LMFDB - Embedded newform 1050.3.c.b.449.10

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:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			449.10
Character	$\chi$	$=$	1050.449
Dual form			1050.3.c.b.449.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +(0.836130 + 2.88113i) q^{3} +2.00000 q^{4} +(-1.18247 - 4.07453i) q^{6} -2.64575i q^{7} -2.82843 q^{8} +(-7.60177 + 4.81799i) q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +(0.836130 + 2.88113i) q^{3} +2.00000 q^{4} +(-1.18247 - 4.07453i) q^{6} -2.64575i q^{7} -2.82843 q^{8} +(-7.60177 + 4.81799i) q^{9} +13.1493i q^{11} +(1.67226 + 5.76225i) q^{12} +6.59929i q^{13} +3.74166i q^{14} +4.00000 q^{16} -21.7341 q^{17} +(10.7505 - 6.81367i) q^{18} +5.34611 q^{19} +(7.62274 - 2.21219i) q^{21} -18.5959i q^{22} -0.0360813 q^{23} +(-2.36493 - 8.14906i) q^{24} -9.33280i q^{26} +(-20.2373 - 17.8732i) q^{27} -5.29150i q^{28} +0.0748258i q^{29} +36.8062 q^{31} -5.65685 q^{32} +(-37.8847 + 10.9945i) q^{33} +30.7366 q^{34} +(-15.2035 + 9.63598i) q^{36} -71.7200i q^{37} -7.56054 q^{38} +(-19.0134 + 5.51786i) q^{39} +3.25149i q^{41} +(-10.7802 + 3.12851i) q^{42} +49.0760i q^{43} +26.2986i q^{44} +0.0510267 q^{46} -58.2461 q^{47} +(3.34452 + 11.5245i) q^{48} -7.00000 q^{49} +(-18.1725 - 62.6186i) q^{51} +13.1986i q^{52} -93.5713 q^{53} +(28.6199 + 25.2765i) q^{54} +7.48331i q^{56} +(4.47004 + 15.4028i) q^{57} -0.105820i q^{58} +49.6848i q^{59} -43.0443 q^{61} -52.0518 q^{62} +(12.7472 + 20.1124i) q^{63} +8.00000 q^{64} +(53.5771 - 15.5486i) q^{66} +68.3846i q^{67} -43.4682 q^{68} +(-0.0301687 - 0.103955i) q^{69} -87.2076i q^{71} +(21.5011 - 13.6273i) q^{72} +1.12498i q^{73} +101.427i q^{74} +10.6922 q^{76} +34.7897 q^{77} +(26.8890 - 7.80343i) q^{78} -70.2593 q^{79} +(34.5740 - 73.2505i) q^{81} -4.59830i q^{82} +0.397403 q^{83} +(15.2455 - 4.42438i) q^{84} -69.4039i q^{86} +(-0.215582 + 0.0625640i) q^{87} -37.1918i q^{88} +1.85426i q^{89} +17.4601 q^{91} -0.0721626 q^{92} +(30.7747 + 106.043i) q^{93} +82.3724 q^{94} +(-4.72986 - 16.2981i) q^{96} -34.4355i q^{97} +9.89949 q^{98} +(-63.3531 - 99.9579i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 64 q^{4} - 16 q^{6} - 16 q^{9}+O(q^{10}) $ 32 * q + 64 * q^4 - 16 * q^6 - 16 * q^9	$ 32 q + 64 q^{4} - 16 q^{6} - 16 q^{9} + 128 q^{16} + 48 q^{19} + 56 q^{21} - 32 q^{24} + 48 q^{31} + 256 q^{34} - 32 q^{36} + 192 q^{39} + 160 q^{46} - 224 q^{49} + 288 q^{51} - 80 q^{54} - 112 q^{61} + 256 q^{64} - 192 q^{66} + 344 q^{69} + 96 q^{76} - 256 q^{79} + 160 q^{81} + 112 q^{84} - 448 q^{91} + 416 q^{94} - 64 q^{96} - 304 q^{99}+O(q^{100}) $ 32 * q + 64 * q^4 - 16 * q^6 - 16 * q^9 + 128 * q^16 + 48 * q^19 + 56 * q^21 - 32 * q^24 + 48 * q^31 + 256 * q^34 - 32 * q^36 + 192 * q^39 + 160 * q^46 - 224 * q^49 + 288 * q^51 - 80 * q^54 - 112 * q^61 + 256 * q^64 - 192 * q^66 + 344 * q^69 + 96 * q^76 - 256 * q^79 + 160 * q^81 + 112 * q^84 - 448 * q^91 + 416 * q^94 - 64 * q^96 - 304 * 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
$3$	0.836130	+	2.88113i	0.278710	+	0.960375i
$3$	0.836130	+	2.88113i	0.278710	+	0.960375i
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$	−1.18247	−	4.07453i	−0.197078	−	0.679088i
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	−2.82843			−0.353553
$9$	−7.60177	+	4.81799i	−0.844642	+	0.535332i
$10$		0			0
$11$			13.1493i			1.19539i	0.801724	+	0.597695i	$0.203917\pi$
$11$			13.1493i			1.19539i	−0.801724	+	0.597695i	$0.796083\pi$
$12$	1.67226	+	5.76225i	0.139355	+	0.480188i
$13$			6.59929i			0.507637i	0.967252	+	0.253819i	$0.0816867\pi$
$13$			6.59929i			0.507637i	−0.967252	+	0.253819i	$0.918313\pi$
$14$			3.74166i			0.267261i
$15$		0			0
$16$	4.00000			0.250000
$17$	−21.7341			−1.27848			−0.639238	−	0.769009i	$-0.720750\pi$
$17$	−21.7341			−1.27848			−0.639238	+	0.769009i	$0.720750\pi$
$18$	10.7505	−	6.81367i	0.597252	−	0.378537i
$19$	5.34611			0.281374			0.140687	−	0.990054i	$-0.455069\pi$
$19$	5.34611			0.281374			0.140687	+	0.990054i	$0.455069\pi$
$20$		0			0
$21$	7.62274	−	2.21219i	0.362988	−	0.105342i
$22$		−	18.5959i		−	0.845268i
$23$	−0.0360813			−0.00156875			−0.000784376	−	1.00000i	$-0.500250\pi$
$23$	−0.0360813			−0.00156875			−0.000784376		1.00000i	$0.500250\pi$
$24$	−2.36493	−	8.14906i	−0.0985388	−	0.339544i
$25$		0			0
$26$		−	9.33280i		−	0.358954i
$27$	−20.2373	−	17.8732i	−0.749530	−	0.661971i
$28$		−	5.29150i		−	0.188982i
$29$			0.0748258i			0.00258020i	0.999999	+	0.00129010i	$0.000410652\pi$
$29$			0.0748258i			0.00258020i	−0.999999	+	0.00129010i	$0.999589\pi$
$30$		0			0
$31$	36.8062			1.18730			0.593648	−	0.804725i	$-0.297687\pi$
$31$	36.8062			1.18730			0.593648	+	0.804725i	$0.297687\pi$
$32$	−5.65685			−0.176777
$33$	−37.8847	+	10.9945i	−1.14802	+	0.333167i
$34$	30.7366			0.904019
$35$		0			0
$36$	−15.2035	+	9.63598i	−0.422321	+	0.267666i
$37$		−	71.7200i		−	1.93838i	−0.246317	−	0.969189i	$-0.579221\pi$
$37$		−	71.7200i		−	1.93838i	0.246317	−	0.969189i	$-0.420779\pi$
$38$	−7.56054			−0.198962
$39$	−19.0134	+	5.51786i	−0.487522	+	0.141484i
$40$		0			0
$41$			3.25149i			0.0793047i	0.999214	+	0.0396523i	$0.0126250\pi$
$41$			3.25149i			0.0793047i	−0.999214	+	0.0396523i	$0.987375\pi$
$42$	−10.7802	+	3.12851i	−0.256671	+	0.0744883i
$43$			49.0760i			1.14130i	0.821193	+	0.570651i	$0.193309\pi$
$43$			49.0760i			1.14130i	−0.821193	+	0.570651i	$0.806691\pi$
$44$			26.2986i			0.597695i
$45$		0			0
$46$	0.0510267			0.00110928
$47$	−58.2461			−1.23928			−0.619639	−	0.784887i	$-0.712721\pi$
$47$	−58.2461			−1.23928			−0.619639	+	0.784887i	$0.712721\pi$
$48$	3.34452	+	11.5245i	0.0696775	+	0.240094i
$49$	−7.00000			−0.142857
$50$		0			0
$51$	−18.1725	−	62.6186i	−0.356324	−	1.22782i
$52$			13.1986i			0.253819i
$53$	−93.5713			−1.76550			−0.882748	−	0.469847i	$-0.844309\pi$
$53$	−93.5713			−1.76550			−0.882748	+	0.469847i	$0.844309\pi$
$54$	28.6199	+	25.2765i	0.529998	+	0.468084i
$55$		0			0
$56$			7.48331i			0.133631i
$57$	4.47004	+	15.4028i	0.0784217	+	0.270225i
$58$		−	0.105820i		−	0.00182448i
$59$			49.6848i			0.842114i	0.907034	+	0.421057i	$0.138341\pi$
$59$			49.6848i			0.842114i	−0.907034	+	0.421057i	$0.861659\pi$
$60$		0			0
$61$	−43.0443			−0.705644			−0.352822	−	0.935690i	$-0.614778\pi$
$61$	−43.0443			−0.705644			−0.352822	+	0.935690i	$0.614778\pi$
$62$	−52.0518			−0.839545
$63$	12.7472	+	20.1124i	0.202337	+	0.319245i
$64$	8.00000			0.125000
$65$		0			0
$66$	53.5771	−	15.5486i	0.811775	−	0.235585i
$67$			68.3846i			1.02067i	0.859977	+	0.510333i	$0.170478\pi$
$67$			68.3846i			1.02067i	−0.859977	+	0.510333i	$0.829522\pi$
$68$	−43.4682			−0.639238
$69$	−0.0301687	−	0.103955i	−0.000437227	−	0.00150659i
$70$		0			0
$71$		−	87.2076i		−	1.22828i	−0.789199	−	0.614138i	$-0.789504\pi$
$71$		−	87.2076i		−	1.22828i	0.789199	−	0.614138i	$-0.210496\pi$
