LMFDB - Embedded newform 1050.3.c.a.449.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(449,1050)]

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, 1, 0]))

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

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

chi := DirichletCharacter("1050.449");

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.c (of order $2$, degree $1$, not 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:	$8$
Coefficient field:	8.0.157351936.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{4} + 16 $ x^8 + x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 5^{4} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			449.8
Root			$0.581861 + 1.28897i$ of defining polynomial
Character	$\chi$	$=$	1050.449
Dual form			1050.3.c.a.449.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +(-1.41421 + 2.64575i) q^{3} +2.00000 q^{4} +(-2.00000 + 3.74166i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(-5.00000 - 7.48331i) q^{9} +O(q^{10})$	\(q+1.41421 q^{2} +(-1.41421 + 2.64575i) q^{3} +2.00000 q^{4} +(-2.00000 + 3.74166i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(-5.00000 - 7.48331i) q^{9} -0.412247i q^{11} +(-2.82843 + 5.29150i) q^{12} -20.5830i q^{13} +3.74166i q^{14} +4.00000 q^{16} +15.8799 q^{17} +(-7.07107 - 10.5830i) q^{18} +16.0000 q^{19} +(-7.00000 - 3.74166i) q^{21} -0.583005i q^{22} +36.0024 q^{23} +(-4.00000 + 7.48331i) q^{24} -29.1088i q^{26} +(26.8701 - 2.64575i) q^{27} +5.29150i q^{28} +20.8010i q^{29} -5.54249 q^{31} +5.65685 q^{32} +(1.09070 + 0.583005i) q^{33} +22.4575 q^{34} +(-10.0000 - 14.9666i) q^{36} +20.0000i q^{37} +22.6274 q^{38} +(54.4575 + 29.1088i) q^{39} +76.1013i q^{41} +(-9.89949 - 5.29150i) q^{42} -51.7490i q^{43} -0.824494i q^{44} +50.9150 q^{46} -8.48528 q^{47} +(-5.65685 + 10.5830i) q^{48} -7.00000 q^{49} +(-22.4575 + 42.0142i) q^{51} -41.1660i q^{52} +50.9117 q^{53} +(38.0000 - 3.74166i) q^{54} +7.48331i q^{56} +(-22.6274 + 42.3320i) q^{57} +29.4170i q^{58} -1.64899i q^{59} -66.9150 q^{61} -7.83826 q^{62} +(19.7990 - 13.2288i) q^{63} +8.00000 q^{64} +(1.54249 + 0.824494i) q^{66} +49.4170i q^{67} +31.7597 q^{68} +(-50.9150 + 95.2533i) q^{69} -87.7385i q^{71} +(-14.1421 - 21.1660i) q^{72} +12.3320i q^{73} +28.2843i q^{74} +32.0000 q^{76} +1.09070 q^{77} +(77.0146 + 41.1660i) q^{78} +84.9150 q^{79} +(-31.0000 + 74.8331i) q^{81} +107.624i q^{82} -4.12247 q^{83} +(-14.0000 - 7.48331i) q^{84} -73.1842i q^{86} +(-55.0342 - 29.4170i) q^{87} -1.16601i q^{88} +31.2014i q^{89} +54.4575 q^{91} +72.0047 q^{92} +(7.83826 - 14.6640i) q^{93} -12.0000 q^{94} +(-8.00000 + 14.9666i) q^{96} -68.8340i q^{97} -9.89949 q^{98} +(-3.08497 + 2.06123i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{4} - 16 q^{6} - 40 q^{9}+O(q^{10}) $ 8 * q + 16 * q^4 - 16 * q^6 - 40 * q^9	$ 8 q + 16 q^{4} - 16 q^{6} - 40 q^{9} + 32 q^{16} + 128 q^{19} - 56 q^{21} - 32 q^{24} - 256 q^{31} - 32 q^{34} - 80 q^{36} + 224 q^{39} - 16 q^{46} - 56 q^{49} + 32 q^{51} + 304 q^{54} - 112 q^{61} + 64 q^{64} + 224 q^{66} + 16 q^{69} + 256 q^{76} + 256 q^{79} - 248 q^{81} - 112 q^{84} + 224 q^{91} - 96 q^{94} - 64 q^{96} - 448 q^{99}+O(q^{100}) $ 8 * q + 16 * q^4 - 16 * q^6 - 40 * q^9 + 32 * q^16 + 128 * q^19 - 56 * q^21 - 32 * q^24 - 256 * q^31 - 32 * q^34 - 80 * q^36 + 224 * q^39 - 16 * q^46 - 56 * q^49 + 32 * q^51 + 304 * q^54 - 112 * q^61 + 64 * q^64 + 224 * q^66 + 16 * q^69 + 256 * q^76 + 256 * q^79 - 248 * q^81 - 112 * q^84 + 224 * q^91 - 96 * q^94 - 64 * q^96 - 448 * 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 $

$2$	1.41421			0.707107
$2$	1.41421			0.707107
$3$	−1.41421	+	2.64575i	−0.471405	+	0.881917i
$3$	−1.41421	+	2.64575i	−0.471405	+	0.881917i
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$	−2.00000	+	3.74166i	−0.333333	+	0.623610i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	2.82843			0.353553
$9$	−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	$-0.00596500\pi$
$12$	−2.82843	+	5.29150i	−0.235702	+	0.440959i
$13$		−	20.5830i		−	1.58331i	−0.610970	−	0.791654i	$-0.709220\pi$
$13$		−	20.5830i		−	1.58331i	0.610970	−	0.791654i	$-0.290780\pi$
$14$			3.74166i			0.267261i
$15$		0			0
$16$	4.00000			0.250000
$17$	15.8799			0.934109			0.467055	−	0.884228i	$-0.345315\pi$
$17$	15.8799			0.934109			0.467055	+	0.884228i	$0.345315\pi$
$18$	−7.07107	−	10.5830i	−0.392837	−	0.587945i
$19$	16.0000			0.842105			0.421053	−	0.907036i	$-0.361661\pi$
$19$	16.0000			0.842105			0.421053	+	0.907036i	$0.361661\pi$
$20$		0			0
$21$	−7.00000	−	3.74166i	−0.333333	−	0.178174i
$22$		−	0.583005i		−	0.0265002i
$23$	36.0024			1.56532			0.782660	−	0.622449i	$-0.213862\pi$
$23$	36.0024			1.56532			0.782660	+	0.622449i	$0.213862\pi$
$24$	−4.00000	+	7.48331i	−0.166667	+	0.311805i
$25$		0			0
$26$		−	29.1088i		−	1.11957i
$27$	26.8701	−	2.64575i	0.995187	−	0.0979908i
$28$			5.29150i			0.188982i
$29$			20.8010i			0.717274i	0.933477	+	0.358637i	$0.116758\pi$
$29$			20.8010i			0.717274i	−0.933477	+	0.358637i	$0.883242\pi$
$30$		0			0
$31$	−5.54249			−0.178790			−0.0893949	−	0.995996i	$-0.528493\pi$
$31$	−5.54249			−0.178790			−0.0893949	+	0.995996i	$0.528493\pi$
$32$	5.65685			0.176777
$33$	1.09070	+	0.583005i	0.0330516	+	0.0176668i
$34$	22.4575			0.660515
$35$		0			0
$36$	−10.0000	−	14.9666i	−0.277778	−	0.415740i
$37$			20.0000i			0.540541i	0.962784	+	0.270270i	$0.0871131\pi$
$37$			20.0000i			0.540541i	−0.962784	+	0.270270i	$0.912887\pi$
$38$	22.6274			0.595458
$39$	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	$0.621471\pi$
$42$	−9.89949	−	5.29150i	−0.235702	−	0.125988i
$43$		−	51.7490i		−	1.20347i	−0.798698	−	0.601733i	$-0.794477\pi$
$43$		−	51.7490i		−	1.20347i	0.798698	−	0.601733i	$-0.205523\pi$
$44$		−	0.824494i		−	0.0187385i
$45$		0			0
$46$	50.9150			1.10685
$47$	−8.48528			−0.180538			−0.0902690	−	0.995917i	$-0.528773\pi$
$47$	−8.48528			−0.180538			−0.0902690	+	0.995917i	$0.528773\pi$
$48$	−5.65685	+	10.5830i	−0.117851	+	0.220479i
$49$	−7.00000			−0.142857
$50$		0			0
$51$	−22.4575	+	42.0142i	−0.440343	+	0.823807i
$52$		−	41.1660i		−	0.791654i
$53$	50.9117			0.960598			0.480299	−	0.877105i	$-0.340528\pi$
$53$	50.9117			0.960598			0.480299	+	0.877105i	$0.340528\pi$
$54$	38.0000	−	3.74166i	0.703704	−	0.0692900i
$55$		0			0
$56$			7.48331i			0.133631i
$57$	−22.6274	+	42.3320i	−0.396972	+	0.742667i
$58$			29.4170i			0.507190i
$59$		−	1.64899i		−	0.0279489i	−0.999902	−	0.0139745i	$-0.995552\pi$
$59$		−	1.64899i		−	0.0279489i	0.999902	−	0.0139745i	$-0.00444836\pi$
$60$		0			0
$61$	−66.9150			−1.09697			−0.548484	−	0.836161i	$-0.684795\pi$
