LMFDB - Embedded newform 29.2.e.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,2,Mod(4,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(14))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("29.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	29.e (of order $14$, degree $6$, 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:	$0.231566165862$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{14})$
Coefficient field:	12.0.7877952219361.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{11} + 13x^{9} - 18x^{8} - 14x^{7} + 57x^{6} - 28x^{5} - 72x^{4} + 104x^{3} - 96x + 64 $ x^12 - 3x^11 + 13x^9 - 18x^8 - 14x^7 + 57x^6 - 28x^5 - 72x^4 + 104x^3 - 96*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			4.1
Root			$0.639551 + 1.26134i$ of defining polynomial
Character	$\chi$	$=$	29.4
Dual form			29.2.e.a.22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.21089 - 0.504621i) q^{2} +(-1.23248 - 2.55926i) q^{3} +(2.83146 + 1.36356i) q^{4} +(0.0128801 - 0.0564316i) q^{5} +(1.43341 + 6.28018i) q^{6} +(1.40728 - 0.677709i) q^{7} +(-2.02596 - 1.61565i) q^{8} +(-3.16036 + 3.96297i) q^{9} +O(q^{10})$	\(q+(-2.21089 - 0.504621i) q^{2} +(-1.23248 - 2.55926i) q^{3} +(2.83146 + 1.36356i) q^{4} +(0.0128801 - 0.0564316i) q^{5} +(1.43341 + 6.28018i) q^{6} +(1.40728 - 0.677709i) q^{7} +(-2.02596 - 1.61565i) q^{8} +(-3.16036 + 3.96297i) q^{9} +(-0.0569531 + 0.118264i) q^{10} +(3.10613 - 2.47705i) q^{11} -8.92699i q^{12} +(-0.252504 - 0.316631i) q^{13} +(-3.45332 + 0.788198i) q^{14} +(-0.160298 + 0.0365869i) q^{15} +(-0.254963 - 0.319714i) q^{16} +5.16843i q^{17} +(8.98701 - 7.16690i) q^{18} +(-1.49728 + 3.10914i) q^{19} +(0.113417 - 0.142221i) q^{20} +(-3.46887 - 2.76633i) q^{21} +(-8.11728 + 3.90908i) q^{22} +(-0.0512209 - 0.224414i) q^{23} +(-1.63793 + 7.17623i) q^{24} +(4.50183 + 2.16797i) q^{25} +(0.398481 + 0.827455i) q^{26} +(5.72931 + 1.30768i) q^{27} +4.90874 q^{28} +(5.00751 - 1.98113i) q^{29} +0.372863 q^{30} +(-4.21005 - 0.960917i) q^{31} +(2.65101 + 5.50488i) q^{32} +(-10.1677 - 4.89649i) q^{33} +(2.60810 - 11.4268i) q^{34} +(-0.0201183 - 0.0881438i) q^{35} +(-14.3522 + 6.91164i) q^{36} +(-4.19898 - 3.34857i) q^{37} +(4.87927 - 6.11841i) q^{38} +(-0.499135 + 1.03647i) q^{39} +(-0.117269 + 0.0935185i) q^{40} +1.46294i q^{41} +(6.27335 + 7.86653i) q^{42} +(6.32061 - 1.44264i) q^{43} +(12.1725 - 2.77829i) q^{44} +(0.182931 + 0.229388i) q^{45} +0.522001i q^{46} +(-7.48524 + 5.96928i) q^{47} +(-0.503996 + 1.04656i) q^{48} +(-2.84329 + 3.56537i) q^{49} +(-8.85904 - 7.06485i) q^{50} +(13.2274 - 6.36997i) q^{51} +(-0.283211 - 1.24083i) q^{52} +(0.398044 - 1.74395i) q^{53} +(-12.0070 - 5.78226i) q^{54} +(-0.0997767 - 0.207188i) q^{55} +(-3.94604 - 0.900657i) q^{56} +9.80247 q^{57} +(-12.0708 + 1.85317i) q^{58} -1.05216 q^{59} +(-0.503764 - 0.114981i) q^{60} +(1.38382 + 2.87352i) q^{61} +(8.82307 + 4.24897i) q^{62} +(-1.76177 + 7.71880i) q^{63} +(-2.90123 - 12.7111i) q^{64} +(-0.0211203 + 0.0101710i) q^{65} +(20.0087 + 15.9564i) q^{66} +(-6.77893 + 8.50052i) q^{67} +(-7.04745 + 14.6342i) q^{68} +(-0.511205 + 0.407672i) q^{69} +0.205028i q^{70} +(-8.38773 - 10.5179i) q^{71} +(12.8056 - 2.92279i) q^{72} +(6.83974 - 1.56113i) q^{73} +(7.59372 + 9.52223i) q^{74} -14.1933i q^{75} +(-8.47898 + 6.76176i) q^{76} +(2.69246 - 5.59095i) q^{77} +(1.62656 - 2.03964i) q^{78} +(3.74078 + 2.98318i) q^{79} +(-0.0213259 + 0.0102700i) q^{80} +(-0.330785 - 1.44926i) q^{81} +(0.738232 - 3.23440i) q^{82} +(-7.58927 - 3.65480i) q^{83} +(-6.04990 - 12.5628i) q^{84} +(0.291662 + 0.0665701i) q^{85} -14.7022 q^{86} +(-11.2419 - 10.3738i) q^{87} -10.2950 q^{88} +(1.10427 + 0.252043i) q^{89} +(-0.288686 - 0.599462i) q^{90} +(-0.569927 - 0.274462i) q^{91} +(0.160971 - 0.705260i) q^{92} +(2.72955 + 11.9589i) q^{93} +(19.5613 - 9.42022i) q^{94} +(0.156168 + 0.124540i) q^{95} +(10.8211 - 13.5693i) q^{96} +(7.46850 - 15.5085i) q^{97} +(8.08536 - 6.44786i) q^{98} +20.1379i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 7 q^{2} - 7 q^{3} - q^{4} - q^{5} - 3 q^{6} - 11 q^{7} + 14 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 7 * q^2 - 7 * q^3 - q^4 - q^5 - 3 * q^6 - 11 * q^7 + 14 * q^8 - 3 * q^9	\( 12 q - 7 q^{2} - 7 q^{3} - q^{4} - q^{5} - 3 q^{6} - 11 q^{7} + 14 q^{8} - 3 q^{9} - 7 q^{10} + 7 q^{11} + 9 q^{13} - 7 q^{14} + 7 q^{15} + 9 q^{16} + 42 q^{18} - 7 q^{19} - 11 q^{20} - 7 q^{21} - 4 q^{22} - 5 q^{23} - 25 q^{24} + 13 q^{25} - 21 q^{26} - 7 q^{27} + 12 q^{28} - 15 q^{29} + 2 q^{30} - 21 q^{31} - 17 q^{33} - 13 q^{34} + 19 q^{35} - 40 q^{36} + 7 q^{37} + 28 q^{38} + 21 q^{39} + 35 q^{40} + 50 q^{42} + 7 q^{43} + 42 q^{44} + 16 q^{45} - 7 q^{47} - 14 q^{48} + 13 q^{49} - 28 q^{50} + 20 q^{51} - 6 q^{52} - 10 q^{53} - 38 q^{54} - 35 q^{55} - 21 q^{56} - 14 q^{57} - 57 q^{58} + 44 q^{59} - 28 q^{60} - 7 q^{61} + 37 q^{62} - 13 q^{63} - 26 q^{64} - 6 q^{65} + 21 q^{66} - 37 q^{67} + 14 q^{68} + 21 q^{69} - 21 q^{71} + 35 q^{72} + 14 q^{73} + 7 q^{76} - 7 q^{77} + 17 q^{78} + 49 q^{79} - 6 q^{80} + q^{81} + 22 q^{82} + 5 q^{83} + 21 q^{84} + 14 q^{85} - 44 q^{86} + 15 q^{87} - 66 q^{88} + 7 q^{89} + 28 q^{90} - 3 q^{91} - 6 q^{92} + 19 q^{93} + 66 q^{94} - 7 q^{95} + 30 q^{96} + 14 q^{97} - 42 q^{98}+O(q^{100}) \) 12 * q - 7 * q^2 - 7 * q^3 - q^4 - q^5 - 3 * q^6 - 11 * q^7 + 14 * q^8 - 3 * q^9 - 7 * q^10 + 7 * q^11 + 9 * q^13 - 7 * q^14 + 7 * q^15 + 9 * q^16 + 42 * q^18 - 7 * q^19 - 11 * q^20 - 7 * q^21 - 4 * q^22 - 5 * q^23 - 25 * q^24 + 13 * q^25 - 21 * q^26 - 7 * q^27 + 12 * q^28 - 15 * q^29 + 2 * q^30 - 21 * q^31 - 17 * q^33 - 13 * q^34 + 19 * q^35 - 40 * q^36 + 7 * q^37 + 28 * q^38 + 21 * q^39 + 35 * q^40 + 50 * q^42 + 7 * q^43 + 42 * q^44 + 16 * q^45 - 7 * q^47 - 14 * q^48 + 13 * q^49 - 28 * q^50 + 20 * q^51 - 6 * q^52 - 10 * q^53 - 38 * q^54 - 35 * q^55 - 21 * q^56 - 14 * q^57 - 57 * q^58 + 44 * q^59 - 28 * q^60 - 7 * q^61 + 37 * q^62 - 13 * q^63 - 26 * q^64 - 6 * q^65 + 21 * q^66 - 37 * q^67 + 14 * q^68 + 21 * q^69 - 21 * q^71 + 35 * q^72 + 14 * q^73 + 7 * q^76 - 7 * q^77 + 17 * q^78 + 49 * q^79 - 6 * q^80 + q^81 + 22 * q^82 + 5 * q^83 + 21 * q^84 + 14 * q^85 - 44 * q^86 + 15 * q^87 - 66 * q^88 + 7 * q^89 + 28 * q^90 - 3 * q^91 - 6 * q^92 + 19 * q^93 + 66 * q^94 - 7 * q^95 + 30 * q^96 + 14 * q^97 - 42 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{14}\right)$

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 $

$2$	−2.21089	−	0.504621i	−1.56334	−	0.356821i	−0.648682	−	0.761060i	$-0.724679\pi$
$2$	−2.21089	−	0.504621i	−1.56334	−	0.356821i	−0.914654	+	0.404239i	$0.867537\pi$
$3$	−1.23248	−	2.55926i	−0.711571	−	1.47759i	−0.871465	−	0.490457i	$-0.836830\pi$
$3$	−1.23248	−	2.55926i	−0.711571	−	1.47759i	0.159895	−	0.987134i	$-0.448885\pi$
$4$	2.83146	+	1.36356i	1.41573	+	0.681779i
$5$	0.0128801	−	0.0564316i	0.00576017	−	0.0252370i	−0.971966	−	0.235121i	$-0.924451\pi$
$5$	0.0128801	−	0.0564316i	0.00576017	−	0.0252370i	0.977726	+	0.209884i	$0.0673086\pi$
$6$	1.43341	+	6.28018i	0.585188	+	2.56387i
$7$	1.40728	−	0.677709i	0.531901	−	0.256150i	−0.148600	−	0.988897i	$-0.547477\pi$
$7$	1.40728	−	0.677709i	0.531901	−	0.256150i	0.680501	+	0.732747i	$0.261762\pi$
$8$	−2.02596	−	1.61565i	−0.716287	−	0.571220i
$9$	−3.16036	+	3.96297i	−1.05345	+	1.32099i
$10$	−0.0569531	+	0.118264i	−0.0180102	+	0.0373985i
$11$	3.10613	−	2.47705i	0.936533	−	0.746860i	−0.0310229	−	0.999519i	$-0.509876\pi$
$11$	3.10613	−	2.47705i	0.936533	−	0.746860i	0.967555	+	0.252659i	$0.0813051\pi$
$12$		−	8.92699i		−	2.57700i
$13$	−0.252504	−	0.316631i	−0.0700321	−	0.0878175i	0.745581	−	0.666415i	$-0.232172\pi$
$13$	−0.252504	−	0.316631i	−0.0700321	−	0.0878175i	−0.815614	+	0.578597i	$0.803600\pi$
$14$	−3.45332	+	0.788198i	−0.922939	+	0.210655i
$15$	−0.160298	+	0.0365869i	−0.0413887	+	0.00944670i
$16$	−0.254963	−	0.319714i	−0.0637408	−	0.0799285i
$17$			5.16843i			1.25353i	0.779209	+	0.626764i	$0.215621\pi$
$17$			5.16843i			1.25353i	−0.779209	+	0.626764i	$0.784379\pi$
$18$	8.98701	−	7.16690i	2.11826	−	1.68926i
$19$	−1.49728	+	3.10914i	−0.343500	+	0.713286i	−0.999126	−	0.0418005i	$-0.986691\pi$
$19$	−1.49728	+	3.10914i	−0.343500	+	0.713286i	0.655626	+	0.755086i	$0.272405\pi$
$20$	0.113417	−	0.142221i	0.0253609	−	0.0318015i
$21$	−3.46887	−	2.76633i	−0.756970	−	0.603663i
$22$	−8.11728	+	3.90908i	−1.73061	+	0.833418i
$23$	−0.0512209	−	0.224414i	−0.0106803	−	0.0467935i	0.969307	−	0.245854i	$-0.0790682\pi$
$23$	−0.0512209	−	0.224414i	−0.0106803	−	0.0467935i	−0.979987	+	0.199060i	$0.936211\pi$
$24$	−1.63793	+	7.17623i	−0.334341	+	1.46484i
$25$	4.50183	+	2.16797i	0.900365	+	0.433593i
$26$	0.398481	+	0.827455i	0.0781486	+	0.162277i
$27$	5.72931	+	1.30768i	1.10261	+	0.251663i
$28$	4.90874			0.927664
$29$	5.00751	−	1.98113i	0.929870	−	0.367887i
$29$	5.00751	−	1.98113i	0.929870	−	0.367887i
$30$	0.372863			0.0680752
$31$	−4.21005	−	0.960917i	−0.756148	−	0.172586i	−0.172967	−	0.984928i	$-0.555335\pi$
$31$	−4.21005	−	0.960917i	−0.756148	−	0.172586i	−0.583182	+	0.812342i	$0.698192\pi$
$32$	2.65101	+	5.50488i	0.468637	+	0.973135i
$33$	−10.1677	−	4.89649i	−1.76996	−	0.852369i
$34$	2.60810	−	11.4268i	0.447285	−	1.95968i
$35$	−0.0201183	−	0.0881438i	−0.00340061	−	0.0148990i
$36$	−14.3522	+	6.91164i	−2.39203	+	1.15194i
$37$	−4.19898	−	3.34857i	−0.690308	−	0.550502i	0.214289	−	0.976770i	$-0.431257\pi$
$37$	−4.19898	−	3.34857i	−0.690308	−	0.550502i	−0.904597	+	0.426268i	$0.859828\pi$
$38$	4.87927	−	6.11841i	0.791521	−	0.992536i
$39$	−0.499135	+	1.03647i	−0.0799256	+	0.165967i
$40$	−0.117269	+	0.0935185i	−0.0185418	+	0.0147866i
$41$			1.46294i			0.228473i	0.993454	+	0.114237i	$0.0364422\pi$
$41$			1.46294i			0.228473i	−0.993454	+	0.114237i	$0.963558\pi$
$42$	6.27335	+	7.86653i	0.967998	+	1.21383i
$43$	6.32061	−	1.44264i	0.963884	−	0.220000i	0.288511	−	0.957477i	$-0.406840\pi$
$43$	6.32061	−	1.44264i	0.963884	−	0.220000i	0.675373	+	0.737476i	$0.263983\pi$
$44$	12.1725	−	2.77829i	1.83507	−	0.418842i
$45$	0.182931	+	0.229388i	0.0272697	+	0.0341951i
$46$			0.522001i			0.0769648i
