LMFDB - Embedded newform 105.3.f.a.29.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(29,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("105.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.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:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.4
Character	$\chi$	$=$	105.29
Dual form			105.3.f.a.29.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.21327 q^{2} +(-1.93400 + 2.29339i) q^{3} +6.32511 q^{4} +(4.77035 + 1.49792i) q^{5} +(6.21446 - 7.36929i) q^{6} -2.64575i q^{7} -7.47120 q^{8} +(-1.51929 - 8.87084i) q^{9} +O(q^{10})$	\(q-3.21327 q^{2} +(-1.93400 + 2.29339i) q^{3} +6.32511 q^{4} +(4.77035 + 1.49792i) q^{5} +(6.21446 - 7.36929i) q^{6} -2.64575i q^{7} -7.47120 q^{8} +(-1.51929 - 8.87084i) q^{9} +(-15.3284 - 4.81322i) q^{10} +17.2644i q^{11} +(-12.2328 + 14.5059i) q^{12} +13.3791i q^{13} +8.50151i q^{14} +(-12.6612 + 8.04331i) q^{15} -1.29344 q^{16} +1.12735 q^{17} +(4.88189 + 28.5044i) q^{18} -14.7926 q^{19} +(30.1730 + 9.47449i) q^{20} +(6.06774 + 5.11688i) q^{21} -55.4751i q^{22} -35.3087 q^{23} +(14.4493 - 17.1344i) q^{24} +(20.5125 + 14.2912i) q^{25} -42.9908i q^{26} +(23.2826 + 13.6719i) q^{27} -16.7347i q^{28} +27.9768i q^{29} +(40.6838 - 25.8453i) q^{30} +4.04305 q^{31} +34.0410 q^{32} +(-39.5939 - 33.3893i) q^{33} -3.62249 q^{34} +(3.96312 - 12.6212i) q^{35} +(-9.60967 - 56.1090i) q^{36} +0.538959i q^{37} +47.5327 q^{38} +(-30.6836 - 25.8753i) q^{39} +(-35.6402 - 11.1912i) q^{40} -36.7247i q^{41} +(-19.4973 - 16.4419i) q^{42} +75.7429i q^{43} +109.199i q^{44} +(6.04025 - 44.5928i) q^{45} +113.456 q^{46} +2.16744 q^{47} +(2.50152 - 2.96637i) q^{48} -7.00000 q^{49} +(-65.9122 - 45.9215i) q^{50} +(-2.18030 + 2.58546i) q^{51} +84.6245i q^{52} +22.1997 q^{53} +(-74.8133 - 43.9314i) q^{54} +(-25.8606 + 82.3570i) q^{55} +19.7669i q^{56} +(28.6089 - 33.9253i) q^{57} -89.8971i q^{58} +58.3106i q^{59} +(-80.0833 + 50.8748i) q^{60} +41.2004 q^{61} -12.9914 q^{62} +(-23.4700 + 4.01966i) q^{63} -104.209 q^{64} +(-20.0409 + 63.8232i) q^{65} +(127.226 + 107.289i) q^{66} -32.9426i q^{67} +7.13062 q^{68} +(68.2870 - 80.9767i) q^{69} +(-12.7346 + 40.5552i) q^{70} -31.4470i q^{71} +(11.3509 + 66.2758i) q^{72} -21.2784i q^{73} -1.73182i q^{74} +(-72.4464 + 19.4040i) q^{75} -93.5649 q^{76} +45.6772 q^{77} +(98.5947 + 83.1442i) q^{78} +114.122 q^{79} +(-6.17017 - 1.93747i) q^{80} +(-76.3835 + 26.9547i) q^{81} +118.006i q^{82} -81.5781 q^{83} +(38.3791 + 32.3648i) q^{84} +(5.37786 + 1.68868i) q^{85} -243.382i q^{86} +(-64.1618 - 54.1072i) q^{87} -128.985i q^{88} -43.2217i q^{89} +(-19.4089 + 143.289i) q^{90} +35.3979 q^{91} -223.331 q^{92} +(-7.81926 + 9.27230i) q^{93} -6.96456 q^{94} +(-70.5660 - 22.1581i) q^{95} +(-65.8353 + 78.0693i) q^{96} -51.9161i q^{97} +22.4929 q^{98} +(153.149 - 26.2296i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 52 q^{4} - 22 q^{9}+O(q^{10}) $ 24 * q + 52 * q^4 - 22 * q^9	$ 24 q + 52 q^{4} - 22 q^{9} - 24 q^{10} + 26 q^{15} + 4 q^{16} + 72 q^{19} + 14 q^{21} - 156 q^{24} - 64 q^{25} - 32 q^{30} - 40 q^{31} - 144 q^{34} + 36 q^{36} + 62 q^{39} - 40 q^{40} + 120 q^{45} - 104 q^{46} - 168 q^{49} + 70 q^{51} + 60 q^{54} - 16 q^{55} - 348 q^{60} + 432 q^{61} - 364 q^{64} + 284 q^{66} + 404 q^{69} + 140 q^{70} + 204 q^{75} + 152 q^{76} + 108 q^{79} - 158 q^{81} + 112 q^{84} + 196 q^{85} - 152 q^{90} - 84 q^{91} + 808 q^{94} - 516 q^{96} + 582 q^{99}+O(q^{100}) $ 24 * q + 52 * q^4 - 22 * q^9 - 24 * q^10 + 26 * q^15 + 4 * q^16 + 72 * q^19 + 14 * q^21 - 156 * q^24 - 64 * q^25 - 32 * q^30 - 40 * q^31 - 144 * q^34 + 36 * q^36 + 62 * q^39 - 40 * q^40 + 120 * q^45 - 104 * q^46 - 168 * q^49 + 70 * q^51 + 60 * q^54 - 16 * q^55 - 348 * q^60 + 432 * q^61 - 364 * q^64 + 284 * q^66 + 404 * q^69 + 140 * q^70 + 204 * q^75 + 152 * q^76 + 108 * q^79 - 158 * q^81 + 112 * q^84 + 196 * q^85 - 152 * q^90 - 84 * q^91 + 808 * q^94 - 516 * q^96 + 582 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−3.21327			−1.60664			−0.803318	−	0.595551i	$-0.796934\pi$
$2$	−3.21327			−1.60664			−0.803318	+	0.595551i	$0.796934\pi$
$3$	−1.93400	+	2.29339i	−0.644667	+	0.764464i
$3$	−1.93400	+	2.29339i	−0.644667	+	0.764464i
$4$	6.32511			1.58128
$5$	4.77035	+	1.49792i	0.954070	+	0.299584i
$5$	4.77035	+	1.49792i	0.954070	+	0.299584i
$6$	6.21446	−	7.36929i	1.03574	−	1.22821i
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	−7.47120			−0.933900
$9$	−1.51929	−	8.87084i	−0.168810	−	0.985649i
$10$	−15.3284	−	4.81322i	−1.53284	−	0.481322i
$11$			17.2644i			1.56949i	0.619820	+	0.784744i	$0.287205\pi$
$11$			17.2644i			1.56949i	−0.619820	+	0.784744i	$0.712795\pi$
$12$	−12.2328	+	14.5059i	−1.01940	+	1.20883i
$13$			13.3791i			1.02916i	0.857441	+	0.514582i	$0.172053\pi$
$13$			13.3791i			1.02916i	−0.857441	+	0.514582i	$0.827947\pi$
$14$			8.50151i			0.607251i
$15$	−12.6612	+	8.04331i	−0.844078	+	0.536221i
$16$	−1.29344			−0.0808401
$17$	1.12735			0.0663148			0.0331574	−	0.999450i	$-0.489444\pi$
$17$	1.12735			0.0663148			0.0331574	+	0.999450i	$0.489444\pi$
$18$	4.88189	+	28.5044i	0.271216	+	1.58358i
$19$	−14.7926			−0.778559			−0.389279	−	0.921120i	$-0.627276\pi$
$19$	−14.7926			−0.778559			−0.389279	+	0.921120i	$0.627276\pi$
$20$	30.1730	+	9.47449i	1.50865	+	0.473725i
$21$	6.06774	+	5.11688i	0.288940	+	0.243661i
$22$		−	55.4751i		−	2.52159i
$23$	−35.3087			−1.53516			−0.767581	−	0.640952i	$-0.778540\pi$
$23$	−35.3087			−1.53516			−0.767581	+	0.640952i	$0.778540\pi$
$24$	14.4493	−	17.1344i	0.602054	−	0.713933i
$25$	20.5125	+	14.2912i	0.820499	+	0.571647i
$26$		−	42.9908i		−	1.65349i
$27$	23.2826	+	13.6719i	0.862319	+	0.506366i
$28$		−	16.7347i		−	0.597667i
$29$			27.9768i			0.964718i	0.875974	+	0.482359i	$0.160220\pi$
$29$			27.9768i			0.964718i	−0.875974	+	0.482359i	$0.839780\pi$
$30$	40.6838	−	25.8453i	1.35613	−	0.861511i
$31$	4.04305			0.130421			0.0652105	−	0.997872i	$-0.479228\pi$
$31$	4.04305			0.130421			0.0652105	+	0.997872i	$0.479228\pi$
$32$	34.0410			1.06378
$33$	−39.5939	−	33.3893i	−1.19982	−	1.01180i
$34$	−3.62249			−0.106544
$35$	3.96312	−	12.6212i	0.113232	−	0.360605i
$36$	−9.60967	−	56.1090i	−0.266935	−	1.55858i
$37$			0.538959i			0.0145665i	0.999973	+	0.00728324i	$0.00231835\pi$
$37$			0.538959i			0.0145665i	−0.999973	+	0.00728324i	$0.997682\pi$
$38$	47.5327			1.25086
$39$	−30.6836	−	25.8753i	−0.786759	−	0.663468i
$40$	−35.6402	−	11.1912i	−0.891006	−	0.279781i
$41$		−	36.7247i		−	0.895723i	−0.894103	−	0.447862i	$-0.852186\pi$
$41$		−	36.7247i		−	0.895723i	0.894103	−	0.447862i	$-0.147814\pi$
$42$	−19.4973	−	16.4419i	−0.464221	−	0.391474i
$43$			75.7429i			1.76146i	0.473616	+	0.880732i	$0.342949\pi$
$43$			75.7429i			1.76146i	−0.473616	+	0.880732i	$0.657051\pi$
$44$			109.199i			2.48179i
$45$	6.04025	−	44.5928i	0.134228	−	0.990951i
$46$	113.456			2.46644
$47$	2.16744			0.0461157			0.0230578	−	0.999734i	$-0.492660\pi$
$47$	2.16744			0.0461157			0.0230578	+	0.999734i	$0.492660\pi$
$48$	2.50152	−	2.96637i	0.0521149	−	0.0617994i
$49$	−7.00000			−0.142857
$50$	−65.9122	−	45.9215i	−1.31824	−	0.918429i
$51$	−2.18030	+	2.58546i	−0.0427510	+	0.0506953i
$52$			84.6245i			1.62739i
$53$	22.1997			0.418863			0.209431	−	0.977823i	$-0.432839\pi$
$53$	22.1997			0.418863			0.209431	+	0.977823i	$0.432839\pi$
$54$	−74.8133	−	43.9314i	−1.38543	−	0.813545i
$55$	−25.8606	+	82.3570i	−0.470193	+	1.49740i
$56$			19.7669i			0.352981i
$57$	28.6089	−	33.9253i	0.501911	−	0.595180i
$58$		−	89.8971i		−	1.54995i
$59$			58.3106i			0.988315i	0.869372	+	0.494158i	$0.164523\pi$
$59$			58.3106i			0.988315i	−0.869372	+	0.494158i	$0.835477\pi$
$60$	−80.0833	+	50.8748i	−1.33472	+	0.847913i
$61$	41.2004			0.675416			0.337708	−	0.941251i	$-0.390348\pi$
$61$	41.2004			0.675416			0.337708	+	0.941251i	$0.390348\pi$
$62$	−12.9914			−0.209539
