LMFDB - Embedded newform 378.2.u.b.169.1

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			169.1
Root			$0.500000 - 0.0126039i$ of defining polynomial
Character	$\chi$	$=$	378.169
Dual form			378.2.u.b.85.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(-1.04508 - 1.38124i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.108876 + 0.617467i) q^{5} +(1.45446 + 0.940501i) q^{6} +(0.766044 + 0.642788i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.815631 + 2.88700i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(-1.04508 - 1.38124i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.108876 + 0.617467i) q^{5} +(1.45446 + 0.940501i) q^{6} +(0.766044 + 0.642788i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.815631 + 2.88700i) q^{9} +(-0.313496 - 0.542992i) q^{10} +(-0.0434396 + 0.246358i) q^{11} +(-1.68842 - 0.386327i) q^{12} +(3.98990 + 1.45220i) q^{13} +(-0.939693 - 0.342020i) q^{14} +(0.739085 - 0.795684i) q^{15} +(0.173648 - 0.984808i) q^{16} +(0.0870455 + 0.150767i) q^{17} +(-0.220968 - 2.99185i) q^{18} +(1.22610 - 2.12366i) q^{19} +(0.480304 + 0.403023i) q^{20} +(0.0872671 - 1.72985i) q^{21} +(-0.0434396 - 0.246358i) q^{22} +(0.0380340 - 0.0319143i) q^{23} +(1.71872 - 0.214444i) q^{24} +(4.32905 - 1.57565i) q^{25} -4.24596 q^{26} +(4.84002 - 1.89055i) q^{27} +1.00000 q^{28} +(0.635836 - 0.231425i) q^{29} +(-0.422372 + 1.00048i) q^{30} +(5.73496 - 4.81221i) q^{31} +(0.173648 + 0.984808i) q^{32} +(0.385677 - 0.197463i) q^{33} +(-0.133361 - 0.111904i) q^{34} +(-0.313496 + 0.542992i) q^{35} +(1.23092 + 2.73584i) q^{36} +(2.59919 + 4.50193i) q^{37} +(-0.425819 + 2.41494i) q^{38} +(-2.16391 - 7.02866i) q^{39} +(-0.589180 - 0.214444i) q^{40} +(11.3770 + 4.14090i) q^{41} +(0.509640 + 1.65538i) q^{42} +(0.237614 - 1.34758i) q^{43} +(0.125079 + 0.216644i) q^{44} +(-1.87143 - 0.189301i) q^{45} +(-0.0248249 + 0.0429980i) q^{46} +(0.339914 + 0.285222i) q^{47} +(-1.54173 + 0.789350i) q^{48} +(0.173648 + 0.984808i) q^{49} +(-3.52908 + 2.96125i) q^{50} +(0.117276 - 0.277794i) q^{51} +(3.98990 - 1.45220i) q^{52} -12.0962 q^{53} +(-3.90153 + 3.43192i) q^{54} -0.156848 q^{55} +(-0.939693 + 0.342020i) q^{56} +(-4.21465 + 0.525859i) q^{57} +(-0.518338 + 0.434937i) q^{58} +(0.847403 + 4.80586i) q^{59} +(0.0547159 - 1.08460i) q^{60} +(-2.13354 - 1.79025i) q^{61} +(-3.74323 + 6.48347i) q^{62} +(-2.48053 + 1.68729i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.462284 + 2.62174i) q^{65} +(-0.294882 + 0.317464i) q^{66} +(-3.13920 - 1.14257i) q^{67} +(0.163592 + 0.0595426i) q^{68} +(-0.0838296 - 0.0191810i) q^{69} +(0.108876 - 0.617467i) q^{70} +(-2.14487 - 3.71502i) q^{71} +(-2.09240 - 2.14986i) q^{72} +(-4.93331 + 8.54475i) q^{73} +(-3.98219 - 3.34146i) q^{74} +(-6.70053 - 4.33278i) q^{75} +(-0.425819 - 2.41494i) q^{76} +(-0.191633 + 0.160799i) q^{77} +(4.43735 + 5.86468i) q^{78} +(5.12170 - 1.86415i) q^{79} +0.626993 q^{80} +(-7.66949 - 4.70945i) q^{81} -12.1072 q^{82} +(5.81583 - 2.11679i) q^{83} +(-1.04508 - 1.38124i) q^{84} +(-0.0836166 + 0.0701627i) q^{85} +(0.237614 + 1.34758i) q^{86} +(-0.984150 - 0.636383i) q^{87} +(-0.191633 - 0.160799i) q^{88} +(3.53501 - 6.12282i) q^{89} +(1.82331 - 0.462182i) q^{90} +(2.12298 + 3.67711i) q^{91} +(0.00862160 - 0.0488955i) q^{92} +(-12.6403 - 2.89222i) q^{93} +(-0.416967 - 0.151763i) q^{94} +(1.44478 + 0.525859i) q^{95} +(1.17878 - 1.26905i) q^{96} +(-2.64647 + 15.0089i) q^{97} +(-0.500000 - 0.866025i) q^{98} +(-0.675805 - 0.326348i) 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 $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$

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 $

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	−1.04508	−	1.38124i	−0.603375	−	0.797458i
$3$	−1.04508	−	1.38124i	−0.603375	−	0.797458i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	0.108876	+	0.617467i	0.0486909	+	0.276140i	0.999426	−	0.0338632i	$-0.0107811\pi$
$5$	0.108876	+	0.617467i	0.0486909	+	0.276140i	−0.950736	+	0.310003i	$0.899670\pi$
$6$	1.45446	+	0.940501i	0.593781	+	0.383958i
$7$	0.766044	+	0.642788i	0.289538	+	0.242951i
$7$	0.766044	+	0.642788i	0.289538	+	0.242951i
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−0.815631	+	2.88700i	−0.271877	+	0.962332i
$10$	−0.313496	−	0.542992i	−0.0991362	−	0.171709i
$11$	−0.0434396	+	0.246358i	−0.0130975	+	0.0742798i	−0.990656	−	0.136385i	$-0.956452\pi$
$11$	−0.0434396	+	0.246358i	−0.0130975	+	0.0742798i	0.977558	+	0.210665i	$0.0675628\pi$
$12$	−1.68842	−	0.386327i	−0.487404	−	0.111523i
$13$	3.98990	+	1.45220i	1.10660	+	0.402769i	0.829745	−	0.558143i	$-0.188486\pi$
$13$	3.98990	+	1.45220i	1.10660	+	0.402769i	0.276854	+	0.960912i	$0.410708\pi$
$14$	−0.939693	−	0.342020i	−0.251143	−	0.0914087i
$15$	0.739085	−	0.795684i	0.190831	−	0.205445i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	0.0870455	+	0.150767i	0.0211116	+	0.0365664i	0.876388	−	0.481605i	$-0.159946\pi$
$17$	0.0870455	+	0.150767i	0.0211116	+	0.0365664i	−0.855277	+	0.518172i	$0.826613\pi$
$18$	−0.220968	−	2.99185i	−0.0520827	−	0.705186i
$19$	1.22610	−	2.12366i	0.281286	−	0.487202i	−0.690416	−	0.723413i	$-0.742572\pi$
$19$	1.22610	−	2.12366i	0.281286	−	0.487202i	0.971702	+	0.236211i	$0.0759057\pi$
$20$	0.480304	+	0.403023i	0.107399	+	0.0901187i
$21$	0.0872671	−	1.72985i	0.0190433	−	0.377484i
$22$	−0.0434396	−	0.246358i	−0.00926136	−	0.0525238i
$23$	0.0380340	−	0.0319143i	0.00793063	−	0.00665459i	−0.638814	−	0.769361i	$-0.720575\pi$
$23$	0.0380340	−	0.0319143i	0.00793063	−	0.00665459i	0.646744	+	0.762707i	$0.276130\pi$
$24$	1.71872	−	0.214444i	0.350833	−	0.0437732i
$25$	4.32905	−	1.57565i	0.865810	−	0.315129i
$26$	−4.24596			−0.832701
$27$	4.84002	−	1.89055i	0.931463	−	0.363837i
$28$	1.00000			0.188982
$29$	0.635836	−	0.231425i	0.118072	−	0.0429746i	−0.282309	−	0.959324i	$-0.591100\pi$
$29$	0.635836	−	0.231425i	0.118072	−	0.0429746i	0.400380	+	0.916349i	$0.368878\pi$
$30$	−0.422372	+	1.00048i	−0.0771143	+	0.182662i
$31$	5.73496	−	4.81221i	1.03003	−	0.864298i	0.0391754	−	0.999232i	$-0.487527\pi$
$31$	5.73496	−	4.81221i	1.03003	−	0.864298i	0.990854	+	0.134935i	$0.0430825\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	0.385677	−	0.197463i	0.0671378	−	0.0343739i
$34$	−0.133361	−	0.111904i	−0.0228713	−	0.0191913i
$35$	−0.313496	+	0.542992i	−0.0529905	+	0.0917823i
$36$	1.23092	+	2.73584i	0.205153	+	0.455974i
$37$	2.59919	+	4.50193i	0.427304	+	0.740113i	0.996633	−	0.0819975i	$-0.0261300\pi$
$37$	2.59919	+	4.50193i	0.427304	+	0.740113i	−0.569328	+	0.822110i	$0.692797\pi$
$38$	−0.425819	+	2.41494i	−0.0690770	+	0.391755i
$39$	−2.16391	−	7.02866i	−0.346503	−	1.12549i
$40$	−0.589180	−	0.214444i	−0.0931576	−	0.0339066i
$41$	11.3770	+	4.14090i	1.77679	+	0.646700i	0.999853	+	0.0171245i	$0.00545118\pi$
$41$	11.3770	+	4.14090i	1.77679	+	0.646700i	0.776940	+	0.629575i	$0.216771\pi$
$42$	0.509640	+	1.65538i	0.0786391	+	0.255430i
$43$	0.237614	−	1.34758i	0.0362358	−	0.205504i	−0.961315	−	0.275452i	$-0.911172\pi$
$43$	0.237614	−	1.34758i	0.0362358	−	0.205504i	0.997551	+	0.0699486i	$0.0222835\pi$
$44$	0.125079	+	0.216644i	0.0188564	+	0.0326603i
$45$	−1.87143	−	0.189301i	−0.278976	−	0.0282193i
$46$	−0.0248249	+	0.0429980i	−0.00366023	+	0.00633971i
$47$	0.339914	+	0.285222i	0.0495816	+	0.0416039i	0.667242	−	0.744841i	$-0.267475\pi$
$47$	0.339914	+	0.285222i	0.0495816	+	0.0416039i	−0.617660	+	0.786445i	$0.711919\pi$
$48$	−1.54173	+	0.789350i	−0.222529	+	0.113933i
$49$	0.173648	+	0.984808i	0.0248069	+	0.140687i
$50$	−3.52908	+	2.96125i	−0.499087	+	0.418783i
$51$	0.117276	−	0.277794i	0.0164219	−	0.0388989i
$52$	3.98990	−	1.45220i	0.553299	−	0.201384i
$53$	−12.0962			−1.66154			−0.830771	−	0.556614i	$-0.812100\pi$
$53$	−12.0962			−1.66154			−0.830771	+	0.556614i	$0.812100\pi$
$54$	−3.90153	+	3.43192i	−0.530931	+	0.467025i
$55$	−0.156848			−0.0211493
$56$	−0.939693	+	0.342020i	−0.125572	+	0.0457044i
$57$	−4.21465	+	0.525859i	−0.558244	+	0.0696517i
$58$	−0.518338	+	0.434937i	−0.0680611	+	0.0571101i
$59$	0.847403	+	4.80586i	0.110323	+	0.625670i	0.988960	+	0.148181i	$0.0473418\pi$