$72$	21.5011	−	13.6273i	0.298626	−	0.189269i
$73$			1.12498i			0.0154107i	0.999970	+	0.00770536i	$0.00245272\pi$
$73$			1.12498i			0.0154107i	−0.999970	+	0.00770536i	$0.997547\pi$
$74$			101.427i			1.37064i
$75$		0			0
$76$	10.6922			0.140687
$77$	34.7897			0.451815
$78$	26.8890	−	7.80343i	0.344730	−	0.100044i
$79$	−70.2593			−0.889358			−0.444679	−	0.895690i	$-0.646682\pi$
$79$	−70.2593			−0.889358			−0.444679	+	0.895690i	$0.646682\pi$
$80$		0			0
$81$	34.5740	−	73.2505i	0.426839	−	0.904328i
$82$		−	4.59830i		−	0.0560769i
$83$	0.397403			0.00478799			0.00239399	−	0.999997i	$-0.499238\pi$
$83$	0.397403			0.00478799			0.00239399	+	0.999997i	$0.499238\pi$
$84$	15.2455	−	4.42438i	0.181494	−	0.0526712i
$85$		0			0
$86$		−	69.4039i		−	0.807022i
$87$	−0.215582	+	0.0625640i	−0.00247796	+	0.000719127i
$88$		−	37.1918i		−	0.422634i
$89$			1.85426i			0.0208344i	0.999946	+	0.0104172i	$0.00331595\pi$
$89$			1.85426i			0.0208344i	−0.999946	+	0.0104172i	$0.996684\pi$
$90$		0			0
$91$	17.4601			0.191869
$92$	−0.0721626			−0.000784376
$93$	30.7747	+	106.043i	0.330911	+	1.14025i
$94$	82.3724			0.876302
$95$		0			0
$96$	−4.72986	−	16.2981i	−0.0492694	−	0.169772i
$97$		−	34.4355i		−	0.355005i	−0.984120	−	0.177502i	$-0.943198\pi$
$97$		−	34.4355i		−	0.355005i	0.984120	−	0.177502i	$-0.0568018\pi$
$98$	9.89949			0.101015
$99$	−63.3531	−	99.9579i	−0.639930	−	1.00968i
$100$		0			0
$101$		−	133.144i		−	1.31826i	−0.752030	−	0.659129i	$-0.770925\pi$
$101$		−	133.144i		−	1.31826i	0.752030	−	0.659129i	$-0.229075\pi$
$102$	25.6998	+	88.5561i	0.251959	+	0.868197i
$103$		−	150.759i		−	1.46368i	−0.681477	−	0.731840i	$-0.738662\pi$
$103$		−	150.759i		−	1.46368i	0.681477	−	0.731840i	$-0.261338\pi$
$104$		−	18.6656i		−	0.179477i
$105$		0			0
$106$	132.330			1.24839
$107$	13.4570			0.125766			0.0628831	−	0.998021i	$-0.479970\pi$
$107$	13.4570			0.125766			0.0628831	+	0.998021i	$0.479970\pi$
$108$	−40.4746	−	35.7464i	−0.374765	−	0.330985i
$109$	24.2335			0.222325			0.111163	−	0.993802i	$-0.464543\pi$
$109$	24.2335			0.222325			0.111163	+	0.993802i	$0.464543\pi$
$110$		0			0
$111$	206.634	−	59.9672i	1.86157	−	0.540245i
$112$		−	10.5830i		−	0.0944911i
$113$	−165.249			−1.46238			−0.731190	−	0.682174i	$-0.761035\pi$
$113$	−165.249			−1.46238			−0.731190	+	0.682174i	$0.761035\pi$
$114$	−6.32159	−	21.7829i	−0.0554525	−	0.191078i
$115$		0			0
$116$			0.149652i			0.00129010i
$117$	−31.7953	−	50.1663i	−0.271755	−	0.428772i
$118$		−	70.2649i		−	0.595465i
$119$			57.5030i			0.483218i
$120$		0			0
$121$	−51.9037			−0.428956
$122$	60.8738			0.498966
$123$	−9.36796	+	2.71867i	−0.0761623	+	0.0221030i
$124$	73.6124			0.593648
$125$		0			0
$126$	−18.0273	−	28.4432i	−0.143074	−	0.225740i
$127$		−	170.551i		−	1.34292i	−0.741041	−	0.671460i	$-0.765668\pi$
$127$		−	170.551i		−	1.34292i	0.741041	−	0.671460i	$-0.234332\pi$
$128$	−11.3137			−0.0883883
$129$	−141.394	+	41.0339i	−1.09608	+	0.318092i
$130$		0			0
$131$			100.138i			0.764410i	0.924078	+	0.382205i	$0.124835\pi$
$131$			100.138i			0.764410i	−0.924078	+	0.382205i	$0.875165\pi$
$132$	−75.7695	+	21.9890i	−0.574011	+	0.166583i
$133$		−	14.1445i		−	0.106349i
$134$		−	96.7105i		−	0.721720i
$135$		0			0
$136$	61.4733			0.452009
$137$	5.58180			0.0407430			0.0203715	−	0.999792i	$-0.493515\pi$
$137$	5.58180			0.0407430			0.0203715	+	0.999792i	$0.493515\pi$
$138$	0.0426649	+	0.147014i	0.000309166	+	0.00106532i
$139$	51.2753			0.368887			0.184443	−	0.982843i	$-0.440952\pi$
$139$	51.2753			0.368887			0.184443	+	0.982843i	$0.440952\pi$
$140$		0			0
$141$	−48.7013	−	167.814i	−0.345399	−	1.19017i
$142$			123.330i			0.868522i
$143$	−86.7759			−0.606824
$144$	−30.4071	+	19.2720i	−0.211160	+	0.133833i
$145$		0			0
$146$		−	1.59097i		−	0.0108970i
$147$	−5.85291	−	20.1679i	−0.0398157	−	0.137196i
$148$		−	143.440i		−	0.969189i
$149$			39.8906i			0.267722i	0.991000	+	0.133861i	$0.0427376\pi$
$149$			39.8906i			0.267722i	−0.991000	+	0.133861i	$0.957262\pi$
$150$		0			0
$151$	−265.474			−1.75811			−0.879053	−	0.476725i	$-0.841824\pi$
$151$	−265.474			−1.75811			−0.879053	+	0.476725i	$0.841824\pi$
$152$	−15.1211			−0.0994808
$153$	165.218	−	104.715i	1.07985	−	0.684409i
$154$	−49.2001			−0.319481
$155$		0			0
$156$	−38.0268	+	11.0357i	−0.243761	+	0.0707418i
$157$			49.9312i			0.318033i	0.987276	+	0.159017i	$0.0508323\pi$
$157$			49.9312i			0.318033i	−0.987276	+	0.159017i	$0.949168\pi$
$158$	99.3616			0.628871
$159$	−78.2377	−	269.591i	−0.492061	−	1.69554i
$160$		0			0
$161$			0.0954622i			0.000592933i
$162$	−48.8950	+	103.592i	−0.301821	+	0.639456i
$163$		−	118.716i		−	0.728318i	−0.931337	−	0.364159i	$-0.881356\pi$
$163$		−	118.716i		−	0.728318i	0.931337	−	0.364159i	$-0.118644\pi$
$164$			6.50298i			0.0396523i
$165$		0			0
$166$	−0.562013			−0.00338562
$167$	−97.0138			−0.580921			−0.290461	−	0.956887i	$-0.593808\pi$
$167$	−97.0138			−0.580921			−0.290461	+	0.956887i	$0.593808\pi$
$168$	−21.5604	+	6.25702i	−0.128336	+	0.0372442i
$169$	125.449			0.742304
$170$		0			0
$171$	−40.6399	+	25.7575i	−0.237660	+	0.150629i
$172$			98.1519i			0.570651i
$173$	−323.468			−1.86976			−0.934879	−	0.354967i	$-0.884492\pi$
$173$	−323.468			−1.86976			−0.934879	+	0.354967i	$0.884492\pi$
$174$	0.304880	−	0.0884789i	0.00175218	−	0.000508500i
$175$		0			0
$176$			52.5971i			0.298847i
$177$	−143.148	+	41.5429i	−0.808746	+	0.234706i
$178$		−	2.62232i		−	0.0147321i
$179$			205.429i			1.14765i	0.818978	+	0.573825i	$0.194541\pi$
$179$			205.429i			1.14765i	−0.818978	+	0.573825i	$0.805459\pi$
$180$		0			0
$181$	−130.267			−0.719709			−0.359854	−	0.933009i	$-0.617174\pi$
$181$	−130.267			−0.719709			−0.359854	+	0.933009i	$0.617174\pi$
$182$	−24.6923			−0.135672
$183$	−35.9906	−	124.016i	−0.196670	−	0.677683i
$184$	0.102053			0.000554638
$185$		0			0
$186$	−43.5220	−	149.968i	−0.233990	−	0.806278i
$187$		−	285.788i		−	1.52828i
$188$	−116.492			−0.619639
$189$	−47.2881	+	53.5429i	−0.250201	+	0.283296i
$190$		0			0
$191$		−	74.1925i		−	0.388442i	−0.980958	−	0.194221i	$-0.937782\pi$
$191$		−	74.1925i		−	0.388442i	0.980958	−	0.194221i	$-0.0622180\pi$
$192$	6.68904	+	23.0490i	0.0348387	+	0.120047i
$193$			350.612i			1.81664i	0.418273	+	0.908321i	$0.362636\pi$
$193$			350.612i			1.81664i	−0.418273	+	0.908321i	$0.637364\pi$
$194$			48.6991i			0.251026i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	265.258			1.34649			0.673244	−	0.739420i	$-0.264900\pi$
$197$	265.258			1.34649			0.673244	+	0.739420i	$0.264900\pi$
$198$	89.5948	+	141.362i	0.452499	+	0.713948i
$199$	−190.615			−0.957865			−0.478933	−	0.877852i	$-0.658976\pi$
$199$	−190.615			−0.957865			−0.478933	+	0.877852i	$0.658976\pi$
$200$		0			0
$201$	−197.025	+	57.1784i	−0.980223	+	0.284470i
$202$			188.294i			0.932149i
$203$	0.197970			0.000975224
