LMFDB - Embedded newform 322.2.i.b.197.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(29,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("322.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.i (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:	$2.57118294509$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			197.1
Root			$-0.841254 + 0.540641i$ of defining polynomial
Character	$\chi$	$=$	322.197
Dual form			322.2.i.b.85.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 + 0.755750i) q^{2} +(0.0741615 + 0.0476607i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(1.57773 - 3.45475i) q^{5} +(0.0125459 + 0.0872586i) q^{6} +(0.959493 + 0.281733i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-1.24302 - 2.72183i) q^{9} +O(q^{10})$	\(q+(0.654861 + 0.755750i) q^{2} +(0.0741615 + 0.0476607i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(1.57773 - 3.45475i) q^{5} +(0.0125459 + 0.0872586i) q^{6} +(0.959493 + 0.281733i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-1.24302 - 2.72183i) q^{9} +(3.64412 - 1.07001i) q^{10} +(2.68996 - 3.10438i) q^{11} +(-0.0577299 + 0.0666238i) q^{12} +(-2.13843 + 0.627899i) q^{13} +(0.415415 + 0.909632i) q^{14} +(0.281663 - 0.181014i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(0.664440 + 4.62128i) q^{17} +(1.24302 - 2.72183i) q^{18} +(-0.773100 + 5.37703i) q^{19} +(3.19505 + 2.05334i) q^{20} +(0.0577299 + 0.0666238i) q^{21} +4.10769 q^{22} +(4.58330 - 1.41187i) q^{23} -0.0881559 q^{24} +(-6.17177 - 7.12260i) q^{25} +(-1.87491 - 1.20493i) q^{26} +(0.0751779 - 0.522874i) q^{27} +(-0.415415 + 0.909632i) q^{28} +(0.831674 + 5.78442i) q^{29} +(0.321251 + 0.0943278i) q^{30} +(-3.89867 + 2.50552i) q^{31} +(-0.415415 - 0.909632i) q^{32} +(0.347449 - 0.102020i) q^{33} +(-3.05742 + 3.52845i) q^{34} +(2.48714 - 2.87031i) q^{35} +(2.87102 - 0.843008i) q^{36} +(-0.274362 - 0.600768i) q^{37} +(-4.56996 + 2.93694i) q^{38} +(-0.188515 - 0.0553531i) q^{39} +(0.540507 + 3.75931i) q^{40} +(-1.69012 + 3.70085i) q^{41} +(-0.0125459 + 0.0872586i) q^{42} +(3.70159 + 2.37887i) q^{43} +(2.68996 + 3.10438i) q^{44} -11.3644 q^{45} +(4.06844 + 2.53925i) q^{46} +9.37437 q^{47} +(-0.0577299 - 0.0666238i) q^{48} +(0.841254 + 0.540641i) q^{49} +(1.34125 - 9.32862i) q^{50} +(-0.170978 + 0.374389i) q^{51} +(-0.317178 - 2.20602i) q^{52} +(-11.1053 - 3.26080i) q^{53} +(0.444393 - 0.285594i) q^{54} +(-6.48083 - 14.1910i) q^{55} +(-0.959493 + 0.281733i) q^{56} +(-0.313607 + 0.361922i) q^{57} +(-3.82694 + 4.41653i) q^{58} +(-8.09519 + 2.37696i) q^{59} +(0.139086 + 0.304557i) q^{60} +(-3.99868 + 2.56979i) q^{61} +(-4.44663 - 1.30565i) q^{62} +(-0.425839 - 2.96177i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-1.20463 + 8.37840i) q^{65} +(0.304632 + 0.195775i) q^{66} +(0.365142 + 0.421396i) q^{67} -4.66880 q^{68} +(0.407195 + 0.113737i) q^{69} +3.79797 q^{70} +(-3.50975 - 4.05046i) q^{71} +(2.51722 + 1.61772i) q^{72} +(2.13088 - 14.8206i) q^{73} +(0.274362 - 0.600768i) q^{74} +(-0.118239 - 0.822373i) q^{75} +(-5.21228 - 1.53046i) q^{76} +(3.45561 - 2.22078i) q^{77} +(-0.0816181 - 0.178719i) q^{78} +(9.49144 - 2.78694i) q^{79} +(-2.48714 + 2.87031i) q^{80} +(-5.84798 + 6.74893i) q^{81} +(-3.90371 + 1.14623i) q^{82} +(-4.35874 - 9.54430i) q^{83} +(-0.0741615 + 0.0476607i) q^{84} +(17.0137 + 4.99567i) q^{85} +(0.626198 + 4.35530i) q^{86} +(-0.214011 + 0.468620i) q^{87} +(-0.584585 + 4.06588i) q^{88} +(3.91643 + 2.51694i) q^{89} +(-7.44209 - 8.58863i) q^{90} -2.22871 q^{91} +(0.745229 + 4.73758i) q^{92} -0.408546 q^{93} +(6.13891 + 7.08467i) q^{94} +(17.3566 + 11.1544i) q^{95} +(0.0125459 - 0.0872586i) q^{96} +(-5.11212 + 11.1940i) q^{97} +(0.142315 + 0.989821i) q^{98} +(-11.7933 - 3.46281i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} + 5 q^{3} - q^{4} + 8 q^{5} - 5 q^{6} + q^{7} + q^{8}+O(q^{10}) $ 10 * q + q^2 + 5 * q^3 - q^4 + 8 * q^5 - 5 * q^6 + q^7 + q^8	\( 10 q + q^{2} + 5 q^{3} - q^{4} + 8 q^{5} - 5 q^{6} + q^{7} + q^{8} + 3 q^{10} + 11 q^{11} + 5 q^{12} - 6 q^{13} - q^{14} + 4 q^{15} - q^{16} - 2 q^{17} - 3 q^{19} + 8 q^{20} - 5 q^{21} - 21 q^{23} + 6 q^{24} - 15 q^{25} - 5 q^{26} - 4 q^{27} + q^{28} + 2 q^{29} - 4 q^{30} + 3 q^{31} + q^{32} - 11 q^{33} + 2 q^{34} + 3 q^{35} - 6 q^{37} - 8 q^{38} + 8 q^{39} + 14 q^{40} - 23 q^{41} + 5 q^{42} - q^{43} + 11 q^{44} - 22 q^{45} - q^{46} + 38 q^{47} + 5 q^{48} - q^{49} + 4 q^{50} + 21 q^{51} + 5 q^{52} - 49 q^{53} + 4 q^{54} + 11 q^{55} - q^{56} - 7 q^{57} - 13 q^{58} + 9 q^{59} + 4 q^{60} + 16 q^{61} - 14 q^{62} - q^{64} + 15 q^{65} + 7 q^{67} - 2 q^{68} - 16 q^{69} + 8 q^{70} - 16 q^{71} + 11 q^{72} - 9 q^{73} + 6 q^{74} - 2 q^{75} - 14 q^{76} + 11 q^{77} - 8 q^{78} + 6 q^{79} - 3 q^{80} - 24 q^{81} - 43 q^{82} - 19 q^{83} - 5 q^{84} + 49 q^{85} + 23 q^{86} - 21 q^{87} - 11 q^{88} + 25 q^{89} - 11 q^{90} + 6 q^{91} + q^{92} - 4 q^{93} - 5 q^{94} + 24 q^{95} - 5 q^{96} + 16 q^{97} + q^{98} - 33 q^{99}+O(q^{100}) \) 10 * q + q^2 + 5 * q^3 - q^4 + 8 * q^5 - 5 * q^6 + q^7 + q^8 + 3 * q^10 + 11 * q^11 + 5 * q^12 - 6 * q^13 - q^14 + 4 * q^15 - q^16 - 2 * q^17 - 3 * q^19 + 8 * q^20 - 5 * q^21 - 21 * q^23 + 6 * q^24 - 15 * q^25 - 5 * q^26 - 4 * q^27 + q^28 + 2 * q^29 - 4 * q^30 + 3 * q^31 + q^32 - 11 * q^33 + 2 * q^34 + 3 * q^35 - 6 * q^37 - 8 * q^38 + 8 * q^39 + 14 * q^40 - 23 * q^41 + 5 * q^42 - q^43 + 11 * q^44 - 22 * q^45 - q^46 + 38 * q^47 + 5 * q^48 - q^49 + 4 * q^50 + 21 * q^51 + 5 * q^52 - 49 * q^53 + 4 * q^54 + 11 * q^55 - q^56 - 7 * q^57 - 13 * q^58 + 9 * q^59 + 4 * q^60 + 16 * q^61 - 14 * q^62 - q^64 + 15 * q^65 + 7 * q^67 - 2 * q^68 - 16 * q^69 + 8 * q^70 - 16 * q^71 + 11 * q^72 - 9 * q^73 + 6 * q^74 - 2 * q^75 - 14 * q^76 + 11 * q^77 - 8 * q^78 + 6 * q^79 - 3 * q^80 - 24 * q^81 - 43 * q^82 - 19 * q^83 - 5 * q^84 + 49 * q^85 + 23 * q^86 - 21 * q^87 - 11 * q^88 + 25 * q^89 - 11 * q^90 + 6 * q^91 + q^92 - 4 * q^93 - 5 * q^94 + 24 * q^95 - 5 * q^96 + 16 * q^97 + q^98 - 33 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{7}{11}\right)$

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 $

$2$	0.654861	+	0.755750i	0.463056	+	0.534396i
$2$	0.654861	+	0.755750i	0.463056	+	0.534396i
$3$	0.0741615	+	0.0476607i	0.0428172	+	0.0275169i	0.561874	−	0.827223i	$-0.310080\pi$
$3$	0.0741615	+	0.0476607i	0.0428172	+	0.0275169i	−0.519057	+	0.854740i	$0.673717\pi$
$4$	−0.142315	+	0.989821i	−0.0711574	+	0.494911i
$5$	1.57773	−	3.45475i	0.705583	−	1.54501i	−0.127484	−	0.991841i	$-0.540690\pi$
$5$	1.57773	−	3.45475i	0.705583	−	1.54501i	0.833067	−	0.553171i	$-0.186583\pi$
$6$	0.0125459	+	0.0872586i	0.00512184	+	0.0356232i
$7$	0.959493	+	0.281733i	0.362654	+	0.106485i
$7$	0.959493	+	0.281733i	0.362654	+	0.106485i
$8$	−0.841254	+	0.540641i	−0.297428	+	0.191145i
$9$	−1.24302	−	2.72183i	−0.414339	−	0.907276i
$10$	3.64412	−	1.07001i	1.15237	−	0.338367i
$11$	2.68996	−	3.10438i	0.811055	−	0.936007i	−0.187878	−	0.982192i	$-0.560161\pi$
$11$	2.68996	−	3.10438i	0.811055	−	0.936007i	0.998933	+	0.0461854i	$0.0147065\pi$
$12$	−0.0577299	+	0.0666238i	−0.0166652	+	0.0192326i
$13$	−2.13843	+	0.627899i	−0.593094	+	0.174148i	−0.564486	−	0.825443i	$-0.690926\pi$
$13$	−2.13843	+	0.627899i	−0.593094	+	0.174148i	−0.0286077	+	0.999591i	$0.509107\pi$
$14$	0.415415	+	0.909632i	0.111024	+	0.243109i
$15$	0.281663	−	0.181014i	0.0727250	−	0.0467375i
$16$	−0.959493	−	0.281733i	−0.239873	−	0.0704331i
$17$	0.664440	+	4.62128i	0.161150	+	1.12083i	0.896470	+	0.443105i	$0.146123\pi$
$17$	0.664440	+	4.62128i	0.161150	+	1.12083i	−0.735320	+	0.677721i	$0.762968\pi$
$18$	1.24302	−	2.72183i	0.292982	−	0.641541i
$19$	−0.773100	+	5.37703i	−0.177361	+	1.23358i	0.685477	+	0.728095i	$0.259594\pi$
$19$	−0.773100	+	5.37703i	−0.177361	+	1.23358i	−0.862838	+	0.505481i	$0.831315\pi$
$20$	3.19505	+	2.05334i	0.714436	+	0.459140i
$21$	0.0577299	+	0.0666238i	0.0125977	+	0.0145385i
$22$	4.10769			0.875762
$23$	4.58330	−	1.41187i	0.955684	−	0.294395i
$23$	4.58330	−	1.41187i	0.955684	−	0.294395i
$24$	−0.0881559			−0.0179948
$25$	−6.17177	−	7.12260i	−1.23435	−	1.42452i
$26$	−1.87491	−	1.20493i	−0.367700	−	0.236306i
$27$	0.0751779	−	0.522874i	0.0144680	−	0.100627i
$28$	−0.415415	+	0.909632i	−0.0785061	+	0.171904i
$29$	0.831674	+	5.78442i	0.154438	+	1.07414i	0.908665	+	0.417526i	$0.137103\pi$
$29$	0.831674	+	5.78442i	0.154438	+	1.07414i	−0.754227	+	0.656614i	$0.771988\pi$
$30$	0.321251	+	0.0943278i	0.0586521	+	0.0172218i
$31$	−3.89867	+	2.50552i	−0.700222	+	0.450005i	−0.841706	−	0.539935i	$-0.818449\pi$
$31$	−3.89867	+	2.50552i	−0.700222	+	0.450005i	0.141485	+	0.989940i	$0.454812\pi$
$32$	−0.415415	−	0.909632i	−0.0734357	−	0.160802i
$33$	0.347449	−	0.102020i	0.0604831	−	0.0177594i
$34$	−3.05742	+	3.52845i	−0.524342	+	0.605123i
$35$	2.48714	−	2.87031i	0.420403	−	0.485171i
$36$	2.87102	−	0.843008i	0.478504	−	0.140501i
$37$	−0.274362	−	0.600768i	−0.0451048	−	0.0987657i	0.885738	−	0.464185i	$-0.153653\pi$
$37$	−0.274362	−	0.600768i	−0.0451048	−	0.0987657i	−0.930843	+	0.365420i	$0.880926\pi$
$38$	−4.56996	+	2.93694i	−0.741346	+	0.476434i
$39$	−0.188515	−	0.0553531i	−0.0301866	−	0.00886358i
$40$	0.540507	+	3.75931i	0.0854617	+	0.594399i
$41$	−1.69012	+	3.70085i	−0.263953	+	0.577976i	−0.994482	−	0.104905i	$-0.966546\pi$
$41$	−1.69012	+	3.70085i	−0.263953	+	0.577976i	0.730529	+	0.682881i	$0.239273\pi$
$42$	−0.0125459	+	0.0872586i	−0.00193587	+	0.0134643i
$43$	3.70159	+	2.37887i	0.564487	+	0.362774i	0.791548	−	0.611107i	$-0.209275\pi$
$43$	3.70159	+	2.37887i	0.564487	+	0.362774i	−0.227061	+	0.973881i	$0.572912\pi$
$44$	2.68996	+	3.10438i	0.405527	+	0.468003i
$45$	−11.3644			−1.69410
$46$	4.06844	+	2.53925i	0.599859	+	0.374392i
$47$	9.37437			1.36739			0.683696	−	0.729767i	$-0.260371\pi$
$47$	9.37437			1.36739			0.683696	+	0.729767i	$0.260371\pi$
$48$	−0.0577299	−	0.0666238i	−0.00833259	−	0.00961632i