$59$	0.847403	+	4.80586i	0.110323	+	0.625670i	−0.878638	+	0.477489i	$0.841547\pi$
$60$	0.0547159	−	1.08460i	0.00706379	−	0.140022i
$61$	−2.13354	−	1.79025i	−0.273171	−	0.229218i	0.495902	−	0.868379i	$-0.334838\pi$
$61$	−2.13354	−	1.79025i	−0.273171	−	0.229218i	−0.769073	+	0.639160i	$0.779282\pi$
$62$	−3.74323	+	6.48347i	−0.475391	+	0.823401i
$63$	−2.48053	+	1.68729i	−0.312518	+	0.212579i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.462284	+	2.62174i	−0.0573392	+	0.325187i
$66$	−0.294882	+	0.317464i	−0.0362974	+	0.0390771i
$67$	−3.13920	−	1.14257i	−0.383514	−	0.139588i	0.143066	−	0.989713i	$-0.454304\pi$
$67$	−3.13920	−	1.14257i	−0.383514	−	0.139588i	−0.526580	+	0.850125i	$0.676526\pi$
$68$	0.163592	+	0.0595426i	0.0198384	+	0.00722060i
$69$	−0.0838296	−	0.0191810i	−0.0100919	−	0.00230913i
$70$	0.108876	−	0.617467i	0.0130132	−	0.0738014i
$71$	−2.14487	−	3.71502i	−0.254549	−	0.440892i	0.710224	−	0.703976i	$-0.248594\pi$
$71$	−2.14487	−	3.71502i	−0.254549	−	0.440892i	−0.964773	+	0.263084i	$0.915260\pi$
$72$	−2.09240	−	2.14986i	−0.246591	−	0.253363i
$73$	−4.93331	+	8.54475i	−0.577401	+	1.00009i	0.418376	+	0.908274i	$0.362600\pi$
$73$	−4.93331	+	8.54475i	−0.577401	+	1.00009i	−0.995776	+	0.0918132i	$0.970734\pi$
$74$	−3.98219	−	3.34146i	−0.462920	−	0.388436i
$75$	−6.70053	−	4.33278i	−0.773710	−	0.500306i
$76$	−0.425819	−	2.41494i	−0.0488448	−	0.277013i
$77$	−0.191633	+	0.160799i	−0.0218386	+	0.0183247i
$78$	4.43735	+	5.86468i	0.502431	+	0.664044i
$79$	5.12170	−	1.86415i	0.576237	−	0.209733i	−0.0374285	−	0.999299i	$-0.511917\pi$
$79$	5.12170	−	1.86415i	0.576237	−	0.209733i	0.613665	+	0.789566i	$0.289694\pi$
$80$	0.626993			0.0700999
$81$	−7.66949	−	4.70945i	−0.852166	−	0.523272i
$82$	−12.1072			−1.33701
$83$	5.81583	−	2.11679i	0.638371	−	0.232348i	−0.00249992	−	0.999997i	$-0.500796\pi$
$83$	5.81583	−	2.11679i	0.638371	−	0.232348i	0.640871	+	0.767649i	$0.278574\pi$
$84$	−1.04508	−	1.38124i	−0.114027	−	0.150705i
$85$	−0.0836166	+	0.0701627i	−0.00906950	+	0.00761021i
$86$	0.237614	+	1.34758i	0.0256226	+	0.145313i
$87$	−0.984150	−	0.636383i	−0.105512	−	0.0682274i
$88$	−0.191633	−	0.160799i	−0.0204281	−	0.0171412i
$89$	3.53501	−	6.12282i	0.374710	−	0.649017i	−0.615573	−	0.788080i	$-0.711075\pi$
$89$	3.53501	−	6.12282i	0.374710	−	0.649017i	0.990284	+	0.139062i	$0.0444088\pi$
$90$	1.82331	−	0.462182i	0.192194	−	0.0487182i
$91$	2.12298	+	3.67711i	0.222549	+	0.385466i
$92$	0.00862160	−	0.0488955i	0.000898864	−	0.00509771i
$93$	−12.6403	−	2.89222i	−1.31074	−	0.299909i
$94$	−0.416967	−	0.151763i	−0.0430068	−	0.0156532i
$95$	1.44478	+	0.525859i	0.148232	+	0.0539520i
$96$	1.17878	−	1.26905i	0.120308	−	0.129522i
$97$	−2.64647	+	15.0089i	−0.268709	+	1.52392i	0.489554	+	0.871973i	$0.337159\pi$
$97$	−2.64647	+	15.0089i	−0.268709	+	1.52392i	−0.758263	+	0.651949i	$0.773952\pi$
$98$	−0.500000	−	0.866025i	−0.0505076	−	0.0874818i
$99$	−0.675805	−	0.326348i	−0.0679210	−	0.0327992i
$100$	2.30344	−	3.98968i	0.230344	−	0.398968i
$101$	1.89098	+	1.58672i	0.188159	+	0.157884i	0.732001	−	0.681303i	$-0.238586\pi$
$101$	1.89098	+	1.58672i	0.188159	+	0.157884i	−0.543842	+	0.839188i	$0.683031\pi$
$102$	−0.0151924	+	0.301151i	−0.00150427	+	0.0298184i
$103$	−1.89237	−	10.7322i	−0.186461	−	1.05747i	−0.924064	−	0.382238i	$-0.875153\pi$
$103$	−1.89237	−	10.7322i	−0.186461	−	1.05747i	0.737603	−	0.675235i	$-0.235958\pi$
$104$	−3.25259	+	2.72925i	−0.318943	+	0.267625i
$105$	1.07763	−	0.134455i	0.105166	−	0.0131215i
$106$	11.3667	−	4.13715i	1.10403	−	0.401835i
$107$	−16.4462			−1.58991			−0.794956	−	0.606667i	$-0.792506\pi$
$107$	−16.4462			−1.58991			−0.794956	+	0.606667i	$0.792506\pi$
$108$	2.49245	−	4.55935i	0.239836	−	0.438724i
$109$	−14.2596			−1.36582			−0.682910	−	0.730502i	$-0.739286\pi$
$109$	−14.2596			−1.36582			−0.682910	+	0.730502i	$0.739286\pi$
$110$	0.147389	−	0.0536451i	0.0140530	−	0.00511486i
$111$	3.50188	−	8.29496i	0.332384	−	0.787323i
$112$	0.766044	−	0.642788i	0.0723844	−	0.0607377i
$113$	0.856231	+	4.85593i	0.0805475	+	0.456807i	0.998229	+	0.0594903i	$0.0189475\pi$
$113$	0.856231	+	4.85593i	0.0805475	+	0.456807i	−0.917681	+	0.397317i	$0.869941\pi$
$114$	3.78062	−	1.93564i	0.354087	−	0.181289i
$115$	0.0238470	+	0.0200100i	0.00222374	+	0.00186594i
$116$	0.338321	−	0.585990i	0.0314123	−	0.0544078i
$117$	−7.44679	+	10.3344i	−0.688456	+	0.955412i
$118$	−2.44000	−	4.22620i	−0.224620	−	0.389054i
$119$	−0.0302306	+	0.171446i	−0.00277123	+	0.0157164i
$120$	0.319540	+	1.03791i	0.0291699	+	0.0947476i
$121$	10.2778	+	3.74082i	0.934347	+	0.340074i
$122$	2.61717	+	0.952572i	0.236948	+	0.0862418i
$123$	−6.17030	−	20.0419i	−0.556357	−	1.80712i
$124$	1.30001	−	7.37273i	0.116744	−	0.662090i
$125$	3.01172	+	5.21645i	0.269377	+	0.466574i
$126$	1.75385	−	2.43393i	0.156246	−	0.216831i
$127$	−9.17226	+	15.8868i	−0.813907	+	1.40973i	0.0962039	+	0.995362i	$0.469330\pi$
$127$	−9.17226	+	15.8868i	−0.813907	+	1.40973i	−0.910110	+	0.414366i	$0.864003\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	−2.10965	+	1.08012i	−0.185744	+	0.0950992i
$130$	−0.462284	−	2.62174i	−0.0405450	−	0.229942i
$131$	16.3481	−	13.7177i	1.42834	−	1.19852i	0.481660	−	0.876358i	$-0.340034\pi$
$131$	16.3481	−	13.7177i	1.42834	−	1.19852i	0.946684	−	0.322165i	$-0.104411\pi$
$132$	0.168519	−	0.399174i	0.0146677	−	0.0347436i
$133$	2.30431	−	0.838700i	0.199809	−	0.0727245i
$134$	3.34066			0.288589
$135$	1.69432	+	2.78272i	0.145824	+	0.239498i
$136$	−0.174091			−0.0149282
$137$	−5.21790	+	1.89916i	−0.445796	+	0.162256i	−0.555157	−	0.831746i	$-0.687342\pi$
$137$	−5.21790	+	1.89916i	−0.445796	+	0.162256i	0.109361	+	0.994002i	$0.465120\pi$
$138$	0.0853343	−	0.0106471i	0.00726414	−	0.000906342i
$139$	−0.678301	+	0.569162i	−0.0575327	+	0.0482757i	−0.671101	−	0.741366i	$-0.734178\pi$
$139$	−0.678301	+	0.569162i	−0.0575327	+	0.0482757i	0.613568	+	0.789642i	$0.289734\pi$
$140$	0.108876	+	0.617467i	0.00920171	+	0.0521855i
$141$	0.0387228	−	0.767581i	0.00326105	−	0.0646420i
$142$	3.28613	+	2.75739i	0.275766	+	0.231395i
$143$	−0.531082	+	0.919862i	−0.0444113	+	0.0769227i
$144$	2.70150	+	1.30456i	0.225125	+	0.108713i
$145$	0.212125	+	0.367411i	0.0176160	+	0.0305118i
$146$	1.71332	−	9.71673i	0.141796	−	0.804162i
$147$	1.17878	−	1.26905i	0.0972239	−	0.104669i
$148$	4.88488	+	1.77795i	0.401535	+	0.146147i
$149$	4.99854	+	1.81932i	0.409497	+	0.149045i	0.538551	−	0.842593i	$-0.318972\pi$
$149$	4.99854	+	1.81932i	0.409497	+	0.149045i	−0.129054	+	0.991638i	$0.541194\pi$
$150$	7.77833	+	1.77976i	0.635098	+	0.145317i
$151$	−1.61648	+	9.16750i	−0.131547	+	0.746040i	0.845655	+	0.533730i	$0.179210\pi$
$151$	−1.61648	+	9.16750i	−0.131547	+	0.746040i	−0.977202	+	0.212311i	$0.931901\pi$
$152$	1.22610	+	2.12366i	0.0994496	+	0.172252i
$153$	−0.506261	+	0.128330i	−0.0409288	+	0.0103748i
$154$	0.125079	−	0.216644i	0.0100792	−	0.0174577i
$155$	3.59578	+	3.01722i	0.288820	+	0.242349i
$156$	−6.17559	−	3.99333i	−0.494443	−	0.319722i
$157$	−1.23178	−	6.98577i	−0.0983067	−	0.557525i	−0.993684	−	0.112216i	$-0.964205\pi$
$157$	−1.23178	−	6.98577i	−0.0983067	−	0.557525i	0.895377	−	0.445309i	$-0.146906\pi$
$158$	−4.17525	+	3.50345i	−0.332165	+	0.278720i
$159$	12.6415	+	16.7077i	1.00253	+	1.32501i
$160$	−0.589180	+	0.214444i	−0.0465788	+	0.0169533i
$161$	0.0496498			0.00391295
$162$	8.81769	+	1.80231i	0.692783	+	0.141603i
$163$	0.0659960			0.00516921			0.00258460	−	0.999997i	$-0.499177\pi$
$163$	0.0659960			0.00516921			0.00258460	+	0.999997i	$0.499177\pi$
$164$	11.3770	−	4.14090i	0.888396	−	0.323350i
$165$	0.163918	+	0.216644i	0.0127610	+	0.0168657i
$166$	−4.74111	+	3.97826i	−0.367982	+	0.308773i
$167$	2.73325	+	15.5010i	0.211505	+	1.19950i	0.886869	+	0.462020i	$0.152875\pi$
$167$	2.73325	+	15.5010i	0.211505	+	1.19950i	−0.675364	+	0.737484i	$0.736014\pi$
$168$	1.45446	+	0.940501i	0.112214	+	0.0725612i
$169$	3.85181	+	3.23205i	0.296293	+	0.248620i
$170$	0.0545769	−	0.0945299i	0.00418586	−	0.00725011i
$171$	5.13096	+	5.27186i	0.392375	+	0.403149i
$172$	−0.684183	−	1.18504i	−0.0521685	−	0.0903584i
