LMFDB - Embedded newform 230.2.g.b.81.1

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			81.1
Root			$-0.138474 - 0.963109i$ of defining polynomial
Character	$\chi$	$=$	230.81
Dual form			230.2.g.b.71.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.841254 + 0.540641i) q^{2} +(-0.420808 + 2.92679i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-1.22833 - 2.68968i) q^{6} +(2.73530 + 3.15671i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-5.51052 - 1.61803i) q^{9} +O(q^{10})$	\(q+(-0.841254 + 0.540641i) q^{2} +(-0.420808 + 2.92679i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-1.22833 - 2.68968i) q^{6} +(2.73530 + 3.15671i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-5.51052 - 1.61803i) q^{9} +(0.654861 - 0.755750i) q^{10} +(0.283012 + 0.181881i) q^{11} +(2.48749 + 1.59861i) q^{12} +(-2.21575 + 2.55712i) q^{13} +(-4.00773 - 1.17677i) q^{14} +(-0.420808 - 2.92679i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-1.82715 - 4.00090i) q^{17} +(5.51052 - 1.61803i) q^{18} +(2.00581 - 4.39211i) q^{19} +(-0.142315 + 0.989821i) q^{20} +(-10.3900 + 6.67727i) q^{21} -0.336417 q^{22} +(-2.79856 - 3.89462i) q^{23} -2.95688 q^{24} +(0.841254 - 0.540641i) q^{25} +(0.481529 - 3.34911i) q^{26} +(3.36951 - 7.37820i) q^{27} +(4.00773 - 1.17677i) q^{28} +(3.04924 + 6.67690i) q^{29} +(1.93635 + 2.23466i) q^{30} +(0.759503 + 5.28246i) q^{31} +(0.959493 + 0.281733i) q^{32} +(-0.651421 + 0.751780i) q^{33} +(3.70014 + 2.37794i) q^{34} +(-3.51385 - 2.25821i) q^{35} +(-3.76097 + 4.34039i) q^{36} +(7.80009 + 2.29031i) q^{37} +(0.687159 + 4.77930i) q^{38} +(-6.55172 - 7.56109i) q^{39} +(-0.415415 - 0.909632i) q^{40} +(0.0346901 - 0.0101859i) q^{41} +(5.13065 - 11.2346i) q^{42} +(-1.80648 + 12.5643i) q^{43} +(0.283012 - 0.181881i) q^{44} +5.74316 q^{45} +(4.45989 + 1.76334i) q^{46} +2.78554 q^{47} +(2.48749 - 1.59861i) q^{48} +(-1.48671 + 10.3403i) q^{49} +(-0.415415 + 0.909632i) q^{50} +(12.4786 - 3.66406i) q^{51} +(1.40558 + 3.07778i) q^{52} +(-0.0676444 - 0.0780658i) q^{53} +(1.15434 + 8.02864i) q^{54} +(-0.322790 - 0.0947797i) q^{55} +(-2.73530 + 3.15671i) q^{56} +(12.0107 + 7.71881i) q^{57} +(-6.17498 - 3.96842i) q^{58} +(-5.00157 + 5.77212i) q^{59} +(-2.83711 - 0.833050i) q^{60} +(-1.30303 - 9.06279i) q^{61} +(-3.49485 - 4.03327i) q^{62} +(-9.96527 - 21.8209i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(1.40558 - 3.07778i) q^{65} +(0.141567 - 0.984622i) q^{66} +(7.18925 - 4.62025i) q^{67} -4.39837 q^{68} +(12.5764 - 6.55191i) q^{69} +4.17692 q^{70} +(12.6504 - 8.12993i) q^{71} +(0.817337 - 5.68470i) q^{72} +(-2.21707 + 4.85471i) q^{73} +(-7.80009 + 2.29031i) q^{74} +(1.22833 + 2.68968i) q^{75} +(-3.16196 - 3.64909i) q^{76} +(0.199979 + 1.39089i) q^{77} +(9.59949 + 2.81867i) q^{78} +(8.98287 - 10.3668i) q^{79} +(0.841254 + 0.540641i) q^{80} +(5.68215 + 3.65170i) q^{81} +(-0.0236762 + 0.0273238i) q^{82} +(-0.0754484 - 0.0221536i) q^{83} +(1.75768 + 12.2250i) q^{84} +(2.88032 + 3.32406i) q^{85} +(-5.27308 - 11.5464i) q^{86} +(-20.8250 + 6.11477i) q^{87} +(-0.139753 + 0.306016i) q^{88} +(-1.30693 + 9.08988i) q^{89} +(-4.83145 + 3.10499i) q^{90} -14.1328 q^{91} +(-4.70523 + 0.927781i) q^{92} -15.7802 q^{93} +(-2.34335 + 1.50598i) q^{94} +(-0.687159 + 4.77930i) q^{95} +(-1.22833 + 2.68968i) q^{96} +(-3.45970 + 1.01586i) q^{97} +(-4.33970 - 9.50261i) q^{98} +(-1.26526 - 1.46018i) 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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{10}{11}\right)$

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 $

$2$	−0.841254	+	0.540641i	−0.594856	+	0.382291i
$2$	−0.841254	+	0.540641i	−0.594856	+	0.382291i
$3$	−0.420808	+	2.92679i	−0.242954	+	1.68978i	0.394184	+	0.919031i	$0.371027\pi$
$3$	−0.420808	+	2.92679i	−0.242954	+	1.68978i	−0.637138	+	0.770749i	$0.719882\pi$
$4$	0.415415	−	0.909632i	0.207708	−	0.454816i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$6$	−1.22833	−	2.68968i	−0.501465	−	1.09806i
$7$	2.73530	+	3.15671i	1.03385	+	1.19312i	0.980898	+	0.194525i	$0.0623166\pi$
$7$	2.73530	+	3.15671i	1.03385	+	1.19312i	0.0529490	+	0.998597i	$0.483138\pi$
$8$	0.142315	+	0.989821i	0.0503159	+	0.349955i
$9$	−5.51052	−	1.61803i	−1.83684	−	0.539345i
$10$	0.654861	−	0.755750i	0.207085	−	0.238989i
$11$	0.283012	+	0.181881i	0.0853314	+	0.0548392i	0.582611	−	0.812751i	$-0.302031\pi$
$11$	0.283012	+	0.181881i	0.0853314	+	0.0548392i	−0.497279	+	0.867590i	$0.665668\pi$
$12$	2.48749	+	1.59861i	0.718076	+	0.461479i
$13$	−2.21575	+	2.55712i	−0.614539	+	0.709216i	−0.974660	−	0.223689i	$-0.928190\pi$
$13$	−2.21575	+	2.55712i	−0.614539	+	0.709216i	0.360121	+	0.932906i	$0.382735\pi$
$14$	−4.00773	−	1.17677i	−1.07111	−	0.314506i
$15$	−0.420808	−	2.92679i	−0.108652	−	0.755693i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	−1.82715	−	4.00090i	−0.443148	−	0.970360i	−0.991010	−	0.133790i	$-0.957285\pi$
$17$	−1.82715	−	4.00090i	−0.443148	−	0.970360i	0.547861	−	0.836569i	$-0.315442\pi$
$18$	5.51052	−	1.61803i	1.29884	−	0.381374i
$19$	2.00581	−	4.39211i	0.460164	−	1.00762i	−0.527286	−	0.849688i	$-0.676790\pi$
$19$	2.00581	−	4.39211i	0.460164	−	1.00762i	0.987450	−	0.157931i	$-0.0504823\pi$
$20$	−0.142315	+	0.989821i	−0.0318226	+	0.221331i
$21$	−10.3900	+	6.67727i	−2.26729	+	1.45710i
$22$	−0.336417			−0.0717244
$23$	−2.79856	−	3.89462i	−0.583541	−	0.812084i
$23$	−2.79856	−	3.89462i	−0.583541	−	0.812084i
$24$	−2.95688			−0.603571
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	0.481529	−	3.34911i	0.0944356	−	0.656814i
$27$	3.36951	−	7.37820i	0.648463	−	1.41994i
$28$	4.00773	−	1.17677i	0.757389	−	0.222389i
$29$	3.04924	+	6.67690i	0.566229	+	1.23987i	0.948781	+	0.315935i	$0.102318\pi$
$29$	3.04924	+	6.67690i	0.566229	+	1.23987i	−0.382552	+	0.923934i	$0.624955\pi$
$30$	1.93635	+	2.23466i	0.353527	+	0.407992i
$31$	0.759503	+	5.28246i	0.136411	+	0.948757i	0.936947	+	0.349472i	$0.113639\pi$
$31$	0.759503	+	5.28246i	0.136411	+	0.948757i	−0.800536	+	0.599285i	$0.795452\pi$
$32$	0.959493	+	0.281733i	0.169616	+	0.0498038i
$33$	−0.651421	+	0.751780i	−0.113398	+	0.130868i
$34$	3.70014	+	2.37794i	0.634569	+	0.407813i
$35$	−3.51385	−	2.25821i	−0.593949	−	0.381708i
$36$	−3.76097	+	4.34039i	−0.626828	+	0.723398i
$37$	7.80009	+	2.29031i	1.28233	+	0.376525i	0.850760	−	0.525555i	$-0.176142\pi$
$37$	7.80009	+	2.29031i	1.28233	+	0.376525i	0.431568	+	0.902080i	$0.357961\pi$
$38$	0.687159	+	4.77930i	0.111472	+	0.775304i
$39$	−6.55172	−	7.56109i	−1.04912	−	1.21074i
$40$	−0.415415	−	0.909632i	−0.0656829	−	0.143825i
$41$	0.0346901	−	0.0101859i	0.00541768	−	0.00159077i	−0.279023	−	0.960285i	$-0.590010\pi$
$41$	0.0346901	−	0.0101859i	0.00541768	−	0.00159077i	0.284440	+	0.958694i	$0.408192\pi$
$42$	5.13065	−	11.2346i	0.791677	−	1.73353i
$43$	−1.80648	+	12.5643i	−0.275485	+	1.91604i	0.111140	+	0.993805i	$0.464550\pi$
$43$	−1.80648	+	12.5643i	−0.275485	+	1.91604i	−0.386625	+	0.922237i	$0.626359\pi$
$44$	0.283012	−	0.181881i	0.0426657	−	0.0274196i
$45$	5.74316			0.856139
$46$	4.45989	+	1.76334i	0.657575	+	0.259991i
$47$	2.78554			0.406313			0.203157	−	0.979146i	$-0.434880\pi$
$47$	2.78554			0.406313			0.203157	+	0.979146i	$0.434880\pi$
$48$	2.48749	−	1.59861i	0.359038	−	0.230740i
$49$	−1.48671	+	10.3403i	−0.212388	+	1.47719i
$50$	−0.415415	+	0.909632i	−0.0587486	+	0.128641i
$51$	12.4786	−	3.66406i	1.74736	−	0.513071i
$52$	1.40558	+	3.07778i	0.194918	+	0.426812i
$53$	−0.0676444	−	0.0780658i	−0.00929167	−	0.0107232i	0.751085	−	0.660206i	$-0.229531\pi$
$53$	−0.0676444	−	0.0780658i	−0.00929167	−	0.0107232i	−0.760376	+	0.649483i	$0.774986\pi$
$54$	1.15434	+	8.02864i	0.157086	+	1.09256i
$55$	−0.322790	−	0.0947797i	−0.0435250	−	0.0127801i
$56$	−2.73530	+	3.15671i	−0.365520	+	0.421832i
$57$	12.0107	+	7.71881i	1.59086	+	1.02238i
$58$	−6.17498	−	3.96842i	−0.810815	−	0.521079i
$59$	−5.00157	+	5.77212i	−0.651149	+	0.751466i	−0.981305	−	0.192460i	$-0.938353\pi$
$59$	−5.00157	+	5.77212i	−0.651149	+	0.751466i	0.330156	+	0.943927i	$0.392899\pi$
$60$	−2.83711	−	0.833050i	−0.366269	−	0.107546i
$61$	−1.30303	−	9.06279i	−0.166836	−	1.16037i	−0.885373	−	0.464882i	$-0.846097\pi$
$61$	−1.30303	−	9.06279i	−0.166836	−	1.16037i	0.718537	−	0.695489i	$-0.244812\pi$
$62$	−3.49485	−	4.03327i	−0.443846	−	0.512225i
$63$	−9.96527	−	21.8209i	−1.25551	−	2.74917i
$64$	−0.959493	+	0.281733i	−0.119937	+	0.0352166i
$65$	1.40558	−	3.07778i	0.174340	−	0.381752i
$66$	0.141567	−	0.984622i	0.0174257	−	0.121199i
$67$	7.18925	−	4.62025i	0.878307	−	0.564454i	−0.0219762	−	0.999758i	$-0.506996\pi$
$67$	7.18925	−	4.62025i	0.878307	−	0.564454i	0.900283	+	0.435305i	$0.143359\pi$
$68$	−4.39837			−0.533380
$69$	12.5764	−	6.55191i	1.51402	−	0.788757i
$70$	4.17692			0.499237
$71$	12.6504	−	8.12993i	1.50133	−	0.964845i	0.506613	−	0.862173i	$-0.330897\pi$
$71$	12.6504	−	8.12993i	1.50133	−	0.964845i	0.994715	−	0.102672i	$-0.0327392\pi$
$72$	0.817337	−	5.68470i	0.0963240	−	0.669948i
$73$	−2.21707	+	4.85471i	−0.259489	+	0.568201i	−0.993872	−	0.110533i	$-0.964744\pi$
$73$	−2.21707	+	4.85471i	−0.259489	+	0.568201i	0.734384	+	0.678735i	$0.237471\pi$
$74$	−7.80009	+	2.29031i	−0.906742	+	0.266244i
$75$	1.22833	+	2.68968i	0.141836	+	0.310577i
