LMFDB - Embedded newform 23.2.c.a.12.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,2,Mod(2,23)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(23, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("23.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	23.c (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:	$0.183655924649$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
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			12.1
Root			$-0.841254 + 0.540641i$ of defining polynomial
Character	$\chi$	$=$	23.12
Dual form			23.2.c.a.2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.11435 + 1.35881i) q^{2} +(-0.226900 + 1.57812i) q^{3} +(1.79329 - 3.92676i) q^{4} +(1.41899 - 0.416652i) q^{5} +(-1.66463 - 3.64502i) q^{6} +(-0.804632 - 0.928595i) q^{7} +(0.828708 + 5.76379i) q^{8} +(0.439490 + 0.129046i) q^{9} +O(q^{10})$	\(q+(-2.11435 + 1.35881i) q^{2} +(-0.226900 + 1.57812i) q^{3} +(1.79329 - 3.92676i) q^{4} +(1.41899 - 0.416652i) q^{5} +(-1.66463 - 3.64502i) q^{6} +(-0.804632 - 0.928595i) q^{7} +(0.828708 + 5.76379i) q^{8} +(0.439490 + 0.129046i) q^{9} +(-2.43409 + 2.80909i) q^{10} +(-2.98325 - 1.91722i) q^{11} +(5.79001 + 3.72101i) q^{12} +(0.0892619 - 0.103014i) q^{13} +(2.96306 + 0.870034i) q^{14} +(0.335560 + 2.33387i) q^{15} +(-3.93020 - 4.53569i) q^{16} +(-2.50680 - 5.48912i) q^{17} +(-1.10459 + 0.324336i) q^{18} +(-1.33703 + 2.92768i) q^{19} +(0.908562 - 6.31919i) q^{20} +(1.64801 - 1.05911i) q^{21} +8.91280 q^{22} +(4.66533 + 1.11118i) q^{23} -9.28400 q^{24} +(-2.36635 + 1.52076i) q^{25} +(-0.0487549 + 0.339098i) q^{26} +(-2.29032 + 5.01511i) q^{27} +(-5.08931 + 1.49436i) q^{28} +(1.90906 + 4.18027i) q^{29} +(-3.88079 - 4.47867i) q^{30} +(-0.409407 - 2.84749i) q^{31} +(3.29862 + 0.968563i) q^{32} +(3.70251 - 4.27292i) q^{33} +(12.7590 + 8.19968i) q^{34} +(-1.52866 - 0.982412i) q^{35} +(1.29487 - 1.49436i) q^{36} +(-3.73811 - 1.09761i) q^{37} +(-1.15122 - 8.00691i) q^{38} +(0.142315 + 0.164240i) q^{39} +(3.57742 + 7.83345i) q^{40} +(-0.981618 + 0.288229i) q^{41} +(-2.04534 + 4.47867i) q^{42} +(0.450518 - 3.13342i) q^{43} +(-12.8783 + 8.27638i) q^{44} +0.677398 q^{45} +(-11.3740 + 3.98989i) q^{46} +0.00935386 q^{47} +(8.04964 - 5.17319i) q^{48} +(0.781348 - 5.43439i) q^{49} +(2.93687 - 6.43084i) q^{50} +(9.23131 - 2.71056i) q^{51} +(-0.244437 - 0.535243i) q^{52} +(6.16090 + 7.11005i) q^{53} +(-1.97204 - 13.7158i) q^{54} +(-5.03201 - 1.47753i) q^{55} +(4.68542 - 5.40726i) q^{56} +(-4.31686 - 2.77428i) q^{57} +(-9.71664 - 6.24450i) q^{58} +(-3.05621 + 3.52706i) q^{59} +(9.76631 + 2.86765i) q^{60} +(1.92941 + 13.4193i) q^{61} +(4.73483 + 5.46429i) q^{62} +(-0.233797 - 0.511943i) q^{63} +(3.22640 - 0.947356i) q^{64} +(0.0837405 - 0.183366i) q^{65} +(-2.02231 + 14.0655i) q^{66} +(8.18185 - 5.25816i) q^{67} -26.0499 q^{68} +(-2.81213 + 7.11034i) q^{69} +4.56705 q^{70} +(-0.585691 + 0.376401i) q^{71} +(-0.379585 + 2.64007i) q^{72} +(-2.20482 + 4.82788i) q^{73} +(9.39514 - 2.75866i) q^{74} +(-1.86302 - 4.07944i) q^{75} +(9.09860 + 10.5003i) q^{76} +(0.620100 + 4.31289i) q^{77} +(-0.524075 - 0.153882i) q^{78} +(7.03002 - 8.11308i) q^{79} +(-7.46670 - 4.79856i) q^{80} +(-6.23879 - 4.00943i) q^{81} +(1.68384 - 1.94325i) q^{82} +(1.68020 + 0.493351i) q^{83} +(-1.20351 - 8.37062i) q^{84} +(-5.84417 - 6.74453i) q^{85} +(3.30518 + 7.23733i) q^{86} +(-7.03014 + 2.06424i) q^{87} +(8.57821 - 18.7837i) q^{88} +(1.25375 - 8.72002i) q^{89} +(-1.43226 + 0.920457i) q^{90} -0.167481 q^{91} +(12.7296 - 16.3270i) q^{92} +4.58658 q^{93} +(-0.0197774 + 0.0127101i) q^{94} +(-0.677398 + 4.71141i) q^{95} +(-2.27697 + 4.98587i) q^{96} +(-17.2863 + 5.07571i) q^{97} +(5.73228 + 12.5519i) q^{98} +(-1.06370 - 1.22758i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 7 q^{2} - 7 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 5 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) $ 10 * q - 7 * q^2 - 7 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 - 5 * q^7 + 4 * q^8 - 2 * q^9	\( 10 q - 7 q^{2} - 7 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 5 q^{7} + 4 q^{8} - 2 q^{9} + q^{10} + 7 q^{11} + 12 q^{12} - 3 q^{13} + 9 q^{14} + 12 q^{15} + q^{16} - 10 q^{17} - 14 q^{18} + 2 q^{19} - 9 q^{20} - 2 q^{21} - 6 q^{22} - 12 q^{23} - 38 q^{24} - 4 q^{25} + 12 q^{26} - 4 q^{27} + 7 q^{28} + 14 q^{29} + 7 q^{30} + 10 q^{31} + 21 q^{32} + 16 q^{33} + 29 q^{34} + 7 q^{35} + 27 q^{36} - 19 q^{37} - 8 q^{38} + q^{39} + q^{40} + 7 q^{41} - 25 q^{42} - 11 q^{43} - 34 q^{44} - 6 q^{45} - 29 q^{46} - 18 q^{47} + 18 q^{48} - 18 q^{49} + 16 q^{50} + 7 q^{51} - 20 q^{52} + 29 q^{53} - 6 q^{54} - q^{55} - 2 q^{56} - 8 q^{57} - 23 q^{58} - 21 q^{59} + 25 q^{60} + 3 q^{61} + 4 q^{62} + 34 q^{63} + 24 q^{64} + 2 q^{65} + 2 q^{66} + 45 q^{67} - 30 q^{68} + 26 q^{69} + 38 q^{70} - 14 q^{71} + 19 q^{72} + 19 q^{73} + 10 q^{74} - 28 q^{75} - 16 q^{76} + 2 q^{77} - 4 q^{78} - 15 q^{79} - 52 q^{80} - 44 q^{81} + 16 q^{82} + 18 q^{83} - 17 q^{84} - 19 q^{85} - 11 q^{86} - 23 q^{87} + 27 q^{88} + 25 q^{89} - 20 q^{90} - 4 q^{91} + 52 q^{92} + 4 q^{93} + 17 q^{94} + 6 q^{95} - 51 q^{96} - 34 q^{97} + 17 q^{98} - 30 q^{99}+O(q^{100}) \) 10 * q - 7 * q^2 - 7 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 - 5 * q^7 + 4 * q^8 - 2 * q^9 + q^10 + 7 * q^11 + 12 * q^12 - 3 * q^13 + 9 * q^14 + 12 * q^15 + q^16 - 10 * q^17 - 14 * q^18 + 2 * q^19 - 9 * q^20 - 2 * q^21 - 6 * q^22 - 12 * q^23 - 38 * q^24 - 4 * q^25 + 12 * q^26 - 4 * q^27 + 7 * q^28 + 14 * q^29 + 7 * q^30 + 10 * q^31 + 21 * q^32 + 16 * q^33 + 29 * q^34 + 7 * q^35 + 27 * q^36 - 19 * q^37 - 8 * q^38 + q^39 + q^40 + 7 * q^41 - 25 * q^42 - 11 * q^43 - 34 * q^44 - 6 * q^45 - 29 * q^46 - 18 * q^47 + 18 * q^48 - 18 * q^49 + 16 * q^50 + 7 * q^51 - 20 * q^52 + 29 * q^53 - 6 * q^54 - q^55 - 2 * q^56 - 8 * q^57 - 23 * q^58 - 21 * q^59 + 25 * q^60 + 3 * q^61 + 4 * q^62 + 34 * q^63 + 24 * q^64 + 2 * q^65 + 2 * q^66 + 45 * q^67 - 30 * q^68 + 26 * q^69 + 38 * q^70 - 14 * q^71 + 19 * q^72 + 19 * q^73 + 10 * q^74 - 28 * q^75 - 16 * q^76 + 2 * q^77 - 4 * q^78 - 15 * q^79 - 52 * q^80 - 44 * q^81 + 16 * q^82 + 18 * q^83 - 17 * q^84 - 19 * q^85 - 11 * q^86 - 23 * q^87 + 27 * q^88 + 25 * q^89 - 20 * q^90 - 4 * q^91 + 52 * q^92 + 4 * q^93 + 17 * q^94 + 6 * q^95 - 51 * q^96 - 34 * q^97 + 17 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/23\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{10}{11}\right)$

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 $

$2$	−2.11435	+	1.35881i	−1.49507	+	0.960826i	−0.499553	+	0.866283i	$0.666502\pi$
$2$	−2.11435	+	1.35881i	−1.49507	+	0.960826i	−0.995521	+	0.0945423i	$0.969861\pi$
$3$	−0.226900	+	1.57812i	−0.131001	+	0.911130i	0.813253	+	0.581910i	$0.197695\pi$
$3$	−0.226900	+	1.57812i	−0.131001	+	0.911130i	−0.944254	+	0.329219i	$0.893214\pi$
$4$	1.79329	−	3.92676i	0.896645	−	1.96338i
$5$	1.41899	−	0.416652i	0.634590	−	0.186332i	0.0514128	−	0.998677i	$-0.483628\pi$
$5$	1.41899	−	0.416652i	0.634590	−	0.186332i	0.583177	+	0.812345i	$0.301809\pi$
$6$	−1.66463	−	3.64502i	−0.679581	−	1.48808i
$7$	−0.804632	−	0.928595i	−0.304122	−	0.350976i	0.583032	−	0.812449i	$-0.301866\pi$
$7$	−0.804632	−	0.928595i	−0.304122	−	0.350976i	−0.887154	+	0.461474i	$0.847321\pi$
$8$	0.828708	+	5.76379i	0.292992	+	2.03781i
$9$	0.439490	+	0.129046i	0.146497	+	0.0430153i
$10$	−2.43409	+	2.80909i	−0.769726	+	0.888311i
$11$	−2.98325	−	1.91722i	−0.899485	−	0.578064i	0.00715262	−	0.999974i	$-0.497723\pi$
$11$	−2.98325	−	1.91722i	−0.899485	−	0.578064i	−0.906637	+	0.421911i	$0.861360\pi$
$12$	5.79001	+	3.72101i	1.67143	+	1.07416i
$13$	0.0892619	−	0.103014i	0.0247568	−	0.0285709i	−0.743236	−	0.669029i	$-0.766710\pi$
$13$	0.0892619	−	0.103014i	0.0247568	−	0.0285709i	0.767993	+	0.640458i	$0.221256\pi$
$14$	2.96306	+	0.870034i	0.791912	+	0.232526i
$15$	0.335560	+	2.33387i	0.0866413	+	0.602603i
$16$	−3.93020	−	4.53569i	−0.982550	−	1.13392i
$17$	−2.50680	−	5.48912i	−0.607988	−	1.33131i	−0.923942	−	0.382534i	$-0.875052\pi$
$17$	−2.50680	−	5.48912i	−0.607988	−	1.33131i	0.315953	−	0.948775i	$-0.397676\pi$
$18$	−1.10459	+	0.324336i	−0.260354	+	0.0764468i
$19$	−1.33703	+	2.92768i	−0.306735	+	0.671655i	−0.998737	−	0.0502399i	$-0.984001\pi$
$19$	−1.33703	+	2.92768i	−0.306735	+	0.671655i	0.692003	+	0.721895i	$0.256729\pi$
$20$	0.908562	−	6.31919i	0.203161	−	1.41301i
$21$	1.64801	−	1.05911i	0.359625	−	0.231117i
$22$	8.91280			1.90021
$23$	4.66533	+	1.11118i	0.972788	+	0.231696i
$23$	4.66533	+	1.11118i	0.972788	+	0.231696i
$24$	−9.28400			−1.89509
$25$	−2.36635	+	1.52076i	−0.473269	+	0.304152i
$26$	−0.0487549	+	0.339098i	−0.00956162	+	0.0665025i
$27$	−2.29032	+	5.01511i	−0.440773	+	0.965158i
$28$	−5.08931	+	1.49436i	−0.961788	+	0.282407i
$29$	1.90906	+	4.18027i	0.354504	+	0.776256i	0.999923	+	0.0124270i	$0.00395575\pi$
$29$	1.90906	+	4.18027i	0.354504	+	0.776256i	−0.645418	+	0.763829i	$0.723317\pi$
$30$	−3.88079	−	4.47867i	−0.708532	−	0.817689i
$31$	−0.409407	−	2.84749i	−0.0735316	−	0.511424i	−0.992986	−	0.118228i	$-0.962279\pi$
$31$	−0.409407	−	2.84749i	−0.0735316	−	0.511424i	0.919455	−	0.393196i	$-0.128631\pi$
$32$	3.29862	+	0.968563i	0.583120	+	0.171219i
$33$	3.70251	−	4.27292i	0.644524	−	0.743821i
$34$	12.7590	+	8.19968i	2.18814	+	1.40623i
$35$	−1.52866	−	0.982412i	−0.258391	−	0.166058i
$36$	1.29487	−	1.49436i	0.215811	−	0.249059i
$37$	−3.73811	−	1.09761i	−0.614542	−	0.180446i	−0.0403759	−	0.999185i	$-0.512856\pi$
$37$	−3.73811	−	1.09761i	−0.614542	−	0.180446i	−0.574166	+	0.818739i	$0.694674\pi$
$38$	−1.15122	−	8.00691i	−0.186753	−	1.29889i
$39$	0.142315	+	0.164240i	0.0227886	+	0.0262995i
$40$	3.57742	+	7.83345i	0.565639	+	1.23858i
$41$	−0.981618	+	0.288229i	−0.153303	+	0.0450138i	−0.357484	−	0.933919i	$-0.616365\pi$
$41$	−0.981618	+	0.288229i	−0.153303	+	0.0450138i	0.204181	+	0.978933i	$0.434547\pi$
$42$	−2.04534	+	4.47867i	−0.315603	+	0.691074i
$43$	0.450518	−	3.13342i	0.0687034	−	0.477842i	−0.926202	−	0.377028i	$-0.876946\pi$
$43$	0.450518	−	3.13342i	0.0687034	−	0.477842i	0.994905	−	0.100814i	$-0.0321448\pi$
$44$	−12.8783	+	8.27638i	−1.94148	+	1.24771i
