LMFDB - Embedded newform 690.3.f.a.229.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(229,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("690.229");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.f (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:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			229.8
Character	$\chi$	$=$	690.229
Dual form			690.3.f.a.229.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +1.73205i q^{3} -2.00000 q^{4} +(3.10921 - 3.91571i) q^{5} -2.44949 q^{6} -3.09410 q^{7} -2.82843i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +1.73205i q^{3} -2.00000 q^{4} +(3.10921 - 3.91571i) q^{5} -2.44949 q^{6} -3.09410 q^{7} -2.82843i q^{8} -3.00000 q^{9} +(5.53765 + 4.39709i) q^{10} -15.9443i q^{11} -3.46410i q^{12} +24.8732i q^{13} -4.37572i q^{14} +(6.78221 + 5.38531i) q^{15} +4.00000 q^{16} -12.6980 q^{17} -4.24264i q^{18} +10.4874i q^{19} +(-6.21842 + 7.83142i) q^{20} -5.35914i q^{21} +22.5487 q^{22} +(-22.9821 + 0.906621i) q^{23} +4.89898 q^{24} +(-5.66561 - 24.3496i) q^{25} -35.1760 q^{26} -5.19615i q^{27} +6.18820 q^{28} -44.7809 q^{29} +(-7.61598 + 9.59150i) q^{30} -50.0174 q^{31} +5.65685i q^{32} +27.6164 q^{33} -17.9577i q^{34} +(-9.62022 + 12.1156i) q^{35} +6.00000 q^{36} -39.1282 q^{37} -14.8314 q^{38} -43.0816 q^{39} +(-11.0753 - 8.79418i) q^{40} +41.3571 q^{41} +7.57897 q^{42} +71.6357 q^{43} +31.8887i q^{44} +(-9.32763 + 11.7471i) q^{45} +(-1.28216 - 32.5016i) q^{46} -17.3085i q^{47} +6.92820i q^{48} -39.4265 q^{49} +(34.4355 - 8.01238i) q^{50} -21.9936i q^{51} -49.7463i q^{52} -39.6184 q^{53} +7.34847 q^{54} +(-62.4335 - 49.5744i) q^{55} +8.75144i q^{56} -18.1647 q^{57} -63.3298i q^{58} +24.0107 q^{59} +(-13.5644 - 10.7706i) q^{60} +76.0777i q^{61} -70.7353i q^{62} +9.28230 q^{63} -8.00000 q^{64} +(97.3961 + 77.3359i) q^{65} +39.0555i q^{66} -76.7774 q^{67} +25.3960 q^{68} +(-1.57031 - 39.8062i) q^{69} +(-17.1341 - 13.6050i) q^{70} +22.9757 q^{71} +8.48528i q^{72} -51.8874i q^{73} -55.3356i q^{74} +(42.1747 - 9.81312i) q^{75} -20.9748i q^{76} +49.3334i q^{77} -60.9265i q^{78} +25.5241i q^{79} +(12.4368 - 15.6628i) q^{80} +9.00000 q^{81} +58.4877i q^{82} -21.6791 q^{83} +10.7183i q^{84} +(-39.4807 + 49.7217i) q^{85} +101.308i q^{86} -77.5628i q^{87} -45.0974 q^{88} -165.958i q^{89} +(-16.6130 - 13.1913i) q^{90} -76.9601i q^{91} +(45.9642 - 1.81324i) q^{92} -86.6327i q^{93} +24.4779 q^{94} +(41.0657 + 32.6076i) q^{95} -9.79796 q^{96} -0.580105 q^{97} -55.7575i q^{98} +47.8330i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 96 q^{4} - 144 q^{9}+O(q^{10}) $ 48 * q - 96 * q^4 - 144 * q^9	$ 48 q - 96 q^{4} - 144 q^{9} + 192 q^{16} + 96 q^{25} + 64 q^{26} - 152 q^{29} - 8 q^{31} + 56 q^{35} + 288 q^{36} - 48 q^{39} + 40 q^{41} - 160 q^{46} + 424 q^{49} + 96 q^{50} + 32 q^{55} + 360 q^{59} - 384 q^{64} + 192 q^{69} - 496 q^{70} - 152 q^{71} + 144 q^{75} + 432 q^{81} - 136 q^{85} + 256 q^{94} + 496 q^{95}+O(q^{100}) $ 48 * q - 96 * q^4 - 144 * q^9 + 192 * q^16 + 96 * q^25 + 64 * q^26 - 152 * q^29 - 8 * q^31 + 56 * q^35 + 288 * q^36 - 48 * q^39 + 40 * q^41 - 160 * q^46 + 424 * q^49 + 96 * q^50 + 32 * q^55 + 360 * q^59 - 384 * q^64 + 192 * q^69 - 496 * q^70 - 152 * q^71 + 144 * q^75 + 432 * q^81 - 136 * q^85 + 256 * q^94 + 496 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$1$	$-1$

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
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	−2.00000			−0.500000
$5$	3.10921	−	3.91571i	0.621842	−	0.783142i
$5$	3.10921	−	3.91571i	0.621842	−	0.783142i
$6$	−2.44949			−0.408248
$7$	−3.09410			−0.442015			−0.221007	−	0.975272i	$-0.570934\pi$
$7$	−3.09410			−0.442015			−0.221007	+	0.975272i	$0.570934\pi$
$8$		−	2.82843i		−	0.353553i
$9$	−3.00000			−0.333333
$10$	5.53765	+	4.39709i	0.553765	+	0.439709i
$11$		−	15.9443i		−	1.44949i	−0.689019	−	0.724743i	$-0.741958\pi$
$11$		−	15.9443i		−	1.44949i	0.689019	−	0.724743i	$-0.258042\pi$
$12$		−	3.46410i		−	0.288675i
$13$			24.8732i			1.91332i	0.291208	+	0.956660i	$0.405943\pi$
$13$			24.8732i			1.91332i	−0.291208	+	0.956660i	$0.594057\pi$
$14$		−	4.37572i		−	0.312551i
$15$	6.78221	+	5.38531i	0.452148	+	0.359021i
$16$	4.00000			0.250000
$17$	−12.6980			−0.746940			−0.373470	−	0.927642i	$-0.621832\pi$
$17$	−12.6980			−0.746940			−0.373470	+	0.927642i	$0.621832\pi$
$18$		−	4.24264i		−	0.235702i
$19$			10.4874i			0.551969i	0.961162	+	0.275984i	$0.0890038\pi$
$19$			10.4874i			0.551969i	−0.961162	+	0.275984i	$0.910996\pi$
$20$	−6.21842	+	7.83142i	−0.310921	+	0.391571i
$21$		−	5.35914i		−	0.255197i
$22$	22.5487			1.02494
$23$	−22.9821	+	0.906621i	−0.999223	+	0.0394183i
$23$	−22.9821	+	0.906621i	−0.999223	+	0.0394183i
$24$	4.89898			0.204124
$25$	−5.66561	−	24.3496i	−0.226624	−	0.973982i
$26$	−35.1760			−1.35292
$27$		−	5.19615i		−	0.192450i
$28$	6.18820			0.221007
$29$	−44.7809			−1.54417			−0.772084	−	0.635520i	$-0.780786\pi$
$29$	−44.7809			−1.54417			−0.772084	+	0.635520i	$0.780786\pi$
$30$	−7.61598	+	9.59150i	−0.253866	+	0.319717i
$31$	−50.0174			−1.61346			−0.806732	−	0.590917i	$-0.798766\pi$
$31$	−50.0174			−1.61346			−0.806732	+	0.590917i	$0.798766\pi$
$32$			5.65685i			0.176777i
$33$	27.6164			0.836861
$34$		−	17.9577i		−	0.528167i
$35$	−9.62022	+	12.1156i	−0.274863	+	0.346160i
$36$	6.00000			0.166667
$37$	−39.1282			−1.05752			−0.528759	−	0.848772i	$-0.677343\pi$
$37$	−39.1282			−1.05752			−0.528759	+	0.848772i	$0.677343\pi$
$38$	−14.8314			−0.390301
$39$	−43.0816			−1.10466
$40$	−11.0753	−	8.79418i	−0.276883	−	0.219854i
$41$	41.3571			1.00871			0.504355	−	0.863497i	$-0.331730\pi$
$41$	41.3571			1.00871			0.504355	+	0.863497i	$0.331730\pi$
$42$	7.57897			0.180452
$43$	71.6357			1.66595			0.832973	−	0.553313i	$-0.186637\pi$
$43$	71.6357			1.66595			0.832973	+	0.553313i	$0.186637\pi$
$44$			31.8887i			0.724743i
$45$	−9.32763	+	11.7471i	−0.207281	+	0.261047i
$46$	−1.28216	−	32.5016i	−0.0278730	−	0.706557i
$47$		−	17.3085i		−	0.368266i	−0.982901	−	0.184133i	$-0.941052\pi$
$47$		−	17.3085i		−	0.368266i	0.982901	−	0.184133i	$-0.0589477\pi$
$48$			6.92820i			0.144338i
$49$	−39.4265			−0.804623
$50$	34.4355	−	8.01238i	0.688709	−	0.160248i
$51$		−	21.9936i		−	0.431246i
$52$		−	49.7463i		−	0.956660i
$53$	−39.6184			−0.747517			−0.373758	−	0.927526i	$-0.621931\pi$
$53$	−39.6184			−0.747517			−0.373758	+	0.927526i	$0.621931\pi$
$54$	7.34847			0.136083
$55$	−62.4335	−	49.5744i	−1.13515	−	0.901352i
$56$			8.75144i			0.156276i
$57$	−18.1647			−0.318679
$58$		−	63.3298i		−	1.09189i
$59$	24.0107			0.406961			0.203481	−	0.979079i	$-0.434775\pi$
$59$	24.0107			0.406961			0.203481	+	0.979079i	$0.434775\pi$
$60$	−13.5644	−	10.7706i	−0.226074	−	0.179510i
$61$			76.0777i			1.24717i	0.781754	+	0.623587i	$0.214325\pi$
$61$			76.0777i			1.24717i	−0.781754	+	0.623587i	$0.785675\pi$
$62$		−	70.7353i		−	1.14089i
$63$	9.28230			0.147338
$64$	−8.00000			−0.125000
$65$	97.3961	+	77.3359i	1.49840	+	1.18978i
$66$			39.0555i			0.591750i
$67$	−76.7774			−1.14593			−0.572966	−	0.819579i	$-0.694207\pi$
