LMFDB - Embedded newform 49.2.g.a.23.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,2,Mod(2,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([26]))

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

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

chi := DirichletCharacter("49.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	49.g (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.391266969904$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			23.3
Character	$\chi$	$=$	49.23
Dual form			49.2.g.a.32.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0658689 - 0.878959i) q^{2} +(-0.269714 + 0.0831957i) q^{3} +(1.20943 + 0.182293i) q^{4} +(-1.49036 - 1.38285i) q^{5} +(0.0553598 + 0.242547i) q^{6} +(-0.607511 + 2.57506i) q^{7} +(0.632162 - 2.76968i) q^{8} +(-2.41289 + 1.64508i) q^{9} +O(q^{10})$	\(q+(0.0658689 - 0.878959i) q^{2} +(-0.269714 + 0.0831957i) q^{3} +(1.20943 + 0.182293i) q^{4} +(-1.49036 - 1.38285i) q^{5} +(0.0553598 + 0.242547i) q^{6} +(-0.607511 + 2.57506i) q^{7} +(0.632162 - 2.76968i) q^{8} +(-2.41289 + 1.64508i) q^{9} +(-1.31364 + 1.21888i) q^{10} +(1.64705 + 1.12294i) q^{11} +(-0.341366 + 0.0514527i) q^{12} +(-3.26094 + 1.57038i) q^{13} +(2.22335 + 0.703594i) q^{14} +(0.517018 + 0.248983i) q^{15} +(-0.0552877 - 0.0170540i) q^{16} +(-0.409339 + 1.04298i) q^{17} +(1.28702 + 2.22919i) q^{18} +(3.73687 - 6.47246i) q^{19} +(-1.55041 - 1.94415i) q^{20} +(-0.0503796 - 0.745071i) q^{21} +(1.09550 - 1.37372i) q^{22} +(-1.94485 - 4.95539i) q^{23} +(0.0599228 + 0.799614i) q^{24} +(-0.0647567 - 0.864118i) q^{25} +(1.16551 + 2.96967i) q^{26} +(1.04187 - 1.30647i) q^{27} +(-1.20416 + 3.00361i) q^{28} +(1.28279 + 1.60857i) q^{29} +(0.252901 - 0.438037i) q^{30} +(2.48025 + 4.29592i) q^{31} +(2.05717 - 5.24158i) q^{32} +(-0.537654 - 0.165844i) q^{33} +(0.889772 + 0.428491i) q^{34} +(4.46634 - 2.99767i) q^{35} +(-3.21812 + 1.54976i) q^{36} +(0.814555 - 0.122774i) q^{37} +(-5.44288 - 3.71089i) q^{38} +(0.748870 - 0.694850i) q^{39} +(-4.77221 + 3.25364i) q^{40} +(-1.33292 + 5.83991i) q^{41} +(-0.658205 - 0.00479541i) q^{42} +(0.518849 + 2.27323i) q^{43} +(1.78729 + 1.65836i) q^{44} +(5.87099 + 0.884909i) q^{45} +(-4.48369 + 1.38304i) q^{46} +(-0.407053 + 5.43174i) q^{47} +0.0163307 q^{48} +(-6.26186 - 3.12876i) q^{49} -0.763790 q^{50} +(0.0236330 - 0.315360i) q^{51} +(-4.23015 + 1.30483i) q^{52} +(-13.4919 - 2.03358i) q^{53} +(-1.07970 - 1.00182i) q^{54} +(-0.901837 - 3.95120i) q^{55} +(6.74805 + 3.31047i) q^{56} +(-0.469406 + 2.05660i) q^{57} +(1.49837 - 1.02157i) q^{58} +(7.41658 - 6.88158i) q^{59} +(0.579911 + 0.395376i) q^{60} +(8.84072 - 1.33252i) q^{61} +(3.93931 - 1.89707i) q^{62} +(-2.77032 - 7.21275i) q^{63} +(-4.57589 - 2.20363i) q^{64} +(7.03159 + 2.16896i) q^{65} +(-0.181185 + 0.461652i) q^{66} +(5.76466 + 9.98468i) q^{67} +(-0.685194 + 1.18679i) q^{68} +(0.936820 + 1.17473i) q^{69} +(-2.34063 - 4.12318i) q^{70} +(-2.62321 + 3.28940i) q^{71} +(3.03102 + 7.72290i) q^{72} +(-0.880793 - 11.7534i) q^{73} +(-0.0542598 - 0.724047i) q^{74} +(0.0893566 + 0.227677i) q^{75} +(5.69938 - 7.14679i) q^{76} +(-3.89223 + 3.55904i) q^{77} +(-0.561417 - 0.703995i) q^{78} +(-4.13300 + 7.15857i) q^{79} +(0.0588155 + 0.101871i) q^{80} +(3.02844 - 7.71633i) q^{81} +(5.04524 + 1.55625i) q^{82} +(8.17636 + 3.93753i) q^{83} +(0.0748902 - 0.910296i) q^{84} +(2.05235 - 0.988358i) q^{85} +(2.03225 - 0.306312i) q^{86} +(-0.479814 - 0.327131i) q^{87} +(4.15138 - 3.85192i) q^{88} +(-14.5109 + 9.89337i) q^{89} +(1.16451 - 5.10207i) q^{90} +(-2.06278 - 9.35113i) q^{91} +(-1.44883 - 6.34774i) q^{92} +(-1.02636 - 0.952322i) q^{93} +(4.74747 + 0.715565i) q^{94} +(-14.5198 + 4.47875i) q^{95} +(-0.118770 + 1.58487i) q^{96} +3.72740 q^{97} +(-3.16251 + 5.29783i) q^{98} -5.82147 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 13 q^{2} - 14 q^{3} - 9 q^{4} - 14 q^{5} - 14 q^{7} - 20 q^{8} + 6 q^{9}+O(q^{10}) $ 48 * q - 13 * q^2 - 14 * q^3 - 9 * q^4 - 14 * q^5 - 14 * q^7 - 20 * q^8 + 6 * q^9	\( 48 q - 13 q^{2} - 14 q^{3} - 9 q^{4} - 14 q^{5} - 14 q^{7} - 20 q^{8} + 6 q^{9} - 14 q^{10} - 3 q^{11} + 21 q^{12} - 14 q^{13} + 21 q^{14} - 12 q^{15} - 3 q^{16} - 7 q^{17} + 2 q^{18} + 21 q^{19} + 14 q^{20} - 14 q^{21} - 20 q^{22} + 15 q^{23} + 28 q^{24} - 4 q^{25} + 7 q^{27} + 28 q^{28} + 12 q^{29} + 11 q^{30} + 35 q^{31} + 45 q^{32} - 14 q^{33} + 70 q^{34} - 12 q^{36} + 15 q^{37} - 28 q^{38} - 7 q^{39} - 42 q^{40} - 42 q^{41} + 28 q^{42} - 30 q^{43} - 50 q^{44} + 7 q^{45} - 78 q^{46} + 21 q^{47} - 84 q^{48} - 70 q^{49} + 40 q^{50} - 52 q^{51} - 70 q^{52} + 11 q^{53} - 77 q^{54} - 7 q^{55} - 28 q^{56} - 12 q^{57} + 16 q^{58} - 28 q^{59} + 56 q^{60} + 7 q^{61} - 28 q^{62} + 35 q^{63} - 32 q^{64} + 14 q^{65} + 154 q^{66} + 11 q^{67} + 77 q^{68} + 70 q^{69} + 70 q^{70} + 19 q^{71} + 170 q^{72} + 7 q^{73} + 34 q^{74} + 112 q^{75} + 119 q^{76} + 7 q^{77} + 28 q^{78} + 15 q^{79} + 70 q^{80} + 64 q^{81} - 14 q^{82} - 84 q^{84} - 26 q^{85} - 33 q^{86} - 112 q^{87} - 77 q^{88} - 14 q^{89} - 182 q^{90} + 84 q^{91} - 38 q^{92} - 80 q^{93} + 14 q^{94} - 61 q^{95} - 70 q^{96} - 161 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q - 13 * q^2 - 14 * q^3 - 9 * q^4 - 14 * q^5 - 14 * q^7 - 20 * q^8 + 6 * q^9 - 14 * q^10 - 3 * q^11 + 21 * q^12 - 14 * q^13 + 21 * q^14 - 12 * q^15 - 3 * q^16 - 7 * q^17 + 2 * q^18 + 21 * q^19 + 14 * q^20 - 14 * q^21 - 20 * q^22 + 15 * q^23 + 28 * q^24 - 4 * q^25 + 7 * q^27 + 28 * q^28 + 12 * q^29 + 11 * q^30 + 35 * q^31 + 45 * q^32 - 14 * q^33 + 70 * q^34 - 12 * q^36 + 15 * q^37 - 28 * q^38 - 7 * q^39 - 42 * q^40 - 42 * q^41 + 28 * q^42 - 30 * q^43 - 50 * q^44 + 7 * q^45 - 78 * q^46 + 21 * q^47 - 84 * q^48 - 70 * q^49 + 40 * q^50 - 52 * q^51 - 70 * q^52 + 11 * q^53 - 77 * q^54 - 7 * q^55 - 28 * q^56 - 12 * q^57 + 16 * q^58 - 28 * q^59 + 56 * q^60 + 7 * q^61 - 28 * q^62 + 35 * q^63 - 32 * q^64 + 14 * q^65 + 154 * q^66 + 11 * q^67 + 77 * q^68 + 70 * q^69 + 70 * q^70 + 19 * q^71 + 170 * q^72 + 7 * q^73 + 34 * q^74 + 112 * q^75 + 119 * q^76 + 7 * q^77 + 28 * q^78 + 15 * q^79 + 70 * q^80 + 64 * q^81 - 14 * q^82 - 84 * q^84 - 26 * q^85 - 33 * q^86 - 112 * q^87 - 77 * q^88 - 14 * q^89 - 182 * q^90 + 84 * q^91 - 38 * q^92 - 80 * q^93 + 14 * q^94 - 61 * q^95 - 70 * q^96 - 161 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{19}{21}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.0658689	−	0.878959i	0.0465763	−	0.621518i	−0.924258	−	0.381768i	$-0.875315\pi$
$2$	0.0658689	−	0.878959i	0.0465763	−	0.621518i	0.970835	−	0.239750i	$-0.0770655\pi$
$3$	−0.269714	+	0.0831957i	−0.155719	+	0.0480330i	−0.371635	−	0.928379i	$-0.621203\pi$
$3$	−0.269714	+	0.0831957i	−0.155719	+	0.0480330i	0.215915	+	0.976412i	$0.430726\pi$
$4$	1.20943	+	0.182293i	0.604716	+	0.0911463i
$5$	−1.49036	−	1.38285i	−0.666510	−	0.618431i	0.272568	−	0.962137i	$-0.412127\pi$
$5$	−1.49036	−	1.38285i	−0.666510	−	0.618431i	−0.939077	+	0.343706i	$0.888318\pi$
$6$	0.0553598	+	0.242547i	0.0226005	+	0.0990195i
$7$	−0.607511	+	2.57506i	−0.229618	+	0.973281i
$7$	−0.607511	+	2.57506i	−0.229618	+	0.973281i
$8$	0.632162	−	2.76968i	0.223503	−	0.979230i
$9$	−2.41289	+	1.64508i	−0.804297	+	0.548361i
$10$	−1.31364	+	1.21888i	−0.415409	+	0.385443i
$11$	1.64705	+	1.12294i	0.496603	+	0.338578i	0.785582	−	0.618757i	$-0.212363\pi$
$11$	1.64705	+	1.12294i	0.496603	+	0.338578i	−0.288979	+	0.957335i	$0.593316\pi$
$12$	−0.341366	+	0.0514527i	−0.0985440	+	0.0148531i
$13$	−3.26094	+	1.57038i	−0.904421	+	0.435546i	−0.827484	−	0.561490i	$-0.810228\pi$
$13$	−3.26094	+	1.57038i	−0.904421	+	0.435546i	−0.0769375	+	0.997036i	$0.524514\pi$
$14$	2.22335	+	0.703594i	0.594217	+	0.188043i
$15$	0.517018	+	0.248983i	0.133494	+	0.0642871i
$16$	−0.0552877	−	0.0170540i	−0.0138219	−	0.00426350i
$17$	−0.409339	+	1.04298i	−0.0992792	+	0.252959i	−0.971881	−	0.235473i	$-0.924336\pi$
$17$	−0.409339	+	1.04298i	−0.0992792	+	0.252959i	0.872602	+	0.488433i	$0.162431\pi$
$18$	1.28702	+	2.22919i	0.303355	+	0.525426i
$19$	3.73687	−	6.47246i	0.857298	−	1.48488i	−0.0171988	−	0.999852i	$-0.505475\pi$
$19$	3.73687	−	6.47246i	0.857298	−	1.48488i	0.874497	−	0.485031i	$-0.161192\pi$
$20$	−1.55041	−	1.94415i	−0.346681	−	0.434725i
$21$	−0.0503796	−	0.745071i	−0.0109937	−	0.162588i
$22$	1.09550	−	1.37372i	0.233562	−	0.292878i
$23$	−1.94485	−	4.95539i	−0.405529	−	1.03327i	−0.977112	−	0.212727i	$-0.931766\pi$
$23$	−1.94485	−	4.95539i	−0.405529	−	1.03327i	0.571583	−	0.820544i	$-0.306330\pi$
$24$	0.0599228	+	0.799614i	0.0122317	+	0.163221i
$25$	−0.0647567	−	0.864118i	−0.0129513	−	0.172824i
$26$	1.16551	+	2.96967i	0.228575	+	0.582400i
$27$	1.04187	−	1.30647i	0.200509	−	0.251430i
$28$	−1.20416	+	3.00361i	−0.227564	+	0.567630i
$29$	1.28279	+	1.60857i	0.238209	+	0.298705i	0.886538	−	0.462656i	$-0.153103\pi$
$29$	1.28279	+	1.60857i	0.238209	+	0.298705i	−0.648329	+	0.761360i	$0.724532\pi$
$30$	0.252901	−	0.438037i	0.0461732	−	0.0799743i
$31$	2.48025	+	4.29592i	0.445466	+	0.771570i	0.998085	−	0.0618646i	$-0.0197047\pi$
$31$	2.48025	+	4.29592i	0.445466	+	0.771570i	−0.552619	+	0.833434i	$0.686371\pi$
$32$	2.05717	−	5.24158i	0.363660	−	0.926590i
$33$	−0.537654	−	0.165844i	−0.0935936	−	0.0288698i
$34$	0.889772	+	0.428491i	0.152595	+	0.0734857i
$35$	4.46634	−	2.99767i	0.754949	−	0.506699i
$36$	−3.21812	+	1.54976i	−0.536353	+	0.258294i
$37$	0.814555	−	0.122774i	0.133912	−	0.0201840i	−0.0817442	−	0.996653i	$-0.526049\pi$
$37$	0.814555	−	0.122774i	0.133912	−	0.0201840i	0.215656	+	0.976469i	$0.430811\pi$
$38$	−5.44288	−	3.71089i	−0.882952	−	0.601986i
$39$	0.748870	−	0.694850i	0.119915	−	0.111265i
$40$	−4.77221	+	3.25364i	−0.754553	+	0.514446i
$41$	−1.33292	+	5.83991i	−0.208167	+	0.912041i	0.757618	+	0.652698i	$0.226363\pi$
$41$	−1.33292	+	5.83991i	−0.208167	+	0.912041i	−0.965785	+	0.259343i	$0.916494\pi$
$42$	−0.658205	−	0.00479541i	−0.101563	−	0.000739948i
$43$	0.518849	+	2.27323i	0.0791238	+	0.346664i	0.998958	−	0.0456439i	$-0.0145339\pi$
$43$	0.518849	+	2.27323i	0.0791238	+	0.346664i	−0.919834	+	0.392308i	$0.871677\pi$
$44$	1.78729	+	1.65836i	0.269444	+	0.250007i
$45$	5.87099	+	0.884909i	0.875195	+	0.131914i
$46$	−4.48369	+	1.38304i	−0.661084	+	0.203918i
