LMFDB - Embedded newform 67.2.e.c.24.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [67,2,Mod(9,67)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(67, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("67.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	67.e (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:	$0.534997693543$
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} - 7 x^{19} + 39 x^{18} - 148 x^{17} + 492 x^{16} - 1282 x^{15} + 2921 x^{14} - 4316 x^{13} + \cdots + 4489 $ x^20 - 7x^19 + 39x^18 - 148x^17 + 492x^16 - 1282x^15 + 2921x^14 - 4316x^13 + 2696x^12 + 9361x^11 - 20998x^10 + 10813x^9 + 44155x^8 - 46933x^7 - 36976x^6 - 49131x^5 + 105828x^4 + 108234x^3 + 143215x^2 + 41004*x + 4489
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			24.2
Root			$1.66916 + 1.92631i$ of defining polynomial
Character	$\chi$	$=$	67.24
Dual form			67.2.e.c.14.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.797176 + 1.74557i) q^{2} +(0.802994 - 0.516053i) q^{3} +(-1.10181 - 1.27155i) q^{4} +(-0.451016 + 3.13689i) q^{5} +(0.260680 + 1.81307i) q^{6} +(1.40141 - 3.06866i) q^{7} +(-0.584585 + 0.171650i) q^{8} +(-0.867756 + 1.90012i) q^{9} +O(q^{10})$	\(q+(-0.797176 + 1.74557i) q^{2} +(0.802994 - 0.516053i) q^{3} +(-1.10181 - 1.27155i) q^{4} +(-0.451016 + 3.13689i) q^{5} +(0.260680 + 1.81307i) q^{6} +(1.40141 - 3.06866i) q^{7} +(-0.584585 + 0.171650i) q^{8} +(-0.867756 + 1.90012i) q^{9} +(-5.11612 - 3.28793i) q^{10} +(0.598388 - 4.16188i) q^{11} +(-1.54093 - 0.452459i) q^{12} +(1.65150 + 0.484925i) q^{13} +(4.23940 + 4.89252i) q^{14} +(1.25664 + 2.75165i) q^{15} +(0.645282 - 4.48803i) q^{16} +(3.22553 - 3.72246i) q^{17} +(-2.62504 - 3.02946i) q^{18} +(-0.0642876 - 0.140770i) q^{19} +(4.48565 - 2.88275i) q^{20} +(-0.458267 - 3.18732i) q^{21} +(6.78784 + 4.36228i) q^{22} +(-0.215503 + 0.138495i) q^{23} +(-0.380838 + 0.439511i) q^{24} +(-4.83917 - 1.42091i) q^{25} +(-2.16301 + 2.49625i) q^{26} +(0.691288 + 4.80801i) q^{27} +(-5.44605 + 1.59911i) q^{28} -9.45314 q^{29} -5.80496 q^{30} +(-6.77696 + 1.98990i) q^{31} +(6.29469 + 4.04535i) q^{32} +(-1.66725 - 3.65077i) q^{33} +(3.92651 + 8.59785i) q^{34} +(8.99398 + 5.78008i) q^{35} +(3.37221 - 0.990169i) q^{36} -0.210230 q^{37} +0.296973 q^{38} +(1.57639 - 0.462871i) q^{39} +(-0.274788 - 1.91119i) q^{40} +(1.99866 - 2.30658i) q^{41} +(5.92901 + 1.74091i) q^{42} +(-2.71169 + 3.12945i) q^{43} +(-5.95136 + 3.82471i) q^{44} +(-5.56909 - 3.57904i) q^{45} +(-0.0699596 - 0.486580i) q^{46} +(4.08294 - 2.62395i) q^{47} +(-1.79791 - 3.93686i) q^{48} +(-2.86870 - 3.31066i) q^{49} +(6.33797 - 7.31440i) q^{50} +(0.669096 - 4.65366i) q^{51} +(-1.20303 - 2.63427i) q^{52} +(6.51756 + 7.52166i) q^{53} +(-8.94380 - 2.62614i) q^{54} +(12.7855 + 3.75415i) q^{55} +(-0.292509 + 2.03444i) q^{56} +(-0.124268 - 0.0798619i) q^{57} +(7.53581 - 16.5011i) q^{58} +(-12.2983 + 3.61111i) q^{59} +(2.11430 - 4.62967i) q^{60} +(1.78213 + 12.3950i) q^{61} +(1.92892 - 13.4160i) q^{62} +(4.61474 + 5.32570i) q^{63} +(-4.45062 + 2.86024i) q^{64} +(-2.26601 + 4.96187i) q^{65} +7.70176 q^{66} +(1.38719 - 8.06695i) q^{67} -8.28723 q^{68} +(-0.101577 + 0.222422i) q^{69} +(-17.2593 + 11.0919i) q^{70} +(-0.0591972 - 0.0683172i) q^{71} +(0.181122 - 1.25973i) q^{72} +(-1.15465 - 8.03075i) q^{73} +(0.167591 - 0.366972i) q^{74} +(-4.61909 + 1.35629i) q^{75} +(-0.108164 + 0.236847i) q^{76} +(-11.9328 - 7.66875i) q^{77} +(-0.448689 + 3.12070i) q^{78} +(4.53757 + 1.33235i) q^{79} +(13.7874 + 4.04835i) q^{80} +(-1.06751 - 1.23197i) q^{81} +(2.43301 + 5.32755i) q^{82} +(1.11684 - 7.76780i) q^{83} +(-3.54793 + 4.09453i) q^{84} +(10.2222 + 11.7970i) q^{85} +(-3.30099 - 7.22817i) q^{86} +(-7.59082 + 4.87832i) q^{87} +(0.364577 + 2.53569i) q^{88} +(-13.6813 - 8.79241i) q^{89} +(10.6870 - 6.86812i) q^{90} +(3.80250 - 4.38832i) q^{91} +(0.413546 + 0.121428i) q^{92} +(-4.41497 + 5.09515i) q^{93} +(1.32546 + 9.21881i) q^{94} +(0.470575 - 0.138173i) q^{95} +7.14221 q^{96} +1.98762 q^{97} +(8.06585 - 2.36835i) q^{98} +(7.38882 + 4.74851i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9	\( 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9} - 9 q^{10} + 3 q^{12} + 12 q^{13} + 6 q^{14} - 11 q^{15} + 8 q^{16} - 4 q^{17} - 2 q^{18} + 4 q^{19} + 2 q^{20} - 53 q^{21} + 2 q^{23} + 11 q^{24} - 3 q^{25} - 31 q^{26} + 47 q^{27} - 5 q^{28} - 6 q^{29} + 44 q^{30} + 16 q^{32} + q^{33} - 8 q^{34} + 34 q^{35} + 9 q^{36} + 24 q^{37} - 14 q^{38} - 22 q^{39} - 11 q^{40} - 6 q^{41} + 59 q^{42} - 22 q^{43} - 22 q^{44} - 46 q^{45} + 15 q^{46} + 16 q^{47} + 5 q^{48} + 42 q^{49} - 17 q^{50} + 22 q^{51} + 2 q^{52} - q^{53} - 60 q^{54} + 20 q^{55} + 11 q^{56} - 52 q^{57} + 10 q^{58} - 26 q^{59} + 44 q^{60} - 26 q^{61} + 11 q^{62} - 42 q^{63} - 6 q^{64} + 9 q^{65} + 2 q^{66} - 22 q^{67} - 52 q^{68} + 62 q^{69} - 42 q^{70} + 20 q^{71} + 11 q^{72} - 55 q^{73} + 37 q^{74} - 70 q^{75} - 3 q^{76} - 70 q^{77} + 22 q^{78} - 34 q^{79} + 40 q^{80} + 42 q^{81} - 12 q^{82} + 56 q^{83} - 29 q^{84} + 41 q^{85} - 33 q^{86} - 10 q^{87} + 11 q^{88} - 3 q^{89} + 18 q^{90} + 12 q^{91} - 18 q^{92} - 69 q^{93} + 32 q^{94} + 74 q^{95} - 12 q^{96} - 14 q^{97} + 95 q^{98} + 81 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9 - 9 * q^10 + 3 * q^12 + 12 * q^13 + 6 * q^14 - 11 * q^15 + 8 * q^16 - 4 * q^17 - 2 * q^18 + 4 * q^19 + 2 * q^20 - 53 * q^21 + 2 * q^23 + 11 * q^24 - 3 * q^25 - 31 * q^26 + 47 * q^27 - 5 * q^28 - 6 * q^29 + 44 * q^30 + 16 * q^32 + q^33 - 8 * q^34 + 34 * q^35 + 9 * q^36 + 24 * q^37 - 14 * q^38 - 22 * q^39 - 11 * q^40 - 6 * q^41 + 59 * q^42 - 22 * q^43 - 22 * q^44 - 46 * q^45 + 15 * q^46 + 16 * q^47 + 5 * q^48 + 42 * q^49 - 17 * q^50 + 22 * q^51 + 2 * q^52 - q^53 - 60 * q^54 + 20 * q^55 + 11 * q^56 - 52 * q^57 + 10 * q^58 - 26 * q^59 + 44 * q^60 - 26 * q^61 + 11 * q^62 - 42 * q^63 - 6 * q^64 + 9 * q^65 + 2 * q^66 - 22 * q^67 - 52 * q^68 + 62 * q^69 - 42 * q^70 + 20 * q^71 + 11 * q^72 - 55 * q^73 + 37 * q^74 - 70 * q^75 - 3 * q^76 - 70 * q^77 + 22 * q^78 - 34 * q^79 + 40 * q^80 + 42 * q^81 - 12 * q^82 + 56 * q^83 - 29 * q^84 + 41 * q^85 - 33 * q^86 - 10 * q^87 + 11 * q^88 - 3 * q^89 + 18 * q^90 + 12 * q^91 - 18 * q^92 - 69 * q^93 + 32 * q^94 + 74 * q^95 - 12 * q^96 - 14 * q^97 + 95 * q^98 + 81 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/67\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{11}\right)$

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 $

$2$	−0.797176	+	1.74557i	−0.563688	+	1.23431i	0.386402	+	0.922330i	$0.373718\pi$
$2$	−0.797176	+	1.74557i	−0.563688	+	1.23431i	−0.950090	+	0.311975i	$0.899010\pi$
$3$	0.802994	−	0.516053i	0.463609	−	0.297943i	−0.287907	−	0.957658i	$-0.592959\pi$
$3$	0.802994	−	0.516053i	0.463609	−	0.297943i	0.751516	+	0.659715i	$0.229323\pi$
$4$	−1.10181	−	1.27155i	−0.550904	−	0.635777i
$5$	−0.451016	+	3.13689i	−0.201701	+	1.40286i	0.597536	+	0.801842i	$0.296146\pi$
$5$	−0.451016	+	3.13689i	−0.201701	+	1.40286i	−0.799237	+	0.601016i	$0.794763\pi$
$6$	0.260680	+	1.81307i	0.106422	+	0.740182i
$7$	1.40141	−	3.06866i	0.529683	−	1.15984i	−0.435958	−	0.899967i	$-0.643590\pi$
$7$	1.40141	−	3.06866i	0.529683	−	1.15984i	0.965642	−	0.259878i	$-0.0836823\pi$
$8$	−0.584585	+	0.171650i	−0.206682	+	0.0606873i
$9$	−0.867756	+	1.90012i	−0.289252	+	0.633374i
$10$	−5.11612	−	3.28793i	−1.61786	−	1.03973i
$11$	0.598388	−	4.16188i	0.180421	−	1.25485i	−0.675349	−	0.737498i	$-0.736007\pi$
$11$	0.598388	−	4.16188i	0.180421	−	1.25485i	0.855770	−	0.517356i	$-0.173084\pi$
$12$	−1.54093	−	0.452459i	−0.444830	−	0.130614i
$13$	1.65150	+	0.484925i	0.458045	+	0.134494i	0.502611	−	0.864512i	$-0.332373\pi$
$13$	1.65150	+	0.484925i	0.458045	+	0.134494i	−0.0445670	+	0.999006i	$0.514191\pi$
$14$	4.23940	+	4.89252i	1.13303	+	1.30758i
$15$	1.25664	+	2.75165i	0.324462	+	0.710473i
$16$	0.645282	−	4.48803i	0.161320	−	1.12201i
$17$	3.22553	−	3.72246i	0.782306	−	0.902830i	−0.214967	−	0.976621i	$-0.568964\pi$
$17$	3.22553	−	3.72246i	0.782306	−	0.902830i	0.997274	+	0.0737915i	$0.0235099\pi$
$18$	−2.62504	−	3.02946i	−0.618728	−	0.714050i
$19$	−0.0642876	−	0.140770i	−0.0147486	−	0.0322949i	0.902114	−	0.431497i	$-0.142014\pi$
$19$	−0.0642876	−	0.140770i	−0.0147486	−	0.0322949i	−0.916863	+	0.399202i	$0.869287\pi$
$20$	4.48565	−	2.88275i	1.00302	−	0.644603i
$21$	−0.458267	−	3.18732i	−0.100002	−	0.695530i
$22$	6.78784	+	4.36228i	1.44717	+	0.930041i
$23$	−0.215503	+	0.138495i	−0.0449354	+	0.0288782i	−0.562916	−	0.826514i	$-0.690320\pi$
$23$	−0.215503	+	0.138495i	−0.0449354	+	0.0288782i	0.517980	+	0.855393i	$0.326684\pi$
$24$	−0.380838	+	0.439511i	−0.0777383	+	0.0897147i
$25$	−4.83917	−	1.42091i	−0.967834	−	0.284182i
$26$	−2.16301	+	2.49625i	−0.424201	+	0.489554i
$27$	0.691288	+	4.80801i	0.133038	+	0.925302i
$28$	−5.44605	+	1.59911i	−1.02921	+	0.302203i
$29$	−9.45314			−1.75540			−0.877702	−	0.479206i	$-0.840925\pi$
$29$	−9.45314			−1.75540			−0.877702	+	0.479206i	$0.840925\pi$
$30$	−5.80496			−1.05984
$31$	−6.77696	+	1.98990i	−1.21718	+	0.357396i	−0.826397	−	0.563088i	$-0.809613\pi$
$31$	−6.77696	+	1.98990i	−1.21718	+	0.357396i	−0.390781	+	0.920484i	$0.627795\pi$
$32$	6.29469	+	4.04535i	1.11275	+	0.715123i
$33$	−1.66725	−	3.65077i	−0.290231	−	0.635517i
$34$	3.92651	+	8.59785i	0.673390	+	1.47452i
$35$	8.99398	+	5.78008i	1.52026	+	0.977012i
$36$	3.37221	−	0.990169i	0.562034	−	0.165028i
$37$	−0.210230			−0.0345617			−0.0172808	−	0.999851i	$-0.505501\pi$
$37$	−0.210230			−0.0345617			−0.0172808	+	0.999851i	$0.505501\pi$
$38$	0.296973			0.0481754
$39$	1.57639	−	0.462871i	0.252425	−	0.0741187i
$40$	−0.274788	−	1.91119i	−0.0434478	−	0.302186i
$41$	1.99866	−	2.30658i	0.312138	−	0.360227i	−0.577904	−	0.816105i	$-0.696129\pi$
$41$	1.99866	−	2.30658i	0.312138	−	0.360227i	0.890042	+	0.455878i	$0.150675\pi$
$42$	5.92901	+	1.74091i	0.914866	+	0.268629i