$67$	−76.7774			−1.14593			−0.572966	+	0.819579i	$0.694207\pi$
$68$	25.3960			0.373470
$69$	−1.57031	−	39.8062i	−0.0227582	−	0.576902i
$70$	−17.1341	−	13.6050i	−0.244772	−	0.194358i
$71$	22.9757			0.323602			0.161801	−	0.986823i	$-0.448270\pi$
$71$	22.9757			0.323602			0.161801	+	0.986823i	$0.448270\pi$
$72$			8.48528i			0.117851i
$73$		−	51.8874i		−	0.710786i	−0.934717	−	0.355393i	$-0.884347\pi$
$73$		−	51.8874i		−	0.710786i	0.934717	−	0.355393i	$-0.115653\pi$
$74$		−	55.3356i		−	0.747779i
$75$	42.1747	−	9.81312i	0.562329	−	0.130842i
$76$		−	20.9748i		−	0.275984i
$77$			49.3334i			0.640694i
$78$		−	60.9265i		−	0.781110i
$79$			25.5241i			0.323090i	0.986865	+	0.161545i	$0.0516478\pi$
$79$			25.5241i			0.323090i	−0.986865	+	0.161545i	$0.948352\pi$
$80$	12.4368	−	15.6628i	0.155461	−	0.195786i
$81$	9.00000			0.111111
$82$			58.4877i			0.713265i
$83$	−21.6791			−0.261194			−0.130597	−	0.991436i	$-0.541689\pi$
$83$	−21.6791			−0.261194			−0.130597	+	0.991436i	$0.541689\pi$
$84$			10.7183i			0.127599i
$85$	−39.4807	+	49.7217i	−0.464479	+	0.584961i
$86$			101.308i			1.17800i
$87$		−	77.5628i		−	0.891526i
$88$	−45.0974			−0.512471
$89$		−	165.958i		−	1.86469i	−0.361566	−	0.932346i	$-0.617758\pi$
$89$		−	165.958i		−	1.86469i	0.361566	−	0.932346i	$-0.382242\pi$
$90$	−16.6130	−	13.1913i	−0.184588	−	0.146570i
$91$		−	76.9601i		−	0.845715i
$92$	45.9642	−	1.81324i	0.499611	−	0.0197092i
$93$		−	86.6327i		−	0.931534i
$94$	24.4779			0.260403
$95$	41.0657	+	32.6076i	0.432270	+	0.343237i
$96$	−9.79796			−0.102062
$97$	−0.580105			−0.00598047			−0.00299023	−	0.999996i	$-0.500952\pi$
$97$	−0.580105			−0.00598047			−0.00299023	+	0.999996i	$0.500952\pi$
$98$		−	55.7575i		−	0.568955i
$99$			47.8330i			0.483162i
$100$	11.3312	+	48.6991i	0.113312	+	0.486991i
$101$	−164.285			−1.62658			−0.813290	−	0.581859i	$-0.802326\pi$
$101$	−164.285			−1.62658			−0.813290	+	0.581859i	$0.802326\pi$
$102$	31.1036			0.304937
$103$	160.952			1.56264			0.781322	−	0.624128i	$-0.214546\pi$
$103$	160.952			1.56264			0.781322	+	0.624128i	$0.214546\pi$
$104$	70.3519			0.676461
$105$	−20.9849	−	16.6627i	−0.199856	−	0.158692i
$106$		−	56.0288i		−	0.528574i
$107$	53.6355			0.501266			0.250633	−	0.968082i	$-0.419361\pi$
$107$	53.6355			0.501266			0.250633	+	0.968082i	$0.419361\pi$
$108$			10.3923i			0.0962250i
$109$		−	77.5961i		−	0.711890i	−0.934507	−	0.355945i	$-0.884159\pi$
$109$		−	77.5961i		−	0.711890i	0.934507	−	0.355945i	$-0.115841\pi$
$110$	70.1087	−	88.2943i	0.637352	−	0.802675i
$111$		−	67.7720i		−	0.610559i
$112$	−12.3764			−0.110504
$113$	−61.1674			−0.541305			−0.270652	−	0.962677i	$-0.587239\pi$
$113$	−61.1674			−0.541305			−0.270652	+	0.962677i	$0.587239\pi$
$114$		−	25.6888i		−	0.225340i
$115$	−67.9062	+	92.8103i	−0.590489	+	0.807046i
$116$	89.5618			0.772084
$117$		−	74.6195i		−	0.637773i
$118$			33.9563i			0.287765i
$119$	39.2889			0.330159
$120$	15.2320	−	19.1830i	0.126933	−	0.159858i
$121$	−133.222			−1.10101
$122$	−107.590			−0.881886
$123$			71.6326i			0.582379i
$124$	100.035			0.806732
$125$	−112.961	−	53.5230i	−0.903691	−	0.428184i
$126$			13.1272i			0.104184i
$127$		−	17.0523i		−	0.134270i	−0.997744	−	0.0671350i	$-0.978614\pi$
$127$		−	17.0523i		−	0.134270i	0.997744	−	0.0671350i	$-0.0213858\pi$
$128$		−	11.3137i		−	0.0883883i
$129$			124.077i			0.961835i
$130$	−109.369	+	137.739i	−0.841304	+	1.05953i
$131$	210.657			1.60807			0.804034	−	0.594583i	$-0.202683\pi$
$131$	210.657			1.60807			0.804034	+	0.594583i	$0.202683\pi$
$132$	−55.2328			−0.418431
$133$		−	32.4491i		−	0.243978i
$134$		−	108.580i		−	0.810296i
$135$	−20.3466	−	16.1559i	−0.150716	−	0.119674i
$136$			35.9153i			0.264083i
$137$	0.388976			0.00283924			0.00141962	−	0.999999i	$-0.499548\pi$
$137$	0.388976			0.00283924			0.00141962	+	0.999999i	$0.499548\pi$
$138$	56.2945	−	2.22076i	0.407931	−	0.0160925i
$139$	113.401			0.815837			0.407918	−	0.913018i	$-0.366255\pi$
$139$	113.401			0.815837			0.407918	+	0.913018i	$0.366255\pi$
$140$	19.2404	−	24.2312i	0.137432	−	0.173080i
$141$	29.9792			0.212618
$142$			32.4926i			0.228821i
$143$	396.586			2.77333
$144$	−12.0000			−0.0833333
$145$	−139.233	+	175.349i	−0.960230	+	1.20930i
$146$	73.3799			0.502602
$147$		−	68.2888i		−	0.464549i
$148$	78.2564			0.528759
$149$			92.8418i			0.623099i	0.950230	+	0.311550i	$0.100848\pi$
$149$			92.8418i			0.623099i	−0.950230	+	0.311550i	$0.899152\pi$
$150$	13.8778	+	59.6440i	0.0925190	+	0.397627i
$151$	−184.936			−1.22474			−0.612372	−	0.790570i	$-0.709784\pi$
$151$	−184.936			−1.22474			−0.612372	+	0.790570i	$0.709784\pi$
$152$	29.6629			0.195150
$153$	38.0940			0.248980
$154$	−69.7680			−0.453039
$155$	−155.515	+	195.854i	−1.00332	+	1.26357i
$156$	86.1631			0.552328
$157$	−176.605			−1.12488			−0.562438	−	0.826840i	$-0.690136\pi$
$157$	−176.605			−1.12488			−0.562438	+	0.826840i	$0.690136\pi$
$158$	−36.0966			−0.228459
$159$		−	68.6210i		−	0.431579i
$160$	22.1506	+	17.5884i	0.138441	+	0.109927i
$161$	71.1090	−	2.80518i	0.441671	−	0.0174235i
$162$			12.7279i			0.0785674i
$163$			282.949i			1.73589i	0.496664	+	0.867943i	$0.334558\pi$
$163$			282.949i			1.73589i	−0.496664	+	0.867943i	$0.665442\pi$
$164$	−82.7142			−0.504355
$165$	85.8653	−	108.138i	0.520396	−	0.655382i
$166$		−	30.6588i		−	0.184692i
$167$			181.294i			1.08559i	0.839864	+	0.542797i	$0.182635\pi$
$167$			181.294i			1.08559i	−0.839864	+	0.542797i	$0.817365\pi$
$168$	−15.1579			−0.0902258
$169$	−449.674			−2.66079
$170$	−70.3171	−	55.8342i	−0.413630	−	0.328436i
$171$		−	31.4622i		−	0.183990i
$172$	−143.271			−0.832973
$173$		−	111.291i		−	0.643300i	−0.946859	−	0.321650i	$-0.895763\pi$
$173$		−	111.291i		−	0.643300i	0.946859	−	0.321650i	$-0.104237\pi$
$174$	109.690			0.630404
$175$	17.5300	+	75.3400i	0.100171	+	0.430514i
$176$		−	63.7774i		−	0.362372i
$177$			41.5878i			0.234959i
$178$	234.700			1.31854
$179$	81.4644			0.455108			0.227554	−	0.973765i	$-0.426927\pi$
$179$	81.4644			0.455108			0.227554	+	0.973765i	$0.426927\pi$
$180$	18.6553	−	23.4943i	0.103640	−	0.130524i
$181$		−	126.722i		−	0.700121i	−0.936727	−	0.350061i	$-0.886161\pi$
$181$		−	126.722i		−	0.700121i	0.936727	−	0.350061i	$-0.113839\pi$
$182$	108.838			0.598011
$183$	−131.770			−0.720057
$184$	2.56431	+	65.0033i	0.0139365	+	0.353279i
$185$	−121.658	+	153.215i	−0.657610	+	0.828188i
$186$	122.517			0.658694
$187$			202.461i			1.08268i
$188$			34.6170i			0.184133i
$189$			16.0774i			0.0850657i
$190$	−46.1141	+	58.0756i	−0.242706	+	0.305661i
$191$			111.905i			0.585888i	0.956130	+	0.292944i	$0.0946350\pi$
$191$			111.905i			0.585888i	−0.956130	+	0.292944i	$0.905365\pi$
$192$		−	13.8564i		−	0.0721688i
$193$			162.315i			0.841011i	0.907290	+	0.420506i	$0.138147\pi$
$193$			162.315i			0.841011i	−0.907290	+	0.420506i	$0.861853\pi$
$194$		−	0.820393i		−	0.00422883i
$195$	−133.950	+	168.695i	−0.686922	+	0.865103i
$196$	78.8531			0.402312
$197$			351.020i			1.78183i	0.454174	+	0.890913i	$0.349934\pi$
$197$			351.020i			1.78183i	−0.454174	+	0.890913i	$0.650066\pi$
$198$	−67.6461			−0.341647
$199$		−	17.0849i		−	0.0858540i	−0.999078	−	0.0429270i	$-0.986332\pi$
