LMFDB - Embedded newform 230.2.g.b.141.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(31,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("230.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.g (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 5 x^{19} + 12 x^{18} + 16 x^{17} - 49 x^{16} + 59 x^{15} - 197 x^{14} + 42 x^{13} + 1625 x^{12} + \cdots + 529 $ x^20 - 5x^19 + 12x^18 + 16x^17 - 49x^16 + 59x^15 - 197x^14 + 42x^13 + 1625x^12 - 5910x^11 + 14651x^10 - 22501x^9 + 26003x^8 - 19607x^7 + 13040x^6 + 348x^5 + 7193x^4 + 10771x^3 + 8781x^2 + 3105*x + 529
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			141.1
Root			$0.588453 + 1.28853i$ of defining polynomial
Character	$\chi$	$=$	230.141
Dual form			230.2.g.b.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 + 0.989821i) q^{2} +(-1.10832 + 2.42687i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-2.55990 - 0.751655i) q^{6} +(-0.986597 + 0.634047i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-2.69677 - 3.11224i) q^{9} +O(q^{10})$	\(q+(0.142315 + 0.989821i) q^{2} +(-1.10832 + 2.42687i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-2.55990 - 0.751655i) q^{6} +(-0.986597 + 0.634047i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-2.69677 - 3.11224i) q^{9} +(-0.841254 - 0.540641i) q^{10} +(0.195880 - 1.36238i) q^{11} +(0.379692 - 2.64082i) q^{12} +(1.43004 + 0.919031i) q^{13} +(-0.768001 - 0.886321i) q^{14} +(-1.10832 - 2.42687i) q^{15} +(0.841254 - 0.540641i) q^{16} +(3.87301 + 1.13722i) q^{17} +(2.69677 - 3.11224i) q^{18} +(-5.55050 + 1.62977i) q^{19} +(0.415415 - 0.909632i) q^{20} +(-0.445292 - 3.09707i) q^{21} +1.37639 q^{22} +(-2.63501 + 4.00708i) q^{23} +2.66797 q^{24} +(-0.142315 - 0.989821i) q^{25} +(-0.706161 + 1.54628i) q^{26} +(2.86219 - 0.840414i) q^{27} +(0.768001 - 0.886321i) q^{28} +(-3.94124 - 1.15725i) q^{29} +(2.24444 - 1.44242i) q^{30} +(1.74115 + 3.81258i) q^{31} +(0.654861 + 0.755750i) q^{32} +(3.08922 + 1.98532i) q^{33} +(-0.574457 + 3.99544i) q^{34} +(0.166903 - 1.16083i) q^{35} +(3.46435 + 2.22640i) q^{36} +(2.83610 + 3.27303i) q^{37} +(-2.40310 - 5.26206i) q^{38} +(-3.81531 + 2.45195i) q^{39} +(0.959493 + 0.281733i) q^{40} +(4.48578 - 5.17686i) q^{41} +(3.00218 - 0.881519i) q^{42} +(-4.90588 + 10.7424i) q^{43} +(0.195880 + 1.36238i) q^{44} +4.11808 q^{45} +(-4.34130 - 2.03792i) q^{46} +11.3658 q^{47} +(0.379692 + 2.64082i) q^{48} +(-2.33655 + 5.11633i) q^{49} +(0.959493 - 0.281733i) q^{50} +(-7.05241 + 8.13892i) q^{51} +(-1.63103 - 0.478915i) q^{52} +(-1.21878 + 0.783263i) q^{53} +(1.23919 + 2.71345i) q^{54} +(0.901341 + 1.04020i) q^{55} +(0.986597 + 0.634047i) q^{56} +(2.19645 - 15.2767i) q^{57} +(0.584577 - 4.06582i) q^{58} +(9.37896 + 6.02749i) q^{59} +(1.74715 + 2.01632i) q^{60} +(-1.22711 - 2.68699i) q^{61} +(-3.52598 + 2.26601i) q^{62} +(4.63394 + 1.36065i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-1.63103 + 0.478915i) q^{65} +(-1.52547 + 3.34032i) q^{66} +(-0.299446 - 2.08269i) q^{67} -4.03652 q^{68} +(-6.80426 - 10.8360i) q^{69} +1.17277 q^{70} +(-0.947942 - 6.59308i) q^{71} +(-1.71071 + 3.74594i) q^{72} +(6.38511 - 1.87484i) q^{73} +(-2.83610 + 3.27303i) q^{74} +(2.55990 + 0.751655i) q^{75} +(4.86650 - 3.12751i) q^{76} +(0.670556 + 1.46831i) q^{77} +(-2.96997 - 3.42753i) q^{78} +(7.13409 + 4.58480i) q^{79} +(-0.142315 + 0.989821i) q^{80} +(0.625564 - 4.35089i) q^{81} +(5.76256 + 3.70338i) q^{82} +(-6.62403 - 7.64454i) q^{83} +(1.29980 + 2.84617i) q^{84} +(-3.39574 + 2.18231i) q^{85} +(-11.3312 - 3.32715i) q^{86} +(7.17665 - 8.28229i) q^{87} +(-1.32063 + 0.387773i) q^{88} +(4.01175 - 8.78452i) q^{89} +(0.586065 + 4.07617i) q^{90} -1.99358 q^{91} +(1.39935 - 4.58714i) q^{92} -11.1824 q^{93} +(1.61752 + 11.2501i) q^{94} +(2.40310 - 5.26206i) q^{95} +(-2.55990 + 0.751655i) q^{96} +(-11.4667 + 13.2333i) q^{97} +(-5.39677 - 1.58464i) q^{98} +(-4.76829 + 3.06439i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9	\( 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9} + 2 q^{10} + 7 q^{11} + 8 q^{12} + 8 q^{13} + 3 q^{14} - 3 q^{15} - 2 q^{16} + 8 q^{17} + 27 q^{18} - q^{19} - 2 q^{20} - 31 q^{21} - 18 q^{22} - 9 q^{23} - 8 q^{24} - 2 q^{25} - 8 q^{26} - 18 q^{27} - 3 q^{28} + 20 q^{29} + 3 q^{30} - 17 q^{31} + 2 q^{32} + 17 q^{33} + 3 q^{34} - 3 q^{35} + 17 q^{36} + 6 q^{37} - 21 q^{38} - 75 q^{39} + 2 q^{40} - 2 q^{41} + 42 q^{42} - 18 q^{43} + 7 q^{44} + 28 q^{45} - 2 q^{46} + 42 q^{47} + 8 q^{48} - 19 q^{49} + 2 q^{50} + 26 q^{51} + 19 q^{52} + 19 q^{53} - 26 q^{54} - 15 q^{55} - 19 q^{56} + 7 q^{57} - 9 q^{58} + 25 q^{59} - 3 q^{60} - 49 q^{61} - 38 q^{62} - 87 q^{63} - 2 q^{64} + 19 q^{65} - 6 q^{66} + 19 q^{67} - 36 q^{68} + 36 q^{69} + 14 q^{70} + 7 q^{71} - 17 q^{72} - 10 q^{73} - 6 q^{74} - 3 q^{75} - q^{76} - 29 q^{77} - 2 q^{78} - 33 q^{79} - 2 q^{80} + 72 q^{81} + 2 q^{82} - 41 q^{83} + 13 q^{84} - 14 q^{85} - 48 q^{86} - 16 q^{87} - 7 q^{88} + 55 q^{89} + 5 q^{90} + 13 q^{92} + 10 q^{93} + 13 q^{94} + 21 q^{95} + 3 q^{96} - 9 q^{97} + 41 q^{98} + 59 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9 + 2 * q^10 + 7 * q^11 + 8 * q^12 + 8 * q^13 + 3 * q^14 - 3 * q^15 - 2 * q^16 + 8 * q^17 + 27 * q^18 - q^19 - 2 * q^20 - 31 * q^21 - 18 * q^22 - 9 * q^23 - 8 * q^24 - 2 * q^25 - 8 * q^26 - 18 * q^27 - 3 * q^28 + 20 * q^29 + 3 * q^30 - 17 * q^31 + 2 * q^32 + 17 * q^33 + 3 * q^34 - 3 * q^35 + 17 * q^36 + 6 * q^37 - 21 * q^38 - 75 * q^39 + 2 * q^40 - 2 * q^41 + 42 * q^42 - 18 * q^43 + 7 * q^44 + 28 * q^45 - 2 * q^46 + 42 * q^47 + 8 * q^48 - 19 * q^49 + 2 * q^50 + 26 * q^51 + 19 * q^52 + 19 * q^53 - 26 * q^54 - 15 * q^55 - 19 * q^56 + 7 * q^57 - 9 * q^58 + 25 * q^59 - 3 * q^60 - 49 * q^61 - 38 * q^62 - 87 * q^63 - 2 * q^64 + 19 * q^65 - 6 * q^66 + 19 * q^67 - 36 * q^68 + 36 * q^69 + 14 * q^70 + 7 * q^71 - 17 * q^72 - 10 * q^73 - 6 * q^74 - 3 * q^75 - q^76 - 29 * q^77 - 2 * q^78 - 33 * q^79 - 2 * q^80 + 72 * q^81 + 2 * q^82 - 41 * q^83 + 13 * q^84 - 14 * q^85 - 48 * q^86 - 16 * q^87 - 7 * q^88 + 55 * q^89 + 5 * q^90 + 13 * q^92 + 10 * q^93 + 13 * q^94 + 21 * q^95 + 3 * q^96 - 9 * q^97 + 41 * q^98 + 59 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$

Coefficient data

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

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

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

$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$3$	−1.10832	+	2.42687i	−0.639887	+	1.40116i	0.260247	+	0.965542i	$0.416196\pi$
$3$	−1.10832	+	2.42687i	−0.639887	+	1.40116i	−0.900133	+	0.435614i	$0.856531\pi$
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	−0.654861	+	0.755750i	−0.292863	+	0.337981i
$5$	−0.654861	+	0.755750i	−0.292863	+	0.337981i
$6$	−2.55990	−	0.751655i	−1.04508	−	0.306862i
$7$	−0.986597	+	0.634047i	−0.372899	+	0.239647i	−0.713645	−	0.700508i	$-0.752957\pi$
$7$	−0.986597	+	0.634047i	−0.372899	+	0.239647i	0.340746	+	0.940155i	$0.389320\pi$
$8$	−0.415415	−	0.909632i	−0.146871	−	0.321603i
$9$	−2.69677	−	3.11224i	−0.898924	−	1.03741i
$10$	−0.841254	−	0.540641i	−0.266028	−	0.170966i
$11$	0.195880	−	1.36238i	0.0590601	−	0.410772i	−0.938748	−	0.344603i	$-0.888013\pi$
$11$	0.195880	−	1.36238i	0.0590601	−	0.410772i	0.997808	−	0.0661685i	$-0.0210775\pi$
$12$	0.379692	−	2.64082i	0.109608	−	0.762338i
$13$	1.43004	+	0.919031i	0.396622	+	0.254893i	0.723715	−	0.690099i	$-0.242433\pi$
$13$	1.43004	+	0.919031i	0.396622	+	0.254893i	−0.327094	+	0.944992i	$0.606069\pi$
$14$	−0.768001	−	0.886321i	−0.205257	−	0.236879i
$15$	−1.10832	−	2.42687i	−0.286166	−	0.626616i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	3.87301	+	1.13722i	0.939344	+	0.275816i	0.715344	−	0.698773i	$-0.246270\pi$
$17$	3.87301	+	1.13722i	0.939344	+	0.275816i	0.224000	+	0.974589i	$0.428088\pi$
$18$	2.69677	−	3.11224i	0.635635	−	0.733562i
$19$	−5.55050	+	1.62977i	−1.27337	+	0.373896i	−0.847455	−	0.530867i	$-0.821866\pi$
$19$	−5.55050	+	1.62977i	−1.27337	+	0.373896i	−0.425916	+	0.904763i	$0.640048\pi$
$20$	0.415415	−	0.909632i	0.0928896	−	0.203400i
$21$	−0.445292	−	3.09707i	−0.0971706	−	0.675837i
$22$	1.37639			0.293446
$23$	−2.63501	+	4.00708i	−0.549438	+	0.835535i
$23$	−2.63501	+	4.00708i	−0.549438	+	0.835535i
$24$	2.66797			0.544598
$25$	−0.142315	−	0.989821i	−0.0284630	−	0.197964i
$26$	−0.706161	+	1.54628i	−0.138489	+	0.303250i
$27$	2.86219	−	0.840414i	0.550828	−	0.161738i
$28$	0.768001	−	0.886321i	0.145139	−	0.167499i
$29$	−3.94124	−	1.15725i	−0.731870	−	0.214896i	−0.105497	−	0.994420i	$-0.533643\pi$
$29$	−3.94124	−	1.15725i	−0.731870	−	0.214896i	−0.626373	+	0.779523i	$0.715461\pi$
$30$	2.24444	−	1.44242i	0.409777	−	0.263348i
$31$	1.74115	+	3.81258i	0.312719	+	0.684760i	0.999097	−	0.0424856i	$-0.0135276\pi$
$31$	1.74115	+	3.81258i	0.312719	+	0.684760i	−0.686378	+	0.727245i	$0.740800\pi$
$32$	0.654861	+	0.755750i	0.115764	+	0.133599i
$33$	3.08922	+	1.98532i	0.537764	+	0.345600i
$34$	−0.574457	+	3.99544i	−0.0985186	+	0.685212i
$35$	0.166903	−	1.16083i	0.0282117	−	0.196217i
$36$	3.46435	+	2.22640i	0.577392	+	0.371067i
$37$	2.83610	+	3.27303i	0.466251	+	0.538083i	0.939365	−	0.342919i	$-0.111416\pi$
$37$	2.83610	+	3.27303i	0.466251	+	0.538083i	−0.473114	+	0.881001i	$0.656870\pi$
$38$	−2.40310	−	5.26206i	−0.389835	−	0.853619i
$39$	−3.81531	+	2.45195i	−0.610938	+	0.392626i
$40$	0.959493	+	0.281733i	0.151709	+	0.0445458i
$41$	4.48578	−	5.17686i	0.700561	−	0.808490i	−0.288267	−	0.957550i	$-0.593079\pi$
$41$	4.48578	−	5.17686i	0.700561	−	0.808490i	0.988828	+	0.149060i	$0.0476246\pi$
$42$	3.00218	−	0.881519i	0.463246	−	0.136021i
$43$	−4.90588	+	10.7424i	−0.748140	+	1.63820i	0.0215401	+	0.999768i	$0.493143\pi$
$43$	−4.90588	+	10.7424i	−0.748140	+	1.63820i	−0.769680	+	0.638430i	$0.779584\pi$
