LMFDB - Embedded newform 966.2.q.e.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} - 9 x^{19} + 42 x^{18} - 126 x^{17} + 277 x^{16} - 538 x^{15} + 1046 x^{14} - 1170 x^{13} + \cdots + 529 $ x^20 - 9x^19 + 42x^18 - 126x^17 + 277x^16 - 538x^15 + 1046x^14 - 1170x^13 - 619x^12 + 2218x^11 + 1660x^10 - 3225x^9 + 2719x^8 + 8761x^7 + 14705x^6 + 21691x^5 + 21163x^4 + 14656x^3 + 7846x^2 + 2622*x + 529
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			$-0.0895295 - 0.622691i$ of defining polynomial
Character	$\chi$	$=$	966.673
Dual form			966.2.q.e.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 + 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.117330 + 0.0754032i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.117330 + 0.0754032i) 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} +(-0.0198486 - 0.138050i) q^{10} +(-1.36267 - 2.98384i) q^{11} +(0.415415 + 0.909632i) q^{12} +(0.379656 + 2.64057i) q^{13} +(-0.841254 - 0.540641i) q^{14} +(0.133820 - 0.0392932i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(0.888717 - 1.02563i) q^{17} +(-0.841254 + 0.540641i) q^{18} +(-3.67555 - 4.24181i) q^{19} +(0.133820 + 0.0392932i) q^{20} +(0.415415 - 0.909632i) q^{21} +3.28027 q^{22} +(-2.46629 + 4.11308i) q^{23} -1.00000 q^{24} +(-2.06899 + 4.53047i) q^{25} +(-2.55966 - 0.751584i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(0.841254 - 0.540641i) q^{28} +(3.00117 - 3.46354i) q^{29} +(-0.0198486 + 0.138050i) q^{30} +(1.90730 - 0.560035i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(0.466831 + 3.24688i) q^{33} +(0.563763 + 1.23447i) q^{34} +(-0.0579379 - 0.126866i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-8.05470 - 5.17644i) q^{37} +(5.38537 - 1.58129i) q^{38} +(0.379656 - 2.64057i) q^{39} +(-0.0913334 + 0.105404i) q^{40} +(5.91238 - 3.79965i) q^{41} +(0.654861 + 0.755750i) q^{42} +(-10.7824 - 3.16600i) q^{43} +(-1.36267 + 2.98384i) q^{44} -0.139470 q^{45} +(-2.71685 - 3.95205i) q^{46} -2.44285 q^{47} +(0.415415 - 0.909632i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(-3.26157 - 3.76405i) q^{50} +(-1.14167 + 0.733708i) q^{51} +(1.74699 - 2.01613i) q^{52} +(0.943820 - 6.56441i) q^{53} +(0.959493 - 0.281733i) q^{54} +(0.384873 + 0.247343i) q^{55} +(0.142315 + 0.989821i) q^{56} +(2.33161 + 5.10551i) q^{57} +(1.90381 + 4.16877i) q^{58} +(-2.11755 - 14.7279i) q^{59} +(-0.117330 - 0.0754032i) q^{60} +(-6.29642 + 1.84879i) q^{61} +(-0.282897 + 1.96759i) q^{62} +(-0.654861 + 0.755750i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-0.243652 - 0.281189i) q^{65} +(-3.14740 - 0.924159i) q^{66} +(-0.751453 + 1.64545i) q^{67} -1.35711 q^{68} +(3.52518 - 3.25163i) q^{69} +0.139470 q^{70} +(3.34252 - 7.31910i) q^{71} +(0.959493 + 0.281733i) q^{72} +(-4.55722 - 5.25931i) q^{73} +(8.05470 - 5.17644i) q^{74} +(3.26157 - 3.76405i) q^{75} +(-0.798774 + 5.55560i) q^{76} +(3.14740 - 0.924159i) q^{77} +(2.24423 + 1.44228i) q^{78} +(-0.319333 - 2.22101i) q^{79} +(-0.0579379 - 0.126866i) q^{80} +(0.415415 + 0.909632i) q^{81} +(1.00020 + 6.95652i) q^{82} +(-3.86065 - 2.48109i) q^{83} +(-0.959493 + 0.281733i) q^{84} +(-0.0269368 + 0.187349i) q^{85} +(7.35907 - 8.49282i) q^{86} +(-3.85539 + 2.47771i) q^{87} +(-2.14812 - 2.47906i) q^{88} +(-9.43260 - 2.76966i) q^{89} +(0.0579379 - 0.126866i) q^{90} -2.66772 q^{91} +(4.72353 - 0.829594i) q^{92} -1.98782 q^{93} +(1.01480 - 2.22210i) q^{94} +(0.751097 + 0.220542i) q^{95} +(0.654861 + 0.755750i) q^{96} +(4.29736 - 2.76175i) q^{97} +(0.654861 - 0.755750i) q^{98} +(0.466831 - 3.24688i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 10 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 + 10 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 10 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} - 10 q^{10} - 3 q^{11} - 2 q^{12} + 6 q^{13} + 2 q^{14} - 12 q^{15} - 2 q^{16} + 14 q^{17} + 2 q^{18} - 13 q^{19} - 12 q^{20} - 2 q^{21} - 8 q^{22} - 2 q^{23} - 20 q^{24} + 22 q^{25} - 28 q^{26} - 2 q^{27} - 2 q^{28} + 26 q^{29} - 10 q^{30} + 15 q^{31} + 2 q^{32} - 14 q^{33} - 3 q^{34} - q^{35} - 2 q^{36} - 26 q^{37} + 2 q^{38} + 6 q^{39} + q^{40} + 40 q^{41} + 2 q^{42} + 8 q^{43} - 3 q^{44} - 12 q^{45} - 20 q^{46} + 36 q^{47} - 2 q^{48} - 2 q^{49} + 11 q^{50} + 3 q^{51} - 27 q^{52} - 5 q^{53} + 2 q^{54} - 7 q^{55} + 2 q^{56} + 9 q^{57} - 15 q^{58} + 13 q^{59} + 10 q^{60} + 59 q^{61} - 4 q^{62} - 2 q^{63} - 2 q^{64} - q^{65} - 8 q^{66} - 26 q^{67} - 8 q^{68} - 35 q^{69} + 12 q^{70} + 13 q^{71} + 2 q^{72} - 34 q^{73} + 26 q^{74} - 11 q^{75} - 2 q^{76} + 8 q^{77} - 6 q^{78} - 27 q^{79} - q^{80} - 2 q^{81} - 40 q^{82} + 41 q^{83} - 2 q^{84} + 51 q^{85} + 14 q^{86} - 7 q^{87} - 8 q^{88} + 43 q^{89} + q^{90} - 16 q^{91} + 9 q^{92} + 4 q^{93} - 3 q^{94} - 26 q^{95} + 2 q^{96} - 8 q^{97} + 2 q^{98} - 14 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 10 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 - 10 * q^10 - 3 * q^11 - 2 * q^12 + 6 * q^13 + 2 * q^14 - 12 * q^15 - 2 * q^16 + 14 * q^17 + 2 * q^18 - 13 * q^19 - 12 * q^20 - 2 * q^21 - 8 * q^22 - 2 * q^23 - 20 * q^24 + 22 * q^25 - 28 * q^26 - 2 * q^27 - 2 * q^28 + 26 * q^29 - 10 * q^30 + 15 * q^31 + 2 * q^32 - 14 * q^33 - 3 * q^34 - q^35 - 2 * q^36 - 26 * q^37 + 2 * q^38 + 6 * q^39 + q^40 + 40 * q^41 + 2 * q^42 + 8 * q^43 - 3 * q^44 - 12 * q^45 - 20 * q^46 + 36 * q^47 - 2 * q^48 - 2 * q^49 + 11 * q^50 + 3 * q^51 - 27 * q^52 - 5 * q^53 + 2 * q^54 - 7 * q^55 + 2 * q^56 + 9 * q^57 - 15 * q^58 + 13 * q^59 + 10 * q^60 + 59 * q^61 - 4 * q^62 - 2 * q^63 - 2 * q^64 - q^65 - 8 * q^66 - 26 * q^67 - 8 * q^68 - 35 * q^69 + 12 * q^70 + 13 * q^71 + 2 * q^72 - 34 * q^73 + 26 * q^74 - 11 * q^75 - 2 * q^76 + 8 * q^77 - 6 * q^78 - 27 * q^79 - q^80 - 2 * q^81 - 40 * q^82 + 41 * q^83 - 2 * q^84 + 51 * q^85 + 14 * q^86 - 7 * q^87 - 8 * q^88 + 43 * q^89 + q^90 - 16 * q^91 + 9 * q^92 + 4 * q^93 - 3 * q^94 - 26 * q^95 + 2 * q^96 - 8 * q^97 + 2 * q^98 - 14 * 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
$5$	−0.117330	+	0.0754032i	−0.0524714	+	0.0337213i	−0.566614	−	0.823984i	$-0.691747\pi$
$5$	−0.117330	+	0.0754032i	−0.0524714	+	0.0337213i	0.514142	+	0.857705i	$0.328110\pi$
$6$	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
$10$	−0.0198486	−	0.138050i	−0.00627669	−	0.0436554i
$11$	−1.36267	−	2.98384i	−0.410862	−	0.899662i	−0.996053	−	0.0887660i	$-0.971708\pi$
$11$	−1.36267	−	2.98384i	−0.410862	−	0.899662i	0.585191	−	0.810896i	$-0.301020\pi$
$12$	0.415415	+	0.909632i	0.119920	+	0.262588i
$13$	0.379656	+	2.64057i	0.105298	+	0.732361i	0.972246	+	0.233963i	$0.0751694\pi$
$13$	0.379656	+	2.64057i	0.105298	+	0.732361i	−0.866948	+	0.498399i	$0.833922\pi$
$14$	−0.841254	−	0.540641i	−0.224834	−	0.144492i
$15$	0.133820	−	0.0392932i	0.0345523	−	0.0101455i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	0.888717	−	1.02563i	0.215546	−	0.248753i	−0.637672	−	0.770308i	$-0.720102\pi$
$17$	0.888717	−	1.02563i	0.215546	−	0.248753i	0.853218	+	0.521555i	$0.174648\pi$
$18$	−0.841254	+	0.540641i	−0.198285	+	0.127430i
$19$	−3.67555	−	4.24181i	−0.843230	−	0.973139i	0.156665	−	0.987652i	$-0.449926\pi$
$19$	−3.67555	−	4.24181i	−0.843230	−	0.973139i	−0.999895	+	0.0145127i	$0.995380\pi$
$20$	0.133820	+	0.0392932i	0.0299232	+	0.00878623i
$21$	0.415415	−	0.909632i	0.0906510	−	0.198498i
$22$	3.28027			0.699356
$23$	−2.46629	+	4.11308i	−0.514257	+	0.857636i
$23$	−2.46629	+	4.11308i	−0.514257	+	0.857636i
$24$	−1.00000			−0.204124
$25$	−2.06899	+	4.53047i	−0.413799	+	0.906093i
$26$	−2.55966	−	0.751584i	−0.501990	−	0.147398i
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$	0.841254	−	0.540641i	0.158982	−	0.102172i
$29$	3.00117	−	3.46354i	0.557303	−	0.643162i	−0.405266	−	0.914199i	$-0.632821\pi$
$29$	3.00117	−	3.46354i	0.557303	−	0.643162i	0.962569	+	0.271037i	$0.0873664\pi$
$30$	−0.0198486	+	0.138050i	−0.00362385	+	0.0252044i
$31$	1.90730	−	0.560035i	0.342562	−	0.100585i	−0.105926	−	0.994374i	$-0.533781\pi$
$31$	1.90730	−	0.560035i	0.342562	−	0.100585i	0.448488	+	0.893789i	$0.351963\pi$
$32$	−0.841254	−	0.540641i	−0.148714	−	0.0955727i
$33$	0.466831	+	3.24688i	0.0812649	+	0.565210i
$34$	0.563763	+	1.23447i	0.0966846	+	0.211710i
$35$	−0.0579379	−	0.126866i	−0.00979330	−	0.0214443i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	−8.05470	−	5.17644i	−1.32418	−	0.851001i	−0.328563	−	0.944482i	$-0.606564\pi$
$37$	−8.05470	−	5.17644i	−1.32418	−	0.851001i	−0.995621	+	0.0934808i	$0.970201\pi$
$38$	5.38537	−	1.58129i	0.873622	−	0.256519i
$39$	0.379656	−	2.64057i	0.0607936	−	0.422829i
$40$	−0.0913334	+	0.105404i	−0.0144411	+	0.0166659i
$41$	5.91238	−	3.79965i	0.923358	−	0.593406i	0.00972817	−	0.999953i	$-0.496903\pi$
$41$	5.91238	−	3.79965i	0.923358	−	0.593406i	0.913630	+	0.406546i	$0.133267\pi$
$42$	0.654861	+	0.755750i	0.101047	+	0.116615i
$43$	−10.7824	−	3.16600i	−1.64430	−	0.482811i	−0.676904	−	0.736072i	$-0.736679\pi$
$43$	−10.7824	−	3.16600i	−1.64430	−	0.482811i	−0.967398	+	0.253261i	$0.918497\pi$
$44$	−1.36267	+	2.98384i	−0.205431	+	0.449831i
$45$	−0.139470			−0.0207910
$46$	−2.71685	−	3.95205i	−0.400578	−	0.582698i
$47$	−2.44285			−0.356327			−0.178163	−	0.984001i	$-0.557016\pi$
$47$	−2.44285			−0.356327			−0.178163	+	0.984001i	$0.557016\pi$
$48$	0.415415	−	0.909632i	0.0599600	−	0.131294i
$49$	−0.959493	−	0.281733i	−0.137070	−	0.0402475i
$50$	−3.26157	−	3.76405i	−0.461255	−	0.532317i
$51$	−1.14167	+	0.733708i	−0.159866	+	0.102740i
$52$	1.74699	−	2.01613i	0.242263	−	0.279587i
$53$	0.943820	−	6.56441i	0.129644	−	0.901691i	−0.816362	−	0.577541i	$-0.804013\pi$
$53$	0.943820	−	6.56441i	0.129644	−	0.901691i	0.946006	−	0.324150i	$-0.105078\pi$
$54$	0.959493	−	0.281733i	0.130570	−	0.0383389i
$55$	0.384873	+	0.247343i	0.0518963	+	0.0333517i
