LMFDB - Embedded newform 966.2.q.d.673.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(85,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.q (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{19} + 10 x^{18} - 14 x^{17} + 77 x^{16} + 12 x^{15} - 226 x^{14} - 793 x^{13} + \cdots + 1849 $ x^20 - 6x^19 + 10x^18 - 14x^17 + 77x^16 + 12x^15 - 226x^14 - 793x^13 + 690x^12 + 6105x^11 + 13883x^10 + 24365x^9 + 36461x^8 + 41912x^7 + 45709x^6 + 33023x^5 + 25949x^4 + 12217x^3 + 2895x^2 - 172*x + 1849
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			673.1
Root			$2.68238 + 1.72386i$ of defining polynomial
Character	$\chi$	$=$	966.673
Dual form			966.2.q.d.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 - 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-1.26697 + 0.814230i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(0.415415 - 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-1.26697 + 0.814230i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(0.214333 + 1.49072i) q^{10} +(1.09428 + 2.39613i) q^{11} +(-0.415415 - 0.909632i) q^{12} +(0.0324836 + 0.225928i) q^{13} +(0.841254 + 0.540641i) q^{14} +(-1.44504 + 0.424302i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-0.344110 + 0.397124i) q^{17} +(0.841254 - 0.540641i) q^{18} +(3.05495 + 3.52559i) q^{19} +(1.44504 + 0.424302i) q^{20} +(-0.415415 + 0.909632i) q^{21} +2.63418 q^{22} +(4.75622 - 0.615128i) q^{23} -1.00000 q^{24} +(-1.13484 + 2.48496i) q^{25} +(0.219006 + 0.0643058i) q^{26} +(0.654861 + 0.755750i) q^{27} +(0.841254 - 0.540641i) q^{28} +(-3.24204 + 3.74152i) q^{29} +(-0.214333 + 1.49072i) q^{30} +(1.60220 - 0.470447i) q^{31} +(0.841254 + 0.540641i) q^{32} +(0.374882 + 2.60736i) q^{33} +(0.218288 + 0.477985i) q^{34} +(-0.625634 - 1.36995i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(6.89839 + 4.43333i) q^{37} +(4.47606 - 1.31429i) q^{38} +(-0.0324836 + 0.225928i) q^{39} +(0.986250 - 1.13819i) q^{40} +(-0.0412942 + 0.0265382i) q^{41} +(0.654861 + 0.755750i) q^{42} +(4.52129 + 1.32757i) q^{43} +(1.09428 - 2.39613i) q^{44} -1.50605 q^{45} +(1.41626 - 4.58194i) q^{46} -5.00790 q^{47} +(-0.415415 + 0.909632i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(1.78897 + 2.06458i) q^{50} +(-0.442054 + 0.284091i) q^{51} +(0.149473 - 0.172501i) q^{52} +(0.865718 - 6.02120i) q^{53} +(0.959493 - 0.281733i) q^{54} +(-3.33741 - 2.14482i) q^{55} +(-0.142315 - 0.989821i) q^{56} +(1.93792 + 4.24346i) q^{57} +(2.05661 + 4.50335i) q^{58} +(-0.0271187 - 0.188614i) q^{59} +(1.26697 + 0.814230i) q^{60} +(1.19326 - 0.350373i) q^{61} +(0.237642 - 1.65284i) q^{62} +(-0.654861 + 0.755750i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-0.225113 - 0.259794i) q^{65} +(2.52747 + 0.742133i) q^{66} +(3.12659 - 6.84628i) q^{67} +0.525470 q^{68} +(4.73686 + 0.749771i) q^{69} -1.50605 q^{70} +(-4.83436 + 10.5858i) q^{71} +(-0.959493 - 0.281733i) q^{72} +(4.58807 + 5.29492i) q^{73} +(6.89839 - 4.43333i) q^{74} +(-1.78897 + 2.06458i) q^{75} +(0.663903 - 4.61755i) q^{76} +(-2.52747 + 0.742133i) q^{77} +(0.192017 + 0.123402i) q^{78} +(-1.14553 - 7.96730i) q^{79} +(-0.625634 - 1.36995i) q^{80} +(0.415415 + 0.909632i) q^{81} +(0.00698575 + 0.0485869i) q^{82} +(-1.70637 - 1.09662i) q^{83} +(0.959493 - 0.281733i) q^{84} +(0.112625 - 0.783327i) q^{85} +(3.08581 - 3.56121i) q^{86} +(-4.16482 + 2.67657i) q^{87} +(-1.72502 - 1.99078i) q^{88} +(-7.18547 - 2.10984i) q^{89} +(-0.625634 + 1.36995i) q^{90} -0.228251 q^{91} +(-3.57954 - 3.19169i) q^{92} +1.66984 q^{93} +(-2.08036 + 4.55535i) q^{94} +(-6.74115 - 1.97938i) q^{95} +(0.654861 + 0.755750i) q^{96} +(-2.01807 + 1.29693i) q^{97} +(-0.654861 + 0.755750i) q^{98} +(-0.374882 + 2.60736i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9} - 10 q^{10} - 7 q^{11} + 2 q^{12} - 8 q^{13} - 2 q^{14} - q^{15} - 2 q^{16} + 13 q^{17} - 2 q^{18} - 8 q^{19} + q^{20} + 2 q^{21} + 4 q^{22} - 20 q^{24} + 16 q^{25} - 8 q^{26} + 2 q^{27} - 2 q^{28} + 3 q^{29} + 10 q^{30} + 9 q^{31} - 2 q^{32} - 4 q^{33} - 9 q^{34} + q^{35} - 2 q^{36} - q^{37} + 3 q^{38} + 8 q^{39} + q^{40} + 10 q^{41} + 2 q^{42} - 15 q^{43} - 7 q^{44} - 10 q^{45} - 28 q^{47} + 2 q^{48} - 2 q^{49} + 5 q^{50} - 2 q^{51} + 3 q^{52} + 38 q^{53} + 2 q^{54} - 8 q^{55} - 2 q^{56} - 14 q^{57} - 19 q^{58} - 10 q^{59} - 12 q^{60} - 6 q^{61} + 20 q^{62} - 2 q^{63} - 2 q^{64} - 36 q^{65} - 4 q^{66} + 36 q^{67} - 20 q^{68} + 11 q^{69} - 10 q^{70} - q^{71} - 2 q^{72} + 65 q^{73} - q^{74} - 5 q^{75} + 14 q^{76} + 4 q^{77} - 14 q^{78} + 10 q^{79} + q^{80} - 2 q^{81} + 10 q^{82} - 14 q^{83} + 2 q^{84} - 5 q^{85} + 51 q^{86} - 3 q^{87} - 7 q^{88} - 18 q^{89} + q^{90} - 30 q^{91} - 11 q^{92} + 2 q^{93} + 38 q^{94} - 73 q^{95} + 2 q^{96} - 20 q^{97} - 2 q^{98} + 4 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9 - 10 * q^10 - 7 * q^11 + 2 * q^12 - 8 * q^13 - 2 * q^14 - q^15 - 2 * q^16 + 13 * q^17 - 2 * q^18 - 8 * q^19 + q^20 + 2 * q^21 + 4 * q^22 - 20 * q^24 + 16 * q^25 - 8 * q^26 + 2 * q^27 - 2 * q^28 + 3 * q^29 + 10 * q^30 + 9 * q^31 - 2 * q^32 - 4 * q^33 - 9 * q^34 + q^35 - 2 * q^36 - q^37 + 3 * q^38 + 8 * q^39 + q^40 + 10 * q^41 + 2 * q^42 - 15 * q^43 - 7 * q^44 - 10 * q^45 - 28 * q^47 + 2 * q^48 - 2 * q^49 + 5 * q^50 - 2 * q^51 + 3 * q^52 + 38 * q^53 + 2 * q^54 - 8 * q^55 - 2 * q^56 - 14 * q^57 - 19 * q^58 - 10 * q^59 - 12 * q^60 - 6 * q^61 + 20 * q^62 - 2 * q^63 - 2 * q^64 - 36 * q^65 - 4 * q^66 + 36 * q^67 - 20 * q^68 + 11 * q^69 - 10 * q^70 - q^71 - 2 * q^72 + 65 * q^73 - q^74 - 5 * q^75 + 14 * q^76 + 4 * q^77 - 14 * q^78 + 10 * q^79 + q^80 - 2 * q^81 + 10 * q^82 - 14 * q^83 + 2 * q^84 - 5 * q^85 + 51 * q^86 - 3 * q^87 - 7 * q^88 - 18 * q^89 + q^90 - 30 * q^91 - 11 * q^92 + 2 * q^93 + 38 * q^94 - 73 * q^95 + 2 * q^96 - 20 * q^97 - 2 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$3$	0.959493	+	0.281733i	0.553964	+	0.162658i
$3$	0.959493	+	0.281733i	0.553964	+	0.162658i
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	−1.26697	+	0.814230i	−0.566604	+	0.364135i	−0.792364	−	0.610048i	$-0.791150\pi$
$5$	−1.26697	+	0.814230i	−0.566604	+	0.364135i	0.225760	+	0.974183i	$0.427514\pi$
$6$	0.654861	−	0.755750i	0.267346	−	0.308533i
$7$	−0.142315	+	0.989821i	−0.0537900	+	0.374117i
$7$	−0.142315	+	0.989821i	−0.0537900	+	0.374117i
$8$	−0.959493	+	0.281733i	−0.339232	+	0.0996075i
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$	0.214333	+	1.49072i	0.0677779	+	0.471406i
$11$	1.09428	+	2.39613i	0.329937	+	0.722461i	0.999799	−	0.0200243i	$-0.00637437\pi$
$11$	1.09428	+	2.39613i	0.329937	+	0.722461i	−0.669863	+	0.742485i	$0.733647\pi$
$12$	−0.415415	−	0.909632i	−0.119920	−	0.262588i
$13$	0.0324836	+	0.225928i	0.00900932	+	0.0626612i	0.993830	−	0.110913i	$-0.0353775\pi$
$13$	0.0324836	+	0.225928i	0.00900932	+	0.0626612i	−0.984821	+	0.173574i	$0.944468\pi$
$14$	0.841254	+	0.540641i	0.224834	+	0.144492i
$15$	−1.44504	+	0.424302i	−0.373108	+	0.109554i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	−0.344110	+	0.397124i	−0.0834589	+	0.0963167i	−0.795943	−	0.605371i	$-0.793025\pi$
$17$	−0.344110	+	0.397124i	−0.0834589	+	0.0963167i	0.712484	+	0.701688i	$0.247570\pi$
$18$	0.841254	−	0.540641i	0.198285	−	0.127430i
$19$	3.05495	+	3.52559i	0.700852	+	0.808827i	0.988867	−	0.148799i	$-0.0475408\pi$
$19$	3.05495	+	3.52559i	0.700852	+	0.808827i	−0.288015	+	0.957626i	$0.592995\pi$
$20$	1.44504	+	0.424302i	0.323121	+	0.0948768i
$21$	−0.415415	+	0.909632i	−0.0906510	+	0.198498i
$22$	2.63418			0.561608
$23$	4.75622	−	0.615128i	0.991740	−	0.128263i
$23$	4.75622	−	0.615128i	0.991740	−	0.128263i
$24$	−1.00000			−0.204124
$25$	−1.13484	+	2.48496i	−0.226968	+	0.496992i
$26$	0.219006	+	0.0643058i	0.0429505	+	0.0126114i
$27$	0.654861	+	0.755750i	0.126028	+	0.145444i
$28$	0.841254	−	0.540641i	0.158982	−	0.102172i
$29$	−3.24204	+	3.74152i	−0.602032	+	0.694782i	−0.972192	−	0.234186i	$-0.924758\pi$
$29$	−3.24204	+	3.74152i	−0.602032	+	0.694782i	0.370160	+	0.928968i	$0.379303\pi$
$30$	−0.214333	+	1.49072i	−0.0391316	+	0.272166i
$31$	1.60220	−	0.470447i	0.287763	−	0.0844948i	−0.134665	−	0.990891i	$-0.542996\pi$
$31$	1.60220	−	0.470447i	0.287763	−	0.0844948i	0.422428	+	0.906396i	$0.361178\pi$
$32$	0.841254	+	0.540641i	0.148714	+	0.0955727i
$33$	0.374882	+	2.60736i	0.0652586	+	0.453884i
$34$	0.218288	+	0.477985i	0.0374361	+	0.0819737i
$35$	−0.625634	−	1.36995i	−0.105751	−	0.231563i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	6.89839	+	4.43333i	1.13409	+	0.728835i	0.966410	−	0.257007i	$-0.0827364\pi$
$37$	6.89839	+	4.43333i	1.13409	+	0.728835i	0.167679	+	0.985842i	$0.446373\pi$
$38$	4.47606	−	1.31429i	0.726113	−	0.213206i
$39$	−0.0324836	+	0.225928i	−0.00520153	+	0.0361774i
$40$	0.986250	−	1.13819i	0.155940	−	0.179964i
$41$	−0.0412942	+	0.0265382i	−0.00644908	+	0.00414457i	−0.543861	−	0.839175i	$-0.683038\pi$
$41$	−0.0412942	+	0.0265382i	−0.00644908	+	0.00414457i	0.537412	+	0.843320i	$0.319402\pi$
$42$	0.654861	+	0.755750i	0.101047	+	0.116615i
$43$	4.52129	+	1.32757i	0.689490	+	0.202452i	0.607664	−	0.794194i	$-0.292107\pi$
$43$	4.52129	+	1.32757i	0.689490	+	0.202452i	0.0818257	+	0.996647i	$0.473925\pi$
$44$	1.09428	−	2.39613i	0.164968	−	0.361230i
$45$	−1.50605			−0.224508
$46$	1.41626	−	4.58194i	0.208817	−	0.675571i
$47$	−5.00790			−0.730478			−0.365239	−	0.930914i	$-0.619013\pi$
$47$	−5.00790			−0.730478			−0.365239	+	0.930914i	$0.619013\pi$
$48$	−0.415415	+	0.909632i	−0.0599600	+	0.131294i
$49$	−0.959493	−	0.281733i	−0.137070	−	0.0402475i
$50$	1.78897	+	2.06458i	0.252998	+	0.291975i
$51$	−0.442054	+	0.284091i	−0.0618999	+	0.0397807i
$52$	0.149473	−	0.172501i	0.0207282	−	0.0239216i
$53$	0.865718	−	6.02120i	0.118916	−	0.827076i	−0.839838	−	0.542837i	$-0.817350\pi$
$53$	0.865718	−	6.02120i	0.118916	−	0.827076i	0.958754	−	0.284239i	$-0.0917408\pi$
