LMFDB - Embedded newform 483.2.q.b.463.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (of order $11$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			463.1
Root			$-0.415415 - 0.909632i$ of defining polynomial
Character	$\chi$	$=$	483.463
Dual form			483.2.q.b.169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.317178 - 2.20602i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-2.84695 + 0.835939i) q^{4} +(0.0577299 - 0.0666238i) q^{5} +(-2.13843 - 0.627899i) q^{6} +(0.841254 - 0.540641i) q^{7} +(0.895412 + 1.96068i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.317178 - 2.20602i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-2.84695 + 0.835939i) q^{4} +(0.0577299 - 0.0666238i) q^{5} +(-2.13843 - 0.627899i) q^{6} +(0.841254 - 0.540641i) q^{7} +(0.895412 + 1.96068i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(-0.165284 - 0.106222i) q^{10} +(0.345139 - 2.40050i) q^{11} +(-0.422268 + 2.93694i) q^{12} +(-4.37102 - 2.80909i) q^{13} +(-1.45949 - 1.68434i) q^{14} +(-0.0366213 - 0.0801894i) q^{15} +(-0.950930 + 0.611126i) q^{16} +(0.959493 + 0.281733i) q^{17} +(-1.45949 + 1.68434i) q^{18} +(-2.58816 + 0.759951i) q^{19} +(-0.108660 + 0.237933i) q^{20} +(-0.142315 - 0.989821i) q^{21} -5.40502 q^{22} +(-2.79310 - 3.89854i) q^{23} +2.15546 q^{24} +(0.710468 + 4.94141i) q^{25} +(-4.81051 + 10.5336i) q^{26} +(-0.959493 + 0.281733i) q^{27} +(-1.94306 + 2.24241i) q^{28} +(6.21307 + 1.82432i) q^{29} +(-0.165284 + 0.106222i) q^{30} +(-0.830830 - 1.81926i) q^{31} +(4.47283 + 5.16192i) q^{32} +(-2.04019 - 1.31115i) q^{33} +(0.317178 - 2.20602i) q^{34} +(0.0125459 - 0.0872586i) q^{35} +(2.49611 + 1.60416i) q^{36} +(-2.36514 - 2.72952i) q^{37} +(2.49738 + 5.46849i) q^{38} +(-4.37102 + 2.80909i) q^{39} +(0.182320 + 0.0535340i) q^{40} +(8.10627 - 9.35513i) q^{41} +(-2.13843 + 0.627899i) q^{42} +(-0.893649 + 1.95682i) q^{43} +(1.02408 + 7.12260i) q^{44} -0.0881559 q^{45} +(-7.71434 + 7.39818i) q^{46} -0.184083 q^{47} +(0.160869 + 1.11887i) q^{48} +(0.415415 - 0.909632i) q^{49} +(10.6755 - 3.13462i) q^{50} +(0.654861 - 0.755750i) q^{51} +(14.7923 + 4.34341i) q^{52} +(4.77023 - 3.06564i) q^{53} +(0.925839 + 2.02730i) q^{54} +(-0.140005 - 0.161575i) q^{55} +(1.81329 + 1.16533i) q^{56} +(-0.383883 + 2.66996i) q^{57} +(2.05384 - 14.2848i) q^{58} +(6.09814 + 3.91903i) q^{59} +(0.171292 + 0.197682i) q^{60} +(-3.16361 - 6.92734i) q^{61} +(-3.74982 + 2.40986i) q^{62} +(-0.959493 - 0.281733i) q^{63} +(8.48816 - 9.79585i) q^{64} +(-0.439490 + 0.129046i) q^{65} +(-2.24533 + 4.91658i) q^{66} +(0.0438528 + 0.305003i) q^{67} -2.96714 q^{68} +(-4.70653 + 0.921186i) q^{69} -0.196474 q^{70} +(0.152711 + 1.06213i) q^{71} +(0.895412 - 1.96068i) q^{72} +(2.04663 - 0.600946i) q^{73} +(-5.27121 + 6.08330i) q^{74} +(4.79001 + 1.40647i) q^{75} +(6.73307 - 4.32708i) q^{76} +(-1.00746 - 2.20602i) q^{77} +(7.58330 + 8.75159i) q^{78} +(9.37454 + 6.02465i) q^{79} +(-0.0141815 + 0.0986348i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-23.2088 - 14.9154i) q^{82} +(-4.90145 - 5.65657i) q^{83} +(1.23259 + 2.69900i) q^{84} +(0.0741615 - 0.0476607i) q^{85} +(4.60023 + 1.35075i) q^{86} +(4.24046 - 4.89375i) q^{87} +(5.01565 - 1.47273i) q^{88} +(-6.22577 + 13.6325i) q^{89} +(0.0279611 + 0.194474i) q^{90} -5.19584 q^{91} +(11.2108 + 8.76406i) q^{92} -2.00000 q^{93} +(0.0583872 + 0.406092i) q^{94} +(-0.0987830 + 0.216305i) q^{95} +(6.55353 - 1.92429i) q^{96} +(-6.53289 + 7.53936i) q^{97} +(-2.13843 - 0.627899i) q^{98} +(-2.04019 + 1.31115i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{2} - q^{3} - q^{4} - 5 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} - q^{9}+O(q^{10}) $ 10 * q + 5 * q^2 - q^3 - q^4 - 5 * q^5 - 6 * q^6 - q^7 + 6 * q^8 - q^9	\( 10 q + 5 q^{2} - q^{3} - q^{4} - 5 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} - q^{9} + 3 q^{10} + 9 q^{11} - 12 q^{12} - 15 q^{13} - 6 q^{14} + 6 q^{15} + 5 q^{16} + q^{17} - 6 q^{18} - 19 q^{19} - 5 q^{20} - q^{21} - 12 q^{22} - 21 q^{23} + 6 q^{24} + 2 q^{25} - 13 q^{26} - q^{27} - q^{28} + 3 q^{30} + 2 q^{31} + 7 q^{32} - 2 q^{33} - 5 q^{34} - 5 q^{35} + 10 q^{36} - 27 q^{37} + 18 q^{38} - 15 q^{39} - 3 q^{40} + 10 q^{41} - 6 q^{42} + 15 q^{43} + 9 q^{44} + 6 q^{45} - 5 q^{46} - 18 q^{47} + 5 q^{48} - q^{49} + 34 q^{50} + q^{51} + 18 q^{52} + 19 q^{53} + 5 q^{54} - 21 q^{55} - 5 q^{56} + 3 q^{57} - 13 q^{59} + 6 q^{60} - 18 q^{61} - 10 q^{62} - q^{63} + 54 q^{64} + 2 q^{65} + 10 q^{66} - 18 q^{67} - 10 q^{68} + q^{69} - 8 q^{70} + 38 q^{71} + 6 q^{72} + 14 q^{73} + 14 q^{74} + 2 q^{75} + 3 q^{76} - 13 q^{77} + 9 q^{78} + 25 q^{79} + 25 q^{80} - q^{81} - 72 q^{82} - 19 q^{83} - q^{84} + 5 q^{85} + 2 q^{86} + 33 q^{87} + q^{88} - 17 q^{89} + 14 q^{90} - 4 q^{91} + 67 q^{92} - 20 q^{93} + 13 q^{94} + 37 q^{95} + 18 q^{96} - 49 q^{97} - 6 q^{98} - 2 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 - q^3 - q^4 - 5 * q^5 - 6 * q^6 - q^7 + 6 * q^8 - q^9 + 3 * q^10 + 9 * q^11 - 12 * q^12 - 15 * q^13 - 6 * q^14 + 6 * q^15 + 5 * q^16 + q^17 - 6 * q^18 - 19 * q^19 - 5 * q^20 - q^21 - 12 * q^22 - 21 * q^23 + 6 * q^24 + 2 * q^25 - 13 * q^26 - q^27 - q^28 + 3 * q^30 + 2 * q^31 + 7 * q^32 - 2 * q^33 - 5 * q^34 - 5 * q^35 + 10 * q^36 - 27 * q^37 + 18 * q^38 - 15 * q^39 - 3 * q^40 + 10 * q^41 - 6 * q^42 + 15 * q^43 + 9 * q^44 + 6 * q^45 - 5 * q^46 - 18 * q^47 + 5 * q^48 - q^49 + 34 * q^50 + q^51 + 18 * q^52 + 19 * q^53 + 5 * q^54 - 21 * q^55 - 5 * q^56 + 3 * q^57 - 13 * q^59 + 6 * q^60 - 18 * q^61 - 10 * q^62 - q^63 + 54 * q^64 + 2 * q^65 + 10 * q^66 - 18 * q^67 - 10 * q^68 + q^69 - 8 * q^70 + 38 * q^71 + 6 * q^72 + 14 * q^73 + 14 * q^74 + 2 * q^75 + 3 * q^76 - 13 * q^77 + 9 * q^78 + 25 * q^79 + 25 * q^80 - q^81 - 72 * q^82 - 19 * q^83 - q^84 + 5 * q^85 + 2 * q^86 + 33 * q^87 + q^88 - 17 * q^89 + 14 * q^90 - 4 * q^91 + 67 * q^92 - 20 * q^93 + 13 * q^94 + 37 * q^95 + 18 * q^96 - 49 * q^97 - 6 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{11}\right)$

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 $

$2$	−0.317178	−	2.20602i	−0.224279	−	1.55989i	−0.721590	−	0.692321i	$-0.756588\pi$
$2$	−0.317178	−	2.20602i	−0.224279	−	1.55989i	0.497311	−	0.867572i	$-0.334321\pi$
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$4$	−2.84695	+	0.835939i	−1.42347	+	0.417970i
$5$	0.0577299	−	0.0666238i	0.0258176	−	0.0297951i	−0.742694	−	0.669631i	$-0.766452\pi$
$5$	0.0577299	−	0.0666238i	0.0258176	−	0.0297951i	0.768512	+	0.639836i	$0.220998\pi$
$6$	−2.13843	−	0.627899i	−0.873010	−	0.256339i
$7$	0.841254	−	0.540641i	0.317964	−	0.204343i
$7$	0.841254	−	0.540641i	0.317964	−	0.204343i
$8$	0.895412	+	1.96068i	0.316576	+	0.693205i
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$	−0.165284	−	0.106222i	−0.0522675	−	0.0335903i
$11$	0.345139	−	2.40050i	0.104063	−	0.723777i	−0.869263	−	0.494351i	$-0.835406\pi$
$11$	0.345139	−	2.40050i	0.104063	−	0.723777i	0.973326	−	0.229426i	$-0.0736850\pi$
$12$	−0.422268	+	2.93694i	−0.121898	+	0.847820i
$13$	−4.37102	−	2.80909i	−1.21230	−	0.779100i	−0.231261	−	0.972892i	$-0.574285\pi$
$13$	−4.37102	−	2.80909i	−1.21230	−	0.779100i	−0.981043	+	0.193792i	$0.937921\pi$
$14$	−1.45949	−	1.68434i	−0.390066	−	0.450160i
$15$	−0.0366213	−	0.0801894i	−0.00945558	−	0.0207048i
$16$	−0.950930	+	0.611126i	−0.237733	+	0.152781i
$17$	0.959493	+	0.281733i	0.232711	+	0.0683302i	0.396009	−	0.918247i	$-0.370395\pi$
$17$	0.959493	+	0.281733i	0.232711	+	0.0683302i	−0.163298	+	0.986577i	$0.552213\pi$
$18$	−1.45949	+	1.68434i	−0.344006	+	0.397004i
$19$	−2.58816	+	0.759951i	−0.593764	+	0.174345i	−0.564789	−	0.825235i	$-0.691042\pi$
$19$	−2.58816	+	0.759951i	−0.593764	+	0.174345i	−0.0289748	+	0.999580i	$0.509224\pi$
$20$	−0.108660	+	0.237933i	−0.0242972	+	0.0532034i
$21$	−0.142315	−	0.989821i	−0.0310556	−	0.215997i
$22$	−5.40502			−1.15235
$23$	−2.79310	−	3.89854i	−0.582402	−	0.812901i
$23$	−2.79310	−	3.89854i	−0.582402	−	0.812901i
$24$	2.15546			0.439982
$25$	0.710468	+	4.94141i	0.142094	+	0.988283i
$26$	−4.81051	+	10.5336i	−0.943419	+	2.06580i
$27$	−0.959493	+	0.281733i	−0.184655	+	0.0542195i
$28$	−1.94306	+	2.24241i	−0.367204	+	0.423776i
$29$	6.21307	+	1.82432i	1.15374	+	0.338768i	0.801996	−	0.597329i	$-0.203771\pi$
$29$	6.21307	+	1.82432i	1.15374	+	0.338768i	0.351741	+	0.936097i	$0.385590\pi$
$30$	−0.165284	+	0.106222i	−0.0301766	+	0.0193933i
$31$	−0.830830	−	1.81926i	−0.149221	−	0.326749i	0.820230	−	0.572035i	$-0.193846\pi$
$31$	−0.830830	−	1.81926i	−0.149221	−	0.326749i	−0.969451	+	0.245285i	$0.921118\pi$
$32$	4.47283	+	5.16192i	0.790692	+	0.912507i
$33$	−2.04019	−	1.31115i	−0.355152	−	0.228242i
$34$	0.317178	−	2.20602i	0.0543956	−	0.378330i
$35$	0.0125459	−	0.0872586i	0.00212064	−	0.0147494i
$36$	2.49611	+	1.60416i	0.416019	+	0.267359i
$37$	−2.36514	−	2.72952i	−0.388827	−	0.448730i	0.527264	−	0.849702i	$-0.323218\pi$
$37$	−2.36514	−	2.72952i	−0.388827	−	0.448730i	−0.916090	+	0.400972i	$0.868673\pi$
$38$	2.49738	+	5.46849i	0.405128	+	0.887106i
$39$	−4.37102	+	2.80909i	−0.699924	+	0.449814i
$40$	0.182320	+	0.0535340i	0.0288273	+	0.00846446i
$41$	8.10627	−	9.35513i	1.26599	−	1.46103i	0.439323	−	0.898329i	$-0.355218\pi$
$41$	8.10627	−	9.35513i	1.26599	−	1.46103i	0.826663	−	0.562697i	$-0.190236\pi$
$42$	−2.13843	+	0.627899i	−0.329967	+	0.0968870i
$43$	−0.893649	+	1.95682i	−0.136280	+	0.298412i	−0.965452	−	0.260582i	$-0.916085\pi$
$43$	−0.893649	+	1.95682i	−0.136280	+	0.298412i	0.829171	+	0.558994i	$0.188813\pi$
$44$	1.02408	+	7.12260i	0.154385	+	1.07377i
$45$	−0.0881559			−0.0131415
$46$	−7.71434	+	7.39818i	−1.13742	+	1.09080i
$47$	−0.184083			−0.0268513			−0.0134257	−	0.999910i	$-0.504274\pi$
$47$	−0.184083			−0.0268513			−0.0134257	+	0.999910i	$0.504274\pi$
$48$	0.160869	+	1.11887i	0.0232194	+	0.161495i
$49$	0.415415	−	0.909632i	0.0593450	−	0.129947i