$47$	−0.407053	+	5.43174i	−0.0593748	+	0.792301i	0.885452	+	0.464731i	$0.153849\pi$
$47$	−0.407053	+	5.43174i	−0.0593748	+	0.792301i	−0.944827	+	0.327570i	$0.893770\pi$
$48$	0.0163307			0.00235713
$49$	−6.26186	−	3.12876i	−0.894551	−	0.446965i
$50$	−0.763790			−0.108016
$51$	0.0236330	−	0.315360i	0.00330928	−	0.0441593i
$52$	−4.23015	+	1.30483i	−0.586616	+	0.180947i
$53$	−13.4919	−	2.03358i	−1.85326	−	0.279334i	−0.874602	−	0.484842i	$-0.838877\pi$
$53$	−13.4919	−	2.03358i	−1.85326	−	0.279334i	−0.978655	+	0.205509i	$0.934115\pi$
$54$	−1.07970	−	1.00182i	−0.146929	−	0.136330i
$55$	−0.901837	−	3.95120i	−0.121604	−	0.532780i
$56$	6.74805	+	3.31047i	0.901746	+	0.442380i
$57$	−0.469406	+	2.05660i	−0.0621743	+	0.272404i
$58$	1.49837	−	1.02157i	0.196745	−	0.134139i
$59$	7.41658	−	6.88158i	0.965556	−	0.895905i	−0.0290552	−	0.999578i	$-0.509250\pi$
$59$	7.41658	−	6.88158i	0.965556	−	0.895905i	0.994611	+	0.103673i	$0.0330594\pi$
$60$	0.579911	+	0.395376i	0.0748661	+	0.0510429i
$61$	8.84072	−	1.33252i	1.13194	−	0.170612i	0.443754	−	0.896149i	$-0.353646\pi$
$61$	8.84072	−	1.33252i	1.13194	−	0.170612i	0.688184	+	0.725536i	$0.258408\pi$
$62$	3.93931	−	1.89707i	0.500292	−	0.240928i
$63$	−2.77032	−	7.21275i	−0.349028	−	0.908721i
$64$	−4.57589	−	2.20363i	−0.571986	−	0.275454i
$65$	7.03159	+	2.16896i	0.872161	+	0.269026i
$66$	−0.181185	+	0.461652i	−0.0223023	+	0.0568254i
$67$	5.76466	+	9.98468i	0.704265	+	1.21982i	0.966956	+	0.254943i	$0.0820567\pi$
$67$	5.76466	+	9.98468i	0.704265	+	1.21982i	−0.262691	+	0.964880i	$0.584610\pi$
$68$	−0.685194	+	1.18679i	−0.0830920	+	0.143920i
$69$	0.936820	+	1.17473i	0.112780	+	0.141421i
$70$	−2.34063	−	4.12318i	−0.279759	−	0.492814i
$71$	−2.62321	+	3.28940i	−0.311318	+	0.390380i	−0.912733	−	0.408556i	$-0.866032\pi$
$71$	−2.62321	+	3.28940i	−0.311318	+	0.390380i	0.601415	+	0.798937i	$0.294604\pi$
$72$	3.03102	+	7.72290i	0.357209	+	0.910153i
$73$	−0.880793	−	11.7534i	−0.103089	−	1.37563i	−0.773575	−	0.633705i	$-0.781533\pi$
$73$	−0.880793	−	11.7534i	−0.103089	−	1.37563i	0.670486	−	0.741922i	$-0.266086\pi$
$74$	−0.0542598	−	0.724047i	−0.00630758	−	0.0841687i
$75$	0.0893566	+	0.227677i	0.0103180	+	0.0262899i
$76$	5.69938	−	7.14679i	0.653763	−	0.819793i
$77$	−3.89223	+	3.55904i	−0.443561	+	0.405591i
$78$	−0.561417	−	0.703995i	−0.0635680	−	0.0797117i
$79$	−4.13300	+	7.15857i	−0.464999	+	0.805402i	−0.999201	−	0.0399547i	$-0.987279\pi$
$79$	−4.13300	+	7.15857i	−0.464999	+	0.805402i	0.534203	+	0.845357i	$0.320612\pi$
$80$	0.0588155	+	0.101871i	0.00657577	+	0.0113896i
$81$	3.02844	−	7.71633i	0.336493	−	0.857370i
$82$	5.04524	+	1.55625i	0.557154	+	0.171859i
$83$	8.17636	+	3.93753i	0.897472	+	0.432200i	0.824975	−	0.565169i	$-0.191189\pi$
$83$	8.17636	+	3.93753i	0.897472	+	0.432200i	0.0724970	+	0.997369i	$0.476903\pi$
$84$	0.0748902	−	0.910296i	0.00817119	−	0.0993215i
$85$	2.05235	−	0.988358i	0.222608	−	0.107202i
$86$	2.03225	−	0.306312i	0.219143	−	0.0330305i
$87$	−0.479814	−	0.327131i	−0.0514414	−	0.0350722i
$88$	4.15138	−	3.85192i	0.442538	−	0.410616i
$89$	−14.5109	+	9.89337i	−1.53815	+	1.04870i	−0.563191	+	0.826327i	$0.690426\pi$
$89$	−14.5109	+	9.89337i	−1.53815	+	1.04870i	−0.974963	+	0.222369i	$0.928621\pi$
$90$	1.16451	−	5.10207i	0.122751	−	0.537805i
$91$	−2.06278	−	9.35113i	−0.216238	−	0.980265i
$92$	−1.44883	−	6.34774i	−0.151051	−	0.661798i
$93$	−1.02636	−	0.952322i	−0.106428	−	0.0987512i
$94$	4.74747	+	0.715565i	0.489664	+	0.0738049i
$95$	−14.5198	+	4.47875i	−1.48969	+	0.459510i
$96$	−0.118770	+	1.58487i	−0.0121219	+	0.161756i
$97$	3.72740			0.378460			0.189230	−	0.981933i	$-0.439401\pi$
$97$	3.72740			0.378460			0.189230	+	0.981933i	$0.439401\pi$
$98$	−3.16251	+	5.29783i	−0.319462	+	0.535161i
$99$	−5.82147			−0.585080
$100$	0.0792035	−	1.05690i	0.00792035	−	0.105690i
$101$	−3.43384	+	1.05920i	−0.341679	+	0.105394i	−0.460846	−	0.887480i	$-0.652454\pi$
$101$	−3.43384	+	1.05920i	−0.341679	+	0.105394i	0.119167	+	0.992874i	$0.461978\pi$
$102$	−0.275632	−	0.0415449i	−0.0272917	−	0.00411355i
$103$	−5.42624	−	5.03481i	−0.534663	−	0.496095i	0.365999	−	0.930615i	$-0.380727\pi$
$103$	−5.42624	−	5.03481i	−0.534663	−	0.496095i	−0.900662	+	0.434521i	$0.856918\pi$
$104$	2.28803	+	10.0245i	0.224359	+	0.982983i
$105$	−0.955240	+	1.18009i	−0.0932219	+	0.115165i
$106$	−2.67613	+	11.7249i	−0.259929	+	1.13882i
$107$	−3.64697	+	2.48646i	−0.352566	+	0.240375i	−0.726632	−	0.687027i	$-0.758916\pi$
$107$	−3.64697	+	2.48646i	−0.352566	+	0.240375i	0.374066	+	0.927402i	$0.377963\pi$
$108$	1.49823	−	1.39016i	0.144168	−	0.133768i
$109$	3.55236	+	2.42196i	0.340255	+	0.231982i	0.721376	−	0.692543i	$-0.243510\pi$
$109$	3.55236	+	2.42196i	0.340255	+	0.231982i	−0.381122	+	0.924525i	$0.624462\pi$
$110$	−3.53235	+	0.532416i	−0.336796	+	0.0507639i
$111$	−0.209482	+	0.100881i	−0.0198832	+	0.00957523i
$112$	0.0775030	−	0.132009i	0.00732334	−	0.0124736i
$113$	11.2558	+	5.42048i	1.05885	+	0.509916i	0.880498	−	0.474050i	$-0.157208\pi$
$113$	11.2558	+	5.42048i	1.05885	+	0.509916i	0.178354	+	0.983966i	$0.442923\pi$
$114$	1.77675	+	0.548055i	0.166408	+	0.0513300i
$115$	−3.95406	+	10.0748i	−0.368718	+	0.939477i
$116$	1.25822	+	2.17930i	0.116823	+	0.202343i
$117$	5.28488	−	9.15368i	0.488587	−	0.846258i
$118$	−5.56010	−	6.97215i	−0.511849	−	0.641838i
$119$	−2.43705	−	1.68769i	−0.223404	−	0.154710i
$120$	1.01644	−	1.27458i	0.0927881	−	0.116353i
$121$	−2.56698	−	6.54055i	−0.233362	−	0.594596i
$122$	−0.588905	−	7.85840i	−0.0533170	−	0.711466i
$123$	−0.126348	−	1.68600i	−0.0113924	−	0.152021i
$124$	2.21658	+	5.64775i	0.199055	+	0.507183i
$125$	−7.43649	+	9.32507i	−0.665140	+	0.834060i
$126$	−6.52218	+	1.95991i	−0.581042	+	0.174602i
$127$	−3.46997	−	4.35120i	−0.307910	−	0.386107i	0.603667	−	0.797237i	$-0.293706\pi$
$127$	−3.46997	−	4.35120i	−0.307910	−	0.386107i	−0.911577	+	0.411130i	$0.865134\pi$
$128$	3.39251	−	5.87600i	0.299858	−	0.519370i
$129$	−0.329063	−	0.569955i	−0.0289724	−	0.0501817i
$130$	2.36959	−	6.03761i	0.207826	−	0.529533i
$131$	14.2825	+	4.40556i	1.24787	+	0.384916i	0.847183	−	0.531301i	$-0.178297\pi$
$131$	14.2825	+	4.40556i	1.24787	+	0.384916i	0.400683	+	0.916217i	$0.368773\pi$
$132$	−0.620024	−	0.298588i	−0.0539662	−	0.0259887i
$133$	14.3968	+	13.5548i	1.24836	+	1.17535i
$134$	9.15583	−	4.40922i	0.790944	−	0.380898i
$135$	−3.35942	+	0.506351i	−0.289133	+	0.0435797i
$136$	2.62995	+	1.79307i	0.225516	+	0.153754i
$137$	−0.612467	+	0.568286i	−0.0523266	+	0.0485520i	−0.705903	−	0.708309i	$-0.749458\pi$
$137$	−0.612467	+	0.568286i	−0.0523266	+	0.0485520i	0.653576	+	0.756861i	$0.273268\pi$
$138$	1.09425	−	0.746047i	0.0931488	−	0.0635078i
$139$	1.31718	−	5.77093i	0.111721	−	0.489484i	−0.887848	−	0.460137i	$-0.847800\pi$
$139$	1.31718	−	5.77093i	0.111721	−	0.489484i	0.999569	−	0.0293465i	$-0.00934262\pi$
$140$	5.94819	−	2.81130i	0.502714	−	0.237598i
$141$	−0.342110	−	1.49888i	−0.0288108	−	0.126229i
$142$	2.71846	+	2.52236i	0.228128	+	0.211672i
$143$	−7.13436	−	1.07533i	−0.596605	−	0.0899237i
$144$	0.161458	−	0.0498033i	0.0134549	−	0.00415028i
$145$	0.312594	−	4.17127i	0.0259595	−	0.346405i
$146$	−10.3887			−0.859778
$147$	1.94921	+	0.322909i	0.160768	+	0.0266331i
$148$	1.00753			0.0828184
$149$	0.681223	−	9.09029i	0.0558079	−	0.744705i	−0.897174	−	0.441678i	$-0.854384\pi$
$149$	0.681223	−	9.09029i	0.0558079	−	0.744705i	0.952982	−	0.303028i	$-0.0979974\pi$
$150$	0.206004	−	0.0635440i	0.0168202	−	0.00518834i
$151$	2.87758	+	0.433725i	0.234174	+	0.0352960i	0.265081	−	0.964226i	$-0.414601\pi$
$151$	2.87758	+	0.433725i	0.234174	+	0.0352960i	−0.0309069	+	0.999522i	$0.509840\pi$
$152$	−15.5643	−	14.4416i	−1.26243	−	1.17137i
$153$	−0.728094	−	3.18999i	−0.0588629	−	0.257895i
$154$	2.87188	+	3.65554i	0.231422	+	0.294572i
$155$	2.24416	−	9.83229i	0.180255	−	0.789749i
$156$	1.03237	−	0.703860i	0.0826560	−	0.0563539i
$157$	3.88611	−	3.60578i	0.310145	−	0.287773i	−0.509707	−	0.860348i	$-0.670246\pi$
$157$	3.88611	−	3.60578i	0.310145	−	0.287773i	0.819852	+	0.572576i	$0.194056\pi$
$158$	6.01985	+	4.10426i	0.478913	+	0.326518i
$159$	3.80814	−	0.573985i	0.302005	−	0.0455199i
$160$	−10.3143	+	4.96709i	−0.815414	+	0.392683i
$161$	13.9420	−	1.99764i	1.09878	−	0.157436i
$162$	−6.58286	−	3.17014i	−0.517198	−	0.249070i
$163$	−4.04529	−	1.24781i	−0.316851	−	0.0977356i	0.132250	−	0.991216i	$-0.457780\pi$
$163$	−4.04529	−	1.24781i	−0.316851	−	0.0977356i	−0.449102	+	0.893481i	$0.648256\pi$
$164$	−2.67665	+	6.81999i	−0.209011	+	0.532552i
$165$	0.571961	+	0.990665i	0.0445271	+	0.0771232i
$166$	3.99949	−	6.92732i	0.310421	−	0.537665i
$167$	5.46726	+	6.85572i	0.423069	+	0.530512i	0.946993	−	0.321253i	$-0.104104\pi$
$167$	5.46726	+	6.85572i	0.423069	+	0.530512i	−0.523924	+	0.851765i	$0.675533\pi$
$168$	−2.09546	−	0.331470i	−0.161668	−	0.0255735i
$169$	0.0622382	−	0.0780442i	0.00478755	−	0.00600340i
$170$	−0.733540	−	1.86903i	−0.0562600	−	0.143348i
$171$	1.63105	+	21.7648i	0.124729	+	1.66440i
$172$	0.213121	+	2.84390i	0.0162503	+	0.216845i
$173$	1.39588	+	3.55665i	0.106127	+	0.270407i	0.974066	−	0.226264i	$-0.0726511\pi$
$173$	1.39588	+	3.55665i	0.106127	+	0.270407i	−0.867939	+	0.496670i	$0.834556\pi$
$174$	−0.319140	+	0.400189i	−0.0241939	+	0.0303382i
$175$	2.26450	+	0.358209i	0.171180	+	0.0270781i
$176$	−0.0719108	−	0.0901733i	−0.00542048	−	0.00679707i
$177$	−1.42784	+	2.47308i	−0.107323	+	0.185888i
$178$	7.74005	+	13.4062i	0.580141	+	1.00483i
$179$	2.23558	−	5.69617i	0.167095	−	0.425752i	−0.822659	−	0.568536i	$-0.807510\pi$
$179$	2.23558	−	5.69617i	0.167095	−	0.425752i	0.989754	+	0.142784i	$0.0456053\pi$
$180$	6.93925	+	2.14047i	0.517221	+	0.159542i
$181$	−20.2282	−	9.74138i	−1.50355	−	0.724071i	−0.512639	−	0.858604i	$-0.671332\pi$
$181$	−20.2282	−	9.74138i	−1.50355	−	0.724071i	−0.990909	+	0.134533i	$0.957047\pi$
$182$	−8.35513	+	1.19715i	−0.619324	+	0.0887384i
$183$	−2.27360	+	1.09491i	−0.168069	+	0.0809380i
$184$	−14.9543	+	2.25400i	−1.10245	+	0.166167i
$185$	−1.38376	−	0.943431i	−0.101736	−	0.0693624i
$186$	−0.904657	+	0.839399i	−0.0663327	+	0.0615477i
$187$	−1.84540	+	1.25817i	−0.134949	+	0.0920066i
$188$	−1.48247	+	6.49512i	−0.108120	+	0.473705i
$189$	2.73128	+	3.47658i	0.198671	+	0.252884i
$190$	2.98024	+	13.0573i	0.216209	+	0.947274i