$49$	0.841254	+	0.540641i	0.120179	+	0.0772344i
$50$	1.34125	−	9.32862i	0.189682	−	1.31927i
$51$	−0.170978	+	0.374389i	−0.0239416	+	0.0524249i
$52$	−0.317178	−	2.20602i	−0.0439847	−	0.305920i
$53$	−11.1053	−	3.26080i	−1.52542	−	0.447905i	−0.591777	−	0.806101i	$-0.701574\pi$
$53$	−11.1053	−	3.26080i	−1.52542	−	0.447905i	−0.933646	+	0.358197i	$0.883392\pi$
$54$	0.444393	−	0.285594i	0.0604742	−	0.0388644i
$55$	−6.48083	−	14.1910i	−0.873875	−	1.91352i
$56$	−0.959493	+	0.281733i	−0.128218	+	0.0376481i
$57$	−0.313607	+	0.361922i	−0.0415383	+	0.0479377i
$58$	−3.82694	+	4.41653i	−0.502502	+	0.579919i
$59$	−8.09519	+	2.37696i	−1.05390	+	0.309454i	−0.762393	−	0.647114i	$-0.775976\pi$
$59$	−8.09519	+	2.37696i	−1.05390	+	0.309454i	−0.291510	+	0.956568i	$0.594158\pi$
$60$	0.139086	+	0.304557i	0.0179560	+	0.0393181i
$61$	−3.99868	+	2.56979i	−0.511978	+	0.329028i	−0.770992	−	0.636845i	$-0.780239\pi$
$61$	−3.99868	+	2.56979i	−0.511978	+	0.329028i	0.259013	+	0.965874i	$0.416603\pi$
$62$	−4.44663	−	1.30565i	−0.564723	−	0.165818i
$63$	−0.425839	−	2.96177i	−0.0536506	−	0.373148i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	−1.20463	+	8.37840i	−0.149416	+	1.03921i
$66$	0.304632	+	0.195775i	0.0374976	+	0.0240983i
$67$	0.365142	+	0.421396i	0.0446092	+	0.0514817i	0.777616	−	0.628740i	$-0.216429\pi$
$67$	0.365142	+	0.421396i	0.0446092	+	0.0514817i	−0.733006	+	0.680222i	$0.761884\pi$
$68$	−4.66880			−0.566175
$69$	0.407195	+	0.113737i	0.0490205	+	0.0136923i
$70$	3.79797			0.453944
$71$	−3.50975	−	4.05046i	−0.416530	−	0.480702i	0.508247	−	0.861212i	$-0.330294\pi$
$71$	−3.50975	−	4.05046i	−0.416530	−	0.480702i	−0.924777	+	0.380510i	$0.875748\pi$
$72$	2.51722	+	1.61772i	0.296658	+	0.190650i
$73$	2.13088	−	14.8206i	0.249401	−	1.73462i	−0.352288	−	0.935892i	$-0.614596\pi$
$73$	2.13088	−	14.8206i	0.249401	−	1.73462i	0.601689	−	0.798730i	$-0.294495\pi$
$74$	0.274362	−	0.600768i	0.0318939	−	0.0698379i
$75$	−0.118239	−	0.822373i	−0.0136531	−	0.0949595i
$76$	−5.21228	−	1.53046i	−0.597889	−	0.175556i
$77$	3.45561	−	2.22078i	0.393803	−	0.253082i
$78$	−0.0816181	−	0.178719i	−0.00924144	−	0.0202359i
$79$	9.49144	−	2.78694i	1.06787	−	0.313555i	0.299854	−	0.953985i	$-0.403062\pi$
$79$	9.49144	−	2.78694i	1.06787	−	0.313555i	0.768017	+	0.640430i	$0.221244\pi$
$80$	−2.48714	+	2.87031i	−0.278071	+	0.320911i
$81$	−5.84798	+	6.74893i	−0.649776	+	0.749881i
$82$	−3.90371	+	1.14623i	−0.431093	+	0.126580i
$83$	−4.35874	−	9.54430i	−0.478434	−	1.04762i	−0.982891	−	0.184187i	$-0.941035\pi$
$83$	−4.35874	−	9.54430i	−0.478434	−	1.04762i	0.504458	−	0.863436i	$-0.331692\pi$
$84$	−0.0741615	+	0.0476607i	−0.00809168	+	0.00520021i
$85$	17.0137	+	4.99567i	1.84539	+	0.541856i
$86$	0.626198	+	4.35530i	0.0675247	+	0.469644i
$87$	−0.214011	+	0.468620i	−0.0229444	+	0.0502413i
$88$	−0.584585	+	4.06588i	−0.0623170	+	0.433424i
$89$	3.91643	+	2.51694i	0.415141	+	0.266795i	0.731496	−	0.681846i	$-0.238823\pi$
$89$	3.91643	+	2.51694i	0.415141	+	0.266795i	−0.316355	+	0.948641i	$0.602459\pi$
$90$	−7.44209	−	8.58863i	−0.784465	−	0.905321i
$91$	−2.22871			−0.233632
$92$	0.745229	+	4.73758i	0.0776955	+	0.493927i
$93$	−0.408546			−0.0423642
$94$	6.13891	+	7.08467i	0.633180	+	0.730728i
$95$	17.3566	+	11.1544i	1.78075	+	1.14442i
$96$	0.0125459	−	0.0872586i	0.00128046	−	0.00890580i
$97$	−5.11212	+	11.1940i	−0.519057	+	1.13658i	0.450738	+	0.892656i	$0.351161\pi$
$97$	−5.11212	+	11.1940i	−0.519057	+	1.13658i	−0.969795	+	0.243920i	$0.921566\pi$
$98$	0.142315	+	0.989821i	0.0143760	+	0.0999871i
$99$	−11.7933	−	3.46281i	−1.18527	−	0.348026i
$100$	7.92844	−	5.09530i	0.792844	−	0.509530i
$101$	4.99756	+	10.9431i	0.497276	+	1.08888i	0.977345	+	0.211652i	$0.0678843\pi$
$101$	4.99756	+	10.9431i	0.497276	+	1.08888i	−0.480069	+	0.877231i	$0.659388\pi$
$102$	−0.394911	+	0.115956i	−0.0391020	+	0.0114814i
$103$	−2.48190	+	2.86426i	−0.244549	+	0.282224i	−0.864733	−	0.502232i	$-0.832512\pi$
$103$	−2.48190	+	2.86426i	−0.244549	+	0.282224i	0.620184	+	0.784456i	$0.287058\pi$
$104$	1.45949	−	1.68434i	0.143115	−	0.165164i
$105$	0.321251	−	0.0943278i	0.0313509	−	0.00920545i
$106$	−4.80805	−	10.5282i	−0.466999	−	1.02258i
$107$	−9.57303	+	6.15221i	−0.925459	+	0.594757i	−0.914237	−	0.405180i	$-0.867209\pi$
$107$	−9.57303	+	6.15221i	−0.925459	+	0.594757i	−0.0112226	+	0.999937i	$0.503572\pi$
$108$	0.506853	+	0.148825i	0.0487719	+	0.0143207i
$109$	0.501401	+	3.48732i	0.0480255	+	0.334025i	0.999642	+	0.0267380i	$0.00851197\pi$
$109$	0.501401	+	3.48732i	0.0480255	+	0.334025i	−0.951617	+	0.307287i	$0.900579\pi$
$110$	6.48083	−	14.1910i	0.617923	−	1.35306i
$111$	0.00828596	−	0.0576301i	0.000786469	−	0.00547001i
$112$	−0.841254	−	0.540641i	−0.0794910	−	0.0510858i
$113$	3.57396	+	4.12457i	0.336210	+	0.388007i	0.898530	−	0.438913i	$-0.144636\pi$
$113$	3.57396	+	4.12457i	0.336210	+	0.388007i	−0.562319	+	0.826920i	$0.690091\pi$
$114$	−0.478891			−0.0448523
$115$	2.35355	−	18.0617i	0.219470	−	1.68426i
$116$	−5.84391			−0.542593
$117$	4.36714	+	5.03994i	0.403742	+	0.465943i
$118$	−7.09761	−	4.56136i	−0.653388	−	0.419907i
$119$	−0.664440	+	4.62128i	−0.0609091	+	0.423632i
$120$	−0.139086	+	0.304557i	−0.0126968	+	0.0278021i
$121$	−0.835830	−	5.81332i	−0.0759845	−	0.528484i
$122$	−4.56070	−	1.33914i	−0.412906	−	0.121240i
$123$	−0.301727	+	0.193908i	−0.0272058	+	0.0174841i
$124$	−1.92518	−	4.21556i	−0.172886	−	0.378568i
$125$	−16.1236	+	4.73432i	−1.44214	+	0.423450i
$126$	1.95949	−	2.26138i	0.174566	−	0.201459i
$127$	13.9653	−	16.1168i	1.23922	−	1.43014i	0.374996	−	0.927026i	$-0.377644\pi$
$127$	13.9653	−	16.1168i	1.23922	−	1.43014i	0.864223	−	0.503109i	$-0.167810\pi$
$128$	0.959493	−	0.281733i	0.0848080	−	0.0249019i
$129$	0.161137	+	0.352841i	0.0141873	+	0.0310659i
$130$	−7.12084	+	4.57628i	−0.624539	+	0.401367i
$131$	2.89215	+	0.849211i	0.252688	+	0.0741959i	0.405623	−	0.914040i	$-0.367054\pi$
$131$	2.89215	+	0.849211i	0.252688	+	0.0741959i	−0.152935	+	0.988236i	$0.548873\pi$
$132$	0.0515346	+	0.358431i	0.00448551	+	0.0311974i
$133$	−2.25667	+	4.94141i	−0.195678	+	0.428475i
$134$	−0.0793529	+	0.551912i	−0.00685505	+	0.0476779i
$135$	−1.68779	−	1.08468i	−0.145262	−	0.0933540i
$136$	−3.05742	−	3.52845i	−0.262171	−	0.302562i
$137$	−3.67024			−0.313569			−0.156785	−	0.987633i	$-0.550113\pi$
$137$	−3.67024			−0.313569			−0.156785	+	0.987633i	$0.550113\pi$
$138$	0.180699	+	0.382219i	0.0153822	+	0.0325366i
$139$	−1.53861			−0.130503			−0.0652515	−	0.997869i	$-0.520785\pi$
$139$	−1.53861			−0.130503			−0.0652515	+	0.997869i	$0.520785\pi$
$140$	2.48714	+	2.87031i	0.210202	+	0.242586i
$141$	0.695217	+	0.446789i	0.0585478	+	0.0376264i
$142$	0.762741	−	5.30498i	0.0640078	−	0.445184i
$143$	−3.80306	+	8.32753i	−0.318028	+	0.696383i
$144$	0.425839	+	2.96177i	0.0354865	+	0.246814i
$145$	21.2959	+	6.25304i	1.76853	+	0.519287i
$146$	12.5961	−	8.09503i	1.04246	−	0.669949i
$147$	0.0366213	+	0.0801894i	0.00302047	+	0.00661391i
$148$	0.633699	−	0.186071i	0.0520897	−	0.0152949i
$149$	12.4948	−	14.4198i	1.02362	−	1.18132i	0.0403417	−	0.999186i	$-0.487155\pi$
$149$	12.4948	−	14.4198i	1.02362	−	1.18132i	0.983274	−	0.182130i	$-0.0582992\pi$
$150$	0.544078	−	0.627899i	0.0444238	−	0.0512678i
$151$	−3.77491	+	1.10841i	−0.307198	+	0.0902014i	−0.431698	−	0.902018i	$-0.642085\pi$
$151$	−3.77491	+	1.10841i	−0.307198	+	0.0902014i	0.124500	+	0.992220i	$0.460267\pi$
$152$	−2.25667	−	4.94141i	−0.183040	−	0.400802i
$153$	11.7524	−	7.55282i	0.950126	−	0.610609i
$154$	3.94130	+	1.15727i	0.317599	+	0.0932554i
$155$	2.50490	+	17.4220i	0.201199	+	1.39937i
$156$	0.0816181	−	0.178719i	0.00653468	−	0.0143090i
$157$	0.693218	−	4.82143i	0.0553248	−	0.384792i	−0.943281	−	0.331997i	$-0.892278\pi$
$157$	0.693218	−	4.82143i	0.0553248	−	0.384792i	0.998605	−	0.0527957i	$-0.0168132\pi$
$158$	8.32180	+	5.34810i	0.662047	+	0.425472i
$159$	−0.668170	−	0.771109i	−0.0529893	−	0.0611530i
$160$	−3.79797			−0.300256
$161$	4.79541	−	0.0634158i	0.377931	−	0.00499787i
$162$	−8.93012			−0.701616
$163$	7.97963	+	9.20898i	0.625013	+	0.721303i	0.976651	−	0.214833i	$-0.0689207\pi$
$163$	7.97963	+	9.20898i	0.625013	+	0.721303i	−0.351638	+	0.936136i	$0.614375\pi$
$164$	−3.42265	−	2.19961i	−0.267264	−	0.171760i
$165$	0.195727	−	1.36131i	0.0152373	−	0.105978i
$166$	4.35874	−	9.54430i	0.338304	−	0.740782i
$167$	2.35311	+	16.3662i	0.182089	+	1.26646i	0.851813	+	0.523846i	$0.175503\pi$
$167$	2.35311	+	16.3662i	0.182089	+	1.26646i	−0.669724	+	0.742610i	$0.733588\pi$
$168$	−0.0845850	−	0.0248364i	−0.00652587	−	0.00191617i
$169$	−6.75767	+	4.34289i	−0.519821	+	0.334069i
$170$	7.36612	+	16.1296i	0.564956	+	1.23708i
$171$	15.5963	−	4.57949i	1.19268	−	0.350203i
$172$	−2.88145	+	3.32537i	−0.219708	+	0.253557i
$173$	−13.7371	+	15.8535i	−1.04441	+	1.20532i	−0.0661792	+	0.997808i	$0.521081\pi$
$173$	−13.7371	+	15.8535i	−1.04441	+	1.20532i	−0.978233	+	0.207508i	$0.933465\pi$
$174$	−0.494307	+	0.145142i	−0.0374733	+	0.0110032i
$175$	−3.91510	−	8.57287i	−0.295954	−	0.648048i
$176$	−3.45561	+	2.22078i	−0.260476	+	0.167398i
$177$	−0.713639	−	0.209543i	−0.0536404	−	0.0157502i
$178$	0.662543	+	4.60808i	0.0496597	+	0.345391i
$179$	−0.758164	+	1.66015i	−0.0566678	+	0.124085i	−0.935848	−	0.352405i	$-0.885364\pi$
$179$	−0.758164	+	1.66015i	−0.0566678	+	0.124085i	0.879180	+	0.476490i	$0.158091\pi$
$180$	1.61732	−	11.2487i	0.120548	−	0.838429i
$181$	−13.5569	−	8.71252i	−1.00768	−	0.647597i	−0.0708883	−	0.997484i	$-0.522583\pi$
$181$	−13.5569	−	8.71252i	−1.00768	−	0.647597i	−0.936792	+	0.349888i	$0.886220\pi$
$182$	−1.45949	−	1.68434i	−0.108185	−	0.124852i
$183$	−0.419026			−0.0309753
$184$	−3.09240	+	3.66566i	−0.227975	+	0.270236i
$185$	−2.50837			−0.184419
$186$	−0.267541	−	0.308758i	−0.0196170	−	0.0226393i
$187$	16.1335	+	10.3684i	1.17980	+	0.758213i
$188$	−1.33411	+	9.27895i	−0.0973001	+	0.676737i
$189$	0.219443	−	0.480513i	0.0159621	−	0.0349522i
$190$	2.93621	+	20.4218i	0.213015	+	1.48155i