$50$	10.6755	−	3.13462i	1.50975	−	0.443302i
$51$	0.654861	−	0.755750i	0.0916988	−	0.105826i
$52$	14.7923	+	4.34341i	2.05132	+	0.602322i
$53$	4.77023	−	3.06564i	0.655242	−	0.421098i	−0.170337	−	0.985386i	$-0.554486\pi$
$53$	4.77023	−	3.06564i	0.655242	−	0.421098i	0.825578	+	0.564288i	$0.190849\pi$
$54$	0.925839	+	2.02730i	0.125991	+	0.275881i
$55$	−0.140005	−	0.161575i	−0.0188783	−	0.0217867i
$56$	1.81329	+	1.16533i	0.242311	+	0.155724i
$57$	−0.383883	+	2.66996i	−0.0508465	+	0.353645i
$58$	2.05384	−	14.2848i	0.269683	−	1.87569i
$59$	6.09814	+	3.91903i	0.793910	+	0.510215i	0.873623	−	0.486603i	$-0.161764\pi$
$59$	6.09814	+	3.91903i	0.793910	+	0.510215i	−0.0797134	+	0.996818i	$0.525401\pi$
$60$	0.171292	+	0.197682i	0.0221137	+	0.0255206i
$61$	−3.16361	−	6.92734i	−0.405059	−	0.886955i	−0.996732	−	0.0807773i	$-0.974260\pi$
$61$	−3.16361	−	6.92734i	−0.405059	−	0.886955i	0.591673	−	0.806178i	$-0.298468\pi$
$62$	−3.74982	+	2.40986i	−0.476227	+	0.306053i
$63$	−0.959493	−	0.281733i	−0.120885	−	0.0354950i
$64$	8.48816	−	9.79585i	1.06102	−	1.22448i
$65$	−0.439490	+	0.129046i	−0.0545121	+	0.0160062i
$66$	−2.24533	+	4.91658i	−0.276381	+	0.605189i
$67$	0.0438528	+	0.305003i	0.00535747	+	0.0372620i	0.992325	−	0.123659i	$-0.0394628\pi$
$67$	0.0438528	+	0.305003i	0.00535747	+	0.0372620i	−0.986967	+	0.160921i	$0.948554\pi$
$68$	−2.96714			−0.359818
$69$	−4.70653	+	0.921186i	−0.566600	+	0.110898i
$70$	−0.196474			−0.0234831
$71$	0.152711	+	1.06213i	0.0181234	+	0.126051i	0.996875	−	0.0790005i	$-0.0251729\pi$
$71$	0.152711	+	1.06213i	0.0181234	+	0.126051i	−0.978751	+	0.205052i	$0.934264\pi$
$72$	0.895412	−	1.96068i	0.105525	−	0.231068i
$73$	2.04663	−	0.600946i	0.239540	−	0.0703354i	−0.159759	−	0.987156i	$-0.551072\pi$
$73$	2.04663	−	0.600946i	0.239540	−	0.0703354i	0.399299	+	0.916821i	$0.369253\pi$
$74$	−5.27121	+	6.08330i	−0.612766	+	0.707169i
$75$	4.79001	+	1.40647i	0.553103	+	0.162406i
$76$	6.73307	−	4.32708i	0.772336	−	0.496350i
$77$	−1.00746	−	2.20602i	−0.114810	−	0.251400i
$78$	7.58330	+	8.75159i	0.858639	+	0.990923i
$79$	9.37454	+	6.02465i	1.05472	+	0.677826i	0.948584	−	0.316526i	$-0.102516\pi$
$79$	9.37454	+	6.02465i	1.05472	+	0.677826i	0.106134	+	0.994352i	$0.466153\pi$
$80$	−0.0141815	+	0.0986348i	−0.00158554	+	0.0110277i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	−23.2088	−	14.9154i	−2.56298	−	1.64713i
$83$	−4.90145	−	5.65657i	−0.538004	−	0.620890i	0.420042	−	0.907505i	$-0.362015\pi$
$83$	−4.90145	−	5.65657i	−0.538004	−	0.620890i	−0.958046	+	0.286615i	$0.907470\pi$
$84$	1.23259	+	2.69900i	0.134487	+	0.294485i
$85$	0.0741615	−	0.0476607i	0.00804394	−	0.00516953i
$86$	4.60023	+	1.35075i	0.496056	+	0.145655i
$87$	4.24046	−	4.89375i	0.454625	−	0.524666i
$88$	5.01565	−	1.47273i	0.534670	−	0.156993i
$89$	−6.22577	+	13.6325i	−0.659931	+	1.44505i	0.222656	+	0.974897i	$0.428527\pi$
$89$	−6.22577	+	13.6325i	−0.659931	+	1.44505i	−0.882587	+	0.470149i	$0.844200\pi$
$90$	0.0279611	+	0.194474i	0.00294736	+	0.0204994i
$91$	−5.19584			−0.544672
$92$	11.2108	+	8.76406i	1.16880	+	0.913716i
$93$	−2.00000			−0.207390
$94$	0.0583872	+	0.406092i	0.00602218	+	0.0418852i
$95$	−0.0987830	+	0.216305i	−0.0101349	+	0.0221924i
$96$	6.55353	−	1.92429i	0.668867	−	0.196397i
$97$	−6.53289	+	7.53936i	−0.663315	+	0.765506i	−0.983315	−	0.181912i	$-0.941772\pi$
$97$	−6.53289	+	7.53936i	−0.663315	+	0.765506i	0.320000	+	0.947417i	$0.396317\pi$
$98$	−2.13843	−	0.627899i	−0.216014	−	0.0634274i
$99$	−2.04019	+	1.31115i	−0.205047	+	0.131776i
$100$	−6.15339	−	13.4740i	−0.615339	−	1.34740i
$101$	−5.27111	−	6.08319i	−0.524495	−	0.605300i	0.430255	−	0.902707i	$-0.358423\pi$
$101$	−5.27111	−	6.08319i	−0.524495	−	0.605300i	−0.954751	+	0.297407i	$0.903878\pi$
$102$	−1.87491	−	1.20493i	−0.185644	−	0.119306i
$103$	2.64823	−	18.4189i	0.260938	−	1.81486i	−0.264895	−	0.964277i	$-0.585337\pi$
$103$	2.64823	−	18.4189i	0.260938	−	1.81486i	0.525833	−	0.850588i	$-0.323754\pi$
$104$	1.59385	−	11.0855i	0.156290	−	1.08702i
$105$	−0.0741615	−	0.0476607i	−0.00723742	−	0.00465121i
$106$	−8.27589	−	9.55088i	−0.803825	−	0.927664i
$107$	−4.21562	−	9.23091i	−0.407539	−	0.892386i	−0.996450	−	0.0841879i	$-0.973170\pi$
$107$	−4.21562	−	9.23091i	−0.407539	−	0.892386i	0.588911	−	0.808198i	$-0.299557\pi$
$108$	2.49611	−	1.60416i	0.240189	−	0.154360i
$109$	16.1175	+	4.73252i	1.54377	+	0.453293i	0.939233	−	0.343281i	$-0.111538\pi$
$109$	16.1175	+	4.73252i	1.54377	+	0.453293i	0.604541	+	0.796574i	$0.293356\pi$
$110$	−0.312031	+	0.360103i	−0.0297510	+	0.0343345i
$111$	−3.46537	+	1.01753i	−0.328919	+	0.0965792i
$112$	−0.469574	+	1.02822i	−0.0443706	+	0.0971580i
$113$	−1.13694	−	7.90762i	−0.106955	−	0.743886i	−0.970759	−	0.240058i	$-0.922834\pi$
$113$	−1.13694	−	7.90762i	−0.106955	−	0.743886i	0.863804	−	0.503828i	$-0.168076\pi$
$114$	6.01176			0.563053
$115$	−0.420981	−	0.0389747i	−0.0392566	−	0.00363441i
$116$	−19.2133			−1.78391
$117$	0.739446	+	5.14296i	0.0683618	+	0.475467i
$118$	6.71128	−	14.6957i	0.617824	−	1.35285i
$119$	0.959493	−	0.281733i	0.0879566	−	0.0258264i
$120$	0.124435	−	0.143605i	0.0113593	−	0.0131093i
$121$	4.91116	+	1.44205i	0.446469	+	0.131095i
$122$	−14.2784	+	9.17620i	−1.29271	+	0.830774i
$123$	−5.14226	−	11.2600i	−0.463662	−	1.01528i
$124$	3.88612	+	4.48482i	0.348984	+	0.402749i
$125$	0.741038	+	0.476236i	0.0662805	+	0.0425959i
$126$	−0.317178	+	2.20602i	−0.0282565	+	0.196528i
$127$	1.62103	−	11.2745i	0.143844	−	1.00045i	−0.782197	−	0.623031i	$-0.785901\pi$
$127$	1.62103	−	11.2745i	0.143844	−	1.00045i	0.926041	−	0.377423i	$-0.123190\pi$
$128$	−12.8103	−	8.23266i	−1.13228	−	0.727671i
$129$	1.40875	+	1.62578i	0.124033	+	0.143142i
$130$	0.424075	+	0.928595i	0.0371939	+	0.0814432i
$131$	8.10128	−	5.20637i	0.707812	−	0.454883i	−0.136566	−	0.990631i	$-0.543607\pi$
$131$	8.10128	−	5.20637i	0.707812	−	0.454883i	0.844378	+	0.535748i	$0.179970\pi$
$132$	6.90436	+	2.02730i	0.600948	+	0.176454i
$133$	−1.76643	+	2.03857i	−0.153169	+	0.176767i
$134$	0.658934	−	0.193480i	0.0569232	−	0.0167142i
$135$	−0.0366213	+	0.0801894i	−0.00315186	+	0.00690161i
$136$	0.306755	+	2.13353i	0.0263040	+	0.182948i
$137$	12.2009			1.04240			0.521198	−	0.853436i	$-0.325485\pi$
$137$	12.2009			1.04240			0.521198	+	0.853436i	$0.325485\pi$
$138$	3.52496	+	10.0905i	0.300065	+	0.858963i
$139$	−4.48141			−0.380109			−0.190054	−	0.981774i	$-0.560866\pi$
$139$	−4.48141			−0.380109			−0.190054	+	0.981774i	$0.560866\pi$
$140$	0.0372254	+	0.258908i	0.00314612	+	0.0218817i
$141$	−0.0764710	+	0.167448i	−0.00644002	+	0.0141017i
$142$	2.29464	−	0.673766i	0.192562	−	0.0565412i
$143$	−8.25181	+	9.52310i	−0.690051	+	0.796361i
$144$	1.08458	+	0.318463i	0.0903821	+	0.0265386i
$145$	0.480223	−	0.308620i	0.0398803	−	0.0256295i
$146$	−1.97485	−	4.32431i	−0.163439	−	0.357882i
$147$	−0.654861	−	0.755750i	−0.0540120	−	0.0623332i
$148$	9.01514	+	5.79368i	0.741040	+	0.476238i
$149$	0.874668	−	6.08345i	0.0716556	−	0.498375i	−0.922114	−	0.386919i	$-0.873539\pi$
$149$	0.874668	−	6.08345i	0.0716556	−	0.498375i	0.993769	−	0.111456i	$-0.0355516\pi$
$150$	1.58343	−	11.0130i	0.129286	−	0.899205i
$151$	8.09964	+	5.20532i	0.659139	+	0.423603i	0.826996	−	0.562208i	$-0.190048\pi$
$151$	8.09964	+	5.20532i	0.659139	+	0.423603i	−0.167856	+	0.985811i	$0.553684\pi$
$152$	−3.80749	−	4.39408i	−0.308828	−	0.356407i
$153$	−0.415415	−	0.909632i	−0.0335843	−	0.0735394i
$154$	−4.54699	+	2.92217i	−0.366407	+	0.235475i
$155$	−0.169170	−	0.0496728i	−0.0135881	−	0.00398981i
$156$	10.0958	−	11.6512i	0.808314	−	0.932845i
$157$	−7.90469	+	2.32103i	−0.630863	+	0.185238i	−0.581505	−	0.813543i	$-0.697536\pi$
$157$	−7.90469	+	2.32103i	−0.630863	+	0.185238i	−0.0493582	+	0.998781i	$0.515718\pi$
$158$	10.3171	−	22.5913i	0.820786	−	1.79727i
$159$	−0.806980	−	5.61267i	−0.0639977	−	0.445114i
$160$	0.602123			0.0476020
$161$	−4.45741	−	1.76959i	−0.351294	−	0.139463i
$162$	2.22871			0.175104
$163$	−1.61476	−	11.2309i	−0.126478	−	0.879672i	−0.949969	−	0.312344i	$-0.898886\pi$
$163$	−1.61476	−	11.2309i	−0.126478	−	0.879672i	0.823491	−	0.567329i	$-0.192023\pi$
$164$	−15.2578	+	33.4099i	−1.19143	+	2.60888i
$165$	−0.205134	+	0.0602328i	−0.0159697	+	0.00468911i
$166$	−10.9239	+	12.6068i	−0.847859	+	0.978481i
$167$	−7.67556	−	2.25375i	−0.593953	−	0.174400i	−0.0290785	−	0.999577i	$-0.509257\pi$
$167$	−7.67556	−	2.25375i	−0.593953	−	0.174400i	−0.564875	+	0.825177i	$0.691075\pi$
$168$	1.81329	−	1.16533i	0.139899	−	0.0899073i
$169$	5.81448	+	12.7319i	0.447268	+	0.979380i
$170$	−0.128663	−	0.148485i	−0.00986800	−	0.0113883i
$171$	2.26921	+	1.45834i	0.173531	+	0.111522i
$172$	0.908390	−	6.31799i	0.0692641	−	0.481743i
$173$	0.226854	−	1.57781i	0.0172474	−	0.119958i	−0.979379	−	0.202033i	$-0.935245\pi$
$173$	0.226854	−	1.57781i	0.0172474	−	0.119958i	0.996626	+	0.0820741i	$0.0261544\pi$
$174$	−12.1407	−	7.80236i	−0.920385	−	0.591496i
$175$	3.26921	+	3.77287i	0.247129	+	0.285203i
$176$	1.13880	+	2.49363i	0.0858404	+	0.187964i
$177$	6.09814	−	3.91903i	0.458364	−	0.294573i
$178$	32.0484	+	9.41025i	2.40213	+	0.705328i
$179$	13.9163	−	16.0602i	1.04015	−	1.20040i	0.0608155	−	0.998149i	$-0.480630\pi$
$179$	13.9163	−	16.0602i	1.04015	−	1.20040i	0.979334	−	0.202248i	$-0.0648247\pi$
$180$	0.250975	−	0.0736930i	0.0187066	−	0.00549275i
$181$	−7.68604	+	16.8301i	−0.571299	+	1.25097i	0.374804	+	0.927104i	$0.377710\pi$
$181$	−7.68604	+	16.8301i	−0.571299	+	1.25097i	−0.946103	+	0.323866i	$0.895017\pi$
$182$	1.64801	+	11.4621i	0.122158	+	0.849631i
$183$	−7.61554			−0.562957
$184$	5.14280	−	8.96718i	0.379132	−	0.661069i
$185$	−0.318390			−0.0234085
$186$	0.634356	+	4.41204i	0.0465133	+	0.323507i
$187$	1.00746	−	2.20602i	0.0736725	−	0.161320i
$188$	0.524075	−	0.153882i	0.0382221	−	0.0112230i
$189$	−0.654861	+	0.755750i	−0.0476341	+	0.0549727i
$190$	0.508505	+	0.149310i	0.0368908	+	0.0108321i