$63$	−23.4700	+	4.01966i	−0.372540	+	0.0638042i
$64$	−104.209			−1.62827
$65$	−20.0409	+	63.8232i	−0.308321	+	0.981895i
$66$	127.226	+	107.289i	1.92767	+	1.62559i
$67$		−	32.9426i		−	0.491680i	−0.969310	−	0.245840i	$-0.920936\pi$
$67$		−	32.9426i		−	0.491680i	0.969310	−	0.245840i	$-0.0790638\pi$
$68$	7.13062			0.104862
$69$	68.2870	−	80.9767i	0.989667	−	1.17358i
$70$	−12.7346	+	40.5552i	−0.181922	+	0.579360i
$71$		−	31.4470i		−	0.442916i	−0.975170	−	0.221458i	$-0.928919\pi$
$71$		−	31.4470i		−	0.442916i	0.975170	−	0.221458i	$-0.0710815\pi$
$72$	11.3509	+	66.2758i	0.157652	+	0.920497i
$73$		−	21.2784i		−	0.291485i	−0.989323	−	0.145742i	$-0.953443\pi$
$73$		−	21.2784i		−	0.291485i	0.989323	−	0.145742i	$-0.0465571\pi$
$74$		−	1.73182i		−	0.0234030i
$75$	−72.4464	+	19.4040i	−0.965952	+	0.258720i
$76$	−93.5649			−1.23112
$77$	45.6772			0.593210
$78$	98.5947	+	83.1442i	1.26403	+	1.06595i
$79$	114.122			1.44458			0.722291	−	0.691589i	$-0.243089\pi$
$79$	114.122			1.44458			0.722291	+	0.691589i	$0.243089\pi$
$80$	−6.17017	−	1.93747i	−0.0771272	−	0.0242184i
$81$	−76.3835	+	26.9547i	−0.943006	+	0.332775i
$82$			118.006i			1.43910i
$83$	−81.5781			−0.982869			−0.491434	−	0.870915i	$-0.663527\pi$
$83$	−81.5781			−0.982869			−0.491434	+	0.870915i	$0.663527\pi$
$84$	38.3791	+	32.3648i	0.456894	+	0.385296i
$85$	5.37786	+	1.68868i	0.0632690	+	0.0198668i
$86$		−	243.382i		−	2.83003i
$87$	−64.1618	−	54.1072i	−0.737492	−	0.621922i
$88$		−	128.985i		−	1.46574i
$89$		−	43.2217i		−	0.485637i	−0.970072	−	0.242818i	$-0.921928\pi$
$89$		−	43.2217i		−	0.485637i	0.970072	−	0.242818i	$-0.0780719\pi$
$90$	−19.4089	+	143.289i	−0.215655	+	1.59210i
$91$	35.3979			0.388988
$92$	−223.331			−2.42752
$93$	−7.81926	+	9.27230i	−0.0840781	+	0.0997022i
$94$	−6.96456			−0.0740911
$95$	−70.5660	−	22.1581i	−0.742800	−	0.233243i
$96$	−65.8353	+	78.0693i	−0.685784	+	0.813222i
$97$		−	51.9161i		−	0.535217i	−0.963528	−	0.267609i	$-0.913767\pi$
$97$		−	51.9161i		−	0.535217i	0.963528	−	0.267609i	$-0.0862334\pi$
$98$	22.4929			0.229519
$99$	153.149	−	26.2296i	1.54696	−	0.264945i
$100$	129.744	+	90.3933i	1.29744	+	0.903933i
$101$		−	12.1734i		−	0.120529i	−0.998182	−	0.0602644i	$-0.980806\pi$
$101$		−	12.1734i		−	0.120529i	0.998182	−	0.0602644i	$-0.0191944\pi$
$102$	7.00589	−	8.30778i	0.0686852	−	0.0814488i
$103$		−	188.798i		−	1.83299i	−0.400050	−	0.916493i	$-0.631007\pi$
$103$		−	188.798i		−	1.83299i	0.400050	−	0.916493i	$-0.368993\pi$
$104$		−	99.9582i		−	0.961137i
$105$	21.2806	+	33.4983i	0.202672	+	0.319031i
$106$	−71.3337			−0.672960
$107$	108.420			1.01327			0.506636	−	0.862160i	$-0.330889\pi$
$107$	108.420			1.01327			0.506636	+	0.862160i	$0.330889\pi$
$108$	147.265	+	86.4761i	1.36356	+	0.800704i
$109$	117.978			1.08237			0.541183	−	0.840905i	$-0.317977\pi$
$109$	117.978			1.08237			0.541183	+	0.840905i	$0.317977\pi$
$110$	83.0971	−	264.635i	0.755428	−	2.40578i
$111$	−1.23605	−	1.04235i	−0.0111355	−	0.00939052i
$112$			3.42213i			0.0305547i
$113$	180.160			1.59433			0.797166	−	0.603760i	$-0.206332\pi$
$113$	180.160			1.59433			0.797166	+	0.603760i	$0.206332\pi$
$114$	−91.9282	+	109.011i	−0.806388	+	0.956237i
$115$	−168.435	−	52.8896i	−1.46465	−	0.459909i
$116$			176.956i			1.52549i
$117$	118.684	−	20.3268i	1.01439	−	0.173733i
$118$		−	187.368i		−	1.58786i
$119$		−	2.98269i		−	0.0250647i
$120$	94.5941	−	60.0932i	0.788284	−	0.500776i
$121$	−177.058			−1.46329
$122$	−132.388			−1.08515
$123$	84.2240	+	71.0255i	0.684748	+	0.577443i
$124$	25.5727			0.206232
$125$	76.4447	+	98.9000i	0.611558	+	0.791200i
$126$	75.4156	−	12.9163i	0.598536	−	0.102510i
$127$			132.415i			1.04264i	0.853361	+	0.521320i	$0.174560\pi$
$127$			132.415i			1.04264i	−0.853361	+	0.521320i	$0.825440\pi$
$128$	198.688			1.55225
$129$	−173.708	−	146.487i	−1.34657	−	1.13556i
$130$	64.3967	−	205.081i	0.495359	−	1.57755i
$131$			108.060i			0.824884i	0.910984	+	0.412442i	$0.135324\pi$
$131$			108.060i			0.824884i	−0.910984	+	0.412442i	$0.864676\pi$
$132$	−250.436	−	211.191i	−1.89724	−	1.59993i
$133$			39.1376i			0.294268i
$134$			105.853i			0.789951i
$135$	90.5869	+	100.095i	0.671014	+	0.741445i
$136$	−8.42267			−0.0619314
$137$	73.5337			0.536742			0.268371	−	0.963316i	$-0.413515\pi$
$137$	73.5337			0.536742			0.268371	+	0.963316i	$0.413515\pi$
$138$	−219.425	+	260.200i	−1.59003	+	1.88551i
$139$	−185.763			−1.33642			−0.668211	−	0.743972i	$-0.732940\pi$
$139$	−185.763			−1.33642			−0.668211	+	0.743972i	$0.732940\pi$
$140$	25.0672	−	79.8302i	0.179051	−	0.570216i
$141$	−4.19182	+	4.97078i	−0.0297292	+	0.0352538i
$142$			101.048i			0.711604i
$143$	−230.982			−1.61526
$144$	1.96511	+	11.4739i	0.0136466	+	0.0796800i
$145$	−41.9070	+	133.459i	−0.289014	+	0.920409i
$146$			68.3733i			0.468310i
$147$	13.5380	−	16.0537i	0.0920952	−	0.109209i
$148$			3.40898i			0.0230336i
$149$			148.078i			0.993812i	0.867804	+	0.496906i	$0.165531\pi$
$149$			148.078i			0.993812i	−0.867804	+	0.496906i	$0.834469\pi$
$150$	232.790	−	62.3503i	1.55193	−	0.415669i
$151$	61.5651			0.407716			0.203858	−	0.979000i	$-0.434652\pi$
$151$	61.5651			0.407716			0.203858	+	0.979000i	$0.434652\pi$
$152$	110.519			0.727096
$153$	−1.71277	−	10.0006i	−0.0111946	−	0.0653631i
$154$	−146.773			−0.953073
$155$	19.2868	+	6.05616i	0.124431	+	0.0390720i
$156$	−194.077	−	163.664i	−1.24408	−	1.04913i
$157$		−	306.467i		−	1.95202i	−0.217735	−	0.976008i	$-0.569867\pi$
$157$		−	306.467i		−	1.95202i	0.217735	−	0.976008i	$-0.430133\pi$
$158$	−366.705			−2.32092
$159$	−42.9343	+	50.9127i	−0.270027	+	0.320205i
$160$	162.387	+	50.9906i	1.01492	+	0.318691i
$161$			93.4181i			0.580236i
$162$	245.441	−	86.6129i	1.51507	−	0.534647i
$163$			77.6609i			0.476447i	0.971210	+	0.238224i	$0.0765651\pi$
$163$			77.6609i			0.476447i	−0.971210	+	0.238224i	$0.923435\pi$
$164$		−	232.287i		−	1.41639i
$165$	−138.863	−	218.587i	−0.841591	−	1.32477i
$166$	262.132			1.57911
$167$	145.821			0.873178			0.436589	−	0.899661i	$-0.356186\pi$
$167$	145.821			0.873178			0.436589	+	0.899661i	$0.356186\pi$
$168$	−45.3333	−	38.2293i	−0.269841	−	0.227555i
$169$	−10.0014			−0.0591797
$170$	−17.2805	−	5.42619i	−0.101650	−	0.0319188i
$171$	22.4743	+	131.223i	0.131428	+	0.767385i
$172$			479.082i			2.78536i
$173$	74.3018			0.429490			0.214745	−	0.976670i	$-0.431108\pi$
$173$	74.3018			0.429490			0.214745	+	0.976670i	$0.431108\pi$
$174$	206.169	+	173.861i	1.18488	+	0.999201i
$175$	37.8109	−	54.2709i	0.216062	−	0.310120i
$176$		−	22.3305i		−	0.126878i
$177$	−133.729	−	112.773i	−0.755531	−	0.637134i
$178$			138.883i			0.780241i
$179$		−	135.620i		−	0.757652i	−0.925468	−	0.378826i	$-0.876328\pi$
$179$		−	135.620i		−	0.757652i	0.925468	−	0.378826i	$-0.123672\pi$
$180$	38.2052	−	282.054i	0.212251	−	1.56697i
$181$	−230.425			−1.27307			−0.636534	−	0.771248i	$-0.719633\pi$
$181$	−230.425			−1.27307			−0.636534	+	0.771248i	$0.719633\pi$
$182$	−113.743			−0.624961
$183$	−79.6815	+	94.4886i	−0.435418	+	0.516331i
$184$	263.798			1.43369
$185$	−0.807317	+	2.57103i	−0.00436388	+	0.0138974i
$186$	25.1254	−	29.7944i	0.135083	−	0.160185i
$187$			19.4630i			0.104080i
$188$	13.7093			0.0729217
$189$	36.1724	−	61.6000i	0.191388	−	0.325926i
$190$	226.748	+	71.2001i	1.19341	+	0.374737i
$191$		−	215.768i		−	1.12967i	−0.825203	−	0.564836i	$-0.808939\pi$
$191$		−	215.768i		−	1.12967i	0.825203	−	0.564836i	$-0.191061\pi$
$192$	201.540	−	238.992i	1.04969	−	1.24475i
$193$			69.4011i			0.359591i	0.983704	+	0.179796i	$0.0575436\pi$
$193$			69.4011i			0.359591i	−0.983704	+	0.179796i	$0.942456\pi$
$194$			166.820i			0.859899i
$195$	−107.613	−	169.396i	−0.551859	−	0.868695i
$196$	−44.2758			−0.225897
$197$	−158.924			−0.806720			−0.403360	−	0.915041i	$-0.632158\pi$
$197$	−158.924			−0.806720			−0.403360	+	0.915041i	$0.632158\pi$
$198$	−492.110	+	84.2827i	−2.48541	+	0.425670i