$61$	−66.9150			−1.09697			−0.548484	+	0.836161i	$0.684795\pi$
$62$	−7.83826			−0.126424
$63$	19.7990	−	13.2288i	0.314270	−	0.209980i
$64$	8.00000			0.125000
$65$		0			0
$66$	1.54249	+	0.824494i	0.0233710	+	0.0124923i
$67$			49.4170i			0.737567i	0.929515	+	0.368784i	$0.120226\pi$
$67$			49.4170i			0.737567i	−0.929515	+	0.368784i	$0.879774\pi$
$68$	31.7597			0.467055
$69$	−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	$-0.212007\pi$
$72$	−14.1421	−	21.1660i	−0.196419	−	0.293972i
$73$			12.3320i			0.168932i	0.996426	+	0.0844659i	$0.0269184\pi$
$73$			12.3320i			0.168932i	−0.996426	+	0.0844659i	$0.973082\pi$
$74$			28.2843i			0.382220i
$75$		0			0
$76$	32.0000			0.421053
$77$	1.09070			0.0141650
$78$	77.0146	+	41.1660i	0.987366	+	0.527769i
$79$	84.9150			1.07487			0.537437	−	0.843304i	$-0.319393\pi$
$79$	84.9150			1.07487			0.537437	+	0.843304i	$0.319393\pi$
$80$		0			0
$81$	−31.0000	+	74.8331i	−0.382716	+	0.923866i
$82$			107.624i			1.31248i
$83$	−4.12247			−0.0496683			−0.0248342	−	0.999692i	$-0.507906\pi$
$83$	−4.12247			−0.0496683			−0.0248342	+	0.999692i	$0.507906\pi$
$84$	−14.0000	−	7.48331i	−0.166667	−	0.0890871i
$85$		0			0
$86$		−	73.1842i		−	0.850979i
$87$	−55.0342	−	29.4170i	−0.632577	−	0.338126i
$88$		−	1.16601i		−	0.0132501i
$89$			31.2014i			0.350578i	0.984517	+	0.175289i	$0.0560860\pi$
$89$			31.2014i			0.350578i	−0.984517	+	0.175289i	$0.943914\pi$
$90$		0			0
$91$	54.4575			0.598434
$92$	72.0047			0.782660
$93$	7.83826	−	14.6640i	0.0842824	−	0.157678i
$94$	−12.0000			−0.127660
$95$		0			0
$96$	−8.00000	+	14.9666i	−0.0833333	+	0.155902i
$97$		−	68.8340i		−	0.709629i	−0.934937	−	0.354814i	$-0.884544\pi$
$97$		−	68.8340i		−	0.709629i	0.934937	−	0.354814i	$-0.115456\pi$
$98$	−9.89949			−0.101015
$99$	−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	$0.755923\pi$
$102$	−31.7597	+	59.4170i	−0.311370	+	0.582520i
$103$		−	39.3725i		−	0.382258i	−0.981565	−	0.191129i	$-0.938785\pi$
$103$		−	39.3725i		−	0.382258i	0.981565	−	0.191129i	$-0.0612148\pi$
$104$		−	58.2175i		−	0.559784i
$105$		0			0
$106$	72.0000			0.679245
$107$	108.007			1.00941			0.504706	−	0.863291i	$-0.331601\pi$
$107$	108.007			1.00941			0.504706	+	0.863291i	$0.331601\pi$
$108$	53.7401	−	5.29150i	0.497594	−	0.0489954i
$109$	123.830			1.13606			0.568028	−	0.823009i	$-0.307707\pi$
$109$	123.830			1.13606			0.568028	+	0.823009i	$0.307707\pi$
$110$		0			0
$111$	−52.9150	−	28.2843i	−0.476712	−	0.254813i
$112$			10.5830i			0.0944911i
$113$	80.4900			0.712301			0.356150	−	0.934429i	$-0.384089\pi$
$113$	80.4900			0.712301			0.356150	+	0.934429i	$0.384089\pi$
$114$	−32.0000	+	59.8665i	−0.280702	+	0.525145i
$115$		0			0
$116$			41.6019i			0.358637i
$117$	−154.029	+	102.915i	−1.31649	+	0.879616i
$118$		−	2.33202i		−	0.0197629i
$119$			42.0142i			0.353060i
$120$		0			0
$121$	120.830			0.998595
$122$	−94.6321			−0.775673
$123$	−201.345	−	107.624i	−1.63695	−	0.874988i
$124$	−11.0850			−0.0893949
$125$		0			0
$126$	28.0000	−	18.7083i	0.222222	−	0.148478i
$127$		−	132.915i		−	1.04658i	−0.852156	−	0.523288i	$-0.824705\pi$
$127$		−	132.915i		−	1.04658i	0.852156	−	0.523288i	$-0.175295\pi$
$128$	11.3137			0.0883883
$129$	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	$0.994991\pi$
$132$	2.18141	+	1.16601i	0.0165258	+	0.00883341i
$133$			42.3320i			0.318286i
$134$			69.8862i			0.521539i
$135$		0			0
$136$	44.9150			0.330258
$137$	99.6420			0.727314			0.363657	−	0.931533i	$-0.381528\pi$
$137$	99.6420			0.727314			0.363657	+	0.931533i	$0.381528\pi$
$138$	−72.0047	+	134.708i	−0.521773	+	0.976149i
$139$	−93.5425			−0.672968			−0.336484	−	0.941689i	$-0.609238\pi$
$139$	−93.5425			−0.672968			−0.336484	+	0.941689i	$0.609238\pi$
$140$		0			0
$141$	12.0000	−	22.4499i	0.0851064	−	0.159219i
$142$		−	124.081i		−	0.873810i
$143$	−8.48528			−0.0593376
$144$	−20.0000	−	29.9333i	−0.138889	−	0.207870i
$145$		0			0
$146$			17.4401i			0.119453i
$147$	9.89949	−	18.5203i	0.0673435	−	0.125988i
$148$			40.0000i			0.270270i
$149$		−	49.8469i		−	0.334543i	−0.985911	−	0.167271i	$-0.946504\pi$
$149$		−	49.8469i		−	0.334543i	0.985911	−	0.167271i	$-0.0534956\pi$
$150$		0			0
$151$	211.660			1.40172			0.700861	−	0.713298i	$-0.252799\pi$
$151$	211.660			1.40172			0.700861	+	0.713298i	$0.252799\pi$
$152$	45.2548			0.297729
$153$	−79.3993	−	118.834i	−0.518950	−	0.776693i
$154$	1.54249			0.0100161
$155$		0			0
$156$	108.915	+	58.2175i	0.698173	+	0.373189i
$157$		−	108.745i		−	0.692644i	−0.938116	−	0.346322i	$-0.887430\pi$
$157$		−	108.745i		−	0.692644i	0.938116	−	0.346322i	$-0.112570\pi$
$158$	120.088			0.760051
$159$	−72.0000	+	134.700i	−0.452830	+	0.847168i
$160$		0			0
$161$			95.2533i			0.591635i
$162$	−43.8406	+	105.830i	−0.270621	+	0.653272i
$163$		−	13.0039i		−	0.0797788i	−0.999204	−	0.0398894i	$-0.987299\pi$
$163$		−	13.0039i		−	0.0797788i	0.999204	−	0.0398894i	$-0.0127006\pi$
$164$			152.203i			0.928065i
$165$		0			0
$166$	−5.83005			−0.0351208
$167$	−156.858			−0.939267			−0.469633	−	0.882862i	$-0.655614\pi$
$167$	−156.858			−0.939267			−0.469633	+	0.882862i	$0.655614\pi$
$168$	−19.7990	−	10.5830i	−0.117851	−	0.0629941i
$169$	−254.660			−1.50686
$170$		0			0
$171$	−80.0000	−	119.733i	−0.467836	−	0.700193i
$172$		−	103.498i		−	0.601733i
$173$	5.45351			0.0315232			0.0157616	−	0.999876i	$-0.494983\pi$
$173$	5.45351			0.0315232			0.0157616	+	0.999876i	$0.494983\pi$
$174$	−77.8301	−	41.6019i	−0.447299	−	0.239091i
$175$		0			0
$176$		−	1.64899i		−	0.00936925i
$177$	4.36281	+	2.33202i	0.0246487	+	0.0131753i
$178$			44.1255i			0.247896i
$179$			1.23674i			0.00690917i	0.999994	+	0.00345458i	$0.00109963\pi$
$179$			1.23674i			0.00690917i	−0.999994	+	0.00345458i	$0.998900\pi$
$180$		0			0
$181$	−186.915			−1.03268			−0.516340	−	0.856384i	$-0.672706\pi$
$181$	−186.915			−1.03268			−0.516340	+	0.856384i	$0.672706\pi$
$182$	77.0146			0.423157
$183$	94.6321	−	177.041i	0.517116	−	0.967435i
$184$	101.830			0.553424
$185$		0			0
$186$	11.0850	−	20.7381i	0.0595966	−	0.111495i
$187$		−	6.54642i		−	0.0350076i
$188$	−16.9706			−0.0902690
$189$	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	$0.630085\pi$
$192$	−11.3137	+	21.1660i	−0.0589256	+	0.110240i
$193$		−	270.494i		−	1.40152i	−0.713395	−	0.700762i	$-0.752844\pi$
$193$		−	270.494i		−	1.40152i	0.713395	−	0.700762i	$-0.247156\pi$
$194$		−	97.3460i		−	0.501783i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	63.5194			0.322434			0.161217	−	0.986919i	$-0.448458\pi$
$197$	63.5194			0.322434			0.161217	+	0.986919i	$0.448458\pi$
$198$	−4.36281	+	2.91503i	−0.0220344	+	0.0147224i
