LMFDB - Embedded newform 91.2.k.b.4.4

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} + 16 x^{2} - 96 x + 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			4.4
Root			$-1.18541 + 0.771231i$ of defining polynomial
Character	$\chi$	$=$	91.4
Dual form			91.2.k.b.23.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.499987i q^{2} +(-0.424801 - 0.735776i) q^{3} +1.75001 q^{4} +(-0.902810 + 0.521238i) q^{5} +(0.367878 - 0.212395i) q^{6} +(2.63491 - 0.239300i) q^{7} +1.87496i q^{8} +(1.13909 - 1.97296i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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	$0.0565655\pi$
$2$			0.499987i			0.353544i	−0.984252	+	0.176772i	$0.943434\pi$
$3$	−0.424801	−	0.735776i	−0.245259	−	0.424801i	0.716946	−	0.697129i	$-0.245540\pi$
$3$	−0.424801	−	0.735776i	−0.245259	−	0.424801i	−0.962204	+	0.272328i	$0.912206\pi$
$4$	1.75001			0.875007
$5$	−0.902810	+	0.521238i	−0.403749	+	0.233105i	−0.688100	−	0.725616i	$-0.741555\pi$
$5$	−0.902810	+	0.521238i	−0.403749	+	0.233105i	0.284351	+	0.958720i	$0.408222\pi$
$6$	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	−0.918677	−	0.395009i	$-0.870742\pi$
$11$	−3.43579	+	1.98365i	−1.03593	+	0.598094i	−0.117251	+	0.993102i	$0.537408\pi$
$12$	−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	−0.159861	−	0.987140i	$-0.551105\pi$
$19$	−4.77160	−	2.75488i	−1.09468	−	0.632014i	−0.934818	+	0.355126i	$0.884438\pi$
$20$	−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	−0.152419	−	0.988316i	$-0.548706\pi$
$29$	4.19880	−	7.27253i	0.779697	−	1.35047i	0.932116	−	0.362159i	$-0.117960\pi$
$30$	−0.221416	+	0.383504i	−0.0404249	+	0.0700179i
$31$	2.46516	+	1.42326i	0.442756	+	0.255625i	0.704766	−	0.709440i	$-0.251052\pi$
$31$	2.46516	+	1.42326i	0.442756	+	0.255625i	−0.262010	+	0.965065i	$0.584385\pi$
$32$			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	$-0.977920\pi$
$37$		−	0.843187i		−	0.138619i	0.997595	−	0.0693095i	$-0.0220796\pi$
$38$	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	0.982133	+	0.188190i	$0.0602621\pi$
$41$	10.4766	+	6.04869i	1.63618	+	0.944647i	0.654044	+	0.756457i	$0.273071\pi$
$42$	0.918499	−	0.647674i	0.141728	−	0.0999382i
$43$	2.41161	+	4.17704i	0.367768	+	0.636993i	0.989216	−	0.146463i	$-0.0467888\pi$
$43$	2.41161	+	4.17704i	0.367768	+	0.636993i	−0.621448	+	0.783455i	$0.713455\pi$
$44$	−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	−0.759378	−	0.650650i	$-0.774496\pi$
$47$	−3.94602	+	2.27824i	−0.575587	+	0.332315i	0.183791	+	0.982965i	$0.441163\pi$
$48$	−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	−0.856264	−	0.516538i	$-0.827220\pi$
$53$	0.139800	−	0.242141i	0.0192030	−	0.0332606i	0.875467	+	0.483278i	$0.160554\pi$
$54$		−	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	$-0.752373\pi$
$59$		−	10.7815i		−	1.40363i	0.712359	−	0.701815i	$-0.247627\pi$
$60$	1.34231	+	0.774983i	0.173292	+	0.100050i
$61$	2.93177	−	5.07797i	0.375374	−	0.650168i	−0.615009	−	0.788520i	$-0.710847\pi$
$61$	2.93177	−	5.07797i	0.375374	−	0.650168i	0.990383	+	0.138353i	$0.0441808\pi$
$62$	−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	−0.746818	−	0.665029i	$-0.768419\pi$
$67$	−4.45524	+	2.57223i	−0.544294	+	0.314248i	0.202523	+	0.979277i	$0.435086\pi$
$68$	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	−0.677887	−	0.735167i	$-0.737104\pi$
$71$	−3.20326	+	1.84940i	−0.380157	+	0.219484i	0.297730	+	0.954650i	$0.403771\pi$
$72$	3.69921	+	2.13574i	0.435956	+	0.251700i