$76$	−3.16196	−	3.64909i	−0.362702	−	0.418580i
$77$	0.199979	+	1.39089i	0.0227897	+	0.158506i
$78$	9.59949	+	2.81867i	1.08693	+	0.319151i
$79$	8.98287	−	10.3668i	1.01065	−	1.16635i	0.0246369	−	0.999696i	$-0.492157\pi$
$79$	8.98287	−	10.3668i	1.01065	−	1.16635i	0.986015	−	0.166658i	$-0.0532975\pi$
$80$	0.841254	+	0.540641i	0.0940550	+	0.0604455i
$81$	5.68215	+	3.65170i	0.631350	+	0.405744i
$82$	−0.0236762	+	0.0273238i	−0.00261460	+	0.00301741i
$83$	−0.0754484	−	0.0221536i	−0.00828154	−	0.00243168i	0.277589	−	0.960700i	$-0.410465\pi$
$83$	−0.0754484	−	0.0221536i	−0.00828154	−	0.00243168i	−0.285871	+	0.958268i	$0.592283\pi$
$84$	1.75768	+	12.2250i	0.191779	+	1.33385i
$85$	2.88032	+	3.32406i	0.312414	+	0.360545i
$86$	−5.27308	−	11.5464i	−0.568611	−	1.24508i
$87$	−20.8250	+	6.11477i	−2.23267	+	0.655572i
$88$	−0.139753	+	0.306016i	−0.0148977	+	0.0326214i
$89$	−1.30693	+	9.08988i	−0.138534	+	0.963526i	0.795401	+	0.606083i	$0.207260\pi$
$89$	−1.30693	+	9.08988i	−0.138534	+	0.963526i	−0.933935	+	0.357442i	$0.883649\pi$
$90$	−4.83145	+	3.10499i	−0.509280	+	0.327294i
$91$	−14.1328			−1.48152
$92$	−4.70523	+	0.927781i	−0.490555	+	0.0967278i
$93$	−15.7802			−1.63633
$94$	−2.34335	+	1.50598i	−0.241698	+	0.155330i
$95$	−0.687159	+	4.77930i	−0.0705011	+	0.490346i
$96$	−1.22833	+	2.68968i	−0.125366	+	0.274514i
$97$	−3.45970	+	1.01586i	−0.351279	+	0.103145i	−0.452612	−	0.891708i	$-0.649508\pi$
$97$	−3.45970	+	1.01586i	−0.351279	+	0.103145i	0.101332	+	0.994853i	$0.467689\pi$
$98$	−4.33970	−	9.50261i	−0.438376	−	0.959909i
$99$	−1.26526	−	1.46018i	−0.127163	−	0.146754i
$100$	−0.142315	−	0.989821i	−0.0142315	−	0.0989821i
$101$	−6.92739	−	2.03407i	−0.689301	−	0.202397i	−0.0817208	−	0.996655i	$-0.526042\pi$
$101$	−6.92739	−	2.03407i	−0.689301	−	0.202397i	−0.607580	+	0.794258i	$0.707860\pi$
$102$	−8.51676	+	9.82887i	−0.843285	+	0.973203i
$103$	4.82800	+	3.10277i	0.475717	+	0.305725i	0.756439	−	0.654064i	$-0.226938\pi$
$103$	4.82800	+	3.10277i	0.475717	+	0.305725i	−0.280722	+	0.959789i	$0.590574\pi$
$104$	−2.84642	−	1.82928i	−0.279115	−	0.179376i
$105$	8.08796	−	9.33401i	0.789304	−	0.910906i
$106$	0.0991116	+	0.0291018i	0.00962657	+	0.00282662i
$107$	1.60918	+	11.1921i	0.155565	+	1.08198i	0.906684	+	0.421811i	$0.138605\pi$
$107$	1.60918	+	11.1921i	0.155565	+	1.08198i	−0.751119	+	0.660167i	$0.770485\pi$
$108$	−5.31170	−	6.13003i	−0.511119	−	0.589863i
$109$	4.59531	+	10.0623i	0.440151	+	0.963796i	0.991571	+	0.129568i	$0.0413591\pi$
$109$	4.59531	+	10.0623i	0.440151	+	0.963796i	−0.551420	+	0.834228i	$0.685914\pi$
$110$	0.322790	−	0.0947797i	0.0307768	−	0.00903689i
$111$	−9.98560	+	21.8654i	−0.947792	+	2.07537i
$112$	0.594438	−	4.13440i	0.0561691	−	0.390665i
$113$	−1.19412	+	0.767412i	−0.112333	+	0.0721921i	−0.595601	−	0.803280i	$-0.703086\pi$
$113$	−1.19412	+	0.767412i	−0.112333	+	0.0721921i	0.483268	+	0.875472i	$0.339450\pi$
$114$	−14.2771			−1.33718
$115$	3.78244	+	2.94841i	0.352715	+	0.274941i
$116$	7.34022			0.681522
$117$	16.3474	−	10.5059i	1.51132	−	0.971268i
$118$	1.08695	−	7.55987i	0.100061	−	0.695942i
$119$	7.63185	−	16.7114i	0.699610	−	1.53193i
$120$	2.83711	−	0.833050i	0.258991	−	0.0760467i
$121$	−4.52255	−	9.90300i	−0.411141	−	0.900273i
$122$	5.99589	+	6.91963i	0.542843	+	0.626474i
$123$	0.0152142	+	0.105817i	0.00137181	+	0.00954118i
$124$	5.12060	+	1.50354i	0.459843	+	0.135022i
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$	20.1806	+	12.9693i	1.79783	+	1.15539i
$127$	−13.4488	−	8.64301i	−1.19339	−	0.766944i	−0.215588	−	0.976485i	$-0.569167\pi$
$127$	−13.4488	−	8.64301i	−1.19339	−	0.766944i	−0.977800	+	0.209541i	$0.932803\pi$
$128$	0.654861	−	0.755750i	0.0578821	−	0.0667995i
$129$	−36.0129	−	10.5743i	−3.17076	−	0.931019i
$130$	0.481529	+	3.34911i	0.0422329	+	0.293736i
$131$	1.72208	+	1.98739i	0.150459	+	0.173639i	0.825976	−	0.563706i	$-0.190625\pi$
$131$	1.72208	+	1.98739i	0.150459	+	0.173639i	−0.675517	+	0.737345i	$0.736079\pi$
$132$	0.413233	+	0.904854i	0.0359673	+	0.0787574i
$133$	19.3511	−	5.68199i	1.67795	−	0.492691i
$134$	−3.55009	+	7.77361i	−0.306681	+	0.671537i
$135$	−1.15434	+	8.02864i	−0.0993501	+	0.690995i
$136$	3.70014	−	2.37794i	0.317285	−	0.203906i
$137$	3.10380			0.265175			0.132588	−	0.991171i	$-0.457671\pi$
$137$	3.10380			0.265175			0.132588	+	0.991171i	$0.457671\pi$
$138$	−7.03769	+	12.3111i	−0.599088	+	1.04799i
$139$	14.9829			1.27084			0.635418	−	0.772168i	$-0.280828\pi$
$139$	14.9829			1.27084			0.635418	+	0.772168i	$0.280828\pi$
$140$	−3.51385	+	2.25821i	−0.296974	+	0.190854i
$141$	−1.17218	+	8.15269i	−0.0987154	+	0.686581i
$142$	−6.24684	+	13.6787i	−0.524223	+	1.14789i
$143$	−1.09218	+	0.320692i	−0.0913323	+	0.0268176i
$144$	2.38579	+	5.22416i	0.198816	+	0.435347i
$145$	−4.80682	−	5.54737i	−0.399185	−	0.460684i
$146$	−0.759536	−	5.28269i	−0.0628596	−	0.437198i
$147$	−29.6383	−	8.70259i	−2.44453	−	0.717778i
$148$	5.32362	−	6.14378i	0.437599	−	0.505016i
$149$	−2.22067	−	1.42714i	−0.181924	−	0.116916i	0.446509	−	0.894779i	$-0.352667\pi$
$149$	−2.22067	−	1.42714i	−0.181924	−	0.116916i	−0.628433	+	0.777864i	$0.716303\pi$
$150$	−2.48749	−	1.59861i	−0.203103	−	0.130526i
$151$	8.15342	−	9.40955i	0.663516	−	0.765738i	−0.319831	−	0.947474i	$-0.603626\pi$
$151$	8.15342	−	9.40955i	0.663516	−	0.765738i	0.983347	+	0.181736i	$0.0581717\pi$
$152$	4.63286	+	1.36033i	0.375774	+	0.110337i
$153$	3.59495	+	25.0034i	0.290634	+	2.02141i
$154$	−0.920203	−	1.06197i	−0.0741520	−	0.0855760i
$155$	−2.21698	−	4.85450i	−0.178072	−	0.389923i
$156$	−9.59949	+	2.81867i	−0.768575	+	0.225674i
$157$	1.72804	−	3.78389i	0.137913	−	0.301987i	−0.828056	−	0.560645i	$-0.810553\pi$
$157$	1.72804	−	3.78389i	0.137913	−	0.301987i	0.965969	+	0.258658i	$0.0832803\pi$
$158$	−1.95216	+	13.5776i	−0.155306	+	1.08018i
$159$	0.256947	−	0.165130i	0.0203772	−	0.0130957i
$160$	−1.00000			−0.0790569
$161$	4.63924	−	19.4872i	0.365624	−	1.53581i
$162$	−6.75438			−0.530675
$163$	8.31811	−	5.34573i	0.651525	−	0.418710i	−0.172698	−	0.984975i	$-0.555249\pi$
$163$	8.31811	−	5.34573i	0.651525	−	0.418710i	0.824223	+	0.566265i	$0.191612\pi$
$164$	0.00514534	−	0.0357866i	0.000401783	−	0.00279446i
$165$	0.413233	−	0.904854i	0.0321701	−	0.0704428i
$166$	0.0754484	−	0.0221536i	0.00585593	−	0.00171946i
$167$	−7.95143	−	17.4112i	−0.615300	−	1.34732i	−0.918889	−	0.394517i	$-0.870912\pi$
$167$	−7.95143	−	17.4112i	−0.615300	−	1.34732i	0.303588	−	0.952803i	$-0.401815\pi$
$168$	−8.08796	−	9.33401i	−0.624000	−	0.720134i
$169$	0.220816	+	1.53581i	0.0169858	+	0.118139i
$170$	−4.22020	−	1.23916i	−0.323675	−	0.0950395i
$171$	−18.1596	+	20.9573i	−1.38870	+	1.60265i
$172$	10.6785	+	6.86264i	0.814226	+	0.523271i
$173$	11.8860	+	7.63865i	0.903673	+	0.580755i	0.907877	−	0.419236i	$-0.137702\pi$
$173$	11.8860	+	7.63865i	0.903673	+	0.580755i	−0.00420433	+	0.999991i	$0.501338\pi$
$174$	14.2132	−	16.4029i	1.07750	−	1.24350i
$175$	4.00773	+	1.17677i	0.302956	+	0.0889558i
$176$	−0.0478772	−	0.332993i	−0.00360888	−	0.0251003i
$177$	−14.7891	−	17.0675i	−1.11161	−	1.28287i
$178$	−3.81490	−	8.35347i	−0.285939	−	0.626119i
$179$	−6.55264	+	1.92403i	−0.489767	+	0.143809i	−0.517286	−	0.855813i	$-0.673058\pi$
$179$	−6.55264	+	1.92403i	−0.489767	+	0.143809i	0.0275186	+	0.999621i	$0.491239\pi$
$180$	2.38579	−	5.22416i	0.177827	−	0.389386i
$181$	−1.14988	+	7.99758i	−0.0854698	+	0.594455i	0.901406	+	0.432975i	$0.142536\pi$
$181$	−1.14988	+	7.99758i	−0.0854698	+	0.594455i	−0.986876	+	0.161481i	$0.948373\pi$
$182$	11.8893	−	7.64077i	0.881292	−	0.566372i
$183$	27.0732			2.00131
$184$	3.45670	−	3.32434i	0.254831	−	0.245074i
$185$	−8.12939			−0.597685
$186$	13.2752	−	8.53143i	0.973383	−	0.625555i
$187$	0.210581	−	1.46463i	0.0153992	−	0.107104i
$188$	1.15716	−	2.53382i	0.0843944	−	0.184798i
$189$	32.5074	−	9.54505i	2.36457	−	0.694300i
$190$	−2.00581	−	4.39211i	−0.145517	−	0.318637i
$191$	0.140669	+	0.162340i	0.0101784	+	0.0117465i	0.760816	−	0.648968i	$-0.224799\pi$
$191$	0.140669	+	0.162340i	0.0101784	+	0.0117465i	−0.750638	+	0.660714i	$0.770254\pi$
$192$	−0.420808	−	2.92679i	−0.0303692	−	0.211223i
$193$	−13.3099	−	3.90814i	−0.958068	−	0.281314i	−0.234926	−	0.972013i	$-0.575485\pi$
$193$	−13.3099	−	3.90814i	−0.958068	−	0.281314i	−0.723142	+	0.690699i	$0.757303\pi$
$194$	2.36127	−	2.72505i	0.169529	−	0.195647i
$195$	8.41654	+	5.40898i	0.602721	+	0.387345i
$196$	8.78829	+	5.64789i	0.627735	+	0.403421i
$197$	9.47436	−	10.9340i	0.675020	−	0.779014i	−0.310133	−	0.950693i	$-0.600374\pi$
$197$	9.47436	−	10.9340i	0.675020	−	0.779014i	0.985153	+	0.171679i	$0.0549191\pi$
$198$	1.85383	+	0.544335i	0.131746	+	0.0386842i
$199$	−1.68606	−	11.7268i	−0.119522	−	0.831291i	−0.958084	−	0.286486i	$-0.907513\pi$
$199$	−1.68606	−	11.7268i	−0.119522	−	0.831291i	0.838563	−	0.544805i	$-0.183396\pi$
$200$	0.654861	+	0.755750i	0.0463056	+	0.0534396i
$201$	10.4972	+	22.9856i	0.740415	+	1.62128i
$202$	6.92739	−	2.03407i	0.487410	−	0.143116i
$203$	−12.7364	+	27.8889i	−0.893921	+	1.95741i
$204$	1.85087	−	12.8731i	0.129587	−	0.901296i
$205$	−0.0304152	+	0.0195467i	−0.00212429	+	0.00136520i
$206$	−5.73905			−0.399859
$207$	9.11992	+	25.9895i	0.633878	+	1.80640i
$208$	3.38355			0.234607
$209$	1.36651	−	0.878202i	0.0945234	−	0.0607465i
