−0.251557	+	1.42665i	0.553202	+	0.833047i	$0.313406\pi$
$991$	−7.91905	+	44.9112i	−0.251557	+	1.42665i	−0.804758	+	0.593602i	$0.797705\pi$
$992$	−11.0210	+	9.24768i	−0.349916	+	0.293614i
$993$	−31.8912	−	26.7599i	−1.01204	−	0.849199i
$994$	−1.77564	−	10.0701i	−0.0563198	−	0.319406i
$995$		0			0
$996$	−26.5808	+	46.0393i	−0.842246	+	1.45881i
$997$	4.51171	+	1.64213i	0.142887	+	0.0520067i	0.412474	−	0.910969i	$-0.364665\pi$
$997$	4.51171	+	1.64213i	0.142887	+	0.0520067i	−0.269587	+	0.962976i	$0.586887\pi$
$998$	−43.6062	−	15.8713i	−1.38033	−	0.502399i
$999$	−1.81408	+	3.14208i	−0.0573950	+	0.0994111i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.l.f.176.1		48
5.2	odd	4		95.2.p.a.24.1	yes	48
5.3	odd	4		95.2.p.a.24.8	yes	48
5.4	even	2	inner	475.2.l.f.176.8		48
15.2	even	4		855.2.da.b.784.8		48
15.8	even	4		855.2.da.b.784.1		48
19.2	odd	18		9025.2.a.ct.1.2		24
19.4	even	9	inner	475.2.l.f.251.1		48
19.17	even	9		9025.2.a.cu.1.23		24
95.2	even	36		1805.2.b.l.1084.2		24
95.4	even	18	inner	475.2.l.f.251.8		48
95.17	odd	36		1805.2.b.k.1084.23		24
95.23	odd	36		95.2.p.a.4.1	✓	48
95.42	odd	36		95.2.p.a.4.8	yes	48
95.59	odd	18		9025.2.a.ct.1.23		24
95.74	even	18		9025.2.a.cu.1.2		24
95.78	even	36		1805.2.b.l.1084.23		24
95.93	odd	36		1805.2.b.k.1084.2		24
285.23	even	36		855.2.da.b.289.8		48
285.137	even	36		855.2.da.b.289.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.4.1	✓	48	95.23	odd	36
95.2.p.a.4.8	yes	48	95.42	odd	36
95.2.p.a.24.1	yes	48	5.2	odd	4
95.2.p.a.24.8	yes	48	5.3	odd	4
475.2.l.f.176.1		48	1.1	even	1	trivial
475.2.l.f.176.8		48	5.4	even	2	inner
475.2.l.f.251.1		48	19.4	even	9	inner
475.2.l.f.251.8		48	95.4	even	18	inner
855.2.da.b.289.1		48	285.137	even	36
855.2.da.b.289.8		48	285.23	even	36
855.2.da.b.784.1		48	15.8	even	4
855.2.da.b.784.8		48	15.2	even	4
1805.2.b.k.1084.2		24	95.93	odd	36
1805.2.b.k.1084.23		24	95.17	odd	36
1805.2.b.l.1084.2		24	95.2	even	36
1805.2.b.l.1084.23		24	95.78	even	36
9025.2.a.ct.1.2		24	19.2	odd	18
9025.2.a.ct.1.23		24	95.59	odd	18
9025.2.a.cu.1.2		24	95.74	even	18
9025.2.a.cu.1.23		24	19.17	even	9

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.22798 + 0.810919i) q^{2} +(-0.396806 + 2.25040i) q^{3} +(2.77422 - 2.32785i) q^{4} +(-0.940815 - 5.33563i) q^{6} +(0.818386 + 1.41749i) q^{7} +(-1.92225 + 3.32944i) q^{8} +(-2.08777 - 0.759885i) q^{9} +O(q^{10})\)	\(q+(-2.22798 + 0.810919i) q^{2} +(-0.396806 + 2.25040i) q^{3} +(2.77422 - 2.32785i) q^{4} +(-0.940815 - 5.33563i) q^{6} +(0.818386 + 1.41749i) q^{7} +(-1.92225 + 3.32944i) q^{8} +(-2.08777 - 0.759885i) q^{9} +(-1.36374 + 2.36206i) q^{11} +(4.13776 + 7.16682i) q^{12} +(-1.07650 - 6.10515i) q^{13} +(-2.97282 - 2.49449i) q^{14} +(0.325107 - 1.84377i) q^{16} +(-2.93608 + 1.06864i) q^{17} +5.26771 q^{18} +(-3.46824 + 2.64032i) q^{19} +(-3.51465 + 1.27923i) q^{21} +(1.12294 - 