$54$	0.959493	−	0.281733i	0.130570	−	0.0383389i
$55$	−3.33741	−	2.14482i	−0.450016	−	0.289208i
$56$	−0.142315	−	0.989821i	−0.0190176	−	0.132270i
$57$	1.93792	+	4.24346i	0.256684	+	0.562060i
$58$	2.05661	+	4.50335i	0.270046	+	0.591318i
$59$	−0.0271187	−	0.188614i	−0.00353055	−	0.0245555i	0.987980	−	0.154582i	$-0.0494030\pi$
$59$	−0.0271187	−	0.188614i	−0.00353055	−	0.0245555i	−0.991511	+	0.130026i	$0.958494\pi$
$60$	1.26697	+	0.814230i	0.163565	+	0.105117i
$61$	1.19326	−	0.350373i	0.152781	−	0.0448606i	−0.204448	−	0.978878i	$-0.565540\pi$
$61$	1.19326	−	0.350373i	0.152781	−	0.0448606i	0.357229	+	0.934017i	$0.383722\pi$
$62$	0.237642	−	1.65284i	0.0301806	−	0.209911i
$63$	−0.654861	+	0.755750i	−0.0825047	+	0.0952155i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	−0.225113	−	0.259794i	−0.0279218	−	0.0322235i
$66$	2.52747	+	0.742133i	0.311110	+	0.0913503i
$67$	3.12659	−	6.84628i	0.381974	−	0.836406i	−0.616811	−	0.787112i	$-0.711576\pi$
$67$	3.12659	−	6.84628i	0.381974	−	0.836406i	0.998784	−	0.0492942i	$-0.0156972\pi$
$68$	0.525470			0.0637226
$69$	4.73686	+	0.749771i	0.570251	+	0.0902618i
$70$	−1.50605			−0.180007
$71$	−4.83436	+	10.5858i	−0.573733	+	1.25630i	0.371053	+	0.928612i	$0.378997\pi$
$71$	−4.83436	+	10.5858i	−0.573733	+	1.25630i	−0.944786	+	0.327688i	$0.893731\pi$
$72$	−0.959493	−	0.281733i	−0.113077	−	0.0332025i
$73$	4.58807	+	5.29492i	0.536993	+	0.619723i	0.957803	−	0.287426i	$-0.0927994\pi$
$73$	4.58807	+	5.29492i	0.536993	+	0.619723i	−0.420810	+	0.907149i	$0.638254\pi$
$74$	6.89839	−	4.43333i	0.801922	−	0.515364i
$75$	−1.78897	+	2.06458i	−0.206572	+	0.238397i
$76$	0.663903	−	4.61755i	0.0761549	−	0.529669i
$77$	−2.52747	+	0.742133i	−0.288032	+	0.0845739i
$78$	0.192017	+	0.123402i	0.0217417	+	0.0139725i
$79$	−1.14553	−	7.96730i	−0.128882	−	0.896392i	−0.946975	−	0.321307i	$-0.895878\pi$
$79$	−1.14553	−	7.96730i	−0.128882	−	0.896392i	0.818094	−	0.575085i	$-0.195031\pi$
$80$	−0.625634	−	1.36995i	−0.0699480	−	0.153165i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	0.00698575	+	0.0485869i	0.000771447	+	0.00536553i
$83$	−1.70637	−	1.09662i	−0.187298	−	0.120369i	0.443631	−	0.896209i	$-0.353690\pi$
$83$	−1.70637	−	1.09662i	−0.187298	−	0.120369i	−0.630930	+	0.775840i	$0.717326\pi$
$84$	0.959493	−	0.281733i	0.104689	−	0.0307395i
$85$	0.112625	−	0.783327i	0.0122159	−	0.0849637i
$86$	3.08581	−	3.56121i	0.332751	−	0.384016i
$87$	−4.16482	+	2.67657i	−0.446516	+	0.286958i
$88$	−1.72502	−	1.99078i	−0.183888	−	0.212218i
$89$	−7.18547	−	2.10984i	−0.761658	−	0.223643i	−0.122238	−	0.992501i	$-0.539007\pi$
$89$	−7.18547	−	2.10984i	−0.761658	−	0.223643i	−0.639420	+	0.768858i	$0.720825\pi$
$90$	−0.625634	+	1.36995i	−0.0659476	+	0.144405i
$91$	−0.228251			−0.0239272
$92$	−3.57954	−	3.19169i	−0.373193	−	0.332756i
$93$	1.66984			0.173154
$94$	−2.08036	+	4.55535i	−0.214573	+	0.469848i
$95$	−6.74115	−	1.97938i	−0.691628	−	0.203080i
$96$	0.654861	+	0.755750i	0.0668364	+	0.0771334i
$97$	−2.01807	+	1.29693i	−0.204904	+	0.131684i	−0.639068	−	0.769150i	$-0.720680\pi$
$97$	−2.01807	+	1.29693i	−0.204904	+	0.131684i	0.434165	+	0.900833i	$0.357044\pi$
$98$	−0.654861	+	0.755750i	−0.0661509	+	0.0763422i
$99$	−0.374882	+	2.60736i	−0.0376771	+	0.262050i
$100$	2.62117	−	0.769645i	0.262117	−	0.0769645i
$101$	−13.3422	−	8.57452i	−1.32760	−	0.853197i	−0.331676	−	0.943393i	$-0.607614\pi$
$101$	−13.3422	−	8.57452i	−1.32760	−	0.853197i	−0.995924	+	0.0901963i	$0.971251\pi$
$102$	0.0747822	+	0.520122i	0.00740454	+	0.0514997i
$103$	−4.50578	−	9.86629i	−0.443968	−	0.972154i	−0.990853	−	0.134946i	$-0.956914\pi$
$103$	−4.50578	−	9.86629i	−0.443968	−	0.972154i	0.546885	−	0.837208i	$-0.315813\pi$
$104$	−0.0948190	−	0.207625i	−0.00929777	−	0.0203593i
$105$	−0.214333	−	1.49072i	−0.0209167	−	0.145479i
$106$	−5.11745	−	3.28878i	−0.497050	−	0.319435i
$107$	−0.528825	+	0.155277i	−0.0511234	+	0.0150112i	−0.307194	−	0.951647i	$-0.599390\pi$
$107$	−0.528825	+	0.155277i	−0.0511234	+	0.0150112i	0.256071	+	0.966658i	$0.417572\pi$
$108$	0.142315	−	0.989821i	0.0136943	−	0.0952456i
$109$	5.68441	−	6.56016i	0.544468	−	0.628350i	−0.415117	−	0.909768i	$-0.636259\pi$
$109$	5.68441	−	6.56016i	0.544468	−	0.628350i	0.959585	+	0.281418i	$0.0908048\pi$
$110$	−3.33741	+	2.14482i	−0.318210	+	0.204501i
$111$	5.36995	+	6.19725i	0.509693	+	0.588217i
$112$	−0.959493	−	0.281733i	−0.0906636	−	0.0266212i
$113$	−3.55441	+	7.78308i	−0.334371	+	0.732170i	−0.999899	−	0.0142024i	$-0.995479\pi$
$113$	−3.55441	+	7.78308i	−0.334371	+	0.732170i	0.665528	+	0.746373i	$0.268206\pi$
$114$	4.66503			0.436920
$115$	−5.52511	+	4.65200i	−0.515219	+	0.433801i
$116$	4.95074			0.459664
$117$	−0.0948190	+	0.207625i	−0.00876602	+	0.0191949i
$118$	−0.182835	−	0.0536852i	−0.0168313	−	0.00494213i
$119$	−0.344110	−	0.397124i	−0.0315445	−	0.0364043i
$120$	1.26697	−	0.814230i	0.115658	−	0.0743286i
$121$	2.65947	−	3.06919i	0.241770	−	0.279017i
$122$	0.176988	−	1.23098i	0.0160237	−	0.111447i
$123$	−0.0470982	+	0.0138293i	−0.00424670	+	0.00124694i
$124$	−1.40476	−	0.902782i	−0.126151	−	0.0810722i
$125$	−1.65718	−	11.5260i	−0.148223	−	1.03091i
$126$	0.415415	+	0.909632i	0.0370081	+	0.0810365i
$127$	8.02017	+	17.5617i	0.711675	+	1.55835i	0.825216	+	0.564817i	$0.191053\pi$
$127$	8.02017	+	17.5617i	0.711675	+	1.55835i	−0.113542	+	0.993533i	$0.536220\pi$
$128$	−0.142315	−	0.989821i	−0.0125790	−	0.0874887i
$129$	3.96412	+	2.54759i	0.349022	+	0.224303i
$130$	−0.329832	+	0.0968475i	−0.0289282	+	0.00849409i
$131$	0.611207	−	4.25104i	0.0534014	−	0.371415i	−0.945544	−	0.325495i	$-0.894469\pi$
$131$	0.611207	−	4.25104i	0.0534014	−	0.371415i	0.998945	−	0.0459198i	$-0.0146219\pi$
$132$	1.72502	−	1.99078i	0.150144	−	0.173275i
$133$	−3.92447	+	2.52211i	−0.340295	+	0.218694i
$134$	−4.92876	−	5.68809i	−0.425780	−	0.491376i
$135$	−1.44504	−	0.424302i	−0.124369	−	0.0365181i
$136$	0.218288	−	0.477985i	0.0187181	−	0.0409868i
$137$	4.31710			0.368835			0.184417	−	0.982848i	$-0.440960\pi$
$137$	4.31710			0.368835			0.184417	+	0.982848i	$0.440960\pi$
$138$	2.64978	−	3.99733i	0.225564	−	0.340276i
$139$	−1.50959			−0.128042			−0.0640209	−	0.997949i	$-0.520392\pi$
$139$	−1.50959			−0.128042			−0.0640209	+	0.997949i	$0.520392\pi$
$140$	−0.625634	+	1.36995i	−0.0528757	+	0.115782i
$141$	−4.80505	−	1.41089i	−0.404658	−	0.118818i
$142$	7.62089	+	8.79497i	0.639531	+	0.738058i
$143$	−0.505807	+	0.325063i	−0.0422977	+	0.0271831i
$144$	−0.654861	+	0.755750i	−0.0545717	+	0.0629791i
$145$	1.06110	−	7.38014i	0.0881199	−	0.612887i
$146$	6.72238	−	1.97387i	0.556348	−	0.163359i
$147$	−0.841254	−	0.540641i	−0.0693854	−	0.0445913i
$148$	−1.16700	−	8.11667i	−0.0959269	−	0.667186i
$149$	0.629266	+	1.37790i	0.0515515	+	0.112882i	0.933655	−	0.358174i	$-0.116600\pi$
$149$	0.629266	+	1.37790i	0.0515515	+	0.112882i	−0.882104	+	0.471056i	$0.843873\pi$
$150$	1.13484	+	2.48496i	0.0926595	+	0.202896i
$151$	−1.60114	−	11.1362i	−0.130299	−	0.906251i	−0.945163	−	0.326599i	$-0.894097\pi$
$151$	−1.60114	−	11.1362i	−0.130299	−	0.906251i	0.814864	−	0.579652i	$-0.196812\pi$
$152$	−3.92447	−	2.52211i	−0.318317	−	0.204570i
$153$	−0.504185	+	0.148042i	−0.0407610	+	0.0119685i
$154$	−0.374882	+	2.60736i	−0.0302089	+	0.210107i
$155$	−1.64688	+	1.90060i	−0.132280	+	0.152660i
$156$	0.192017	−	0.123402i	0.0153737	−	0.00988007i
$157$	−0.842563	−	0.972370i	−0.0672439	−	0.0776036i	0.721131	−	0.692799i	$-0.243623\pi$
$157$	−0.842563	−	0.972370i	−0.0672439	−	0.0776036i	−0.788375	+	0.615195i	$0.789077\pi$
$158$	−7.72318	−	2.26773i	−0.614423	−	0.180411i
$159$	2.52702	−	5.53340i	0.200406	−	0.438827i
$160$	−1.50605			−0.119063
$161$	−0.0680135	+	4.79535i	−0.00536021	+	0.377926i
$162$	1.00000			0.0785674
$163$	−0.790942	+	1.73192i	−0.0619514	+	0.135655i	−0.938075	−	0.346431i	$-0.887393\pi$
$163$	−0.790942	+	1.73192i	−0.0619514	+	0.135655i	0.876124	+	0.482086i	$0.160121\pi$
$164$	0.0470982	+	0.0138293i	0.00367775	+	0.00107989i
$165$	−2.59796	−	2.99820i	−0.202251	−	0.233410i
$166$	−1.70637	+	1.09662i	−0.132440	+	0.0851140i
$167$	−12.4350	+	14.3508i	−0.962250	+	1.11050i	0.0315715	+	0.999501i	$0.489949\pi$
$167$	−12.4350	+	14.3508i	−0.962250	+	1.11050i	−0.993821	+	0.110994i	$0.964597\pi$
$168$	0.142315	−	0.989821i	0.0109798	−	0.0763664i
$169$	12.4234	−	3.64785i	0.955648	−	0.280603i
$170$	−0.665753	−	0.427854i	−0.0510609	−	0.0328149i
$171$	0.663903	+	4.61755i	0.0507699	+	0.353113i
$172$	−1.95750	−	4.28633i	−0.149258	−	0.326830i
$173$	−7.36777	−	16.1332i	−0.560161	−	1.22658i	−0.951873	−	0.306493i	$-0.900844\pi$
$173$	−7.36777	−	16.1332i	−0.560161	−	1.22658i	0.391712	−	0.920088i	$-0.371883\pi$
$174$	0.704563	+	4.90034i	0.0534128	+	0.371494i
$175$	−2.29816	−	1.47694i	−0.173725	−	0.111646i
$176$	−2.52747	+	0.742133i	−0.190515	+	0.0559404i
$177$	0.0271187	−	0.188614i	0.00203836	−	0.0141771i
$178$	−4.90413	+	5.65967i	−0.367580	+	0.424210i
$179$	12.5255	−	8.04964i	0.936199	−	0.601658i	0.0188841	−	0.999822i	$-0.493989\pi$
$179$	12.5255	−	8.04964i	0.936199	−	0.601658i	0.917315	+	0.398163i	$0.130352\pi$
$180$	0.986250	+	1.13819i	0.0735107	+	0.0848359i
$181$	2.21743	+	0.651097i	0.164821	+	0.0483957i	0.363102	−	0.931749i	$-0.381718\pi$
$181$	2.21743	+	0.651097i	0.164821	+	0.0483957i	−0.198281	+	0.980145i	$0.563536\pi$
$182$	−0.0948190	+	0.207625i	−0.00702845	+	0.0153902i
$183$	1.24364			0.0919322
$184$	−4.39026	+	1.93019i	−0.323654	+	0.142296i
$185$	−12.3498			−0.907973
$186$	0.693675	−	1.51894i	0.0508627	−	0.111374i
$187$	−1.32811	−	0.389969i	−0.0971212	−	0.0285174i
$188$	3.27948	+	3.78472i	0.239181	+	0.276029i
$189$	−0.841254	+	0.540641i	−0.0611922	+	0.0393258i
$190$	−4.60089	+	5.30971i	−0.333783	+	0.385206i
$191$	2.81432	−	19.5740i	0.203637	−	1.41633i	−0.589738	−	0.807595i	$-0.700769\pi$
$191$	2.81432	−	19.5740i	0.203637	−	1.41633i	0.793375	−	0.608733i	$-0.208322\pi$
