LMFDB - Embedded newform 378.2.u.b.337.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(43,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("378.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.u (of order $9$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			337.2
Root			$0.500000 - 1.00210i$ of defining polynomial
Character	$\chi$	$=$	378.337
Dual form			378.2.u.b.295.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{2} +(1.65667 + 0.505425i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.31259 + 1.10139i) q^{5} +(-0.210069 + 1.71926i) q^{6} +(-0.939693 - 0.342020i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.48909 + 1.67464i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{2} +(1.65667 + 0.505425i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.31259 + 1.10139i) q^{5} +(-0.210069 + 1.71926i) q^{6} +(-0.939693 - 0.342020i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.48909 + 1.67464i) q^{9} +(-0.856730 + 1.48390i) q^{10} +(-0.960783 + 0.806193i) q^{11} +(-1.72962 + 0.0916693i) q^{12} +(-0.652160 + 3.69858i) q^{13} +(0.173648 - 0.984808i) q^{14} +(1.61785 + 2.48805i) q^{15} +(0.766044 - 0.642788i) q^{16} +(3.04828 - 5.27978i) q^{17} +(-1.21697 + 2.74207i) q^{18} +(1.39513 + 2.41644i) q^{19} +(-1.61013 - 0.586038i) q^{20} +(-1.38389 - 1.04156i) q^{21} +(-0.960783 - 0.806193i) q^{22} +(-2.42118 + 0.881236i) q^{23} +(-0.390623 - 1.68743i) q^{24} +(-0.358420 - 2.03270i) q^{25} -3.75564 q^{26} +(3.27719 + 4.03237i) q^{27} +1.00000 q^{28} +(-0.744954 - 4.22485i) q^{29} +(-2.16932 + 2.02531i) q^{30} +(-1.67121 + 0.608270i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-1.99917 + 0.849989i) q^{33} +(5.72890 + 2.08515i) q^{34} +(-0.856730 - 1.48390i) q^{35} +(-2.91174 - 0.722330i) q^{36} +(0.699704 - 1.21192i) q^{37} +(-2.13746 + 1.79354i) q^{38} +(-2.94977 + 5.79770i) q^{39} +(0.297539 - 1.68743i) q^{40} +(0.568290 - 3.22293i) q^{41} +(0.785424 - 1.54373i) q^{42} +(5.86201 - 4.91881i) q^{43} +(0.627106 - 1.08618i) q^{44} +(1.42271 + 4.93957i) q^{45} +(-1.28828 - 2.23137i) q^{46} +(-6.56218 - 2.38844i) q^{47} +(1.59396 - 0.677707i) q^{48} +(0.766044 + 0.642788i) q^{49} +(1.93958 - 0.705949i) q^{50} +(7.71852 - 7.20616i) q^{51} +(-0.652160 - 3.69858i) q^{52} -3.54440 q^{53} +(-3.40203 + 3.92762i) q^{54} -2.14904 q^{55} +(0.173648 + 0.984808i) q^{56} +(1.08994 + 4.70836i) q^{57} +(4.03130 - 1.46727i) q^{58} +(-6.26285 - 5.25516i) q^{59} +(-2.37124 - 1.78467i) q^{60} +(10.9885 + 3.99950i) q^{61} +(-0.889232 - 1.54019i) q^{62} +(-1.76622 - 2.42497i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-4.92960 + 4.13643i) q^{65} +(-1.18423 - 1.82120i) q^{66} +(-2.70516 + 15.3417i) q^{67} +(-1.05866 + 6.00394i) q^{68} +(-4.45648 + 0.236191i) q^{69} +(1.31259 - 1.10139i) q^{70} +(5.68458 - 9.84598i) q^{71} +(0.205737 - 2.99294i) q^{72} +(-3.34614 - 5.79569i) q^{73} +(1.31501 + 0.478626i) q^{74} +(0.433595 - 3.54866i) q^{75} +(-2.13746 - 1.79354i) q^{76} +(1.17857 - 0.428966i) q^{77} +(-6.22184 - 1.89819i) q^{78} +(-0.215477 - 1.22203i) q^{79} +1.71346 q^{80} +(3.39115 + 8.33667i) q^{81} +3.27265 q^{82} +(-0.957482 - 5.43015i) q^{83} +(1.65667 + 0.505425i) q^{84} +(9.81623 - 3.57282i) q^{85} +(5.86201 + 4.91881i) q^{86} +(0.901202 - 7.37568i) q^{87} +(1.17857 + 0.428966i) q^{88} +(-8.40393 - 14.5560i) q^{89} +(-4.61748 + 2.25885i) q^{90} +(1.87782 - 3.25248i) q^{91} +(1.97376 - 1.65618i) q^{92} +(-3.07607 + 0.163030i) q^{93} +(1.21264 - 6.87724i) q^{94} +(-0.830211 + 4.70836i) q^{95} +(0.944200 + 1.45206i) q^{96} +(11.1167 - 9.32799i) q^{97} +(-0.500000 + 0.866025i) q^{98} +(-3.74156 + 0.397719i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} - 6 q^{6} - 6 q^{8} + 9 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 - 6 * q^6 - 6 * q^8 + 9 * q^9	$ 12 q + 3 q^{3} - 6 q^{6} - 6 q^{8} + 9 q^{9} + 3 q^{11} - 6 q^{12} + 12 q^{13} + 9 q^{15} - 9 q^{18} + 12 q^{19} - 9 q^{20} + 3 q^{21} + 3 q^{22} + 12 q^{23} + 3 q^{24} - 24 q^{25} - 18 q^{26} + 18 q^{27} + 12 q^{28} - 3 q^{29} + 21 q^{31} - 27 q^{33} + 9 q^{34} + 15 q^{37} + 15 q^{38} - 48 q^{39} + 9 q^{40} + 12 q^{41} + 3 q^{42} + 21 q^{43} + 12 q^{44} - 9 q^{45} - 6 q^{46} + 12 q^{47} + 3 q^{48} + 21 q^{50} - 9 q^{51} + 12 q^{52} - 42 q^{53} - 27 q^{54} - 12 q^{55} + 33 q^{57} - 3 q^{58} + 18 q^{59} - 18 q^{60} + 9 q^{62} + 9 q^{63} - 6 q^{64} - 36 q^{65} - 9 q^{66} - 33 q^{67} - 18 q^{68} + 9 q^{69} + 24 q^{71} - 18 q^{72} + 9 q^{73} - 36 q^{74} - 33 q^{75} + 15 q^{76} + 3 q^{77} - 21 q^{78} + 9 q^{81} - 24 q^{82} + 15 q^{83} + 3 q^{84} - 24 q^{85} + 21 q^{86} + 3 q^{88} - 51 q^{89} + 9 q^{91} - 6 q^{92} - 30 q^{93} - 15 q^{94} - 45 q^{95} + 3 q^{96} + 48 q^{97} - 6 q^{98} + 36 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 - 6 * q^6 - 6 * q^8 + 9 * q^9 + 3 * q^11 - 6 * q^12 + 12 * q^13 + 9 * q^15 - 9 * q^18 + 12 * q^19 - 9 * q^20 + 3 * q^21 + 3 * q^22 + 12 * q^23 + 3 * q^24 - 24 * q^25 - 18 * q^26 + 18 * q^27 + 12 * q^28 - 3 * q^29 + 21 * q^31 - 27 * q^33 + 9 * q^34 + 15 * q^37 + 15 * q^38 - 48 * q^39 + 9 * q^40 + 12 * q^41 + 3 * q^42 + 21 * q^43 + 12 * q^44 - 9 * q^45 - 6 * q^46 + 12 * q^47 + 3 * q^48 + 21 * q^50 - 9 * q^51 + 12 * q^52 - 42 * q^53 - 27 * q^54 - 12 * q^55 + 33 * q^57 - 3 * q^58 + 18 * q^59 - 18 * q^60 + 9 * q^62 + 9 * q^63 - 6 * q^64 - 36 * q^65 - 9 * q^66 - 33 * q^67 - 18 * q^68 + 9 * q^69 + 24 * q^71 - 18 * q^72 + 9 * q^73 - 36 * q^74 - 33 * q^75 + 15 * q^76 + 3 * q^77 - 21 * q^78 + 9 * q^81 - 24 * q^82 + 15 * q^83 + 3 * q^84 - 24 * q^85 + 21 * q^86 + 3 * q^88 - 51 * q^89 + 9 * q^91 - 6 * q^92 - 30 * q^93 - 15 * q^94 - 45 * q^95 + 3 * q^96 + 48 * q^97 - 6 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

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 $

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	1.65667	+	0.505425i	0.956477	+	0.291807i
$3$	1.65667	+	0.505425i	0.956477	+	0.291807i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	1.31259	+	1.10139i	0.587006	+	0.492557i	0.887240	−	0.461309i	$-0.152620\pi$
$5$	1.31259	+	1.10139i	0.587006	+	0.492557i	−0.300233	+	0.953866i	$0.597064\pi$
$6$	−0.210069	+	1.71926i	−0.0857604	+	0.701887i
$7$	−0.939693	−	0.342020i	−0.355170	−	0.129271i
$7$	−0.939693	−	0.342020i	−0.355170	−	0.129271i
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	2.48909	+	1.67464i	0.829697	+	0.558214i
$10$	−0.856730	+	1.48390i	−0.270922	+	0.469250i
$11$	−0.960783	+	0.806193i	−0.289687	+	0.243076i	−0.776036	−	0.630688i	$-0.782773\pi$
$11$	−0.960783	+	0.806193i	−0.289687	+	0.243076i	0.486349	+	0.873764i	$0.338328\pi$
$12$	−1.72962	+	0.0916693i	−0.499299	+	0.0264626i
$13$	−0.652160	+	3.69858i	−0.180877	+	1.02580i	0.750263	+	0.661140i	$0.229927\pi$
$13$	−0.652160	+	3.69858i	−0.180877	+	1.02580i	−0.931140	+	0.364663i	$0.881184\pi$
$14$	0.173648	−	0.984808i	0.0464094	−	0.263201i
$15$	1.61785	+	2.48805i	0.417726	+	0.642412i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	3.04828	−	5.27978i	0.739317	−	1.28053i	−0.213486	−	0.976946i	$-0.568482\pi$
$17$	3.04828	−	5.27978i	0.739317	−	1.28053i	0.952803	−	0.303588i	$-0.0981848\pi$
$18$	−1.21697	+	2.74207i	−0.286844	+	0.646313i
$19$	1.39513	+	2.41644i	0.320065	+	0.554368i	0.980501	−	0.196514i	$-0.0629620\pi$
$19$	1.39513	+	2.41644i	0.320065	+	0.554368i	−0.660436	+	0.750882i	$0.729629\pi$
$20$	−1.61013	−	0.586038i	−0.360035	−	0.131042i
$21$	−1.38389	−	1.04156i	−0.301990	−	0.227287i
$22$	−0.960783	−	0.806193i	−0.204840	−	0.171881i
$23$	−2.42118	+	0.881236i	−0.504850	+	0.183750i	−0.581874	−	0.813279i	$-0.697680\pi$
$23$	−2.42118	+	0.881236i	−0.504850	+	0.183750i	0.0770242	+	0.997029i	$0.475458\pi$
$24$	−0.390623	−	1.68743i	−0.0797355	−	0.344445i
$25$	−0.358420	−	2.03270i	−0.0716839	−	0.406540i
$26$	−3.75564			−0.736542
$27$	3.27719	+	4.03237i	0.630695	+	0.776031i
$28$	1.00000			0.188982
$29$	−0.744954	−	4.22485i	−0.138335	−	0.784534i	−0.972479	−	0.232989i	$-0.925149\pi$
$29$	−0.744954	−	4.22485i	−0.138335	−	0.784534i	0.834145	−	0.551545i	$-0.185962\pi$
$30$	−2.16932	+	2.02531i	−0.396061	+	0.369770i
$31$	−1.67121	+	0.608270i	−0.300158	+	0.109249i	−0.487709	−	0.873006i	$-0.662167\pi$
$31$	−1.67121	+	0.608270i	−0.300158	+	0.109249i	0.187551	+	0.982255i	$0.439945\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	−1.99917	+	0.849989i	−0.348010	+	0.147964i
$34$	5.72890	+	2.08515i	0.982497	+	0.357600i
$35$	−0.856730	−	1.48390i	−0.144814	−	0.250825i
$36$	−2.91174	−	0.722330i	−0.485290	−	0.120388i
$37$	0.699704	−	1.21192i	0.115031	−	0.199239i	−0.802761	−	0.596300i	$-0.796637\pi$
$37$	0.699704	−	1.21192i	0.115031	−	0.199239i	0.917792	+	0.397062i	$0.129970\pi$
$38$	−2.13746	+	1.79354i	−0.346742	+	0.290951i
$39$	−2.94977	+	5.79770i	−0.472341	+	0.928375i
$40$	0.297539	−	1.68743i	0.0470451	−	0.266806i
$41$	0.568290	−	3.22293i	0.0887519	−	0.503337i	−0.907732	−	0.419551i	$-0.862188\pi$
$41$	0.568290	−	3.22293i	0.0887519	−	0.503337i	0.996484	−	0.0837863i	$-0.0267013\pi$
$42$	0.785424	−	1.54373i	0.121194	−	0.238203i
$43$	5.86201	−	4.91881i	0.893949	−	0.750112i	−0.0750495	−	0.997180i	$-0.523911\pi$
$43$	5.86201	−	4.91881i	0.893949	−	0.750112i	0.968998	+	0.247068i	$0.0794670\pi$
$44$	0.627106	−	1.08618i	0.0945399	−	0.163748i
$45$	1.42271	+	4.93957i	0.212085	+	0.736348i
$46$	−1.28828	−	2.23137i	−0.189947	−	0.328997i
$47$	−6.56218	−	2.38844i	−0.957193	−	0.348390i	−0.184260	−	0.982878i	$-0.558989\pi$
$47$	−6.56218	−	2.38844i	−0.957193	−	0.348390i	−0.772933	+	0.634488i	$0.781211\pi$
$48$	1.59396	−	0.677707i	0.230069	−	0.0978186i
$49$	0.766044	+	0.642788i	0.109435	+	0.0918268i
$50$	1.93958	−	0.705949i	0.274298	−	0.0998362i
$51$	7.71852	−	7.20616i	1.08081	−	1.00906i
$52$	−0.652160	−	3.69858i	−0.0904383	−	0.512901i