$173$	2.41378	−	13.6892i	0.183517	−	1.04077i	−0.744330	−	0.667812i	$-0.767231\pi$
$173$	2.41378	−	13.6892i	0.183517	−	1.04077i	0.927847	−	0.372962i	$-0.121658\pi$
$174$	1.14245	+	0.261405i	0.0866093	+	0.0198171i
$175$	4.32905	+	1.57565i	0.327246	+	0.119108i
$176$	0.235072	+	0.0855594i	0.0177193	+	0.00644928i
$177$	5.75243	−	6.19296i	0.432379	−	0.465491i
$178$	−1.22770	+	6.96261i	−0.0920197	+	0.521870i
$179$	−2.97554	−	5.15378i	−0.222402	−	0.385212i	0.733135	−	0.680083i	$-0.238056\pi$
$179$	−2.97554	−	5.15378i	−0.222402	−	0.385212i	−0.955537	+	0.294872i	$0.904723\pi$
$180$	−1.55528	+	1.05792i	−0.115924	+	0.0788526i
$181$	−7.23503	+	12.5314i	−0.537776	+	0.931455i	0.461248	+	0.887271i	$0.347402\pi$
$181$	−7.23503	+	12.5314i	−0.537776	+	0.931455i	−0.999023	+	0.0441833i	$0.985931\pi$
$182$	−3.25259	−	2.72925i	−0.241098	−	0.202306i
$183$	−0.243051	+	4.81787i	−0.0179668	+	0.356147i
$184$	0.00862160	+	0.0488955i	0.000635593	+	0.00360462i
$185$	−2.49680	+	2.09507i	−0.183569	+	0.154032i
$186$	12.8672	−	1.60543i	0.943466	−	0.117716i
$187$	−0.0409240	+	0.0148951i	−0.00299266	+	0.00108924i
$188$	0.443727			0.0323621
$189$	4.92290	+	1.66286i	0.358088	+	0.120955i
$190$	−1.53751			−0.111543
$191$	6.63560	−	2.41516i	0.480135	−	0.174755i	−0.0906027	−	0.995887i	$-0.528879\pi$
$191$	6.63560	−	2.41516i	0.480135	−	0.174755i	0.570738	+	0.821132i	$0.306657\pi$
$192$	−0.673648	+	1.59568i	−0.0486164	+	0.115158i
$193$	−9.10006	+	7.63586i	−0.655037	+	0.549641i	−0.908595	−	0.417679i	$-0.862844\pi$
$193$	−9.10006	+	7.63586i	−0.655037	+	0.549641i	0.253558	+	0.967320i	$0.418399\pi$
$194$	−2.64647	−	15.0089i	−0.190006	−	1.07758i
$195$	4.10437	−	2.10140i	0.293920	−	0.150484i
$196$	0.766044	+	0.642788i	0.0547175	+	0.0459134i
$197$	12.5895	−	21.8056i	0.896964	−	1.55359i	0.0656101	−	0.997845i	$-0.479101\pi$
$197$	12.5895	−	21.8056i	0.896964	−	1.55359i	0.831354	−	0.555743i	$-0.187566\pi$
$198$	0.746666	+	0.0755275i	0.0530633	+	0.00536751i
$199$	3.85284	+	6.67331i	0.273121	+	0.473059i	0.969659	−	0.244461i	$-0.0786109\pi$
$199$	3.85284	+	6.67331i	0.273121	+	0.473059i	−0.696539	+	0.717519i	$0.745278\pi$
$200$	−0.799976	+	4.53689i	−0.0565669	+	0.320807i
$201$	1.70253	+	5.53005i	0.120088	+	0.390060i
$202$	−2.31963	−	0.844275i	−0.163208	−	0.0594030i
$203$	0.635836	+	0.231425i	0.0446269	+	0.0162429i
$204$	−0.0887236	−	0.288186i	−0.00621190	−	0.0201770i
$205$	−1.31818	+	7.47579i	−0.0920659	+	0.522131i
$206$	5.44887	+	9.43772i	0.379641	+	0.657557i
$207$	0.0611147	+	0.135834i	0.00424777	+	0.00944113i
$208$	2.12298	−	3.67711i	0.147202	−	0.254962i
$209$	0.469921	+	0.394310i	0.0325051	+	0.0272750i
$210$	−0.966652	+	0.494917i	−0.0667054	+	0.0341525i
$211$	−4.37530	−	24.8135i	−0.301208	−	1.70823i	−0.640839	−	0.767675i	$-0.721413\pi$
$211$	−4.37530	−	24.8135i	−0.301208	−	1.70823i	0.339631	−	0.940559i	$-0.389698\pi$
$212$	−9.26624	+	7.77530i	−0.636408	+	0.534009i
$213$	−2.88977	+	6.84505i	−0.198004	+	0.469015i
$214$	15.4544	−	5.62493i	1.05644	−	0.384512i
$215$	0.857955			0.0585121
$216$	−0.782746	+	5.13686i	−0.0532591	+	0.349519i
$217$	7.48646			0.508214
$218$	13.3996	−	4.87706i	0.907537	−	0.330317i
$219$	16.9580	−	2.11584i	1.14592	−	0.142975i
$220$	−0.120152	+	0.100820i	−0.00810067	+	0.00679727i
$221$	0.128358	+	0.727954i	0.00863428	+	0.0489675i
$222$	−0.453648	+	8.99243i	−0.0304469	+	0.603532i
$223$	−17.6697	−	14.8267i	−1.18325	−	0.992866i	−0.999952	−	0.00980949i	$-0.996877\pi$
$223$	−17.6697	−	14.8267i	−1.18325	−	0.992866i	−0.183300	−	0.983057i	$-0.558678\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	1.01797	+	13.7831i	0.0678649	+	0.918873i
$226$	−2.46542	−	4.27023i	−0.163997	−	0.284052i
$227$	0.0444521	−	0.252100i	0.00295039	−	0.0167325i	−0.983297	−	0.182008i	$-0.941740\pi$
$227$	0.0444521	−	0.252100i	0.00295039	−	0.0167325i	0.986247	+	0.165276i	$0.0528514\pi$
$228$	−2.89059	+	3.11195i	−0.191434	+	0.206094i
$229$	−17.3377	−	6.31041i	−1.14571	−	0.417004i	−0.301737	−	0.953391i	$-0.597566\pi$
$229$	−17.3377	−	6.31041i	−1.14571	−	0.417004i	−0.843972	+	0.536388i	$0.819789\pi$
$230$	−0.0292527	−	0.0106471i	−0.00192886	−	0.000702049i
$231$	0.422372	+	0.0966431i	0.0277901	+	0.00635865i
$232$	−0.117498	+	0.666363i	−0.00771410	+	0.0437489i
$233$	−11.7883	−	20.4179i	−0.772275	−	1.33762i	−0.936314	−	0.351165i	$-0.885786\pi$
$233$	−11.7883	−	20.4179i	−0.772275	−	1.33762i	0.164039	−	0.986454i	$-0.447548\pi$
$234$	3.46314	−	12.2581i	0.226392	−	0.801335i
$235$	−0.139107	+	0.240940i	−0.00907432	+	0.0157172i
$236$	3.73830	+	3.13680i	0.243342	+	0.204189i
$237$	−7.92740	−	5.12611i	−0.514940	−	0.332977i
$238$	−0.0302306	−	0.171446i	−0.00195956	−	0.0111132i
$239$	−7.11168	+	5.96740i	−0.460016	+	0.385999i	−0.843137	−	0.537699i	$-0.819294\pi$
$239$	−7.11168	+	5.96740i	−0.460016	+	0.385999i	0.383121	+	0.923698i	$0.374849\pi$
$240$	−0.655255	−	0.866025i	−0.0422965	−	0.0559017i
$241$	14.8989	−	5.42276i	0.959723	−	0.349311i	0.185798	−	0.982588i	$-0.440513\pi$
$241$	14.8989	−	5.42276i	0.959723	−	0.349311i	0.773925	+	0.633277i	$0.218291\pi$
$242$	−10.9374			−0.703084
$243$	1.51034	+	15.5151i	0.0968884	+	0.995295i
$244$	−2.78514			−0.178300
$245$	−0.589180	+	0.214444i	−0.0376414	+	0.0137003i
$246$	12.6529	+	16.7229i	0.806721	+	1.06621i
$247$	7.97600	−	6.69265i	0.507500	−	0.425843i
$248$	1.30001	+	7.37273i	0.0825508	+	0.468169i
$249$	−9.00178	−	5.82084i	−0.570465	−	0.368881i
$250$	−4.61423	−	3.87179i	−0.291829	−	0.244874i
$251$	4.96806	−	8.60493i	0.313581	−	0.543139i	−0.665554	−	0.746350i	$-0.731805\pi$
$251$	4.96806	−	8.60493i	0.313581	−	0.543139i	0.979135	+	0.203211i	$0.0651379\pi$
$252$	−0.815631	+	2.88700i	−0.0513799	+	0.181864i
$253$	0.00621017	+	0.0107563i	0.000390430	+	0.000676245i
$254$	3.18549	−	18.0658i	0.199876	−	1.13355i
$255$	0.184297	+	0.0421690i	0.0115411	+	0.00264073i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	14.3247	+	5.21378i	0.893553	+	0.325227i	0.747666	−	0.664075i	$-0.231174\pi$
$257$	14.3247	+	5.21378i	0.893553	+	0.325227i	0.145887	+	0.989301i	$0.453396\pi$
$258$	1.61300	−	1.73652i	0.100421	−	0.108111i
$259$	−0.902689	+	5.11941i	−0.0560904	+	0.318104i
$260$	1.33109	+	2.30552i	0.0825509	+	0.142982i
$261$	0.149516	+	2.02441i	0.00925484	+	0.125308i
$262$	−10.6705	+	18.4818i	−0.659225	+	1.14181i
$263$	8.20749	+	6.88690i	0.506096	+	0.424665i	0.859753	−	0.510711i	$-0.170618\pi$
$263$	8.20749	+	6.88690i	0.506096	+	0.424665i	−0.353657	+	0.935375i	$0.615062\pi$
$264$	−0.0218307	+	0.432738i	−0.00134358	+	0.0266332i
$265$	−1.31699	−	7.46901i	−0.0809020	−	0.458818i
$266$	−1.87849	+	1.57624i	−0.115178	+	0.0966455i
$267$	−12.1514	+	1.51612i	−0.743655	+	0.0927853i
$268$	−3.13920	+	1.14257i	−0.191757	+	0.0697938i
$269$	−13.9193			−0.848677			−0.424339	−	0.905504i	$-0.639493\pi$
$269$	−13.9193			−0.848677			−0.424339	+	0.905504i	$0.639493\pi$
$270$	−2.54388	−	2.03541i	−0.154816	−	0.123871i
$271$	−4.99999			−0.303728			−0.151864	−	0.988401i	$-0.548528\pi$
$271$	−4.99999			−0.303728			−0.151864	+	0.988401i	$0.548528\pi$
$272$	0.163592	−	0.0595426i	0.00991922	−	0.00361030i
$273$	2.86028	−	6.77520i	0.173112	−	0.410054i
$274$	4.25367	−	3.56926i	0.256974	−	0.215627i
$275$	0.200121	+	1.13494i	0.0120678	+	0.0684397i
$276$	−0.0765465	+	0.0391911i	−0.00460756	+	0.00235902i
$277$	6.45026	+	5.41241i	0.387558	+	0.325200i	0.815661	−	0.578530i	$-0.196373\pi$
$277$	6.45026	+	5.41241i	0.387558	+	0.325200i	−0.428103	+	0.903730i	$0.640818\pi$
$278$	0.442730	−	0.766830i	0.0265532	−	0.0459914i
$279$	9.21520	+	20.4818i	0.551700	+	1.22621i
$280$	−0.313496	−	0.542992i	−0.0187350	−	0.0324500i
$281$	4.06049	−	23.0282i	0.242229	−	1.37375i	−0.584613	−	0.811312i	$-0.698754\pi$
$281$	4.06049	−	23.0282i	0.242229	−	1.37375i	0.826842	−	0.562435i	$-0.190135\pi$
$282$	0.226141	+	0.734534i	0.0134665	+	0.0437409i
$283$	−15.3148	−	5.57412i	−0.910369	−	0.331347i	−0.155969	−	0.987762i	$-0.549850\pi$
$283$	−15.3148	−	5.57412i	−0.910369	−	0.331347i	−0.754400	+	0.656415i	$0.772072\pi$
$284$	−4.03103	−	1.46718i	−0.239198	−	0.0870609i
$285$	−0.783575	−	2.54515i	−0.0464150	−	0.150762i
$286$	0.184443	−	1.04603i	0.0109063	−	0.0618529i