$192$	0.959493	−	0.281733i	0.0692454	−	0.0203323i
$193$	8.44799	+	5.42920i	0.608100	+	0.390802i	0.808144	−	0.588985i	$-0.200472\pi$
$193$	8.44799	+	5.42920i	0.608100	+	0.390802i	−0.200044	+	0.979787i	$0.564109\pi$
$194$	0.341396	+	2.37446i	0.0245108	+	0.170477i
$195$	−0.142802	−	0.312692i	−0.0102262	−	0.0223924i
$196$	0.415415	+	0.909632i	0.0296725	+	0.0649737i
$197$	1.61074	+	11.2029i	0.114760	+	0.798176i	0.963181	+	0.268854i	$0.0866448\pi$
$197$	1.61074	+	11.2029i	0.114760	+	0.798176i	−0.848421	+	0.529323i	$0.822446\pi$
$198$	2.21601	+	1.42414i	0.157485	+	0.101209i
$199$	−7.70616	+	2.26273i	−0.546275	+	0.160401i	−0.543214	−	0.839594i	$-0.682793\pi$
$199$	−7.70616	+	2.26273i	−0.546275	+	0.160401i	−0.00306151	+	0.999995i	$0.500975\pi$
$200$	0.388780	−	2.70402i	0.0274909	−	0.191203i
$201$	4.92876	−	5.68809i	0.347648	−	0.401207i
$202$	−13.3422	+	8.57452i	−0.938755	+	0.603301i
$203$	−3.24204	−	3.74152i	−0.227547	−	0.262603i
$204$	0.504185	+	0.148042i	0.0353000	+	0.0103650i
$205$	0.0307102	−	0.0672460i	0.00214489	−	0.00469666i
$206$	−10.8465			−0.755709
$207$	4.33375	+	2.05393i	0.301216	+	0.142758i
$208$	−0.228251			−0.0158264
$209$	−5.10483	+	11.1780i	−0.353109	+	0.773200i
$210$	−1.44504	−	0.424302i	−0.0997172	−	0.0292796i
$211$	6.30652	+	7.27812i	0.434159	+	0.501046i	0.930098	−	0.367311i	$-0.119722\pi$
$211$	6.30652	+	7.27812i	0.434159	+	0.501046i	−0.495939	+	0.868357i	$0.665176\pi$
$212$	−5.11745	+	3.28878i	−0.351468	+	0.225875i
$213$	−7.62089	+	8.79497i	−0.522175	+	0.602622i
$214$	−0.0784368	+	0.545540i	−0.00536183	+	0.0372924i
$215$	−6.80926	+	1.99938i	−0.464388	+	0.136357i
$216$	−0.841254	−	0.540641i	−0.0572401	−	0.0367859i
$217$	0.237642	+	1.65284i	0.0161322	+	0.112202i
$218$	−3.60594	−	7.89592i	−0.244225	−	0.534779i
$219$	2.91047	+	6.37305i	0.196672	+	0.430651i
$220$	0.564590	+	3.92681i	0.0380646	+	0.264745i
$221$	−0.100899	−	0.0648441i	−0.00678723	−	0.00436189i
$222$	7.86797	−	2.31024i	0.528064	−	0.155053i
$223$	2.46215	−	17.1246i	0.164878	−	1.14675i	−0.724399	−	0.689381i	$-0.757883\pi$
$223$	2.46215	−	17.1246i	0.164878	−	1.14675i	0.889277	−	0.457369i	$-0.151208\pi$
$224$	−0.654861	+	0.755750i	−0.0437547	+	0.0504956i
$225$	−2.29816	+	1.47694i	−0.153211	+	0.0984625i
$226$	5.60318	+	6.46641i	0.372718	+	0.430140i
$227$	−9.45032	−	2.77486i	−0.627240	−	0.184174i	−0.0473620	−	0.998878i	$-0.515081\pi$
$227$	−9.45032	−	2.77486i	−0.627240	−	0.184174i	−0.579878	+	0.814704i	$0.696900\pi$
$228$	1.93792	−	4.24346i	0.128342	−	0.281030i
$229$	17.1018			1.13012			0.565059	−	0.825050i	$-0.308853\pi$
$229$	17.1018			1.13012			0.565059	+	0.825050i	$0.308853\pi$
$230$	1.93639	+	6.95833i	0.127682	+	0.458819i
$231$	−2.63418			−0.173316
$232$	2.05661	−	4.50335i	0.135023	−	0.295659i
$233$	−5.82232	−	1.70959i	−0.381433	−	0.111999i	0.0853945	−	0.996347i	$-0.472785\pi$
$233$	−5.82232	−	1.70959i	−0.381433	−	0.111999i	−0.466828	+	0.884348i	$0.654603\pi$
$234$	0.149473	+	0.172501i	0.00977134	+	0.0112767i
$235$	6.34484	−	4.07758i	0.413892	−	0.265992i
$236$	−0.124786	+	0.144011i	−0.00812290	+	0.00937432i
$237$	1.14553	−	7.96730i	0.0744099	−	0.517532i
$238$	−0.504185	+	0.148042i	−0.0326815	+	0.00959614i
$239$	−13.6277	−	8.75800i	−0.881503	−	0.566508i	0.0197478	−	0.999805i	$-0.493714\pi$
$239$	−13.6277	−	8.75800i	−0.881503	−	0.566508i	−0.901251	+	0.433297i	$0.857350\pi$
$240$	−0.214333	−	1.49072i	−0.0138351	−	0.0962253i
$241$	2.55651	+	5.59797i	0.164679	+	0.360597i	0.973924	−	0.226875i	$-0.0728507\pi$
$241$	2.55651	+	5.59797i	0.164679	+	0.360597i	−0.809245	+	0.587471i	$0.800123\pi$
$242$	−1.68705	−	3.69412i	−0.108448	−	0.237467i
$243$	0.142315	+	0.989821i	0.00912950	+	0.0634971i
$244$	−1.04621	−	0.672360i	−0.0669769	−	0.0430434i
$245$	1.44504	−	0.424302i	0.0923202	−	0.0271077i
$246$	−0.00698575	+	0.0485869i	−0.000445395	+	0.00309779i
$247$	−0.697295	+	0.804722i	−0.0443678	+	0.0512032i
$248$	−1.40476	+	0.902782i	−0.0892021	+	0.0573267i
$249$	−1.32830	−	1.53294i	−0.0841774	−	0.0971459i
$250$	−11.1728	−	3.28063i	−0.706630	−	0.207485i
$251$	−9.38466	+	20.5495i	−0.592355	+	1.29708i	0.341654	+	0.939826i	$0.389013\pi$
$251$	−9.38466	+	20.5495i	−0.592355	+	1.29708i	−0.934009	+	0.357250i	$0.883714\pi$
$252$	1.00000			0.0629941
$253$	6.67854	+	10.7234i	0.419876	+	0.674174i
$254$	19.3064			1.21139
$255$	0.328752	−	0.719867i	0.0205873	−	0.0450798i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	8.99267	+	10.3781i	0.560947	+	0.647368i	0.963398	−	0.268074i	$-0.0863871\pi$
$257$	8.99267	+	10.3781i	0.560947	+	0.647368i	−0.402451	+	0.915441i	$0.631842\pi$
$258$	3.96412	−	2.54759i	0.246796	−	0.158606i
$259$	−5.36995	+	6.19725i	−0.333672	+	0.385078i
$260$	−0.0489217	+	0.340258i	−0.00303399	+	0.0211019i
$261$	−4.75020	+	1.39478i	−0.294030	+	0.0863349i
$262$	−3.61298	−	2.32192i	−0.223210	−	0.143449i
$263$	−3.66281	−	25.4754i	−0.225859	−	1.57088i	−0.715282	−	0.698835i	$-0.753702\pi$
$263$	−3.66281	−	25.4754i	−0.225859	−	1.57088i	0.489424	−	0.872046i	$-0.337207\pi$
$264$	−1.09428	−	2.39613i	−0.0673480	−	0.147472i
$265$	3.80581	+	8.33355i	0.233789	+	0.511926i
$266$	0.663903	+	4.61755i	0.0407065	+	0.283120i
$267$	−6.30000	−	4.04876i	−0.385554	−	0.247780i
$268$	−7.22155	+	2.12044i	−0.441126	+	0.129526i
$269$	1.83149	−	12.7383i	0.111668	−	0.776669i	−0.854629	−	0.519239i	$-0.826215\pi$
$269$	1.83149	−	12.7383i	0.111668	−	0.776669i	0.966297	−	0.257430i	$-0.0828755\pi$
$270$	−0.986250	+	1.13819i	−0.0600213	+	0.0692682i
$271$	−7.14303	+	4.59055i	−0.433908	+	0.278856i	−0.739307	−	0.673369i	$-0.764847\pi$
$271$	−7.14303	+	4.59055i	−0.433908	+	0.278856i	0.305399	+	0.952225i	$0.401210\pi$
$272$	−0.344110	−	0.397124i	−0.0208647	−	0.0240792i
$273$	−0.219006	−	0.0643058i	−0.0132548	−	0.00389197i
$274$	1.79339	−	3.92697i	0.108342	−	0.237237i
$275$	−7.19611			−0.433942
$276$	−2.53534	−	4.07088i	−0.152610	−	0.245038i
$277$	−16.7175			−1.00446			−0.502229	−	0.864735i	$-0.667487\pi$
$277$	−16.7175			−1.00446			−0.502229	+	0.864735i	$0.667487\pi$
$278$	−0.627107	+	1.37317i	−0.0376114	+	0.0823574i
$279$	1.60220	+	0.470447i	0.0959210	+	0.0281649i
$280$	0.986250	+	1.13819i	0.0589397	+	0.0680200i
$281$	11.6220	−	7.46901i	0.693310	−	0.445564i	−0.145951	−	0.989292i	$-0.546624\pi$
$281$	11.6220	−	7.46901i	0.693310	−	0.445564i	0.839261	+	0.543728i	$0.182988\pi$
$282$	−3.27948	+	3.78472i	−0.195290	+	0.225377i
$283$	−0.112803	+	0.784559i	−0.00670541	+	0.0466372i	−0.992899	−	0.118957i	$-0.962045\pi$
$283$	−0.112803	+	0.784559i	−0.00670541	+	0.0466372i	0.986194	+	0.165594i	$0.0529541\pi$
$284$	11.1660	−	3.27864i	0.662581	−	0.194551i
$285$	−5.91043	−	3.79841i	−0.350104	−	0.224998i
$286$	0.0855674	+	0.595134i	0.00505971	+	0.0351910i
$287$	−0.0203913	−	0.0446507i	−0.00120366	−	0.00263565i
$288$	0.415415	+	0.909632i	0.0244786	+	0.0536006i
$289$	2.38006	+	16.5537i	0.140003	+	0.973744i
$290$	−6.27241	−	4.03104i	−0.368329	−	0.236711i
$291$	−2.30171	+	0.675843i	−0.134929	+	0.0396186i
$292$	0.997084	−	6.93487i	0.0583499	−	0.405832i
$293$	11.3864	−	13.1406i	0.665201	−	0.767682i	−0.318417	−	0.947951i	$-0.603151\pi$
$293$	11.3864	−	13.1406i	0.665201	−	0.767682i	0.983617	+	0.180268i	$0.0576966\pi$
$294$	−0.841254	+	0.540641i	−0.0490629	+	0.0315308i
$295$	0.187934	+	0.216887i	0.0109419	+	0.0126277i
$296$	−7.86797	−	2.31024i	−0.457317	−	0.134280i
$297$	−1.09428	+	2.39613i	−0.0634963	+	0.139038i
$298$	1.51479			0.0877494
$299$	0.293474	+	1.05458i	0.0169720	+	0.0609880i
$300$	2.73183			0.157722
$301$	−1.95750	+	4.28633i	−0.112829	+	0.247060i
$302$	−10.7950	−	3.16969i	−0.621182	−	0.182395i
$303$	−10.3860	−	11.9861i	−0.596663	−	0.688585i
$304$	−3.92447	+	2.52211i	−0.225084	+	0.144653i
$305$	−1.22654	+	1.41550i	−0.0702312	+	0.0810511i
$306$	−0.0747822	+	0.520122i	−0.00427502	+	0.0297334i
$307$	−25.2822	+	7.42353i	−1.44293	+	0.423683i	−0.907198	−	0.420703i	$-0.861783\pi$
$307$	−25.2822	+	7.42353i	−1.44293	+	0.423683i	−0.535734	+	0.844387i	$0.679965\pi$
$308$	2.21601	+	1.42414i	0.126269	+	0.0811481i
$309$	−1.54361	−	10.7361i	−0.0878130	−	0.610753i
$310$	1.04471	+	2.28759i	0.0593353	+	0.129926i
$311$	3.48039	+	7.62099i	0.197355	+	0.432147i	0.982274	−	0.187452i	$-0.0600228\pi$
$311$	3.48039	+	7.62099i	0.197355	+	0.432147i	−0.784919	+	0.619598i	$0.787296\pi$
$312$	−0.0324836	−	0.225928i	−0.00183902	−	0.0127907i
$313$	22.4705	+	14.4409i	1.27011	+	0.816250i	0.989634	−	0.143611i	$-0.0458715\pi$
$313$	22.4705	+	14.4409i	1.27011	+	0.816250i	0.280476	+	0.959861i	$0.409508\pi$
$314$	−1.23451	+	0.362485i	−0.0696676	+	0.0204562i
$315$	0.214333	−	1.49072i	0.0120763	−	0.0839923i
$316$	−5.27113	+	6.08320i	−0.296524	+	0.342207i
$317$	5.20451	−	3.34473i	0.292314	−	0.187859i	−0.386262	−	0.922389i	$-0.626234\pi$
$317$	5.20451	−	3.34473i	0.292314	−	0.187859i	0.678576	+	0.734530i	$0.262597\pi$
$318$	−3.98360	−	4.59732i	−0.223389	−	0.257805i
$319$	−12.5129	−	3.67410i	−0.700585	−	0.205710i
$320$	−0.625634	+	1.36995i	−0.0349740	+	0.0765824i
$321$	−0.551150			−0.0307622
$322$	4.33375	+	2.05393i	0.241510	+	0.114461i
$323$	−2.45134			−0.136396
$324$	0.415415	−	0.909632i	0.0230786	−	0.0505351i
$325$	−0.598285	−	0.175672i	−0.0331869	−	0.00974455i
$326$	1.24684	+	1.43893i	0.0690562	+	0.0796951i
$327$	7.30237	−	4.69295i	0.403822	−	0.259521i
$328$	0.0321449	−	0.0370971i	0.00177490	−	0.00204835i
$329$	0.712699	−	4.95693i	0.0392924	−	0.273284i
$330$	−3.80649	+	1.11769i	−0.209540	+	0.0615266i
$331$	−23.1057	−	14.8491i	−1.27001	−	0.816183i	−0.280385	−	0.959888i	$-0.590462\pi$
$331$	−23.1057	−	14.8491i	−1.27001	−	0.816183i	−0.989621	+	0.143705i	$0.954098\pi$
$332$	0.288666	+	2.00772i	0.0158426	+	0.110188i
$333$	3.40646	+	7.45910i	0.186673	+	0.408756i
$334$	7.88822	+	17.2728i	0.431624	+	0.945126i
$335$	1.61316	+	11.2198i	0.0881362	+	0.613001i
$336$	−0.841254	−	0.540641i	−0.0458941	−	0.0294944i
