LMFDB - Embedded newform 224.2.bd.a.109.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(37,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("224.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.bd (of order $24$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			109.6
Character	$\chi$	$=$	224.109
Dual form			224.2.bd.a.37.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16516 - 0.801498i) q^{2} +(1.71349 + 2.23306i) q^{3} +(0.715201 + 1.86775i) q^{4} +(1.90405 + 1.46103i) q^{5} +(-0.206695 - 3.97523i) q^{6} +(-0.262719 - 2.63268i) q^{7} +(0.663674 - 2.74946i) q^{8} +(-1.27406 + 4.75485i) q^{9} +O(q^{10})$	\(q+(-1.16516 - 0.801498i) q^{2} +(1.71349 + 2.23306i) q^{3} +(0.715201 + 1.86775i) q^{4} +(1.90405 + 1.46103i) q^{5} +(-0.206695 - 3.97523i) q^{6} +(-0.262719 - 2.63268i) q^{7} +(0.663674 - 2.74946i) q^{8} +(-1.27406 + 4.75485i) q^{9} +(-1.04751 - 3.22843i) q^{10} +(2.49657 + 0.328680i) q^{11} +(-2.94531 + 4.79745i) q^{12} +(-1.76220 - 0.729927i) q^{13} +(-1.80397 + 3.27806i) q^{14} +6.75532i q^{15} +(-2.97698 + 2.67163i) q^{16} +(-5.05929 - 2.92098i) q^{17} +(5.29549 - 4.51901i) q^{18} +(0.908918 + 6.90392i) q^{19} +(-1.36706 + 4.60122i) q^{20} +(5.42875 - 5.09772i) q^{21} +(-2.64547 - 2.38396i) q^{22} +(0.497314 - 1.85600i) q^{23} +(7.27690 - 3.22914i) q^{24} +(0.196710 + 0.734131i) q^{25} +(1.46821 + 2.26288i) q^{26} +(-4.99959 + 2.07090i) q^{27} +(4.72928 - 2.37359i) q^{28} +(3.54360 - 8.55501i) q^{29} +(5.41438 - 7.87103i) q^{30} +(-2.59366 + 4.49234i) q^{31} +(5.60996 - 0.726841i) q^{32} +(3.54388 + 6.13818i) q^{33} +(3.55373 + 7.45843i) q^{34} +(3.34619 - 5.39659i) q^{35} +(-9.79208 + 1.02105i) q^{36} +(-2.70513 - 2.07572i) q^{37} +(4.47444 - 8.77267i) q^{38} +(-1.38953 - 5.18581i) q^{39} +(5.28072 - 4.26547i) q^{40} +(-4.86955 - 4.86955i) q^{41} +(-10.4112 + 1.58853i) q^{42} +(1.94703 + 4.70055i) q^{43} +(1.17166 + 4.89804i) q^{44} +(-9.37286 + 7.19205i) q^{45} +(-2.06703 + 1.76394i) q^{46} +(3.40104 - 1.96359i) q^{47} +(-11.0669 - 2.06996i) q^{48} +(-6.86196 + 1.38331i) q^{49} +(0.359206 - 1.01304i) q^{50} +(-2.14630 - 16.3028i) q^{51} +(0.102994 - 3.81339i) q^{52} +(4.89856 + 0.644908i) q^{53} +(7.48514 + 1.59423i) q^{54} +(4.27339 + 4.27339i) q^{55} +(-7.41280 - 1.02490i) q^{56} +(-13.8594 + 13.8594i) q^{57} +(-10.9857 + 7.12777i) q^{58} +(-0.694133 + 5.27246i) q^{59} +(-12.6172 + 4.83141i) q^{60} +(-7.60241 + 1.00088i) q^{61} +(6.62263 - 3.15549i) q^{62} +(12.8527 + 2.10499i) q^{63} +(-7.11907 - 3.64949i) q^{64} +(-2.28887 - 3.96445i) q^{65} +(0.790550 - 9.99238i) q^{66} +(-4.18604 - 5.45536i) q^{67} +(1.83725 - 11.5386i) q^{68} +(4.99670 - 2.06970i) q^{69} +(-8.22421 + 3.60594i) q^{70} +(7.62970 - 7.62970i) q^{71} +(12.2277 + 6.65864i) q^{72} +(10.2082 - 2.73527i) q^{73} +(1.48823 + 4.58671i) q^{74} +(-1.30230 + 1.69719i) q^{75} +(-12.2447 + 6.63532i) q^{76} +(0.209410 - 6.65901i) q^{77} +(-2.53739 + 7.15602i) q^{78} +(7.49333 - 4.32628i) q^{79} +(-9.57166 + 0.737475i) q^{80} +(-0.401905 - 0.232040i) q^{81} +(1.77087 + 9.57674i) q^{82} +(-9.84868 - 4.07946i) q^{83} +(13.4039 + 6.49365i) q^{84} +(-5.36551 - 12.9535i) q^{85} +(1.49888 - 7.03744i) q^{86} +(25.1757 - 6.74582i) q^{87} +(2.56060 - 6.64609i) q^{88} +(-3.81526 - 1.02230i) q^{89} +(16.6853 - 0.867564i) q^{90} +(-1.45870 + 4.83106i) q^{91} +(3.82222 - 0.398556i) q^{92} +(-14.4759 + 1.90578i) q^{93} +(-5.53658 - 0.438028i) q^{94} +(-8.35621 + 14.4734i) q^{95} +(11.2357 + 11.2819i) q^{96} +12.6228 q^{97} +(9.10401 + 3.88807i) q^{98} +(-4.74360 + 11.4521i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{8}\right)$

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 $

$2$	−1.16516	−	0.801498i	−0.823893	−	0.566745i
$2$	−1.16516	−	0.801498i	−0.823893	−	0.566745i
$3$	1.71349	+	2.23306i	0.989282	+	1.28926i	0.957095	+	0.289775i	$0.0935805\pi$
$3$	1.71349	+	2.23306i	0.989282	+	1.28926i	0.0321868	+	0.999482i	$0.489753\pi$
$4$	0.715201	+	1.86775i	0.357600	+	0.933875i
$5$	1.90405	+	1.46103i	0.851518	+	0.653393i	0.939432	−	0.342735i	$-0.111353\pi$
$5$	1.90405	+	1.46103i	0.851518	+	0.653393i	−0.0879138	+	0.996128i	$0.528020\pi$
$6$	−0.206695	−	3.97523i	−0.0843828	−	1.62288i
$7$	−0.262719	−	2.63268i	−0.0992986	−	0.995058i
$7$	−0.262719	−	2.63268i	−0.0992986	−	0.995058i
$8$	0.663674	−	2.74946i	0.234644	−	0.972081i
$9$	−1.27406	+	4.75485i	−0.424686	+	1.58495i
$10$	−1.04751	−	3.22843i	−0.331253	−	1.02092i
$11$	2.49657	+	0.328680i	0.752745	+	0.0991007i	0.497128	−	0.867677i	$-0.334388\pi$
$11$	2.49657	+	0.328680i	0.752745	+	0.0991007i	0.255617	+	0.966778i	$0.417721\pi$
$12$	−2.94531	+	4.79745i	−0.850237	+	1.38490i
$13$	−1.76220	−	0.729927i	−0.488746	−	0.202445i	0.124681	−	0.992197i	$-0.460209\pi$
$13$	−1.76220	−	0.729927i	−0.488746	−	0.202445i	−0.613427	+	0.789752i	$0.710209\pi$
$14$	−1.80397	+	3.27806i	−0.482132	+	0.876098i
$15$			6.75532i			1.74422i
$16$	−2.97698	+	2.67163i	−0.744244	+	0.667908i
$17$	−5.05929	−	2.92098i	−1.22706	−	0.708442i	−0.260645	−	0.965435i	$-0.583935\pi$
$17$	−5.05929	−	2.92098i	−1.22706	−	0.708442i	−0.966413	+	0.256992i	$0.917268\pi$
$18$	5.29549	−	4.51901i	1.24816	−	1.06514i
$19$	0.908918	+	6.90392i	0.208520	+	1.58387i	0.700753	+	0.713404i	$0.252847\pi$
$19$	0.908918	+	6.90392i	0.208520	+	1.58387i	−0.492233	+	0.870463i	$0.663819\pi$
$20$	−1.36706	+	4.60122i	−0.305684	+	1.02886i
$21$	5.42875	−	5.09772i	1.18465	−	1.11241i
$22$	−2.64547	−	2.38396i	−0.564017	−	0.508263i
$23$	0.497314	−	1.85600i	0.103697	−	0.387003i	−0.894497	−	0.447074i	$-0.852466\pi$
$23$	0.497314	−	1.85600i	0.103697	−	0.387003i	0.998194	+	0.0600710i	$0.0191327\pi$
$24$	7.27690	−	3.22914i	1.48539	−	0.659146i
$25$	0.196710	+	0.734131i	0.0393420	+	0.146826i
$26$	1.46821	+	2.26288i	0.287940	+	0.443788i
$27$	−4.99959	+	2.07090i	−0.962171	+	0.398544i
$28$	4.72928	−	2.37359i	0.893750	−	0.448566i
$29$	3.54360	−	8.55501i	0.658030	−	1.58862i	−0.142813	−	0.989750i	$-0.545615\pi$
$29$	3.54360	−	8.55501i	0.658030	−	1.58862i	0.800843	−	0.598875i	$-0.204385\pi$
$30$	5.41438	−	7.87103i	0.988525	−	1.43705i
$31$	−2.59366	+	4.49234i	−0.465834	+	0.806849i	−0.999239	−	0.0390116i	$-0.987579\pi$
$31$	−2.59366	+	4.49234i	−0.465834	+	0.806849i	0.533404	+	0.845860i	$0.320912\pi$
$32$	5.60996	−	0.726841i	0.991711	−	0.128489i
$33$	3.54388	+	6.13818i	0.616910	+	1.06852i
$34$	3.55373	+	7.45843i	0.609459	+	1.27911i
$35$	3.34619	−	5.39659i	0.565609	−	0.912191i
$36$	−9.79208	+	1.02105i	−1.63201	+	0.170175i
$37$	−2.70513	−	2.07572i	−0.444721	−	0.341247i	0.362001	−	0.932178i	$-0.382094\pi$
$37$	−2.70513	−	2.07572i	−0.444721	−	0.341247i	−0.806722	+	0.590931i	$0.798760\pi$
$38$	4.47444	−	8.77267i	0.725850	−	1.42312i
$39$	−1.38953	−	5.18581i	−0.222504	−	0.830394i
$40$	5.28072	−	4.26547i	0.834955	−	0.674430i
$41$	−4.86955	−	4.86955i	−0.760496	−	0.760496i	0.215916	−	0.976412i	$-0.430726\pi$
$41$	−4.86955	−	4.86955i	−0.760496	−	0.760496i	−0.976412	+	0.215916i	$0.930726\pi$
$42$	−10.4112	+	1.58853i	−1.60648	+	0.245115i
$43$	1.94703	+	4.70055i	0.296920	+	0.716827i	0.999984	+	0.00570089i	$0.00181466\pi$
$43$	1.94703	+	4.70055i	0.296920	+	0.716827i	−0.703064	+	0.711126i	$0.748185\pi$
$44$	1.17166	+	4.89804i	0.176634	+	0.738408i
$45$	−9.37286	+	7.19205i	−1.39722	+	1.07213i
$46$	−2.06703	+	1.76394i	−0.304767	+	0.260079i
$47$	3.40104	−	1.96359i	0.496093	−	0.286419i	−0.231006	−	0.972952i	$-0.574202\pi$
$47$	3.40104	−	1.96359i	0.496093	−	0.286419i	0.727099	+	0.686533i	$0.240868\pi$
$48$	−11.0669	−	2.06996i	−1.59737	−	0.298772i
$49$	−6.86196	+	1.38331i	−0.980280	+	0.197616i
$50$	0.359206	−	1.01304i	0.0507994	−	0.143266i
$51$	−2.14630	−	16.3028i	−0.300542	−	2.28284i
$52$	0.102994	−	3.81339i	0.0142827	−	0.528822i
$53$	4.89856	+	0.644908i	0.672869	+	0.0885849i	0.459216	−	0.888325i	$-0.348130\pi$
$53$	4.89856	+	0.644908i	0.672869	+	0.0885849i	0.213653	+	0.976910i	$0.431464\pi$
$54$	7.48514	+	1.59423i	1.01860	+	0.216947i
$55$	4.27339	+	4.27339i	0.576224	+	0.576224i
$56$	−7.41280	−	1.02490i	−0.990577	−	0.136958i
$57$	−13.8594	+	13.8594i	−1.83573	+	1.83573i
$58$	−10.9857	+	7.12777i	−1.44249	+	0.935922i
$59$	−0.694133	+	5.27246i	−0.0903684	+	0.686416i	0.884962	+	0.465664i	$0.154184\pi$
$59$	−0.694133	+	5.27246i	−0.0903684	+	0.686416i	−0.975330	+	0.220752i	$0.929149\pi$
$60$	−12.6172	+	4.83141i	−1.62888	+	0.623732i
$61$	−7.60241	+	1.00088i	−0.973389	+	0.128149i	−0.600412	−	0.799691i	$-0.704997\pi$
$61$	−7.60241	+	1.00088i	−0.973389	+	0.128149i	−0.372978	+	0.927840i	$0.621663\pi$
$62$	6.62263	−	3.15549i	0.841075	−	0.400748i
$63$	12.8527	+	2.10499i	1.61929	+	0.265204i
$64$	−7.11907	−	3.64949i	−0.889884	−	0.456186i
$65$	−2.28887	−	3.96445i	−0.283900	−	0.491729i
$66$	0.790550	−	9.99238i	0.0973099	−	1.22998i
$67$	−4.18604	−	5.45536i	−0.511407	−	0.666478i	0.464270	−	0.885694i	$-0.346317\pi$
$67$	−4.18604	−	5.45536i	−0.511407	−	0.666478i	−0.975676	+	0.219216i	$0.929650\pi$
$68$	1.83725	−	11.5386i	0.222800	−	1.39926i
$69$	4.99670	−	2.06970i	0.601532	−	0.249163i
$70$	−8.22421	+	3.60594i	−0.982981	+	0.430992i
$71$	7.62970	−	7.62970i	0.905478	−	0.905478i	−0.0904250	−	0.995903i	$-0.528823\pi$
$71$	7.62970	−	7.62970i	0.905478	−	0.905478i	0.995903	+	0.0904250i	$0.0288225\pi$
$72$	12.2277	+	6.65864i	1.44105	+	0.784729i
$73$	10.2082	−	2.73527i	1.19478	−	0.320139i	0.394004	−	0.919109i	$-0.371090\pi$