$43$	−2.71169	+	3.12945i	−0.413529	+	0.477237i	−0.923855	−	0.382744i	$-0.874979\pi$
$43$	−2.71169	+	3.12945i	−0.413529	+	0.477237i	0.510326	+	0.859981i	$0.329525\pi$
$44$	−5.95136	+	3.82471i	−0.897202	+	0.576597i
$45$	−5.56909	−	3.57904i	−0.830191	−	0.533531i
$46$	−0.0699596	−	0.486580i	−0.0103150	−	0.0717423i
$47$	4.08294	−	2.62395i	0.595558	−	0.382742i	−0.207859	−	0.978159i	$-0.566649\pi$
$47$	4.08294	−	2.62395i	0.595558	−	0.382742i	0.803417	+	0.595417i	$0.203013\pi$
$48$	−1.79791	−	3.93686i	−0.259505	−	0.568237i
$49$	−2.86870	−	3.31066i	−0.409815	−	0.472951i
$50$	6.33797	−	7.31440i	0.896324	−	1.03441i
$51$	0.669096	−	4.65366i	0.0936921	−	0.651643i
$52$	−1.20303	−	2.63427i	−0.166830	−	0.365307i
$53$	6.51756	+	7.52166i	0.895255	+	1.03318i	0.999255	+	0.0386023i	$0.0122905\pi$
$53$	6.51756	+	7.52166i	0.895255	+	1.03318i	−0.103999	+	0.994577i	$0.533164\pi$
$54$	−8.94380	−	2.62614i	−1.21710	−	0.357372i
$55$	12.7855	+	3.75415i	1.72399	+	0.506209i
$56$	−0.292509	+	2.03444i	−0.0390882	+	0.271864i
$57$	−0.124268	−	0.0798619i	−0.0164596	−	0.0105780i
$58$	7.53581	−	16.5011i	0.989501	−	2.16670i
$59$	−12.2983	+	3.61111i	−1.60111	+	0.470127i	−0.955854	−	0.293843i	$-0.905066\pi$
$59$	−12.2983	+	3.61111i	−1.60111	+	0.470127i	−0.645252	+	0.763970i	$0.723248\pi$
$60$	2.11430	−	4.62967i	0.272955	−	0.597688i
$61$	1.78213	+	12.3950i	0.228178	+	1.58701i	0.705777	+	0.708434i	$0.250598\pi$
$61$	1.78213	+	12.3950i	0.228178	+	1.58701i	−0.477599	+	0.878578i	$0.658493\pi$
$62$	1.92892	−	13.4160i	0.244974	−	1.70383i
$63$	4.61474	+	5.32570i	0.581403	+	0.670975i
$64$	−4.45062	+	2.86024i	−0.556327	+	0.357530i
$65$	−2.26601	+	4.96187i	−0.281064	+	0.615444i
$66$	7.70176			0.948021
$67$	1.38719	−	8.06695i	0.169472	−	0.985535i
$67$	1.38719	−	8.06695i	0.169472	−	0.985535i
$68$	−8.28723			−1.00497
$69$	−0.101577	+	0.222422i	−0.0122284	+	0.0267764i
$70$	−17.2593	+	11.0919i	−2.06288	+	1.32573i
$71$	−0.0591972	−	0.0683172i	−0.00702541	−	0.00810776i	0.752226	−	0.658905i	$-0.228980\pi$
$71$	−0.0591972	−	0.0683172i	−0.00702541	−	0.00810776i	−0.759251	+	0.650797i	$0.774435\pi$
$72$	0.181122	−	1.25973i	0.0213454	−	0.148461i
$73$	−1.15465	−	8.03075i	−0.135141	−	0.939929i	−0.938708	−	0.344714i	$-0.887976\pi$
$73$	−1.15465	−	8.03075i	−0.135141	−	0.939929i	0.803567	−	0.595215i	$-0.202933\pi$
$74$	0.167591	−	0.366972i	0.0194820	−	0.0426597i
$75$	−4.61909	+	1.35629i	−0.533367	+	0.156611i
$76$	−0.108164	+	0.236847i	−0.0124073	+	0.0271682i
$77$	−11.9328	−	7.66875i	−1.35987	−	0.873935i
$78$	−0.448689	+	3.12070i	−0.0508040	+	0.353349i
$79$	4.53757	+	1.33235i	0.510517	+	0.149901i	0.526838	−	0.849966i	$-0.323377\pi$
$79$	4.53757	+	1.33235i	0.510517	+	0.149901i	−0.0163217	+	0.999867i	$0.505196\pi$
$80$	13.7874	+	4.04835i	1.54148	+	0.452619i
$81$	−1.06751	−	1.23197i	−0.118612	−	0.136885i
$82$	2.43301	+	5.32755i	0.268681	+	0.588330i
$83$	1.11684	−	7.76780i	0.122589	−	0.852627i	−0.832016	−	0.554752i	$-0.812813\pi$
$83$	1.11684	−	7.76780i	0.122589	−	0.852627i	0.954605	−	0.297875i	$-0.0962778\pi$
$84$	−3.54793	+	4.09453i	−0.387110	+	0.446749i
$85$	10.2222	+	11.7970i	1.10875	+	1.27957i
$86$	−3.30099	−	7.22817i	−0.355955	−	0.779433i
$87$	−7.59082	+	4.87832i	−0.813821	+	0.523011i
$88$	0.364577	+	2.53569i	0.0388640	+	0.270305i
$89$	−13.6813	−	8.79241i	−1.45021	−	0.931993i	−0.999221	−	0.0394638i	$-0.987435\pi$
$89$	−13.6813	−	8.79241i	−1.45021	−	0.931993i	−0.450989	−	0.892530i	$-0.648929\pi$
$90$	10.6870	−	6.86812i	1.12651	−	0.723963i
$91$	3.80250	−	4.38832i	0.398611	−	0.460021i
$92$	0.413546	+	0.121428i	0.0431152	+	0.0126598i
$93$	−4.41497	+	5.09515i	−0.457811	+	0.528342i
$94$	1.32546	+	9.21881i	0.136711	+	0.950848i
$95$	0.470575	−	0.138173i	0.0482800	−	0.0141763i
$96$	7.14221			0.728949
$97$	1.98762			0.201812			0.100906	−	0.994896i	$-0.467826\pi$
$97$	1.98762			0.201812			0.100906	+	0.994896i	$0.467826\pi$
$98$	8.06585	−	2.36835i	0.814774	−	0.239239i
$99$	7.38882	+	4.74851i	0.742604	+	0.477243i
$100$	3.52507	+	7.71883i	0.352507	+	0.771883i
$101$	−3.19667	−	6.99972i	−0.318080	−	0.696498i	0.681289	−	0.732015i	$-0.261420\pi$
$101$	−3.19667	−	6.99972i	−0.318080	−	0.696498i	−0.999369	+	0.0355163i	$0.988692\pi$
$102$	7.58991	+	4.87774i	0.751513	+	0.482968i
$103$	2.22090	−	0.652116i	0.218832	−	0.0642549i	−0.170479	−	0.985361i	$-0.554531\pi$
$103$	2.22090	−	0.652116i	0.218832	−	0.0642549i	0.389311	+	0.921106i	$0.372713\pi$
$104$	−1.04868			−0.102832
$105$	10.2049			0.995900
$106$	−18.3252	+	5.38077i	−1.77990	+	0.522627i
$107$	1.79543	+	12.4875i	0.173571	+	1.20721i	0.871264	+	0.490814i	$0.163300\pi$
$107$	1.79543	+	12.4875i	0.173571	+	1.20721i	−0.697694	+	0.716396i	$0.745790\pi$
$108$	5.35198	−	6.17651i	0.514994	−	0.594335i
$109$	15.6766	+	4.60307i	1.50155	+	0.440894i	0.926205	−	0.377019i	$-0.123051\pi$
$109$	15.6766	+	4.60307i	1.50155	+	0.440894i	0.575341	+	0.817913i	$0.304869\pi$
$110$	−16.7454	+	19.3252i	−1.59661	+	1.84259i
$111$	−0.168814	+	0.108490i	−0.0160231	+	0.0102974i
$112$	−12.8679	−	8.26973i	−1.21591	−	0.781416i
$113$	0.128861	+	0.896251i	0.0121223	+	0.0843122i	0.994984	−	0.100030i	$-0.0318938\pi$
$113$	0.128861	+	0.896251i	0.0121223	+	0.0843122i	−0.982862	+	0.184342i	$0.940985\pi$
$114$	0.238468	−	0.153254i	0.0223345	−	0.0143535i
$115$	−0.337248	−	0.738470i	−0.0314485	−	0.0688627i
$116$	10.4155	+	12.0202i	0.967059	+	1.11605i
$117$	−2.35452	+	2.71726i	−0.217675	+	0.251211i
$118$	3.50047	−	24.3463i	0.322244	−	2.24126i
$119$	−6.90268	−	15.1148i	−0.632768	−	1.38557i
$120$	−1.20693	−	1.39287i	−0.110177	−	0.127151i
$121$	−6.40876	−	1.88178i	−0.582614	−	0.171071i
$122$	−23.0570	−	6.77013i	−2.08748	−	0.612939i
$123$	0.414597	−	2.88358i	0.0373829	−	0.260004i
$124$	9.99717	+	6.42479i	0.897772	+	0.576963i
$125$	0.0572238	−	0.125303i	0.00511825	−	0.0112074i
$126$	−12.9751	+	3.80985i	−1.15592	+	0.339408i
$127$	−1.79814	+	3.93739i	−0.159559	+	0.349386i	−0.972479	−	0.232989i	$-0.925149\pi$
$127$	−1.79814	+	3.93739i	−0.159559	+	0.349386i	0.812920	+	0.582376i	$0.197877\pi$
$128$	0.684919	+	4.76371i	0.0605388	+	0.421057i
$129$	−0.562505	+	3.91231i	−0.0495258	+	0.344460i
$130$	−6.85488	−	7.91096i	−0.601213	−	0.693837i
$131$	15.1221	−	9.71836i	1.32122	−	0.849097i	0.325870	−	0.945414i	$-0.394343\pi$
$131$	15.1221	−	9.71836i	1.32122	−	0.849097i	0.995351	+	0.0963172i	$0.0307063\pi$
$132$	−2.80516	+	6.14244i	−0.244158	+	0.534631i
$133$	−0.522069			−0.0452692
$134$	12.9756	+	8.85222i	1.12092	+	0.764715i
$135$	−15.3940			−1.32490
$136$	−1.24664	+	2.72976i	−0.106898	+	0.234075i
$137$	−6.24620	+	4.01419i	−0.533649	+	0.342955i	−0.779550	−	0.626339i	$-0.784552\pi$
$137$	−6.24620	+	4.01419i	−0.533649	+	0.342955i	0.245901	+	0.969295i	$0.420916\pi$
$138$	−0.307278	−	0.354618i	−0.0261573	−	0.0301871i
$139$	0.242425	−	1.68610i	0.0205622	−	0.143013i	−0.976954	−	0.213450i	$-0.931530\pi$
$139$	0.242425	−	1.68610i	0.0205622	−	0.143013i	0.997516	+	0.0704362i	$0.0224391\pi$
$140$	−2.55995	−	17.8049i	−0.216356	−	1.50479i
$141$	1.92448	−	4.21403i	0.162071	−	0.354885i
$142$	0.166443	−	0.0488721i	0.0139676	−	0.00410125i
$143$	3.00644	−	6.58318i	0.251411	−	0.550514i
$144$	7.96786	+	5.12063i	0.663988	+	0.426719i
$145$	4.26352	−	29.6534i	0.354066	−	2.46258i
$146$	14.9387	+	4.38640i	1.23634	+	0.363021i
$147$	−4.01203	−	1.17804i	−0.330907	−	0.0971629i
$148$	0.231634	+	0.267319i	0.0190402	+	0.0219735i
$149$	6.34126	+	13.8854i	0.519496	+	1.13754i	0.969630	+	0.244577i	$0.0786490\pi$
$149$	6.34126	+	13.8854i	0.519496	+	1.13754i	−0.450134	+	0.892961i	$0.648624\pi$
$150$	1.31473	−	9.14415i	0.107347	−	0.746617i
$151$	−7.77283	+	8.97033i	−0.632544	+	0.729995i	−0.978038	−	0.208426i	$-0.933166\pi$
$151$	−7.77283	+	8.97033i	−0.632544	+	0.729995i	0.345494	+	0.938421i	$0.387711\pi$
$152$	0.0617447	+	0.0712572i	0.00500816	+	0.00577972i
$153$	4.27415	+	9.35909i	0.345545	+	0.756638i
$154$	22.8989	−	14.7162i	1.84525	−	1.18587i
$155$	−3.18556	−	22.1560i	−0.255870	−	1.77961i
$156$	−2.32545	−	1.49448i	−0.186185	−	0.119654i
$157$	1.91845	−	1.23291i	0.153109	−	0.0983973i	−0.461843	−	0.886962i	$-0.652812\pi$
$157$	1.91845	−	1.23291i	0.153109	−	0.0983973i	0.614952	+	0.788564i	$0.289175\pi$
$158$	−5.94295	+	6.85853i	−0.472796	+	0.545636i
$159$	9.11514	+	2.67645i	0.722877	+	0.212256i
$160$	−15.5288	+	17.9212i	−1.22766	+	1.41679i
$161$	0.122987	+	0.855393i	0.00969273	+	0.0674144i
$162$	3.00148	−	0.881313i	0.235818	−	0.0692425i
$163$	−4.08535			−0.319989			−0.159995	−	0.987118i	$-0.551148\pi$
$163$	−4.08535			−0.319989			−0.159995	+	0.987118i	$0.551148\pi$
$164$	−5.13508			−0.400982
$165$	12.2040	−	3.58342i	0.950080	−	0.278969i
$166$	12.6689	+	8.14183i	0.983300	+	0.631928i
$167$	−3.93362	−	8.61342i	−0.304392	−	0.666526i	0.694188	−	0.719794i	$-0.255764\pi$
$167$	−3.93362	−	8.61342i	−0.304392	−	0.666526i	−0.998580	+	0.0532675i	$0.983036\pi$
$168$	0.814998	+	1.78460i	0.0628785	+	0.137685i
$169$	−8.44399	−	5.42662i	−0.649537	−	0.417432i
$170$	−28.7414	+	8.43923i	−2.20436	+	0.647260i
$171$	0.323266			0.0247208
$172$	6.96703			0.531231
$173$	5.39745	−	1.58483i	0.410361	−	0.120493i	−0.0700353	−	0.997545i	$-0.522311\pi$
$173$	5.39745	−	1.58483i	0.410361	−	0.120493i	0.480396	+	0.877052i	$0.340493\pi$
$174$	−2.46424	−	17.1392i	−0.186814	−	1.29932i
$175$	−11.1420	+	12.8585i	−0.842252	+	0.972011i
$176$	−18.2925	−	5.37117i	−1.37885	−	0.404867i
$177$	−8.01196	+	9.24630i	−0.602216	+	0.694994i
$178$	26.2541	−	16.8725i	1.96783	−	1.26465i
$179$	15.9030	+	10.2203i	1.18865	+	0.763899i	0.976957	−	0.213437i	$-0.0684660\pi$
$179$	15.9030	+	10.2203i	1.18865	+	0.763899i	0.211693	+	0.977336i	$0.432102\pi$
$180$	1.58513	+	11.0248i	0.118148	+	0.821741i
$181$	7.19238	−	4.62226i	0.534605	−	0.343570i	−0.245321	−	0.969442i	$-0.578893\pi$
$181$	7.19238	−	4.62226i	0.534605	−	0.343570i	0.779926	+	0.625872i	$0.215257\pi$
$182$	4.62887	+	10.1358i	0.343114	+	0.751316i
$183$	7.82750	+	9.03341i	0.578625	+	0.667769i
