LMFDB - Embedded newform 1050.3.c.c.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:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +(-0.922735 + 2.85457i) q^{3} +2.00000 q^{4} +(1.30494 - 4.03697i) q^{6} -2.64575i q^{7} -2.82843 q^{8} +(-7.29712 - 5.26802i) q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +(-0.922735 + 2.85457i) q^{3} +2.00000 q^{4} +(1.30494 - 4.03697i) q^{6} -2.64575i q^{7} -2.82843 q^{8} +(-7.29712 - 5.26802i) q^{9} -4.58314i q^{11} +(-1.84547 + 5.70914i) q^{12} +20.4597i q^{13} +3.74166i q^{14} +4.00000 q^{16} +4.97301 q^{17} +(10.3197 + 7.45010i) q^{18} -6.22537 q^{19} +(7.55248 + 2.44133i) q^{21} +6.48154i q^{22} -0.140044 q^{23} +(2.60989 - 8.07394i) q^{24} -28.9343i q^{26} +(21.7712 - 15.9691i) q^{27} -5.29150i q^{28} -1.76265i q^{29} -29.7354 q^{31} -5.65685 q^{32} +(13.0829 + 4.22902i) q^{33} -7.03290 q^{34} +(-14.5942 - 10.5360i) q^{36} +38.8333i q^{37} +8.80401 q^{38} +(-58.4035 - 18.8788i) q^{39} -68.8223i q^{41} +(-10.6808 - 3.45256i) q^{42} -20.3093i q^{43} -9.16628i q^{44} +0.198053 q^{46} -57.3078 q^{47} +(-3.69094 + 11.4183i) q^{48} -7.00000 q^{49} +(-4.58877 + 14.1958i) q^{51} +40.9193i q^{52} -41.0342 q^{53} +(-30.7892 + 22.5838i) q^{54} +7.48331i q^{56} +(5.74437 - 17.7708i) q^{57} +2.49277i q^{58} -79.4508i q^{59} -19.1096 q^{61} +42.0522 q^{62} +(-13.9379 + 19.3064i) q^{63} +8.00000 q^{64} +(-18.5020 - 5.98074i) q^{66} +67.5134i q^{67} +9.94602 q^{68} +(0.129224 - 0.399767i) q^{69} +30.8958i q^{71} +(20.6394 + 14.9002i) q^{72} -111.327i q^{73} -54.9186i q^{74} -12.4507 q^{76} -12.1259 q^{77} +(82.5950 + 26.6987i) q^{78} +20.9159 q^{79} +(25.4960 + 76.8827i) q^{81} +97.3294i q^{82} +156.468 q^{83} +(15.1050 + 4.88265i) q^{84} +28.7216i q^{86} +(5.03162 + 1.62646i) q^{87} +12.9631i q^{88} -133.632i q^{89} +54.1312 q^{91} -0.280089 q^{92} +(27.4379 - 84.8817i) q^{93} +81.0455 q^{94} +(5.21978 - 16.1479i) q^{96} -20.1609i q^{97} +9.89949 q^{98} +(-24.1441 + 33.4437i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9}+O(q^{10}) $ 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9	$ 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9} + 128 q^{16} - 96 q^{19} + 56 q^{21} + 64 q^{24} - 320 q^{34} + 16 q^{36} - 312 q^{39} + 64 q^{46} - 224 q^{49} + 168 q^{51} + 64 q^{54} + 224 q^{61} + 256 q^{64} - 16 q^{69} - 192 q^{76} - 16 q^{79} - 248 q^{81} + 112 q^{84} - 112 q^{91} - 64 q^{94} + 128 q^{96} + 104 q^{99}+O(q^{100}) $ 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9 + 128 * q^16 - 96 * q^19 + 56 * q^21 + 64 * q^24 - 320 * q^34 + 16 * q^36 - 312 * q^39 + 64 * q^46 - 224 * q^49 + 168 * q^51 + 64 * q^54 + 224 * q^61 + 256 * q^64 - 16 * q^69 - 192 * q^76 - 16 * q^79 - 248 * q^81 + 112 * q^84 - 112 * q^91 - 64 * q^94 + 128 * q^96 + 104 * 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
$3$	−0.922735	+	2.85457i	−0.307578	+	0.951523i
$3$	−0.922735	+	2.85457i	−0.307578	+	0.951523i
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$	1.30494	−	4.03697i	0.217491	−	0.672828i
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	−2.82843			−0.353553
$9$	−7.29712	−	5.26802i	−0.810791	−	0.585335i
$10$		0			0
$11$		−	4.58314i		−	0.416649i	−0.978060	−	0.208325i	$-0.933199\pi$
$11$		−	4.58314i		−	0.416649i	0.978060	−	0.208325i	$-0.0668010\pi$
$12$	−1.84547	+	5.70914i	−0.153789	+	0.475761i
$13$			20.4597i			1.57382i	0.617068	+	0.786910i	$0.288320\pi$
$13$			20.4597i			1.57382i	−0.617068	+	0.786910i	$0.711680\pi$
$14$			3.74166i			0.267261i
$15$		0			0
$16$	4.00000			0.250000
$17$	4.97301			0.292530			0.146265	−	0.989245i	$-0.453275\pi$
$17$	4.97301			0.292530			0.146265	+	0.989245i	$0.453275\pi$
$18$	10.3197	+	7.45010i	0.573316	+	0.413895i
$19$	−6.22537			−0.327651			−0.163826	−	0.986489i	$-0.552383\pi$
$19$	−6.22537			−0.327651			−0.163826	+	0.986489i	$0.552383\pi$
$20$		0			0
$21$	7.55248	+	2.44133i	0.359642	+	0.116254i
$22$			6.48154i			0.294615i
$23$	−0.140044			−0.00608889			−0.00304445	−	0.999995i	$-0.500969\pi$
$23$	−0.140044			−0.00608889			−0.00304445	+	0.999995i	$0.500969\pi$
$24$	2.60989	−	8.07394i	0.108745	−	0.336414i
$25$		0			0
$26$		−	28.9343i		−	1.11286i
$27$	21.7712	−	15.9691i	0.806342	−	0.591450i
$28$		−	5.29150i		−	0.188982i
$29$		−	1.76265i		−	0.0607812i	−0.999538	−	0.0303906i	$-0.990325\pi$
$29$		−	1.76265i		−	0.0607812i	0.999538	−	0.0303906i	$-0.00967511\pi$
$30$		0			0
$31$	−29.7354			−0.959207			−0.479603	−	0.877485i	$-0.659219\pi$
$31$	−29.7354			−0.959207			−0.479603	+	0.877485i	$0.659219\pi$
$32$	−5.65685			−0.176777
$33$	13.0829	+	4.22902i	0.396451	+	0.128152i
$34$	−7.03290			−0.206850
$35$		0			0
$36$	−14.5942	−	10.5360i	−0.405396	−	0.292668i
$37$			38.8333i			1.04955i	0.851242	+	0.524774i	$0.175850\pi$
$37$			38.8333i			1.04955i	−0.851242	+	0.524774i	$0.824150\pi$
$38$	8.80401			0.231684
$39$	−58.4035	−	18.8788i	−1.49753	−	0.484073i
$40$		0			0
$41$		−	68.8223i		−	1.67859i	−0.543675	−	0.839296i	$-0.682968\pi$
$41$		−	68.8223i		−	1.67859i	0.543675	−	0.839296i	$-0.317032\pi$
$42$	−10.6808	−	3.45256i	−0.254305	−	0.0822037i
$43$		−	20.3093i		−	0.472308i	−0.971716	−	0.236154i	$-0.924113\pi$
$43$		−	20.3093i		−	0.472308i	0.971716	−	0.236154i	$-0.0758870\pi$
$44$		−	9.16628i		−	0.208325i
$45$		0			0
$46$	0.198053			0.00430550
$47$	−57.3078			−1.21932			−0.609658	−	0.792665i	$-0.708693\pi$
$47$	−57.3078			−1.21932			−0.609658	+	0.792665i	$0.708693\pi$
$48$	−3.69094	+	11.4183i	−0.0768946	+	0.237881i
$49$	−7.00000			−0.142857
$50$		0			0
$51$	−4.58877	+	14.1958i	−0.0899758	+	0.278349i
$52$			40.9193i			0.786910i
$53$	−41.0342			−0.774230			−0.387115	−	0.922032i	$-0.626528\pi$
$53$	−41.0342			−0.774230			−0.387115	+	0.922032i	$0.626528\pi$
$54$	−30.7892	+	22.5838i	−0.570170	+	0.418218i
$55$		0			0
$56$			7.48331i			0.133631i
$57$	5.74437	−	17.7708i	0.100778	−	0.311768i
$58$			2.49277i			0.0429788i
$59$		−	79.4508i		−	1.34662i	−0.739358	−	0.673312i	$-0.764871\pi$
$59$		−	79.4508i		−	1.34662i	0.739358	−	0.673312i	$-0.235129\pi$
$60$		0			0
$61$	−19.1096			−0.313273			−0.156636	−	0.987656i	$-0.550065\pi$
$61$	−19.1096			−0.313273			−0.156636	+	0.987656i	$0.550065\pi$
$62$	42.0522			0.678261
$63$	−13.9379	+	19.3064i	−0.221236	+	0.306450i
$64$	8.00000			0.125000
$65$		0			0
$66$	−18.5020	−	5.98074i	−0.280333	−	0.0906173i
$67$			67.5134i			1.00766i	0.863802	+	0.503831i	$0.168077\pi$
$67$			67.5134i			1.00766i	−0.863802	+	0.503831i	$0.831923\pi$
$68$	9.94602			0.146265
$69$	0.129224	−	0.399767i	0.00187281	−	0.00579372i
$70$		0			0
$71$			30.8958i			0.435152i	0.976043	+	0.217576i	$0.0698150\pi$
$71$			30.8958i			0.435152i	−0.976043	+	0.217576i	$0.930185\pi$
$72$	20.6394	+	14.9002i	0.286658	+	0.206947i
$73$		−	111.327i		−	1.52502i	−0.646975	−	0.762511i	$-0.723966\pi$