$53$	−3.54440			−0.486861			−0.243431	−	0.969918i	$-0.578273\pi$
$53$	−3.54440			−0.486861			−0.243431	+	0.969918i	$0.578273\pi$
$54$	−3.40203	+	3.92762i	−0.462958	+	0.534481i
$55$	−2.14904			−0.289777
$56$	0.173648	+	0.984808i	0.0232047	+	0.131600i
$57$	1.08994	+	4.70836i	0.144366	+	0.623638i
$58$	4.03130	−	1.46727i	0.529336	−	0.192662i
$59$	−6.26285	−	5.25516i	−0.815354	−	0.684163i	0.136525	−	0.990637i	$-0.456407\pi$
$59$	−6.26285	−	5.25516i	−0.815354	−	0.684163i	−0.951879	+	0.306473i	$0.900851\pi$
$60$	−2.37124	−	1.78467i	−0.306126	−	0.230400i
$61$	10.9885	+	3.99950i	1.40694	+	0.512083i	0.930229	−	0.366979i	$-0.119608\pi$
$61$	10.9885	+	3.99950i	1.40694	+	0.512083i	0.476708	+	0.879062i	$0.341830\pi$
$62$	−0.889232	−	1.54019i	−0.112933	−	0.195605i
$63$	−1.76622	−	2.42497i	−0.222523	−	0.305517i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−4.92960	+	4.13643i	−0.611442	+	0.513061i
$66$	−1.18423	−	1.82120i	−0.145768	−	0.224174i
$67$	−2.70516	+	15.3417i	−0.330488	+	1.87429i	0.137422	+	0.990513i	$0.456118\pi$
$67$	−2.70516	+	15.3417i	−0.330488	+	1.87429i	−0.467910	+	0.883776i	$0.654993\pi$
$68$	−1.05866	+	6.00394i	−0.128381	+	0.728085i
$69$	−4.45648	+	0.236191i	−0.536497	+	0.0284341i
$70$	1.31259	−	1.10139i	0.156884	−	0.131641i
$71$	5.68458	−	9.84598i	0.674635	−	1.16850i	−0.301940	−	0.953327i	$-0.597634\pi$
$71$	5.68458	−	9.84598i	0.674635	−	1.16850i	0.976575	−	0.215176i	$-0.0690324\pi$
$72$	0.205737	−	2.99294i	0.0242463	−	0.352721i
$73$	−3.34614	−	5.79569i	−0.391636	−	0.678334i	0.601029	−	0.799227i	$-0.294757\pi$
$73$	−3.34614	−	5.79569i	−0.391636	−	0.678334i	−0.992666	+	0.120893i	$0.961424\pi$
$74$	1.31501	+	0.478626i	0.152867	+	0.0556391i
$75$	0.433595	−	3.54866i	0.0500672	−	0.409764i
$76$	−2.13746	−	1.79354i	−0.245184	−	0.205734i
$77$	1.17857	−	0.428966i	0.134311	−	0.0488852i
$78$	−6.22184	−	1.89819i	−0.704485	−	0.214928i
$79$	−0.215477	−	1.22203i	−0.0242430	−	0.137489i	0.970284	−	0.241969i	$-0.0777932\pi$
$79$	−0.215477	−	1.22203i	−0.0242430	−	0.137489i	−0.994527	+	0.104480i	$0.966682\pi$
$80$	1.71346			0.191571
$81$	3.39115	+	8.33667i	0.376794	+	0.926297i
$82$	3.27265			0.361404
$83$	−0.957482	−	5.43015i	−0.105097	−	0.596037i	−0.991181	−	0.132512i	$-0.957696\pi$
$83$	−0.957482	−	5.43015i	−0.105097	−	0.596037i	0.886084	−	0.463525i	$-0.153415\pi$
$84$	1.65667	+	0.505425i	0.180757	+	0.0551464i
$85$	9.81623	−	3.57282i	1.06472	−	0.387526i
$86$	5.86201	+	4.91881i	0.632117	+	0.530409i
$87$	0.901202	−	7.37568i	0.0966190	−	0.790756i
$88$	1.17857	+	0.428966i	0.125636	+	0.0457279i
$89$	−8.40393	−	14.5560i	−0.890815	−	1.54294i	−0.838900	−	0.544286i	$-0.816801\pi$
$89$	−8.40393	−	14.5560i	−0.890815	−	1.54294i	−0.0519154	−	0.998651i	$-0.516533\pi$
$90$	−4.61748	+	2.25885i	−0.486725	+	0.238103i
$91$	1.87782	−	3.25248i	0.196849	−	0.340953i
$92$	1.97376	−	1.65618i	0.205779	−	0.172669i
$93$	−3.07607	+	0.163030i	−0.318974	+	0.0169055i
$94$	1.21264	−	6.87724i	0.125074	−	0.709333i
$95$	−0.830211	+	4.70836i	−0.0851779	+	0.483068i
$96$	0.944200	+	1.45206i	0.0963670	+	0.148201i
$97$	11.1167	−	9.32799i	1.12873	−	0.947114i	0.129714	−	0.991551i	$-0.458594\pi$
$97$	11.1167	−	9.32799i	1.12873	−	0.947114i	0.999012	+	0.0444373i	$0.0141495\pi$
$98$	−0.500000	+	0.866025i	−0.0505076	+	0.0874818i
$99$	−3.74156	+	0.397719i	−0.376041	+	0.0399723i
$100$	1.03203	+	1.78753i	0.103203	+	0.178753i
$101$	12.7918	+	4.65583i	1.27283	+	0.463272i	0.888055	−	0.459738i	$-0.152057\pi$
$101$	12.7918	+	4.65583i	1.27283	+	0.463272i	0.384775	+	0.923010i	$0.374279\pi$
$102$	8.43699	+	6.34992i	0.835386	+	0.628736i
$103$	−0.375422	−	0.315016i	−0.0369914	−	0.0310395i	0.624105	−	0.781341i	$-0.285464\pi$
$103$	−0.375422	−	0.315016i	−0.0369914	−	0.0310395i	−0.661096	+	0.750301i	$0.729908\pi$
$104$	3.52915	−	1.28450i	0.346061	−	0.125956i
$105$	−0.669316	−	2.89134i	−0.0653185	−	0.282166i
$106$	−0.615479	−	3.49056i	−0.0597806	−	0.339033i
$107$	4.10282			0.396635			0.198317	−	0.980138i	$-0.436452\pi$
$107$	4.10282			0.396635			0.198317	+	0.980138i	$0.436452\pi$
$108$	−4.45870	−	2.66833i	−0.429039	−	0.256760i
$109$	−10.5320			−1.00878			−0.504390	−	0.863476i	$-0.668283\pi$
$109$	−10.5320			−1.00878			−0.504390	+	0.863476i	$0.668283\pi$
$110$	−0.373177	−	2.11639i	−0.0355811	−	0.201790i
$111$	1.77171	−	1.65410i	0.168164	−	0.157001i
$112$	−0.939693	+	0.342020i	−0.0887926	+	0.0323179i
$113$	5.22859	+	4.38731i	0.491865	+	0.412723i	0.854694	−	0.519132i	$-0.173745\pi$
$113$	5.22859	+	4.38731i	0.491865	+	0.412723i	−0.362829	+	0.931856i	$0.618189\pi$
$114$	−4.44757	+	1.89098i	−0.416553	+	0.177106i
$115$	−4.14859	−	1.50996i	−0.386858	−	0.140805i
$116$	2.14501	+	3.71527i	0.199159	+	0.344954i
$117$	−7.81709	+	8.11398i	−0.722690	+	0.750137i
$118$	4.08779	−	7.08026i	0.376311	−	0.651790i
$119$	−4.67024	+	3.91880i	−0.428120	+	0.359235i
$120$	1.34579	−	2.64512i	0.122853	−	0.241466i
$121$	−1.63697	+	9.28373i	−0.148816	+	0.843976i
$122$	−2.03060	+	11.5161i	−0.183842	+	1.04262i
$123$	2.57042	−	5.05209i	0.231767	−	0.455532i
$124$	1.36238	−	1.14317i	0.122346	−	0.102660i
$125$	6.05199	−	10.4823i	0.541306	−	0.937570i
$126$	2.08143	−	2.16048i	0.185428	−	0.192471i
$127$	3.33416	+	5.77494i	0.295859	+	0.512443i	0.975184	−	0.221394i	$-0.0710607\pi$
$127$	3.33416	+	5.77494i	0.295859	+	0.512443i	−0.679325	+	0.733837i	$0.737727\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	12.1975	−	5.18603i	1.07393	−	0.456604i
$130$	−4.92960	−	4.13643i	−0.432355	−	0.362789i
$131$	0.116911	−	0.0425522i	0.0102146	−	0.00371780i	−0.336908	−	0.941538i	$-0.609381\pi$
$131$	0.116911	−	0.0425522i	0.0102146	−	0.00371780i	0.347122	+	0.937820i	$0.387159\pi$
$132$	1.58789	−	1.48248i	0.138208	−	0.129034i
$133$	−0.484523	−	2.74787i	−0.0420135	−	0.238270i
$134$	−15.5784			−1.34577
$135$	−0.139625	+	8.90230i	−0.0120170	+	0.766188i
$136$	−6.09656			−0.522776
$137$	−0.543640	−	3.08313i	−0.0464463	−	0.263410i	0.952738	−	0.303793i	$-0.0982532\pi$
$137$	−0.543640	−	3.08313i	−0.0464463	−	0.263410i	−0.999184	+	0.0403833i	$0.987142\pi$
$138$	−1.00646	−	4.34776i	−0.0856758	−	0.370106i
$139$	−6.99391	+	2.54557i	−0.593215	+	0.215913i	−0.621143	−	0.783697i	$-0.713331\pi$
$139$	−6.99391	+	2.54557i	−0.593215	+	0.215913i	0.0279276	+	0.999610i	$0.491109\pi$
$140$	1.31259	+	1.10139i	0.110934	+	0.0930845i
$141$	−9.66417	−	7.27354i	−0.813870	−	0.612542i
$142$	10.6835	+	3.88848i	0.896540	+	0.326314i
$143$	−2.35519	−	4.07930i	−0.196951	−	0.341128i
$144$	2.98319	−	0.317107i	0.248599	−	0.0264256i
$145$	3.67539	−	6.36596i	0.305224	−	0.528664i
$146$	5.12659	−	4.30172i	0.424279	−	0.356013i
$147$	0.944200	+	1.45206i	0.0778763	+	0.119764i
$148$	−0.243005	+	1.37815i	−0.0199749	+	0.113283i
$149$	−2.78633	+	15.8020i	−0.228265	+	1.29455i	0.628080	+	0.778149i	$0.283841\pi$
$149$	−2.78633	+	15.8020i	−0.228265	+	1.29455i	−0.856345	+	0.516405i	$0.827270\pi$
$150$	3.57004	−	0.189211i	0.291493	−	0.0154490i
$151$	−13.3844	+	11.2309i	−1.08921	+	0.913955i	−0.996653	−	0.0817521i	$-0.973948\pi$
$151$	−13.3844	+	11.2309i	−1.08921	+	0.913955i	−0.0925568	+	0.995707i	$0.529504\pi$
$152$	1.39513	−	2.41644i	0.113160	−	0.195999i
$153$	16.4292	−	8.03707i	1.32822	−	0.649759i
$154$	0.627106	+	1.08618i	0.0505337	+	0.0875269i
$155$	−2.86355	−	1.04225i	−0.230006	−	0.0837153i
$156$	0.788945	−	6.45694i	0.0631661	−	0.516969i
$157$	−8.98089	−	7.53586i	−0.716753	−	0.601427i	0.209732	−	0.977759i	$-0.432741\pi$
$157$	−8.98089	−	7.53586i	−0.716753	−	0.601427i	−0.926485	+	0.376332i	$0.877185\pi$
$158$	1.16605	−	0.424406i	0.0927656	−	0.0337639i
$159$	−5.87190	−	1.79143i	−0.465672	−	0.142070i
$160$	0.297539	+	1.68743i	0.0235225	+	0.133403i
$161$	2.57656			0.203061
$162$	−7.62115	+	4.78728i	−0.598774	+	0.376124i
$163$	−24.0423			−1.88314			−0.941568	−	0.336822i	$-0.890648\pi$
$163$	−24.0423			−1.88314			−0.941568	+	0.336822i	$0.890648\pi$
$164$	0.568290	+	3.22293i	0.0443760	+	0.251669i
$165$	−3.56025	−	1.08618i	−0.277165	−	0.0845590i
$166$	5.18139	−	1.88587i	0.402154	−	0.146372i
$167$	−5.63531	−	4.72858i	−0.436073	−	0.365909i	0.398164	−	0.917314i	$-0.369647\pi$
$167$	−5.63531	−	4.72858i	−0.436073	−	0.365909i	−0.834237	+	0.551405i	$0.814092\pi$
$168$	−0.210069	+	1.71926i	−0.0162072	+	0.132644i
$169$	−1.03820	−	0.377875i	−0.0798617	−	0.0290673i
$170$	5.22311	+	9.04669i	0.400594	+	0.693849i
$171$	−0.574060	+	8.35107i	−0.0438994	+	0.638622i
$172$	−3.82616	+	6.62710i	−0.291742	+	0.505312i
$173$	−15.9462	+	13.3804i	−1.21237	+	1.01730i	−0.213177	+	0.977014i	$0.568381\pi$
$173$	−15.9462	+	13.3804i	−1.21237	+	1.01730i	−0.999188	+	0.0402822i	$0.987174\pi$
$174$	7.42012	−	0.393263i	0.562518	−	0.0298132i
$175$	−0.358420	+	2.03270i	−0.0270940	+	0.153658i
$176$	−0.217792	+	1.23516i	−0.0164167	+	0.0931036i
$177$	−7.71938	−	11.8715i	−0.580224	−	0.892313i
$178$	12.8756	−	10.8039i	0.965065	−	0.809786i
$179$	−4.93356	+	8.54517i	−0.368751	+	0.638696i	−0.989371	−	0.145416i	$-0.953548\pi$
$179$	−4.93356	+	8.54517i	−0.368751	+	0.638696i	0.620619	+	0.784112i	$0.286881\pi$
$180$	−3.02634	−	4.15508i	−0.225570	−	0.309702i
$181$	0.189393	+	0.328038i	0.0140775	+	0.0243829i	0.872978	−	0.487759i	$-0.162186\pi$
$181$	0.189393	+	0.328038i	0.0140775	+	0.0243829i	−0.858901	+	0.512142i	$0.828852\pi$
$182$	3.52915	+	1.28450i	0.261598	+	0.0952138i
$183$	16.1829	+	12.1797i	1.19627	+	0.900350i
$184$	1.97376	+	1.65618i	0.145508	+	0.122095i
$185$	2.25322	−	0.820106i	0.165660	−	0.0602954i
$186$	−0.694708	−	3.00103i	−0.0509385	−	0.220046i
$187$	1.32778	+	7.53022i	0.0970970	+	0.550664i
$188$	6.98333			0.509312
$189$	−1.70040	−	4.91006i	−0.123686	−	0.357154i
$190$	−4.78100			−0.346850
$191$	2.26465	+	12.8435i	0.163865	+	0.929322i	0.950227	+	0.311557i	$0.100851\pi$