$73$	5.72686	+	3.30640i	0.670278	+	0.386985i	0.796182	−	0.605057i	$-0.206850\pi$
$73$	5.72686	+	3.30640i	0.670278	+	0.386985i	−0.125904	+	0.992042i	$0.540183\pi$
$74$	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	−0.977705	−	0.209985i	$-0.932658\pi$
$79$	−5.96135	−	10.3254i	−0.670705	−	1.16169i	0.307000	−	0.951710i	$-0.400675\pi$
$80$	−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	$-0.949596\pi$
$83$		−	2.87321i		−	0.315376i	0.987489	−	0.157688i	$-0.0504040\pi$
$84$	−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	$0.0295258\pi$
$89$			1.74765i			0.185250i	−0.995701	+	0.0926252i	$0.970474\pi$
$90$	−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	−0.376435	−	0.926443i	$-0.622850\pi$
$97$	2.34079	−	1.35145i	0.237671	−	0.137219i	0.614106	+	0.789224i	$0.289517\pi$
$98$	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	0.996488	+	0.0837401i	$0.0266866\pi$
$101$	5.73612	+	9.93524i	0.570765	+	0.988594i	−0.425723	+	0.904854i	$0.639980\pi$
$102$	0.0522517	−	0.0301676i	0.00517369	−	0.00298703i
$103$	2.08475	+	3.61090i	0.205417	+	0.355792i	0.950265	−	0.311441i	$-0.100812\pi$
$103$	2.08475	+	3.61090i	0.205417	+	0.355792i	−0.744849	+	0.667233i	$0.767478\pi$
$104$	−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	0.742400	−	0.669957i	$-0.233688\pi$
$109$	5.56886	+	3.21518i	0.533400	+	0.307958i	−0.209000	+	0.977916i	$0.567021\pi$
$110$	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	−0.999835	−	0.0181892i	$-0.994210\pi$
$113$	−5.48164	−	9.49448i	−0.515670	−	0.893166i	0.484165	−	0.874977i	$-0.339123\pi$
$114$	−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	−0.907125	−	0.420862i	$-0.861728\pi$
$127$	−1.00394	+	1.73887i	−0.0890849	+	0.154300i	0.818040	+	0.575162i	$0.195061\pi$
$128$			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	0.998676	+	0.0514449i	$0.0163826\pi$
$131$	6.22511	+	10.7822i	0.543890	+	0.942046i	−0.454785	+	0.890601i	$0.650284\pi$
$132$	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	$-0.928068\pi$
$137$		−	5.24518i		−	0.448126i	0.974575	−	0.224063i	$-0.0719321\pi$
$138$	−1.61535	+	0.932620i	−0.137507	+	0.0793899i
$139$	10.3693	+	17.9601i	0.879510	+	1.52336i	0.851880	+	0.523737i	$0.175463\pi$
$139$	10.3693	+	17.9601i	0.879510	+	1.52336i	0.0276301	+	0.999618i	$0.491204\pi$
$140$	−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	0.500403	−	0.865792i	$-0.333185\pi$
$149$	0.00985188	+	0.00568799i	0.000807098	+	0.000465978i	−0.499596	+	0.866258i	$0.666518\pi$
$150$			1.66231i			0.135727i
$151$	−16.3726	−	9.45271i	−1.33238	−	0.769251i	−0.346717	−	0.937970i	$-0.612704\pi$
$151$	−16.3726	−	9.45271i	−1.33238	−	0.769251i	−0.985664	+	0.168719i	$0.946037\pi$
$152$	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	0.136198	+	0.990682i	$0.456512\pi$
$157$	−9.89687	+	17.1419i	−0.789856	+	1.36807i	−0.926054	+	0.377390i	$0.876822\pi$
$158$	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	0.771365	−	0.636393i	$-0.219574\pi$
$163$	7.73581	+	4.46627i	0.605915	+	0.349825i	−0.165450	+	0.986218i	$0.552908\pi$
$164$	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	0.691269	−	0.722597i	$-0.257052\pi$
$167$	5.31279	+	3.06734i	0.411116	+	0.237358i	−0.280153	+	0.959955i	$0.590385\pi$
$168$	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	0.126535	−	0.991962i	$-0.459614\pi$
$173$	12.1314	−	21.0122i	0.922332	−	1.59753i	0.795797	−	0.605563i	$-0.207052\pi$
$174$		−	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	0.778315	−	0.627874i	$-0.216075\pi$