$73$		−	111.327i		−	1.52502i	0.646975	−	0.762511i	$-0.276034\pi$
$74$		−	54.9186i		−	0.742143i
$75$		0			0
$76$	−12.4507			−0.163826
$77$	−12.1259			−0.157479
$78$	82.5950	+	26.6987i	1.05891	+	0.342291i
$79$	20.9159			0.264759			0.132379	−	0.991199i	$-0.457738\pi$
$79$	20.9159			0.264759			0.132379	+	0.991199i	$0.457738\pi$
$80$		0			0
$81$	25.4960	+	76.8827i	0.314765	+	0.949170i
$82$			97.3294i			1.18694i
$83$	156.468			1.88516			0.942579	−	0.333984i	$-0.108393\pi$
$83$	156.468			1.88516			0.942579	+	0.333984i	$0.108393\pi$
$84$	15.1050	+	4.88265i	0.179821	+	0.0581268i
$85$		0			0
$86$			28.7216i			0.333972i
$87$	5.03162	+	1.62646i	0.0578347	+	0.0186950i
$88$			12.9631i			0.147308i
$89$		−	133.632i		−	1.50148i	−0.660598	−	0.750739i	$-0.729697\pi$
$89$		−	133.632i		−	1.50148i	0.660598	−	0.750739i	$-0.270303\pi$
$90$		0			0
$91$	54.1312			0.594848
$92$	−0.280089			−0.00304445
$93$	27.4379	−	84.8817i	0.295031	−	0.912707i
$94$	81.0455			0.862186
$95$		0			0
$96$	5.21978	−	16.1479i	0.0543727	−	0.168207i
$97$		−	20.1609i		−	0.207845i	−0.994585	−	0.103922i	$-0.966861\pi$
$97$		−	20.1609i		−	0.207845i	0.994585	−	0.103922i	$-0.0331393\pi$
$98$	9.89949			0.101015
$99$	−24.1441	+	33.4437i	−0.243880	+	0.337816i
$100$		0			0
$101$			95.9087i			0.949591i	0.880096	+	0.474796i	$0.157478\pi$
$101$			95.9087i			0.949591i	−0.880096	+	0.474796i	$0.842522\pi$
$102$	6.48950	−	20.0759i	0.0636225	−	0.196822i
$103$		−	136.017i		−	1.32056i	−0.751021	−	0.660278i	$-0.770438\pi$
$103$		−	136.017i		−	1.32056i	0.751021	−	0.660278i	$-0.229562\pi$
$104$		−	57.8687i		−	0.556429i
$105$		0			0
$106$	58.0311			0.547463
$107$	−77.0597			−0.720184			−0.360092	−	0.932917i	$-0.617255\pi$
$107$	−77.0597			−0.720184			−0.360092	+	0.932917i	$0.617255\pi$
$108$	43.5425	−	31.9383i	0.403171	−	0.295725i
$109$	−148.111			−1.35881			−0.679406	−	0.733762i	$-0.737763\pi$
$109$	−148.111			−1.35881			−0.679406	+	0.733762i	$0.737763\pi$
$110$		0			0
$111$	−110.852	−	35.8328i	−0.998669	−	0.322818i
$112$		−	10.5830i		−	0.0944911i
$113$	86.9193			0.769198			0.384599	−	0.923084i	$-0.374340\pi$
$113$	86.9193			0.769198			0.384599	+	0.923084i	$0.374340\pi$
$114$	−8.12376	+	25.1316i	−0.0712611	+	0.220453i
$115$		0			0
$116$		−	3.52531i		−	0.0303906i
$117$	107.782	−	149.297i	0.921213	−	1.27604i
$118$			112.360i			0.952207i
$119$		−	13.1573i		−	0.110566i
$120$		0			0
$121$	99.9948			0.826403
$122$	27.0251			0.221517
$123$	196.458	+	63.5047i	1.59722	+	0.516298i
$124$	−59.4708			−0.479603
$125$		0			0
$126$	19.7111	−	27.3033i	0.156437	−	0.216693i
$127$		−	244.384i		−	1.92429i	−0.272546	−	0.962143i	$-0.587866\pi$
$127$		−	244.384i		−	1.92429i	0.272546	−	0.962143i	$-0.412134\pi$
$128$	−11.3137			−0.0883883
$129$	57.9742	+	18.7401i	0.449412	+	0.145272i
$130$		0			0
$131$		−	258.568i		−	1.97380i	−0.161334	−	0.986900i	$-0.551580\pi$
$131$		−	258.568i		−	1.97380i	0.161334	−	0.986900i	$-0.448420\pi$
$132$	26.1658	+	8.45805i	0.198226	+	0.0640761i
$133$			16.4708i			0.123841i
$134$		−	95.4784i		−	0.712525i
$135$		0			0
$136$	−14.0658			−0.103425
$137$	−217.042			−1.58425			−0.792123	−	0.610361i	$-0.791024\pi$
$137$	−217.042			−1.58425			−0.792123	+	0.610361i	$0.791024\pi$
$138$	−0.182750	+	0.565355i	−0.00132428	+	0.00409678i
$139$	110.593			0.795636			0.397818	−	0.917464i	$-0.369768\pi$
$139$	110.593			0.795636			0.397818	+	0.917464i	$0.369768\pi$
$140$		0			0
$141$	52.8799	−	163.589i	0.375035	−	1.16021i
$142$		−	43.6933i		−	0.307699i
$143$	93.7695			0.655731
$144$	−29.1885	−	21.0721i	−0.202698	−	0.146334i
$145$		0			0
$146$			157.440i			1.07835i
$147$	6.45914	−	19.9820i	0.0439397	−	0.135932i
$148$			77.6666i			0.524774i
$149$		−	42.4042i		−	0.284592i	−0.989824	−	0.142296i	$-0.954552\pi$
$149$		−	42.4042i		−	0.284592i	0.989824	−	0.142296i	$-0.0454485\pi$
$150$		0			0
$151$	106.207			0.703357			0.351678	−	0.936121i	$-0.385611\pi$
$151$	106.207			0.703357			0.351678	+	0.936121i	$0.385611\pi$
$152$	17.6080			0.115842
$153$	−36.2886	−	26.1979i	−0.237181	−	0.171228i
$154$	17.1485			0.111354
$155$		0			0
$156$	−116.807	−	37.7577i	−0.748763	−	0.242036i
$157$			106.522i			0.678487i	0.940699	+	0.339244i	$0.110171\pi$
$157$			106.522i			0.678487i	−0.940699	+	0.339244i	$0.889829\pi$
$158$	−29.5796			−0.187213
$159$	37.8637	−	117.135i	0.238136	−	0.736697i
$160$		0			0
$161$			0.370523i			0.00230138i
$162$	−36.0567	−	108.729i	−0.222572	−	0.671164i
$163$		−	143.209i		−	0.878584i	−0.898344	−	0.439292i	$-0.855229\pi$
$163$		−	143.209i		−	0.878584i	0.898344	−	0.439292i	$-0.144771\pi$
$164$		−	137.645i		−	0.839296i
$165$		0			0
$166$	−221.279			−1.33301
$167$	−134.374			−0.804636			−0.402318	−	0.915500i	$-0.631795\pi$
$167$	−134.374			−0.804636			−0.402318	+	0.915500i	$0.631795\pi$
$168$	−21.3616	−	6.90511i	−0.127153	−	0.0411019i
$169$	−249.598			−1.47691
$170$		0			0
$171$	45.4273	+	32.7954i	0.265657	+	0.191786i
$172$		−	40.6185i		−	0.236154i
$173$	−271.155			−1.56737			−0.783686	−	0.621157i	$-0.786663\pi$
$173$	−271.155			−1.56737			−0.783686	+	0.621157i	$0.786663\pi$
$174$	−7.11578	−	2.30016i	−0.0408953	−	0.0132193i
$175$		0			0
$176$		−	18.3326i		−	0.104162i
$177$	226.798	+	73.3120i	1.28134	+	0.414192i
$178$			188.984i			1.06171i
$179$			101.035i			0.564441i	0.959350	+	0.282221i	$0.0910710\pi$
$179$			101.035i			0.564441i	−0.959350	+	0.282221i	$0.908929\pi$
$180$		0			0
$181$	245.254			1.35499			0.677496	−	0.735526i	$-0.263065\pi$
$181$	245.254			1.35499			0.677496	+	0.735526i	$0.263065\pi$
$182$	−76.5531			−0.420621
$183$	17.6331	−	54.5498i	0.0963558	−	0.298086i
$184$	0.396106			0.00215275
$185$		0			0
$186$	−38.8030	+	120.041i	−0.208618	+	0.645381i
$187$		−	22.7920i		−	0.121882i
$188$	−114.616			−0.609658
$189$	−42.2504	−	57.6012i	−0.223547	−	0.304769i
$190$		0			0
$191$		−	33.8884i		−	0.177426i	−0.996057	−	0.0887132i	$-0.971725\pi$
$191$		−	33.8884i		−	0.177426i	0.996057	−	0.0887132i	$-0.0282755\pi$
$192$	−7.38188	+	22.8365i	−0.0384473	+	0.118940i
$193$		−	304.046i		−	1.57537i	−0.616080	−	0.787684i	$-0.711280\pi$
$193$		−	304.046i		−	1.57537i	0.616080	−	0.787684i	$-0.288720\pi$
$194$			28.5119i			0.146968i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	251.710			1.27772			0.638859	−	0.769324i	$-0.279407\pi$
$197$	251.710			1.27772			0.638859	+	0.769324i	$0.279407\pi$
$198$	34.1449	−	47.2966i	0.172449	−	0.238872i
$199$	371.292			1.86579			0.932895	−	0.360148i	$-0.117274\pi$
$199$	371.292			1.86579			0.932895	+	0.360148i	$0.117274\pi$
$200$		0			0
$201$	−192.722	−	62.2970i	−0.958814	−	0.309935i
$202$		−	135.635i		−	0.671463i
$203$	−4.66354			−0.0229731
$204$	−9.17753	+	28.3916i	−0.0449879	+	0.139174i
$205$		0			0
$206$			192.358i			0.933775i
$207$	1.02192	+	0.737757i	0.00493682	+	0.00356404i
$208$			81.8387i			0.393455i