$199$	387.755			1.94852			0.974258	−	0.225436i	$-0.0723806\pi$
$199$	387.755			1.94852			0.974258	+	0.225436i	$0.0723806\pi$
$200$	−153.253	−	106.772i	−0.766264	−	0.533862i
$201$	75.5502	+	63.7109i	0.375872	+	0.316970i
$202$			39.1164i			0.193646i
$203$	74.0197			0.364629
$204$	−13.7906	+	16.3533i	−0.0676011	+	0.0801633i
$205$	55.0105	−	175.189i	0.268344	−	0.854583i
$206$			606.658i			2.94494i
$207$	53.6441	+	313.218i	0.259150	+	1.51313i
$208$		−	17.3051i		−	0.0831978i
$209$		−	255.385i		−	1.22194i
$210$	−68.3803	−	107.639i	−0.325620	−	0.512567i
$211$	10.6368			0.0504113			0.0252057	−	0.999682i	$-0.491976\pi$
$211$	10.6368			0.0504113			0.0252057	+	0.999682i	$0.491976\pi$
$212$	140.416			0.662338
$213$	72.1203	+	60.8185i	0.338593	+	0.285533i
$214$	−348.383			−1.62796
$215$	−113.457	+	361.320i	−0.527705	+	1.68056i
$216$	−173.949	−	102.145i	−0.805320	−	0.472895i
$217$		−	10.6969i		−	0.0492945i
$218$	−379.095			−1.73897
$219$	48.7997	+	41.1524i	0.222830	+	0.187911i
$220$	−163.571	+	520.917i	−0.743505	+	2.36781i
$221$			15.0830i			0.0682489i
$222$	3.97175	+	3.34934i	0.0178908	+	0.0150871i
$223$			301.077i			1.35012i	0.737762	+	0.675061i	$0.235883\pi$
$223$			301.077i			1.35012i	−0.737762	+	0.675061i	$0.764117\pi$
$224$		−	90.0640i		−	0.402071i
$225$	95.6104	−	203.675i	0.424935	−	0.905224i
$226$	−578.901			−2.56151
$227$	8.10157			0.0356897			0.0178449	−	0.999841i	$-0.494320\pi$
$227$	8.10157			0.0356897			0.0178449	+	0.999841i	$0.494320\pi$
$228$	180.954	−	214.581i	0.793660	−	0.941144i
$229$	162.381			0.709089			0.354544	−	0.935039i	$-0.384636\pi$
$229$	162.381			0.709089			0.354544	+	0.935039i	$0.384636\pi$
$230$	541.227	+	169.948i	2.35316	+	0.738906i
$231$	−88.3397	+	104.756i	−0.382423	+	0.453488i
$232$		−	209.020i		−	0.900950i
$233$	191.254			0.820831			0.410416	−	0.911899i	$-0.365384\pi$
$233$	191.254			0.820831			0.410416	+	0.911899i	$0.365384\pi$
$234$	−381.364	+	65.3155i	−1.62976	+	0.279126i
$235$	10.3394	+	3.24664i	0.0439976	+	0.0138155i
$236$			368.821i			1.56280i
$237$	−220.712	+	261.727i	−0.931274	+	1.10433i
$238$			9.58420i			0.0402698i
$239$			152.829i			0.639453i	0.947510	+	0.319727i	$0.103591\pi$
$239$			152.829i			0.639453i	−0.947510	+	0.319727i	$0.896409\pi$
$240$	16.3765	−	10.4036i	0.0682354	−	0.0433481i
$241$	−62.7182			−0.260242			−0.130121	−	0.991498i	$-0.541537\pi$
$241$	−62.7182			−0.260242			−0.130121	+	0.991498i	$0.541537\pi$
$242$	568.936			2.35097
$243$	85.9080	−	227.308i	0.353531	−	0.935423i
$244$	260.597			1.06802
$245$	−33.3925	−	10.4854i	−0.136296	−	0.0427977i
$246$	−270.635	−	228.224i	−1.10014	−	0.927740i
$247$		−	197.912i		−	0.801265i
$248$	−30.2064			−0.121800
$249$	157.772	−	187.090i	0.633623	−	0.751367i
$250$	−245.638	−	317.792i	−0.982550	−	1.27117i
$251$		−	332.777i		−	1.32580i	−0.748707	−	0.662902i	$-0.769325\pi$
$251$		−	332.777i		−	1.32580i	0.748707	−	0.662902i	$-0.230675\pi$
$252$	−148.450	+	25.4248i	−0.589089	+	0.100892i
$253$		−	609.582i		−	2.40942i
$254$		−	425.486i		−	1.67514i
$255$	−14.2736	+	9.06764i	−0.0559749	+	0.0355594i
$256$	−221.602			−0.865634
$257$	−122.355			−0.476091			−0.238046	−	0.971254i	$-0.576507\pi$
$257$	−122.355			−0.476091			−0.238046	+	0.971254i	$0.576507\pi$
$258$	558.171	+	470.702i	2.16345	+	1.82443i
$259$	1.42595			0.00550561
$260$	−126.761	+	403.689i	−0.487541	+	1.55265i
$261$	248.178	−	42.5049i	0.950873	−	0.162854i
$262$		−	347.226i		−	1.32529i
$263$	−179.362			−0.681986			−0.340993	−	0.940066i	$-0.610763\pi$
$263$	−179.362			−0.681986			−0.340993	+	0.940066i	$0.610763\pi$
$264$	295.814	+	249.458i	1.12051	+	0.944916i
$265$	105.900	+	33.2534i	0.399624	+	0.125484i
$266$		−	125.760i		−	0.472781i
$267$	99.1242	+	83.5907i	0.371252	+	0.313074i
$268$		−	208.365i		−	0.777482i
$269$		−	11.5851i		−	0.0430673i	−0.999768	−	0.0215337i	$-0.993145\pi$
$269$		−	11.5851i		−	0.0430673i	0.999768	−	0.0215337i	$-0.00685491\pi$
$270$	−291.080	−	321.633i	−1.07807	−	1.19123i
$271$	193.585			0.714334			0.357167	−	0.934041i	$-0.383743\pi$
$271$	193.585			0.714334			0.357167	+	0.934041i	$0.383743\pi$
$272$	−1.45817			−0.00536090
$273$	−68.4595	+	81.1812i	−0.250767	+	0.297367i
$274$	−236.284			−0.862349
$275$	−246.728	+	354.135i	−0.897193	+	1.28776i
$276$	431.923	−	512.186i	1.56494	−	1.85575i
$277$			64.2191i			0.231838i	0.993259	+	0.115919i	$0.0369813\pi$
$277$			64.2191i			0.231838i	−0.993259	+	0.115919i	$0.963019\pi$
$278$	596.906			2.14714
$279$	−6.14256	−	35.8653i	−0.0220164	−	0.128549i
$280$	−29.6093	+	94.2952i	−0.105747	+	0.336769i
$281$			290.982i			1.03552i	0.855525	+	0.517761i	$0.173234\pi$
$281$			290.982i			1.03552i	−0.855525	+	0.517761i	$0.826766\pi$
$282$	13.4695	−	15.9725i	0.0477640	−	0.0566400i
$283$		−	61.1607i		−	0.216116i	−0.994145	−	0.108058i	$-0.965537\pi$
$283$		−	61.1607i		−	0.216116i	0.994145	−	0.108058i	$-0.0344631\pi$
$284$		−	198.906i		−	0.700372i
$285$	187.292	−	118.982i	0.657164	−	0.417479i
$286$	742.209			2.59513
$287$	−97.1643			−0.338552
$288$	−51.7181	−	301.972i	−0.179577	−	1.04851i
$289$	−287.729			−0.995602
$290$	134.659	−	428.841i	0.464340	−	1.47876i
$291$	119.064	+	100.406i	0.409154	+	0.345037i
$292$		−	134.588i		−	0.460919i
$293$	190.963			0.651752			0.325876	−	0.945412i	$-0.394341\pi$
$293$	190.963			0.651752			0.325876	+	0.945412i	$0.394341\pi$
$294$	−43.5013	+	51.5850i	−0.147963	+	0.175459i
$295$	−87.3445	+	278.162i	−0.296083	+	0.942922i
$296$		−	4.02667i		−	0.0136036i
$297$	−236.036	+	401.959i	−0.794734	+	1.35340i
$298$		−	475.815i		−	1.59669i
$299$		−	472.400i		−	1.57993i
$300$	−458.231	+	122.732i	−1.52744	+	0.409108i
$301$	200.397			0.665770
$302$	−197.825			−0.655050
$303$	27.9184	+	23.5434i	0.0921399	+	0.0777009i
$304$	19.1334			0.0629388
$305$	196.540	+	61.7148i	0.644394	+	0.202344i
$306$	5.50361	+	32.1345i	0.0179856	+	0.105015i
$307$		−	205.128i		−	0.668170i	−0.942543	−	0.334085i	$-0.891573\pi$
$307$		−	205.128i		−	0.668170i	0.942543	−	0.334085i	$-0.108427\pi$
$308$	288.913			0.938030
$309$	432.987	+	365.134i	1.40125	+	1.18167i
$310$	−61.9736	−	19.4601i	−0.199915	−	0.0627745i
$311$		−	491.365i		−	1.57995i	−0.613138	−	0.789976i	$-0.710093\pi$
$311$		−	491.365i		−	1.57995i	0.613138	−	0.789976i	$-0.289907\pi$
$312$	229.243	+	193.319i	0.734754	+	0.619613i
$313$			177.985i			0.568643i	0.958729	+	0.284321i	$0.0917683\pi$
$313$			177.985i			0.568643i	−0.958729	+	0.284321i	$0.908232\pi$
$314$			984.760i			3.13618i
$315$	−117.981	−	15.9810i	−0.374544	−	0.0507333i
$316$	721.834			2.28429
$317$	−384.532			−1.21304			−0.606518	−	0.795070i	$-0.707434\pi$
$317$	−384.532			−1.21304			−0.606518	+	0.795070i	$0.707434\pi$
$318$	137.959	−	163.596i	0.433835	−	0.514453i
$319$	−483.002			−1.51411
$320$	−497.114	−	156.097i	−1.55348	−	0.487802i
$321$	−209.685	+	248.650i	−0.653223	+	0.774610i
$322$		−	300.178i		−	0.932228i
$323$	−16.6765			−0.0516300
$324$	−483.134	+	170.492i	−1.49115	+	0.526209i
$325$	−191.204	+	274.439i	−0.588319	+	0.844429i
$326$		−	249.545i		−	0.765477i
$327$	−228.169	+	270.569i	−0.697765	+	0.827429i
$328$			274.377i			0.836516i
$329$		−	5.73450i		−	0.0174301i
$330$	446.203	+	702.379i	1.35213	+	2.12842i
$331$	−48.0782			−0.145251			−0.0726257	−	0.997359i	$-0.523138\pi$
$331$	−48.0782			−0.145251			−0.0726257	+	0.997359i	$0.523138\pi$
$332$	−515.990			−1.55419
$333$	4.78102	−	0.818835i	0.0143574	−	0.00245896i
$334$	−468.562			−1.40288
$335$	49.3453	−	157.148i	0.147299	−	0.469097i
$336$	−7.84828	−	6.61839i	−0.0233580	−	0.0196976i
$337$		−	68.1215i		−	0.202141i	−0.994879	−	0.101070i	$-0.967773\pi$
$337$		−	68.1215i		−	0.202141i	0.994879	−	0.101070i	$-0.0322267\pi$
$338$	32.1371			0.0950802
$339$	−348.428	+	413.176i	−1.02781	+	1.21881i
$340$	34.0156	+	10.6811i	0.100046	+	0.0314150i
$341$			69.8007i			0.204694i
$342$	−72.2159	−	421.655i	−0.211158	−	1.23291i
$343$			18.5203i			0.0539949i