$199$	88.0000			0.442211			0.221106	−	0.975250i	$-0.429033\pi$
$199$	88.0000			0.442211			0.221106	+	0.975250i	$0.429033\pi$
$200$		0			0
$201$	−130.745	−	69.8862i	−0.650473	−	0.347692i
$202$			198.207i			0.981220i
$203$	−55.0342			−0.271104
$204$	−44.9150	+	84.0283i	−0.220172	+	0.411904i
$205$		0			0
$206$		−	55.6812i		−	0.270297i
$207$	−180.012	−	269.417i	−0.869622	−	1.30153i
$208$		−	82.3320i		−	0.395827i
$209$		−	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	$0.854619\pi$
$212$	101.823			0.480299
$213$	232.134	+	124.081i	1.08983	+	0.582540i
$214$	152.745			0.713762
$215$		0			0
$216$	76.0000	−	7.48331i	0.351852	−	0.0346450i
$217$		−	14.6640i		−	0.0675762i
$218$	175.122			0.803313
$219$	−32.6275	−	17.4401i	−0.148984	−	0.0796352i
$220$		0			0
$221$		−	326.855i		−	1.47898i
$222$	−74.8331	−	40.0000i	−0.337086	−	0.180180i
$223$			230.494i			1.03361i	0.856104	+	0.516803i	$0.172878\pi$
$223$			230.494i			1.03361i	−0.856104	+	0.516803i	$0.827122\pi$
$224$			14.9666i			0.0668153i
$225$		0			0
$226$	113.830			0.503673
$227$	258.441			1.13850			0.569252	−	0.822163i	$-0.307233\pi$
$227$	258.441			1.13850			0.569252	+	0.822163i	$0.307233\pi$
$228$	−45.2548	+	84.6640i	−0.198486	+	0.371334i
$229$	37.0850			0.161943			0.0809716	−	0.996716i	$-0.474198\pi$
$229$	37.0850			0.161943			0.0809716	+	0.996716i	$0.474198\pi$
$230$		0			0
$231$	−1.54249	+	2.88573i	−0.00667743	+	0.0124923i
$232$			58.8340i			0.253595i
$233$	82.6714			0.354813			0.177406	−	0.984138i	$-0.443229\pi$
$233$	82.6714			0.354813			0.177406	+	0.984138i	$0.443229\pi$
$234$	−217.830	+	145.544i	−0.930898	+	0.621982i
$235$		0			0
$236$		−	3.29798i		−	0.0139745i
$237$	−120.088	+	224.664i	−0.506700	+	0.947950i
$238$			59.4170i			0.249651i
$239$		−	168.469i		−	0.704891i	−0.935832	−	0.352445i	$-0.885350\pi$
$239$		−	168.469i		−	0.704891i	0.935832	−	0.352445i	$-0.114650\pi$
$240$		0			0
$241$	−130.000			−0.539419			−0.269710	−	0.962942i	$-0.586928\pi$
$241$	−130.000			−0.539419			−0.269710	+	0.962942i	$0.586928\pi$
$242$	170.879			0.706114
$243$	−154.149	−	187.848i	−0.634359	−	0.773038i
$244$	−133.830			−0.548484
$245$		0			0
$246$	−284.745	−	152.203i	−1.15750	−	0.618710i
$247$		−	329.328i		−	1.33331i
$248$	−15.6765			−0.0632118
$249$	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	$-0.0767417\pi$
$252$	39.5980	−	26.4575i	0.157135	−	0.104990i
$253$		−	14.8419i		−	0.0586635i
$254$		−	187.970i		−	0.740040i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−223.889			−0.871165			−0.435583	−	0.900149i	$-0.643458\pi$
$257$	−223.889			−0.871165			−0.435583	+	0.900149i	$0.643458\pi$
$258$	193.627	+	103.498i	0.750493	+	0.401155i
$259$	−52.9150			−0.204305
$260$		0			0
$261$	155.660	−	104.005i	0.596399	−	0.398486i
$262$			5.83005i			0.0222521i
$263$	−214.434			−0.815337			−0.407668	−	0.913130i	$-0.633658\pi$
$263$	−214.434			−0.815337			−0.407668	+	0.913130i	$0.633658\pi$
$264$	3.08497	+	1.64899i	0.0116855	+	0.00624617i
$265$		0			0
$266$			59.8665i			0.225062i
$267$	−82.5512	−	44.1255i	−0.309181	−	0.165264i
$268$			98.8340i			0.368784i
$269$		−	382.156i		−	1.42065i	−0.703872	−	0.710326i	$-0.748547\pi$
$269$		−	382.156i		−	1.42065i	0.703872	−	0.710326i	$-0.251453\pi$
$270$		0			0
$271$	114.458			0.422352			0.211176	−	0.977448i	$-0.432271\pi$
$271$	114.458			0.422352			0.211176	+	0.977448i	$0.432271\pi$
$272$	63.5194			0.233527
$273$	−77.0146	+	144.081i	−0.282105	+	0.527769i
$274$	140.915			0.514288
$275$		0			0
$276$	−101.830	+	190.507i	−0.368949	+	0.690241i
$277$		−	230.494i		−	0.832109i	−0.909340	−	0.416054i	$-0.863413\pi$
$277$		−	230.494i		−	0.832109i	0.909340	−	0.416054i	$-0.136587\pi$
$278$	−132.289			−0.475860
$279$	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	$-0.0420038\pi$
$282$	16.9706	−	31.7490i	0.0601793	−	0.112585i
$283$		−	141.166i		−	0.498820i	−0.968398	−	0.249410i	$-0.919763\pi$
$283$		−	141.166i		−	0.498820i	0.968398	−	0.249410i	$-0.0802366\pi$
$284$		−	175.477i		−	0.617877i
$285$		0			0
$286$	−12.0000			−0.0419580
$287$	−201.345			−0.701551
$288$	−28.2843	−	42.3320i	−0.0982093	−	0.146986i
$289$	−36.8301			−0.127440
$290$		0			0
$291$	182.118	+	97.3460i	0.625834	+	0.334522i
$292$			24.6640i			0.0844659i
$293$	−329.595			−1.12490			−0.562449	−	0.826832i	$-0.690141\pi$
$293$	−329.595			−1.12490			−0.562449	+	0.826832i	$0.690141\pi$
$294$	14.0000	−	26.1916i	0.0476190	−	0.0890871i
$295$		0			0
$296$			56.5685i			0.191110i
$297$	−1.09070	−	11.0771i	−0.00367240	−	0.0372966i
$298$		−	70.4941i		−	0.236557i
$299$		−	741.037i		−	2.47838i
$300$		0			0
$301$	136.915			0.454867
$302$	299.333			0.991168
$303$	−370.810	−	198.207i	−1.22380	−	0.654147i
$304$	64.0000			0.210526
$305$		0			0
$306$	−112.288	−	168.057i	−0.366953	−	0.549205i
$307$		−	105.830i		−	0.344723i	−0.985034	−	0.172362i	$-0.944860\pi$
$307$		−	105.830i		−	0.344723i	0.985034	−	0.172362i	$-0.0551398\pi$
$308$	2.18141			0.00708249
$309$	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	$-0.212539\pi$
$312$	154.029	+	82.3320i	0.493683	+	0.263885i
$313$			79.3281i			0.253444i	0.991938	+	0.126722i	$0.0404457\pi$
$313$			79.3281i			0.253444i	−0.991938	+	0.126722i	$0.959554\pi$
$314$		−	153.789i		−	0.489773i
$315$		0			0
$316$	169.830			0.537437
$317$	411.176			1.29708			0.648542	−	0.761179i	$-0.275379\pi$
$317$	411.176			1.29708			0.648542	+	0.761179i	$0.275379\pi$
$318$	−101.823	+	190.494i	−0.320199	+	0.599038i
$319$	8.57513			0.0268813
$320$		0			0
$321$	−152.745	+	285.760i	−0.475841	+	0.890218i
$322$			134.708i			0.418349i
$323$	254.078			0.786618
$324$	−62.0000	+	149.666i	−0.191358	+	0.461933i
$325$		0			0
$326$		−	18.3903i		−	0.0564121i
$327$	−175.122	+	327.624i	−0.535542	+	1.00191i
$328$			215.247i			0.656241i
$329$		−	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	$0.764896\pi$
$332$	−8.24494			−0.0248342
$333$	149.666	−	100.000i	0.449448	−	0.300300i
$334$	−221.830			−0.664162
$335$		0			0
$336$	−28.0000	−	14.9666i	−0.0833333	−	0.0445435i
$337$			500.316i			1.48462i	0.670058	+	0.742309i	$0.266269\pi$
$337$			500.316i			1.48462i	−0.670058	+	0.742309i	$0.733731\pi$
$338$	−360.144			−1.06551
$339$	−113.830	+	212.957i	−0.335782	+	0.628190i
$340$		0			0
$341$			2.28487i			0.00670051i
$342$	−113.137	−	169.328i	−0.330810	−	0.495111i
$343$		−	18.5203i		−	0.0539949i
$344$		−	146.368i		−	0.425489i
$345$		0			0
$346$	7.71243			0.0222903
$347$	192.860			0.555792			0.277896	−	0.960611i	$-0.410363\pi$
$347$	192.860			0.555792			0.277896	+	0.960611i	$0.410363\pi$
$348$	−110.068	−	58.8340i	−0.316288	−	0.169063i
$349$	−148.405			−0.425230			−0.212615	−	0.977136i	$-0.568198\pi$