$209$			28.5318i			0.136516i
$210$		0			0
$211$	219.180			1.03877			0.519383	−	0.854542i	$-0.326162\pi$
$211$	219.180			1.03877			0.519383	+	0.854542i	$0.326162\pi$
$212$	−82.0683			−0.387115
$213$	−88.1942	−	28.5086i	−0.414057	−	0.133843i
$214$	108.979			0.509247
$215$		0			0
$216$	−61.5783	+	45.1676i	−0.285085	+	0.209109i
$217$			78.6725i			0.362546i
$218$	209.460			0.960826
$219$	317.789	+	102.725i	1.45109	+	0.469064i
$220$		0			0
$221$			101.746i			0.460390i
$222$	156.769	+	50.6753i	0.706166	+	0.228267i
$223$			224.223i			1.00549i	0.864436	+	0.502743i	$0.167676\pi$
$223$			224.223i			1.00549i	−0.864436	+	0.502743i	$0.832324\pi$
$224$			14.9666i			0.0668153i
$225$		0			0
$226$	−122.922			−0.543905
$227$	−386.312			−1.70181			−0.850907	−	0.525317i	$-0.823947\pi$
$227$	−386.312			−1.70181			−0.850907	+	0.525317i	$0.823947\pi$
$228$	11.4887	−	35.5415i	0.0503892	−	0.155884i
$229$	−159.911			−0.698300			−0.349150	−	0.937067i	$-0.613530\pi$
$229$	−159.911			−0.698300			−0.349150	+	0.937067i	$0.613530\pi$
$230$		0			0
$231$	11.1889	−	34.6141i	0.0484370	−	0.149844i
$232$			4.98554i			0.0214894i
$233$	−285.263			−1.22431			−0.612153	−	0.790739i	$-0.709696\pi$
$233$	−285.263			−1.22431			−0.612153	+	0.790739i	$0.709696\pi$
$234$	−152.427	+	211.137i	−0.651396	+	0.902296i
$235$		0			0
$236$		−	158.902i		−	0.673312i
$237$	−19.2999	+	59.7060i	−0.0814340	+	0.251924i
$238$			18.6073i			0.0781819i
$239$		−	277.247i		−	1.16003i	−0.814606	−	0.580015i	$-0.803047\pi$
$239$		−	277.247i		−	1.16003i	0.814606	−	0.580015i	$-0.196953\pi$
$240$		0			0
$241$	−66.8596			−0.277426			−0.138713	−	0.990333i	$-0.544296\pi$
$241$	−66.8596			−0.277426			−0.138713	+	0.990333i	$0.544296\pi$
$242$	−141.414			−0.584355
$243$	−242.993	+	1.83761i	−0.999971	+	0.00756219i
$244$	−38.2193			−0.156636
$245$		0			0
$246$	−277.833	−	89.8092i	−1.12940	−	0.365078i
$247$		−	127.369i		−	0.515664i
$248$	84.1044			0.339131
$249$	−144.379	+	446.649i	−0.579833	+	1.79377i
$250$		0			0
$251$		−	351.334i		−	1.39974i	−0.714271	−	0.699869i	$-0.753242\pi$
$251$		−	351.334i		−	1.39974i	0.714271	−	0.699869i	$-0.246758\pi$
$252$	−27.8757	+	38.6127i	−0.110618	+	0.153225i
$253$			0.641844i			0.00253693i
$254$			345.611i			1.36068i
$255$		0			0
$256$	16.0000			0.0625000
$257$	130.747			0.508745			0.254372	−	0.967106i	$-0.418131\pi$
$257$	130.747			0.508745			0.254372	+	0.967106i	$0.418131\pi$
$258$	−81.9879	−	26.5024i	−0.317782	−	0.102723i
$259$	102.743			0.396692
$260$		0			0
$261$	−9.28569	+	12.8623i	−0.0355774	+	0.0492808i
$262$			365.670i			1.39569i
$263$	−183.496			−0.697704			−0.348852	−	0.937178i	$-0.613428\pi$
$263$	−183.496			−0.697704			−0.348852	+	0.937178i	$0.613428\pi$
$264$	−37.0040	−	11.9615i	−0.140167	−	0.0453087i
$265$		0			0
$266$		−	23.2932i		−	0.0875685i
$267$	381.461	+	123.307i	1.42869	+	0.461822i
$268$			135.027i			0.503831i
$269$		−	176.353i		−	0.655587i	−0.944749	−	0.327794i	$-0.893695\pi$
$269$		−	176.353i		−	0.655587i	0.944749	−	0.327794i	$-0.106305\pi$
$270$		0			0
$271$	−228.813			−0.844329			−0.422164	−	0.906519i	$-0.638729\pi$
$271$	−228.813			−0.844329			−0.422164	+	0.906519i	$0.638729\pi$
$272$	19.8920			0.0731325
$273$	−49.9487	+	154.521i	−0.182962	+	0.566012i
$274$	306.943			1.12023
$275$		0			0
$276$	0.258448	−	0.799533i	0.000936405	−	0.00289686i
$277$		−	21.1361i		−	0.0763035i	−0.999272	−	0.0381517i	$-0.987853\pi$
$277$		−	21.1361i		−	0.0763035i	0.999272	−	0.0381517i	$-0.0121470\pi$
$278$	−156.403			−0.562599
$279$	216.983	+	156.647i	0.777716	+	0.561458i
$280$		0			0
$281$			439.326i			1.56344i	0.623631	+	0.781719i	$0.285657\pi$
$281$			439.326i			1.56344i	−0.623631	+	0.781719i	$0.714343\pi$
$282$	−74.7835	+	231.350i	−0.265190	+	0.820390i
$283$		−	76.8388i		−	0.271515i	−0.990742	−	0.135758i	$-0.956653\pi$
$283$		−	76.8388i		−	0.271515i	0.990742	−	0.135758i	$-0.0433468\pi$
$284$			61.7916i			0.217576i
$285$		0			0
$286$	−132.610			−0.463672
$287$	−182.087			−0.634448
$288$	41.2788	+	29.8004i	0.143329	+	0.103474i
$289$	−264.269			−0.914426
$290$		0			0
$291$	57.5508	+	18.6032i	0.197769	+	0.0639285i
$292$		−	222.653i		−	0.762511i
$293$	−255.154			−0.870834			−0.435417	−	0.900229i	$-0.643399\pi$
$293$	−255.154			−0.870834			−0.435417	+	0.900229i	$0.643399\pi$
$294$	−9.13461	+	28.2588i	−0.0310701	+	0.0961183i
$295$		0			0
$296$		−	109.837i		−	0.371071i
$297$	−73.1889	−	99.7806i	−0.246427	−	0.335962i
$298$			59.9686i			0.201237i
$299$		−	2.86526i		−	0.00958282i
$300$		0			0
$301$	−53.7332			−0.178516
$302$	−150.199			−0.497348
$303$	−273.778	−	88.4983i	−0.903558	−	0.292074i
$304$	−24.9015			−0.0819128
$305$		0			0
$306$	51.3199	+	37.0494i	0.167712	+	0.121077i
$307$			162.522i			0.529389i	0.964332	+	0.264695i	$0.0852712\pi$
$307$			162.522i			0.529389i	−0.964332	+	0.264695i	$0.914729\pi$
$308$	−24.2517			−0.0787393
$309$	388.271	+	125.508i	1.25654	+	0.406174i
$310$		0			0
$311$			130.962i			0.421099i	0.977583	+	0.210550i	$0.0675254\pi$
$311$			130.962i			0.421099i	−0.977583	+	0.210550i	$0.932475\pi$
$312$	165.190	+	53.3974i	0.529455	+	0.171146i
$313$			206.265i			0.658994i	0.944157	+	0.329497i	$0.106879\pi$
$313$			206.265i			0.658994i	−0.944157	+	0.329497i	$0.893121\pi$
$314$		−	150.646i		−	0.479763i
$315$		0			0
$316$	41.8319			0.132379
$317$	−220.246			−0.694783			−0.347392	−	0.937720i	$-0.612933\pi$
$317$	−220.246			−0.694783			−0.347392	+	0.937720i	$0.612933\pi$
$318$	−53.5473	+	165.654i	−0.168388	+	0.520924i
$319$	−8.07849			−0.0253244
$320$		0			0
$321$	71.1057	−	219.972i	0.221513	−	0.685272i
$322$		−	0.523998i		−	0.00162732i
$323$	−30.9588			−0.0958478
$324$	50.9919	+	153.765i	0.157383	+	0.474585i
$325$		0			0
$326$			202.528i			0.621253i
$327$	136.667	−	422.792i	0.417941	−	1.29294i
$328$			194.659i			0.593472i
$329$			151.622i			0.460858i
$330$		0			0
$331$	533.158			1.61075			0.805375	−	0.592765i	$-0.201964\pi$
$331$	533.158			1.61075			0.805375	+	0.592765i	$0.201964\pi$
$332$	312.936			0.942579
$333$	204.574	−	283.371i	0.614338	−	0.850965i
$334$	190.034			0.568963
$335$		0			0
$336$	30.2099	+	9.76531i	0.0899105	+	0.0290634i
$337$			507.809i			1.50685i	0.657533	+	0.753425i	$0.271600\pi$
$337$			507.809i			1.50685i	−0.657533	+	0.753425i	$0.728400\pi$
$338$	352.985			1.04433
$339$	−80.2035	+	248.117i	−0.236588	+	0.731909i
$340$		0			0
$341$			136.282i			0.399653i
$342$	−64.2439	−	46.3797i	−0.187848	−	0.135613i
$343$			18.5203i			0.0539949i
$344$			57.4433i			0.166986i
$345$		0			0
$346$	383.472			1.10830
$347$	361.202			1.04093			0.520464	−	0.853883i	$-0.325759\pi$
$347$	361.202			1.04093			0.520464	+	0.853883i	$0.325759\pi$
$348$	10.0632	+	3.25292i	0.0289173	+	0.00934748i
$349$	−283.631			−0.812698			−0.406349	−	0.913718i	$-0.633198\pi$