$191$	−10.4264	−	9.67431i	−0.754429	−	0.700008i	0.205994	−	0.978553i	$-0.433957\pi$
$191$	−10.4264	−	9.67431i	−0.754429	−	0.700008i	−0.960423	+	0.278545i	$0.910148\pi$
$192$	1.41751	+	0.213656i	0.102300	+	0.0154193i
$193$	6.27185	−	1.93461i	0.451457	−	0.139256i	−0.0606845	−	0.998157i	$-0.519328\pi$
$193$	6.27185	−	1.93461i	0.451457	−	0.139256i	0.512142	+	0.858901i	$0.328852\pi$
$194$	0.245519	−	3.27623i	0.0176273	−	0.235219i
$195$	−2.07696			−0.148734
$196$	−7.00294	−	4.92551i	−0.500210	−	0.351822i
$197$	17.7880			1.26734			0.633670	−	0.773603i	$-0.281548\pi$
$197$	17.7880			1.26734			0.633670	+	0.773603i	$0.281548\pi$
$198$	−0.383453	+	5.11683i	−0.0272509	+	0.363637i
$199$	−15.0295	+	4.63598i	−1.06541	+	0.328636i	−0.777410	−	0.628994i	$-0.783467\pi$
$199$	−15.0295	+	4.63598i	−1.06541	+	0.328636i	−0.288002	+	0.957630i	$0.592991\pi$
$200$	−2.43427	−	0.366907i	−0.172129	−	0.0259442i
$201$	−2.38549	−	2.21341i	−0.168259	−	0.156122i
$202$	0.704808	+	3.08797i	0.0495901	+	0.217269i
$203$	−4.92148	+	2.32605i	−0.345421	+	0.163256i
$204$	0.0860704	−	0.377099i	0.00602613	−	0.0264022i
$205$	10.0623	−	6.86034i	0.702779	−	0.479147i
$206$	−4.78281	+	4.43780i	−0.333234	+	0.309196i
$207$	12.8447	+	8.75740i	0.892771	+	0.608681i
$208$	0.207071	−	0.0312109i	0.0143578	−	0.00216409i
$209$	13.4230	−	6.46416i	0.928486	−	0.447135i
$210$	0.974332	+	0.917348i	0.0672353	+	0.0633030i
$211$	−8.40082	−	4.04562i	−0.578336	−	0.278512i	0.121761	−	0.992559i	$-0.461146\pi$
$211$	−8.40082	−	4.04562i	−0.578336	−	0.278512i	−0.700097	+	0.714047i	$0.746860\pi$
$212$	−15.9468	−	4.91895i	−1.09523	−	0.337835i
$213$	0.433852	−	1.10544i	0.0297270	−	0.0757432i
$214$	1.94528	+	3.36932i	0.132976	+	0.230322i
$215$	2.37027	−	4.10542i	0.161651	−	0.279988i
$216$	−2.95987	−	3.71155i	−0.201393	−	0.252539i
$217$	−12.5690	+	3.77697i	−0.853241	+	0.256397i
$218$	2.36279	−	2.96285i	0.160028	−	0.200669i
$219$	1.21539	+	3.09677i	0.0821285	+	0.209260i
$220$	−0.370435	−	4.94311i	−0.0249747	−	0.333264i
$221$	−0.303049	−	4.04390i	−0.0203853	−	0.272022i
$222$	0.0748722	+	0.190771i	0.00502509	+	0.0128037i
$223$	−3.60573	+	4.52144i	−0.241457	+	0.302778i	−0.887763	−	0.460301i	$-0.847742\pi$
$223$	−3.60573	+	4.52144i	−0.241457	+	0.302778i	0.646306	+	0.763079i	$0.276313\pi$
$224$	12.2476	+	8.48166i	0.818329	+	0.566705i
$225$	1.57780	+	1.97849i	0.105186	+	0.131900i
$226$	5.50579	−	9.53630i	0.366239	−	0.634345i
$227$	−6.63933	−	11.4997i	−0.440668	−	0.763259i	0.557071	−	0.830465i	$-0.311925\pi$
$227$	−6.63933	−	11.4997i	−0.440668	−	0.763259i	−0.997739	+	0.0672056i	$0.978592\pi$
$228$	−0.942618	+	2.40175i	−0.0624264	+	0.159060i
$229$	−20.4642	−	6.31236i	−1.35231	−	0.417132i	−0.467875	−	0.883795i	$-0.654980\pi$
$229$	−20.4642	−	6.31236i	−1.35231	−	0.417132i	−0.884436	+	0.466662i	$0.845456\pi$
$230$	8.59486	+	4.13906i	0.566728	+	0.272922i
$231$	0.753690	−	1.28374i	0.0495892	−	0.0844639i
$232$	5.26617	−	2.53605i	0.345741	−	0.166500i
$233$	23.6339	−	3.56224i	1.54831	−	0.233370i	0.681429	−	0.731885i	$-0.261359\pi$
$233$	23.6339	−	3.56224i	1.54831	−	0.233370i	0.866881	+	0.498514i	$0.166121\pi$
$234$	−7.69760	−	5.24813i	−0.503208	−	0.343081i
$235$	8.11796	−	7.53237i	0.529557	−	0.491357i
$236$	10.2243	−	6.97081i	0.665546	−	0.453761i
$237$	0.519165	−	2.27461i	0.0337234	−	0.147752i
$238$	−1.64394	+	2.03090i	−0.106561	+	0.131644i
$239$	−2.60391	−	11.4085i	−0.168433	−	0.737954i	−0.986625	−	0.163008i	$-0.947880\pi$
$239$	−2.60391	−	11.4085i	−0.168433	−	0.737954i	0.818192	−	0.574946i	$-0.194977\pi$
$240$	−0.0243386	−	0.0225829i	−0.00157105	−	0.00145772i
$241$	12.7510	+	1.92191i	0.821366	+	0.123801i	0.546263	−	0.837614i	$-0.316050\pi$
$241$	12.7510	+	1.92191i	0.821366	+	0.123801i	0.275103	+	0.961415i	$0.411288\pi$
$242$	−5.91796	+	1.82545i	−0.380421	+	0.117344i
$243$	−0.549475	+	7.33224i	−0.0352489	+	0.470363i
$244$	10.9352			0.700051
$245$	5.00582	+	13.3222i	0.319810	+	0.851125i
$246$	−1.49024			−0.0950145
$247$	−2.02147	+	26.9746i	−0.128623	+	1.71635i
$248$	13.4662	−	4.15379i	0.855107	−	0.263766i
$249$	−2.53286	−	0.381768i	−0.160514	−	0.0241935i
$250$	7.70652	+	7.15060i	0.487403	+	0.452244i
$251$	−2.83406	−	12.4168i	−0.178884	−	0.783744i	−0.982146	−	0.188118i	$-0.939761\pi$
$251$	−2.83406	−	12.4168i	−0.178884	−	0.783744i	0.803262	−	0.595626i	$-0.203096\pi$
$252$	−2.03569	−	9.22834i	−0.128236	−	0.581331i
$253$	2.36134	−	10.3457i	0.148456	−	0.650429i
$254$	−4.05309	+	2.76335i	−0.254314	+	0.173388i
$255$	−0.471319	+	0.437320i	−0.0295151	+	0.0273860i
$256$	−13.3340	−	9.09096i	−0.833375	−	0.568185i
$257$	−15.8576	+	2.39015i	−0.989172	+	0.149094i	−0.623645	−	0.781707i	$-0.714349\pi$
$257$	−15.8576	+	2.39015i	−0.989172	+	0.149094i	−0.365526	+	0.930801i	$0.619111\pi$
$258$	−0.522642	+	0.251691i	−0.0325382	+	0.0156696i
$259$	−0.178700	+	2.17211i	−0.0111039	+	0.134969i
$260$	8.10884	+	3.90501i	0.502889	+	0.242179i
$261$	−5.74148	−	1.77101i	−0.355389	−	0.109623i
$262$	4.81308	−	12.2635i	0.297353	−	0.757643i
$263$	3.50137	+	6.06455i	0.215904	+	0.373956i	0.953552	−	0.301229i	$-0.0973970\pi$
$263$	3.50137	+	6.06455i	0.215904	+	0.373956i	−0.737648	+	0.675185i	$0.764064\pi$
$264$	−0.799221	+	1.38429i	−0.0491886	+	0.0851972i
$265$	17.2957	+	21.6881i	1.06247	+	1.33229i
$266$	12.8624	−	11.7613i	0.788643	−	0.721133i
$267$	3.09071	−	3.87562i	0.189148	−	0.237184i
$268$	5.15183	+	13.1266i	0.314698	+	0.801838i
$269$	−1.42342	−	18.9942i	−0.0867874	−	1.15810i	−0.855254	−	0.518208i	$-0.826599\pi$
$269$	−1.42342	−	18.9942i	−0.0867874	−	1.15810i	0.768467	−	0.639890i	$-0.221020\pi$
$270$	0.223780	+	2.98614i	0.0136188	+	0.181731i
$271$	3.40664	+	8.67999i	0.206939	+	0.527272i	0.996230	−	0.0867470i	$-0.0276472\pi$
$271$	3.40664	+	8.67999i	0.206939	+	0.527272i	−0.789291	+	0.614019i	$0.789552\pi$
$272$	0.0404183	−	0.0506830i	0.00245072	−	0.00307311i
$273$	1.33433	+	2.35051i	0.0807575	+	0.142260i
$274$	0.459158	+	0.575765i	0.0277387	+	0.0347833i
$275$	0.863693	−	1.49596i	0.0520826	−	0.0902098i
$276$	0.918874	+	1.59154i	0.0553097	+	0.0957993i
$277$	−2.82229	+	7.19108i	−0.169575	+	0.432070i	−0.990246	−	0.139331i	$-0.955505\pi$
$277$	−2.82229	+	7.19108i	−0.169575	+	0.432070i	0.820671	+	0.571401i	$0.193600\pi$
$278$	−4.98565	−	1.53787i	−0.299019	−	0.0922352i
$279$	−13.0517	−	6.28537i	−0.781386	−	0.376296i
$280$	−5.47914	−	14.2654i	−0.327441	−	0.852518i
$281$	−26.3988	+	12.7130i	−1.57482	+	0.758394i	−0.998277	−	0.0586722i	$-0.981313\pi$
$281$	−26.3988	+	12.7130i	−1.57482	+	0.758394i	−0.576544	+	0.817066i	$0.695599\pi$
$282$	−1.33999	+	0.201971i	−0.0797952	+	0.0120272i
$283$	−3.34674	−	2.28177i	−0.198943	−	0.135637i	0.459751	−	0.888048i	$-0.347939\pi$
$283$	−3.34674	−	2.28177i	−0.198943	−	0.135637i	−0.658694	+	0.752411i	$0.728891\pi$
$284$	−3.77223	+	3.50011i	−0.223840	+	0.207694i
$285$	3.54356	−	2.41596i	0.209903	−	0.143109i
$286$	−1.41510	+	6.19998i	−0.0836769	+	0.366612i
$287$	−14.2283	−	6.98016i	−0.839873	−	0.412026i
$288$	3.65911	+	16.0316i	0.215615	+	0.944671i
$289$	11.5416	+	10.7091i	0.678920	+	0.629946i
$290$	−3.64579	−	0.549514i	−0.214088	−	0.0322686i
$291$	−1.00533	+	0.310103i	−0.0589335	+	0.0181786i
$292$	1.07729	−	14.3755i	0.0630437	−	0.841260i
$293$	−6.82335			−0.398624			−0.199312	−	0.979936i	$-0.563871\pi$
$293$	−6.82335			−0.398624			−0.199312	+	0.979936i	$0.563871\pi$
$294$	0.412216	−	1.69200i	0.0240409	−	0.0986797i
$295$	−20.5696			−1.19761
$296$	0.174884	−	2.33367i	0.0101650	−	0.135642i
$297$	3.18309	−	0.981854i	0.184702	−	0.0569730i
$298$	−7.94511	−	1.19753i	−0.460248	−	0.0693712i
$299$	14.1239	+	13.1051i	0.816807	+	0.757886i
$300$	0.0665669	+	0.291649i	0.00384324	+	0.0168384i
$301$	−6.16890	−	0.0449441i	−0.355570	−	0.00259053i
$302$	0.570769	−	2.50070i	0.0328440	−	0.143899i
$303$	0.838032	−	0.571360i	0.0481437	−	0.0328238i
$304$	−0.316984	+	0.294119i	−0.0181803	+	0.0168689i
$305$	−15.0185	−	10.2395i	−0.859959	−	0.586310i
$306$	−2.85183	+	0.429844i	−0.163028	+	0.0245725i
$307$	24.0748	−	11.5938i	1.37402	−	0.661694i	0.406306	−	0.913737i	$-0.366817\pi$
$307$	24.0748	−	11.5938i	1.37402	−	0.661694i	0.967716	+	0.252043i	$0.0811024\pi$
$308$	−5.35617	+	3.59490i	−0.305196	+	0.204838i
$309$	1.88240	+	0.906518i	0.107086	+	0.0515700i
$310$	−8.49436	−	2.62016i	−0.482447	−	0.148815i
$311$	−1.49322	+	3.80465i	−0.0846725	+	0.215742i	−0.966939	−	0.255009i	$-0.917922\pi$
$311$	−1.49322	+	3.80465i	−0.0846725	+	0.215742i	0.882266	+	0.470751i	$0.156017\pi$
$312$	−1.45111	−	2.51339i	−0.0821527	−	0.142293i
$313$	−13.7747	+	23.8585i	−0.778593	+	1.34856i	0.154159	+	0.988046i	$0.450733\pi$
$313$	−13.7747	+	23.8585i	−0.778593	+	1.34856i	−0.932752	+	0.360517i	$0.882600\pi$
$314$	−2.91336	−	3.65324i	−0.164410	−	0.206164i
$315$	−5.84539	+	14.5805i	−0.329350	+	0.821521i
$316$	−6.30354	+	7.90438i	−0.354602	+	0.444656i
$317$	2.31786	+	5.90580i	0.130184	+	0.331703i	0.981072	−	0.193644i	$-0.0620307\pi$
$317$	2.31786	+	5.90580i	0.130184	+	0.331703i	−0.850888	+	0.525347i	$0.823935\pi$
$318$	−0.253671	−	3.38500i	−0.0142252	−	0.189822i
$319$	0.306495	+	4.08989i	0.0171604	+	0.228990i
$320$	3.77243	+	9.61199i	0.210885	+	0.537327i
$321$	0.776775	−	0.974045i	0.0433554	−	0.0543659i
$322$	−0.837505	−	12.3860i	−0.0466723	−	0.690244i
$323$	5.22098	+	6.54690i	0.290503	+	0.364279i
$324$	5.06932	−	8.78032i	0.281629	−	0.487795i
$325$	1.56817	+	2.71614i	0.0869862	+	0.150664i
$326$	−1.36323	+	3.47345i	−0.0755022	+	0.192376i
$327$	−1.15962	−	0.357694i	−0.0641270	−	0.0197806i
$328$	15.3321	+	7.38354i	0.846572	+	0.407688i
$329$	−13.7398	−	4.34803i	−0.757498	−	0.239715i
$330$	0.908428	−	0.437476i	0.0500073	−	0.0240823i
$331$	5.92680	−	0.893321i	0.325766	−	0.0491014i	0.0158769	−	0.999874i	$-0.494946\pi$
$331$	5.92680	−	0.893321i	0.325766	−	0.0491014i	0.309890	+	0.950773i	$0.399708\pi$
$332$	9.17097	+	6.25266i	0.503322	+	0.343159i
$333$	−1.76346	+	1.63625i	−0.0966369	+	0.0896660i
$334$	6.38602	−	4.35391i	0.349427	−	0.238236i
$335$	5.21592	−	22.8525i	0.284976	−	1.24856i
$336$	−0.00992107	+	0.0420524i	−0.000541239	+	0.00229415i
$337$	−1.51230	−	6.62581i	−0.0823801	−	0.360931i	0.916890	−	0.399141i	$-0.130692\pi$
$337$	−1.51230	−	6.62581i	−0.0823801	−	0.360931i	−0.999270	+	0.0382101i	$0.987834\pi$