$199$		−	17.0849i		−	0.0858540i	0.999078	−	0.0429270i	$-0.0136683\pi$
$200$	−68.8709	+	16.0248i	−0.344355	+	0.0801238i
$201$		−	132.982i		−	0.661604i
$202$		−	232.333i		−	1.15017i
$203$	138.557			0.682545
$204$			43.9871i			0.215623i
$205$	128.588	−	161.942i	0.627258	−	0.789963i
$206$			227.621i			1.10496i
$207$	68.9464	−	2.71986i	0.333074	−	0.0131394i
$208$			99.4926i			0.478330i
$209$	167.215			0.800071
$210$	23.5646	−	29.6771i	0.112212	−	0.141319i
$211$	−167.474			−0.793717			−0.396858	−	0.917880i	$-0.629900\pi$
$211$	−167.474			−0.793717			−0.396858	+	0.917880i	$0.629900\pi$
$212$	79.2368			0.373758
$213$			39.7951i			0.186832i
$214$			75.8520i			0.354449i
$215$	222.731	−	280.505i	1.03596	−	1.30467i
$216$	−14.6969			−0.0680414
$217$	154.759			0.713175
$218$	109.737			0.503383
$219$	89.8716			0.410373
$220$	124.867	+	99.1487i	0.567577	+	0.450676i
$221$		−	315.839i		−	1.42914i
$222$	95.8441			0.431730
$223$		−	53.1179i		−	0.238197i	−0.992882	−	0.119098i	$-0.962000\pi$
$223$		−	53.1179i		−	0.238197i	0.992882	−	0.119098i	$-0.0380004\pi$
$224$		−	17.5029i		−	0.0781379i
$225$	16.9968	+	73.0487i	0.0755414	+	0.324661i
$226$		−	86.5038i		−	0.382760i
$227$	−371.776			−1.63778			−0.818889	−	0.573951i	$-0.805410\pi$
$227$	−371.776			−1.63778			−0.818889	+	0.573951i	$0.805410\pi$
$228$	36.3294			0.159340
$229$		−	297.261i		−	1.29808i	−0.760752	−	0.649042i	$-0.775170\pi$
$229$		−	297.261i		−	1.29808i	0.760752	−	0.649042i	$-0.224830\pi$
$230$	−131.254	−	96.0339i	−0.570668	−	0.417539i
$231$	−85.4480			−0.369905
$232$			126.660i			0.545946i
$233$			180.942i			0.776575i	0.921538	+	0.388287i	$0.126933\pi$
$233$			180.942i			0.776575i	−0.921538	+	0.388287i	$0.873067\pi$
$234$	105.528			0.450974
$235$	−67.7751	−	53.8158i	−0.288405	−	0.229003i
$236$	−48.0214			−0.203481
$237$	−44.2091			−0.186536
$238$			55.5628i			0.233457i
$239$	339.522			1.42059			0.710296	−	0.703903i	$-0.248561\pi$
$239$	339.522			1.42059			0.710296	+	0.703903i	$0.248561\pi$
$240$	27.1289	+	21.5412i	0.113037	+	0.0897552i
$241$			33.1123i			0.137395i	0.997638	+	0.0686977i	$0.0218844\pi$
$241$			33.1123i			0.137395i	−0.997638	+	0.0686977i	$0.978116\pi$
$242$		−	188.405i		−	0.778532i
$243$			15.5885i			0.0641500i
$244$		−	152.155i		−	0.623587i
$245$	−122.585	+	154.383i	−0.500349	+	0.630135i
$246$	−101.304			−0.411804
$247$	−260.855			−1.05609
$248$			141.471i			0.570446i
$249$		−	37.5492i		−	0.150800i
$250$	75.6930	−	159.752i	0.302772	−	0.639006i
$251$			21.2171i			0.0845304i	0.999106	+	0.0422652i	$0.0134574\pi$
$251$			21.2171i			0.0845304i	−0.999106	+	0.0422652i	$0.986543\pi$
$252$	−18.5646			−0.0736691
$253$	14.4555	+	366.435i	0.0571363	+	1.44836i
$254$	24.1156			0.0949432
$255$	−86.1205	−	68.3826i	−0.337727	−	0.268167i
$256$	16.0000			0.0625000
$257$		−	368.667i		−	1.43450i	−0.696815	−	0.717251i	$-0.745400\pi$
$257$		−	368.667i		−	1.43450i	0.696815	−	0.717251i	$-0.254600\pi$
$258$	−175.471			−0.680120
$259$	121.067			0.467439
$260$	−194.792	−	154.672i	−0.749201	−	0.594892i
$261$	134.343			0.514723
$262$			297.914i			1.13708i
$263$	182.829			0.695169			0.347584	−	0.937649i	$-0.387002\pi$
$263$	182.829			0.695169			0.347584	+	0.937649i	$0.387002\pi$
$264$		−	78.1110i		−	0.295875i
$265$	−123.182	+	155.134i	−0.464837	+	0.585412i
$266$	45.8900			0.172519
$267$	287.447			1.07658
$268$	153.555			0.572966
$269$	−231.329			−0.859958			−0.429979	−	0.902839i	$-0.641479\pi$
$269$	−231.329			−0.859958			−0.429979	+	0.902839i	$0.641479\pi$
$270$	22.8479	−	28.7745i	0.0846220	−	0.106572i
$271$	241.547			0.891318			0.445659	−	0.895203i	$-0.352969\pi$
$271$	241.547			0.891318			0.445659	+	0.895203i	$0.352969\pi$
$272$	−50.7919			−0.186735
$273$	133.299			0.488274
$274$			0.550095i			0.00200765i
$275$	−388.238	+	90.3344i	−1.41177	+	0.328489i
$276$	3.14063	+	79.6124i	0.0113791	+	0.288451i
$277$			217.095i			0.783737i	0.920021	+	0.391869i	$0.128171\pi$
$277$			217.095i			0.783737i	−0.920021	+	0.391869i	$0.871829\pi$
$278$			160.374i			0.576884i
$279$	150.052			0.537821
$280$	34.2681	+	27.2101i	0.122386	+	0.0971789i
$281$			262.796i			0.935218i	0.883935	+	0.467609i	$0.154885\pi$
$281$			262.796i			0.935218i	−0.883935	+	0.467609i	$0.845115\pi$
$282$			42.3970i			0.150344i
$283$	−71.0126			−0.250928			−0.125464	−	0.992098i	$-0.540042\pi$
$283$	−71.0126			−0.250928			−0.125464	+	0.992098i	$0.540042\pi$
$284$	−45.9514			−0.161801
$285$	−56.4780	+	71.1278i	−0.198168	+	0.249571i
$286$			560.858i			1.96104i
$287$	−127.963			−0.445864
$288$		−	16.9706i		−	0.0589256i
$289$	−127.761			−0.442080
$290$	−247.981	−	196.906i	−0.855107	−	0.678985i
$291$		−	1.00477i		−	0.00345282i
$292$			103.775i			0.355393i
$293$	491.470			1.67737			0.838687	−	0.544614i	$-0.183324\pi$
$293$	491.470			1.67737			0.838687	+	0.544614i	$0.183324\pi$
$294$	96.5749			0.328486
$295$	74.6544	−	94.0190i	0.253066	−	0.318708i
$296$			110.671i			0.373889i
$297$	−82.8493			−0.278954
$298$	−131.298			−0.440598
$299$	−22.5505	−	571.638i	−0.0754198	−	1.91183i
$300$	−84.3493	+	19.6262i	−0.281164	+	0.0654208i
$301$	−221.648			−0.736372
$302$		−	261.539i		−	0.866025i
$303$		−	284.549i		−	0.939106i
$304$			41.9496i			0.137992i
$305$	297.898	+	236.542i	0.976715	+	0.775546i
$306$			53.8730i			0.176056i
$307$		−	357.082i		−	1.16313i	−0.813498	−	0.581567i	$-0.802440\pi$
$307$		−	357.082i		−	1.16313i	0.813498	−	0.581567i	$-0.197560\pi$
$308$		−	98.6669i		−	0.320347i
$309$			278.778i			0.902193i
$310$	−276.979	−	219.931i	−0.893481	−	0.709455i
$311$	137.819			0.443149			0.221575	−	0.975143i	$-0.428880\pi$
$311$	137.819			0.443149			0.221575	+	0.975143i	$0.428880\pi$
$312$			121.853i			0.390555i
$313$	476.224			1.52148			0.760740	−	0.649056i	$-0.224836\pi$
$313$	476.224			1.52148			0.760740	+	0.649056i	$0.224836\pi$
$314$		−	249.758i		−	0.795407i
$315$	28.8606	−	36.3468i	0.0916211	−	0.115387i
$316$		−	51.0483i		−	0.161545i
$317$			290.212i			0.915495i	0.889082	+	0.457748i	$0.151344\pi$
$317$			290.212i			0.915495i	−0.889082	+	0.457748i	$0.848656\pi$
$318$	97.0448			0.305172
$319$			714.002i			2.23825i
$320$	−24.8737	+	31.3257i	−0.0777303	+	0.0978928i
$321$			92.8994i			0.289406i
$322$	3.96712	+	100.563i	0.0123202	+	0.312309i
$323$		−	133.169i		−	0.412288i
$324$	−18.0000			−0.0555556
$325$	605.650	−	140.922i	1.86354	−	0.433605i
$326$	−400.151			−1.22746
$327$	134.400			0.411010
$328$		−	116.975i		−	0.356633i
$329$			53.5542i			0.162779i
$330$	152.930	+	121.432i	0.463425	+	0.367975i
$331$	124.642			0.376561			0.188280	−	0.982115i	$-0.439709\pi$
$331$	124.642			0.376561			0.188280	+	0.982115i	$0.439709\pi$
$332$	43.3581			0.130597
$333$	117.385			0.352506
$334$	−256.389			−0.767631
$335$	−238.717	+	300.638i	−0.712589	+	0.897428i
$336$		−	21.4366i		−	0.0637993i
$337$	281.809			0.836228			0.418114	−	0.908395i	$-0.362691\pi$
$337$	281.809			0.836228			0.418114	+	0.908395i	$0.362691\pi$
$338$		−	635.935i		−	1.88146i
$339$		−	105.945i		−	0.312522i
$340$	78.9615	−	99.4433i	0.232240	−	0.292480i
$341$			797.495i			2.33869i
$342$	44.4943			0.130100
$343$	273.601			0.797670
