LMFDB - Embedded newform 91.2.k.b.23.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(4,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("91.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.k (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.3
Root			$-1.18541 - 0.771231i$ of defining polynomial
Character	$\chi$	$=$	91.23
Dual form			91.2.k.b.4.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.499987i q^{2} +(-0.424801 + 0.735776i) q^{3} +1.75001 q^{4} +(-0.902810 - 0.521238i) q^{5} +(0.367878 + 0.212395i) q^{6} +(2.63491 + 0.239300i) q^{7} -1.87496i q^{8} +(1.13909 + 1.97296i) q^{9} +O(q^{10})$	\(q-0.499987i q^{2} +(-0.424801 + 0.735776i) q^{3} +1.75001 q^{4} +(-0.902810 - 0.521238i) q^{5} +(0.367878 + 0.212395i) q^{6} +(2.63491 + 0.239300i) q^{7} -1.87496i q^{8} +(1.13909 + 1.97296i) q^{9} +(-0.260612 + 0.451393i) q^{10} +(-3.43579 - 1.98365i) q^{11} +(-0.743407 + 1.28762i) q^{12} +(-3.57504 - 0.468096i) q^{13} +(0.119647 - 1.31742i) q^{14} +(0.767029 - 0.442844i) q^{15} +2.56257 q^{16} +0.142035 q^{17} +(0.986453 - 0.569529i) q^{18} +(-4.77160 + 2.75488i) q^{19} +(-1.57993 - 0.912173i) q^{20} +(-1.29538 + 1.83705i) q^{21} +(-0.991800 + 1.71785i) q^{22} -4.39098 q^{23} +(1.37955 + 0.796483i) q^{24} +(-1.95662 - 3.38897i) q^{25} +(-0.234042 + 1.78747i) q^{26} -4.48435 q^{27} +(4.61112 + 0.418779i) q^{28} +(4.19880 + 7.27253i) q^{29} +(-0.221416 - 0.383504i) q^{30} +(2.46516 - 1.42326i) q^{31} -5.03117i q^{32} +(2.91905 - 1.68531i) q^{33} -0.0710158i q^{34} +(-2.25409 - 1.58946i) q^{35} +(1.99342 + 3.45271i) q^{36} +0.843187i q^{37} +(1.37740 + 2.38574i) q^{38} +(1.86309 - 2.43158i) q^{39} +(-0.977298 + 1.69273i) q^{40} +(10.4766 - 6.04869i) q^{41} +(0.918499 + 0.647674i) q^{42} +(2.41161 - 4.17704i) q^{43} +(-6.01267 - 3.47142i) q^{44} -2.37494i q^{45} +2.19543i q^{46} +(-3.94602 - 2.27824i) q^{47} +(-1.08858 + 1.88548i) q^{48} +(6.88547 + 1.26107i) q^{49} +(-1.69444 + 0.978285i) q^{50} +(-0.0603367 + 0.104506i) q^{51} +(-6.25636 - 0.819175i) q^{52} +(0.139800 + 0.242141i) q^{53} +2.24211i q^{54} +(2.06791 + 3.58172i) q^{55} +(0.448678 - 4.94034i) q^{56} -4.68111i q^{57} +(3.63617 - 2.09934i) q^{58} +10.7815i q^{59} +(1.34231 - 0.774983i) q^{60} +(2.93177 + 5.07797i) q^{61} +(-0.711612 - 1.23255i) q^{62} +(2.52926 + 5.47115i) q^{63} +2.60963 q^{64} +(2.98359 + 2.28605i) q^{65} +(-0.842634 - 1.45949i) q^{66} +(-4.45524 - 2.57223i) q^{67} +0.248564 q^{68} +(1.86529 - 3.23078i) q^{69} +(-0.794706 + 1.12701i) q^{70} +(-3.20326 - 1.84940i) q^{71} +(3.69921 - 2.13574i) q^{72} +(5.72686 - 3.30640i) q^{73} +0.421582 q^{74} +3.32470 q^{75} +(-8.35036 + 4.82108i) q^{76} +(-8.57829 - 6.04892i) q^{77} +(-1.21576 - 0.931521i) q^{78} +(-5.96135 + 10.3254i) q^{79} +(-2.31352 - 1.33571i) q^{80} +(-1.51231 + 2.61940i) q^{81} +(-3.02426 - 5.23818i) q^{82} +2.87321i q^{83} +(-2.26694 + 3.21486i) q^{84} +(-0.128231 - 0.0740342i) q^{85} +(-2.08846 - 1.20578i) q^{86} -7.13461 q^{87} +(-3.71926 + 6.44195i) q^{88} -1.74765i q^{89} -1.18744 q^{90} +(-9.30787 - 2.08890i) q^{91} -7.68427 q^{92} +2.41841i q^{93} +(-1.13909 + 1.97296i) q^{94} +5.74379 q^{95} +(3.70181 + 2.13724i) q^{96} +(2.34079 + 1.35145i) q^{97} +(0.630517 - 3.44264i) q^{98} -9.03822i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} - 8 q^{4} - 3 q^{5} - 9 q^{6} - 3 q^{7} - q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 - 8 * q^4 - 3 * q^5 - 9 * q^6 - 3 * q^7 - q^9	$ 12 q - 3 q^{3} - 8 q^{4} - 3 q^{5} - 9 q^{6} - 3 q^{7} - q^{9} + 12 q^{10} + 12 q^{11} - q^{12} - 2 q^{13} + 4 q^{14} - 12 q^{15} + 16 q^{16} - 34 q^{17} + 3 q^{18} + 9 q^{19} - 3 q^{20} + 21 q^{21} - 15 q^{22} - 6 q^{23} + 15 q^{24} - 5 q^{25} - 6 q^{26} + 12 q^{27} - 9 q^{28} - q^{29} + 11 q^{30} + 18 q^{31} - 6 q^{33} - 6 q^{35} - 13 q^{36} + 19 q^{38} - 4 q^{39} - q^{40} - 6 q^{41} - 8 q^{42} + 11 q^{43} - 33 q^{44} - 15 q^{47} + 19 q^{48} - 3 q^{49} + 18 q^{50} + 4 q^{51} - 7 q^{52} - 8 q^{53} - 15 q^{55} + 27 q^{56} - 24 q^{58} - 30 q^{60} + 5 q^{61} + 41 q^{62} - 30 q^{63} + 2 q^{64} + 21 q^{65} - 34 q^{66} + 15 q^{67} + 22 q^{68} + 7 q^{69} + 3 q^{70} + 30 q^{71} + 57 q^{72} + 42 q^{73} + 66 q^{74} - 2 q^{75} - 45 q^{76} - 19 q^{77} + 44 q^{78} - 35 q^{79} - 63 q^{80} + 14 q^{81} + 5 q^{82} - 12 q^{84} - 21 q^{85} - 57 q^{86} - 20 q^{87} - 14 q^{88} - 7 q^{91} - 66 q^{92} + q^{94} - 4 q^{95} + 21 q^{96} - 3 q^{97} - 18 q^{98}+O(q^{100}) $ 12 * q - 3 * q^3 - 8 * q^4 - 3 * q^5 - 9 * q^6 - 3 * q^7 - q^9 + 12 * q^10 + 12 * q^11 - q^12 - 2 * q^13 + 4 * q^14 - 12 * q^15 + 16 * q^16 - 34 * q^17 + 3 * q^18 + 9 * q^19 - 3 * q^20 + 21 * q^21 - 15 * q^22 - 6 * q^23 + 15 * q^24 - 5 * q^25 - 6 * q^26 + 12 * q^27 - 9 * q^28 - q^29 + 11 * q^30 + 18 * q^31 - 6 * q^33 - 6 * q^35 - 13 * q^36 + 19 * q^38 - 4 * q^39 - q^40 - 6 * q^41 - 8 * q^42 + 11 * q^43 - 33 * q^44 - 15 * q^47 + 19 * q^48 - 3 * q^49 + 18 * q^50 + 4 * q^51 - 7 * q^52 - 8 * q^53 - 15 * q^55 + 27 * q^56 - 24 * q^58 - 30 * q^60 + 5 * q^61 + 41 * q^62 - 30 * q^63 + 2 * q^64 + 21 * q^65 - 34 * q^66 + 15 * q^67 + 22 * q^68 + 7 * q^69 + 3 * q^70 + 30 * q^71 + 57 * q^72 + 42 * q^73 + 66 * q^74 - 2 * q^75 - 45 * q^76 - 19 * q^77 + 44 * q^78 - 35 * q^79 - 63 * q^80 + 14 * q^81 + 5 * q^82 - 12 * q^84 - 21 * q^85 - 57 * q^86 - 20 * q^87 - 14 * q^88 - 7 * q^91 - 66 * q^92 + q^94 - 4 * q^95 + 21 * q^96 - 3 * q^97 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	0.499987i		−	0.353544i	−0.984252	−	0.176772i	$-0.943434\pi$
$2$		−	0.499987i		−	0.353544i	0.984252	−	0.176772i	$-0.0565655\pi$
$3$	−0.424801	+	0.735776i	−0.245259	+	0.424801i	−0.962204	−	0.272328i	$-0.912206\pi$
$3$	−0.424801	+	0.735776i	−0.245259	+	0.424801i	0.716946	+	0.697129i	$0.245540\pi$
$4$	1.75001			0.875007
$5$	−0.902810	−	0.521238i	−0.403749	−	0.233105i	0.284351	−	0.958720i	$-0.408222\pi$
$5$	−0.902810	−	0.521238i	−0.403749	−	0.233105i	−0.688100	+	0.725616i	$0.741555\pi$
$6$	0.367878	+	0.212395i	0.150186	+	0.0867098i
$7$	2.63491	+	0.239300i	0.995901	+	0.0904471i
$7$	2.63491	+	0.239300i	0.995901	+	0.0904471i
$8$		−	1.87496i		−	0.662897i
$9$	1.13909	+	1.97296i	0.379696	+	0.657653i
$10$	−0.260612	+	0.451393i	−0.0824127	+	0.142743i
$11$	−3.43579	−	1.98365i	−1.03593	−	0.598094i	−0.117251	−	0.993102i	$-0.537408\pi$
$11$	−3.43579	−	1.98365i	−1.03593	−	0.598094i	−0.918677	+	0.395009i	$0.870742\pi$
$12$	−0.743407	+	1.28762i	−0.214603	+	0.371703i
$13$	−3.57504	−	0.468096i	−0.991537	−	0.129827i
$13$	−3.57504	−	0.468096i	−0.991537	−	0.129827i
$14$	0.119647	−	1.31742i	0.0319770	−	0.352095i
$15$	0.767029	−	0.442844i	0.198046	−	0.114342i
$16$	2.56257			0.640643
$17$	0.142035			0.0344486			0.0172243	−	0.999852i	$-0.494517\pi$
$17$	0.142035			0.0344486			0.0172243	+	0.999852i	$0.494517\pi$
$18$	0.986453	−	0.569529i	0.232509	−	0.134239i
$19$	−4.77160	+	2.75488i	−1.09468	+	0.632014i	−0.934818	−	0.355126i	$-0.884438\pi$
$19$	−4.77160	+	2.75488i	−1.09468	+	0.632014i	−0.159861	+	0.987140i	$0.551105\pi$
$20$	−1.57993	−	0.912173i	−0.353283	−	0.203968i
$21$	−1.29538	+	1.83705i	−0.282676	+	0.400877i
$22$	−0.991800	+	1.71785i	−0.211452	+	0.366246i
$23$	−4.39098			−0.915582			−0.457791	−	0.889060i	$-0.651359\pi$
$23$	−4.39098			−0.915582			−0.457791	+	0.889060i	$0.651359\pi$
$24$	1.37955	+	0.796483i	0.281599	+	0.162581i
$25$	−1.95662	−	3.38897i	−0.391325	−	0.677794i
$26$	−0.234042	+	1.78747i	−0.0458994	+	0.350552i
$27$	−4.48435			−0.863013
$28$	4.61112	+	0.418779i	0.871420	+	0.0791418i
$29$	4.19880	+	7.27253i	0.779697	+	1.35047i	0.932116	+	0.362159i	$0.117960\pi$
$29$	4.19880	+	7.27253i	0.779697	+	1.35047i	−0.152419	+	0.988316i	$0.548706\pi$
$30$	−0.221416	−	0.383504i	−0.0404249	−	0.0700179i
$31$	2.46516	−	1.42326i	0.442756	−	0.255625i	−0.262010	−	0.965065i	$-0.584385\pi$
$31$	2.46516	−	1.42326i	0.442756	−	0.255625i	0.704766	+	0.709440i	$0.251052\pi$
$32$		−	5.03117i		−	0.889393i
$33$	2.91905	−	1.68531i	0.508141	−	0.293376i
$34$		−	0.0710158i		−	0.0121791i
$35$	−2.25409	−	1.58946i	−0.381010	−	0.268667i
$36$	1.99342	+	3.45271i	0.332237	+	0.575451i
$37$			0.843187i			0.138619i	0.997595	+	0.0693095i	$0.0220796\pi$
$37$			0.843187i			0.138619i	−0.997595	+	0.0693095i	$0.977920\pi$
$38$	1.37740	+	2.38574i	0.223445	+	0.387017i
$39$	1.86309	−	2.43158i	0.298334	−	0.389364i
$40$	−0.977298	+	1.69273i	−0.154524	+	0.267644i
$41$	10.4766	−	6.04869i	1.63618	−	0.944647i	0.654044	−	0.756457i	$-0.273071\pi$
$41$	10.4766	−	6.04869i	1.63618	−	0.944647i	0.982133	−	0.188190i	$-0.0602621\pi$
$42$	0.918499	+	0.647674i	0.141728	+	0.0999382i
$43$	2.41161	−	4.17704i	0.367768	−	0.636993i	−0.621448	−	0.783455i	$-0.713455\pi$
$43$	2.41161	−	4.17704i	0.367768	−	0.636993i	0.989216	+	0.146463i	$0.0467888\pi$
$44$	−6.01267	−	3.47142i	−0.906444	−	0.523336i
$45$		−	2.37494i		−	0.354036i
$46$			2.19543i			0.323699i
$47$	−3.94602	−	2.27824i	−0.575587	−	0.332315i	0.183791	−	0.982965i	$-0.441163\pi$
$47$	−3.94602	−	2.27824i	−0.575587	−	0.332315i	−0.759378	+	0.650650i	$0.774496\pi$
$48$	−1.08858	+	1.88548i	−0.157123	+	0.272146i
$49$	6.88547	+	1.26107i	0.983639	+	0.180153i
$50$	−1.69444	+	0.978285i	−0.239630	+	0.138350i
$51$	−0.0603367	+	0.104506i	−0.00844883	+	0.0146338i
$52$	−6.25636	−	0.819175i	−0.867601	−	0.113599i
$53$	0.139800	+	0.242141i	0.0192030	+	0.0332606i	0.875467	−	0.483278i	$-0.160554\pi$