$204$	−36.3450	−	125.237i	−0.178162	−	0.613908i
$205$		0			0
$206$			213.205i			1.03498i
$207$	0.274282	−	0.173839i	0.00132503	−	0.000839804i
$208$			26.3971i			0.126909i
$209$			70.2975i			0.336352i
$210$		0			0
$211$	66.1196			0.313363			0.156682	−	0.987649i	$-0.449920\pi$
$211$	66.1196			0.313363			0.156682	+	0.987649i	$0.449920\pi$
$212$	−187.143			−0.882748
$213$	251.256	−	72.9168i	1.17961	−	0.342333i
$214$	−19.0311			−0.0889301
$215$		0			0
$216$	57.2397	+	50.5531i	0.264999	+	0.234042i
$217$		−	97.3800i		−	0.448756i
$218$	−34.2713			−0.157208
$219$	−3.24122	+	0.940632i	−0.0148001	+	0.00429512i
$220$		0			0
$221$		−	143.429i		−	0.649002i
$222$	−292.225	+	84.8065i	−1.31633	+	0.382011i
$223$		−	35.9671i		−	0.161288i	−0.996743	−	0.0806438i	$-0.974302\pi$
$223$		−	35.9671i		−	0.161288i	0.996743	−	0.0806438i	$-0.0256976\pi$
$224$			14.9666i			0.0668153i
$225$		0			0
$226$	233.697			1.03406
$227$	429.252			1.89098			0.945489	−	0.325653i	$-0.105584\pi$
$227$	429.252			1.89098			0.945489	+	0.325653i	$0.105584\pi$
$228$	8.94008	+	30.8056i	0.0392109	+	0.135112i
$229$	157.761			0.688914			0.344457	−	0.938802i	$-0.388063\pi$
$229$	157.761			0.688914			0.344457	+	0.938802i	$0.388063\pi$
$230$		0			0
$231$	29.0887	+	100.234i	0.125925	+	0.433912i
$232$		−	0.211639i		−	0.000912238i
$233$	365.653			1.56932			0.784662	−	0.619924i	$-0.212836\pi$
$233$	365.653			1.56932			0.784662	+	0.619924i	$0.212836\pi$
$234$	44.9653	+	70.9458i	0.192160	+	0.303187i
$235$		0			0
$236$			99.3695i			0.421057i
$237$	−58.7459	−	202.426i	−0.247873	−	0.854118i
$238$		−	81.3215i		−	0.341687i
$239$		−	208.754i		−	0.873447i	−0.899596	−	0.436723i	$-0.856139\pi$
$239$		−	208.754i		−	0.873447i	0.899596	−	0.436723i	$-0.143861\pi$
$240$		0			0
$241$	−136.568			−0.566671			−0.283335	−	0.959021i	$-0.591441\pi$
$241$	−136.568			−0.566671			−0.283335	+	0.959021i	$0.591441\pi$
$242$	73.4029			0.303318
$243$	239.952	+	38.3650i	0.987458	+	0.157881i
$244$	−86.0886			−0.352822
$245$		0			0
$246$	13.2483	−	3.84478i	0.0538549	−	0.0156292i
$247$			35.2805i			0.142836i
$248$	−104.104			−0.419773
$249$	0.332280	+	1.14497i	0.00133446	+	0.00459827i
$250$		0			0
$251$			492.617i			1.96262i	0.192442	+	0.981308i	$0.438359\pi$
$251$			492.617i			1.96262i	−0.192442	+	0.981308i	$0.561641\pi$
$252$	25.4944	+	40.2248i	0.101168	+	0.159622i
$253$		−	0.474443i		−	0.00187527i
$254$			241.195i			0.949588i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−500.659			−1.94809			−0.974045	−	0.226353i	$-0.927320\pi$
$257$	−500.659			−1.94809			−0.974045	+	0.226353i	$0.927320\pi$
$258$	199.961	−	58.0307i	0.775044	−	0.224925i
$259$	−189.753			−0.732638
$260$		0			0
$261$	−0.360510	−	0.568809i	−0.00138126	−	0.00217934i
$262$		−	141.616i		−	0.540519i
$263$	−10.3435			−0.0393288			−0.0196644	−	0.999807i	$-0.506260\pi$
$263$	−10.3435			−0.0393288			−0.0196644	+	0.999807i	$0.506260\pi$
$264$	107.154	−	31.0972i	0.405887	−	0.117792i
$265$		0			0
$266$			20.0033i			0.0752004i
$267$	−5.34236	+	1.55040i	−0.0200088	+	0.00580675i
$268$			136.769i			0.510333i
$269$		−	61.7933i		−	0.229715i	−0.993382	−	0.114857i	$-0.963359\pi$
$269$		−	61.7933i		−	0.229715i	0.993382	−	0.114857i	$-0.0366411\pi$
$270$		0			0
$271$	−318.697			−1.17600			−0.588002	−	0.808860i	$-0.700085\pi$
$271$	−318.697			−1.17600			−0.588002	+	0.808860i	$0.700085\pi$
$272$	−86.9364			−0.319619
$273$	14.5989	+	50.3047i	0.0534758	+	0.184266i
$274$	−7.89385			−0.0288097
$275$		0			0
$276$	−0.0603373	−	0.207910i	−0.000218613	−	0.000753296i
$277$			92.2140i			0.332903i	0.986050	+	0.166451i	$0.0532309\pi$
$277$			92.2140i			0.332903i	−0.986050	+	0.166451i	$0.946769\pi$
$278$	−72.5142			−0.260842
$279$	−279.792	+	177.332i	−1.00284	+	0.635598i
$280$		0			0
$281$			301.330i			1.07235i	0.844108	+	0.536174i	$0.180131\pi$
$281$			301.330i			1.07235i	−0.844108	+	0.536174i	$0.819869\pi$
$282$	68.8740	+	237.325i	0.244234	+	0.841579i
$283$		−	338.612i		−	1.19651i	−0.801307	−	0.598254i	$-0.795862\pi$
$283$		−	338.612i		−	1.19651i	0.801307	−	0.598254i	$-0.204138\pi$
$284$		−	174.415i		−	0.614138i
$285$		0			0
$286$	122.720			0.429090
$287$	8.60264			0.0299744
$288$	43.0021	−	27.2547i	0.149313	−	0.0946343i
$289$	183.371			0.634500
$290$		0			0
$291$	99.2130	−	28.7925i	0.340938	−	0.0989434i
$292$			2.24997i			0.00770536i
$293$	−129.520			−0.442046			−0.221023	−	0.975269i	$-0.570940\pi$
$293$	−129.520			−0.442046			−0.221023	+	0.975269i	$0.570940\pi$
$294$	8.27726	+	28.5217i	0.0281539	+	0.0970126i
$295$		0			0
$296$			202.855i			0.685320i
$297$	235.020	−	266.106i	0.791313	−	0.895980i
$298$		−	56.4139i		−	0.189308i
$299$		−	0.238111i		−	0.000796358i
$300$		0			0
$301$	129.843			0.431371
$302$	375.437			1.24317
$303$	383.605	−	111.326i	1.26602	−	0.367411i
$304$	21.3844			0.0703435
$305$		0			0
$306$	−233.653	+	148.089i	−0.763572	+	0.483950i
$307$		−	407.440i		−	1.32717i	−0.748102	−	0.663584i	$-0.769035\pi$
$307$		−	407.440i		−	1.32717i	0.748102	−	0.663584i	$-0.230965\pi$
$308$	69.5795			0.225907
$309$	434.356	−	126.054i	1.40568	−	0.407942i
$310$		0			0
$311$			2.87311i			0.00923831i	0.999989	+	0.00461915i	$0.00147033\pi$
$311$			2.87311i			0.00923831i	−0.999989	+	0.00461915i	$0.998530\pi$
$312$	53.7779	−	15.6069i	0.172365	−	0.0500220i
$313$			620.686i			1.98302i	0.130026	+	0.991511i	$0.458494\pi$
$313$			620.686i			1.98302i	−0.130026	+	0.991511i	$0.541506\pi$
$314$		−	70.6134i		−	0.224883i
$315$		0			0
$316$	−140.519			−0.444679
$317$	372.444			1.17490			0.587452	−	0.809259i	$-0.300131\pi$
$317$	372.444			1.17490			0.587452	+	0.809259i	$0.300131\pi$
$318$	110.645	+	381.259i	0.347940	+	1.19893i
$319$	−0.983905			−0.00308434
$320$		0			0
$321$	11.2518	+	38.7713i	0.0350523	+	0.120783i
$322$		−	0.135004i		−	0.000419267i
$323$	−116.193			−0.359730
$324$	69.1479	−	146.501i	0.213419	−	0.452164i
$325$		0			0
$326$			167.890i			0.514999i
$327$	20.2623	+	69.8197i	0.0619643	+	0.213516i
$328$		−	9.19661i		−	0.0280384i
$329$			154.105i			0.468403i
$330$		0			0
$331$	−220.489			−0.666131			−0.333066	−	0.942904i	$-0.608083\pi$
$331$	−220.489			−0.666131			−0.333066	+	0.942904i	$0.608083\pi$
$332$	0.794806			0.00239399
$333$	345.546	+	545.199i	1.03768	+	1.63724i
$334$	137.198			0.410773
$335$		0			0
$336$	30.4910	−	8.84876i	0.0907469	−	0.0263356i
$337$			127.041i			0.376975i	0.982076	+	0.188487i	$0.0603585\pi$
$337$			127.041i			0.376975i	−0.982076	+	0.188487i	$0.939642\pi$
$338$	−177.412			−0.524888
$339$	−138.170	−	476.103i	−0.407580	−	1.40443i
$340$		0			0
$341$			483.975i			1.41928i
$342$	57.4735	−	36.4266i	0.168051	−	0.106511i
$343$			18.5203i			0.0539949i
$344$		−	138.808i		−	0.403511i
$345$		0			0
$346$	457.453			1.32212
$347$	668.267			1.92584			0.962921	−	0.269782i	$-0.0869517\pi$
$347$	668.267			1.92584			0.962921	+	0.269782i	$0.0869517\pi$
