LMFDB - Embedded newform 378.2.u.b.295.1

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			295.1
Root			$0.500000 - 1.68614i$ of defining polynomial
Character	$\chi$	$=$	378.295
Dual form			378.2.u.b.337.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 - 0.984808i) q^{2} +(-0.390623 - 1.68743i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.393151 - 0.329893i) q^{5} +(-1.72962 + 0.0916693i) q^{6} +(-0.939693 + 0.342020i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.69483 + 1.31830i) q^{9} +O(q^{10})$	\(q+(0.173648 - 0.984808i) q^{2} +(-0.390623 - 1.68743i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.393151 - 0.329893i) q^{5} +(-1.72962 + 0.0916693i) q^{6} +(-0.939693 + 0.342020i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.69483 + 1.31830i) q^{9} +(-0.256611 - 0.444463i) q^{10} +(-2.36944 - 1.98820i) q^{11} +(-0.210069 + 1.71926i) q^{12} +(-0.932962 - 5.29109i) q^{13} +(0.173648 + 0.984808i) q^{14} +(-0.710244 - 0.534550i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-2.52734 - 4.37748i) q^{17} +(0.830315 + 2.88281i) q^{18} +(-2.98025 + 5.16195i) q^{19} +(-0.482271 + 0.175532i) q^{20} +(0.944200 + 1.45206i) q^{21} +(-2.36944 + 1.98820i) q^{22} +(4.07388 + 1.48277i) q^{23} +(1.65667 + 0.505425i) q^{24} +(-0.822502 + 4.66464i) q^{25} -5.37272 q^{26} +(3.27719 + 4.03237i) q^{27} +1.00000 q^{28} +(0.663702 - 3.76404i) q^{29} +(-0.649762 + 0.606630i) q^{30} +(7.88809 + 2.87103i) q^{31} +(0.766044 - 0.642788i) q^{32} +(-2.42938 + 4.77489i) q^{33} +(-4.74984 + 1.72880i) q^{34} +(-0.256611 + 0.444463i) q^{35} +(2.98319 - 0.317107i) q^{36} +(-3.24546 - 5.62131i) q^{37} +(4.56601 + 3.83134i) q^{38} +(-8.56390 + 3.64113i) q^{39} +(0.0891201 + 0.505425i) q^{40} +(-1.73466 - 9.83777i) q^{41} +(1.59396 - 0.677707i) q^{42} +(-5.49764 - 4.61307i) q^{43} +(1.54654 + 2.67869i) q^{44} +(-0.624578 + 1.40729i) q^{45} +(2.16767 - 3.75451i) q^{46} +(12.7397 - 4.63687i) q^{47} +(0.785424 - 1.54373i) q^{48} +(0.766044 - 0.642788i) q^{49} +(4.45095 + 1.62001i) q^{50} +(-6.39944 + 5.97464i) q^{51} +(-0.932962 + 5.29109i) q^{52} -2.76100 q^{53} +(4.54019 - 2.52719i) q^{54} -1.58744 q^{55} +(0.173648 - 0.984808i) q^{56} +(9.87457 + 3.01259i) q^{57} +(-3.59161 - 1.30724i) q^{58} +(4.66659 - 3.91573i) q^{59} +(0.484584 + 0.745231i) q^{60} +(-5.17672 + 1.88417i) q^{61} +(4.19717 - 7.26970i) q^{62} +(2.08143 - 2.16048i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.11229 - 1.77242i) q^{65} +(4.28049 + 3.22162i) q^{66} +(0.300081 + 1.70184i) q^{67} +(0.877735 + 4.97788i) q^{68} +(0.910720 - 7.45358i) q^{69} +(0.393151 + 0.329893i) q^{70} +(-1.26583 - 2.19248i) q^{71} +(0.205737 - 2.99294i) q^{72} +(4.87689 - 8.44701i) q^{73} +(-6.09948 + 2.22003i) q^{74} +(8.19254 - 0.434201i) q^{75} +(4.56601 - 3.83134i) q^{76} +(2.90655 + 1.05790i) q^{77} +(2.09870 + 9.06607i) q^{78} +(-1.55175 + 8.80041i) q^{79} +0.513222 q^{80} +(5.52420 - 7.10516i) q^{81} -9.98953 q^{82} +(1.50665 - 8.54461i) q^{83} +(-0.390623 - 1.68743i) q^{84} +(-2.43772 - 0.887259i) q^{85} +(-5.49764 + 4.61307i) q^{86} +(-6.61081 + 0.350370i) q^{87} +(2.90655 - 1.05790i) q^{88} +(-0.964307 + 1.67023i) q^{89} +(1.27746 + 0.859463i) q^{90} +(2.68636 + 4.65291i) q^{91} +(-3.32106 - 2.78670i) q^{92} +(1.76339 - 14.4321i) q^{93} +(-2.35420 - 13.3513i) q^{94} +(0.531201 + 3.01259i) q^{95} +(-1.38389 - 1.04156i) q^{96} +(11.3975 + 9.56361i) q^{97} +(-0.500000 - 0.866025i) q^{98} +(9.00626 + 2.23423i) 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 $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$1$

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
$3$	−0.390623	−	1.68743i	−0.225526	−	0.974237i
$3$	−0.390623	−	1.68743i	−0.225526	−	0.974237i
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	0.393151	−	0.329893i	0.175822	−	0.147533i	−0.550630	−	0.834750i	$-0.685612\pi$
$5$	0.393151	−	0.329893i	0.175822	−	0.147533i	0.726452	+	0.687217i	$0.241168\pi$
$6$	−1.72962	+	0.0916693i	−0.706116	+	0.0374238i
$7$	−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
$9$	−2.69483	+	1.31830i	−0.898276	+	0.439432i
$10$	−0.256611	−	0.444463i	−0.0811475	−	0.140552i
$11$	−2.36944	−	1.98820i	−0.714413	−	0.599464i	0.211421	−	0.977395i	$-0.432191\pi$
$11$	−2.36944	−	1.98820i	−0.714413	−	0.599464i	−0.925834	+	0.377932i	$0.876635\pi$
$12$	−0.210069	+	1.71926i	−0.0606418	+	0.496309i
$13$	−0.932962	−	5.29109i	−0.258757	−	1.46748i	−0.786241	−	0.617920i	$-0.787976\pi$
$13$	−0.932962	−	5.29109i	−0.258757	−	1.46748i	0.527484	−	0.849565i	$-0.323135\pi$
$14$	0.173648	+	0.984808i	0.0464094	+	0.263201i
$15$	−0.710244	−	0.534550i	−0.183384	−	0.138020i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−2.52734	−	4.37748i	−0.612969	−	1.06169i	−0.990737	−	0.135794i	$-0.956642\pi$
$17$	−2.52734	−	4.37748i	−0.612969	−	1.06169i	0.377768	−	0.925900i	$-0.376692\pi$
$18$	0.830315	+	2.88281i	0.195707	+	0.679484i
$19$	−2.98025	+	5.16195i	−0.683717	+	1.18423i	0.290122	+	0.956990i	$0.406304\pi$
$19$	−2.98025	+	5.16195i	−0.683717	+	1.18423i	−0.973838	+	0.227242i	$0.927029\pi$
$20$	−0.482271	+	0.175532i	−0.107839	+	0.0392502i
$21$	0.944200	+	1.45206i	0.206041	+	0.316866i
$22$	−2.36944	+	1.98820i	−0.505166	+	0.423885i
$23$	4.07388	+	1.48277i	0.849462	+	0.309179i	0.729821	−	0.683638i	$-0.239603\pi$
$23$	4.07388	+	1.48277i	0.849462	+	0.309179i	0.119641	+	0.992817i	$0.461826\pi$
$24$	1.65667	+	0.505425i	0.338166	+	0.103169i
$25$	−0.822502	+	4.66464i	−0.164500	+	0.932929i
$26$	−5.37272			−1.05368
$27$	3.27719	+	4.03237i	0.630695	+	0.776031i
$28$	1.00000			0.188982
$29$	0.663702	−	3.76404i	0.123246	−	0.698965i	−0.859088	−	0.511829i	$-0.828968\pi$
$29$	0.663702	−	3.76404i	0.123246	−	0.698965i	0.982334	−	0.187136i	$-0.0599207\pi$
$30$	−0.649762	+	0.606630i	−0.118630	+	0.110755i
$31$	7.88809	+	2.87103i	1.41674	+	0.515652i	0.933101	−	0.359614i	$-0.117092\pi$
$31$	7.88809	+	2.87103i	1.41674	+	0.515652i	0.483642	+	0.875266i	$0.339314\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$	−2.42938	+	4.77489i	−0.422901	+	0.831202i
$34$	−4.74984	+	1.72880i	−0.814591	+	0.296487i
$35$	−0.256611	+	0.444463i	−0.0433752	+	0.0751280i
$36$	2.98319	−	0.317107i	0.497199	−	0.0528511i
$37$	−3.24546	−	5.62131i	−0.533551	−	0.924137i	−0.999232	−	0.0391846i	$-0.987524\pi$
$37$	−3.24546	−	5.62131i	−0.533551	−	0.924137i	0.465681	−	0.884953i	$-0.345809\pi$
$38$	4.56601	+	3.83134i	0.740705	+	0.621525i
$39$	−8.56390	+	3.64113i	−1.37132	+	0.583047i
$40$	0.0891201	+	0.505425i	0.0140911	+	0.0799147i
$41$	−1.73466	−	9.83777i	−0.270909	−	1.53640i	−0.751664	−	0.659546i	$-0.770748\pi$
$41$	−1.73466	−	9.83777i	−0.270909	−	1.53640i	0.480755	−	0.876855i	$-0.340363\pi$
$42$	1.59396	−	0.677707i	0.245954	−	0.104572i
$43$	−5.49764	−	4.61307i	−0.838383	−	0.703487i	0.118817	−	0.992916i	$-0.462090\pi$
$43$	−5.49764	−	4.61307i	−0.838383	−	0.703487i	−0.957199	+	0.289430i	$0.906534\pi$
$44$	1.54654	+	2.67869i	0.233150	+	0.403828i
$45$	−0.624578	+	1.40729i	−0.0931066	+	0.209787i
$46$	2.16767	−	3.75451i	0.319605	−	0.553572i
$47$	12.7397	−	4.63687i	1.85828	−	0.676357i	0.878021	−	0.478623i	$-0.158864\pi$
$47$	12.7397	−	4.63687i	1.85828	−	0.676357i	0.980256	−	0.197734i	$-0.0633583\pi$
$48$	0.785424	−	1.54373i	0.113366	−	0.222819i
$49$	0.766044	−	0.642788i	0.109435	−	0.0918268i
$50$	4.45095	+	1.62001i	0.629460	+	0.229105i
$51$	−6.39944	+	5.97464i	−0.896101	+	0.836617i
$52$	−0.932962	+	5.29109i	−0.129379	+	0.733742i
$53$	−2.76100			−0.379253			−0.189627	−	0.981856i	$-0.560728\pi$
$53$	−2.76100			−0.379253			−0.189627	+	0.981856i	$0.560728\pi$
$54$	4.54019	−	2.52719i	0.617842	−	0.343907i
$55$	−1.58744			−0.214050
$56$	0.173648	−	0.984808i	0.0232047	−	0.131600i
$57$	9.87457	+	3.01259i	1.30792	+	0.399027i
$58$	−3.59161	−	1.30724i	−0.471601	−	0.171649i
$59$	4.66659	−	3.91573i	0.607538	−	0.509785i	−0.286321	−	0.958134i	$-0.592432\pi$
$59$	4.66659	−	3.91573i	0.607538	−	0.509785i	0.893859	+	0.448349i	$0.147988\pi$
$60$	0.484584	+	0.745231i	0.0625595	+	0.0962089i
$61$	−5.17672	+	1.88417i	−0.662812	+	0.241244i	−0.651450	−	0.758692i	$-0.725839\pi$
$61$	−5.17672	+	1.88417i	−0.662812	+	0.241244i	−0.0113618	+	0.999935i	$0.503617\pi$
$62$	4.19717	−	7.26970i	0.533041	−	0.923253i
$63$	2.08143	−	2.16048i	0.262235	−	0.272195i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−2.11229	−	1.77242i	−0.261997	−	0.219842i
$66$	4.28049	+	3.22162i	0.526892	+	0.396555i
$67$	0.300081	+	1.70184i	0.0366607	+	0.207913i	0.997636	−	0.0687214i	$-0.0218920\pi$
$67$	0.300081	+	1.70184i	0.0366607	+	0.207913i	−0.960975	+	0.276635i	$0.910781\pi$
$68$	0.877735	+	4.97788i	0.106441	+	0.603657i
$69$	0.910720	−	7.45358i	0.109638	−	0.897306i
$70$	0.393151	+	0.329893i	0.0469905	+	0.0394297i
$71$	−1.26583	−	2.19248i	−0.150226	−	0.260200i	0.781084	−	0.624426i	$-0.214667\pi$
$71$	−1.26583	−	2.19248i	−0.150226	−	0.260200i	−0.931311	+	0.364226i	$0.881334\pi$
$72$	0.205737	−	2.99294i	0.0242463	−	0.352721i
$73$	4.87689	−	8.44701i	0.570796	−	0.988648i	−0.425688	−	0.904870i	$-0.639968\pi$
$73$	4.87689	−	8.44701i	0.570796	−	0.988648i	0.996484	−	0.0837783i	$-0.0266987\pi$
$74$	−6.09948	+	2.22003i	−0.709050	+	0.258073i