$184$	0.102207	−	0.117953i	0.00753479	−	0.00869562i
$185$	0.0948173	−	0.659469i	0.00697111	−	0.0484851i
$186$	−5.37443	−	11.7684i	−0.394073	−	0.862899i
$187$	−13.5623	−	15.6518i	−0.991775	−	1.14457i
$188$	−7.83511	−	2.30059i	−0.571434	−	0.167788i
$189$	15.7229	+	4.61667i	1.14368	+	0.335813i
$190$	−0.133940	+	0.931570i	−0.00971700	+	0.0675832i
$191$	2.64534	+	1.70006i	0.191410	+	0.123012i	0.632836	−	0.774286i	$-0.281891\pi$
$191$	2.64534	+	1.70006i	0.191410	+	0.123012i	−0.441426	+	0.897298i	$0.645527\pi$
$192$	−2.09778	+	4.59351i	−0.151395	+	0.331508i
$193$	12.1572	−	3.56968i	0.875094	−	0.256951i	0.186814	−	0.982395i	$-0.440184\pi$
$193$	12.1572	−	3.56968i	0.875094	−	0.256951i	0.688281	+	0.725444i	$0.258366\pi$
$194$	−1.58448	+	3.46953i	−0.113759	+	0.249097i
$195$	0.740995	+	5.15373i	0.0530637	+	0.369066i
$196$	−1.04892	+	7.29542i	−0.0749231	+	0.521102i
$197$	4.70267	+	5.42717i	0.335051	+	0.386670i	0.898127	−	0.439735i	$-0.144928\pi$
$197$	4.70267	+	5.42717i	0.335051	+	0.386670i	−0.563076	+	0.826405i	$0.690382\pi$
$198$	−14.1790	+	9.11232i	−1.00766	+	0.647584i
$199$	−6.26816	+	13.7253i	−0.444338	+	0.972964i	0.546444	+	0.837496i	$0.315981\pi$
$199$	−6.26816	+	13.7253i	−0.444338	+	0.972964i	−0.990782	+	0.135468i	$0.956746\pi$
$200$	3.07280			0.217280
$201$	−3.04907	−	7.19358i	−0.215065	−	0.507396i
$202$	14.7668			1.03899
$203$	−13.2477	+	29.0085i	−0.929809	+	2.03600i
$204$	−6.65460	+	4.27665i	−0.465915	+	0.299425i
$205$	6.33404	+	7.30987i	0.442389	+	0.510544i
$206$	−0.632135	+	4.39660i	−0.0440429	+	0.306325i
$207$	−0.0761537	−	0.529661i	−0.00529305	−	0.0368140i
$208$	3.24204	−	7.09909i	0.224795	−	0.492233i
$209$	−0.624338	+	0.183322i	−0.0431864	+	0.0126807i
$210$	−8.13513	+	17.8135i	−0.561377	+	1.22924i
$211$	−4.40588	−	2.83149i	−0.303313	−	0.194928i	0.380126	−	0.924935i	$-0.375880\pi$
$211$	−4.40588	−	2.83149i	−0.303313	−	0.194928i	−0.683440	+	0.730007i	$0.739517\pi$
$212$	2.38310	−	16.5749i	0.163672	−	1.13837i
$213$	−0.0827903	−	0.0243094i	−0.00567270	−	0.00166565i
$214$	−23.2290	−	6.82066i	−1.58791	−	0.466251i
$215$	−8.59373	−	9.91769i	−0.586087	−	0.676381i
$216$	−1.22941	−	2.69203i	−0.0836507	−	0.183170i
$217$	−3.39099	+	23.5849i	−0.230195	+	1.60104i
$218$	−20.5320	+	23.6952i	−1.39060	+	1.60484i
$219$	−5.07147	−	5.85279i	−0.342698	−	0.395495i
$220$	−9.31352	−	20.3938i	−0.627917	−	1.37495i
$221$	7.13209	−	4.58352i	0.479756	−	0.308321i
$222$	−0.0548029	−	0.381162i	−0.00367813	−	0.0255819i
$223$	−3.41537	−	2.19493i	−0.228710	−	0.146983i	0.421267	−	0.906936i	$-0.361585\pi$
$223$	−3.41537	−	2.19493i	−0.228710	−	0.146983i	−0.649978	+	0.759953i	$0.725222\pi$
$224$	21.2352	−	13.6471i	1.41884	−	0.911833i
$225$	6.89912	−	7.96201i	0.459941	−	0.530800i
$226$	−1.66719	−	0.489532i	−0.110900	−	0.0325632i
$227$	4.57279	−	5.27728i	0.303507	−	0.350265i	−0.583424	−	0.812168i	$-0.698287\pi$
$227$	4.57279	−	5.27728i	0.303507	−	0.350265i	0.886931	+	0.461902i	$0.152833\pi$
$228$	0.0353702	+	0.246005i	0.00234245	+	0.0162921i
$229$	−17.5677	+	5.15834i	−1.16090	+	0.340872i	−0.804784	−	0.593568i	$-0.797719\pi$
$229$	−17.5677	+	5.15834i	−1.16090	+	0.340872i	−0.356121	+	0.934440i	$0.615901\pi$
$230$	1.55790			0.102725
$231$	−13.5395			−0.890831
$232$	5.52617	−	1.62263i	0.362811	−	0.106531i
$233$	7.87730	+	5.06243i	0.516059	+	0.331651i	0.772611	−	0.634879i	$-0.218950\pi$
$233$	7.87730	+	5.06243i	0.516059	+	0.331651i	−0.256552	+	0.966530i	$0.582587\pi$
$234$	−2.86620	−	6.27611i	−0.187370	−	0.410282i
$235$	6.38955	+	13.9912i	0.416808	+	0.912683i
$236$	18.1421	+	11.6592i	1.18095	+	0.758951i
$237$	4.33121	−	1.27176i	0.281342	−	0.0826095i
$238$	31.8865			2.06690
$239$	−6.22139			−0.402428			−0.201214	−	0.979547i	$-0.564489\pi$
$239$	−6.22139			−0.402428			−0.201214	+	0.979547i	$0.564489\pi$
$240$	13.1604	−	3.86424i	0.849499	−	0.249435i
$241$	−0.383421	−	2.66675i	−0.0246983	−	0.171781i	0.973739	−	0.227668i	$-0.0731102\pi$
$241$	−0.383421	−	2.66675i	−0.0246983	−	0.171781i	−0.998437	+	0.0558876i	$0.982201\pi$
$242$	8.39369	−	9.68683i	0.539567	−	0.622693i
$243$	−15.4750	−	4.54388i	−0.992724	−	0.291490i
$244$	13.7973	−	15.9229i	0.883282	−	1.01936i
$245$	11.6790	−	7.50563i	0.746143	−	0.479517i
$246$	4.70299	+	3.02243i	0.299852	+	0.192703i
$247$	−0.0379082	−	0.263657i	−0.00241204	−	0.0167761i
$248$	3.62014	−	2.32653i	0.229879	−	0.147735i
$249$	−3.11178	−	6.81385i	−0.197201	−	0.431810i
$250$	0.173107	+	0.199776i	0.0109483	+	0.0126350i
$251$	9.05314	−	10.4479i	0.571429	−	0.659465i	−0.394310	−	0.918977i	$-0.629016\pi$
$251$	9.05314	−	10.4479i	0.571429	−	0.659465i	0.965740	+	0.259513i	$0.0835619\pi$
$252$	1.68735	−	11.7358i	0.106293	−	0.739285i
$253$	0.447446	+	0.979770i	0.0281307	+	0.0615976i
$254$	−5.43955	−	6.27758i	−0.341308	−	0.393890i
$255$	14.2962	+	4.19775i	0.895265	+	0.262873i
$256$	−19.0137	−	5.58293i	−1.18836	−	0.348933i
$257$	−1.03527	+	7.20045i	−0.0645783	+	0.449152i	0.931719	+	0.363179i	$0.118309\pi$
$257$	−1.03527	+	7.20045i	−0.0645783	+	0.449152i	−0.996298	+	0.0859724i	$0.972600\pi$
$258$	−6.38080	−	4.10069i	−0.397251	−	0.255298i
$259$	−0.294619	+	0.645126i	−0.0183067	+	0.0400862i
$260$	8.80599	−	2.58567i	0.546124	−	0.160357i
$261$	8.20302	−	17.9621i	0.507754	−	1.11183i
$262$	4.90915	+	34.1439i	0.303288	+	2.10942i
$263$	2.91480	−	20.2729i	0.179734	−	1.25008i	−0.677643	−	0.735391i	$-0.736999\pi$
$263$	2.91480	−	20.2729i	0.179734	−	1.25008i	0.857378	−	0.514688i	$-0.172092\pi$
$264$	1.60130	+	1.84800i	0.0985533	+	0.113737i
$265$	−26.5341	+	17.0524i	−1.62998	+	1.04752i
$266$	0.416181	−	0.911309i	0.0255177	−	0.0558760i
$267$	−15.5233			−0.950012
$268$	−11.7860	+	7.12434i	−0.719943	+	0.435188i
$269$	6.18415			0.377054			0.188527	−	0.982068i	$-0.439629\pi$
$269$	6.18415			0.377054			0.188527	+	0.982068i	$0.439629\pi$
$270$	12.2717	−	26.8713i	0.746831	−	1.63533i
$271$	6.63095	−	4.26145i	0.402801	−	0.258865i	−0.323518	−	0.946222i	$-0.604866\pi$
$271$	6.63095	−	4.26145i	0.402801	−	0.258865i	0.726319	+	0.687357i	$0.241229\pi$
$272$	−14.6252	−	16.8783i	−0.886780	−	1.02340i
$273$	0.788781	−	5.48609i	0.0477392	−	0.332033i
$274$	−2.02773	−	14.1032i	−0.122500	−	0.852006i
$275$	−8.80935	+	19.2898i	−0.531224	+	1.16322i
$276$	0.394739	−	0.115906i	0.0237605	−	0.00697671i
$277$	−9.86976	+	21.6118i	−0.593016	+	1.29852i	0.340586	+	0.940213i	$0.389375\pi$
$277$	−9.86976	+	21.6118i	−0.593016	+	1.29852i	−0.933602	+	0.358311i	$0.883353\pi$
$278$	2.74996	+	1.76729i	0.164932	+	0.105995i
$279$	2.09971	−	14.6038i	0.125706	−	0.874306i
$280$	−6.24989	−	1.83513i	−0.373503	−	0.109670i
$281$	−13.6183	−	3.99869i	−0.812399	−	0.238542i	−0.150959	−	0.988540i	$-0.548236\pi$
$281$	−13.6183	−	3.99869i	−0.812399	−	0.238542i	−0.661440	+	0.749998i	$0.730054\pi$
$282$	5.82174	+	6.71864i	0.346679	+	0.400089i
$283$	2.39697	+	5.24862i	0.142485	+	0.311998i	0.967398	−	0.253261i	$-0.0815033\pi$
$283$	2.39697	+	5.24862i	0.142485	+	0.311998i	−0.824913	+	0.565260i	$0.808776\pi$
$284$	−0.0216451	+	0.150545i	−0.00128440	+	0.00893319i
$285$	0.306564	−	0.353794i	0.0181593	−	0.0209569i
$286$	9.09476	+	10.4959i	0.537784	+	0.620636i
$287$	−4.27716	−	9.36568i	−0.252473	−	0.552838i
$288$	−13.1489	+	8.45029i	−0.774806	+	0.497938i
$289$	−1.03332	−	7.18688i	−0.0607834	−	0.422758i
$290$	48.3634	+	31.0813i	2.84000	+	1.82515i
$291$	1.59605	−	1.02572i	0.0935618	−	0.0601285i
$292$	−8.93934	+	10.3165i	−0.523135	+	0.603730i
$293$	5.98076	+	1.75611i	0.349400	+	0.102593i	0.451723	−	0.892158i	$-0.350809\pi$
$293$	5.98076	+	1.75611i	0.349400	+	0.102593i	−0.102323	+	0.994751i	$0.532628\pi$
$294$	5.25464	−	6.06418i	0.306457	−	0.353670i
$295$	−5.78091	−	40.2071i	−0.336578	−	2.34095i
$296$	0.122898	−	0.0360860i	0.00714328	−	0.00209746i
$297$	20.4240			1.18512
$298$	−29.2931			−1.69690
$299$	−0.423063	+	0.124222i	−0.0244664	+	0.00718397i
$300$	6.81394	+	4.37906i	0.393403	+	0.252825i
$301$	5.80305	+	12.7069i	0.334482	+	0.732414i
$302$	−9.46203	−	20.7190i	−0.544479	−	1.19224i
$303$	−6.17913	−	3.97109i	−0.354982	−	0.228133i
$304$	−0.673265	+	0.197688i	−0.0386144	+	0.0113382i
$305$	−39.6854			−2.27238
$306$	−19.7442			−1.12870
$307$	−20.5215	+	6.02566i	−1.17122	+	0.343903i	−0.808785	−	0.588105i	$-0.799874\pi$
$307$	−20.5215	+	6.02566i	−1.17122	+	0.343903i	−0.362440	+	0.932007i	$0.618056\pi$
$308$	3.39643	+	23.6227i	0.193530	+	1.34603i
$309$	1.44685	−	1.66975i	0.0823082	−	0.0949887i
$310$	41.2144	+	12.1016i	2.34082	+	0.687326i
$311$	−2.49852	+	2.88345i	−0.141678	+	0.163506i	−0.822154	−	0.569265i	$-0.807228\pi$
$311$	−2.49852	+	2.88345i	−0.141678	+	0.163506i	0.680476	+	0.732771i	$0.261773\pi$
$312$	−0.842085	+	0.541175i	−0.0476737	+	0.0306380i
$313$	3.55971	+	2.28769i	0.201207	+	0.129308i	0.637364	−	0.770563i	$-0.280025\pi$
$313$	3.55971	+	2.28769i	0.201207	+	0.129308i	−0.436158	+	0.899870i	$0.643661\pi$
$314$	0.622796	+	4.33164i	0.0351464	+	0.244449i
$315$	−18.7874	+	12.0739i	−1.05855	+	0.680290i
$316$	−3.30537	−	7.23776i	−0.185942	−	0.407156i
$317$	5.55718	+	6.41333i	0.312122	+	0.360208i	0.890037	−	0.455889i	$-0.150679\pi$
$317$	5.55718	+	6.41333i	0.312122	+	0.360208i	−0.577914	+	0.816098i	$0.696133\pi$
$318$	−11.9383	+	13.7775i	−0.669466	+	0.772605i
$319$	−5.65665	+	39.3429i	−0.316711	+	2.20278i
$320$	−6.96494	−	15.2511i	−0.389352	−	0.852562i
$321$	7.88592	+	9.10084i	0.440149	+	0.507959i
$322$	−1.59119	−	0.467216i	−0.0886736	−	0.0260369i
$323$	−0.731374	−	0.214751i	−0.0406947	−	0.0119490i
$324$	−0.390327	+	2.71478i	−0.0216848	+	0.150821i
$325$	−7.30287	−	4.69327i	−0.405090	−	0.260336i
$326$	3.25674	−	7.13126i	0.180374	−	0.394964i
$327$	14.9637	−	4.39373i	0.827492	−	0.242974i
$328$	−0.772464	+	1.69146i	−0.0426522	+	0.0933953i
$329$	−2.33013	−	16.2064i	−0.128464	−	0.893487i
$330$	−3.47362	+	24.1595i	−0.191216	+	1.32994i
$331$	10.0364	+	11.5826i	0.551649	+	0.636637i	0.961267	−	0.275620i	$-0.0888833\pi$
$331$	10.0364	+	11.5826i	0.551649	+	0.636637i	−0.409618	+	0.912257i	$0.634338\pi$
