LMFDB - Embedded newform 155.2.q.b.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [155,2,Mod(41,155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(155, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("155.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 155 = 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	155.q (of order $15$, degree $8$, 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:	$1.23768123133$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			81.2
Character	$\chi$	$=$	155.81
Dual form			155.2.q.b.111.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.55894 - 1.13264i) q^{2} +(-0.439495 - 0.195676i) q^{3} +(0.529393 + 1.62930i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.463517 + 0.802834i) q^{6} +(-2.49772 + 2.77400i) q^{7} +(-0.170807 + 0.525691i) q^{8} +(-1.85252 - 2.05744i) q^{9} +O(q^{10})$	\(q+(-1.55894 - 1.13264i) q^{2} +(-0.439495 - 0.195676i) q^{3} +(0.529393 + 1.62930i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.463517 + 0.802834i) q^{6} +(-2.49772 + 2.77400i) q^{7} +(-0.170807 + 0.525691i) q^{8} +(-1.85252 - 2.05744i) q^{9} +(1.76036 - 0.783763i) q^{10} +(1.92380 + 0.408916i) q^{11} +(0.0861498 - 0.819660i) q^{12} +(0.484249 + 4.60732i) q^{13} +(7.03573 - 1.49549i) q^{14} +(0.389208 - 0.282776i) q^{15} +(3.63363 - 2.63999i) q^{16} +(-3.33092 + 0.708008i) q^{17} +(0.557647 + 5.30565i) q^{18} +(-0.873384 + 8.30970i) q^{19} +(-1.67571 - 0.356184i) q^{20} +(1.64054 - 0.730416i) q^{21} +(-2.53593 - 2.81643i) q^{22} +(2.10357 - 6.47411i) q^{23} +(0.177934 - 0.197616i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(4.46350 - 7.73101i) q^{26} +(0.857578 + 2.63935i) q^{27} +(-5.84197 - 2.60101i) q^{28} +(-5.12053 - 3.72029i) q^{29} -0.927033 q^{30} +(-3.06803 + 4.64620i) q^{31} -7.54926 q^{32} +(-0.765485 - 0.556157i) q^{33} +(5.99461 + 2.66897i) q^{34} +(-1.15349 - 3.55009i) q^{35} +(2.37148 - 4.10752i) q^{36} +(-3.28791 - 5.69482i) q^{37} +(10.7734 - 11.9651i) q^{38} +(0.688717 - 2.11965i) q^{39} +(-0.369858 - 0.410769i) q^{40} +(-8.16651 + 3.63596i) q^{41} +(-3.38480 - 0.719461i) q^{42} +(-0.0738348 + 0.702492i) q^{43} +(0.352197 + 3.35093i) q^{44} +(2.70806 - 0.575615i) q^{45} +(-10.6121 + 7.71017i) q^{46} +(2.03315 - 1.47717i) q^{47} +(-2.11355 + 0.449248i) q^{48} +(-0.724769 - 6.89572i) q^{49} +(-0.201422 + 1.91640i) q^{50} +(1.60246 + 0.340614i) q^{51} +(-7.25037 + 3.22807i) q^{52} +(4.16026 + 4.62043i) q^{53} +(1.65251 - 5.08591i) q^{54} +(-1.31603 + 1.46160i) q^{55} +(-1.03164 - 1.78685i) q^{56} +(2.00986 - 3.48117i) q^{57} +(3.76887 + 11.5994i) q^{58} +(0.810429 + 0.360826i) q^{59} +(0.666772 + 0.484438i) q^{60} +10.1791 q^{61} +(10.0453 - 3.76819i) q^{62} +10.3344 q^{63} +(4.50157 + 3.27058i) q^{64} +(-4.23218 - 1.88429i) q^{65} +(0.563420 + 1.73403i) q^{66} +(0.271777 - 0.470731i) q^{67} +(-2.91692 - 5.05226i) q^{68} +(-2.19134 + 2.43373i) q^{69} +(-2.22273 + 6.84086i) q^{70} +(8.27069 + 9.18553i) q^{71} +(1.39800 - 0.622431i) q^{72} +(-10.0825 - 2.14311i) q^{73} +(-1.32451 + 12.6019i) q^{74} +(0.0502873 + 0.478452i) q^{75} +(-14.0014 + 2.97609i) q^{76} +(-5.93944 + 4.31526i) q^{77} +(-3.47446 + 2.52434i) q^{78} +(12.8102 - 2.72290i) q^{79} +(0.469481 + 4.46681i) q^{80} +(-0.728622 + 6.93238i) q^{81} +(16.8493 + 3.58143i) q^{82} +(-0.791033 + 0.352191i) q^{83} +(2.05856 + 2.28626i) q^{84} +(1.05231 - 3.23866i) q^{85} +(0.910771 - 1.01151i) q^{86} +(1.52248 + 2.63701i) q^{87} +(-0.543562 + 0.941478i) q^{88} +(-0.461178 - 1.41936i) q^{89} +(-4.87365 - 2.16989i) q^{90} +(-13.9902 - 10.1645i) q^{91} +11.6619 q^{92} +(2.25753 - 1.44165i) q^{93} -4.84266 q^{94} +(-6.75972 - 4.91122i) q^{95} +(3.31786 + 1.47721i) q^{96} +(0.330979 + 1.01865i) q^{97} +(-6.68046 + 11.5709i) q^{98} +(-2.72256 - 4.71562i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 2 q^{2} + 3 q^{3} - 2 q^{4} - 20 q^{5} - 12 q^{6} - 2 q^{7} - 31 q^{8} + 6 q^{9}+O(q^{10}) $ 40 * q + 2 * q^2 + 3 * q^3 - 2 * q^4 - 20 * q^5 - 12 * q^6 - 2 * q^7 - 31 * q^8 + 6 * q^9	\( 40 q + 2 q^{2} + 3 q^{3} - 2 q^{4} - 20 q^{5} - 12 q^{6} - 2 q^{7} - 31 q^{8} + 6 q^{9} - q^{10} + 16 q^{11} - q^{12} + 2 q^{13} - 10 q^{14} - 6 q^{15} - 16 q^{16} + 4 q^{17} + 37 q^{18} - 9 q^{19} + q^{20} - 24 q^{21} - 2 q^{22} - 4 q^{23} + 110 q^{24} - 20 q^{25} - 4 q^{26} - 9 q^{27} + 38 q^{28} - 22 q^{29} + 24 q^{30} - 6 q^{31} - 60 q^{32} + 9 q^{33} - 16 q^{34} + 4 q^{35} - q^{36} - 38 q^{37} - 32 q^{38} - 55 q^{39} + 8 q^{40} - 24 q^{41} - 68 q^{42} + 26 q^{43} - 52 q^{44} + 6 q^{45} - 50 q^{46} + 4 q^{47} + 105 q^{48} + 93 q^{49} - q^{50} - 42 q^{51} + 15 q^{52} + 13 q^{53} + 102 q^{54} + q^{55} + 5 q^{56} - 36 q^{57} - 37 q^{58} + 31 q^{59} + 17 q^{60} + 68 q^{61} + 47 q^{62} - 10 q^{63} - 23 q^{64} + 2 q^{65} - 2 q^{67} - 28 q^{68} - 48 q^{69} - 10 q^{70} - 30 q^{71} + 39 q^{72} + 25 q^{73} + 50 q^{74} + 3 q^{75} + 14 q^{76} - 64 q^{77} - 22 q^{78} + 49 q^{79} - 7 q^{80} + 25 q^{81} - 66 q^{82} - 18 q^{83} - 18 q^{84} + 7 q^{85} + 163 q^{86} - 36 q^{87} - 124 q^{88} + 4 q^{89} - 23 q^{90} - 37 q^{91} + 110 q^{92} + 7 q^{93} - 94 q^{94} - 12 q^{95} + 22 q^{96} + 46 q^{97} - 13 q^{98} + 17 q^{99}+O(q^{100}) \) 40 * q + 2 * q^2 + 3 * q^3 - 2 * q^4 - 20 * q^5 - 12 * q^6 - 2 * q^7 - 31 * q^8 + 6 * q^9 - q^10 + 16 * q^11 - q^12 + 2 * q^13 - 10 * q^14 - 6 * q^15 - 16 * q^16 + 4 * q^17 + 37 * q^18 - 9 * q^19 + q^20 - 24 * q^21 - 2 * q^22 - 4 * q^23 + 110 * q^24 - 20 * q^25 - 4 * q^26 - 9 * q^27 + 38 * q^28 - 22 * q^29 + 24 * q^30 - 6 * q^31 - 60 * q^32 + 9 * q^33 - 16 * q^34 + 4 * q^35 - q^36 - 38 * q^37 - 32 * q^38 - 55 * q^39 + 8 * q^40 - 24 * q^41 - 68 * q^42 + 26 * q^43 - 52 * q^44 + 6 * q^45 - 50 * q^46 + 4 * q^47 + 105 * q^48 + 93 * q^49 - q^50 - 42 * q^51 + 15 * q^52 + 13 * q^53 + 102 * q^54 + q^55 + 5 * q^56 - 36 * q^57 - 37 * q^58 + 31 * q^59 + 17 * q^60 + 68 * q^61 + 47 * q^62 - 10 * q^63 - 23 * q^64 + 2 * q^65 - 2 * q^67 - 28 * q^68 - 48 * q^69 - 10 * q^70 - 30 * q^71 + 39 * q^72 + 25 * q^73 + 50 * q^74 + 3 * q^75 + 14 * q^76 - 64 * q^77 - 22 * q^78 + 49 * q^79 - 7 * q^80 + 25 * q^81 - 66 * q^82 - 18 * q^83 - 18 * q^84 + 7 * q^85 + 163 * q^86 - 36 * q^87 - 124 * q^88 + 4 * q^89 - 23 * q^90 - 37 * q^91 + 110 * q^92 + 7 * q^93 - 94 * q^94 - 12 * q^95 + 22 * q^96 + 46 * q^97 - 13 * q^98 + 17 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/155\mathbb{Z}\right)^\times$.

$n$	$32$	$96$
$\chi(n)$	$1$	$e\left(\frac{2}{15}\right)$

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 $

$2$	−1.55894	−	1.13264i	−1.10234	−	0.800894i	−0.120896	−	0.992665i	$-0.538577\pi$
$2$	−1.55894	−	1.13264i	−1.10234	−	0.800894i	−0.981440	+	0.191771i	$0.938577\pi$
$3$	−0.439495	−	0.195676i	−0.253743	−	0.112974i	0.275924	−	0.961180i	$-0.411016\pi$
$3$	−0.439495	−	0.195676i	−0.253743	−	0.112974i	−0.529667	+	0.848206i	$0.677683\pi$
$4$	0.529393	+	1.62930i	0.264696	+	0.814652i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	0.463517	+	0.802834i	0.189230	+	0.327756i
$7$	−2.49772	+	2.77400i	−0.944050	+	1.04847i	0.0547003	+	0.998503i	$0.482580\pi$
$7$	−2.49772	+	2.77400i	−0.944050	+	1.04847i	−0.998751	+	0.0499713i	$0.984087\pi$
$8$	−0.170807	+	0.525691i	−0.0603896	+	0.185860i
$9$	−1.85252	−	2.05744i	−0.617508	−	0.685812i
$10$	1.76036	−	0.783763i	0.556675	−	0.247848i
$11$	1.92380	+	0.408916i	0.580047	+	0.123293i	0.488586	−	0.872516i	$-0.337513\pi$
$11$	1.92380	+	0.408916i	0.580047	+	0.123293i	0.0914610	+	0.995809i	$0.470846\pi$
$12$	0.0861498	−	0.819660i	0.0248693	−	0.236616i
$13$	0.484249	+	4.60732i	0.134307	+	1.27784i	0.829291	+	0.558817i	$0.188745\pi$
$13$	0.484249	+	4.60732i	0.134307	+	1.27784i	−0.694984	+	0.719025i	$0.744589\pi$
$14$	7.03573	−	1.49549i	1.88038	−	0.399687i
$15$	0.389208	−	0.282776i	0.100493	−	0.0730125i
$16$	3.63363	−	2.63999i	0.908408	−	0.659997i
$17$	−3.33092	+	0.708008i	−0.807866	+	0.171717i	−0.593289	−	0.804990i	$-0.702171\pi$
$17$	−3.33092	+	0.708008i	−0.807866	+	0.171717i	−0.214577	+	0.976707i	$0.568837\pi$
$18$	0.557647	+	5.30565i	0.131439	+	1.25055i
$19$	−0.873384	+	8.30970i	−0.200368	+	1.90638i	0.183553	+	0.983010i	$0.441240\pi$
$19$	−0.873384	+	8.30970i	−0.200368	+	1.90638i	−0.383922	+	0.923366i	$0.625427\pi$
$20$	−1.67571	−	0.356184i	−0.374701	−	0.0796452i
$21$	1.64054	−	0.730416i	0.357996	−	0.159390i
$22$	−2.53593	−	2.81643i	−0.540662	−	0.600466i
$23$	2.10357	−	6.47411i	0.438624	−	1.34995i	−0.450703	−	0.892674i	$-0.648827\pi$
$23$	2.10357	−	6.47411i	0.438624	−	1.34995i	0.889327	−	0.457272i	$-0.151173\pi$
$24$	0.177934	−	0.197616i	0.0363207	−	0.0403382i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	4.46350	−	7.73101i	0.875365	−	1.51618i
$27$	0.857578	+	2.63935i	0.165041	+	0.507944i
$28$	−5.84197	−	2.60101i	−1.10403	−	0.491545i
$29$	−5.12053	−	3.72029i	−0.950859	−	0.690840i	0.000150605	−	1.00000i	$-0.499952\pi$
$29$	−5.12053	−	3.72029i	−0.950859	−	0.690840i	−0.951010	+	0.309160i	$0.899952\pi$
$30$	−0.927033			−0.169252
$31$	−3.06803	+	4.64620i	−0.551034	+	0.834483i
$31$	−3.06803	+	4.64620i	−0.551034	+	0.834483i
$32$	−7.54926			−1.33453
$33$	−0.765485	−	0.556157i	−0.133254	−	0.0968145i
$34$	5.99461	+	2.66897i	1.02807	+	0.457725i
$35$	−1.15349	−	3.55009i	−0.194976	−	0.600075i
$36$	2.37148	−	4.10752i	0.395246	−	0.684586i
$37$	−3.28791	−	5.69482i	−0.540529	−	0.936223i	−0.998874	−	0.0474489i	$-0.984891\pi$
$37$	−3.28791	−	5.69482i	−0.540529	−	0.936223i	0.458345	−	0.888774i	$-0.348442\pi$
$38$	10.7734	−	11.9651i	1.74768	−	1.94099i
$39$	0.688717	−	2.11965i	0.110283	−	0.339416i
$40$	−0.369858	−	0.410769i	−0.0584797	−	0.0649483i
$41$	−8.16651	+	3.63596i	−1.27539	+	0.567842i	−0.928942	−	0.370226i	$-0.879280\pi$
$41$	−8.16651	+	3.63596i	−1.27539	+	0.567842i	−0.346452	+	0.938068i	$0.612614\pi$
$42$	−3.38480	−	0.719461i	−0.522286	−	0.111015i
$43$	−0.0738348	+	0.702492i	−0.0112597	+	0.107129i	−0.998708	−	0.0508123i	$-0.983819\pi$
$43$	−0.0738348	+	0.702492i	−0.0112597	+	0.107129i	0.987449	+	0.157941i	$0.0504857\pi$
$44$	0.352197	+	3.35093i	0.0530956	+	0.505171i