$44$	0.195880	+	1.36238i	0.0295300	+	0.205386i
$45$	4.11808			0.613888
$46$	−4.34130	−	2.03792i	−0.640090	−	0.300475i
$47$	11.3658			1.65787			0.828937	−	0.559343i	$-0.188946\pi$
$47$	11.3658			1.65787			0.828937	+	0.559343i	$0.188946\pi$
$48$	0.379692	+	2.64082i	0.0548039	+	0.381169i
$49$	−2.33655	+	5.11633i	−0.333792	+	0.730904i
$50$	0.959493	−	0.281733i	0.135693	−	0.0398430i
$51$	−7.05241	+	8.13892i	−0.987536	+	1.13968i
$52$	−1.63103	−	0.478915i	−0.226184	−	0.0664135i
$53$	−1.21878	+	0.783263i	−0.167412	+	0.107589i	−0.621664	−	0.783284i	$-0.713543\pi$
$53$	−1.21878	+	0.783263i	−0.167412	+	0.107589i	0.454252	+	0.890873i	$0.349907\pi$
$54$	1.23919	+	2.71345i	0.168633	+	0.369254i
$55$	0.901341	+	1.04020i	0.121537	+	0.140261i
$56$	0.986597	+	0.634047i	0.131840	+	0.0847282i
$57$	2.19645	−	15.2767i	0.290927	−	2.02344i
$58$	0.584577	−	4.06582i	0.0767587	−	0.533868i
$59$	9.37896	+	6.02749i	1.22104	+	0.784713i	0.982471	−	0.186414i	$-0.0596866\pi$
$59$	9.37896	+	6.02749i	1.22104	+	0.784713i	0.238565	+	0.971126i	$0.423323\pi$
$60$	1.74715	+	2.01632i	0.225556	+	0.260306i
$61$	−1.22711	−	2.68699i	−0.157115	−	0.344034i	0.814662	−	0.579937i	$-0.196923\pi$
$61$	−1.22711	−	2.68699i	−0.157115	−	0.344034i	−0.971777	+	0.235902i	$0.924195\pi$
$62$	−3.52598	+	2.26601i	−0.447800	+	0.287784i
$63$	4.63394	+	1.36065i	0.583821	+	0.171425i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	−1.63103	+	0.478915i	−0.202305	+	0.0594021i
$66$	−1.52547	+	3.34032i	−0.187773	+	0.411164i
$67$	−0.299446	−	2.08269i	−0.0365831	−	0.254441i	0.963320	−	0.268355i	$-0.0864800\pi$
$67$	−0.299446	−	2.08269i	−0.0365831	−	0.254441i	−0.999903	+	0.0139139i	$0.995571\pi$
$68$	−4.03652			−0.489500
$69$	−6.80426	−	10.8360i	−0.819137	−	1.30450i
$70$	1.17277			0.140173
$71$	−0.947942	−	6.59308i	−0.112500	−	0.782455i	−0.965474	−	0.260501i	$-0.916112\pi$
$71$	−0.947942	−	6.59308i	−0.112500	−	0.782455i	0.852974	−	0.521954i	$-0.174797\pi$
$72$	−1.71071	+	3.74594i	−0.201610	+	0.441463i
$73$	6.38511	−	1.87484i	0.747321	−	0.219433i	0.114170	−	0.993461i	$-0.463579\pi$
$73$	6.38511	−	1.87484i	0.747321	−	0.219433i	0.633151	+	0.774028i	$0.281761\pi$
$74$	−2.83610	+	3.27303i	−0.329689	+	0.380482i
$75$	2.55990	+	0.751655i	0.295592	+	0.0867937i
$76$	4.86650	−	3.12751i	0.558226	−	0.358750i
$77$	0.670556	+	1.46831i	0.0764170	+	0.167330i
$78$	−2.96997	−	3.42753i	−0.336283	−	0.388091i
$79$	7.13409	+	4.58480i	0.802647	+	0.515830i	0.876479	−	0.481441i	$-0.159886\pi$
$79$	7.13409	+	4.58480i	0.802647	+	0.515830i	−0.0738313	+	0.997271i	$0.523523\pi$
$80$	−0.142315	+	0.989821i	−0.0159113	+	0.110665i
$81$	0.625564	−	4.35089i	0.0695071	−	0.483432i
$82$	5.76256	+	3.70338i	0.636369	+	0.408969i
$83$	−6.62403	−	7.64454i	−0.727082	−	0.839098i	0.265058	−	0.964233i	$-0.414609\pi$
$83$	−6.62403	−	7.64454i	−0.727082	−	0.839098i	−0.992140	+	0.125135i	$0.960064\pi$
$84$	1.29980	+	2.84617i	0.141820	+	0.310542i
$85$	−3.39574	+	2.18231i	−0.368320	+	0.236705i
$86$	−11.3312	−	3.32715i	−1.22188	−	0.358775i
$87$	7.17665	−	8.28229i	0.769418	−	0.887955i
$88$	−1.32063	+	0.387773i	−0.140780	+	0.0413367i
$89$	4.01175	−	8.78452i	0.425245	−	0.931157i	−0.568829	−	0.822456i	$-0.692604\pi$
$89$	4.01175	−	8.78452i	0.425245	−	0.931157i	0.994074	−	0.108701i	$-0.0346692\pi$
$90$	0.586065	+	4.07617i	0.0617766	+	0.429666i
$91$	−1.99358			−0.208984
$92$	1.39935	−	4.58714i	0.145892	−	0.478242i
$93$	−11.1824			−1.15956
$94$	1.61752	+	11.2501i	0.166835	+	1.16036i
$95$	2.40310	−	5.26206i	0.246553	−	0.539876i
$96$	−2.55990	+	0.751655i	−0.261269	+	0.0767155i
$97$	−11.4667	+	13.2333i	−1.16427	+	1.34364i	−0.235987	+	0.971756i	$0.575832\pi$
$97$	−11.4667	+	13.2333i	−1.16427	+	1.34364i	−0.928281	+	0.371880i	$0.878713\pi$
$98$	−5.39677	−	1.58464i	−0.545156	−	0.160072i
$99$	−4.76829	+	3.06439i	−0.479231	+	0.307983i
$100$	0.415415	+	0.909632i	0.0415415	+	0.0909632i
$101$	8.47323	+	9.77863i	0.843118	+	0.973010i	0.999893	−	0.0146246i	$-0.00465532\pi$
$101$	8.47323	+	9.77863i	0.843118	+	0.973010i	−0.156775	+	0.987634i	$0.550110\pi$
$102$	−9.05974	−	5.82234i	−0.897048	−	0.576498i
$103$	2.09043	−	14.5393i	0.205976	−	1.43260i	−0.580139	−	0.814517i	$-0.697002\pi$
$103$	2.09043	−	14.5393i	0.205976	−	1.43260i	0.786115	−	0.618080i	$-0.212089\pi$
$104$	0.241920	−	1.68259i	0.0237222	−	0.164991i
$105$	2.63222	+	1.69162i	0.256878	+	0.165085i
$106$	−0.948741	−	1.09491i	−0.0921498	−	0.106347i
$107$	−1.58156	−	3.46314i	−0.152895	−	0.334794i	0.817649	−	0.575717i	$-0.195277\pi$
$107$	−1.58156	−	3.46314i	−0.152895	−	0.334794i	−0.970544	+	0.240923i	$0.922550\pi$
$108$	−2.50948	+	1.61274i	−0.241475	+	0.155186i
$109$	13.0731	+	3.83862i	1.25218	+	0.367673i	0.839578	−	0.543239i	$-0.182802\pi$
$109$	13.0731	+	3.83862i	1.25218	+	0.367673i	0.412601	+	0.910912i	$0.364620\pi$
$110$	−0.901341	+	1.04020i	−0.0859395	+	0.0991795i
$111$	−11.0865	+	3.25530i	−1.05229	+	0.308979i
$112$	−0.487186	+	1.06679i	−0.0460348	+	0.100802i
$113$	−1.21679	−	8.46297i	−0.114466	−	0.796130i	−0.963484	−	0.267766i	$-0.913715\pi$
$113$	−1.21679	−	8.46297i	−0.114466	−	0.796130i	0.849018	−	0.528364i	$-0.177194\pi$
$114$	15.4338			1.44550
$115$	−1.30279	−	4.61549i	−0.121486	−	0.430397i
$116$	4.10763			0.381384
$117$	−0.996246	−	6.92905i	−0.0921030	−	0.640591i
$118$	−4.63138	+	10.1413i	−0.426353	+	0.933582i
$119$	−4.54216	+	1.33370i	−0.416379	+	0.122260i
$120$	−1.74715	+	2.01632i	−0.159492	+	0.184064i
$121$	8.73672	+	2.56533i	0.794248	+	0.233212i
$122$	2.48501	−	1.59702i	0.224982	−	0.144587i
$123$	7.59194	+	16.6240i	0.684542	+	1.49894i
$124$	−2.74475	−	3.16761i	−0.246485	−	0.284459i
$125$	0.841254	+	0.540641i	0.0752440	+	0.0483564i
$126$	−0.687319	+	4.78041i	−0.0612312	+	0.425873i
$127$	−1.31373	+	9.13718i	−0.116574	+	0.810793i	0.844708	+	0.535228i	$0.179774\pi$
$127$	−1.31373	+	9.13718i	−0.116574	+	0.810793i	−0.961282	+	0.275566i	$0.911135\pi$
$128$	−0.841254	−	0.540641i	−0.0743570	−	0.0477863i
$129$	−20.6331	−	23.8119i	−1.81665	−	2.09652i
$130$	−0.706161	−	1.54628i	−0.0619344	−	0.135617i
$131$	6.75165	−	4.33902i	0.589894	−	0.379102i	−0.211376	−	0.977405i	$-0.567794\pi$
$131$	6.75165	−	4.33902i	0.589894	−	0.379102i	0.801270	+	0.598303i	$0.204158\pi$
$132$	−3.52341	−	1.03457i	−0.306674	−	0.0900475i
$133$	4.44275	−	5.12721i	0.385235	−	0.444585i
$134$	2.01888	−	0.592795i	0.174404	−	0.0512097i
$135$	−1.23919	+	2.71345i	−0.106653	+	0.233537i
$136$	−0.574457	−	3.99544i	−0.0492593	−	0.342606i
$137$	−19.3731			−1.65516			−0.827578	−	0.561350i	$-0.810282\pi$
$137$	−19.3731			−1.65516			−0.827578	+	0.561350i	$0.810282\pi$
$138$	9.75731	−	8.27712i	0.830598	−	0.704596i
$139$	−13.7448			−1.16582			−0.582908	−	0.812538i	$-0.698085\pi$
$139$	−13.7448			−1.16582			−0.582908	+	0.812538i	$0.698085\pi$
$140$	0.166903	+	1.16083i	0.0141058	+	0.0981083i
$141$	−12.5969	+	27.5834i	−1.06085	+	2.32294i
$142$	6.39107	−	1.87659i	0.536327	−	0.157480i
$143$	1.53218	−	1.76823i	0.128128	−	0.147867i
$144$	−3.95127	−	1.16020i	−0.329273	−	0.0966832i
$145$	3.45556	−	2.22075i	0.286968	−	0.184423i
$146$	2.76445	+	6.05331i	0.228788	+	0.500975i
$147$	−9.82705	−	11.3410i	−0.810521	−	0.935391i
$148$	−3.64333	−	2.34143i	−0.299480	−	0.192464i
$149$	0.914701	−	6.36188i	0.0749352	−	0.521186i	−0.917434	−	0.397887i	$-0.869744\pi$
$149$	0.914701	−	6.36188i	0.0749352	−	0.521186i	0.992370	−	0.123299i	$-0.0393473\pi$
$150$	−0.379692	+	2.64082i	−0.0310017	+	0.215622i
$151$	−2.49140	−	1.60112i	−0.202747	−	0.130298i	0.435328	−	0.900272i	$-0.356633\pi$
$151$	−2.49140	−	1.60112i	−0.202747	−	0.130298i	−0.638075	+	0.769975i	$0.720269\pi$
$152$	3.78825	+	4.37188i	0.307268	+	0.354606i
$153$	−6.90534	−	15.1206i	−0.558263	−	1.22243i
$154$	−1.35794	+	0.872694i	−0.109426	+	0.0703237i
$155$	−4.02156	−	1.18084i	−0.323020	−	0.0948472i
$156$	2.96997	−	3.42753i	0.237788	−	0.274422i
$157$	10.8297	−	3.17989i	0.864306	−	0.253783i	0.180614	−	0.983554i	$-0.442192\pi$
$157$	10.8297	−	3.17989i	0.864306	−	0.253783i	0.683692	+	0.729771i	$0.260373\pi$
$158$	−3.52285	+	7.71396i	−0.280263	+	0.613689i
$159$	−0.550086	−	3.82593i	−0.0436246	−	0.303416i
$160$	−1.00000			−0.0790569
$161$	0.0590124	−	5.62410i	0.00465083	−	0.443241i
$162$	4.39563			0.345353
$163$	2.56533	+	17.8423i	0.200933	+	1.39752i	0.801525	+	0.597961i	$0.204022\pi$
$163$	2.56533	+	17.8423i	0.200933	+	1.39752i	−0.600593	+	0.799555i	$0.705069\pi$
$164$	−2.84558	+	6.23096i	−0.222203	+	0.486556i
$165$	−3.52341	+	1.03457i	−0.274297	+	0.0805410i
$166$	6.62403	−	7.64454i	0.514125	−	0.593332i
$167$	9.44476	+	2.77323i	0.730858	+	0.214599i	0.625928	−	0.779881i	$-0.284720\pi$
$167$	9.44476	+	2.77323i	0.730858	+	0.214599i	0.104929	+	0.994480i	$0.466538\pi$
$168$	−2.63222	+	1.69162i	−0.203080	+	0.130511i
$169$	−4.20000	−	9.19671i	−0.323077	−	0.707440i
$170$	−2.64336	−	3.05060i	−0.202736	−	0.233970i
$171$	20.0407	+	12.8794i	1.53255	+	0.984909i
$172$	1.68068	−	11.6894i	0.128151	−	0.891307i
$173$	−1.46763	+	10.2076i	−0.111582	+	0.776069i	0.854800	+	0.518958i	$0.173680\pi$
$173$	−1.46763	+	10.2076i	−0.111582	+	0.776069i	−0.966382	+	0.257111i	$0.917229\pi$
$174$	9.21934	+	5.92491i	0.698916	+	0.449166i
$175$	0.768001	+	0.886321i	0.0580554	+	0.0669995i
$176$	−0.571771	−	1.25200i	−0.0430989	−	0.0943734i
$177$	−25.0228	+	16.0812i	−1.88083	+	1.20874i
$178$	9.26603	+	2.72075i	0.694519	+	0.203929i
$179$	9.60745	−	11.0876i	0.718095	−	0.828726i	−0.272982	−	0.962019i	$-0.588010\pi$
$179$	9.60745	−	11.0876i	0.718095	−	0.828726i	0.991077	+	0.133294i	$0.0425553\pi$
$180$	−3.95127	+	1.16020i	−0.294511	+	0.0864761i
$181$	1.21321	−	2.65655i	0.0901769	−	0.197460i	−0.859170	−	0.511691i	$-0.829019\pi$
$181$	1.21321	−	2.65655i	0.0901769	−	0.197460i	0.949347	+	0.314231i	$0.101747\pi$
$182$	−0.283716	−	1.97329i	−0.0210305	−	0.146270i
$183$	7.88102			0.582582
$184$	4.73959	+	0.732287i	0.349408	+	0.0539849i