$191$	2.26465	+	12.8435i	0.163865	+	0.929322i	−0.786363	+	0.617765i	$0.788038\pi$
$192$	−1.26604	+	1.18200i	−0.0913689	+	0.0853037i
$193$	14.2127	−	5.17299i	1.02305	−	0.372360i	0.224620	−	0.974446i	$-0.427886\pi$
$193$	14.2127	−	5.17299i	1.02305	−	0.372360i	0.798431	+	0.602087i	$0.205664\pi$
$194$	11.1167	+	9.32799i	0.798130	+	0.669711i
$195$	−10.2574	+	4.36114i	−0.734545	+	0.312308i
$196$	−0.939693	−	0.342020i	−0.0671209	−	0.0244300i
$197$	10.4828	+	18.1567i	0.746868	+	1.29361i	0.949317	+	0.314320i	$0.101777\pi$
$197$	10.4828	+	18.1567i	0.746868	+	1.29361i	−0.202449	+	0.979293i	$0.564890\pi$
$198$	−1.04139	−	3.61565i	−0.0740085	−	0.256953i
$199$	−9.49884	+	16.4525i	−0.673355	+	1.16628i	0.303592	+	0.952802i	$0.401814\pi$
$199$	−9.49884	+	16.4525i	−0.673355	+	1.16628i	−0.976947	+	0.213483i	$0.931519\pi$
$200$	−1.58116	+	1.32675i	−0.111805	+	0.0938154i
$201$	−12.2356	+	24.0489i	−0.863035	+	1.69628i
$202$	−2.36383	+	13.4059i	−0.166318	+	0.943237i
$203$	−0.744954	+	4.22485i	−0.0522855	+	0.296526i
$204$	−4.78839	+	9.41146i	−0.335254	+	0.658934i
$205$	4.29563	−	3.60446i	0.300020	−	0.251747i
$206$	0.245039	−	0.424420i	0.0170727	−	0.0295708i
$207$	−7.50228	−	1.86113i	−0.521444	−	0.129357i
$208$	1.87782	+	3.25248i	0.130203	+	0.225519i
$209$	−3.28853	−	1.19693i	−0.227472	−	0.0827931i
$210$	2.73119	−	1.16122i	0.188470	−	0.0801320i
$211$	15.7543	+	13.2194i	1.08457	+	0.910063i	0.996292	−	0.0860332i	$-0.0274191\pi$
$211$	15.7543	+	13.2194i	1.08457	+	0.910063i	0.0882782	+	0.996096i	$0.471864\pi$
$212$	3.33065	−	1.21226i	0.228750	−	0.0832582i
$213$	14.3939	−	13.4384i	0.986251	−	0.920782i
$214$	0.712448	+	4.04049i	0.0487019	+	0.276202i
$215$	13.1119			0.894226
$216$	1.85354	−	4.85432i	0.126118	−	0.330294i
$217$	1.77846			0.120730
$218$	−1.82886	−	10.3720i	−0.123866	−	0.702478i
$219$	−2.61416	−	11.2927i	−0.176648	−	0.763093i
$220$	2.01944	−	0.735016i	0.136151	−	0.0495548i
$221$	17.5397	+	14.7176i	1.17985	+	0.990012i
$222$	1.93663	+	1.45756i	0.129978	+	0.0978253i
$223$	−26.2670	−	9.56040i	−1.75897	−	0.640212i	−0.759026	−	0.651061i	$-0.774324\pi$
$223$	−26.2670	−	9.56040i	−1.75897	−	0.640212i	−0.999941	+	0.0108493i	$0.996547\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$	2.51190	−	5.65980i	0.167460	−	0.377320i
$226$	−3.41272	+	5.91101i	−0.227011	+	0.393194i
$227$	−7.36444	+	6.17950i	−0.488795	+	0.410148i	−0.853594	−	0.520939i	$-0.825582\pi$
$227$	−7.36444	+	6.17950i	−0.488795	+	0.410148i	0.364799	+	0.931086i	$0.381138\pi$
$228$	−2.63456	−	4.05163i	−0.174478	−	0.268326i
$229$	−3.11049	+	17.6404i	−0.205547	+	1.16571i	0.691031	+	0.722826i	$0.257157\pi$
$229$	−3.11049	+	17.6404i	−0.205547	+	1.16571i	−0.896577	+	0.442887i	$0.853954\pi$
$230$	0.766628	−	4.34776i	0.0505499	−	0.286683i
$231$	2.16932	−	0.114973i	0.142731	−	0.00756465i
$232$	−3.28635	+	2.75757i	−0.215759	+	0.181043i
$233$	−2.35161	+	4.07311i	−0.154059	+	0.266838i	−0.932716	−	0.360612i	$-0.882568\pi$
$233$	−2.35161	+	4.07311i	−0.154059	+	0.266838i	0.778657	+	0.627450i	$0.215901\pi$
$234$	−9.34813	−	6.28935i	−0.611106	−	0.411148i
$235$	−5.98282	−	10.3626i	−0.390276	−	0.675979i
$236$	7.68253	+	2.79621i	0.500090	+	0.182018i
$237$	0.260671	−	2.13340i	0.0169324	−	0.138579i
$238$	−4.67024	−	3.91880i	−0.302727	−	0.254018i
$239$	−23.6469	+	8.60676i	−1.52959	+	0.556725i	−0.963521	−	0.267633i	$-0.913759\pi$
$239$	−23.6469	+	8.60676i	−1.52959	+	0.556725i	−0.566069	+	0.824358i	$0.691536\pi$
$240$	2.83863	+	0.866025i	0.183233	+	0.0559017i
$241$	0.650035	+	3.68653i	0.0418724	+	0.237470i	0.998560	−	0.0536463i	$-0.0170843\pi$
$241$	0.650035	+	3.68653i	0.0418724	+	0.237470i	−0.956688	+	0.291117i	$0.905973\pi$
$242$	−9.42695			−0.605987
$243$	1.40444	+	15.5251i	0.0900948	+	0.995933i
$244$	−11.6937			−0.748615
$245$	0.297539	+	1.68743i	0.0190091	+	0.107806i
$246$	5.42169	+	1.65408i	0.345674	+	0.105460i
$247$	−9.84723	+	3.58410i	−0.626565	+	0.228051i
$248$	1.36238	+	1.14317i	0.0865114	+	0.0725917i
$249$	1.15831	−	9.47989i	0.0734046	−	0.600764i
$250$	11.3740	+	4.13980i	0.719356	+	0.261824i
$251$	−10.6347	−	18.4199i	−0.671258	−	1.16265i	−0.977548	−	0.210715i	$-0.932421\pi$
$251$	−10.6347	−	18.4199i	−0.671258	−	1.16265i	0.306289	−	0.951938i	$-0.400913\pi$
$252$	2.48909	+	1.67464i	0.156798	+	0.105493i
$253$	1.61578	−	2.79861i	0.101583	−	0.175947i
$254$	−5.10824	+	4.28632i	−0.320519	+	0.268948i
$255$	18.0680	−	0.957597i	1.13146	−	0.0599670i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	5.55886	−	31.5259i	0.346752	−	1.96653i	0.118274	−	0.992981i	$-0.462264\pi$
$257$	5.55886	−	31.5259i	0.346752	−	1.96653i	0.228478	−	0.973549i	$-0.426625\pi$
$258$	7.22531	+	11.1116i	0.449828	+	0.691781i
$259$	−1.07201	+	0.899522i	−0.0666114	+	0.0558936i
$260$	3.21757	−	5.57299i	0.199545	−	0.345622i
$261$	5.22084	−	11.7636i	0.323162	−	0.728146i
$262$	0.0622071	+	0.107746i	0.00384317	+	0.00665656i
$263$	9.60132	+	3.49459i	0.592043	+	0.215486i	0.620628	−	0.784105i	$-0.286878\pi$
$263$	9.60132	+	3.49459i	0.592043	+	0.215486i	−0.0285849	+	0.999591i	$0.509100\pi$
$264$	1.73570	+	1.30634i	0.106825	+	0.0803994i
$265$	−4.65233	−	3.90377i	−0.285791	−	0.239807i
$266$	2.62199	−	0.954325i	0.160764	−	0.0585134i
$267$	−6.56553	−	28.3621i	−0.401804	−	1.73573i
$268$	−2.70516	−	15.3417i	−0.165244	−	0.937144i
$269$	18.4643			1.12579			0.562894	−	0.826529i	$-0.309688\pi$
$269$	18.4643			1.12579			0.562894	+	0.826529i	$0.309688\pi$
$270$	−8.79130	+	1.40836i	−0.535022	+	0.0857103i
$271$	12.7983			0.777443			0.388722	−	0.921355i	$-0.372917\pi$
$271$	12.7983			0.777443			0.388722	+	0.921355i	$0.372917\pi$
$272$	−1.05866	−	6.00394i	−0.0641905	−	0.364043i
$273$	4.75481	−	4.43918i	0.287774	−	0.268671i
$274$	2.94189	−	1.07076i	0.177726	−	0.0646871i
$275$	1.98311	+	1.66403i	0.119586	+	0.100345i
$276$	4.10694	−	1.74615i	0.247209	−	0.105106i
$277$	−13.9464	−	5.07608i	−0.837959	−	0.304992i	−0.112838	−	0.993613i	$-0.535994\pi$
$277$	−13.9464	−	5.07608i	−0.837959	−	0.304992i	−0.725121	+	0.688621i	$0.758216\pi$
$278$	−3.72138	−	6.44562i	−0.223194	−	0.386583i
$279$	−5.17843	−	1.28464i	−0.310024	−	0.0769092i
$280$	−0.856730	+	1.48390i	−0.0511994	+	0.0886800i
$281$	3.72253	−	3.12358i	0.222068	−	0.186337i	−0.524966	−	0.851123i	$-0.675922\pi$
$281$	3.72253	−	3.12358i	0.222068	−	0.186337i	0.747034	+	0.664786i	$0.231477\pi$
$282$	5.48487	−	10.7804i	0.326619	−	0.641963i
$283$	−3.25925	+	18.4841i	−0.193742	+	1.09877i	0.720456	+	0.693501i	$0.243933\pi$
$283$	−3.25925	+	18.4841i	−0.193742	+	1.09877i	−0.914198	+	0.405267i	$0.867178\pi$
$284$	−1.97423	+	11.1964i	−0.117149	+	0.664386i
$285$	−3.75511	+	7.38058i	−0.222433	+	0.437188i
$286$	3.60835	−	3.02777i	0.213366	−	0.179036i
$287$	−1.63632	+	2.83420i	−0.0965892	+	0.167297i
$288$	0.830315	+	2.88281i	0.0489268	+	0.169871i
$289$	−10.0840	−	17.4661i	−0.593179	−	1.02742i
$290$	6.90747	+	2.51411i	0.405621	+	0.147634i
$291$	23.1312	−	9.83473i	1.35598	−	0.576522i
$292$	5.12659	+	4.30172i	0.300011	+	0.251739i
$293$	13.7105	−	4.99021i	0.800975	−	0.291531i	0.0910848	−	0.995843i	$-0.470967\pi$
$293$	13.7105	−	4.99021i	0.800975	−	0.291531i	0.709891	+	0.704312i	$0.248744\pi$
$294$	−1.26604	+	1.18200i	−0.0738372	+	0.0689358i
$295$	−2.43255	−	13.7957i	−0.141629	−	0.803217i
$296$	−1.39941			−0.0813389
$297$	−6.39954	−	1.23219i	−0.371339	−	0.0714989i
$298$	−16.0458			−0.929509
$299$	−1.68033	−	9.52962i	−0.0971760	−	0.551112i
$300$	0.806267	+	3.48295i	0.0465498	+	0.201088i
$301$	−7.19082	+	2.61725i	−0.414472	+	0.150856i
$302$	−13.3844	−	11.2309i	−0.770187	−	0.646264i
$303$	18.8386	+	14.1784i	1.08225	+	0.814530i
$304$	2.62199	+	0.954325i	0.150381	+	0.0547343i
$305$	10.0184	+	17.3523i	0.573651	+	0.993592i
$306$	10.7679	+	14.7840i	0.615558	+	0.845143i
$307$	5.33942	−	9.24814i	0.304737	−	0.527819i	−0.672466	−	0.740128i	$-0.734765\pi$
$307$	5.33942	−	9.24814i	0.304737	−	0.527819i	0.977203	+	0.212309i	$0.0680982\pi$
$308$	−0.960783	+	0.806193i	−0.0547457	+	0.0459371i
$309$	−0.462732	−	0.711625i	−0.0263239	−	0.0404829i
$310$	0.529163	−	3.00103i	0.0300544	−	0.170447i
$311$	2.66283	−	15.1016i	0.150995	−	0.856336i	−0.811361	−	0.584545i	$-0.801273\pi$
$311$	2.66283	−	15.1016i	0.150995	−	0.856336i	0.962356	−	0.271791i	$-0.0876158\pi$
$312$	6.49584	−	0.344277i	0.367755	−	0.0194908i
$313$	−9.95410	+	8.35248i	−0.562639	+	0.472110i	−0.879194	−	0.476464i	$-0.841918\pi$
$313$	−9.95410	+	8.35248i	−0.562639	+	0.472110i	0.316555	+	0.948574i	$0.397474\pi$
$314$	5.86186	−	10.1530i	0.330804	−	0.572969i
$315$	0.352522	−	5.12828i	0.0198624	−	0.288946i
$316$	0.620440	+	1.07463i	0.0349025	+	0.0604529i
$317$	−9.15813	−	3.33328i	−0.514372	−	0.187216i	0.0717752	−	0.997421i	$-0.477134\pi$
$317$	−9.15813	−	3.33328i	−0.514372	−	0.187216i	−0.586147	+	0.810205i	$0.699356\pi$
$318$	0.744570	−	6.09377i	0.0417534	−	0.341722i
$319$	4.12178	+	3.45858i	0.230775	+	0.193643i
$320$	−1.61013	+	0.586038i	−0.0900087	+	0.0327605i
$321$	6.79701	+	2.07367i	0.379372	+	0.115741i
$322$	0.447415	+	2.53742i	0.0249335	+	0.141405i
$323$	17.0110			0.946517
$324$	−6.03795	−	6.67407i	−0.335441	−	0.370782i
$325$	7.75185			0.429995
$326$	−4.17490	−	23.6770i	−0.231226	−	1.31135i
$327$	−17.4480	−	5.32312i	−0.964875	−	0.294369i
$328$	−3.07528	+	1.11931i	−0.169804	+	0.0618037i
$329$	5.34954	+	4.48880i	0.294930	+	0.247475i
$330$	0.451448	−	3.69477i	0.0248514	−	0.203391i
$331$	2.79680	+	1.01795i	0.153726	+	0.0559517i	0.417737	−	0.908568i	$-0.362823\pi$
$331$	2.79680	+	1.01795i	0.153726	+	0.0559517i	−0.264011	+	0.964520i	$0.585046\pi$
$332$	2.75696	+	4.77520i	0.151308	+	0.262073i
$333$	3.77116	−	1.84483i	0.206658	−	0.101096i
$334$	3.67818	−	6.37080i	0.201261	−	0.348595i
$335$	−20.4480	+	17.1579i	−1.11719	+	0.937435i
$336$	−1.72962	+	0.0916693i	−0.0943587	+	0.00500097i