$45$	2.70806	−	0.575615i	0.403693	−	0.0858076i
$46$	−10.6121	+	7.71017i	−1.56467	+	1.13680i
$47$	2.03315	−	1.47717i	0.296566	−	0.215468i	−0.429545	−	0.903046i	$-0.641326\pi$
$47$	2.03315	−	1.47717i	0.296566	−	0.215468i	0.726111	+	0.687578i	$0.241326\pi$
$48$	−2.11355	+	0.449248i	−0.305064	+	0.0648434i
$49$	−0.724769	−	6.89572i	−0.103538	−	0.985103i
$50$	−0.201422	+	1.91640i	−0.0284853	+	0.271020i
$51$	1.60246	+	0.340614i	0.224390	+	0.0476955i
$52$	−7.25037	+	3.22807i	−1.00545	+	0.447653i
$53$	4.16026	+	4.62043i	0.571455	+	0.634665i	0.957713	−	0.287726i	$-0.0928992\pi$
$53$	4.16026	+	4.62043i	0.571455	+	0.634665i	−0.386258	+	0.922391i	$0.626232\pi$
$54$	1.65251	−	5.08591i	0.224878	−	0.692105i
$55$	−1.31603	+	1.46160i	−0.177453	+	0.197082i
$56$	−1.03164	−	1.78685i	−0.137859	−	0.238778i
$57$	2.00986	−	3.48117i	0.266212	−	0.461093i
$58$	3.76887	+	11.5994i	0.494877	+	1.52307i
$59$	0.810429	+	0.360826i	0.105509	+	0.0469756i	0.458812	−	0.888533i	$-0.348275\pi$
$59$	0.810429	+	0.360826i	0.105509	+	0.0469756i	−0.353303	+	0.935509i	$0.614942\pi$
$60$	0.666772	+	0.484438i	0.0860799	+	0.0625407i
$61$	10.1791			1.30330			0.651651	−	0.758519i	$-0.274077\pi$
$61$	10.1791			1.30330			0.651651	+	0.758519i	$0.274077\pi$
$62$	10.0453	−	3.76819i	1.27576	−	0.478561i
$63$	10.3344			1.30202
$64$	4.50157	+	3.27058i	0.562696	+	0.408823i
$65$	−4.23218	−	1.88429i	−0.524938	−	0.233717i
$66$	0.563420	+	1.73403i	0.0693523	+	0.213444i
$67$	0.271777	−	0.470731i	0.0332028	−	0.0575090i	−0.848946	−	0.528479i	$-0.822763\pi$
$67$	0.271777	−	0.470731i	0.0332028	−	0.0575090i	0.882149	+	0.470970i	$0.156096\pi$
$68$	−2.91692	−	5.05226i	−0.353729	−	0.612677i
$69$	−2.19134	+	2.43373i	−0.263806	+	0.292986i
$70$	−2.22273	+	6.84086i	−0.265667	+	0.817640i
$71$	8.27069	+	9.18553i	0.981550	+	1.09012i	0.995921	+	0.0902247i	$0.0287585\pi$
$71$	8.27069	+	9.18553i	0.981550	+	1.09012i	−0.0143717	+	0.999897i	$0.504575\pi$
$72$	1.39800	−	0.622431i	0.164756	−	0.0733542i
$73$	−10.0825	−	2.14311i	−1.18007	−	0.250832i	−0.424209	−	0.905564i	$-0.639448\pi$
$73$	−10.0825	−	2.14311i	−1.18007	−	0.250832i	−0.755861	+	0.654733i	$0.772781\pi$
$74$	−1.32451	+	12.6019i	−0.153971	+	1.46494i
$75$	0.0502873	+	0.478452i	0.00580668	+	0.0552469i
$76$	−14.0014	+	2.97609i	−1.60607	+	0.341380i
$77$	−5.93944	+	4.31526i	−0.676863	+	0.491769i
$78$	−3.47446	+	2.52434i	−0.393405	+	0.285826i
$79$	12.8102	−	2.72290i	1.44126	−	0.306350i	0.580044	−	0.814585i	$-0.303035\pi$
$79$	12.8102	−	2.72290i	1.44126	−	0.306350i	0.861218	+	0.508236i	$0.169702\pi$
$80$	0.469481	+	4.46681i	0.0524895	+	0.499405i
$81$	−0.728622	+	6.93238i	−0.0809580	+	0.770264i
$82$	16.8493	+	3.58143i	1.86069	+	0.395503i
$83$	−0.791033	+	0.352191i	−0.0868271	+	0.0386579i	−0.449691	−	0.893184i	$-0.648466\pi$
$83$	−0.791033	+	0.352191i	−0.0868271	+	0.0386579i	0.362864	+	0.931842i	$0.381799\pi$
$84$	2.05856	+	2.28626i	0.224607	+	0.249452i
$85$	1.05231	−	3.23866i	0.114139	−	0.351282i
$86$	0.910771	−	1.01151i	0.0982109	−	0.109074i
$87$	1.52248	+	2.63701i	0.163227	+	0.282717i
$88$	−0.543562	+	0.941478i	−0.0579440	+	0.100362i
$89$	−0.461178	−	1.41936i	−0.0488847	−	0.150452i	0.923634	−	0.383275i	$-0.125204\pi$
$89$	−0.461178	−	1.41936i	−0.0488847	−	0.150452i	−0.972519	+	0.232823i	$0.925204\pi$
$90$	−4.87365	−	2.16989i	−0.513728	−	0.228727i
$91$	−13.9902	−	10.1645i	−1.46658	−	1.06553i
$92$	11.6619			1.21584
$93$	2.25753	−	1.44165i	0.234095	−	0.149492i
$94$	−4.84266			−0.499482
$95$	−6.75972	−	4.91122i	−0.693532	−	0.503881i
$96$	3.31786	+	1.47721i	0.338628	+	0.150767i
$97$	0.330979	+	1.01865i	0.0336058	+	0.103428i	0.966452	−	0.256846i	$-0.0826833\pi$
$97$	0.330979	+	1.01865i	0.0336058	+	0.103428i	−0.932847	+	0.360274i	$0.882683\pi$
$98$	−6.68046	+	11.5709i	−0.674829	+	1.16884i
$99$	−2.72256	−	4.71562i	−0.273628	−	0.473938i
$100$	1.14632	−	1.27312i	0.114632	−	0.127312i
$101$	0.386821	−	1.19051i	0.0384901	−	0.118460i	−0.929965	−	0.367647i	$-0.880163\pi$
$101$	0.386821	−	1.19051i	0.0384901	−	0.118460i	0.968455	+	0.249187i	$0.0801634\pi$
$102$	−2.11235	−	2.34600i	−0.209154	−	0.232289i
$103$	2.12944	−	0.948089i	0.209820	−	0.0934180i	−0.299136	−	0.954211i	$-0.596698\pi$
$103$	2.12944	−	0.948089i	0.209820	−	0.0934180i	0.508956	+	0.860793i	$0.330032\pi$
$104$	−2.50474	−	0.532400i	−0.245610	−	0.0522061i
$105$	−0.187712	+	1.78596i	−0.0183188	+	0.174292i
$106$	−1.25232	−	11.9150i	−0.121636	−	1.15729i
$107$	6.39902	−	1.36015i	0.618617	−	0.131491i	0.112065	−	0.993701i	$-0.464253\pi$
$107$	6.39902	−	1.36015i	0.618617	−	0.131491i	0.506551	+	0.862210i	$0.330920\pi$
$108$	−3.84631	+	2.79451i	−0.370111	+	0.268902i
$109$	4.55769	−	3.31136i	0.436548	−	0.317171i	−0.347714	−	0.937601i	$-0.613042\pi$
$109$	4.55769	−	3.31136i	0.436548	−	0.317171i	0.784262	+	0.620430i	$0.213042\pi$
$110$	3.70707	−	0.787962i	0.353455	−	0.0751292i
$111$	0.330680	+	3.14621i	0.0313868	+	0.298625i
$112$	−1.75247	+	16.6737i	−0.165593	+	1.57551i
$113$	3.87804	+	0.824303i	0.364815	+	0.0775439i	0.386672	−	0.922217i	$-0.373625\pi$
$113$	3.87804	+	0.824303i	0.364815	+	0.0775439i	−0.0218570	+	0.999761i	$0.506958\pi$
$114$	−7.07614	+	3.15050i	−0.662741	+	0.295071i
$115$	4.55496	+	5.05880i	0.424753	+	0.471736i
$116$	3.35070	−	10.3124i	0.311105	−	0.957482i
$117$	8.58220	−	9.53150i	0.793424	−	0.881187i
$118$	−0.854725	−	1.48043i	−0.0786838	−	0.136284i
$119$	6.35569	−	11.0084i	0.582625	−	1.00914i
$120$	0.0821733	+	0.252904i	0.00750136	+	0.0230868i
$121$	−6.51522	−	2.90076i	−0.592292	−	0.263706i
$122$	−15.8686	−	11.5292i	−1.43668	−	1.04381i
$123$	4.30061			0.387773
$124$	−9.19427	−	2.53908i	−0.825670	−	0.228016i
$125$	1.00000			0.0894427
$126$	−16.1107	−	11.7051i	−1.43526	−	1.04278i
$127$	14.3771	+	6.40111i	1.27576	+	0.568007i	0.929047	−	0.369962i	$-0.120629\pi$
$127$	14.3771	+	6.40111i	1.27576	+	0.568007i	0.346718	+	0.937969i	$0.387296\pi$
$128$	1.35241	+	4.16228i	0.119537	+	0.367897i
$129$	0.169911	−	0.294294i	0.0149598	−	0.0259111i
$130$	4.46350	+	7.73101i	0.391475	+	0.678055i
$131$	−7.95573	+	8.83573i	−0.695095	+	0.771982i	−0.982587	−	0.185801i	$-0.940512\pi$
$131$	−7.95573	+	8.83573i	−0.695095	+	0.771982i	0.287492	+	0.957783i	$0.407179\pi$
$132$	0.500907	−	1.54163i	0.0435983	−	0.134182i
$133$	−20.8696	−	23.1781i	−1.80963	−	2.00980i
$134$	−0.956850	+	0.426017i	−0.0826593	+	0.0368023i
$135$	−2.71453	−	0.576992i	−0.233630	−	0.0496596i
$136$	0.196752	−	1.87197i	0.0168713	−	0.160520i
$137$	0.622276	+	5.92056i	0.0531646	+	0.505827i	0.988408	+	0.151822i	$0.0485140\pi$
$137$	0.622276	+	5.92056i	0.0531646	+	0.505827i	−0.935243	+	0.354006i	$0.884819\pi$
$138$	6.17268	−	1.31204i	0.525453	−	0.111689i
$139$	−8.88605	+	6.45610i	−0.753705	+	0.547599i	−0.896973	−	0.442085i	$-0.854239\pi$
$139$	−8.88605	+	6.45610i	−0.753705	+	0.547599i	0.143268	+	0.989684i	$0.454239\pi$
$140$	5.17353	−	3.75879i	0.437243	−	0.317675i
$141$	−1.18261	+	0.251371i	−0.0995935	+	0.0211693i
$142$	−2.48964	−	23.6873i	−0.208926	−	1.98780i
$143$	−0.952410	+	9.06158i	−0.0796445	+	0.757767i
$144$	−12.1630	−	2.58533i	−1.01358	−	0.215444i
$145$	5.78213	−	2.57437i	0.480180	−	0.213790i
$146$	13.2907	+	14.7608i	1.09994	+	1.22161i
$147$	−1.03079	+	3.17246i	−0.0850184	+	0.261660i
$148$	7.53800	−	8.37180i	0.619620	−	0.688158i
$149$	−1.18504	−	2.05254i	−0.0970819	−	0.168151i	0.813394	−	0.581714i	$-0.197618\pi$
$149$	−1.18504	−	2.05254i	−0.0970819	−	0.168151i	−0.910476	+	0.413563i	$0.864284\pi$
$150$	0.463517	−	0.802834i	0.0378460	−	0.0655511i
$151$	1.07415	+	3.30589i	0.0874130	+	0.269030i	0.985202	−	0.171396i	$-0.0548277\pi$
$151$	1.07415	+	3.30589i	0.0874130	+	0.269030i	−0.897789	+	0.440425i	$0.854828\pi$
$152$	−4.21916	−	1.87849i	−0.342219	−	0.152366i
$153$	7.62729	+	5.54155i	0.616630	+	0.448008i
$154$	14.1468			1.13998
$155$	−2.48972	−	4.98009i	−0.199979	−	0.400011i
$156$	3.81816			0.305697
$157$	5.63714	+	4.09562i	0.449893	+	0.326866i	0.789554	−	0.613682i	$-0.210312\pi$
$157$	5.63714	+	4.09562i	0.449893	+	0.326866i	−0.339661	+	0.940548i	$0.610312\pi$
$158$	−23.0544	−	10.2645i	−1.83411	−	0.816598i
$159$	−0.924305	−	2.84472i	−0.0733022	−	0.225601i
$160$	3.77463	−	6.53785i	0.298411	−	0.516863i
$161$	12.7051	+	22.0058i	1.00130	+	1.73430i
$162$	8.98773	−	9.98188i	0.706143	−	0.784251i
$163$	−1.02830	+	3.16477i	−0.0805425	+	0.247884i	−0.983217	−	0.182440i	$-0.941601\pi$
$163$	−1.02830	+	3.16477i	−0.0805425	+	0.247884i	0.902675	+	0.430324i	$0.141601\pi$
$164$	−10.2474	−	11.3809i	−0.800186	−	0.888696i
$165$	0.864389	−	0.384851i	0.0672926	−	0.0299606i
$166$	1.63208	+	0.346908i	0.126674	+	0.0269253i
$167$	−1.88413	+	17.9263i	−0.145799	+	1.38718i	0.639846	+	0.768503i	$0.278998\pi$
$167$	−1.88413	+	17.9263i	−0.145799	+	1.38718i	−0.785644	+	0.618678i	$0.787668\pi$
$168$	0.103757	+	0.987180i	0.00800501	+	0.0761626i
$169$	−8.27702	+	1.75934i	−0.636694	+	0.135334i
$170$	−5.30870	+	3.85700i	−0.407159	+	0.295818i
$171$	18.7146	−	13.5970i	1.43114	−	1.03979i
$172$	−1.18366	+	0.251595i	−0.0902532	+	0.0191839i
$173$	−2.57509	−	24.5003i	−0.195780	−	1.86273i	−0.446656	−	0.894706i	$-0.647385\pi$
$173$	−2.57509	−	24.5003i	−0.195780	−	1.86273i	0.250875	−	0.968019i	$-0.419282\pi$
$174$	0.613321	−	5.83536i	0.0464957	−	0.442377i
$175$	3.65122	+	0.776090i	0.276006	+	0.0586669i
$176$	8.06990	−	3.59295i	0.608292	−	0.270829i
$177$	−0.285575	−	0.317163i	−0.0214651	−	0.0238394i
$178$	−0.888668	+	2.73504i	−0.0666085	+	0.205000i
$179$	−8.52831	+	9.47165i	−0.637436	+	0.707944i	−0.972146	−	0.234377i	$-0.924695\pi$
$179$	−8.52831	+	9.47165i	−0.637436	+	0.707944i	0.334710	+	0.942321i	$0.391362\pi$
$180$	2.37148	+	4.10752i	0.176759	+	0.306156i
$181$	5.90699	−	10.2312i	0.439063	−	0.760479i	−0.558555	−	0.829468i	$-0.688644\pi$
$181$	5.90699	−	10.2312i	0.439063	−	0.760479i	0.997617	+	0.0689887i	$0.0219772\pi$
$182$	10.2973	+	31.6917i	0.763283	+	2.34914i
$183$	−4.47367	−	1.99181i	−0.330704	−	0.147239i
$184$	3.04408	+	2.21165i	0.224413	+	0.163045i
$185$	6.57582			0.483464
$186$	−5.15221	−	0.309525i	−0.377779	−	0.0226955i