$53$	0.139800	+	0.242141i	0.0192030	+	0.0332606i	−0.856264	+	0.516538i	$0.827220\pi$
$54$			2.24211i			0.305113i
$55$	2.06791	+	3.58172i	0.278837	+	0.482959i
$56$	0.448678	−	4.94034i	0.0599571	−	0.660180i
$57$		−	4.68111i		−	0.620028i
$58$	3.63617	−	2.09934i	0.477452	−	0.275657i
$59$			10.7815i			1.40363i	0.712359	+	0.701815i	$0.247627\pi$
$59$			10.7815i			1.40363i	−0.712359	+	0.701815i	$0.752373\pi$
$60$	1.34231	−	0.774983i	0.173292	−	0.100050i
$61$	2.93177	+	5.07797i	0.375374	+	0.650168i	0.990383	−	0.138353i	$-0.0441808\pi$
$61$	2.93177	+	5.07797i	0.375374	+	0.650168i	−0.615009	+	0.788520i	$0.710847\pi$
$62$	−0.711612	−	1.23255i	−0.0903748	−	0.156534i
$63$	2.52926	+	5.47115i	0.318657	+	0.689300i
$64$	2.60963			0.326204
$65$	2.98359	+	2.28605i	0.370069	+	0.283549i
$66$	−0.842634	−	1.45949i	−0.103721	−	0.179650i
$67$	−4.45524	−	2.57223i	−0.544294	−	0.314248i	0.202523	−	0.979277i	$-0.435086\pi$
$67$	−4.45524	−	2.57223i	−0.544294	−	0.314248i	−0.746818	+	0.665029i	$0.768419\pi$
$68$	0.248564			0.0301428
$69$	1.86529	−	3.23078i	0.224555	−	0.388940i
$70$	−0.794706	+	1.12701i	−0.0949856	+	0.134704i
$71$	−3.20326	−	1.84940i	−0.380157	−	0.219484i	0.297730	−	0.954650i	$-0.403771\pi$
$71$	−3.20326	−	1.84940i	−0.380157	−	0.219484i	−0.677887	+	0.735167i	$0.737104\pi$
$72$	3.69921	−	2.13574i	0.435956	−	0.251700i
$73$	5.72686	−	3.30640i	0.670278	−	0.386985i	−0.125904	−	0.992042i	$-0.540183\pi$
$73$	5.72686	−	3.30640i	0.670278	−	0.386985i	0.796182	+	0.605057i	$0.206850\pi$
$74$	0.421582			0.0490079
$75$	3.32470			0.383903
$76$	−8.35036	+	4.82108i	−0.957852	+	0.553016i
$77$	−8.57829	−	6.04892i	−0.977587	−	0.689339i
$78$	−1.21576	−	0.931521i	−0.137657	−	0.105474i
$79$	−5.96135	+	10.3254i	−0.670705	+	1.16169i	0.307000	+	0.951710i	$0.400675\pi$
$79$	−5.96135	+	10.3254i	−0.670705	+	1.16169i	−0.977705	+	0.209985i	$0.932658\pi$
$80$	−2.31352	−	1.33571i	−0.258659	−	0.149337i
$81$	−1.51231	+	2.61940i	−0.168035	+	0.291045i
$82$	−3.02426	−	5.23818i	−0.333974	−	0.578460i
$83$			2.87321i			0.315376i	0.987489	+	0.157688i	$0.0504040\pi$
$83$			2.87321i			0.315376i	−0.987489	+	0.157688i	$0.949596\pi$
$84$	−2.26694	+	3.21486i	−0.247343	+	0.350770i
$85$	−0.128231	−	0.0740342i	−0.0139086	−	0.00803013i
$86$	−2.08846	−	1.20578i	−0.225205	−	0.130022i
$87$	−7.13461			−0.764910
$88$	−3.71926	+	6.44195i	−0.396475	+	0.686714i
$89$		−	1.74765i		−	0.185250i	−0.995701	−	0.0926252i	$-0.970474\pi$
$89$		−	1.74765i		−	0.185250i	0.995701	−	0.0926252i	$-0.0295258\pi$
$90$	−1.18744			−0.125167
$91$	−9.30787	−	2.08890i	−0.975730	−	0.218976i
$92$	−7.68427			−0.801141
$93$			2.41841i			0.250777i
$94$	−1.13909	+	1.97296i	−0.117488	+	0.203495i
$95$	5.74379			0.589301
$96$	3.70181	+	2.13724i	0.377815	+	0.218131i
$97$	2.34079	+	1.35145i	0.237671	+	0.137219i	0.614106	−	0.789224i	$-0.289517\pi$
$97$	2.34079	+	1.35145i	0.237671	+	0.137219i	−0.376435	+	0.926443i	$0.622850\pi$
$98$	0.630517	−	3.44264i	0.0636919	−	0.347759i
$99$		−	9.03822i		−	0.908376i
$100$	−3.42412	−	5.93074i	−0.342412	−	0.593074i
$101$	5.73612	−	9.93524i	0.570765	−	0.988594i	−0.425723	−	0.904854i	$-0.639980\pi$
$101$	5.73612	−	9.93524i	0.570765	−	0.988594i	0.996488	−	0.0837401i	$-0.0266866\pi$
$102$	0.0522517	+	0.0301676i	0.00517369	+	0.00298703i
$103$	2.08475	−	3.61090i	0.205417	−	0.355792i	−0.744849	−	0.667233i	$-0.767478\pi$
$103$	2.08475	−	3.61090i	0.205417	−	0.355792i	0.950265	+	0.311441i	$0.100812\pi$
$104$	−0.877660	+	6.70304i	−0.0860617	+	0.657287i
$105$	2.12702	−	0.983303i	0.207576	−	0.0959606i
$106$	0.121067	−	0.0698982i	0.0117591	−	0.00678911i
$107$	8.48742			0.820510			0.410255	−	0.911971i	$-0.365440\pi$
$107$	8.48742			0.820510			0.410255	+	0.911971i	$0.365440\pi$
$108$	−7.84767			−0.755142
$109$	5.56886	−	3.21518i	0.533400	−	0.307958i	−0.209000	−	0.977916i	$-0.567021\pi$
$109$	5.56886	−	3.21518i	0.533400	−	0.307958i	0.742400	+	0.669957i	$0.233688\pi$
$110$	1.79081	−	1.03393i	0.170747	−	0.0985810i
$111$	−0.620397	−	0.358186i	−0.0588855	−	0.0339975i
$112$	6.75214	+	0.613225i	0.638018	+	0.0579443i
$113$	−5.48164	+	9.49448i	−0.515670	+	0.893166i	0.484165	+	0.874977i	$0.339123\pi$
$113$	−5.48164	+	9.49448i	−0.515670	+	0.893166i	−0.999835	+	0.0181892i	$0.994210\pi$
$114$	−2.34049			−0.219207
$115$	3.96422	+	2.28874i	0.369665	+	0.213426i
$116$	7.34795	+	12.7270i	0.682240	+	1.18167i
$117$	−3.14875	−	7.58661i	−0.291102	−	0.701382i
$118$	5.39060			0.496245
$119$	0.374250	+	0.0339891i	0.0343074	+	0.00311578i
$120$	−0.830314	−	1.43815i	−0.0757969	−	0.131284i
$121$	2.36975	+	4.10453i	0.215432	+	0.373139i
$122$	2.53892	−	1.46584i	0.229863	−	0.132711i
$123$			10.2780i			0.926732i
$124$	4.31406	−	2.49073i	0.387414	−	0.223674i
$125$			9.29184i			0.831087i
$126$	2.73550	−	1.26460i	0.243698	−	0.112659i
$127$	−1.00394	−	1.73887i	−0.0890849	−	0.154300i	0.818040	−	0.575162i	$-0.195061\pi$
$127$	−1.00394	−	1.73887i	−0.0890849	−	0.154300i	−0.907125	+	0.420862i	$0.861728\pi$
$128$		−	11.3671i		−	1.00472i
$129$	2.04891	+	3.54882i	0.180397	+	0.312456i
$130$	1.14299	−	1.49175i	0.100247	−	0.130836i
$131$	6.22511	−	10.7822i	0.543890	−	0.942046i	−0.454785	−	0.890601i	$-0.650284\pi$
$131$	6.22511	−	10.7822i	0.543890	−	0.942046i	0.998676	−	0.0514449i	$-0.0163826\pi$
$132$	5.10838	−	2.94932i	0.444627	−	0.256706i
$133$	−13.2320	+	6.11702i	−1.14736	+	0.530413i
$134$	−1.28608	+	2.22756i	−0.111101	+	0.192432i
$135$	4.04851	+	2.33741i	0.348441	+	0.201172i
$136$		−	0.266310i		−	0.0228359i
$137$			5.24518i			0.448126i	0.974575	+	0.224063i	$0.0719321\pi$
$137$			5.24518i			0.448126i	−0.974575	+	0.224063i	$0.928068\pi$
$138$	−1.61535	−	0.932620i	−0.137507	−	0.0793899i
$139$	10.3693	−	17.9601i	0.879510	−	1.52336i	0.0276301	−	0.999618i	$-0.491204\pi$
$139$	10.3693	−	17.9601i	0.879510	−	1.52336i	0.851880	−	0.523737i	$-0.175463\pi$
$140$	−3.94468	−	2.78157i	−0.333387	−	0.235085i
$141$	3.35255	−	1.93559i	0.282335	−	0.163006i
$142$	−0.924676	+	1.60159i	−0.0775971	+	0.134402i
$143$	11.3545	+	8.69991i	0.949513	+	0.727523i
$144$	2.91900	+	5.05585i	0.243250	+	0.421321i
$145$		−	8.75428i		−	0.727004i
$146$	−1.65316	−	2.86335i	−0.136816	−	0.236973i
$147$	−3.85282	+	4.53046i	−0.317775	+	0.373666i
$148$			1.47559i			0.121293i
$149$	0.00985188	−	0.00568799i	0.000807098	−	0.000465978i	−0.499596	−	0.866258i	$-0.666518\pi$
$149$	0.00985188	−	0.00568799i	0.000807098	−	0.000465978i	0.500403	+	0.865792i	$0.333185\pi$
$150$		−	1.66231i		−	0.135727i
$151$	−16.3726	+	9.45271i	−1.33238	+	0.769251i	−0.985664	−	0.168719i	$-0.946037\pi$
$151$	−16.3726	+	9.45271i	−1.33238	+	0.769251i	−0.346717	+	0.937970i	$0.612704\pi$
$152$	5.16529	+	8.94654i	0.418960	+	0.725660i
$153$	0.161791	+	0.280230i	0.0130800	+	0.0226553i
$154$	−3.02438	+	4.28903i	−0.243712	+	0.345620i
$155$	−2.96743			−0.238350
$156$	3.26044	−	4.25530i	0.261044	−	0.340696i
$157$	−9.89687	−	17.1419i	−0.789856	−	1.36807i	−0.926054	−	0.377390i	$-0.876822\pi$
$157$	−9.89687	−	17.1419i	−0.789856	−	1.36807i	0.136198	−	0.990682i	$-0.456512\pi$
$158$	5.16255	+	2.98060i	0.410710	+	0.237124i
$159$	−0.237549			−0.0188388
$160$	−2.62243	+	4.54219i	−0.207321	+	0.359091i
$161$	−11.5698	−	1.05076i	−0.911830	−	0.0828117i
$162$	1.30967	+	0.756136i	0.102897	+	0.0594076i
$163$	7.73581	−	4.46627i	0.605915	−	0.349825i	−0.165450	−	0.986218i	$-0.552908\pi$
$163$	7.73581	−	4.46627i	0.605915	−	0.349825i	0.771365	+	0.636393i	$0.219574\pi$
$164$	18.3343	−	10.5853i	1.43167	−	0.826572i
$165$	−3.51380			−0.273549
$166$	1.43657			0.111499
$167$	5.31279	−	3.06734i	0.411116	−	0.237358i	−0.280153	−	0.959955i	$-0.590385\pi$
$167$	5.31279	−	3.06734i	0.411116	−	0.237358i	0.691269	+	0.722597i	$0.257052\pi$
$168$	3.44438	+	2.42879i	0.265740	+	0.187385i
$169$	12.5618	+	3.34692i	0.966290	+	0.257456i
$170$	−0.0370161	+	0.0641138i	−0.00283900	+	0.00491730i
$171$	−10.8705	−	6.27611i	−0.831291	−	0.479946i
$172$	4.22036	−	7.30987i	0.321799	−	0.557373i
$173$	12.1314	+	21.0122i	0.922332	+	1.59753i	0.795797	+	0.605563i	$0.207052\pi$
$173$	12.1314	+	21.0122i	0.922332	+	1.59753i	0.126535	+	0.991962i	$0.459614\pi$
$174$			3.56721i			0.270429i
$175$	−4.34454	−	9.39784i	−0.328416	−	0.710410i
$176$	−8.80446	−	5.08325i	−0.663661	−	0.383165i
$177$	−7.93277	−	4.57999i	−0.596263	−	0.344253i
$178$	−0.873801			−0.0654942
$179$	−2.06838	+	3.58253i	−0.154598	+	0.267771i	−0.932912	−	0.360103i	$-0.882741\pi$
$179$	−2.06838	+	3.58253i	−0.154598	+	0.267771i	0.778315	+	0.627874i	$0.216075\pi$
$180$		−	4.15618i		−	0.309784i
$181$	−7.86568			−0.584651			−0.292326	−	0.956319i	$-0.594429\pi$
$181$	−7.86568			−0.584651			−0.292326	+	0.956319i	$0.594429\pi$
$182$	−1.04442	+	4.65381i	−0.0774176	+	0.344964i
$183$	−4.98167			−0.368256
$184$			8.23289i			0.606937i
$185$	0.439501	−	0.761237i	0.0323127	−	0.0559673i
$186$	1.20917			0.0886608
$187$	−0.488003	−	0.281749i	−0.0356863	−	0.0206035i
$188$	−6.90560	−	3.98695i	−0.503642	−	0.290778i
$189$	−11.8158	−	1.07311i	−0.859476	−	0.0780570i
$190$		−	2.87182i		−	0.208344i
$191$	3.23933	+	5.61069i	0.234390	+	0.405975i	0.959095	−	0.283084i	$-0.0913574\pi$
$191$	3.23933	+	5.61069i	0.234390	+	0.405975i	−0.724705	+	0.689059i	$0.758024\pi$
$192$	−1.10857	+	1.92011i	−0.0800044	+	0.138572i
$193$	4.18228	+	2.41464i	0.301047	+	0.173810i	0.642913	−	0.765939i	$-0.277726\pi$
$193$	4.18228	+	2.41464i	0.301047	+	0.173810i	−0.341866	+	0.939749i	$0.611059\pi$
