LMFDB - Embedded newform 105.3.f.a.29.12

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			29.12
Character	$\chi$	$=$	105.29
Dual form			105.3.f.a.29.11

$q$-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} +(14.3716 + 4.29603i) 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} +(-7.26727 - 2.17236i) 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} +(-26.3355 + 36.4889i) 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} +(-53.8118 - 16.0856i) 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} +(18.2818 - 72.7377i) 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} +(13.3170 - 18.4512i) 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	$-0.540348\pi$
$2$	−0.505667			−0.252834			−0.126417	+	0.991977i	$0.540348\pi$
$3$	−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	$-0.791802\pi$
$11$		−	13.3853i		−	1.21685i	0.793612	−	0.608424i	$-0.208198\pi$
$12$	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
$15$	14.3716	+	4.29603i	0.958110	+	0.286402i
$16$	12.9970			0.812312
$17$	−21.9449			−1.29088			−0.645438	−	0.763813i	$-0.723325\pi$
$17$	−21.9449			−1.29088			−0.645438	+	0.763813i	$0.723325\pi$
$18$	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	$-0.730609\pi$
$23$	−30.4863			−1.32549			−0.662745	+	0.748845i	$0.730609\pi$
$24$	−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	$0.0269293\pi$
$29$			4.90100i			0.169000i	−0.996423	+	0.0845000i	$0.973071\pi$
$30$	−7.26727	−	2.17236i	−0.242242	−	0.0724120i
$31$	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	$0.0533629\pi$
$41$			13.6825i			0.333721i	−0.985981	+	0.166860i	$0.946637\pi$
$42$	−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
$45$	−26.3355	+	36.4889i	−0.585234	+	0.810864i
$46$	15.4159			0.335128
$47$	75.3743			1.60371			0.801854	−	0.597519i	$-0.203847\pi$
$47$	75.3743			1.60371			0.801854	+	0.597519i	$0.203847\pi$
$48$	−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	$-0.718339\pi$
$53$	−67.1397			−1.26679			−0.633394	+	0.773830i	$0.718339\pi$
$54$	−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	$-0.826272\pi$
$59$		−	61.2523i		−	1.03818i	0.854721	−	0.519088i	$-0.173728\pi$
$60$	−53.8118	−	16.0856i	−0.896863	−	0.268094i
$61$	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	$-0.724149\pi$
$71$		−	108.224i		−	1.52428i	0.647413	−	0.762140i	$-0.275851\pi$
$72$	−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
$75$	18.2818	−	72.7377i	0.243758	−	0.969836i
$76$	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	$-0.333544\pi$
$83$	82.9049			0.998855			0.499427	+	0.866356i	$0.333544\pi$
$84$	−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	$0.147190\pi$
$89$			79.4072i			0.892216i	−0.894979	+	0.446108i	$0.852810\pi$
$90$	13.3170	−	18.4512i	0.147967	−	0.205014i
$91$	−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	$0.0811272\pi$
$101$			50.9279i			0.504237i	−0.967696	+	0.252118i	$0.918873\pi$
$102$	−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
$105$	11.3662	−	38.0238i	0.108250	−	0.362131i
$106$	33.9504			0.320287
$107$	−105.419			−0.985223			−0.492612	−	0.870249i	$-0.663958\pi$
$107$	−105.419			−0.985223			−0.492612	+	0.870249i	$0.663958\pi$
$108$	−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	$-0.467880\pi$
$113$	22.7668			0.201476			0.100738	+	0.994913i	$0.467880\pi$
$114$	−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
$120$	56.2799	+	16.8234i	0.468999	+	0.140195i
$121$	−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	$0.164262\pi$
$131$			129.282i			0.986886i	−0.869778	+	0.493443i	$0.835738\pi$
$132$	−142.013	−	49.3898i	−1.07585	−	0.374165i
$133$			11.5562i			0.0868886i
$134$		−	48.9465i		−	0.365272i
$135$	−77.4397	−	110.581i	−0.573627	−	0.819116i
$136$	−85.9371			−0.631890
$137$	115.143			0.840462			0.420231	−	0.907417i	$-0.361949\pi$
$137$	115.143			0.840462			0.420231	+	0.907417i	$0.361949\pi$
$138$	−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	$0.0477666\pi$
$149$			44.5512i			0.299001i	−0.988762	+	0.149501i	$0.952233\pi$
$150$	−9.24453	+	36.7811i	−0.0616302	+	0.245207i
$151$	−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