$47$	−7.48524	+	5.96928i	−1.09184	+	0.870709i	−0.992242	−	0.124319i	$-0.960325\pi$
$47$	−7.48524	+	5.96928i	−1.09184	+	0.870709i	−0.0995928	+	0.995028i	$0.531754\pi$
$48$	−0.503996	+	1.04656i	−0.0727455	+	0.151058i
$49$	−2.84329	+	3.56537i	−0.406184	+	0.509339i
$50$	−8.85904	−	7.06485i	−1.25286	−	0.999121i
$51$	13.2274	−	6.36997i	1.85220	−	0.891974i
$52$	−0.283211	−	1.24083i	−0.0392743	−	0.172072i
$53$	0.398044	−	1.74395i	0.0546756	−	0.239549i	−0.940205	−	0.340610i	$-0.889366\pi$
$53$	0.398044	−	1.74395i	0.0546756	−	0.239549i	0.994880	+	0.101061i	$0.0322236\pi$
$54$	−12.0070	−	5.78226i	−1.63394	−	0.786866i
$55$	−0.0997767	−	0.207188i	−0.0134539	−	0.0279373i
$56$	−3.94604	−	0.900657i	−0.527311	−	0.120355i
$57$	9.80247			1.29837
$58$	−12.0708	+	1.85317i	−1.58497	+	0.243333i
$59$	−1.05216			−0.136980			−0.0684900	−	0.997652i	$-0.521818\pi$
$59$	−1.05216			−0.136980			−0.0684900	+	0.997652i	$0.521818\pi$
$60$	−0.503764	−	0.114981i	−0.0650357	−	0.0148440i
$61$	1.38382	+	2.87352i	0.177179	+	0.367917i	0.970578	−	0.240785i	$-0.0774049\pi$
$61$	1.38382	+	2.87352i	0.177179	+	0.367917i	−0.793399	+	0.608702i	$0.791691\pi$
$62$	8.82307	+	4.24897i	1.12053	+	0.539619i
$63$	−1.76177	+	7.71880i	−0.221962	+	0.972478i
$64$	−2.90123	−	12.7111i	−0.362653	−	1.58889i
$65$	−0.0211203	+	0.0101710i	−0.00261964	+	0.00126155i
$66$	20.0087	+	15.9564i	2.46290	+	1.96410i
$67$	−6.77893	+	8.50052i	−0.828179	+	1.03850i	0.170409	+	0.985373i	$0.445491\pi$
$67$	−6.77893	+	8.50052i	−0.828179	+	1.03850i	−0.998588	+	0.0531298i	$0.983080\pi$
$68$	−7.04745	+	14.6342i	−0.854628	+	1.77465i
$69$	−0.511205	+	0.407672i	−0.0615418	+	0.0490780i
$70$			0.205028i			0.0245056i
$71$	−8.38773	−	10.5179i	−0.995440	−	1.24824i	−0.968606	−	0.248603i	$-0.920029\pi$
$71$	−8.38773	−	10.5179i	−0.995440	−	1.24824i	−0.0268346	−	0.999640i	$-0.508543\pi$
$72$	12.8056	−	2.92279i	1.50915	−	0.344454i
$73$	6.83974	−	1.56113i	0.800531	−	0.182716i	0.197363	−	0.980330i	$-0.436762\pi$
$73$	6.83974	−	1.56113i	0.800531	−	0.182716i	0.603167	+	0.797615i	$0.293905\pi$
$74$	7.59372	+	9.52223i	0.882752	+	1.10694i
$75$		−	14.1933i		−	1.63890i
$76$	−8.47898	+	6.76176i	−0.972605	+	0.775627i
$77$	2.69246	−	5.59095i	0.306834	−	0.637148i
$78$	1.62656	−	2.03964i	0.184171	−	0.230943i
$79$	3.74078	+	2.98318i	0.420871	+	0.335634i	0.810916	−	0.585162i	$-0.198969\pi$
$79$	3.74078	+	2.98318i	0.420871	+	0.335634i	−0.390045	+	0.920796i	$0.627541\pi$
$80$	−0.0213259	+	0.0102700i	−0.00238431	+	0.00114822i
$81$	−0.330785	−	1.44926i	−0.0367539	−	0.161029i
$82$	0.738232	−	3.23440i	0.0815241	−	0.357180i
$83$	−7.58927	−	3.65480i	−0.833030	−	0.401166i	−0.0317796	−	0.999495i	$-0.510117\pi$
$83$	−7.58927	−	3.65480i	−0.833030	−	0.401166i	−0.801251	+	0.598329i	$0.795832\pi$
$84$	−6.04990	−	12.5628i	−0.660099	−	1.37071i
$85$	0.291662	+	0.0665701i	0.0316352	+	0.00722054i
$86$	−14.7022			−1.58537
$87$	−11.2419	−	10.3738i	−1.20526	−	1.11219i
$88$	−10.2950			−1.09745
$89$	1.10427	+	0.252043i	0.117053	+	0.0267165i	0.280646	−	0.959811i	$-0.409451\pi$
$89$	1.10427	+	0.252043i	0.117053	+	0.0267165i	−0.163593	+	0.986528i	$0.552308\pi$
$90$	−0.288686	−	0.599462i	−0.0304301	−	0.0631888i
$91$	−0.569927	−	0.274462i	−0.0597446	−	0.0287715i
$92$	0.160971	−	0.705260i	0.0167824	−	0.0735284i
$93$	2.72955	+	11.9589i	0.283041	+	1.24009i
$94$	19.5613	−	9.42022i	2.01759	−	0.971621i
$95$	0.156168	+	0.124540i	0.0160225	+	0.0127775i
$96$	10.8211	−	13.5693i	1.10443	−	1.38491i
$97$	7.46850	−	15.5085i	0.758311	−	1.57465i	−0.0588689	−	0.998266i	$-0.518749\pi$
$97$	7.46850	−	15.5085i	0.758311	−	1.57465i	0.817180	−	0.576383i	$-0.195536\pi$
$98$	8.08536	−	6.44786i	0.816745	−	0.651332i
$99$			20.1379i			2.02393i
$100$	9.79057	+	12.2770i	0.979057	+	1.22770i
$101$	−6.08315	+	1.38844i	−0.605296	+	0.138155i	−0.514175	−	0.857685i	$-0.671902\pi$
$101$	−6.08315	+	1.38844i	−0.605296	+	0.138155i	−0.0911203	+	0.995840i	$0.529045\pi$
$102$	−32.4587	+	7.40848i	−3.21389	+	0.733549i
$103$	8.23659	+	10.3284i	0.811576	+	1.01768i	0.999371	+	0.0354755i	$0.0112946\pi$
$103$	8.23659	+	10.3284i	0.811576	+	1.01768i	−0.187795	+	0.982208i	$0.560134\pi$
$104$			1.04944i			0.102906i
$105$	−0.200788	+	0.160123i	−0.0195949	+	0.0156264i
$106$	−1.76006	+	3.65481i	−0.170953	+	0.354987i
$107$	5.77864	−	7.24619i	0.558642	−	0.700516i	−0.419664	−	0.907680i	$-0.637852\pi$
$107$	5.77864	−	7.24619i	0.558642	−	0.700516i	0.978306	+	0.207164i	$0.0664234\pi$
$108$	14.4392	+	11.5149i	1.38941	+	1.10802i
$109$	−5.18545	+	2.49718i	−0.496676	+	0.239187i	−0.665414	−	0.746474i	$-0.731745\pi$
$109$	−5.18545	+	2.49718i	−0.496676	+	0.239187i	0.168738	+	0.985661i	$0.446031\pi$
$110$	0.116044	+	0.508420i	0.0110643	+	0.0484760i
$111$	−3.39474	+	14.8733i	−0.322215	+	1.41171i
$112$	−0.575477	−	0.277135i	−0.0543775	−	0.0261868i
$113$	3.49809	+	7.26385i	0.329072	+	0.683326i	0.998210	−	0.0598131i	$-0.0190505\pi$
$113$	3.49809	+	7.26385i	0.329072	+	0.683326i	−0.669137	+	0.743139i	$0.733336\pi$
$114$	−21.6722	−	4.94654i	−2.02979	−	0.463286i
$115$	−0.0133237			−0.00124245
$116$	16.8799	+	1.21853i	1.56726	+	0.113138i
$117$	2.05280			0.189782
$118$	2.32622	+	0.530944i	0.214146	+	0.0488774i
$119$	3.50269	+	7.27341i	0.321091	+	0.666753i
$120$	0.383869	+	0.184862i	0.0350423	+	0.0168755i
$121$	1.06450	−	4.66388i	0.0967727	−	0.423989i
$122$	−1.60942	−	7.05135i	−0.145710	−	0.638399i
$123$	3.74405	−	1.80304i	0.337590	−	0.162575i
$124$	−10.6103	−	8.46144i	−0.952834	−	0.759860i
$125$	0.360772	−	0.452394i	0.0322685	−	0.0404634i
$126$	7.79014	−	16.1764i	0.694001	−	1.44111i
$127$	−13.7396	+	10.9570i	−1.21920	+	0.972277i	−0.999994	−	0.00340252i	$-0.998917\pi$
$127$	−13.7396	+	10.9570i	−1.21920	+	0.972277i	−0.219202	+	0.975679i	$0.570346\pi$
$128$			17.3469i			1.53327i
$129$	−11.4821	−	14.3981i	−1.01094	−	1.26768i
$130$	0.0518270	−	0.0118292i	0.00454553	−	0.00103749i
$131$	−3.26398	+	0.744983i	−0.285176	+	0.0650895i	−0.362716	−	0.931900i	$-0.618150\pi$
$131$	−3.26398	+	0.744983i	−0.285176	+	0.0650895i	0.0775403	+	0.996989i	$0.475293\pi$
$132$	−22.1126	−	27.7284i	−1.92466	−	2.41345i
$133$			5.39014i			0.467385i
$134$	19.2770	−	15.3729i	1.66528	−	1.32802i
$135$	0.147589	−	0.306471i	0.0127024	−	0.0263768i
$136$	8.35039	−	10.4711i	0.716040	−	0.897885i
$137$	−4.31618	−	3.44204i	−0.368756	−	0.294073i	0.421526	−	0.906816i	$-0.361495\pi$
$137$	−4.31618	−	3.44204i	−0.368756	−	0.294073i	−0.790282	+	0.612743i	$0.790066\pi$
$138$	1.33594	−	0.643354i	0.113723	−	0.0547659i
$139$	0.132958	+	0.582528i	0.0112774	+	0.0494094i	0.980254	−	0.197745i	$-0.0633617\pi$
$139$	0.132958	+	0.582528i	0.0112774	+	0.0494094i	−0.968976	+	0.247154i	$0.920505\pi$
$140$	0.0632252	−	0.277008i	0.00534351	−	0.0234114i
$141$	24.5024	+	11.7997i	2.06347	+	0.993715i
$142$	13.2368	+	27.4865i	1.11081	+	2.30662i
$143$	−1.56862	−	0.358028i	−0.131175	−	0.0299398i
$144$	2.07279			0.172733
$145$	−0.0473010	−	0.308099i	−0.00392814	−	0.0255862i
$146$	−15.9097			−1.31669
$147$	12.6290	+	2.88249i	1.04162	+	0.237744i
$148$	−7.32325	−	15.2069i	−0.601968	−	1.25000i
$149$	4.60312	+	2.21675i	0.377102	+	0.181603i	0.612827	−	0.790217i	$-0.290032\pi$
$149$	4.60312	+	2.21675i	0.377102	+	0.181603i	−0.235725	+	0.971820i	$0.575746\pi$
$150$	−7.16225	+	31.3799i	−0.584796	+	2.56216i
$151$	−1.73572	−	7.60469i	−0.141251	−	0.618861i	−0.995145	−	0.0984149i	$-0.968623\pi$
$151$	−1.73572	−	7.60469i	−0.141251	−	0.618861i	0.853894	−	0.520446i	$-0.174234\pi$
$152$	8.05673	−	3.87992i	0.653487	−	0.314703i
$153$	−20.4823	−	16.3341i	−1.65590	−	1.32053i
$154$	−8.77405	+	11.0023i	−0.707033	+	0.886591i
$155$	−0.108452	+	0.225203i	−0.00871109	+	0.0180888i
$156$	−2.82656	+	2.25411i	−0.226306	+	0.180473i
$157$		−	18.8577i		−	1.50501i	−0.658588	−	0.752504i	$-0.728846\pi$
$157$		−	18.8577i		−	1.50501i	0.658588	−	0.752504i	$-0.271154\pi$
$158$	−6.76509	−	8.48315i	−0.538202	−	0.674884i
$159$	−4.95380	+	1.13067i	−0.392862	+	0.0896681i
$160$	0.344795	−	0.0786971i	0.0272584	−	0.00622155i
$161$	−0.224169	−	0.281099i	−0.0176670	−	0.0221537i
$162$			3.37109i			0.264858i
$163$	−1.76850	+	1.41033i	−0.138520	+	0.110466i	−0.690298	−	0.723525i	$-0.742521\pi$
$163$	−1.76850	+	1.41033i	−0.138520	+	0.110466i	0.551779	+	0.833991i	$0.313949\pi$
$164$	−1.99481	+	4.14226i	−0.155768	+	0.323456i
$165$	−0.407277	+	0.510710i	−0.0317065	+	0.0397587i
$166$	14.9347	+	11.9101i	1.15916	+	0.924400i
$167$	10.5728	−	5.09159i	0.818147	−	0.393999i	0.0224905	−	0.999747i	$-0.492840\pi$
$167$	10.5728	−	5.09159i	0.818147	−	0.393999i	0.795656	+	0.605748i	$0.207126\pi$
$168$	2.55838	+	11.2090i	0.197383	+	0.864792i
$169$	2.85628	−	12.5142i	0.219714	−	0.962628i
$170$	−0.611241	−	0.294358i	−0.0468801	−	0.0225762i
$171$	−7.58947	−	15.7597i	−0.580381	−	1.20517i
$172$	19.8636	+	4.53375i	1.51459	+	0.345695i
$173$	−19.2889			−1.46651			−0.733254	−	0.679954i	$-0.762000\pi$
$173$	−19.2889			−1.46651			−0.733254	+	0.679954i	$0.762000\pi$
$174$	19.6197	+	28.6083i	1.48737	+	2.16879i
$175$	7.80457			0.589970
$176$	−1.58390	−	0.361514i	−0.119391	−	0.0272501i
$177$	1.29677	+	2.69276i	0.0974710	+	0.202401i
$178$	−2.31424	−	1.11448i	−0.173460	−	0.0835337i
$179$	0.202580	−	0.887562i	0.0151416	−	0.0663395i	−0.966793	−	0.255562i	$-0.917740\pi$
$179$	0.202580	−	0.887562i	0.0151416	−	0.0663395i	0.981934	+	0.189222i	$0.0605967\pi$
$180$	0.205177	+	0.898938i	0.0152930	+	0.0670029i
$181$	−4.74107	+	2.28318i	−0.352401	+	0.169707i	−0.601706	−	0.798718i	$-0.705512\pi$
$181$	−4.74107	+	2.28318i	−0.352401	+	0.169707i	0.249305	+	0.968425i	$0.419798\pi$
$182$	1.12155	+	0.894404i	0.0831346	+	0.0662976i
$183$	5.64858	−	7.08310i	0.417555	−	0.523598i
$184$	−0.258803	+	0.537409i	−0.0190792	+	0.0396183i
$185$	−0.243049	+	0.193825i	−0.0178693	+	0.0142503i
$186$		−	27.8173i		−	2.03966i
$187$	12.8025	+	16.0538i	0.936210	+	1.17397i
$188$	−29.3336	+	6.69520i	−2.13937	+	0.488298i
$189$	8.94895	−	2.04254i	0.650940	−	0.148573i
$190$	−0.282426	−	0.354150i	−0.0204893	−	0.0256928i
$191$		−	10.3088i		−	0.745920i	−0.927847	−	0.372960i	$-0.878343\pi$
$191$		−	10.3088i		−	0.745920i	0.927847	−	0.372960i	$-0.121657\pi$