$73$	10.2082	−	2.73527i	1.19478	−	0.320139i	0.800772	+	0.598970i	$0.204423\pi$
$74$	1.48823	+	4.58671i	0.173003	+	0.533194i
$75$	−1.30230	+	1.69719i	−0.150376	+	0.195974i
$76$	−12.2447	+	6.63532i	−1.40457	+	0.761123i
$77$	0.209410	−	6.65901i	0.0238645	−	0.758865i
$78$	−2.53739	+	7.15602i	−0.287303	+	0.810259i
$79$	7.49333	−	4.32628i	0.843066	−	0.486744i	−0.0152392	−	0.999884i	$-0.504851\pi$
$79$	7.49333	−	4.32628i	0.843066	−	0.486744i	0.858305	+	0.513139i	$0.171518\pi$
$80$	−9.57166	+	0.737475i	−1.07014	+	0.0824522i
$81$	−0.401905	−	0.232040i	−0.0446561	−	0.0257822i
$82$	1.77087	+	9.57674i	0.195560	+	1.05757i
$83$	−9.84868	−	4.07946i	−1.08103	−	0.447779i	−0.230162	−	0.973152i	$-0.573926\pi$
$83$	−9.84868	−	4.07946i	−1.08103	−	0.447779i	−0.850872	+	0.525374i	$0.823926\pi$
$84$	13.4039	+	6.49365i	1.46249	+	0.708516i
$85$	−5.36551	−	12.9535i	−0.581971	−	1.40500i
$86$	1.49888	−	7.03744i	0.161628	−	0.758867i
$87$	25.1757	−	6.74582i	2.69912	−	0.723228i
$88$	2.56060	−	6.64609i	0.272961	−	0.708476i
$89$	−3.81526	−	1.02230i	−0.404417	−	0.108363i	0.0508757	−	0.998705i	$-0.483799\pi$
$89$	−3.81526	−	1.02230i	−0.404417	−	0.108363i	−0.455293	+	0.890342i	$0.650465\pi$
$90$	16.6853	−	0.867564i	1.75879	−	0.0914492i
$91$	−1.45870	+	4.83106i	−0.152913	+	0.506433i
$92$	3.82222	−	0.398556i	0.398494	−	0.0415523i
$93$	−14.4759	+	1.90578i	−1.50108	+	0.197620i
$94$	−5.53658	−	0.438028i	−0.571054	−	0.0451791i
$95$	−8.35621	+	14.4734i	−0.857329	+	1.48494i
$96$	11.2357	+	11.2819i	1.14674	+	1.15146i
$97$	12.6228			1.28165			0.640824	−	0.767687i	$-0.278593\pi$
$97$	12.6228			1.28165			0.640824	+	0.767687i	$0.278593\pi$
$98$	9.10401	+	3.88807i	0.919643	+	0.392754i
$99$	−4.74360	+	11.4521i	−0.476750	+	1.15098i
$100$	−1.23049	+	0.892456i	−0.123049	+	0.0892456i
$101$	−0.337706	+	2.56513i	−0.0336030	+	0.255240i	−0.999998	−	0.00182026i	$-0.999421\pi$
$101$	−0.337706	+	2.56513i	−0.0336030	+	0.255240i	0.966395	+	0.257060i	$0.0827539\pi$
$102$	−10.5658	+	20.7156i	−1.04617	+	2.05115i
$103$	−8.19958	−	2.19707i	−0.807929	−	0.216484i	−0.168866	−	0.985639i	$-0.554011\pi$
$103$	−8.19958	−	2.19707i	−0.807929	−	0.216484i	−0.639062	+	0.769155i	$0.720677\pi$
$104$	−3.17643	+	4.36066i	−0.311475	+	0.427598i
$105$	17.7846	−	1.77475i	1.73559	−	0.173198i
$106$	−5.19072	−	4.67761i	−0.504167	−	0.454330i
$107$	−0.311724	+	0.406246i	−0.0301355	+	0.0392733i	−0.808178	−	0.588938i	$-0.799546\pi$
$107$	−0.311724	+	0.406246i	−0.0301355	+	0.0392733i	0.778043	+	0.628212i	$0.216213\pi$
$108$	−7.44362	−	7.85687i	−0.716263	−	0.756027i
$109$	−5.02982	+	3.85952i	−0.481770	+	0.369675i	−0.820907	−	0.571062i	$-0.806532\pi$
$109$	−5.02982	+	3.85952i	−0.481770	+	0.369675i	0.339137	+	0.940737i	$0.389865\pi$
$110$	−1.55407	−	8.40431i	−0.148175	−	0.801319i
$111$		−	9.59744i		−	0.910949i
$112$	7.81565	+	7.13552i	0.738509	+	0.674243i
$113$			12.0501i			1.13358i	0.823862	+	0.566791i	$0.191815\pi$
$113$			12.0501i			1.13358i	−0.823862	+	0.566791i	$0.808185\pi$
$114$	27.2568	−	5.04016i	2.55283	−	0.472054i
$115$	3.65859	−	2.80733i	0.341165	−	0.261785i
$116$	18.5130	+	0.500008i	1.71889	+	0.0464245i
$117$	5.71584	−	7.44902i	0.528429	−	0.688662i
$118$	5.03465	−	5.58692i	0.463477	−	0.514318i
$119$	−6.36083	+	14.0869i	−0.583096	+	1.29134i
$120$	18.5735	+	4.48333i	1.69552	+	0.409270i
$121$	−4.50034	−	1.20586i	−0.409122	−	0.109624i
$122$	9.66024	+	4.92714i	0.874597	+	0.446082i
$123$	2.53008	−	19.2179i	0.228130	−	1.73282i
$124$	−10.2456	−	1.63137i	−0.920078	−	0.146501i
$125$	3.89417	−	9.40136i	0.348305	−	0.840883i
$126$	−13.2883	−	12.7541i	−1.18382	−	1.13622i
$127$	4.16383			0.369481			0.184740	−	0.982787i	$-0.440856\pi$
$127$	4.16383			0.369481			0.184740	+	0.982787i	$0.440856\pi$
$128$	5.36981	+	9.95817i	0.474629	+	0.880186i
$129$	−7.16039	+	12.4022i	−0.630437	+	1.09195i
$130$	−0.510590	+	6.45375i	−0.0447817	+	0.566031i
$131$	5.87422	−	0.773355i	0.513233	−	0.0675684i	0.130538	−	0.991443i	$-0.458329\pi$
$131$	5.87422	−	0.773355i	0.513233	−	0.0675684i	0.382695	+	0.923875i	$0.374996\pi$
$132$	−8.92999	+	11.0091i	−0.777256	+	0.958220i
$133$	17.9370	−	4.20668i	1.55533	−	0.364765i
$134$	0.504955	+	9.71148i	0.0436215	+	0.838944i
$135$	−12.5451	−	3.36145i	−1.07971	−	0.289308i
$136$	−11.3888	+	11.9717i	−0.976586	+	1.02657i
$137$	0.764393	−	0.204819i	0.0653065	−	0.0174988i	−0.226018	−	0.974123i	$-0.572571\pi$
$137$	0.764393	−	0.204819i	0.0653065	−	0.0174988i	0.291324	+	0.956624i	$0.405904\pi$
$138$	−7.48082	−	1.59331i	−0.636810	−	0.135632i
$139$	4.52992	+	10.9362i	0.384223	+	0.927597i	0.991139	+	0.132830i	$0.0424065\pi$
$139$	4.52992	+	10.9362i	0.384223	+	0.927597i	−0.606916	+	0.794766i	$0.707593\pi$
$140$	12.4727	+	2.39019i	1.05413	+	0.202008i
$141$	10.2125	+	4.23014i	0.860044	+	0.356242i
$142$	−15.0050	+	2.77464i	−1.25919	+	0.232842i
$143$	−4.15954	−	2.40151i	−0.347838	−	0.200825i
$144$	−8.91037	−	17.5589i	−0.742531	−	1.46324i
$145$	19.2463	−	11.1119i	1.59832	−	0.922791i
$146$	−14.0865	−	4.99480i	−1.16580	−	0.413372i
$147$	−14.8469	−	12.9529i	−1.22455	−	1.06833i
$148$	1.94221	−	6.53707i	0.159649	−	0.537344i
$149$	−8.48224	+	11.0543i	−0.694892	+	0.905601i	−0.998892	−	0.0470715i	$-0.985011\pi$
$149$	−8.48224	+	11.0543i	−0.694892	+	0.905601i	0.304000	+	0.952672i	$0.401678\pi$
$150$	2.87768	−	0.933707i	0.234962	−	0.0762369i
$151$	−17.1811	+	4.60367i	−1.39818	+	0.374642i	−0.877692	−	0.479226i	$-0.840918\pi$
$151$	−17.1811	+	4.60367i	−1.39818	+	0.374642i	−0.520490	+	0.853868i	$0.674251\pi$
$152$	19.5853	+	2.08291i	1.58858	+	0.168947i
$153$	20.3347	−	20.3347i	1.64396	−	1.64396i
$154$	−5.58118	+	7.59098i	−0.449745	+	0.611699i
$155$	−11.5019	+	4.76425i	−0.923856	+	0.382674i
$156$	8.69200	−	6.30420i	0.695917	−	0.504740i
$157$	−2.38799	−	3.11209i	−0.190583	−	0.248372i	0.688282	−	0.725443i	$-0.258365\pi$
$157$	−2.38799	−	3.11209i	−0.190583	−	0.248372i	−0.878865	+	0.477071i	$0.841698\pi$
$158$	−12.1984	−	0.965083i	−0.970456	−	0.0767779i
$159$	6.95350	+	12.0438i	0.551448	+	0.955137i
$160$	11.7436	+	6.81239i	0.928414	+	0.538567i
$161$	−5.01690	−	0.821659i	−0.395387	−	0.0647558i
$162$	0.282304	+	0.592490i	0.0221799	+	0.0465504i
$163$	−7.11973	+	0.937331i	−0.557661	+	0.0734174i	−0.404088	−	0.914720i	$-0.632411\pi$
$163$	−7.11973	+	0.937331i	−0.557661	+	0.0734174i	−0.153572	+	0.988137i	$0.549078\pi$
$164$	5.61239	−	12.5778i	0.438254	−	0.982161i
$165$	−2.22034	+	16.8651i	−0.172853	+	1.31295i
$166$	8.20562	+	12.6469i	0.636880	+	0.981592i
$167$	−7.05741	+	7.05741i	−0.546119	+	0.546119i	−0.925316	−	0.379197i	$-0.876200\pi$
$167$	−7.05741	+	7.05741i	−0.546119	+	0.546119i	0.379197	+	0.925316i	$0.376200\pi$
$168$	−10.4131	−	18.3094i	−0.803385	−	1.41260i
$169$	−6.61984	−	6.61984i	−0.509218	−	0.509218i
$170$	−4.13051	+	19.3933i	−0.316796	+	1.48740i
$171$	−33.9851	−	4.47423i	−2.59891	−	0.342153i
$172$	−7.38693	+	6.99841i	−0.563248	+	0.533623i
$173$	−0.856088	−	6.50263i	−0.0650871	−	0.494386i	−0.992678	−	0.120789i	$-0.961458\pi$
$173$	−0.856088	−	6.50263i	−0.0650871	−	0.494386i	0.927591	−	0.373597i	$-0.121876\pi$
$174$	−34.7406	−	12.3183i	−2.63367	−	0.933851i
$175$	1.88105	−	0.710743i	0.142194	−	0.0537271i
$176$	−8.31034	+	5.69145i	−0.626416	+	0.429009i
$177$	−12.9631	+	7.48425i	−0.974367	+	0.562551i
$178$	3.62603	+	4.24907i	0.271782	+	0.318481i
$179$	15.7076	−	12.0529i	1.17404	−	0.900874i	0.177512	−	0.984119i	$-0.443195\pi$
$179$	15.7076	−	12.0529i	1.17404	−	0.900874i	0.996529	+	0.0832449i	$0.0265284\pi$
$180$	−20.1364	−	12.3624i	−1.50088	−	0.921438i
$181$	5.19916	+	12.5519i	0.386450	+	0.932973i	0.990686	+	0.136168i	$0.0434786\pi$
$181$	5.19916	+	12.5519i	0.386450	+	0.932973i	−0.604236	+	0.796806i	$0.706521\pi$
$182$	5.57170	−	4.45982i	0.413002	−	0.330584i
$183$	−15.2616	−	15.2616i	−1.12817	−	1.12817i
$184$	−4.77295	−	2.59912i	−0.351866	−	0.191610i
$185$	−2.11802	−	7.90457i	−0.155720	−	0.581155i
$186$	18.3942	+	9.38183i	1.34873	+	0.687909i
$187$	−11.6708	−	8.95533i	−0.853454	−	0.654879i
$188$	6.09993	+	4.94793i	0.444883	+	0.360865i
$189$	6.76549	+	12.6182i	0.492117	+	0.917841i
$190$	21.3367	−	10.1663i	1.54793	−	0.737543i
$191$	3.35172	+	5.80536i	0.242522	+	0.420061i	0.961432	−	0.275042i	$-0.0886919\pi$
$191$	3.35172	+	5.80536i	0.242522	+	0.420061i	−0.718910	+	0.695103i	$0.755359\pi$
$192$	−4.04891	−	22.1507i	−0.292205	−	1.59859i
$193$	−6.41438	+	11.1100i	−0.461717	+	0.799718i	−0.999047	−	0.0436545i	$-0.986100\pi$
$193$	−6.41438	+	11.1100i	−0.461717	+	0.799718i	0.537329	+	0.843373i	$0.319433\pi$
$194$	−14.7076	−	10.1171i	−1.05594	−	0.726368i
$195$	4.93089	−	11.9042i	0.353108	−	0.852478i
$196$	−7.49135	−	11.8271i	−0.535097	−	0.844791i
$197$	−7.51399	+	3.11240i	−0.535349	+	0.221749i	−0.633944	−	0.773379i	$-0.718565\pi$
$197$	−7.51399	+	3.11240i	−0.535349	+	0.221749i	0.0985949	+	0.995128i	$0.468565\pi$
$198$	14.7059	−	9.54152i	1.04510	−	0.678086i
$199$	6.12203	+	22.8477i	0.433980	+	1.61963i	0.743497	+	0.668740i	$0.233166\pi$
$199$	6.12203	+	22.8477i	0.433980	+	1.61963i	−0.309517	+	0.950894i	$0.600167\pi$
$200$	2.14902	−	0.0536226i	0.151958	−	0.00379169i
$201$	5.00941	−	18.6954i	0.353336	−	1.31867i
$202$	2.44943	−	2.71812i	0.172341	−	0.191246i
$203$	−23.4535	−	7.08158i	−1.64611	−	0.497030i
$204$	28.9144	−	15.6685i	2.02441	−	1.09701i
$205$	−2.15732	−	16.3864i	−0.150673	−	1.14448i
$206$	7.79288	+	9.13189i	0.542956	+	0.636249i
$207$	8.19140	+	4.72931i	0.569342	+	0.328710i