$191$	15.4622	−	9.93693i	1.11880	−	0.719011i	0.155609	−	0.987819i	$-0.450266\pi$
$191$	15.4622	−	9.93693i	1.11880	−	0.719011i	0.963194	+	0.268808i	$0.0866296\pi$
$192$	−5.38451	−	11.7904i	−0.388594	−	0.850902i
$193$	16.7854	+	19.3713i	1.20824	+	1.39438i	0.895809	+	0.444438i	$0.146597\pi$
$193$	16.7854	+	19.3713i	1.20824	+	1.39438i	0.312428	+	0.949942i	$0.398858\pi$
$194$	18.7041	+	12.0204i	1.34287	+	0.863013i
$195$	−0.0651865	+	0.453382i	−0.00466810	+	0.0324674i
$196$	−0.422268	+	2.93694i	−0.0301620	+	0.209781i
$197$	11.2382	+	7.22237i	0.800690	+	0.514572i	0.875841	−	0.482600i	$-0.160307\pi$
$197$	11.2382	+	7.22237i	0.800690	+	0.514572i	−0.0751507	+	0.997172i	$0.523944\pi$
$198$	3.53953	+	4.08484i	0.251544	+	0.290297i
$199$	7.11549	+	15.5807i	0.504404	+	1.10449i	0.975013	+	0.222148i	$0.0713068\pi$
$199$	7.11549	+	15.5807i	0.504404	+	1.10449i	−0.470609	+	0.882342i	$0.655966\pi$
$200$	−9.05237	+	5.81760i	−0.640099	+	0.411367i
$201$	0.295657	+	0.0868128i	0.0208541	+	0.00612330i
$202$	−11.7478	+	13.5576i	−0.826570	+	0.953913i
$203$	6.21307	−	1.82432i	0.436072	−	0.128042i
$204$	−1.23259	+	2.69900i	−0.0862988	+	0.188968i
$205$	−0.155301	−	1.08014i	−0.0108467	−	0.0754403i
$206$	−41.4724			−2.88952
$207$	−1.11722	+	4.66388i	−0.0776524	+	0.324162i
$208$	5.87324			0.407236
$209$	0.930986	+	6.47515i	0.0643976	+	0.447895i
$210$	−0.0816181	+	0.178719i	−0.00563219	+	0.0123328i
$211$	−23.3048	+	6.84292i	−1.60437	+	0.471086i	−0.956759	−	0.290883i	$-0.906051\pi$
$211$	−23.3048	+	6.84292i	−1.60437	+	0.471086i	−0.647613	+	0.761969i	$0.724233\pi$
$212$	−11.0179	+	12.7153i	−0.756713	+	0.873293i
$213$	1.02958	+	0.302312i	0.0705458	+	0.0207141i
$214$	−19.0265	+	12.2276i	−1.30062	+	0.835860i
$215$	0.0787805	+	0.172505i	0.00537278	+	0.0117648i
$216$	−1.41153	−	1.62899i	−0.0960424	−	0.110839i
$217$	−1.68251	−	1.08128i	−0.114216	−	0.0734022i
$218$	5.32793	−	37.0566i	0.360853	−	2.50979i
$219$	0.303563	−	2.11132i	0.0205129	−	0.142670i
$220$	0.533654	+	0.342959i	0.0359790	+	0.0231223i
$221$	−3.40255	−	3.92676i	−0.228881	−	0.264142i
$222$	3.34382	+	7.32195i	0.224423	+	0.491417i
$223$	14.9754	−	9.62408i	1.00282	−	0.644476i	0.0672983	−	0.997733i	$-0.478562\pi$
$223$	14.9754	−	9.62408i	1.00282	−	0.644476i	0.935526	+	0.353257i	$0.114926\pi$
$224$	6.55353	+	1.92429i	0.437876	+	0.128572i
$225$	3.26921	−	3.77287i	0.217948	−	0.251525i
$226$	−17.0838	+	5.01625i	−1.13640	+	0.333676i
$227$	−4.24212	+	9.28894i	−0.281559	+	0.616529i	−0.996585	−	0.0825689i	$-0.973688\pi$
$227$	−4.24212	+	9.28894i	−0.281559	+	0.616529i	0.715026	+	0.699098i	$0.246415\pi$
$228$	−1.13903	−	7.92215i	−0.0754343	−	0.524657i
$229$	0.658210			0.0434957			0.0217479	−	0.999763i	$-0.493077\pi$
$229$	0.658210			0.0434957			0.0217479	+	0.999763i	$0.493077\pi$
$230$	0.0475467	+	0.941055i	0.00313514	+	0.0620513i
$231$	−2.42518			−0.159565
$232$	1.98635	+	13.8154i	0.130410	+	0.907022i
$233$	−7.97784	+	17.4690i	−0.522645	+	1.14443i	0.445783	+	0.895141i	$0.352925\pi$
$233$	−7.97784	+	17.4690i	−0.522645	+	1.14443i	−0.968428	+	0.249293i	$0.919802\pi$
$234$	11.1109	−	3.26247i	0.726345	−	0.213274i
$235$	−0.0106271	+	0.0122643i	−0.000693236	+	0.000800037i
$236$	−20.6371	−	6.05961i	−1.34336	−	0.394447i
$237$	9.37454	−	6.02465i	0.608942	−	0.391343i
$238$	−0.925839	−	2.02730i	−0.0600132	−	0.131411i
$239$	−3.65938	−	4.22315i	−0.236706	−	0.273173i	0.624952	−	0.780664i	$-0.285119\pi$
$239$	−3.65938	−	4.22315i	−0.236706	−	0.273173i	−0.861657	+	0.507490i	$0.830573\pi$
$240$	0.0838301	+	0.0538744i	0.00541121	+	0.00347757i
$241$	−1.70162	+	11.8350i	−0.109611	+	0.762362i	0.858676	+	0.512520i	$0.171288\pi$
$241$	−1.70162	+	11.8350i	−0.109611	+	0.762362i	−0.968287	+	0.249842i	$0.919621\pi$
$242$	1.62348	−	11.2915i	0.104361	−	0.725846i
$243$	0.841254	+	0.540641i	0.0539664	+	0.0346821i
$244$	14.7975	+	17.0772i	0.947311	+	1.09325i
$245$	−0.0366213	−	0.0801894i	−0.00233965	−	0.00512312i
$246$	−23.2088	+	14.9154i	−1.47974	+	0.950969i
$247$	13.4477	+	3.94859i	0.855654	+	0.251243i
$248$	2.82306	−	3.25798i	0.179264	−	0.206882i
$249$	−7.18153	+	2.10869i	−0.455111	+	0.133633i
$250$	0.815547	−	1.78580i	0.0515797	−	0.112944i
$251$	−0.716671	−	4.98456i	−0.0452359	−	0.314623i	−0.999859	−	0.0168053i	$-0.994650\pi$
$251$	−0.716671	−	4.98456i	−0.0452359	−	0.314623i	0.954623	−	0.297817i	$-0.0962586\pi$
$252$	2.96714			0.186912
$253$	−10.3224	+	5.35930i	−0.648966	+	0.336936i
$254$	−25.3860			−1.59286
$255$	−0.0125459	−	0.0872586i	−0.000785654	−	0.00546435i
$256$	−3.32927	+	7.29008i	−0.208079	+	0.455630i
$257$	−0.817990	+	0.240184i	−0.0510248	+	0.0149822i	−0.307145	−	0.951663i	$-0.599374\pi$
$257$	−0.817990	+	0.240184i	−0.0510248	+	0.0149822i	0.256121	+	0.966645i	$0.417556\pi$
$258$	3.13969	−	3.62340i	0.195469	−	0.225583i
$259$	−3.46537	−	1.01753i	−0.215328	−	0.0632260i
$260$	1.14333	−	0.734774i	0.0709064	−	0.0455688i
$261$	−2.68996	−	5.89020i	−0.166505	−	0.364594i
$262$	−14.0549	−	16.2202i	−0.868316	−	1.00209i
$263$	19.5164	+	12.5424i	1.20343	+	0.773398i	0.979546	−	0.201218i	$-0.0644900\pi$
$263$	19.5164	+	12.5424i	1.20343	+	0.773398i	0.223884	+	0.974616i	$0.428126\pi$
$264$	0.743936	−	5.17419i	0.0457861	−	0.318449i
$265$	0.0711401	−	0.494790i	0.00437010	−	0.0303947i
$266$	5.05742	+	3.25020i	0.310090	+	0.199283i
$267$	9.81431	+	11.3263i	0.600626	+	0.693160i
$268$	−0.379810	−	0.831668i	−0.0232006	−	0.0508022i
$269$	−21.1222	+	13.5744i	−1.28784	+	0.827647i	−0.991834	−	0.127537i	$-0.959293\pi$
$269$	−21.1222	+	13.5744i	−1.28784	+	0.827647i	−0.296011	+	0.955185i	$0.595656\pi$
$270$	0.188515	+	0.0553531i	0.0114727	+	0.00336868i
$271$	−5.00687	+	5.77824i	−0.304146	+	0.351003i	−0.887163	−	0.461457i	$-0.847327\pi$
$271$	−5.00687	+	5.77824i	−0.304146	+	0.351003i	0.583017	+	0.812460i	$0.301872\pi$
$272$	−1.08458	+	0.318463i	−0.0657626	+	0.0193096i
$273$	−2.15843	+	4.72631i	−0.130634	+	0.286049i
$274$	−3.86987	−	26.9155i	−0.233787	−	1.62603i
$275$	12.1071			0.730083
$276$	12.6292	−	6.55694i	0.760188	−	0.394681i
$277$	8.19180			0.492198			0.246099	−	0.969245i	$-0.420851\pi$
$277$	8.19180			0.492198			0.246099	+	0.969245i	$0.420851\pi$
$278$	1.42141	+	9.88610i	0.0852503	+	0.592929i
$279$	−0.830830	+	1.81926i	−0.0497405	+	0.108916i
$280$	0.182320	−	0.0535340i	0.0108957	−	0.00319927i
$281$	−18.2906	+	21.1085i	−1.09113	+	1.25923i	−0.127540	+	0.991833i	$0.540708\pi$
$281$	−18.2906	+	21.1085i	−1.09113	+	1.25923i	−0.963587	+	0.267394i	$0.913837\pi$
$282$	0.393649	+	0.115586i	0.0234415	+	0.00688303i
$283$	−19.2623	+	12.3791i	−1.14503	+	0.735863i	−0.968643	−	0.248459i	$-0.920076\pi$
$283$	−19.2623	+	12.3791i	−1.14503	+	0.735863i	−0.176383	+	0.984322i	$0.556440\pi$
$284$	−1.32263	−	2.89616i	−0.0784837	−	0.171855i
$285$	0.155722	+	0.179712i	0.00922416	+	0.0106452i
$286$	23.6255	+	15.1832i	1.39700	+	0.897799i
$287$	1.76166	−	12.2526i	0.103988	−	0.723249i
$288$	0.972039	−	6.76068i	0.0572779	−	0.398377i
$289$	−13.4601	−	8.65025i	−0.791768	−	0.508838i
$290$	−0.833140	−	0.961494i	−0.0489236	−	0.0564609i
$291$	4.14418	+	9.07449i	0.242936	+	0.531956i
$292$	−5.32430	+	3.42172i	−0.311581	+	0.200241i
$293$	9.63304	+	2.82851i	0.562768	+	0.165244i	0.550729	−	0.834684i	$-0.314350\pi$
$293$	9.63304	+	2.82851i	0.562768	+	0.165244i	0.0120387	+	0.999928i	$0.496168\pi$
$294$	−1.45949	+	1.68434i	−0.0851194	+	0.0982330i
$295$	0.613146	−	0.180036i	0.0356987	−	0.0104821i
$296$	3.23394	−	7.08133i	0.187969	−	0.411594i
$297$	0.345139	+	2.40050i	0.0200270	+	0.139291i
$298$	−13.6976			−0.793483
$299$	1.25740	+	24.8866i	0.0727171	+	1.43923i
$300$	−14.8126			−0.855207
$301$	0.306151	+	2.12932i	0.0176462	+	0.122732i
$302$	8.91403	−	19.5190i	0.512945	−	1.12319i
$303$	−7.72316	+	2.26772i	−0.443684	+	0.130277i
$304$	1.99673	−	2.30435i	0.114520	−	0.132164i
$305$	−0.644161	−	0.189143i	−0.0368845	−	0.0108303i
$306$	−1.87491	+	1.20493i	−0.107181	+	0.0688813i
$307$	2.49269	+	5.45824i	0.142266	+	0.311518i	0.967330	−	0.253521i	$-0.0815885\pi$
$307$	2.49269	+	5.45824i	0.142266	+	0.311518i	−0.825064	+	0.565039i	$0.808861\pi$
$308$	4.71228	+	5.43826i	0.268507	+	0.309873i
$309$	−15.6543	−	10.0604i	−0.890541	−	0.572316i
$310$	−0.0559223	+	0.388948i	−0.00317617	+	0.0220908i
$311$	1.22818	−	8.54215i	0.0696435	−	0.484381i	−0.924913	−	0.380180i	$-0.875862\pi$
$311$	1.22818	−	8.54215i	0.0696435	−	0.484381i	0.994556	−	0.104202i	$-0.0332287\pi$
$312$	−9.42158	−	6.05488i	−0.533392	−	0.342790i
$313$	9.36577	+	10.8087i	0.529385	+	0.610943i	0.955955	−	0.293512i	$-0.0948239\pi$
$313$	9.36577	+	10.8087i	0.529385	+	0.610943i	−0.426571	+	0.904454i	$0.640278\pi$
$314$	7.62743	+	16.7017i	0.430441	+	0.942534i
$315$	−0.0741615	+	0.0476607i	−0.00417853	+	0.00268538i
$316$	−31.7251	−	9.31532i	−1.78467	−	0.524028i
$317$	5.40750	−	6.24059i	0.303716	−	0.350507i	−0.583291	−	0.812263i	$-0.698235\pi$
$317$	5.40750	−	6.24059i	0.303716	−	0.350507i	0.887007	+	0.461757i	$0.152781\pi$
$318$	−12.1257	+	3.56043i	−0.679976	+	0.199659i
$319$	6.52365	−	14.2848i	0.365254	−	0.799795i
$320$	−0.162617	−	1.13103i	−0.00909057	−	0.0632263i
$321$	−10.1480			−0.566404
$322$	−2.48996	+	10.3944i	−0.138760	+	0.579259i
$323$	−2.69742			−0.150088
$324$	−0.422268	−	2.93694i	−0.0234593	−	0.163163i
$325$	10.7754	−	23.5948i	0.597711	−	1.30880i
$326$	−24.2635	+	7.12439i	−1.34383	+	0.394584i
$327$	11.0003	−	12.6950i	0.608317	−	0.702036i
$328$	25.6009	+	7.51709i	1.41357	+	0.415062i
$329$	−0.154861	+	0.0995230i	−0.00853775	+	0.00548688i
$330$	0.197939	+	0.433426i	0.0108962	+	0.0238593i
$331$	−0.322764	−	0.372489i	−0.0177407	−	0.0204739i	0.746810	−	0.665038i	$-0.231584\pi$
$331$	−0.322764	−	0.372489i	−0.0177407	−	0.0204739i	−0.764551	+	0.644564i	$0.777039\pi$
$332$	18.6827	+	12.0067i	1.02535	+	0.658951i
$333$	−0.513994	+	3.57491i	−0.0281667	+	0.195904i
$334$	−2.53730	+	17.6473i	−0.138835	+	0.965618i
$335$	0.0228520	+	0.0146861i	0.00124854	+	0.000802388i