$349$	−283.631			−0.812698			−0.406349	+	0.913718i	$0.633198\pi$
$350$		0			0
$351$	326.723	+	445.432i	0.930836	+	1.26904i
$352$			25.9262i			0.0736539i
$353$	54.6557			0.154832			0.0774161	−	0.996999i	$-0.475333\pi$
$353$	54.6557			0.154832			0.0774161	+	0.996999i	$0.475333\pi$
$354$	−320.741	−	103.679i	−0.906047	−	0.292878i
$355$		0			0
$356$		−	267.263i		−	0.750739i
$357$	37.5585	+	12.1407i	0.105206	+	0.0340077i
$358$		−	142.885i		−	0.399120i
$359$		−	74.6193i		−	0.207853i	−0.994585	−	0.103927i	$-0.966859\pi$
$359$		−	74.6193i		−	0.207853i	0.994585	−	0.103927i	$-0.0331407\pi$
$360$		0			0
$361$	−322.245			−0.892645
$362$	−346.841			−0.958124
$363$	−92.2687	+	285.442i	−0.254184	+	0.786342i
$364$	108.262			0.297424
$365$		0			0
$366$	−24.9370	+	77.1450i	−0.0681339	+	0.210779i
$367$		−	592.999i		−	1.61580i	−0.589318	−	0.807901i	$-0.700603\pi$
$367$		−	592.999i		−	1.61580i	0.589318	−	0.807901i	$-0.299397\pi$
$368$	−0.560178			−0.00152222
$369$	−362.557	+	502.204i	−0.982539	+	1.36099i
$370$		0			0
$371$			108.566i			0.292631i
$372$	54.8758	−	169.763i	0.147516	−	0.456353i
$373$			477.906i			1.28125i	0.767855	+	0.640624i	$0.221324\pi$
$373$			477.906i			1.28125i	−0.767855	+	0.640624i	$0.778676\pi$
$374$			32.2328i			0.0861838i
$375$		0			0
$376$	162.091			0.431093
$377$	36.0633			0.0956586
$378$	59.7511	+	81.4605i	0.158072	+	0.215504i
$379$	−155.751			−0.410952			−0.205476	−	0.978662i	$-0.565874\pi$
$379$	−155.751			−0.410952			−0.205476	+	0.978662i	$0.565874\pi$
$380$		0			0
$381$	697.612	+	225.502i	1.83100	+	0.591868i
$382$			47.9255i			0.125459i
$383$	−204.995			−0.535235			−0.267618	−	0.963525i	$-0.586236\pi$
$383$	−204.995			−0.535235			−0.267618	+	0.963525i	$0.586236\pi$
$384$	10.4396	−	32.2958i	0.0271863	−	0.0841035i
$385$		0			0
$386$			429.986i			1.11395i
$387$	−106.990	+	148.199i	−0.276459	+	0.382943i
$388$		−	40.3219i		−	0.103922i
$389$			161.706i			0.415696i	0.978161	+	0.207848i	$0.0666460\pi$
$389$			161.706i			0.415696i	−0.978161	+	0.207848i	$0.933354\pi$
$390$		0			0
$391$	−0.696442			−0.00178118
$392$	19.7990			0.0505076
$393$	738.099	+	238.589i	1.87812	+	0.607098i
$394$	−355.972			−0.903483
$395$		0			0
$396$	−48.2881	+	66.8875i	−0.121940	+	0.168908i
$397$			487.130i			1.22703i	0.789684	+	0.613514i	$0.210244\pi$
$397$			487.130i			1.22703i	−0.789684	+	0.613514i	$0.789756\pi$
$398$	−525.087			−1.31931
$399$	−47.0170	−	15.1982i	−0.117837	−	0.0380906i
$400$		0			0
$401$			504.622i			1.25841i	0.777240	+	0.629205i	$0.216619\pi$
$401$			504.622i			1.25841i	−0.777240	+	0.629205i	$0.783381\pi$
$402$	272.550	+	88.1012i	0.677984	+	0.219157i
$403$		−	608.376i		−	1.50962i
$404$			191.817i			0.474796i
$405$		0			0
$406$	6.59525			0.0162444
$407$	177.978			0.437293
$408$	12.9790	−	40.1518i	0.0318113	−	0.0984112i
$409$	93.2305			0.227947			0.113974	−	0.993484i	$-0.463642\pi$
$409$	93.2305			0.227947			0.113974	+	0.993484i	$0.463642\pi$
$410$		0			0
$411$	200.272	−	619.560i	0.487280	−	1.50745i
$412$		−	272.035i		−	0.660278i
$413$	−210.207			−0.508976
$414$	−1.44522	−	1.04335i	−0.00349086	−	0.00252016i
$415$		0			0
$416$		−	115.737i		−	0.278215i
$417$	−102.048	+	315.696i	−0.244720	+	0.757066i
$418$		−	40.3500i		−	0.0965311i
$419$			213.512i			0.509575i	0.966997	+	0.254787i	$0.0820055\pi$
$419$			213.512i			0.509575i	−0.966997	+	0.254787i	$0.917995\pi$
$420$		0			0
$421$	−415.349			−0.986578			−0.493289	−	0.869866i	$-0.664205\pi$
$421$	−415.349			−0.986578			−0.493289	+	0.869866i	$0.664205\pi$
$422$	−309.967			−0.734518
$423$	418.182	+	301.899i	0.988610	+	0.713708i
$424$	116.062			0.273732
$425$		0			0
$426$	124.725	+	40.3173i	0.292783	+	0.0946415i
$427$			50.5593i			0.118406i
$428$	−154.119			−0.360092
$429$	−86.5244	+	267.672i	−0.201689	+	0.623943i
$430$		0			0
$431$			375.874i			0.872098i	0.899923	+	0.436049i	$0.143623\pi$
$431$			375.874i			0.872098i	−0.899923	+	0.436049i	$0.856377\pi$
$432$	87.0849	−	63.8766i	0.201585	−	0.147862i
$433$		−	448.441i		−	1.03566i	−0.855483	−	0.517830i	$-0.826740\pi$
$433$		−	448.441i		−	1.03566i	0.855483	−	0.517830i	$-0.173260\pi$
$434$		−	111.260i		−	0.256359i
$435$		0			0
$436$	−296.221			−0.679406
$437$	0.871829			0.00199503
$438$	−449.422	−	145.275i	−1.02608	−	0.331678i
$439$	−409.075			−0.931833			−0.465916	−	0.884829i	$-0.654275\pi$
$439$	−409.075			−0.931833			−0.465916	+	0.884829i	$0.654275\pi$
$440$		0			0
$441$	51.0799	+	36.8761i	0.115827	+	0.0836193i
$442$		−	143.891i		−	0.325545i
$443$	−142.814			−0.322380			−0.161190	−	0.986923i	$-0.551533\pi$
$443$	−142.814			−0.322380			−0.161190	+	0.986923i	$0.551533\pi$
$444$	−221.705	−	71.6656i	−0.499335	−	0.161409i
$445$		0			0
$446$		−	317.100i		−	0.710986i
$447$	121.046	+	39.1278i	0.270796	+	0.0875343i
$448$		−	21.1660i		−	0.0472456i
$449$			435.581i			0.970114i	0.874483	+	0.485057i	$0.161201\pi$
$449$			435.581i			0.970114i	−0.874483	+	0.485057i	$0.838799\pi$
$450$		0			0
$451$	−315.422			−0.699384
$452$	173.839			0.384599
$453$	−98.0008	+	303.175i	−0.216337	+	0.669260i
$454$	546.327			1.20336
$455$		0			0
$456$	−16.2475	+	50.2633i	−0.0356305	+	0.110226i
$457$		−	403.048i		−	0.881943i	−0.897521	−	0.440972i	$-0.854634\pi$
$457$		−	403.048i		−	0.881943i	0.897521	−	0.440972i	$-0.145366\pi$
$458$	226.148			0.493773
$459$	108.268	−	79.4147i	0.235879	−	0.173017i
$460$		0			0
$461$		−	862.233i		−	1.87035i	−0.354181	−	0.935177i	$-0.615240\pi$
$461$		−	862.233i		−	1.87035i	0.354181	−	0.935177i	$-0.384760\pi$
$462$	−15.8236	+	48.9517i	−0.0342501	+	0.105956i
$463$		−	85.0507i		−	0.183695i	−0.995773	−	0.0918474i	$-0.970723\pi$
$463$		−	85.0507i		−	0.183695i	0.995773	−	0.0918474i	$-0.0292772\pi$
$464$		−	7.05061i		−	0.0151953i
$465$		0			0
$466$	403.423			0.865715
$467$	−509.615			−1.09125			−0.545627	−	0.838028i	$-0.683708\pi$
$467$	−509.615			−1.09125			−0.545627	+	0.838028i	$0.683708\pi$
$468$	215.564	−	298.593i	0.460606	−	0.638020i
$469$	178.624			0.380861
$470$		0			0
$471$	−304.076	−	98.2920i	−0.645596	−	0.208688i
$472$			224.721i			0.476104i
$473$	−93.0802			−0.196787
$474$	27.2941	−	84.4370i	0.0575826	−	0.178137i
$475$		0			0
$476$		−	26.3147i		−	0.0552830i
$477$	299.431	+	216.169i	0.627739	+	0.453184i
$478$			392.087i			0.820266i
$479$		−	207.378i		−	0.432940i	−0.976289	−	0.216470i	$-0.930546\pi$
$479$		−	207.378i		−	0.432940i	0.976289	−	0.216470i	$-0.0694543\pi$
$480$		0			0
$481$	−794.516			−1.65180
$482$	94.5537			0.196170
$483$	−1.05768	−	0.341894i	−0.00218982	−	0.000707856i
$484$	199.990			0.413202
$485$		0			0
$486$	343.644	−	2.59878i	0.707087	−	0.00534728i
$487$			28.4608i			0.0584411i	0.999573	+	0.0292206i	$0.00930252\pi$
$487$			28.4608i			0.0584411i	−0.999573	+	0.0292206i	$0.990697\pi$
$488$	54.0502			0.110759
$489$	408.801	+	132.144i	0.835993	+	0.270233i