$179$	−2.06838	−	3.58253i	−0.154598	−	0.267771i	−0.932912	+	0.360103i	$0.882741\pi$
$180$			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	−0.724705	−	0.689059i	$-0.758024\pi$
$191$	3.23933	−	5.61069i	0.234390	−	0.405975i	0.959095	+	0.283084i	$0.0913574\pi$
$192$	−1.10857	−	1.92011i	−0.0800044	−	0.138572i
$193$	4.18228	−	2.41464i	0.301047	−	0.173810i	−0.341866	−	0.939749i	$-0.611059\pi$
$193$	4.18228	−	2.41464i	0.301047	−	0.173810i	0.642913	+	0.765939i	$0.277726\pi$
$194$	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	−0.992586	−	0.121545i	$-0.961215\pi$
$197$	−22.3748	−	12.9181i	−1.59414	−	0.920377i	−0.601554	−	0.798832i	$-0.705452\pi$
$198$	−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	0.358024	+	0.933713i	$0.383451\pi$
$211$	−9.14557	+	15.8406i	−0.629607	+	1.09051i	−0.987631	+	0.156799i	$0.949883\pi$
$212$	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	0.127674	−	0.991816i	$-0.459249\pi$
$223$	−9.96682	−	5.75435i	−0.667428	−	0.385340i	−0.795101	+	0.606477i	$0.792582\pi$
$224$	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	$-0.797476\pi$
$227$		−	17.9045i		−	1.18836i	0.804332	−	0.594181i	$-0.202524\pi$
$228$			8.19200i			0.542528i
$229$	−3.34589	+	1.93175i	−0.221103	+	0.127654i	−0.606461	−	0.795113i	$-0.707411\pi$
$229$	−3.34589	+	1.93175i	−0.221103	+	0.127654i	0.385358	+	0.922767i	$0.374078\pi$
$230$	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	0.904935	+	0.425549i	$0.139919\pi$
$233$	12.5321	+	21.7062i	0.821004	+	1.42202i	−0.0839312	+	0.996472i	$0.526748\pi$
$234$	−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	$-0.918774\pi$
$239$		−	7.80462i		−	0.504839i	0.967618	−	0.252419i	$-0.0812263\pi$
$240$	1.96557	+	1.13482i	0.126877	+	0.0732524i
$241$		−	21.7653i		−	1.40202i	−0.713150	−	0.701012i	$-0.752732\pi$
$241$		−	21.7653i		−	1.40202i	0.713150	−	0.701012i	$-0.247268\pi$
$242$	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	0.961390	−	0.275191i	$-0.0887411\pi$
$251$	3.83990	+	6.65090i	0.242372	+	0.419801i	−0.719017	+	0.694992i	$0.755408\pi$
$252$	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	0.988198	−	0.153181i	$-0.0489518\pi$
$263$	5.86158	+	10.1525i	0.361440	+	0.626033i	−0.626758	+	0.779214i	$0.715618\pi$
$264$	−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	$0.0248108\pi$
$271$			2.56369i			0.155733i	−0.996964	+	0.0778665i	$0.975189\pi$
$272$	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	$-0.938349\pi$
$281$		−	6.45288i		−	0.384947i	0.981302	−	0.192473i	$-0.0616509\pi$
$282$	−0.967771	+	1.67623i	−0.0576299	+	0.0998180i
$283$	11.0873	+	19.2037i	0.659071	+	1.14154i	0.980857	+	0.194731i	$0.0623835\pi$
$283$	11.0873	+	19.2037i	0.659071	+	1.14154i	−0.321786	+	0.946812i	$0.604283\pi$
$284$	−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	−0.965874	−	0.259014i	$-0.916602\pi$
$293$	−20.9600	+	12.1013i	−1.22450	+	0.706964i	−0.258624	+	0.965978i	$0.583269\pi$
$294$	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	$-0.756191\pi$
$307$		−	24.2924i		−	1.38644i	0.720726	−	0.693220i	$-0.243809\pi$
$308$	−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	−0.803952	−	0.594694i	$-0.797273\pi$
$311$	1.99355	−	3.45294i	0.113044	−	0.195798i	0.916996	+	0.398896i	$0.130607\pi$
$312$	−4.55911	+	3.49322i	−0.258109	+	0.197764i
$313$	−14.2377	−	24.6604i	−0.804763	−	1.39389i	−0.916451	−	0.400147i	$-0.868959\pi$
$313$	−14.2377	−	24.6604i	−0.804763	−	1.39389i	0.111688	−	0.993743i	$-0.464374\pi$
$314$	−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	−0.849709	−	0.527252i	$-0.823222\pi$