$336$	0.740237	+	0.854279i	0.0403832	+	0.0466047i
$337$	7.93786	+	17.3815i	0.432403	+	0.946830i	0.992931	+	0.118695i	$0.0378710\pi$
$337$	7.93786	+	17.3815i	0.432403	+	0.946830i	−0.560528	+	0.828135i	$0.689402\pi$
$338$	26.2427	−	16.8652i	1.42742	−	0.917344i
$339$	−7.66533	−	2.25074i	−0.416323	−	0.122244i
$340$	−0.171292	+	0.197682i	−0.00928963	+	0.0107208i
$341$	−4.65389	+	1.36650i	−0.252022	+	0.0740004i
$342$	2.49738	−	5.46849i	0.135043	−	0.295702i
$343$	−0.142315	−	0.989821i	−0.00768428	−	0.0534453i
$344$	−4.63688			−0.250004
$345$	−0.210334	+	0.366747i	−0.0113240	+	0.0197450i
$346$	−3.55263			−0.190991
$347$	−2.92237	−	20.3255i	−0.156881	−	1.09113i	−0.904337	−	0.426819i	$-0.859634\pi$
$347$	−2.92237	−	20.3255i	−0.156881	−	1.09113i	0.747456	−	0.664311i	$-0.231275\pi$
$348$	−7.98149	+	17.4770i	−0.427853	+	0.936867i
$349$	22.5464	−	6.62023i	1.20688	−	0.354373i	0.384402	−	0.923166i	$-0.374408\pi$
$349$	22.5464	−	6.62023i	1.20688	−	0.354373i	0.822481	+	0.568793i	$0.192589\pi$
$350$	7.28612	−	8.40863i	0.389460	−	0.449460i
$351$	4.98538	+	1.46384i	0.266100	+	0.0781339i
$352$	13.9349	−	8.95543i	0.742734	−	0.477326i
$353$	−12.0267	−	26.3347i	−0.640115	−	1.40166i	−0.899946	−	0.436002i	$-0.856394\pi$
$353$	−12.0267	−	26.3347i	−0.640115	−	1.40166i	0.259831	−	0.965654i	$-0.416333\pi$
$354$	−10.5797	−	12.2096i	−0.562303	−	0.648933i
$355$	0.0795788	+	0.0511422i	0.00422360	+	0.00271435i
$356$	6.32847	−	44.0155i	0.335408	−	2.33282i
$357$	0.142315	−	0.989821i	0.00753210	−	0.0523869i
$358$	−39.8431	−	25.6056i	−2.10577	−	1.35330i
$359$	11.4911	+	13.2615i	0.606479	+	0.699914i	0.973081	−	0.230464i	$-0.0740244\pi$
$359$	11.4911	+	13.2615i	0.606479	+	0.699914i	−0.366602	+	0.930378i	$0.619479\pi$
$360$	−0.0789359	−	0.172846i	−0.00416029	−	0.00910976i
$361$	−9.86279	+	6.33843i	−0.519094	+	0.333602i
$362$	39.5654	+	11.6174i	2.07951	+	0.610599i
$363$	3.35190	−	3.86830i	0.175929	−	0.203033i
$364$	14.7923	−	4.34341i	0.775327	−	0.227656i
$365$	0.0781145	−	0.171047i	0.00408870	−	0.00895301i
$366$	2.41548	+	16.8001i	0.126259	+	0.878153i
$367$	−13.9832			−0.729917			−0.364958	−	0.931024i	$-0.618917\pi$
$367$	−13.9832			−0.729917			−0.364958	+	0.931024i	$0.618917\pi$
$368$	5.03854	+	2.00030i	0.262652	+	0.104273i
$369$	−12.3786			−0.644405
$370$	0.100986	+	0.702376i	0.00525003	+	0.0365148i
$371$	2.35556	−	5.15796i	0.122295	−	0.267788i
$372$	5.69389	−	1.67188i	0.295215	−	0.0866828i
$373$	−0.452630	+	0.522363i	−0.0234363	+	0.0270469i	−0.767347	−	0.641232i	$-0.778423\pi$
$373$	−0.452630	+	0.522363i	−0.0234363	+	0.0270469i	0.743910	+	0.668279i	$0.232969\pi$
$374$	−5.18608	−	1.52277i	−0.268166	−	0.0787406i
$375$	0.741038	−	0.476236i	0.0382671	−	0.0245927i
$376$	−0.164830	−	0.360928i	−0.00850048	−	0.0186135i
$377$	−22.0328	−	25.4272i	−1.13475	−	1.30957i
$378$	1.87491	+	1.20493i	0.0964349	+	0.0619749i
$379$	0.498652	−	3.46820i	0.0256140	−	0.178150i	−0.972998	−	0.230812i	$-0.925862\pi$
$379$	0.498652	−	3.46820i	0.0256140	−	0.178150i	0.998612	+	0.0526626i	$0.0167708\pi$
$380$	0.100413	−	0.698384i	0.00515105	−	0.0358264i
$381$	−9.58228	−	6.15816i	−0.490915	−	0.315492i
$382$	−26.8253	−	30.9581i	−1.37250	−	1.58395i
$383$	−7.73204	−	16.9308i	−0.395089	−	0.865124i	−0.997745	−	0.0671230i	$-0.978618\pi$
$383$	−7.73204	−	16.9308i	−0.395089	−	0.865124i	0.602656	−	0.798001i	$-0.294109\pi$
$384$	−12.8103	+	8.23266i	−0.653721	+	0.420121i
$385$	−0.205134	−	0.0602328i	−0.0104546	−	0.00306975i
$386$	37.4097	−	43.1731i	1.90410	−	2.19745i
$387$	2.06408	−	0.606069i	0.104923	−	0.0308082i
$388$	12.2963	−	26.9253i	0.624253	−	1.36692i
$389$	2.55697	+	17.7841i	0.129644	+	0.901692i	0.946005	+	0.324151i	$0.105079\pi$
$389$	2.55697	+	17.7841i	0.129644	+	0.901692i	−0.816362	+	0.577541i	$0.804012\pi$
$390$	1.02085			0.0516926
$391$	−1.58162	−	4.52753i	−0.0799859	−	0.228967i
$392$	2.15546			0.108867
$393$	−1.37049	−	9.53199i	−0.0691322	−	0.480825i
$394$	12.3682	−	27.0825i	0.623100	−	1.36440i
$395$	0.942576	−	0.276765i	0.0474261	−	0.0139256i
$396$	4.71228	−	5.43826i	0.236801	−	0.273283i
$397$	28.4338	+	8.34892i	1.42705	+	0.419020i	0.901884	−	0.431978i	$-0.142184\pi$
$397$	28.4338	+	8.34892i	1.42705	+	0.419020i	0.525168	+	0.850998i	$0.324002\pi$
$398$	32.1146	−	20.6388i	1.60976	−	1.03453i
$399$	1.12055	+	2.45366i	0.0560976	+	0.122837i
$400$	−3.69543	−	4.26476i	−0.184772	−	0.213238i
$401$	18.9823	+	12.1992i	0.947930	+	0.609198i	0.920633	−	0.390429i	$-0.127673\pi$
$401$	18.9823	+	12.1992i	0.947930	+	0.609198i	0.0272976	+	0.999627i	$0.491310\pi$
$402$	0.0977350	−	0.679762i	0.00487458	−	0.0339034i
$403$	−1.47889	+	10.2859i	−0.0736688	+	0.512378i
$404$	20.0917	+	12.9122i	0.999602	+	0.642405i
$405$	0.0577299	+	0.0666238i	0.00286862	+	0.00331056i
$406$	−5.99514	−	13.1275i	−0.297534	−	0.651508i
$407$	−7.36850	+	4.73545i	−0.365243	+	0.234728i
$408$	2.06815	+	0.607265i	0.102389	+	0.0300641i
$409$	6.73611	−	7.77388i	0.333079	−	0.384394i	−0.564363	−	0.825527i	$-0.690878\pi$
$409$	6.73611	−	7.77388i	0.333079	−	0.384394i	0.897442	+	0.441133i	$0.145423\pi$
$410$	−2.33356	+	0.685194i	−0.115246	+	0.0338393i
$411$	5.06845	−	11.0983i	0.250008	−	0.547441i
$412$	7.85767	+	54.6513i	0.387120	+	2.69248i
$413$	7.24887			0.356694
$414$	10.6430	+	0.985337i	0.523074	+	0.0484267i
$415$	−0.659822			−0.0323894
$416$	−5.05056	−	35.1274i	−0.247624	−	1.72226i
$417$	−1.86165	+	4.07644i	−0.0911652	+	0.199624i
$418$	13.9890	−	4.10755i	0.684226	−	0.200907i
$419$	−14.5377	+	16.7774i	−0.710212	+	0.819628i	−0.990094	−	0.140406i	$-0.955159\pi$
$419$	−14.5377	+	16.7774i	−0.710212	+	0.819628i	0.279882	+	0.960034i	$0.409705\pi$
$420$	0.250975	+	0.0736930i	0.0122463	+	0.00359585i
$421$	−14.9458	+	9.60509i	−0.728414	+	0.468123i	−0.851555	−	0.524266i	$-0.824340\pi$
$421$	−14.9458	+	9.60509i	−0.728414	+	0.468123i	0.123141	+	0.992389i	$0.460703\pi$
$422$	22.4874	+	49.2406i	1.09467	+	2.39699i
$423$	0.120549	+	0.139121i	0.00586129	+	0.00676429i
$424$	10.2821	+	6.60788i	0.499341	+	0.320907i
$425$	−0.710468	+	4.94141i	−0.0344628	+	0.239694i
$426$	0.340347	−	2.36717i	0.0164899	−	0.114690i
$427$	−6.40660	−	4.11727i	−0.310037	−	0.199249i
$428$	19.7181	+	22.7559i	0.953111	+	1.09995i
$429$	5.23459	+	11.4621i	0.252728	+	0.553398i
$430$	0.355563	−	0.228506i	0.0171468	−	0.0110196i
$431$	−25.5341	−	7.49748i	−1.22993	−	0.361141i	−0.398708	−	0.917078i	$-0.630541\pi$
$431$	−25.5341	−	7.49748i	−1.22993	−	0.361141i	−0.831225	+	0.555937i	$0.812360\pi$
$432$	0.740237	−	0.854279i	0.0356147	−	0.0411015i
$433$	−6.76513	+	1.98642i	−0.325111	+	0.0954613i	−0.440215	−	0.897892i	$-0.645098\pi$
$433$	−6.76513	+	1.98642i	−0.325111	+	0.0954613i	0.115104	+	0.993353i	$0.463280\pi$
$434$	−1.85168	+	4.05461i	−0.0888833	+	0.194627i
$435$	−0.0812393	−	0.565031i	−0.00389512	−	0.0270912i
$436$	−49.8417			−2.38698
$437$	10.1917	+	7.96740i	0.487534	+	0.381132i
$438$	−4.75391			−0.227151
$439$	−0.541875	−	3.76883i	−0.0258623	−	0.179876i	0.972796	−	0.231664i	$-0.0744171\pi$
$439$	−0.541875	−	3.76883i	−0.0258623	−	0.179876i	−0.998658	+	0.0517880i	$0.983508\pi$
$440$	0.191434	−	0.419182i	0.00912625	−	0.0199837i
$441$	−0.959493	+	0.281733i	−0.0456901	+	0.0134158i
$442$	−7.58330	+	8.75159i	−0.360701	+	0.416271i
$443$	−8.19441	−	2.40610i	−0.389328	−	0.114317i	0.0812094	−	0.996697i	$-0.474122\pi$
$443$	−8.19441	−	2.40610i	−0.389328	−	0.114317i	−0.470537	+	0.882380i	$0.655940\pi$
$444$	9.01514	−	5.79368i	0.427840	−	0.274956i
$445$	0.548839	+	1.20179i	0.0260174	+	0.0569703i
$446$	−25.9808	−	29.9834i	−1.23023	−	1.41976i
$447$	−5.17035	−	3.32278i	−0.244549	−	0.157162i
$448$	1.84465	−	12.8298i	0.0871516	−	0.606153i
$449$	0.833319	−	5.79586i	0.0393268	−	0.273524i	−0.960664	−	0.277712i	$-0.910424\pi$
$449$	0.833319	−	5.79586i	0.0393268	−	0.273524i	0.999991	+	0.00418805i	$0.00133310\pi$
$450$	−9.35997	−	6.01529i	−0.441233	−	0.283563i
$451$	−19.6592	−	22.6879i	−0.925714	−	1.06833i
$452$	9.84711	+	21.5622i	0.463169	+	1.01420i
$453$	8.09964	−	5.20532i	0.380554	−	0.244567i
$454$	21.8371	+	6.41196i	1.02487	+	0.300928i
$455$	−0.299955	+	0.346167i	−0.0140621	+	0.0162286i
$456$	−5.57868	+	1.63805i	−0.261246	+	0.0767086i
$457$	−9.02988	+	19.7727i	−0.422400	+	0.924927i	0.572099	+	0.820184i	$0.306129\pi$
$457$	−9.02988	+	19.7727i	−0.422400	+	0.924927i	−0.994499	+	0.104743i	$0.966598\pi$
$458$	−0.208770	−	1.45203i	−0.00975517	−	0.0678487i
$459$	−1.00000			−0.0466760
$460$	1.23109	−	0.240955i	0.0573999	−	0.0112346i
$461$	−24.6617			−1.14861			−0.574304	−	0.818642i	$-0.694727\pi$
$461$	−24.6617			−1.14861			−0.574304	+	0.818642i	$0.694727\pi$
$462$	0.769214	+	5.35000i	0.0357871	+	0.248905i
$463$	−3.65448	+	8.00220i	−0.169838	+	0.371894i	−0.975343	−	0.220696i	$-0.929167\pi$
$463$	−3.65448	+	8.00220i	−0.169838	+	0.371894i	0.805504	+	0.592590i	$0.201894\pi$
$464$	−7.02308	+	2.06216i	−0.326038	+	0.0957335i
$465$	−0.115460	+	0.133248i	−0.00535432	+	0.00617921i
$466$	41.0675	+	12.0585i	1.90241	+	0.558599i
$467$	0.866156	−	0.556645i	0.0400809	−	0.0257584i	−0.520447	−	0.853894i	$-0.674235\pi$
$467$	0.866156	−	0.556645i	0.0400809	−	0.0257584i	0.560528	+	0.828136i	$0.310598\pi$
$468$	−6.40436	−	14.0236i	−0.296042	−	0.648241i
$469$	0.201788	+	0.232876i	0.00931771	+	0.0107532i
$470$	0.0304261	+	0.0195536i	0.00140345	+	0.000901943i
$471$	−1.17245	+	8.15455i	−0.0540235	+	0.375742i
$472$	−2.22362	+	15.4656i	−0.102351	+	0.711864i
$473$	4.38890	+	2.82058i	0.201802	+	0.129690i
$474$	−16.2639	−	18.7696i	−0.747026	−	0.862114i
$475$	−5.59404	−	12.2492i	−0.256672	−	0.562033i
$476$	−2.49611	+	1.60416i	−0.114409	+	0.0735263i
$477$	−5.44069	−	1.59753i	−0.249112	−	0.0731460i
$478$	−8.15570	+	9.41218i	−0.373033	+	0.430503i
$479$	23.8624	−	7.00662i	1.09030	−	0.320141i	0.313307	−	0.949652i	$-0.398563\pi$
$479$	23.8624	−	7.00662i	1.09030	−	0.320141i	0.776991	+	0.629511i	$0.216745\pi$
$480$	0.250131	−	0.547710i	0.0114169	−	0.0249994i