$187$	−6.69753			−0.489772
$188$	3.48310	+	2.53062i	0.254031	+	0.184564i
$189$	−9.46356	−	4.21345i	−0.688373	−	0.306483i
$190$	4.97536	+	15.3126i	0.360951	+	1.11089i
$191$	−5.67383	+	9.82737i	−0.410544	+	0.711083i	−0.994949	−	0.100379i	$-0.967995\pi$
$191$	−5.67383	+	9.82737i	−0.410544	+	0.711083i	0.584405	+	0.811462i	$0.301328\pi$
$192$	−1.33844	−	2.31825i	−0.0965939	−	0.167306i
$193$	−6.10936	+	6.78513i	−0.439761	+	0.488404i	−0.921756	−	0.387770i	$-0.873246\pi$
$193$	−6.10936	+	6.78513i	−0.439761	+	0.488404i	0.481995	+	0.876174i	$0.339912\pi$
$194$	0.637781	−	1.96289i	0.0457900	−	0.140927i
$195$	1.49131	+	1.65627i	0.106795	+	0.118608i
$196$	10.8515	−	4.83141i	0.775109	−	0.345101i
$197$	7.35424	+	1.56319i	0.523968	+	0.111373i	0.462299	−	0.886724i	$-0.347025\pi$
$197$	7.35424	+	1.56319i	0.523968	+	0.111373i	0.0616684	+	0.998097i	$0.480358\pi$
$198$	−1.09677	+	10.4350i	−0.0779438	+	0.741585i
$199$	0.660402	+	6.28330i	0.0468146	+	0.445412i	0.992673	+	0.120832i	$0.0385562\pi$
$199$	0.660402	+	6.28330i	0.0468146	+	0.445412i	−0.945858	+	0.324580i	$0.894777\pi$
$200$	0.540666	−	0.114922i	0.0382308	−	0.00812622i
$201$	−0.211555	+	0.153704i	−0.0149220	+	0.0108414i
$202$	−1.95144	+	1.41781i	−0.137303	+	0.0997566i
$203$	23.1098	−	4.91213i	1.62199	−	0.344764i
$204$	0.293369	+	2.79122i	0.0205399	+	0.195424i
$205$	0.934417	−	8.89038i	0.0652625	−	0.620931i
$206$	−4.39351	−	0.933869i	−0.306110	−	0.0650658i
$207$	−17.2170	+	7.66550i	−1.19666	+	0.532789i
$208$	13.9229	+	15.4629i	0.965377	+	1.07216i
$209$	−5.07818	+	15.6290i	−0.351265	+	1.08108i
$210$	2.31547	−	2.57159i	0.159783	−	0.177457i
$211$	1.84218	+	3.19074i	0.126821	+	0.219660i	0.922443	−	0.386133i	$-0.126189\pi$
$211$	1.84218	+	3.19074i	0.126821	+	0.219660i	−0.795622	+	0.605793i	$0.792856\pi$
$212$	−5.32568	+	9.22434i	−0.365769	+	0.633530i
$213$	−1.83754	−	5.65537i	−0.125906	−	0.387499i
$214$	−11.5162	−	5.12736i	−0.787234	−	0.350499i
$215$	−0.571458	−	0.415189i	−0.0389731	−	0.0283156i
$216$	−1.53397			−0.104373
$217$	−5.22550	−	20.1156i	−0.354730	−	1.36554i
$218$	−10.8557			−0.735242
$219$	4.01187	+	2.91479i	0.271097	+	0.196963i
$220$	−3.07809	−	1.37045i	−0.207525	−	0.0923959i
$221$	−4.87502	−	15.0038i	−0.327929	−	1.00926i
$222$	3.04800	−	5.27929i	0.204568	−	0.354323i
$223$	1.66236	+	2.87928i	0.111320	+	0.192811i	0.916303	−	0.400487i	$-0.131159\pi$
$223$	1.66236	+	2.87928i	0.111320	+	0.192811i	−0.804983	+	0.593298i	$0.797826\pi$
$224$	18.8560	−	20.9417i	1.25987	−	1.39922i
$225$	−0.855531	+	2.63305i	−0.0570354	+	0.175537i
$226$	−5.11199	−	5.67744i	−0.340044	−	0.377658i
$227$	4.52835	−	2.01615i	0.300557	−	0.133817i	−0.250917	−	0.968009i	$-0.580732\pi$
$227$	4.52835	−	2.01615i	0.300557	−	0.133817i	0.551474	+	0.834192i	$0.314066\pi$
$228$	6.73589	+	1.43176i	0.446095	+	0.0948204i
$229$	−1.63773	+	15.5819i	−0.108224	+	1.02968i	0.796777	+	0.604274i	$0.206537\pi$
$229$	−1.63773	+	15.5819i	−0.108224	+	1.02968i	−0.905001	+	0.425410i	$0.860130\pi$
$230$	−1.37113	−	13.0455i	−0.0904099	−	0.860193i
$231$	3.45475	−	0.734330i	0.227306	−	0.0483153i
$232$	2.83035	−	2.05637i	0.185821	−	0.135007i
$233$	−6.09365	+	4.42730i	−0.399208	+	0.290042i	−0.769219	−	0.638986i	$-0.779354\pi$
$233$	−6.09365	+	4.42730i	−0.399208	+	0.290042i	0.370010	+	0.929028i	$0.379354\pi$
$234$	−24.1748	+	5.13852i	−1.58036	+	0.335915i
$235$	0.262692	+	2.49935i	0.0171361	+	0.163039i
$236$	−0.158860	+	1.51145i	−0.0103409	+	0.0983873i
$237$	−6.16283	−	1.30995i	−0.400319	−	0.0850904i
$238$	−22.3766	+	9.96271i	−1.45046	+	0.645786i
$239$	−8.61778	−	9.57102i	−0.557438	−	0.619098i	0.396887	−	0.917867i	$-0.370090\pi$
$239$	−8.61778	−	9.57102i	−0.557438	−	0.619098i	−0.954325	+	0.298770i	$0.903424\pi$
$240$	0.667713	−	2.05501i	0.0431007	−	0.132650i
$241$	1.27545	−	1.41653i	0.0821592	−	0.0912470i	−0.700663	−	0.713492i	$-0.747113\pi$
$241$	1.27545	−	1.41653i	0.0821592	−	0.0912470i	0.782823	+	0.622245i	$0.213779\pi$
$242$	6.87132	+	11.9015i	0.441705	+	0.765055i
$243$	5.83949	−	10.1143i	0.374604	−	0.648833i
$244$	5.38875	+	16.5849i	0.344980	+	1.06174i
$245$	6.33425	+	2.82019i	0.404681	+	0.180175i
$246$	−6.70439	−	4.87102i	−0.427456	−	0.310565i
$247$	−38.7084			−2.46296
$248$	−1.91843	−	2.40644i	−0.121820	−	0.152809i
$249$	0.416570			0.0263991
$250$	−1.55894	−	1.13264i	−0.0985959	−	0.0716341i
$251$	6.00944	+	2.67557i	0.379312	+	0.168881i	0.587531	−	0.809202i	$-0.300100\pi$
$251$	6.00944	+	2.67557i	0.379312	+	0.168881i	−0.208219	+	0.978082i	$0.566767\pi$
$252$	5.47097	+	16.8379i	0.344639	+	1.06069i
$253$	6.69420	−	11.5947i	0.420861	−	0.728953i
$254$	−15.1629	−	26.2630i	−0.951408	−	1.64789i
$255$	−1.09621	+	1.21747i	−0.0686474	+	0.0762407i
$256$	6.04492	−	18.6043i	0.377807	−	1.16277i
$257$	8.83955	+	9.81732i	0.551396	+	0.612387i	0.952831	−	0.303500i	$-0.0981552\pi$
$257$	8.83955	+	9.81732i	0.551396	+	0.612387i	−0.401435	+	0.915887i	$0.631489\pi$
$258$	−0.598208	+	0.266339i	−0.0372428	+	0.0165816i
$259$	24.0097	+	5.10343i	1.49189	+	0.317112i
$260$	0.829592	−	7.89304i	0.0514491	−	0.489506i
$261$	1.83166	+	17.4271i	0.113377	+	1.07871i
$262$	22.4102	−	4.76343i	1.38450	−	0.294285i
$263$	−14.5787	+	10.5920i	−0.898960	+	0.653132i	−0.938199	−	0.346097i	$-0.887507\pi$
$263$	−14.5787	+	10.5920i	−0.898960	+	0.653132i	0.0392390	+	0.999230i	$0.487507\pi$
$264$	0.423118	−	0.307413i	0.0260411	−	0.0189200i
$265$	−6.08154	+	1.29267i	−0.373586	+	0.0794082i
$266$	6.28218	+	59.7709i	0.385185	+	3.66479i
$267$	−0.0750489	+	0.714043i	−0.00459292	+	0.0436987i
$268$	0.910841	+	0.193605i	0.0556385	+	0.0118263i
$269$	−18.8610	+	8.39745i	−1.14997	+	0.512002i	−0.891054	−	0.453897i	$-0.850033\pi$
$269$	−18.8610	+	8.39745i	−1.14997	+	0.512002i	−0.258920	+	0.965899i	$0.583367\pi$
$270$	3.57827	+	3.97407i	0.217767	+	0.241854i
$271$	6.83481	−	21.0354i	0.415185	−	1.27781i	−0.496900	−	0.867808i	$-0.665529\pi$
$271$	6.83481	−	21.0354i	0.415185	−	1.27781i	0.912085	−	0.410000i	$-0.134471\pi$
$272$	−10.2342	+	11.3662i	−0.620539	+	0.689179i
$273$	4.15970	+	7.20481i	0.251756	+	0.436055i
$274$	5.73574	−	9.93460i	0.346509	−	0.600171i
$275$	−0.607767	−	1.87052i	−0.0366497	−	0.112796i
$276$	−5.12535	−	2.28195i	−0.308510	−	0.137358i
$277$	22.8754	+	16.6200i	1.37445	+	0.998597i	0.997375	+	0.0724150i	$0.0230706\pi$
$277$	22.8754	+	16.6200i	1.37445	+	0.998597i	0.377076	+	0.926182i	$0.376929\pi$
$278$	21.1652			1.26941
$279$	15.2429	−	2.29493i	0.912567	−	0.137394i
$280$	2.06328			0.123304
$281$	−21.1411	−	15.3599i	−1.26117	−	0.916294i	−0.262356	−	0.964971i	$-0.584500\pi$
$281$	−21.1411	−	15.3599i	−1.26117	−	0.916294i	−0.998815	+	0.0486769i	$0.984500\pi$
$282$	2.12832	+	0.947591i	0.126740	+	0.0564282i
$283$	−5.79518	−	17.8357i	−0.344488	−	1.06022i	−0.961857	−	0.273551i	$-0.911802\pi$
$283$	−5.79518	−	17.8357i	−0.344488	−	1.06022i	0.617370	−	0.786673i	$-0.288198\pi$
$284$	−10.5876	+	18.3382i	−0.628257	+	1.08817i
$285$	2.00986	+	3.48117i	0.119054	+	0.206207i
$286$	11.7482	−	13.0477i	0.694686	−	0.771527i
$287$	10.3115	−	31.7355i	0.608669	−	1.87329i
$288$	13.9852	+	15.5321i	0.824085	+	0.915240i
$289$	−4.93653	+	2.19789i	−0.290384	+	0.129287i
$290$	−11.9298	−	2.53576i	−0.700542	−	0.148905i
$291$	0.0538612	−	0.512455i	0.00315740	−	0.0300407i
$292$	−1.84584	−	17.5620i	−0.108020	−	1.02774i
$293$	−20.7954	+	4.42020i	−1.21488	+	0.258231i	−0.770402	−	0.637559i	$-0.779944\pi$
$293$	−20.7954	+	4.42020i	−1.21488	+	0.258231i	−0.444478	+	0.895790i	$0.646611\pi$
$294$	5.20018	−	3.77815i	0.303281	−	0.220346i
$295$	−0.717699	+	0.521439i	−0.0417861	+	0.0303594i
$296$	3.55532	−	0.755707i	0.206649	−	0.0439245i
$297$	0.570533	+	5.42826i	0.0331057	+	0.314979i
$298$	−0.477383	+	4.54200i	−0.0276541	+	0.263111i
$299$	30.8470	+	6.55673i	1.78393	+	0.379186i
$300$	−0.752922	+	0.335222i	−0.0434700	+	0.0193541i
$301$	−1.76429	−	1.95945i	−0.101692	−	0.112941i
$302$	2.06984	−	6.37030i	0.119106	−	0.366569i
$303$	−0.402960	+	0.447533i	−0.0231495	+	0.0257101i
$304$	18.7639	+	32.5001i	1.07619	+	1.86401i
$305$	−5.08956	+	8.81538i	−0.291427	+	0.504767i
$306$	−5.61392	−	17.2779i	−0.320927	−	0.987710i
$307$	−7.72484	−	3.43932i	−0.440880	−	0.196292i	0.174278	−	0.984697i	$-0.444241\pi$
$307$	−7.72484	−	3.43932i	−0.440880	−	0.196292i	−0.615158	+	0.788404i	$0.710908\pi$
$308$	−10.1752	−	7.39269i	−0.579784	−	0.421238i
$309$	−1.12140			−0.0637941
$310$	−1.75931	+	10.5836i	−0.0999222	+	0.601108i
$311$	−5.13480			−0.291168			−0.145584	−	0.989346i	$-0.546506\pi$
$311$	−5.13480			−0.291168			−0.145584	+	0.989346i	$0.546506\pi$
$312$	0.996645	+	0.724105i	0.0564239	+	0.0409944i
$313$	18.5996	+	8.28107i	1.05131	+	0.468074i	0.858314	−	0.513126i	$-0.171512\pi$
$313$	18.5996	+	8.28107i	1.05131	+	0.468074i	0.192997	+	0.981199i	$0.438179\pi$
$314$	−4.14911	−	12.7697i	−0.234148	−	0.720633i
$315$	−5.16721	+	8.94988i	−0.291140	+	0.504268i
$316$	11.2181	+	19.4302i	0.631065	+	1.09304i
$317$	15.7524	−	17.4948i	0.884744	−	0.982608i	−0.115198	−	0.993343i	$-0.536750\pi$
$317$	15.7524	−	17.4948i	0.884744	−	0.982608i	0.999942	+	0.0107345i	$0.00341696\pi$
$318$	−1.78109	+	5.48164i	−0.0998788	+	0.307395i
$319$	−8.32959	−	9.25094i	−0.466367	−	0.517953i
$320$	−5.08319	+	2.26318i	−0.284159	+	0.126516i
$321$	−3.07849	−	0.654353i	−0.171825	−	0.0365224i
$322$	5.11815	−	48.6960i	0.285223	−	2.71372i
$323$	−2.97416	−	28.2973i	−0.165487	−	1.57450i
$324$	−11.6807	+	2.48280i	−0.648926	+	0.137934i
$325$	3.74794	−	2.72303i	0.207898	−	0.151047i
$326$	5.18759	−	3.76900i	0.287314	−	0.208746i
$327$	−2.65104	+	0.563495i	−0.146603	+	0.0311614i
$328$	−0.516494	−	4.91411i	−0.0285186	−	0.271336i
$329$	−0.980574	+	9.32953i	−0.0540608	+	0.514354i
$330$	−1.78342	−	0.379078i	−0.0981743	−	0.0208676i
$331$	24.0596	−	10.7120i	1.32243	−	0.588786i	0.380562	−	0.924755i	$-0.375731\pi$
$331$	24.0596	−	10.7120i	1.32243	−	0.588786i	0.941873	+	0.335969i	$0.109064\pi$
$332$	−0.992592	−	1.10239i	−0.0544756	−	0.0605013i
$333$	−5.62581	+	17.3145i	−0.308293	+	0.948827i
$334$	23.2413	−	25.8120i	1.27170	−	1.41237i
$335$	0.271777	+	0.470731i	0.0148488	+	0.0257188i