$191$	12.5484	+	3.68453i	0.907968	+	0.266603i	0.702185	−	0.711994i	$-0.252208\pi$
$191$	12.5484	+	3.68453i	0.907968	+	0.266603i	0.205782	+	0.978598i	$0.434026\pi$
$192$	0.0741615	−	0.0476607i	0.00535214	−	0.00343961i
$193$	−10.5844	−	23.1766i	−0.761882	−	1.66829i	−0.743755	−	0.668453i	$-0.766957\pi$
$193$	−10.5844	−	23.1766i	−0.761882	−	1.66829i	−0.0181272	−	0.999836i	$-0.505770\pi$
$194$	−11.8076	+	3.46702i	−0.847734	+	0.248917i
$195$	−0.488658	+	0.563941i	−0.0349935	+	0.0403846i
$196$	−0.654861	+	0.755750i	−0.0467758	+	0.0539821i
$197$	21.2117	−	6.22832i	1.51127	−	0.443750i	0.582014	−	0.813179i	$-0.302265\pi$
$197$	21.2117	−	6.22832i	1.51127	−	0.443750i	0.929259	+	0.369429i	$0.120447\pi$
$198$	−5.10592	−	11.1804i	−0.362862	−	0.794558i
$199$	10.5921	−	6.80712i	0.750853	−	0.482544i	−0.108392	−	0.994108i	$-0.534570\pi$
$199$	10.5921	−	6.80712i	0.750853	−	0.482544i	0.859245	+	0.511564i	$0.170934\pi$
$200$	9.04279	+	2.65520i	0.639422	+	0.187751i
$201$	0.00699543	+	0.0486543i	0.000493419	+	0.00343181i
$202$	−4.99756	+	10.9431i	−0.351627	+	0.769956i
$203$	−0.831674	+	5.78442i	−0.0583721	+	0.405987i
$204$	−0.346245	−	0.222518i	−0.0242420	−	0.0155794i
$205$	10.1190	+	11.6779i	0.706739	+	0.815621i
$206$	−3.78996			−0.264059
$207$	−9.53998	−	10.7200i	−0.663075	−	0.745089i
$208$	2.22871			0.154533
$209$	14.6128	+	16.8640i	1.01079	+	1.16651i
$210$	0.281663	+	0.181014i	0.0194366	+	0.0124911i
$211$	3.54282	−	24.6409i	0.243898	−	1.69635i	−0.388293	−	0.921536i	$-0.626935\pi$
$211$	3.54282	−	24.6409i	0.243898	−	1.69635i	0.632191	−	0.774813i	$-0.282156\pi$
$212$	4.80805	−	10.5282i	0.330218	−	0.723077i
$213$	−0.0672401	−	0.467665i	−0.00460722	−	0.0320439i
$214$	−10.9185	−	3.20597i	−0.746375	−	0.219156i
$215$	14.0585	−	9.03486i	0.958783	−	0.616172i
$216$	0.219443	+	0.480513i	0.0149312	+	0.0326948i
$217$	−4.44663	+	1.30565i	−0.301857	+	0.0886332i
$218$	−2.30719	+	2.66264i	−0.156263	+	0.180337i
$219$	0.864390	−	0.997559i	0.0584101	−	0.0674088i
$220$	14.9689	−	4.39527i	1.00920	−	0.296329i
$221$	−4.32256	−	9.46508i	−0.290767	−	0.636690i
$222$	0.0489801	−	0.0314776i	0.00328733	−	0.00211264i
$223$	7.09814	+	2.08420i	0.475327	+	0.139569i	0.510616	−	0.859809i	$-0.329417\pi$
$223$	7.09814	+	2.08420i	0.475327	+	0.139569i	−0.0352897	+	0.999377i	$0.511235\pi$
$224$	−0.142315	−	0.989821i	−0.00950881	−	0.0661352i
$225$	−11.7149	+	25.6520i	−0.780992	+	1.71013i
$226$	−0.776697	+	5.40204i	−0.0516651	+	0.359339i
$227$	3.88185	+	2.49471i	0.257647	+	0.165580i	0.663088	−	0.748541i	$-0.269246\pi$
$227$	3.88185	+	2.49471i	0.257647	+	0.165580i	−0.405441	+	0.914121i	$0.632882\pi$
$228$	−0.313607	−	0.361922i	−0.0207691	−	0.0239689i
$229$	−18.1000			−1.19608			−0.598041	−	0.801466i	$-0.704054\pi$
$229$	−18.1000			−1.19608			−0.598041	+	0.801466i	$0.704054\pi$
$230$	15.1914	−	10.0492i	1.00169	−	0.662625i
$231$	0.362117			0.0238256
$232$	−3.82694	−	4.41653i	−0.251251	−	0.289959i
$233$	−23.1106	−	14.8523i	−1.51403	−	0.973007i	−0.992825	−	0.119575i	$-0.961847\pi$
$233$	−23.1106	−	14.8523i	−1.51403	−	0.973007i	−0.521204	−	0.853432i	$-0.674517\pi$
$234$	−0.949069	+	6.60092i	−0.0620426	+	0.431516i
$235$	14.7902	−	32.3861i	0.964809	−	2.11264i
$236$	−1.20070	−	8.35107i	−0.0781590	−	0.543608i
$237$	0.836727	+	0.245685i	0.0543513	+	0.0159590i
$238$	−3.92765	+	2.52414i	−0.254591	+	0.163616i
$239$	7.96559	+	17.4422i	0.515251	+	1.12824i	0.971206	+	0.238240i	$0.0765705\pi$
$239$	7.96559	+	17.4422i	0.515251	+	1.12824i	−0.455955	+	0.890003i	$0.650702\pi$
$240$	−0.321251	+	0.0943278i	−0.0207367	+	0.00608883i
$241$	−11.9500	+	13.7911i	−0.769769	+	0.888360i	−0.996326	−	0.0856374i	$-0.972707\pi$
$241$	−11.9500	+	13.7911i	−0.769769	+	0.888360i	0.226558	+	0.973998i	$0.427253\pi$
$242$	3.84606	−	4.43859i	0.247234	−	0.285324i
$243$	−2.27591	+	0.668268i	−0.146000	+	0.0428694i
$244$	−1.97457	−	4.32370i	−0.126409	−	0.276796i
$245$	3.19505	−	2.05334i	0.204124	−	0.131183i
$246$	−0.344135	−	0.101047i	−0.0219413	−	0.00644254i
$247$	−1.72301	−	11.9838i	−0.109633	−	0.762513i
$248$	1.92518	−	4.21556i	0.122249	−	0.267688i
$249$	0.131638	−	0.915560i	0.00834220	−	0.0580213i
$250$	−14.1367	−	9.08509i	−0.894082	−	0.574592i
$251$	−7.38960	−	8.52805i	−0.466427	−	0.538286i	0.472987	−	0.881069i	$-0.343176\pi$
$251$	−7.38960	−	8.52805i	−0.466427	−	0.538286i	−0.939414	+	0.342784i	$0.888630\pi$
$252$	2.99223			0.188493
$253$	7.94592	−	18.0262i	0.499556	−	1.13330i
$254$	21.3256			1.33809
$255$	1.02366	+	1.18137i	0.0641043	+	0.0739803i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	2.81612	−	19.5865i	0.175664	−	1.22177i	−0.690990	−	0.722864i	$-0.742825\pi$
$257$	2.81612	−	19.5865i	0.175664	−	1.22177i	0.866655	−	0.498909i	$-0.166266\pi$
$258$	−0.161137	+	0.352841i	−0.0100319	+	0.0219669i
$259$	−0.0939921	−	0.653729i	−0.00584038	−	0.0406208i
$260$	−8.12168	−	2.38474i	−0.503685	−	0.147895i
$261$	14.7104	−	9.45381i	0.910552	−	0.585176i
$262$	1.25216	+	2.74185i	0.0773588	+	0.169392i
$263$	−16.8407	+	4.94488i	−1.03844	+	0.304915i	−0.756140	−	0.654410i	$-0.772917\pi$
$263$	−16.8407	+	4.94488i	−1.03844	+	0.304915i	−0.282304	+	0.959325i	$0.591099\pi$
$264$	−0.237136	+	0.273670i	−0.0145947	+	0.0168432i
$265$	−28.7864	+	33.2212i	−1.76833	+	2.04076i
$266$	−5.21228	+	1.53046i	−0.319585	+	0.0938387i
$267$	0.170489	+	0.373320i	0.0104338	+	0.0228468i
$268$	−0.469072	+	0.301454i	−0.0286531	+	0.0184143i
$269$	−4.95533	−	1.45502i	−0.302132	−	0.0887139i	0.127153	−	0.991883i	$-0.459416\pi$
$269$	−4.95533	−	1.45502i	−0.302132	−	0.0887139i	−0.429285	+	0.903169i	$0.641234\pi$
$270$	−0.285523	−	1.98586i	−0.0173764	−	0.120855i
$271$	−8.02027	+	17.5619i	−0.487196	+	1.06681i	0.493225	+	0.869902i	$0.335818\pi$
$271$	−8.02027	+	17.5619i	−0.487196	+	1.06681i	−0.980422	+	0.196910i	$0.936909\pi$
$272$	0.664440	−	4.62128i	0.0402876	−	0.280206i
$273$	−0.165284	−	0.106222i	−0.0100035	−	0.00642883i
$274$	−2.40349	−	2.77378i	−0.145200	−	0.167570i
$275$	−38.7131			−2.33449
$276$	−0.170529	+	0.386864i	−0.0102646	+	0.0232865i
$277$	−24.2784			−1.45875			−0.729374	−	0.684116i	$-0.760188\pi$
$277$	−24.2784			−1.45875			−0.729374	+	0.684116i	$0.760188\pi$
$278$	−1.00757	−	1.16280i	−0.0604303	−	0.0697403i
$279$	11.6657	+	7.49709i	0.698408	+	0.448839i
$280$	−0.540507	+	3.75931i	−0.0323015	+	0.224662i
$281$	5.78119	−	12.6590i	0.344877	−	0.755175i	−0.655123	−	0.755522i	$-0.727383\pi$
$281$	5.78119	−	12.6590i	0.344877	−	0.755175i	1.00000		0.000347260i	$0.000110536\pi$
$282$	0.117610	+	0.817994i	0.00700356	+	0.0487109i
$283$	−23.4143	−	6.87507i	−1.39184	−	0.408680i	−0.501964	−	0.864888i	$-0.667389\pi$
$283$	−23.4143	−	6.87507i	−1.39184	−	0.408680i	−0.889873	+	0.456208i	$0.849207\pi$
$284$	4.50872	−	2.89758i	0.267544	−	0.171940i
$285$	0.755563	+	1.65445i	0.0447557	+	0.0980012i
$286$	−8.78400	+	2.57922i	−0.519409	+	0.152512i
$287$	−2.66431	+	3.07478i	−0.157269	+	0.181499i
$288$	−1.95949	+	2.26138i	−0.115464	+	0.133253i
$289$	−4.60337	+	1.35167i	−0.270786	+	0.0795101i
$290$	9.22012	+	20.1892i	0.541424	+	1.18555i
$291$	−0.912635	+	0.586515i	−0.0534996	+	0.0343821i
$292$	14.3665	+	4.21839i	0.840736	+	0.246862i
$293$	−2.68388	−	18.6668i	−0.156794	−	1.09053i	−0.904493	−	0.426489i	$-0.859750\pi$
$293$	−2.68388	−	18.6668i	−0.156794	−	1.09053i	0.747699	−	0.664038i	$-0.231159\pi$
$294$	−0.0366213	+	0.0801894i	−0.00213580	+	0.00467674i
$295$	−4.56023	+	31.7171i	−0.265507	+	1.84664i
$296$	0.555607	+	0.357067i	0.0322940	+	0.0207541i
$297$	−1.42097	−	1.63989i	−0.0824533	−	0.0951562i
$298$	19.0801			1.10528
$299$	−8.91455	+	5.89704i	−0.515541	+	0.341034i
$300$	0.830830			0.0479680
$301$	2.88145	+	3.32537i	0.166084	+	0.191671i
$302$	−3.30972	−	2.12703i	−0.190453	−	0.122397i
$303$	−0.150931	+	1.04975i	−0.00867075	+	0.0603064i
$304$	2.25667	−	4.94141i	0.129429	−	0.283410i
$305$	2.56916	+	17.8689i	0.147110	+	1.02317i
$306$	13.4042	+	3.93584i	0.766269	+	0.224997i
$307$	9.00209	−	5.78529i	0.513777	−	0.330184i	−0.257929	−	0.966164i	$-0.583040\pi$
$307$	9.00209	−	5.78529i	0.513777	−	0.330184i	0.771706	+	0.635980i	$0.219404\pi$
$308$	1.70640	+	3.73648i	0.0972309	+	0.212906i
$309$	−0.320574	+	0.0941290i	−0.0182368	+	0.00535481i
$310$	−11.5263	+	13.3020i	−0.654649	+	0.755506i
$311$	12.5314	−	14.4620i	0.710593	−	0.820068i	−0.279550	−	0.960131i	$-0.590185\pi$
$311$	12.5314	−	14.4620i	0.710593	−	0.820068i	0.990143	+	0.140064i	$0.0447307\pi$
$312$	0.188515	−	0.0553531i	0.0106726	−	0.00313375i
$313$	−3.10853	−	6.80673i	−0.175705	−	0.384739i	0.801206	−	0.598389i	$-0.204192\pi$
$313$	−3.10853	−	6.80673i	−0.175705	−	0.384739i	−0.976910	+	0.213650i	$0.931465\pi$
$314$	4.09776	−	2.63347i	0.231250	−	0.148615i
$315$	−10.9040	−	3.20172i	−0.614373	−	0.180396i
$316$	1.40780	+	9.79146i	0.0791949	+	0.550812i
$317$	1.98194	−	4.33985i	0.111317	−	0.243750i	−0.845772	−	0.533545i	$-0.820860\pi$
$317$	1.98194	−	4.33985i	0.111317	−	0.243750i	0.957089	+	0.289794i	$0.0935869\pi$
$318$	0.145207	−	1.00994i	0.00814282	−	0.0566345i
$319$	20.1942	+	12.9781i	1.13066	+	0.726631i
$320$	−2.48714	−	2.87031i	−0.139035	−	0.160455i
$321$	−1.00317			−0.0559914
$322$	3.18825	+	3.58260i	0.177674	+	0.199651i
$323$	−25.3624			−1.41120
$324$	−5.84798	−	6.74893i	−0.324888	−	0.374941i
$325$	17.6702	+	11.3559i	0.980165	+	0.629913i
$326$	−1.73414	+	12.0612i	−0.0960451	+	0.668008i
$327$	−0.129023	+	0.282522i	−0.00713501	+	0.0156235i
$328$	−0.579010	−	4.02711i	−0.0319705	−	0.222360i
$329$	8.99464	+	2.64106i	0.495891	+	0.145607i
$330$	1.15698	−	0.743548i	0.0636898	−	0.0409310i
$331$	−5.13691	−	11.2483i	−0.282350	−	0.618260i	0.714318	−	0.699821i	$-0.246737\pi$
$331$	−5.13691	−	11.2483i	−0.282350	−	0.618260i	−0.996668	+	0.0815607i	$0.974010\pi$
$332$	10.0675	−	2.95608i	0.552524	−	0.162236i
$333$	−1.29415	+	1.49353i	−0.0709190	+	0.0818449i
$334$	−10.8278	+	12.4959i	−0.592471	+	0.683748i
$335$	2.03192	−	0.596624i	0.111015	−	0.0325971i
