LMFDB - Embedded newform 105.3.f.a.29.14

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			29.14
Character	$\chi$	$=$	105.29
Dual form			105.3.f.a.29.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.505667 q^{2} +(0.985457 + 2.83353i) q^{3} -3.74430 q^{4} +(0.221081 + 4.99511i) q^{5} +(0.498313 + 1.43282i) q^{6} -2.64575i q^{7} -3.91604 q^{8} +(-7.05775 + 5.58464i) q^{9} +O(q^{10})$	\(q+0.505667 q^{2} +(0.985457 + 2.83353i) q^{3} -3.74430 q^{4} +(0.221081 + 4.99511i) q^{5} +(0.498313 + 1.43282i) q^{6} -2.64575i q^{7} -3.91604 q^{8} +(-7.05775 + 5.58464i) q^{9} +(0.111793 + 2.52586i) q^{10} +13.3853i q^{11} +(-3.68985 - 10.6096i) q^{12} -3.27000i q^{13} -1.33787i q^{14} +(-13.9359 + 5.54890i) q^{15} +12.9970 q^{16} +21.9449 q^{17} +(-3.56887 + 2.82397i) q^{18} -4.36782 q^{19} +(-0.827792 - 18.7032i) q^{20} +(7.49681 - 2.60727i) q^{21} +6.76852i q^{22} +30.4863 q^{23} +(-3.85909 - 11.0962i) q^{24} +(-24.9022 + 2.20864i) q^{25} -1.65353i q^{26} +(-22.7793 - 14.4949i) q^{27} +9.90649i q^{28} -4.90100i q^{29} +(-7.04694 + 2.80590i) q^{30} +29.2074 q^{31} +22.2363 q^{32} +(-37.9277 + 13.1907i) q^{33} +11.0968 q^{34} +(13.2158 - 0.584924i) q^{35} +(26.4263 - 20.9106i) q^{36} +24.8760i q^{37} -2.20867 q^{38} +(9.26564 - 3.22245i) q^{39} +(-0.865761 - 19.5611i) q^{40} -13.6825i q^{41} +(3.79089 - 1.31841i) q^{42} -64.9582i q^{43} -50.1187i q^{44} +(-29.4562 - 34.0196i) q^{45} +15.4159 q^{46} -75.3743 q^{47} +(12.8080 + 36.8273i) q^{48} -7.00000 q^{49} +(-12.5923 + 1.11684i) q^{50} +(21.6258 + 62.1815i) q^{51} +12.2439i q^{52} +67.1397 q^{53} +(-11.5188 - 7.32960i) q^{54} +(-66.8612 + 2.95924i) q^{55} +10.3609i q^{56} +(-4.30430 - 12.3763i) q^{57} -2.47828i q^{58} +61.2523i q^{59} +(52.1802 - 20.7768i) q^{60} +46.8643 q^{61} +14.7693 q^{62} +(14.7756 + 18.6730i) q^{63} -40.7438 q^{64} +(16.3340 - 0.722934i) q^{65} +(-19.1788 + 6.67009i) q^{66} +96.7958i q^{67} -82.1683 q^{68} +(30.0429 + 86.3836i) q^{69} +(6.68281 - 0.295777i) q^{70} +108.224i q^{71} +(27.6384 - 21.8697i) q^{72} -50.7288i q^{73} +12.5790i q^{74} +(-30.7983 - 68.3847i) q^{75} +16.3544 q^{76} +35.4142 q^{77} +(4.68533 - 1.62949i) q^{78} -59.8158 q^{79} +(2.87338 + 64.9214i) q^{80} +(18.6236 - 78.8299i) q^{81} -6.91882i q^{82} -82.9049 q^{83} +(-28.0703 + 9.76242i) q^{84} +(4.85159 + 109.617i) q^{85} -32.8473i q^{86} +(13.8871 - 4.82972i) q^{87} -52.4175i q^{88} -79.4072i q^{89} +(-14.8950 - 17.2026i) q^{90} -8.65161 q^{91} -114.150 q^{92} +(28.7827 + 82.7601i) q^{93} -38.1143 q^{94} +(-0.965641 - 21.8178i) q^{95} +(21.9129 + 63.0072i) q^{96} -103.792i q^{97} -3.53967 q^{98} +(-74.7522 - 94.4703i) 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 $

$2$	0.505667			0.252834			0.126417	−	0.991977i	$-0.459652\pi$
$2$	0.505667			0.252834			0.126417	+	0.991977i	$0.459652\pi$
$3$	0.985457	+	2.83353i	0.328486	+	0.944509i
$3$	0.985457	+	2.83353i	0.328486	+	0.944509i
$4$	−3.74430			−0.936075
$5$	0.221081	+	4.99511i	0.0442161	+	0.999022i
$5$	0.221081	+	4.99511i	0.0442161	+	0.999022i
$6$	0.498313	+	1.43282i	0.0830522	+	0.238804i
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	−3.91604			−0.489505
$9$	−7.05775	+	5.58464i	−0.784194	+	0.620515i
$10$	0.111793	+	2.52586i	0.0111793	+	0.252586i
$11$			13.3853i			1.21685i	0.793612	+	0.608424i	$0.208198\pi$
$11$			13.3853i			1.21685i	−0.793612	+	0.608424i	$0.791802\pi$
$12$	−3.68985	−	10.6096i	−0.307487	−	0.884131i
$13$		−	3.27000i		−	0.251539i	−0.992060	−	0.125769i	$-0.959860\pi$
$13$		−	3.27000i		−	0.251539i	0.992060	−	0.125769i	$-0.0401399\pi$
$14$		−	1.33787i		−	0.0955622i
$15$	−13.9359	+	5.54890i	−0.929061	+	0.369927i
$16$	12.9970			0.812312
$17$	21.9449			1.29088			0.645438	−	0.763813i	$-0.276675\pi$
$17$	21.9449			1.29088			0.645438	+	0.763813i	$0.276675\pi$
$18$	−3.56887	+	2.82397i	−0.198271	+	0.156887i
$19$	−4.36782			−0.229886			−0.114943	−	0.993372i	$-0.536668\pi$
$19$	−4.36782			−0.229886			−0.114943	+	0.993372i	$0.536668\pi$
$20$	−0.827792	−	18.7032i	−0.0413896	−	0.935160i
$21$	7.49681	−	2.60727i	0.356991	−	0.124156i
$22$			6.76852i			0.307660i
$23$	30.4863			1.32549			0.662745	−	0.748845i	$-0.269391\pi$
$23$	30.4863			1.32549			0.662745	+	0.748845i	$0.269391\pi$
$24$	−3.85909	−	11.0962i	−0.160795	−	0.462342i
$25$	−24.9022	+	2.20864i	−0.996090	+	0.0883458i
$26$		−	1.65353i		−	0.0635974i
$27$	−22.7793	−	14.4949i	−0.843679	−	0.536848i
$28$			9.90649i			0.353803i
$29$		−	4.90100i		−	0.169000i	−0.996423	−	0.0845000i	$-0.973071\pi$
$29$		−	4.90100i		−	0.169000i	0.996423	−	0.0845000i	$-0.0269293\pi$
$30$	−7.04694	+	2.80590i	−0.234898	+	0.0935300i
$31$	29.2074			0.942176			0.471088	−	0.882086i	$-0.343861\pi$
$31$	29.2074			0.942176			0.471088	+	0.882086i	$0.343861\pi$
$32$	22.2363			0.694885
$33$	−37.9277	+	13.1907i	−1.14932	+	0.399717i
$34$	11.0968			0.326377
$35$	13.2158	−	0.584924i	0.377595	−	0.0167121i
$36$	26.4263	−	20.9106i	0.734065	−	0.580849i
$37$			24.8760i			0.672323i	0.941804	+	0.336162i	$0.109129\pi$
$37$			24.8760i			0.672323i	−0.941804	+	0.336162i	$0.890871\pi$
$38$	−2.20867			−0.0581228
$39$	9.26564	−	3.22245i	0.237580	−	0.0826268i
$40$	−0.865761	−	19.5611i	−0.0216440	−	0.489026i
$41$		−	13.6825i		−	0.333721i	−0.985981	−	0.166860i	$-0.946637\pi$
$41$		−	13.6825i		−	0.333721i	0.985981	−	0.166860i	$-0.0533629\pi$
$42$	3.79089	−	1.31841i	0.0902593	−	0.0313908i
$43$		−	64.9582i		−	1.51066i	−0.655347	−	0.755328i	$-0.727477\pi$
$43$		−	64.9582i		−	1.51066i	0.655347	−	0.755328i	$-0.272523\pi$
$44$		−	50.1187i		−	1.13906i
$45$	−29.4562	−	34.0196i	−0.654582	−	0.755991i
$46$	15.4159			0.335128
$47$	−75.3743			−1.60371			−0.801854	−	0.597519i	$-0.796153\pi$
$47$	−75.3743			−1.60371			−0.801854	+	0.597519i	$0.796153\pi$
$48$	12.8080	+	36.8273i	0.266833	+	0.767236i
$49$	−7.00000			−0.142857
$50$	−12.5923	+	1.11684i	−0.251845	+	0.0223368i
$51$	21.6258	+	62.1815i	0.424034	+	1.21924i
$52$			12.2439i			0.235459i
$53$	67.1397			1.26679			0.633394	−	0.773830i	$-0.281661\pi$
$53$	67.1397			1.26679			0.633394	+	0.773830i	$0.281661\pi$
$54$	−11.5188	−	7.32960i	−0.213310	−	0.135733i
$55$	−66.8612	+	2.95924i	−1.21566	+	0.0538043i
$56$			10.3609i			0.185016i
$57$	−4.30430	−	12.3763i	−0.0755141	−	0.217129i
$58$		−	2.47828i		−	0.0427289i
$59$			61.2523i			1.03818i	0.854721	+	0.519088i	$0.173728\pi$
$59$			61.2523i			1.03818i	−0.854721	+	0.519088i	$0.826272\pi$
$60$	52.1802	−	20.7768i	0.869671	−	0.346279i
$61$	46.8643			0.768267			0.384133	−	0.923278i	$-0.374500\pi$
$61$	46.8643			0.768267			0.384133	+	0.923278i	$0.374500\pi$
$62$	14.7693			0.238214
$63$	14.7756	+	18.6730i	0.234533	+	0.296398i
$64$	−40.7438			−0.636621
$65$	16.3340	−	0.722934i	0.251293	−	0.0111221i
$66$	−19.1788	+	6.67009i	−0.290588	+	0.101062i
$67$			96.7958i			1.44471i	0.691520	+	0.722357i	$0.256941\pi$
$67$			96.7958i			1.44471i	−0.691520	+	0.722357i	$0.743059\pi$
$68$	−82.1683			−1.20836
$69$	30.0429	+	86.3836i	0.435404	+	1.25194i
$70$	6.68281	−	0.295777i	0.0954687	−	0.00422539i
$71$			108.224i			1.52428i	0.647413	+	0.762140i	$0.275851\pi$
$71$			108.224i			1.52428i	−0.647413	+	0.762140i	$0.724149\pi$
$72$	27.6384	−	21.8697i	0.383867	−	0.303745i
$73$		−	50.7288i		−	0.694915i	−0.937696	−	0.347457i	$-0.887045\pi$
$73$		−	50.7288i		−	0.694915i	0.937696	−	0.347457i	$-0.112955\pi$
$74$			12.5790i			0.169986i
$75$	−30.7983	−	68.3847i	−0.410645	−	0.911795i
$76$	16.3544			0.215190
$77$	35.4142			0.459925
$78$	4.68533	−	1.62949i	0.0600683	−	0.0208908i
$79$	−59.8158			−0.757162			−0.378581	−	0.925568i	$-0.623588\pi$
$79$	−59.8158			−0.757162			−0.378581	+	0.925568i	$0.623588\pi$
