LMFDB - Embedded newform 1050.3.e.a.701.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(701,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1050.701");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.e (of order $2$, degree $1$, 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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 8x^{2} + 9 $ x^4 + 8*x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			701.4
Root			$1.16372i$ of defining polynomial
Character	$\chi$	$=$	1050.701
Dual form			1050.3.e.a.701.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +(2.64575 + 1.41421i) q^{3} -2.00000 q^{4} +(-2.00000 + 3.74166i) q^{6} -2.64575 q^{7} -2.82843i q^{8} +(5.00000 + 7.48331i) q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +(2.64575 + 1.41421i) q^{3} -2.00000 q^{4} +(-2.00000 + 3.74166i) q^{6} -2.64575 q^{7} -2.82843i q^{8} +(5.00000 + 7.48331i) q^{9} -0.412247i q^{11} +(-5.29150 - 2.82843i) q^{12} -20.5830 q^{13} -3.74166i q^{14} +4.00000 q^{16} +15.8799i q^{17} +(-10.5830 + 7.07107i) q^{18} -16.0000 q^{19} +(-7.00000 - 3.74166i) q^{21} +0.583005 q^{22} -36.0024i q^{23} +(4.00000 - 7.48331i) q^{24} -29.1088i q^{26} +(2.64575 + 26.8701i) q^{27} +5.29150 q^{28} -20.8010i q^{29} -5.54249 q^{31} +5.65685i q^{32} +(0.583005 - 1.09070i) q^{33} -22.4575 q^{34} +(-10.0000 - 14.9666i) q^{36} -20.0000 q^{37} -22.6274i q^{38} +(-54.4575 - 29.1088i) q^{39} +76.1013i q^{41} +(5.29150 - 9.89949i) q^{42} -51.7490 q^{43} +0.824494i q^{44} +50.9150 q^{46} -8.48528i q^{47} +(10.5830 + 5.65685i) q^{48} +7.00000 q^{49} +(-22.4575 + 42.0142i) q^{51} +41.1660 q^{52} -50.9117i q^{53} +(-38.0000 + 3.74166i) q^{54} +7.48331i q^{56} +(-42.3320 - 22.6274i) q^{57} +29.4170 q^{58} +1.64899i q^{59} -66.9150 q^{61} -7.83826i q^{62} +(-13.2288 - 19.7990i) q^{63} -8.00000 q^{64} +(1.54249 + 0.824494i) q^{66} -49.4170 q^{67} -31.7597i q^{68} +(50.9150 - 95.2533i) q^{69} -87.7385i q^{71} +(21.1660 - 14.1421i) q^{72} +12.3320 q^{73} -28.2843i q^{74} +32.0000 q^{76} +1.09070i q^{77} +(41.1660 - 77.0146i) q^{78} -84.9150 q^{79} +(-31.0000 + 74.8331i) q^{81} -107.624 q^{82} +4.12247i q^{83} +(14.0000 + 7.48331i) q^{84} -73.1842i q^{86} +(29.4170 - 55.0342i) q^{87} -1.16601 q^{88} -31.2014i q^{89} +54.4575 q^{91} +72.0047i q^{92} +(-14.6640 - 7.83826i) q^{93} +12.0000 q^{94} +(-8.00000 + 14.9666i) q^{96} +68.8340 q^{97} +9.89949i q^{98} +(3.08497 - 2.06123i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{4} - 8 q^{6} + 20 q^{9}+O(q^{10}) $ 4 * q - 8 * q^4 - 8 * q^6 + 20 * q^9	$ 4 q - 8 q^{4} - 8 q^{6} + 20 q^{9} - 40 q^{13} + 16 q^{16} - 64 q^{19} - 28 q^{21} - 40 q^{22} + 16 q^{24} - 128 q^{31} - 40 q^{33} + 16 q^{34} - 40 q^{36} - 80 q^{37} - 112 q^{39} - 80 q^{43} - 8 q^{46} + 28 q^{49} + 16 q^{51} + 80 q^{52} - 152 q^{54} + 160 q^{58} - 56 q^{61} - 32 q^{64} + 112 q^{66} - 240 q^{67} - 8 q^{69} - 120 q^{73} + 128 q^{76} + 80 q^{78} - 128 q^{79} - 124 q^{81} - 240 q^{82} + 56 q^{84} + 160 q^{87} + 80 q^{88} + 112 q^{91} + 280 q^{93} + 48 q^{94} - 32 q^{96} + 360 q^{97} + 224 q^{99}+O(q^{100}) $ 4 * q - 8 * q^4 - 8 * q^6 + 20 * q^9 - 40 * q^13 + 16 * q^16 - 64 * q^19 - 28 * q^21 - 40 * q^22 + 16 * q^24 - 128 * q^31 - 40 * q^33 + 16 * q^34 - 40 * q^36 - 80 * q^37 - 112 * q^39 - 80 * q^43 - 8 * q^46 + 28 * q^49 + 16 * q^51 + 80 * q^52 - 152 * q^54 + 160 * q^58 - 56 * q^61 - 32 * q^64 + 112 * q^66 - 240 * q^67 - 8 * q^69 - 120 * q^73 + 128 * q^76 + 80 * q^78 - 128 * q^79 - 124 * q^81 - 240 * q^82 + 56 * q^84 + 160 * q^87 + 80 * q^88 + 112 * q^91 + 280 * q^93 + 48 * q^94 - 32 * q^96 + 360 * q^97 + 224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$	2.64575	+	1.41421i	0.881917	+	0.471405i
$3$	2.64575	+	1.41421i	0.881917	+	0.471405i
$4$	−2.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	−2.00000	+	3.74166i	−0.333333	+	0.623610i
$7$	−2.64575			−0.377964
$7$	−2.64575			−0.377964
$8$		−	2.82843i		−	0.353553i
$9$	5.00000	+	7.48331i	0.555556	+	0.831479i
$10$		0			0
$11$		−	0.412247i		−	0.0374770i	−0.999824	−	0.0187385i	$-0.994035\pi$
$11$		−	0.412247i		−	0.0374770i	0.999824	−	0.0187385i	$-0.00596500\pi$
$12$	−5.29150	−	2.82843i	−0.440959	−	0.235702i
$13$	−20.5830			−1.58331			−0.791654	−	0.610970i	$-0.790780\pi$
$13$	−20.5830			−1.58331			−0.791654	+	0.610970i	$0.790780\pi$
$14$		−	3.74166i		−	0.267261i
$15$		0			0
$16$	4.00000			0.250000
$17$			15.8799i			0.934109i	0.884228	+	0.467055i	$0.154685\pi$
$17$			15.8799i			0.934109i	−0.884228	+	0.467055i	$0.845315\pi$
$18$	−10.5830	+	7.07107i	−0.587945	+	0.392837i
$19$	−16.0000			−0.842105			−0.421053	−	0.907036i	$-0.638339\pi$
$19$	−16.0000			−0.842105			−0.421053	+	0.907036i	$0.638339\pi$
$20$		0			0
$21$	−7.00000	−	3.74166i	−0.333333	−	0.178174i
$22$	0.583005			0.0265002
$23$		−	36.0024i		−	1.56532i	−0.622449	−	0.782660i	$-0.713862\pi$
$23$		−	36.0024i		−	1.56532i	0.622449	−	0.782660i	$-0.286138\pi$
$24$	4.00000	−	7.48331i	0.166667	−	0.311805i
$25$		0			0
$26$		−	29.1088i		−	1.11957i
$27$	2.64575	+	26.8701i	0.0979908	+	0.995187i
$28$	5.29150			0.188982
$29$		−	20.8010i		−	0.717274i	−0.933477	−	0.358637i	$-0.883242\pi$
$29$		−	20.8010i		−	0.717274i	0.933477	−	0.358637i	$-0.116758\pi$
$30$		0			0
$31$	−5.54249			−0.178790			−0.0893949	−	0.995996i	$-0.528493\pi$
$31$	−5.54249			−0.178790			−0.0893949	+	0.995996i	$0.528493\pi$
$32$			5.65685i			0.176777i
$33$	0.583005	−	1.09070i	0.0176668	−	0.0330516i
$34$	−22.4575			−0.660515
$35$		0			0
$36$	−10.0000	−	14.9666i	−0.277778	−	0.415740i
$37$	−20.0000			−0.540541			−0.270270	−	0.962784i	$-0.587113\pi$
$37$	−20.0000			−0.540541			−0.270270	+	0.962784i	$0.587113\pi$
$38$		−	22.6274i		−	0.595458i
$39$	−54.4575	−	29.1088i	−1.39635	−	0.746379i
$40$		0			0
$41$			76.1013i			1.85613i	0.372418	+	0.928065i	$0.378529\pi$
$41$			76.1013i			1.85613i	−0.372418	+	0.928065i	$0.621471\pi$
$42$	5.29150	−	9.89949i	0.125988	−	0.235702i
$43$	−51.7490			−1.20347			−0.601733	−	0.798698i	$-0.705523\pi$
$43$	−51.7490			−1.20347			−0.601733	+	0.798698i	$0.705523\pi$
$44$			0.824494i			0.0187385i
$45$		0			0
$46$	50.9150			1.10685
$47$		−	8.48528i		−	0.180538i	−0.995917	−	0.0902690i	$-0.971227\pi$
$47$		−	8.48528i		−	0.180538i	0.995917	−	0.0902690i	$-0.0287727\pi$
$48$	10.5830	+	5.65685i	0.220479	+	0.117851i
$49$	7.00000			0.142857
$50$		0			0
$51$	−22.4575	+	42.0142i	−0.440343	+	0.823807i
$52$	41.1660			0.791654
$53$		−	50.9117i		−	0.960598i	−0.877105	−	0.480299i	$-0.840528\pi$
$53$		−	50.9117i		−	0.960598i	0.877105	−	0.480299i	$-0.159472\pi$
$54$	−38.0000	+	3.74166i	−0.703704	+	0.0692900i
$55$		0			0
$56$			7.48331i			0.133631i
$57$	−42.3320	−	22.6274i	−0.742667	−	0.396972i
$58$	29.4170			0.507190
$59$			1.64899i			0.0279489i	0.999902	+	0.0139745i	$0.00444836\pi$
$59$			1.64899i			0.0279489i	−0.999902	+	0.0139745i	$0.995552\pi$
$60$		0			0
$61$	−66.9150			−1.09697			−0.548484	−	0.836161i	$-0.684795\pi$
$61$	−66.9150			−1.09697			−0.548484	+	0.836161i	$0.684795\pi$
$62$		−	7.83826i		−	0.126424i