$338$	−0.0644981	−	0.0598455i	−0.00350823	−	0.00325517i
$339$	−3.48679	−	0.525549i	−0.189376	−	0.0285439i
$340$	2.66234	−	0.821224i	0.144386	−	0.0445371i
$341$	−0.738960	+	9.86074i	−0.0400169	+	0.533989i
$342$	19.2378			1.04026
$343$	11.8609	−	14.2239i	0.640428	−	0.768019i
$344$	6.62411			0.357148
$345$	0.228286	−	3.04626i	0.0122905	−	0.164005i
$346$	3.21809	−	0.992649i	0.173006	−	0.0533652i
$347$	13.2639	+	1.99922i	0.712045	+	0.107324i	0.495069	−	0.868853i	$-0.335143\pi$
$347$	13.2639	+	1.99922i	0.712045	+	0.107324i	0.216976	+	0.976177i	$0.430381\pi$
$348$	−0.520668	−	0.483110i	−0.0279107	−	0.0258974i
$349$	−1.84229	−	8.07162i	−0.0986157	−	0.432064i	0.901384	−	0.433021i	$-0.142552\pi$
$349$	−1.84229	−	8.07162i	−0.0986157	−	0.432064i	−1.00000		0.000957302i	$0.999695\pi$
$350$	0.464011	−	1.96680i	0.0248024	−	0.105130i
$351$	−1.34583	+	5.89645i	−0.0718349	+	0.314729i
$352$	9.27422	−	6.32306i	0.494318	−	0.337020i
$353$	−2.87036	+	2.66330i	−0.152774	+	0.141753i	−0.752857	−	0.658185i	$-0.771325\pi$
$353$	−2.87036	+	2.66330i	−0.152774	+	0.141753i	0.600083	+	0.799938i	$0.295134\pi$
$354$	2.07969	+	1.41791i	0.110534	+	0.0753609i
$355$	8.45829	−	1.27488i	0.448919	−	0.0676637i
$356$	−19.3534	+	9.32013i	−1.02573	+	0.493966i
$357$	0.797715	+	0.252441i	0.0422195	+	0.0133606i
$358$	−4.85945	−	2.34019i	−0.256830	−	0.123683i
$359$	28.8513	+	8.89945i	1.52271	+	0.469695i	0.939478	−	0.342608i	$-0.111310\pi$
$359$	28.8513	+	8.89945i	1.52271	+	0.469695i	0.583235	+	0.812303i	$0.301787\pi$
$360$	6.16233	−	15.7014i	0.324783	−	0.827534i
$361$	−18.4285	−	31.9190i	−0.969919	−	1.67995i
$362$	−9.89467	+	17.1381i	−0.520053	+	0.900757i
$363$	1.23649	+	1.55052i	0.0648991	+	0.0813809i
$364$	−0.790146	−	11.6856i	−0.0414149	−	0.612491i
$365$	−14.9405	+	18.7348i	−0.782020	+	0.980623i
$366$	0.812620	+	2.07052i	0.0424763	+	0.108228i
$367$	1.44656	+	19.3031i	0.0755100	+	1.00761i	0.898333	+	0.439314i	$0.144779\pi$
$367$	1.44656	+	19.3031i	0.0755100	+	1.00761i	−0.822823	+	0.568297i	$0.807602\pi$
$368$	0.0230169	+	0.307140i	0.00119984	+	0.0160108i
$369$	−6.39094	−	16.2838i	−0.332699	−	0.847703i
$370$	−0.920384	+	1.15412i	−0.0478485	+	0.0600001i
$371$	13.4331	−	33.5071i	0.697411	−	1.73960i
$372$	−1.06771	−	1.33887i	−0.0553582	−	0.0694170i
$373$	−8.10061	+	14.0307i	−0.419434	+	0.726481i	−0.995883	−	0.0906525i	$-0.971105\pi$
$373$	−8.10061	+	14.0307i	−0.419434	+	0.726481i	0.576449	+	0.817133i	$0.304438\pi$
$374$	0.984326	+	1.70490i	0.0508983	+	0.0881584i
$375$	1.22992	−	3.13378i	0.0635128	−	0.161828i
$376$	14.7869	+	4.56115i	0.762575	+	0.235223i
$377$	−6.70919	−	3.23098i	−0.345541	−	0.166404i
$378$	3.23567	−	2.17168i	0.166425	−	0.111699i
$379$	1.58848	−	0.764970i	0.0815946	−	0.0392939i	−0.392641	−	0.919692i	$-0.628439\pi$
$379$	1.58848	−	0.764970i	0.0815946	−	0.0392939i	0.474236	+	0.880398i	$0.342724\pi$
$380$	−18.3771	+	2.76990i	−0.942725	+	0.142093i
$381$	1.29790	+	0.884893i	0.0664934	+	0.0453344i
$382$	−9.19009	+	8.52716i	−0.470206	+	0.436287i
$383$	10.3539	−	7.05918i	0.529060	−	0.360707i	−0.269138	−	0.963102i	$-0.586739\pi$
$383$	10.3539	−	7.05918i	0.529060	−	0.360707i	0.798199	+	0.602394i	$0.205786\pi$
$384$	−0.426149	+	1.86708i	−0.0217468	+	0.0952790i
$385$	10.7225	+	0.0781194i	0.546467	+	0.00398134i
$386$	−1.28732	−	5.64013i	−0.0655230	−	0.287075i
$387$	−4.99157	−	4.63150i	−0.253736	−	0.235433i
$388$	4.50803	+	0.679477i	0.228861	+	0.0344952i
$389$	16.8248	−	5.18977i	0.853053	−	0.263132i	0.162763	−	0.986665i	$-0.447959\pi$
$389$	16.8248	−	5.18977i	0.853053	−	0.263132i	0.690290	+	0.723533i	$0.257483\pi$
$390$	−0.136807	+	1.82556i	−0.00692750	+	0.0924411i
$391$	5.96447			0.301636
$392$	−12.6242	+	15.3655i	−0.637617	+	0.776074i
$393$	−4.21871			−0.212806
$394$	1.17167	−	15.6349i	0.0590281	−	0.787675i
$395$	16.0589	−	4.95352i	0.808011	−	0.249239i
$396$	−7.04067	−	1.06121i	−0.353807	−	0.0533278i
$397$	4.19877	+	3.89589i	0.210730	+	0.195529i	0.778475	−	0.627676i	$-0.215994\pi$
$397$	4.19877	+	3.89589i	0.210730	+	0.195529i	−0.567745	+	0.823204i	$0.692184\pi$
$398$	3.08486	+	13.5157i	0.154630	+	0.677479i
$399$	−5.01070	−	2.45816i	−0.250849	−	0.123062i
$400$	−0.0111564	+	0.0488795i	−0.000557821	+	0.00244397i
$401$	3.22300	−	2.19741i	0.160949	−	0.109733i	−0.480167	−	0.877177i	$-0.659424\pi$
$401$	3.22300	−	2.19741i	0.160949	−	0.109733i	0.641116	+	0.767444i	$0.278472\pi$
$402$	−2.10263	+	1.95095i	−0.104869	+	0.0973046i
$403$	−14.8342	−	10.1138i	−0.738943	−	0.503803i
$404$	−4.34607	+	0.655065i	−0.216225	+	0.0325907i
$405$	−15.1840	+	7.31224i	−0.754500	+	0.363348i
$406$	1.72033	+	4.47900i	0.0853783	+	0.222289i
$407$	1.47948	+	0.712479i	0.0733350	+	0.0353163i
$408$	−0.858508	−	0.264815i	−0.0425025	−	0.0131103i
$409$	8.42068	−	21.4555i	0.416376	−	1.06091i	−0.556759	−	0.830674i	$-0.687955\pi$
$409$	8.42068	−	21.4555i	0.416376	−	1.06091i	0.973135	−	0.230235i	$-0.0739494\pi$
$410$	−5.36717	−	9.29620i	−0.265065	−	0.459107i
$411$	0.117912	−	0.204229i	0.00581616	−	0.0100739i
$412$	−5.64485	−	7.07842i	−0.278102	−	0.348729i
$413$	13.2148	+	23.2788i	0.650259	+	1.14547i
$414$	8.54346	−	10.7132i	0.419888	−	0.526523i
$415$	−6.74071	−	17.1750i	−0.330888	−	0.843090i
$416$	1.52300	+	20.3230i	0.0746712	+	0.996418i
$417$	0.124856	+	1.66608i	0.00611420	+	0.0815884i
$418$	−4.79758	−	12.2240i	−0.234657	−	0.597896i
$419$	−1.69685	+	2.12778i	−0.0828965	+	0.103949i	−0.821550	−	0.570136i	$-0.806890\pi$
$419$	−1.69685	+	2.12778i	−0.0828965	+	0.103949i	0.738654	+	0.674085i	$0.235462\pi$
$420$	−1.37042	+	1.25311i	−0.0668696	+	0.0611454i
$421$	3.17877	+	3.98606i	0.154924	+	0.194269i	0.853236	−	0.521525i	$-0.174637\pi$
$421$	3.17877	+	3.98606i	0.154924	+	0.194269i	−0.698312	+	0.715793i	$0.746065\pi$
$422$	−4.10929	+	7.11749i	−0.200037	+	0.346474i
$423$	−7.95349	−	13.7758i	−0.386712	−	0.669805i
$424$	−14.1614	+	36.0828i	−0.687740	+	1.75233i
$425$	0.927763	+	0.286177i	0.0450031	+	0.0138816i
$426$	−0.943055	−	0.454152i	−0.0456912	−	0.0220037i
$427$	−1.93951	+	23.5749i	−0.0938595	+	1.14087i
$428$	−4.86403	+	2.34239i	−0.235112	+	0.113224i
$429$	2.01370	−	0.303516i	0.0972222	−	0.0146539i
$430$	−3.45237	−	2.35379i	−0.166488	−	0.113510i
$431$	−10.7225	+	9.94903i	−0.516485	+	0.479228i	−0.894812	−	0.446444i	$-0.852690\pi$
$431$	−10.7225	+	9.94903i	−0.516485	+	0.479228i	0.378326	+	0.925672i	$0.376500\pi$
$432$	−0.0798832	+	0.0544635i	−0.00384338	+	0.00262037i
$433$	−3.42780	+	15.0182i	−0.164729	+	0.721727i	0.823319	+	0.567580i	$0.192120\pi$
$433$	−3.42780	+	15.0182i	−0.164729	+	0.721727i	−0.988048	+	0.154147i	$0.950737\pi$
$434$	2.49189	+	11.2964i	0.119615	+	0.542246i
$435$	0.262721	+	1.15106i	0.0125965	+	0.0551889i
$436$	3.85483	+	3.57676i	0.184613	+	0.171296i
$437$	−39.3412	−	5.92974i	−1.88195	−	0.283658i
$438$	2.80199	−	0.864298i	0.133884	−	0.0412978i
$439$	0.321848	−	4.29476i	0.0153609	−	0.204978i	−0.984243	−	0.176823i	$-0.943418\pi$
$439$	0.321848	−	4.29476i	0.0153609	−	0.204978i	0.999604	−	0.0281544i	$-0.00896302\pi$
$440$	−11.5137			−0.548893
$441$	20.2563	−	2.75192i	0.964584	−	0.131044i
$442$	−3.57439			−0.170016
$443$	−0.174580	+	2.32961i	−0.00829454	+	0.110683i	−0.999814	−	0.0192735i	$-0.993865\pi$
$443$	−0.174580	+	2.32961i	−0.00829454	+	0.110683i	0.991520	+	0.129956i	$0.0414837\pi$
$444$	−0.271744	+	0.0838221i	−0.0128964	+	0.00397802i
$445$	35.3076	+	5.32176i	1.67374	+	0.252276i
$446$	3.73665	+	3.46711i	0.176936	+	0.164172i
$447$	0.572537	+	2.50845i	0.0270801	+	0.118646i
$448$	8.45439	−	10.4445i	0.399432	−	0.493454i
$449$	−3.93304	+	17.2318i	−0.185612	+	0.813219i	0.793283	+	0.608853i	$0.208370\pi$
$449$	−3.93304	+	17.2318i	−0.185612	+	0.813219i	−0.978895	+	0.204365i	$0.934487\pi$
$450$	1.84294	−	1.25650i	0.0868771	−	0.0592318i
$451$	−8.75323	+	8.12181i	−0.412174	+	0.382441i
$452$	12.6250	+	8.60755i	0.593828	+	0.404865i
$453$	−0.812205	+	0.122420i	−0.0381607	+	0.00575181i
$454$	−10.5450	+	5.07823i	−0.494904	+	0.238333i
$455$	−9.85696	+	16.7891i	−0.462102	+	0.787084i
$456$	5.39939	+	2.60021i	0.252850	+	0.121766i
$457$	1.20613	+	0.372040i	0.0564202	+	0.0174033i	0.322837	−	0.946455i	$-0.395364\pi$
$457$	1.20613	+	0.372040i	0.0564202	+	0.0174033i	−0.266417	+	0.963858i	$0.585840\pi$
$458$	−6.89625	+	17.5714i	−0.322241	+	0.821056i
$459$	0.936137	+	1.62144i	0.0436951	+	0.0756822i
$460$	−6.61872	+	11.4640i	−0.308599	+	0.534509i
$461$	−5.47928	−	6.87080i	−0.255195	−	0.320005i	0.637686	−	0.770296i	$-0.279892\pi$
$461$	−5.47928	−	6.87080i	−0.255195	−	0.320005i	−0.892882	+	0.450291i	$0.851320\pi$
$462$	−1.07871	−	0.747021i	−0.0501861	−	0.0347546i
$463$	22.6266	−	28.3729i	1.05155	−	1.31860i	0.105553	−	0.994414i	$-0.466339\pi$
$463$	22.6266	−	28.3729i	1.05155	−	1.31860i	0.945994	−	0.324185i	$-0.105090\pi$
$464$	−0.0434902	−	0.110811i	−0.00201898	−	0.00514428i
$465$	0.212724	+	2.83861i	0.00986485	+	0.131637i
$466$	−1.57432	−	21.0079i	−0.0729291	−	0.973172i
$467$	−10.8812	−	27.7249i	−0.503522	−	1.28295i	−0.926323	−	0.376731i	$-0.877048\pi$
$467$	−10.8812	−	27.7249i	−0.503522	−	1.28295i	0.422800	−	0.906223i	$-0.361047\pi$
$468$	8.06035	−	10.1074i	0.372590	−	0.467213i
$469$	−29.2132	+	8.77853i	−1.34894	+	0.405355i
$470$	−6.08592	−	7.63150i	−0.280722	−	0.352015i
$471$	−0.748151	+	1.29584i	−0.0344730	+	0.0597089i
$472$	−14.3713	−	24.8918i	−0.661493	−	1.14574i
$473$	−1.69812	+	4.32675i	−0.0780798	+	0.198944i
$474$	−1.96509	−	0.606151i	−0.0902597	−	0.0278414i
$475$	−5.83495	−	2.80997i	−0.267726	−	0.128930i
$476$	−2.63979	−	2.48540i	−0.120995	−	0.113918i
$477$	35.8999	−	17.2885i	1.64375	−	0.791586i
$478$	−10.1991	+	1.53727i	−0.466496	+	0.0703130i
$479$	30.8915	+	21.0614i	1.41147	+	0.962322i	0.998673	+	0.0514977i	$0.0163995\pi$
$479$	30.8915	+	21.0614i	1.41147	+	0.962322i	0.412794	+	0.910824i	$0.364553\pi$
$480$	2.36866	−	2.19779i	0.108114	−	0.100315i
$481$	−2.46341	+	1.67952i	−0.112322	+	0.0765797i
$482$	2.52917	−	11.0810i	0.115201	−	0.504727i
$483$	−3.59414	+	1.69870i	−0.163539	+	0.0772936i
$484$	−1.91229	−	8.37829i	−0.0869223	−	0.380832i
$485$	−5.55517	−	5.15444i	−0.252247	−	0.234051i
$486$	6.40854	+	0.965932i	0.290697	+	0.0438156i
$487$	31.9034	−	9.84090i	1.44568	−	0.445934i	0.530055	−	0.847963i	$-0.322171\pi$
$487$	31.9034	−	9.84090i	1.44568	−	0.445934i	0.915627	+	0.402029i	$0.131695\pi$