$194$	0.675708	−	1.17036i	0.0485130	−	0.0840270i
$195$	−2.94945	+	1.22414i	−0.211214	+	0.0876626i
$196$	12.0497	+	2.20689i	0.860690	+	0.157635i
$197$	−22.3748	+	12.9181i	−1.59414	+	0.920377i	−0.601554	+	0.798832i	$0.705452\pi$
$197$	−22.3748	+	12.9181i	−1.59414	+	0.920377i	−0.992586	+	0.121545i	$0.961215\pi$
$198$	−4.51899			−0.321151
$199$	−17.1146			−1.21322			−0.606612	−	0.794998i	$-0.707472\pi$
$199$	−17.1146			−1.21322			−0.606612	+	0.794998i	$0.707472\pi$
$200$	−6.35417	+	3.66858i	−0.449308	+	0.259408i
$201$	3.78518	−	2.18537i	0.266986	−	0.154144i
$202$	−4.96749	−	2.86798i	−0.349511	−	0.201790i
$203$	9.32312	+	20.1672i	0.654355	+	1.41546i
$204$	−0.105590	+	0.182887i	−0.00739278	+	0.0128047i
$205$	−12.6112			−0.880806
$206$	−1.80540	−	1.04235i	−0.125788	−	0.0726238i
$207$	−5.00171	−	8.66322i	−0.347643	−	0.602136i
$208$	−9.16129	−	1.19953i	−0.635221	−	0.0831725i
$209$	21.8589			1.51201
$210$	−0.491638	−	1.06348i	−0.0339263	−	0.0733873i
$211$	−9.14557	−	15.8406i	−0.629607	−	1.09051i	−0.987631	−	0.156799i	$-0.949883\pi$
$211$	−9.14557	−	15.8406i	−0.629607	−	1.09051i	0.358024	−	0.933713i	$-0.383451\pi$
$212$	0.244652	+	0.423750i	0.0168028	+	0.0291032i
$213$	2.72149	−	1.57125i	0.186474	−	0.107661i
$214$		−	4.24360i		−	0.290086i
$215$	−4.35446	+	2.51405i	−0.296972	+	0.171457i
$216$			8.40796i			0.572089i
$217$	6.83606	−	3.16025i	0.464062	−	0.214532i
$218$	−1.60755	−	2.78435i	−0.108877	−	0.188580i
$219$			5.61825i			0.379646i
$220$	3.61887	+	6.26806i	0.243984	+	0.422593i
$221$	−0.507782	−	0.0664862i	−0.0341571	−	0.00447235i
$222$	−0.179088	+	0.310190i	−0.0120196	+	0.0208186i
$223$	−9.96682	+	5.75435i	−0.667428	+	0.385340i	−0.795101	−	0.606477i	$-0.792582\pi$
$223$	−9.96682	+	5.75435i	−0.667428	+	0.385340i	0.127674	+	0.991816i	$0.459249\pi$
$224$	1.20396	−	13.2567i	0.0804430	−	0.885747i
$225$	4.45753	−	7.72067i	0.297169	−	0.514712i
$226$	4.74711	+	2.74075i	0.315773	+	0.182312i
$227$			17.9045i			1.18836i	0.804332	+	0.594181i	$0.202524\pi$
$227$			17.9045i			1.18836i	−0.804332	+	0.594181i	$0.797476\pi$
$228$		−	8.19200i		−	0.542528i
$229$	−3.34589	−	1.93175i	−0.221103	−	0.127654i	0.385358	−	0.922767i	$-0.374078\pi$
$229$	−3.34589	−	1.93175i	−0.221103	−	0.127654i	−0.606461	+	0.795113i	$0.707411\pi$
$230$	1.14434	−	1.98206i	0.0754556	−	0.130693i
$231$	8.09472	−	3.74212i	0.532593	−	0.246213i
$232$	13.6357	−	7.87256i	0.895226	−	0.516859i
$233$	12.5321	−	21.7062i	0.821004	−	1.42202i	−0.0839312	−	0.996472i	$-0.526748\pi$
$233$	12.5321	−	21.7062i	0.821004	−	1.42202i	0.904935	−	0.425549i	$-0.139919\pi$
$234$	−3.79320	+	1.57433i	−0.247969	+	0.102917i
$235$	2.37501	+	4.11363i	0.154928	+	0.268344i
$236$			18.8678i			1.22819i
$237$	−5.06477	−	8.77245i	−0.328992	−	0.569832i
$238$	0.0169941	−	0.187120i	0.00110156	−	0.0121292i
$239$			7.80462i			0.504839i	0.967618	+	0.252419i	$0.0812263\pi$
$239$			7.80462i			0.504839i	−0.967618	+	0.252419i	$0.918774\pi$
$240$	1.96557	−	1.13482i	0.126877	−	0.0732524i
$241$			21.7653i			1.40202i	0.713150	+	0.701012i	$0.247268\pi$
$241$			21.7653i			1.40202i	−0.713150	+	0.701012i	$0.752732\pi$
$242$	2.05221	−	1.18484i	0.131921	−	0.0761647i
$243$	−8.01138	−	13.8761i	−0.513930	−	0.890154i
$244$	5.13063	+	8.88652i	0.328455	+	0.568901i
$245$	−5.55895	−	4.72747i	−0.355149	−	0.302027i
$246$	5.13884			0.327640
$247$	18.3482	−	7.61524i	1.16747	−	0.484546i
$248$	−2.66855	−	4.62207i	−0.169453	−	0.293502i
$249$	−2.11404	−	1.22054i	−0.133972	−	0.0773488i
$250$	4.64579			0.293826
$251$	3.83990	−	6.65090i	0.242372	−	0.419801i	−0.719017	−	0.694992i	$-0.755408\pi$
$251$	3.83990	−	6.65090i	0.242372	−	0.419801i	0.961390	+	0.275191i	$0.0887411\pi$
$252$	4.42624	+	9.57458i	0.278827	+	0.603142i
$253$	15.0865	+	8.71017i	0.948478	+	0.547604i
$254$	−0.869411	+	0.501955i	−0.0545517	+	0.0314954i
$255$	0.108945	−	0.0628995i	0.00682241	−	0.00393892i
$256$	−0.464141			−0.0290088
$257$	−13.6237			−0.849826			−0.424913	−	0.905234i	$-0.639695\pi$
$257$	−13.6237			−0.849826			−0.424913	+	0.905234i	$0.639695\pi$
$258$	1.77436	−	1.02443i	0.110467	−	0.0637781i
$259$	−0.201775	+	2.22172i	−0.0125377	+	0.138051i
$260$	5.22132	+	4.00061i	0.323813	+	0.248107i
$261$	−9.56560	+	16.5681i	−0.592096	+	1.02554i
$262$	−5.39096	−	3.11247i	−0.333055	−	0.192289i
$263$	5.86158	−	10.1525i	0.361440	−	0.626033i	−0.626758	−	0.779214i	$-0.715618\pi$
$263$	5.86158	−	10.1525i	0.361440	−	0.626033i	0.988198	+	0.153181i	$0.0489518\pi$
$264$	−3.15989	−	5.47309i	−0.194478	−	0.336845i
$265$		−	0.291476i		−	0.0179052i
$266$	3.05843	+	6.61580i	0.187524	+	0.405641i
$267$	1.28588	+	0.742403i	0.0786945	+	0.0454343i
$268$	−7.79673	−	4.50144i	−0.476261	−	0.274970i
$269$	9.19876			0.560858			0.280429	−	0.959875i	$-0.409523\pi$
$269$	9.19876			0.560858			0.280429	+	0.959875i	$0.409523\pi$
$270$	1.16867	−	2.02420i	0.0711232	−	0.123189i
$271$		−	2.56369i		−	0.155733i	−0.996964	−	0.0778665i	$-0.975189\pi$
$271$		−	2.56369i		−	0.155733i	0.996964	−	0.0778665i	$-0.0248108\pi$
$272$	0.363976			0.0220693
$273$	5.49095	−	5.96115i	0.332328	−	0.360785i
$274$	2.62252			0.158432
$275$			15.5250i			0.936195i
$276$	3.26428	−	5.65391i	0.196487	−	0.340325i
$277$	0.933882			0.0561115			0.0280558	−	0.999606i	$-0.491068\pi$
$277$	0.933882			0.0561115			0.0280558	+	0.999606i	$0.491068\pi$
$278$	−8.97981	−	5.18450i	−0.538573	−	0.310945i
$279$	5.61607	+	3.24244i	0.336226	+	0.194120i
$280$	−2.98016	+	4.22632i	−0.178099	+	0.252571i
$281$			6.45288i			0.384947i	0.981302	+	0.192473i	$0.0616509\pi$
$281$			6.45288i			0.384947i	−0.981302	+	0.192473i	$0.938349\pi$
$282$	−0.967771	−	1.67623i	−0.0576299	−	0.0998180i
$283$	11.0873	−	19.2037i	0.659071	−	1.14154i	−0.321786	−	0.946812i	$-0.604283\pi$
$283$	11.0873	−	19.2037i	0.659071	−	1.14154i	0.980857	−	0.194731i	$-0.0623835\pi$
$284$	−5.60575	−	3.23648i	−0.332640	−	0.192050i
$285$	−2.43997	+	4.22615i	−0.144531	+	0.250335i
$286$	4.34984	−	5.67711i	0.257211	−	0.335695i
$287$	29.0524	−	13.4307i	1.71491	−	0.792788i
$288$	9.92629	−	5.73094i	0.584912	−	0.337699i
$289$	−16.9798			−0.998813
$290$	−4.37702			−0.257028
$291$	−1.98873	+	1.14820i	−0.116582	+	0.0673085i
$292$	10.0221	−	5.78625i	0.586498	−	0.338615i
$293$	−20.9600	−	12.1013i	−1.22450	−	0.706964i	−0.258624	−	0.965978i	$-0.583269\pi$
$293$	−20.9600	−	12.1013i	−1.22450	−	0.706964i	−0.965874	+	0.259014i	$0.916602\pi$
$294$	2.26517	+	1.92636i	0.132107	+	0.112347i
$295$	5.61972	−	9.73364i	0.327193	−	0.566714i
$296$	1.58094			0.0918902
$297$	15.4073	+	8.89539i	0.894020	+	0.516163i
$298$	−0.00284392	−	0.00492581i	−0.000164744	−	0.000285345i
$299$	15.6979	+	2.05540i	0.907833	+	0.118867i
$300$	5.81827			0.335918
$301$	7.35395	−	10.4290i	0.423875	−	0.601118i
$302$	4.72623	+	8.18607i	0.271964	+	0.471055i
$303$	4.87341	+	8.44100i	0.279970	+	0.484923i
$304$	−12.2276	+	7.05959i	−0.701299	+	0.404895i
$305$		−	6.11259i		−	0.350006i
$306$	0.140111	−	0.0808933i	0.00800963	−	0.00462436i
$307$			24.2924i			1.38644i	0.720726	+	0.693220i	$0.243809\pi$
$307$			24.2924i			1.38644i	−0.720726	+	0.693220i	$0.756191\pi$
$308$	−15.0121	−	10.5857i	−0.855395	−	0.603176i
$309$	1.77121	+	3.06782i	0.100761	+	0.174522i
$310$			1.48367i			0.0842671i
$311$	1.99355	+	3.45294i	0.113044	+	0.195798i	0.916996	−	0.398896i	$-0.130607\pi$
$311$	1.99355	+	3.45294i	0.113044	+	0.195798i	−0.803952	+	0.594694i	$0.797273\pi$
$312$	−4.55911	−	3.49322i	−0.258109	−	0.197764i
$313$	−14.2377	+	24.6604i	−0.804763	+	1.39389i	0.111688	+	0.993743i	$0.464374\pi$
$313$	−14.2377	+	24.6604i	−0.804763	+	1.39389i	−0.916451	+	0.400147i	$0.868959\pi$
$314$	−8.57071	+	4.94830i	−0.483673	+	0.279249i
$315$	0.568325	−	6.25775i	0.0320215	−	0.352585i
$316$	−10.4324	+	18.0695i	−0.586871	+	1.01649i
$317$	−14.5632	−	8.40806i	−0.817950	−	0.472244i	0.0317591	−	0.999496i	$-0.489889\pi$
$317$	−14.5632	−	8.40806i	−0.817950	−	0.472244i	−0.849709	+	0.527252i	$0.823222\pi$
$318$			0.118771i			0.00666036i
$319$		−	33.3158i		−	1.86533i
$320$	−2.35600	−	1.36024i	−0.131704	−	0.0760396i
$321$	−3.60546	+	6.24485i	−0.201237	+	0.348553i
$322$	−0.525367	+	5.78476i	−0.0292776	+	0.322372i
$323$	−0.677736	+	0.391291i	−0.0377102	+	0.0217720i
$324$	−2.64657	+	4.58399i	−0.147031	+	0.254666i
$325$	5.40863	+	13.0316i	0.300017	+	0.722862i
$326$	−2.23308	−	3.86780i	−0.123679	−	0.214218i
$327$			5.46324i			0.302118i
$328$	−11.3410	−	19.6432i	−0.626204	−	1.08462i
$329$	−9.85222	−	6.94723i	−0.543171	−	0.383013i
$330$			1.75685i			0.0967115i
$331$	5.37730	−	3.10459i	0.295563	−	0.170644i	−0.344885	−	0.938645i	$-0.612082\pi$
$331$	5.37730	−	3.10459i	0.295563	−	0.170644i	0.640448	+	0.768002i	$0.278749\pi$
$332$			5.02816i			0.275956i
$333$	−1.66357	+	0.960464i	−0.0911632	+	0.0526331i
$334$	−1.53363	−	2.65633i	−0.0839165	−	0.145348i
$335$	2.68149	+	4.64448i	0.146505	+	0.253755i
$336$	−3.31951	+	4.70757i	−0.181094	+	0.256819i
$337$	7.69650			0.419255			0.209628	−	0.977781i	$-0.432775\pi$
$337$	7.69650			0.419255			0.209628	+	0.977781i	$0.432775\pi$
$338$	1.67342	−	6.28072i	0.0910219	−	0.341626i
$339$	−4.65721	−	8.06653i	−0.252945	−	0.438114i
$340$	−0.224406	−	0.129561i	−0.0121701	−	0.00702642i
$341$	−11.2930			−0.611552
$342$	−3.13797	+	5.43513i	−0.169682	+	0.293898i
$343$	17.8408	+	4.97049i	0.963313	+	0.268381i
$344$	−7.83177	−	4.52167i	−0.422261	−	0.243792i
$345$	−3.36801	+	1.94452i	−0.181327	+	0.104689i