$45$	0.677398			0.100981
$46$	−11.3740	+	3.98989i	−1.67701	+	0.588277i
$47$	0.00935386			0.00136440			0.000682200	−	1.00000i	$-0.499783\pi$
$47$	0.00935386			0.00136440			0.000682200		1.00000i	$0.499783\pi$
$48$	8.04964	−	5.17319i	1.16187	−	0.746686i
$49$	0.781348	−	5.43439i	0.111621	−	0.776342i
$50$	2.93687	−	6.43084i	0.415336	−	0.909458i
$51$	9.23131	−	2.71056i	1.29264	−	0.379554i
$52$	−0.244437	−	0.535243i	−0.0338974	−	0.0742249i
$53$	6.16090	+	7.11005i	0.846264	+	0.976641i	0.999934	−	0.0114813i	$-0.00365468\pi$
$53$	6.16090	+	7.11005i	0.846264	+	0.976641i	−0.153670	+	0.988122i	$0.549109\pi$
$54$	−1.97204	−	13.7158i	−0.268360	−	1.86649i
$55$	−5.03201	−	1.47753i	−0.678516	−	0.199230i
$56$	4.68542	−	5.40726i	0.626116	−	0.722576i
$57$	−4.31686	−	2.77428i	−0.571783	−	0.367462i
$58$	−9.71664	−	6.24450i	−1.27586	−	0.819944i
$59$	−3.05621	+	3.52706i	−0.397885	+	0.459184i	−0.918974	−	0.394319i	$-0.870981\pi$
$59$	−3.05621	+	3.52706i	−0.397885	+	0.459184i	0.521089	+	0.853502i	$0.325526\pi$
$60$	9.76631	+	2.86765i	1.26082	+	0.370212i
$61$	1.92941	+	13.4193i	0.247036	+	1.71817i	0.615167	+	0.788397i	$0.289088\pi$
$61$	1.92941	+	13.4193i	0.247036	+	1.71817i	−0.368132	+	0.929774i	$0.620002\pi$
$62$	4.73483	+	5.46429i	0.601324	+	0.693965i
$63$	−0.233797	−	0.511943i	−0.0294556	−	0.0644988i
$64$	3.22640	−	0.947356i	0.403300	−	0.118419i
$65$	0.0837405	−	0.183366i	0.0103867	−	0.0227438i
$66$	−2.02231	+	14.0655i	−0.248929	+	1.73134i
$67$	8.18185	−	5.25816i	0.999572	−	0.642386i	0.0648980	−	0.997892i	$-0.479328\pi$
$67$	8.18185	−	5.25816i	0.999572	−	0.642386i	0.934674	+	0.355506i	$0.115691\pi$
$68$	−26.0499			−3.15901
$69$	−2.81213	+	7.11034i	−0.338541	+	0.855984i
$70$	4.56705			0.545867
$71$	−0.585691	+	0.376401i	−0.0695087	+	0.0446705i	−0.574934	−	0.818200i	$-0.694972\pi$
$71$	−0.585691	+	0.376401i	−0.0695087	+	0.0446705i	0.505425	+	0.862871i	$0.331336\pi$
$72$	−0.379585	+	2.64007i	−0.0447345	+	0.311135i
$73$	−2.20482	+	4.82788i	−0.258055	+	0.565061i	−0.993670	−	0.112339i	$-0.964166\pi$
$73$	−2.20482	+	4.82788i	−0.258055	+	0.565061i	0.735615	+	0.677399i	$0.236893\pi$
$74$	9.39514	−	2.75866i	1.09216	−	0.320688i
$75$	−1.86302	−	4.07944i	−0.215123	−	0.471054i
$76$	9.09860	+	10.5003i	1.04368	+	1.20447i
$77$	0.620100	+	4.31289i	0.0706670	+	0.491500i
$78$	−0.524075	−	0.153882i	−0.0593399	−	0.0174238i
$79$	7.03002	−	8.11308i	0.790939	−	0.912792i	−0.206909	−	0.978360i	$-0.566340\pi$
$79$	7.03002	−	8.11308i	0.790939	−	0.912792i	0.997848	+	0.0655679i	$0.0208859\pi$
$80$	−7.46670	−	4.79856i	−0.834803	−	0.536495i
$81$	−6.23879	−	4.00943i	−0.693199	−	0.445492i
$82$	1.68384	−	1.94325i	0.185949	−	0.214596i
$83$	1.68020	+	0.493351i	0.184426	+	0.0541523i	0.372641	−	0.927975i	$-0.378452\pi$
$83$	1.68020	+	0.493351i	0.184426	+	0.0541523i	−0.188216	+	0.982128i	$0.560270\pi$
$84$	−1.20351	−	8.37062i	−0.131314	−	0.913309i
$85$	−5.84417	−	6.74453i	−0.633889	−	0.731547i
$86$	3.30518	+	7.23733i	0.356407	+	0.780421i
$87$	−7.03014	+	2.06424i	−0.753710	+	0.221309i
$88$	8.57821	−	18.7837i	0.914440	−	2.00234i
$89$	1.25375	−	8.72002i	0.132897	−	0.924321i	−0.808854	−	0.588010i	$-0.799912\pi$
$89$	1.25375	−	8.72002i	0.132897	−	0.924321i	0.941751	−	0.336311i	$-0.109179\pi$
$90$	−1.43226	+	0.920457i	−0.150973	+	0.0970247i
$91$	−0.167481			−0.0175568
$92$	12.7296	−	16.3270i	1.32715	−	1.70220i
$93$	4.58658			0.475606
$94$	−0.0197774	+	0.0127101i	−0.00203988	+	0.00131095i
$95$	−0.677398	+	4.71141i	−0.0694996	+	0.483380i
$96$	−2.27697	+	4.98587i	−0.232392	+	0.508868i
$97$	−17.2863	+	5.07571i	−1.75516	+	0.515360i	−0.991482	−	0.130242i	$-0.958425\pi$
$97$	−17.2863	+	5.07571i	−1.75516	+	0.515360i	−0.763674	+	0.645602i	$0.776606\pi$
$98$	5.73228	+	12.5519i	0.579048	+	1.26794i
$99$	−1.06370	−	1.22758i	−0.106906	−	0.123376i
$100$	1.72810	+	12.0192i	0.172810	+	1.20192i
$101$	1.24246	+	0.364820i	0.123630	+	0.0363009i	0.342962	−	0.939349i	$-0.388570\pi$
$101$	1.24246	+	0.364820i	0.123630	+	0.0363009i	−0.219333	+	0.975650i	$0.570388\pi$
$102$	−15.8351	+	18.2747i	−1.56791	+	1.80946i
$103$	−3.19601	−	2.05395i	−0.314912	−	0.202382i	0.373631	−	0.927578i	$-0.378113\pi$
$103$	−3.19601	−	2.05395i	−0.314912	−	0.202382i	−0.688543	+	0.725196i	$0.741749\pi$
$104$	0.667721	+	0.429119i	0.0654755	+	0.0420785i
$105$	1.89722	−	2.18951i	0.185150	−	0.213674i
$106$	−22.6875	−	6.66166i	−2.20361	−	0.647038i
$107$	−0.815153	−	5.66952i	−0.0788038	−	0.548093i	−0.990530	−	0.137295i	$-0.956159\pi$
$107$	−0.815153	−	5.66952i	−0.0788038	−	0.548093i	0.911726	−	0.410798i	$-0.134750\pi$
$108$	15.5859	+	17.9871i	1.49975	+	1.73081i
$109$	−0.579577	−	1.26910i	−0.0555134	−	0.121557i	0.879843	−	0.475265i	$-0.157648\pi$
$109$	−0.579577	−	1.26910i	−0.0555134	−	0.121557i	−0.935356	+	0.353708i	$0.884921\pi$
$110$	12.6471	−	3.71353i	1.20586	−	0.354072i
$111$	2.58034	−	5.65016i	0.244915	−	0.536289i
$112$	−1.04946	+	7.29913i	−0.0991643	+	0.689703i
$113$	4.37102	−	2.80909i	0.411191	−	0.264257i	−0.318651	−	0.947872i	$-0.603230\pi$
$113$	4.37102	−	2.80909i	0.411191	−	0.264257i	0.729842	+	0.683616i	$0.239593\pi$
$114$	12.8971			1.20792
$115$	7.08301	−	0.367076i	0.660494	−	0.0342300i
$116$	19.8384			1.84195
$117$	0.0525233	−	0.0337547i	0.00485578	−	0.00312062i
$118$	1.66930	−	11.6103i	0.153672	−	1.06881i
$119$	−3.08012	+	6.74453i	−0.282354	+	0.618270i
$120$	−13.1739	+	3.86820i	−1.20260	+	0.353116i
$121$	0.654502	+	1.43316i	0.0595002	+	0.130287i
$122$	−22.3138	−	25.7515i	−2.02020	−	2.33143i
$123$	−0.232132	−	1.61451i	−0.0209306	−	0.145576i
$124$	−11.9156	−	3.49873i	−1.07005	−	0.314195i
$125$	−7.56652	+	8.73223i	−0.676770	+	0.781035i
$126$	1.18996	+	0.764743i	0.106010	+	0.0681287i
$127$	16.5455	+	10.6332i	1.46818	+	0.943542i	0.998144	+	0.0608938i	$0.0193951\pi$
$127$	16.5455	+	10.6332i	1.46818	+	0.943542i	0.470035	+	0.882648i	$0.344241\pi$
$128$	−10.0371	+	11.5835i	−0.887166	+	1.02384i
$129$	4.84270	+	1.42195i	0.426376	+	0.125195i
$130$	0.0721032	+	0.501489i	0.00632387	+	0.0439835i
$131$	4.58349	+	5.28962i	0.400461	+	0.462157i	0.919786	−	0.392420i	$-0.128362\pi$
$131$	4.58349	+	5.28962i	0.400461	+	0.462157i	−0.519325	+	0.854577i	$0.673817\pi$
$132$	−10.1391	−	22.2014i	−0.882492	−	1.93239i
$133$	3.79444	−	1.11415i	0.329020	−	0.0966089i
$134$	−10.1545	+	22.2352i	−0.877213	+	1.92083i
$135$	−1.16038	+	8.07063i	−0.0998698	+	0.694610i
$136$	29.5607	−	18.9975i	2.53481	−	1.62903i
$137$	12.3878			1.05836			0.529180	−	0.848510i	$-0.322500\pi$
$137$	12.3878			1.05836			0.529180	+	0.848510i	$0.322500\pi$
$138$	−3.71577	−	18.8549i	−0.316307	−	1.60504i
$139$	−12.5126			−1.06131			−0.530654	−	0.847589i	$-0.678054\pi$
$139$	−12.5126			−1.06131			−0.530654	+	0.847589i	$0.678054\pi$
$140$	−6.59903	+	4.24094i	−0.557720	+	0.358425i
$141$	−0.00212239	+	0.0147615i	−0.000178737	+	0.00124315i
$142$	0.726900	−	1.59169i	0.0610001	−	0.133572i
$143$	−0.463791	+	0.136181i	−0.0387842	+	0.0113881i
$144$	−1.14197	−	2.50057i	−0.0951644	−	0.208381i
$145$	4.45065	+	5.13633i	0.369607	+	0.426549i
$146$	−1.89842	−	13.2038i	−0.157114	−	1.09275i
$147$	8.39886	+	2.46613i	0.692726	+	0.203403i
$148$	−11.0136	+	12.7103i	−0.905310	+	1.04478i
$149$	−2.99653	−	1.92575i	−0.245485	−	0.157764i	0.412113	−	0.911133i	$-0.364791\pi$
$149$	−2.99653	−	1.92575i	−0.245485	−	0.157764i	−0.657598	+	0.753369i	$0.728427\pi$
$150$	9.48228	+	6.09389i	0.774225	+	0.497564i
$151$	3.67654	−	4.24295i	0.299192	−	0.345286i	−0.586170	−	0.810188i	$-0.699365\pi$
$151$	3.67654	−	4.24295i	0.299192	−	0.345286i	0.885362	+	0.464902i	$0.153910\pi$
$152$	−17.9825	−	5.28014i	−1.45857	−	0.428276i
$153$	−0.393365	−	2.73591i	−0.0318016	−	0.221185i
$154$	−7.17152	−	8.27638i	−0.577898	−	0.666930i
$155$	−1.76735	−	3.86996i	−0.141957	−	0.310843i
$156$	0.900143	−	0.264306i	0.0720691	−	0.0211614i
$157$	6.05902	−	13.2674i	0.483563	−	1.05885i	−0.497906	−	0.867231i	$-0.665897\pi$
$157$	6.05902	−	13.2674i	0.483563	−	1.05885i	0.981469	−	0.191623i	$-0.0613752\pi$
$158$	−3.83980	+	26.7064i	−0.305478	+	2.12465i
$159$	−12.6184	+	8.10938i	−1.00071	+	0.643116i
$160$	5.08426			0.401946
$161$	−2.72204	−	5.22629i	−0.214527	−	0.411889i
$162$	18.6391			1.46442
$163$	10.4067	−	6.68797i	0.815115	−	0.523843i	−0.0654010	−	0.997859i	$-0.520833\pi$
$163$	10.4067	−	6.68797i	0.815115	−	0.523843i	0.880516	+	0.474016i	$0.157196\pi$
$164$	−0.628520	+	4.37145i	−0.0490792	+	0.341353i
$165$	3.47349	−	7.60588i	0.270411	−	0.592117i
$166$	−4.22290	+	1.23996i	−0.327761	+	0.0962393i
$167$	−4.90552	−	10.7416i	−0.379601	−	0.831209i	−0.998938	−	0.0460841i	$-0.985326\pi$
$167$	−4.90552	−	10.7416i	−0.379601	−	0.831209i	0.619337	−	0.785125i	$-0.287401\pi$
$168$	7.47021	+	8.62108i	0.576339	+	0.665131i
$169$	1.84745	+	12.8493i	0.142111	+	0.988407i
$170$	21.5212	+	6.31919i	1.65060	+	0.484660i
$171$	−0.965415	+	1.11415i	−0.0738271	+	0.0852010i
$172$	−11.4963	−	7.38821i	−0.876583	−	0.563346i
$173$	−2.05672	−	1.32177i	−0.156370	−	0.100493i	0.460116	−	0.887859i	$-0.347808\pi$
$173$	−2.05672	−	1.32177i	−0.156370	−	0.100493i	−0.616486	+	0.787366i	$0.711444\pi$
$174$	12.0593	−	13.9172i	0.914213	−	1.05506i
$175$	3.31621	+	0.973726i	0.250682	+	0.0736068i
$176$	3.02886	+	21.0662i	0.228309	+	1.58792i
$177$	−4.87267	−	5.62337i	−0.366253	−	0.422678i
$178$	9.19801	+	20.1408i	0.689420	+	1.50962i
$179$	−20.7763	+	6.10048i	−1.55290	+	0.455972i	−0.941965	−	0.335712i	$-0.891023\pi$
$179$	−20.7763	+	6.10048i	−1.55290	+	0.455972i	−0.610932	+	0.791683i	$0.709205\pi$
$180$	1.21477	−	2.65998i	0.0905437	−	0.198263i
$181$	0.210389	−	1.46329i	0.0156381	−	0.108766i	−0.980507	−	0.196483i	$-0.937048\pi$
$181$	0.210389	−	1.46329i	0.0156381	−	0.108766i	0.996145	+	0.0877171i	$0.0279572\pi$
$182$	0.354114	−	0.227575i	0.0262487	−	0.0168690i
$183$	−21.6151			−1.59784
$184$	−2.53838	+	27.8108i	−0.187132	+	2.05024i
$185$	−5.76165			−0.423605
$186$	−9.69765	+	6.23230i	−0.711066	+	0.456975i
$187$	−3.04545	+	21.1815i	−0.222705	+	1.54895i
$188$	0.0167742	−	0.0367303i	0.00122338	−	0.00267883i
$189$	6.49987	−	1.90853i	0.472796	−	0.138825i
$190$	−4.96966	−	10.8820i	−0.360537	−	0.789466i
$191$	−7.45216	−	8.60025i	−0.539219	−	0.622292i	0.419118	−	0.907932i	$-0.362339\pi$
