LMFDB - Embedded newform 637.2.bz.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(4,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 7]))

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

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

chi := DirichletCharacter("637.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bz (of order $42$, degree $12$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$756$
Relative dimension:	$63$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			4.1
Character	$\chi$	$=$	637.4
Dual form			637.2.bz.a.478.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.21061 - 2.51386i) q^{2} +(2.20537 - 0.680267i) q^{3} +(-3.60692 + 4.52294i) q^{4} +(0.0440739 + 0.142884i) q^{5} +(-4.37994 - 4.72045i) q^{6} +(-1.16487 + 2.37551i) q^{7} +(10.2962 + 2.35003i) q^{8} +(1.92218 - 1.31052i) q^{9} +(0.305834 - 0.283773i) q^{10} +(-0.0535545 + 0.0785500i) q^{11} +(-4.87780 + 12.4284i) q^{12} +(3.58603 - 0.374655i) q^{13} +(7.38191 + 0.0525022i) q^{14} +(0.194399 + 0.285130i) q^{15} +(-3.98241 - 17.4481i) q^{16} +(4.51976 + 5.66760i) q^{17} +(-5.62146 - 3.24555i) q^{18} +(2.18665 + 1.26246i) q^{19} +(-0.805228 - 0.316029i) q^{20} +(-0.952992 + 6.03131i) q^{21} +(0.262297 + 0.0395349i) q^{22} +(-1.75652 + 2.20260i) q^{23} +(24.3055 - 1.82145i) q^{24} +(4.11272 - 2.80401i) q^{25} +(-5.28312 - 8.56122i) q^{26} +(-0.969253 + 1.21540i) q^{27} +(-6.54270 - 13.8370i) q^{28} +(1.32861 - 0.200255i) q^{29} +(0.481436 - 0.833872i) q^{30} +(-5.80247 - 3.35006i) q^{31} +(-22.5270 + 17.9647i) q^{32} +(-0.0646725 + 0.209663i) q^{33} +(8.77587 - 18.2233i) q^{34} +(-0.390764 - 0.0617436i) q^{35} +(-1.00575 + 13.4208i) q^{36} +(4.25886 - 3.39633i) q^{37} +(0.526472 - 7.02528i) q^{38} +(7.65366 - 3.26571i) q^{39} +(0.118010 + 1.57474i) q^{40} +(4.90796 - 5.28952i) q^{41} +(16.3156 - 4.90588i) q^{42} +(1.02469 - 0.950773i) q^{43} +(-0.162110 - 0.525548i) q^{44} +(0.271970 + 0.216889i) q^{45} +(7.66349 + 1.74914i) q^{46} +(-0.980734 + 1.43847i) q^{47} +(-20.6520 - 35.7703i) q^{48} +(-4.28614 - 5.53435i) q^{49} +(-12.0278 - 6.94424i) q^{50} +(13.8232 + 9.42451i) q^{51} +(-11.2400 + 17.5708i) q^{52} +(5.24041 + 13.3523i) q^{53} +(4.22874 + 0.965182i) q^{54} +(-0.0135839 - 0.00419008i) q^{55} +(-17.5763 + 21.7212i) q^{56} +(5.68119 + 1.29669i) q^{57} +(-2.11184 - 3.09750i) q^{58} +(-7.57230 + 1.72833i) q^{59} +(-1.99081 - 0.149190i) q^{60} +(2.92847 - 0.441395i) q^{61} +(-1.39704 + 18.6422i) q^{62} +(0.874064 + 6.09275i) q^{63} +(40.1833 + 19.3512i) q^{64} +(0.211583 + 0.495875i) q^{65} +(0.605357 - 0.0912428i) q^{66} +(1.17280 - 0.677116i) q^{67} -41.9367 q^{68} +(-2.37541 + 6.05245i) q^{69} +(0.317848 + 1.05707i) q^{70} +(1.51701 - 10.0647i) q^{71} +(22.8708 - 8.97614i) q^{72} +(-6.29968 - 9.23993i) q^{73} +(-13.6937 - 6.59454i) q^{74} +(7.16260 - 8.98162i) q^{75} +(-13.5971 + 5.33648i) q^{76} +(-0.124213 - 0.218720i) q^{77} +(-17.4751 - 15.2867i) q^{78} +(2.84793 + 4.93277i) q^{79} +(2.31753 - 1.33803i) q^{80} +(-3.86057 + 9.83657i) q^{81} +(-19.2387 - 5.93436i) q^{82} +(-0.109670 + 0.227732i) q^{83} +(-23.8419 - 26.0648i) q^{84} +(-0.610607 + 0.895596i) q^{85} +(-3.63061 - 1.42491i) q^{86} +(2.79384 - 1.34544i) q^{87} +(-0.736002 + 0.682910i) q^{88} +(-4.83820 + 10.0466i) q^{89} +(0.215978 - 0.946262i) q^{90} +(-3.28728 + 8.95510i) q^{91} +(-3.62662 - 15.8892i) q^{92} +(-15.0755 - 3.44089i) q^{93} +(4.80340 + 0.723996i) q^{94} +(-0.0840118 + 0.368080i) q^{95} +(-37.4596 + 54.9432i) q^{96} +(5.28921 - 3.05373i) q^{97} +(-8.72371 + 17.4747i) q^{98} +0.221171i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 756 q - 21 q^{2} - 5 q^{3} + 115 q^{4} - 15 q^{6} - 14 q^{7} + 50 q^{9} - 16 q^{10} - 24 q^{11} - 26 q^{12} - 10 q^{13} - 38 q^{14} - 6 q^{15} - 125 q^{16} + 15 q^{17} - 9 q^{18} - 27 q^{19} - 15 q^{20}+ \cdots + 105 q^{98}+O(q^{100}) $ 756 * q - 21 * q^2 - 5 * q^3 + 115 * q^4 - 15 * q^6 - 14 * q^7 + 50 * q^9 - 16 * q^10 - 24 * q^11 - 26 * q^12 - 10 * q^13 - 38 * q^14 - 6 * q^15 - 125 * q^16 + 15 * q^17 - 9 * q^18 - 27 * q^19 - 15 * q^20 - 16 * q^21 - q^22 - 5 * q^23 - 39 * q^24 - 79 * q^25 - 34 * q^26 - 50 * q^27 - 142 * q^28 - 3 * q^29 - 11 * q^30 - 15 * q^31 - 21 * q^32 - 6 * q^33 - 12 * q^35 - 84 * q^36 + 7 * q^37 - 2 * q^38 - 6 * q^39 - 24 * q^40 - 6 * q^41 + 88 * q^42 - 5 * q^43 + 108 * q^44 - 21 * q^45 - 21 * q^46 + 63 * q^47 - 154 * q^48 - 34 * q^49 + 135 * q^50 + 26 * q^51 + 89 * q^52 + 16 * q^53 - 21 * q^54 - 4 * q^55 + 58 * q^56 - 63 * q^57 - 18 * q^58 - 21 * q^59 + 15 * q^60 - 75 * q^61 - 87 * q^62 + 147 * q^63 + 4 * q^64 - 20 * q^65 + 85 * q^66 - 27 * q^67 + 312 * q^68 - 182 * q^69 - 228 * q^70 - 30 * q^71 - 120 * q^72 + 6 * q^73 - 43 * q^74 + 83 * q^75 + 21 * q^76 + 3 * q^77 + 79 * q^78 + 12 * q^79 + 57 * q^80 + 72 * q^81 - 248 * q^82 + 147 * q^83 - 14 * q^84 - 24 * q^85 - 60 * q^86 - 37 * q^87 + 70 * q^88 - 126 * q^89 + 117 * q^90 - 55 * q^91 + 88 * q^92 - 21 * q^93 + 210 * q^94 + 9 * q^95 - 12 * q^96 - 156 * q^97 + 105 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{21}\right)$

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 $

$2$	−1.21061	−	2.51386i	−0.856031	−	1.77757i	−0.575697	−	0.817663i	$-0.695269\pi$
$2$	−1.21061	−	2.51386i	−0.856031	−	1.77757i	−0.280334	−	0.959903i	$-0.590445\pi$
$3$	2.20537	−	0.680267i	1.27327	−	0.392752i	0.416824	−	0.908987i	$-0.363143\pi$
$3$	2.20537	−	0.680267i	1.27327	−	0.392752i	0.856447	+	0.516235i	$0.172667\pi$
$4$	−3.60692	+	4.52294i	−1.80346	+	2.26147i
$5$	0.0440739	+	0.142884i	0.0197105	+	0.0638997i	0.964894	−	0.262641i	$-0.0845933\pi$
$5$	0.0440739	+	0.142884i	0.0197105	+	0.0638997i	−0.945183	+	0.326540i	$0.894117\pi$
$6$	−4.37994	−	4.72045i	−1.78810	−	1.92712i
$7$	−1.16487	+	2.37551i	−0.440281	+	0.897860i
$7$	−1.16487	+	2.37551i	−0.440281	+	0.897860i
$8$	10.2962	+	2.35003i	3.64025	+	0.830863i
$9$	1.92218	−	1.31052i	0.640726	−	0.436839i
$10$	0.305834	−	0.283773i	0.0967132	−	0.0897368i
$11$	−0.0535545	+	0.0785500i	−0.0161473	+	0.0236837i	−0.834228	−	0.551420i	$-0.814086\pi$
$11$	−0.0535545	+	0.0785500i	−0.0161473	+	0.0236837i	0.818080	+	0.575104i	$0.195038\pi$
$12$	−4.87780	+	12.4284i	−1.40810	+	3.58778i
$13$	3.58603	−	0.374655i	0.994587	−	0.103910i
$13$	3.58603	−	0.374655i	0.994587	−	0.103910i
$14$	7.38191	+	0.0525022i	1.97290	+	0.0140318i
$15$	0.194399	+	0.285130i	0.0501935	+	0.0736204i
$16$	−3.98241	−	17.4481i	−0.995602	−	4.36202i
$17$	4.51976	+	5.66760i	1.09620	+	1.37460i	0.920771	+	0.390104i	$0.127561\pi$
$17$	4.51976	+	5.66760i	1.09620	+	1.37460i	0.175432	+	0.984492i	$0.443868\pi$
$18$	−5.62146	−	3.24555i	−1.32499	−	0.764984i
$19$	2.18665	+	1.26246i	0.501652	+	0.289629i	0.729396	−	0.684092i	$-0.239801\pi$
$19$	2.18665	+	1.26246i	0.501652	+	0.289629i	−0.227743	+	0.973721i	$0.573135\pi$
$20$	−0.805228	−	0.316029i	−0.180054	−	0.0706661i
$21$	−0.952992	+	6.03131i	−0.207960	+	1.31614i
$22$	0.262297	+	0.0395349i	0.0559219	+	0.00842888i
$23$	−1.75652	+	2.20260i	−0.366259	+	0.459274i	−0.930476	−	0.366352i	$-0.880607\pi$
$23$	−1.75652	+	2.20260i	−0.366259	+	0.459274i	0.564217	+	0.825626i	$0.309178\pi$
$24$	24.3055	−	1.82145i	4.96134	−	0.371801i
$25$	4.11272	−	2.80401i	0.822544	−	0.560801i
$26$	−5.28312	−	8.56122i	−1.03610	−	1.67899i
$27$	−0.969253	+	1.21540i	−0.186533	+	0.233905i
$28$	−6.54270	−	13.8370i	−1.23645	−	2.61494i
$29$	1.32861	−	0.200255i	0.246716	−	0.0371864i	−0.0245200	−	0.999699i	$-0.507806\pi$
$29$	1.32861	−	0.200255i	0.246716	−	0.0371864i	0.271236	+	0.962513i	$0.412568\pi$
$30$	0.481436	−	0.833872i	0.0878978	−	0.152244i
$31$	−5.80247	−	3.35006i	−1.04215	−	0.601688i	−0.121711	−	0.992566i	$-0.538838\pi$
$31$	−5.80247	−	3.35006i	−1.04215	−	0.601688i	−0.920443	+	0.390878i	$0.872172\pi$
$32$	−22.5270	+	17.9647i	−3.98225	+	3.17574i
$33$	−0.0646725	+	0.209663i	−0.0112580	+	0.0364977i
$34$	8.77587	−	18.2233i	1.50505	−	3.12527i
$35$	−0.390764	−	0.0617436i	−0.0660512	−	0.0104366i
$36$	−1.00575	+	13.4208i	−0.167625	+	2.23681i
$37$	4.25886	−	3.39633i	0.700153	−	0.558353i	−0.207418	−	0.978252i	$-0.566506\pi$
$37$	4.25886	−	3.39633i	0.700153	−	0.558353i	0.907571	+	0.419899i	$0.137935\pi$
$38$	0.526472	−	7.02528i	0.0854050	−	1.13965i
$39$	7.65366	−	3.26571i	1.22557	−	0.522932i
$40$	0.118010	+	1.57474i	0.0186590	+	0.248988i
$41$	4.90796	−	5.28952i	0.766494	−	0.826085i	−0.222361	−	0.974964i	$-0.571376\pi$
$41$	4.90796	−	5.28952i	0.766494	−	0.826085i	0.988855	+	0.148880i	$0.0475668\pi$
$42$	16.3156	−	4.90588i	2.51755	−	0.756994i
$43$	1.02469	−	0.950773i	0.156264	−	0.144991i	−0.598166	−	0.801372i	$-0.704104\pi$
$43$	1.02469	−	0.950773i	0.156264	−	0.144991i	0.754430	+	0.656380i	$0.227913\pi$
$44$	−0.162110	−	0.525548i	−0.0244390	−	0.0792293i
$45$	0.271970	+	0.216889i	0.0405429	+	0.0323319i
$46$	7.66349	+	1.74914i	1.12992	+	0.257897i
$47$	−0.980734	+	1.43847i	−0.143055	+	0.209823i	−0.891079	−	0.453849i	$-0.850051\pi$
$47$	−0.980734	+	1.43847i	−0.143055	+	0.209823i	0.748024	+	0.663672i	$0.231003\pi$
$48$	−20.6520	−	35.7703i	−2.98086	−	5.16300i
$49$	−4.28614	−	5.53435i	−0.612306	−	0.790621i
$50$	−12.0278	−	6.94424i	−1.70098	−	0.982063i
$51$	13.8232	+	9.42451i	1.93564	+	1.31970i
$52$	−11.2400	+	17.5708i	−1.55871	+	2.43663i
$53$	5.24041	+	13.3523i	0.719825	+	1.83409i	0.519783	+	0.854298i	$0.326013\pi$
$53$	5.24041	+	13.3523i	0.719825	+	1.83409i	0.200042	+	0.979787i	$0.435892\pi$
$54$	4.22874	+	0.965182i	0.575459	+	0.131345i
$55$	−0.0135839	−	0.00419008i	−0.00183165	−	0.000564990i
$56$	−17.5763	+	21.7212i	−2.34873	+	2.90262i
$57$	5.68119	+	1.29669i	0.752492	+	0.171751i
$58$	−2.11184	−	3.09750i	−0.277298	−	0.406721i
$59$	−7.57230	+	1.72833i	−0.985829	+	0.225009i	−0.684900	−	0.728637i	$-0.740154\pi$