$344$		−	565.891i		−	1.64503i
$345$	447.050	−	283.999i	1.29580	−	0.823185i
$346$	−238.752			−0.690034
$347$	−438.220			−1.26288			−0.631442	−	0.775424i	$-0.717536\pi$
$347$	−438.220			−1.26288			−0.631442	+	0.775424i	$0.717536\pi$
$348$	−405.830	−	342.234i	−1.16618	−	0.983430i
$349$	−104.860			−0.300460			−0.150230	−	0.988651i	$-0.548001\pi$
$349$	−104.860			−0.300460			−0.150230	+	0.988651i	$0.548001\pi$
$350$	−121.497	+	174.387i	−0.347134	+	0.498249i
$351$	−182.918	+	311.501i	−0.521134	+	0.887468i
$352$			587.696i			1.66959i
$353$	97.8668			0.277243			0.138621	−	0.990345i	$-0.455733\pi$
$353$	97.8668			0.277243			0.138621	+	0.990345i	$0.455733\pi$
$354$	429.707	+	362.369i	1.21386	+	1.02364i
$355$	47.1050	−	150.013i	0.132690	−	0.422572i
$356$		−	273.382i		−	0.767926i
$357$	6.84048	+	5.76853i	0.0191610	+	0.0161583i
$358$			435.783i			1.21727i
$359$			0.751929i			0.00209451i	0.999999	+	0.00104726i	$0.000333352\pi$
$359$			0.751929i			0.00209451i	−0.999999	+	0.00104726i	$0.999667\pi$
$360$	−45.1279	+	333.162i	−0.125355	+	0.925449i
$361$	−142.179			−0.393846
$362$	740.419			2.04536
$363$	342.430	−	406.064i	0.943334	−	1.11863i
$364$	223.895			0.615097
$365$	31.8733	−	101.505i	0.0873241	−	0.278097i
$366$	256.038	−	303.617i	0.699558	−	0.829556i
$367$			595.624i			1.62295i	0.584385	+	0.811476i	$0.301336\pi$
$367$			595.624i			1.62295i	−0.584385	+	0.811476i	$0.698664\pi$
$368$	45.6698			0.124103
$369$	−325.778	+	55.7954i	−0.882868	+	0.151207i
$370$	2.59413	−	8.26140i	0.00701116	−	0.0223281i
$371$		−	58.7349i		−	0.158315i
$372$	−49.4577	+	58.6483i	−0.132951	+	0.157657i
$373$			491.021i			1.31641i	0.752838	+	0.658206i	$0.228684\pi$
$373$			491.021i			1.31641i	−0.752838	+	0.658206i	$0.771316\pi$
$374$		−	62.5399i		−	0.167219i
$375$	−374.660	−	15.9549i	−0.999094	−	0.0425464i
$376$	−16.1934			−0.0430674
$377$	−374.306			−0.992854
$378$	−116.232	+	197.937i	−0.307491	+	0.523644i
$379$	459.206			1.21163			0.605813	−	0.795607i	$-0.292848\pi$
$379$	459.206			1.21163			0.605813	+	0.795607i	$0.292848\pi$
$380$	−446.337	−	140.153i	−1.17457	−	0.368822i
$381$	−303.680	−	256.091i	−0.797061	−	0.672156i
$382$			693.319i			1.81497i
$383$	−12.7226			−0.0332182			−0.0166091	−	0.999862i	$-0.505287\pi$
$383$	−12.7226			−0.0332182			−0.0166091	+	0.999862i	$0.505287\pi$
$384$	−384.263	+	455.670i	−1.00068	+	1.18664i
$385$	217.896	+	68.4207i	0.565964	+	0.177716i
$386$		−	223.004i		−	0.577732i
$387$	671.903	−	115.075i	1.73618	−	0.297352i
$388$		−	328.375i		−	0.846327i
$389$			407.135i			1.04662i	0.852143	+	0.523310i	$0.175303\pi$
$389$			407.135i			1.04662i	−0.852143	+	0.523310i	$0.824697\pi$
$390$	345.788	+	544.314i	0.886636	+	1.39568i
$391$	−39.8054			−0.101804
$392$	52.2984			0.133414
$393$	−247.824	−	208.988i	−0.630594	−	0.531775i
$394$	510.665			1.29611
$395$	544.402	+	170.945i	1.37823	+	0.432773i
$396$	968.686	−	165.905i	2.44618	−	0.418951i
$397$			204.803i			0.515876i	0.966161	+	0.257938i	$0.0830430\pi$
$397$			204.803i			0.515876i	−0.966161	+	0.257938i	$0.916957\pi$
$398$	−1245.96			−3.13055
$399$	−89.7578	−	75.6921i	−0.224957	−	0.189704i
$400$	−26.5317	−	18.4848i	−0.0663293	−	0.0462121i
$401$			86.8627i			0.216615i	0.994117	+	0.108308i	$0.0345431\pi$
$401$			86.8627i			0.216615i	−0.994117	+	0.108308i	$0.965457\pi$
$402$	−242.763	−	204.720i	−0.603889	−	0.509255i
$403$			54.0926i			0.134225i
$404$		−	76.9981i		−	0.190589i
$405$	−404.752	+	14.1673i	−0.999388	+	0.0349810i
$406$	−237.845			−0.585826
$407$	−9.30479			−0.0228619
$408$	16.2895	−	19.3165i	0.0399251	−	0.0473443i
$409$	524.233			1.28174			0.640872	−	0.767648i	$-0.278573\pi$
$409$	524.233			1.28174			0.640872	+	0.767648i	$0.278573\pi$
$410$	−176.764	+	562.931i	−0.431131	+	1.37300i
$411$	−142.214	+	168.642i	−0.346020	+	0.410320i
$412$		−	1194.17i		−	2.89846i
$413$	154.275			0.373548
$414$	−172.373	−	1006.45i	−0.416360	−	2.43105i
$415$	−389.156	−	122.197i	−0.937725	−	0.294451i
$416$			455.439i			1.09481i
$417$	359.265	−	426.027i	0.861547	−	1.02165i
$418$			820.621i			1.96321i
$419$		−	578.937i		−	1.38171i	−0.722993	−	0.690856i	$-0.757234\pi$
$419$		−	578.937i		−	1.38171i	0.722993	−	0.690856i	$-0.242766\pi$
$420$	134.602	+	211.880i	0.320481	+	0.504477i
$421$	−301.013			−0.714996			−0.357498	−	0.933914i	$-0.616370\pi$
$421$	−301.013			−0.714996			−0.357498	+	0.933914i	$0.616370\pi$
$422$	−34.1789			−0.0809926
$423$	−3.29296	−	19.2270i	−0.00778478	−	0.0454539i
$424$	−165.859			−0.391176
$425$	23.1248	+	16.1112i	0.0544113	+	0.0379087i
$426$	−231.742	−	195.426i	−0.543995	−	0.458747i
$427$		−	109.006i		−	0.255283i
$428$	685.769			1.60226
$429$	446.720	−	529.733i	1.04130	−	1.23481i
$430$	364.567	−	1161.02i	0.847830	−	2.70005i
$431$		−	484.437i		−	1.12398i	−0.827143	−	0.561992i	$-0.810035\pi$
$431$		−	484.437i		−	1.12398i	0.827143	−	0.561992i	$-0.189965\pi$
$432$	−30.1147	−	17.6838i	−0.0697100	−	0.0409347i
$433$		−	152.214i		−	0.351534i	−0.984432	−	0.175767i	$-0.943760\pi$
$433$		−	152.214i		−	0.351534i	0.984432	−	0.175767i	$-0.0562405\pi$
$434$			34.3721i			0.0791983i
$435$	−225.026	−	354.219i	−0.517302	−	0.814297i
$436$	746.223			1.71152
$437$	522.308			1.19521
$438$	−156.807	−	132.234i	−0.358006	−	0.301904i
$439$	46.7623			0.106520			0.0532600	−	0.998581i	$-0.483039\pi$
$439$	46.7623			0.106520			0.0532600	+	0.998581i	$0.483039\pi$
$440$	193.210	−	615.306i	0.439113	−	1.39842i
$441$	10.6350	+	62.0959i	0.0241157	+	0.140807i
$442$		−	48.4658i		−	0.109651i
$443$	477.576			1.07805			0.539025	−	0.842290i	$-0.318793\pi$
$443$	477.576			1.07805			0.539025	+	0.842290i	$0.318793\pi$
$444$	−7.81812	−	6.59296i	−0.0176084	−	0.0148490i
$445$	64.7425	−	206.183i	0.145489	−	0.463332i
$446$		−	967.443i		−	2.16915i
$447$	−339.601	−	286.383i	−0.759733	−	0.640678i
$448$			275.711i			0.615427i
$449$			313.516i			0.698253i	0.937076	+	0.349127i	$0.113522\pi$
$449$			313.516i			0.698253i	−0.937076	+	0.349127i	$0.886478\pi$
$450$	−307.222	+	654.464i	−0.682716	+	1.45436i
$451$	634.028			1.40583
$452$	1139.53			2.52108
$453$	−119.067	+	141.193i	−0.262841	+	0.311684i
$454$	−26.0325			−0.0573404
$455$	168.860	+	53.0231i	0.371121	+	0.116534i
$456$	−213.743	+	253.462i	−0.468735	+	0.555839i
$457$			433.599i			0.948793i	0.880311	+	0.474397i	$0.157334\pi$
$457$			433.599i			0.948793i	−0.880311	+	0.474397i	$0.842666\pi$
$458$	−521.775			−1.13925
$459$	26.2477	+	15.4130i	0.0571845	+	0.0335796i
$460$	−1065.37	−	334.532i	−2.31602	−	0.727244i
$461$			511.370i			1.10926i	0.832096	+	0.554631i	$0.187141\pi$
$461$			511.370i			1.10926i	−0.832096	+	0.554631i	$0.812859\pi$
$462$	283.859	−	336.608i	0.614414	−	0.728590i
$463$			452.337i			0.976969i	0.872573	+	0.488484i	$0.162450\pi$
$463$			452.337i			0.976969i	−0.872573	+	0.488484i	$0.837550\pi$
$464$		−	36.1864i		−	0.0779880i
$465$	−51.1898	+	32.5195i	−0.110086	+	0.0699344i
$466$	−614.550			−1.31878
$467$	380.108			0.813936			0.406968	−	0.913442i	$-0.366586\pi$
$467$	380.108			0.813936			0.406968	+	0.913442i	$0.366586\pi$
$468$	750.690	−	128.569i	1.60404	−	0.274720i
$469$	−87.1578			−0.185838
$470$	−33.2234	−	10.4323i	−0.0706881	−	0.0221965i
$471$	702.848	+	592.706i	1.49225	+	1.25840i
$472$		−	435.650i		−	0.922987i
$473$	−1307.65			−2.76459
$474$	709.207	−	840.998i	1.49622	−	1.77426i
$475$	−303.433	−	211.404i	−0.638807	−	0.445061i
$476$		−	18.8659i		−	0.0396342i
$477$	−33.7278	−	196.930i	−0.0707082	−	0.412851i
$478$		−	491.082i		−	1.02737i
$479$			699.921i			1.46121i	0.682799	+	0.730607i	$0.260763\pi$
$479$			699.921i			1.46121i	−0.682799	+	0.730607i	$0.739237\pi$
$480$	−430.999	+	273.802i	−0.897914	+	0.570421i
$481$	−7.21081			−0.0149913
$482$	201.531			0.418113
$483$	−214.244	−	180.671i	−0.443570	−	0.374059i
$484$	−1119.91			−2.31387
$485$	77.7660	−	247.658i	0.160342	−	0.510635i
$486$	−276.045	+	730.401i	−0.567995	+	1.50288i