$337$	−2.03813	+	11.5588i	−0.111024	+	0.629650i	0.877618	+	0.479361i	$0.159131\pi$
$337$	−2.03813	+	11.5588i	−0.111024	+	0.629650i	−0.988642	+	0.150289i	$0.951980\pi$
$338$	0.191852	−	1.08805i	0.0104354	−	0.0591819i
$339$	6.44458	+	9.91097i	0.350022	+	0.538290i
$340$	−8.00226	+	6.71470i	−0.433984	+	0.364156i
$341$	1.11529	−	1.93173i	0.0603961	−	0.104609i
$342$	−8.32388	+	0.884810i	−0.450104	+	0.0478450i
$343$	−0.500000	−	0.866025i	−0.0269975	−	0.0467610i
$344$	−7.19082	−	2.61725i	−0.387703	−	0.141112i
$345$	−6.10965	−	4.59830i	−0.328933	−	0.247564i
$346$	−15.9462	−	13.3804i	−0.857272	−	0.719337i
$347$	25.1905	−	9.16860i	1.35230	−	0.492196i	0.438634	−	0.898666i	$-0.355462\pi$
$347$	25.1905	−	9.16860i	1.35230	−	0.492196i	0.913664	+	0.406469i	$0.133240\pi$
$348$	1.67578	+	7.23910i	0.0898312	+	0.388057i
$349$	1.34593	+	7.63313i	0.0720458	+	0.408592i	0.999407	+	0.0344255i	$0.0109601\pi$
$349$	1.34593	+	7.63313i	0.0720458	+	0.408592i	−0.927361	+	0.374167i	$0.877929\pi$
$350$	−2.06406			−0.110328
$351$	−17.0513	+	9.49120i	−0.910132	+	0.506603i
$352$	−1.25421			−0.0668498
$353$	0.305997	+	1.73539i	0.0162866	+	0.0923657i	0.991868	−	0.127274i	$-0.0406228\pi$
$353$	0.305997	+	1.73539i	0.0162866	+	0.0923657i	−0.975581	+	0.219640i	$0.929512\pi$
$354$	10.3506	−	9.66356i	0.550130	−	0.513612i
$355$	18.3058	−	6.66275i	0.971569	−	0.353622i
$356$	12.8756	+	10.8039i	0.682404	+	0.572605i
$357$	−9.71769	+	4.13168i	−0.514315	+	0.218672i
$358$	−9.27205	−	3.37475i	−0.490043	−	0.178361i
$359$	−8.54676	−	14.8034i	−0.451081	−	0.781295i	0.547373	−	0.836889i	$-0.315628\pi$
$359$	−8.54676	−	14.8034i	−0.451081	−	0.781295i	−0.998453	+	0.0555942i	$0.982295\pi$
$360$	3.56644	−	3.70189i	0.187968	−	0.195107i
$361$	5.60723	−	9.71200i	0.295117	−	0.511158i
$362$	−0.290167	+	0.243479i	−0.0152508	+	0.0127970i
$363$	−7.40415	+	14.5527i	−0.388617	+	0.763818i
$364$	−0.652160	+	3.69858i	−0.0341825	+	0.193858i
$365$	1.99122	−	11.2927i	0.104225	−	0.591089i
$366$	−9.18455	+	18.0520i	−0.480084	+	0.943594i
$367$	−10.9253	+	9.16739i	−0.570295	+	0.478534i	−0.881744	−	0.471729i	$-0.843630\pi$
$367$	−10.9253	+	9.16739i	−0.570295	+	0.478534i	0.311449	+	0.950263i	$0.399186\pi$
$368$	−1.28828	+	2.23137i	−0.0671563	+	0.116318i
$369$	6.81178	−	7.07049i	0.354607	−	0.368075i
$370$	1.19891	+	2.07658i	0.0623286	+	0.107956i
$371$	3.33065	+	1.21226i	0.172919	+	0.0629373i
$372$	2.83480	−	1.20528i	0.146978	−	0.0624907i
$373$	−24.2229	−	20.3254i	−1.25422	−	1.05241i	−0.996273	−	0.0862515i	$-0.972511\pi$
$373$	−24.2229	−	20.3254i	−1.25422	−	1.05241i	−0.257942	−	0.966160i	$-0.583044\pi$
$374$	−7.18525	+	2.61522i	−0.371541	+	0.135230i
$375$	15.3242	−	14.3069i	0.791337	−	0.738807i
$376$	1.21264	+	6.87724i	0.0625372	+	0.354666i
$377$	16.1118			0.829798
$378$	4.54019	−	2.52719i	0.233522	−	0.129984i
$379$	28.6868			1.47354			0.736770	−	0.676144i	$-0.236350\pi$
$379$	28.6868			1.47354			0.736770	+	0.676144i	$0.236350\pi$
$380$	−0.830211	−	4.70836i	−0.0425889	−	0.241534i
$381$	2.60480	+	11.2523i	0.133448	+	0.576474i
$382$	−12.2551	+	4.46050i	−0.627026	+	0.228219i
$383$	−5.73043	−	4.80840i	−0.292811	−	0.245698i	0.484534	−	0.874773i	$-0.338989\pi$
$383$	−5.73043	−	4.80840i	−0.292811	−	0.245698i	−0.777345	+	0.629075i	$0.783434\pi$
$384$	−1.38389	−	1.04156i	−0.0706215	−	0.0531518i
$385$	2.01944	+	0.735016i	0.102920	+	0.0374599i
$386$	7.56241	+	13.0985i	0.384916	+	0.666695i
$387$	22.8283	−	2.42660i	1.16043	−	0.123351i
$388$	−7.25589	+	12.5676i	−0.368362	+	0.638022i
$389$	−8.45937	+	7.09826i	−0.428907	+	0.359896i	−0.831539	−	0.555466i	$-0.812540\pi$
$389$	−8.45937	+	7.09826i	−0.428907	+	0.359896i	0.402632	+	0.915362i	$0.368095\pi$
$390$	−6.07605	−	9.34423i	−0.307673	−	0.473163i
$391$	−2.72769	+	15.4695i	−0.137945	+	0.782327i
$392$	0.173648	−	0.984808i	0.00877056	−	0.0497403i
$393$	0.215190	−	0.0114050i	0.0108549	−	0.000575304i
$394$	−16.0606	+	13.4764i	−0.809120	+	0.678932i
$395$	1.06310	−	1.84134i	0.0534903	−	0.0926479i
$396$	3.37989	−	1.65342i	0.169846	−	0.0830876i
$397$	−15.9992	−	27.7114i	−0.802977	−	1.39080i	−0.917648	−	0.397394i	$-0.869915\pi$
$397$	−15.9992	−	27.7114i	−0.802977	−	1.39080i	0.114671	−	0.993404i	$-0.463419\pi$
$398$	−17.8520	−	6.49759i	−0.894839	−	0.325695i
$399$	0.586148	−	4.79719i	0.0293441	−	0.240160i
$400$	−1.58116	−	1.32675i	−0.0790579	−	0.0663375i
$401$	−0.622863	+	0.226704i	−0.0311043	+	0.0113210i	−0.357525	−	0.933903i	$-0.616379\pi$
$401$	−0.622863	+	0.226704i	−0.0311043	+	0.0113210i	0.326421	+	0.945224i	$0.394157\pi$
$402$	−25.8082	−	7.87371i	−1.28720	−	0.392705i
$403$	−1.15984	−	6.57780i	−0.0577759	−	0.327663i
$404$	−13.6127			−0.677259
$405$	−4.73076	+	14.6776i	−0.235073	+	0.729335i
$406$	−4.29002			−0.212910
$407$	0.304780	+	1.72849i	0.0151074	+	0.0856781i
$408$	−10.1000	−	3.08136i	−0.500023	−	0.152550i
$409$	24.2399	−	8.82259i	1.19858	−	0.436249i	0.335854	−	0.941914i	$-0.390975\pi$
$409$	24.2399	−	8.82259i	1.19858	−	0.436249i	0.862730	+	0.505665i	$0.168753\pi$
$410$	4.29563	+	3.60446i	0.212146	+	0.178012i
$411$	0.657663	−	5.38250i	0.0324401	−	0.265499i
$412$	0.460523	+	0.167617i	0.0226883	+	0.00825788i
$413$	4.08779	+	7.08026i	0.201147	+	0.348397i
$414$	0.530094	−	7.71148i	0.0260527	−	0.378999i
$415$	4.72394	−	8.18210i	0.231889	−	0.401644i
$416$	−2.87699	+	2.41408i	−0.141056	+	0.118360i
$417$	−12.8732	+	0.682272i	−0.630402	+	0.0334110i
$418$	0.607695	−	3.44641i	0.0297234	−	0.168570i
$419$	−1.58766	+	9.00409i	−0.0775624	+	0.439878i	0.921153	+	0.389201i	$0.127249\pi$
$419$	−1.58766	+	9.00409i	−0.0775624	+	0.439878i	−0.998715	+	0.0506769i	$0.983862\pi$
$420$	1.61785	+	2.48805i	0.0789429	+	0.121404i
$421$	17.8021	−	14.9377i	0.867620	−	0.728019i	−0.0959758	−	0.995384i	$-0.530597\pi$
$421$	17.8021	−	14.9377i	0.867620	−	0.728019i	0.963596	+	0.267364i	$0.0861527\pi$
$422$	−10.2829	+	17.8105i	−0.500563	+	0.867001i
$423$	−12.3341	−	16.9343i	−0.599704	−	0.823376i
$424$	1.77220	+	3.06954i	0.0860657	+	0.149070i
$425$	−11.8248	−	4.30386i	−0.573585	−	0.208768i
$426$	15.7337	+	11.8416i	0.762299	+	0.573729i
$427$	−8.95793	−	7.51660i	−0.433505	−	0.363754i
$428$	−3.85539	+	1.40325i	−0.186357	+	0.0678286i
$429$	−1.83998	−	7.94842i	−0.0888350	−	0.383753i
$430$	2.27686	+	12.9127i	0.109800	+	0.622707i
$431$	−5.99707			−0.288869			−0.144434	−	0.989514i	$-0.546136\pi$
$431$	−5.99707			−0.288869			−0.144434	+	0.989514i	$0.546136\pi$
$432$	5.10243	+	0.982441i	0.245491	+	0.0472677i
$433$	12.6815			0.609432			0.304716	−	0.952443i	$-0.401438\pi$
$433$	12.6815			0.609432			0.304716	+	0.952443i	$0.401438\pi$
$434$	0.308827	+	1.75145i	0.0148242	+	0.0840721i
$435$	9.30641	−	8.68864i	0.446208	−	0.416588i
$436$	9.89681	−	3.60215i	0.473971	−	0.172511i
$437$	−5.50730	−	4.62117i	−0.263450	−	0.221061i
$438$	10.6672	−	4.53541i	0.509700	−	0.216710i
$439$	18.8863	+	6.87404i	0.901392	+	0.328080i	0.750811	−	0.660518i	$-0.229663\pi$
$439$	18.8863	+	6.87404i	0.901392	+	0.328080i	0.150582	+	0.988598i	$0.451885\pi$
$440$	1.07452	+	1.86113i	0.0512258	+	0.0887257i
$441$	0.830315	+	2.88281i	0.0395388	+	0.137277i
$442$	−11.4482	+	19.8289i	−0.544538	+	0.943167i
$443$	25.1520	−	21.1050i	1.19501	−	1.00273i	0.195247	−	0.980754i	$-0.437449\pi$
$443$	25.1520	−	21.1050i	1.19501	−	1.00273i	0.999759	−	0.0219748i	$-0.00699536\pi$
$444$	−1.09913	+	2.16031i	−0.0521623	+	0.102524i
$445$	5.00100	−	28.3621i	0.237070	−	1.34449i
$446$	4.85394	−	27.5281i	0.229841	−	1.30349i
$447$	−12.6028	+	24.7704i	−0.596090	+	1.17160i
$448$	0.766044	−	0.642788i	0.0361922	−	0.0303689i
$449$	−17.8043	+	30.8380i	−0.840238	+	1.45533i	0.0494557	+	0.998776i	$0.484251\pi$
$449$	−17.8043	+	30.8380i	−0.840238	+	1.45533i	−0.889694	+	0.456558i	$0.849082\pi$
$450$	6.01000	+	1.49093i	0.283314	+	0.0702831i
$451$	2.05230	+	3.55469i	0.0966390	+	0.167384i
$452$	−6.41382	−	2.33444i	−0.301681	−	0.109803i
$453$	−27.8499	+	11.8410i	−1.30850	+	0.556338i
$454$	−7.36444	−	6.17950i	−0.345630	−	0.290018i
$455$	6.04705	−	2.20095i	0.283490	−	0.103182i
$456$	3.53259	−	3.29809i	0.165429	−	0.154447i
$457$	2.80215	+	15.8918i	0.131079	+	0.743385i	0.977510	+	0.210888i	$0.0676354\pi$
$457$	2.80215	+	15.8918i	0.131079	+	0.743385i	−0.846431	+	0.532498i	$0.821253\pi$
$458$	−17.9126			−0.837000
$459$	31.2798	−	5.01102i	1.46002	−	0.233894i
$460$	4.41483			0.205843
$461$	6.57323	+	37.2786i	0.306146	+	1.73624i	0.618062	+	0.786129i	$0.287918\pi$
$461$	6.57323	+	37.2786i	0.306146	+	1.73624i	−0.311916	+	0.950110i	$0.600971\pi$
$462$	0.489924	+	2.11639i	0.0227933	+	0.0984636i
$463$	29.4281	−	10.7110i	1.36764	−	0.497781i	0.449233	−	0.893414i	$-0.351697\pi$
$463$	29.4281	−	10.7110i	1.36764	−	0.497781i	0.918408	+	0.395634i	$0.129475\pi$
$464$	−3.28635	−	2.75757i	−0.152565	−	0.128017i
$465$	−4.21717	−	3.17397i	−0.195567	−	0.147189i
$466$	−4.41958	−	1.60860i	−0.204733	−	0.0745168i
$467$	−13.1073	−	22.7024i	−0.606531	−	1.05054i	−0.991807	−	0.127742i	$-0.959227\pi$
$467$	−13.1073	−	22.7024i	−0.606531	−	1.05054i	0.385276	−	0.922801i	$-0.374106\pi$
$468$	4.57052	−	10.2982i	0.211272	−	0.476037i
$469$	7.78919	−	13.4913i	0.359672	−	0.622969i
$470$	9.16622	−	7.69137i	0.422806	−	0.354776i
$471$	−11.0695	−	17.0236i	−0.510057	−	0.784405i
$472$	−1.41967	+	8.05137i	−0.0653458	+	0.370594i
$473$	−1.66661	+	9.45182i	−0.0766309	+	0.434595i
$474$	2.14626	−	0.113751i	0.0985808	−	0.00522474i
$475$	4.41184	−	3.70198i	0.202429	−	0.169858i
$476$	3.04828	−	5.27978i	0.139718	−	0.241998i
$477$	−8.82234	−	5.93561i	−0.403947	−	0.271773i
$478$	−12.5822	−	21.7931i	−0.575499	−	0.996793i
$479$	4.62221	+	1.68235i	0.211194	+	0.0768683i	0.445451	−	0.895306i	$-0.353043\pi$
$479$	4.62221	+	1.68235i	0.211194	+	0.0768683i	−0.234257	+	0.972175i	$0.575266\pi$
$480$	−0.359945	+	2.94589i	−0.0164292	+	0.134461i