$490$		0			0
$491$			757.575i			1.54292i	0.636277	+	0.771461i	$0.280474\pi$
$491$			757.575i			1.54292i	−0.636277	+	0.771461i	$0.719526\pi$
$492$	392.916	+	127.009i	0.798609	+	0.258149i
$493$		−	8.76569i		−	0.0177803i
$494$			180.127i			0.364630i
$495$		0			0
$496$	−118.942			−0.239802
$497$	81.7426			0.164472
$498$	204.182	−	631.657i	0.410004	−	1.26839i
$499$	165.989			0.332643			0.166322	−	0.986072i	$-0.446811\pi$
$499$	165.989			0.332643			0.166322	+	0.986072i	$0.446811\pi$
$500$		0			0
$501$	123.992	−	383.580i	0.247488	−	0.765629i
$502$			496.861i			0.989764i
$503$	−842.529			−1.67501			−0.837504	−	0.546431i	$-0.815986\pi$
$503$	−842.529			−1.67501			−0.837504	+	0.546431i	$0.815986\pi$
$504$	39.4222	−	54.6067i	0.0782187	−	0.108347i
$505$		0			0
$506$		−	0.907704i		−	0.00179388i
$507$	230.313	−	712.494i	0.454265	−	1.40531i
$508$		−	488.768i		−	0.962143i
$509$			119.739i			0.235244i	0.993058	+	0.117622i	$0.0375271\pi$
$509$			119.739i			0.235244i	−0.993058	+	0.117622i	$0.962473\pi$
$510$		0			0
$511$	−294.543			−0.576404
$512$	−22.6274			−0.0441942
$513$	−135.534	+	99.4139i	−0.264199	+	0.193789i
$514$	−184.905			−0.359737
$515$		0			0
$516$	115.948	+	37.4801i	0.224706	+	0.0726359i
$517$			262.650i			0.508027i
$518$	−145.301			−0.280504
$519$	250.205	−	774.032i	0.482090	−	1.49139i
$520$		0			0
$521$		−	320.580i		−	0.615316i	−0.951497	−	0.307658i	$-0.900455\pi$
$521$		−	320.580i		−	0.615316i	0.951497	−	0.307658i	$-0.0995452\pi$
$522$	13.1320	−	18.1900i	0.0251570	−	0.0348468i
$523$		−	341.396i		−	0.652764i	−0.945238	−	0.326382i	$-0.894170\pi$
$523$		−	341.396i		−	0.652764i	0.945238	−	0.326382i	$-0.105830\pi$
$524$		−	517.136i		−	0.986900i
$525$		0			0
$526$	259.503			0.493351
$527$	−147.874			−0.280597
$528$	52.3316	+	16.9161i	0.0991128	+	0.0320381i
$529$	−528.980			−0.999963
$530$		0			0
$531$	−418.548	+	579.762i	−0.788227	+	1.09183i
$532$			32.9416i			0.0619203i
$533$	1408.08			2.64180
$534$	−539.467	−	174.382i	−1.01024	−	0.326558i
$535$		0			0
$536$		−	190.957i		−	0.356263i
$537$	−288.411	−	93.2284i	−0.537079	−	0.173610i
$538$			249.401i			0.463570i
$539$			32.0820i			0.0595213i
$540$		0			0
$541$	−158.832			−0.293590			−0.146795	−	0.989167i	$-0.546896\pi$
$541$	−158.832			−0.293590			−0.146795	+	0.989167i	$0.546896\pi$
$542$	323.591			0.597031
$543$	−226.304	+	700.093i	−0.416766	+	1.28931i
$544$	−28.1316			−0.0517125
$545$		0			0
$546$	70.6382	−	218.526i	0.129374	−	0.400231i
$547$		−	350.423i		−	0.640628i	−0.947312	−	0.320314i	$-0.896212\pi$
$547$		−	350.423i		−	0.640628i	0.947312	−	0.320314i	$-0.103788\pi$
$548$	−434.083			−0.792123
$549$	139.445	+	100.670i	0.253999	+	0.183370i
$550$		0			0
$551$			10.9732i			0.0199150i
$552$	−0.365500	+	1.13071i	−0.000662138	+	0.00204839i
$553$		−	55.3384i		−	0.100069i
$554$			29.8909i			0.0539547i
$555$		0			0
$556$	221.187			0.397818
$557$	206.230			0.370251			0.185125	−	0.982715i	$-0.440731\pi$
$557$	206.230			0.370251			0.185125	+	0.982715i	$0.440731\pi$
$558$	−306.860	−	221.532i	−0.549928	−	0.397010i
$559$	415.521			0.743328
$560$		0			0
$561$	65.0613	+	21.0310i	0.115974	+	0.0374884i
$562$		−	621.301i		−	1.10552i
$563$	1075.62			1.91051			0.955253	−	0.295789i	$-0.0955826\pi$
$563$	1075.62			1.91051			0.955253	+	0.295789i	$0.0955826\pi$
$564$	105.760	−	327.178i	0.187517	−	0.580103i
$565$		0			0
$566$			108.666i			0.191990i
$567$	203.413	−	67.4560i	0.358752	−	0.118970i
$568$		−	87.3865i		−	0.153849i
$569$		−	969.357i		−	1.70362i	−0.523854	−	0.851808i	$-0.675506\pi$
$569$		−	969.357i		−	1.70362i	0.523854	−	0.851808i	$-0.324494\pi$
$570$		0			0
$571$	−961.564			−1.68400			−0.842000	−	0.539477i	$-0.818622\pi$
$571$	−961.564			−1.68400			−0.842000	+	0.539477i	$0.818622\pi$
$572$	187.539			0.327865
$573$	96.7369	+	31.2700i	0.168825	+	0.0545725i
$574$	257.509			0.448623
$575$		0			0
$576$	−58.3770	−	42.1441i	−0.101349	−	0.0731669i
$577$		−	985.988i		−	1.70882i	−0.519601	−	0.854409i	$-0.673920\pi$
$577$		−	985.988i		−	1.70882i	0.519601	−	0.854409i	$-0.326080\pi$
$578$	373.733			0.646597
$579$	867.920	+	280.554i	1.49900	+	0.484549i
$580$		0			0
$581$		−	413.976i		−	0.712523i
$582$	−81.3891	−	26.3089i	−0.139844	−	0.0452043i
$583$			188.065i			0.322582i
$584$			314.879i			0.539177i
$585$		0			0
$586$	360.843			0.615772
$587$	−665.664			−1.13401			−0.567005	−	0.823714i	$-0.691898\pi$
$587$	−665.664			−1.13401			−0.567005	+	0.823714i	$0.691898\pi$
$588$	12.9183	−	39.9640i	0.0219699	−	0.0679659i
$589$	185.114			0.314285
$590$		0			0
$591$	−232.262	+	718.525i	−0.392998	+	1.21578i
$592$			155.333i			0.262387i
$593$	−485.553			−0.818808			−0.409404	−	0.912353i	$-0.634263\pi$
$593$	−485.553			−0.818808			−0.409404	+	0.912353i	$0.634263\pi$
$594$	103.505	+	141.111i	0.174250	+	0.237561i
$595$		0			0
$596$		−	84.8084i		−	0.142296i
$597$	−342.604	+	1059.88i	−0.573876	+	1.77534i
$598$			4.05209i			0.00677608i
$599$		−	701.599i		−	1.17128i	−0.810570	−	0.585642i	$-0.800842\pi$
$599$		−	701.599i		−	1.17128i	0.810570	−	0.585642i	$-0.199158\pi$
$600$		0			0
$601$	63.1246			0.105033			0.0525163	−	0.998620i	$-0.483276\pi$
$601$	63.1246			0.105033			0.0525163	+	0.998620i	$0.483276\pi$
$602$	75.9903			0.126230
$603$	355.662	−	492.654i	0.589821	−	0.817004i
$604$	212.414			0.351678
$605$		0			0
$606$	387.181	+	125.156i	0.638912	+	0.206527i
$607$			234.302i			0.386001i	0.981199	+	0.193000i	$0.0618218\pi$
$607$			234.302i			0.386001i	−0.981199	+	0.193000i	$0.938178\pi$
$608$	35.2160			0.0579211
$609$	4.30321	−	13.3124i	0.00706603	−	0.0218594i
$610$		0			0
$611$		−	1172.50i		−	1.91898i
$612$	−72.5773	−	52.3958i	−0.118590	−	0.0856141i
$613$		−	15.8710i		−	0.0258908i	−0.999916	−	0.0129454i	$-0.995879\pi$
$613$		−	15.8710i		−	0.0258908i	0.999916	−	0.0129454i	$-0.00412076\pi$
$614$		−	229.842i		−	0.374335i
$615$		0			0
$616$	34.2971			0.0556771
$617$	−307.663			−0.498644			−0.249322	−	0.968421i	$-0.580208\pi$
$617$	−307.663			−0.498644			−0.249322	+	0.968421i	$0.580208\pi$
$618$	−549.098	−	177.495i	−0.888508	−	0.287209i
$619$	−0.497116			−0.000803095			−0.000401548	−	1.00000i	$-0.500128\pi$
$619$	−0.497116			−0.000803095			−0.000401548		1.00000i	$0.500128\pi$
$620$		0			0
$621$	−3.04894	+	2.23639i	−0.00490973	+	0.00360127i
$622$		−	185.208i		−	0.297762i
$623$	−353.556			−0.567506
$624$	−233.614	−	75.5154i	−0.374381	−	0.121018i
$625$		0			0
$626$		−	291.703i		−	0.465979i
$627$	−81.4459	−	26.3272i	−0.129898	−	0.0419892i
$628$			213.045i			0.339244i
$629$			193.118i			0.307024i
$630$		0			0
$631$	414.758			0.657302			0.328651	−	0.944451i	$-0.393406\pi$
$631$	414.758			0.657302			0.328651	+	0.944451i	$0.393406\pi$
$632$	−59.1592			−0.0936064
$633$	−202.245	+	625.663i	−0.319502	+	0.988409i
$634$	311.475			0.491286
$635$		0			0