$488$	1.89810	−	25.3283i	0.0859228	−	1.14656i
$489$	1.19488			0.0540344
$490$	12.0394	−	3.52239i	0.543885	−	0.159125i
$491$	−1.56442			−0.0706015			−0.0353007	−	0.999377i	$-0.511239\pi$
$491$	−1.56442			−0.0706015			−0.0353007	+	0.999377i	$0.511239\pi$
$492$	0.154535	−	2.06213i	0.00696699	−	0.0929680i
$493$	−2.20280	+	0.679475i	−0.0992093	+	0.0306020i
$494$	23.5764	+	3.55357i	1.06075	+	0.159883i
$495$	8.67609	+	8.05024i	0.389961	+	0.361831i
$496$	−0.0638647	−	0.279810i	−0.00286761	−	0.0125638i
$497$	−6.87677	−	8.75327i	−0.308465	−	0.392638i
$498$	−0.502395	+	2.20113i	−0.0225128	+	0.0986352i
$499$	−26.8259	+	18.2896i	−1.20089	+	0.818753i	−0.987408	−	0.158193i	$-0.949433\pi$
$499$	−26.8259	+	18.2896i	−1.20089	+	0.818753i	−0.213483	+	0.976947i	$0.568481\pi$
$500$	−10.6938	+	9.92242i	−0.478242	+	0.443744i
$501$	−2.04496	−	1.39423i	−0.0913621	−	0.0622896i
$502$	−11.1006	+	1.67314i	−0.495442	+	0.0746759i
$503$	23.6844	−	11.4058i	1.05604	−	0.508561i	0.176455	−	0.984309i	$-0.443537\pi$
$503$	23.6844	−	11.4058i	1.05604	−	0.508561i	0.879582	+	0.475748i	$0.157823\pi$
$504$	−21.7283	+	3.11329i	−0.967856	+	0.138677i
$505$	6.58237	+	3.16990i	0.292912	+	0.141059i
$506$	−8.93791	−	2.75698i	−0.397339	−	0.122563i
$507$	−0.0102936	+	0.0262275i	−0.000457153	+	0.00116481i
$508$	−3.40350	−	5.89503i	−0.151006	−	0.261550i
$509$	9.44590	−	16.3608i	0.418682	−	0.725179i	−0.577125	−	0.816656i	$-0.695826\pi$
$509$	9.44590	−	16.3608i	0.418682	−	0.725179i	0.995807	+	0.0914771i	$0.0291588\pi$
$510$	0.353341	+	0.443076i	0.0156462	+	0.0196197i
$511$	30.8007	+	4.87221i	1.36254	+	0.215534i
$512$	−0.408092	+	0.511731i	−0.0180353	+	0.0226155i
$513$	−4.56270	−	11.6256i	−0.201448	−	0.513282i
$514$	1.05632	+	14.0956i	0.0465924	+	0.621732i
$515$	1.12465	+	15.0074i	0.0495579	+	0.661304i
$516$	−0.294081	−	0.749307i	−0.0129462	−	0.0329864i
$517$	−6.76994	+	8.48924i	−0.297742	+	0.373356i
$518$	1.89743	+	0.300145i	0.0833682	+	0.0131876i
$519$	−0.672386	−	0.843145i	−0.0295145	−	0.0370100i
$520$	10.4524	−	18.1041i	0.458369	−	0.793918i
$521$	7.75661	+	13.4348i	0.339823	+	0.588591i	0.984399	−	0.175949i	$-0.0562994\pi$
$521$	7.75661	+	13.4348i	0.339823	+	0.588591i	−0.644576	+	0.764540i	$0.722966\pi$
$522$	−1.93483	+	4.92987i	−0.0846853	+	0.215775i
$523$	−34.6951	−	10.7020i	−1.51711	−	0.467967i	−0.579301	−	0.815113i	$-0.696675\pi$
$523$	−34.6951	−	10.7020i	−1.51711	−	0.467967i	−0.937811	+	0.347146i	$0.887151\pi$
$524$	16.4706	+	7.93182i	0.719521	+	0.346503i
$525$	−0.640567	+	0.0917822i	−0.0279566	+	0.00400570i
$526$	5.56112	−	2.67809i	0.242476	−	0.116770i
$527$	−5.49581	+	0.828360i	−0.239401	+	0.0360839i
$528$	0.0268974	+	0.0183383i	0.00117056	+	0.000798073i
$529$	−3.91331	+	3.63102i	−0.170144	+	0.157870i
$530$	20.2022	−	13.7736i	0.877527	−	0.598288i
$531$	−6.57464	+	28.8054i	−0.285315	+	1.25005i
$532$	14.9410	+	19.0180i	0.647773	+	0.824534i
$533$	−4.82433	−	21.1368i	−0.208965	−	0.915536i
$534$	−3.20293	−	2.97189i	−0.138604	−	0.128606i
$535$	8.87372	+	1.33750i	0.383644	+	0.0578251i
$536$	31.2986	−	9.65434i	1.35189	−	0.417004i
$537$	−0.129071	+	1.72233i	−0.00556981	+	0.0743239i
$538$	−16.7889			−0.723821
$539$	−6.80018	−	12.1849i	−0.292904	−	0.524840i
$540$	−4.15529			−0.178815
$541$	1.71802	−	22.9253i	0.0738633	−	0.985637i	−0.829985	−	0.557785i	$-0.811651\pi$
$541$	1.71802	−	22.9253i	0.0738633	−	0.985637i	0.903849	−	0.427852i	$-0.140730\pi$
$542$	7.85374	−	2.42256i	0.337347	−	0.104058i
$543$	6.26626	+	0.944486i	0.268911	+	0.0405318i
$544$	4.62477	+	4.29116i	0.198286	+	0.183982i
$545$	−1.94509	−	8.52199i	−0.0833184	−	0.365042i
$546$	2.15390	−	1.01800i	0.0921783	−	0.0435663i
$547$	−0.402078	+	1.76162i	−0.0171916	+	0.0753213i	−0.982796	−	0.184694i	$-0.940871\pi$
$547$	−0.402078	+	1.76162i	−0.0171916	+	0.0753213i	0.965604	+	0.260016i	$0.0837277\pi$
$548$	−0.844331	+	0.575655i	−0.0360680	+	0.0245908i
$549$	−19.1396	+	17.7589i	−0.816858	+	0.757933i
$550$	−1.25800	−	0.857688i	−0.0536412	−	0.0365719i
$551$	15.2051	−	2.29180i	0.647758	−	0.0976338i
$552$	3.84586	−	1.85207i	0.163691	−	0.0788293i
$553$	−15.9229	−	14.9916i	−0.677110	−	0.637509i
$554$	6.13476	+	2.95435i	0.260641	+	0.125518i
$555$	0.451708	+	0.139334i	0.0191739	+	0.00591438i
$556$	2.64503	−	6.73943i	0.112174	−	0.285816i
$557$	−0.0865296	−	0.149874i	−0.00366638	−	0.00635035i	0.864186	−	0.503172i	$-0.167834\pi$
$557$	−0.0865296	−	0.149874i	−0.00366638	−	0.00635035i	−0.867853	+	0.496821i	$0.834500\pi$
$558$	−6.38429	+	11.0579i	−0.270268	+	0.468119i
$559$	−5.26178	−	6.59806i	−0.222549	−	0.279068i
$560$	−0.298056	+	0.0895653i	−0.0125952	+	0.00378482i
$561$	0.393055	−	0.492875i	0.0165948	−	0.0208092i
$562$	9.43534	+	24.0409i	0.398006	+	1.01410i
$563$	−0.508314	−	6.78298i	−0.0214229	−	0.285869i	−0.997618	−	0.0689759i	$-0.978027\pi$
$563$	−0.508314	−	6.78298i	−0.0214229	−	0.285869i	0.976195	−	0.216893i	$-0.0695922\pi$
$564$	−0.140524	−	1.87516i	−0.00591711	−	0.0789584i
$565$	−9.27940	−	23.6435i	−0.390387	−	0.994691i
$566$	−2.22602	+	2.79134i	−0.0935667	+	0.117329i
$567$	18.0302	+	12.4862i	0.757197	+	0.524370i
$568$	7.45230	+	9.34489i	0.312692	+	0.392103i
$569$	−15.8713	+	27.4899i	−0.665358	+	1.15243i	0.313830	+	0.949479i	$0.398388\pi$
$569$	−15.8713	+	27.4899i	−0.665358	+	1.15243i	−0.979188	+	0.202955i	$0.934945\pi$
$570$	−1.89012	−	3.27378i	−0.0791684	−	0.137124i
$571$	−13.0140	+	33.1590i	−0.544617	+	1.38766i	0.348275	+	0.937392i	$0.386768\pi$
$571$	−13.0140	+	33.1590i	−0.544617	+	1.38766i	−0.892892	+	0.450270i	$0.851328\pi$
$572$	−8.43250	−	2.60108i	−0.352580	−	0.108757i
$573$	3.61701	+	1.74186i	0.151103	+	0.0727672i
$574$	−7.07248	+	12.0464i	−0.295200	+	0.502805i
$575$	−4.15610	+	2.00147i	−0.173322	+	0.0834672i
$576$	14.6663	−	2.21059i	0.611095	−	0.0921078i
$577$	−0.103690	−	0.0706949i	−0.00431669	−	0.00294307i	0.561160	−	0.827707i	$-0.310355\pi$
$577$	−0.103690	−	0.0706949i	−0.00431669	−	0.00294307i	−0.565476	+	0.824764i	$0.691308\pi$
$578$	10.1731	−	9.43923i	0.423144	−	0.392620i
$579$	−1.53065	+	1.04358i	−0.0636117	+	0.0433697i
$580$	1.13845	−	4.98789i	0.0472717	−	0.207111i
$581$	−15.1066	+	18.6625i	−0.626728	+	0.774252i
$582$	0.206348	+	0.904070i	0.00855340	+	0.0374749i
$583$	−19.9382	−	18.5000i	−0.825757	−	0.766190i
$584$	−33.1099	−	4.99051i	−1.37010	−	0.206509i
$585$	−20.5346	+	6.33408i	−0.849000	+	0.261882i
$586$	−0.449446	+	5.99744i	−0.0185664	+	0.247752i
$587$	−21.6190			−0.892311			−0.446155	−	0.894956i	$-0.647207\pi$
$587$	−21.6190			−0.892311			−0.446155	+	0.894956i	$0.647207\pi$
$588$	2.29857	+	0.745862i	0.0947915	+	0.0307588i
$589$	37.0735			1.52759
$590$	−1.35490	+	18.0798i	−0.0557802	+	0.744335i
$591$	−4.79766	+	1.47988i	−0.197349	+	0.0608742i
$592$	−0.0471286	−	0.00710350i	−0.00193698	−	0.000291952i
$593$	30.7265	+	28.5101i	1.26179	+	1.17077i	0.977247	+	0.212103i	$0.0680313\pi$
$593$	30.7265	+	28.5101i	1.26179	+	1.17077i	0.284540	+	0.958664i	$0.408159\pi$
$594$	−0.653343	−	2.86248i	−0.0268070	−	0.117449i
$595$	1.29826	+	5.88535i	0.0532233	+	0.241276i
$596$	2.48098	−	10.8699i	0.101625	−	0.445248i
$597$	3.66796	−	2.50078i	0.150120	−	0.102350i
$598$	12.4491	−	11.5511i	0.509083	−	0.472360i
$599$	−7.57891	−	5.16722i	−0.309666	−	0.211127i	0.398508	−	0.917165i	$-0.369528\pi$
$599$	−7.57891	−	5.16722i	−0.309666	−	0.211127i	−0.708174	+	0.706038i	$0.750481\pi$
$600$	0.687081	−	0.103561i	0.0280499	−	0.00422785i
$601$	−17.0184	+	8.19563i	−0.694195	+	0.334307i	−0.747491	−	0.664272i	$-0.768742\pi$
$601$	−17.0184	+	8.19563i	−0.694195	+	0.334307i	0.0532960	+	0.998579i	$0.483027\pi$
$602$	−0.445843	+	5.41925i	−0.0181712	+	0.220872i
$603$	−30.3351	−	14.6086i	−1.23534	−	0.594909i
$604$	3.40117	+	1.04912i	0.138392	+	0.0426881i
$605$	−5.21890	+	13.2975i	−0.212178	+	0.540622i
$606$	−0.447002	−	0.774230i	−0.0181582	−	0.0314509i
$607$	−10.8325	+	18.7625i	−0.439678	+	0.761545i	−0.997664	−	0.0683051i	$-0.978241\pi$
$607$	−10.8325	+	18.7625i	−0.439678	+	0.761545i	0.557986	+	0.829850i	$0.311574\pi$
$608$	−26.2385	−	32.9021i	−1.06411	−	1.33436i
$609$	1.13387	−	1.03681i	0.0459469	−	0.0420138i
$610$	−9.98933	+	12.5262i	−0.404456	+	0.507172i
$611$	−7.20255	−	18.3518i	−0.291384	−	0.742435i
$612$	−0.299069	−	3.99080i	−0.0120892	−	0.161318i
$613$	1.85572	+	24.7628i	0.0749517	+	1.00016i	0.900224	+	0.435426i	$0.143402\pi$
$613$	1.85572	+	24.7628i	0.0749517	+	1.00016i	−0.825273	+	0.564735i	$0.808979\pi$
$614$	−8.60471	−	21.9244i	−0.347258	−	0.884798i
$615$	−2.14318	+	2.68746i	−0.0864214	+	0.108369i
$616$	7.39690	+	13.0301i	0.298030	+	0.524999i
$617$	−18.7007	−	23.4499i	−0.752862	−	0.944059i	0.246825	−	0.969060i	$-0.420613\pi$
$617$	−18.7007	−	23.4499i	−0.752862	−	0.944059i	−0.999687	+	0.0250006i	$0.992041\pi$
$618$	0.920784	−	1.59484i	0.0370394	−	0.0641540i
$619$	−10.7544	−	18.6272i	−0.432256	−	0.748690i	0.564811	−	0.825220i	$-0.308949\pi$
$619$	−10.7544	−	18.6272i	−0.432256	−	0.748690i	−0.997067	+	0.0765305i	$0.975616\pi$
$620$	4.50651	−	11.4824i	0.180986	−	0.461144i
$621$	−8.50035	−	2.62201i	−0.341107	−	0.105218i
$622$	3.24577	+	1.56308i	0.130144	+	0.0626739i
$623$	−16.6605	−	43.3768i	−0.667488	−	1.73785i
$624$	−0.0532533	+	0.0256454i	−0.00213184	+	0.00102664i
$625$	19.6940	−	2.96839i	0.787758	−	0.118735i
$626$	20.0633	+	13.6789i	0.801892	+	0.546721i
$627$	−3.08257	+	2.86021i	−0.123106	+	0.114226i
$628$	5.35729	−	3.65254i	0.213779	−	0.145752i
$629$	−0.205378	+	0.899818i	−0.00818894	+	0.0358781i
$630$	12.4307	+	6.09826i	0.495250	+	0.242960i
$631$	8.96758	+	39.2895i	0.356994	+	1.56409i	0.760638	+	0.649176i	$0.224886\pi$
$631$	8.96758	+	39.2895i	0.356994	+	1.56409i	−0.403644	+	0.914916i	$0.632257\pi$
$632$	17.2142	+	15.9725i	0.684745	+	0.635351i
$633$	2.60239	+	0.392248i	0.103436	+	0.0155904i
$634$	5.34363	−	1.64829i	0.212223	−	0.0654621i
$635$	−0.845568	+	11.2833i	−0.0335553	+	0.447765i
$636$	4.71032			0.186776
$637$	25.3329	+	0.369150i	1.00373	+	0.0146262i
$638$	3.61504			0.143121
$639$	0.918188	−	12.2524i	0.0363229	−	0.484696i
$640$	−13.1817	+	4.06602i	−0.521053	+	0.160724i
$641$	−15.7961	−	2.38088i	−0.623908	−	0.0940389i	−0.170523	−	0.985354i	$-0.554546\pi$
$641$	−15.7961	−	2.38088i	−0.623908	−	0.0940389i	−0.453385	+	0.891315i	$0.649784\pi$