$317$	−14.5632	+	8.40806i	−0.817950	+	0.472244i	0.0317591	+	0.999496i	$0.489889\pi$
$318$		−	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	0.640448	−	0.768002i	$-0.278749\pi$
$331$	5.37730	+	3.10459i	0.295563	+	0.170644i	−0.344885	+	0.938645i	$0.612082\pi$
$332$		−	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	0.0763028	−	0.997085i	$-0.475688\pi$
$349$	−13.9933	−	8.07906i	−0.749046	−	0.432462i	−0.825349	+	0.564623i	$0.809022\pi$
$350$	−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	−0.747451	−	0.664317i	$-0.768723\pi$
$353$	−10.2558	+	5.92119i	−0.545861	+	0.315153i	0.201590	+	0.979470i	$0.435389\pi$
$354$	−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	−0.997394	−	0.0721417i	$-0.977017\pi$
$359$	−27.1631	+	15.6826i	−1.43362	+	0.827698i	−0.436221	+	0.899840i	$0.643683\pi$
$360$	−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	−0.987870	−	0.155285i	$-0.950370\pi$
$367$	−12.0387	−	20.8517i	−0.628415	−	1.08845i	0.359454	−	0.933163i	$-0.382963\pi$
$368$	−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	−0.523470	−	0.852044i	$-0.675363\pi$
$373$	9.19612	−	15.9281i	0.476157	−	0.824728i	0.999627	+	0.0273160i	$0.00869604\pi$
$374$	−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	0.307963	−	0.951398i	$-0.400353\pi$
$379$	−7.04719	−	4.06870i	−0.361990	−	0.208995i	−0.669953	+	0.742403i	$0.733686\pi$
$380$	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	−0.0846992	−	0.996407i	$-0.526993\pi$
$383$	−19.3739	−	11.1856i	−0.989962	−	0.571555i	−0.905263	+	0.424852i	$0.860326\pi$
$384$	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	0.456393	+	0.889778i	$0.349141\pi$
$389$	−10.6973	+	18.5283i	−0.542374	+	0.939420i	−0.998767	+	0.0496415i	$0.984192\pi$
$390$	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	0.525782	−	0.850619i	$-0.323773\pi$
$397$	1.03640	+	0.598365i	0.0520154	+	0.0300311i	−0.473767	+	0.880650i	$0.657106\pi$
$398$		−	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	$0.360685\pi$
$401$			36.2749i			1.81148i	−0.423831	+	0.905741i	$0.639315\pi$
$402$	−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	$0.118162\pi$
$409$			14.6723i			0.725500i	−0.931887	+	0.362750i	$0.881838\pi$
$410$		−	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	−0.784414	−	0.620238i	$-0.787036\pi$
$419$	2.96674	−	5.13855i	0.144935	−	0.251034i	0.929349	+	0.369203i	$0.120369\pi$
$420$	3.72232	+	1.72079i	0.181630	+	0.0839661i
$421$			2.63174i			0.128263i	0.997941	+	0.0641317i	$0.0204278\pi$
$421$			2.63174i			0.128263i	−0.997941	+	0.0641317i	$0.979572\pi$
$422$	−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	−0.0526738	−	0.998612i	$-0.516774\pi$
$431$	16.3139	−	9.41883i	0.785812	−	0.453689i	0.838486	+	0.544923i	$0.183441\pi$
$432$	−11.4915			−0.552884
$433$	9.56773	+	16.5718i	0.459796	+	0.796389i	0.998950	−	0.0458176i	$-0.0145893\pi$
$433$	9.56773	+	16.5718i	0.459796	+	0.796389i	−0.539154	+	0.842207i	$0.681256\pi$
$434$	−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	0.999996	−	0.00296930i	$-0.000945159\pi$
$443$	10.4696	+	18.1339i	0.497426	+	0.861568i	−0.502569	+	0.864537i	$0.667612\pi$
$444$	−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	−0.0883746	−	0.996087i	$-0.528167\pi$
$449$	15.4700	−	8.93162i	0.730075	−	0.421509i	0.818450	+	0.574578i	$0.194834\pi$
$450$	−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	$-0.950922\pi$
$457$		−	6.56597i		−	0.307143i	0.988138	−	0.153571i	$-0.0490775\pi$