$346$	10.5058	−	6.06553i	0.564795	−	0.326085i
$347$	30.4094			1.63246			0.816231	−	0.577725i	$-0.196059\pi$
$347$	30.4094			1.63246			0.816231	+	0.577725i	$0.196059\pi$
$348$	−12.4857			−0.669302
$349$	−13.9933	+	8.07906i	−0.749046	+	0.432462i	−0.825349	−	0.564623i	$-0.809022\pi$
$349$	−13.9933	+	8.07906i	−0.749046	+	0.432462i	0.0763028	+	0.997085i	$0.475688\pi$
$350$	−4.69880	+	2.17221i	−0.251161	+	0.116110i
$351$	16.0317	+	2.09911i	0.855709	+	0.112042i
$352$	−9.98008	+	17.2860i	−0.531940	+	0.921347i
$353$	−10.2558	−	5.92119i	−0.545861	−	0.315153i	0.201590	−	0.979470i	$-0.435389\pi$
$353$	−10.2558	−	5.92119i	−0.545861	−	0.315153i	−0.747451	+	0.664317i	$0.768723\pi$
$354$	−2.28993	+	3.96628i	−0.121709	+	0.210805i
$355$	1.92796	+	3.33932i	0.102325	+	0.177233i
$356$		−	3.05841i		−	0.162095i
$357$	−0.183990	+	0.260926i	−0.00973779	+	0.0138097i
$358$	1.79122	+	1.03416i	0.0946688	+	0.0546571i
$359$	−27.1631	−	15.6826i	−1.43362	−	0.827698i	−0.436221	−	0.899840i	$-0.643683\pi$
$359$	−27.1631	−	15.6826i	−1.43362	−	0.827698i	−0.997394	+	0.0721417i	$0.977017\pi$
$360$	−4.45292			−0.234689
$361$	5.67876	−	9.83591i	0.298882	−	0.517679i
$362$			3.93273i			0.206700i
$363$	−4.02669			−0.211346
$364$	−16.2889	−	3.65560i	−0.853770	−	0.191605i
$365$	−6.89369			−0.360832
$366$			2.49077i			0.130195i
$367$	−12.0387	+	20.8517i	−0.628415	+	1.08845i	0.359454	+	0.933163i	$0.382963\pi$
$367$	−12.0387	+	20.8517i	−0.628415	+	1.08845i	−0.987870	+	0.155285i	$0.950370\pi$
$368$	−11.2522			−0.586562
$369$	23.8676	+	13.7800i	1.24250	+	0.717358i
$370$	−0.380608	−	0.219744i	−0.0197869	−	0.0114240i
$371$	0.310416	+	0.671473i	0.0161160	+	0.0348611i
$372$			4.23225i			0.219432i
$373$	9.19612	+	15.9281i	0.476157	+	0.824728i	0.999627	−	0.0273160i	$-0.00869604\pi$
$373$	9.19612	+	15.9281i	0.476157	+	0.824728i	−0.523470	+	0.852044i	$0.675363\pi$
$374$	−0.140871	+	0.243995i	−0.00728425	+	0.0126167i
$375$	−6.83672	−	3.94718i	−0.353046	−	0.203831i
$376$	−4.27160	+	7.39862i	−0.220291	+	0.381555i
$377$	−11.6066	−	27.9650i	−0.597771	−	1.44027i
$378$	−0.536539	+	5.90776i	−0.0275966	+	0.303862i
$379$	−7.04719	+	4.06870i	−0.361990	+	0.208995i	−0.669953	−	0.742403i	$-0.733686\pi$
$379$	−7.04719	+	4.06870i	−0.361990	+	0.208995i	0.307963	+	0.951398i	$0.400353\pi$
$380$	10.0517			0.515642
$381$	1.70589			0.0873955
$382$	2.80527	−	1.61962i	0.143530	−	0.0828671i
$383$	−19.3739	+	11.1856i	−0.989962	+	0.571555i	−0.905263	−	0.424852i	$-0.860326\pi$
$383$	−19.3739	+	11.1856i	−0.989962	+	0.571555i	−0.0846992	+	0.996407i	$0.526993\pi$
$384$	8.36365	+	4.82876i	0.426806	+	0.246417i
$385$	4.59164	+	9.93236i	0.234012	+	0.506200i
$386$	1.20729	−	2.09108i	0.0614493	−	0.106433i
$387$	10.9882			0.558560
$388$	4.09641	+	2.36506i	0.207963	+	0.120068i
$389$	−10.6973	−	18.5283i	−0.542374	−	0.939420i	−0.998767	−	0.0496415i	$-0.984192\pi$
$389$	−10.6973	−	18.5283i	−0.542374	−	0.939420i	0.456393	−	0.889778i	$-0.349141\pi$
$390$	0.612054	+	1.47469i	0.0309926	+	0.0746736i
$391$	−0.623674			−0.0315406
$392$	2.36445	−	12.9100i	0.119423	−	0.652051i
$393$	5.28886	+	9.16058i	0.266788	+	0.462090i
$394$	6.45888	+	11.1871i	0.325394	+	0.563599i
$395$	10.7639	−	6.21456i	0.541592	−	0.312689i
$396$		−	15.8170i		−	0.794835i
$397$	1.03640	−	0.598365i	0.0520154	−	0.0300311i	−0.473767	−	0.880650i	$-0.657106\pi$
$397$	1.03640	−	0.598365i	0.0520154	−	0.0300311i	0.525782	+	0.850619i	$0.323773\pi$
$398$			8.55708i			0.428928i
$399$	1.12019	−	12.3343i	0.0560797	−	0.617486i
$400$	−5.01399	−	8.68449i	−0.250699	−	0.434224i
$401$		−	36.2749i		−	1.81148i	−0.423831	−	0.905741i	$-0.639315\pi$
$401$		−	36.2749i		−	1.81148i	0.423831	−	0.905741i	$-0.360685\pi$
$402$	−1.09266	−	1.89254i	−0.0544968	−	0.0943913i
$403$	−9.47926	+	3.93428i	−0.472196	+	0.195980i
$404$	10.0383	−	17.3868i	0.499423	−	0.865026i
$405$	2.73066	−	1.57655i	0.135688	−	0.0783393i
$406$	10.0833	−	4.66144i	0.500428	−	0.231343i
$407$	1.67259	−	2.89701i	0.0829072	−	0.143599i
$408$	0.195945	+	0.113129i	0.00970071	+	0.00560071i
$409$		−	14.6723i		−	0.725500i	−0.931887	−	0.362750i	$-0.881838\pi$
$409$		−	14.6723i		−	0.725500i	0.931887	−	0.362750i	$-0.118162\pi$
$410$			6.30544i			0.311404i
$411$	−3.85928	−	2.22816i	−0.190364	−	0.109907i
$412$	3.64834	−	6.31912i	0.179741	−	0.311321i
$413$	−2.58002	+	28.4082i	−0.126954	+	1.39788i
$414$	−4.33150	+	2.50079i	−0.212881	+	0.122907i
$415$	1.49763	−	2.59397i	0.0735156	−	0.127333i
$416$	−2.35507	+	17.9866i	−0.115467	+	0.881866i
$417$	8.80975	+	15.2589i	0.431415	+	0.747233i
$418$		−	10.9292i		−	0.534563i
$419$	2.96674	+	5.13855i	0.144935	+	0.251034i	0.929349	−	0.369203i	$-0.120369\pi$
$419$	2.96674	+	5.13855i	0.144935	+	0.251034i	−0.784414	+	0.620238i	$0.787036\pi$
$420$	3.72232	−	1.72079i	0.181630	−	0.0839661i
$421$		−	2.63174i		−	0.128263i	−0.997941	−	0.0641317i	$-0.979572\pi$
$421$		−	2.63174i		−	0.128263i	0.997941	−	0.0641317i	$-0.0204278\pi$
$422$	−7.92008	+	4.57266i	−0.385544	+	0.222594i
$423$		−	10.3805i		−	0.504715i
$424$	0.454004	−	0.262119i	0.0220484	−	0.0127296i
$425$	−0.277910	−	0.481354i	−0.0134806	−	0.0233491i
$426$	−0.785606	−	1.36071i	−0.0380628	−	0.0659266i
$427$	6.50978	+	14.0816i	0.315030	+	0.681454i
$428$	14.8531			0.717952
$429$	−11.2246	+	4.65866i	−0.541929	+	0.224922i
$430$	1.25699	+	2.17717i	0.0606175	+	0.104993i
$431$	16.3139	+	9.41883i	0.785812	+	0.453689i	0.838486	−	0.544923i	$-0.183441\pi$
$431$	16.3139	+	9.41883i	0.785812	+	0.453689i	−0.0526738	+	0.998612i	$0.516774\pi$
$432$	−11.4915			−0.552884
$433$	9.56773	−	16.5718i	0.459796	−	0.796389i	−0.539154	−	0.842207i	$-0.681256\pi$
$433$	9.56773	−	16.5718i	0.459796	−	0.796389i	0.998950	+	0.0458176i	$0.0145893\pi$
$434$	−1.58008	−	3.41794i	−0.0758463	−	0.164066i
$435$	6.44119	+	3.71883i	0.308832	+	0.178304i
$436$	9.74557	−	5.62661i	0.466728	−	0.269466i
$437$	20.9520	−	12.0966i	1.00227	−	0.578660i
$438$	2.80905			0.134222
$439$	1.26511			0.0603803			0.0301901	−	0.999544i	$-0.490389\pi$
$439$	1.26511			0.0603803			0.0301901	+	0.999544i	$0.490389\pi$
$440$	6.71557	−	3.87724i	0.320152	−	0.184840i
$441$	5.35512	+	15.0212i	0.255006	+	0.715296i
$442$	−0.0332422	+	0.253884i	−0.00158117	+	0.0120760i
$443$	10.4696	−	18.1339i	0.497426	−	0.861568i	−0.502569	−	0.864537i	$-0.667612\pi$
$443$	10.4696	−	18.1339i	0.497426	−	0.861568i	0.999996	+	0.00296930i	$0.000945159\pi$
$444$	−1.08570	−	0.626831i	−0.0515252	−	0.0297481i
$445$	−0.910940	+	1.57779i	−0.0431827	+	0.0747946i
$446$	2.87710	+	4.98328i	0.136234	+	0.235965i
$447$			0.00966505i			0.000457141i
$448$	6.87614	+	0.624486i	0.324867	+	0.0295042i
$449$	15.4700	+	8.93162i	0.730075	+	0.421509i	0.818450	−	0.574578i	$-0.194834\pi$
$449$	15.4700	+	8.93162i	0.730075	+	0.421509i	−0.0883746	+	0.996087i	$0.528167\pi$
$450$	−3.86023	−	2.22871i	−0.181973	−	0.105062i
$451$	−47.9940			−2.25995
$452$	−9.59295	+	16.6155i	−0.451214	+	0.781526i
$453$		−	16.0621i		−	0.754662i
$454$	8.95199			0.420138
$455$	7.31443	+	6.73749i	0.342906	+	0.315858i
$456$	−8.77687			−0.411015
$457$			6.56597i			0.307143i	0.988138	+	0.153571i	$0.0490775\pi$
$457$			6.56597i			0.307143i	−0.988138	+	0.153571i	$0.950922\pi$
$458$	−0.965850	+	1.67290i	−0.0451312	+	0.0781695i
$459$	−0.636936			−0.0297296
$460$	6.93744	+	4.00533i	0.323460	+	0.186749i
$461$	−4.42854	−	2.55682i	−0.206258	−	0.119083i	0.393313	−	0.919404i	$-0.371329\pi$
$461$	−4.42854	−	2.55682i	−0.206258	−	0.119083i	−0.599571	+	0.800322i	$0.704662\pi$
$462$	−1.87101	−	4.04725i	−0.0870472	−	0.188295i
$463$		−	33.3239i		−	1.54869i	−0.632761	−	0.774347i	$-0.718079\pi$
$463$		−	33.3239i		−	1.54869i	0.632761	−	0.774347i	$-0.281921\pi$
$464$	10.7597	+	18.6364i	0.499508	+	0.865173i
$465$	1.26057	−	2.18336i	0.0584574	−	0.101251i
$466$	−10.8528	−	6.26587i	−0.502747	−	0.290261i
$467$	−6.47472	+	11.2145i	−0.299614	+	0.518947i	−0.976048	−	0.217557i	$-0.930191\pi$
$467$	−6.47472	+	11.2145i	−0.299614	+	0.518947i	0.676433	+	0.736504i	$0.263525\pi$
$468$	−5.51035	−	13.2767i	−0.254716	−	0.613714i
$469$	−11.1236	−	7.84374i	−0.513641	−	0.362190i
$470$	2.05676	−	1.18747i	0.0948713	−	0.0547740i
$471$	16.8168			0.774877
$472$	20.2148			0.930463
$473$	−16.5716	+	9.56761i	−0.761962	+	0.439919i
$474$	−4.38611	+	2.53232i	−0.201461	+	0.116313i
$475$	18.6724	+	10.7805i	0.856750	+	0.494645i
$476$	0.654942	+	0.0594814i	0.0300192	+	0.00272633i
$477$	−0.318489	+	0.551640i	−0.0145826	+	0.0252578i
$478$	3.90221			0.178483
$479$	23.3930	+	13.5060i	1.06885	+	0.617104i	0.927868	−	0.372908i	$-0.121639\pi$
$479$	23.3930	+	13.5060i	1.06885	+	0.617104i	0.140987	+	0.990012i	$0.454973\pi$
$480$	−2.22802	−	3.85905i	−0.101695	−	0.176141i
$481$	0.394692	−	3.01442i	0.0179964	−	0.137446i
$482$	10.8823			0.495677
$483$	5.68799	−	8.06644i	0.258813	−	0.367036i
$484$	4.14710	+	7.18299i	0.188505	+	0.326499i
$485$	−1.40886	−	2.44021i	−0.0639729	−	0.110804i
$486$	−6.93788	+	4.00558i	−0.314708	+	0.181697i
$487$			32.0838i			1.45386i	0.686713	+	0.726928i	$0.259053\pi$
$487$			32.0838i			1.45386i	−0.686713	+	0.726928i	$0.740947\pi$
$488$	9.52097	−	5.49694i	0.430994	−	0.248835i
$489$			7.58910i			0.343191i
$490$	−2.36367	+	2.77940i	−0.106780	+	0.125561i
$491$	−14.3020	−	24.7718i	−0.645440	−	1.11793i	−0.984200	−	0.177061i	$-0.943341\pi$
$491$	−14.3020	−	24.7718i	−0.645440	−	1.11793i	0.338760	−	0.940873i	$-0.389992\pi$
$492$			17.9866i			0.810897i