$80$	2.87338	+	64.9214i	0.0359173	+	0.811517i
$81$	18.6236	−	78.8299i	0.229922	−	0.973209i
$82$		−	6.91882i		−	0.0843758i
$83$	−82.9049			−0.998855			−0.499427	−	0.866356i	$-0.666456\pi$
$83$	−82.9049			−0.998855			−0.499427	+	0.866356i	$0.666456\pi$
$84$	−28.0703	+	9.76242i	−0.334170	+	0.116219i
$85$	4.85159	+	109.617i	0.0570775	+	1.28961i
$86$		−	32.8473i		−	0.381945i
$87$	13.8871	−	4.82972i	0.159622	−	0.0555141i
$88$		−	52.4175i		−	0.595653i
$89$		−	79.4072i		−	0.892216i	−0.894979	−	0.446108i	$-0.852810\pi$
$89$		−	79.4072i		−	0.892216i	0.894979	−	0.446108i	$-0.147190\pi$
$90$	−14.8950	−	17.2026i	−0.165500	−	0.191140i
$91$	−8.65161			−0.0950726
$92$	−114.150			−1.24076
$93$	28.7827	+	82.7601i	0.309491	+	0.889893i
$94$	−38.1143			−0.405472
$95$	−0.965641	−	21.8178i	−0.0101646	−	0.229661i
$96$	21.9129	+	63.0072i	0.228260	+	0.656325i
$97$		−	103.792i		−	1.07003i	−0.844844	−	0.535013i	$-0.820307\pi$
$97$		−	103.792i		−	1.07003i	0.844844	−	0.535013i	$-0.179693\pi$
$98$	−3.53967			−0.0361191
$99$	−74.7522	−	94.4703i	−0.755073	−	0.954245i
$100$	93.2415	−	8.26983i	0.932415	−	0.0826983i
$101$		−	50.9279i		−	0.504237i	−0.967696	−	0.252118i	$-0.918873\pi$
$101$		−	50.9279i		−	0.504237i	0.967696	−	0.252118i	$-0.0811272\pi$
$102$	10.9354	+	31.4431i	0.107210	+	0.308266i
$103$		−	47.3487i		−	0.459696i	−0.973227	−	0.229848i	$-0.926177\pi$
$103$		−	47.3487i		−	0.459696i	0.973227	−	0.229848i	$-0.0738229\pi$
$104$			12.8055i			0.123129i
$105$	14.6810	+	36.8710i	0.139819	+	0.351152i
$106$	33.9504			0.320287
$107$	105.419			0.985223			0.492612	−	0.870249i	$-0.336042\pi$
$107$	105.419			0.985223			0.492612	+	0.870249i	$0.336042\pi$
$108$	85.2927	+	54.2733i	0.789747	+	0.502530i
$109$	134.280			1.23193			0.615964	−	0.787775i	$-0.288767\pi$
$109$	134.280			1.23193			0.615964	+	0.787775i	$0.288767\pi$
$110$	−33.8095	+	1.49639i	−0.307359	+	0.0136035i
$111$	−70.4867	+	24.5142i	−0.635015	+	0.220849i
$112$		−	34.3868i		−	0.307025i
$113$	−22.7668			−0.201476			−0.100738	−	0.994913i	$-0.532120\pi$
$113$	−22.7668			−0.201476			−0.100738	+	0.994913i	$0.532120\pi$
$114$	−2.17655	−	6.25832i	−0.0190925	−	0.0548975i
$115$	6.73992	+	152.282i	0.0586080	+	1.32419i
$116$			18.3508i			0.158197i
$117$	18.2618	+	23.0788i	0.156084	+	0.197255i
$118$			30.9733i			0.262486i
$119$		−	58.0607i		−	0.487905i
$120$	54.5736	−	21.7297i	0.454780	−	0.181081i
$121$	−58.1670			−0.480719
$122$	23.6977			0.194244
$123$	38.7699	−	13.4836i	0.315202	−	0.109622i
$124$	−109.361			−0.881947
$125$	−16.5378	−	123.901i	−0.132303	−	0.991209i
$126$	7.47152	+	9.44235i	0.0592978	+	0.0749393i
$127$		−	62.4984i		−	0.492113i	−0.969255	−	0.246057i	$-0.920865\pi$
$127$		−	62.4984i		−	0.492113i	0.969255	−	0.246057i	$-0.0791349\pi$
$128$	−109.548			−0.855844
$129$	184.061	−	64.0135i	1.42683	−	0.496229i
$130$	8.25958	−	0.365564i	0.0635352	−	0.00281203i
$131$		−	129.282i		−	0.986886i	−0.869778	−	0.493443i	$-0.835738\pi$
$131$		−	129.282i		−	0.986886i	0.869778	−	0.493443i	$-0.164262\pi$
$132$	142.013	−	49.3898i	1.07585	−	0.374165i
$133$			11.5562i			0.0868886i
$134$			48.9465i			0.365272i
$135$	67.3676	−	116.990i	0.499019	−	0.866591i
$136$	−85.9371			−0.631890
$137$	−115.143			−0.840462			−0.420231	−	0.907417i	$-0.638051\pi$
$137$	−115.143			−0.840462			−0.420231	+	0.907417i	$0.638051\pi$
$138$	15.1917	+	43.6814i	0.110085	+	0.316532i
$139$	263.818			1.89797			0.948987	−	0.315316i	$-0.102111\pi$
$139$	263.818			1.89797			0.948987	+	0.315316i	$0.102111\pi$
$140$	−49.4840	+	2.19013i	−0.353457	+	0.0156438i
$141$	−74.2781	−	213.575i	−0.526795	−	1.51472i
$142$			54.7253i			0.385389i
$143$	43.7700			0.306084
$144$	−91.7295	+	72.5835i	−0.637010	+	0.504052i
$145$	24.4810	−	1.08352i	0.168835	−	0.00747252i
$146$		−	25.6519i		−	0.175698i
$147$	−6.89820	−	19.8347i	−0.0469265	−	0.134930i
$148$		−	93.1431i		−	0.629345i
$149$		−	44.5512i		−	0.299001i	−0.988762	−	0.149501i	$-0.952233\pi$
$149$		−	44.5512i		−	0.299001i	0.988762	−	0.149501i	$-0.0477666\pi$
$150$	−15.5737	−	34.5799i	−0.103825	−	0.230533i
$151$	−197.815			−1.31003			−0.655017	−	0.755614i	$-0.727339\pi$
$151$	−197.815			−1.31003			−0.655017	+	0.755614i	$0.727339\pi$
$152$	17.1046			0.112530
$153$	−154.882	+	122.554i	−1.01230	+	0.801009i
$154$	17.9078			0.116285
$155$	6.45720	+	145.894i	0.0416593	+	0.941254i
$156$	−34.6933	+	12.0658i	−0.222393	+	0.0773449i
$157$		−	193.760i		−	1.23414i	−0.786909	−	0.617069i	$-0.788320\pi$
$157$		−	193.760i		−	1.23414i	0.786909	−	0.617069i	$-0.211680\pi$
$158$	−30.2469			−0.191436
$159$	66.1633	+	190.242i	0.416121	+	1.19649i
$160$	4.91602	+	111.073i	0.0307251	+	0.694205i
$161$		−	80.6591i		−	0.500988i
$162$	9.41737	−	39.8617i	0.0581319	−	0.246060i
$163$		−	37.0528i		−	0.227318i	−0.993520	−	0.113659i	$-0.963743\pi$
$163$		−	37.0528i		−	0.227318i	0.993520	−	0.113659i	$-0.0362571\pi$
$164$			51.2316i			0.312388i
$165$	−74.2739	−	186.537i	−0.450145	−	1.13053i
$166$	−41.9223			−0.252544
$167$	−53.8763			−0.322612			−0.161306	−	0.986904i	$-0.551571\pi$
$167$	−53.8763			−0.322612			−0.161306	+	0.986904i	$0.551571\pi$
$168$	−29.3578	+	10.2102i	−0.174749	+	0.0607749i
$169$	158.307			0.936728
$170$	2.45329	+	55.4298i	0.0144311	+	0.326058i
$171$	30.8270	−	24.3927i	0.180275	−	0.142647i
$172$			243.223i			1.41409i
$173$	212.646			1.22917			0.614584	−	0.788852i	$-0.289324\pi$
$173$	212.646			1.22917			0.614584	+	0.788852i	$0.289324\pi$
$174$	7.02226	−	2.44223i	0.0403578	−	0.0140358i
$175$	5.84352	+	65.8852i	0.0333916	+	0.376487i
$176$			173.969i			0.988460i
$177$	−173.560	+	60.3615i	−0.980566	+	0.341026i
$178$		−	40.1536i		−	0.225582i
$179$			227.092i			1.26867i	0.773058	+	0.634335i	$0.218726\pi$
$179$			227.092i			1.26867i	−0.773058	+	0.634335i	$0.781274\pi$
$180$	110.293	+	127.380i	0.612738	+	0.707664i
$181$	−197.563			−1.09151			−0.545754	−	0.837946i	$-0.683757\pi$
$181$	−197.563			−1.09151			−0.545754	+	0.837946i	$0.683757\pi$
$182$	−4.37484			−0.0240376
$183$	46.1827	+	132.791i	0.252365	+	0.725635i
$184$	−119.385			−0.648834
$185$	−124.258	+	5.49959i	−0.671666	+	0.0297275i
$186$	14.5545	+	41.8491i	0.0782498	+	0.224995i
$187$			293.740i			1.57080i
$188$	282.224			1.50119
$189$	−38.3499	+	60.2684i	−0.202910	+	0.318881i
$190$	−0.488293	−	11.0325i	−0.00256996	−	0.0580660i
$191$			131.748i			0.689779i	0.938643	+	0.344889i	$0.112084\pi$
$191$			131.748i			0.689779i	−0.938643	+	0.344889i	$0.887916\pi$
$192$	−40.1512	−	115.449i	−0.209121	−	0.601295i
$193$		−	261.426i		−	1.35454i	−0.735734	−	0.677271i	$-0.763163\pi$
$193$		−	261.426i		−	1.35454i	0.735734	−	0.677271i	$-0.236837\pi$
$194$		−	52.4845i		−	0.270539i
$195$	18.1449	+	45.5704i	0.0930509	+	0.233695i
$196$	26.2101			0.133725
$197$	390.509			1.98228			0.991139	−	0.132831i	$-0.0424068\pi$
$197$	390.509			1.98228			0.991139	+	0.132831i	$0.0424068\pi$
$198$	−37.7998	−	47.7705i	−0.190908	−	0.241265i
$199$	−141.883			−0.712979			−0.356489	−	0.934299i	$-0.616026\pi$
$199$	−141.883			−0.712979			−0.356489	+	0.934299i	$0.616026\pi$
$200$	97.5182	−	8.64914i	0.487591	−	0.0432457i
$201$	−274.274	+	95.3881i	−1.36455	+	0.474568i
$202$		−	25.7526i		−	0.127488i
$203$	−12.9668			−0.0638760
$204$	−80.9733	−	232.826i	−0.396928	−	1.14130i
$205$	68.3458	−	3.02495i	0.333394	−	0.0147558i
$206$		−	23.9427i		−	0.116227i
$207$	−215.164	+	170.255i	−1.03944	+	0.822487i
$208$		−	42.5002i		−	0.204328i
$209$		−	58.4648i		−	0.279736i
$210$	7.42371	+	18.6444i	0.0353510	+	0.0887831i
$211$	−115.598			−0.547860			−0.273930	−	0.961750i	$-0.588324\pi$
$211$	−115.598			−0.547860			−0.273930	+	0.961750i	$0.588324\pi$