$208$	7.19612	−	2.53497i	0.498961	−	0.175769i
$209$			17.5349i			1.21291i
$210$	−22.1443	−	12.1864i	−1.52810	−	0.840943i
$211$	11.1803	+	4.63103i	0.769683	+	0.318813i	0.732744	−	0.680505i	$-0.238239\pi$
$211$	11.1803	+	4.63103i	0.769683	+	0.318813i	0.0369388	+	0.999318i	$0.488239\pi$
$212$	2.29893	+	9.61053i	0.157891	+	0.660054i
$213$	30.1109	+	3.96418i	2.06317	+	0.271621i
$214$	0.688814	−	0.223496i	0.0470864	−	0.0152779i
$215$	−3.16040	+	11.7948i	−0.215537	+	0.804397i
$216$	2.37576	+	15.1206i	0.161650	+	1.02882i
$217$	12.5083	+	5.64803i	0.849118	+	0.383413i
$218$	8.95395	−	0.465567i	0.606438	−	0.0315322i
$219$	23.5996	+	18.1086i	1.59471	+	1.22366i
$220$	−4.92529	+	11.0380i	−0.332063	+	0.744179i
$221$	6.78337	+	8.84026i	0.456299	+	0.594660i
$222$	−7.69233	+	11.1826i	−0.516276	+	0.750525i
$223$	−16.0197			−1.07276			−0.536380	−	0.843977i	$-0.680209\pi$
$223$	−16.0197			−1.07276			−0.536380	+	0.843977i	$0.680209\pi$
$224$	−3.38738	−	14.5783i	−0.226329	−	0.974051i
$225$	−3.74130			−0.249420
$226$	9.65817	−	14.0404i	0.642452	−	0.933951i
$227$	14.1416	+	18.4296i	0.938608	+	1.22322i	0.974620	+	0.223867i	$0.0718681\pi$
$227$	14.1416	+	18.4296i	0.938608	+	1.22322i	−0.0360112	+	0.999351i	$0.511465\pi$
$228$	−35.7982	−	15.9737i	−2.37080	−	1.05788i
$229$	−15.0628	−	11.5581i	−0.995375	−	0.763778i	−0.0236079	−	0.999721i	$-0.507515\pi$
$229$	−15.0628	−	11.5581i	−0.995375	−	0.763778i	−0.971767	+	0.235943i	$0.924182\pi$
$230$	−6.51292	+	0.338643i	−0.429449	+	0.0223295i
$231$	15.2288	−	10.9425i	1.00198	−	0.719964i
$232$	−21.1699	−	15.4207i	−1.38987	−	1.01242i
$233$	−1.35571	+	5.05959i	−0.0888157	+	0.331465i	−0.996009	−	0.0892485i	$-0.971553\pi$
$233$	−1.35571	+	5.05959i	−0.0888157	+	0.331465i	0.907194	+	0.420713i	$0.138220\pi$
$234$	−12.6302	+	4.09808i	−0.825665	+	0.267900i
$235$	9.34463	+	1.23024i	0.609576	+	0.0802523i
$236$	−10.3441	+	2.47440i	−0.673342	+	0.161070i
$237$	22.5006	+	9.32004i	1.46157	+	0.605401i
$238$	18.7020	−	11.3153i	1.21227	−	0.733461i
$239$		−	1.07070i		−	0.0692579i	−0.999400	−	0.0346290i	$-0.988975\pi$
$239$		−	1.07070i		−	0.0692579i	0.999400	−	0.0346290i	$-0.0110249\pi$
$240$	−18.0477	−	20.1104i	−1.16498	−	1.29812i
$241$	20.0585	+	11.5808i	1.29208	+	0.745983i	0.979023	−	0.203752i	$-0.0653135\pi$
$241$	20.0585	+	11.5808i	1.29208	+	0.745983i	0.313057	+	0.949734i	$0.398647\pi$
$242$	4.27713	+	5.01204i	0.274944	+	0.322186i
$243$	1.94853	+	14.8006i	0.124998	+	0.949457i
$244$	−7.30664	−	13.4836i	−0.467760	−	0.863197i
$245$	−15.0866	−	7.39164i	−0.963847	−	0.472234i
$246$	−18.3511	+	20.3641i	−1.17002	+	1.29837i
$247$	3.43766	−	12.8295i	0.218733	−	0.816323i
$248$	10.6302	+	10.1126i	0.675017	+	0.642151i
$249$	−7.76591	−	28.9828i	−0.492145	−	1.83671i
$250$	−12.0725	+	7.83293i	−0.763532	+	0.495398i
$251$	17.9949	−	7.45374i	1.13583	−	0.470476i	0.266071	−	0.963954i	$-0.414275\pi$
$251$	17.9949	−	7.45374i	1.13583	−	0.470476i	0.869758	+	0.493478i	$0.164275\pi$
$252$	5.26067	+	25.5111i	0.331391	+	1.60705i
$253$	1.85161	−	4.47018i	0.116410	−	0.281038i
$254$	−4.85154	−	3.33731i	−0.304413	−	0.209401i
$255$	19.7322	−	34.1771i	1.23568	−	2.14025i
$256$	1.72476	−	15.9068i	0.107798	−	0.994173i
$257$	2.67709	+	4.63685i	0.166992	+	0.289239i	0.937361	−	0.348360i	$-0.113261\pi$
$257$	2.67709	+	4.63685i	0.166992	+	0.289239i	−0.770369	+	0.637599i	$0.779928\pi$
$258$	18.2833	−	8.71148i	1.13827	−	0.542353i
$259$	−4.75401	+	7.66707i	−0.295400	+	0.476409i
$260$	5.76759	−	7.11042i	0.357691	−	0.440969i
$261$	36.1630	+	27.7489i	2.23843	+	1.71761i
$262$	−7.46425	−	3.80709i	−0.461143	−	0.235203i
$263$	−4.04719	−	15.1043i	−0.249561	−	0.931373i	−0.971036	−	0.238933i	$-0.923202\pi$
$263$	−4.04719	−	15.1043i	−0.249561	−	0.931373i	0.721475	−	0.692440i	$-0.243464\pi$
$264$	19.2287	−	5.67001i	1.18344	−	0.348965i
$265$	8.38489	+	8.38489i	0.515080	+	0.515080i
$266$	−24.2711	−	9.47500i	−1.48816	−	0.580950i
$267$	−4.25455	−	10.2714i	−0.260374	−	0.628599i
$268$	7.19538	−	11.7202i	0.439528	−	0.715922i
$269$	−12.9654	+	9.94868i	−0.790513	+	0.606582i	−0.923087	−	0.384591i	$-0.874342\pi$
$269$	−12.9654	+	9.94868i	−0.790513	+	0.606582i	0.132574	+	0.991173i	$0.457676\pi$
$270$	11.9229	+	13.9715i	0.725604	+	0.850280i
$271$	−6.21779	+	3.58984i	−0.377704	+	0.218068i	−0.676819	−	0.736150i	$-0.736642\pi$
$271$	−6.21779	+	3.58984i	−0.377704	+	0.218068i	0.299115	+	0.954217i	$0.403309\pi$
$272$	22.8652	−	4.82087i	1.38640	−	0.292308i
$273$	−13.2875	+	5.02060i	−0.804196	+	0.303861i
$274$	−1.05480	−	0.374013i	−0.0637230	−	0.0225950i
$275$	0.249806	+	1.89747i	0.0150639	+	0.114421i
$276$	7.43933	+	7.85233i	0.447795	+	0.472655i
$277$	−1.51574	−	0.199551i	−0.0910718	−	0.0119898i	0.0848525	−	0.996394i	$-0.472958\pi$
$277$	−1.51574	−	0.199551i	−0.0910718	−	0.0119898i	−0.175924	+	0.984404i	$0.556291\pi$
$278$	3.48726	−	16.3732i	0.209152	−	0.981997i
$279$	−18.0560	−	18.0560i	−1.08098	−	1.08098i
$280$	−12.6169	−	12.7818i	−0.754007	−	0.763858i
$281$	−20.6059	+	20.6059i	−1.22925	+	1.22925i	−0.264997	+	0.964249i	$0.585371\pi$
$281$	−20.6059	+	20.6059i	−1.22925	+	1.22925i	−0.964249	+	0.264997i	$0.914629\pi$
$282$	−8.50870	−	13.1141i	−0.506686	−	0.780930i
$283$	−0.145302	+	1.10368i	−0.00863728	+	0.0656067i	−0.995221	−	0.0976514i	$-0.968867\pi$
$283$	−0.145302	+	1.10368i	−0.00863728	+	0.0656067i	0.986583	+	0.163258i	$0.0522003\pi$
$284$	19.7071	+	8.79359i	1.16940	+	0.521804i
$285$	−46.6382	+	6.14003i	−2.76261	+	0.363704i
$286$	2.92173	+	6.13202i	0.172765	+	0.362594i
$287$	−11.5406	+	14.0993i	−0.681221	+	0.832253i
$288$	−3.69140	+	27.6006i	−0.217518	+	1.62638i
$289$	8.56428	+	14.8338i	0.503781	+	0.872575i
$290$	−31.3312	−	2.47878i	−1.83983	−	0.145559i
$291$	21.6290	+	28.1874i	1.26791	+	1.65237i
$292$	12.4097	+	17.1100i	0.726222	+	1.00129i
$293$	−19.5257	+	8.08783i	−1.14071	+	0.472496i	−0.871407	−	0.490561i	$-0.836792\pi$
$293$	−19.5257	+	8.08783i	−1.14071	+	0.472496i	−0.269299	+	0.963057i	$0.586792\pi$
$294$	6.91730	+	26.9919i	0.403425	+	1.57420i
$295$	−9.02490	+	9.02490i	−0.525450	+	0.525450i
$296$	−7.50244	+	6.06006i	−0.436071	+	0.352234i
$297$	−13.1625	+	3.52688i	−0.763765	+	0.204650i
$298$	18.7431	−	6.08150i	1.08576	−	0.352292i
$299$	−2.23111	+	2.90764i	−0.129028	+	0.168153i
$300$	−4.10133	−	1.21854i	−0.236790	−	0.0703522i
$301$	11.8635	−	6.36083i	0.683801	−	0.366632i
$302$	23.7086	+	8.40664i	1.36428	+	0.483748i
$303$	−6.30674	+	3.64120i	−0.362313	+	0.209181i
$304$	−21.1506	−	18.1245i	−1.21307	−	1.03951i
$305$	−15.9377	−	9.20164i	−0.912591	−	0.526884i
$306$	−39.9914	+	7.39496i	−2.28615	+	0.422742i
$307$	14.5688	+	6.03459i	0.831485	+	0.344412i	0.757491	−	0.652846i	$-0.226425\pi$
$307$	14.5688	+	6.03459i	0.831485	+	0.344412i	0.0739948	+	0.997259i	$0.476425\pi$
$308$	12.5871	−	4.37141i	0.717219	−	0.249084i
$309$	−9.14368	−	22.0748i	−0.520166	−	1.25579i
$310$	17.2201	+	3.66765i	0.978037	+	0.208308i
$311$	−4.54949	+	1.21903i	−0.257978	+	0.0691250i	−0.385490	−	0.922712i	$-0.625968\pi$
$311$	−4.54949	+	1.21903i	−0.257978	+	0.0691250i	0.127512	+	0.991837i	$0.459301\pi$
$312$	−15.1804	+	0.378784i	−0.859420	+	0.0214444i
$313$	−2.49854	−	0.669481i	−0.141226	−	0.0378413i	0.187514	−	0.982262i	$-0.439957\pi$
$313$	−2.49854	−	0.669481i	−0.141226	−	0.0378413i	−0.328739	+	0.944421i	$0.606624\pi$
$314$	0.288059	+	5.54006i	0.0162561	+	0.312644i
$315$	21.3968	+	22.7862i	1.20557	+	1.28386i
$316$	13.4396	+	10.9015i	0.756039	+	0.613258i
$317$	0.0966973	−	0.0127304i	0.00543106	−	0.000715013i	−0.127810	−	0.991799i	$-0.540795\pi$
$317$	0.0966973	−	0.0127304i	0.00543106	−	0.000715013i	0.133241	+	0.991084i	$0.457461\pi$
$318$	1.55115	−	19.6062i	0.0869842	−	1.09946i
$319$	11.6587	−	20.1935i	0.652762	−	1.13062i
$320$	−8.22308	−	17.3500i	−0.459684	−	0.969895i
$321$	−1.44131			−0.0804459
$322$	5.18694	+	4.97840i	0.289057	+	0.277436i
$323$	15.5677	−	37.5839i	0.866213	−	2.09122i
$324$	0.145950	−	0.916613i	0.00810831	−	0.0509229i
$325$	0.189220	−	1.43727i	0.0104960	−	0.0797253i
$326$	9.04691	+	4.61431i	0.501062	+	0.255563i
$327$	−17.2371	−	4.61866i	−0.953212	−	0.255412i
$328$	−16.6204	+	10.1568i	−0.917710	+	0.560818i
$329$	−6.06302	−	8.43796i	−0.334265	−	0.465200i
$330$	16.1044	−	17.8710i	0.886520	−	0.983766i
$331$	−11.6822	+	15.2246i	−0.642113	+	0.836818i	−0.995107	−	0.0988075i	$-0.968497\pi$
$331$	−11.6822	+	15.2246i	−0.642113	+	0.836818i	0.352993	+	0.935626i	$0.385164\pi$
$332$	0.575618	−	21.3125i	0.0315911	−	1.16968i
$333$	13.3162	−	10.2179i	0.729726	−	0.559938i
$334$	13.8795	−	2.56652i	0.759454	−	0.140434i
$335$		−	16.5032i		−	0.901668i
$336$	−2.54203	+	29.6794i	−0.138679	+	1.61914i
$337$		−	23.0585i		−	1.25608i	−0.778183	−	0.628038i	$-0.783858\pi$
$337$		−	23.0585i		−	1.25608i	0.778183	−	0.628038i	$-0.216142\pi$
$338$	2.40739	+	13.0190i	0.130945	+	0.708138i
$339$	−26.9087	+	20.6477i	−1.46148	+	1.12143i
$340$	20.3564	−	19.2858i	1.10398	−	1.04592i
$341$	−7.95179	+	10.3630i	−0.430614	+	0.561187i
$342$	36.0120	+	32.4522i	1.94731	+	1.75481i
$343$	5.44457	+	17.7019i	0.293979	+	0.955812i
$344$	14.2162	−	2.23366i	0.766485	−	0.120431i
$345$	12.5379	+	3.35951i	0.675016	+	0.180870i
$346$	−4.21437	+	8.26277i	−0.226566	+	0.444209i
$347$	3.79981	−	28.8624i	0.203984	−	1.54941i	−0.516709	−	0.856161i	$-0.672843\pi$
$347$	3.79981	−	28.8624i	0.203984	−	1.54941i	0.720694	−	0.693254i	$-0.243823\pi$
$348$	30.6052	+	42.1973i	1.64061	+	2.26202i