$337$	8.23330	−	2.41752i	0.448497	−	0.131690i	−0.0496817	−	0.998765i	$-0.515821\pi$
$337$	8.23330	−	2.41752i	0.448497	−	0.131690i	0.498178	+	0.867075i	$0.334002\pi$
$338$	1.84268	−	12.8161i	0.100228	−	0.697105i
$339$	−5.60318	+	6.46641i	−0.304323	+	0.351207i
$340$	−0.665753	+	0.427854i	−0.0361055	+	0.0232036i
$341$	2.88050	+	3.32427i	0.155988	+	0.180019i
$342$	4.47606	+	1.31429i	0.242038	+	0.0710687i
$343$	0.415415	−	0.909632i	0.0224303	−	0.0491155i
$344$	−4.71216			−0.254063
$345$	−6.61193	+	2.90696i	−0.355974	+	0.156505i
$346$	−17.7359			−0.953489
$347$	3.13904	−	6.87354i	0.168512	−	0.368991i	−0.806469	−	0.591276i	$-0.798624\pi$
$347$	3.13904	−	6.87354i	0.168512	−	0.368991i	0.974982	+	0.222285i	$0.0713516\pi$
$348$	4.75020	+	1.39478i	0.254637	+	0.0747682i
$349$	3.09687	+	3.57398i	0.165772	+	0.191311i	0.832557	−	0.553939i	$-0.186876\pi$
$349$	3.09687	+	3.57398i	0.165772	+	0.191311i	−0.666786	+	0.745249i	$0.732330\pi$
$350$	−2.29816	+	1.47694i	−0.122842	+	0.0789456i
$351$	−0.149473	+	0.172501i	−0.00797827	+	0.00920741i
$352$	−0.374882	+	2.60736i	−0.0199813	+	0.138973i
$353$	21.2013	−	6.22527i	1.12843	−	0.331338i	0.336341	−	0.941740i	$-0.390810\pi$
$353$	21.2013	−	6.22527i	1.12843	−	0.331338i	0.792092	+	0.610402i	$0.208992\pi$
$354$	−0.160304	−	0.103021i	−0.00852007	−	0.00547552i
$355$	−2.49428	−	17.3481i	−0.132383	−	0.920741i
$356$	3.11097	+	6.81207i	0.164881	+	0.361039i
$357$	−0.218288	−	0.477985i	−0.0115530	−	0.0252976i
$358$	−2.11894	−	14.7375i	−0.111989	−	0.778902i
$359$	11.3329	+	7.28324i	0.598130	+	0.384395i	0.804389	−	0.594102i	$-0.202493\pi$
$359$	11.3329	+	7.28324i	0.598130	+	0.384395i	−0.206259	+	0.978497i	$0.566129\pi$
$360$	1.44504	−	0.424302i	0.0761603	−	0.0223627i
$361$	−0.393146	+	2.73439i	−0.0206919	+	0.143915i
$362$	1.51341	−	1.74657i	0.0795433	−	0.0917978i
$363$	3.41643	−	2.19561i	0.179316	−	0.115239i
$364$	0.149473	+	0.172501i	0.00783451	+	0.00904150i
$365$	−10.1242	−	2.97274i	−0.529925	−	0.155600i
$366$	0.516625	−	1.13125i	0.0270044	−	0.0591314i
$367$	−31.3164			−1.63470			−0.817350	−	0.576141i	$-0.804558\pi$
$367$	−31.3164			−1.63470			−0.817350	+	0.576141i	$0.804558\pi$
$368$	−0.0680135	+	4.79535i	−0.00354545	+	0.249975i
$369$	−0.0490866			−0.00255534
$370$	−5.13028	+	11.2337i	−0.266711	+	0.584015i
$371$	5.83671	+	1.71381i	0.303027	+	0.0889767i
$372$	−1.09351	−	1.26198i	−0.0566959	−	0.0654305i
$373$	17.2941	−	11.1142i	0.895455	−	0.575474i	−0.00998433	−	0.999950i	$-0.503178\pi$
$373$	17.2941	−	11.1142i	0.895455	−	0.575474i	0.905439	+	0.424476i	$0.139542\pi$
$374$	−0.906446	+	1.04609i	−0.0468712	+	0.0540923i
$375$	1.65718	−	11.5260i	0.0855765	−	0.595198i
$376$	4.80505	−	1.41089i	0.247801	−	0.0727611i
$377$	−0.950627	−	0.610931i	−0.0489598	−	0.0314645i
$378$	0.142315	+	0.989821i	0.00731989	+	0.0509109i
$379$	4.63198	+	10.1426i	0.237929	+	0.520991i	0.990499	−	0.137521i	$-0.0439134\pi$
$379$	4.63198	+	10.1426i	0.237929	+	0.520991i	−0.752570	+	0.658512i	$0.771186\pi$
$380$	2.91860	+	6.39084i	0.149721	+	0.327843i
$381$	2.74759	+	19.1099i	0.140763	+	0.979029i
$382$	−16.6361	−	10.6913i	−0.851175	−	0.547017i
$383$	−4.16379	+	1.22260i	−0.212760	+	0.0624719i	−0.386376	−	0.922342i	$-0.626273\pi$
$383$	−4.16379	+	1.22260i	−0.212760	+	0.0624719i	0.173616	+	0.984813i	$0.444455\pi$
$384$	0.142315	−	0.989821i	0.00726247	−	0.0505116i
$385$	2.59796	−	2.99820i	0.132404	−	0.152802i
$386$	8.44799	−	5.42920i	0.429992	−	0.276339i
$387$	3.08581	+	3.56121i	0.156861	+	0.181027i
$388$	2.30171	+	0.675843i	0.116852	+	0.0343107i
$389$	7.53202	−	16.4928i	0.381888	−	0.836219i	−0.616902	−	0.787040i	$-0.711612\pi$
$389$	7.53202	−	16.4928i	0.381888	−	0.836219i	0.998790	−	0.0491786i	$-0.0156603\pi$
$390$	−0.343757			−0.0174068
$391$	−1.39238	+	2.10048i	−0.0704157	+	0.106226i
$392$	1.00000			0.0505076
$393$	1.78410	−	3.90664i	0.0899962	−	0.197064i
$394$	10.8597	+	3.18869i	0.547103	+	0.160644i
$395$	7.93856	+	9.16158i	0.399432	+	0.460969i
$396$	2.21601	−	1.42414i	0.111359	−	0.0715659i
$397$	9.05132	−	10.4458i	0.454273	−	0.524259i	−0.481697	−	0.876338i	$-0.659980\pi$
$397$	9.05132	−	10.4458i	0.454273	−	0.524259i	0.935970	+	0.352079i	$0.114525\pi$
$398$	−1.14300	+	7.94974i	−0.0572934	+	0.398485i
$399$	−4.47606	+	1.31429i	−0.224083	+	0.0657968i
$400$	−2.29816	−	1.47694i	−0.114908	−	0.0738469i
$401$	0.0189033	+	0.131475i	0.000943985	+	0.00656556i	0.990288	−	0.139031i	$-0.0443989\pi$
$401$	0.0189033	+	0.131475i	0.000943985	+	0.00656556i	−0.989344	+	0.145597i	$0.953490\pi$
$402$	−3.12659	−	6.84628i	−0.155940	−	0.341461i
$403$	0.158332	+	0.346699i	0.00788709	+	0.0172703i
$404$	2.25710	+	15.6985i	0.112295	+	0.781029i
$405$	−1.26697	−	0.814230i	−0.0629560	−	0.0404594i
$406$	−4.75020	+	1.39478i	−0.235748	+	0.0692219i
$407$	−3.07409	+	21.3807i	−0.152377	+	1.05980i
$408$	0.344110	−	0.397124i	0.0170360	−	0.0196606i
$409$	3.66814	−	2.35737i	0.181378	−	0.116565i	−0.446801	−	0.894633i	$-0.647437\pi$
$409$	3.66814	−	2.35737i	0.181378	−	0.116565i	0.628179	+	0.778069i	$0.283800\pi$
$410$	−0.0484116	−	0.0558700i	−0.00239088	−	0.00275922i
$411$	4.14222	+	1.21627i	0.204321	+	0.0599940i
$412$	−4.50578	+	9.86629i	−0.221984	+	0.486077i
$413$	0.190554			0.00937655
$414$	3.66862	−	3.08888i	0.180303	−	0.151810i
$415$	3.05481			0.149955
$416$	−0.0948190	+	0.207625i	−0.00464889	+	0.0101796i
$417$	−1.44844	−	0.425301i	−0.0709305	−	0.0208271i
$418$	8.04726	+	9.28704i	0.393604	+	0.454244i
$419$	−11.8954	+	7.64471i	−0.581129	+	0.373469i	−0.797933	−	0.602746i	$-0.794073\pi$
$419$	−11.8954	+	7.64471i	−0.581129	+	0.373469i	0.216804	+	0.976215i	$0.430437\pi$
$420$	−0.986250	+	1.13819i	−0.0481241	+	0.0555381i
$421$	1.54923	−	10.7751i	0.0755047	−	0.525147i	−0.916607	−	0.399790i	$-0.869083\pi$
$421$	1.54923	−	10.7751i	0.0755047	−	0.525147i	0.992112	−	0.125357i	$-0.0400077\pi$
$422$	9.24023	−	2.71318i	0.449807	−	0.132075i
$423$	−4.21292	−	2.70748i	−0.204839	−	0.131642i
$424$	0.865718	+	6.02120i	0.0420430	+	0.292415i
$425$	−0.596326	−	1.30577i	−0.0289261	−	0.0633392i
$426$	4.83436	+	10.5858i	0.234225	+	0.512882i
$427$	0.176988	+	1.23098i	0.00856504	+	0.0595712i
$428$	0.463657	+	0.297974i	0.0224117	+	0.0144031i
$429$	−0.576899	+	0.169393i	−0.0278530	+	0.00817836i
$430$	−1.00997	+	7.02449i	−0.0487051	+	0.338751i
$431$	19.9482	−	23.0214i	0.960869	−	1.10890i	−0.0331230	−	0.999451i	$-0.510545\pi$
$431$	19.9482	−	23.0214i	0.960869	−	1.10890i	0.993992	−	0.109451i	$-0.0349092\pi$
$432$	−0.841254	+	0.540641i	−0.0404748	+	0.0260116i
$433$	0.937158	+	1.08154i	0.0450369	+	0.0519754i	0.777821	−	0.628486i	$-0.216325\pi$
$433$	0.937158	+	1.08154i	0.0450369	+	0.0519754i	−0.732784	+	0.680461i	$0.761780\pi$
$434$	1.60220	+	0.470447i	0.0769079	+	0.0225822i
$435$	3.09735	−	6.78225i	0.148506	−	0.325184i
$436$	−8.68034			−0.415713
$437$	16.6987	+	14.8893i	0.798806	+	0.712253i
$438$	7.00618			0.334768
$439$	12.1719	−	26.6527i	0.580932	−	1.27206i	−0.359837	−	0.933015i	$-0.617168\pi$
$439$	12.1719	−	26.6527i	0.580932	−	1.27206i	0.940769	−	0.339048i	$-0.110105\pi$
$440$	3.80649	+	1.11769i	0.181467	+	0.0532836i
$441$	−0.654861	−	0.755750i	−0.0311838	−	0.0359881i
$442$	−0.100899	+	0.0648441i	−0.00479929	+	0.00308432i
$443$	22.0022	−	25.3919i	1.04536	−	1.20641i	0.0673741	−	0.997728i	$-0.478538\pi$
$443$	22.0022	−	25.3919i	1.04536	−	1.20641i	0.977984	−	0.208680i	$-0.0669166\pi$
$444$	1.16700	−	8.11667i	0.0553834	−	0.385200i
$445$	10.8216	−	3.17752i	0.512995	−	0.150629i
$446$	−14.5543	−	9.35347i	−0.689166	−	0.442900i
$447$	0.215577	+	1.49937i	0.0101964	+	0.0709178i
$448$	0.415415	+	0.909632i	0.0196265	+	0.0429761i
$449$	10.1682	+	22.2652i	0.479865	+	1.05076i	0.982501	+	0.186259i	$0.0596365\pi$
$449$	10.1682	+	22.2652i	0.479865	+	1.05076i	−0.502636	+	0.864498i	$0.667636\pi$
$450$	0.388780	+	2.70402i	0.0183272	+	0.127469i
$451$	−0.108776	−	0.0699063i	−0.00512208	−	0.00329176i
$452$	8.20970	−	2.41059i	0.386152	−	0.113384i
$453$	1.60114	−	11.1362i	0.0752283	−	0.523224i
$454$	−6.44991	+	7.44359i	−0.302709	+	0.349345i
$455$	0.289187	−	0.185849i	0.0135573	−	0.00871273i
$456$	−3.05495	−	3.52559i	−0.143061	−	0.165101i
$457$	22.1496	+	6.50371i	1.03611	+	0.304231i	0.755195	−	0.655500i	$-0.227542\pi$
$457$	22.1496	+	6.50371i	1.03611	+	0.304231i	0.280920	+	0.959731i	$0.409360\pi$
$458$	7.10434	−	15.5563i	0.331964	−	0.726900i
$459$	−0.525470			−0.0245269
$460$	7.13393	+	1.12919i	0.332621	+	0.0526487i
$461$	21.0810			0.981841			0.490921	−	0.871204i	$-0.336661\pi$
$461$	21.0810			0.981841			0.490921	+	0.871204i	$0.336661\pi$
$462$	−1.09428	+	2.39613i	−0.0509103	+	0.111478i
$463$	17.6799	+	5.19129i	0.821655	+	0.241260i	0.665428	−	0.746462i	$-0.268249\pi$
$463$	17.6799	+	5.19129i	0.821655	+	0.241260i	0.156226	+	0.987721i	$0.450067\pi$
$464$	−3.24204	−	3.74152i	−0.150508	−	0.173696i
$465$	−2.11563	+	1.35963i	−0.0981098	+	0.0630513i
$466$	−3.97378	+	4.58598i	−0.184082	+	0.212442i
$467$	−1.09687	+	7.62890i	−0.0507571	+	0.353024i	0.948577	+	0.316545i	$0.102523\pi$
$467$	−1.09687	+	7.62890i	−0.0507571	+	0.353024i	−0.999334	+	0.0364780i	$0.988386\pi$
$468$	0.219006	−	0.0643058i	0.0101235	−	0.00297254i
$469$	6.33163	+	4.06909i	0.292368	+	0.187893i
$470$	−1.07336	−	7.46536i	−0.0495103	−	0.344351i
$471$	−0.534485	−	1.17036i	−0.0246278	−	0.0539273i
$472$	0.0791590	+	0.173334i	0.00364359	+	0.00797834i
$473$	1.76651	+	12.2863i	0.0812240	+	0.564926i
$474$	−6.77145	−	4.35174i	−0.311023	−	0.199882i
$475$	−12.2278	+	3.59042i	−0.561052	+	0.164740i
$476$	−0.0747822	+	0.520122i	−0.00342764	+	0.0238397i
$477$	3.98360	−	4.59732i	0.182396	−	0.210497i
$478$	−13.6277	+	8.75800i	−0.623317	+	0.400581i
$479$	14.1189	+	16.2941i	0.645110	+	0.744496i	0.980270	−	0.197665i	$-0.0633358\pi$
$479$	14.1189	+	16.2941i	0.645110	+	0.744496i	−0.335160	+	0.942161i	$0.608790\pi$