$191$	−7.45216	−	8.60025i	−0.539219	−	0.622292i	−0.958337	+	0.285640i	$0.907794\pi$
$192$	0.762975	+	5.30661i	0.0550630	+	0.382971i
$193$	−1.60409	−	0.471002i	−0.115465	−	0.0339035i	0.223490	−	0.974706i	$-0.428255\pi$
$193$	−1.60409	−	0.471002i	−0.115465	−	0.0339035i	−0.338954	+	0.940803i	$0.610073\pi$
$194$	29.6524	−	34.2207i	2.12892	−	2.45690i
$195$	0.270374	+	0.173759i	0.0193619	+	0.0124431i
$196$	−19.9384	−	12.8136i	−1.42417	−	0.915258i
$197$	10.0068	−	11.5485i	0.712957	−	0.822796i	−0.277485	−	0.960730i	$-0.589501\pi$
$197$	10.0068	−	11.5485i	0.712957	−	0.822796i	0.990441	+	0.137934i	$0.0440462\pi$
$198$	3.91709	+	1.15016i	0.278375	+	0.0817384i
$199$	−0.539112	−	3.74960i	−0.0382166	−	0.265802i	0.961750	−	0.273927i	$-0.0883228\pi$
$199$	−0.539112	−	3.74960i	−0.0382166	−	0.265802i	−0.999967	+	0.00812498i	$0.997414\pi$
$200$	−10.7263	−	12.3788i	−0.758466	−	0.875317i
$201$	6.44156	+	14.1050i	0.454352	+	0.994893i
$202$	−3.12272	+	0.916915i	−0.219714	+	0.0645139i
$203$	2.34568	−	5.13633i	0.164635	−	0.360499i
$204$	5.91071	−	41.1099i	0.413833	−	2.87827i
$205$	−1.27281	+	0.817986i	−0.0888970	+	0.0571306i
$206$	9.54842			0.665270
$207$	1.90697	+	1.09039i	0.132544	+	0.0757875i
$208$	−0.818056			−0.0567220
$209$	9.60169	−	6.17063i	0.664163	−	0.426831i
$210$	−1.03626	+	7.20736i	−0.0715089	+	0.497355i
$211$	1.01253	−	2.21713i	0.0697054	−	0.152634i	−0.871572	−	0.490267i	$-0.836899\pi$
$211$	1.01253	−	2.21713i	0.0697054	−	0.152634i	0.941278	+	0.337634i	$0.109626\pi$
$212$	38.9677	−	11.4420i	2.67631	−	0.785837i
$213$	−0.461113	−	1.00970i	−0.0315950	−	0.0691833i
$214$	9.42733	+	10.8797i	0.644439	+	0.743722i
$215$	−0.666267	−	4.63399i	−0.0454390	−	0.316036i
$216$	−30.8040	−	9.04488i	−2.09595	−	0.615426i
$217$	−2.31474	+	2.67135i	−0.157135	+	0.181343i
$218$	2.94989	+	1.89578i	0.199792	+	0.128399i
$219$	−7.11872	−	4.57492i	−0.481038	−	0.309145i
$220$	−14.8258	+	17.1098i	−0.999552	+	1.15354i
$221$	−0.789217	−	0.231735i	−0.0530885	−	0.0155882i
$222$	2.22175	+	15.4526i	0.149114	+	1.03711i
$223$	9.24303	+	10.6670i	0.618959	+	0.714317i	0.975509	−	0.219959i	$-0.0705924\pi$
$223$	9.24303	+	10.6670i	0.618959	+	0.714317i	−0.356550	+	0.934276i	$0.616047\pi$
$224$	−1.75478	−	3.84242i	−0.117246	−	0.256733i
$225$	−1.23623	+	0.362991i	−0.0824156	+	0.0241994i
$226$	−5.42487	+	11.8788i	−0.360857	+	0.790166i
$227$	−2.01729	+	14.0305i	−0.133892	+	0.931239i	0.806521	+	0.591205i	$0.201348\pi$
$227$	−2.01729	+	14.0305i	−0.133892	+	0.931239i	−0.940413	+	0.340034i	$0.889561\pi$
$228$	−18.6353	+	11.9762i	−1.23415	+	0.793142i
$229$	−15.9629			−1.05486			−0.527428	−	0.849600i	$-0.676844\pi$
$229$	−15.9629			−1.05486			−0.527428	+	0.849600i	$0.676844\pi$
$230$	−14.4772	+	10.4006i	−0.954598	+	0.685796i
$231$	−6.94697			−0.457077
$232$	−22.5121	+	14.4677i	−1.47799	+	0.949849i
$233$	2.87393	−	19.9886i	0.188277	−	1.30950i	−0.648189	−	0.761480i	$-0.724473\pi$
$233$	2.87393	−	19.9886i	0.188277	−	1.30950i	0.836466	−	0.548019i	$-0.184618\pi$
$234$	−0.0651865	+	0.142739i	−0.00426138	+	0.00933111i
$235$	0.0132730	−	0.00389730i	0.000865835	−	0.000254232i
$236$	8.36922	+	18.3260i	0.544790	+	1.19292i
$237$	11.2083	+	12.9351i	0.728059	+	0.840224i
$238$	−2.65208	−	18.4456i	−0.171909	−	1.19565i
$239$	20.3406	+	5.97254i	1.31572	+	0.386331i	0.862948	−	0.505293i	$-0.168616\pi$
$239$	20.3406	+	5.97254i	1.31572	+	0.386331i	0.452776	+	0.891624i	$0.350434\pi$
$240$	9.26691	−	10.6946i	0.598177	−	0.690333i
$241$	18.8313	+	12.1021i	1.21303	+	0.779567i	0.981163	−	0.193181i	$-0.0618803\pi$
$241$	18.8313	+	12.1021i	1.21303	+	0.779567i	0.231867	+	0.972748i	$0.425517\pi$
$242$	−3.33124	−	2.14086i	−0.214140	−	0.137620i
$243$	−3.08846	+	3.56427i	−0.198125	+	0.228648i
$244$	56.1545	+	16.4884i	3.59492	+	1.05556i
$245$	−1.15553	−	8.03688i	−0.0738240	−	0.513457i
$246$	2.68463	+	3.09823i	0.171166	+	0.197536i
$247$	0.182246	+	0.399062i	0.0115960	+	0.0253917i
$248$	16.0730	−	4.71947i	1.02064	−	0.299687i
$249$	−1.15980	+	2.53962i	−0.0734996	+	0.160942i
$250$	4.13284	−	28.7445i	0.261384	−	1.81796i
$251$	−16.9509	+	10.8937i	−1.06993	+	0.687601i	−0.952210	−	0.305446i	$-0.901195\pi$
$251$	−16.9509	+	10.8937i	−1.06993	+	0.687601i	−0.117719	+	0.993047i	$0.537558\pi$
$252$	−2.42954			−0.153047
$253$	−11.7875	−	12.2594i	−0.741073	−	0.770741i
$254$	−49.4316			−3.10162
$255$	11.9697	−	7.69248i	0.749574	−	0.481722i
$256$	4.52519	−	31.4734i	0.282824	−	1.96709i
$257$	0.868886	−	1.90260i	0.0541996	−	0.118681i	−0.880595	−	0.473870i	$-0.842856\pi$
$257$	0.868886	−	1.90260i	0.0541996	−	0.118681i	0.934794	+	0.355190i	$0.115584\pi$
$258$	−12.1713	+	3.57383i	−0.757755	+	0.222497i
$259$	1.98857	+	4.35437i	0.123564	+	0.270567i
$260$	−0.569863	−	0.657657i	−0.0353414	−	0.0407862i
$261$	0.299569	+	2.08354i	0.0185428	+	0.128968i
$262$	−16.8787	−	4.95604i	−1.04277	−	0.306185i
$263$	−3.70302	+	4.27351i	−0.228338	+	0.263516i	−0.858344	−	0.513074i	$-0.828507\pi$
$263$	−3.70302	+	4.27351i	−0.228338	+	0.263516i	0.630007	+	0.776590i	$0.283052\pi$
$264$	27.6965	+	17.7995i	1.70460	+	1.09548i
$265$	11.7046	+	7.52212i	0.719010	+	0.462080i
$266$	−6.50887	+	7.51164i	−0.399084	+	0.460568i
$267$	13.4768	+	3.95714i	0.824766	+	0.242173i
$268$	−5.97507	−	41.5575i	−0.364986	−	2.53853i
$269$	−18.6359	−	21.5070i	−1.13625	−	1.31131i	−0.943994	−	0.329963i	$-0.892964\pi$
$269$	−18.6359	−	21.5070i	−1.13625	−	1.31131i	−0.192260	−	0.981344i	$-0.561582\pi$
$270$	−8.51302	−	18.6409i	−0.518086	−	1.13445i
$271$	27.6649	−	8.12315i	1.68052	−	0.493446i	0.704244	−	0.709958i	$-0.251286\pi$
$271$	27.6649	−	8.12315i	1.68052	−	0.493446i	0.976280	+	0.216512i	$0.0694680\pi$
$272$	−15.0448	+	32.9434i	−0.912223	+	1.99749i
$273$	0.0380014	−	0.264306i	0.00229995	−	0.0159965i
$274$	−26.1922	+	16.8327i	−1.58233	+	1.01690i
$275$	9.97504			0.601517
$276$	22.8776	+	23.7935i	1.37707	+	1.43220i
$277$	−1.64325			−0.0987332			−0.0493666	−	0.998781i	$-0.515720\pi$
$277$	−1.64325			−0.0987332			−0.0493666	+	0.998781i	$0.515720\pi$
$278$	26.4561	−	17.0023i	1.58673	−	1.01973i
$279$	0.187527	−	1.30428i	0.0112269	−	0.0780849i
$280$	4.39560	−	9.62502i	0.262687	−	0.575205i
$281$	−24.8545	+	7.29795i	−1.48270	+	0.435359i	−0.920203	−	0.391442i	$-0.871976\pi$
$281$	−24.8545	+	7.29795i	−1.48270	+	0.435359i	−0.562494	+	0.826801i	$0.690158\pi$
$282$	−0.0155707	−	0.0340950i	−0.000927221	−	0.00203033i
$283$	−9.28827	−	10.7192i	−0.552130	−	0.637192i	0.409248	−	0.912423i	$-0.365791\pi$
$283$	−9.28827	−	10.7192i	−0.552130	−	0.637192i	−0.961378	+	0.275231i	$0.911246\pi$
$284$	0.427721	+	2.97486i	0.0253805	+	0.176526i
$285$	−7.28148	−	2.13803i	−0.431317	−	0.126646i
$286$	0.795573	−	0.918141i	0.0470432	−	0.0542908i
$287$	1.05749	+	0.679607i	0.0624216	+	0.0401159i
$288$	1.32472	+	0.851349i	0.0780601	+	0.0501662i
$289$	−12.7138	+	14.6725i	−0.747872	+	0.863090i
$290$	−16.3896	−	4.81241i	−0.962428	−	0.282594i
$291$	−4.08784	−	28.4316i	−0.239633	−	1.66669i
$292$	15.0040	+	17.3156i	0.878045	+	1.01332i
$293$	9.52164	+	20.8495i	0.556260	+	1.21804i	0.953797	+	0.300453i	$0.0971380\pi$
$293$	9.52164	+	20.8495i	0.556260	+	1.21804i	−0.397536	+	0.917586i	$0.630135\pi$
$294$	−21.1092	+	6.19821i	−1.23111	+	0.361487i
$295$	−2.86717	+	6.27822i	−0.166933	+	0.365532i
$296$	3.22858	−	22.4553i	0.187658	−	1.30519i
$297$	16.4477	−	10.5703i	0.954391	−	0.613350i
$298$	8.95245			0.518602
$299$	0.530902	−	0.381407i	0.0307029	−	0.0220574i
$300$	−19.3599			−1.11775
$301$	−3.27218	+	2.10290i	−0.188605	+	0.121209i
$302$	−2.00813	+	13.9668i	−0.115555	+	0.803700i
$303$	−0.857645	+	1.87798i	−0.0492704	+	0.107887i
$304$	18.5338	−	5.44202i	1.06299	−	0.312121i
$305$	8.32900	+	18.2380i	0.476917	+	1.04430i
$306$	4.54930	+	5.25017i	0.260066	+	0.300132i
$307$	−0.574582	−	3.99630i	−0.0327931	−	0.228081i	0.966833	−	0.255408i	$-0.0822097\pi$
$307$	−0.574582	−	3.99630i	−0.0327931	−	0.228081i	−0.999627	+	0.0273266i	$0.991301\pi$
$308$	18.0477	+	5.29928i	1.02836	+	0.301955i
$309$	3.96656	−	4.57765i	0.225650	−	0.260414i
$310$	8.99537	+	5.78097i	0.510903	+	0.328337i
$311$	−0.708410	−	0.455267i	−0.0401702	−	0.0258158i	0.520402	−	0.853922i	$-0.325782\pi$
$311$	−0.708410	−	0.455267i	−0.0401702	−	0.0258158i	−0.560572	+	0.828106i	$0.689419\pi$
$312$	−0.828708	+	0.956380i	−0.0469163	+	0.0541443i
$313$	−25.6293	−	7.52544i	−1.44865	−	0.425363i	−0.539557	−	0.841949i	$-0.681408\pi$
$313$	−25.6293	−	7.52544i	−1.44865	−	0.425363i	−0.909096	+	0.416586i	$0.863226\pi$
$314$	5.21701	+	36.2851i	0.294413	+	2.04769i
$315$	−0.545056	−	0.629028i	−0.0307104	−	0.0354417i
$316$	−19.2512	−	42.1543i	−1.08297	−	2.37136i
$317$	−1.23027	+	0.361241i	−0.0690991	+	0.0202893i	−0.316099	−	0.948726i	$-0.602373\pi$
$317$	−1.23027	+	0.361241i	−0.0690991	+	0.0202893i	0.247000	+	0.969015i	$0.420555\pi$
$318$	15.6607	−	34.2922i	0.878210	−	1.92301i
$319$	2.31927	−	16.1309i	0.129854	−	0.903157i
$320$	4.18350	−	2.68857i	0.233865	−	0.150296i
$321$	9.13215			0.509707
$322$	12.8569	+	7.35148i	0.716487	+	0.409682i
$323$	19.4220			1.08067
$324$	−26.9320	+	17.3081i	−1.49622	+	0.961564i
$325$	−0.0545656	+	0.379512i	−0.00302675	+	0.0210515i
$326$	−12.9157	+	28.2815i	−0.715336	+	1.56637i
$327$	2.13430	−	0.626686i	0.118027	−	0.0346558i
$328$	−2.47477	−	5.41898i	−0.136646	−	0.299213i
$329$	−0.00752642	−	0.00868595i	−0.000414945	−	0.000478872i
$330$	2.99078	+	20.8013i	0.164637	+	1.14508i
$331$	−3.33242	−	0.978486i	−0.183166	−	0.0537825i	0.188863	−	0.982003i	$-0.439520\pi$
$331$	−3.33242	−	0.978486i	−0.183166	−	0.0537825i	−0.372029	+	0.928221i	$0.621338\pi$
$332$	4.95035	−	5.71301i	0.271686	−	0.313542i
$333$	−1.50122	−	0.964778i	−0.0822665	−	0.0528695i
$334$	24.9678	+	16.0458i	1.36618	+	0.877989i
$335$	9.41911	−	10.8702i	0.514621	−	0.593904i
$336$	−11.2808	−	3.31234i	−0.615418	−	0.180703i
$337$	2.65405	+	18.4593i	0.144575	+	1.00554i	0.924911	+	0.380183i	$0.124139\pi$
$337$	2.65405	+	18.4593i	0.144575	+	1.00554i	−0.780336	+	0.625360i	$0.784952\pi$
$338$	−21.3659	−	24.6576i	−1.16215	−	1.34120i
$339$	3.44130	+	7.53539i	0.186906	+	0.409266i
$340$	−36.9644	+	10.8537i	−2.00468	+	0.588626i
$341$	−4.23790	+	9.27970i	−0.229495	+	0.502524i
$342$	0.527310	−	3.66752i	0.0285137	−	0.198317i
$343$	−12.9106	+	8.29716i	−0.697109	+	0.448004i