$493$	0.596378	+	1.03296i	0.0268595	+	0.0465220i
$494$	−3.80752	−	9.17385i	−0.171308	−	0.412751i
$495$	−4.71106	+	8.15980i	−0.211746	+	0.366756i
$496$	6.31716	−	3.64721i	0.283649	−	0.163765i
$497$	−7.99773	−	5.63954i	−0.358747	−	0.252968i
$498$	−0.610255	+	1.05699i	−0.0273462	+	0.0473650i
$499$	1.55726	+	0.899082i	0.0697123	+	0.0402484i	0.534451	−	0.845199i	$-0.320518\pi$
$499$	1.55726	+	0.899082i	0.0697123	+	0.0402484i	−0.464739	+	0.885448i	$0.653852\pi$
$500$			16.2608i			0.727207i
$501$			5.21204i			0.232857i
$502$	−3.32536	−	1.91990i	−0.148418	−	0.0856893i
$503$	−14.5386	+	25.1816i	−0.648245	+	1.12279i	0.335297	+	0.942112i	$0.391163\pi$
$503$	−14.5386	+	25.1816i	−0.648245	+	1.12279i	−0.983542	+	0.180681i	$0.942170\pi$
$504$	10.2582	−	4.74226i	0.456935	−	0.211237i
$505$	−10.3572	+	5.97976i	−0.460891	+	0.266096i
$506$	4.35497	−	7.54303i	0.193602	−	0.335329i
$507$	−7.79884	+	7.82088i	−0.346359	+	0.347338i
$508$	−1.75690	−	3.04304i	−0.0779499	−	0.135013i
$509$		−	23.1913i		−	1.02794i	−0.857809	−	0.513969i	$-0.828175\pi$
$509$		−	23.1913i		−	1.02794i	0.857809	−	0.513969i	$-0.171825\pi$
$510$	−0.0314489	−	0.0544711i	−0.00139258	−	0.00241202i
$511$	15.8810	−	7.34163i	0.702532	−	0.324774i
$512$		−	22.5022i		−	0.994464i
$513$	21.3975	−	12.3539i	0.944723	−	0.545436i
$514$			6.81169i			0.300451i
$515$	−3.76427	+	2.17330i	−0.165874	+	0.0957671i
$516$	3.58562	+	6.21048i	0.157848	+	0.273401i
$517$	9.03847	+	15.6551i	0.397511	+	0.688510i
$518$	1.11083	+	0.100885i	0.0488070	+	0.00443262i
$519$	−20.6137			−0.904840
$520$	4.28624	−	5.59410i	0.187964	−	0.245318i
$521$	−16.6255	−	28.7962i	−0.728376	−	1.26158i	−0.957569	−	0.288203i	$-0.906942\pi$
$521$	−16.6255	−	28.7962i	−0.728376	−	1.26158i	0.229193	−	0.973381i	$-0.426391\pi$
$522$	8.28383	+	4.78267i	0.362574	+	0.209332i
$523$	38.7121			1.69276			0.846380	−	0.532579i	$-0.178777\pi$
$523$	38.7121			1.69276			0.846380	+	0.532579i	$0.178777\pi$
$524$	10.8940	−	18.8690i	0.475908	−	0.824296i
$525$	8.76027	+	0.795602i	0.382330	+	0.0347229i
$526$	−5.07614	−	2.93071i	−0.221330	−	0.127785i
$527$	0.350140	−	0.202153i	0.0152523	−	0.00880594i
$528$	7.48028	−	4.31874i	0.325537	−	0.187949i
$529$	−3.71931			−0.161709
$530$	−0.145734			−0.00633029
$531$	−21.2714	+	12.2811i	−0.923102	+	0.532953i
$532$	−23.1561	+	10.7049i	−1.00394	+	0.464115i
$533$	−40.2857	+	16.7202i	−1.74497	+	0.724233i
$534$	0.371191	−	0.642922i	0.0160630	−	0.0278220i
$535$	−7.66253	−	4.42396i	−0.331280	−	0.191265i
$536$	−4.82283	+	8.35338i	−0.208314	+	0.360811i
$537$	−1.75730	−	3.04372i	−0.0758329	−	0.131346i
$538$		−	4.59926i		−	0.198288i
$539$	−21.1555	−	17.9911i	−0.911231	−	0.774933i
$540$	7.08495	+	4.09050i	0.304888	+	0.176027i
$541$	−19.6306	−	11.3337i	−0.843986	−	0.487275i	0.0146313	−	0.999893i	$-0.495343\pi$
$541$	−19.6306	−	11.3337i	−0.843986	−	0.487275i	−0.858617	+	0.512618i	$0.828676\pi$
$542$	−1.28181			−0.0550585
$543$	3.34135	−	5.78738i	0.143391	−	0.248360i
$544$		−	0.714603i		−	0.0306384i
$545$	−6.70349			−0.287146
$546$	−2.98049	−	2.74540i	−0.127553	−	0.117492i
$547$	−9.21134			−0.393848			−0.196924	−	0.980419i	$-0.563095\pi$
$547$	−9.21134			−0.393848			−0.196924	+	0.980419i	$0.563095\pi$
$548$			9.17913i			0.392113i
$549$	−6.67909	+	11.5685i	−0.285056	+	0.493732i
$550$	7.76231			0.330986
$551$	−40.0699	−	23.1344i	−1.70704	−	0.985558i
$552$	−6.05757	−	3.49734i	−0.257827	−	0.148857i
$553$	−18.1785	+	25.7798i	−0.773027	+	1.09627i
$554$		−	0.466928i		−	0.0198379i
$555$	0.373400	+	0.646748i	0.0158500	+	0.0274529i
$556$	18.1464	−	31.4304i	0.769577	−	1.33295i
$557$	9.81039	+	5.66403i	0.415680	+	0.239993i	0.693227	−	0.720719i	$-0.256188\pi$
$557$	9.81039	+	5.66403i	0.415680	+	0.239993i	−0.277547	+	0.960712i	$0.589522\pi$
$558$	1.62118	−	2.80796i	0.0686299	−	0.118871i
$559$	−10.5769	+	13.8042i	−0.447354	+	0.583855i
$560$	−5.77627	−	4.07310i	−0.244092	−	0.172120i
$561$	0.414608	−	0.239374i	0.0175048	−	0.0101064i
$562$	3.22636			0.136096
$563$	−32.6386			−1.37555			−0.687777	−	0.725922i	$-0.741414\pi$
$563$	−32.6386			−1.37555			−0.687777	+	0.725922i	$0.741414\pi$
$564$	5.86700	−	3.38732i	0.247045	−	0.142632i
$565$	9.89776	−	5.71448i	0.416402	−	0.240410i
$566$	−9.60161	−	5.54349i	−0.403586	−	0.233010i
$567$	−4.61162	+	6.53998i	−0.193670	+	0.274653i
$568$	−3.46755	+	6.00597i	−0.145495	+	0.252005i
$569$	−35.0091			−1.46766			−0.733829	−	0.679335i	$-0.762269\pi$
$569$	−35.0091			−1.46766			−0.733829	+	0.679335i	$0.762269\pi$
$570$	2.11302	+	1.21995i	0.0885046	+	0.0510981i
$571$	13.1273	+	22.7371i	0.549360	+	0.951519i	0.998319	+	0.0579663i	$0.0184616\pi$
$571$	13.1273	+	22.7371i	0.549360	+	0.951519i	−0.448959	+	0.893552i	$0.648205\pi$
$572$	19.8706	+	15.2250i	0.830830	+	0.636587i
$573$	−5.50428			−0.229945
$574$	−6.71516	−	14.5258i	−0.280285	−	0.606296i
$575$	8.59149	+	14.8809i	0.358290	+	0.620576i
$576$	2.97260	+	5.14870i	0.123858	+	0.214529i
$577$	21.2806	−	12.2863i	0.885922	−	0.511487i	0.0133154	−	0.999911i	$-0.495761\pi$
$577$	21.2806	−	12.2863i	0.885922	−	0.511487i	0.872606	+	0.488424i	$0.162428\pi$
$578$			8.48969i			0.353124i
$579$	−3.55327	+	2.05148i	−0.147669	+	0.0852567i
$580$		−	15.3201i		−	0.636133i
$581$	−0.687561	+	7.57065i	−0.0285248	+	0.314083i
$582$	0.574083	+	0.994341i	0.0237965	+	0.0412167i
$583$		−	1.10926i		−	0.0459408i
$584$	−6.19936	−	10.7376i	−0.256531	−	0.444325i
$585$	−1.11170	+	8.49051i	−0.0459632	+	0.351039i
$586$	−6.05048	+	10.4797i	−0.249943	+	0.432914i
$587$	17.7777	−	10.2640i	0.733765	−	0.423639i	−0.0860331	−	0.996292i	$-0.527419\pi$
$587$	17.7777	−	10.2640i	0.733765	−	0.423639i	0.819798	+	0.572653i	$0.194086\pi$
$588$	−6.74248	+	7.92837i	−0.278055	+	0.326961i
$589$	−7.84184	+	13.5825i	−0.323117	+	0.559656i
$590$	−4.86669	−	2.80978i	−0.200358	−	0.115677i
$591$		−	21.9505i		−	0.902923i
$592$			2.16073i			0.0888054i
$593$	33.1545	+	19.1417i	1.36149	+	0.786057i	0.989822	−	0.142308i	$-0.0454524\pi$
$593$	33.1545	+	19.1417i	1.36149	+	0.786057i	0.371669	+	0.928365i	$0.378786\pi$
$594$	4.44757	−	7.70342i	0.182486	−	0.316075i
$595$	−0.320160	−	0.225759i	−0.0131253	−	0.00925521i
$596$	0.0172409	−	0.00995405i	0.000706216	−	0.000407734i
$597$	7.27030	−	12.5925i	0.297554	−	0.515378i
$598$	1.02767	−	7.84874i	0.0420247	−	0.320959i
$599$	−7.03567	−	12.1861i	−0.287470	−	0.497912i	0.685735	−	0.727851i	$-0.259481\pi$
$599$	−7.03567	−	12.1861i	−0.287470	−	0.497912i	−0.973205	+	0.229939i	$0.926147\pi$
$600$		−	6.23367i		−	0.254488i
$601$	10.1171	+	17.5233i	0.412685	+	0.714791i	0.995182	−	0.0980417i	$-0.0312579\pi$
$601$	10.1171	+	17.5233i	0.412685	+	0.714791i	−0.582498	+	0.812832i	$0.697925\pi$
$602$	−5.21437	−	3.67688i	−0.212522	−	0.149858i
$603$		−	11.7200i		−	0.477276i
$604$	−28.6522	+	16.5424i	−1.16584	+	0.673099i
$605$		−	4.94082i		−	0.200873i
$606$	4.22039	−	2.43664i	0.171441	−	0.0989818i
$607$	−3.27563	−	5.67356i	−0.132954	−	0.230283i	0.791860	−	0.610703i	$-0.209113\pi$
$607$	−3.27563	−	5.67356i	−0.132954	−	0.230283i	−0.924814	+	0.380420i	$0.875780\pi$
$608$	13.8603	+	24.0067i	0.562108	+	0.973600i
$609$	−18.7990	−	1.70731i	−0.761775	−	0.0691839i
$610$	−3.05621			−0.123742
$611$	13.0407	+	9.99190i	0.527572	+	0.404229i
$612$	0.283136	+	0.490406i	0.0114451	+	0.0198235i
$613$	28.8598	+	16.6622i	1.16564	+	0.672980i	0.952648	−	0.304075i	$-0.0983472\pi$
$613$	28.8598	+	16.6622i	1.16564	+	0.672980i	0.212988	+	0.977055i	$0.431681\pi$
$614$	12.1459			0.490168
$615$	5.35726	−	9.27904i	0.216025	−	0.374167i
$616$	−11.3415	+	16.0839i	−0.456961	+	0.648040i
$617$	5.85466	+	3.38019i	0.235700	+	0.136081i	0.613199	−	0.789929i	$-0.289883\pi$
$617$	5.85466	+	3.38019i	0.235700	+	0.136081i	−0.377499	+	0.926010i	$0.623216\pi$
$618$	1.53387	−	0.885581i	0.0617013	−	0.0356233i
$619$	15.2582	−	8.80931i	0.613278	−	0.354076i	−0.160970	−	0.986959i	$-0.551462\pi$
$619$	15.2582	−	8.80931i	0.613278	−	0.354076i	0.774247	+	0.632883i	$0.218129\pi$
$620$	−5.19304			−0.208558
$621$	19.6907			0.790159
$622$	1.72642	−	0.996751i	0.0692233	−	0.0399661i
$623$	0.418213	−	4.60489i	0.0167554	−	0.184491i
$624$	4.77431	−	6.23110i	0.191125	−	0.249444i
$625$	−4.93986	+	8.55609i	−0.197594	+	0.342244i
$626$	12.3299	+	7.11866i	0.492801	+	0.284519i
$627$	−9.28569	+	16.0833i	−0.370835	+	0.642304i
$628$	−17.3197	−	29.9985i	−0.691130	−	1.19707i
$629$			0.119762i			0.00477524i
$630$	−3.12879	−	0.284155i	−0.124654	−	0.0113210i
$631$	13.6416	+	7.87596i	0.543062	+	0.313537i	0.746319	−	0.665588i	$-0.231819\pi$
$631$	13.6416	+	7.87596i	0.543062	+	0.313537i	−0.203257	+	0.979125i	$0.565153\pi$
$632$	19.3596	+	11.1773i	0.770084	+	0.444608i
$633$	15.5402			0.617667
$634$	−4.20392	+	7.28140i	−0.166959	+	0.289181i
$635$			2.09316i			0.0830644i
$636$	−0.415713			−0.0164841
$637$	−24.0255	−	7.73143i	−0.951925	−	0.306330i
$638$	−16.6575			−0.659475
$639$		−	8.42653i		−	0.333348i
$640$	−5.92497	+	10.2623i	−0.234205	+	0.405655i
$641$	20.9405			0.827099			0.413550	−	0.910482i	$-0.364289\pi$
$641$	20.9405			0.827099			0.413550	+	0.910482i	$0.364289\pi$
$642$	3.12234	+	1.80268i	0.123229	+	0.0711463i
$643$	−16.3952	−	9.46576i	−0.646563	−	0.373293i	0.140575	−	0.990070i	$-0.455105\pi$
$643$	−16.3952	−	9.46576i	−0.646563	−	0.373293i	−0.787138	+	0.616777i	$0.788438\pi$
$644$	−20.2473	−	1.83885i	−0.797857	−	0.0724608i
$645$		−	4.27188i		−	0.168205i
$646$	0.195640	+	0.338859i	0.00769736	+	0.0133322i