$287$	6.05359	+	10.4851i	0.357332	+	0.618917i
$288$	−2.98477	−	0.301918i	−0.175879	−	0.0177907i
$289$	8.48485	−	14.6962i	0.499109	−	0.864481i
$290$	−0.324994	−	0.272703i	−0.0190843	−	0.0160136i
$291$	23.4966	−	12.0300i	1.37739	−	0.705213i
$292$	1.71332	+	9.71673i	0.100265	+	0.568629i
$293$	11.5162	−	9.66323i	0.672783	−	0.564532i	−0.241104	−	0.970499i	$-0.577510\pi$
$293$	11.5162	−	9.66323i	0.672783	−	0.564532i	0.913888	+	0.405967i	$0.133065\pi$
$294$	−0.673648	+	1.59568i	−0.0392880	+	0.0930620i
$295$	−2.87520	+	1.04649i	−0.167401	+	0.0609289i
$296$	−5.19838			−0.302150
$297$	0.255504	+	1.27450i	0.0148259	+	0.0739543i
$298$	−5.31934			−0.308141
$299$	0.198098	−	0.0721016i	0.0114563	−	0.00416975i
$300$	−7.91796	+	0.987918i	−0.457144	+	0.0570375i
$301$	1.04823	−	0.879569i	0.0604189	−	0.0506975i
$302$	−1.61648	−	9.16750i	−0.0930178	−	0.527530i
$303$	0.215418	−	4.27013i	0.0123755	−	0.245312i
$304$	−1.87849	−	1.57624i	−0.107739	−	0.0904036i
$305$	0.873130	−	1.51230i	0.0499953	−	0.0865943i
$306$	0.431839	−	0.293742i	0.0246866	−	0.0167921i
$307$	−7.53035	−	13.0429i	−0.429780	−	0.744400i	0.567074	−	0.823667i	$-0.308075\pi$
$307$	−7.53035	−	13.0429i	−0.429780	−	0.744400i	−0.996853	+	0.0792666i	$0.974742\pi$
$308$	−0.0434396	+	0.246358i	−0.00247520	+	0.0140376i
$309$	−12.8460	+	13.8298i	−0.730784	+	0.786748i
$310$	−4.41088	−	1.60543i	−0.250521	−	0.0911822i
$311$	−29.3274	−	10.6743i	−1.66300	−	0.605284i	−0.672173	−	0.740394i	$-0.734639\pi$
$311$	−29.3274	−	10.6743i	−1.66300	−	0.605284i	−0.990831	+	0.135110i	$0.956861\pi$
$312$	7.16895	+	1.64033i	0.405862	+	0.0928653i
$313$	−3.06803	+	17.3997i	−0.173416	+	0.983489i	0.766541	+	0.642195i	$0.221976\pi$
$313$	−3.06803	+	17.3997i	−0.173416	+	0.983489i	−0.939957	+	0.341293i	$0.889135\pi$
$314$	3.54677	+	6.14318i	0.200156	+	0.346680i
$315$	−1.31192	−	1.34794i	−0.0739182	−	0.0759480i
$316$	2.72520	−	4.72019i	0.153305	−	0.265531i
$317$	−17.8698	−	14.9945i	−1.00367	−	0.842177i	−0.0161786	−	0.999869i	$-0.505150\pi$
$317$	−17.8698	−	14.9945i	−1.00367	−	0.842177i	−0.987488	+	0.157693i	$0.949594\pi$
$318$	−17.5935	−	11.3765i	−0.986593	−	0.637962i
$319$	0.0293931	+	0.166697i	0.00164570	+	0.00933321i
$320$	0.480304	−	0.403023i	0.0268498	−	0.0225297i
$321$	17.1875	+	22.7161i	0.959314	+	1.26789i
$322$	−0.0466555	+	0.0169812i	−0.00260001	+	0.000946327i
$323$	0.426905			0.0237536
$324$	−8.90235	+	1.32221i	−0.494575	+	0.0734560i
$325$	19.5606			1.08503
$326$	−0.0620160	+	0.0225720i	−0.00343475	+	0.00125015i
$327$	14.9024	+	19.6959i	0.824102	+	1.08918i
$328$	−9.27464	+	7.78234i	−0.512106	+	0.429708i
$329$	0.0770523	+	0.436986i	0.00424803	+	0.0240918i
$330$	−0.228129	−	0.147515i	−0.0125581	−	0.00812046i
$331$	−10.2229	−	8.57801i	−0.561900	−	0.471490i	0.317047	−	0.948410i	$-0.397309\pi$
$331$	−10.2229	−	8.57801i	−0.561900	−	0.471490i	−0.878947	+	0.476920i	$0.841753\pi$
$332$	3.09454	−	5.35990i	0.169835	−	0.294163i
$333$	−15.1170	+	3.83194i	−0.828408	+	0.209989i
$334$	−7.87007	−	13.6314i	−0.430631	−	0.745875i
$335$	0.363718	−	2.06275i	0.0198721	−	0.112700i
$336$	−1.68842	−	0.386327i	−0.0921107	−	0.0210759i
$337$	−24.2530	−	8.82736i	−1.32114	−	0.480857i	−0.417319	−	0.908760i	$-0.637030\pi$
$337$	−24.2530	−	8.82736i	−1.32114	−	0.480857i	−0.903825	+	0.427903i	$0.859253\pi$
$338$	−4.72495	−	1.71974i	−0.257003	−	0.0935415i
$339$	5.81236	−	6.25747i	0.315684	−	0.339859i
$340$	−0.0189543	+	0.107495i	−0.00102794	+	0.00582976i
$341$	0.936403	+	1.62190i	0.0507090	+	0.0878306i
$342$	−6.62461	−	3.19904i	−0.358218	−	0.172984i
$343$	−0.500000	+	0.866025i	−0.0269975	+	0.0467610i
$344$	1.04823	+	0.879569i	0.0565167	+	0.0474232i
$345$	0.00271663	−	0.0538504i	0.000146259	−	0.00289921i
$346$	2.41378	+	13.6892i	0.129766	+	0.735939i
$347$	1.46706	−	1.23101i	0.0787557	−	0.0660839i	−0.602560	−	0.798074i	$-0.705853\pi$
$347$	1.46706	−	1.23101i	0.0787557	−	0.0660839i	0.681316	+	0.731990i	$0.261408\pi$
$348$	−1.16296	+	0.145102i	−0.0623413	+	0.00777828i
$349$	−18.8097	+	6.84616i	−1.00686	+	0.366466i	−0.792226	−	0.610228i	$-0.791078\pi$
$349$	−18.8097	+	6.84616i	−1.00686	+	0.366466i	−0.214633	+	0.976695i	$0.568855\pi$
$350$	−4.60688			−0.246248
$351$	22.0567	−	0.514405i	1.17730	−	0.0274569i
$352$	−0.250159			−0.0133335
$353$	−16.6145	+	6.04720i	−0.884303	+	0.321860i	−0.743945	−	0.668241i	$-0.767048\pi$
$353$	−16.6145	+	6.04720i	−0.884303	+	0.321860i	−0.140358	+	0.990101i	$0.544825\pi$
$354$	−3.28740	+	7.78692i	−0.174724	+	0.413870i
$355$	2.06038	−	1.72886i	0.109354	−	0.0917585i
$356$	−1.22770	−	6.96261i	−0.0650678	−	0.369018i
$357$	0.268401	−	0.137419i	0.0142053	−	0.00727297i
$358$	4.55879	+	3.82528i	0.240939	+	0.202172i
$359$	−15.1563	+	26.2515i	−0.799918	+	1.38550i	0.119750	+	0.992804i	$0.461791\pi$
$359$	−15.1563	+	26.2515i	−0.799918	+	1.38550i	−0.919669	+	0.392695i	$0.871543\pi$
$360$	1.09965	−	1.52605i	0.0579568	−	0.0804301i
$361$	6.49337	+	11.2468i	0.341756	+	0.591939i
$362$	2.51270	−	14.2502i	0.132065	−	0.748975i
$363$	−5.57414	−	18.1055i	−0.292567	−	0.950294i
$364$	3.98990	+	1.45220i	0.209127	+	0.0761162i
$365$	−5.81322	−	2.11584i	−0.304278	−	0.110748i
$366$	−1.41942	−	4.61044i	−0.0741940	−	0.240992i
$367$	−1.70454	+	9.66691i	−0.0889761	+	0.504609i	0.907451	+	0.420157i	$0.138025\pi$
$367$	−1.70454	+	9.66691i	−0.0889761	+	0.504609i	−0.996428	+	0.0844517i	$0.973086\pi$
$368$	−0.0248249	−	0.0429980i	−0.00129409	−	0.00224143i
$369$	−21.2342	+	29.4680i	−1.10541	+	1.53404i
$370$	1.62967	−	2.82268i	0.0847227	−	0.146744i
$371$	−9.26624	−	7.77530i	−0.481079	−	0.403673i
$372$	−11.5421	+	5.90944i	−0.598430	+	0.306390i
$373$	2.83376	+	16.0710i	0.146726	+	0.832126i	0.965965	+	0.258673i	$0.0832853\pi$
$373$	2.83376	+	16.0710i	0.146726	+	0.832126i	−0.819239	+	0.573453i	$0.805604\pi$
$374$	0.0333615	−	0.0279937i	0.00172508	−	0.00144752i
$375$	4.05768	−	9.61149i	0.209538	−	0.496335i
$376$	−0.416967	+	0.151763i	−0.0215034	+	0.00782660i
$377$	2.87300			0.147967
$378$	−5.19474	+	0.121152i	−0.267189	+	0.00623137i
$379$	−28.4011			−1.45887			−0.729433	−	0.684052i	$-0.760216\pi$
$379$	−28.4011			−1.45887			−0.729433	+	0.684052i	$0.760216\pi$
$380$	1.44478	−	0.525859i	0.0741159	−	0.0269760i
$381$	31.5292	−	3.93387i	1.61529	−	0.201539i
$382$	−5.40939	+	4.53902i	−0.276769	+	0.232236i
$383$	1.84496	+	10.4633i	0.0942731	+	0.534649i	0.994968	+	0.100196i	$0.0319471\pi$
$383$	1.84496	+	10.4633i	0.0942731	+	0.534649i	−0.900695	+	0.434453i	$0.856942\pi$
$384$	0.0872671	−	1.72985i	0.00445333	−	0.0882761i
$385$	−0.120152	−	0.100820i	−0.00612353	−	0.00513825i
$386$	5.93964	−	10.2878i	0.302320	−	0.523633i
$387$	3.69664	+	1.78512i	0.187911	+	0.0907426i
$388$	7.62021	+	13.1986i	0.386858	+	0.670057i
$389$	−6.23887	+	35.3824i	−0.316323	+	1.79396i	0.248379	+	0.968663i	$0.420102\pi$
$389$	−6.23887	+	35.3824i	−0.316323	+	1.79396i	−0.564702	+	0.825295i	$0.691009\pi$
$390$	−3.13812	+	3.37844i	−0.158905	+	0.171074i
$391$	0.00812231	+	0.00295628i	0.000410763	+	0.000149505i
$392$	−0.939693	−	0.342020i	−0.0474616	−	0.0172746i
$393$	−36.0325	−	8.24460i	−1.81760	−	0.415885i
$394$	−4.37229	+	24.7965i	−0.220273	+	1.24923i
$395$	1.70868	+	2.95952i	0.0859731	+	0.148910i
$396$	−0.727469	+	0.184402i	−0.0365567	+	0.00926656i
$397$	12.5480	−	21.7337i	0.629765	−	1.09078i	−0.357834	−	0.933785i	$-0.616485\pi$
$397$	12.5480	−	21.7337i	0.629765	−	1.09078i	0.987599	−	0.157000i	$-0.0501821\pi$
$398$	−5.90289	−	4.95312i	−0.295885	−	0.248277i
$399$	−3.56662	−	2.30629i	−0.178554	−	0.115459i
$400$	−0.799976	−	4.53689i	−0.0399988	−	0.226845i
$401$	13.4481	−	11.2843i	0.671565	−	0.563510i	−0.241963	−	0.970285i	$-0.577791\pi$
$401$	13.4481	−	11.2843i	0.671565	−	0.563510i	0.913528	+	0.406775i	$0.133347\pi$
$402$	−3.49125	−	4.61425i	−0.174128	−	0.230138i
$403$	29.8702	−	10.8719i	1.48794	−	0.541567i
$404$	2.46849			0.122812
$405$	2.07291	−	5.24841i	0.103003	−	0.260795i
$406$	−0.676642			−0.0335812
$407$	−1.22200	+	0.444770i	−0.0605721	+	0.0220464i
$408$	0.181938	+	0.240461i	0.00900729	+	0.0119046i
$409$	25.1441	−	21.0984i	1.24329	−	1.04325i	0.246034	−	0.969261i	$-0.420872\pi$
$409$	25.1441	−	21.0984i	1.24329	−	1.04325i	0.997259	−	0.0739858i	$-0.0235720\pi$