$63$	−13.2288	−	19.7990i	−0.209980	−	0.314270i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	1.54249	+	0.824494i	0.0233710	+	0.0124923i
$67$	−49.4170			−0.737567			−0.368784	−	0.929515i	$-0.620226\pi$
$67$	−49.4170			−0.737567			−0.368784	+	0.929515i	$0.620226\pi$
$68$		−	31.7597i		−	0.467055i
$69$	50.9150	−	95.2533i	0.737899	−	1.38048i
$70$		0			0
$71$		−	87.7385i		−	1.23575i	−0.786275	−	0.617877i	$-0.787993\pi$
$71$		−	87.7385i		−	1.23575i	0.786275	−	0.617877i	$-0.212007\pi$
$72$	21.1660	−	14.1421i	0.293972	−	0.196419i
$73$	12.3320			0.168932			0.0844659	−	0.996426i	$-0.473082\pi$
$73$	12.3320			0.168932			0.0844659	+	0.996426i	$0.473082\pi$
$74$		−	28.2843i		−	0.382220i
$75$		0			0
$76$	32.0000			0.421053
$77$			1.09070i			0.0141650i
$78$	41.1660	−	77.0146i	0.527769	−	0.987366i
$79$	−84.9150			−1.07487			−0.537437	−	0.843304i	$-0.680607\pi$
$79$	−84.9150			−1.07487			−0.537437	+	0.843304i	$0.680607\pi$
$80$		0			0
$81$	−31.0000	+	74.8331i	−0.382716	+	0.923866i
$82$	−107.624			−1.31248
$83$			4.12247i			0.0496683i	0.999692	+	0.0248342i	$0.00790577\pi$
$83$			4.12247i			0.0496683i	−0.999692	+	0.0248342i	$0.992094\pi$
$84$	14.0000	+	7.48331i	0.166667	+	0.0890871i
$85$		0			0
$86$		−	73.1842i		−	0.850979i
$87$	29.4170	−	55.0342i	0.338126	−	0.632577i
$88$	−1.16601			−0.0132501
$89$		−	31.2014i		−	0.350578i	−0.984517	−	0.175289i	$-0.943914\pi$
$89$		−	31.2014i		−	0.350578i	0.984517	−	0.175289i	$-0.0560860\pi$
$90$		0			0
$91$	54.4575			0.598434
$92$			72.0047i			0.782660i
$93$	−14.6640	−	7.83826i	−0.157678	−	0.0842824i
$94$	12.0000			0.127660
$95$		0			0
$96$	−8.00000	+	14.9666i	−0.0833333	+	0.155902i
$97$	68.8340			0.709629			0.354814	−	0.934937i	$-0.384544\pi$
$97$	68.8340			0.709629			0.354814	+	0.934937i	$0.384544\pi$
$98$			9.89949i			0.101015i
$99$	3.08497	−	2.06123i	0.0311614	−	0.0208206i
$100$		0			0
$101$			140.153i			1.38766i	0.720141	+	0.693828i	$0.244077\pi$
$101$			140.153i			1.38766i	−0.720141	+	0.693828i	$0.755923\pi$
$102$	−59.4170	−	31.7597i	−0.582520	−	0.311370i
$103$	−39.3725			−0.382258			−0.191129	−	0.981565i	$-0.561215\pi$
$103$	−39.3725			−0.382258			−0.191129	+	0.981565i	$0.561215\pi$
$104$			58.2175i			0.559784i
$105$		0			0
$106$	72.0000			0.679245
$107$			108.007i			1.00941i	0.863291	+	0.504706i	$0.168399\pi$
$107$			108.007i			1.00941i	−0.863291	+	0.504706i	$0.831601\pi$
$108$	−5.29150	−	53.7401i	−0.0489954	−	0.497594i
$109$	−123.830			−1.13606			−0.568028	−	0.823009i	$-0.692293\pi$
$109$	−123.830			−1.13606			−0.568028	+	0.823009i	$0.692293\pi$
$110$		0			0
$111$	−52.9150	−	28.2843i	−0.476712	−	0.254813i
$112$	−10.5830			−0.0944911
$113$		−	80.4900i		−	0.712301i	−0.934429	−	0.356150i	$-0.884089\pi$
$113$		−	80.4900i		−	0.712301i	0.934429	−	0.356150i	$-0.115911\pi$
$114$	32.0000	−	59.8665i	0.280702	−	0.525145i
$115$		0			0
$116$			41.6019i			0.358637i
$117$	−102.915	−	154.029i	−0.879616	−	1.31649i
$118$	−2.33202			−0.0197629
$119$		−	42.0142i		−	0.353060i
$120$		0			0
$121$	120.830			0.998595
$122$		−	94.6321i		−	0.775673i
$123$	−107.624	+	201.345i	−0.874988	+	1.63695i
$124$	11.0850			0.0893949
$125$		0			0
$126$	28.0000	−	18.7083i	0.222222	−	0.148478i
$127$	132.915			1.04658			0.523288	−	0.852156i	$-0.324705\pi$
$127$	132.915			1.04658			0.523288	+	0.852156i	$0.324705\pi$
$128$		−	11.3137i		−	0.0883883i
$129$	−136.915	−	73.1842i	−1.06136	−	0.567319i
$130$		0			0
$131$			4.12247i			0.0314692i	0.999876	+	0.0157346i	$0.00500869\pi$
$131$			4.12247i			0.0314692i	−0.999876	+	0.0157346i	$0.994991\pi$
$132$	−1.16601	+	2.18141i	−0.00883341	+	0.0165258i
$133$	42.3320			0.318286
$134$		−	69.8862i		−	0.521539i
$135$		0			0
$136$	44.9150			0.330258
$137$			99.6420i			0.727314i	0.931533	+	0.363657i	$0.118472\pi$
$137$			99.6420i			0.727314i	−0.931533	+	0.363657i	$0.881528\pi$
$138$	134.708	+	72.0047i	0.976149	+	0.521773i
$139$	93.5425			0.672968			0.336484	−	0.941689i	$-0.390762\pi$
$139$	93.5425			0.672968			0.336484	+	0.941689i	$0.390762\pi$
$140$		0			0
$141$	12.0000	−	22.4499i	0.0851064	−	0.159219i
$142$	124.081			0.873810
$143$			8.48528i			0.0593376i
$144$	20.0000	+	29.9333i	0.138889	+	0.207870i
$145$		0			0
$146$			17.4401i			0.119453i
$147$	18.5203	+	9.89949i	0.125988	+	0.0673435i
$148$	40.0000			0.270270
$149$			49.8469i			0.334543i	0.985911	+	0.167271i	$0.0534956\pi$
$149$			49.8469i			0.334543i	−0.985911	+	0.167271i	$0.946504\pi$
$150$		0			0
$151$	211.660			1.40172			0.700861	−	0.713298i	$-0.252799\pi$
$151$	211.660			1.40172			0.700861	+	0.713298i	$0.252799\pi$
$152$			45.2548i			0.297729i
$153$	−118.834	+	79.3993i	−0.776693	+	0.518950i
$154$	−1.54249			−0.0100161
$155$		0			0
$156$	108.915	+	58.2175i	0.698173	+	0.373189i
$157$	108.745			0.692644			0.346322	−	0.938116i	$-0.387430\pi$
$157$	108.745			0.692644			0.346322	+	0.938116i	$0.387430\pi$
$158$		−	120.088i		−	0.760051i
$159$	72.0000	−	134.700i	0.452830	−	0.847168i
$160$		0			0
$161$			95.2533i			0.591635i
$162$	−105.830	−	43.8406i	−0.653272	−	0.270621i
$163$	−13.0039			−0.0797788			−0.0398894	−	0.999204i	$-0.512701\pi$
$163$	−13.0039			−0.0797788			−0.0398894	+	0.999204i	$0.512701\pi$
$164$		−	152.203i		−	0.928065i
$165$		0			0
$166$	−5.83005			−0.0351208
$167$		−	156.858i		−	0.939267i	−0.882862	−	0.469633i	$-0.844386\pi$
$167$		−	156.858i		−	0.939267i	0.882862	−	0.469633i	$-0.155614\pi$
$168$	−10.5830	+	19.7990i	−0.0629941	+	0.117851i
$169$	254.660			1.50686
$170$		0			0
$171$	−80.0000	−	119.733i	−0.467836	−	0.700193i
$172$	103.498			0.601733
$173$		−	5.45351i		−	0.0315232i	−0.999876	−	0.0157616i	$-0.994983\pi$
$173$		−	5.45351i		−	0.0315232i	0.999876	−	0.0157616i	$-0.00501728\pi$
$174$	77.8301	+	41.6019i	0.447299	+	0.239091i
$175$		0			0
$176$		−	1.64899i		−	0.00936925i
$177$	−2.33202	+	4.36281i	−0.0131753	+	0.0246487i
$178$	44.1255			0.247896
$179$		−	1.23674i		−	0.00690917i	−0.999994	−	0.00345458i	$-0.998900\pi$
$179$		−	1.23674i		−	0.00690917i	0.999994	−	0.00345458i	$-0.00109963\pi$
$180$		0			0
$181$	−186.915			−1.03268			−0.516340	−	0.856384i	$-0.672706\pi$
$181$	−186.915			−1.03268			−0.516340	+	0.856384i	$0.672706\pi$
$182$			77.0146i			0.423157i
$183$	−177.041	−	94.6321i	−0.967435	−	0.517116i
$184$	−101.830			−0.553424
$185$		0			0
$186$	11.0850	−	20.7381i	0.0595966	−	0.111495i
$187$	6.54642			0.0350076
$188$			16.9706i			0.0902690i
$189$	−7.00000	−	71.0915i	−0.0370370	−	0.376145i
$190$		0			0
$191$			350.542i			1.83530i	0.397392	+	0.917649i	$0.369915\pi$
$191$			350.542i			1.83530i	−0.397392	+	0.917649i	$0.630085\pi$
$192$	−21.1660	−	11.3137i	−0.110240	−	0.0589256i
$193$	−270.494			−1.40152			−0.700762	−	0.713395i	$-0.747156\pi$
$193$	−270.494			−1.40152			−0.700762	+	0.713395i	$0.747156\pi$
$194$			97.3460i			0.501783i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$			63.5194i			0.322434i	0.986919	+	0.161217i	$0.0515419\pi$
$197$			63.5194i			0.322434i	−0.986919	+	0.161217i	$0.948458\pi$
$198$	2.91503	+	4.36281i	0.0147224	+	0.0220344i
$199$	−88.0000			−0.442211			−0.221106	−	0.975250i	$-0.570967\pi$
$199$	−88.0000			−0.442211			−0.221106	+	0.975250i	$0.570967\pi$
