LMFDB - Embedded newform 1050.3.e.e.701.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1050.701");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			701.15
Character	$\chi$	$=$	1050.701
Dual form			1050.3.e.e.701.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +(-0.554262 - 2.94835i) q^{3} -2.00000 q^{4} +(4.16960 - 0.783844i) q^{6} +2.64575 q^{7} -2.82843i q^{8} +(-8.38559 + 3.26832i) q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +(-0.554262 - 2.94835i) q^{3} -2.00000 q^{4} +(4.16960 - 0.783844i) q^{6} +2.64575 q^{7} -2.82843i q^{8} +(-8.38559 + 3.26832i) q^{9} +2.58444i q^{11} +(1.10852 + 5.89671i) q^{12} -0.180526 q^{13} +3.74166i q^{14} +4.00000 q^{16} +7.25119i q^{17} +(-4.62210 - 11.8590i) q^{18} +21.4338 q^{19} +(-1.46644 - 7.80061i) q^{21} -3.65495 q^{22} -11.8858i q^{23} +(-8.33921 + 1.56769i) q^{24} -0.255303i q^{26} +(14.2840 + 22.9122i) q^{27} -5.29150 q^{28} +29.5458i q^{29} -49.5193 q^{31} +5.65685i q^{32} +(7.61985 - 1.43246i) q^{33} -10.2547 q^{34} +(16.7712 - 6.53664i) q^{36} +43.2958 q^{37} +30.3120i q^{38} +(0.100059 + 0.532256i) q^{39} -20.7847i q^{41} +(11.0317 - 2.07386i) q^{42} +74.2183 q^{43} -5.16888i q^{44} +16.8091 q^{46} +7.05106i q^{47} +(-2.21705 - 11.7934i) q^{48} +7.00000 q^{49} +(21.3791 - 4.01906i) q^{51} +0.361053 q^{52} +55.0572i q^{53} +(-32.4027 + 20.2006i) q^{54} -7.48331i q^{56} +(-11.8799 - 63.1944i) q^{57} -41.7841 q^{58} -100.110i q^{59} +8.44678 q^{61} -70.0309i q^{62} +(-22.1862 + 8.64716i) q^{63} -8.00000 q^{64} +(2.02580 + 10.7761i) q^{66} +85.7646 q^{67} -14.5024i q^{68} +(-35.0435 + 6.58784i) q^{69} -97.8086i q^{71} +(9.24420 + 23.7180i) q^{72} +17.8312 q^{73} +61.2295i q^{74} -42.8676 q^{76} +6.83779i q^{77} +(-0.752723 + 0.141505i) q^{78} +110.652 q^{79} +(59.6362 - 54.8136i) q^{81} +29.3940 q^{82} +3.08611i q^{83} +(2.93288 + 15.6012i) q^{84} +104.961i q^{86} +(87.1115 - 16.3761i) q^{87} +7.30991 q^{88} -80.1881i q^{89} -0.477628 q^{91} +23.7716i q^{92} +(27.4467 + 146.001i) q^{93} -9.97171 q^{94} +(16.6784 - 3.13538i) q^{96} +105.794 q^{97} +9.89949i q^{98} +(-8.44678 - 21.6721i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 48 q^{4} - 44 q^{9}+O(q^{10}) $ 24 * q - 48 * q^4 - 44 * q^9	$ 24 q - 48 q^{4} - 44 q^{9} + 96 q^{16} + 80 q^{19} - 28 q^{21} + 224 q^{31} - 128 q^{34} + 88 q^{36} + 92 q^{39} - 144 q^{46} + 168 q^{49} - 284 q^{51} + 144 q^{54} - 192 q^{64} + 224 q^{66} + 152 q^{69} - 160 q^{76} + 72 q^{79} - 212 q^{81} + 56 q^{84} + 168 q^{91} + 128 q^{94} + 876 q^{99}+O(q^{100}) $ 24 * q - 48 * q^4 - 44 * q^9 + 96 * q^16 + 80 * q^19 - 28 * q^21 + 224 * q^31 - 128 * q^34 + 88 * q^36 + 92 * q^39 - 144 * q^46 + 168 * q^49 - 284 * q^51 + 144 * q^54 - 192 * q^64 + 224 * q^66 + 152 * q^69 - 160 * q^76 + 72 * q^79 - 212 * q^81 + 56 * q^84 + 168 * q^91 + 128 * q^94 + 876 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$	−0.554262	−	2.94835i	−0.184754	−	0.982785i
$3$	−0.554262	−	2.94835i	−0.184754	−	0.982785i
$4$	−2.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	4.16960	−	0.783844i	0.694934	−	0.130641i
$7$	2.64575			0.377964
$7$	2.64575			0.377964
$8$		−	2.82843i		−	0.353553i
$9$	−8.38559	+	3.26832i	−0.931732	+	0.363147i
$10$		0			0
$11$			2.58444i			0.234949i	0.993076	+	0.117475i	$0.0374799\pi$
$11$			2.58444i			0.234949i	−0.993076	+	0.117475i	$0.962520\pi$
$12$	1.10852	+	5.89671i	0.0923769	+	0.491392i
$13$	−0.180526			−0.0138866			−0.00694332	−	0.999976i	$-0.502210\pi$
$13$	−0.180526			−0.0138866			−0.00694332	+	0.999976i	$0.502210\pi$
$14$			3.74166i			0.267261i
$15$		0			0
$16$	4.00000			0.250000
$17$			7.25119i			0.426541i	0.976993	+	0.213270i	$0.0684115\pi$
$17$			7.25119i			0.426541i	−0.976993	+	0.213270i	$0.931589\pi$
$18$	−4.62210	−	11.8590i	−0.256783	−	0.658834i
$19$	21.4338			1.12809			0.564047	−	0.825743i	$-0.309244\pi$
$19$	21.4338			1.12809			0.564047	+	0.825743i	$0.309244\pi$
$20$		0			0
$21$	−1.46644	−	7.80061i	−0.0698304	−	0.371458i
$22$	−3.65495			−0.166134
$23$		−	11.8858i		−	0.516774i	−0.966042	−	0.258387i	$-0.916809\pi$
$23$		−	11.8858i		−	0.516774i	0.966042	−	0.258387i	$-0.0831909\pi$
$24$	−8.33921	+	1.56769i	−0.347467	+	0.0653203i
$25$		0			0
$26$		−	0.255303i		−	0.00981934i
$27$	14.2840	+	22.9122i	0.529036	+	0.848599i
$28$	−5.29150			−0.188982
$29$			29.5458i			1.01882i	0.860524	+	0.509410i	$0.170136\pi$
$29$			29.5458i			1.01882i	−0.860524	+	0.509410i	$0.829864\pi$
$30$		0			0
$31$	−49.5193			−1.59740			−0.798699	−	0.601731i	$-0.794478\pi$
$31$	−49.5193			−1.59740			−0.798699	+	0.601731i	$0.794478\pi$
$32$			5.65685i			0.176777i
$33$	7.61985	−	1.43246i	0.230905	−	0.0434078i
$34$	−10.2547			−0.301610
$35$		0			0
$36$	16.7712	−	6.53664i	0.465866	−	0.181573i
$37$	43.2958			1.17016			0.585078	−	0.810977i	$-0.301064\pi$
$37$	43.2958			1.17016			0.585078	+	0.810977i	$0.301064\pi$
$38$			30.3120i			0.797683i
$39$	0.100059	+	0.532256i	0.00256561	+	0.0136476i
$40$		0			0
$41$		−	20.7847i		−	0.506944i	−0.967343	−	0.253472i	$-0.918427\pi$
$41$		−	20.7847i		−	0.506944i	0.967343	−	0.253472i	$-0.0815726\pi$
$42$	11.0317	−	2.07386i	0.262660	−	0.0493775i
$43$	74.2183			1.72601			0.863004	−	0.505197i	$-0.168580\pi$
$43$	74.2183			1.72601			0.863004	+	0.505197i	$0.168580\pi$
$44$		−	5.16888i		−	0.117475i
$45$		0			0
$46$	16.8091			0.365414
$47$			7.05106i			0.150023i	0.997183	+	0.0750113i	$0.0238993\pi$
$47$			7.05106i			0.150023i	−0.997183	+	0.0750113i	$0.976101\pi$
$48$	−2.21705	−	11.7934i	−0.0461885	−	0.245696i
$49$	7.00000			0.142857
$50$		0			0
$51$	21.3791	−	4.01906i	0.419198	−	0.0788050i
$52$	0.361053			0.00694332
$53$			55.0572i			1.03882i	0.854526	+	0.519408i	$0.173847\pi$
$53$			55.0572i			1.03882i	−0.854526	+	0.519408i	$0.826153\pi$
$54$	−32.4027	+	20.2006i	−0.600050	+	0.374085i
$55$		0			0
$56$		−	7.48331i		−	0.133631i
$57$	−11.8799	−	63.1944i	−0.208420	−	1.10867i
$58$	−41.7841			−0.720415
$59$		−	100.110i		−	1.69678i	−0.529375	−	0.848388i	$-0.677573\pi$
$59$		−	100.110i		−	1.69678i	0.529375	−	0.848388i	$-0.322427\pi$
$60$		0			0
$61$	8.44678			0.138472			0.0692359	−	0.997600i	$-0.477944\pi$
$61$	8.44678			0.138472			0.0692359	+	0.997600i	$0.477944\pi$
$62$		−	70.0309i		−	1.12953i
$63$	−22.1862	+	8.64716i	−0.352162	+	0.137256i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	2.02580	+	10.7761i	0.0306939	+	0.163274i
$67$	85.7646			1.28007			0.640034	−	0.768347i	$-0.278920\pi$
$67$	85.7646			1.28007			0.640034	+	0.768347i	$0.278920\pi$
$68$		−	14.5024i		−	0.213270i
$69$	−35.0435	+	6.58784i	−0.507877	+	0.0954759i
$70$		0			0
$71$		−	97.8086i		−	1.37759i	−0.724958	−	0.688793i	$-0.758141\pi$
$71$		−	97.8086i		−	1.37759i	0.724958	−	0.688793i	$-0.241859\pi$
$72$	9.24420	+	23.7180i	0.128392	+	0.329417i