$344$		−	202.616i		−	0.589001i
$345$	−160.752	−	117.617i	−0.465948	−	0.340919i
$346$	157.389			0.454882
$347$			31.0131i			0.0893749i	0.999001	+	0.0446874i	$0.0142292\pi$
$347$			31.0131i			0.0893749i	−0.999001	+	0.0446874i	$0.985771\pi$
$348$			155.126i			0.445763i
$349$	226.092			0.647828			0.323914	−	0.946087i	$-0.395001\pi$
$349$	226.092			0.647828			0.323914	+	0.946087i	$0.395001\pi$
$350$	−106.547	+	24.7911i	−0.304420	+	0.0708318i
$351$	129.245			0.368219
$352$	90.1949			0.256235
$353$			230.573i			0.653180i	0.945166	+	0.326590i	$0.105900\pi$
$353$			230.573i			0.653180i	−0.945166	+	0.326590i	$0.894100\pi$
$354$	−58.8140			−0.166141
$355$	71.4364	−	89.9663i	0.201229	−	0.253426i
$356$			331.915i			0.932346i
$357$			68.0503i			0.190617i
$358$			115.208i			0.321810i
$359$		−	569.575i		−	1.58656i	−0.608858	−	0.793279i	$-0.708372\pi$
$359$		−	569.575i		−	1.58656i	0.608858	−	0.793279i	$-0.291628\pi$
$360$	33.2259	+	26.3825i	0.0922942	+	0.0732848i
$361$	251.014			0.695331
$362$	179.212			0.495061
$363$		−	230.748i		−	0.635669i
$364$			153.920i			0.422858i
$365$	−203.176	−	161.329i	−0.556647	−	0.441997i
$366$		−	186.351i		−	0.509157i
$367$	−707.351			−1.92739			−0.963693	−	0.267012i	$-0.913964\pi$
$367$	−707.351			−1.92739			−0.963693	+	0.267012i	$0.913964\pi$
$368$	−91.9285	+	3.62648i	−0.249806	+	0.00985458i
$369$	−124.071			−0.336236
$370$	−216.678	−	172.050i	−0.585617	−	0.465000i
$371$	122.583			0.330413
$372$			173.265i			0.465767i
$373$	−476.230			−1.27676			−0.638378	−	0.769723i	$-0.720394\pi$
$373$	−476.230			−1.27676			−0.638378	+	0.769723i	$0.720394\pi$
$374$	−286.323			−0.765570
$375$	92.7046	−	195.655i	0.247212	−	0.521747i
$376$	−48.9558			−0.130202
$377$		−	1113.84i		−	2.95449i
$378$	−22.7369			−0.0601506
$379$			218.771i			0.577232i	0.957445	+	0.288616i	$0.0931950\pi$
$379$			218.771i			0.577232i	−0.957445	+	0.288616i	$0.906805\pi$
$380$	−82.1313	−	65.2151i	−0.216135	−	0.171619i
$381$	29.5354			0.0775208
$382$	−158.257			−0.414286
$383$	25.9382			0.0677238			0.0338619	−	0.999427i	$-0.489219\pi$
$383$	25.9382			0.0677238			0.0338619	+	0.999427i	$0.489219\pi$
$384$	19.5959			0.0510310
$385$	193.176	+	153.388i	0.501755	+	0.398411i
$386$	−229.548			−0.594685
$387$	−214.907			−0.555315
$388$	1.16021			0.00299023
$389$		−	117.093i		−	0.301011i	−0.988609	−	0.150505i	$-0.951910\pi$
$389$		−	117.093i		−	0.301011i	0.988609	−	0.150505i	$-0.0480901\pi$
$390$	−238.571	−	189.434i	−0.611720	−	0.485727i
$391$	291.827	−	11.5123i	0.746360	−	0.0294431i
$392$			111.515i			0.284477i
$393$			364.869i			0.928419i
$394$	−496.417			−1.25994
$395$	99.9452	+	79.3600i	0.253026	+	0.200911i
$396$		−	95.6661i		−	0.241581i
$397$			184.113i			0.463760i	0.972744	+	0.231880i	$0.0744876\pi$
$397$			184.113i			0.463760i	−0.972744	+	0.231880i	$0.925512\pi$
$398$	24.1618			0.0607079
$399$	56.2035			0.140861
$400$	−22.6624	−	97.3982i	−0.0566561	−	0.243496i
$401$		−	483.910i		−	1.20676i	−0.797454	−	0.603379i	$-0.793821\pi$
$401$		−	483.910i		−	1.20676i	0.797454	−	0.603379i	$-0.206179\pi$
$402$	188.066			0.467825
$403$		−	1244.09i		−	3.08707i
$404$	328.569			0.813290
$405$	27.9829	−	35.2414i	0.0690936	−	0.0870158i
$406$			195.949i			0.482632i
$407$			623.873i			1.53286i
$408$	−62.2072			−0.152469
$409$	−587.697			−1.43691			−0.718457	−	0.695572i	$-0.755151\pi$
$409$	−587.697			−1.43691			−0.718457	+	0.695572i	$0.755151\pi$
$410$	229.021	+	181.851i	0.558588	+	0.443538i
$411$			0.673726i			0.00163924i
$412$	−321.905			−0.781322
$413$	−74.2915			−0.179883
$414$	3.84647	+	97.5049i	0.00929098	+	0.235519i
$415$	−67.4048	+	84.8890i	−0.162421	+	0.204552i
$416$	−140.704			−0.338230
$417$			196.417i			0.471024i
$418$			236.477i			0.565736i
$419$			249.476i			0.595408i	0.954658	+	0.297704i	$0.0962208\pi$
$419$			249.476i			0.595408i	−0.954658	+	0.297704i	$0.903779\pi$
$420$	41.9697	+	33.3254i	0.0999279	+	0.0793462i
$421$		−	297.570i		−	0.706816i	−0.935469	−	0.353408i	$-0.885023\pi$
$421$		−	297.570i		−	0.706816i	0.935469	−	0.353408i	$-0.114977\pi$
$422$		−	236.844i		−	0.561243i
$423$			51.9255i			0.122755i
$424$			112.058i			0.264287i
$425$	71.9418	+	309.190i	0.169275	+	0.727507i
$426$	−56.2788			−0.132110
$427$		−	235.392i		−	0.551269i
$428$	−107.271			−0.250633
$429$			686.908i			1.60118i
$430$	396.694	+	314.989i	0.922543	+	0.732531i
$431$		−	83.3118i		−	0.193299i	−0.995318	−	0.0966495i	$-0.969187\pi$
$431$		−	83.3118i		−	0.193299i	0.995318	−	0.0966495i	$-0.0308126\pi$
$432$		−	20.7846i		−	0.0481125i
$433$	574.608			1.32704			0.663520	−	0.748159i	$-0.269062\pi$
$433$	574.608			1.32704			0.663520	+	0.748159i	$0.269062\pi$
$434$			218.862i			0.504291i
$435$	−303.714	−	241.159i	−0.698192	−	0.554389i
$436$			155.192i			0.355945i
$437$	−9.50810	−	241.023i	−0.0217577	−	0.551540i
$438$			127.098i			0.290177i
$439$	−196.774			−0.448231			−0.224116	−	0.974563i	$-0.571949\pi$
$439$	−196.774			−0.448231			−0.224116	+	0.974563i	$0.571949\pi$
$440$	−140.217	+	176.589i	−0.318676	+	0.401338i
$441$	118.280			0.268208
$442$	446.664			1.01055
$443$			13.1466i			0.0296764i	0.999890	+	0.0148382i	$0.00472332\pi$
$443$			13.1466i			0.0296764i	−0.999890	+	0.0148382i	$0.995277\pi$
$444$			135.544i			0.305279i
$445$	−649.842	−	515.997i	−1.46032	−	1.15954i
$446$	75.1201			0.168431
$447$	−160.807			−0.359747
$448$	24.7528			0.0552518
$449$	7.26549			0.0161815			0.00809074	−	0.999967i	$-0.497425\pi$
$449$	7.26549			0.0161815			0.00809074	+	0.999967i	$0.497425\pi$
$450$	−103.306	+	24.0371i	−0.229570	+	0.0534159i
$451$		−	659.412i		−	1.46211i
$452$	122.335			0.270652
$453$		−	320.319i		−	0.707106i
$454$		−	525.770i		−	1.15808i
$455$	−301.354	−	239.285i	−0.662315	−	0.525901i
$456$			51.3776i			0.112670i
$457$	−635.868			−1.39140			−0.695698	−	0.718334i	$-0.744905\pi$
$457$	−635.868			−1.39140			−0.695698	+	0.718334i	$0.744905\pi$
$458$	420.391			0.917885
$459$			65.9807i			0.143749i
$460$	135.812	−	185.621i	0.295244	−	0.403523i
$461$	−638.029			−1.38401			−0.692006	−	0.721892i	$-0.743273\pi$
$461$	−638.029			−1.38401			−0.692006	+	0.721892i	$0.743273\pi$
$462$		−	120.842i		−	0.261562i
$463$		−	593.754i		−	1.28241i	−0.767371	−	0.641203i	$-0.778436\pi$
$463$		−	593.754i		−	1.28241i	0.767371	−	0.641203i	$-0.221564\pi$
$464$	−179.124			−0.386042
$465$	−339.229	−	269.359i	−0.729524	−	0.579267i
$466$	−255.891			−0.549121
$467$	596.261			1.27679			0.638395	−	0.769709i	$-0.279599\pi$
$467$	596.261			1.27679			0.638395	+	0.769709i	$0.279599\pi$
$468$			149.239i			0.318887i
$469$	237.557			0.506519
$470$	76.1070	−	95.8484i	0.161930	−	0.203933i
$471$		−	305.890i		−	0.649447i
$472$		−	67.9125i		−	0.143882i
$473$		−	1142.18i		−	2.41477i
$474$		−	62.5211i		−	0.131901i
$475$	255.364	−	59.4175i	0.537608	−	0.125090i
$476$	−78.5777			−0.165079
$477$	118.855			0.249172
$478$			480.156i			1.00451i
$479$			203.911i			0.425702i	0.977085	+	0.212851i	$0.0682750\pi$
$479$			203.911i			0.425702i	−0.977085	+	0.212851i	$0.931725\pi$
$480$	−30.4639	+	38.3660i	−0.0634665	+	0.0799291i
$481$		−	973.242i		−	2.02337i
$482$	−46.8279			−0.0971533