$336$	−0.0366213	−	0.0801894i	−0.00199786	−	0.00437469i
$337$	−11.5063	+	7.39462i	−0.626786	+	0.402811i	−0.815118	−	0.579295i	$-0.803328\pi$
$337$	−11.5063	+	7.39462i	−0.626786	+	0.402811i	0.188332	+	0.982105i	$0.439692\pi$
$338$	−7.70748	−	2.26312i	−0.419231	−	0.123097i
$339$	0.0684704	+	0.476222i	0.00371880	+	0.0258648i
$340$	−7.36612	+	16.1296i	−0.399484	+	0.874748i
$341$	−2.70918	+	18.8427i	−0.146710	+	1.02039i
$342$	13.6744	+	8.78798i	0.739425	+	0.475200i
$343$	0.654861	+	0.755750i	0.0353592	+	0.0408066i
$344$	−4.40009			−0.237237
$345$	1.03538	−	1.22731i	0.0557428	−	0.0660762i
$346$	−20.9771			−1.12774
$347$	2.69602	+	3.11137i	0.144730	+	0.167027i	0.823486	−	0.567337i	$-0.192026\pi$
$347$	2.69602	+	3.11137i	0.144730	+	0.167027i	−0.678756	+	0.734364i	$0.737481\pi$
$348$	−0.433393	−	0.278525i	−0.0232323	−	0.0149305i
$349$	0.467197	−	3.24943i	0.0250085	−	0.173938i	−0.973489	−	0.228733i	$-0.926542\pi$
$349$	0.467197	−	3.24943i	0.0250085	−	0.173938i	0.998498	+	0.0547955i	$0.0174507\pi$
$350$	3.91510	−	8.57287i	0.209271	−	0.458239i
$351$	0.167549	+	1.16533i	0.00894313	+	0.0622008i
$352$	−3.94130	−	1.15727i	−0.210072	−	0.0616827i
$353$	27.1757	−	17.4647i	1.44641	−	0.929554i	0.447028	−	0.894520i	$-0.352482\pi$
$353$	27.1757	−	17.4647i	1.44641	−	0.929554i	0.999386	−	0.0350341i	$-0.0111540\pi$
$354$	−0.308972	−	0.676554i	−0.0164217	−	0.0359584i
$355$	−19.5308	+	5.73476i	−1.03659	+	0.304369i
$356$	−3.04869	+	3.51837i	−0.161580	+	0.186473i
$357$	−0.269529	+	0.311053i	−0.0142650	+	0.0164627i
$358$	−1.75115	+	0.514183i	−0.0925510	+	0.0271754i
$359$	12.3596	+	27.0637i	0.652313	+	1.42837i	0.889515	+	0.456906i	$0.151043\pi$
$359$	12.3596	+	27.0637i	0.652313	+	1.42837i	−0.237201	+	0.971460i	$0.576230\pi$
$360$	9.56033	−	6.14405i	0.503874	−	0.323820i
$361$	−10.0844	−	2.96105i	−0.530758	−	0.155845i
$362$	−2.29343	−	15.9511i	−0.120540	−	0.838374i
$363$	0.215081	−	0.470961i	0.0112888	−	0.0247190i
$364$	0.317178	−	2.20602i	0.0166247	−	0.115627i
$365$	−47.8396	−	30.7446i	−2.50404	−	1.60925i
$366$	−0.274404	−	0.316679i	−0.0143433	−	0.0165531i
$367$	−18.2422			−0.952234			−0.476117	−	0.879382i	$-0.657956\pi$
$367$	−18.2422			−0.952234			−0.476117	+	0.879382i	$0.657956\pi$
$368$	−4.79541	+	0.0634158i	−0.249978	+	0.00330578i
$369$	12.1739			0.633750
$370$	−1.64264	−	1.89570i	−0.0853966	−	0.0985529i
$371$	−9.73674	−	6.25742i	−0.505506	−	0.324869i
$372$	0.0581422	−	0.404388i	0.00301453	−	0.0209665i
$373$	8.98806	−	19.6811i	0.465384	−	1.01905i	−0.520843	−	0.853652i	$-0.674382\pi$
$373$	8.98806	−	19.6811i	0.465384	−	1.01905i	0.986227	−	0.165396i	$-0.0528903\pi$
$374$	2.72931	+	18.9828i	0.141129	+	0.981576i
$375$	−1.42139	−	0.417358i	−0.0734003	−	0.0215523i
$376$	−7.88622	+	5.06817i	−0.406701	+	0.261371i
$377$	−5.41051	−	11.8474i	−0.278656	−	0.610171i
$378$	0.506853	−	0.148825i	0.0260697	−	0.00765475i
$379$	−10.0115	+	11.5538i	−0.514254	+	0.593481i	−0.952183	−	0.305529i	$-0.901167\pi$
$379$	−10.0115	+	11.5538i	−0.514254	+	0.593481i	0.437929	+	0.899010i	$0.355712\pi$
$380$	−13.5109	+	15.5925i	−0.693097	+	0.799876i
$381$	1.80382	−	0.529651i	0.0924127	−	0.0271348i
$382$	5.43285	+	11.8963i	0.277969	+	0.608666i
$383$	7.00416	−	4.50130i	0.357896	−	0.230006i	−0.349320	−	0.937004i	$-0.613587\pi$
$383$	7.00416	−	4.50130i	0.357896	−	0.230006i	0.707216	+	0.706998i	$0.249951\pi$
$384$	0.0845850	+	0.0248364i	0.00431646	+	0.00126743i
$385$	−2.22023	−	15.4421i	−0.113154	−	0.787001i
$386$	10.5844	−	23.1766i	0.538732	−	1.17966i
$387$	1.87373	−	13.0321i	0.0952469	−	0.662457i
$388$	−10.3525	−	6.65316i	−0.525569	−	0.337763i
$389$	22.2455	+	25.6726i	1.12789	+	1.30165i	0.948108	+	0.317948i	$0.102994\pi$
$389$	22.2455	+	25.6726i	1.12789	+	1.30165i	0.179782	+	0.983707i	$0.442461\pi$
$390$	−0.746201			−0.0377853
$391$	9.56998	+	20.2426i	0.483974	+	1.02371i
$392$	−1.00000			−0.0505076
$393$	0.174012	+	0.200820i	0.00877774	+	0.0101300i
$394$	18.5978	+	11.9521i	0.936942	+	0.602136i
$395$	5.34677	−	37.1876i	0.269025	−	1.87111i
$396$	5.10592	−	11.1804i	0.256582	−	0.561837i
$397$	−1.10287	−	7.67064i	−0.0553515	−	0.384978i	−0.998600	−	0.0528913i	$-0.983156\pi$
$397$	−1.10287	−	7.67064i	−0.0553515	−	0.384978i	0.943249	−	0.332087i	$-0.107753\pi$
$398$	12.0808	+	3.54725i	0.605557	+	0.177807i
$399$	−0.402869	+	0.258908i	−0.0201687	+	0.0129616i
$400$	3.91510	+	8.57287i	0.195755	+	0.428644i
$401$	−28.3680	+	8.32959i	−1.41663	+	0.415960i	−0.898361	−	0.439258i	$-0.855241\pi$
$401$	−28.3680	+	8.32959i	−1.41663	+	0.415960i	−0.518268	+	0.855218i	$0.673423\pi$
$402$	−0.0321894	+	0.0371486i	−0.00160546	+	0.00185280i
$403$	6.76381	−	7.80585i	0.336929	−	0.388837i
$404$	−11.5430	+	3.38932i	−0.574285	+	0.168625i
$405$	14.0893	+	30.8513i	0.700105	+	1.53302i
$406$	−4.91621	+	3.15945i	−0.243987	+	0.156801i
$407$	−2.60304	−	0.764321i	−0.129028	−	0.0378860i
$408$	−0.0585743	−	0.407393i	−0.00289986	−	0.0201690i
$409$	6.39859	−	14.0110i	0.316390	−	0.692797i	−0.682899	−	0.730513i	$-0.739281\pi$
$409$	6.39859	−	14.0110i	0.316390	−	0.692797i	0.999289	+	0.0377160i	$0.0120082\pi$
$410$	−2.19906	+	15.2948i	−0.108604	+	0.755357i
$411$	−0.272190	−	0.174926i	−0.0134261	−	0.00862846i
$412$	−2.48190	−	2.86426i	−0.122274	−	0.141112i
$413$	−8.43694			−0.415155
$414$	1.85425	−	14.2299i	0.0911313	−	0.699363i
$415$	−39.8501			−1.95617
$416$	1.45949	+	1.68434i	0.0715575	+	0.0825818i
$417$	−0.114105	−	0.0733311i	−0.00558777	−	0.00359104i
$418$	−3.17565	+	22.0872i	−0.155326	+	1.08032i
$419$	14.5943	−	31.9571i	0.712980	−	1.56121i	−0.110509	−	0.993875i	$-0.535248\pi$
$419$	14.5943	−	31.9571i	0.712980	−	1.56121i	0.823489	−	0.567332i	$-0.192024\pi$
$420$	0.0476489	+	0.331405i	0.00232503	+	0.0161709i
$421$	−4.32709	−	1.27055i	−0.210890	−	0.0619228i	0.174581	−	0.984643i	$-0.444143\pi$
$421$	−4.32709	−	1.27055i	−0.210890	−	0.0619228i	−0.385471	+	0.922720i	$0.625961\pi$
$422$	20.9424	−	13.4589i	1.01946	−	0.655167i
$423$	−11.6525	−	25.5154i	−0.566564	−	1.24060i
$424$	11.1053	−	3.26080i	0.539319	−	0.158358i
$425$	28.8148	−	33.2540i	1.39772	−	1.61306i
$426$	0.309405	−	0.357072i	0.0149907	−	0.0173002i
$427$	−4.56070	+	1.33914i	−0.220708	+	0.0648056i
$428$	−4.72721	−	10.3511i	−0.228498	−	0.500341i
$429$	−0.678936	+	0.436326i	−0.0327793	+	0.0210660i
$430$	16.0345	+	4.70814i	0.773251	+	0.227047i
$431$	2.95603	+	20.5596i	0.142387	+	0.990322i	0.928259	+	0.371933i	$0.121305\pi$
$431$	2.95603	+	20.5596i	0.142387	+	0.990322i	−0.785873	+	0.618388i	$0.787786\pi$
$432$	−0.219443	+	0.480513i	−0.0105580	+	0.0231187i
$433$	2.88552	−	20.0692i	0.138669	−	0.964465i	−0.795072	−	0.606515i	$-0.792567\pi$
$433$	2.88552	−	20.0692i	0.138669	−	0.964465i	0.933741	−	0.357950i	$-0.116524\pi$
$434$	−3.89867	−	2.50552i	−0.187142	−	0.120269i
$435$	1.28131	+	1.47871i	0.0614342	+	0.0708988i
$436$	−3.52318			−0.168730
$437$	4.04832	+	25.7360i	0.193658	+	1.23112i
$438$	1.31996			0.0630701
$439$	8.61302	+	9.93996i	0.411077	+	0.474408i	0.923098	−	0.384565i	$-0.125648\pi$
$439$	8.61302	+	9.93996i	0.411077	+	0.474408i	−0.512021	+	0.858973i	$0.671103\pi$
$440$	13.1243	+	8.43446i	0.625676	+	0.402097i
$441$	0.425839	−	2.96177i	0.0202780	−	0.141037i
$442$	4.32256	−	9.46508i	0.205603	−	0.450208i
$443$	−2.95658	−	20.5635i	−0.140471	−	0.977000i	−0.931116	−	0.364724i	$-0.881163\pi$
$443$	−2.95658	−	20.5635i	−0.140471	−	0.977000i	0.790644	−	0.612276i	$-0.209746\pi$
$444$	0.0558643	+	0.0164032i	0.00265120	+	0.000778463i
$445$	14.8745	−	9.55925i	0.705118	−	0.453152i
$446$	3.07316	+	6.72928i	0.145518	+	0.318641i
$447$	1.61389	−	0.473882i	0.0763345	−	0.0224138i
$448$	0.654861	−	0.755750i	0.0309393	−	0.0357058i
$449$	13.6277	−	15.7272i	0.643131	−	0.742212i	−0.336795	−	0.941578i	$-0.609343\pi$
$449$	13.6277	−	15.7272i	0.643131	−	0.742212i	0.979925	+	0.199366i	$0.0638882\pi$
$450$	−27.0581	+	7.94497i	−1.27553	+	0.374530i
$451$	6.94250	+	15.2020i	0.326909	+	0.715832i
$452$	−4.59122	+	2.95060i	−0.215953	+	0.138784i
$453$	−0.332780	−	0.0977132i	−0.0156354	−	0.00459096i
$454$	0.656692	+	4.56740i	0.0308201	+	0.214359i
$455$	−3.51630	+	7.69963i	−0.164847	+	0.360964i
$456$	0.0681534	−	0.474017i	0.00319157	−	0.0221979i
$457$	14.9415	+	9.60235i	0.698936	+	0.449179i	0.841253	−	0.540642i	$-0.181819\pi$
$457$	14.9415	+	9.60235i	0.698936	+	0.449179i	−0.142317	+	0.989821i	$0.545455\pi$
$458$	−11.8530	−	13.6791i	−0.553854	−	0.639181i
$459$	2.46630			0.115117
$460$	17.5429	+	4.90005i	0.817943	+	0.228466i
$461$	22.4456			1.04540			0.522699	−	0.852518i	$-0.324925\pi$
$461$	22.4456			1.04540			0.522699	+	0.852518i	$0.324925\pi$
$462$	0.237136	+	0.273670i	0.0110326	+	0.0127323i
$463$	11.9229	+	7.66237i	0.554103	+	0.356100i	0.787532	−	0.616273i	$-0.211358\pi$
$463$	11.9229	+	7.66237i	0.554103	+	0.356100i	−0.233429	+	0.972374i	$0.574995\pi$
$464$	0.831674	−	5.78442i	0.0386095	−	0.268535i
$465$	−0.644576	+	1.41142i	−0.0298915	+	0.0654533i
$466$	−3.90963	−	27.1921i	−0.181110	−	1.25965i
$467$	14.7364	+	4.32698i	0.681917	+	0.200229i	0.604303	−	0.796755i	$-0.293452\pi$
$467$	14.7364	+	4.32698i	0.681917	+	0.200229i	0.0776141	+	0.996983i	$0.475270\pi$
$468$	−5.61015	+	3.60543i	−0.259329	+	0.166661i
$469$	0.231630	+	0.507199i	0.0106957	+	0.0234203i
$470$	34.1613	−	10.0307i	1.57575	−	0.462681i
$471$	0.281203	−	0.324525i	0.0129571	−	0.0149533i
$472$	5.52502	−	6.37622i	0.254310	−	0.293489i
$473$	17.3421	−	5.09209i	0.797389	−	0.234135i
$474$	0.362263	+	0.793246i	0.0166393	+	0.0364350i
$475$	43.0698	−	27.6793i	1.97618	−	1.27001i
$476$	−4.47968	−	1.31535i	−0.205326	−	0.0602891i
$477$	4.92869	+	34.2798i	0.225669	+	1.56956i
$478$	−7.96559	+	17.4422i	−0.364338	+	0.797788i
$479$	−4.08654	+	28.4225i	−0.186719	+	1.29866i	0.653715	+	0.756741i	$0.273210\pi$
$479$	−4.08654	+	28.4225i	−0.186719	+	1.29866i	−0.840433	+	0.541915i	$0.817699\pi$
$480$	−0.281663	−	0.181014i	−0.0128561	−	0.00826211i
$481$	0.963925	+	1.11243i	0.0439512	+	0.0507224i