$73$	17.8312			0.244264			0.122132	−	0.992514i	$-0.461027\pi$
$73$	17.8312			0.244264			0.122132	+	0.992514i	$0.461027\pi$
$74$			61.2295i			0.827426i
$75$		0			0
$76$	−42.8676			−0.564047
$77$			6.83779i			0.0888025i
$78$	−0.752723	+	0.141505i	−0.00965030	+	0.00181416i
$79$	110.652			1.40066			0.700328	−	0.713821i	$-0.253037\pi$
$79$	110.652			1.40066			0.700328	+	0.713821i	$0.253037\pi$
$80$		0			0
$81$	59.6362	−	54.8136i	0.736249	−	0.676711i
$82$	29.3940			0.358464
$83$			3.08611i			0.0371820i	0.999827	+	0.0185910i	$0.00591804\pi$
$83$			3.08611i			0.0371820i	−0.999827	+	0.0185910i	$0.994082\pi$
$84$	2.93288	+	15.6012i	0.0349152	+	0.185729i
$85$		0			0
$86$			104.961i			1.22047i
$87$	87.1115	−	16.3761i	1.00128	−	0.188231i
$88$	7.30991			0.0830671
$89$		−	80.1881i		−	0.900990i	−0.892779	−	0.450495i	$-0.851248\pi$
$89$		−	80.1881i		−	0.900990i	0.892779	−	0.450495i	$-0.148752\pi$
$90$		0			0
$91$	−0.477628			−0.00524866
$92$			23.7716i			0.258387i
$93$	27.4467	+	146.001i	0.295125	+	1.56990i
$94$	−9.97171			−0.106082
$95$		0			0
$96$	16.6784	−	3.13538i	0.173733	−	0.0326602i
$97$	105.794			1.09066			0.545328	−	0.838223i	$-0.316405\pi$
$97$	105.794			1.09066			0.545328	+	0.838223i	$0.316405\pi$
$98$			9.89949i			0.101015i
$99$	−8.44678	−	21.6721i	−0.0853210	−	0.218910i
$100$		0			0
$101$			120.653i			1.19459i	0.802022	+	0.597294i	$0.203757\pi$
$101$			120.653i			1.19459i	−0.802022	+	0.597294i	$0.796243\pi$
$102$	5.68380	+	30.2346i	0.0557236	+	0.296417i
$103$	173.031			1.67992			0.839958	−	0.542652i	$-0.182580\pi$
$103$	173.031			1.67992			0.839958	+	0.542652i	$0.182580\pi$
$104$			0.510606i			0.00490967i
$105$		0			0
$106$	−77.8627			−0.734554
$107$			82.1335i			0.767603i	0.923416	+	0.383802i	$0.125385\pi$
$107$			82.1335i			0.767603i	−0.923416	+	0.383802i	$0.874615\pi$
$108$	−28.5679	−	45.8244i	−0.264518	−	0.424300i
$109$	−63.4890			−0.582468			−0.291234	−	0.956652i	$-0.594066\pi$
$109$	−63.4890			−0.582468			−0.291234	+	0.956652i	$0.594066\pi$
$110$		0			0
$111$	−23.9972	−	127.651i	−0.216191	−	1.15001i
$112$	10.5830			0.0944911
$113$		−	145.494i		−	1.28755i	−0.765213	−	0.643777i	$-0.777366\pi$
$113$		−	145.494i		−	1.28755i	0.765213	−	0.643777i	$-0.222634\pi$
$114$	89.3704	−	16.8008i	0.783951	−	0.147375i
$115$		0			0
$116$		−	59.0916i		−	0.509410i
$117$	1.51382	−	0.590018i	0.0129386	−	0.00504289i
$118$	141.577			1.19980
$119$			19.1848i			0.161217i
$120$		0			0
$121$	114.321			0.944799
$122$			11.9456i			0.0979144i
$123$	−61.2807	+	11.5202i	−0.498217	+	0.0936599i
$124$	99.0387			0.798699
$125$		0			0
$126$	−12.2289	−	31.3760i	−0.0970550	−	0.249016i
$127$	153.065			1.20523			0.602616	−	0.798031i	$-0.294125\pi$
$127$	153.065			1.20523			0.602616	+	0.798031i	$0.294125\pi$
$128$		−	11.3137i		−	0.0883883i
$129$	−41.1364	−	218.822i	−0.318887	−	1.69629i
$130$		0			0
$131$			176.646i			1.34844i	0.738529	+	0.674222i	$0.235521\pi$
$131$			176.646i			1.34844i	−0.738529	+	0.674222i	$0.764479\pi$
$132$	−15.2397	+	2.86491i	−0.115452	+	0.0217039i
$133$	56.7085			0.426380
$134$			121.289i			0.905145i
$135$		0			0
$136$	20.5095			0.150805
$137$			229.315i			1.67383i	0.547333	+	0.836915i	$0.315643\pi$
$137$			229.315i			1.67383i	−0.547333	+	0.836915i	$0.684357\pi$
$138$	−9.31661	−	49.5591i	−0.0675117	−	0.359124i
$139$	−7.93236			−0.0570673			−0.0285337	−	0.999593i	$-0.509084\pi$
$139$	−7.93236			−0.0570673			−0.0285337	+	0.999593i	$0.509084\pi$
$140$		0			0
$141$	20.7890	−	3.90813i	0.147440	−	0.0277173i
$142$	138.322			0.974101
$143$		−	0.466560i		−	0.00326266i
$144$	−33.5424	+	13.0733i	−0.232933	+	0.0907866i
$145$		0			0
$146$			25.2172i			0.172720i
$147$	−3.87983	−	20.6385i	−0.0263934	−	0.140398i
$148$	−86.5916			−0.585078
$149$		−	111.886i		−	0.750910i	−0.926841	−	0.375455i	$-0.877487\pi$
$149$		−	111.886i		−	0.750910i	0.926841	−	0.375455i	$-0.122513\pi$
$150$		0			0
$151$	−73.7503			−0.488412			−0.244206	−	0.969723i	$-0.578527\pi$
$151$	−73.7503			−0.488412			−0.244206	+	0.969723i	$0.578527\pi$
$152$		−	60.6239i		−	0.398842i
$153$	−23.6992	−	60.8055i	−0.154897	−	0.397421i
$154$	−9.67010			−0.0627928
$155$		0			0
$156$	−0.200118	−	1.06451i	−0.00128281	−	0.00682379i
$157$	52.3958			0.333731			0.166866	−	0.985980i	$-0.446635\pi$
$157$	52.3958			0.333731			0.166866	+	0.985980i	$0.446635\pi$
$158$			156.485i			0.990414i
$159$	162.328	−	30.5161i	1.02093	−	0.191925i
$160$		0			0
$161$		−	31.4469i		−	0.195322i
$162$	77.5181	+	84.3383i	0.478507	+	0.520607i
$163$	−16.9135			−0.103764			−0.0518819	−	0.998653i	$-0.516522\pi$
$163$	−16.9135			−0.103764			−0.0518819	+	0.998653i	$0.516522\pi$
$164$			41.5694i			0.253472i
$165$		0			0
$166$	−4.36442			−0.0262917
$167$			2.03625i			0.0121931i	0.999981	+	0.00609657i	$0.00194061\pi$
$167$			2.03625i			0.0121931i	−0.999981	+	0.00609657i	$0.998059\pi$
$168$	−22.0635	+	4.14771i	−0.131330	+	0.0246888i
$169$	−168.967			−0.999807
$170$		0			0
$171$	−179.735	+	70.0525i	−1.05108	+	0.409664i
$172$	−148.437			−0.863004
$173$		−	258.927i		−	1.49669i	−0.663312	−	0.748343i	$-0.730850\pi$
$173$		−	258.927i		−	1.49669i	0.663312	−	0.748343i	$-0.269150\pi$
$174$	23.1593	+	123.194i	0.133099	+	0.708013i
$175$		0			0
$176$			10.3378i			0.0587373i
$177$	−295.159	+	55.4870i	−1.66757	+	0.313486i
$178$	113.403			0.637096
$179$			38.3599i			0.214301i	0.994243	+	0.107150i	$0.0341727\pi$
$179$			38.3599i			0.214301i	−0.994243	+	0.107150i	$0.965827\pi$
$180$		0			0
$181$	213.719			1.18077			0.590384	−	0.807122i	$-0.298976\pi$
$181$	213.719			1.18077			0.590384	+	0.807122i	$0.298976\pi$
$182$		−	0.675468i		−	0.00371136i
$183$	−4.68173	−	24.9041i	−0.0255832	−	0.136088i
$184$	−33.6181			−0.182707
$185$		0			0
$186$	−206.476	+	38.8154i	−1.11009	+	0.208685i
$187$	−18.7403			−0.100215
$188$		−	14.1021i		−	0.0750113i
$189$	37.7918	+	60.6199i	0.199957	+	0.320740i
$190$		0			0
$191$			245.546i			1.28558i	0.766043	+	0.642790i	$0.222223\pi$
$191$			245.546i			1.28558i	−0.766043	+	0.642790i	$0.777777\pi$
$192$	4.43409	+	23.5868i	0.0230942	+	0.122848i
$193$	−32.9007			−0.170470			−0.0852350	−	0.996361i	$-0.527164\pi$
$193$	−32.9007			−0.170470			−0.0852350	+	0.996361i	$0.527164\pi$
$194$			149.615i			0.771210i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$		−	219.340i		−	1.11340i	−0.830714	−	0.556700i	$-0.812067\pi$
$197$		−	219.340i		−	1.11340i	0.830714	−	0.556700i	$-0.187933\pi$
$198$	30.6489	−	11.9456i	0.154793	−	0.0603311i
$199$	−100.635			−0.505703			−0.252852	−	0.967505i	$-0.581368\pi$
$199$	−100.635			−0.505703			−0.252852	+	0.967505i	$0.581368\pi$
$200$		0			0
$201$	−47.5360	−	252.864i	−0.236498	−	1.25803i
$202$	−170.630			−0.844701
$203$			78.1708i			0.385078i
$204$	−42.7582	+	8.03811i	−0.209599	+	0.0394025i
$205$		0			0