$56$	0.142315	+	0.989821i	0.0190176	+	0.132270i
$57$	2.33161	+	5.10551i	0.308829	+	0.676242i
$58$	1.90381	+	4.16877i	0.249983	+	0.547386i
$59$	−2.11755	−	14.7279i	−0.275682	−	1.91741i	−0.384080	−	0.923300i	$-0.625481\pi$
$59$	−2.11755	−	14.7279i	−0.275682	−	1.91741i	0.108398	−	0.994108i	$-0.465428\pi$
$60$	−0.117330	−	0.0754032i	−0.0151472	−	0.00973451i
$61$	−6.29642	+	1.84879i	−0.806173	+	0.236714i	−0.658752	−	0.752360i	$-0.728915\pi$
$61$	−6.29642	+	1.84879i	−0.806173	+	0.236714i	−0.147421	+	0.989074i	$0.547097\pi$
$62$	−0.282897	+	1.96759i	−0.0359280	+	0.249884i
$63$	−0.654861	+	0.755750i	−0.0825047	+	0.0952155i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	−0.243652	−	0.281189i	−0.0302213	−	0.0348773i
$66$	−3.14740	−	0.924159i	−0.387418	−	0.113756i
$67$	−0.751453	+	1.64545i	−0.0918046	+	0.201024i	−0.949964	−	0.312359i	$-0.898881\pi$
$67$	−0.751453	+	1.64545i	−0.0918046	+	0.201024i	0.858159	+	0.513383i	$0.171608\pi$
$68$	−1.35711			−0.164574
$69$	3.52518	−	3.25163i	0.424382	−	0.391451i
$70$	0.139470			0.0166698
$71$	3.34252	−	7.31910i	0.396684	−	0.868618i	−0.600911	−	0.799316i	$-0.705195\pi$
$71$	3.34252	−	7.31910i	0.396684	−	0.868618i	0.997596	−	0.0693021i	$-0.0220772\pi$
$72$	0.959493	+	0.281733i	0.113077	+	0.0332025i
$73$	−4.55722	−	5.25931i	−0.533382	−	0.615555i	0.423548	−	0.905873i	$-0.360784\pi$
$73$	−4.55722	−	5.25931i	−0.533382	−	0.615555i	−0.956930	+	0.290318i	$0.906239\pi$
$74$	8.05470	−	5.17644i	0.936339	−	0.601749i
$75$	3.26157	−	3.76405i	0.376613	−	0.434635i
$76$	−0.798774	+	5.55560i	−0.0916257	+	0.637271i
$77$	3.14740	−	0.924159i	0.358679	−	0.105318i
$78$	2.24423	+	1.44228i	0.254109	+	0.163306i
$79$	−0.319333	−	2.22101i	−0.0359278	−	0.249883i	0.963940	−	0.266118i	$-0.0857412\pi$
$79$	−0.319333	−	2.22101i	−0.0359278	−	0.249883i	−0.999868	+	0.0162348i	$0.994832\pi$
$80$	−0.0579379	−	0.126866i	−0.00647766	−	0.0141841i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	1.00020	+	6.95652i	0.110453	+	0.768219i
$83$	−3.86065	−	2.48109i	−0.423761	−	0.272335i	0.311332	−	0.950301i	$-0.399225\pi$
$83$	−3.86065	−	2.48109i	−0.423761	−	0.272335i	−0.735093	+	0.677967i	$0.762861\pi$
$84$	−0.959493	+	0.281733i	−0.104689	+	0.0307395i
$85$	−0.0269368	+	0.187349i	−0.00292170	+	0.0203209i
$86$	7.35907	−	8.49282i	0.793549	−	0.915804i
$87$	−3.85539	+	2.47771i	−0.413341	+	0.265638i
$88$	−2.14812	−	2.47906i	−0.228990	−	0.264269i
$89$	−9.43260	−	2.76966i	−0.999853	−	0.293583i	−0.259457	−	0.965755i	$-0.583544\pi$
$89$	−9.43260	−	2.76966i	−0.999853	−	0.293583i	−0.740396	+	0.672171i	$0.765362\pi$
$90$	0.0579379	−	0.126866i	0.00610719	−	0.0133729i
$91$	−2.66772			−0.279653
$92$	4.72353	−	0.829594i	0.492462	−	0.0864911i
$93$	−1.98782			−0.206128
$94$	1.01480	−	2.22210i	0.104668	−	0.229192i
$95$	0.751097	+	0.220542i	0.0770610	+	0.0226271i
$96$	0.654861	+	0.755750i	0.0668364	+	0.0771334i
$97$	4.29736	−	2.76175i	0.436331	−	0.280413i	−0.303979	−	0.952679i	$-0.598315\pi$
$97$	4.29736	−	2.76175i	0.436331	−	0.280413i	0.740310	+	0.672266i	$0.234679\pi$
$98$	0.654861	−	0.755750i	0.0661509	−	0.0763422i
$99$	0.466831	−	3.24688i	0.0469183	−	0.326324i
$100$	4.77880	−	1.40318i	0.477880	−	0.140318i
$101$	8.31914	+	5.34639i	0.827786	+	0.531985i	0.884574	−	0.466401i	$-0.154450\pi$
$101$	8.31914	+	5.34639i	0.827786	+	0.531985i	−0.0567880	+	0.998386i	$0.518086\pi$
$102$	−0.193137	−	1.34330i	−0.0191234	−	0.133006i
$103$	−2.76255	−	6.04915i	−0.272202	−	0.596040i	0.723326	−	0.690507i	$-0.242613\pi$
$103$	−2.76255	−	6.04915i	−0.272202	−	0.596040i	−0.995528	+	0.0944670i	$0.969885\pi$
$104$	1.10821	+	2.42664i	0.108669	+	0.237952i
$105$	0.0198486	+	0.138050i	0.00193703	+	0.0134723i
$106$	5.57912	+	3.58548i	0.541892	+	0.348253i
$107$	1.42617	−	0.418761i	0.137873	−	0.0404832i	−0.212068	−	0.977255i	$-0.568020\pi$
$107$	1.42617	−	0.418761i	0.137873	−	0.0404832i	0.349941	+	0.936772i	$0.386202\pi$
$108$	−0.142315	+	0.989821i	−0.0136943	+	0.0952456i
$109$	−8.51957	+	9.83211i	−0.816027	+	0.941746i	−0.999145	−	0.0413454i	$-0.986836\pi$
$109$	−8.51957	+	9.83211i	−0.816027	+	0.941746i	0.183118	+	0.983091i	$0.441381\pi$
$110$	−0.384873	+	0.247343i	−0.0366962	+	0.0235832i
$111$	6.27005	+	7.23603i	0.595127	+	0.686813i
$112$	−0.959493	−	0.281733i	−0.0906636	−	0.0266212i
$113$	−5.39188	+	11.8066i	−0.507226	+	1.11067i	0.466827	+	0.884349i	$0.345397\pi$
$113$	−5.39188	+	11.8066i	−0.507226	+	1.11067i	−0.974053	+	0.226321i	$0.927330\pi$
$114$	−5.61273			−0.525680
$115$	−0.0207700	−	0.668552i	−0.00193681	−	0.0623428i
$116$	−4.58291			−0.425513
$117$	−1.10821	+	2.42664i	−0.102454	+	0.224343i
$118$	14.2766	+	4.19199i	1.31427	+	0.385904i
$119$	0.888717	+	1.02563i	0.0814686	+	0.0940197i
$120$	0.117330	−	0.0754032i	0.0107107	−	0.00688334i
$121$	0.157046	−	0.181241i	0.0142769	−	0.0164765i
$122$	0.933903	−	6.49544i	0.0845516	−	0.588069i
$123$	−6.74337	+	1.98003i	−0.608029	+	0.178534i
$124$	−1.67226	−	1.07470i	−0.150174	−	0.0965108i
$125$	−0.198100	−	1.37782i	−0.0177186	−	0.123236i
$126$	−0.415415	−	0.909632i	−0.0370081	−	0.0810365i
$127$	5.13482	+	11.2437i	0.455642	+	0.997717i	0.988459	+	0.151487i	$0.0484060\pi$
$127$	5.13482	+	11.2437i	0.455642	+	0.997717i	−0.532817	+	0.846230i	$0.678867\pi$
$128$	0.142315	+	0.989821i	0.0125790	+	0.0874887i
$129$	9.45368	+	6.07551i	0.832350	+	0.534919i
$130$	0.356996	−	0.104823i	0.0313106	−	0.00919362i
$131$	2.17386	−	15.1195i	0.189931	−	1.32100i	−0.642250	−	0.766495i	$-0.721999\pi$
$131$	2.17386	−	15.1195i	0.189931	−	1.32100i	0.832181	−	0.554504i	$-0.187092\pi$
$132$	2.14812	−	2.47906i	0.186970	−	0.215775i
$133$	4.72173	−	3.03447i	0.409426	−	0.263122i
$134$	−1.18459	−	1.36709i	−0.102333	−	0.118099i
$135$	0.133820	+	0.0392932i	0.0115174	+	0.00338182i
$136$	0.563763	−	1.23447i	0.0483423	−	0.105855i
$137$	−13.7564			−1.17529			−0.587645	−	0.809119i	$-0.699945\pi$
$137$	−13.7564			−1.17529			−0.587645	+	0.809119i	$0.699945\pi$
$138$	1.49338	+	4.55739i	0.127125	+	0.387951i
$139$	10.9938			0.932483			0.466242	−	0.884657i	$-0.345608\pi$
$139$	10.9938			0.932483			0.466242	+	0.884657i	$0.345608\pi$
$140$	−0.0579379	+	0.126866i	−0.00489665	+	0.0107222i
$141$	2.34390	+	0.688231i	0.197392	+	0.0579595i
$142$	5.26916	+	6.08093i	0.442178	+	0.510300i
$143$	7.36168	−	4.73107i	0.615615	−	0.395632i
$144$	−0.654861	+	0.755750i	−0.0545717	+	0.0629791i
$145$	−0.0909646	+	0.632673i	−0.00755420	+	0.0525406i
$146$	6.67717	−	1.96059i	0.552606	−	0.162260i
$147$	0.841254	+	0.540641i	0.0693854	+	0.0445913i
$148$	1.36261	+	9.47718i	0.112006	+	0.779019i
$149$	3.14190	+	6.87981i	0.257395	+	0.563616i	0.993576	−	0.113169i	$-0.0361000\pi$
$149$	3.14190	+	6.87981i	0.257395	+	0.563616i	−0.736181	+	0.676785i	$0.763373\pi$
$150$	2.06899	+	4.53047i	0.168933	+	0.369911i
$151$	−0.0898232	−	0.624734i	−0.00730971	−	0.0508402i	0.985840	−	0.167688i	$-0.0536301\pi$
$151$	−0.0898232	−	0.624734i	−0.00730971	−	0.0508402i	−0.993150	+	0.116848i	$0.962721\pi$
$152$	−4.72173	−	3.03447i	−0.382982	−	0.246128i
$153$	1.30214	−	0.382342i	0.105271	−	0.0309105i
$154$	−0.466831	+	3.24688i	−0.0376183	+	0.261641i
$155$	−0.181555	+	0.209525i	−0.0145828	+	0.0168295i
$156$	−2.24423	+	1.44228i	−0.179682	+	0.115475i
$157$	12.9655	+	14.9630i	1.03476	+	1.19418i	0.980676	+	0.195639i	$0.0626782\pi$
$157$	12.9655	+	14.9630i	1.03476	+	1.19418i	0.0540832	+	0.998536i	$0.482776\pi$
$158$	2.15296	+	0.632166i	0.171280	+	0.0502924i
$159$	−2.75500	+	6.03260i	−0.218485	+	0.478416i
$160$	0.139470			0.0110261
$161$	−3.72022	−	3.02654i	−0.293195	−	0.238525i
$162$	−1.00000			−0.0785674
$163$	−9.54244	+	20.8950i	−0.747422	+	1.63663i	0.0235227	+	0.999723i	$0.492512\pi$
$163$	−9.54244	+	20.8950i	−0.747422	+	1.63663i	−0.770945	+	0.636902i	$0.780215\pi$
$164$	−6.74337	−	1.98003i	−0.526569	−	0.154615i
$165$	−0.299598	−	0.345755i	−0.0233237	−	0.0269170i
$166$	3.86065	−	2.48109i	0.299644	−	0.192570i
$167$	10.9736	−	12.6642i	0.849160	−	0.979983i	−0.150803	−	0.988564i	$-0.548186\pi$
$167$	10.9736	−	12.6642i	0.849160	−	0.979983i	0.999963	+	0.00858069i	$0.00273135\pi$
$168$	0.142315	−	0.989821i	0.0109798	−	0.0763664i
$169$	5.64495	−	1.65751i	0.434227	−	0.127501i
$170$	−0.159229	−	0.102330i	−0.0122123	−	0.00784837i
$171$	−0.798774	−	5.55560i	−0.0610838	−	0.424847i
$172$	4.66827	+	10.2221i	0.355952	+	0.779427i
$173$	−5.22665	−	11.4448i	−0.397375	−	0.870129i	−0.997530	−	0.0702454i	$-0.977622\pi$
$173$	−5.22665	−	11.4448i	−0.397375	−	0.870129i	0.600155	−	0.799884i	$-0.295105\pi$
$174$	−0.652217	−	4.53627i	−0.0494444	−	0.343893i
$175$	−4.18990	−	2.69269i	−0.316727	−	0.203548i
$176$	3.14740	−	0.924159i	0.237244	−	0.0696611i
$177$	−2.11755	+	14.7279i	−0.159165	+	1.10702i
$178$	6.43781	−	7.42963i	0.482535	−	0.556875i
$179$	−17.3313	+	11.1382i	−1.29540	+	0.832505i	−0.992704	−	0.120580i	$-0.961524\pi$
$179$	−17.3313	+	11.1382i	−1.29540	+	0.832505i	−0.302700	+	0.953086i	$0.597888\pi$
$180$	0.0913334	+	0.105404i	0.00680759	+	0.00785638i
$181$	1.95732	+	0.574721i	0.145487	+	0.0427187i	0.353665	−	0.935372i	$-0.384935\pi$
$181$	1.95732	+	0.574721i	0.145487	+	0.0427187i	−0.208178	+	0.978091i	$0.566753\pi$
$182$	1.10821	−	2.42664i	0.0821461	−	0.179875i
$183$	6.56223			0.485094
$184$	−1.20760	+	4.64130i	−0.0890256	+	0.342161i
$185$	1.33537			0.0981787
$186$	0.825772	−	1.80819i	0.0605486	−	0.132583i
$187$	−4.27136	−	1.25418i	−0.312353	−	0.0917151i
$188$	1.59973	+	1.84619i	0.116672	+	0.134647i
$189$	0.841254	−	0.540641i	0.0611922	−	0.0393258i
$190$	−0.512629	+	0.591606i	−0.0371900	+	0.0429196i
$191$	−0.270286	+	1.87988i	−0.0195572	+	0.136024i	−0.997261	−	0.0739667i	$-0.976434\pi$
$191$	−0.270286	+	1.87988i	−0.0195572	+	0.136024i	0.977703	+	0.209990i	$0.0673432\pi$
$192$	−0.959493	+	0.281733i	−0.0692454	+	0.0203323i
$193$	−14.3575	−	9.22700i	−1.03347	−	0.664174i	−0.0901099	−	0.995932i	$-0.528722\pi$