$344$	18.4337			0.993880
$345$	−1.02784	+	11.2611i	−0.0553372	+	0.606280i
$346$	6.14468			0.330340
$347$	−12.1831	+	7.82962i	−0.654025	+	0.420316i	−0.825135	−	0.564936i	$-0.808901\pi$
$347$	−12.1831	+	7.82962i	−0.654025	+	0.420316i	0.171110	+	0.985252i	$0.445265\pi$
$348$	−4.50133	+	31.3074i	−0.241297	+	1.67825i
$349$	11.7770	−	25.7880i	0.630407	−	1.38040i	−0.277296	−	0.960785i	$-0.589438\pi$
$349$	11.7770	−	25.7880i	0.630407	−	1.38040i	0.907703	−	0.419614i	$-0.137835\pi$
$350$	−8.33474	+	2.44730i	−0.445511	+	0.130814i
$351$	0.312186	+	0.683593i	0.0166633	+	0.0364875i
$352$	−7.98368	−	9.21366i	−0.425532	−	0.491090i
$353$	1.58229	+	11.0051i	0.0842170	+	0.585742i	0.987610	+	0.156928i	$0.0501592\pi$
$353$	1.58229	+	11.0051i	0.0842170	+	0.585742i	−0.903393	+	0.428813i	$0.858932\pi$
$354$	17.9437	+	5.26873i	0.953695	+	0.280030i
$355$	−0.674259	+	0.778137i	−0.0357860	+	0.0412992i
$356$	−31.9931	−	20.5607i	−1.69563	−	1.08972i
$357$	−9.94482	−	6.39114i	−0.526335	−	0.338255i
$358$	35.6391	−	41.1297i	1.88359	−	2.17377i
$359$	3.68663	+	1.08249i	0.194573	+	0.0571317i	0.377567	−	0.925982i	$-0.376761\pi$
$359$	3.68663	+	1.08249i	0.194573	+	0.0571317i	−0.182994	+	0.983114i	$0.558579\pi$
$360$	0.561365	+	3.90438i	0.0295865	+	0.205779i
$361$	5.65870	+	6.53049i	0.297826	+	0.343710i
$362$	1.54350	+	3.37979i	0.0811246	+	0.177638i
$363$	−2.41021	+	0.707701i	−0.126503	+	0.0371447i
$364$	−0.300342	+	0.657657i	−0.0157422	+	0.0344706i
$365$	−1.11706	+	7.76934i	−0.0584697	+	0.406666i
$366$	45.7021	−	29.3709i	2.38889	−	1.53524i
$367$	−8.47757			−0.442525			−0.221263	−	0.975214i	$-0.571018\pi$
$367$	−8.47757			−0.442525			−0.221263	+	0.975214i	$0.571018\pi$
$368$	−13.2957	−	25.5276i	−0.693088	−	1.33072i
$369$	−0.468606			−0.0243947
$370$	12.1822	−	7.82901i	0.633321	−	0.407011i
$371$	1.64511	−	11.4420i	0.0854096	−	0.594037i
$372$	8.22507	−	18.0104i	0.426450	−	0.933795i
$373$	1.88469	−	0.553395i	0.0975855	−	0.0286537i	−0.232575	−	0.972578i	$-0.574715\pi$
$373$	1.88469	−	0.553395i	0.0975855	−	0.0286537i	0.330161	+	0.943925i	$0.392897\pi$
$374$	−22.3426	−	48.9235i	−1.15531	−	2.52977i
$375$	−12.0637	−	13.9222i	−0.622967	−	0.718942i
$376$	0.00775161	+	0.0539137i	0.000399759	+	0.00278038i
$377$	0.601032	+	0.176479i	0.0309547	+	0.00908912i
$378$	−11.1497	+	12.8674i	−0.573478	+	0.661829i
$379$	−15.2611	−	9.80773i	−0.783911	−	0.503789i	0.0864184	−	0.996259i	$-0.472458\pi$
$379$	−15.2611	−	9.80773i	−0.783911	−	0.503789i	−0.870330	+	0.492470i	$0.836094\pi$
$380$	17.2858	+	11.1089i	0.886742	+	0.569874i
$381$	−20.5346	+	23.6982i	−1.05202	+	1.21410i
$382$	27.4426	+	8.05788i	1.40409	+	0.412277i
$383$	2.85984	+	19.8906i	0.146131	+	1.01636i	0.922476	+	0.386055i	$0.126162\pi$
$383$	2.85984	+	19.8906i	0.146131	+	1.01636i	−0.776345	+	0.630308i	$0.782929\pi$
$384$	−16.0027	−	18.4681i	−0.816635	−	0.942447i
$385$	2.67689	+	5.86157i	0.136427	+	0.298733i
$386$	4.03161	−	1.18379i	0.205203	−	0.0602532i
$387$	0.602354	−	1.31897i	0.0306194	−	0.0670471i
$388$	−11.0682	+	76.9813i	−0.561904	+	3.90813i
$389$	14.6099	−	9.38921i	0.740751	−	0.476052i	−0.115048	−	0.993360i	$-0.536702\pi$
$389$	14.6099	−	9.38921i	0.740751	−	0.476052i	0.855799	+	0.517308i	$0.173066\pi$
$390$	−0.807771			−0.0409031
$391$	−5.59566	−	28.3941i	−0.282985	−	1.43595i
$392$	31.9702			1.61474
$393$	−9.38767	+	6.03309i	−0.473545	+	0.304329i
$394$	−5.46573	+	38.0150i	−0.275360	+	1.91517i
$395$	6.59517	−	14.4414i	0.331839	−	0.726626i
$396$	−6.72792	+	1.97550i	−0.338091	+	0.0992724i
$397$	−15.0230	−	32.8958i	−0.753984	−	1.65099i	−0.759072	−	0.651007i	$-0.774347\pi$
$397$	−15.0230	−	32.8958i	−0.753984	−	1.65099i	0.00508792	−	0.999987i	$-0.498380\pi$
$398$	6.23488	+	7.19544i	0.312526	+	0.360675i
$399$	0.897305	+	6.24089i	0.0449214	+	0.312435i
$400$	16.1979	+	4.75613i	0.809895	+	0.237807i
$401$	−13.2156	+	15.2516i	−0.659955	+	0.761628i	−0.982770	−	0.184834i	$-0.940825\pi$
$401$	−13.2156	+	15.2516i	−0.659955	+	0.761628i	0.322815	+	0.946462i	$0.395371\pi$
$402$	−32.7858	−	21.0702i	−1.63521	−	1.05088i
$403$	−0.329875	−	0.211998i	−0.0164322	−	0.0105604i
$404$	3.66065	−	4.22462i	0.182124	−	0.210183i
$405$	−10.5233	−	3.08992i	−0.522906	−	0.153539i
$406$	2.01970	+	14.0474i	0.100236	+	0.697158i
$407$	9.04738	+	10.4412i	0.448462	+	0.517553i
$408$	23.2731	+	50.9610i	1.15219	+	2.52295i
$409$	23.9248	−	7.02495i	1.18301	−	0.347362i	0.369673	−	0.929162i	$-0.379470\pi$
$409$	23.9248	−	7.02495i	1.18301	−	0.347362i	0.813332	+	0.581800i	$0.197651\pi$
$410$	1.57968	−	3.45902i	0.0780150	−	0.170829i
$411$	−2.81079	+	19.5495i	−0.138646	+	0.964303i
$412$	−13.7967	+	8.86662i	−0.679716	+	0.436827i
$413$	5.73433			0.282168
$414$	−5.51366	+	0.285745i	−0.270982	+	0.0140436i
$415$	2.58973			0.127125
$416$	0.394217	−	0.253348i	0.0193281	−	0.0124214i
$417$	2.83911	−	19.7465i	0.139032	−	0.966989i
$418$	−11.9166	+	26.0938i	−0.582862	+	1.27629i
$419$	31.8114	−	9.34068i	1.55409	−	0.456322i	0.611770	−	0.791036i	$-0.290458\pi$
$419$	31.8114	−	9.34068i	1.55409	−	0.456322i	0.942320	+	0.334714i	$0.108640\pi$
$420$	−5.19540	−	11.3763i	−0.253510	−	0.555109i
$421$	−6.45551	−	7.45006i	−0.314622	−	0.363093i	0.576309	−	0.817232i	$-0.304493\pi$
$421$	−6.45551	−	7.45006i	−0.314622	−	0.363093i	−0.890931	+	0.454139i	$0.849947\pi$
$422$	0.871819	+	6.06364i	0.0424395	+	0.295173i
$423$	0.00411093	+	0.00120708i	0.000199880	+	5.86902e-5i
$424$	−35.8753	+	41.4023i	−1.74226	+	2.01067i
$425$	14.2796	+	9.17693i	0.692661	+	0.445147i
$426$	2.34695	+	1.50829i	0.113710	+	0.0730769i
$427$	10.9087	−	12.5893i	0.527907	−	0.609238i
$428$	−23.7246	−	6.96618i	−1.14677	−	0.336723i
$429$	−0.109677	−	0.762819i	−0.00529524	−	0.0368292i
$430$	7.70545	+	8.89256i	0.371590	+	0.428837i
$431$	−16.5212	−	36.1764i	−0.795798	−	1.74256i	−0.659253	−	0.751922i	$-0.729127\pi$
$431$	−16.5212	−	36.1764i	−0.795798	−	1.74256i	−0.136546	−	0.990634i	$-0.543600\pi$
$432$	31.7484	−	9.32218i	1.52750	−	0.448513i
$433$	−6.78963	+	14.8672i	−0.326289	+	0.714473i	−0.999692	−	0.0248024i	$-0.992104\pi$
$433$	−6.78963	+	14.8672i	−0.326289	+	0.714473i	0.673404	+	0.739275i	$0.264832\pi$
$434$	1.26431	−	8.79349i	0.0606889	−	0.422101i
$435$	−9.11561	+	5.85824i	−0.437060	+	0.280881i
$436$	−6.02278			−0.288439
$437$	−9.49082	+	12.1729i	−0.454008	+	0.582309i
$438$	21.2679			1.01622
$439$	−19.8964	+	12.7867i	−0.949605	+	0.610274i	−0.921103	−	0.389320i	$-0.872710\pi$
$439$	−19.8964	+	12.7867i	−0.949605	+	0.610274i	−0.0285021	+	0.999594i	$0.509074\pi$
$440$	4.34611	−	30.2279i	0.207193	−	1.44106i
$441$	1.04468	−	2.28753i	0.0497468	−	0.108930i
$442$	1.98357	−	0.582428i	0.0943487	−	0.0277033i
$443$	8.14964	+	17.8452i	0.387201	+	0.847852i	0.998409	+	0.0563819i	$0.0179564\pi$
$443$	8.14964	+	17.8452i	0.387201	+	0.847852i	−0.611208	+	0.791470i	$0.709316\pi$
$444$	−17.5595	−	20.2647i	−0.833337	−	0.961722i
$445$	−1.85416	−	12.8960i	−0.0878956	−	0.611328i
$446$	−34.0375	−	9.99432i	−1.61172	−	0.473245i
$447$	3.71898	−	4.29193i	0.175902	−	0.203002i
$448$	−3.47577	−	2.23374i	−0.164215	−	0.105534i
$449$	−3.75626	−	2.41400i	−0.177269	−	0.113924i	0.448997	−	0.893533i	$-0.351781\pi$
$449$	−3.75626	−	2.41400i	−0.177269	−	0.113924i	−0.626266	+	0.779609i	$0.715418\pi$
$450$	2.12060	−	2.44730i	0.0999660	−	0.115367i
$451$	3.48101	+	1.02212i	0.163915	+	0.0481297i
$452$	−3.19209	−	22.2014i	−0.150143	−	1.04427i
$453$	5.86169	+	6.76475i	0.275406	+	0.317836i
$454$	−14.7996	−	32.4066i	−0.694580	−	1.52092i
$455$	−0.237653	+	0.0697813i	−0.0111414	+	0.00327140i
$456$	12.4129	−	27.1806i	0.581289	−	1.27285i
$457$	1.44712	−	10.0649i	0.0676935	−	0.470818i	−0.927574	−	0.373641i	$-0.878109\pi$
$457$	1.44712	−	10.0649i	0.0676935	−	0.470818i	0.995267	−	0.0971778i	$-0.0309815\pi$
$458$	33.7512	−	21.6906i	1.57709	−	1.01353i
$459$	33.2699			1.55291
$460$	11.2605	−	28.4715i	0.525022	−	1.32749i
$461$	30.3196			1.41213			0.706063	−	0.708149i	$-0.250469\pi$
$461$	30.3196			1.41213			0.706063	+	0.708149i	$0.250469\pi$
$462$	14.6884	−	9.43964i	0.683364	−	0.439172i
$463$	−4.92409	+	34.2478i	−0.228842	+	1.59163i	0.474157	+	0.880440i	$0.342753\pi$
$463$	−4.92409	+	34.2478i	−0.228842	+	1.59163i	−0.702999	+	0.711191i	$0.748156\pi$
$464$	11.4574	−	25.0882i	0.531897	−	1.16469i
$465$	6.50829	−	1.91101i	0.301815	−	0.0886208i
$466$	21.0843	+	46.1682i	0.976711	+	2.13870i
$467$	7.38214	+	8.51944i	0.341605	+	0.394233i	0.900393	−	0.435078i	$-0.143279\pi$
$467$	7.38214	+	8.51944i	0.341605	+	0.394233i	−0.558788	+	0.829310i	$0.688734\pi$
$468$	−0.0383569	−	0.266778i	−0.00177305	−	0.0123318i
$469$	−11.4661	−	3.36674i	−0.529454	−	0.155462i
$470$	−0.0227681	+	0.0262758i	−0.00105021	+	0.00121201i
$471$	19.5628	+	12.5723i	0.901407	+	0.579299i
$472$	−22.8619	−	14.6925i	−1.05230	−	0.676275i
$473$	−7.35147	+	8.48405i	−0.338021	+	0.390097i
$474$	−41.2747	−	12.1194i	−1.89581	−	0.556660i
$475$	−1.28842	−	8.96119i	−0.0591170	−	0.411167i
$476$	20.9606	+	24.1898i	0.960726	+	1.10874i
$477$	1.79013	+	3.91984i	0.0819645	+	0.179477i
$478$	−51.1228	+	15.0110i	−2.33830	+	0.686587i
$479$	−7.02430	+	15.3811i	−0.320948	+	0.702779i	−0.999495	−	0.0317785i	$-0.989883\pi$
$479$	−7.02430	+	15.3811i	−0.320948	+	0.702779i	0.678547	+	0.734557i	$0.262610\pi$
$480$	−1.15362	+	8.02358i	−0.0526552	+	0.366225i
$481$	−0.446740	+	0.287102i	−0.0203696	+	0.0130907i
$482$	−56.2605			−2.56260
$483$	8.86536	−	3.10987i	0.403388	−	0.141504i
$484$	6.80138			0.309154
$485$	−22.4142	+	14.4047i	−1.01778	+	0.654085i
$486$	1.68692	−	11.7328i	0.0765201	−	0.532209i
$487$	−14.8126	+	32.4350i	−0.671221	+	1.46977i	0.200463	+	0.979701i	$0.435755\pi$
$487$	−14.8126	+	32.4350i	−0.671221	+	1.46977i	−0.871684	+	0.490068i	$0.836972\pi$
$488$	−75.7473	+	22.2414i	−3.42892	+	1.00682i
$489$	8.19317	+	17.9405i	0.370508	+	0.811299i
$490$	13.3638	+	15.4227i	0.603715	+	0.696725i
$491$	−1.74891	−	12.1640i	−0.0789274	−	0.548952i	−0.990468	−	0.137742i	$-0.956015\pi$
$491$	−1.74891	−	12.1640i	−0.0789274	−	0.548952i	0.911541	−	0.411210i	$-0.134894\pi$
$492$	−6.75608	−	1.98376i	−0.304588	−	0.0894350i
$493$	18.1604	−	20.9582i	0.817902	−	0.943909i
$494$	−0.927582	−	0.596121i	−0.0417339	−	0.0268207i
$495$	−2.02085	−	1.29872i	−0.0908305	−	0.0583732i