$481$	4.02608	+	3.37828i	0.183573	+	0.154036i
$482$	−3.51765	+	1.28032i	−0.160224	+	0.0583169i
$483$	4.26850	+	1.30226i	0.194224	+	0.0592548i
$484$	−1.63697	−	9.28373i	−0.0744078	−	0.421988i
$485$	24.8653			1.12908
$486$	−15.0453	+	4.07900i	−0.682470	+	0.185027i
$487$	4.88965			0.221571			0.110786	−	0.993844i	$-0.464663\pi$
$487$	4.88965			0.221571			0.110786	+	0.993844i	$0.464663\pi$
$488$	−2.03060	−	11.5161i	−0.0919208	−	0.521309i
$489$	−39.8300	−	12.1516i	−1.80118	−	0.549513i
$490$	−1.61013	+	0.586038i	−0.0727380	+	0.0264745i
$491$	−23.1798	−	19.4502i	−1.04609	−	0.877775i	−0.0534147	−	0.998572i	$-0.517011\pi$
$491$	−23.1798	−	19.4502i	−1.04609	−	0.877775i	−0.992677	+	0.120797i	$0.961455\pi$
$492$	−0.687483	+	5.62655i	−0.0309941	+	0.253664i
$493$	−24.5771	−	8.94532i	−1.10690	−	0.402877i
$494$	−5.23960	−	9.07526i	−0.235741	−	0.408315i
$495$	−5.34916	−	3.59888i	−0.240427	−	0.161758i
$496$	−0.889232	+	1.54019i	−0.0399277	+	0.0691568i
$497$	−8.70928	+	7.30795i	−0.390664	+	0.327806i
$498$	9.53701	−	0.505457i	0.427363	−	0.0226501i
$499$	−5.49178	+	31.1454i	−0.245846	+	1.39426i	0.572674	+	0.819783i	$0.305906\pi$
$499$	−5.49178	+	31.1454i	−0.245846	+	1.39426i	−0.818520	+	0.574478i	$0.805205\pi$
$500$	−2.10183	+	11.9201i	−0.0939968	+	0.533083i
$501$	−6.94588	−	10.6819i	−0.310319	−	0.477233i
$502$	16.2934	−	13.6717i	0.727208	−	0.610200i
$503$	−9.71695	+	16.8303i	−0.433257	+	0.750424i	−0.997152	−	0.0754231i	$-0.975969\pi$
$503$	−9.71695	+	16.8303i	−0.433257	+	0.750424i	0.563894	+	0.825847i	$0.309303\pi$
$504$	−1.21697	+	2.74207i	−0.0542083	+	0.122142i
$505$	11.6624	+	20.1999i	0.518971	+	0.898885i
$506$	3.03667	+	1.10526i	0.134996	+	0.0491347i
$507$	−1.52897	−	1.15075i	−0.0679039	−	0.0511064i
$508$	−5.10824	−	4.28632i	−0.226641	−	0.190175i
$509$	17.0878	−	6.21944i	0.757402	−	0.275672i	0.0656851	−	0.997840i	$-0.479077\pi$
$509$	17.0878	−	6.21944i	0.757402	−	0.275672i	0.691717	+	0.722169i	$0.256855\pi$
$510$	4.08053	+	17.6272i	0.180689	+	0.780547i
$511$	1.16210	+	6.59061i	0.0514084	+	0.291551i
$512$	1.00000			0.0441942
$513$	−5.17187	+	13.5448i	−0.228343	+	0.598017i
$514$	32.0122			1.41200
$515$	−0.145818	−	0.826972i	−0.00642549	−	0.0364408i
$516$	−9.68817	+	9.04506i	−0.426498	+	0.398187i
$517$	8.23037	−	2.99561i	0.361971	−	0.131747i
$518$	−1.07201	−	0.899522i	−0.0471014	−	0.0395227i
$519$	−33.1803	+	14.1073i	−1.45645	+	0.619243i
$520$	6.04705	+	2.20095i	0.265181	+	0.0965179i
$521$	5.19696	+	9.00140i	0.227683	+	0.394359i	0.957121	−	0.289688i	$-0.0935517\pi$
$521$	5.19696	+	9.00140i	0.227683	+	0.394359i	−0.729438	+	0.684047i	$0.760218\pi$
$522$	12.4914	+	3.09881i	0.546735	+	0.135631i
$523$	17.0844	−	29.5910i	0.747048	−	1.29392i	−0.202184	−	0.979347i	$-0.564804\pi$
$523$	17.0844	−	29.5910i	0.747048	−	1.29392i	0.949232	−	0.314577i	$-0.101863\pi$
$524$	−0.0953068	+	0.0799719i	−0.00416350	+	0.00349359i
$525$	−1.62116	+	3.18635i	−0.0707532	+	0.139064i
$526$	−1.77425	+	10.0623i	−0.0773611	+	0.438736i
$527$	−1.88278	+	10.6778i	−0.0820153	+	0.465132i
$528$	−0.985089	+	1.93617i	−0.0428705	+	0.0842609i
$529$	−12.5335	+	10.5169i	−0.544935	+	0.457255i
$530$	3.03660	−	5.25954i	0.131901	−	0.228460i
$531$	−6.78830	−	23.5686i	−0.294587	−	1.02279i
$532$	1.39513	+	2.41644i	0.0604865	+	0.104766i
$533$	11.5497	+	4.20373i	0.500271	+	0.182084i
$534$	26.7911	−	11.3908i	1.15936	−	0.492929i
$535$	5.38531	+	4.51881i	0.232827	+	0.195365i
$536$	14.6389	−	5.32812i	0.632304	−	0.230140i
$537$	−12.4922	+	11.6630i	−0.539078	+	0.503294i
$538$	3.20629	+	18.1838i	0.138233	+	0.783958i
$539$	−1.25421			−0.0540228
$540$	−2.91356	−	8.41318i	−0.125380	−	0.362046i
$541$	27.8490			1.19732			0.598662	−	0.801002i	$-0.295699\pi$
$541$	27.8490			1.19732			0.598662	+	0.801002i	$0.295699\pi$
$542$	2.22241	+	12.6039i	0.0954606	+	0.541384i
$543$	0.147962	+	0.639174i	0.00634967	+	0.0274296i
$544$	5.72890	−	2.08515i	0.245624	−	0.0894000i
$545$	−13.8241	−	11.5998i	−0.592160	−	0.496881i
$546$	5.19740	+	3.91172i	0.222428	+	0.167406i
$547$	−10.3695	−	3.77418i	−0.443367	−	0.161372i	0.110683	−	0.993856i	$-0.464696\pi$
$547$	−10.3695	−	3.77418i	−0.443367	−	0.161372i	−0.554050	+	0.832483i	$0.686918\pi$
$548$	1.56535	+	2.71126i	0.0668684	+	0.115819i
$549$	20.6537	+	28.3570i	0.881479	+	1.21025i
$550$	−1.29438	+	2.24194i	−0.0551927	+	0.0955965i
$551$	9.16976	−	7.69434i	0.390645	−	0.327790i
$552$	2.43279	+	3.74133i	0.103546	+	0.159242i
$553$	−0.215477	+	1.22203i	−0.00916300	+	0.0519659i
$554$	2.57719	−	14.6160i	0.109495	−	0.620974i
$555$	4.14734	−	0.219807i	0.176045	−	0.00933030i
$556$	5.70148	−	4.78411i	0.241797	−	0.202892i
$557$	−18.1741	+	31.4784i	−0.770059	+	1.33378i	0.167470	+	0.985877i	$0.446440\pi$
$557$	−18.1741	+	31.4784i	−0.770059	+	1.33378i	−0.937530	+	0.347905i	$0.886893\pi$
$558$	0.365896	−	5.32283i	0.0154896	−	0.225333i
$559$	14.3697	+	24.8890i	0.607772	+	1.05269i
$560$	−1.61013	−	0.586038i	−0.0680402	−	0.0247646i
$561$	−1.60627	+	13.1462i	−0.0678168	+	0.555032i
$562$	3.72253	+	3.12358i	0.157026	+	0.131760i
$563$	−24.2070	+	8.81062i	−1.02020	+	0.371323i	−0.797343	−	0.603527i	$-0.793762\pi$
$563$	−24.2070	+	8.81062i	−1.02020	+	0.371323i	−0.222860	+	0.974850i	$0.571539\pi$
$564$	11.5690	+	3.52955i	0.487145	+	0.148621i
$565$	2.03084	+	11.5174i	0.0854379	+	0.484543i
$566$	−18.7693			−0.788932
$567$	−0.335327	−	8.99375i	−0.0140824	−	0.377702i
$568$	−11.3692			−0.477039
$569$	1.63546	+	9.27514i	0.0685620	+	0.388834i	0.999707	+	0.0241864i	$0.00769952\pi$
$569$	1.63546	+	9.27514i	0.0685620	+	0.388834i	−0.931145	+	0.364648i	$0.881189\pi$
$570$	−7.92052	−	2.41644i	−0.331754	−	0.101213i
$571$	43.2087	−	15.7267i	1.80823	−	0.658140i	0.810890	−	0.585199i	$-0.198984\pi$
$571$	43.2087	−	15.7267i	1.80823	−	0.658140i	0.997336	−	0.0729416i	$-0.0232387\pi$
$572$	3.60835	+	3.02777i	0.150873	+	0.126597i
$573$	−2.73964	+	22.4220i	−0.114450	+	0.936692i
$574$	−3.07528	−	1.11931i	−0.128360	−	0.0467192i
$575$	2.65908	+	4.60567i	0.110891	+	0.192070i
$576$	−2.69483	+	1.31830i	−0.112285	+	0.0549290i
$577$	−16.4242	+	28.4475i	−0.683747	+	1.18428i	0.290082	+	0.957002i	$0.406317\pi$
$577$	−16.4242	+	28.4475i	−0.683747	+	1.18428i	−0.973829	+	0.227283i	$0.927016\pi$
$578$	15.4496	−	12.9638i	0.642621	−	0.539223i
$579$	26.1602	−	1.38648i	1.08718	−	0.0576202i
$580$	−1.27645	+	7.23910i	−0.0530017	+	0.300587i
$581$	−0.957482	+	5.43015i	−0.0397231	+	0.225281i
$582$	13.7020	+	21.0720i	0.567967	+	0.873463i
$583$	3.40540	−	2.85747i	0.141037	−	0.118344i
$584$	−3.34614	+	5.79569i	−0.138464	+	0.239827i
$585$	−19.1973	+	2.04062i	−0.793709	+	0.0843694i
$586$	7.29520	+	12.6357i	0.301362	+	0.521974i
$587$	23.7564	+	8.64661i	0.980530	+	0.356884i	0.782046	−	0.623220i	$-0.214176\pi$
$587$	23.7564	+	8.64661i	0.980530	+	0.356884i	0.198484	+	0.980104i	$0.436398\pi$
$588$	−1.38389	−	1.04156i	−0.0570708	−	0.0429531i
$589$	−3.80140	−	3.18975i	−0.156634	−	0.131431i
$590$	13.1637	−	4.79120i	0.541941	−	0.197250i
$591$	8.18963	+	35.3779i	0.336876	+	1.45525i
$592$	−0.243005	−	1.37815i	−0.00998743	−	0.0566415i
$593$	−38.9252			−1.59847			−0.799234	−	0.601021i	$-0.794761\pi$
$593$	−38.9252			−1.59847			−0.799234	+	0.601021i	$0.794761\pi$
$594$	0.102202	−	6.51628i	0.00419341	−	0.267366i
$595$	−10.4462			−0.428253
$596$	−2.78633	−	15.8020i	−0.114132	−	0.647277i
$597$	−24.0519	+	22.4553i	−0.984379	+	0.919035i
$598$	9.09306	−	3.30960i	0.371843	−	0.135340i
$599$	−19.7740	−	16.5923i	−0.807942	−	0.677944i	0.142174	−	0.989842i	$-0.454591\pi$
$599$	−19.7740	−	16.5923i	−0.807942	−	0.677944i	−0.950116	+	0.311898i	$0.899035\pi$
$600$	−3.29003	+	1.39883i	−0.134315	+	0.0571068i
$601$	33.7633	+	12.2889i	1.37724	+	0.501273i	0.921339	−	0.388760i	$-0.127097\pi$
$601$	33.7633	+	12.2889i	1.37724	+	0.501273i	0.455896	+	0.890033i	$0.349319\pi$
$602$	−3.82616	−	6.62710i	−0.155943	−	0.270100i
$603$	−32.4253	+	33.6568i	−1.32046	+	1.37061i
$604$	8.73607	−	15.1313i	0.355466	−	0.615684i
$605$	−12.3737	+	10.3828i	−0.503062	+	0.422119i
$606$	−10.6918	+	21.0144i	−0.434323	+	0.853652i
$607$	0.858112	−	4.86659i	0.0348297	−	0.197529i	−0.962428	−	0.271537i	$-0.912468\pi$
$607$	0.858112	−	4.86659i	0.0348297	−	0.197529i	0.997258	+	0.0740083i	$0.0235791\pi$
$608$	−0.484523	+	2.74787i	−0.0196500	+	0.111441i
$609$	−3.36948	+	6.62264i	−0.136538	+	0.268363i
$610$	−15.3491	+	12.8794i	−0.621465	+	0.521471i
$611$	13.1134	−	22.7131i	0.530513	−	0.918875i
$612$	−12.6895	+	13.1715i	−0.512945	+	0.532426i
$613$	−3.00127	−	5.19836i	−0.121220	−	0.209960i	0.799029	−	0.601293i	$-0.205347\pi$
$613$	−3.00127	−	5.19836i	−0.121220	−	0.209960i	−0.920249	+	0.391333i	$0.872014\pi$
$614$	10.0348	+	3.65238i	0.404973	+	0.147398i
$615$	8.93822	−	3.80028i	0.360424	−	0.153242i
$616$	−0.960783	−	0.806193i	−0.0387110	−	0.0324824i
$617$	−39.7116	+	14.4539i	−1.59873	+	0.581890i	−0.979167	−	0.203057i	$-0.934912\pi$
$617$	−39.7116	+	14.4539i	−1.59873	+	0.581890i	−0.619563	+	0.784947i	$0.712690\pi$
$618$	0.620461	−	0.579274i	0.0249586	−	0.0233018i
$619$	−4.67530	−	26.5149i	−0.187916	−	1.06572i	−0.922151	−	0.386830i	$-0.873570\pi$
$619$	−4.67530	−	26.5149i	−0.187916	−	1.06572i	0.734235	−	0.678895i	$-0.237541\pi$
$620$	3.04733			0.122384
$621$	−11.4881	−	6.87511i	−0.461002	−	0.275889i
$622$	15.3346			0.614862
$623$	2.91866	+	16.5525i	0.116933	+	0.663163i
$624$	1.46704	+	6.33737i	0.0587285	+	0.253698i
$625$	9.79102	−	3.56364i	0.391641	−	0.142546i
$626$	−9.95410	−	8.35248i	−0.397846	−	0.333832i
$627$	−4.84304	−	3.64501i	−0.193412	−	0.145568i
$628$	11.0167	+	4.00975i	0.439614	+	0.160006i
$629$	−4.26579	−	7.38856i	−0.170088	−	0.294601i
$630$	5.11158	−	0.543349i	0.203650	−	0.0216476i
$631$	−9.17121	+	15.8850i	−0.365100	+	0.632372i	−0.988792	−	0.149298i	$-0.952299\pi$