$487$		−	290.607i		−	0.596729i	−0.954452	−	0.298365i	$-0.903559\pi$
$487$		−	290.607i		−	0.596729i	0.954452	−	0.298365i	$-0.0964411\pi$
$488$	−307.816			−0.630771
$489$	−178.107	−	150.196i	−0.364227	−	0.307150i
$490$	107.299	+	33.6925i	0.218978	+	0.0687602i
$491$		−	747.159i		−	1.52171i	−0.648923	−	0.760854i	$-0.724780\pi$
$491$		−	747.159i		−	1.52171i	0.648923	−	0.760854i	$-0.275220\pi$
$492$	532.726	+	449.244i	1.08278	+	0.913097i
$493$			31.5397i			0.0639751i
$494$			635.946i			1.28734i
$495$	769.866	+	104.281i	1.55528	+	0.210669i
$496$	−5.22945			−0.0105433
$497$	−83.2010			−0.167406
$498$	−506.964	+	601.172i	−1.01800	+	1.20717i
$499$	−243.049			−0.487072			−0.243536	−	0.969892i	$-0.578307\pi$
$499$	−243.049			−0.487072			−0.243536	+	0.969892i	$0.578307\pi$
$500$	483.521	+	625.553i	0.967042	+	1.25111i
$501$	−282.017	+	334.424i	−0.562909	+	0.667513i
$502$			1069.30i			2.13008i
$503$	−610.132			−1.21299			−0.606493	−	0.795089i	$-0.707424\pi$
$503$	−610.132			−1.21299			−0.606493	+	0.795089i	$0.707424\pi$
$504$	175.349	−	30.0317i	0.347915	−	0.0595867i
$505$	18.2348	−	58.0714i	0.0361084	−	0.114993i
$506$			1958.75i			3.87105i
$507$	19.3427	−	22.9371i	0.0381512	−	0.0452408i
$508$			837.542i			1.64870i
$509$			292.158i			0.573985i	0.957933	+	0.286992i	$0.0926554\pi$
$509$			292.158i			0.573985i	−0.957933	+	0.286992i	$0.907345\pi$
$510$	45.8649	−	29.1368i	0.0899312	−	0.0571309i
$511$	−56.2974			−0.110171
$512$	−82.6843			−0.161493
$513$	−344.411	−	202.243i	−0.671366	−	0.394235i
$514$	393.161			0.764905
$515$	282.803	−	900.631i	0.549133	−	1.74880i
$516$	−1098.72	−	926.545i	−2.12931	−	1.79563i
$517$			37.4194i			0.0723780i
$518$	−4.58197			−0.00884551
$519$	−143.700	+	170.403i	−0.276878	+	0.328330i
$520$	149.729	−	476.836i	0.287941	−	0.916992i
$521$		−	1002.34i		−	1.92388i	−0.273266	−	0.961939i	$-0.588104\pi$
$521$		−	1002.34i		−	1.92388i	0.273266	−	0.961939i	$-0.411896\pi$
$522$	−797.463	+	136.580i	−1.52771	+	0.261647i
$523$		−	429.640i		−	0.821491i	−0.911750	−	0.410746i	$-0.865268\pi$
$523$		−	429.640i		−	0.821491i	0.911750	−	0.410746i	$-0.134732\pi$
$524$			683.490i			1.30437i
$525$	51.3382	+	191.675i	0.0977870	+	0.365096i
$526$	576.339			1.09570
$527$	4.55794			0.00864885
$528$	51.2125	+	43.1871i	0.0969933	+	0.0817937i
$529$	717.705			1.35672
$530$	−340.287	−	106.852i	−0.642051	−	0.201608i
$531$	517.264	−	88.5906i	0.974131	−	0.166837i
$532$			247.549i			0.465318i
$533$	491.344			0.921847
$534$	−318.513	−	268.600i	−0.596466	−	0.502996i
$535$	517.202	+	162.405i	0.966733	+	0.303560i
$536$			246.121i			0.459180i
$537$	311.029	+	262.289i	0.579198	+	0.488433i
$538$			37.2261i			0.0691935i
$539$		−	120.851i		−	0.224212i
$540$	572.972	+	633.112i	1.06106	+	1.17243i
$541$	−112.287			−0.207554			−0.103777	−	0.994601i	$-0.533093\pi$
$541$	−112.287			−0.207554			−0.103777	+	0.994601i	$0.533093\pi$
$542$	−622.039			−1.14767
$543$	445.643	−	528.456i	0.820705	−	0.973215i
$544$	38.3762			0.0705444
$545$	562.796	+	176.721i	1.03265	+	0.324259i
$546$	219.979	−	260.857i	0.402892	−	0.477760i
$547$		−	840.540i		−	1.53664i	−0.640068	−	0.768318i	$-0.721094\pi$
$547$		−	840.540i		−	1.53664i	0.640068	−	0.768318i	$-0.278906\pi$
$548$	465.109			0.848739
$549$	−62.5953	−	365.482i	−0.114017	−	0.665723i
$550$	792.804	−	1137.93i	1.44146	−	2.06897i
$551$		−	413.850i		−	0.751090i
$552$	−510.186	+	604.993i	−0.924250	+	1.09600i
$553$		−	301.939i		−	0.546001i
$554$		−	206.353i		−	0.372479i
$555$	−4.33502	−	6.82386i	−0.00781084	−	0.0122952i
$556$	−1174.97			−2.11325
$557$	47.9220			0.0860358			0.0430179	−	0.999074i	$-0.486303\pi$
$557$	47.9220			0.0860358			0.0430179	+	0.999074i	$0.486303\pi$
$558$	19.7377	+	115.245i	0.0353723	+	0.206532i
$559$	−1013.38			−1.81284
$560$	−5.12607	+	16.3247i	−0.00915369	+	0.0291513i
$561$	−44.6363	−	37.6415i	−0.0795656	−	0.0670971i
$562$		−	935.003i		−	1.66371i
$563$	540.314			0.959705			0.479852	−	0.877349i	$-0.340690\pi$
$563$	540.314			0.959705			0.479852	+	0.877349i	$0.340690\pi$
$564$	−26.5137	+	31.4407i	−0.0470102	+	0.0557460i
$565$	859.424	+	269.864i	1.52110	+	0.477636i
$566$			196.526i			0.347219i
$567$	71.3155	+	202.092i	0.125777	+	0.356423i
$568$			234.947i			0.413639i
$569$		−	245.668i		−	0.431754i	−0.976421	−	0.215877i	$-0.930739\pi$
$569$		−	245.668i		−	0.431754i	0.976421	−	0.215877i	$-0.0692610\pi$
$570$	−601.819	+	382.320i	−1.05582	+	0.670737i
$571$	−497.374			−0.871058			−0.435529	−	0.900175i	$-0.643439\pi$
$571$	−497.374			−0.871058			−0.435529	+	0.900175i	$0.643439\pi$
$572$	−1460.99			−2.55417
$573$	494.839	+	417.294i	0.863594	+	0.728262i
$574$	312.215			0.543929
$575$	−724.269	−	504.603i	−1.25960	−	0.877571i
$576$	158.324	+	924.422i	0.274868	+	1.60490i
$577$		−	271.133i		−	0.469902i	−0.972007	−	0.234951i	$-0.924507\pi$
$577$		−	271.133i		−	0.469902i	0.972007	−	0.234951i	$-0.0754929\pi$
$578$	924.551			1.59957
$579$	−159.164	−	134.222i	−0.274894	−	0.231816i
$580$	−265.066	+	844.144i	−0.457011	+	1.45542i
$581$			215.835i			0.371489i
$582$	−382.585	−	322.631i	−0.657362	−	0.554348i
$583$			383.264i			0.657400i
$584$			158.975i			0.272218i
$585$	596.613	+	80.8133i	1.01985	+	0.138142i
$586$	−613.617			−1.04713
$587$	450.508			0.767476			0.383738	−	0.923442i	$-0.374637\pi$
$587$	450.508			0.767476			0.383738	+	0.923442i	$0.374637\pi$
$588$	85.6293	−	101.542i	0.145628	−	0.172690i
$589$	−59.8073			−0.101540
$590$	280.661	−	893.810i	0.475697	−	1.51493i
$591$	307.359	−	364.475i	0.520066	−	0.616708i
$592$		−	0.697113i		−	0.00117756i
$593$	−820.458			−1.38357			−0.691786	−	0.722103i	$-0.743176\pi$
$593$	−820.458			−1.38357			−0.691786	+	0.722103i	$0.743176\pi$
$594$	758.448	−	1291.60i	1.27685	−	2.17442i
$595$	4.46783	−	14.2285i	0.00750896	−	0.0239134i
$596$			936.609i			1.57149i
$597$	−749.917	+	889.273i	−1.25614	+	1.48957i
$598$			1517.95i			2.53838i
$599$			944.746i			1.57720i	0.614903	+	0.788602i	$0.289195\pi$
$599$			944.746i			1.57720i	−0.614903	+	0.788602i	$0.710805\pi$
$600$	541.262	−	144.971i	0.902103	−	0.241619i
$601$	790.903			1.31598			0.657989	−	0.753028i	$-0.271407\pi$
$601$	790.903			1.31598			0.657989	+	0.753028i	$0.271407\pi$
$602$	−643.930			−1.06965
$603$	−292.228	+	50.0493i	−0.484624	+	0.0830005i
$604$	389.406			0.644711
$605$	−844.629	−	265.219i	−1.39608	−	0.438378i
$606$	−89.7093	−	75.6512i	−0.148035	−	0.124837i
$607$		−	698.813i		−	1.15126i	−0.817712	−	0.575628i	$-0.804758\pi$
$607$		−	698.813i		−	1.15126i	0.817712	−	0.575628i	$-0.195242\pi$
$608$	−503.555			−0.828216
$609$	−143.154	+	169.756i	−0.235064	+	0.278746i
$610$	−631.537	−	198.306i	−1.03531	−	0.325092i
$611$			28.9984i			0.0474606i
$612$	−10.8335	−	63.2546i	−0.0177018	−	0.103357i
$613$		−	303.996i		−	0.495914i	−0.968771	−	0.247957i	$-0.920241\pi$
$613$		−	303.996i		−	0.495914i	0.968771	−	0.247957i	$-0.0797592\pi$
$614$			659.132i			1.07351i
$615$	295.388	+	464.977i	0.480305	+	0.756060i
$616$	−341.264			−0.553999
$617$	154.508			0.250419			0.125209	−	0.992130i	$-0.460040\pi$
$617$	154.508			0.250419			0.125209	+	0.992130i	$0.460040\pi$
$618$	−1391.30	−	1173.28i	−2.25130	−	1.89850i
$619$	−247.956			−0.400575			−0.200287	−	0.979737i	$-0.564188\pi$
$619$	−247.956			−0.400575			−0.200287	+	0.979737i	$0.564188\pi$
$620$	121.991	+	38.3059i	0.196760	+	0.0617837i
$621$	−822.079	−	482.736i	−1.32380	−	0.777353i
$622$			1578.89i			2.53841i
$623$	−114.354			−0.183553
$624$	39.6875	+	33.4681i	0.0636017	+	0.0536349i
$625$	216.524	+	586.295i	0.346438	+	0.938073i
$626$		−	571.915i		−	0.913602i
$627$	585.698	+	493.915i	0.934127	+	0.787743i
$628$		−	1938.43i		−	3.08668i
$629$			0.607597i			0.000965973i
$630$	379.106	+	51.3512i	0.601756	+	0.0815099i
$631$	207.352			0.328609			0.164305	−	0.986410i	$-0.447462\pi$
$631$	207.352			0.328609			0.164305	+	0.986410i	$0.447462\pi$
$632$	−852.629			−1.34910