$75$	8.19254	−	0.434201i	0.945993	−	0.0501372i
$76$	4.56601	−	3.83134i	0.523757	−	0.439485i
$77$	2.90655	+	1.05790i	0.331232	+	0.120559i
$78$	2.09870	+	9.06607i	0.237631	+	1.02653i
$79$	−1.55175	+	8.80041i	−0.174586	+	0.990124i	0.764036	+	0.645174i	$0.223215\pi$
$79$	−1.55175	+	8.80041i	−0.174586	+	0.990124i	−0.938621	+	0.344950i	$0.887896\pi$
$80$	0.513222			0.0573800
$81$	5.52420	−	7.10516i	0.613800	−	0.789462i
$82$	−9.98953			−1.10316
$83$	1.50665	−	8.54461i	0.165376	−	0.937893i	−0.783300	−	0.621643i	$-0.786465\pi$
$83$	1.50665	−	8.54461i	0.165376	−	0.937893i	0.948676	−	0.316249i	$-0.102424\pi$
$84$	−0.390623	−	1.68743i	−0.0426204	−	0.184114i
$85$	−2.43772	−	0.887259i	−0.264408	−	0.0962367i
$86$	−5.49764	+	4.61307i	−0.592826	+	0.497440i
$87$	−6.61081	+	0.350370i	−0.708753	+	0.0375636i
$88$	2.90655	−	1.05790i	0.309839	−	0.112772i
$89$	−0.964307	+	1.67023i	−0.102216	+	0.177044i	−0.912597	−	0.408859i	$-0.865927\pi$
$89$	−0.964307	+	1.67023i	−0.102216	+	0.177044i	0.810381	+	0.585903i	$0.199260\pi$
$90$	1.27746	+	0.859463i	0.134656	+	0.0905954i
$91$	2.68636	+	4.65291i	0.281607	+	0.487757i
$92$	−3.32106	−	2.78670i	−0.346244	−	0.290533i
$93$	1.76339	−	14.4321i	0.182855	−	1.49654i
$94$	−2.35420	−	13.3513i	−0.242817	−	1.37709i
$95$	0.531201	+	3.01259i	0.0545000	+	0.309085i
$96$	−1.38389	−	1.04156i	−0.141243	−	0.106304i
$97$	11.3975	+	9.56361i	1.15724	+	0.971038i	0.999864	−	0.0165013i	$-0.00525278\pi$
$97$	11.3975	+	9.56361i	1.15724	+	0.971038i	0.157374	+	0.987539i	$0.449697\pi$
$98$	−0.500000	−	0.866025i	−0.0505076	−	0.0874818i
$99$	9.00626	+	2.23423i	0.905163	+	0.224548i
$100$	2.36830	−	4.10202i	0.236830	−	0.410202i
$101$	5.76899	−	2.09974i	0.574036	−	0.208932i	−0.0386575	−	0.999253i	$-0.512308\pi$
$101$	5.76899	−	2.09974i	0.574036	−	0.208932i	0.612694	+	0.790320i	$0.290086\pi$
$102$	4.77262	+	7.33971i	0.472560	+	0.726739i
$103$	−2.42271	+	2.03290i	−0.238717	+	0.200307i	−0.754296	−	0.656535i	$-0.772021\pi$
$103$	−2.42271	+	2.03290i	−0.238717	+	0.200307i	0.515579	+	0.856842i	$0.327577\pi$
$104$	5.04870	+	1.83758i	0.495066	+	0.180189i
$105$	0.850238	+	0.259395i	0.0829747	+	0.0253144i
$106$	−0.479443	+	2.71906i	−0.0465677	+	0.264098i
$107$	−10.2826			−0.994053			−0.497027	−	0.867735i	$-0.665575\pi$
$107$	−10.2826			−0.994053			−0.497027	+	0.867735i	$0.665575\pi$
$108$	−1.70040	−	4.91006i	−0.163621	−	0.472470i
$109$	−13.2045			−1.26476			−0.632382	−	0.774657i	$-0.717922\pi$
$109$	−13.2045			−1.26476			−0.632382	+	0.774657i	$0.717922\pi$
$110$	−0.275656	+	1.56332i	−0.0262828	+	0.149057i
$111$	−8.21780	+	7.67230i	−0.779999	+	0.728222i
$112$	−0.939693	−	0.342020i	−0.0887926	−	0.0323179i
$113$	12.2719	−	10.2973i	1.15444	−	0.968691i	0.154627	−	0.987973i	$-0.450582\pi$
$113$	12.2719	−	10.2973i	1.15444	−	0.968691i	0.999814	+	0.0192821i	$0.00613805\pi$
$114$	4.68152	−	9.20142i	0.438465	−	0.861792i
$115$	2.09080	−	0.760991i	0.194969	−	0.0709627i
$116$	−1.91105	+	3.31004i	−0.177437	+	0.307330i
$117$	9.48939	+	13.0287i	0.877295	+	1.20450i
$118$	−3.04590	−	5.27565i	−0.280398	−	0.485663i
$119$	3.87211	+	3.24908i	0.354955	+	0.297843i
$120$	0.818056	−	0.347814i	0.0746780	−	0.0317509i
$121$	−0.248809	−	1.41107i	−0.0226190	−	0.128279i
$122$	0.956620	+	5.42526i	0.0866083	+	0.491180i
$123$	−15.9229	+	6.76997i	−1.43572	+	0.610428i
$124$	−6.43043	−	5.39577i	−0.577470	−	0.484555i
$125$	2.49852	+	4.32756i	0.223474	+	0.387069i
$126$	−1.76622	−	2.42497i	−0.157347	−	0.216033i
$127$	1.75096	−	3.03275i	0.155372	−	0.269113i	−0.777822	−	0.628484i	$-0.783676\pi$
$127$	1.75096	−	3.03275i	0.155372	−	0.269113i	0.933195	+	0.359372i	$0.117009\pi$
$128$	−0.939693	+	0.342020i	−0.0830579	+	0.0302306i
$129$	−5.63672	+	11.0788i	−0.496286	+	0.975438i
$130$	−2.11229	+	1.77242i	−0.185260	+	0.155452i
$131$	1.06148	+	0.386349i	0.0927424	+	0.0337555i	0.387975	−	0.921670i	$-0.373175\pi$
$131$	1.06148	+	0.386349i	0.0927424	+	0.0337555i	−0.295232	+	0.955426i	$0.595397\pi$
$132$	3.91598	−	3.65603i	0.340842	−	0.318217i
$133$	1.03503	−	5.86995i	0.0897485	−	0.508989i
$134$	1.72810			0.149285
$135$	2.61868	+	0.504210i	0.225380	+	0.0433955i
$136$	5.05467			0.433435
$137$	−2.42814	+	13.7707i	−0.207450	+	1.17651i	0.686087	+	0.727519i	$0.259327\pi$
$137$	−2.42814	+	13.7707i	−0.207450	+	1.17651i	−0.893537	+	0.448989i	$0.851784\pi$
$138$	−7.18220	−	2.19119i	−0.611389	−	0.186526i
$139$	19.0114	+	6.91960i	1.61253	+	0.586913i	0.981938	−	0.189202i	$-0.0605900\pi$
$139$	19.0114	+	6.91960i	1.61253	+	0.586913i	0.630592	+	0.776115i	$0.282812\pi$
$140$	0.393151	−	0.329893i	0.0332273	−	0.0278810i
$141$	−12.8008	−	19.6861i	−1.07802	−	1.65787i
$142$	−2.37898	+	0.865878i	−0.199640	+	0.0726629i
$143$	−8.30913	+	14.3918i	−0.694844	+	1.20351i
$144$	−2.91174	−	0.722330i	−0.242645	−	0.0601941i
$145$	−0.980795	−	1.69879i	−0.0814506	−	0.141077i
$146$	−7.47182	−	6.26960i	−0.618372	−	0.518876i
$147$	−1.38389	−	1.04156i	−0.114142	−	0.0859062i
$148$	1.12714	+	6.39232i	0.0926501	+	0.525445i
$149$	2.96384	+	16.8088i	0.242808	+	1.37703i	0.825530	+	0.564359i	$0.190876\pi$
$149$	2.96384	+	16.8088i	0.242808	+	1.37703i	−0.582722	+	0.812671i	$0.698012\pi$
$150$	0.995015	−	8.14347i	0.0812426	−	0.664912i
$151$	−3.26353	−	2.73842i	−0.265582	−	0.222850i	0.500265	−	0.865872i	$-0.333236\pi$
$151$	−3.26353	−	2.73842i	−0.265582	−	0.222850i	−0.765847	+	0.643022i	$0.777680\pi$
$152$	−2.98025	−	5.16195i	−0.241730	−	0.418689i
$153$	12.5815	+	8.46477i	1.01716	+	0.684336i
$154$	1.54654	−	2.67869i	0.124624	−	0.215855i
$155$	4.04834	−	1.47348i	0.325171	−	0.118352i
$156$	9.29277	−	0.492513i	0.744017	−	0.0394326i
$157$	3.23919	−	2.71801i	0.258516	−	0.216921i	−0.504313	−	0.863521i	$-0.668254\pi$
$157$	3.23919	−	2.71801i	0.258516	−	0.216921i	0.762829	+	0.646600i	$0.223810\pi$
$158$	8.39725	+	3.05635i	0.668050	+	0.243150i
$159$	1.07851	+	4.65900i	0.0855314	+	0.369482i
$160$	0.0891201	−	0.505425i	0.00704556	−	0.0399574i
$161$	−4.33533			−0.341672
$162$	−6.03795	−	6.67407i	−0.474386	−	0.524364i
$163$	7.92166			0.620473			0.310236	−	0.950659i	$-0.399592\pi$
$163$	7.92166			0.620473			0.310236	+	0.950659i	$0.399592\pi$
$164$	−1.73466	+	9.83777i	−0.135454	+	0.768201i
$165$	0.620089	+	2.67869i	0.0482739	+	0.208536i
$166$	−8.15317	−	2.96751i	−0.632809	−	0.230324i
$167$	−3.52901	+	2.96119i	−0.273083	+	0.229144i	−0.769036	−	0.639206i	$-0.779263\pi$
$167$	−3.52901	+	2.96119i	−0.273083	+	0.229144i	0.495953	+	0.868349i	$0.334819\pi$
$168$	−1.72962	+	0.0916693i	−0.133443	+	0.00707244i
$169$	−14.9092	+	5.42652i	−1.14686	+	0.417424i
$170$	−1.29709	+	2.24662i	−0.0994819	+	0.172308i
$171$	1.22630	−	17.8394i	0.0937772	−	1.36421i
$172$	3.58833	+	6.21517i	0.273608	+	0.473902i
$173$	−13.8989	−	11.6626i	−1.05671	−	0.886688i	−0.0629298	−	0.998018i	$-0.520044\pi$
$173$	−13.8989	−	11.6626i	−1.05671	−	0.886688i	−0.993783	+	0.111330i	$0.964489\pi$
$174$	−0.802908	+	6.57122i	−0.0608683	+	0.498163i
$175$	−0.822502	−	4.66464i	−0.0621753	−	0.352614i
$176$	−0.537108	−	3.04609i	−0.0404861	−	0.229608i
$177$	−8.43039	−	6.34496i	−0.633667	−	0.476916i
$178$	1.47740	+	1.23969i	0.110736	+	0.0929186i
$179$	−4.86117	−	8.41980i	−0.363341	−	0.629325i	0.625167	−	0.780491i	$-0.285031\pi$
$179$	−4.86117	−	8.41980i	−0.363341	−	0.629325i	−0.988508	+	0.151165i	$0.951697\pi$
$180$	1.06823	−	1.10880i	0.0796215	−	0.0826454i
$181$	2.02362	−	3.50501i	0.150414	−	0.260525i	−0.780965	−	0.624574i	$-0.785273\pi$
$181$	2.02362	−	3.50501i	0.150414	−	0.260525i	0.931380	+	0.364049i	$0.118606\pi$
$182$	5.04870	−	1.83758i	0.374235	−	0.136210i
$183$	5.20155	+	7.99935i	0.384510	+	0.591329i
$184$	−3.32106	+	2.78670i	−0.244832	+	0.205438i
$185$	−3.13039	−	1.13937i	−0.230151	−	0.0837679i
$186$	−13.9066	−	4.24271i	−1.01968	−	0.311090i
$187$	−2.71491	+	15.3970i	−0.198534	+	1.12594i
$188$	−13.5573			−0.988768
$189$	−4.45870	−	2.66833i	−0.324323	−	0.194092i
$190$	3.05906			0.221928
$191$	−0.774454	+	4.39215i	−0.0560375	+	0.317805i	−0.999922	−	0.0124705i	$-0.996030\pi$
$191$	−0.774454	+	4.39215i	−0.0560375	+	0.317805i	0.943885	+	0.330275i	$0.107142\pi$
$192$	−1.26604	+	1.18200i	−0.0913689	+	0.0853037i
$193$	24.2997	+	8.84437i	1.74913	+	0.636632i	0.999677	−	0.0254240i	$-0.00809358\pi$
$193$	24.2997	+	8.84437i	1.74913	+	0.636632i	0.749455	+	0.662056i	$0.230316\pi$
$194$	11.3975	−	9.56361i	0.818291	−	0.686627i
$195$	−2.16572	+	4.25668i	−0.155091	+	0.304827i
$196$	−0.939693	+	0.342020i	−0.0671209	+	0.0244300i
$197$	−4.47758	+	7.75539i	−0.319014	+	0.552549i	−0.980283	−	0.197601i	$-0.936685\pi$
$197$	−4.47758	+	7.75539i	−0.319014	+	0.552549i	0.661268	+	0.750149i	$0.270018\pi$
$198$	3.76420	−	8.48147i	0.267510	−	0.602752i
$199$	6.23620	+	10.8014i	0.442072	+	0.765692i	0.997843	−	0.0656438i	$-0.0209101\pi$
$199$	6.23620	+	10.8014i	0.442072	+	0.765692i	−0.555771	+	0.831336i	$0.687577\pi$
$200$	−3.62845	−	3.04463i	−0.256570	−	0.215288i
$201$	2.75452	−	1.17114i	0.194289	−	0.0826060i
$202$	−1.06607	−	6.04596i	−0.0750082	−	0.425393i
$203$	0.663702	+	3.76404i	0.0465828	+	0.264184i
$204$	8.05696	−	3.42559i	0.564100	−	0.239839i
$205$	−3.92739	−	3.29547i	−0.274301	−	0.230166i
$206$	1.58131	+	2.73891i	0.110175	+	0.190829i
$207$	−12.9331	+	1.37476i	−0.898915	+	0.0955526i
$208$	2.68636	−	4.65291i	0.186265	−	0.322621i