$193$	−14.3575	−	9.22700i	−1.03347	−	0.664174i	−0.943364	+	0.331758i	$0.892358\pi$
$194$	0.726984	+	5.05629i	0.0521944	+	0.363020i
$195$	0.154562	+	0.338444i	0.0110684	+	0.0242365i
$196$	0.415415	+	0.909632i	0.0296725	+	0.0649737i
$197$	3.54523	+	24.6576i	0.252587	+	1.75678i	0.582556	+	0.812791i	$0.302053\pi$
$197$	3.54523	+	24.6576i	0.252587	+	1.75678i	−0.329969	+	0.943992i	$0.607038\pi$
$198$	2.75954	+	1.77345i	0.196112	+	0.126034i
$199$	−20.9822	+	6.16094i	−1.48739	+	0.436738i	−0.921708	−	0.387885i	$-0.873206\pi$
$199$	−20.9822	+	6.16094i	−1.48739	+	0.436738i	−0.565684	+	0.824622i	$0.691388\pi$
$200$	−0.708806	+	4.92985i	−0.0501201	+	0.348593i
$201$	1.18459	−	1.36709i	0.0835546	−	0.0964272i
$202$	−8.31914	+	5.34639i	−0.585333	+	0.376171i
$203$	3.00117	+	3.46354i	0.210641	+	0.243093i
$204$	1.30214	+	0.382342i	0.0911678	+	0.0267693i
$205$	−0.407191	+	0.891624i	−0.0284395	+	0.0622737i
$206$	6.65010			0.463335
$207$	−4.29847	+	2.12676i	−0.298765	+	0.147820i
$208$	−2.66772			−0.184973
$209$	−7.64832	+	16.7475i	−0.529045	+	1.15845i
$210$	−0.133820	−	0.0392932i	−0.00923449	−	0.00271149i
$211$	−14.6369	−	16.8919i	−1.00765	−	1.16289i	−0.986608	−	0.163110i	$-0.947847\pi$
$211$	−14.6369	−	16.8919i	−1.00765	−	1.16289i	−0.0210408	−	0.999779i	$-0.506698\pi$
$212$	−5.57912	+	3.58548i	−0.383176	+	0.246252i
$213$	−5.26916	+	6.08093i	−0.361037	+	0.416659i
$214$	−0.211534	+	1.47125i	−0.0144602	+	0.100573i
$215$	1.50382	−	0.441562i	0.102560	−	0.0301143i
$216$	−0.841254	−	0.540641i	−0.0572401	−	0.0367859i
$217$	0.282897	+	1.96759i	0.0192043	+	0.133569i
$218$	−5.40445	−	11.8341i	−0.366035	−	0.801505i
$219$	2.89090	+	6.33018i	0.195349	+	0.427754i
$220$	−0.0651090	−	0.452843i	−0.00438964	−	0.0305307i
$221$	3.04566	+	1.95733i	0.204873	+	0.131664i
$222$	−9.18680	+	2.69749i	−0.616577	+	0.181043i
$223$	−1.62950	+	11.3334i	−0.109119	+	0.758941i	0.859633	+	0.510912i	$0.170692\pi$
$223$	−1.62950	+	11.3334i	−0.109119	+	0.758941i	−0.968752	+	0.248030i	$0.920217\pi$
$224$	0.654861	−	0.755750i	0.0437547	−	0.0504956i
$225$	−4.18990	+	2.69269i	−0.279327	+	0.179513i
$226$	−8.49977	−	9.80926i	−0.565396	−	0.652502i
$227$	−0.702722	−	0.206338i	−0.0466413	−	0.0136951i	0.258329	−	0.966057i	$-0.416828\pi$
$227$	−0.702722	−	0.206338i	−0.0466413	−	0.0136951i	−0.304970	+	0.952362i	$0.598646\pi$
$228$	2.33161	−	5.10551i	0.154415	−	0.338121i
$229$	16.9378			1.11928			0.559642	−	0.828735i	$-0.310939\pi$
$229$	16.9378			1.11928			0.559642	+	0.828735i	$0.310939\pi$
$230$	0.616764	+	0.258833i	0.0406682	+	0.0170670i
$231$	−3.28027			−0.215826
$232$	1.90381	−	4.16877i	0.124991	−	0.273693i
$233$	18.4502	+	5.41745i	1.20871	+	0.354909i	0.823177	−	0.567785i	$-0.192199\pi$
$233$	18.4502	+	5.41745i	1.20871	+	0.354909i	0.385533	+	0.922694i	$0.374018\pi$
$234$	−1.74699	−	2.01613i	−0.114204	−	0.131798i
$235$	0.286619	−	0.184199i	0.0186970	−	0.0120158i
$236$	−9.74389	+	11.2451i	−0.634273	+	0.731991i
$237$	−0.319333	+	2.22101i	−0.0207429	+	0.144270i
$238$	−1.30214	+	0.382342i	−0.0844049	+	0.0247835i
$239$	−6.72576	−	4.32238i	−0.435053	−	0.279592i	0.304728	−	0.952439i	$-0.401435\pi$
$239$	−6.72576	−	4.32238i	−0.435053	−	0.279592i	−0.739781	+	0.672848i	$0.765071\pi$
$240$	0.0198486	+	0.138050i	0.00128122	+	0.00891111i
$241$	3.25174	+	7.12032i	0.209463	+	0.458660i	0.984980	−	0.172666i	$-0.0552382\pi$
$241$	3.25174	+	7.12032i	0.209463	+	0.458660i	−0.775517	+	0.631326i	$0.782511\pi$
$242$	0.0996234	+	0.218145i	0.00640403	+	0.0140229i
$243$	−0.142315	−	0.989821i	−0.00912950	−	0.0634971i
$244$	5.52050	+	3.54781i	0.353414	+	0.227125i
$245$	0.133820	−	0.0392932i	0.00854948	−	0.00251035i
$246$	1.00020	−	6.95652i	0.0637702	−	0.443532i
$247$	9.80535	−	11.3160i	0.623899	−	0.720018i
$248$	1.67226	−	1.07470i	0.106189	−	0.0682435i
$249$	3.00526	+	3.46826i	0.190451	+	0.219792i
$250$	1.33560	+	0.392168i	0.0844709	+	0.0248029i
$251$	7.18991	−	15.7437i	0.453823	−	0.993734i	−0.535029	−	0.844834i	$-0.679699\pi$
$251$	7.18991	−	15.7437i	0.453823	−	0.993734i	0.988852	−	0.148900i	$-0.0475733\pi$
$252$	1.00000			0.0629941
$253$	15.6335	+	1.75424i	0.982871	+	0.110288i
$254$	−12.3607			−0.775580
$255$	0.0786280	−	0.172171i	0.00492388	−	0.0107818i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	5.66666	+	6.53968i	0.353477	+	0.407934i	0.904444	−	0.426593i	$-0.140286\pi$
$257$	5.66666	+	6.53968i	0.353477	+	0.407934i	−0.550967	+	0.834527i	$0.685741\pi$
$258$	−9.45368	+	6.07551i	−0.588560	+	0.378245i
$259$	6.27005	−	7.23603i	0.389602	−	0.449625i
$260$	−0.0529506	+	0.368280i	−0.00328386	+	0.0228397i
$261$	4.39727	−	1.29116i	0.272184	−	0.0799206i
$262$	12.8502	+	8.25829i	0.793885	+	0.510199i
$263$	−1.30373	−	9.06766i	−0.0803916	−	0.559136i	−0.989716	−	0.143048i	$-0.954310\pi$
$263$	−1.30373	−	9.06766i	−0.0803916	−	0.559136i	0.909324	−	0.416088i	$-0.136599\pi$
$264$	1.36267	+	2.98384i	0.0838668	+	0.183643i
$265$	0.384239	+	0.841366i	0.0236036	+	0.0516847i
$266$	0.798774	+	5.55560i	0.0489760	+	0.340635i
$267$	8.27021	+	5.31494i	0.506128	+	0.325269i
$268$	1.73565	−	0.509632i	0.106022	−	0.0311307i
$269$	−0.296048	+	2.05906i	−0.0180504	+	0.125543i	−0.996854	−	0.0792568i	$-0.974745\pi$
$269$	−0.296048	+	2.05906i	−0.0180504	+	0.125543i	0.978804	+	0.204800i	$0.0656544\pi$
$270$	−0.0913334	+	0.105404i	−0.00555837	+	0.00641471i
$271$	−20.4939	+	13.1706i	−1.24491	+	0.800058i	−0.986146	−	0.165881i	$-0.946953\pi$
$271$	−20.4939	+	13.1706i	−1.24491	+	0.800058i	−0.258769	+	0.965939i	$0.583317\pi$
$272$	0.888717	+	1.02563i	0.0538864	+	0.0621882i
$273$	2.55966	+	0.751584i	0.154918	+	0.0454879i
$274$	5.71463	−	12.5133i	0.345233	−	0.755955i
$275$	16.3376			0.985191
$276$	−4.76592	−	0.534784i	−0.286875	−	0.0321902i
$277$	−3.40773			−0.204750			−0.102375	−	0.994746i	$-0.532644\pi$
$277$	−3.40773			−0.204750			−0.102375	+	0.994746i	$0.532644\pi$
$278$	−4.56700	+	10.0003i	−0.273910	+	0.599780i
$279$	1.90730	+	0.560035i	0.114187	+	0.0335284i
$280$	−0.0913334	−	0.105404i	−0.00545821	−	0.00629912i
$281$	−16.9553	+	10.8965i	−1.01147	+	0.650030i	−0.937772	−	0.347251i	$-0.887115\pi$
$281$	−16.9553	+	10.8965i	−1.01147	+	0.650030i	−0.0736944	+	0.997281i	$0.523479\pi$
$282$	−1.59973	+	1.84619i	−0.0952624	+	0.109939i
$283$	−0.830406	+	5.77560i	−0.0493625	+	0.343324i	0.950141	+	0.311820i	$0.100939\pi$
$283$	−0.830406	+	5.77560i	−0.0493625	+	0.343324i	−0.999504	+	0.0315037i	$0.989970\pi$
$284$	−7.72030	+	2.26688i	−0.458115	+	0.134515i
$285$	−0.658539	−	0.423217i	−0.0390085	−	0.0250692i
$286$	1.24538	+	8.66178i	0.0736406	+	0.512182i
$287$	2.91956	+	6.39295i	0.172336	+	0.377364i
$288$	−0.415415	−	0.909632i	−0.0244786	−	0.0536006i
$289$	2.15724	+	15.0040i	0.126897	+	0.882586i
$290$	−0.537711	−	0.345566i	−0.0315755	−	0.0202923i
$291$	−4.90136	+	1.43917i	−0.287323	+	0.0843656i
$292$	−0.990378	+	6.88823i	−0.0579575	+	0.403103i
$293$	14.5537	−	16.7958i	0.850235	−	0.981224i	−0.149737	−	0.988726i	$-0.547843\pi$
$293$	14.5537	−	16.7958i	0.850235	−	0.981224i	0.999972	+	0.00750220i	$0.00238805\pi$
$294$	−0.841254	+	0.540641i	−0.0490629	+	0.0315308i
$295$	1.35898	+	1.56835i	0.0791229	+	0.0913127i
$296$	−9.18680	−	2.69749i	−0.533972	−	0.156788i
$297$	−1.36267	+	2.98384i	−0.0790704	+	0.173140i
$298$	−7.56329			−0.438130
$299$	−11.7972	−	4.95085i	−0.682250	−	0.286315i
$300$	−4.98055			−0.287552
$301$	4.66827	−	10.2221i	0.269075	−	0.589191i
$302$	0.605592	+	0.177818i	0.0348479	+	0.0102323i
$303$	−6.47591	−	7.47359i	−0.372031	−	0.429347i
$304$	4.72173	−	3.03447i	0.270810	−	0.174039i
$305$	0.599351	−	0.691688i	0.0343187	−	0.0396059i
$306$	−0.193137	+	1.34330i	−0.0110409	+	0.0767911i
$307$	12.8793	−	3.78170i	0.735059	−	0.215833i	0.107285	−	0.994228i	$-0.465784\pi$
$307$	12.8793	−	3.78170i	0.735059	−	0.215833i	0.627774	+	0.778395i	$0.283966\pi$
$308$	−2.75954	−	1.77345i	−0.157239	−	0.101052i
$309$	0.946408	+	6.58241i	0.0538393	+	0.374461i
$310$	−0.115170	−	0.252188i	−0.00654124	−	0.0143233i
$311$	4.31047	+	9.43862i	0.244424	+	0.535215i	0.991589	−	0.129424i	$-0.0413128\pi$
$311$	4.31047	+	9.43862i	0.244424	+	0.535215i	−0.747165	+	0.664639i	$0.768585\pi$
$312$	−0.379656	−	2.64057i	−0.0214938	−	0.149493i
$313$	−10.3736	−	6.66672i	−0.586351	−	0.376825i	0.213572	−	0.976927i	$-0.431490\pi$
$313$	−10.3736	−	6.66672i	−0.586351	−	0.376825i	−0.799923	+	0.600102i	$0.795127\pi$
$314$	−18.9969	+	5.57798i	−1.07206	+	0.314784i
$315$	0.0198486	−	0.138050i	0.00111834	−	0.00777826i
$316$	−1.46941	+	1.69579i	−0.0826608	+	0.0953957i
$317$	9.48187	−	6.09363i	0.532555	−	0.342252i	−0.246566	−	0.969126i	$-0.579302\pi$
$317$	9.48187	−	6.09363i	0.532555	−	0.342252i	0.779121	+	0.626874i	$0.215666\pi$
$318$	−4.34298	−	5.01206i	−0.243542	−	0.281063i
$319$	−14.4243	−	4.23534i	−0.807603	−	0.237134i
$320$	−0.0579379	+	0.126866i	−0.00323883	+	0.00709204i
$321$	−1.48638			−0.0829616
$322$	4.29847	−	2.12676i	0.239545	−	0.118520i
$323$	−7.61708			−0.423826
$324$	0.415415	−	0.909632i	0.0230786	−	0.0505351i
$325$	−12.7485	−	3.74330i	−0.707160	−	0.207641i
$326$	−15.0427	−	17.3602i	−0.833139	−	0.961494i
$327$	10.9445	−	7.03360i	0.605232	−	0.388959i
$328$	4.60240	−	5.31145i	0.254125	−	0.293276i
$329$	0.347654	−	2.41799i	0.0191668	−	0.133308i
$330$	0.438967	−	0.128892i	0.0241644	−	0.00709530i
$331$	−17.1416	−	11.0162i	−0.942186	−	0.605506i	−0.0231722	−	0.999731i	$-0.507377\pi$
$331$	−17.1416	−	11.0162i	−0.942186	−	0.605506i	−0.919014	+	0.394225i	$0.871013\pi$
$332$	0.653105	+	4.54245i	0.0358438	+	0.249299i
$333$	−3.97745	−	8.70940i	−0.217963	−	0.477272i
$334$	6.96115	+	15.2428i	0.380897	+	0.834049i
$335$	−0.0359046	−	0.249722i	−0.00196168	−	0.0136438i
$336$	0.841254	+	0.540641i	0.0458941	+	0.0294944i
$337$	24.4360	−	7.17507i	1.33112	−	0.390851i	0.462624	−	0.886555i	$-0.346908\pi$