$212$	−251.391			−1.18581
$213$	−306.655	+	106.650i	−1.43970	+	0.500704i
$214$	53.3069			0.249098
$215$	324.473	−	14.3610i	1.50918	−	0.0667954i
$216$	89.2048	+	56.7626i	0.412985	+	0.262790i
$217$		−	77.2756i		−	0.356109i
$218$	67.9011			0.311473
$219$	143.741	−	49.9910i	0.656353	−	0.228270i
$220$	250.348	−	11.0803i	1.13795	−	0.0503649i
$221$		−	71.7598i		−	0.324705i
$222$	−35.6428	+	12.3960i	−0.160553	+	0.0558379i
$223$		−	72.6912i		−	0.325970i	−0.986629	−	0.162985i	$-0.947888\pi$
$223$		−	72.6912i		−	0.325970i	0.986629	−	0.162985i	$-0.0521122\pi$
$224$		−	58.8318i		−	0.262642i
$225$	163.419	−	154.658i	0.726308	−	0.687369i
$226$	−11.5125			−0.0509400
$227$	−97.0030			−0.427326			−0.213663	−	0.976907i	$-0.568539\pi$
$227$	−97.0030			−0.427326			−0.213663	+	0.976907i	$0.568539\pi$
$228$	16.1166	+	46.3408i	0.0706869	+	0.203249i
$229$	−15.2371			−0.0665374			−0.0332687	−	0.999446i	$-0.510592\pi$
$229$	−15.2371			−0.0665374			−0.0332687	+	0.999446i	$0.510592\pi$
$230$	3.40816	+	77.0042i	0.0148181	+	0.334801i
$231$	34.8992	+	100.347i	0.151079	+	0.434404i
$232$			19.1925i			0.0827263i
$233$	19.9430			0.0855921			0.0427960	−	0.999084i	$-0.486373\pi$
$233$	19.9430			0.0855921			0.0427960	+	0.999084i	$0.486373\pi$
$234$	9.23438	+	11.6702i	0.0394632	+	0.0498727i
$235$	−16.6638	−	376.503i	−0.0709098	−	1.60214i
$236$		−	229.347i		−	0.971810i
$237$	−58.9459	−	169.490i	−0.248717	−	0.715146i
$238$		−	29.3594i		−	0.123359i
$239$			312.826i			1.30890i	0.756107	+	0.654448i	$0.227099\pi$
$239$			312.826i			1.30890i	−0.756107	+	0.654448i	$0.772901\pi$
$240$	−181.125	+	72.1190i	−0.754687	+	0.300496i
$241$	86.9196			0.360662			0.180331	−	0.983606i	$-0.442283\pi$
$241$	86.9196			0.360662			0.180331	+	0.983606i	$0.442283\pi$
$242$	−29.4132			−0.121542
$243$	241.720	−	24.9129i	0.994731	−	0.102522i
$244$	−175.474			−0.719155
$245$	−1.54756	−	34.9658i	−0.00631659	−	0.142717i
$246$	19.6047	−	6.81820i	0.0796937	−	0.0277163i
$247$			14.2828i			0.0578251i
$248$	−114.378			−0.461200
$249$	−81.6992	−	234.913i	−0.328109	−	0.943427i
$250$	−8.36264	−	62.6528i	−0.0334506	−	0.250611i
$251$		−	239.629i		−	0.954695i	−0.878714	−	0.477348i	$-0.841598\pi$
$251$		−	239.629i		−	0.954695i	0.878714	−	0.477348i	$-0.158402\pi$
$252$	−55.3241	−	69.9175i	−0.219540	−	0.277450i
$253$			408.069i			1.61292i
$254$		−	31.6034i		−	0.124423i
$255$	−305.822	+	121.770i	−1.19930	+	0.477530i
$256$	107.580			0.420235
$257$	195.470			0.760584			0.380292	−	0.924867i	$-0.375824\pi$
$257$	195.470			0.760584			0.380292	+	0.924867i	$0.375824\pi$
$258$	93.0736	−	32.3696i	0.360750	−	0.125463i
$259$	65.8156			0.254114
$260$	−61.1595	+	2.70688i	−0.235229	+	0.0104111i
$261$	27.3703	+	34.5900i	0.104867	+	0.132529i
$262$		−	65.3737i		−	0.249518i
$263$	−314.308			−1.19509			−0.597544	−	0.801836i	$-0.703857\pi$
$263$	−314.308			−1.19509			−0.597544	+	0.801836i	$0.703857\pi$
$264$	148.526	−	51.6552i	0.562600	−	0.195664i
$265$	14.8433	+	335.370i	0.0560124	+	1.26555i
$266$			5.84358i			0.0219684i
$267$	225.002	−	78.2524i	0.842706	−	0.293080i
$268$		−	362.433i		−	1.35236i
$269$			11.6841i			0.0434354i	0.999764	+	0.0217177i	$0.00691350\pi$
$269$			11.6841i			0.0434354i	−0.999764	+	0.0217177i	$0.993087\pi$
$270$	34.0656	−	59.1579i	0.126169	−	0.219103i
$271$	396.895			1.46456			0.732278	−	0.681006i	$-0.238457\pi$
$271$	396.895			1.46456			0.732278	+	0.681006i	$0.238457\pi$
$272$	285.218			1.04859
$273$	−8.52579	−	24.5146i	−0.0312300	−	0.0897970i
$274$	−58.2242			−0.212497
$275$	−29.5634	−	333.325i	−0.107503	−	1.21209i
$276$	−112.490	−	323.446i	−0.407571	−	1.17191i
$277$			465.546i			1.68067i	0.542067	+	0.840336i	$0.317642\pi$
$277$			465.546i			1.68067i	−0.542067	+	0.840336i	$0.682358\pi$
$278$	133.404			0.479872
$279$	−206.139	+	163.113i	−0.738849	+	0.584634i
$280$	−51.7537	+	2.29059i	−0.184835	+	0.00818067i
$281$			22.8385i			0.0812758i	0.999174	+	0.0406379i	$0.0129390\pi$
$281$			22.8385i			0.0812758i	−0.999174	+	0.0406379i	$0.987061\pi$
$282$	−37.5600	−	107.998i	−0.133192	−	0.382972i
$283$			267.163i			0.944039i	0.881588	+	0.472020i	$0.156475\pi$
$283$			267.163i			0.944039i	−0.881588	+	0.472020i	$0.843525\pi$
$284$		−	405.223i		−	1.42684i
$285$	60.8696	−	24.2366i	0.213578	−	0.0850408i
$286$	22.1331			0.0773884
$287$	−36.2006			−0.126135
$288$	−156.938	+	124.182i	−0.544925	+	0.431187i
$289$	192.579			0.666362
$290$	12.3793	−	0.547899i	0.0426871	−	0.00188931i
$291$	294.099	−	102.283i	1.01065	−	0.351488i
$292$			189.944i			0.650493i
$293$	−76.4961			−0.261079			−0.130539	−	0.991443i	$-0.541671\pi$
$293$	−76.4961			−0.261079			−0.130539	+	0.991443i	$0.541671\pi$
$294$	−3.48819	−	10.0298i	−0.0118646	−	0.0341148i
$295$	−305.962	+	13.5417i	−1.03716	+	0.0459041i
$296$		−	97.4152i		−	0.329106i
$297$	194.019	−	304.909i	0.653263	−	1.02663i
$298$		−	22.5281i		−	0.0755976i
$299$		−	99.6901i		−	0.333412i
$300$	115.318	+	256.053i	0.384394	+	0.853509i
$301$	−171.863			−0.570974
$302$	−100.029			−0.331221
$303$	144.306	−	50.1873i	0.476256	−	0.165635i
$304$	−56.7686			−0.186739
$305$	10.3608	+	234.092i	0.0339698	+	0.767515i
$306$	−78.3186	+	61.9717i	−0.255943	+	0.202522i
$307$		−	430.795i		−	1.40324i	−0.712551	−	0.701621i	$-0.752460\pi$
$307$		−	430.795i		−	1.40324i	0.712551	−	0.701621i	$-0.247540\pi$
$308$	−132.602			−0.430525
$309$	134.164	−	46.6601i	0.434187	−	0.151003i
$310$	3.26520	+	73.7740i	0.0105329	+	0.237981i
$311$			548.295i			1.76301i	0.472178	+	0.881503i	$0.343468\pi$
$311$			548.295i			1.76301i	−0.472178	+	0.881503i	$0.656532\pi$
$312$	−36.2846	+	12.6192i	−0.116297	+	0.0404462i
$313$		−	265.497i		−	0.848234i	−0.905607	−	0.424117i	$-0.860584\pi$
$313$		−	265.497i		−	0.848234i	0.905607	−	0.424117i	$-0.139416\pi$
$314$		−	97.9779i		−	0.312032i
$315$	−90.0073	+	77.9338i	−0.285738	+	0.247409i
$316$	223.968			0.708760
$317$	−43.2820			−0.136536			−0.0682681	−	0.997667i	$-0.521747\pi$
$317$	−43.2820			−0.136536			−0.0682681	+	0.997667i	$0.521747\pi$
$318$	33.4566	+	96.1993i	0.105210	+	0.302514i
$319$	65.6015			0.205647
$320$	−9.00766	−	203.520i	−0.0281489	−	0.635999i
$321$	103.886	+	298.707i	0.323632	+	0.930552i
$322$		−	40.7867i		−	0.126667i
$323$	−95.8515			−0.296754
$324$	−69.7325	+	295.163i	−0.215224	+	0.910997i
$325$	7.22227	+	81.4304i	0.0222224	+	0.250555i
$326$		−	18.7364i		−	0.0574737i
$327$	132.327	+	380.486i	0.404670	+	1.16357i
$328$			53.5814i			0.163358i
$329$			199.422i			0.606145i
$330$	−37.5579	−	94.3256i	−0.113812	−	0.285835i
$331$	113.106			0.341711			0.170855	−	0.985296i	$-0.445347\pi$
$331$	113.106			0.341711			0.170855	+	0.985296i	$0.445347\pi$
$332$	310.421			0.935003
$333$	−138.923	−	175.568i	−0.417187	−	0.527232i
$334$	−27.2435			−0.0815673
$335$	−483.506	+	21.3997i	−1.44330	+	0.0638796i
$336$	97.4359	−	33.8867i	0.289988	−	0.100853i
$337$		−	497.637i		−	1.47667i	−0.674436	−	0.738334i	$-0.735613\pi$
$337$		−	497.637i		−	1.47667i	0.674436	−	0.738334i	$-0.264387\pi$
$338$	80.0507			0.236836
$339$	−22.4357	−	64.5105i	−0.0661821	−	0.190296i
$340$	−18.1658	−	410.440i	−0.0534289	−	1.20718i
$341$			390.951i			1.14648i
$342$	15.5882	−	12.3346i	0.0455796	−	0.0360661i
$343$			18.5203i			0.0539949i
$344$			254.379i			0.739474i
$345$	−424.854	+	169.165i	−1.23146	+	0.490334i
$346$	107.528			0.310775
$347$	−515.457			−1.48547			−0.742734	−	0.669587i	$-0.766471\pi$
$347$	−515.457			−1.48547			−0.742734	+	0.669587i	$0.766471\pi$
$348$	−51.9975	+	18.0839i	−0.149418	+	0.0519653i
$349$	−346.338			−0.992373			−0.496187	−	0.868216i	$-0.665267\pi$
$349$	−346.338			−0.992373			−0.496187	+	0.868216i	$0.665267\pi$