$192$	−28.9554	+	23.0911i	−2.08967	+	1.66646i
$193$	−1.17581	+	2.44160i	−0.0846368	+	0.175750i	−0.938992	−	0.343940i	$-0.888238\pi$
$193$	−1.17581	+	2.44160i	−0.0846368	+	0.175750i	0.854355	+	0.519690i	$0.173953\pi$
$194$	−24.3379	+	30.5188i	−1.74736	+	2.19112i
$195$	0.0520604	+	0.0415168i	0.00372812	+	0.00297308i
$196$	−12.9122	+	6.21820i	−0.922302	+	0.444157i
$197$	3.28855	+	14.4081i	0.234300	+	1.02653i	0.946030	+	0.324080i	$0.105055\pi$
$197$	3.28855	+	14.4081i	0.234300	+	1.02653i	−0.711730	+	0.702453i	$0.752088\pi$
$198$	10.1620	−	44.5226i	0.722182	−	3.16409i
$199$	−13.5173	−	6.50959i	−0.958216	−	0.461453i	−0.111657	−	0.993747i	$-0.535616\pi$
$199$	−13.5173	−	6.50959i	−0.958216	−	0.461453i	−0.846560	+	0.532294i	$0.821330\pi$
$200$	−5.61786	−	11.6656i	−0.397243	−	0.824883i
$201$	30.1099	+	6.87240i	2.12379	+	0.484741i
$202$	14.1498			0.995577
$203$	5.70432	−	6.18163i	0.400365	−	0.433866i
$204$	46.1385			3.23034
$205$	0.0825561	+	0.0188429i	0.00576597	+	0.00131604i
$206$	−12.9983	−	26.9912i	−0.905634	−	1.88057i
$207$	1.05122	+	0.506241i	0.0730649	+	0.0351862i
$208$	−0.0368518	+	0.161458i	−0.00255521	+	0.0111951i
$209$	3.05076	+	13.3662i	0.211025	+	0.924562i
$210$	0.524722	−	0.252693i	0.0362093	−	0.0174375i
$211$	9.36088	+	7.46505i	0.644430	+	0.513916i	0.890293	−	0.455389i	$-0.150500\pi$
$211$	9.36088	+	7.46505i	0.644430	+	0.513916i	−0.245863	+	0.969305i	$0.579071\pi$
$212$	3.50501	−	4.39515i	0.240725	−	0.301860i
$213$	−16.5803	+	34.4294i	−1.13607	+	2.35907i
$214$	−16.4325	+	13.1045i	−1.12330	+	0.895805i
$215$		−	0.375263i		−	0.0255927i
$216$	−9.49462	−	11.9059i	−0.646027	−	0.810093i
$217$	−6.57594	+	1.50091i	−0.446404	+	0.101889i
$218$	12.7246	−	2.90430i	0.861818	−	0.196704i
$219$	−12.4251	−	15.5806i	−0.839613	−	1.05284i
$220$		−	0.722696i		−	0.0487241i
$221$	1.63648	−	1.30505i	0.110082	−	0.0877872i
$222$	15.0108	−	31.1703i	1.00746	−	2.09201i
$223$	8.33685	−	10.4541i	0.558277	−	0.700057i	−0.419962	−	0.907542i	$-0.637956\pi$
$223$	8.33685	−	10.4541i	0.558277	−	0.700057i	0.978238	+	0.207485i	$0.0665279\pi$
$224$	7.46142	+	5.95028i	0.498537	+	0.397570i
$225$	−22.8190	+	10.9890i	−1.52127	+	0.732603i
$226$	−4.06839	−	17.8248i	−0.270625	−	1.18569i
$227$	0.472258	−	2.06910i	0.0313448	−	0.137331i	−0.956834	−	0.290634i	$-0.906134\pi$
$227$	0.472258	−	2.06910i	0.0313448	−	0.137331i	0.988179	+	0.153303i	$0.0489910\pi$
$228$	27.7553	+	13.3662i	1.83814	+	0.885200i
$229$	−11.8839	−	24.6772i	−0.785312	−	1.63072i	−0.775978	−	0.630760i	$-0.782743\pi$
$229$	−11.8839	−	24.6772i	−0.785312	−	1.63072i	−0.00933352	−	0.999956i	$-0.502971\pi$
$230$	0.0294573	+	0.00672344i	0.00194236	+	0.000443331i
$231$	−17.6271			−1.15978
$232$	−13.3459	−	4.07669i	−0.876198	−	0.267648i
$233$	17.4774			1.14498			0.572492	−	0.819910i	$-0.305977\pi$
$233$	17.4774			1.14498			0.572492	+	0.819910i	$0.305977\pi$
$234$	−4.53852	−	1.03589i	−0.296692	−	0.0677181i
$235$	0.240445	+	0.499289i	0.0156849	+	0.0325700i
$236$	−2.97915	−	1.43468i	−0.193926	−	0.0933900i
$237$	3.02431	−	13.2503i	0.196450	−	0.860703i
$238$	−4.07375	−	17.8482i	−0.264062	−	1.15693i
$239$	−15.5439	+	7.48555i	−1.00545	+	0.484200i	−0.862785	−	0.505571i	$-0.831282\pi$
$239$	−15.5439	+	7.48555i	−1.00545	+	0.484200i	−0.142667	+	0.989771i	$0.545568\pi$
$240$	0.0525674	+	0.0419211i	0.00339321	+	0.00270599i
$241$	−13.7085	+	17.1899i	−0.883040	+	1.10730i	0.110507	+	0.993875i	$0.464753\pi$
$241$	−13.7085	+	17.1899i	−0.883040	+	1.10730i	−0.993547	+	0.113422i	$0.963819\pi$
$242$	−4.70698	+	9.77415i	−0.302576	+	0.628306i
$243$	10.4823	−	8.35934i	0.672439	−	0.536252i
$244$			10.0232i			0.641667i
$245$	0.164578	+	0.206374i	0.0105145	+	0.0131847i
$246$	−9.18755	+	2.09700i	−0.585777	+	0.133700i
$247$	1.36252	−	0.310986i	0.0866950	−	0.0197876i
$248$	6.97691	+	8.74877i	0.443034	+	0.555548i
$249$			23.9274i			1.51634i
$250$	−1.02592	+	0.818141i	−0.0648846	+	0.0517438i
$251$	−4.23936	+	8.80311i	−0.267586	+	0.555648i	−0.990857	−	0.134917i	$-0.956923\pi$
$251$	−4.23936	+	8.80311i	−0.267586	+	0.555648i	0.723271	+	0.690564i	$0.242638\pi$
$252$	−15.5134	+	19.4532i	−0.977252	+	1.22544i
$253$	−0.714983	−	0.570180i	−0.0449506	−	0.0358469i
$254$	35.9060	−	17.2914i	2.25294	−	1.08496i
$255$	−0.189097	−	0.828487i	−0.0118417	−	0.0518819i
$256$	2.95119	−	12.9300i	0.184449	−	0.808124i
$257$	13.8769	+	6.68278i	0.865620	+	0.416861i	0.813352	−	0.581772i	$-0.197641\pi$
$257$	13.8769	+	6.68278i	0.865620	+	0.416861i	0.0522684	+	0.998633i	$0.483355\pi$
$258$	18.1201	+	37.6267i	1.12811	+	2.34254i
$259$	−8.17849	−	1.86669i	−0.508187	−	0.115990i
$260$	−0.0736698			−0.00456880
$261$	−7.97437	+	26.1057i	−0.493601	+	1.61590i
$262$	7.59225			0.469050
$263$	30.2162	+	6.89666i	1.86321	+	0.425266i	0.997202	−	0.0747599i	$-0.0238190\pi$
$263$	30.2162	+	6.89666i	1.86321	+	0.425266i	0.866010	+	0.500026i	$0.166676\pi$
$264$	12.6883	+	26.3475i	0.780911	+	1.62158i
$265$	−0.0932867	−	0.0449245i	−0.00573056	−	0.00275969i
$266$	2.71998	−	11.9170i	0.166773	−	0.730679i
$267$	−0.715945	−	3.13676i	−0.0438151	−	0.191967i
$268$	−30.7852	+	14.8254i	−1.88050	+	0.905603i
$269$	10.8322	+	8.63841i	0.660453	+	0.526693i	0.895371	−	0.445322i	$-0.146911\pi$
$269$	10.8322	+	8.63841i	0.660453	+	0.526693i	−0.234918	+	0.972015i	$0.575482\pi$
$270$	−0.480954	+	0.603097i	−0.0292699	+	0.0367033i
$271$	11.6447	−	24.1804i	0.707362	−	1.46885i	−0.168203	−	0.985752i	$-0.553796\pi$
$271$	11.6447	−	24.1804i	0.707362	−	1.46885i	0.875565	−	0.483100i	$-0.160489\pi$
$272$	1.65242	−	1.31776i	0.100193	−	0.0799009i
$273$			1.79686i			0.108751i
$274$	7.80567	+	9.78800i	0.471558	+	0.591315i
$275$	19.3534	−	4.41729i	1.16705	−	0.266373i
$276$	−2.00334	+	0.457249i	−0.120587	+	0.0275232i
$277$	−14.0636	−	17.6352i	−0.845002	−	1.05960i	−0.997456	−	0.0712885i	$-0.977289\pi$
$277$	−14.0636	−	17.6352i	−0.845002	−	1.05960i	0.152454	−	0.988311i	$-0.451283\pi$
$278$		−	1.35500i		−	0.0812675i
$279$	17.1134	−	13.6475i	1.02455	−	0.817053i
$280$	−0.101651	+	0.211080i	−0.00607481	+	0.0126145i
$281$	−2.05756	+	2.58010i	−0.122744	+	0.153916i	−0.839406	−	0.543504i	$-0.817097\pi$
$281$	−2.05756	+	2.58010i	−0.122744	+	0.153916i	0.716663	+	0.697420i	$0.245669\pi$
$282$	−48.2176	−	38.4523i	−2.87132	−	2.28980i
$283$	−15.9189	+	7.66611i	−0.946277	+	0.455703i	−0.842380	−	0.538885i	$-0.818846\pi$
$283$	−15.9189	+	7.66611i	−0.946277	+	0.455703i	−0.103898	+	0.994588i	$0.533132\pi$
$284$	−9.40775	−	41.2180i	−0.558247	−	2.44584i
$285$	0.126257	−	0.553169i	0.00747883	−	0.0327669i
$286$	3.28738	+	1.58312i	0.194387	+	0.0936118i
$287$	0.991449	+	2.05877i	0.0585234	+	0.121525i
$288$	−30.1938	−	6.89155i	−1.77919	−	0.406088i
$289$	−9.71265			−0.571332
$290$	−0.0508957	+	0.705041i	−0.00298870	+	0.0414015i
$291$	−48.8951			−2.86628
$292$	21.4951	+	4.90611i	1.25790	+	0.287109i
$293$	−5.87226	−	12.1939i	−0.343061	−	0.712374i	0.656042	−	0.754725i	$-0.272230\pi$
$293$	−5.87226	−	12.1939i	−0.343061	−	0.712374i	−0.999103	+	0.0423508i	$0.986515\pi$
$294$	−26.4668	−	12.7457i	−1.54357	−	0.743346i
$295$	−0.0135520	+	0.0593752i	−0.000789028	+	0.00345696i
$296$	3.09685	+	13.5682i	0.180001	+	0.788635i
$297$	21.0351	−	10.1300i	1.22058	−	0.587802i
$298$	−9.05838	−	7.22382i	−0.524738	−	0.418464i
$299$	−0.0581227	+	0.0728835i	−0.00336132	+	0.00421496i
$300$	19.3534	−	40.1878i	1.11737	−	2.32024i
$301$	7.91716	−	6.31373i	0.456338	−	0.363917i
$302$			17.6890i			1.01789i
$303$	11.0507	+	13.8572i	0.634847	+	0.796073i
$304$	1.37579	−	0.314014i	0.0789068	−	0.0180100i
$305$	0.179981	−	0.0410795i	0.0103057	−	0.00235221i
$306$	37.0416	+	46.4487i	2.11753	+	2.65530i
$307$			6.51865i			0.372039i	0.982546	+	0.186020i	$0.0595588\pi$
$307$			6.51865i			0.372039i	−0.982546	+	0.186020i	$0.940441\pi$
$308$	15.2472	−	12.1592i	0.868788	−	0.692835i
$309$	16.2816	−	33.8091i	0.926227	−	1.92333i
$310$	0.353418	−	0.443172i	0.0200728	−	0.0251705i
$311$	19.1908	+	15.3042i	1.08821	+	0.867820i	0.991835	−	0.127525i	$-0.0407034\pi$
$311$	19.1908	+	15.3042i	1.08821	+	0.867820i	0.0963761	+	0.995345i	$0.469275\pi$
$312$	2.68580	−	1.29341i	0.152053	−	0.0732251i
$313$	−0.439360	−	1.92496i	−0.0248341	−	0.108805i	0.960992	−	0.276577i	$-0.0892001\pi$
$313$	−0.439360	−	1.92496i	−0.0248341	−	0.108805i	−0.985826	+	0.167772i	$0.946343\pi$
$314$	−9.51599	+	41.6923i	−0.537019	+	2.35283i
$315$	0.412892	+	0.198838i	0.0232638	+	0.0112033i
$316$	6.52413	+	13.5475i	0.367011	+	0.762107i
$317$	−28.9366	−	6.60459i	−1.62524	−	0.370951i	−0.689680	−	0.724114i	$-0.742249\pi$
$317$	−28.9366	−	6.60459i	−1.62524	−	0.370951i	−0.935562	+	0.353163i	$0.885106\pi$
$318$	11.5229			0.646170
$319$	10.6466	−	18.5575i	0.596094	−	1.03902i
$320$	−0.754675			−0.0421876
$321$	−25.6669	−	5.85831i	−1.43259	−	0.326979i
$322$	0.353765	+	0.734600i	0.0197145	+	0.0409377i
$323$	−16.0694	−	7.73860i	−0.894123	−	0.430587i
$324$	1.03955	−	4.55457i	0.0577529	−	0.253032i
$325$	−0.450287	−	1.97284i	−0.0249774	−	0.109433i
$326$	4.62165	−	2.22567i	0.255969	−	0.123268i
$327$	12.7819	+	10.1932i	0.706840	+	0.563686i
$328$	2.36361	−	2.96387i	0.130508	−	0.163652i
$329$	−6.48838	+	13.4733i	−0.357716	+	0.742805i
$330$	1.15816	−	0.923602i	0.0637546	−	0.0508426i
$331$			28.3740i			1.55958i	0.626044	+	0.779788i	$0.284673\pi$
$331$			28.3740i			1.55958i	−0.626044	+	0.779788i	$0.715327\pi$
$332$	−16.5051	−	20.6968i	−0.905838	−	1.13588i
$333$	26.5406	−	6.05772i	1.45442	−	0.331961i
$334$	−25.9446	+	5.92168i	−1.41963	+	0.324020i
$335$	0.392384	+	0.492034i	0.0214382	+	0.0268827i
$336$			1.81436i			0.0989814i
$337$	−3.14082	+	2.50472i	−0.171091	+	0.136441i	−0.705292	−	0.708917i	$-0.749184\pi$
$337$	−3.14082	+	2.50472i	−0.171091	+	0.136441i	0.534201	+	0.845358i	$0.320613\pi$
$338$	−12.6298	+	26.2261i	−0.686972	+	1.42651i
$339$	14.2788	−	17.9051i	0.775518	−	0.972469i
$340$	0.735057	+	0.586189i	0.0398641	+	0.0317905i
$341$	−15.4572	+	7.44380i	−0.837055	+	0.403104i
$342$	8.82681	+	38.6728i	0.477299	+	2.09118i
$343$	−4.01799	+	17.6040i	−0.216951	+	0.950525i
$344$	−15.1361	−	7.28918i	−0.816086	−	0.393006i
$345$	0.0164212	+	0.0340990i	0.000884088	+	0.00183583i