$633$	−20.5715	+	24.3943i	−0.0324985	+	0.0385376i
$634$	1235.61			1.94891
$635$	−198.347	+	631.668i	−0.312358	+	0.994752i
$636$	−271.564	+	322.028i	−0.426987	+	0.506333i
$637$		−	93.6540i		−	0.147024i
$638$	1552.02			2.43263
$639$	−278.961	+	47.7771i	−0.436559	+	0.0747685i
$640$	947.812	+	297.619i	1.48096	+	0.465029i
$641$			962.715i			1.50190i	0.660362	+	0.750948i	$0.270403\pi$
$641$			962.715i			1.50190i	−0.660362	+	0.750948i	$0.729597\pi$
$642$	673.773	−	798.979i	1.04949	−	1.24452i
$643$			143.679i			0.223452i	0.993739	+	0.111726i	$0.0356378\pi$
$643$			143.679i			0.223452i	−0.993739	+	0.111726i	$0.964362\pi$
$644$			590.879i			0.917515i
$645$	−609.224	−	958.994i	−0.944533	−	1.48681i
$646$	53.5861			0.0829506
$647$	657.715			1.01656			0.508280	−	0.861192i	$-0.330281\pi$
$647$	657.715			1.01656			0.508280	+	0.861192i	$0.330281\pi$
$648$	570.677	−	201.384i	0.880674	−	0.310778i
$649$	−1006.69			−1.55115
$650$	614.389	−	881.848i	0.945215	−	1.35669i
$651$	24.5322	+	20.6878i	0.0376839	+	0.0317785i
$652$			491.213i			0.753395i
$653$	659.701			1.01026			0.505131	−	0.863043i	$-0.331444\pi$
$653$	659.701			1.01026			0.505131	+	0.863043i	$0.331444\pi$
$654$	733.169	−	869.413i	1.12105	−	1.32938i
$655$	−161.865	+	515.483i	−0.247122	+	0.786998i
$656$			47.5012i			0.0724104i
$657$	−188.757	+	32.3281i	−0.287302	+	0.0492056i
$658$			18.4265i			0.0280038i
$659$		−	52.2447i		−	0.0792787i	−0.999214	−	0.0396394i	$-0.987379\pi$
$659$		−	52.2447i		−	0.0792787i	0.999214	−	0.0396394i	$-0.0126209\pi$
$660$	−878.321	−	1382.59i	−1.33079	−	2.09483i
$661$	−1226.43			−1.85542			−0.927708	−	0.373307i	$-0.878224\pi$
$661$	−1226.43			−1.85542			−0.927708	+	0.373307i	$0.878224\pi$
$662$	154.488			0.233366
$663$	−34.5912	−	29.1705i	−0.0521738	−	0.0439978i
$664$	609.486			0.917901
$665$	−58.6249	+	186.700i	−0.0881577	+	0.280752i
$666$	−15.3627	+	2.63114i	−0.0230671	+	0.00395066i
$667$		−	987.826i		−	1.48100i
$668$	922.332			1.38074
$669$	−690.488	−	582.284i	−1.03212	−	0.870379i
$670$	−158.560	+	504.958i	−0.236656	+	0.753668i
$671$			711.298i			1.06006i
$672$	206.552	+	174.184i	0.307369	+	0.259202i
$673$			1025.65i			1.52400i	0.647575	+	0.762001i	$0.275783\pi$
$673$			1025.65i			1.52400i	−0.647575	+	0.762001i	$0.724217\pi$
$674$			218.893i			0.324767i
$675$	282.197	+	613.180i	0.418069	+	0.908415i
$676$	−63.2598			−0.0935795
$677$	−139.833			−0.206549			−0.103274	−	0.994653i	$-0.532932\pi$
$677$	−139.833			−0.206549			−0.103274	+	0.994653i	$0.532932\pi$
$678$	1119.60	−	1327.65i	1.65132	−	1.95818i
$679$	−137.357			−0.202293
$680$	−40.1791	−	12.6165i	−0.0590869	−	0.0185536i
$681$	−15.6684	+	18.5801i	−0.0230080	+	0.0272835i
$682$		−	224.289i		−	0.328869i
$683$	357.970			0.524114			0.262057	−	0.965052i	$-0.415599\pi$
$683$	357.970			0.524114			0.262057	+	0.965052i	$0.415599\pi$
$684$	142.152	+	829.999i	0.207825	+	1.21345i
$685$	350.782	+	110.147i	0.512090	+	0.160799i
$686$		−	59.5106i		−	0.0867502i
$687$	−314.045	+	372.404i	−0.457126	+	0.542073i
$688$		−	97.9691i		−	0.142397i
$689$			297.013i			0.431079i
$690$	−1436.49	+	912.565i	−2.08187	+	1.32256i
$691$	1042.49			1.50867			0.754335	−	0.656489i	$-0.227959\pi$
$691$	1042.49			1.50867			0.754335	+	0.656489i	$0.227959\pi$
$692$	469.967			0.679143
$693$	−69.3969	−	405.195i	−0.100140	−	0.584697i
$694$	1408.12			2.02899
$695$	−886.153	−	278.257i	−1.27504	−	0.400370i
$696$	479.366	+	404.246i	0.688744	+	0.580813i
$697$		−	41.4016i		−	0.0593997i
$698$	336.945			0.482729
$699$	−369.885	+	438.620i	−0.529163	+	0.627496i
$700$	239.158	−	343.269i	0.341655	−	0.490385i
$701$			873.071i			1.24546i	0.782435	+	0.622732i	$0.213977\pi$
$701$			873.071i			1.24546i	−0.782435	+	0.622732i	$0.786023\pi$
$702$	587.765	−	1000.94i	0.837272	−	1.42584i
$703$		−	7.97262i		−	0.0113409i
$704$		−	1799.10i		−	2.55555i
$705$	−27.4423	+	17.4334i	−0.0389252	+	0.0247282i
$706$	−314.472			−0.445428
$707$	−32.2078			−0.0455556
$708$	−845.850	−	713.299i	−1.19470	−	1.00748i
$709$	−1305.07			−1.84072			−0.920362	−	0.391067i	$-0.872106\pi$
$709$	−1305.07			−1.84072			−0.920362	+	0.391067i	$0.872106\pi$
$710$	−151.361	+	482.033i	−0.213185	+	0.678920i
$711$	−173.384	−	1012.36i	−0.243860	−	1.42385i
$712$			322.918i			0.453536i
$713$	−142.755			−0.200217
$714$	−21.9803	−	18.5358i	−0.0307848	−	0.0259606i
$715$	−1101.87	−	345.993i	−1.54107	−	0.483906i
$716$		−	857.809i		−	1.19806i
$717$	−350.497	−	295.572i	−0.488839	−	0.412234i
$718$		−	2.41615i		−	0.00336512i
$719$		−	566.466i		−	0.787852i	−0.919142	−	0.393926i	$-0.871117\pi$
$719$		−	566.466i		−	0.787852i	0.919142	−	0.393926i	$-0.128883\pi$
$720$	−7.81271	+	57.6782i	−0.0108510	+	0.0801086i
$721$	−499.511			−0.692804
$722$	456.858			0.632767
$723$	121.297	−	143.837i	0.167769	−	0.198945i
$724$	−1457.47			−2.01307
$725$	−399.822	+	573.874i	−0.551479	+	0.791551i
$726$	−1100.32	+	1304.79i	−1.51559	+	1.79723i
$727$			347.597i			0.478125i	0.971004	+	0.239062i	$0.0768400\pi$
$727$			347.597i			0.478125i	−0.971004	+	0.239062i	$0.923160\pi$
$728$	−264.465			−0.363276
$729$	355.160	+	636.634i	0.487188	+	0.873297i
$730$	−102.418	+	326.164i	−0.140298	+	0.446801i
$731$			85.3889i			0.116811i
$732$	−503.994	+	597.651i	−0.688517	+	0.816463i
$733$			170.822i			0.233044i	0.993188	+	0.116522i	$0.0371746\pi$
$733$			170.822i			0.233044i	−0.993188	+	0.116522i	$0.962825\pi$
$734$		−	1913.90i		−	2.60749i
$735$	88.6282	−	56.3032i	0.120583	−	0.0766029i
$736$	−1201.94			−1.63307
$737$	568.732			0.771686
$738$	1046.81	−	179.286i	1.41845	−	0.242934i
$739$	837.328			1.13306			0.566528	−	0.824043i	$-0.308286\pi$
$739$	837.328			1.13306			0.566528	+	0.824043i	$0.308286\pi$
$740$	−5.10637	+	16.2620i	−0.00690050	+	0.0219757i
$741$	453.891	+	382.763i	0.612538	+	0.516549i
$742$			188.731i			0.254355i
$743$	593.407			0.798664			0.399332	−	0.916806i	$-0.369242\pi$
$743$	593.407			0.798664			0.399332	+	0.916806i	$0.369242\pi$
$744$	58.4193	−	69.2752i	0.0785205	−	0.0931118i
$745$	−221.809	+	706.384i	−0.297730	+	0.948166i
$746$		−	1577.78i		−	2.11499i
$747$	123.941	+	723.666i	0.165918	+	0.968763i
$748$			123.106i			0.164580i
$749$		−	286.853i		−	0.382981i
$750$	1203.89	+	51.2675i	1.60518	+	0.0683566i
$751$	1071.84			1.42722			0.713611	−	0.700542i	$-0.247059\pi$
$751$	1071.84			1.42722			0.713611	+	0.700542i	$0.247059\pi$
$752$	−2.80345			−0.00372800
$753$	763.187	+	643.590i	1.01353	+	0.854701i
$754$	1202.75			1.59515
$755$	293.687	+	92.2194i	0.388989	+	0.122145i
$756$	228.794	−	389.627i	0.302638	−	0.515379i
$757$		−	298.341i		−	0.394110i	−0.980392	−	0.197055i	$-0.936862\pi$
$757$		−	298.341i		−	0.394110i	0.980392	−	0.197055i	$-0.0631378\pi$
$758$	−1475.55			−1.94664
$759$	1398.01	+	1178.93i	1.84191	+	1.55327i
$760$	527.212	+	165.548i	0.693701	+	0.217826i
$761$			201.735i			0.265092i	0.991177	+	0.132546i	$0.0423152\pi$
$761$			201.735i			0.265092i	−0.991177	+	0.132546i	$0.957685\pi$
$762$	975.807	+	822.891i	1.28059	+	1.07991i
$763$		−	312.140i		−	0.409096i
$764$		−	1364.75i		−	1.78633i
$765$	6.80948	−	50.2718i	0.00890129	−	0.0657147i
$766$	40.8810			0.0533695
$767$	−780.145			−1.01714
$768$	428.579	−	508.221i	0.558045	−	0.661746i
$769$	969.762			1.26107			0.630535	−	0.776161i	$-0.282836\pi$
$769$	969.762			1.26107			0.630535	+	0.776161i	$0.282836\pi$
$770$	−700.160	−	219.854i	−0.909298	−	0.285525i
$771$	236.635	−	280.609i	0.306920	−	0.363954i
$772$			438.969i			0.568613i
$773$	−1150.02			−1.48773			−0.743866	−	0.668328i	$-0.767010\pi$
$773$	−1150.02			−1.48773			−0.743866	+	0.668328i	$0.767010\pi$
$774$	−2159.01	+	369.768i	−2.78941	+	0.477737i
$775$	82.9330	+	57.7800i	0.107010	+	0.0745548i
$776$			387.876i			0.499840i
$777$	−2.75779	+	3.27027i	−0.00354928	+	0.00420884i
$778$		−	1308.23i		−	1.68154i
$779$			543.254i			0.697373i
$780$	−680.661	−	1071.45i	−0.872642	−	1.37365i
$781$	542.912			0.695150