$209$	17.3245	−	6.30560i	1.19836	−	0.436167i
$210$	0.403097	−	0.792278i	0.0278163	−	0.0546723i
$211$	−6.02509	+	5.05565i	−0.414784	+	0.348045i	−0.826175	−	0.563414i	$-0.809488\pi$
$211$	−6.02509	+	5.05565i	−0.414784	+	0.348045i	0.411391	+	0.911459i	$0.365043\pi$
$212$	2.59450	+	0.944319i	0.178191	+	0.0648561i
$213$	−3.20519	+	2.99243i	−0.219616	+	0.205038i
$214$	−1.78555	+	10.1263i	−0.122058	+	0.692223i
$215$	−3.68322			−0.251194
$216$	−5.13073	+	0.821942i	−0.349102	+	0.0559261i
$217$	−8.39433			−0.569844
$218$	−2.29294	+	13.0039i	−0.155297	+	0.880736i
$219$	−16.1588	−	4.92980i	−1.09191	−	0.333125i
$220$	1.49170	+	0.542936i	0.100571	+	0.0366047i
$221$	−20.8037	+	17.4564i	−1.39941	+	1.17424i
$222$	6.12873	+	9.42524i	0.411333	+	0.632580i
$223$	−16.0603	+	5.84548i	−1.07548	+	0.391442i	−0.818223	−	0.574902i	$-0.805040\pi$
$223$	−16.0603	+	5.84548i	−1.07548	+	0.391442i	−0.257255	+	0.966343i	$0.582818\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	−3.93287	−	13.6547i	−0.262192	−	0.910314i
$226$	−8.00990	−	13.8735i	−0.532810	−	0.922855i
$227$	−5.05684	−	4.24319i	−0.335634	−	0.281630i	0.459357	−	0.888252i	$-0.348080\pi$
$227$	−5.05684	−	4.24319i	−0.335634	−	0.281630i	−0.794991	+	0.606621i	$0.792524\pi$
$228$	−8.24869	−	6.20821i	−0.546283	−	0.411149i
$229$	−0.828025	−	4.69596i	−0.0547174	−	0.310318i	0.945149	−	0.326638i	$-0.105916\pi$
$229$	−0.828025	−	4.69596i	−0.0547174	−	0.310318i	−0.999867	+	0.0163204i	$0.994805\pi$
$230$	−0.386365	−	2.19119i	−0.0254762	−	0.144482i
$231$	0.649762	−	5.31783i	0.0427512	−	0.349887i
$232$	2.92791	+	2.45680i	0.192226	+	0.161297i
$233$	9.05529	+	15.6842i	0.593232	+	1.02751i	0.993794	+	0.111238i	$0.0354816\pi$
$233$	9.05529	+	15.6842i	0.593232	+	1.02751i	−0.400562	+	0.916270i	$0.631185\pi$
$234$	14.4785	−	7.08282i	0.946492	−	0.463019i
$235$	3.47895	−	6.02573i	0.226942	−	0.393075i
$236$	−5.72442	+	2.08352i	−0.372628	+	0.135625i
$237$	15.4562	−	0.819172i	1.00399	−	0.0532110i
$238$	3.87211	−	3.24908i	0.250991	−	0.210607i
$239$	−22.1658	−	8.06771i	−1.43379	−	0.521857i	−0.495775	−	0.868451i	$-0.665116\pi$
$239$	−22.1658	−	8.06771i	−1.43379	−	0.521857i	−0.938015	+	0.346595i	$0.887338\pi$
$240$	−0.200476	−	0.866025i	−0.0129407	−	0.0559017i
$241$	3.78666	−	21.4752i	0.243921	−	1.38334i	−0.579066	−	0.815281i	$-0.696583\pi$
$241$	3.78666	−	21.4752i	0.243921	−	1.38334i	0.822986	−	0.568061i	$-0.192306\pi$
$242$	−1.43283			−0.0921061
$243$	−14.1473	−	6.54625i	−0.907551	−	0.419942i
$244$	5.50895			0.352675
$245$	0.0891201	−	0.505425i	0.00569367	−	0.0322904i
$246$	3.90214	+	16.8566i	0.248791	+	1.07474i
$247$	30.0928	+	10.9529i	1.91476	+	0.696915i
$248$	−6.43043	+	5.39577i	−0.408333	+	0.342632i
$249$	−15.0069	+	0.795362i	−0.951027	+	0.0504040i
$250$	4.69568	−	1.70909i	0.296981	−	0.108092i
$251$	−4.88921	+	8.46835i	−0.308604	+	0.534518i	−0.978057	−	0.208336i	$-0.933195\pi$
$251$	−4.88921	+	8.46835i	−0.308604	+	0.534518i	0.669453	+	0.742854i	$0.266528\pi$
$252$	−2.69483	+	1.31830i	−0.169758	+	0.0830448i
$253$	−6.70477	−	11.6130i	−0.421525	−	0.730103i
$254$	−2.68262	−	2.25099i	−0.168323	−	0.141240i
$255$	−0.544956	+	4.46007i	−0.0341264	+	0.279300i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	2.11629	+	12.0021i	0.132011	+	0.748670i	0.976895	+	0.213720i	$0.0685582\pi$
$257$	2.11629	+	12.0021i	0.132011	+	0.748670i	−0.844884	+	0.534949i	$0.820331\pi$
$258$	9.93173	+	7.47491i	0.618322	+	0.465367i
$259$	4.97234	+	4.17229i	0.308966	+	0.259253i
$260$	1.37870	+	2.38798i	0.0855032	+	0.148096i
$261$	3.17356	+	11.0184i	0.196438	+	0.682022i
$262$	0.564804	−	0.978270i	0.0348937	−	0.0604377i
$263$	−3.15523	+	1.14841i	−0.194560	+	0.0708140i	−0.437462	−	0.899237i	$-0.644123\pi$
$263$	−3.15523	+	1.14841i	−0.194560	+	0.0708140i	0.242903	+	0.970051i	$0.421900\pi$
$264$	−2.92049	−	4.49135i	−0.179744	−	0.276424i
$265$	−1.08549	+	0.910835i	−0.0666812	+	0.0559522i
$266$	−5.60104	−	2.03861i	−0.343422	−	0.124995i
$267$	3.19507	+	0.974769i	0.195535	+	0.0596549i
$268$	0.300081	−	1.70184i	0.0183304	−	0.103957i
$269$	6.33461			0.386228			0.193114	−	0.981176i	$-0.438141\pi$
$269$	6.33461			0.386228			0.193114	+	0.981176i	$0.438141\pi$
$270$	0.951279	−	2.49134i	0.0578930	−	0.151618i
$271$	−26.6659			−1.61984			−0.809918	−	0.586543i	$-0.800488\pi$
$271$	−26.6659			−1.61984			−0.809918	+	0.586543i	$0.800488\pi$
$272$	0.877735	−	4.97788i	0.0532205	−	0.301828i
$273$	6.80210	−	6.35057i	0.411682	−	0.384354i
$274$	13.1398	+	4.78251i	0.793806	+	0.288922i
$275$	11.2231	−	9.41729i	0.676778	−	0.567884i
$276$	−3.40507	+	6.69259i	−0.204961	+	0.402847i
$277$	27.0491	−	9.84506i	1.62522	−	0.591532i	0.640855	−	0.767662i	$-0.278580\pi$
$277$	27.0491	−	9.84506i	1.62522	−	0.591532i	0.984367	+	0.176130i	$0.0563577\pi$
$278$	10.1158	−	17.5210i	0.606704	−	1.05084i
$279$	−25.0419	+	2.66190i	−1.49922	+	0.159364i
$280$	−0.256611	−	0.444463i	−0.0153354	−	0.0265618i
$281$	−3.47016	−	2.91181i	−0.207012	−	0.173704i	0.533387	−	0.845871i	$-0.320919\pi$
$281$	−3.47016	−	2.91181i	−0.207012	−	0.173704i	−0.740399	+	0.672167i	$0.765363\pi$
$282$	−21.6098	+	9.18788i	−1.28685	+	0.547130i
$283$	1.89488	+	10.7464i	0.112639	+	0.638808i	0.987892	+	0.155143i	$0.0495837\pi$
$283$	1.89488	+	10.7464i	0.112639	+	0.638808i	−0.875253	+	0.483665i	$0.839305\pi$
$284$	0.439618	+	2.49320i	0.0260865	+	0.147944i
$285$	4.87603	−	2.07315i	0.288831	−	0.122803i
$286$	12.7303	+	10.6820i	0.752760	+	0.631640i
$287$	4.99477	+	8.65119i	0.294832	+	0.510663i
$288$	−1.21697	+	2.74207i	−0.0717109	+	0.161578i
$289$	−4.27487	+	7.40428i	−0.251463	+	0.435546i
$290$	−1.84329	+	0.670904i	−0.108242	+	0.0393968i
$291$	11.6858	−	22.9682i	0.685034	−	1.34642i
$292$	−7.47182	+	6.26960i	−0.437255	+	0.366901i
$293$	7.55989	+	2.75158i	0.441654	+	0.160749i	0.553269	−	0.833003i	$-0.313380\pi$
$293$	7.55989	+	2.75158i	0.441654	+	0.160749i	−0.111615	+	0.993751i	$0.535602\pi$
$294$	−1.26604	+	1.18200i	−0.0738372	+	0.0689358i
$295$	0.542901	−	3.07895i	0.0316089	−	0.179263i
$296$	6.49093			0.377277
$297$	0.252047	−	16.0702i	0.0146252	−	0.932485i
$298$	17.0681			0.988728
$299$	4.04470	−	22.9386i	0.233911	−	1.32658i
$300$	−7.84697	−	2.39400i	−0.453045	−	0.138218i
$301$	6.74386	+	2.45456i	0.388709	+	0.141479i
$302$	−3.26353	+	2.73842i	−0.187795	+	0.157579i
$303$	−5.79666	−	8.91455i	−0.333010	−	0.512128i
$304$	−5.60104	+	2.03861i	−0.321242	+	0.116922i
$305$	−1.41366	+	2.44853i	−0.0809459	+	0.140202i
$306$	10.5209	−	10.9205i	0.601442	−	0.624284i
$307$	6.95649	+	12.0490i	0.397028	+	0.687673i	0.993358	−	0.115067i	$-0.0367082\pi$
$307$	6.95649	+	12.0490i	0.397028	+	0.687673i	−0.596330	+	0.802740i	$0.703375\pi$
$308$	−2.36944	−	1.98820i	−0.135011	−	0.113288i
$309$	4.37673	+	3.29406i	0.248984	+	0.187392i
$310$	−0.748103	−	4.24271i	−0.0424894	−	0.240969i
$311$	−5.87079	−	33.2949i	−0.332902	−	1.88798i	−0.447039	−	0.894514i	$-0.647521\pi$
$311$	−5.87079	−	33.2949i	−0.332902	−	1.88798i	0.114137	−	0.993465i	$-0.463590\pi$
$312$	1.12864	−	9.23712i	0.0638968	−	0.522949i
$313$	3.00461	+	2.52117i	0.169831	+	0.142505i	0.723742	−	0.690071i	$-0.242421\pi$
$313$	3.00461	+	2.52117i	0.169831	+	0.142505i	−0.553911	+	0.832576i	$0.686865\pi$
$314$	−2.11423	−	3.66196i	−0.119313	−	0.206656i
$315$	0.105589	−	1.53604i	0.00594925	−	0.0865461i
$316$	4.46809	−	7.73895i	0.251349	−	0.435350i
$317$	−4.59946	+	1.67407i	−0.258332	+	0.0940250i	−0.467939	−	0.883761i	$-0.655003\pi$
$317$	−4.59946	+	1.67407i	−0.258332	+	0.0940250i	0.209608	+	0.977786i	$0.432781\pi$
$318$	4.77550	−	0.253099i	0.267797	−	0.0141931i
$319$	−9.05626	+	7.59910i	−0.507053	+	0.425468i
$320$	−0.482271	−	0.175532i	−0.0269598	−	0.00981255i
$321$	4.01660	+	17.3511i	0.224185	+	0.968443i
$322$	−0.752822	+	4.26947i	−0.0419532	+	0.237928i
$323$	30.1284			1.67639
$324$	−7.62115	+	4.78728i	−0.423397	+	0.265960i
$325$	25.4484			1.41162
$326$	1.37558	−	7.80132i	0.0761865	−	0.432075i
$327$	5.15798	+	22.2817i	0.285237	+	1.23218i
$328$	9.38709	+	3.41662i	0.518315	+	0.188651i
$329$	−10.3855	+	8.71447i	−0.572571	+	0.480444i
$330$	2.74567	−	0.145519i	0.151144	−	0.00801058i
$331$	20.5155	−	7.46702i	1.12763	−	0.410425i	0.290200	−	0.956966i	$-0.406278\pi$
$331$	20.5155	−	7.46702i	1.12763	−	0.410425i	0.837432	+	0.546541i	$0.184056\pi$
$332$	−4.33821	+	7.51400i	−0.238090	+	0.412385i
$333$	16.1565	+	10.8700i	0.885371	+	0.595671i
$334$	2.30340	+	3.98960i	0.126036	+	0.218301i
$335$	0.679403	+	0.570086i	0.0371197	+	0.0311472i
$336$	−0.210069	+	1.71926i	−0.0114602	+	0.0937936i
$337$	−0.914925	−	5.18880i	−0.0498391	−	0.282652i	0.949695	−	0.313177i	$-0.101393\pi$
$337$	−0.914925	−	5.18880i	−0.0498391	−	0.282652i	−0.999534	+	0.0305249i	$0.990282\pi$
$338$	2.75511	+	15.6250i	0.149858	+	0.849890i
$339$	−22.1697	−	16.6855i	−1.20409	−	0.906234i
$340$	1.98725	+	1.66750i	0.107774	+	0.0904329i
$341$	−12.9822	−	22.4858i	−0.703025	−	1.21767i
$342$	−17.3554	−	4.30545i	−0.938475	−	0.232812i
$343$	−0.500000	+	0.866025i	−0.0269975	+	0.0467610i
$344$	6.74386	−	2.45456i	0.363604	−	0.132341i
$345$	−2.10083	−	3.23082i	−0.113105	−	0.173942i
$346$	−13.8989	+	11.6626i	−0.747209	+	0.626983i
$347$	16.2565	+	5.91688i	0.872694	+	0.317635i	0.739258	−	0.673423i	$-0.235177\pi$