$631$	−9.17121	+	15.8850i	−0.365100	+	0.632372i	0.623692	+	0.781670i	$0.285632\pi$
$632$	−0.950569	+	0.797622i	−0.0378116	+	0.0317277i
$633$	19.4182	+	29.8628i	0.771804	+	1.18694i
$634$	1.69235	−	9.59781i	0.0672119	−	0.381178i
$635$	−1.98409	+	11.2523i	−0.0787362	+	0.446535i
$636$	6.13048	−	0.324913i	0.243089	−	0.0128836i
$637$	−2.87699	+	2.41408i	−0.113990	+	0.0956493i
$638$	−2.69030	+	4.65974i	−0.106510	+	0.184481i
$639$	30.6379	−	14.9879i	1.21202	−	0.592912i
$640$	−0.856730	−	1.48390i	−0.0338652	−	0.0586563i
$641$	2.30577	+	0.839230i	0.0910723	+	0.0331476i	0.387154	−	0.922015i	$-0.373458\pi$
$641$	2.30577	+	0.839230i	0.0910723	+	0.0331476i	−0.296082	+	0.955162i	$0.595680\pi$
$642$	−0.861878	+	7.05384i	−0.0340156	+	0.278393i
$643$	−15.7539	−	13.2191i	−0.621275	−	0.521312i	0.276929	−	0.960890i	$-0.410683\pi$
$643$	−15.7539	−	13.2191i	−0.621275	−	0.521312i	−0.898204	+	0.439579i	$0.855128\pi$
$644$	−2.42118	+	0.881236i	−0.0954077	+	0.0347256i
$645$	21.7221	+	6.62710i	0.855307	+	0.260942i
$646$	2.95393	+	16.7526i	0.116221	+	0.659120i
$647$	34.4411			1.35402			0.677010	−	0.735974i	$-0.263275\pi$
$647$	34.4411			1.35402			0.677010	+	0.735974i	$0.263275\pi$
$648$	5.52420	−	7.10516i	0.217011	−	0.279117i
$649$	10.2539			0.402501
$650$	1.34610	+	7.63408i	0.0527982	+	0.299433i
$651$	2.94632	+	0.898880i	0.115475	+	0.0352299i
$652$	22.5924	−	8.22294i	0.884785	−	0.322035i
$653$	1.89648	+	1.59133i	0.0742149	+	0.0622737i	0.679140	−	0.734008i	$-0.262353\pi$
$653$	1.89648	+	1.59133i	0.0742149	+	0.0622737i	−0.604926	+	0.796282i	$0.706797\pi$
$654$	2.21244	−	18.1072i	0.0865134	−	0.708049i
$655$	0.200322	+	0.0729114i	0.00782725	+	0.00284889i
$656$	−1.63632	−	2.83420i	−0.0638877	−	0.110657i
$657$	1.37685	−	20.0296i	0.0537161	−	0.781428i
$658$	−3.49166	+	6.04774i	−0.136119	+	0.235765i
$659$	26.9032	−	22.5745i	1.04800	−	0.879378i	0.0551197	−	0.998480i	$-0.482446\pi$
$659$	26.9032	−	22.5745i	1.04800	−	0.879378i	0.992882	+	0.119102i	$0.0380015\pi$
$660$	3.71704	−	0.197001i	0.144685	−	0.00766826i
$661$	3.92439	−	22.2563i	0.152641	−	0.865671i	−0.808270	−	0.588812i	$-0.799596\pi$
$661$	3.92439	−	22.2563i	0.152641	−	0.865671i	0.960911	−	0.276858i	$-0.0892932\pi$
$662$	−0.516827	+	2.93107i	−0.0200871	+	0.113919i
$663$	21.6189	+	33.2472i	0.839607	+	1.29121i
$664$	−4.22391	+	3.54428i	−0.163919	+	0.137545i
$665$	2.39050	−	4.14046i	0.0926995	−	0.160560i
$666$	2.47166	+	3.39352i	0.0957749	+	0.131496i
$667$	5.52675	+	9.57261i	0.213997	+	0.370653i
$668$	6.91273	+	2.51603i	0.267461	+	0.0973480i
$669$	−38.6836	−	29.1144i	−1.49559	−	1.12563i
$670$	−20.4480	−	17.1579i	−0.789974	−	0.662867i
$671$	−13.7820	+	5.01622i	−0.532046	+	0.193649i
$672$	−0.390623	−	1.68743i	−0.0150686	−	0.0650940i
$673$	−6.10431	−	34.6192i	−0.235304	−	1.33447i	−0.841973	−	0.539520i	$-0.818606\pi$
$673$	−6.10431	−	34.6192i	−0.235304	−	1.33447i	0.606669	−	0.794954i	$-0.292505\pi$
$674$	−11.7371			−0.452098
$675$	7.02199	−	8.10682i	0.270277	−	0.312032i
$676$	1.10483			0.0424935
$677$	−6.38106	−	36.1888i	−0.245244	−	1.39085i	−0.819925	−	0.572470i	$-0.805985\pi$
$677$	−6.38106	−	36.1888i	−0.245244	−	1.39085i	0.574681	−	0.818377i	$-0.305126\pi$
$678$	−8.64131	+	8.06769i	−0.331868	+	0.309838i
$679$	−13.6366	+	4.96332i	−0.523325	+	0.190475i
$680$	−8.00226	−	6.71470i	−0.306873	−	0.257497i
$681$	−15.3237	+	6.51520i	−0.587205	+	0.249663i
$682$	2.09605	+	0.762901i	0.0802620	+	0.0292130i
$683$	3.40776	+	5.90241i	0.130394	+	0.225849i	0.923829	−	0.382806i	$-0.125042\pi$
$683$	3.40776	+	5.90241i	0.130394	+	0.225849i	−0.793434	+	0.608656i	$0.791709\pi$
$684$	−2.31679	−	8.04378i	−0.0885848	−	0.307562i
$685$	2.68216	−	4.64564i	0.102480	−	0.177501i
$686$	0.766044	−	0.642788i	0.0292477	−	0.0245417i
$687$	−14.0690	+	27.6522i	−0.536764	+	1.05500i
$688$	1.32881	−	7.53606i	0.0506604	−	0.287310i
$689$	2.31152	−	13.1093i	0.0880618	−	0.499423i
$690$	3.46751	−	6.81532i	0.132006	−	0.259455i
$691$	−4.27495	+	3.58711i	−0.162627	+	0.136460i	−0.720469	−	0.693487i	$-0.756074\pi$
$691$	−4.27495	+	3.58711i	−0.162627	+	0.136460i	0.557843	+	0.829947i	$0.311629\pi$
$692$	10.4081	−	18.0274i	0.395658	−	0.685299i
$693$	3.65194	+	0.905955i	0.138726	+	0.0344144i
$694$	13.4036	+	23.2157i	0.508794	+	0.881257i
$695$	−11.9838	−	4.36174i	−0.454571	−	0.165450i
$696$	−6.83813	+	2.90738i	−0.259199	+	0.110204i
$697$	−15.2841	−	12.8248i	−0.578925	−	0.485776i
$698$	−7.28345	+	2.65096i	−0.275683	+	0.100340i
$699$	−5.95449	+	5.55923i	−0.225220	+	0.210269i
$700$	−0.358420	−	2.03270i	−0.0135470	−	0.0768288i
$701$	17.6988			0.668473			0.334237	−	0.942489i	$-0.391521\pi$
$701$	17.6988			0.668473			0.334237	+	0.942489i	$0.391521\pi$
$702$	−12.3079	−	15.1441i	−0.464533	−	0.571579i
$703$	3.90471			0.147269
$704$	−0.217792	−	1.23516i	−0.00820834	−	0.0465518i
$705$	−4.67405	−	20.1912i	−0.176035	−	0.760444i
$706$	−1.65589	+	0.602696i	−0.0623204	+	0.0226828i
$707$	−10.4280	−	8.75009i	−0.392184	−	0.329081i
$708$	11.3141	+	8.51533i	0.425211	+	0.320026i
$709$	−7.27144	−	2.64659i	−0.273085	−	0.0993947i	0.201848	−	0.979417i	$-0.435305\pi$
$709$	−7.27144	−	2.64659i	−0.273085	−	0.0993947i	−0.474933	+	0.880022i	$0.657528\pi$
$710$	9.74029	+	16.8707i	0.365547	+	0.633145i
$711$	1.51012	−	3.40259i	0.0566339	−	0.127607i
$712$	−8.40393	+	14.5560i	−0.314951	+	0.545511i
$713$	3.51026	−	2.94546i	0.131460	−	0.110308i
$714$	−5.75637	−	8.85259i	−0.215427	−	0.331300i
$715$	1.40152	−	7.94842i	0.0524139	−	0.297254i
$716$	1.71341	−	9.71721i	0.0640330	−	0.363149i
$717$	−43.5251	+	2.30681i	−1.62547	+	0.0861494i
$718$	13.0944	−	10.9875i	0.488678	−	0.410050i
$719$	0.415956	−	0.720458i	0.0155126	−	0.0268685i	−0.858165	−	0.513374i	$-0.828395\pi$
$719$	0.415956	−	0.720458i	0.0155126	−	0.0268685i	0.873677	+	0.486506i	$0.161729\pi$
$720$	4.26496	+	2.86943i	0.158946	+	0.106937i
$721$	0.245039	+	0.424420i	0.00912574	+	0.0158062i
$722$	10.5381	+	3.83557i	0.392189	+	0.142745i
$723$	−0.786374	+	6.43590i	−0.0292456	+	0.239354i
$724$	−0.290167	−	0.243479i	−0.0107840	−	0.00904882i
$725$	−8.32083	+	3.02854i	−0.309028	+	0.112477i
$726$	−15.6173	−	4.76462i	−0.579613	−	0.176832i
$727$	2.54091	+	14.4102i	0.0942371	+	0.534445i	0.994978	+	0.100089i	$0.0319128\pi$
$727$	2.54091	+	14.4102i	0.0942371	+	0.534445i	−0.900741	+	0.434356i	$0.856976\pi$
$728$	−3.75564			−0.139193
$729$	−5.52007	+	26.4297i	−0.204447	+	0.978878i
$730$	11.4670			0.424411
$731$	−8.10118	−	45.9441i	−0.299633	−	1.69930i
$732$	−19.3726	−	5.91031i	−0.716034	−	0.218451i
$733$	8.82838	−	3.21327i	0.326084	−	0.118685i	−0.173791	−	0.984783i	$-0.555602\pi$
$733$	8.82838	−	3.21327i	0.326084	−	0.118685i	0.499874	+	0.866098i	$0.333379\pi$
$734$	−10.9253	−	9.16739i	−0.403259	−	0.338375i
$735$	−0.359945	+	2.94589i	−0.0132768	+	0.108661i
$736$	−2.42118	−	0.881236i	−0.0892457	−	0.0324828i
$737$	−9.76931	−	16.9209i	−0.359857	−	0.623291i
$738$	8.14592	+	5.48052i	0.299856	+	0.201741i
$739$	19.3348	−	33.4889i	0.711242	−	1.23191i	−0.253149	−	0.967427i	$-0.581466\pi$
$739$	19.3348	−	33.4889i	0.711242	−	1.23191i	0.964391	−	0.264481i	$-0.0852005\pi$
$740$	−1.83684	+	1.54129i	−0.0675237	+	0.0566591i
$741$	−18.1251	+	0.960621i	−0.665842	+	0.0352893i
$742$	−0.615479	+	3.49056i	−0.0225950	+	0.128142i
$743$	0.115651	−	0.655890i	0.00424282	−	0.0240623i	−0.982613	−	0.185666i	$-0.940556\pi$
$743$	0.115651	−	0.655890i	0.00424282	−	0.0240623i	0.986856	+	0.161604i	$0.0516668\pi$
$744$	1.67922	+	2.58244i	0.0615634	+	0.0946769i
$745$	−21.0615	+	17.6727i	−0.771634	+	0.647478i
$746$	15.8104	−	27.3844i	0.578860	−	1.00261i
$747$	6.71030	−	15.1196i	0.245517	−	0.553197i
$748$	−3.82319	−	6.62197i	−0.139790	−	0.242123i
$749$	−3.85539	−	1.40325i	−0.140873	−	0.0512736i
$750$	16.7506	+	12.6070i	0.611645	+	0.460342i
$751$	−13.7199	−	11.5123i	−0.500645	−	0.420091i	0.357178	−	0.934036i	$-0.383739\pi$
$751$	−13.7199	−	11.5123i	−0.500645	−	0.420091i	−0.857823	+	0.513945i	$0.828183\pi$
$752$	−6.56218	+	2.38844i	−0.239298	+	0.0870974i
$753$	−8.30833	−	35.8907i	−0.302772	−	1.30793i
$754$	2.79778	+	15.8670i	0.101889	+	0.577842i
$755$	−29.9378			−1.08955
$756$	3.27719	+	4.03237i	0.119190	+	0.146656i
$757$	−39.4556			−1.43404			−0.717019	−	0.697053i	$-0.754494\pi$
$757$	−39.4556			−1.43404			−0.717019	+	0.697053i	$0.754494\pi$
$758$	4.98140	+	28.2509i	0.180933	+	1.02612i
$759$	4.09129	−	3.81971i	0.148505	−	0.138647i
$760$	4.49267	−	1.63520i	0.162966	−	0.0593148i
$761$	23.4940	+	19.7138i	0.851657	+	0.714625i	0.960154	−	0.279472i	$-0.0901594\pi$
$761$	23.4940	+	19.7138i	0.851657	+	0.714625i	−0.108497	+	0.994097i	$0.534604\pi$
$762$	−10.6291	+	4.51917i	−0.385050	+	0.163712i
$763$	9.89681	+	3.60215i	0.358289	+	0.130406i
$764$	−6.52081	−	11.2944i	−0.235915	−	0.408616i
$765$	30.4167	+	7.54561i	1.09972	+	0.272812i
$766$	3.74027	−	6.47834i	0.135141	−	0.234072i
$767$	23.5210	−	19.7365i	0.849295	−	0.712643i
$768$	0.785424	−	1.54373i	0.0283415	−	0.0557046i
$769$	3.91627	−	22.2102i	0.141224	−	0.800922i	−0.829097	−	0.559104i	$-0.811145\pi$
$769$	3.91627	−	22.2102i	0.141224	−	0.800922i	0.970322	−	0.241818i	$-0.0777437\pi$
$770$	−0.373177	+	2.11639i	−0.0134484	+	0.0762696i
$771$	25.1432	−	49.4183i	0.905508	−	1.77976i
$772$	−11.5863	+	9.72204i	−0.416999	+	0.349904i
$773$	−23.3947	+	40.5209i	−0.841450	+	1.45743i	0.0472189	+	0.998885i	$0.484964\pi$
$773$	−23.3947	+	40.5209i	−0.841450	+	1.45743i	−0.888669	+	0.458550i	$0.848369\pi$
$774$	6.35383	+	22.0601i	0.228384	+	0.792936i
$775$	1.83542	+	3.17905i	0.0659304	+	0.114195i
$776$	−13.6366	−	4.96332i	−0.489526	−	0.178173i
$777$	−2.23060	+	0.948388i	−0.0800224	+	0.0340232i
$778$	−8.45937	−	7.09826i	−0.303283	−	0.254485i
$779$	8.58084	−	3.12317i	0.307440	−	0.111899i
$780$	8.14717	−	7.60635i	0.291715	−	0.272351i
$781$	2.47611	+	14.0427i	0.0886021	+	0.502488i