$481$	2.67064	+	18.5747i	0.121770	+	0.846932i
$482$	26.6481			1.21379
$483$	−3.46135	+	3.31949i	−0.157497	+	0.151042i
$484$	−15.1873			−0.690331
$485$	0.125158	+	0.870492i	0.00568313	+	0.0395270i
$486$	0.925839	−	2.02730i	0.0419969	−	0.0919604i
$487$	−25.0571	+	7.35743i	−1.13545	+	0.333397i	−0.794846	−	0.606811i	$-0.792448\pi$
$487$	−25.0571	+	7.35743i	−1.13545	+	0.333397i	−0.340600	+	0.940208i	$0.610630\pi$
$488$	10.7496	−	12.4057i	0.486610	−	0.561578i
$489$	−10.8868	−	3.19665i	−0.492317	−	0.144557i
$490$	−0.165284	+	0.106222i	−0.00746678	+	0.00479861i
$491$	−3.15048	−	6.89859i	−0.142179	−	0.311329i	0.825124	−	0.564952i	$-0.191105\pi$
$491$	−3.15048	−	6.89859i	−0.142179	−	0.311329i	−0.967303	+	0.253622i	$0.918378\pi$
$492$	24.0524	+	27.7580i	1.08437	+	1.25143i
$493$	5.44742	+	3.50085i	0.245340	+	0.157670i
$494$	4.44537	−	30.9182i	0.200007	−	1.39108i
$495$	−0.0304261	+	0.211618i	−0.00136755	+	0.00951152i
$496$	1.90186	+	1.22225i	0.0853961	+	0.0548807i
$497$	0.702697	+	0.810955i	0.0315203	+	0.0363763i
$498$	6.92964	+	15.1738i	0.310525	+	0.679954i
$499$	13.4014	−	8.61256i	0.599929	−	0.385551i	−0.205139	−	0.978733i	$-0.565765\pi$
$499$	13.4014	−	8.61256i	0.599929	−	0.385551i	0.805069	+	0.593182i	$0.202128\pi$
$500$	−2.50780	−	0.736357i	−0.112152	−	0.0329309i
$501$	−5.23863	+	6.04570i	−0.234045	+	0.270102i
$502$	−10.7687	+	3.16199i	−0.480632	+	0.141126i
$503$	9.92594	−	21.7348i	0.442576	−	0.969106i	−0.548542	−	0.836123i	$-0.684817\pi$
$503$	9.92594	−	21.7348i	0.442576	−	0.969106i	0.991118	−	0.132983i	$-0.0424557\pi$
$504$	−0.306755	−	2.13353i	−0.0136639	−	0.0950348i
$505$	−0.709586			−0.0315761
$506$	15.0968	+	21.0717i	0.671133	+	0.936749i
$507$	13.9968			0.621620
$508$	4.80983	+	33.4531i	0.213402	+	1.48424i
$509$	−3.22145	+	7.05399i	−0.142788	+	0.312663i	−0.967492	−	0.252903i	$-0.918615\pi$
$509$	−3.22145	+	7.05399i	−0.142788	+	0.312663i	0.824703	+	0.565565i	$0.191342\pi$
$510$	−0.188515	+	0.0553531i	−0.00834759	+	0.00245107i
$511$	1.39684	−	1.61204i	0.0617926	−	0.0713125i
$512$	−12.0835	−	3.54804i	−0.534020	−	0.156803i
$513$	2.26921	−	1.45834i	0.100188	−	0.0643871i
$514$	0.789299	+	1.72832i	0.0348145	+	0.0762331i
$515$	−1.07425	−	1.23975i	−0.0473372	−	0.0546301i
$516$	−5.36969	−	3.45089i	−0.236387	−	0.151917i
$517$	−0.0635344	+	0.441891i	−0.00279424	+	0.0194344i
$518$	−1.14554	+	7.96743i	−0.0503323	+	0.350069i
$519$	−1.34099	−	0.861799i	−0.0588627	−	0.0378288i
$520$	−0.646543	−	0.746151i	−0.0283528	−	0.0327209i
$521$	0.0253717	+	0.0555563i	0.00111156	+	0.00243397i	0.910187	−	0.414198i	$-0.135938\pi$
$521$	0.0253717	+	0.0555563i	0.00111156	+	0.00243397i	−0.909075	+	0.416632i	$0.863211\pi$
$522$	−12.1407	+	7.80236i	−0.531385	+	0.341500i
$523$	29.5757	+	8.68421i	1.29326	+	0.379734i	0.854771	−	0.519005i	$-0.173697\pi$
$523$	29.5757	+	8.68421i	1.29326	+	0.379734i	0.438484	+	0.898739i	$0.355516\pi$
$524$	−18.7117	+	21.5944i	−0.817424	+	0.943358i
$525$	4.79001	−	1.40647i	0.209053	−	0.0613835i
$526$	21.4787	−	47.0317i	0.936514	−	2.05068i
$527$	−0.284630	−	1.97964i	−0.0123987	−	0.0862346i
$528$	2.74136			0.119302
$529$	−7.39715	+	21.7780i	−0.321615	+	0.946870i
$530$	−1.11408			−0.0483926
$531$	−1.03162	−	7.17509i	−0.0447686	−	0.311372i
$532$	3.32482	−	7.28034i	0.144149	−	0.315643i
$533$	−61.7120	+	18.1203i	−2.67305	+	0.784877i
$534$	21.8732	−	25.2431i	0.946548	−	1.09237i
$535$	−0.858365	−	0.252039i	−0.0371104	−	0.0108966i
$536$	−0.558746	+	0.359084i	−0.0241342	+	0.0155101i
$537$	−8.82786	−	19.3303i	−0.380950	−	0.834165i
$538$	36.6450	+	42.2906i	1.57988	+	1.82328i
$539$	−2.04019	−	1.31115i	−0.0878773	−	0.0564753i
$540$	0.0372254	−	0.258908i	0.00160193	−	0.0111416i
$541$	−2.36013	+	16.4151i	−0.101470	+	0.705739i	0.874051	+	0.485834i	$0.161484\pi$
$541$	−2.36013	+	16.4151i	−0.101470	+	0.705739i	−0.975521	+	0.219905i	$0.929425\pi$
$542$	14.3350	+	9.21255i	0.615741	+	0.395713i
$543$	12.1163	+	13.9829i	0.519960	+	0.600065i
$544$	2.83737	+	6.21297i	0.121651	+	0.266379i
$545$	1.24576	−	0.800600i	0.0533624	−	0.0342939i
$546$	11.1109	+	3.26247i	0.475505	+	0.139621i
$547$	6.02779	−	6.95644i	0.257730	−	0.297436i	−0.612108	−	0.790774i	$-0.709678\pi$
$547$	6.02779	−	6.95644i	0.257730	−	0.297436i	0.869838	+	0.493338i	$0.164224\pi$
$548$	−34.7354	+	10.1992i	−1.48382	+	0.435689i
$549$	−3.16361	+	6.92734i	−0.135020	+	0.295652i
$550$	−3.84009	−	26.7084i	−0.163742	−	1.13885i
$551$	−17.4668			−0.744110
$552$	−6.02043	−	8.40316i	−0.256247	−	0.357662i
$553$	11.1435			0.473871
$554$	−2.59826	−	18.0713i	−0.110390	−	0.767776i
$555$	−0.132264	+	0.289618i	−0.00561430	+	0.0122936i
$556$	12.7583	−	3.74619i	0.541074	−	0.158874i
$557$	24.2320	−	27.9652i	1.02674	−	1.18492i	0.0441746	−	0.999024i	$-0.485934\pi$
$557$	24.2320	−	27.9652i	1.02674	−	1.18492i	0.982568	−	0.185901i	$-0.0595203\pi$
$558$	4.27686	+	1.25580i	0.181054	+	0.0531622i
$559$	9.40303	−	6.04296i	0.397706	−	0.255590i
$560$	0.0413957	+	0.0906440i	0.00174929	+	0.00383041i
$561$	−1.58816	−	1.83283i	−0.0670520	−	0.0773821i
$562$	52.3672	+	33.6544i	2.20898	+	1.41962i
$563$	−2.14315	+	14.9059i	−0.0903230	+	0.628210i	0.893499	+	0.449064i	$0.148243\pi$
$563$	−2.14315	+	14.9059i	−0.0903230	+	0.628210i	−0.983822	+	0.179146i	$0.942667\pi$
$564$	0.0777324	−	0.540641i	0.00327313	−	0.0227651i
$565$	−0.592471	−	0.380758i	−0.0249255	−	0.0160186i
$566$	33.4182	+	38.5667i	1.40467	+	1.62108i
$567$	0.415415	+	0.909632i	0.0174458	+	0.0382010i
$568$	−1.94575	+	1.25046i	−0.0816418	+	0.0524680i
$569$	−20.8197	−	6.11323i	−0.872809	−	0.256280i	−0.185499	−	0.982644i	$-0.559390\pi$
$569$	−20.8197	−	6.11323i	−0.872809	−	0.256280i	−0.687310	+	0.726365i	$0.741208\pi$
$570$	0.347058	−	0.400526i	0.0145367	−	0.0167762i
$571$	−10.4034	+	3.05471i	−0.435368	+	0.127836i	−0.492070	−	0.870556i	$-0.663760\pi$
$571$	−10.4034	+	3.05471i	−0.435368	+	0.127836i	0.0567022	+	0.998391i	$0.481941\pi$
$572$	15.5317	−	34.0098i	0.649415	−	1.42202i
$573$	−2.61573	−	18.1928i	−0.109274	−	0.760016i
$574$	−27.5883			−1.15151
$575$	17.2799	−	16.5717i	0.720620	−	0.691086i
$576$	−12.9618			−0.540074
$577$	5.37829	+	37.4068i	0.223901	+	1.55727i	0.723077	+	0.690767i	$0.242727\pi$
$577$	5.37829	+	37.4068i	0.223901	+	1.55727i	−0.499176	+	0.866500i	$0.666364\pi$
$578$	−14.8134	+	32.4369i	−0.616157	+	1.34920i
$579$	24.5937	−	7.22136i	1.02208	−	0.300109i
$580$	−1.10918	+	1.28006i	−0.0460562	+	0.0531517i
$581$	−7.18153	−	2.10869i	−0.297940	−	0.0874832i
$582$	18.7041	−	12.0204i	0.775309	−	0.498261i
$583$	−5.71267	−	12.5090i	−0.236594	−	0.518070i
$584$	3.01084	+	3.47470i	0.124590	+	0.143784i
$585$	0.385331	+	0.247638i	0.0159315	+	0.0102386i
$586$	3.18438	−	22.1478i	0.131545	−	0.914919i
$587$	−2.56605	+	17.8473i	−0.105912	+	0.736635i	0.865787	+	0.500413i	$0.166818\pi$
$587$	−2.56605	+	17.8473i	−0.105912	+	0.736635i	−0.971699	+	0.236222i	$0.924091\pi$
$588$	2.49611	+	1.60416i	0.102938	+	0.0661542i
$589$	3.53287	+	4.07715i	0.145569	+	0.167996i
$590$	−0.591639	−	1.29551i	−0.0243574	−	0.0533353i
$591$	11.2382	−	7.22237i	0.462279	−	0.297088i
$592$	3.91716	+	1.15018i	0.160994	+	0.0472722i
$593$	−8.59418	+	9.91821i	−0.352921	+	0.407292i	−0.904255	−	0.426992i	$-0.859573\pi$
$593$	−8.59418	+	9.91821i	−0.352921	+	0.407292i	0.551335	+	0.834284i	$0.314119\pi$
$594$	5.18608	−	1.52277i	0.212787	−	0.0624800i
$595$	0.0366213	−	0.0801894i	0.00150133	−	0.00328745i
$596$	2.59526	+	18.0504i	0.106306	+	0.739374i
$597$	17.1286			0.701028
$598$	54.5017	−	10.6673i	2.22874	−	0.436220i
$599$	21.5544			0.880690			0.440345	−	0.897829i	$-0.354856\pi$
$599$	21.5544			0.880690			0.440345	+	0.897829i	$0.354856\pi$
$600$	1.53139	+	10.6510i	0.0625187	+	0.434827i
$601$	19.0771	−	41.7731i	0.778172	−	1.70396i	0.0703982	−	0.997519i	$-0.477573\pi$
$601$	19.0771	−	41.7731i	0.778172	−	1.70396i	0.707773	−	0.706439i	$-0.249700\pi$
$602$	4.60023	−	1.35075i	0.187491	−	0.0550525i
$603$	0.201788	−	0.232876i	0.00821745	−	0.00948344i
$604$	−27.4106	−	8.04847i	−1.11532	−	0.327488i
$605$	0.379595	−	0.243951i	0.0154327	−	0.00991802i
$606$	7.45227	+	16.3182i	0.302728	+	0.662881i
$607$	−21.8569	−	25.2242i	−0.887145	−	1.02382i	−0.999545	−	0.0301573i	$-0.990399\pi$
$607$	−21.8569	−	25.2242i	−0.887145	−	1.02382i	0.112400	−	0.993663i	$-0.464146\pi$
$608$	−15.4992	−	9.96072i	−0.628575	−	0.403961i
$609$	0.921540	−	6.40945i	0.0373427	−	0.259724i
$610$	−0.212939	+	1.48102i	−0.00862165	+	0.0599649i
$611$	0.804632	+	0.517106i	0.0325519	+	0.0209199i
$612$	1.94306	+	2.24241i	0.0785436	+	0.0906441i
$613$	−0.306262	−	0.670620i	−0.0123698	−	0.0270861i	0.903346	−	0.428912i	$-0.141103\pi$
$613$	−0.306262	−	0.670620i	−0.0123698	−	0.0270861i	−0.915716	+	0.401826i	$0.868376\pi$
$614$	11.2504	−	7.23017i	0.454028	−	0.291786i
$615$	−1.04704	−	0.307440i	−0.0422209	−	0.0123972i
$616$	3.42321	−	3.95060i	0.137925	−	0.159174i
$617$	−5.02233	+	1.47469i	−0.202191	+	0.0593687i	−0.381260	−	0.924468i	$-0.624510\pi$
$617$	−5.02233	+	1.47469i	−0.202191	+	0.0593687i	0.179069	+	0.983837i	$0.442692\pi$
$618$	−17.2283	+	37.7246i	−0.693022	+	1.51751i
$619$	−4.44731	−	30.9317i	−0.178753	−	1.24325i	−0.859654	−	0.510876i	$-0.829321\pi$
$619$	−4.44731	−	30.9317i	−0.178753	−	1.24325i	0.680902	−	0.732375i	$-0.261588\pi$
$620$	0.523141			0.0210099
$621$	3.77831	+	2.95371i	0.151618	+	0.118528i
$622$	−19.2337			−0.771203
$623$	2.13285	+	14.8343i	0.0854510	+	0.594325i
$624$	2.43983	−	5.34249i	0.0976715	−	0.213871i
$625$	−23.8755	+	7.01049i	−0.955021	+	0.280420i
$626$	20.8736	−	24.0894i	0.834275	−	0.962805i
$627$	6.27675	+	1.84302i	0.250669	+	0.0736031i
$628$	20.5640	−	13.2157i	0.820593	−	0.527363i
$629$	−1.50034	−	3.28529i	−0.0598226	−	0.130993i
$630$	0.128663	+	0.148485i	0.00512605	+	0.00591578i
$631$	23.0684	+	14.8251i	0.918337	+	0.590179i	0.912175	−	0.409802i	$-0.134402\pi$
$631$	23.0684	+	14.8251i	0.918337	+	0.590179i	0.00616250	+	0.999981i	$0.498038\pi$