$349$	2.50585	−	6.04966i	0.134135	−	0.323831i	−0.842513	−	0.538676i	$-0.818925\pi$
$349$	2.50585	−	6.04966i	0.134135	−	0.323831i	0.976648	+	0.214845i	$0.0689247\pi$
$350$	−2.76138	−	0.679527i	−0.147602	−	0.0363222i
$351$	10.3219			0.550940
$352$	14.2446	+	0.0292714i	0.759239	+	0.00156017i
$353$	6.63400	−	11.4904i	0.353092	−	0.611574i	−0.633697	−	0.773581i	$-0.718464\pi$
$353$	6.63400	−	11.4904i	0.353092	−	0.611574i	0.986790	+	0.162008i	$0.0517969\pi$
$354$	21.1027	+	1.66955i	1.12160	+	0.0887354i
$355$	25.6746	−	3.38012i	1.36266	−	0.179398i
$356$	−0.819286	−	7.85710i	−0.0434221	−	0.416426i
$357$	−42.3560	+	9.93356i	−2.24172	+	0.525740i
$358$	−27.9622	+	1.45392i	−1.47785	+	0.0768418i
$359$	−26.2813	−	7.04206i	−1.38708	−	0.371666i	−0.513389	−	0.858156i	$-0.671610\pi$
$359$	−26.2813	−	7.04206i	−1.38708	−	0.371666i	−0.873686	+	0.486490i	$0.838277\pi$
$360$	13.5537	+	30.5435i	0.714345	+	1.60978i
$361$	−28.4854	+	7.63263i	−1.49923	+	0.401717i
$362$	4.00245	−	18.7921i	0.210364	−	0.987689i
$363$	−5.01851	−	12.1158i	−0.263404	−	0.635912i
$364$	−10.0665	+	0.730702i	−0.527627	+	0.0382992i
$365$	23.4332	+	9.70635i	1.22655	+	0.508053i
$366$	5.55009	+	30.0145i	0.290108	+	1.56888i
$367$	−15.6885	−	9.05776i	−0.818933	−	0.472811i	0.0311155	−	0.999516i	$-0.490094\pi$
$367$	−15.6885	−	9.05776i	−0.818933	−	0.472811i	−0.850048	+	0.526705i	$0.823427\pi$
$368$	3.47806	+	6.85391i	0.181306	+	0.357285i
$369$	29.3581	−	16.9499i	1.52832	−	0.882376i
$370$	−3.86766	+	10.9077i	−0.201070	+	0.567064i
$371$	0.410886	−	13.0658i	0.0213321	−	0.678340i
$372$	−13.9127	−	25.6743i	−0.721338	−	1.33115i
$373$	12.7858	−	16.6627i	0.662022	−	0.862764i	−0.334811	−	0.942285i	$-0.608673\pi$
$373$	12.7858	−	16.6627i	0.662022	−	0.862764i	0.996833	+	0.0795215i	$0.0253392\pi$
$374$	6.42070	+	19.7885i	0.332006	+	1.02324i
$375$	27.6664	−	7.41319i	1.42869	−	0.382815i
$376$	−3.14164	−	10.6542i	−0.162018	−	0.549449i
$377$	−12.4891	+	12.4891i	−0.643219	+	0.643219i
$378$	2.23060	−	20.1248i	0.114730	−	1.03511i
$379$	−26.0016	+	10.7702i	−1.33561	+	0.553229i	−0.932251	−	0.361812i	$-0.882158\pi$
$379$	−26.0016	+	10.7702i	−1.33561	+	0.553229i	−0.403361	+	0.915041i	$0.632158\pi$
$380$	−33.0090	−	5.25593i	−1.69333	−	0.269624i
$381$	7.13467	+	9.29809i	0.365520	+	0.476355i
$382$	0.747685	−	9.45058i	0.0382549	−	0.483534i
$383$	2.85738	+	4.94912i	0.146005	+	0.252888i	0.929748	−	0.368198i	$-0.120025\pi$
$383$	2.85738	+	4.94912i	0.146005	+	0.252888i	−0.783742	+	0.621086i	$0.786692\pi$
$384$	−13.0361	+	29.0543i	−0.665245	+	1.48267i
$385$	10.1278	−	12.3732i	0.516158	−	0.630595i
$386$	16.3785	−	7.80387i	0.833642	−	0.397206i
$387$	−24.8311	+	3.26907i	−1.26223	+	0.166176i
$388$	9.02782	+	23.5762i	0.458318	+	1.19690i
$389$	2.28731	−	17.3738i	0.115971	−	0.880889i	−0.830255	−	0.557384i	$-0.811805\pi$
$389$	2.28731	−	17.3738i	0.115971	−	0.880889i	0.946226	−	0.323505i	$-0.104861\pi$
$390$	−15.2865	+	9.91823i	−0.774061	+	0.502229i
$391$	−7.93740	+	7.93740i	−0.401412	+	0.401412i
$392$	−0.750745	+	19.7848i	−0.0379183	+	0.999281i
$393$	11.7923	+	11.7923i	0.594845	+	0.594845i
$394$	11.2496	+	2.39601i	0.566746	+	0.120709i
$395$	20.5885	+	2.71053i	1.03592	+	0.136382i
$396$	−24.7822	−	0.669330i	−1.24535	−	0.0336351i
$397$	0.336576	+	2.55655i	0.0168923	+	0.128309i	0.997813	−	0.0660979i	$-0.0210550\pi$
$397$	0.336576	+	2.55655i	0.0168923	+	0.128309i	−0.980921	+	0.194407i	$0.937722\pi$
$398$	11.1793	−	31.5281i	0.560366	−	1.58036i
$399$	40.1285	+	32.8462i	2.00894	+	1.64437i
$400$	−2.54693	−	1.65995i	−0.127346	−	0.0829977i
$401$	18.2466	−	10.5347i	0.911190	−	0.526076i	0.0303763	−	0.999539i	$-0.490329\pi$
$401$	18.2466	−	10.5347i	0.911190	−	0.526076i	0.880814	+	0.473463i	$0.156996\pi$
$402$	−20.8211	+	17.7681i	−1.03846	+	0.886191i
$403$	7.84962	−	6.02322i	0.391017	−	0.300038i
$404$	−5.03255	+	1.20383i	−0.250379	+	0.0598930i
$405$	−0.426231	−	1.02901i	−0.0211796	−	0.0511320i
$406$	21.6513	+	27.0491i	1.07453	+	1.34243i
$407$	−6.07131	−	6.07131i	−0.300944	−	0.300944i
$408$	−46.2482	−	4.91854i	−2.28963	−	0.243504i
$409$	−3.41503	−	12.7451i	−0.168862	−	0.630203i	−0.997516	−	0.0704414i	$-0.977559\pi$
$409$	−3.41503	−	12.7451i	−0.168862	−	0.630203i	0.828653	−	0.559762i	$-0.189107\pi$
$410$	−10.6201	+	20.8219i	−0.524489	+	1.02832i
$411$	1.76715	+	1.35598i	0.0871670	+	0.0668856i
$412$	−1.76077	−	16.8861i	−0.0867469	−	0.831919i
$413$	14.0630	+	0.442249i	0.691997	+	0.0217616i
$414$	−5.75377	−	12.0758i	−0.282782	−	0.593493i
$415$	−12.7922	−	22.1567i	−0.627944	−	1.08763i
$416$	−10.4164	−	2.81402i	−0.510707	−	0.137969i
$417$	−16.6592	+	28.8546i	−0.815805	+	1.41302i
$418$	14.0542	−	20.4309i	0.687412	−	0.999310i
$419$	−7.42662	+	17.9294i	−0.362814	+	0.875911i	0.632072	+	0.774910i	$0.282205\pi$
$419$	−7.42662	+	17.9294i	−0.362814	+	0.875911i	−0.994886	+	0.101001i	$0.967795\pi$
$420$	16.0343	+	31.9478i	0.782395	+	1.55889i
$421$	37.0445	−	15.3443i	1.80544	−	0.747836i	0.821282	−	0.570523i	$-0.193259\pi$
$421$	37.0445	−	15.3443i	1.80544	−	0.747836i	0.984154	−	0.177314i	$-0.0567407\pi$
$422$	−9.31508	−	14.3569i	−0.453451	−	0.698882i
$423$	5.00346	+	18.6732i	0.243277	+	0.907921i
$424$	5.02420	−	13.0404i	0.243997	−	0.633298i
$425$	1.14917	−	4.28877i	0.0557430	−	0.208036i
$426$	−31.9068	−	28.7528i	−1.54589	−	1.39308i
$427$	4.63228	+	19.7517i	0.224172	+	0.955854i
$428$	−0.981711	−	0.291674i	−0.0474528	−	0.0140986i
$429$	−1.76460	−	13.4035i	−0.0851957	−	0.647125i
$430$	13.1359	−	11.2098i	0.633468	−	0.540582i
$431$	−12.3186	−	7.11214i	−0.593366	−	0.342580i	0.173062	−	0.984911i	$-0.444634\pi$
$431$	−12.3186	−	7.11214i	−0.593366	−	0.342580i	−0.766427	+	0.642331i	$0.777967\pi$
$432$	9.35097	−	19.5221i	0.449899	−	0.939256i
$433$			4.61159i			0.221619i	0.993842	+	0.110809i	$0.0353443\pi$
$433$			4.61159i			0.221619i	−0.993842	+	0.110809i	$0.964656\pi$
$434$	−10.0473	−	16.6062i	−0.482285	−	0.797125i
$435$	57.7918	+	23.9381i	2.77090	+	1.14775i
$436$	−10.8060	−	6.63412i	−0.517511	−	0.317717i
$437$	13.2657	+	1.74646i	0.634584	+	0.0835446i
$438$	−12.9833	−	40.0144i	−0.620366	−	1.91196i
$439$	4.50964	−	16.8302i	0.215233	−	0.803262i	−0.770851	−	0.637016i	$-0.780169\pi$
$439$	4.50964	−	16.8302i	0.215233	−	0.803262i	0.986084	−	0.166246i	$-0.0531647\pi$
$440$	14.5857	−	8.91339i	0.695344	−	0.424929i
$441$	2.16511	−	34.3900i	0.103100	−	1.63762i
$442$	−0.818266	−	15.7372i	−0.0389209	−	0.748542i
$443$	−0.128970	−	0.0989625i	−0.00612757	−	0.00470185i	0.605693	−	0.795698i	$-0.292896\pi$
$443$	−0.128970	−	0.0989625i	−0.00612757	−	0.00470185i	−0.611821	+	0.790997i	$0.709563\pi$
$444$	17.9256	−	6.86410i	0.850712	−	0.325756i
$445$	−5.77086	−	7.52073i	−0.273565	−	0.356517i
$446$	18.6656	+	12.8398i	0.883840	+	0.607981i
$447$	−39.2190			−1.85500
$448$	−7.73760	+	19.7010i	−0.365567	+	0.930785i
$449$	11.6567			0.550116			0.275058	−	0.961428i	$-0.411303\pi$
$449$	11.6567			0.550116			0.275058	+	0.961428i	$0.411303\pi$
$450$	4.35922	+	2.99865i	0.205496	+	0.141358i
$451$	−10.5567	−	13.7577i	−0.497093	−	0.647825i
$452$	−22.5066	+	8.61827i	−1.05862	+	0.405369i
$453$	−39.7199	−	30.4782i	−1.86621	−	1.43199i
$454$	−1.70587	−	32.8079i	−0.0800605	−	1.53975i
$455$	−9.83577	+	7.06740i	−0.461108	+	0.331325i
$456$	28.9078	+	47.3041i	1.35373	+	2.21522i
$457$	7.02008	−	26.1993i	0.328386	−	1.22555i	−0.582479	−	0.812846i	$-0.697917\pi$
$457$	7.02008	−	26.1993i	0.328386	−	1.22555i	0.910864	−	0.412706i	$-0.135416\pi$
$458$	8.28677	+	25.5398i	0.387215	+	1.19340i
$459$	31.3434	+	4.12644i	1.46299	+	0.192606i
$460$	7.86002	+	4.82552i	0.366475	+	0.224991i
$461$	7.81215	+	3.23590i	0.363848	+	0.150711i	0.557115	−	0.830435i	$-0.311908\pi$
$461$	7.81215	+	3.23590i	0.363848	+	0.150711i	−0.193267	+	0.981146i	$0.561908\pi$
$462$	−26.5144	+	0.543931i	−1.23356	+	0.0253060i
$463$			28.9645i			1.34609i	0.739600	+	0.673046i	$0.235015\pi$
$463$			28.9645i			1.34609i	−0.739600	+	0.673046i	$0.764985\pi$
$464$	12.3066	+	34.9352i	0.571321	+	1.62183i
$465$	−30.3472	−	17.5210i	−1.40732	−	0.812515i
$466$	5.63488	−	4.80863i	0.261031	−	0.222756i
$467$	−3.39774	−	25.8084i	−0.157229	−	1.19427i	−0.870064	−	0.492939i	$-0.835923\pi$
$467$	−3.39774	−	25.8084i	−0.157229	−	1.19427i	0.712835	−	0.701331i	$-0.247411\pi$
$468$	18.0009	+	5.34820i	0.832091	+	0.247221i
$469$	−13.2624	+	12.4537i	−0.612402	+	0.575059i
$470$	−9.90196	−	8.92314i	−0.456743	−	0.411594i
$471$	2.85769	−	10.6651i	0.131676	−	0.491420i
$472$	14.0358	+	5.40769i	0.646048	+	0.248909i
$473$	3.31593	+	12.3752i	0.152467	+	0.569013i
$474$	−18.7468	−	28.8935i	−0.861068	−	1.32712i
$475$	−4.88959	+	2.02533i	−0.224350	+	0.0929287i
$476$	−30.8600	−	1.80549i	−1.41447	−	0.0827544i
$477$	−9.30750	+	22.4703i	−0.426161	+	1.02884i
$478$	−0.858166	+	1.24754i	−0.0392516	+	0.0570612i
$479$	−6.63509	+	11.4923i	−0.303165	+	0.525097i	−0.976851	−	0.213920i	$-0.931377\pi$
$479$	−6.63509	+	11.4923i	−0.303165	+	0.525097i	0.673686	+	0.739018i	$0.264710\pi$
$480$	4.91004	+	37.8971i	0.224112	+	1.72976i
$481$	3.25186	+	5.63238i	0.148272	+	0.256815i
$482$	−14.0894	−	29.5703i	−0.641754	−	1.34689i
$483$	−6.76158	−	12.6109i	−0.307662	−	0.573817i
$484$	−0.966399	−	9.26795i	−0.0439272	−	0.421270i
$485$	24.0344	+	18.4423i	1.09135	+	0.837420i
$486$	9.59228	−	18.8068i	0.435115	−	0.853094i
$487$	4.00836	+	14.9594i	0.181636	+	0.677875i	0.995326	+	0.0965753i	$0.0307889\pi$