$782$	−15.7082			−0.561723
$783$	14.5948	−	16.8495i	0.521576	−	0.602154i
$784$	1.00000			0.0357143
$785$	−3.48827	−	19.7829i	−0.124502	−	0.706083i
$786$	0.0485990	+	0.209940i	0.00173347	+	0.00748831i
$787$	−35.5802	+	12.9501i	−1.26830	+	0.461622i	−0.886545	−	0.462643i	$-0.846901\pi$
$787$	−35.5802	+	12.9501i	−1.26830	+	0.461622i	−0.381752	+	0.924265i	$0.624679\pi$
$788$	−16.0606	−	13.4764i	−0.572134	−	0.480077i
$789$	14.1399	+	10.6421i	0.503395	+	0.378870i
$790$	1.99797	+	0.727203i	0.0710847	+	0.0258727i
$791$	−3.41272	−	5.91101i	−0.121342	−	0.210171i
$792$	2.21521	+	3.04143i	0.0787142	+	0.108072i
$793$	−21.9588	+	38.0337i	−0.779778	+	1.35062i
$794$	24.5122	−	20.5682i	0.869906	−	0.729938i
$795$	−5.73430	−	8.81866i	−0.203375	−	0.312766i
$796$	3.29891	−	18.7091i	0.116927	−	0.663125i
$797$	2.04003	−	11.5696i	0.0722617	−	0.409816i	−0.927123	−	0.374756i	$-0.877727\pi$
$797$	2.04003	−	11.5696i	0.0722617	−	0.409816i	0.999385	−	0.0350605i	$-0.0111624\pi$
$798$	4.82610	−	0.255781i	0.170842	−	0.00905455i
$799$	−32.6138	+	27.3662i	−1.15379	+	0.968148i
$800$	1.03203	−	1.78753i	0.0364877	−	0.0631986i
$801$	3.45800	−	50.3049i	0.122182	−	1.77744i
$802$	−0.331419	−	0.574034i	−0.0117028	−	0.0202698i
$803$	7.88735	+	2.87076i	0.278339	+	0.101307i
$804$	3.27254	−	26.7834i	0.115414	−	0.944577i
$805$	3.38196	+	2.83780i	0.119198	+	0.100019i
$806$	6.27646	−	2.28445i	0.221079	−	0.0804661i
$807$	30.5892	+	9.33232i	1.07679	+	0.328513i
$808$	−2.36383	−	13.4059i	−0.0831591	−	0.471619i
$809$	21.1089			0.742150			0.371075	−	0.928603i	$-0.378989\pi$
$809$	21.1089			0.742150			0.371075	+	0.928603i	$0.378989\pi$
$810$	−15.2761	−	2.11015i	−0.536747	−	0.0741432i
$811$	21.5118			0.755383			0.377692	−	0.925931i	$-0.376718\pi$
$811$	21.5118			0.755383			0.377692	+	0.925931i	$0.376718\pi$
$812$	−0.744954	−	4.22485i	−0.0261428	−	0.148263i
$813$	21.2026	+	6.46860i	0.743607	+	0.226864i
$814$	−1.64931	+	0.600299i	−0.0578082	+	0.0210405i
$815$	−31.5576	−	26.4799i	−1.10541	−	0.927552i
$816$	1.28070	−	10.4816i	0.0448335	−	0.366930i
$817$	20.0643	+	7.30279i	0.701960	+	0.255492i
$818$	12.8978	+	22.3396i	0.450960	+	0.781085i
$819$	10.1208	−	4.95104i	0.353650	−	0.173003i
$820$	−2.80378	+	4.85628i	−0.0979121	+	0.169589i
$821$	18.7703	−	15.7501i	0.655086	−	0.549683i	−0.253523	−	0.967329i	$-0.581589\pi$
$821$	18.7703	−	15.7501i	0.655086	−	0.549683i	0.908610	+	0.417646i	$0.137145\pi$
$822$	5.41493	−	0.286989i	0.188867	−	0.0100099i
$823$	−2.30464	+	13.0703i	−0.0803348	+	0.455602i	0.917931	+	0.396739i	$0.129858\pi$
$823$	−2.30464	+	13.0703i	−0.0803348	+	0.455602i	−0.998266	+	0.0588621i	$0.981253\pi$
$824$	−0.0851012	+	0.482633i	−0.00296464	+	0.0168133i
$825$	2.44431	+	3.75905i	0.0851000	+	0.130873i
$826$	−6.26285	+	5.25516i	−0.217913	+	0.182850i
$827$	−7.74580	+	13.4161i	−0.269348	+	0.466524i	−0.968694	−	0.248259i	$-0.920141\pi$
$827$	−7.74580	+	13.4161i	−0.269348	+	0.466524i	0.699346	+	0.714784i	$0.253475\pi$
$828$	7.68638	−	0.817044i	0.267120	−	0.0283943i
$829$	0.649236	+	1.12451i	0.0225489	+	0.0390558i	0.877080	−	0.480345i	$-0.159489\pi$
$829$	0.649236	+	1.12451i	0.0225489	+	0.0390558i	−0.854531	+	0.519401i	$0.826155\pi$
$830$	8.87810	+	3.23137i	0.308163	+	0.112162i
$831$	−20.5390	−	15.4582i	−0.712490	−	0.536241i
$832$	−2.87699	−	2.41408i	−0.0997416	−	0.0836931i
$833$	5.72890	−	2.08515i	0.198494	−	0.0722461i
$834$	−2.90731	−	12.5591i	−0.100672	−	0.434887i
$835$	−2.18881	−	12.4133i	−0.0757468	−	0.429582i
$836$	3.49958			0.121035
$837$	−7.92964	−	4.74552i	−0.274089	−	0.164029i
$838$	−9.14299			−0.315839
$839$	4.64390	+	26.3368i	0.160325	+	0.909249i	0.953755	+	0.300587i	$0.0971824\pi$
$839$	4.64390	+	26.3368i	0.160325	+	0.909249i	−0.793429	+	0.608662i	$0.791706\pi$
$840$	−2.16932	+	2.02531i	−0.0748485	+	0.0698800i
$841$	9.95673	−	3.62395i	0.343335	−	0.124964i
$842$	17.8021	+	14.9377i	0.613500	+	0.514787i
$843$	7.74573	−	3.29326i	0.266777	−	0.113426i
$844$	−19.3255	−	7.03391i	−0.665211	−	0.242117i
$845$	−0.946542	−	1.63946i	−0.0325620	−	0.0563991i
$846$	14.5353	−	15.0873i	0.499733	−	0.518713i
$847$	4.71347	−	8.16398i	0.161957	−	0.280518i
$848$	−2.71517	+	2.27830i	−0.0932393	+	0.0782371i
$849$	−14.7418	+	28.9748i	−0.505939	+	0.994411i
$850$	2.18513	−	12.3925i	0.0749493	−	0.425058i
$851$	−0.626116	+	3.55088i	−0.0214630	+	0.121723i
$852$	−8.92960	+	17.5509i	−0.305923	+	0.601285i
$853$	34.0714	−	28.5893i	1.16658	−	0.978878i	0.166607	−	0.986023i	$-0.446719\pi$
$853$	34.0714	−	28.5893i	1.16658	−	0.978878i	0.999974	+	0.00714556i	$0.00227452\pi$
$854$	5.84687	−	10.1271i	0.200076	−	0.346542i
$855$	−9.95129	+	10.3292i	−0.340327	+	0.353252i
$856$	−2.05141	−	3.55315i	−0.0701158	−	0.121444i
$857$	−5.55120	−	2.02047i	−0.189625	−	0.0690180i	0.245462	−	0.969406i	$-0.421060\pi$
$857$	−5.55120	−	2.02047i	−0.189625	−	0.0690180i	−0.435087	+	0.900388i	$0.643283\pi$
$858$	7.50815	−	3.19225i	0.256324	−	0.108982i
$859$	−20.3020	−	17.0354i	−0.692694	−	0.581239i	0.226991	−	0.973897i	$-0.427111\pi$
$859$	−20.3020	−	17.0354i	−0.692694	−	0.581239i	−0.919685	+	0.392658i	$0.871556\pi$
$860$	−12.3212	+	4.48454i	−0.420149	+	0.152922i
$861$	−4.14332	+	3.86828i	−0.141204	+	0.131831i
$862$	−1.04138	−	5.90596i	−0.0354695	−	0.201158i
$863$	−29.4642			−1.00297			−0.501487	−	0.865165i	$-0.667214\pi$
$863$	−29.4642			−1.00297			−0.501487	+	0.865165i	$0.667214\pi$
$864$	−0.0814873	+	5.19551i	−0.00277225	+	0.176755i
$865$	−35.6678			−1.21274
$866$	2.20211	+	12.4888i	0.0748308	+	0.424386i
$867$	−7.87811	−	34.0322i	−0.267555	−	1.15579i
$868$	−1.67121	+	0.608270i	−0.0567245	+	0.0206460i
$869$	1.19222	+	1.00039i	0.0404432	+	0.0339358i
$870$	10.1727	+	7.65626i	0.344886	+	0.259571i
$871$	−54.9784	−	20.0105i	−1.86287	−	0.678030i
$872$	5.26598	+	9.12095i	0.178329	+	0.308874i
$873$	43.2914	−	4.60178i	1.46519	−	0.155747i
$874$	3.59464	−	6.22609i	0.121590	−	0.210601i
$875$	−9.27218	+	7.78029i	−0.313457	+	0.263022i
$876$	6.31885	+	9.71762i	0.213494	+	0.328328i
$877$	3.82766	−	21.7077i	0.129251	−	0.733018i	−0.849441	−	0.527684i	$-0.823061\pi$
$877$	3.82766	−	21.7077i	0.129251	−	0.733018i	0.978692	−	0.205334i	$-0.0658282\pi$
$878$	−3.49004	+	19.7930i	−0.117783	+	0.667982i
$879$	25.2359	−	1.33749i	0.851186	−	0.0451125i
$880$	−1.64626	+	1.38138i	−0.0554955	+	0.0465663i
$881$	1.49650	−	2.59201i	0.0504182	−	0.0873269i	−0.839715	−	0.543028i	$-0.817278\pi$
$881$	1.49650	−	2.59201i	0.0504182	−	0.0873269i	0.890133	+	0.455701i	$0.150611\pi$
$882$	−2.69483	+	1.31830i	−0.0907396	+	0.0443893i
$883$	20.2298	+	35.0390i	0.680786	+	1.17916i	0.974741	+	0.223336i	$0.0716949\pi$
$883$	20.2298	+	35.0390i	0.680786	+	1.17916i	−0.293956	+	0.955819i	$0.594972\pi$
$884$	−21.5157	−	7.83106i	−0.723650	−	0.263387i
$885$	2.94276	−	24.0844i	0.0989198	−	0.809587i
$886$	25.1520	+	21.1050i	0.844997	+	0.709036i
$887$	−1.58338	+	0.576305i	−0.0531648	+	0.0193504i	−0.368466	−	0.929641i	$-0.620117\pi$
$887$	−1.58338	+	0.576305i	−0.0531648	+	0.0193504i	0.315301	+	0.948992i	$0.397895\pi$
$888$	−2.31835	−	0.707296i	−0.0777988	−	0.0237353i
$889$	−1.15794	−	6.56702i	−0.0388362	−	0.220251i
$890$	28.7996			0.965365
$891$	−9.97912	−	5.27581i	−0.334313	−	0.176746i
$892$	27.9527			0.935927
$893$	−3.38359	−	19.1893i	−0.113227	−	0.642144i
$894$	−26.5826	−	8.10995i	−0.889054	−	0.271237i
$895$	−15.8873	+	5.78250i	−0.531053	+	0.193288i
$896$	0.766044	+	0.642788i	0.0255917	+	0.0214740i
$897$	2.03276	−	16.6367i	0.0678720	−	0.555483i
$898$	−33.4612	−	12.1789i	−1.11661	−	0.406414i
$899$	3.81482	+	6.60747i	0.127231	+	0.220371i
$900$	−0.424653	+	6.17759i	−0.0141551	+	0.205920i
$901$	−10.8043	+	18.7137i	−0.359945	+	0.623443i
$902$	−3.14431	+	2.63839i	−0.104694	+	0.0878486i
$903$	−13.2356	+	0.701482i	−0.440454	+	0.0233439i
$904$	1.18523	−	6.72175i	0.0394200	−	0.223562i
$905$	−0.112704	+	0.639174i	−0.00374640	+	0.0212469i
$906$	−16.4972	−	25.3706i	−0.548082	−	0.842883i
$907$	12.2402	−	10.2708i	0.406430	−	0.341035i	−0.416543	−	0.909116i	$-0.636758\pi$
$907$	12.2402	−	10.2708i	0.406430	−	0.341035i	0.822973	+	0.568081i	$0.192314\pi$
$908$	4.80679	−	8.32561i	0.159519	−	0.276295i
$909$	24.0431	+	33.0104i	0.797458	+	1.09489i
$910$	3.21757	+	5.57299i	0.106661	+	0.184743i
$911$	28.5440	+	10.3892i	0.945706	+	0.344209i	0.768417	−	0.639950i	$-0.221045\pi$
$911$	28.5440	+	10.3892i	0.945706	+	0.344209i	0.177289	+	0.984159i	$0.443267\pi$
$912$	3.86142	+	2.90622i	0.127864	+	0.0962344i
$913$	5.29768	+	4.44528i	0.175328	+	0.147117i
$914$	−15.1637	+	5.51915i	−0.501572	+	0.182557i
$915$	7.82681	+	33.8106i	0.258746	+	1.11774i
$916$	−3.11049	−	17.6404i	−0.102773	−	0.582857i
$917$	−0.124414			−0.00410852
$918$	10.3666	+	29.9345i	0.342148	+	0.987985i
$919$	22.9564			0.757262			0.378631	−	0.925548i	$-0.376395\pi$
$919$	22.9564			0.757262			0.378631	+	0.925548i	$0.376395\pi$
$920$	0.766628	+	4.34776i	0.0252750	+	0.143341i
$921$	13.5199	−	12.6224i	0.445495	−	0.415923i
$922$	−35.5709	+	12.9467i	−1.17146	+	0.426378i
$923$	32.7089	+	27.4460i	1.07663	+	0.903397i
$924$	−1.99917	+	0.849989i	−0.0657678	+	0.0279626i
$925$	−2.71426	−	0.987910i	−0.0892444	−	0.0324823i
$926$	15.6584	+	27.1211i	0.514567	+	0.891255i
$927$	−0.406920	−	1.41280i	−0.0133650	−	0.0464025i
$928$	2.14501	−	3.71527i	0.0704134	−	0.121960i
$929$	−3.77717	+	3.16942i	−0.123925	+	0.103985i	−0.702644	−	0.711542i	$-0.747997\pi$
$929$	−3.77717	+	3.16942i	−0.123925	+	0.103985i	0.578719	+	0.815527i	$0.303553\pi$
$930$	2.39344	−	4.70426i	0.0784841	−	0.154259i
$931$	−0.484523	+	2.74787i	−0.0158796	+	0.0900578i
$932$	0.816706	−	4.63177i	0.0267521	−	0.151719i
$933$	12.0442	−	23.6725i	0.394308	−	0.775004i
$934$	20.0815	−	16.8504i	0.657086	−	0.551361i
$935$	−6.55089	+	11.3465i	−0.214237	+	0.371069i