$458$	−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	−0.599571	−	0.800322i	$-0.704662\pi$
$461$	−4.42854	+	2.55682i	−0.206258	+	0.119083i	0.393313	+	0.919404i	$0.371329\pi$
$462$	−1.87101	+	4.04725i	−0.0870472	+	0.188295i
$463$			33.3239i			1.54869i	0.632761	+	0.774347i	$0.281921\pi$
$463$			33.3239i			1.54869i	−0.632761	+	0.774347i	$0.718079\pi$
$464$	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	0.676433	−	0.736504i	$-0.263525\pi$
$467$	−6.47472	−	11.2145i	−0.299614	−	0.518947i	−0.976048	+	0.217557i	$0.930191\pi$
$468$	−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	0.140987	−	0.990012i	$-0.454973\pi$
$479$	23.3930	−	13.5060i	1.06885	−	0.617104i	0.927868	+	0.372908i	$0.121639\pi$
$480$	−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	$-0.740947\pi$
$487$		−	32.0838i		−	1.45386i	0.686713	−	0.726928i	$-0.259053\pi$
$488$	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	0.338760	+	0.940873i	$0.389992\pi$
$491$	−14.3020	+	24.7718i	−0.645440	+	1.11793i	−0.984200	+	0.177061i	$0.943341\pi$
$492$		−	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	−0.464739	−	0.885448i	$-0.653852\pi$
$499$	1.55726	−	0.899082i	0.0697123	−	0.0402484i	0.534451	+	0.845199i	$0.320518\pi$
$500$		−	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	−0.983542	−	0.180681i	$-0.942170\pi$
$503$	−14.5386	−	25.1816i	−0.648245	−	1.12279i	0.335297	−	0.942112i	$-0.391163\pi$
$504$	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	$0.171825\pi$
$509$			23.1913i			1.02794i	−0.857809	+	0.513969i	$0.828175\pi$
$510$	−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	0.229193	+	0.973381i	$0.426391\pi$
$521$	−16.6255	+	28.7962i	−0.728376	+	1.26158i	−0.957569	+	0.288203i	$0.906942\pi$
$522$	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	−0.858617	−	0.512618i	$-0.828676\pi$
$541$	−19.6306	+	11.3337i	−0.843986	+	0.487275i	0.0146313	+	0.999893i	$0.495343\pi$
$542$	−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	−0.277547	−	0.960712i	$-0.589522\pi$
$557$	9.81039	−	5.66403i	0.415680	−	0.239993i	0.693227	+	0.720719i	$0.256188\pi$
$558$	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	−0.448959	−	0.893552i	$-0.648205\pi$
$571$	13.1273	−	22.7371i	0.549360	−	0.951519i	0.998319	−	0.0579663i	$-0.0184616\pi$
$572$	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	0.872606	−	0.488424i	$-0.162428\pi$
$577$	21.2806	+	12.2863i	0.885922	+	0.511487i	0.0133154	+	0.999911i	$0.495761\pi$
$578$		−	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	0.819798	−	0.572653i	$-0.194086\pi$
$587$	17.7777	+	10.2640i	0.733765	+	0.423639i	−0.0860331	+	0.996292i	$0.527419\pi$
$588$	−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	0.371669	−	0.928365i	$-0.378786\pi$
$593$	33.1545	−	19.1417i	1.36149	−	0.786057i	0.989822	+	0.142308i	$0.0454524\pi$
$594$	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	−0.973205	−	0.229939i	$-0.926147\pi$
$599$	−7.03567	+	12.1861i	−0.287470	+	0.497912i	0.685735	+	0.727851i	$0.259481\pi$
$600$			6.23367i			0.254488i
$601$	10.1171	−	17.5233i	0.412685	−	0.714791i	−0.582498	−	0.812832i	$-0.697925\pi$
$601$	10.1171	−	17.5233i	0.412685	−	0.714791i	0.995182	+	0.0980417i	$0.0312579\pi$
$602$	−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	−0.924814	−	0.380420i	$-0.875780\pi$
$607$	−3.27563	+	5.67356i	−0.132954	+	0.230283i	0.791860	+	0.610703i	$0.209113\pi$
$608$	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	0.212988	−	0.977055i	$-0.431681\pi$
$613$	28.8598	−	16.6622i	1.16564	−	0.672980i	0.952648	+	0.304075i	$0.0983472\pi$