$496$	−11.3063	+	13.0481i	−0.507667	+	0.585879i
$497$	0.820790	+	0.241006i	0.0368175	+	0.0108106i
$498$	−0.998627	−	6.94561i	−0.0447496	−	0.311240i
$499$	18.0998	+	20.8883i	0.810260	+	0.935089i	0.998897	−	0.0469574i	$-0.0149525\pi$
$499$	18.0998	+	20.8883i	0.810260	+	0.935089i	−0.188637	+	0.982047i	$0.560407\pi$
$500$	20.7204	+	45.3713i	0.926644	+	2.02907i
$501$	18.0646	−	5.30425i	0.807068	−	0.236976i
$502$	21.0377	−	46.0661i	0.938957	−	2.05603i
$503$	1.88678	−	13.1228i	0.0841273	−	0.585118i	−0.903534	−	0.428515i	$-0.859037\pi$
$503$	1.88678	−	13.1228i	0.0841273	−	0.585118i	0.987662	−	0.156603i	$-0.0500542\pi$
$504$	2.75698	−	1.77181i	0.122806	−	0.0789225i
$505$	1.91504			0.0852181
$506$	41.5811	+	9.90368i	1.84851	+	0.440272i
$507$	−20.6969			−0.919183
$508$	71.4248	−	45.9020i	3.16896	−	2.03657i
$509$	1.59792	−	11.1137i	0.0708264	−	0.492608i	−0.923274	−	0.384143i	$-0.874497\pi$
$509$	1.59792	−	11.1137i	0.0708264	−	0.492608i	0.994100	−	0.108466i	$-0.0345938\pi$
$510$	−14.8556	+	32.5293i	−0.657818	+	1.44042i
$511$	6.25721	−	1.83728i	0.276803	−	0.0812767i
$512$	20.4643	+	44.8107i	0.904405	+	1.98037i
$513$	−11.6204	−	13.4107i	−0.513053	−	0.592095i
$514$	0.748138	+	5.20341i	0.0329989	+	0.229513i
$515$	−5.39087	−	1.58290i	−0.237550	−	0.0697510i
$516$	14.2680	−	16.4662i	0.628114	−	0.724882i
$517$	−0.0279049	−	0.0179334i	−0.00122726	−	0.000788710i
$518$	−10.1213	−	6.50457i	−0.444705	−	0.285795i
$519$	2.55259	−	2.94585i	0.112046	−	0.129308i
$520$	1.12628	+	0.330706i	0.0493907	+	0.0145024i
$521$	−3.73291	−	25.9630i	−0.163542	−	1.13746i	−0.891890	−	0.452252i	$-0.850621\pi$
$521$	−3.73291	−	25.9630i	−0.163542	−	1.13746i	0.728348	−	0.685207i	$-0.240288\pi$
$522$	−3.46454	−	3.99829i	−0.151639	−	0.175001i
$523$	−11.9266	−	26.1157i	−0.521516	−	1.14196i	−0.968862	−	0.247600i	$-0.920358\pi$
$523$	−11.9266	−	26.1157i	−0.521516	−	1.14196i	0.447346	−	0.894361i	$-0.352369\pi$
$524$	28.9906	−	8.51240i	1.26646	−	0.371866i
$525$	−2.28911	+	5.01244i	−0.0999048	+	0.218761i
$526$	2.02259	−	14.0674i	0.0881891	−	0.613368i
$527$	−14.6039	+	9.38537i	−0.636156	+	0.408833i
$528$	−33.9323			−1.47671
$529$	20.5306	+	10.3680i	0.892634	+	0.450782i
$530$	−34.9689			−1.51895
$531$	−1.79833	+	1.15572i	−0.0780408	+	0.0501538i
$532$	2.42954	−	16.8978i	0.105334	−	0.732614i
$533$	−0.0579295	+	0.126848i	−0.00250921	+	0.00549440i
$534$	−33.8717	+	9.94564i	−1.46577	+	0.430390i
$535$	−3.51891	−	7.70533i	−0.152136	−	0.333130i
$536$	37.0873	+	42.8010i	1.60193	+	1.84872i
$537$	−4.91316	−	34.1718i	−0.212019	−	1.47462i
$538$	68.6270	+	20.1507i	2.95872	+	0.868759i
$539$	−12.7499	+	14.7142i	−0.549177	+	0.633784i
$540$	29.6105	+	19.0295i	1.27423	+	0.818900i
$541$	4.46715	+	2.87087i	0.192058	+	0.123428i	0.633136	−	0.774041i	$-0.281767\pi$
$541$	4.46715	+	2.87087i	0.192058	+	0.123428i	−0.441078	+	0.897469i	$0.645404\pi$
$542$	−47.4556	+	54.7666i	−2.03839	+	2.35243i
$543$	2.26152	+	0.664041i	0.0970509	+	0.0284967i
$544$	−2.95242	−	20.5346i	−0.126584	−	0.880412i
$545$	−1.35118	−	1.55935i	−0.0578783	−	0.0667951i
$546$	0.278793	+	0.610473i	0.0119313	+	0.0261258i
$547$	−28.9227	+	8.49246i	−1.23664	+	0.363111i	−0.833754	−	0.552137i	$-0.813813\pi$
$547$	−28.9227	+	8.49246i	−1.23664	+	0.363111i	−0.402890	+	0.915248i	$0.631994\pi$
$548$	22.2149	−	48.6438i	0.948973	−	2.07796i
$549$	−0.883755	+	6.14665i	−0.0377178	+	0.262333i
$550$	−21.0908	+	13.5542i	−0.899313	+	0.577953i
$551$	−14.7909			−0.630115
$552$	−43.3129	−	10.3161i	−1.84352	−	0.439084i
$553$	−13.1903			−0.560910
$554$	3.47441	−	2.23287i	0.147613	−	0.0948654i
$555$	1.30732	−	9.09260i	0.0554926	−	0.385959i
$556$	−22.4388	+	49.1341i	−0.951616	+	2.08375i
$557$	4.10236	−	1.20456i	0.173823	−	0.0510389i	−0.193663	−	0.981068i	$-0.562037\pi$
$557$	4.10236	−	1.20456i	0.173823	−	0.0510389i	0.367486	+	0.930029i	$0.380219\pi$
$558$	1.37577	+	3.01251i	0.0582409	+	0.127530i
$559$	−0.282571	−	0.326105i	−0.0119515	−	0.0137928i
$560$	1.55203	+	10.7946i	0.0655853	+	0.456156i
$561$	−32.7361	−	9.61217i	−1.38212	−	0.405826i
$562$	42.6347	−	49.2031i	1.79844	−	2.07551i
$563$	−12.2601	−	7.87909i	−0.516701	−	0.332064i	0.256164	−	0.966633i	$-0.417541\pi$
$563$	−12.2601	−	7.87909i	−0.516701	−	0.332064i	−0.772866	+	0.634569i	$0.781178\pi$
$564$	0.0541589	+	0.0348058i	0.00228050	+	0.00146559i
$565$	5.03201	−	5.80725i	0.211698	−	0.244313i
$566$	34.2041	+	10.0432i	1.43771	+	0.422149i
$567$	1.29680	+	9.01942i	0.0544604	+	0.378780i
$568$	−2.65486	−	3.06387i	−0.111395	−	0.128557i
$569$	−7.60317	−	16.6486i	−0.318742	−	0.697947i	0.680658	−	0.732602i	$-0.261694\pi$
$569$	−7.60317	−	16.6486i	−0.318742	−	0.697947i	−0.999399	+	0.0346549i	$0.988967\pi$
$570$	18.3008	−	5.37360i	0.766536	−	0.225075i
$571$	−14.8587	+	32.5360i	−0.621816	+	1.36159i	0.292374	+	0.956304i	$0.405555\pi$
$571$	−14.8587	+	32.5360i	−0.621816	+	1.36159i	−0.914191	+	0.405284i	$0.867173\pi$
$572$	−0.296961	+	2.06541i	−0.0124166	+	0.0863590i
$573$	15.2631	−	9.80903i	0.637627	−	0.409778i
$574$	−3.15937			−0.131869
$575$	−12.7296	+	4.46541i	−0.530861	+	0.186220i
$576$	1.54022			0.0641760
$577$	22.0299	−	14.1578i	0.917117	−	0.589395i	0.00529727	−	0.999986i	$-0.498314\pi$
$577$	22.0299	−	14.1578i	0.917117	−	0.589395i	0.911820	+	0.410591i	$0.134677\pi$
$578$	6.94429	−	48.2986i	0.288844	−	2.00896i
$579$	1.10727	−	2.42457i	0.0460164	−	0.100762i
$580$	28.1504	−	8.26571i	1.16888	−	0.343215i
$581$	−0.893818	−	1.95719i	−0.0370818	−	0.0811979i
$582$	47.2763	+	54.5598i	1.95967	+	2.26157i
$583$	−4.74797	−	33.0229i	−0.196641	−	1.36767i
$584$	−29.6540	−	8.70721i	−1.22709	−	0.360307i
$585$	0.0604658	−	0.0697813i	0.00249995	−	0.00288510i
$586$	−48.4627	−	31.1451i	−2.00197	−	1.28659i
$587$	−29.6020	−	19.0240i	−1.22180	−	0.785206i	−0.239209	−	0.970968i	$-0.576888\pi$
$587$	−29.6020	−	19.0240i	−1.22180	−	0.785206i	−0.982595	+	0.185762i	$0.940525\pi$
$588$	24.7455	−	28.5578i	1.02049	−	1.17770i
$589$	8.88391	+	2.60855i	0.366055	+	0.107483i
$590$	−2.46872	−	17.1703i	−0.101636	−	0.706891i
$591$	15.9544	+	18.4124i	0.656276	+	0.757383i
$592$	9.71312	+	21.2688i	0.399207	+	0.874141i
$593$	16.8283	−	4.94124i	0.691057	−	0.202913i	0.0826978	−	0.996575i	$-0.473646\pi$
$593$	16.8283	−	4.94124i	0.691057	−	0.202913i	0.608359	+	0.793662i	$0.291828\pi$
$594$	−20.4132	+	44.6986i	−0.837563	+	1.83401i
$595$	−1.56053	+	10.8537i	−0.0639755	+	0.444960i
$596$	−12.9356	+	8.31320i	−0.529863	+	0.340522i
$597$	6.03966			0.247187
$598$	−0.604255	+	1.52783i	−0.0247098	+	0.0624775i
$599$	38.0735			1.55564			0.777821	−	0.628486i	$-0.216325\pi$
$599$	38.0735			1.55564			0.777821	+	0.628486i	$0.216325\pi$
$600$	21.9692	−	14.1187i	0.896887	−	0.576394i
$601$	−2.45730	+	17.0909i	−0.100235	+	0.697153i	0.876295	+	0.481774i	$0.160008\pi$
$601$	−2.45730	+	17.0909i	−0.100235	+	0.697153i	−0.976531	+	0.215378i	$0.930902\pi$
$602$	4.06110	−	8.89256i	0.165518	−	0.362434i
$603$	4.27439	−	1.25507i	0.174067	−	0.0511106i
$604$	−10.0679	−	22.0457i	−0.409659	−	0.897027i
$605$	1.52586	+	1.76093i	0.0620349	+	0.0715921i
$606$	−0.738458	−	5.13609i	−0.0299978	−	0.208639i
$607$	−24.0606	−	7.06483i	−0.976589	−	0.286752i	−0.245773	−	0.969327i	$-0.579042\pi$
$607$	−24.0606	−	7.06483i	−0.976589	−	0.286752i	−0.730816	+	0.682575i	$0.760860\pi$
$608$	−7.24598	+	8.36231i	−0.293863	+	0.339137i
$609$	7.57352	+	4.86721i	0.306894	+	0.197229i
$610$	−42.3924	−	27.2440i	−1.71642	−	1.10308i
$611$	0.000834943	0	0.000963576i	3.37782e−5	0	3.89821e-5i
$612$	−11.4487	−	3.36163i	−0.462785	−	0.135886i
$613$	4.65605	+	32.3836i	0.188056	+	1.30796i	0.837033	+	0.547152i	$0.184288\pi$
$613$	4.65605	+	32.3836i	0.188056	+	1.30796i	−0.648977	+	0.760808i	$0.724803\pi$
$614$	6.64510	+	7.66885i	0.268174	+	0.309490i
$615$	−1.00208	−	2.19425i	−0.0404078	−	0.0884808i
$616$	−24.3447	+	7.14825i	−0.980877	+	0.288011i
$617$	8.50218	−	18.6172i	0.342285	−	0.749499i	−0.657708	−	0.753273i	$-0.728474\pi$
$617$	8.50218	−	18.6172i	0.342285	−	0.749499i	0.999993	+	0.00377365i	$0.00120119\pi$
$618$	−2.16654	+	15.0686i	−0.0871509	+	0.606148i
$619$	−0.207398	+	0.133287i	−0.00833605	+	0.00535725i	−0.544802	−	0.838565i	$-0.683395\pi$
$619$	−0.207398	+	0.133287i	−0.00833605	+	0.00535725i	0.536466	+	0.843922i	$0.319759\pi$
$620$	−18.3658			−0.737588
$621$	−16.2578	+	20.8522i	−0.652402	+	0.836769i
$622$	2.11645			0.0848620
$623$	−9.10618	+	5.85219i	−0.364831	+	0.234463i
$624$	0.185617	−	1.29099i	0.00743062	−	0.0516811i
$625$	−1.25593	+	2.75009i	−0.0502371	+	0.110004i
$626$	64.4150	−	18.9140i	2.57454	−	0.755954i
$627$	7.55939	+	16.5528i	0.301893	+	0.661054i
$628$	−41.2323	−	47.5846i	−1.64535	−	1.89883i
$629$	3.34579	+	23.2705i	0.133405	+	0.927854i
$630$	2.00717	+	0.589359i	0.0799677	+	0.0234806i
$631$	2.03793	−	2.35190i	0.0811288	−	0.0936277i	−0.713734	−	0.700417i	$-0.752997\pi$
$631$	2.03793	−	2.35190i	0.0811288	−	0.0936277i	0.794863	+	0.606789i	$0.207543\pi$
$632$	52.5879	+	33.7962i	2.09183	+	1.34434i
$633$	3.26916	+	2.10096i	0.129937	+	0.0835058i
$634$	2.11038	−	2.43550i	0.0838138	−	0.0967262i
$635$	27.9082	+	8.19459i	1.10750	+	0.325193i
$636$	9.21504	+	64.0920i	0.365400	+	2.54141i
$637$	−0.490073	−	0.565574i	−0.0194174	−	0.0224089i
$638$	17.0151	+	37.2579i	0.673634	+	1.47505i
$639$	−0.305979	+	0.0898434i	−0.0121043	+	0.00355415i
$640$	−9.41628	+	20.6188i	−0.372211	+	0.815029i
$641$	0.472771	−	3.28820i	0.0186733	−	0.129876i	−0.978352	−	0.206946i	$-0.933647\pi$
$641$	0.472771	−	3.28820i	0.0186733	−	0.129876i	0.997026	+	0.0770703i	$0.0245566\pi$
$642$	−19.3086	+	12.4089i	−0.762050	+	0.489739i
$643$	−4.99919			−0.197149			−0.0985744	−	0.995130i	$-0.531428\pi$
$643$	−4.99919			−0.197149			−0.0985744	+	0.995130i	$0.531428\pi$
$644$	−25.4038	+	1.31655i	−1.00105	+	0.0518792i
$645$	7.46418			0.293902
$646$	−41.0651	+	26.3909i	−1.61568	+	1.03834i
$647$	−2.35177	+	16.3569i	−0.0924574	+	0.643056i	0.889916	+	0.456125i	$0.150763\pi$
$647$	−2.35177	+	16.3569i	−0.0924574	+	0.643056i	−0.982373	+	0.186931i	$0.940146\pi$
$648$	17.9393	−	39.2817i	0.704724	−	1.54313i
$649$	15.8796	−	4.66267i	0.623329	−	0.183026i
$650$	−0.400315	−	0.876567i	−0.0157016	−	0.0343818i
$651$	−3.69051	−	4.25908i	−0.144642	−	0.166926i
$652$	−7.59984	−	52.8580i	−0.297633	−	2.07008i