$206$			244.703i			1.18788i
$207$	38.8466	+	99.6694i	0.187665	+	0.481495i
$208$	−0.722106			−0.00347166
$209$			55.3944i			0.265045i
$210$		0			0
$211$	119.865			0.568082			0.284041	−	0.958812i	$-0.408325\pi$
$211$	119.865			0.568082			0.284041	+	0.958812i	$0.408325\pi$
$212$		−	110.114i		−	0.519408i
$213$	−288.375	+	54.2116i	−1.35387	+	0.254514i
$214$	−116.154			−0.542777
$215$		0			0
$216$	64.8054	−	40.4012i	0.300025	−	0.187042i
$217$	−131.016			−0.603760
$218$		−	89.7870i		−	0.411867i
$219$	−9.88317	−	52.5728i	−0.0451286	−	0.240059i
$220$		0			0
$221$		−	1.30903i		−	0.00592322i
$222$	180.526	−	33.9372i	0.813182	−	0.152870i
$223$	−315.561			−1.41507			−0.707536	−	0.706677i	$-0.750193\pi$
$223$	−315.561			−1.41507			−0.707536	+	0.706677i	$0.750193\pi$
$224$			14.9666i			0.0668153i
$225$		0			0
$226$	205.759			0.910438
$227$		−	315.509i		−	1.38991i	−0.719054	−	0.694954i	$-0.755425\pi$
$227$		−	315.509i		−	1.38991i	0.719054	−	0.694954i	$-0.244575\pi$
$228$	23.7599	+	126.389i	0.104210	+	0.554337i
$229$	−66.8556			−0.291946			−0.145973	−	0.989289i	$-0.546631\pi$
$229$	−66.8556			−0.291946			−0.145973	+	0.989289i	$0.546631\pi$
$230$		0			0
$231$	20.1602	−	3.78992i	0.0872737	−	0.0164066i
$232$	83.5681			0.360207
$233$			301.826i			1.29539i	0.761900	+	0.647695i	$0.224267\pi$
$233$			301.826i			1.29539i	−0.761900	+	0.647695i	$0.775733\pi$
$234$	0.834411	+	2.14086i	0.00356586	+	0.00914899i
$235$		0			0
$236$			200.220i			0.848388i
$237$	−61.3301	−	326.241i	−0.258777	−	1.37654i
$238$	−27.1315			−0.113998
$239$			241.028i			1.00849i	0.863562	+	0.504243i	$0.168229\pi$
$239$			241.028i			1.00849i	−0.863562	+	0.504243i	$0.831771\pi$
$240$		0			0
$241$	−196.843			−0.816775			−0.408388	−	0.912809i	$-0.633909\pi$
$241$	−196.843			−0.816775			−0.408388	+	0.912809i	$0.633909\pi$
$242$			161.674i			0.668074i
$243$	−194.664	−	145.448i	−0.801086	−	0.598550i
$244$	−16.8936			−0.0692359
$245$		0			0
$246$	−16.2920	−	86.6640i	−0.0662275	−	0.352293i
$247$	−3.86937			−0.0156654
$248$			140.062i			0.564766i
$249$	9.09894	−	1.71051i	0.0365419	−	0.00686952i
$250$		0			0
$251$			349.301i			1.39164i	0.718217	+	0.695819i	$0.244959\pi$
$251$			349.301i			1.39164i	−0.718217	+	0.695819i	$0.755041\pi$
$252$	44.3724	−	17.2943i	0.176081	−	0.0686282i
$253$	30.7182			0.121416
$254$			216.466i			0.852228i
$255$		0			0
$256$	16.0000			0.0625000
$257$			4.18732i			0.0162931i	0.999967	+	0.00814653i	$0.00259315\pi$
$257$			4.18732i			0.0162931i	−0.999967	+	0.00814653i	$0.997407\pi$
$258$	309.461	−	58.1756i	1.19946	−	0.225487i
$259$	114.550			0.442278
$260$		0			0
$261$	−96.5651	−	247.759i	−0.369981	−	0.949267i
$262$	−249.815			−0.953493
$263$			268.485i			1.02086i	0.859921	+	0.510428i	$0.170513\pi$
$263$			268.485i			1.02086i	−0.859921	+	0.510428i	$0.829487\pi$
$264$	−4.05160	−	21.5522i	−0.0153470	−	0.0816371i
$265$		0			0
$266$			80.1979i			0.301496i
$267$	−236.423	+	44.4452i	−0.885479	+	0.166461i
$268$	−171.529			−0.640034
$269$			59.1206i			0.219779i	0.993944	+	0.109890i	$0.0350497\pi$
$269$			59.1206i			0.219779i	−0.993944	+	0.109890i	$0.964950\pi$
$270$		0			0
$271$	−206.348			−0.761433			−0.380717	−	0.924692i	$-0.624323\pi$
$271$	−206.348			−0.761433			−0.380717	+	0.924692i	$0.624323\pi$
$272$			29.0048i			0.106635i
$273$	0.264731	+	1.40822i	0.000969710	+	0.00515830i
$274$	−324.300			−1.18358
$275$		0			0
$276$	70.0871	−	13.1757i	0.253939	−	0.0477380i
$277$	−370.482			−1.33748			−0.668740	−	0.743496i	$-0.733166\pi$
$277$	−370.482			−1.33748			−0.668740	+	0.743496i	$0.733166\pi$
$278$		−	11.2180i		−	0.0403527i
$279$	415.249	−	161.845i	1.48835	−	0.580090i
$280$		0			0
$281$			71.0258i			0.252761i	0.991982	+	0.126380i	$0.0403360\pi$
$281$			71.0258i			0.252761i	−0.991982	+	0.126380i	$0.959664\pi$
$282$	5.52693	+	29.4001i	0.0195991	+	0.104256i
$283$	255.816			0.903944			0.451972	−	0.892032i	$-0.350721\pi$
$283$	255.816			0.903944			0.451972	+	0.892032i	$0.350721\pi$
$284$			195.617i			0.688793i
$285$		0			0
$286$	0.659816			0.00230705
$287$		−	54.9912i		−	0.191607i
$288$	−18.4884	−	47.4361i	−0.0641958	−	0.164709i
$289$	236.420			0.818063
$290$		0			0
$291$	−58.6373	−	311.917i	−0.201503	−	1.07188i
$292$	−35.6625			−0.122132
$293$		−	162.409i		−	0.554297i	−0.960827	−	0.277148i	$-0.910611\pi$
$293$		−	162.409i		−	0.554297i	0.960827	−	0.277148i	$-0.0893894\pi$
$294$	29.1872	−	5.48691i	0.0992763	−	0.0186630i
$295$		0			0
$296$		−	122.459i		−	0.413713i
$297$	−59.2152	+	36.9161i	−0.199378	+	0.124297i
$298$	158.230			0.530973
$299$			2.14570i			0.00717625i
$300$		0			0
$301$	196.363			0.652370
$302$		−	104.299i		−	0.345360i
$303$	355.729	−	66.8735i	1.17402	−	0.220705i
$304$	85.7352			0.282024
$305$		0			0
$306$	85.9919	−	33.5157i	0.281019	−	0.109529i
$307$	532.774			1.73542			0.867709	−	0.497072i	$-0.165592\pi$
$307$	532.774			1.73542			0.867709	+	0.497072i	$0.165592\pi$
$308$		−	13.6756i		−	0.0444012i
$309$	−95.9046	−	510.158i	−0.310371	−	1.65100i
$310$		0			0
$311$		−	353.139i		−	1.13549i	−0.823203	−	0.567747i	$-0.807815\pi$
$311$		−	353.139i		−	1.13549i	0.823203	−	0.567747i	$-0.192185\pi$
$312$	1.50545	−	0.283009i	0.00482515	−	0.000907081i
$313$	113.835			0.363689			0.181845	−	0.983327i	$-0.441793\pi$
$313$	113.835			0.363689			0.181845	+	0.983327i	$0.441793\pi$
$314$			74.0989i			0.235984i
$315$		0			0
$316$	−221.304			−0.700328
$317$			73.1423i			0.230733i	0.993323	+	0.115366i	$0.0368042\pi$
$317$			73.1423i			0.230733i	−0.993323	+	0.115366i	$0.963196\pi$
$318$	43.1563	+	229.567i	0.135712	+	0.721908i
$319$	−76.3594			−0.239371
$320$		0			0
$321$	242.159	−	45.5235i	0.754389	−	0.141818i
$322$	44.4726			0.138114
$323$			155.420i			0.481178i
$324$	−119.272	+	109.627i	−0.368125	+	0.338355i
$325$		0			0
$326$		−	23.9193i		−	0.0733720i
$327$	35.1895	+	187.188i	0.107613	+	0.572441i
$328$	−58.7880			−0.179232
$329$			18.6554i			0.0567032i
$330$		0			0
$331$	−244.549			−0.738818			−0.369409	−	0.929267i	$-0.620440\pi$
$331$	−244.549			−0.738818			−0.369409	+	0.929267i	$0.620440\pi$
$332$		−	6.17222i		−	0.0185910i
$333$	−363.061	+	141.505i	−1.09027	+	0.424938i
$334$	−2.87970			−0.00862185
$335$		0			0
$336$	−5.86575	−	31.2025i	−0.0174576	−	0.0928644i
$337$	−360.620			−1.07009			−0.535045	−	0.844824i	$-0.679705\pi$
$337$	−360.620			−1.07009			−0.535045	+	0.844824i	$0.679705\pi$
$338$		−	238.956i		−	0.706970i
$339$	−428.967	+	80.6415i	−1.26539	+	0.237881i
$340$		0			0
$341$		−	127.980i		−	0.375308i
$342$	−99.0692	−	254.184i	−0.289676	−	0.743227i
$343$	18.5203			0.0539949
$344$		−	209.921i		−	0.610236i
$345$		0			0
$346$	366.178			1.05832
$347$			320.079i			0.922417i	0.887292	+	0.461209i	$0.152584\pi$
$347$			320.079i			0.922417i	−0.887292	+	0.461209i	$0.847416\pi$