$349$	−148.405			−0.425230			−0.212615	+	0.977136i	$0.568198\pi$
$350$		0			0
$351$	−54.4575	−	553.067i	−0.155150	−	1.57569i
$352$		−	2.33202i		−	0.00662506i
$353$	163.771			0.463942			0.231971	−	0.972723i	$-0.425483\pi$
$353$	163.771			0.463942			0.231971	+	0.972723i	$0.425483\pi$
$354$	6.16995	+	3.29798i	0.0174292	+	0.00931632i
$355$		0			0
$356$			62.4029i			0.175289i
$357$	−111.159	−	59.4170i	−0.311370	−	0.166434i
$358$			1.74902i			0.00488552i
$359$		−	334.877i		−	0.932804i	−0.884573	−	0.466402i	$-0.845550\pi$
$359$		−	334.877i		−	0.932804i	0.884573	−	0.466402i	$-0.154450\pi$
$360$		0			0
$361$	−105.000			−0.290859
$362$	−264.338			−0.730215
$363$	−170.879	+	319.686i	−0.470742	+	0.880678i
$364$	108.915			0.299217
$365$		0			0
$366$	133.830	−	250.373i	0.365656	−	0.684080i
$367$			326.996i			0.890997i	0.895283	+	0.445499i	$0.146974\pi$
$367$			326.996i			0.890997i	−0.895283	+	0.445499i	$0.853026\pi$
$368$	144.009			0.391330
$369$	569.490	−	380.507i	1.54333	−	1.03118i
$370$		0			0
$371$			134.700i			0.363072i
$372$	15.6765	−	29.3281i	0.0421412	−	0.0788389i
$373$			305.336i			0.818595i	0.912401	+	0.409298i	$0.134226\pi$
$373$			305.336i			0.818595i	−0.912401	+	0.409298i	$0.865774\pi$
$374$		−	9.25804i		−	0.0247541i
$375$		0			0
$376$	−24.0000			−0.0638298
$377$	428.146			1.13567
$378$	9.89949	+	100.539i	0.0261891	+	0.265975i
$379$	−199.660			−0.526808			−0.263404	−	0.964686i	$-0.584845\pi$
$379$	−199.660			−0.526808			−0.263404	+	0.964686i	$0.584845\pi$
$380$		0			0
$381$	351.660	+	187.970i	0.922992	+	0.493360i
$382$			495.741i			1.29775i
$383$	−529.489			−1.38248			−0.691239	−	0.722626i	$-0.742935\pi$
$383$	−529.489			−1.38248			−0.691239	+	0.722626i	$0.742935\pi$
$384$	−16.0000	+	29.9333i	−0.0416667	+	0.0779512i
$385$		0			0
$386$		−	382.536i		−	0.991027i
$387$	−387.254	+	258.745i	−1.00066	+	0.668592i
$388$		−	137.668i		−	0.354814i
$389$		−	238.704i		−	0.613636i	−0.951768	−	0.306818i	$-0.900736\pi$
$389$		−	238.704i		−	0.613636i	0.951768	−	0.306818i	$-0.0992643\pi$
$390$		0			0
$391$	571.712			1.46218
$392$	−19.7990			−0.0505076
$393$	−10.9070	−	5.83005i	−0.0277533	−	0.0148347i
$394$	89.8301			0.227995
$395$		0			0
$396$	−6.16995	+	4.12247i	−0.0155807	+	0.0104103i
$397$			320.583i			0.807514i	0.914866	+	0.403757i	$0.132296\pi$
$397$			320.583i			0.807514i	−0.914866	+	0.403757i	$0.867704\pi$
$398$	124.451			0.312690
$399$	−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	$0.906540\pi$
$402$	−184.901	−	98.8340i	−0.459954	−	0.245856i
$403$			114.081i			0.283079i
$404$			280.306i			0.693828i
$405$		0			0
$406$	−77.8301			−0.191700
$407$	8.24494			0.0202578
$408$	−63.5194	+	118.834i	−0.155685	+	0.291260i
$409$	−528.980			−1.29335			−0.646675	−	0.762765i	$-0.723841\pi$
$409$	−528.980			−1.29335			−0.646675	+	0.762765i	$0.723841\pi$
$410$		0			0
$411$	−140.915	+	263.628i	−0.342859	+	0.641430i
$412$		−	78.7451i		−	0.191129i
$413$	4.36281			0.0105637
$414$	−254.575	−	381.013i	−0.614916	−	0.920322i
$415$		0			0
$416$		−	116.435i		−	0.279892i
$417$	132.289	−	247.490i	0.317240	−	0.593502i
$418$		−	9.32808i		−	0.0223160i
$419$			89.7998i			0.214319i	0.994242	+	0.107160i	$0.0341756\pi$
$419$			89.7998i			0.214319i	−0.994242	+	0.107160i	$0.965824\pi$
$420$		0			0
$421$	−777.150			−1.84596			−0.922981	−	0.384845i	$-0.874255\pi$
$421$	−777.150			−1.84596			−0.922981	+	0.384845i	$0.874255\pi$
$422$	−535.626			−1.26926
$423$	42.4264	+	63.4980i	0.100299	+	0.150114i
$424$	144.000			0.339623
$425$		0			0
$426$	328.288	+	175.477i	0.770628	+	0.411918i
$427$		−	177.041i		−	0.414615i
$428$	216.014			0.504706
$429$	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	$0.907917\pi$
$432$	107.480	−	10.5830i	0.248797	−	0.0244977i
$433$			796.996i			1.84064i	0.391169	+	0.920319i	$0.372071\pi$
$433$			796.996i			1.84064i	−0.391169	+	0.920319i	$0.627929\pi$
$434$		−	20.7381i		−	0.0477836i
$435$		0			0
$436$	247.660			0.568028
$437$	576.038			1.31816
$438$	−46.1422	−	24.6640i	−0.105347	−	0.0563106i
$439$	−553.830			−1.26157			−0.630786	−	0.775957i	$-0.717267\pi$
$439$	−553.830			−1.26157			−0.630786	+	0.775957i	$0.717267\pi$
$440$		0			0
$441$	35.0000	+	52.3832i	0.0793651	+	0.118783i
$442$		−	462.243i		−	1.04580i
$443$	−773.981			−1.74714			−0.873568	−	0.486702i	$-0.838200\pi$
$443$	−773.981			−1.74714			−0.873568	+	0.486702i	$0.838200\pi$
$444$	−105.830	−	56.5685i	−0.238356	−	0.127407i
$445$		0			0
$446$			325.968i			0.730870i
$447$	131.882	+	70.4941i	0.295039	+	0.157705i
$448$			21.1660i			0.0472456i
$449$			677.174i			1.50818i	0.656770	+	0.754091i	$0.271922\pi$
$449$			677.174i			1.50818i	−0.656770	+	0.754091i	$0.728078\pi$
$450$		0			0
$451$	31.3725			0.0695622
$452$	160.980			0.356150
$453$	−299.333	+	560.000i	−0.660778	+	1.23620i
$454$	365.490			0.805044
$455$		0			0
$456$	−64.0000	+	119.733i	−0.140351	+	0.262572i
$457$			834.664i			1.82640i	0.407514	+	0.913199i	$0.366396\pi$
$457$			834.664i			1.82640i	−0.407514	+	0.913199i	$0.633604\pi$
$458$	52.4461			0.114511
$459$	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	$0.877121\pi$
$462$	−2.18141	+	4.08104i	−0.00472166	+	0.00883341i
$463$		−	317.668i		−	0.686108i	−0.939316	−	0.343054i	$-0.888539\pi$
$463$		−	317.668i		−	0.686108i	0.939316	−	0.343054i	$-0.111461\pi$
$464$			83.2038i			0.179319i
$465$		0			0
$466$	116.915			0.250891
$467$	547.421			1.17221			0.586104	−	0.810236i	$-0.300661\pi$
$467$	547.421			1.17221			0.586104	+	0.810236i	$0.300661\pi$
$468$	−308.058	+	205.830i	−0.658244	+	0.439808i
$469$	−130.745			−0.278774
$470$		0			0
$471$	287.712	+	153.789i	0.610854	+	0.326515i
$472$		−	4.66404i		−	0.00988144i
$473$	−21.3334			−0.0451023
$474$	−169.830	+	317.723i	−0.358291	+	0.670302i
$475$		0			0
$476$			84.0283i			0.176530i
$477$	−254.558	−	380.988i	−0.533665	−	0.798717i
$478$		−	238.251i		−	0.498433i
$479$		−	135.524i		−	0.282931i	−0.989943	−	0.141466i	$-0.954818\pi$
$479$		−	135.524i		−	0.282931i	0.989943	−	0.141466i	$-0.0451815\pi$
$480$		0			0
$481$	411.660			0.855842
$482$	−183.848			−0.381427
$483$	−252.017	−	134.708i	−0.521773	−	0.278900i
$484$	241.660			0.499298
$485$		0			0
$486$	−218.000	−	265.658i	−0.448560	−	0.546621i
$487$			23.4980i			0.0482506i	0.999709	+	0.0241253i	$0.00768006\pi$
$487$			23.4980i			0.0482506i	−0.999709	+	0.0241253i	$0.992320\pi$
$488$	−189.264			−0.387837
$489$	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	$-0.0335801\pi$
$492$	−402.690	−	215.247i	−0.818476	−	0.437494i
$493$			330.316i			0.670013i
$494$		−	465.740i		−	0.942794i
$495$		0			0
$496$	−22.1699			−0.0446975