$59$	−7.57230	+	1.72833i	−0.985829	+	0.225009i	−0.300930	+	0.953646i	$0.597297\pi$
$60$	−1.99081	−	0.149190i	−0.257012	−	0.0192604i
$61$	2.92847	−	0.441395i	0.374952	−	0.0565149i	0.0411368	−	0.999154i	$-0.486902\pi$
$61$	2.92847	−	0.441395i	0.374952	−	0.0565149i	0.333815	+	0.942639i	$0.391664\pi$
$62$	−1.39704	+	18.6422i	−0.177424	+	2.36756i
$63$	0.874064	+	6.09275i	0.110122	+	0.767614i
$64$	40.1833	+	19.3512i	5.02291	+	2.41891i
$65$	0.211583	+	0.495875i	0.0262436	+	0.0615057i
$66$	0.605357	−	0.0912428i	0.0745142	−	0.0112312i
$67$	1.17280	−	0.677116i	0.143280	−	0.0827229i	−0.426646	−	0.904419i	$-0.640305\pi$
$67$	1.17280	−	0.677116i	0.143280	−	0.0827229i	0.569926	+	0.821696i	$0.306972\pi$
$68$	−41.9367			−5.08557
$69$	−2.37541	+	6.05245i	−0.285966	+	0.728630i
$70$	0.317848	+	1.05707i	0.0379901	+	0.126344i
$71$	1.51701	−	10.0647i	0.180036	−	1.19446i	−0.698084	−	0.716016i	$-0.745964\pi$
$71$	1.51701	−	10.0647i	0.180036	−	1.19446i	0.878119	−	0.478442i	$-0.158798\pi$
$72$	22.8708	−	8.97614i	2.69535	−	1.05785i
$73$	−6.29968	−	9.23993i	−0.737322	−	1.08145i	−0.993389	−	0.114793i	$-0.963379\pi$
$73$	−6.29968	−	9.23993i	−0.737322	−	1.08145i	0.256068	−	0.966659i	$-0.417573\pi$
$74$	−13.6937	−	6.59454i	−1.59186	−	0.766600i
$75$	7.16260	−	8.98162i	0.827066	−	1.03711i
$76$	−13.5971	+	5.33648i	−1.55970	+	0.612136i
$77$	−0.124213	−	0.218720i	−0.0141553	−	0.0249255i
$78$	−17.4751	−	15.2867i	−1.97867	−	1.73088i
$79$	2.84793	+	4.93277i	0.320418	+	0.554980i	0.980574	−	0.196148i	$-0.0628434\pi$
$79$	2.84793	+	4.93277i	0.320418	+	0.554980i	−0.660157	+	0.751128i	$0.729510\pi$
$80$	2.31753	−	1.33803i	0.259108	−	0.149596i
$81$	−3.86057	+	9.83657i	−0.428952	+	1.09295i
$82$	−19.2387	−	5.93436i	−2.12456	−	0.655341i
$83$	−0.109670	+	0.227732i	−0.0120378	+	0.0249968i	−0.906901	−	0.421344i	$-0.861559\pi$
$83$	−0.109670	+	0.227732i	−0.0120378	+	0.0249968i	0.894863	+	0.446340i	$0.147273\pi$
$84$	−23.8419	−	26.0648i	−2.60136	−	2.84390i
$85$	−0.610607	+	0.895596i	−0.0662296	+	0.0971410i
$86$	−3.63061	−	1.42491i	−0.391498	−	0.153652i
$87$	2.79384	−	1.34544i	0.299531	−	0.144247i
$88$	−0.736002	+	0.682910i	−0.0784580	+	0.0727984i
$89$	−4.83820	+	10.0466i	−0.512848	+	1.06494i	0.470364	+	0.882472i	$0.344123\pi$
$89$	−4.83820	+	10.0466i	−0.512848	+	1.06494i	−0.983212	+	0.182467i	$0.941592\pi$
$90$	0.215978	−	0.946262i	0.0227661	−	0.0997448i
$91$	−3.28728	+	8.95510i	−0.344600	+	0.938750i
$92$	−3.62662	−	15.8892i	−0.378101	−	1.65657i
$93$	−15.0755	−	3.44089i	−1.56326	−	0.356803i
$94$	4.80340	+	0.723996i	0.495433	+	0.0746745i
$95$	−0.0840118	+	0.368080i	−0.00861942	+	0.0377642i
$96$	−37.4596	+	54.9432i	−3.82321	+	5.60762i
$97$	5.28921	−	3.05373i	0.537038	−	0.310059i	−0.206840	−	0.978375i	$-0.566318\pi$
$97$	5.28921	−	3.05373i	0.537038	−	0.310059i	0.743878	+	0.668316i	$0.232985\pi$
$98$	−8.72371	+	17.4747i	−0.881228	+	1.76521i
$99$			0.221171i			0.0222285i
$100$	−2.15192	+	28.7154i	−0.215192	+	2.87154i
$101$	4.25745	−	1.31325i	0.423632	−	0.130673i	−0.0756064	−	0.997138i	$-0.524089\pi$
$101$	4.25745	−	1.31325i	0.423632	−	0.130673i	0.499239	+	0.866464i	$0.333613\pi$
$102$	6.95735	−	46.1590i	0.688881	−	4.57042i
$103$	−6.74657	+	2.08104i	−0.664759	+	0.205051i	−0.608729	−	0.793378i	$-0.708320\pi$
$103$	−6.74657	+	2.08104i	−0.664759	+	0.205051i	−0.0560301	+	0.998429i	$0.517844\pi$
$104$	37.8029	+	4.56979i	3.70688	+	0.448105i
$105$	−0.903781	+	0.129656i	−0.0882000	+	0.0126531i
$106$	27.2218	−	29.3381i	2.64401	−	2.84957i
$107$	0.634342	+	0.305483i	0.0613242	+	0.0295322i	0.464294	−	0.885681i	$-0.346308\pi$
$107$	0.634342	+	0.305483i	0.0613242	+	0.0295322i	−0.402970	+	0.915213i	$0.632022\pi$
$108$	−2.00118	−	8.76774i	−0.192564	−	0.843676i
$109$	−12.8592	−	0.963663i	−1.23169	−	0.0923021i	−0.557067	−	0.830468i	$-0.688073\pi$
$109$	−12.8592	−	0.963663i	−1.23169	−	0.0923021i	−0.674620	+	0.738166i	$0.735692\pi$
$110$	0.00591155	+	0.0392206i	0.000563644	+	0.00373953i
$111$	7.08196	−	10.3873i	0.672190	−	0.985921i
$112$	46.0871	+	10.8645i	4.35482	+	1.02660i
$113$	0.00563538	+	0.0751990i	0.000530132	+	0.00707412i	0.997463	−	0.0711926i	$-0.0226805\pi$
$113$	0.00563538	+	0.0751990i	0.000530132	+	0.00707412i	−0.996932	+	0.0782667i	$0.975061\pi$
$114$	−3.61800	−	15.8515i	−0.338857	−	1.48463i
$115$	−0.392134	−	0.153901i	−0.0365666	−	0.0143514i
$116$	−3.88644	+	6.73151i	−0.360847	+	0.625005i
$117$	6.40200	−	5.41971i	0.591865	−	0.501053i
$118$	13.5119	+	16.9433i	1.24387	+	1.55976i
$119$	−18.7284	+	4.13473i	−1.71683	+	0.379030i
$120$	1.33150	+	3.39260i	0.121548	+	0.309700i
$121$	4.01545	+	10.2312i	0.365041	+	0.930109i
$122$	−4.65484	−	6.82739i	−0.421429	−	0.618123i
$123$	7.22558	−	15.0041i	0.651509	−	1.35287i
$124$	36.0812	−	14.1608i	3.24018	−	1.27168i
$125$	1.16644	+	0.930203i	0.104329	+	0.0831998i
$126$	14.2582	−	9.57321i	1.27022	−	0.852850i
$127$	−7.09752	+	1.06978i	−0.629803	+	0.0949275i	−0.456184	−	0.889885i	$-0.650784\pi$
$127$	−7.09752	+	1.06978i	−0.629803	+	0.0949275i	−0.173619	+	0.984813i	$0.555546\pi$
$128$		−	66.8156i		−	5.90572i
$129$	1.61304	−	2.79387i	0.142020	−	0.245986i
$130$	0.990415	−	1.13220i	0.0868651	−	0.0993005i
$131$	2.13007	−	1.97641i	0.186105	−	0.172680i	−0.581618	−	0.813462i	$-0.697580\pi$
$131$	2.13007	−	1.97641i	0.186105	−	0.172680i	0.767723	+	0.640782i	$0.221390\pi$
$132$	−0.715025	−	1.04875i	−0.0622349	−	0.0912819i
$133$	−5.54617	+	3.72381i	−0.480914	+	0.322896i
$134$	−3.12198	−	2.12853i	−0.269698	−	0.183877i
$135$	−0.216381	−	0.0849232i	−0.0186231	−	0.00730902i
$136$	33.2172	+	68.9762i	2.84835	+	5.91466i
$137$	20.0310	−	4.57194i	1.71136	−	0.390607i	0.749041	−	0.662524i	$-0.230515\pi$
$137$	20.0310	−	4.57194i	1.71136	−	0.390607i	0.962321	+	0.271916i	$0.0876574\pi$
$138$	18.0907	−	1.35571i	1.53998	−	0.115406i
$139$	11.0750	−	3.41619i	0.939372	−	0.289758i	0.212994	−	0.977054i	$-0.431679\pi$
$139$	11.0750	−	3.41619i	0.939372	−	0.289758i	0.726378	+	0.687296i	$0.241202\pi$
$140$	1.68872	−	1.54470i	0.142723	−	0.130551i
$141$	−1.18434	+	3.83953i	−0.0997391	+	0.323346i
$142$	−27.1377	+	8.37086i	−2.27734	+	0.702467i
$143$	−0.162619	+	0.301747i	−0.0135989	+	0.0252334i
$144$	−30.5209	−	28.3193i	−2.54341	−	2.35994i
$145$	0.0871702	+	0.181011i	0.00723909	+	0.0150321i
$146$	−15.6014	+	27.0224i	−1.29118	+	2.23639i
$147$	−13.2174	−	9.28956i	−1.09015	−	0.766190i
$148$			31.5129i			2.59034i
$149$	−18.1891	−	1.36309i	−1.49011	−	0.111668i	−0.695385	−	0.718637i	$-0.744766\pi$
$149$	−18.1891	−	1.36309i	−1.49011	−	0.111668i	−0.794726	+	0.606969i	$0.792385\pi$
$150$	−31.2496	−	7.13252i	−2.55152	−	0.582368i
$151$	−2.94773	+	1.15690i	−0.239883	+	0.0941471i	−0.482237	−	0.876041i	$-0.660176\pi$
$151$	−2.94773	+	1.15690i	−0.239883	+	0.0941471i	0.242354	+	0.970188i	$0.422080\pi$
$152$	19.5473	+	18.1373i	1.58550	+	1.47113i
$153$	16.1153	+	4.97090i	1.30284	+	0.401874i
$154$	−0.399459	+	0.577038i	−0.0321893	+	0.0464990i
$155$	0.222932	−	0.976731i	0.0179064	−	0.0784529i
$156$	−12.8356	+	46.3962i	−1.02767	+	3.71467i
$157$	−10.9109	−	3.36557i	−0.870787	−	0.268602i	−0.173012	−	0.984920i	$-0.555350\pi$
$157$	−10.9109	−	3.36557i	−0.870787	−	0.268602i	−0.697774	+	0.716318i	$0.745826\pi$
$158$	8.95254	−	13.1310i	0.712226	−	1.04464i
$159$	20.6402	+	25.8820i	1.63687	+	2.05257i
$160$	−3.55973	−	2.42698i	−0.281421	−	0.191870i
$161$	−3.18620	−	6.73838i	−0.251107	−	0.531059i
$162$	29.4014	−	2.20333i	2.30999	−	0.173110i
$163$	5.29990	−	17.1818i	0.415120	−	1.34579i	−0.470919	−	0.882176i	$-0.656078\pi$
$163$	5.29990	−	17.1818i	0.415120	−	1.34579i	0.886039	−	0.463610i	$-0.153446\pi$
$164$	6.22155	+	41.2773i	0.485822	+	3.22322i
$165$	−0.0328079			−0.00255409
$166$	0.705252			0.0547382
$167$	1.83757	+	12.1915i	0.142195	+	0.943405i	0.940168	+	0.340711i	$0.110668\pi$
$167$	1.83757	+	12.1915i	0.142195	+	0.943405i	−0.797973	+	0.602694i	$0.794094\pi$
$168$	−23.9860	+	59.8599i	−1.85056	+	4.61829i
$169$	12.7193	−	2.68705i	0.978405	−	0.206696i
$170$	2.99061	+	0.450761i	0.229369	+	0.0345718i
$171$	5.85761	−	0.438967i	0.447943	−	0.0335687i
$172$	0.604311	+	8.06397i	0.0460783	+	0.614872i
$173$	1.22856	+	3.13032i	0.0934058	+	0.237994i	0.969939	−	0.243347i	$-0.0782452\pi$
$173$	1.22856	+	3.13032i	0.0934058	+	0.237994i	−0.876534	+	0.481341i	$0.840150\pi$
$174$	−6.76450	−	5.39451i	−0.512816	−	0.408957i
$175$	1.87016	+	13.0361i	0.141371	+	0.985439i
$176$	1.58382	+	0.621604i	0.119385	+	0.0468552i
$177$	−15.5240	+	8.96278i	−1.16685	+	0.673684i
$178$	31.1129			2.33201
$179$	4.95915	−	12.6357i	0.370664	−	0.944436i	−0.616875	−	0.787061i	$-0.711602\pi$
$179$	4.95915	−	12.6357i	0.370664	−	0.944436i	0.987539	−	0.157375i	$-0.0503032\pi$
$180$	−1.96195	+	0.447803i	−0.146235	+	0.0333772i
$181$	−10.8992	−	5.24877i	−0.810129	−	0.390138i	−0.0175041	−	0.999847i	$-0.505572\pi$
$181$	−10.8992	−	5.24877i	−0.810129	−	0.390138i	−0.792625	+	0.609709i	$0.791286\pi$
$182$	26.4915	−	2.57739i	1.96368	−	0.191049i
$183$	6.15809	−	2.96558i	0.455219	−	0.219222i
$184$	−23.2616	+	18.5505i	−1.71487	+	1.36756i
$185$	0.672987	+	0.458834i	0.0494790	+	0.0337342i
$186$	9.60067	+	42.0633i	0.703955	+	3.08423i
$187$	−0.687244	+	0.0515018i	−0.0502562	+	0.00376618i
$188$	−2.96869	−	9.62426i	−0.216514	−	0.701922i
$189$	−1.75815	−	3.71827i	−0.127887	−	0.270464i
$190$	1.02701	−	0.234407i	0.0745068	−	0.0170057i
$191$	7.42488	+	6.88929i	0.537246	+	0.498491i	0.901483	−	0.432815i	$-0.142480\pi$
$191$	7.42488	+	6.88929i	0.537246	+	0.498491i	−0.364237	+	0.931306i	$0.618670\pi$
$192$	101.783	+	15.3413i	7.34556	+	1.10716i
$193$	−2.23162	−	7.23473i	−0.160635	−	0.520767i	0.839095	−	0.543985i	$-0.183085\pi$
$193$	−2.23162	−	7.23473i	−0.160635	−	0.520767i	−0.999730	+	0.0232175i	$0.992609\pi$
$194$	−14.0798	−	9.59944i	−1.01087	−	0.689200i