$336$	4.03284	−	6.98508i	0.220009	−	0.381067i
$337$	4.55410	+	14.0161i	0.248078	+	0.763504i	0.995115	+	0.0987222i	$0.0314755\pi$
$337$	4.55410	+	14.0161i	0.248078	+	0.763504i	−0.747038	+	0.664782i	$0.768524\pi$
$338$	14.8961	+	6.63215i	0.810239	+	0.360742i
$339$	−1.54308	−	1.12112i	−0.0838088	−	0.0608906i
$340$	5.83385			0.316385
$341$	−7.80217	+	7.68379i	−0.422511	+	0.416100i
$342$	−44.5754			−2.41036
$343$	−0.200208	−	0.145460i	−0.0108102	−	0.00785409i
$344$	−0.356682	−	0.158805i	−0.0192310	−	0.00856220i
$345$	−1.01200	−	3.11462i	−0.0544842	−	0.167685i
$346$	−23.7355	+	41.1111i	−1.27603	+	2.21015i
$347$	−6.48529	−	11.2329i	−0.348149	−	0.603012i	0.637772	−	0.770225i	$-0.279856\pi$
$347$	−6.48529	−	11.2329i	−0.348149	−	0.603012i	−0.985921	+	0.167214i	$0.946523\pi$
$348$	−3.49050	+	3.87660i	−0.187111	+	0.207807i
$349$	7.49297	−	23.0610i	0.401089	−	1.23443i	−0.523027	−	0.852316i	$-0.675197\pi$
$349$	7.49297	−	23.0610i	0.401089	−	1.23443i	0.924117	−	0.382110i	$-0.124803\pi$
$350$	−4.81300	−	5.34537i	−0.257265	−	0.285722i
$351$	−11.7451	+	5.22924i	−0.626906	+	0.279116i
$352$	−14.5232	−	3.08701i	−0.774092	−	0.164538i
$353$	−0.804663	+	7.65586i	−0.0428279	+	0.407480i	0.952015	+	0.306052i	$0.0990080\pi$
$353$	−0.804663	+	7.65586i	−0.0428279	+	0.407480i	−0.994843	+	0.101429i	$0.967659\pi$
$354$	0.0859636	+	0.817889i	0.00456892	+	0.0434703i
$355$	−12.0902	+	2.56986i	−0.641683	+	0.136394i
$356$	2.06842	−	1.50280i	0.109626	−	0.0796480i
$357$	−4.94737	+	3.59448i	−0.261843	+	0.190240i
$358$	24.0230	−	5.10625i	1.26966	−	0.269874i
$359$	−1.44135	−	13.7136i	−0.0760718	−	0.723774i	−0.964379	−	0.264525i	$-0.914785\pi$
$359$	−1.44135	−	13.7136i	−0.0760718	−	0.723774i	0.888307	−	0.459250i	$-0.151882\pi$
$360$	−0.159960	+	1.52192i	−0.00843065	+	0.0802123i
$361$	−49.7035	−	10.5648i	−2.61597	−	0.556042i
$362$	−20.7968	+	9.25935i	−1.09306	+	0.486661i
$363$	2.29580	+	2.54974i	0.120498	+	0.133827i
$364$	9.15474	−	28.1754i	0.479838	−	1.47679i
$365$	6.89724	−	7.66017i	0.361018	−	0.400951i
$366$	4.71819	+	8.17215i	0.246624	+	0.427165i
$367$	−14.3643	+	24.8797i	−0.749810	+	1.29871i	0.198103	+	0.980181i	$0.436522\pi$
$367$	−14.3643	+	24.8797i	−0.749810	+	1.29871i	−0.947913	+	0.318528i	$0.896811\pi$
$368$	−9.44800	−	29.0779i	−0.492511	−	1.51579i
$369$	22.6094	+	10.0664i	1.17700	+	0.524034i
$370$	−10.2513	−	7.44800i	−0.532939	−	0.387203i
$371$	−23.2082			−1.20491
$372$	3.54400	+	2.91501i	0.183748	+	0.151136i
$373$	0.584104			0.0302437			0.0151219	−	0.999886i	$-0.495186\pi$
$373$	0.584104			0.0302437			0.0151219	+	0.999886i	$0.495186\pi$
$374$	10.4410	+	7.58585i	0.539893	+	0.392255i
$375$	−0.439495	−	0.195676i	−0.0226954	−	0.0101047i
$376$	0.429259	+	1.32112i	0.0221373	+	0.0681317i
$377$	14.6610	−	25.3935i	0.755077	−	1.30783i
$378$	9.98081	+	17.2873i	0.513357	+	0.889161i
$379$	−0.497769	+	0.552829i	−0.0255687	+	0.0283969i	−0.755794	−	0.654810i	$-0.772749\pi$
$379$	−0.497769	+	0.552829i	−0.0255687	+	0.0283969i	0.730225	+	0.683207i	$0.239415\pi$
$380$	4.42333	−	13.6136i	0.226912	−	0.698363i
$381$	−5.06614	−	5.62652i	−0.259546	−	0.288255i
$382$	19.9760	−	8.89388i	1.02206	−	0.455050i
$383$	−20.4194	−	4.34027i	−1.04338	−	0.221778i	−0.345819	−	0.938301i	$-0.612399\pi$
$383$	−20.4194	−	4.34027i	−1.04338	−	0.221778i	−0.697563	+	0.716524i	$0.745732\pi$
$384$	0.220081	−	2.09393i	0.0112310	−	0.106856i
$385$	−0.767402	−	7.30134i	−0.0391104	−	0.372111i
$386$	17.2092	−	3.65793i	0.875925	−	0.186184i
$387$	1.58211	−	1.14947i	0.0804233	−	0.0584310i
$388$	−1.48447	+	1.07853i	−0.0753625	+	0.0547540i
$389$	20.6277	−	4.38455i	1.04587	−	0.222305i	0.347227	−	0.937781i	$-0.387123\pi$
$389$	20.6277	−	4.38455i	1.04587	−	0.222305i	0.698638	+	0.715476i	$0.253790\pi$
$390$	−0.448915	−	4.27114i	−0.0227317	−	0.216278i
$391$	−2.42308	+	23.0541i	−0.122541	+	1.16590i
$392$	3.74882	+	0.796836i	0.189344	+	0.0402463i
$393$	5.22545	−	2.32652i	0.263589	−	0.117357i
$394$	−9.69428	−	10.7666i	−0.488391	−	0.542413i
$395$	−4.04701	+	12.4554i	−0.203627	+	0.626700i
$396$	6.24187	−	6.93230i	0.313666	−	0.348361i
$397$	−11.1789	−	19.3623i	−0.561051	−	0.971768i	−0.997405	−	0.0719934i	$-0.977064\pi$
$397$	−11.1789	−	19.3623i	−0.561051	−	0.971768i	0.436354	−	0.899775i	$-0.356269\pi$
$398$	6.08716	−	10.5433i	0.305122	−	0.528487i
$399$	4.63672	+	14.2703i	0.232126	+	0.714411i
$400$	−4.10311	−	1.82682i	−0.205156	−	0.0913412i
$401$	5.69932	+	4.14080i	0.284610	+	0.206781i	0.720926	−	0.693012i	$-0.243717\pi$
$401$	5.69932	+	4.14080i	0.284610	+	0.206781i	−0.436316	+	0.899794i	$0.643717\pi$
$402$	0.503892			0.0251319
$403$	−22.8923	−	11.8855i	−1.14034	−	0.592058i
$404$	2.14448			0.106692
$405$	−5.63930	−	4.09719i	−0.280219	−	0.203591i
$406$	−41.5903	−	18.5172i	−2.06409	−	0.918994i
$407$	−3.99657	−	12.3002i	−0.198102	−	0.609697i
$408$	−0.452770	+	0.784221i	−0.0224155	+	0.0388247i
$409$	16.3360	+	28.2948i	0.807763	+	1.39909i	0.914410	+	0.404789i	$0.132655\pi$
$409$	16.3360	+	28.2948i	0.807763	+	1.39909i	−0.106647	+	0.994297i	$0.534012\pi$
$410$	−11.5263	+	12.8012i	−0.569241	+	0.632207i
$411$	0.885023	−	2.72382i	0.0436550	−	0.134356i
$412$	2.67204	+	2.96760i	0.131642	+	0.146203i
$413$	−3.02516	+	1.34689i	−0.148858	+	0.0662760i
$414$	35.5225	+	7.55053i	1.74583	+	0.371088i
$415$	0.0905105	−	0.861150i	0.00444299	−	0.0422722i
$416$	−3.65572	−	34.7819i	−0.179237	−	1.70532i
$417$	5.16868	−	1.09864i	0.253111	−	0.0538005i
$418$	25.6186	−	18.6130i	1.25304	−	0.910390i
$419$	−13.2851	+	9.65217i	−0.649018	+	0.471539i	−0.862937	−	0.505312i	$-0.831377\pi$
$419$	−13.2851	+	9.65217i	−0.649018	+	0.471539i	0.213918	+	0.976852i	$0.431377\pi$
$420$	−3.00924	+	0.639634i	−0.146836	+	0.0312110i
$421$	2.30738	+	21.9533i	0.112455	+	1.06994i	0.894608	+	0.446851i	$0.147455\pi$
$421$	2.30738	+	21.9533i	0.112455	+	1.06994i	−0.782154	+	0.623086i	$0.785879\pi$
$422$	0.742108	−	7.06069i	0.0361253	−	0.343709i
$423$	−6.80565	−	1.44659i	−0.330902	−	0.0703354i
$424$	−3.13952	+	1.39781i	−0.152469	+	0.0678835i
$425$	2.27861	+	2.53066i	0.110529	+	0.122755i
$426$	−3.54086	+	10.8976i	−0.171555	+	0.527992i
$427$	−25.4246	+	28.2369i	−1.23038	+	1.36648i
$428$	5.60370	+	9.70589i	0.270865	+	0.469152i
$429$	2.19171	−	3.79616i	0.105817	−	0.183280i
$430$	0.420611	+	1.29451i	0.0202837	+	0.0624267i
$431$	26.7577	+	11.9133i	1.28887	+	0.573844i	0.932726	−	0.360585i	$-0.117423\pi$
$431$	26.7577	+	11.9133i	1.28887	+	0.573844i	0.356149	+	0.934429i	$0.384090\pi$
$432$	10.0840	+	7.32644i	0.485166	+	0.352493i
$433$	17.3298			0.832818			0.416409	−	0.909177i	$-0.363288\pi$
$433$	17.3298			0.832818			0.416409	+	0.909177i	$0.363288\pi$
$434$	−14.6375	+	37.2776i	−0.702620	+	1.78938i
$435$	−3.04496			−0.145995
$436$	7.80802	+	5.67286i	0.373936	+	0.271681i
$437$	51.9607	+	23.1344i	2.48562	+	1.10667i
$438$	−2.95286	−	9.08796i	−0.141093	−	0.434239i
$439$	−0.134251	+	0.232529i	−0.00640743	+	0.0110980i	−0.869211	−	0.494441i	$-0.835373\pi$
$439$	−0.134251	+	0.232529i	−0.00640743	+	0.0110980i	0.862804	+	0.505539i	$0.168706\pi$
$440$	−0.543562	−	0.941478i	−0.0259133	−	0.0448832i
$441$	−12.8449	+	14.2657i	−0.611660	+	0.679317i
$442$	−9.39394	+	28.9116i	−0.446824	+	1.37518i
$443$	21.2889	+	23.6437i	1.01147	+	1.12335i	0.992341	+	0.123531i	$0.0394220\pi$
$443$	21.2889	+	23.6437i	1.01147	+	1.12335i	0.0191268	+	0.999817i	$0.493911\pi$
$444$	−4.95108	+	2.20436i	−0.234968	+	0.104614i
$445$	1.45979	+	0.310288i	0.0692007	+	0.0147091i
$446$	0.669668	−	6.37147i	0.0317097	−	0.301698i
$447$	0.119185	+	1.13397i	0.00563723	+	0.0536347i
$448$	−20.3163	+	4.31836i	−0.959854	+	0.204023i
$449$	−0.319768	+	0.232325i	−0.0150908	+	0.0109641i	−0.595305	−	0.803500i	$-0.702969\pi$
$449$	−0.319768	+	0.232325i	−0.0150908	+	0.0109641i	0.580214	+	0.814464i	$0.302969\pi$
$450$	4.31601	−	3.13576i	0.203459	−	0.147821i
$451$	−17.1975	+	3.65544i	−0.809799	+	0.172128i
$452$	0.709967	+	6.75488i	0.0333940	+	0.317723i
$453$	0.174800	−	1.66311i	0.00821281	−	0.0781396i
$454$	−9.34298	−	1.98591i	−0.438488	−	0.0932034i
$455$	15.7978	−	7.03365i	0.740615	−	0.329743i
$456$	1.48672	+	1.65117i	0.0696222	+	0.0773233i
$457$	−10.4764	+	32.2431i	−0.490066	+	1.50827i	0.334442	+	0.942416i	$0.391452\pi$
$457$	−10.4764	+	32.2431i	−0.490066	+	1.50827i	−0.824507	+	0.565851i	$0.808548\pi$
$458$	20.2018	−	22.4363i	0.943967	−	1.04838i
$459$	−4.72520	−	8.18429i	−0.220554	−	0.382010i
$460$	−5.83096	+	10.0995i	−0.271870	+	0.470892i
$461$	−4.04048	−	12.4353i	−0.188184	−	0.579171i	0.811805	−	0.583929i	$-0.198485\pi$
$461$	−4.04048	−	12.4353i	−0.188184	−	0.579171i	−0.999989	+	0.00475812i	$0.998485\pi$
$462$	−6.21747	−	2.76820i	−0.289263	−	0.128788i
$463$	13.7425	+	9.98447i	0.638666	+	0.464018i	0.859392	−	0.511318i	$-0.170843\pi$
$463$	13.7425	+	9.98447i	0.638666	+	0.464018i	−0.220726	+	0.975336i	$0.570843\pi$
$464$	−28.4276			−1.31972
$465$	0.119735	+	2.67590i	0.00555256	+	0.124092i
$466$	14.5141			0.672355
$467$	−20.2664	−	14.7244i	−0.937816	−	0.681364i	0.0100776	−	0.999949i	$-0.496792\pi$
$467$	−20.2664	−	14.7244i	−0.937816	−	0.681364i	−0.947894	+	0.318586i	$0.896792\pi$
$468$	20.0731	+	8.93710i	0.927877	+	0.413118i
$469$	0.626986	+	1.92967i	0.0289515	+	0.0891037i
$470$	2.42133	−	4.19386i	0.111688	−	0.193448i
$471$	−1.67608	−	2.90306i	−0.0772298	−	0.133766i
$472$	−0.328111	+	0.364404i	−0.0151025	+	0.0167730i
$473$	−0.429303	+	1.32126i	−0.0197394	+	0.0607516i
$474$	8.12378	+	9.02237i	0.373138	+	0.414411i
$475$	7.63310	−	3.39848i	0.350231	−	0.155933i
$476$	21.3007	+	4.52759i	0.976314	+	0.207522i
$477$	1.79927	−	17.1189i	0.0823830	−	0.783822i
$478$	2.59412	+	24.6814i	0.118652	+	1.12890i
$479$	16.1908	−	3.44147i	0.739778	−	0.157245i	0.177416	−	0.984136i	$-0.443226\pi$
$479$	16.1908	−	3.44147i	0.739778	−	0.157245i	0.562362	+	0.826891i	$0.309893\pi$
$480$	−2.93823	+	2.13475i	−0.134111	+	0.0974376i
$481$	24.6457	−	17.9062i	1.12375	−	0.816451i
$482$	−3.59277	+	0.763667i	−0.163646	+	0.0347841i
$483$	−1.27781	−	12.1575i	−0.0581423	−	0.553187i
$484$	1.27711	−	12.1509i	0.0580505	−	0.552314i