$483$	4.85871	+	123.164i	0.0100594	+	0.254999i
$484$	266.444			0.550505
$485$	−1.80367	+	2.27153i	−0.00371891	+	0.00468356i
$486$	−22.0454			−0.0453609
$487$		−	390.999i		−	0.802873i	−0.915887	−	0.401436i	$-0.868511\pi$
$487$		−	390.999i		−	0.802873i	0.915887	−	0.401436i	$-0.131489\pi$
$488$	215.180			0.440943
$489$	−490.083			−1.00221
$490$	−218.330	−	173.362i	−0.445572	−	0.353800i
$491$	449.372			0.915217			0.457609	−	0.889154i	$-0.348706\pi$
$491$	449.372			0.915217			0.457609	+	0.889154i	$0.348706\pi$
$492$		−	143.265i		−	0.291189i
$493$	568.627			1.15340
$494$		−	368.905i		−	0.746770i
$495$	187.300	+	148.723i	0.378385	+	0.300451i
$496$	−200.070			−0.403366
$497$	−71.0892			−0.143037
$498$	53.1027			0.106632
$499$	770.506			1.54410			0.772050	−	0.635561i	$-0.219231\pi$
$499$	770.506			1.54410			0.772050	+	0.635561i	$0.219231\pi$
$500$	225.923	+	107.046i	0.451846	+	0.214092i
$501$	−314.011			−0.626768
$502$	−30.0055			−0.0597720
$503$	−185.848			−0.369480			−0.184740	−	0.982787i	$-0.559144\pi$
$503$	−185.848			−0.369480			−0.184740	+	0.982787i	$0.559144\pi$
$504$		−	26.2543i		−	0.0520919i
$505$	−510.795	+	643.291i	−1.01148	+	1.27384i
$506$	−518.217	+	20.4431i	−1.02414	+	0.0404015i
$507$		−	778.858i		−	1.53621i
$508$			34.1046i			0.0671350i
$509$	−110.051			−0.216210			−0.108105	−	0.994139i	$-0.534478\pi$
$509$	−110.051			−0.216210			−0.108105	+	0.994139i	$0.534478\pi$
$510$	96.7076	−	121.793i	0.189623	−	0.238809i
$511$			160.545i			0.314178i
$512$			22.6274i			0.0441942i
$513$	54.4942			0.106226
$514$	521.374			1.01435
$515$	500.435	−	630.243i	0.971718	−	1.22377i
$516$		−	248.153i		−	0.480917i
$517$	−275.973			−0.533796
$518$			171.214i			0.330529i
$519$	192.761			0.371409
$520$	218.739	−	275.478i	0.420652	−	0.529765i
$521$		−	39.4422i		−	0.0757049i	−0.999283	−	0.0378524i	$-0.987948\pi$
$521$		−	39.4422i		−	0.0757049i	0.999283	−	0.0378524i	$-0.0120517\pi$
$522$			189.989i			0.363964i
$523$	−288.174			−0.551003			−0.275501	−	0.961301i	$-0.588844\pi$
$523$	−288.174			−0.551003			−0.275501	+	0.961301i	$0.588844\pi$
$524$	−421.314			−0.804034
$525$	−130.493	+	30.3628i	−0.248558	+	0.0578339i
$526$			258.560i			0.491558i
$527$	635.120			1.20516
$528$	110.466			0.209215
$529$	527.356	−	41.6722i	0.996892	−	0.0787753i
$530$	−219.393	−	174.206i	−0.413949	−	0.328690i
$531$	−72.0321			−0.135654
$532$			64.8982i			0.121989i
$533$			1028.68i			1.92998i
$534$			406.512i			0.761258i
$535$	166.764	−	210.021i	0.311709	−	0.392563i
$536$			217.159i			0.405148i
$537$			141.100i			0.262757i
$538$		−	327.148i		−	0.608082i
$539$			628.630i			1.16629i
$540$	40.6933	+	32.3119i	0.0753579	+	0.0598368i
$541$	−153.598			−0.283915			−0.141958	−	0.989873i	$-0.545340\pi$
$541$	−153.598			−0.283915			−0.141958	+	0.989873i	$0.545340\pi$
$542$			341.599i			0.630257i
$543$	219.489			0.404215
$544$		−	71.8307i		−	0.132042i
$545$	−303.844	−	241.263i	−0.557512	−	0.442684i
$546$			188.513i			0.345262i
$547$		−	756.260i		−	1.38256i	−0.722588	−	0.691279i	$-0.757047\pi$
$547$		−	756.260i		−	1.38256i	0.722588	−	0.691279i	$-0.242953\pi$
$548$	−0.777952			−0.00141962
$549$		−	228.233i		−	0.415725i
$550$	−127.752	−	549.051i	−0.232277	−	0.998275i
$551$		−	469.635i		−	0.852333i
$552$	−112.589	+	4.44152i	−0.203965	+	0.00804623i
$553$		−	78.9743i		−	0.142811i
$554$	−307.019			−0.554186
$555$	−265.376	−	210.718i	−0.478154	−	0.379671i
$556$	−226.803			−0.407918
$557$	276.554			0.496506			0.248253	−	0.968695i	$-0.420144\pi$
$557$	276.554			0.496506			0.248253	+	0.968695i	$0.420144\pi$
$558$			212.206i			0.380297i
$559$			1781.81i			3.18749i
$560$	−38.4809	+	48.4624i	−0.0687158	+	0.0865401i
$561$	−350.673			−0.625086
$562$	−371.650			−0.661299
$563$	−535.076			−0.950401			−0.475201	−	0.879878i	$-0.657624\pi$
$563$	−535.076			−0.950401			−0.475201	+	0.879878i	$0.657624\pi$
$564$	−59.9584			−0.106309
$565$	−190.183	+	239.514i	−0.336606	+	0.423919i
$566$		−	100.427i		−	0.177433i
$567$	−27.8469			−0.0491127
$568$		−	64.9851i		−	0.114410i
$569$		−	94.4406i		−	0.165976i	−0.996551	−	0.0829882i	$-0.973554\pi$
$569$		−	94.4406i		−	0.165976i	0.996551	−	0.0829882i	$-0.0264464\pi$
$570$	−100.590	−	79.8719i	−0.176474	−	0.140126i
$571$		−	594.892i		−	1.04184i	−0.853605	−	0.520921i	$-0.825589\pi$
$571$		−	594.892i		−	1.04184i	0.853605	−	0.520921i	$-0.174411\pi$
$572$	−793.173			−1.38667
$573$	−193.825			−0.338263
$574$		−	180.967i		−	0.315274i
$575$	152.284	+	554.468i	0.264841	+	0.964292i
$576$	24.0000			0.0416667
$577$			511.175i			0.885919i	0.896542	+	0.442960i	$0.146071\pi$
$577$			511.175i			0.885919i	−0.896542	+	0.442960i	$0.853929\pi$
$578$		−	180.682i		−	0.312598i
$579$	−281.138			−0.485558
$580$	278.467	−	350.698i	0.480115	−	0.604652i
$581$	67.0772			0.115451
$582$	1.42096			0.00244152
$583$			631.689i			1.08351i
$584$	−146.760			−0.251301
$585$	−292.188	−	232.008i	−0.499467	−	0.396594i
$586$			695.044i			1.18608i
$587$			492.563i			0.839119i	0.907728	+	0.419560i	$0.137815\pi$
$587$			492.563i			0.839119i	−0.907728	+	0.419560i	$0.862185\pi$
$588$			136.578i			0.232275i
$589$		−	524.553i		−	0.890582i
$590$	132.963	+	105.577i	0.225361	+	0.178944i
$591$	−607.984			−1.02874
$592$	−156.513			−0.264380
$593$			535.477i			0.902996i	0.892272	+	0.451498i	$0.149110\pi$
$593$			535.477i			0.902996i	−0.892272	+	0.451498i	$0.850890\pi$
$594$		−	117.167i		−	0.197250i
$595$	122.157	−	153.844i	0.205307	−	0.258561i
$596$		−	185.684i		−	0.311550i
$597$	29.5920			0.0495678
$598$	808.418	−	31.8913i	1.35187	−	0.0533299i
$599$	−522.025			−0.871495			−0.435747	−	0.900069i	$-0.643516\pi$
$599$	−522.025			−0.871495			−0.435747	+	0.900069i	$0.643516\pi$
$600$	−27.7557	−	119.288i	−0.0462595	−	0.198813i
$601$	500.049			0.832028			0.416014	−	0.909358i	$-0.363427\pi$
$601$	500.049			0.832028			0.416014	+	0.909358i	$0.363427\pi$
$602$		−	313.458i		−	0.520694i
$603$	230.332			0.381977
$604$	369.873			0.612372
$605$	−414.216	+	521.660i	−0.684655	+	0.862248i
$606$	402.413			0.664048
$607$			232.429i			0.382915i	0.981501	+	0.191457i	$0.0613214\pi$
$607$			232.429i			0.382915i	−0.981501	+	0.191457i	$0.938679\pi$
$608$	−59.3257			−0.0975752
$609$			239.987i			0.394068i
$610$	−334.520	+	421.292i	−0.548394	+	0.690642i
$611$	430.517			0.704610
$612$	−76.1879			−0.124490
$613$	654.378			1.06750			0.533751	−	0.845642i	$-0.320782\pi$
$613$	654.378			1.06750			0.533751	+	0.845642i	$0.320782\pi$
$614$	504.991			0.822460
$615$	280.493	+	222.721i	0.456085	+	0.362148i
$616$	139.536			0.226520
$617$	−675.896			−1.09546			−0.547728	−	0.836657i	$-0.684507\pi$
$617$	−675.896			−1.09546			−0.547728	+	0.836657i	$0.684507\pi$
$618$	−394.251			−0.637947
$619$			1153.52i			1.86352i	0.363075	+	0.931760i	$0.381727\pi$
$619$			1153.52i			1.86352i	−0.363075	+	0.931760i	$0.618273\pi$
$620$	311.029	−	391.707i	0.501660	−	0.631786i
$621$	4.71094	+	119.419i	0.00758606	+	0.192301i
$622$			194.906i			0.313354i
$623$			513.490i			0.824221i
$624$	−172.326			−0.276164
$625$	−560.802	+	275.910i	−0.897283	+	0.441456i
$626$			673.482i			1.07585i
$627$			289.625i			0.461921i