$480$	−1.44504	−	0.424302i	−0.0659567	−	0.0193666i
$481$	−0.777529	+	1.70255i	−0.0354523	+	0.0776296i
$482$	6.15410			0.280312
$483$	−1.41626	+	4.58194i	−0.0644423	+	0.208486i
$484$	−4.06112			−0.184596
$485$	1.50082	−	3.28634i	0.0681488	−	0.149225i
$486$	0.959493	+	0.281733i	0.0435235	+	0.0127796i
$487$	17.9503	+	20.7157i	0.813405	+	0.938719i	0.999036	−	0.0439006i	$-0.0139785\pi$
$487$	17.9503	+	20.7157i	0.813405	+	0.938719i	−0.185631	+	0.982619i	$0.559433\pi$
$488$	−1.04621	+	0.672360i	−0.0473598	+	0.0304363i
$489$	−1.24684	+	1.43893i	−0.0563841	+	0.0650708i
$490$	0.214333	−	1.49072i	0.00968256	−	0.0673437i
$491$	−2.46095	+	0.722601i	−0.111061	+	0.0326105i	−0.336791	−	0.941579i	$-0.609342\pi$
$491$	−2.46095	+	0.722601i	−0.111061	+	0.0326105i	0.225730	+	0.974190i	$0.427523\pi$
$492$	0.0412942	+	0.0265382i	0.00186169	+	0.00119643i
$493$	−0.370227	−	2.57499i	−0.0166742	−	0.115972i
$494$	0.442334	+	0.968576i	0.0199015	+	0.0435783i
$495$	−1.64803	−	3.60868i	−0.0740734	−	0.162198i
$496$	0.237642	+	1.65284i	0.0106705	+	0.0742147i
$497$	−9.79002	−	6.29166i	−0.439142	−	0.282220i
$498$	−1.94620	+	0.571456i	−0.0872114	+	0.0256076i
$499$	5.08290	−	35.3524i	0.227542	−	1.58259i	−0.480871	−	0.876791i	$-0.659680\pi$
$499$	5.08290	−	35.3524i	0.227542	−	1.58259i	0.708413	−	0.705798i	$-0.249411\pi$
$500$	−7.62551	+	8.80031i	−0.341023	+	0.393562i
$501$	−15.9744	+	10.2661i	−0.713683	+	0.458656i
$502$	14.7940	+	17.0732i	0.660288	+	0.762013i
$503$	0.963848	+	0.283011i	0.0429759	+	0.0126188i	0.303150	−	0.952943i	$-0.401962\pi$
$503$	0.963848	+	0.283011i	0.0429759	+	0.0126188i	−0.260174	+	0.965562i	$0.583780\pi$
$504$	0.415415	−	0.909632i	0.0185041	−	0.0405182i
$505$	23.8858			1.06290
$506$	12.5287	−	1.62036i	0.556969	−	0.0720336i
$507$	12.9479			0.575036
$508$	8.02017	−	17.5617i	0.355837	−	0.779175i
$509$	12.2057	+	3.58392i	0.541009	+	0.158854i	0.540809	−	0.841146i	$-0.318118\pi$
$509$	12.2057	+	3.58392i	0.541009	+	0.158854i	0.000199715		1.00000i	$0.499936\pi$
$510$	−0.518245	−	0.598087i	−0.0229483	−	0.0264837i
$511$	−5.89397	+	3.78783i	−0.260734	+	0.167564i
$512$	−0.654861	+	0.755750i	−0.0289410	+	0.0333997i
$513$	−0.663903	+	4.61755i	−0.0293120	+	0.203870i
$514$	13.1759	−	3.86880i	0.581166	−	0.170646i
$515$	13.7421	+	8.83151i	0.605549	+	0.389163i
$516$	−0.670611	−	4.66420i	−0.0295220	−	0.205330i
$517$	−5.48003	−	11.9996i	−0.241011	−	0.527741i
$518$	3.40646	+	7.45910i	0.149671	+	0.327734i
$519$	−2.52408	−	17.5554i	−0.110795	−	0.770596i
$520$	0.289187	+	0.185849i	0.0126817	+	0.00815002i
$521$	18.3966	−	5.40173i	0.805970	−	0.236654i	0.147306	−	0.989091i	$-0.452940\pi$
$521$	18.3966	−	5.40173i	0.805970	−	0.236654i	0.658664	+	0.752437i	$0.271122\pi$
$522$	−0.704563	+	4.90034i	−0.0308379	+	0.214482i
$523$	20.5613	−	23.7290i	0.899084	−	1.03760i	−0.100008	−	0.994987i	$-0.531887\pi$
$523$	20.5613	−	23.7290i	0.899084	−	1.03760i	0.999092	−	0.0426116i	$-0.0135678\pi$
$524$	−3.61298	+	2.32192i	−0.157834	+	0.101433i
$525$	−1.78897	−	2.06458i	−0.0780769	−	0.0901055i
$526$	−24.6948	−	7.25106i	−1.07675	−	0.316161i
$527$	−0.364506	+	0.798156i	−0.0158781	+	0.0347682i
$528$	−2.63418			−0.114638
$529$	22.2432	−	5.85137i	0.967097	−	0.254407i
$530$	9.16145			0.397948
$531$	0.0791590	−	0.173334i	0.00343521	−	0.00752205i
$532$	4.47606	+	1.31429i	0.194062	+	0.0569817i
$533$	−0.00733711	−	0.00846747i	−0.000317805	−	0.000366767i
$534$	−6.30000	+	4.04876i	−0.272627	+	0.175207i
$535$	0.543572	−	0.627315i	0.0235007	−	0.0271212i
$536$	−1.07112	+	7.44982i	−0.0462654	+	0.321783i
$537$	14.2860	−	4.19474i	0.616485	−	0.181016i
$538$	−10.8263	−	6.95767i	−0.466757	−	0.299967i
$539$	−0.374882	−	2.60736i	−0.0161473	−	0.112307i
$540$	0.625634	+	1.36995i	0.0269230	+	0.0589531i
$541$	1.61165	+	3.52903i	0.0692904	+	0.151725i	0.941108	−	0.338105i	$-0.109786\pi$
$541$	1.61165	+	3.52903i	0.0692904	+	0.151725i	−0.871818	+	0.489830i	$0.837059\pi$
$542$	1.20839	+	8.40451i	0.0519046	+	0.361005i
$543$	1.94418	+	1.24945i	0.0834326	+	0.0536189i
$544$	−0.504185	+	0.148042i	−0.0216168	+	0.00634725i
$545$	−1.86048	+	12.9399i	−0.0796942	+	0.554285i
$546$	−0.149473	+	0.172501i	−0.00639685	+	0.00738235i
$547$	−14.5178	+	9.33002i	−0.620736	+	0.398923i	−0.812869	−	0.582446i	$-0.802096\pi$
$547$	−14.5178	+	9.33002i	−0.620736	+	0.398923i	0.192134	+	0.981369i	$0.438459\pi$
$548$	−2.82710	−	3.26264i	−0.120768	−	0.139373i
$549$	1.19326	+	0.350373i	0.0509271	+	0.0149535i
$550$	−2.98937	+	6.54582i	−0.127467	+	0.279115i
$551$	−23.0953			−0.983894
$552$	−4.75622	+	0.615128i	−0.202438	+	0.0261816i
$553$	8.04923			0.342288
$554$	−6.94471	+	15.2068i	−0.295052	+	0.646075i
$555$	−11.8495	−	3.47933i	−0.502984	−	0.147689i
$556$	0.988572	+	1.14087i	0.0419248	+	0.0483838i
$557$	22.5981	−	14.5229i	0.957513	−	0.615356i	0.0342042	−	0.999415i	$-0.489110\pi$
$557$	22.5981	−	14.5229i	0.957513	−	0.615356i	0.923309	+	0.384059i	$0.125474\pi$
$558$	1.09351	−	1.26198i	0.0462920	−	0.0534238i
$559$	−0.153068	+	1.06461i	−0.00647408	+	0.0450282i
$560$	1.44504	−	0.424302i	0.0610641	−	0.0179300i
$561$	−1.16445	−	0.748345i	−0.0491630	−	0.0315951i
$562$	−1.96609	−	13.6745i	−0.0829347	−	0.576823i
$563$	18.6815	+	40.9068i	0.787331	+	1.72401i	0.684137	+	0.729354i	$0.260179\pi$
$563$	18.6815	+	40.9068i	0.787331	+	1.72401i	0.103195	+	0.994661i	$0.467094\pi$
$564$	2.08036	+	4.55535i	0.0875989	+	0.191815i
$565$	−1.83389	−	12.7550i	−0.0771524	−	0.536607i
$566$	0.666800	+	0.428526i	0.0280277	+	0.0180123i
$567$	−0.959493	+	0.281733i	−0.0402949	+	0.0118317i
$568$	1.65618	−	11.5190i	0.0694917	−	0.483325i
$569$	−13.8716	+	16.0087i	−0.581530	+	0.671121i	−0.967933	−	0.251209i	$-0.919172\pi$
$569$	−13.8716	+	16.0087i	−0.581530	+	0.671121i	0.386403	+	0.922330i	$0.373717\pi$
$570$	−5.91043	+	3.79841i	−0.247561	+	0.159098i
$571$	−6.07372	−	7.00945i	−0.254177	−	0.293336i	0.614292	−	0.789079i	$-0.289442\pi$
$571$	−6.07372	−	7.00945i	−0.254177	−	0.293336i	−0.868470	+	0.495742i	$0.834896\pi$
$572$	0.576899	+	0.169393i	0.0241214	+	0.00708267i
$573$	8.21497	−	17.9883i	0.343185	−	0.751471i
$574$	−0.0490866			−0.00204883
$575$	−3.86899	+	12.5171i	−0.161348	+	0.521998i
$576$	1.00000			0.0416667
$577$	−4.87762	+	10.6805i	−0.203058	+	0.444635i	−0.983575	−	0.180500i	$-0.942229\pi$
$577$	−4.87762	+	10.6805i	−0.203058	+	0.444635i	0.780517	+	0.625134i	$0.214956\pi$
$578$	16.0464	+	4.71166i	0.667444	+	0.195979i
$579$	6.57621	+	7.58935i	0.273298	+	0.315403i
$580$	−6.27241	+	4.03104i	−0.260448	+	0.167380i
$581$	1.32830	−	1.53294i	0.0551070	−	0.0635969i
$582$	−0.341396	+	2.37446i	−0.0141513	+	0.0984247i
$583$	15.3749	−	4.51448i	0.636764	−	0.186971i
$584$	−5.89397	−	3.78783i	−0.243894	−	0.156741i
$585$	−0.0489217	−	0.340258i	−0.00202266	−	0.0140679i
$586$	−7.22303	−	15.8162i	−0.298381	−	0.653363i
$587$	−0.390729	−	0.855577i	−0.0161271	−	0.0353134i	0.901397	−	0.432993i	$-0.142543\pi$
$587$	−0.390729	−	0.855577i	−0.0161271	−	0.0353134i	−0.917524	+	0.397680i	$0.869815\pi$
$588$	0.142315	+	0.989821i	0.00586897	+	0.0408195i
$589$	6.55323	+	4.21150i	0.270021	+	0.173532i
$590$	0.275358	−	0.0808524i	0.0113363	−	0.00332864i
$591$	−1.61074	+	11.2029i	−0.0662570	+	0.460827i
$592$	−5.36995	+	6.19725i	−0.220703	+	0.254705i
$593$	−6.90648	+	4.43852i	−0.283615	+	0.182268i	−0.674712	−	0.738081i	$-0.735732\pi$
$593$	−6.90648	+	4.43852i	−0.283615	+	0.182268i	0.391097	+	0.920350i	$0.372096\pi$
$594$	1.72502	+	1.99078i	0.0707784	+	0.0816826i
$595$	0.759326	+	0.222958i	0.0311293	+	0.00914039i
$596$	0.629266	−	1.37790i	0.0257757	−	0.0564410i
$597$	−8.03149			−0.328707
$598$	1.08119	+	0.171136i	0.0442133	+	0.00699828i
$599$	11.2572			0.459957			0.229979	−	0.973196i	$-0.426134\pi$
$599$	11.2572			0.459957			0.229979	+	0.973196i	$0.426134\pi$
$600$	1.13484	−	2.48496i	0.0463297	−	0.101448i
$601$	−9.84521	−	2.89081i	−0.401594	−	0.117919i	0.0746969	−	0.997206i	$-0.476201\pi$
$601$	−9.84521	−	2.89081i	−0.401594	−	0.117919i	−0.476291	+	0.879288i	$0.658019\pi$
$602$	3.08581	+	3.56121i	0.125768	+	0.145144i
$603$	6.33163	−	4.06909i	0.257844	−	0.165706i
$604$	−7.36765	+	8.50273i	−0.299786	+	0.345971i
$605$	−0.870430	+	6.05397i	−0.0353880	+	0.246129i
$606$	−15.2175	+	4.46826i	−0.618168	+	0.181511i
$607$	−20.9868	−	13.4874i	−0.851829	−	0.547437i	0.0403157	−	0.999187i	$-0.487164\pi$
$607$	−20.9868	−	13.4874i	−0.851829	−	0.547437i	−0.892145	+	0.451750i	$0.850800\pi$
$608$	0.663903	+	4.61755i	0.0269248	+	0.187266i
$609$	−2.05661	−	4.50335i	−0.0833380	−	0.182485i
$610$	0.778060	+	1.70371i	0.0315027	+	0.0689814i
$611$	−0.162674	−	1.13143i	−0.00658110	−	0.0457726i
$612$	0.442054	+	0.284091i	0.0178690	+	0.0114837i
$613$	−8.07079	+	2.36980i	−0.325976	+	0.0957152i	−0.440626	−	0.897691i	$-0.645244\pi$
$613$	−8.07079	+	2.36980i	−0.325976	+	0.0957152i	0.114650	+	0.993406i	$0.463425\pi$
$614$	−3.74993	+	26.0814i	−0.151335	+	1.05256i
$615$	0.0484116	−	0.0558700i	0.00195214	−	0.00225290i
$616$	2.21601	−	1.42414i	0.0892856	−	0.0573804i
$617$	−1.86405	−	2.15123i	−0.0750440	−	0.0866054i	0.716986	−	0.697088i	$-0.245521\pi$
$617$	−1.86405	−	2.15123i	−0.0750440	−	0.0866054i	−0.792030	+	0.610482i	$0.790976\pi$
$618$	−10.4071	−	3.05580i	−0.418635	−	0.122922i
$619$	15.7645	−	34.5195i	0.633629	−	1.38745i	−0.271550	−	0.962424i	$-0.587536\pi$
$619$	15.7645	−	34.5195i	0.633629	−	1.38745i	0.905179	−	0.425030i	$-0.139737\pi$
$620$	2.51485			0.100999
$621$	3.57954	+	3.19169i	0.143642	+	0.128078i
$622$	8.37810			0.335931
$623$	3.11097	−	6.81207i	0.124638	−	0.272920i
$624$	−0.219006	−	0.0643058i	−0.00876724	−	0.00257429i
$625$	2.53954	+	2.93078i	0.101581	+	0.117231i
$626$	22.4705	−	14.4409i	0.898103	−	0.577176i
$627$	−8.04726	+	9.28704i	−0.321377	+	0.370888i
$628$	−0.183107	+	1.27353i	−0.00730674	+	0.0508195i
$629$	−4.13439	+	1.21397i	−0.164849	+	0.0484040i
$630$	−1.26697	−	0.814230i	−0.0504771	−	0.0324397i