$485$	−1.04766	−	0.222688i	−0.0475720	−	0.0101117i
$486$	−20.5592	+	9.15355i	−0.932585	+	0.415214i
$487$	−6.24753	−	6.93858i	−0.283103	−	0.314417i	0.584775	−	0.811196i	$-0.301183\pi$
$487$	−6.24753	−	6.93858i	−0.283103	−	0.314417i	−0.867877	+	0.496778i	$0.834516\pi$
$488$	−1.73867	+	5.35108i	−0.0787059	+	0.242232i
$489$	1.07120	−	1.18969i	0.0484414	−	0.0537997i
$490$	−6.68046	−	11.5709i	−0.301793	−	0.522720i
$491$	−7.10684	+	12.3094i	−0.320727	+	0.555516i	−0.980638	−	0.195828i	$-0.937261\pi$
$491$	−7.10684	+	12.3094i	−0.320727	+	0.555516i	0.659911	+	0.751344i	$0.270594\pi$
$492$	2.27671	+	7.00700i	0.102642	+	0.315900i
$493$	19.6901	+	8.76659i	0.886796	+	0.394827i
$494$	60.3440	+	43.8425i	2.71501	+	1.97257i
$495$	5.44513			0.244740
$496$	1.11784	+	24.9821i	0.0501925	+	1.12173i
$497$	−46.1385			−2.06960
$498$	−0.649408	−	0.471822i	−0.0291006	−	0.0211429i
$499$	−5.91676	−	2.63431i	−0.264871	−	0.117928i	0.270005	−	0.962859i	$-0.412975\pi$
$499$	−5.91676	−	2.63431i	−0.264871	−	0.117928i	−0.534875	+	0.844931i	$0.679641\pi$
$500$	0.529393	+	1.62930i	0.0236752	+	0.0728647i
$501$	4.33582	−	7.50986i	0.193710	−	0.335516i
$502$	−6.33790	−	10.9776i	−0.282874	−	0.489952i
$503$	−7.91917	+	8.79513i	−0.353098	+	0.392155i	−0.893360	−	0.449342i	$-0.851659\pi$
$503$	−7.91917	+	8.79513i	−0.353098	+	0.392155i	0.540262	+	0.841497i	$0.318325\pi$
$504$	−1.76520	+	5.43272i	−0.0786282	+	0.241993i
$505$	0.837603	+	0.930252i	0.0372728	+	0.0413957i
$506$	−23.5684	+	10.4933i	−1.04774	+	0.466486i
$507$	3.98197	+	0.846394i	0.176846	+	0.0375897i
$508$	−2.81820	+	26.8134i	−0.125038	+	1.18965i
$509$	3.55552	+	33.8285i	0.157596	+	1.49942i	0.732255	+	0.681030i	$0.238468\pi$
$509$	3.55552	+	33.8285i	0.157596	+	1.49942i	−0.574660	+	0.818393i	$0.694866\pi$
$510$	3.08787	−	0.656347i	0.136733	−	0.0290635i
$511$	31.1283	−	22.6160i	1.37704	−	1.00047i
$512$	−23.4143	+	17.0115i	−1.03478	+	0.751808i
$513$	−22.6812	+	4.82104i	−1.00140	+	0.212854i
$514$	−2.66088	−	25.3166i	−0.117366	−	1.11667i
$515$	−0.243652	+	2.31820i	−0.0107366	+	0.102152i
$516$	0.569444	+	0.121039i	0.0250684	+	0.00532844i
$517$	4.51541	−	2.01039i	0.198588	−	0.0884169i
$518$	−31.6494	−	35.1502i	−1.39059	−	1.54441i
$519$	−3.66238	+	11.2717i	−0.160761	+	0.494771i
$520$	1.71344	−	1.90297i	0.0751395	−	0.0834509i
$521$	14.9977	+	25.9768i	0.657062	+	1.13806i	0.981373	+	0.192114i	$0.0615343\pi$
$521$	14.9977	+	25.9768i	0.657062	+	1.13806i	−0.324311	+	0.945951i	$0.605132\pi$
$522$	16.8831	−	29.2424i	0.738953	−	1.27990i
$523$	9.17299	+	28.2316i	0.401107	+	1.23448i	0.924103	+	0.382145i	$0.124814\pi$
$523$	9.17299	+	28.2316i	0.401107	+	1.23448i	−0.522996	+	0.852335i	$0.675186\pi$
$524$	−18.6078	−	8.28473i	−0.812886	−	0.361920i
$525$	−1.45283	−	1.05554i	−0.0634067	−	0.0460677i
$526$	34.7242			1.51405
$527$	6.92980	−	17.6483i	0.301867	−	0.768773i
$528$	−4.24974			−0.184946
$529$	−18.8818	−	13.7184i	−0.820947	−	0.596453i
$530$	10.9449	+	4.87297i	0.475415	+	0.211668i
$531$	−0.758963	−	2.33585i	−0.0329362	−	0.101367i
$532$	26.7159	−	46.2733i	1.15828	−	2.00620i
$533$	−20.7067	−	35.8650i	−0.896906	−	1.55349i
$534$	0.925746	−	1.02815i	0.0400610	−	0.0444922i
$535$	−2.02158	+	6.22179i	−0.0874007	+	0.268992i
$536$	0.201038	+	0.223275i	0.00868352	+	0.00964402i
$537$	5.60152	−	2.49396i	0.241724	−	0.107622i
$538$	38.9144	+	8.27150i	1.67772	+	0.356610i
$539$	1.42546	−	13.5623i	0.0613989	−	0.584171i
$540$	−0.496960	−	4.72826i	−0.0213857	−	0.203472i
$541$	24.3197	−	5.16931i	1.04558	−	0.222246i	0.347068	−	0.937840i	$-0.387177\pi$
$541$	24.3197	−	5.16931i	1.04558	−	0.222246i	0.698516	+	0.715594i	$0.253844\pi$
$542$	−34.4805	+	25.0515i	−1.48106	+	1.07605i
$543$	−4.59809	+	3.34071i	−0.197323	+	0.143364i
$544$	25.1460	−	5.34494i	1.07812	−	0.229162i
$545$	0.588874	+	5.60276i	0.0252246	+	0.239996i
$546$	1.67571	−	15.9433i	0.0717136	−	0.682309i
$547$	−8.82102	−	1.87497i	−0.377160	−	0.0801677i	0.0154314	−	0.999881i	$-0.495088\pi$
$547$	−8.82102	−	1.87497i	−0.377160	−	0.0801677i	−0.392591	+	0.919713i	$0.628421\pi$
$548$	−9.31696	+	4.14818i	−0.398001	+	0.177201i
$549$	−18.8571	−	20.9429i	−0.804800	−	0.893821i
$550$	−1.17114	+	3.60440i	−0.0499375	+	0.153692i
$551$	35.3866	−	39.3009i	1.50752	−	1.67427i
$552$	−0.905092	−	1.56766i	−0.0385233	−	0.0667243i
$553$	−24.4430	+	42.3366i	−1.03942	+	1.80034i
$554$	−16.8370	−	51.8190i	−0.715336	−	2.20158i
$555$	−2.89004	−	1.28673i	−0.122675	−	0.0546186i
$556$	−15.2232	−	11.0603i	−0.645606	−	0.469060i
$557$	14.6276			0.619791			0.309896	−	0.950771i	$-0.399706\pi$
$557$	14.6276			0.619791			0.309896	+	0.950771i	$0.399706\pi$
$558$	−26.3620	−	13.6869i	−1.11599	−	0.579415i
$559$	−3.27236			−0.138406
$560$	−13.5636	−	9.85451i	−0.573166	−	0.416429i
$561$	2.94353	+	1.31054i	0.124276	+	0.0553312i
$562$	15.5605	+	47.8902i	0.656379	+	2.02013i
$563$	2.75356	−	4.76930i	0.116049	−	0.201002i	−0.802150	−	0.597123i	$-0.796311\pi$
$563$	2.75356	−	4.76930i	0.116049	−	0.201002i	0.918198	+	0.396121i	$0.129644\pi$
$564$	−1.03562	−	1.79375i	−0.0436076	−	0.0755306i
$565$	−2.65289	+	2.94633i	−0.111608	+	0.123953i
$566$	−11.1670	+	34.3686i	−0.469386	+	1.44462i
$567$	−17.4105	−	19.3363i	−0.731173	−	0.812050i
$568$	−6.24145	+	2.77887i	−0.261885	+	0.116599i
$569$	−7.11922	−	1.51324i	−0.298453	−	0.0634382i	0.0562513	−	0.998417i	$-0.482085\pi$
$569$	−7.11922	−	1.51324i	−0.298453	−	0.0634382i	−0.354705	+	0.934978i	$0.615419\pi$
$570$	0.809656	−	7.70337i	0.0339128	−	0.322658i
$571$	−2.69380	−	25.6298i	−0.112732	−	1.07257i	−0.893905	−	0.448257i	$-0.852045\pi$
$571$	−2.69380	−	25.6298i	−0.112732	−	1.07257i	0.781173	−	0.624315i	$-0.214622\pi$
$572$	−15.2683	+	3.24537i	−0.638398	+	0.135696i
$573$	4.41660	−	3.20885i	0.184506	−	0.134052i
$574$	−52.0198	+	37.7946i	−2.17126	+	1.57752i
$575$	−6.65853	+	1.41531i	−0.277680	+	0.0590227i
$576$	−1.61025	−	15.3205i	−0.0670939	−	0.638356i
$577$	2.81962	−	26.8269i	0.117382	−	1.11682i	−0.764263	−	0.644905i	$-0.776897\pi$
$577$	2.81962	−	26.8269i	0.117382	−	1.11682i	0.881645	−	0.471913i	$-0.156436\pi$
$578$	10.1852	+	2.16492i	0.423647	+	0.0900489i
$579$	4.01272	−	1.78658i	0.166763	−	0.0742477i
$580$	7.25545	+	8.05799i	0.301266	+	0.334590i
$581$	0.998804	−	3.07400i	0.0414374	−	0.127531i
$582$	−0.664391	+	0.737881i	−0.0275399	+	0.0305862i
$583$	6.11412	+	10.5900i	0.253221	+	0.438592i
$584$	2.84878	−	4.93424i	0.117883	−	0.204180i
$585$	3.96342	+	12.1981i	0.163867	+	0.504331i
$586$	37.4252	+	16.6628i	1.54602	+	0.688333i
$587$	7.97688	+	5.79554i	0.329241	+	0.239208i	0.740109	−	0.672487i	$-0.234774\pi$
$587$	7.97688	+	5.79554i	0.329241	+	0.239208i	−0.410867	+	0.911695i	$0.634774\pi$
$588$	−5.71459			−0.235666
$589$	−35.9290	−	29.5523i	−1.48043	−	1.21768i
$590$	1.70945			0.0703769
$591$	−2.92627	−	2.12606i	−0.120371	−	0.0874545i
$592$	−26.9813	−	12.0129i	−1.10893	−	0.493725i
$593$	−5.63986	−	17.3577i	−0.231601	−	0.712795i	−0.997554	−	0.0698986i	$-0.977732\pi$
$593$	−5.63986	−	17.3577i	−0.231601	−	0.712795i	0.765953	−	0.642897i	$-0.222268\pi$
$594$	5.25881	−	9.10852i	0.215771	−	0.373727i
$595$	6.35569	+	11.0084i	0.260558	+	0.451300i
$596$	2.71686	−	3.01738i	0.111287	−	0.123597i
$597$	0.939247	−	2.89071i	0.0384408	−	0.118309i
$598$	−40.6622	−	45.1599i	−1.66280	−	1.84673i
$599$	−7.33563	+	3.26603i	−0.299726	+	0.133447i	−0.551089	−	0.834446i	$-0.685788\pi$
$599$	−7.33563	+	3.26603i	−0.299726	+	0.133447i	0.251364	+	0.967893i	$0.419121\pi$
$600$	−0.260108	−	0.0552876i	−0.0106188	−	0.00225711i
$601$	3.75182	−	35.6962i	0.153040	−	1.45608i	−0.601000	−	0.799249i	$-0.705231\pi$
$601$	3.75182	−	35.6962i	0.153040	−	1.45608i	0.754040	−	0.656828i	$-0.228102\pi$
$602$	0.531087	+	5.05296i	0.0216455	+	0.205943i
$603$	−1.47197	+	0.312878i	−0.0599434	+	0.0127414i
$604$	−4.81765	+	3.50023i	−0.196027	+	0.142422i
$605$	5.76974	−	4.19196i	0.234573	−	0.170428i
$606$	1.13508	−	0.241269i	0.0461095	−	0.00980088i
$607$	−0.395307	−	3.76109i	−0.0160450	−	0.152658i	0.983566	−	0.180549i	$-0.0577875\pi$
$607$	−0.395307	−	3.76109i	−0.0160450	−	0.152658i	−0.999611	+	0.0278912i	$0.991121\pi$
$608$	6.59341	−	62.7321i	0.267398	−	2.54412i
$609$	−11.1178	−	2.36316i	−0.450516	−	0.0957602i
$610$	17.9189	−	7.97801i	0.725516	−	0.323020i
$611$	7.79036	+	8.65207i	0.315164	+	0.350025i
$612$	−4.99104	+	15.3608i	−0.201751	+	0.620925i
$613$	−6.04544	+	6.71414i	−0.244173	+	0.271181i	−0.852757	−	0.522308i	$-0.825071\pi$
$613$	−6.04544	+	6.71414i	−0.244173	+	0.271181i	0.608584	+	0.793489i	$0.291738\pi$
$614$	8.14706	+	14.1111i	0.328788	+	0.569478i
$615$	−2.15031	+	3.72444i	−0.0867087	+	0.150184i
$616$	−1.25399	−	3.85939i	−0.0505248	−	0.155499i
$617$	16.7520	+	7.45846i	0.674409	+	0.300266i	0.715219	−	0.698901i	$-0.246327\pi$
$617$	16.7520	+	7.45846i	0.674409	+	0.300266i	−0.0408097	+	0.999167i	$0.512994\pi$
$618$	1.74819	+	1.27013i	0.0703225	+	0.0510923i
$619$	24.1536			0.970815			0.485408	−	0.874288i	$-0.338671\pi$
$619$	24.1536			0.970815			0.485408	+	0.874288i	$0.338671\pi$
$620$	6.79604	−	6.69293i	0.272936	−	0.268794i
$621$	18.8914			0.758087
$622$	8.00483	+	5.81585i	0.320965	+	0.233194i
$623$	5.08920	+	2.26586i	0.203894	+	0.0907796i
$624$	−3.09331	−	9.52024i	−0.123832	−	0.381115i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−19.6162	−	33.9762i	−0.784020	−	1.35796i
$627$	5.29006	−	5.87521i	0.211265	−	0.234633i
$628$	−3.68875	+	11.3528i	−0.147197	+	0.453026i
$629$	14.9837	+	16.6411i	0.597441	+	0.663525i
$630$	18.1923	−	8.09974i	0.724799	−	0.322701i
$631$	−48.0388	−	10.2110i	−1.91240	−	0.406492i	−0.912400	−	0.409299i	$-0.865773\pi$
$631$	−48.0388	−	10.2110i	−1.91240	−	0.406492i	−0.999996	+	0.00280714i	$0.999106\pi$
$632$	−0.756678	+	7.19931i	−0.0300990	+	0.286373i
$633$	−0.185276	−	1.76279i	−0.00736407	−	0.0700644i
$634$	−44.3723	+	9.43163i	−1.76225	+	0.374578i
$635$	−12.7321	+	9.25041i	−0.505258	+	0.367091i
$636$	4.14559	−	3.01195i	0.164383	−	0.119431i
$637$	31.4199	−	6.67850i	1.24490	−	0.264612i
$638$	2.50737	+	23.8560i	0.0992677	+	0.944469i
$639$	3.57699	−	34.0328i	0.141504	−	1.34632i