$348$	−174.223	+	32.7522i	−0.500641	+	0.0941155i
$349$	656.250			1.88037			0.940187	−	0.340660i	$-0.110650\pi$
$349$	656.250			1.88037			0.940187	+	0.340660i	$0.110650\pi$
$350$		0			0
$351$	−2.57863	−	4.13625i	−0.00734654	−	0.0117842i
$352$	−14.6198			−0.0415336
$353$		−	307.348i		−	0.870673i	−0.900268	−	0.435337i	$-0.856629\pi$
$353$		−	307.348i		−	0.870673i	0.900268	−	0.435337i	$-0.143371\pi$
$354$	−78.4705	−	417.418i	−0.221668	−	1.17915i
$355$		0			0
$356$			160.376i			0.450495i
$357$	56.5637	−	10.6334i	0.158442	−	0.0297855i
$358$	−54.2490			−0.151534
$359$		−	149.072i		−	0.415244i	−0.978209	−	0.207622i	$-0.933428\pi$
$359$		−	149.072i		−	0.415244i	0.978209	−	0.207622i	$-0.0665723\pi$
$360$		0			0
$361$	98.4076			0.272597
$362$			302.245i			0.834930i
$363$	−63.3635	−	337.058i	−0.174555	−	0.928534i
$364$	0.955256			0.00262433
$365$		0			0
$366$	35.2197	−	6.62096i	0.0962287	−	0.0180901i
$367$	−394.930			−1.07610			−0.538052	−	0.842912i	$-0.680840\pi$
$367$	−394.930			−1.07610			−0.538052	+	0.842912i	$0.680840\pi$
$368$		−	47.5432i		−	0.129193i
$369$	67.9311	+	174.292i	0.184095	+	0.472336i
$370$		0			0
$371$			145.668i			0.392635i
$372$	−54.8933	−	292.001i	−0.147563	−	0.784949i
$373$	−567.874			−1.52245			−0.761225	−	0.648488i	$-0.775402\pi$
$373$	−567.874			−1.52245			−0.761225	+	0.648488i	$0.775402\pi$
$374$		−	26.5028i		−	0.0708630i
$375$		0			0
$376$	19.9434			0.0530410
$377$		−	5.33379i		−	0.0141480i
$378$	−85.7295	+	53.4457i	−0.226798	+	0.141391i
$379$	−641.443			−1.69246			−0.846230	−	0.532817i	$-0.821133\pi$
$379$	−641.443			−1.69246			−0.846230	+	0.532817i	$0.821133\pi$
$380$		0			0
$381$	−84.8378	−	451.289i	−0.222671	−	1.18448i
$382$	−347.254			−0.909042
$383$		−	340.090i		−	0.887963i	−0.896036	−	0.443982i	$-0.853566\pi$
$383$		−	340.090i		−	0.887963i	0.896036	−	0.443982i	$-0.146434\pi$
$384$	−33.3568	+	6.27075i	−0.0868667	+	0.0163301i
$385$		0			0
$386$		−	46.5286i		−	0.120541i
$387$	−622.365	+	242.569i	−1.60818	+	0.626794i
$388$	−211.587			−0.545328
$389$		−	432.582i		−	1.11204i	−0.831170	−	0.556018i	$-0.812328\pi$
$389$		−	432.582i		−	1.11204i	0.831170	−	0.556018i	$-0.187672\pi$
$390$		0			0
$391$	86.1862			0.220425
$392$		−	19.7990i		−	0.0505076i
$393$	520.815	−	97.9081i	1.32523	−	0.249130i
$394$	310.193			0.787292
$395$		0			0
$396$	16.8936	+	43.3441i	0.0426605	+	0.109455i
$397$	−471.352			−1.18728			−0.593642	−	0.804729i	$-0.702310\pi$
$397$	−471.352			−1.18728			−0.593642	+	0.804729i	$0.702310\pi$
$398$		−	142.319i		−	0.357586i
$399$	−31.4313	−	167.197i	−0.0787753	−	0.419039i
$400$		0			0
$401$		−	180.124i		−	0.449186i	−0.974453	−	0.224593i	$-0.927895\pi$
$401$		−	180.124i		−	0.449186i	0.974453	−	0.224593i	$-0.0721053\pi$
$402$	357.604	−	67.2261i	0.889563	−	0.167229i
$403$	8.93955			0.0221825
$404$		−	241.307i		−	0.597294i
$405$		0			0
$406$	−110.550			−0.272291
$407$			111.896i			0.274928i
$408$	−11.3676	−	60.4692i	−0.0278618	−	0.148209i
$409$	−259.241			−0.633842			−0.316921	−	0.948452i	$-0.602649\pi$
$409$	−259.241			−0.633842			−0.316921	+	0.948452i	$0.602649\pi$
$410$		0			0
$411$	676.101	−	127.100i	1.64501	−	0.309246i
$412$	−346.063			−0.839958
$413$		−	264.866i		−	0.641321i
$414$	−140.954	+	54.9374i	−0.340468	+	0.132699i
$415$		0			0
$416$		−	1.02121i		−	0.00245484i
$417$	4.39660	+	23.3874i	0.0105434	+	0.0560849i
$418$	−78.3395			−0.187415
$419$			146.134i			0.348769i	0.984678	+	0.174384i	$0.0557935\pi$
$419$			146.134i			0.348769i	−0.984678	+	0.174384i	$0.944207\pi$
$420$		0			0
$421$	−599.808			−1.42472			−0.712361	−	0.701813i	$-0.752374\pi$
$421$	−599.808			−1.42472			−0.712361	+	0.701813i	$0.752374\pi$
$422$			169.515i			0.401695i
$423$	−23.0451	−	59.1273i	−0.0544802	−	0.139781i
$424$	155.725			0.367277
$425$		0			0
$426$	−76.6667	−	407.823i	−0.179969	−	0.957331i
$427$	22.3481			0.0523374
$428$		−	164.267i		−	0.383802i
$429$	−1.37558	+	0.258596i	−0.00320649	+	0.000602789i
$430$		0			0
$431$			825.631i			1.91562i	0.287409	+	0.957808i	$0.407206\pi$
$431$			825.631i			1.91562i	−0.287409	+	0.957808i	$0.592794\pi$
$432$	57.1359	+	91.6487i	0.132259	+	0.212150i
$433$	−185.307			−0.427962			−0.213981	−	0.976838i	$-0.568643\pi$
$433$	−185.307			−0.427962			−0.213981	+	0.976838i	$0.568643\pi$
$434$		−	185.284i		−	0.426923i
$435$		0			0
$436$	126.978			0.291234
$437$		−	254.758i		−	0.582970i
$438$	74.3492	−	13.9769i	0.169747	−	0.0319108i
$439$	809.103			1.84306			0.921529	−	0.388309i	$-0.126941\pi$
$439$	809.103			1.84306			0.921529	+	0.388309i	$0.126941\pi$
$440$		0			0
$441$	−58.6991	+	22.8782i	−0.133105	+	0.0518781i
$442$	1.85125			0.00418835
$443$			449.922i			1.01563i	0.861467	+	0.507813i	$0.169546\pi$
$443$			449.922i			1.01563i	−0.861467	+	0.507813i	$0.830454\pi$
$444$	47.9944	+	255.303i	0.108095	+	0.575006i
$445$		0			0
$446$		−	446.271i		−	1.00061i
$447$	−329.878	+	62.0138i	−0.737983	+	0.138733i
$448$	−21.1660			−0.0472456
$449$		−	676.008i		−	1.50559i	−0.658257	−	0.752793i	$-0.728706\pi$
$449$		−	676.008i		−	1.50559i	0.658257	−	0.752793i	$-0.271294\pi$
$450$		0			0
$451$	53.7169			0.119106
$452$			290.987i			0.643777i
$453$	40.8769	+	217.442i	0.0902361	+	0.480004i
$454$	446.198			0.982814
$455$		0			0
$456$	−178.741	+	33.6015i	−0.391975	+	0.0736875i
$457$	588.327			1.28737			0.643683	−	0.765292i	$-0.277405\pi$
$457$	588.327			1.28737			0.643683	+	0.765292i	$0.277405\pi$
$458$		−	94.5481i		−	0.206437i
$459$	−166.141	+	103.576i	−0.361962	+	0.225655i
$460$		0			0
$461$		−	344.268i		−	0.746785i	−0.927673	−	0.373393i	$-0.878194\pi$
$461$		−	344.268i		−	0.746785i	0.927673	−	0.373393i	$-0.121806\pi$
$462$	5.35976	+	28.5109i	0.0116012	+	0.0617119i
$463$	−220.223			−0.475643			−0.237821	−	0.971309i	$-0.576433\pi$
$463$	−220.223			−0.475643			−0.237821	+	0.971309i	$0.576433\pi$
$464$			118.183i			0.254705i
$465$		0			0
$466$	−426.846			−0.915978
$467$		−	595.502i		−	1.27516i	−0.770382	−	0.637582i	$-0.779935\pi$
$467$		−	595.502i		−	1.27516i	0.770382	−	0.637582i	$-0.220065\pi$
$468$	−3.02764	+	1.18004i	−0.00646932	+	0.00252144i
$469$	226.912			0.483820
$470$		0			0
$471$	−29.0410	−	154.481i	−0.0616581	−	0.327986i
$472$	−283.153			−0.599901
$473$			191.813i			0.405524i
$474$	461.374	−	86.7338i	0.973364	−	0.182983i
$475$		0			0
$476$		−	38.3697i		−	0.0806086i
$477$	−179.945	−	461.687i	−0.377242	−	0.967898i
$478$	−340.865			−0.713108
$479$			710.354i			1.48299i	0.670956	+	0.741497i	$0.265884\pi$
$479$			710.354i			1.48299i	−0.670956	+	0.741497i	$0.734116\pi$
$480$		0			0
$481$	−7.81604			−0.0162496
$482$		−	278.378i		−	0.577547i
$483$	−92.7165	+	17.4298i	−0.191960	+	0.0360865i
$484$	−228.641			−0.472399
$485$		0			0
$486$	205.694	−	275.296i	0.423239	−	0.566453i
$487$	325.987			0.669378			0.334689	−	0.942329i	$-0.391369\pi$