$200$		0			0
$201$	−130.745	−	69.8862i	−0.650473	−	0.347692i
$202$	−198.207			−0.981220
$203$			55.0342i			0.271104i
$204$	44.9150	−	84.0283i	0.220172	−	0.411904i
$205$		0			0
$206$		−	55.6812i		−	0.270297i
$207$	269.417	−	180.012i	1.30153	−	0.869622i
$208$	−82.3320			−0.395827
$209$			6.59595i			0.0315596i
$210$		0			0
$211$	−378.745			−1.79500			−0.897500	−	0.441014i	$-0.854619\pi$
$211$	−378.745			−1.79500			−0.897500	+	0.441014i	$0.854619\pi$
$212$			101.823i			0.480299i
$213$	124.081	−	232.134i	0.582540	−	1.08983i
$214$	−152.745			−0.713762
$215$		0			0
$216$	76.0000	−	7.48331i	0.351852	−	0.0346450i
$217$	14.6640			0.0675762
$218$		−	175.122i		−	0.803313i
$219$	32.6275	+	17.4401i	0.148984	+	0.0796352i
$220$		0			0
$221$		−	326.855i		−	1.47898i
$222$	40.0000	−	74.8331i	0.180180	−	0.337086i
$223$	230.494			1.03361			0.516803	−	0.856104i	$-0.327122\pi$
$223$	230.494			1.03361			0.516803	+	0.856104i	$0.327122\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	113.830			0.503673
$227$			258.441i			1.13850i	0.822163	+	0.569252i	$0.192767\pi$
$227$			258.441i			1.13850i	−0.822163	+	0.569252i	$0.807233\pi$
$228$	84.6640	+	45.2548i	0.371334	+	0.198486i
$229$	−37.0850			−0.161943			−0.0809716	−	0.996716i	$-0.525802\pi$
$229$	−37.0850			−0.161943			−0.0809716	+	0.996716i	$0.525802\pi$
$230$		0			0
$231$	−1.54249	+	2.88573i	−0.00667743	+	0.0124923i
$232$	−58.8340			−0.253595
$233$		−	82.6714i		−	0.354813i	−0.984138	−	0.177406i	$-0.943229\pi$
$233$		−	82.6714i		−	0.354813i	0.984138	−	0.177406i	$-0.0567707\pi$
$234$	217.830	−	145.544i	0.930898	−	0.621982i
$235$		0			0
$236$		−	3.29798i		−	0.0139745i
$237$	−224.664	−	120.088i	−0.947950	−	0.506700i
$238$	59.4170			0.249651
$239$			168.469i			0.704891i	0.935832	+	0.352445i	$0.114650\pi$
$239$			168.469i			0.704891i	−0.935832	+	0.352445i	$0.885350\pi$
$240$		0			0
$241$	−130.000			−0.539419			−0.269710	−	0.962942i	$-0.586928\pi$
$241$	−130.000			−0.539419			−0.269710	+	0.962942i	$0.586928\pi$
$242$			170.879i			0.706114i
$243$	−187.848	+	154.149i	−0.773038	+	0.634359i
$244$	133.830			0.548484
$245$		0			0
$246$	−284.745	−	152.203i	−1.15750	−	0.618710i
$247$	329.328			1.33331
$248$			15.6765i			0.0632118i
$249$	−5.83005	+	10.9070i	−0.0234139	+	0.0438033i
$250$		0			0
$251$		−	119.859i		−	0.477525i	−0.971078	−	0.238763i	$-0.923258\pi$
$251$		−	119.859i		−	0.477525i	0.971078	−	0.238763i	$-0.0767417\pi$
$252$	26.4575	+	39.5980i	0.104990	+	0.157135i
$253$	−14.8419			−0.0586635
$254$			187.970i			0.740040i
$255$		0			0
$256$	16.0000			0.0625000
$257$		−	223.889i		−	0.871165i	−0.900149	−	0.435583i	$-0.856542\pi$
$257$		−	223.889i		−	0.871165i	0.900149	−	0.435583i	$-0.143458\pi$
$258$	103.498	−	193.627i	0.401155	−	0.750493i
$259$	52.9150			0.204305
$260$		0			0
$261$	155.660	−	104.005i	0.596399	−	0.398486i
$262$	−5.83005			−0.0222521
$263$			214.434i			0.815337i	0.913130	+	0.407668i	$0.133658\pi$
$263$			214.434i			0.815337i	−0.913130	+	0.407668i	$0.866342\pi$
$264$	−3.08497	−	1.64899i	−0.0116855	−	0.00624617i
$265$		0			0
$266$			59.8665i			0.225062i
$267$	44.1255	−	82.5512i	0.165264	−	0.309181i
$268$	98.8340			0.368784
$269$			382.156i			1.42065i	0.703872	+	0.710326i	$0.251453\pi$
$269$			382.156i			1.42065i	−0.703872	+	0.710326i	$0.748547\pi$
$270$		0			0
$271$	114.458			0.422352			0.211176	−	0.977448i	$-0.432271\pi$
$271$	114.458			0.422352			0.211176	+	0.977448i	$0.432271\pi$
$272$			63.5194i			0.233527i
$273$	144.081	+	77.0146i	0.527769	+	0.282105i
$274$	−140.915			−0.514288
$275$		0			0
$276$	−101.830	+	190.507i	−0.368949	+	0.690241i
$277$	230.494			0.832109			0.416054	−	0.909340i	$-0.363413\pi$
$277$	230.494			0.832109			0.416054	+	0.909340i	$0.363413\pi$
$278$			132.289i			0.475860i
$279$	−27.7124	−	41.4762i	−0.0993277	−	0.148660i
$280$		0			0
$281$		−	73.9458i		−	0.263152i	−0.991306	−	0.131576i	$-0.957996\pi$
$281$		−	73.9458i		−	0.263152i	0.991306	−	0.131576i	$-0.0420038\pi$
$282$	31.7490	+	16.9706i	0.112585	+	0.0601793i
$283$	−141.166			−0.498820			−0.249410	−	0.968398i	$-0.580237\pi$
$283$	−141.166			−0.498820			−0.249410	+	0.968398i	$0.580237\pi$
$284$			175.477i			0.617877i
$285$		0			0
$286$	−12.0000			−0.0419580
$287$		−	201.345i		−	0.701551i
$288$	−42.3320	+	28.2843i	−0.146986	+	0.0982093i
$289$	36.8301			0.127440
$290$		0			0
$291$	182.118	+	97.3460i	0.625834	+	0.334522i
$292$	−24.6640			−0.0844659
$293$			329.595i			1.12490i	0.826832	+	0.562449i	$0.190141\pi$
$293$			329.595i			1.12490i	−0.826832	+	0.562449i	$0.809859\pi$
$294$	−14.0000	+	26.1916i	−0.0476190	+	0.0890871i
$295$		0			0
$296$			56.5685i			0.191110i
$297$	11.0771	−	1.09070i	0.0372966	−	0.00367240i
$298$	−70.4941			−0.236557
$299$			741.037i			2.47838i
$300$		0			0
$301$	136.915			0.454867
$302$			299.333i			0.991168i
$303$	−198.207	+	370.810i	−0.654147	+	1.22380i
$304$	−64.0000			−0.210526
$305$		0			0
$306$	−112.288	−	168.057i	−0.366953	−	0.549205i
$307$	105.830			0.344723			0.172362	−	0.985034i	$-0.444860\pi$
$307$	105.830			0.344723			0.172362	+	0.985034i	$0.444860\pi$
$308$		−	2.18141i		−	0.00708249i
$309$	−104.170	−	55.6812i	−0.337120	−	0.180198i
$310$		0			0
$311$		−	385.136i		−	1.23838i	−0.785242	−	0.619189i	$-0.787461\pi$
$311$		−	385.136i		−	1.23838i	0.785242	−	0.619189i	$-0.212539\pi$
$312$	−82.3320	+	154.029i	−0.263885	+	0.493683i
$313$	79.3281			0.253444			0.126722	−	0.991938i	$-0.459554\pi$
$313$	79.3281			0.253444			0.126722	+	0.991938i	$0.459554\pi$
$314$			153.789i			0.489773i
$315$		0			0
$316$	169.830			0.537437
$317$			411.176i			1.29708i	0.761179	+	0.648542i	$0.224621\pi$
$317$			411.176i			1.29708i	−0.761179	+	0.648542i	$0.775379\pi$
$318$	190.494	+	101.823i	0.599038	+	0.320199i
$319$	−8.57513			−0.0268813
$320$		0			0
$321$	−152.745	+	285.760i	−0.475841	+	0.890218i
$322$	−134.708			−0.418349
$323$		−	254.078i		−	0.786618i
$324$	62.0000	−	149.666i	0.191358	−	0.461933i
$325$		0			0
$326$		−	18.3903i		−	0.0564121i
$327$	−327.624	−	175.122i	−1.00191	−	0.535542i
$328$	215.247			0.656241
$329$			22.4499i			0.0682369i
$330$		0			0
$331$	−489.490			−1.47882			−0.739411	−	0.673254i	$-0.764896\pi$
$331$	−489.490			−1.47882			−0.739411	+	0.673254i	$0.764896\pi$
$332$		−	8.24494i		−	0.0248342i
$333$	−100.000	−	149.666i	−0.300300	−	0.449448i
$334$	221.830			0.664162
$335$		0			0
$336$	−28.0000	−	14.9666i	−0.0833333	−	0.0445435i
$337$	−500.316			−1.48462			−0.742309	−	0.670058i	$-0.766269\pi$
$337$	−500.316			−1.48462			−0.742309	+	0.670058i	$0.766269\pi$
$338$			360.144i			1.06551i
$339$	113.830	−	212.957i	0.335782	−	0.628190i
$340$		0			0
$341$			2.28487i			0.00670051i
$342$	169.328	−	113.137i	0.495111	−	0.330810i
$343$	−18.5203			−0.0539949
$344$			146.368i			0.425489i
$345$		0			0
$346$	7.71243			0.0222903
$347$			192.860i			0.555792i	0.960611	+	0.277896i	$0.0896371\pi$
$347$			192.860i			0.555792i	−0.960611	+	0.277896i	$0.910363\pi$
$348$	−58.8340	+	110.068i	−0.169063	+	0.316288i
$349$	148.405			0.425230			0.212615	−	0.977136i	$-0.431802\pi$
$349$	148.405			0.425230			0.212615	+	0.977136i	$0.431802\pi$