$631$	−4.33365	−	30.1412i	−0.172520	−	1.19990i	−0.873537	−	0.486758i	$-0.838179\pi$
$631$	−4.33365	−	30.1412i	−0.172520	−	1.19990i	0.701017	−	0.713145i	$-0.252730\pi$
$632$	3.34377	+	7.32184i	0.133008	+	0.291247i
$633$	4.00058	+	8.76005i	0.159009	+	0.348181i
$634$	−0.880446	−	6.12364i	−0.0349670	−	0.243201i
$635$	−24.4605	−	15.7198i	−0.970687	−	0.623823i
$636$	−5.83671	+	1.71381i	−0.231441	+	0.0679571i
$637$	0.0324836	−	0.225928i	0.00128705	−	0.00895160i
$638$	−8.54011	+	9.85581i	−0.338106	+	0.390195i
$639$	−9.79002	+	6.29166i	−0.387287	+	0.248894i
$640$	0.986250	+	1.13819i	0.0389850	+	0.0449910i
$641$	20.3479	+	5.97467i	0.803693	+	0.235985i	0.657680	−	0.753297i	$-0.271538\pi$
$641$	20.3479	+	5.97467i	0.803693	+	0.235985i	0.146012	+	0.989283i	$0.453356\pi$
$642$	−0.228956	+	0.501344i	−0.00903617	+	0.0197865i
$643$	−36.0428			−1.42139			−0.710695	−	0.703501i	$-0.751619\pi$
$643$	−36.0428			−1.42139			−0.710695	+	0.703501i	$0.751619\pi$
$644$	3.66862	−	3.08888i	0.144564	−	0.121719i
$645$	−7.09673			−0.279433
$646$	−1.01832	+	2.22981i	−0.0400653	+	0.0877308i
$647$	1.99851	+	0.586817i	0.0785697	+	0.0230701i	0.320781	−	0.947153i	$-0.396055\pi$
$647$	1.99851	+	0.586817i	0.0785697	+	0.0230701i	−0.242211	+	0.970223i	$0.577873\pi$
$648$	−0.654861	−	0.755750i	−0.0257254	−	0.0296886i
$649$	0.422269	−	0.271376i	0.0165755	−	0.0106524i
$650$	−0.408334	+	0.471243i	−0.0160162	+	0.0184837i
$651$	−0.237642	+	1.65284i	−0.00931394	+	0.0647799i
$652$	1.82686	−	0.536413i	0.0715452	−	0.0210076i
$653$	−30.1222	−	19.3584i	−1.17877	−	0.757552i	−0.203614	−	0.979051i	$-0.565269\pi$
$653$	−30.1222	−	19.3584i	−1.17877	−	0.757552i	−0.975161	+	0.221499i	$0.928905\pi$
$654$	−1.23534	−	8.59199i	−0.0483057	−	0.335973i
$655$	2.68694	+	5.88358i	0.104988	+	0.229891i
$656$	−0.0203913	−	0.0446507i	−0.000796146	−	0.00174332i
$657$	0.997084	+	6.93487i	0.0388999	+	0.270555i
$658$	−4.21292	−	2.70748i	−0.164237	−	0.105548i
$659$	−5.44132	+	1.59772i	−0.211964	+	0.0622382i	−0.385991	−	0.922503i	$-0.626140\pi$
$659$	−5.44132	+	1.59772i	−0.211964	+	0.0622382i	0.174027	+	0.984741i	$0.444322\pi$
$660$	−0.564590	+	3.92681i	−0.0219766	+	0.152851i
$661$	30.8712	−	35.6272i	1.20075	−	1.38574i	0.298563	−	0.954390i	$-0.403493\pi$
$661$	30.8712	−	35.6272i	1.20075	−	1.38574i	0.902186	−	0.431348i	$-0.141962\pi$
$662$	−23.1057	+	14.8491i	−0.898030	+	0.577129i
$663$	−0.0785435	−	0.0906441i	−0.00305038	−	0.00352032i
$664$	1.94620	+	0.571456i	0.0755273	+	0.0221768i
$665$	2.91860	−	6.39084i	0.113178	−	0.247826i
$666$	8.20013			0.317749
$667$	−13.1184	+	19.7897i	−0.507945	+	0.766262i
$668$	18.9888			0.734698
$669$	7.18698	−	15.7373i	0.277865	−	0.608439i
$670$	10.8760	+	3.19348i	0.420176	+	0.123375i
$671$	2.14529	+	2.47580i	0.0828182	+	0.0955772i
$672$	−0.841254	+	0.540641i	−0.0324521	+	0.0208557i
$673$	−9.81188	+	11.3235i	−0.378220	+	0.436489i	−0.912662	−	0.408716i	$-0.865977\pi$
$673$	−9.81188	+	11.3235i	−0.378220	+	0.436489i	0.534441	+	0.845206i	$0.320522\pi$
$674$	1.22119	−	8.49355i	0.0470384	−	0.327159i
$675$	−2.62117	+	0.769645i	−0.100889	+	0.0296236i
$676$	−10.8925	−	7.00016i	−0.418941	−	0.269237i
$677$	0.493847	+	3.43478i	0.0189801	+	0.132009i	0.997108	−	0.0759934i	$-0.0242128\pi$
$677$	0.493847	+	3.43478i	0.0189801	+	0.132009i	−0.978128	+	0.208003i	$0.933304\pi$
$678$	3.55441	+	7.78308i	0.136506	+	0.298907i
$679$	−0.996531	−	2.18210i	−0.0382434	−	0.0837413i
$680$	0.112625	+	0.783327i	0.00431899	+	0.0300392i
$681$	−8.28574	−	5.32492i	−0.317510	−	0.204052i
$682$	4.22047	−	1.23924i	0.161610	−	0.0474530i
$683$	−0.471942	+	3.28243i	−0.0180584	+	0.125599i	−0.996856	−	0.0792288i	$-0.974754\pi$
$683$	−0.471942	+	3.28243i	−0.0180584	+	0.125599i	0.978798	+	0.204827i	$0.0656633\pi$
$684$	3.05495	−	3.52559i	0.116809	−	0.134804i
$685$	−5.46962	+	3.51511i	−0.208983	+	0.134305i
$686$	−0.654861	−	0.755750i	−0.0250027	−	0.0288547i
$687$	16.4091	+	4.81813i	0.626044	+	0.183823i
$688$	−1.95750	+	4.28633i	−0.0746291	+	0.163415i
$689$	1.38848			0.0528969
$690$	−0.102431	+	7.22201i	−0.00389950	+	0.274937i
$691$	−33.7285			−1.28309			−0.641546	−	0.767084i	$-0.721707\pi$
$691$	−33.7285			−1.28309			−0.641546	+	0.767084i	$0.721707\pi$
$692$	−7.36777	+	16.1332i	−0.280080	+	0.613291i
$693$	−2.52747	−	0.742133i	−0.0960108	−	0.0281913i
$694$	−4.94838	−	5.71074i	−0.187838	−	0.216777i
$695$	1.91260	−	1.22915i	0.0725491	−	0.0466244i
$696$	3.24204	−	3.74152i	0.122889	−	0.141822i
$697$	0.00367080	−	0.0255310i	0.000139042	−	0.000967055i
$698$	4.53749	−	1.33233i	0.171747	−	0.0504293i
$699$	−5.10483	−	3.28068i	−0.193082	−	0.124087i
$700$	0.388780	+	2.70402i	0.0146945	+	0.102202i
$701$	17.3420	+	37.9736i	0.654997	+	1.43424i	0.887112	+	0.461555i	$0.152708\pi$
$701$	17.3420	+	37.9736i	0.654997	+	1.43424i	−0.232114	+	0.972688i	$0.574564\pi$
$702$	0.0948190	+	0.207625i	0.00357871	+	0.00783629i
$703$	5.44409	+	37.8645i	0.205328	+	1.42809i
$704$	2.21601	+	1.42414i	0.0835190	+	0.0536744i
$705$	7.23662	−	2.12486i	0.272547	−	0.0800270i
$706$	3.14464	−	21.8715i	0.118350	−	0.823144i
$707$	10.3860	−	11.9861i	0.390607	−	0.450785i
$708$	−0.160304	+	0.103021i	−0.00602460	+	0.00387177i
$709$	−5.22038	−	6.02463i	−0.196055	−	0.226260i	0.649207	−	0.760612i	$-0.275101\pi$
$709$	−5.22038	−	6.02463i	−0.196055	−	0.226260i	−0.845262	+	0.534352i	$0.820556\pi$
$710$	−16.8165	−	4.93778i	−0.631113	−	0.185312i
$711$	3.34377	−	7.32184i	0.125401	−	0.274590i
$712$	7.48882			0.280655
$713$	7.33101	−	3.22311i	0.274548	−	0.120706i
$714$	−0.525470			−0.0196652
$715$	0.376165	−	0.823686i	0.0140678	−	0.0308041i
$716$	−14.2860	−	4.19474i	−0.533891	−	0.156765i
$717$	−10.6083	−	12.2426i	−0.396173	−	0.457209i
$718$	11.3329	−	7.28324i	0.422942	−	0.271808i
$719$	−17.9926	+	20.7646i	−0.671011	+	0.774388i	−0.984534	−	0.175192i	$-0.943945\pi$
$719$	−17.9926	+	20.7646i	−0.671011	+	0.774388i	0.313523	+	0.949581i	$0.398491\pi$
$720$	0.214333	−	1.49072i	0.00798770	−	0.0555557i
$721$	10.4071	−	3.05580i	0.387581	−	0.113804i
$722$	2.32397	+	1.49352i	0.0864892	+	0.0555832i
$723$	0.875820	+	6.09146i	0.0325721	+	0.226544i
$724$	−0.960044	−	2.10220i	−0.0356797	−	0.0781278i
$725$	−5.61830	−	12.3024i	−0.208659	−	0.456899i
$726$	−0.577957	−	4.01978i	−0.0214500	−	0.149188i
$727$	8.92488	+	5.73567i	0.331006	+	0.212724i	0.695578	−	0.718451i	$-0.255148\pi$
$727$	8.92488	+	5.73567i	0.331006	+	0.212724i	−0.364572	+	0.931175i	$0.618785\pi$
$728$	0.219006	−	0.0643058i	0.00811689	−	0.00238333i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−6.90985	+	7.97439i	−0.255745	+	0.295145i
$731$	−2.08303	+	1.33868i	−0.0770436	+	0.0495129i
$732$	−0.814408	−	0.939877i	−0.0301014	−	0.0347389i
$733$	11.0748	+	3.25185i	0.409057	+	0.120110i	0.479786	−	0.877386i	$-0.340714\pi$
$733$	11.0748	+	3.25185i	0.409057	+	0.120110i	−0.0707291	+	0.997496i	$0.522533\pi$
$734$	−13.0093	+	28.4864i	−0.480181	+	1.05145i
$735$	1.50605			0.0555513
$736$	4.33375	+	2.05393i	0.159744	+	0.0757088i
$737$	19.8259			0.730297
$738$	−0.0203913	+	0.0446507i	−0.000750614	+	0.00164362i
$739$	−1.09999	−	0.322986i	−0.0404637	−	0.0118812i	0.261438	−	0.965220i	$-0.415803\pi$
$739$	−1.09999	−	0.322986i	−0.0404637	−	0.0118812i	−0.301902	+	0.953339i	$0.597621\pi$
$740$	8.08738	+	9.33334i	0.297298	+	0.343100i
$741$	−0.895766	+	0.575674i	−0.0329068	+	0.0211479i
$742$	3.98360	−	4.59732i	0.146242	−	0.168773i
$743$	−0.0170263	+	0.118420i	−0.000624633	+	0.00434442i	−0.990131	−	0.140142i	$-0.955244\pi$
$743$	−0.0170263	+	0.118420i	−0.000624633	+	0.00434442i	0.989507	+	0.144487i	$0.0461531\pi$
$744$	−1.60220	+	0.470447i	−0.0587394	+	0.0172474i
$745$	−1.91919	−	1.23339i	−0.0703135	−	0.0451878i
$746$	−2.92564	−	20.3483i	−0.107115	−	0.745004i
$747$	−0.842613	−	1.84507i	−0.0308296	−	0.0675074i
$748$	0.575010	+	1.25910i	0.0210244	+	0.0460371i
$749$	−0.0784368	−	0.545540i	−0.00286602	−	0.0199336i
$750$	−9.79596	−	6.29548i	−0.357698	−	0.229879i
$751$	−20.3469	+	5.97440i	−0.742471	+	0.218009i	−0.631026	−	0.775762i	$-0.717366\pi$
$751$	−20.3469	+	5.97440i	−0.742471	+	0.218009i	−0.111445	+	0.993771i	$0.535548\pi$
$752$	0.712699	−	4.95693i	0.0259895	−	0.180761i
$753$	−14.7940	+	17.0732i	−0.539123	+	0.622181i
$754$	−0.950627	+	0.610931i	−0.0346198	+	0.0222488i
$755$	11.0960	+	12.8055i	0.403826	+	0.466039i
$756$	0.959493	+	0.281733i	0.0348964	+	0.0102465i
$757$	−20.0231	+	43.8444i	−0.727751	+	1.59355i	0.0749615	+	0.997186i	$0.476117\pi$
$757$	−20.0231	+	43.8444i	−0.727751	+	1.59355i	−0.802713	+	0.596366i	$0.796611\pi$
$758$	11.1502			0.404995
$759$	3.38689	+	12.1706i	0.122936	+	0.441764i
$760$	7.02575			0.254851
$761$	−7.88685	+	17.2698i	−0.285898	+	0.626029i	−0.997029	−	0.0770306i	$-0.975456\pi$
$761$	−7.88685	+	17.2698i	−0.285898	+	0.626029i	0.711131	+	0.703060i	$0.248183\pi$
$762$	18.5243	+	5.43924i	0.671066	+	0.197043i
$763$	5.68441	+	6.56016i	0.205790	+	0.237494i
$764$	−16.6361	+	10.6913i	−0.601872	+	0.386799i
$765$	0.518245	−	0.598087i	0.0187372	−	0.0216239i
$766$	−0.617586	+	4.29540i	−0.0223143	+	0.155199i
$767$	0.0417324	−	0.0122537i	0.00150687	−	0.000442456i
$768$	−0.841254	−	0.540641i	−0.0303561	−	0.0195087i
$769$	−2.72412	−	18.9467i	−0.0982342	−	0.683234i	−0.978119	−	0.208047i	$-0.933289\pi$
$769$	−2.72412	−	18.9467i	−0.0982342	−	0.683234i	0.879885	−	0.475187i	$-0.157620\pi$
$770$	−1.64803	−	3.60868i	−0.0593909	−	0.130048i
$771$	5.70456	+	12.4912i	0.205445	+	0.449861i
$772$	−1.42915	−	9.93994i	−0.0514361	−	0.357746i
$773$	6.66091	+	4.28071i	0.239576	+	0.153966i	0.654920	−	0.755698i	$-0.272702\pi$
$773$	6.66091	+	4.28071i	0.239576	+	0.153966i	−0.415344	+	0.909665i	$0.636339\pi$
$774$	4.52129	−	1.32757i	0.162514	−	0.0477185i
$775$	−0.649198	+	4.51527i	−0.0233199	+	0.162193i
$776$	1.57093	−	1.81295i	0.0563932	−	0.0650812i
$777$	−6.89839	+	4.43333i	−0.247478	+	0.159045i