$487$	325.987			0.669378			0.334689	+	0.942329i	$0.391369\pi$
$488$		−	23.8911i		−	0.0489572i
$489$	9.37450	+	49.8670i	0.0191708	+	0.101977i
$490$		0			0
$491$			573.407i			1.16784i	0.811813	+	0.583918i	$0.198481\pi$
$491$			573.407i			1.16784i	−0.811813	+	0.583918i	$0.801519\pi$
$492$	122.561	−	23.0403i	0.249108	−	0.0468299i
$493$	−214.242			−0.434568
$494$		−	5.47211i		−	0.0110771i
$495$		0			0
$496$	−198.077			−0.399350
$497$		−	258.777i		−	0.520679i
$498$	2.41903	+	12.8678i	0.00485749	+	0.0258390i
$499$	−410.671			−0.822989			−0.411494	−	0.911412i	$-0.634993\pi$
$499$	−410.671			−0.822989			−0.411494	+	0.911412i	$0.634993\pi$
$500$		0			0
$501$	6.00360	−	1.12862i	0.0119832	−	0.00225273i
$502$	−493.987			−0.984037
$503$			903.370i			1.79596i	0.440032	+	0.897982i	$0.354967\pi$
$503$			903.370i			1.79596i	−0.440032	+	0.897982i	$0.645033\pi$
$504$	24.4579	+	62.7520i	0.0485275	+	0.124508i
$505$		0			0
$506$			43.4420i			0.0858538i
$507$	93.6521	+	498.176i	0.184718	+	0.982595i
$508$	−306.129			−0.602616
$509$			323.535i			0.635628i	0.948153	+	0.317814i	$0.102949\pi$
$509$			323.535i			0.635628i	−0.948153	+	0.317814i	$0.897051\pi$
$510$		0			0
$511$	47.1770			0.0923230
$512$			22.6274i			0.0441942i
$513$	306.160	+	491.095i	0.596803	+	0.957300i
$514$	−5.92176			−0.0115209
$515$		0			0
$516$	82.2728	+	437.644i	0.159443	+	0.848147i
$517$	−18.2231			−0.0352477
$518$			161.998i			0.312738i
$519$	−763.408	+	143.513i	−1.47092	+	0.276519i
$520$		0			0
$521$		−	687.287i		−	1.31917i	−0.751631	−	0.659584i	$-0.770732\pi$
$521$		−	687.287i		−	1.31917i	0.751631	−	0.659584i	$-0.229268\pi$
$522$	350.384	−	136.564i	0.671233	−	0.261616i
$523$	760.416			1.45395			0.726975	−	0.686664i	$-0.240926\pi$
$523$	760.416			1.45395			0.726975	+	0.686664i	$0.240926\pi$
$524$		−	353.292i		−	0.674222i
$525$		0			0
$526$	−379.695			−0.721854
$527$		−	359.074i		−	0.681355i
$528$	30.4794	−	5.72983i	0.0577262	−	0.0108519i
$529$	387.728			0.732945
$530$		0			0
$531$	327.191	+	839.480i	0.616179	+	1.58094i
$532$	−113.417			−0.213190
$533$			3.75219i			0.00703975i
$534$	−62.8550	−	334.353i	−0.117706	−	0.626128i
$535$		0			0
$536$		−	242.579i		−	0.452572i
$537$	113.098	−	21.2614i	0.210612	−	0.0395929i
$538$	−83.6091			−0.155407
$539$			18.0911i			0.0335642i
$540$		0			0
$541$	472.370			0.873142			0.436571	−	0.899670i	$-0.356193\pi$
$541$	472.370			0.873142			0.436571	+	0.899670i	$0.356193\pi$
$542$		−	291.821i		−	0.538415i
$543$	−118.456	−	630.120i	−0.218152	−	1.16044i
$544$	−41.0189			−0.0754024
$545$		0			0
$546$	−1.99152	+	0.374386i	−0.00364747	+	0.000685688i
$547$	536.508			0.980818			0.490409	−	0.871492i	$-0.336847\pi$
$547$	536.508			0.980818			0.490409	+	0.871492i	$0.336847\pi$
$548$		−	458.629i		−	0.836915i
$549$	−70.8312	+	27.6068i	−0.129019	+	0.0502856i
$550$		0			0
$551$			633.278i			1.14933i
$552$	18.6332	+	99.1181i	0.0337558	+	0.179562i
$553$	292.757			0.529398
$554$		−	523.941i		−	0.945741i
$555$		0			0
$556$	15.8647			0.0285337
$557$			288.061i			0.517165i	0.965989	+	0.258583i	$0.0832554\pi$
$557$			288.061i			0.517165i	−0.965989	+	0.258583i	$0.916745\pi$
$558$	228.883	+	587.250i	0.410185	+	1.05242i
$559$	−13.3984			−0.0239685
$560$		0			0
$561$	10.3870	+	55.2530i	0.0185152	+	0.0984902i
$562$	−100.446			−0.178729
$563$		−	16.4938i		−	0.0292963i	−0.999893	−	0.0146482i	$-0.995337\pi$
$563$		−	16.4938i		−	0.0292963i	0.999893	−	0.0146482i	$-0.00466282\pi$
$564$	−41.5781	+	7.81627i	−0.0737200	+	0.0138586i
$565$		0			0
$566$			361.779i			0.639185i
$567$	157.783	−	145.023i	0.278276	−	0.255773i
$568$	−276.645			−0.487050
$569$			1076.66i			1.89219i	0.323889	+	0.946095i	$0.395009\pi$
$569$			1076.66i			1.89219i	−0.323889	+	0.946095i	$0.604991\pi$
$570$		0			0
$571$	1009.39			1.76775			0.883876	−	0.467721i	$-0.154925\pi$
$571$	1009.39			1.76775			0.883876	+	0.467721i	$0.154925\pi$
$572$			0.933120i			0.00163133i
$573$	723.956	−	136.097i	1.26345	−	0.237516i
$574$	77.7693			0.135487
$575$		0			0
$576$	67.0847	−	26.1466i	0.116467	−	0.0453933i
$577$	901.098			1.56169			0.780847	−	0.624722i	$-0.214788\pi$
$577$	901.098			1.56169			0.780847	+	0.624722i	$0.214788\pi$
$578$			334.349i			0.578458i
$579$	18.2356	+	97.0030i	0.0314950	+	0.167535i
$580$		0			0
$581$			8.16507i			0.0140535i
$582$	441.117	−	82.9257i	0.757933	−	0.142484i
$583$	−142.292			−0.244069
$584$		−	50.4344i		−	0.0863602i
$585$		0			0
$586$	229.681			0.391947
$587$		−	265.739i		−	0.452707i	−0.974045	−	0.226354i	$-0.927319\pi$
$587$		−	265.739i		−	0.452707i	0.974045	−	0.226354i	$-0.0726805\pi$
$588$	7.75966	+	41.2770i	0.0131967	+	0.0701989i
$589$	−1061.39			−1.80202
$590$		0			0
$591$	−646.691	+	121.572i	−1.09423	+	0.205705i
$592$	173.183			0.292539
$593$			548.447i			0.924869i	0.886653	+	0.462435i	$0.153024\pi$
$593$			548.447i			0.924869i	−0.886653	+	0.462435i	$0.846976\pi$
$594$	−52.2073	−	83.7430i	−0.0878910	−	0.140981i
$595$		0			0
$596$			223.771i			0.375455i
$597$	55.7781	+	296.708i	0.0934306	+	0.496998i
$598$	−3.03448			−0.00507438
$599$		−	237.976i		−	0.397289i	−0.980072	−	0.198644i	$-0.936346\pi$
$599$		−	237.976i		−	0.397289i	0.980072	−	0.198644i	$-0.0636538\pi$
$600$		0			0
$601$	−566.317			−0.942291			−0.471146	−	0.882055i	$-0.656159\pi$
$601$	−566.317			−0.942291			−0.471146	+	0.882055i	$0.656159\pi$
$602$			277.700i			0.461295i
$603$	−719.186	+	280.306i	−1.19268	+	0.464852i
$604$	147.501			0.244206
$605$		0			0
$606$	94.5734	+	503.077i	0.156062	+	0.830159i
$607$	60.4291			0.0995537			0.0497769	−	0.998760i	$-0.484149\pi$
$607$	60.4291			0.0995537			0.0497769	+	0.998760i	$0.484149\pi$
$608$			121.248i			0.199421i
$609$	230.475	−	43.3271i	0.378449	−	0.0711446i
$610$		0			0
$611$		−	1.27290i		−	0.00208331i
$612$	47.3984	+	121.611i	0.0774484	+	0.198711i
$613$	307.983			0.502419			0.251210	−	0.967933i	$-0.419172\pi$
$613$	307.983			0.502419			0.251210	+	0.967933i	$0.419172\pi$
$614$			753.456i			1.22713i
$615$		0			0
$616$	19.3402			0.0313964
$617$			780.226i			1.26455i	0.774745	+	0.632274i	$0.217878\pi$
$617$			780.226i			1.26455i	−0.774745	+	0.632274i	$0.782122\pi$
$618$	721.472	−	135.630i	1.16743	−	0.219465i
$619$	−838.604			−1.35477			−0.677386	−	0.735627i	$-0.736887\pi$
$619$	−838.604			−1.35477			−0.677386	+	0.735627i	$0.736887\pi$
$620$		0			0
$621$	272.330	−	169.776i	0.438534	−	0.273392i
$622$	499.413			0.802916
$623$		−	212.158i		−	0.340542i
$624$	0.400235	+	2.12902i	0.000641403	+	0.00341190i
$625$		0			0
$626$			160.987i			0.257167i
$627$	163.322	−	30.7030i	0.260482	−	0.0489681i
$628$	−104.792			−0.166866
$629$			313.946i			0.499119i
$630$		0			0
$631$	−433.178			−0.686494			−0.343247	−	0.939245i	$-0.611527\pi$
$631$	−433.178			−0.686494			−0.343247	+	0.939245i	$0.611527\pi$