$647$	−18.8384	+	32.6291i	−0.740614	+	1.28278i	0.211601	+	0.977356i	$0.432132\pi$
$647$	−18.8384	+	32.6291i	−0.740614	+	1.28278i	−0.952216	+	0.305426i	$0.901201\pi$
$648$	4.91126	+	2.83552i	0.192933	+	0.111390i
$649$	21.3867	−	37.0429i	0.839503	−	1.45406i
$650$	6.51562	−	2.70424i	0.255563	−	0.106069i
$651$	−0.578727	+	6.37229i	−0.0226821	+	0.249750i
$652$	13.5378	−	7.81604i	0.530180	−	0.306100i
$653$	29.0326			1.13613			0.568066	−	0.822983i	$-0.307692\pi$
$653$	29.0326			1.13613			0.568066	+	0.822983i	$0.307692\pi$
$654$	2.73155			0.106812
$655$	−11.2402	+	6.48952i	−0.439190	+	0.253567i
$656$	26.8472	−	15.5002i	1.04821	−	0.605182i
$657$	13.0468	+	7.53257i	0.509004	+	0.293874i
$658$	−3.47352	+	4.92598i	−0.135412	+	0.192035i
$659$	0.709152	−	1.22829i	0.0276247	−	0.0478473i	−0.851883	−	0.523733i	$-0.824539\pi$
$659$	0.709152	−	1.22829i	0.0276247	−	0.0478473i	0.879507	+	0.475886i	$0.157872\pi$
$660$	−6.14919			−0.239357
$661$	−3.97764	−	2.29649i	−0.154712	−	0.0893231i	0.420645	−	0.907225i	$-0.361804\pi$
$661$	−3.97764	−	2.29649i	−0.154712	−	0.0893231i	−0.575357	+	0.817902i	$0.695137\pi$
$662$	−1.55225	−	2.68858i	−0.0603300	−	0.104495i
$663$	0.264625	−	0.345370i	0.0102772	−	0.0134131i
$664$	5.38715			0.209062
$665$	15.1344	+	1.37449i	0.586885	+	0.0533005i
$666$	0.480219	+	0.831764i	0.0186081	+	0.0322302i
$667$	−18.4368	−	31.9335i	−0.713877	−	1.23647i
$668$	9.29746	−	5.36789i	0.359730	−	0.207690i
$669$		−	9.77780i		−	0.378032i
$670$	2.32218	−	1.34071i	0.0897135	−	0.0517961i
$671$		−	23.2624i		−	0.898036i
$672$	9.24249	+	6.51728i	0.356537	+	0.251410i
$673$	−2.10111	−	3.63924i	−0.0809920	−	0.140282i	0.822684	−	0.568499i	$-0.192475\pi$
$673$	−2.10111	−	3.63924i	−0.0809920	−	0.140282i	−0.903676	+	0.428216i	$0.859142\pi$
$674$		−	3.84815i		−	0.148225i
$675$	8.77418	+	15.1973i	0.337718	+	0.584945i
$676$	21.9833	+	5.85716i	0.845510	+	0.225275i
$677$	−4.04354	+	7.00361i	−0.155406	+	0.269171i	−0.933207	−	0.359340i	$-0.883002\pi$
$677$	−4.04354	+	7.00361i	−0.155406	+	0.269171i	0.777801	+	0.628511i	$0.216335\pi$
$678$	−4.03316	+	2.32854i	−0.154892	+	0.0894272i
$679$	5.84435	+	4.12110i	0.224285	+	0.158153i
$680$	−0.138811	+	0.240427i	−0.00532315	+	0.00921997i
$681$	−13.1737	−	7.60583i	−0.504817	−	0.291456i
$682$			5.64636i			0.216210i
$683$			24.6865i			0.944604i	0.881437	+	0.472302i	$0.156577\pi$
$683$			24.6865i			0.944604i	−0.881437	+	0.472302i	$0.843423\pi$
$684$	−19.0236	−	10.9833i	−0.727386	−	0.419956i
$685$	2.73398	−	4.73540i	0.104460	−	0.180930i
$686$	2.48518	−	8.92016i	0.0948846	−	0.340573i
$687$	2.84267	−	1.64122i	0.108455	−	0.0626164i
$688$	6.17994	−	10.7040i	0.235608	−	0.408085i
$689$	−0.386445	−	0.931102i	−0.0147224	−	0.0354722i
$690$	0.972234	+	1.68396i	0.0370123	+	0.0641072i
$691$			11.2567i			0.428225i	0.976809	+	0.214113i	$0.0686859\pi$
$691$			11.2567i			0.428225i	−0.976809	+	0.214113i	$0.931314\pi$
$692$	21.2301	+	36.7716i	0.807047	+	1.39785i
$693$	2.16285	−	23.8149i	0.0821599	−	0.904652i
$694$		−	15.2043i		−	0.577147i
$695$	−18.7230	+	10.8097i	−0.710202	+	0.410035i
$696$			13.3771i			0.507057i
$697$	1.48805	−	0.859128i	0.0563640	−	0.0325418i
$698$	4.03942	+	6.99648i	0.152894	+	0.264821i
$699$	10.6473	+	18.4416i	0.402717	+	0.697526i
$700$	−7.60300	−	16.4463i	−0.287366	−	0.621614i
$701$	22.2305			0.839635			0.419818	−	0.907608i	$-0.362094\pi$
$701$	22.2305			0.839635			0.419818	+	0.907608i	$0.362094\pi$
$702$	1.04953	−	8.01564i	0.0396118	−	0.302531i
$703$	−2.32288	−	4.02335i	−0.0876091	−	0.151743i
$704$	−8.96614	−	5.17660i	−0.337924	−	0.195101i
$705$	−4.03562			−0.151990
$706$	−2.96052	+	5.12776i	−0.111420	+	0.192986i
$707$	17.4916	−	24.8058i	0.657841	−	0.932918i
$708$	−13.8825	−	8.01504i	−0.521734	−	0.301224i
$709$	20.5889	−	11.8870i	0.773234	−	0.446427i	−0.0607929	−	0.998150i	$-0.519363\pi$
$709$	20.5889	−	11.8870i	0.773234	−	0.446427i	0.834027	+	0.551723i	$0.186030\pi$
$710$	1.66961	−	0.963952i	0.0626595	−	0.0361765i
$711$	−27.1620			−1.01866
$712$	−3.27677			−0.122802
$713$	−10.8245	+	6.24951i	−0.405380	+	0.234046i
$714$	0.130459	+	0.0919926i	0.00488232	+	0.00344274i
$715$	−5.71626	−	13.7728i	−0.213776	−	0.515072i
$716$	−3.61969	+	6.26948i	−0.135274	+	0.234301i
$717$	−5.74246	−	3.31541i	−0.214456	−	0.123816i
$718$	−7.84111	+	13.5812i	−0.292628	+	0.506846i
$719$	10.3904	+	17.9967i	0.387496	+	0.671163i	0.992112	−	0.125354i	$-0.0400068\pi$
$719$	10.3904	+	17.9967i	0.387496	+	0.671163i	−0.604616	+	0.796517i	$0.706673\pi$
$720$		−	6.08597i		−	0.226811i
$721$	6.35722	−	9.01550i	0.236755	−	0.335755i
$722$	−4.91782	−	2.83931i	−0.183022	−	0.105668i
$723$	−16.0144	−	9.24589i	−0.595580	−	0.343859i
$724$	−13.7650			−0.511574
$725$	16.4309	−	28.4592i	0.610229	−	1.05695i
$726$			2.01329i			0.0747203i
$727$	−26.7719			−0.992915			−0.496457	−	0.868061i	$-0.665366\pi$
$727$	−26.7719			−0.992915			−0.496457	+	0.868061i	$0.665366\pi$
$728$	−3.91659	+	17.4519i	−0.145159	+	0.646809i
$729$	4.53910			0.168115
$730$			3.44675i			0.127570i
$731$	0.342535	−	0.593287i	0.0126691	−	0.0219435i
$732$	−8.71799			−0.322226
$733$	4.55224	+	2.62824i	0.168141	+	0.0970761i	0.581709	−	0.813397i	$-0.302384\pi$
$733$	4.55224	+	2.62824i	0.168141	+	0.0970761i	−0.413568	+	0.910473i	$0.635718\pi$
$734$	10.4255	+	6.01919i	0.384814	+	0.222172i
$735$	5.83981	−	2.08191i	0.215405	−	0.0767926i
$736$			22.0917i			0.814312i
$737$	10.2048	+	17.6753i	0.375900	+	0.651078i
$738$	6.88981	−	11.9335i	0.253617	−	0.439278i
$739$	6.19209	+	3.57501i	0.227780	+	0.131509i	0.609547	−	0.792750i	$-0.291351\pi$
$739$	6.19209	+	3.57501i	0.227780	+	0.131509i	−0.381768	+	0.924258i	$0.624685\pi$
$740$	0.769132	−	1.33218i	0.0282738	−	0.0489717i
$741$	−2.19121	+	16.7351i	−0.0804960	+	0.614780i
$742$	0.335727	−	0.155204i	0.0123249	−	0.00569771i
$743$	−0.618032	+	0.356821i	−0.0226734	+	0.0130905i	−0.511294	−	0.859406i	$-0.670834\pi$
$743$	−0.618032	+	0.356821i	−0.0226734	+	0.0130905i	0.488620	+	0.872496i	$0.337500\pi$
$744$	4.53441			0.166240
$745$	−0.0118592			−0.000434486
$746$	7.96386	−	4.59794i	0.291578	−	0.168342i
$747$	−5.66873	+	3.27284i	−0.207408	+	0.119747i
$748$	−0.854012	−	0.493064i	−0.0312258	−	0.0180282i
$749$	22.3636	+	2.03104i	0.817147	+	0.0742127i
$750$	−1.97354	+	3.41827i	−0.0720634	+	0.124817i
$751$	25.7013			0.937854			0.468927	−	0.883237i	$-0.344641\pi$
$751$	25.7013			0.937854			0.468927	+	0.883237i	$0.344641\pi$
$752$	−10.1120	−	5.83815i	−0.368746	−	0.212896i
$753$	3.26238	+	5.65062i	0.118888	+	0.205920i
$754$	−13.9821	+	5.80315i	−0.509199	+	0.211338i
$755$	19.7084			0.717263
$756$	−20.6779	−	1.87795i	−0.752047	−	0.0683004i
$757$	−8.19425	−	14.1928i	−0.297825	−	0.515848i	0.677813	−	0.735234i	$-0.262928\pi$
$757$	−8.19425	−	14.1928i	−0.297825	−	0.515848i	−0.975638	+	0.219386i	$0.929594\pi$
$758$	2.03430	+	3.52350i	0.0738889	+	0.127979i
$759$	−12.8175	+	7.40018i	−0.465245	+	0.268609i
$760$		−	10.7694i		−	0.390646i
$761$	7.20531	−	4.15999i	0.261192	−	0.150800i	−0.363686	−	0.931522i	$-0.618482\pi$
$761$	7.20531	−	4.15999i	0.261192	−	0.150800i	0.624878	+	0.780722i	$0.285149\pi$
$762$		−	0.852923i		−	0.0308981i
$763$	15.4428	−	7.13907i	0.559067	−	0.258452i
$764$	5.66888	+	9.81878i	0.205093	+	0.355231i
$765$		−	0.337326i		−	0.0121960i
$766$	5.59263	+	9.68671i	0.202070	+	0.349995i
$767$	5.04678	−	38.5442i	0.182229	−	1.39175i
$768$	0.197167	−	0.341504i	0.00711466	−	0.0123230i
$769$	22.1346	−	12.7794i	0.798194	−	0.460838i	−0.0446452	−	0.999003i	$-0.514216\pi$
$769$	22.1346	−	12.7794i	0.798194	−	0.460838i	0.842839	+	0.538165i	$0.180882\pi$
$770$	4.96605	−	2.29576i	0.178964	−	0.0827334i
$771$	5.78738	−	10.0240i	0.208427	−	0.361007i
$772$	7.31905	+	4.22565i	0.263418	+	0.152085i
$773$			8.40077i			0.302155i	0.988522	+	0.151077i	$0.0482742\pi$
$773$			8.40077i			0.302155i	−0.988522	+	0.151077i	$0.951726\pi$
$774$		−	5.49394i		−	0.197476i
$775$	−9.64678	−	5.56957i	−0.346523	−	0.200065i
$776$	2.53392	−	4.38887i	0.0909623	−	0.157551i
$777$	−1.54897	−	1.09225i	−0.0555691	−	0.0391842i
$778$	−9.26388	+	5.34850i	−0.332126	+	0.191753i
$779$	−33.3269	+	57.7238i	−1.19406	+	2.06817i
$780$	−5.16158	+	2.14226i	−0.184814	+	0.0767053i
$781$	7.33714	+	12.7083i	0.262544	+	0.454739i
$782$			0.311829i			0.0111510i
$783$	−18.8289	−	32.6125i	−0.672889	−	1.16548i
$784$	17.6445	+	3.23158i	0.630162	+	0.115414i
$785$			20.6345i			0.736476i
$786$	4.58017	−	2.64436i	0.163369	−	0.0943212i
$787$		−	35.0644i		−	1.24991i	−0.780660	−	0.624956i	$-0.785117\pi$
$787$		−	35.0644i		−	1.24991i	0.780660	−	0.624956i	$-0.214883\pi$
$788$	−39.1562	+	22.6069i	−1.39488	+	0.805336i
$789$	4.98000	+	8.62562i	0.177293	+	0.307080i
$790$	−3.10720	−	5.38182i	−0.110549	−	0.191477i
$791$	−16.7157	+	23.7053i	−0.594340	+	0.842864i
$792$	−16.9463			−0.602160
$793$	−8.10420	−	19.5263i	−0.287788	−	0.693399i
$794$	−0.299175	−	0.518186i	−0.0106173	−	0.0183897i
$795$	0.214461	+	0.123819i	0.00760616	+	0.00439142i
$796$	−29.9508			−1.06158
$797$	−12.2876	+	21.2828i	−0.435250	+	0.753875i	−0.997316	−	0.0732173i	$-0.976673\pi$
$797$	−12.2876	+	21.2828i	−0.435250	+	0.753875i	0.562066	+	0.827092i	$0.310007\pi$
$798$	−6.16697	−	0.560080i	−0.218309	−	0.0198266i
$799$	−0.560475	−	0.323590i	−0.0198282	−	0.0114478i
$800$	−17.0505	+	9.84409i	−0.602825	+	0.348041i
$801$	3.44804	−	1.99073i	0.121831	−	0.0703389i