$210$	−1.75768	+	12.2250i	−0.121292	+	0.843602i
$211$	9.11646	−	19.9623i	0.627603	−	1.37426i	−0.282255	−	0.959340i	$-0.591082\pi$
$211$	9.11646	−	19.9623i	0.627603	−	1.37426i	0.909858	−	0.414920i	$-0.136190\pi$
$212$	−0.0991116	+	0.0291018i	−0.00680702	+	0.00199872i
$213$	18.4712	+	40.4462i	1.26562	+	2.77133i
$214$	−7.40462	−	8.54538i	−0.506169	−	0.584150i
$215$	−1.80648	−	12.5643i	−0.123201	−	0.856880i
$216$	7.78264	+	2.28519i	0.529541	+	0.155487i
$217$	−14.5977	+	16.8466i	−0.990956	+	1.14362i
$218$	−9.30593	−	5.98056i	−0.630277	−	0.405054i
$219$	−13.2757	−	8.53180i	−0.897092	−	0.576526i
$220$	−0.220307	+	0.254247i	−0.0148531	+	0.0171413i
$221$	14.2793	+	4.19277i	0.960527	+	0.282036i
$222$	−3.42092	−	23.7930i	−0.229597	−	1.59688i
$223$	−13.6397	−	15.7411i	−0.913385	−	1.05410i	−0.998333	−	0.0577166i	$-0.981618\pi$
$223$	−13.6397	−	15.7411i	−0.913385	−	1.05410i	0.0849485	−	0.996385i	$-0.472927\pi$
$224$	1.73516	+	3.79946i	0.115935	+	0.253862i
$225$	−5.51052	+	1.61803i	−0.367368	+	0.107869i
$226$	0.589661	−	1.29118i	0.0392236	−	0.0858878i
$227$	−3.64401	+	25.3447i	−0.241862	+	1.68218i	0.400903	+	0.916120i	$0.368696\pi$
$227$	−3.64401	+	25.3447i	−0.241862	+	1.68218i	−0.642765	+	0.766064i	$0.722213\pi$
$228$	12.0107	−	7.71881i	0.795428	−	0.511191i
$229$	−2.00258			−0.132334			−0.0661670	−	0.997809i	$-0.521077\pi$
$229$	−2.00258			−0.132334			−0.0661670	+	0.997809i	$0.521077\pi$
$230$	−4.77602	−	0.435418i	−0.314922	−	0.0287106i
$231$	−4.15498			−0.273377
$232$	−6.17498	+	3.96842i	−0.405408	+	0.260540i
$233$	0.227176	−	1.58005i	0.0148828	−	0.103512i	−0.981026	−	0.193876i	$-0.937894\pi$
$233$	0.227176	−	1.58005i	0.0148828	−	0.103512i	0.995909	+	0.0903640i	$0.0288031\pi$
$234$	−8.07245	+	17.6762i	−0.527712	+	1.15553i
$235$	−2.67271	+	0.784779i	−0.174348	+	0.0511933i
$236$	3.17278	+	6.94741i	0.206530	+	0.452238i
$237$	26.5613	+	30.6534i	1.72534	+	1.99115i
$238$	2.61456	+	18.1846i	0.169476	+	1.17873i
$239$	20.5589	+	6.03663i	1.32984	+	0.390477i	0.868035	−	0.496503i	$-0.165383\pi$
$239$	20.5589	+	6.03663i	1.32984	+	0.390477i	0.461808	+	0.886980i	$0.347201\pi$
$240$	−1.93635	+	2.23466i	−0.124991	+	0.144247i
$241$	−8.89620	−	5.71724i	−0.573054	−	0.368280i	0.221789	−	0.975095i	$-0.428811\pi$
$241$	−8.89620	−	5.71724i	−0.573054	−	0.368280i	−0.794843	+	0.606815i	$0.792447\pi$
$242$	9.15858	+	5.88586i	0.588736	+	0.378357i
$243$	2.85628	−	3.29632i	0.183230	−	0.211459i
$244$	−8.78510	−	2.57954i	−0.562408	−	0.165138i
$245$	−1.48671	−	10.3403i	−0.0949827	−	0.660619i
$246$	−0.0700078	−	0.0807934i	−0.00446354	−	0.00515120i
$247$	6.78675	+	14.8609i	0.431830	+	0.945577i
$248$	−5.12060	+	1.50354i	−0.325158	+	0.0954751i
$249$	0.0965883	−	0.211499i	0.00612103	−	0.0134032i
$250$	0.142315	−	0.989821i	0.00900078	−	0.0626018i
$251$	6.82341	−	4.38514i	0.430690	−	0.276787i	−0.307283	−	0.951618i	$-0.599420\pi$
$251$	6.82341	−	4.38514i	0.430690	−	0.276787i	0.737972	+	0.674831i	$0.235783\pi$
$252$	−23.9887			−1.51115
$253$	−0.0836713	−	1.61123i	−0.00526037	−	0.101297i
$254$	15.9866			1.00309
$255$	−10.9409	+	7.03128i	−0.685145	+	0.440316i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	−3.68002	+	8.05812i	−0.229553	+	0.502652i	−0.989000	−	0.147918i	$-0.952743\pi$
$257$	−3.68002	+	8.05812i	−0.229553	+	0.502652i	0.759446	+	0.650570i	$0.225470\pi$
$258$	36.0129	−	10.5743i	2.24207	−	0.658330i
$259$	14.1058	+	30.8873i	0.876489	+	1.91924i
$260$	−2.21575	−	2.55712i	−0.137415	−	0.158586i
$261$	−5.99943	−	41.7269i	−0.371355	−	2.58283i
$262$	−2.52317	−	0.740869i	−0.155882	−	0.0457711i
$263$	7.88502	−	9.09980i	0.486211	−	0.561118i	−0.458638	−	0.888623i	$-0.651663\pi$
$263$	7.88502	−	9.09980i	0.486211	−	0.561118i	0.944849	+	0.327505i	$0.106208\pi$
$264$	−0.836834	−	0.537801i	−0.0515036	−	0.0330993i
$265$	0.0868980	+	0.0558460i	0.00533810	+	0.00343059i
$266$	−13.2072	+	15.2420i	−0.809788	+	0.934546i
$267$	−26.0542	−	7.65020i	−1.59449	−	0.468184i
$268$	−1.21621	−	8.45889i	−0.0742916	−	0.516709i
$269$	−15.8134	−	18.2496i	−0.964157	−	1.11270i	−0.993580	−	0.113130i	$-0.963912\pi$
$269$	−15.8134	−	18.2496i	−0.964157	−	1.11270i	0.0294228	−	0.999567i	$-0.490633\pi$
$270$	−3.36951	−	7.37820i	−0.205062	−	0.449023i
$271$	−8.76831	+	2.57461i	−0.532637	+	0.156396i	−0.536981	−	0.843594i	$-0.680435\pi$
$271$	−8.76831	+	2.57461i	−0.532637	+	0.156396i	0.00434432	+	0.999991i	$0.498617\pi$
$272$	−1.82715	+	4.00090i	−0.110787	+	0.242590i
$273$	5.94720	−	41.3637i	0.359941	−	2.50345i
$274$	−2.61108	+	1.67804i	−0.157741	+	0.101374i
$275$	0.336417			0.0202867
$276$	−0.735415	−	14.1616i	−0.0442668	−	0.852430i
$277$	−24.5138			−1.47289			−0.736446	−	0.676497i	$-0.763497\pi$
$277$	−24.5138			−1.47289			−0.736446	+	0.676497i	$0.763497\pi$
$278$	−12.6045	+	8.10039i	−0.755965	+	0.485829i
$279$	4.36194	−	30.3380i	0.261143	−	1.81629i
$280$	1.73516	−	3.79946i	0.103695	−	0.227061i
$281$	15.7944	−	4.63765i	0.942213	−	0.276659i	0.225672	−	0.974203i	$-0.427542\pi$
$281$	15.7944	−	4.63765i	0.942213	−	0.276659i	0.716541	+	0.697545i	$0.245724\pi$
$282$	−3.42158	−	7.49221i	−0.203752	−	0.446155i
$283$	13.4420	+	15.5129i	0.799045	+	0.922147i	0.998328	−	0.0577952i	$-0.0184070\pi$
$283$	13.4420	+	15.5129i	0.799045	+	0.922147i	−0.199284	+	0.979942i	$0.563862\pi$
$284$	−2.14007	−	14.8845i	−0.126990	−	0.883234i
$285$	−13.6988	−	4.02234i	−0.811448	−	0.238263i
$286$	0.745418	−	0.860258i	0.0440775	−	0.0508681i
$287$	0.127042	+	0.0816448i	0.00749904	+	0.00481934i
$288$	−4.83145	−	3.10499i	−0.284696	−	0.182963i
$289$	−1.53606	+	1.77271i	−0.0903567	+	0.104277i
$290$	7.04289	+	2.06798i	0.413573	+	0.121436i
$291$	−1.51733	−	10.5533i	−0.0889477	−	0.618645i
$292$	3.49500	+	4.03344i	0.204529	+	0.236039i
$293$	−7.75531	−	16.9818i	−0.453070	−	0.992085i	−0.989013	−	0.147830i	$-0.952771\pi$
$293$	−7.75531	−	16.9818i	−0.453070	−	0.992085i	0.535943	−	0.844254i	$-0.319956\pi$
$294$	29.6383	−	8.70259i	1.72854	−	0.507545i
$295$	3.17278	−	6.94741i	0.184726	−	0.404494i
$296$	−1.15693	+	8.04665i	−0.0672454	+	0.467702i
$297$	2.29557	−	1.47527i	0.133202	−	0.0856040i
$298$	2.63971			0.152915
$299$	16.1599	+	1.47326i	0.934552	+	0.0852008i
$300$	2.95688			0.170716
$301$	−44.6031	+	28.6647i	−2.57088	+	1.65221i
$302$	−1.77191	+	12.3239i	−0.101962	+	0.709160i
$303$	8.86838	−	19.4190i	0.509475	−	1.11559i
$304$	−4.63286	+	1.36033i	−0.265713	+	0.0780203i
$305$	3.80353	+	8.32858i	0.217790	+	0.476893i
$306$	−16.5421	−	19.0906i	−0.945650	−	1.09134i
$307$	−1.27563	−	8.87223i	−0.0728043	−	0.506365i	−0.993296	−	0.115602i	$-0.963120\pi$
$307$	−1.27563	−	8.87223i	−0.0728043	−	0.506365i	0.920491	−	0.390763i	$-0.127789\pi$
$308$	1.34827	+	0.395887i	0.0768247	+	0.0225578i
$309$	−11.1128	+	12.8249i	−0.632185	+	0.729580i
$310$	4.48958	+	2.88528i	0.254991	+	0.163873i
$311$	22.7048	+	14.5915i	1.28747	+	0.827409i	0.991790	−	0.127877i	$-0.0408162\pi$
$311$	22.7048	+	14.5915i	1.28747	+	0.827409i	0.295684	+	0.955286i	$0.404453\pi$
$312$	6.55172	−	7.56109i	0.370918	−	0.428062i
$313$	−15.6564	−	4.59714i	−0.884954	−	0.259846i	−0.192490	−	0.981299i	$-0.561656\pi$
$313$	−15.6564	−	4.59714i	−0.884954	−	0.259846i	−0.692463	+	0.721453i	$0.743475\pi$
$314$	0.592002	+	4.11746i	0.0334086	+	0.232362i
$315$	15.7093	+	18.1295i	0.885117	+	1.02148i
$316$	−5.69834	−	12.4776i	−0.320557	−	0.701921i
$317$	7.18608	−	2.11002i	0.403610	−	0.118511i	−0.0736254	−	0.997286i	$-0.523457\pi$
$317$	7.18608	−	2.11002i	0.403610	−	0.118511i	0.477236	+	0.878775i	$0.341639\pi$
$318$	−0.126882	+	0.277832i	−0.00711518	+	0.0155801i
$319$	−0.351429	+	2.44424i	−0.0196762	+	0.136851i
$320$	0.841254	−	0.540641i	0.0470275	−	0.0302227i
$321$	−33.4340			−1.86610
$322$	6.63279	+	18.9018i	0.369631	+	1.05336i
$323$	−21.2373			−1.18167
$324$	5.68215	−	3.65170i	0.315675	−	0.202872i
$325$	−0.481529	+	3.34911i	−0.0267104	+	0.185775i
$326$	−4.10752	+	8.99422i	−0.227495	+	0.498144i
$327$	−31.3840	+	9.21518i	−1.73554	+	0.509601i
$328$	0.0150192	+	0.0328874i	0.000829295	+	0.00181590i
$329$	7.61930	+	8.79314i	0.420066	+	0.484782i
$330$	0.141567	+	0.984622i	0.00779302	+	0.0542016i
$331$	4.51093	+	1.32453i	0.247943	+	0.0728026i	0.403343	−	0.915049i	$-0.367848\pi$
$331$	4.51093	+	1.32453i	0.247943	+	0.0728026i	−0.155400	+	0.987852i	$0.549666\pi$
$332$	−0.0514941	+	0.0594273i	−0.00282610	+	0.00326150i
$333$	−39.2768	−	25.2416i	−2.15235	−	1.38323i
$334$	16.1024	+	10.3484i	0.881083	+	0.566238i
$335$	−5.59636	+	6.45854i	−0.305762	+	0.352868i
$336$	11.8504	+	3.47958i	0.646491	+	0.189827i
$337$	0.0695908	+	0.484015i	0.00379085	+	0.0263660i	0.991629	−	0.129119i	$-0.0412150\pi$
$337$	0.0695908	+	0.484015i	0.00379085	+	0.0263660i	−0.987838	+	0.155485i	$0.950306\pi$
$338$	−1.01608	−	1.17262i	−0.0552677	−	0.0637823i
$339$	−1.74356	−	3.81786i	−0.0946970	−	0.207358i
$340$	4.22020	−	1.23916i	0.228873	−	0.0672031i
$341$	−0.745830	+	1.63314i	−0.0403889	+	0.0884394i
$342$	3.94646	−	27.4483i	0.213400	−	1.48423i
$343$	−12.1110	+	7.78329i	−0.653934	+	0.420258i
$344$	−12.6935			−0.684389
$345$	−10.2211	+	9.82969i	−0.550283	+	0.529212i
$346$	−14.1289			−0.759573
$347$	20.4941	−	13.1708i	1.10018	−	0.707044i	0.141049	−	0.990003i	$-0.454952\pi$
$347$	20.4941	−	13.1708i	1.10018	−	0.707044i	0.959132	+	0.282959i	$0.0913160\pi$