$350$	2.95488	+	33.3160i	0.00844251	+	0.0951885i
$351$	−47.3983	+	74.4884i	−0.135038	+	0.212218i
$352$			297.640i			0.845569i
$353$	−172.050			−0.487393			−0.243697	−	0.969852i	$-0.578360\pi$
$353$	−172.050			−0.487393			−0.243697	+	0.969852i	$0.578360\pi$
$354$	−87.7637	+	30.5229i	−0.247920	+	0.0862228i
$355$	−540.590	+	23.9262i	−1.52279	+	0.0673977i
$356$			297.324i			0.835181i
$357$	164.517	−	57.2164i	0.460831	−	0.160270i
$358$			114.833i			0.320762i
$359$		−	18.7897i		−	0.0523391i	−0.999658	−	0.0261695i	$-0.991669\pi$
$359$		−	18.7897i		−	0.0523391i	0.999658	−	0.0261695i	$-0.00833097\pi$
$360$	115.352	+	133.222i	0.320421	+	0.370061i
$361$	−341.922			−0.947153
$362$	−99.9011			−0.275970
$363$	−57.3211	−	164.818i	−0.157909	−	0.454043i
$364$	32.3942			0.0889951
$365$	253.396	−	11.2152i	0.694235	−	0.0307264i
$366$	23.3531	+	67.1482i	0.0638063	+	0.183465i
$367$		−	386.638i		−	1.05351i	−0.850017	−	0.526755i	$-0.823409\pi$
$367$		−	386.638i		−	1.05351i	0.850017	−	0.526755i	$-0.176591\pi$
$368$	396.230			1.07671
$369$	76.4121	+	96.5680i	0.207079	+	0.261702i
$370$	−62.8333	+	2.78096i	−0.169820	+	0.00751612i
$371$		−	177.635i		−	0.478801i
$372$	−107.771	−	309.879i	−0.289707	−	0.833007i
$373$			247.808i			0.664364i	0.943215	+	0.332182i	$0.107785\pi$
$373$			247.808i			0.664364i	−0.943215	+	0.332182i	$0.892215\pi$
$374$			148.535i			0.397151i
$375$	334.780	−	168.960i	0.892747	−	0.450559i
$376$	295.169			0.785024
$377$	−16.0263			−0.0425100
$378$	−19.3923	+	30.4758i	−0.0513024	+	0.0806238i
$379$	125.931			0.332271			0.166135	−	0.986103i	$-0.446871\pi$
$379$	125.931			0.332271			0.166135	+	0.986103i	$0.446871\pi$
$380$	3.61565	+	81.6923i	0.00951487	+	0.214980i
$381$	177.091	−	61.5895i	0.464805	−	0.161652i
$382$			66.6205i			0.174399i
$383$	−247.866			−0.647170			−0.323585	−	0.946199i	$-0.604888\pi$
$383$	−247.866			−0.647170			−0.323585	+	0.946199i	$0.604888\pi$
$384$	−107.955	−	310.407i	−0.281133	−	0.808352i
$385$	7.82940	+	176.898i	0.0203361	+	0.459476i
$386$		−	132.195i		−	0.342474i
$387$	362.768	+	458.459i	0.937385	+	1.18465i
$388$			388.630i			1.00162i
$389$			313.757i			0.806574i	0.915074	+	0.403287i	$0.132132\pi$
$389$			313.757i			0.806574i	−0.915074	+	0.403287i	$0.867868\pi$
$390$	9.17529	+	23.0435i	0.0235264	+	0.0590859i
$391$	669.018			1.71104
$392$	27.4123			0.0699293
$393$	366.324	−	127.402i	0.932123	−	0.324178i
$394$	197.467			0.501187
$395$	−13.2241	−	298.786i	−0.0334787	−	0.756421i
$396$	279.895	+	353.725i	0.706805	+	0.893245i
$397$			165.635i			0.417218i	0.977999	+	0.208609i	$0.0668936\pi$
$397$			165.635i			0.417218i	−0.977999	+	0.208609i	$0.933106\pi$
$398$	−71.7455			−0.180265
$399$	−32.7447	+	11.3881i	−0.0820670	+	0.0285416i
$400$	−323.654	+	28.7057i	−0.809136	+	0.0717643i
$401$		−	279.659i		−	0.697405i	−0.937234	−	0.348702i	$-0.886622\pi$
$401$		−	279.659i		−	0.697405i	0.937234	−	0.348702i	$-0.113378\pi$
$402$	−138.691	+	48.2347i	−0.345003	+	0.119987i
$403$		−	95.5084i		−	0.236993i
$404$			190.689i			0.472003i
$405$	397.882	+	75.5994i	0.982424	+	0.186665i
$406$	−6.55690			−0.0161500
$407$	−332.973			−0.818115
$408$	−84.6873	−	243.505i	−0.207567	−	0.596826i
$409$	−294.392			−0.719784			−0.359892	−	0.932994i	$-0.617186\pi$
$409$	−294.392			−0.719784			−0.359892	+	0.932994i	$0.617186\pi$
$410$	34.5603	−	1.52962i	0.0842933	−	0.00373077i
$411$	−113.469	−	326.262i	−0.276080	−	0.793824i
$412$			177.288i			0.430310i
$413$	162.058			0.392393
$414$	−108.802	+	86.0923i	−0.262806	+	0.207952i
$415$	−18.3287	−	414.119i	−0.0441655	−	0.997878i
$416$		−	72.7128i		−	0.174790i
$417$	259.982	+	747.536i	0.623457	+	1.79265i
$418$		−	29.5637i		−	0.0707266i
$419$		−	605.580i		−	1.44530i	−0.691215	−	0.722649i	$-0.742924\pi$
$419$		−	605.580i		−	1.44530i	0.691215	−	0.722649i	$-0.257076\pi$
$420$	−54.9701	−	138.056i	−0.130881	−	0.328705i
$421$	182.276			0.432959			0.216479	−	0.976287i	$-0.430543\pi$
$421$	182.276			0.432959			0.216479	+	0.976287i	$0.430543\pi$
$422$	−58.4543			−0.138517
$423$	531.973	−	420.938i	1.25762	−	0.995126i
$424$	−262.922			−0.620099
$425$	−546.477	+	48.4685i	−1.28583	+	0.114043i
$426$	−155.066	+	53.9294i	−0.364004	+	0.126595i
$427$		−	123.991i		−	0.290378i
$428$	−394.720			−0.922243
$429$	43.1335	+	124.024i	0.100544	+	0.289099i
$430$	164.076	−	7.26189i	0.381571	−	0.0168881i
$431$			391.145i			0.907530i	0.891121	+	0.453765i	$0.149919\pi$
$431$			391.145i			0.907530i	−0.891121	+	0.453765i	$0.850081\pi$
$432$	−296.063	−	188.390i	−0.685330	−	0.436088i
$433$			482.337i			1.11394i	0.830532	+	0.556971i	$0.188036\pi$
$433$			482.337i			1.11394i	−0.830532	+	0.556971i	$0.811964\pi$
$434$		−	39.0758i		−	0.0900363i
$435$	27.1952	+	68.2999i	0.0625176	+	0.157011i
$436$	−502.785			−1.15318
$437$	−133.159			−0.304711
$438$	72.6853	−	25.2788i	0.165948	−	0.0577142i
$439$	−288.605			−0.657414			−0.328707	−	0.944432i	$-0.606613\pi$
$439$	−288.605			−0.657414			−0.328707	+	0.944432i	$0.606613\pi$
$440$	261.831	−	11.5885i	0.595071	−	0.0263375i
$441$	49.4042	−	39.0925i	0.112028	−	0.0886450i
$442$		−	36.2866i		−	0.0820964i
$443$	−201.332			−0.454473			−0.227236	−	0.973840i	$-0.572969\pi$
$443$	−201.332			−0.454473			−0.227236	+	0.973840i	$0.572969\pi$
$444$	263.923	−	91.7885i	0.594422	−	0.206731i
$445$	396.648	−	17.5554i	0.891343	−	0.0394503i
$446$		−	36.7576i		−	0.0824161i
$447$	126.237	−	43.9033i	0.282410	−	0.0982177i
$448$			107.798i			0.240620i
$449$		−	551.114i		−	1.22743i	−0.789530	−	0.613713i	$-0.789675\pi$
$449$		−	551.114i		−	1.22743i	0.789530	−	0.613713i	$-0.210325\pi$
$450$	82.6358	−	78.2055i	0.183635	−	0.173790i
$451$	183.145			0.406087
$452$	85.2459			0.188597
$453$	−194.938	−	560.515i	−0.430327	−	1.23734i
$454$	−49.0513			−0.108042
$455$	−1.91270	−	43.2157i	−0.00420374	−	0.0949796i
$456$	16.8558	+	48.4663i	0.0369645	+	0.106286i
$457$		−	173.162i		−	0.378909i	−0.981889	−	0.189455i	$-0.939328\pi$
$457$		−	173.162i		−	0.378909i	0.981889	−	0.189455i	$-0.0606720\pi$
$458$	−7.70489			−0.0168229
$459$	−499.890	−	318.089i	−1.08909	−	0.693005i
$460$	−25.2363	−	570.190i	−0.0548615	−	1.23954i
$461$		−	191.372i		−	0.415124i	−0.978222	−	0.207562i	$-0.933447\pi$
$461$		−	191.372i		−	0.415124i	0.978222	−	0.207562i	$-0.0665529\pi$
$462$	17.6474	+	50.7423i	0.0381978	+	0.109832i
$463$			304.688i			0.658073i	0.944317	+	0.329037i	$0.106724\pi$
$463$			304.688i			0.658073i	−0.944317	+	0.329037i	$0.893276\pi$
$464$		−	63.6982i		−	0.137281i
$465$	−407.032	+	162.069i	−0.875338	+	0.348536i
$466$	10.0845			0.0216406
$467$	−490.114			−1.04949			−0.524747	−	0.851258i	$-0.675840\pi$
$467$	−490.114			−1.04949			−0.524747	+	0.851258i	$0.675840\pi$
$468$	−68.3776	−	86.4141i	−0.146106	−	0.184646i
$469$	256.098			0.546051
$470$	−8.42634	−	190.385i	−0.0179284	−	0.405075i
$471$	549.023	−	190.942i	1.16565	−	0.405397i
$472$		−	239.867i		−	0.508192i
$473$	869.487			1.83824
$474$	−29.8070	−	85.7054i	−0.0628840	−	0.180813i
$475$	108.769	−	9.64697i	0.228987	−	0.0203094i
$476$			217.397i			0.456716i
$477$	−473.855	+	374.951i	−0.993408	+	0.786061i
$478$			158.186i			0.330933i
$479$		−	639.298i		−	1.33465i	−0.744766	−	0.667325i	$-0.767439\pi$
$479$		−	639.298i		−	1.33465i	0.744766	−	0.667325i	$-0.232561\pi$
$480$	−309.883	+	123.387i	−0.645590	+	0.257057i
$481$	81.3444			0.169115
$482$	43.9524			0.0911876
$483$	228.550	−	79.4860i	0.473188	−	0.164567i
$484$	217.795			0.449989
$485$	518.455	−	22.9465i	1.06898	−	0.0473124i
$486$	122.230	−	12.5976i	0.251501	−	0.0259211i
$487$			423.604i			0.869824i	0.900473	+	0.434912i	$0.143220\pi$
$487$			423.604i			0.869824i	−0.900473	+	0.434912i	$0.856780\pi$