$410$	−1.31818	−	7.47579i	−0.0651004	−	0.369203i
$411$	8.07630	+	5.22239i	0.398375	+	0.257602i
$412$	−8.34815	−	7.00493i	−0.411284	−	0.345108i
$413$	−2.44000	+	4.22620i	−0.120065	+	0.207958i
$414$	−0.103887	−	0.106740i	−0.00510577	−	0.00524598i
$415$	1.94025	+	3.36062i	0.0952433	+	0.164966i
$416$	−0.737303	+	4.18146i	−0.0361493	+	0.205013i
$417$	1.49502	+	0.342077i	0.0732116	+	0.0167516i
$418$	−0.576443	−	0.209808i	−0.0281948	−	0.0102621i
$419$	−9.93869	−	3.61739i	−0.485537	−	0.176721i	0.0876406	−	0.996152i	$-0.472067\pi$
$419$	−9.93869	−	3.61739i	−0.485537	−	0.176721i	−0.573178	+	0.819431i	$0.694290\pi$
$420$	0.739085	−	0.795684i	0.0360636	−	0.0388254i
$421$	−2.89699	+	16.4297i	−0.141191	+	0.800733i	0.829156	+	0.559017i	$0.188821\pi$
$421$	−2.89699	+	16.4297i	−0.141191	+	0.800733i	−0.970347	+	0.241716i	$0.922290\pi$
$422$	12.5982	+	21.8207i	0.613269	+	1.06221i
$423$	−1.10068	+	0.748696i	−0.0535169	+	0.0364028i
$424$	6.04811	−	10.4756i	0.293722	−	0.508741i
$425$	0.614380	+	0.515526i	0.0298018	+	0.0250067i
$426$	0.374353	−	7.42061i	0.0181375	−	0.359530i
$427$	−0.483634	−	2.74282i	−0.0234047	−	0.132734i
$428$	−12.5985	+	10.5714i	−0.608972	+	0.510988i
$429$	1.82557	−	0.227775i	0.0881393	−	0.0109971i
$430$	−0.806214	+	0.293438i	−0.0388791	+	0.0141508i
$431$	15.4219			0.742847			0.371423	−	0.928464i	$-0.378870\pi$
$431$	15.4219			0.742847			0.371423	+	0.928464i	$0.378870\pi$
$432$	−1.02137	−	5.09478i	−0.0491406	−	0.245123i
$433$	40.5518			1.94879			0.974396	−	0.224837i	$-0.0721850\pi$
$433$	40.5518			1.94879			0.974396	+	0.224837i	$0.0721850\pi$
$434$	−7.03497	+	2.56052i	−0.337690	+	0.122909i
$435$	0.285795	−	0.676967i	0.0137028	−	0.0324581i
$436$	−10.9235	+	9.16588i	−0.523140	+	0.438966i
$437$	−0.0211418	−	0.119901i	−0.00101135	−	0.00573566i
$438$	−15.2117	+	7.78822i	−0.726841	+	0.372136i
$439$	−26.3958	−	22.1487i	−1.25980	−	1.05710i	−0.995703	−	0.0926032i	$-0.970481\pi$
$439$	−26.3958	−	22.1487i	−1.25980	−	1.05710i	−0.264098	−	0.964496i	$-0.585074\pi$
$440$	0.0784239	−	0.135834i	0.00373871	−	0.00647564i
$441$	−2.98477	−	0.301918i	−0.142132	−	0.0143771i
$442$	−0.369592	−	0.640152i	−0.0175797	−	0.0304489i
$443$	−4.22885	+	23.9830i	−0.200919	+	1.13947i	0.702815	+	0.711372i	$0.251926\pi$
$443$	−4.22885	+	23.9830i	−0.200919	+	1.13947i	−0.903734	+	0.428094i	$0.859185\pi$
$444$	−2.64930	−	8.60527i	−0.125730	−	0.408388i
$445$	4.16552	+	1.51612i	0.197464	+	0.0718712i
$446$	21.6751	+	7.88910i	1.02635	+	0.373560i
$447$	−2.71095	−	8.80550i	−0.128223	−	0.416486i
$448$	0.173648	−	0.984808i	0.00820411	−	0.0465278i
$449$	−5.10430	−	8.84090i	−0.240887	−	0.417228i	0.720080	−	0.693891i	$-0.244105\pi$
$449$	−5.10430	−	8.84090i	−0.240887	−	0.417228i	−0.960967	+	0.276663i	$0.910772\pi$
$450$	−5.67068	−	12.6037i	−0.267318	−	0.594145i
$451$	−1.51436	+	2.62295i	−0.0713084	+	0.123510i
$452$	3.77724	+	3.16948i	0.177667	+	0.149080i
$453$	14.3518	−	7.34799i	0.674308	−	0.345239i
$454$	0.0444521	+	0.252100i	0.00208624	+	0.0118317i
$455$	−2.03935	+	1.71122i	−0.0956063	+	0.0802232i
$456$	1.65192	−	3.91292i	0.0773581	−	0.183239i
$457$	13.5197	−	4.92076i	0.632423	−	0.230183i	−0.00586237	−	0.999983i	$-0.501866\pi$
$457$	13.5197	−	4.92076i	0.632423	−	0.230183i	0.638286	+	0.769800i	$0.279644\pi$
$458$	18.4504			0.862131
$459$	0.706335	+	0.565153i	0.0329689	+	0.0263791i
$460$	0.0311301			0.00145145
$461$	6.22607	−	2.26611i	0.289977	−	0.105543i	−0.192936	−	0.981211i	$-0.561801\pi$
$461$	6.22607	−	2.26611i	0.289977	−	0.105543i	0.482913	+	0.875668i	$0.339579\pi$
$462$	−0.429954	+	0.0536451i	−0.0200033	+	0.00249580i
$463$	2.90393	−	2.43669i	0.134957	−	0.113242i	−0.572810	−	0.819688i	$-0.694147\pi$
$463$	2.90393	−	2.43669i	0.134957	−	0.113242i	0.707767	+	0.706445i	$0.249702\pi$
$464$	−0.117498	−	0.666363i	−0.00545469	−	0.0309351i
$465$	0.409628	−	8.11985i	0.0189961	−	0.376549i
$466$	18.0607	+	15.1547i	0.836644	+	0.702028i
$467$	−6.74689	+	11.6860i	−0.312209	+	0.540761i	−0.978840	−	0.204626i	$-0.934402\pi$
$467$	−6.74689	+	11.6860i	−0.312209	+	0.540761i	0.666632	+	0.745387i	$0.267735\pi$
$468$	0.938222	+	12.7033i	0.0433693	+	0.587209i
$469$	−1.67033	−	2.89310i	−0.0771287	−	0.133591i
$470$	0.0483113	−	0.273987i	0.00222843	−	0.0126381i
$471$	−8.36170	+	9.00204i	−0.385287	+	0.414792i
$472$	−4.58570	−	1.66906i	−0.211074	−	0.0768246i
$473$	0.321665	+	0.117077i	0.0147902	+	0.00538318i
$474$	9.20255	+	2.10564i	0.422687	+	0.0967151i
$475$	1.96170	−	11.1253i	0.0900089	−	0.510466i
$476$	0.0870455	+	0.150767i	0.00398972	+	0.00691040i
$477$	9.86605	−	34.9217i	0.451735	−	1.59896i
$478$	4.64182	−	8.03986i	0.212312	−	0.367735i
$479$	−10.5269	−	8.83309i	−0.480985	−	0.403594i	0.369797	−	0.929112i	$-0.379427\pi$
$479$	−10.5269	−	8.83309i	−0.480985	−	0.403594i	−0.850782	+	0.525518i	$0.823872\pi$
$480$	0.911937	+	0.589687i	0.0416240	+	0.0269154i
$481$	3.83278	+	21.7368i	0.174760	+	0.991113i
$482$	−12.1457	+	10.1915i	−0.553222	+	0.464208i
$483$	−0.0518878	−	0.0685781i	−0.00236098	−	0.00312041i
$484$	10.2778	−	3.74082i	0.467173	−	0.170037i
$485$	−9.55563			−0.433899
$486$	−6.72574	−	14.0629i	−0.305086	−	0.637905i
$487$	23.4159			1.06108			0.530538	−	0.847661i	$-0.321990\pi$
$487$	23.4159			1.06108			0.530538	+	0.847661i	$0.321990\pi$
$488$	2.61717	−	0.952572i	0.118474	−	0.0431209i
$489$	−0.0689709	−	0.0911562i	−0.00311897	−	0.00412222i
$490$	0.480304	−	0.403023i	0.0216979	−	0.0182067i
$491$	1.49114	+	8.45670i	0.0672944	+	0.381646i	0.999791	+	0.0204657i	$0.00651489\pi$
$491$	1.49114	+	8.45670i	0.0672944	+	0.381646i	−0.932496	+	0.361180i	$0.882374\pi$
$492$	−17.6094	−	11.3868i	−0.793894	−	0.513357i
$493$	0.0902380	+	0.0757187i	0.00406411	+	0.00341020i
$494$	−5.20596	+	9.01699i	−0.234227	+	0.405694i
$495$	0.127930	−	0.452819i	0.00575002	−	0.0203527i
$496$	−3.74323	−	6.48347i	−0.168076	−	0.291116i
$497$	0.744905	−	4.22457i	0.0334136	−	0.189498i
$498$	10.4497	+	2.39101i	0.468264	+	0.107144i
$499$	31.0769	+	11.3111i	1.39119	+	0.506353i	0.925552	−	0.378621i	$-0.123601\pi$
$499$	31.0769	+	11.3111i	1.39119	+	0.506353i	0.465641	+	0.884974i	$0.345824\pi$
$500$	5.66019	+	2.06014i	0.253131	+	0.0921322i
$501$	18.5541	−	19.9750i	0.828937	−	0.892417i
$502$	−1.72539	+	9.78517i	−0.0770079	+	0.436734i
$503$	15.8634	+	27.4762i	0.707314	+	1.22510i	0.965850	+	0.259102i	$0.0834265\pi$
$503$	15.8634	+	27.4762i	0.707314	+	1.22510i	−0.258536	+	0.966002i	$0.583240\pi$
$504$	−0.220968	−	2.99185i	−0.00984270	−	0.133268i
$505$	−0.773864	+	1.34037i	−0.0344365	+	0.0596458i
$506$	−0.00951453	−	0.00798364i	−0.000422972	−	0.000354916i
$507$	0.438795	−	8.69801i	0.0194876	−	0.386292i
$508$	3.18549	+	18.0658i	0.141333	+	0.801541i
$509$	23.2571	−	19.5150i	1.03085	−	0.864989i	0.0399017	−	0.999204i	$-0.487296\pi$
$509$	23.2571	−	19.5150i	1.03085	−	0.864989i	0.990952	+	0.134214i	$0.0428511\pi$
$510$	−0.187605	+	0.0234074i	−0.00830730	+	0.00103650i
$511$	−9.27160	+	3.37459i	−0.410151	+	0.149283i
$512$	1.00000			0.0441942
$513$	1.91945	−	12.5966i	0.0847456	−	0.556152i
$514$	−15.2441			−0.672387
$515$	6.42073	−	2.33696i	0.282931	−	0.102979i
$516$	−0.921797	+	2.18348i	−0.0405799	+	0.0961222i
$517$	−0.0850326	+	0.0713508i	−0.00373973	+	0.00313801i
$518$	−0.902689	−	5.11941i	−0.0396619	−	0.224934i
$519$	−21.4307	+	10.9723i	−0.940703	+	0.481631i
$520$	−2.03935	−	1.71122i	−0.0894315	−	0.0750420i
$521$	11.8470	−	20.5197i	0.519028	−	0.898983i	−0.480727	−	0.876870i	$-0.659627\pi$
$521$	11.8470	−	20.5197i	0.519028	−	0.898983i	0.999755	−	0.0221129i	$-0.00703933\pi$
$522$	−0.832890	−	1.85119i	−0.0364546	−	0.0810243i
$523$	−10.7941	−	18.6960i	−0.471994	−	0.817518i	0.527492	−	0.849560i	$-0.323132\pi$
$523$	−10.7941	−	18.6960i	−0.471994	−	0.817518i	−0.999487	+	0.0320416i	$0.989799\pi$
$524$	3.70582	−	21.0168i	0.161890	−	0.918122i
$525$	−2.34785	−	7.62612i	−0.102469	−	0.332831i
$526$	−10.0680	−	3.66444i	−0.438985	−	0.159777i
$527$	1.22473	+	0.445764i	0.0533499	+	0.0194178i
$528$	−0.127491	−	0.414107i	−0.00554833	−	0.0180217i
$529$	−3.99348	+	22.6482i	−0.173630	+	0.984702i
$530$	3.79212	+	6.56814i	0.164719	+	0.285302i