$350$		0			0
$351$	−54.4575	−	553.067i	−0.155150	−	1.57569i
$352$	2.33202			0.00662506
$353$		−	163.771i		−	0.463942i	−0.972723	−	0.231971i	$-0.925483\pi$
$353$		−	163.771i		−	0.463942i	0.972723	−	0.231971i	$-0.0745174\pi$
$354$	−6.16995	−	3.29798i	−0.0174292	−	0.00931632i
$355$		0			0
$356$			62.4029i			0.175289i
$357$	59.4170	−	111.159i	0.166434	−	0.311370i
$358$	1.74902			0.00488552
$359$			334.877i			0.932804i	0.884573	+	0.466402i	$0.154450\pi$
$359$			334.877i			0.932804i	−0.884573	+	0.466402i	$0.845550\pi$
$360$		0			0
$361$	−105.000			−0.290859
$362$		−	264.338i		−	0.730215i
$363$	319.686	+	170.879i	0.880678	+	0.470742i
$364$	−108.915			−0.299217
$365$		0			0
$366$	133.830	−	250.373i	0.365656	−	0.684080i
$367$	−326.996			−0.890997			−0.445499	−	0.895283i	$-0.646974\pi$
$367$	−326.996			−0.890997			−0.445499	+	0.895283i	$0.646974\pi$
$368$		−	144.009i		−	0.391330i
$369$	−569.490	+	380.507i	−1.54333	+	1.03118i
$370$		0			0
$371$			134.700i			0.363072i
$372$	29.3281	+	15.6765i	0.0788389	+	0.0421412i
$373$	305.336			0.818595			0.409298	−	0.912401i	$-0.365774\pi$
$373$	305.336			0.818595			0.409298	+	0.912401i	$0.365774\pi$
$374$			9.25804i			0.0247541i
$375$		0			0
$376$	−24.0000			−0.0638298
$377$			428.146i			1.13567i
$378$	100.539	−	9.89949i	0.265975	−	0.0261891i
$379$	199.660			0.526808			0.263404	−	0.964686i	$-0.415155\pi$
$379$	199.660			0.526808			0.263404	+	0.964686i	$0.415155\pi$
$380$		0			0
$381$	351.660	+	187.970i	0.922992	+	0.493360i
$382$	−495.741			−1.29775
$383$			529.489i			1.38248i	0.722626	+	0.691239i	$0.242935\pi$
$383$			529.489i			1.38248i	−0.722626	+	0.691239i	$0.757065\pi$
$384$	16.0000	−	29.9333i	0.0416667	−	0.0779512i
$385$		0			0
$386$		−	382.536i		−	0.991027i
$387$	−258.745	−	387.254i	−0.668592	−	1.00066i
$388$	−137.668			−0.354814
$389$			238.704i			0.613636i	0.951768	+	0.306818i	$0.0992643\pi$
$389$			238.704i			0.613636i	−0.951768	+	0.306818i	$0.900736\pi$
$390$		0			0
$391$	571.712			1.46218
$392$		−	19.7990i		−	0.0505076i
$393$	−5.83005	+	10.9070i	−0.0148347	+	0.0277533i
$394$	−89.8301			−0.227995
$395$		0			0
$396$	−6.16995	+	4.12247i	−0.0155807	+	0.0104103i
$397$	−320.583			−0.807514			−0.403757	−	0.914866i	$-0.632296\pi$
$397$	−320.583			−0.807514			−0.403757	+	0.914866i	$0.632296\pi$
$398$		−	124.451i		−	0.312690i
$399$	112.000	+	59.8665i	0.280702	+	0.150041i
$400$		0			0
$401$			232.108i			0.578824i	0.957205	+	0.289412i	$0.0934598\pi$
$401$			232.108i			0.578824i	−0.957205	+	0.289412i	$0.906540\pi$
$402$	98.8340	−	184.901i	0.245856	−	0.459954i
$403$	114.081			0.283079
$404$		−	280.306i		−	0.693828i
$405$		0			0
$406$	−77.8301			−0.191700
$407$			8.24494i			0.0202578i
$408$	118.834	+	63.5194i	0.291260	+	0.155685i
$409$	528.980			1.29335			0.646675	−	0.762765i	$-0.276159\pi$
$409$	528.980			1.29335			0.646675	+	0.762765i	$0.276159\pi$
$410$		0			0
$411$	−140.915	+	263.628i	−0.342859	+	0.641430i
$412$	78.7451			0.191129
$413$		−	4.36281i		−	0.0105637i
$414$	254.575	+	381.013i	0.614916	+	0.920322i
$415$		0			0
$416$		−	116.435i		−	0.279892i
$417$	247.490	+	132.289i	0.593502	+	0.317240i
$418$	−9.32808			−0.0223160
$419$		−	89.7998i		−	0.214319i	−0.994242	−	0.107160i	$-0.965824\pi$
$419$		−	89.7998i		−	0.214319i	0.994242	−	0.107160i	$-0.0341756\pi$
$420$		0			0
$421$	−777.150			−1.84596			−0.922981	−	0.384845i	$-0.874255\pi$
$421$	−777.150			−1.84596			−0.922981	+	0.384845i	$0.874255\pi$
$422$		−	535.626i		−	1.26926i
$423$	63.4980	−	42.4264i	0.150114	−	0.100299i
$424$	−144.000			−0.339623
$425$		0			0
$426$	328.288	+	175.477i	0.770628	+	0.411918i
$427$	177.041			0.414615
$428$		−	216.014i		−	0.504706i
$429$	−12.0000	+	22.4499i	−0.0279720	+	0.0523309i
$430$		0			0
$431$			245.901i			0.570537i	0.958448	+	0.285268i	$0.0920827\pi$
$431$			245.901i			0.570537i	−0.958448	+	0.285268i	$0.907917\pi$
$432$	10.5830	+	107.480i	0.0244977	+	0.248797i
$433$	796.996			1.84064			0.920319	−	0.391169i	$-0.127929\pi$
$433$	796.996			1.84064			0.920319	+	0.391169i	$0.127929\pi$
$434$			20.7381i			0.0477836i
$435$		0			0
$436$	247.660			0.568028
$437$			576.038i			1.31816i
$438$	−24.6640	+	46.1422i	−0.0563106	+	0.105347i
$439$	553.830			1.26157			0.630786	−	0.775957i	$-0.282733\pi$
$439$	553.830			1.26157			0.630786	+	0.775957i	$0.282733\pi$
$440$		0			0
$441$	35.0000	+	52.3832i	0.0793651	+	0.118783i
$442$	462.243			1.04580
$443$			773.981i			1.74714i	0.486702	+	0.873568i	$0.338200\pi$
$443$			773.981i			1.74714i	−0.486702	+	0.873568i	$0.661800\pi$
$444$	105.830	+	56.5685i	0.238356	+	0.127407i
$445$		0			0
$446$			325.968i			0.730870i
$447$	−70.4941	+	131.882i	−0.157705	+	0.295039i
$448$	21.1660			0.0472456
$449$		−	677.174i		−	1.50818i	−0.656770	−	0.754091i	$-0.728078\pi$
$449$		−	677.174i		−	1.50818i	0.656770	−	0.754091i	$-0.271922\pi$
$450$		0			0
$451$	31.3725			0.0695622
$452$			160.980i			0.356150i
$453$	560.000	+	299.333i	1.23620	+	0.660778i
$454$	−365.490			−0.805044
$455$		0			0
$456$	−64.0000	+	119.733i	−0.140351	+	0.262572i
$457$	−834.664			−1.82640			−0.913199	−	0.407514i	$-0.866396\pi$
$457$	−834.664			−1.82640			−0.913199	+	0.407514i	$0.866396\pi$
$458$		−	52.4461i		−	0.114511i
$459$	−426.693	+	42.0142i	−0.929614	+	0.0915341i
$460$		0			0
$461$			347.150i			0.753036i	0.926409	+	0.376518i	$0.122879\pi$
$461$			347.150i			0.753036i	−0.926409	+	0.376518i	$0.877121\pi$
$462$	−4.08104	−	2.18141i	−0.00883341	−	0.00472166i
$463$	−317.668			−0.686108			−0.343054	−	0.939316i	$-0.611461\pi$
$463$	−317.668			−0.686108			−0.343054	+	0.939316i	$0.611461\pi$
$464$		−	83.2038i		−	0.179319i
$465$		0			0
$466$	116.915			0.250891
$467$			547.421i			1.17221i	0.810236	+	0.586104i	$0.199339\pi$
$467$			547.421i			1.17221i	−0.810236	+	0.586104i	$0.800661\pi$
$468$	205.830	+	308.058i	0.439808	+	0.658244i
$469$	130.745			0.278774
$470$		0			0
$471$	287.712	+	153.789i	0.610854	+	0.326515i
$472$	4.66404			0.00988144
$473$			21.3334i			0.0451023i
$474$	169.830	−	317.723i	0.358291	−	0.670302i
$475$		0			0
$476$			84.0283i			0.176530i
$477$	380.988	−	254.558i	0.798717	−	0.533665i
$478$	−238.251			−0.498433
$479$			135.524i			0.282931i	0.989943	+	0.141466i	$0.0451815\pi$
$479$			135.524i			0.282931i	−0.989943	+	0.141466i	$0.954818\pi$
$480$		0			0
$481$	411.660			0.855842
$482$		−	183.848i		−	0.381427i
$483$	−134.708	+	252.017i	−0.278900	+	0.521773i
$484$	−241.660			−0.499298
$485$		0			0
$486$	−218.000	−	265.658i	−0.448560	−	0.546621i
$487$	−23.4980			−0.0482506			−0.0241253	−	0.999709i	$-0.507680\pi$
$487$	−23.4980			−0.0482506			−0.0241253	+	0.999709i	$0.507680\pi$
$488$			189.264i			0.387837i
$489$	−34.4052	−	18.3903i	−0.0703582	−	0.0376081i
$490$		0			0
$491$		−	103.404i		−	0.210599i	−0.994441	−	0.105299i	$-0.966420\pi$
$491$		−	103.404i		−	0.210599i	0.994441	−	0.105299i	$-0.0335801\pi$
$492$	215.247	−	402.690i	0.437494	−	0.818476i
$493$	330.316			0.670013
$494$			465.740i			0.942794i
$495$		0			0
$496$	−22.1699			−0.0446975
$497$			232.134i			0.467071i
$498$	−15.4249	−	8.24494i	−0.0309736	−	0.0165561i