$195$	0.803945	+	0.949655i	0.0575717	+	0.0680062i
$196$	40.4913	+	0.576000i	2.89224	+	0.0411428i
$197$	−1.55409	−	0.897253i	−0.110724	−	0.0639266i	0.443615	−	0.896217i	$-0.353696\pi$
$197$	−1.55409	−	0.897253i	−0.110724	−	0.0639266i	−0.554339	+	0.832291i	$0.687029\pi$
$198$	0.555993	−	0.267752i	0.0395127	−	0.0190283i
$199$	3.20907	−	14.0598i	0.227485	−	0.996676i	−0.724198	−	0.689592i	$-0.757790\pi$
$199$	3.20907	−	14.0598i	0.227485	−	0.996676i	0.951683	−	0.307084i	$-0.0993532\pi$
$200$	48.9348	−	19.2055i	3.46021	−	1.35803i
$201$	2.12584	−	2.29111i	0.149945	−	0.161602i
$202$	−8.45544	−	9.11279i	−0.594923	−	0.641174i
$203$	−1.07195	+	3.38939i	−0.0752360	+	0.237889i
$204$	−92.4858	+	28.5281i	−6.47530	+	1.99737i
$205$	0.972102	+	0.468140i	0.0678945	+	0.0326963i
$206$	13.3989	+	14.4406i	0.933546	+	1.00612i
$207$	−0.489786	+	6.53574i	−0.0340425	+	0.454265i
$208$	−20.8180	−	61.0773i	−1.44347	−	4.23495i
$209$	−0.216272	+	0.104151i	−0.0149598	+	0.00720427i
$210$	1.42006	+	2.11501i	0.0979937	+	0.145950i
$211$	−10.5595	+	7.19931i	−0.726943	+	0.495621i	−0.869356	−	0.494186i	$-0.835466\pi$
$211$	−10.5595	+	7.19931i	−0.726943	+	0.495621i	0.142413	+	0.989807i	$0.454514\pi$
$212$	−79.2936	−	24.4588i	−5.44591	−	1.67984i
$213$	−3.50110	−	23.2283i	−0.239892	−	1.59158i
$214$		−	1.96447i		−	0.134288i
$215$	0.181012	+	0.104508i	0.0123449	+	0.00712736i
$216$	−12.8358	+	10.2362i	−0.873368	+	0.696488i
$217$	14.7172	−	9.88146i	0.999072	−	0.670797i
$218$	13.1449	+	33.4928i	0.890288	+	2.26842i
$219$	−20.1787	−	16.0920i	−1.36355	−	1.08740i
$220$	0.0679476	−	0.0463259i	0.00458103	−	0.00312329i
$221$	18.3314	+	18.6309i	1.23310	+	1.25325i
$222$	−34.6858	−	5.22804i	−2.32796	−	0.350883i
$223$	8.92795	−	3.50396i	0.597860	−	0.234643i	−0.0470613	−	0.998892i	$-0.514986\pi$
$223$	8.92795	−	3.50396i	0.597860	−	0.234643i	0.644921	+	0.764249i	$0.276890\pi$
$224$	−16.4343	−	74.4399i	−1.09806	−	4.97372i
$225$	4.23068	−	10.7796i	0.282045	−	0.718639i
$226$	0.182217	−	0.105203i	0.0121209	−	0.00699801i
$227$			15.5078i			1.02929i	0.857405	+	0.514643i	$0.172076\pi$
$227$			15.5078i			1.02929i	−0.857405	+	0.514643i	$0.827924\pi$
$228$	−26.3565	+	21.0186i	−1.74550	+	1.39199i
$229$	8.30581	+	8.95153i	0.548863	+	0.591534i	0.945168	−	0.326585i	$-0.105898\pi$
$229$	8.30581	+	8.95153i	0.548863	+	0.591534i	−0.396304	+	0.918119i	$0.629708\pi$
$230$	0.0878354	+	1.17208i	0.00579170	+	0.0772848i
$231$	−0.422723	−	0.397862i	−0.0278131	−	0.0261774i
$232$	14.1502	+	1.06041i	0.929004	+	0.0696192i
$233$	10.4159	−	26.5392i	0.682365	−	1.73864i	0.00830088	−	0.999966i	$-0.497358\pi$
$233$	10.4159	−	26.5392i	0.682365	−	1.73864i	0.674064	−	0.738673i	$-0.264547\pi$
$234$	−21.3747	−	9.53256i	−1.39731	−	0.623163i
$235$	−0.248760	−	0.0767322i	−0.0162273	−	0.00500546i
$236$	19.4956	−	40.4830i	1.26905	−	2.63522i
$237$	9.63635	+	8.94122i	0.625948	+	0.580795i
$238$	33.0669	+	42.0750i	2.14341	+	2.72732i
$239$	−22.5990	+	5.15807i	−1.46181	+	0.333648i	−0.878162	−	0.478363i	$-0.841230\pi$
$239$	−22.5990	+	5.15807i	−1.46181	+	0.333648i	−0.583643	+	0.812010i	$0.698373\pi$
$240$	4.20080	−	4.52738i	0.271160	−	0.292241i
$241$	−13.8063	−	11.0102i	−0.889343	−	0.709227i	0.0681528	−	0.997675i	$-0.478289\pi$
$241$	−13.8063	−	11.0102i	−0.889343	−	0.709227i	−0.957496	+	0.288448i	$0.906861\pi$
$242$	20.8586	−	22.4803i	1.34084	−	1.44509i
$243$	−1.47398	+	19.6689i	−0.0945557	+	1.26176i
$244$	−8.56635	+	14.8374i	−0.548405	+	0.949864i
$245$	0.601863	−	0.856342i	0.0384516	−	0.0547097i
$246$	−46.4655			−2.96253
$247$	8.31439	+	3.70800i	0.529032	+	0.235934i
$248$	−51.8705	−	48.1288i	−3.29378	−	3.05618i
$249$	−0.0869442	+	0.576837i	−0.00550986	+	0.0365556i
$250$	0.926296	−	4.05837i	0.0585841	−	0.256674i
$251$	7.01508	−	6.50904i	0.442788	−	0.410847i	−0.427017	−	0.904244i	$-0.640435\pi$
$251$	7.01508	−	6.50904i	0.442788	−	0.410847i	0.869804	+	0.493397i	$0.164245\pi$
$252$	−30.7098	−	18.0227i	−1.93454	−	1.13533i
$253$	−0.0789451	−	0.255934i	−0.00496324	−	0.0160904i
$254$	11.2816	+	16.5471i	0.707870	+	1.03825i
$255$	−0.737370	+	2.39049i	−0.0461759	+	0.149699i
$256$	−87.5983	+	42.1851i	−5.47489	+	2.63657i
$257$	−9.04027	−	11.3361i	−0.563916	−	0.707129i	0.415360	−	0.909657i	$-0.363656\pi$
$257$	−9.04027	−	11.3361i	−0.563916	−	0.707129i	−0.979276	+	0.202528i	$0.935084\pi$
$258$	−8.97615	−	0.672669i	−0.558830	−	0.0418786i
$259$	3.10700	+	14.0733i	0.193060	+	0.874471i
$260$	−3.00597	−	0.831607i	−0.186423	−	0.0515741i
$261$	2.29138	−	2.12609i	0.141833	−	0.131602i
$262$	−7.54710	−	2.96202i	−0.466262	−	0.182994i
$263$	−14.0381	−	24.3146i	−0.865624	−	1.49930i	−0.866426	−	0.499305i	$-0.833589\pi$
$263$	−14.0381	−	24.3146i	−0.865624	−	1.49930i	0.000802136	−	1.00000i	$-0.499745\pi$
$264$	−1.15860	+	2.00675i	−0.0713066	+	0.123507i
$265$	−1.67687	+	1.33726i	−0.103009	+	0.0821473i
$266$	16.0754	+	9.43420i	0.985645	+	0.578448i
$267$	−3.83563	+	25.4478i	−0.234737	+	1.55738i
$268$	−1.16764	+	7.74681i	−0.0713252	+	0.473212i
$269$	−23.5240	−	11.3286i	−1.43429	−	0.690715i	−0.454496	−	0.890749i	$-0.650181\pi$
$269$	−23.5240	−	11.3286i	−1.43429	−	0.690715i	−0.979789	+	0.200033i	$0.935895\pi$
$270$	0.0484679	+	0.646759i	0.00294966	+	0.0393605i
$271$	−0.514099	−	0.409980i	−0.0312293	−	0.0249045i	0.607751	−	0.794128i	$-0.292072\pi$
$271$	−0.514099	−	0.409980i	−0.0312293	−	0.0249045i	−0.638980	+	0.769223i	$0.720643\pi$
$272$	80.8891	−	101.432i	4.90462	−	6.15020i
$273$	−1.15780	+	21.9855i	−0.0700734	+	1.33062i
$274$	−35.7429	−	44.8202i	−2.15931	−	2.70769i
$275$			0.473221i			0.0285363i
$276$	−18.8069	−	32.5746i	−1.13205	−	1.96076i
$277$	−15.0873	−	18.9189i	−0.906508	−	1.13673i	−0.990119	−	0.140227i	$-0.955217\pi$
$277$	−15.0873	−	18.9189i	−0.906508	−	1.13673i	0.0836114	−	0.996498i	$-0.473355\pi$
$278$	−21.9954	−	23.7054i	−1.31919	−	1.42175i
$279$	−15.5437	+	1.16484i	−0.930576	+	0.0697370i
$280$	−3.87827	−	1.55403i	−0.231771	−	0.0928712i
$281$	−3.94628	−	8.19454i	−0.235415	−	0.488845i	0.749473	−	0.662035i	$-0.230307\pi$
$281$	−3.94628	−	8.19454i	−0.235415	−	0.488845i	−0.984889	+	0.173190i	$0.944593\pi$
$282$	11.0858	−	1.67091i	0.660149	−	0.0995015i
$283$	−13.4157	−	9.14668i	−0.797481	−	0.543713i	0.0946390	−	0.995512i	$-0.469830\pi$
$283$	−13.4157	−	9.14668i	−0.797481	−	0.543713i	−0.892120	+	0.451798i	$0.850783\pi$
$284$	40.0502	+	43.1639i	2.37654	+	2.56130i
$285$	0.0651152	+	0.868902i	0.00385709	+	0.0514693i
$286$	0.955418	+	0.0435028i	0.0564951	+	0.00257237i
$287$	6.84819	+	17.8206i	0.404236	+	1.05191i
$288$	−19.7579	+	64.0534i	−1.16424	+	3.77438i
$289$	−7.91061	+	34.6586i	−0.465330	+	2.03874i
$290$	0.349506	−	0.438267i	0.0205237	−	0.0257359i
$291$	9.58731	−	10.3327i	0.562018	−	0.605712i
$292$	64.5141	+	4.83466i	3.77540	+	0.282927i
$293$	−12.8445	+	7.41579i	−0.750385	+	0.433235i	−0.825833	−	0.563915i	$-0.809295\pi$
$293$	−12.8445	+	7.41579i	−0.750385	+	0.433235i	0.0754480	+	0.997150i	$0.475961\pi$
$294$	−7.35156	+	44.4726i	−0.428752	+	2.59369i
$295$	−0.580692	−	1.00579i	−0.0338092	−	0.0585592i
$296$	51.8315	−	24.9607i	3.01264	−	1.45081i
$297$	−0.0435622	−	0.141225i	−0.00252773	−	0.00819472i
$298$	18.5933	+	47.3750i	1.07708	+	2.74436i
$299$	−5.47371	+	8.55669i	−0.316553	+	0.494846i
$300$	14.7884	+	64.7920i	0.853806	+	3.74077i
$301$	1.06494	+	3.54169i	0.0613822	+	0.204140i
$302$	6.47683	+	6.00962i	0.372700	+	0.345815i
$303$	8.49590	−	5.79240i	0.488077	−	0.332765i
$304$	13.3194	−	43.1805i	0.763921	−	2.47657i
$305$	0.192137	+	0.398977i	0.0110018	+	0.0228454i
$306$	−7.01317	−	46.5293i	−0.400916	−	2.65991i
$307$	−0.863237	−	1.79253i	−0.0492675	−	0.102305i	0.874882	−	0.484336i	$-0.160939\pi$
$307$	−0.863237	−	1.79253i	−0.0492675	−	0.102305i	−0.924149	+	0.382031i	$0.875225\pi$
$308$	1.43728	+	0.227102i	0.0818969	+	0.0129403i
$309$	−13.4630	+	9.17893i	−0.765885	+	0.522171i
$310$	−2.72525	+	0.622020i	−0.154784	+	0.0353283i
$311$	−13.0681	+	1.96970i	−0.741024	+	0.111691i	−0.508696	−	0.860946i	$-0.669872\pi$
$311$	−13.0681	+	1.96970i	−0.741024	+	0.111691i	−0.232328	+	0.972637i	$0.574634\pi$
$312$	86.4780	−	15.6379i	4.89585	−	0.885324i
$313$	5.65496	+	9.79469i	0.319637	+	0.553628i	0.980412	−	0.196956i	$-0.0631055\pi$
$313$	5.65496	+	9.79469i	0.319637	+	0.553628i	−0.660775	+	0.750584i	$0.729772\pi$
$314$	4.74830	+	31.5029i	0.267962	+	1.77781i
$315$	−0.832034	+	0.393421i	−0.0468798	+	0.0221668i
$316$	−32.5829	−	4.91108i	−1.83293	−	0.276270i
$317$	−1.74620	+	11.5853i	−0.0980765	+	0.650695i	0.884737	+	0.466091i	$0.154338\pi$
$317$	−1.74620	+	11.5853i	−0.0980765	+	0.650695i	−0.982813	+	0.184604i	$0.940900\pi$
$318$	40.0764	−	83.2195i	2.24737	−	4.66672i
$319$	−0.0554228	+	0.115087i	−0.00310308	+	0.00644361i
$320$	−0.993952	+	6.59444i	−0.0555636	+	0.368640i
$321$	1.60677	+	0.242181i	0.0896811	+	0.0135172i
$322$	−13.0821	+	16.1672i	−0.729037	+	0.900963i
$323$	2.72800	+	18.0991i	0.151790	+	1.00706i
$324$	−30.5654	−	52.9409i	−1.69808	−	2.94116i
$325$	13.6978	−	11.5961i	0.759818	−	0.643236i
$326$	−49.6088	+	7.47733i	−2.74758	+	0.414131i
$327$	−29.0148	+	6.62244i	−1.60452	+	0.366222i
$328$	62.9638	−	42.9280i	3.47659	−	2.37030i
$329$	−2.27468	−	4.00539i	−0.125407	−	0.220824i
$330$	0.0397176	+	0.0824744i	0.00218638	+	0.00454007i
$331$	−1.17568	−	7.80011i	−0.0646211	−	0.428733i	−0.997626	−	0.0688686i	$-0.978061\pi$
$331$	−1.17568	−	7.80011i	−0.0646211	−	0.428733i	0.933005	−	0.359864i	$-0.117177\pi$
$332$	−0.634446	−	1.31744i	−0.0348197	−	0.0723039i
$333$	3.73534	−	12.1097i	0.204695	−	0.663606i
$334$	28.4231	−	19.3785i	1.55524	−	1.06034i
$335$	0.148439	+	0.137731i	0.00811010	+	0.00752507i
$336$	109.030	−	7.39127i	5.94807	−	0.403227i
$337$	3.77430	+	16.5363i	0.205599	+	0.900789i	0.967455	+	0.253042i	$0.0814312\pi$
$337$	3.77430	+	16.5363i	0.205599	+	0.900789i	−0.761856	+	0.647746i	$0.775712\pi$