$531$	−14.5657	−	1.47336i	−0.632096	−	0.0639384i
$532$	1.22610	−	2.12366i	0.0531581	−	0.0920725i
$533$	39.3797	+	33.0435i	1.70573	+	1.43127i
$534$	10.9001	−	5.58072i	0.471691	−	0.241501i
$535$	−1.79060	−	10.1550i	−0.0774143	−	0.439038i
$536$	2.55910	−	2.14734i	0.110536	−	0.0927508i
$537$	−4.00893	+	9.49602i	−0.172998	+	0.409783i
$538$	13.0799	−	4.76069i	0.563915	−	0.205248i
$539$	−0.250159			−0.0107751
$540$	3.08662	+	1.04260i	0.132827	+	0.0448664i
$541$	14.9833			0.644184			0.322092	−	0.946708i	$-0.395614\pi$
$541$	14.9833			0.644184			0.322092	+	0.946708i	$0.395614\pi$
$542$	4.69846	−	1.71010i	0.201816	−	0.0734550i
$543$	24.8700	−	3.10302i	1.06728	−	0.133163i
$544$	−0.133361	+	0.111904i	−0.00571782	+	0.00479782i
$545$	−1.55253	−	8.80483i	−0.0665030	−	0.377157i
$546$	−0.370533	+	7.34488i	−0.0158573	+	0.314332i
$547$	−27.0650	−	22.7102i	−1.15722	−	0.971020i	−0.157353	−	0.987542i	$-0.550296\pi$
$547$	−27.0650	−	22.7102i	−1.15722	−	0.971020i	−0.999863	+	0.0165225i	$0.994740\pi$
$548$	−2.77639	+	4.80885i	−0.118601	+	0.205424i
$549$	6.90863	−	4.69933i	0.294853	−	0.200562i
$550$	−0.576226	−	0.998053i	−0.0245704	−	0.0425571i
$551$	0.288127	−	1.63405i	0.0122746	−	0.0696129i
$552$	0.0585261	−	0.0630080i	0.00249103	−	0.00268180i
$553$	5.12170	+	1.86415i	0.217797	+	0.0792716i
$554$	−7.91241	−	2.87988i	−0.336166	−	0.122354i
$555$	5.50314	+	1.25917i	0.233595	+	0.0534489i
$556$	−0.153758	+	0.872007i	−0.00652081	+	0.0369813i
$557$	0.176302	+	0.305364i	0.00747014	+	0.0129387i	0.869736	−	0.493517i	$-0.164289\pi$
$557$	0.176302	+	0.305364i	0.00747014	+	0.0129387i	−0.862266	+	0.506455i	$0.830955\pi$
$558$	−15.6646	−	16.0948i	−0.663137	−	0.681348i
$559$	2.90501	−	5.03163i	0.122869	−	0.212815i
$560$	0.480304	+	0.403023i	0.0202966	+	0.0170308i
$561$	0.0633424	+	0.0409592i	0.00267432	+	0.00172930i
$562$	4.06049	+	23.0282i	0.171282	+	0.971386i
$563$	−30.4124	+	25.5191i	−1.28173	+	1.07550i	−0.288729	+	0.957411i	$0.593233\pi$
$563$	−30.4124	+	25.5191i	−1.28173	+	1.07550i	−0.993003	+	0.118089i	$0.962323\pi$
$564$	−0.463728	−	0.612892i	−0.0195265	−	0.0258074i
$565$	−2.90515	+	1.05739i	−0.122221	+	0.0444847i
$566$	16.2976			0.685041
$567$	−2.84800	−	8.53750i	−0.119605	−	0.358541i
$568$	4.28974			0.179993
$569$	−34.6626	+	12.6161i	−1.45313	+	0.528896i	−0.943464	−	0.331475i	$-0.892454\pi$
$569$	−34.6626	+	12.6161i	−1.45313	+	0.528896i	−0.509667	+	0.860372i	$0.670231\pi$
$570$	1.60681	+	2.12366i	0.0673020	+	0.0889504i
$571$	−7.33363	+	6.15365i	−0.306903	+	0.257522i	−0.783211	−	0.621757i	$-0.786419\pi$
$571$	−7.33363	+	6.15365i	−0.306903	+	0.257522i	0.476308	+	0.879279i	$0.341975\pi$
$572$	0.184443	+	1.04603i	0.00771195	+	0.0437366i
$573$	−10.2706	−	6.64131i	−0.429061	−	0.277445i
$574$	−9.27464	−	7.78234i	−0.387116	−	0.324829i
$575$	0.114365	−	0.198087i	0.00476936	−	0.00826078i
$576$	2.90803	−	0.737141i	0.121168	−	0.0307142i
$577$	2.17563	+	3.76831i	0.0905728	+	0.156877i	0.907752	−	0.419507i	$-0.137797\pi$
$577$	2.17563	+	3.76831i	0.0905728	+	0.156877i	−0.817179	+	0.576383i	$0.804464\pi$
$578$	−2.94676	+	16.7119i	−0.122569	+	0.695123i
$579$	20.0572	+	4.58929i	0.833548	+	0.190724i
$580$	0.398664	+	0.145102i	0.0165536	+	0.00602503i
$581$	5.81583	+	2.11679i	0.241281	+	0.0878193i
$582$	−17.9651	+	19.3408i	−0.744676	+	0.801704i
$583$	0.525455	−	2.98000i	0.0217621	−	0.123419i
$584$	−4.93331	−	8.54475i	−0.204142	−	0.353584i
$585$	−7.19190	−	3.47299i	−0.297349	−	0.143590i
$586$	−7.51666	+	13.0192i	−0.310510	+	0.537820i
$587$	−18.7090	−	15.6987i	−0.772201	−	0.647954i	0.169070	−	0.985604i	$-0.445923\pi$
$587$	−18.7090	−	15.6987i	−0.772201	−	0.647954i	−0.941272	+	0.337650i	$0.890368\pi$
$588$	0.0872671	−	1.72985i	0.00359884	−	0.0713379i
$589$	−3.18788	−	18.0794i	−0.131354	−	0.744947i
$590$	2.34388	−	1.96675i	0.0964962	−	0.0809699i
$591$	−43.2758	+	5.39949i	−1.78013	+	0.222105i
$592$	4.88488	−	1.77795i	0.200767	−	0.0730733i
$593$	12.9536			0.531941			0.265970	−	0.963981i	$-0.414308\pi$
$593$	12.9536			0.531941			0.265970	+	0.963981i	$0.414308\pi$
$594$	−0.676002	−	1.11026i	−0.0277367	−	0.0455543i
$595$	−0.109154			−0.00447487
$596$	4.99854	−	1.81932i	0.204748	−	0.0745223i
$597$	5.19092	−	12.2958i	0.212450	−	0.503234i
$598$	−0.161491	+	0.135507i	−0.00660384	+	0.00554128i
$599$	0.631798	+	3.58311i	0.0258146	+	0.146402i	0.994991	−	0.0999669i	$-0.0318737\pi$
$599$	0.631798	+	3.58311i	0.0258146	+	0.146402i	−0.969176	+	0.246369i	$0.920763\pi$
$600$	7.10256	−	3.63644i	0.289961	−	0.148457i
$601$	−22.2215	−	18.6460i	−0.906434	−	0.760588i	0.0650034	−	0.997885i	$-0.479294\pi$
$601$	−22.2215	−	18.6460i	−0.906434	−	0.760588i	−0.971437	+	0.237297i	$0.923739\pi$
$602$	−0.684183	+	1.18504i	−0.0278852	+	0.0482986i
$603$	5.85903	−	8.13093i	0.238598	−	0.331117i
$604$	4.65446	+	8.06176i	0.189387	+	0.328028i
$605$	−1.19082	+	6.75350i	−0.0484139	+	0.274569i
$606$	1.25804	+	4.08629i	0.0511045	+	0.165994i
$607$	6.10716	+	2.22282i	0.247882	+	0.0902217i	0.462973	−	0.886372i	$-0.346783\pi$
$607$	6.10716	+	2.22282i	0.247882	+	0.0902217i	−0.215091	+	0.976594i	$0.569005\pi$
$608$	2.30431	+	0.838700i	0.0934521	+	0.0340138i
$609$	−0.344844	−	1.12010i	−0.0139738	−	0.0453886i
$610$	−0.303235	+	1.71973i	−0.0122776	+	0.0696298i
$611$	0.942023	+	1.63163i	0.0381102	+	0.0660088i
$612$	−0.305330	+	0.423725i	−0.0123422	+	0.0171281i
$613$	7.49041	−	12.9738i	0.302535	−	0.524005i	−0.674175	−	0.738572i	$-0.735501\pi$
$613$	7.49041	−	12.9738i	0.302535	−	0.524005i	0.976709	+	0.214566i	$0.0688339\pi$
$614$	11.5372	+	9.68083i	0.465602	+	0.390687i
$615$	11.7034	−	5.99204i	0.471928	−	0.241623i
$616$	−0.0434396	−	0.246358i	−0.00175023	−	0.00992606i
$617$	3.98099	−	3.34045i	0.160269	−	0.134481i	−0.559127	−	0.829082i	$-0.688863\pi$
$617$	3.98099	−	3.34045i	0.160269	−	0.134481i	0.719395	+	0.694601i	$0.244419\pi$
$618$	7.34124	−	17.3893i	0.295308	−	0.699501i
$619$	5.82097	−	2.11866i	0.233965	−	0.0851561i	−0.222377	−	0.974961i	$-0.571382\pi$
$619$	5.82097	−	2.11866i	0.233965	−	0.0851561i	0.456342	+	0.889805i	$0.349159\pi$
$620$	4.69396			0.188514
$621$	0.123750	−	0.226371i	0.00496590	−	0.00908395i
$622$	31.2096			1.25139
$623$	6.64365	−	2.41809i	0.266172	−	0.0968787i
$624$	−7.29764	+	0.910521i	−0.292139	+	0.0364500i
$625$	14.7523	−	12.3786i	0.590092	−	0.495146i
$626$	−3.06803	−	17.3997i	−0.122623	−	0.695431i
$627$	0.0535330	−	1.06116i	0.00213790	−	0.0423785i
$628$	−5.43396	−	4.55964i	−0.216839	−	0.181949i
$629$	−0.452496	+	0.783745i	−0.0180422	+	0.0312500i
$630$	1.69382	+	0.817950i	0.0674835	+	0.0325879i
$631$	20.7579	+	35.9538i	0.826360	+	1.43130i	0.900876	+	0.434077i	$0.142925\pi$
$631$	20.7579	+	35.9538i	0.826360	+	1.43130i	−0.0745161	+	0.997220i	$0.523741\pi$
$632$	−0.946453	+	5.36760i	−0.0376479	+	0.213512i
$633$	−29.7009	+	31.9754i	−1.18050	+	1.27091i
$634$	21.9205	+	7.97842i	0.870576	+	0.316864i
$635$	−10.8082	−	3.93387i	−0.428912	−	0.156111i
$636$	20.4234	+	4.67309i	0.809842	+	0.185300i
$637$	−0.737303	+	4.18146i	−0.0292130	+	0.165675i
$638$	−0.0846340	−	0.146590i	−0.00335069	−	0.00580357i
$639$	12.4747	−	3.16214i	0.493490	−	0.125092i
$640$	−0.313496	+	0.542992i	−0.0123920	+	0.0214636i
$641$	7.01815	+	5.88893i	0.277200	+	0.232599i	0.770779	−	0.637102i	$-0.219867\pi$
$641$	7.01815	+	5.88893i	0.277200	+	0.232599i	−0.493579	+	0.869701i	$0.664312\pi$
$642$	−23.9203	−	15.4677i	−0.944061	−	0.610460i
$643$	3.67117	+	20.8202i	0.144777	+	0.821069i	0.967546	+	0.252694i	$0.0813166\pi$
$643$	3.67117	+	20.8202i	0.144777	+	0.821069i	−0.822770	+	0.568375i	$0.807572\pi$
$644$	0.0380340	−	0.0319143i	0.00149875	−	0.00125760i
$645$	−0.896629	−	1.18504i	−0.0353047	−	0.0466609i
$646$	−0.401159	+	0.146010i	−0.0157834	+	0.00574469i
$647$	−10.4626			−0.411329			−0.205664	−	0.978623i	$-0.565935\pi$
$647$	−10.4626			−0.411329			−0.205664	+	0.978623i	$0.565935\pi$
$648$	7.91325	−	4.28725i	0.310862	−	0.168419i
$649$	−1.22078			−0.0479196
$650$	−18.3810	+	6.69013i	−0.720961	+	0.262409i
$651$	−7.82393	−	10.3406i	−0.306644	−	0.405279i
$652$	0.0505559	−	0.0424214i	0.00197992	−	0.00166135i
$653$	7.06892	+	40.0899i	0.276628	+	1.56884i	0.733742	+	0.679429i	$0.237772\pi$