$632$	−3.41833	+	23.7750i	−0.135974	+	0.945719i
$633$	−3.45664	+	24.0415i	−0.137389	+	0.955563i
$634$	−15.4820	−	9.94970i	−0.614870	−	0.395153i
$635$	−0.657571	−	0.758877i	−0.0260949	−	0.0301151i
$636$	6.98928	+	15.3044i	0.277143	+	0.606858i
$637$	−4.37102	+	2.80909i	−0.173186	+	0.111300i
$638$	−33.5817	−	9.86049i	−1.32951	−	0.390381i
$639$	0.702697	−	0.810955i	0.0277983	−	0.0320809i
$640$	−1.28803	+	0.378199i	−0.0509137	+	0.0149496i
$641$	−4.94042	+	10.8180i	−0.195135	+	0.427286i	−0.981755	−	0.190152i	$-0.939102\pi$
$641$	−4.94042	+	10.8180i	−0.195135	+	0.427286i	0.786620	+	0.617438i	$0.211829\pi$
$642$	3.21871	+	22.3866i	0.127032	+	0.883530i
$643$	−47.9287			−1.89012			−0.945062	−	0.326892i	$-0.893999\pi$
$643$	−47.9287			−1.89012			−0.945062	+	0.326892i	$0.893999\pi$
$644$	14.1693	+	1.31181i	0.558348	+	0.0516924i
$645$	0.189643			0.00746718
$646$	0.855563	+	5.95057i	0.0336617	+	0.234122i
$647$	−2.38129	+	5.21430i	−0.0936183	+	0.204995i	−0.950648	−	0.310272i	$-0.899580\pi$
$647$	−2.38129	+	5.21430i	−0.0936183	+	0.204995i	0.857030	+	0.515267i	$0.172307\pi$
$648$	−2.06815	+	0.607265i	−0.0812447	+	0.0238556i
$649$	11.5123	−	13.2859i	0.451899	−	0.521519i
$650$	−55.4684	−	16.2870i	−2.17565	−	0.638828i
$651$	−1.68251	+	1.08128i	−0.0659427	+	0.0423788i
$652$	13.9855	+	30.6239i	0.547714	+	1.19933i
$653$	−20.4380	−	23.5867i	−0.799801	−	0.923019i	0.198570	−	0.980087i	$-0.436370\pi$
$653$	−20.4380	−	23.5867i	−0.799801	−	0.923019i	−0.998370	+	0.0570678i	$0.981825\pi$
$654$	−31.4945	−	20.2403i	−1.23153	−	0.791459i
$655$	0.120817	−	0.840301i	0.00472071	−	0.0328333i
$656$	−1.99133	+	13.8500i	−0.0777485	+	0.540753i
$657$	−1.79442	−	1.15321i	−0.0700071	−	0.0449909i
$658$	0.268668	+	0.310060i	0.0104738	+	0.0120874i
$659$	19.1680	+	41.9721i	0.746681	+	1.63500i	0.772241	+	0.635329i	$0.219136\pi$
$659$	19.1680	+	41.9721i	0.746681	+	1.63500i	−0.0255607	+	0.999673i	$0.508137\pi$
$660$	0.533654	−	0.342959i	0.0207725	−	0.0133497i
$661$	−25.1849	−	7.39496i	−0.979581	−	0.287631i	−0.247529	−	0.968880i	$-0.579619\pi$
$661$	−25.1849	−	7.39496i	−0.979581	−	0.287631i	−0.732051	+	0.681250i	$0.761437\pi$
$662$	−0.719346	+	0.830169i	−0.0279582	+	0.0322654i
$663$	−4.98538	+	1.46384i	−0.193616	+	0.0568508i
$664$	6.70191	−	14.6751i	0.260085	−	0.569506i
$665$	0.0338416	+	0.235373i	0.00131232	+	0.00912738i
$666$	8.04936			0.311906
$667$	−10.2416	−	29.3174i	−0.396555	−	1.13517i
$668$	23.7359			0.918370
$669$	−2.53338	−	17.6201i	−0.0979462	−	0.681231i
$670$	0.0251497	−	0.0550703i	0.000971619	−	0.00212755i
$671$	−17.7209	+	5.20334i	−0.684109	+	0.200873i
$672$	4.47283	−	5.16192i	0.172543	−	0.199125i
$673$	46.2145	+	13.5698i	1.78144	+	0.523078i	0.995460	−	0.0951767i	$-0.0303416\pi$
$673$	46.2145	+	13.5698i	1.78144	+	0.523078i	0.785978	+	0.618254i	$0.212160\pi$
$674$	35.8262	−	23.0241i	1.37998	−	0.886856i
$675$	−2.07385	−	4.54109i	−0.0798224	−	0.174787i
$676$	−27.1966	−	31.3866i	−1.04602	−	1.20718i
$677$	−26.2290	−	16.8564i	−1.00806	−	0.647843i	−0.0711716	−	0.997464i	$-0.522674\pi$
$677$	−26.2290	−	16.8564i	−1.00806	−	0.647843i	−0.936891	+	0.349622i	$0.886310\pi$
$678$	−2.53392	+	17.6238i	−0.0973145	+	0.676837i
$679$	−1.41973	+	9.87446i	−0.0544843	+	0.378947i
$680$	0.159852	+	0.102731i	0.00613006	+	0.00393955i
$681$	6.68728	+	7.71753i	0.256257	+	0.295737i
$682$	4.49065	+	9.83316i	0.171956	+	0.376531i
$683$	9.82892	−	6.31667i	0.376093	−	0.241700i	−0.338914	−	0.940817i	$-0.610060\pi$
$683$	9.82892	−	6.31667i	0.376093	−	0.241700i	0.715007	+	0.699117i	$0.246423\pi$
$684$	−7.67941	−	2.25488i	−0.293630	−	0.0862175i
$685$	0.704357	−	0.812872i	0.0269121	−	0.0310582i
$686$	−2.13843	+	0.627899i	−0.0816456	+	0.0239733i
$687$	0.273430	−	0.598728i	0.0104320	−	0.0228429i
$688$	−0.346064	−	2.40693i	−0.0131936	−	0.0917634i
$689$	−29.4624			−1.12243
$690$	0.875765	+	0.347678i	0.0333398	+	0.0132359i
$691$	7.03174			0.267500			0.133750	−	0.991015i	$-0.457298\pi$
$691$	7.03174			0.267500			0.133750	+	0.991015i	$0.457298\pi$
$692$	0.673108	+	4.68157i	0.0255877	+	0.177967i
$693$	−1.00746	+	2.20602i	−0.0382701	+	0.0837999i
$694$	−43.9116	+	12.8936i	−1.66686	+	0.489435i
$695$	−0.258711	+	0.298569i	−0.00981348	+	0.0113254i
$696$	13.3920	+	3.93226i	0.507624	+	0.149052i
$697$	10.4136	−	6.69238i	0.394441	−	0.253492i
$698$	−21.7556	−	47.6382i	−0.823462	−	1.80313i
$699$	12.5763	+	14.5138i	0.475678	+	0.548962i
$700$	−12.4612	−	8.00831i	−0.470988	−	0.302686i
$701$	−5.71091	+	39.7202i	−0.215698	+	1.50021i	0.537974	+	0.842961i	$0.319190\pi$
$701$	−5.71091	+	39.7202i	−0.215698	+	1.50021i	−0.753672	+	0.657251i	$0.771719\pi$
$702$	1.64801	−	11.4621i	0.0622001	−	0.432611i
$703$	8.19566	+	5.26703i	0.309105	+	0.198650i
$704$	−20.5853	−	23.7567i	−0.775838	−	0.895365i
$705$	0.00674137	+	0.0147615i	0.000253895	+	0.000555952i
$706$	−54.2804	+	34.8839i	−2.04287	+	1.31287i
$707$	−7.72316	−	2.26772i	−0.290459	−	0.0852866i
$708$	−14.0850	+	16.2550i	−0.529347	+	0.610899i
$709$	−26.3639	+	7.74115i	−0.990118	+	0.290725i	−0.736395	−	0.676552i	$-0.763473\pi$
$709$	−26.3639	+	7.74115i	−0.990118	+	0.290725i	−0.253723	+	0.967277i	$0.581655\pi$
$710$	0.0875802	−	0.191774i	0.00328682	−	0.00719714i
$711$	−1.58589	−	11.0301i	−0.0594755	−	0.413662i
$712$	−32.3037			−1.21063
$713$	−4.77187	+	8.32041i	−0.178708	+	0.311602i
$714$	−2.22871			−0.0834073
$715$	0.158089	+	1.09953i	0.00591220	+	0.0411202i
$716$	−26.1935	+	57.3557i	−0.978896	+	2.14348i
$717$	−5.36168	+	1.57433i	−0.200236	+	0.0587945i
$718$	25.6104	−	29.5560i	0.955771	−	1.10302i
$719$	−18.6235	−	5.46835i	−0.694539	−	0.203935i	−0.0846368	−	0.996412i	$-0.526973\pi$
$719$	−18.6235	−	5.46835i	−0.694539	−	0.203935i	−0.609902	+	0.792477i	$0.708791\pi$
$720$	0.0838301	−	0.0538744i	0.00312416	−	0.00200778i
$721$	−7.73016	−	16.9267i	−0.287886	−	0.630383i
$722$	17.1110	+	19.7471i	0.636805	+	0.734912i
$723$	10.0586	+	6.46430i	0.374085	+	0.240410i
$724$	7.81283	−	54.3394i	0.290361	−	2.01951i
$725$	−4.60054	+	31.9975i	−0.170860	+	1.18836i
$726$	−9.59671	−	6.16743i	−0.356167	−	0.228895i
$727$	20.3654	+	23.5029i	0.755311	+	0.871675i	0.995072	−	0.0991567i	$-0.0316145\pi$
$727$	20.3654	+	23.5029i	0.755311	+	0.871675i	−0.239761	+	0.970832i	$0.577069\pi$
$728$	−4.65242	−	10.1874i	−0.172430	−	0.377570i
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$	−0.402110	−	0.118070i	−0.0148827	−	0.00436997i
$731$	−1.40875	+	1.62578i	−0.0521045	+	0.0601318i
$732$	21.6810	−	6.36613i	0.801354	−	0.235299i
$733$	11.0720	−	24.2443i	0.408953	−	0.895483i	−0.587330	−	0.809347i	$-0.699821\pi$
$733$	11.0720	−	24.2443i	0.408953	−	0.895483i	0.996283	−	0.0861354i	$-0.0274518\pi$
$734$	4.43516	+	30.8472i	0.163705	+	1.13859i
$735$	−0.0881559			−0.00325168
$736$	7.63086	−	31.8553i	0.281277	−	1.17420i
$737$	0.747293			0.0275269
$738$	3.92623	+	27.3075i	0.144526	+	1.00520i
$739$	12.0412	−	26.3666i	0.442944	−	0.969913i	−0.548104	−	0.836410i	$-0.684650\pi$
$739$	12.0412	−	26.3666i	0.442944	−	0.969913i	0.991048	−	0.133503i	$-0.0426225\pi$
$740$	0.906440	−	0.266155i	0.0333214	−	0.00978405i
$741$	9.17812	−	10.5921i	0.337167	−	0.389111i
$742$	−12.1257	−	3.56043i	−0.445149	−	0.130708i
$743$	−37.0104	+	23.7852i	−1.35778	+	0.872593i	−0.998168	−	0.0605082i	$-0.980728\pi$
$743$	−37.0104	+	23.7852i	−1.35778	+	0.872593i	−0.359614	+	0.933101i	$0.617092\pi$
$744$	−1.79082	−	3.92136i	−0.0656548	−	0.143764i
$745$	−0.354808	−	0.409470i	−0.0129992	−	0.0150018i
$746$	1.29591	+	0.832830i	0.0474466	+	0.0304921i
$747$	−1.06519	+	7.40853i	−0.0389731	+	0.271064i
$748$	−1.02408	+	7.12260i	−0.0374439	+	0.260428i
$749$	−8.53701	−	5.48640i	−0.311935	−	0.200469i
$750$	−1.28563	−	1.48370i	−0.0469446	−	0.0541769i
$751$	−18.1784	−	39.8051i	−0.663339	−	1.45251i	−0.879378	−	0.476124i	$-0.842041\pi$
$751$	−18.1784	−	39.8051i	−0.663339	−	1.45251i	0.216039	−	0.976385i	$-0.430686\pi$
$752$	0.175050	−	0.112498i	0.00638343	−	0.00410238i
$753$	−4.83183	−	1.41875i	−0.176082	−	0.0517022i
$754$	−49.1046	+	56.6698i	−1.78828	+	2.06379i
$755$	0.814389	−	0.239126i	0.0296387	−	0.00870270i
$756$	1.23259	−	2.69900i	0.0448290	−	0.0981618i
$757$	−3.79984	−	26.4285i	−0.138108	−	0.960559i	−0.934547	−	0.355840i	$-0.884195\pi$
$757$	−3.79984	−	26.4285i	−0.138108	−	0.960559i	0.796439	−	0.604719i	$-0.206714\pi$
$758$	−7.80910			−0.283639
$759$	0.586894	+	11.6159i	0.0213029	+	0.421632i
$760$	−0.512556			−0.0185923
$761$	5.05497	+	35.1581i	0.183242	+	1.27448i	0.849033	+	0.528340i	$0.177185\pi$
$761$	5.05497	+	35.1581i	0.183242	+	1.27448i	−0.665791	+	0.746139i	$0.731906\pi$
$762$	−10.5457	+	23.0920i	−0.382032	+	0.836533i
$763$	16.1175	−	4.73252i	0.583492	−	0.171329i
$764$	−35.7133	+	41.2153i	−1.29206	+	1.49112i
$765$	−0.0845850	−	0.0248364i	−0.00305818	−	0.000897962i
$766$	−34.8973	+	22.4271i	−1.26089	+	0.810326i
$767$	−15.6462	−	34.2604i	−0.564951	−	1.23707i
$768$	5.24826	+	6.05681i	0.189380	+	0.218556i
$769$	−16.1802	−	10.3984i	−0.583472	−	0.374974i	0.215355	−	0.976536i	$-0.430909\pi$
$769$	−16.1802	−	10.3984i	−0.583472	−	0.374974i	−0.798827	+	0.601561i	$0.794545\pi$
$770$	−0.0678108	+	0.471635i	−0.00244373	+	0.0169965i
$771$	−0.121327	+	0.843846i	−0.00436948	+	0.0303904i
$772$	−63.9803	−	41.1176i	−2.30270	−	1.47986i
$773$	18.9533	+	21.8733i	0.681704	+	0.786728i	0.986160	−	0.165798i	$-0.0530201\pi$
$773$	18.9533	+	21.8733i	0.681704	+	0.786728i	−0.304456	+	0.952526i	$0.598475\pi$
$774$	−1.99168	−	4.36118i	−0.0715895	−	0.156759i
$775$	8.39946	−	5.39801i	0.301718	−	0.193902i
$776$	−20.6319	−	6.05807i	−0.740642	−	0.217472i
$777$	−2.36514	+	2.72952i	−0.0848490	+	0.0979210i
$778$	38.4212	−	11.2815i	1.37747	−	0.404461i
$779$	−13.8708	+	30.3729i	−0.496974	+	1.08822i
$780$	−0.193417	−	1.34525i	−0.00692545	−	0.0481676i
$781$	2.60233			0.0931189
$782$	−9.48617	+	4.92512i	−0.339225	+	0.176122i
$783$	−6.47536			−0.231411
$784$	0.160869	+	1.11887i	0.00574532	+	0.0399596i