$936$	10.9355	+	2.71281i	0.357436	+	0.0886710i
$937$	1.54514	+	2.67627i	0.0504776	+	0.0874298i	0.890160	−	0.455648i	$-0.150592\pi$
$937$	1.54514	+	2.67627i	0.0504776	+	0.0874298i	−0.839683	+	0.543077i	$0.817259\pi$
$938$	14.6389	+	5.32812i	0.477977	+	0.173969i
$939$	−20.7122	+	8.80623i	−0.675917	+	0.287380i
$940$	9.16622	+	7.69137i	0.298969	+	0.250865i
$941$	25.5251	−	9.29039i	0.832096	−	0.302858i	0.109377	−	0.994000i	$-0.465114\pi$
$941$	25.5251	−	9.29039i	0.832096	−	0.302858i	0.722719	+	0.691142i	$0.242892\pi$
$942$	14.8428	−	13.8575i	0.483603	−	0.451501i
$943$	1.46423	+	8.30408i	0.0476820	+	0.270418i
$944$	−8.17558			−0.266092
$945$	3.17597	−	8.31767i	0.103314	−	0.270574i
$946$	−9.59763			−0.312046
$947$	4.76379	+	27.0168i	0.154802	+	0.877928i	0.958966	+	0.283520i	$0.0915024\pi$
$947$	4.76379	+	27.0168i	0.154802	+	0.877928i	−0.804164	+	0.594408i	$0.797387\pi$
$948$	0.484716	+	2.09390i	0.0157428	+	0.0680066i
$949$	23.6180	−	8.59627i	0.766674	−	0.279047i
$950$	4.41184	+	3.70198i	0.143139	+	0.120108i
$951$	−13.4872	−	10.1509i	−0.437354	−	0.329165i
$952$	5.72890	+	2.08515i	0.185675	+	0.0675800i
$953$	4.78950	+	8.29565i	0.155147	+	0.268723i	0.933113	−	0.359584i	$-0.117082\pi$
$953$	4.78950	+	8.29565i	0.155147	+	0.268723i	−0.777966	+	0.628307i	$0.783748\pi$
$954$	4.31345	−	9.71902i	0.139653	−	0.314665i
$955$	−11.1731	+	19.3525i	−0.361555	+	0.626231i
$956$	19.2771	−	16.1754i	0.623467	−	0.523151i
$957$	5.08036	+	7.81297i	0.164225	+	0.252557i
$958$	−0.854149	+	4.84412i	−0.0275963	+	0.156506i
$959$	−0.543640	+	3.08313i	−0.0175550	+	0.0995596i
$960$	−2.96364	+	0.157072i	−0.0956511	+	0.00506946i
$961$	−21.3244	+	17.8933i	−0.687885	+	0.577204i
$962$	−2.62784	+	4.55155i	−0.0847248	+	0.146748i
$963$	10.2123	+	6.87076i	0.329087	+	0.221407i
$964$	−1.87170	−	3.24188i	−0.0602834	−	0.104414i
$965$	24.3528	+	8.86371i	0.783946	+	0.285333i
$966$	−0.541256	+	4.42979i	−0.0174146	+	0.142526i
$967$	−21.0791	−	17.6874i	−0.677857	−	0.568790i	0.237522	−	0.971382i	$-0.423665\pi$
$967$	−21.0791	−	17.6874i	−0.677857	−	0.568790i	−0.915379	+	0.402592i	$0.868109\pi$
$968$	8.85844	−	3.22421i	0.284721	−	0.103630i
$969$	28.1815	+	8.59778i	0.905322	+	0.276201i
$970$	4.31782	+	24.4876i	0.138637	+	0.786249i
$971$	5.63993			0.180994			0.0904970	−	0.995897i	$-0.471154\pi$
$971$	5.63993			0.180994			0.0904970	+	0.995897i	$0.471154\pi$
$972$	−6.62963	−	14.1084i	−0.212645	−	0.452528i
$973$	7.44276			0.238604
$974$	0.849079	+	4.81537i	0.0272062	+	0.154294i
$975$	12.8422	+	3.91798i	0.411281	+	0.125476i
$976$	10.9885	−	3.99950i	0.351734	−	0.128021i
$977$	−25.9217	−	21.7509i	−0.829309	−	0.695873i	0.125823	−	0.992053i	$-0.459843\pi$
$977$	−25.9217	−	21.7509i	−0.829309	−	0.695873i	−0.955132	+	0.296180i	$0.904287\pi$
$978$	5.05055	−	41.3350i	0.161499	−	1.32175i
$979$	19.8093	+	7.21001i	0.633109	+	0.230433i
$980$	−0.856730	−	1.48390i	−0.0273672	−	0.0474014i
$981$	−26.2150	−	17.6373i	−0.836981	−	0.563115i
$982$	15.1296	−	26.2052i	0.482804	−	0.836241i
$983$	22.1965	−	18.6251i	0.707958	−	0.594047i	−0.216068	−	0.976378i	$-0.569323\pi$
$983$	22.1965	−	18.6251i	0.707958	−	0.594047i	0.924025	+	0.382331i	$0.124879\pi$
$984$	−5.66045	+	0.300001i	−0.180449	+	0.00956369i
$985$	−6.23808	+	35.3779i	−0.198762	+	1.12723i
$986$	4.54166	−	25.7570i	0.144636	−	0.820271i
$987$	6.59365	+	10.1402i	0.209878	+	0.322767i
$988$	8.02754	−	6.73591i	0.255390	−	0.214298i
$989$	−9.85833	+	17.0751i	−0.313477	+	0.542957i
$990$	2.61533	−	5.89284i	0.0831207	−	0.187287i
$991$	18.2070	+	31.5355i	0.578366	+	1.00176i	0.995667	+	0.0929906i	$0.0296427\pi$
$991$	18.2070	+	31.5355i	0.578366	+	1.00176i	−0.417301	+	0.908768i	$0.637024\pi$
$992$	−1.67121	−	0.608270i	−0.0530610	−	0.0193126i
$993$	4.11886	+	3.09998i	0.130708	+	0.0983748i
$994$	−8.70928	−	7.30795i	−0.276242	−	0.231794i
$995$	−30.5886	+	11.1334i	−0.969725	+	0.352951i
$996$	2.15386	+	9.30435i	0.0682477	+	0.294819i
$997$	−3.27169	−	18.5547i	−0.103615	−	0.587632i	−0.991764	−	0.128076i	$-0.959120\pi$
$997$	−3.27169	−	18.5547i	−0.103615	−	0.587632i	0.888149	−	0.459556i	$-0.151991\pi$
$998$	−31.6259			−1.00110
$999$	7.17999	−	1.15023i	0.227165	−	0.0363917i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.b.337.2	yes	12
27.25	even	9	inner	378.2.u.b.295.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.b.295.2	✓	12	27.25	even	9	inner
378.2.u.b.337.2	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(1.65667 + 0.505425i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.31259 + 1.10139i) q^{5} +(-0.210069 + 1.71926i) q^{6} +(-0.939693 - 0.342020i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.48909 + 1.67464i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{2} +(1.65667 + 0.505425i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.31259 + 1.10139i) q^{5} +(-0.210069 + 1.71926i) q^{6} +(-0.939693 - 0.342020i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.48909 + 1.67464i) q^{9} +(-0.856730 + 1.48390i) q^{10} +(-0.960783 + 0.806193i) q^{11} +(-1.72962 + 0.0916693i) q^{12} +(-0.652160 + 3.69858i) q^{13} +(0.173648 - 0.984808i) q^{14} +(1.61785 + 2.48805i) q^{15} +(0.766044 - 0.642788i) q^{16} +(3.04828 - 5.27978i) q^{17} +(-1.21697 + 2.74207i) q^{18} +(1.39513 + 2.41644i) q^{19} +(-1.61013 - 0.586038i) q^{20} +(-1.38389 - 1.04156i) q^{21} +(-0.960783 - 0.806193i) q^{22} +(-2.42118 + 0.881236i) q^{23} +(-0.390623 - 1.68743i) q^{24} +(-0.358420 - 2.03270i) q^{25} -3.75564 q^{26} +(3.27719 + 4.03237i) q^{27} +1.00000 q^{28} +(-0.744954 - 4.22485i) q^{29} +(-2.16932 + 2.02531i) q^{30} +(-1.67121 + 0.608270i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-1.99917 + 0.849989i) q^{33} +(5.72890 + 2.08515i) q^{34} +(-0.856730 - 1.48390i) q^{35} +(-2.91174 - 0.722330i) q^{36} +(0.699704 - 1.21192i) q^{37} +(-2.13746 + 1.79354i) q^{38} +(-2.94977 + 5.79770i) q^{39} +(0.297539 - 1.68743i) q^{40} +(0.568290 - 3.22293i) q^{41} +(0.785424 - 1.54373i) q^{42} +(5.86201 - 4.91881i) q^{43} +(0.627106 - 1.08618i) q^{44} +(1.42271 + 4.93957i) q^{45} +(-1.28828 - 2.23137i) q^{46} +(-6.56218 - 2.38844i) q^{47} +(1.59396 - 0.677707i) q^{48} +(0.766044 + 0.642788i) q^{49} +(1.93958 - 0.705949i) q^{50} +(7.71852 - 7.20616i) q^{51} +(-0.652160 - 3.69858i) q^{52} -3.54440 q^{53} +(-3.40203 + 3.92762i) q^{54} -2.14904 q^{55} +(0.173648 + 0.984808i) q^{56} +(1.08994 + 4.70836i) q^{57} +(4.03130 - 1.46727i) q^{58} +(-6.26285 - 5.25516i) q^{59} +(-2.37124 - 1.78467i) q^{60} +(10.9885 + 3.99950i) q^{61} +(-0.889232 - 1.54019i) q^{62} +(-1.76622 - 2.42497i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-4.92960 + 4.13643i) q^{65} +(-1.18423 - 1.82120i) q^{66} +(-2.70516 + 15.3417i) q^{67} +(-1.05866 + 6.00394i) q^{68} +(-4.45648 + 0.236191i) q^{69} +(1.31259 - 1.10139i) q^{70} +(5.68458 - 9.84598i) q^{71} +(0.205737 - 2.99294i) q^{72} +(-3.34614 - 5.79569i) q^{73} +(1.31501 + 0.478626i) q^{74} +(0.433595 - 3.54866i) q^{75} +(-2.13746 - 1.79354i) q^{76} +(1.17857 - 0.428966i) q^{77} +(-6.22184 - 1.89819i) q^{78} +(-0.215477 - 1.22203i) q^{79} +1.71346 q^{80} +(3.39115 + 8.33667i) q^{81} +3.27265 q^{82} +(-0.957482 - 5.43015i) q^{83} +(1.65667 + 0.505425i) q^{84} +(9.81623 - 3.57282i) q^{85} +(5.86201 + 4.91881i) q^{86} +(0.901202 - 7.37568i) q^{87} +(1.17857 + 0.428966i) q^{88} +(-8.40393 - 14.5560i) q^{89} +(-4.61748 + 2.25885i) q^{90} +(1.87782 - 3.25248i) q^{91} +(1.97376 - 1.65618i) q^{92} +(-3.07607 + 0.163030i) q^{93} +(1.21264 - 6.87724i) q^{94} +(-0.830211 + 4.70836i) q^{95} +(0.944200 + 1.45206i) q^{96} +(11.1167 - 9.32799i) q^{97} +(-0.500000 + 0.866025i) q^{98} +(-3.74156 + 0.397719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} - 6 q^{6} - 6 q^{8} + 9 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 - 6 * q^6 - 6 * q^8 + 9 * q^9	\( 12 q + 3 q^{3} - 6 q^{6} - 6 q^{8} + 9 q^{9} + 3 q^{11} - 6 q^{12} + 12 q^{13} + 9 q^{15} - 9 q^{18} + 12 q^{19} - 9 q^{20} + 3 q^{21} + 3 q^{22} + 12 q^{23} + 3 q^{24} - 24 q^{25} - 18 q^{26} + 18 q^{27} + 12 q^{28} - 3 q^{29} + 21 q^{31} - 27 q^{33} + 9 q^{34} + 15 q^{37} + 15 q^{38} - 48 q^{39} + 9 q^{40} + 12 q^{41} + 3 q^{42} + 21 q^{43} + 12 q^{44} - 9 q^{45} - 6 q^{46} + 12 q^{47} + 3 q^{48} + 21 q^{50} - 9 q^{51} + 12 q^{52} - 42 q^{53} - 27 q^{54} - 12 q^{55} + 33 q^{57} - 3 q^{58} + 18 q^{59} - 18 q^{60} + 9 q^{62} + 9 q^{63} - 6 q^{64} - 36 q^{65} - 9 q^{66} - 33 q^{67} - 18 q^{68} + 9 q^{69} + 24 q^{71} - 18 q^{72} + 9 q^{73} - 36 q^{74} - 33 q^{75} + 15 q^{76} + 3 q^{77} - 21 q^{78} + 9 q^{81} - 24 q^{82} + 15 q^{83} + 3 q^{84} - 24 q^{85} + 21 q^{86} + 3 q^{88} - 51 q^{89} + 9 q^{91} - 6 q^{92} - 30 q^{93} - 15 q^{94} - 45 q^{95} + 3 q^{96} + 48 q^{97} - 6 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 - 6 * q^6 - 6 * q^8 + 9 * q^9 + 3 * q^11 - 6 * q^12 + 12 * q^13 + 9 * q^15 - 9 * q^18 + 12 * q^19 - 9 * q^20 + 3 * q^21 + 3 * q^22 + 12 * q^23 + 3 * q^24 - 24 * q^25 - 18 * q^26 + 18 * q^27 + 12 * q^28 - 3 * q^29 + 21 * q^31 - 27 * q^33 + 9 * q^34 + 15 * q^37 + 15 * q^38 - 48 * q^39 + 9 * q^40 + 12 * q^41 + 3 * q^42 + 21 * q^43 + 12 * q^44 - 9 * q^45 - 6 * q^46 + 12 * q^47 + 3 * q^48 + 21 * q^50 - 9 * q^51 + 12 * q^52 - 42 * q^53 - 27 * q^54 - 12 * q^55 + 33 * q^57 - 3 * q^58 + 18 * q^59 - 18 * q^60 + 9 * q^62 + 9 * q^63 - 6 * q^64 - 36 * q^65 - 9 * q^66 - 33 * q^67 - 18 * q^68 + 9 * q^69 + 24 * q^71 - 18 * q^72 + 9 * q^73 - 36 * q^74 - 33 * q^75 + 15 * q^76 + 3 * q^77 - 21 * q^78 + 9 * q^81 - 24 * q^82 + 15 * q^83 + 3 * q^84 - 24 * q^85 + 21 * q^86 + 3 * q^88 - 51 * q^89 + 9 * q^91 - 6 * q^92 - 30 * q^93 - 15 * q^94 - 45 * q^95 + 3 * q^96 + 48 * q^97 - 6 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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