$185$	−4.33084			−0.318410
$186$	−1.59142	−	11.0686i	−0.116689	−	0.811587i
$187$	2.30797	−	5.05374i	0.168775	−	0.369566i
$188$	−10.9054	+	3.20212i	−0.795359	+	0.233538i
$189$	−2.29096	+	2.64391i	−0.166643	+	0.192316i
$190$	5.55050	+	1.62977i	0.402675	+	0.118236i
$191$	11.4002	−	7.32646i	0.824889	−	0.530124i	−0.0587607	−	0.998272i	$-0.518715\pi$
$191$	11.4002	−	7.32646i	0.824889	−	0.530124i	0.883650	+	0.468148i	$0.155079\pi$
$192$	−1.10832	−	2.42687i	−0.0799858	−	0.175145i
$193$	7.61908	+	8.79289i	0.548434	+	0.632926i	0.960517	−	0.278220i	$-0.0897444\pi$
$193$	7.61908	+	8.79289i	0.548434	+	0.632926i	−0.412084	+	0.911146i	$0.635199\pi$
$194$	−14.7305	−	9.46670i	−1.05759	−	0.679669i
$195$	0.645436	−	4.48910i	0.0462206	−	0.321471i
$196$	0.800465	−	5.56736i	0.0571761	−	0.397669i
$197$	14.7591	+	9.48512i	1.05155	+	0.675787i	0.947816	−	0.318819i	$-0.103286\pi$
$197$	14.7591	+	9.48512i	1.05155	+	0.675787i	0.103729	+	0.994606i	$0.466922\pi$
$198$	−3.71180	−	4.28364i	−0.263786	−	0.304425i
$199$	6.44357	+	14.1094i	0.456772	+	1.00019i	0.988211	+	0.153095i	$0.0489241\pi$
$199$	6.44357	+	14.1094i	0.456772	+	1.00019i	−0.531439	+	0.847096i	$0.678349\pi$
$200$	−0.841254	+	0.540641i	−0.0594856	+	0.0382291i
$201$	5.38631	+	1.58156i	0.379921	+	0.111555i
$202$	−8.47323	+	9.77863i	−0.596174	+	0.688022i
$203$	4.62217	−	1.35719i	0.324413	−	0.0952562i
$204$	4.47374	−	9.79613i	0.313225	−	0.685866i
$205$	0.974853	+	6.78025i	0.0680867	+	0.473553i
$206$	14.6888			1.02342
$207$	19.5770	−	2.60540i	1.36070	−	0.181088i
$208$	1.69989			0.117866
$209$	1.13313	+	7.88111i	0.0783804	+	0.545148i
$210$	−1.29980	+	2.84617i	−0.0896948	+	0.196404i
$211$	−23.7743	+	6.98076i	−1.63669	+	0.480575i	−0.965433	−	0.260651i	$-0.916063\pi$
$211$	−23.7743	+	6.98076i	−1.63669	+	0.480575i	−0.671255	+	0.741226i	$0.734245\pi$
$212$	0.948741	−	1.09491i	0.0651598	−	0.0751984i
$213$	17.0512	+	5.00669i	1.16833	+	0.343052i
$214$	3.20281	−	2.05832i	0.218939	−	0.140704i
$215$	−4.90588	−	10.7424i	−0.334578	−	0.732624i
$216$	−1.95346	−	2.25442i	−0.132916	−	0.153394i
$217$	−4.13517	−	2.65751i	−0.280713	−	0.180404i
$218$	−1.93905	+	13.4864i	−0.131329	+	0.913411i
$219$	−2.52673	+	17.5738i	−0.170741	+	1.18753i
$220$	−1.15789	−	0.744130i	−0.0780649	−	0.0501693i
$221$	4.49343	+	5.18569i	0.302261	+	0.348827i
$222$	−4.79994	−	10.5104i	−0.322151	−	0.705412i
$223$	20.4455	−	13.1395i	1.36913	−	0.879887i	0.370333	−	0.928899i	$-0.379243\pi$
$223$	20.4455	−	13.1395i	1.36913	−	0.879887i	0.998798	+	0.0490116i	$0.0156071\pi$
$224$	−1.12526	−	0.330408i	−0.0751849	−	0.0220763i
$225$	−2.69677	+	3.11224i	−0.179785	+	0.207483i
$226$	8.20367	−	2.40881i	0.545700	−	0.160232i
$227$	−11.6147	+	25.4326i	−0.770893	+	1.68802i	−0.0462166	+	0.998931i	$0.514716\pi$
$227$	−11.6147	+	25.4326i	−0.770893	+	1.68802i	−0.724677	+	0.689089i	$0.758011\pi$
$228$	2.19645	+	15.2767i	0.145464	+	1.01172i
$229$	4.89042			0.323168			0.161584	−	0.986859i	$-0.448340\pi$
$229$	4.89042			0.323168			0.161584	+	0.986859i	$0.448340\pi$
$230$	4.38310	−	1.94638i	0.289013	−	0.128340i
$231$	−4.30660			−0.283354
$232$	0.584577	+	4.06582i	0.0383793	+	0.266934i
$233$	2.24981	−	4.92639i	0.147390	−	0.322738i	−0.821509	−	0.570195i	$-0.806868\pi$
$233$	2.24981	−	4.92639i	0.147390	−	0.322738i	0.968899	+	0.247457i	$0.0795948\pi$
$234$	6.71674	−	1.97221i	0.439087	−	0.128928i
$235$	−7.44302	+	8.58970i	−0.485529	+	0.560330i
$236$	−10.6972	−	3.14098i	−0.696328	−	0.204460i
$237$	−19.0336	+	12.2321i	−1.23636	+	0.794562i
$238$	−1.96654	−	4.30612i	−0.127472	−	0.279124i
$239$	−7.24953	−	8.36640i	−0.468933	−	0.541177i	0.471182	−	0.882036i	$-0.343828\pi$
$239$	−7.24953	−	8.36640i	−0.468933	−	0.541177i	−0.940114	+	0.340859i	$0.889282\pi$
$240$	−2.24444	−	1.44242i	−0.144878	−	0.0931075i
$241$	−0.0656020	+	0.456272i	−0.00422580	+	0.0293911i	−0.991825	−	0.127604i	$-0.959271\pi$
$241$	−0.0656020	+	0.456272i	−0.00422580	+	0.0293911i	0.987599	+	0.156995i	$0.0501806\pi$
$242$	−1.29586	+	9.01288i	−0.0833008	+	0.579370i
$243$	17.3942	+	11.1786i	1.11584	+	0.717105i
$244$	1.93442	+	2.23243i	0.123838	+	0.142917i
$245$	−2.33655	−	5.11633i	−0.149277	−	0.326870i
$246$	−15.3744	+	9.88051i	−0.980234	+	0.629958i
$247$	−9.43525	−	2.77044i	−0.600350	−	0.176279i
$248$	2.74475	−	3.16761i	0.174292	−	0.201143i
$249$	25.8939	−	7.60313i	1.64096	−	0.481829i
$250$	−0.415415	+	0.909632i	−0.0262732	+	0.0575302i
$251$	−1.87860	−	13.0659i	−0.118576	−	0.824715i	−0.959126	−	0.282980i	$-0.908677\pi$
$251$	−1.87860	−	13.0659i	−0.118576	−	0.824715i	0.840550	−	0.541734i	$-0.182232\pi$
$252$	−4.82957			−0.304234
$253$	4.94301	+	4.37478i	0.310764	+	0.275040i
$254$	−9.23114			−0.579213
$255$	−1.53264	−	10.6597i	−0.0959774	−	0.667537i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	6.25156	−	1.83562i	0.389962	−	0.114503i	−0.0808733	−	0.996724i	$-0.525771\pi$
$257$	6.25156	−	1.83562i	0.389962	−	0.114503i	0.470835	+	0.882221i	$0.343953\pi$
$258$	20.6331	−	23.8119i	1.28456	−	1.48247i
$259$	−4.87334	−	1.43094i	−0.302815	−	0.0889144i
$260$	1.43004	−	0.919031i	0.0886873	−	0.0569959i
$261$	7.02698	+	15.3869i	0.434959	+	0.952428i
$262$	5.25572	+	6.06542i	0.324699	+	0.374723i
$263$	−4.72655	−	3.03757i	−0.291451	−	0.187304i	0.386742	−	0.922188i	$-0.373600\pi$
$263$	−4.72655	−	3.03757i	−0.291451	−	0.187304i	−0.678193	+	0.734884i	$0.737237\pi$
$264$	0.522603	−	3.63478i	0.0321640	−	0.223706i
$265$	0.206181	−	1.43402i	0.0126656	−	0.0880912i
$266$	5.70729	+	3.66785i	0.349936	+	0.224890i
$267$	16.8726	+	19.4720i	1.03259	+	1.19167i
$268$	0.874078	+	1.91396i	0.0533928	+	0.116914i
$269$	23.6133	−	15.1753i	1.43973	−	0.925256i	0.440099	−	0.897949i	$-0.354943\pi$
$269$	23.6133	−	15.1753i	1.43973	−	0.925256i	0.999627	−	0.0273064i	$-0.00869297\pi$
$270$	−2.86219	−	0.840414i	−0.174187	−	0.0511460i
$271$	−0.485696	+	0.560524i	−0.0295040	+	0.0340494i	−0.770310	−	0.637670i	$-0.779898\pi$
$271$	−0.485696	+	0.560524i	−0.0295040	+	0.0340494i	0.740806	+	0.671719i	$0.234444\pi$
$272$	3.87301	−	1.13722i	0.234836	−	0.0689541i
$273$	2.20952	−	4.83817i	0.133726	−	0.292820i
$274$	−2.75708	−	19.1759i	−0.166561	−	1.15846i
$275$	−1.37639			−0.0829992
$276$	9.58148	+	8.48004i	0.576738	+	0.510438i
$277$	−2.31510			−0.139101			−0.0695505	−	0.997578i	$-0.522157\pi$
$277$	−2.31510			−0.139101			−0.0695505	+	0.997578i	$0.522157\pi$
$278$	−1.95608	−	13.6049i	−0.117318	−	0.815966i
$279$	7.17019	−	15.7005i	0.429268	−	0.939966i
$280$	−1.12526	+	0.330408i	−0.0672474	+	0.0197456i
$281$	−6.59874	+	7.61535i	−0.393648	+	0.454294i	−0.917630	−	0.397435i	$-0.869900\pi$
$281$	−6.59874	+	7.61535i	−0.393648	+	0.454294i	0.523982	+	0.851729i	$0.324446\pi$
$282$	−29.0953	−	8.54317i	−1.73260	−	0.508738i
$283$	14.2015	−	9.12676i	0.844193	−	0.542530i	−0.0455657	−	0.998961i	$-0.514509\pi$
$283$	14.2015	−	9.12676i	0.844193	−	0.542530i	0.889759	+	0.456432i	$0.150873\pi$
$284$	2.76703	+	6.05895i	0.164193	+	0.359533i
$285$	10.1070	+	11.6641i	0.598685	+	0.690919i
$286$	1.96829	+	1.26494i	0.116387	+	0.0747975i
$287$	−1.14328	+	7.95168i	−0.0674856	+	0.469373i
$288$	0.586065	−	4.07617i	0.0345342	−	0.240191i
$289$	−0.594339	−	0.381958i	−0.0349611	−	0.0224681i
$290$	2.68992	+	3.10434i	0.157958	+	0.182293i
$291$	−19.4068	−	42.4949i	−1.13765	−	2.49110i
$292$	−5.59827	+	3.59779i	−0.327614	+	0.210545i
$293$	−25.0317	−	7.34998i	−1.46237	−	0.429391i	−0.548759	−	0.835980i	$-0.684900\pi$
$293$	−25.0317	−	7.34998i	−1.46237	−	0.429391i	−0.913611	+	0.406590i	$0.866718\pi$
$294$	9.82705	−	11.3410i	0.573125	−	0.661421i
$295$	−10.6972	+	3.14098i	−0.622814	+	0.182875i
$296$	1.79909	−	3.93947i	0.104570	−	0.228977i
$297$	−0.584315	−	4.06400i	−0.0339054	−	0.235817i
$298$	6.42730			0.372324
$299$	−7.45080	+	3.30863i	−0.430891	+	0.191343i
$300$	−2.66797			−0.154036
$301$	−1.97105	−	13.7090i	−0.113610	−	0.790172i
$302$	1.23026	−	2.69390i	0.0707937	−	0.155017i
$303$	−33.1225	+	9.72565i	−1.90284	+	0.558724i
$304$	−3.78825	+	4.37188i	−0.217271	+	0.250744i
$305$	2.83428	+	0.832220i	0.162290	+	0.0476528i
$306$	13.9839	−	8.98693i	0.799409	−	0.513749i
$307$	−12.0462	−	26.3775i	−0.687513	−	1.50544i	−0.854481	−	0.519482i	$-0.826125\pi$
$307$	−12.0462	−	26.3775i	−0.687513	−	1.50544i	0.166968	−	0.985962i	$-0.446602\pi$
$308$	−1.05707	−	1.21992i	−0.0602319	−	0.0695113i
$309$	32.9681	+	21.1873i	1.87549	+	1.20531i
$310$	0.596490	−	4.14868i	0.0338784	−	0.235629i
$311$	−2.37281	+	16.5033i	−0.134550	+	0.935815i	0.804969	+	0.593317i	$0.202182\pi$
$311$	−2.37281	+	16.5033i	−0.134550	+	0.935815i	−0.939519	+	0.342498i	$0.888727\pi$
$312$	3.81531	+	2.45195i	0.215999	+	0.138814i
$313$	−10.6623	−	12.3049i	−0.602669	−	0.695517i	0.369651	−	0.929171i	$-0.379477\pi$
$313$	−10.6623	−	12.3049i	−0.602669	−	0.695517i	−0.972320	+	0.233654i	$0.924932\pi$
$314$	4.68875	+	10.2669i	0.264602	+	0.579397i
$315$	−4.06289	+	2.61106i	−0.228918	+	0.147117i
$316$	−8.13679	−	2.38918i	−0.457730	−	0.134402i
$317$	−22.3428	+	25.7849i	−1.25490	+	1.44823i	−0.411075	+	0.911601i	$0.634847\pi$
$317$	−22.3428	+	25.7849i	−1.25490	+	1.44823i	−0.843821	+	0.536626i	$0.819699\pi$
$318$	3.70870	−	1.08897i	0.207974	−	0.0610666i
$319$	−2.34862	+	5.14277i	−0.131498	+	0.287940i
$320$	−0.142315	−	0.989821i	−0.00795564	−	0.0553327i
$321$	10.1575			0.566934
$322$	5.57525	−	0.741981i	0.310697	−	0.0413490i
$323$	−23.3506			−1.29926
$324$	0.625564	+	4.35089i	0.0347535	+	0.241716i
$325$	0.706161	−	1.54628i	0.0391707	−	0.0857720i
$326$	−17.2956	+	5.07845i	−0.957915	+	0.281269i
$327$	−23.8050	+	27.4724i	−1.31642	+	1.51923i
$328$	−6.57250	−	1.92986i	−0.362906	−	0.106559i
$329$	−11.2135	+	7.20646i	−0.618219	+	0.397305i
$330$	−1.52547	−	3.34032i	−0.0839744	−	0.183878i
$331$	−22.3494	−	25.7926i	−1.22844	−	1.41769i	−0.876317	−	0.481736i	$-0.840007\pi$
$331$	−22.3494	−	25.7926i	−1.22844	−	1.41769i	−0.352119	−	0.935955i	$-0.614539\pi$