$653$	−14.3422	−	4.21124i	−0.561253	−	0.164799i	−0.0112130	−	0.999937i	$-0.503569\pi$
$653$	−14.3422	−	4.21124i	−0.561253	−	0.164799i	−0.550040	+	0.835138i	$0.685387\pi$
$654$	−3.66111	+	4.22514i	−0.143161	+	0.165216i
$655$	8.70783	+	5.59618i	0.340243	+	0.218661i
$656$	5.16527	+	3.31952i	0.201670	+	0.129605i
$657$	−1.59202	+	1.83728i	−0.0621104	+	0.0716793i
$658$	0.0277161	+	0.00813818i	0.00108049	+	0.000317259i
$659$	−1.87862	−	13.0661i	−0.0731806	−	0.508982i	−0.993137	−	0.116961i	$-0.962685\pi$
$659$	−1.87862	−	13.0661i	−0.0731806	−	0.508982i	0.919956	−	0.392022i	$-0.128224\pi$
$660$	−23.6375	−	27.2791i	−0.920087	−	1.06184i
$661$	16.2711	+	35.6287i	0.632871	+	1.38579i	0.905777	+	0.423754i	$0.139288\pi$
$661$	16.2711	+	35.6287i	0.632871	+	1.38579i	−0.272906	+	0.962041i	$0.587985\pi$
$662$	8.37549	−	2.45927i	0.325523	−	0.0955821i
$663$	0.544780	−	1.19290i	0.0211575	−	0.0463284i
$664$	−1.45118	+	10.0931i	−0.0563165	+	0.391690i
$665$	4.92005	−	3.16192i	0.190791	−	0.122614i
$666$	4.48507			0.173793
$667$	4.26140	+	21.6236i	0.165002	+	0.837270i
$668$	−50.9766			−1.97235
$669$	−18.9311	+	12.1663i	−0.731920	+	0.470376i
$670$	−5.14472	+	35.7823i	−0.198758	+	1.38239i
$671$	19.9719	−	43.7324i	0.771007	−	1.68827i
$672$	6.46198	−	1.89741i	0.249276	−	0.0731941i
$673$	−9.39052	−	20.5624i	−0.361978	−	0.792621i	−0.999749	−	0.0223951i	$-0.992871\pi$
$673$	−9.39052	−	20.5624i	−0.361978	−	0.792621i	0.637771	−	0.770226i	$-0.279856\pi$
$674$	−30.6944	−	35.4232i	−1.18230	−	1.36445i
$675$	−2.20707	−	15.3505i	−0.0849501	−	0.590841i
$676$	53.7690	+	15.7880i	2.06804	+	0.607231i
$677$	0.750532	−	0.866160i	0.0288453	−	0.0332892i	−0.741144	−	0.671347i	$-0.765716\pi$
$677$	0.750532	−	0.866160i	0.0288453	−	0.0332892i	0.769989	+	0.638057i	$0.220262\pi$
$678$	−17.5153	−	11.2564i	−0.672671	−	0.432300i
$679$	18.6224	+	11.9679i	0.714661	+	0.459285i
$680$	34.0309	−	39.2738i	1.30503	−	1.50608i
$681$	−21.6842	−	6.36705i	−0.830939	−	0.243986i
$682$	−3.64896	−	25.3791i	−0.139726	−	0.971815i
$683$	−10.7108	−	12.3609i	−0.409837	−	0.472978i	0.512877	−	0.858462i	$-0.328580\pi$
$683$	−10.7108	−	12.3609i	−0.409837	−	0.472978i	−0.922714	+	0.385485i	$0.874034\pi$
$684$	2.64372	+	5.78894i	0.101085	+	0.221346i
$685$	17.5781	−	5.16139i	0.671625	−	0.197207i
$686$	16.0234	−	35.0863i	0.611775	−	1.33960i
$687$	3.62197	−	25.1914i	0.138187	−	0.961111i
$688$	−15.9829	+	10.2716i	−0.609341	+	0.391600i
$689$	1.28237			0.0488543
$690$	−13.1286	−	25.2067i	−0.499796	−	0.959602i
$691$	30.8862			1.17497			0.587483	−	0.809236i	$-0.300119\pi$
$691$	30.8862			1.17497			0.587483	+	0.809236i	$0.300119\pi$
$692$	−8.87859	+	5.70592i	−0.337513	+	0.216907i
$693$	−0.284033	+	1.97550i	−0.0107895	+	0.0750429i
$694$	15.1205	−	33.1092i	0.573965	−	1.25681i
$695$	−17.7552	+	5.21341i	−0.673495	+	0.197756i
$696$	−17.7238	−	38.8096i	−0.671817	−	1.47107i
$697$	4.04284	+	4.66569i	0.153134	+	0.176726i
$698$	10.1403	+	70.5276i	0.383817	+	2.66951i
$699$	30.8924	+	9.07083i	1.16846	+	0.343090i
$700$	9.77050	−	11.2758i	0.369290	−	0.426184i
$701$	8.48984	+	5.45609i	0.320657	+	0.206074i	0.691060	−	0.722798i	$-0.257144\pi$
$701$	8.48984	+	5.45609i	0.320657	+	0.206074i	−0.370403	+	0.928871i	$0.620780\pi$
$702$	−1.58895	−	1.02115i	−0.0599709	−	0.0385410i
$703$	8.21140	−	9.47646i	0.309699	−	0.357411i
$704$	−11.4415	−	3.35951i	−0.431216	−	0.126616i
$705$	0.00313878	+	0.0218307i	0.000118213	+	0.000822192i
$706$	−18.2994	−	21.1186i	−0.688706	−	0.794809i
$707$	−0.660955	−	1.44729i	−0.0248578	−	0.0544309i
$708$	−30.8197	+	9.04948i	−1.15828	+	0.340100i
$709$	11.1003	−	24.3063i	0.416881	−	0.912841i	−0.578395	−	0.815757i	$-0.696321\pi$
$709$	11.1003	−	24.3063i	0.416881	−	0.912841i	0.995276	−	0.0970848i	$-0.0309518\pi$
$710$	0.368281	−	2.56145i	0.0138213	−	0.0961294i
$711$	4.13659	−	2.65842i	0.155134	−	0.0996986i
$712$	51.2994			1.92253
$713$	1.25404	−	13.7394i	0.0469642	−	0.514544i
$714$	29.7112			1.11191
$715$	−0.601373	+	0.386479i	−0.0224901	+	0.0144535i
$716$	−13.3029	+	92.5236i	−0.497152	+	3.45777i
$717$	−14.0407	+	30.7448i	−0.524359	+	1.14819i
$718$	−9.26574	+	2.72067i	−0.345794	+	0.101534i
$719$	−6.61782	−	14.4910i	−0.246803	−	0.540423i	0.745170	−	0.666875i	$-0.232368\pi$
$719$	−6.61782	−	14.4910i	−0.246803	−	0.540423i	−0.991973	+	0.126452i	$0.959641\pi$
$720$	−2.66231	−	3.07247i	−0.0992184	−	0.114504i
$721$	0.664324	+	4.62047i	0.0247407	+	0.172075i
$722$	−20.8382	−	6.11865i	−0.775517	−	0.227712i
$723$	−23.3715	+	26.9721i	−0.869194	+	1.00310i
$724$	−5.36870	−	3.45025i	−0.199526	−	0.128228i
$725$	−10.8747	−	6.98873i	−0.403875	−	0.259555i
$726$	4.13440	−	4.77135i	0.153442	−	0.177081i
$727$	−27.8024	−	8.16353i	−1.03113	−	0.302769i	−0.277963	−	0.960592i	$-0.589659\pi$
$727$	−27.8024	−	8.16353i	−1.03113	−	0.302769i	−0.753172	+	0.657823i	$0.771477\pi$
$728$	−0.138793	−	0.965325i	−0.00514401	−	0.0357773i
$729$	−19.4935	−	22.4968i	−0.721983	−	0.833213i
$730$	−8.19521	−	17.9450i	−0.303318	−	0.664174i
$731$	−18.3291	+	5.38191i	−0.677926	+	0.199057i
$732$	−38.7622	+	84.8774i	−1.43269	+	3.13716i
$733$	−2.34706	+	16.3242i	−0.0866907	+	0.602947i	0.899448	+	0.437027i	$0.143969\pi$
$733$	−2.34706	+	16.3242i	−0.0866907	+	0.602947i	−0.986139	+	0.165920i	$0.946941\pi$
$734$	17.9246	−	11.5194i	0.661608	−	0.425190i
$735$	12.9454			0.477497
$736$	14.3129	+	8.18402i	0.527581	+	0.301667i
$737$	−34.4896			−1.27044
$738$	0.990800	−	0.636748i	0.0364718	−	0.0234390i
$739$	2.76567	−	19.2356i	0.101737	−	0.707594i	−0.873563	−	0.486710i	$-0.838197\pi$
$739$	2.76567	−	19.2356i	0.101737	−	0.707594i	0.975300	−	0.220884i	$-0.0708942\pi$
$740$	−10.3323	+	22.6246i	−0.379823	+	0.831697i
$741$	−0.671120	+	0.197059i	−0.0246542	+	0.00723913i
$742$	12.0691	+	26.4277i	0.443072	+	0.970193i
$743$	34.8401	+	40.2076i	1.27816	+	1.47507i	0.803994	+	0.594638i	$0.202705\pi$
$743$	34.8401	+	40.2076i	1.27816	+	1.47507i	0.474165	+	0.880436i	$0.342750\pi$
$744$	3.80093	+	26.4361i	0.139349	+	0.969193i
$745$	−5.05440	−	1.48410i	−0.185179	−	0.0543734i
$746$	−3.23294	+	3.73101i	−0.118366	+	0.136602i
$747$	0.674766	+	0.433646i	0.0246884	+	0.0158663i
$748$	77.7134	+	49.9434i	2.84148	+	1.82611i
$749$	−4.60879	+	5.31882i	−0.168401	+	0.194346i
$750$	44.4246	+	13.0443i	1.62216	+	0.476309i
$751$	2.00349	+	13.9346i	0.0731084	+	0.508480i	0.993167	+	0.116700i	$0.0372316\pi$
$751$	2.00349	+	13.9346i	0.0731084	+	0.508480i	−0.920059	+	0.391780i	$0.871859\pi$
$752$	−0.0367625	−	0.0424262i	−0.00134059	−	0.00154713i
$753$	−13.3454	−	29.2223i	−0.486333	−	1.06492i
$754$	−1.51060	+	0.443551i	−0.0550126	+	0.0161532i
$755$	3.44912	−	7.55252i	0.125526	−	0.274864i
$756$	4.16180	−	28.9460i	0.151363	−	1.05275i
$757$	15.5541	−	9.99604i	0.565325	−	0.363312i	−0.226546	−	0.974000i	$-0.572743\pi$
$757$	15.5541	−	9.99604i	0.565325	−	0.363312i	0.791871	+	0.610688i	$0.209107\pi$
$758$	45.5943			1.65606
$759$	22.0214	−	15.8205i	0.799326	−	0.574246i
$760$	−27.7169			−1.00540
$761$	−15.1093	+	9.71017i	−0.547712	+	0.351993i	−0.785049	−	0.619434i	$-0.787362\pi$
$761$	−15.1093	+	9.71017i	−0.547712	+	0.351993i	0.237336	+	0.971428i	$0.423726\pi$
$762$	11.2160	−	78.0092i	0.406314	−	2.82597i
$763$	−0.712130	+	1.55935i	−0.0257808	+	0.0564522i
$764$	−47.1350	+	13.8401i	−1.70528	+	0.500716i
$765$	−1.69810	−	3.71832i	−0.0613950	−	0.134436i
$766$	−33.0743	−	38.1698i	−1.19502	−	1.37913i
$767$	0.0905320	+	0.629664i	0.00326892	+	0.0227358i
$768$	48.6421	+	14.2826i	1.75522	+	0.515379i
$769$	−9.54325	+	11.0135i	−0.344138	+	0.397157i	−0.901263	−	0.433272i	$-0.857359\pi$
$769$	−9.54325	+	11.0135i	−0.344138	+	0.397157i	0.557125	+	0.830429i	$0.311904\pi$
$770$	−13.6247	−	8.75604i	−0.490999	−	0.315546i
$771$	2.80538	+	1.80291i	0.101033	+	0.0649301i
$772$	−4.72610	+	5.45421i	−0.170096	+	0.196301i
$773$	4.50784	+	1.32362i	0.162136	+	0.0476073i	0.361793	−	0.932258i	$-0.382165\pi$
$773$	4.50784	+	1.32362i	0.162136	+	0.0476073i	−0.199657	+	0.979866i	$0.563983\pi$
$774$	0.518645	+	3.60726i	0.0186423	+	0.129660i
$775$	5.29914	+	6.11553i	0.190351	+	0.219676i
$776$	−43.5806	−	95.4282i	−1.56445	−	3.42567i
$777$	−7.32293	+	2.15021i	−0.262709	+	0.0771383i
$778$	−18.1323	+	39.7042i	−0.650075	+	1.42347i
$779$	0.468606	−	3.25923i	0.0167896	−	0.116774i
$780$	1.16717	−	0.750092i	0.0417913	−	0.0268576i
$781$	2.46891			0.0883445
$782$	50.4134	+	52.4316i	1.80278	+	1.87495i
$783$	−25.3369			−0.905466
$784$	−27.7196	+	17.8143i	−0.989986	+	0.636225i
$785$	3.06978	−	21.3508i	0.109565	−	0.762042i
$786$	11.6510	−	25.5122i	0.415578	−	0.909989i
$787$	−16.3778	+	4.80896i	−0.583806	+	0.171421i	−0.560281	−	0.828302i	$-0.689307\pi$
$787$	−16.3778	+	4.80896i	−0.583806	+	0.171421i	−0.0235244	+	0.999723i	$0.507489\pi$
$788$	−27.4030	−	60.0042i	−0.976191	−	2.13756i
$789$	−5.90391	−	6.81347i	−0.210185	−	0.242566i
$790$	5.67865	+	39.4959i	0.202037	+	1.40520i
$791$	−6.12557	−	1.79863i	−0.217800	−	0.0639519i
$792$	6.19400	−	7.14825i	0.220094	−	0.254002i
$793$	1.55460	+	0.999080i	0.0552054	+	0.0354784i
$794$	76.4632	+	49.1399i	2.71358	+	1.74391i
$795$	−14.5266	+	16.7646i	−0.515206	+	0.594579i
$796$	−15.6906	−	4.60717i	−0.556137	−	0.163297i
$797$	2.87492	+	19.9955i	0.101835	+	0.708278i	0.975218	+	0.221245i	$0.0710120\pi$
$797$	2.87492	+	19.9955i	0.101835	+	0.708278i	−0.873383	+	0.487034i	$0.838079\pi$
$798$	−10.3774	−	11.9762i	−0.367357	−	0.423952i
$799$	−0.0234482	−	0.0513445i	−0.000829539	−	0.00181644i
$800$	−9.27863	+	2.72445i	−0.328049	+	0.0963240i
$801$	1.67630	−	3.67058i	0.0592290	−	0.129693i
$802$	7.21835	−	50.2048i	0.254889	−	1.77279i
$803$	15.8336	−	10.1757i	0.558757	−	0.359091i
$804$	66.9386			2.36074
$805$	−6.04008	−	6.28189i	−0.212885	−	0.221407i
$806$	0.985537			0.0347141
$807$	38.1692	−	24.5299i	1.34362	−	0.863492i
$808$	−1.07311	+	7.46361i	−0.0377517	+	0.262569i
$809$	−9.49680	+	20.7951i	−0.333890	+	0.731116i	−0.999890	−	0.0148352i	$-0.995278\pi$
$809$	−9.49680	+	20.7951i	−0.333890	+	0.731116i	0.666000	+	0.745951i	$0.268005\pi$
$810$	26.4486	−	7.76600i	0.929308	−	0.272869i
$811$	−3.74985	−	8.21104i	−0.131675	−	0.288328i	0.832298	−	0.554329i	$-0.187025\pi$
$811$	−3.74985	−	8.21104i	−0.131675	−	0.288328i	−0.963973	+	0.266000i	$0.914298\pi$