$165$	57.5037	−	192.369i	0.348508	−	1.16587i
$166$	−41.9223			−0.252544
$167$	53.8763			0.322612			0.161306	−	0.986904i	$-0.448429\pi$
$167$	53.8763			0.322612			0.161306	+	0.986904i	$0.448429\pi$
$168$	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	$-0.710676\pi$
$173$	−212.646			−1.22917			−0.614584	+	0.788852i	$0.710676\pi$
$174$	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	$-0.781274\pi$
$179$		−	227.092i		−	1.26867i	0.773058	−	0.634335i	$-0.218726\pi$
$180$	98.6082	−	136.625i	0.547823	−	0.759030i
$181$	−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	$-0.887916\pi$
$191$		−	131.748i		−	0.689779i	0.938643	−	0.344889i	$-0.112084\pi$
$192$	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
$195$	14.0480	−	46.9953i	0.0720411	−	0.241001i
$196$	26.2101			0.133725
$197$	−390.509			−1.98228			−0.991139	−	0.132831i	$-0.957593\pi$
$197$	−390.509			−1.98228			−0.991139	+	0.132831i	$0.957593\pi$
$198$	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
$210$	−5.74753	+	19.2274i	−0.0273692	+	0.0915590i
$211$	−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
$225$	188.088	+	123.482i	0.835948	+	0.548809i
$226$	−11.5125			−0.0509400
$227$	97.0030			0.427326			0.213663	−	0.976907i	$-0.431461\pi$
$227$	97.0030			0.427326			0.213663	+	0.976907i	$0.431461\pi$
$228$	−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	$-0.513627\pi$
$233$	−19.9430			−0.0855921			−0.0427960	+	0.999084i	$0.513627\pi$
$234$	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	$-0.772901\pi$
$239$		−	312.826i		−	1.30890i	0.756107	−	0.654448i	$-0.227099\pi$
$240$	186.788	+	55.8354i	0.778284	+	0.232648i
$241$	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	$0.158402\pi$
$251$			239.629i			0.954695i	−0.878714	+	0.477348i	$0.841598\pi$
$252$	55.3241	−	69.9175i	0.219540	−	0.277450i
$253$			408.069i			1.61292i
$254$			31.6034i			0.124423i
$255$	−315.384	−	94.2759i	−1.23680	−	0.369709i
$256$	107.580			0.420235
$257$	−195.470			−0.760584			−0.380292	−	0.924867i	$-0.624176\pi$
$257$	−195.470			−0.760584			−0.380292	+	0.924867i	$0.624176\pi$
$258$	−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	$-0.296143\pi$
$263$	314.308			1.19509			0.597544	+	0.801836i	$0.296143\pi$
$264$	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	$-0.993087\pi$
$269$		−	11.6841i		−	0.0434354i	0.999764	−	0.0217177i	$-0.00691350\pi$
$270$	39.1587	+	55.9171i	0.145032	+	0.207100i
$271$	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	$-0.987061\pi$
$281$		−	22.8385i		−	0.0812758i	0.999174	−	0.0406379i	$-0.0129390\pi$
$282$	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
$285$	−62.7728	−	18.7643i	−0.220256	−	0.0658396i
$286$	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	$-0.458329\pi$
$293$	76.4961			0.261079			0.130539	+	0.991443i	$0.458329\pi$
$294$	−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
$300$	−68.4527	+	272.352i	−0.228176	+	0.907839i
$301$	−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	$-0.656532\pi$
$311$		−	548.295i		−	1.76301i	0.472178	−	0.881503i	$-0.343468\pi$
$312$	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
$315$	96.5405	+	69.6773i	0.306478	+	0.221198i
$316$	223.968			0.708760
$317$	43.2820			0.136536			0.0682681	−	0.997667i	$-0.478253\pi$
$317$	43.2820			0.136536			0.0682681	+	0.997667i	$0.478253\pi$
$318$	−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
$330$	−29.0778	+	97.2748i	−0.0881144	+	0.294772i
$331$	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
$345$	−438.138	−	130.970i	−1.26996	−	0.379623i
$346$	107.528			0.310775
$347$	515.457			1.48547			0.742734	−	0.669587i	$-0.233529\pi$
$347$	515.457			1.48547			0.742734	+	0.669587i	$0.233529\pi$
$348$	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	$-0.421640\pi$
$353$	172.050			0.487393			0.243697	+	0.969852i	$0.421640\pi$
$354$	−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	$0.00833097\pi$
$359$			18.7897i			0.0523391i	−0.999658	+	0.0261695i	$0.991669\pi$
$360$	−103.131	+	142.892i	−0.286475	+	0.396922i
$361$	−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