$487$	4.00836	+	14.9594i	0.181636	+	0.677875i	−0.813690	+	0.581299i	$0.802544\pi$
$488$	−2.29365	+	21.5668i	−0.103829	+	0.976283i
$489$	−14.2927	−	14.2927i	−0.646337	−	0.646337i
$490$	11.6539	+	20.7043i	0.526470	+	0.935326i
$491$	3.85714	+	9.31196i	0.174070	+	0.420243i	0.986703	−	0.162533i	$-0.0519665\pi$
$491$	3.85714	+	9.31196i	0.174070	+	0.420243i	−0.812633	+	0.582776i	$0.801966\pi$
$492$	37.7037	−	9.01909i	1.69981	−	0.406612i
$493$	−42.9171	+	32.9315i	−1.93289	+	1.48316i
$494$	−14.2883	+	12.1932i	−0.642859	+	0.548597i
$495$	−25.7639	+	14.8748i	−1.15800	+	0.668572i
$496$	−4.28064	−	20.3029i	−0.192206	−	0.911627i
$497$	−22.0910	−	18.0820i	−0.990916	−	0.811090i
$498$	−14.1811	+	39.9940i	−0.635471	+	1.79217i
$499$	0.979674	+	7.44137i	0.0438562	+	0.333121i	0.999282	+	0.0378896i	$0.0120635\pi$
$499$	0.979674	+	7.44137i	0.0438562	+	0.333121i	−0.955426	+	0.295232i	$0.904603\pi$
$500$	20.3445	+	0.549474i	0.909833	+	0.0245732i
$501$	−27.8524	−	3.66684i	−1.24435	−	0.163822i
$502$	−26.9411	−	5.73809i	−1.20244	−	0.256103i
$503$	7.48218	+	7.48218i	0.333614	+	0.333614i	0.853957	−	0.520343i	$-0.174196\pi$
$503$	7.48218	+	7.48218i	0.333614	+	0.333614i	−0.520343	+	0.853957i	$0.674196\pi$
$504$	14.3176	−	33.9410i	0.637756	−	1.51185i
$505$	−4.39075	+	4.39075i	−0.195386	+	0.195386i
$506$	−5.74027	+	3.72442i	−0.255186	+	0.165571i
$507$	3.43948	−	26.1255i	0.152753	−	1.16027i
$508$	2.97798	+	7.77700i	0.132126	+	0.345049i
$509$	17.0736	−	2.24778i	0.756772	−	0.0996309i	0.257740	−	0.966214i	$-0.417022\pi$
$509$	17.0736	−	2.24778i	0.756772	−	0.0996309i	0.499032	+	0.866583i	$0.333689\pi$
$510$	−50.3841	+	24.0065i	−2.23104	+	1.06303i
$511$	−9.88296	−	26.1562i	−0.437196	−	1.15708i
$512$	−14.7589	+	17.1515i	−0.652256	+	0.757999i
$513$	−18.8415	−	32.6345i	−0.831873	−	1.44085i
$514$	0.597191	−	7.54836i	0.0263409	−	0.332944i
$515$	−12.4024	−	16.1632i	−0.546517	−	0.712235i
$516$	−28.2853	−	4.50378i	−1.24519	−	0.198268i
$517$	9.13634	−	3.78439i	0.401816	−	0.166437i
$518$	11.6843	−	5.12304i	0.513380	−	0.225093i
$519$	13.0539	−	13.0539i	0.573001	−	0.573001i
$520$	−12.4192	+	3.66207i	−0.544616	+	0.160592i
$521$	−0.744652	+	0.199529i	−0.0326238	+	0.00874152i	−0.275094	−	0.961417i	$-0.588709\pi$
$521$	−0.744652	+	0.199529i	−0.0326238	+	0.00874152i	0.242470	+	0.970159i	$0.422042\pi$
$522$	−19.8951	−	61.3165i	−0.870784	−	2.68375i
$523$	18.1156	−	23.6087i	0.792138	−	1.03233i	−0.206410	−	0.978466i	$-0.566178\pi$
$523$	18.1156	−	23.6087i	0.792138	−	1.03233i	0.998548	−	0.0538690i	$-0.0171553\pi$
$524$	5.64568	+	10.4185i	0.246633	+	0.455133i
$525$	4.81028	+	2.98264i	0.209938	+	0.130173i
$526$	−7.39047	+	20.8428i	−0.322240	+	0.908789i
$527$	26.2441	−	15.1520i	1.14321	−	0.660034i
$528$	−26.9490	−	8.80527i	−1.17280	−	0.383200i
$529$	16.7212	+	9.65397i	0.727007	+	0.419738i
$530$	−3.04927	−	16.4902i	−0.132452	−	0.716290i
$531$	−24.1854	−	10.0179i	−1.04956	−	0.434741i
$532$	20.6856	+	30.4932i	0.896833	+	1.32205i
$533$	5.02670	+	12.1355i	0.217731	+	0.525648i
$534$	−3.27527	+	15.3778i	−0.141735	+	0.665465i
$535$	−1.18708	+	0.318076i	−0.0513218	+	0.0137516i
$536$	−17.7775	+	7.88879i	−0.767869	+	0.340744i
$537$	53.8295	+	14.4236i	2.32292	+	0.622423i
$538$	23.0806	−	1.20009i	0.995075	−	0.0517396i
$539$	−17.5860	+	1.19814i	−0.757484	+	0.0516077i
$540$	−2.69393	−	25.8353i	−0.115928	−	1.11177i
$541$	11.3104	−	1.48905i	0.486274	−	0.0640192i	0.116597	−	0.993179i	$-0.462802\pi$
$541$	11.3104	−	1.48905i	0.486274	−	0.0640192i	0.369678	+	0.929160i	$0.379468\pi$
$542$	10.1220	+	0.800803i	0.434776	+	0.0343974i
$543$	−19.1204	+	33.1175i	−0.820534	+	1.42121i
$544$	−30.5055	−	12.7093i	−1.30791	−	0.544907i
$545$	−15.2159			−0.651779
$546$	19.5061	+	4.80010i	0.834783	+	0.205425i
$547$	−3.53300	+	8.52942i	−0.151060	+	0.364692i	−0.981236	−	0.192810i	$-0.938240\pi$
$547$	−3.53300	+	8.52942i	−0.151060	+	0.364692i	0.830176	+	0.557502i	$0.188240\pi$
$548$	0.929244	+	1.28121i	0.0396954	+	0.0547305i
$549$	4.92690	−	37.4235i	0.210275	−	1.59720i
$550$	1.22975	−	2.41107i	0.0524368	−	0.102808i
$551$	62.2839	+	16.6889i	2.65338	+	0.710972i
$552$	−2.37438	−	15.1118i	−0.101060	−	0.643202i
$553$	−13.3583	−	18.5909i	−0.568054	−	0.790566i
$554$	1.60614	+	1.44737i	0.0682383	+	0.0614928i
$555$	14.0222	−	18.2740i	0.595207	−	0.775689i
$556$	−17.1863	+	16.2823i	−0.728861	+	0.690525i
$557$	−35.3300	+	27.1097i	−1.49698	+	1.14867i	−0.546679	+	0.837342i	$0.684108\pi$
$557$	−35.3300	+	27.1097i	−1.49698	+	1.14867i	−0.950301	+	0.311332i	$0.899225\pi$
$558$	6.56628	+	35.5099i	0.277973	+	1.50325i
$559$		−	9.70450i		−	0.410456i
$560$	4.45619	+	25.0053i	0.188308	+	1.05667i
$561$		−	41.4064i		−	1.74818i
$562$	40.5248	−	7.49361i	1.70944	−	0.316099i
$563$	25.9783	−	19.9338i	1.09485	−	0.840112i	0.106810	−	0.994279i	$-0.465936\pi$
$563$	25.9783	−	19.9338i	1.09485	−	0.840112i	0.988045	+	0.154168i	$0.0492697\pi$
$564$	−0.596879	+	22.0997i	−0.0251331	+	0.930565i
$565$	−17.6056	+	22.9441i	−0.740674	+	0.965266i
$566$	1.05389	−	1.16950i	0.0442985	−	0.0491578i
$567$	−0.505298	+	1.11905i	−0.0212205	+	0.0469955i
$568$	−15.9139	−	26.0412i	−0.667733	−	1.09266i
$569$	−13.4522	−	3.60452i	−0.563947	−	0.151109i	−0.0344280	−	0.999407i	$-0.510961\pi$
$569$	−13.4522	−	3.60452i	−0.563947	−	0.151109i	−0.529519	+	0.848298i	$0.677628\pi$
$570$	59.2622	+	30.2263i	2.48222	+	1.26604i
$571$	−2.99406	+	22.7421i	−0.125297	+	0.951728i	0.807131	+	0.590373i	$0.201019\pi$
$571$	−2.99406	+	22.7421i	−0.125297	+	0.951728i	−0.932428	+	0.361355i	$0.882314\pi$
$572$	1.51052	−	9.48655i	0.0631578	−	0.396653i
$573$	−7.22057	+	17.4320i	−0.301644	+	0.728232i
$574$	24.7472	−	7.17813i	1.03293	−	0.299609i
$575$	1.46037			0.0609018
$576$	26.4229	−	29.2005i	1.10095	−	1.21669i
$577$	5.25492	−	9.10178i	0.218765	−	0.378912i	−0.735666	−	0.677345i	$-0.763131\pi$
$577$	5.25492	−	9.10178i	0.218765	−	0.378912i	0.954431	+	0.298433i	$0.0964638\pi$
$578$	1.91047	−	24.1480i	0.0794653	−	1.00442i
$579$	−35.8003	+	4.71320i	−1.48781	+	0.195874i
$580$	34.5192	+	28.0001i	1.43333	+	1.16264i
$581$	−8.15245	+	27.0001i	−0.338221	+	1.12015i
$582$	−2.60906	−	50.1784i	−0.108149	−	2.07996i
$583$	12.0176	+	3.22012i	0.497720	+	0.133364i
$584$	−0.745628	−	29.8823i	−0.0308543	−	1.23654i
$585$	21.7665	−	5.83232i	0.899934	−	0.241137i
$586$	29.2330	+	6.22623i	1.20760	+	0.257203i
$587$	1.98416	+	4.79017i	0.0818949	+	0.197712i	0.959523	−	0.281631i	$-0.0908753\pi$
$587$	1.98416	+	4.79017i	0.0818949	+	0.197712i	−0.877628	+	0.479342i	$0.840875\pi$
$588$	13.5742	−	36.9942i	0.559791	−	1.52561i
$589$	−33.3722	−	13.8232i	−1.37508	−	0.569576i
$590$	17.7489	−	3.28202i	0.730711	−	0.135119i
$591$	−19.8253	−	11.4461i	−0.815503	−	0.470831i
$592$	13.5987	−	1.04775i	0.558902	−	0.0430622i
$593$	−26.8166	+	15.4826i	−1.10123	+	0.635793i	−0.936543	−	0.350554i	$-0.885993\pi$
$593$	−26.8166	+	15.4826i	−1.10123	+	0.635793i	−0.164683	+	0.986347i	$0.552660\pi$
$594$	18.1632	+	6.44033i	0.745245	+	0.264250i
$595$	−32.6927	+	17.5288i	−1.34027	+	0.718610i
$596$	−26.7131	−	7.93667i	−1.09421	−	0.325099i
$597$	−40.5303	+	52.8201i	−1.65880	+	2.16178i
$598$	4.93007	−	1.59964i	0.201606	−	0.0654140i
$599$	−1.01301	+	0.271435i	−0.0413905	+	0.0110905i	−0.279455	−	0.960159i	$-0.590154\pi$
$599$	−1.01301	+	0.271435i	−0.0413905	+	0.0110905i	0.238064	+	0.971249i	$0.423487\pi$
$600$	3.80205	+	4.70700i	0.155218	+	0.192162i
$601$	8.02007	−	8.02007i	0.327145	−	0.327145i	−0.524355	−	0.851500i	$-0.675693\pi$
$601$	8.02007	−	8.02007i	0.327145	−	0.327145i	0.851500	+	0.524355i	$0.175693\pi$
$602$	−18.9211	−	2.09719i	−0.771166	−	0.0854749i
$603$	31.2727	−	12.9536i	1.27352	−	0.527510i
$604$	−20.8865	−	28.7975i	−0.849859	−	1.17175i
$605$	−6.80709	−	8.87117i	−0.276747	−	0.360664i
$606$	10.2668	+	0.812259i	0.417060	+	0.0329958i
$607$	11.2174	+	19.4291i	0.455300	+	0.788603i	0.998705	−	0.0508676i	$-0.0161986\pi$
$607$	11.2174	+	19.4291i	0.455300	+	0.788603i	−0.543405	+	0.839470i	$0.682865\pi$
$608$	10.1170	+	38.0701i	0.410301	+	1.54395i
$609$	−24.3737	−	64.5073i	−0.987672	−	2.61397i
$610$	11.1949	+	23.4954i	0.453268	+	0.951303i
$611$	−7.42659	+	0.977729i	−0.300448	+	0.0395547i
$612$	52.5234	+	23.4367i	2.12313	+	0.947372i
$613$	1.07911	−	8.19667i	0.0435849	−	0.331060i	−0.955736	−	0.294224i	$-0.904939\pi$
$613$	1.07911	−	8.19667i	0.0435849	−	0.331060i	0.999321	−	0.0368360i	$-0.0117279\pi$
$614$	−12.1383	−	18.7081i	−0.489861	−	0.754999i
$615$	32.8953	−	32.8953i	1.32647	−	1.32647i
$616$	−18.1697	−	4.99518i	−0.732079	−	0.201261i
$617$	28.3687	+	28.3687i	1.14208	+	1.14208i	0.988069	+	0.154010i	$0.0492189\pi$
$617$	28.3687	+	28.3687i	1.14208	+	1.14208i	0.154010	+	0.988069i	$0.450781\pi$
$618$	−7.03905	+	33.0493i	−0.283152	+	1.32944i
$619$	3.01949	+	0.397523i	0.121363	+	0.0159778i	0.190963	−	0.981597i	$-0.438839\pi$
$619$	3.01949	+	0.397523i	0.121363	+	0.0159778i	−0.0695998	+	0.997575i	$0.522172\pi$
$620$	−17.1246	−	18.0753i	−0.687740	−	0.725921i
$621$	1.35722	+	10.3091i	0.0544634	+	0.413691i
$622$	6.27795	+	2.22604i	0.251723	+	0.0892561i
$623$	−1.68903	+	10.3129i	−0.0676696	+	0.413179i
$624$	17.9912	+	11.7257i	0.720224	+	0.469404i
$625$	24.4414	−	14.1112i	0.977656	−	0.564450i
$626$	2.37461	+	2.78263i	0.0949086	+	0.111216i
$627$	−39.1564	+	30.0458i	−1.56376	+	1.19991i
$628$	4.10471	−	6.68594i	0.163796	−	0.266798i
$629$	7.62291	+	18.4033i	0.303945	+	0.733789i