$499$	−64.3399			−0.128938			−0.0644688	−	0.997920i	$-0.520535\pi$
$499$	−64.3399			−0.128938			−0.0644688	+	0.997920i	$0.520535\pi$
$500$		0			0
$501$	221.830	−	415.006i	0.442775	−	0.828355i
$502$	169.506			0.337661
$503$		−	546.940i		−	1.08736i	−0.839294	−	0.543678i	$-0.817031\pi$
$503$		−	546.940i		−	1.08736i	0.839294	−	0.543678i	$-0.182969\pi$
$504$	−56.0000	+	37.4166i	−0.111111	+	0.0742392i
$505$		0			0
$506$		−	20.9896i		−	0.0414814i
$507$	673.767	+	360.144i	1.32893	+	0.710343i
$508$	−265.830			−0.523288
$509$		−	63.5453i		−	0.124843i	−0.998050	−	0.0624217i	$-0.980118\pi$
$509$		−	63.5453i		−	0.124843i	0.998050	−	0.0624217i	$-0.0198824\pi$
$510$		0			0
$511$	−32.6275			−0.0638502
$512$			22.6274i			0.0441942i
$513$	−42.3320	−	429.921i	−0.0825186	−	0.838052i
$514$	316.627			0.616007
$515$		0			0
$516$	273.830	+	146.368i	0.530678	+	0.283660i
$517$	−3.49803			−0.00676602
$518$			74.8331i			0.144466i
$519$	7.71243	−	14.4286i	0.0148602	−	0.0278009i
$520$		0			0
$521$		−	642.297i		−	1.23282i	−0.787427	−	0.616408i	$-0.788587\pi$
$521$		−	642.297i		−	1.23282i	0.787427	−	0.616408i	$-0.211413\pi$
$522$	147.085	+	220.137i	0.281772	+	0.421718i
$523$	112.376			0.214869			0.107434	−	0.994212i	$-0.465736\pi$
$523$	112.376			0.214869			0.107434	+	0.994212i	$0.465736\pi$
$524$		−	8.24494i		−	0.0157346i
$525$		0			0
$526$	−303.255			−0.576530
$527$		−	88.0139i		−	0.167009i
$528$	2.33202	−	4.36281i	0.00441671	−	0.00826290i
$529$	−767.170			−1.45023
$530$		0			0
$531$	−12.3399	+	8.24494i	−0.0232390	+	0.0155272i
$532$	−84.6640			−0.159143
$533$		−	1566.39i		−	2.93883i
$534$	116.745	+	62.4029i	0.218624	+	0.116859i
$535$		0			0
$536$			139.772i			0.260769i
$537$	1.74902	−	3.27211i	0.00325701	−	0.00609331i
$538$	−540.450			−1.00455
$539$		−	2.88573i		−	0.00535386i
$540$		0			0
$541$	−33.1503			−0.0612759			−0.0306380	−	0.999531i	$-0.509754\pi$
$541$	−33.1503			−0.0612759			−0.0306380	+	0.999531i	$0.509754\pi$
$542$			161.867i			0.298648i
$543$	−494.531	−	264.338i	−0.910738	−	0.486810i
$544$	−89.8301			−0.165129
$545$		0			0
$546$	−108.915	+	203.761i	−0.199478	+	0.373189i
$547$	919.911			1.68174			0.840869	−	0.541238i	$-0.182044\pi$
$547$	919.911			1.68174			0.840869	+	0.541238i	$0.182044\pi$
$548$		−	199.284i		−	0.363657i
$549$	−334.575	−	500.746i	−0.609426	−	0.912106i
$550$		0			0
$551$			332.815i			0.604021i
$552$	−269.417	−	144.009i	−0.488074	−	0.260887i
$553$	224.664			0.406264
$554$			325.968i			0.588390i
$555$		0			0
$556$	−187.085			−0.336484
$557$		−	725.371i		−	1.30228i	−0.758957	−	0.651141i	$-0.774291\pi$
$557$		−	725.371i		−	1.30228i	0.758957	−	0.651141i	$-0.225709\pi$
$558$	58.6562	−	39.1913i	0.105119	−	0.0702353i
$559$	1065.15			1.90546
$560$		0			0
$561$	17.3202	+	9.25804i	0.0308738	+	0.0165027i
$562$	104.575			0.186077
$563$		−	728.773i		−	1.29445i	−0.762301	−	0.647223i	$-0.775930\pi$
$563$		−	728.773i		−	1.29445i	0.762301	−	0.647223i	$-0.224070\pi$
$564$	−24.0000	+	44.8999i	−0.0425532	+	0.0796097i
$565$		0			0
$566$		−	199.639i		−	0.352719i
$567$	82.0183	−	197.990i	0.144653	−	0.349189i
$568$	−248.162			−0.436905
$569$			167.044i			0.293574i	0.989168	+	0.146787i	$0.0468932\pi$
$569$			167.044i			0.293574i	−0.989168	+	0.146787i	$0.953107\pi$
$570$		0			0
$571$	−72.9150			−0.127697			−0.0638485	−	0.997960i	$-0.520337\pi$
$571$	−72.9150			−0.127697			−0.0638485	+	0.997960i	$0.520337\pi$
$572$		−	16.9706i		−	0.0296688i
$573$	−495.741	+	927.447i	−0.865168	+	1.61858i
$574$	284.745			0.496072
$575$		0			0
$576$	−40.0000	−	59.8665i	−0.0694444	−	0.103935i
$577$	−552.154			−0.956940			−0.478470	−	0.878104i	$-0.658808\pi$
$577$	−552.154			−0.956940			−0.478470	+	0.878104i	$0.658808\pi$
$578$			52.0856i			0.0901134i
$579$	−715.660	−	382.536i	−1.23603	−	0.660685i
$580$		0			0
$581$		−	10.9070i		−	0.0187729i
$582$	−137.668	+	257.553i	−0.236543	+	0.442531i
$583$	−20.9882			−0.0360003
$584$		−	34.8802i		−	0.0597264i
$585$		0			0
$586$	−466.118			−0.795423
$587$		−	1115.21i		−	1.89985i	−0.312474	−	0.949926i	$-0.601158\pi$
$587$		−	1115.21i		−	1.89985i	0.312474	−	0.949926i	$-0.398842\pi$
$588$	−37.0405	−	19.7990i	−0.0629941	−	0.0336718i
$589$	88.6798			0.150560
$590$		0			0
$591$	−89.8301	+	168.057i	−0.151997	+	0.284360i
$592$	−80.0000			−0.135135
$593$			957.506i			1.61468i	0.590086	+	0.807340i	$0.299094\pi$
$593$			957.506i			1.61468i	−0.590086	+	0.807340i	$0.700906\pi$
$594$	1.54249	+	15.6654i	0.00259678	+	0.0263727i
$595$		0			0
$596$		−	99.6937i		−	0.167271i
$597$	−232.826	−	124.451i	−0.389993	−	0.208460i
$598$	−1047.98			−1.75248
$599$		−	610.047i		−	1.01844i	−0.860636	−	0.509221i	$-0.829933\pi$
$599$		−	610.047i		−	1.01844i	0.860636	−	0.509221i	$-0.170067\pi$
$600$		0			0
$601$	−974.470			−1.62142			−0.810708	−	0.585451i	$-0.800917\pi$
$601$	−974.470			−1.62142			−0.810708	+	0.585451i	$0.800917\pi$
$602$			193.627i			0.321640i
$603$	−247.085	−	369.803i	−0.409759	−	0.613272i
$604$	−423.320			−0.700861
$605$		0			0
$606$	−524.405	−	280.306i	−0.865355	−	0.462552i
$607$	1096.15			1.80584			0.902921	−	0.429806i	$-0.141418\pi$
$607$	1096.15			1.80584			0.902921	+	0.429806i	$0.141418\pi$
$608$		−	90.5097i		−	0.148865i
$609$	−77.8301	+	145.607i	−0.127800	+	0.239091i
$610$		0			0
$611$			174.653i			0.285847i
$612$	237.668	−	158.799i	0.388346	−	0.259475i
$613$	311.166			0.507612			0.253806	−	0.967255i	$-0.418318\pi$
$613$	311.166			0.507612			0.253806	+	0.967255i	$0.418318\pi$
$614$			149.666i			0.243756i
$615$		0			0
$616$	3.08497			0.00500807
$617$			905.503i			1.46759i	0.679371	+	0.733795i	$0.262253\pi$
$617$			905.503i			1.46759i	−0.679371	+	0.733795i	$0.737747\pi$
$618$	78.7451	−	147.319i	0.127419	−	0.238380i
$619$	54.7974			0.0885257			0.0442628	−	0.999020i	$-0.485906\pi$
$619$	54.7974			0.0885257			0.0442628	+	0.999020i	$0.485906\pi$
$620$		0			0
$621$	967.385	−	95.2533i	1.55779	−	0.153387i
$622$	544.664			0.875666
$623$			82.5512i			0.132506i
$624$	−217.830	−	116.435i	−0.349087	−	0.186595i
$625$		0			0
$626$			112.187i			0.179212i
$627$	−9.32808	+	17.4512i	−0.0148773	+	0.0278329i
$628$	−217.490			−0.346322
$629$		−	317.597i		−	0.504924i
$630$		0			0
$631$	181.490			0.287623			0.143812	−	0.989605i	$-0.454064\pi$
$631$	181.490			0.287623			0.143812	+	0.989605i	$0.454064\pi$
$632$			240.176i			0.380025i
$633$	−1002.07	−	535.626i	−1.58304	−	0.846171i
$634$	−581.490			−0.917177
$635$		0			0
$636$	−144.000	+	269.399i	−0.226415	+	0.423584i
$637$	−144.081			−0.226187
$638$		−	12.1271i		−	0.0190079i
$639$	656.575	−	438.693i	1.02750	−	0.686530i
$640$		0			0
$641$		−	837.621i		−	1.30674i	−0.757038	−	0.653371i	$-0.773354\pi$
$641$		−	837.621i		−	1.30674i	0.757038	−	0.653371i	$-0.226646\pi$
$642$	−404.125	−	216.014i	−0.629479	−	0.336471i
$643$	−59.0118			−0.0917758			−0.0458879	−	0.998947i	$-0.514612\pi$
$643$	−59.0118			−0.0917758			−0.0458879	+	0.998947i	$0.514612\pi$
$644$		−	190.507i		−	0.295818i
$645$		0			0
$646$	359.320			0.556223
$647$		−	547.661i		−	0.846462i	−0.906022	−	0.423231i	$-0.860896\pi$