$332$	−11.1077	+	7.13850i	−0.609616	+	0.391776i
$333$	0.182429	−	0.399463i	0.00999703	−	0.0218904i
$334$	18.1711			0.994279
$335$	24.6795	+	7.98978i	1.34838	+	0.436528i
$336$	−14.6005			−0.796523
$337$	9.63638	−	21.1007i	0.524927	−	1.14943i	−0.442613	−	0.896713i	$-0.645949\pi$
$337$	9.63638	−	21.1007i	0.524927	−	1.14943i	0.967540	−	0.252717i	$-0.0813241\pi$
$338$	16.2039	−	10.4136i	0.881375	−	0.566426i
$339$	0.565988	+	0.653185i	0.0307402	+	0.0354761i
$340$	3.73767	−	25.9961i	0.202704	−	1.40984i
$341$	4.22645	+	29.3956i	0.228875	+	1.59186i
$342$	−0.257700	+	0.564284i	−0.0139348	+	0.0305130i
$343$	8.47855	−	2.48953i	0.457799	−	0.134422i
$344$	1.04804	−	2.29489i	0.0565066	−	0.123732i
$345$	−0.651898	−	0.418950i	−0.0350970	−	0.0225555i
$346$	−1.53627	+	10.6850i	−0.0825906	+	0.574431i
$347$	9.96384	+	2.92565i	0.534887	+	0.157057i	0.538010	−	0.842938i	$-0.319176\pi$
$347$	9.96384	+	2.92565i	0.534887	+	0.157057i	−0.00312362	+	0.999995i	$0.500994\pi$
$348$	14.5667	+	4.27716i	0.780856	+	0.229280i
$349$	−8.85734	−	10.2219i	−0.474122	−	0.547166i	0.467431	−	0.884029i	$-0.345180\pi$
$349$	−8.85734	−	10.2219i	−0.474122	−	0.547166i	−0.941554	+	0.336863i	$0.890634\pi$
$350$	−13.5633	−	29.6995i	−0.724990	−	1.58751i
$351$	−1.18986	+	8.27567i	−0.0635101	+	0.441722i
$352$	20.6029	−	23.7770i	1.09814	−	1.26732i
$353$	20.3415	+	23.4753i	1.08267	+	1.24946i	0.966618	+	0.256221i	$0.0824776\pi$
$353$	20.3415	+	23.4753i	1.08267	+	1.24946i	0.116049	+	0.993243i	$0.462977\pi$
$354$	−9.75313	−	21.3564i	−0.518373	−	1.13508i
$355$	0.241002	−	0.154883i	0.0127911	−	0.00822032i
$356$	3.89409	+	27.0840i	0.206386	+	1.43545i
$357$	−13.3428	−	8.57492i	−0.706178	−	0.453833i
$358$	−30.5177	+	19.6126i	−1.61291	+	1.03656i
$359$	19.0812	−	22.0209i	1.00707	−	1.16222i	0.0203473	−	0.999793i	$-0.493523\pi$
$359$	19.0812	−	22.0209i	1.00707	−	1.16222i	0.986721	−	0.162426i	$-0.0519317\pi$
$360$	3.86995	+	1.13632i	0.203964	+	0.0598893i
$361$	12.4267	−	14.3411i	0.654035	−	0.754797i
$362$	2.33490	+	16.2396i	0.122719	+	0.853532i
$363$	−6.11730	+	1.79620i	−0.321075	+	0.0942761i
$364$	−9.76962			−0.512067
$365$	25.7123			1.34584
$366$	−22.0084	+	6.46224i	−1.15040	+	0.337786i
$367$	−11.5123	−	7.39849i	−0.600936	−	0.386198i	0.204513	−	0.978864i	$-0.434439\pi$
$367$	−11.5123	−	7.39849i	−0.600936	−	0.386198i	−0.805448	+	0.592666i	$0.798075\pi$
$368$	0.482511	+	1.05655i	0.0251526	+	0.0550765i
$369$	2.64843	+	5.79924i	0.137872	+	0.301897i
$370$	1.07556	+	0.691223i	0.0559159	+	0.0359350i
$371$	32.2152	−	9.45924i	1.67253	−	0.491099i
$372$	11.3432			0.588118
$373$	−29.9015			−1.54824			−0.774120	−	0.633039i	$-0.781807\pi$
$373$	−29.9015			−1.54824			−0.774120	+	0.633039i	$0.781807\pi$
$374$	38.1328	−	11.1968i	1.97180	−	0.578973i
$375$	−0.0187124	−	0.130148i	−0.000966306	−	0.00672081i
$376$	−1.93643	+	2.23476i	−0.0998636	+	0.115249i
$377$	−15.6119	−	4.58407i	−0.804053	−	0.236091i
$378$	−20.5927	+	23.7652i	−1.05917	+	1.22235i
$379$	−1.29495	+	0.832214i	−0.0665171	+	0.0427480i	−0.573477	−	0.819222i	$-0.694406\pi$
$379$	−1.29495	+	0.832214i	−0.0665171	+	0.0427480i	0.506960	+	0.861970i	$0.330769\pi$
$380$	−0.694178	−	0.446121i	−0.0356106	−	0.0228855i
$381$	0.588001	+	4.08964i	0.0301242	+	0.209518i
$382$	−5.07638	+	3.26239i	−0.259730	+	0.166918i
$383$	−7.99828	−	17.5138i	−0.408693	−	0.894913i	−0.996314	−	0.0857767i	$-0.972663\pi$
$383$	−7.99828	−	17.5138i	−0.408693	−	0.894913i	0.587621	−	0.809136i	$-0.300064\pi$
$384$	3.00832	+	3.47178i	0.153517	+	0.177169i
$385$	29.4379	−	33.9731i	1.50029	−	1.73143i
$386$	−3.46030	+	24.0669i	−0.176125	+	1.22497i
$387$	−3.59326	−	7.86814i	−0.182656	−	0.399960i
$388$	−2.18997	−	2.52736i	−0.111179	−	0.128307i
$389$	−34.6895	−	10.1857i	−1.75883	−	0.516438i	−0.766736	−	0.641963i	$-0.778120\pi$
$389$	−34.6895	−	10.1857i	−1.75883	−	0.516438i	−0.992090	+	0.125525i	$0.959939\pi$
$390$	−9.58691	−	2.81497i	−0.485452	−	0.142542i
$391$	−0.179568	+	1.24892i	−0.00908113	+	0.0631606i
$392$	2.24527	+	1.44295i	0.113403	+	0.0728800i
$393$	7.12774	−	15.6076i	0.359547	−	0.787298i
$394$	−13.2224	+	3.88244i	−0.666133	+	0.195594i
$395$	−6.22595	+	13.6329i	−0.313261	+	0.685947i
$396$	−2.10308	−	14.6272i	−0.105684	−	0.735046i
$397$	−0.965354	+	6.71418i	−0.0484497	+	0.336975i	0.951151	+	0.308725i	$0.0999024\pi$
$397$	−0.965354	+	6.71418i	−0.0484497	+	0.336975i	−0.999601	+	0.0282497i	$0.991007\pi$
$398$	−18.9617	−	21.8830i	−0.950467	−	1.09690i
$399$	−0.419219	+	0.269416i	−0.0209872	+	0.0134876i
$400$	−9.49971	+	20.8015i	−0.474986	+	1.04007i
$401$	2.58618			0.129148			0.0645738	−	0.997913i	$-0.479431\pi$
$401$	2.58618			0.129148			0.0645738	+	0.997913i	$0.479431\pi$
$402$	14.9875	+	0.412180i	0.747511	+	0.0205577i
$403$	−12.1571			−0.605589
$404$	−5.37841	+	11.7771i	−0.267586	+	0.585932i
$405$	4.34600	−	2.79301i	0.215955	−	0.138786i
$406$	−40.0756	−	46.2497i	−1.98892	−	2.29533i
$407$	−0.125799	+	0.874954i	−0.00623564	+	0.0433699i
$408$	0.407656	+	2.83531i	0.0201820	+	0.140369i
$409$	11.3332	−	24.8162i	0.560391	−	1.22708i	−0.391367	−	0.920235i	$-0.627998\pi$
$409$	11.3332	−	24.8162i	0.560391	−	1.22708i	0.951758	−	0.306850i	$-0.0992749\pi$
$410$	−17.8092	+	5.22927i	−0.879536	+	0.258255i
$411$	−2.94413	+	6.44674i	−0.145223	+	0.317994i
$412$	−3.27621	−	2.10549i	−0.161407	−	0.103730i
$413$	−6.15372	+	42.8001i	−0.302805	+	2.10605i
$414$	0.985268	+	0.289301i	0.0484233	+	0.0142184i
$415$	23.8630	+	7.00681i	1.17139	+	0.343951i
$416$	8.43400	+	9.73336i	0.413511	+	0.477217i
$417$	−0.675453	−	1.47904i	−0.0330771	−	0.0724287i
$418$	0.177705	−	1.23597i	0.00869184	−	0.0604531i
$419$	−3.30483	+	3.81398i	−0.161452	+	0.186325i	−0.830711	−	0.556704i	$-0.812066\pi$
$419$	−3.30483	+	3.81398i	−0.161452	+	0.186325i	0.669260	+	0.743029i	$0.266611\pi$
$420$	−11.2439	−	12.9761i	−0.548645	−	0.633171i
$421$	11.4739	+	25.1243i	0.559204	+	1.22449i	0.952349	+	0.305009i	$0.0986596\pi$
$421$	11.4739	+	25.1243i	0.559204	+	1.22449i	−0.393145	+	0.919476i	$0.628613\pi$
$422$	8.45482	−	5.43359i	0.411574	−	0.264503i
$423$	1.44282	+	10.0350i	0.0701523	+	0.487920i
$424$	−5.10116	−	3.27831i	−0.247734	−	0.159209i
$425$	−20.8982	+	13.4304i	−1.01371	+	0.651472i
$426$	0.108432	−	0.125137i	0.00525356	−	0.00606293i
$427$	40.5334	+	11.9017i	1.96155	+	0.575963i
$428$	13.9003	−	16.0418i	0.671896	−	0.775409i
$429$	−0.983119	−	6.83774i	−0.0474654	−	0.330129i
$430$	24.1627	−	7.09482i	1.16523	−	0.342143i
$431$	−21.5609			−1.03855			−0.519276	−	0.854607i	$-0.673798\pi$
$431$	−21.5609			−1.03855			−0.519276	+	0.854607i	$0.673798\pi$
$432$	22.0246			1.05966
$433$	15.3946	−	4.52027i	0.739818	−	0.217230i	0.109955	−	0.993937i	$-0.464929\pi$
$433$	15.3946	−	4.52027i	0.739818	−	0.217230i	0.629863	+	0.776706i	$0.283111\pi$
$434$	−38.4658	−	24.7205i	−1.84642	−	1.18662i
$435$	−11.8792	−	26.0117i	−0.569562	−	1.24717i
$436$	−11.4196	−	25.0053i	−0.546898	−	1.19754i
$437$	0.0333501	+	0.0214328i	0.00159535	+	0.00102527i
$438$	14.2593	−	4.18691i	0.681336	−	0.200058i
$439$	19.3905			0.925460			0.462730	−	0.886499i	$-0.346870\pi$
$439$	19.3905			0.925460			0.462730	+	0.886499i	$0.346870\pi$
$440$	−8.11859			−0.387038
$441$	8.77999	−	2.57804i	0.418095	−	0.122764i
$442$	2.31533	+	16.1034i	0.110129	+	0.765962i
$443$	−6.28367	+	7.25174i	−0.298546	+	0.344541i	−0.885127	−	0.465350i	$-0.845928\pi$
$443$	−6.28367	+	7.25174i	−0.298546	+	0.344541i	0.586580	+	0.809891i	$0.300474\pi$
$444$	0.323951	+	0.0951207i	0.0153741	+	0.00451423i
$445$	33.7512	−	38.9510i	1.59996	−	1.84645i
$446$	6.55405	−	4.21203i	0.310343	−	0.199446i
$447$	12.2576	+	7.87749i	0.579765	+	0.372592i
$448$	2.53996	+	17.6658i	0.120002	+	0.834630i
$449$	−2.89707	+	1.86183i	−0.136721	+	0.0878654i	−0.607213	−	0.794539i	$-0.707713\pi$
$449$	−2.89707	+	1.86183i	−0.136721	+	0.0878654i	0.470492	+	0.882404i	$0.344076\pi$
$450$	8.39844	+	18.3900i	0.395906	+	0.866914i
$451$	−8.40373	−	9.69842i	−0.395716	−	0.456681i
$452$	0.997651	−	1.15135i	0.0469255	−	0.0541550i
$453$	−1.61238	+	11.2143i	−0.0757560	+	0.526894i
$454$	5.56655	+	12.1890i	0.261251	+	0.572060i
$455$	12.0507	+	13.9072i	0.564944	+	0.651981i
$456$	0.0863532	+	0.0253556i	0.00404386	+	0.00118738i
$457$	−15.8967	−	4.66769i	−0.743616	−	0.218345i	−0.112088	−	0.993698i	$-0.535754\pi$
$457$	−15.8967	−	4.66769i	−0.743616	−	0.218345i	−0.631528	+	0.775353i	$0.717572\pi$
$458$	5.00028	−	34.7777i	0.233648	−	1.62506i
$459$	20.1274	+	12.9351i	0.939467	+	0.603759i
$460$	−0.567422	+	1.24248i	−0.0264562	+	0.0579310i
$461$	−2.40080	+	0.704939i	−0.111816	+	0.0328323i	−0.337162	−	0.941447i	$-0.609467\pi$
$461$	−2.40080	+	0.704939i	−0.111816	+	0.0328323i	0.225346	+	0.974279i	$0.427649\pi$
$462$	10.7933	−	23.6341i	0.502151	−	1.09956i
$463$	−2.98479	−	20.7597i	−0.138715	−	0.964784i	−0.933675	−	0.358122i	$-0.883417\pi$
$463$	−2.98479	−	20.7597i	−0.138715	−	0.964784i	0.794960	−	0.606662i	$-0.207492\pi$
$464$	−6.09994	+	42.4260i	−0.283183	+	1.96958i
$465$	−13.9917	−	16.1472i	−0.648848	−	0.748811i
$466$	−15.1164	+	9.71474i	−0.700255	+	0.450027i
$467$	15.1370	−	33.1454i	0.700458	−	1.53379i	−0.138958	−	0.990298i	$-0.544375\pi$
$467$	15.1370	−	33.1454i	0.700458	−	1.53379i	0.839416	−	0.543490i	$-0.182897\pi$
$468$	6.04937			0.279632
$469$	−22.8107	−	15.5619i	−1.05330	−	0.718583i
$470$	−29.5162			−1.36148
$471$	0.904257	−	1.98005i	0.0416660	−	0.0912357i
$472$	6.56957	−	4.22201i	0.302389	−	0.194334i
$473$	11.4018	+	13.1583i	0.524254	+	0.605022i
$474$	−1.23279	+	8.57424i	−0.0566239	+	0.393828i
$475$	0.111077	+	0.772558i	0.00509657	+	0.0354474i
$476$	−11.6138	+	25.4307i	−0.532318	+	1.16561i
$477$	−19.9477	+	5.85718i	−0.913343	+	0.268182i
$478$	4.95954	−	10.8599i	0.226844	−	0.496719i
$479$	−0.0352892	−	0.0226790i	−0.00161241	−	0.00103623i	0.539834	−	0.841771i	$-0.318487\pi$
$479$	−0.0352892	−	0.0226790i	−0.00161241	−	0.00103623i	−0.541447	+	0.840735i	$0.682123\pi$