$782$	127.905			0.163562
$783$	−382.496	+	651.374i	−0.488500	+	0.831895i
$784$	9.05410			0.0115486
$785$	459.062	−	1461.95i	0.584792	−	1.86236i
$786$	796.324	+	671.534i	1.01314	+	0.854369i
$787$		−	1034.39i		−	1.31434i	−0.753740	−	0.657172i	$-0.771752\pi$
$787$		−	1034.39i		−	1.31434i	0.753740	−	0.657172i	$-0.228248\pi$
$788$	−1005.21			−1.27565
$789$	346.887	−	411.348i	0.439653	−	0.521353i
$790$	−1749.31	−	549.294i	−2.21432	−	0.695309i
$791$		−	476.657i		−	0.602601i
$792$	−1144.21	+	195.966i	−1.44471	+	0.247432i
$793$			551.226i			0.695114i
$794$		−	658.087i		−	0.828825i
$795$	−281.074	+	178.559i	−0.353553	+	0.224603i
$796$	2452.59			3.08114
$797$	479.466			0.601588			0.300794	−	0.953689i	$-0.402748\pi$
$797$	479.466			0.601588			0.300794	+	0.953689i	$0.402748\pi$
$798$	288.416	+	243.219i	0.361424	+	0.304786i
$799$	2.44346			0.00305815
$800$	698.265	+	486.486i	0.872831	+	0.608108i
$801$	−383.413	+	65.6662i	−0.478667	+	0.0819803i
$802$		−	279.113i		−	0.348022i
$803$	367.358			0.457482
$804$	477.863	+	402.978i	0.594357	+	0.501217i
$805$	−139.933	+	445.637i	−0.173829	+	0.553586i
$806$		−	173.814i		−	0.215650i
$807$	26.5692	+	22.4056i	0.0329234	+	0.0277641i
$808$			90.9499i			0.112562i
$809$		−	501.244i		−	0.619584i	−0.950804	−	0.309792i	$-0.899741\pi$
$809$		−	501.244i		−	0.619584i	0.950804	−	0.309792i	$-0.100259\pi$
$810$	1300.58	−	45.5233i	1.60565	−	0.0562016i
$811$	−923.160			−1.13830			−0.569149	−	0.822234i	$-0.692727\pi$
$811$	−923.160			−1.13830			−0.569149	+	0.822234i	$0.692727\pi$
$812$	468.183			0.576580
$813$	−374.392	+	443.965i	−0.460507	+	0.546082i
$814$	29.8988			0.0367307
$815$	−116.330	+	370.470i	−0.142736	+	0.454564i
$816$	2.82009	−	3.34414i	0.00345599	−	0.00409821i
$817$		−	1120.44i		−	1.37140i
$818$	−1684.50			−2.05930
$819$	−53.7796	−	314.009i	−0.0656650	−	0.383405i
$820$	347.947	−	1108.09i	0.424326	−	1.35133i
$821$			489.040i			0.595664i	0.954618	+	0.297832i	$0.0962635\pi$
$821$			489.040i			0.595664i	−0.954618	+	0.297832i	$0.903736\pi$
$822$	456.973	−	541.891i	0.555928	−	0.659235i
$823$		−	708.795i		−	0.861233i	−0.902535	−	0.430617i	$-0.858296\pi$
$823$		−	708.795i		−	0.861233i	0.902535	−	0.430617i	$-0.141704\pi$
$824$			1410.54i			1.71183i
$825$	−334.998	−	1250.74i	−0.406058	−	1.51605i
$826$	−495.728			−0.600155
$827$	−406.217			−0.491194			−0.245597	−	0.969372i	$-0.578984\pi$
$827$	−406.217			−0.491194			−0.245597	+	0.969372i	$0.578984\pi$
$828$	339.305	+	1981.14i	0.409789	+	2.39268i
$829$	−445.483			−0.537374			−0.268687	−	0.963228i	$-0.586590\pi$
$829$	−445.483			−0.537374			−0.268687	+	0.963228i	$0.586590\pi$
$830$	1250.46	+	392.653i	1.50658	+	0.473076i
$831$	−147.280	−	124.200i	−0.177232	−	0.149458i
$832$		−	1394.23i		−	1.67576i
$833$	−7.89147			−0.00947355
$834$	−1154.42	+	1368.94i	−1.38419	+	1.64141i
$835$	695.616	+	218.428i	0.833073	+	0.261590i
$836$		−	1615.34i		−	1.93222i
$837$	94.1328	+	55.2761i	0.112465	+	0.0660407i
$838$			1860.28i			2.21991i
$839$		−	102.860i		−	0.122599i	−0.998119	−	0.0612993i	$-0.980476\pi$
$839$		−	102.860i		−	0.122599i	0.998119	−	0.0612993i	$-0.0195244\pi$
$840$	−158.992	−	250.273i	−0.189276	−	0.297944i
$841$	58.2972			0.0693189
$842$	967.237			1.14874
$843$	−667.335	−	562.758i	−0.791619	−	0.667566i
$844$	67.2788			0.0797143
$845$	−47.7100	−	14.9812i	−0.0564616	−	0.0177293i
$846$	10.5812	+	61.7815i	0.0125073	+	0.0730278i
$847$			468.452i			0.553072i
$848$	−28.7141			−0.0338609
$849$	140.265	+	118.285i	0.165213	+	0.139322i
$850$	−74.3062	−	51.7696i	−0.0874191	−	0.0609055i
$851$		−	19.0300i		−	0.0223619i
$852$	456.169	+	384.684i	0.535409	+	0.451507i
$853$		−	40.3354i		−	0.0472865i	−0.999720	−	0.0236433i	$-0.992473\pi$
$853$		−	40.3354i		−	0.0472865i	0.999720	−	0.0236433i	$-0.00752659\pi$
$854$			350.266i			0.410147i
$855$	−89.3510	+	659.644i	−0.104504	+	0.771513i
$856$	−810.029			−0.946295
$857$	861.111			1.00480			0.502399	−	0.864636i	$-0.332451\pi$
$857$	861.111			1.00480			0.502399	+	0.864636i	$0.332451\pi$
$858$	−1435.43	+	1702.17i	−1.67300	+	1.98389i
$859$	−466.583			−0.543170			−0.271585	−	0.962414i	$-0.587548\pi$
$859$	−466.583			−0.543170			−0.271585	+	0.962414i	$0.587548\pi$
$860$	−717.626	+	2285.39i	−0.834448	+	2.65743i
$861$	187.916	−	222.836i	0.218253	−	0.258810i
$862$			1556.63i			1.80583i
$863$	−477.492			−0.553293			−0.276646	−	0.960972i	$-0.589223\pi$
$863$	−477.492			−0.553293			−0.276646	+	0.960972i	$0.589223\pi$
$864$	792.563	+	465.404i	0.917318	+	0.538662i
$865$	354.445	+	111.298i	0.409764	+	0.128668i
$866$			489.105i			0.564787i
$867$	556.468	−	659.875i	0.641832	−	0.761102i
$868$		−	67.6591i		−	0.0779483i
$869$			1970.24i			2.26725i
$870$	723.070	+	1138.20i	0.831115	+	1.30828i
$871$	440.743			0.506020
$872$	−881.436			−1.01082
$873$	−460.539	+	78.8756i	−0.527536	+	0.0903500i
$874$	−1678.32			−1.92027
$875$	261.665	−	202.254i	0.299045	−	0.231147i
$876$	308.663	+	260.294i	0.352356	+	0.297139i
$877$		−	102.947i		−	0.117385i	−0.998276	−	0.0586925i	$-0.981307\pi$
$877$		−	102.947i		−	0.117385i	0.998276	−	0.0586925i	$-0.0186932\pi$
$878$	−150.260			−0.171139
$879$	−369.323	+	437.954i	−0.420163	+	0.498241i
$880$	33.4492	−	106.524i	0.0380104	−	0.121050i
$881$			168.738i			0.191530i	0.995404	+	0.0957651i	$0.0305298\pi$
$881$			168.738i			0.191530i	−0.995404	+	0.0957651i	$0.969470\pi$
$882$	−34.1732	−	199.531i	−0.0387451	−	0.226225i
$883$			541.823i			0.613617i	0.951771	+	0.306808i	$0.0992610\pi$
$883$			541.823i			0.613617i	−0.951771	+	0.306808i	$0.900739\pi$
$884$			95.4016i			0.107920i
$885$	−469.010	−	738.280i	−0.529955	−	0.834215i
$886$	−1534.58			−1.73203
$887$	−508.508			−0.573289			−0.286645	−	0.958037i	$-0.592540\pi$
$887$	−508.508			−0.573289			−0.286645	+	0.958037i	$0.592540\pi$
$888$	9.23474	+	7.78759i	0.0103995	+	0.00876981i
$889$	350.338			0.394081
$890$	−208.035	+	662.520i	−0.233748	+	0.744405i
$891$	−465.356	−	1318.71i	−0.522285	−	1.48004i
$892$			1904.35i			2.13492i
$893$	−32.0621			−0.0359038
$894$	1091.23	+	920.226i	1.22061	+	1.02934i
$895$	203.147	−	646.954i	0.226980	−	0.722853i
$896$		−	525.679i		−	0.586696i
$897$	1083.40	+	913.622i	1.20780	+	1.01853i
$898$		−	1007.41i		−	1.12184i
$899$			113.112i			0.125820i
$900$	604.746	−	1288.27i	0.671940	−	1.43141i
$901$	25.0269			0.0277768
$902$	−2037.30			−2.25865
$903$	−387.568	+	459.589i	−0.429200	+	0.508957i
$904$	−1346.01			−1.48895
$905$	−1099.21	−	345.158i	−1.21460	−	0.381390i
$906$	382.594	−	453.691i	0.422289	−	0.500762i
$907$			764.628i			0.843030i	0.906821	+	0.421515i	$0.138501\pi$
$907$			764.628i			0.843030i	−0.906821	+	0.421515i	$0.861499\pi$
$908$	51.2433			0.0564354
$909$	−107.988	+	18.4949i	−0.118799	+	0.0203464i
$910$	−542.594	−	170.378i	−0.596257	−	0.187228i
$911$		−	660.093i		−	0.724580i	−0.932065	−	0.362290i	$-0.881995\pi$
$911$		−	660.093i		−	0.724580i	0.932065	−	0.362290i	$-0.118005\pi$
$912$	−37.0040	+	43.8804i	−0.0405745	+	0.0481144i
$913$		−	1408.39i		−	1.54260i
$914$		−	1393.27i		−	1.52436i
$915$	−521.645	+	331.387i	−0.570104	+	0.362172i
$916$	1027.08			1.12127
$917$	285.900			0.311777
$918$	−84.3410	−	49.5262i	−0.0918747	−	0.0539501i
$919$	−638.298			−0.694557			−0.347278	−	0.937762i	$-0.612894\pi$
$919$	−638.298			−0.694557			−0.347278	+	0.937762i	$0.612894\pi$
$920$	1258.41	+	395.148i	1.36784	+	0.429509i
$921$	470.439	+	396.718i	0.510792	+	0.430747i
$922$		−	1643.17i		−	1.78218i
$923$	420.734			0.455833
$924$	−558.758	+	662.591i	−0.604717	+	0.717090i
$925$	−7.70237	+	11.0554i	−0.00832689	+	0.0119518i
$926$		−	1453.48i		−	1.56963i
$927$	−1674.79	+	286.838i	−1.80668	+	0.309426i
$928$			952.359i			1.02625i
$929$		−	140.139i		−	0.150849i	−0.997152	−	0.0754246i	$-0.975969\pi$
$929$		−	140.139i		−	0.150849i	0.997152	−	0.0754246i	$-0.0240312\pi$
$930$	164.487	−	104.494i	0.176867	−	0.112359i
$931$	103.548			0.111223
$932$	1209.70			1.29796