$332$	8.50943	+	5.46868i	0.467016	+	0.300133i
$333$	2.53815	−	17.6532i	0.139090	−	0.967391i
$334$	−1.40087	+	9.74330i	−0.0766525	+	0.533130i
$335$	1.77009	+	1.13757i	0.0967102	+	0.0621519i
$336$	−2.04901	−	2.36468i	−0.111782	−	0.129004i
$337$	−3.25687	−	7.13155i	−0.177413	−	0.388480i	0.799945	−	0.600074i	$-0.204862\pi$
$337$	−3.25687	−	7.13155i	−0.177413	−	0.388480i	−0.977358	+	0.211593i	$0.932135\pi$
$338$	8.50538	−	5.46608i	0.462632	−	0.297315i
$339$	21.8872	+	6.42665i	1.18875	+	0.349048i
$340$	2.64336	−	3.05060i	0.143356	−	0.165442i
$341$	5.53522	−	1.62529i	0.299749	−	0.0880143i
$342$	−9.89618	+	21.6696i	−0.535124	+	1.17176i
$343$	−2.10708	−	14.6551i	−0.113772	−	0.791299i
$344$	11.8096			0.636730
$345$	12.6451	+	1.95372i	0.680790	+	0.105185i
$346$	−10.3126			−0.554407
$347$	−2.28569	−	15.8973i	−0.122702	−	0.853413i	−0.954474	−	0.298295i	$-0.903582\pi$
$347$	−2.28569	−	15.8973i	−0.122702	−	0.853413i	0.831771	−	0.555118i	$-0.187327\pi$
$348$	−4.55255	+	9.96870i	−0.244042	+	0.534378i
$349$	−14.9268	+	4.38291i	−0.799014	+	0.234612i	−0.655656	−	0.755059i	$-0.727608\pi$
$349$	−14.9268	+	4.38291i	−0.799014	+	0.234612i	−0.143357	+	0.989671i	$0.545790\pi$
$350$	−0.768001	+	0.886321i	−0.0410514	+	0.0473758i
$351$	4.86541	+	1.42861i	0.259696	+	0.0762537i
$352$	1.15789	−	0.744130i	0.0617157	−	0.0396623i
$353$	5.93569	+	12.9974i	0.315925	+	0.691779i	0.999265	−	0.0383205i	$-0.0122008\pi$
$353$	5.93569	+	12.9974i	0.315925	+	0.691779i	−0.683340	+	0.730100i	$0.739474\pi$
$354$	−19.4786	−	22.4795i	−1.03528	−	1.19477i
$355$	5.60349	+	3.60114i	0.297402	+	0.191129i
$356$	−1.37437	+	9.55892i	−0.0728412	+	0.506622i
$357$	1.79743	−	12.5014i	0.0951301	−	0.661644i
$358$	12.3420	+	7.93174i	0.652296	+	0.419205i
$359$	3.77323	+	4.35454i	0.199143	+	0.229824i	0.846534	−	0.532335i	$-0.178685\pi$
$359$	3.77323	+	4.35454i	0.199143	+	0.229824i	−0.647391	+	0.762158i	$0.724140\pi$
$360$	−1.71071	−	3.74594i	−0.0901626	−	0.197428i
$361$	12.1681	−	7.81993i	0.640424	−	0.411575i
$362$	2.80217	+	0.822791i	0.147279	+	0.0432449i
$363$	−15.9088	+	18.3597i	−0.834995	+	0.963636i
$364$	1.91283	−	0.561657i	0.100259	−	0.0294388i
$365$	−2.76445	+	6.05331i	−0.144698	+	0.316845i
$366$	1.12159	+	7.80080i	0.0586262	+	0.407755i
$367$	−30.9168			−1.61384			−0.806921	−	0.590660i	$-0.798868\pi$
$367$	−30.9168			−1.61384			−0.806921	+	0.590660i	$0.798868\pi$
$368$	−0.0503188	+	4.79557i	−0.00262305	+	0.249986i
$369$	−28.2088			−1.46849
$370$	−0.616342	−	4.28676i	−0.0320421	−	0.222858i
$371$	0.705819	−	1.54553i	0.0366443	−	0.0802399i
$372$	10.7294	−	3.15044i	0.556295	−	0.163343i
$373$	−8.56476	+	9.88426i	−0.443466	+	0.511787i	−0.932842	−	0.360286i	$-0.882679\pi$
$373$	−8.56476	+	9.88426i	−0.443466	+	0.511787i	0.489376	+	0.872073i	$0.337225\pi$
$374$	5.33076	+	1.56525i	0.275647	+	0.0809373i
$375$	−2.24444	+	1.44242i	−0.115903	+	0.0744860i
$376$	−4.72153	−	10.3387i	−0.243494	−	0.533178i
$377$	−4.57258	−	5.27704i	−0.235500	−	0.271781i
$378$	−2.94304	−	1.89138i	−0.151374	−	0.0972819i
$379$	−0.975770	+	6.78663i	−0.0501219	+	0.348606i	0.949293	+	0.314394i	$0.101801\pi$
$379$	−0.975770	+	6.78663i	−0.0501219	+	0.348606i	−0.999415	+	0.0342119i	$0.989108\pi$
$380$	−0.823266	+	5.72594i	−0.0422327	+	0.293735i
$381$	−20.7188	−	13.3151i	−1.06145	−	0.682155i
$382$	8.87431	+	10.2415i	0.454049	+	0.524001i
$383$	0.0767508	+	0.168061i	0.00392178	+	0.00858751i	0.911583	−	0.411117i	$-0.134861\pi$
$383$	0.0767508	+	0.168061i	0.00392178	+	0.00858751i	−0.907661	+	0.419704i	$0.862134\pi$
$384$	2.24444	−	1.44242i	0.114536	−	0.0736080i
$385$	−1.54880	−	0.454768i	−0.0789341	−	0.0231771i
$386$	−7.61908	+	8.79289i	−0.387801	+	0.447546i
$387$	46.6629	−	13.7015i	2.37201	−	0.696485i
$388$	7.27398	−	15.9278i	0.369280	−	0.808611i
$389$	3.65512	+	25.4219i	0.185322	+	1.28894i	0.843929	+	0.536455i	$0.180237\pi$
$389$	3.65512	+	25.4219i	0.185322	+	1.28894i	−0.658607	+	0.752487i	$0.728854\pi$
$390$	4.53527			0.229652
$391$	−14.7624	+	12.5229i	−0.746565	+	0.633311i
$392$	5.62461			0.284086
$393$	3.04730	+	21.1944i	0.153716	+	1.06912i
$394$	−7.28813	+	15.9588i	−0.367171	+	0.803992i
$395$	−8.13679	+	2.38918i	−0.409406	+	0.120213i
$396$	3.71180	−	4.28364i	0.186525	−	0.215261i
$397$	−0.0737127	−	0.0216440i	−0.00369954	−	0.00108628i	0.279882	−	0.960034i	$-0.409705\pi$
$397$	−0.0737127	−	0.0216440i	−0.00369954	−	0.00108628i	−0.283582	+	0.958948i	$0.591523\pi$
$398$	−13.0488	+	8.38596i	−0.654078	+	0.420350i
$399$	7.51912	+	16.4646i	0.376427	+	0.824259i
$400$	−0.654861	−	0.755750i	−0.0327430	−	0.0377875i
$401$	14.5348	+	9.34096i	0.725834	+	0.466465i	0.850662	−	0.525713i	$-0.176202\pi$
$401$	14.5348	+	9.34096i	0.725834	+	0.466465i	−0.124828	+	0.992178i	$0.539838\pi$
$402$	−0.798913	+	5.55656i	−0.0398462	+	0.277136i
$403$	−1.01397	+	7.05231i	−0.0505094	+	0.351301i
$404$	−10.8850	−	6.99534i	−0.541547	−	0.348031i
$405$	2.87853	+	3.32200i	0.143035	+	0.165071i
$406$	2.00118	+	4.38197i	0.0993169	+	0.217474i
$407$	5.01463	−	3.22271i	0.248566	−	0.159744i
$408$	10.3331	+	3.03407i	0.511565	+	0.150209i
$409$	7.59726	−	8.76771i	0.375660	−	0.433535i	−0.536165	−	0.844113i	$-0.680128\pi$
$409$	7.59726	−	8.76771i	0.375660	−	0.433535i	0.911826	+	0.410578i	$0.134673\pi$
$410$	−6.57250	+	1.92986i	−0.324593	+	0.0953090i
$411$	21.4715	−	47.0161i	1.05911	−	2.31913i
$412$	2.09043	+	14.5393i	0.102988	+	0.716299i
$413$	−13.0750			−0.643377
$414$	5.36499	+	19.0070i	0.263675	+	0.934142i
$415$	10.1152			0.496535
$416$	0.241920	+	1.68259i	0.0118611	+	0.0824957i
$417$	15.2336	−	33.3568i	0.745990	−	1.63349i
$418$	−7.63963	+	2.24320i	−0.373666	+	0.109718i
$419$	26.0096	−	30.0167i	1.27065	−	1.46641i	0.452116	−	0.891959i	$-0.350669\pi$
$419$	26.0096	−	30.0167i	1.27065	−	1.46641i	0.818537	−	0.574453i	$-0.194785\pi$
$420$	−3.00218	−	0.881519i	−0.146491	−	0.0430137i
$421$	10.4853	−	6.73846i	0.511020	−	0.328413i	−0.259591	−	0.965719i	$-0.583588\pi$
$421$	10.4853	−	6.73846i	0.511020	−	0.328413i	0.770611	+	0.637306i	$0.219951\pi$
$422$	−10.2931	−	22.5388i	−0.501062	−	1.09717i
$423$	−30.6510	−	35.3731i	−1.49030	−	1.71990i
$424$	1.21878	+	0.783263i	0.0591892	+	0.0380386i
$425$	0.574457	−	3.99544i	0.0278653	−	0.193807i
$426$	−2.52909	+	17.5902i	−0.122535	+	0.852247i
$427$	2.91434	+	1.87293i	0.141035	+	0.0906377i
$428$	2.49317	+	2.87728i	0.120512	+	0.139078i
$429$	2.59314	+	5.67818i	0.125198	+	0.274145i
$430$	9.93486	−	6.38475i	0.479101	−	0.307900i
$431$	−1.68521	−	0.494823i	−0.0811738	−	0.0238348i	0.240893	−	0.970552i	$-0.422560\pi$
$431$	−1.68521	−	0.494823i	−0.0811738	−	0.0238348i	−0.322067	+	0.946717i	$0.604378\pi$
$432$	1.95346	−	2.25442i	0.0939861	−	0.108466i
$433$	−0.460315	+	0.135161i	−0.0221213	+	0.00649541i	−0.292775	−	0.956182i	$-0.594579\pi$
$433$	−0.460315	+	0.135161i	−0.0221213	+	0.00649541i	0.270653	+	0.962677i	$0.412760\pi$
$434$	2.04197	−	4.47128i	0.0980175	−	0.214628i
$435$	1.55963	+	10.8475i	0.0747788	+	0.520098i
$436$	−13.6250			−0.652521
$437$	8.09498	−	26.5358i	0.387236	−	1.26938i
$438$	−17.7545			−0.848343
$439$	0.480627	+	3.34283i	0.0229391	+	0.159545i	0.998071	−	0.0620796i	$-0.0197733\pi$
$439$	0.480627	+	3.34283i	0.0229391	+	0.159545i	−0.975132	+	0.221624i	$0.928864\pi$
$440$	0.571771	−	1.25200i	0.0272581	−	0.0596870i
$441$	22.2244	−	6.52566i	1.05830	−	0.310746i
$442$	−4.49343	+	5.18569i	−0.213730	+	0.246658i
$443$	−7.04267	−	2.06791i	−0.334607	−	0.0982495i	0.110113	−	0.993919i	$-0.464879\pi$
$443$	−7.04267	−	2.06791i	−0.334607	−	0.0982495i	−0.444720	+	0.895670i	$0.646697\pi$
$444$	9.72032	−	6.24687i	0.461306	−	0.296463i
$445$	4.01175	+	8.78452i	0.190175	+	0.416426i
$446$	15.9155	+	18.3674i	0.753620	+	0.869723i
$447$	14.4257	+	9.27084i	0.682313	+	0.438496i
$448$	0.166903	−	1.16083i	0.00788541	−	0.0548442i
$449$	−3.89467	+	27.0881i	−0.183801	+	1.27836i	0.663872	+	0.747846i	$0.268912\pi$
$449$	−3.89467	+	27.0881i	−0.183801	+	1.27836i	−0.847673	+	0.530518i	$0.821997\pi$
$450$	−3.46435	−	2.22640i	−0.163311	−	0.104954i
$451$	−6.17416	−	7.12536i	−0.290730	−	0.335520i
$452$	3.55180	+	7.77735i	0.167063	+	0.365816i
$453$	6.64698	−	4.27175i	0.312302	−	0.200705i
$454$	−26.8267	−	7.87702i	−1.25904	−	0.369687i
$455$	1.30552	−	1.50665i	0.0612037	−	0.0706328i
$456$	−14.8086	+	4.34819i	−0.693475	+	0.203623i
$457$	6.89481	−	15.0975i	0.322526	−	0.706233i	−0.677033	−	0.735953i	$-0.736734\pi$
$457$	6.89481	−	15.0975i	0.322526	−	0.706233i	0.999558	+	0.0297204i	$0.00946170\pi$
$458$	0.695980	+	4.84065i	0.0325210	+	0.226189i
$459$	12.0410			0.562027
$460$	2.55035	+	4.06149i	0.118911	+	0.189368i
$461$	29.5586			1.37668			0.688339	−	0.725389i	$-0.258340\pi$
$461$	29.5586			1.37668			0.688339	+	0.725389i	$0.258340\pi$
$462$	−0.612893	−	4.26277i	−0.0285144	−	0.198322i
$463$	11.4452	−	25.0615i	0.531903	−	1.16470i	−0.432831	−	0.901475i	$-0.642485\pi$
$463$	11.4452	−	25.0615i	0.531903	−	1.16470i	0.964733	−	0.263229i	$-0.0847876\pi$
$464$	−3.94124	+	1.15725i	−0.182968	+	0.0537241i
$465$	7.32291	−	8.45109i	0.339592	−	0.391910i
$466$	5.19642	+	1.52581i	0.240720	+	0.0706817i
$467$	4.62494	−	2.97227i	0.214017	−	0.137540i	−0.429241	−	0.903190i	$-0.641219\pi$
$467$	4.62494	−	2.97227i	0.214017	−	0.137540i	0.643258	+	0.765650i	$0.277582\pi$
$468$	2.90803	+	6.36770i	0.134424	+	0.294347i
$469$	1.61596	+	1.86491i	0.0746179	+	0.0861137i
$470$	−9.56152	−	6.14482i	−0.441040	−	0.283439i
$471$	−4.28556	+	29.8067i	−0.197468	+	1.37342i
$472$	1.58664	−	11.0353i	0.0730309	−	0.507941i
$473$	13.6742	+	8.78787i	0.628740	+	0.404067i
$474$	−14.8164	−	17.0990i	−0.680539	−	0.785384i
$475$	2.40310	+	5.26206i	0.110262	+	0.241440i
$476$	3.98242	−	2.55935i	0.182534	−	0.117307i
$477$	5.72447	+	1.68086i	0.262106	+	0.0769612i
$478$	7.24953	−	8.36640i	0.331586	−	0.382670i
$479$	20.6173	−	6.05379i	0.942029	−	0.276605i	0.225564	−	0.974228i	$-0.427577\pi$