$338$	−22.1529	−	28.7215i	−1.20496	−	1.56224i
$339$	0.0635834	+	0.162008i	0.00345338	+	0.00879906i
$340$	−1.84831	−	5.99208i	−0.100239	−	0.324966i
$341$	0.573895	−	0.276373i	0.0310782	−	0.0149665i
$342$	−8.19479	−	14.1938i	−0.443123	−	0.767512i
$343$	18.1397	−	3.73499i	0.979453	−	0.201670i
$344$	12.7847	−	7.38126i	0.689306	−	0.397971i
$345$	−0.969493	−	0.0726535i	−0.0521958	−	0.00391153i
$346$	6.38188	−	6.87803i	0.343092	−	0.369765i
$347$	−4.47969	+	5.61735i	−0.240482	+	0.301555i	−0.887396	−	0.461008i	$-0.847488\pi$
$347$	−4.47969	+	5.61735i	−0.240482	+	0.301555i	0.646914	+	0.762563i	$0.276059\pi$
$348$	−3.99181	+	17.4893i	−0.213984	+	0.937524i
$349$	8.84494	−	28.6746i	0.473459	−	1.53492i	−0.332592	−	0.943071i	$-0.607923\pi$
$349$	8.84494	−	28.6746i	0.473459	−	1.53492i	0.806051	−	0.591846i	$-0.201601\pi$
$350$	30.5070	−	20.4830i	1.63067	−	1.09486i
$351$	−3.02041	+	4.72161i	−0.161218	+	0.252021i
$352$	−0.204704	−	2.73159i	−0.0109108	−	0.145594i
$353$	13.0879	+	14.1054i	0.696599	+	0.750755i	0.977948	−	0.208851i	$-0.0669723\pi$
$353$	13.0879	+	14.1054i	0.696599	+	0.750755i	−0.281349	+	0.959606i	$0.590782\pi$
$354$	41.3247	+	28.1747i	2.19638	+	1.49747i
$355$	1.50494	−	0.226834i	0.0798741	−	0.0120391i
$356$	−27.9892	−	58.1203i	−1.48343	−	3.08037i
$357$	−38.4904	+	21.8589i	−2.03713	+	1.15690i
$358$	−37.7679	+	2.83032i	−1.99610	+	0.149587i
$359$	−4.49617	−	4.84572i	−0.237299	−	0.255747i	0.603163	−	0.797618i	$-0.293907\pi$
$359$	−4.49617	−	4.84572i	−0.237299	−	0.255747i	−0.840462	+	0.541871i	$0.817716\pi$
$360$	2.29056	+	2.87227i	0.120723	+	0.151382i
$361$	−6.31237	−	10.9333i	−0.332230	−	0.575439i
$362$			33.7532i			1.77403i
$363$	15.8155	+	19.8320i	0.830098	+	1.04091i
$364$	−28.6464	−	47.1685i	−1.50148	−	2.47230i
$365$	1.04259	−	1.30736i	0.0545716	−	0.0684306i
$366$	−14.9101	−	11.8904i	−0.779362	−	0.621521i
$367$	1.00003	+	13.3444i	0.0522009	+	0.696573i	0.960505	+	0.278262i	$0.0897585\pi$
$367$	1.00003	+	13.3444i	0.0522009	+	0.696573i	−0.908304	+	0.418310i	$0.862622\pi$
$368$	45.4263	+	21.8762i	2.36801	+	1.14037i
$369$	2.50195	−	16.5994i	0.130246	−	0.864129i
$370$	0.338720	−	2.24726i	0.0176092	−	0.116830i
$371$	−37.8231	−	3.10511i	−1.96368	−	0.161209i
$372$	69.9392	−	55.7746i	3.62618	−	2.89178i
$373$	5.25732	−	9.10595i	0.272214	−	0.471488i	−0.697215	−	0.716862i	$-0.745578\pi$
$373$	5.25732	−	9.10595i	0.272214	−	0.471488i	0.969428	+	0.245374i	$0.0789109\pi$
$374$	0.961452	+	1.66528i	0.0497155	+	0.0861098i
$375$	3.20521	+	1.25795i	0.165516	+	0.0649604i
$376$	−13.4783	+	12.5060i	−0.695089	+	0.644948i
$377$	4.68940	−	1.21589i	0.241516	−	0.0626215i
$378$	−7.21875	+	8.92112i	−0.371292	+	0.458853i
$379$	1.23644	+	0.0926580i	0.0635114	+	0.00475952i	0.106448	−	0.994318i	$-0.466052\pi$
$379$	1.23644	+	0.0926580i	0.0635114	+	0.00475952i	−0.0429365	+	0.999078i	$0.513671\pi$
$380$	−1.36178	−	1.70762i	−0.0698577	−	0.0875988i
$381$	−14.9249	+	7.18746i	−0.764626	+	0.368225i
$382$	8.33004	−	27.0053i	0.426202	−	1.38171i
$383$	−0.891159	−	1.30709i	−0.0455361	−	0.0667892i	0.802796	−	0.596254i	$-0.203345\pi$
$383$	−0.891159	−	1.30709i	−0.0455361	−	0.0667892i	−0.848332	+	0.529465i	$0.822393\pi$
$384$	−45.4524	−	147.353i	−2.31948	−	7.51958i
$385$	0.0257771	−	0.0273879i	0.00131372	−	0.00139582i
$386$	−15.4855	+	14.3684i	−0.788190	+	0.731333i
$387$	0.723629	−	3.17043i	0.0367842	−	0.161162i
$388$	−5.26595	+	34.9373i	−0.267338	+	1.77367i
$389$	−4.86433	−	4.51344i	−0.246631	−	0.228840i	0.547164	−	0.837025i	$-0.315707\pi$
$389$	−4.86433	−	4.51344i	−0.246631	−	0.228840i	−0.793795	+	0.608185i	$0.791898\pi$
$390$	1.41403	−	3.17067i	0.0716023	−	0.160553i
$391$	−20.4225			−1.03281
$392$	−31.1250	−	67.0552i	−1.57205	−	3.38680i
$393$	3.35310	−	5.80774i	0.169141	−	0.292962i
$394$	−0.374172	+	4.99298i	−0.0188505	+	0.251543i
$395$	−0.579295	+	0.624331i	−0.0291475	+	0.0314135i
$396$	−1.00034	−	0.797748i	−0.0502692	−	0.0400883i
$397$	−14.3798	+	15.4978i	−0.721704	+	0.777812i	−0.982235	−	0.187654i	$-0.939912\pi$
$397$	−14.3798	+	15.4978i	−0.721704	+	0.777812i	0.260531	+	0.965465i	$0.416102\pi$
$398$	−39.2294	+	8.95385i	−1.96639	+	0.448816i
$399$	−9.69818	+	11.9853i	−0.485516	+	0.600014i
$400$	−65.3030	−	60.5923i	−3.26515	−	3.02962i
$401$	−2.34640	+	4.87236i	−0.117174	+	0.243314i	−0.951304	−	0.308253i	$-0.900256\pi$
$401$	−2.34640	+	4.87236i	−0.117174	+	0.243314i	0.834131	+	0.551567i	$0.185970\pi$
$402$	−8.33308	−	2.57042i	−0.415616	−	0.128201i
$403$	−22.0630	−	9.83949i	−1.09903	−	0.490140i
$404$	−9.41656	+	23.9930i	−0.468491	+	1.19370i
$405$	−1.57564	−	0.118078i	−0.0782942	−	0.00586734i
$406$	9.81817	−	1.40851i	0.487267	−	0.0699032i
$407$	0.0387005	+	0.516423i	0.00191831	+	0.0255981i
$408$	120.178	+	129.521i	5.94972	+	6.41227i
$409$	3.90240	−	3.11206i	0.192961	−	0.153882i	−0.522244	−	0.852796i	$-0.674905\pi$
$409$	3.90240	−	3.11206i	0.192961	−	0.153882i	0.715205	+	0.698915i	$0.246333\pi$
$410$		−	3.01046i		−	0.148676i
$411$	41.0656	−	23.7092i	2.02562	−	1.16949i
$412$	14.9219	−	38.0205i	0.735151	−	1.87314i
$413$	4.71510	−	20.0014i	0.232015	−	0.984204i
$414$	17.0229	−	6.68098i	0.836628	−	0.328352i
$415$	−0.0373728	−	0.00563304i	−0.00183456	−	0.000276515i
$416$	−74.0521	+	72.8619i	−3.63070	+	3.57235i
$417$	22.1006	−	15.0679i	1.08227	−	0.737880i
$418$	0.523641	+	0.417590i	0.0256121	+	0.0204250i
$419$	12.4545	+	31.7335i	0.608441	+	1.55028i	0.819664	+	0.572844i	$0.194160\pi$
$419$	12.4545	+	31.7335i	0.608441	+	1.55028i	−0.211224	+	0.977438i	$0.567745\pi$
$420$	2.67344	−	4.55541i	0.130451	−	0.222281i
$421$	−7.73838	+	6.17115i	−0.377146	+	0.300764i	−0.793655	−	0.608368i	$-0.791825\pi$
$421$	−7.73838	+	6.17115i	−0.377146	+	0.300764i	0.416510	+	0.909131i	$0.363253\pi$
$422$	30.8814	+	17.8294i	1.50328	+	0.867922i
$423$			4.05027i			0.196931i
$424$	22.5777	+	149.793i	1.09647	+	7.27460i
$425$	34.4805	+	10.6358i	1.67255	+	0.515913i
$426$	−54.1542	+	36.9217i	−2.62378	+	1.78886i
$427$	−2.36275	+	7.47079i	−0.114341	+	0.361537i
$428$	−3.66970	+	1.76724i	−0.177382	+	0.0854226i
$429$	−0.153367	+	0.776089i	−0.00740461	+	0.0374699i
$430$	0.0435817	−	0.581557i	0.00210170	−	0.0280452i
$431$	−13.7750	−	14.8459i	−0.663517	−	0.715101i	0.308181	−	0.951328i	$-0.400280\pi$
$431$	−13.7750	−	14.8459i	−0.663517	−	0.715101i	−0.971698	+	0.236226i	$0.924089\pi$
$432$	25.0664	+	12.0713i	1.20601	+	0.580783i
$433$	8.02837	−	2.47642i	0.385819	−	0.119009i	−0.0957770	−	0.995403i	$-0.530534\pi$
$433$	8.02837	−	2.47642i	0.385819	−	0.119009i	0.481596	+	0.876394i	$0.340057\pi$
$434$	−42.6574	−	25.0345i	−2.04762	−	1.20169i
$435$	0.315378	+	0.339897i	0.0151212	+	0.0162968i
$436$	50.7407	−	54.6855i	2.43004	−	2.61896i
$437$	−6.62160	+	2.59878i	−0.316754	+	0.124317i
$438$	−16.0244	+	70.2076i	−0.765677	+	3.35465i
$439$	11.2299	−	5.40805i	0.535976	−	0.258112i	−0.146258	−	0.989246i	$-0.546723\pi$
$439$	11.2299	−	5.40805i	0.535976	−	0.258112i	0.682234	+	0.731134i	$0.261009\pi$
$440$	−0.130015	−	0.0750645i	−0.00619824	−	0.00357856i
$441$	−15.4916	−	5.02093i	−0.737695	−	0.239092i
$442$	24.6431	−	68.6372i	1.17215	−	3.26474i
$443$	−30.5165	−	20.8058i	−1.44988	−	0.988512i	−0.995200	−	0.0978576i	$-0.968801\pi$
$443$	−30.5165	−	20.8058i	−1.44988	−	0.988512i	−0.454681	−	0.890655i	$-0.650247\pi$
$444$	21.4372	+	69.4976i	1.01736	+	3.29821i
$445$	−1.64874	−	0.248508i	−0.0781578	−	0.0117804i
$446$	−19.6167	−	18.2017i	−0.928879	−	0.861873i
$447$	−41.0410	+	9.36734i	−1.94117	+	0.443060i
$448$	−92.7776	+	72.9142i	−4.38333	+	3.44487i
$449$	6.04920	+	19.6110i	0.285479	+	0.925502i	0.978791	+	0.204863i	$0.0656750\pi$
$449$	6.04920	+	19.6110i	0.285479	+	0.925502i	−0.693311	+	0.720638i	$0.743849\pi$
$450$	−32.2201	+	2.41456i	−1.51887	+	0.113823i
$451$	0.152649	+	0.668798i	0.00718795	+	0.0314925i
$452$	−0.360447	−	0.245748i	−0.0169540	−	0.0115590i
$453$	−5.71384	+	4.55663i	−0.268460	+	0.214089i
$454$	38.9843	−	18.7738i	1.82962	−	0.881100i
$455$	−1.42443	−	0.0750131i	−0.0667781	−	0.00351667i
$456$	55.4472	+	26.7020i	2.59655	+	1.25043i
$457$	12.5916	−	2.87394i	0.589008	−	0.134437i	0.0823785	−	0.996601i	$-0.473748\pi$
$457$	12.5916	−	2.87394i	0.589008	−	0.134437i	0.506629	+	0.862164i	$0.330891\pi$
$458$	12.4478	−	31.7164i	0.581647	−	1.48201i
$459$	−11.2692			−0.526002
$460$	2.11048	−	1.21849i	0.0984017	−	0.0568123i
$461$	30.0315	+	11.7865i	1.39871	+	0.548951i	0.940469	−	0.339879i	$-0.110386\pi$
$461$	30.0315	+	11.7865i	1.39871	+	0.548951i	0.458236	+	0.888830i	$0.348481\pi$
$462$	−0.488415	+	1.54432i	−0.0227231	+	0.0718483i
$463$	−0.544781	−	0.434449i	−0.0253181	−	0.0201905i	0.610749	−	0.791824i	$-0.290868\pi$
$463$	−0.544781	−	0.434449i	−0.0253181	−	0.0201905i	−0.636067	+	0.771634i	$0.719440\pi$
$464$	−8.78511	−	22.3841i	−0.407839	−	1.03916i
$465$	−0.172789	−	2.30571i	−0.00801289	−	0.106925i
$466$	−79.3252	+	5.94460i	−3.67467	+	0.275378i
$467$	29.2697	+	4.41170i	1.35444	+	0.204149i	0.785823	−	0.618452i	$-0.212240\pi$
$467$	29.2697	+	4.41170i	1.35444	+	0.204149i	0.568619	+	0.822601i	$0.307478\pi$
$468$	1.42151	+	48.5044i	0.0657095	+	2.24212i
$469$	0.242337	+	3.57476i	0.0111901	+	0.165067i
$470$	0.108257	+	0.718239i	0.00499353	+	0.0331299i
$471$	−26.3521			−1.21424
$472$	−82.0273			−3.77561
$473$	0.0198065	+	0.131408i	0.000910704	+	0.00604212i
$474$	10.8111	−	35.0487i	0.496570	−	1.60984i
$475$	12.5330	−	0.939222i	0.575055	−	0.0430944i
$476$	48.8509	−	99.6211i	2.23908	−	4.56613i
$477$	27.5715	+	18.7979i	1.26241	+	0.860698i
$478$	40.3252	+	50.5662i	1.84443	+	2.31284i
$479$	2.11983	−	3.10921i	0.0968573	−	0.142064i	−0.774751	−	0.632266i	$-0.782125\pi$
$479$	2.11983	−	3.10921i	0.0968573	−	0.142064i	0.871608	+	0.490203i	$0.163077\pi$
$480$	−9.50151	−	2.93083i	−0.433682	−	0.133773i