$632$		−	312.971i		−	0.495207i
$633$	−66.4368	−	353.406i	−0.104955	−	0.558303i
$634$	−103.439			−0.163153
$635$		0			0
$636$	−324.656	+	61.0322i	−0.510466	+	0.0959626i
$637$	−1.26368			−0.00198381
$638$		−	107.988i		−	0.169261i
$639$	319.670	+	820.183i	0.500266	+	1.28354i
$640$		0			0
$641$			571.035i			0.890850i	0.895319	+	0.445425i	$0.146947\pi$
$641$			571.035i			0.890850i	−0.895319	+	0.445425i	$0.853053\pi$
$642$	64.3799	+	342.464i	0.100280	+	0.533433i
$643$	194.578			0.302609			0.151304	−	0.988487i	$-0.451653\pi$
$643$	194.578			0.302609			0.151304	+	0.988487i	$0.451653\pi$
$644$			62.8937i			0.0976611i
$645$		0			0
$646$	−219.798			−0.340244
$647$		−	432.986i		−	0.669220i	−0.942357	−	0.334610i	$-0.891395\pi$
$647$		−	432.986i		−	0.669220i	0.942357	−	0.334610i	$-0.108605\pi$
$648$	−155.036	−	168.677i	−0.239253	−	0.260303i
$649$	258.728			0.398656
$650$		0			0
$651$	72.6171	+	386.281i	0.111547	+	0.593366i
$652$	33.8270			0.0518819
$653$		−	870.907i		−	1.33370i	−0.745192	−	0.666850i	$-0.767642\pi$
$653$		−	870.907i		−	1.33370i	0.745192	−	0.666850i	$-0.232358\pi$
$654$	−264.724	+	49.7655i	−0.404777	+	0.0760940i
$655$		0			0
$656$		−	83.1388i		−	0.126736i
$657$	−149.525	+	58.2782i	−0.227588	+	0.0887035i
$658$	−26.3827			−0.0400952
$659$			95.3946i			0.144757i	0.997377	+	0.0723783i	$0.0230589\pi$
$659$			95.3946i			0.144757i	−0.997377	+	0.0723783i	$0.976941\pi$
$660$		0			0
$661$	−532.252			−0.805222			−0.402611	−	0.915371i	$-0.631897\pi$
$661$	−532.252			−0.805222			−0.402611	+	0.915371i	$0.631897\pi$
$662$		−	345.844i		−	0.522423i
$663$	−3.85949	+	0.725546i	−0.00582125	+	0.00109434i
$664$	8.72883			0.0131458
$665$		0			0
$666$	−200.118	−	513.446i	−0.300477	−	0.770939i
$667$	351.175			0.526500
$668$		−	4.07251i		−	0.00609657i
$669$	174.903	+	930.386i	0.261440	+	1.39071i
$670$		0			0
$671$			21.8302i			0.0325339i
$672$	44.1269	−	8.29543i	0.0656651	−	0.0123444i
$673$	256.746			0.381494			0.190747	−	0.981639i	$-0.438909\pi$
$673$	256.746			0.381494			0.190747	+	0.981639i	$0.438909\pi$
$674$		−	509.994i		−	0.756667i
$675$		0			0
$676$	337.935			0.499904
$677$			962.182i			1.42124i	0.703574	+	0.710622i	$0.251586\pi$
$677$			962.182i			1.42124i	−0.703574	+	0.710622i	$0.748414\pi$
$678$	−114.044	−	606.651i	−0.168207	−	0.894765i
$679$	279.903			0.412229
$680$		0			0
$681$	−930.233	+	174.875i	−1.36598	+	0.256791i
$682$	180.991			0.265383
$683$		−	981.986i		−	1.43775i	−0.695137	−	0.718877i	$-0.744656\pi$
$683$		−	981.986i		−	1.43775i	0.695137	−	0.718877i	$-0.255344\pi$
$684$	359.470	−	140.105i	0.525541	−	0.204832i
$685$		0			0
$686$			26.1916i			0.0381802i
$687$	37.0555	+	197.114i	0.0539381	+	0.286920i
$688$	296.873			0.431502
$689$		−	9.93928i		−	0.0144257i
$690$		0			0
$691$	−38.5649			−0.0558103			−0.0279052	−	0.999611i	$-0.508884\pi$
$691$	−38.5649			−0.0558103			−0.0279052	+	0.999611i	$0.508884\pi$
$692$			517.853i			0.748343i
$693$	−22.3481	−	57.3389i	−0.0322483	−	0.0827401i
$694$	−452.660			−0.652247
$695$		0			0
$696$	−46.3186	−	246.388i	−0.0665497	−	0.354006i
$697$	150.714			0.216232
$698$			928.078i			1.32962i
$699$	889.889	−	167.290i	1.27309	−	0.239328i
$700$		0			0
$701$		−	301.635i		−	0.430293i	−0.976582	−	0.215146i	$-0.930977\pi$
$701$		−	301.635i		−	0.430293i	0.976582	−	0.215146i	$-0.0690228\pi$
$702$	5.84955	−	3.64674i	0.00833269	−	0.00519478i
$703$	927.993			1.32005
$704$		−	20.6755i		−	0.0293687i
$705$		0			0
$706$	434.655			0.615659
$707$			319.219i			0.451512i
$708$	590.318	−	110.974i	0.833783	−	0.156743i
$709$	910.699			1.28448			0.642242	−	0.766502i	$-0.278005\pi$
$709$	910.699			1.28448			0.642242	+	0.766502i	$0.278005\pi$
$710$		0			0
$711$	−927.881	+	361.646i	−1.30504	+	0.508644i
$712$	−226.806			−0.318548
$713$			588.577i			0.825493i
$714$	15.0379	+	79.9932i	0.0210615	+	0.112035i
$715$		0			0
$716$		−	76.7197i		−	0.107150i
$717$	710.637	−	133.593i	0.991125	−	0.186322i
$718$	210.820			0.293622
$719$			526.394i			0.732119i	0.930591	+	0.366060i	$0.119293\pi$
$719$			526.394i			0.732119i	−0.930591	+	0.366060i	$0.880707\pi$
$720$		0			0
$721$	457.798			0.634948
$722$			139.169i			0.192755i
$723$	109.102	+	580.362i	0.150902	+	0.802714i
$724$	−427.438			−0.590384
$725$		0			0
$726$	476.672	−	89.6096i	0.656573	−	0.123429i
$727$	348.251			0.479025			0.239513	−	0.970893i	$-0.423012\pi$
$727$	348.251			0.479025			0.239513	+	0.970893i	$0.423012\pi$
$728$			1.35094i			0.00185568i
$729$	−320.936	+	654.554i	−0.440242	+	0.897879i
$730$		0			0
$731$			538.171i			0.736212i
$732$	9.36345	+	49.8082i	0.0127916	+	0.0680440i
$733$	−1270.52			−1.73332			−0.866658	−	0.498903i	$-0.833736\pi$
$733$	−1270.52			−1.73332			−0.866658	+	0.498903i	$0.833736\pi$
$734$		−	558.515i		−	0.760920i
$735$		0			0
$736$	67.2362			0.0913536
$737$			221.654i			0.300751i
$738$	−246.486	+	96.0690i	−0.333992	+	0.130175i
$739$	−1072.31			−1.45103			−0.725514	−	0.688207i	$-0.758398\pi$
$739$	−1072.31			−1.45103			−0.725514	+	0.688207i	$0.758398\pi$
$740$		0			0
$741$	2.14464	+	11.4083i	0.00289425	+	0.0153958i
$742$	−206.005			−0.277635
$743$			205.210i			0.276191i	0.990419	+	0.138095i	$0.0440981\pi$
$743$			205.210i			0.276191i	−0.990419	+	0.138095i	$0.955902\pi$
$744$	412.952	−	77.6309i	0.555043	−	0.104343i
$745$		0			0
$746$		−	803.094i		−	1.07653i
$747$	−10.0864	−	25.8788i	−0.0135025	−	0.0346437i
$748$	37.4806			0.0501077
$749$			217.305i			0.290127i
$750$		0			0
$751$	−167.702			−0.223306			−0.111653	−	0.993747i	$-0.535614\pi$
$751$	−167.702			−0.223306			−0.111653	+	0.993747i	$0.535614\pi$
$752$			28.2043i			0.0375057i
$753$	1029.86	−	193.604i	1.36768	−	0.257111i
$754$	7.54312			0.0100041
$755$		0			0
$756$	−75.5837	−	121.240i	−0.0999784	−	0.160370i
$757$	468.004			0.618236			0.309118	−	0.951024i	$-0.399966\pi$
$757$	468.004			0.618236			0.309118	+	0.951024i	$0.399966\pi$
$758$		−	907.137i		−	1.19675i
$759$	−17.0259	−	90.5680i	−0.0224320	−	0.119325i
$760$		0			0
$761$		−	252.487i		−	0.331784i	−0.986144	−	0.165892i	$-0.946950\pi$
$761$		−	252.487i		−	0.331784i	0.986144	−	0.165892i	$-0.0530503\pi$
$762$	638.218	−	119.979i	0.837557	−	0.157452i
$763$	−167.976			−0.220152
$764$		−	491.091i		−	0.642790i
$765$		0			0
$766$	480.960			0.627885
$767$			18.0725i			0.0235625i
$768$	−8.86818	−	47.1737i	−0.0115471	−	0.0614241i
$769$	−146.391			−0.190366			−0.0951828	−	0.995460i	$-0.530344\pi$
$769$	−146.391			−0.190366			−0.0951828	+	0.995460i	$0.530344\pi$
$770$		0			0
$771$	12.3457	−	2.32087i	0.0160126	−	0.00301021i
$772$	65.8014			0.0852350
$773$		−	1105.53i		−	1.43018i	−0.699032	−	0.715091i	$-0.746385\pi$
$773$		−	1105.53i		−	1.43018i	0.699032	−	0.715091i	$-0.253615\pi$
$774$	−343.045	−	880.156i	−0.443210	−	1.13715i
$775$		0			0
$776$		−	299.229i		−	0.385605i