$480$	−3.22125	+	22.4043i	−0.147029	+	1.02261i
$481$	−0.347196	−	0.101946i	−0.0158308	−	0.00464834i
$482$	4.96066	+	1.45658i	0.225952	+	0.0663455i
$483$	0.540186	+	0.623408i	0.0245793	+	0.0283660i
$484$	4.66843	+	10.2224i	0.212202	+	0.464657i
$485$	−0.896447	+	6.23493i	−0.0407056	+	0.283113i
$486$	20.2680	−	23.3905i	0.919375	−	1.06101i
$487$	9.73604	+	11.2360i	0.441182	+	0.509151i	0.932173	−	0.362014i	$-0.117911\pi$
$487$	9.73604	+	11.2360i	0.441182	+	0.509151i	−0.490991	+	0.871165i	$0.663365\pi$
$488$	−3.16940	−	6.94001i	−0.143472	−	0.314159i
$489$	−3.28051	+	2.10826i	−0.148350	+	0.0953386i
$490$	3.79141	+	26.3698i	0.171278	+	1.19127i
$491$	29.3907	+	18.8883i	1.32639	+	0.852416i	0.995817	−	0.0913655i	$-0.0291232\pi$
$491$	29.3907	+	18.8883i	1.32639	+	0.852416i	0.330569	+	0.943782i	$0.392760\pi$
$492$	−4.12344	+	2.64997i	−0.185899	+	0.119470i
$493$	−30.4914	+	35.1890i	−1.37326	+	1.58483i
$494$	0.490452	+	0.144010i	0.0220665	+	0.00647930i
$495$	−18.2280	+	21.0362i	−0.819288	+	0.945508i
$496$	4.55767	+	31.6993i	0.204645	+	1.42334i
$497$	−0.292602	+	0.0859156i	−0.0131250	+	0.00385384i
$498$	14.3747			0.644146
$499$	9.61045			0.430223			0.215111	−	0.976590i	$-0.430989\pi$
$499$	9.61045			0.430223			0.215111	+	0.976590i	$0.430989\pi$
$500$	−0.222379	+	0.0652963i	−0.00994508	+	0.00292014i
$501$	−7.60365	−	4.88657i	−0.339706	−	0.218316i
$502$	11.0206	+	24.1317i	0.491873	+	1.07705i
$503$	−5.84867	−	12.8068i	−0.260779	−	0.571027i	0.733273	−	0.679935i	$-0.237992\pi$
$503$	−5.84867	−	12.8068i	−0.260779	−	0.571027i	−0.994052	+	0.108908i	$0.965265\pi$
$504$	−3.61186	−	2.32120i	−0.160885	−	0.103395i
$505$	23.3991	−	6.87059i	1.04124	−	0.305737i
$506$	−2.06695			−0.0918872
$507$	−9.58090			−0.425503
$508$	6.98781	−	2.05181i	0.310034	−	0.0910341i
$509$	−2.59033	−	18.0161i	−0.114814	−	0.798550i	−0.963126	−	0.269052i	$-0.913290\pi$
$509$	−2.59033	−	18.0161i	−0.114814	−	0.798550i	0.848311	−	0.529498i	$-0.177620\pi$
$510$	−18.7241	+	21.6087i	−0.829116	+	0.956851i
$511$	−26.2618	−	7.71116i	−1.16175	−	0.341122i
$512$	18.5994	−	21.4648i	0.821984	−	0.948620i
$513$	0.632384	−	0.406408i	0.0279204	−	0.0179434i
$514$	−11.7436	−	7.54716i	−0.517988	−	0.332891i
$515$	1.04395	+	7.26083i	0.0460020	+	0.319951i
$516$	5.59448	−	3.59536i	0.246283	−	0.158277i
$517$	−8.47737	−	18.5629i	−0.372834	−	0.816393i
$518$	−0.891250	−	1.02856i	−0.0391593	−	0.0451922i
$519$	3.51626	−	4.05798i	0.154347	−	0.178126i
$520$	0.472972	−	3.28959i	0.0207412	−	0.144258i
$521$	8.31122	+	18.1990i	0.364121	+	0.797314i	0.999681	+	0.0252621i	$0.00804203\pi$
$521$	8.31122	+	18.1990i	0.364121	+	0.797314i	−0.635560	+	0.772052i	$0.719231\pi$
$522$	24.8149	+	28.6379i	1.08612	+	1.25345i
$523$	−21.6361	−	6.35293i	−0.946080	−	0.277794i	−0.227926	−	0.973678i	$-0.573194\pi$
$523$	−21.6361	−	6.35293i	−0.946080	−	0.277794i	−0.718154	+	0.695884i	$0.755013\pi$
$524$	−29.0190	−	8.52076i	−1.26770	−	0.372231i
$525$	−2.31126	+	16.0751i	−0.100871	+	0.701577i
$526$	33.0641	+	21.2490i	1.44166	+	0.926502i
$527$	−14.4520	+	31.6455i	−0.629539	+	1.37850i
$528$	−17.4606	+	5.12690i	−0.759875	+	0.223120i
$529$	−9.52728	+	20.8618i	−0.414230	+	0.907037i
$530$	−8.61390	−	59.9110i	−0.374164	−	2.60237i
$531$	3.81039	−	26.5019i	0.165357	−	1.15008i
$532$	0.575220	+	0.663839i	0.0249390	+	0.0287811i
$533$	4.41931	−	2.84012i	0.191422	−	0.123019i
$534$	12.3748	−	27.0971i	0.535510	−	1.17260i
$535$	−39.9816			−1.72855
$536$	0.573758	+	4.95393i	0.0247826	+	0.213977i
$537$	18.0443			0.778667
$538$	−4.92985	+	10.7949i	−0.212541	+	0.465400i
$539$	−15.4952	+	9.95814i	−0.667424	+	0.428927i
$540$	16.9612	+	19.5743i	0.729893	+	0.842342i
$541$	3.12108	−	21.7076i	0.134186	−	0.933282i	−0.805829	−	0.592148i	$-0.798280\pi$
$541$	3.12108	−	21.7076i	0.134186	−	0.933282i	0.940015	−	0.341134i	$-0.110811\pi$
$542$	2.15264	+	14.9719i	0.0924636	+	0.643099i
$543$	3.39011	−	7.42330i	0.145483	−	0.318564i
$544$	35.3624	−	10.3833i	1.51615	−	0.445182i
$545$	−21.5097	+	47.0997i	−0.921374	+	2.01753i
$546$	8.94757	+	5.75025i	0.382921	+	0.246088i
$547$	−6.05332	+	42.1018i	−0.258821	+	1.80014i	0.282438	+	0.959286i	$0.408857\pi$
$547$	−6.05332	+	42.1018i	−0.258821	+	1.80014i	−0.541259	+	0.840856i	$0.682052\pi$
$548$	11.9864	+	3.51952i	0.512033	+	0.150346i
$549$	−25.0984	−	7.36955i	−1.07117	−	0.314525i
$550$	−26.6491	−	30.7547i	−1.13632	−	1.31139i
$551$	0.607720	+	1.33072i	0.0258897	+	0.0566906i
$552$	0.0212015	−	0.147460i	0.000902397	−	0.00627631i
$553$	10.4475	−	12.0571i	0.444274	−	0.512720i
$554$	−29.8569	−	34.4567i	−1.26850	−	1.46393i
$555$	−0.264183	−	0.578481i	−0.0112140	−	0.0245551i
$556$	−2.41108	+	1.54951i	−0.102252	+	0.0657137i
$557$	−5.38786	−	37.4734i	−0.228291	−	1.58780i	−0.705305	−	0.708904i	$-0.749190\pi$
$557$	−5.38786	−	37.4734i	−0.228291	−	1.58780i	0.477014	−	0.878896i	$-0.341719\pi$
$558$	23.8181	+	15.3070i	1.00830	+	0.647996i
$559$	−5.99591	+	3.85334i	−0.253600	+	0.162979i
$560$	31.7448	−	36.6355i	1.34146	−	1.54813i
$561$	−18.9676	−	5.56939i	−0.800813	−	0.235140i
$562$	17.8362	−	20.5840i	0.752373	−	0.868285i
$563$	−1.83182	−	12.7406i	−0.0772020	−	0.536951i	−0.991317	−	0.131496i	$-0.958022\pi$
$563$	−1.83182	−	12.7406i	−0.0772020	−	0.536951i	0.914115	−	0.405456i	$-0.132887\pi$
$564$	−7.47878	+	2.19597i	−0.314913	+	0.0924669i
$565$	−2.86955			−0.120723
$566$	−11.0726			−0.465418
$567$	−5.27650	+	1.54932i	−0.221592	+	0.0650654i
$568$	0.0463324	+	0.0297760i	0.00194406	+	0.00124937i
$569$	−9.41018	−	20.6054i	−0.394495	−	0.863824i	−0.997799	−	0.0663127i	$-0.978877\pi$
$569$	−9.41018	−	20.6054i	−0.394495	−	0.863824i	0.603304	−	0.797512i	$-0.293851\pi$
$570$	0.373187	+	0.817165i	0.0156311	+	0.0342273i
$571$	−7.77224	−	4.99492i	−0.325258	−	0.209031i	0.367813	−	0.929900i	$-0.380107\pi$
$571$	−7.77224	−	4.99492i	−0.325258	−	0.209031i	−0.693071	+	0.720869i	$0.743743\pi$
$572$	−11.6834	+	3.43055i	−0.488507	+	0.143439i
$573$	3.00152			0.125390
$574$	19.7581			0.824687
$575$	1.23964	−	0.363992i	0.0516967	−	0.0151795i
$576$	−1.57275	−	10.9387i	−0.0655311	−	0.455779i
$577$	−7.43789	+	8.58379i	−0.309644	+	0.357348i	−0.889147	−	0.457622i	$-0.848701\pi$
$577$	−7.43789	+	8.58379i	−0.309644	+	0.357348i	0.579503	+	0.814970i	$0.303247\pi$
$578$	13.3689	+	3.92548i	0.556075	+	0.163278i
$579$	7.92002	−	9.14019i	0.329145	−	0.379853i
$580$	−42.4035	+	27.2511i	−1.76071	+	1.13154i
$581$	−22.2716	−	14.3131i	−0.923982	−	0.593807i
$582$	0.518132	+	3.60369i	0.0214773	+	0.149378i
$583$	35.2043	−	22.6244i	1.45801	−	0.937008i
$584$	2.05347	+	4.49646i	0.0849730	+	0.186065i
$585$	−7.46180	−	8.61138i	−0.308508	−	0.356037i
$586$	−7.83313	+	9.03991i	−0.323584	+	0.373435i
$587$	6.32989	−	44.0254i	0.261263	−	1.81712i	−0.262134	−	0.965032i	$-0.584426\pi$
$587$	6.32989	−	44.0254i	0.261263	−	1.81712i	0.523396	−	0.852089i	$-0.324665\pi$
$588$	2.92255	+	6.39948i	0.120524	+	0.263910i
$589$	0.715793	+	0.826069i	0.0294937	+	0.0340376i
$590$	74.7928	+	21.9611i	3.07917	+	0.904126i
$591$	6.57692	+	1.93116i	0.270538	+	0.0794373i
$592$	−0.135658	+	0.943521i	−0.00557550	+	0.0387785i
$593$	−14.7394	−	9.47243i	−0.605274	−	0.388986i	0.201808	−	0.979425i	$-0.435318\pi$
$593$	−14.7394	−	9.47243i	−0.605274	−	0.388986i	−0.807082	+	0.590439i	$0.798955\pi$
$594$	−16.2815	+	35.6516i	−0.668039	+	1.46280i
$595$	50.5265	−	14.8359i	2.07138	−	0.608213i
$596$	10.6692	−	23.3623i	0.437028	−	0.956958i
$597$	2.04971	+	14.2561i	0.0838892	+	0.583462i
$598$	0.120416	−	0.837513i	0.00492419	−	0.0342485i
$599$	29.4304	+	33.9645i	1.20249	+	1.38775i	0.900736	+	0.434366i	$0.143028\pi$
$599$	29.4304	+	33.9645i	1.20249	+	1.38775i	0.301757	+	0.953385i	$0.402427\pi$
$600$	2.46744	−	1.58573i	0.100733	−	0.0647372i
$601$	−3.10916	+	6.80811i	−0.126825	+	0.277709i	−0.962384	−	0.271692i	$-0.912417\pi$
$601$	−3.10916	+	6.80811i	−0.126825	+	0.277709i	0.835559	+	0.549401i	$0.185144\pi$
$602$	−26.8068			−1.09257
$603$	14.1244	+	9.63597i	0.575192	+	0.392407i
$604$	19.9704			0.812585
$605$	8.79339	−	19.2548i	0.357502	−	0.782820i
$606$	11.8577	−	7.62046i	0.481685	−	0.309560i
$607$	1.81327	+	2.09262i	0.0735983	+	0.0849369i	0.791355	−	0.611358i	$-0.209376\pi$
$607$	1.81327	+	2.09262i	0.0735983	+	0.0849369i	−0.717756	+	0.696294i	$0.754831\pi$
$608$	0.164794	−	1.14617i	0.00668329	−	0.0464833i
$609$	4.33207	+	30.1302i	0.175544	+	1.22094i
$610$	31.6362	−	69.2736i	1.28091	−	2.80481i
$611$	8.01541	−	2.35354i	0.324269	−	0.0952139i
$612$	7.19129	−	15.7467i	0.290691	−	0.636524i
$613$	26.5959	+	17.0922i	1.07420	+	0.690346i	0.953210	−	0.302307i	$-0.0977569\pi$
$613$	26.5959	+	17.0922i	1.07420	+	0.690346i	0.120989	+	0.992654i	$0.461393\pi$
$614$	5.84103	−	40.6253i	0.235725	−	1.63950i
$615$	8.85848	+	2.60109i	0.357209	+	0.104886i
$616$	8.29208	+	2.43477i	0.334097	+	0.0980999i
$617$	24.8719	+	28.7037i	1.00131	+	1.15557i	0.987811	+	0.155659i	$0.0497500\pi$
$617$	24.8719	+	28.7037i	1.00131	+	1.15557i	0.0134942	+	0.999909i	$0.495705\pi$
$618$	1.76128	+	3.85666i	0.0708489	+	0.155137i
$619$	0.0890205	−	0.619152i	0.00357804	−	0.0248858i	−0.987954	−	0.154746i	$-0.950544\pi$
$619$	0.0890205	−	0.619152i	0.00357804	−	0.0248858i	0.991532	+	0.129861i	$0.0414530\pi$
$620$	−24.6627	+	28.4623i	−0.990478	+	1.14307i
$621$	−0.814860	−	0.940399i	−0.0326992	−	0.0377369i
$622$	−3.04151	−	6.65997i	−0.121953	−	0.267040i
$623$	−46.1540	+	29.6614i	−1.84912	+	1.18836i
$624$	−1.06016	−	7.37359i	−0.0424405	−	0.295180i
$625$	−20.8469	−	13.3975i	−0.833877	−	0.535900i
$626$	−6.83103	+	4.39004i	−0.273023	+	0.175461i
$627$	−0.406736	+	0.469398i	−0.0162435	+	0.0187460i
$628$	−3.68148	−	1.08098i	−0.146907	−	0.0431358i
$629$	−0.678105	+	0.782575i	−0.0270378	+	0.0312033i
$630$	−6.09905	−	42.4198i	−0.242992	−	1.69005i
$631$	−11.1477	+	3.27325i	−0.443782	+	0.130306i	−0.495986	−	0.868330i	$-0.665193\pi$
$631$	−11.1477	+	3.27325i	−0.443782	+	0.130306i	0.0522045	+	0.998636i	$0.483375\pi$
$632$	−2.88129			−0.114612