$346$	42.6457	+	9.73360i	2.29265	+	0.523281i
$347$	3.55272			0.190720			0.0953601	−	0.995443i	$-0.469600\pi$
$347$	3.55272			0.190720			0.0953601	+	0.995443i	$0.469600\pi$
$348$	−17.6856	−	44.7020i	−0.948045	−	2.39628i
$349$	3.34203			0.178895			0.0894473	−	0.995992i	$-0.471490\pi$
$349$	3.34203			0.178895			0.0894473	+	0.995992i	$0.471490\pi$
$350$	−17.2550	−	3.93835i	−0.922321	−	0.210514i
$351$	−1.03263	−	2.14427i	−0.0551175	−	0.114453i
$352$	21.8703	+	10.5322i	1.16569	+	0.561366i
$353$	2.78493	−	12.2016i	0.148227	−	0.649424i	−0.845151	−	0.534528i	$-0.820489\pi$
$353$	2.78493	−	12.2016i	0.148227	−	0.649424i	0.993378	−	0.114896i	$-0.0366535\pi$
$354$	−1.50818	−	6.60778i	−0.0801590	−	0.351200i
$355$	−0.701575	+	0.337861i	−0.0372358	+	0.0179318i
$356$	2.78302	+	2.21939i	0.147500	+	0.117627i
$357$	14.2976	−	17.9286i	0.756709	−	0.948883i
$358$	−0.895765	+	1.86008i	−0.0473426	+	0.0983080i
$359$	−14.3825	+	11.4697i	−0.759080	+	0.605346i	−0.924635	−	0.380855i	$-0.875630\pi$
$359$	−14.3825	+	11.4697i	−0.759080	+	0.605346i	0.165555	+	0.986201i	$0.447058\pi$
$360$		−	0.760284i		−	0.0400705i
$361$	4.42141	+	5.54428i	0.232706	+	0.291804i
$362$	11.6341	−	2.65541i	0.611476	−	0.139566i
$363$	−13.2481	+	3.02378i	−0.695343	+	0.158708i
$364$	−1.23948	−	1.55426i	−0.0649663	−	0.0814652i
$365$		−	0.406084i		−	0.0212554i
$366$	−16.0627	+	12.8096i	−0.839609	+	0.669566i
$367$	4.26516	−	8.85669i	0.222639	−	0.462316i	−0.759491	−	0.650518i	$-0.774552\pi$
$367$	4.26516	−	8.85669i	0.222639	−	0.462316i	0.982130	+	0.188202i	$0.0602661\pi$
$368$	−0.0586887	+	0.0735933i	−0.00305936	+	0.00383631i
$369$	−5.79760	−	4.62343i	−0.301811	−	0.240686i
$370$	0.635162	−	0.305878i	0.0330205	−	0.0159018i
$371$	−0.621729	−	2.72397i	−0.0322786	−	0.141422i
$372$	−8.57810	+	37.5831i	−0.444754	+	1.94859i
$373$	−19.9832	−	9.62338i	−1.03469	−	0.498280i	−0.162120	−	0.986771i	$-0.551833\pi$
$373$	−19.9832	−	9.62338i	−1.03469	−	0.498280i	−0.872569	+	0.488491i	$0.837547\pi$
$374$	−20.2038	−	41.9536i	−1.04471	−	2.16937i
$375$	−1.60244	−	0.365746i	−0.0827496	−	0.0188871i
$376$	24.8091			1.27943
$377$	−1.89170	−	1.08528i	−0.0974277	−	0.0558950i
$378$	−20.8159			−1.07065
$379$	−8.48209	−	1.93598i	−0.435696	−	0.0994447i	−0.000953214	−	1.00000i	$-0.500303\pi$
$379$	−8.48209	−	1.93598i	−0.435696	−	0.0994447i	−0.434742	+	0.900555i	$0.643161\pi$
$380$	0.272366	+	0.565574i	0.0139721	+	0.0290134i
$381$	44.9757	+	21.6591i	2.30417	+	1.10963i
$382$	−5.20205	+	22.7917i	−0.266160	+	1.16612i
$383$	1.13179	+	4.95869i	0.0578317	+	0.253377i	0.995577	−	0.0939456i	$-0.0299480\pi$
$383$	1.13179	+	4.95869i	0.0578317	+	0.253377i	−0.937746	+	0.347323i	$0.887091\pi$
$384$	44.3954	−	21.3797i	2.26554	−	1.09103i
$385$	−0.280827	−	0.223952i	−0.0143123	−	0.0114136i
$386$	3.83167	−	4.80477i	0.195027	−	0.244556i
$387$	−14.2583	+	29.6076i	−0.724790	+	1.50504i
$388$	42.2934	−	33.7279i	2.14712	−	1.71227i
$389$		−	29.8408i		−	1.51299i	−0.654000	−	0.756494i	$-0.726910\pi$
$389$		−	29.8408i		−	1.51299i	0.654000	−	0.756494i	$-0.273090\pi$
$390$	−0.0941496	−	0.118060i	−0.00476745	−	0.00597819i
$391$	1.15987	−	0.264732i	0.0586569	−	0.0133881i
$392$	11.5208	−	2.62955i	0.581888	−	0.132812i
$393$	5.92939	+	7.43522i	0.299098	+	0.375057i
$394$		−	33.5142i		−	1.68842i
$395$	0.216527	−	0.172675i	0.0108947	−	0.00868820i
$396$	−27.4591	+	57.0195i	−1.37987	+	2.86534i
$397$	−1.82220	+	2.28497i	−0.0914537	+	0.114679i	−0.825453	−	0.564471i	$-0.809080\pi$
$397$	−1.82220	+	2.28497i	−0.0914537	+	0.114679i	0.733999	+	0.679150i	$0.237652\pi$
$398$	26.6004	+	21.2131i	1.33336	+	1.06332i
$399$	13.7948	−	6.64322i	0.690604	−	0.332577i
$400$	−0.454672	−	1.99205i	−0.0227336	−	0.0996024i
$401$	4.54850	−	19.9283i	0.227141	−	0.995171i	−0.724817	−	0.688942i	$-0.758075\pi$
$401$	4.54850	−	19.9283i	0.227141	−	0.995171i	0.951958	−	0.306229i	$-0.0990674\pi$
$402$	−63.1018	−	30.3882i	−3.14723	−	1.51563i
$403$	0.758802	+	1.57567i	0.0377986	+	0.0784896i
$404$	−19.1174	−	4.36341i	−0.951125	−	0.217088i
$405$	−0.0860448			−0.00427560
$406$	−15.7310	+	10.7884i	−0.780717	+	0.535419i
$407$	−21.3372			−1.05764
$408$	−37.0898	−	8.46551i	−1.83622	−	0.419105i
$409$	14.5837	+	30.2833i	0.721116	+	1.49741i	0.861741	+	0.507349i	$0.169374\pi$
$409$	14.5837	+	30.2833i	0.721116	+	1.49741i	−0.140625	+	0.990063i	$0.544911\pi$
$410$	−0.173014	−	0.0833192i	−0.00854455	−	0.00411484i
$411$	−3.48949	+	15.2885i	−0.172124	+	0.754124i
$412$	9.23824	+	40.4754i	0.455135	+	1.99408i
$413$	−1.48069	+	0.713061i	−0.0728598	+	0.0350874i
$414$	−2.06867	−	1.64971i	−0.101670	−	0.0810789i
$415$	−0.303997	+	0.381200i	−0.0149226	+	0.0187124i
$416$	1.07362	−	2.22940i	0.0526387	−	0.109305i
$417$	1.32698	−	1.05823i	0.0649823	−	0.0518216i
$418$		−	31.0907i		−	1.52070i
$419$	4.69488	+	5.88719i	0.229360	+	0.287608i	0.883173	−	0.469048i	$-0.155403\pi$
$419$	4.69488	+	5.88719i	0.229360	+	0.287608i	−0.653813	+	0.756656i	$0.726832\pi$
$420$	−0.786859	+	0.179596i	−0.0383948	+	0.00876336i
$421$	19.8646	−	4.53398i	0.968144	−	0.220972i	0.290918	−	0.956748i	$-0.406039\pi$
$421$	19.8646	−	4.53398i	0.968144	−	0.220972i	0.677226	+	0.735775i	$0.263182\pi$
$422$	−16.9289	−	21.2281i	−0.824084	−	1.03337i
$423$		−	48.5289i		−	2.35956i
$424$	−3.62403	+	2.89007i	−0.175999	+	0.140354i
$425$	−11.2050	+	23.2674i	−0.543521	+	1.12863i
$426$	54.0312	−	67.7529i	2.61782	−	3.28264i
$427$	3.89482	+	3.10602i	0.188484	+	0.150311i
$428$	26.2426	−	12.6378i	1.26848	−	0.610869i
$429$	1.01700	+	4.45578i	0.0491013	+	0.215127i
$430$	−0.189366	+	0.829666i	−0.00913203	+	0.0400100i
$431$	−10.6631	−	5.13509i	−0.513625	−	0.247349i	0.159072	−	0.987267i	$-0.449150\pi$
$431$	−10.6631	−	5.13509i	−0.513625	−	0.247349i	−0.672697	+	0.739918i	$0.734864\pi$
$432$	−1.04268	−	2.16515i	−0.0501660	−	0.104171i
$433$	−16.6685	−	3.80447i	−0.801037	−	0.182831i	−0.197642	−	0.980274i	$-0.563328\pi$
$433$	−16.6685	−	3.80447i	−0.801037	−	0.182831i	−0.603394	+	0.797443i	$0.706186\pi$
$434$	15.2961			0.734235
$435$	−0.730208	+	0.500780i	−0.0350108	+	0.0240106i
$436$	−18.0874			−0.866230
$437$	0.774425	+	0.176758i	0.0370458	+	0.00845546i
$438$	19.6083	+	40.7171i	0.936921	+	1.94554i
$439$	16.8940	+	8.13573i	0.806308	+	0.388297i	0.791176	−	0.611588i	$-0.209469\pi$
$439$	16.8940	+	8.13573i	0.806308	+	0.388297i	0.0151314	+	0.999886i	$0.495183\pi$
$440$	−0.132601	+	0.580961i	−0.00632148	+	0.0276962i
$441$	−5.14363	−	22.5357i	−0.244935	−	1.07313i
$442$	−4.27664	+	2.05952i	−0.203419	+	0.0979614i
$443$	−2.66122	−	2.12225i	−0.126438	−	0.100831i	0.558229	−	0.829687i	$-0.311481\pi$
$443$	−2.66122	−	2.12225i	−0.126438	−	0.100831i	−0.684667	+	0.728856i	$0.740052\pi$
$444$	−29.8927	+	37.4843i	−1.41864	+	1.77892i
$445$	0.0284464	−	0.0590695i	0.00134849	−	0.00280016i
$446$	−23.7072	+	18.9059i	−1.12257	+	0.895219i
$447$		−	14.5127i		−	0.686427i
$448$	−12.6973	−	15.9219i	−0.599889	−	0.752237i
$449$	0.135791	−	0.0309934i	0.00640836	−	0.00146267i	−0.219316	−	0.975654i	$-0.570382\pi$
$449$	0.135791	−	0.0309934i	0.00640836	−	0.00146267i	0.225724	+	0.974191i	$0.427525\pi$
$450$	55.9956	−	12.7806i	2.63966	−	0.602484i
$451$	3.62379	+	4.54408i	0.170637	+	0.213973i
$452$			25.3371i			1.19176i
$453$	−17.3232	+	13.8148i	−0.813914	+	0.649075i
$454$	−2.08822	+	4.33623i	−0.0980050	+	0.203509i
$455$	−0.0228291	+	0.0286268i	−0.00107024	+	0.00134204i
$456$	−19.8595	−	15.8374i	−0.930005	−	0.741654i
$457$	28.9026	−	13.9188i	1.35201	−	0.651093i	0.389169	−	0.921166i	$-0.372762\pi$
$457$	28.9026	−	13.9188i	1.35201	−	0.651093i	0.962840	+	0.270073i	$0.0870480\pi$
$458$	13.8214	+	60.5555i	0.645831	+	2.82957i
$459$	−6.75864	+	29.6115i	−0.315466	+	1.38215i
$460$	−0.0377256	−	0.0181677i	−0.00175896	−	0.000847073i
$461$	−0.314786	−	0.653661i	−0.0146611	−	0.0304440i	0.893510	−	0.449044i	$-0.148235\pi$
$461$	−0.314786	−	0.653661i	−0.0146611	−	0.0304440i	−0.908171	+	0.418600i	$0.862521\pi$
$462$	38.9716	+	8.89502i	1.81312	+	0.413834i
$463$	9.14813			0.425150			0.212575	−	0.977145i	$-0.431815\pi$
$463$	9.14813			0.425150			0.212575	+	0.977145i	$0.431815\pi$
$464$	−1.91013	−	1.09585i	−0.0886753	−	0.0508737i
$465$	0.710019			0.0329263
$466$	−38.6407	−	8.81948i	−1.78999	−	0.408554i
$467$	−13.3047	−	27.6274i	−0.615667	−	1.27844i	−0.942766	−	0.333455i	$-0.891785\pi$
$467$	−13.3047	−	27.6274i	−0.615667	−	1.27844i	0.327099	−	0.944990i	$-0.393929\pi$
$468$	5.81242	+	2.79911i	0.268679	+	0.129389i
$469$	−3.77897	+	16.5567i	−0.174496	+	0.764519i
$470$	−0.279646	−	1.22521i	−0.0128991	−	0.0565146i
$471$	−48.2618	+	23.2417i	−2.22379	+	1.07092i
$472$	2.13165	+	1.69993i	0.0981170	+	0.0782457i
$473$	16.0591	−	20.1375i	0.738399	−	0.925924i
$474$	−13.3728	+	27.7689i	−0.614234	+	1.27547i
$475$	−13.4810	+	10.7507i	−0.618551	+	0.493278i
$476$			25.3705i			1.16285i
$477$	5.65324	+	7.08894i	0.258844	+	0.324580i
$478$	38.1433	−	8.70595i	1.74463	−	0.398201i
$479$	−5.16447	+	1.17876i	−0.235971	+	0.0538588i	−0.338871	−	0.940833i	$-0.610045\pi$
$479$	−5.16447	+	1.17876i	−0.235971	+	0.0538588i	0.102900	+	0.994692i	$0.467188\pi$
$480$	−0.626358	−	0.785428i	−0.0285892	−	0.0358497i
$481$			2.17506i			0.0991740i
$482$	38.9823	−	31.0873i	1.77559	−	1.41599i
$483$	−0.443124	+	0.920156i	−0.0201628	+	0.0418686i
$484$	9.37355	−	11.7541i	0.426070	−	0.534275i
$485$	−0.778973	−	0.621210i	−0.0353713	−	0.0282077i
$486$	−27.3935	+	13.1920i	−1.24259	+	0.598401i
$487$	0.774725	+	3.39429i	0.0351062	+	0.153810i	0.989443	−	0.144922i	$-0.0462933\pi$
$487$	0.774725	+	3.39429i	0.0351062	+	0.153810i	−0.954337	+	0.298733i	$0.903436\pi$
$488$	1.83905	−	8.05742i	0.0832500	−	0.364742i
$489$	5.78905	+	2.78786i	0.261790	+	0.126071i
$490$	−0.259722	−	0.539319i	−0.0117331	−	0.0243639i
$491$	5.70489	+	1.30210i	0.257458	+	0.0587631i	0.349302	−	0.937010i	$-0.386419\pi$
$491$	5.70489	+	1.30210i	0.257458	+	0.0587631i	−0.0918437	+	0.995773i	$0.529276\pi$
$492$	13.0597			0.588776
$493$	10.2393	+	25.8809i	0.461157	+	1.16562i
$494$	−3.16931			−0.142594
$495$	1.13641	+	0.259379i	0.0510779	+	0.0116582i
$496$	0.766191	+	1.59101i	0.0344030	+	0.0714385i
$497$	−18.9319	−	9.11713i	−0.849213	−	0.408959i