$488$	−183.522			−0.376070
$489$	104.990	−	36.5140i	0.214704	−	0.0746707i
$490$	−0.782553	−	17.6810i	−0.00159705	−	0.0360838i
$491$		−	464.645i		−	0.946324i	−0.880976	−	0.473162i	$-0.843113\pi$
$491$		−	464.645i		−	0.946324i	0.880976	−	0.473162i	$-0.156887\pi$
$492$	−145.166	+	50.4865i	−0.295053	+	0.102615i
$493$		−	107.552i		−	0.218158i
$494$			7.22234i			0.0146201i
$495$	455.363	−	394.281i	0.919926	−	0.796527i
$496$	379.609			0.765340
$497$	286.333			0.576123
$498$	−41.3126	−	118.788i	−0.0829571	−	0.238530i
$499$	−286.547			−0.574243			−0.287121	−	0.957894i	$-0.592698\pi$
$499$	−286.547			−0.574243			−0.287121	+	0.957894i	$0.592698\pi$
$500$	61.9226	+	463.923i	0.123845	+	0.927846i
$501$	−53.0927	−	152.660i	−0.105974	−	0.304710i
$502$		−	121.172i		−	0.241379i
$503$	−161.645			−0.321362			−0.160681	−	0.987006i	$-0.551369\pi$
$503$	−161.645			−0.321362			−0.160681	+	0.987006i	$0.551369\pi$
$504$	−57.8617	−	73.1244i	−0.114805	−	0.145088i
$505$	254.391	−	11.2592i	0.503744	−	0.0222954i
$506$			206.347i			0.407800i
$507$	156.005	+	448.567i	0.307702	+	0.884748i
$508$			234.013i			0.460655i
$509$			267.397i			0.525337i	0.964886	+	0.262668i	$0.0846026\pi$
$509$			267.397i			0.525337i	−0.964886	+	0.262668i	$0.915397\pi$
$510$	−154.644	+	61.5752i	−0.303224	+	0.120736i
$511$	−134.216			−0.262653
$512$	492.592			0.962094
$513$	99.4961	+	63.3112i	0.193950	+	0.123414i
$514$	98.8428			0.192301
$515$	236.512	−	10.4679i	0.459246	−	0.0203260i
$516$	−689.179	+	239.686i	−1.33562	+	0.464508i
$517$		−	1008.91i		−	1.95147i
$518$	33.2808			0.0642486
$519$	209.553	+	602.538i	0.403764	+	1.16096i
$520$	−63.9647	+	2.83104i	−0.123009	+	0.00544430i
$521$		−	214.253i		−	0.411234i	−0.978633	−	0.205617i	$-0.934080\pi$
$521$		−	214.253i		−	0.411234i	0.978633	−	0.205617i	$-0.0659201\pi$
$522$	13.8403	+	17.4910i	0.0265139	+	0.0335078i
$523$			102.499i			0.195983i	0.995187	+	0.0979915i	$0.0312418\pi$
$523$			102.499i			0.195983i	−0.995187	+	0.0979915i	$0.968758\pi$
$524$			484.071i			0.923800i
$525$	−180.929	+	81.4848i	−0.344626	+	0.155209i
$526$	−158.935			−0.302158
$527$	640.954			1.21623
$528$	−492.946	+	171.439i	−0.933609	+	0.324695i
$529$	400.412			0.756923
$530$	7.50577	+	169.586i	0.0141618	+	0.319973i
$531$	−342.072	−	432.304i	−0.644203	−	0.814131i
$532$		−	43.2698i		−	0.0813342i
$533$	−44.7419			−0.0839436
$534$	113.776	−	39.5697i	0.213064	−	0.0741005i
$535$	23.3061	+	526.579i	0.0435627	+	0.984259i
$536$		−	379.056i		−	0.707195i
$537$	−643.471	+	223.789i	−1.19827	+	0.416740i
$538$			5.90828i			0.0109819i
$539$		−	93.6973i		−	0.173835i
$540$	−252.244	+	438.045i	−0.467119	+	0.811194i
$541$	−485.925			−0.898198			−0.449099	−	0.893482i	$-0.648255\pi$
$541$	−485.925			−0.898198			−0.449099	+	0.893482i	$0.648255\pi$
$542$	200.697			0.370289
$543$	−194.690	−	559.800i	−0.358545	−	1.03094i
$544$	487.974			0.897010
$545$	29.6867	+	670.744i	0.0544710	+	1.23072i
$546$	−4.31121	−	12.3962i	−0.00789600	−	0.0227037i
$547$		−	220.793i		−	0.403644i	−0.979422	−	0.201822i	$-0.935314\pi$
$547$		−	220.793i		−	0.403644i	0.979422	−	0.201822i	$-0.0646862\pi$
$548$	431.131			0.786735
$549$	−330.756	+	261.720i	−0.602470	+	0.476721i
$550$	−14.9493	−	168.551i	−0.0271805	−	0.306457i
$551$			21.4067i			0.0388507i
$552$	−117.649	−	338.282i	−0.213133	−	0.612829i
$553$			158.258i			0.286180i
$554$			235.411i			0.424930i
$555$	−138.034	−	346.669i	−0.248710	−	0.624629i
$556$	−987.815			−1.77665
$557$	110.854			0.199020			0.0995102	−	0.995037i	$-0.468272\pi$
$557$	110.854			0.199020			0.0995102	+	0.995037i	$0.468272\pi$
$558$	−104.238	+	82.4809i	−0.186806	+	0.147815i
$559$	−212.413			−0.379988
$560$	171.766	−	7.60225i	0.306725	−	0.0135755i
$561$	−832.319	+	289.468i	−1.48364	+	0.515985i
$562$			11.5487i			0.0205493i
$563$	801.536			1.42369			0.711844	−	0.702338i	$-0.247860\pi$
$563$	801.536			1.42369			0.711844	+	0.702338i	$0.247860\pi$
$564$	278.120	+	799.690i	0.493120	+	1.41789i
$565$	−5.03331	−	113.723i	−0.00890851	−	0.201279i
$566$			135.096i			0.238685i
$567$	−208.564	−	49.2735i	−0.367838	−	0.0869022i
$568$		−	423.809i		−	0.746142i
$569$			943.932i			1.65893i	0.558557	+	0.829466i	$0.311355\pi$
$569$			943.932i			1.65893i	−0.558557	+	0.829466i	$0.688645\pi$
$570$	30.7798	−	12.2557i	0.0539996	−	0.0215012i
$571$	−7.63540			−0.0133720			−0.00668599	−	0.999978i	$-0.502128\pi$
$571$	−7.63540			−0.0133720			−0.00668599	+	0.999978i	$0.502128\pi$
$572$	−163.888			−0.286518
$573$	−373.311	+	129.832i	−0.651502	+	0.226582i
$574$	−18.3055			−0.0318911
$575$	−759.176	+	67.3333i	−1.32031	+	0.117101i
$576$	287.559	−	227.539i	0.499235	−	0.395033i
$577$			182.959i			0.317087i	0.987352	+	0.158544i	$0.0506798\pi$
$577$			182.959i			0.317087i	−0.987352	+	0.158544i	$0.949320\pi$
$578$	97.3807			0.168479
$579$	740.759	−	257.624i	1.27938	−	0.444947i
$580$	−91.6643	+	4.05701i	−0.158042	+	0.00699484i
$581$			219.346i			0.377532i
$582$	148.716	−	51.7212i	0.255526	−	0.0888680i
$583$			898.687i			1.54149i
$584$			198.656i			0.340164i
$585$	−111.244	+	96.3218i	−0.190161	+	0.164653i
$586$	−38.6816			−0.0660095
$587$	−169.335			−0.288475			−0.144237	−	0.989543i	$-0.546073\pi$
$587$	−169.335			−0.288475			−0.144237	+	0.989543i	$0.546073\pi$
$588$	25.8289	+	74.2670i	0.0439267	+	0.126304i
$589$	−127.573			−0.216593
$590$	−154.715	+	6.84760i	−0.262229	+	0.0116061i
$591$	384.829	+	1106.52i	0.651150	+	1.87228i
$592$			323.313i			0.546136i
$593$	−435.205			−0.733904			−0.366952	−	0.930240i	$-0.619599\pi$
$593$	−435.205			−0.733904			−0.366952	+	0.930240i	$0.619599\pi$
$594$	98.1091	−	154.182i	0.165167	−	0.259566i
$595$	290.020	−	12.8361i	0.487428	−	0.0215733i
$596$			166.813i			0.279888i
$597$	−139.819	−	402.029i	−0.234203	−	0.673415i
$598$		−	50.4100i		−	0.0842977i
$599$		−	519.702i		−	0.867615i	−0.901006	−	0.433808i	$-0.857170\pi$
$599$		−	519.702i		−	0.867615i	0.901006	−	0.433808i	$-0.142830\pi$
$600$	120.608	+	267.797i	0.201013	+	0.446328i
$601$	−804.056			−1.33786			−0.668932	−	0.743324i	$-0.733248\pi$
$601$	−804.056			−1.33786			−0.668932	+	0.743324i	$0.733248\pi$
$602$	−86.9057			−0.144362
$603$	−540.570	−	683.161i	−0.896467	−	1.13294i
$604$	740.679			1.22629
$605$	−12.8596	−	290.551i	−0.0212555	−	0.480249i
$606$	72.9706	−	25.3781i	0.120414	−	0.0418780i
$607$		−	629.795i		−	1.03755i	−0.854910	−	0.518777i	$-0.826387\pi$
$607$		−	629.795i		−	1.03755i	0.854910	−	0.518777i	$-0.173613\pi$
$608$	−97.1243			−0.159744
$609$	−12.7782	−	36.7419i	−0.0209823	−	0.0603315i
$610$	5.23911	+	118.373i	0.00858870	+	0.194054i
$611$			246.474i			0.403395i
$612$	579.923	−	458.880i	0.947587	−	0.749804i
$613$		−	155.397i		−	0.253502i	−0.991935	−	0.126751i	$-0.959545\pi$
$613$		−	155.397i		−	0.253502i	0.991935	−	0.126751i	$-0.0404549\pi$
$614$		−	217.839i		−	0.354787i
$615$	75.9231	+	190.679i	0.123452	+	0.310047i
$616$	−138.684			−0.225136
$617$	220.169			0.356838			0.178419	−	0.983955i	$-0.442902\pi$
$617$	220.169			0.356838			0.178419	+	0.983955i	$0.442902\pi$
$618$	67.8422	−	23.5945i	0.109777	−	0.0381788i
$619$	286.630			0.463053			0.231526	−	0.972829i	$-0.425628\pi$
$619$	286.630			0.463053			0.231526	+	0.972829i	$0.425628\pi$
$620$	−24.1777	−	546.272i	−0.0389963	−	0.881085i
$621$	−694.457	−	441.895i	−1.11829	−	0.711587i
$622$			277.255i			0.445747i
$623$	−210.092			−0.337226
$624$	120.425	−	41.8821i	0.192989	−	0.0671187i
$625$	615.244	−	110.000i	0.984390	−	0.176001i
$626$		−	134.253i		−	0.214462i
$627$	165.661	−	57.6145i	0.264213	−	0.0918892i
$628$			725.494i			1.15525i
$629$			545.900i			0.867886i