$633$	−4.99910			−0.198696
$634$	−15.6250	+	4.58791i	−0.620547	+	0.182209i
$635$	−11.5401	−	7.41640i	−0.457956	−	0.294311i
$636$	−6.63988	−	14.5393i	−0.263289	−	0.576522i
$637$	−3.13225	−	6.85867i	−0.124104	−	0.271750i
$638$	−64.1664	−	41.2372i	−2.54037	−	1.63260i
$639$	0.181180	−	0.0531991i	0.00716735	−	0.00210452i
$640$	−15.2521			−0.602894
$641$	−20.3647			−0.804356			−0.402178	−	0.915561i	$-0.631747\pi$
$641$	−20.3647			−0.804356			−0.402178	+	0.915561i	$0.631747\pi$
$642$	−22.1726	+	6.51047i	−0.875083	+	0.256948i
$643$	−4.60008	−	31.9943i	−0.181409	−	1.26173i	−0.853434	−	0.521201i	$-0.825484\pi$
$643$	−4.60008	−	31.9943i	−0.181409	−	1.26173i	0.672024	−	0.740529i	$-0.265425\pi$
$644$	0.952170	−	1.09886i	0.0375208	−	0.0433013i
$645$	−12.0188	−	3.52903i	−0.473238	−	0.138955i
$646$	0.957896	−	1.10547i	0.0376879	−	0.0434942i
$647$	−9.36607	+	6.01921i	−0.368218	+	0.236639i	−0.711644	−	0.702540i	$-0.752049\pi$
$647$	−9.36607	+	6.01921i	−0.368218	+	0.236639i	0.343426	+	0.939180i	$0.388413\pi$
$648$	0.835515	+	0.536953i	0.0328221	+	0.0210935i
$649$	7.66986	+	53.3450i	0.301068	+	2.09398i
$650$	14.0141	−	9.00632i	0.549678	−	0.353257i
$651$	9.44809	+	20.6884i	0.370300	+	0.810844i
$652$	4.50127	+	5.19474i	0.176283	+	0.203442i
$653$	1.88062	−	2.17035i	0.0735943	−	0.0849324i	−0.717758	−	0.696292i	$-0.754832\pi$
$653$	1.88062	−	2.17035i	0.0735943	−	0.0849324i	0.791353	+	0.611360i	$0.209377\pi$
$654$	−4.25910	+	29.6227i	−0.166544	+	1.15834i
$655$	23.6651	+	51.8193i	0.924672	+	2.02475i
$656$	−9.06230	−	10.4584i	−0.353823	−	0.408334i
$657$	16.2614	+	4.77476i	0.634416	+	0.186281i
$658$	30.1469	+	8.85193i	1.17525	+	0.345084i
$659$	1.74479	−	12.1353i	0.0679675	−	0.472724i	−0.927203	−	0.374560i	$-0.877794\pi$
$659$	1.74479	−	12.1353i	0.0679675	−	0.472724i	0.995170	−	0.0981644i	$-0.0312971\pi$
$660$	−18.0030	−	11.5698i	−0.700764	−	0.450354i
$661$	−5.77342	+	12.6420i	−0.224560	+	0.491718i	−0.988056	−	0.154095i	$-0.950754\pi$
$661$	−5.77342	+	12.6420i	−0.224560	+	0.491718i	0.763496	+	0.645812i	$0.223481\pi$
$662$	−28.2190	+	8.28584i	−1.09676	+	0.322038i
$663$	3.36169	−	7.36108i	0.130557	−	0.285880i
$664$	0.680452	+	4.73265i	0.0264067	+	0.183662i
$665$	0.235462	−	1.63767i	0.00913081	−	0.0635062i
$666$	0.551864	+	0.636885i	0.0213843	+	0.0246788i
$667$	2.03718	−	1.30921i	0.0788798	−	0.0506930i
$668$	−6.61834	+	14.4921i	−0.256071	+	0.560718i
$669$	−3.87522			−0.149825
$670$	−33.6206	+	36.7105i	−1.29888	+	1.41825i
$671$	52.6528			2.03264
$672$	10.0092	−	21.9170i	0.386112	−	0.845468i
$673$	−0.585759	+	0.376444i	−0.0225793	+	0.0145109i	−0.551882	−	0.833922i	$-0.686090\pi$
$673$	−0.585759	+	0.376444i	−0.0225793	+	0.0145109i	0.529302	+	0.848433i	$0.322454\pi$
$674$	29.1509	+	33.6420i	1.12285	+	1.29584i
$675$	3.48649	−	24.2490i	0.134195	−	0.933346i
$676$	2.40341	+	16.7161i	0.0924388	+	0.642926i
$677$	−10.8812	+	23.8266i	−0.418200	+	0.915731i	0.576896	+	0.816818i	$0.304264\pi$
$677$	−10.8812	+	23.8266i	−0.418200	+	0.915731i	−0.995096	+	0.0989130i	$0.968463\pi$
$678$	−1.59137	+	0.467269i	−0.0611163	+	0.0179454i
$679$	2.78547	−	6.09932i	0.106896	−	0.234070i
$680$	−8.00068	−	5.14173i	−0.306812	−	0.197176i
$681$	0.948567	−	6.59743i	0.0363492	−	0.252814i
$682$	−54.6814	−	16.0559i	−2.09386	−	0.614812i
$683$	0.0105453	+	0.00309639i	0.000403506	+	0.000118480i	0.281934	−	0.959434i	$-0.409024\pi$
$683$	0.0105453	+	0.00309639i	0.000403506	+	0.000118480i	−0.281531	+	0.959552i	$0.590842\pi$
$684$	−0.356177	−	0.411051i	−0.0136188	−	0.0157169i
$685$	−9.77492	−	21.4041i	−0.373480	−	0.817808i
$686$	−2.41325	+	16.7845i	−0.0921382	+	0.640835i
$687$	−11.4448	+	13.2080i	−0.436645	+	0.503915i
$688$	12.2953	+	14.1895i	0.468754	+	0.540970i
$689$	7.11632	+	15.5826i	0.271110	+	0.593649i
$690$	1.25098	−	0.803958i	0.0476241	−	0.0306062i
$691$	−0.723532	−	5.03227i	−0.0275244	−	0.191437i	0.971420	−	0.237366i	$-0.0762841\pi$
$691$	−0.723532	−	5.03227i	−0.0275244	−	0.191437i	−0.998945	+	0.0459295i	$0.985375\pi$
$692$	−7.96216	−	5.11697i	−0.302676	−	0.194518i
$693$	24.9263	−	16.0192i	0.946873	−	0.608518i
$694$	−13.0499	+	15.0603i	−0.495366	+	0.571682i
$695$	5.17978	+	1.52092i	0.196480	+	0.0576918i
$696$	3.60012	−	4.15476i	0.136462	−	0.157486i
$697$	−2.13940	−	14.8799i	−0.0810357	−	0.563616i
$698$	24.9039	−	7.31245i	0.942627	−	0.276780i
$699$	8.93791			0.338063
$700$	28.6266			1.08198
$701$	−8.09253	+	2.37618i	−0.305650	+	0.0897471i	−0.430961	−	0.902370i	$-0.641825\pi$
$701$	−8.09253	+	2.37618i	−0.305650	+	0.0897471i	0.125311	+	0.992118i	$0.460007\pi$
$702$	−13.4972	−	8.67415i	−0.509420	−	0.327385i
$703$	0.0135152	+	0.0295942i	0.000509736	+	0.00111617i
$704$	9.24077	+	20.2345i	0.348275	+	0.762615i
$705$	12.3510	+	7.93748i	0.465164	+	0.298943i
$706$	−57.1935	+	16.7935i	−2.15251	+	0.632033i
$707$	−25.9596			−0.976312
$708$	20.5848			0.773624
$709$	31.5905	−	9.27582i	1.18641	−	0.348361i	0.371767	−	0.928326i	$-0.378752\pi$
$709$	31.5905	−	9.27582i	1.18641	−	0.348361i	0.814641	+	0.579965i	$0.196934\pi$
$710$	0.0782377	+	0.544155i	0.00293621	+	0.0204218i
$711$	−6.46913	+	7.46577i	−0.242611	+	0.279988i
$712$	9.50707	+	2.79153i	0.356292	+	0.104617i
$713$	1.18486	−	1.36740i	0.0443734	−	0.0512097i
$714$	25.6047	−	16.4551i	0.958232	−	0.615818i
$715$	19.2947	+	12.4000i	0.721583	+	0.463733i
$716$	−4.52648	−	31.4824i	−0.169162	−	1.17655i
$717$	−4.99574	+	3.21057i	−0.186569	+	0.119901i
$718$	23.2280	+	50.8621i	0.866860	+	1.89816i
$719$	−16.9925	−	19.6104i	−0.633712	−	0.731343i	0.344538	−	0.938772i	$-0.388036\pi$
$719$	−16.9925	−	19.6104i	−0.633712	−	0.731343i	−0.978250	+	0.207430i	$0.933490\pi$
$720$	−19.6565	+	22.6848i	−0.732553	+	0.845411i
$721$	1.11127	−	7.72908i	0.0413860	−	0.287846i
$722$	15.1272	+	33.1240i	0.562978	+	1.23275i
$723$	−1.68407	−	1.94352i	−0.0626313	−	0.0722804i
$724$	−13.8021	−	4.05265i	−0.512950	−	0.150616i
$725$	45.7454	+	13.4321i	1.69894	+	0.498854i
$726$	1.74116	−	12.1101i	0.0646207	−	0.449447i
$727$	9.37205	+	6.02305i	0.347590	+	0.223383i	0.702773	−	0.711414i	$-0.251945\pi$
$727$	9.37205	+	6.02305i	0.347590	+	0.223383i	−0.355183	+	0.934797i	$0.615581\pi$
$728$	−1.46963	+	3.21805i	−0.0544682	+	0.119269i
$729$	−10.0790	+	2.95945i	−0.373295	+	0.109609i
$730$	−20.4972	+	44.8827i	−0.758637	+	1.66118i
$731$	2.90264	+	20.1883i	0.107358	+	0.746692i
$732$	2.86208	−	19.9062i	0.105785	−	0.735753i
$733$	−20.9736	−	24.2048i	−0.774677	−	0.894025i	0.222036	−	0.975039i	$-0.428730\pi$
$733$	−20.9736	−	24.2048i	−0.774677	−	0.894025i	−0.996713	+	0.0810134i	$0.974184\pi$
$734$	22.0919	−	14.1976i	0.815426	−	0.524043i
$735$	5.50486	−	12.0540i	0.203050	−	0.444617i
$736$	−1.91678			−0.0706535
$737$	−32.7436	−	10.6005i	−1.20613	−	0.390474i
$738$	−12.2343			−0.450349
$739$	−14.6094	+	31.9901i	−0.537415	+	1.17677i	0.425001	+	0.905193i	$0.360274\pi$
$739$	−14.6094	+	31.9901i	−0.537415	+	1.17677i	−0.962416	+	0.271581i	$0.912454\pi$
$740$	−0.943021	+	0.606043i	−0.0346661	+	0.0222786i
$741$	−0.166501	−	0.192153i	−0.00611657	−	0.00705890i
$742$	−9.16940	+	63.7746i	−0.336619	+	2.34124i
$743$	−2.96508	−	20.6226i	−0.108778	−	0.756570i	−0.969073	−	0.246773i	$-0.920630\pi$
$743$	−2.96508	−	20.6226i	−0.108778	−	0.756570i	0.860295	−	0.509797i	$-0.170279\pi$
$744$	1.70634	−	3.73637i	0.0625576	−	0.136982i
$745$	−46.4170	+	13.6293i	−1.70059	+	0.499337i
$746$	23.8367	−	52.1951i	0.872724	−	1.91100i
$747$	13.7906	+	8.86269i	0.504572	+	0.324269i
$748$	−4.95898	+	34.4905i	−0.181318	+	1.26110i
$749$	40.8360	+	11.9905i	1.49211	+	0.438124i
$750$	0.242099	+	0.0710868i	0.00884022	+	0.00259572i
$751$	−26.9498	−	31.1017i	−0.983413	−	1.13492i	−0.990853	−	0.134947i	$-0.956914\pi$
$751$	−26.9498	−	31.1017i	−0.983413	−	1.13492i	0.00744006	−	0.999972i	$-0.497632\pi$
$752$	−9.14171	−	20.0176i	−0.333364	−	0.729965i
$753$	1.87796	−	13.0615i	0.0684366	−	0.475987i
$754$	20.4472	−	23.5974i	0.744644	−	0.859365i
$755$	−24.6332	−	28.4282i	−0.896494	−	1.03461i
$756$	−11.4533	−	25.0792i	−0.416553	−	0.912123i
$757$	29.7366	−	19.1106i	1.08080	−	0.694586i	0.126055	−	0.992023i	$-0.459768\pi$
$757$	29.7366	−	19.1106i	1.08080	−	0.694586i	0.954741	+	0.297437i	$0.0961319\pi$
$758$	−0.420386	−	2.92385i	−0.0152691	−	0.106199i
$759$	0.864910	+	0.555844i	0.0313942	+	0.0201758i
$760$	−0.251374	+	0.161548i	−0.00911828	+	0.00585996i
$761$	22.3677	−	25.8137i	0.810828	−	0.935746i	−0.188095	−	0.982151i	$-0.560231\pi$
$761$	22.3677	−	25.8137i	0.810828	−	0.935746i	0.998923	+	0.0464054i	$0.0147766\pi$
$762$	−7.60749	−	2.23376i	−0.275590	−	0.0809206i
$763$	36.0946	−	41.6554i	1.30671	−	1.50803i
$764$	−0.752944	−	5.23684i	−0.0272405	−	0.189462i
$765$	−31.2861	+	9.18643i	−1.13115	+	0.332136i
$766$	36.9476			1.33497
$767$	−22.0618			−0.796607
$768$	−18.1490	+	5.32903i	−0.654895	+	0.192295i
$769$	−10.4407	−	6.70981i	−0.376500	−	0.241962i	0.338681	−	0.940901i	$-0.390019\pi$
$769$	−10.4407	−	6.70981i	−0.376500	−	0.241962i	−0.715181	+	0.698939i	$0.753656\pi$
$770$	35.8354	+	78.4685i	1.29142	+	2.82781i
$771$	2.88450	+	6.31618i	0.103883	+	0.227471i
$772$	−17.9339	−	11.5254i	−0.645456	−	0.414810i
$773$	1.05186	−	0.308855i	0.0378328	−	0.0111087i	−0.262761	−	0.964861i	$-0.584633\pi$
$773$	1.05186	−	0.308855i	0.0378328	−	0.0111087i	0.300594	+	0.953752i	$0.402815\pi$
$774$	16.5988			0.596633
$775$	35.6223			1.27959
$776$	−1.16193	+	0.341174i	−0.0417109	+	0.0122474i
$777$	0.0963418	+	0.670072i	0.00345624	+	0.0240387i
$778$	45.4336	−	52.4331i	1.62887	−	1.87982i
$779$	−0.453187	−	0.133068i	−0.0162371	−	0.00476764i
$780$	5.73681	−	6.62064i	0.205411	−	0.237057i
$781$	−0.319751	+	0.205491i	−0.0114416	+	0.00735306i
$782$	−2.03693	−	1.30906i	−0.0728406	−	0.0468118i
$783$	−6.53484	−	45.4508i	−0.233536	−	1.62428i
$784$	−16.7095	+	10.7385i	−0.596767	+	0.383519i
$785$	3.00226	+	6.57403i	0.107155	+	0.234637i
$786$	21.5621	+	24.8840i	0.769094	+	0.887582i
$787$	−4.08315	+	4.71220i	−0.145548	+	0.167972i	−0.823843	−	0.566819i	$-0.808174\pi$