$498$	12.0743	−	52.9008i	0.541061	−	2.37054i
$499$	−5.27783	−	23.1237i	−0.236268	−	1.03516i	−0.944328	−	0.329005i	$-0.893287\pi$
$499$	−5.27783	−	23.1237i	−0.236268	−	1.03516i	0.708060	−	0.706152i	$-0.249571\pi$
$500$	1.63838	−	0.789001i	0.0732704	−	0.0352852i
$501$	−26.0614	−	20.7833i	−1.16434	−	0.928529i
$502$	13.8150	−	17.3234i	0.616593	−	0.773183i
$503$	8.38962	−	17.4212i	0.374075	−	0.776774i	−0.625920	−	0.779887i	$-0.715277\pi$
$503$	8.38962	−	17.4212i	0.374075	−	0.776774i	0.999995	+	0.00311266i	$0.000990793\pi$
$504$	16.0402	−	12.7916i	0.714487	−	0.569784i
$505$			0.361165i			0.0160716i
$506$	1.29302	+	1.62140i	0.0574819	+	0.0720801i
$507$	−35.5473	+	8.11345i	−1.57871	+	0.360331i
$508$	−53.8437	+	12.2895i	−2.38893	+	0.545257i
$509$	24.2136	+	30.3629i	1.07325	+	1.34581i	0.934693	+	0.355456i	$0.115674\pi$
$509$	24.2136	+	30.3629i	1.07325	+	1.34581i	0.138555	+	0.990355i	$0.455754\pi$
$510$			1.92712i			0.0853342i
$511$	8.56742	−	6.83229i	0.379000	−	0.302243i
$512$	2.00362	−	4.16055i	0.0885482	−	0.183872i
$513$	−12.6441	+	15.8553i	−0.558253	+	0.700027i
$514$	−27.3081	−	21.7775i	−1.20451	−	0.960565i
$515$	0.688934	−	0.331773i	0.0303581	−	0.0146197i
$516$	−12.8784	−	56.4240i	−0.566941	−	2.48393i
$517$	−8.46389	+	37.0827i	−0.372241	+	1.63090i
$518$	17.1398	+	8.25408i	0.753078	+	0.362663i
$519$	23.7731	+	49.3654i	1.04352	+	2.16690i
$520$	0.0592216	+	0.0135170i	0.00259704	+	0.000592758i
$521$	33.3472			1.46097			0.730484	−	0.682930i	$-0.239294\pi$
$521$	33.3472			1.46097			0.730484	+	0.682930i	$0.239294\pi$
$522$	30.8039	−	53.6928i	1.34825	−	2.35007i
$523$	31.8103			1.39097			0.695484	−	0.718542i	$-0.255190\pi$
$523$	31.8103			1.39097			0.695484	+	0.718542i	$0.255190\pi$
$524$	−10.2577	−	2.34124i	−0.448108	−	0.102278i
$525$	−9.61894	−	19.9739i	−0.419805	−	0.871734i
$526$	−63.3246	−	30.4955i	−2.76108	−	1.32967i
$527$	4.96643	−	21.7594i	0.216341	−	0.947853i
$528$	1.02691	+	4.49917i	0.0446903	+	0.195801i
$529$	20.6745	−	9.95634i	0.898893	−	0.432884i
$530$	0.183577	+	0.146398i	0.00797407	+	0.00635911i
$531$	3.32522	−	4.16969i	0.144302	−	0.180949i
$532$	−7.34977	+	15.2620i	−0.318653	+	0.661689i
$533$	0.463212	−	0.369399i	0.0200640	−	0.0160005i
$534$			7.29632i			0.315742i
$535$	−0.334484	−	0.419430i	−0.0144610	−	0.0181335i
$536$	27.4678	−	6.26934i	1.18643	−	0.270794i
$537$	−2.52118	+	0.575443i	−0.108797	+	0.0248322i
$538$	−19.5897	−	24.5648i	−0.844574	−	1.05906i
$539$			18.1175i			0.780375i
$540$	0.835781	−	0.666513i	0.0359663	−	0.0286821i
$541$	16.8087	−	34.9037i	0.722664	−	1.50063i	−0.137441	−	0.990510i	$-0.543888\pi$
$541$	16.8087	−	34.9037i	0.722664	−	1.50063i	0.860105	−	0.510117i	$-0.170398\pi$
$542$	−37.9470	+	47.5840i	−1.62996	+	2.04391i
$543$	11.6865	+	9.31969i	0.501517	+	0.399946i
$544$	−28.4516	+	13.7016i	−1.21985	+	0.587450i
$545$	0.0741305	+	0.324787i	0.00317540	+	0.0139123i
$546$	0.906735	−	3.97267i	0.0388047	−	0.170014i
$547$	−5.39730	−	2.59920i	−0.230772	−	0.111134i	0.314925	−	0.949117i	$-0.398021\pi$
$547$	−5.39730	−	2.59920i	−0.230772	−	0.111134i	−0.545697	+	0.837983i	$0.683735\pi$
$548$	−7.52765	−	15.6313i	−0.321565	−	0.667737i
$549$	−15.7610	−	3.59735i	−0.672665	−	0.153531i
$550$	−45.0173			−1.91954
$551$	−1.33803	+	18.5353i	−0.0570022	+	0.789632i
$552$	1.69434			0.0721159
$553$	7.28605	+	1.66299i	0.309834	+	0.0707176i
$554$	22.1940	+	46.0864i	0.942934	+	1.95802i
$555$	0.795601	+	0.383141i	0.0337714	+	0.0162634i
$556$	−0.417845	+	1.83070i	−0.0177206	+	0.0776389i
$557$	0.417760	+	1.83032i	0.0177010	+	0.0775533i	0.983007	−	0.183568i	$-0.0587648\pi$
$557$	0.417760	+	1.83032i	0.0177010	+	0.0775533i	−0.965306	+	0.261122i	$0.915908\pi$
$558$	−44.7226	+	21.5373i	−1.89326	+	0.911746i
$559$	−2.05277	−	1.63703i	−0.0868227	−	0.0692388i
$560$	−0.0230514	+	0.0289055i	−0.000974099	+	0.00122148i
$561$	25.3071	−	52.5508i	1.06847	−	2.21870i
$562$	5.85101	−	4.66602i	0.246810	−	0.196824i
$563$		−	26.4739i		−	1.11574i	−0.829927	−	0.557872i	$-0.811618\pi$
$563$		−	26.4739i		−	1.11574i	0.829927	−	0.557872i	$-0.188382\pi$
$564$	53.2877	+	66.8207i	2.24382	+	2.81366i
$565$	0.454966	−	0.103843i	0.0191406	−	0.00436871i
$566$	39.0633	−	8.91595i	1.64195	−	0.374765i
$567$	−1.44769	−	1.81534i	−0.0607971	−	0.0762372i
$568$			34.8605i			1.46271i
$569$	−9.99580	+	7.97139i	−0.419046	+	0.334178i	−0.810207	−	0.586144i	$-0.800645\pi$
$569$	−9.99580	+	7.97139i	−0.419046	+	0.334178i	0.391161	+	0.920322i	$0.372074\pi$
$570$	−0.558282	+	1.15928i	−0.0233838	+	0.0485570i
$571$	−23.7265	+	29.7521i	−0.992924	+	1.24509i	−0.0234924	+	0.999724i	$0.507479\pi$
$571$	−23.7265	+	29.7521i	−0.992924	+	1.24509i	−0.969431	+	0.245363i	$0.921093\pi$
$572$	−3.95329	−	3.15264i	−0.165295	−	0.131819i
$573$	−26.3830	+	12.7054i	−1.10216	+	0.530775i
$574$	−1.15309	−	5.05201i	−0.0481290	−	0.210867i
$575$	0.255933	−	1.12132i	0.0106731	−	0.0467621i
$576$	59.5426	+	28.6742i	2.48094	+	1.19476i
$577$	0.0443670	+	0.0921290i	0.00184702	+	0.00383538i	0.901890	−	0.431965i	$-0.142180\pi$
$577$	0.0443670	+	0.0921290i	0.00184702	+	0.00383538i	−0.900043	+	0.435800i	$0.856465\pi$
$578$	21.4736	+	4.90121i	0.893184	+	0.203863i
$579$	7.69786			0.319912
$580$	0.286179	−	0.936865i	0.0118829	−	0.0389012i
$581$	−13.1571			−0.545848
$582$	108.102	+	24.6735i	4.48096	+	1.02275i
$583$	−3.08347	−	6.40289i	−0.127704	−	0.265181i
$584$	−16.3793	−	7.88785i	−0.677780	−	0.326402i
$585$	0.0264404	−	0.115843i	0.00109318	−	0.00478951i
$586$	6.82964	+	29.9226i	0.282130	+	1.23609i
$587$	0.662492	−	0.319039i	0.0273440	−	0.0131682i	−0.420162	−	0.907449i	$-0.638027\pi$
$587$	0.662492	−	0.319039i	0.0273440	−	0.0131682i	0.447506	+	0.894281i	$0.352312\pi$
$588$	31.8280	+	25.3820i	1.31257	+	1.04674i
$589$	9.29127	−	11.6509i	0.382840	−	0.480066i
$590$	0.0599240	−	0.124433i	0.00246703	−	0.00512285i
$591$	32.8210	−	26.1739i	1.35008	−	1.07665i
$592$			2.19624i			0.0902647i
$593$	−27.9046	−	34.9913i	−1.14590	−	1.43692i	−0.881297	−	0.472562i	$-0.843329\pi$
$593$	−27.9046	−	34.9913i	−1.14590	−	1.43692i	−0.264607	−	0.964356i	$-0.585242\pi$
$594$	−51.6182	+	11.7815i	−2.11792	+	0.483402i
$595$	0.455565	−	0.103980i	0.0186763	−	0.00426275i
$596$	10.0109	+	12.5532i	0.410061	+	0.514201i
$597$			42.6173i			1.74421i
$598$	0.165281	−	0.131808i	0.00675886	−	0.00539001i
$599$	1.76159	−	3.65797i	0.0719764	−	0.149461i	−0.861876	−	0.507119i	$-0.830710\pi$
$599$	1.76159	−	3.65797i	0.0719764	−	0.149461i	0.933853	+	0.357658i	$0.116425\pi$
$600$	−22.9315	+	28.7552i	−0.936174	+	1.17393i
$601$	−34.7392	−	27.7036i	−1.41704	−	1.13005i	−0.972120	−	0.234483i	$-0.924660\pi$
$601$	−34.7392	−	27.7036i	−1.41704	−	1.13005i	−0.444921	−	0.895570i	$-0.646768\pi$
$602$	−20.6900	+	9.96379i	−0.843262	+	0.406094i
$603$	−12.2634	−	53.7294i	−0.499404	−	2.18803i
$604$	5.45481	−	23.8991i	0.221953	−	0.972441i
$605$	−0.249479	−	0.120143i	−0.0101428	−	0.00488450i
$606$	−17.4393	−	36.2131i	−0.708423	−	1.47106i
$607$	−9.45849	−	2.15884i	−0.383908	−	0.0876246i	0.0262110	−	0.999656i	$-0.491656\pi$
$607$	−9.45849	−	2.15884i	−0.383908	−	0.0876246i	−0.410119	+	0.912032i	$0.634513\pi$
$608$	−21.0848			−0.855100
$609$	−22.8509	−	6.98013i	−0.925964	−	0.282849i
$610$	−0.418648			−0.0169506
$611$	3.78012	+	0.862787i	0.152927	+	0.0349046i
$612$	−35.7223	−	74.1781i	−1.44399	−	2.99847i
$613$	−1.60828	−	0.774505i	−0.0649576	−	0.0312820i	0.401123	−	0.916024i	$-0.368620\pi$
$613$	−1.60828	−	0.774505i	−0.0649576	−	0.0312820i	−0.466081	+	0.884742i	$0.654334\pi$
$614$	3.28945	−	14.4120i	0.132751	−	0.581622i
$615$	−0.0535245	−	0.234506i	−0.00215832	−	0.00945621i
$616$	−14.4879	+	6.97699i	−0.583733	+	0.281111i
$617$	−6.80982	−	5.43065i	−0.274153	−	0.218630i	0.476756	−	0.879036i	$-0.341813\pi$
$617$	−6.80982	−	5.43065i	−0.274153	−	0.218630i	−0.750909	+	0.660406i	$0.770384\pi$
$618$	−53.0576	+	66.5321i	−2.13429	+	2.67631i
$619$	−6.16293	+	12.7975i	−0.247709	+	0.514373i	−0.987336	−	0.158644i	$-0.949288\pi$
$619$	−6.16293	+	12.7975i	−0.247709	+	0.514373i	0.739627	+	0.673017i	$0.235002\pi$
$620$	−0.614155	+	0.489772i	−0.0246651	+	0.0196697i
$621$		−	1.35272i		−	0.0542826i
$622$	−34.7060	−	43.5199i	−1.39158	−	1.74499i
$623$	1.72483	−	0.393681i	0.0691038	−	0.0157725i
$624$	0.458633	−	0.104680i	0.0183600	−	0.00419056i
$625$	15.5559	+	19.5065i	0.622237	+	0.780260i
$626$			4.47759i			0.178961i
$627$	30.4477	−	24.2813i	1.21597	−	0.969700i
$628$	25.7135	−	53.3947i	1.02608	−	2.13068i
$629$	17.3069	−	21.7021i	0.690070	−	0.865320i
$630$	−0.812522	−	0.647964i	−0.0323716	−	0.0258155i
$631$	14.9293	−	7.18958i	0.594327	−	0.286213i	−0.112441	−	0.993658i	$-0.535867\pi$
$631$	14.9293	−	7.18958i	0.594327	−	0.286213i	0.706768	+	0.707446i	$0.250153\pi$
$632$	−2.75892	−	12.0876i	−0.109744	−	0.480820i
$633$	7.56798	−	33.1575i	0.300800	−	1.31789i
$634$	60.6429	+	29.2041i	2.40844	+	1.15984i
$635$	0.441352	+	0.916478i	0.0175145	+	0.0363693i
$636$	−15.5682	−	3.55334i	−0.617319	−	0.140899i
$637$	1.84685			0.0731748
$638$	−32.9029	+	35.6561i	−1.30264	+	1.41164i
$639$	68.1903			2.69757
$640$	0.978915	+	0.223431i	0.0386950	+	0.00883189i
$641$	3.16628	+	6.57486i	0.125061	+	0.259691i	0.954094	−	0.299509i	$-0.0968227\pi$
$641$	3.16628	+	6.57486i	0.125061	+	0.259691i	−0.829033	+	0.559200i	$0.811108\pi$
$642$	53.7906	+	25.9042i	2.12294	+	1.02236i
$643$	−7.53691	+	33.0214i	−0.297227	+	1.30224i	0.577010	+	0.816737i	$0.304219\pi$
$643$	−7.53691	+	33.0214i	−0.297227	+	1.30224i	−0.874237	+	0.485499i	$0.838638\pi$
$644$	−0.251430	−	1.10159i	−0.00990774	−	0.0434086i
$645$	−0.960398	+	0.462503i	−0.0378156	+	0.0182110i
$646$	31.6225	+	25.2181i	1.24417	+	0.992194i
$647$	−20.8525	+	26.1482i	−0.819795	+	1.02799i	0.179228	+	0.983807i	$0.442640\pi$
$647$	−20.8525	+	26.1482i	−0.819795	+	1.02799i	−0.999023	+	0.0441829i	$0.985932\pi$
$648$	−1.67135	+	3.47059i	−0.0656568	+	0.136338i
$649$	−3.26815	+	2.60627i	−0.128286	+	0.102305i
$650$			4.58895i			0.179993i
$651$	11.9459	+	14.9797i	0.468198	+	0.587101i
$652$	−6.93051	+	1.58184i	−0.271420	+	0.0619497i
$653$	−23.1601	+	5.28615i	−0.906326	+	0.206863i	−0.650184	−	0.759776i	$-0.725308\pi$