$347$	16.2565	+	5.91688i	0.872694	+	0.317635i	0.133436	+	0.991057i	$0.457399\pi$
$348$	6.33196	+	1.93179i	0.339429	+	0.103555i
$349$	1.89577	−	10.7514i	0.101478	−	0.575511i	−0.891090	−	0.453826i	$-0.850059\pi$
$349$	1.89577	−	10.7514i	0.101478	−	0.575511i	0.992569	−	0.121686i	$-0.0388300\pi$
$350$	−4.73660			−0.253182
$351$	18.2782	−	21.1020i	0.975616	−	1.12634i
$352$	−3.09308			−0.164862
$353$	2.51607	−	14.2694i	0.133917	−	0.759482i	−0.841691	−	0.539960i	$-0.818439\pi$
$353$	2.51607	−	14.2694i	0.133917	−	0.759482i	0.975608	−	0.219521i	$-0.0704496\pi$
$354$	−7.71249	+	7.20052i	−0.409914	+	0.382704i
$355$	−1.22095	−	0.444388i	−0.0648011	−	0.0235857i
$356$	1.47740	−	1.23969i	0.0783022	−	0.0657034i
$357$	3.97006	−	7.80306i	0.210118	−	0.412982i
$358$	−9.13602	+	3.32524i	−0.482854	+	0.175744i
$359$	−12.3652	+	21.4171i	−0.652609	+	1.13035i	0.329878	+	0.944024i	$0.392992\pi$
$359$	−12.3652	+	21.4171i	−0.652609	+	1.13035i	−0.982487	+	0.186329i	$0.940341\pi$
$360$	−0.906463	−	1.24455i	−0.0477748	−	0.0655934i
$361$	−8.26380	−	14.3133i	−0.434937	−	0.753333i
$362$	−3.10036	−	2.60151i	−0.162951	−	0.136732i
$363$	−2.28388	+	0.971042i	−0.119873	+	0.0509665i
$364$	−0.932962	−	5.29109i	−0.0489005	−	0.277329i
$365$	−0.869257	−	4.92980i	−0.0454990	−	0.258038i
$366$	8.78106	−	3.73346i	0.458993	−	0.195151i
$367$	7.71748	+	6.47573i	0.402849	+	0.338031i	0.821594	−	0.570073i	$-0.193085\pi$
$367$	7.71748	+	6.47573i	0.402849	+	0.338031i	−0.418745	+	0.908104i	$0.637530\pi$
$368$	2.16767	+	3.75451i	0.112997	+	0.195717i
$369$	17.6437	+	24.2243i	0.918494	+	1.26107i
$370$	−1.66564	+	2.88498i	−0.0865927	+	0.149983i
$371$	2.59450	−	0.944319i	0.134699	−	0.0490266i
$372$	−6.59311	+	12.9586i	−0.341837	+	0.671872i
$373$	15.5677	−	13.0628i	0.806065	−	0.676369i	−0.143600	−	0.989636i	$-0.545868\pi$
$373$	15.5677	−	13.0628i	0.806065	−	0.676369i	0.949665	+	0.313267i	$0.101424\pi$
$374$	14.6917	+	5.34732i	0.759687	+	0.276504i
$375$	6.32647	−	5.90652i	0.326698	−	0.305011i
$376$	−2.35420	+	13.3513i	−0.121409	+	0.688543i
$377$	−20.5351			−1.05761
$378$	−3.40203	+	3.92762i	−0.174982	+	0.202015i
$379$	−7.76186			−0.398700			−0.199350	−	0.979928i	$-0.563883\pi$
$379$	−7.76186			−0.398700			−0.199350	+	0.979928i	$0.563883\pi$
$380$	0.531201	−	3.01259i	0.0272500	−	0.154543i
$381$	−5.80151	−	1.76996i	−0.297220	−	0.0906776i
$382$	4.19094	+	1.52538i	0.214427	+	0.0780451i
$383$	−6.07023	+	5.09353i	−0.310174	+	0.260267i	−0.784564	−	0.620048i	$-0.787113\pi$
$383$	−6.07023	+	5.09353i	−0.310174	+	0.260267i	0.474390	+	0.880315i	$0.342669\pi$
$384$	0.944200	+	1.45206i	0.0481835	+	0.0741003i
$385$	1.49170	−	0.542936i	0.0760243	−	0.0276706i
$386$	12.9296	−	22.3947i	0.658100	−	1.13986i
$387$	20.8966	+	5.18392i	1.06223	+	0.263513i
$388$	−7.43917	−	12.8850i	−0.377667	−	0.654138i
$389$	−5.08046	−	4.26301i	−0.257589	−	0.216143i	0.504843	−	0.863211i	$-0.331550\pi$
$389$	−5.08046	−	4.26301i	−0.257589	−	0.216143i	−0.762432	+	0.647068i	$0.775995\pi$
$390$	3.81594	+	2.87199i	0.193228	+	0.145429i
$391$	−3.80527	−	21.5808i	−0.192441	−	1.09139i
$392$	0.173648	+	0.984808i	0.00877056	+	0.0497403i
$393$	0.237296	−	1.94210i	0.0119700	−	0.0979658i
$394$	6.86005	+	5.75626i	0.345604	+	0.289996i
$395$	2.29312	+	3.97180i	0.115379	+	0.199843i
$396$	−7.69897	−	5.17981i	−0.386888	−	0.260295i
$397$	−14.0377	+	24.3140i	−0.704531	+	1.22028i	0.262329	+	0.964978i	$0.415509\pi$
$397$	−14.0377	+	24.3140i	−0.704531	+	1.22028i	−0.966861	+	0.255305i	$0.917824\pi$
$398$	11.7202	−	4.26581i	0.587482	−	0.213826i
$399$	−10.3094	+	0.546395i	−0.516117	+	0.0273540i
$400$	−3.62845	+	3.04463i	−0.181422	+	0.152231i
$401$	−8.34329	−	3.03671i	−0.416644	−	0.151646i	0.125187	−	0.992133i	$-0.460047\pi$
$401$	−8.34329	−	3.03671i	−0.416644	−	0.151646i	−0.541832	+	0.840487i	$0.682269\pi$
$402$	−0.675033	−	2.91604i	−0.0336676	−	0.145439i
$403$	7.83159	−	44.4152i	0.390119	−	2.21248i
$404$	−6.13923			−0.305438
$405$	−0.172097	−	4.61579i	−0.00855157	−	0.229361i
$406$	3.82211			0.189688
$407$	−3.48633	+	19.7720i	−0.172811	+	0.980060i
$408$	−1.97447	−	8.52940i	−0.0977508	−	0.422268i
$409$	1.49844	+	0.545386i	0.0740929	+	0.0269676i	0.378801	−	0.925478i	$-0.376337\pi$
$409$	1.49844	+	0.545386i	0.0740929	+	0.0269676i	−0.304708	+	0.952446i	$0.598559\pi$
$410$	−3.92739	+	3.29547i	−0.193960	+	0.162752i
$411$	24.1855	−	1.28182i	1.19298	−	0.0632276i
$412$	2.97190	−	1.08168i	0.146415	−	0.0532906i
$413$	−3.04590	+	5.27565i	−0.149879	+	0.259598i
$414$	−0.891938	+	12.9754i	−0.0438364	+	0.637705i
$415$	−2.22647	−	3.85635i	−0.109293	−	0.189301i
$416$	−4.11574	−	3.45351i	−0.201791	−	0.169323i
$417$	4.25003	−	34.7834i	0.208125	−	1.70335i
$418$	−3.20144	−	18.1562i	−0.156587	−	0.888051i
$419$	2.23949	+	12.7008i	0.109406	+	0.620474i	0.989369	+	0.145430i	$0.0464566\pi$
$419$	2.23949	+	12.7008i	0.109406	+	0.620474i	−0.879962	+	0.475043i	$0.842432\pi$
$420$	−0.710244	−	0.534550i	−0.0346564	−	0.0260834i
$421$	−24.8963	−	20.8905i	−1.21337	−	1.01814i	−0.999145	−	0.0413543i	$-0.986833\pi$
$421$	−24.8963	−	20.8905i	−1.21337	−	1.01814i	−0.214226	−	0.976784i	$-0.568723\pi$
$422$	3.93260	+	6.81146i	0.191436	+	0.331577i
$423$	−28.2185	+	29.2903i	−1.37203	+	1.42414i
$424$	1.38050	−	2.39110i	0.0670431	−	0.116122i
$425$	22.4981	−	8.18864i	1.09132	−	0.397207i
$426$	2.39039	+	3.67613i	0.115815	+	0.178109i
$427$	4.22010	−	3.54109i	0.204225	−	0.171365i
$428$	9.66245	+	3.51684i	0.467052	+	0.169993i
$429$	27.5309	+	8.39928i	1.32921	+	0.405521i
$430$	−0.639585	+	3.62727i	−0.0308435	+	0.174922i
$431$	19.5805			0.943162			0.471581	−	0.881823i	$-0.343684\pi$
$431$	19.5805			0.943162			0.471581	+	0.881823i	$0.343684\pi$
$432$	−0.0814873	+	5.19551i	−0.00392056	+	0.249969i
$433$	−3.07569			−0.147808			−0.0739041	−	0.997265i	$-0.523546\pi$
$433$	−3.07569			−0.147808			−0.0739041	+	0.997265i	$0.523546\pi$
$434$	−1.45766	+	8.26680i	−0.0699699	+	0.396819i
$435$	−2.48346	+	2.31861i	−0.119073	+	0.111169i
$436$	12.4082	+	4.51621i	0.594244	+	0.216287i
$437$	−19.7952	+	16.6101i	−0.946931	+	0.794570i
$438$	−7.66084	+	15.0572i	−0.366049	+	0.719461i
$439$	18.4782	−	6.72550i	0.881914	−	0.320991i	0.138932	−	0.990302i	$-0.455633\pi$
$439$	18.4782	−	6.72550i	0.881914	−	0.320991i	0.742982	+	0.669311i	$0.233411\pi$
$440$	0.793719	−	1.37476i	0.0378391	−	0.0655392i
$441$	−1.21697	+	2.74207i	−0.0579512	+	0.130575i
$442$	13.5787	+	23.5189i	0.645871	+	1.11868i
$443$	20.0199	+	16.7987i	0.951176	+	0.798131i	0.979495	−	0.201468i	$-0.0645711\pi$
$443$	20.0199	+	16.7987i	0.951176	+	0.798131i	−0.0283195	+	0.999599i	$0.509016\pi$
$444$	10.3463	−	4.39895i	0.491013	−	0.208765i
$445$	0.171878	+	0.974769i	0.00814781	+	0.0462085i
$446$	2.96783	+	16.8314i	0.140531	+	0.796989i
$447$	27.2059	−	11.5672i	1.28679	−	0.547108i
$448$	0.766044	+	0.642788i	0.0361922	+	0.0303689i
$449$	11.2401	+	19.4685i	0.530455	+	0.918775i	0.999369	+	0.0355311i	$0.0113123\pi$
$449$	11.2401	+	19.4685i	0.530455	+	0.918775i	−0.468913	+	0.883244i	$0.655354\pi$
$450$	−14.1302	+	1.50201i	−0.666104	+	0.0708053i
$451$	−15.4492	+	26.7588i	−0.727476	+	1.26002i
$452$	−15.0537	+	5.47909i	−0.708066	+	0.257715i
$453$	−3.34609	+	6.57665i	−0.157213	+	0.308998i
$454$	−5.05684	+	4.24319i	−0.237329	+	0.199143i
$455$	2.59110	+	0.943085i	0.121473	+	0.0442125i
$456$	−7.54626	+	7.04533i	−0.353386	+	0.329928i
$457$	−4.41730	+	25.0517i	−0.206633	+	1.17187i	0.688218	+	0.725504i	$0.258393\pi$
$457$	−4.41730	+	25.0517i	−0.206633	+	1.17187i	−0.894850	+	0.446367i	$0.852718\pi$
$458$	−4.76841			−0.222813
$459$	9.36906	−	24.5370i	0.437310	−	1.14529i
$460$	−2.22499			−0.103741
$461$	0.234704	−	1.33107i	0.0109313	−	0.0619943i	−0.978854	−	0.204559i	$-0.934424\pi$
$461$	0.234704	−	1.33107i	0.0109313	−	0.0619943i	0.989785	+	0.142565i	$0.0455350\pi$
$462$	−5.12421	−	1.56332i	−0.238400	−	0.0727323i
$463$	7.33409	+	2.66939i	0.340844	+	0.124057i	0.506770	−	0.862081i	$-0.330839\pi$
$463$	7.33409	+	2.66939i	0.340844	+	0.124057i	−0.165926	+	0.986138i	$0.553061\pi$
$464$	2.92791	−	2.45680i	0.135925	−	0.114054i
$465$	−4.06776	−	6.25571i	−0.188638	−	0.290102i
$466$	17.0184	−	6.19418i	0.788361	−	0.286940i
$467$	10.5654	−	18.2997i	0.488907	−	0.846811i	−0.511012	−	0.859574i	$-0.670729\pi$
$467$	10.5654	−	18.2997i	0.488907	−	0.846811i	0.999919	+	0.0127624i	$0.00406250\pi$
$468$	−4.46105	−	15.4885i	−0.206212	−	0.715956i
$469$	−0.864048	−	1.49658i	−0.0398980	−	0.0691054i
$470$	−5.33007	−	4.47246i	−0.245858	−	0.206299i
$471$	−5.85174	−	4.40419i	−0.269634	−	0.202934i
$472$	1.05783	+	5.99925i	0.0486906	+	0.276138i
$473$	3.85465	+	21.8608i	0.177237	+	1.00516i
$474$	1.87722	−	15.3636i	0.0862234	−	0.705676i
$475$	−21.6274	−	18.1475i	−0.992332	−	0.832666i
$476$	−2.52734	−	4.37748i	−0.115840	−	0.200641i
$477$	7.44043	−	3.63982i	0.340674	−	0.166656i
$478$	−11.7942	+	20.4282i	−0.539454	+	0.934362i
$479$	8.92520	−	3.24851i	0.407803	−	0.148428i	−0.129970	−	0.991518i	$-0.541488\pi$
$479$	8.92520	−	3.24851i	0.407803	−	0.148428i	0.537773	+	0.843090i	$0.319266\pi$
$480$	−0.887681	+	0.0470467i	−0.0405169	+	0.00214738i
$481$	−26.7150	+	22.4165i	−1.21810	+	1.02211i
$482$	−20.4914	−	7.45827i	−0.933359	−	0.339715i
$483$	1.69348	+	7.31556i	0.0770559	+	0.332870i