$479$	20.6173	−	6.05379i	0.942029	−	0.276605i	0.716464	+	0.697624i	$0.245759\pi$
$480$	1.10832	−	2.42687i	0.0505875	−	0.110771i
$481$	1.04772	+	7.28702i	0.0477717	+	0.332260i
$482$	−0.460964			−0.0209963
$483$	13.5836	+	6.37650i	0.618074	+	0.290141i
$484$	−9.10556			−0.413889
$485$	−2.49195	−	17.3319i	−0.113154	−	0.787002i
$486$	−8.58933	+	18.8080i	−0.389620	+	0.853148i
$487$	3.60843	−	1.05953i	0.163514	−	0.0480119i	−0.198951	−	0.980009i	$-0.563754\pi$
$487$	3.60843	−	1.05953i	0.163514	−	0.0480119i	0.362465	+	0.931997i	$0.381935\pi$
$488$	−1.93442	+	2.23243i	−0.0875669	+	0.101058i
$489$	−46.1442	−	13.5492i	−2.08671	−	0.612714i
$490$	4.73172	−	3.04089i	0.213757	−	0.137374i
$491$	−4.22014	−	9.24082i	−0.190452	−	0.417032i	0.790184	−	0.612870i	$-0.209985\pi$
$491$	−4.22014	−	9.24082i	−0.190452	−	0.417032i	−0.980636	+	0.195837i	$0.937258\pi$
$492$	−11.9679	−	13.8117i	−0.539556	−	0.622681i
$493$	−13.9484	−	8.96411i	−0.628206	−	0.403723i
$494$	1.39946	−	9.73348i	0.0629648	−	0.437930i
$495$	0.806651	−	5.61038i	0.0362563	−	0.252168i
$496$	3.52598	+	2.26601i	0.158321	+	0.101747i
$497$	5.11557	+	5.90368i	0.229464	+	0.264816i
$498$	11.2108	+	24.5483i	0.502369	+	1.10003i
$499$	29.0054	−	18.6407i	1.29846	−	0.834471i	0.305418	−	0.952218i	$-0.401204\pi$
$499$	29.0054	−	18.6407i	1.29846	−	0.834471i	0.993044	+	0.117748i	$0.0375675\pi$
$500$	−0.959493	−	0.281733i	−0.0429098	−	0.0125995i
$501$	−17.1981	+	19.8476i	−0.768353	+	0.886727i
$502$	12.6656	−	3.71895i	0.565293	−	0.165985i
$503$	12.1254	−	26.5509i	0.540644	−	1.18385i	−0.420372	−	0.907352i	$-0.638100\pi$
$503$	12.1254	−	26.5509i	0.540644	−	1.18385i	0.961016	−	0.276493i	$-0.0891724\pi$
$504$	−0.687319	−	4.78041i	−0.0306156	−	0.212936i
$505$	−12.9390			−0.575777
$506$	−3.62679	+	5.51529i	−0.161231	+	0.245185i
$507$	26.9742			1.19797
$508$	−1.31373	−	9.13718i	−0.0582872	−	0.405397i
$509$	−13.2034	+	28.9113i	−0.585229	+	1.28147i	0.353054	+	0.935603i	$0.385143\pi$
$509$	−13.2034	+	28.9113i	−0.585229	+	1.28147i	−0.938283	+	0.345869i	$0.887584\pi$
$510$	10.3331	−	3.03407i	0.457557	−	0.134351i
$511$	−5.11080	+	5.89818i	−0.226088	+	0.260920i
$512$	0.959493	+	0.281733i	0.0424040	+	0.0124509i
$513$	−14.5169	+	9.32943i	−0.640936	+	0.411905i
$514$	2.70663	+	5.92669i	0.119384	+	0.261415i
$515$	9.61911	+	11.1010i	0.423869	+	0.489170i
$516$	26.5059	+	17.0343i	1.16686	+	0.749895i
$517$	2.22634	−	15.4845i	0.0979141	−	0.681008i
$518$	0.722828	−	5.02738i	0.0317592	−	0.220890i
$519$	−23.1460	−	14.8750i	−1.01599	−	0.652940i
$520$	1.11319	+	1.28469i	0.0488167	+	0.0563375i
$521$	2.61911	+	5.73505i	0.114745	+	0.251257i	0.958288	−	0.285806i	$-0.0922611\pi$
$521$	2.61911	+	5.73505i	0.114745	+	0.251257i	−0.843542	+	0.537063i	$0.819534\pi$
$522$	−14.2303	+	9.14524i	−0.622842	+	0.400276i
$523$	18.9172	+	5.55459i	0.827192	+	0.242885i	0.667810	−	0.744332i	$-0.267232\pi$
$523$	18.9172	+	5.55459i	0.827192	+	0.242885i	0.159382	+	0.987217i	$0.449050\pi$
$524$	−5.25572	+	6.06542i	−0.229597	+	0.264969i
$525$	−3.00218	+	0.881519i	−0.131026	+	0.0384726i
$526$	2.33399	−	5.11073i	0.101767	−	0.222838i
$527$	2.40775	+	16.7462i	0.104883	+	0.729478i
$528$	3.67216			0.159810
$529$	−9.11344	−	21.1174i	−0.396237	−	0.918148i
$530$	1.44877			0.0629304
$531$	−6.53391	−	45.4444i	−0.283548	−	1.97212i
$532$	−2.81829	+	6.17119i	−0.122188	+	0.267555i
$533$	11.1725	−	3.28055i	0.483937	−	0.142097i
$534$	−16.8726	+	19.4720i	−0.730150	+	0.842638i
$535$	3.65296	+	1.07261i	0.157931	+	0.0463729i
$536$	−1.77009	+	1.13757i	−0.0764561	+	0.0491354i
$537$	16.2601	+	35.6046i	0.701675	+	1.53645i
$538$	18.3814	+	21.2132i	0.792477	+	0.914568i
$539$	6.51268	+	4.18544i	0.280521	+	0.180280i
$540$	0.424528	−	2.95266i	0.0182688	−	0.127062i
$541$	−6.19614	+	43.0951i	−0.266393	+	1.85280i	0.215412	+	0.976523i	$0.430891\pi$
$541$	−6.19614	+	43.0951i	−0.266393	+	1.85280i	−0.481805	+	0.876279i	$0.660019\pi$
$542$	−0.623940	−	0.400982i	−0.0268005	−	0.0172236i
$543$	5.10250	+	5.88860i	0.218969	+	0.252704i
$544$	1.67683	+	3.67175i	0.0718936	+	0.157425i
$545$	−11.4621	+	7.36625i	−0.490983	+	0.315536i
$546$	5.10338	+	1.49849i	0.218404	+	0.0641293i
$547$	6.28449	−	7.25268i	0.268705	−	0.310102i	−0.605321	−	0.795982i	$-0.706955\pi$
$547$	6.28449	−	7.25268i	0.268705	−	0.310102i	0.874026	+	0.485879i	$0.161501\pi$
$548$	18.5884	−	5.45804i	0.794056	−	0.233156i
$549$	−5.05334	+	11.0653i	−0.215671	+	0.472254i
$550$	−0.195880	−	1.36238i	−0.00835236	−	0.0580919i
$551$	23.7619			1.01229
$552$	−7.03014	+	10.6908i	−0.299223	+	0.455030i
$553$	−9.94545			−0.422924
$554$	−0.329474	−	2.29154i	−0.0139980	−	0.0973582i
$555$	4.79994	−	10.5104i	0.203746	−	0.446142i
$556$	13.1880	−	3.87235i	0.559296	−	0.164224i
$557$	2.17811	−	2.51367i	0.0922895	−	0.106508i	−0.707726	−	0.706487i	$-0.750279\pi$
$557$	2.17811	−	2.51367i	0.0922895	−	0.106508i	0.800016	+	0.599979i	$0.204824\pi$
$558$	16.5611	+	4.86279i	0.701089	+	0.205858i
$559$	−16.8882	+	10.8534i	−0.714294	+	0.459049i
$560$	−0.487186	−	1.06679i	−0.0205874	−	0.0450801i
$561$	9.70684	+	11.2023i	0.409823	+	0.472961i
$562$	−8.47694	−	5.44780i	−0.357578	−	0.229801i
$563$	−0.336134	+	2.33786i	−0.0141663	+	0.0985291i	−0.995678	−	0.0928739i	$-0.970395\pi$
$563$	−0.336134	+	2.33786i	−0.0141663	+	0.0985291i	0.981512	+	0.191403i	$0.0613037\pi$
$564$	4.31551	−	30.0150i	0.181716	−	1.26386i
$565$	7.19272	+	4.62248i	0.302600	+	0.194469i
$566$	11.0550	+	12.7581i	0.464674	+	0.536263i
$567$	2.14149	+	4.68921i	0.0899342	+	0.196928i
$568$	−5.60349	+	3.60114i	−0.235117	+	0.151101i
$569$	−23.8201	−	6.99420i	−0.998589	−	0.293212i	−0.258712	−	0.965954i	$-0.583298\pi$
$569$	−23.8201	−	6.99420i	−0.998589	−	0.293212i	−0.739877	+	0.672742i	$0.765116\pi$
$570$	−10.1070	+	11.6641i	−0.423334	+	0.488554i
$571$	−25.3656	+	7.44800i	−1.06152	+	0.311689i	−0.765461	−	0.643482i	$-0.777489\pi$
$571$	−25.3656	+	7.44800i	−1.06152	+	0.311689i	−0.296055	+	0.955171i	$0.595671\pi$
$572$	−0.971949	+	2.12827i	−0.0406392	+	0.0889875i
$573$	5.14538	+	35.7869i	0.214951	+	1.49502i
$574$	−8.03345			−0.335310
$575$	4.34130	+	2.03792i	0.181045	+	0.0849872i
$576$	4.11808			0.171587
$577$	−2.56390	−	17.8323i	−0.106736	−	0.742368i	−0.970957	−	0.239255i	$-0.923097\pi$
$577$	−2.56390	−	17.8323i	−0.106736	−	0.742368i	0.864221	−	0.503113i	$-0.167812\pi$
$578$	0.293487	−	0.642647i	0.0122075	−	0.0267306i
$579$	−29.7836	+	8.74525i	−1.23776	+	0.363440i
$580$	−2.68992	+	3.10434i	−0.111693	+	0.128901i
$581$	11.3823	+	3.34213i	0.472216	+	0.138655i
$582$	39.3005	−	25.2569i	1.62906	−	1.04693i
$583$	0.828363	+	1.81386i	0.0343073	+	0.0751225i
$584$	−4.35789	−	5.02927i	−0.180331	−	0.208113i
$585$	5.88903	+	3.78465i	0.243481	+	0.156476i
$586$	3.71278	−	25.8230i	0.153374	−	1.06674i
$587$	−2.87662	+	20.0073i	−0.118731	+	0.825790i	0.840226	+	0.542237i	$0.182422\pi$
$587$	−2.87662	+	20.0073i	−0.118731	+	0.825790i	−0.958956	+	0.283553i	$0.908487\pi$
$588$	12.6241	+	8.11303i	0.520610	+	0.334576i
$589$	−15.8779	−	18.3240i	−0.654236	−	0.755029i
$590$	−4.63138	−	10.1413i	−0.190671	−	0.417511i
$591$	−39.3770	+	25.3061i	−1.61975	+	1.04095i
$592$	4.15541	+	1.22014i	0.170786	+	0.0501474i
$593$	−22.1185	+	25.5261i	−0.908297	+	1.04823i	0.0903337	+	0.995912i	$0.471207\pi$
$593$	−22.1185	+	25.5261i	−0.908297	+	1.04823i	−0.998630	+	0.0523188i	$0.983339\pi$
$594$	3.93947	−	1.15673i	0.161639	−	0.0474614i
$595$	1.96654	−	4.30612i	0.0806202	−	0.176534i
$596$	0.914701	+	6.36188i	0.0374676	+	0.260593i
$597$	−41.3833			−1.69371
$598$	−4.33532	−	6.90410i	−0.177284	−	0.282330i
$599$	18.3116			0.748193			0.374096	−	0.927390i	$-0.377953\pi$
$599$	18.3116			0.748193			0.374096	+	0.927390i	$0.377953\pi$
$600$	−0.379692	−	2.64082i	−0.0155009	−	0.107811i
$601$	−11.2375	+	24.6066i	−0.458385	+	1.00372i	0.529467	+	0.848330i	$0.322392\pi$
$601$	−11.2375	+	24.6066i	−0.458385	+	1.00372i	−0.987853	+	0.155393i	$0.950335\pi$
$602$	13.2889	−	3.90198i	0.541616	−	0.159033i
$603$	−5.67430	+	6.54849i	−0.231075	+	0.266675i
$604$	2.84157	+	0.834359i	0.115622	+	0.0339496i
$605$	−7.66009	+	4.92284i	−0.311427	+	0.200142i
$606$	−14.3405	−	31.4013i	−0.582542	−	1.27559i
$607$	6.79272	+	7.83922i	0.275708	+	0.318184i	0.876669	−	0.481094i	$-0.159761\pi$
$607$	6.79272	+	7.83922i	0.275708	+	0.318184i	−0.600961	+	0.799279i	$0.705215\pi$
$608$	−4.86650	−	3.12751i	−0.197363	−	0.126837i
$609$	−1.82909	+	12.7216i	−0.0741186	+	0.515506i
$610$	−0.420389	+	2.92387i	−0.0170210	+	0.118384i
$611$	16.2536	+	10.4455i	0.657548	+	0.422581i
$612$	10.8856	+	12.5626i	0.440023	+	0.507814i
$613$	11.7654	+	25.7627i	0.475202	+	1.04055i	0.983755	+	0.179516i	$0.0574531\pi$
$613$	11.7654	+	25.7627i	0.475202	+	1.04055i	−0.508553	+	0.861030i	$0.669820\pi$
$614$	24.3947	−	15.6775i	0.984489	−	0.632693i
$615$	−17.5353	−	5.14882i	−0.707090	−	0.207620i
$616$	1.05707	−	1.21992i	0.0425904	−	0.0491519i
$617$	23.8318	−	6.99764i	0.959430	−	0.281714i	0.235722	−	0.971820i	$-0.424254\pi$
$617$	23.8318	−	6.99764i	0.959430	−	0.281714i	0.723708	+	0.690106i	$0.242436\pi$
$618$	−16.2798	+	35.6478i	−0.654870	+	1.43397i
$619$	−2.78598	−	19.3769i	−0.111978	−	0.778824i	−0.965992	−	0.258573i	$-0.916748\pi$
$619$	−2.78598	−	19.3769i	−0.111978	−	0.778824i	0.854014	−	0.520251i	$-0.174161\pi$
$620$	4.19134			0.168328
$621$	−4.17428	+	13.6835i	−0.167508	+	0.549101i
$622$	−16.6730			−0.668525
$623$	1.61182	+	11.2104i	0.0645760	+	0.449136i
$624$	−1.88402	+	4.12542i	−0.0754211	+	0.165149i
$625$	−0.959493	+	0.281733i	−0.0383797	+	0.0112693i
$626$	10.6623	−	12.3049i	0.426151	−	0.491805i
$627$	−20.3823	−	5.98479i	−0.813992	−	0.239010i
$628$	−9.49516	+	6.10217i	−0.378898	+	0.243503i
$629$	7.26209	+	15.9018i	0.289558	+	0.634044i
$630$	−3.16269	−	3.64994i	−0.126005	−	0.145417i
$631$	−14.4459	−	9.28379i	−0.575080	−	0.369582i	0.220539	−	0.975378i	$-0.429218\pi$