$482$	−18.2482			−0.831182
$483$	0.358657	+	0.223850i	0.0163195	+	0.0101855i
$484$	5.87310			0.266959
$485$	30.6069	+	35.3222i	1.38979	+	1.60390i
$486$	−1.99545	−	1.28240i	−0.0905154	−	0.0581707i
$487$	−1.08629	+	7.55529i	−0.0492243	+	0.342363i	0.950295	+	0.311352i	$0.100782\pi$
$487$	−1.08629	+	7.55529i	−0.0492243	+	0.342363i	−0.999519	+	0.0310110i	$0.990127\pi$
$488$	1.97457	−	4.32370i	0.0893844	−	0.195725i
$489$	0.152875	+	1.06327i	0.00691323	+	0.0480826i
$490$	3.64412	+	1.07001i	0.164625	+	0.0483382i
$491$	−36.3072	+	23.3332i	−1.63852	+	1.05301i	−0.696448	+	0.717607i	$0.745237\pi$
$491$	−36.3072	+	23.3332i	−1.63852	+	1.05301i	−0.942074	+	0.335406i	$0.891126\pi$
$492$	−0.148994	−	0.326252i	−0.00671718	−	0.0147086i
$493$	−26.1788	+	7.68680i	−1.17904	+	0.346196i
$494$	7.92844	−	9.14990i	0.356717	−	0.411674i
$495$	−30.5698	+	35.2794i	−1.37401	+	1.58569i
$496$	4.44663	−	1.30565i	0.199660	−	0.0586254i
$497$	−2.22643	−	4.87520i	−0.0998690	−	0.218683i
$498$	0.778139	−	0.500079i	0.0348692	−	0.0224091i
$499$	−10.8263	−	3.17888i	−0.484651	−	0.142306i	0.0302739	−	0.999542i	$-0.490362\pi$
$499$	−10.8263	−	3.17888i	−0.484651	−	0.142306i	−0.514925	+	0.857235i	$0.672180\pi$
$500$	−2.39150	−	16.6333i	−0.106951	−	0.743862i
$501$	−0.605515	+	1.32589i	−0.0270524	+	0.0592365i
$502$	1.60591	−	11.1694i	0.0716754	−	0.498513i
$503$	22.9552	+	14.7524i	1.02352	+	0.657779i	0.940859	−	0.338799i	$-0.110021\pi$
$503$	22.9552	+	14.7524i	1.02352	+	0.657779i	0.0826649	+	0.996577i	$0.473657\pi$
$504$	1.95949	+	2.26138i	0.0872828	+	0.100730i
$505$	45.6906			2.03321
$506$	18.8268	−	5.79952i	0.836952	−	0.257820i
$507$	−0.708144			−0.0314498
$508$	13.9653	+	16.1168i	0.619610	+	0.715068i
$509$	−21.1382	−	13.5847i	−0.936933	−	0.602130i	−0.0194096	−	0.999812i	$-0.506179\pi$
$509$	−21.1382	−	13.5847i	−0.936933	−	0.602130i	−0.917524	+	0.397681i	$0.869815\pi$
$510$	−0.222463	+	1.54727i	−0.00985084	+	0.0685141i
$511$	6.22002	−	13.6199i	0.275157	−	0.602511i
$512$	0.142315	+	0.989821i	0.00628949	+	0.0437443i
$513$	2.75339	+	0.808467i	0.121565	+	0.0356947i
$514$	16.6467	−	10.6982i	0.734253	−	0.471876i
$515$	5.97954	+	13.0934i	0.263490	+	0.576963i
$516$	−0.372182	+	0.109282i	−0.0163844	+	0.00481089i
$517$	25.2167	−	29.1016i	1.10903	−	1.27989i
$518$	0.432504	−	0.499136i	0.0190031	−	0.0219308i
$519$	−1.77435	+	0.520996i	−0.0778853	+	0.0228692i
$520$	−3.51630	−	7.69963i	−0.154200	−	0.337651i
$521$	−24.5221	+	15.7594i	−1.07433	+	0.690431i	−0.953241	−	0.302210i	$-0.902276\pi$
$521$	−24.5221	+	15.7594i	−1.07433	+	0.690431i	−0.121091	+	0.992641i	$0.538639\pi$
$522$	16.7780	+	4.92646i	0.734352	+	0.215625i
$523$	−3.02593	−	21.0458i	−0.132315	−	0.920268i	−0.942527	−	0.334131i	$-0.891557\pi$
$523$	−3.02593	−	21.0458i	−0.132315	−	0.920268i	0.810212	−	0.586137i	$-0.199352\pi$
$524$	−1.25216	+	2.74185i	−0.0547010	+	0.119778i
$525$	0.118239	−	0.822373i	0.00516039	−	0.0358913i
$526$	−14.7654	−	9.48916i	−0.643803	−	0.413747i
$527$	−14.1692	−	16.3521i	−0.617218	−	0.712307i
$528$	−0.362117			−0.0157591
$529$	19.0132	−	12.9420i	0.826663	−	0.562698i
$530$	−43.9580			−1.90941
$531$	16.5321	+	19.0791i	0.717433	+	0.827962i
$532$	−4.56996	−	2.93694i	−0.198133	−	0.127332i
$533$	1.29044	−	8.97524i	0.0558954	−	0.388761i
$534$	−0.170489	+	0.373320i	−0.00737780	+	0.0161551i
$535$	6.15069	+	42.7790i	0.265917	+	1.84950i
$536$	−0.535001	−	0.157090i	−0.0231085	−	0.00678527i
$537$	−0.135350	+	0.0869844i	−0.00584080	+	0.00375365i
$538$	−2.14542	−	4.69782i	−0.0924958	−	0.202537i
$539$	3.94130	−	1.15727i	0.169764	−	0.0498471i
$540$	1.31383	−	1.51624i	0.0565383	−	0.0652487i
$541$	18.9084	−	21.8215i	0.812937	−	0.938179i	−0.186079	−	0.982535i	$-0.559578\pi$
$541$	18.9084	−	21.8215i	0.812937	−	0.938179i	0.999016	+	0.0443559i	$0.0141236\pi$
$542$	−18.5246	+	5.43931i	−0.795699	+	0.233638i
$543$	−0.590159	−	1.29227i	−0.0253261	−	0.0554565i
$544$	3.92765	−	2.52414i	0.168396	−	0.108222i
$545$	12.8389	+	3.76984i	0.549958	+	0.161482i
$546$	−0.0279611	−	0.194474i	−0.00119663	−	0.00832272i
$547$	15.1962	−	33.2751i	0.649743	−	1.42274i	−0.242035	−	0.970267i	$-0.577815\pi$
$547$	15.1962	−	33.2751i	0.649743	−	1.42274i	0.891779	−	0.452472i	$-0.149458\pi$
$548$	0.522329	−	3.63288i	0.0223128	−	0.155189i
$549$	11.9650	+	7.68941i	0.510652	+	0.328176i
$550$	−25.3517	−	29.2574i	−1.08100	−	1.24754i
$551$	−31.7460			−1.35242
$552$	−0.404045	+	0.124465i	−0.0171973	+	0.00529757i
$553$	9.89214			0.420657
$554$	−15.8990	−	18.3484i	−0.675482	−	0.779548i
$555$	−0.186025	−	0.119551i	−0.00789631	−	0.00507465i
$556$	0.218967	−	1.52295i	0.00928626	−	0.0645874i
$557$	−8.01587	+	17.5523i	−0.339643	+	0.743715i	−0.999974	−	0.00726019i	$-0.997689\pi$
$557$	−8.01587	+	17.5523i	−0.339643	+	0.743715i	0.660330	+	0.750975i	$0.270416\pi$
$558$	1.97349	+	13.7259i	0.0835444	+	0.581064i
$559$	−9.40928	−	2.76281i	−0.397970	−	0.116855i
$560$	−3.19505	+	2.05334i	−0.135016	+	0.0867693i
$561$	0.702323	+	1.53787i	0.0296521	+	0.0649290i
$562$	13.3529	−	3.92078i	0.563260	−	0.165388i
$563$	−1.39018	+	1.60435i	−0.0585890	+	0.0676154i	−0.784288	−	0.620397i	$-0.786971\pi$
$563$	−1.39018	+	1.60435i	−0.0585890	+	0.0676154i	0.725698	+	0.688013i	$0.241517\pi$
$564$	−0.541181	+	0.624556i	−0.0227878	+	0.0262986i
$565$	19.8881	−	5.83969i	0.836700	−	0.245677i
$566$	−10.1373	−	22.1976i	−0.426102	−	0.933034i
$567$	−7.51249	+	4.82799i	−0.315495	+	0.202756i
$568$	5.14243	+	1.50995i	0.215772	+	0.0633563i
$569$	1.37394	+	9.55597i	0.0575986	+	0.400607i	0.998142	+	0.0609331i	$0.0194076\pi$
$569$	1.37394	+	9.55597i	0.0575986	+	0.400607i	−0.940543	+	0.339674i	$0.889683\pi$
$570$	−0.755563	+	1.65445i	−0.0316470	+	0.0692973i
$571$	0.389461	−	2.70876i	0.0162984	−	0.113358i	−0.980048	−	0.198760i	$-0.936308\pi$
$571$	0.389461	−	2.70876i	0.0162984	−	0.113358i	0.996347	+	0.0854023i	$0.0272176\pi$
$572$	−7.70154	−	4.94948i	−0.322017	−	0.206948i
$573$	0.754998	+	0.871314i	0.0315405	+	0.0363997i
$574$	−4.06852			−0.169817
$575$	−38.3432	−	23.9313i	−1.59902	−	0.998003i
$576$	−2.99223			−0.124676
$577$	−6.70277	−	7.73541i	−0.279040	−	0.322029i	0.598878	−	0.800840i	$-0.295613\pi$
$577$	−6.70277	−	7.73541i	−0.279040	−	0.322029i	−0.877918	+	0.478811i	$0.841068\pi$
$578$	−4.03609	−	2.59384i	−0.167879	−	0.107889i
$579$	0.319658	−	2.22327i	0.0132845	−	0.0923960i
$580$	−9.22012	+	20.1892i	−0.382845	+	0.838313i
$581$	−1.49324	−	10.3857i	−0.0619499	−	0.430871i
$582$	−1.04091	−	0.305638i	−0.0431470	−	0.0126691i
$583$	−39.9955	+	25.7035i	−1.65644	+	1.06453i
$584$	6.22002	+	13.6199i	0.257386	+	0.563597i
$585$	24.3019	−	7.13569i	1.00476	−	0.295024i
$586$	12.3499	−	14.2525i	0.510168	−	0.588766i
$587$	5.60610	−	6.46978i	0.231389	−	0.267037i	−0.628167	−	0.778078i	$-0.716195\pi$
$587$	5.60610	−	6.46978i	0.231389	−	0.267037i	0.859556	+	0.511042i	$0.170740\pi$
$588$	−0.0845850	+	0.0248364i	−0.00348823	+	0.00102424i
$589$	−10.4582	−	22.9003i	−0.430923	−	0.943589i
$590$	−26.9565	+	17.3239i	−1.10978	+	0.713213i
$591$	1.86994	+	0.549064i	0.0769190	+	0.0225855i
$592$	0.0939921	+	0.653729i	0.00386305	+	0.0268681i
$593$	6.84546	−	14.9895i	0.281109	−	0.615544i	−0.715428	−	0.698686i	$-0.753768\pi$
$593$	6.84546	−	14.9895i	0.281109	−	0.615544i	0.996538	+	0.0831424i	$0.0264956\pi$
$594$	0.308807	−	2.14780i	0.0126705	−	0.0881254i
$595$	14.9171	+	9.58662i	0.611540	+	0.393013i
$596$	12.4948	+	14.4198i	0.511808	+	0.590658i
$597$	1.10996			0.0454275
$598$	−10.2945	−	2.87543i	−0.420972	−	0.117585i
$599$	20.7767			0.848913			0.424457	−	0.905448i	$-0.360465\pi$
$599$	20.7767			0.848913			0.424457	+	0.905448i	$0.360465\pi$
$600$	0.544078	+	0.627899i	0.0222119	+	0.0256339i
$601$	−9.86340	−	6.33882i	−0.402337	−	0.258566i	0.323787	−	0.946130i	$-0.395044\pi$
$601$	−9.86340	−	6.33882i	−0.402337	−	0.258566i	−0.726124	+	0.687564i	$0.758680\pi$
$602$	−0.626198	+	4.35530i	−0.0255219	+	0.177509i
$603$	0.693090	−	1.51766i	0.0282248	−	0.0618037i
$604$	−0.559905	−	3.89423i	−0.0227822	−	0.158454i
$605$	−21.4023	−	6.28428i	−0.870127	−	0.255492i
$606$	−0.892184	+	0.573372i	−0.0362425	+	0.0232916i
$607$	4.90212	+	10.7341i	0.198971	+	0.435686i	0.982647	−	0.185484i	$-0.0593852\pi$
$607$	4.90212	+	10.7341i	0.198971	+	0.435686i	−0.783676	+	0.621169i	$0.786658\pi$
$608$	5.21228	−	1.53046i	0.211386	−	0.0620684i
$609$	−0.337368	+	0.389343i	−0.0136708	+	0.0157770i
$610$	−11.8220	+	13.6433i	−0.478657	+	0.552400i
$611$	−20.0464	+	5.88616i	−0.810991	+	0.238129i
$612$	5.80340	+	12.7077i	0.234588	+	0.513677i
$613$	−11.0192	+	7.08158i	−0.445060	+	0.286022i	−0.743913	−	0.668277i	$-0.767032\pi$
$613$	−11.0192	+	7.08158i	−0.445060	+	0.286022i	0.298853	+	0.954299i	$0.403396\pi$
$614$	10.2674	+	3.01477i	0.414357	+	0.121666i
$615$	0.193860	+	1.34833i	0.00781720	+	0.0543698i
$616$	−1.70640	+	3.73648i	−0.0687526	+	0.150547i
$617$	1.46720	−	10.2046i	0.0590672	−	0.410821i	−0.938740	−	0.344627i	$-0.888005\pi$
$617$	1.46720	−	10.2046i	0.0590672	−	0.410821i	0.997807	−	0.0661940i	$-0.0210856\pi$
$618$	−0.281069	−	0.180632i	−0.0113063	−	0.00726609i
$619$	16.3377	+	18.8547i	0.656666	+	0.757833i	0.982229	−	0.187688i	$-0.0600993\pi$
$619$	16.3377	+	18.8547i	0.656666	+	0.757833i	−0.325563	+	0.945520i	$0.605554\pi$
$620$	−17.6011			−0.706878
$621$	−0.393667	−	2.50263i	−0.0157973	−	0.100427i
$622$	19.1360			0.767285
$623$	3.04869	+	3.51837i	0.122143	+	0.140961i
$624$	0.165284	+	0.106222i	0.00661667	+	0.00425227i
$625$	−2.37657	+	16.5294i	−0.0950630	+	0.661178i
$626$	3.10853	−	6.80673i	0.124242	−	0.272052i
$627$	0.279953	+	1.94711i	0.0111802	+	0.0777602i
$628$	4.67370	+	1.37232i	0.186501	+	0.0547617i
$629$	2.59402	−	1.66708i	0.103430	−	0.0664707i
$630$	−4.72094	−	10.3374i	−0.188087	−	0.411852i
$631$	−25.0757	+	7.36289i	−0.998248	+	0.293112i	−0.739737	−	0.672896i	$-0.765050\pi$
$631$	−25.0757	+	7.36289i	−0.998248	+	0.293112i	−0.258511	+	0.966008i	$0.583232\pi$
$632$	−6.47798	+	7.47598i	−0.257680	+	0.297379i