$337$	24.4360	−	7.17507i	1.33112	−	0.390851i	0.868492	+	0.495704i	$0.165090\pi$
$338$	−0.837276	+	5.82338i	−0.0455418	+	0.316750i
$339$	8.49977	−	9.80926i	0.461644	−	0.532766i
$340$	0.159229	−	0.102330i	0.00863540	−	0.00554964i
$341$	−4.27009	−	4.92795i	−0.231238	−	0.266863i
$342$	5.38537	+	1.58129i	0.291207	+	0.0855062i
$343$	0.415415	−	0.909632i	0.0224303	−	0.0491155i
$344$	−11.2376			−0.605891
$345$	−0.168424	+	0.647322i	−0.00906765	+	0.0348507i
$346$	12.5817			0.676399
$347$	−2.25112	+	4.92926i	−0.120846	+	0.264616i	−0.960381	−	0.278689i	$-0.910100\pi$
$347$	−2.25112	+	4.92926i	−0.120846	+	0.264616i	0.839535	+	0.543305i	$0.182827\pi$
$348$	4.39727	+	1.29116i	0.235719	+	0.0692132i
$349$	−8.66948	−	10.0051i	−0.464066	−	0.535561i	0.474685	−	0.880156i	$-0.342562\pi$
$349$	−8.66948	−	10.0051i	−0.464066	−	0.535561i	−0.938752	+	0.344594i	$0.888016\pi$
$350$	4.18990	−	2.69269i	0.223960	−	0.143930i
$351$	1.74699	−	2.01613i	0.0932472	−	0.107613i
$352$	−0.466831	+	3.24688i	−0.0248822	+	0.173059i
$353$	29.4164	−	8.63743i	1.56568	−	0.459724i	0.619938	−	0.784651i	$-0.287158\pi$
$353$	29.4164	−	8.63743i	1.56568	−	0.459724i	0.945739	+	0.324927i	$0.105340\pi$
$354$	−12.5173	−	8.04438i	−0.665287	−	0.427554i
$355$	0.159707	+	1.11078i	0.00847635	+	0.0589543i
$356$	4.08387	+	8.94242i	0.216445	+	0.473947i
$357$	−0.563763	−	1.23447i	−0.0298375	−	0.0653350i
$358$	−2.93194	−	20.3921i	−0.154958	−	1.07776i
$359$	−4.18943	−	2.69238i	−0.221110	−	0.142098i	0.425397	−	0.905007i	$-0.360134\pi$
$359$	−4.18943	−	2.69238i	−0.221110	−	0.142098i	−0.646507	+	0.762908i	$0.723771\pi$
$360$	−0.133820	+	0.0392932i	−0.00705296	+	0.00207094i
$361$	−1.77932	+	12.3754i	−0.0936483	+	0.651338i
$362$	−1.33589	+	1.54169i	−0.0702126	+	0.0810296i
$363$	−0.201747	+	0.129655i	−0.0105889	+	0.00680510i
$364$	1.74699	+	2.01613i	0.0915669	+	0.105674i
$365$	0.931265	+	0.273444i	0.0487446	+	0.0143127i
$366$	−2.72605	+	5.96922i	−0.142493	+	0.312016i
$367$	29.7743			1.55420			0.777102	−	0.629374i	$-0.216689\pi$
$367$	29.7743			1.55420			0.777102	+	0.629374i	$0.216689\pi$
$368$	−3.72022	−	3.02654i	−0.193930	−	0.157769i
$369$	7.02806			0.365866
$370$	−0.554734	+	1.21470i	−0.0288393	+	0.0631492i
$371$	6.36327	+	1.86843i	0.330365	+	0.0970038i
$372$	1.30175	+	1.50230i	0.0674925	+	0.0778905i
$373$	6.61548	−	4.25151i	0.342537	−	0.220135i	−0.358050	−	0.933703i	$-0.616558\pi$
$373$	6.61548	−	4.25151i	0.342537	−	0.220135i	0.700586	+	0.713568i	$0.252922\pi$
$374$	2.91523	−	3.36436i	0.150743	−	0.173967i
$375$	−0.198100	+	1.37782i	−0.0102299	+	0.0711502i
$376$	−2.34390	+	0.688231i	−0.120877	+	0.0354928i
$377$	10.2851	+	6.60984i	0.529710	+	0.340424i
$378$	0.142315	+	0.989821i	0.00731989	+	0.0509109i
$379$	9.02148	+	19.7543i	0.463402	+	1.01471i	0.986699	+	0.162559i	$0.0519746\pi$
$379$	9.02148	+	19.7543i	0.463402	+	1.01471i	−0.523297	+	0.852150i	$0.675298\pi$
$380$	−0.325190	−	0.712066i	−0.0166819	−	0.0365282i
$381$	−1.75911	−	12.2349i	−0.0901221	−	0.626813i
$382$	−1.59772	−	1.02679i	−0.0817465	−	0.0525353i
$383$	−34.2370	+	10.0529i	−1.74943	+	0.513679i	−0.990502	−	0.137496i	$-0.956095\pi$
$383$	−34.2370	+	10.0529i	−1.74943	+	0.513679i	−0.758928	+	0.651175i	$0.774276\pi$
$384$	0.142315	−	0.989821i	0.00726247	−	0.0505116i
$385$	−0.299598	+	0.345755i	−0.0152689	+	0.0176213i
$386$	14.3575	−	9.22700i	0.730777	−	0.469642i
$387$	−7.35907	−	8.49282i	−0.374083	−	0.431714i
$388$	−4.90136	−	1.43917i	−0.248829	−	0.0730627i
$389$	−10.4478	+	22.8774i	−0.529723	+	1.15993i	0.435902	+	0.899994i	$0.356429\pi$
$389$	−10.4478	+	22.8774i	−0.529723	+	1.15993i	−0.965625	+	0.259938i	$0.916298\pi$
$390$	−0.372067			−0.0188403
$391$	2.02668	+	6.18488i	0.102493	+	0.312783i
$392$	−1.00000			−0.0505076
$393$	−6.34547	+	13.8946i	−0.320086	+	0.700891i
$394$	−23.9021	−	7.01829i	−1.20417	−	0.353576i
$395$	0.204939	+	0.236512i	0.0103116	+	0.0119002i
$396$	−2.75954	+	1.77345i	−0.138672	+	0.0891192i
$397$	20.3987	−	23.5413i	1.02378	−	1.18151i	0.0405430	−	0.999178i	$-0.487091\pi$
$397$	20.3987	−	23.5413i	1.02378	−	1.18151i	0.983238	−	0.182328i	$-0.0583633\pi$
$398$	3.11215	−	21.6455i	0.155998	−	1.08499i
$399$	−5.38537	+	1.58129i	−0.269606	+	0.0791634i
$400$	−4.18990	−	2.69269i	−0.209495	−	0.134634i
$401$	2.17573	+	15.1326i	0.108651	+	0.755684i	0.969193	+	0.246304i	$0.0792162\pi$
$401$	2.17573	+	15.1326i	0.108651	+	0.755684i	−0.860542	+	0.509380i	$0.829875\pi$
$402$	0.751453	+	1.64545i	0.0374791	+	0.0820677i
$403$	2.20293	+	4.82374i	0.109736	+	0.240288i
$404$	−1.40735	−	9.78833i	−0.0700182	−	0.486987i
$405$	−0.117330	−	0.0754032i	−0.00583015	−	0.00374681i
$406$	−4.39727	+	1.29116i	−0.218233	+	0.0640790i
$407$	−4.46974	+	31.0877i	−0.221557	+	1.54096i
$408$	−0.888717	+	1.02563i	−0.0439980	+	0.0507765i
$409$	−17.4456	+	11.2116i	−0.862631	+	0.554379i	−0.895491	−	0.445081i	$-0.853175\pi$
$409$	−17.4456	+	11.2116i	−0.862631	+	0.554379i	0.0328592	+	0.999460i	$0.489539\pi$
$410$	−0.641896	−	0.740788i	−0.0317010	−	0.0365849i
$411$	13.1992	+	3.87563i	0.651068	+	0.191171i
$412$	−2.76255	+	6.04915i	−0.136101	+	0.298020i
$413$	14.8793			0.732164
$414$	−0.148921	−	4.79352i	−0.00731905	−	0.235589i
$415$	0.640050			0.0314188
$416$	1.10821	−	2.42664i	0.0543345	−	0.118976i
$417$	−10.5485	−	3.09732i	−0.516562	−	0.151676i
$418$	−12.0568	−	13.9143i	−0.589718	−	0.680571i
$419$	−7.00646	+	4.50278i	−0.342288	+	0.219975i	−0.700479	−	0.713673i	$-0.747030\pi$
$419$	−7.00646	+	4.50278i	−0.342288	+	0.219975i	0.358191	+	0.933648i	$0.383394\pi$
$420$	0.0913334	−	0.105404i	0.00445661	−	0.00514321i
$421$	3.78529	−	26.3272i	0.184484	−	1.28311i	−0.661517	−	0.749930i	$-0.730087\pi$
$421$	3.78529	−	26.3272i	0.184484	−	1.28311i	0.846001	−	0.533181i	$-0.179004\pi$
$422$	21.4458	−	6.29707i	1.04397	−	0.306537i
$423$	−2.05506	−	1.32071i	−0.0999204	−	0.0642149i
$424$	−0.943820	−	6.56441i	−0.0458359	−	0.318796i
$425$	2.80785	+	6.14833i	0.136201	+	0.298238i
$426$	−3.34252	−	7.31910i	−0.161946	−	0.354612i
$427$	−0.933903	−	6.49544i	−0.0451947	−	0.314336i
$428$	−1.25042	−	0.803597i	−0.0604414	−	0.0388433i
$429$	−8.39638	+	2.46540i	−0.405381	+	0.119031i
$430$	−0.223051	+	1.55136i	−0.0107565	+	0.0748130i
$431$	22.1060	−	25.5117i	1.06481	−	1.22886i	0.0923652	−	0.995725i	$-0.470557\pi$
$431$	22.1060	−	25.5117i	1.06481	−	1.22886i	0.972445	−	0.233132i	$-0.0748973\pi$
$432$	0.841254	−	0.540641i	0.0404748	−	0.0260116i
$433$	23.4293	+	27.0388i	1.12594	+	1.29940i	0.949034	+	0.315175i	$0.102063\pi$
$433$	23.4293	+	27.0388i	1.12594	+	1.29940i	0.176905	+	0.984228i	$0.443391\pi$
$434$	−1.90730	−	0.560035i	−0.0915535	−	0.0268825i
$435$	0.265524	−	0.581418i	0.0127309	−	0.0278768i
$436$	13.0098			0.623054
$437$	26.5119	−	4.65628i	1.26824	−	0.222740i
$438$	−6.95906			−0.332517
$439$	12.2959	−	26.9243i	0.586851	−	1.28502i	−0.350475	−	0.936572i	$-0.613980\pi$
$439$	12.2959	−	26.9243i	0.586851	−	1.28502i	0.937326	−	0.348453i	$-0.113293\pi$
$440$	0.438967	+	0.128892i	0.0209270	+	0.00614471i
$441$	−0.654861	−	0.755750i	−0.0311838	−	0.0359881i
$442$	−3.04566	+	1.95733i	−0.144867	+	0.0931006i
$443$	15.0807	−	17.4041i	0.716507	−	0.826893i	−0.274376	−	0.961623i	$-0.588471\pi$
$443$	15.0807	−	17.4041i	0.716507	−	0.826893i	0.990882	+	0.134730i	$0.0430166\pi$
$444$	1.36261	−	9.47718i	0.0646667	−	0.449767i
$445$	1.31556	−	0.386284i	0.0623637	−	0.0183116i
$446$	−9.63232	−	6.19031i	−0.456103	−	0.293120i
$447$	−1.07637	−	7.48631i	−0.0509105	−	0.354090i
$448$	0.415415	+	0.909632i	0.0196265	+	0.0429761i
$449$	−6.45235	−	14.1287i	−0.304505	−	0.666773i	0.694083	−	0.719895i	$-0.255810\pi$
$449$	−6.45235	−	14.1287i	−0.304505	−	0.666773i	−0.998588	+	0.0531219i	$0.983083\pi$
$450$	−0.708806	−	4.92985i	−0.0334134	−	0.232396i
$451$	−19.3942	−	12.4639i	−0.913238	−	0.586902i
$452$	12.4538	−	3.65675i	0.585775	−	0.171999i
$453$	−0.0898232	+	0.624734i	−0.00422026	+	0.0293526i
$454$	0.479613	−	0.553503i	0.0225093	−	0.0259772i
$455$	0.313003	−	0.201155i	0.0146738	−	0.00943027i
$456$	3.67555	+	4.24181i	0.172124	+	0.198641i
$457$	−19.5427	−	5.73824i	−0.914167	−	0.268424i	−0.209373	−	0.977836i	$-0.567142\pi$
$457$	−19.5427	−	5.73824i	−0.914167	−	0.268424i	−0.704794	+	0.709412i	$0.748960\pi$
$458$	−7.03623	+	15.4072i	−0.328781	+	0.719931i
$459$	−1.35711			−0.0633444
$460$	−0.491656	+	0.453505i	−0.0229236	+	0.0211448i
$461$	−1.65506			−0.0770837			−0.0385418	−	0.999257i	$-0.512271\pi$
$461$	−1.65506			−0.0770837			−0.0385418	+	0.999257i	$0.512271\pi$
$462$	1.36267	−	2.98384i	0.0633973	−	0.138821i
$463$	12.5119	+	3.67384i	0.581479	+	0.170738i	0.559227	−	0.829015i	$-0.311098\pi$
$463$	12.5119	+	3.67384i	0.581479	+	0.170738i	0.0222523	+	0.999752i	$0.492916\pi$
$464$	3.00117	+	3.46354i	0.139326	+	0.160791i
$465$	0.233231	−	0.149888i	0.0108158	−	0.00695090i
$466$	−12.5924	+	14.5324i	−0.583330	+	0.673199i
$467$	1.45443	−	10.1158i	0.0673031	−	0.468103i	−0.928100	−	0.372331i	$-0.878559\pi$
$467$	1.45443	−	10.1158i	0.0673031	−	0.468103i	0.995403	−	0.0957727i	$-0.0305322\pi$
$468$	2.55966	−	0.751584i	0.118320	−	0.0347420i
$469$	−1.52176	−	0.977977i	−0.0702684	−	0.0451588i
$470$	0.0484873	+	0.337237i	0.00223655	+	0.0155556i
$471$	−8.22474	−	18.0097i	−0.378976	−	0.829842i
$472$	−6.18110	−	13.5347i	−0.284508	−	0.622986i
$473$	5.24607	+	36.4872i	0.241214	+	1.67768i
$474$	−1.88765	−	1.21312i	−0.0867026	−	0.0557204i
$475$	26.8221	−	7.87568i	1.23068	−	0.361361i
$476$	0.193137	−	1.34330i	0.00885240	−	0.0615698i
$477$	4.34298	−	5.01206i	0.198851	−	0.229487i
$478$	6.72576	−	4.32238i	0.307629	−	0.197701i
$479$	8.94906	+	10.3278i	0.408893	+	0.471888i	0.922421	−	0.386185i	$-0.126207\pi$
$479$	8.94906	+	10.3278i	0.408893	+	0.471888i	−0.513528	+	0.858073i	$0.671662\pi$
$480$	−0.133820	−	0.0392932i	−0.00610804	−	0.00179348i
$481$	10.6107	−	23.2342i	0.483807	−	1.05939i
$482$	−7.82769			−0.356542