$642$	−0.804980	−	0.746912i	−0.0317700	−	0.0294783i
$643$	5.04636	+	22.1096i	0.199009	+	0.871916i	0.971528	+	0.236924i	$0.0761393\pi$
$643$	5.04636	+	22.1096i	0.199009	+	0.871916i	−0.772519	+	0.634992i	$0.781004\pi$
$644$	17.2260	+	0.125502i	0.678799	+	0.00494545i
$645$	−0.297740	+	1.30448i	−0.0117235	+	0.0513640i
$646$	6.09836	−	4.15779i	0.239937	−	0.163586i
$647$	26.0305	−	24.1528i	1.02336	−	0.949543i	0.0246228	−	0.999697i	$-0.492162\pi$
$647$	26.0305	−	24.1528i	1.02336	−	0.949543i	0.998742	+	0.0501534i	$0.0159710\pi$
$648$	−19.4573	−	13.2658i	−0.764356	−	0.521129i
$649$	19.9430	−	3.00593i	0.782832	−	0.117993i
$650$	2.49067	−	1.19944i	0.0976921	−	0.0470460i
$651$	3.07581	−	2.06439i	0.120551	−	0.0809098i
$652$	−4.66503	−	2.24656i	−0.182697	−	0.0879821i
$653$	10.1546	+	3.13229i	0.397382	+	0.122576i	0.487004	−	0.873400i	$-0.338090\pi$
$653$	10.1546	+	3.13229i	0.397382	+	0.122576i	−0.0896221	+	0.995976i	$0.528566\pi$
$654$	−0.390781	+	0.995695i	−0.0152808	+	0.0389347i
$655$	−15.1938	−	26.3165i	−0.593671	−	1.02827i
$656$	0.173288	−	0.300144i	0.00676576	−	0.0117186i
$657$	21.4605	+	26.9106i	0.837254	+	1.04988i
$658$	−4.72676	+	11.7903i	−0.184268	+	0.459634i
$659$	−18.0931	+	22.6881i	−0.704808	+	0.883802i	−0.997372	−	0.0724441i	$-0.976920\pi$
$659$	−18.0931	+	22.6881i	−0.704808	+	0.883802i	0.292564	+	0.956246i	$0.405492\pi$
$660$	0.511157	+	1.30241i	0.0198967	+	0.0506961i
$661$	0.606333	+	8.09095i	0.0235836	+	0.314701i	0.996503	+	0.0835568i	$0.0266280\pi$
$661$	0.606333	+	8.09095i	0.0235836	+	0.314701i	−0.972919	+	0.231145i	$0.925753\pi$
$662$	−0.394801	−	5.26825i	−0.0153444	−	0.204757i
$663$	0.418172	+	1.06548i	0.0162404	+	0.0413800i
$664$	16.0745	−	20.1568i	0.623811	−	0.782234i
$665$	−2.71213	−	40.1101i	−0.105172	−	1.55540i
$666$	1.32204	+	1.65779i	0.0512280	+	0.0642379i
$667$	5.47628	−	9.48519i	0.212042	−	0.367268i
$668$	5.36253	+	9.28817i	0.207482	+	0.359370i
$669$	0.596350	−	1.51947i	0.0230562	−	0.0587463i
$670$	−19.7428	−	6.08985i	−0.762731	−	0.235271i
$671$	16.0574	+	7.73284i	0.619889	+	0.298523i
$672$	−4.00899	−	1.26867i	−0.154650	−	0.0489400i
$673$	−12.9761	+	6.24897i	−0.500193	+	0.240880i	−0.666929	−	0.745121i	$-0.732392\pi$
$673$	−12.9761	+	6.24897i	−0.500193	+	0.240880i	0.166736	+	0.986002i	$0.446677\pi$
$674$	−5.92342	+	0.892812i	−0.228162	+	0.0343898i
$675$	−1.19641	−	0.815699i	−0.0460498	−	0.0313963i
$676$	0.0894998	−	0.0830436i	0.00344230	−	0.00319399i
$677$	17.9144	−	12.2139i	0.688508	−	0.469417i	−0.167841	−	0.985814i	$-0.553680\pi$
$677$	17.9144	−	12.2139i	0.688508	−	0.469417i	0.856349	+	0.516397i	$0.172727\pi$
$678$	−0.691607	+	3.03013i	−0.0265610	+	0.116371i
$679$	−2.26444	+	9.59827i	−0.0869011	+	0.368348i
$680$	−1.44002	−	6.30915i	−0.0552223	−	0.241945i
$681$	2.74744	+	2.54925i	0.105282	+	0.0976875i
$682$	8.61851	+	1.29903i	0.330020	+	0.0497425i
$683$	−4.64443	+	1.43262i	−0.177714	+	0.0548176i	−0.382335	−	0.924024i	$-0.624880\pi$
$683$	−4.64443	+	1.43262i	−0.177714	+	0.0548176i	0.204621	+	0.978841i	$0.434404\pi$
$684$	−1.99492	+	26.6204i	−0.0762777	+	1.01786i
$685$	1.69865			0.0649022
$686$	−11.7210	−	11.3621i	−0.447508	−	0.433809i
$687$	6.04463			0.230617
$688$	0.0100816	−	0.134530i	0.000384358	−	0.00512891i
$689$	47.1898	−	14.5561i	1.79779	−	0.554544i
$690$	−2.66250	−	0.401308i	−0.101360	−	0.0152775i
$691$	23.9530	+	22.2251i	0.911215	+	0.845484i	0.988453	−	0.151529i	$-0.0484197\pi$
$691$	23.9530	+	22.2251i	0.911215	+	0.845484i	−0.0772383	+	0.997013i	$0.524610\pi$
$692$	1.03987	+	4.55598i	0.0395300	+	0.173192i
$693$	3.53661	−	14.9906i	0.134345	−	0.569447i
$694$	2.63091	−	11.5268i	0.0998679	−	0.437550i
$695$	−9.94341	+	6.77930i	−0.377175	+	0.257154i
$696$	−1.20937	+	1.12213i	−0.0458410	+	0.0425343i
$697$	−5.54528	−	3.78071i	−0.210042	−	0.143204i
$698$	−7.21597	+	1.08763i	−0.273128	+	0.0411675i
$699$	−6.07803	+	2.92702i	−0.229892	+	0.110710i
$700$	2.67345	+	0.846030i	0.101047	+	0.0319769i
$701$	17.6281	+	8.48923i	0.665803	+	0.320634i	0.736081	−	0.676894i	$-0.236674\pi$
$701$	17.6281	+	8.48923i	0.665803	+	0.320634i	−0.0702781	+	0.997527i	$0.522389\pi$
$702$	5.09409	+	1.57132i	0.192264	+	0.0593056i
$703$	2.24924	−	5.73096i	0.0848316	−	0.216147i
$704$	−5.06216	−	8.76792i	−0.190787	−	0.330453i
$705$	−1.56286	+	2.70696i	−0.0588609	+	0.101950i
$706$	2.15186	+	2.69835i	0.0809865	+	0.101554i
$707$	−0.641403	−	9.48580i	−0.0241224	−	0.356750i
$708$	−2.17769	+	2.73074i	−0.0818428	+	0.102628i
$709$	−12.3708	−	31.5204i	−0.464597	−	1.18377i	−0.950766	−	0.309908i	$-0.899702\pi$
$709$	−12.3708	−	31.5204i	−0.464597	−	1.18377i	0.486170	−	0.873864i	$-0.338394\pi$
$710$	−0.563431	−	7.51846i	−0.0211452	−	0.282163i
$711$	−1.80395	−	24.0720i	−0.0676532	−	0.902770i
$712$	18.2282	+	46.4448i	0.683133	+	1.74059i
$713$	16.4643	−	20.6455i	0.616591	−	0.773181i
$714$	0.274430	−	0.684530i	0.0102703	−	0.0256179i
$715$	9.14575	+	11.4684i	0.342031	+	0.428894i
$716$	3.74216	−	6.48160i	0.139851	−	0.242229i
$717$	1.65145	+	2.86039i	0.0616745	+	0.106823i
$718$	9.72265	−	24.7729i	0.362846	−	0.924517i
$719$	−12.9175	−	3.98453i	−0.481742	−	0.148598i	0.0443663	−	0.999015i	$-0.485873\pi$
$719$	−12.9175	−	3.98453i	−0.481742	−	0.148598i	−0.526108	+	0.850418i	$0.676349\pi$
$720$	−0.309502	−	0.149048i	−0.0115345	−	0.00555471i
$721$	16.2614	−	10.9142i	0.605608	−	0.406465i
$722$	−29.2694	+	14.0954i	−1.08929	+	0.524576i
$723$	−3.59902	+	0.542465i	−0.133849	+	0.0201745i
$724$	−22.6888	−	15.4690i	−0.843223	−	0.574900i
$725$	1.30693	−	1.21265i	0.0485381	−	0.0450368i
$726$	1.44429	−	0.984697i	0.0536025	−	0.0365455i
$727$	4.10803	−	17.9985i	0.152358	−	0.667526i	−0.839837	−	0.542838i	$-0.817350\pi$
$727$	4.10803	−	17.9985i	0.152358	−	0.667526i	0.992196	−	0.124688i	$-0.0397931\pi$
$728$	−27.2037	−	0.198195i	−1.00824	−	0.00734559i
$729$	5.07185	+	22.2212i	0.187846	+	0.823008i
$730$	15.4830	+	14.3661i	0.573051	+	0.531713i
$731$	−2.58331	−	0.389371i	−0.0955472	−	0.0144014i
$732$	−2.94936	+	0.909757i	−0.109011	+	0.0336256i
$733$	1.06286	−	14.1828i	0.0392575	−	0.523855i	−0.942561	−	0.334033i	$-0.891590\pi$
$733$	1.06286	−	14.1828i	0.0392575	−	0.523855i	0.981819	−	0.189821i	$-0.0607908\pi$
$734$	17.0619			0.629765
$735$	−2.45849	−	3.17672i	−0.0906827	−	0.117175i
$736$	−29.9750			−1.10489
$737$	−1.71751	+	22.9186i	−0.0632653	+	0.844217i
$738$	−14.7338	+	4.54477i	−0.542358	+	0.167295i
$739$	−22.1816	−	3.34334i	−0.815964	−	0.122987i	−0.272217	−	0.962236i	$-0.587757\pi$
$739$	−22.1816	−	3.34334i	−0.815964	−	0.122987i	−0.543747	+	0.839249i	$0.682995\pi$
$740$	−1.50158	−	1.39326i	−0.0551993	−	0.0512174i
$741$	−1.69895	−	7.44360i	−0.0624126	−	0.273447i
$742$	−28.5665	−	14.0142i	−1.04871	−	0.514477i
$743$	−1.99719	+	8.75028i	−0.0732700	+	0.321017i	−0.998259	−	0.0589761i	$-0.981216\pi$
$743$	−1.99719	+	8.75028i	−0.0732700	+	0.321017i	0.924989	+	0.379993i	$0.124074\pi$
$744$	−3.28645	+	2.24067i	−0.120487	+	0.0821468i
$745$	−13.5858	+	12.6058i	−0.497745	+	0.461840i
$746$	11.7988	+	8.04429i	0.431985	+	0.294522i
$747$	−26.2062	+	3.94996i	−0.958836	+	0.144521i
$748$	−2.46124	+	1.18527i	−0.0899918	+	0.0433378i
$749$	−4.18721	−	10.9017i	−0.152997	−	0.398340i
$750$	−2.67345	−	1.28747i	−0.0976207	−	0.0470116i
$751$	21.4956	+	6.63051i	0.784386	+	0.241951i	0.660978	−	0.750405i	$-0.270142\pi$
$751$	21.4956	+	6.63051i	0.784386	+	0.241951i	0.123407	+	0.992356i	$0.460618\pi$
$752$	0.115138	−	0.293367i	0.00419865	−	0.0106980i
$753$	1.79741	+	3.11321i	0.0655013	+	0.113452i
$754$	−3.28182	+	5.68428i	−0.119517	+	0.207009i
$755$	−3.68885	−	4.62567i	−0.134251	−	0.168345i
$756$	2.66954	+	4.70258i	0.0970904	+	0.171031i
$757$	1.47107	−	1.84466i	0.0534669	−	0.0670454i	−0.754379	−	0.656439i	$-0.772062\pi$
$757$	1.47107	−	1.84466i	0.0534669	−	0.0670454i	0.807846	+	0.589394i	$0.200633\pi$
$758$	−0.567746	−	1.44659i	−0.0206215	−	0.0525426i
$759$	0.223832	+	2.98683i	0.00812459	+	0.108415i
$760$	3.22588	+	43.0464i	0.117015	+	1.56146i
$761$	5.12400	+	13.0557i	0.185745	+	0.473270i	0.993167	−	0.116704i	$-0.0372330\pi$
$761$	5.12400	+	13.0557i	0.185745	+	0.473270i	−0.807422	+	0.589975i	$0.799138\pi$
$762$	0.863275	−	1.08251i	0.0312732	−	0.0392153i
$763$	−8.39479	+	7.67617i	−0.303912	+	0.277896i
$764$	−10.8465	−	13.6011i	−0.392412	−	0.492070i
$765$	−3.32616	+	5.76108i	−0.120258	+	0.208292i
$766$	−5.52273	−	9.56565i	−0.199544	−	0.345621i
$767$	−13.3783	+	34.0873i	−0.483061	+	1.23082i
$768$	4.35269	+	1.34263i	0.157064	+	0.0484479i
$769$	17.5379	+	8.44581i	0.632433	+	0.304564i	0.722499	−	0.691372i	$-0.242993\pi$
$769$	17.5379	+	8.44581i	0.632433	+	0.304564i	−0.0900657	+	0.995936i	$0.528708\pi$
$770$	0.774940	−	9.41946i	0.0279269	−	0.339454i
$771$	4.07817	−	1.96394i	0.146872	−	0.0707297i
$772$	7.93804	−	1.19647i	0.285696	−	0.0430618i
$773$	7.04361	+	4.80225i	0.253341	+	0.172725i	0.683331	−	0.730109i	$-0.260531\pi$
$773$	7.04361	+	4.80225i	0.253341	+	0.172725i	−0.429990	+	0.902834i	$0.641483\pi$
$774$	−4.39969	+	4.08232i	−0.158144	+	0.146736i
$775$	3.55157	−	2.42142i	0.127576	−	0.0869799i
$776$	2.35632	−	10.3237i	0.0845869	−	0.370599i
$777$	−0.132513	−	0.600716i	−0.00475386	−	0.0215506i
$778$	−3.45337	−	15.1302i	−0.123809	−	0.542443i
$779$	32.8176	+	30.4503i	1.17581	+	1.09099i
$780$	−2.51195	−	0.378615i	−0.0899421	−	0.0135566i
$781$	−8.01434	+	2.47210i	−0.286776	+	0.0884585i
$782$	0.392873	−	5.24252i	0.0140491	−	0.187472i
$783$	3.43806			0.122866
$784$	0.292846	+	0.279771i	0.0104588	+	0.00999184i
$785$	−10.7780			−0.384682
$786$	−0.277881	+	3.70807i	−0.00991170	+	0.132262i
$787$	−7.77607	+	2.39860i	−0.277187	+	0.0855009i	−0.430232	−	0.902718i	$-0.641568\pi$
$787$	−7.77607	+	2.39860i	−0.277187	+	0.0855009i	0.153045	+	0.988219i	$0.451092\pi$
$788$	21.5133	+	3.24262i	0.766381	+	0.115513i
$789$	−1.44891	−	1.34439i	−0.0515826	−	0.0478616i
$790$	−3.29616	−	14.4414i	−0.117272	−	0.513802i
$791$	−20.7961	+	25.6912i	−0.739423	+	0.913475i
$792$	−3.68011	+	16.1236i	−0.130767	+	0.572928i
$793$	−26.7364	+	18.2286i	−0.949439	+	0.647317i
$794$	3.70089	−	3.43392i	0.131340	−	0.121865i
$795$	−6.46924	−	4.41065i	−0.229440	−	0.156430i
$796$	−19.0222	+	2.86714i	−0.674225	+	0.101623i
$797$	20.7141	−	9.97537i	0.733730	−	0.353346i	−0.0294198	−	0.999567i	$-0.509366\pi$