$653$	−23.1601	+	5.28615i	−0.906326	+	0.206863i	−0.256141	+	0.966639i	$0.582451\pi$
$654$	−23.1156	−	28.9861i	−0.903893	−	1.13345i
$655$			0.193787i			0.00757189i
$656$	0.467723	−	0.372997i	0.0182615	−	0.0145631i
$657$	−15.4294	+	32.0394i	−0.601956	+	1.24998i
$658$	21.1440	−	26.5137i	0.824278	−	1.03361i
$659$	−3.85540	−	3.07458i	−0.150185	−	0.119769i	0.545515	−	0.838101i	$-0.316334\pi$
$659$	−3.85540	−	3.07458i	−0.150185	−	0.119769i	−0.695700	+	0.718333i	$0.744906\pi$
$660$	−1.84957	+	0.890706i	−0.0719944	+	0.0346707i
$661$	5.22326	+	22.8846i	0.203161	+	0.890107i	0.968997	+	0.247071i	$0.0794682\pi$
$661$	5.22326	+	22.8846i	0.203161	+	0.890107i	−0.765836	+	0.643036i	$0.777675\pi$
$662$	14.3181	−	62.7318i	0.556489	−	2.43814i
$663$	−5.35690	−	2.57975i	−0.208045	−	0.100189i
$664$	9.47070	+	19.6661i	0.367535	+	0.763193i
$665$	0.304174	+	0.0694258i	0.0117954	+	0.00269222i
$666$	−61.7352			−2.39219
$667$	−0.701082	−	1.02228i	−0.0271460	−	0.0395827i
$668$	36.8790			1.42689
$669$	−37.0297	−	8.45179i	−1.43165	−	0.326765i
$670$	−0.619227	−	1.28584i	−0.0239228	−	0.0496762i
$671$	11.4162	+	5.49774i	0.440717	+	0.212238i
$672$	6.03232	−	26.4293i	0.232702	−	1.01953i
$673$	6.65990	+	29.1789i	0.256720	+	1.12477i	0.924733	+	0.380616i	$0.124288\pi$
$673$	6.65990	+	29.1789i	0.256720	+	1.12477i	−0.668013	+	0.744150i	$0.732855\pi$
$674$	8.20794	−	3.95274i	0.316158	−	0.152254i
$675$	22.9573	+	18.3079i	0.883629	+	0.704670i
$676$	25.1512	−	31.5386i	0.967353	−	1.21302i
$677$	−9.55250	+	19.8360i	−0.367132	+	0.762358i	−0.999928	−	0.0119603i	$-0.996193\pi$
$677$	−9.55250	+	19.8360i	−0.367132	+	0.762358i	0.632796	+	0.774318i	$0.281907\pi$
$678$	−40.6041	+	32.3807i	−1.55939	+	1.24357i
$679$		−	26.8862i		−	1.03180i
$680$	−0.483344	−	0.606094i	−0.0185354	−	0.0232426i
$681$	−5.87741	+	1.34148i	−0.225223	+	0.0514056i
$682$	37.9305	−	8.65739i	1.45243	−	0.331508i
$683$	−2.87871	−	3.60979i	−0.110151	−	0.138125i	0.723700	−	0.690115i	$-0.242440\pi$
$683$	−2.87871	−	3.60979i	−0.110151	−	0.138125i	−0.833851	+	0.551990i	$0.813869\pi$
$684$		−	54.9715i		−	2.10189i
$685$	−0.249832	+	0.199235i	−0.00954561	+	0.00761237i
$686$	17.7667	−	36.8929i	0.678335	−	1.40858i
$687$	−48.5088	+	60.8282i	−1.85073	+	2.32074i
$688$	−2.07275	−	1.65297i	−0.0790230	−	0.0630188i
$689$	−0.652694	+	0.314321i	−0.0248657	+	0.0119747i
$690$	−0.0190984	−	0.0836756i	−0.000727064	−	0.00318547i
$691$	7.95421	−	34.8497i	0.302592	−	1.32574i	−0.563606	−	0.826044i	$-0.690586\pi$
$691$	7.95421	−	34.8497i	0.302592	−	1.32574i	0.866199	−	0.499700i	$-0.166556\pi$
$692$	−54.6157	−	26.3015i	−2.07618	−	0.999834i
$693$	13.6476	+	28.3396i	0.518430	+	1.07653i
$694$	−7.85468	−	1.79278i	−0.298160	−	0.0680530i
$695$	0.0345855			0.00131190
$696$	6.01513	+	39.1800i	0.228003	+	1.48511i
$697$	−7.56111			−0.286398
$698$	−7.38886	−	1.68646i	−0.279672	−	0.0638334i
$699$	−21.5405	−	44.7293i	−0.814737	−	1.69182i
$700$	22.0983	+	10.6420i	0.835237	+	0.402229i
$701$	−0.811010	+	3.55327i	−0.0306314	+	0.134205i	−0.987932	−	0.154891i	$-0.950497\pi$
$701$	−0.811010	+	3.55327i	−0.0306314	+	0.134205i	0.957300	+	0.289096i	$0.0933546\pi$
$702$	1.20098	+	5.26183i	0.0453280	+	0.198595i
$703$	16.6982	−	8.04145i	0.629786	−	0.303289i
$704$	−40.4976	−	32.2958i	−1.52631	−	1.21719i
$705$	0.981470	−	1.23072i	0.0369643	−	0.0463518i
$706$	−12.3143	+	25.5710i	−0.463457	+	0.962377i
$707$	−7.61972	+	6.07652i	−0.286569	+	0.228531i
$708$			9.39266i			0.352998i
$709$	13.0877	+	16.4114i	0.491518	+	0.616344i	0.964293	−	0.264839i	$-0.0853188\pi$
$709$	13.0877	+	16.4114i	0.491518	+	0.616344i	−0.472774	+	0.881184i	$0.656747\pi$
$710$	1.72160	−	0.392944i	0.0646104	−	0.0147469i
$711$	−23.6445	+	5.39670i	−0.886737	+	0.202392i
$712$	−1.83000	−	2.29475i	−0.0685822	−	0.0859994i
$713$			0.994013i			0.0372261i
$714$	−40.6576	+	32.4233i	−1.52157	+	1.21341i
$715$	−0.0404081	+	0.0839083i	−0.00151118	+	0.00313799i
$716$	1.78384	−	2.23686i	0.0666651	−	0.0835954i
$717$	38.3150	+	30.5552i	1.43090	+	1.14110i
$718$	37.5860	−	18.1005i	1.40270	−	0.675503i
$719$	−5.39677	−	23.6448i	−0.201266	−	0.881803i	−0.970167	−	0.242436i	$-0.922054\pi$
$719$	−5.39677	−	23.6448i	−0.201266	−	0.881803i	0.768902	−	0.639367i	$-0.220803\pi$
$720$	0.0266979	−	0.116971i	0.000994970	−	0.00435925i
$721$	18.5908	+	8.95286i	0.692357	+	0.333422i
$722$	−6.97750	−	14.4889i	−0.259676	−	0.539222i
$723$	60.8888	+	13.8975i	2.26448	+	0.516852i
$724$	−16.5374			−0.614607
$725$	26.8379	+	1.93738i	0.996736	+	0.0719526i
$726$	30.8159			1.14368
$727$	−30.1601	−	6.88385i	−1.11858	−	0.255308i	−0.377025	−	0.926203i	$-0.623053\pi$
$727$	−30.1601	−	6.88385i	−1.11858	−	0.255308i	−0.741552	+	0.670895i	$0.765910\pi$
$728$	0.711216	+	1.47686i	0.0263594	+	0.0547359i
$729$	−38.3309	−	18.4592i	−1.41966	−	0.683673i
$730$	−0.204919	+	0.897808i	−0.00758439	+	0.0332294i
$731$	7.45617	+	32.6676i	0.275776	+	1.20826i
$732$	25.6519	−	12.3533i	0.948122	−	0.456591i
$733$	14.4717	+	11.5408i	0.534523	+	0.426268i	0.853191	−	0.521598i	$-0.174664\pi$
$733$	14.4717	+	11.5408i	0.534523	+	0.426268i	−0.318668	+	0.947866i	$0.603235\pi$
$734$	−13.8991	+	17.4289i	−0.513024	+	0.643312i
$735$	0.325327	−	0.675548i	0.0119999	−	0.0249180i
$736$	1.09958	−	0.876889i	0.0405312	−	0.0323225i
$737$			43.1955i			1.59113i
$738$	10.4848	+	13.1475i	0.385950	+	0.483966i
$739$	−33.1954	+	7.57663i	−1.22111	+	0.278711i	−0.784037	−	0.620714i	$-0.786843\pi$
$739$	−33.1954	+	7.57663i	−1.22111	+	0.278711i	−0.437075	+	0.899425i	$0.643986\pi$
$740$	−0.952473	+	0.217396i	−0.0350136	+	0.00799163i
$741$	−2.47517	−	3.10376i	−0.0909276	−	0.114020i
$742$			6.33614i			0.232607i
$743$	−27.2288	+	21.7142i	−0.998927	+	0.796618i	−0.979140	−	0.203187i	$-0.934870\pi$
$743$	−27.2288	+	21.7142i	−0.998927	+	0.796618i	−0.0197868	+	0.999804i	$0.506299\pi$
$744$	13.7915	−	28.6384i	0.505622	−	1.04994i
$745$	0.184383	−	0.231209i	0.00675528	−	0.00847086i
$746$	39.3244	+	31.3602i	1.43977	+	1.14818i
$747$	38.4687	−	18.5255i	1.40750	−	0.677814i
$748$	14.3594	+	62.9125i	0.525030	+	2.30031i
$749$	3.22135	−	14.1136i	0.117705	−	0.515701i
$750$	3.35826	+	1.61725i	0.122626	+	0.0590536i
$751$	−21.0818	−	43.7769i	−0.769287	−	1.59744i	−0.801525	−	0.597961i	$-0.795978\pi$
$751$	−21.0818	−	43.7769i	−0.769287	−	1.59744i	0.0322376	−	0.999480i	$-0.489737\pi$
$752$	3.81692	+	0.871188i	0.139189	+	0.0317690i
$753$	27.7544			1.01143
$754$	3.63469	+	3.35404i	0.132368	+	0.122147i
$755$	−0.451501			−0.0164318
$756$	28.1237	+	6.41904i	1.02285	+	0.233458i
$757$	13.0563	+	27.1118i	0.474541	+	0.985394i	0.991588	+	0.129437i	$0.0413171\pi$
$757$	13.0563	+	27.1118i	0.474541	+	0.985394i	−0.517047	+	0.855957i	$0.672969\pi$
$758$	17.7760	+	8.56048i	0.645654	+	0.310931i
$759$	−0.578041	+	2.53256i	−0.0209816	+	0.0919262i
$760$	−0.115178	−	0.504628i	−0.00417795	−	0.0183048i
$761$	8.85531	−	4.26449i	0.321005	−	0.154588i	−0.266441	−	0.963851i	$-0.585848\pi$
$761$	8.85531	−	4.26449i	0.321005	−	0.154588i	0.587446	+	0.809263i	$0.300133\pi$
$762$	−88.5066	−	70.5816i	−3.20625	−	2.55690i
$763$	−5.60500	+	7.02845i	−0.202915	+	0.254447i
$764$	14.0567	−	29.1890i	0.508552	−	1.05602i
$765$	−1.18557	+	0.945464i	−0.0428645	+	0.0341833i
$766$		−	11.5342i		−	0.416749i
$767$	0.265676	+	0.333147i	0.00959300	+	0.0120292i
$768$	−36.7285	+	8.38305i	−1.32533	+	0.302497i
$769$	−29.2236	+	6.67010i	−1.05383	+	0.240530i	−0.714137	−	0.700006i	$-0.753181\pi$
$769$	−29.2236	+	6.67010i	−1.05383	+	0.240530i	−0.339694	+	0.940536i	$0.610323\pi$
$770$	0.507867	+	0.636844i	0.0183022	+	0.0229503i
$771$		−	43.7511i		−	1.57566i
$772$	−6.65852	+	5.30999i	−0.239645	+	0.191111i
$773$	−7.33911	+	15.2398i	−0.263969	+	0.548138i	−0.990257	−	0.139253i	$-0.955530\pi$
$773$	−7.33911	+	15.2398i	−0.263969	+	0.548138i	0.726287	+	0.687391i	$0.241244\pi$
$774$	46.4642	−	58.2642i	1.67012	−	2.09426i
$775$	−16.8697	−	13.4531i	−0.605977	−	0.483251i
$776$	−40.1872	+	19.3532i	−1.44264	+	0.694738i
$777$	5.30245	+	23.2316i	0.190224	+	0.833427i
$778$	−15.0583	+	65.9747i	−0.539866	+	2.36531i
$779$	−4.54849	−	2.19044i	−0.162967	−	0.0784806i
$780$	0.0907962	+	0.188540i	0.00325103	+	0.00675083i
$781$	−52.1067	−	11.8930i	−1.86452	−	0.425565i
$782$	−2.69792			−0.0964776
$783$	31.2802	−	4.80232i	1.11786	−	0.171621i
$784$	1.86483			0.0666012
$785$	−1.06417	−	0.242890i	−0.0379818	−	0.00866910i
$786$	−9.35726	−	19.4306i	−0.333763	−	0.693065i
$787$	−18.0155	−	8.67579i	−0.642182	−	0.309259i	0.0843036	−	0.996440i	$-0.473133\pi$
$787$	−18.0155	−	8.67579i	−0.642182	−	0.309259i	−0.726486	+	0.687181i	$0.758848\pi$
$788$	−10.3349	+	45.2800i	−0.368164	+	1.61303i
$789$	−19.5904	−	85.8312i	−0.697437	−	3.05567i
$790$	−0.565853	+	0.272500i	−0.0201321	+	0.00969513i
$791$	9.84556	+	7.85157i	0.350068	+	0.279170i
$792$	32.5358	−	40.7986i	1.15611	−	1.44972i
$793$	0.560425	−	1.16374i	0.0199013	−	0.0413255i
$794$	5.18173	−	4.13230i	0.183893	−	0.146650i
$795$			0.294114i			0.0104311i
$796$	−29.3975	−	36.8632i	−1.04197	−	1.30658i
$797$	39.2904	−	8.96777i	1.39174	−	0.317655i	0.540017	−	0.841654i	$-0.318418\pi$
$797$	39.2904	−	8.96777i	1.39174	−	0.317655i	0.851719	+	0.523999i	$0.175560\pi$
$798$	−33.8511	+	7.72629i	−1.19832	+	0.273508i
$799$	−30.8518	−	38.6869i	−1.09146	−	1.36865i
$800$			30.5293i			1.07937i
$801$	−4.48874	+	3.57965i	−0.158602	+	0.126481i
$802$	−20.1125	+	41.7640i	−0.710196	+	1.47474i
$803$	17.3781	−	21.7914i	0.613260	−	0.769003i
$804$	75.8840	+	60.5155i	2.67622	+	2.13422i
$805$	−0.0187502	+	0.00902962i	−0.000660858	+	0.000318252i
$806$	−0.882512	−	3.86654i	−0.0310851	−	0.136193i
$807$	8.75751	−	38.3692i	0.308279	−	1.35066i
$808$	14.5675	+	7.01532i	0.512482	+	0.246798i
$809$	21.7442	+	45.1522i	0.764484	+	1.58747i	0.808542	+	0.588439i	$0.200257\pi$
$809$	21.7442	+	45.1522i	0.764484	+	1.58747i	−0.0440579	+	0.999029i	$0.514029\pi$
$810$	0.190236	+	0.0434201i	0.00668420	+	0.00152563i
$811$	24.7764			0.870017			0.435009	−	0.900426i	$-0.356745\pi$
$811$	24.7764			0.870017			0.435009	+	0.900426i	$0.356745\pi$
$812$	24.5805	−	9.72486i	0.862608	−	0.341276i
$813$	−76.2357			−2.67370
$814$	47.1741	+	10.7672i	1.65345	+	0.377390i