$375$	−367.375	−	75.2389i	−0.979666	−	0.200637i
$376$	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	$-0.395112\pi$
$383$	247.866			0.647170			0.323585	+	0.946199i	$0.395112\pi$
$384$	−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	$-0.867868\pi$
$389$		−	313.757i		−	0.806574i	0.915074	−	0.403287i	$-0.132132\pi$
$390$	−7.10362	+	23.7640i	−0.0182144	+	0.0609333i
$391$	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	$0.113378\pi$
$401$			279.659i			0.697405i	−0.937234	+	0.348702i	$0.886622\pi$
$402$	138.691	+	48.2347i	0.345003	+	0.119987i
$403$		−	95.5084i		−	0.236993i
$404$		−	190.689i		−	0.472003i
$405$	389.647	−	110.455i	0.962091	−	0.272728i
$406$	−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	$0.257076\pi$
$419$			605.580i			1.44530i	−0.691215	+	0.722649i	$0.742924\pi$
$420$	−42.5585	+	142.373i	−0.101330	+	0.338982i
$421$	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	$-0.850081\pi$
$431$		−	391.145i		−	0.907530i	0.891121	−	0.453765i	$-0.149919\pi$
$432$	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
$435$	−21.0548	+	70.4354i	−0.0484019	+	0.161921i
$436$	−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	$-0.427031\pi$
$443$	201.332			0.454473			0.227236	+	0.973840i	$0.427031\pi$
$444$	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	$0.210325\pi$
$449$			551.114i			1.22743i	−0.789530	+	0.613713i	$0.789675\pi$
$450$	−95.1101	−	62.4408i	−0.211356	−	0.138757i
$451$	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	$0.0665529\pi$
$461$			191.372i			0.415124i	−0.978222	+	0.207562i	$0.933447\pi$
$462$	−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
$465$	419.759	+	125.476i	0.902707	+	0.269841i
$466$	10.0845			0.0216406
$467$	490.114			1.04949			0.524747	−	0.851258i	$-0.324160\pi$
$467$	490.114			1.04949			0.524747	+	0.851258i	$0.324160\pi$
$468$	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	$0.232561\pi$
$479$			639.298i			1.33465i	−0.744766	+	0.667325i	$0.767439\pi$
$480$	−319.572	−	95.5278i	−0.665776	−	0.199016i
$481$	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	$0.156887\pi$
$491$			464.645i			0.946324i	−0.880976	+	0.473162i	$0.843113\pi$
$492$	145.166	+	50.4865i	0.295053	+	0.102615i
$493$		−	107.552i		−	0.218158i
$494$		−	7.22234i		−	0.0146201i
$495$	488.416	+	352.510i	0.986698	+	0.712141i
$496$	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	$-0.448631\pi$
$503$	161.645			0.321362			0.160681	+	0.987006i	$0.448631\pi$
$504$	−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	$-0.915397\pi$
$509$		−	267.397i		−	0.525337i	0.964886	−	0.262668i	$-0.0846026\pi$
$510$	159.480	+	47.6722i	0.312705	+	0.0934750i
$511$	−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	$0.0659201\pi$
$521$			214.253i			0.411234i	−0.978633	+	0.205617i	$0.934080\pi$
$522$	−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
$525$	−192.446	−	48.3692i	−0.366564	−	0.0921318i
$526$	−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
$540$	289.958	+	414.047i	0.536958	+	0.766754i
$541$	−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
$555$	−106.868	+	357.508i	−0.192555	+	0.644159i
$556$	−987.815			−1.77665
$557$	−110.854			−0.199020			−0.0995102	−	0.995037i	$-0.531728\pi$
$557$	−110.854			−0.199020			−0.0995102	+	0.995037i	$0.531728\pi$
$558$	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	$-0.752140\pi$
$563$	−801.536			−1.42369			−0.711844	+	0.702338i	$0.752140\pi$
$564$	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	$-0.688645\pi$
$569$		−	943.932i		−	1.65893i	0.558557	−	0.829466i	$-0.311355\pi$
$570$	31.7422	+	9.48849i	0.0556880	+	0.0166465i
$571$	−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
$585$	119.319	+	86.1173i	0.203964	+	0.147209i
$586$	−38.6816			−0.0660095
$587$	169.335			0.288475			0.144237	−	0.989543i	$-0.453927\pi$
$587$	169.335			0.288475			0.144237	+	0.989543i	$0.453927\pi$
$588$	−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	$-0.380401\pi$
$593$	435.205			0.733904			0.366952	+	0.930240i	$0.380401\pi$
$594$	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	$0.142830\pi$