$348$	−0.431165	+	0.125128i	−0.00123898	+	0.000359563i
$349$	154.424			0.442474			0.221237	−	0.975220i	$-0.428991\pi$
$349$	154.424			0.442474			0.221237	+	0.975220i	$0.428991\pi$
$350$		0			0
$351$	117.950	−	133.552i	0.336041	−	0.380489i
$352$		−	74.3836i		−	0.211317i
$353$	−417.578			−1.18294			−0.591470	−	0.806327i	$-0.701452\pi$
$353$	−417.578			−1.18294			−0.591470	+	0.806327i	$0.701452\pi$
$354$	202.442	−	58.7505i	0.571870	−	0.165962i
$355$		0			0
$356$			3.70852i			0.0104172i
$357$	−165.673	+	48.0800i	−0.464071	+	0.134678i
$358$		−	290.521i		−	0.811511i
$359$			585.625i			1.63127i	0.578568	+	0.815634i	$0.303612\pi$
$359$			585.625i			1.63127i	−0.578568	+	0.815634i	$0.696388\pi$
$360$		0			0
$361$	−332.419			−0.920829
$362$	184.226			0.508911
$363$	−43.3982	−	149.541i	−0.119554	−	0.411959i
$364$	34.9201			0.0959345
$365$		0			0
$366$	50.8984	+	175.385i	0.139067	+	0.479194i
$367$			404.551i			1.10232i	0.834400	+	0.551159i	$0.185814\pi$
$367$			404.551i			1.10232i	−0.834400	+	0.551159i	$0.814186\pi$
$368$	−0.144325			−0.000392188
$369$	−15.6657	−	24.7171i	−0.0424543	−	0.0669840i
$370$		0			0
$371$			247.566i			0.667295i
$372$	61.5495	+	212.086i	0.165456	+	0.570125i
$373$			234.337i			0.628251i	0.949382	+	0.314125i	$0.101711\pi$
$373$			234.337i			0.628251i	−0.949382	+	0.314125i	$0.898289\pi$
$374$			404.165i			1.08065i
$375$		0			0
$376$	164.745			0.438151
$377$	−0.493797			−0.00130981
$378$	66.8754	−	75.7211i	0.176919	−	0.200320i
$379$	169.108			0.446196			0.223098	−	0.974796i	$-0.428383\pi$
$379$	169.108			0.446196			0.223098	+	0.974796i	$0.428383\pi$
$380$		0			0
$381$	491.378	−	142.603i	1.28971	−	0.374285i
$382$			104.924i			0.274670i
$383$	388.986			1.01563			0.507814	−	0.861467i	$-0.330454\pi$
$383$	388.986			1.01563			0.507814	+	0.861467i	$0.330454\pi$
$384$	−9.45973	−	32.5962i	−0.0246347	−	0.0848860i
$385$		0			0
$386$		−	495.840i		−	1.28456i
$387$	−236.447	−	373.064i	−0.610975	−	0.963991i
$388$		−	68.8710i		−	0.177502i
$389$		−	289.809i		−	0.745010i	−0.928030	−	0.372505i	$-0.878499\pi$
$389$		−	289.809i		−	0.745010i	0.928030	−	0.372505i	$-0.121501\pi$
$390$		0			0
$391$	0.784194			0.00200561
$392$	19.7990			0.0505076
$393$	−288.509	+	83.7281i	−0.734120	+	0.213049i
$394$	−375.132			−0.952111
$395$		0			0
$396$	−126.706	−	199.916i	−0.319965	−	0.504838i
$397$			603.647i			1.52052i	0.649618	+	0.760260i	$0.274929\pi$
$397$			603.647i			1.52052i	−0.649618	+	0.760260i	$0.725071\pi$
$398$	269.571			0.677313
$399$	40.7520	−	11.8266i	0.102135	−	0.0296406i
$400$		0			0
$401$			331.427i			0.826500i	0.910618	+	0.413250i	$0.135606\pi$
$401$			331.427i			0.826500i	−0.910618	+	0.413250i	$0.864394\pi$
$402$	278.635	−	80.8625i	0.693122	−	0.201150i
$403$			242.895i			0.602716i
$404$		−	266.288i		−	0.659129i
$405$		0			0
$406$	−0.279972			−0.000689587
$407$	943.067			2.31712
$408$	51.3996	+	177.112i	0.125979	+	0.434099i
$409$	−254.348			−0.621877			−0.310939	−	0.950430i	$-0.600643\pi$
$409$	−254.348			−0.621877			−0.310939	+	0.950430i	$0.600643\pi$
$410$		0			0
$411$	4.66711	+	16.0819i	0.0113555	+	0.0391286i
$412$		−	301.518i		−	0.731840i
$413$	131.454			0.318289
$414$	−0.387893	+	0.245846i	−0.000936940	+	0.000593831i
$415$		0			0
$416$		−	37.3312i		−	0.0897385i
$417$	42.8728	+	147.730i	0.102812	+	0.354270i
$418$		−	99.4157i		−	0.237836i
$419$		−	460.686i		−	1.09949i	−0.835333	−	0.549745i	$-0.814725\pi$
$419$		−	460.686i		−	1.09949i	0.835333	−	0.549745i	$-0.185275\pi$
$420$		0			0
$421$	504.134			1.19747			0.598734	−	0.800948i	$-0.295671\pi$
$421$	504.134			1.19747			0.598734	+	0.800948i	$0.295671\pi$
$422$	−93.5072			−0.221581
$423$	442.773	−	280.629i	1.04675	−	0.663425i
$424$	264.660			0.624197
$425$		0			0
$426$	−355.330	+	103.120i	−0.834107	+	0.242066i
$427$			113.884i			0.266708i
$428$	26.9140			0.0628831
$429$	−72.5559	−	250.012i	−0.169128	−	0.582779i
$430$		0			0
$431$			112.652i			0.261373i	0.991424	+	0.130687i	$0.0417182\pi$
$431$			112.652i			0.261373i	−0.991424	+	0.130687i	$0.958282\pi$
$432$	−80.9492	−	71.4928i	−0.187382	−	0.165493i
$433$			653.844i			1.51003i	0.655707	+	0.755016i	$0.272371\pi$
$433$			653.844i			1.51003i	−0.655707	+	0.755016i	$0.727629\pi$
$434$			137.716i			0.317318i
$435$		0			0
$436$	48.4669			0.111163
$437$	−0.192895			−0.000441406
$438$	4.58377	−	1.33025i	0.0104652	−	0.00303711i
$439$	224.009			0.510271			0.255136	−	0.966905i	$-0.417880\pi$
$439$	224.009			0.510271			0.255136	+	0.966905i	$0.417880\pi$
$440$		0			0
$441$	53.2124	−	33.7259i	0.120663	−	0.0764760i
$442$			202.840i			0.458914i
$443$	−446.483			−1.00786			−0.503931	−	0.863744i	$-0.668113\pi$
$443$	−446.483			−1.00786			−0.503931	+	0.863744i	$0.668113\pi$
$444$	413.269	−	119.934i	0.930785	−	0.270123i
$445$		0			0
$446$			50.8652i			0.114048i
$447$	−114.930	+	33.3537i	−0.257114	+	0.0746169i
$448$		−	21.1660i		−	0.0472456i
$449$		−	320.507i		−	0.713823i	−0.934138	−	0.356912i	$-0.883830\pi$
$449$		−	320.507i		−	0.713823i	0.934138	−	0.356912i	$-0.116170\pi$
$450$		0			0
$451$	−42.7548			−0.0948000
$452$	−330.498			−0.731190
$453$	−221.971	−	764.864i	−0.490001	−	1.68844i
$454$	−607.054			−1.33712
$455$		0			0
$456$	−12.6432	−	43.5657i	−0.0277263	−	0.0955389i
$457$			490.633i			1.07360i	0.843711	+	0.536798i	$0.180366\pi$
$457$			490.633i			1.07360i	−0.843711	+	0.536798i	$0.819634\pi$
$458$	−223.108			−0.487136
$459$	439.839	+	388.458i	0.958256	+	0.846313i
$460$		0			0
$461$			746.588i			1.61950i	0.586778	+	0.809748i	$0.300396\pi$
$461$			746.588i			1.61950i	−0.586778	+	0.809748i	$0.699604\pi$
$462$	−41.1377	−	141.752i	−0.0890426	−	0.306822i
$463$		−	20.3890i		−	0.0440366i	−0.999758	−	0.0220183i	$-0.992991\pi$
$463$		−	20.3890i		−	0.0440366i	0.999758	−	0.0220183i	$-0.00700921\pi$
$464$			0.299303i			0.000645050i
$465$		0			0
$466$	−517.111			−1.10968
$467$	−506.079			−1.08368			−0.541840	−	0.840482i	$-0.682272\pi$
$467$	−506.079			−1.08368			−0.541840	+	0.840482i	$0.682272\pi$
$468$	−63.5906	−	100.333i	−0.135877	−	0.214386i
$469$	180.929			0.385776
$470$		0			0
$471$	−143.858	+	41.7490i	−0.305431	+	0.0886390i
$472$		−	140.530i		−	0.297732i
$473$	−645.314			−1.36430
$474$	83.0792	+	286.273i	0.175273	+	0.603952i
$475$		0			0
$476$			115.006i			0.241609i
$477$	711.308	−	450.826i	1.49121	−	0.945127i
$478$			295.222i			0.617620i
$479$		−	604.281i		−	1.26155i	−0.775967	−	0.630774i	$-0.782738\pi$
$479$		−	604.281i		−	1.26155i	0.775967	−	0.630774i	$-0.217262\pi$
$480$		0			0
$481$	473.301			0.983993
$482$	193.136			0.400697
$483$	−0.275039	+	0.0798188i	−0.000569438	+	0.000165256i
$484$	−103.807			−0.214478
$485$		0			0
$486$	−339.344	−	54.2563i	−0.698238	−	0.111638i
$487$			717.441i			1.47319i	0.676337	+	0.736593i	$0.263566\pi$
$487$			717.441i			1.47319i	−0.676337	+	0.736593i	$0.736434\pi$
$488$	121.748			0.249483