$497$	232.134			0.467071
$498$	8.24494	−	15.4249i	0.0165561	−	0.0309736i
$499$	64.3399			0.128938			0.0644688	−	0.997920i	$-0.479465\pi$
$499$	64.3399			0.128938			0.0644688	+	0.997920i	$0.479465\pi$
$500$		0			0
$501$	221.830	−	415.006i	0.442775	−	0.828355i
$502$		−	169.506i		−	0.337661i
$503$	546.940			1.08736			0.543678	−	0.839294i	$-0.317031\pi$
$503$	546.940			1.08736			0.543678	+	0.839294i	$0.317031\pi$
$504$	56.0000	−	37.4166i	0.111111	−	0.0742392i
$505$		0			0
$506$		−	20.9896i		−	0.0414814i
$507$	360.144	−	673.767i	0.710343	−	1.32893i
$508$		−	265.830i		−	0.523288i
$509$			63.5453i			0.124843i	0.998050	+	0.0624217i	$0.0198824\pi$
$509$			63.5453i			0.124843i	−0.998050	+	0.0624217i	$0.980118\pi$
$510$		0			0
$511$	−32.6275			−0.0638502
$512$	22.6274			0.0441942
$513$	429.921	−	42.3320i	0.838052	−	0.0825186i
$514$	−316.627			−0.616007
$515$		0			0
$516$	273.830	+	146.368i	0.530678	+	0.283660i
$517$			3.49803i			0.00676602i
$518$	−74.8331			−0.144466
$519$	−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	$-0.211413\pi$
$522$	220.137	−	147.085i	0.421718	−	0.281772i
$523$			112.376i			0.214869i	0.994212	+	0.107434i	$0.0342636\pi$
$523$			112.376i			0.214869i	−0.994212	+	0.107434i	$0.965736\pi$
$524$			8.24494i			0.0157346i
$525$		0			0
$526$	−303.255			−0.576530
$527$	−88.0139			−0.167009
$528$	4.36281	+	2.33202i	0.00826290	+	0.00441671i
$529$	767.170			1.45023
$530$		0			0
$531$	−12.3399	+	8.24494i	−0.0232390	+	0.0155272i
$532$			84.6640i			0.159143i
$533$	1566.39			2.93883
$534$	−116.745	−	62.4029i	−0.218624	−	0.116859i
$535$		0			0
$536$			139.772i			0.260769i
$537$	−3.27211	−	1.74902i	−0.00609331	−	0.00325701i
$538$		−	540.450i		−	1.00455i
$539$			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	$0.509754\pi$
$542$	161.867			0.298648
$543$	264.338	−	494.531i	0.486810	−	0.910738i
$544$	89.8301			0.165129
$545$		0			0
$546$	−108.915	+	203.761i	−0.199478	+	0.373189i
$547$		−	919.911i		−	1.68174i	−0.541238	−	0.840869i	$-0.682044\pi$
$547$		−	919.911i		−	1.68174i	0.541238	−	0.840869i	$-0.317956\pi$
$548$	199.284			0.363657
$549$	334.575	+	500.746i	0.609426	+	0.912106i
$550$		0			0
$551$			332.815i			0.604021i
$552$	−144.009	+	269.417i	−0.260887	+	0.488074i
$553$			224.664i			0.406264i
$554$		−	325.968i		−	0.588390i
$555$		0			0
$556$	−187.085			−0.336484
$557$	−725.371			−1.30228			−0.651141	−	0.758957i	$-0.725709\pi$
$557$	−725.371			−1.30228			−0.651141	+	0.758957i	$0.725709\pi$
$558$	39.1913	+	58.6562i	0.0702353	+	0.105119i
$559$	−1065.15			−1.90546
$560$		0			0
$561$	17.3202	+	9.25804i	0.0308738	+	0.0165027i
$562$		−	104.575i		−	0.186077i
$563$	728.773			1.29445			0.647223	−	0.762301i	$-0.275930\pi$
$563$	728.773			1.29445			0.647223	+	0.762301i	$0.275930\pi$
$564$	24.0000	−	44.8999i	0.0425532	−	0.0796097i
$565$		0			0
$566$		−	199.639i		−	0.352719i
$567$	−197.990	−	82.0183i	−0.349189	−	0.144653i
$568$		−	248.162i		−	0.436905i
$569$		−	167.044i		−	0.293574i	−0.989168	−	0.146787i	$-0.953107\pi$
$569$		−	167.044i		−	0.293574i	0.989168	−	0.146787i	$-0.0468932\pi$
$570$		0			0
$571$	−72.9150			−0.127697			−0.0638485	−	0.997960i	$-0.520337\pi$
$571$	−72.9150			−0.127697			−0.0638485	+	0.997960i	$0.520337\pi$
$572$	−16.9706			−0.0296688
$573$	−927.447	−	495.741i	−1.61858	−	0.865168i
$574$	−284.745			−0.496072
$575$		0			0
$576$	−40.0000	−	59.8665i	−0.0694444	−	0.103935i
$577$			552.154i			0.956940i	0.878104	+	0.478470i	$0.158808\pi$
$577$			552.154i			0.956940i	−0.878104	+	0.478470i	$0.841192\pi$
$578$	−52.0856			−0.0901134
$579$	715.660	+	382.536i	1.23603	+	0.660685i
$580$		0			0
$581$		−	10.9070i		−	0.0187729i
$582$	257.553	+	137.668i	0.442531	+	0.236543i
$583$		−	20.9882i		−	0.0360003i
$584$			34.8802i			0.0597264i
$585$		0			0
$586$	−466.118			−0.795423
$587$	−1115.21			−1.89985			−0.949926	−	0.312474i	$-0.898842\pi$
$587$	−1115.21			−1.89985			−0.949926	+	0.312474i	$0.898842\pi$
$588$	19.7990	−	37.0405i	0.0336718	−	0.0629941i
$589$	−88.6798			−0.150560
$590$		0			0
$591$	−89.8301	+	168.057i	−0.151997	+	0.284360i
$592$			80.0000i			0.135135i
$593$	−957.506			−1.61468			−0.807340	−	0.590086i	$-0.799094\pi$
$593$	−957.506			−1.61468			−0.807340	+	0.590086i	$0.799094\pi$
$594$	−1.54249	−	15.6654i	−0.00259678	−	0.0263727i
$595$		0			0
$596$		−	99.6937i		−	0.167271i
$597$	−124.451	+	232.826i	−0.208460	+	0.389993i
$598$		−	1047.98i		−	1.75248i
$599$			610.047i			1.01844i	0.860636	+	0.509221i	$0.170067\pi$
$599$			610.047i			1.01844i	−0.860636	+	0.509221i	$0.829933\pi$
$600$		0			0
$601$	−974.470			−1.62142			−0.810708	−	0.585451i	$-0.800917\pi$
$601$	−974.470			−1.62142			−0.810708	+	0.585451i	$0.800917\pi$
$602$	193.627			0.321640
$603$	369.803	−	247.085i	0.613272	−	0.409759i
$604$	423.320			0.700861
$605$		0			0
$606$	−524.405	−	280.306i	−0.865355	−	0.462552i
$607$		−	1096.15i		−	1.80584i	−0.429806	−	0.902921i	$-0.641418\pi$
$607$		−	1096.15i		−	1.80584i	0.429806	−	0.902921i	$-0.358582\pi$
$608$	90.5097			0.148865
$609$	77.8301	−	145.607i	0.127800	−	0.239091i
$610$		0			0
$611$			174.653i			0.285847i
$612$	−158.799	−	237.668i	−0.259475	−	0.388346i
$613$			311.166i			0.507612i	0.967255	+	0.253806i	$0.0816824\pi$
$613$			311.166i			0.507612i	−0.967255	+	0.253806i	$0.918318\pi$
$614$		−	149.666i		−	0.243756i
$615$		0			0
$616$	3.08497			0.00500807
$617$	905.503			1.46759			0.733795	−	0.679371i	$-0.237747\pi$
$617$	905.503			1.46759			0.733795	+	0.679371i	$0.237747\pi$
$618$	147.319	+	78.7451i	0.238380	+	0.127419i
$619$	−54.7974			−0.0885257			−0.0442628	−	0.999020i	$-0.514094\pi$
$619$	−54.7974			−0.0885257			−0.0442628	+	0.999020i	$0.514094\pi$
$620$		0			0
$621$	967.385	−	95.2533i	1.55779	−	0.153387i
$622$		−	544.664i		−	0.875666i
$623$	−82.5512			−0.132506
$624$	217.830	+	116.435i	0.349087	+	0.186595i
$625$		0			0
$626$			112.187i			0.179212i
$627$	17.4512	+	9.32808i	0.0278329	+	0.0148773i
$628$		−	217.490i		−	0.346322i
$629$			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	$0.454064\pi$
$632$	240.176			0.380025
$633$	535.626	−	1002.07i	0.846171	−	1.58304i
$634$	581.490			0.917177
$635$		0			0
$636$	−144.000	+	269.399i	−0.226415	+	0.423584i
$637$			144.081i			0.226187i
$638$	12.1271			0.0190079
$639$	−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	$-0.226646\pi$
$642$	−216.014	+	404.125i	−0.336471	+	0.629479i
$643$		−	59.0118i		−	0.0917758i	−0.998947	−	0.0458879i	$-0.985388\pi$
$643$		−	59.0118i		−	0.0917758i	0.998947	−	0.0458879i	$-0.0146117\pi$
$644$			190.507i			0.295818i
$645$		0			0
$646$	359.320			0.556223
$647$	−547.661			−0.846462			−0.423231	−	0.906022i	$-0.639104\pi$