$802$	−18.1370			−0.640439
$803$	−26.2350			−0.925814
$804$	6.62411	−	3.82443i	0.233615	−	0.134877i
$805$	9.89765	+	6.97926i	0.348846	+	0.245987i
$806$	1.96709	+	4.73951i	0.0692877	+	0.166942i
$807$	−3.90764	+	6.76823i	−0.137555	+	0.238253i
$808$	−18.6282	−	10.7550i	−0.655336	−	0.378358i
$809$	15.9006	−	27.5406i	0.559035	−	0.968277i	−0.438542	−	0.898711i	$-0.644505\pi$
$809$	15.9006	−	27.5406i	0.559035	−	0.968277i	0.997577	−	0.0695667i	$-0.0221617\pi$
$810$	−0.788253	−	1.36529i	−0.0276964	−	0.0479715i
$811$			10.3633i			0.363905i	0.983307	+	0.181953i	$0.0582418\pi$
$811$			10.3633i			0.363905i	−0.983307	+	0.181953i	$0.941758\pi$
$812$	16.3156	+	35.2929i	0.572565	+	1.23854i
$813$	1.88630	+	1.08906i	0.0661555	+	0.0381949i
$814$	−1.44847	−	0.836272i	−0.0507687	−	0.0293113i
$815$	−9.31196			−0.326184
$816$	−0.154617	+	0.267805i	−0.00541269	+	0.00937505i
$817$			26.5749i			0.929737i
$818$	−7.33597			−0.256496
$819$	−6.48118	−	20.7435i	−0.226471	−	0.724836i
$820$	−22.0698			−0.770711
$821$		−	4.05592i		−	0.141552i	−0.997492	−	0.0707762i	$-0.977452\pi$
$821$		−	4.05592i		−	0.141552i	0.997492	−	0.0707762i	$-0.0225476\pi$
$822$	−1.11405	+	1.92959i	−0.0388569	+	0.0673021i
$823$	−8.71697			−0.303854			−0.151927	−	0.988392i	$-0.548548\pi$
$823$	−8.71697			−0.303854			−0.151927	+	0.988392i	$0.548548\pi$
$824$	−6.77027	−	3.90882i	−0.235854	−	0.136170i
$825$	−11.4230	−	6.59505i	−0.397696	−	0.229610i
$826$	14.2037	+	1.28997i	0.494211	+	0.0448839i
$827$		−	23.5788i		−	0.819915i	−0.912105	−	0.409957i	$-0.865544\pi$
$827$		−	23.5788i		−	0.819915i	0.912105	−	0.409957i	$-0.134456\pi$
$828$	−8.75307	−	15.1608i	−0.304190	−	0.526873i
$829$	−14.5203	+	25.1499i	−0.504311	+	0.873492i	0.495677	+	0.868507i	$0.334920\pi$
$829$	−14.5203	+	25.1499i	−0.504311	+	0.873492i	−0.999988	+	0.00498467i	$0.998413\pi$
$830$	−1.29695	−	0.748793i	−0.0450177	−	0.0259910i
$831$	−0.396714	+	0.687128i	−0.0137618	+	0.0238362i
$832$	−9.32953	−	1.22156i	−0.323443	−	0.0423499i
$833$	0.977980	+	0.179116i	0.0338850	+	0.00620601i
$834$	7.62926	−	4.40475i	0.264180	−	0.152524i
$835$	−6.39526			−0.221317
$836$	38.2534			1.32302
$837$	−11.0546	+	6.38240i	−0.382104	+	0.220608i
$838$	2.56921	−	1.48333i	0.0887517	−	0.0512408i
$839$	−10.0090	−	5.77871i	−0.345550	−	0.199503i	0.317174	−	0.948367i	$-0.397266\pi$
$839$	−10.0090	−	5.77871i	−0.345550	−	0.199503i	−0.662723	+	0.748864i	$0.730600\pi$
$840$	−1.84365	−	3.98807i	−0.0636120	−	0.137602i
$841$	−20.7598	+	35.9570i	−0.715855	+	1.23990i
$842$	−1.31584			−0.0453467
$843$	−4.74788	−	2.74119i	−0.163526	−	0.0944116i
$844$	−16.0049	−	27.7212i	−0.550910	−	0.954205i
$845$	−9.59635	−	9.56930i	−0.330124	−	0.329194i
$846$	−5.19009			−0.178439
$847$	5.26186	+	11.3821i	0.180800	+	0.391095i
$848$	0.358248	+	0.620504i	0.0123023	+	0.0213082i
$849$	9.41977	+	16.3155i	0.323286	+	0.559947i
$850$	−0.240670	+	0.138951i	−0.00825493	+	0.00476598i
$851$		−	3.70241i		−	0.126917i
$852$	4.76265	−	2.74972i	0.163166	−	0.0942038i
$853$		−	1.51845i		−	0.0519906i	−0.999662	−	0.0259953i	$-0.991725\pi$
$853$		−	1.51845i		−	0.0519906i	0.999662	−	0.0259953i	$-0.00827550\pi$
$854$	7.04059	−	3.25480i	0.240924	−	0.111377i
$855$	6.54269	+	11.3323i	0.223755	+	0.387556i
$856$		−	15.9136i		−	0.543914i
$857$	−3.00060	−	5.19718i	−0.102498	−	0.177532i	0.810215	−	0.586133i	$-0.199350\pi$
$857$	−3.00060	−	5.19718i	−0.102498	−	0.177532i	−0.912713	+	0.408600i	$0.866017\pi$
$858$	2.32927	+	5.61215i	0.0795199	+	0.191596i
$859$	−0.838021	+	1.45150i	−0.0285929	+	0.0495244i	−0.879968	−	0.475033i	$-0.842436\pi$
$859$	−0.838021	+	1.45150i	−0.0285929	+	0.0495244i	0.851375	+	0.524558i	$0.175769\pi$
$860$	−7.62036	+	4.39962i	−0.259852	+	0.150026i
$861$	−2.45952	+	27.0815i	−0.0838202	+	0.922933i
$862$	4.70929	−	8.15673i	0.160399	−	0.277819i
$863$	36.4167	+	21.0252i	1.23964	+	0.715706i	0.969021	−	0.246980i	$-0.0794383\pi$
$863$	36.4167	+	21.0252i	1.23964	+	0.715706i	0.270619	+	0.962687i	$0.412772\pi$
$864$			22.5615i			0.767558i
$865$		−	25.2933i		−	0.859999i
$866$	−8.28567	−	4.78374i	−0.281559	−	0.162558i
$867$	7.21304	−	12.4934i	0.244968	−	0.424297i
$868$	11.9632	−	5.53048i	0.406057	−	0.187717i
$869$	40.9639	−	23.6505i	1.38960	−	0.802288i
$870$	1.85936	−	3.22051i	0.0630383	−	0.109186i
$871$	14.7236	+	11.2813i	0.498890	+	0.382253i
$872$	−6.02832	−	10.4414i	−0.204145	−	0.353589i
$873$			6.15770i			0.208407i
$874$	−6.04815	−	10.4757i	−0.204582	−	0.354346i
$875$	−2.22354	+	24.4831i	−0.0751694	+	0.827681i
$876$			9.83201i			0.332193i
$877$	26.7281	−	15.4315i	0.902545	−	0.521084i	0.0245198	−	0.999699i	$-0.492194\pi$
$877$	26.7281	−	15.4315i	0.902545	−	0.521084i	0.878025	+	0.478615i	$0.158861\pi$
$878$		−	0.632537i		−	0.0213471i
$879$	17.8077	−	10.2813i	0.600638	−	0.346778i
$880$	5.29917	+	9.17843i	0.178635	+	0.309405i
$881$	−27.8669	−	48.2669i	−0.938860	−	1.62615i	−0.767601	−	0.640928i	$-0.778550\pi$
$881$	−27.8669	−	48.2669i	−0.938860	−	1.62615i	−0.171260	−	0.985226i	$-0.554784\pi$
$882$	7.51041	−	2.67749i	0.252889	−	0.0901558i
$883$	−2.92007			−0.0982681			−0.0491341	−	0.998792i	$-0.515646\pi$
$883$	−2.92007			−0.0982681			−0.0491341	+	0.998792i	$0.515646\pi$
$884$	−0.888625	−	0.116352i	−0.0298877	−	0.00391333i
$885$	4.77452	+	8.26971i	0.160494	+	0.277983i
$886$	−9.06671	−	5.23467i	−0.304602	−	0.175862i
$887$	1.87909			0.0630937			0.0315468	−	0.999502i	$-0.489957\pi$
$887$	1.87909			0.0630937			0.0315468	+	0.999502i	$0.489957\pi$
$888$	−0.671584	+	1.16322i	−0.0225369	+	0.0390350i
$889$	−2.22917	−	4.82200i	−0.0747639	−	0.161725i
$890$	0.788876	+	0.455458i	0.0264432	+	0.0152670i
$891$	10.3920	−	5.99980i	0.348144	−	0.201001i
$892$	−17.4421	+	10.0702i	−0.584004	+	0.337175i
$893$	25.1051			0.840111
$894$	0.00483239			0.000161619
$895$	3.73470	−	2.15623i	0.124837	−	0.0720748i
$896$	2.72015	−	29.9513i	0.0908740	−	1.00060i
$897$	−8.18080	+	10.6770i	−0.273149	+	0.356495i
$898$	4.46569	−	7.73480i	0.149022	−	0.258114i
$899$	20.7014	+	11.9520i	0.690431	+	0.398621i
$900$	7.80074	−	13.5113i	0.260025	−	0.450376i
$901$	0.0198566	+	0.0343926i	0.000661518	+	0.00114578i
$902$			23.9964i			0.798991i
$903$	4.54946	+	9.84111i	0.151396	+	0.327492i
$904$	17.8017	+	10.2778i	0.592077	+	0.341836i
$905$	7.10121	+	4.09989i	0.236052	+	0.136285i
$906$	−8.03082			−0.266806
$907$	−17.8082	+	30.8447i	−0.591311	+	1.02418i	0.402745	+	0.915312i	$0.368056\pi$
$907$	−17.8082	+	30.8447i	−0.591311	+	1.02418i	−0.994056	+	0.108868i	$0.965277\pi$
$908$			31.3331i			1.03982i
$909$	26.1358			0.866869
$910$	3.36866	−	3.65712i	0.111670	−	0.121232i
$911$	44.2844			1.46721			0.733604	−	0.679577i	$-0.237837\pi$
$911$	44.2844			1.46721			0.733604	+	0.679577i	$0.237837\pi$
$912$		−	11.9957i		−	0.397217i
$913$	5.69946	−	9.87175i	0.188624	−	0.326707i
$914$	3.28290			0.108589
$915$	4.49750	+	2.59663i	0.148683	+	0.0858420i
$916$	−5.85535	−	3.38059i	−0.193466	−	0.111698i
$917$	18.9828	−	26.9204i	0.626866	−	0.888991i
$918$			0.318459i			0.0105107i
$919$	−13.0564	−	22.6144i	−0.430691	−	0.745979i	0.566242	−	0.824239i	$-0.308397\pi$
$919$	−13.0564	−	22.6144i	−0.430691	−	0.745979i	−0.996933	+	0.0782603i	$0.975063\pi$
$920$	4.29129	−	7.43274i	0.141480	−	0.245050i
$921$	−17.8738	−	10.3194i	−0.588961	−	0.340037i
$922$	−1.27838	+	2.21421i	−0.0421010	+	0.0729211i
$923$	10.5861	+	8.11111i	0.348445	+	0.266981i
$924$	14.1659	−	6.54875i	0.466023	−	0.215438i
$925$	2.85753	−	1.64980i	0.0939551	−	0.0542450i
$926$	−16.6615			−0.547531
$927$	9.49887			0.311984
$928$	36.5893	−	21.1248i	1.20110	−	0.693457i
$929$	−8.68030	+	5.01157i	−0.284791	+	0.164424i	−0.635591	−	0.772026i	$-0.719243\pi$
$929$	−8.68030	+	5.01157i	−0.284791	+	0.164424i	0.350799	+	0.936451i	$0.385910\pi$
$930$	−1.09165	−	0.630266i	−0.0357967	−	0.0206672i
$931$	−36.3288	+	12.9514i	−1.19063	+	0.424464i
$932$	21.9313	−	37.9861i	0.718384	−	1.24428i
$933$	−3.38745			−0.110900
$934$	5.60712	+	3.23727i	0.183471	+	0.105927i
$935$	0.293716	+	0.508731i	0.00960554	+	0.0166373i
$936$	−14.2246	+	5.90377i	−0.464944	+	0.192971i
$937$	−0.916838			−0.0299518			−0.0149759	−	0.999888i	$-0.504767\pi$
$937$	−0.916838			−0.0299518			−0.0149759	+	0.999888i	$0.504767\pi$
$938$	−3.92177	+	5.56166i	−0.128050	+	0.181595i
$939$	−12.0964	−	20.9515i	−0.394750	−	0.683728i
$940$	4.15629	+	7.19891i	0.135563	+	0.234803i
$941$	−14.8001	+	8.54482i	−0.482468	+	0.278553i	−0.721445	−	0.692472i	$-0.756522\pi$
$941$	−14.8001	+	8.54482i	−0.482468	+	0.278553i	0.238976	+	0.971025i	$0.423188\pi$
$942$		−	8.40817i		−	0.273953i
$943$	−46.0027	+	26.5597i	−1.49805	+	0.864902i
$944$			27.6284i			0.899227i
$945$	10.1081	+	7.12767i	0.328817	+	0.231863i
$946$	4.78368	+	8.28557i	0.155531	+	0.269387i
$947$		−	21.7555i		−	0.706957i	−0.935443	−	0.353479i	$-0.884999\pi$
$947$		−	21.7555i		−	0.706957i	0.935443	−	0.353479i	$-0.115001\pi$
$948$	−8.86342	−	15.3519i	−0.287871	−	0.498607i
$949$	−22.0214	+	9.13979i	−0.714846	+	0.296690i
$950$	5.39012	−	9.33597i	0.174879	−	0.302899i
$951$	12.3729	−	7.14350i	0.401219	−	0.231644i
$952$	0.0637281	−	0.701702i	0.00206544	−	0.0227423i
$953$	−8.90406	+	15.4223i	−0.288431	+	0.499577i	−0.973435	−	0.228962i	$-0.926467\pi$
$953$	−8.90406	+	15.4223i	−0.288431	+	0.499577i	0.685005	+	0.728539i	$0.259800\pi$
$954$	0.275812	+	0.159240i	0.00892976	+	0.00515560i
$955$		−	6.75385i		−	0.218549i
$956$			13.6582i			0.441737i