$630$	−6.66757	−	43.6991i	−0.265642	−	1.74101i
$631$	8.79911	+	8.79911i	0.350287	+	0.350287i	0.860216	−	0.509929i	$-0.170328\pi$
$631$	8.79911	+	8.79911i	0.350287	+	0.350287i	−0.509929	+	0.860216i	$0.670328\pi$
$632$	−6.92181	−	23.4739i	−0.275335	−	0.933740i
$633$	8.81591	+	32.9014i	0.350401	+	1.30771i
$634$	−0.122871	−	0.0626697i	−0.00487985	−	0.00248893i
$635$	7.92816	+	6.08349i	0.314619	+	0.241416i
$636$	−17.5217	+	21.6011i	−0.694780	+	0.856541i
$637$	13.1018	+	2.57106i	0.519114	+	0.101869i
$638$	−29.7693	+	14.1842i	−1.17858	+	0.561559i
$639$	26.5574	+	45.9987i	1.05059	+	1.81968i
$640$	−4.32480	+	26.8063i	−0.170953	+	1.05961i
$641$	6.70187	−	11.6080i	0.264708	−	0.458488i	−0.702779	−	0.711408i	$-0.748058\pi$
$641$	6.70187	−	11.6080i	0.264708	−	0.458488i	0.967487	+	0.252920i	$0.0813911\pi$
$642$	1.67935	+	1.15520i	0.0662788	+	0.0455923i
$643$	13.9500	−	33.6784i	0.550136	−	1.32815i	−0.367241	−	0.930126i	$-0.619698\pi$
$643$	13.9500	−	33.6784i	0.550136	−	1.32815i	0.917377	−	0.398019i	$-0.130302\pi$
$644$	−2.05344	−	9.95797i	−0.0809169	−	0.392399i
$645$	−31.7537	+	13.1528i	−1.25030	+	0.517892i
$646$	−48.2623	+	31.3137i	−1.89886	+	1.23202i
$647$	−4.88005	−	18.2126i	−0.191855	−	0.716012i	−0.993059	−	0.117620i	$-0.962473\pi$
$647$	−4.88005	−	18.2126i	−0.191855	−	0.716012i	0.801204	−	0.598391i	$-0.204193\pi$
$648$	−0.904719	+	0.951023i	−0.0355407	+	0.0373597i
$649$	−3.46591	+	12.9349i	−0.136049	+	0.507741i
$650$	−1.37244	+	1.52299i	−0.0538315	+	0.0597366i
$651$	8.82040	+	37.6095i	0.345699	+	1.47403i
$652$	−6.84274	−	12.6275i	−0.267982	−	0.494531i
$653$	−4.96634	−	37.7231i	−0.194348	−	1.47622i	−0.759108	−	0.650964i	$-0.774365\pi$
$653$	−4.96634	−	37.7231i	−0.194348	−	1.47622i	0.564760	−	0.825255i	$-0.308969\pi$
$654$	16.3821	+	19.1970i	0.640591	+	0.750661i
$655$	12.3147	+	7.10990i	0.481176	+	0.277807i
$656$	27.5062	+	1.48688i	1.07394	+	0.0580530i
$657$			52.0232i			2.02962i
$658$	0.301381	+	14.6911i	0.0117491	+	0.572718i
$659$	28.0384	+	11.6139i	1.09222	+	0.452413i	0.854781	−	0.518989i	$-0.173691\pi$
$659$	28.0384	+	11.6139i	1.09222	+	0.452413i	0.237441	+	0.971402i	$0.423691\pi$
$660$	−33.0878	+	7.91493i	−1.28794	+	0.308088i
$661$	30.7880	+	4.05331i	1.19751	+	0.157656i	0.702792	−	0.711396i	$-0.251937\pi$
$661$	30.7880	+	4.05331i	1.19751	+	0.157656i	0.494722	+	0.869051i	$0.335270\pi$
$662$	25.8141	−	8.37580i	1.00330	−	0.325535i
$663$	−8.11761	+	30.2953i	−0.315262	+	1.17657i
$664$	−17.7526	+	24.3711i	−0.688935	+	0.945784i
$665$	40.2990	+	18.1968i	1.56273	+	0.705640i
$666$	−23.7052	+	1.23257i	−0.918558	+	0.0477611i
$667$	−14.1158	−	10.8314i	−0.546567	−	0.419395i
$668$	−18.2289	−	8.13401i	−0.705299	−	0.314714i
$669$	−27.4496	−	35.7730i	−1.06126	−	1.38306i
$670$	−13.2273	+	19.2289i	−0.511015	+	0.742878i
$671$	−19.3089			−0.745413
$672$	26.7499	−	32.5439i	1.03190	−	1.25541i
$673$	13.9793			0.538863			0.269431	−	0.963020i	$-0.413164\pi$
$673$	13.9793			0.538863			0.269431	+	0.963020i	$0.413164\pi$
$674$	−18.4813	+	26.8669i	−0.711875	+	1.03487i
$675$	−2.50378	−	3.26299i	−0.0963704	−	0.125592i
$676$	7.62968	−	17.0987i	0.293449	−	0.657643i
$677$	23.0998	+	17.7251i	0.887799	+	0.681232i	0.948450	−	0.316927i	$-0.102651\pi$
$677$	23.0998	+	17.7251i	0.887799	+	0.681232i	−0.0606508	+	0.998159i	$0.519318\pi$
$678$	47.9021	−	2.49070i	1.83967	−	0.0956548i
$679$	−3.31625	−	33.2317i	−0.127266	−	1.27531i
$680$	−39.1761	+	6.15537i	−1.50233	+	0.236048i
$681$	−16.9231	+	63.1579i	−0.648495	+	2.42021i
$682$	17.5710	−	5.70119i	0.672829	−	0.218310i
$683$	13.7542	+	1.81077i	0.526289	+	0.0692873i	0.388989	−	0.921242i	$-0.372824\pi$
$683$	13.7542	+	1.81077i	0.526289	+	0.0692873i	0.137300	+	0.990530i	$0.456158\pi$
$684$	−15.9495	−	66.6756i	−0.609843	−	2.54941i
$685$	1.75469	+	0.726817i	0.0670433	+	0.0277702i
$686$	7.84422	−	24.9894i	0.299494	−	0.954098i
$687$		−	53.4406i		−	2.03889i
$688$	−18.3544	−	8.79167i	−0.699755	−	0.335179i
$689$	−8.16150	−	4.71205i	−0.310929	−	0.179515i
$690$	−11.9160	−	13.9635i	−0.453634	−	0.531580i
$691$	−1.09459	−	8.31426i	−0.0416403	−	0.316289i	−0.999571	−	0.0292898i	$-0.990675\pi$
$691$	−1.09459	−	8.31426i	−0.0416403	−	0.316289i	0.957931	−	0.287000i	$-0.0926579\pi$
$692$	11.5330	−	6.24965i	0.438419	−	0.237576i
$693$	31.3958	+	9.47968i	1.19263	+	0.360103i
$694$	−27.5605	+	30.5838i	−1.04618	+	1.16095i
$695$	−7.35292	+	27.4415i	−0.278912	+	1.04091i
$696$	−1.83889	−	73.6967i	−0.0697031	−	2.79347i
$697$	10.4126	+	38.8603i	0.394405	+	1.47194i
$698$	−7.76851	+	5.04039i	−0.294043	+	0.190782i
$699$	−13.6214	+	5.64215i	−0.515207	+	0.213406i
$700$	2.67282	+	3.00500i	0.101023	+	0.113578i
$701$	10.2240	−	24.6829i	0.386155	−	0.932260i	−0.604592	−	0.796535i	$-0.706664\pi$
$701$	10.2240	−	24.6829i	0.386155	−	0.932260i	0.990747	−	0.135724i	$-0.0433362\pi$
$702$	−12.0266	−	8.27296i	−0.453916	−	0.312243i
$703$	11.8719	−	20.5627i	0.447756	−	0.775536i
$704$	−16.5738	−	11.4511i	−0.624647	−	0.431580i
$705$	13.2647	+	22.9751i	0.499577	+	0.865293i
$706$	−16.9392	+	8.07106i	−0.637516	+	0.303758i
$707$	6.84188	+	0.215160i	0.257315	+	0.00809194i
$708$	−23.2499	−	18.8591i	−0.873786	−	0.708768i
$709$	−12.3050	−	9.44197i	−0.462125	−	0.354601i	0.351308	−	0.936260i	$-0.385737\pi$
$709$	−12.3050	−	9.44197i	−0.462125	−	0.354601i	−0.813433	+	0.581659i	$0.802404\pi$
$710$	−32.6242	−	16.6397i	−1.22436	−	0.624478i
$711$	11.0239	+	41.1416i	0.413427	+	1.54293i
$712$	−5.34286	+	9.81145i	−0.200232	+	0.367700i
$713$	7.04793	+	7.04793i	0.263947	+	0.263947i
$714$	57.3133	+	22.3741i	2.14490	+	0.837328i
$715$	−4.41130	−	10.6498i	−0.164973	−	0.398281i
$716$	33.7458	+	20.7176i	1.26114	+	0.774255i
$717$	2.39094	−	1.83463i	0.0892913	−	0.0685156i
$718$	24.9778	+	29.2696i	0.932162	+	1.09233i
$719$	−31.1442	+	17.9811i	−1.16148	+	0.670583i	−0.951659	−	0.307157i	$-0.900622\pi$
$719$	−31.1442	+	17.9811i	−1.16148	+	0.670583i	−0.209824	+	0.977739i	$0.567289\pi$
$720$	8.68826	−	46.4514i	0.323792	−	1.73114i
$721$	−3.62999	+	22.1640i	−0.135188	+	0.825432i
$722$	39.3076	+	13.9377i	1.46288	+	0.518708i
$723$	8.50939	+	64.6352i	0.316468	+	2.40381i
$724$	−19.7253	+	18.6878i	−0.733085	+	0.694528i
$725$	6.97755	+	0.918613i	0.259140	+	0.0341164i
$726$	−3.86339	+	18.1391i	−0.143384	+	0.673207i
$727$	20.7270	+	20.7270i	0.768722	+	0.768722i	0.977882	−	0.209159i	$-0.0670728\pi$
$727$	20.7270	+	20.7270i	0.768722	+	0.768722i	−0.209159	+	0.977882i	$0.567073\pi$
$728$	12.3147	+	7.21688i	0.456414	+	0.267475i
$729$	−30.6962	+	30.6962i	−1.13690	+	1.13690i
$730$	−19.5238	−	30.0911i	−0.722609	−	1.11372i
$731$	3.87963	−	29.4687i	0.143493	−	1.08994i
$732$	17.5898	−	39.4201i	0.650137	−	1.45701i
$733$	32.0545	−	4.22005i	1.18396	−	0.155871i	0.487275	−	0.873249i	$-0.337991\pi$
$733$	32.0545	−	4.22005i	1.18396	−	0.155871i	0.696685	+	0.717377i	$0.254658\pi$
$734$	11.0198	+	23.1280i	0.406750	+	0.853672i
$735$	−9.34469	−	46.3547i	−0.344684	−	1.70982i
$736$	1.44090	−	10.7736i	0.0531121	−	0.397119i
$737$	−8.65769	−	14.9956i	−0.318910	−	0.552369i
$738$	−47.7922	−	3.78109i	−1.75925	−	0.139184i
$739$	−20.6995	−	26.9761i	−0.761444	−	0.992333i	−0.999776	−	0.0211493i	$-0.993267\pi$
$739$	−20.6995	−	26.9761i	−0.761444	−	0.992333i	0.238332	−	0.971184i	$-0.423399\pi$
$740$	13.2489	−	9.60929i	0.487041	−	0.353244i
$741$	34.5394	−	14.3067i	1.26884	−	0.525570i
$742$	−10.9509	+	14.8944i	−0.402021	+	0.546790i
$743$	−20.9462	+	20.9462i	−0.768440	+	0.768440i	−0.977832	−	0.209392i	$-0.932852\pi$
$743$	−20.9462	+	20.9462i	−0.768440	+	0.768440i	0.209392	+	0.977832i	$0.432852\pi$
$744$	−4.36737	+	41.0656i	−0.160116	+	1.50554i
$745$	−32.3012	+	8.65509i	−1.18343	+	0.317098i
$746$	−28.2526	+	9.16700i	−1.03440	+	0.335628i
$747$	31.9450	−	41.6315i	1.16881	−	1.52322i
$748$	8.37934	−	28.2030i	0.306379	−	1.03120i
$749$	1.15141	+	0.713939i	0.0420716	+	0.0260867i
$750$	−38.1775	−	13.5370i	−1.39404	−	0.494302i
$751$	44.3472	−	25.6039i	1.61825	−	0.934299i	0.630881	−	0.775879i	$-0.282693\pi$
$751$	44.3472	−	25.6039i	1.61825	−	0.934299i	0.987372	−	0.158420i	$-0.0506398\pi$
$752$	−4.87882	+	14.9319i	−0.177912	+	0.544510i
$753$	47.4787	+	27.4118i	1.73022	+	0.998942i
$754$	24.5617	−	4.54180i	0.894485	−	0.165403i
$755$	−39.4399	−	16.3366i	−1.43537	−	0.594548i
$756$	−18.7290	+	21.6608i	−0.681167	+	0.787795i
$757$	4.82278	+	11.6432i	0.175287	+	0.423180i	0.986967	−	0.160922i	$-0.0514467\pi$
$757$	4.82278	+	11.6432i	0.175287	+	0.423180i	−0.811680	+	0.584102i	$0.801447\pi$
$758$	38.9283	+	8.29120i	1.41394	+	0.301150i
$759$	13.1549	−	3.52484i	0.477492	−	0.127944i
$760$	34.2482	+	32.5807i	1.24231	+	1.18183i
$761$	−41.4678	−	11.1113i	−1.50321	−	0.402783i	−0.589034	−	0.808108i	$-0.700492\pi$
$761$	−41.4678	−	11.1113i	−1.50321	−	0.402783i	−0.914173	+	0.405325i	$0.867158\pi$
$762$	−0.860643	−	16.5522i	−0.0311778	−	0.599623i
$763$	11.4823	+	12.2279i	0.415687	+	0.442681i
$764$	−8.44580	+	10.4122i	−0.305558	+	0.376699i
$765$	68.4279	−	9.00870i	2.47401	−	0.325710i
$766$	0.637409	−	8.05671i	0.0230305	−	0.291101i
$767$	5.07171	−	8.78446i	0.183129	−	0.317188i
$768$	38.4761	−	23.4045i	1.38839	−	0.844538i
$769$	2.39948			0.0865273			0.0432637	−	0.999064i	$-0.486224\pi$
$769$	2.39948			0.0865273			0.0432637	+	0.999064i	$0.486224\pi$
$770$	−21.7175	+	6.29935i	−0.782645	+	0.227013i
$771$	−5.76721	+	13.9233i	−0.207701	+	0.501435i
$772$	−25.3383	−	4.03455i	−0.911947	−	0.145207i