$348$	−3.08882	+	21.4832i	−0.165578	+	1.15162i
$349$	−11.8661	+	25.9831i	−0.635176	+	1.39084i	0.268773	+	0.963203i	$0.413382\pi$
$349$	−11.8661	+	25.9831i	−0.635176	+	1.39084i	−0.903950	+	0.427639i	$0.859346\pi$
$350$	−4.00773	+	1.17677i	−0.214222	+	0.0629012i
$351$	11.4009	+	24.9645i	0.608535	+	1.33251i
$352$	0.220307	+	0.254247i	0.0117424	+	0.0135514i
$353$	−0.116419	−	0.809711i	−0.00619635	−	0.0430966i	0.986489	−	0.163829i	$-0.0523847\pi$
$353$	−0.116419	−	0.809711i	−0.00619635	−	0.0430966i	−0.992685	+	0.120733i	$0.961476\pi$
$354$	21.6687	+	6.36251i	1.15168	+	0.338164i
$355$	−9.84752	+	11.3646i	−0.522652	+	0.603173i
$356$	7.72553	+	4.96490i	0.409452	+	0.263139i
$357$	45.6992	+	29.3691i	2.41866	+	1.55438i
$358$	4.47222	−	5.16122i	0.236364	−	0.272779i
$359$	26.3159	+	7.72704i	1.38890	+	0.407818i	0.888858	−	0.458184i	$-0.151500\pi$
$359$	26.3159	+	7.72704i	1.38890	+	0.407818i	0.500042	+	0.866001i	$0.333318\pi$
$360$	0.817337	+	5.68470i	0.0430774	+	0.299610i
$361$	−2.82499	−	3.26021i	−0.148684	−	0.171590i
$362$	−3.35648	−	7.34966i	−0.176413	−	0.386290i
$363$	30.8871	−	9.06927i	1.62115	−	0.476013i
$364$	−5.87098	+	12.8557i	−0.307723	+	0.673819i
$365$	0.759536	−	5.28269i	0.0397559	−	0.276508i
$366$	−22.7754	+	14.6369i	−1.19049	+	0.765081i
$367$	3.94426			0.205889			0.102944	−	0.994687i	$-0.467174\pi$
$367$	3.94426			0.205889			0.102944	+	0.994687i	$0.467174\pi$
$368$	−1.11069	+	4.66545i	−0.0578985	+	0.243203i
$369$	−0.207642			−0.0108094
$370$	6.83888	−	4.39508i	0.355536	−	0.228489i
$371$	0.0614029	−	0.427067i	0.00318788	−	0.0221722i
$372$	−6.55534	+	14.3542i	−0.339879	+	0.744230i
$373$	13.3654	−	3.92444i	0.692036	−	0.203200i	0.0832430	−	0.996529i	$-0.473472\pi$
$373$	13.3654	−	3.92444i	0.692036	−	0.203200i	0.608793	+	0.793329i	$0.291654\pi$
$374$	0.614684	+	1.34597i	0.0317846	+	0.0695985i
$375$	−1.93635	−	2.23466i	−0.0999925	−	0.115398i
$376$	0.396424	+	2.75719i	0.0204440	+	0.142191i
$377$	−23.8299	−	6.99710i	−1.22730	−	0.360369i
$378$	−22.1866	+	25.6047i	−1.14115	+	1.31696i
$379$	−23.2415	−	14.9364i	−1.19384	−	0.767233i	−0.215958	−	0.976403i	$-0.569288\pi$
$379$	−23.2415	−	14.9364i	−1.19384	−	0.767233i	−0.977879	+	0.209170i	$0.932924\pi$
$380$	4.06195	+	2.61045i	0.208373	+	0.133913i
$381$	30.9556	−	35.7247i	1.58590	−	1.83023i
$382$	−0.206106	−	0.0605181i	−0.0105453	−	0.00309637i
$383$	−0.634727	−	4.41462i	−0.0324330	−	0.225577i	0.967158	−	0.254176i	$-0.0818043\pi$
$383$	−0.634727	−	4.41462i	−0.0324330	−	0.225577i	−0.999591	+	0.0285995i	$0.990895\pi$
$384$	1.93635	+	2.23466i	0.0988138	+	0.114037i
$385$	−0.583736	−	1.27820i	−0.0297500	−	0.0651433i
$386$	13.3099	−	3.90814i	0.677456	−	0.198919i
$387$	30.2841	−	66.3130i	1.53943	−	3.37088i
$388$	−0.513153	+	3.56906i	−0.0260514	+	0.181191i
$389$	14.4125	−	9.26233i	0.730741	−	0.469619i	−0.121617	−	0.992577i	$-0.538808\pi$
$389$	14.4125	−	9.26233i	0.730741	−	0.469619i	0.852358	+	0.522958i	$0.175172\pi$
$390$	−10.0048			−0.506611
$391$	−10.4686	+	18.3128i	−0.529418	+	0.926118i
$392$	−10.4467			−0.527636
$393$	−6.54132	+	4.20385i	−0.329966	+	0.212056i
$394$	−2.05897	+	14.3205i	−0.103730	+	0.721455i
$395$	−5.69834	+	12.4776i	−0.286715	+	0.627817i
$396$	−1.85383	+	0.544335i	−0.0931587	+	0.0273539i
$397$	−13.0290	−	28.5295i	−0.653905	−	1.43185i	−0.888094	−	0.459662i	$-0.847971\pi$
$397$	−13.0290	−	28.5295i	−0.653905	−	1.43185i	0.234189	−	0.972191i	$-0.424757\pi$
$398$	7.75839	+	8.95366i	0.388893	+	0.448806i
$399$	8.48687	+	59.0275i	0.424875	+	2.95507i
$400$	−0.959493	−	0.281733i	−0.0479746	−	0.0140866i
$401$	4.59322	−	5.30086i	0.229375	−	0.264712i	−0.629382	−	0.777096i	$-0.716692\pi$
$401$	4.59322	−	5.30086i	0.229375	−	0.264712i	0.858757	+	0.512384i	$0.171237\pi$
$402$	−21.2578	−	13.6615i	−1.06024	−	0.681376i
$403$	−15.1907	−	9.76248i	−0.756704	−	0.486304i
$404$	−4.72799	+	5.45639i	−0.235226	+	0.271466i
$405$	−6.48078	−	1.90293i	−0.322033	−	0.0945574i
$406$	−4.36330	−	30.3474i	−0.216547	−	1.50612i
$407$	1.79096	+	2.06688i	0.0887745	+	0.102451i
$408$	5.40266	+	11.8302i	0.267472	+	0.585681i
$409$	29.1815	−	8.56845i	1.44293	−	0.423683i	0.535733	−	0.844387i	$-0.320035\pi$
$409$	29.1815	−	8.56845i	1.44293	−	0.423683i	0.907198	+	0.420705i	$0.138217\pi$
$410$	0.0150192	−	0.0328874i	0.000741744	−	0.00162419i
$411$	−1.30610	+	9.08415i	−0.0644253	+	0.448088i
$412$	4.82800	−	3.10277i	0.237858	−	0.152862i
$413$	−31.9017			−1.56978
$414$	−21.7232	−	16.9332i	−1.06764	−	0.832221i
$415$	0.0786336			0.00385997
$416$	−2.84642	+	1.82928i	−0.139557	+	0.0896880i
$417$	−6.30495	+	43.8519i	−0.308755	+	2.14744i
$418$	−0.674789	+	1.47758i	−0.0330050	+	0.0722709i
$419$	−16.3927	+	4.81332i	−0.800834	+	0.235146i	−0.656444	−	0.754375i	$-0.727940\pi$
$419$	−16.3927	+	4.81332i	−0.800834	+	0.235146i	−0.144390	+	0.989521i	$0.546122\pi$
$420$	−5.13065	−	11.2346i	−0.250350	−	0.548190i
$421$	0.633995	+	0.731670i	0.0308990	+	0.0356594i	0.770989	−	0.636849i	$-0.219762\pi$
$421$	0.633995	+	0.731670i	0.0308990	+	0.0356594i	−0.740090	+	0.672508i	$0.765217\pi$
$422$	3.12316	+	21.7221i	0.152033	+	1.05741i
$423$	−15.3498	−	4.50711i	−0.746333	−	0.219143i
$424$	0.0676444	−	0.0780658i	0.00328510	−	0.00379121i
$425$	−3.70014	−	2.37794i	−0.179483	−	0.115347i
$426$	−37.4058	−	24.0393i	−1.81232	−	1.16471i
$427$	25.0444	−	28.9027i	1.21198	−	1.39870i
$428$	10.8491	+	3.18560i	0.524413	+	0.153982i
$429$	−0.479000	−	3.33152i	−0.0231263	−	0.160847i
$430$	8.31249	+	9.59313i	0.400864	+	0.462622i
$431$	8.77307	+	19.2103i	0.422584	+	0.925329i	0.994472	+	0.104998i	$0.0334836\pi$
$431$	8.77307	+	19.2103i	0.422584	+	0.925329i	−0.571889	+	0.820331i	$0.693789\pi$
$432$	−7.78264	+	2.28519i	−0.374442	+	0.109946i
$433$	5.03037	−	11.0150i	0.241744	−	0.529345i	−0.749403	−	0.662114i	$-0.769659\pi$
$433$	5.03037	−	11.0150i	0.241744	−	0.529345i	0.991147	+	0.132769i	$0.0423867\pi$
$434$	3.17238	−	22.0644i	0.152279	−	1.05912i
$435$	18.2587	−	11.7342i	0.875438	−	0.562610i
$436$	11.0620			0.529773
$437$	−22.7190	+	4.47974i	−1.08680	+	0.214295i
$438$	15.7809			0.754041
$439$	−3.09398	+	1.98838i	−0.147668	+	0.0949003i	−0.612388	−	0.790557i	$-0.709791\pi$
$439$	−3.09398	+	1.98838i	−0.147668	+	0.0949003i	0.464721	+	0.885457i	$0.346155\pi$
$440$	0.0478772	−	0.332993i	0.00228246	−	0.0158748i
$441$	24.9236	−	54.5750i	1.18684	−	2.59881i
$442$	−14.2793	+	4.19277i	−0.679195	+	0.199430i
$443$	6.04071	+	13.2273i	0.287003	+	0.628448i	0.997137	−	0.0756183i	$-0.0240930\pi$
$443$	6.04071	+	13.2273i	0.287003	+	0.628448i	−0.710134	+	0.704066i	$0.751366\pi$
$444$	15.7413	+	18.1665i	0.747050	+	0.862142i
$445$	−1.30693	−	9.08988i	−0.0619543	−	0.430902i
$446$	19.9848	+	5.86805i	0.946306	+	0.277860i
$447$	5.11140	−	5.89887i	0.241761	−	0.279007i
$448$	−3.51385	−	2.25821i	−0.166014	−	0.106691i
$449$	−18.8937	−	12.1422i	−0.891648	−	0.573027i	0.0126546	−	0.999920i	$-0.495972\pi$
$449$	−18.8937	−	12.1422i	−0.891648	−	0.573027i	−0.904302	+	0.426893i	$0.859608\pi$
$450$	3.76097	−	4.34039i	0.177294	−	0.204608i
$451$	0.0116703	+	0.00342672i	0.000549535	+	0.000161358i
$452$	0.202009	+	1.40500i	0.00950169	+	0.0660857i
$453$	24.1087	+	27.8229i	1.13273	+	1.30724i
$454$	−10.6368	−	23.2914i	−0.499211	−	1.09312i
$455$	13.5603	−	3.98167i	0.635718	−	0.186664i
$456$	−5.93094	+	12.9869i	−0.277742	+	0.608170i
$457$	1.83076	−	12.7332i	0.0856392	−	0.595634i	−0.901136	−	0.433537i	$-0.857265\pi$
$457$	1.83076	−	12.7332i	0.0856392	−	0.595634i	0.986775	−	0.162096i	$-0.0518256\pi$
$458$	1.68467	−	1.08267i	0.0787197	−	0.0505901i
$459$	−35.6760			−1.66521
$460$	4.25325	−	2.21582i	0.198309	−	0.103313i
$461$	−8.65375			−0.403045			−0.201523	−	0.979484i	$-0.564589\pi$
$461$	−8.65375			−0.403045			−0.201523	+	0.979484i	$0.564589\pi$
$462$	3.49539	−	2.24635i	0.162620	−	0.104510i
$463$	1.35527	−	9.42613i	0.0629849	−	0.438070i	−0.933790	−	0.357821i	$-0.883520\pi$
$463$	1.35527	−	9.42613i	0.0629849	−	0.438070i	0.996775	−	0.0802481i	$-0.0255713\pi$
$464$	3.04924	−	6.67690i	0.141557	−	0.309967i
$465$	15.1410	−	4.44580i	0.702148	−	0.206169i
$466$	0.663125	+	1.45204i	0.0307187	+	0.0672645i
$467$	−1.90226	−	2.19532i	−0.0880260	−	0.101587i	0.710028	−	0.704174i	$-0.248682\pi$
$467$	−1.90226	−	2.19532i	−0.0880260	−	0.101587i	−0.798054	+	0.602586i	$0.794137\pi$
$468$	−2.76550	−	19.2345i	−0.127835	−	0.889113i
$469$	34.2495	+	10.0566i	1.58150	+	0.464369i
$470$	1.82414	−	2.10517i	0.0841415	−	0.0971044i
$471$	10.3475	+	6.64991i	0.476786	+	0.306412i
$472$	−6.42517	−	4.12920i	−0.295742	−	0.190062i
$473$	−2.79647	+	3.22729i	−0.128582	+	0.148391i
$474$	−38.9172	−	11.4271i	−1.78753	−	0.524866i
$475$	−0.687159	−	4.77930i	−0.0315290	−	0.219289i
$476$	−12.0309	−	13.8843i	−0.551433	−	0.636388i
$477$	0.246443	+	0.539634i	0.0112838	+	0.0247081i
$478$	−20.5589	+	6.03663i	−0.940341	+	0.276109i
$479$	−12.1910	+	26.6945i	−0.557020	+	1.21970i	0.396405	+	0.918076i	$0.370257\pi$
$479$	−12.1910	+	26.6945i	−0.557020	+	1.21970i	−0.953426	+	0.301628i	$0.902470\pi$
$480$	0.420808	−	2.92679i	0.0192072	−	0.133589i
$481$	−23.1397	+	14.8710i	−1.05508	+	0.678058i
$482$	10.5749			0.481675
$483$	55.0826	+	21.7784i	2.50635	+	0.990954i
$484$	−10.8868			−0.494856
$485$	3.03336	−	1.94942i	0.137738	−	0.0885186i