$636$	75.7273	−	234.270i	0.119068	−	0.368349i
$637$		−	143.218i		−	0.224831i
$638$	11.4247			0.0179071
$639$	162.760	−	225.450i	0.254710	−	0.352818i
$640$		0			0
$641$			636.221i			0.992544i	0.868167	+	0.496272i	$0.165298\pi$
$641$			636.221i			0.992544i	−0.868167	+	0.496272i	$0.834702\pi$
$642$	−100.559	+	311.088i	−0.156633	+	0.484560i
$643$			556.821i			0.865974i	0.901400	+	0.432987i	$0.142540\pi$
$643$			556.821i			0.865974i	−0.901400	+	0.432987i	$0.857460\pi$
$644$			0.741046i			0.00115069i
$645$		0			0
$646$	43.7824			0.0677746
$647$	−528.501			−0.816848			−0.408424	−	0.912792i	$-0.633922\pi$
$647$	−528.501			−0.816848			−0.408424	+	0.912792i	$0.633922\pi$
$648$	−72.1135	−	217.457i	−0.111286	−	0.335582i
$649$	−364.134			−0.561070
$650$		0			0
$651$	−224.576	−	72.5938i	−0.344971	−	0.111511i
$652$		−	286.418i		−	0.439292i
$653$	−476.577			−0.729826			−0.364913	−	0.931042i	$-0.618901\pi$
$653$	−476.577			−0.729826			−0.364913	+	0.931042i	$0.618901\pi$
$654$	−193.276	+	597.918i	−0.295529	+	0.914248i
$655$		0			0
$656$		−	275.289i		−	0.419648i
$657$	−586.471	+	812.364i	−0.892649	+	1.23647i
$658$		−	214.426i		−	0.325876i
$659$			247.290i			0.375250i	0.982241	+	0.187625i	$0.0600790\pi$
$659$			247.290i			0.375250i	−0.982241	+	0.187625i	$0.939921\pi$
$660$		0			0
$661$	72.2288			0.109272			0.0546360	−	0.998506i	$-0.482600\pi$
$661$	72.2288			0.109272			0.0546360	+	0.998506i	$0.482600\pi$
$662$	−754.000			−1.13897
$663$	−290.441	−	93.8846i	−0.438071	−	0.141606i
$664$	−442.559			−0.666504
$665$		0			0
$666$	−289.312	+	400.747i	−0.434402	+	0.601723i
$667$			0.246850i			0.000370090i
$668$	−268.748			−0.402318
$669$	−640.061	−	206.899i	−0.956743	−	0.309266i
$670$		0			0
$671$			87.5821i			0.130525i
$672$	−42.7233	−	13.8102i	−0.0635763	−	0.0205509i
$673$			309.647i			0.460099i	0.973179	+	0.230050i	$0.0738889\pi$
$673$			309.647i			0.460099i	−0.973179	+	0.230050i	$0.926111\pi$
$674$		−	718.150i		−	1.06550i
$675$		0			0
$676$	−499.196			−0.738455
$677$	−155.619			−0.229866			−0.114933	−	0.993373i	$-0.536665\pi$
$677$	−155.619			−0.229866			−0.114933	+	0.993373i	$0.536665\pi$
$678$	113.425	−	350.891i	0.167293	−	0.517538i
$679$	−53.3408			−0.0785579
$680$		0			0
$681$	356.463	−	1102.75i	0.523441	−	1.61931i
$682$		−	192.731i		−	0.282597i
$683$	625.573			0.915919			0.457960	−	0.888973i	$-0.348580\pi$
$683$	625.573			0.915919			0.457960	+	0.888973i	$0.348580\pi$
$684$	90.8546	+	65.5908i	0.132828	+	0.0958929i
$685$		0			0
$686$		−	26.1916i		−	0.0381802i
$687$	147.555	−	456.476i	0.214782	−	0.664448i
$688$		−	81.2370i		−	0.118077i
$689$		−	839.545i		−	1.21850i
$690$		0			0
$691$	186.932			0.270523			0.135262	−	0.990810i	$-0.456812\pi$
$691$	186.932			0.270523			0.135262	+	0.990810i	$0.456812\pi$
$692$	−542.311			−0.783686
$693$	88.4838	+	63.8792i	0.127682	+	0.0921778i
$694$	−510.817			−0.736048
$695$		0			0
$696$	−14.2316	−	4.60033i	−0.0204476	−	0.00660967i
$697$		−	342.254i		−	0.491038i
$698$	401.115			0.574664
$699$	263.222	−	814.304i	0.376570	−	1.16496i
$700$		0			0
$701$			20.0020i			0.0285336i	0.999898	+	0.0142668i	$0.00454141\pi$
$701$			20.0020i			0.0285336i	−0.999898	+	0.0142668i	$0.995459\pi$
$702$	−462.057	−	629.936i	−0.658200	−	0.897345i
$703$		−	241.752i		−	0.343886i
$704$		−	36.6651i		−	0.0520811i
$705$		0			0
$706$	−77.2949			−0.109483
$707$	253.751			0.358912
$708$	453.596	+	146.624i	0.640672	+	0.207096i
$709$	−168.823			−0.238114			−0.119057	−	0.992887i	$-0.537987\pi$
$709$	−168.823			−0.238114			−0.119057	+	0.992887i	$0.537987\pi$
$710$		0			0
$711$	−152.626	−	110.186i	−0.214664	−	0.154973i
$712$			377.967i			0.530853i
$713$	4.16428			0.00584050
$714$	−53.1158	−	17.1696i	−0.0743919	−	0.0240471i
$715$		0			0
$716$			202.070i			0.282221i
$717$	791.422	+	255.826i	1.10380	+	0.356800i
$718$			105.528i			0.146974i
$719$		−	244.215i		−	0.339659i	−0.985473	−	0.169830i	$-0.945678\pi$
$719$		−	244.215i		−	0.339659i	0.985473	−	0.169830i	$-0.0543217\pi$
$720$		0			0
$721$	−359.868			−0.499124
$722$	455.723			0.631195
$723$	61.6936	−	190.855i	0.0853301	−	0.263977i
$724$	490.507			0.677496
$725$		0			0
$726$	130.488	−	403.676i	0.179735	−	0.556028i
$727$			187.393i			0.257762i	0.991660	+	0.128881i	$0.0411386\pi$
$727$			187.393i			0.257762i	−0.991660	+	0.128881i	$0.958861\pi$
$728$	−153.106			−0.210311
$729$	218.973	−	695.336i	0.300374	−	0.953822i
$730$		0			0
$731$		−	100.998i		−	0.138164i
$732$	35.2662	−	109.100i	0.0481779	−	0.149043i
$733$			771.777i			1.05290i	0.850206	+	0.526451i	$0.176478\pi$
$733$			771.777i			1.05290i	−0.850206	+	0.526451i	$0.823522\pi$
$734$			838.628i			1.14254i
$735$		0			0
$736$	0.792211			0.00107637
$737$	309.423			0.419842
$738$	512.733	−	710.224i	0.694760	−	0.962364i
$739$	−534.142			−0.722791			−0.361395	−	0.932413i	$-0.617699\pi$
$739$	−534.142			−0.722791			−0.361395	+	0.932413i	$0.617699\pi$
$740$		0			0
$741$	363.584	+	117.528i	0.490666	+	0.158607i
$742$		−	153.536i		−	0.206922i
$743$	983.813			1.32411			0.662054	−	0.749456i	$-0.269685\pi$
$743$	983.813			1.32411			0.662054	+	0.749456i	$0.269685\pi$
$744$	−77.6061	+	240.082i	−0.104309	+	0.322691i
$745$		0			0
$746$		−	675.860i		−	0.905979i
$747$	−1141.77	−	824.277i	−1.52847	−	1.10345i
$748$		−	45.5840i		−	0.0609412i
$749$			203.881i			0.272204i
$750$		0			0
$751$	261.058			0.347614			0.173807	−	0.984780i	$-0.444393\pi$
$751$	261.058			0.347614			0.173807	+	0.984780i	$0.444393\pi$
$752$	−229.231			−0.304829
$753$	1002.91	+	324.188i	1.33188	+	0.430529i
$754$	−51.0012			−0.0676409
$755$		0			0
$756$	−84.5008	−	115.202i	−0.111774	−	0.152384i
$757$			870.719i			1.15022i	0.818075	+	0.575111i	$0.195041\pi$
$757$			870.719i			1.15022i	−0.818075	+	0.575111i	$0.804959\pi$
$758$	220.265			0.290587
$759$	−1.83219	−	0.592251i	−0.00241395	−	0.000780305i
$760$		0			0
$761$			497.495i			0.653739i	0.945070	+	0.326869i	$0.105994\pi$
$761$			497.495i			0.653739i	−0.945070	+	0.326869i	$0.894006\pi$
$762$	−986.572	−	318.908i	−1.29471	−	0.418514i
$763$			391.864i			0.513583i
$764$		−	67.7769i		−	0.0887132i
$765$		0			0
$766$	289.907			0.378469
$767$	1625.54			2.11934
$768$	−14.7638	+	45.6731i	−0.0192236	+	0.0594702i
$769$	−1119.67			−1.45601			−0.728003	−	0.685574i	$-0.759551\pi$
$769$	−1119.67			−1.45601			−0.728003	+	0.685574i	$0.759551\pi$
$770$		0			0
$771$	−120.645	+	373.227i	−0.156479	+	0.484082i
$772$		−	608.092i		−	0.787684i
$773$	1029.28			1.33154			0.665768	−	0.746159i	$-0.268104\pi$
$773$	1029.28			1.33154			0.665768	+	0.746159i	$0.268104\pi$
$774$	151.306	−	209.585i	0.195486	−	0.270782i
$775$		0			0
$776$			57.0237i			0.0734842i
$777$	−94.8047	+	293.288i	−0.122014	+	0.377461i
$778$		−	228.687i		−	0.293942i
$779$			428.444i			0.549993i
$780$		0			0
$781$	141.600			0.181306
$782$	0.984918			0.00125949