$797$	20.7141	−	9.97537i	0.733730	−	0.353346i	0.763150	+	0.646221i	$0.223652\pi$
$798$	−2.49067	+	4.24228i	−0.0881687	+	0.150175i
$799$	−5.49856	−	2.64797i	−0.194525	−	0.0936784i
$800$	−4.66256	−	1.43821i	−0.164846	−	0.0508484i
$801$	18.7379	−	47.7433i	0.662070	−	1.68693i
$802$	−1.71913	−	2.97763i	−0.0607047	−	0.105144i
$803$	11.7476	−	20.3474i	0.414563	−	0.718045i
$804$	−2.48160	−	3.11183i	−0.0875192	−	0.109746i
$805$	−23.5410	−	16.3025i	−0.829711	−	0.574586i
$806$	−9.86670	+	12.3725i	−0.347540	+	0.435801i
$807$	1.96415	+	5.00458i	0.0691414	+	0.176169i
$808$	0.762902	+	10.1802i	0.0268388	+	0.358139i
$809$	−1.29728	−	17.3110i	−0.0456099	−	0.608622i	−0.972442	−	0.233146i	$-0.925098\pi$
$809$	−1.29728	−	17.3110i	−0.0456099	−	0.608622i	0.926832	−	0.375476i	$-0.122521\pi$
$810$	5.42700	+	13.8278i	0.190685	+	0.485859i
$811$	−8.15099	+	10.2210i	−0.286220	+	0.358909i	−0.904068	−	0.427389i	$-0.859433\pi$
$811$	−8.15099	+	10.2210i	−0.286220	+	0.358909i	0.617848	+	0.786298i	$0.288005\pi$
$812$	−6.37622	+	1.91604i	−0.223762	+	0.0672399i
$813$	−1.64096	−	2.05769i	−0.0575508	−	0.0721665i
$814$	0.723691	−	1.25347i	0.0253653	−	0.0439341i
$815$	4.30340	+	7.45372i	0.150742	+	0.261092i
$816$	−0.00668477	+	0.0170325i	−0.000234014	+	0.000596257i
$817$	16.6522	+	5.13654i	0.582588	+	0.179705i
$818$	−18.3039	−	8.81468i	−0.639980	−	0.308198i
$819$	20.3606	+	19.1698i	0.711458	+	0.669849i
$820$	13.4202	−	6.46284i	0.468654	−	0.225692i
$821$	−10.1999	+	1.53739i	−0.355979	+	0.0536551i	−0.324597	−	0.945852i	$-0.605229\pi$
$821$	−10.1999	+	1.53739i	−0.355979	+	0.0536551i	−0.0313814	+	0.999507i	$0.509991\pi$
$822$	−0.171742	−	0.117092i	−0.00599020	−	0.00408405i
$823$	−11.4821	+	10.6538i	−0.400240	+	0.371368i	−0.854457	−	0.519523i	$-0.826110\pi$
$823$	−11.4821	+	10.6538i	−0.400240	+	0.371368i	0.454217	+	0.890891i	$0.349919\pi$
$824$	−17.3751	+	11.8461i	−0.605290	+	0.412680i
$825$	−0.108492	+	0.475336i	−0.00377722	+	0.0165491i
$826$	21.3315	−	10.0819i	0.742218	−	0.350795i
$827$	1.48144	+	6.49060i	0.0515146	+	0.225700i	0.994132	−	0.108175i	$-0.0345007\pi$
$827$	1.48144	+	6.49060i	0.0515146	+	0.225700i	−0.942617	+	0.333875i	$0.891644\pi$
$828$	13.9384	+	12.9330i	0.484394	+	0.449452i
$829$	17.1579	+	2.58614i	0.595919	+	0.0898204i	0.440075	−	0.897961i	$-0.354952\pi$
$829$	17.1579	+	2.58614i	0.595919	+	0.0898204i	0.155845	+	0.987782i	$0.450190\pi$
$830$	−15.5402	+	4.79350i	−0.539407	+	0.166385i
$831$	0.162944	−	2.17434i	0.00565246	−	0.0754269i
$832$	18.3822			0.637289
$833$	5.82644	−	5.25026i	0.201874	−	0.181911i
$834$	1.47264			0.0509934
$835$	1.33227	−	17.7779i	0.0461051	−	0.615230i
$836$	17.4125	−	5.37106i	0.602225	−	0.185762i
$837$	8.19658	+	1.23544i	0.283315	+	0.0427029i
$838$	1.75846	+	1.63162i	0.0607451	+	0.0563632i
$839$	6.97366	+	30.5536i	0.240758	+	1.05483i	0.940329	+	0.340265i	$0.110517\pi$
$839$	6.97366	+	30.5536i	0.240758	+	1.05483i	−0.699572	+	0.714562i	$0.746626\pi$
$840$	2.66461	+	3.39172i	0.0919379	+	0.117025i
$841$	5.51116	−	24.1460i	0.190040	−	0.832620i
$842$	3.71296	−	2.53145i	0.127957	−	0.0872397i
$843$	6.06246	−	5.62514i	0.208802	−	0.193740i
$844$	−9.42273	−	6.42431i	−0.324344	−	0.221134i
$845$	−0.200681	+	0.0302478i	−0.00690364	+	0.00104056i
$846$	−12.6323	+	6.08339i	−0.434307	+	0.209151i
$847$	18.4018	−	2.63666i	0.632293	−	0.0905967i
$848$	0.711256	+	0.342523i	0.0244246	+	0.0117623i
$849$	1.09249	+	0.336990i	0.0374943	+	0.0115655i
$850$	0.312648	−	0.796615i	0.0107238	−	0.0273237i
$851$	−2.19258	−	3.79766i	−0.0751607	−	0.130182i
$852$	0.726227	−	1.25786i	0.0248801	−	0.0430936i
$853$	3.71287	+	4.65580i	0.127126	+	0.159411i	0.841321	−	0.540536i	$-0.181778\pi$
$853$	3.71287	+	4.65580i	0.127126	+	0.159411i	−0.714195	+	0.699947i	$0.753207\pi$
$854$	20.5936	+	3.25760i	0.704699	+	0.111473i
$855$	27.6667	−	34.6929i	0.946181	−	1.18647i
$856$	4.58123	+	11.6728i	0.156583	+	0.398968i
$857$	−2.57175	−	34.3177i	−0.0878495	−	1.17227i	−0.850685	−	0.525677i	$-0.823812\pi$
$857$	−2.57175	−	34.3177i	−0.0878495	−	1.17227i	0.762835	−	0.646593i	$-0.223807\pi$
$858$	−0.134138	−	1.78995i	−0.00457940	−	0.0611078i
$859$	−3.78291	−	9.63870i	−0.129071	−	0.328868i	0.851700	−	0.524030i	$-0.175572\pi$
$859$	−3.78291	−	9.63870i	−0.129071	−	0.328868i	−0.980771	+	0.195162i	$0.937477\pi$
$860$	3.61506	−	4.53315i	0.123273	−	0.154579i
$861$	4.41830	+	0.698909i	0.150575	+	0.0238188i
$862$	8.03851	+	10.0800i	0.273793	+	0.343325i
$863$	−6.04299	+	10.4668i	−0.205706	+	0.356293i	−0.950357	−	0.311160i	$-0.899282\pi$
$863$	−6.04299	+	10.4668i	−0.205706	+	0.356293i	0.744652	+	0.667453i	$0.232616\pi$
$864$	−4.70465	−	8.14869i	−0.160055	−	0.277224i
$865$	2.83795	−	7.23098i	0.0964933	−	0.245861i
$866$	12.9746	+	4.00212i	0.440893	+	0.135998i
$867$	−4.00389	−	1.92817i	−0.135979	−	0.0654841i
$868$	−15.8899	+	2.27675i	−0.539338	+	0.0772779i
$869$	−14.8459	+	7.14939i	−0.503611	+	0.242527i
$870$	1.02904	−	0.155102i	0.0348876	−	0.00525846i
$871$	−34.4780	−	23.5067i	−1.16824	−	0.796494i
$872$	8.95372	−	8.30784i	0.303211	−	0.281339i
$873$	−8.99381	+	6.13187i	−0.304394	+	0.207532i
$874$	−7.80336	+	34.1887i	−0.263952	+	1.15645i
$875$	−19.4948	−	24.8145i	−0.659046	−	0.838883i
$876$	0.905415	+	3.96688i	0.0305911	+	0.134029i
$877$	−40.1349	−	37.2398i	−1.35526	−	1.25750i	−0.937072	−	0.349137i	$-0.886475\pi$
$877$	−40.1349	−	37.2398i	−1.35526	−	1.25750i	−0.418188	−	0.908360i	$-0.637335\pi$
$878$	−3.75371	−	0.565781i	−0.126682	−	0.0190942i
$879$	1.84035	−	0.567673i	0.0620735	−	0.0191471i
$880$	−0.0175234	+	0.233833i	−0.000590712	+	0.00788251i
$881$	14.9335			0.503124			0.251562	−	0.967841i	$-0.419056\pi$
$881$	14.9335			0.503124			0.251562	+	0.967841i	$0.419056\pi$
$882$	−1.08457	−	17.9857i	−0.0365194	−	0.605609i
$883$	−10.8928			−0.366570			−0.183285	−	0.983060i	$-0.558673\pi$
$883$	−10.8928			−0.366570			−0.183285	+	0.983060i	$0.558673\pi$
$884$	0.370657	−	4.94607i	0.0124665	−	0.166354i
$885$	5.54790	−	1.71130i	0.186491	−	0.0575247i
$886$	2.03613	+	0.306897i	0.0684050	+	0.0103104i
$887$	−40.2092	−	37.3087i	−1.35009	−	1.25270i	−0.940222	−	0.340561i	$-0.889383\pi$
$887$	−40.2092	−	37.3087i	−1.35009	−	1.25270i	−0.409872	−	0.912143i	$-0.634426\pi$
$888$	0.146983	+	0.643972i	0.00493241	+	0.0216103i
$889$	13.3127	−	6.29197i	0.446492	−	0.211026i
$890$	7.00328	−	30.6834i	0.234750	−	1.02851i
$891$	13.6529	−	9.30841i	0.457390	−	0.311844i
$892$	−5.18511	+	4.81107i	−0.173610	+	0.161087i
$893$	33.6356	+	22.9324i	1.12557	+	0.767403i
$894$	2.24254	−	0.338008i	0.0750016	−	0.0113047i
$895$	−11.2088	+	5.39787i	−0.374669	+	0.180431i
$896$	13.0701	+	12.3057i	0.436640	+	0.411103i
$897$	−4.89970	−	2.35957i	−0.163596	−	0.0787837i
$898$	14.8870	+	4.59202i	0.496785	+	0.153238i
$899$	−3.72865	+	9.50045i	−0.124357	+	0.316858i
$900$	1.54757	+	2.68047i	0.0515857	+	0.0893491i
$901$	7.64374	−	13.2393i	0.254650	−	0.441066i
$902$	6.56217	+	8.22871i	0.218497	+	0.273986i
$903$	1.66758	−	0.501104i	0.0554935	−	0.0166757i
$904$	22.1285	−	27.7482i	0.735982	−	0.922892i
$905$	16.6764	+	42.4908i	0.554342	+	1.41244i
$906$	0.0541033	+	0.721959i	0.00179746	+	0.0239855i
$907$	−1.95619	−	26.1035i	−0.0649541	−	0.866753i	−0.930586	−	0.366072i	$-0.880702\pi$
$907$	−1.95619	−	26.1035i	−0.0649541	−	0.866753i	0.865632	−	0.500680i	$-0.166917\pi$
$908$	−5.93352	−	15.1184i	−0.196911	−	0.501720i
$909$	6.54301	−	8.20467i	0.217018	−	0.272132i
$910$	14.1076	+	9.76974i	0.467664	+	0.323864i
$911$	27.8205	+	34.8858i	0.921734	+	1.15582i	0.987443	+	0.157979i	$0.0504978\pi$
$911$	27.8205	+	34.8858i	0.921734	+	1.15582i	−0.0657087	+	0.997839i	$0.520931\pi$
$912$	0.0610257	−	0.105700i	0.00202076	−	0.00350006i
$913$	9.04525	+	15.6668i	0.299354	+	0.518496i
$914$	0.406454	−	1.03563i	0.0134443	−	0.0342556i
$915$	4.90259	+	1.51225i	0.162074	+	0.0499934i
$916$	−23.5993	−	11.3648i	−0.779744	−	0.375505i
$917$	−20.0214	+	34.1018i	−0.661164	+	1.12614i
$918$	1.48684	−	0.716024i	0.0490730	−	0.0236323i
$919$	32.3241	−	4.87207i	1.06627	−	0.160715i	0.407613	−	0.913155i	$-0.366361\pi$
$919$	32.3241	−	4.87207i	1.06627	−	0.160715i	0.658661	+	0.752440i	$0.271123\pi$
$920$	25.4043	+	17.3204i	0.837555	+	0.571035i
$921$	−5.52875	+	5.12993i	−0.182179	+	0.169037i
$922$	−6.40006	+	4.36349i	−0.210775	+	0.143704i
$923$	3.38850	−	14.8460i	0.111534	−	0.488661i
$924$	1.14555	−	1.41520i	0.0376859	−	0.0465568i
$925$	−0.158839	−	0.695921i	−0.00522261	−	0.0228817i
$926$	−23.4482	−	21.7567i	−0.770555	−	0.714970i
$927$	21.3756	+	3.22185i	0.702067	+	0.105820i
$928$	11.0704	−	3.41477i	0.363404	−	0.112095i
$929$	−2.18613	+	29.1719i	−0.0717247	+	0.957100i	0.839012	+	0.544113i	$0.183134\pi$
$929$	−2.18613	+	29.1719i	−0.0717247	+	0.957100i	−0.910737	+	0.412987i	$0.864485\pi$
$930$	2.50903			0.0822744
$931$	−43.6505	+	28.8378i	−1.43059	+	0.945122i
$932$	29.2330			0.957559
$933$	0.0862102	−	1.15040i	0.00282240	−	0.0376622i
$934$	−25.0857	+	7.73793i	−0.820831	+	0.253193i
$935$	4.49017	+	0.676785i	0.146844	+	0.0221332i
$936$	−22.0119	−	20.4240i	−0.719481	−	0.667581i
$937$	−5.73292	−	25.1176i	−0.187286	−	0.820555i	−0.978039	−	0.208420i	$-0.933168\pi$
$937$	−5.73292	−	25.1176i	−0.187286	−	0.820555i	0.790753	−	0.612135i	$-0.209689\pi$
$938$	5.79172	+	26.2555i	0.189106	+	0.857271i
$939$	1.73031	−	7.58097i	0.0564664	−	0.247396i
$940$	11.1912	−	7.63004i	0.365017	−	0.248864i
$941$	−44.7390	+	41.5117i	−1.45845	+	1.35324i	−0.659809	+	0.751434i	$0.729363\pi$
$941$	−44.7390	+	41.5117i	−1.45845	+	1.35324i	−0.798640	+	0.601809i	$0.794447\pi$
$942$	1.08971	+	0.742949i	0.0355045	+	0.0242066i
$943$	31.5314	−	4.75259i	1.02680	−	0.154766i
$944$	−0.527404	+	0.253984i	−0.0171655	+	0.00826649i
$945$	0.737002	−	8.95832i	0.0239747	−	0.291414i
$946$	3.69118	+	1.77758i	0.120011	+	0.0577940i
$947$	−50.4968	−	15.5762i	−1.64092	−	0.506158i	−0.669361	−	0.742937i	$-0.733432\pi$
$947$	−50.4968	−	15.5762i	−1.64092	−	0.506158i	−0.971563	+	0.236779i	$0.923908\pi$
$948$	1.04254	−	2.65635i	0.0338601	−	0.0862742i
$949$	21.3295	+	36.9438i	0.692385	+	1.19925i
$950$	−2.85419	+	4.94360i	−0.0926020	+	0.160391i
$951$	−1.11650	−	1.40004i	−0.0362048	−	0.0453994i
$952$	−6.21498	+	5.68296i	−0.201429	+	0.184186i
$953$	−33.3284	+	41.7925i	−1.07961	+	1.35379i	−0.148560	+	0.988903i	$0.547464\pi$