$484$	−0.248809	+	1.41107i	−0.0113095	+	0.0641394i
$485$	7.63589			0.346728
$486$	−8.90345	+	12.7956i	−0.403869	+	0.580422i
$487$	−3.92885			−0.178033			−0.0890166	−	0.996030i	$-0.528372\pi$
$487$	−3.92885			−0.178033			−0.0890166	+	0.996030i	$0.528372\pi$
$488$	0.956620	−	5.42526i	0.0433041	−	0.245590i
$489$	−3.09438	−	13.3672i	−0.139933	−	0.604487i
$490$	−0.482271	−	0.175532i	−0.0217868	−	0.00792974i
$491$	23.7854	−	19.9584i	1.07342	−	0.900708i	0.0780641	−	0.996948i	$-0.475126\pi$
$491$	23.7854	−	19.9584i	1.07342	−	0.900708i	0.995358	+	0.0962401i	$0.0306817\pi$
$492$	17.2781	−	0.915733i	0.778958	−	0.0412844i
$493$	−18.1544	+	6.60766i	−0.817633	+	0.297594i
$494$	16.0120	−	27.7337i	0.720416	−	1.24780i
$495$	4.27787	−	2.09271i	0.192276	−	0.0940604i
$496$	4.19717	+	7.26970i	0.188458	+	0.326419i
$497$	1.93936	+	1.62732i	0.0869923	+	0.0729952i
$498$	−1.82265	+	14.9171i	−0.0816749	+	0.668450i
$499$	−2.97273	−	16.8592i	−0.133078	−	0.754721i	−0.976179	−	0.216966i	$-0.930384\pi$
$499$	−2.97273	−	16.8592i	−0.133078	−	0.754721i	0.843101	−	0.537754i	$-0.180727\pi$
$500$	−0.867727	−	4.92112i	−0.0388059	−	0.220079i
$501$	6.37531	+	4.79824i	0.284828	+	0.214370i
$502$	7.49070	+	6.28544i	0.334326	+	0.280533i
$503$	−12.9850	−	22.4906i	−0.578971	−	1.00281i	−0.995598	−	0.0937298i	$-0.970121\pi$
$503$	−12.9850	−	22.4906i	−0.578971	−	1.00281i	0.416626	−	0.909078i	$-0.363212\pi$
$504$	0.830315	+	2.88281i	0.0369852	+	0.128410i
$505$	1.57540	−	2.72866i	0.0701042	−	0.121424i
$506$	−12.6008	+	4.58633i	−0.560176	+	0.203887i
$507$	14.9807	+	23.0385i	0.665318	+	1.02318i
$508$	−2.68262	+	2.25099i	−0.119022	+	0.0998714i
$509$	−14.6986	−	5.34985i	−0.651503	−	0.237128i	−0.00493966	−	0.999988i	$-0.501572\pi$
$509$	−14.6986	−	5.34985i	−0.651503	−	0.237128i	−0.646564	+	0.762860i	$0.723795\pi$
$510$	4.29768	+	1.31116i	0.190304	+	0.0580591i
$511$	−1.69372	+	9.60559i	−0.0749260	+	0.424926i
$512$	1.00000			0.0441942
$513$	−30.5817	+	4.89919i	−1.35022	+	0.216304i
$514$	12.1872			0.537556
$515$	−0.281853	+	1.59847i	−0.0124199	+	0.0704370i
$516$	9.08597	−	8.48284i	0.399988	−	0.373436i
$517$	−39.4050	−	14.3422i	−1.73303	−	0.630771i
$518$	4.97234	−	4.17229i	0.218472	−	0.183320i
$519$	−14.2505	+	28.0090i	−0.625528	+	1.22946i
$520$	2.59110	−	0.943085i	0.113627	−	0.0413570i
$521$	3.00491	−	5.20465i	0.131647	−	0.228020i	−0.792664	−	0.609658i	$-0.791307\pi$
$521$	3.00491	−	5.20465i	0.131647	−	0.228020i	0.924312	+	0.381638i	$0.124640\pi$
$522$	11.4021	−	1.21202i	0.499056	−	0.0530485i
$523$	−19.4382	−	33.6680i	−0.849974	−	1.47220i	−0.881230	−	0.472687i	$-0.843284\pi$
$523$	−19.4382	−	33.6680i	−0.849974	−	1.47220i	0.0312557	−	0.999511i	$-0.490049\pi$
$524$	−0.865330	−	0.726098i	−0.0378021	−	0.0317198i
$525$	−7.54996	+	3.21003i	−0.329507	+	0.140097i
$526$	0.583063	+	3.30671i	0.0254228	+	0.144180i
$527$	−7.36800	−	41.7860i	−0.320955	−	1.82023i
$528$	−4.93026	+	2.09620i	−0.214562	+	0.0912256i
$529$	−3.22114	−	2.70286i	−0.140050	−	0.117516i
$530$	0.708504	+	1.22717i	0.0307755	+	0.0533046i
$531$	−7.41356	+	16.7042i	−0.321721	+	0.724899i
$532$	−2.98025	+	5.16195i	−0.129210	+	0.223799i
$533$	−50.4342	+	18.3565i	−2.18455	+	0.795110i
$534$	1.51478	−	2.97726i	0.0655509	−	0.128839i
$535$	−4.04260	+	3.39214i	−0.174777	+	0.146655i
$536$	−1.62388	−	0.591044i	−0.0701409	−	0.0255292i
$537$	−12.3089	+	11.4918i	−0.531169	+	0.495910i
$538$	1.09999	−	6.23838i	0.0474241	−	0.268955i
$539$	−3.09308			−0.133229
$540$	−2.28830	−	1.36944i	−0.0984730	−	0.0589315i
$541$	−11.6829			−0.502287			−0.251144	−	0.967950i	$-0.580807\pi$
$541$	−11.6829			−0.502287			−0.251144	+	0.967950i	$0.580807\pi$
$542$	−4.63048	+	26.2607i	−0.198896	+	1.12800i
$543$	−6.70492	−	2.04557i	−0.287736	−	0.0877840i
$544$	−4.74984	−	1.72880i	−0.203648	−	0.0741217i
$545$	−5.19137	+	4.35607i	−0.222374	+	0.186594i
$546$	−5.07292	−	7.80152i	−0.217101	−	0.333874i
$547$	−30.4578	+	11.0857i	−1.30228	+	0.473992i	−0.897739	−	0.440528i	$-0.854791\pi$
$547$	−30.4578	+	11.0857i	−1.30228	+	0.473992i	−0.404542	+	0.914519i	$0.632569\pi$
$548$	6.99156	−	12.1097i	0.298664	−	0.517302i
$549$	11.4665	−	11.9020i	0.489378	−	0.507964i
$550$	−7.32535	−	12.6879i	−0.312354	−	0.541013i
$551$	17.4518	+	14.6438i	0.743471	+	0.623847i
$552$	5.99963	+	4.51550i	0.255361	+	0.192192i
$553$	−1.55175	−	8.80041i	−0.0659871	−	0.374232i
$554$	−4.99847	−	28.3477i	−0.212365	−	1.20438i
$555$	−0.699801	+	5.72736i	−0.0297049	+	0.243113i
$556$	−15.4983	−	13.0046i	−0.657273	−	0.551518i
$557$	18.7993	+	32.5613i	0.796550	+	1.37967i	0.921850	+	0.387546i	$0.126677\pi$
$557$	18.7993	+	32.5613i	0.796550	+	1.37967i	−0.125300	+	0.992119i	$0.539989\pi$
$558$	−1.72703	+	25.1237i	−0.0731108	+	1.06357i
$559$	−19.2791	+	33.3924i	−0.815418	+	1.41235i
$560$	−0.482271	+	0.175532i	−0.0203797	+	0.00741759i
$561$	27.0418	−	1.43321i	1.14171	−	0.0605100i
$562$	−3.47016	+	2.91181i	−0.146380	+	0.122827i
$563$	−26.2543	−	9.55578i	−1.10649	−	0.402728i	−0.276783	−	0.960933i	$-0.589268\pi$
$563$	−26.2543	−	9.55578i	−1.10649	−	0.402728i	−0.829703	+	0.558205i	$0.811490\pi$
$564$	5.29579	+	22.8770i	0.222993	+	0.963295i
$565$	1.42769	−	8.09681i	0.0600632	−	0.340635i
$566$	10.9122			0.458674
$567$	−2.76094	+	8.56605i	−0.115949	+	0.359740i
$568$	2.53166			0.106226
$569$	−2.21987	+	12.5895i	−0.0930616	+	0.527778i	0.902263	+	0.431187i	$0.141905\pi$
$569$	−2.21987	+	12.5895i	−0.0930616	+	0.527778i	−0.995324	+	0.0965914i	$0.969206\pi$
$570$	−1.19494	−	5.16195i	−0.0500505	−	0.216210i
$571$	9.72516	+	3.53967i	0.406985	+	0.148131i	0.537397	−	0.843329i	$-0.319408\pi$
$571$	9.72516	+	3.53967i	0.406985	+	0.148131i	−0.130412	+	0.991460i	$0.541630\pi$
$572$	12.7303	−	10.6820i	0.532282	−	0.446637i
$573$	7.71395	−	0.408836i	0.322255	−	0.0170794i
$574$	9.38709	−	3.41662i	0.391809	−	0.142607i
$575$	−10.2674	+	17.7836i	−0.428179	+	0.741628i
$576$	2.48909	+	1.67464i	0.103712	+	0.0697768i
$577$	−10.5631	−	18.2958i	−0.439748	−	0.761665i	0.557922	−	0.829893i	$-0.311599\pi$
$577$	−10.5631	−	18.2958i	−0.439748	−	0.761665i	−0.997670	+	0.0682282i	$0.978265\pi$
$578$	6.54947	+	5.49566i	0.272422	+	0.228589i
$579$	5.43223	−	44.4588i	0.225756	−	1.84765i
$580$	0.340627	+	1.93179i	0.0141438	+	0.0802132i
$581$	1.50665	+	8.54461i	0.0625062	+	0.354490i
$582$	−20.5900	−	15.4966i	−0.853484	−	0.642357i
$583$	6.54203	+	5.48942i	0.270943	+	0.227348i
$584$	4.87689	+	8.44701i	0.201807	+	0.349540i
$585$	8.02883	+	1.99175i	0.331951	+	0.0823487i
$586$	4.02253	−	6.96723i	0.166169	−	0.287814i
$587$	2.62900	−	0.956877i	0.108510	−	0.0394945i	−0.287194	−	0.957872i	$-0.592723\pi$
$587$	2.62900	−	0.956877i	0.108510	−	0.0394945i	0.395705	+	0.918378i	$0.370500\pi$
$588$	0.944200	+	1.45206i	0.0389381	+	0.0598821i
$589$	−38.3286	+	32.1615i	−1.57930	+	1.32519i
$590$	−2.93790	−	1.06931i	−0.120951	−	0.0440227i
$591$	14.8357	+	4.52616i	0.610260	+	0.186181i
$592$	1.12714	−	6.39232i	0.0463251	−	0.262723i
$593$	36.6385			1.50456			0.752281	−	0.658842i	$-0.228954\pi$
$593$	36.6385			1.50456			0.752281	+	0.658842i	$0.228954\pi$
$594$	−15.7822	−	3.03877i	−0.647553	−	0.124682i
$595$	2.59417			0.106351
$596$	2.96384	−	16.8088i	0.121404	−	0.688515i
$597$	15.7906	−	14.7424i	0.646267	−	0.603367i
$598$	−21.8878	−	7.96650i	−0.895058	−	0.325775i
$599$	7.47015	−	6.26820i	0.305222	−	0.256112i	−0.477292	−	0.878745i	$-0.658382\pi$
$599$	7.47015	−	6.26820i	0.305222	−	0.256112i	0.782514	+	0.622633i	$0.213937\pi$
$600$	−3.72024	+	7.31205i	−0.151878	+	0.298513i
$601$	−20.2947	+	7.38665i	−0.827836	+	0.301308i	−0.720971	−	0.692966i	$-0.756304\pi$
$601$	−20.2947	+	7.38665i	−0.827836	+	0.301308i	−0.106866	+	0.994273i	$0.534082\pi$
$602$	3.58833	−	6.21517i	0.146249	−	0.253312i
$603$	−3.05220	−	4.19058i	−0.124295	−	0.170654i
$604$	2.13012	+	3.68947i	0.0866732	+	0.150122i
$605$	−0.563320	−	0.472682i	−0.0229022	−	0.0192173i
$606$	−9.78570	+	4.16060i	−0.397517	+	0.169013i
$607$	−1.42435	−	8.07788i	−0.0578125	−	0.327871i	0.942161	−	0.335161i	$-0.108791\pi$
$607$	−1.42435	−	8.07788i	−0.0578125	−	0.327871i	−0.999973	+	0.00728976i	$0.997680\pi$
$608$	1.03503	+	5.86995i	0.0419760	+	0.238058i
$609$	6.09229	−	2.59027i	0.246872	−	0.104963i
$610$	2.16585	+	1.81736i	0.0876927	+	0.0735829i
$611$	−36.4198	−	63.0809i	−1.47339	−	2.55198i
$612$	−8.92766	−	12.2574i	−0.360879	−	0.495477i
$613$	18.8418	−	32.6349i	0.761012	−	1.31811i	−0.181318	−	0.983425i	$-0.558036\pi$
$613$	18.8418	−	32.6349i	0.761012	−	1.31811i	0.942330	−	0.334686i	$-0.108630\pi$
$614$	13.0739	−	4.75852i	0.527621	−	0.192038i
$615$	−4.02675	+	7.91448i	−0.162374	+	0.319143i
$616$	−2.36944	+	1.98820i	−0.0954674	+	0.0801067i
$617$	−42.3929	−	15.4298i	−1.70667	−	0.621179i	−0.710117	−	0.704084i	$-0.751358\pi$
$617$	−42.3929	−	15.4298i	−1.70667	−	0.621179i	−0.996557	+	0.0829055i	$0.973580\pi$
$618$	4.00402	−	3.73823i	0.161065	−	0.150374i
$619$	3.45021	−	19.5671i	0.138676	−	0.786468i	−0.833554	−	0.552438i	$-0.813697\pi$
$619$	3.45021	−	19.5671i	0.138676	−	0.786468i	0.972229	−	0.234030i	$-0.0751914\pi$
$620$	−4.30816			−0.173020
$621$	7.37179	+	21.2867i	0.295820	+	0.854207i
$622$	−33.8085			−1.35560
$623$	0.334900	−	1.89931i	0.0134175	−	0.0760944i
$624$	−8.90080	−	2.71551i	−0.356317	−	0.108707i