$483$	2.71685	+	3.95205i	0.123621	+	0.179825i
$484$	−0.239817			−0.0109008
$485$	−0.295963	+	0.648069i	−0.0134390	+	0.0294273i
$486$	0.959493	+	0.281733i	0.0435235	+	0.0127796i
$487$	−12.9173	−	14.9074i	−0.585339	−	0.675518i	0.383405	−	0.923580i	$-0.374751\pi$
$487$	−12.9173	−	14.9074i	−0.585339	−	0.675518i	−0.968744	+	0.248063i	$0.920206\pi$
$488$	−5.52050	+	3.54781i	−0.249901	+	0.160602i
$489$	15.0427	−	17.3602i	0.680255	−	0.785056i
$490$	−0.0198486	+	0.138050i	−0.000896670	+	0.00623648i
$491$	30.1984	−	8.86705i	1.36284	−	0.400164i	0.483074	−	0.875580i	$-0.339520\pi$
$491$	30.1984	−	8.86705i	1.36284	−	0.400164i	0.879761	+	0.475415i	$0.157702\pi$
$492$	5.91238	+	3.79965i	0.266551	+	0.171302i
$493$	−0.885129	−	6.15621i	−0.0398642	−	0.277262i
$494$	6.22008	+	13.6201i	0.279855	+	0.612797i
$495$	0.190052	+	0.416156i	0.00854221	+	0.0187048i
$496$	0.282897	+	1.96759i	0.0127024	+	0.0883475i
$497$	6.76892	+	4.35012i	0.303627	+	0.195129i
$498$	−4.40327	+	1.29292i	−0.197315	+	0.0579369i
$499$	3.18549	−	22.1556i	0.142602	−	0.991819i	−0.785332	−	0.619075i	$-0.787508\pi$
$499$	3.18549	−	22.1556i	0.142602	−	0.991819i	0.927934	−	0.372744i	$-0.121583\pi$
$500$	−0.911557	+	1.05199i	−0.0407661	+	0.0470466i
$501$	−14.0970	+	9.05957i	−0.629806	+	0.404752i
$502$	11.3342	+	13.0803i	0.505869	+	0.583804i
$503$	−35.9902	−	10.5677i	−1.60472	−	0.471189i	−0.647868	−	0.761753i	$-0.724339\pi$
$503$	−35.9902	−	10.5677i	−1.60472	−	0.471189i	−0.956856	+	0.290563i	$0.906157\pi$
$504$	−0.415415	+	0.909632i	−0.0185041	+	0.0405182i
$505$	−1.37922			−0.0613743
$506$	−8.09011	+	13.4920i	−0.359649	+	0.599793i
$507$	−5.88327			−0.261285
$508$	5.13482	−	11.2437i	0.227821	−	0.498858i
$509$	−11.4885	−	3.37334i	−0.509220	−	0.149521i	0.0170223	−	0.999855i	$-0.494581\pi$
$509$	−11.4885	−	3.37334i	−0.509220	−	0.149521i	−0.526242	+	0.850335i	$0.676400\pi$
$510$	0.123949	+	0.143045i	0.00548857	+	0.00633415i
$511$	5.85433	−	3.76235i	0.258980	−	0.166437i
$512$	0.654861	−	0.755750i	0.0289410	−	0.0333997i
$513$	−0.798774	+	5.55560i	−0.0352667	+	0.245286i
$514$	−8.30272	+	2.43790i	−0.366217	+	0.107531i
$515$	0.780254	+	0.501439i	0.0343821	+	0.0220960i
$516$	−1.59928	−	11.1232i	−0.0704043	−	0.489673i
$517$	3.32881	+	7.28908i	0.146401	+	0.320573i
$518$	3.97745	+	8.70940i	0.174759	+	0.382669i
$519$	1.79057	+	12.4537i	0.0785973	+	0.546656i
$520$	−0.313003	−	0.201155i	−0.0137261	−	0.00882121i
$521$	−5.75568	+	1.69002i	−0.252161	+	0.0740411i	−0.405370	−	0.914153i	$-0.632857\pi$
$521$	−5.75568	+	1.69002i	−0.252161	+	0.0740411i	0.153209	+	0.988194i	$0.451039\pi$
$522$	−0.652217	+	4.53627i	−0.0285467	+	0.198547i
$523$	15.0713	−	17.3932i	0.659020	−	0.760550i	−0.323597	−	0.946195i	$-0.604892\pi$
$523$	15.0713	−	17.3932i	0.659020	−	0.760550i	0.982617	+	0.185646i	$0.0594376\pi$
$524$	−12.8502	+	8.25829i	−0.561361	+	0.360765i
$525$	3.26157	+	3.76405i	0.142346	+	0.164276i
$526$	8.78982	+	2.58093i	0.383255	+	0.112534i
$527$	1.12066	−	2.45391i	0.0488168	−	0.106894i
$528$	−3.28027			−0.142756
$529$	−10.8348	−	20.2881i	−0.471079	−	0.882091i
$530$	−0.924953			−0.0401774
$531$	6.18110	−	13.5347i	0.268237	−	0.587357i
$532$	−5.38537	−	1.58129i	−0.233485	−	0.0685575i
$533$	12.2779	+	14.1695i	0.531815	+	0.613748i
$534$	−8.27021	+	5.31494i	−0.357887	+	0.230000i
$535$	−0.135756	+	0.156671i	−0.00586925	+	0.00677347i
$536$	−0.257436	+	1.79051i	−0.0111196	+	0.0773382i
$537$	19.7673	−	5.80419i	0.853020	−	0.250469i
$538$	−1.75001	−	1.12466i	−0.0754481	−	0.0484876i
$539$	0.466831	+	3.24688i	0.0201079	+	0.139853i
$540$	−0.0579379	−	0.126866i	−0.00249325	−	0.00545946i
$541$	−11.7328	−	25.6912i	−0.504431	−	1.10455i	−0.975004	−	0.222189i	$-0.928680\pi$
$541$	−11.7328	−	25.6912i	−0.504431	−	1.10455i	0.470573	−	0.882361i	$-0.344047\pi$
$542$	−3.46695	−	24.1132i	−0.148918	−	1.03575i
$543$	−1.71612	−	1.10288i	−0.0736457	−	0.0473292i
$544$	−1.30214	+	0.382342i	−0.0558286	+	0.0163928i
$545$	0.258226	−	1.79600i	0.0110612	−	0.0769322i
$546$	−1.74699	+	2.01613i	−0.0747641	+	0.0862823i
$547$	−17.0141	+	10.9343i	−0.727469	+	0.467516i	−0.851228	−	0.524796i	$-0.824141\pi$
$547$	−17.0141	+	10.9343i	−0.727469	+	0.467516i	0.123759	+	0.992312i	$0.460505\pi$
$548$	9.00854	+	10.3964i	0.384826	+	0.444113i
$549$	−6.29642	−	1.84879i	−0.268724	−	0.0789046i
$550$	−6.78686	+	14.8612i	−0.289393	+	0.633682i
$551$	−25.7226			−1.09582
$552$	2.46629	−	4.11308i	0.104972	−	0.175064i
$553$	2.24385			0.0954183
$554$	1.41562	−	3.09978i	0.0601440	−	0.131697i
$555$	−1.28128	−	0.376218i	−0.0543874	−	0.0159696i
$556$	−7.19942	−	8.30857i	−0.305323	−	0.352362i
$557$	−32.7023	+	21.0165i	−1.38564	+	0.890497i	−0.999490	−	0.0319382i	$-0.989832\pi$
$557$	−32.7023	+	21.0165i	−1.38564	+	0.890497i	−0.386151	+	0.922436i	$0.626196\pi$
$558$	−1.30175	+	1.50230i	−0.0551074	+	0.0635973i
$559$	4.26643	−	29.6737i	0.180451	−	1.25506i
$560$	0.133820	−	0.0392932i	0.00565495	−	0.00166044i
$561$	3.74500	+	2.40676i	0.158114	+	0.101614i
$562$	−2.86832	−	19.9496i	−0.120993	−	0.841524i
$563$	15.1516	+	33.1775i	0.638565	+	1.39826i	0.901215	+	0.433372i	$0.142676\pi$
$563$	15.1516	+	33.1775i	0.638565	+	1.39826i	−0.262650	+	0.964891i	$0.584596\pi$
$564$	−1.01480	−	2.22210i	−0.0427307	−	0.0935672i
$565$	−0.257626	−	1.79183i	−0.0108384	−	0.0753827i
$566$	−4.90871	−	3.15464i	−0.206329	−	0.132599i
$567$	−0.959493	+	0.281733i	−0.0402949	+	0.0118317i
$568$	1.14510	−	7.96433i	0.0480472	−	0.334176i
$569$	16.6167	−	19.1767i	0.696608	−	0.803928i	−0.291682	−	0.956515i	$-0.594215\pi$
$569$	16.6167	−	19.1767i	0.696608	−	0.803928i	0.988290	+	0.152587i	$0.0487604\pi$
$570$	0.658539	−	0.423217i	0.0275832	−	0.0177266i
$571$	6.73628	+	7.77408i	0.281905	+	0.325335i	0.878988	−	0.476844i	$-0.158219\pi$
$571$	6.73628	+	7.77408i	0.281905	+	0.325335i	−0.597083	+	0.802179i	$0.703674\pi$
$572$	−8.39638	−	2.46540i	−0.351070	−	0.103084i
$573$	0.788962	−	1.72759i	0.0329594	−	0.0721710i
$574$	−7.02806			−0.293345
$575$	−13.5314	−	19.6834i	−0.564299	−	0.820854i
$576$	1.00000			0.0416667
$577$	−8.25670	+	18.0796i	−0.343731	+	0.752666i	−0.999998	−	0.00186284i	$-0.999407\pi$
$577$	−8.25670	+	18.0796i	−0.343731	+	0.752666i	0.656267	+	0.754528i	$0.272134\pi$
$578$	−14.5442	−	4.27057i	−0.604961	−	0.177632i
$579$	11.1764	+	12.8982i	0.464474	+	0.536031i
$580$	0.537711	−	0.345566i	0.0223273	−	0.0143489i
$581$	3.00526	−	3.46826i	0.124679	−	0.143887i
$582$	0.726984	−	5.05629i	0.0301345	−	0.209590i
$583$	−20.8733	+	6.12894i	−0.864482	+	0.253835i
$584$	−5.85433	−	3.76235i	−0.242254	−	0.155687i
$585$	−0.0529506	−	0.368280i	−0.00218924	−	0.0152265i
$586$	9.23222	+	20.2157i	0.381379	+	0.835105i
$587$	−9.80140	−	21.4621i	−0.404547	−	0.885835i	−0.996789	−	0.0800745i	$-0.974484\pi$
$587$	−9.80140	−	21.4621i	−0.404547	−	0.885835i	0.592242	−	0.805760i	$-0.298243\pi$
$588$	−0.142315	−	0.989821i	−0.00586897	−	0.0408195i
$589$	−9.38596	−	6.03199i	−0.386742	−	0.248544i
$590$	−1.99116	+	0.584657i	−0.0819747	+	0.0240700i
$591$	3.54523	−	24.6576i	0.145831	−	1.01428i
$592$	6.27005	−	7.23603i	0.257698	−	0.297399i
$593$	−18.5347	+	11.9116i	−0.761130	+	0.489149i	−0.862723	−	0.505677i	$-0.831243\pi$
$593$	−18.5347	+	11.9116i	−0.761130	+	0.489149i	0.101592	+	0.994826i	$0.467606\pi$
$594$	−2.14812	−	2.47906i	−0.0881385	−	0.101717i
$595$	−0.181609	−	0.0533252i	−0.00744524	−	0.00218612i
$596$	3.14190	−	6.87981i	0.128697	−	0.281808i
$597$	21.8681			0.895000
$598$	9.40419	−	8.67445i	0.384566	−	0.354725i
$599$	4.97057			0.203092			0.101546	−	0.994831i	$-0.467621\pi$
$599$	4.97057			0.203092			0.101546	+	0.994831i	$0.467621\pi$
$600$	2.06899	−	4.53047i	0.0844663	−	0.184955i
$601$	3.96471	+	1.16414i	0.161724	+	0.0474864i	0.361592	−	0.932336i	$-0.382233\pi$
$601$	3.96471	+	1.16414i	0.161724	+	0.0474864i	−0.199868	+	0.979823i	$0.564051\pi$
$602$	7.35907	+	8.49282i	0.299933	+	0.346141i
$603$	−1.52176	+	0.977977i	−0.0619709	+	0.0398263i
$604$	−0.413321	+	0.476998i	−0.0168178	+	0.0194088i
$605$	−0.00476003	+	0.0331068i	−0.000193523	+	0.00134598i
$606$	9.48841	−	2.78605i	0.385440	−	0.113175i
$607$	33.4882	+	21.5216i	1.35924	+	0.873533i	0.998256	−	0.0590367i	$-0.0188029\pi$
$607$	33.4882	+	21.5216i	1.35924	+	0.873533i	0.360989	+	0.932570i	$0.382439\pi$
$608$	0.798774	+	5.55560i	0.0323946	+	0.225309i
$609$	−1.90381	−	4.16877i	−0.0771463	−	0.168927i
$610$	0.380202	+	0.832526i	0.0153939	+	0.0337080i
$611$	−0.927444	−	6.45052i	−0.0375204	−	0.260960i
$612$	−1.14167	−	0.733708i	−0.0461494	−	0.0296584i
$613$	−39.7674	+	11.6768i	−1.60619	+	0.471621i	−0.957261	−	0.289226i	$-0.906602\pi$
$613$	−39.7674	+	11.6768i	−1.60619	+	0.471621i	−0.648931	+	0.760847i	$0.724784\pi$
$614$	−1.91029	+	13.2864i	−0.0770932	+	0.536195i
$615$	0.641896	−	0.740788i	0.0258838	−	0.0298715i
$616$	2.75954	−	1.77345i	0.111185	−	0.0714543i
$617$	−8.99879	−	10.3852i	−0.362278	−	0.418091i	0.545124	−	0.838356i	$-0.316483\pi$
$617$	−8.99879	−	10.3852i	−0.362278	−	0.418091i	−0.907401	+	0.420265i	$0.861937\pi$
$618$	−6.38073	−	1.87355i	−0.256671	−	0.0753653i
$619$	−7.01776	+	15.3667i	−0.282067	+	0.617642i	−0.996639	−	0.0819210i	$-0.973894\pi$
$619$	−7.01776	+	15.3667i	−0.282067	+	0.617642i	0.714571	+	0.699563i	$0.246622\pi$
$620$	0.277242			0.0111343
$621$	4.72353	−	0.829594i	0.189549	−	0.0332904i
$622$	−10.3763			−0.416052
$623$	4.08387	−	8.94242i	0.163617	−	0.358271i
$624$	2.55966	+	0.751584i	0.102468	+	0.0300874i
$625$	−16.1807	−	18.6735i	−0.647228	−	0.746941i
$626$	10.3736	−	6.66672i	0.414613	−	0.266456i
$627$	12.0568	−	13.9143i	0.481503	−	0.555684i
$628$	2.81767	−	19.5973i	0.112437	−	0.782019i
$629$	−12.4675	+	3.66078i	−0.497111	+	0.145965i
$630$	0.117330	+	0.0754032i	0.00467452	+	0.00300413i
$631$	0.951082	+	6.61492i	0.0378620	+	0.263336i	0.999956	−	0.00938213i	$-0.00298647\pi$
$631$	0.951082	+	6.61492i	0.0378620	+	0.263336i	−0.962094	+	0.272718i	$0.912077\pi$