$815$	0.0568088	+	0.117965i	0.00198992	+	0.00413212i
$816$	−5.40906	−	2.60487i	−0.189355	−	0.0911885i
$817$	−4.97838	+	21.8117i	−0.174171	+	0.763095i
$818$	−16.9613	−	74.3122i	−0.593037	−	2.59827i
$819$	2.88886	−	1.39120i	0.100945	−	0.0486126i
$820$	0.208061	+	0.165923i	0.00726579	+	0.00579428i
$821$	22.1885	−	27.8235i	0.774384	−	0.971047i	−0.225611	−	0.974218i	$-0.572438\pi$
$821$	22.1885	−	27.8235i	0.774384	−	0.971047i	0.999995	+	0.00317052i	$0.00100921\pi$
$822$	15.4298	−	32.0402i	0.538175	−	1.11753i
$823$	12.0433	−	9.60419i	0.419802	−	0.334781i	−0.390699	−	0.920519i	$-0.627767\pi$
$823$	12.0433	−	9.60419i	0.419802	−	0.334781i	0.810501	+	0.585738i	$0.199195\pi$
$824$		−	34.2324i		−	1.19254i
$825$	−35.1576	−	44.0863i	−1.22403	−	1.53489i
$826$	3.63346	−	0.829313i	0.126424	−	0.0288555i
$827$	40.3885	−	9.21841i	1.40445	−	0.320556i	0.547864	−	0.836567i	$-0.315441\pi$
$827$	40.3885	−	9.21841i	1.40445	−	0.320556i	0.856581	+	0.516012i	$0.172584\pi$
$828$	2.28620	+	2.86680i	0.0794508	+	0.0996282i
$829$		−	4.64043i		−	0.161169i	−0.996748	−	0.0805844i	$-0.974321\pi$
$829$		−	4.64043i		−	0.161169i	0.996748	−	0.0805844i	$-0.0256787\pi$
$830$	0.864465	−	0.689388i	0.0300060	−	0.0239290i
$831$	−27.8001	+	57.7276i	−0.964376	+	2.00255i
$832$	−3.29215	+	4.12823i	−0.114135	+	0.143120i
$833$	−18.4274	−	14.6953i	−0.638470	−	0.509163i
$834$	−3.46780	+	1.67000i	−0.120080	+	0.0578275i
$835$	−0.151147	−	0.662219i	−0.00523067	−	0.0229170i
$836$	−9.58754	+	42.0058i	−0.331592	+	1.45280i
$837$	−22.8641	−	11.0108i	−0.790300	−	0.380588i
$838$	−7.40906	−	15.3851i	−0.255942	−	0.531468i
$839$	34.5374	+	7.88295i	1.19237	+	0.272150i	0.772248	−	0.635321i	$-0.219132\pi$
$839$	34.5374	+	7.88295i	1.19237	+	0.272150i	0.420117	+	0.907470i	$0.361989\pi$
$840$	0.665493			0.0229617
$841$	21.1502	−	19.8411i	0.729318	−	0.684175i
$842$	−46.2065			−1.59238
$843$	9.13904	+	2.08593i	0.314765	+	0.0718431i
$844$	16.3259	+	33.9011i	0.561960	+	1.16692i
$845$	−0.669404	−	0.322368i	−0.0230282	−	0.0110898i
$846$	−24.4887	+	107.292i	−0.841939	+	3.68878i
$847$	−1.66271	−	7.28479i	−0.0571313	−	0.250308i
$848$	−0.659050	+	0.317382i	−0.0226319	+	0.0108989i
$849$	39.2392	+	31.2922i	1.34669	+	1.07395i
$850$	36.5142	−	45.7873i	1.25243	−	1.57049i
$851$	−0.536390	+	1.11383i	−0.0183872	+	0.0381814i
$852$	−93.8930	+	74.8772i	−3.21672	+	2.56525i
$853$			25.5045i			0.873256i	0.899642	+	0.436628i	$0.143827\pi$
$853$			25.5045i			0.873256i	−0.899642	+	0.436628i	$0.856173\pi$
$854$	−7.04367	−	8.83248i	−0.241029	−	0.302241i
$855$	−0.987098	+	0.225299i	−0.0337580	+	0.00770505i
$856$	−23.4147	+	5.34424i	−0.800296	+	0.182662i
$857$	−22.3127	−	27.9793i	−0.762189	−	0.955754i	0.237690	−	0.971341i	$-0.423610\pi$
$857$	−22.3127	−	27.9793i	−0.762189	−	0.955754i	−0.999879	+	0.0155868i	$0.995038\pi$
$858$		−	10.3644i		−	0.353836i
$859$	23.1233	−	18.4402i	0.788956	−	0.629171i	−0.143830	−	0.989602i	$-0.545942\pi$
$859$	23.1233	−	18.4402i	0.788956	−	0.629171i	0.932786	+	0.360431i	$0.117370\pi$
$860$	0.511693	−	1.06254i	0.0174486	−	0.0362324i
$861$	4.04699	−	5.07476i	0.137921	−	0.172947i
$862$	20.9837	+	16.7340i	0.714709	+	0.569961i
$863$	−36.2241	+	17.4446i	−1.23308	+	0.593822i	−0.932926	−	0.360068i	$-0.882754\pi$
$863$	−36.2241	+	17.4446i	−1.23308	+	0.593822i	−0.300158	+	0.953890i	$0.597039\pi$
$864$	7.98986	+	35.0058i	0.271820	+	1.19092i
$865$	−0.248444	+	1.08850i	−0.00844734	+	0.0370102i
$866$	34.9324	+	16.8225i	1.18705	+	0.571654i
$867$	11.9706	+	24.8572i	0.406543	+	0.844196i
$868$	−20.6661	−	4.71689i	−0.701452	−	0.160102i
$869$	19.0088			0.644831
$870$	1.86711	−	0.738691i	0.0633011	−	0.0250440i
$871$	4.40323			0.149198
$872$	14.5401	+	3.31869i	0.492390	+	0.112385i
$873$	37.8565	+	78.6099i	1.28125	+	2.66054i
$874$	−1.62297	−	0.781583i	−0.0548979	−	0.0264374i
$875$	0.201115	−	0.881143i	0.00679893	−	0.0297881i
$876$	−13.9362	−	61.0583i	−0.470859	−	2.06297i
$877$	46.9427	−	22.6064i	1.58514	−	0.763364i	0.586237	−	0.810139i	$-0.300609\pi$
$877$	46.9427	−	22.6064i	1.58514	−	0.763364i	0.998905	+	0.0467750i	$0.0148944\pi$
$878$	−33.2454	−	26.5123i	−1.12198	−	0.894747i
$879$	−23.9699	+	30.0573i	−0.808485	+	1.01381i
$880$	−0.0408016	+	0.0847254i	−0.00137542	+	0.00285609i
$881$	35.3863	−	28.2196i	1.19219	−	0.950743i	0.192660	−	0.981266i	$-0.438289\pi$
$881$	35.3863	−	28.2196i	1.19219	−	0.950743i	0.999534	+	0.0305225i	$0.00971713\pi$
$882$			52.4196i			1.76506i
$883$	21.1350	+	26.5025i	0.711251	+	0.891880i	0.997808	−	0.0661830i	$-0.0210821\pi$
$883$	21.1350	+	26.5025i	0.711251	+	0.891880i	−0.286557	+	0.958063i	$0.592511\pi$
$884$	6.41314	−	1.46376i	0.215697	−	0.0492315i
$885$	0.168659	−	0.0384954i	0.00566942	−	0.00129401i
$886$	4.81273	+	6.03497i	0.161687	+	0.202749i
$887$			30.4108i			1.02110i	0.859850	+	0.510548i	$0.170557\pi$
$887$			30.4108i			1.02110i	−0.859850	+	0.510548i	$0.829443\pi$
$888$	30.9078	−	24.6481i	1.03720	−	0.827137i
$889$	−11.9098	+	24.7310i	−0.399443	+	0.829452i
$890$	−0.0926995	+	0.116241i	−0.00310729	+	0.00389642i
$891$	−4.61737	−	3.68223i	−0.154688	−	0.123359i
$892$	37.8601	−	18.2325i	1.26765	−	0.610469i
$893$	−7.35181	−	32.2104i	−0.246019	−	1.07788i
$894$	−7.32341	+	32.0860i	−0.244932	+	1.07312i
$895$	−0.0474772	−	0.0228638i	−0.00158699	−	0.000764254i
$896$	11.7562	+	24.4120i	0.392746	+	0.815546i
$897$	0.258163	+	0.0589240i	0.00861981	+	0.00196742i
$898$	−0.315858			−0.0105403
$899$	−22.9856	+	3.52888i	−0.766612	+	0.117695i
$900$	−79.5951			−2.65317
$901$	9.01346	+	2.05726i	0.300282	+	0.0685374i
$902$	−5.71875	−	11.8751i	−0.190414	−	0.395398i
$903$	−25.9162	−	12.4806i	−0.862437	−	0.415328i
$904$	4.64886	−	20.3680i	0.154619	−	0.677430i
$905$	0.0677778	+	0.296954i	0.00225301	+	0.00987108i
$906$	45.2709	−	21.8013i	1.50402	−	0.724300i
$907$	−12.4174	−	9.90255i	−0.412313	−	0.328809i	0.395267	−	0.918566i	$-0.370652\pi$
$907$	−12.4174	−	9.90255i	−0.412313	−	0.328809i	−0.807580	+	0.589757i	$0.799223\pi$
$908$	4.15851	−	5.21460i	0.138005	−	0.173053i
$909$	13.7226	−	28.4953i	0.455150	−	0.945129i
$910$	0.0649183	−	0.0517706i	0.00215202	−	0.00171618i
$911$			24.9672i			0.827199i	0.910459	+	0.413600i	$0.135729\pi$
$911$			24.9672i			0.827199i	−0.910459	+	0.413600i	$0.864271\pi$
$912$	−2.49927	−	3.13399i	−0.0827591	−	0.103777i
$913$	−32.6264	+	7.44675i	−1.07977	+	0.246452i
$914$	−70.9243	+	16.1880i	−2.34597	+	0.535452i
$915$	−0.326956	−	0.409990i	−0.0108088	−	0.0135538i
$916$		−	86.0768i		−	2.84406i
$917$	−4.08845	+	3.26043i	−0.135012	+	0.107669i
$918$	29.8852	−	62.0573i	0.986359	−	2.04819i
$919$	8.39456	−	10.5264i	0.276911	−	0.347236i	−0.623855	−	0.781540i	$-0.714434\pi$
$919$	8.39456	−	10.5264i	0.276911	−	0.347236i	0.900766	+	0.434305i	$0.143006\pi$
$920$	0.0269934	+	0.0215265i	0.000889947	+	0.000709709i
$921$	16.6830	−	8.03409i	0.549722	−	0.264732i
$922$	0.366107	+	1.60402i	0.0120571	+	0.0528256i
$923$	−1.21234	+	5.31162i	−0.0399048	+	0.174834i
$924$	−49.9104	−	24.0356i	−1.64193	−	0.790712i
$925$	−11.6435	−	24.1779i	−0.382835	−	0.794966i
$926$	−20.2255	−	4.61634i	−0.664651	−	0.151702i
$927$	−66.9616			−2.19931
$928$	24.1809	+	22.3137i	0.793776	+	0.732484i
$929$	7.53667			0.247270			0.123635	−	0.992328i	$-0.460545\pi$
$929$	7.53667			0.247270			0.123635	+	0.992328i	$0.460545\pi$
$930$	−1.56977	−	0.358291i	−0.0514749	−	0.0117488i
$931$	−6.82803	−	14.1785i	−0.223780	−	0.464683i
$932$	49.4865	+	23.8315i	1.62099	+	0.780625i
$933$	15.5152	−	67.9764i	0.507944	−	2.22545i
$934$	15.4738	+	67.7950i	0.506317	+	2.21832i
$935$	1.07084	−	0.515689i	0.0350202	−	0.0168648i
$936$	−4.15891	−	3.31662i	−0.135938	−	0.108407i
$937$	22.7346	−	28.5083i	0.742708	−	0.931326i	−0.256674	−	0.966498i	$-0.582627\pi$
$937$	22.7346	−	28.5083i	0.742708	−	0.931326i	0.999381	+	0.0351723i	$0.0111980\pi$
$938$	16.7098	−	34.6982i	0.545593	−	1.13294i
$939$	−4.38499	+	3.49691i	−0.143099	+	0.114117i
$940$			1.74158i			0.0568039i
$941$	21.9323	+	27.5023i	0.714973	+	0.896548i	0.998042	−	0.0625515i	$-0.0199238\pi$
$941$	21.9323	+	27.5023i	0.714973	+	0.896548i	−0.283068	+	0.959100i	$0.591352\pi$
$942$	118.430	−	27.0308i	3.85865	−	0.880712i
$943$	0.328304	−	0.0749333i	0.0106911	−	0.00244016i
$944$	0.268263	+	0.336391i	0.00873122	+	0.0109486i
$945$		−	0.531311i		−	0.0172836i
$946$	−45.6668	+	36.4180i	−1.48476	+	1.18405i
$947$	−4.51096	+	9.36711i	−0.146587	+	0.304390i	−0.961314	−	0.275453i	$-0.911172\pi$
$947$	−4.51096	+	9.36711i	−0.146587	+	0.304390i	0.814728	+	0.579843i	$0.196886\pi$
$948$	26.6308	−	33.3940i	0.864928	−	1.08459i
$949$	−2.22136	−	1.77148i	−0.0721085	−	0.0575046i
$950$	35.2301	−	16.9659i	1.14302	−	0.550447i
$951$	18.7608	+	82.1964i	0.608361	+	2.66540i
$952$	4.65498	−	20.3948i	0.150869	−	0.660999i
$953$	−48.4858	−	23.3495i	−1.57061	−	0.756366i	−0.572625	−	0.819818i	$-0.694075\pi$
$953$	−48.4858	−	23.3495i	−1.57061	−	0.756366i	−0.997985	+	0.0634519i	$0.979789\pi$
$954$	−8.92146	−	18.5256i	−0.288843	−	0.599789i
$955$	−0.581743	−	0.132779i	−0.0188248	−	0.00429663i
$956$	−54.2189			−1.75356
$957$	−60.6152	−	4.37571i	−1.95941	−	0.141446i
$958$	12.0129			0.388119
$959$	−8.40676	−	1.91879i	−0.271468	−	0.0619609i
$960$	0.930120	+	1.93141i	0.0300195	+	0.0623361i
$961$	−11.1288	−	5.35937i	−0.358995	−	0.172883i
$962$	1.09758	−	4.80881i	0.0353874	−	0.155042i
$963$	10.4538	+	45.8012i	0.336870	+	1.47592i
$964$	−62.2543	+	29.9801i	−2.00508	+	0.965594i
$965$	0.122639	+	0.0978010i	0.00394788	+	0.00314833i
$966$	1.44403	−	1.81075i	0.0464609	−	0.0582601i
$967$	5.16092	−	10.7168i	0.165964	−	0.344628i	−0.801356	−	0.598188i	$-0.795887\pi$
$967$	5.16092	−	10.7168i	0.165964	−	0.344628i	0.967319	+	0.253561i	$0.0816017\pi$
$968$	−9.69185	+	7.72899i	−0.311508	+	0.248419i
$969$			50.6634i			1.62754i
$970$	1.40875	+	1.76651i	0.0452322	+	0.0567194i
$971$	−48.8341	+	11.1461i	−1.56716	+	0.357694i	−0.915979	−	0.401226i	$-0.868584\pi$
$971$	−48.8341	+	11.1461i	−1.56716	+	0.357694i	−0.651183	+	0.758921i	$0.725727\pi$
$972$	41.0785	−	9.37591i	1.31759	−	0.300732i
$973$	0.581894	+	0.729672i	0.0186547	+	0.0233922i
$974$		−	7.89535i		−	0.252983i
$975$	−4.49404	+	3.58388i	−0.143924	+	0.114776i