$628$	353.211			0.562438
$629$	496.849			0.789903
$630$	51.4022	+	40.8151i	0.0815908	+	0.0647859i
$631$			210.863i			0.334173i	0.985942	+	0.167086i	$0.0534359\pi$
$631$			210.863i			0.334173i	−0.985942	+	0.167086i	$0.946564\pi$
$632$	72.1932			0.114230
$633$		−	290.074i		−	0.458253i
$634$	−410.422			−0.647353
$635$	−66.7719	−	53.0192i	−0.105153	−	0.0834947i
$636$			137.242i			0.215789i
$637$		−	980.662i		−	1.53950i
$638$	−1009.75			−1.58268
$639$	−68.9272			−0.107867
$640$	−44.3012	−	35.1767i	−0.0692207	−	0.0549636i
$641$		−	358.037i		−	0.558560i	−0.960210	−	0.279280i	$-0.909904\pi$
$641$		−	358.037i		−	0.558560i	0.960210	−	0.279280i	$-0.0900958\pi$
$642$	−131.380			−0.204641
$643$	−1177.59			−1.83141			−0.915703	−	0.401855i	$-0.868366\pi$
$643$	−1177.59			−1.83141			−0.915703	+	0.401855i	$0.868366\pi$
$644$	−142.218	+	5.61036i	−0.220835	+	0.00871173i
$645$	485.848	+	385.781i	0.753253	+	0.598109i
$646$	188.329			0.291531
$647$		−	556.482i		−	0.860096i	−0.902806	−	0.430048i	$-0.858497\pi$
$647$		−	556.482i		−	0.860096i	0.902806	−	0.430048i	$-0.141503\pi$
$648$		−	25.4558i		−	0.0392837i
$649$		−	382.835i		−	0.589884i
$650$	199.293	+	856.519i	0.306605	+	1.31772i
$651$			268.050i			0.411752i
$652$		−	565.899i		−	0.867943i
$653$			1076.49i			1.64853i	0.566204	+	0.824265i	$0.308412\pi$
$653$			1076.49i			1.64853i	−0.566204	+	0.824265i	$0.691588\pi$
$654$			190.071i			0.290628i
$655$	654.977	−	824.872i	0.999965	−	1.25935i
$656$	165.428			0.252177
$657$			155.662i			0.236929i
$658$	−75.7371			−0.115102
$659$		−	1142.54i		−	1.73375i	−0.498526	−	0.866875i	$-0.666125\pi$
$659$		−	1142.54i		−	1.73375i	0.498526	−	0.866875i	$-0.333875\pi$
$660$	−171.731	+	216.276i	−0.260198	+	0.327691i
$661$			1194.32i			1.80684i	0.428754	+	0.903421i	$0.358953\pi$
$661$			1194.32i			1.80684i	−0.428754	+	0.903421i	$0.641047\pi$
$662$			176.270i			0.266269i
$663$	547.049			0.825112
$664$			61.3177i			0.0923459i
$665$	−127.061	−	100.891i	−0.191070	−	0.151716i
$666$			166.007i			0.249260i
$667$	1029.16	−	40.5993i	1.54297	−	0.0608685i
$668$		−	362.588i		−	0.542797i
$669$	92.0029			0.137523
$670$	−425.167	−	337.597i	−0.634577	−	0.503877i
$671$	1213.01			1.80776
$672$	30.3159			0.0451129
$673$		−	481.936i		−	0.716100i	−0.933702	−	0.358050i	$-0.883442\pi$
$673$		−	481.936i		−	0.716100i	0.933702	−	0.358050i	$-0.116558\pi$
$674$			398.538i			0.591302i
$675$	−126.524	+	29.4394i	−0.187443	+	0.0436139i
$676$	899.348			1.33040
$677$	−180.841			−0.267121			−0.133560	−	0.991041i	$-0.542641\pi$
$677$	−180.841			−0.267121			−0.133560	+	0.991041i	$0.542641\pi$
$678$	149.829			0.220987
$679$	1.79490			0.00264345
$680$	140.634	+	111.668i	0.206815	+	0.164218i
$681$		−	643.935i		−	0.945572i
$682$	−1127.83			−1.65371
$683$		−	18.5491i		−	0.0271582i	−0.999908	−	0.0135791i	$-0.995678\pi$
$683$		−	18.5491i		−	0.0271582i	0.999908	−	0.0135791i	$-0.00432250\pi$
$684$			62.9244i			0.0919948i
$685$	1.20941	−	1.52312i	0.00176556	−	0.00222353i
$686$			386.930i			0.564038i
$687$	514.872			0.749450
$688$	286.543			0.416487
$689$		−	985.434i		−	1.43024i
$690$	166.336	−	227.338i	0.241066	−	0.329475i
$691$	−502.845			−0.727706			−0.363853	−	0.931456i	$-0.618539\pi$
$691$	−502.845			−0.727706			−0.363853	+	0.931456i	$0.618539\pi$
$692$			222.582i			0.321650i
$693$		−	148.000i		−	0.213565i
$694$	−43.8591			−0.0631976
$695$	352.589	−	444.047i	0.507322	−	0.638916i
$696$	−219.381			−0.315202
$697$	−525.152			−0.753446
$698$			319.742i			0.458084i
$699$	−313.401			−0.448356
$700$	−35.0599	−	150.680i	−0.0500856	−	0.215257i
$701$		−	183.664i		−	0.262002i	−0.991382	−	0.131001i	$-0.958181\pi$
$701$		−	183.664i		−	0.262002i	0.991382	−	0.131001i	$-0.0418192\pi$
$702$			182.780i			0.260370i
$703$		−	410.353i		−	0.583717i
$704$			127.555i			0.181186i
$705$	93.2116	−	117.390i	0.132215	−	0.166510i
$706$	−326.079			−0.461868
$707$	508.313			0.718972
$708$		−	83.1755i		−	0.117480i
$709$			39.2008i			0.0552903i	0.999618	+	0.0276452i	$0.00880085\pi$
$709$			39.2008i			0.0552903i	−0.999618	+	0.0276452i	$0.991199\pi$
$710$	127.232	+	101.026i	0.179199	+	0.142291i
$711$		−	76.5724i		−	0.107697i
$712$	−469.399			−0.659268
$713$	1149.51	−	45.3468i	1.61221	−	0.0636000i
$714$	−96.2377			−0.134787
$715$	1233.07	−	1552.92i	1.72457	−	2.17191i
$716$	−162.929			−0.227554
$717$			588.069i			0.820179i
$718$	805.500			1.12187
$719$	−44.6052			−0.0620378			−0.0310189	−	0.999519i	$-0.509875\pi$
$719$	−44.6052			−0.0620378			−0.0310189	+	0.999519i	$0.509875\pi$
$720$	−37.3105	+	46.9885i	−0.0518202	+	0.0652619i
$721$	−498.003			−0.690711
$722$			354.988i			0.491673i
$723$	−57.3522			−0.0793253
$724$			253.444i			0.350061i
$725$	253.711	+	1090.39i	0.349946	+	1.50399i
$726$	326.327			0.449486
$727$	−966.099			−1.32889			−0.664443	−	0.747339i	$-0.731331\pi$
$727$	−966.099			−1.32889			−0.664443	+	0.747339i	$0.731331\pi$
$728$	−217.676			−0.299005
$729$	−27.0000			−0.0370370
$730$	228.153	−	287.334i	0.312539	−	0.393609i
$731$	−909.629			−1.24436
$732$	263.541			0.360028
$733$	58.5900			0.0799317			0.0399659	−	0.999201i	$-0.487275\pi$
$733$	58.5900			0.0799317			0.0399659	+	0.999201i	$0.487275\pi$
$734$		−	1000.35i		−	1.36287i
$735$	−267.399	−	212.324i	−0.363808	−	0.288876i
$736$	−5.12862	−	130.007i	−0.00696824	−	0.176639i
$737$			1224.17i			1.66101i
$738$		−	175.463i		−	0.237755i
$739$	−513.758			−0.695207			−0.347603	−	0.937642i	$-0.613004\pi$
$739$	−513.758			−0.695207			−0.347603	+	0.937642i	$0.613004\pi$
$740$	243.316	−	306.429i	0.328805	−	0.414094i
$741$		−	451.814i		−	0.609735i
$742$			173.359i			0.233637i
$743$	−474.006			−0.637962			−0.318981	−	0.947761i	$-0.603341\pi$
$743$	−474.006			−0.637962			−0.318981	+	0.947761i	$0.603341\pi$
$744$	−245.034			−0.329347
$745$	363.542	+	288.665i	0.487976	+	0.387470i
$746$		−	673.491i		−	0.902803i
$747$	65.0372			0.0870645
$748$		−	404.922i		−	0.541340i
$749$	−165.954			−0.221567
$750$	276.698	+	131.104i	0.368930	+	0.174805i
$751$		−	870.368i		−	1.15894i	−0.814992	−	0.579472i	$-0.803259\pi$
$751$		−	870.368i		−	1.15894i	0.814992	−	0.579472i	$-0.196741\pi$
$752$		−	69.2340i		−	0.0920665i
$753$	−36.7491			−0.0488036
$754$	1575.21			2.08914
$755$	−575.006	+	724.157i	−0.761597	+	0.959149i
$756$		−	32.1548i		−	0.0425329i
$757$	439.359			0.580395			0.290197	−	0.956967i	$-0.406279\pi$
$757$	439.359			0.580395			0.290197	+	0.956967i	$0.406279\pi$
$758$	−309.389			−0.408164
$759$	−634.684	+	25.0376i	−0.836211	+	0.0329877i
$760$	92.2281	−	116.151i	0.121353	−	0.152831i
$761$	−814.037			−1.06969			−0.534847	−	0.844949i	$-0.679631\pi$
$761$	−814.037			−1.06969			−0.534847	+	0.844949i	$0.679631\pi$
$762$			41.7694i			0.0548155i
$763$			240.090i			0.314666i
$764$		−	223.809i		−	0.292944i
$765$	118.442	−	149.165i	0.154826	−	0.194987i
$766$			36.6822i			0.0478880i
$767$			597.222i			0.778647i
$768$			27.7128i			0.0360844i
$769$			1396.26i			1.81568i	0.419320	+	0.907838i	$0.362269\pi$
$769$			1396.26i			1.81568i	−0.419320	+	0.907838i	$0.637731\pi$
$770$	−216.923	+	273.191i	−0.281719	+	0.354794i
$771$	638.550			0.828210