$640$	−4.28084	−	0.909921i	−0.169215	−	0.0359678i
$641$	40.7919	−	18.1617i	1.61118	−	0.717344i	0.613787	−	0.789472i	$-0.289646\pi$
$641$	40.7919	−	18.1617i	1.61118	−	0.717344i	0.997395	+	0.0721276i	$0.0229789\pi$
$642$	4.05803	+	4.50690i	0.160158	+	0.177873i
$643$	9.37820	−	28.8631i	0.369840	−	1.13825i	−0.577054	−	0.816706i	$-0.695798\pi$
$643$	9.37820	−	28.8631i	0.369840	−	1.13825i	0.946894	−	0.321545i	$-0.104202\pi$
$644$	−29.1282	+	32.3502i	−1.14781	+	1.27478i
$645$	0.169911	+	0.294294i	0.00669023	+	0.0115878i
$646$	−27.4140	+	47.4824i	−1.07859	+	1.86817i
$647$	5.90248	+	18.1660i	0.232050	+	0.714178i	0.997499	+	0.0706807i	$0.0225171\pi$
$647$	5.90248	+	18.1660i	0.232050	+	0.714178i	−0.765449	+	0.643497i	$0.777483\pi$
$648$	−3.51984	−	1.56713i	−0.138272	−	0.0615628i
$649$	1.41155	+	1.02555i	0.0554083	+	0.0402565i
$650$	−8.92701			−0.350146
$651$	−1.63957	+	9.86323i	−0.0642596	+	0.386571i
$652$	−5.70075			−0.223259
$653$	39.5163	+	28.7102i	1.54639	+	1.12352i	0.946164	+	0.323689i	$0.104923\pi$
$653$	39.5163	+	28.7102i	1.54639	+	1.12352i	0.600227	+	0.799830i	$0.295077\pi$
$654$	4.77104	+	2.12420i	0.186562	+	0.0830629i
$655$	−3.67410	−	11.3077i	−0.143559	−	0.441830i
$656$	−20.0752	+	34.7712i	−0.783804	+	1.35759i
$657$	14.2688	+	24.7143i	0.556679	+	0.964197i
$658$	12.0956	−	13.4335i	0.471536	−	0.523694i
$659$	−1.24620	+	3.83541i	−0.0485450	+	0.149406i	−0.972391	−	0.233359i	$-0.925028\pi$
$659$	−1.24620	+	3.83541i	−0.0485450	+	0.149406i	0.923846	+	0.382765i	$0.125028\pi$
$660$	1.08464	+	1.20461i	0.0422195	+	0.0468895i
$661$	−6.02581	+	2.68286i	−0.234377	+	0.104351i	−0.520565	−	0.853822i	$-0.674279\pi$
$661$	−6.02581	+	2.68286i	−0.234377	+	0.104351i	0.286188	+	0.958174i	$0.407612\pi$
$662$	−49.6402	−	10.5514i	−1.92932	−	0.410090i
$663$	−0.793328	+	7.54801i	−0.0308103	+	0.293140i
$664$	−0.0500292	−	0.475996i	−0.00194151	−	0.0184722i
$665$	30.5076	−	6.48460i	1.18304	−	0.251462i
$666$	28.3813	−	20.6202i	1.09975	−	0.799016i
$667$	−34.8569	+	25.3251i	−1.34967	+	0.980590i
$668$	−30.2049	+	6.42025i	−1.16866	+	0.248407i
$669$	−0.167191	−	1.59071i	−0.00646397	−	0.0615006i
$670$	0.109483	−	1.04167i	0.00422971	−	0.0402430i
$671$	19.5826	+	4.16240i	0.755976	+	0.160688i
$672$	−12.3849	+	5.51410i	−0.477757	+	0.212711i
$673$	9.35566	+	10.3905i	0.360634	+	0.400525i	0.895970	−	0.444115i	$-0.146482\pi$
$673$	9.35566	+	10.3905i	0.360634	+	0.400525i	−0.535336	+	0.844639i	$0.679815\pi$
$674$	8.77554	−	27.0083i	0.338021	−	1.04032i
$675$	1.85696	−	2.06236i	0.0714743	−	0.0793803i
$676$	−7.24829	−	12.5544i	−0.278780	−	0.482862i
$677$	−0.839447	+	1.45396i	−0.0322626	+	0.0558804i	−0.881706	−	0.471800i	$-0.843605\pi$
$677$	−0.839447	+	1.45396i	−0.0322626	+	0.0558804i	0.849443	+	0.527680i	$0.176938\pi$
$678$	1.13576	+	3.49550i	0.0436185	+	0.134244i
$679$	−3.65242	−	1.62616i	−0.140167	−	0.0624064i
$680$	1.52280	+	1.10638i	0.0583966	+	0.0424276i
$681$	−2.38470			−0.0913819
$682$	20.8660	−	3.14154i	0.799002	−	0.120296i
$683$	24.2589			0.928240			0.464120	−	0.885772i	$-0.346371\pi$
$683$	24.2589			0.928240			0.464120	+	0.885772i	$0.346371\pi$
$684$	32.0610	+	23.2937i	1.22588	+	0.890657i
$685$	−5.43849	−	2.42137i	−0.207794	−	0.0925159i
$686$	0.147359	+	0.453526i	0.00562621	+	0.0173157i
$687$	3.76878	−	6.52773i	0.143788	−	0.249048i
$688$	1.58628	+	2.74752i	0.0604764	+	0.104748i
$689$	−19.2732	+	21.4051i	−0.734252	+	0.815469i
$690$	−1.95008	+	6.00172i	−0.0742382	+	0.228482i
$691$	−13.0183	−	14.4582i	−0.495238	−	0.550018i	0.442768	−	0.896636i	$-0.353996\pi$
$691$	−13.0183	−	14.4582i	−0.495238	−	0.550018i	−0.938006	+	0.346619i	$0.887330\pi$
$692$	38.5552	−	17.1659i	1.46565	−	0.652549i
$693$	19.8813	+	4.22591i	0.755230	+	0.160529i
$694$	−2.61256	+	24.8568i	−0.0991713	+	0.943552i
$695$	−1.14812	−	10.9236i	−0.0435505	−	0.414356i
$696$	−1.64631	+	0.349933i	−0.0624031	+	0.0132642i
$697$	24.6277	−	17.8931i	0.932840	−	0.677748i
$698$	−37.8008	+	27.4639i	−1.43078	+	1.03952i
$699$	3.54445	−	0.753395i	0.134063	−	0.0284960i
$700$	0.668442	+	6.35980i	0.0252647	+	0.240378i
$701$	−0.330435	+	3.14388i	−0.0124803	+	0.118743i	−0.998988	−	0.0449708i	$-0.985681\pi$
$701$	−0.330435	+	3.14388i	−0.0124803	+	0.118743i	0.986508	+	0.163713i	$0.0523472\pi$
$702$	24.2327	+	5.15081i	0.914603	+	0.194405i
$703$	50.1939	−	22.3478i	1.89310	−	0.842862i
$704$	7.32272	+	8.13270i	0.275985	+	0.306513i
$705$	0.373610	−	1.14985i	0.0140710	−	0.0433060i
$706$	9.92572	−	11.0236i	0.373559	−	0.414880i
$707$	2.33631	+	4.04661i	0.0878660	+	0.152188i
$708$	0.365573	−	0.633192i	0.0137391	−	0.0237968i
$709$	−9.74311	−	29.9862i	−0.365910	−	1.12616i	−0.949409	−	0.314042i	$-0.898317\pi$
$709$	−9.74311	−	29.9862i	−0.365910	−	1.12616i	0.583499	−	0.812114i	$-0.301683\pi$
$710$	21.7587	+	9.68758i	0.816588	+	0.363568i
$711$	−29.3334	−	21.3120i	−1.10009	−	0.799262i
$712$	0.824917			0.0309151
$713$	23.6263	+	29.6364i	0.884810	+	1.10989i
$714$	11.7839			0.441000
$715$	−7.37135	−	5.35560i	−0.275673	−	0.200288i
$716$	−19.9470	−	8.88098i	−0.745455	−	0.331898i
$717$	1.91466	+	5.89271i	0.0715042	+	0.220067i
$718$	−13.2855	+	23.0111i	−0.495810	+	0.858768i
$719$	−7.22080	−	12.5068i	−0.269290	−	0.466425i	0.699388	−	0.714742i	$-0.253456\pi$
$719$	−7.22080	−	12.5068i	−0.269290	−	0.466425i	−0.968679	+	0.248317i	$0.920122\pi$
$720$	8.32046	−	9.24081i	0.310085	−	0.344384i
$721$	−2.68876	+	8.27514i	−0.100135	+	0.308182i
$722$	65.5186	+	72.7658i	2.43835	+	2.70806i
$723$	−0.837738	+	0.372985i	−0.0311558	+	0.0138715i
$724$	19.7968	+	4.20795i	0.735744	+	0.156387i
$725$	−0.661595	+	6.29466i	−0.0245710	+	0.233778i
$726$	−0.691080	−	6.57519i	−0.0256484	−	0.244028i
$727$	0.218860	−	0.0465201i	0.00811706	−	0.00172533i	−0.203851	−	0.979002i	$-0.565346\pi$
$727$	0.218860	−	0.0465201i	0.00811706	−	0.00172533i	0.211968	+	0.977277i	$0.432013\pi$
$728$	7.73303	−	5.61838i	0.286605	−	0.208231i
$729$	12.3724	−	8.98904i	0.458235	−	0.332927i
$730$	−19.4286	+	4.12967i	−0.719083	+	0.152846i
$731$	−0.251432	−	2.39222i	−0.00929955	−	0.0884794i
$732$	0.876929	−	8.34342i	0.0324122	−	0.308382i
$733$	−39.0270	−	8.29544i	−1.44149	−	0.306399i	−0.580187	−	0.814484i	$-0.697020\pi$
$733$	−39.0270	−	8.29544i	−1.44149	−	0.306399i	−0.861307	+	0.508085i	$0.830354\pi$
$734$	50.5727	−	22.5164i	1.86667	−	0.831096i
$735$	−2.23203	−	2.47892i	−0.0823297	−	0.0914364i
$736$	−15.8804	+	48.8748i	−0.585359	+	1.80155i
$737$	0.715333	−	0.794458i	0.0263496	−	0.0292642i
$738$	−23.8452	−	41.3011i	−0.877753	−	1.52031i
$739$	5.75932	−	9.97544i	0.211860	−	0.366953i	−0.740437	−	0.672126i	$-0.765381\pi$
$739$	5.75932	−	9.97544i	0.211860	−	0.366953i	0.952297	+	0.305174i	$0.0987145\pi$
$740$	3.48119	+	10.7140i	0.127971	+	0.393855i
$741$	17.0122	+	7.57430i	0.624957	+	0.278249i
$742$	36.1802	+	26.2865i	1.32822	+	0.965007i
$743$	−44.3036			−1.62534			−0.812670	−	0.582724i	$-0.801987\pi$
$743$	−44.3036			−1.62534			−0.812670	+	0.582724i	$0.801987\pi$
$744$	0.372257	+	1.43301i	0.0136476	+	0.0525367i
$745$	2.37007			0.0868327
$746$	−0.910582	−	0.661576i	−0.0333388	−	0.0242220i
$747$	2.19002	+	0.975059i	0.0801286	+	0.0356755i
$748$	−3.54562	−	10.9123i	−0.129641	−	0.398993i
$749$	−12.2099	+	21.1482i	−0.446140	+	0.772738i
$750$	0.463517	+	0.802834i	0.0169252	+	0.0293154i
$751$	−31.4541	+	34.9333i	−1.14778	+	1.27474i	−0.191754	+	0.981443i	$0.561418\pi$
$751$	−31.4541	+	34.9333i	−1.14778	+	1.27474i	−0.956023	+	0.293293i	$0.905249\pi$
$752$	3.48801	−	10.7350i	0.127195	−	0.391465i
$753$	−2.11757	−	2.35180i	−0.0771687	−	0.0857045i
$754$	−51.6171	+	22.9814i	−1.87978	+	0.836934i
$755$	−3.40006	−	0.722705i	−0.123741	−	0.0263019i
$756$	1.85505	−	17.6496i	0.0674673	−	0.641909i
$757$	1.88216	+	17.9076i	0.0684082	+	0.650861i	0.973975	+	0.226657i	$0.0727795\pi$
$757$	1.88216	+	17.9076i	0.0684082	+	0.650861i	−0.905566	+	0.424204i	$0.860554\pi$
$758$	1.40215	−	0.298035i	0.0509282	−	0.0108251i
$759$	−5.21087	+	3.78592i	−0.189143	+	0.137420i
$760$	3.73640	−	2.71465i	0.135533	−	0.0984708i
$761$	−23.9385	+	5.08828i	−0.867769	+	0.184450i	−0.620222	−	0.784426i	$-0.712958\pi$
$761$	−23.9385	+	5.08828i	−0.867769	+	0.184450i	−0.247546	+	0.968876i	$0.579624\pi$
$762$	1.52501	+	14.5095i	0.0552452	+	0.525623i
$763$	−2.19814	+	20.9139i	−0.0795780	+	0.757134i
$764$	−19.0155	−	4.04186i	−0.687955	−	0.146229i
$765$	−8.61277	+	3.83465i	−0.311395	+	0.138642i
$766$	26.9166	+	29.8939i	0.972537	+	1.08011i
$767$	−1.26999	+	3.90864i	−0.0458568	+	0.141133i
$768$	−6.29713	+	6.99367i	−0.227228	+	0.252362i
$769$	−5.29984	−	9.17960i	−0.191117	−	0.331025i	0.754503	−	0.656296i	$-0.227878\pi$
$769$	−5.29984	−	9.17960i	−0.191117	−	0.331025i	−0.945621	+	0.325271i	$0.894544\pi$
$770$	−7.07342	+	12.2515i	−0.254908	+	0.441514i
$771$	−1.96393	−	6.04435i	−0.0707292	−	0.217682i
$772$	−14.2893	−	6.36200i	−0.514283	−	0.228973i
$773$	−16.0546	−	11.6644i	−0.577444	−	0.419538i	0.260358	−	0.965512i	$-0.416160\pi$
$773$	−16.0546	−	11.6644i	−0.577444	−	0.419538i	−0.837802	+	0.545975i	$0.816160\pi$
$774$	−3.76835			−0.135451
$775$	5.55774	+	0.333888i	0.199640	+	0.0119936i
$776$	−0.592028			−0.0212526
$777$	−9.55355	−	6.94106i	−0.342732	−	0.249009i
$778$	−37.1234	−	16.5284i	−1.33094	−	0.592572i
$779$	−23.0813	−	71.0368i	−0.826972	−	2.54516i
$780$	−1.90908	+	3.30662i	−0.0683560	+	0.118396i
$781$	12.1550	+	21.0531i	0.434941	+	0.753339i
$782$	29.8893	−	33.1954i	1.06884	−	1.18707i
$783$	5.42789	−	16.7053i	0.193977	−	0.597000i
$784$	−20.8382	−	23.1431i	−0.744220	−	0.826540i
$785$	−6.36549	+	2.83410i	−0.227194	+	0.101153i
$786$	−10.7812	−	2.29162i	−0.384554	−	0.0817395i
$787$	2.50315	−	23.8159i	0.0892276	−	0.848944i	−0.854773	−	0.519002i	$-0.826304\pi$
$787$	2.50315	−	23.8159i	0.0892276	−	0.848944i	0.944001	−	0.329943i	$-0.107029\pi$
$788$	1.34637	+	12.8098i	0.0479623	+	0.456331i
$789$	8.47986	−	1.80245i	0.301891	−	0.0641689i
$790$	20.4165	−	14.8334i	0.726386	−	0.527750i
$791$	−11.9729	+	8.69881i	−0.425707	+	0.309294i
$792$	2.94399	−	0.625765i	0.104610	−	0.0222356i
$793$	4.92923	+	46.8985i	0.175042	+	1.66541i
$794$	−4.50332	+	42.8463i	−0.159817	+	1.52056i