$630$	−45.5138	+	39.4086i	−0.0722441	+	0.0625533i
$631$	152.418			0.241549			0.120775	−	0.992680i	$-0.461462\pi$
$631$	152.418			0.241549			0.120775	+	0.992680i	$0.461462\pi$
$632$	234.241			0.370634
$633$	−113.917	−	327.551i	−0.179964	−	0.517458i
$634$	−21.8863			−0.0345209
$635$	312.186	−	13.8172i	0.491632	−	0.0217593i
$636$	−247.735	−	712.324i	−0.389521	−	1.12001i
$637$			22.8900i			0.0359341i
$638$	33.1725			0.0519946
$639$	−604.391	−	763.817i	−0.945839	−	1.19533i
$640$	−24.2189	−	547.205i	−0.0378421	−	0.855007i
$641$		−	151.830i		−	0.236864i	−0.992962	−	0.118432i	$-0.962213\pi$
$641$		−	151.830i		−	0.236864i	0.992962	−	0.118432i	$-0.0377867\pi$
$642$	52.5316	+	151.046i	0.0818250	+	0.235275i
$643$			853.138i			1.32681i	0.748261	+	0.663404i	$0.230889\pi$
$643$			853.138i			1.32681i	−0.748261	+	0.663404i	$0.769111\pi$
$644$			302.012i			0.468962i
$645$	360.447	+	905.252i	0.558832	+	1.40349i
$646$	−48.4690			−0.0750294
$647$	483.979			0.748035			0.374017	−	0.927422i	$-0.377980\pi$
$647$	483.979			0.748035			0.374017	+	0.927422i	$0.377980\pi$
$648$	−72.9310	+	308.701i	−0.112548	+	0.476391i
$649$	−819.883			−1.26330
$650$	3.65207	+	41.1767i	0.00561856	+	0.0633487i
$651$	218.963	−	76.1518i	0.336348	−	0.116977i
$652$			138.737i			0.212787i
$653$	−270.349			−0.414010			−0.207005	−	0.978340i	$-0.566372\pi$
$653$	−270.349			−0.414010			−0.207005	+	0.978340i	$0.566372\pi$
$654$	66.9136	+	192.399i	0.102314	+	0.294189i
$655$	645.778	−	28.5818i	0.985921	−	0.0436363i
$656$		−	177.832i		−	0.271085i
$657$	283.302	+	358.031i	0.431205	+	0.544948i
$658$			100.841i			0.153254i
$659$		−	853.530i		−	1.29519i	−0.761985	−	0.647594i	$-0.775775\pi$
$659$		−	853.530i		−	1.29519i	0.761985	−	0.647594i	$-0.224225\pi$
$660$	278.104	+	698.450i	0.421369	+	1.05826i
$661$	−541.060			−0.818548			−0.409274	−	0.912412i	$-0.634218\pi$
$661$	−541.060			−0.818548			−0.409274	+	0.912412i	$0.634218\pi$
$662$	57.1941			0.0863960
$663$	203.333	−	70.7162i	0.306687	−	0.106661i
$664$	324.659			0.488944
$665$	−57.7244	+	2.55485i	−0.0868036	+	0.00384187i
$666$	−70.2489	−	88.7791i	−0.105479	−	0.133302i
$667$		−	149.413i		−	0.224008i
$668$	201.729			0.301989
$669$	205.973	−	71.6341i	0.307881	−	0.107076i
$670$	−244.493	+	10.8211i	−0.364915	+	0.0161509i
$671$			627.294i			0.934864i
$672$	166.701	−	57.9762i	0.248068	−	0.0862741i
$673$		−	688.054i		−	1.02237i	−0.859471	−	0.511184i	$-0.829207\pi$
$673$		−	688.054i		−	1.02237i	0.859471	−	0.511184i	$-0.170793\pi$
$674$		−	251.639i		−	0.373351i
$675$	599.271	+	310.644i	0.887808	+	0.460214i
$676$	−592.749			−0.876848
$677$	429.973			0.635116			0.317558	−	0.948239i	$-0.397137\pi$
$677$	429.973			0.635116			0.317558	+	0.948239i	$0.397137\pi$
$678$	−11.3450	−	32.6208i	−0.0167331	−	0.0481133i
$679$	−274.609			−0.404432
$680$	−18.9990	−	429.265i	−0.0279397	−	0.631272i
$681$	−95.5923	−	274.861i	−0.140370	−	0.403613i
$682$			197.691i			0.289870i
$683$	−530.037			−0.776042			−0.388021	−	0.921650i	$-0.626841\pi$
$683$	−530.037			−0.776042			−0.388021	+	0.921650i	$0.626841\pi$
$684$	−115.426	+	91.3337i	−0.168751	+	0.133529i
$685$	−25.4559	−	575.153i	−0.0371620	−	0.839640i
$686$			9.36509i			0.0136517i
$687$	−15.0155	−	43.1746i	−0.0218566	−	0.0628452i
$688$		−	844.261i		−	1.22712i
$689$		−	219.547i		−	0.318646i
$690$	−214.835	+	85.5414i	−0.311355	+	0.123973i
$691$	1231.27			1.78187			0.890936	−	0.454129i	$-0.150049\pi$
$691$	1231.27			1.78187			0.890936	+	0.454129i	$0.150049\pi$
$692$	−796.210			−1.15059
$693$	−249.945	+	197.776i	−0.360671	+	0.285391i
$694$	−260.650			−0.375576
$695$	58.3251	+	1317.80i	0.0839210	+	1.89612i
$696$	−54.3825	+	18.9134i	−0.0781358	+	0.0271744i
$697$		−	300.262i		−	0.430792i
$698$	−175.132			−0.250905
$699$	19.6529	+	56.5089i	0.0281158	+	0.0808425i
$700$	−21.8799	−	246.694i	−0.0312570	−	0.352420i
$701$		−	511.428i		−	0.729570i	−0.931092	−	0.364785i	$-0.881143\pi$
$701$		−	511.428i		−	0.729570i	0.931092	−	0.364785i	$-0.118857\pi$
$702$	−23.9678	+	37.6664i	−0.0341422	+	0.0536558i
$703$		−	108.654i		−	0.154557i
$704$		−	545.369i		−	0.774672i
$705$	1050.41	−	418.245i	1.48994	−	0.593255i
$706$	−87.0000			−0.123229
$707$	−134.743			−0.190584
$708$	649.861	−	226.012i	0.917883	−	0.319226i
$709$	−33.6210			−0.0474203			−0.0237102	−	0.999719i	$-0.507548\pi$
$709$	−33.6210			−0.0474203			−0.0237102	+	0.999719i	$0.507548\pi$
$710$	−273.359	+	12.0987i	−0.385012	+	0.0170404i
$711$	422.165	−	334.049i	0.593762	−	0.469830i
$712$			310.962i			0.436744i
$713$	890.426			1.24884
$714$	83.1907	−	28.9324i	0.116514	−	0.0405216i
$715$	9.67671	+	218.636i	0.0135339	+	0.305785i
$716$		−	850.300i		−	1.18757i
$717$	−886.401	+	308.277i	−1.23626	+	0.429953i
$718$		−	9.50135i		−	0.0132331i
$719$			366.444i			0.509658i	0.966986	+	0.254829i	$0.0820191\pi$
$719$			366.444i			0.509658i	−0.966986	+	0.254829i	$0.917981\pi$
$720$	−382.842	−	442.152i	−0.531725	−	0.614100i
$721$	−125.273			−0.173749
$722$	−172.899			−0.239472
$723$	85.6555	+	246.289i	0.118472	+	0.340649i
$724$	739.735			1.02173
$725$	10.8246	+	122.046i	0.0149304	+	0.168339i
$726$	−28.9854	−	83.3430i	−0.0399248	−	0.114797i
$727$			400.035i			0.550255i	0.961408	+	0.275128i	$0.0887201\pi$
$727$			400.035i			0.550255i	−0.961408	+	0.275128i	$0.911280\pi$
$728$	33.8801			0.0465385
$729$	308.796	+	660.368i	0.423588	+	0.905855i
$730$	128.134	−	5.67114i	0.175526	−	0.00776868i
$731$		−	1425.50i		−	1.95007i
$732$	−172.922	−	497.210i	−0.236232	−	0.679249i
$733$			315.918i			0.430993i	0.976505	+	0.215497i	$0.0691370\pi$
$733$			315.918i			0.430993i	−0.976505	+	0.215497i	$0.930863\pi$
$734$		−	195.510i		−	0.266363i
$735$	97.5514	−	38.8423i	0.132723	−	0.0528467i
$736$	677.902			0.921063
$737$	−1295.64			−1.75800
$738$	38.6391	+	48.8313i	0.0523565	+	0.0661671i
$739$	−22.7831			−0.0308296			−0.0154148	−	0.999881i	$-0.504907\pi$
$739$	−22.7831			−0.0308296			−0.0154148	+	0.999881i	$0.504907\pi$
$740$	465.260	−	20.5921i	0.628729	−	0.0278272i
$741$	−40.4707	+	14.0751i	−0.0546163	+	0.0189947i
$742$		−	89.8242i		−	0.121057i
$743$	369.322			0.497069			0.248534	−	0.968623i	$-0.420051\pi$
$743$	369.322			0.497069			0.248534	+	0.968623i	$0.420051\pi$
$744$	−112.714	−	324.092i	−0.151497	−	0.435607i
$745$	222.538	−	9.84941i	0.298709	−	0.0132207i
$746$			125.308i			0.167974i
$747$	585.122	−	462.994i	0.783296	−	0.619805i
$748$		−	1099.85i		−	1.47039i
$749$		−	278.912i		−	0.372379i
$750$	169.287	−	85.4374i	0.225716	−	0.113917i
$751$	69.7646			0.0928956			0.0464478	−	0.998921i	$-0.485210\pi$
$751$	69.7646			0.0928956			0.0464478	+	0.998921i	$0.485210\pi$
$752$	−979.639			−1.30271
$753$	678.994	−	236.144i	0.901718	−	0.313604i
$754$	−8.10396			−0.0107480
$755$	−43.7331	−	988.108i	−0.0579246	−	1.30875i
$756$	143.594	−	225.663i	0.189939	−	0.298496i
$757$			1079.71i			1.42630i	0.701010	+	0.713152i	$0.252733\pi$
$757$			1079.71i			1.42630i	−0.701010	+	0.713152i	$0.747267\pi$
$758$	63.6790			0.0840092
$759$	−1156.27	+	402.134i	−1.52342	+	0.529821i
$760$	3.78149	+	85.4392i	0.00497565	+	0.112420i
$761$			949.374i			1.24753i	0.781610	+	0.623767i	$0.214399\pi$
$761$			949.374i			1.24753i	−0.781610	+	0.623767i	$0.785601\pi$
$762$	89.5491	−	31.1438i	0.117518	−	0.0408711i
$763$		−	355.272i		−	0.465625i
$764$		−	493.303i		−	0.645685i
$765$	−646.414	−	746.556i	−0.844985	−	0.975890i
$766$	−125.338			−0.163626
$767$	200.295			0.261141
$768$	106.016	+	304.831i	0.138041	+	0.396916i
$769$	181.128			0.235537			0.117769	−	0.993041i	$-0.462426\pi$
$769$	181.128			0.235537			0.117769	+	0.993041i	$0.462426\pi$
$770$	3.95907	+	89.4516i	0.00514165	+	0.116171i