$772$		−	324.630i		−	0.420506i
$773$	60.6538			0.0784654			0.0392327	−	0.999230i	$-0.487509\pi$
$773$	60.6538			0.0784654			0.0392327	+	0.999230i	$0.487509\pi$
$774$		−	303.924i		−	0.392667i
$775$	283.379	+	1217.90i	0.365650	+	1.57149i
$776$			1.64079i			0.00211441i
$777$			209.693i			0.269876i
$778$	165.595			0.212847
$779$			433.728i			0.556776i
$780$	267.899	−	337.390i	0.343461	−	0.432551i
$781$		−	366.333i		−	0.469056i
$782$	16.2808	+	412.705i	0.0208194	+	0.527756i
$783$			232.688i			0.297175i
$784$	−157.706			−0.201156
$785$	−549.104	+	691.536i	−0.699495	+	0.880938i
$786$	−516.002			−0.656491
$787$	910.682			1.15716			0.578578	−	0.815627i	$-0.303608\pi$
$787$	910.682			1.15716			0.578578	+	0.815627i	$0.303608\pi$
$788$		−	702.039i		−	0.890913i
$789$			316.670i			0.401356i
$790$	−112.232	+	141.344i	−0.142066	+	0.178916i
$791$	189.258			0.239265
$792$	135.292			0.170824
$793$	−1892.29			−2.38624
$794$	−260.374			−0.327928
$795$	−268.700	−	213.357i	−0.337988	−	0.268374i
$796$			34.1699i			0.0429270i
$797$	554.031			0.695146			0.347573	−	0.937653i	$-0.387006\pi$
$797$	554.031			0.695146			0.347573	+	0.937653i	$0.387006\pi$
$798$			79.4837i			0.0996037i
$799$			219.783i			0.275073i
$800$	137.742	−	32.0495i	0.172177	−	0.0400619i
$801$			497.873i			0.621564i
$802$	684.352			0.853307
$803$	−827.311			−1.03027
$804$			265.965i			0.330802i
$805$	210.109	−	287.164i	0.261005	−	0.356726i
$806$	1759.41			2.18289
$807$		−	400.673i		−	0.496497i
$808$			464.667i			0.575083i
$809$	91.9575			0.113668			0.0568341	−	0.998384i	$-0.481899\pi$
$809$	91.9575			0.113668			0.0568341	+	0.998384i	$0.481899\pi$
$810$	49.8389	+	39.5738i	0.0615295	+	0.0488565i
$811$	11.1806			0.0137862			0.00689311	−	0.999976i	$-0.497806\pi$
$811$	11.1806			0.0137862			0.00689311	+	0.999976i	$0.497806\pi$
$812$	−277.113			−0.341273
$813$			418.372i			0.514602i
$814$	−882.290			−1.08389
$815$	1107.95	+	879.749i	1.35945	+	1.07945i
$816$		−	87.9742i		−	0.107812i
$817$			751.272i			0.919550i
$818$		−	831.130i		−	1.01605i
$819$			230.880i			0.281905i
$820$	−257.176	+	323.885i	−0.313629	+	0.394982i
$821$	−1163.60			−1.41730			−0.708651	−	0.705559i	$-0.750696\pi$
$821$	−1163.60			−1.41730			−0.708651	+	0.705559i	$0.750696\pi$
$822$	−0.952793			−0.00115912
$823$		−	261.580i		−	0.317837i	−0.987292	−	0.158918i	$-0.949199\pi$
$823$		−	261.580i		−	0.317837i	0.987292	−	0.158918i	$-0.0508007\pi$
$824$		−	455.242i		−	0.552478i
$825$	−156.464	−	672.448i	−0.189653	−	0.815088i
$826$		−	105.064i		−	0.127196i
$827$	−773.865			−0.935750			−0.467875	−	0.883795i	$-0.654980\pi$
$827$	−773.865			−0.935750			−0.467875	+	0.883795i	$0.654980\pi$
$828$	−137.893	+	5.43973i	−0.166537	+	0.00656972i
$829$	1240.96			1.49693			0.748466	−	0.663173i	$-0.230791\pi$
$829$	1240.96			1.49693			0.748466	+	0.663173i	$0.230791\pi$
$830$	−120.051	−	95.3248i	−0.144640	−	0.114849i
$831$	−376.020			−0.452491
$832$		−	198.985i		−	0.239165i
$833$	500.638			0.601006
$834$	−277.775			−0.333064
$835$	709.896	+	563.682i	0.850175	+	0.675068i
$836$	−334.430			−0.400036
$837$			259.898i			0.310511i
$838$	−352.812			−0.421017
$839$		−	634.862i		−	0.756689i	−0.925665	−	0.378344i	$-0.876493\pi$
$839$		−	634.862i		−	0.756689i	0.925665	−	0.378344i	$-0.123507\pi$
$840$	−47.1292	+	59.3541i	−0.0561062	+	0.0706597i
$841$	1164.33			1.38446
$842$	420.827			0.499795
$843$	−455.177			−0.539948
$844$	334.949			0.396858
$845$	−1398.13	+	1760.79i	−1.65459	+	2.08378i
$846$	−73.4337			−0.0868011
$847$	412.203			0.486663
$848$	−158.474			−0.186879
$849$		−	122.997i		−	0.144873i
$850$	−437.261	+	101.741i	−0.514425	+	0.119695i
$851$	899.249	−	35.4744i	1.05670	−	0.0416856i
$852$		−	79.5902i		−	0.0934158i
$853$			228.755i			0.268177i	0.990969	+	0.134089i	$0.0428107\pi$
$853$			228.755i			0.268177i	−0.990969	+	0.134089i	$0.957189\pi$
$854$	332.895			0.389806
$855$	−123.197	−	97.8227i	−0.144090	−	0.114412i
$856$		−	151.704i		−	0.177224i
$857$		−	820.109i		−	0.956953i	−0.878100	−	0.478477i	$-0.841189\pi$
$857$		−	820.109i		−	0.956953i	0.878100	−	0.478477i	$-0.158811\pi$
$858$	−971.434			−1.13221
$859$	1282.12			1.49257			0.746286	−	0.665626i	$-0.231835\pi$
$859$	1282.12			1.49257			0.746286	+	0.665626i	$0.231835\pi$
$860$	−445.461	+	561.010i	−0.517978	+	0.652337i
$861$		−	221.638i		−	0.257420i
$862$	117.821			0.136683
$863$			216.368i			0.250717i	0.992112	+	0.125358i	$0.0400080\pi$
$863$			216.368i			0.250717i	−0.992112	+	0.125358i	$0.959992\pi$
$864$	29.3939			0.0340207
$865$	−435.783	−	346.027i	−0.503795	−	0.400031i
$866$			812.619i			0.938359i
$867$		−	221.289i		−	0.255235i
$868$	−309.518			−0.356587
$869$	406.966			0.468315
$870$	341.050	−	429.516i	0.392012	−	0.493696i
$871$		−	1909.70i		−	2.19253i
$872$	−219.475			−0.251691
$873$	1.74032			0.00199349
$874$	340.858	−	13.4465i	0.389997	−	0.0153850i
$875$	349.514	+	165.606i	0.399445	+	0.189264i
$876$	−179.743			−0.205186
$877$			957.335i			1.09160i	0.837915	+	0.545801i	$0.183774\pi$
$877$			957.335i			1.09160i	−0.837915	+	0.545801i	$0.816226\pi$
$878$		−	278.280i		−	0.316947i
$879$			851.252i			0.968432i
$880$	−249.734	−	198.297i	−0.283789	−	0.225338i
$881$			802.836i			0.911278i	0.890165	+	0.455639i	$0.150589\pi$
$881$			802.836i			0.911278i	−0.890165	+	0.455639i	$0.849411\pi$
$882$			167.273i			0.189652i
$883$			188.170i			0.213103i	0.994307	+	0.106552i	$0.0339809\pi$
$883$			188.170i			0.213103i	−0.994307	+	0.106552i	$0.966019\pi$
$884$			631.678i			0.714568i
$885$	162.846	+	129.305i	0.184006	+	0.146107i
$886$	−18.5922			−0.0209844
$887$			1228.23i			1.38470i	0.721564	+	0.692348i	$0.243424\pi$
$887$			1228.23i			1.38470i	−0.721564	+	0.692348i	$0.756576\pi$
$888$	−191.688			−0.215865
$889$			52.7615i			0.0593493i
$890$	729.731	−	919.016i	0.819922	−	1.03260i
$891$		−	143.499i		−	0.161054i
$892$			106.236i			0.119098i
$893$	181.521			0.203271
$894$		−	227.415i		−	0.254379i
$895$	253.290	−	318.991i	0.283006	−	0.356415i
$896$			35.0058i			0.0390689i
$897$	990.106	−	39.0587i	1.10380	−	0.0435437i
$898$			10.2749i			0.0114420i
$899$	2239.82			2.49146
$900$	−33.9936	−	146.097i	−0.0377707	−	0.162330i
$901$	503.074			0.558350
$902$	932.549			1.03387
$903$		−	383.906i		−	0.425145i
$904$			173.008i			0.191380i
$905$	−496.207	−	394.005i	−0.548295	−	0.435365i
$906$	453.000			0.499999
$907$	969.640			1.06906			0.534531	−	0.845149i	$-0.320488\pi$
$907$	969.640			1.06906			0.534531	+	0.845149i	$0.320488\pi$
$908$	743.552			0.818889
$909$	492.854			0.542193
$910$	338.400	−	426.178i	0.371868	−	0.468328i
$911$			82.3091i			0.0903503i	0.998979	+	0.0451751i	$0.0143846\pi$
$911$			82.3091i			0.0903503i	−0.998979	+	0.0451751i	$0.985615\pi$
$912$	−72.6589			−0.0796698
$913$			345.659i			0.378596i
$914$		−	899.254i		−	0.983866i
$915$	−409.702	+	515.975i	−0.447762	+	0.563907i
$916$			594.523i			0.649042i
$917$	−651.794			−0.710790
$918$	−93.3108			−0.101646
$919$		−	1404.90i		−	1.52872i	−0.644788	−	0.764362i	$-0.723054\pi$
$919$		−	1404.90i		−	1.52872i	0.644788	−	0.764362i	$-0.276946\pi$
$920$	262.507	+	192.068i	0.285334	+	0.208769i
$921$	618.485			0.671536