$795$	2.92575	+	0.621888i	0.103766	+	0.0220561i
$796$	−9.88780	+	4.40233i	−0.350464	+	0.156036i
$797$	−32.2965	−	35.8689i	−1.14400	−	1.27054i	−0.957611	−	0.288066i	$-0.906988\pi$
$797$	−32.2965	−	35.8689i	−1.14400	−	1.27054i	−0.186390	−	0.982476i	$-0.559679\pi$
$798$	8.93474	−	27.4983i	0.316286	−	0.973429i
$799$	−5.72641	+	6.35983i	−0.202586	+	0.224995i
$800$	3.77463	+	6.53785i	0.133453	+	0.231148i
$801$	−2.06590	+	3.57824i	−0.0729949	+	0.126431i
$802$	−4.19487	−	12.9105i	−0.148126	−	0.455885i
$803$	−18.5204	−	8.24580i	−0.653570	−	0.290988i
$804$	−0.362426	−	0.263318i	−0.0127818	−	0.00928652i
$805$	−25.4102			−0.895590
$806$	22.2257	+	44.4573i	0.782867	+	1.56594i
$807$	9.93249			0.349640
$808$	0.559770	+	0.406696i	0.0196926	+	0.0143075i
$809$	−1.63377	−	0.727400i	−0.0574402	−	0.0255740i	0.377816	−	0.925881i	$-0.376675\pi$
$809$	−1.63377	−	0.727400i	−0.0574402	−	0.0255740i	−0.435256	+	0.900307i	$0.643342\pi$
$810$	4.15070	+	12.7745i	0.145841	+	0.448852i
$811$	3.85523	−	6.67745i	0.135375	−	0.234477i	−0.790365	−	0.612636i	$-0.790109\pi$
$811$	3.85523	−	6.67745i	0.135375	−	0.234477i	0.925741	+	0.378159i	$0.123443\pi$
$812$	20.2375	+	35.0524i	0.710197	+	1.23010i
$813$	−7.11998	+	7.90754i	−0.249709	+	0.277330i
$814$	−7.70120	+	23.7019i	−0.269927	+	0.830749i
$815$	−2.22663	−	2.47292i	−0.0779953	−	0.0866226i
$816$	6.72198	−	2.99282i	0.235316	−	0.104770i
$817$	−5.77301	−	1.22709i	−0.201972	−	0.0429305i
$818$	6.58084	−	62.6125i	0.230094	−	2.18920i
$819$	5.00444	+	47.6141i	0.174869	+	1.66377i
$820$	14.9798	−	3.18406i	0.523118	−	0.111192i
$821$	−14.9438	+	10.8573i	−0.521542	+	0.378923i	−0.817185	−	0.576376i	$-0.804466\pi$
$821$	−14.9438	+	10.8573i	−0.521542	+	0.378923i	0.295642	+	0.955299i	$0.404466\pi$
$822$	−4.46479	+	3.24386i	−0.155728	+	0.113143i
$823$	34.6643	−	7.36813i	1.20832	−	0.256837i	0.440649	−	0.897679i	$-0.354748\pi$
$823$	34.6643	−	7.36813i	1.20832	−	0.256837i	0.767672	+	0.640843i	$0.221415\pi$
$824$	0.134677	+	1.28137i	0.00469171	+	0.0446387i
$825$	−0.0989039	+	0.941008i	−0.00344339	+	0.0327617i
$826$	6.24157	+	1.32669i	0.217172	+	0.0461613i
$827$	21.8080	−	9.70957i	0.758340	−	0.337635i	0.00912218	−	0.999958i	$-0.497096\pi$
$827$	21.8080	−	9.70957i	0.758340	−	0.337635i	0.749218	+	0.662324i	$0.230430\pi$
$828$	−21.6040	−	23.9937i	−0.750790	−	0.833837i
$829$	−4.64106	+	14.2837i	−0.161191	+	0.496094i	−0.998735	−	0.0502750i	$-0.983990\pi$
$829$	−4.64106	+	14.2837i	−0.161191	+	0.496094i	0.837545	+	0.546369i	$0.183990\pi$
$830$	−1.11647	+	1.23996i	−0.0387532	+	0.0430398i
$831$	−6.80151	−	11.7806i	−0.235942	−	0.408663i
$832$	−12.8888	+	22.3240i	−0.446837	+	0.773944i
$833$	7.29638	+	22.4559i	0.252804	+	0.778052i
$834$	−9.30201	−	4.14152i	−0.322102	−	0.143409i
$835$	−14.5826	−	10.5949i	−0.504652	−	0.366651i
$836$	−28.1528			−0.973685
$837$	−14.8940	−	4.11313i	−0.514813	−	0.142170i
$838$	31.6430			1.09309
$839$	2.99776	+	2.17800i	0.103494	+	0.0751930i	0.638329	−	0.769764i	$-0.279626\pi$
$839$	2.99776	+	2.17800i	0.103494	+	0.0751930i	−0.534834	+	0.844957i	$0.679626\pi$
$840$	−0.906801	−	0.403734i	−0.0312876	−	0.0139301i
$841$	3.41785	+	10.5191i	0.117857	+	0.362726i
$842$	21.2680	−	36.8372i	0.732943	−	1.26949i
$843$	6.28584	+	10.8874i	0.216496	+	0.374982i
$844$	−4.22345	+	4.69062i	−0.145377	+	0.161458i
$845$	2.61488	−	8.04778i	0.0899547	−	0.276852i
$846$	8.97114	+	9.96346i	0.308434	+	0.342551i
$847$	24.3199	−	10.8279i	0.835642	−	0.372052i
$848$	27.3147	+	5.80592i	0.937991	+	0.199376i
$849$	−0.943068	+	8.97269i	−0.0323660	+	0.307942i
$850$	−0.685907	−	6.52597i	−0.0235264	−	0.223839i
$851$	−43.7853	+	9.30685i	−1.50094	+	0.319035i
$852$	8.24153	−	5.98782i	0.282350	−	0.205139i
$853$	10.9839	−	7.98030i	0.376083	−	0.273240i	−0.383646	−	0.923480i	$-0.625332\pi$
$853$	10.9839	−	7.98030i	0.376083	−	0.273240i	0.759729	+	0.650240i	$0.225332\pi$
$854$	71.6175	−	15.2228i	2.45070	−	0.520912i
$855$	2.41801	+	23.0059i	0.0826943	+	0.786784i
$856$	−0.377980	+	3.59624i	−0.0129191	+	0.122917i
$857$	29.1782	+	6.20202i	0.996709	+	0.211857i	0.677258	−	0.735746i	$-0.263168\pi$
$857$	29.1782	+	6.20202i	0.996709	+	0.211857i	0.319451	+	0.947603i	$0.396501\pi$
$858$	−7.71640	+	3.43556i	−0.263434	+	0.117288i
$859$	8.92455	+	9.91171i	0.304502	+	0.338183i	0.875903	−	0.482488i	$-0.160267\pi$
$859$	8.92455	+	9.91171i	0.304502	+	0.338183i	−0.571401	+	0.820671i	$0.693600\pi$
$860$	0.373942	−	1.15088i	0.0127513	−	0.0392446i
$861$	−10.7417	+	11.9299i	−0.366077	+	0.406570i
$862$	−28.2202	−	48.8789i	−0.961185	−	1.66482i
$863$	3.38945	−	5.87070i	0.115378	−	0.199841i	−0.802553	−	0.596581i	$-0.796525\pi$
$863$	3.38945	−	5.87070i	0.115378	−	0.199841i	0.917931	+	0.396740i	$0.129859\pi$
$864$	−6.47408	−	19.9252i	−0.220253	−	0.677868i
$865$	22.5054	+	10.0201i	0.765208	+	0.340693i
$866$	−27.0161	−	19.6284i	−0.918046	−	0.666999i
$867$	2.59966			0.0882890
$868$	30.0081	−	19.1630i	1.01854	−	0.650434i
$869$	25.7577			0.873770
$870$	4.74691	+	3.44883i	0.160935	+	0.116926i
$871$	2.30042	+	1.02421i	0.0779468	+	0.0347041i
$872$	0.962264	+	2.96155i	0.0325864	+	0.100291i
$873$	1.48266	−	2.56804i	0.0501803	−	0.0869149i
$874$	−54.8007	−	94.9176i	−1.85366	−	3.21064i
$875$	−2.49772	+	2.77400i	−0.0844384	+	0.0937784i
$876$	−2.62523	+	8.07962i	−0.0886982	+	0.272985i
$877$	23.5105	+	26.1110i	0.793893	+	0.881707i	0.995204	−	0.0978202i	$-0.0311870\pi$
$877$	23.5105	+	26.1110i	0.793893	+	0.881707i	−0.201311	+	0.979527i	$0.564520\pi$
$878$	0.472658	−	0.210441i	0.0159515	−	0.00710204i
$879$	10.0044	+	2.12650i	0.337440	+	0.0717251i
$880$	−0.923363	+	8.78522i	−0.0311266	+	0.296150i
$881$	−3.91222	−	37.2222i	−0.131806	−	1.25405i	−0.837858	−	0.545889i	$-0.816192\pi$
$881$	−3.91222	−	37.2222i	−0.131806	−	1.25405i	0.706052	−	0.708160i	$-0.250475\pi$
$882$	36.1821	−	7.69075i	1.21832	−	0.258961i
$883$	−41.9273	+	30.4620i	−1.41097	+	1.02513i	−0.417784	+	0.908546i	$0.637193\pi$
$883$	−41.9273	+	30.4620i	−1.41097	+	1.02513i	−0.993181	+	0.116580i	$0.962807\pi$
$884$	21.8649	−	15.8858i	0.735396	−	0.534296i
$885$	0.417458	−	0.0887335i	0.0140327	−	0.00298274i
$886$	−6.40839	−	60.9717i	−0.215294	−	2.04839i
$887$	0.615173	−	5.85298i	0.0206555	−	0.196524i	−0.979328	−	0.202279i	$-0.935165\pi$
$887$	0.615173	−	5.85298i	0.0206555	−	0.196524i	0.999983	+	0.00575514i	$0.00183193\pi$
$888$	−1.71042	−	0.363561i	−0.0573979	−	0.0122003i
$889$	−53.6668	+	23.8940i	−1.79993	+	0.801379i
$890$	−1.92428	−	2.13713i	−0.0645020	−	0.0716367i
$891$	−4.23648	+	13.0385i	−0.141927	+	0.436808i
$892$	−3.81119	+	4.23275i	−0.127608	+	0.141723i
$893$	10.4991	+	18.1850i	0.351340	+	0.608539i
$894$	1.09857	−	1.90277i	0.0367416	−	0.0636383i
$895$	−3.93853	−	12.1216i	−0.131651	−	0.405179i
$896$	−14.9241	−	6.64464i	−0.498579	−	0.221982i
$897$	−12.2741	−	8.91767i	−0.409821	−	0.297752i
$898$	0.761638			0.0254162
$899$	32.9951	−	12.3771i	1.10045	−	0.412800i
$900$	−4.74295			−0.158098
$901$	−17.1288	−	12.4448i	−0.570642	−	0.414596i
$902$	30.9501	+	13.7799i	1.03053	+	0.458820i
$903$	0.391982	+	1.20640i	0.0130444	+	0.0401464i
$904$	−1.09573	+	1.89785i	−0.0364433	+	0.0631217i
$905$	5.90699	+	10.2312i	0.196355	+	0.340097i
$906$	−2.15620	+	2.39470i	−0.0716348	+	0.0795585i
$907$	−14.4273	+	44.4028i	−0.479052	+	1.47437i	0.361362	+	0.932425i	$0.382312\pi$
$907$	−14.4273	+	44.4028i	−0.479052	+	1.47437i	−0.840414	+	0.541945i	$0.817688\pi$
$908$	5.68220	+	6.31072i	0.188570	+	0.209429i
$909$	−3.16600	+	1.40959i	−0.105009	+	0.0467532i
$910$	−32.5944	−	6.92816i	−1.08050	−	0.229666i
$911$	−3.87824	+	36.8990i	−0.128492	+	1.22252i	0.720251	+	0.693713i	$0.244027\pi$
$911$	−3.87824	+	36.8990i	−0.128492	+	1.22252i	−0.848743	+	0.528805i	$0.822640\pi$
$912$	−1.88718	−	17.9553i	−0.0624907	−	0.594559i
$913$	−1.66580	+	0.354077i	−0.0551300	+	0.0117183i
$914$	52.8517	−	38.3990i	1.74818	−	1.27013i
$915$	3.96179	−	2.87841i	0.130973	−	0.0951573i
$916$	−26.2547	+	5.58061i	−0.867480	+	0.184389i
$917$	−4.63914	−	44.1384i	−0.153198	−	1.45758i
$918$	−1.90352	+	18.1107i	−0.0628254	+	0.597744i
$919$	11.2480	+	2.39084i	0.371038	+	0.0788666i	0.389657	−	0.920960i	$-0.372594\pi$
$919$	11.2480	+	2.39084i	0.371038	+	0.0788666i	−0.0186189	+	0.999827i	$0.505927\pi$
$920$	−3.43739	+	1.53042i	−0.113327	+	0.0504566i
$921$	2.72204	+	3.02313i	0.0896942	+	0.0996155i
$922$	−7.78583	+	23.9623i	−0.256413	+	0.789157i
$923$	−38.3156	+	42.5538i	−1.26117	+	1.40068i
$924$	3.02537	+	5.24009i	0.0995272	+	0.172386i
$925$	−3.28791	+	5.69482i	−0.108106	+	0.187245i
$926$	−10.1149	−	31.1304i	−0.332395	−	1.02301i
$927$	−5.89548	−	2.62484i	−0.193633	−	0.0862110i
$928$	38.6563	+	28.0854i	1.26895	+	0.921949i
$929$	−24.6485			−0.808691			−0.404346	−	0.914606i	$-0.632501\pi$
$929$	−24.6485			−0.808691			−0.404346	+	0.914606i	$0.632501\pi$
$930$	2.84416	−	4.30718i	0.0932638	−	0.141238i
$931$	57.9344			1.89872
$932$	−10.4393	−	7.58463i	−0.341952	−	0.248443i
$933$	2.25672	+	1.00476i	0.0738817	+	0.0328942i
$934$	14.9167	+	45.9088i	0.488089	+	1.50218i
$935$	3.34876	−	5.80023i	0.109516	−	0.189688i
$936$	3.54472	+	6.13964i	0.115863	+	0.200680i
$937$	−22.6216	+	25.1238i	−0.739016	+	0.820760i	−0.989066	−	0.147473i	$-0.952886\pi$
$937$	−22.6216	+	25.1238i	−0.739016	+	0.820760i	0.250051	+	0.968233i	$0.419553\pi$
$938$	1.20817	−	3.71838i	0.0394483	−	0.121409i
$939$	−6.55402	−	7.27898i	−0.213882	−	0.237541i
$940$	−3.93313	+	1.75114i	−0.128285	+	0.0571159i
$941$	37.5168	+	7.97444i	1.22301	+	0.259959i	0.773779	−	0.633455i	$-0.218364\pi$
$941$	37.5168	+	7.97444i	1.22301	+	0.259959i	0.449233	+	0.893415i	$0.351697\pi$
$942$	−0.675198	+	6.42408i	−0.0219991	+	0.209308i
$943$	6.36085	+	60.5194i	0.207138	+	1.97078i
$944$	3.89738	−	0.828413i	0.126849	−	0.0269626i
$945$	8.38073	−	6.08896i	0.272625	−	0.198074i
$946$	2.16576	−	1.57352i	0.0704150	−	0.0511595i
$947$	−16.9927	+	3.61191i	−0.552188	+	0.117371i	−0.475551	−	0.879688i	$-0.657751\pi$
$947$	−16.9927	+	3.61191i	−0.552188	+	0.117371i	−0.0766365	+	0.997059i	$0.524418\pi$
$948$	−1.12825	−	10.7346i	−0.0366439	−	0.348644i