$486$	−0.620729	+	4.31727i	−0.0281568	+	0.195835i
$487$	−4.70301	+	10.2982i	−0.213114	+	0.466654i	−0.985755	−	0.168189i	$-0.946208\pi$
$487$	−4.70301	+	10.2982i	−0.213114	+	0.466654i	0.772641	+	0.634843i	$0.218935\pi$
$488$	8.78510	−	2.57954i	0.397683	−	0.116770i
$489$	12.1455	+	26.5949i	0.549237	+	1.20266i
$490$	6.84111	+	7.89506i	0.309050	+	0.356662i
$491$	1.28476	+	8.93570i	0.0579804	+	0.403262i	0.998057	+	0.0623004i	$0.0198437\pi$
$491$	1.28476	+	8.93570i	0.0579804	+	0.403262i	−0.940077	+	0.340962i	$0.889247\pi$
$492$	0.102575	+	0.0301186i	0.00462442	+	0.00135785i
$493$	21.1422	−	24.3994i	0.952195	−	1.09889i
$494$	−13.7438	−	8.83260i	−0.618362	−	0.397397i
$495$	1.62538	+	1.04457i	0.0730556	+	0.0469500i
$496$	3.49485	−	4.03327i	0.156923	−	0.181099i
$497$	60.2665	+	17.6958i	2.70332	+	0.793767i
$498$	0.0330897	+	0.230144i	0.00148278	+	0.0103130i
$499$	−25.6770	−	29.6328i	−1.14946	−	1.32655i	−0.936980	−	0.349382i	$-0.886391\pi$
$499$	−25.6770	−	29.6328i	−1.14946	−	1.32655i	−0.212480	−	0.977165i	$-0.568154\pi$
$500$	0.415415	+	0.909632i	0.0185779	+	0.0406800i
$501$	54.3049	−	15.9454i	2.42617	−	0.712386i
$502$	−3.36943	+	7.37802i	−0.150385	+	0.329297i
$503$	−0.128365	+	0.892799i	−0.00572352	+	0.0398080i	−0.992483	−	0.122382i	$-0.960947\pi$
$503$	−0.128365	+	0.892799i	−0.00572352	+	0.0398080i	0.986760	+	0.162190i	$0.0518558\pi$
$504$	20.1806	−	12.9693i	0.898915	−	0.577697i
$505$	7.21985			0.321279
$506$	0.941486	+	1.31022i	0.0418541	+	0.0582462i
$507$	−4.58791			−0.203756
$508$	−13.4488	+	8.64301i	−0.596694	+	0.383472i
$509$	5.35005	−	37.2104i	0.237137	−	1.64932i	−0.428862	−	0.903370i	$-0.641085\pi$
$509$	5.35005	−	37.2104i	0.237137	−	1.64932i	0.665999	−	0.745953i	$-0.268006\pi$
$510$	5.40266	−	11.8302i	0.239234	−	0.523849i
$511$	−21.3893	+	6.28045i	−0.946205	+	0.277831i
$512$	−0.415415	−	0.909632i	−0.0183589	−	0.0402004i
$513$	−25.6473	−	29.5985i	−1.13235	−	1.30681i
$514$	−1.26072	−	8.76849i	−0.0556079	−	0.386762i
$515$	−5.50658	−	1.61688i	−0.242649	−	0.0712482i
$516$	−24.5791	+	28.3658i	−1.08203	+	1.24873i
$517$	0.788343	+	0.506638i	0.0346713	+	0.0222819i
$518$	−28.5654	−	18.3579i	−1.25509	−	0.806600i
$519$	−27.3584	+	31.5733i	−1.20090	+	1.38591i
$520$	3.24649	+	0.953256i	0.142368	+	0.0418030i
$521$	−4.40966	−	30.6699i	−0.193191	−	1.34367i	−0.823495	−	0.567324i	$-0.807979\pi$
$521$	−4.40966	−	30.6699i	−0.193191	−	1.34367i	0.630304	−	0.776348i	$-0.282930\pi$
$522$	27.6063	+	31.8594i	1.20830	+	1.39445i
$523$	2.51118	+	5.49873i	0.109806	+	0.240443i	0.956556	−	0.291550i	$-0.0941708\pi$
$523$	2.51118	+	5.49873i	0.109806	+	0.240443i	−0.846749	+	0.531992i	$0.821444\pi$
$524$	2.52317	−	0.740869i	0.110225	−	0.0323650i
$525$	−5.13065	+	11.2346i	−0.223920	+	0.490316i
$526$	−1.71358	+	11.9182i	−0.0747156	+	0.519658i
$527$	19.7468	−	12.6905i	0.860186	−	0.552808i
$528$	0.994747			0.0432908
$529$	−7.33608	+	21.7987i	−0.318960	+	0.947768i
$530$	−0.103296			−0.00448689
$531$	36.9007	−	23.7147i	1.60136	−	1.02913i
$532$	2.87021	−	19.9627i	0.124439	−	0.865495i
$533$	−0.0508181	+	0.111276i	−0.00220117	+	0.00481990i
$534$	26.0542	−	7.65020i	1.12747	−	0.331056i
$535$	−4.69716	−	10.2854i	−0.203076	−	0.444675i
$536$	5.59636	+	6.45854i	0.241726	+	0.278967i
$537$	−2.87382	−	19.9878i	−0.124014	−	0.862538i
$538$	23.1695	+	6.80318i	0.998909	+	0.293306i
$539$	−2.30147	+	2.65603i	−0.0991312	+	0.114404i
$540$	6.82357	+	4.38524i	0.293640	+	0.188711i
$541$	4.80968	+	3.09099i	0.206784	+	0.132892i	0.639934	−	0.768430i	$-0.278962\pi$
$541$	4.80968	+	3.09099i	0.206784	+	0.132892i	−0.433150	+	0.901322i	$0.642598\pi$
$542$	5.98443	−	6.90640i	0.257053	−	0.296655i
$543$	−22.9233	−	6.73090i	−0.983734	−	0.288850i
$544$	−0.625953	−	4.35360i	−0.0268375	−	0.186659i
$545$	−7.24405	−	8.36008i	−0.310301	−	0.358107i
$546$	17.3598	+	38.0127i	0.742931	+	1.62679i
$547$	−17.8530	+	5.24212i	−0.763341	+	0.224137i	−0.640154	−	0.768246i	$-0.721130\pi$
$547$	−17.8530	+	5.24212i	−0.763341	+	0.224137i	−0.123187	+	0.992384i	$0.539311\pi$
$548$	1.28936	−	2.82331i	0.0550789	−	0.120606i
$549$	−7.48352	+	52.0490i	−0.319389	+	2.22140i
$550$	−0.283012	+	0.181881i	−0.0120677	+	0.00775543i
$551$	35.4418			1.50987
$552$	8.27503	+	11.5159i	0.352208	+	0.490150i
$553$	57.2957			2.43646
$554$	20.6223	−	13.2532i	0.876158	−	0.563073i
$555$	3.42092	−	23.7930i	0.145210	−	1.00996i
$556$	6.22414	−	13.6290i	0.263962	−	0.577997i
$557$	−37.1046	+	10.8949i	−1.57217	+	0.461631i	−0.947633	−	0.319362i	$-0.896531\pi$
$557$	−37.1046	+	10.8949i	−1.57217	+	0.461631i	−0.624539	+	0.780994i	$0.714713\pi$
$558$	12.7324	+	27.8802i	0.539008	+	1.18026i
$559$	−28.1257	−	32.4588i	−1.18959	−	1.37286i
$560$	0.594438	+	4.13440i	0.0251196	+	0.174710i
$561$	4.19803	+	1.23265i	0.177241	+	0.0520427i
$562$	−10.7798	+	12.4405i	−0.454717	+	0.524772i
$563$	24.0105	+	15.4306i	1.01192	+	0.650322i	0.937890	−	0.346934i	$-0.112777\pi$
$563$	24.0105	+	15.4306i	1.01192	+	0.650322i	0.0740314	+	0.997256i	$0.476413\pi$
$564$	6.92901	+	4.45300i	0.291764	+	0.187505i
$565$	0.929542	−	1.07275i	0.0391061	−	0.0451309i
$566$	−19.6950	−	5.78299i	−0.827845	−	0.243077i
$567$	4.01506	+	27.9254i	0.168617	+	1.17275i
$568$	9.84752	+	11.3646i	0.413193	+	0.476850i
$569$	0.572420	+	1.25342i	0.0239971	+	0.0525463i	0.921251	−	0.388969i	$-0.127169\pi$
$569$	0.572420	+	1.25342i	0.0239971	+	0.0525463i	−0.897254	+	0.441515i	$0.854441\pi$
$570$	13.6988	−	4.02234i	0.573780	−	0.168477i
$571$	−12.2136	+	26.7441i	−0.511124	+	1.11921i	0.461568	+	0.887105i	$0.347287\pi$
$571$	−12.2136	+	26.7441i	−0.511124	+	1.11921i	−0.972692	+	0.232100i	$0.925440\pi$
$572$	−0.161995	+	1.12670i	−0.00677334	+	0.0471096i
$573$	−0.534329	+	0.343393i	−0.0223219	+	0.0143454i
$574$	−0.151015			−0.00630324
$575$	−4.45989	−	1.76334i	−0.185990	−	0.0735365i
$576$	5.74316			0.239298
$577$	−20.0046	+	12.8562i	−0.832801	+	0.535209i	−0.886167	−	0.463366i	$-0.846642\pi$
$577$	−20.0046	+	12.8562i	−0.832801	+	0.535209i	0.0533655	+	0.998575i	$0.483005\pi$
$578$	0.333818	−	2.32176i	0.0138850	−	0.0965724i
$579$	17.0392	−	37.3107i	0.708126	−	1.55058i
$580$	−7.04289	+	2.06798i	−0.292440	+	0.0858681i
$581$	−0.136441	−	0.298765i	−0.00566055	−	0.0123949i
$582$	6.98200	+	8.05766i	0.289413	+	0.334001i
$583$	−0.00494552	−	0.0343968i	−0.000204822	−	0.00142457i
$584$	−5.12082	−	1.50361i	−0.211901	−	0.0622198i
$585$	−12.7254	+	14.6859i	−0.526131	+	0.607188i
$586$	15.7052	+	10.0931i	0.648776	+	0.416943i
$587$	−8.10561	−	5.20916i	−0.334554	−	0.215005i	0.362568	−	0.931957i	$-0.381900\pi$
$587$	−8.10561	−	5.20916i	−0.334554	−	0.215005i	−0.697122	+	0.716952i	$0.745537\pi$
$588$	−20.2284	+	23.3448i	−0.834203	+	0.962722i
$589$	24.7245	+	7.25978i	1.01876	+	0.299134i
$590$	1.08695	+	7.55987i	0.0447488	+	0.311235i
$591$	28.0146	+	32.3305i	1.15237	+	1.32990i
$592$	−3.37707	−	7.39475i	−0.138797	−	0.303923i
$593$	−26.9616	+	7.91663i	−1.10718	+	0.325097i	−0.783701	−	0.621139i	$-0.786670\pi$
$593$	−26.9616	+	7.91663i	−1.10718	+	0.325097i	−0.323478	+	0.946236i	$0.604852\pi$
$594$	−1.13356	+	2.48216i	−0.0465106	+	0.101844i
$595$	−2.61456	+	18.1846i	−0.107186	+	0.745497i
$596$	−2.22067	+	1.42714i	−0.0909622	+	0.0584578i
$597$	35.0313			1.43374
$598$	−14.3911	+	7.49732i	−0.588495	+	0.306588i
$599$	−24.3918			−0.996624			−0.498312	−	0.866998i	$-0.666047\pi$
$599$	−24.3918			−0.996624			−0.498312	+	0.866998i	$0.666047\pi$
$600$	−2.48749	+	1.59861i	−0.101551	+	0.0652630i
$601$	−2.24293	+	15.5999i	−0.0914909	+	0.636333i	0.891547	+	0.452929i	$0.149621\pi$
$601$	−2.24293	+	15.5999i	−0.0914909	+	0.636333i	−0.983038	+	0.183404i	$0.941288\pi$
$602$	22.0252	−	48.2285i	0.897682	−	1.96565i
$603$	−47.0922	+	13.8275i	−1.91774	+	0.563100i
$604$	−5.17217	−	11.3255i	−0.210453	−	0.460827i
$605$	7.12935	+	8.22771i	0.289849	+	0.334504i
$606$	3.03817	+	21.1309i	0.123417	+	0.858386i
$607$	31.1610	+	9.14968i	1.26478	+	0.371374i	0.844273	−	0.535913i	$-0.180033\pi$
$607$	31.1610	+	9.14968i	1.26478	+	0.371374i	0.420511	+	0.907287i	$0.361851\pi$
$608$	3.16196	−	3.64909i	0.128234	−	0.147990i
$609$	−76.2651	−	49.0126i	−3.09042	−	1.98609i
$610$	−7.70250	−	4.95010i	−0.311865	−	0.200424i
$611$	−6.17208	+	7.12296i	−0.249696	+	0.288164i
$612$	24.2373	+	7.11671i	0.979734	+	0.287676i
$613$	0.0204662	+	0.142346i	0.000826623	+	0.00574929i	0.990231	−	0.139440i	$-0.0445301\pi$
$613$	0.0204662	+	0.142346i	0.000826623	+	0.00574929i	−0.989404	+	0.145189i	$0.953621\pi$
$614$	5.86982	+	6.77413i	0.236887	+	0.273382i
$615$	−0.0444099	−	0.0972441i	−0.00179078	−	0.00392126i
$616$	−1.34827	+	0.395887i	−0.0543233	+	0.0159508i
$617$	12.0410	−	26.3661i	0.484752	−	1.06146i	−0.496377	−	0.868107i	$-0.665337\pi$
$617$	12.0410	−	26.3661i	0.484752	−	1.06146i	0.981129	−	0.193353i	$-0.0619361\pi$
$618$	2.41504	−	16.7970i	0.0971472	−	0.675674i
$619$	−0.143050	+	0.0919324i	−0.00574965	+	0.00369507i	−0.543512	−	0.839401i	$-0.682906\pi$
$619$	−0.143050	+	0.0919324i	−0.00574965	+	0.00369507i	0.537763	+	0.843096i	$0.319270\pi$
$620$	−5.33678			−0.214330
$621$	−38.1651	+	7.52541i	−1.53151	+	0.301984i
$622$	−26.9893			−1.08217
$623$	−32.2689	+	20.7380i	−1.29283	+	0.830849i
$624$	−1.42383	+	9.90292i	−0.0569986	+	0.396434i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	15.6564	−	4.59714i	0.625757	−	0.183739i