$812$	−15.9626	−	18.4218i	−0.560178	−	0.646480i
$813$	6.54217	+	45.5018i	0.229444	+	1.59582i
$814$	−33.3171	−	9.78277i	−1.16776	−	0.342886i
$815$	11.9804	−	13.8261i	0.419655	−	0.484307i
$816$	−48.5751	−	31.2173i	−1.70047	−	1.09283i
$817$	8.57129	+	5.50843i	0.299872	+	0.192716i
$818$	−41.0399	+	47.3626i	−1.43493	+	1.65599i
$819$	−0.0736063	−	0.0216128i	−0.00257201	−	0.000755211i
$820$	0.929513	+	6.46490i	0.0324600	+	0.225764i
$821$	11.7980	+	13.6156i	0.411753	+	0.475189i	0.923307	−	0.384063i	$-0.125475\pi$
$821$	11.7980	+	13.6156i	0.411753	+	0.475189i	−0.511554	+	0.859251i	$0.670930\pi$
$822$	−20.6210	−	45.1538i	−0.719242	−	1.57492i
$823$	28.0049	−	8.22299i	0.976191	−	0.286636i	0.245540	−	0.969386i	$-0.421035\pi$
$823$	28.0049	−	8.22299i	0.976191	−	0.286636i	0.730651	+	0.682751i	$0.239217\pi$
$824$	9.18997	−	20.1232i	0.320148	−	0.701026i
$825$	−2.26333	+	15.7418i	−0.0787992	+	0.548060i
$826$	−12.1244	+	7.79188i	−0.421862	+	0.271114i
$827$	13.2576			0.461011			0.230506	−	0.973071i	$-0.425962\pi$
$827$	13.2576			0.461011			0.230506	+	0.973071i	$0.425962\pi$
$828$	7.70147	−	5.53283i	0.267644	−	0.192279i
$829$	−33.0687			−1.14852			−0.574261	−	0.818672i	$-0.694710\pi$
$829$	−33.0687			−1.14852			−0.574261	+	0.818672i	$0.694710\pi$
$830$	−5.47561	+	3.51896i	−0.190061	+	0.122145i
$831$	0.372853	−	2.59325i	0.0129341	−	0.0899587i
$832$	0.190404	−	0.416926i	0.00660106	−	0.0144543i
$833$	−31.7888	+	9.33402i	−1.10142	+	0.323405i
$834$	20.8289	+	45.6088i	0.721245	+	1.57931i
$835$	−11.4364	−	13.1983i	−0.395772	−	0.456745i
$836$	−7.01196	−	48.7692i	−0.242514	−	1.68672i
$837$	15.2181	+	4.46845i	0.526016	+	0.154452i
$838$	−54.5684	+	62.9753i	−1.88503	+	2.17544i
$839$	−24.5147	−	15.7546i	−0.846340	−	0.543910i	0.0440909	−	0.999028i	$-0.485961\pi$
$839$	−24.5147	−	15.7546i	−0.846340	−	0.543910i	−0.890431	+	0.455118i	$0.849597\pi$
$840$	14.1921	+	9.12071i	0.489674	+	0.314694i
$841$	5.16085	−	5.95594i	0.177960	−	0.205377i
$842$	23.7725	+	6.98022i	0.819253	+	0.240554i
$843$	−5.87757	−	40.8794i	−0.202434	−	1.40796i
$844$	−6.89037	−	7.95191i	−0.237176	−	0.273716i
$845$	7.97518	+	17.4632i	0.274355	+	0.600753i
$846$	−0.0103322	+	0.00303379i	−0.000355227	+	0.000104304i
$847$	0.804191	−	1.76093i	0.0276323	−	0.0605064i
$848$	8.03546	−	55.8879i	0.275939	−	1.91920i
$849$	19.0238	−	12.2258i	0.652894	−	0.419590i
$850$	−42.6618			−1.46329
$851$	−16.2199	−	9.27441i	−0.556011	−	0.317923i
$852$	−4.79175			−0.164163
$853$	7.98123	−	5.12923i	0.273272	−	0.175621i	−0.396826	−	0.917894i	$-0.629888\pi$
$853$	7.98123	−	5.12923i	0.273272	−	0.175621i	0.670098	+	0.742273i	$0.266252\pi$
$854$	−5.95832	+	41.4410i	−0.203889	+	1.41808i
$855$	−0.905698	+	1.98320i	−0.0309742	+	0.0678241i
$856$	32.0024	−	9.39674i	1.09382	−	0.321174i
$857$	14.7858	+	32.3765i	0.505074	+	1.10596i	0.974787	+	0.223139i	$0.0716304\pi$
$857$	14.7858	+	32.3765i	0.505074	+	1.10596i	−0.469712	+	0.882820i	$0.655642\pi$
$858$	1.26842	+	1.46384i	0.0433033	+	0.0499746i
$859$	6.11026	+	42.4978i	0.208479	+	1.45001i	0.778122	+	0.628113i	$0.216172\pi$
$859$	6.11026	+	42.4978i	0.208479	+	1.45001i	−0.569643	+	0.821892i	$0.692919\pi$
$860$	−19.3914	−	5.69382i	−0.661240	−	0.194158i
$861$	−1.31245	+	1.51465i	−0.0447281	+	0.0516190i
$862$	84.0886	+	54.0405i	2.86407	+	1.84063i
$863$	21.9447	+	14.1030i	0.747007	+	0.480072i	0.857936	−	0.513756i	$-0.171746\pi$
$863$	21.9447	+	14.1030i	0.747007	+	0.480072i	−0.110929	+	0.993828i	$0.535383\pi$
$864$	−12.4124	+	14.3246i	−0.422277	+	0.487334i
$865$	−3.46918	−	1.01864i	−0.117956	−	0.0346349i
$866$	−5.84608	−	40.6604i	−0.198658	−	1.38170i
$867$	−20.2703	−	23.3932i	−0.688415	−	0.794473i
$868$	6.33875	+	13.8799i	0.215151	+	0.471116i
$869$	−36.5269	+	10.7253i	−1.23909	+	0.363830i
$870$	11.3134	−	24.7728i	0.383559	−	0.839877i
$871$	0.188665	−	1.31220i	0.00639268	−	0.0444621i
$872$	6.83450	−	4.39227i	0.231445	−	0.148741i
$873$	−8.25216			−0.279293
$874$	3.52626	−	38.6341i	0.119278	−	1.30682i
$875$	14.1970			0.479945
$876$	−30.7305	+	19.7493i	−1.03829	+	0.667267i
$877$	−0.778553	+	5.41496i	−0.0262899	+	0.182850i	−0.998735	−	0.0502814i	$-0.983988\pi$
$877$	−0.778553	+	5.41496i	−0.0262899	+	0.182850i	0.972445	+	0.233132i	$0.0748973\pi$
$878$	24.6934	−	54.0710i	0.833362	−	1.82481i
$879$	−35.0635	+	10.2956i	−1.18266	+	0.347261i
$880$	13.0752	+	28.6306i	0.440764	+	0.965139i
$881$	−9.31297	−	10.7477i	−0.313762	−	0.362100i	0.576862	−	0.816842i	$-0.304277\pi$
$881$	−9.31297	−	10.7477i	−0.313762	−	0.362100i	−0.890624	+	0.454741i	$0.849732\pi$
$882$	0.899504	+	6.25618i	0.0302879	+	0.210657i
$883$	16.1172	+	4.73243i	0.542386	+	0.159259i	0.541438	−	0.840741i	$-0.317880\pi$
$883$	16.1172	+	4.73243i	0.542386	+	0.159259i	0.000947742		1.00000i	$0.499698\pi$
$884$	−2.32526	+	2.68350i	−0.0782070	+	0.0902557i
$885$	−9.25724	−	5.94927i	−0.311179	−	0.199982i
$886$	−41.4795	−	26.6573i	−1.39353	−	0.895568i
$887$	27.0365	−	31.2018i	0.907797	−	1.04765i	−0.0908606	−	0.995864i	$-0.528962\pi$
$887$	27.0365	−	31.2018i	0.907797	−	1.04765i	0.998658	−	0.0517904i	$-0.0164928\pi$
$888$	34.7047	+	10.1902i	1.16461	+	0.341961i
$889$	−3.43916	−	23.9199i	−0.115346	−	0.802248i
$890$	21.4436	+	24.7472i	0.718790	+	0.829528i
$891$	10.9249	+	23.9223i	0.365999	+	0.801426i
$892$	58.4623	−	17.1661i	1.95746	−	0.574763i
$893$	−0.0125063	+	0.0273851i	−0.000418509	+	0.000916407i
$894$	−2.03131	+	14.1281i	−0.0679372	+	0.472513i
$895$	−26.9396	+	17.3130i	−0.900490	+	0.578710i
$896$	18.8326			0.629152
$897$	0.481446	+	0.924371i	0.0160750	+	0.0308638i
$898$	11.2222			0.374491
$899$	11.1217	−	7.14747i	0.370929	−	0.238381i
$900$	−0.791548	+	5.50534i	−0.0263849	+	0.183511i
$901$	23.5838	−	51.6414i	0.785692	−	1.72042i
$902$	−8.74896	+	2.56893i	−0.291309	+	0.0855359i
$903$	−2.57618	−	5.64105i	−0.0857300	−	0.187722i
$904$	19.8133	+	22.8657i	0.658980	+	0.760503i
$905$	−0.311143	−	2.16405i	−0.0103427	−	0.0719354i
$906$	−21.5857	−	6.33814i	−0.717137	−	0.210571i
$907$	18.2757	−	21.0913i	0.606836	−	0.700326i	−0.366315	−	0.930491i	$-0.619381\pi$
$907$	18.2757	−	21.0913i	0.606836	−	0.700326i	0.973152	+	0.230164i	$0.0739264\pi$
$908$	51.4769	+	33.0822i	1.70832	+	1.09787i
$909$	0.498971	+	0.320669i	0.0165498	+	0.0106359i
$910$	0.407663	−	0.470469i	0.0135139	−	0.0155959i
$911$	−3.57987	−	1.05115i	−0.118607	−	0.0348260i	0.221891	−	0.975072i	$-0.428777\pi$
$911$	−3.57987	−	1.05115i	−0.118607	−	0.0348260i	−0.340497	+	0.940246i	$0.610595\pi$
$912$	4.38286	+	30.4834i	0.145131	+	1.00941i
$913$	−4.06659	−	4.69310i	−0.134585	−	0.155319i
$914$	10.6167	+	23.2472i	0.351168	+	0.768950i
$915$	−30.6716	+	9.00599i	−1.01397	+	0.297729i
$916$	−28.6261	+	62.6823i	−0.945832	+	2.07108i
$917$	1.22390	−	8.51240i	0.0404167	−	0.281104i
$918$	−70.3444	+	45.2076i	−2.32171	+	1.49207i
$919$	−35.9581			−1.18615			−0.593074	−	0.805148i	$-0.702086\pi$
$919$	−35.9581			−1.18615			−0.593074	+	0.805148i	$0.702086\pi$
$920$	7.98549	+	40.5208i	0.263274	+	1.33593i
$921$	6.43703			0.212107
$922$	−64.1065	+	41.1987i	−2.11123	+	1.35681i
$923$	−0.0135055	+	0.0939325i	−0.000444537	+	0.00309182i
$924$	−12.4579	+	27.2791i	−0.409836	+	0.897416i
$925$	10.5149	−	3.08744i	0.345727	−	0.101515i
$926$	−36.1251	−	79.1029i	−1.18714	−	2.59948i
$927$	−1.13956	−	1.31512i	−0.0374281	−	0.0431943i
$928$	2.24843	+	15.6382i	0.0738084	+	0.513348i
$929$	34.4476	+	10.1147i	1.13019	+	0.331853i	0.792782	−	0.609505i	$-0.208632\pi$
$929$	34.4476	+	10.1147i	1.13019	+	0.331853i	0.337407	+	0.941359i	$0.390450\pi$
$930$	−11.1641	+	12.8841i	−0.366086	+	0.422486i
$931$	14.8655	+	9.55346i	0.487196	+	0.313102i
$932$	−73.3367	−	47.1306i	−2.40222	−	1.54382i
$933$	0.879206	−	1.01466i	0.0287839	−	0.0332184i
$934$	−27.1848	−	7.98217i	−0.889513	−	0.261185i
$935$	4.50388	+	31.3252i	0.147293	+	1.02444i
$936$	0.238081	+	0.274760i	0.00778193	+	0.00898082i
$937$	10.2606	+	22.4676i	0.335200	+	0.733986i	0.999914	−	0.0131122i	$-0.00417385\pi$
$937$	10.2606	+	22.4676i	0.335200	+	0.733986i	−0.664714	+	0.747098i	$0.731447\pi$
$938$	28.8181	−	8.46176i	0.940945	−	0.276286i
$939$	17.6913	−	38.7386i	0.577335	−	1.26419i
$940$	0.00849856	−	0.0591088i	0.000277193	−	0.00192792i
$941$	−43.5130	+	27.9641i	−1.41848	+	0.911605i	−0.418491	+	0.908221i	$0.637441\pi$
$941$	−43.5130	+	27.9641i	−1.41848	+	0.911605i	−0.999994	+	0.00338366i	$0.998923\pi$
$942$	−58.4460			−1.90428
$943$	−4.89984	+	0.253934i	−0.159561	+	0.00826922i
$944$	28.0092			0.911621
$945$	8.42803	−	5.41637i	0.274164	−	0.176194i
$946$	4.01538	−	27.9276i	0.130551	−	0.908003i
$947$	−16.1916	+	35.4546i	−0.526155	+	1.15212i	0.440901	+	0.897556i	$0.354659\pi$
$947$	−16.1916	+	35.4546i	−0.526155	+	1.15212i	−0.967056	+	0.254563i	$0.918068\pi$
$948$	70.8927	−	20.8160i	2.30249	−	0.676072i
$949$	0.300532	+	0.658073i	0.00975567	+	0.0213619i
$950$	14.9008	+	17.1964i	0.483444	+	0.557925i
$951$	−0.290934	−	2.02349i	−0.00943418	−	0.0656162i
$952$	−41.4266	−	12.1639i	−1.34264	−	0.394235i
$953$	14.2405	−	16.4344i	0.461294	−	0.532361i	−0.476676	−	0.879079i	$-0.658158\pi$
$953$	14.2405	−	16.4344i	0.461294	−	0.532361i	0.937969	+	0.346718i	$0.112704\pi$
$954$	−9.11130	−	5.85548i	−0.294989	−	0.189578i
$955$	−14.1578	−	9.09868i	−0.458136	−	0.294426i
$956$	59.9293	−	69.1621i	1.93825	−	2.23686i
$957$	24.9303	+	7.32020i	0.805882	+	0.236628i
$958$	−6.04814	−	42.0657i	−0.195406	−	1.35908i
$959$	−9.96761	−	11.5032i	−0.321871	−	0.371459i
$960$	3.29366	+	7.21211i	0.106302	+	0.232770i
$961$	21.8037	−	6.40215i	0.703346	−	0.206521i
$962$	0.554448	−	1.21407i	0.0178761	−	0.0391433i
$963$	0.373376	−	2.59689i	0.0120319	−	0.0836836i
$964$	81.2921	−	52.2433i	2.61824	−	1.68264i
$965$	−2.47242			−0.0795900
$966$	−14.5188	+	18.6217i	−0.467134	+	0.599144i
$967$	−8.23067			−0.264680			−0.132340	−	0.991204i	$-0.542249\pi$
$967$	−8.23067			−0.264680			−0.132340	+	0.991204i	$0.542249\pi$
$968$	−7.71803	+	4.96008i	−0.248067	+	0.159423i
$969$	−4.40686	+	30.6504i	−0.141569	+	0.984632i
$970$	27.8182	−	60.9134i	0.893189	−	1.95581i
$971$	57.6332	−	16.9226i	1.84954	−	0.543073i	0.849661	−	0.527329i	$-0.176806\pi$
$971$	57.6332	−	16.9226i	1.84954	−	0.543073i	0.999876	−	0.0157441i	$-0.00501173\pi$