$773$	0.664020	−	5.04373i	0.0238831	−	0.181411i	−0.975345	−	0.220684i	$-0.929171\pi$
$773$	0.664020	−	5.04373i	0.0238831	−	0.181411i	0.999228	+	0.0392735i	$0.0125044\pi$
$774$	31.5523	+	16.0931i	1.13413	+	0.578453i
$775$	−3.80817	−	1.02039i	−0.136793	−	0.0366537i
$776$	8.37741	−	34.7058i	0.300731	−	1.24587i
$777$	−25.2669	+	2.52143i	−0.906447	+	0.0904559i
$778$	−16.5902	+	18.4101i	−0.594787	+	0.660032i
$779$	29.1929	−	38.0450i	1.04595	−	1.36310i
$780$	25.7607	+	0.695756i	0.922379	+	0.0249121i
$781$	21.5558	−	16.5404i	0.771328	−	0.591860i
$782$	15.6102	−	2.88654i	0.558219	−	0.103222i
$783$			50.1099i			1.79078i
$784$	16.7322	−	22.4507i	0.597578	−	0.801811i
$785$		−	9.41452i		−	0.336019i
$786$	−4.28843	−	23.1915i	−0.152963	−	0.827214i
$787$	−33.7494	+	25.8968i	−1.20304	+	0.923122i	−0.998446	−	0.0557260i	$-0.982253\pi$
$787$	−33.7494	+	25.8968i	−1.20304	+	0.923122i	−0.204590	+	0.978848i	$0.565586\pi$
$788$	−11.1872	−	11.8083i	−0.398527	−	0.420652i
$789$	26.7941	−	34.9187i	0.953894	−	1.24314i
$790$	−21.8165	−	19.6599i	−0.776195	−	0.699467i
$791$	31.7241	−	3.16580i	1.12798	−	0.112563i
$792$	28.3388	+	20.6428i	1.00698	+	0.733510i
$793$	14.1275	+	3.78546i	0.501683	+	0.134426i
$794$	1.65690	−	3.24855i	0.0588013	−	0.115287i
$795$	−4.35656	+	33.0913i	−0.154511	+	1.17363i
$796$	−38.2954	+	27.7752i	−1.35734	+	0.984464i
$797$	−2.45911	+	5.93682i	−0.0871061	+	0.210293i	−0.961430	−	0.275051i	$-0.911305\pi$
$797$	−2.45911	+	5.93682i	−0.0871061	+	0.210293i	0.874324	+	0.485343i	$0.161305\pi$
$798$	−20.4300	−	70.4341i	−0.723214	−	2.49334i
$799$	−22.9425			−0.811646
$800$	1.63713	+	3.97547i	0.0578813	+	0.140554i
$801$	9.72174	−	16.8385i	0.343501	−	0.594961i
$802$	−29.7037	−	2.35002i	−1.04887	−	0.0829820i
$803$	26.3844	−	3.47358i	0.931087	−	0.122580i
$804$	38.5010	−	4.01462i	1.35782	−	0.141585i
$805$	−8.35198	−	8.89433i	−0.294368	−	0.313484i
$806$	−13.9737	+	0.726571i	−0.492202	+	0.0255924i
$807$	−44.4320	−	11.9055i	−1.56408	−	0.419094i
$808$	6.82860	+	2.63092i	0.240229	+	0.0925554i
$809$	37.5771	−	10.0687i	1.32114	−	0.353998i	0.471735	−	0.881741i	$-0.343628\pi$
$809$	37.5771	−	10.0687i	1.32114	−	0.353998i	0.849404	+	0.527742i	$0.176961\pi$
$810$	−0.328124	+	1.54059i	−0.0115291	+	0.0541307i
$811$	13.4053	+	32.3632i	0.470723	+	1.13642i	0.963845	+	0.266465i	$0.0858556\pi$
$811$	13.4053	+	32.3632i	0.470723	+	1.13642i	−0.493122	+	0.869960i	$0.664144\pi$
$812$	−3.54736	−	48.8701i	−0.124488	−	1.71500i
$813$	−18.6704	−	7.73355i	−0.654801	−	0.271227i
$814$	2.20791	+	11.9402i	0.0773872	+	0.418504i
$815$	−14.9258	−	8.61742i	−0.522829	−	0.301855i
$816$	49.9444	+	42.7988i	1.74841	+	1.49826i
$817$	−30.6825	+	17.7146i	−1.07345	+	0.619754i
$818$	−6.23609	+	17.5872i	−0.218040	+	0.614922i
$819$	−21.1125	−	13.0909i	−0.737731	−	0.457434i
$820$	29.0628	−	15.7489i	1.01492	−	0.549976i
$821$	22.3420	−	29.1167i	0.779742	−	1.01618i	−0.219436	−	0.975627i	$-0.570422\pi$
$821$	22.3420	−	29.1167i	0.779742	−	1.01618i	0.999177	−	0.0405524i	$-0.0129118\pi$
$822$	−0.972197	−	2.99630i	−0.0339092	−	0.104508i
$823$	−23.3807	+	6.26484i	−0.815000	+	0.218378i	−0.642159	−	0.766571i	$-0.721961\pi$
$823$	−23.3807	+	6.26484i	−0.815000	+	0.218378i	−0.172840	+	0.984950i	$0.555294\pi$
$824$	−11.4826	+	21.0863i	−0.400016	+	0.734576i
$825$	−3.80911	+	3.80911i	−0.132616	+	0.132616i
$826$	−16.0313	−	11.7868i	−0.557799	−	0.410115i
$827$	−11.9206	+	4.93769i	−0.414521	+	0.171700i	−0.580190	−	0.814481i	$-0.697022\pi$
$827$	−11.9206	+	4.93769i	−0.414521	+	0.171700i	0.165669	+	0.986181i	$0.447022\pi$
$828$	−2.97466	+	18.6819i	−0.103377	+	0.649241i
$829$	21.4230	+	27.9190i	0.744053	+	0.969668i	0.999996	+	0.00297653i	$0.000947461\pi$
$829$	21.4230	+	27.9190i	0.744053	+	0.969668i	−0.255943	+	0.966692i	$0.582386\pi$
$830$	−2.85361	+	36.0691i	−0.0990504	+	1.25198i
$831$	−2.15159	−	3.72666i	−0.0746377	−	0.129276i
$832$	9.88136	+	11.6275i	0.342575	+	0.403112i
$833$	38.7573	+	13.0451i	1.34286	+	0.451986i
$834$	42.5376	−	20.2679i	1.47296	−	0.701821i
$835$	−23.7488	+	3.12659i	−0.821861	+	0.108200i
$836$	−32.7507	+	12.5410i	−1.13271	+	0.433738i
$837$	3.66403	−	27.8311i	0.126647	−	0.961982i
$838$	23.0236	−	14.9383i	0.795338	−	0.516034i
$839$	20.8066	−	20.8066i	0.718325	−	0.718325i	−0.249937	−	0.968262i	$-0.580410\pi$
$839$	20.8066	−	20.8066i	0.718325	−	0.718325i	0.968262	+	0.249937i	$0.0804099\pi$
$840$	6.92353	−	50.0758i	0.238884	−	1.72778i
$841$	−40.1249	−	40.1249i	−1.38362	−	1.38362i
$842$	−55.4612	−	11.8125i	−1.91132	−	0.407085i
$843$	−81.3222	−	10.7063i	−2.80088	−	0.368743i
$844$	−0.653445	+	24.1941i	−0.0224925	+	0.832795i
$845$	−2.93273	−	22.2763i	−0.100889	−	0.766328i
$846$	9.13668	−	25.7675i	0.314125	−	0.885906i
$847$	−1.99232	+	12.1647i	−0.0684569	+	0.417986i
$848$	−16.3059	+	11.1673i	−0.559945	+	0.383486i
$849$	−2.71354	+	1.56667i	−0.0931286	+	0.0537678i
$850$	−4.77641	+	4.07605i	−0.163830	+	0.139807i
$851$	−5.19784	+	3.98844i	−0.178180	+	0.136722i
$852$	14.1313	+	59.0749i	0.484129	+	2.02387i
$853$	−16.1928	−	39.0928i	−0.554430	−	1.33851i	−0.914121	−	0.405441i	$-0.867118\pi$
$853$	−16.1928	−	39.0928i	−0.554430	−	1.33851i	0.359691	−	0.933072i	$-0.382882\pi$
$854$	10.4336	−	26.7267i	0.357031	−	0.914570i
$855$	−58.1725	−	58.1725i	−1.98946	−	1.98946i
$856$	0.910076	+	1.12669i	0.0311057	+	0.0385094i
$857$	−11.9490	−	44.5944i	−0.408171	−	1.52332i	−0.798131	−	0.602483i	$-0.794178\pi$
$857$	−11.9490	−	44.5944i	−0.408171	−	1.52332i	0.389960	−	0.920832i	$-0.372489\pi$
$858$	−8.68681	+	17.0315i	−0.296563	+	0.581446i
$859$	−1.30660	−	1.00259i	−0.0445808	−	0.0342080i	0.586231	−	0.810144i	$-0.300611\pi$
$859$	−1.30660	−	1.00259i	−0.0445808	−	0.0342080i	−0.630811	+	0.775936i	$0.717278\pi$
$860$	−24.2900	+	2.53280i	−0.828282	+	0.0863677i
$861$	−51.2592	−	1.61198i	−1.74691	−	0.0549360i
$862$	8.65277	+	18.1601i	0.294715	+	0.618536i
$863$	−11.8511	−	20.5267i	−0.403415	−	0.698736i	0.590720	−	0.806877i	$-0.298844\pi$
$863$	−11.8511	−	20.5267i	−0.403415	−	0.698736i	−0.994136	+	0.108140i	$0.965510\pi$
$864$	−26.5423	+	15.2516i	−0.902987	+	0.518869i
$865$	7.87051	−	13.6321i	0.267605	−	0.463506i
$866$	3.69618	−	5.37324i	0.125601	−	0.182590i
$867$	−18.4499	+	44.5420i	−0.626592	+	1.51273i
$868$	−1.60316	+	27.4018i	−0.0544149	+	0.930078i
$869$	20.1296	−	8.33796i	0.682850	−	0.282846i
$870$	−48.1504	−	74.2118i	−1.63245	−	2.51602i
$871$	3.39463	+	12.6689i	0.115023	+	0.429270i
$872$	7.27344	+	16.3908i	0.246310	+	0.555061i
$873$	−16.0822	+	60.0194i	−0.544299	+	2.03135i
$874$	−14.0569	−	12.6673i	−0.475481	−	0.428479i
$875$	−25.7738	−	7.78217i	−0.871313	−	0.263085i
$876$	−16.9439	+	57.0293i	−0.572480	+	1.92684i
$877$	5.75133	+	43.6857i	0.194208	+	1.47516i	0.759629	+	0.650357i	$0.225381\pi$
$877$	5.75133	+	43.6857i	0.194208	+	1.47516i	−0.565420	+	0.824803i	$0.691286\pi$
$878$	−18.7438	+	15.9954i	−0.632574	+	0.539820i
$879$	−51.5177	−	29.7437i	−1.73765	−	1.00323i
$880$	−24.1387	−	1.30485i	−0.813716	−	0.0439865i
$881$		−	24.7572i		−	0.834091i	−0.908886	−	0.417045i	$-0.863066\pi$
$881$		−	24.7572i		−	0.834091i	0.908886	−	0.417045i	$-0.136934\pi$
$882$	−30.0862	+	38.3346i	−1.01306	+	1.29079i
$883$	−32.9264	−	13.6386i	−1.10806	−	0.458975i	−0.247793	−	0.968813i	$-0.579705\pi$
$883$	−32.9264	−	13.6386i	−1.10806	−	0.458975i	−0.860270	+	0.509838i	$0.829705\pi$
$884$	−11.6599	+	18.9922i	−0.392166	+	0.638777i
$885$	−35.6172	−	4.68909i	−1.19726	−	0.157622i
$886$	0.0709530	+	0.218677i	0.00238371	+	0.00734659i
$887$	−8.13062	+	30.3439i	−0.273000	+	1.01885i	0.684170	+	0.729322i	$0.260164\pi$
$887$	−8.13062	+	30.3439i	−0.273000	+	1.01885i	−0.957170	+	0.289526i	$0.906502\pi$
$888$	−26.3878	−	6.36957i	−0.885516	−	0.213749i
$889$	−1.09392	−	10.9620i	−0.0366889	−	0.367655i
$890$	0.696128	+	13.3882i	0.0233343	+	0.448773i
$891$	−0.927118	−	0.711403i	−0.0310596	−	0.0238329i
$892$	−11.4573	−	29.9208i	−0.383620	−	1.00182i
$893$	16.6477	+	21.6958i	0.557096	+	0.726021i
$894$	45.6965	+	31.4340i	1.52832	+	1.05131i
$895$	47.5177			1.58834
$896$	24.8059	−	16.7532i	0.828706	−	0.559684i
$897$	−10.3159			−0.344438
$898$	−13.5820	−	9.34286i	−0.453237	−	0.311775i
$899$	29.2412	+	38.1078i	0.975247	+	1.27097i
$900$	−2.67578	−	6.98782i	−0.0891928	−	0.232927i
$901$	−22.8995	−	17.5714i	−0.762892	−	0.585388i
$902$	1.27343	+	24.4911i	0.0424006	+	0.815464i
$903$	34.5320	+	15.5927i	1.14915	+	0.518893i
$904$	33.1314	+	7.99736i	1.10193	+	0.265988i
$905$	−8.43921	+	31.4956i	−0.280529	+	1.04695i
$906$	21.8519	+	67.3474i	0.725981	+	2.23747i
$907$	−2.17761	−	0.286688i	−0.0723065	−	0.00951933i	0.0942861	−	0.995545i	$-0.469943\pi$
$907$	−2.17761	−	0.286688i	−0.0723065	−	0.00951933i	−0.166593	+	0.986026i	$0.553276\pi$
$908$	−24.3079	+	39.5938i	−0.806686	+	1.31397i
$909$	−11.7666	−	4.87387i	−0.390272	−	0.161656i
$910$	17.1248	−	0.351307i	0.567680	−	0.0116457i
$911$		−	9.57871i		−	0.317357i	−0.987330	−	0.158678i	$-0.949277\pi$
$911$		−	9.57871i		−	0.317357i	0.987330	−	0.158678i	$-0.0507233\pi$
$912$	4.23188	−	78.2865i	0.140132	−	2.59232i
$913$	−23.2471	−	13.4217i	−0.769367	−	0.444194i
$914$	−29.1782	+	24.8998i	−0.965130	+	0.823613i
$915$	−6.76124	−	51.3567i	−0.223520	−	1.69780i
$916$	10.8147	−	36.3998i	0.357326	−	1.20268i
$917$	−3.57926	−	15.2617i	−0.118198	−	0.503987i
$918$	−33.2128	−	29.9297i	−1.09619	−	0.987826i
$919$	−4.14276	+	15.4610i	−0.136657	+	0.510011i	0.863328	+	0.504642i	$0.168376\pi$