$777$	−63.4906	−	337.734i	−0.0817125	−	0.434664i
$778$	611.764			0.786328
$779$		−	445.495i		−	0.571881i
$780$		0			0
$781$	252.781			0.323663
$782$			121.886i			0.155864i
$783$	−676.958	+	422.031i	−0.864570	+	0.538993i
$784$	28.0000			0.0357143
$785$		0			0
$786$	138.463	+	736.544i	0.176162	+	0.937079i
$787$	−1176.01			−1.49430			−0.747150	−	0.664655i	$-0.768578\pi$
$787$	−1176.01			−1.49430			−0.747150	+	0.664655i	$0.768578\pi$
$788$			438.679i			0.556700i
$789$	791.589	−	148.811i	1.00328	−	0.188607i
$790$		0			0
$791$		−	384.940i		−	0.486650i
$792$	−61.2979	+	23.8911i	−0.0773963	+	0.0301655i
$793$	−1.52487			−0.00192291
$794$		−	666.592i		−	0.839536i
$795$		0			0
$796$	201.270			0.252852
$797$			1123.49i			1.40965i	0.709383	+	0.704823i	$0.248973\pi$
$797$			1123.49i			1.40965i	−0.709383	+	0.704823i	$0.751027\pi$
$798$	236.452	−	44.4506i	0.296306	−	0.0557025i
$799$	−51.1286			−0.0639907
$800$		0			0
$801$	262.080	+	672.424i	0.327191	+	0.839481i
$802$	254.733			0.317623
$803$			46.0838i			0.0573896i
$804$	95.0720	+	505.729i	0.118249	+	0.629016i
$805$		0			0
$806$			12.6424i			0.0156854i
$807$	174.308	−	32.7683i	0.215996	−	0.0406050i
$808$	341.259			0.422351
$809$		−	539.089i		−	0.666365i	−0.942862	−	0.333182i	$-0.891878\pi$
$809$		−	539.089i		−	0.666365i	0.942862	−	0.333182i	$-0.108122\pi$
$810$		0			0
$811$	435.885			0.537467			0.268733	−	0.963215i	$-0.413395\pi$
$811$	435.885			0.537467			0.268733	+	0.963215i	$0.413395\pi$
$812$		−	156.342i		−	0.192539i
$813$	114.371	+	608.388i	0.140678	+	0.748325i
$814$	−158.244			−0.194403
$815$		0			0
$816$	85.5163	−	16.0762i	0.104799	−	0.0197013i
$817$	1590.78			1.94710
$818$		−	366.623i		−	0.448194i
$819$	4.00519	−	1.56104i	0.00489034	−	0.00190603i
$820$		0			0
$821$		−	811.354i		−	0.988251i	−0.869391	−	0.494126i	$-0.835488\pi$
$821$		−	811.354i		−	0.988251i	0.869391	−	0.494126i	$-0.164512\pi$
$822$	179.747	+	956.151i	0.218670	+	1.16320i
$823$	283.495			0.344465			0.172233	−	0.985056i	$-0.444902\pi$
$823$	283.495			0.344465			0.172233	+	0.985056i	$0.444902\pi$
$824$		−	489.406i		−	0.593940i
$825$		0			0
$826$	374.577			0.453483
$827$			406.820i			0.491923i	0.969280	+	0.245962i	$0.0791037\pi$
$827$			406.820i			0.491923i	−0.969280	+	0.245962i	$0.920896\pi$
$828$	−77.6931	−	199.339i	−0.0938323	−	0.240747i
$829$	−553.326			−0.667462			−0.333731	−	0.942668i	$-0.608308\pi$
$829$	−553.326			−0.667462			−0.333731	+	0.942668i	$0.608308\pi$
$830$		0			0
$831$	205.344	+	1092.31i	0.247105	+	1.31446i
$832$	1.44421			0.00173583
$833$			50.7583i			0.0609344i
$834$	−33.0748	+	6.21773i	−0.0396580	+	0.00745532i
$835$		0			0
$836$		−	110.789i		−	0.132522i
$837$	−707.333	−	1134.60i	−0.845081	−	1.35555i
$838$	−206.665			−0.246617
$839$			1325.58i			1.57996i	0.613136	+	0.789978i	$0.289908\pi$
$839$			1325.58i			1.57996i	−0.613136	+	0.789978i	$0.710092\pi$
$840$		0			0
$841$	−31.9535			−0.0379946
$842$		−	848.256i		−	1.00743i
$843$	209.409	−	39.3669i	0.248409	−	0.0466985i
$844$	−239.731			−0.284041
$845$		0			0
$846$	83.6186	−	32.5907i	0.0988400	−	0.0385233i
$847$	302.464			0.357100
$848$			220.229i			0.259704i
$849$	−141.789	−	754.237i	−0.167007	−	0.888382i
$850$		0			0
$851$		−	514.605i		−	0.604706i
$852$	576.749	−	108.423i	0.676936	−	0.127257i
$853$	273.098			0.320162			0.160081	−	0.987104i	$-0.448825\pi$
$853$	273.098			0.320162			0.160081	+	0.987104i	$0.448825\pi$
$854$			31.6050i			0.0370082i
$855$		0			0
$856$	232.309			0.271389
$857$		−	1236.47i		−	1.44278i	−0.692527	−	0.721392i	$-0.743503\pi$
$857$		−	1236.47i		−	1.44278i	0.692527	−	0.721392i	$-0.256497\pi$
$858$	−0.365710	−	1.94537i	−0.000426236	−	0.00226733i
$859$	1117.68			1.30114			0.650569	−	0.759447i	$-0.274530\pi$
$859$	1117.68			1.30114			0.650569	+	0.759447i	$0.274530\pi$
$860$		0			0
$861$	−162.133	+	30.4795i	−0.188308	+	0.0354001i
$862$	−1167.62			−1.35455
$863$			95.0081i			0.110090i	0.998484	+	0.0550452i	$0.0175303\pi$
$863$			95.0081i			0.110090i	−0.998484	+	0.0550452i	$0.982470\pi$
$864$	−129.611	+	80.8023i	−0.150013	+	0.0935212i
$865$		0			0
$866$		−	262.064i		−	0.302615i
$867$	−131.039	−	697.051i	−0.151140	−	0.803980i
$868$	262.032			0.301880
$869$			285.973i			0.329083i
$870$		0			0
$871$	−15.4828			−0.0177759
$872$			179.574i			0.205934i
$873$	−887.141	+	345.767i	−1.01620	+	0.396068i
$874$	360.282			0.412222
$875$		0			0
$876$	19.7663	+	105.146i	0.0225643	+	0.120029i
$877$	749.945			0.855125			0.427563	−	0.903986i	$-0.359372\pi$
$877$	749.945			0.855125			0.427563	+	0.903986i	$0.359372\pi$
$878$			1144.24i			1.30324i
$879$	−478.839	+	90.0171i	−0.544755	+	0.102408i
$880$		0			0
$881$		−	1369.06i		−	1.55399i	−0.629508	−	0.776994i	$-0.716744\pi$
$881$		−	1369.06i		−	1.55399i	0.629508	−	0.776994i	$-0.283256\pi$
$882$	−32.3547	−	83.0131i	−0.0366833	−	0.0941191i
$883$	−1039.06			−1.17673			−0.588367	−	0.808594i	$-0.700229\pi$
$883$	−1039.06			−1.17673			−0.588367	+	0.808594i	$0.700229\pi$
$884$			2.61806i			0.00296161i
$885$		0			0
$886$	−636.286			−0.718156
$887$		−	217.425i		−	0.245124i	−0.992461	−	0.122562i	$-0.960889\pi$
$887$		−	217.425i		−	0.245124i	0.992461	−	0.122562i	$-0.0391111\pi$
$888$	−361.053	+	67.8743i	−0.406591	+	0.0764351i
$889$	404.971			0.455535
$890$		0			0
$891$	141.662	+	154.126i	0.158993	+	0.172981i
$892$	631.122			0.707536
$893$			151.131i			0.169240i
$894$	−87.7008	−	466.518i	−0.0980994	−	0.521833i
$895$		0			0
$896$		−	29.9333i		−	0.0334077i
$897$	6.32628	−	1.18928i	0.00705271	−	0.00132584i
$898$	956.020			1.06461
$899$		−	1463.09i		−	1.62746i
$900$		0			0
$901$	−399.230			−0.443097
$902$			75.9671i			0.0842208i
$903$	−108.837	−	578.949i	−0.120528	−	0.641139i
$904$	−411.518			−0.455219
$905$		0			0
$906$	−307.509	+	57.8087i	−0.339414	+	0.0638065i
$907$	331.700			0.365711			0.182855	−	0.983140i	$-0.441466\pi$
$907$	331.700			0.365711			0.182855	+	0.983140i	$0.441466\pi$
$908$			631.019i			0.694954i
$909$	−394.334	−	1011.75i	−0.433810	−	1.11304i
$910$		0			0
$911$		−	500.840i		−	0.549769i	−0.961477	−	0.274885i	$-0.911360\pi$
$911$		−	500.840i		−	0.549769i	0.961477	−	0.274885i	$-0.0886396\pi$
$912$	−47.5197	−	252.778i	−0.0521049	−	0.277169i
$913$	−7.97587			−0.00873589
$914$			832.020i			0.910306i
$915$		0			0
$916$	133.711			0.145973
$917$			467.362i			0.509664i
$918$	−146.478	−	234.958i	−0.159562	−	0.255946i
$919$	634.767			0.690715			0.345357	−	0.938471i	$-0.387758\pi$
$919$	634.767			0.690715			0.345357	+	0.938471i	$0.387758\pi$
$920$		0			0
$921$	−295.296	−	1570.81i	−0.320625	−	1.70554i
$922$	486.868			0.528057
$923$			17.6570i			0.0191301i
$924$	−40.3205	+	7.57985i	−0.0436369	+	0.00820330i
$925$		0			0
$926$		−	311.442i		−	0.336330i
$927$	−1450.97	+	565.521i	−1.56523	+	0.610055i
$928$	−167.136			−0.180104