$647$		−	547.661i		−	0.846462i	0.906022	−	0.423231i	$-0.139104\pi$
$648$	211.660	+	87.6812i	0.326636	+	0.135311i
$649$	0.679790			0.00104744
$650$		0			0
$651$	38.7974	+	20.7381i	0.0595966	+	0.0318557i
$652$	26.0079			0.0398894
$653$			764.895i			1.17136i	0.810544	+	0.585678i	$0.199172\pi$
$653$			764.895i			1.17136i	−0.810544	+	0.585678i	$0.800828\pi$
$654$	247.660	−	463.330i	0.378685	−	0.708455i
$655$		0			0
$656$			304.405i			0.464032i
$657$	61.6601	+	92.2844i	0.0938510	+	0.140463i
$658$	−31.7490			−0.0482508
$659$		−	1050.80i		−	1.59454i	−0.603623	−	0.797270i	$-0.706277\pi$
$659$		−	1050.80i		−	1.59454i	0.603623	−	0.797270i	$-0.293723\pi$
$660$		0			0
$661$	−145.085			−0.219493			−0.109747	−	0.993960i	$-0.535004\pi$
$661$	−145.085			−0.219493			−0.109747	+	0.993960i	$0.535004\pi$
$662$		−	692.244i		−	1.04569i
$663$	462.243	−	864.778i	0.697199	−	1.30434i
$664$	11.6601			0.0175604
$665$		0			0
$666$	211.660	−	141.421i	0.317808	−	0.212344i
$667$	−748.884			−1.12276
$668$			313.715i			0.469633i
$669$	609.830	+	325.968i	0.911555	+	0.487246i
$670$		0			0
$671$			27.5855i			0.0411111i
$672$	21.1660	−	39.5980i	0.0314970	−	0.0589256i
$673$	−323.498			−0.480681			−0.240340	−	0.970689i	$-0.577259\pi$
$673$	−323.498			−0.480681			−0.240340	+	0.970689i	$0.577259\pi$
$674$		−	707.554i		−	1.04978i
$675$		0			0
$676$	−509.320			−0.753432
$677$			166.434i			0.245840i	0.992417	+	0.122920i	$0.0392258\pi$
$677$			166.434i			0.245840i	−0.992417	+	0.122920i	$0.960774\pi$
$678$	301.166	+	160.980i	0.444198	+	0.237434i
$679$	−182.118			−0.268214
$680$		0			0
$681$	−365.490	+	683.769i	−0.536696	+	1.00407i
$682$	−3.23130			−0.00473797
$683$		−	973.506i		−	1.42534i	−0.701501	−	0.712669i	$-0.747486\pi$
$683$		−	973.506i		−	1.42534i	0.701501	−	0.712669i	$-0.252514\pi$
$684$	160.000	+	239.466i	0.233918	+	0.350097i
$685$		0			0
$686$		−	26.1916i		−	0.0381802i
$687$	−98.1176	−	52.4461i	−0.142820	−	0.0763407i
$688$	−206.996			−0.300866
$689$			1047.92i			1.52092i
$690$		0			0
$691$	1268.86			1.83627			0.918135	−	0.396268i	$-0.129695\pi$
$691$	1268.86			1.83627			0.918135	+	0.396268i	$0.129695\pi$
$692$			10.9070i			0.0157616i
$693$	−8.16207	+	5.45351i	−0.0117779	+	0.00786943i
$694$	−272.745			−0.393004
$695$		0			0
$696$	−155.660	−	83.2038i	−0.223650	−	0.119546i
$697$	−1208.48			−1.73383
$698$			209.877i			0.300683i
$699$	116.915	−	218.728i	0.167260	−	0.312916i
$700$		0			0
$701$		−	798.940i		−	1.13971i	−0.821744	−	0.569857i	$-0.806998\pi$
$701$		−	798.940i		−	1.13971i	0.821744	−	0.569857i	$-0.193002\pi$
$702$	782.154	−	77.0146i	1.11418	−	0.109707i
$703$	320.000			0.455192
$704$			3.29798i			0.00468462i
$705$		0			0
$706$	231.608			0.328056
$707$		−	370.810i		−	0.524484i
$708$	4.66404	−	8.72562i	0.00658763	−	0.0123243i
$709$	−651.490			−0.918886			−0.459443	−	0.888207i	$-0.651951\pi$
$709$	−651.490			−0.918886			−0.459443	+	0.888207i	$0.651951\pi$
$710$		0			0
$711$	−424.575	−	635.446i	−0.597152	−	0.893735i
$712$	−88.2510			−0.123948
$713$			199.543i			0.279863i
$714$	157.203	+	84.0283i	0.220172	+	0.117687i
$715$		0			0
$716$			2.47348i			0.00345458i
$717$	−238.251	+	445.727i	−0.332289	+	0.621655i
$718$	−473.587			−0.659592
$719$		−	878.587i		−	1.22196i	−0.791647	−	0.610979i	$-0.790776\pi$
$719$		−	878.587i		−	1.22196i	0.791647	−	0.610979i	$-0.209224\pi$
$720$		0			0
$721$	104.170			0.144480
$722$		−	148.492i		−	0.205668i
$723$	−343.948	−	183.848i	−0.475723	−	0.254285i
$724$	373.830			0.516340
$725$		0			0
$726$	−241.660	+	452.105i	−0.332865	+	0.622734i
$727$	−442.782			−0.609053			−0.304527	−	0.952504i	$-0.598498\pi$
$727$	−442.782			−0.609053			−0.304527	+	0.952504i	$0.598498\pi$
$728$		−	154.029i		−	0.211578i
$729$	−715.000	+	142.183i	−0.980796	+	0.195038i
$730$		0			0
$731$		−	821.767i		−	1.12417i
$732$	354.081	+	189.264i	0.483717	+	0.258558i
$733$	−962.559			−1.31318			−0.656589	−	0.754249i	$-0.728001\pi$
$733$	−962.559			−1.31318			−0.656589	+	0.754249i	$0.728001\pi$
$734$		−	462.442i		−	0.630030i
$735$		0			0
$736$	203.660			0.276712
$737$			20.3720i			0.0276418i
$738$	−538.118	−	805.381i	−0.729157	−	1.09130i
$739$	1224.81			1.65739			0.828694	−	0.559701i	$-0.189084\pi$
$739$	1224.81			1.65739			0.828694	+	0.559701i	$0.189084\pi$
$740$		0			0
$741$	871.320	+	465.740i	1.17587	+	0.628529i
$742$	−190.494			−0.256731
$743$		−	1447.24i		−	1.94783i	−0.226908	−	0.973916i	$-0.572862\pi$
$743$		−	1447.24i		−	1.94783i	0.226908	−	0.973916i	$-0.427138\pi$
$744$	−22.1699	+	41.4762i	−0.0297983	+	0.0557475i
$745$		0			0
$746$			431.810i			0.578834i
$747$	−30.8497	+	20.6123i	−0.0412982	+	0.0275935i
$748$	−13.0928			−0.0175038
$749$		−	285.760i		−	0.381522i
$750$		0			0
$751$	−684.915			−0.912004			−0.456002	−	0.889979i	$-0.650719\pi$
$751$	−684.915			−0.912004			−0.456002	+	0.889979i	$0.650719\pi$
$752$		−	33.9411i		−	0.0451345i
$753$	169.506	−	317.117i	0.225107	−	0.421137i
$754$	−605.490			−0.803037
$755$		0			0
$756$	14.0000	+	142.183i	0.0185185	+	0.188073i
$757$	907.135			1.19833			0.599164	−	0.800626i	$-0.295500\pi$
$757$	907.135			1.19833			0.599164	+	0.800626i	$0.295500\pi$
$758$			282.362i			0.372509i
$759$	−39.2679	−	20.9896i	−0.0517363	−	0.0276542i
$760$		0			0
$761$			1451.51i			1.90737i	0.300808	+	0.953685i	$0.402744\pi$
$761$			1451.51i			1.90737i	−0.300808	+	0.953685i	$0.597256\pi$
$762$	−265.830	+	497.322i	−0.348858	+	0.652654i
$763$	327.624			0.429389
$764$		−	701.084i		−	0.917649i
$765$		0			0
$766$	−748.810			−0.977559
$767$		−	33.9411i		−	0.0442518i
$768$	42.3320	+	22.6274i	0.0551198	+	0.0294628i
$769$	−1089.32			−1.41654			−0.708271	−	0.705941i	$-0.750524\pi$
$769$	−1089.32			−1.41654			−0.708271	+	0.705941i	$0.750524\pi$
$770$		0			0
$771$	316.627	−	592.356i	0.410671	−	0.768295i
$772$	540.988			0.700762
$773$		−	1019.58i		−	1.31900i	−0.751707	−	0.659498i	$-0.770769\pi$
$773$		−	1019.58i		−	1.31900i	0.751707	−	0.659498i	$-0.229231\pi$
$774$	547.660	−	365.921i	0.707571	−	0.472766i
$775$		0			0
$776$		−	194.692i		−	0.250892i
$777$	140.000	+	74.8331i	0.180180	+	0.0963104i
$778$	−337.579			−0.433906
$779$		−	1217.62i		−	1.56306i
$780$		0			0
$781$	−36.1699			−0.0463124
$782$			808.523i			1.03392i
$783$	558.923	−	55.0342i	0.713822	−	0.0702863i
$784$	28.0000			0.0357143
$785$		0			0
$786$	−15.4249	−	8.24494i	−0.0196245	−	0.0104897i
$787$	1267.00			1.60991			0.804956	−	0.593334i	$-0.202189\pi$
$787$	1267.00			1.60991			0.804956	+	0.593334i	$0.202189\pi$
$788$		−	127.039i		−	0.161217i
$789$	−303.255	+	567.338i	−0.384354	+	0.719060i
$790$		0			0
$791$			212.957i			0.269224i
$792$	−5.83005	−	8.72562i	−0.00736118	−	0.0110172i
$793$	1377.31			1.73684
$794$		−	453.373i		−	0.570999i
$795$		0			0
$796$	176.000			0.221106
$797$		−	922.123i		−	1.15699i	−0.815685	−	0.578496i	$-0.803640\pi$
$797$		−	922.123i		−	1.15699i	0.815685	−	0.578496i	$-0.196360\pi$
$798$	−84.6640	+	158.392i	−0.106095	+	0.198486i
$799$	134.745			0.168642
$800$		0			0
$801$	233.490	−	156.007i	0.291498	−	0.194766i
$802$	−328.251			−0.409291
$803$		−	5.08384i		−	0.00633106i
$804$	261.490	+	139.772i	0.325237	+	0.173846i