$489$	342.035	−	99.2619i	0.699459	−	0.202990i
$490$		0			0
$491$		−	246.844i		−	0.502737i	−0.967891	−	0.251369i	$-0.919119\pi$
$491$		−	246.844i		−	0.502737i	0.967891	−	0.251369i	$-0.0808806\pi$
$492$	−18.7359	+	5.43734i	−0.0380811	+	0.0110515i
$493$		−	1.62627i		−	0.00329872i
$494$		−	49.8942i		−	0.101000i
$495$		0			0
$496$	147.225			0.296824
$497$	−230.730			−0.464245
$498$	−0.469915	−	1.61923i	−0.000943605	−	0.00325146i
$499$	−33.1929			−0.0665188			−0.0332594	−	0.999447i	$-0.510589\pi$
$499$	−33.1929			−0.0665188			−0.0332594	+	0.999447i	$0.510589\pi$
$500$		0			0
$501$	−81.1161	−	279.509i	−0.161908	−	0.557902i
$502$		−	696.665i		−	1.38778i
$503$	153.381			0.304932			0.152466	−	0.988309i	$-0.451279\pi$
$503$	153.381			0.304932			0.152466	+	0.988309i	$0.451279\pi$
$504$	−36.0545	−	56.8865i	−0.0715368	−	0.112870i
$505$		0			0
$506$			0.670964i			0.00132602i
$507$	104.892	+	361.436i	0.206888	+	0.712891i
$508$		−	341.102i		−	0.671460i
$509$			1003.81i			1.97213i	0.166362	+	0.986065i	$0.446798\pi$
$509$			1003.81i			1.97213i	−0.166362	+	0.986065i	$0.553202\pi$
$510$		0			0
$511$	2.97643			0.00582471
$512$	−22.6274			−0.0441942
$513$	−108.191	−	95.5521i	−0.210898	−	0.186261i
$514$	708.039			1.37751
$515$		0			0
$516$	−282.788	+	82.0677i	−0.548039	+	0.159046i
$517$		−	765.894i		−	1.48142i
$518$	268.352			0.518053
$519$	−270.461	−	931.952i	−0.521120	−	1.79567i
$520$		0			0
$521$		−	760.122i		−	1.45897i	−0.683999	−	0.729483i	$-0.739761\pi$
$521$		−	760.122i		−	1.45897i	0.683999	−	0.729483i	$-0.260239\pi$
$522$	0.509838	+	0.804417i	0.000976701	+	0.00154103i
$523$			546.015i			1.04401i	0.852943	+	0.522003i	$0.174815\pi$
$523$			546.015i			1.04401i	−0.852943	+	0.522003i	$0.825185\pi$
$524$			200.275i			0.382205i
$525$		0			0
$526$	14.6279			0.0278097
$527$	−799.949			−1.51793
$528$	−151.539	+	43.9780i	−0.287006	+	0.0832917i
$529$	−528.999			−0.999998
$530$		0			0
$531$	−239.381	−	377.692i	−0.450811	−	0.711285i
$532$		−	28.2889i		−	0.0531747i
$533$	−21.4575			−0.0402580
$534$	7.55523	−	2.19260i	0.0141484	−	0.00410599i
$535$		0			0
$536$		−	193.421i		−	0.360860i
$537$	−591.868	+	171.765i	−1.10217	+	0.319861i
$538$			87.3890i			0.162433i
$539$		−	92.0450i		−	0.170770i
$540$		0			0
$541$	−939.855			−1.73725			−0.868627	−	0.495466i	$-0.834997\pi$
$541$	−939.855			−1.73725			−0.868627	+	0.495466i	$0.834997\pi$
$542$	450.705			0.831560
$543$	−108.920	−	375.316i	−0.200590	−	0.691190i
$544$	122.947			0.226005
$545$		0			0
$546$	−20.6459	−	71.1415i	−0.0378131	−	0.130296i
$547$			614.161i			1.12278i	0.827551	+	0.561390i	$0.189733\pi$
$547$			614.161i			1.12278i	−0.827551	+	0.561390i	$0.810267\pi$
$548$	11.1636			0.0203715
$549$	327.213	−	207.387i	0.596016	−	0.377754i
$550$		0			0
$551$			0.400027i			0.000726001i
$552$	0.0853298	+	0.294029i	0.000154583	+	0.000532660i
$553$			185.889i			0.336146i
$554$		−	130.410i		−	0.235398i
$555$		0			0
$556$	102.551			0.184443
$557$	39.5004			0.0709164			0.0354582	−	0.999371i	$-0.488711\pi$
$557$	39.5004			0.0709164			0.0354582	+	0.999371i	$0.488711\pi$
$558$	395.686	−	250.785i	0.709115	−	0.449436i
$559$	−323.866			−0.579367
$560$		0			0
$561$	823.390	−	238.956i	1.46772	−	0.425946i
$562$		−	426.145i		−	0.758264i
$563$	392.566			0.697276			0.348638	−	0.937257i	$-0.386644\pi$
$563$	392.566			0.697276			0.348638	+	0.937257i	$0.386644\pi$
$564$	−97.4025	−	335.628i	−0.172699	−	0.595086i
$565$		0			0
$566$			478.869i			0.846058i
$567$	−193.803	−	91.4741i	−0.341804	−	0.161330i
$568$			246.660i			0.434261i
$569$			369.392i			0.649194i	0.945852	+	0.324597i	$0.105229\pi$
$569$			369.392i			0.649194i	−0.945852	+	0.324597i	$0.894771\pi$
$570$		0			0
$571$	−106.110			−0.185831			−0.0929156	−	0.995674i	$-0.529619\pi$
$571$	−106.110			−0.185831			−0.0929156	+	0.995674i	$0.529619\pi$
$572$	−173.552			−0.303412
$573$	213.758	−	62.0346i	0.373051	−	0.108263i
$574$	−12.1660			−0.0211951
$575$		0			0
$576$	−60.8142	+	38.5439i	−0.105580	+	0.0669165i
$577$			323.982i			0.561494i	0.959782	+	0.280747i	$0.0905823\pi$
$577$			323.982i			0.561494i	−0.959782	+	0.280747i	$0.909418\pi$
$578$	−259.325			−0.448659
$579$	−1010.16	+	293.157i	−1.74466	+	0.506316i
$580$		0			0
$581$		−	1.05143i		−	0.00180969i
$582$	−140.308	+	40.7188i	−0.241080	+	0.0699635i
$583$		−	1230.40i		−	2.11046i
$584$		−	3.18193i		−	0.00544851i
$585$		0			0
$586$	183.168			0.312574
$587$	−1118.07			−1.90471			−0.952356	−	0.304987i	$-0.901348\pi$
$587$	−1118.07			−1.90471			−0.952356	+	0.304987i	$0.901348\pi$
$588$	−11.7058	−	40.3358i	−0.0199078	−	0.0685982i
$589$	196.770			0.334074
$590$		0			0
$591$	221.790	+	764.242i	0.375280	+	1.29313i
$592$		−	286.880i		−	0.484595i
$593$	594.281			1.00216			0.501080	−	0.865401i	$-0.332936\pi$
$593$	594.281			1.00216			0.501080	+	0.865401i	$0.332936\pi$
$594$	−332.368	+	376.331i	−0.559543	+	0.633554i
$595$		0			0
$596$			79.7813i			0.133861i
$597$	−159.379	−	549.186i	−0.266967	−	0.919910i
$598$			0.336740i			0.000563110i
$599$		−	277.589i		−	0.463421i	−0.972785	−	0.231710i	$-0.925568\pi$
$599$		−	277.589i		−	0.463421i	0.972785	−	0.231710i	$-0.0744322\pi$
$600$		0			0
$601$	589.923			0.981569			0.490784	−	0.871281i	$-0.336710\pi$
$601$	589.923			0.981569			0.490784	+	0.871281i	$0.336710\pi$
$602$	−183.625			−0.305026
$603$	−329.476	−	519.845i	−0.546395	−	0.862097i
$604$	−530.948			−0.879053
$605$		0			0
$606$	−542.499	+	157.438i	−0.895213	+	0.259799i
$607$		−	15.8946i		−	0.0261856i	−0.999914	−	0.0130928i	$-0.995832\pi$
$607$		−	15.8946i		−	0.0261856i	0.999914	−	0.0130928i	$-0.00416768\pi$
$608$	−30.2422			−0.0497404
$609$	0.165529	+	0.570378i	0.000271804	+	0.000936581i
$610$		0			0
$611$		−	384.382i		−	0.629104i
$612$	330.435	−	209.429i	0.539927	−	0.342205i
$613$		−	229.877i		−	0.375003i	−0.982264	−	0.187502i	$-0.939961\pi$
$613$		−	229.877i		−	0.375003i	0.982264	−	0.187502i	$-0.0600390\pi$
$614$			576.208i			0.938449i
$615$		0			0
$616$	−98.4002			−0.159741
$617$	948.107			1.53664			0.768320	−	0.640066i	$-0.221093\pi$
$617$	948.107			1.53664			0.768320	+	0.640066i	$0.221093\pi$
$618$	−614.272	+	178.267i	−0.993967	+	0.288459i
$619$	−888.371			−1.43517			−0.717585	−	0.696471i	$-0.754753\pi$
$619$	−888.371			−1.43517			−0.717585	+	0.696471i	$0.754753\pi$
$620$		0			0
$621$	0.730188	+	0.644889i	0.00117583	+	0.00103847i
$622$		−	4.06320i		−	0.00653247i
$623$	4.90591			0.00787466
$624$	−76.0535	+	22.0714i	−0.121881	+	0.0353709i
$625$		0			0
$626$		−	877.782i		−	1.40221i
$627$	−202.536	+	58.7778i	−0.323024	+	0.0937445i
$628$			99.8624i			0.159017i
$629$			1558.77i			2.47817i
$630$		0			0
$631$	0.357000			0.000565768			0.000282884	−	1.00000i	$-0.499910\pi$
$631$	0.357000			0.000565768			0.000282884		1.00000i	$0.499910\pi$
$632$	198.723			0.314436
$633$	55.2846	+	190.499i	0.0873374	+	0.300946i