$632$	−0.932130	−	2.04108i	−0.0370781	−	0.0811898i
$633$	9.28504	+	20.3314i	0.369047	+	0.808100i
$634$	1.60405	+	11.1564i	0.0637049	+	0.443077i
$635$	−1.45028	−	0.932037i	−0.0575525	−	0.0369867i
$636$	6.36327	−	1.86843i	0.252320	−	0.0740879i
$637$	0.379656	−	2.64057i	0.0150425	−	0.104623i
$638$	9.84465	−	11.3613i	0.389754	−	0.449800i
$639$	6.76892	−	4.35012i	0.267774	−	0.172088i
$640$	−0.0913334	−	0.105404i	−0.00361027	−	0.00416647i
$641$	19.5980	+	5.75449i	0.774075	+	0.227289i	0.644832	−	0.764324i	$-0.276927\pi$
$641$	19.5980	+	5.75449i	0.774075	+	0.227289i	0.129242	+	0.991613i	$0.458745\pi$
$642$	0.617464	−	1.35206i	0.0243694	−	0.0533615i
$643$	−33.5671			−1.32376			−0.661879	−	0.749611i	$-0.730241\pi$
$643$	−33.5671			−1.32376			−0.661879	+	0.749611i	$0.730241\pi$
$644$	0.148921	+	4.79352i	0.00586830	+	0.188891i
$645$	−1.56731			−0.0617127
$646$	3.16425	−	6.92874i	0.124496	−	0.272608i
$647$	−0.273325	−	0.0802554i	−0.0107455	−	0.00315516i	0.276355	−	0.961056i	$-0.410873\pi$
$647$	−0.273325	−	0.0802554i	−0.0107455	−	0.00315516i	−0.287101	+	0.957900i	$0.592691\pi$
$648$	0.654861	+	0.755750i	0.0257254	+	0.0296886i
$649$	−41.0601	+	26.3877i	−1.61175	+	1.03581i
$650$	8.70094	−	10.0414i	0.341279	−	0.393857i
$651$	0.282897	−	1.96759i	0.0110876	−	0.0771160i
$652$	22.0404	−	6.47164i	0.863168	−	0.253449i
$653$	−16.0076	−	10.2875i	−0.626427	−	0.402580i	0.188558	−	0.982062i	$-0.439619\pi$
$653$	−16.0076	−	10.2875i	−0.626427	−	0.402580i	−0.814985	+	0.579482i	$0.803255\pi$
$654$	1.85148	+	12.8773i	0.0723986	+	0.503543i
$655$	0.885002	+	1.93788i	0.0345799	+	0.0757194i
$656$	2.91956	+	6.39295i	0.113990	+	0.249603i
$657$	−0.990378	−	6.88823i	−0.0386383	−	0.268735i
$658$	2.05506	+	1.32071i	0.0801145	+	0.0514865i
$659$	−35.4340	+	10.4043i	−1.38031	+	0.405296i	−0.885877	−	0.463919i	$-0.846443\pi$
$659$	−35.4340	+	10.4043i	−1.38031	+	0.405296i	−0.494434	+	0.869215i	$0.664625\pi$
$660$	−0.0651090	+	0.452843i	−0.00253436	+	0.0176269i
$661$	4.83226	−	5.57673i	0.187953	−	0.216910i	−0.653950	−	0.756537i	$-0.726890\pi$
$661$	4.83226	−	5.57673i	0.187953	−	0.216910i	0.841904	+	0.539628i	$0.181435\pi$
$662$	17.1416	−	11.0162i	0.666226	−	0.428158i
$663$	−2.37085	−	2.73611i	−0.0920761	−	0.106262i
$664$	−4.40327	−	1.29292i	−0.170880	−	0.0501749i
$665$	−0.325190	+	0.712066i	−0.0126103	+	0.0276127i
$666$	9.57464			0.371010
$667$	6.84403	+	20.8861i	0.265002	+	0.808714i
$668$	−16.7571			−0.648352
$669$	4.75648	−	10.4152i	0.183896	−	0.402677i
$670$	0.242071	+	0.0710784i	0.00935201	+	0.00274600i
$671$	14.0965	+	16.2682i	0.544188	+	0.628027i
$672$	−0.841254	+	0.540641i	−0.0324521	+	0.0208557i
$673$	−6.19002	+	7.14367i	−0.238608	+	0.275368i	−0.862406	−	0.506217i	$-0.831043\pi$
$673$	−6.19002	+	7.14367i	−0.238608	+	0.275368i	0.623798	+	0.781586i	$0.285589\pi$
$674$	−3.62443	+	25.2084i	−0.139608	+	0.970993i
$675$	4.77880	−	1.40318i	0.183936	−	0.0540085i
$676$	−4.94932	−	3.18073i	−0.190358	−	0.122336i
$677$	−1.41314	−	9.82858i	−0.0543112	−	0.377743i	−0.998790	−	0.0491715i	$-0.984342\pi$
$677$	−1.41314	−	9.82858i	−0.0543112	−	0.377743i	0.944479	−	0.328571i	$-0.106567\pi$
$678$	5.39188	+	11.8066i	0.207074	+	0.453429i
$679$	2.12206	+	4.64666i	0.0814371	+	0.178322i
$680$	0.0269368	+	0.187349i	0.00103298	+	0.00718452i
$681$	0.616125	+	0.395959i	0.0236099	+	0.0151732i
$682$	6.25648	−	1.83707i	0.239573	−	0.0703449i
$683$	0.185334	−	1.28902i	0.00709159	−	0.0493231i	−0.985968	−	0.166932i	$-0.946614\pi$
$683$	0.185334	−	1.28902i	0.00709159	−	0.0493231i	0.993060	+	0.117609i	$0.0375230\pi$
$684$	−3.67555	+	4.24181i	−0.140538	+	0.162190i
$685$	1.61404	−	1.03728i	0.0616692	−	0.0396324i
$686$	0.654861	+	0.755750i	0.0250027	+	0.0288547i
$687$	−16.2517	−	4.77194i	−0.620042	−	0.182061i
$688$	4.66827	−	10.2221i	0.177976	−	0.389714i
$689$	17.6921			0.674015
$690$	−0.518859	−	0.422112i	−0.0197526	−	0.0160695i
$691$	31.9617			1.21588			0.607940	−	0.793983i	$-0.291996\pi$
$691$	31.9617			1.21588			0.607940	+	0.793983i	$0.291996\pi$
$692$	−5.22665	+	11.4448i	−0.198687	+	0.435064i
$693$	3.14740	+	0.924159i	0.119560	+	0.0351059i
$694$	−3.54866	−	4.09537i	−0.134705	−	0.155458i
$695$	−1.28990	+	0.828968i	−0.0489287	+	0.0314446i
$696$	−3.00117	+	3.46354i	−0.113759	+	0.131285i
$697$	1.35738	−	9.44075i	0.0514143	−	0.357594i
$698$	12.7024	−	3.72976i	0.480793	−	0.141173i
$699$	−16.1765	−	10.3960i	−0.611852	−	0.393214i
$700$	0.708806	+	4.92985i	0.0267903	+	0.186331i
$701$	12.2828	+	26.8956i	0.463915	+	1.01583i	0.986578	+	0.163293i	$0.0522117\pi$
$701$	12.2828	+	26.8956i	0.463915	+	1.01583i	−0.522662	+	0.852540i	$0.675061\pi$
$702$	1.10821	+	2.42664i	0.0418267	+	0.0915878i
$703$	7.64797	+	53.1928i	0.288449	+	2.00620i
$704$	−2.75954	−	1.77345i	−0.104004	−	0.0668394i
$705$	−0.326904	+	0.0959876i	−0.0123119	+	0.00361510i
$706$	−4.36313	+	30.3462i	−0.164208	+	1.14209i
$707$	−6.47591	+	7.47359i	−0.243552	+	0.281073i
$708$	12.5173	−	8.04438i	0.470429	−	0.302326i
$709$	−19.4380	−	22.4326i	−0.730008	−	0.842474i	0.262464	−	0.964942i	$-0.415465\pi$
$709$	−19.4380	−	22.4326i	−0.730008	−	0.842474i	−0.992473	+	0.122467i	$0.960919\pi$
$710$	−1.07675	−	0.316162i	−0.0404097	−	0.0118654i
$711$	0.932130	−	2.04108i	0.0349576	−	0.0765465i
$712$	−9.83081			−0.368425
$713$	−2.40050	+	9.22610i	−0.0898995	+	0.345520i
$714$	1.35711			0.0507885
$715$	−0.507006	+	1.11019i	−0.0189609	+	0.0415187i
$716$	19.7673	+	5.80419i	0.738737	+	0.216913i
$717$	5.23556	+	6.04216i	0.195526	+	0.225649i
$718$	4.18943	−	2.69238i	0.156348	−	0.100479i
$719$	9.82261	−	11.3359i	0.366321	−	0.422757i	−0.542426	−	0.840103i	$-0.682494\pi$
$719$	9.82261	−	11.3359i	0.366321	−	0.422757i	0.908748	+	0.417346i	$0.137040\pi$
$720$	0.0198486	−	0.138050i	0.000739715	−	0.00514483i
$721$	6.38073	−	1.87355i	0.237631	−	0.0697747i
$722$	−10.5179	−	6.75946i	−0.391437	−	0.251561i
$723$	−1.11400	−	7.74802i	−0.0414300	−	0.288152i
$724$	−0.847427	−	1.85561i	−0.0314944	−	0.0689631i
$725$	9.48202	+	20.7627i	0.352154	+	0.771109i
$726$	−0.0341295	−	0.237376i	−0.00126666	−	0.00880983i
$727$	17.8277	+	11.4571i	0.661192	+	0.424922i	0.827741	−	0.561111i	$-0.189626\pi$
$727$	17.8277	+	11.4571i	0.661192	+	0.424922i	−0.166549	+	0.986033i	$0.553262\pi$
$728$	−2.55966	+	0.751584i	−0.0948673	+	0.0278555i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−0.635595	+	0.733515i	−0.0235244	+	0.0271486i
$731$	−12.8297	+	8.24513i	−0.474522	+	0.304957i
$732$	−4.29735	−	4.95940i	−0.158835	−	0.183305i
$733$	−14.6569	−	4.30366i	−0.541366	−	0.158959i	−0.000393645	−	1.00000i	$-0.500125\pi$
$733$	−14.6569	−	4.30366i	−0.541366	−	0.158959i	−0.540972	+	0.841041i	$0.681943\pi$
$734$	−12.3687	+	27.0836i	−0.456536	+	0.999675i
$735$	−0.139470			−0.00514443
$736$	4.29847	−	2.12676i	0.158444	−	0.0783935i
$737$	5.93375			0.218573
$738$	−2.91956	+	6.39295i	−0.107471	+	0.235328i
$739$	21.1567	+	6.21215i	0.778260	+	0.228518i	0.646653	−	0.762784i	$-0.276168\pi$
$739$	21.1567	+	6.21215i	0.778260	+	0.228518i	0.131607	+	0.991302i	$0.457986\pi$
$740$	−0.874484	−	1.00921i	−0.0321467	−	0.0370992i
$741$	−12.5962	+	8.09511i	−0.462735	+	0.297381i
$742$	−4.34298	+	5.01206i	−0.159436	+	0.183999i
$743$	−5.67425	+	39.4653i	−0.208168	+	1.44784i	0.570961	+	0.820977i	$0.306571\pi$
$743$	−5.67425	+	39.4653i	−0.208168	+	1.44784i	−0.779129	+	0.626863i	$0.784339\pi$
$744$	−1.90730	+	0.560035i	−0.0699252	+	0.0205319i
$745$	−0.887398	−	0.570296i	−0.0325117	−	0.0208940i
$746$	1.11914	+	7.78380i	0.0409747	+	0.284985i
$747$	−1.90641	−	4.17445i	−0.0697517	−	0.152735i
$748$	1.84930	+	4.04939i	0.0676170	+	0.148061i
$749$	0.211534	+	1.47125i	0.00772928	+	0.0537583i
$750$	−1.17101	−	0.752565i	−0.0427594	−	0.0274798i
$751$	11.6962	−	3.43430i	0.426799	−	0.125320i	−0.0612766	−	0.998121i	$-0.519517\pi$
$751$	11.6962	−	3.43430i	0.426799	−	0.125320i	0.488076	+	0.872801i	$0.337699\pi$
$752$	0.347654	−	2.41799i	0.0126776	−	0.0881750i
$753$	−11.3342	+	13.0803i	−0.413040	+	0.476674i
$754$	−10.2851	+	6.60984i	−0.374562	+	0.240716i
$755$	0.0576459	+	0.0665269i	0.00209795	+	0.00242116i
$756$	−0.959493	−	0.281733i	−0.0348964	−	0.0102465i
$757$	3.99992	−	8.75861i	0.145380	−	0.318337i	−0.822908	−	0.568174i	$-0.807650\pi$
$757$	3.99992	−	8.75861i	0.145380	−	0.318337i	0.968288	+	0.249837i	$0.0803772\pi$
$758$	−21.7168			−0.788789
$759$	−14.5060	−	6.08765i	−0.526535	−	0.220968i
$760$	0.782807			0.0283954
$761$	−2.04839	+	4.48534i	−0.0742539	+	0.162593i	−0.943119	−	0.332456i	$-0.892123\pi$
$761$	−2.04839	+	4.48534i	−0.0742539	+	0.162593i	0.868865	+	0.495049i	$0.164850\pi$
$762$	11.8600	+	3.48241i	0.429643	+	0.126155i
$763$	−8.51957	−	9.83211i	−0.308429	−	0.355946i
$764$	1.59772	−	1.02679i	0.0578035	−	0.0371481i
$765$	−0.123949	+	0.143045i	−0.00448140	+	0.00517181i
$766$	5.07814	−	35.3192i	0.183481	−	1.27614i
$767$	38.0860	−	11.1831i	1.37521	−	0.403797i
$768$	0.841254	+	0.540641i	0.0303561	+	0.0195087i
$769$	−6.12232	−	42.5817i	−0.220776	−	1.53553i	−0.735112	−	0.677945i	$-0.762871\pi$
$769$	−6.12232	−	42.5817i	−0.220776	−	1.53553i	0.514336	−	0.857589i	$-0.328038\pi$
$770$	−0.190052	−	0.416156i	−0.00684900	−	0.0149972i
$771$	−3.59468	−	7.87126i	−0.129459	−	0.283476i
$772$	2.42886	+	16.8931i	0.0874164	+	0.607995i
$773$	−33.6154	−	21.6033i	−1.20906	−	0.777017i	−0.228561	−	0.973530i	$-0.573402\pi$
$773$	−33.6154	−	21.6033i	−1.20906	−	0.777017i	−0.980501	+	0.196512i	$0.937038\pi$
$774$	10.7824	−	3.16600i	0.387566	−	0.113800i
$775$	−1.40898	+	9.79969i	−0.0506121	+	0.352015i
$776$	3.34521	−	3.86058i	0.120086	−	0.138587i
$777$	−8.05470	+	5.17644i	−0.288961	+	0.185704i
$778$	−16.4699	−	19.0073i	−0.590474	−	0.681443i
$779$	−37.8487	−	11.1134i	−1.35607	−	0.398178i
$780$	0.154562	−	0.338444i	0.00553421	−	0.0121182i
$781$	−26.3938			−0.944445