$627$	1.99527	+	4.36904i	0.0796835	+	0.174482i
$628$	−2.72409	−	3.14377i	−0.108703	−	0.125450i
$629$	−5.08862	−	35.3921i	−0.202896	−	1.41118i
$630$	−23.0170	−	6.75840i	−0.917019	−	0.269261i
$631$	11.3593	−	13.1093i	0.452205	−	0.521872i	−0.483172	−	0.875526i	$-0.660515\pi$
$631$	11.3593	−	13.1093i	0.452205	−	0.521872i	0.935376	+	0.353654i	$0.115061\pi$
$632$	11.5397	+	7.41609i	0.459023	+	0.294996i
$633$	54.5890	+	35.0822i	2.16972	+	1.39439i
$634$	−4.90455	+	5.66015i	−0.194785	+	0.224793i
$635$	15.3390	+	4.50395i	0.608711	+	0.178734i
$636$	−0.0434678	−	0.302325i	−0.00172361	−	0.0119880i
$637$	−23.1472	−	26.7133i	−0.917126	−	1.05842i
$638$	−1.02582	−	2.24622i	−0.0406125	−	0.0889289i
$639$	−82.8649	+	24.3313i	−3.27808	+	0.962532i
$640$	−0.415415	+	0.909632i	−0.0164207	+	0.0359564i
$641$	0.258461	−	1.79764i	0.0102086	−	0.0710024i	−0.984080	−	0.177724i	$-0.943126\pi$
$641$	0.258461	−	1.79764i	0.0102086	−	0.0710024i	0.994289	+	0.106722i	$0.0340355\pi$
$642$	28.1264	−	18.0758i	1.11006	−	0.713393i
$643$	−35.4114			−1.39649			−0.698244	−	0.715860i	$-0.746035\pi$
$643$	−35.4114			−1.39649			−0.698244	+	0.715860i	$0.746035\pi$
$644$	−15.7990	−	12.3153i	−0.622566	−	0.485290i
$645$	37.5333			1.47787
$646$	17.8659	−	11.4817i	0.702926	−	0.451743i
$647$	−5.29168	+	36.8044i	−0.208037	+	1.44693i	0.571514	+	0.820592i	$0.306356\pi$
$647$	−5.29168	+	36.8044i	−0.208037	+	1.44693i	−0.779551	+	0.626339i	$0.784553\pi$
$648$	−2.80587	+	6.14400i	−0.110225	+	0.241359i
$649$	−2.46535	+	0.723891i	−0.0967733	+	0.0284152i
$650$	−1.40558	−	3.07778i	−0.0551313	−	0.120721i
$651$	−43.1637	−	49.8135i	−1.69172	−	1.95235i
$652$	−1.40718	−	9.78712i	−0.0551092	−	0.383293i
$653$	−13.4690	−	3.95485i	−0.527082	−	0.154765i	0.00735601	−	0.999973i	$-0.497658\pi$
$653$	−13.4690	−	3.95485i	−0.527082	−	0.154765i	−0.534438	+	0.845208i	$0.679477\pi$
$654$	21.4198	−	24.7198i	0.837581	−	0.966620i
$655$	−2.21224	−	1.42172i	−0.0864392	−	0.0555511i
$656$	−0.0304152	−	0.0195467i	−0.00118751	−	0.000763169i
$657$	20.0723	−	23.1647i	0.783096	−	0.903741i
$658$	−11.1637	−	3.27796i	−0.435206	−	0.127788i
$659$	4.40027	+	30.6045i	0.171410	+	1.19218i	0.875908	+	0.482478i	$0.160263\pi$
$659$	4.40027	+	30.6045i	0.171410	+	1.19218i	−0.704498	+	0.709706i	$0.748828\pi$
$660$	−0.651421	−	0.751780i	−0.0253565	−	0.0292630i
$661$	1.38324	+	3.02888i	0.0538019	+	0.117810i	0.934624	−	0.355638i	$-0.115736\pi$
$661$	1.38324	+	3.02888i	0.0538019	+	0.117810i	−0.880822	+	0.473448i	$0.843009\pi$
$662$	−4.51093	+	1.32453i	−0.175322	+	0.0514792i
$663$	−18.2802	+	40.0280i	−0.709943	+	1.55456i
$664$	0.0111907	−	0.0778332i	0.000434284	−	0.00302051i
$665$	−16.9664	+	10.9037i	−0.657930	+	0.422826i
$666$	46.6884			1.80914
$667$	17.4705	−	30.5613i	0.676459	−	1.18334i
$668$	−19.1409			−0.740585
$669$	51.8105	−	33.2966i	2.00311	−	1.28732i
$670$	1.21621	−	8.45889i	0.0469861	−	0.326796i
$671$	1.27957	−	2.80188i	0.0493974	−	0.108165i
$672$	−11.8504	+	3.47958i	−0.457138	+	0.134228i
$673$	0.696404	+	1.52491i	0.0268444	+	0.0587811i	0.922579	−	0.385808i	$-0.126077\pi$
$673$	0.696404	+	1.52491i	0.0268444	+	0.0587811i	−0.895735	+	0.444589i	$0.853350\pi$
$674$	−0.320222	−	0.369555i	−0.0123345	−	0.0142347i
$675$	−1.15434	−	8.02864i	−0.0444307	−	0.309022i
$676$	1.48875	+	0.437137i	0.0572597	+	0.0168130i
$677$	19.3075	−	22.2821i	0.742048	−	0.856369i	−0.251724	−	0.967799i	$-0.580998\pi$
$677$	19.3075	−	22.2821i	0.742048	−	0.856369i	0.993772	+	0.111430i	$0.0355430\pi$
$678$	3.53086	+	2.26915i	0.135602	+	0.0871461i
$679$	−12.6701	−	8.14257i	−0.486234	−	0.312483i
$680$	−2.88032	+	3.32406i	−0.110455	+	0.127472i
$681$	−72.6450	−	21.3305i	−2.78376	−	0.817386i
$682$	−0.255510	−	1.77711i	−0.00978398	−	0.0680491i
$683$	−23.2842	−	26.8714i	−0.890947	−	1.02821i	−0.999418	−	0.0341079i	$-0.989141\pi$
$683$	−23.2842	−	26.8714i	−0.890947	−	1.02821i	0.108471	−	0.994100i	$-0.465404\pi$
$684$	11.5197	+	25.2246i	0.440466	+	0.964485i
$685$	−2.97807	+	0.874440i	−0.113786	+	0.0334106i
$686$	5.98049	−	13.0954i	0.228336	−	0.499986i
$687$	0.842701	−	5.86111i	0.0321510	−	0.223615i
$688$	10.6785	−	6.86264i	0.407113	−	0.261636i
$689$	0.349507			0.0133151
$690$	3.28417	−	13.7952i	0.125026	−	0.525173i
$691$	15.4571			0.588018			0.294009	−	0.955803i	$-0.405011\pi$
$691$	15.4571			0.588018			0.294009	+	0.955803i	$0.405011\pi$
$692$	11.8860	−	7.63865i	0.451837	−	0.290378i
$693$	1.14851	−	7.98808i	0.0436284	−	0.303442i
$694$	−10.1201	+	22.1599i	−0.384153	+	0.841178i
$695$	−14.3760	+	4.22118i	−0.545314	+	0.160119i
$696$	−9.01624	−	19.7428i	−0.341760	−	0.748349i
$697$	−0.104137	−	0.120180i	−0.00394446	−	0.00455215i
$698$	−4.06514	−	28.2736i	−0.153868	−	1.07017i
$699$	4.52886	+	1.32979i	0.171297	+	0.0502974i
$700$	2.73530	−	3.15671i	0.103385	−	0.119312i
$701$	24.7444	+	15.9022i	0.934581	+	0.600619i	0.916853	−	0.399224i	$-0.130720\pi$
$701$	24.7444	+	15.9022i	0.934581	+	0.600619i	0.0177279	+	0.999843i	$0.494357\pi$
$702$	−23.0879	−	14.8377i	−0.871396	−	0.560012i
$703$	25.7048	−	29.6649i	0.969475	−	1.11883i
$704$	−0.322790	−	0.0947797i	−0.0121656	−	0.00357215i
$705$	−1.17218	−	8.15269i	−0.0441469	−	0.307048i
$706$	0.535701	+	0.618231i	0.0201614	+	0.0232674i
$707$	−12.5276	−	27.4315i	−0.471147	−	1.03167i
$708$	−21.6687	+	6.36251i	−0.814361	+	0.239118i
$709$	−5.75700	+	12.6061i	−0.216209	+	0.473431i	−0.986396	−	0.164387i	$-0.947435\pi$
$709$	−5.75700	+	12.6061i	−0.216209	+	0.473431i	0.770187	+	0.637818i	$0.220163\pi$
$710$	2.14007	−	14.8845i	0.0803154	−	0.558606i
$711$	−66.2741	+	42.5918i	−2.48547	+	1.59732i
$712$	−9.18336			−0.344161
$713$	18.4476	−	17.7413i	0.690869	−	0.664415i
$714$	−54.3228			−2.03298
$715$	0.957586	−	0.615403i	0.0358117	−	0.0230148i
$716$	−0.971907	+	6.75976i	−0.0363219	+	0.252624i
$717$	−26.3193	+	57.6312i	−0.982911	+	2.15228i
$718$	−26.3159	+	7.72704i	−0.982100	+	0.288371i
$719$	−0.548352	−	1.20072i	−0.0204501	−	0.0447794i	0.899131	−	0.437679i	$-0.144199\pi$
$719$	−0.548352	−	1.20072i	−0.0204501	−	0.0447794i	−0.919581	+	0.392899i	$0.871472\pi$
$720$	−3.76097	−	4.34039i	−0.140163	−	0.161757i
$721$	3.41151	+	23.7276i	0.127051	+	0.883661i
$722$	4.13913	+	1.21536i	0.154043	+	0.0452310i
$723$	20.4767	−	23.6314i	0.761538	−	0.878861i
$724$	6.79718	+	4.36828i	0.252615	+	0.162346i
$725$	6.17498	+	3.96842i	0.229333	+	0.147383i
$726$	−21.0807	+	24.3284i	−0.782377	+	0.902911i
$727$	2.05794	+	0.604266i	0.0763248	+	0.0224110i	0.319672	−	0.947528i	$-0.396427\pi$
$727$	2.05794	+	0.604266i	0.0763248	+	0.0224110i	−0.243347	+	0.969939i	$0.578245\pi$
$728$	−2.01131	−	13.9890i	−0.0745440	−	0.518465i
$729$	21.7152	+	25.0607i	0.804268	+	0.928175i
$730$	2.21707	+	4.85471i	0.0820576	+	0.179681i
$731$	53.5693	−	15.7294i	1.98133	−	0.581771i
$732$	11.2466	−	24.6266i	0.415686	−	0.910226i
$733$	2.17623	−	15.1360i	0.0803810	−	0.559062i	−0.909340	−	0.416053i	$-0.863413\pi$
$733$	2.17623	−	15.1360i	0.0803810	−	0.559062i	0.989721	−	0.143009i	$-0.0456779\pi$
$734$	−3.31812	+	2.13243i	−0.122474	+	0.0787094i
$735$	30.8895			1.13938
$736$	−1.58796	−	4.52530i	−0.0585331	−	0.166805i
$737$	2.87498			0.105901
$738$	0.174679	−	0.112260i	0.00643003	−	0.00413233i
$739$	−1.28095	+	8.90921i	−0.0471205	+	0.327730i	0.952603	+	0.304216i	$0.0983946\pi$
$739$	−1.28095	+	8.90921i	−0.0471205	+	0.327730i	−0.999724	+	0.0235142i	$0.992515\pi$
$740$	−3.37707	+	7.39475i	−0.124144	+	0.271837i
$741$	−46.3506	+	13.6098i	−1.70273	+	0.499967i
$742$	0.179234	+	0.392468i	0.00657990	+	0.0144080i
$743$	−9.49363	−	10.9562i	−0.348287	−	0.401945i	0.554394	−	0.832254i	$-0.312950\pi$
$743$	−9.49363	−	10.9562i	−0.348287	−	0.401945i	−0.902682	+	0.430309i	$0.858405\pi$
$744$	−2.24576	−	15.6196i	−0.0823336	−	0.572643i
$745$	2.53279	+	0.743694i	0.0927942	+	0.0272468i
$746$	−9.12200	+	10.5274i	−0.333980	+	0.385434i
$747$	0.379914	+	0.244156i	0.0139003	+	0.00893321i
$748$	−1.24479	−	0.799979i	−0.0455141	−	0.0292501i
$749$	−30.9285	+	35.6934i	−1.13010	+	1.30421i
$750$	2.83711	+	0.833050i	0.103597	+	0.0304187i
$751$	4.53321	+	31.5292i	0.165419	+	1.15052i	0.888206	+	0.459446i	$0.151952\pi$
$751$	4.53321	+	31.5292i	0.165419	+	1.15052i	−0.722787	+	0.691071i	$0.757139\pi$
$752$	−1.82414	−	2.10517i	−0.0665197	−	0.0767678i
$753$	9.96301	+	21.8160i	0.363072	+	0.795018i
$754$	23.8299	−	6.99710i	0.867835	−	0.254819i
$755$	−5.17217	+	11.3255i	−0.188235	+	0.412176i
$756$	4.82160	−	33.5350i	0.175360	−	1.21965i
$757$	−40.0457	+	25.7358i	−1.45548	+	0.935383i	−0.456528	+	0.889709i	$0.650907\pi$
$757$	−40.0457	+	25.7358i	−1.45548	+	0.935383i	−0.998956	+	0.0456739i	$0.985456\pi$
$758$	27.6273			1.00347
$759$	4.75094	+	0.433131i	0.172448	+	0.0157217i
$760$	−4.82844			−0.175146
$761$	−38.2980	+	24.6126i	−1.38830	+	0.892207i	−0.999575	−	0.0291458i	$-0.990721\pi$
$761$	−38.2980	+	24.6126i	−1.38830	+	0.892207i	−0.388727	+	0.921353i	$0.627085\pi$
$762$	−6.72730	+	46.7894i	−0.243704	+	1.69500i
$763$	−19.1942	+	42.0295i	−0.694878	+	1.52157i
$764$	0.206106	−	0.0605181i	0.00745664	−	0.00218947i
$765$	−10.4936	−	22.9778i	−0.379397	−	0.830763i
$766$	2.92069	+	3.37066i	0.105529	+	0.121787i
$767$	−3.67773	−	25.5792i	−0.132795	−	0.923611i
$768$	−2.83711	−	0.833050i	−0.102375	−	0.0300601i