$634$	−526.716			−0.830782
$635$		0			0
$636$	−156.475	−	539.181i	−0.246031	−	0.847770i
$637$		−	46.1950i		−	0.0725196i
$638$	1.39145			0.00218096
$639$	420.165	+	662.932i	0.657536	+	1.03745i
$640$		0			0
$641$			149.546i			0.233301i	0.993173	+	0.116650i	$0.0372157\pi$
$641$			149.546i			0.233301i	−0.993173	+	0.116650i	$0.962784\pi$
$642$	−15.9124	−	54.8309i	−0.0247857	−	0.0854063i
$643$		−	908.812i		−	1.41339i	−0.707517	−	0.706696i	$-0.750185\pi$
$643$		−	908.812i		−	1.41339i	0.707517	−	0.706696i	$-0.249815\pi$
$644$			0.190924i			0.000296466i
$645$		0			0
$646$	164.321			0.254367
$647$	−1149.33			−1.77640			−0.888200	−	0.459457i	$-0.848044\pi$
$647$	−1149.33			−1.77640			−0.888200	+	0.459457i	$0.848044\pi$
$648$	−97.7899	+	207.184i	−0.150910	+	0.319728i
$649$	−653.319			−1.00665
$650$		0			0
$651$	280.564	−	81.4223i	0.430974	−	0.125073i
$652$		−	237.432i		−	0.364159i
$653$	66.4470			0.101757			0.0508783	−	0.998705i	$-0.483798\pi$
$653$	66.4470			0.101757			0.0508783	+	0.998705i	$0.483798\pi$
$654$	−28.6552	−	98.7399i	−0.0438154	−	0.150978i
$655$		0			0
$656$			13.0060i			0.0198262i
$657$	−5.42016	−	8.55187i	−0.00824986	−	0.0130165i
$658$		−	217.937i		−	0.331211i
$659$			85.5834i			0.129869i	0.997890	+	0.0649343i	$0.0206838\pi$
$659$			85.5834i			0.129869i	−0.997890	+	0.0649343i	$0.979316\pi$
$660$		0			0
$661$	379.290			0.573813			0.286906	−	0.957959i	$-0.407373\pi$
$661$	379.290			0.573813			0.286906	+	0.957959i	$0.407373\pi$
$662$	311.819			0.471026
$663$	413.238	−	119.926i	0.623286	−	0.180883i
$664$	−1.12403			−0.00169281
$665$		0			0
$666$	−488.676	−	771.028i	−0.733748	−	1.15770i
$667$		−	0.00269981i		−	4.04769e-6i
$668$	−194.028			−0.290461
$669$	103.626	−	30.0732i	0.154897	−	0.0449524i
$670$		0			0
$671$		−	566.001i		−	0.843519i
$672$	−43.1207	+	12.5140i	−0.0641678	+	0.0186221i
$673$			282.112i			0.419186i	0.977789	+	0.209593i	$0.0672139\pi$
$673$			282.112i			0.419186i	−0.977789	+	0.209593i	$0.932786\pi$
$674$		−	179.662i		−	0.266562i
$675$		0			0
$676$	250.899			0.371152
$677$	−523.122			−0.772706			−0.386353	−	0.922351i	$-0.626265\pi$
$677$	−523.122			−0.772706			−0.386353	+	0.922351i	$0.626265\pi$
$678$	195.401	+	673.311i	0.288202	+	0.993085i
$679$	−91.1077			−0.134179
$680$		0			0
$681$	358.910	+	1236.73i	0.527034	+	1.81605i
$682$		−	684.444i		−	1.00358i
$683$	367.122			0.537514			0.268757	−	0.963208i	$-0.413387\pi$
$683$	367.122			0.537514			0.268757	+	0.963208i	$0.413387\pi$
$684$	−81.2798	+	51.5150i	−0.118830	+	0.0753143i
$685$		0			0
$686$		−	26.1916i		−	0.0381802i
$687$	131.909	+	454.530i	0.192007	+	0.661616i
$688$			196.304i			0.285325i
$689$		−	617.504i		−	0.896232i
$690$		0			0
$691$	−1053.75			−1.52496			−0.762481	−	0.647011i	$-0.776019\pi$
$691$	−1053.75			−1.52496			−0.762481	+	0.647011i	$0.776019\pi$
$692$	−646.936			−0.934879
$693$	−264.464	+	167.617i	−0.381622	+	0.241871i
$694$	−945.073			−1.36178
$695$		0			0
$696$	0.609759	−	0.176958i	0.000876091	−	0.000254250i
$697$		−	70.6682i		−	0.101389i
$698$	−218.388			−0.312877
$699$	305.733	+	1053.49i	0.437386	+	1.50714i
$700$		0			0
$701$		−	671.905i		−	0.958495i	−0.877680	−	0.479248i	$-0.840910\pi$
$701$		−	671.905i		−	0.958495i	0.877680	−	0.479248i	$-0.159090\pi$
$702$	−166.807	+	188.871i	−0.237617	+	0.269047i
$703$		−	383.423i		−	0.545409i
$704$			105.194i			0.149424i
$705$		0			0
$706$	590.544			0.836464
$707$	−352.266			−0.498254
$708$	−286.296	+	83.0858i	−0.404373	+	0.117353i
$709$	1008.50			1.42243			0.711214	−	0.702976i	$-0.248146\pi$
$709$	1008.50			1.42243			0.711214	+	0.702976i	$0.248146\pi$
$710$		0			0
$711$	534.095	−	338.509i	0.751189	−	0.476102i
$712$		−	5.24464i		−	0.00736607i
$713$	−1.32802			−0.00186257
$714$	234.298	−	67.9953i	0.328148	−	0.0952315i
$715$		0			0
$716$			410.858i			0.573825i
$717$	601.446	−	174.545i	0.838837	−	0.243438i
$718$		−	828.200i		−	1.15348i
$719$			718.569i			0.999401i	0.866198	+	0.499701i	$0.166557\pi$
$719$			718.569i			0.999401i	−0.866198	+	0.499701i	$0.833443\pi$
$720$		0			0
$721$	−398.871			−0.553219
$722$	470.112			0.651124
$723$	−114.188	−	393.469i	−0.157937	−	0.544217i
$724$	−260.534			−0.359854
$725$		0			0
$726$	61.3743	+	211.483i	0.0845376	+	0.291299i
$727$			830.204i			1.14196i	0.820964	+	0.570979i	$0.193436\pi$
$727$			830.204i			1.14196i	−0.820964	+	0.570979i	$0.806564\pi$
$728$	−49.3845			−0.0678359
$729$	90.0970	+	723.411i	0.123590	+	0.992333i
$730$		0			0
$731$		−	1066.62i		−	1.45913i
$732$	−71.9812	−	248.032i	−0.0983350	−	0.338842i
$733$			922.108i			1.25799i	0.777408	+	0.628996i	$0.216534\pi$
$733$			922.108i			1.25799i	−0.777408	+	0.628996i	$0.783466\pi$
$734$		−	572.122i		−	0.779457i
$735$		0			0
$736$	0.204107			0.000277319
$737$	−899.209			−1.22009
$738$	22.1546	+	34.9553i	0.0300198	+	0.0473649i
$739$	676.120			0.914913			0.457456	−	0.889232i	$-0.348761\pi$
$739$	676.120			0.914913			0.457456	+	0.889232i	$0.348761\pi$
$740$		0			0
$741$	−101.648	+	29.4991i	−0.137176	+	0.0398098i
$742$		−	350.112i		−	0.471849i
$743$	−745.720			−1.00366			−0.501831	−	0.864966i	$-0.667340\pi$
$743$	−745.720			−1.00366			−0.501831	+	0.864966i	$0.667340\pi$
$744$	−87.0441	−	299.936i	−0.116995	−	0.403139i
$745$		0			0
$746$		−	331.403i		−	0.444240i
$747$	−3.02097	+	1.91468i	−0.00404413	+	0.00256316i
$748$		−	571.575i		−	0.764138i
$749$		−	35.6038i		−	0.0475352i
$750$		0			0
$751$	−440.356			−0.586360			−0.293180	−	0.956057i	$-0.594714\pi$
$751$	−440.356			−0.586360			−0.293180	+	0.956057i	$0.594714\pi$
$752$	−232.984			−0.309819
$753$	−1419.29	+	411.891i	−1.88485	+	0.547001i
$754$	0.698334			0.000926172
$755$		0			0
$756$	−94.5761	+	107.086i	−0.125101	+	0.141648i
$757$			664.394i			0.877667i	0.898568	+	0.438833i	$0.144608\pi$
$757$			664.394i			0.877667i	−0.898568	+	0.438833i	$0.855392\pi$
$758$	−239.155			−0.315509
$759$	1.36693	−	0.396696i	0.00180096	−	0.000522656i
$760$		0			0
$761$		−	997.255i		−	1.31045i	−0.755432	−	0.655227i	$-0.772573\pi$
$761$		−	997.255i		−	1.31045i	0.755432	−	0.655227i	$-0.227427\pi$
$762$	−694.914	+	201.670i	−0.911961	+	0.264659i
$763$		−	64.1157i		−	0.0840311i
$764$		−	148.385i		−	0.194221i
$765$		0			0
$766$	−550.109			−0.718158
$767$	−327.884			−0.427489
$768$	13.3781	+	46.0980i	0.0174194	+	0.0600235i
$769$	772.797			1.00494			0.502469	−	0.864595i	$-0.332425\pi$
$769$	772.797			1.00494			0.502469	+	0.864595i	$0.332425\pi$
$770$		0			0
$771$	−418.616	−	1442.46i	−0.542952	−	1.87090i
$772$			701.224i			0.908321i
$773$	−396.911			−0.513468			−0.256734	−	0.966482i	$-0.582646\pi$
$773$	−396.911			−0.513468			−0.256734	+	0.966482i	$0.582646\pi$
$774$	334.387	+	527.593i	0.432025	+	0.681644i
$775$		0			0
$776$			97.3983i			0.125513i
$777$	−158.658	−	546.703i	−0.204194	−	0.703608i
$778$			409.852i			0.526802i
$779$			17.3828i			0.0223143i
$780$		0			0