$481$	14.0000	−	13.7750i	0.638344	−	0.628084i
$482$	−10.9639	+	48.0361i	−0.499393	+	2.18799i
$483$	−11.6106	−	12.6932i	−0.528302	−	0.577559i
$484$	−60.7585	−	18.7415i	−2.76175	−	0.851887i
$485$	0.669445	+	0.621154i	0.0303979	+	0.0282052i
$486$	51.2291	−	20.1059i	2.32380	−	0.912024i
$487$	−38.1117	−	8.69875i	−1.72701	−	0.394178i	−0.760200	−	0.649689i	$-0.774899\pi$
$487$	−38.1117	−	8.69875i	−1.72701	−	0.394178i	−0.966806	+	0.255512i	$0.917756\pi$
$488$	31.1893	+	2.33731i	1.41187	+	0.105805i
$489$		−	41.4977i		−	1.87659i
$490$	−2.88134	−	0.476302i	−0.130166	−	0.0215171i
$491$	−12.8502	+	22.2572i	−0.579921	+	1.00445i	0.415566	+	0.909563i	$0.363583\pi$
$491$	−12.8502	+	22.2572i	−0.579921	+	1.00445i	−0.995488	+	0.0948904i	$0.969750\pi$
$492$	41.8004	+	86.7994i	1.88451	+	3.91322i
$493$	7.13995	+	6.62490i	0.321567	+	0.298371i
$494$	−0.744107	−	25.3901i	−0.0334790	−	1.14236i
$495$	−0.0316019	+	0.00974788i	−0.00142040	+	0.000438135i
$496$	−35.3442	+	114.583i	−1.58700	+	5.14493i
$497$	22.1417	+	15.3277i	0.993190	+	0.687543i
$498$	1.55534	−	0.479759i	0.0696965	−	0.0214985i
$499$	−34.9881	+	2.62200i	−1.56628	+	0.117377i	−0.829404	−	0.558649i	$-0.811320\pi$
$499$	−34.9881	+	2.62200i	−1.56628	+	0.117377i	−0.736878	+	0.676025i	$0.763701\pi$
$500$	−8.41450	+	1.92055i	−0.376308	+	0.0858898i
$501$	12.3460	+	25.6367i	0.551577	+	1.14536i
$502$	−24.8553	−	9.75500i	−1.10935	−	0.435387i
$503$	10.0092	+	6.82418i	0.446290	+	0.304275i	0.765532	−	0.643398i	$-0.222476\pi$
$503$	10.0092	+	6.82418i	0.446290	+	0.304275i	−0.319242	+	0.947673i	$0.603428\pi$
$504$	−5.31866	+	64.7861i	−0.236912	+	2.88580i
$505$	0.375285	+	0.550442i	0.0167000	+	0.0244944i
$506$	−0.547809	+	0.508293i	−0.0243531	+	0.0225964i
$507$	26.2228	−	14.5784i	1.16459	−	0.647451i
$508$	20.7617	−	35.9602i	0.921150	−	1.59548i
$509$			34.6879i			1.53752i	0.639540	+	0.768758i	$0.279125\pi$
$509$			34.6879i			1.53752i	−0.639540	+	0.768758i	$0.720875\pi$
$510$	6.90203	−	1.04031i	0.305627	−	0.0460659i
$511$	29.2879	−	4.20164i	1.29562	−	0.185869i
$512$	107.618	+	85.8222i	4.75607	+	3.79284i
$513$	−3.65382	+	1.43402i	−0.161320	+	0.0633135i
$514$	−17.5532	+	36.4496i	−0.774238	+	1.60772i
$515$	−0.594696	−	0.872258i	−0.0262054	−	0.0384363i
$516$	6.81838	+	17.3729i	0.300162	+	0.764801i
$517$	−0.0604693	−	0.154073i	−0.00265944	−	0.00677614i
$518$	31.6169	−	24.8478i	1.38917	−	1.09175i
$519$	4.83889	+	6.06777i	0.212404	+	0.266346i
$520$	1.01317	+	5.60284i	0.0444304	+	0.245701i
$521$	8.90067	−	15.4164i	0.389945	−	0.675405i	−0.602497	−	0.798122i	$-0.705827\pi$
$521$	8.90067	−	15.4164i	0.389945	−	0.675405i	0.992442	+	0.122717i	$0.0391606\pi$
$522$	−8.11865	−	3.18633i	−0.355344	−	0.139462i
$523$	−5.89761	−	25.8391i	−0.257885	−	1.12987i	−0.923508	−	0.383579i	$-0.874692\pi$
$523$	−5.89761	−	25.8391i	−0.257885	−	1.12987i	0.665624	−	0.746288i	$-0.268166\pi$
$524$	1.25621	+	16.7629i	0.0548777	+	0.732292i
$525$	12.9924	+	27.4773i	0.567037	+	1.19921i
$526$	−44.1289	+	64.7252i	−1.92411	+	2.82215i
$527$	−7.23898	−	48.0275i	−0.315335	−	2.09211i
$528$	3.91577	+	0.293446i	0.170412	+	0.0127706i
$529$	3.35188	+	14.6855i	0.145734	+	0.638501i
$530$	5.39172	+	2.59652i	0.234202	+	0.112786i
$531$	−12.2903	+	13.2458i	−0.533353	+	0.574818i
$532$	3.16204	−	38.5165i	0.137092	−	1.66990i
$533$	15.6184	−	20.8072i	0.676506	−	0.901259i
$534$	68.6155	−	21.1651i	2.96928	−	0.915903i
$535$	−0.0156907	+	0.104101i	−0.000678370	+	0.00450069i
$536$	13.6666	−	4.21559i	0.590307	−	0.182086i
$537$	2.34111	−	31.2399i	0.101026	−	1.34810i
$538$			72.8505i			3.14081i
$539$	0.664265	−	0.0402875i	0.0286119	−	0.00173531i
$540$	1.16457	−	0.672366i	0.0501152	−	0.0289340i
$541$	18.6042	−	27.2874i	0.799858	−	1.17318i	−0.181951	−	0.983308i	$-0.558241\pi$
$541$	18.6042	−	27.2874i	0.799858	−	1.17318i	0.981809	−	0.189869i	$-0.0608063\pi$
$542$	−0.408258	+	1.78870i	−0.0175362	+	0.0768311i
$543$	−27.6073	−	4.16113i	−1.18474	−	0.178571i
$544$	−203.634	−	46.4780i	−8.73072	−	1.99273i
$545$	−0.429063	−	1.87985i	−0.0183790	−	0.0805238i
$546$	56.6701	−	23.7054i	2.42526	−	1.01450i
$547$	6.74243	−	29.5405i	0.288286	−	1.26306i	−0.598591	−	0.801055i	$-0.704272\pi$
$547$	6.74243	−	29.5405i	0.288286	−	1.26306i	0.886876	−	0.462007i	$-0.152870\pi$
$548$	−51.5716	+	107.090i	−2.20303	+	4.57464i
$549$	5.05058	−	4.68625i	0.215553	−	0.200004i
$550$	1.18961	−	0.572887i	0.0507252	−	0.0244280i
$551$	3.15801	+	1.23943i	0.134536	+	0.0528014i
$552$	−38.6811	+	56.7348i	−1.64638	+	2.41479i
$553$	−15.0353	+	1.01926i	−0.639368	+	0.0433435i
$554$	−29.2945	+	60.8307i	−1.24461	+	2.58445i
$555$	1.79631	+	0.554090i	0.0762493	+	0.0235198i
$556$	−24.4956	+	62.4136i	−1.03884	+	2.64693i
$557$	−12.7649	+	7.36981i	−0.540866	+	0.312269i	−0.745430	−	0.666584i	$-0.767756\pi$
$557$	−12.7649	+	7.36981i	−0.540866	+	0.312269i	0.204564	+	0.978853i	$0.434422\pi$
$558$	21.7456	+	37.6644i	0.920563	+	1.59446i
$559$	3.31836	−	3.79341i	0.140352	−	0.160444i
$560$	0.478875	+	7.06396i	0.0202361	+	0.298507i
$561$	−1.48059	+	0.581089i	−0.0625106	+	0.0245336i
$562$	−15.8225	+	19.8408i	−0.667432	+	0.836933i
$563$	−15.3412	−	7.38794i	−0.646556	−	0.311365i	0.0817137	−	0.996656i	$-0.473961\pi$
$563$	−15.3412	−	7.38794i	−0.646556	−	0.311365i	−0.728269	+	0.685291i	$0.759675\pi$
$564$	−13.0941	−	19.2056i	−0.551362	−	0.808700i
$565$	−0.0104964	+	0.00411952i	−0.000441585	+	0.000173310i
$566$	−6.75225	+	44.7982i	−0.283818	+	1.88301i
$567$	−18.8699	−	20.6292i	−0.792459	−	0.866345i
$568$	39.2717	−	100.063i	1.64780	−	4.19854i
$569$	15.4549			0.647903			0.323951	−	0.946074i	$-0.394989\pi$
$569$	15.4549			0.647903			0.323951	+	0.946074i	$0.394989\pi$
$570$	2.10547	−	1.21559i	0.0881883	−	0.0509155i
$571$	31.5691	−	4.75827i	1.32112	−	0.199127i	0.549654	−	0.835393i	$-0.314760\pi$
$571$	31.5691	−	4.75827i	1.32112	−	0.199127i	0.771470	+	0.636265i	$0.219522\pi$
$572$	−0.778231	−	1.82390i	−0.0325395	−	0.0762609i
$573$	21.0612	+	10.1425i	0.879843	+	0.423710i
$574$	36.5078	−	38.7891i	1.52381	−	1.61903i
$575$	−1.04795	+	13.9840i	−0.0437027	+	0.583172i
$576$	102.600	−	15.4644i	4.27498	−	0.644350i
$577$	14.2503	+	1.06791i	0.593249	+	0.0444579i	0.367972	−	0.929837i	$-0.380052\pi$
$577$	14.2503	+	1.06791i	0.593249	+	0.0444579i	0.225277	+	0.974295i	$0.427671\pi$
$578$	96.7035	−	22.0719i	4.02234	−	0.918072i
$579$	−9.84309	−	14.4372i	−0.409065	−	0.599988i
$580$	−1.13312	−	0.258626i	−0.0470501	−	0.0107389i
$581$	−0.413228	−	0.525800i	−0.0171436	−	0.0218139i
$582$	−37.5813	−	11.5923i	−1.55780	−	0.480517i
$583$	−1.32947	−	0.303444i	−0.0550612	−	0.0125674i
$584$	−43.1484	−	109.940i	−1.78549	−	4.54937i
$585$	1.05655	+	0.675876i	0.0436831	+	0.0279440i
$586$	34.1919	+	23.3117i	1.41246	+	0.962996i
$587$	−21.1222	−	12.1949i	−0.871807	−	0.503338i	−0.00385899	−	0.999993i	$-0.501228\pi$
$587$	−21.1222	−	12.1949i	−0.871807	−	0.503338i	−0.867948	+	0.496654i	$0.834562\pi$
$588$	89.6901	−	26.2746i	3.69876	−	1.08355i
$589$	−8.45865	−	14.6508i	−0.348533	−	0.603676i
$590$	−1.82542	+	2.67739i	−0.0751511	+	0.110226i
$591$	−4.03771	−	0.921581i	−0.166089	−	0.0379088i
$592$	−76.2199	−	60.7833i	−3.13262	−	2.49818i
$593$	−2.22540	−	7.21457i	−0.0913862	−	0.296267i	0.898328	−	0.439325i	$-0.144782\pi$
$593$	−2.22540	−	7.21457i	−0.0913862	−	0.296267i	−0.989714	+	0.143059i	$0.954306\pi$
$594$	−0.302283	+	0.280478i	−0.0124028	+	0.0115081i
$595$	−1.41622	−	2.49376i	−0.0580594	−	0.102234i
$596$	71.7719	−	77.3517i	2.93989	−	3.16845i
$597$	−2.48726	−	33.1902i	−0.101797	−	1.35838i
$598$	28.1368	+	3.40132i	1.15060	+	0.139090i
$599$	−0.0939302	+	1.25341i	−0.00383788	+	0.0512130i	−0.998794	−	0.0490990i	$-0.984365\pi$
$599$	−0.0939302	+	1.25341i	−0.00383788	+	0.0512130i	0.994956	+	0.100312i	$0.0319841\pi$
$600$	94.8545	−	75.6439i	3.87242	−	3.08815i
$601$	−0.329244	+	4.39345i	−0.0134301	+	0.179213i	0.986455	+	0.164034i	$0.0524507\pi$
$601$	−0.329244	+	4.39345i	−0.0134301	+	0.179213i	−0.999885	+	0.0151785i	$0.995168\pi$
$602$	7.61408	−	6.96472i	0.310327	−	0.283861i
$603$	1.36696	−	2.83851i	0.0556668	−	0.115593i
$604$	5.39966	−	17.5053i	0.219709	−	0.712279i
$605$	−1.28490	+	1.02467i	−0.0522386	+	0.0416589i
$606$	−24.8465	−	14.3451i	−1.00932	−	0.582731i
$607$	15.4092	−	26.6895i	0.625441	−	1.08330i	−0.363015	−	0.931783i	$-0.618253\pi$
$607$	15.4092	−	26.6895i	0.625441	−	1.08330i	0.988455	−	0.151512i	$-0.0484142\pi$
$608$	−71.9385	+	10.8430i	−2.91749	+	0.439741i
$609$	−0.0583497	+	8.20408i	−0.00236445	+	0.332446i
$610$	0.770369	−	0.966012i	0.0311913	−	0.0391127i
$611$	−2.97801	+	5.52585i	−0.120478	+	0.223552i
$612$	−80.6097	+	54.9588i	−3.25845	+	2.22158i
$613$	−19.4075	+	1.45439i	−0.783860	+	0.0587422i	−0.460646	−	0.887584i	$-0.652382\pi$
$613$	−19.4075	+	1.45439i	−0.783860	+	0.0587422i	−0.323214	+	0.946326i	$0.604763\pi$
$614$	−3.46112	+	4.34011i	−0.139680	+	0.175153i
$615$	2.46230	+	0.371133i	0.0992897	+	0.0149655i
$616$	−0.764914	−	2.54389i	−0.0308193	−	0.102496i
$617$	13.6770	+	5.36782i	0.550614	+	0.216100i	0.624305	−	0.781181i	$-0.285382\pi$
$617$	13.6770	+	5.36782i	0.550614	+	0.216100i	−0.0736903	+	0.997281i	$0.523478\pi$
$618$	39.3730	+	22.7320i	1.58381	+	0.914416i
$619$	−3.80614	−	2.19747i	−0.152982	−	0.0883240i	0.421555	−	0.906803i	$-0.361484\pi$
$619$	−3.80614	−	2.19747i	−0.152982	−	0.0883240i	−0.574537	+	0.818479i	$0.694818\pi$
$620$	3.61359	+	4.53130i	0.145125	+	0.181982i
$621$	−0.974544	−	4.26976i	−0.0391071	−	0.171339i
$622$	20.7719	+	30.4668i	0.832878	+	1.22161i
$623$	−18.2300	−	23.1962i	−0.730370	−	0.929338i
$624$	−87.4603	−	120.536i	−3.50121	−	4.82531i
$625$	9.01118	−	22.9601i	0.360447	−	0.918405i
$626$	17.7765	−	26.0733i	0.710491	−	1.04210i
$627$	−0.406108	+	0.376814i	−0.0162184	+	0.0150485i
$628$	54.5772	−	37.2101i	2.17787	−	1.48484i