$785$	−0.301701	+	0.660633i	−0.0107682	+	0.0235790i
$786$	−20.5931	+	6.04667i	−0.734531	+	0.215678i
$787$	−16.6330	+	19.1955i	−0.592901	+	0.684244i	−0.970327	−	0.241795i	$-0.922264\pi$
$787$	−16.6330	+	19.1955i	−0.592901	+	0.684244i	0.377426	+	0.926040i	$0.376809\pi$
$788$	−38.0321	−	11.1672i	−1.35484	−	0.397816i
$789$	19.5164	−	12.5424i	0.694801	−	0.446521i
$790$	−0.909515	−	1.99156i	−0.0323591	−	0.0708565i
$791$	−5.23164	−	6.03764i	−0.186016	−	0.214674i
$792$	−4.39756	−	2.82614i	−0.156261	−	0.100423i
$793$	−5.63128	+	39.1664i	−0.199973	+	1.39084i
$794$	9.39932	−	65.3737i	0.333570	−	2.32003i
$795$	−0.420524	−	0.270254i	−0.0149145	−	0.00958494i
$796$	−33.2820	−	38.4094i	−1.17965	−	1.36139i
$797$	−21.8315	−	47.8044i	−0.773313	−	1.69332i	−0.719219	−	0.694783i	$-0.755500\pi$
$797$	−21.8315	−	47.8044i	−0.773313	−	1.69332i	−0.0540934	−	0.998536i	$-0.517227\pi$
$798$	5.05742	−	3.25020i	0.179031	−	0.115056i
$799$	−0.176627	−	0.0518623i	−0.00624860	−	0.00183475i
$800$	−22.3294	+	25.7695i	−0.789463	+	0.911089i
$801$	14.3798	−	4.22229i	0.508085	−	0.149187i
$802$	20.8909	−	45.7447i	0.737683	−	1.61530i
$803$	−0.736194	−	5.12034i	−0.0259797	−	0.180693i
$804$	−0.914291			−0.0322445
$805$	−0.375223	+	0.194812i	−0.0132249	+	0.00686621i
$806$	23.1600			0.815777
$807$	3.57324	+	24.8525i	0.125784	+	0.874848i
$808$	7.20736	−	15.7819i	0.253554	−	0.555206i
$809$	3.41442	−	1.00256i	0.120044	−	0.0352482i	−0.221159	−	0.975238i	$-0.570984\pi$
$809$	3.41442	−	1.00256i	0.120044	−	0.0352482i	0.341203	+	0.939990i	$0.389166\pi$
$810$	0.128663	−	0.148485i	0.00452076	−	0.00521723i
$811$	33.5489	+	9.85084i	1.17806	+	0.345910i	0.811426	−	0.584455i	$-0.198692\pi$
$811$	33.5489	+	9.85084i	1.17806	+	0.345910i	0.366634	+	0.930365i	$0.380510\pi$
$812$	−16.1633	+	10.3875i	−0.567219	+	0.364529i
$813$	3.17614	+	6.95478i	0.111392	+	0.243915i
$814$	12.7836	+	14.7531i	0.448066	+	0.517096i
$815$	−0.841465	−	0.540777i	−0.0294752	−	0.0189426i
$816$	−0.160869	+	1.11887i	−0.00563154	+	0.0391682i
$817$	0.825817	−	5.74368i	0.0288917	−	0.200946i
$818$	−19.2859	−	12.3943i	−0.674316	−	0.433356i
$819$	3.40255	+	3.92676i	0.118895	+	0.137212i
$820$	1.34506	+	2.94528i	0.0469717	+	0.102854i
$821$	32.1110	−	20.6365i	1.12068	−	0.720218i	0.157087	−	0.987585i	$-0.449790\pi$
$821$	32.1110	−	20.6365i	1.12068	−	0.720218i	0.963595	+	0.267366i	$0.0861534\pi$
$822$	−26.0908	−	7.66095i	−0.910021	−	0.267206i
$823$	33.4953	−	38.6556i	1.16757	−	1.34745i	0.241364	−	0.970435i	$-0.422405\pi$
$823$	33.4953	−	38.6556i	1.16757	−	1.34745i	0.926207	−	0.377015i	$-0.123049\pi$
$824$	38.4848	−	11.3001i	1.34068	−	0.393659i
$825$	5.02945	−	11.0130i	0.175103	−	0.383422i
$826$	−2.29918	−	15.9912i	−0.0799988	−	0.556404i
$827$	32.4723			1.12917			0.564586	−	0.825375i	$-0.309036\pi$
$827$	32.4723			1.12917			0.564586	+	0.825375i	$0.309036\pi$
$828$	−0.718048	−	14.2118i	−0.0249539	−	0.493893i
$829$	35.6620			1.23859			0.619296	−	0.785158i	$-0.287418\pi$
$829$	35.6620			1.23859			0.619296	+	0.785158i	$0.287418\pi$
$830$	0.209281	+	1.45558i	0.00726426	+	0.0505240i
$831$	3.40300	−	7.45153i	0.118049	−	0.258491i
$832$	−64.6193	+	18.9739i	−2.24027	+	0.657803i
$833$	0.654861	−	0.755750i	0.0226896	−	0.0261852i
$834$	9.58319	+	2.81388i	0.331839	+	0.0974366i
$835$	−0.593263	+	0.381267i	−0.0205307	+	0.0131943i
$836$	−8.06330	−	17.6562i	−0.278875	−	0.610651i
$837$	1.30972	+	1.51150i	0.0452706	+	0.0522451i
$838$	41.6223	+	26.7490i	1.43782	+	0.924030i
$839$	−7.29064	+	50.7075i	−0.251701	+	1.75062i	0.336297	+	0.941756i	$0.390825\pi$
$839$	−7.29064	+	50.7075i	−0.251701	+	1.75062i	−0.587998	+	0.808862i	$0.700084\pi$
$840$	0.0270422	−	0.188083i	0.000933046	−	0.00648948i
$841$	10.8777	+	6.99067i	0.375093	+	0.241058i
$842$	25.9295	+	29.9243i	0.893590	+	1.03126i
$843$	11.6028	+	25.4065i	0.399621	+	0.875047i
$844$	60.6274	−	38.9629i	2.08688	−	1.34116i
$845$	1.18392	+	0.347630i	0.0407280	+	0.0119588i
$846$	0.268668	−	0.310060i	0.00923701	−	0.0106601i
$847$	4.91116	−	1.44205i	0.168749	−	0.0495493i
$848$	−2.66266	+	5.83042i	−0.0914363	+	0.200218i
$849$	3.25860	+	22.6641i	0.111835	+	0.777829i
$850$	11.1262			0.381626
$851$	−4.03504	+	16.8444i	−0.138319	+	0.577419i
$852$	−3.18388			−0.109078
$853$	6.03827	+	41.9971i	0.206746	+	1.43795i	0.783681	+	0.621163i	$0.213340\pi$
$853$	6.03827	+	41.9971i	0.206746	+	1.43795i	−0.576935	+	0.816790i	$0.695751\pi$
$854$	−7.05076	+	15.4390i	−0.241272	+	0.528312i
$855$	0.228161	−	0.0669942i	0.00780295	−	0.00229115i
$856$	14.3241	−	16.5309i	0.489589	−	0.565016i
$857$	23.2607	+	6.82995i	0.794570	+	0.233307i	0.653732	−	0.756726i	$-0.273202\pi$
$857$	23.2607	+	6.82995i	0.794570	+	0.233307i	0.140838	+	0.990033i	$0.455020\pi$
$858$	23.6255	−	15.1832i	0.806560	−	0.518345i
$859$	−21.8037	−	47.7434i	−0.743932	−	1.62898i	−0.776976	−	0.629530i	$-0.783247\pi$
$859$	−21.8037	−	47.7434i	−0.743932	−	1.62898i	0.0330439	−	0.999454i	$-0.489480\pi$
$860$	−0.368488	−	0.425257i	−0.0125653	−	0.0145012i
$861$	−10.4136	−	6.69238i	−0.354893	−	0.228076i
$862$	−8.44076	+	58.7068i	−0.287493	+	1.99956i
$863$	7.13200	−	49.6041i	0.242776	−	1.68854i	−0.395285	−	0.918559i	$-0.629354\pi$
$863$	7.13200	−	49.6041i	0.242776	−	1.68854i	0.638061	−	0.769986i	$-0.279737\pi$
$864$	−5.74593	−	3.69269i	−0.195481	−	0.125628i
$865$	−0.0920233	−	0.106200i	−0.00312888	−	0.00361093i
$866$	6.52784	+	14.2940i	0.221825	+	0.485729i
$867$	−13.4601	+	8.65025i	−0.457127	+	0.293778i
$868$	5.69389	+	1.67188i	0.193263	+	0.0567472i
$869$	17.6977	−	20.4242i	0.600352	−	0.692844i
$870$	−1.22070	+	0.358431i	−0.0413858	+	0.0121520i
$871$	0.665097	−	1.45636i	0.0225360	−	0.0493469i
$872$	5.15284	+	35.8388i	0.174497	+	1.21365i
$873$	9.97600			0.337636
$874$	14.3437	−	25.0102i	0.485182	−	0.845981i
$875$	0.880874			0.0297790
$876$	0.900712	+	6.26459i	0.0304322	+	0.211661i
$877$	0.610592	−	1.33701i	0.0206182	−	0.0451476i	−0.899043	−	0.437861i	$-0.855736\pi$
$877$	0.610592	−	1.33701i	0.0206182	−	0.0451476i	0.919661	+	0.392713i	$0.128464\pi$
$878$	−8.14225	+	2.39078i	−0.274787	+	0.0806849i
$879$	6.57462	−	7.58751i	0.221756	−	0.255920i
$880$	0.231878	+	0.0680855i	0.00781660	+	0.00229516i
$881$	36.6247	−	23.5372i	1.23392	−	0.792990i	0.249420	−	0.968395i	$-0.419760\pi$
$881$	36.6247	−	23.5372i	1.23392	−	0.792990i	0.984496	+	0.175406i	$0.0561237\pi$
$882$	0.925839	+	2.02730i	0.0311746	+	0.0682629i
$883$	25.9197	+	29.9129i	0.872267	+	1.00665i	0.999890	+	0.0148266i	$0.00471962\pi$
$883$	25.9197	+	29.9129i	0.872267	+	1.00665i	−0.127624	+	0.991823i	$0.540735\pi$
$884$	12.9694	+	8.33494i	0.436209	+	0.280334i
$885$	0.0909436	−	0.632526i	0.00305703	−	0.0212621i
$886$	−2.70881	+	18.8402i	−0.0910044	+	0.632949i
$887$	33.2219	+	21.3504i	1.11548	+	0.716878i	0.962481	−	0.271348i	$-0.0874695\pi$
$887$	33.2219	+	21.3504i	1.11548	+	0.716878i	0.153002	+	0.988226i	$0.451106\pi$
$888$	−5.09798	−	5.88338i	−0.171077	−	0.197433i
$889$	−4.73178	−	10.3611i	−0.158699	−	0.347502i
$890$	2.47709	−	1.59193i	0.0830324	−	0.0533617i
$891$	2.32694	+	0.683252i	0.0779556	+	0.0228898i
$892$	−34.5889	+	39.9178i	−1.15812	+	1.33655i
$893$	0.476436	−	0.139894i	0.0159433	−	0.00468138i
$894$	−5.69021	+	12.4598i	−0.190309	+	0.416719i
$895$	−0.266609	−	1.85431i	−0.00891176	−	0.0619827i
$896$	−15.2276			−0.508718
$897$	23.1600	+	9.19452i	0.773291	+	0.306996i
$898$	−13.0501			−0.435488
$899$	−1.84308	−	12.8189i	−0.0614702	−	0.427535i
$900$	−6.15339	+	13.4740i	−0.205113	+	0.449135i
$901$	5.44069	−	1.59753i	0.181256	−	0.0532215i
$902$	−43.8145	+	50.5647i	−1.45886	+	1.68362i
$903$	2.06408	+	0.606069i	0.0686883	+	0.0201687i
$904$	14.4863	−	9.30977i	0.481806	−	0.309638i
$905$	0.677570	+	1.48367i	0.0225232	+	0.0493189i
$906$	−14.0521	−	16.2170i	−0.466849	−	0.538773i
$907$	−32.1380	−	20.6539i	−1.06713	−	0.685800i	−0.115577	−	0.993299i	$-0.536872\pi$
$907$	−32.1380	−	20.6539i	−1.06713	−	0.685800i	−0.951549	+	0.307499i	$0.900508\pi$
$908$	4.31210	−	29.9913i	0.143102	−	0.995296i
$909$	−1.14552	+	7.96728i	−0.0379946	+	0.264258i
$910$	0.858791	+	0.551912i	0.0284686	+	0.0182957i
$911$	21.4741	+	24.7824i	0.711469	+	0.821079i	0.990254	−	0.139275i	$-0.0444771\pi$
$911$	21.4741	+	24.7824i	0.711469	+	0.821079i	−0.278785	+	0.960354i	$0.589932\pi$
$912$	−1.26664	−	2.77355i	−0.0419426	−	0.0918415i
$913$	−15.2703	+	9.81360i	−0.505372	+	0.324783i
$914$	46.4831	+	13.6487i	1.53752	+	0.451458i
$915$	−0.439644	+	0.507376i	−0.0145342	+	0.0167733i
$916$	−1.87389	+	0.550223i	−0.0619150	+	0.0181799i
$917$	4.00045	−	8.75976i	0.132106	−	0.289273i
$918$	0.317178	+	2.20602i	0.0104684	+	0.0728096i
$919$	34.5038			1.13817			0.569087	−	0.822277i	$-0.307297\pi$
$919$	34.5038			1.13817			0.569087	+	0.822277i	$0.307297\pi$
$920$	−0.300534	−	0.860307i	−0.00990832	−	0.0283635i
$921$	6.00049			0.197723
$922$	7.82214	+	54.4042i	0.257608	+	1.79171i
$923$	2.31610	−	5.07155i	0.0762354	−	0.166932i
$924$	6.90436	−	2.02730i	0.227137	−	0.0666934i
$925$	11.8073	−	13.6264i	0.388223	−	0.448033i
$926$	18.8122	+	5.52375i	0.618206	+	0.181522i
$927$	−15.6543	+	10.0604i	−0.514154	+	0.330427i
$928$	18.3730	+	40.2312i	0.603123	+	1.32066i
$929$	−3.29417	−	3.80167i	−0.108078	−	0.124729i	0.699133	−	0.714992i	$-0.253570\pi$
$929$	−3.29417	−	3.80167i	−0.108078	−	0.124729i	−0.807211	+	0.590263i	$0.799024\pi$
$930$	0.330568	+	0.212443i	0.0108398	+	0.00696630i
$931$	−0.383883	+	2.66996i	−0.0125813	+	0.0875046i
$932$	8.10944	−	56.4024i	0.265633	−	1.84752i
$933$	−7.26001	−	4.66573i	−0.237682	−	0.152749i
$934$	−1.50270	−	1.73420i	−0.0491697	−	0.0567449i
$935$	−0.0888133	−	0.194474i	−0.00290450	−	0.00635998i
$936$	−9.42158	+	6.05488i	−0.307954	+	0.197910i
$937$	41.3783	+	12.1498i	1.35177	+	0.396916i	0.875855	−	0.482574i	$-0.160298\pi$
$937$	41.3783	+	12.1498i	1.35177	+	0.396916i	0.475917	+	0.879490i	$0.342116\pi$
$938$	0.449727	−	0.519012i	0.0146841	−	0.0169464i
$939$	13.7226	−	4.02932i	0.447820	−	0.131492i