$769$	1.79650	−	2.07327i	0.0647833	−	0.0747639i	−0.722433	−	0.691441i	$-0.756976\pi$
$769$	1.79650	−	2.07327i	0.0647833	−	0.0747639i	0.787216	+	0.616677i	$0.211522\pi$
$770$	1.18212	+	0.759702i	0.0426006	+	0.0273778i
$771$	−22.0358	−	14.1616i	−0.793600	−	0.510016i
$772$	−9.08411	+	10.4836i	−0.326944	+	0.377314i
$773$	−5.92689	−	1.74029i	−0.213175	−	0.0625939i	0.173401	−	0.984851i	$-0.444524\pi$
$773$	−5.92689	−	1.74029i	−0.213175	−	0.0625939i	−0.386576	+	0.922257i	$0.626342\pi$
$774$	10.3749	+	72.1589i	0.372917	+	2.59370i
$775$	3.49485	+	4.03327i	0.125539	+	0.144879i
$776$	−1.49789	−	3.27991i	−0.0537710	−	0.117742i
$777$	−96.3363	+	28.2869i	−3.45605	+	1.01479i
$778$	−7.11694	+	15.5839i	−0.255155	+	0.558711i
$779$	0.0248440	−	0.172794i	0.000890128	−	0.00619097i
$780$	8.41654	−	5.40898i	0.301360	−	0.193673i
$781$	5.05890			0.181022
$782$	−1.09393	−	21.0654i	−0.0391189	−	0.753299i
$783$	59.5379			2.12771
$784$	8.78829	−	5.64789i	0.313867	−	0.201710i
$785$	−0.592002	+	4.11746i	−0.0211294	+	0.146959i
$786$	3.23014	−	7.07301i	0.115215	−	0.252286i
$787$	36.2825	−	10.6535i	1.29333	−	0.379756i	0.438531	−	0.898716i	$-0.355499\pi$
$787$	36.2825	−	10.6535i	1.29333	−	0.379756i	0.854799	+	0.518960i	$0.173681\pi$
$788$	−6.01012	−	13.1603i	−0.214102	−	0.468817i
$789$	23.3151	+	26.9070i	0.830039	+	0.957916i
$790$	−1.95216	−	13.5776i	−0.0694549	−	0.483069i
$791$	−5.68876	−	1.67037i	−0.202269	−	0.0593916i
$792$	1.26526	−	1.46018i	0.0449589	−	0.0518853i
$793$	26.0618	+	16.7489i	0.925481	+	0.594771i
$794$	26.3849	+	16.9565i	0.936364	+	0.601764i
$795$	−0.200017	+	0.230831i	−0.00709386	+	0.00818675i
$796$	−11.3675	−	3.33779i	−0.402910	−	0.118305i
$797$	2.88669	+	20.0773i	0.102252	+	0.711176i	0.974870	+	0.222774i	$0.0715111\pi$
$797$	2.88669	+	20.0773i	0.102252	+	0.711176i	−0.872619	+	0.488402i	$0.837580\pi$
$798$	−39.0523	−	45.0687i	−1.38244	−	1.59542i
$799$	−5.08960	−	11.1447i	−0.180057	−	0.394270i
$800$	0.959493	−	0.281733i	0.0339232	−	0.00996075i
$801$	21.9096	−	47.9753i	0.774137	−	1.69512i
$802$	−0.998202	+	6.94265i	−0.0352478	+	0.245154i
$803$	−1.51044	+	0.970700i	−0.0533022	+	0.0342553i
$804$	25.2692			0.891175
$805$	1.03885	+	20.0048i	0.0366148	+	0.705078i
$806$	18.0572			0.636039
$807$	60.0670	−	38.6027i	2.11446	−	1.35888i
$808$	1.02749	−	7.14636i	0.0361470	−	0.251408i
$809$	−15.7461	+	34.4790i	−0.553602	+	1.21222i	0.401478	+	0.915869i	$0.368497\pi$
$809$	−15.7461	+	34.4790i	−0.553602	+	1.21222i	−0.955079	+	0.296350i	$0.904231\pi$
$810$	6.48078	−	1.90293i	0.227712	−	0.0668621i
$811$	−13.6122	−	29.8067i	−0.477991	−	1.04665i	−0.983011	−	0.183546i	$-0.941242\pi$
$811$	−13.6122	−	29.8067i	−0.477991	−	1.04665i	0.505021	−	0.863107i	$-0.331485\pi$
$812$	20.0777	+	23.1709i	0.704589	+	0.813139i
$813$	−3.84555	−	26.7464i	−0.134869	−	0.938036i
$814$	−2.62409	−	0.770502i	−0.0919742	−	0.0270061i
$815$	−6.47511	+	7.47267i	−0.226813	+	0.261756i
$816$	−10.9409	−	7.03128i	−0.383008	−	0.246144i
$817$	51.5604	+	33.1359i	1.80387	+	1.15928i
$818$	−19.9166	+	22.9849i	−0.696366	+	0.803649i
$819$	77.8791	+	22.8674i	2.72132	+	0.799051i
$820$	0.00514534	+	0.0357866i	0.000179683	+	0.00124972i
$821$	−4.08405	−	4.71324i	−0.142534	−	0.164493i	0.679994	−	0.733218i	$-0.261982\pi$
$821$	−4.08405	−	4.71324i	−0.142534	−	0.164493i	−0.822528	+	0.568725i	$0.807437\pi$
$822$	−3.81250	−	8.34820i	−0.132976	−	0.291177i
$823$	18.0149	−	5.28966i	0.627961	−	0.184386i	0.0477594	−	0.998859i	$-0.484792\pi$
$823$	18.0149	−	5.28966i	0.627961	−	0.184386i	0.580202	+	0.814473i	$0.302974\pi$
$824$	−2.38409	+	5.22043i	−0.0830537	+	0.181862i
$825$	−0.141567	+	0.984622i	−0.00492874	+	0.0342801i
$826$	26.8374	−	17.2474i	0.933793	−	0.600112i
$827$	−27.9060			−0.970385			−0.485193	−	0.874407i	$-0.661250\pi$
$827$	−27.9060			−0.970385			−0.485193	+	0.874407i	$0.661250\pi$
$828$	27.4295	+	2.50068i	0.953240	+	0.0869045i
$829$	40.8497			1.41877			0.709384	−	0.704822i	$-0.248973\pi$
$829$	40.8497			1.41877			0.709384	+	0.704822i	$0.248973\pi$
$830$	−0.0661508	+	0.0425125i	−0.00229613	+	0.00147563i
$831$	10.3156	−	71.7466i	0.357845	−	2.48886i
$832$	1.40558	−	3.07778i	0.0487296	−	0.106703i
$833$	44.0870	−	12.9451i	1.52752	−	0.448522i
$834$	−18.4041	−	40.2993i	−0.637280	−	1.39545i
$835$	12.5347	+	14.4658i	0.433779	+	0.500608i
$836$	−0.231172	−	1.60784i	−0.00799526	−	0.0556083i
$837$	41.5342	+	12.1955i	1.43563	+	0.421539i
$838$	11.1881	−	12.9118i	0.386487	−	0.446029i
$839$	30.1264	+	19.3610i	1.04008	+	0.668417i	0.945006	−	0.327053i	$-0.106056\pi$
$839$	30.1264	+	19.3610i	1.04008	+	0.668417i	0.0950715	+	0.995470i	$0.469692\pi$
$840$	10.3900	+	6.67727i	0.358490	+	0.230388i
$841$	−16.2921	+	18.8021i	−0.561798	+	0.648350i
$842$	−0.928921	−	0.272756i	−0.0320127	−	0.00939979i
$843$	6.92700	+	48.1783i	0.238578	+	1.65935i
$844$	−14.3712	−	16.5853i	−0.494677	−	0.570888i
$845$	−0.644559	−	1.41139i	−0.0221735	−	0.0485532i
$846$	15.3498	−	4.50711i	0.527737	−	0.154958i
$847$	18.8903	−	41.3640i	0.649079	−	1.42129i
$848$	−0.0147005	+	0.102244i	−0.000504818	+	0.00351109i
$849$	−51.0595	+	32.8139i	−1.75236	+	1.12617i
$850$	4.39837			0.150863
$851$	−12.9092	−	36.7880i	−0.442520	−	1.26108i
$852$	44.4644			1.52332
$853$	−29.2548	+	18.8009i	−1.00167	+	0.643732i	−0.935223	−	0.354058i	$-0.884802\pi$
$853$	−29.2548	+	18.8009i	−1.00167	+	0.643732i	−0.0664433	+	0.997790i	$0.521165\pi$
$854$	−5.44266	+	37.8545i	−0.186244	+	1.29536i
$855$	11.5197	−	25.2246i	0.393965	−	0.862662i
$856$	−10.8491	+	3.18560i	−0.370816	+	0.108881i
$857$	9.95264	+	21.7932i	0.339976	+	0.744443i	0.999977	−	0.00682190i	$-0.00217149\pi$
$857$	9.95264	+	21.7932i	0.339976	+	0.744443i	−0.660001	+	0.751265i	$0.729444\pi$
$858$	2.20411	+	2.54368i	0.0752472	+	0.0868399i
$859$	−1.16703	−	8.11689i	−0.0398186	−	0.276945i	0.960178	−	0.279388i	$-0.0901314\pi$
$859$	−1.16703	−	8.11689i	−0.0398186	−	0.276945i	−0.999997	+	0.00244304i	$0.999222\pi$
$860$	−12.1793	−	3.57618i	−0.415312	−	0.121947i
$861$	−0.292417	+	0.337467i	−0.00996555	+	0.0115009i
$862$	−17.7663	−	11.4177i	−0.605121	−	0.388888i
$863$	−30.7182	−	19.7414i	−1.04566	−	0.672006i	−0.0992807	−	0.995059i	$-0.531654\pi$
$863$	−30.7182	−	19.7414i	−1.04566	−	0.672006i	−0.946381	+	0.323054i	$0.895291\pi$
$864$	5.31170	−	6.13003i	0.180708	−	0.208548i
$865$	−13.5566	−	3.98056i	−0.460937	−	0.135343i
$866$	1.72333	+	11.9860i	0.0585610	+	0.407301i
$867$	−4.54196	−	5.24170i	−0.154253	−	0.178018i
$868$	9.26014	+	20.2769i	0.314309	+	0.688242i
$869$	4.42778	−	1.30011i	0.150202	−	0.0441034i
$870$	−9.01624	+	19.7428i	−0.305679	+	0.669344i
$871$	−4.11509	+	28.6211i	−0.139434	+	0.969788i
$872$	−9.30593	+	5.98056i	−0.315138	+	0.202527i
$873$	20.7084			0.700875
$874$	16.6905	−	16.0514i	0.564564	−	0.542946i
$875$	−4.17692			−0.141206
$876$	−13.2757	+	8.53180i	−0.448546	+	0.288263i
$877$	7.49962	−	52.1610i	0.253244	−	1.76135i	−0.325215	−	0.945640i	$-0.605437\pi$
$877$	7.49962	−	52.1610i	0.253244	−	1.76135i	0.578459	−	0.815711i	$-0.303654\pi$
$878$	1.52782	−	3.34547i	0.0515616	−	0.112904i
$879$	52.9655	−	15.5521i	1.78648	−	0.524558i
$880$	0.139753	+	0.306016i	0.00471107	+	0.0103158i
$881$	−7.12293	−	8.22030i	−0.239978	−	0.276949i	0.622966	−	0.782249i	$-0.285927\pi$
$881$	−7.12293	−	8.22030i	−0.239978	−	0.276949i	−0.862944	+	0.505300i	$0.831382\pi$
$882$	8.53844	+	59.3861i	0.287504	+	1.99963i
$883$	−15.7716	−	4.63096i	−0.530757	−	0.155844i	0.00536378	−	0.999986i	$-0.498293\pi$
$883$	−15.7716	−	4.63096i	−0.530757	−	0.155844i	−0.536121	+	0.844141i	$0.680111\pi$
$884$	9.74569	−	11.2471i	0.327783	−	0.378282i
$885$	18.9985	+	12.2096i	0.638626	+	0.410420i
$886$	−12.2330	−	7.86166i	−0.410975	−	0.264118i
$887$	−1.80191	+	2.07952i	−0.0605023	+	0.0698234i	−0.785194	−	0.619250i	$-0.787437\pi$
$887$	−1.80191	+	2.07952i	−0.0605023	+	0.0698234i	0.724692	+	0.689073i	$0.241982\pi$
$888$	−23.0640	−	6.77219i	−0.773976	−	0.227260i
$889$	−9.50304	−	66.0951i	−0.318722	−	2.21676i
$890$	6.01382	+	6.94032i	0.201584	+	0.232640i
$891$	0.943944	+	2.06695i	0.0316233	+	0.0692454i
$892$	−19.9848	+	5.86805i	−0.669139	+	0.196477i
$893$	5.58727	−	12.2344i	0.186971	−	0.409409i
$894$	−1.11081	+	7.72588i	−0.0371512	+	0.258392i
$895$	5.74515	−	3.69218i	0.192039	−	0.123416i
$896$	4.17692			0.139541
$897$	−11.1121	+	46.6766i	−0.371023	+	1.55849i
$898$	22.4590			0.749465
$899$	−32.9545	+	21.1786i	−1.09909	+	0.706345i
$900$	−0.817337	+	5.68470i	−0.0272446	+	0.189490i
$901$	−0.188737	+	0.413276i	−0.00628773	+	0.0137682i
$902$	−0.0116703	+	0.00342672i	−0.000388580	+	0.000114097i
$903$	−65.1261	−	142.606i	−2.16726	−	4.74564i
$904$	−0.929542	−	1.07275i	−0.0309161	−	0.0356791i
$905$	−1.14988	−	7.99758i	−0.0382232	−	0.265849i
$906$	−35.3237	−	10.3720i	−1.17355	−	0.344586i
$907$	−11.6935	+	13.4950i	−0.388276	+	0.448094i	−0.915914	−	0.401375i	$-0.868532\pi$
$907$	−11.6935	+	13.4950i	−0.388276	+	0.448094i	0.527638	+	0.849469i	$0.323078\pi$
$908$	21.5405	+	13.8433i	0.714848	+	0.459405i
$909$	34.8823	+	22.4175i	1.15697	+	0.743542i
$910$	−9.25502	+	10.6809i	−0.306801	+	0.354067i
$911$	19.4315	+	5.70560i	0.643794	+	0.189035i	0.587302	−	0.809368i	$-0.300190\pi$
$911$	19.4315	+	5.70560i	0.643794	+	0.189035i	0.0564921	+	0.998403i	$0.482008\pi$
$912$	−2.03185	−	14.1318i	−0.0672813	−	0.467951i