$957$	24.5130	+	14.1526i	0.792392	+	0.457488i
$958$	6.75281	−	11.6962i	0.218173	−	0.377887i
$959$	−1.25517	+	13.8206i	−0.0405317	+	0.446289i
$960$	2.00166	−	1.15566i	0.0646034	−	0.0372988i
$961$	−11.4487	+	19.8297i	−0.369311	+	0.639666i
$962$	−1.50717	−	0.197341i	−0.0485931	−	0.00636253i
$963$	9.66793	+	16.7453i	0.311545	+	0.539611i
$964$			38.0895i			1.22678i
$965$	−2.51720	−	4.35992i	−0.0810316	−	0.140351i
$966$	−4.03311	−	2.84392i	−0.129763	−	0.0915017i
$967$			35.3813i			1.13779i	0.822412	+	0.568893i	$0.192628\pi$
$967$			35.3813i			1.13779i	−0.822412	+	0.568893i	$0.807372\pi$
$968$	7.69582	−	4.44318i	0.247353	−	0.142809i
$969$		−	0.664883i		−	0.0213591i
$970$	−1.22007	+	0.704409i	−0.0391742	+	0.0226172i
$971$	−24.8533	−	43.0472i	−0.797582	−	1.38145i	−0.921187	−	0.389120i	$-0.872779\pi$
$971$	−24.8533	−	43.0472i	−0.797582	−	1.38145i	0.123605	−	0.992331i	$-0.460554\pi$
$972$	−14.0200	−	24.2834i	−0.449693	−	0.778890i
$973$	31.6199	−	44.8418i	1.01369	−	1.43756i
$974$	16.0415			0.514002
$975$	−11.8859	−	1.55628i	−0.380654	−	0.0498408i
$976$	7.51287	+	13.0127i	0.240481	+	0.416526i
$977$	−53.0701	−	30.6401i	−1.69786	−	0.980262i	−0.947783	−	0.318917i	$-0.896681\pi$
$977$	−53.0701	−	30.6401i	−1.69786	−	0.980262i	−0.750081	−	0.661346i	$-0.769986\pi$
$978$	3.79445			0.121333
$979$	−3.46673	+	6.00455i	−0.110797	+	0.191906i
$980$	−9.72825	−	8.27314i	−0.310757	−	0.264276i
$981$	12.6868	+	7.32475i	0.405060	+	0.233861i
$982$	−12.3856	+	7.15080i	−0.395239	+	0.228191i
$983$	−6.05318	+	3.49481i	−0.193067	+	0.111467i	−0.593417	−	0.804895i	$-0.702222\pi$
$983$	−6.05318	+	3.49481i	−0.193067	+	0.111467i	0.400351	+	0.916362i	$0.368888\pi$
$984$	19.2707			0.614328
$985$	26.9336			0.858176
$986$	0.516464	−	0.298181i	0.0164476	−	0.00949601i
$987$	9.29684	−	4.29785i	0.295922	−	0.136802i
$988$	32.1096	−	13.3268i	1.02154	−	0.423981i
$989$	−10.5893	+	18.3413i	−0.336722	+	0.583219i
$990$	4.07979	+	2.35547i	0.129664	+	0.0748617i
$991$	16.3671	−	28.3486i	0.519917	−	0.900522i	−0.479815	−	0.877370i	$-0.659296\pi$
$991$	16.3671	−	28.3486i	0.519917	−	0.900522i	0.999732	−	0.0231525i	$-0.00737033\pi$
$992$	−7.16066	−	12.4026i	−0.227351	−	0.393784i
$993$			5.27532i			0.167407i
$994$	−2.81970	+	3.99876i	−0.0894353	+	0.126833i
$995$	15.4512	+	8.92078i	0.489838	+	0.282808i
$996$	−3.69960	−	2.13597i	−0.117226	−	0.0676807i
$997$	57.7897			1.83022			0.915109	−	0.403207i	$-0.132104\pi$
$997$	57.7897			1.83022			0.915109	+	0.403207i	$0.132104\pi$
$998$	0.449529	−	0.778607i	0.0142296	−	0.0246464i
$999$		−	3.78114i		−	0.119630i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.k.b.23.3	yes	12
3.2	odd	2		819.2.bm.f.478.4		12
7.2	even	3		637.2.q.g.491.3		12
7.3	odd	6		637.2.u.g.361.4		12
7.4	even	3		91.2.u.b.88.4	yes	12
7.5	odd	6		637.2.q.i.491.3		12
7.6	odd	2		637.2.k.i.569.3		12
13.2	odd	12		1183.2.e.j.170.8		24
13.4	even	6		91.2.u.b.30.4	yes	12
13.11	odd	12		1183.2.e.j.170.5		24
21.11	odd	6		819.2.do.e.361.3		12
39.17	odd	6		819.2.do.e.667.3		12
91.2	odd	12		8281.2.a.cp.1.5		12
91.4	even	6	inner	91.2.k.b.4.4	✓	12
91.11	odd	12		1183.2.e.j.508.5		24
91.17	odd	6		637.2.k.i.459.4		12
91.30	even	6		637.2.q.g.589.3		12
91.37	odd	12		8281.2.a.cp.1.8		12
91.54	even	12		8281.2.a.co.1.5		12
91.67	odd	12		1183.2.e.j.508.8		24
91.69	odd	6		637.2.u.g.30.4		12
91.82	odd	6		637.2.q.i.589.3		12
91.89	even	12		8281.2.a.co.1.8		12
273.95	odd	6		819.2.bm.f.550.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.4	✓	12	91.4	even	6	inner
91.2.k.b.23.3	yes	12	1.1	even	1	trivial
91.2.u.b.30.4	yes	12	13.4	even	6
91.2.u.b.88.4	yes	12	7.4	even	3
637.2.k.i.459.4		12	91.17	odd	6
637.2.k.i.569.3		12	7.6	odd	2
637.2.q.g.491.3		12	7.2	even	3
637.2.q.g.589.3		12	91.30	even	6
637.2.q.i.491.3		12	7.5	odd	6
637.2.q.i.589.3		12	91.82	odd	6
637.2.u.g.30.4		12	91.69	odd	6
637.2.u.g.361.4		12	7.3	odd	6
819.2.bm.f.478.4		12	3.2	odd	2
819.2.bm.f.550.3		12	273.95	odd	6
819.2.do.e.361.3		12	21.11	odd	6
819.2.do.e.667.3		12	39.17	odd	6
1183.2.e.j.170.5		24	13.11	odd	12
1183.2.e.j.170.8		24	13.2	odd	12
1183.2.e.j.508.5		24	91.11	odd	12
1183.2.e.j.508.8		24	91.67	odd	12
8281.2.a.co.1.5		12	91.54	even	12
8281.2.a.co.1.8		12	91.89	even	12
8281.2.a.cp.1.5		12	91.2	odd	12
8281.2.a.cp.1.8		12	91.37	odd	12

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.499987i q^{2} +(-0.424801 + 0.735776i) q^{3} +1.75001 q^{4} +(-0.902810 - 0.521238i) q^{5} +(0.367878 + 0.212395i) q^{6} +(2.63491 + 0.239300i) q^{7} -1.87496i q^{8} +(1.13909 + 1.97296i) q^{9} +O(q^{10})\)	\(q-0.499987i q^{2} +(-0.424801 + 0.735776i) q^{3} +1.75001 q^{4} +(-0.902810 - 0.521238i) q^{5} +(0.367878 + 0.212395i) q^{6} +(2.63491 + 0.239300i) q^{7} -1.87496i q^{8} +(1.13909 + 1.97296i) q^{9} +(-0.260612 + 0.451393i) q^{10} +(-3.43579 - 1.98365i) q^{11} +(-0.743407 + 1.28762i) q^{12} +(-3.57504 - 0.468096i) q^{13} +(0.119647 - 1.31742i) q^{14} +(0.767029 - 0.442844i) q^{15} +2.56257 q^{16} +0.142035 q^{17} +(0.986453 - 0.569529i) q^{18} +(-4.77160 + 2.75488i) q^{19} +(-1.57993 - 0.912173i) q^{20} +(-1.29538 + 1.83705i) q^{21} +(-0.991800 + 1.71785i) q^{22} -4.39098 q^{23} +(1.37955 + 0.796483i) q^{24} +(-1.95662 - 3.38897i) q^{25} +(-0.234042 + 1.78747i) q^{26} -4.48435 q^{27} +(4.61112 + 0.418779i) q^{28} +(4.19880 + 7.27253i) q^{29} +(-0.221416 - 0.383504i) q^{30} +(2.46516 - 1.42326i) q^{31} -5.03117i q^{32} +(2.91905 - 1.68531i) q^{33} -0.0710158i q^{34} +(-2.25409 - 1.58946i) q^{35} +(1.99342 + 3.45271i) q^{36} +0.843187i q^{37} +(1.37740 + 2.38574i) q^{38} +(1.86309 - 2.43158i) q^{39} +(-0.977298 + 1.69273i) q^{40} +(10.4766 - 6.04869i) q^{41} +(0.918499 + 0.647674i) q^{42} +(2.41161 - 4.17704i) q^{43} +(-6.01267 - 3.47142i) q^{44} -2.37494i q^{45} +2.19543i q^{46} +(-3.94602 - 2.27824i) q^{47} +(-1.08858 + 1.88548i) q^{48} +(6.88547 + 1.26107i) q^{49} +(-1.69444 + 0.978285i) q^{50} +(-0.0603367 + 0.104506i) q^{51} +(-6.25636 - 0.819175i) q^{52} +(0.139800 + 0.242141i) q^{53} +2.24211i q^{54} +(2.06791 + 3.58172i) q^{55} +(0.448678 - 4.94034i) q^{56} -4.68111i q^{57} +(3.63617 - 2.09934i) q^{58} +10.7815i q^{59} +(1.34231 - 0.774983i) q^{60} +(2.93177 + 5.07797i) q^{61} +(-0.711612 - 1.23255i) q^{62} +(2.52926 + 5.47115i) q^{63} +2.60963 q^{64} +(2.98359 + 2.28605i) q^{65} +(-0.842634 - 1.45949i) q^{66} +(-4.45524 - 2.57223i) q^{67} +0.248564 q^{68} +(1.86529 - 3.23078i) q^{69} +(-0.794706 + 1.12701i) q^{70} +(-3.20326 - 1.84940i) q^{71} +(3.69921 - 2.13574i) q^{72} +(5.72686 - 3.30640i) q^{73} +0.421582 q^{74} +3.32470 q^{75} +(-8.35036 + 4.82108i) q^{76} +(-8.57829 - 6.04892i) q^{77} +(-1.21576 - 0.931521i) q^{78} +(-5.96135 + 10.3254i) q^{79} +(-2.31352 - 1.33571i) q^{80} +(-1.51231 + 2.61940i) q^{81} +(-3.02426 - 5.23818i) q^{82} +2.87321i q^{83} +(-2.26694 + 3.21486i) q^{84} +(-0.128231 - 0.0740342i) q^{85} +(-2.08846 - 1.20578i) q^{86} -7.13461 q^{87} +(-3.71926 + 6.44195i) q^{88} -1.74765i q^{89} -1.18744 q^{90} +(-9.30787 - 2.08890i) q^{91} -7.68427 q^{92} +2.41841i q^{93} +(-1.13909 + 1.97296i) q^{94} +5.74379 q^{95} +(3.70181 + 2.13724i) q^{96} +(2.34079 + 1.35145i) q^{97} +(0.630517 - 3.44264i) q^{98} -9.03822i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} - 8 q^{4} - 3 q^{5} - 9 q^{6} - 3 q^{7} - q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 - 8 * q^4 - 3 * q^5 - 9 * q^6 - 3 * q^7 - q^9	\( 12 q - 3 q^{3} - 8 q^{4} - 3 q^{5} - 9 q^{6} - 3 q^{7} - q^{9} + 12 q^{10} + 12 q^{11} - q^{12} - 2 q^{13} + 4 q^{14} - 12 q^{15} + 16 q^{16} - 34 q^{17} + 3 q^{18} + 9 q^{19} - 3 q^{20} + 21 q^{21} - 15 q^{22} - 6 q^{23} + 15 q^{24} - 5 q^{25} - 6 q^{26} + 12 q^{27} - 9 q^{28} - q^{29} + 11 q^{30} + 18 q^{31} - 6 q^{33} - 6 q^{35} - 13 q^{36} + 19 q^{38} - 4 q^{39} - q^{40} - 6 q^{41} - 8 q^{42} + 11 q^{43} - 33 q^{44} - 15 q^{47} + 19 q^{48} - 3 q^{49} + 18 q^{50} + 4 q^{51} - 7 q^{52} - 8 q^{53} - 15 q^{55} + 27 q^{56} - 24 q^{58} - 30 q^{60} + 5 q^{61} + 41 q^{62} - 30 q^{63} + 2 q^{64} + 21 q^{65} - 34 q^{66} + 15 q^{67} + 22 q^{68} + 7 q^{69} + 3 q^{70} + 30 q^{71} + 57 q^{72} + 42 q^{73} + 66 q^{74} - 2 q^{75} - 45 q^{76} - 19 q^{77} + 44 q^{78} - 35 q^{79} - 63 q^{80} + 14 q^{81} + 5 q^{82} - 12 q^{84} - 21 q^{85} - 57 q^{86} - 20 q^{87} - 14 q^{88} - 7 q^{91} - 66 q^{92} + q^{94} - 4 q^{95} + 21 q^{96} - 3 q^{97} - 18 q^{98}+O(q^{100}) \) 12 * q - 3 * q^3 - 8 * q^4 - 3 * q^5 - 9 * q^6 - 3 * q^7 - q^9 + 12 * q^10 + 12 * q^11 - q^12 - 2 * q^13 + 4 * q^14 - 12 * q^15 + 16 * q^16 - 34 * q^17 + 3 * q^18 + 9 * q^19 - 3 * q^20 + 21 * q^21 - 15 * q^22 - 6 * q^23 + 15 * q^24 - 5 * q^25 - 6 * q^26 + 12 * q^27 - 9 * q^28 - q^29 + 11 * q^30 + 18 * q^31 - 6 * q^33 - 6 * q^35 - 13 * q^36 + 19 * q^38 - 4 * q^39 - q^40 - 6 * q^41 - 8 * q^42 + 11 * q^43 - 33 * q^44 - 15 * q^47 + 19 * q^48 - 3 * q^49 + 18 * q^50 + 4 * q^51 - 7 * q^52 - 8 * q^53 - 15 * q^55 + 27 * q^56 - 24 * q^58 - 30 * q^60 + 5 * q^61 + 41 * q^62 - 30 * q^63 + 2 * q^64 + 21 * q^65 - 34 * q^66 + 15 * q^67 + 22 * q^68 + 7 * q^69 + 3 * q^70 + 30 * q^71 + 57 * q^72 + 42 * q^73 + 66 * q^74 - 2 * q^75 - 45 * q^76 - 19 * q^77 + 44 * q^78 - 35 * q^79 - 63 * q^80 + 14 * q^81 + 5 * q^82 - 12 * q^84 - 21 * q^85 - 57 * q^86 - 20 * q^87 - 14 * q^88 - 7 * q^91 - 66 * q^92 + q^94 - 4 * q^95 + 21 * q^96 - 3 * q^97 - 18 * q^98

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