$778$	−11.8735	−	13.7027i	−0.425685	−	0.491266i
$779$	−0.219715	−	0.0645140i	−0.00787209	−	0.00231145i
$780$	−0.142802	+	0.312692i	−0.00511312	+	0.0111962i
$781$	−30.6550			−1.09692
$782$	1.33225	+	2.13912i	0.0476411	+	0.0764949i
$783$	−4.95074			−0.176925
$784$	0.415415	−	0.909632i	0.0148363	−	0.0324869i
$785$	1.85923	+	0.545920i	0.0663588	+	0.0194847i
$786$	−2.81246	−	3.24576i	−0.100317	−	0.115772i
$787$	−23.2424	+	14.9370i	−0.828503	+	0.532447i	−0.884802	−	0.465967i	$-0.845706\pi$
$787$	−23.2424	+	14.9370i	−0.828503	+	0.532447i	0.0562989	+	0.998414i	$0.482070\pi$
$788$	7.41181	−	8.55368i	0.264035	−	0.304712i
$789$	3.66281	−	25.4754i	0.130400	−	0.906949i
$790$	11.6315	−	3.41531i	0.413829	−	0.121511i
$791$	−7.19801	−	4.62588i	−0.255932	−	0.164477i
$792$	−0.374882	−	2.60736i	−0.0133209	−	0.0926486i
$793$	0.117920	+	0.258209i	0.00418747	+	0.00916929i
$794$	−5.74176	−	12.5727i	−0.203768	−	0.446189i
$795$	1.30381	+	9.06820i	0.0462414	+	0.321616i
$796$	6.75652	+	4.34215i	0.239479	+	0.153904i
$797$	−51.2014	+	15.0341i	−1.81365	+	0.532535i	−0.998883	−	0.0472558i	$-0.984952\pi$
$797$	−51.2014	+	15.0341i	−1.81365	+	0.532535i	−0.814765	+	0.579791i	$0.803134\pi$
$798$	−0.663903	+	4.61755i	−0.0235019	+	0.163459i
$799$	1.72327	−	1.98876i	0.0609649	−	0.0703572i
$800$	−2.29816	+	1.47694i	−0.0812522	+	0.0522176i
$801$	−4.90413	−	5.65967i	−0.173279	−	0.199975i
$802$	0.127447	+	0.0374218i	0.00450030	+	0.00132141i
$803$	−7.66670	+	16.7877i	−0.270552	+	0.592426i
$804$	−7.52642			−0.265437
$805$	−3.81834	−	6.13092i	−0.134579	−	0.216087i
$806$	0.381142			0.0134252
$807$	5.34610	−	11.7063i	0.188192	−	0.412082i
$808$	15.2175	+	4.46826i	0.535349	+	0.157193i
$809$	11.5227	+	13.2979i	0.405117	+	0.467530i	0.921246	−	0.388981i	$-0.127173\pi$
$809$	11.5227	+	13.2979i	0.405117	+	0.467530i	−0.516129	+	0.856511i	$0.672627\pi$
$810$	−1.26697	+	0.814230i	−0.0445166	+	0.0286091i
$811$	4.56546	−	5.26883i	0.160315	−	0.185013i	−0.669909	−	0.742443i	$-0.733667\pi$
$811$	4.56546	−	5.26883i	0.160315	−	0.185013i	0.830224	+	0.557430i	$0.188212\pi$
$812$	−0.704563	+	4.90034i	−0.0247253	+	0.171968i
$813$	−8.14700	+	2.39217i	−0.285728	+	0.0838972i
$814$	18.1716	+	11.6782i	0.636913	+	0.409319i
$815$	−0.408085	−	2.83829i	−0.0142946	−	0.0994211i
$816$	−0.218288	−	0.477985i	−0.00764162	−	0.0167328i
$817$	9.13181	+	19.9959i	0.319482	+	0.699567i
$818$	−0.620540	−	4.31595i	−0.0216967	−	0.150904i
$819$	−0.192017	−	0.123402i	−0.00670963	−	0.00431201i
$820$	−0.0709320	+	0.0208275i	−0.00247705	+	0.000727329i
$821$	−3.37275	+	23.4580i	−0.117710	+	0.818690i	0.842357	+	0.538920i	$0.181167\pi$
$821$	−3.37275	+	23.4580i	−0.117710	+	0.818690i	−0.960067	+	0.279770i	$0.909742\pi$
$822$	2.82710	−	3.26264i	0.0986064	−	0.113798i
$823$	−35.9777	+	23.1215i	−1.25410	+	0.805964i	−0.987466	−	0.157833i	$-0.949549\pi$
$823$	−35.9777	+	23.1215i	−1.25410	+	0.805964i	−0.266638	+	0.963797i	$0.585913\pi$
$824$	7.10292	+	8.19721i	0.247442	+	0.285563i
$825$	−6.90462	−	2.02738i	−0.240388	−	0.0705843i
$826$	0.0791590	−	0.173334i	0.00275429	−	0.00603106i
$827$	−34.6162			−1.20372			−0.601861	−	0.798601i	$-0.705574\pi$
$827$	−34.6162			−1.20372			−0.601861	+	0.798601i	$0.705574\pi$
$828$	−1.28575	−	4.62027i	−0.0446828	−	0.160565i
$829$	−55.8301			−1.93906			−0.969529	−	0.244975i	$-0.921220\pi$
$829$	−55.8301			−1.93906			−0.969529	+	0.244975i	$0.921220\pi$
$830$	1.26901	−	2.77875i	0.0440481	−	0.0964519i
$831$	−16.0403	−	4.70987i	−0.556433	−	0.163384i
$832$	0.149473	+	0.172501i	0.00518204	+	0.00598039i
$833$	0.442054	−	0.284091i	0.0153163	−	0.00984316i
$834$	−0.988572	+	1.14087i	−0.0342314	+	0.0395052i
$835$	4.06991	−	28.3069i	0.140845	−	0.979600i
$836$	11.7907	−	3.46207i	0.407791	−	0.119738i
$837$	1.40476	+	0.902782i	0.0485555	+	0.0312047i
$838$	2.01235	+	13.9962i	0.0695153	+	0.483490i
$839$	−2.60036	−	5.69400i	−0.0897745	−	0.196579i	0.859419	−	0.511272i	$-0.170826\pi$
$839$	−2.60036	−	5.69400i	−0.0897745	−	0.196579i	−0.949193	+	0.314693i	$0.898098\pi$
$840$	0.625634	+	1.36995i	0.0215864	+	0.0472677i
$841$	0.639025	+	4.44451i	0.0220353	+	0.153259i
$842$	−9.15781	−	5.88537i	−0.315599	−	0.202823i
$843$	13.2555	−	3.89216i	0.456543	−	0.134053i
$844$	1.37054	−	9.53230i	0.0471759	−	0.328115i
$845$	−12.7699	+	14.7372i	−0.439297	+	0.506976i
$846$	−4.21292	+	2.70748i	−0.144843	+	0.0930850i
$847$	2.65947	+	3.06919i	0.0913804	+	0.105459i
$848$	5.83671	+	1.71381i	0.200433	+	0.0588526i
$849$	−0.329269	+	0.720999i	−0.0113005	+	0.0247446i
$850$	−1.43549			−0.0492371
$851$	35.5373	+	16.8425i	1.21820	+	0.577353i
$852$	11.6374			0.398691
$853$	15.5700	−	34.0936i	0.533108	−	1.16734i	−0.431127	−	0.902291i	$-0.641884\pi$
$853$	15.5700	−	34.0936i	0.533108	−	1.16734i	0.964234	−	0.265052i	$-0.0853890\pi$
$854$	1.19326	+	0.350373i	0.0408325	+	0.0119895i
$855$	−4.60089	−	5.30971i	−0.157347	−	0.181588i
$856$	0.463657	−	0.297974i	0.0158475	−	0.0101846i
$857$	−11.7084	+	13.5122i	−0.399950	+	0.461567i	−0.919625	−	0.392797i	$-0.871507\pi$
$857$	−11.7084	+	13.5122i	−0.399950	+	0.461567i	0.519675	+	0.854364i	$0.326053\pi$
$858$	−0.0855674	+	0.595134i	−0.00292122	+	0.0203175i
$859$	33.4023	−	9.80779i	1.13967	−	0.334637i	0.343169	−	0.939274i	$-0.388500\pi$
$859$	33.4023	−	9.80779i	1.13967	−	0.334637i	0.796502	+	0.604637i	$0.206682\pi$
$860$	5.97015	+	3.83678i	0.203580	+	0.130833i
$861$	−0.00698575	−	0.0485869i	−0.000238074	−	0.00165584i
$862$	−12.6542	−	27.7089i	−0.431005	−	0.943770i
$863$	−13.4940	−	29.5477i	−0.459340	−	1.00582i	−0.987637	−	0.156755i	$-0.949897\pi$
$863$	−13.4940	−	29.5477i	−0.459340	−	1.00582i	0.528297	−	0.849060i	$-0.322831\pi$
$864$	0.142315	+	0.989821i	0.00484165	+	0.0336744i
$865$	22.4708	+	14.4411i	0.764030	+	0.491012i
$866$	1.37311	−	0.403182i	0.0466602	−	0.0137007i
$867$	−2.38006	+	16.5537i	−0.0808310	+	0.562192i
$868$	1.09351	−	1.26198i	0.0371162	−	0.0428343i
$869$	17.8372	−	11.4633i	0.605085	−	0.388864i
$870$	−4.88266	−	5.63489i	−0.165538	−	0.191041i
$871$	1.64833	+	0.483993i	0.0558515	+	0.0163995i
$872$	−3.60594	+	7.89592i	−0.122113	+	0.267389i
$873$	−2.39888			−0.0811898
$874$	20.4807	−	9.00441i	0.692769	−	0.304579i
$875$	11.6445			0.393655
$876$	2.91047	−	6.37305i	0.0983358	−	0.215325i
$877$	−25.7469	−	7.55996i	−0.869409	−	0.255282i	−0.183545	−	0.983011i	$-0.558757\pi$
$877$	−25.7469	−	7.55996i	−0.869409	−	0.255282i	−0.685864	+	0.727730i	$0.740576\pi$
$878$	−19.1878	−	22.1439i	−0.647555	−	0.747319i
$879$	14.6273	−	9.40040i	0.493367	−	0.317068i
$880$	2.59796	−	2.99820i	0.0875771	−	0.101069i
$881$	4.92276	−	34.2385i	0.165852	−	1.15353i	−0.721494	−	0.692421i	$-0.756544\pi$
$881$	4.92276	−	34.2385i	0.165852	−	1.15353i	0.887346	−	0.461105i	$-0.152547\pi$
$882$	−0.959493	+	0.281733i	−0.0323078	+	0.00948643i
$883$	−2.04854	−	1.31652i	−0.0689389	−	0.0443043i	0.505717	−	0.862699i	$-0.331228\pi$
$883$	−2.04854	−	1.31652i	−0.0689389	−	0.0443043i	−0.574656	+	0.818395i	$0.694864\pi$
$884$	0.0170691	+	0.118718i	0.000574097	+	0.00399294i
$885$	0.119217	+	0.261049i	0.00400743	+	0.00877506i
$886$	−13.9573	−	30.5621i	−0.468903	−	1.02676i
$887$	2.13050	+	14.8179i	0.0715352	+	0.497538i	0.993818	+	0.111022i	$0.0354125\pi$
$887$	2.13050	+	14.8179i	0.0715352	+	0.497538i	−0.922283	+	0.386516i	$0.873678\pi$
$888$	−6.89839	−	4.43333i	−0.231495	−	0.148773i
$889$	−18.5243	+	5.43924i	−0.621287	+	0.182426i
$890$	1.60510	−	11.1637i	0.0538030	−	0.374208i
$891$	−1.72502	+	1.99078i	−0.0577903	+	0.0666935i
$892$	−14.5543	+	9.35347i	−0.487314	+	0.313177i
$893$	−15.2989	−	17.6558i	−0.511957	−	0.590830i
$894$	1.45343	+	0.426765i	0.0486099	+	0.0142732i
$895$	−9.31511	+	20.3972i	−0.311370	+	0.681805i
$896$	1.00000			0.0334077
$897$	−0.0155242	+	1.09454i	−0.000518337	+	0.0365458i
$898$	24.4771			0.816812
$899$	−3.43420	+	7.51985i	−0.114537	+	0.250801i
$900$	2.62117	+	0.769645i	0.0873723	+	0.0256548i
$901$	2.09326	+	2.41575i	0.0697367	+	0.0804804i
$902$	−0.108776	+	0.0699063i	−0.00362185	+	0.00232762i
$903$	−3.08581	+	3.56121i	−0.102689	+	0.118510i
$904$	1.21769	−	8.46920i	0.0404997	−	0.281681i
$905$	−3.33956	+	0.980582i	−0.111011	+	0.0325957i
$906$	−9.46471	−	6.08260i	−0.314444	−	0.202081i
$907$	−4.02764	−	28.0129i	−0.133736	−	0.930153i	−0.940624	−	0.339449i	$-0.889759\pi$
$907$	−4.02764	−	28.0129i	−0.133736	−	0.930153i	0.806889	−	0.590704i	$-0.201150\pi$
$908$	4.09154	+	8.95922i	0.135783	+	0.297322i
$909$	−6.58845	−	14.4267i	−0.218525	−	0.478503i
$910$	−0.0489217	−	0.340258i	−0.00162174	−	0.0112794i
$911$	−13.4316	−	8.63195i	−0.445008	−	0.285989i	0.298884	−	0.954290i	$-0.403386\pi$
$911$	−13.4316	−	8.63195i	−0.445008	−	0.285989i	−0.743892	+	0.668300i	$0.767022\pi$
$912$	−4.47606	+	1.31429i	−0.148217	+	0.0435205i
$913$	0.760398	−	5.28868i	0.0251655	−	0.175030i
$914$	15.1173	−	17.4462i	0.500035	−	0.577071i
$915$	−1.57564	+	1.01260i	−0.0520892	+	0.0334757i
$916$	−11.1993	−	12.9247i	−0.370035	−	0.427043i
$917$	4.12078	+	1.20997i	0.136080	+	0.0399568i
$918$	−0.218288	+	0.477985i	−0.00720459	+	0.0157758i
$919$	−16.9266			−0.558357			−0.279178	−	0.960239i	$-0.590062\pi$
$919$	−16.9266			−0.558357			−0.279178	+	0.960239i	$0.590062\pi$
$920$	3.99069	−	6.02017i	0.131569	−	0.198479i
$921$	−26.3496			−0.868248
$922$	8.75737	−	19.1760i	0.288409	−	0.631527i
$923$	−2.54866	−	0.748354i	−0.0838901	−	0.0246324i
$924$	1.72502	+	1.99078i	0.0567489	+	0.0654918i
$925$	−18.8452	+	12.1111i	−0.619627	+	0.398210i
$926$	12.0667	−	13.9257i	0.396535	−	0.457626i
$927$	1.54361	−	10.7361i	0.0506989	−	0.352618i
$928$	−4.75020	+	1.39478i	−0.155933	+	0.0457860i
$929$	−43.7997	−	28.1484i	−1.43702	−	0.923518i	−0.999707	−	0.0242105i	$-0.992293\pi$
$929$	−43.7997	−	28.1484i	−1.43702	−	0.923518i	−0.437316	−	0.899308i	$-0.644071\pi$
$930$	0.357900	+	2.48925i	0.0117360	+	0.0816258i
$931$	−1.93792	−	4.24346i	−0.0635129	−	0.139074i