$913$	−0.0173235	−	0.0199924i	−0.000573324	−	0.000661651i
$914$	5.34395	+	11.7016i	0.176762	+	0.387055i
$915$	−25.9765	+	7.62739i	−0.858757	+	0.252154i
$916$	−0.831900	+	1.82161i	−0.0274868	+	0.0601876i
$917$	−1.56319	+	10.8722i	−0.0516210	+	0.359032i
$918$	30.0126	−	19.2879i	0.990563	−	0.636596i
$919$	31.7762			1.04820			0.524100	−	0.851657i	$-0.324402\pi$
$919$	31.7762			1.04820			0.524100	+	0.851657i	$0.324402\pi$
$920$	−2.38010	+	4.16355i	−0.0784697	+	0.137268i
$921$	26.5039			0.873334
$922$	7.28000	−	4.67857i	0.239754	−	0.154081i
$923$	−7.24103	+	50.3625i	−0.238342	+	1.65770i
$924$	−1.72604	+	3.77950i	−0.0567826	+	0.124336i
$925$	7.80009	−	2.29031i	0.256466	−	0.0753051i
$926$	3.95602	+	8.66249i	0.130003	+	0.284667i
$927$	−21.5844	−	24.9097i	−0.708925	−	0.818143i
$928$	1.04462	+	7.26550i	0.0342914	+	0.238502i
$929$	−0.365395	−	0.107290i	−0.0119882	−	0.00352006i	0.275733	−	0.961234i	$-0.411079\pi$
$929$	−0.365395	−	0.107290i	−0.0119882	−	0.00352006i	−0.287721	+	0.957714i	$0.592898\pi$
$930$	−10.3338	+	11.9259i	−0.338860	+	0.391066i
$931$	42.4338	+	27.2705i	1.39071	+	0.893755i
$932$	−1.34289	−	0.863022i	−0.0439878	−	0.0282692i
$933$	−52.2607	+	60.3120i	−1.71094	+	1.97453i
$934$	2.78716	+	0.818385i	0.0911987	+	0.0267784i
$935$	0.210581	+	1.46463i	0.00688675	+	0.0478984i
$936$	12.7254	+	14.6859i	0.415943	+	0.480024i
$937$	−15.1992	−	33.2815i	−0.496535	−	1.08726i	−0.977580	−	0.210564i	$-0.932470\pi$
$937$	−15.1992	−	33.2815i	−0.496535	−	1.08726i	0.481045	−	0.876696i	$-0.340257\pi$
$938$	−34.2495	+	10.0566i	−1.11829	+	0.328359i
$939$	20.0432	−	43.8885i	0.654085	−	1.43225i
$940$	−0.396424	+	2.75719i	−0.0129299	+	0.0899297i
$941$	35.9790	−	23.1223i	1.17288	−	0.753766i	0.198818	−	0.980036i	$-0.436290\pi$
$941$	35.9790	−	23.1223i	1.17288	−	0.753766i	0.974064	+	0.226271i	$0.0726534\pi$
$942$	−12.3000			−0.400757
$943$	−0.136753	−	0.106599i	−0.00445328	−	0.00347133i
$944$	7.63761			0.248583
$945$	−28.5015	+	18.3168i	−0.927154	+	0.595846i
$946$	0.607730	−	4.22686i	0.0197590	−	0.137427i
$947$	−9.60619	+	21.0346i	−0.312159	+	0.683533i	−0.999066	−	0.0432123i	$-0.986241\pi$
$947$	−9.60619	+	21.0346i	−0.312159	+	0.683533i	0.686907	+	0.726746i	$0.258968\pi$
$948$	38.9172	−	11.4271i	1.26397	−	0.371136i
$949$	−7.50158	−	16.4262i	−0.243511	−	0.533216i
$950$	3.16196	+	3.64909i	0.102587	+	0.118392i
$951$	3.15162	+	21.9200i	0.102198	+	0.710806i
$952$	17.6274	+	5.17589i	0.571309	+	0.167751i
$953$	13.5055	−	15.5862i	0.437486	−	0.504886i	−0.493598	−	0.869690i	$-0.664319\pi$
$953$	13.5055	−	15.5862i	0.437486	−	0.504886i	0.931084	+	0.364804i	$0.118864\pi$
$954$	−0.499069	−	0.320732i	−0.0161580	−	0.0103841i
$955$	−0.180707	−	0.116133i	−0.00584754	−	0.00375799i
$956$	14.0316	−	16.1933i	0.453814	−	0.523729i
$957$	−7.00589	−	2.05711i	−0.226468	−	0.0664971i
$958$	−4.17644	−	29.0478i	−0.134935	−	0.938492i
$959$	8.48981	+	9.79777i	0.274150	+	0.316386i
$960$	1.22833	+	2.68968i	0.0396443	+	0.0868089i
$961$	2.41678	−	0.709631i	0.0779607	−	0.0228913i
$962$	11.4265	−	25.0205i	0.368405	−	0.806694i
$963$	9.24176	−	64.2778i	0.297811	−	2.07132i
$964$	−8.89620	+	5.71724i	−0.286527	+	0.184140i
$965$	13.8718			0.446549
$966$	−58.1128	+	11.4587i	−1.86975	+	0.368678i
$967$	39.2594			1.26250			0.631249	−	0.775580i	$-0.282543\pi$
$967$	39.2594			1.26250			0.631249	+	0.775580i	$0.282543\pi$
$968$	9.15858	−	5.88586i	0.294368	−	0.189179i
$969$	8.93682	−	62.1570i	0.287092	−	1.99677i
$970$	−1.49789	+	3.27991i	−0.0480942	+	0.105312i
$971$	−30.3583	+	8.91400i	−0.974245	+	0.286064i	−0.729847	−	0.683611i	$-0.760409\pi$
$971$	−30.3583	+	8.91400i	−0.974245	+	0.286064i	−0.244398	+	0.969675i	$0.578590\pi$
$972$	−1.81190	−	3.96751i	−0.0581167	−	0.127258i
$973$	40.9829	+	47.2967i	1.31385	+	1.51626i
$974$	−1.61118	−	11.2060i	−0.0516255	−	0.359063i
$975$	−9.59949	−	2.81867i	−0.307430	−	0.0902695i
$976$	−5.99589	+	6.91963i	−0.191924	+	0.221492i
$977$	−39.0494	−	25.0955i	−1.24930	−	0.802876i	−0.262518	−	0.964927i	$-0.584553\pi$
$977$	−39.0494	−	25.0955i	−1.24930	−	0.802876i	−0.986782	+	0.162051i	$0.948189\pi$
$978$	−24.5957	−	15.8067i	−0.786484	−	0.505442i
$979$	−2.02315	+	2.33484i	−0.0646603	+	0.0746219i
$980$	−10.0235	−	2.94316i	−0.320189	−	0.0940159i
$981$	−9.04136	−	62.8840i	−0.288668	−	2.00773i
$982$	−5.91181	−	6.82260i	−0.188654	−	0.217718i
$983$	12.7840	+	27.9931i	0.407747	+	0.892841i	0.996426	+	0.0844738i	$0.0269209\pi$
$983$	12.7840	+	27.9931i	0.407747	+	0.892841i	−0.588679	+	0.808367i	$0.700352\pi$
$984$	−0.102575	+	0.0301186i	−0.00326996	+	0.000960146i
$985$	−6.01012	+	13.1603i	−0.191498	+	0.419323i
$986$	−4.59463	+	31.9564i	−0.146323	+	1.01770i
$987$	−28.9419	+	18.5998i	−0.921231	+	0.592039i
$988$	16.3373			0.519758
$989$	53.9888	−	28.1265i	1.71674	−	0.894372i
$990$	−1.93210			−0.0614061
$991$	7.41452	−	4.76502i	0.235530	−	0.151366i	−0.417552	−	0.908653i	$-0.637112\pi$
$991$	7.41452	−	4.76502i	0.235530	−	0.151366i	0.653082	+	0.757287i	$0.273476\pi$
$992$	−0.759503	+	5.28246i	−0.0241142	+	0.167718i
$993$	−5.77485	+	12.6451i	−0.183259	+	0.401282i
$994$	−60.2665	+	17.6958i	−1.91154	+	0.561278i
$995$	4.92158	+	10.7768i	0.156025	+	0.341646i
$996$	−0.152262	−	0.175720i	−0.00482460	−	0.00556789i
$997$	2.08714	+	14.5164i	0.0661005	+	0.459739i	0.995810	+	0.0914455i	$0.0291487\pi$
$997$	2.08714	+	14.5164i	0.0661005	+	0.459739i	−0.929710	+	0.368293i	$0.879942\pi$
$998$	37.6216	+	11.0467i	1.19089	+	0.349677i
$999$	43.1809	−	49.8334i	1.36618	−	1.57666i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.g.b.81.1	yes	20
23.2	even	11	inner	230.2.g.b.71.1	✓	20
23.5	odd	22		5290.2.a.bi.1.9		10
23.18	even	11		5290.2.a.bj.1.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.b.71.1	✓	20	23.2	even	11	inner
230.2.g.b.81.1	yes	20	1.1	even	1	trivial
5290.2.a.bi.1.9		10	23.5	odd	22
5290.2.a.bj.1.9		10	23.18	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)

\(f(q)\)	\(=\)	\(q+(-0.841254 + 0.540641i) q^{2} +(-0.420808 + 2.92679i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-1.22833 - 2.68968i) q^{6} +(2.73530 + 3.15671i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-5.51052 - 1.61803i) q^{9} +O(q^{10})\)	\(q+(-0.841254 + 0.540641i) q^{2} +(-0.420808 + 2.92679i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-1.22833 - 2.68968i) q^{6} +(2.73530 + 3.15671i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-5.51052 - 1.61803i) q^{9} +(0.654861 - 0.755750i) q^{10} +(0.283012 + 0.181881i) q^{11} +(2.48749 + 1.59861i) q^{12} +(-2.21575 + 2.55712i) q^{13} +(-4.00773 - 1.17677i) q^{14} +(-0.420808 - 2.92679i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-1.82715 - 4.00090i) q^{17} +(5.51052 - 1.61803i) q^{18} +(2.00581 - 4.39211i) q^{19} +(-0.142315 + 0.989821i) q^{20} +(-10.3900 + 6.67727i) q^{21} -0.336417 q^{22} +(-2.79856 - 3.89462i) q^{23} -2.95688 q^{24} +(0.841254 - 0.540641i) q^{25} +(0.481529 - 3.34911i) q^{26} +(3.36951 - 7.37820i) q^{27} +(4.00773 - 1.17677i) q^{28} +(3.04924 + 6.67690i) q^{29} +(1.93635 + 2.23466i) q^{30} +(0.759503 + 5.28246i) q^{31} +(0.959493 + 0.281733i) q^{32} +(-0.651421 + 0.751780i) q^{33} +(3.70014 + 2.37794i) q^{34} +(-3.51385 - 2.25821i) q^{35} +(-3.76097 + 4.34039i) q^{36} +(7.80009 + 2.29031i) q^{37} +(0.687159 + 4.77930i) q^{38} +(-6.55172 - 7.56109i) q^{39} +(-0.415415 - 0.909632i) q^{40} +(0.0346901 - 0.0101859i) q^{41} +(5.13065 - 11.2346i) q^{42} +(-1.80648 + 12.5643i) q^{43} +(0.283012 - 0.181881i) q^{44} +5.74316 q^{45} +(4.45989 + 1.76334i) q^{46} +2.78554 q^{47} +(2.48749 - 1.59861i) q^{48} +(-1.48671 + 10.3403i) q^{49} +(-0.415415 + 0.909632i) q^{50} +(12.4786 - 3.66406i) q^{51} +(1.40558 + 3.07778i) q^{52} +(-0.0676444 - 0.0780658i) q^{53} +(1.15434 + 8.02864i) q^{54} +(-0.322790 - 0.0947797i) q^{55} +(-2.73530 + 3.15671i) q^{56} +(12.0107 + 7.71881i) q^{57} +(-6.17498 - 3.96842i) q^{58} +(-5.00157 + 5.77212i) q^{59} +(-2.83711 - 0.833050i) q^{60} +(-1.30303 - 9.06279i) q^{61} +(-3.49485 - 4.03327i) q^{62} +(-9.96527 - 21.8209i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(1.40558 - 3.07778i) q^{65} +(0.141567 - 0.984622i) q^{66} +(7.18925 - 4.62025i) q^{67} -4.39837 q^{68} +(12.5764 - 6.55191i) q^{69} +4.17692 q^{70} +(12.6504 - 8.12993i) q^{71} +(0.817337 - 5.68470i) q^{72} +(-2.21707 + 4.85471i) q^{73} +(-7.80009 + 2.29031i) q^{74} +(1.22833 + 2.68968i) q^{75} +(-3.16196 - 3.64909i) q^{76} +(0.199979 + 1.39089i) q^{77} +(9.59949 + 2.81867i) q^{78} +(8.98287 - 10.3668i) q^{79} +(0.841254 + 0.540641i) q^{80} +(5.68215 + 3.65170i) q^{81} +(-0.0236762 + 0.0273238i) q^{82} +(-0.0754484 - 0.0221536i) q^{83} +(1.75768 + 12.2250i) q^{84} +(2.88032 + 3.32406i) q^{85} +(-5.27308 - 11.5464i) q^{86} +(-20.8250 + 6.11477i) q^{87} +(-0.139753 + 0.306016i) q^{88} +(-1.30693 + 9.08988i) q^{89} +(-4.83145 + 3.10499i) q^{90} -14.1328 q^{91} +(-4.70523 + 0.927781i) q^{92} -15.7802 q^{93} +(-2.34335 + 1.50598i) q^{94} +(-0.687159 + 4.77930i) q^{95} +(-1.22833 + 2.68968i) q^{96} +(-3.45970 + 1.01586i) q^{97} +(-4.33970 - 9.50261i) q^{98} +(-1.26526 - 1.46018i) 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

Varieties

Fields

Representations

Groups

Database

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