$629$	38.4981	+	8.78694i	1.53502	+	0.350358i
$630$	1.99627	+	1.61533i	0.0795334	+	0.0643565i
$631$	18.1785	+	19.5918i	0.723676	+	0.779938i	0.982555	−	0.185972i	$-0.0595434\pi$
$631$	18.1785	+	19.5918i	0.723676	+	0.779938i	−0.258879	+	0.965910i	$0.583353\pi$
$632$	17.7307	+	57.4814i	0.705288	+	2.28649i
$633$	−18.3900	+	23.0604i	−0.730939	+	0.916568i
$634$	31.2377	−	9.63557i	1.24061	−	0.382677i
$635$	−0.465670	−	0.966973i	−0.0184795	−	0.0383732i
$636$	−191.510			−7.59388
$637$	−17.4437	−	18.2405i	−0.691145	−	0.722716i
$638$	0.356407			0.0141103
$639$	−10.2740	−	21.3342i	−0.406433	−	0.843967i
$640$	9.54689	−	2.94482i	0.377374	−	0.116404i
$641$	8.51977	−	10.6835i	0.336511	−	0.421971i	−0.584570	−	0.811344i	$-0.698737\pi$
$641$	8.51977	−	10.6835i	0.336511	−	0.421971i	0.921080	+	0.389372i	$0.127308\pi$
$642$	−1.33636	−	4.33237i	−0.0527419	−	0.170985i
$643$	−1.93919	−	2.08995i	−0.0764742	−	0.0824196i	0.693655	−	0.720307i	$-0.255999\pi$
$643$	−1.93919	−	2.08995i	−0.0764742	−	0.0824196i	−0.770130	+	0.637887i	$0.779809\pi$
$644$	41.9697	+	9.89387i	1.65384	+	0.389873i
$645$	0.470292	+	0.107341i	0.0185177	+	0.00422655i
$646$	42.1960	−	28.7688i	1.66018	−	1.13189i
$647$	4.49300	−	4.16890i	0.176638	−	0.163896i	−0.586899	−	0.809660i	$-0.699651\pi$
$647$	4.49300	−	4.16890i	0.176638	−	0.163896i	0.763537	+	0.645764i	$0.223461\pi$
$648$	−62.8654	+	92.2066i	−2.46959	+	3.62222i
$649$	0.269770	−	0.687364i	0.0105894	−	0.0269814i
$650$	−45.7337	−	20.3960i	−1.79382	−	0.799997i
$651$	25.7349	−	31.8039i	1.00863	−	1.24649i
$652$	58.5961	+	85.9447i	2.29480	+	3.36586i
$653$	4.31006	+	18.8836i	0.168666	+	0.738973i	0.986533	+	0.163565i	$0.0522995\pi$
$653$	4.31006	+	18.8836i	0.168666	+	0.738973i	−0.817867	+	0.575408i	$0.804843\pi$
$654$	51.7735	+	64.9219i	2.02450	+	2.53865i
$655$	0.376279	+	0.217245i	0.0147024	+	0.00848845i
$656$	−111.837	−	64.5694i	−4.36652	−	2.52101i
$657$	−24.2182	−	9.50494i	−0.944842	−	0.370823i
$658$	−7.31522	+	10.5672i	−0.285177	+	0.411952i
$659$	−24.1249	−	3.63624i	−0.939772	−	0.141648i	−0.338747	−	0.940878i	$-0.610003\pi$
$659$	−24.1249	−	3.63624i	−0.939772	−	0.141648i	−0.601026	+	0.799230i	$0.705241\pi$
$660$	0.118336	−	0.148388i	0.00460621	−	0.00577600i
$661$	44.4950	−	3.33444i	1.73066	−	0.129695i	0.828187	−	0.560451i	$-0.189372\pi$
$661$	44.4950	−	3.33444i	1.73066	−	0.129695i	0.902468	+	0.430757i	$0.141753\pi$
$662$	−18.1851	+	12.3984i	−0.706783	+	0.481877i
$663$	53.1015	+	28.6177i	2.06229	+	1.11142i
$664$	−1.66436	+	2.08704i	−0.0645895	+	0.0809927i
$665$	−0.776515	−	0.628337i	−0.0301120	−	0.0243659i
$666$	−34.9640	+	5.26998i	−1.35483	+	0.204208i
$667$	−1.89264	+	3.27814i	−0.0732832	+	0.126930i
$668$	−61.7693	−	35.6625i	−2.38993	−	1.37982i
$669$	17.3058	−	13.8009i	0.669081	−	0.533574i
$670$	0.166535	−	0.539894i	0.00643382	−	0.0208579i
$671$	−0.122161	+	0.253670i	−0.00471597	+	0.00979281i
$672$	−86.8827	−	152.988i	−3.35157	−	5.90163i
$673$	2.40271	−	32.0619i	0.0926176	−	1.23590i	−0.736351	−	0.676600i	$-0.763453\pi$
$673$	2.40271	−	32.0619i	0.0926176	−	1.23590i	0.828968	−	0.559296i	$-0.188928\pi$
$674$	37.0006	−	29.5070i	1.42521	−	1.13657i
$675$	−0.578265	+	7.71641i	−0.0222574	+	0.297005i
$676$	−33.7241	+	67.2205i	−1.29708	+	2.58540i
$677$	3.06973	+	40.9627i	0.117979	+	1.57432i	0.671192	+	0.741283i	$0.265782\pi$
$677$	3.06973	+	40.9627i	0.117979	+	1.57432i	−0.553213	+	0.833040i	$0.686598\pi$
$678$	0.330290	−	0.355968i	0.0126847	−	0.0136709i
$679$	1.09292	+	16.1218i	0.0419423	+	0.618698i
$680$	−8.39159	+	7.78626i	−0.321803	+	0.298589i
$681$	10.5494	+	34.2003i	0.404254	+	1.31056i
$682$	−1.38953	−	1.10811i	−0.0532077	−	0.0424317i
$683$	26.0274	+	5.94058i	0.995911	+	0.227310i	0.689262	−	0.724512i	$-0.257935\pi$
$683$	26.0274	+	5.94058i	0.995911	+	0.227310i	0.306649	+	0.951823i	$0.400792\pi$
$684$	−19.1425	+	28.0770i	−0.731934	+	1.07355i
$685$	1.53610	+	2.66061i	0.0586914	+	0.101657i
$686$	−31.3494	−	41.0791i	−1.19692	−	1.56841i
$687$	24.4068	+	14.0913i	0.931178	+	0.537616i
$688$	−20.6699	−	14.0925i	−0.788031	−	0.537271i
$689$	23.7948	+	45.9186i	0.906509	+	1.74936i
$690$	0.991038	+	2.52512i	0.0377282	+	0.0961298i
$691$	13.6251	+	3.10983i	0.518321	+	0.118303i	0.473676	−	0.880699i	$-0.342927\pi$
$691$	13.6251	+	3.10983i	0.518321	+	0.118303i	0.0446458	+	0.999003i	$0.485784\pi$
$692$	−18.5896	−	5.73413i	−0.706670	−	0.217979i
$693$	−0.525396	−	0.257636i	−0.0199581	−	0.00978680i
$694$	19.5444	+	4.46088i	0.741895	+	0.169333i
$695$	0.976240	+	1.43188i	0.0370309	+	0.0543143i
$696$	31.9277	−	7.28729i	1.21022	−	0.276224i
$697$	52.1617	+	3.90898i	1.97577	+	0.148063i
$698$	−82.7917	+	12.4788i	−3.13371	+	0.472331i
$699$	4.91711	−	65.6142i	0.185982	−	2.48176i
$700$	−65.7072	−	38.5617i	−2.48350	−	1.45750i
$701$	19.3285	+	9.30811i	0.730027	+	0.351562i	0.761695	−	0.647936i	$-0.224368\pi$
$701$	19.3285	+	9.30811i	0.730027	+	0.351562i	−0.0316679	+	0.999498i	$0.510082\pi$
$702$	15.5260	+	1.87686i	0.585992	+	0.0708375i
$703$	13.6004	−	2.04993i	0.512949	−	0.0773146i
$704$	−3.67204	+	2.12005i	−0.138395	+	0.0799024i
$705$	−0.600806			−0.0226277
$706$	19.6146	−	49.9773i	0.738206	−	1.88092i
$707$	−1.83975	+	11.6434i	−0.0691907	+	0.437896i
$708$	15.4557	−	102.542i	0.580863	−	3.85377i
$709$	−18.6122	+	7.30475i	−0.698996	+	0.274336i	−0.688112	−	0.725605i	$-0.741560\pi$
$709$	−18.6122	+	7.30475i	−0.698996	+	0.274336i	−0.0108848	+	0.999941i	$0.503465\pi$
$710$	−2.39213	−	3.50861i	−0.0897750	−	0.131676i
$711$	11.9387	+	5.74938i	0.447737	+	0.215619i
$712$	−73.4248	+	92.0718i	−2.75171	+	3.45054i
$713$	17.5710	−	6.89610i	0.658038	−	0.258261i
$714$	101.547	+	70.2967i	3.80030	+	2.63079i
$715$	−0.0502822	−	0.00993650i	−0.00188045	−	0.000371604i
$716$	39.2632	+	68.0059i	1.46734	+	2.54150i
$717$	−46.3302	+	26.7488i	−1.73023	+	0.998951i
$718$	−6.73834	+	17.1690i	−0.251473	+	0.640742i
$719$	20.7936	+	6.41398i	0.775471	+	0.239201i	0.657135	−	0.753773i	$-0.271768\pi$
$719$	20.7936	+	6.41398i	0.775471	+	0.239201i	0.118336	+	0.992974i	$0.462244\pi$
$720$	2.70120	−	5.60909i	0.100668	−	0.209039i
$721$	2.91535	−	18.4507i	0.108573	−	0.687141i
$722$	−19.8431	+	29.1044i	−0.738482	+	1.08315i
$723$	−37.9379	−	14.8895i	−1.41092	−	0.553747i
$724$	63.0524	−	30.3644i	2.34332	−	1.12848i
$725$	4.90267	−	4.54901i	0.182081	−	0.168946i
$726$	30.7084	−	63.7667i	1.13970	−	2.36660i
$727$	−11.0621	+	48.4662i	−0.410271	+	1.79751i	0.172648	+	0.984984i	$0.444768\pi$
$727$	−11.0621	+	48.4662i	−0.410271	+	1.79751i	−0.582919	+	0.812530i	$0.698090\pi$
$728$	−54.8911	+	84.4781i	−2.03440	+	3.13097i
$729$	3.07524	+	13.4735i	0.113898	+	0.499019i
$730$	−4.54870	−	1.03821i	−0.168355	−	0.0384259i
$731$	10.0199	+	1.51026i	0.370601	+	0.0558591i
$732$	−8.79862	+	38.5493i	−0.325206	+	1.42482i
$733$	0.975914	−	1.43140i	0.0360462	−	0.0528701i	−0.807793	−	0.589467i	$-0.799338\pi$
$733$	0.975914	−	1.43140i	0.0360462	−	0.0528701i	0.843839	+	0.536597i	$0.180290\pi$
$734$	32.3353	−	18.6688i	1.19352	−	0.689078i
$735$	0.744790	−	2.29798i	0.0274720	−	0.0847622i
$736$		−	81.1734i		−	2.99209i
$737$	−0.00962121	+	0.128386i	−0.000354402	+	0.00472916i
$738$	−44.7573	+	13.8058i	−1.64754	+	0.508199i
$739$	3.38121	−	22.4329i	0.124380	−	0.825207i	−0.836445	−	0.548051i	$-0.815370\pi$
$739$	3.38121	−	22.4329i	0.124380	−	0.825207i	0.960825	−	0.277156i	$-0.0893919\pi$
$740$	−4.50269	+	1.38890i	−0.165522	+	0.0510569i
$741$	20.8587	+	2.52150i	0.766265	+	0.0926298i
$742$	37.9832	+	98.8410i	1.39441	+	3.62857i
$743$	−20.3058	+	21.8844i	−0.744947	+	0.802861i	−0.985840	−	0.167690i	$-0.946369\pi$
$743$	−20.3058	+	21.8844i	−0.744947	+	0.802861i	0.240893	+	0.970552i	$0.422560\pi$
$744$	−147.134	−	70.8560i	−5.39419	−	2.59771i
$745$	−0.606902	−	2.65901i	−0.0222352	−	0.0974187i
$746$	−29.2556	−	2.19241i	−1.07112	−	0.0802697i
$747$	0.0876417	+	0.581465i	0.00320664	+	0.0212747i
$748$	2.24590	−	3.29413i	0.0821181	−	0.120445i
$749$	−1.46461	+	1.15104i	−0.0535156	+	0.0420581i
$750$	−0.717947	−	9.58033i	−0.0262157	−	0.349824i
$751$	−0.889377	−	3.89662i	−0.0324538	−	0.142190i	0.956105	−	0.293023i	$-0.0946613\pi$
$751$	−0.889377	−	3.89662i	−0.0324538	−	0.142190i	−0.988559	+	0.150834i	$0.951804\pi$
$752$	29.0042	+	11.3833i	1.05768	+	0.415107i
$753$	11.0430	−	19.1270i	0.402428	−	0.697025i
$754$	−8.73361	−	10.3165i	−0.318059	−	0.375705i
$755$	−0.295221	−	0.370195i	−0.0107442	−	0.0134728i
$756$	23.1590	+	5.45947i	0.842285	+	0.198559i
$757$	−12.0215	−	30.6302i	−0.436927	−	1.11327i	−0.964575	−	0.263810i	$-0.915021\pi$
$757$	−12.0215	−	30.6302i	−0.436927	−	1.11327i	0.527647	−	0.849464i	$-0.323074\pi$
$758$	−1.26391	−	3.22039i	−0.0459073	−	0.116970i
$759$	−0.348206	−	0.510725i	−0.0126391	−	0.0185381i
$760$	−1.73000	+	3.59238i	−0.0627537	+	0.130309i
$761$	−13.4851	+	5.29250i	−0.488833	+	0.191853i	−0.596939	−	0.802286i	$-0.703617\pi$
$761$	−13.4851	+	5.29250i	−0.488833	+	0.191853i	0.108106	+	0.994139i	$0.465521\pi$
$762$	36.1365	+	28.8179i	1.30909	+	1.04396i
$763$	17.2685	−	29.4246i	0.625162	−	1.06524i
$764$	−57.9408	+	8.73317i	−2.09623	+	0.315955i
$765$			2.52171i			0.0911724i
$766$	−2.20699	+	3.82262i	−0.0797419	+	0.138117i
$767$	−26.5070	+	9.03484i	−0.957112	+	0.326229i
$768$	−164.489	+	152.624i	−5.93550	+	5.50734i
$769$	−11.4090	−	16.7339i	−0.411418	−	0.603439i	0.563470	−	0.826137i	$-0.309466\pi$
$769$	−11.4090	−	16.7339i	−0.411418	−	0.603439i	−0.974888	+	0.222698i	$0.928514\pi$
$770$	−0.100055	−	0.0316440i	−0.00360574	−	0.00114037i
$771$	−27.6487	−	18.8506i	−0.995745	−	0.678887i
$772$	40.7715	+	16.0017i	1.46740	+	0.575912i
$773$	−7.47726	−	15.5267i	−0.268938	−	0.558457i	0.722138	−	0.691749i	$-0.243159\pi$
$773$	−7.47726	−	15.5267i	−0.268938	−	0.558457i	−0.991077	+	0.133292i	$0.957445\pi$
$774$	−8.84604	+	2.01905i	−0.317964	+	0.0725733i