$782$	−6.46787	−	0.725760i	−0.231291	−	0.0259531i
$783$	−4.58291			−0.163780
$784$	0.415415	−	0.909632i	0.0148363	−	0.0324869i
$785$	−2.64949	−	0.777961i	−0.0945644	−	0.0277666i
$786$	−10.0030	−	11.5441i	−0.356795	−	0.411764i
$787$	−10.0118	+	6.43416i	−0.356881	+	0.229353i	−0.706779	−	0.707434i	$-0.749852\pi$
$787$	−10.0118	+	6.43416i	−0.356881	+	0.229353i	0.349898	+	0.936788i	$0.386216\pi$
$788$	16.3134	−	18.8266i	0.581139	−	0.670670i
$789$	−1.30373	+	9.06766i	−0.0464141	+	0.322817i
$790$	−0.300273	+	0.0881682i	−0.0106832	+	0.00313688i
$791$	−10.9191	−	7.01725i	−0.388237	−	0.249505i
$792$	−0.466831	−	3.24688i	−0.0165881	−	0.115373i
$793$	−7.27234	−	15.9242i	−0.258248	−	0.565485i
$794$	12.9400	+	28.3347i	0.459225	+	1.00556i
$795$	−0.131634	−	0.915538i	−0.00466859	−	0.0324708i
$796$	18.3966	+	11.8228i	0.652049	+	0.419047i
$797$	14.6309	−	4.29601i	0.518252	−	0.152173i	−0.0121379	−	0.999926i	$-0.503864\pi$
$797$	14.6309	−	4.29601i	0.518252	−	0.152173i	0.530390	+	0.847754i	$0.322046\pi$
$798$	0.798774	−	5.55560i	0.0282763	−	0.196666i
$799$	−2.17101	+	2.50547i	−0.0768046	+	0.0886373i
$800$	4.18990	−	2.69269i	0.148135	−	0.0952009i
$801$	−6.43781	−	7.42963i	−0.227469	−	0.262513i
$802$	−14.6689	−	4.30718i	−0.517977	−	0.152092i
$803$	−9.48293	+	20.7647i	−0.334645	+	0.732771i
$804$	−1.80892			−0.0637957
$805$	0.664703	+	0.0745863i	0.0234277	+	0.00262882i
$806$	−5.30296			−0.186789
$807$	0.864161	−	1.89225i	0.0304199	−	0.0666103i
$808$	9.48841	+	2.78605i	0.333801	+	0.0980128i
$809$	16.9276	+	19.5354i	0.595141	+	0.686829i	0.970789	−	0.239933i	$-0.0771254\pi$
$809$	16.9276	+	19.5354i	0.595141	+	0.686829i	−0.375648	+	0.926762i	$0.622580\pi$
$810$	0.117330	−	0.0754032i	0.00412254	−	0.00264940i
$811$	−28.6519	+	33.0661i	−1.00611	+	1.16111i	−0.0191992	+	0.999816i	$0.506112\pi$
$811$	−28.6519	+	33.0661i	−1.00611	+	1.16111i	−0.986907	+	0.161292i	$0.948434\pi$
$812$	0.652217	−	4.53627i	0.0228883	−	0.159192i
$813$	23.3743	−	6.86332i	0.819773	−	0.240707i
$814$	−26.4216	−	16.9801i	−0.926076	−	0.595153i
$815$	−0.455941	−	3.17114i	−0.0159709	−	0.111080i
$816$	−0.563763	−	1.23447i	−0.0197357	−	0.0432151i
$817$	26.2017	+	57.3738i	0.916682	+	2.00725i
$818$	−2.95128	−	20.5266i	−0.103189	−	0.717695i
$819$	−2.24423	−	1.44228i	−0.0784197	−	0.0503973i
$820$	0.940498	−	0.276155i	0.0328436	−	0.00964375i
$821$	−4.25075	+	29.5646i	−0.148352	+	1.03181i	0.770565	+	0.637362i	$0.219974\pi$
$821$	−4.25075	+	29.5646i	−0.148352	+	1.03181i	−0.918917	+	0.394451i	$0.870935\pi$
$822$	−9.00854	+	10.3964i	−0.314209	+	0.362617i
$823$	15.7014	−	10.0907i	0.547316	−	0.351739i	−0.237578	−	0.971368i	$-0.576354\pi$
$823$	15.7014	−	10.0907i	0.547316	−	0.351739i	0.784894	+	0.619630i	$0.212717\pi$
$824$	−4.35489	−	5.02581i	−0.151710	−	0.175082i
$825$	−15.6758	−	4.60282i	−0.545760	−	0.160250i
$826$	−6.18110	+	13.5347i	−0.215068	+	0.470933i
$827$	11.4038			0.396548			0.198274	−	0.980147i	$-0.436466\pi$
$827$	11.4038			0.396548			0.198274	+	0.980147i	$0.436466\pi$
$828$	4.42220	+	1.85584i	0.153682	+	0.0644948i
$829$	−1.83129			−0.0636033			−0.0318016	−	0.999494i	$-0.510124\pi$
$829$	−1.83129			−0.0636033			−0.0318016	+	0.999494i	$0.510124\pi$
$830$	−0.265886	+	0.582210i	−0.00922905	+	0.0202088i
$831$	3.26969	+	0.960068i	0.113424	+	0.0333044i
$832$	1.74699	+	2.01613i	0.0605658	+	0.0698967i
$833$	−1.14167	+	0.733708i	−0.0395566	+	0.0254215i
$834$	7.19942	−	8.30857i	0.249295	−	0.287702i
$835$	−0.332606	+	2.31332i	−0.0115103	+	0.0800559i
$836$	17.6655	−	5.18705i	0.610973	−	0.179398i
$837$	−1.67226	−	1.07470i	−0.0578019	−	0.0371470i
$838$	−1.18528	−	8.24382i	−0.0409449	−	0.284778i
$839$	−6.06300	−	13.2761i	−0.209318	−	0.458342i	0.775631	−	0.631186i	$-0.217432\pi$
$839$	−6.06300	−	13.2761i	−0.209318	−	0.458342i	−0.984949	+	0.172844i	$0.944704\pi$
$840$	0.0579379	+	0.126866i	0.00199905	+	0.00437730i
$841$	1.13808	+	7.91550i	0.0392441	+	0.272948i
$842$	22.3756	+	14.3799i	0.771115	+	0.495566i
$843$	19.3384	−	5.67826i	0.666049	−	0.195570i
$844$	−3.18091	+	22.1237i	−0.109491	+	0.761530i
$845$	−0.537339	+	0.620122i	−0.0184850	+	0.0213329i
$846$	2.05506	−	1.32071i	0.0706544	−	0.0454068i
$847$	0.157046	+	0.181241i	0.00539618	+	0.00622752i
$848$	6.36327	+	1.86843i	0.218516	+	0.0641620i
$849$	2.42394	−	5.30770i	0.0831896	−	0.182160i
$850$	−6.75914			−0.231837
$851$	41.1563	−	20.3630i	1.41082	−	0.698034i
$852$	8.04623			0.275659
$853$	18.3991	−	40.2885i	0.629974	−	1.37945i	−0.278064	−	0.960563i	$-0.589693\pi$
$853$	18.3991	−	40.2885i	0.629974	−	1.37945i	0.908038	−	0.418888i	$-0.137580\pi$
$854$	6.29642	+	1.84879i	0.215459	+	0.0632644i
$855$	0.512629	+	0.591606i	0.0175316	+	0.0202325i
$856$	1.25042	−	0.803597i	0.0427385	−	0.0274664i
$857$	−20.1725	+	23.2804i	−0.689081	+	0.795242i	−0.987234	−	0.159276i	$-0.949084\pi$
$857$	−20.1725	+	23.2804i	−0.689081	+	0.795242i	0.298153	+	0.954518i	$0.403629\pi$
$858$	1.24538	−	8.66178i	0.0425164	−	0.295708i
$859$	−7.62602	+	2.23920i	−0.260197	+	0.0764006i	−0.409229	−	0.912432i	$-0.634202\pi$
$859$	−7.62602	+	2.23920i	−0.260197	+	0.0764006i	0.149032	+	0.988832i	$0.452384\pi$
$860$	−1.31850	−	0.847351i	−0.0449606	−	0.0288944i
$861$	−1.00020	−	6.95652i	−0.0340866	−	0.237078i
$862$	14.0231	+	30.7063i	0.477629	+	1.04586i
$863$	11.6140	+	25.4311i	0.395345	+	0.865686i	0.997721	+	0.0674731i	$0.0214937\pi$
$863$	11.6140	+	25.4311i	0.395345	+	0.865686i	−0.602376	+	0.798213i	$0.705779\pi$
$864$	0.142315	+	0.989821i	0.00484165	+	0.0336744i
$865$	1.47621	+	0.948703i	0.0501927	+	0.0322569i
$866$	−34.3282	+	10.0797i	−1.16652	+	0.342522i
$867$	2.15724	−	15.0040i	0.0732639	−	0.509561i
$868$	1.30175	−	1.50230i	0.0441842	−	0.0509913i
$869$	−6.19200	+	3.97936i	−0.210049	+	0.134990i
$870$	0.418573	+	0.483059i	0.0141910	+	0.0163772i
$871$	−4.63022	−	1.35956i	−0.156889	−	0.0460668i
$872$	−5.40445	+	11.8341i	−0.183018	+	0.400753i
$873$	5.10828			0.172889
$874$	−6.77794	+	26.0504i	−0.229267	+	0.881167i
$875$	1.39199			0.0470577
$876$	2.89090	−	6.33018i	0.0976744	−	0.213877i
$877$	40.5717	+	11.9129i	1.37001	+	0.402271i	0.882280	−	0.470725i	$-0.156008\pi$
$877$	40.5717	+	11.9129i	1.37001	+	0.402271i	0.487728	+	0.872996i	$0.337826\pi$
$878$	19.3833	+	22.3695i	0.654153	+	0.754933i
$879$	−18.6961	+	12.0152i	−0.630604	+	0.405264i
$880$	−0.299598	+	0.345755i	−0.0100995	+	0.0116554i
$881$	−4.11425	+	28.6152i	−0.138613	+	0.964072i	0.795210	+	0.606335i	$0.207361\pi$
$881$	−4.11425	+	28.6152i	−0.138613	+	0.964072i	−0.933822	+	0.357737i	$0.883548\pi$
$882$	0.959493	−	0.281733i	0.0323078	−	0.00948643i
$883$	−25.2741	−	16.2427i	−0.850540	−	0.546609i	0.0412031	−	0.999151i	$-0.486881\pi$
$883$	−25.2741	−	16.2427i	−0.850540	−	0.546609i	−0.891743	+	0.452542i	$0.850517\pi$
$884$	−0.515235	−	3.58354i	−0.0173292	−	0.120527i
$885$	−0.862078	−	1.88769i	−0.0289784	−	0.0634539i
$886$	9.56655	+	20.9478i	0.321395	+	0.703756i
$887$	3.97892	+	27.6740i	0.133599	+	0.929203i	0.940809	+	0.338938i	$0.110068\pi$
$887$	3.97892	+	27.6740i	0.133599	+	0.929203i	−0.807210	+	0.590265i	$0.799023\pi$
$888$	8.05470	+	5.17644i	0.270298	+	0.173710i
$889$	−11.8600	+	3.48241i	−0.397772	+	0.116796i
$890$	−0.195128	+	1.35715i	−0.00654072	+	0.0454917i
$891$	2.14812	−	2.47906i	0.0719648	−	0.0830518i
$892$	9.63232	−	6.19031i	0.322514	−	0.207267i
$893$	8.97884	+	10.3621i	0.300465	+	0.346755i
$894$	7.25692	+	2.13083i	0.242708	+	0.0712655i
$895$	1.19362	−	2.61367i	0.0398985	−	0.0873654i
$896$	−1.00000			−0.0334077
$897$	9.92451	+	8.07396i	0.331370	+	0.269582i
$898$	15.5323			0.518319
$899$	3.78444	−	8.28678i	0.126218	−	0.276379i
$900$	4.77880	+	1.40318i	0.159293	+	0.0467728i
$901$	−5.89389	−	6.80192i	−0.196354	−	0.226605i
$902$	19.3942	−	12.4639i	0.645756	−	0.415002i
$903$	−7.35907	+	8.49282i	−0.244895	+	0.282623i
$904$	−1.84718	+	12.8474i	−0.0614362	+	0.427298i
$905$	−0.272988	+	0.0801564i	−0.00907441	+	0.00266449i
$906$	−0.530964	−	0.341230i	−0.0176401	−	0.0113366i
$907$	2.18110	+	15.1699i	0.0724224	+	0.503709i	0.993455	+	0.114223i	$0.0364380\pi$
$907$	2.18110	+	15.1699i	0.0724224	+	0.503709i	−0.921033	+	0.389485i	$0.872653\pi$
$908$	0.304245	+	0.666204i	0.0100967	+	0.0221088i
$909$	4.10803	+	8.99534i	0.136255	+	0.298356i
$910$	0.0529506	+	0.368280i	0.00175530	+	0.0122084i
$911$	−29.6884	−	19.0796i	−0.983621	−	0.632135i	−0.0531831	−	0.998585i	$-0.516937\pi$
$911$	−29.6884	−	19.0796i	−0.983621	−	0.632135i	−0.930438	+	0.366450i	$0.880573\pi$
$912$	−5.38537	+	1.58129i	−0.178327	+	0.0523617i
$913$	−2.14236	+	14.9005i	−0.0709019	+	0.493133i
$914$	13.3380	−	15.3929i	0.441182	−	0.509151i
$915$	−0.769944	+	0.494813i	−0.0254536	+	0.0163580i
$916$	−11.0919	−	12.8008i	−0.366487	−	0.422949i
$917$	14.6563	+	4.30347i	0.483992	+	0.142113i
$918$	0.563763	−	1.23447i	0.0186070	−	0.0407436i
$919$	12.5487			0.413944			0.206972	−	0.978347i	$-0.433639\pi$
$919$	12.5487			0.413944			0.206972	+	0.978347i	$0.433639\pi$
$920$	−0.208281	−	0.635619i	−0.00686684	−	0.0209557i
$921$	−13.4230			−0.442303
$922$	0.687535	−	1.50549i	0.0226428	−	0.0495808i
$923$	20.5956	+	6.04741i	0.677912	+	0.199053i
$924$	2.14812	+	2.47906i	0.0706680	+	0.0815552i
$925$	40.1168	−	25.7815i	1.31903	−	0.847691i
$926$	−8.53949	+	9.85509i	−0.280625	+	0.323858i
$927$	0.946408	−	6.58241i	0.0310841	−	0.216195i
$928$	−4.39727	+	1.29116i	−0.144348	+	0.0423843i
$929$	−8.13901	−	5.23062i	−0.267032	−	0.171611i	0.400272	−	0.916396i	$-0.368916\pi$
$929$	−8.13901	−	5.23062i	−0.267032	−	0.171611i	−0.667304	+	0.744785i	$0.732552\pi$
$930$	0.0394556	+	0.274420i	0.00129380	+	0.00899858i
$931$	2.33161	+	5.10551i	0.0764154	+	0.167326i
$932$	−7.98804	−	17.4914i	−0.261657	−	0.572949i
$933$	−1.47670	−	10.2707i	−0.0483451	−	0.336247i
$934$	8.59746	+	5.52525i	0.281318	+	0.180792i
$935$	0.595726	−	0.174921i	0.0194823	−	0.00572053i