$633$	1.43714	−	1.65855i	0.0571213	−	0.0659215i
$634$	4.57774	−	1.34415i	0.181805	−	0.0533828i
$635$	−33.6461	−	73.6746i	−1.33520	−	2.92369i
$636$	0.858351	−	0.551629i	0.0340358	−	0.0218735i
$637$	−2.13843	−	0.627899i	−0.0847276	−	0.0248783i
$638$	3.41626	+	23.7606i	0.135251	+	0.940691i
$639$	−6.66199	+	14.5877i	−0.263544	+	0.577081i
$640$	0.540507	−	3.75931i	0.0213654	−	0.148600i
$641$	5.24194	+	3.36879i	0.207044	+	0.133059i	0.640054	−	0.768330i	$-0.278912\pi$
$641$	5.24194	+	3.36879i	0.207044	+	0.133059i	−0.433010	+	0.901389i	$0.642548\pi$
$642$	−0.656936	−	0.758144i	−0.0259272	−	0.0299216i
$643$	25.9092			1.02176			0.510880	−	0.859652i	$-0.329320\pi$
$643$	25.9092			1.02176			0.510880	+	0.859652i	$0.329320\pi$
$644$	−0.619688	+	4.75563i	−0.0244191	+	0.187398i
$645$	1.47321			0.0580075
$646$	−16.6089	−	19.1677i	−0.653467	−	0.754141i
$647$	24.5281	+	15.7632i	0.964297	+	0.619716i	0.925184	−	0.379519i	$-0.123910\pi$
$647$	24.5281	+	15.7632i	0.964297	+	0.619716i	0.0391131	+	0.999235i	$0.487547\pi$
$648$	1.27089	−	8.83922i	0.0499252	−	0.347237i
$649$	−14.3968	+	31.5245i	−0.565122	+	1.23745i
$650$	2.98926	+	20.7908i	0.117248	+	0.815481i
$651$	−0.391997	−	0.115101i	−0.0153636	−	0.00451115i
$652$	−10.2509	+	6.58783i	−0.401455	+	0.257999i
$653$	−6.46388	−	14.1539i	−0.252951	−	0.553885i	0.739973	−	0.672637i	$-0.234838\pi$
$653$	−6.46388	−	14.1539i	−0.252951	−	0.553885i	−0.992924	+	0.118751i	$0.962111\pi$
$654$	−0.298008	+	0.0875031i	−0.0116530	+	0.00342164i
$655$	7.49684	−	8.65182i	0.292926	−	0.338055i
$656$	2.66431	−	3.07478i	0.104024	−	0.120050i
$657$	−42.9879	+	12.6224i	−1.67712	+	0.492446i
$658$	3.89425	+	8.52723i	0.151814	+	0.332426i
$659$	−2.17065	+	1.39499i	−0.0845566	+	0.0543412i	−0.582236	−	0.813020i	$-0.697822\pi$
$659$	−2.17065	+	1.39499i	−0.0845566	+	0.0543412i	0.497679	+	0.867361i	$0.334186\pi$
$660$	1.31960	+	0.387469i	0.0513653	+	0.0150822i
$661$	6.82418	+	47.4632i	0.265430	+	1.84611i	0.490094	+	0.871669i	$0.336962\pi$
$661$	6.82418	+	47.4632i	0.265430	+	1.84611i	−0.224664	+	0.974436i	$0.572129\pi$
$662$	5.13691	−	11.2483i	0.199652	−	0.437176i
$663$	0.130545	−	0.907960i	0.00506995	−	0.0352623i
$664$	8.82684	+	5.67267i	0.342548	+	0.220142i
$665$	13.5109	+	15.5925i	0.523932	+	0.604650i
$666$	−1.97622			−0.0765771
$667$	11.9787	+	25.3375i	0.463816	+	0.981073i
$668$	−16.5345			−0.639739
$669$	0.427074	+	0.492870i	0.0165116	+	0.0190554i
$670$	1.78152	+	1.14491i	0.0688261	+	0.0442319i
$671$	−2.77867	+	19.3261i	−0.107269	+	0.746075i
$672$	0.0366213	−	0.0801894i	0.00141270	−	0.00309338i
$673$	4.30651	+	29.9524i	0.166004	+	1.15458i	0.887043	+	0.461687i	$0.152756\pi$
$673$	4.30651	+	29.9524i	0.166004	+	1.15458i	−0.721039	+	0.692895i	$0.756335\pi$
$674$	−13.1235	−	3.85340i	−0.505498	−	0.148427i
$675$	−4.18820	+	2.69159i	−0.161204	+	0.103599i
$676$	−3.33697	−	7.30695i	−0.128345	−	0.281037i
$677$	−27.1081	+	7.95965i	−1.04185	+	0.305914i	−0.757519	−	0.652813i	$-0.773589\pi$
$677$	−27.1081	+	7.95965i	−1.04185	+	0.305914i	−0.284329	+	0.958727i	$0.591771\pi$
$678$	−0.315066	+	0.363606i	−0.0121000	+	0.0139642i
$679$	−8.05875	+	9.30030i	−0.309267	+	0.356913i
$680$	−17.0137	+	4.99567i	−0.652445	+	0.191575i
$681$	0.168984	+	0.370023i	0.00647548	+	0.0141793i
$682$	−16.0145	+	10.2919i	−0.613227	+	0.394097i
$683$	−24.2286	−	7.11417i	−0.927083	−	0.272216i	−0.216868	−	0.976201i	$-0.569584\pi$
$683$	−24.2286	−	7.11417i	−0.927083	−	0.272216i	−0.710215	+	0.703985i	$0.751402\pi$
$684$	2.31329	+	16.0893i	0.0884509	+	0.615190i
$685$	−5.79065	+	12.6798i	−0.221249	+	0.484468i
$686$	−0.142315	+	0.989821i	−0.00543361	+	0.0377916i
$687$	−1.34232	−	0.862659i	−0.0512128	−	0.0329125i
$688$	−2.88145	−	3.32537i	−0.109854	−	0.126778i
$689$	25.7952			0.982721
$690$	1.60557	−	0.0212325i	0.0611229	−	0.000808306i
$691$	22.8305			0.868514			0.434257	−	0.900789i	$-0.357011\pi$
$691$	22.8305			0.868514			0.434257	+	0.900789i	$0.357011\pi$
$692$	−13.7371	−	15.8535i	−0.522206	−	0.602658i
$693$	−10.3400	−	6.64509i	−0.392783	−	0.252426i
$694$	−0.585901	+	4.07503i	−0.0222405	+	0.154686i
$695$	−2.42751	+	5.31551i	−0.0920808	+	0.201629i
$696$	−0.0733170	−	0.509931i	−0.00277907	−	0.0193289i
$697$	−18.2257	−	5.35154i	−0.690346	−	0.202704i
$698$	2.76170	−	1.77484i	0.104532	−	0.0671786i
$699$	−1.00605	−	2.20294i	−0.0380522	−	0.0833228i
$700$	9.04279	−	2.65520i	0.341785	−	0.100357i
$701$	22.1672	−	25.5823i	0.837243	−	0.966230i	−0.162547	−	0.986701i	$-0.551971\pi$
$701$	22.1672	−	25.5823i	0.837243	−	0.966230i	0.999790	+	0.0204708i	$0.00651652\pi$
$702$	−0.770978	+	0.889756i	−0.0290987	+	0.0335817i
$703$	3.44246	−	1.01080i	0.129835	−	0.0381229i
$704$	−1.70640	−	3.73648i	−0.0643122	−	0.140824i
$705$	2.64041	−	1.69689i	0.0994436	−	0.0639085i
$706$	30.9952	+	9.10102i	1.16652	+	0.342521i
$707$	1.71209	+	11.9078i	0.0643897	+	0.447840i
$708$	0.308972	−	0.676554i	0.0116119	−	0.0254264i
$709$	−0.891544	+	6.20082i	−0.0334826	+	0.232877i	−0.999690	−	0.0248883i	$-0.992077\pi$
$709$	−0.891544	+	6.20082i	−0.0334826	+	0.232877i	0.966208	+	0.257765i	$0.0829861\pi$
$710$	−17.1240	−	11.0049i	−0.642652	−	0.413007i
$711$	−19.3836	−	22.3699i	−0.726941	−	0.838935i
$712$	−4.65547			−0.174471
$713$	−14.3313	+	16.9880i	−0.536711	+	0.636205i
$714$	−0.411583			−0.0154031
$715$	22.7694	+	26.2772i	0.851525	+	0.982713i
$716$	−1.53535	−	0.986710i	−0.0573788	−	0.0368751i
$717$	−0.240568	+	1.67319i	−0.00898417	+	0.0624863i
$718$	−12.3596	+	27.0637i	−0.461255	+	1.01001i
$719$	−5.34043	−	37.1435i	−0.199164	−	1.38522i	−0.806717	−	0.590939i	$-0.798758\pi$
$719$	−5.34043	−	37.1435i	−0.199164	−	1.38522i	0.607552	−	0.794280i	$-0.292152\pi$
$720$	10.9040	+	3.20172i	0.406370	+	0.119321i
$721$	−3.18832	+	2.04901i	−0.118739	+	0.0763090i
$722$	−4.36607	−	9.56035i	−0.162488	−	0.355800i
$723$	−1.54352	+	0.453219i	−0.0574042	+	0.0168554i
$724$	10.5532	−	12.1790i	0.392206	−	0.452630i
$725$	36.0672	−	41.6238i	1.33950	−	1.54587i
$726$	0.496776	−	0.145867i	0.0184371	−	0.00541362i
$727$	3.83184	+	8.39056i	0.142115	+	0.311189i	0.967283	−	0.253698i	$-0.0816471\pi$
$727$	3.83184	+	8.39056i	0.142115	+	0.311189i	−0.825168	+	0.564887i	$0.808920\pi$
$728$	1.87491	−	1.20493i	0.0694887	−	0.0446577i
$729$	25.5045	+	7.48880i	0.944612	+	0.277363i
$730$	−8.09302	−	56.2882i	−0.299536	−	2.08332i
$731$	−8.53393	+	18.6867i	−0.315639	+	0.691153i
$732$	0.0596336	−	0.414761i	0.00220412	−	0.0153300i
$733$	6.64500	+	4.27048i	0.245439	+	0.157734i	0.657577	−	0.753387i	$-0.271581\pi$
$733$	6.64500	+	4.27048i	0.245439	+	0.157734i	−0.412138	+	0.911121i	$0.635218\pi$
$734$	−11.9461	−	13.7865i	−0.440938	−	0.508870i
$735$	0.334813			0.0123498
$736$	−3.18825	−	3.58260i	−0.117521	−	0.132056i
$737$	2.29039			0.0843677
$738$	7.97223	+	9.20044i	0.293462	+	0.338673i
$739$	−25.3281	−	16.2774i	−0.931711	−	0.598774i	−0.0156777	−	0.999877i	$-0.504991\pi$
$739$	−25.3281	−	16.2774i	−0.931711	−	0.598774i	−0.916033	+	0.401103i	$0.868627\pi$
$740$	0.356979	−	2.48284i	0.0131228	−	0.0912711i
$741$	0.443376	−	0.970858i	0.0162878	−	0.0356654i
$742$	−1.64716	−	11.4563i	−0.0604693	−	0.420573i
$743$	−5.64370	−	1.65714i	−0.207047	−	0.0607945i	0.176564	−	0.984289i	$-0.443502\pi$
$743$	−5.64370	−	1.65714i	−0.207047	−	0.0607945i	−0.383612	+	0.923495i	$0.625320\pi$
$744$	0.343691	−	0.220877i	0.0126003	−	0.00809773i
$745$	−30.1033	−	65.9171i	−1.10290	−	2.41502i
$746$	20.7599	−	6.09566i	0.760074	−	0.223178i
$747$	−20.5600	+	23.7275i	−0.752250	+	0.868142i
$748$	−12.5589	+	14.4938i	−0.459199	+	0.529944i
$749$	−10.9185	+	3.20597i	−0.398954	+	0.117144i
$750$	−0.615395	−	1.34753i	−0.0224711	−	0.0492047i
$751$	4.85264	−	3.11860i	0.177075	−	0.113799i	−0.449101	−	0.893481i	$-0.648256\pi$
$751$	4.85264	−	3.11860i	0.177075	−	0.113799i	0.626176	+	0.779682i	$0.284619\pi$
$752$	−8.99464	−	2.64106i	−0.328001	−	0.0963097i
$753$	−0.141571	−	0.984646i	−0.00515912	−	0.0358825i
$754$	5.41051	−	11.8474i	0.197039	−	0.431456i
$755$	−2.12650	+	14.7901i	−0.0773913	+	0.538269i
$756$	0.444393	+	0.285594i	0.0161624	+	0.0103869i
$757$	−17.3605	−	20.0351i	−0.630979	−	0.728189i	0.346773	−	0.937949i	$-0.387277\pi$
$757$	−17.3605	−	20.0351i	−0.630979	−	0.728189i	−0.977753	+	0.209760i	$0.932732\pi$
$758$	−15.2879			−0.555282
$759$	1.44842	−	0.958142i	0.0525744	−	0.0347783i
$760$	−20.6318			−0.748393
$761$	25.5688	+	29.5080i	0.926869	+	1.06966i	0.997394	+	0.0721533i	$0.0229871\pi$
$761$	25.5688	+	29.5080i	0.926869	+	1.06966i	−0.0705250	+	0.997510i	$0.522467\pi$
$762$	1.58154	+	1.01639i	0.0572930	+	0.0368200i
$763$	−0.501401	+	3.48732i	−0.0181519	+	0.126249i
$764$	−5.43285	+	11.8963i	−0.196553	+	0.430392i
$765$	−7.55095	−	52.5180i	−0.273005	−	1.89879i
$766$	7.98861	+	2.34567i	0.288640	+	0.0847524i
$767$	15.8185	−	10.1659i	0.571173	−	0.367070i
$768$	0.0366213	+	0.0801894i	0.00132146	+	0.00289359i
$769$	−46.5966	+	13.6820i	−1.68031	+	0.493385i	−0.976231	−	0.216732i	$-0.930460\pi$
$769$	−46.5966	+	13.6820i	−1.68031	+	0.493385i	−0.704084	+	0.710117i	$0.748642\pi$
$770$	10.2164	−	11.7903i	0.368173	−	0.424895i
$771$	1.14235	−	1.31835i	0.0411409	−	0.0474791i
$772$	24.4470	−	7.17829i	0.879867	−	0.258352i
$773$	−7.94719	−	17.4019i	−0.285841	−	0.625904i	0.711182	−	0.703008i	$-0.248160\pi$
$773$	−7.94719	−	17.4019i	−0.285841	−	0.625904i	−0.997023	+	0.0771038i	$0.975433\pi$
$774$	11.0760	−	7.11812i	0.398119	−	0.255855i
$775$	41.9075	+	12.3052i	1.50536	+	0.442014i
$776$	−1.75133	−	12.1808i	−0.0628692	−	0.437265i
$777$	0.0241866	−	0.0529613i	0.000867689	−	0.00189997i
$778$	−4.83440	+	33.6240i	−0.173322	+	1.20548i
$779$	−18.5930	−	11.9490i	−0.666162	−	0.428116i
$780$	−0.488658	−	0.563941i	−0.0174967	−	0.0201923i
$781$	−22.0153			−0.787769
$782$	−9.03134	+	20.4886i	−0.322960	+	0.732670i
$783$	3.08705			0.110322
$784$	−0.654861	−	0.755750i	−0.0233879	−	0.0269911i
$785$	−15.5631	−	10.0018i	−0.555473	−	0.356981i
$786$	−0.0378164	+	0.263019i	−0.00134887	+	0.00938157i