$775$	−33.2575	+	2.49230i	−1.19464	+	0.0895262i
$776$	61.6350	−	19.0119i	2.21257	−	0.682486i
$777$	16.4257	+	28.9232i	0.589268	+	1.03761i
$778$	−5.45734	+	17.6922i	−0.195655	+	0.634298i
$779$	17.4098	−	5.37022i	0.623772	−	0.192408i
$780$	−7.19500	+	0.210863i	−0.257622	+	0.00755012i
$781$	0.709338	+	0.658170i	0.0253821	+	0.0235512i
$782$	24.7237	+	51.3393i	0.884118	+	1.83589i
$783$	−1.04436	+	1.80889i	−0.0373225	+	0.0646445i
$784$	−79.4944	+	96.8249i	−2.83909	+	3.45803i
$785$		−	1.70733i		−	0.0609373i
$786$	−18.6591	−	1.39831i	−0.665549	−	0.0498760i
$787$	35.1057	+	8.01264i	1.25138	+	0.285620i	0.796340	−	0.604850i	$-0.206767\pi$
$787$	35.1057	+	8.01264i	1.25138	+	0.285620i	0.455043	+	0.890470i	$0.349624\pi$
$788$	9.66370	−	3.79272i	0.344255	−	0.135110i
$789$	−47.4996	−	44.0731i	−1.69103	−	1.56905i
$790$	2.27078	+	0.700443i	0.0807907	+	0.0249206i
$791$	−0.185201	−	0.0742103i	−0.00658498	−	0.00263861i
$792$	−0.519760	+	2.27722i	−0.0184689	+	0.0809174i
$793$	10.3362	−	2.68002i	0.367049	−	0.0951704i
$794$	56.3676	+	17.3871i	2.00041	+	0.617045i
$795$	−2.78843	+	4.08988i	−0.0988954	+	0.145053i
$796$	52.0170	+	65.2272i	1.84369	+	2.31192i
$797$	−17.6607	−	12.0408i	−0.625573	−	0.426508i	0.208608	−	0.977999i	$-0.433107\pi$
$797$	−17.6607	−	12.0408i	−0.625573	−	0.426508i	−0.834181	+	0.551491i	$0.814059\pi$
$798$	41.8699	+	9.87036i	1.48218	+	0.349407i
$799$	−12.5854	+	0.943143i	−0.445239	+	0.0333660i
$800$	−42.2742	+	137.050i	−1.49462	+	4.84544i
$801$	3.86641	+	25.6519i	0.136613	+	0.906366i
$802$	15.0890			0.532811
$803$	1.06317			0.0375186
$804$	2.69481	+	17.8789i	0.0950386	+	0.630540i
$805$	0.822380	−	0.752244i	0.0289851	−	0.0265131i
$806$	1.97455	+	67.3749i	0.0695506	+	2.37318i
$807$	−59.5856	−	8.98109i	−2.09751	−	0.316149i
$808$	46.9216	−	3.51629i	1.65070	−	0.123703i
$809$	0.638325	+	8.51785i	0.0224423	+	0.299472i	0.997119	+	0.0758530i	$0.0241680\pi$
$809$	0.638325	+	8.51785i	0.0224423	+	0.299472i	−0.974677	+	0.223619i	$0.928213\pi$
$810$	1.61066	+	4.10388i	0.0565927	+	0.144196i
$811$	−31.8388	−	25.3906i	−1.11801	−	0.891583i	−0.123104	−	0.992394i	$-0.539285\pi$
$811$	−31.8388	−	25.3906i	−1.11801	−	0.891583i	−0.994906	+	0.100811i	$0.967856\pi$
$812$	−11.4636	−	17.0736i	−0.402293	−	0.599167i
$813$	−1.41267	−	0.554433i	−0.0495446	−	0.0194448i
$814$	1.25136	−	0.722474i	0.0438602	−	0.0253227i
$815$	2.68860			0.0941776
$816$	109.390	−	278.721i	3.82941	−	9.75718i
$817$	3.44095	−	0.785375i	0.120384	−	0.0274768i
$818$	−12.5476	−	6.04259i	−0.438716	−	0.211274i
$819$	5.41710	+	21.5213i	0.189289	+	0.752016i
$820$	−5.62367	+	2.70821i	−0.196387	+	0.0945750i
$821$	15.4595	−	12.3286i	0.539541	−	0.430270i	−0.315427	−	0.948950i	$-0.602148\pi$
$821$	15.4595	−	12.3286i	0.539541	−	0.430270i	0.854968	+	0.518680i	$0.173576\pi$
$822$	−109.316	−	74.5304i	−3.81283	−	2.59955i
$823$	−11.3051	−	49.5309i	−0.394071	−	1.72654i	−0.650080	−	0.759866i	$-0.725265\pi$
$823$	−11.3051	−	49.5309i	−0.394071	−	1.72654i	0.256009	−	0.966674i	$-0.417592\pi$
$824$	−74.3544	+	5.57209i	−2.59026	+	0.194113i
$825$	0.321917	+	1.04363i	0.0112077	+	0.0363345i
$826$	−55.9888	+	12.3608i	−1.94810	+	0.430087i
$827$	−23.5074	+	5.36540i	−0.817431	+	0.186573i	−0.610738	−	0.791833i	$-0.709127\pi$
$827$	−23.5074	+	5.36540i	−0.817431	+	0.186573i	−0.206693	+	0.978406i	$0.566270\pi$
$828$	−27.7941	−	25.7892i	−0.965913	−	0.896236i
$829$	30.1047	+	4.53756i	1.04558	+	0.157596i	0.649299	−	0.760533i	$-0.275062\pi$
$829$	30.1047	+	4.53756i	1.04558	+	0.157596i	0.396281	+	0.918129i	$0.370300\pi$
$830$	0.0310832	+	0.100769i	0.00107891	+	0.00349775i
$831$	−46.1430	−	31.4597i	−1.60068	−	1.09133i
$832$	151.349	+	54.3394i	5.24707	+	1.88388i
$833$	11.9941	−	49.3061i	0.415572	−	1.70835i
$834$	−64.6339	−	37.3164i	−2.23809	−	1.29216i
$835$	−1.66098	+	0.799886i	−0.0574806	+	0.0276812i
$836$	0.309007	−	1.35385i	0.0106872	−	0.0468238i
$837$	9.69573	−	3.80529i	0.335133	−	0.131530i
$838$	64.6959	−	69.7256i	2.23488	−	2.40863i
$839$	−0.620050	−	0.668255i	−0.0214065	−	0.0230707i	0.722258	−	0.691624i	$-0.243104\pi$
$839$	−0.620050	−	0.668255i	−0.0214065	−	0.0230707i	−0.743664	+	0.668553i	$0.766914\pi$
$840$	−9.61018	−	0.788955i	−0.331583	−	0.0272215i
$841$	−25.9865	+	8.01578i	−0.896087	+	0.276406i
$842$	24.8816	+	11.9823i	0.857475	+	0.412938i
$843$	−14.2775	−	15.3875i	−0.491743	−	0.529973i
$844$	5.52509	−	73.7271i	0.190181	−	2.53779i
$845$	0.944525	+	1.69895i	0.0324926	+	0.0584458i
$846$	10.1818	−	4.90330i	0.350058	−	0.168579i
$847$	−28.9819	−	2.37928i	−0.995828	−	0.0817532i
$848$	212.103	−	144.609i	7.28365	−	4.96591i
$849$	−35.8088	−	11.0455i	−1.22895	−	0.379082i
$850$	−15.0055	−	99.5549i	−0.514684	−	3.41470i
$851$			15.3463i			0.526064i
$852$	117.688	+	67.9475i	4.03194	+	2.32784i
$853$	26.1203	−	20.8303i	0.894342	−	0.713214i	−0.0642688	−	0.997933i	$-0.520471\pi$
$853$	26.1203	−	20.8303i	0.894342	−	0.713214i	0.958611	+	0.284718i	$0.0919001\pi$
$854$	21.6409	−	3.10459i	0.740535	−	0.106237i
$855$	0.320890	+	0.817613i	0.0109742	+	0.0279618i
$856$	5.81340	+	4.63603i	0.198698	+	0.158456i
$857$	20.7170	−	14.1246i	0.707680	−	0.482488i	−0.155209	−	0.987882i	$-0.549605\pi$
$857$	20.7170	−	14.1246i	0.707680	−	0.482488i	0.862889	+	0.505394i	$0.168653\pi$
$858$	2.13664	−	0.553999i	0.0729438	−	0.0189132i
$859$	31.4931	+	4.74682i	1.07453	+	0.161960i	0.662389	−	0.749160i	$-0.269543\pi$
$859$	31.4931	+	4.74682i	1.07453	+	0.161960i	0.412142	+	0.911120i	$0.364781\pi$
$860$	−1.12558	+	0.441757i	−0.0383819	+	0.0150638i
$861$	27.2255	+	34.6423i	0.927843	+	1.18061i
$862$	−20.6443	+	52.6009i	−0.703149	+	1.79159i
$863$	32.6574	−	18.8547i	1.11167	−	0.641823i	0.172409	−	0.985026i	$-0.444845\pi$
$863$	32.6574	−	18.8547i	1.11167	−	0.641823i	0.939261	+	0.343202i	$0.111512\pi$
$864$		−	44.7918i		−	1.52385i
$865$	−0.393126	+	0.313508i	−0.0133667	+	0.0106596i
$866$	−15.9446	−	17.1842i	−0.541820	−	0.583943i
$867$	6.13129	+	81.8164i	0.208230	+	2.77863i
$868$	−8.39074	+	102.207i	−0.284800	+	3.46913i
$869$	−0.539989	−	0.0404666i	−0.0183179	−	0.00137273i
$870$	0.472652	−	1.20430i	0.0160244	−	0.0408295i
$871$	3.95202	−	2.86756i	0.133909	−	0.0971635i
$872$	−130.136	−	40.1416i	−4.40695	−	1.35936i
$873$	6.16483	−	12.8014i	0.208648	−	0.433262i
$874$	14.5491	+	13.4996i	0.492132	+	0.456632i
$875$	−3.56846	+	1.68732i	−0.120636	+	0.0570419i
$876$	145.566	−	33.2246i	4.91823	−	1.12255i
$877$	−16.9496	+	18.2674i	−0.572348	+	0.616845i	−0.951186	−	0.308618i	$-0.900133\pi$
$877$	−16.9496	+	18.2674i	−0.572348	+	0.616845i	0.378838	+	0.925463i	$0.376324\pi$
$878$	−27.1902	−	21.6834i	−0.917623	−	0.731780i
$879$	−23.2822	+	25.0923i	−0.785289	+	0.846341i
$880$	−0.0190122	+	0.253700i	−0.000640899	+	0.00855221i
$881$	14.2191	−	24.6282i	0.479054	−	0.829746i	−0.520657	−	0.853766i	$-0.674313\pi$
$881$	14.2191	−	24.6282i	0.479054	−	0.829746i	0.999711	+	0.0240194i	$0.00764635\pi$
$882$	6.13238	+	45.0220i	0.206488	+	1.51597i
$883$	−6.88478			−0.231691			−0.115846	−	0.993267i	$-0.536958\pi$
$883$	−6.88478			−0.231691			−0.115846	+	0.993267i	$0.536958\pi$
$884$	−150.386	+	15.7118i	−5.05804	+	0.528444i
$885$	−1.96484	−	1.82311i	−0.0660475	−	0.0612831i
$886$	−15.3592	+	101.902i	−0.516003	+	3.42346i
$887$	−4.99529	+	21.8858i	−0.167725	+	0.734853i	0.819178	+	0.573540i	$0.194430\pi$
$887$	−4.99529	+	21.8858i	−0.167725	+	0.734853i	−0.986903	+	0.161313i	$0.948427\pi$
$888$	97.3277	−	90.3069i	3.26610	−	3.03050i
$889$	5.72643	−	18.1064i	0.192058	−	0.607270i
$890$	1.37127	+	4.44555i	0.0459650	+	0.149015i
$891$	−0.565912	−	0.830041i	−0.0189588	−	0.0278074i
$892$	−16.3542	+	53.0191i	−0.547580	+	1.77521i
$893$	−3.96054	+	1.90730i	−0.132535	+	0.0638253i
$894$	73.2328	+	91.8310i	2.44927	+	3.07129i
$895$	2.02401	+	0.151679i	0.0676552	+	0.00507005i
$896$	158.721	+	77.8316i	5.30251	+	2.60017i
$897$	−6.25073	+	22.5943i	−0.208706	+	0.754400i
$898$	41.9761	−	38.9481i	1.40076	−	1.29972i
$899$	−8.38006	−	3.28893i	−0.279491	−	0.109692i
$900$	33.4957	+	58.0163i	1.11652	+	1.93388i
$901$	−51.9904	+	90.0499i	−1.73205	+	3.00000i
$902$	1.49646	−	1.19339i	0.0498268	−	0.0397356i
$903$	4.75789	+	7.08630i	0.158333	+	0.235817i
$904$	−0.118697	+	0.787505i	−0.00394781	+	0.0261920i
$905$	0.269596	−	1.78865i	0.00896168	−	0.0594569i
$906$	18.3720	+	8.84747i	0.610367	+	0.293937i
$907$	0.984837	+	13.1417i	0.0327010	+	0.436364i	0.989393	+	0.145263i	$0.0464027\pi$
$907$	0.984837	+	13.1417i	0.0327010	+	0.436364i	−0.956692	+	0.291101i	$0.905978\pi$
$908$	−70.1407	−	55.9353i	−2.32770	−	1.85628i
$909$	6.46254	−	8.10377i	0.214349	−	0.268785i
$910$	1.53585	+	3.67161i	0.0509130	+	0.121713i
$911$	−15.9684	−	20.0237i	−0.529057	−	0.663416i	0.443448	−	0.896300i	$-0.353755\pi$
$911$	−15.9684	−	20.0237i	−0.529057	−	0.663416i	−0.972504	+	0.232884i	$0.925184\pi$
$912$		−	104.290i		−	3.45338i
$913$	−0.0120150	−	0.0208106i	−0.000397639	−	0.000688731i
$914$	−22.4681	−	28.1741i	−0.743180	−	0.931918i
$915$	0.695145	+	0.749188i	0.0229808	+	0.0247674i
$916$	−70.4457	+	5.27917i	−2.32759	+	0.174429i
$917$	2.21374	+	7.36228i	0.0731042	+	0.243124i
$918$	13.6426	+	28.3292i	0.450274	+	0.935003i
$919$	−47.0588	+	7.09298i	−1.55233	+	0.233976i	−0.868508	−	0.495675i	$-0.834921\pi$
$919$	−47.0588	+	7.09298i	−1.55233	+	0.233976i	−0.683820	+	0.729651i	$0.739682\pi$
$920$	−3.67580	−	2.50612i	−0.121188	−	0.0826243i
$921$	−3.12316	−	3.36596i	−0.102911	−	0.110912i
$922$	−6.72686	−	89.7637i	−0.221537	−	2.95621i
$923$	1.66926	−	36.6606i	0.0549443	−	1.20670i
$924$	3.32423	−	0.476893i	0.109359	−	0.0156886i
$925$	7.99219	−	25.9100i	0.262781	−	0.851917i
$926$	−0.432624	+	1.89545i	−0.0142169	+	0.0622884i
$927$	−10.2409	+	12.8416i	−0.336354	+	0.421775i
$928$	−26.3320	+	28.3792i	−0.864391	+	0.931592i
$929$	−52.5409	−	3.93740i	−1.72381	−	0.129182i	−0.824321	−	0.566122i	$-0.808443\pi$