$940$	0.0200026	−	0.0437995i	0.000652412	−	0.00142858i
$941$	−4.44514	−	30.9166i	−0.144907	−	1.00785i	−0.924395	−	0.381436i	$-0.875430\pi$
$941$	−4.44514	−	30.9166i	−0.144907	−	1.00785i	0.779488	−	0.626417i	$-0.215479\pi$
$942$	18.3610			0.598233
$943$	−59.1129	−	5.47273i	−1.92498	−	0.178216i
$944$	−8.19393			−0.266690
$945$	0.0125459	+	0.0872586i	0.000408118	+	0.00283852i
$946$	4.83019	−	10.5766i	0.157043	−	0.343876i
$947$	19.8437	−	5.82665i	0.644835	−	0.189341i	0.0570673	−	0.998370i	$-0.481825\pi$
$947$	19.8437	−	5.82665i	0.644835	−	0.189341i	0.587768	+	0.809030i	$0.300007\pi$
$948$	−21.6526	+	24.9884i	−0.703243	+	0.811586i
$949$	−10.6340	−	3.12242i	−0.345194	−	0.101358i
$950$	−25.2478	+	16.2258i	−0.819146	+	0.526433i
$951$	−3.43028	−	7.51128i	−0.111235	−	0.243570i
$952$	1.41153	+	1.62899i	0.0457479	+	0.0527959i
$953$	−12.3143	−	7.91392i	−0.398899	−	0.256357i	0.325777	−	0.945447i	$-0.394374\pi$
$953$	−12.3143	−	7.91392i	−0.398899	−	0.256357i	−0.724676	+	0.689090i	$0.758011\pi$
$954$	−1.79852	+	12.5090i	−0.0582293	+	0.404994i
$955$	0.230592	−	1.60381i	0.00746180	−	0.0518979i
$956$	13.9484	+	8.96407i	0.451123	+	0.289919i
$957$	−10.2839	−	11.8682i	−0.332431	−	0.383646i
$958$	−23.0254	−	50.4185i	−0.743916	−	1.62895i
$959$	10.2641	−	6.59632i	0.331444	−	0.213006i
$960$	−1.09637	−	0.321924i	−0.0353852	−	0.0103900i
$961$	17.6812	−	20.4052i	0.570363	−	0.658234i
$962$	40.1291	−	11.7830i	1.29381	−	0.379898i
$963$	−4.21562	+	9.23091i	−0.135846	+	0.297462i
$964$	−5.04894	−	35.1162i	−0.162615	−	1.13102i
$965$	2.25961			0.0727394
$966$	8.42074	+	6.58295i	0.270933	+	0.211803i
$967$	58.1937			1.87138			0.935692	−	0.352819i	$-0.114777\pi$
$967$	58.1937			1.87138			0.935692	+	0.352819i	$0.114777\pi$
$968$	1.57012	+	10.9204i	0.0504656	+	0.350996i
$969$	−1.12055	+	2.45366i	−0.0359972	+	0.0788229i
$970$	1.88063	−	0.552202i	0.0603833	−	0.0177301i
$971$	28.0207	−	32.3376i	0.899227	−	1.03776i	−0.0998583	−	0.995002i	$-0.531839\pi$
$971$	28.0207	−	32.3376i	0.899227	−	1.03776i	0.999085	−	0.0427616i	$-0.0136156\pi$
$972$	−2.84695	−	0.835939i	−0.0913159	−	0.0268128i
$973$	−3.77001	+	2.42284i	−0.120861	+	0.0776725i
$974$	24.1782	+	52.9429i	0.774720	+	1.69640i
$975$	−16.9863	−	19.6033i	−0.543998	−	0.627807i
$976$	7.24185	+	4.65405i	0.231806	+	0.148973i
$977$	−1.39186	+	9.68060i	−0.0445295	+	0.309710i	0.955368	+	0.295417i	$0.0954587\pi$
$977$	−1.39186	+	9.68060i	−0.0445295	+	0.309710i	−0.999898	+	0.0142924i	$0.995450\pi$
$978$	−3.59883	+	25.0304i	−0.115078	+	0.800384i
$979$	30.5761	+	19.6501i	0.977216	+	0.628019i
$980$	0.171292	+	0.197682i	0.00547173	+	0.00631472i
$981$	−6.97810	−	15.2799i	−0.222794	−	0.487850i
$982$	−14.2192	+	9.13812i	−0.453752	+	0.291609i
$983$	26.7633	+	7.85842i	0.853617	+	0.250645i	0.679133	−	0.734015i	$-0.262356\pi$
$983$	26.7633	+	7.85842i	0.853617	+	0.250645i	0.174484	+	0.984660i	$0.444174\pi$
$984$	17.4728	−	20.1647i	0.557012	−	0.642826i
$985$	1.12996	−	0.331787i	0.0360036	−	0.0105716i
$986$	5.99514	−	13.1275i	0.190924	−	0.418066i
$987$	0.0261978	+	0.182210i	0.000833885	+	0.00579980i
$988$	−41.5855			−1.32301
$989$	10.1248	−	1.98167i	0.321949	−	0.0630135i
$990$	0.476484			0.0151437
$991$	7.63185	+	53.0807i	0.242434	+	1.68616i	0.639830	+	0.768516i	$0.279005\pi$
$991$	7.63185	+	53.0807i	0.242434	+	1.68616i	−0.397396	+	0.917647i	$0.630086\pi$
$992$	5.67474	−	12.4259i	0.180173	−	0.394524i
$993$	−0.472909	+	0.138859i	−0.0150073	+	0.00440654i
$994$	1.56611	−	1.80738i	0.0496738	−	0.0573267i
$995$	1.44882	+	0.425413i	0.0459308	+	0.0134865i
$996$	18.6827	−	12.0067i	0.591984	−	0.380445i
$997$	−9.90898	−	21.6976i	−0.313821	−	0.687171i	0.685336	−	0.728227i	$-0.259655\pi$
$997$	−9.90898	−	21.6976i	−0.313821	−	0.687171i	−0.999157	+	0.0410554i	$0.986928\pi$
$998$	−23.2501	−	26.8321i	−0.735970	−	0.849355i
$999$	3.03833	+	1.95262i	0.0961286	+	0.0617781i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.b.463.1	yes	10
23.8	even	11	inner	483.2.q.b.169.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.b.169.1	✓	10	23.8	even	11	inner
483.2.q.b.463.1	yes	10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.317178 - 2.20602i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-2.84695 + 0.835939i) q^{4} +(0.0577299 - 0.0666238i) q^{5} +(-2.13843 - 0.627899i) q^{6} +(0.841254 - 0.540641i) q^{7} +(0.895412 + 1.96068i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.317178 - 2.20602i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-2.84695 + 0.835939i) q^{4} +(0.0577299 - 0.0666238i) q^{5} +(-2.13843 - 0.627899i) q^{6} +(0.841254 - 0.540641i) q^{7} +(0.895412 + 1.96068i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(-0.165284 - 0.106222i) q^{10} +(0.345139 - 2.40050i) q^{11} +(-0.422268 + 2.93694i) q^{12} +(-4.37102 - 2.80909i) q^{13} +(-1.45949 - 1.68434i) q^{14} +(-0.0366213 - 0.0801894i) q^{15} +(-0.950930 + 0.611126i) q^{16} +(0.959493 + 0.281733i) q^{17} +(-1.45949 + 1.68434i) q^{18} +(-2.58816 + 0.759951i) q^{19} +(-0.108660 + 0.237933i) q^{20} +(-0.142315 - 0.989821i) q^{21} -5.40502 q^{22} +(-2.79310 - 3.89854i) q^{23} +2.15546 q^{24} +(0.710468 + 4.94141i) q^{25} +(-4.81051 + 10.5336i) q^{26} +(-0.959493 + 0.281733i) q^{27} +(-1.94306 + 2.24241i) q^{28} +(6.21307 + 1.82432i) q^{29} +(-0.165284 + 0.106222i) q^{30} +(-0.830830 - 1.81926i) q^{31} +(4.47283 + 5.16192i) q^{32} +(-2.04019 - 1.31115i) q^{33} +(0.317178 - 2.20602i) q^{34} +(0.0125459 - 0.0872586i) q^{35} +(2.49611 + 1.60416i) q^{36} +(-2.36514 - 2.72952i) q^{37} +(2.49738 + 5.46849i) q^{38} +(-4.37102 + 2.80909i) q^{39} +(0.182320 + 0.0535340i) q^{40} +(8.10627 - 9.35513i) q^{41} +(-2.13843 + 0.627899i) q^{42} +(-0.893649 + 1.95682i) q^{43} +(1.02408 + 7.12260i) q^{44} -0.0881559 q^{45} +(-7.71434 + 7.39818i) q^{46} -0.184083 q^{47} +(0.160869 + 1.11887i) q^{48} +(0.415415 - 0.909632i) q^{49} +(10.6755 - 3.13462i) q^{50} +(0.654861 - 0.755750i) q^{51} +(14.7923 + 4.34341i) q^{52} +(4.77023 - 3.06564i) q^{53} +(0.925839 + 2.02730i) q^{54} +(-0.140005 - 0.161575i) q^{55} +(1.81329 + 1.16533i) q^{56} +(-0.383883 + 2.66996i) q^{57} +(2.05384 - 14.2848i) q^{58} +(6.09814 + 3.91903i) q^{59} +(0.171292 + 0.197682i) q^{60} +(-3.16361 - 6.92734i) q^{61} +(-3.74982 + 2.40986i) q^{62} +(-0.959493 - 0.281733i) q^{63} +(8.48816 - 9.79585i) q^{64} +(-0.439490 + 0.129046i) q^{65} +(-2.24533 + 4.91658i) q^{66} +(0.0438528 + 0.305003i) q^{67} -2.96714 q^{68} +(-4.70653 + 0.921186i) q^{69} -0.196474 q^{70} +(0.152711 + 1.06213i) q^{71} +(0.895412 - 1.96068i) q^{72} +(2.04663 - 0.600946i) q^{73} +(-5.27121 + 6.08330i) q^{74} +(4.79001 + 1.40647i) q^{75} +(6.73307 - 4.32708i) q^{76} +(-1.00746 - 2.20602i) q^{77} +(7.58330 + 8.75159i) q^{78} +(9.37454 + 6.02465i) q^{79} +(-0.0141815 + 0.0986348i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-23.2088 - 14.9154i) q^{82} +(-4.90145 - 5.65657i) q^{83} +(1.23259 + 2.69900i) q^{84} +(0.0741615 - 0.0476607i) q^{85} +(4.60023 + 1.35075i) q^{86} +(4.24046 - 4.89375i) q^{87} +(5.01565 - 1.47273i) q^{88} +(-6.22577 + 13.6325i) q^{89} +(0.0279611 + 0.194474i) q^{90} -5.19584 q^{91} +(11.2108 + 8.76406i) q^{92} -2.00000 q^{93} +(0.0583872 + 0.406092i) q^{94} +(-0.0987830 + 0.216305i) q^{95} +(6.55353 - 1.92429i) q^{96} +(-6.53289 + 7.53936i) q^{97} +(-2.13843 - 0.627899i) q^{98} +(-2.04019 + 1.31115i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{2} - q^{3} - q^{4} - 5 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} - q^{9}+O(q^{10}) \) 10 * q + 5 * q^2 - q^3 - q^4 - 5 * q^5 - 6 * q^6 - q^7 + 6 * q^8 - q^9	\( 10 q + 5 q^{2} - q^{3} - q^{4} - 5 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} - q^{9} + 3 q^{10} + 9 q^{11} - 12 q^{12} - 15 q^{13} - 6 q^{14} + 6 q^{15} + 5 q^{16} + q^{17} - 6 q^{18} - 19 q^{19} - 5 q^{20} - q^{21} - 12 q^{22} - 21 q^{23} + 6 q^{24} + 2 q^{25} - 13 q^{26} - q^{27} - q^{28} + 3 q^{30} + 2 q^{31} + 7 q^{32} - 2 q^{33} - 5 q^{34} - 5 q^{35} + 10 q^{36} - 27 q^{37} + 18 q^{38} - 15 q^{39} - 3 q^{40} + 10 q^{41} - 6 q^{42} + 15 q^{43} + 9 q^{44} + 6 q^{45} - 5 q^{46} - 18 q^{47} + 5 q^{48} - q^{49} + 34 q^{50} + q^{51} + 18 q^{52} + 19 q^{53} + 5 q^{54} - 21 q^{55} - 5 q^{56} + 3 q^{57} - 13 q^{59} + 6 q^{60} - 18 q^{61} - 10 q^{62} - q^{63} + 54 q^{64} + 2 q^{65} + 10 q^{66} - 18 q^{67} - 10 q^{68} + q^{69} - 8 q^{70} + 38 q^{71} + 6 q^{72} + 14 q^{73} + 14 q^{74} + 2 q^{75} + 3 q^{76} - 13 q^{77} + 9 q^{78} + 25 q^{79} + 25 q^{80} - q^{81} - 72 q^{82} - 19 q^{83} - q^{84} + 5 q^{85} + 2 q^{86} + 33 q^{87} + q^{88} - 17 q^{89} + 14 q^{90} - 4 q^{91} + 67 q^{92} - 20 q^{93} + 13 q^{94} + 37 q^{95} + 18 q^{96} - 49 q^{97} - 6 q^{98} - 2 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 - q^3 - q^4 - 5 * q^5 - 6 * q^6 - q^7 + 6 * q^8 - q^9 + 3 * q^10 + 9 * q^11 - 12 * q^12 - 15 * q^13 - 6 * q^14 + 6 * q^15 + 5 * q^16 + q^17 - 6 * q^18 - 19 * q^19 - 5 * q^20 - q^21 - 12 * q^22 - 21 * q^23 + 6 * q^24 + 2 * q^25 - 13 * q^26 - q^27 - q^28 + 3 * q^30 + 2 * q^31 + 7 * q^32 - 2 * q^33 - 5 * q^34 - 5 * q^35 + 10 * q^36 - 27 * q^37 + 18 * q^38 - 15 * q^39 - 3 * q^40 + 10 * q^41 - 6 * q^42 + 15 * q^43 + 9 * q^44 + 6 * q^45 - 5 * q^46 - 18 * q^47 + 5 * q^48 - q^49 + 34 * q^50 + q^51 + 18 * q^52 + 19 * q^53 + 5 * q^54 - 21 * q^55 - 5 * q^56 + 3 * q^57 - 13 * q^59 + 6 * q^60 - 18 * q^61 - 10 * q^62 - q^63 + 54 * q^64 + 2 * q^65 + 10 * q^66 - 18 * q^67 - 10 * q^68 + q^69 - 8 * q^70 + 38 * q^71 + 6 * q^72 + 14 * q^73 + 14 * q^74 + 2 * q^75 + 3 * q^76 - 13 * q^77 + 9 * q^78 + 25 * q^79 + 25 * q^80 - q^81 - 72 * q^82 - 19 * q^83 - q^84 + 5 * q^85 + 2 * q^86 + 33 * q^87 + q^88 - 17 * q^89 + 14 * q^90 - 4 * q^91 + 67 * q^92 - 20 * q^93 + 13 * q^94 + 37 * q^95 + 18 * q^96 - 49 * q^97 - 6 * q^98 - 2 * q^99

Introduction

L-functions

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