$783$	−28.1481	−	38.3751i	−0.0359490	−	0.0490104i
$784$	−28.0000			−0.0357143
$785$		0			0
$786$	−1043.83	−	337.416i	−1.32803	−	0.429283i
$787$		−	180.973i		−	0.229953i	−0.993368	−	0.114977i	$-0.963321\pi$
$787$		−	180.973i		−	0.229953i	0.993368	−	0.114977i	$-0.0366793\pi$
$788$	503.421			0.638859
$789$	169.318	−	523.802i	0.214599	−	0.663881i
$790$		0			0
$791$		−	229.967i		−	0.290729i
$792$	68.2897	−	94.5932i	0.0862244	−	0.119436i
$793$		−	390.977i		−	0.493035i
$794$		−	688.906i		−	0.867639i
$795$		0			0
$796$	742.584			0.932895
$797$	1063.75			1.33469			0.667343	−	0.744750i	$-0.267431\pi$
$797$	1063.75			1.33469			0.667343	+	0.744750i	$0.267431\pi$
$798$	66.4921	+	21.4935i	0.0833234	+	0.0269342i
$799$	−284.992			−0.356686
$800$		0			0
$801$	−703.974	+	975.126i	−0.878869	+	1.21739i
$802$		−	713.643i		−	0.889830i
$803$	−510.226			−0.635399
$804$	−385.443	−	124.594i	−0.479407	−	0.154968i
$805$		0			0
$806$			860.374i			1.06746i
$807$	503.412	+	162.727i	0.623806	+	0.201644i
$808$		−	271.271i		−	0.335731i
$809$			652.710i			0.806811i	0.915021	+	0.403406i	$0.132174\pi$
$809$			652.710i			0.806811i	−0.915021	+	0.403406i	$0.867826\pi$
$810$		0			0
$811$	188.572			0.232518			0.116259	−	0.993219i	$-0.462910\pi$
$811$	188.572			0.232518			0.116259	+	0.993219i	$0.462910\pi$
$812$	−9.32709			−0.0114866
$813$	211.134	−	653.163i	0.259697	−	0.803398i
$814$	−251.700			−0.309213
$815$		0			0
$816$	−18.3551	+	56.7832i	−0.0224940	+	0.0695872i
$817$			126.433i			0.154752i
$818$	−131.848			−0.161183
$819$	−395.002	−	285.164i	−0.482298	−	0.348186i
$820$		0			0
$821$		−	1051.42i		−	1.28066i	−0.768099	−	0.640332i	$-0.778797\pi$
$821$		−	1051.42i		−	1.28066i	0.768099	−	0.640332i	$-0.221203\pi$
$822$	−283.227	+	876.191i	−0.344559	+	1.06593i
$823$			296.725i			0.360541i	0.983617	+	0.180271i	$0.0576973\pi$
$823$			296.725i			0.360541i	−0.983617	+	0.180271i	$0.942303\pi$
$824$			384.715i			0.466887i
$825$		0			0
$826$	297.278			0.359900
$827$	483.556			0.584711			0.292355	−	0.956310i	$-0.405561\pi$
$827$	483.556			0.584711			0.292355	+	0.956310i	$0.405561\pi$
$828$	2.04384	+	1.47551i	0.00246841	+	0.00178202i
$829$	−1009.43			−1.21765			−0.608826	−	0.793303i	$-0.708359\pi$
$829$	−1009.43			−1.21765			−0.608826	+	0.793303i	$0.708359\pi$
$830$		0			0
$831$	60.3343	+	19.5030i	0.0726045	+	0.0234693i
$832$			163.677i			0.196728i
$833$	−34.8111			−0.0417900
$834$	144.318	−	446.462i	0.173043	−	0.535326i
$835$		0			0
$836$			57.0635i			0.0682578i
$837$	−647.376	+	474.849i	−0.773448	+	0.567323i
$838$		−	301.951i		−	0.360324i
$839$		−	402.644i		−	0.479909i	−0.970784	−	0.239954i	$-0.922868\pi$
$839$		−	402.644i		−	0.479909i	0.970784	−	0.239954i	$-0.0771325\pi$
$840$		0			0
$841$	837.893			0.996306
$842$	587.393			0.697616
$843$	−1254.09	−	405.381i	−1.48765	−	0.480879i
$844$	438.359			0.519383
$845$		0			0
$846$	−591.399	−	426.949i	−0.699053	−	0.504668i
$847$		−	264.561i		−	0.312351i
$848$	−164.137			−0.193557
$849$	219.342	+	70.9018i	0.258353	+	0.0835121i
$850$		0			0
$851$		−	5.43839i		−	0.00639058i
$852$	−176.388	−	57.0172i	−0.207029	−	0.0669217i
$853$			544.670i			0.638534i	0.947665	+	0.319267i	$0.103437\pi$
$853$			544.670i			0.638534i	−0.947665	+	0.319267i	$0.896563\pi$
$854$		−	71.5017i		−	0.0837256i
$855$		0			0
$856$	217.958			0.254624
$857$	1535.83			1.79210			0.896051	−	0.443951i	$-0.146423\pi$
$857$	1535.83			1.79210			0.896051	+	0.443951i	$0.146423\pi$
$858$	122.364	−	378.545i	0.142615	−	0.441194i
$859$	710.763			0.827430			0.413715	−	0.910406i	$-0.364231\pi$
$859$	710.763			0.827430			0.413715	+	0.910406i	$0.364231\pi$
$860$		0			0
$861$	168.018	−	519.779i	0.195142	−	0.603692i
$862$		−	531.566i		−	0.616666i
$863$	746.122			0.864568			0.432284	−	0.901738i	$-0.357708\pi$
$863$	746.122			0.864568			0.432284	+	0.901738i	$0.357708\pi$
$864$	−123.157	+	90.3352i	−0.142542	+	0.104555i
$865$		0			0
$866$			634.191i			0.732322i
$867$	243.850	−	754.374i	0.281258	−	0.870097i
$868$			157.345i			0.181273i
$869$		−	95.8607i		−	0.110312i
$870$		0			0
$871$	−1381.30			−1.58588
$872$	418.920			0.480413
$873$	−106.208	+	147.117i	−0.121659	+	0.168519i
$874$	−1.23295			−0.00141070
$875$		0			0
$876$	635.579	+	205.450i	0.725547	+	0.234532i
$877$			1221.75i			1.39310i	0.717506	+	0.696552i	$0.245284\pi$
$877$			1221.75i			1.39310i	−0.717506	+	0.696552i	$0.754716\pi$
$878$	578.519			0.658905
$879$	235.440	−	728.355i	0.267849	−	0.828618i
$880$		0			0
$881$		−	213.476i		−	0.242311i	−0.992634	−	0.121155i	$-0.961340\pi$
$881$		−	213.476i		−	0.242311i	0.992634	−	0.121155i	$-0.0386599\pi$
$882$	−72.2378	−	52.1507i	−0.0819023	−	0.0591278i
$883$		−	1084.76i		−	1.22850i	−0.789112	−	0.614249i	$-0.789459\pi$
$883$		−	1084.76i		−	1.22850i	0.789112	−	0.614249i	$-0.210541\pi$
$884$			203.492i			0.230195i
$885$		0			0
$886$	201.970			0.227957
$887$	167.255			0.188563			0.0942813	−	0.995546i	$-0.469945\pi$
$887$	167.255			0.188563			0.0942813	+	0.995546i	$0.469945\pi$
$888$	313.538	+	101.351i	0.353083	+	0.114133i
$889$	−646.580			−0.727311
$890$		0			0
$891$	352.364	−	116.852i	0.395471	−	0.131147i
$892$			448.447i			0.502743i
$893$	356.762			0.399510
$894$	−171.184	−	55.3351i	−0.191481	−	0.0618961i
$895$		0			0
$896$			29.9333i			0.0334077i
$897$	8.17909	+	2.64388i	0.00911827	+	0.00294747i
$898$		−	616.005i		−	0.685974i
$899$			52.4132i			0.0583017i
$900$		0			0
$901$	−204.063			−0.226485
$902$	446.074			0.494539
$903$	49.5815	−	153.385i	0.0549076	−	0.169862i
$904$	−245.845			−0.271952
$905$		0			0
$906$	138.594	−	428.754i	0.152974	−	0.473238i
$907$		−	660.255i		−	0.727955i	−0.931408	−	0.363977i	$-0.881419\pi$
$907$		−	660.255i		−	0.727955i	0.931408	−	0.363977i	$-0.118581\pi$
$908$	−772.623			−0.850907
$909$	505.249	−	699.858i	0.555829	−	0.769920i
$910$		0			0
$911$			1120.41i			1.22987i	0.788577	+	0.614936i	$0.210818\pi$
$911$			1120.41i			1.22987i	−0.788577	+	0.614936i	$0.789182\pi$
$912$	22.9775	−	71.0830i	0.0251946	−	0.0779419i
$913$		−	717.115i		−	0.785449i
$914$			569.996i			0.623628i
$915$		0			0
$916$	−319.821			−0.349150
$917$	−684.106			−0.746026
$918$	−153.115	+	112.309i	−0.166792	+	0.122341i
$919$	470.684			0.512170			0.256085	−	0.966654i	$-0.417567\pi$
$919$	470.684			0.512170			0.256085	+	0.966654i	$0.417567\pi$
$920$		0			0
$921$	−463.932	−	149.965i	−0.503726	−	0.162829i
$922$			1219.38i			1.32254i
$923$	−632.118			−0.684851
$924$	22.3779	−	69.2281i	0.0242185	−	0.0749222i
$925$		0			0
$926$			120.280i			0.129892i
$927$	−716.542	+	992.535i	−0.772969	+	1.07070i
$928$			9.97107i			0.0107447i
$929$			121.743i			0.131048i	0.997851	+	0.0655238i	$0.0208718\pi$
$929$			121.743i			0.131048i	−0.997851	+	0.0655238i	$0.979128\pi$
$930$		0			0
$931$	43.5776			0.0468073
$932$	−570.527			−0.612153