$929$	−52.5409	−	3.93740i	−1.72381	−	0.129182i	−0.899491	+	0.436940i	$0.856062\pi$
$930$	−5.58704	+	3.22568i	−0.183206	+	0.105774i
$931$	−2.38539	−	17.5128i	−0.0781780	−	0.573958i
$932$	82.4658	+	142.835i	2.70126	+	4.67872i
$933$	−27.4801	+	13.2337i	−0.899658	+	0.433252i
$934$	−24.3438	−	78.9208i	−0.796555	−	2.58237i
$935$	−0.0376483	−	0.0959264i	−0.00123123	−	0.00313713i
$936$	78.6526	−	40.7574i	2.57084	−	1.33220i
$937$	−3.76987	−	16.5169i	−0.123156	−	0.539582i	−0.998433	−	0.0559602i	$-0.982178\pi$
$937$	−3.76987	−	16.5169i	−0.123156	−	0.539582i	0.875277	−	0.483622i	$-0.160679\pi$
$938$	8.69306	−	4.93684i	0.283838	−	0.161194i
$939$	19.1343	+	17.7540i	0.624424	+	0.579381i
$940$	1.24431	−	0.848358i	0.0405850	−	0.0276704i
$941$	13.6145	−	44.1372i	0.443821	−	1.43883i	−0.407026	−	0.913417i	$-0.633434\pi$
$941$	13.6145	−	44.1372i	0.443821	−	1.43883i	0.850846	−	0.525414i	$-0.176090\pi$
$942$	31.9021	+	66.2455i	1.03943	+	2.15839i
$943$	3.02980	+	20.1014i	0.0986639	+	0.654592i
$944$	60.3119	+	125.239i	1.96299	+	4.07618i
$945$	0.453792	−	0.415091i	0.0147619	−	0.0135029i
$946$	0.306362	−	0.208874i	0.00996068	−	0.00679108i
$947$	−11.5888	+	2.64507i	−0.376586	+	0.0859532i	−0.406624	−	0.913596i	$-0.633294\pi$
$947$	−11.5888	+	2.64507i	−0.376586	+	0.0859532i	0.0300386	+	0.999549i	$0.490437\pi$
$948$	−75.1982	+	11.3343i	−2.44232	+	0.368121i
$949$	−26.0526	−	30.7745i	−0.845704	−	0.998982i
$950$	−17.5337	−	30.3693i	−0.568868	−	0.985309i
$951$	4.03007	+	26.7377i	0.130684	+	0.867031i
$952$	−202.548	−	1.44058i	−6.56461	−	0.0466893i
$953$	27.9716	+	4.21604i	0.906089	+	0.136571i	0.585524	−	0.810655i	$-0.300889\pi$
$953$	27.9716	+	4.21604i	0.906089	+	0.136571i	0.320566	+	0.947226i	$0.396127\pi$
$954$	13.8770	−	92.0677i	0.449284	−	2.98080i
$955$	−0.657126	+	1.36454i	−0.0212641	+	0.0441554i
$956$	58.1831	−	120.819i	1.88178	−	3.90755i
$957$	−0.0439382	+	0.291511i	−0.00142032	+	0.00942320i
$958$	−10.3824	−	1.56489i	−0.335440	−	0.0505595i
$959$	−12.4728	+	52.9096i	−0.402769	+	1.70854i
$960$	2.29395	+	15.2193i	0.0740368	+	0.491202i
$961$	6.94575	+	12.0304i	0.224056	+	0.388077i
$962$	−51.5768	−	18.5178i	−1.66290	−	0.597039i
$963$	1.61966	−	0.244124i	0.0521928	−	0.00786680i
$964$	99.5967	−	22.7323i	3.20779	−	0.732158i
$965$	0.935372	−	0.637726i	0.0301107	−	0.0205291i
$966$	−17.8529	+	44.5540i	−0.574406	+	1.43350i
$967$	7.88263	+	16.3684i	0.253488	+	0.526374i	0.988415	−	0.151772i	$-0.0484980\pi$
$967$	7.88263	+	16.3684i	0.253488	+	0.526374i	−0.734927	+	0.678146i	$0.762784\pi$
$968$	17.3001	+	114.779i	0.556046	+	3.68912i
$969$	18.3285	+	38.0594i	0.588795	+	1.22265i
$970$	0.751057	−	2.43487i	0.0241150	−	0.0781788i
$971$	22.7999	−	15.5447i	0.731684	−	0.498854i	−0.139248	−	0.990258i	$-0.544469\pi$
$971$	22.7999	−	15.5447i	0.731684	−	0.498854i	0.870932	+	0.491404i	$0.163516\pi$
$972$	−83.6445	−	77.6108i	−2.68290	−	2.48937i
$973$	−4.78578	+	30.2883i	−0.153425	+	0.970999i
$974$	24.2710	+	106.338i	0.777693	+	3.40729i
$975$	22.3203	−	34.8919i	0.714822	−	1.11743i
$976$	−19.3638	−	49.3383i	−0.619821	−	1.57928i
$977$	−1.83373	−	5.94481i	−0.0586662	−	0.190191i	0.921496	−	0.388388i	$-0.126968\pi$
$977$	−1.83373	−	5.94481i	−0.0586662	−	0.190191i	−0.980162	+	0.198196i	$0.936492\pi$
$978$	−104.319	+	50.2375i	−3.33576	+	1.60642i
$979$	−0.530055	−	0.918082i	−0.0169406	−	0.0293420i
$980$	1.70231	+	5.81095i	0.0543783	+	0.185624i
$981$	−25.9805	+	14.9999i	−0.829494	+	0.478909i
$982$	71.5080	+	5.35878i	2.28191	+	0.171006i
$983$	−1.70940	+	1.84230i	−0.0545214	+	0.0587601i	−0.759724	−	0.650246i	$-0.774666\pi$
$983$	−1.70940	+	1.84230i	−0.0545214	+	0.0587601i	0.705202	+	0.709006i	$0.250856\pi$
$984$	109.656	−	137.504i	3.49570	−	4.38347i
$985$	0.0597085	−	0.261600i	0.00190247	−	0.00833527i
$986$	8.01037	−	25.9690i	0.255102	−	0.827021i
$987$	−7.74125	−	7.28597i	−0.246407	−	0.231915i
$988$	−46.7604	+	24.2310i	−1.48765	+	0.770892i
$989$	0.294290	+	3.92703i	0.00935789	+	0.124872i
$990$	0.0627623	+	0.0676417i	0.00199472	+	0.00214979i
$991$	14.0744	+	9.59574i	0.447087	+	0.304819i	0.765854	−	0.643014i	$-0.222316\pi$
$991$	14.0744	+	9.59574i	0.447087	+	0.304819i	−0.318767	+	0.947833i	$0.603269\pi$
$992$	190.895	−	28.7728i	6.06092	−	0.913537i
$993$	−7.89896	−	16.4024i	−0.250666	−	0.520513i
$994$	11.7268	−	74.2169i	0.371952	−	2.35402i
$995$	2.15037	−	0.161148i	0.0681712	−	0.00510872i
$996$	−2.29540	−	2.47385i	−0.0727325	−	0.0783869i
$997$	−16.9109	−	21.2056i	−0.535574	−	0.671589i	0.438260	−	0.898848i	$-0.355595\pi$
$997$	−16.9109	−	21.2056i	−0.535574	−	0.671589i	−0.973834	+	0.227259i	$0.927024\pi$
$998$	48.9483	+	84.7809i	1.54943	+	2.68369i
$999$			8.46814i			0.267920i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bz.a.4.1	yes	756
13.10	even	6		637.2.bp.a.543.1	✓	756
49.37	even	21		637.2.bp.a.576.1	yes	756
637.478	even	42	inner	637.2.bz.a.478.1	yes	756

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bp.a.543.1	✓	756	13.10	even	6
637.2.bp.a.576.1	yes	756	49.37	even	21
637.2.bz.a.4.1	yes	756	1.1	even	1	trivial
637.2.bz.a.478.1	yes	756	637.478	even	42	inner

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bz (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21061 - 2.51386i) q^{2} +(2.20537 - 0.680267i) q^{3} +(-3.60692 + 4.52294i) q^{4} +(0.0440739 + 0.142884i) q^{5} +(-4.37994 - 4.72045i) q^{6} +(-1.16487 + 2.37551i) q^{7} +(10.2962 + 2.35003i) q^{8} +(1.92218 - 1.31052i) q^{9} +(0.305834 - 0.283773i) q^{10} +(-0.0535545 + 0.0785500i) q^{11} +(-4.87780 + 12.4284i) q^{12} +(3.58603 - 0.374655i) q^{13} +(7.38191 + 0.0525022i) q^{14} +(0.194399 + 0.285130i) q^{15} +(-3.98241 - 17.4481i) q^{16} +(4.51976 + 5.66760i) q^{17} +(-5.62146 - 3.24555i) q^{18} +(2.18665 + 1.26246i) q^{19} +(-0.805228 - 0.316029i) q^{20} +(-0.952992 + 6.03131i) q^{21} +(0.262297 + 0.0395349i) q^{22} +(-1.75652 + 2.20260i) q^{23} +(24.3055 - 1.82145i) q^{24} +(4.11272 - 2.80401i) q^{25} +(-5.28312 - 8.56122i) q^{26} +(-0.969253 + 1.21540i) q^{27} +(-6.54270 - 13.8370i) q^{28} +(1.32861 - 0.200255i) q^{29} +(0.481436 - 0.833872i) q^{30} +(-5.80247 - 3.35006i) q^{31} +(-22.5270 + 17.9647i) q^{32} +(-0.0646725 + 0.209663i) q^{33} +(8.77587 - 18.2233i) q^{34} +(-0.390764 - 0.0617436i) q^{35} +(-1.00575 + 13.4208i) q^{36} +(4.25886 - 3.39633i) q^{37} +(0.526472 - 7.02528i) q^{38} +(7.65366 - 3.26571i) q^{39} +(0.118010 + 1.57474i) q^{40} +(4.90796 - 5.28952i) q^{41} +(16.3156 - 4.90588i) q^{42} +(1.02469 - 0.950773i) q^{43} +(-0.162110 - 0.525548i) q^{44} +(0.271970 + 0.216889i) q^{45} +(7.66349 + 1.74914i) q^{46} +(-0.980734 + 1.43847i) q^{47} +(-20.6520 - 35.7703i) q^{48} +(-4.28614 - 5.53435i) q^{49} +(-12.0278 - 6.94424i) q^{50} +(13.8232 + 9.42451i) q^{51} +(-11.2400 + 17.5708i) q^{52} +(5.24041 + 13.3523i) q^{53} +(4.22874 + 0.965182i) q^{54} +(-0.0135839 - 0.00419008i) q^{55} +(-17.5763 + 21.7212i) q^{56} +(5.68119 + 1.29669i) q^{57} +(-2.11184 - 3.09750i) q^{58} +(-7.57230 + 1.72833i) q^{59} +(-1.99081 - 0.149190i) q^{60} +(2.92847 - 0.441395i) q^{61} +(-1.39704 + 18.6422i) q^{62} +(0.874064 + 6.09275i) q^{63} +(40.1833 + 19.3512i) q^{64} +(0.211583 + 0.495875i) q^{65} +(0.605357 - 0.0912428i) q^{66} +(1.17280 - 0.677116i) q^{67} -41.9367 q^{68} +(-2.37541 + 6.05245i) q^{69} +(0.317848 + 1.05707i) q^{70} +(1.51701 - 10.0647i) q^{71} +(22.8708 - 8.97614i) q^{72} +(-6.29968 - 9.23993i) q^{73} +(-13.6937 - 6.59454i) q^{74} +(7.16260 - 8.98162i) q^{75} +(-13.5971 + 5.33648i) q^{76} +(-0.124213 - 0.218720i) q^{77} +(-17.4751 - 15.2867i) q^{78} +(2.84793 + 4.93277i) q^{79} +(2.31753 - 1.33803i) q^{80} +(-3.86057 + 9.83657i) q^{81} +(-19.2387 - 5.93436i) q^{82} +(-0.109670 + 0.227732i) q^{83} +(-23.8419 - 26.0648i) q^{84} +(-0.610607 + 0.895596i) q^{85} +(-3.63061 - 1.42491i) q^{86} +(2.79384 - 1.34544i) q^{87} +(-0.736002 + 0.682910i) q^{88} +(-4.83820 + 10.0466i) q^{89} +(0.215978 - 0.946262i) q^{90} +(-3.28728 + 8.95510i) q^{91} +(-3.62662 - 15.8892i) q^{92} +(-15.0755 - 3.44089i) q^{93} +(4.80340 + 0.723996i) q^{94} +(-0.0840118 + 0.368080i) q^{95} +(-37.4596 + 54.9432i) q^{96} +(5.28921 - 3.05373i) q^{97} +(-8.72371 + 17.4747i) q^{98} +0.221171i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 756 q - 21 q^{2} - 5 q^{3} + 115 q^{4} - 15 q^{6} - 14 q^{7} + 50 q^{9} - 16 q^{10} - 24 q^{11} - 26 q^{12} - 10 q^{13} - 38 q^{14} - 6 q^{15} - 125 q^{16} + 15 q^{17} - 9 q^{18} - 27 q^{19} - 15 q^{20}+ \cdots + 105 q^{98}+O(q^{100}) \) 756 * q - 21 * q^2 - 5 * q^3 + 115 * q^4 - 15 * q^6 - 14 * q^7 + 50 * q^9 - 16 * q^10 - 24 * q^11 - 26 * q^12 - 10 * q^13 - 38 * q^14 - 6 * q^15 - 125 * q^16 + 15 * q^17 - 9 * q^18 - 27 * q^19 - 15 * q^20 - 16 * q^21 - q^22 - 5 * q^23 - 39 * q^24 - 79 * q^25 - 34 * q^26 - 50 * q^27 - 142 * q^28 - 3 * q^29 - 11 * q^30 - 15 * q^31 - 21 * q^32 - 6 * q^33 - 12 * q^35 - 84 * q^36 + 7 * q^37 - 2 * q^38 - 6 * q^39 - 24 * q^40 - 6 * q^41 + 88 * q^42 - 5 * q^43 + 108 * q^44 - 21 * q^45 - 21 * q^46 + 63 * q^47 - 154 * q^48 - 34 * q^49 + 135 * q^50 + 26 * q^51 + 89 * q^52 + 16 * q^53 - 21 * q^54 - 4 * q^55 + 58 * q^56 - 63 * q^57 - 18 * q^58 - 21 * q^59 + 15 * q^60 - 75 * q^61 - 87 * q^62 + 147 * q^63 + 4 * q^64 - 20 * q^65 + 85 * q^66 - 27 * q^67 + 312 * q^68 - 182 * q^69 - 228 * q^70 - 30 * q^71 - 120 * q^72 + 6 * q^73 - 43 * q^74 + 83 * q^75 + 21 * q^76 + 3 * q^77 + 79 * q^78 + 12 * q^79 + 57 * q^80 + 72 * q^81 - 248 * q^82 + 147 * q^83 - 14 * q^84 - 24 * q^85 - 60 * q^86 - 37 * q^87 + 70 * q^88 - 126 * q^89 + 117 * q^90 - 55 * q^91 + 88 * q^92 - 21 * q^93 + 210 * q^94 + 9 * q^95 - 12 * q^96 - 156 * q^97 + 105 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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