$625$	−19.8448	−	7.22293i	−0.793793	−	0.288917i
$626$	3.00461	−	2.52117i	0.120088	−	0.100766i
$627$	−17.4076	−	26.7707i	−0.695192	−	1.06912i
$628$	−3.97346	+	1.44622i	−0.158558	+	0.0577105i
$629$	−16.4048	+	28.4139i	−0.654101	+	1.13294i
$630$	−1.49437	−	0.370715i	−0.0595371	−	0.0147697i
$631$	17.5749	+	30.4407i	0.699647	+	1.21182i	0.968589	+	0.248668i	$0.0799929\pi$
$631$	17.5749	+	30.4407i	0.699647	+	1.21182i	−0.268941	+	0.963157i	$0.586674\pi$
$632$	−6.84550	−	5.74406i	−0.272300	−	0.228486i
$633$	10.8846	+	8.19205i	0.432623	+	0.325605i
$634$	0.849946	+	4.82029i	0.0337557	+	0.191438i
$635$	−0.312091	−	1.76996i	−0.0123850	−	0.0702386i
$636$	0.580002	−	4.74690i	0.0229986	−	0.188227i
$637$	−4.11574	−	3.45351i	−0.163072	−	0.136833i
$638$	5.91105	+	10.2382i	0.234021	+	0.405336i
$639$	6.30153	+	4.23962i	0.249285	+	0.167717i
$640$	−0.256611	+	0.444463i	−0.0101434	+	0.0175690i
$641$	7.69810	−	2.80188i	0.304057	−	0.110668i	−0.185486	−	0.982647i	$-0.559386\pi$
$641$	7.69810	−	2.80188i	0.304057	−	0.110668i	0.489543	+	0.871979i	$0.337164\pi$
$642$	17.7850	−	0.942595i	0.701916	−	0.0372013i
$643$	7.84382	−	6.58174i	0.309330	−	0.259559i	−0.474885	−	0.880048i	$-0.657510\pi$
$643$	7.84382	−	6.58174i	0.309330	−	0.259559i	0.784215	+	0.620489i	$0.213066\pi$
$644$	4.07388	+	1.48277i	0.160533	+	0.0584293i
$645$	1.43875	+	6.21517i	0.0566507	+	0.244722i
$646$	5.23174	−	29.6707i	0.205840	−	1.16738i
$647$	22.9408			0.901895			0.450947	−	0.892551i	$-0.351086\pi$
$647$	22.9408			0.901895			0.450947	+	0.892551i	$0.351086\pi$
$648$	3.39115	+	8.33667i	0.133217	+	0.327495i
$649$	−18.8424			−0.739630
$650$	4.41907	−	25.0618i	0.173330	−	0.983005i
$651$	3.27901	+	14.1648i	0.128515	+	0.555163i
$652$	−7.44393	−	2.70937i	−0.291527	−	0.106107i
$653$	−18.0260	+	15.1256i	−0.705412	+	0.591911i	−0.923308	−	0.384061i	$-0.874525\pi$
$653$	−18.0260	+	15.1256i	−0.705412	+	0.591911i	0.217895	+	0.975972i	$0.430081\pi$
$654$	22.8388	−	1.21045i	0.893069	−	0.0473323i
$655$	0.544777	−	0.198283i	0.0212862	−	0.00774755i
$656$	4.99477	−	8.65119i	0.195013	−	0.337772i
$657$	−2.00671	+	29.1924i	−0.0782893	+	1.13890i
$658$	6.77865	+	11.7410i	0.264259	+	0.457711i
$659$	15.2377	+	12.7859i	0.593575	+	0.498068i	0.889373	−	0.457182i	$-0.151141\pi$
$659$	15.2377	+	12.7859i	0.593575	+	0.498068i	−0.295798	+	0.955250i	$0.595586\pi$
$660$	0.333472	−	2.72923i	0.0129804	−	0.106235i
$661$	−2.83097	−	16.0552i	−0.110112	−	0.624477i	−0.989055	−	0.147549i	$-0.952862\pi$
$661$	−2.83097	−	16.0552i	−0.110112	−	0.624477i	0.878943	−	0.476928i	$-0.158250\pi$
$662$	−3.79111	−	21.5004i	−0.147346	−	0.835638i
$663$	37.5828	+	28.2859i	1.45960	+	1.09853i
$664$	6.64653	+	5.57710i	0.257935	+	0.216433i
$665$	−1.52953	−	2.64923i	−0.0593127	−	0.102733i
$666$	13.5104	−	14.0235i	0.523517	−	0.543400i
$667$	8.28505	−	14.3501i	0.320799	−	0.555639i
$668$	4.32897	−	1.57562i	0.167493	−	0.0609624i
$669$	16.1373	+	24.8172i	0.623906	+	0.959490i
$670$	0.679403	−	0.570086i	0.0262476	−	0.0220244i
$671$	16.0120	+	5.82791i	0.618138	+	0.224984i
$672$	1.65667	+	0.505425i	0.0639073	+	0.0194972i
$673$	4.81479	−	27.3060i	0.185597	−	1.05257i	−0.739590	−	0.673058i	$-0.764981\pi$
$673$	4.81479	−	27.3060i	0.185597	−	1.05257i	0.925187	−	0.379513i	$-0.123908\pi$
$674$	−5.26884			−0.202948
$675$	−21.5051	+	11.9703i	−0.827731	+	0.460736i
$676$	15.8661			0.610234
$677$	3.75569	−	21.2996i	0.144343	−	0.818610i	−0.823549	−	0.567245i	$-0.808009\pi$
$677$	3.75569	−	21.2996i	0.144343	−	0.818610i	0.967892	−	0.251365i	$-0.0808796\pi$
$678$	−20.2818	+	18.9354i	−0.778917	+	0.727211i
$679$	−13.9811	−	5.08869i	−0.536544	−	0.195286i
$680$	1.98725	−	1.66750i	0.0762076	−	0.0639457i
$681$	−5.18476	+	10.1905i	−0.198681	+	0.390502i
$682$	−24.3985	+	8.88034i	−0.934268	+	0.340046i
$683$	8.72771	−	15.1168i	0.333957	−	0.578430i	−0.649327	−	0.760509i	$-0.724949\pi$
$683$	8.72771	−	15.1168i	0.333957	−	0.578430i	0.983284	+	0.182079i	$0.0582828\pi$
$684$	−7.25378	+	16.3441i	−0.277355	+	0.624934i
$685$	3.58822	+	6.21498i	0.137099	+	0.237462i
$686$	0.766044	+	0.642788i	0.0292477	+	0.0245417i
$687$	−7.60066	+	3.23158i	−0.289983	+	0.123293i
$688$	−1.24621	−	7.06763i	−0.0475115	−	0.269451i
$689$	2.57591	+	14.6087i	0.0981345	+	0.556548i
$690$	−3.54654	+	1.50789i	−0.135015	+	0.0574044i
$691$	3.38648	+	2.84159i	0.128828	+	0.108099i	0.704925	−	0.709282i	$-0.250981\pi$
$691$	3.38648	+	2.84159i	0.128828	+	0.108099i	−0.576097	+	0.817381i	$0.695425\pi$
$692$	9.07186	+	15.7129i	0.344860	+	0.597316i
$693$	−9.22727	+	0.980837i	−0.350515	+	0.0372589i
$694$	8.64990	−	14.9821i	0.328346	−	0.568711i
$695$	9.75709	−	3.55129i	0.370108	−	0.134708i
$696$	3.00198	−	5.90031i	0.113790	−	0.223651i
$697$	−38.6805	+	32.4568i	−1.46513	+	1.22939i
$698$	−10.2589	−	3.73394i	−0.388305	−	0.141332i
$699$	22.9288	−	21.4068i	0.867247	−	0.809678i
$700$	−0.822502	+	4.66464i	−0.0310877	+	0.176307i
$701$	16.3363			0.617014			0.308507	−	0.951222i	$-0.400171\pi$
$701$	16.3363			0.617014			0.308507	+	0.951222i	$0.400171\pi$
$702$	−17.6074	−	21.6648i	−0.664549	−	0.817685i
$703$	38.6892			1.45919
$704$	−0.537108	+	3.04609i	−0.0202430	+	0.114804i
$705$	−11.5269	−	3.51670i	−0.434130	−	0.132447i
$706$	−13.6157	−	4.95570i	−0.512432	−	0.186510i
$707$	−4.70293	+	3.94622i	−0.176872	+	0.148413i
$708$	5.75187	+	8.84567i	0.216169	+	0.332441i
$709$	26.2680	−	9.56078i	0.986517	−	0.359063i	0.202146	−	0.979355i	$-0.435208\pi$
$709$	26.2680	−	9.56078i	0.986517	−	0.359063i	0.784370	+	0.620293i	$0.212986\pi$
$710$	−0.649651	+	1.12523i	−0.0243810	+	0.0422291i
$711$	−7.41984	−	25.7613i	−0.278266	−	0.966123i
$712$	−0.964307	−	1.67023i	−0.0361389	−	0.0625944i
$713$	27.8780	+	23.3925i	1.04404	+	0.876054i
$714$	−6.99512	−	5.26473i	−0.261786	−	0.197028i
$715$	1.48102	+	8.39928i	0.0553870	+	0.314115i
$716$	1.68827	+	9.57464i	0.0630935	+	0.357821i
$717$	−4.95520	+	40.5547i	−0.185055	+	1.51454i
$718$	18.9446	+	15.8964i	0.707005	+	0.593247i
$719$	−10.0464	−	17.4008i	−0.374666	−	0.648941i	0.615611	−	0.788050i	$-0.288909\pi$
$719$	−10.0464	−	17.4008i	−0.374666	−	0.648941i	−0.990277	+	0.139109i	$0.955576\pi$
$720$	−1.38305	+	0.676578i	−0.0515431	+	0.0252146i
$721$	1.58131	−	2.73891i	0.0588912	−	0.102002i
$722$	−15.5309	+	5.65277i	−0.577999	+	0.210374i
$723$	−37.7171	+	1.99899i	−1.40271	+	0.0743432i
$724$	−3.10036	+	2.60151i	−0.115224	+	0.0966845i
$725$	17.0120	+	6.19187i	0.631811	+	0.229960i
$726$	0.559698	+	2.41781i	0.0207723	+	0.0897332i
$727$	−5.47673	+	31.0601i	−0.203121	+	1.15195i	0.697249	+	0.716829i	$0.254407\pi$
$727$	−5.47673	+	31.0601i	−0.203121	+	1.15195i	−0.900370	+	0.435126i	$0.856704\pi$
$728$	−5.37272			−0.199126
$729$	−5.52007	+	26.4297i	−0.204447	+	0.978878i
$730$	−5.00585			−0.185275
$731$	−6.29921	+	35.7246i	−0.232985	+	1.32132i
$732$	−2.15192	−	9.29597i	−0.0795373	−	0.343589i
$733$	30.1139	+	10.9606i	1.11228	+	0.404838i	0.831830	−	0.555030i	$-0.187293\pi$
$733$	30.1139	+	10.9606i	1.11228	+	0.404838i	0.280452	+	0.959868i	$0.409516\pi$
$734$	7.71748	−	6.47573i	0.284857	−	0.239024i
$735$	−0.887681	+	0.0470467i	−0.0327426	+	0.00173534i
$736$	4.07388	−	1.48277i	0.150165	−	0.0546557i
$737$	2.67257	−	4.62903i	0.0984455	−	0.170513i
$738$	26.9201	−	13.1691i	0.990941	−	0.484763i
$739$	23.4176	+	40.5605i	0.861431	+	1.49204i	0.870548	+	0.492084i	$0.163765\pi$
$739$	23.4176	+	40.5605i	0.861431	+	1.49204i	−0.00911643	+	0.999958i	$0.502902\pi$
$740$	2.55191	+	2.14131i	0.0938102	+	0.0787161i
$741$	6.72728	−	55.0579i	0.247133	−	2.02260i
$742$	−0.479443	−	2.71906i	−0.0176009	−	0.0998198i
$743$	−7.11612	−	40.3575i	−0.261065	−	1.48057i	−0.780011	−	0.625766i	$-0.784786\pi$
$743$	−7.11612	−	40.3575i	−0.261065	−	1.48057i	0.518946	−	0.854807i	$-0.326325\pi$
$744$	11.6168	+	8.74318i	0.425894	+	0.320541i
$745$	6.71034	+	5.63064i	0.245848	+	0.206291i
$746$	−10.1611	−	17.5995i	−0.372024	−	0.644365i
$747$	7.20417	+	25.0125i	0.263587	+	0.915158i
$748$	7.81726	−	13.5399i	0.285827	−	0.495068i
$749$	9.66245	−	3.51684i	0.353058	−	0.128503i
$750$	−4.71820	−	7.25602i	−0.172284	−	0.264952i
$751$	−16.1793	+	13.5761i	−0.590393	+	0.495398i	−0.888341	−	0.459184i	$-0.848142\pi$
$751$	−16.1793	+	13.5761i	−0.590393	+	0.495398i	0.297949	+	0.954582i	$0.403698\pi$
$752$	12.7397	+	4.63687i	0.464569	+	0.169089i
$753$	16.1996	+	4.94226i	0.590345	+	0.180106i
$754$	−3.56588	+	20.2231i	−0.129862	+	0.736483i
$755$	−2.18644			−0.0795728
$756$	3.27719	+	4.03237i	0.119190	+	0.146656i
$757$	48.2596			1.75402			0.877012	−	0.480468i	$-0.159533\pi$
$757$	48.2596			1.75402			0.877012	+	0.480468i	$0.159533\pi$
$758$	−1.34783	+	7.64394i	−0.0489555	+	0.277640i
$759$	−16.9771	+	15.8501i	−0.616229	+	0.575323i
$760$	−2.87458	−	1.04626i	−0.104272	−	0.0379519i
$761$	27.2550	−	22.8697i	0.987994	−	0.829025i	0.00271790	−	0.999996i	$-0.499135\pi$
$761$	27.2550	−	22.8697i	0.987994	−	0.829025i	0.985276	+	0.170971i	$0.0546904\pi$
$762$	−2.75049	+	5.40602i	−0.0996397	+	0.195839i
$763$	12.4082	−	4.51621i	0.449206	−	0.163498i
$764$	2.22995	−	3.86239i	0.0806768	−	0.139736i
$765$	7.73891	−	0.822629i	0.279801	−	0.0297422i
$766$	3.96206	+	6.86250i	0.143155	+	0.247952i
$767$	−25.0722	−	21.0381i	−0.905306	−	0.759642i
$768$	1.59396	−	0.677707i	0.0575171	−	0.0244546i