$771$	192.627	+	553.870i	0.249841	+	0.718378i
$772$			978.859i			1.26795i
$773$	−1300.73			−1.68271			−0.841354	−	0.540484i	$-0.818241\pi$
$773$	−1300.73			−1.68271			−0.841354	+	0.540484i	$0.818241\pi$
$774$	183.440	+	231.828i	0.237003	+	0.299519i
$775$	−727.331	+	64.5088i	−0.938492	+	0.0832372i
$776$			406.456i			0.523783i
$777$	64.8584	+	186.490i	0.0834729	+	0.240013i
$778$			158.657i			0.203929i
$779$			59.7630i			0.0767176i
$780$	−67.9400	−	170.629i	−0.0871026	−	0.218756i
$781$	−1448.61			−1.85482
$782$	338.301			0.432609
$783$	−71.0395	+	111.641i	−0.0907274	+	0.142582i
$784$	−90.9789			−0.116045
$785$	967.851	−	42.8365i	1.23293	−	0.0545688i
$786$	185.238	−	64.4230i	0.235672	−	0.0819631i
$787$		−	320.350i		−	0.407052i	−0.979070	−	0.203526i	$-0.934760\pi$
$787$		−	320.350i		−	0.407052i	0.979070	−	0.203526i	$-0.0652401\pi$
$788$	−1462.18			−1.85556
$789$	−309.737	−	890.600i	−0.392569	−	1.12877i
$790$	−6.68700	−	151.086i	−0.00846456	−	0.191249i
$791$			60.2354i			0.0761510i
$792$	292.733	+	369.949i	0.369612	+	0.467108i
$793$		−	153.246i		−	0.193249i
$794$			83.7564i			0.105487i
$795$	−935.653	+	372.552i	−1.17692	+	0.468619i
$796$	531.252			0.667402
$797$	1111.52			1.39464			0.697318	−	0.716762i	$-0.254377\pi$
$797$	1111.52			1.39464			0.697318	+	0.716762i	$0.254377\pi$
$798$	−16.5579	+	5.75860i	−0.0207493	+	0.00721629i
$799$	−1654.08			−2.07019
$800$	−553.734	+	49.1121i	−0.692168	+	0.0613901i
$801$	443.460	+	560.436i	0.553633	+	0.699670i
$802$		−	141.415i		−	0.176327i
$803$	679.022			0.845606
$804$	1026.96	−	357.162i	1.27732	−	0.444231i
$805$	402.901	−	17.8322i	0.500498	−	0.0221517i
$806$		−	48.2955i		−	0.0599199i
$807$	−33.1072	+	11.5142i	−0.0410251	+	0.0142679i
$808$			199.436i			0.246826i
$809$			1116.08i			1.37958i	0.724011	+	0.689789i	$0.242297\pi$
$809$			1116.08i			1.37958i	−0.724011	+	0.689789i	$0.757703\pi$
$810$	201.196	+	38.2282i	0.248390	+	0.0471952i
$811$	503.412			0.620730			0.310365	−	0.950617i	$-0.399549\pi$
$811$	503.412			0.620730			0.310365	+	0.950617i	$0.399549\pi$
$812$	48.5517			0.0597927
$813$	391.123	+	1124.61i	0.481086	+	1.38329i
$814$	−168.374			−0.206847
$815$	185.083	−	8.19166i	0.227096	−	0.0100511i
$816$	281.070	+	808.172i	0.344448	+	0.990406i
$817$			283.726i			0.347278i
$818$	−148.864			−0.181986
$819$	61.0609	−	48.3161i	0.0745554	−	0.0589940i
$820$	−255.907	+	11.3263i	−0.312082	+	0.0138126i
$821$			958.269i			1.16720i	0.812042	+	0.583599i	$0.198356\pi$
$821$			958.269i			1.16720i	−0.812042	+	0.583599i	$0.801644\pi$
$822$	−57.3774	−	164.980i	−0.0698022	−	0.200705i
$823$			566.080i			0.687825i	0.939002	+	0.343913i	$0.111752\pi$
$823$			566.080i			0.687825i	−0.939002	+	0.343913i	$0.888248\pi$
$824$			185.419i			0.225023i
$825$	915.351	−	412.246i	1.10952	−	0.499692i
$826$	81.9477			0.0992102
$827$	−747.453			−0.903813			−0.451906	−	0.892065i	$-0.649256\pi$
$827$	−747.453			−0.903813			−0.451906	+	0.892065i	$0.649256\pi$
$828$	805.640	−	637.485i	0.972995	−	0.769909i
$829$	1574.43			1.89919			0.949597	−	0.313475i	$-0.101493\pi$
$829$	1574.43			1.89919			0.949597	+	0.313475i	$0.101493\pi$
$830$	−9.26821	−	209.407i	−0.0111665	−	0.252297i
$831$	−1319.14	+	458.775i	−1.58741	+	0.552076i
$832$			133.232i			0.160135i
$833$	−153.614			−0.184411
$834$	131.464	+	378.005i	0.157631	+	0.453243i
$835$	−11.9110	−	269.118i	−0.0142647	−	0.322297i
$836$			218.910i			0.261854i
$837$	−665.326	−	423.359i	−0.794894	−	0.505805i
$838$		−	306.222i		−	0.365420i
$839$			1460.41i			1.74065i	0.492475	+	0.870326i	$0.336092\pi$
$839$			1460.41i			1.74065i	−0.492475	+	0.870326i	$0.663908\pi$
$840$	−57.4915	−	144.388i	−0.0684422	−	0.171891i
$841$	816.980			0.971439
$842$	92.1708			0.109467
$843$	−64.7135	+	22.5064i	−0.0767657	+	0.0266979i
$844$	432.835			0.512838
$845$	34.9986	+	790.761i	0.0414185	+	0.935812i
$846$	269.001	−	212.855i	0.317969	−	0.251601i
$847$			153.895i			0.181695i
$848$	872.614			1.02903
$849$	−757.014	+	263.278i	−0.891654	+	0.310103i
$850$	−276.336	+	24.5089i	−0.325101	+	0.0288340i
$851$			758.375i			0.891157i
$852$	1148.21	−	399.329i	1.34766	−	0.468696i
$853$			73.4996i			0.0861660i	0.999071	+	0.0430830i	$0.0137180\pi$
$853$			73.4996i			0.0861660i	−0.999071	+	0.0430830i	$0.986282\pi$
$854$		−	62.6983i		−	0.0734172i
$855$	128.660	+	148.592i	0.150479	+	0.173791i
$856$	−412.825			−0.482272
$857$	−713.562			−0.832627			−0.416314	−	0.909221i	$-0.636678\pi$
$857$	−713.562			−0.832627			−0.416314	+	0.909221i	$0.636678\pi$
$858$	21.8112	+	62.7147i	0.0254210	+	0.0730940i
$859$	−416.180			−0.484493			−0.242247	−	0.970215i	$-0.577884\pi$
$859$	−416.180			−0.484493			−0.242247	+	0.970215i	$0.577884\pi$
$860$	−1214.93	+	53.7719i	−1.41270	+	0.0625255i
$861$	−35.6742	−	102.575i	−0.0414334	−	0.119135i
$862$			197.790i			0.229454i
$863$	−1163.66			−1.34839			−0.674197	−	0.738552i	$-0.735510\pi$
$863$	−1163.66			−1.34839			−0.674197	+	0.738552i	$0.735510\pi$
$864$	−506.528	−	322.313i	−0.586260	−	0.373048i
$865$	47.0119	+	1062.19i	0.0543490	+	1.22797i
$866$			243.902i			0.281642i
$867$	189.778	+	545.677i	0.218890	+	0.629385i
$868$			289.343i			0.333345i
$869$		−	800.654i		−	0.921351i
$870$	13.7517	+	34.5370i	0.0158066	+	0.0396977i
$871$	316.522			0.363401
$872$	−525.846			−0.603035
$873$	579.643	+	732.541i	0.663967	+	0.839108i
$874$	−67.3340			−0.0770412
$875$	−327.812	+	43.7550i	−0.374642	+	0.0500057i
$876$	−538.211	+	187.181i	−0.614396	+	0.213677i
$877$		−	1584.74i		−	1.80700i	−0.428590	−	0.903499i	$-0.640989\pi$
$877$		−	1584.74i		−	1.80700i	0.428590	−	0.903499i	$-0.359011\pi$
$878$	−145.938			−0.166216
$879$	−75.3836	−	216.754i	−0.0857606	−	0.246591i
$880$	−868.994	+	38.4612i	−0.987493	+	0.0437059i
$881$		−	1264.13i		−	1.43488i	−0.696620	−	0.717440i	$-0.745314\pi$
$881$		−	1264.13i		−	1.43488i	0.696620	−	0.717440i	$-0.254686\pi$
$882$	24.9821	−	19.7678i	0.0283244	−	0.0224125i
$883$			187.970i			0.212877i	0.994319	+	0.106439i	$0.0339447\pi$
$883$			187.970i			0.212877i	−0.994319	+	0.106439i	$0.966055\pi$
$884$			268.690i			0.303948i
$885$	−339.883	−	853.607i	−0.384049	−	0.964528i
$886$	−101.807			−0.114906
$887$	594.855			0.670637			0.335318	−	0.942105i	$-0.391156\pi$
$887$	594.855			0.670637			0.335318	+	0.942105i	$0.391156\pi$
$888$	276.029	−	95.9985i	0.310843	−	0.108106i
$889$	−165.355			−0.186001
$890$	200.572	−	8.87719i	0.225362	−	0.00997437i
$891$	1055.16	+	249.284i	1.18425	+	0.279780i
$892$			272.178i			0.305132i
$893$	329.222			0.368669
$894$	63.8340	−	22.2005i	0.0714027	−	0.0248327i
$895$	−1134.35	+	50.2056i	−1.26743	+	0.0560957i
$896$			289.837i			0.323479i
$897$	282.475	−	98.2403i	0.314910	−	0.109521i
$898$		−	278.680i		−	0.310334i
$899$		−	143.146i		−	0.159228i
$900$	−611.891	+	579.086i	−0.679879	+	0.643429i
$901$	1473.37			1.63527
$902$	92.6107			0.102673
$903$	−169.364	−	486.979i	−0.187557	−	0.539290i
$904$	89.1559			0.0986238
$905$	−43.6773	−	986.848i	−0.0482622	−	1.09044i
$906$	−98.5740	−	283.434i	−0.108801	−	0.312841i
$907$		−	1551.71i		−	1.71082i	−0.517956	−	0.855408i	$-0.673307\pi$
$907$		−	1551.71i		−	1.71082i	0.517956	−	0.855408i	$-0.326693\pi$
$908$	363.208			0.400009
$909$	284.414	+	359.436i	0.312887	+	0.395420i
$910$	−0.967192	−	21.8528i	−0.00106285	−	0.0240141i
$911$		−	291.382i		−	0.319848i	−0.987129	−	0.159924i	$-0.948875\pi$
$911$		−	291.382i		−	0.319848i	0.987129	−	0.159924i	$-0.0511250\pi$
$912$	−55.9430	−	160.855i	−0.0613410	−	0.176376i
$913$		−	1109.71i		−	1.21545i
$914$		−	87.5622i		−	0.0958010i
$915$	−653.096	+	260.045i	−0.713767	+	0.284203i
$916$	57.0521			0.0622840
$917$	−342.048			−0.373008