$976$	0.565883	−	1.17507i	0.0181135	−	0.0376130i
$977$	8.61138	−	10.7983i	0.275502	−	0.345469i	−0.624760	−	0.780817i	$-0.714803\pi$
$977$	8.61138	−	10.7983i	0.275502	−	0.345469i	0.900262	+	0.435348i	$0.143375\pi$
$978$	−11.3921	−	9.08493i	−0.364281	−	0.290504i
$979$	4.05433	−	1.95246i	0.129577	−	0.0624010i
$980$	0.184592	+	0.808749i	0.00589656	+	0.0258345i
$981$	6.49165	−	28.4418i	0.207262	−	0.908076i
$982$	−11.9558	−	5.75762i	−0.381525	−	0.183733i
$983$	5.05705	+	10.5011i	0.161295	+	0.334932i	0.965916	−	0.258857i	$-0.0833458\pi$
$983$	5.05705	+	10.5011i	0.161295	+	0.334932i	−0.804621	+	0.593789i	$0.797631\pi$
$984$	−10.4984	−	2.39619i	−0.334677	−	0.0763879i
$985$	0.855428			0.0272562
$986$	−9.57799	−	62.3869i	−0.305025	−	1.98680i
$987$	42.4784			1.35210
$988$	4.28196	+	0.977329i	0.136227	+	0.0310930i
$989$	−0.647495	−	1.34454i	−0.0205891	−	0.0427538i
$990$	−2.38159	−	1.14692i	−0.0756920	−	0.0364514i
$991$	1.54324	−	6.76136i	0.0490225	−	0.214782i	−0.944484	−	0.328558i	$-0.893437\pi$
$991$	1.54324	−	6.76136i	0.0490225	−	0.214782i	0.993506	+	0.113776i	$0.0362946\pi$
$992$	−5.87117	−	25.7233i	−0.186410	−	0.816715i
$993$	72.6165	−	34.9703i	2.30442	−	1.10975i
$994$	37.2557	+	29.7104i	1.18168	+	0.942358i
$995$	−0.541451	+	0.678958i	−0.0171652	+	0.0215244i
$996$	−32.6264	+	67.7493i	−1.03381	+	2.14672i
$997$	−18.7405	+	14.9450i	−0.593516	+	0.473314i	−0.873588	−	0.486665i	$-0.838213\pi$
$997$	−18.7405	+	14.9450i	−0.593516	+	0.473314i	0.280072	+	0.959979i	$0.409642\pi$
$998$			53.7872i			1.70260i
$999$	−19.6784	−	24.6759i	−0.622597	−	0.780712i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.2.e.a.4.1	✓	12
3.2	odd	2		261.2.o.a.91.2		12
4.3	odd	2		464.2.y.d.33.2		12
5.2	odd	4		725.2.p.a.149.4		24
5.3	odd	4		725.2.p.a.149.1		24
5.4	even	2		725.2.q.a.526.2		12
29.2	odd	28		841.2.d.l.190.1		24
29.3	odd	28		841.2.d.m.645.1		24
29.4	even	14		841.2.e.f.267.1		12
29.5	even	14		841.2.e.a.651.1		12
29.6	even	14		841.2.b.e.840.2		12
29.7	even	7		841.2.e.i.196.2		12
29.8	odd	28		841.2.d.k.778.1		24
29.9	even	14		841.2.e.e.63.2		12
29.10	odd	28		841.2.d.k.574.1		24
29.11	odd	28		841.2.d.l.571.1		24
29.12	odd	4		841.2.d.m.605.4		24
29.13	even	14		841.2.e.h.270.2		12
29.14	odd	28		841.2.a.k.1.11		12
29.15	odd	28		841.2.a.k.1.2		12
29.16	even	7		841.2.e.a.270.1		12
29.17	odd	4		841.2.d.m.605.1		24
29.18	odd	28		841.2.d.l.571.4		24
29.19	odd	28		841.2.d.k.574.4		24
29.20	even	7		841.2.e.f.63.1		12
29.21	odd	28		841.2.d.k.778.4		24
29.22	even	14	inner	29.2.e.a.22.1	yes	12
29.23	even	7		841.2.b.e.840.11		12
29.24	even	7		841.2.e.h.651.2		12
29.25	even	7		841.2.e.e.267.2		12
29.26	odd	28		841.2.d.m.645.4		24
29.27	odd	28		841.2.d.l.190.4		24
29.28	even	2		841.2.e.i.236.2		12
87.14	even	28		7569.2.a.bp.1.2		12
87.44	even	28		7569.2.a.bp.1.11		12
87.80	odd	14		261.2.o.a.109.2		12
116.51	odd	14		464.2.y.d.225.2		12
145.22	odd	28		725.2.p.a.399.1		24
145.109	even	14		725.2.q.a.51.2		12
145.138	odd	28		725.2.p.a.399.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.e.a.4.1	✓	12	1.1	even	1	trivial
29.2.e.a.22.1	yes	12	29.22	even	14	inner
261.2.o.a.91.2		12	3.2	odd	2
261.2.o.a.109.2		12	87.80	odd	14
464.2.y.d.33.2		12	4.3	odd	2
464.2.y.d.225.2		12	116.51	odd	14
725.2.p.a.149.1		24	5.3	odd	4
725.2.p.a.149.4		24	5.2	odd	4
725.2.p.a.399.1		24	145.22	odd	28
725.2.p.a.399.4		24	145.138	odd	28
725.2.q.a.51.2		12	145.109	even	14
725.2.q.a.526.2		12	5.4	even	2
841.2.a.k.1.2		12	29.15	odd	28
841.2.a.k.1.11		12	29.14	odd	28
841.2.b.e.840.2		12	29.6	even	14
841.2.b.e.840.11		12	29.23	even	7
841.2.d.k.574.1		24	29.10	odd	28
841.2.d.k.574.4		24	29.19	odd	28
841.2.d.k.778.1		24	29.8	odd	28
841.2.d.k.778.4		24	29.21	odd	28
841.2.d.l.190.1		24	29.2	odd	28
841.2.d.l.190.4		24	29.27	odd	28
841.2.d.l.571.1		24	29.11	odd	28
841.2.d.l.571.4		24	29.18	odd	28
841.2.d.m.605.1		24	29.17	odd	4
841.2.d.m.605.4		24	29.12	odd	4
841.2.d.m.645.1		24	29.3	odd	28
841.2.d.m.645.4		24	29.26	odd	28
841.2.e.a.270.1		12	29.16	even	7
841.2.e.a.651.1		12	29.5	even	14
841.2.e.e.63.2		12	29.9	even	14
841.2.e.e.267.2		12	29.25	even	7
841.2.e.f.63.1		12	29.20	even	7
841.2.e.f.267.1		12	29.4	even	14
841.2.e.h.270.2		12	29.13	even	14
841.2.e.h.651.2		12	29.24	even	7
841.2.e.i.196.2		12	29.7	even	7
841.2.e.i.236.2		12	29.28	even	2
7569.2.a.bp.1.2		12	87.14	even	28
7569.2.a.bp.1.11		12	87.44	even	28

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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	29.e (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.21089 - 0.504621i) q^{2} +(-1.23248 - 2.55926i) q^{3} +(2.83146 + 1.36356i) q^{4} +(0.0128801 - 0.0564316i) q^{5} +(1.43341 + 6.28018i) q^{6} +(1.40728 - 0.677709i) q^{7} +(-2.02596 - 1.61565i) q^{8} +(-3.16036 + 3.96297i) q^{9} +O(q^{10})\)	\(q+(-2.21089 - 0.504621i) q^{2} +(-1.23248 - 2.55926i) q^{3} +(2.83146 + 1.36356i) q^{4} +(0.0128801 - 0.0564316i) q^{5} +(1.43341 + 6.28018i) q^{6} +(1.40728 - 0.677709i) q^{7} +(-2.02596 - 1.61565i) q^{8} +(-3.16036 + 3.96297i) q^{9} +(-0.0569531 + 0.118264i) q^{10} +(3.10613 - 2.47705i) q^{11} -8.92699i q^{12} +(-0.252504 - 0.316631i) q^{13} +(-3.45332 + 0.788198i) q^{14} +(-0.160298 + 0.0365869i) q^{15} +(-0.254963 - 0.319714i) q^{16} +5.16843i q^{17} +(8.98701 - 7.16690i) q^{18} +(-1.49728 + 3.10914i) q^{19} +(0.113417 - 0.142221i) q^{20} +(-3.46887 - 2.76633i) q^{21} +(-8.11728 + 3.90908i) q^{22} +(-0.0512209 - 0.224414i) q^{23} +(-1.63793 + 7.17623i) q^{24} +(4.50183 + 2.16797i) q^{25} +(0.398481 + 0.827455i) q^{26} +(5.72931 + 1.30768i) q^{27} +4.90874 q^{28} +(5.00751 - 1.98113i) q^{29} +0.372863 q^{30} +(-4.21005 - 0.960917i) q^{31} +(2.65101 + 5.50488i) q^{32} +(-10.1677 - 4.89649i) q^{33} +(2.60810 - 11.4268i) q^{34} +(-0.0201183 - 0.0881438i) q^{35} +(-14.3522 + 6.91164i) q^{36} +(-4.19898 - 3.34857i) q^{37} +(4.87927 - 6.11841i) q^{38} +(-0.499135 + 1.03647i) q^{39} +(-0.117269 + 0.0935185i) q^{40} +1.46294i q^{41} +(6.27335 + 7.86653i) q^{42} +(6.32061 - 1.44264i) q^{43} +(12.1725 - 2.77829i) q^{44} +(0.182931 + 0.229388i) q^{45} +0.522001i q^{46} +(-7.48524 + 5.96928i) q^{47} +(-0.503996 + 1.04656i) q^{48} +(-2.84329 + 3.56537i) q^{49} +(-8.85904 - 7.06485i) q^{50} +(13.2274 - 6.36997i) q^{51} +(-0.283211 - 1.24083i) q^{52} +(0.398044 - 1.74395i) q^{53} +(-12.0070 - 5.78226i) q^{54} +(-0.0997767 - 0.207188i) q^{55} +(-3.94604 - 0.900657i) q^{56} +9.80247 q^{57} +(-12.0708 + 1.85317i) q^{58} -1.05216 q^{59} +(-0.503764 - 0.114981i) q^{60} +(1.38382 + 2.87352i) q^{61} +(8.82307 + 4.24897i) q^{62} +(-1.76177 + 7.71880i) q^{63} +(-2.90123 - 12.7111i) q^{64} +(-0.0211203 + 0.0101710i) q^{65} +(20.0087 + 15.9564i) q^{66} +(-6.77893 + 8.50052i) q^{67} +(-7.04745 + 14.6342i) q^{68} +(-0.511205 + 0.407672i) q^{69} +0.205028i q^{70} +(-8.38773 - 10.5179i) q^{71} +(12.8056 - 2.92279i) q^{72} +(6.83974 - 1.56113i) q^{73} +(7.59372 + 9.52223i) q^{74} -14.1933i q^{75} +(-8.47898 + 6.76176i) q^{76} +(2.69246 - 5.59095i) q^{77} +(1.62656 - 2.03964i) q^{78} +(3.74078 + 2.98318i) q^{79} +(-0.0213259 + 0.0102700i) q^{80} +(-0.330785 - 1.44926i) q^{81} +(0.738232 - 3.23440i) q^{82} +(-7.58927 - 3.65480i) q^{83} +(-6.04990 - 12.5628i) q^{84} +(0.291662 + 0.0665701i) q^{85} -14.7022 q^{86} +(-11.2419 - 10.3738i) q^{87} -10.2950 q^{88} +(1.10427 + 0.252043i) q^{89} +(-0.288686 - 0.599462i) q^{90} +(-0.569927 - 0.274462i) q^{91} +(0.160971 - 0.705260i) q^{92} +(2.72955 + 11.9589i) q^{93} +(19.5613 - 9.42022i) q^{94} +(0.156168 + 0.124540i) q^{95} +(10.8211 - 13.5693i) q^{96} +(7.46850 - 15.5085i) q^{97} +(8.08536 - 6.44786i) q^{98} +20.1379i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 7 q^{2} - 7 q^{3} - q^{4} - q^{5} - 3 q^{6} - 11 q^{7} + 14 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 7 * q^2 - 7 * q^3 - q^4 - q^5 - 3 * q^6 - 11 * q^7 + 14 * q^8 - 3 * q^9	\( 12 q - 7 q^{2} - 7 q^{3} - q^{4} - q^{5} - 3 q^{6} - 11 q^{7} + 14 q^{8} - 3 q^{9} - 7 q^{10} + 7 q^{11} + 9 q^{13} - 7 q^{14} + 7 q^{15} + 9 q^{16} + 42 q^{18} - 7 q^{19} - 11 q^{20} - 7 q^{21} - 4 q^{22} - 5 q^{23} - 25 q^{24} + 13 q^{25} - 21 q^{26} - 7 q^{27} + 12 q^{28} - 15 q^{29} + 2 q^{30} - 21 q^{31} - 17 q^{33} - 13 q^{34} + 19 q^{35} - 40 q^{36} + 7 q^{37} + 28 q^{38} + 21 q^{39} + 35 q^{40} + 50 q^{42} + 7 q^{43} + 42 q^{44} + 16 q^{45} - 7 q^{47} - 14 q^{48} + 13 q^{49} - 28 q^{50} + 20 q^{51} - 6 q^{52} - 10 q^{53} - 38 q^{54} - 35 q^{55} - 21 q^{56} - 14 q^{57} - 57 q^{58} + 44 q^{59} - 28 q^{60} - 7 q^{61} + 37 q^{62} - 13 q^{63} - 26 q^{64} - 6 q^{65} + 21 q^{66} - 37 q^{67} + 14 q^{68} + 21 q^{69} - 21 q^{71} + 35 q^{72} + 14 q^{73} + 7 q^{76} - 7 q^{77} + 17 q^{78} + 49 q^{79} - 6 q^{80} + q^{81} + 22 q^{82} + 5 q^{83} + 21 q^{84} + 14 q^{85} - 44 q^{86} + 15 q^{87} - 66 q^{88} + 7 q^{89} + 28 q^{90} - 3 q^{91} - 6 q^{92} + 19 q^{93} + 66 q^{94} - 7 q^{95} + 30 q^{96} + 14 q^{97} - 42 q^{98}+O(q^{100}) \) 12 * q - 7 * q^2 - 7 * q^3 - q^4 - q^5 - 3 * q^6 - 11 * q^7 + 14 * q^8 - 3 * q^9 - 7 * q^10 + 7 * q^11 + 9 * q^13 - 7 * q^14 + 7 * q^15 + 9 * q^16 + 42 * q^18 - 7 * q^19 - 11 * q^20 - 7 * q^21 - 4 * q^22 - 5 * q^23 - 25 * q^24 + 13 * q^25 - 21 * q^26 - 7 * q^27 + 12 * q^28 - 15 * q^29 + 2 * q^30 - 21 * q^31 - 17 * q^33 - 13 * q^34 + 19 * q^35 - 40 * q^36 + 7 * q^37 + 28 * q^38 + 21 * q^39 + 35 * q^40 + 50 * q^42 + 7 * q^43 + 42 * q^44 + 16 * q^45 - 7 * q^47 - 14 * q^48 + 13 * q^49 - 28 * q^50 + 20 * q^51 - 6 * q^52 - 10 * q^53 - 38 * q^54 - 35 * q^55 - 21 * q^56 - 14 * q^57 - 57 * q^58 + 44 * q^59 - 28 * q^60 - 7 * q^61 + 37 * q^62 - 13 * q^63 - 26 * q^64 - 6 * q^65 + 21 * q^66 - 37 * q^67 + 14 * q^68 + 21 * q^69 - 21 * q^71 + 35 * q^72 + 14 * q^73 + 7 * q^76 - 7 * q^77 + 17 * q^78 + 49 * q^79 - 6 * q^80 + q^81 + 22 * q^82 + 5 * q^83 + 21 * q^84 + 14 * q^85 - 44 * q^86 + 15 * q^87 - 66 * q^88 + 7 * q^89 + 28 * q^90 - 3 * q^91 - 6 * q^92 + 19 * q^93 + 66 * q^94 - 7 * q^95 + 30 * q^96 + 14 * q^97 - 42 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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