$936$	−0.379656	+	2.64057i	−0.0124095	+	0.0863096i
$937$	−11.6882	+	13.4889i	−0.381836	+	0.440662i	−0.913837	−	0.406082i	$-0.866895\pi$
$937$	−11.6882	+	13.4889i	−0.381836	+	0.440662i	0.532001	+	0.846744i	$0.321440\pi$
$938$	1.52176	−	0.977977i	0.0496873	−	0.0319321i
$939$	8.07518	+	9.31926i	0.263524	+	0.304122i
$940$	−0.326904	−	0.0959876i	−0.0106624	−	0.00313077i
$941$	10.7196	−	23.4727i	0.349450	−	0.765188i	−0.650534	−	0.759477i	$-0.725455\pi$
$941$	10.7196	−	23.4727i	0.349450	−	0.765188i	0.999984	−	0.00571103i	$-0.00181789\pi$
$942$	19.7989			0.645082
$943$	1.04662	+	33.6891i	0.0340827	+	1.09707i
$944$	14.8793			0.484281
$945$	−0.0579379	+	0.126866i	−0.00188472	+	0.00412696i
$946$	−35.3692	−	10.3853i	−1.14995	−	0.337657i
$947$	11.2749	+	13.0120i	0.366386	+	0.422832i	0.908769	−	0.417299i	$-0.137023\pi$
$947$	11.2749	+	13.0120i	0.366386	+	0.422832i	−0.542383	+	0.840131i	$0.682478\pi$
$948$	1.88765	−	1.21312i	0.0613080	−	0.0394002i
$949$	12.1574	−	14.0304i	0.394645	−	0.455445i
$950$	−3.97833	+	27.6699i	−0.129074	+	0.897731i
$951$	−10.8146	+	3.17544i	−0.350686	+	0.102971i
$952$	1.14167	+	0.733708i	0.0370018	+	0.0237796i
$953$	−6.43572	−	44.7614i	−0.208474	−	1.44997i	−0.778141	−	0.628090i	$-0.783837\pi$
$953$	−6.43572	−	44.7614i	−0.208474	−	1.44997i	0.569667	−	0.821875i	$-0.307072\pi$
$954$	2.75500	+	6.03260i	0.0891963	+	0.195313i
$955$	−0.110037	−	0.240946i	−0.00356070	−	0.00779684i
$956$	1.13780	+	7.91355i	0.0367990	+	0.255942i
$957$	12.6467	+	8.12756i	0.408811	+	0.262727i
$958$	−13.1120	+	3.85004i	−0.423631	+	0.124389i
$959$	1.95774	−	13.6164i	0.0632188	−	0.439697i
$960$	0.0913334	−	0.105404i	0.00294777	−	0.00340191i
$961$	−22.7547	+	14.6236i	−0.734022	+	0.471727i
$962$	16.7267	+	19.3037i	0.539292	+	0.622376i
$963$	1.42617	+	0.418761i	0.0459577	+	0.0134944i
$964$	3.25174	−	7.12032i	0.104732	−	0.229330i
$965$	2.38030			0.0766247
$966$	−4.72353	+	0.829594i	−0.151977	+	0.0266917i
$967$	−8.68669			−0.279345			−0.139673	−	0.990198i	$-0.544605\pi$
$967$	−8.68669			−0.279345			−0.139673	+	0.990198i	$0.544605\pi$
$968$	0.0996234	−	0.218145i	0.00320202	−	0.00701144i
$969$	7.30853	+	2.14598i	0.234784	+	0.0689388i
$970$	−0.466557	−	0.538435i	−0.0149802	−	0.0172881i
$971$	20.7773	−	13.3527i	0.666774	−	0.428510i	−0.162987	−	0.986628i	$-0.552113\pi$
$971$	20.7773	−	13.3527i	0.666774	−	0.428510i	0.829761	+	0.558118i	$0.188477\pi$
$972$	−0.654861	+	0.755750i	−0.0210047	+	0.0242407i
$973$	−1.56458	+	10.8819i	−0.0501582	+	0.348858i
$974$	18.9263	−	5.55725i	0.606437	−	0.178066i
$975$	11.1775	+	7.18334i	0.357966	+	0.230051i
$976$	−0.933903	−	6.49544i	−0.0298935	−	0.207914i
$977$	−12.1177	−	26.5340i	−0.387679	−	0.848898i	−0.998372	−	0.0570312i	$-0.981837\pi$
$977$	−12.1177	−	26.5340i	−0.387679	−	0.848898i	0.610694	−	0.791867i	$-0.290891\pi$
$978$	9.54244	+	20.8950i	0.305134	+	0.668150i
$979$	4.58933	+	31.9195i	0.146676	+	1.02015i
$980$	−0.117330	−	0.0754032i	−0.00374796	−	0.00240867i
$981$	−12.4828	+	3.66527i	−0.398544	+	0.117023i
$982$	−4.47912	+	31.1529i	−0.142934	+	0.994130i
$983$	−15.8725	+	18.3179i	−0.506255	+	0.584250i	−0.950136	−	0.311836i	$-0.899056\pi$
$983$	−15.8725	+	18.3179i	−0.506255	+	0.584250i	0.443881	+	0.896086i	$0.353601\pi$
$984$	−5.91238	+	3.79965i	−0.188480	+	0.121129i
$985$	−2.27522	−	2.62575i	−0.0724946	−	0.0836633i
$986$	5.96758	+	1.75224i	0.190046	+	0.0558027i
$987$	−1.01480	+	2.22210i	−0.0323014	+	0.0707301i
$988$	−14.9732			−0.476360
$989$	39.6146	−	36.5406i	1.25967	−	1.16192i
$990$	−0.457499			−0.0145403
$991$	−12.0978	+	26.4904i	−0.384298	+	0.841496i	0.614326	+	0.789053i	$0.289428\pi$
$991$	−12.0978	+	26.4904i	−0.384298	+	0.841496i	−0.998624	+	0.0524433i	$0.983299\pi$
$992$	−1.90730	−	0.560035i	−0.0605570	−	0.0177811i
$993$	13.3436	+	15.3993i	0.423446	+	0.488683i
$994$	−6.76892	+	4.35012i	−0.214697	+	0.137977i
$995$	1.99728	−	2.30499i	0.0633181	−	0.0730730i
$996$	0.653105	−	4.54245i	0.0206944	−	0.143933i
$997$	18.1153	−	5.31914i	0.573719	−	0.168459i	0.0180125	−	0.999838i	$-0.494266\pi$
$997$	18.1153	−	5.31914i	0.573719	−	0.168459i	0.555706	+	0.831379i	$0.312448\pi$
$998$	18.8301	+	12.1014i	0.596056	+	0.383062i
$999$	1.36261	+	9.47718i	0.0431112	+	0.299845i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.e.211.1	✓	20	23.4	even	11	inner
966.2.q.e.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)

\(f(q)\)	\(=\)	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.117330 + 0.0754032i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.117330 + 0.0754032i) 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} +(-0.0198486 - 0.138050i) q^{10} +(-1.36267 - 2.98384i) q^{11} +(0.415415 + 0.909632i) q^{12} +(0.379656 + 2.64057i) q^{13} +(-0.841254 - 0.540641i) q^{14} +(0.133820 - 0.0392932i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(0.888717 - 1.02563i) q^{17} +(-0.841254 + 0.540641i) q^{18} +(-3.67555 - 4.24181i) q^{19} +(0.133820 + 0.0392932i) q^{20} +(0.415415 - 0.909632i) q^{21} +3.28027 q^{22} +(-2.46629 + 4.11308i) q^{23} -1.00000 q^{24} +(-2.06899 + 4.53047i) q^{25} +(-2.55966 - 0.751584i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(0.841254 - 0.540641i) q^{28} +(3.00117 - 3.46354i) q^{29} +(-0.0198486 + 0.138050i) q^{30} +(1.90730 - 0.560035i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(0.466831 + 3.24688i) q^{33} +(0.563763 + 1.23447i) q^{34} +(-0.0579379 - 0.126866i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-8.05470 - 5.17644i) q^{37} +(5.38537 - 1.58129i) q^{38} +(0.379656 - 2.64057i) q^{39} +(-0.0913334 + 0.105404i) q^{40} +(5.91238 - 3.79965i) q^{41} +(0.654861 + 0.755750i) q^{42} +(-10.7824 - 3.16600i) q^{43} +(-1.36267 + 2.98384i) q^{44} -0.139470 q^{45} +(-2.71685 - 3.95205i) q^{46} -2.44285 q^{47} +(0.415415 - 0.909632i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(-3.26157 - 3.76405i) q^{50} +(-1.14167 + 0.733708i) q^{51} +(1.74699 - 2.01613i) q^{52} +(0.943820 - 6.56441i) q^{53} +(0.959493 - 0.281733i) q^{54} +(0.384873 + 0.247343i) q^{55} +(0.142315 + 0.989821i) q^{56} +(2.33161 + 5.10551i) q^{57} +(1.90381 + 4.16877i) q^{58} +(-2.11755 - 14.7279i) q^{59} +(-0.117330 - 0.0754032i) q^{60} +(-6.29642 + 1.84879i) q^{61} +(-0.282897 + 1.96759i) q^{62} +(-0.654861 + 0.755750i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-0.243652 - 0.281189i) q^{65} +(-3.14740 - 0.924159i) q^{66} +(-0.751453 + 1.64545i) q^{67} -1.35711 q^{68} +(3.52518 - 3.25163i) q^{69} +0.139470 q^{70} +(3.34252 - 7.31910i) q^{71} +(0.959493 + 0.281733i) q^{72} +(-4.55722 - 5.25931i) q^{73} +(8.05470 - 5.17644i) q^{74} +(3.26157 - 3.76405i) q^{75} +(-0.798774 + 5.55560i) q^{76} +(3.14740 - 0.924159i) q^{77} +(2.24423 + 1.44228i) q^{78} +(-0.319333 - 2.22101i) q^{79} +(-0.0579379 - 0.126866i) q^{80} +(0.415415 + 0.909632i) q^{81} +(1.00020 + 6.95652i) q^{82} +(-3.86065 - 2.48109i) q^{83} +(-0.959493 + 0.281733i) q^{84} +(-0.0269368 + 0.187349i) q^{85} +(7.35907 - 8.49282i) q^{86} +(-3.85539 + 2.47771i) q^{87} +(-2.14812 - 2.47906i) q^{88} +(-9.43260 - 2.76966i) q^{89} +(0.0579379 - 0.126866i) q^{90} -2.66772 q^{91} +(4.72353 - 0.829594i) q^{92} -1.98782 q^{93} +(1.01480 - 2.22210i) q^{94} +(0.751097 + 0.220542i) q^{95} +(0.654861 + 0.755750i) q^{96} +(4.29736 - 2.76175i) q^{97} +(0.654861 - 0.755750i) q^{98} +(0.466831 - 3.24688i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 10 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 10 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 10 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} - 10 q^{10} - 3 q^{11} - 2 q^{12} + 6 q^{13} + 2 q^{14} - 12 q^{15} - 2 q^{16} + 14 q^{17} + 2 q^{18} - 13 q^{19} - 12 q^{20} - 2 q^{21} - 8 q^{22} - 2 q^{23} - 20 q^{24} + 22 q^{25} - 28 q^{26} - 2 q^{27} - 2 q^{28} + 26 q^{29} - 10 q^{30} + 15 q^{31} + 2 q^{32} - 14 q^{33} - 3 q^{34} - q^{35} - 2 q^{36} - 26 q^{37} + 2 q^{38} + 6 q^{39} + q^{40} + 40 q^{41} + 2 q^{42} + 8 q^{43} - 3 q^{44} - 12 q^{45} - 20 q^{46} + 36 q^{47} - 2 q^{48} - 2 q^{49} + 11 q^{50} + 3 q^{51} - 27 q^{52} - 5 q^{53} + 2 q^{54} - 7 q^{55} + 2 q^{56} + 9 q^{57} - 15 q^{58} + 13 q^{59} + 10 q^{60} + 59 q^{61} - 4 q^{62} - 2 q^{63} - 2 q^{64} - q^{65} - 8 q^{66} - 26 q^{67} - 8 q^{68} - 35 q^{69} + 12 q^{70} + 13 q^{71} + 2 q^{72} - 34 q^{73} + 26 q^{74} - 11 q^{75} - 2 q^{76} + 8 q^{77} - 6 q^{78} - 27 q^{79} - q^{80} - 2 q^{81} - 40 q^{82} + 41 q^{83} - 2 q^{84} + 51 q^{85} + 14 q^{86} - 7 q^{87} - 8 q^{88} + 43 q^{89} + q^{90} - 16 q^{91} + 9 q^{92} + 4 q^{93} - 3 q^{94} - 26 q^{95} + 2 q^{96} - 8 q^{97} + 2 q^{98} - 14 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 10 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 - 10 * q^10 - 3 * q^11 - 2 * q^12 + 6 * q^13 + 2 * q^14 - 12 * q^15 - 2 * q^16 + 14 * q^17 + 2 * q^18 - 13 * q^19 - 12 * q^20 - 2 * q^21 - 8 * q^22 - 2 * q^23 - 20 * q^24 + 22 * q^25 - 28 * q^26 - 2 * q^27 - 2 * q^28 + 26 * q^29 - 10 * q^30 + 15 * q^31 + 2 * q^32 - 14 * q^33 - 3 * q^34 - q^35 - 2 * q^36 - 26 * q^37 + 2 * q^38 + 6 * q^39 + q^40 + 40 * q^41 + 2 * q^42 + 8 * q^43 - 3 * q^44 - 12 * q^45 - 20 * q^46 + 36 * q^47 - 2 * q^48 - 2 * q^49 + 11 * q^50 + 3 * q^51 - 27 * q^52 - 5 * q^53 + 2 * q^54 - 7 * q^55 + 2 * q^56 + 9 * q^57 - 15 * q^58 + 13 * q^59 + 10 * q^60 + 59 * q^61 - 4 * q^62 - 2 * q^63 - 2 * q^64 - q^65 - 8 * q^66 - 26 * q^67 - 8 * q^68 - 35 * q^69 + 12 * q^70 + 13 * q^71 + 2 * q^72 - 34 * q^73 + 26 * q^74 - 11 * q^75 - 2 * q^76 + 8 * q^77 - 6 * q^78 - 27 * q^79 - q^80 - 2 * q^81 - 40 * q^82 + 41 * q^83 - 2 * q^84 + 51 * q^85 + 14 * q^86 - 7 * q^87 - 8 * q^88 + 43 * q^89 + q^90 - 16 * q^91 + 9 * q^92 + 4 * q^93 - 3 * q^94 - 26 * q^95 + 2 * q^96 - 8 * q^97 + 2 * q^98 - 14 * q^99

Introduction

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