$599$			519.702i			0.867615i	−0.901006	+	0.433808i	$0.857170\pi$
$600$	71.5924	−	284.844i	0.119321	−	0.474740i
$601$	−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
$615$	−58.7806	+	196.641i	−0.0955782	+	0.319741i
$616$	−138.684			−0.225136
$617$	−220.169			−0.356838			−0.178419	−	0.983955i	$-0.557098\pi$
$617$	−220.169			−0.356838			−0.178419	+	0.983955i	$0.557098\pi$
$618$	−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
$630$	−48.8174	−	35.2335i	−0.0774879	−	0.0559263i
$631$	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	$0.0377867\pi$
$641$			151.830i			0.236864i	−0.992962	+	0.118432i	$0.962213\pi$
$642$	−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
$645$	279.062	−	933.556i	0.432655	−	1.44737i
$646$	−48.4690			−0.0750294
$647$	−483.979			−0.748035			−0.374017	−	0.927422i	$-0.622020\pi$
$647$	−483.979			−0.748035			−0.374017	+	0.927422i	$0.622020\pi$
$648$	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	$-0.433628\pi$
$653$	270.349			0.414010			0.207005	+	0.978340i	$0.433628\pi$
$654$	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	$0.224225\pi$
$659$			853.530i			1.29519i	−0.761985	+	0.647594i	$0.775775\pi$
$660$	−215.311	+	720.288i	−0.326229	+	1.09135i
$661$	−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
$675$	−535.242	+	411.267i	−0.792952	+	0.609285i
$676$	−592.749			−0.876848
$677$	−429.973			−0.635116			−0.317558	−	0.948239i	$-0.602863\pi$
$677$	−429.973			−0.635116			−0.317558	+	0.948239i	$0.602863\pi$
$678$	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	$-0.373159\pi$
$683$	530.037			0.776042			0.388021	+	0.921650i	$0.373159\pi$
$684$	−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
$690$	221.552	+	66.2272i	0.321090	+	0.0959814i
$691$	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	$0.118857\pi$
$701$			511.428i			0.729570i	−0.931092	+	0.364785i	$0.881143\pi$
$702$	23.9678	+	37.6664i	0.0341422	+	0.0536558i
$703$		−	108.654i		−	0.154557i
$704$			545.369i			0.774672i
$705$	1083.25	+	323.810i	1.53653	+	0.459305i
$706$	−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	$-0.917981\pi$
$719$		−	366.444i		−	0.509658i	0.966986	−	0.254829i	$-0.0820191\pi$
$720$	−342.283	+	474.246i	−0.475393	+	0.658675i
$721$	−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
$735$	−100.602	−	30.0722i	−0.136873	−	0.0409146i
$736$	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	$-0.579949\pi$
$743$	−369.322			−0.497069			−0.248534	+	0.968623i	$0.579949\pi$
$744$	−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
$750$	185.769	+	38.0459i	0.247692	+	0.0507278i
$751$	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	$-0.785601\pi$
$761$		−	949.374i		−	1.24753i	0.781610	−	0.623767i	$-0.214399\pi$
$762$	−89.5491	−	31.1438i	−0.117518	−	0.0408711i
$763$		−	355.272i		−	0.465625i
$764$			493.303i			0.645685i
$765$	577.931	−	800.745i	0.755465	−	1.04673i
$766$	−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	$-0.181759\pi$
$773$	1300.73			1.68271			0.841354	+	0.540484i	$0.181759\pi$
$774$	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
$780$	−52.6000	+	175.964i	−0.0674359	+	0.225595i
$781$	−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
$795$	−964.908	−	288.434i	−1.21372	−	0.362810i
$796$	531.252			0.667402
$797$	−1111.52			−1.39464			−0.697318	−	0.716762i	$-0.745623\pi$
$797$	−1111.52			−1.39464			−0.697318	+	0.716762i	$0.745623\pi$
$798$	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	$-0.757703\pi$
$809$		−	1116.08i		−	1.37958i	0.724011	−	0.689789i	$-0.242297\pi$
$810$	−197.032	+	55.8535i	−0.243249	+	0.0689549i
$811$	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	$-0.801644\pi$
$821$		−	958.269i		−	1.16720i	0.812042	−	0.583599i	$-0.198356\pi$
$822$	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
$825$	−973.618	−	244.708i	−1.18014	−	0.296616i
$826$	81.9477			0.0992102
$827$	747.453			0.903813			0.451906	−	0.892065i	$-0.350744\pi$
$827$	747.453			0.903813			0.451906	+	0.892065i	$0.350744\pi$
$828$	−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	$-0.663908\pi$
$839$		−	1460.41i		−	1.74065i	0.492475	−	0.870326i	$-0.336092\pi$