$614$	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	−0.377499	−	0.926010i	$-0.623216\pi$
$617$	5.85466	−	3.38019i	0.235700	−	0.136081i	0.613199	+	0.789929i	$0.289883\pi$
$618$	1.53387	+	0.885581i	0.0617013	+	0.0356233i
$619$	15.2582	+	8.80931i	0.613278	+	0.354076i	0.774247	−	0.632883i	$-0.218129\pi$
$619$	15.2582	+	8.80931i	0.613278	+	0.354076i	−0.160970	+	0.986959i	$0.551462\pi$
$620$	−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	−0.203257	−	0.979125i	$-0.565153\pi$
$631$	13.6416	−	7.87596i	0.543062	−	0.313537i	0.746319	+	0.665588i	$0.231819\pi$
$632$	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	−0.787138	−	0.616777i	$-0.788438\pi$
$643$	−16.3952	+	9.46576i	−0.646563	+	0.373293i	0.140575	+	0.990070i	$0.455105\pi$
$644$	−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	−0.952216	−	0.305426i	$-0.901201\pi$
$647$	−18.8384	−	32.6291i	−0.740614	−	1.28278i	0.211601	−	0.977356i	$-0.432132\pi$
$648$	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	0.879507	−	0.475886i	$-0.157872\pi$
$659$	0.709152	+	1.22829i	0.0276247	+	0.0478473i	−0.851883	+	0.523733i	$0.824539\pi$
$660$	−6.14919			−0.239357
$661$	−3.97764	+	2.29649i	−0.154712	+	0.0893231i	−0.575357	−	0.817902i	$-0.695137\pi$
$661$	−3.97764	+	2.29649i	−0.154712	+	0.0893231i	0.420645	+	0.907225i	$0.361804\pi$
$662$	−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	−0.903676	−	0.428216i	$-0.859142\pi$
$673$	−2.10111	+	3.63924i	−0.0809920	+	0.140282i	0.822684	+	0.568499i	$0.192475\pi$
$674$			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	0.777801	−	0.628511i	$-0.216335\pi$
$677$	−4.04354	−	7.00361i	−0.155406	−	0.269171i	−0.933207	+	0.359340i	$0.883002\pi$
$678$	−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	$-0.843423\pi$
$683$		−	24.6865i		−	0.944604i	0.881437	−	0.472302i	$-0.156577\pi$
$684$	−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	$-0.931314\pi$
$691$		−	11.2567i		−	0.428225i	0.976809	−	0.214113i	$-0.0686859\pi$
$692$	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	0.834027	−	0.551723i	$-0.186030\pi$
$709$	20.5889	+	11.8870i	0.773234	+	0.446427i	−0.0607929	+	0.998150i	$0.519363\pi$
$710$	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	−0.604616	−	0.796517i	$-0.706673\pi$
$719$	10.3904	−	17.9967i	0.387496	−	0.671163i	0.992112	+	0.125354i	$0.0400068\pi$
$720$			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	−0.413568	−	0.910473i	$-0.635718\pi$
$733$	4.55224	−	2.62824i	0.168141	−	0.0970761i	0.581709	+	0.813397i	$0.302384\pi$
$734$	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	−0.381768	−	0.924258i	$-0.624685\pi$
$739$	6.19209	−	3.57501i	0.227780	−	0.131509i	0.609547	+	0.792750i	$0.291351\pi$
$740$	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	0.488620	−	0.872496i	$-0.337500\pi$
$743$	−0.618032	−	0.356821i	−0.0226734	−	0.0130905i	−0.511294	+	0.859406i	$0.670834\pi$
$744$	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	−0.975638	−	0.219386i	$-0.929594\pi$
$757$	−8.19425	+	14.1928i	−0.297825	+	0.515848i	0.677813	+	0.735234i	$0.262928\pi$
$758$	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	0.624878	−	0.780722i	$-0.285149\pi$
$761$	7.20531	+	4.15999i	0.261192	+	0.150800i	−0.363686	+	0.931522i	$0.618482\pi$
$762$			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

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

Introduction

L-functions

Modular forms

Varieties

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