$787$	−4.08315	+	4.71220i	−0.145548	+	0.167972i	0.678294	+	0.734790i	$0.262720\pi$
$788$	1.71950	−	11.9594i	0.0612547	−	0.426036i
$789$	−8.12131	−	17.7832i	−0.289126	−	0.633098i
$790$	−18.8341	−	21.7357i	−0.670086	−	0.773320i
$791$	2.93088	+	0.860583i	0.104210	+	0.0305988i
$792$	−5.13447	−	1.50762i	−0.182446	−	0.0535708i
$793$	−3.06744	+	21.3345i	−0.108928	+	0.757611i
$794$	−10.9505	−	7.03748i	−0.388620	−	0.249751i
$795$	−12.5068	+	27.3860i	−0.443570	+	0.971282i
$796$	24.3588	−	7.15240i	0.863376	−	0.253510i
$797$	−2.68772	+	5.88528i	−0.0952039	+	0.208467i	−0.951242	−	0.308445i	$-0.900191\pi$
$797$	−2.68772	+	5.88528i	−0.0952039	+	0.208467i	0.856038	+	0.516912i	$0.172919\pi$
$798$	−0.136093	−	0.946548i	−0.00481764	−	0.0335074i
$799$	3.40211	−	23.6622i	0.120358	−	0.837109i
$800$	−24.7130	−	28.5203i	−0.873736	−	1.00835i
$801$	28.5786	−	18.3664i	1.00978	−	0.648944i
$802$	−2.06164	+	4.51436i	−0.0727990	+	0.159408i
$803$	−34.1140			−1.20386
$804$	−5.78754	+	11.8030i	−0.204111	+	0.416260i
$805$	−2.73874			−0.0965278
$806$	9.69136	−	21.2211i	0.341364	−	0.747482i
$807$	4.96584	−	3.19135i	0.174806	−	0.112341i
$808$	3.07022	+	3.54323i	0.108010	+	0.124650i
$809$	−2.66295	+	18.5212i	−0.0936242	+	0.651171i	0.887929	+	0.459981i	$0.152144\pi$
$809$	−2.66295	+	18.5212i	−0.0936242	+	0.651171i	−0.981553	+	0.191190i	$0.938765\pi$
$810$	1.41086	+	9.81277i	0.0495727	+	0.344786i
$811$	−21.5074	+	47.0946i	−0.755227	+	1.65372i	0.00151131	+	0.999999i	$0.499519\pi$
$811$	−21.5074	+	47.0946i	−0.755227	+	1.65372i	−0.756738	+	0.653718i	$0.773208\pi$
$812$	51.4823	−	15.1166i	1.80668	−	0.530488i
$813$	3.12548	−	6.84384i	0.109615	−	0.240024i
$814$	−1.42701	−	0.917084i	−0.0500167	−	0.0321438i
$815$	1.84256	−	12.8153i	0.0645420	−	0.448899i
$816$	−20.4540	−	6.00585i	−0.716034	−	0.210247i
$817$	0.614862	+	0.180540i	0.0215113	+	0.00631629i
$818$	34.2840	+	39.5658i	1.19871	+	1.38339i
$819$	5.03870	+	11.0332i	0.176066	+	0.385532i
$820$	2.31600	−	16.1082i	0.0808783	−	0.562521i
$821$	2.18425	−	2.52076i	0.0762310	−	0.0879752i	−0.716353	−	0.697738i	$-0.754190\pi$
$821$	2.18425	−	2.52076i	0.0762310	−	0.0879752i	0.792584	+	0.609763i	$0.208735\pi$
$822$	−8.90626	−	10.2784i	−0.310642	−	0.358499i
$823$	−0.116426	−	0.254938i	−0.00405836	−	0.00888657i	0.907592	−	0.419853i	$-0.137918\pi$
$823$	−0.116426	−	0.254938i	−0.00405836	−	0.00888657i	−0.911650	+	0.410967i	$0.865191\pi$
$824$	−1.18637	+	0.762435i	−0.0413292	+	0.0265607i
$825$	2.88070	+	20.0357i	0.100293	+	0.697553i
$826$	−69.8049	−	44.8609i	−2.42882	−	1.56091i
$827$	−19.3832	+	12.4569i	−0.674022	+	0.433167i	−0.832373	−	0.554215i	$-0.813018\pi$
$827$	−19.3832	+	12.4569i	−0.674022	+	0.433167i	0.158352	+	0.987383i	$0.449382\pi$
$828$	−0.589586	+	0.680418i	−0.0204895	+	0.0236462i
$829$	−41.6695	−	12.2353i	−1.44724	−	0.424948i	−0.538612	−	0.842554i	$-0.681051\pi$
$829$	−41.6695	−	12.2353i	−1.44724	−	0.424948i	−0.908628	+	0.417606i	$0.862869\pi$
$830$	−31.2539	+	36.0689i	−1.08484	+	1.25197i
$831$	3.22745	+	22.4474i	0.111959	+	0.778693i
$832$	−8.73721	+	2.56547i	−0.302908	+	0.0889418i
$833$	−21.5769			−0.747595
$834$	3.12022			0.108044
$835$	28.7934	−	8.45451i	0.996438	−	0.292581i
$836$	0.921004	+	0.591894i	0.0318536	+	0.0204711i
$837$	−14.2523	−	31.2081i	−0.492630	−	1.07871i
$838$	−4.02304	−	8.80923i	−0.138974	−	0.304310i
$839$	33.3034	+	21.4028i	1.14976	+	0.738907i	0.969592	−	0.244728i	$-0.0786988\pi$
$839$	33.3034	+	21.4028i	1.14976	+	0.738907i	0.180170	+	0.983635i	$0.442335\pi$
$840$	−5.96566	+	1.75167i	−0.205835	+	0.0604385i
$841$	60.3619			2.08145
$842$	−53.0030			−1.82661
$843$	−12.9989	+	3.81683i	−0.447707	+	0.131459i
$844$	1.25404	+	8.72207i	0.0431660	+	0.300226i
$845$	20.8311	−	24.0403i	0.716610	−	0.827012i
$846$	−18.6670	−	5.48113i	−0.641786	−	0.188445i
$847$	−14.7558	+	17.0292i	−0.507017	+	0.585129i
$848$	37.9631	−	24.3974i	1.30366	−	0.837811i
$849$	4.63332	+	2.97765i	0.159015	+	0.102193i
$850$	−6.78428	−	47.1857i	−0.232699	−	1.61846i
$851$	0.0453052	−	0.0291159i	0.00155304	−	0.000998080i
$852$	0.0603082	+	0.132057i	0.00206613	+	0.00452419i
$853$	−14.5266	−	16.7645i	−0.497380	−	0.574007i	0.450443	−	0.892805i	$-0.351266\pi$
$853$	−14.5266	−	16.7645i	−0.497380	−	0.574007i	−0.947823	+	0.318798i	$0.896721\pi$
$854$	−53.0875	+	61.2662i	−1.81662	+	2.09649i
$855$	−0.145798	+	1.01405i	−0.00498620	+	0.0346798i
$856$	−3.19305	−	6.99181i	−0.109136	−	0.238975i
$857$	1.52627	+	1.76141i	0.0521364	+	0.0601686i	0.781219	−	0.624257i	$-0.214598\pi$
$857$	1.52627	+	1.76141i	0.0521364	+	0.0601686i	−0.729082	+	0.684426i	$0.760053\pi$
$858$	12.7195	+	3.73478i	0.434236	+	0.127503i
$859$	−18.1184	−	5.32004i	−0.618192	−	0.181518i	−0.0423825	−	0.999101i	$-0.513495\pi$
$859$	−18.1184	−	5.32004i	−0.618192	−	0.181518i	−0.575809	+	0.817584i	$0.695313\pi$
$860$	−3.14224	+	21.8548i	−0.107150	+	0.745242i
$861$	−8.26772	−	5.31334i	−0.281763	−	0.181078i
$862$	17.1878	−	37.6361i	0.585419	−	1.28189i
$863$	−11.4435	+	3.36011i	−0.389540	+	0.114379i	−0.470637	−	0.882327i	$-0.655976\pi$
$863$	−11.4435	+	3.36011i	−0.389540	+	0.114379i	0.0810968	+	0.996706i	$0.474158\pi$
$864$	−15.0986	+	33.0614i	−0.513666	+	1.12477i
$865$	2.53711	+	17.6460i	0.0862643	+	0.599981i
$866$	−4.38176	+	30.4758i	−0.148898	+	1.03561i
$867$	−4.53856	−	5.23778i	−0.154138	−	0.177884i
$868$	33.7256	−	21.6742i	1.14472	−	0.735669i
$869$	8.26031	−	18.0876i	0.280212	−	0.613578i
$870$	54.8751			1.86044
$871$	6.20282	−	12.6499i	0.210174	−	0.428626i
$872$	−9.95442			−0.337099
$873$	−1.72477	+	3.77671i	−0.0583745	+	0.127822i
$874$	−0.0639984	+	0.0411293i	−0.00216478	+	0.00139122i
$875$	−0.304317	−	0.351201i	−0.0102878	−	0.0118728i
$876$	−1.85435	+	12.8973i	−0.0626527	+	0.435759i
$877$	−6.64943	−	46.2478i	−0.224535	−	1.56168i	−0.720574	−	0.693378i	$-0.756122\pi$
$877$	−6.64943	−	46.2478i	−0.224535	−	1.56168i	0.496039	−	0.868300i	$-0.334787\pi$
$878$	−15.4577	+	33.8476i	−0.521671	+	1.14230i
$879$	5.70876	−	1.67624i	0.192552	−	0.0565383i
$880$	25.0990	−	54.9591i	0.846086	−	1.85267i
$881$	40.8217	+	26.2345i	1.37532	+	0.883864i	0.999090	−	0.0426625i	$-0.0135840\pi$
$881$	40.8217	+	26.2345i	1.37532	+	0.883864i	0.376230	+	0.926526i	$0.377220\pi$
$882$	−2.49904	+	17.3812i	−0.0841472	+	0.585257i
$883$	−30.9664	−	9.09256i	−1.04210	−	0.305989i	−0.284480	−	0.958682i	$-0.591821\pi$
$883$	−30.9664	−	9.09256i	−1.04210	−	0.305989i	−0.757623	+	0.652693i	$0.773639\pi$
$884$	−13.6864	−	4.01868i	−0.460323	−	0.135163i
$885$	−25.3910	−	29.3028i	−0.853511	−	0.985004i
$886$	−7.64925	−	16.7495i	−0.256981	−	0.562711i
$887$	0.157540	−	1.09571i	0.00528967	−	0.0367905i	−0.987006	−	0.160686i	$-0.948630\pi$
$887$	0.157540	−	1.09571i	0.00528967	−	0.0367905i	0.992295	+	0.123895i	$0.0395386\pi$
$888$	0.0800638	−	0.0923985i	0.00268676	−	0.00310069i
$889$	9.56256	+	11.0358i	0.320718	+	0.370128i
$890$	41.0861	+	89.9660i	1.37721	+	3.01567i
$891$	−5.76608	+	3.70564i	−0.193171	+	0.124144i
$892$	0.972116	+	6.76122i	0.0325489	+	0.226382i
$893$	−0.631856	−	0.406069i	−0.0211443	−	0.0135886i
$894$	−23.5222	+	15.1168i	−0.786699	+	0.505581i
$895$	−39.2323	+	45.2765i	−1.31139	+	1.51343i
$896$	15.5781	+	4.57414i	0.520427	+	0.152811i
$897$	−0.275612	+	0.318073i	−0.00920241	+	0.0106201i
$898$	−0.940490	−	6.54125i	−0.0313845	−	0.218284i
$899$	64.0636	−	18.8108i	2.13664	−	0.627374i
$900$	−17.7256			−0.590854
$901$	49.0217			1.63315
$902$	23.6285	−	6.93796i	0.786744	−	0.231009i
$903$	11.2172	+	7.20889i	0.373287	+	0.239897i
$904$	−0.229172	−	0.501816i	−0.00762213	−	0.0166901i
$905$	11.2556	+	24.6464i	0.374150	+	0.819273i
$906$	−18.2900	−	11.7543i	−0.607646	−	0.390510i
$907$	27.0681	−	7.94791i	0.898781	−	0.263906i	0.200470	−	0.979700i	$-0.435753\pi$
$907$	27.0681	−	7.94791i	0.898781	−	0.263906i	0.698312	+	0.715794i	$0.253935\pi$
$908$	−11.7487			−0.389894
$909$	16.0742			0.533149
$910$	−33.8826	+	9.94882i	−1.12320	+	0.329800i
$911$	7.95455	+	55.3251i	0.263546	+	1.83300i	0.505633	+	0.862749i	$0.331259\pi$
$911$	7.95455	+	55.3251i	0.263546	+	1.83300i	−0.242087	+	0.970255i	$0.577832\pi$
$912$	−0.438610	+	0.506183i	−0.0145238	+	0.0167614i
$913$	−31.6604	−	9.29632i	−1.04781	−	0.307663i
$914$	20.8202	−	24.0278i	0.688673	−	0.794770i
$915$	−31.8671	+	20.4797i	−1.05349	+	0.677040i
$916$	25.9153	+	16.6548i	0.856266	+	0.550289i
$917$	−8.63013	−	60.0239i	−0.284992	−	1.98216i
$918$	−38.6242	+	24.8223i	−1.27479	+	0.819257i
$919$	−23.0502	−	50.4729i	−0.760356	−	1.66495i	−0.746808	−	0.665040i	$-0.768414\pi$
$919$	−23.0502	−	50.4729i	−0.760356	−	1.66495i	−0.0135487	−	0.999908i	$-0.504313\pi$
$920$	0.323908	+	0.373810i	0.0106789	+	0.0123242i
$921$	−13.3691	+	15.4288i	−0.440527	+	0.508395i
$922$	0.683339	−	4.75273i	0.0225046	−	0.156523i
$923$	−0.0646356	−	0.141532i	−0.00212751	−	0.00465859i
$924$	14.9179	+	17.2162i	0.490762	+	0.566370i
$925$	1.01734	+	0.298718i	0.0334500	+	0.00982180i
$926$	38.6169	+	11.3389i	1.26903	+	0.372621i
$927$	−0.688103	+	4.78586i	−0.0226003	+	0.157188i
$928$	−59.5046	−	38.2413i	−1.95333	−	1.25533i
$929$	10.2759	−	22.5011i	0.337142	−	0.738237i	−0.662803	−	0.748794i	$-0.730633\pi$
$929$	10.2759	−	22.5011i	0.337142	−	0.738237i	0.999944	+	0.0105570i	$0.00336045\pi$
$930$	39.3400	−	11.5513i	1.29001	−	0.378781i
$931$	−0.281620	+	0.616662i	−0.00922973	+	0.0202103i
$932$	−2.24211	−	15.5942i	−0.0734429	−	0.510806i
$933$	−0.518287	+	3.60477i	−0.0169680	+	0.118015i
$934$	45.7909	+	52.8455i	1.49832	+	1.72916i
$935$	55.2146	−	35.4843i	1.80571	−	1.16046i
$936$	0.909999	−	1.99262i	0.0297443	−	0.0651308i
$937$	34.2720			1.11962			0.559810	−	0.828621i	$-0.310874\pi$
$937$	34.2720			1.11962			0.559810	+	0.828621i	$0.310874\pi$
$938$	45.3486	−	27.4121i	1.48068	−	0.895038i
$939$	4.03899			0.131808
$940$	10.7505	−	23.5402i	0.350641	−	0.767798i
$941$	−15.6246	+	10.0413i	−0.509346	+	0.327337i	−0.769945	−	0.638110i	$-0.779716\pi$