$953$	−33.3284	+	41.7925i	−1.07961	+	1.35379i	−0.931052	+	0.364887i	$0.881107\pi$
$954$	−12.8312	−	32.6933i	−0.415425	−	1.05849i
$955$	2.16099	+	28.8364i	0.0699280	+	0.933125i
$956$	−1.06957	−	14.2725i	−0.0345925	−	0.461605i
$957$	−0.422927	−	1.07760i	−0.0136713	−	0.0348339i
$958$	20.5469	−	25.7650i	0.663841	−	0.832430i
$959$	−1.09129	−	1.92238i	−0.0352396	−	0.0620768i
$960$	−1.81715	−	2.27864i	−0.0586483	−	0.0735426i
$961$	3.19672	−	5.53689i	0.103120	−	0.178609i
$962$	1.31397	+	2.27586i	0.0423641	+	0.0733768i
$963$	4.70931	−	11.9991i	0.151755	−	0.386667i
$964$	15.0712	+	4.64884i	0.485409	+	0.149729i
$965$	−12.0226	−	5.78978i	−0.387021	−	0.186380i
$966$	1.25635	+	3.27099i	0.0404223	+	0.105242i
$967$	31.0375	−	14.9469i	0.998100	−	0.480659i	0.137807	−	0.990459i	$-0.455995\pi$
$967$	31.0375	−	14.9469i	0.998100	−	0.480659i	0.860293	+	0.509800i	$0.170280\pi$
$968$	−19.7380	+	2.97502i	−0.634403	+	0.0956209i
$969$	−1.95284	−	1.33143i	−0.0627344	−	0.0427716i
$970$	−4.89645	+	4.54325i	−0.157216	+	0.145875i
$971$	−24.0376	+	16.3886i	−0.771404	+	0.525934i	−0.883876	−	0.467721i	$-0.845075\pi$
$971$	−24.0376	+	16.3886i	−0.771404	+	0.525934i	0.112473	+	0.993655i	$0.464123\pi$
$972$	−2.00117	+	8.76768i	−0.0641874	+	0.281223i
$973$	14.0603	+	6.89771i	0.450752	+	0.221130i
$974$	−6.54830	−	28.6900i	−0.209821	−	0.919287i
$975$	−0.648927	−	0.602116i	−0.0207823	−	0.0192831i
$976$	−0.511508	−	0.0770974i	−0.0163730	−	0.00246783i
$977$	−4.82826	+	1.48932i	−0.154470	+	0.0476476i	−0.371026	−	0.928623i	$-0.620994\pi$
$977$	−4.82826	+	1.48932i	−0.154470	+	0.0476476i	0.216556	+	0.976270i	$0.430518\pi$
$978$	0.0787054	−	1.05025i	0.00251672	−	0.0335833i
$979$	−35.0098			−1.11892
$980$	3.62566	+	17.0248i	0.115818	+	0.543838i
$981$	−12.5558			−0.400875
$982$	−0.103047	+	1.37506i	−0.00328836	+	0.0438801i
$983$	−35.7982	+	11.0423i	−1.14179	+	0.352194i	−0.807262	−	0.590193i	$-0.799052\pi$
$983$	−35.7982	+	11.0423i	−1.14179	+	0.352194i	−0.334523	+	0.942387i	$0.608575\pi$
$984$	−4.74955	−	0.715879i	−0.151410	−	0.0228214i
$985$	−26.5105	−	24.5982i	−0.844695	−	0.783762i
$986$	0.452134	+	1.98093i	0.0143989	+	0.0630856i
$987$	4.06754	+	0.0296344i	0.129471	+	0.000943275i
$988$	−7.36210	+	32.2555i	−0.234220	+	1.02618i
$989$	10.2557	−	6.99219i	0.326111	−	0.222339i
$990$	7.64731	−	7.09567i	0.243047	−	0.225515i
$991$	11.6974	+	7.97515i	0.371580	+	0.253339i	0.734684	−	0.678410i	$-0.237331\pi$
$991$	11.6974	+	7.97515i	0.371580	+	0.253339i	−0.363104	+	0.931749i	$0.618283\pi$
$992$	27.6197	−	4.16300i	0.876927	−	0.132175i
$993$	−1.52422	+	0.734025i	−0.0483696	+	0.0232936i
$994$	−8.14673	+	5.46783i	−0.258398	+	0.173429i
$995$	28.8102	+	13.8743i	0.913346	+	0.439844i
$996$	−2.99373	−	0.923444i	−0.0948600	−	0.0292604i
$997$	−13.6960	+	34.8969i	−0.433757	+	1.10519i	0.532229	+	0.846600i	$0.321355\pi$
$997$	−13.6960	+	34.8969i	−0.433757	+	1.10519i	−0.965986	+	0.258594i	$0.916741\pi$
$998$	14.3088	+	24.7835i	0.452937	+	0.784509i
$999$	0.688262	−	1.19210i	0.0217756	−	0.0377165i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.2.g.a.23.3	✓	48
3.2	odd	2		441.2.bb.d.415.2		48
4.3	odd	2		784.2.bg.c.513.2		48
7.2	even	3		343.2.e.d.148.3		48
7.3	odd	6		343.2.g.h.263.3		48
7.4	even	3		343.2.g.i.263.3		48
7.5	odd	6		343.2.e.c.148.3		48
7.6	odd	2		343.2.g.g.275.3		48
49.9	even	21		2401.2.a.h.1.16		24
49.12	odd	42		343.2.e.c.197.3		48
49.17	odd	42		343.2.g.g.116.3		48
49.20	odd	14		343.2.g.h.30.3		48
49.29	even	7		343.2.g.i.30.3		48
49.32	even	21	inner	49.2.g.a.32.3	yes	48
49.37	even	21		343.2.e.d.197.3		48
49.40	odd	42		2401.2.a.i.1.16		24
147.32	odd	42		441.2.bb.d.424.2		48
196.179	odd	42		784.2.bg.c.81.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.23.3	✓	48	1.1	even	1	trivial
49.2.g.a.32.3	yes	48	49.32	even	21	inner
343.2.e.c.148.3		48	7.5	odd	6
343.2.e.c.197.3		48	49.12	odd	42
343.2.e.d.148.3		48	7.2	even	3
343.2.e.d.197.3		48	49.37	even	21
343.2.g.g.116.3		48	49.17	odd	42
343.2.g.g.275.3		48	7.6	odd	2
343.2.g.h.30.3		48	49.20	odd	14
343.2.g.h.263.3		48	7.3	odd	6
343.2.g.i.30.3		48	49.29	even	7
343.2.g.i.263.3		48	7.4	even	3
441.2.bb.d.415.2		48	3.2	odd	2
441.2.bb.d.424.2		48	147.32	odd	42
784.2.bg.c.81.2		48	196.179	odd	42
784.2.bg.c.513.2		48	4.3	odd	2
2401.2.a.h.1.16		24	49.9	even	21
2401.2.a.i.1.16		24	49.40	odd	42

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	49.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0658689 - 0.878959i) q^{2} +(-0.269714 + 0.0831957i) q^{3} +(1.20943 + 0.182293i) q^{4} +(-1.49036 - 1.38285i) q^{5} +(0.0553598 + 0.242547i) q^{6} +(-0.607511 + 2.57506i) q^{7} +(0.632162 - 2.76968i) q^{8} +(-2.41289 + 1.64508i) q^{9} +O(q^{10})\)	\(q+(0.0658689 - 0.878959i) q^{2} +(-0.269714 + 0.0831957i) q^{3} +(1.20943 + 0.182293i) q^{4} +(-1.49036 - 1.38285i) q^{5} +(0.0553598 + 0.242547i) q^{6} +(-0.607511 + 2.57506i) q^{7} +(0.632162 - 2.76968i) q^{8} +(-2.41289 + 1.64508i) q^{9} +(-1.31364 + 1.21888i) q^{10} +(1.64705 + 1.12294i) q^{11} +(-0.341366 + 0.0514527i) q^{12} +(-3.26094 + 1.57038i) q^{13} +(2.22335 + 0.703594i) q^{14} +(0.517018 + 0.248983i) q^{15} +(-0.0552877 - 0.0170540i) q^{16} +(-0.409339 + 1.04298i) q^{17} +(1.28702 + 2.22919i) q^{18} +(3.73687 - 6.47246i) q^{19} +(-1.55041 - 1.94415i) q^{20} +(-0.0503796 - 0.745071i) q^{21} +(1.09550 - 1.37372i) q^{22} +(-1.94485 - 4.95539i) q^{23} +(0.0599228 + 0.799614i) q^{24} +(-0.0647567 - 0.864118i) q^{25} +(1.16551 + 2.96967i) q^{26} +(1.04187 - 1.30647i) q^{27} +(-1.20416 + 3.00361i) q^{28} +(1.28279 + 1.60857i) q^{29} +(0.252901 - 0.438037i) q^{30} +(2.48025 + 4.29592i) q^{31} +(2.05717 - 5.24158i) q^{32} +(-0.537654 - 0.165844i) q^{33} +(0.889772 + 0.428491i) q^{34} +(4.46634 - 2.99767i) q^{35} +(-3.21812 + 1.54976i) q^{36} +(0.814555 - 0.122774i) q^{37} +(-5.44288 - 3.71089i) q^{38} +(0.748870 - 0.694850i) q^{39} +(-4.77221 + 3.25364i) q^{40} +(-1.33292 + 5.83991i) q^{41} +(-0.658205 - 0.00479541i) q^{42} +(0.518849 + 2.27323i) q^{43} +(1.78729 + 1.65836i) q^{44} +(5.87099 + 0.884909i) q^{45} +(-4.48369 + 1.38304i) q^{46} +(-0.407053 + 5.43174i) q^{47} +0.0163307 q^{48} +(-6.26186 - 3.12876i) q^{49} -0.763790 q^{50} +(0.0236330 - 0.315360i) q^{51} +(-4.23015 + 1.30483i) q^{52} +(-13.4919 - 2.03358i) q^{53} +(-1.07970 - 1.00182i) q^{54} +(-0.901837 - 3.95120i) q^{55} +(6.74805 + 3.31047i) q^{56} +(-0.469406 + 2.05660i) q^{57} +(1.49837 - 1.02157i) q^{58} +(7.41658 - 6.88158i) q^{59} +(0.579911 + 0.395376i) q^{60} +(8.84072 - 1.33252i) q^{61} +(3.93931 - 1.89707i) q^{62} +(-2.77032 - 7.21275i) q^{63} +(-4.57589 - 2.20363i) q^{64} +(7.03159 + 2.16896i) q^{65} +(-0.181185 + 0.461652i) q^{66} +(5.76466 + 9.98468i) q^{67} +(-0.685194 + 1.18679i) q^{68} +(0.936820 + 1.17473i) q^{69} +(-2.34063 - 4.12318i) q^{70} +(-2.62321 + 3.28940i) q^{71} +(3.03102 + 7.72290i) q^{72} +(-0.880793 - 11.7534i) q^{73} +(-0.0542598 - 0.724047i) q^{74} +(0.0893566 + 0.227677i) q^{75} +(5.69938 - 7.14679i) q^{76} +(-3.89223 + 3.55904i) q^{77} +(-0.561417 - 0.703995i) q^{78} +(-4.13300 + 7.15857i) q^{79} +(0.0588155 + 0.101871i) q^{80} +(3.02844 - 7.71633i) q^{81} +(5.04524 + 1.55625i) q^{82} +(8.17636 + 3.93753i) q^{83} +(0.0748902 - 0.910296i) q^{84} +(2.05235 - 0.988358i) q^{85} +(2.03225 - 0.306312i) q^{86} +(-0.479814 - 0.327131i) q^{87} +(4.15138 - 3.85192i) q^{88} +(-14.5109 + 9.89337i) q^{89} +(1.16451 - 5.10207i) q^{90} +(-2.06278 - 9.35113i) q^{91} +(-1.44883 - 6.34774i) q^{92} +(-1.02636 - 0.952322i) q^{93} +(4.74747 + 0.715565i) q^{94} +(-14.5198 + 4.47875i) q^{95} +(-0.118770 + 1.58487i) q^{96} +3.72740 q^{97} +(-3.16251 + 5.29783i) q^{98} -5.82147 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 13 q^{2} - 14 q^{3} - 9 q^{4} - 14 q^{5} - 14 q^{7} - 20 q^{8} + 6 q^{9}+O(q^{10}) \) 48 * q - 13 * q^2 - 14 * q^3 - 9 * q^4 - 14 * q^5 - 14 * q^7 - 20 * q^8 + 6 * q^9	\( 48 q - 13 q^{2} - 14 q^{3} - 9 q^{4} - 14 q^{5} - 14 q^{7} - 20 q^{8} + 6 q^{9} - 14 q^{10} - 3 q^{11} + 21 q^{12} - 14 q^{13} + 21 q^{14} - 12 q^{15} - 3 q^{16} - 7 q^{17} + 2 q^{18} + 21 q^{19} + 14 q^{20} - 14 q^{21} - 20 q^{22} + 15 q^{23} + 28 q^{24} - 4 q^{25} + 7 q^{27} + 28 q^{28} + 12 q^{29} + 11 q^{30} + 35 q^{31} + 45 q^{32} - 14 q^{33} + 70 q^{34} - 12 q^{36} + 15 q^{37} - 28 q^{38} - 7 q^{39} - 42 q^{40} - 42 q^{41} + 28 q^{42} - 30 q^{43} - 50 q^{44} + 7 q^{45} - 78 q^{46} + 21 q^{47} - 84 q^{48} - 70 q^{49} + 40 q^{50} - 52 q^{51} - 70 q^{52} + 11 q^{53} - 77 q^{54} - 7 q^{55} - 28 q^{56} - 12 q^{57} + 16 q^{58} - 28 q^{59} + 56 q^{60} + 7 q^{61} - 28 q^{62} + 35 q^{63} - 32 q^{64} + 14 q^{65} + 154 q^{66} + 11 q^{67} + 77 q^{68} + 70 q^{69} + 70 q^{70} + 19 q^{71} + 170 q^{72} + 7 q^{73} + 34 q^{74} + 112 q^{75} + 119 q^{76} + 7 q^{77} + 28 q^{78} + 15 q^{79} + 70 q^{80} + 64 q^{81} - 14 q^{82} - 84 q^{84} - 26 q^{85} - 33 q^{86} - 112 q^{87} - 77 q^{88} - 14 q^{89} - 182 q^{90} + 84 q^{91} - 38 q^{92} - 80 q^{93} + 14 q^{94} - 61 q^{95} - 70 q^{96} - 161 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q - 13 * q^2 - 14 * q^3 - 9 * q^4 - 14 * q^5 - 14 * q^7 - 20 * q^8 + 6 * q^9 - 14 * q^10 - 3 * q^11 + 21 * q^12 - 14 * q^13 + 21 * q^14 - 12 * q^15 - 3 * q^16 - 7 * q^17 + 2 * q^18 + 21 * q^19 + 14 * q^20 - 14 * q^21 - 20 * q^22 + 15 * q^23 + 28 * q^24 - 4 * q^25 + 7 * q^27 + 28 * q^28 + 12 * q^29 + 11 * q^30 + 35 * q^31 + 45 * q^32 - 14 * q^33 + 70 * q^34 - 12 * q^36 + 15 * q^37 - 28 * q^38 - 7 * q^39 - 42 * q^40 - 42 * q^41 + 28 * q^42 - 30 * q^43 - 50 * q^44 + 7 * q^45 - 78 * q^46 + 21 * q^47 - 84 * q^48 - 70 * q^49 + 40 * q^50 - 52 * q^51 - 70 * q^52 + 11 * q^53 - 77 * q^54 - 7 * q^55 - 28 * q^56 - 12 * q^57 + 16 * q^58 - 28 * q^59 + 56 * q^60 + 7 * q^61 - 28 * q^62 + 35 * q^63 - 32 * q^64 + 14 * q^65 + 154 * q^66 + 11 * q^67 + 77 * q^68 + 70 * q^69 + 70 * q^70 + 19 * q^71 + 170 * q^72 + 7 * q^73 + 34 * q^74 + 112 * q^75 + 119 * q^76 + 7 * q^77 + 28 * q^78 + 15 * q^79 + 70 * q^80 + 64 * q^81 - 14 * q^82 - 84 * q^84 - 26 * q^85 - 33 * q^86 - 112 * q^87 - 77 * q^88 - 14 * q^89 - 182 * q^90 + 84 * q^91 - 38 * q^92 - 80 * q^93 + 14 * q^94 - 61 * q^95 - 70 * q^96 - 161 * q^98 - 16 * q^99

Introduction

L-functions

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