$647$	−547.661			−0.846462			−0.423231	+	0.906022i	$0.639104\pi$
$648$	−87.6812	+	211.660i	−0.135311	+	0.326636i
$649$	−0.679790			−0.00104744
$650$		0			0
$651$	38.7974	+	20.7381i	0.0595966	+	0.0318557i
$652$		−	26.0079i		−	0.0398894i
$653$	−764.895			−1.17136			−0.585678	−	0.810544i	$-0.699172\pi$
$653$	−764.895			−1.17136			−0.585678	+	0.810544i	$0.699172\pi$
$654$	−247.660	+	463.330i	−0.378685	+	0.708455i
$655$		0			0
$656$			304.405i			0.464032i
$657$	92.2844	−	61.6601i	0.140463	−	0.0938510i
$658$		−	31.7490i		−	0.0482508i
$659$			1050.80i			1.59454i	0.603623	+	0.797270i	$0.293723\pi$
$659$			1050.80i			1.59454i	−0.603623	+	0.797270i	$0.706277\pi$
$660$		0			0
$661$	−145.085			−0.219493			−0.109747	−	0.993960i	$-0.535004\pi$
$661$	−145.085			−0.219493			−0.109747	+	0.993960i	$0.535004\pi$
$662$	−692.244			−1.04569
$663$	864.778	+	462.243i	1.30434	+	0.697199i
$664$	−11.6601			−0.0175604
$665$		0			0
$666$	211.660	−	141.421i	0.317808	−	0.212344i
$667$			748.884i			1.12276i
$668$	−313.715			−0.469633
$669$	−609.830	−	325.968i	−0.911555	−	0.487246i
$670$		0			0
$671$			27.5855i			0.0411111i
$672$	−39.5980	−	21.1660i	−0.0589256	−	0.0314970i
$673$		−	323.498i		−	0.480681i	−0.970689	−	0.240340i	$-0.922741\pi$
$673$		−	323.498i		−	0.480681i	0.970689	−	0.240340i	$-0.0772590\pi$
$674$			707.554i			1.04978i
$675$		0			0
$676$	−509.320			−0.753432
$677$	166.434			0.245840			0.122920	−	0.992417i	$-0.460774\pi$
$677$	166.434			0.245840			0.122920	+	0.992417i	$0.460774\pi$
$678$	−160.980	+	301.166i	−0.237434	+	0.444198i
$679$	182.118			0.268214
$680$		0			0
$681$	−365.490	+	683.769i	−0.536696	+	1.00407i
$682$			3.23130i			0.00473797i
$683$	973.506			1.42534			0.712669	−	0.701501i	$-0.247486\pi$
$683$	973.506			1.42534			0.712669	+	0.701501i	$0.247486\pi$
$684$	−160.000	−	239.466i	−0.233918	−	0.350097i
$685$		0			0
$686$		−	26.1916i		−	0.0381802i
$687$	−52.4461	+	98.1176i	−0.0763407	+	0.142820i
$688$		−	206.996i		−	0.300866i
$689$		−	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	$0.129695\pi$
$692$	10.9070			0.0157616
$693$	−5.45351	−	8.16207i	−0.00786943	−	0.0117779i
$694$	272.745			0.393004
$695$		0			0
$696$	−155.660	−	83.2038i	−0.223650	−	0.119546i
$697$			1208.48i			1.73383i
$698$	−209.877			−0.300683
$699$	−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	$-0.193002\pi$
$702$	−77.0146	−	782.154i	−0.109707	−	1.11418i
$703$			320.000i			0.455192i
$704$		−	3.29798i		−	0.00468462i
$705$		0			0
$706$	231.608			0.328056
$707$	−370.810			−0.524484
$708$	8.72562	+	4.66404i	0.0123243	+	0.00658763i
$709$	651.490			0.918886			0.459443	−	0.888207i	$-0.348049\pi$
$709$	651.490			0.918886			0.459443	+	0.888207i	$0.348049\pi$
$710$		0			0
$711$	−424.575	−	635.446i	−0.597152	−	0.893735i
$712$			88.2510i			0.123948i
$713$	−199.543			−0.279863
$714$	−157.203	−	84.0283i	−0.220172	−	0.117687i
$715$		0			0
$716$			2.47348i			0.00345458i
$717$	445.727	+	238.251i	0.621655	+	0.332289i
$718$		−	473.587i		−	0.659592i
$719$			878.587i			1.22196i	0.791647	+	0.610979i	$0.209224\pi$
$719$			878.587i			1.22196i	−0.791647	+	0.610979i	$0.790776\pi$
$720$		0			0
$721$	104.170			0.144480
$722$	−148.492			−0.205668
$723$	183.848	−	343.948i	0.254285	−	0.475723i
$724$	−373.830			−0.516340
$725$		0			0
$726$	−241.660	+	452.105i	−0.332865	+	0.622734i
$727$			442.782i			0.609053i	0.952504	+	0.304527i	$0.0984982\pi$
$727$			442.782i			0.609053i	−0.952504	+	0.304527i	$0.901502\pi$
$728$	154.029			0.211578
$729$	715.000	−	142.183i	0.980796	−	0.195038i
$730$		0			0
$731$		−	821.767i		−	1.12417i
$732$	189.264	−	354.081i	0.258558	−	0.483717i
$733$		−	962.559i		−	1.31318i	−0.754249	−	0.656589i	$-0.771999\pi$
$733$		−	962.559i		−	1.31318i	0.754249	−	0.656589i	$-0.228001\pi$
$734$			462.442i			0.630030i
$735$		0			0
$736$	203.660			0.276712
$737$	20.3720			0.0276418
$738$	805.381	−	538.118i	1.09130	−	0.729157i
$739$	−1224.81			−1.65739			−0.828694	−	0.559701i	$-0.810916\pi$
$739$	−1224.81			−1.65739			−0.828694	+	0.559701i	$0.810916\pi$
$740$		0			0
$741$	871.320	+	465.740i	1.17587	+	0.628529i
$742$			190.494i			0.256731i
$743$	1447.24			1.94783			0.973916	−	0.226908i	$-0.0728617\pi$
$743$	1447.24			1.94783			0.973916	+	0.226908i	$0.0728617\pi$
$744$	22.1699	−	41.4762i	0.0297983	−	0.0557475i
$745$		0			0
$746$			431.810i			0.578834i
$747$	20.6123	+	30.8497i	0.0275935	+	0.0412982i
$748$		−	13.0928i		−	0.0175038i
$749$			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	$0.650719\pi$
$752$	−33.9411			−0.0451345
$753$	317.117	+	169.506i	0.421137	+	0.225107i
$754$	605.490			0.803037
$755$		0			0
$756$	14.0000	+	142.183i	0.0185185	+	0.188073i
$757$		−	907.135i		−	1.19833i	−0.800626	−	0.599164i	$-0.795500\pi$
$757$		−	907.135i		−	1.19833i	0.800626	−	0.599164i	$-0.204500\pi$
$758$	−282.362			−0.372509
$759$	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	$0.597256\pi$
$762$	497.322	+	265.830i	0.652654	+	0.348858i
$763$			327.624i			0.429389i
$764$			701.084i			0.917649i
$765$		0			0
$766$	−748.810			−0.977559
$767$	−33.9411			−0.0442518
$768$	−22.6274	+	42.3320i	−0.0294628	+	0.0551198i
$769$	1089.32			1.41654			0.708271	−	0.705941i	$-0.249476\pi$
$769$	1089.32			1.41654			0.708271	+	0.705941i	$0.249476\pi$
$770$		0			0
$771$	316.627	−	592.356i	0.410671	−	0.768295i
$772$		−	540.988i		−	0.700762i
$773$	1019.58			1.31900			0.659498	−	0.751707i	$-0.270769\pi$
$773$	1019.58			1.31900			0.659498	+	0.751707i	$0.270769\pi$
$774$	−547.660	+	365.921i	−0.707571	+	0.472766i
$775$		0			0
$776$		−	194.692i		−	0.250892i
$777$	74.8331	−	140.000i	0.0963104	−	0.180180i
$778$		−	337.579i		−	0.433906i
$779$			1217.62i			1.56306i
$780$		0			0
$781$	−36.1699			−0.0463124
$782$	808.523			1.03392
$783$	55.0342	+	558.923i	0.0702863	+	0.713822i
$784$	−28.0000			−0.0357143
$785$		0			0
$786$	−15.4249	−	8.24494i	−0.0196245	−	0.0104897i
$787$		−	1267.00i		−	1.60991i	−0.593334	−	0.804956i	$-0.702189\pi$
$787$		−	1267.00i		−	1.60991i	0.593334	−	0.804956i	$-0.297811\pi$
$788$	127.039			0.161217
$789$	303.255	−	567.338i	0.384354	−	0.719060i
$790$		0			0
$791$			212.957i			0.269224i
$792$	−8.72562	+	5.83005i	−0.0110172	+	0.00736118i
$793$			1377.31i			1.73684i
$794$			453.373i			0.570999i
$795$		0			0
$796$	176.000			0.221106
$797$	−922.123			−1.15699			−0.578496	−	0.815685i	$-0.696360\pi$
$797$	−922.123			−1.15699			−0.578496	+	0.815685i	$0.696360\pi$
$798$	−158.392	−	84.6640i	−0.198486	−	0.106095i
$799$	−134.745			−0.168642
$800$		0			0
$801$	233.490	−	156.007i	0.291498	−	0.194766i
$802$			328.251i			0.409291i
$803$	5.08384			0.00633106