$941$	−15.6246	+	10.0413i	−0.509346	+	0.327337i	0.260599	+	0.965447i	$0.416080\pi$
$942$	2.73546	+	3.15689i	0.0891261	+	0.102857i
$943$	−0.111267	+	0.773878i	−0.00362335	+	0.0252009i
$944$	8.27092	+	57.5255i	0.269195	+	1.87230i
$945$	−21.5733	+	47.2388i	−0.701778	+	1.53668i
$946$	−32.0580	+	9.41309i	−1.04230	+	0.306046i
$947$	−2.16073	+	4.73134i	−0.0702143	+	0.153748i	−0.941485	−	0.337055i	$-0.890569\pi$
$947$	−2.16073	+	4.73134i	−0.0702143	+	0.153748i	0.871271	+	0.490803i	$0.163296\pi$
$948$	−6.38927	−	4.10613i	−0.207514	−	0.133361i
$949$	1.98741	−	13.8227i	0.0645140	−	0.448705i
$950$	−1.43710	−	0.421971i	−0.0466258	−	0.0136906i
$951$	7.77200	+	2.28207i	0.252024	+	0.0740011i
$952$	6.62965	+	7.65102i	0.214868	+	0.247971i
$953$	7.29464	+	15.9730i	0.236297	+	0.517417i	0.990215	−	0.139551i	$-0.0445659\pi$
$953$	7.29464	+	15.9730i	0.236297	+	0.517417i	−0.753918	+	0.656968i	$0.771839\pi$
$954$	5.67771	−	39.4893i	0.183823	−	1.27851i
$955$	−6.52599	+	7.53139i	−0.211176	+	0.243710i
$956$	6.85478	+	7.91083i	0.221699	+	0.255855i
$957$	15.7607	+	34.5112i	0.509473	+	1.11559i
$958$	0.0677195	−	0.0435207i	0.00218792	−	0.00140609i
$959$	3.56470	+	24.7930i	0.115110	+	0.800608i
$960$	−13.4632	−	8.65226i	−0.434522	−	0.279250i
$961$	15.8887	−	10.2110i	0.512537	−	0.329388i
$962$	0.454730	−	0.524787i	0.0146611	−	0.0169198i
$963$	−25.2857	−	7.42455i	−0.814820	−	0.239253i
$964$	−2.96847	+	3.42579i	−0.0956079	+	0.110337i
$965$	5.71457	+	39.7457i	0.183959	+	1.27946i
$966$	−1.51883	+	0.445967i	−0.0488674	+	0.0143488i
$967$	32.3574			1.04055			0.520273	−	0.854000i	$-0.325830\pi$
$967$	32.3574			1.04055			0.520273	+	0.854000i	$0.325830\pi$
$968$	4.06947			0.130798
$969$	−0.698112	+	0.204984i	−0.0224266	+	0.00658504i
$970$	−10.1689	−	6.53514i	−0.326503	−	0.209831i
$971$	−2.69074	−	5.89190i	−0.0863500	−	0.189080i	0.861531	−	0.507705i	$-0.169506\pi$
$971$	−2.69074	−	5.89190i	−0.0863500	−	0.189080i	−0.947881	+	0.318625i	$0.896779\pi$
$972$	11.2727	+	24.6838i	0.361573	+	0.791734i
$973$	−4.83434	−	3.10684i	−0.154982	−	0.0996009i
$974$	−27.3745	+	8.03789i	−0.877137	+	0.257551i
$975$	−8.28614			−0.265369
$976$	56.7790			1.81745
$977$	−6.67545	+	1.96009i	−0.213567	+	0.0627088i	−0.386766	−	0.922178i	$-0.626408\pi$
$977$	−6.67545	+	1.96009i	−0.213567	+	0.0627088i	0.173199	+	0.984887i	$0.444590\pi$
$978$	−1.06497	−	7.40701i	−0.0340539	−	0.236850i
$979$	−44.7796	+	51.6785i	−1.43116	+	1.65165i
$980$	−22.4118	−	6.58070i	−0.715919	−	0.210213i
$981$	−22.3499	+	25.7931i	−0.713576	+	0.823510i
$982$	−56.4004	+	36.2464i	−1.79981	+	1.15667i
$983$	−29.7392	−	19.1122i	−0.948532	−	0.609585i	−0.0277304	−	0.999615i	$-0.508828\pi$
$983$	−29.7392	−	19.1122i	−0.948532	−	0.609585i	−0.920802	+	0.390031i	$0.872464\pi$
$984$	0.252599	+	1.75687i	0.00805257	+	0.0560068i
$985$	−19.1454	+	12.3040i	−0.610023	+	0.392038i
$986$	−37.1178	−	81.2767i	−1.18207	−	2.58838i
$987$	−10.2344	−	11.8112i	−0.325766	−	0.375954i
$988$	−0.293487	+	0.338702i	−0.00933706	+	0.0107755i
$989$	0.150962	−	1.04996i	0.00480030	−	0.0333868i
$990$	−22.1893	−	48.5878i	−0.705223	−	1.54422i
$991$	−33.2163	−	38.3336i	−1.05515	−	1.21771i	−0.975296	−	0.220901i	$-0.929100\pi$
$991$	−33.2163	−	38.3336i	−1.05515	−	1.21771i	−0.0798532	−	0.996807i	$-0.525445\pi$
$992$	−50.7087	−	14.8894i	−1.61000	−	0.472739i
$993$	14.0364	+	4.12145i	0.445431	+	0.130790i
$994$	0.0832832	−	0.579247i	0.00264158	−	0.0183726i
$995$	−40.2278	−	25.8528i	−1.27531	−	0.819590i
$996$	−5.23559	+	11.4644i	−0.165896	+	0.363262i
$997$	11.0148	−	3.23425i	0.348843	−	0.102430i	−0.102617	−	0.994721i	$-0.532722\pi$
$997$	11.0148	−	3.23425i	0.348843	−	0.102430i	0.451460	+	0.892291i	$0.350903\pi$
$998$	−7.66121	+	16.7757i	−0.242511	+	0.531026i
$999$	−0.145330	−	1.01079i	−0.00459803	−	0.0319800i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	67.2.e.c.24.2	yes	20
3.2	odd	2		603.2.u.c.91.2		20
67.9	even	11		4489.2.a.l.1.2		10
67.14	even	11	inner	67.2.e.c.14.2	✓	20
67.58	odd	22		4489.2.a.m.1.9		10
201.14	odd	22		603.2.u.c.550.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.e.c.14.2	✓	20	67.14	even	11	inner
67.2.e.c.24.2	yes	20	1.1	even	1	trivial
603.2.u.c.91.2		20	3.2	odd	2
603.2.u.c.550.2		20	201.14	odd	22
4489.2.a.l.1.2		10	67.9	even	11
4489.2.a.m.1.9		10	67.58	odd	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:	\( N \)	\(=\)	\( 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	67.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.797176 + 1.74557i) q^{2} +(0.802994 - 0.516053i) q^{3} +(-1.10181 - 1.27155i) q^{4} +(-0.451016 + 3.13689i) q^{5} +(0.260680 + 1.81307i) q^{6} +(1.40141 - 3.06866i) q^{7} +(-0.584585 + 0.171650i) q^{8} +(-0.867756 + 1.90012i) q^{9} +O(q^{10})\)	\(q+(-0.797176 + 1.74557i) q^{2} +(0.802994 - 0.516053i) q^{3} +(-1.10181 - 1.27155i) q^{4} +(-0.451016 + 3.13689i) q^{5} +(0.260680 + 1.81307i) q^{6} +(1.40141 - 3.06866i) q^{7} +(-0.584585 + 0.171650i) q^{8} +(-0.867756 + 1.90012i) q^{9} +(-5.11612 - 3.28793i) q^{10} +(0.598388 - 4.16188i) q^{11} +(-1.54093 - 0.452459i) q^{12} +(1.65150 + 0.484925i) q^{13} +(4.23940 + 4.89252i) q^{14} +(1.25664 + 2.75165i) q^{15} +(0.645282 - 4.48803i) q^{16} +(3.22553 - 3.72246i) q^{17} +(-2.62504 - 3.02946i) q^{18} +(-0.0642876 - 0.140770i) q^{19} +(4.48565 - 2.88275i) q^{20} +(-0.458267 - 3.18732i) q^{21} +(6.78784 + 4.36228i) q^{22} +(-0.215503 + 0.138495i) q^{23} +(-0.380838 + 0.439511i) q^{24} +(-4.83917 - 1.42091i) q^{25} +(-2.16301 + 2.49625i) q^{26} +(0.691288 + 4.80801i) q^{27} +(-5.44605 + 1.59911i) q^{28} -9.45314 q^{29} -5.80496 q^{30} +(-6.77696 + 1.98990i) q^{31} +(6.29469 + 4.04535i) q^{32} +(-1.66725 - 3.65077i) q^{33} +(3.92651 + 8.59785i) q^{34} +(8.99398 + 5.78008i) q^{35} +(3.37221 - 0.990169i) q^{36} -0.210230 q^{37} +0.296973 q^{38} +(1.57639 - 0.462871i) q^{39} +(-0.274788 - 1.91119i) q^{40} +(1.99866 - 2.30658i) q^{41} +(5.92901 + 1.74091i) q^{42} +(-2.71169 + 3.12945i) q^{43} +(-5.95136 + 3.82471i) q^{44} +(-5.56909 - 3.57904i) q^{45} +(-0.0699596 - 0.486580i) q^{46} +(4.08294 - 2.62395i) q^{47} +(-1.79791 - 3.93686i) q^{48} +(-2.86870 - 3.31066i) q^{49} +(6.33797 - 7.31440i) q^{50} +(0.669096 - 4.65366i) q^{51} +(-1.20303 - 2.63427i) q^{52} +(6.51756 + 7.52166i) q^{53} +(-8.94380 - 2.62614i) q^{54} +(12.7855 + 3.75415i) q^{55} +(-0.292509 + 2.03444i) q^{56} +(-0.124268 - 0.0798619i) q^{57} +(7.53581 - 16.5011i) q^{58} +(-12.2983 + 3.61111i) q^{59} +(2.11430 - 4.62967i) q^{60} +(1.78213 + 12.3950i) q^{61} +(1.92892 - 13.4160i) q^{62} +(4.61474 + 5.32570i) q^{63} +(-4.45062 + 2.86024i) q^{64} +(-2.26601 + 4.96187i) q^{65} +7.70176 q^{66} +(1.38719 - 8.06695i) q^{67} -8.28723 q^{68} +(-0.101577 + 0.222422i) q^{69} +(-17.2593 + 11.0919i) q^{70} +(-0.0591972 - 0.0683172i) q^{71} +(0.181122 - 1.25973i) q^{72} +(-1.15465 - 8.03075i) q^{73} +(0.167591 - 0.366972i) q^{74} +(-4.61909 + 1.35629i) q^{75} +(-0.108164 + 0.236847i) q^{76} +(-11.9328 - 7.66875i) q^{77} +(-0.448689 + 3.12070i) q^{78} +(4.53757 + 1.33235i) q^{79} +(13.7874 + 4.04835i) q^{80} +(-1.06751 - 1.23197i) q^{81} +(2.43301 + 5.32755i) q^{82} +(1.11684 - 7.76780i) q^{83} +(-3.54793 + 4.09453i) q^{84} +(10.2222 + 11.7970i) q^{85} +(-3.30099 - 7.22817i) q^{86} +(-7.59082 + 4.87832i) q^{87} +(0.364577 + 2.53569i) q^{88} +(-13.6813 - 8.79241i) q^{89} +(10.6870 - 6.86812i) q^{90} +(3.80250 - 4.38832i) q^{91} +(0.413546 + 0.121428i) q^{92} +(-4.41497 + 5.09515i) q^{93} +(1.32546 + 9.21881i) q^{94} +(0.470575 - 0.138173i) q^{95} +7.14221 q^{96} +1.98762 q^{97} +(8.06585 - 2.36835i) q^{98} +(7.38882 + 4.74851i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9	\( 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9} - 9 q^{10} + 3 q^{12} + 12 q^{13} + 6 q^{14} - 11 q^{15} + 8 q^{16} - 4 q^{17} - 2 q^{18} + 4 q^{19} + 2 q^{20} - 53 q^{21} + 2 q^{23} + 11 q^{24} - 3 q^{25} - 31 q^{26} + 47 q^{27} - 5 q^{28} - 6 q^{29} + 44 q^{30} + 16 q^{32} + q^{33} - 8 q^{34} + 34 q^{35} + 9 q^{36} + 24 q^{37} - 14 q^{38} - 22 q^{39} - 11 q^{40} - 6 q^{41} + 59 q^{42} - 22 q^{43} - 22 q^{44} - 46 q^{45} + 15 q^{46} + 16 q^{47} + 5 q^{48} + 42 q^{49} - 17 q^{50} + 22 q^{51} + 2 q^{52} - q^{53} - 60 q^{54} + 20 q^{55} + 11 q^{56} - 52 q^{57} + 10 q^{58} - 26 q^{59} + 44 q^{60} - 26 q^{61} + 11 q^{62} - 42 q^{63} - 6 q^{64} + 9 q^{65} + 2 q^{66} - 22 q^{67} - 52 q^{68} + 62 q^{69} - 42 q^{70} + 20 q^{71} + 11 q^{72} - 55 q^{73} + 37 q^{74} - 70 q^{75} - 3 q^{76} - 70 q^{77} + 22 q^{78} - 34 q^{79} + 40 q^{80} + 42 q^{81} - 12 q^{82} + 56 q^{83} - 29 q^{84} + 41 q^{85} - 33 q^{86} - 10 q^{87} + 11 q^{88} - 3 q^{89} + 18 q^{90} + 12 q^{91} - 18 q^{92} - 69 q^{93} + 32 q^{94} + 74 q^{95} - 12 q^{96} - 14 q^{97} + 95 q^{98} + 81 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9 - 9 * q^10 + 3 * q^12 + 12 * q^13 + 6 * q^14 - 11 * q^15 + 8 * q^16 - 4 * q^17 - 2 * q^18 + 4 * q^19 + 2 * q^20 - 53 * q^21 + 2 * q^23 + 11 * q^24 - 3 * q^25 - 31 * q^26 + 47 * q^27 - 5 * q^28 - 6 * q^29 + 44 * q^30 + 16 * q^32 + q^33 - 8 * q^34 + 34 * q^35 + 9 * q^36 + 24 * q^37 - 14 * q^38 - 22 * q^39 - 11 * q^40 - 6 * q^41 + 59 * q^42 - 22 * q^43 - 22 * q^44 - 46 * q^45 + 15 * q^46 + 16 * q^47 + 5 * q^48 + 42 * q^49 - 17 * q^50 + 22 * q^51 + 2 * q^52 - q^53 - 60 * q^54 + 20 * q^55 + 11 * q^56 - 52 * q^57 + 10 * q^58 - 26 * q^59 + 44 * q^60 - 26 * q^61 + 11 * q^62 - 42 * q^63 - 6 * q^64 + 9 * q^65 + 2 * q^66 - 22 * q^67 - 52 * q^68 + 62 * q^69 - 42 * q^70 + 20 * q^71 + 11 * q^72 - 55 * q^73 + 37 * q^74 - 70 * q^75 - 3 * q^76 - 70 * q^77 + 22 * q^78 - 34 * q^79 + 40 * q^80 + 42 * q^81 - 12 * q^82 + 56 * q^83 - 29 * q^84 + 41 * q^85 - 33 * q^86 - 10 * q^87 + 11 * q^88 - 3 * q^89 + 18 * q^90 + 12 * q^91 - 18 * q^92 - 69 * q^93 + 32 * q^94 + 74 * q^95 - 12 * q^96 - 14 * q^97 + 95 * q^98 + 81 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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