$933$	−373.840	−	120.843i	−0.400686	−	0.129521i
$934$	720.705			0.771632
$935$		0			0
$936$	−304.853	+	422.275i	−0.325698	+	0.451148i
$937$			1283.85i			1.37017i	0.728462	+	0.685087i	$0.240236\pi$
$937$			1283.85i			1.37017i	−0.728462	+	0.685087i	$0.759764\pi$
$938$	−252.612			−0.269309
$939$	−588.798	−	190.328i	−0.627048	−	0.202692i
$940$		0			0
$941$			385.136i			0.409283i	0.978837	+	0.204642i	$0.0656029\pi$
$941$			385.136i			0.409283i	−0.978837	+	0.204642i	$0.934397\pi$
$942$	430.028	+	139.006i	0.456505	+	0.147565i
$943$			9.63818i			0.0102208i
$944$		−	317.803i		−	0.336656i
$945$		0			0
$946$	131.635			0.139149
$947$	−880.115			−0.929372			−0.464686	−	0.885476i	$-0.653833\pi$
$947$	−880.115			−0.929372			−0.464686	+	0.885476i	$0.653833\pi$
$948$	−38.5997	+	119.412i	−0.0407170	+	0.125962i
$949$	2277.70			2.40011
$950$		0			0
$951$	203.229	−	628.708i	0.213700	−	0.661102i
$952$			37.2146i			0.0390910i
$953$	974.386			1.02244			0.511220	−	0.859450i	$-0.329194\pi$
$953$	974.386			1.02244			0.511220	+	0.859450i	$0.329194\pi$
$954$	−423.460	−	305.709i	−0.443878	−	0.320449i
$955$		0			0
$956$		−	554.495i		−	0.580015i
$957$	7.45430	−	23.0606i	0.00778924	−	0.0240968i
$958$			293.277i			0.306135i
$959$			574.238i			0.598789i
$960$		0			0
$961$	−76.8058			−0.0799228
$962$	1123.62			1.16800
$963$	562.314	+	405.952i	0.583919	+	0.421549i
$964$	−133.719			−0.138713
$965$		0			0
$966$	1.49579	+	0.483512i	0.00154844	+	0.000500530i
$967$			848.123i			0.877066i	0.898715	+	0.438533i	$0.144502\pi$
$967$			848.123i			0.877066i	−0.898715	+	0.438533i	$0.855498\pi$
$968$	−282.828			−0.292178
$969$	28.5668	−	88.3741i	0.0294807	−	0.0912013i
$970$		0			0
$971$		−	591.259i		−	0.608917i	−0.952526	−	0.304459i	$-0.901524\pi$
$971$		−	591.259i		−	0.608917i	0.952526	−	0.304459i	$-0.0984755\pi$
$972$	−485.986	+	3.67523i	−0.499986	+	0.00378110i
$973$		−	292.603i		−	0.300722i
$974$		−	40.2497i		−	0.0413241i
$975$		0			0
$976$	−76.4385			−0.0783182
$977$	618.460			0.633020			0.316510	−	0.948589i	$-0.397489\pi$
$977$	618.460			0.633020			0.316510	+	0.948589i	$0.397489\pi$
$978$	−578.131	−	186.880i	−0.591136	−	0.191084i
$979$	−612.453			−0.625590
$980$		0			0
$981$	1080.78	+	780.249i	1.10171	+	0.795361i
$982$		−	1071.37i		−	1.09101i
$983$	1865.84			1.89811			0.949053	−	0.315118i	$-0.102044\pi$
$983$	1865.84			1.89811			0.949053	+	0.315118i	$0.102044\pi$
$984$	−555.667	−	179.618i	−0.564702	−	0.182539i
$985$		0			0
$986$			12.3966i			0.0125726i
$987$	−432.816	−	139.907i	−0.438517	−	0.141750i
$988$		−	254.738i		−	0.257832i
$989$			2.84420i			0.00287583i
$990$		0			0
$991$	659.640			0.665631			0.332816	−	0.942992i	$-0.392001\pi$
$991$	659.640			0.665631			0.332816	+	0.942992i	$0.392001\pi$
$992$	168.209			0.169565
$993$	−491.964	+	1521.94i	−0.495432	+	1.53267i
$994$	−115.601			−0.116299
$995$		0			0
$996$	−288.757	+	893.298i	−0.289917	+	0.896885i
$997$			1049.99i			1.05315i	0.850129	+	0.526575i	$0.176524\pi$
$997$			1049.99i			1.05315i	−0.850129	+	0.526575i	$0.823476\pi$
$998$	−234.744			−0.235214
$999$	620.135	+	845.448i	0.620755	+	0.846294i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.c.c.449.10		32
3.2	odd	2	inner	1050.3.c.c.449.24		32
5.2	odd	4		210.3.e.a.71.8	✓	16
5.3	odd	4		1050.3.e.d.701.9		16
5.4	even	2	inner	1050.3.c.c.449.23		32
15.2	even	4		210.3.e.a.71.16	yes	16
15.8	even	4		1050.3.e.d.701.1		16
15.14	odd	2	inner	1050.3.c.c.449.9		32
20.7	even	4		1680.3.l.c.1121.1		16
60.47	odd	4		1680.3.l.c.1121.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.e.a.71.8	✓	16	5.2	odd	4
210.3.e.a.71.16	yes	16	15.2	even	4
1050.3.c.c.449.9		32	15.14	odd	2	inner
1050.3.c.c.449.10		32	1.1	even	1	trivial
1050.3.c.c.449.23		32	5.4	even	2	inner
1050.3.c.c.449.24		32	3.2	odd	2	inner
1050.3.e.d.701.1		16	15.8	even	4
1050.3.e.d.701.9		16	5.3	odd	4
1680.3.l.c.1121.1		16	20.7	even	4
1680.3.l.c.1121.2		16	60.47	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)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +(-0.922735 + 2.85457i) q^{3} +2.00000 q^{4} +(1.30494 - 4.03697i) q^{6} -2.64575i q^{7} -2.82843 q^{8} +(-7.29712 - 5.26802i) q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +(-0.922735 + 2.85457i) q^{3} +2.00000 q^{4} +(1.30494 - 4.03697i) q^{6} -2.64575i q^{7} -2.82843 q^{8} +(-7.29712 - 5.26802i) q^{9} -4.58314i q^{11} +(-1.84547 + 5.70914i) q^{12} +20.4597i q^{13} +3.74166i q^{14} +4.00000 q^{16} +4.97301 q^{17} +(10.3197 + 7.45010i) q^{18} -6.22537 q^{19} +(7.55248 + 2.44133i) q^{21} +6.48154i q^{22} -0.140044 q^{23} +(2.60989 - 8.07394i) q^{24} -28.9343i q^{26} +(21.7712 - 15.9691i) q^{27} -5.29150i q^{28} -1.76265i q^{29} -29.7354 q^{31} -5.65685 q^{32} +(13.0829 + 4.22902i) q^{33} -7.03290 q^{34} +(-14.5942 - 10.5360i) q^{36} +38.8333i q^{37} +8.80401 q^{38} +(-58.4035 - 18.8788i) q^{39} -68.8223i q^{41} +(-10.6808 - 3.45256i) q^{42} -20.3093i q^{43} -9.16628i q^{44} +0.198053 q^{46} -57.3078 q^{47} +(-3.69094 + 11.4183i) q^{48} -7.00000 q^{49} +(-4.58877 + 14.1958i) q^{51} +40.9193i q^{52} -41.0342 q^{53} +(-30.7892 + 22.5838i) q^{54} +7.48331i q^{56} +(5.74437 - 17.7708i) q^{57} +2.49277i q^{58} -79.4508i q^{59} -19.1096 q^{61} +42.0522 q^{62} +(-13.9379 + 19.3064i) q^{63} +8.00000 q^{64} +(-18.5020 - 5.98074i) q^{66} +67.5134i q^{67} +9.94602 q^{68} +(0.129224 - 0.399767i) q^{69} +30.8958i q^{71} +(20.6394 + 14.9002i) q^{72} -111.327i q^{73} -54.9186i q^{74} -12.4507 q^{76} -12.1259 q^{77} +(82.5950 + 26.6987i) q^{78} +20.9159 q^{79} +(25.4960 + 76.8827i) q^{81} +97.3294i q^{82} +156.468 q^{83} +(15.1050 + 4.88265i) q^{84} +28.7216i q^{86} +(5.03162 + 1.62646i) q^{87} +12.9631i q^{88} -133.632i q^{89} +54.1312 q^{91} -0.280089 q^{92} +(27.4379 - 84.8817i) q^{93} +81.0455 q^{94} +(5.21978 - 16.1479i) q^{96} -20.1609i q^{97} +9.89949 q^{98} +(-24.1441 + 33.4437i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9}+O(q^{10}) \) 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9	\( 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9} + 128 q^{16} - 96 q^{19} + 56 q^{21} + 64 q^{24} - 320 q^{34} + 16 q^{36} - 312 q^{39} + 64 q^{46} - 224 q^{49} + 168 q^{51} + 64 q^{54} + 224 q^{61} + 256 q^{64} - 16 q^{69} - 192 q^{76} - 16 q^{79} - 248 q^{81} + 112 q^{84} - 112 q^{91} - 64 q^{94} + 128 q^{96} + 104 q^{99}+O(q^{100}) \) 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9 + 128 * q^16 - 96 * q^19 + 56 * q^21 + 64 * q^24 - 320 * q^34 + 16 * q^36 - 312 * q^39 + 64 * q^46 - 224 * q^49 + 168 * q^51 + 64 * q^54 + 224 * q^61 + 256 * q^64 - 16 * q^69 - 192 * q^76 - 16 * q^79 - 248 * q^81 + 112 * q^84 - 112 * q^91 - 64 * q^94 + 128 * q^96 + 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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