$929$		−	1222.10i		−	1.31551i	−0.753234	−	0.657753i	$-0.771507\pi$
$929$		−	1222.10i		−	1.31551i	0.753234	−	0.657753i	$-0.228493\pi$
$930$		0			0
$931$	150.037			0.161156
$932$		−	603.651i		−	0.647695i
$933$	−1041.18	+	195.731i	−1.11595	+	0.209787i
$934$	842.167			0.901678
$935$		0			0
$936$	−1.66882	−	4.28173i	−0.00178293	−	0.00457450i
$937$	−689.991			−0.736383			−0.368191	−	0.929750i	$-0.620023\pi$
$937$	−689.991			−0.736383			−0.368191	+	0.929750i	$0.620023\pi$
$938$			320.902i			0.342113i
$939$	−63.0942	−	335.625i	−0.0671930	−	0.357428i
$940$		0			0
$941$			83.4328i			0.0886639i	0.999017	+	0.0443320i	$0.0141159\pi$
$941$			83.4328i			0.0886639i	−0.999017	+	0.0443320i	$0.985884\pi$
$942$	218.470	−	41.0701i	0.231921	−	0.0435989i
$943$	−247.043			−0.261975
$944$		−	400.439i		−	0.424194i
$945$		0			0
$946$	−271.265			−0.286749
$947$		−	528.948i		−	0.558551i	−0.960211	−	0.279276i	$-0.909906\pi$
$947$		−	528.948i		−	0.558551i	0.960211	−	0.279276i	$-0.0900943\pi$
$948$	122.660	+	652.482i	0.129388	+	0.688272i
$949$	−3.21901			−0.00339200
$950$		0			0
$951$	215.649	−	40.5400i	0.226761	−	0.0426288i
$952$	54.2629			0.0569989
$953$			1017.29i			1.06746i	0.845654	+	0.533732i	$0.179211\pi$
$953$			1017.29i			1.06746i	−0.845654	+	0.533732i	$0.820789\pi$
$954$	652.924	−	254.480i	0.684407	−	0.266751i
$955$		0			0
$956$		−	482.057i		−	0.504243i
$957$	42.3231	+	225.135i	0.0442247	+	0.235250i
$958$	−1004.59			−1.04864
$959$			606.710i			0.632648i
$960$		0			0
$961$	1491.17			1.55168
$962$		−	11.0535i		−	0.0114902i
$963$	−268.439	−	688.738i	−0.278752	−	0.715200i
$964$	393.686			0.408388
$965$		0			0
$966$	−24.6494	−	131.121i	−0.0255170	−	0.135736i
$967$	−12.4388			−0.0128633			−0.00643164	−	0.999979i	$-0.502047\pi$
$967$	−12.4388			−0.0128633			−0.00643164	+	0.999979i	$0.502047\pi$
$968$		−	323.348i		−	0.334037i
$969$	458.235	−	86.1436i	0.472894	−	0.0888995i
$970$		0			0
$971$		−	855.268i		−	0.880812i	−0.897799	−	0.440406i	$-0.854835\pi$
$971$		−	855.268i		−	0.880812i	0.897799	−	0.440406i	$-0.145165\pi$
$972$	389.328	+	290.895i	0.400543	+	0.299275i
$973$	−20.9870			−0.0215694
$974$			461.016i			0.473322i
$975$		0			0
$976$	33.7871			0.0346180
$977$		−	939.920i		−	0.962047i	−0.876708	−	0.481023i	$-0.840265\pi$
$977$		−	939.920i		−	0.962047i	0.876708	−	0.481023i	$-0.159735\pi$
$978$	−70.5225	+	13.2575i	−0.0721089	+	0.0135558i
$979$	207.242			0.211687
$980$		0			0
$981$	532.393	−	207.502i	0.542704	−	0.211521i
$982$	−810.920			−0.825784
$983$		−	564.622i		−	0.574387i	−0.957873	−	0.287194i	$-0.907278\pi$
$983$		−	564.622i		−	0.574387i	0.957873	−	0.287194i	$-0.0927223\pi$
$984$	32.5839	+	173.328i	0.0331138	+	0.176146i
$985$		0			0
$986$		−	302.984i		−	0.307286i
$987$	55.0026	−	10.3399i	0.0557271	−	0.0104761i
$988$	7.73873			0.00783272
$989$		−	882.144i		−	0.891956i
$990$		0			0
$991$	−1156.30			−1.16680			−0.583400	−	0.812185i	$-0.698278\pi$
$991$	−1156.30			−1.16680			−0.583400	+	0.812185i	$0.698278\pi$
$992$		−	280.124i		−	0.282383i
$993$	135.544	+	721.016i	0.136499	+	0.726099i
$994$	365.966			0.368175
$995$		0			0
$996$	−18.1979	+	3.42102i	−0.0182710	+	0.00343476i
$997$	807.864			0.810295			0.405148	−	0.914251i	$-0.367220\pi$
$997$	807.864			0.810295			0.405148	+	0.914251i	$0.367220\pi$
$998$		−	580.777i		−	0.581941i
$999$	618.436	+	992.001i	0.619055	+	0.992994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.e.e.701.15		24
3.2	odd	2	inner	1050.3.e.e.701.13		24
5.2	odd	4		210.3.c.a.29.2	yes	24
5.3	odd	4		210.3.c.a.29.23	yes	24
5.4	even	2	inner	1050.3.e.e.701.14		24
15.2	even	4		210.3.c.a.29.24	yes	24
15.8	even	4		210.3.c.a.29.1	✓	24
15.14	odd	2	inner	1050.3.e.e.701.16		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.c.a.29.1	✓	24	15.8	even	4
210.3.c.a.29.2	yes	24	5.2	odd	4
210.3.c.a.29.23	yes	24	5.3	odd	4
210.3.c.a.29.24	yes	24	15.2	even	4
1050.3.e.e.701.13		24	3.2	odd	2	inner
1050.3.e.e.701.14		24	5.4	even	2	inner
1050.3.e.e.701.15		24	1.1	even	1	trivial
1050.3.e.e.701.16		24	15.14	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +(-0.554262 - 2.94835i) q^{3} -2.00000 q^{4} +(4.16960 - 0.783844i) q^{6} +2.64575 q^{7} -2.82843i q^{8} +(-8.38559 + 3.26832i) q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} +(-0.554262 - 2.94835i) q^{3} -2.00000 q^{4} +(4.16960 - 0.783844i) q^{6} +2.64575 q^{7} -2.82843i q^{8} +(-8.38559 + 3.26832i) q^{9} +2.58444i q^{11} +(1.10852 + 5.89671i) q^{12} -0.180526 q^{13} +3.74166i q^{14} +4.00000 q^{16} +7.25119i q^{17} +(-4.62210 - 11.8590i) q^{18} +21.4338 q^{19} +(-1.46644 - 7.80061i) q^{21} -3.65495 q^{22} -11.8858i q^{23} +(-8.33921 + 1.56769i) q^{24} -0.255303i q^{26} +(14.2840 + 22.9122i) q^{27} -5.29150 q^{28} +29.5458i q^{29} -49.5193 q^{31} +5.65685i q^{32} +(7.61985 - 1.43246i) q^{33} -10.2547 q^{34} +(16.7712 - 6.53664i) q^{36} +43.2958 q^{37} +30.3120i q^{38} +(0.100059 + 0.532256i) q^{39} -20.7847i q^{41} +(11.0317 - 2.07386i) q^{42} +74.2183 q^{43} -5.16888i q^{44} +16.8091 q^{46} +7.05106i q^{47} +(-2.21705 - 11.7934i) q^{48} +7.00000 q^{49} +(21.3791 - 4.01906i) q^{51} +0.361053 q^{52} +55.0572i q^{53} +(-32.4027 + 20.2006i) q^{54} -7.48331i q^{56} +(-11.8799 - 63.1944i) q^{57} -41.7841 q^{58} -100.110i q^{59} +8.44678 q^{61} -70.0309i q^{62} +(-22.1862 + 8.64716i) q^{63} -8.00000 q^{64} +(2.02580 + 10.7761i) q^{66} +85.7646 q^{67} -14.5024i q^{68} +(-35.0435 + 6.58784i) q^{69} -97.8086i q^{71} +(9.24420 + 23.7180i) q^{72} +17.8312 q^{73} +61.2295i q^{74} -42.8676 q^{76} +6.83779i q^{77} +(-0.752723 + 0.141505i) q^{78} +110.652 q^{79} +(59.6362 - 54.8136i) q^{81} +29.3940 q^{82} +3.08611i q^{83} +(2.93288 + 15.6012i) q^{84} +104.961i q^{86} +(87.1115 - 16.3761i) q^{87} +7.30991 q^{88} -80.1881i q^{89} -0.477628 q^{91} +23.7716i q^{92} +(27.4467 + 146.001i) q^{93} -9.97171 q^{94} +(16.6784 - 3.13538i) q^{96} +105.794 q^{97} +9.89949i q^{98} +(-8.44678 - 21.6721i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 48 q^{4} - 44 q^{9}+O(q^{10}) \) 24 * q - 48 * q^4 - 44 * q^9	\( 24 q - 48 q^{4} - 44 q^{9} + 96 q^{16} + 80 q^{19} - 28 q^{21} + 224 q^{31} - 128 q^{34} + 88 q^{36} + 92 q^{39} - 144 q^{46} + 168 q^{49} - 284 q^{51} + 144 q^{54} - 192 q^{64} + 224 q^{66} + 152 q^{69} - 160 q^{76} + 72 q^{79} - 212 q^{81} + 56 q^{84} + 168 q^{91} + 128 q^{94} + 876 q^{99}+O(q^{100}) \) 24 * q - 48 * q^4 - 44 * q^9 + 96 * q^16 + 80 * q^19 - 28 * q^21 + 224 * q^31 - 128 * q^34 + 88 * q^36 + 92 * q^39 - 144 * q^46 + 168 * q^49 - 284 * q^51 + 144 * q^54 - 192 * q^64 + 224 * q^66 + 152 * q^69 - 160 * q^76 + 72 * q^79 - 212 * q^81 + 56 * q^84 + 168 * q^91 + 128 * q^94 + 876 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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