$787$	−10.1839	+	22.2997i	−0.363018	+	0.794900i	0.636699	+	0.771113i	$0.280300\pi$
$787$	−10.1839	+	22.2997i	−0.363018	+	0.794900i	−0.999717	+	0.0237868i	$0.992428\pi$
$788$	3.14619	+	21.8822i	0.112078	+	0.779521i
$789$	−1.48461	−	0.435921i	−0.0528535	−	0.0155192i
$790$	31.6059	−	20.3119i	1.12449	−	0.722665i
$791$	2.26717	+	4.96440i	0.0806112	+	0.176514i
$792$	11.7933	−	3.46281i	0.419055	−	0.123046i
$793$	6.93731	−	8.00609i	0.246351	−	0.284305i
$794$	5.07486	−	5.85670i	0.180100	−	0.207846i
$795$	−3.71819	+	1.09176i	−0.131870	+	0.0387207i
$796$	5.23042	+	11.4530i	0.185387	+	0.405942i
$797$	−16.4413	+	10.5662i	−0.582382	+	0.374274i	−0.798411	−	0.602113i	$-0.794326\pi$
$797$	−16.4413	+	10.5662i	−0.582382	+	0.374274i	0.216029	+	0.976387i	$0.430689\pi$
$798$	−0.459493	−	0.134919i	−0.0162659	−	0.00477609i
$799$	6.22870	+	43.3216i	0.220356	+	1.53261i
$800$	−3.91510	+	8.57287i	−0.138420	+	0.303097i
$801$	1.98248	−	13.7884i	0.0700474	−	0.487191i
$802$	−24.8722	−	15.9844i	−0.878266	−	0.564428i
$803$	−40.2769	−	46.4820i	−1.42134	−	1.64031i
$804$	−0.0491546			−0.00173355
$805$	7.34679	−	16.6670i	0.258940	−	0.587435i
$806$	10.3286			0.363810
$807$	−0.298148	−	0.344081i	−0.0104953	−	0.0121122i
$808$	−10.1205	−	6.50407i	−0.356039	−	0.228812i
$809$	−0.170403	+	1.18518i	−0.00599105	+	0.0416687i	−0.992598	−	0.121449i	$-0.961246\pi$
$809$	−0.170403	+	1.18518i	−0.00599105	+	0.0416687i	0.986607	+	0.163118i	$0.0521550\pi$
$810$	−14.0893	+	30.8513i	−0.495049	+	1.08401i
$811$	−0.183705	−	1.27770i	−0.00645075	−	0.0448660i	0.986342	−	0.164711i	$-0.0526692\pi$
$811$	−0.183705	−	1.27770i	−0.00645075	−	0.0448660i	−0.992793	+	0.119845i	$0.961760\pi$
$812$	−5.60719	−	1.64642i	−0.196774	−	0.0577780i
$813$	−1.43181	+	0.920167i	−0.0502157	+	0.0322717i
$814$	−1.12699	−	2.46777i	−0.0395010	−	0.0864952i
$815$	44.4045	−	13.0383i	1.55542	−	0.456713i
$816$	0.269529	−	0.311053i	0.00943541	−	0.0108890i
$817$	−15.6529	+	18.0645i	−0.547627	+	0.631995i
$818$	14.7790	−	4.33949i	0.516734	−	0.151727i
$819$	2.77032	+	6.06616i	0.0968028	+	0.211969i
$820$	−12.9991	+	8.35403i	−0.453949	+	0.291735i
$821$	29.6019	+	8.69190i	1.03311	+	0.303349i	0.753976	−	0.656902i	$-0.228133\pi$
$821$	29.6019	+	8.69190i	1.03311	+	0.303349i	0.279137	+	0.960251i	$0.409952\pi$
$822$	−0.0460464	−	0.320260i	−0.00160605	−	0.0111703i
$823$	−4.03064	+	8.82587i	−0.140499	+	0.307650i	−0.966781	−	0.255607i	$-0.917725\pi$
$823$	−4.03064	+	8.82587i	−0.140499	+	0.307650i	0.826282	+	0.563257i	$0.190452\pi$
$824$	0.539368	−	3.75138i	0.0187898	−	0.130686i
$825$	−2.87102	−	1.84509i	−0.0999562	−	0.0642379i
$826$	−5.52502	−	6.37622i	−0.192240	−	0.221857i
$827$	0.260876			0.00907155			0.00453578	−	0.999990i	$-0.498556\pi$
$827$	0.260876			0.00907155			0.00453578	+	0.999990i	$0.498556\pi$
$828$	11.9685	−	7.91727i	0.415935	−	0.275144i
$829$	−0.888401			−0.0308555			−0.0154277	−	0.999881i	$-0.504911\pi$
$829$	−0.888401			−0.0308555			−0.0154277	+	0.999881i	$0.504911\pi$
$830$	−26.0963	−	30.1167i	−0.905815	−	1.04537i
$831$	−1.80052	−	1.15712i	−0.0624594	−	0.0401402i
$832$	−0.317178	+	2.20602i	−0.0109962	+	0.0764801i
$833$	−1.93949	+	4.24689i	−0.0671994	+	0.147146i
$834$	−0.0193032	−	0.134257i	−0.000668416	−	0.00464893i
$835$	60.2538	+	17.6921i	2.08517	+	0.612260i
$836$	−18.7720	+	12.0640i	−0.649242	+	0.417243i
$837$	1.01698	+	2.22687i	0.0351519	+	0.0769719i
$838$	33.7088	−	9.89781i	1.16445	−	0.341914i
$839$	20.8151	−	24.0219i	0.718616	−	0.829328i	−0.272524	−	0.962149i	$-0.587858\pi$
$839$	20.8151	−	24.0219i	0.718616	−	0.829328i	0.991140	+	0.132822i	$0.0424037\pi$
$840$	−0.219256	+	0.253035i	−0.00756505	+	0.00873054i
$841$	−4.94257	+	1.45127i	−0.170433	+	0.0500438i
$842$	−1.87343	−	4.10223i	−0.0645625	−	0.141372i
$843$	1.03208	−	0.663278i	0.0355467	−	0.0228445i
$844$	23.8859	+	7.01353i	0.822186	+	0.241416i
$845$	4.34182	+	30.1980i	0.149363	+	1.03884i
$846$	11.6525	−	25.5154i	0.400621	−	0.877238i
$847$	0.835830	−	5.81332i	0.0287194	−	0.199748i
$848$	9.73674	+	6.25742i	0.334361	+	0.214881i
$849$	−1.40877	−	1.62581i	−0.0483489	−	0.0557976i
$850$	44.0014			1.50923
$851$	−2.10569	−	2.36614i	−0.0721821	−	0.0811101i
$852$	0.472474			0.0161867
$853$	−8.85098	−	10.2146i	−0.303052	−	0.349740i	0.583714	−	0.811959i	$-0.301599\pi$
$853$	−8.85098	−	10.2146i	−0.303052	−	0.349740i	−0.886766	+	0.462219i	$0.847053\pi$
$854$	−3.99868	−	2.56979i	−0.136832	−	0.0879365i
$855$	8.78581	−	61.1066i	0.300468	−	2.08980i
$856$	4.72721	−	10.3511i	0.161573	−	0.353795i
$857$	−7.01504	−	48.7907i	−0.239629	−	1.66666i	−0.653959	−	0.756530i	$-0.726893\pi$
$857$	−7.01504	−	48.7907i	−0.239629	−	1.66666i	0.414330	−	0.910127i	$-0.364016\pi$
$858$	−0.774362	−	0.227373i	−0.0264363	−	0.00776239i
$859$	−45.5848	+	29.2955i	−1.55533	+	0.999551i	−0.571470	+	0.820623i	$0.693627\pi$
$859$	−45.5848	+	29.2955i	−1.55533	+	0.999551i	−0.983862	+	0.178928i	$0.942737\pi$
$860$	6.94216	+	15.2012i	0.236726	+	0.518357i
$861$	−0.344135	+	0.101047i	−0.0117281	+	0.00344368i
$862$	−13.6021	+	15.6977i	−0.463290	+	0.534666i
$863$	32.7434	−	37.7879i	1.11460	−	1.28632i	0.160431	−	0.987047i	$-0.448712\pi$
$863$	32.7434	−	37.7879i	1.11460	−	1.28632i	0.954169	−	0.299269i	$-0.0967429\pi$
$864$	−0.506853	+	0.148825i	−0.0172435	+	0.00506314i
$865$	33.0963	+	72.4708i	1.12531	+	2.46408i
$866$	17.0569	−	10.9618i	0.579618	−	0.372498i
$867$	−0.405814	−	0.119158i	−0.0137822	−	0.00404681i
$868$	−0.659538	−	4.58719i	−0.0223862	−	0.155699i
$869$	16.8799	−	36.9618i	0.572612	−	1.25384i
$870$	−0.278456	+	1.93670i	−0.00944053	+	0.0656603i
$871$	−1.04542	−	0.671853i	−0.0354229	−	0.0227649i
$872$	−2.30719	−	2.66264i	−0.0781314	−	0.0901685i
$873$	36.8225			1.24625
$874$	−16.7989	+	19.9130i	−0.568232	+	0.673569i
$875$	−16.8043			−0.568089
$876$	0.864390	+	0.997559i	0.0292050	+	0.0337044i
$877$	−0.888158	−	0.570784i	−0.0299910	−	0.0192740i	0.525559	−	0.850757i	$-0.323856\pi$
$877$	−0.888158	−	0.570784i	−0.0299910	−	0.0192740i	−0.555550	+	0.831483i	$0.687492\pi$
$878$	−1.87179	+	13.0186i	−0.0631698	+	0.439356i
$879$	0.690632	−	1.51227i	0.0232945	−	0.0510077i
$880$	2.22023	+	15.4421i	0.0748441	+	0.520552i
$881$	−28.1356	−	8.26136i	−0.947912	−	0.278332i	−0.228995	−	0.973428i	$-0.573544\pi$
$881$	−28.1356	−	8.26136i	−0.947912	−	0.278332i	−0.718918	+	0.695095i	$0.755362\pi$
$882$	2.51722	−	1.61772i	0.0847593	−	0.0544715i
$883$	−2.39826	−	5.25146i	−0.0807080	−	0.176726i	0.864976	−	0.501813i	$-0.167334\pi$
$883$	−2.39826	−	5.25146i	−0.0807080	−	0.176726i	−0.945684	+	0.325087i	$0.894606\pi$
$884$	9.98390	−	2.93154i	0.335795	−	0.0985983i
$885$	−1.84985	+	2.13484i	−0.0621820	+	0.0717619i
$886$	13.6047	−	15.7006i	0.457058	−	0.527473i
$887$	−2.68433	+	0.788190i	−0.0901309	+	0.0264648i	−0.326487	−	0.945202i	$-0.605865\pi$
$887$	−2.68433	+	0.788190i	−0.0901309	+	0.0264648i	0.236356	+	0.971666i	$0.424047\pi$
$888$	0.0241866	+	0.0529613i	0.000811649	+	0.00177726i
$889$	17.9402	−	11.5295i	0.601696	−	0.386686i
$890$	16.9651	+	4.98140i	0.568672	+	0.166977i
$891$	5.22041	+	36.3088i	0.174890	+	1.21639i
$892$	−3.07316	+	6.72928i	−0.102897	+	0.225313i
$893$	−7.24733	+	50.4063i	−0.242523	+	1.68678i
$894$	1.41501	+	0.909372i	0.0473250	+	0.0304140i
$895$	4.53922	+	5.23854i	0.151729	+	0.175105i
$896$	1.00000			0.0334077
$897$	−0.942173	+	0.0124595i	−0.0314582	+	0.000416012i
$898$	20.8101			0.694441
$899$	−17.7354	−	20.4678i	−0.591509	−	0.682638i
$900$	−23.7237	−	15.2463i	−0.790790	−	0.508210i
$901$	7.69028	−	53.4871i	0.256200	−	1.78191i
$902$	−6.94250	+	15.2020i	−0.231160	+	0.506170i
$903$	0.0552031	+	0.383946i	0.00183704	+	0.0127769i
$904$	−5.23652	−	1.53758i	−0.174164	−	0.0511392i
$905$	−51.4888	+	33.0899i	−1.71155	+	1.09994i
$906$	−0.144078	−	0.315487i	−0.00478668	−	0.0104814i
$907$	−24.6739	+	7.24490i	−0.819282	+	0.240563i	−0.664407	−	0.747371i	$-0.731316\pi$
$907$	−24.6739	+	7.24490i	−0.819282	+	0.240563i	−0.154875	+	0.987934i	$0.549498\pi$
$908$	−3.02177	+	3.48730i	−0.100281	+	0.115730i
$909$	23.5733	−	27.2050i	0.781876	−	0.902333i
$910$	−8.12168	+	2.38474i	−0.269231	+	0.0790534i
$911$	16.3067	+	35.7067i	0.540266	+	1.18302i	0.961181	+	0.275917i	$0.0889816\pi$
$911$	16.3067	+	35.7067i	0.540266	+	1.18302i	−0.420916	+	0.907100i	$0.638291\pi$
$912$	0.402869	−	0.258908i	0.0133403	−	0.00857331i
$913$	−41.3540	−	12.1426i	−1.36862	−	0.401863i
$914$	2.52766	+	17.5803i	0.0836076	+	0.581503i
$915$	−0.661111	+	1.44763i	−0.0218556	+	0.0478572i
$916$	2.57590	−	17.9158i	0.0851101	−	0.591954i
$917$	2.53574	+	1.62962i	0.0837376	+	0.0538149i
$918$	1.61508	+	1.86390i	0.0533056	+	0.0615180i
$919$	24.8012			0.818116			0.409058	−	0.912508i	$-0.365857\pi$
$919$	24.8012			0.818116			0.409058	+	0.912508i	$0.365857\pi$
$920$	7.78496	+	16.4669i	0.256663	+	0.542898i
$921$	0.943340			0.0310841
$922$	14.6988	+	16.9633i	0.484078	+	0.558656i
$923$	10.0486	+	6.45786i	0.330755	+	0.212563i
$924$	−0.0515346	+	0.358431i	−0.00169536	+	0.0117915i
$925$	−2.58574	+	5.66197i	−0.0850185	+	0.186164i
$926$	2.01699	+	14.0285i	0.0662825	+	0.461005i
$927$	10.8811	+	3.19497i	0.357381	+	0.104937i
$928$	4.91621	−	3.15945i	0.161382	−	0.103714i
$929$	−3.21206	−	7.03343i	−0.105384	−	0.230760i	0.849593	−	0.527439i	$-0.176848\pi$
$929$	−3.21206	−	7.03343i	−0.105384	−	0.230760i	−0.954977	+	0.296680i	$0.904121\pi$
$930$	−1.48879	+	0.437149i	−0.0488194	+	0.0143347i
$931$	−3.55742	+	4.10548i	−0.116590	+	0.134552i
$932$	17.9901	−	20.7617i	0.589286	−	0.680072i
$933$	1.61862	−	0.475270i	0.0529913	−	0.0155596i
$934$	6.38014	+	13.9706i	0.208765	+	0.457131i
$935$	61.2747	−	39.3788i	2.00390	−	1.28783i
$936$	−6.39867	−	1.87882i	−0.209147	−	0.0614111i
$937$	−1.67348	−	11.6393i	−0.0546703	−	0.380240i	−0.998726	−	0.0504552i	$-0.983933\pi$
$937$	−1.67348	−	11.6393i	−0.0546703	−	0.380240i	0.944056	−	0.329785i	$-0.106976\pi$
$938$	−0.231630	+	0.507199i	−0.00756299	+	0.0165606i
$939$	0.0938804	−	0.652952i	0.00306367	−	0.0213083i