$804$	−261.490	−	139.772i	−0.325237	−	0.173846i
$805$		0			0
$806$			161.335i			0.200167i
$807$	1011.09	+	540.450i	1.25290	+	0.669702i
$808$			396.413i			0.490610i
$809$			706.855i			0.873740i	0.899525	+	0.436870i	$0.143913\pi$
$809$			706.855i			0.873740i	−0.899525	+	0.436870i	$0.856087\pi$
$810$		0			0
$811$	833.778			1.02809			0.514043	−	0.857764i	$-0.328147\pi$
$811$	833.778			1.02809			0.514043	+	0.857764i	$0.328147\pi$
$812$	−110.068			−0.135552
$813$	−161.867	+	302.826i	−0.199099	+	0.372480i
$814$	11.6601			0.0143245
$815$		0			0
$816$	−89.8301	+	168.057i	−0.110086	+	0.205952i
$817$		−	827.984i		−	1.01344i
$818$	−748.091			−0.914537
$819$	−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	$-0.0489002\pi$
$822$	−199.284	+	372.826i	−0.242438	+	0.453560i
$823$		−	38.9229i		−	0.0472939i	−0.999720	−	0.0236470i	$-0.992472\pi$
$823$		−	38.9229i		−	0.0472939i	0.999720	−	0.0236470i	$-0.00752776\pi$
$824$		−	111.362i		−	0.135148i
$825$		0			0
$826$	6.16995			0.00746967
$827$	−108.007			−0.130601			−0.0653005	−	0.997866i	$-0.520801\pi$
$827$	−108.007			−0.130601			−0.0653005	+	0.997866i	$0.520801\pi$
$828$	−360.024	−	538.834i	−0.434811	−	0.650766i
$829$	1410.58			1.70154			0.850769	−	0.525540i	$-0.176137\pi$
$829$	1410.58			1.70154			0.850769	+	0.525540i	$0.176137\pi$
$830$		0			0
$831$	609.830	+	325.968i	0.733851	+	0.392260i
$832$		−	164.664i		−	0.197914i
$833$	−111.159			−0.133444
$834$	187.085	−	350.004i	0.224323	−	0.419669i
$835$		0			0
$836$		−	13.1919i		−	0.0157798i
$837$	−148.927	+	14.6640i	−0.177929	+	0.0175198i
$838$			126.996i			0.151547i
$839$		−	299.906i		−	0.357456i	−0.983899	−	0.178728i	$-0.942802\pi$
$839$		−	299.906i		−	0.357456i	0.983899	−	0.178728i	$-0.0571982\pi$
$840$		0			0
$841$	408.320			0.485517
$842$	−1099.06			−1.30529
$843$	195.642	+	104.575i	0.232078	+	0.124051i
$844$	−757.490			−0.897500
$845$		0			0
$846$	60.0000	+	89.7998i	0.0709220	+	0.106146i
$847$			319.686i			0.377434i
$848$	203.647			0.240149
$849$	373.490	+	199.639i	0.439918	+	0.235146i
$850$		0			0
$851$			720.047i			0.846119i
$852$	464.269	+	248.162i	0.544916	+	0.291270i
$853$			13.7648i			0.0161369i	0.999967	+	0.00806844i	$0.00256829\pi$
$853$			13.7648i			0.0161369i	−0.999967	+	0.00806844i	$0.997432\pi$
$854$		−	250.373i		−	0.293177i
$855$		0			0
$856$	305.490			0.356881
$857$	−252.506			−0.294640			−0.147320	−	0.989089i	$-0.547065\pi$
$857$	−252.506			−0.294640			−0.147320	+	0.989089i	$0.547065\pi$
$858$	16.9706	−	31.7490i	0.0197792	−	0.0370035i
$859$	−674.510			−0.785227			−0.392613	−	0.919704i	$-0.628429\pi$
$859$	−674.510			−0.785227			−0.392613	+	0.919704i	$0.628429\pi$
$860$		0			0
$861$	284.745	−	532.709i	0.330714	−	0.618710i
$862$			347.757i			0.403430i
$863$	477.718			0.553555			0.276777	−	0.960934i	$-0.410734\pi$
$863$	477.718			0.553555			0.276777	+	0.960934i	$0.410734\pi$
$864$	152.000	−	14.9666i	0.175926	−	0.0173225i
$865$		0			0
$866$			1127.12i			1.30153i
$867$	52.0856	−	97.4432i	0.0600756	−	0.112391i
$868$		−	29.3281i		−	0.0337881i
$869$		−	35.0060i		−	0.0402830i
$870$		0			0
$871$	1017.15			1.16780
$872$	350.244			0.401656
$873$	−515.106	+	344.170i	−0.590042	+	0.394238i
$874$	814.640			0.932083
$875$		0			0
$876$	−65.2549	−	34.8802i	−0.0744919	−	0.0398176i
$877$			1533.14i			1.74817i	0.485776	+	0.874083i	$0.338537\pi$
$877$			1533.14i			1.74817i	−0.485776	+	0.874083i	$0.661463\pi$
$878$	−783.234			−0.892066
$879$	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	$0.716961\pi$
$882$	49.4975	+	74.0810i	0.0561196	+	0.0839921i
$883$		−	944.486i		−	1.06963i	−0.844968	−	0.534817i	$-0.820381\pi$
$883$		−	944.486i		−	1.06963i	0.844968	−	0.534817i	$-0.179619\pi$
$884$		−	653.710i		−	0.739491i
$885$		0			0
$886$	−1094.58			−1.23541
$887$	−1326.86			−1.49590			−0.747951	−	0.663754i	$-0.768962\pi$
$887$	−1326.86			−1.49590			−0.747951	+	0.663754i	$0.768962\pi$
$888$	−149.666	−	80.0000i	−0.168543	−	0.0900901i
$889$	351.660			0.395568
$890$		0			0
$891$	30.8497	+	12.7797i	0.0346237	+	0.0143430i
$892$			460.988i			0.516803i
$893$	−135.765			−0.152032
$894$	186.510	+	99.6937i	0.208624	+	0.111514i
$895$		0			0
$896$			29.9333i			0.0334077i
$897$	1960.60	+	1047.98i	2.18573	+	1.16832i
$898$			957.668i			1.06645i
$899$		−	115.289i		−	0.128241i
$900$		0			0
$901$	808.470			0.897304
$902$	44.3675			0.0491879
$903$	−193.627	+	362.243i	−0.214426	+	0.401155i
$904$	227.660			0.251836
$905$		0			0
$906$	−423.320	+	791.960i	−0.467241	+	0.874128i
$907$		−	1219.64i		−	1.34470i	−0.740233	−	0.672351i	$-0.765285\pi$
$907$		−	1219.64i		−	1.34470i	0.740233	−	0.672351i	$-0.234715\pi$
$908$	516.881			0.569252
$909$	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	$0.988847\pi$
$912$	−90.5097	+	169.328i	−0.0992431	+	0.185667i
$913$			1.69948i			0.00186142i
$914$			1180.39i			1.29146i
$915$		0			0
$916$	74.1699			0.0809716
$917$	−10.9070			−0.0118943
$918$	603.435	−	59.4170i	0.657336	−	0.0647244i
$919$	−981.385			−1.06788			−0.533942	−	0.845521i	$-0.679290\pi$
$919$	−981.385			−1.06788			−0.533942	+	0.845521i	$0.679290\pi$
$920$		0			0
$921$	280.000	+	149.666i	0.304017	+	0.162504i
$922$			490.944i			0.532477i
$923$	−1805.92			−1.95658
$924$	−3.08497	+	5.77146i	−0.00333872	+	0.00624617i
$925$		0			0
$926$		−	449.250i		−	0.485152i
$927$	−294.637	+	196.863i	−0.317839	+	0.212365i
$928$			117.668i			0.126797i
$929$		−	340.931i		−	0.366987i	−0.983021	−	0.183493i	$-0.941259\pi$
$929$		−	340.931i		−	0.366987i	0.983021	−	0.183493i	$-0.0587406\pi$
$930$		0			0
$931$	−112.000			−0.120301
$932$	165.343			0.177406
$933$	1018.97	+	544.664i	1.09215	+	0.583777i
$934$	774.170			0.828876
$935$		0			0
$936$	−435.660	+	291.088i	−0.465449	+	0.310991i
$937$			1010.00i			1.07791i	0.842335	+	0.538954i	$0.181180\pi$
$937$			1010.00i			1.07791i	−0.842335	+	0.538954i	$0.818820\pi$
$938$	−184.901			−0.197123
$939$	−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	$-0.0490838\pi$
$942$	406.887	+	217.490i	0.431939	+	0.230881i
$943$			2739.83i			2.90544i
$944$		−	6.59595i		−	0.00698724i
$945$		0			0
$946$	−30.1699			−0.0318921
$947$	−828.054			−0.874397			−0.437199	−	0.899365i	$-0.644029\pi$
$947$	−828.054			−0.874397			−0.437199	+	0.899365i	$0.644029\pi$
$948$	−240.176	+	449.328i	−0.253350	+	0.473975i
$949$	253.830			0.267471
$950$		0			0
$951$	−581.490	+	1087.87i	−0.611451	+	1.14392i
$952$			118.834i			0.124826i
$953$	−102.785			−0.107854			−0.0539269	−	0.998545i	$-0.517174\pi$
$953$	−102.785			−0.107854			−0.0539269	+	0.998545i	$0.517174\pi$
$954$	−360.000	−	538.799i	−0.377358	−	0.564778i
$955$		0			0
$956$		−	336.938i		−	0.352445i