$653$	7.06892	+	40.0899i	0.276628	+	1.56884i	−0.457113	+	0.889408i	$0.651117\pi$
$654$	−20.7400	−	13.4112i	−0.810999	−	0.524418i
$655$	10.2502	+	8.60091i	0.400507	+	0.336065i
$656$	6.05359	−	10.4851i	0.236353	−	0.409375i
$657$	−20.6449	−	21.2118i	−0.805434	−	0.827552i
$658$	−0.221863	−	0.384279i	−0.00864914	−	0.0149807i
$659$	−6.80705	+	38.6047i	−0.265165	+	1.50383i	0.503400	+	0.864054i	$0.332082\pi$
$659$	−6.80705	+	38.6047i	−0.265165	+	1.50383i	−0.768565	+	0.639772i	$0.779029\pi$
$660$	0.264824	+	0.0605945i	0.0103083	+	0.00235864i
$661$	−20.3201	−	7.39592i	−0.790361	−	0.287668i	−0.0848749	−	0.996392i	$-0.527049\pi$
$661$	−20.3201	−	7.39592i	−0.790361	−	0.287668i	−0.705486	+	0.708724i	$0.749271\pi$
$662$	12.5402	+	4.56426i	0.487389	+	0.177395i
$663$	0.871333	−	0.938060i	0.0338398	−	0.0364312i
$664$	−1.07472	+	6.09505i	−0.0417073	+	0.236534i
$665$	0.768754	+	1.33152i	0.0298110	+	0.0516342i
$666$	12.8948	−	8.77118i	0.499662	−	0.339876i
$667$	0.0167976	−	0.0290943i	0.000650405	−	0.00112653i
$668$	12.0576	+	10.1176i	0.466524	+	0.391460i
$669$	−2.01292	+	39.9011i	−0.0778240	+	1.54266i
$670$	0.363718	+	2.06275i	0.0140517	+	0.0796910i
$671$	0.533723	−	0.447847i	0.0206042	−	0.0172889i
$672$	1.71872	−	0.214444i	0.0663012	−	0.00827236i
$673$	39.4535	−	14.3599i	1.52082	−	0.553534i	0.559468	−	0.828852i	$-0.311006\pi$
$673$	39.4535	−	14.3599i	1.52082	−	0.553534i	0.961353	+	0.275319i	$0.0887833\pi$
$674$	25.8095			0.994144
$675$	17.9739	−	15.8105i	0.691814	−	0.608545i
$676$	5.02818			0.193392
$677$	−24.4066	+	8.88328i	−0.938022	+	0.341412i	−0.765385	−	0.643573i	$-0.777451\pi$
$677$	−24.4066	+	8.88328i	−0.938022	+	0.341412i	−0.172638	+	0.984985i	$0.555229\pi$
$678$	−3.32165	+	7.86805i	−0.127567	+	0.302171i
$679$	−11.6748	+	9.79636i	−0.448039	+	0.375950i
$680$	−0.0189543	−	0.107495i	−0.000726866	−	0.00412226i
$681$	−0.394666	+	0.202065i	−0.0151236	+	0.00774316i
$682$	−1.43465	−	1.20382i	−0.0549357	−	0.0460965i
$683$	1.47362	−	2.55239i	0.0563866	−	0.0976645i	−0.836454	−	0.548037i	$-0.815375\pi$
$683$	1.47362	−	2.55239i	0.0563866	−	0.0976645i	0.892841	+	0.450372i	$0.148709\pi$
$684$	7.31923	+	0.740362i	0.279858	+	0.0283085i
$685$	−1.74078	−	3.01511i	−0.0665116	−	0.115201i
$686$	0.173648	−	0.984808i	0.00662992	−	0.0376001i
$687$	9.40306	+	30.5423i	0.358749	+	1.16526i
$688$	−1.28584	−	0.468009i	−0.0490223	−	0.0178427i
$689$	−48.2627	−	17.5662i	−1.83866	−	0.669218i
$690$	0.0158651	+	0.0515319i	0.000603974	+	0.00196179i
$691$	4.08584	−	23.1720i	0.155433	−	0.881504i	−0.802956	−	0.596038i	$-0.796741\pi$
$691$	4.08584	−	23.1720i	0.155433	−	0.881504i	0.958389	−	0.285465i	$-0.0921482\pi$
$692$	−6.95021	−	12.0381i	−0.264207	−	0.457621i
$693$	−0.307924	−	0.684396i	−0.0116971	−	0.0259980i
$694$	−0.957552	+	1.65853i	−0.0363482	+	0.0629569i
$695$	−0.425290	−	0.356860i	−0.0161322	−	0.0135365i
$696$	1.04320	−	0.534108i	0.0395424	−	0.0202453i
$697$	0.366007	+	2.07573i	0.0138635	+	0.0786238i
$698$	15.3338	−	12.8666i	0.580392	−	0.487007i
$699$	−15.8823	+	37.6206i	−0.600723	+	1.42294i
$700$	4.32905	−	1.57565i	0.163623	−	0.0595538i
$701$	43.0461			1.62583			0.812914	−	0.582383i	$-0.197880\pi$
$701$	43.0461			1.62583			0.812914	+	0.582383i	$0.197880\pi$
$702$	−20.5505	+	8.02721i	−0.775630	+	0.302967i
$703$	12.7474			0.480779
$704$	0.235072	−	0.0855594i	0.00885963	−	0.00322464i
$705$	0.478172	−	0.0596612i	0.0180090	−	0.00224697i
$706$	13.5443	−	11.3650i	0.509747	−	0.427728i
$707$	0.428650	+	2.43099i	0.0161210	+	0.0914269i
$708$	0.425864	−	8.44167i	0.0160049	−	0.317258i
$709$	−13.8074	−	11.5858i	−0.518548	−	0.435114i	0.345577	−	0.938390i	$-0.387683\pi$
$709$	−13.8074	−	11.5858i	−0.518548	−	0.435114i	−0.864125	+	0.503277i	$0.832128\pi$
$710$	−1.34482	+	2.32929i	−0.0504701	+	0.0874167i
$711$	1.20437	+	16.3068i	0.0451672	+	0.611553i
$712$	3.53501	+	6.12282i	0.132480	+	0.229462i
$713$	0.0645453	−	0.366054i	0.00241724	−	0.0137088i
$714$	−0.205214	+	0.220930i	−0.00767996	+	0.00826809i
$715$	−0.625807	−	0.227775i	−0.0234038	−	0.00851830i
$716$	−5.59218	−	2.03539i	−0.208990	−	0.0760660i
$717$	15.6746	+	3.58652i	0.585380	+	0.133941i
$718$	5.26372	−	29.8521i	0.196440	−	1.11407i
$719$	16.2275	+	28.1068i	0.605182	+	1.04821i	0.992023	+	0.126059i	$0.0402330\pi$
$719$	16.2275	+	28.1068i	0.605182	+	1.04821i	−0.386841	+	0.922147i	$0.626434\pi$
$720$	−0.511395	+	1.81013i	−0.0190586	+	0.0674594i
$721$	5.44887	−	9.43772i	0.202927	−	0.351479i
$722$	−9.94842	−	8.34772i	−0.370242	−	0.310670i
$723$	−23.0606	−	14.9117i	−0.857633	−	0.554573i
$724$	2.51270	+	14.2502i	0.0933837	+	0.529606i
$725$	2.38792	−	2.00370i	0.0886852	−	0.0744157i
$726$	11.4304	+	15.1072i	0.424223	+	0.560680i
$727$	−26.5268	+	9.65498i	−0.983826	+	0.358083i	−0.783327	−	0.621610i	$-0.786479\pi$
$727$	−26.5268	+	9.65498i	−0.983826	+	0.358083i	−0.200500	+	0.979694i	$0.564257\pi$
$728$	−4.24596			−0.157366
$729$	19.8516	−	18.3006i	0.735246	−	0.677801i
$730$	6.18630			0.228965
$731$	0.223854	−	0.0814761i	0.00827953	−	0.00301350i
$732$	2.91068	+	3.84693i	0.107582	+	0.142187i
$733$	−21.8457	+	18.3308i	−0.806891	+	0.677062i	−0.949864	−	0.312665i	$-0.898778\pi$
$733$	−21.8457	+	18.3308i	−0.806891	+	0.677062i	0.142973	+	0.989727i	$0.454334\pi$
$734$	−1.70454	−	9.66691i	−0.0629156	−	0.356812i
$735$	0.911937	+	0.589687i	0.0336373	+	0.0217509i
$736$	0.0380340	+	0.0319143i	0.00140195	+	0.00117638i
$737$	0.417848	−	0.723734i	0.0153916	−	0.0266591i
$738$	9.87499	−	34.9534i	0.363503	−	1.28665i
$739$	−9.56401	−	16.5653i	−0.351818	−	0.609366i	0.634750	−	0.772717i	$-0.281103\pi$
$739$	−9.56401	−	16.5653i	−0.351818	−	0.609366i	−0.986568	+	0.163351i	$0.947770\pi$
$740$	−0.565980	+	3.20983i	−0.0208058	+	0.117996i
$741$	−17.5797	−	4.02240i	−0.645805	−	0.147767i
$742$	11.3667	+	4.13715i	0.417285	+	0.151879i
$743$	−33.0997	−	12.0473i	−1.21431	−	0.441973i	−0.346114	−	0.938193i	$-0.612499\pi$
$743$	−33.0997	−	12.0473i	−1.21431	−	0.441973i	−0.868197	+	0.496219i	$0.834721\pi$
$744$	8.82487	−	9.50068i	0.323536	−	0.348312i
$745$	−0.579149	+	3.28452i	−0.0212184	+	0.120335i
$746$	−8.15947	−	14.1326i	−0.298740	−	0.517432i
$747$	1.36759	+	18.5168i	0.0500375	+	0.677495i
$748$	−0.0217752	+	0.0377157i	−0.000796180	+	0.00137902i
$749$	−12.5985	−	10.5714i	−0.460340	−	0.386271i
$750$	−0.525649	+	10.4197i	−0.0191940	+	0.380472i
$751$	7.86664	+	44.6139i	0.287058	+	1.62798i	0.697842	+	0.716252i	$0.254144\pi$
$751$	7.86664	+	44.6139i	0.287058	+	1.62798i	−0.410784	+	0.911733i	$0.634745\pi$
$752$	0.339914	−	0.285222i	0.0123954	−	0.0104010i
$753$	−17.0775	+	2.13074i	−0.622337	+	0.0776486i
$754$	−2.69973	+	0.982623i	−0.0983185	+	0.0357850i
$755$	−5.83662			−0.212416
$756$	4.84002	−	1.89055i	0.176030	−	0.0687587i
$757$	−28.8426			−1.04830			−0.524151	−	0.851626i	$-0.675617\pi$
$757$	−28.8426			−1.04830			−0.524151	+	0.851626i	$0.675617\pi$
$758$	26.6883	−	9.71375i	0.969363	−	0.352819i
$759$	0.00836694	−	0.0198189i	0.000303701	−	0.000719380i
$760$	−1.17780	+	0.988291i	−0.0427233	+	0.0358491i
$761$	−5.28082	−	29.9490i	−0.191430	−	1.08565i	−0.917412	−	0.397938i	$-0.869726\pi$
$761$	−5.28082	−	29.9490i	−0.191430	−	1.08565i	0.725983	−	0.687713i	$-0.241385\pi$
$762$	−28.2823	+	14.4802i	−1.02456	+	0.524564i
$763$	−10.9235	−	9.16588i	−0.395456	−	0.331827i
$764$	3.53073	−	6.11541i	0.127737	−	0.221248i
$765$	−0.134359	−	0.298628i	−0.00485776	−	0.0107969i
$766$	−5.31235	−	9.20127i	−0.191943	−	0.332455i
$767$	−3.59804	+	20.4055i	−0.129918	+	0.736800i
$768$	0.509640	+	1.65538i	0.0183900	+	0.0597332i
$769$	46.4767	+	16.9161i	1.67599	+	0.610012i	0.992752	−	0.120181i	$-0.0383475\pi$
$769$	46.4767	+	16.9161i	1.67599	+	0.610012i	0.683241	+	0.730193i	$0.260570\pi$
$770$	0.147389	+	0.0536451i	0.00531152	+	0.00193323i
$771$	−7.76899	−	25.2347i	−0.279793	−	0.908804i
$772$	−2.06282	+	11.6988i	−0.0742424	+	0.421049i
$773$	−1.01084	−	1.75082i	−0.0363572	−	0.0629726i	0.847274	−	0.531156i	$-0.178242\pi$
$773$	−1.01084	−	1.75082i	−0.0363572	−	0.0629726i	−0.883631	+	0.468183i	$0.844909\pi$
$774$	−4.08426	−	0.413135i	−0.146806	−	0.0148498i
$775$	17.2446	−	29.8686i	0.619445	−	1.07291i