$769$	−1.86313	−	10.5663i	−0.0671861	−	0.381031i	−0.999797	−	0.0201477i	$-0.993586\pi$
$769$	−1.86313	−	10.5663i	−0.0671861	−	0.381031i	0.932611	−	0.360883i	$-0.117525\pi$
$770$	−0.275656	−	1.56332i	−0.00993395	−	0.0563382i
$771$	19.4260	−	8.25938i	0.699610	−	0.297454i
$772$	−19.8093	−	16.6220i	−0.712952	−	0.598238i
$773$	2.35031	+	4.07086i	0.0845350	+	0.146419i	0.905193	−	0.425001i	$-0.139726\pi$
$773$	2.35031	+	4.07086i	0.0845350	+	0.146419i	−0.820658	+	0.571420i	$0.806393\pi$
$774$	8.73382	−	19.6789i	0.313931	−	0.707345i
$775$	−19.8803	+	34.4337i	−0.714122	+	1.23690i
$776$	−13.9811	+	5.08869i	−0.501891	+	0.182673i
$777$	5.09813	−	10.0203i	0.182894	−	0.359475i
$778$	−5.08046	+	4.26301i	−0.182143	+	0.152836i
$779$	55.9518	+	20.3648i	2.00468	+	0.729644i
$780$	3.49099	−	3.25925i	0.124997	−	0.116700i
$781$	−1.35977	+	7.71167i	−0.0486566	+	0.275945i
$782$	−21.9137			−0.783632
$783$	17.3531	−	9.65918i	0.620149	−	0.345191i
$784$	1.00000			0.0357143
$785$	0.376841	−	2.13717i	0.0134500	−	0.0762790i
$786$	−1.87139	−	0.570932i	−0.0667501	−	0.0203645i
$787$	40.6653	+	14.8010i	1.44956	+	0.527597i	0.942469	−	0.334294i	$-0.108498\pi$
$787$	40.6653	+	14.8010i	1.44956	+	0.527597i	0.507093	+	0.861891i	$0.330720\pi$
$788$	6.86005	−	5.75626i	0.244379	−	0.205058i
$789$	3.17036	+	4.87563i	0.112868	+	0.173577i
$790$	4.30966	−	1.56859i	0.153331	−	0.0558078i
$791$	−8.00990	+	13.8735i	−0.284799	+	0.493287i
$792$	−6.43803	+	6.68254i	−0.228765	+	0.237454i
$793$	14.7990	+	25.6327i	0.525529	+	0.910242i
$794$	21.5070	+	18.0465i	0.763254	+	0.640446i
$795$	1.96099	+	1.47590i	0.0695490	+	0.0523446i
$796$	−2.16581	−	12.2829i	−0.0767651	−	0.435356i
$797$	−4.90734	−	27.8309i	−0.173827	−	0.985821i	−0.939489	−	0.342579i	$-0.888700\pi$
$797$	−4.90734	−	27.8309i	−0.173827	−	0.985821i	0.765662	−	0.643243i	$-0.222411\pi$
$798$	−1.25212	+	10.2477i	−0.0443245	+	0.362764i
$799$	−52.4953	−	44.0488i	−1.85715	−	1.55833i
$800$	2.36830	+	4.10202i	0.0837321	+	0.145028i
$801$	0.396787	−	5.77222i	0.0140198	−	0.203951i
$802$	−4.43937	+	7.68922i	−0.156760	+	0.271516i
$803$	−28.3498	+	10.3185i	−1.00044	+	0.364131i
$804$	−2.98896	+	0.158413i	−0.105412	+	0.00558681i
$805$	−1.70444	+	1.43019i	−0.0600736	+	0.0504077i
$806$	−42.3805	−	15.4252i	−1.49279	−	0.543331i
$807$	−2.47444	−	10.6892i	−0.0871045	−	0.376278i
$808$	−1.06607	+	6.04596i	−0.0375041	+	0.212696i
$809$	37.0879			1.30394			0.651970	−	0.758245i	$-0.273943\pi$
$809$	37.0879			1.30394			0.651970	+	0.758245i	$0.273943\pi$
$810$	−4.57555	−	0.632041i	−0.160768	−	0.0222077i
$811$	−26.3365			−0.924801			−0.462401	−	0.886671i	$-0.653012\pi$
$811$	−26.3365			−0.924801			−0.462401	+	0.886671i	$0.653012\pi$
$812$	0.663702	−	3.76404i	0.0232914	−	0.132092i
$813$	10.4163	+	44.9967i	0.365315	+	1.57810i
$814$	18.8662	+	6.86673i	0.661260	+	0.240679i
$815$	3.11441	−	2.61330i	0.109093	−	0.0915399i
$816$	−8.74268	+	0.463358i	−0.306055	+	0.0162208i
$817$	40.1968	−	14.6304i	1.40631	−	0.511854i
$818$	0.797302	−	1.38097i	0.0278770	−	0.0482844i
$819$	−13.3732	−	8.99738i	−0.467297	−	0.314394i
$820$	2.56342	+	4.43998i	0.0895186	+	0.155051i
$821$	−14.3169	−	12.0133i	−0.499663	−	0.419267i	0.357811	−	0.933794i	$-0.383523\pi$
$821$	−14.3169	−	12.0133i	−0.499663	−	0.419267i	−0.857474	+	0.514527i	$0.827968\pi$
$822$	2.93742	−	24.0407i	0.102454	−	0.838515i
$823$	−0.940761	−	5.33532i	−0.0327929	−	0.185978i	0.964011	−	0.265861i	$-0.0856563\pi$
$823$	−0.940761	−	5.33532i	−0.0327929	−	0.185978i	−0.996804	+	0.0798836i	$0.974545\pi$
$824$	−0.549184	−	3.11458i	−0.0191317	−	0.108501i
$825$	−20.2750	−	15.2596i	−0.705885	−	0.531270i
$826$	4.66659	+	3.91573i	0.162371	+	0.136246i
$827$	17.1585	+	29.7193i	0.596658	+	1.03344i	0.993311	+	0.115473i	$0.0368384\pi$
$827$	17.1585	+	29.7193i	0.596658	+	1.03344i	−0.396653	+	0.917969i	$0.629828\pi$
$828$	12.6234	+	3.13154i	0.438692	+	0.108828i
$829$	−8.22115	+	14.2395i	−0.285532	+	0.494557i	−0.972738	−	0.231906i	$-0.925504\pi$
$829$	−8.22115	+	14.2395i	−0.285532	+	0.494557i	0.687206	+	0.726463i	$0.258837\pi$
$830$	−4.18439	+	1.52299i	−0.145242	+	0.0528638i
$831$	−27.1788	−	41.7977i	−0.942823	−	1.44995i
$832$	−4.11574	+	3.45351i	−0.142688	+	0.119729i
$833$	−4.74984	−	1.72880i	−0.164572	−	0.0598994i
$834$	−33.5170	−	10.2255i	−1.16060	−	0.354081i
$835$	−0.410558	+	2.32839i	−0.0142079	+	0.0805772i
$836$	−18.4363			−0.637634
$837$	14.2737	+	41.2166i	0.493371	+	1.42466i
$838$	12.8967			0.445509
$839$	−9.20255	+	52.1903i	−0.317707	+	1.80181i	0.238912	+	0.971041i	$0.423209\pi$
$839$	−9.20255	+	52.1903i	−0.317707	+	1.80181i	−0.556620	+	0.830767i	$0.687902\pi$
$840$	−0.649762	+	0.606630i	−0.0224189	+	0.0209307i
$841$	13.5236	+	4.92218i	0.466330	+	0.169730i
$842$	−24.8963	+	20.8905i	−0.857982	+	0.719933i
$843$	−3.55795	+	6.99306i	−0.122542	+	0.240854i
$844$	7.39087	−	2.69005i	0.254404	−	0.0925955i
$845$	−4.07141	+	7.05189i	−0.140061	+	0.242592i
$846$	23.9452	+	32.8760i	0.823252	+	1.13030i
$847$	0.716417	+	1.24087i	0.0246164	+	0.0426368i
$848$	−2.11505	−	1.77474i	−0.0726312	−	0.0609448i
$849$	17.3936	−	7.39527i	0.596947	−	0.253805i
$850$	−4.15748	−	23.5783i	−0.142600	−	0.808727i
$851$	−4.88651	−	27.7128i	−0.167508	−	0.949983i
$852$	4.03537	−	1.71572i	0.138249	−	0.0587797i
$853$	23.6973	+	19.8844i	0.811379	+	0.680828i	0.950936	−	0.309386i	$-0.100124\pi$
$853$	23.6973	+	19.8844i	0.811379	+	0.680828i	−0.139558	+	0.990214i	$0.544568\pi$
$854$	−2.75448	−	4.77089i	−0.0942563	−	0.163257i
$855$	−5.40297	−	7.41813i	−0.184778	−	0.253695i
$856$	5.14128	−	8.90496i	0.175725	−	0.304365i
$857$	−40.2822	+	14.6615i	−1.37601	+	0.500828i	−0.920967	−	0.389640i	$-0.872599\pi$
$857$	−40.2822	+	14.6615i	−1.37601	+	0.500828i	−0.455046	+	0.890468i	$0.650377\pi$
$858$	13.0524	−	25.6541i	0.445601	−	0.875818i
$859$	28.4683	−	23.8878i	0.971327	−	0.815040i	−0.0114313	−	0.999935i	$-0.503639\pi$
$859$	28.4683	−	23.8878i	0.971327	−	0.815040i	0.982758	+	0.184894i	$0.0591943\pi$
$860$	3.46110	+	1.25974i	0.118022	+	0.0429566i
$861$	12.6472	−	11.8077i	0.431015	−	0.402404i
$862$	3.40013	−	19.2831i	0.115809	−	0.656784i
$863$	4.75542			0.161876			0.0809381	−	0.996719i	$-0.474208\pi$
$863$	4.75542			0.161876			0.0809381	+	0.996719i	$0.474208\pi$
$864$	5.10243	+	0.982441i	0.173588	+	0.0334233i
$865$	−9.31176			−0.316609
$866$	−0.534088	+	3.02896i	−0.0181491	+	0.102928i
$867$	14.1641	+	4.32125i	0.481037	+	0.146757i
$868$	7.88809	+	2.87103i	0.267739	+	0.0974491i
$869$	21.1737	−	17.7669i	0.718269	−	0.602699i
$870$	1.85213	+	2.84835i	0.0627932	+	0.0965682i
$871$	8.72464	−	3.17551i	0.295623	−	0.107598i
$872$	6.60226	−	11.4354i	0.223581	−	0.387253i
$873$	−43.3219	−	10.7471i	−1.46622	−	0.363733i
$874$	12.9204	+	22.3788i	0.437038	+	0.756973i
$875$	−3.82795	−	3.21204i	−0.129408	−	0.108587i
$876$	13.4982	+	10.1591i	0.456061	+	0.343245i
$877$	−8.73062	−	49.5138i	−0.294812	−	1.67196i	−0.667965	−	0.744193i	$-0.732834\pi$
$877$	−8.73062	−	49.5138i	−0.294812	−	1.67196i	0.373153	−	0.927770i	$-0.378277\pi$
$878$	−3.41463	−	19.3653i	−0.115238	−	0.653547i
$879$	1.69002	−	13.8316i	0.0570030	−	0.466528i
$880$	−1.21605	−	1.02039i	−0.0409930	−	0.0343972i
$881$	−1.75568	−	3.04092i	−0.0591503	−	0.102451i	0.834934	−	0.550350i	$-0.185506\pi$
$881$	−1.75568	−	3.04092i	−0.0591503	−	0.102451i	−0.894084	+	0.447899i	$0.852172\pi$
$882$	2.48909	+	1.67464i	0.0838121	+	0.0563881i
$883$	18.2682	−	31.6415i	0.614775	−	1.06482i	−0.375649	−	0.926762i	$-0.622580\pi$
$883$	18.2682	−	31.6415i	0.614775	−	1.06482i	0.990424	−	0.138059i	$-0.0440865\pi$
$884$	25.5195	−	9.28835i	0.858315	−	0.312401i
$885$	−5.40757	+	0.286599i	−0.181774	+	0.00963392i
$886$	20.0199	−	16.7987i	0.672583	−	0.564364i
$887$	10.1177	+	3.68254i	0.339719	+	0.123648i	0.506246	−	0.862389i	$-0.331033\pi$
$887$	10.1177	+	3.68254i	0.339719	+	0.123648i	−0.166527	+	0.986037i	$0.553255\pi$
$888$	−2.53550	−	10.9530i	−0.0850859	−	0.367558i
$889$	−0.608101	+	3.44871i	−0.0203951	+	0.115666i
$890$	0.989807			0.0331784
$891$	−27.2157	+	5.85205i	−0.911760	+	0.196051i
$892$	17.0910			0.572250
$893$	−14.0322	+	79.5807i	−0.469571	+	2.66307i
$894$	−6.66718	−	28.8012i	−0.222984	−	0.963256i
$895$	−4.68881	−	1.70659i	−0.156729	−	0.0570449i
$896$	0.766044	−	0.642788i	0.0255917	−	0.0214740i
$897$	−40.2873	+	2.13521i	−1.34515	+	0.0712925i
$898$	21.1246	−	7.68871i	0.704936	−	0.256576i
$899$	16.0420	−	27.7856i	0.535031	−	0.926702i
$900$	−0.974495	+	14.1764i	−0.0324832	+	0.472545i
$901$	6.97799	+	12.0862i	0.232470	+	0.402651i
$902$	23.6696	+	19.8611i	0.788111	+	0.661304i
$903$	1.50760	−	12.3386i	0.0501697	−	0.410602i
$904$	2.78181	+	15.7764i	0.0925216	+	0.524716i
$905$	−0.360690	−	2.04557i	−0.0119897	−	0.0679972i
$906$	5.89570	+	4.43728i	0.195871	+	0.147419i
$907$	9.00607	+	7.55699i	0.299041	+	0.250926i	0.779945	−	0.625848i	$-0.215247\pi$
$907$	9.00607	+	7.55699i	0.299041	+	0.250926i	−0.480904	+	0.876773i	$0.659691\pi$
$908$	3.30062	+	5.71684i	0.109535	+	0.189720i
$909$	−12.7784	+	13.2637i	−0.423832	+	0.439928i
$910$	1.37870	−	2.38798i	0.0457034	−	0.0791606i
$911$	15.4343	−	5.61763i	0.511361	−	0.186120i	−0.0734358	−	0.997300i	$-0.523396\pi$
$911$	15.4343	−	5.61763i	0.511361	−	0.186120i	0.584797	+	0.811180i	$0.301174\pi$