$840$	44.5106	−	148.903i	0.0529888	−	0.177265i
$841$	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
$855$	115.029	−	159.377i	0.134537	−	0.186406i
$856$	−412.825			−0.482272
$857$	713.562			0.832627			0.416314	−	0.909221i	$-0.363322\pi$
$857$	713.562			0.832627			0.416314	+	0.909221i	$0.363322\pi$
$858$	−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	$-0.264490\pi$
$863$	1163.66			1.34839			0.674197	+	0.738552i	$0.264490\pi$
$864$	−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
$870$	10.6467	−	35.6169i	0.0122376	−	0.0409390i
$871$	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	$0.254686\pi$
$881$			1264.13i			1.43488i	−0.696620	+	0.717440i	$0.745314\pi$
$882$	−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
$885$	263.142	−	880.297i	0.297335	−	0.994685i
$886$	−101.807			−0.114906
$887$	−594.855			−0.670637			−0.335318	−	0.942105i	$-0.608844\pi$
$887$	−594.855			−0.670637			−0.335318	+	0.942105i	$0.608844\pi$
$888$	−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
$900$	−704.259	−	462.354i	−0.782510	−	0.513726i
$901$	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	$0.0511250\pi$
$911$			291.382i			0.319848i	−0.987129	+	0.159924i	$0.948875\pi$
$912$	55.9430	−	160.855i	0.0613410	−	0.176376i
$913$		−	1109.71i		−	1.21545i
$914$			87.5622i			0.0958010i
$915$	673.517	+	201.330i	0.736084	+	0.220033i
$916$	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	$0.0359187\pi$
$929$			209.216i			0.225205i	−0.993640	+	0.112603i	$0.964081\pi$
$930$	−212.258	−	63.4491i	−0.228235	−	0.0682249i
$931$	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	$-0.879862\pi$
$941$		−	693.569i		−	0.737055i	0.929617	−	0.368528i	$-0.120138\pi$
$942$	−277.623	−	96.5530i	−0.294717	−	0.102498i
$943$		−	417.130i		−	0.442343i
$944$		−	796.096i		−	0.843322i
$945$	−292.569	+	204.886i	−0.309597	+	0.216811i
$946$	439.671			0.464769
$947$	−176.761			−0.186654			−0.0933268	−	0.995636i	$-0.529750\pi$
$947$	−176.761			−0.186654			−0.0933268	+	0.995636i	$0.529750\pi$
$948$	−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	$-0.457673\pi$
$953$	252.704			0.265167			0.132583	+	0.991172i	$0.457673\pi$
$954$	−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
$960$	−585.555	−	175.036i	−0.609953	−	0.182330i
$961$	−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	$-0.955032\pi$
$971$		−	273.436i		−	0.281602i	0.990038	−	0.140801i	$-0.0449678\pi$
$972$	905.071	+	93.2814i	0.931143	+	0.0959685i
$973$		−	697.998i		−	0.717367i
$974$		−	214.203i		−	0.219921i
$975$	−237.852	−	59.7816i	−0.243951	−	0.0613145i
$976$	609.094			0.624072
$977$	−1014.54			−1.03842			−0.519212	−	0.854646i	$-0.673774\pi$
$977$	−1014.54			−1.03842			−0.519212	+	0.854646i	$0.673774\pi$
$978$	−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	$-0.840563\pi$
$983$	−1724.49			−1.75432			−0.877158	+	0.480202i	$0.840563\pi$
$984$	−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
$990$	−246.976	−	178.253i	−0.249471	−	0.180053i
$991$	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.29.12	yes	24
3.2	odd	2	inner	105.3.f.a.29.14	yes	24
5.2	odd	4		525.3.c.e.176.12		24
5.3	odd	4		525.3.c.e.176.13		24
5.4	even	2	inner	105.3.f.a.29.13	yes	24
15.2	even	4		525.3.c.e.176.14		24
15.8	even	4		525.3.c.e.176.11		24
15.14	odd	2	inner	105.3.f.a.29.11	✓	24

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

\(f(q)\)	\(=\)	\(q-0.505667 q^{2} +(-0.985457 + 2.83353i) q^{3} -3.74430 q^{4} +(-0.221081 - 4.99511i) q^{5} +(0.498313 - 1.43282i) q^{6} -2.64575i q^{7} +3.91604 q^{8} +(-7.05775 - 5.58464i) q^{9} +O(q^{10})\)	\(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} +(14.3716 + 4.29603i) 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} +(-7.26727 - 2.17236i) 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} +(-26.3355 + 36.4889i) 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} +(-53.8118 - 16.0856i) 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} +(18.2818 - 72.7377i) 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} +(13.3170 - 18.4512i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more