$972$	8.45752	+	18.5194i	0.271275	+	0.594010i
$973$	10.0681	+	11.6192i	0.322767	+	0.372493i
$974$	−12.7541	−	88.7065i	−0.408667	−	2.84234i
$975$	−0.586535	−	0.172222i	−0.0187842	−	0.00551553i
$976$	53.2830	−	61.4919i	1.70555	−	1.96831i
$977$	−25.9794	−	16.6960i	−0.831155	−	0.534151i	0.0544895	−	0.998514i	$-0.482647\pi$
$977$	−25.9794	−	16.6960i	−0.831155	−	0.534151i	−0.885645	+	0.464363i	$0.846283\pi$
$978$	−41.7011	−	26.7997i	−1.33345	−	0.856959i
$979$	−20.4585	+	23.6103i	−0.653855	+	0.754589i
$980$	−33.6311	−	9.87497i	−1.07431	−	0.315444i
$981$	−0.0909466	−	0.632548i	−0.00290370	−	0.0201957i
$982$	20.2264	+	23.3425i	0.645450	+	0.744889i
$983$	11.4863	+	25.1514i	0.366355	+	0.802206i	0.999601	+	0.0282549i	$0.00899501\pi$
$983$	11.4863	+	25.1514i	0.366355	+	0.802206i	−0.633246	+	0.773951i	$0.718278\pi$
$984$	9.11334	−	2.67592i	0.290523	−	0.0853052i
$985$	9.38785	−	20.5565i	0.299122	−	0.654985i
$986$	−9.91920	+	68.9896i	−0.315892	+	2.19708i
$987$	0.0154152	−	0.00990677i	0.000490672	−	0.000315336i
$988$	1.89384			0.0602510
$989$	5.58359	−	14.1178i	0.177548	−	0.448921i
$990$	6.03751			0.191885
$991$	4.66167	−	2.99587i	0.148083	−	0.0951671i	−0.464501	−	0.885572i	$-0.653766\pi$
$991$	4.66167	−	2.99587i	0.148083	−	0.0951671i	0.612584	+	0.790405i	$0.290130\pi$
$992$	1.40749	−	9.78933i	0.0446879	−	0.310811i
$993$	2.30030	−	5.03695i	0.0729977	−	0.159843i
$994$	−2.06292	+	0.605728i	−0.0654319	+	0.0192125i
$995$	−2.32727	−	5.09601i	−0.0737795	−	0.161555i
$996$	7.89259	+	9.10854i	0.250086	+	0.288615i
$997$	−0.316460	−	2.20103i	−0.0100224	−	0.0697073i	0.984196	−	0.177080i	$-0.0566652\pi$
$997$	−0.316460	−	2.20103i	−0.0100224	−	0.0697073i	−0.994219	+	0.107373i	$0.965756\pi$
$998$	−66.6527	−	19.5710i	−2.10986	−	0.619510i
$999$	14.0661	−	16.2332i	0.445032	−	0.513595i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.2.c.a.12.1	yes	10
3.2	odd	2		207.2.i.c.127.1		10
4.3	odd	2		368.2.m.c.81.1		10
5.2	odd	4		575.2.p.b.449.1		20
5.3	odd	4		575.2.p.b.449.2		20
5.4	even	2		575.2.k.b.426.1		10
23.2	even	11	inner	23.2.c.a.2.1	✓	10
23.3	even	11		529.2.c.i.177.1		10
23.4	even	11		529.2.c.g.399.1		10
23.5	odd	22		529.2.a.j.1.1		5
23.6	even	11		529.2.c.d.501.1		10
23.7	odd	22		529.2.c.h.266.1		10
23.8	even	11		529.2.c.d.170.1		10
23.9	even	11		529.2.c.b.466.1		10
23.10	odd	22		529.2.c.c.487.1		10
23.11	odd	22		529.2.c.f.118.1		10
23.12	even	11		529.2.c.g.118.1		10
23.13	even	11		529.2.c.b.487.1		10
23.14	odd	22		529.2.c.c.466.1		10
23.15	odd	22		529.2.c.e.170.1		10
23.16	even	11		529.2.c.i.266.1		10
23.17	odd	22		529.2.c.e.501.1		10
23.18	even	11		529.2.a.i.1.1		5
23.19	odd	22		529.2.c.f.399.1		10
23.20	odd	22		529.2.c.h.177.1		10
23.21	odd	22		529.2.c.a.255.1		10
23.22	odd	2		529.2.c.a.334.1		10
69.2	odd	22		207.2.i.c.163.1		10
69.5	even	22		4761.2.a.bn.1.5		5
69.41	odd	22		4761.2.a.bo.1.5		5
92.51	even	22		8464.2.a.bt.1.2		5
92.71	odd	22		368.2.m.c.209.1		10
92.87	odd	22		8464.2.a.bs.1.2		5
115.2	odd	44		575.2.p.b.324.2		20
115.48	odd	44		575.2.p.b.324.1		20
115.94	even	22		575.2.k.b.301.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.2.c.a.2.1	✓	10	23.2	even	11	inner
23.2.c.a.12.1	yes	10	1.1	even	1	trivial
207.2.i.c.127.1		10	3.2	odd	2
207.2.i.c.163.1		10	69.2	odd	22
368.2.m.c.81.1		10	4.3	odd	2
368.2.m.c.209.1		10	92.71	odd	22
529.2.a.i.1.1		5	23.18	even	11
529.2.a.j.1.1		5	23.5	odd	22
529.2.c.a.255.1		10	23.21	odd	22
529.2.c.a.334.1		10	23.22	odd	2
529.2.c.b.466.1		10	23.9	even	11
529.2.c.b.487.1		10	23.13	even	11
529.2.c.c.466.1		10	23.14	odd	22
529.2.c.c.487.1		10	23.10	odd	22
529.2.c.d.170.1		10	23.8	even	11
529.2.c.d.501.1		10	23.6	even	11
529.2.c.e.170.1		10	23.15	odd	22
529.2.c.e.501.1		10	23.17	odd	22
529.2.c.f.118.1		10	23.11	odd	22
529.2.c.f.399.1		10	23.19	odd	22
529.2.c.g.118.1		10	23.12	even	11
529.2.c.g.399.1		10	23.4	even	11
529.2.c.h.177.1		10	23.20	odd	22
529.2.c.h.266.1		10	23.7	odd	22
529.2.c.i.177.1		10	23.3	even	11
529.2.c.i.266.1		10	23.16	even	11
575.2.k.b.301.1		10	115.94	even	22
575.2.k.b.426.1		10	5.4	even	2
575.2.p.b.324.1		20	115.48	odd	44
575.2.p.b.324.2		20	115.2	odd	44
575.2.p.b.449.1		20	5.2	odd	4
575.2.p.b.449.2		20	5.3	odd	4
4761.2.a.bn.1.5		5	69.5	even	22
4761.2.a.bo.1.5		5	69.41	odd	22
8464.2.a.bs.1.2		5	92.87	odd	22
8464.2.a.bt.1.2		5	92.51	even	22

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

\(f(q)\)	\(=\)	\(q+(-2.11435 + 1.35881i) q^{2} +(-0.226900 + 1.57812i) q^{3} +(1.79329 - 3.92676i) q^{4} +(1.41899 - 0.416652i) q^{5} +(-1.66463 - 3.64502i) q^{6} +(-0.804632 - 0.928595i) q^{7} +(0.828708 + 5.76379i) q^{8} +(0.439490 + 0.129046i) q^{9} +O(q^{10})\)	\(q+(-2.11435 + 1.35881i) q^{2} +(-0.226900 + 1.57812i) q^{3} +(1.79329 - 3.92676i) q^{4} +(1.41899 - 0.416652i) q^{5} +(-1.66463 - 3.64502i) q^{6} +(-0.804632 - 0.928595i) q^{7} +(0.828708 + 5.76379i) q^{8} +(0.439490 + 0.129046i) q^{9} +(-2.43409 + 2.80909i) q^{10} +(-2.98325 - 1.91722i) q^{11} +(5.79001 + 3.72101i) q^{12} +(0.0892619 - 0.103014i) q^{13} +(2.96306 + 0.870034i) q^{14} +(0.335560 + 2.33387i) q^{15} +(-3.93020 - 4.53569i) q^{16} +(-2.50680 - 5.48912i) q^{17} +(-1.10459 + 0.324336i) q^{18} +(-1.33703 + 2.92768i) q^{19} +(0.908562 - 6.31919i) q^{20} +(1.64801 - 1.05911i) q^{21} +8.91280 q^{22} +(4.66533 + 1.11118i) q^{23} -9.28400 q^{24} +(-2.36635 + 1.52076i) q^{25} +(-0.0487549 + 0.339098i) q^{26} +(-2.29032 + 5.01511i) q^{27} +(-5.08931 + 1.49436i) q^{28} +(1.90906 + 4.18027i) q^{29} +(-3.88079 - 4.47867i) q^{30} +(-0.409407 - 2.84749i) q^{31} +(3.29862 + 0.968563i) q^{32} +(3.70251 - 4.27292i) q^{33} +(12.7590 + 8.19968i) q^{34} +(-1.52866 - 0.982412i) q^{35} +(1.29487 - 1.49436i) q^{36} +(-3.73811 - 1.09761i) q^{37} +(-1.15122 - 8.00691i) q^{38} +(0.142315 + 0.164240i) q^{39} +(3.57742 + 7.83345i) q^{40} +(-0.981618 + 0.288229i) q^{41} +(-2.04534 + 4.47867i) q^{42} +(0.450518 - 3.13342i) q^{43} +(-12.8783 + 8.27638i) q^{44} +0.677398 q^{45} +(-11.3740 + 3.98989i) q^{46} +0.00935386 q^{47} +(8.04964 - 5.17319i) q^{48} +(0.781348 - 5.43439i) q^{49} +(2.93687 - 6.43084i) q^{50} +(9.23131 - 2.71056i) q^{51} +(-0.244437 - 0.535243i) q^{52} +(6.16090 + 7.11005i) q^{53} +(-1.97204 - 13.7158i) q^{54} +(-5.03201 - 1.47753i) q^{55} +(4.68542 - 5.40726i) q^{56} +(-4.31686 - 2.77428i) q^{57} +(-9.71664 - 6.24450i) q^{58} +(-3.05621 + 3.52706i) q^{59} +(9.76631 + 2.86765i) q^{60} +(1.92941 + 13.4193i) q^{61} +(4.73483 + 5.46429i) q^{62} +(-0.233797 - 0.511943i) q^{63} +(3.22640 - 0.947356i) q^{64} +(0.0837405 - 0.183366i) q^{65} +(-2.02231 + 14.0655i) q^{66} +(8.18185 - 5.25816i) q^{67} -26.0499 q^{68} +(-2.81213 + 7.11034i) q^{69} +4.56705 q^{70} +(-0.585691 + 0.376401i) q^{71} +(-0.379585 + 2.64007i) q^{72} +(-2.20482 + 4.82788i) q^{73} +(9.39514 - 2.75866i) q^{74} +(-1.86302 - 4.07944i) q^{75} +(9.09860 + 10.5003i) q^{76} +(0.620100 + 4.31289i) q^{77} +(-0.524075 - 0.153882i) q^{78} +(7.03002 - 8.11308i) q^{79} +(-7.46670 - 4.79856i) q^{80} +(-6.23879 - 4.00943i) q^{81} +(1.68384 - 1.94325i) q^{82} +(1.68020 + 0.493351i) q^{83} +(-1.20351 - 8.37062i) q^{84} +(-5.84417 - 6.74453i) q^{85} +(3.30518 + 7.23733i) q^{86} +(-7.03014 + 2.06424i) q^{87} +(8.57821 - 18.7837i) q^{88} +(1.25375 - 8.72002i) q^{89} +(-1.43226 + 0.920457i) q^{90} -0.167481 q^{91} +(12.7296 - 16.3270i) q^{92} +4.58658 q^{93} +(-0.0197774 + 0.0127101i) q^{94} +(-0.677398 + 4.71141i) q^{95} +(-2.27697 + 4.98587i) q^{96} +(-17.2863 + 5.07571i) q^{97} +(5.73228 + 12.5519i) q^{98} +(-1.06370 - 1.22758i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 7 q^{2} - 7 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 5 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 10 * q - 7 * q^2 - 7 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 - 5 * q^7 + 4 * q^8 - 2 * q^9	\( 10 q - 7 q^{2} - 7 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 5 q^{7} + 4 q^{8} - 2 q^{9} + q^{10} + 7 q^{11} + 12 q^{12} - 3 q^{13} + 9 q^{14} + 12 q^{15} + q^{16} - 10 q^{17} - 14 q^{18} + 2 q^{19} - 9 q^{20} - 2 q^{21} - 6 q^{22} - 12 q^{23} - 38 q^{24} - 4 q^{25} + 12 q^{26} - 4 q^{27} + 7 q^{28} + 14 q^{29} + 7 q^{30} + 10 q^{31} + 21 q^{32} + 16 q^{33} + 29 q^{34} + 7 q^{35} + 27 q^{36} - 19 q^{37} - 8 q^{38} + q^{39} + q^{40} + 7 q^{41} - 25 q^{42} - 11 q^{43} - 34 q^{44} - 6 q^{45} - 29 q^{46} - 18 q^{47} + 18 q^{48} - 18 q^{49} + 16 q^{50} + 7 q^{51} - 20 q^{52} + 29 q^{53} - 6 q^{54} - q^{55} - 2 q^{56} - 8 q^{57} - 23 q^{58} - 21 q^{59} + 25 q^{60} + 3 q^{61} + 4 q^{62} + 34 q^{63} + 24 q^{64} + 2 q^{65} + 2 q^{66} + 45 q^{67} - 30 q^{68} + 26 q^{69} + 38 q^{70} - 14 q^{71} + 19 q^{72} + 19 q^{73} + 10 q^{74} - 28 q^{75} - 16 q^{76} + 2 q^{77} - 4 q^{78} - 15 q^{79} - 52 q^{80} - 44 q^{81} + 16 q^{82} + 18 q^{83} - 17 q^{84} - 19 q^{85} - 11 q^{86} - 23 q^{87} + 27 q^{88} + 25 q^{89} - 20 q^{90} - 4 q^{91} + 52 q^{92} + 4 q^{93} + 17 q^{94} + 6 q^{95} - 51 q^{96} - 34 q^{97} + 17 q^{98} - 30 q^{99}+O(q^{100}) \) 10 * q - 7 * q^2 - 7 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 - 5 * q^7 + 4 * q^8 - 2 * q^9 + q^10 + 7 * q^11 + 12 * q^12 - 3 * q^13 + 9 * q^14 + 12 * q^15 + q^16 - 10 * q^17 - 14 * q^18 + 2 * q^19 - 9 * q^20 - 2 * q^21 - 6 * q^22 - 12 * q^23 - 38 * q^24 - 4 * q^25 + 12 * q^26 - 4 * q^27 + 7 * q^28 + 14 * q^29 + 7 * q^30 + 10 * q^31 + 21 * q^32 + 16 * q^33 + 29 * q^34 + 7 * q^35 + 27 * q^36 - 19 * q^37 - 8 * q^38 + q^39 + q^40 + 7 * q^41 - 25 * q^42 - 11 * q^43 - 34 * q^44 - 6 * q^45 - 29 * q^46 - 18 * q^47 + 18 * q^48 - 18 * q^49 + 16 * q^50 + 7 * q^51 - 20 * q^52 + 29 * q^53 - 6 * q^54 - q^55 - 2 * q^56 - 8 * q^57 - 23 * q^58 - 21 * q^59 + 25 * q^60 + 3 * q^61 + 4 * q^62 + 34 * q^63 + 24 * q^64 + 2 * q^65 + 2 * q^66 + 45 * q^67 - 30 * q^68 + 26 * q^69 + 38 * q^70 - 14 * q^71 + 19 * q^72 + 19 * q^73 + 10 * q^74 - 28 * q^75 - 16 * q^76 + 2 * q^77 - 4 * q^78 - 15 * q^79 - 52 * q^80 - 44 * q^81 + 16 * q^82 + 18 * q^83 - 17 * q^84 - 19 * q^85 - 11 * q^86 - 23 * q^87 + 27 * q^88 + 25 * q^89 - 20 * q^90 - 4 * q^91 + 52 * q^92 + 4 * q^93 + 17 * q^94 + 6 * q^95 - 51 * q^96 - 34 * q^97 + 17 * q^98 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more