$949$	4.99153	−	47.4912i	0.162032	−	1.54163i
$950$	−15.7488	−	3.34750i	−0.510958	−	0.108607i
$951$	−10.3464	+	4.60653i	−0.335506	+	0.149377i
$952$	4.70141	+	5.22145i	0.152374	+	0.169228i
$953$	8.69390	−	26.7571i	0.281623	−	0.866746i	−0.705768	−	0.708443i	$-0.749398\pi$
$953$	8.69390	−	26.7571i	0.281623	−	0.866746i	0.987391	−	0.158303i	$-0.0506022\pi$
$954$	−22.1945	+	24.6494i	−0.718572	+	0.798055i
$955$	−5.67383	−	9.82737i	−0.183601	−	0.318006i
$956$	11.0319	−	19.1078i	0.356797	−	0.617991i
$957$	1.85063	+	5.69564i	0.0598223	+	0.184114i
$958$	−29.1385	−	12.9733i	−0.941421	−	0.419147i
$959$	−17.9779	−	13.0617i	−0.580537	−	0.421785i
$960$	2.67689			0.0863962
$961$	−12.1744	−	28.5094i	−0.392723	−	0.919657i
$962$	−58.7024			−1.89264
$963$	−14.6528	−	10.6459i	−0.472179	−	0.343058i
$964$	2.98318	+	1.32820i	0.0960818	+	0.0427784i
$965$	−2.82142	−	8.68343i	−0.0908246	−	0.279529i
$966$	−11.7780	+	20.4001i	−0.378952	+	0.656364i
$967$	17.3521	+	30.0546i	0.558005	+	0.966492i	0.997663	+	0.0683271i	$0.0217662\pi$
$967$	17.3521	+	30.0546i	0.558005	+	0.966492i	−0.439658	+	0.898165i	$0.644901\pi$
$968$	2.63775	−	2.92952i	0.0847806	−	0.0941584i
$969$	−4.22996	+	13.0185i	−0.135886	+	0.418214i
$970$	1.38102	+	1.53378i	0.0443419	+	0.0492466i
$971$	2.28281	−	1.01637i	0.0732589	−	0.0326170i	−0.369780	−	0.929119i	$-0.620567\pi$
$971$	2.28281	−	1.01637i	0.0732589	−	0.0326170i	0.443039	+	0.896502i	$0.353900\pi$
$972$	19.5706	+	4.15987i	0.627729	+	0.133428i
$973$	4.28567	−	40.7755i	0.137392	−	1.30720i
$974$	1.88063	+	17.8930i	0.0602593	+	0.573329i
$975$	−2.18003	+	0.463380i	−0.0698169	+	0.0148400i
$976$	36.9872	−	26.8728i	1.18393	−	0.860176i
$977$	9.55608	−	6.94290i	0.305726	−	0.222123i	−0.424334	−	0.905506i	$-0.639492\pi$
$977$	9.55608	−	6.94290i	0.305726	−	0.222123i	0.730060	+	0.683383i	$0.239492\pi$
$978$	−3.01742	+	0.641373i	−0.0964865	+	0.0205088i
$979$	−0.306814	−	2.91914i	−0.00980582	−	0.0932961i
$980$	−1.24164	+	11.8134i	−0.0396627	+	0.377366i
$981$	−15.2562	−	3.24280i	−0.487091	−	0.103534i
$982$	25.0212	−	11.1402i	0.798459	−	0.355497i
$983$	0.387248	+	0.430082i	0.0123513	+	0.0137175i	0.749289	−	0.662243i	$-0.230395\pi$
$983$	0.387248	+	0.430082i	0.0123513	+	0.0137175i	−0.736938	+	0.675961i	$0.763729\pi$
$984$	−0.734577	+	2.26079i	−0.0234174	+	0.0720715i
$985$	−5.03088	+	5.58736i	−0.160297	+	0.178028i
$986$	−20.7663	−	35.9682i	−0.661333	−	1.14546i
$987$	2.25652	−	3.90841i	0.0718259	−	0.124406i
$988$	−20.4920	−	63.0678i	−0.651936	−	2.00645i
$989$	4.39269	+	1.95575i	0.139680	+	0.0621893i
$990$	−8.48862	−	6.16734i	−0.269786	−	0.196011i
$991$	53.0123			1.68399			0.841996	−	0.539484i	$-0.181381\pi$
$991$	53.0123			1.68399			0.841996	+	0.539484i	$0.181381\pi$
$992$	23.1613	−	35.0754i	0.735373	−	1.11365i
$993$	−12.6702			−0.402075
$994$	71.9271	+	52.2581i	2.28139	+	1.65753i
$995$	−5.77170	−	2.56973i	−0.182975	−	0.0814658i
$996$	0.220529	+	0.678720i	0.00698774	+	0.0215061i
$997$	28.3302	−	49.0693i	0.897226	−	1.55404i	0.0662011	−	0.997806i	$-0.478912\pi$
$997$	28.3302	−	49.0693i	0.897226	−	1.55404i	0.831025	−	0.556235i	$-0.187755\pi$
$998$	6.24015	+	10.8083i	0.197529	+	0.342129i
$999$	12.2110	−	13.5617i	0.386339	−	0.429073i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	155.2.q.b.81.2	✓	40
5.2	odd	4		775.2.ck.b.174.8		80
5.3	odd	4		775.2.ck.b.174.3		80
5.4	even	2		775.2.bl.b.701.4		40
31.7	even	15		4805.2.a.ba.1.16		20
31.18	even	15	inner	155.2.q.b.111.2	yes	40
31.24	odd	30		4805.2.a.z.1.16		20
155.18	odd	60		775.2.ck.b.49.8		80
155.49	even	30		775.2.bl.b.576.4		40
155.142	odd	60		775.2.ck.b.49.3		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.q.b.81.2	✓	40	1.1	even	1	trivial
155.2.q.b.111.2	yes	40	31.18	even	15	inner
775.2.bl.b.576.4		40	155.49	even	30
775.2.bl.b.701.4		40	5.4	even	2
775.2.ck.b.49.3		80	155.142	odd	60
775.2.ck.b.49.8		80	155.18	odd	60
775.2.ck.b.174.3		80	5.3	odd	4
775.2.ck.b.174.8		80	5.2	odd	4
4805.2.a.z.1.16		20	31.24	odd	30
4805.2.a.ba.1.16		20	31.7	even	15

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:	\( N \)	\(=\)	\( 155 = 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	155.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.55894 - 1.13264i) q^{2} +(-0.439495 - 0.195676i) q^{3} +(0.529393 + 1.62930i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.463517 + 0.802834i) q^{6} +(-2.49772 + 2.77400i) q^{7} +(-0.170807 + 0.525691i) q^{8} +(-1.85252 - 2.05744i) q^{9} +O(q^{10})\)	\(q+(-1.55894 - 1.13264i) q^{2} +(-0.439495 - 0.195676i) q^{3} +(0.529393 + 1.62930i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.463517 + 0.802834i) q^{6} +(-2.49772 + 2.77400i) q^{7} +(-0.170807 + 0.525691i) q^{8} +(-1.85252 - 2.05744i) q^{9} +(1.76036 - 0.783763i) q^{10} +(1.92380 + 0.408916i) q^{11} +(0.0861498 - 0.819660i) q^{12} +(0.484249 + 4.60732i) q^{13} +(7.03573 - 1.49549i) q^{14} +(0.389208 - 0.282776i) q^{15} +(3.63363 - 2.63999i) q^{16} +(-3.33092 + 0.708008i) q^{17} +(0.557647 + 5.30565i) q^{18} +(-0.873384 + 8.30970i) q^{19} +(-1.67571 - 0.356184i) q^{20} +(1.64054 - 0.730416i) q^{21} +(-2.53593 - 2.81643i) q^{22} +(2.10357 - 6.47411i) q^{23} +(0.177934 - 0.197616i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(4.46350 - 7.73101i) q^{26} +(0.857578 + 2.63935i) q^{27} +(-5.84197 - 2.60101i) q^{28} +(-5.12053 - 3.72029i) q^{29} -0.927033 q^{30} +(-3.06803 + 4.64620i) q^{31} -7.54926 q^{32} +(-0.765485 - 0.556157i) q^{33} +(5.99461 + 2.66897i) q^{34} +(-1.15349 - 3.55009i) q^{35} +(2.37148 - 4.10752i) q^{36} +(-3.28791 - 5.69482i) q^{37} +(10.7734 - 11.9651i) q^{38} +(0.688717 - 2.11965i) q^{39} +(-0.369858 - 0.410769i) q^{40} +(-8.16651 + 3.63596i) q^{41} +(-3.38480 - 0.719461i) q^{42} +(-0.0738348 + 0.702492i) q^{43} +(0.352197 + 3.35093i) q^{44} +(2.70806 - 0.575615i) q^{45} +(-10.6121 + 7.71017i) q^{46} +(2.03315 - 1.47717i) q^{47} +(-2.11355 + 0.449248i) q^{48} +(-0.724769 - 6.89572i) q^{49} +(-0.201422 + 1.91640i) q^{50} +(1.60246 + 0.340614i) q^{51} +(-7.25037 + 3.22807i) q^{52} +(4.16026 + 4.62043i) q^{53} +(1.65251 - 5.08591i) q^{54} +(-1.31603 + 1.46160i) q^{55} +(-1.03164 - 1.78685i) q^{56} +(2.00986 - 3.48117i) q^{57} +(3.76887 + 11.5994i) q^{58} +(0.810429 + 0.360826i) q^{59} +(0.666772 + 0.484438i) q^{60} +10.1791 q^{61} +(10.0453 - 3.76819i) q^{62} +10.3344 q^{63} +(4.50157 + 3.27058i) q^{64} +(-4.23218 - 1.88429i) q^{65} +(0.563420 + 1.73403i) q^{66} +(0.271777 - 0.470731i) q^{67} +(-2.91692 - 5.05226i) q^{68} +(-2.19134 + 2.43373i) q^{69} +(-2.22273 + 6.84086i) q^{70} +(8.27069 + 9.18553i) q^{71} +(1.39800 - 0.622431i) q^{72} +(-10.0825 - 2.14311i) q^{73} +(-1.32451 + 12.6019i) q^{74} +(0.0502873 + 0.478452i) q^{75} +(-14.0014 + 2.97609i) q^{76} +(-5.93944 + 4.31526i) q^{77} +(-3.47446 + 2.52434i) q^{78} +(12.8102 - 2.72290i) q^{79} +(0.469481 + 4.46681i) q^{80} +(-0.728622 + 6.93238i) q^{81} +(16.8493 + 3.58143i) q^{82} +(-0.791033 + 0.352191i) q^{83} +(2.05856 + 2.28626i) q^{84} +(1.05231 - 3.23866i) q^{85} +(0.910771 - 1.01151i) q^{86} +(1.52248 + 2.63701i) q^{87} +(-0.543562 + 0.941478i) q^{88} +(-0.461178 - 1.41936i) q^{89} +(-4.87365 - 2.16989i) q^{90} +(-13.9902 - 10.1645i) q^{91} +11.6619 q^{92} +(2.25753 - 1.44165i) q^{93} -4.84266 q^{94} +(-6.75972 - 4.91122i) q^{95} +(3.31786 + 1.47721i) q^{96} +(0.330979 + 1.01865i) q^{97} +(-6.68046 + 11.5709i) q^{98} +(-2.72256 - 4.71562i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 2 q^{2} + 3 q^{3} - 2 q^{4} - 20 q^{5} - 12 q^{6} - 2 q^{7} - 31 q^{8} + 6 q^{9}+O(q^{10}) \) 40 * q + 2 * q^2 + 3 * q^3 - 2 * q^4 - 20 * q^5 - 12 * q^6 - 2 * q^7 - 31 * q^8 + 6 * q^9	\( 40 q + 2 q^{2} + 3 q^{3} - 2 q^{4} - 20 q^{5} - 12 q^{6} - 2 q^{7} - 31 q^{8} + 6 q^{9} - q^{10} + 16 q^{11} - q^{12} + 2 q^{13} - 10 q^{14} - 6 q^{15} - 16 q^{16} + 4 q^{17} + 37 q^{18} - 9 q^{19} + q^{20} - 24 q^{21} - 2 q^{22} - 4 q^{23} + 110 q^{24} - 20 q^{25} - 4 q^{26} - 9 q^{27} + 38 q^{28} - 22 q^{29} + 24 q^{30} - 6 q^{31} - 60 q^{32} + 9 q^{33} - 16 q^{34} + 4 q^{35} - q^{36} - 38 q^{37} - 32 q^{38} - 55 q^{39} + 8 q^{40} - 24 q^{41} - 68 q^{42} + 26 q^{43} - 52 q^{44} + 6 q^{45} - 50 q^{46} + 4 q^{47} + 105 q^{48} + 93 q^{49} - q^{50} - 42 q^{51} + 15 q^{52} + 13 q^{53} + 102 q^{54} + q^{55} + 5 q^{56} - 36 q^{57} - 37 q^{58} + 31 q^{59} + 17 q^{60} + 68 q^{61} + 47 q^{62} - 10 q^{63} - 23 q^{64} + 2 q^{65} - 2 q^{67} - 28 q^{68} - 48 q^{69} - 10 q^{70} - 30 q^{71} + 39 q^{72} + 25 q^{73} + 50 q^{74} + 3 q^{75} + 14 q^{76} - 64 q^{77} - 22 q^{78} + 49 q^{79} - 7 q^{80} + 25 q^{81} - 66 q^{82} - 18 q^{83} - 18 q^{84} + 7 q^{85} + 163 q^{86} - 36 q^{87} - 124 q^{88} + 4 q^{89} - 23 q^{90} - 37 q^{91} + 110 q^{92} + 7 q^{93} - 94 q^{94} - 12 q^{95} + 22 q^{96} + 46 q^{97} - 13 q^{98} + 17 q^{99}+O(q^{100}) \) 40 * q + 2 * q^2 + 3 * q^3 - 2 * q^4 - 20 * q^5 - 12 * q^6 - 2 * q^7 - 31 * q^8 + 6 * q^9 - q^10 + 16 * q^11 - q^12 + 2 * q^13 - 10 * q^14 - 6 * q^15 - 16 * q^16 + 4 * q^17 + 37 * q^18 - 9 * q^19 + q^20 - 24 * q^21 - 2 * q^22 - 4 * q^23 + 110 * q^24 - 20 * q^25 - 4 * q^26 - 9 * q^27 + 38 * q^28 - 22 * q^29 + 24 * q^30 - 6 * q^31 - 60 * q^32 + 9 * q^33 - 16 * q^34 + 4 * q^35 - q^36 - 38 * q^37 - 32 * q^38 - 55 * q^39 + 8 * q^40 - 24 * q^41 - 68 * q^42 + 26 * q^43 - 52 * q^44 + 6 * q^45 - 50 * q^46 + 4 * q^47 + 105 * q^48 + 93 * q^49 - q^50 - 42 * q^51 + 15 * q^52 + 13 * q^53 + 102 * q^54 + q^55 + 5 * q^56 - 36 * q^57 - 37 * q^58 + 31 * q^59 + 17 * q^60 + 68 * q^61 + 47 * q^62 - 10 * q^63 - 23 * q^64 + 2 * q^65 - 2 * q^67 - 28 * q^68 - 48 * q^69 - 10 * q^70 - 30 * q^71 + 39 * q^72 + 25 * q^73 + 50 * q^74 + 3 * q^75 + 14 * q^76 - 64 * q^77 - 22 * q^78 + 49 * q^79 - 7 * q^80 + 25 * q^81 - 66 * q^82 - 18 * q^83 - 18 * q^84 + 7 * q^85 + 163 * q^86 - 36 * q^87 - 124 * q^88 + 4 * q^89 - 23 * q^90 - 37 * q^91 + 110 * q^92 + 7 * q^93 - 94 * q^94 - 12 * q^95 + 22 * q^96 + 46 * q^97 - 13 * q^98 + 17 * q^99

Introduction

L-functions

Modular forms

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