$933$	1126.89	+	950.300i	1.20782	+	1.01854i
$934$	−1221.39			−1.30770
$935$	−29.1540	+	92.8454i	−0.0311807	+	0.0992999i
$936$	−886.713	+	151.865i	−0.947343	+	0.162249i
$937$		−	521.950i		−	0.557044i	−0.960430	−	0.278522i	$-0.910155\pi$
$937$		−	521.950i		−	0.557044i	0.960430	−	0.278522i	$-0.0898445\pi$
$938$	280.062			0.298573
$939$	−408.190	−	344.223i	−0.434707	−	0.366585i
$940$	65.3980	+	20.5354i	0.0695724	+	0.0218461i
$941$			754.599i			0.801912i	0.916097	+	0.400956i	$0.131322\pi$
$941$			754.599i			0.801912i	−0.916097	+	0.400956i	$0.868678\pi$
$942$	−2258.44	−	1904.53i	−2.39749	−	2.02179i
$943$			1296.70i			1.37508i
$944$		−	75.4214i		−	0.0798955i
$945$	264.827	−	239.670i	0.280240	−	0.253619i
$946$	4201.84			4.44169
$947$	−1457.66			−1.53924			−0.769619	−	0.638504i	$-0.779554\pi$
$947$	−1457.66			−1.53924			−0.769619	+	0.638504i	$0.779554\pi$
$948$	−1396.03	+	1655.45i	−1.47260	+	1.74625i
$949$	284.687			0.299986
$950$	975.013	+	679.298i	1.02633	+	0.715051i
$951$	743.686	−	881.884i	0.782004	−	0.927322i
$952$			22.2843i			0.0234079i
$953$	436.033			0.457537			0.228769	−	0.973481i	$-0.426530\pi$
$953$	436.033			0.457537			0.228769	+	0.973481i	$0.426530\pi$
$954$	108.377	+	632.790i	0.113602	+	0.663302i
$955$	323.202	−	1029.29i	0.338431	−	1.07779i
$956$			966.662i			1.01115i
$957$	934.126	−	1107.71i	0.976098	−	1.15748i
$958$		−	2249.04i		−	2.34764i
$959$		−	194.552i		−	0.202870i
$960$	1319.41	−	838.186i	1.37438	−	0.873110i
$961$	−944.654			−0.982990
$962$	23.1703			0.0240855
$963$	−164.722	−	961.778i	−0.171050	−	0.998731i
$964$	−396.700			−0.411514
$965$	−103.957	+	331.068i	−0.107728	+	0.343075i
$966$	688.425	+	580.543i	0.712655	+	0.600976i
$967$		−	16.8991i		−	0.0174758i	−0.999962	−	0.00873791i	$-0.997219\pi$
$967$		−	16.8991i		−	0.0174758i	0.999962	−	0.00873791i	$-0.00278140\pi$
$968$	1322.84			1.36657
$969$	32.2523	−	38.2457i	0.0332841	−	0.0394693i
$970$	−249.883	+	795.792i	−0.257612	+	0.820404i
$971$			144.690i			0.149011i	0.997221	+	0.0745056i	$0.0237379\pi$
$971$			144.690i			0.149011i	−0.997221	+	0.0745056i	$0.976262\pi$
$972$	543.377	−	1437.75i	0.559030	−	1.47916i
$973$			491.482i			0.505120i
$974$			933.799i			0.958726i
$975$	−259.609	−	969.271i	−0.266265	−	0.994124i
$976$	−53.2903			−0.0546007
$977$	786.805			0.805327			0.402664	−	0.915348i	$-0.368084\pi$
$977$	786.805			0.805327			0.402664	+	0.915348i	$0.368084\pi$
$978$	572.305	+	482.621i	0.585179	+	0.493477i
$979$	746.195			0.762201
$980$	−211.211	−	66.3214i	−0.215521	−	0.0676749i
$981$	−179.242	−	1046.56i	−0.182714	−	1.06683i
$982$			2400.82i			2.44483i
$983$	205.990			0.209553			0.104776	−	0.994496i	$-0.466587\pi$
$983$	205.990			0.209553			0.104776	+	0.994496i	$0.466587\pi$
$984$	−629.254	−	530.646i	−0.639486	−	0.539274i
$985$	−758.123	−	238.055i	−0.769668	−	0.241680i
$986$		−	101.346i		−	0.102785i
$987$	13.1515	+	11.0905i	0.0133247	+	0.0112366i
$988$		−	1251.82i		−	1.26702i
$989$		−	2674.38i		−	2.70413i
$990$	−2473.79	−	335.083i	−2.49877	−	0.338468i
$991$	514.024			0.518692			0.259346	−	0.965784i	$-0.416493\pi$
$991$	514.024			0.518692			0.259346	+	0.965784i	$0.416493\pi$
$992$	137.629			0.138739
$993$	92.9833	−	110.262i	0.0936388	−	0.111039i
$994$	267.347			0.268961
$995$	1849.73	+	580.825i	1.85902	+	0.583743i
$996$	997.925	−	1183.37i	1.00193	−	1.18812i
$997$			1267.89i			1.27170i	0.771812	+	0.635851i	$0.219351\pi$
$997$			1267.89i			1.27170i	−0.771812	+	0.635851i	$0.780649\pi$
$998$	780.982			0.782547
$999$	−7.36859	+	12.5484i	−0.00737596	+	0.0125609i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.f.a.29.4	yes	24
3.2	odd	2	inner	105.3.f.a.29.22	yes	24
5.2	odd	4		525.3.c.e.176.4		24
5.3	odd	4		525.3.c.e.176.21		24
5.4	even	2	inner	105.3.f.a.29.21	yes	24
15.2	even	4		525.3.c.e.176.22		24
15.8	even	4		525.3.c.e.176.3		24
15.14	odd	2	inner	105.3.f.a.29.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.f.a.29.3	✓	24	15.14	odd	2	inner
105.3.f.a.29.4	yes	24	1.1	even	1	trivial
105.3.f.a.29.21	yes	24	5.4	even	2	inner
105.3.f.a.29.22	yes	24	3.2	odd	2	inner
525.3.c.e.176.3		24	15.8	even	4
525.3.c.e.176.4		24	5.2	odd	4
525.3.c.e.176.21		24	5.3	odd	4
525.3.c.e.176.22		24	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.21327 q^{2} +(-1.93400 + 2.29339i) q^{3} +6.32511 q^{4} +(4.77035 + 1.49792i) q^{5} +(6.21446 - 7.36929i) q^{6} -2.64575i q^{7} -7.47120 q^{8} +(-1.51929 - 8.87084i) q^{9} +O(q^{10})\)	\(q-3.21327 q^{2} +(-1.93400 + 2.29339i) q^{3} +6.32511 q^{4} +(4.77035 + 1.49792i) q^{5} +(6.21446 - 7.36929i) q^{6} -2.64575i q^{7} -7.47120 q^{8} +(-1.51929 - 8.87084i) q^{9} +(-15.3284 - 4.81322i) q^{10} +17.2644i q^{11} +(-12.2328 + 14.5059i) q^{12} +13.3791i q^{13} +8.50151i q^{14} +(-12.6612 + 8.04331i) q^{15} -1.29344 q^{16} +1.12735 q^{17} +(4.88189 + 28.5044i) q^{18} -14.7926 q^{19} +(30.1730 + 9.47449i) q^{20} +(6.06774 + 5.11688i) q^{21} -55.4751i q^{22} -35.3087 q^{23} +(14.4493 - 17.1344i) q^{24} +(20.5125 + 14.2912i) q^{25} -42.9908i q^{26} +(23.2826 + 13.6719i) q^{27} -16.7347i q^{28} +27.9768i q^{29} +(40.6838 - 25.8453i) q^{30} +4.04305 q^{31} +34.0410 q^{32} +(-39.5939 - 33.3893i) q^{33} -3.62249 q^{34} +(3.96312 - 12.6212i) q^{35} +(-9.60967 - 56.1090i) q^{36} +0.538959i q^{37} +47.5327 q^{38} +(-30.6836 - 25.8753i) q^{39} +(-35.6402 - 11.1912i) q^{40} -36.7247i q^{41} +(-19.4973 - 16.4419i) q^{42} +75.7429i q^{43} +109.199i q^{44} +(6.04025 - 44.5928i) q^{45} +113.456 q^{46} +2.16744 q^{47} +(2.50152 - 2.96637i) q^{48} -7.00000 q^{49} +(-65.9122 - 45.9215i) q^{50} +(-2.18030 + 2.58546i) q^{51} +84.6245i q^{52} +22.1997 q^{53} +(-74.8133 - 43.9314i) q^{54} +(-25.8606 + 82.3570i) q^{55} +19.7669i q^{56} +(28.6089 - 33.9253i) q^{57} -89.8971i q^{58} +58.3106i q^{59} +(-80.0833 + 50.8748i) q^{60} +41.2004 q^{61} -12.9914 q^{62} +(-23.4700 + 4.01966i) q^{63} -104.209 q^{64} +(-20.0409 + 63.8232i) q^{65} +(127.226 + 107.289i) q^{66} -32.9426i q^{67} +7.13062 q^{68} +(68.2870 - 80.9767i) q^{69} +(-12.7346 + 40.5552i) q^{70} -31.4470i q^{71} +(11.3509 + 66.2758i) q^{72} -21.2784i q^{73} -1.73182i q^{74} +(-72.4464 + 19.4040i) q^{75} -93.5649 q^{76} +45.6772 q^{77} +(98.5947 + 83.1442i) q^{78} +114.122 q^{79} +(-6.17017 - 1.93747i) q^{80} +(-76.3835 + 26.9547i) q^{81} +118.006i q^{82} -81.5781 q^{83} +(38.3791 + 32.3648i) q^{84} +(5.37786 + 1.68868i) q^{85} -243.382i q^{86} +(-64.1618 - 54.1072i) q^{87} -128.985i q^{88} -43.2217i q^{89} +(-19.4089 + 143.289i) q^{90} +35.3979 q^{91} -223.331 q^{92} +(-7.81926 + 9.27230i) q^{93} -6.96456 q^{94} +(-70.5660 - 22.1581i) q^{95} +(-65.8353 + 78.0693i) q^{96} -51.9161i q^{97} +22.4929 q^{98} +(153.149 - 26.2296i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 52 q^{4} - 22 q^{9}+O(q^{10}) \) 24 * q + 52 * q^4 - 22 * q^9	\( 24 q + 52 q^{4} - 22 q^{9} - 24 q^{10} + 26 q^{15} + 4 q^{16} + 72 q^{19} + 14 q^{21} - 156 q^{24} - 64 q^{25} - 32 q^{30} - 40 q^{31} - 144 q^{34} + 36 q^{36} + 62 q^{39} - 40 q^{40} + 120 q^{45} - 104 q^{46} - 168 q^{49} + 70 q^{51} + 60 q^{54} - 16 q^{55} - 348 q^{60} + 432 q^{61} - 364 q^{64} + 284 q^{66} + 404 q^{69} + 140 q^{70} + 204 q^{75} + 152 q^{76} + 108 q^{79} - 158 q^{81} + 112 q^{84} + 196 q^{85} - 152 q^{90} - 84 q^{91} + 808 q^{94} - 516 q^{96} + 582 q^{99}+O(q^{100}) \) 24 * q + 52 * q^4 - 22 * q^9 - 24 * q^10 + 26 * q^15 + 4 * q^16 + 72 * q^19 + 14 * q^21 - 156 * q^24 - 64 * q^25 - 32 * q^30 - 40 * q^31 - 144 * q^34 + 36 * q^36 + 62 * q^39 - 40 * q^40 + 120 * q^45 - 104 * q^46 - 168 * q^49 + 70 * q^51 + 60 * q^54 - 16 * q^55 - 348 * q^60 + 432 * q^61 - 364 * q^64 + 284 * q^66 + 404 * q^69 + 140 * q^70 + 204 * q^75 + 152 * q^76 + 108 * q^79 - 158 * q^81 + 112 * q^84 + 196 * q^85 - 152 * q^90 - 84 * q^91 + 808 * q^94 - 516 * q^96 + 582 * q^99

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