$631$	−14.4459	−	9.28379i	−0.575080	−	0.369582i	−0.795620	+	0.605796i	$0.792855\pi$
$632$	1.20687	−	8.39399i	0.0480068	−	0.333895i
$633$	9.40800	−	65.4341i	0.373934	−	2.60077i
$634$	−28.7022	−	18.4458i	−1.13991	−	0.732576i
$635$	−6.04511	−	6.97643i	−0.239893	−	0.276851i
$636$	1.60569	+	3.51598i	0.0636698	+	0.139417i
$637$	−8.04342	+	5.16919i	−0.318692	+	0.204811i
$638$	−5.42467	−	1.59283i	−0.214765	−	0.0630606i
$639$	−17.9629	+	20.7303i	−0.710601	+	0.820077i
$640$	0.959493	−	0.281733i	0.0379273	−	0.0111365i
$641$	−4.98275	+	10.9107i	−0.196807	+	0.430947i	−0.982146	−	0.188119i	$-0.939761\pi$
$641$	−4.98275	+	10.9107i	−0.196807	+	0.430947i	0.785340	+	0.619065i	$0.212488\pi$
$642$	1.44556	+	10.0541i	0.0570516	+	0.396803i
$643$	−3.12046			−0.123059			−0.0615295	−	0.998105i	$-0.519598\pi$
$643$	−3.12046			−0.123059			−0.0615295	+	0.998105i	$0.519598\pi$
$644$	1.52787	+	5.41291i	0.0602065	+	0.213298i
$645$	31.5077			1.24061
$646$	−3.32313	−	23.1129i	−0.130747	−	0.909365i
$647$	19.3251	−	42.3160i	0.759747	−	1.66361i	0.0117323	−	0.999931i	$-0.496265\pi$
$647$	19.3251	−	42.3160i	0.759747	−	1.66361i	0.748015	−	0.663682i	$-0.231007\pi$
$648$	−4.21758	+	1.23839i	−0.165682	+	0.0486487i
$649$	10.0489	−	11.5970i	0.394452	−	0.455222i
$650$	1.63103	+	0.478915i	0.0639744	+	0.0187846i
$651$	11.0325	−	7.09017i	0.432398	−	0.277886i
$652$	−7.48818	−	16.3968i	−0.293260	−	0.642149i
$653$	−12.1147	−	13.9811i	−0.474083	−	0.547121i	0.467460	−	0.884014i	$-0.345169\pi$
$653$	−12.1147	−	13.9811i	−0.474083	−	0.547121i	−0.941543	+	0.336893i	$0.890624\pi$
$654$	−30.5806	−	19.6530i	−1.19580	−	0.768492i
$655$	−1.14218	+	7.94401i	−0.0446285	+	0.310398i
$656$	0.974853	−	6.78025i	0.0380616	−	0.264724i
$657$	−23.0541	−	14.8160i	−0.899428	−	0.578027i
$658$	−8.72895	−	10.0737i	−0.340290	−	0.392716i
$659$	−9.64380	−	21.1170i	−0.375669	−	0.822600i	−0.999168	−	0.0407765i	$-0.987017\pi$
$659$	−9.64380	−	21.1170i	−0.375669	−	0.822600i	0.623499	−	0.781824i	$-0.285710\pi$
$660$	3.08922	−	1.98532i	0.120248	−	0.0772785i
$661$	5.43968	+	1.59723i	0.211579	+	0.0621252i	0.385804	−	0.922581i	$-0.373924\pi$
$661$	5.43968	+	1.59723i	0.211579	+	0.0621252i	−0.174225	+	0.984706i	$0.555742\pi$
$662$	22.3494	−	25.7926i	0.868635	−	1.00246i
$663$	−17.5652	+	5.15759i	−0.682174	+	0.200304i
$664$	−4.20200	+	9.20109i	−0.163069	+	0.357072i
$665$	0.965502	+	6.71522i	0.0374406	+	0.260405i
$666$	17.8348			0.691083
$667$	15.0224	−	12.7435i	0.581670	−	0.493431i
$668$	−9.84349			−0.380856
$669$	9.22789	+	64.1814i	0.356771	+	2.48140i
$670$	−0.874078	+	1.91396i	−0.0337686	+	0.0739428i
$671$	−3.90106	+	1.14546i	−0.150599	+	0.0442198i
$672$	2.04901	−	2.36468i	0.0790422	−	0.0912195i
$673$	15.1374	+	4.44473i	0.583502	+	0.171332i	0.560144	−	0.828395i	$-0.310746\pi$
$673$	15.1374	+	4.44473i	0.583502	+	0.171332i	0.0233585	+	0.999727i	$0.492564\pi$
$674$	6.59546	−	4.23864i	0.254048	−	0.163266i
$675$	−1.23919	−	2.71345i	−0.0476965	−	0.104441i
$676$	6.62088	+	7.64091i	0.254649	+	0.293881i
$677$	−43.4525	−	27.9252i	−1.67002	−	1.07325i	−0.900764	−	0.434308i	$-0.856993\pi$
$677$	−43.4525	−	27.9252i	−1.67002	−	1.07325i	−0.769252	−	0.638946i	$-0.779371\pi$
$678$	−3.24637	+	22.5790i	−0.124676	+	0.867141i
$679$	2.92249	−	20.3264i	0.112155	−	0.780054i
$680$	3.39574	+	2.18231i	0.130221	+	0.0836877i
$681$	−48.8490	−	56.3747i	−1.87190	−	2.16028i
$682$	2.39649	+	5.24758i	0.0917663	+	0.200940i
$683$	24.3809	−	15.6687i	0.932911	−	0.599545i	0.0165345	−	0.999863i	$-0.494737\pi$
$683$	24.3809	−	15.6687i	0.932911	−	0.599545i	0.916376	+	0.400318i	$0.131100\pi$
$684$	−22.8574	−	6.71154i	−0.873975	−	0.256622i
$685$	12.6867	−	14.6412i	0.484734	−	0.559412i
$686$	14.2060	−	4.17127i	0.542389	−	0.159260i
$687$	−5.42014	+	11.8684i	−0.206791	+	0.452809i
$688$	1.68068	+	11.6894i	0.0640753	+	0.445654i
$689$	−2.46275			−0.0938232
$690$	−0.134249	+	12.7944i	−0.00511078	+	0.487076i
$691$	32.0052			1.21754			0.608768	−	0.793348i	$-0.291664\pi$
$691$	32.0052			1.21754			0.608768	+	0.793348i	$0.291664\pi$
$692$	−1.46763	−	10.2076i	−0.0557910	−	0.388035i
$693$	2.76141	−	6.04664i	0.104897	−	0.229693i
$694$	15.4102	−	4.52485i	0.584964	−	0.171761i
$695$	9.00091	−	10.3876i	0.341424	−	0.394024i
$696$	−10.5151	−	3.08752i	−0.398575	−	0.117032i
$697$	23.2607	−	14.9488i	0.881063	−	0.566225i
$698$	−6.46260	−	14.1511i	−0.244613	−	0.535628i
$699$	9.46223	+	10.9200i	0.357894	+	0.413032i
$700$	−0.986597	−	0.634047i	−0.0372899	−	0.0239647i
$701$	2.20418	−	15.3304i	0.0832507	−	0.579021i	−0.904911	−	0.425602i	$-0.860062\pi$
$701$	2.20418	−	15.3304i	0.0832507	−	0.579021i	0.988161	−	0.153419i	$-0.0490285\pi$
$702$	−0.721652	+	5.01920i	−0.0272370	+	0.189437i
$703$	−21.0760	−	13.5447i	−0.794898	−	0.510850i
$704$	0.901341	+	1.04020i	0.0339706	+	0.0392041i
$705$	−12.5969	−	27.5834i	−0.474427	−	1.03885i
$706$	−12.0203	+	7.72499i	−0.452391	+	0.290734i
$707$	−14.5598	−	4.27514i	−0.547577	−	0.160783i
$708$	19.4786	−	22.4795i	0.732052	−	0.844833i
$709$	−10.9287	+	3.20897i	−0.410437	+	0.120515i	−0.480432	−	0.877032i	$-0.659520\pi$
$709$	−10.9287	+	3.20897i	−0.410437	+	0.120515i	0.0699945	+	0.997547i	$0.477702\pi$
$710$	−2.76703	+	6.05895i	−0.103845	+	0.227388i
$711$	−4.97001	−	34.5672i	−0.186390	−	1.29637i
$712$	−9.65722			−0.361920
$713$	−19.8653	−	3.06927i	−0.743960	−	0.114945i
$714$	12.6300			0.472664
$715$	0.332975	+	2.31589i	0.0124526	+	0.0866095i
$716$	−6.09455	+	13.3452i	−0.227764	+	0.498734i
$717$	28.3390	−	8.32107i	1.05834	−	0.310756i
$718$	−3.77323	+	4.35454i	−0.140816	+	0.162510i
$719$	−21.3863	−	6.27960i	−0.797576	−	0.234190i	−0.142542	−	0.989789i	$-0.545528\pi$
$719$	−21.3863	−	6.27960i	−0.797576	−	0.234190i	−0.655034	+	0.755599i	$0.727346\pi$
$720$	3.46435	−	2.22640i	0.129109	−	0.0829732i
$721$	7.15618	+	15.6698i	0.266510	+	0.583575i
$722$	9.47203	+	10.9313i	0.352512	+	0.406821i
$723$	−1.03461	−	0.664902i	−0.0384774	−	0.0247280i
$724$	−0.415626	+	2.89074i	−0.0154466	+	0.107434i
$725$	−0.584577	+	4.06582i	−0.0217106	+	0.151001i
$726$	−20.4369	−	13.1340i	−0.758485	−	0.487449i
$727$	31.6343	+	36.5079i	1.17325	+	1.35400i	0.922521	+	0.385947i	$0.126125\pi$
$727$	31.6343	+	36.5079i	1.17325	+	1.35400i	0.250730	+	0.968057i	$0.419329\pi$
$728$	0.828164	+	1.81343i	0.0306938	+	0.0672101i
$729$	−35.3137	+	22.6947i	−1.30791	+	0.840545i
$730$	−6.38511	−	1.87484i	−0.236324	−	0.0693909i
$731$	−31.2170	+	36.0263i	−1.15460	+	1.33248i
$732$	−7.56178	+	2.22034i	−0.279492	+	0.0820661i
$733$	5.33867	−	11.6901i	0.197188	−	0.431782i	−0.785047	−	0.619436i	$-0.787361\pi$
$733$	5.33867	−	11.6901i	0.197188	−	0.431782i	0.982235	+	0.187654i	$0.0600884\pi$
$734$	−4.39991	−	30.6021i	−0.162404	−	1.12954i
$735$	15.0063			0.553516
$736$	−4.75392	+	0.632674i	−0.175232	+	0.0233207i
$737$	−2.89606			−0.106678
$738$	−4.01453	−	27.9216i	−0.147777	−	1.02781i
$739$	2.37021	−	5.19003i	0.0871894	−	0.190918i	−0.861015	−	0.508580i	$-0.830170\pi$
$739$	2.37021	−	5.19003i	0.0871894	−	0.190918i	0.948204	+	0.317662i	$0.102898\pi$
$740$	4.15541	−	1.22014i	0.152756	−	0.0448532i
$741$	17.1807	−	19.8276i	0.631150	−	0.728386i
$742$	1.63025	+	0.478684i	0.0598482	+	0.0175730i
$743$	4.03647	−	2.59408i	0.148084	−	0.0951676i	−0.464501	−	0.885573i	$-0.653766\pi$
$743$	4.03647	−	2.59408i	0.148084	−	0.0951676i	0.612585	+	0.790405i	$0.290130\pi$
$744$	4.64533	+	10.1719i	0.170306	+	0.372919i
$745$	4.20899	+	4.85743i	0.154205	+	0.177963i
$746$	−11.0025	−	7.07090i	−0.402832	−	0.258884i
$747$	−5.92815	+	41.2312i	−0.216900	+	1.50857i
$748$	−0.790674	+	5.49926i	−0.0289099	+	0.201073i
$749$	3.75616	+	2.41393i	0.137247	+	0.0882032i
$750$	−1.74715	−	2.01632i	−0.0637969	−	0.0736256i
$751$	12.7939	+	28.0148i	0.466858	+	1.02228i	0.985871	+	0.167509i	$0.0535723\pi$
$751$	12.7939	+	28.0148i	0.466858	+	1.02228i	−0.519013	+	0.854766i	$0.673700\pi$
$752$	9.56152	−	6.14482i	0.348673	−	0.224078i
$753$	33.7915	+	9.92207i	1.23143	+	0.361580i
$754$	4.57258	−	5.27704i	0.166524	−	0.192178i
$755$	2.84157	−	0.834359i	0.103415	−	0.0303654i
$756$	1.45329	−	3.18226i	0.0528555	−	0.115737i
$757$	−5.90824	−	41.0927i	−0.214739	−	1.49354i	−0.757047	−	0.653361i	$-0.773358\pi$
$757$	−5.90824	−	41.0927i	−0.214739	−	1.49354i	0.542308	−	0.840180i	$-0.317551\pi$
$758$	−6.85642			−0.249036
$759$	−16.0955	+	7.14742i	−0.584229	+	0.259435i
$760$	−5.78482			−0.209838
$761$	−0.409351	−	2.84710i	−0.0148390	−	0.103207i	0.981056	−	0.193725i	$-0.0620569\pi$
$761$	−0.409351	−	2.84710i	−0.0148390	−	0.103207i	−0.995895	+	0.0905177i	$0.971148\pi$
$762$	10.2310	−	22.4028i	0.370631	−	0.811568i
$763$	−15.3318	+	4.50182i	−0.555048	+	0.162977i
$764$	−8.87431	+	10.2415i	−0.321061	+	0.370524i
$765$	15.9494	+	4.68317i	0.576652	+	0.169320i
$766$	−0.155427	+	0.0998872i	−0.00561582	+	0.00360907i
$767$	7.87284	+	17.2391i	0.284272	+	0.622468i
$768$	1.74715	+	2.01632i	0.0630449	+	0.0727577i
$769$	4.43212	+	2.84835i	0.159826	+	0.102714i	0.618109	−	0.786092i	$-0.287899\pi$
$769$	4.43212	+	2.84835i	0.159826	+	0.102714i	−0.458283	+	0.888806i	$0.651535\pi$
$770$	0.229722	−	1.59775i	0.00827862	−	0.0575791i
$771$	−2.47388	+	17.2062i	−0.0890946	+	0.619666i
$772$	−9.78770	−	6.29017i	−0.352267	−	0.226388i
$773$	−27.9918	−	32.3042i	−1.00679	−	1.16190i	−0.986774	−	0.162102i	$-0.948173\pi$
$773$	−27.9918	−	32.3042i	−1.00679	−	1.16190i	−0.0200193	−	0.999800i	$-0.506373\pi$
$774$	20.2028	+	44.2380i	0.726176	+	1.59010i
$775$	3.52598	−	2.26601i	0.126657	−	0.0813975i
$776$	16.8009	+	4.93318i	0.603116	+	0.177091i
$777$	8.87392	−	10.2410i	0.318350	−	0.367395i
$778$	−24.6430	+	7.23583i	−0.883494	+	0.259417i
$779$	−16.4612	+	36.0450i	−0.589783	+	1.29145i
$780$	0.645436	+	4.48910i	0.0231103	+	0.160736i
$781$	−9.16794			−0.328055
$782$	−14.4963	−	12.8299i	−0.518388	−	0.458797i
$783$	−12.2531			−0.437892
$784$	0.800465	+	5.56736i	0.0285881	+	0.198834i