$781$	1146.72			1.46827
$782$	−1.10902			−0.00141818
$783$	1.33738	−	1.51427i	0.00170802	−	0.00193394i
$784$	−28.0000			−0.0357143
$785$		0			0
$786$	408.014	−	118.409i	0.519101	−	0.150648i
$787$			439.897i			0.558954i	0.960152	+	0.279477i	$0.0901611\pi$
$787$			439.897i			0.558954i	−0.960152	+	0.279477i	$0.909839\pi$
$788$	530.516			0.673244
$789$	−8.64849	−	29.8009i	−0.0109613	−	0.0377704i
$790$		0			0
$791$			437.208i			0.552728i
$792$	179.190	+	282.724i	0.226250	+	0.356974i
$793$		−	284.062i		−	0.358211i
$794$		−	853.686i		−	1.07517i
$795$		0			0
$796$	−381.230			−0.478933
$797$	−334.640			−0.419875			−0.209938	−	0.977715i	$-0.567326\pi$
$797$	−334.640			−0.419875			−0.209938	+	0.977715i	$0.567326\pi$
$798$	−57.6320	+	16.7254i	−0.0722206	+	0.0209591i
$799$	1265.92			1.58439
$800$		0			0
$801$	−8.93381	−	14.0957i	−0.0111533	−	0.0175976i
$802$		−	468.708i		−	0.584424i
$803$	−14.7927			−0.0184218
$804$	−394.049	+	114.357i	−0.490111	+	0.142235i
$805$		0			0
$806$		−	343.505i		−	0.426185i
$807$	178.034	−	51.6672i	0.220613	−	0.0640238i
$808$			376.588i			0.466074i
$809$		−	1320.59i		−	1.63238i	−0.577786	−	0.816188i	$-0.696083\pi$
$809$		−	1320.59i		−	1.63238i	0.577786	−	0.816188i	$-0.303917\pi$
$810$		0			0
$811$	−223.003			−0.274973			−0.137486	−	0.990504i	$-0.543902\pi$
$811$	−223.003			−0.274973			−0.137486	+	0.990504i	$0.543902\pi$
$812$	0.395941			0.000487612
$813$	−266.472	−	918.206i	−0.327764	−	1.12940i
$814$	−1333.70			−1.63845
$815$		0			0
$816$	−72.6901	−	250.475i	−0.0890810	−	0.306954i
$817$			262.365i			0.321133i
$818$	359.702			0.439734
$819$	−132.728	+	84.1224i	−0.162060	+	0.102714i
$820$		0			0
$821$		−	994.157i		−	1.21091i	−0.795879	−	0.605455i	$-0.792991\pi$
$821$		−	994.157i		−	1.21091i	0.795879	−	0.605455i	$-0.207009\pi$
$822$	−6.60028	−	22.7432i	−0.00802954	−	0.0276681i
$823$		−	934.961i		−	1.13604i	−0.823015	−	0.568020i	$-0.807710\pi$
$823$		−	934.961i		−	1.13604i	0.823015	−	0.568020i	$-0.192290\pi$
$824$			426.411i			0.517489i
$825$		0			0
$826$	−185.903			−0.225065
$827$	1521.18			1.83940			0.919701	−	0.392620i	$-0.128431\pi$
$827$	1521.18			1.83940			0.919701	+	0.392620i	$0.128431\pi$
$828$	0.548564	−	0.347679i	0.000662517	−	0.000419902i
$829$	456.738			0.550951			0.275476	−	0.961308i	$-0.411165\pi$
$829$	456.738			0.550951			0.275476	+	0.961308i	$0.411165\pi$
$830$		0			0
$831$	−265.680	+	77.1029i	−0.319712	+	0.0927833i
$832$			52.7943i			0.0634547i
$833$	152.139			0.182639
$834$	−60.6312	−	208.922i	−0.0726993	−	0.250507i
$835$		0			0
$836$			140.595i			0.168176i
$837$	−744.858	−	657.844i	−0.889914	−	0.785955i
$838$			651.509i			0.777457i
$839$		−	2.18653i		−	0.00260612i	−0.999999	−	0.00130306i	$-0.999585\pi$
$839$		−	2.18653i		−	0.00260612i	0.999999	−	0.00130306i	$-0.000414777\pi$
$840$		0			0
$841$	840.994			0.999993
$842$	−712.953			−0.846737
$843$	−868.169	+	251.951i	−1.02986	+	0.298874i
$844$	132.239			0.156682
$845$		0			0
$846$	−626.176	+	396.869i	−0.740161	+	0.469113i
$847$			137.324i			0.162130i
$848$	−374.285			−0.441374
$849$	975.582	−	283.123i	1.14910	−	0.333478i
$850$		0			0
$851$			2.58775i			0.00304084i
$852$	502.512	−	145.834i	0.589803	−	0.171166i
$853$			332.545i			0.389854i	0.980818	+	0.194927i	$0.0624469\pi$
$853$			332.545i			0.389854i	−0.980818	+	0.194927i	$0.937553\pi$
$854$		−	161.057i		−	0.188591i
$855$		0			0
$856$	−38.0621			−0.0444651
$857$	642.439			0.749637			0.374819	−	0.927098i	$-0.377705\pi$
$857$	642.439			0.749637			0.374819	+	0.927098i	$0.377705\pi$
$858$	102.610	+	353.571i	0.119592	+	0.412087i
$859$	−701.861			−0.817067			−0.408534	−	0.912743i	$-0.633960\pi$
$859$	−701.861			−0.817067			−0.408534	+	0.912743i	$0.633960\pi$
$860$		0			0
$861$	7.19292	+	24.7853i	0.00835415	+	0.0287866i
$862$		−	159.314i		−	0.184819i
$863$	−30.0470			−0.0348169			−0.0174085	−	0.999848i	$-0.505542\pi$
$863$	−30.0470			−0.0348169			−0.0174085	+	0.999848i	$0.505542\pi$
$864$	114.479	+	101.106i	0.132499	+	0.117021i
$865$		0			0
$866$		−	924.674i		−	1.06775i
$867$	153.322	+	528.314i	0.176842	+	0.609358i
$868$		−	194.760i		−	0.224378i
$869$		−	923.859i		−	1.06313i
$870$		0			0
$871$	−451.290			−0.518128
$872$	−68.5426			−0.0786039
$873$	165.910	+	261.771i	0.190046	+	0.299852i
$874$	0.272794			0.000312121
$875$		0			0
$876$	−6.48244	+	1.88126i	−0.00740004	+	0.00214756i
$877$		−	1620.09i		−	1.84731i	−0.383222	−	0.923656i	$-0.625185\pi$
$877$		−	1620.09i		−	1.84731i	0.383222	−	0.923656i	$-0.374815\pi$
$878$	−316.797			−0.360816
$879$	−108.295	−	373.162i	−0.123203	−	0.424531i
$880$		0			0
$881$			730.844i			0.829562i	0.909921	+	0.414781i	$0.136142\pi$
$881$			730.844i			0.829562i	−0.909921	+	0.414781i	$0.863858\pi$
$882$	−75.2537	+	47.6957i	−0.0853217	+	0.0540767i
$883$			926.897i			1.04971i	0.851191	+	0.524857i	$0.175881\pi$
$883$			926.897i			1.04971i	−0.851191	+	0.524857i	$0.824119\pi$
$884$		−	286.859i		−	0.324501i
$885$		0			0
$886$	631.422			0.712666
$887$	251.570			0.283619			0.141809	−	0.989894i	$-0.454708\pi$
$887$	251.570			0.283619			0.141809	+	0.989894i	$0.454708\pi$
$888$	−584.450	+	169.613i	−0.658165	+	0.191006i
$889$	−451.235			−0.507576
$890$		0			0
$891$	963.192	+	454.623i	1.08102	+	0.510239i
$892$		−	71.9343i		−	0.0806438i
$893$	−311.390			−0.348701
$894$	162.535	−	47.1693i	0.181807	−	0.0527621i
$895$		0			0
$896$			29.9333i			0.0334077i
$897$	0.686028	−	0.199092i	0.000764802	−	0.000221953i
$898$			453.265i			0.504749i
$899$			2.75405i			0.00306346i
$900$		0			0
$901$	2033.69			2.25714
$902$	60.4644			0.0670337
$903$	108.565	+	374.093i	0.120227	+	0.414278i
$904$	467.395			0.517029
$905$		0			0
$906$	313.914	+	1081.68i	0.346483	+	1.19391i
$907$		−	143.092i		−	0.157764i	−0.996884	−	0.0788819i	$-0.974865\pi$
$907$		−	143.092i		−	0.157764i	0.996884	−	0.0788819i	$-0.0251350\pi$
$908$	858.504			0.945489
$909$	641.486	+	1012.13i	0.705705	+	1.11345i
$910$		0			0
$911$		−	1031.21i		−	1.13196i	−0.824421	−	0.565978i	$-0.808499\pi$
$911$		−	1031.21i		−	1.13196i	0.824421	−	0.565978i	$-0.191501\pi$
$912$	17.8802	+	61.6112i	0.0196054	+	0.0675562i
$913$			5.22556i			0.00572351i
$914$		−	693.860i		−	0.759147i
$915$		0			0
$916$	315.523			0.344457
$917$	264.939			0.288920
$918$	−622.027	−	549.362i	−0.677589	−	0.598434i
$919$	1628.79			1.77235			0.886177	−	0.463348i	$-0.153352\pi$
$919$	1628.79			1.77235			0.886177	+	0.463348i	$0.153352\pi$
$920$		0			0
$921$	1173.89	−	340.673i	1.27458	−	0.369895i
$922$		−	1055.83i		−	1.14516i
$923$	575.508			0.623519
$924$	58.1775	+	200.467i	0.0629626	+	0.216956i
$925$		0			0
$926$			28.8343i			0.0311386i
$927$	726.355	+	1146.04i	0.783555	+	1.23629i
$928$		−	0.423279i		−	0.000456119i
$929$			172.508i			0.185692i	0.995680	+	0.0928461i	$0.0295965\pi$
$929$			172.508i			0.185692i	−0.995680	+	0.0928461i	$0.970404\pi$