6.36852i) q^{22} +(-5.59139 + 4.69173i) q^{23} +(-6.72981 - 5.64698i) q^{24} +(7.34921 + 12.7292i) q^{26} +(-0.889189 + 1.54012i) q^{27} +(5.57008 + 2.02734i) q^{28} +(-2.09149 - 0.761241i) q^{29} +(-2.21333 - 3.83360i) q^{31} +(-0.564364 - 3.20067i) q^{32} +(-4.77445 - 4.00624i) q^{33} +(5.67494 - 4.76184i) q^{34} +(-7.56083 + 2.75192i) q^{36} +2.04016 q^{37} +(5.58609 - 8.69505i) q^{38} +14.1662 q^{39} +(0.681538 - 3.86519i) q^{41} +(6.79323 - 5.70020i) q^{42} +(-0.362229 - 0.303946i) q^{43} +(1.71522 + 9.72747i) q^{44} +(8.65289 - 14.9872i) q^{46} +(2.16280 + 0.787194i) q^{47} +(4.02022 + 1.46324i) q^{48} +(2.16049 - 3.74208i) q^{49} +(-1.23982 - 7.03139i) q^{51} +(-17.1983 - 14.4311i) q^{52} +(4.87501 - 4.09062i) q^{53} +(0.732183 - 4.15242i) q^{54} -6.29258 q^{56} +(-4.56556 - 8.85263i) q^{57} +5.27711 q^{58} +(-11.5263 + 4.19524i) q^{59} +(-3.66993 + 3.07944i) q^{61} +(8.03999 + 6.74636i) q^{62} +(-0.631473 - 3.58126i) q^{63} +(5.72509 + 9.91615i) q^{64} +(13.8861 + 5.05414i) q^{66} +(-0.630496 - 0.229482i) q^{67} +(-5.65769 + 9.79940i) q^{68} +(-8.33957 - 14.4446i) q^{69} +(2.01848 + 1.69370i) q^{71} +(6.54321 - 5.49040i) q^{72} +(1.13097 - 6.41403i) q^{73} +(-4.54543 + 1.65440i) q^{74} +(-3.47540 + 15.3984i) q^{76} -4.46426 q^{77} +(-31.5620 + 11.4876i) q^{78} +(0.715459 - 4.05757i) q^{79} +(-8.21894 - 6.89651i) q^{81} +(1.61590 + 9.16425i) q^{82} +(3.21198 + 5.56331i) q^{83} +(-6.77258 + 11.7304i) q^{84} +(1.05351 + 0.383448i) q^{86} +(2.54302 - 4.40463i) q^{87} +(-5.24290 - 9.08097i) q^{88} +(3.00487 + 17.0415i) q^{89} +(7.77297 - 6.52229i) q^{91} +(-4.59011 + 26.0318i) q^{92} +(9.50539 - 3.45968i) q^{93} -5.45702 q^{94} +7.42673 q^{96} +(-0.122107 + 0.0444434i) q^{97} +(-1.77901 + 10.0893i) q^{98} +(4.64207 - 3.89516i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9}+O(q^{10}) \) 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9	\( 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 42 q^{16} - 12 q^{19} - 54 q^{21} - 24 q^{24} + 12 q^{26} - 42 q^{31} + 36 q^{34} + 18 q^{36} + 48 q^{39} + 6 q^{41} + 6 q^{44} - 6 q^{46} - 12 q^{49} + 108 q^{51} - 24 q^{54} + 36 q^{56} + 36 q^{59} + 48 q^{61} + 180 q^{66} - 66 q^{69} - 24 q^{71} - 84 q^{74} + 66 q^{76} - 48 q^{79} - 78 q^{81} + 54 q^{84} - 42 q^{86} + 12 q^{89} - 30 q^{91} + 72 q^{94} - 240 q^{96} + 36 q^{99}+O(q^{100}) \) 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9 - 12 * q^11 - 6 * q^14 - 42 * q^16 - 12 * q^19 - 54 * q^21 - 24 * q^24 + 12 * q^26 - 42 * q^31 + 36 * q^34 + 18 * q^36 + 48 * q^39 + 6 * q^41 + 6 * q^44 - 6 * q^46 - 12 * q^49 + 108 * q^51 - 24 * q^54 + 36 * q^56 + 36 * q^59 + 48 * q^61 + 180 * q^66 - 66 * q^69 - 24 * q^71 - 84 * q^74 + 66 * q^76 - 48 * q^79 - 78 * q^81 + 54 * q^84 - 42 * q^86 + 12 * q^89 - 30 * q^91 + 72 * q^94 - 240 * q^96 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more