$805$		0			0
$806$			161.335i			0.200167i
$807$	−540.450	+	1011.09i	−0.669702	+	1.25290i
$808$	396.413			0.490610
$809$		−	706.855i		−	0.873740i	−0.899525	−	0.436870i	$-0.856087\pi$
$809$		−	706.855i		−	0.873740i	0.899525	−	0.436870i	$-0.143913\pi$
$810$		0			0
$811$	833.778			1.02809			0.514043	−	0.857764i	$-0.328147\pi$
$811$	833.778			1.02809			0.514043	+	0.857764i	$0.328147\pi$
$812$		−	110.068i		−	0.135552i
$813$	302.826	+	161.867i	0.372480	+	0.199099i
$814$	−11.6601			−0.0143245
$815$		0			0
$816$	−89.8301	+	168.057i	−0.110086	+	0.205952i
$817$	827.984			1.01344
$818$			748.091i			0.914537i
$819$	272.288	+	407.523i	0.332463	+	0.497586i
$820$		0			0
$821$		−	251.260i		−	0.306042i	−0.988223	−	0.153021i	$-0.951100\pi$
$821$		−	251.260i		−	0.306042i	0.988223	−	0.153021i	$-0.0489002\pi$
$822$	−372.826	−	199.284i	−0.453560	−	0.242438i
$823$	−38.9229			−0.0472939			−0.0236470	−	0.999720i	$-0.507528\pi$
$823$	−38.9229			−0.0472939			−0.0236470	+	0.999720i	$0.507528\pi$
$824$			111.362i			0.135148i
$825$		0			0
$826$	6.16995			0.00746967
$827$		−	108.007i		−	0.130601i	−0.997866	−	0.0653005i	$-0.979199\pi$
$827$		−	108.007i		−	0.130601i	0.997866	−	0.0653005i	$-0.0208006\pi$
$828$	−538.834	+	360.024i	−0.650766	+	0.434811i
$829$	−1410.58			−1.70154			−0.850769	−	0.525540i	$-0.823863\pi$
$829$	−1410.58			−1.70154			−0.850769	+	0.525540i	$0.823863\pi$
$830$		0			0
$831$	609.830	+	325.968i	0.733851	+	0.392260i
$832$	164.664			0.197914
$833$			111.159i			0.133444i
$834$	−187.085	+	350.004i	−0.224323	+	0.419669i
$835$		0			0
$836$		−	13.1919i		−	0.0157798i
$837$	−14.6640	−	148.927i	−0.0175198	−	0.177929i
$838$	126.996			0.151547
$839$			299.906i			0.357456i	0.983899	+	0.178728i	$0.0571982\pi$
$839$			299.906i			0.357456i	−0.983899	+	0.178728i	$0.942802\pi$
$840$		0			0
$841$	408.320			0.485517
$842$		−	1099.06i		−	1.30529i
$843$	104.575	−	195.642i	0.124051	−	0.232078i
$844$	757.490			0.897500
$845$		0			0
$846$	60.0000	+	89.7998i	0.0709220	+	0.106146i
$847$	−319.686			−0.377434
$848$		−	203.647i		−	0.240149i
$849$	−373.490	−	199.639i	−0.439918	−	0.235146i
$850$		0			0
$851$			720.047i			0.846119i
$852$	−248.162	+	464.269i	−0.291270	+	0.544916i
$853$	13.7648			0.0161369			0.00806844	−	0.999967i	$-0.497432\pi$
$853$	13.7648			0.0161369			0.00806844	+	0.999967i	$0.497432\pi$
$854$			250.373i			0.293177i
$855$		0			0
$856$	305.490			0.356881
$857$		−	252.506i		−	0.294640i	−0.989089	−	0.147320i	$-0.952935\pi$
$857$		−	252.506i		−	0.294640i	0.989089	−	0.147320i	$-0.0470647\pi$
$858$	−31.7490	−	16.9706i	−0.0370035	−	0.0197792i
$859$	674.510			0.785227			0.392613	−	0.919704i	$-0.371571\pi$
$859$	674.510			0.785227			0.392613	+	0.919704i	$0.371571\pi$
$860$		0			0
$861$	284.745	−	532.709i	0.330714	−	0.618710i
$862$	−347.757			−0.403430
$863$		−	477.718i		−	0.553555i	−0.960934	−	0.276777i	$-0.910734\pi$
$863$		−	477.718i		−	0.553555i	0.960934	−	0.276777i	$-0.0892664\pi$
$864$	−152.000	+	14.9666i	−0.175926	+	0.0173225i
$865$		0			0
$866$			1127.12i			1.30153i
$867$	97.4432	+	52.0856i	0.112391	+	0.0600756i
$868$	−29.3281			−0.0337881
$869$			35.0060i			0.0402830i
$870$		0			0
$871$	1017.15			1.16780
$872$			350.244i			0.401656i
$873$	344.170	+	515.106i	0.394238	+	0.590042i
$874$	−814.640			−0.932083
$875$		0			0
$876$	−65.2549	−	34.8802i	−0.0744919	−	0.0398176i
$877$	−1533.14			−1.74817			−0.874083	−	0.485776i	$-0.838537\pi$
$877$	−1533.14			−1.74817			−0.874083	+	0.485776i	$0.838537\pi$
$878$			783.234i			0.892066i
$879$	−466.118	+	872.026i	−0.530282	+	0.992066i
$880$		0			0
$881$			1368.30i			1.55313i	0.630039	+	0.776563i	$0.283039\pi$
$881$			1368.30i			1.55313i	−0.630039	+	0.776563i	$0.716961\pi$
$882$	−74.0810	+	49.4975i	−0.0839921	+	0.0561196i
$883$	−944.486			−1.06963			−0.534817	−	0.844968i	$-0.679619\pi$
$883$	−944.486			−1.06963			−0.534817	+	0.844968i	$0.679619\pi$
$884$			653.710i			0.739491i
$885$		0			0
$886$	−1094.58			−1.23541
$887$		−	1326.86i		−	1.49590i	−0.663754	−	0.747951i	$-0.731038\pi$
$887$		−	1326.86i		−	1.49590i	0.663754	−	0.747951i	$-0.268962\pi$
$888$	−80.0000	+	149.666i	−0.0900901	+	0.168543i
$889$	−351.660			−0.395568
$890$		0			0
$891$	30.8497	+	12.7797i	0.0346237	+	0.0143430i
$892$	−460.988			−0.516803
$893$			135.765i			0.152032i
$894$	−186.510	−	99.6937i	−0.208624	−	0.111514i
$895$		0			0
$896$			29.9333i			0.0334077i
$897$	−1047.98	+	1960.60i	−1.16832	+	2.18573i
$898$	957.668			1.06645
$899$			115.289i			0.128241i
$900$		0			0
$901$	808.470			0.897304
$902$			44.3675i			0.0491879i
$903$	362.243	+	193.627i	0.401155	+	0.214426i
$904$	−227.660			−0.251836
$905$		0			0
$906$	−423.320	+	791.960i	−0.467241	+	0.874128i
$907$	1219.64			1.34470			0.672351	−	0.740233i	$-0.265285\pi$
$907$	1219.64			1.34470			0.672351	+	0.740233i	$0.265285\pi$
$908$		−	516.881i		−	0.569252i
$909$	−1048.81	+	700.766i	−1.15381	+	0.770920i
$910$		0			0
$911$			63.8282i			0.0700639i	0.999386	+	0.0350320i	$0.0111533\pi$
$911$			63.8282i			0.0700639i	−0.999386	+	0.0350320i	$0.988847\pi$
$912$	−169.328	−	90.5097i	−0.185667	−	0.0992431i
$913$	1.69948			0.00186142
$914$		−	1180.39i		−	1.29146i
$915$		0			0
$916$	74.1699			0.0809716
$917$		−	10.9070i		−	0.0118943i
$918$	−59.4170	−	603.435i	−0.0647244	−	0.657336i
$919$	981.385			1.06788			0.533942	−	0.845521i	$-0.320710\pi$
$919$	981.385			1.06788			0.533942	+	0.845521i	$0.320710\pi$
$920$		0			0
$921$	280.000	+	149.666i	0.304017	+	0.162504i
$922$	−490.944			−0.532477
$923$			1805.92i			1.95658i
$924$	3.08497	−	5.77146i	0.00333872	−	0.00624617i
$925$		0			0
$926$		−	449.250i		−	0.485152i
$927$	−196.863	−	294.637i	−0.212365	−	0.317839i
$928$	117.668			0.126797
$929$			340.931i			0.366987i	0.983021	+	0.183493i	$0.0587406\pi$
$929$			340.931i			0.366987i	−0.983021	+	0.183493i	$0.941259\pi$
$930$		0			0
$931$	−112.000			−0.120301
$932$			165.343i			0.177406i
$933$	544.664	−	1018.97i	0.583777	−	1.09215i
$934$	−774.170			−0.828876
$935$		0			0
$936$	−435.660	+	291.088i	−0.465449	+	0.310991i
$937$	−1010.00			−1.07791			−0.538954	−	0.842335i	$-0.681180\pi$
$937$	−1010.00			−1.07791			−0.538954	+	0.842335i	$0.681180\pi$
$938$			184.901i			0.197123i
$939$	209.882	+	112.187i	0.223517	+	0.119475i
$940$		0			0
$941$		−	289.058i		−	0.307182i	−0.988135	−	0.153591i	$-0.950916\pi$
$941$		−	289.058i		−	0.307182i	0.988135	−	0.153591i	$-0.0490838\pi$
$942$	−217.490	+	406.887i	−0.230881	+	0.431939i
$943$	2739.83			2.90544
$944$			6.59595i			0.00698724i
$945$		0			0
$946$	−30.1699			−0.0318921
$947$		−	828.054i		−	0.874397i	−0.899365	−	0.437199i	$-0.855971\pi$
$947$		−	828.054i		−	0.874397i	0.899365	−	0.437199i	$-0.144029\pi$
$948$	449.328	+	240.176i	0.473975	+	0.253350i
$949$	−253.830			−0.267471
$950$		0			0
$951$	−581.490	+	1087.87i	−0.611451	+	1.14392i
$952$	−118.834			−0.124826
$953$			102.785i			0.107854i	0.998545	+	0.0539269i	$0.0171738\pi$
$953$			102.785i			0.107854i	−0.998545	+	0.0539269i	$0.982826\pi$
$954$	360.000	+	538.799i	0.377358	+	0.564778i
$955$		0			0
$956$		−	336.938i		−	0.352445i