$918$	−252.778	−	160.847i	−0.275357	−	0.175215i
$919$	−325.437			−0.354121			−0.177060	−	0.984200i	$-0.556659\pi$
$919$	−325.437			−0.354121			−0.177060	+	0.984200i	$0.556659\pi$
$920$	−26.3938	−	596.343i	−0.0286889	−	0.648199i
$921$	1220.67	−	424.530i	1.32537	−	0.460945i
$922$		−	96.7708i		−	0.104957i
$923$	353.892			0.383415
$924$	−130.673	−	375.730i	−0.141421	−	0.406634i
$925$	−54.9421	−	619.467i	−0.0593969	−	0.669694i
$926$			154.071i			0.166383i
$927$	264.425	+	334.175i	0.285248	+	0.360491i
$928$		−	108.980i		−	0.117436i
$929$		−	209.216i		−	0.225205i	−0.993640	−	0.112603i	$-0.964081\pi$
$929$		−	209.216i		−	0.225205i	0.993640	−	0.112603i	$-0.0359187\pi$
$930$	−205.823	+	81.9532i	−0.221315	+	0.0881217i
$931$	30.5748			0.0328408
$932$	−74.6724			−0.0801206
$933$	−1553.61	+	540.321i	−1.66517	+	0.579122i
$934$	−247.834			−0.265347
$935$	−1467.26	+	64.9401i	−1.56926	+	0.0694547i
$936$	−71.5138	−	90.3777i	−0.0764037	−	0.0965574i
$937$			1312.63i			1.40089i	0.713707	+	0.700444i	$0.247015\pi$
$937$			1312.63i			1.40089i	−0.713707	+	0.700444i	$0.752985\pi$
$938$	129.500			0.138060
$939$	752.294	−	261.636i	0.801165	−	0.278633i
$940$	62.3943	+	1409.74i	0.0663769	+	1.49972i
$941$			693.569i			0.737055i	0.929617	+	0.368528i	$0.120138\pi$
$941$			693.569i			0.737055i	−0.929617	+	0.368528i	$0.879862\pi$
$942$	277.623	−	96.5530i	0.294717	−	0.102498i
$943$		−	417.130i		−	0.442343i
$944$			796.096i			0.843322i
$945$	−309.526	−	178.238i	−0.327541	−	0.188611i
$946$	439.671			0.464769
$947$	176.761			0.186654			0.0933268	−	0.995636i	$-0.470250\pi$
$947$	176.761			0.186654			0.0933268	+	0.995636i	$0.470250\pi$
$948$	220.711	+	634.620i	0.232818	+	0.669430i
$949$	−165.883			−0.174798
$950$	55.0008	−	4.87816i	0.0578955	−	0.00513490i
$951$	−42.6525	−	122.641i	−0.0448502	−	0.128960i
$952$			227.368i			0.238832i
$953$	−252.704			−0.265167			−0.132583	−	0.991172i	$-0.542327\pi$
$953$	−252.704			−0.265167			−0.132583	+	0.991172i	$0.542327\pi$
$954$	−239.613	+	189.601i	−0.251167	+	0.198743i
$955$	−658.095	+	29.1269i	−0.689104	+	0.0304993i
$956$		−	1171.31i		−	1.22522i
$957$	64.6474	+	185.884i	0.0675522	+	0.194236i
$958$		−	323.272i		−	0.337445i
$959$			304.640i			0.317665i
$960$	567.802	−	226.083i	0.591460	−	0.235503i
$961$	−107.925			−0.112305
$962$	41.1332			0.0427580
$963$	−744.020	+	588.726i	−0.772606	+	0.611346i
$964$	−325.453			−0.337607
$965$	1305.85	−	57.7963i	1.35322	−	0.0598925i
$966$	115.570	−	40.1935i	0.119638	−	0.0416082i
$967$		−	1691.10i		−	1.74881i	−0.485198	−	0.874404i	$-0.661253\pi$
$967$		−	1691.10i		−	1.74881i	0.485198	−	0.874404i	$-0.338747\pi$
$968$	227.784			0.235314
$969$	−94.4575	−	271.598i	−0.0974794	−	0.280287i
$970$	262.166	−	11.6033i	0.270274	−	0.0119622i
$971$			273.436i			0.281602i	0.990038	+	0.140801i	$0.0449678\pi$
$971$			273.436i			0.281602i	−0.990038	+	0.140801i	$0.955032\pi$
$972$	−905.071	+	93.2814i	−0.931143	+	0.0959685i
$973$		−	697.998i		−	0.717367i
$974$			214.203i			0.219921i
$975$	−223.618	+	100.711i	−0.229352	+	0.103293i
$976$	609.094			0.624072
$977$	1014.54			1.03842			0.519212	−	0.854646i	$-0.326226\pi$
$977$	1014.54			1.03842			0.519212	+	0.854646i	$0.326226\pi$
$978$	53.0901	−	18.4639i	0.0542844	−	0.0188793i
$979$	1062.89			1.08569
$980$	5.79455	+	130.922i	0.00591280	+	0.133594i
$981$	−947.715	+	749.905i	−0.966070	+	0.764430i
$982$		−	234.956i		−	0.239263i
$983$	1724.49			1.75432			0.877158	−	0.480202i	$-0.159437\pi$
$983$	1724.49			1.75432			0.877158	+	0.480202i	$0.159437\pi$
$984$	−151.824	+	52.8022i	−0.154293	+	0.0536607i
$985$	86.3339	+	1950.63i	0.0876486	+	1.98034i
$986$		−	54.3855i		−	0.0551577i
$987$	−565.067	+	196.521i	−0.572509	+	0.199110i
$988$		−	53.4791i		−	0.0541286i
$989$		−	1980.33i		−	2.00236i
$990$	230.262	−	199.375i	0.232588	−	0.201389i
$991$	944.002			0.952576			0.476288	−	0.879289i	$-0.341982\pi$
$991$	944.002			0.952576			0.476288	+	0.879289i	$0.341982\pi$
$992$	649.466			0.654704
$993$	111.461	+	320.490i	0.112247	+	0.322749i
$994$	144.789			0.145663
$995$	−31.3675	−	708.720i	−0.0315252	−	0.712281i
$996$	305.907	+	879.586i	0.307135	+	0.883119i
$997$			1175.44i			1.17898i	0.807777	+	0.589489i	$0.200671\pi$
$997$			1175.44i			1.17898i	−0.807777	+	0.589489i	$0.799329\pi$
$998$	−144.898			−0.145188
$999$	360.575	−	566.658i	0.360935	−	0.567225i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.f.a.29.14	yes	24
3.2	odd	2	inner	105.3.f.a.29.12	yes	24
5.2	odd	4		525.3.c.e.176.14		24
5.3	odd	4		525.3.c.e.176.11		24
5.4	even	2	inner	105.3.f.a.29.11	✓	24
15.2	even	4		525.3.c.e.176.12		24
15.8	even	4		525.3.c.e.176.13		24
15.14	odd	2	inner	105.3.f.a.29.13	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.f.a.29.11	✓	24	5.4	even	2	inner
105.3.f.a.29.12	yes	24	3.2	odd	2	inner
105.3.f.a.29.13	yes	24	15.14	odd	2	inner
105.3.f.a.29.14	yes	24	1.1	even	1	trivial
525.3.c.e.176.11		24	5.3	odd	4
525.3.c.e.176.12		24	15.2	even	4
525.3.c.e.176.13		24	15.8	even	4
525.3.c.e.176.14		24	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.505667 q^{2} +(0.985457 + 2.83353i) q^{3} -3.74430 q^{4} +(0.221081 + 4.99511i) q^{5} +(0.498313 + 1.43282i) q^{6} -2.64575i q^{7} -3.91604 q^{8} +(-7.05775 + 5.58464i) q^{9} +O(q^{10})\)	\(q+0.505667 q^{2} +(0.985457 + 2.83353i) q^{3} -3.74430 q^{4} +(0.221081 + 4.99511i) q^{5} +(0.498313 + 1.43282i) q^{6} -2.64575i q^{7} -3.91604 q^{8} +(-7.05775 + 5.58464i) q^{9} +(0.111793 + 2.52586i) q^{10} +13.3853i q^{11} +(-3.68985 - 10.6096i) q^{12} -3.27000i q^{13} -1.33787i q^{14} +(-13.9359 + 5.54890i) q^{15} +12.9970 q^{16} +21.9449 q^{17} +(-3.56887 + 2.82397i) q^{18} -4.36782 q^{19} +(-0.827792 - 18.7032i) q^{20} +(7.49681 - 2.60727i) q^{21} +6.76852i q^{22} +30.4863 q^{23} +(-3.85909 - 11.0962i) q^{24} +(-24.9022 + 2.20864i) q^{25} -1.65353i q^{26} +(-22.7793 - 14.4949i) q^{27} +9.90649i q^{28} -4.90100i q^{29} +(-7.04694 + 2.80590i) q^{30} +29.2074 q^{31} +22.2363 q^{32} +(-37.9277 + 13.1907i) q^{33} +11.0968 q^{34} +(13.2158 - 0.584924i) q^{35} +(26.4263 - 20.9106i) q^{36} +24.8760i q^{37} -2.20867 q^{38} +(9.26564 - 3.22245i) q^{39} +(-0.865761 - 19.5611i) q^{40} -13.6825i q^{41} +(3.79089 - 1.31841i) q^{42} -64.9582i q^{43} -50.1187i q^{44} +(-29.4562 - 34.0196i) q^{45} +15.4159 q^{46} -75.3743 q^{47} +(12.8080 + 36.8273i) q^{48} -7.00000 q^{49} +(-12.5923 + 1.11684i) q^{50} +(21.6258 + 62.1815i) q^{51} +12.2439i q^{52} +67.1397 q^{53} +(-11.5188 - 7.32960i) q^{54} +(-66.8612 + 2.95924i) q^{55} +10.3609i q^{56} +(-4.30430 - 12.3763i) q^{57} -2.47828i q^{58} +61.2523i q^{59} +(52.1802 - 20.7768i) q^{60} +46.8643 q^{61} +14.7693 q^{62} +(14.7756 + 18.6730i) q^{63} -40.7438 q^{64} +(16.3340 - 0.722934i) q^{65} +(-19.1788 + 6.67009i) q^{66} +96.7958i q^{67} -82.1683 q^{68} +(30.0429 + 86.3836i) q^{69} +(6.68281 - 0.295777i) q^{70} +108.224i q^{71} +(27.6384 - 21.8697i) q^{72} -50.7288i q^{73} +12.5790i q^{74} +(-30.7983 - 68.3847i) q^{75} +16.3544 q^{76} +35.4142 q^{77} +(4.68533 - 1.62949i) q^{78} -59.8158 q^{79} +(2.87338 + 64.9214i) q^{80} +(18.6236 - 78.8299i) q^{81} -6.91882i q^{82} -82.9049 q^{83} +(-28.0703 + 9.76242i) q^{84} +(4.85159 + 109.617i) q^{85} -32.8473i q^{86} +(13.8871 - 4.82972i) q^{87} -52.4175i q^{88} -79.4072i q^{89} +(-14.8950 - 17.2026i) q^{90} -8.65161 q^{91} -114.150 q^{92} +(28.7827 + 82.7601i) q^{93} -38.1143 q^{94} +(-0.965641 - 21.8178i) q^{95} +(21.9129 + 63.0072i) q^{96} -103.792i q^{97} -3.53967 q^{98} +(-74.7522 - 94.4703i) 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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