$785$	−4.68875	+	10.2669i	−0.167349	+	0.366443i
$786$	−20.5450	+	6.03256i	−0.732816	+	0.215174i
$787$	−30.7864	+	35.5294i	−1.09742	+	1.26649i	−0.136205	+	0.990681i	$0.543490\pi$
$787$	−30.7864	+	35.5294i	−1.09742	+	1.26649i	−0.961213	+	0.275807i	$0.911055\pi$
$788$	−16.8336	−	4.94278i	−0.599671	−	0.176079i
$789$	12.6103	−	8.10415i	0.448939	−	0.288516i
$790$	−3.52285	−	7.71396i	−0.125337	−	0.274450i
$791$	6.56641	+	7.57804i	0.233475	+	0.269444i
$792$	4.76829	+	3.06439i	0.169434	+	0.108888i
$793$	0.714615	−	4.97026i	0.0253767	−	0.176499i
$794$	0.0109333	−	0.0760427i	0.000388008	−	0.00269865i
$795$	3.25167	+	2.08972i	0.115325	+	0.0741149i
$796$	−10.1576	−	11.7225i	−0.360028	−	0.415495i
$797$	19.3081	+	42.2789i	0.683930	+	1.49760i	0.858425	+	0.512939i	$0.171443\pi$
$797$	19.3081	+	42.2789i	0.683930	+	1.49760i	−0.174495	+	0.984658i	$0.555829\pi$
$798$	−15.2269	+	9.78574i	−0.539026	+	0.346411i
$799$	44.0199	+	12.9254i	1.55731	+	0.457268i
$800$	0.654861	−	0.755750i	0.0231528	−	0.0267198i
$801$	−38.1583	+	11.2043i	−1.34826	+	0.395884i
$802$	−7.17736	+	15.7162i	−0.253441	+	0.554959i
$803$	−1.30352	−	9.06617i	−0.0460002	−	0.319938i
$804$	−5.61370			−0.197980
$805$	4.21177	+	3.72760i	0.148445	+	0.131381i
$806$	−7.12483			−0.250961
$807$	10.6576	+	74.1255i	0.375167	+	2.60934i
$808$	5.37505	−	11.7697i	0.189093	−	0.414057i
$809$	26.5697	−	7.80157i	0.934141	−	0.274289i	0.220972	−	0.975280i	$-0.429077\pi$
$809$	26.5697	−	7.80157i	0.934141	−	0.274289i	0.713169	+	0.700992i	$0.247259\pi$
$810$	−2.87853	+	3.32200i	−0.101141	+	0.116723i
$811$	30.6545	+	9.00097i	1.07642	+	0.316067i	0.771448	−	0.636293i	$-0.219533\pi$
$811$	30.6545	+	9.00097i	1.07642	+	0.316067i	0.304977	+	0.952360i	$0.401351\pi$
$812$	−4.05257	+	2.60443i	−0.142217	+	0.0913976i
$813$	−0.822015	−	1.79996i	−0.0288293	−	0.0631274i
$814$	3.90356	+	4.50495i	0.136820	+	0.157898i
$815$	−15.1642	−	9.74547i	−0.531180	−	0.341369i
$816$	−1.53264	+	10.6597i	−0.0536530	+	0.373165i
$817$	9.72244	−	67.6210i	0.340145	−	2.36576i
$818$	9.75967	+	6.27216i	0.341239	+	0.219301i
$819$	5.37624	+	6.20451i	0.187861	+	0.216803i
$820$	−2.84558	−	6.23096i	−0.0993720	−	0.217594i
$821$	16.2467	−	10.4411i	0.567014	−	0.364398i	−0.225508	−	0.974241i	$-0.572404\pi$
$821$	16.2467	−	10.4411i	0.567014	−	0.364398i	0.792522	+	0.609843i	$0.208768\pi$
$822$	49.5933	+	14.5619i	1.72976	+	0.507905i
$823$	5.25485	−	6.06442i	0.183173	−	0.211392i	−0.656736	−	0.754121i	$-0.728063\pi$
$823$	5.25485	−	6.06442i	0.183173	−	0.211392i	0.839908	+	0.542728i	$0.182609\pi$
$824$	−14.0938	+	4.13831i	−0.490980	+	0.144165i
$825$	1.52547	−	3.34032i	0.0531101	−	0.116295i
$826$	−1.86076	−	12.9419i	−0.0647442	−	0.450306i
$827$	25.9685			0.903015			0.451507	−	0.892267i	$-0.350886\pi$
$827$	25.9685			0.903015			0.451507	+	0.892267i	$0.350886\pi$
$828$	−18.0500	+	8.01535i	−0.627281	+	0.278553i
$829$	48.8480			1.69656			0.848281	−	0.529546i	$-0.177638\pi$
$829$	48.8480			1.69656			0.848281	+	0.529546i	$0.177638\pi$
$830$	1.43954	+	10.0122i	0.0499672	+	0.347529i
$831$	2.56587	−	5.61846i	0.0890089	−	0.194902i
$832$	−1.63103	+	0.478915i	−0.0565459	+	0.0166034i
$833$	−14.8679	+	17.1584i	−0.515141	+	0.594504i
$834$	35.1853	+	10.3313i	1.21837	+	0.357745i
$835$	−8.28087	+	5.32179i	−0.286571	+	0.184168i
$836$	−3.30760	−	7.24263i	−0.114396	−	0.250491i
$837$	8.18764	+	9.44903i	0.283006	+	0.326606i
$838$	33.4127	+	21.4731i	1.15422	+	0.741775i
$839$	−6.93915	+	48.2628i	−0.239566	+	1.66622i	0.414704	+	0.909956i	$0.363885\pi$
$839$	−6.93915	+	48.2628i	−0.239566	+	1.66622i	−0.654270	+	0.756261i	$0.727024\pi$
$840$	0.445292	−	3.09707i	0.0153640	−	0.106859i
$841$	−10.2022	−	6.55656i	−0.351800	−	0.226088i
$842$	8.16208	+	9.41954i	0.281284	+	0.324619i
$843$	−11.1680	−	24.4545i	−0.384647	−	0.842259i
$844$	20.8445	−	13.3960i	0.717499	−	0.461108i
$845$	9.70083	+	2.84842i	0.333719	+	0.0979886i
$846$	30.6510	−	35.3731i	1.05380	−	1.21615i
$847$	−10.2462	+	3.00855i	−0.352063	+	0.103375i
$848$	−0.601840	+	1.31784i	−0.0206673	+	0.0452550i
$849$	6.40973	+	44.5806i	0.219981	+	1.53000i
$850$	4.03652			0.138452
$851$	−20.5884	+	2.74001i	−0.705763	+	0.0939262i
$852$	−17.7711			−0.608826
$853$	3.35218	+	23.3150i	0.114777	+	0.798289i	0.963164	+	0.268913i	$0.0866646\pi$
$853$	3.35218	+	23.3150i	0.114777	+	0.798289i	−0.848388	+	0.529375i	$0.822426\pi$
$854$	−1.43912	+	3.15123i	−0.0492456	+	0.107833i
$855$	−22.8574	+	6.71154i	−0.781707	+	0.229530i
$856$	−2.49317	+	2.87728i	−0.0852149	+	0.0983433i
$857$	−3.78954	−	1.11271i	−0.129448	−	0.0380095i	0.216367	−	0.976312i	$-0.430579\pi$
$857$	−3.78954	−	1.11271i	−0.129448	−	0.0380095i	−0.345815	+	0.938303i	$0.612398\pi$
$858$	−5.25134	+	3.37483i	−0.179278	+	0.115215i
$859$	4.53442	+	9.92899i	0.154712	+	0.338773i	0.971078	−	0.238763i	$-0.0767418\pi$
$859$	4.53442	+	9.92899i	0.154712	+	0.338773i	−0.816366	+	0.577535i	$0.804015\pi$
$860$	7.73364	+	8.92509i	0.263715	+	0.304343i
$861$	−18.0306	−	11.5876i	−0.614481	−	0.394903i
$862$	0.249956	−	1.73848i	0.00851353	−	0.0592129i
$863$	0.789598	−	5.49177i	0.0268782	−	0.186942i	−0.971959	−	0.235150i	$-0.924442\pi$
$863$	0.789598	−	5.49177i	0.0268782	−	0.186942i	0.998837	+	0.0482078i	$0.0153510\pi$
$864$	2.50948	+	1.61274i	0.0853741	+	0.0548666i
$865$	−6.75329	−	7.79372i	−0.229619	−	0.264994i
$866$	−0.199295	−	0.436395i	−0.00677231	−	0.0148293i
$867$	1.58568	−	1.01905i	0.0538525	−	0.0346089i
$868$	4.71637	+	1.38485i	0.160084	+	0.0470049i
$869$	7.64365	−	8.82124i	0.259293	−	0.299240i
$870$	−10.5151	+	3.08752i	−0.356496	+	0.104677i
$871$	1.48584	−	3.25353i	0.0503457	−	0.110242i
$872$	−1.93905	−	13.4864i	−0.0656644	−	0.456706i
$873$	72.1083			2.44049
$874$	27.4177	+	4.23615i	0.927418	+	0.143290i
$875$	−1.17277			−0.0396469
$876$	−2.52673	−	17.5738i	−0.0853703	−	0.593763i
$877$	−5.06133	+	11.0828i	−0.170909	+	0.374238i	−0.975632	−	0.219412i	$-0.929586\pi$
$877$	−5.06133	+	11.0828i	−0.170909	+	0.374238i	0.804724	+	0.593650i	$0.202314\pi$
$878$	−3.24041	+	0.951469i	−0.109358	+	0.0321105i
$879$	45.5806	−	52.6028i	1.53739	−	1.77425i
$880$	1.32063	+	0.387773i	0.0445185	+	0.0130718i
$881$	0.684913	−	0.440167i	0.0230753	−	0.0148296i	−0.529052	−	0.848589i	$-0.677452\pi$
$881$	0.684913	−	0.440167i	0.0230753	−	0.0148296i	0.552128	+	0.833760i	$0.313816\pi$
$882$	9.62210	+	21.0695i	0.323993	+	0.709446i
$883$	−5.24052	−	6.04788i	−0.176357	−	0.203527i	0.660688	−	0.750660i	$-0.270265\pi$
$883$	−5.24052	−	6.04788i	−0.176357	−	0.203527i	−0.837046	+	0.547133i	$0.815719\pi$
$884$	−5.77239	−	3.70969i	−0.194146	−	0.124770i
$885$	4.23311	−	29.4419i	0.142294	−	0.989679i
$886$	1.04459	−	7.26528i	0.0350937	−	0.244082i
$887$	−22.0881	−	14.1952i	−0.741646	−	0.476627i	0.114459	−	0.993428i	$-0.463486\pi$
$887$	−22.0881	−	14.1952i	−0.741646	−	0.476627i	−0.856106	+	0.516801i	$0.827123\pi$
$888$	7.56663	+	8.73236i	0.253919	+	0.293039i
$889$	−4.49728	−	9.84768i	−0.150834	−	0.330281i
$890$	−8.12417	+	5.22109i	−0.272323	+	0.175011i
$891$	−5.80501	−	1.70451i	−0.194475	−	0.0571031i
$892$	−15.9155	+	18.3674i	−0.532890	+	0.614987i
$893$	−63.0859	+	18.5237i	−2.11109	+	0.619871i
$894$	−7.12349	+	15.5983i	−0.238245	+	0.521684i
$895$	2.08790	+	14.5217i	0.0697908	+	0.485406i
$896$	1.17277			0.0391795
$897$	0.228209	−	21.7492i	0.00761969	−	0.726184i
$898$	−27.3666			−0.913235
$899$	−2.45016	−	17.0412i	−0.0817174	−	0.568357i
$900$	1.71071	−	3.74594i	0.0570238	−	0.124865i
$901$	−5.61110	+	1.64757i	−0.186933	+	0.0548884i
$902$	6.17416	−	7.12536i	0.205577	−	0.237249i
$903$	35.4545	+	10.4104i	1.17985	+	0.346436i
$904$	−7.19272	+	4.62248i	−0.239226	+	0.153741i
$905$	1.21321	+	2.65655i	0.0403284	+	0.0883068i
$906$	5.17424	+	5.97139i	0.171903	+	0.198386i
$907$	−10.6829	−	6.86551i	−0.354721	−	0.227966i	0.351128	−	0.936327i	$-0.385798\pi$
$907$	−10.6829	−	6.86551i	−0.354721	−	0.227966i	−0.705849	+	0.708362i	$0.749435\pi$
$908$	3.97901	−	27.6746i	0.132048	−	0.918415i
$909$	7.58308	−	52.7415i	0.251515	−	1.74932i
$910$	1.67711	+	1.07781i	0.0555956	+	0.0357291i
$911$	9.46767	+	10.9263i	0.313678	+	0.362004i	0.890594	−	0.454800i	$-0.150289\pi$
$911$	9.46767	+	10.9263i	0.313678	+	0.362004i	−0.576916	+	0.816804i	$0.695744\pi$
$912$	−6.41142	−	14.0390i	−0.212303	−	0.464879i
$913$	−11.7123	+	7.52701i	−0.387619	+	0.249108i
$914$	15.9251	+	4.67603i	0.526755	+	0.154669i
$915$	−5.16097	+	5.95608i	−0.170616	+	0.196902i
$916$	−4.69233	+	1.37779i	−0.155039	+	0.0455235i
$917$	−3.91001	+	8.56173i	−0.129120	+	0.282733i
$918$	1.71362	+	11.9185i	0.0565578	+	0.393368i
$919$	−50.8130			−1.67617			−0.838084	−	0.545542i	$-0.816324\pi$
$919$	−50.8130			−1.67617			−0.838084	+	0.545542i	$0.816324\pi$
$920$	−3.65720	+	3.10240i	−0.120574	+	0.102283i
$921$	77.3659			2.54929
$922$	4.20662	+	29.2577i	0.138538	+	0.963551i
$923$	4.70365	−	10.2996i	0.154823	−	0.339014i
$924$	4.13215	−	1.21331i	0.135938	−	0.0399150i
$925$	2.83610	−	3.27303i	0.0932502	−	0.107617i
$926$	26.4352	+	7.76207i	0.868714	+	0.255077i
$927$	−50.8871	+	32.7032i	−1.67135	+	1.07411i
$928$	−1.70637	−	3.73643i	−0.0560144	−	0.122654i
$929$	4.56068	+	5.26331i	0.149631	+	0.172684i	0.825617	−	0.564231i	$-0.190827\pi$
$929$	4.56068	+	5.26331i	0.149631	+	0.172684i	−0.675986	+	0.736915i	$0.736282\pi$
$930$	9.40723	+	6.04566i	0.308475	+	0.198245i
$931$	4.63055	−	32.2062i	0.151760	−	1.05552i
$932$	−0.770749	+	5.36068i	−0.0252467	+	0.175595i
$933$	−37.4215	−	24.0494i	−1.22513	−	0.787341i
$934$	3.60021	+	4.15487i	0.117803	+	0.135951i
$935$	2.30797	+	5.05374i	0.0754786	+	0.165275i
$936$	−5.88903	+	3.78465i	−0.192489	+	0.123705i
$937$	23.3252	+	6.84888i	0.762000	+	0.223743i	0.639569	−	0.768734i	$-0.279113\pi$
$937$	23.3252	+	6.84888i	0.762000	+	0.223743i	0.122431	+	0.992477i	$0.460931\pi$
$938$	−1.61596	+	1.86491i	−0.0527629	+	0.0608916i