$957$	−22.6877	−	12.1271i	−0.0237071	−	0.0126720i
$958$	−191.660			−0.200063
$959$		−	263.628i		−	0.274899i
$960$		0			0
$961$	−930.281			−0.968034
$962$			582.175i			0.605172i
$963$	−808.251	+	540.035i	−0.839305	+	0.560784i
$964$	260.000			0.269710
$965$		0			0
$966$	−356.405	−	190.507i	−0.368949	−	0.197212i
$967$	184.753			0.191058			0.0955289	−	0.995427i	$-0.469546\pi$
$967$	184.753			0.191058			0.0955289	+	0.995427i	$0.469546\pi$
$968$		−	341.759i		−	0.353057i
$969$	359.320	−	672.227i	0.370815	−	0.693732i
$970$		0			0
$971$		−	1469.33i		−	1.51321i	−0.653871	−	0.756606i	$-0.726856\pi$
$971$		−	1469.33i		−	1.51321i	0.653871	−	0.756606i	$-0.273144\pi$
$972$	375.697	−	308.299i	0.386519	−	0.317180i
$973$	−247.490			−0.254358
$974$		−	33.2312i		−	0.0341183i
$975$		0			0
$976$	−267.660			−0.274242
$977$			663.072i			0.678682i	0.940663	+	0.339341i	$0.110204\pi$
$977$			663.072i			0.678682i	−0.940663	+	0.339341i	$0.889796\pi$
$978$	26.0079	−	48.6563i	0.0265929	−	0.0497508i
$979$	−12.8627			−0.0131386
$980$		0			0
$981$	−619.150	−	926.659i	−0.631142	−	0.944607i
$982$	146.235			0.148916
$983$			1899.26i			1.93211i	0.258342	+	0.966053i	$0.416824\pi$
$983$			1899.26i			1.93211i	−0.258342	+	0.966053i	$0.583176\pi$
$984$	569.490	+	304.405i	0.578750	+	0.309355i
$985$		0			0
$986$			467.138i			0.473771i
$987$	−31.7490	+	59.3970i	−0.0321672	+	0.0601793i
$988$	−658.656			−0.666656
$989$			1863.09i			1.88381i
$990$		0			0
$991$	−257.725			−0.260066			−0.130033	−	0.991510i	$-0.541508\pi$
$991$	−257.725			−0.260066			−0.130033	+	0.991510i	$0.541508\pi$
$992$		−	31.3530i		−	0.0316059i
$993$	−1295.07	−	692.244i	−1.30420	−	0.697123i
$994$	−328.288			−0.330269
$995$		0			0
$996$	11.6601	−	21.8141i	0.0117069	−	0.0219017i
$997$	−1235.74			−1.23946			−0.619730	−	0.784815i	$-0.712758\pi$
$997$	−1235.74			−1.23946			−0.619730	+	0.784815i	$0.712758\pi$
$998$		−	90.9904i		−	0.0911727i
$999$	−52.9150	−	537.401i	−0.0529680	−	0.537939i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.e.a.701.4		4
3.2	odd	2	inner	1050.3.e.a.701.2		4
5.2	odd	4		1050.3.c.a.449.2		8
5.3	odd	4		1050.3.c.a.449.8		8
5.4	even	2		42.3.b.a.29.1	✓	4
15.2	even	4		1050.3.c.a.449.5		8
15.8	even	4		1050.3.c.a.449.3		8
15.14	odd	2		42.3.b.a.29.3	yes	4
20.19	odd	2		336.3.d.b.113.4		4
35.4	even	6		294.3.h.d.275.4		8
35.9	even	6		294.3.h.d.263.2		8
35.19	odd	6		294.3.h.g.263.1		8
35.24	odd	6		294.3.h.g.275.3		8
35.34	odd	2		294.3.b.h.197.2		4
40.19	odd	2		1344.3.d.e.449.1		4
40.29	even	2		1344.3.d.c.449.4		4
45.4	even	6		1134.3.q.a.1079.3		8
45.14	odd	6		1134.3.q.a.1079.2		8
45.29	odd	6		1134.3.q.a.701.3		8
45.34	even	6		1134.3.q.a.701.2		8
60.59	even	2		336.3.d.b.113.3		4
105.44	odd	6		294.3.h.d.263.4		8
105.59	even	6		294.3.h.g.275.1		8
105.74	odd	6		294.3.h.d.275.2		8
105.89	even	6		294.3.h.g.263.3		8
105.104	even	2		294.3.b.h.197.4		4
120.29	odd	2		1344.3.d.c.449.3		4
120.59	even	2		1344.3.d.e.449.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.b.a.29.1	✓	4	5.4	even	2
42.3.b.a.29.3	yes	4	15.14	odd	2
294.3.b.h.197.2		4	35.34	odd	2
294.3.b.h.197.4		4	105.104	even	2
294.3.h.d.263.2		8	35.9	even	6
294.3.h.d.263.4		8	105.44	odd	6
294.3.h.d.275.2		8	105.74	odd	6
294.3.h.d.275.4		8	35.4	even	6
294.3.h.g.263.1		8	35.19	odd	6
294.3.h.g.263.3		8	105.89	even	6
294.3.h.g.275.1		8	105.59	even	6
294.3.h.g.275.3		8	35.24	odd	6
336.3.d.b.113.3		4	60.59	even	2
336.3.d.b.113.4		4	20.19	odd	2
1050.3.c.a.449.2		8	5.2	odd	4
1050.3.c.a.449.3		8	15.8	even	4
1050.3.c.a.449.5		8	15.2	even	4
1050.3.c.a.449.8		8	5.3	odd	4
1050.3.e.a.701.2		4	3.2	odd	2	inner
1050.3.e.a.701.4		4	1.1	even	1	trivial
1134.3.q.a.701.2		8	45.34	even	6
1134.3.q.a.701.3		8	45.29	odd	6
1134.3.q.a.1079.2		8	45.14	odd	6
1134.3.q.a.1079.3		8	45.4	even	6
1344.3.d.c.449.3		4	120.29	odd	2
1344.3.d.c.449.4		4	40.29	even	2
1344.3.d.e.449.1		4	40.19	odd	2
1344.3.d.e.449.2		4	120.59	even	2

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +(2.64575 + 1.41421i) q^{3} -2.00000 q^{4} +(-2.00000 + 3.74166i) q^{6} -2.64575 q^{7} -2.82843i q^{8} +(5.00000 + 7.48331i) q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} +(2.64575 + 1.41421i) q^{3} -2.00000 q^{4} +(-2.00000 + 3.74166i) q^{6} -2.64575 q^{7} -2.82843i q^{8} +(5.00000 + 7.48331i) q^{9} -0.412247i q^{11} +(-5.29150 - 2.82843i) q^{12} -20.5830 q^{13} -3.74166i q^{14} +4.00000 q^{16} +15.8799i q^{17} +(-10.5830 + 7.07107i) q^{18} -16.0000 q^{19} +(-7.00000 - 3.74166i) q^{21} +0.583005 q^{22} -36.0024i q^{23} +(4.00000 - 7.48331i) q^{24} -29.1088i q^{26} +(2.64575 + 26.8701i) q^{27} +5.29150 q^{28} -20.8010i q^{29} -5.54249 q^{31} +5.65685i q^{32} +(0.583005 - 1.09070i) q^{33} -22.4575 q^{34} +(-10.0000 - 14.9666i) q^{36} -20.0000 q^{37} -22.6274i q^{38} +(-54.4575 - 29.1088i) q^{39} +76.1013i q^{41} +(5.29150 - 9.89949i) q^{42} -51.7490 q^{43} +0.824494i q^{44} +50.9150 q^{46} -8.48528i q^{47} +(10.5830 + 5.65685i) q^{48} +7.00000 q^{49} +(-22.4575 + 42.0142i) q^{51} +41.1660 q^{52} -50.9117i q^{53} +(-38.0000 + 3.74166i) q^{54} +7.48331i q^{56} +(-42.3320 - 22.6274i) q^{57} +29.4170 q^{58} +1.64899i q^{59} -66.9150 q^{61} -7.83826i q^{62} +(-13.2288 - 19.7990i) q^{63} -8.00000 q^{64} +(1.54249 + 0.824494i) q^{66} -49.4170 q^{67} -31.7597i q^{68} +(50.9150 - 95.2533i) q^{69} -87.7385i q^{71} +(21.1660 - 14.1421i) q^{72} +12.3320 q^{73} -28.2843i q^{74} +32.0000 q^{76} +1.09070i q^{77} +(41.1660 - 77.0146i) q^{78} -84.9150 q^{79} +(-31.0000 + 74.8331i) q^{81} -107.624 q^{82} +4.12247i q^{83} +(14.0000 + 7.48331i) q^{84} -73.1842i q^{86} +(29.4170 - 55.0342i) q^{87} -1.16601 q^{88} -31.2014i q^{89} +54.4575 q^{91} +72.0047i q^{92} +(-14.6640 - 7.83826i) q^{93} +12.0000 q^{94} +(-8.00000 + 14.9666i) q^{96} +68.8340 q^{97} +9.89949i q^{98} +(3.08497 - 2.06123i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{4} - 8 q^{6} + 20 q^{9}+O(q^{10}) \) 4 * q - 8 * q^4 - 8 * q^6 + 20 * q^9	\( 4 q - 8 q^{4} - 8 q^{6} + 20 q^{9} - 40 q^{13} + 16 q^{16} - 64 q^{19} - 28 q^{21} - 40 q^{22} + 16 q^{24} - 128 q^{31} - 40 q^{33} + 16 q^{34} - 40 q^{36} - 80 q^{37} - 112 q^{39} - 80 q^{43} - 8 q^{46} + 28 q^{49} + 16 q^{51} + 80 q^{52} - 152 q^{54} + 160 q^{58} - 56 q^{61} - 32 q^{64} + 112 q^{66} - 240 q^{67} - 8 q^{69} - 120 q^{73} + 128 q^{76} + 80 q^{78} - 128 q^{79} - 124 q^{81} - 240 q^{82} + 56 q^{84} + 160 q^{87} + 80 q^{88} + 112 q^{91} + 280 q^{93} + 48 q^{94} - 32 q^{96} + 360 q^{97} + 224 q^{99}+O(q^{100}) \) 4 * q - 8 * q^4 - 8 * q^6 + 20 * q^9 - 40 * q^13 + 16 * q^16 - 64 * q^19 - 28 * q^21 - 40 * q^22 + 16 * q^24 - 128 * q^31 - 40 * q^33 + 16 * q^34 - 40 * q^36 - 80 * q^37 - 112 * q^39 - 80 * q^43 - 8 * q^46 + 28 * q^49 + 16 * q^51 + 80 * q^52 - 152 * q^54 + 160 * q^58 - 56 * q^61 - 32 * q^64 + 112 * q^66 - 240 * q^67 - 8 * q^69 - 120 * q^73 + 128 * q^76 + 80 * q^78 - 128 * q^79 - 124 * q^81 - 240 * q^82 + 56 * q^84 + 160 * q^87 + 80 * q^88 + 112 * q^91 + 280 * q^93 + 48 * q^94 - 32 * q^96 + 360 * q^97 + 224 * q^99

Introduction

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