$930$		0			0
$931$	−37.4228			−0.0401963
$932$	731.305			0.784662
$933$	−8.27780	+	2.40230i	−0.00887224	+	0.00257481i
$934$	715.703			0.766278
$935$		0			0
$936$	89.9307	+	141.892i	0.0960798	+	0.151594i
$937$			525.532i			0.560866i	0.959874	+	0.280433i	$0.0904781\pi$
$937$			525.532i			0.560866i	−0.959874	+	0.280433i	$0.909522\pi$
$938$	−255.872			−0.272785
$939$	−1788.27	+	518.974i	−1.90444	+	0.552688i
$940$		0			0
$941$		−	550.315i		−	0.584820i	−0.956293	−	0.292410i	$-0.905543\pi$
$941$		−	550.315i		−	0.584820i	0.956293	−	0.292410i	$-0.0944571\pi$
$942$	203.446	−	59.0420i	0.215973	−	0.0626772i
$943$		−	0.117318i		−	0.000124409i
$944$			198.739i			0.210529i
$945$		0			0
$946$	912.611			0.964706
$947$	−474.200			−0.500739			−0.250370	−	0.968150i	$-0.580552\pi$
$947$	−474.200			−0.500739			−0.250370	+	0.968150i	$0.580552\pi$
$948$	−117.492	−	404.852i	−0.123936	−	0.427059i
$949$	−7.42409			−0.00782306
$950$		0			0
$951$	311.412	+	1073.06i	0.327457	+	1.12835i
$952$		−	162.643i		−	0.170844i
$953$	1221.11			1.28134			0.640668	−	0.767818i	$-0.278658\pi$
$953$	1221.11			1.28134			0.640668	+	0.767818i	$0.278658\pi$
$954$	−1005.94	+	637.564i	−1.05445	+	0.668306i
$955$		0			0
$956$		−	417.508i		−	0.436723i
$957$	−0.822672	−	2.83476i	−0.000859637	−	0.00296213i
$958$			854.583i			0.892049i
$959$		−	14.7680i		−	0.0153994i
$960$		0			0
$961$	393.695			0.409672
$962$	−669.348			−0.695788
$963$	−102.297	+	64.8356i	−0.106227	+	0.0673267i
$964$	−273.135			−0.283335
$965$		0			0
$966$	0.388963	−	0.112881i	0.000402653	−	0.000116854i
$967$		−	311.468i		−	0.322097i	−0.986946	−	0.161049i	$-0.948512\pi$
$967$		−	311.468i		−	0.322097i	0.986946	−	0.161049i	$-0.0514876\pi$
$968$	146.806			0.151659
$969$	−97.1522	−	334.766i	−0.100260	−	0.345476i
$970$		0			0
$971$			468.904i			0.482909i	0.970412	+	0.241454i	$0.0776244\pi$
$971$			468.904i			0.482909i	−0.970412	+	0.241454i	$0.922376\pi$
$972$	479.905	+	76.7299i	0.493729	+	0.0789403i
$973$		−	135.662i		−	0.139426i
$974$		−	1014.62i		−	1.04170i
$975$		0			0
$976$	−172.177			−0.176411
$977$	665.977			0.681655			0.340827	−	0.940126i	$-0.389293\pi$
$977$	665.977			0.681655			0.340827	+	0.940126i	$0.389293\pi$
$978$	−483.711	+	140.377i	−0.494592	+	0.143535i
$979$	−24.3822			−0.0249052
$980$		0			0
$981$	−184.217	+	116.757i	−0.187785	+	0.119018i
$982$			349.090i			0.355489i
$983$	−1055.82			−1.07408			−0.537038	−	0.843558i	$-0.680457\pi$
$983$	−1055.82			−1.07408			−0.537038	+	0.843558i	$0.680457\pi$
$984$	26.4966	−	7.68956i	0.0269274	−	0.00781459i
$985$		0			0
$986$			2.29989i			0.00233255i
$987$	−443.995	+	128.851i	−0.449843	+	0.130549i
$988$			70.5610i			0.0714180i
$989$		−	1.77073i		−	0.00179042i
$990$		0			0
$991$	−763.035			−0.769964			−0.384982	−	0.922924i	$-0.625792\pi$
$991$	−763.035			−0.769964			−0.384982	+	0.922924i	$0.625792\pi$
$992$	−208.207			−0.209886
$993$	−184.358	−	635.258i	−0.185657	−	0.639736i
$994$	326.301			0.328271
$995$		0			0
$996$	0.664561	+	2.28994i	0.000667230	+	0.00229913i
$997$		−	485.324i		−	0.486784i	−0.969928	−	0.243392i	$-0.921740\pi$
$997$		−	485.324i		−	0.486784i	0.969928	−	0.243392i	$-0.0782602\pi$
$998$	46.9418			0.0470359
$999$	−1281.87	+	1451.42i	−1.28315	+	1.45287i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.c.b.449.10		32
3.2	odd	2	inner	1050.3.c.b.449.24		32
5.2	odd	4		1050.3.e.b.701.8	✓	16
5.3	odd	4		1050.3.e.c.701.9	yes	16
5.4	even	2	inner	1050.3.c.b.449.23		32
15.2	even	4		1050.3.e.b.701.16	yes	16
15.8	even	4		1050.3.e.c.701.1	yes	16
15.14	odd	2	inner	1050.3.c.b.449.9		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.c.b.449.9		32	15.14	odd	2	inner
1050.3.c.b.449.10		32	1.1	even	1	trivial
1050.3.c.b.449.23		32	5.4	even	2	inner
1050.3.c.b.449.24		32	3.2	odd	2	inner
1050.3.e.b.701.8	✓	16	5.2	odd	4
1050.3.e.b.701.16	yes	16	15.2	even	4
1050.3.e.c.701.1	yes	16	15.8	even	4
1050.3.e.c.701.9	yes	16	5.3	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)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +(0.836130 + 2.88113i) q^{3} +2.00000 q^{4} +(-1.18247 - 4.07453i) q^{6} -2.64575i q^{7} -2.82843 q^{8} +(-7.60177 + 4.81799i) q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +(0.836130 + 2.88113i) q^{3} +2.00000 q^{4} +(-1.18247 - 4.07453i) q^{6} -2.64575i q^{7} -2.82843 q^{8} +(-7.60177 + 4.81799i) q^{9} +13.1493i q^{11} +(1.67226 + 5.76225i) q^{12} +6.59929i q^{13} +3.74166i q^{14} +4.00000 q^{16} -21.7341 q^{17} +(10.7505 - 6.81367i) q^{18} +5.34611 q^{19} +(7.62274 - 2.21219i) q^{21} -18.5959i q^{22} -0.0360813 q^{23} +(-2.36493 - 8.14906i) q^{24} -9.33280i q^{26} +(-20.2373 - 17.8732i) q^{27} -5.29150i q^{28} +0.0748258i q^{29} +36.8062 q^{31} -5.65685 q^{32} +(-37.8847 + 10.9945i) q^{33} +30.7366 q^{34} +(-15.2035 + 9.63598i) q^{36} -71.7200i q^{37} -7.56054 q^{38} +(-19.0134 + 5.51786i) q^{39} +3.25149i q^{41} +(-10.7802 + 3.12851i) q^{42} +49.0760i q^{43} +26.2986i q^{44} +0.0510267 q^{46} -58.2461 q^{47} +(3.34452 + 11.5245i) q^{48} -7.00000 q^{49} +(-18.1725 - 62.6186i) q^{51} +13.1986i q^{52} -93.5713 q^{53} +(28.6199 + 25.2765i) q^{54} +7.48331i q^{56} +(4.47004 + 15.4028i) q^{57} -0.105820i q^{58} +49.6848i q^{59} -43.0443 q^{61} -52.0518 q^{62} +(12.7472 + 20.1124i) q^{63} +8.00000 q^{64} +(53.5771 - 15.5486i) q^{66} +68.3846i q^{67} -43.4682 q^{68} +(-0.0301687 - 0.103955i) q^{69} -87.2076i q^{71} +(21.5011 - 13.6273i) q^{72} +1.12498i q^{73} +101.427i q^{74} +10.6922 q^{76} +34.7897 q^{77} +(26.8890 - 7.80343i) q^{78} -70.2593 q^{79} +(34.5740 - 73.2505i) q^{81} -4.59830i q^{82} +0.397403 q^{83} +(15.2455 - 4.42438i) q^{84} -69.4039i q^{86} +(-0.215582 + 0.0625640i) q^{87} -37.1918i q^{88} +1.85426i q^{89} +17.4601 q^{91} -0.0721626 q^{92} +(30.7747 + 106.043i) q^{93} +82.3724 q^{94} +(-4.72986 - 16.2981i) q^{96} -34.4355i q^{97} +9.89949 q^{98} +(-63.3531 - 99.9579i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 64 q^{4} - 16 q^{6} - 16 q^{9}+O(q^{10}) \) 32 * q + 64 * q^4 - 16 * q^6 - 16 * q^9	\( 32 q + 64 q^{4} - 16 q^{6} - 16 q^{9} + 128 q^{16} + 48 q^{19} + 56 q^{21} - 32 q^{24} + 48 q^{31} + 256 q^{34} - 32 q^{36} + 192 q^{39} + 160 q^{46} - 224 q^{49} + 288 q^{51} - 80 q^{54} - 112 q^{61} + 256 q^{64} - 192 q^{66} + 344 q^{69} + 96 q^{76} - 256 q^{79} + 160 q^{81} + 112 q^{84} - 448 q^{91} + 416 q^{94} - 64 q^{96} - 304 q^{99}+O(q^{100}) \) 32 * q + 64 * q^4 - 16 * q^6 - 16 * q^9 + 128 * q^16 + 48 * q^19 + 56 * q^21 - 32 * q^24 + 48 * q^31 + 256 * q^34 - 32 * q^36 + 192 * q^39 + 160 * q^46 - 224 * q^49 + 288 * q^51 - 80 * q^54 - 112 * q^61 + 256 * q^64 - 192 * q^66 + 344 * q^69 + 96 * q^76 - 256 * q^79 + 160 * q^81 + 112 * q^84 - 448 * q^91 + 416 * q^94 - 64 * q^96 - 304 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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