$922$		−	902.310i		−	0.978644i
$923$			571.479i			0.619153i
$924$	170.896			0.184952
$925$	221.685	+	952.754i	0.239659	+	1.03000i
$926$	839.695			0.906798
$927$	−482.857			−0.520881
$928$		−	253.319i		−	0.272973i
$929$	−1680.30			−1.80872			−0.904361	−	0.426769i	$-0.859652\pi$
$929$	−1680.30			−1.80872			−0.904361	+	0.426769i	$0.859652\pi$
$930$	380.932	−	479.742i	0.409604	−	0.515851i
$931$		−	413.482i		−	0.444127i
$932$		−	361.884i		−	0.388287i
$933$			238.710i			0.255852i
$934$			843.240i			0.902827i
$935$	792.780	+	629.494i	0.847893	+	0.673256i
$936$	−211.056			−0.225487
$937$	283.310			0.302359			0.151180	−	0.988506i	$-0.451693\pi$
$937$	283.310			0.302359			0.151180	+	0.988506i	$0.451693\pi$
$938$			335.957i			0.358163i
$939$			824.843i			0.878427i
$940$	135.550	+	107.632i	0.144202	+	0.114502i
$941$		−	1715.42i		−	1.82297i	−0.411328	−	0.911487i	$-0.634935\pi$
$941$		−	1715.42i		−	1.82297i	0.411328	−	0.911487i	$-0.365065\pi$
$942$	432.593			0.459228
$943$	−950.474	+	37.4952i	−1.00793	+	0.0397616i
$944$	96.0428			0.101740
$945$	62.9546	+	49.9881i	0.0666186	+	0.0528975i
$946$	1615.29			1.70750
$947$			451.702i			0.476982i	0.971145	+	0.238491i	$0.0766528\pi$
$947$			451.702i			0.476982i	−0.971145	+	0.238491i	$0.923347\pi$
$948$	88.4182			0.0932682
$949$	1290.60			1.35996
$950$	84.0291	+	361.139i	0.0884516	+	0.380146i
$951$	−502.662			−0.528562
$952$		−	111.126i		−	0.116729i
$953$	−844.626			−0.886281			−0.443141	−	0.896452i	$-0.646136\pi$
$953$	−844.626			−0.886281			−0.443141	+	0.896452i	$0.646136\pi$
$954$			168.087i			0.176191i
$955$	438.187	+	347.935i	0.458834	+	0.364330i
$956$	−679.043			−0.710296
$957$	−1236.69			−1.29226
$958$	−288.374			−0.301017
$959$	−1.20353			−0.00125499
$960$	−54.2577	−	43.0825i	−0.0565184	−	0.0448776i
$961$	1540.74			1.60327
$962$	1376.37			1.43074
$963$	−160.906			−0.167089
$964$		−	66.2246i		−	0.0686977i
$965$	635.580	+	504.672i	0.658632	+	0.522976i
$966$	−174.181	+	6.87125i	−0.180311	+	0.00711310i
$967$		−	910.755i		−	0.941836i	−0.882177	−	0.470918i	$-0.843923\pi$
$967$		−	910.755i		−	0.941836i	0.882177	−	0.470918i	$-0.156077\pi$
$968$			376.809i			0.389266i
$969$	230.655			0.238034
$970$	−3.21242	−	2.55077i	−0.00331178	−	0.00262966i
$971$		−	1833.23i		−	1.88798i	−0.329979	−	0.943988i	$-0.607042\pi$
$971$		−	1833.23i		−	1.88798i	0.329979	−	0.943988i	$-0.392958\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	−350.875			−0.360612
$974$	552.956			0.567717
$975$	244.083	+	1049.02i	0.250342	+	1.07592i
$976$			304.311i			0.311794i
$977$	−494.521			−0.506163			−0.253082	−	0.967445i	$-0.581444\pi$
$977$	−494.521			−0.506163			−0.253082	+	0.967445i	$0.581444\pi$
$978$		−	693.081i		−	0.708672i
$979$	−2646.09			−2.70285
$980$	245.171	−	308.766i	0.250174	−	0.315067i
$981$			232.788i			0.237297i
$982$			635.507i			0.647156i
$983$	−484.584			−0.492965			−0.246482	−	0.969147i	$-0.579275\pi$
$983$	−484.584			−0.492965			−0.246482	+	0.969147i	$0.579275\pi$
$984$	202.607			0.205902
$985$	1374.49	+	1091.39i	1.39542	+	1.10801i
$986$			804.160i			0.815579i
$987$	−92.7587			−0.0939804
$988$	521.710			0.528046
$989$	−1646.34	+	64.9464i	−1.66465	+	0.0656688i
$990$	−210.326	+	264.883i	−0.212451	+	0.267558i
$991$	−517.471			−0.522171			−0.261085	−	0.965316i	$-0.584080\pi$
$991$	−517.471			−0.522171			−0.261085	+	0.965316i	$0.584080\pi$
$992$		−	282.941i		−	0.285223i
$993$			215.886i			0.217408i
$994$		−	100.535i		−	0.101142i
$995$	−66.8997	−	53.1207i	−0.0672359	−	0.0533876i
$996$			75.0985i			0.0754001i
$997$		−	21.9492i		−	0.0220152i	−0.999939	−	0.0110076i	$-0.996496\pi$
$997$		−	21.9492i		−	0.0220152i	0.999939	−	0.0110076i	$-0.00350391\pi$
$998$			1089.66i			1.09184i
$999$			203.316i			0.203520i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.f.a.229.8	yes	48
5.4	even	2	inner	690.3.f.a.229.5	✓	48
23.22	odd	2	inner	690.3.f.a.229.7	yes	48
115.114	odd	2	inner	690.3.f.a.229.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.f.a.229.5	✓	48	5.4	even	2	inner
690.3.f.a.229.6	yes	48	115.114	odd	2	inner
690.3.f.a.229.7	yes	48	23.22	odd	2	inner
690.3.f.a.229.8	yes	48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +1.73205i q^{3} -2.00000 q^{4} +(3.10921 - 3.91571i) q^{5} -2.44949 q^{6} -3.09410 q^{7} -2.82843i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} +1.73205i q^{3} -2.00000 q^{4} +(3.10921 - 3.91571i) q^{5} -2.44949 q^{6} -3.09410 q^{7} -2.82843i q^{8} -3.00000 q^{9} +(5.53765 + 4.39709i) q^{10} -15.9443i q^{11} -3.46410i q^{12} +24.8732i q^{13} -4.37572i q^{14} +(6.78221 + 5.38531i) q^{15} +4.00000 q^{16} -12.6980 q^{17} -4.24264i q^{18} +10.4874i q^{19} +(-6.21842 + 7.83142i) q^{20} -5.35914i q^{21} +22.5487 q^{22} +(-22.9821 + 0.906621i) q^{23} +4.89898 q^{24} +(-5.66561 - 24.3496i) q^{25} -35.1760 q^{26} -5.19615i q^{27} +6.18820 q^{28} -44.7809 q^{29} +(-7.61598 + 9.59150i) q^{30} -50.0174 q^{31} +5.65685i q^{32} +27.6164 q^{33} -17.9577i q^{34} +(-9.62022 + 12.1156i) q^{35} +6.00000 q^{36} -39.1282 q^{37} -14.8314 q^{38} -43.0816 q^{39} +(-11.0753 - 8.79418i) q^{40} +41.3571 q^{41} +7.57897 q^{42} +71.6357 q^{43} +31.8887i q^{44} +(-9.32763 + 11.7471i) q^{45} +(-1.28216 - 32.5016i) q^{46} -17.3085i q^{47} +6.92820i q^{48} -39.4265 q^{49} +(34.4355 - 8.01238i) q^{50} -21.9936i q^{51} -49.7463i q^{52} -39.6184 q^{53} +7.34847 q^{54} +(-62.4335 - 49.5744i) q^{55} +8.75144i q^{56} -18.1647 q^{57} -63.3298i q^{58} +24.0107 q^{59} +(-13.5644 - 10.7706i) q^{60} +76.0777i q^{61} -70.7353i q^{62} +9.28230 q^{63} -8.00000 q^{64} +(97.3961 + 77.3359i) q^{65} +39.0555i q^{66} -76.7774 q^{67} +25.3960 q^{68} +(-1.57031 - 39.8062i) q^{69} +(-17.1341 - 13.6050i) q^{70} +22.9757 q^{71} +8.48528i q^{72} -51.8874i q^{73} -55.3356i q^{74} +(42.1747 - 9.81312i) q^{75} -20.9748i q^{76} +49.3334i q^{77} -60.9265i q^{78} +25.5241i q^{79} +(12.4368 - 15.6628i) q^{80} +9.00000 q^{81} +58.4877i q^{82} -21.6791 q^{83} +10.7183i q^{84} +(-39.4807 + 49.7217i) q^{85} +101.308i q^{86} -77.5628i q^{87} -45.0974 q^{88} -165.958i q^{89} +(-16.6130 - 13.1913i) q^{90} -76.9601i q^{91} +(45.9642 - 1.81324i) q^{92} -86.6327i q^{93} +24.4779 q^{94} +(41.0657 + 32.6076i) q^{95} -9.79796 q^{96} -0.580105 q^{97} -55.7575i q^{98} +47.8330i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 96 q^{4} - 144 q^{9}+O(q^{10}) \) 48 * q - 96 * q^4 - 144 * q^9	\( 48 q - 96 q^{4} - 144 q^{9} + 192 q^{16} + 96 q^{25} + 64 q^{26} - 152 q^{29} - 8 q^{31} + 56 q^{35} + 288 q^{36} - 48 q^{39} + 40 q^{41} - 160 q^{46} + 424 q^{49} + 96 q^{50} + 32 q^{55} + 360 q^{59} - 384 q^{64} + 192 q^{69} - 496 q^{70} - 152 q^{71} + 144 q^{75} + 432 q^{81} - 136 q^{85} + 256 q^{94} + 496 q^{95}+O(q^{100}) \) 48 * q - 96 * q^4 - 144 * q^9 + 192 * q^16 + 96 * q^25 + 64 * q^26 - 152 * q^29 - 8 * q^31 + 56 * q^35 + 288 * q^36 - 48 * q^39 + 40 * q^41 - 160 * q^46 + 424 * q^49 + 96 * q^50 + 32 * q^55 + 360 * q^59 - 384 * q^64 + 192 * q^69 - 496 * q^70 - 152 * q^71 + 144 * q^75 + 432 * q^81 - 136 * q^85 + 256 * q^94 + 496 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more