$939$	41.6798	−	12.2383i	1.36017	−	0.399381i
$940$	4.72153	−	10.3387i	0.153999	−	0.337211i
$941$	−1.89744	−	13.1970i	−0.0618547	−	0.430209i	−0.997093	−	0.0761907i	$-0.975724\pi$
$941$	−1.89744	−	13.1970i	−0.0618547	−	0.430209i	0.935239	−	0.354018i	$-0.115185\pi$
$942$	−30.1132			−0.981141
$943$	8.92406	+	31.6160i	0.290607	+	1.02956i
$944$	11.1488			0.362862
$945$	−0.497874	−	3.46279i	−0.0161958	−	0.112645i
$946$	−6.75239	+	14.7857i	−0.219539	+	0.480723i
$947$	−33.4561	+	9.82358i	−1.08718	+	0.319224i	−0.775746	−	0.631046i	$-0.782626\pi$
$947$	−33.4561	+	9.82358i	−1.08718	+	0.319224i	−0.311430	+	0.950269i	$0.600808\pi$
$948$	14.8164	−	17.0990i	0.481214	−	0.555350i
$949$	10.8540	+	3.18702i	0.352336	+	0.103455i
$950$	−4.86650	+	3.12751i	−0.157890	+	0.101470i
$951$	−37.8140	−	82.8010i	−1.22620	−	2.68501i
$952$	3.10005	+	3.57765i	0.100473	+	0.115952i
$953$	−29.8213	−	19.1650i	−0.966006	−	0.620814i	−0.0403520	−	0.999186i	$-0.512848\pi$
$953$	−29.8213	−	19.1650i	−0.966006	−	0.620814i	−0.925654	+	0.378371i	$0.876484\pi$
$954$	−0.849071	+	5.90542i	−0.0274897	+	0.191195i
$955$	−1.92857	+	13.4135i	−0.0624071	+	0.434051i
$956$	9.31296	+	5.98507i	0.301203	+	0.193571i
$957$	−9.87784	−	11.3996i	−0.319305	−	0.368498i
$958$	8.92632	+	19.5459i	0.288396	+	0.631499i
$959$	19.1135	−	12.2835i	0.617206	−	0.396654i
$960$	2.55990	+	0.751655i	0.0826205	+	0.0242596i
$961$	8.79651	−	10.1517i	0.283758	−	0.327475i
$962$	−7.06374	+	2.07410i	−0.227744	+	0.0668718i
$963$	−6.51300	+	14.2615i	−0.209879	+	0.459570i
$964$	−0.0656020	−	0.456272i	−0.00211290	−	0.0146955i
$965$	−11.6347			−0.374533
$966$	−4.37845	+	14.3528i	−0.140874	+	0.461793i
$967$	14.9989			0.482331			0.241165	−	0.970484i	$-0.422470\pi$
$967$	14.9989			0.482331			0.241165	+	0.970484i	$0.422470\pi$
$968$	−1.29586	−	9.01288i	−0.0416504	−	0.289685i
$969$	25.8798	−	56.6689i	0.831380	−	1.82047i
$970$	16.8009	−	4.93318i	0.539443	−	0.158395i
$971$	7.69888	−	8.88498i	0.247069	−	0.285133i	−0.618646	−	0.785670i	$-0.712319\pi$
$971$	7.69888	−	8.88498i	0.247069	−	0.285133i	0.865715	+	0.500537i	$0.166864\pi$
$972$	−19.8390	−	5.82524i	−0.636335	−	0.186845i
$973$	13.5606	−	8.71484i	0.434731	−	0.279385i
$974$	1.56228	+	3.42091i	0.0500587	+	0.109613i
$975$	2.96997	+	3.42753i	0.0951151	+	0.109769i
$976$	−2.48501	−	1.59702i	−0.0795432	−	0.0511193i
$977$	−6.05678	+	42.1258i	−0.193773	+	1.34772i	0.628135	+	0.778104i	$0.283818\pi$
$977$	−6.05678	+	42.1258i	−0.193773	+	1.34772i	−0.821909	+	0.569619i	$0.807091\pi$
$978$	6.84425	−	47.6028i	0.218855	−	1.52217i
$979$	−11.1820	−	7.18623i	−0.357378	−	0.229673i
$980$	3.68334	+	4.25080i	0.117660	+	0.135787i
$981$	−23.3085	−	51.0386i	−0.744185	−	1.62954i
$982$	8.54618	−	5.49229i	0.272719	−	0.175266i
$983$	−5.35889	−	1.57351i	−0.170922	−	0.0501872i	0.195152	−	0.980773i	$-0.437480\pi$
$983$	−5.35889	−	1.57351i	−0.170922	−	0.0501872i	−0.366074	+	0.930586i	$0.619298\pi$
$984$	11.9679	−	13.8117i	0.381524	−	0.440302i
$985$	−16.8336	+	4.94278i	−0.536362	+	0.157490i
$986$	6.88780	−	15.0822i	0.219352	−	0.480315i
$987$	−5.06110	−	35.2007i	−0.161097	−	1.12045i
$988$	9.83358			0.312848
$989$	−30.1186	−	47.9646i	−0.957715	−	1.52518i
$990$	5.66807			0.180143
$991$	6.87182	+	47.7946i	0.218291	+	1.51824i	0.744346	+	0.667794i	$0.232761\pi$
$991$	6.87182	+	47.7946i	0.218291	+	1.51824i	−0.526055	+	0.850450i	$0.676330\pi$
$992$	−1.74115	+	3.81258i	−0.0552815	+	0.121050i
$993$	87.3657	−	25.6529i	2.77247	−	0.814070i
$994$	−5.11557	+	5.90368i	−0.162256	+	0.187253i
$995$	−14.8828	−	4.37000i	−0.471818	−	0.138538i
$996$	−22.7029	+	14.5903i	−0.719370	+	0.462311i
$997$	2.19041	+	4.79634i	0.0693711	+	0.151901i	0.941141	−	0.338014i	$-0.109755\pi$
$997$	2.19041	+	4.79634i	0.0693711	+	0.151901i	−0.871770	+	0.489915i	$0.837028\pi$
$998$	22.5788	+	26.0574i	0.714720	+	0.824831i
$999$	10.8681	+	6.98453i	0.343853	+	0.220981i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.g.b.141.1	yes	20
23.8	even	11	inner	230.2.g.b.31.1	✓	20
23.10	odd	22		5290.2.a.bi.1.1		10
23.13	even	11		5290.2.a.bj.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.b.31.1	✓	20	23.8	even	11	inner
230.2.g.b.141.1	yes	20	1.1	even	1	trivial
5290.2.a.bi.1.1		10	23.10	odd	22
5290.2.a.bj.1.1		10	23.13	even	11

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 + 0.989821i) q^{2} +(-1.10832 + 2.42687i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-2.55990 - 0.751655i) q^{6} +(-0.986597 + 0.634047i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-2.69677 - 3.11224i) q^{9} +O(q^{10})\)	\(q+(0.142315 + 0.989821i) q^{2} +(-1.10832 + 2.42687i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-2.55990 - 0.751655i) q^{6} +(-0.986597 + 0.634047i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-2.69677 - 3.11224i) q^{9} +(-0.841254 - 0.540641i) q^{10} +(0.195880 - 1.36238i) q^{11} +(0.379692 - 2.64082i) q^{12} +(1.43004 + 0.919031i) q^{13} +(-0.768001 - 0.886321i) q^{14} +(-1.10832 - 2.42687i) q^{15} +(0.841254 - 0.540641i) q^{16} +(3.87301 + 1.13722i) q^{17} +(2.69677 - 3.11224i) q^{18} +(-5.55050 + 1.62977i) q^{19} +(0.415415 - 0.909632i) q^{20} +(-0.445292 - 3.09707i) q^{21} +1.37639 q^{22} +(-2.63501 + 4.00708i) q^{23} +2.66797 q^{24} +(-0.142315 - 0.989821i) q^{25} +(-0.706161 + 1.54628i) q^{26} +(2.86219 - 0.840414i) q^{27} +(0.768001 - 0.886321i) q^{28} +(-3.94124 - 1.15725i) q^{29} +(2.24444 - 1.44242i) q^{30} +(1.74115 + 3.81258i) q^{31} +(0.654861 + 0.755750i) q^{32} +(3.08922 + 1.98532i) q^{33} +(-0.574457 + 3.99544i) q^{34} +(0.166903 - 1.16083i) q^{35} +(3.46435 + 2.22640i) q^{36} +(2.83610 + 3.27303i) q^{37} +(-2.40310 - 5.26206i) q^{38} +(-3.81531 + 2.45195i) q^{39} +(0.959493 + 0.281733i) q^{40} +(4.48578 - 5.17686i) q^{41} +(3.00218 - 0.881519i) q^{42} +(-4.90588 + 10.7424i) q^{43} +(0.195880 + 1.36238i) q^{44} +4.11808 q^{45} +(-4.34130 - 2.03792i) q^{46} +11.3658 q^{47} +(0.379692 + 2.64082i) q^{48} +(-2.33655 + 5.11633i) q^{49} +(0.959493 - 0.281733i) q^{50} +(-7.05241 + 8.13892i) q^{51} +(-1.63103 - 0.478915i) q^{52} +(-1.21878 + 0.783263i) q^{53} +(1.23919 + 2.71345i) q^{54} +(0.901341 + 1.04020i) q^{55} +(0.986597 + 0.634047i) q^{56} +(2.19645 - 15.2767i) q^{57} +(0.584577 - 4.06582i) q^{58} +(9.37896 + 6.02749i) q^{59} +(1.74715 + 2.01632i) q^{60} +(-1.22711 - 2.68699i) q^{61} +(-3.52598 + 2.26601i) q^{62} +(4.63394 + 1.36065i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-1.63103 + 0.478915i) q^{65} +(-1.52547 + 3.34032i) q^{66} +(-0.299446 - 2.08269i) q^{67} -4.03652 q^{68} +(-6.80426 - 10.8360i) q^{69} +1.17277 q^{70} +(-0.947942 - 6.59308i) q^{71} +(-1.71071 + 3.74594i) q^{72} +(6.38511 - 1.87484i) q^{73} +(-2.83610 + 3.27303i) q^{74} +(2.55990 + 0.751655i) q^{75} +(4.86650 - 3.12751i) q^{76} +(0.670556 + 1.46831i) q^{77} +(-2.96997 - 3.42753i) q^{78} +(7.13409 + 4.58480i) q^{79} +(-0.142315 + 0.989821i) q^{80} +(0.625564 - 4.35089i) q^{81} +(5.76256 + 3.70338i) q^{82} +(-6.62403 - 7.64454i) q^{83} +(1.29980 + 2.84617i) q^{84} +(-3.39574 + 2.18231i) q^{85} +(-11.3312 - 3.32715i) q^{86} +(7.17665 - 8.28229i) q^{87} +(-1.32063 + 0.387773i) q^{88} +(4.01175 - 8.78452i) q^{89} +(0.586065 + 4.07617i) q^{90} -1.99358 q^{91} +(1.39935 - 4.58714i) q^{92} -11.1824 q^{93} +(1.61752 + 11.2501i) q^{94} +(2.40310 - 5.26206i) q^{95} +(-2.55990 + 0.751655i) q^{96} +(-11.4667 + 13.2333i) q^{97} +(-5.39677 - 1.58464i) q^{98} +(-4.76829 + 3.06439i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9	\( 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9} + 2 q^{10} + 7 q^{11} + 8 q^{12} + 8 q^{13} + 3 q^{14} - 3 q^{15} - 2 q^{16} + 8 q^{17} + 27 q^{18} - q^{19} - 2 q^{20} - 31 q^{21} - 18 q^{22} - 9 q^{23} - 8 q^{24} - 2 q^{25} - 8 q^{26} - 18 q^{27} - 3 q^{28} + 20 q^{29} + 3 q^{30} - 17 q^{31} + 2 q^{32} + 17 q^{33} + 3 q^{34} - 3 q^{35} + 17 q^{36} + 6 q^{37} - 21 q^{38} - 75 q^{39} + 2 q^{40} - 2 q^{41} + 42 q^{42} - 18 q^{43} + 7 q^{44} + 28 q^{45} - 2 q^{46} + 42 q^{47} + 8 q^{48} - 19 q^{49} + 2 q^{50} + 26 q^{51} + 19 q^{52} + 19 q^{53} - 26 q^{54} - 15 q^{55} - 19 q^{56} + 7 q^{57} - 9 q^{58} + 25 q^{59} - 3 q^{60} - 49 q^{61} - 38 q^{62} - 87 q^{63} - 2 q^{64} + 19 q^{65} - 6 q^{66} + 19 q^{67} - 36 q^{68} + 36 q^{69} + 14 q^{70} + 7 q^{71} - 17 q^{72} - 10 q^{73} - 6 q^{74} - 3 q^{75} - q^{76} - 29 q^{77} - 2 q^{78} - 33 q^{79} - 2 q^{80} + 72 q^{81} + 2 q^{82} - 41 q^{83} + 13 q^{84} - 14 q^{85} - 48 q^{86} - 16 q^{87} - 7 q^{88} + 55 q^{89} + 5 q^{90} + 13 q^{92} + 10 q^{93} + 13 q^{94} + 21 q^{95} + 3 q^{96} - 9 q^{97} + 41 q^{98} + 59 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9 + 2 * q^10 + 7 * q^11 + 8 * q^12 + 8 * q^13 + 3 * q^14 - 3 * q^15 - 2 * q^16 + 8 * q^17 + 27 * q^18 - q^19 - 2 * q^20 - 31 * q^21 - 18 * q^22 - 9 * q^23 - 8 * q^24 - 2 * q^25 - 8 * q^26 - 18 * q^27 - 3 * q^28 + 20 * q^29 + 3 * q^30 - 17 * q^31 + 2 * q^32 + 17 * q^33 + 3 * q^34 - 3 * q^35 + 17 * q^36 + 6 * q^37 - 21 * q^38 - 75 * q^39 + 2 * q^40 - 2 * q^41 + 42 * q^42 - 18 * q^43 + 7 * q^44 + 28 * q^45 - 2 * q^46 + 42 * q^47 + 8 * q^48 - 19 * q^49 + 2 * q^50 + 26 * q^51 + 19 * q^52 + 19 * q^53 - 26 * q^54 - 15 * q^55 - 19 * q^56 + 7 * q^57 - 9 * q^58 + 25 * q^59 - 3 * q^60 - 49 * q^61 - 38 * q^62 - 87 * q^63 - 2 * q^64 + 19 * q^65 - 6 * q^66 + 19 * q^67 - 36 * q^68 + 36 * q^69 + 14 * q^70 + 7 * q^71 - 17 * q^72 - 10 * q^73 - 6 * q^74 - 3 * q^75 - q^76 - 29 * q^77 - 2 * q^78 - 33 * q^79 - 2 * q^80 + 72 * q^81 + 2 * q^82 - 41 * q^83 + 13 * q^84 - 14 * q^85 - 48 * q^86 - 16 * q^87 - 7 * q^88 + 55 * q^89 + 5 * q^90 + 13 * q^92 + 10 * q^93 + 13 * q^94 + 21 * q^95 + 3 * q^96 - 9 * q^97 + 41 * q^98 + 59 * q^99

Introduction

L-functions

Modular forms

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Database

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