$932$	2.52079	+	5.51976i	0.0825712	+	0.180806i
$933$	1.19233	+	8.29282i	0.0390351	+	0.271495i
$934$	6.48384	+	4.16691i	0.212158	+	0.136345i
$935$	2.00020	−	0.587311i	0.0654134	−	0.0192071i
$936$	0.0324836	−	0.225928i	0.00106176	−	0.00738469i
$937$	31.3529	−	36.1832i	1.02426	−	1.18205i	0.0411248	−	0.999154i	$-0.486906\pi$
$937$	31.3529	−	36.1832i	1.02426	−	1.18205i	0.983131	−	0.182901i	$-0.0585487\pi$
$938$	6.33163	−	4.06909i	0.206735	−	0.132861i
$939$	17.4918	+	20.1867i	0.570825	+	0.658767i
$940$	−7.23662	−	2.12486i	−0.236033	−	0.0693054i
$941$	2.13061	−	4.66539i	0.0694560	−	0.152087i	−0.871720	−	0.490005i	$-0.836995\pi$
$941$	2.13061	−	4.66539i	0.0694560	−	0.152087i	0.941176	+	0.337917i	$0.109722\pi$
$942$	−1.28663			−0.0419207
$943$	−0.180080	+	0.151623i	−0.00586421	+	0.00493752i
$944$	0.190554			0.00620200
$945$	0.625634	−	1.36995i	0.0203519	−	0.0445644i
$946$	11.9099	+	3.49705i	0.387223	+	0.113699i
$947$	13.4566	+	15.5297i	0.437279	+	0.504647i	0.931023	−	0.364960i	$-0.118917\pi$
$947$	13.4566	+	15.5297i	0.437279	+	0.504647i	−0.493744	+	0.869607i	$0.664372\pi$
$948$	−6.77145	+	4.35174i	−0.219926	+	0.141338i
$949$	−1.04723	+	1.20857i	−0.0339946	+	0.0392319i
$950$	−1.81367	+	12.6143i	−0.0588432	+	0.409263i
$951$	5.93601	−	1.74297i	0.192488	−	0.0565196i
$952$	0.442054	+	0.284091i	0.0143270	+	0.00920743i
$953$	−6.65215	−	46.2667i	−0.215484	−	1.49873i	−0.754428	−	0.656383i	$-0.772085\pi$
$953$	−6.65215	−	46.2667i	−0.215484	−	1.49873i	0.538943	−	0.842342i	$-0.318824\pi$
$954$	−2.52702	−	5.53340i	−0.0818153	−	0.179150i
$955$	12.3721	+	27.0911i	0.400352	+	0.876649i
$956$	2.30540	+	16.0344i	0.0745619	+	0.518590i
$957$	−10.9709	−	7.05056i	−0.354638	−	0.227912i
$958$	20.6868	−	6.07420i	0.668361	−	0.196249i
$959$	−0.614387	+	4.27316i	−0.0198396	+	0.137987i
$960$	−0.986250	+	1.13819i	−0.0318311	+	0.0367350i
$961$	−23.7331	+	15.2524i	−0.765585	+	0.492012i
$962$	1.22570	+	1.41453i	0.0395181	+	0.0456063i
$963$	−0.528825	−	0.155277i	−0.0170411	−	0.00500373i
$964$	2.55651	−	5.59797i	0.0823395	−	0.180298i
$965$	−15.1239			−0.486857
$966$	3.57954	+	3.19169i	0.115170	+	0.102691i
$967$	−53.4284			−1.71814			−0.859071	−	0.511856i	$-0.828958\pi$
$967$	−53.4284			−1.71814			−0.859071	+	0.511856i	$0.828958\pi$
$968$	−1.68705	+	3.69412i	−0.0542238	+	0.118734i
$969$	−2.35204	−	0.690621i	−0.0755584	−	0.0221859i
$970$	−2.36590	−	2.73039i	−0.0759644	−	0.0876675i
$971$	36.1463	−	23.2298i	1.15999	−	0.745480i	0.188386	−	0.982095i	$-0.439674\pi$
$971$	36.1463	−	23.2298i	1.15999	−	0.745480i	0.971604	+	0.236615i	$0.0760379\pi$
$972$	0.654861	−	0.755750i	0.0210047	−	0.0242407i
$973$	0.214837	−	1.49423i	0.00688736	−	0.0479027i
$974$	26.3005	−	7.72252i	0.842722	−	0.247446i
$975$	−0.524558	−	0.337113i	−0.0167993	−	0.0107963i
$976$	0.176988	+	1.23098i	0.00566524	+	0.0394026i
$977$	22.7573	+	49.8315i	0.728070	+	1.59425i	0.802238	+	0.597004i	$0.203642\pi$
$977$	22.7573	+	49.8315i	0.728070	+	1.59425i	−0.0741685	+	0.997246i	$0.523630\pi$
$978$	0.790942	+	1.73192i	0.0252915	+	0.0553807i
$979$	−2.80743	−	19.5261i	−0.0897257	−	0.624056i
$980$	−1.26697	−	0.814230i	−0.0404717	−	0.0260096i
$981$	8.32873	−	2.44553i	0.265916	−	0.0780799i
$982$	−0.365016	+	2.53874i	−0.0116481	+	0.0810145i
$983$	10.4413	−	12.0499i	0.333026	−	0.384333i	−0.564397	−	0.825503i	$-0.690891\pi$
$983$	10.4413	−	12.0499i	0.333026	−	0.384333i	0.897423	+	0.441171i	$0.145437\pi$
$984$	0.0412942	−	0.0265382i	0.00131641	−	0.000846007i
$985$	−11.1625	−	12.8822i	−0.355667	−	0.410462i
$986$	−2.49609	−	0.732917i	−0.0794916	−	0.0233408i
$987$	2.08036	−	4.55535i	0.0662185	−	0.144998i
$988$	1.06480			0.0338758
$989$	22.3209	+	3.53304i	0.709762	+	0.112344i
$990$	−3.96719			−0.126086
$991$	−3.78139	+	8.28010i	−0.120120	+	0.263026i	−0.960135	−	0.279537i	$-0.909819\pi$
$991$	−3.78139	+	8.28010i	−0.120120	+	0.263026i	0.840015	+	0.542563i	$0.182546\pi$
$992$	1.60220	+	0.470447i	0.0508698	+	0.0149367i
$993$	−17.9863	−	20.7573i	−0.570778	−	0.658713i
$994$	−9.79002	+	6.29166i	−0.310521	+	0.199559i
$995$	7.92106	−	9.14139i	0.251114	−	0.289802i
$996$	−0.288666	+	2.00772i	−0.00914675	+	0.0636170i
$997$	42.4186	−	12.4552i	1.34341	−	0.394461i	0.470525	−	0.882387i	$-0.344065\pi$
$997$	42.4186	−	12.4552i	1.34341	−	0.394461i	0.872885	+	0.487926i	$0.162246\pi$
$998$	−30.0461	−	19.3095i	−0.951093	−	0.611231i
$999$	1.16700	+	8.11667i	0.0369223	+	0.256800i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.d.673.1	yes	20
23.4	even	11	inner	966.2.q.d.211.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.d.211.1	✓	20	23.4	even	11	inner
966.2.q.d.673.1	yes	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415415 - 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-1.26697 + 0.814230i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(0.415415 - 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-1.26697 + 0.814230i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(0.214333 + 1.49072i) q^{10} +(1.09428 + 2.39613i) q^{11} +(-0.415415 - 0.909632i) q^{12} +(0.0324836 + 0.225928i) q^{13} +(0.841254 + 0.540641i) q^{14} +(-1.44504 + 0.424302i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-0.344110 + 0.397124i) q^{17} +(0.841254 - 0.540641i) q^{18} +(3.05495 + 3.52559i) q^{19} +(1.44504 + 0.424302i) q^{20} +(-0.415415 + 0.909632i) q^{21} +2.63418 q^{22} +(4.75622 - 0.615128i) q^{23} -1.00000 q^{24} +(-1.13484 + 2.48496i) q^{25} +(0.219006 + 0.0643058i) q^{26} +(0.654861 + 0.755750i) q^{27} +(0.841254 - 0.540641i) q^{28} +(-3.24204 + 3.74152i) q^{29} +(-0.214333 + 1.49072i) q^{30} +(1.60220 - 0.470447i) q^{31} +(0.841254 + 0.540641i) q^{32} +(0.374882 + 2.60736i) q^{33} +(0.218288 + 0.477985i) q^{34} +(-0.625634 - 1.36995i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(6.89839 + 4.43333i) q^{37} +(4.47606 - 1.31429i) q^{38} +(-0.0324836 + 0.225928i) q^{39} +(0.986250 - 1.13819i) q^{40} +(-0.0412942 + 0.0265382i) q^{41} +(0.654861 + 0.755750i) q^{42} +(4.52129 + 1.32757i) q^{43} +(1.09428 - 2.39613i) q^{44} -1.50605 q^{45} +(1.41626 - 4.58194i) q^{46} -5.00790 q^{47} +(-0.415415 + 0.909632i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(1.78897 + 2.06458i) q^{50} +(-0.442054 + 0.284091i) q^{51} +(0.149473 - 0.172501i) q^{52} +(0.865718 - 6.02120i) q^{53} +(0.959493 - 0.281733i) q^{54} +(-3.33741 - 2.14482i) q^{55} +(-0.142315 - 0.989821i) q^{56} +(1.93792 + 4.24346i) q^{57} +(2.05661 + 4.50335i) q^{58} +(-0.0271187 - 0.188614i) q^{59} +(1.26697 + 0.814230i) q^{60} +(1.19326 - 0.350373i) q^{61} +(0.237642 - 1.65284i) q^{62} +(-0.654861 + 0.755750i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-0.225113 - 0.259794i) q^{65} +(2.52747 + 0.742133i) q^{66} +(3.12659 - 6.84628i) q^{67} +0.525470 q^{68} +(4.73686 + 0.749771i) q^{69} -1.50605 q^{70} +(-4.83436 + 10.5858i) q^{71} +(-0.959493 - 0.281733i) q^{72} +(4.58807 + 5.29492i) q^{73} +(6.89839 - 4.43333i) q^{74} +(-1.78897 + 2.06458i) q^{75} +(0.663903 - 4.61755i) q^{76} +(-2.52747 + 0.742133i) q^{77} +(0.192017 + 0.123402i) q^{78} +(-1.14553 - 7.96730i) q^{79} +(-0.625634 - 1.36995i) q^{80} +(0.415415 + 0.909632i) q^{81} +(0.00698575 + 0.0485869i) q^{82} +(-1.70637 - 1.09662i) q^{83} +(0.959493 - 0.281733i) q^{84} +(0.112625 - 0.783327i) q^{85} +(3.08581 - 3.56121i) q^{86} +(-4.16482 + 2.67657i) q^{87} +(-1.72502 - 1.99078i) q^{88} +(-7.18547 - 2.10984i) q^{89} +(-0.625634 + 1.36995i) q^{90} -0.228251 q^{91} +(-3.57954 - 3.19169i) q^{92} +1.66984 q^{93} +(-2.08036 + 4.55535i) q^{94} +(-6.74115 - 1.97938i) q^{95} +(0.654861 + 0.755750i) q^{96} +(-2.01807 + 1.29693i) q^{97} +(-0.654861 + 0.755750i) q^{98} +(-0.374882 + 2.60736i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9} - 10 q^{10} - 7 q^{11} + 2 q^{12} - 8 q^{13} - 2 q^{14} - q^{15} - 2 q^{16} + 13 q^{17} - 2 q^{18} - 8 q^{19} + q^{20} + 2 q^{21} + 4 q^{22} - 20 q^{24} + 16 q^{25} - 8 q^{26} + 2 q^{27} - 2 q^{28} + 3 q^{29} + 10 q^{30} + 9 q^{31} - 2 q^{32} - 4 q^{33} - 9 q^{34} + q^{35} - 2 q^{36} - q^{37} + 3 q^{38} + 8 q^{39} + q^{40} + 10 q^{41} + 2 q^{42} - 15 q^{43} - 7 q^{44} - 10 q^{45} - 28 q^{47} + 2 q^{48} - 2 q^{49} + 5 q^{50} - 2 q^{51} + 3 q^{52} + 38 q^{53} + 2 q^{54} - 8 q^{55} - 2 q^{56} - 14 q^{57} - 19 q^{58} - 10 q^{59} - 12 q^{60} - 6 q^{61} + 20 q^{62} - 2 q^{63} - 2 q^{64} - 36 q^{65} - 4 q^{66} + 36 q^{67} - 20 q^{68} + 11 q^{69} - 10 q^{70} - q^{71} - 2 q^{72} + 65 q^{73} - q^{74} - 5 q^{75} + 14 q^{76} + 4 q^{77} - 14 q^{78} + 10 q^{79} + q^{80} - 2 q^{81} + 10 q^{82} - 14 q^{83} + 2 q^{84} - 5 q^{85} + 51 q^{86} - 3 q^{87} - 7 q^{88} - 18 q^{89} + q^{90} - 30 q^{91} - 11 q^{92} + 2 q^{93} + 38 q^{94} - 73 q^{95} + 2 q^{96} - 20 q^{97} - 2 q^{98} + 4 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9 - 10 * q^10 - 7 * q^11 + 2 * q^12 - 8 * q^13 - 2 * q^14 - q^15 - 2 * q^16 + 13 * q^17 - 2 * q^18 - 8 * q^19 + q^20 + 2 * q^21 + 4 * q^22 - 20 * q^24 + 16 * q^25 - 8 * q^26 + 2 * q^27 - 2 * q^28 + 3 * q^29 + 10 * q^30 + 9 * q^31 - 2 * q^32 - 4 * q^33 - 9 * q^34 + q^35 - 2 * q^36 - q^37 + 3 * q^38 + 8 * q^39 + q^40 + 10 * q^41 + 2 * q^42 - 15 * q^43 - 7 * q^44 - 10 * q^45 - 28 * q^47 + 2 * q^48 - 2 * q^49 + 5 * q^50 - 2 * q^51 + 3 * q^52 + 38 * q^53 + 2 * q^54 - 8 * q^55 - 2 * q^56 - 14 * q^57 - 19 * q^58 - 10 * q^59 - 12 * q^60 - 6 * q^61 + 20 * q^62 - 2 * q^63 - 2 * q^64 - 36 * q^65 - 4 * q^66 + 36 * q^67 - 20 * q^68 + 11 * q^69 - 10 * q^70 - q^71 - 2 * q^72 + 65 * q^73 - q^74 - 5 * q^75 + 14 * q^76 + 4 * q^77 - 14 * q^78 + 10 * q^79 + q^80 - 2 * q^81 + 10 * q^82 - 14 * q^83 + 2 * q^84 - 5 * q^85 + 51 * q^86 - 3 * q^87 - 7 * q^88 - 18 * q^89 + q^90 - 30 * q^91 - 11 * q^92 + 2 * q^93 + 38 * q^94 - 73 * q^95 + 2 * q^96 - 20 * q^97 - 2 * q^98 + 4 * q^99

Introduction

L-functions

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