$940$	29.9516	+	19.2487i	0.976914	+	0.627824i
$941$	25.8825	+	29.8700i	0.843745	+	0.973734i	0.999902	−	0.0139986i	$-0.00445605\pi$
$941$	25.8825	+	29.8700i	0.843745	+	0.973734i	−0.156157	+	0.987732i	$0.549911\pi$
$942$	0.429409			0.0139909
$943$	−2.52121	+	19.3483i	−0.0821019	+	0.630069i
$944$	8.43694			0.274599
$945$	−1.31383	−	1.51624i	−0.0427390	−	0.0493234i
$946$	15.2050	+	9.77165i	0.494357	+	0.317704i
$947$	−6.06903	+	42.2110i	−0.197217	+	1.37167i	0.615096	+	0.788452i	$0.289117\pi$
$947$	−6.06903	+	42.2110i	−0.197217	+	1.37167i	−0.812313	+	0.583221i	$0.801792\pi$
$948$	−0.362263	+	0.793246i	−0.0117658	+	0.0257634i
$949$	4.74911	+	33.0308i	0.154163	+	1.07223i
$950$	49.1234	+	14.4239i	1.59377	+	0.467974i
$951$	0.353824	−	0.227389i	0.0114735	−	0.00737359i
$952$	−1.93949	−	4.24689i	−0.0628592	−	0.137643i
$953$	32.8742	−	9.65273i	1.06490	−	0.312682i	0.298076	−	0.954542i	$-0.403655\pi$
$953$	32.8742	−	9.65273i	1.06490	−	0.312682i	0.766822	+	0.641860i	$0.221837\pi$
$954$	−22.6793	+	26.1733i	−0.734271	+	0.847393i
$955$	32.5271	−	37.5383i	1.05255	−	1.21471i
$956$	−18.3983	+	5.40223i	−0.595044	+	0.174721i
$957$	0.879092	+	1.92494i	0.0284170	+	0.0622246i
$958$	−24.1564	+	15.5244i	−0.780458	+	0.501570i
$959$	−3.52157	−	1.03402i	−0.113717	−	0.0333904i
$960$	−0.0476489	−	0.331405i	−0.00153786	−	0.0106961i
$961$	−3.95589	+	8.66219i	−0.127609	+	0.279426i
$962$	−0.209481	+	1.45697i	−0.00675393	+	0.0469746i
$963$	28.6447	+	18.4088i	0.923062	+	0.593216i
$964$	−11.9500	−	13.7911i	−0.384884	−	0.444180i
$965$	−96.7688			−3.11510
$966$	0.0656963	+	0.417645i	0.00211374	+	0.0134375i
$967$	−22.5965			−0.726655			−0.363328	−	0.931661i	$-0.618359\pi$
$967$	−22.5965			−0.726655			−0.363328	+	0.931661i	$0.618359\pi$
$968$	3.84606	+	4.43859i	0.123617	+	0.142662i
$969$	−1.88092	−	1.20879i	−0.0604237	−	0.0388320i
$970$	−6.65151	+	46.2623i	−0.213567	+	1.48539i
$971$	−5.04084	+	11.0379i	−0.161768	+	0.354223i	−0.973107	−	0.230353i	$-0.926012\pi$
$971$	−5.04084	+	11.0379i	−0.161768	+	0.354223i	0.811339	+	0.584576i	$0.198739\pi$
$972$	−0.337570	−	2.34785i	−0.0108276	−	0.0753073i
$973$	−1.47628	−	0.433476i	−0.0473275	−	0.0138966i
$974$	−6.42127	+	4.12670i	−0.205751	+	0.132228i
$975$	0.769214	+	1.68434i	0.0246346	+	0.0539422i
$976$	4.56070	−	1.33914i	0.145984	−	0.0428649i
$977$	−32.7076	+	37.7466i	−1.04641	+	1.20762i	−0.0687044	+	0.997637i	$0.521887\pi$
$977$	−32.7076	+	37.7466i	−1.04641	+	1.20762i	−0.977705	+	0.209984i	$0.932659\pi$
$978$	−0.703452	+	0.811826i	−0.0224939	+	0.0259593i
$979$	18.3486	−	5.38763i	0.586424	−	0.172190i
$980$	1.57773	+	3.45475i	0.0503988	+	0.110358i
$981$	8.86863	−	5.69952i	0.283154	−	0.181972i
$982$	−41.4102	−	12.1591i	−1.32145	−	0.388014i
$983$	−3.76888	−	26.2131i	−0.120208	−	0.836068i	−0.957319	−	0.289034i	$-0.906666\pi$
$983$	−3.76888	−	26.2131i	−0.120208	−	0.836068i	0.837110	−	0.547034i	$-0.184243\pi$
$984$	0.148994	−	0.326252i	0.00474977	−	0.0104005i
$985$	11.9491	−	83.1079i	0.380730	−	2.64804i
$986$	−22.9528	−	14.7509i	−0.730966	−	0.469763i
$987$	0.541181	+	0.624556i	0.0172260	+	0.0198798i
$988$	12.1071			0.385177
$989$	20.3241	+	5.67689i	0.646270	+	0.180515i
$990$	−46.6813			−1.48363
$991$	−0.569484	−	0.657220i	−0.0180903	−	0.0208773i	0.746632	−	0.665237i	$-0.231669\pi$
$991$	−0.569484	−	0.657220i	−0.0180903	−	0.0208773i	−0.764723	+	0.644360i	$0.777124\pi$
$992$	3.89867	+	2.50552i	0.123783	+	0.0795504i
$993$	0.155139	−	1.07902i	0.00492319	−	0.0342415i
$994$	2.22643	−	4.87520i	0.0706181	−	0.154632i
$995$	−6.80543	−	47.3328i	−0.215747	−	1.50055i
$996$	0.887507	+	0.260596i	0.0281217	+	0.00825729i
$997$	−31.2174	+	20.0622i	−0.988666	+	0.635377i	−0.931788	−	0.363004i	$-0.881751\pi$
$997$	−31.2174	+	20.0622i	−0.988666	+	0.635377i	−0.0568788	+	0.998381i	$0.518115\pi$
$998$	−4.68727	−	10.2637i	−0.148373	−	0.324891i
$999$	−0.334752	+	0.0982920i	−0.0105911	+	0.00310982i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.b.197.1	yes	10
23.4	even	11		7406.2.a.bf.1.4		5
23.16	even	11	inner	322.2.i.b.85.1	✓	10
23.19	odd	22		7406.2.a.be.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.b.85.1	✓	10	23.16	even	11	inner
322.2.i.b.197.1	yes	10	1.1	even	1	trivial
7406.2.a.be.1.4		5	23.19	odd	22
7406.2.a.bf.1.4		5	23.4	even	11

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 + 0.755750i) q^{2} +(0.0741615 + 0.0476607i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(1.57773 - 3.45475i) q^{5} +(0.0125459 + 0.0872586i) q^{6} +(0.959493 + 0.281733i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-1.24302 - 2.72183i) q^{9} +O(q^{10})\)	\(q+(0.654861 + 0.755750i) q^{2} +(0.0741615 + 0.0476607i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(1.57773 - 3.45475i) q^{5} +(0.0125459 + 0.0872586i) q^{6} +(0.959493 + 0.281733i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-1.24302 - 2.72183i) q^{9} +(3.64412 - 1.07001i) q^{10} +(2.68996 - 3.10438i) q^{11} +(-0.0577299 + 0.0666238i) q^{12} +(-2.13843 + 0.627899i) q^{13} +(0.415415 + 0.909632i) q^{14} +(0.281663 - 0.181014i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(0.664440 + 4.62128i) q^{17} +(1.24302 - 2.72183i) q^{18} +(-0.773100 + 5.37703i) q^{19} +(3.19505 + 2.05334i) q^{20} +(0.0577299 + 0.0666238i) q^{21} +4.10769 q^{22} +(4.58330 - 1.41187i) q^{23} -0.0881559 q^{24} +(-6.17177 - 7.12260i) q^{25} +(-1.87491 - 1.20493i) q^{26} +(0.0751779 - 0.522874i) q^{27} +(-0.415415 + 0.909632i) q^{28} +(0.831674 + 5.78442i) q^{29} +(0.321251 + 0.0943278i) q^{30} +(-3.89867 + 2.50552i) q^{31} +(-0.415415 - 0.909632i) q^{32} +(0.347449 - 0.102020i) q^{33} +(-3.05742 + 3.52845i) q^{34} +(2.48714 - 2.87031i) q^{35} +(2.87102 - 0.843008i) q^{36} +(-0.274362 - 0.600768i) q^{37} +(-4.56996 + 2.93694i) q^{38} +(-0.188515 - 0.0553531i) q^{39} +(0.540507 + 3.75931i) q^{40} +(-1.69012 + 3.70085i) q^{41} +(-0.0125459 + 0.0872586i) q^{42} +(3.70159 + 2.37887i) q^{43} +(2.68996 + 3.10438i) q^{44} -11.3644 q^{45} +(4.06844 + 2.53925i) q^{46} +9.37437 q^{47} +(-0.0577299 - 0.0666238i) q^{48} +(0.841254 + 0.540641i) q^{49} +(1.34125 - 9.32862i) q^{50} +(-0.170978 + 0.374389i) q^{51} +(-0.317178 - 2.20602i) q^{52} +(-11.1053 - 3.26080i) q^{53} +(0.444393 - 0.285594i) q^{54} +(-6.48083 - 14.1910i) q^{55} +(-0.959493 + 0.281733i) q^{56} +(-0.313607 + 0.361922i) q^{57} +(-3.82694 + 4.41653i) q^{58} +(-8.09519 + 2.37696i) q^{59} +(0.139086 + 0.304557i) q^{60} +(-3.99868 + 2.56979i) q^{61} +(-4.44663 - 1.30565i) q^{62} +(-0.425839 - 2.96177i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-1.20463 + 8.37840i) q^{65} +(0.304632 + 0.195775i) q^{66} +(0.365142 + 0.421396i) q^{67} -4.66880 q^{68} +(0.407195 + 0.113737i) q^{69} +3.79797 q^{70} +(-3.50975 - 4.05046i) q^{71} +(2.51722 + 1.61772i) q^{72} +(2.13088 - 14.8206i) q^{73} +(0.274362 - 0.600768i) q^{74} +(-0.118239 - 0.822373i) q^{75} +(-5.21228 - 1.53046i) q^{76} +(3.45561 - 2.22078i) q^{77} +(-0.0816181 - 0.178719i) q^{78} +(9.49144 - 2.78694i) q^{79} +(-2.48714 + 2.87031i) q^{80} +(-5.84798 + 6.74893i) q^{81} +(-3.90371 + 1.14623i) q^{82} +(-4.35874 - 9.54430i) q^{83} +(-0.0741615 + 0.0476607i) q^{84} +(17.0137 + 4.99567i) q^{85} +(0.626198 + 4.35530i) q^{86} +(-0.214011 + 0.468620i) q^{87} +(-0.584585 + 4.06588i) q^{88} +(3.91643 + 2.51694i) q^{89} +(-7.44209 - 8.58863i) q^{90} -2.22871 q^{91} +(0.745229 + 4.73758i) q^{92} -0.408546 q^{93} +(6.13891 + 7.08467i) q^{94} +(17.3566 + 11.1544i) q^{95} +(0.0125459 - 0.0872586i) q^{96} +(-5.11212 + 11.1940i) q^{97} +(0.142315 + 0.989821i) q^{98} +(-11.7933 - 3.46281i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} + 5 q^{3} - q^{4} + 8 q^{5} - 5 q^{6} + q^{7} + q^{8}+O(q^{10}) \) 10 * q + q^2 + 5 * q^3 - q^4 + 8 * q^5 - 5 * q^6 + q^7 + q^8	\( 10 q + q^{2} + 5 q^{3} - q^{4} + 8 q^{5} - 5 q^{6} + q^{7} + q^{8} + 3 q^{10} + 11 q^{11} + 5 q^{12} - 6 q^{13} - q^{14} + 4 q^{15} - q^{16} - 2 q^{17} - 3 q^{19} + 8 q^{20} - 5 q^{21} - 21 q^{23} + 6 q^{24} - 15 q^{25} - 5 q^{26} - 4 q^{27} + q^{28} + 2 q^{29} - 4 q^{30} + 3 q^{31} + q^{32} - 11 q^{33} + 2 q^{34} + 3 q^{35} - 6 q^{37} - 8 q^{38} + 8 q^{39} + 14 q^{40} - 23 q^{41} + 5 q^{42} - q^{43} + 11 q^{44} - 22 q^{45} - q^{46} + 38 q^{47} + 5 q^{48} - q^{49} + 4 q^{50} + 21 q^{51} + 5 q^{52} - 49 q^{53} + 4 q^{54} + 11 q^{55} - q^{56} - 7 q^{57} - 13 q^{58} + 9 q^{59} + 4 q^{60} + 16 q^{61} - 14 q^{62} - q^{64} + 15 q^{65} + 7 q^{67} - 2 q^{68} - 16 q^{69} + 8 q^{70} - 16 q^{71} + 11 q^{72} - 9 q^{73} + 6 q^{74} - 2 q^{75} - 14 q^{76} + 11 q^{77} - 8 q^{78} + 6 q^{79} - 3 q^{80} - 24 q^{81} - 43 q^{82} - 19 q^{83} - 5 q^{84} + 49 q^{85} + 23 q^{86} - 21 q^{87} - 11 q^{88} + 25 q^{89} - 11 q^{90} + 6 q^{91} + q^{92} - 4 q^{93} - 5 q^{94} + 24 q^{95} - 5 q^{96} + 16 q^{97} + q^{98} - 33 q^{99}+O(q^{100}) \) 10 * q + q^2 + 5 * q^3 - q^4 + 8 * q^5 - 5 * q^6 + q^7 + q^8 + 3 * q^10 + 11 * q^11 + 5 * q^12 - 6 * q^13 - q^14 + 4 * q^15 - q^16 - 2 * q^17 - 3 * q^19 + 8 * q^20 - 5 * q^21 - 21 * q^23 + 6 * q^24 - 15 * q^25 - 5 * q^26 - 4 * q^27 + q^28 + 2 * q^29 - 4 * q^30 + 3 * q^31 + q^32 - 11 * q^33 + 2 * q^34 + 3 * q^35 - 6 * q^37 - 8 * q^38 + 8 * q^39 + 14 * q^40 - 23 * q^41 + 5 * q^42 - q^43 + 11 * q^44 - 22 * q^45 - q^46 + 38 * q^47 + 5 * q^48 - q^49 + 4 * q^50 + 21 * q^51 + 5 * q^52 - 49 * q^53 + 4 * q^54 + 11 * q^55 - q^56 - 7 * q^57 - 13 * q^58 + 9 * q^59 + 4 * q^60 + 16 * q^61 - 14 * q^62 - q^64 + 15 * q^65 + 7 * q^67 - 2 * q^68 - 16 * q^69 + 8 * q^70 - 16 * q^71 + 11 * q^72 - 9 * q^73 + 6 * q^74 - 2 * q^75 - 14 * q^76 + 11 * q^77 - 8 * q^78 + 6 * q^79 - 3 * q^80 - 24 * q^81 - 43 * q^82 - 19 * q^83 - 5 * q^84 + 49 * q^85 + 23 * q^86 - 21 * q^87 - 11 * q^88 + 25 * q^89 - 11 * q^90 + 6 * q^91 + q^92 - 4 * q^93 - 5 * q^94 + 24 * q^95 - 5 * q^96 + 16 * q^97 + q^98 - 33 * q^99

Introduction

L-functions

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