$919$	−4.14276	+	15.4610i	−0.136657	+	0.510011i	−0.999986	+	0.00536900i	$0.998291\pi$
$920$	−5.29054	−	11.9223i	−0.174424	−	0.393066i
$921$	11.4878	+	42.8732i	0.378537	+	1.41272i
$922$	−6.50885	−	10.0318i	−0.214358	−	0.330379i
$923$	−19.0142	+	7.87592i	−0.625859	+	0.259239i
$924$	31.3295	+	20.6175i	1.03066	+	0.678265i
$925$	0.991725	−	2.39424i	0.0326077	−	0.0787220i
$926$	23.2150	−	33.7483i	0.762891	−	1.10904i
$927$	20.8935	−	36.1886i	0.686232	−	1.18859i
$928$	13.6613	−	50.5689i	0.448455	−	1.66001i
$929$	−7.44890	−	12.9019i	−0.244391	−	0.423297i	0.717570	−	0.696487i	$-0.245255\pi$
$929$	−7.44890	−	12.9019i	−0.244391	−	0.423297i	−0.961960	+	0.273190i	$0.911921\pi$
$930$	21.3164	+	44.7380i	0.698991	+	1.46702i
$931$	−15.7872	−	46.1171i	−0.517405	−	1.51143i
$932$	−10.4197	+	1.08649i	−0.341307	+	0.0355892i
$933$	−10.5177	−	8.07049i	−0.344333	−	0.264216i
$934$	−16.7265	+	32.7942i	−0.547307	+	1.07306i
$935$	−9.13783	−	34.1028i	−0.298839	−	1.11528i
$936$	−16.6873	−	20.6592i	−0.545443	−	0.675267i
$937$	9.57260	+	9.57260i	0.312723	+	0.312723i	0.845964	−	0.533240i	$-0.179026\pi$
$937$	9.57260	+	9.57260i	0.312723	+	0.312723i	−0.533240	+	0.845964i	$0.679026\pi$
$938$	25.4345	−	3.88077i	0.830466	−	0.126712i
$939$	−2.78622	−	6.72653i	−0.0909248	−	0.219512i
$940$	4.38550	+	18.3333i	0.143039	+	0.597966i
$941$	27.9699	−	21.4621i	0.911793	−	0.699643i	−0.0423157	−	0.999104i	$-0.513474\pi$
$941$	27.9699	−	21.4621i	0.911793	−	0.699643i	0.954109	+	0.299461i	$0.0968069\pi$
$942$	−11.8777	+	10.1361i	−0.386996	+	0.330251i
$943$	−11.4596	+	6.61619i	−0.373175	+	0.215453i
$944$	−12.0197	−	17.5505i	−0.391207	−	0.571219i
$945$	−5.55377	+	33.9103i	−0.180664	+	1.10310i
$946$	6.05512	−	17.0768i	0.196869	−	0.555216i
$947$	1.84458	+	14.0110i	0.0599409	+	0.455296i	0.994926	+	0.100609i	$0.0320792\pi$
$947$	1.84458	+	14.0110i	0.0599409	+	0.455296i	−0.934985	+	0.354687i	$0.884587\pi$
$948$	−1.31507	+	48.6911i	−0.0427116	+	1.58141i
$949$	−19.9854	−	2.63112i	−0.648752	−	0.0854098i
$950$	7.32046	+	1.55916i	0.237507	+	0.0505857i
$951$	0.194117	+	0.194117i	0.00629468	+	0.00629468i
$952$	34.5098	+	26.8379i	1.11847	+	0.869822i
$953$	18.4907	−	18.4907i	0.598972	−	0.598972i	−0.341067	−	0.940039i	$-0.610788\pi$
$953$	18.4907	−	18.4907i	0.598972	−	0.598972i	0.940039	+	0.341067i	$0.110788\pi$
$954$	28.8546	−	18.7216i	0.934203	−	0.606133i
$955$	−2.09995	+	15.9507i	−0.0679527	+	0.516152i
$956$	1.99980	−	0.765767i	0.0646782	−	0.0247667i
$957$	65.0702	−	8.56666i	2.10342	−	0.276921i
$958$	16.9420	−	8.07238i	0.547372	−	0.260807i
$959$	−0.740041	−	1.95859i	−0.0238972	−	0.0632461i
$960$	24.6535	−	48.0916i	0.795687	−	1.55215i
$961$	2.04590	+	3.54360i	0.0659967	+	0.114310i
$962$	0.725407	−	9.16899i	0.0233881	−	0.295620i
$963$	−1.53449	−	1.99978i	−0.0494481	−	0.0644421i
$964$	−7.28413	+	45.7468i	−0.234606	+	1.47340i
$965$	−28.4454	+	11.7825i	−0.915691	+	0.379292i
$966$	−2.22931	+	20.1132i	−0.0717270	+	0.647130i
$967$	−7.51714	+	7.51714i	−0.241735	+	0.241735i	−0.817568	−	0.575833i	$-0.804678\pi$
$967$	−7.51714	+	7.51714i	−0.241735	+	0.241735i	0.575833	+	0.817568i	$0.304678\pi$
$968$	−6.30223	+	11.5732i	−0.202561	+	0.371977i
$969$	110.602	−	29.6357i	3.55305	−	0.952037i
$970$	−13.2225	−	40.7518i	−0.424550	−	1.30846i
$971$	8.92282	−	11.6284i	0.286347	−	0.373174i	−0.627926	−	0.778273i	$-0.716096\pi$
$971$	8.92282	−	11.6284i	0.286347	−	0.373174i	0.914273	+	0.405098i	$0.132763\pi$
$972$	−26.2502	+	14.2248i	−0.841975	+	0.456259i
$973$	27.6014	−	14.7990i	0.884859	−	0.474433i
$974$	7.31955	−	20.6428i	0.234533	−	0.661438i
$975$	3.53373	−	2.04020i	0.113170	−	0.0653387i
$976$	19.9582	−	23.2904i	0.638847	−	0.745509i
$977$	23.1140	+	13.3449i	0.739482	+	0.426940i	0.821881	−	0.569659i	$-0.192925\pi$
$977$	23.1140	+	13.3449i	0.739482	+	0.426940i	−0.0823987	+	0.996599i	$0.526258\pi$
$978$	5.19772	+	28.1088i	0.166205	+	0.898821i
$979$	−9.18907	−	3.80624i	−0.293684	−	0.121648i
$980$	3.01579	−	33.4645i	0.0963358	−	1.06898i
$981$	−11.9432	−	28.8333i	−0.381315	−	0.920577i
$982$	2.96933	−	13.9414i	0.0947551	−	0.444889i
$983$	18.0879	−	4.84665i	0.576916	−	0.154584i	0.0414494	−	0.999141i	$-0.486802\pi$
$983$	18.0879	−	4.84665i	0.576916	−	0.154584i	0.535466	+	0.844556i	$0.320136\pi$
$984$	−51.1597	−	19.7108i	−1.63091	−	0.628356i
$985$	−18.8543	−	5.05200i	−0.600749	−	0.160970i
$986$	76.3999	−	3.97246i	2.43307	−	0.126509i
$987$	8.45357	−	27.9974i	0.269080	−	0.891167i
$988$	26.4209	−	2.75500i	0.840562	−	0.0876482i
$989$	9.69251	−	1.27604i	0.308204	−	0.0405758i
$990$	41.9412	+	3.31819i	1.33298	+	0.105459i
$991$	25.6294	−	44.3914i	0.814144	−	1.41014i	−0.0957966	−	0.995401i	$-0.530540\pi$
$991$	25.6294	−	44.3914i	0.814144	−	1.41014i	0.909941	−	0.414738i	$-0.136127\pi$
$992$	−11.2851	+	27.0871i	−0.358302	+	0.860015i
$993$	−54.0147			−1.71410
$994$	11.2468	+	38.7744i	0.356728	+	1.22985i
$995$	−21.7246	+	52.4478i	−0.688716	+	1.66271i
$996$	48.5784	−	35.2333i	1.53926	−	1.11641i
$997$	1.24381	−	9.44767i	0.0393918	−	0.299211i	−0.960396	−	0.278637i	$-0.910117\pi$
$997$	1.24381	−	9.44767i	0.0393918	−	0.299211i	0.999788	−	0.0205737i	$-0.00654929\pi$
$998$	4.82276	−	9.45560i	0.152662	−	0.299312i
$999$	17.8232	+	4.77570i	0.563900	+	0.151096i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.bd.a.109.6	yes	240
4.3	odd	2		896.2.bh.a.529.3		240
7.2	even	3	inner	224.2.bd.a.205.16	yes	240
28.23	odd	6		896.2.bh.a.401.28		240
32.5	even	8	inner	224.2.bd.a.165.16	yes	240
32.27	odd	8		896.2.bh.a.753.28		240
224.37	even	24	inner	224.2.bd.a.37.6	✓	240
224.219	odd	24		896.2.bh.a.625.3		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.6	✓	240	224.37	even	24	inner
224.2.bd.a.109.6	yes	240	1.1	even	1	trivial
224.2.bd.a.165.16	yes	240	32.5	even	8	inner
224.2.bd.a.205.16	yes	240	7.2	even	3	inner
896.2.bh.a.401.28		240	28.23	odd	6
896.2.bh.a.529.3		240	4.3	odd	2
896.2.bh.a.625.3		240	224.219	odd	24
896.2.bh.a.753.28		240	32.27	odd	8

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.bd (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16516 - 0.801498i) q^{2} +(1.71349 + 2.23306i) q^{3} +(0.715201 + 1.86775i) q^{4} +(1.90405 + 1.46103i) q^{5} +(-0.206695 - 3.97523i) q^{6} +(-0.262719 - 2.63268i) q^{7} +(0.663674 - 2.74946i) q^{8} +(-1.27406 + 4.75485i) q^{9} +O(q^{10})\)	\(q+(-1.16516 - 0.801498i) q^{2} +(1.71349 + 2.23306i) q^{3} +(0.715201 + 1.86775i) q^{4} +(1.90405 + 1.46103i) q^{5} +(-0.206695 - 3.97523i) q^{6} +(-0.262719 - 2.63268i) q^{7} +(0.663674 - 2.74946i) q^{8} +(-1.27406 + 4.75485i) q^{9} +(-1.04751 - 3.22843i) q^{10} +(2.49657 + 0.328680i) q^{11} +(-2.94531 + 4.79745i) q^{12} +(-1.76220 - 0.729927i) q^{13} +(-1.80397 + 3.27806i) q^{14} +6.75532i q^{15} +(-2.97698 + 2.67163i) q^{16} +(-5.05929 - 2.92098i) q^{17} +(5.29549 - 4.51901i) q^{18} +(0.908918 + 6.90392i) q^{19} +(-1.36706 + 4.60122i) q^{20} +(5.42875 - 5.09772i) q^{21} +(-2.64547 - 2.38396i) q^{22} +(0.497314 - 1.85600i) q^{23} +(7.27690 - 3.22914i) q^{24} +(0.196710 + 0.734131i) q^{25} +(1.46821 + 2.26288i) q^{26} +(-4.99959 + 2.07090i) q^{27} +(4.72928 - 2.37359i) q^{28} +(3.54360 - 8.55501i) q^{29} +(5.41438 - 7.87103i) q^{30} +(-2.59366 + 4.49234i) q^{31} +(5.60996 - 0.726841i) q^{32} +(3.54388 + 6.13818i) q^{33} +(3.55373 + 7.45843i) q^{34} +(3.34619 - 5.39659i) q^{35} +(-9.79208 + 1.02105i) q^{36} +(-2.70513 - 2.07572i) q^{37} +(4.47444 - 8.77267i) q^{38} +(-1.38953 - 5.18581i) q^{39} +(5.28072 - 4.26547i) q^{40} +(-4.86955 - 4.86955i) q^{41} +(-10.4112 + 1.58853i) q^{42} +(1.94703 + 4.70055i) q^{43} +(1.17166 + 4.89804i) q^{44} +(-9.37286 + 7.19205i) q^{45} +(-2.06703 + 1.76394i) q^{46} +(3.40104 - 1.96359i) q^{47} +(-11.0669 - 2.06996i) q^{48} +(-6.86196 + 1.38331i) q^{49} +(0.359206 - 1.01304i) q^{50} +(-2.14630 - 16.3028i) q^{51} +(0.102994 - 3.81339i) q^{52} +(4.89856 + 0.644908i) q^{53} +(7.48514 + 1.59423i) q^{54} +(4.27339 + 4.27339i) q^{55} +(-7.41280 - 1.02490i) q^{56} +(-13.8594 + 13.8594i) q^{57} +(-10.9857 + 7.12777i) q^{58} +(-0.694133 + 5.27246i) q^{59} +(-12.6172 + 4.83141i) q^{60} +(-7.60241 + 1.00088i) q^{61} +(6.62263 - 3.15549i) q^{62} +(12.8527 + 2.10499i) q^{63} +(-7.11907 - 3.64949i) q^{64} +(-2.28887 - 3.96445i) q^{65} +(0.790550 - 9.99238i) q^{66} +(-4.18604 - 5.45536i) q^{67} +(1.83725 - 11.5386i) q^{68} +(4.99670 - 2.06970i) q^{69} +(-8.22421 + 3.60594i) q^{70} +(7.62970 - 7.62970i) q^{71} +(12.2277 + 6.65864i) q^{72} +(10.2082 - 2.73527i) q^{73} +(1.48823 + 4.58671i) q^{74} +(-1.30230 + 1.69719i) q^{75} +(-12.2447 + 6.63532i) q^{76} +(0.209410 - 6.65901i) q^{77} +(-2.53739 + 7.15602i) q^{78} +(7.49333 - 4.32628i) q^{79} +(-9.57166 + 0.737475i) q^{80} +(-0.401905 - 0.232040i) q^{81} +(1.77087 + 9.57674i) q^{82} +(-9.84868 - 4.07946i) q^{83} +(13.4039 + 6.49365i) q^{84} +(-5.36551 - 12.9535i) q^{85} +(1.49888 - 7.03744i) q^{86} +(25.1757 - 6.74582i) q^{87} +(2.56060 - 6.64609i) q^{88} +(-3.81526 - 1.02230i) q^{89} +(16.6853 - 0.867564i) q^{90} +(-1.45870 + 4.83106i) q^{91} +(3.82222 - 0.398556i) q^{92} +(-14.4759 + 1.90578i) q^{93} +(-5.53658 - 0.438028i) q^{94} +(-8.35621 + 14.4734i) q^{95} +(11.2357 + 11.2819i) q^{96} +12.6228 q^{97} +(9.10401 + 3.88807i) q^{98} +(-4.74360 + 11.4521i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Introduction

L-functions

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