$912$	5.62790	+	8.65503i	0.186359	+	0.286597i
$913$	−20.5583	+	17.2504i	−0.680379	+	0.570906i
$914$	23.9041	+	8.70038i	0.790677	+	0.287783i
$915$	4.68392	+	1.42900i	0.154846	+	0.0472412i
$916$	−0.828025	+	4.69596i	−0.0273587	+	0.155159i
$917$	−1.12961			−0.0373030
$918$	−22.5373	−	13.4875i	−0.743841	−	0.445155i
$919$	45.1583			1.48964			0.744818	−	0.667268i	$-0.232536\pi$
$919$	45.1583			1.48964			0.744818	+	0.667268i	$0.232536\pi$
$920$	−0.386365	+	2.19119i	−0.0127381	+	0.0722412i
$921$	17.6145	−	16.4452i	0.580416	−	0.541888i
$922$	−1.27010	−	0.462277i	−0.0418284	−	0.0152243i
$923$	−10.4196	+	8.74312i	−0.342967	+	0.287783i
$924$	−2.42938	+	4.77489i	−0.0799208	+	0.157082i
$925$	28.8908	−	10.5154i	0.949924	−	0.345744i
$926$	3.90239	−	6.75913i	0.128240	−	0.222119i
$927$	3.84883	−	8.67215i	0.126412	−	0.284831i
$928$	−1.91105	−	3.31004i	−0.0627334	−	0.108658i
$929$	−26.1182	−	21.9157i	−0.856909	−	0.719032i	0.104391	−	0.994536i	$-0.466711\pi$
$929$	−26.1182	−	21.9157i	−0.856909	−	0.719032i	−0.961300	+	0.275504i	$0.911155\pi$
$930$	−6.86703	+	2.91967i	−0.225179	+	0.0957397i
$931$	1.03503	+	5.86995i	0.0339218	+	0.192380i
$932$	−3.14487	−	17.8354i	−0.103014	−	0.584219i
$933$	−53.8895	+	22.9123i	−1.76426	+	0.750114i
$934$	−16.1871	−	13.5826i	−0.529657	−	0.444435i
$935$	4.01199	+	6.94898i	0.131206	+	0.227256i
$936$	−16.0279	+	1.70372i	−0.523887	+	0.0556879i
$937$	17.2919	−	29.9505i	0.564903	−	0.978441i	−0.432156	−	0.901799i	$-0.642247\pi$
$937$	17.2919	−	29.9505i	0.564903	−	0.978441i	0.997059	−	0.0766419i	$-0.0244198\pi$
$938$	−1.62388	+	0.591044i	−0.0530215	+	0.0192983i
$939$	3.08062	−	6.05489i	0.100532	−	0.197594i
$940$	−5.33007	+	4.47246i	−0.173848	+	0.145875i
$941$	−38.8668	−	14.1464i	−1.26702	−	0.461158i	−0.380903	−	0.924615i	$-0.624387\pi$
$941$	−38.8668	−	14.1464i	−1.26702	−	0.461158i	−0.886119	+	0.463457i	$0.846609\pi$
$942$	−5.35343	+	4.99806i	−0.174424	+	0.162846i
$943$	7.52034	−	42.6500i	0.244896	−	1.38887i
$944$	6.09180			0.198271
$945$	−2.63320	+	0.421839i	−0.0856582	+	0.0137224i
$946$	22.1980			0.721720
$947$	9.28641	−	52.6659i	0.301768	−	1.71141i	−0.336574	−	0.941657i	$-0.609268\pi$
$947$	9.28641	−	52.6659i	0.301768	−	1.71141i	0.638342	−	0.769753i	$-0.279621\pi$
$948$	−14.8043	−	4.51657i	−0.480820	−	0.146691i
$949$	−49.2439	−	17.9233i	−1.59852	−	0.581815i
$950$	−21.6274	+	18.1475i	−0.701685	+	0.588784i
$951$	4.62152	+	7.10734i	0.149863	+	0.230471i
$952$	−4.74984	+	1.72880i	−0.153943	+	0.0560307i
$953$	27.8257	−	48.1954i	0.901361	−	1.56120i	0.0756330	−	0.997136i	$-0.475902\pi$
$953$	27.8257	−	48.1954i	0.901361	−	1.56120i	0.825728	−	0.564068i	$-0.190764\pi$
$954$	−2.29250	−	7.95944i	−0.0742225	−	0.257696i
$955$	1.14446	+	1.98226i	0.0370339	+	0.0641445i
$956$	18.0698	+	15.1623i	0.584418	+	0.490385i
$957$	16.3605	+	12.3134i	0.528860	+	0.398036i
$958$	−1.64931	−	9.35371i	−0.0532868	−	0.302205i
$959$	−2.42814	−	13.7707i	−0.0784088	−	0.444678i
$960$	−0.107812	+	0.882365i	−0.00347962	+	0.0284782i
$961$	30.2318	+	25.3675i	0.975219	+	0.818306i
$962$	17.4370	+	30.2017i	0.562190	+	0.973741i
$963$	27.7097	−	13.5555i	0.892934	−	0.436818i
$964$	−10.9033	+	18.8850i	−0.351171	+	0.608245i
$965$	12.4711	−	4.53913i	0.401460	−	0.146120i
$966$	7.49849	−	0.397417i	0.241260	−	0.0127867i
$967$	−9.86883	+	8.28093i	−0.317360	+	0.266297i	−0.787526	−	0.616281i	$-0.788638\pi$
$967$	−9.86883	+	8.28093i	−0.317360	+	0.266297i	0.470166	+	0.882578i	$0.344194\pi$
$968$	1.34642	+	0.490058i	0.0432757	+	0.0157511i
$969$	−11.7688	−	50.8395i	−0.378069	−	1.63320i
$970$	1.32596	−	7.51989i	0.0425740	−	0.241449i
$971$	−47.5803			−1.52692			−0.763462	−	0.645852i	$-0.776502\pi$
$971$	−47.5803			−1.52692			−0.763462	+	0.645852i	$0.776502\pi$
$972$	11.0552	+	10.9901i	0.354595	+	0.352509i
$973$	−20.2316			−0.648594
$974$	−0.682238	+	3.86916i	−0.0218603	+	0.123976i
$975$	−9.94073	−	42.9424i	−0.318358	−	1.37526i
$976$	−5.17672	−	1.88417i	−0.165703	−	0.0603109i
$977$	−8.66712	+	7.27258i	−0.277286	+	0.232670i	−0.770815	−	0.637059i	$-0.780151\pi$
$977$	−8.66712	+	7.27258i	−0.277286	+	0.232670i	0.493530	+	0.869729i	$0.335706\pi$
$978$	−13.7015	+	0.726173i	−0.438125	+	0.0232205i
$979$	5.60561	−	2.04027i	0.179156	−	0.0652074i
$980$	−0.256611	+	0.444463i	−0.00819714	+	0.0141979i
$981$	35.5839	−	17.4074i	1.13611	−	0.555777i
$982$	−15.5248	−	26.8898i	−0.495418	−	0.858089i
$983$	−0.720355	−	0.604449i	−0.0229757	−	0.0192789i	0.631227	−	0.775598i	$-0.282551\pi$
$983$	−0.720355	−	0.604449i	−0.0229757	−	0.0192789i	−0.654203	+	0.756319i	$0.726996\pi$
$984$	2.09849	−	17.1746i	0.0668975	−	0.547508i
$985$	0.798084	+	4.52616i	0.0254291	+	0.144215i
$986$	3.35480	+	19.0260i	0.106839	+	0.605912i
$987$	18.7618	+	14.1207i	0.597196	+	0.449467i
$988$	−24.5319	−	20.5847i	−0.780463	−	0.654886i
$989$	−15.5566	−	26.9448i	−0.494671	−	0.856796i
$990$	−1.31807	−	4.57628i	−0.0418912	−	0.145444i
$991$	1.65170	−	2.86083i	0.0524681	−	0.0908774i	−0.838598	−	0.544750i	$-0.816625\pi$
$991$	1.65170	−	2.86083i	0.0524681	−	0.0908774i	0.891067	+	0.453873i	$0.149958\pi$
$992$	7.88809	−	2.87103i	0.250447	−	0.0911553i
$993$	−20.6139	−	31.7016i	−0.654161	−	1.00602i
$994$	1.93936	−	1.62732i	0.0615129	−	0.0516154i
$995$	6.01508	+	2.18931i	0.190691	+	0.0694057i
$996$	14.3739	+	4.38528i	0.455456	+	0.138953i
$997$	−6.05978	+	34.3667i	−0.191915	+	1.08840i	0.724829	+	0.688929i	$0.241919\pi$
$997$	−6.05978	+	34.3667i	−0.191915	+	1.08840i	−0.916744	+	0.399475i	$0.869192\pi$
$998$	−17.1193			−0.541901
$999$	12.0312	−	31.5090i	0.380651	−	0.996901i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.b.295.1	✓	12
27.13	even	9	inner	378.2.u.b.337.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.b.295.1	✓	12	1.1	even	1	trivial
378.2.u.b.337.1	yes	12	27.13	even	9	inner

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)

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{2} +(-0.390623 - 1.68743i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.393151 - 0.329893i) q^{5} +(-1.72962 + 0.0916693i) q^{6} +(-0.939693 + 0.342020i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.69483 + 1.31830i) q^{9} +O(q^{10})\)	\(q+(0.173648 - 0.984808i) q^{2} +(-0.390623 - 1.68743i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.393151 - 0.329893i) q^{5} +(-1.72962 + 0.0916693i) q^{6} +(-0.939693 + 0.342020i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.69483 + 1.31830i) q^{9} +(-0.256611 - 0.444463i) q^{10} +(-2.36944 - 1.98820i) q^{11} +(-0.210069 + 1.71926i) q^{12} +(-0.932962 - 5.29109i) q^{13} +(0.173648 + 0.984808i) q^{14} +(-0.710244 - 0.534550i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-2.52734 - 4.37748i) q^{17} +(0.830315 + 2.88281i) q^{18} +(-2.98025 + 5.16195i) q^{19} +(-0.482271 + 0.175532i) q^{20} +(0.944200 + 1.45206i) q^{21} +(-2.36944 + 1.98820i) q^{22} +(4.07388 + 1.48277i) q^{23} +(1.65667 + 0.505425i) q^{24} +(-0.822502 + 4.66464i) q^{25} -5.37272 q^{26} +(3.27719 + 4.03237i) q^{27} +1.00000 q^{28} +(0.663702 - 3.76404i) q^{29} +(-0.649762 + 0.606630i) q^{30} +(7.88809 + 2.87103i) q^{31} +(0.766044 - 0.642788i) q^{32} +(-2.42938 + 4.77489i) q^{33} +(-4.74984 + 1.72880i) q^{34} +(-0.256611 + 0.444463i) q^{35} +(2.98319 - 0.317107i) q^{36} +(-3.24546 - 5.62131i) q^{37} +(4.56601 + 3.83134i) q^{38} +(-8.56390 + 3.64113i) q^{39} +(0.0891201 + 0.505425i) q^{40} +(-1.73466 - 9.83777i) q^{41} +(1.59396 - 0.677707i) q^{42} +(-5.49764 - 4.61307i) q^{43} +(1.54654 + 2.67869i) q^{44} +(-0.624578 + 1.40729i) q^{45} +(2.16767 - 3.75451i) q^{46} +(12.7397 - 4.63687i) q^{47} +(0.785424 - 1.54373i) q^{48} +(0.766044 - 0.642788i) q^{49} +(4.45095 + 1.62001i) q^{50} +(-6.39944 + 5.97464i) q^{51} +(-0.932962 + 5.29109i) q^{52} -2.76100 q^{53} +(4.54019 - 2.52719i) q^{54} -1.58744 q^{55} +(0.173648 - 0.984808i) q^{56} +(9.87457 + 3.01259i) q^{57} +(-3.59161 - 1.30724i) q^{58} +(4.66659 - 3.91573i) q^{59} +(0.484584 + 0.745231i) q^{60} +(-5.17672 + 1.88417i) q^{61} +(4.19717 - 7.26970i) q^{62} +(2.08143 - 2.16048i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.11229 - 1.77242i) q^{65} +(4.28049 + 3.22162i) q^{66} +(0.300081 + 1.70184i) q^{67} +(0.877735 + 4.97788i) q^{68} +(0.910720 - 7.45358i) q^{69} +(0.393151 + 0.329893i) q^{70} +(-1.26583 - 2.19248i) q^{71} +(0.205737 - 2.99294i) q^{72} +(4.87689 - 8.44701i) q^{73} +(-6.09948 + 2.22003i) q^{74} +(8.19254 - 0.434201i) q^{75} +(4.56601 - 3.83134i) q^{76} +(2.90655 + 1.05790i) q^{77} +(2.09870 + 9.06607i) q^{78} +(-1.55175 + 8.80041i) q^{79} +0.513222 q^{80} +(5.52420 - 7.10516i) q^{81} -9.98953 q^{82} +(1.50665 - 8.54461i) q^{83} +(-0.390623 - 1.68743i) q^{84} +(-2.43772 - 0.887259i) q^{85} +(-5.49764 + 4.61307i) q^{86} +(-6.61081 + 0.350370i) q^{87} +(2.90655 - 1.05790i) q^{88} +(-0.964307 + 1.67023i) q^{89} +(1.27746 + 0.859463i) q^{90} +(2.68636 + 4.65291i) q^{91} +(-3.32106 - 2.78670i) q^{92} +(1.76339 - 14.4321i) q^{93} +(-2.35420 - 13.3513i) q^{94} +(0.531201 + 3.01259i) q^{95} +(-1.38389 - 1.04156i) q^{96} +(11.3975 + 9.56361i) q^{97} +(-0.500000 - 0.866025i) q^{98} +(9.00626 + 2.23423i) 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

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