$957$	−12.1271	+	22.6877i	−0.0126720	+	0.0237071i
$958$		−	191.660i		−	0.200063i
$959$			263.628i			0.274899i
$960$		0			0
$961$	−930.281			−0.968034
$962$	582.175			0.605172
$963$	−540.035	−	808.251i	−0.560784	−	0.839305i
$964$	−260.000			−0.269710
$965$		0			0
$966$	−356.405	−	190.507i	−0.368949	−	0.197212i
$967$		−	184.753i		−	0.191058i	−0.995427	−	0.0955289i	$-0.969546\pi$
$967$		−	184.753i		−	0.191058i	0.995427	−	0.0955289i	$-0.0304542\pi$
$968$	341.759			0.353057
$969$	−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	$-0.273144\pi$
$972$	−308.299	−	375.697i	−0.317180	−	0.386519i
$973$		−	247.490i		−	0.254358i
$974$			33.2312i			0.0341183i
$975$		0			0
$976$	−267.660			−0.274242
$977$	663.072			0.678682			0.339341	−	0.940663i	$-0.389796\pi$
$977$	663.072			0.678682			0.339341	+	0.940663i	$0.389796\pi$
$978$	48.6563	+	26.0079i	0.0497508	+	0.0265929i
$979$	12.8627			0.0131386
$980$		0			0
$981$	−619.150	−	926.659i	−0.631142	−	0.944607i
$982$		−	146.235i		−	0.148916i
$983$	−1899.26			−1.93211			−0.966053	−	0.258342i	$-0.916824\pi$
$983$	−1899.26			−1.93211			−0.966053	+	0.258342i	$0.916824\pi$
$984$	−569.490	−	304.405i	−0.578750	−	0.309355i
$985$		0			0
$986$			467.138i			0.473771i
$987$	59.3970	+	31.7490i	0.0601793	+	0.0321672i
$988$		−	658.656i		−	0.666656i
$989$		−	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	$0.541508\pi$
$992$	−31.3530			−0.0316059
$993$	692.244	−	1295.07i	0.697123	−	1.30420i
$994$	328.288			0.330269
$995$		0			0
$996$	11.6601	−	21.8141i	0.0117069	−	0.0219017i
$997$			1235.74i			1.23946i	0.784815	+	0.619730i	$0.212758\pi$
$997$			1235.74i			1.23946i	−0.784815	+	0.619730i	$0.787242\pi$
$998$	90.9904			0.0911727
$999$	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.c.a.449.8		8
3.2	odd	2	inner	1050.3.c.a.449.3		8
5.2	odd	4		1050.3.e.a.701.4		4
5.3	odd	4		42.3.b.a.29.1	✓	4
5.4	even	2	inner	1050.3.c.a.449.2		8
15.2	even	4		1050.3.e.a.701.2		4
15.8	even	4		42.3.b.a.29.3	yes	4
15.14	odd	2	inner	1050.3.c.a.449.5		8
20.3	even	4		336.3.d.b.113.4		4
35.3	even	12		294.3.h.g.275.3		8
35.13	even	4		294.3.b.h.197.2		4
35.18	odd	12		294.3.h.d.275.4		8
35.23	odd	12		294.3.h.d.263.2		8
35.33	even	12		294.3.h.g.263.1		8
40.3	even	4		1344.3.d.e.449.1		4
40.13	odd	4		1344.3.d.c.449.4		4
45.13	odd	12		1134.3.q.a.1079.3		8
45.23	even	12		1134.3.q.a.1079.2		8
45.38	even	12		1134.3.q.a.701.3		8
45.43	odd	12		1134.3.q.a.701.2		8
60.23	odd	4		336.3.d.b.113.3		4
105.23	even	12		294.3.h.d.263.4		8
105.38	odd	12		294.3.h.g.275.1		8
105.53	even	12		294.3.h.d.275.2		8
105.68	odd	12		294.3.h.g.263.3		8
105.83	odd	4		294.3.b.h.197.4		4
120.53	even	4		1344.3.d.c.449.3		4
120.83	odd	4		1344.3.d.e.449.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.b.a.29.1	✓	4	5.3	odd	4
42.3.b.a.29.3	yes	4	15.8	even	4
294.3.b.h.197.2		4	35.13	even	4
294.3.b.h.197.4		4	105.83	odd	4
294.3.h.d.263.2		8	35.23	odd	12
294.3.h.d.263.4		8	105.23	even	12
294.3.h.d.275.2		8	105.53	even	12
294.3.h.d.275.4		8	35.18	odd	12
294.3.h.g.263.1		8	35.33	even	12
294.3.h.g.263.3		8	105.68	odd	12
294.3.h.g.275.1		8	105.38	odd	12
294.3.h.g.275.3		8	35.3	even	12
336.3.d.b.113.3		4	60.23	odd	4
336.3.d.b.113.4		4	20.3	even	4
1050.3.c.a.449.2		8	5.4	even	2	inner
1050.3.c.a.449.3		8	3.2	odd	2	inner
1050.3.c.a.449.5		8	15.14	odd	2	inner
1050.3.c.a.449.8		8	1.1	even	1	trivial
1050.3.e.a.701.2		4	15.2	even	4
1050.3.e.a.701.4		4	5.2	odd	4
1134.3.q.a.701.2		8	45.43	odd	12
1134.3.q.a.701.3		8	45.38	even	12
1134.3.q.a.1079.2		8	45.23	even	12
1134.3.q.a.1079.3		8	45.13	odd	12
1344.3.d.c.449.3		4	120.53	even	4
1344.3.d.c.449.4		4	40.13	odd	4
1344.3.d.e.449.1		4	40.3	even	4
1344.3.d.e.449.2		4	120.83	odd	4

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.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +(-1.41421 + 2.64575i) q^{3} +2.00000 q^{4} +(-2.00000 + 3.74166i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(-5.00000 - 7.48331i) q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} +(-1.41421 + 2.64575i) q^{3} +2.00000 q^{4} +(-2.00000 + 3.74166i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(-5.00000 - 7.48331i) q^{9} -0.412247i q^{11} +(-2.82843 + 5.29150i) q^{12} -20.5830i q^{13} +3.74166i q^{14} +4.00000 q^{16} +15.8799 q^{17} +(-7.07107 - 10.5830i) q^{18} +16.0000 q^{19} +(-7.00000 - 3.74166i) q^{21} -0.583005i q^{22} +36.0024 q^{23} +(-4.00000 + 7.48331i) q^{24} -29.1088i q^{26} +(26.8701 - 2.64575i) q^{27} +5.29150i q^{28} +20.8010i q^{29} -5.54249 q^{31} +5.65685 q^{32} +(1.09070 + 0.583005i) q^{33} +22.4575 q^{34} +(-10.0000 - 14.9666i) q^{36} +20.0000i q^{37} +22.6274 q^{38} +(54.4575 + 29.1088i) q^{39} +76.1013i q^{41} +(-9.89949 - 5.29150i) q^{42} -51.7490i q^{43} -0.824494i q^{44} +50.9150 q^{46} -8.48528 q^{47} +(-5.65685 + 10.5830i) q^{48} -7.00000 q^{49} +(-22.4575 + 42.0142i) q^{51} -41.1660i q^{52} +50.9117 q^{53} +(38.0000 - 3.74166i) q^{54} +7.48331i q^{56} +(-22.6274 + 42.3320i) q^{57} +29.4170i q^{58} -1.64899i q^{59} -66.9150 q^{61} -7.83826 q^{62} +(19.7990 - 13.2288i) q^{63} +8.00000 q^{64} +(1.54249 + 0.824494i) q^{66} +49.4170i q^{67} +31.7597 q^{68} +(-50.9150 + 95.2533i) q^{69} -87.7385i q^{71} +(-14.1421 - 21.1660i) q^{72} +12.3320i q^{73} +28.2843i q^{74} +32.0000 q^{76} +1.09070 q^{77} +(77.0146 + 41.1660i) q^{78} +84.9150 q^{79} +(-31.0000 + 74.8331i) q^{81} +107.624i q^{82} -4.12247 q^{83} +(-14.0000 - 7.48331i) q^{84} -73.1842i q^{86} +(-55.0342 - 29.4170i) q^{87} -1.16601i q^{88} +31.2014i q^{89} +54.4575 q^{91} +72.0047 q^{92} +(7.83826 - 14.6640i) q^{93} -12.0000 q^{94} +(-8.00000 + 14.9666i) q^{96} -68.8340i q^{97} -9.89949 q^{98} +(-3.08497 + 2.06123i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{4} - 16 q^{6} - 40 q^{9}+O(q^{10}) \) 8 * q + 16 * q^4 - 16 * q^6 - 40 * q^9	\( 8 q + 16 q^{4} - 16 q^{6} - 40 q^{9} + 32 q^{16} + 128 q^{19} - 56 q^{21} - 32 q^{24} - 256 q^{31} - 32 q^{34} - 80 q^{36} + 224 q^{39} - 16 q^{46} - 56 q^{49} + 32 q^{51} + 304 q^{54} - 112 q^{61} + 64 q^{64} + 224 q^{66} + 16 q^{69} + 256 q^{76} + 256 q^{79} - 248 q^{81} - 112 q^{84} + 224 q^{91} - 96 q^{94} - 64 q^{96} - 448 q^{99}+O(q^{100}) \) 8 * q + 16 * q^4 - 16 * q^6 - 40 * q^9 + 32 * q^16 + 128 * q^19 - 56 * q^21 - 32 * q^24 - 256 * q^31 - 32 * q^34 - 80 * q^36 + 224 * q^39 - 16 * q^46 - 56 * q^49 + 32 * q^51 + 304 * q^54 - 112 * q^61 + 64 * q^64 + 224 * q^66 + 16 * q^69 + 256 * q^76 + 256 * q^79 - 248 * q^81 - 112 * q^84 + 224 * q^91 - 96 * q^94 - 64 * q^96 - 448 * q^99

Introduction

L-functions

Modular forms

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