$776$	−11.6748	−	9.79636i	−0.419102	−	0.351669i
$777$	8.01449	−	4.10334i	0.287518	−	0.147207i
$778$	−6.23887	−	35.3824i	−0.223674	−	1.26852i
$779$	22.7432	−	19.0838i	0.814860	−	0.683749i
$780$	1.79338	−	4.24800i	0.0642132	−	0.152103i
$781$	1.00840	−	0.367027i	0.0360833	−	0.0131333i
$782$	−0.00864358			−0.000309094
$783$	2.63994	−	2.32218i	0.0943437	−	0.0829881i
$784$	1.00000			0.0357143
$785$	4.17937	−	1.52117i	0.149168	−	0.0542928i
$786$	36.6793	−	4.57645i	1.30831	−	0.163237i
$787$	20.8346	−	17.4823i	0.742673	−	0.623177i	−0.190881	−	0.981613i	$-0.561135\pi$
$787$	20.8346	−	17.4823i	0.742673	−	0.623177i	0.933554	+	0.358437i	$0.116690\pi$
$788$	−4.37229	−	24.7965i	−0.155756	−	0.883338i
$789$	0.934991	−	18.5338i	0.0332865	−	0.659822i
$790$	−2.61785	−	2.19664i	−0.0931390	−	0.0781529i
$791$	−2.46542	+	4.27023i	−0.0876602	+	0.151832i
$792$	0.620528	−	0.422090i	0.0220495	−	0.0149983i
$793$	−5.91279	−	10.2412i	−0.209969	−	0.363677i
$794$	−4.35787	+	24.7147i	−0.154655	+	0.877092i
$795$	−8.94013	+	9.62476i	−0.317074	+	0.341355i
$796$	7.24097	+	2.63550i	0.256649	+	0.0934127i
$797$	9.14436	+	3.32827i	0.323910	+	0.117893i	0.498857	−	0.866684i	$-0.333753\pi$
$797$	9.14436	+	3.32827i	0.323910	+	0.117893i	−0.174947	+	0.984578i	$0.555976\pi$
$798$	4.14033	+	0.947349i	0.146566	+	0.0335358i
$799$	−0.0134141	+	0.0760752i	−0.000474557	+	0.00269135i
$800$	2.30344	+	3.98968i	0.0814389	+	0.141056i
$801$	14.7933	+	15.1995i	0.522695	+	0.537049i
$802$	−8.77761	+	15.2033i	−0.309948	+	0.536846i
$803$	−1.89077	−	1.58654i	−0.0667238	−	0.0559879i
$804$	4.85887	+	3.14190i	0.171359	+	0.110806i
$805$	0.00540568	+	0.0306571i	0.000190525	+	0.00108052i
$806$	−24.3504	+	20.4324i	−0.857707	+	0.719702i
$807$	14.5468	+	19.2259i	0.512071	+	0.676784i
$808$	−2.31963	+	0.844275i	−0.0816042	+	0.0297015i
$809$	−45.0259			−1.58303			−0.791513	−	0.611152i	$-0.790706\pi$
$809$	−45.0259			−1.58303			−0.791513	+	0.611152i	$0.790706\pi$
$810$	−0.152833	+	5.64086i	−0.00537001	+	0.198200i
$811$	−30.9730			−1.08761			−0.543805	−	0.839212i	$-0.683017\pi$
$811$	−30.9730			−1.08761			−0.543805	+	0.839212i	$0.683017\pi$
$812$	0.635836	−	0.231425i	0.0223135	−	0.00812144i
$813$	5.22537	+	6.90618i	0.183262	+	0.242210i
$814$	0.996180	−	0.835895i	0.0349161	−	0.0292981i
$815$	0.00718539	+	0.0407504i	0.000251693	+	0.00142742i
$816$	−0.253209	−	0.163733i	−0.00886407	−	0.00573179i
$817$	−2.57046	−	2.15687i	−0.0899291	−	0.0754595i
$818$	−16.4116	+	28.4258i	−0.573819	+	0.993883i
$819$	−12.3474	+	3.12987i	−0.431452	+	0.109367i
$820$	3.79556	+	6.57410i	0.132547	+	0.229577i
$821$	−5.53289	+	31.3786i	−0.193099	+	1.09512i	0.722000	+	0.691893i	$0.243223\pi$
$821$	−5.53289	+	31.3786i	−0.193099	+	1.09512i	−0.915100	+	0.403228i	$0.867888\pi$
$822$	−9.37540	−	2.14519i	−0.327005	−	0.0748220i
$823$	23.2299	+	8.45499i	0.809743	+	0.294722i	0.713518	−	0.700637i	$-0.247101\pi$
$823$	23.2299	+	8.45499i	0.809743	+	0.294722i	0.0962253	+	0.995360i	$0.469323\pi$
$824$	10.2405	+	3.72725i	0.356746	+	0.129845i
$825$	1.35848	−	1.46252i	0.0472963	−	0.0509183i
$826$	0.847403	−	4.80586i	0.0294849	−	0.167217i
$827$	−19.0382	−	32.9751i	−0.662022	−	1.14666i	−0.980083	−	0.198586i	$-0.936365\pi$
$827$	−19.0382	−	32.9751i	−0.662022	−	1.14666i	0.318061	−	0.948070i	$-0.396968\pi$
$828$	0.134129	+	0.0647712i	0.00466131	+	0.00225096i
$829$	15.7838	−	27.3383i	0.548194	−	0.949499i	−0.450205	−	0.892925i	$-0.648649\pi$
$829$	15.7838	−	27.3383i	0.548194	−	0.949499i	0.998398	−	0.0565737i	$-0.0180176\pi$
$830$	−2.97264	−	2.49434i	−0.103182	−	0.0865799i
$831$	0.734808	−	14.5657i	0.0254902	−	0.505279i
$832$	−0.737303	−	4.18146i	−0.0255614	−	0.144966i
$833$	−0.133361	+	0.111904i	−0.00462070	+	0.00387723i
$834$	−1.52186	+	0.189881i	−0.0526977	+	0.00657506i
$835$	−9.27378	+	3.37538i	−0.320932	+	0.116810i
$836$	0.613438			0.0212162
$837$	18.6596	−	34.1334i	0.644971	−	1.17982i
$838$	10.5765			0.365360
$839$	−38.9174	+	14.1648i	−1.34358	+	0.489023i	−0.910938	−	0.412543i	$-0.864641\pi$
$839$	−38.9174	+	14.1648i	−1.34358	+	0.489023i	−0.432641	+	0.901566i	$0.642418\pi$
$840$	−0.422372	+	1.00048i	−0.0145732	+	0.0345198i
$841$	−21.8646	+	18.3465i	−0.753950	+	0.632639i
$842$	−2.89699	−	16.4297i	−0.0998370	−	0.566204i
$843$	−36.0509	+	18.4577i	−1.24166	+	0.635718i
$844$	−19.3015	−	16.1959i	−0.664385	−	0.557485i
$845$	−1.57632	+	2.73026i	−0.0542269	+	0.0939238i
$846$	0.778232	−	1.08000i	0.0267562	−	0.0371311i
$847$	5.46871	+	9.47208i	0.187907	+	0.325465i
$848$	−2.10049	+	11.9124i	−0.0721310	+	0.409075i
$849$	8.30592	+	26.9787i	0.285059	+	0.925907i
$850$	−0.753649	−	0.274306i	−0.0258499	−	0.00940861i
$851$	0.242533	+	0.0882749i	0.00831394	+	0.00302603i
$852$	2.18622	+	7.10112i	0.0748987	+	0.243281i
$853$	1.95657	−	11.0962i	0.0669915	−	0.379928i	−0.932817	−	0.360351i	$-0.882657\pi$
$853$	1.95657	−	11.0962i	0.0669915	−	0.379928i	0.999808	−	0.0195769i	$-0.00623192\pi$
$854$	1.39257	+	2.41200i	0.0476527	+	0.0825369i
$855$	−2.69656	+	3.74218i	−0.0922205	+	0.127980i
$856$	8.22309	−	14.2428i	0.281060	−	0.486809i
$857$	−15.9612	−	13.3931i	−0.545226	−	0.457499i	0.328095	−	0.944645i	$-0.393593\pi$
$857$	−15.9612	−	13.3931i	−0.545226	−	0.457499i	−0.873320	+	0.487146i	$0.838038\pi$
$858$	−1.63757	+	0.838420i	−0.0559057	+	0.0286232i
$859$	4.93230	+	27.9725i	0.168288	+	0.954409i	0.945609	+	0.325305i	$0.105467\pi$
$859$	4.93230	+	27.9725i	0.168288	+	0.954409i	−0.777321	+	0.629104i	$0.783422\pi$
$860$	0.657232	−	0.551483i	0.0224114	−	0.0188054i
$861$	8.15598	−	19.3192i	0.277955	−	0.658396i
$862$	−14.4918	+	5.27460i	−0.493594	+	0.179654i
$863$	24.0745			0.819505			0.409752	−	0.912197i	$-0.365615\pi$
$863$	24.0745			0.819505			0.409752	+	0.912197i	$0.365615\pi$
$864$	2.70229	+	4.43820i	0.0919338	+	0.150991i
$865$	8.71547			0.296335
$866$	−38.1062	+	13.8695i	−1.29490	+	0.471305i
$867$	−29.1662	+	3.63905i	−0.990537	+	0.123589i
$868$	5.73496	−	4.81221i	0.194657	−	0.163337i
$869$	0.236764	+	1.34275i	0.00803165	+	0.0455498i
$870$	−0.0370231	+	0.733889i	−0.00125520	+	0.0248812i
$871$	−10.8658	−	9.11751i	−0.368174	−	0.308935i
$872$	7.12979	−	12.3492i	0.241445	−	0.418195i
$873$	−41.1721	−	19.8821i	−1.39346	−	0.672906i
$874$	0.0608755	+	0.105439i	0.00205914	+	0.00356654i
$875$	−1.04596	+	5.93193i	−0.0353599	+	0.200536i
$876$	11.6306	−	12.5212i	0.392960	−	0.423053i
$877$	−46.8390	−	17.0480i	−1.58164	−	0.575671i	−0.606082	−	0.795402i	$-0.707260\pi$
$877$	−46.8390	−	17.0480i	−1.58164	−	0.575671i	−0.975560	+	0.219732i	$0.929482\pi$
$878$	32.3792	+	11.7851i	1.09275	+	0.397727i
$879$	−25.3825	−	5.80778i	−0.856131	−	0.195891i
$880$	−0.0272363	+	0.154465i	−0.000918136	+	0.00520701i
$881$	−23.4713	−	40.6535i	−0.790769	−	1.36965i	−0.925491	−	0.378769i	$-0.876348\pi$
$881$	−23.4713	−	40.6535i	−0.790769	−	1.36965i	0.134723	−	0.990883i	$-0.456986\pi$
$882$	2.90803	−	0.737141i	0.0979184	−	0.0248208i
$883$	−18.0309	+	31.2304i	−0.606788	+	1.05099i	0.384978	+	0.922926i	$0.374209\pi$
$883$	−18.0309	+	31.2304i	−0.606788	+	1.05099i	−0.991766	+	0.128062i	$0.959124\pi$
$884$	0.566247	+	0.475138i	0.0190450	+	0.0159806i
$885$	4.45025	+	2.87767i	0.149594	+	0.0967320i
$886$	−4.22885	−	23.9830i	−0.142071	−	0.805725i
$887$	−1.12872	+	0.947106i	−0.0378986	+	0.0318007i	−0.661540	−	0.749910i	$-0.730097\pi$
$887$	−1.12872	+	0.947106i	−0.0378986	+	0.0318007i	0.623642	+	0.781710i	$0.285652\pi$
$888$	5.43271	+	7.18020i	0.182310	+	0.240952i
$889$	−17.2382	+	6.27420i	−0.578151	+	0.210430i
$890$	−4.43285			−0.148589
$891$	1.49337	−	1.68487i	0.0500298	−	0.0564452i
$892$	−23.0662			−0.772313
$893$	1.02248	−	0.372154i	0.0342161	−	0.0124536i
$894$	5.55911	+	7.34727i	0.185925	+	0.245729i
$895$	2.85833	−	2.39842i	0.0955433	−	0.0801704i
$896$	0.173648	+	0.984808i	0.00580118	+	0.0329001i
$897$	−0.306617	−	0.198268i	−0.0102376	−	0.00661998i
$898$	7.82024	+	6.56196i	0.260965	+	0.218975i
$899$	2.53283	−	4.38699i	0.0844746	−	0.146314i
$900$	9.63942	+	9.90413i	0.321314	+	0.330138i
$901$	−1.05292	−	1.82371i	−0.0350779	−	0.0607567i
$902$	0.525931	−	2.98270i	0.0175116	−	0.0993132i
$903$	−2.31037	−	0.528636i	−0.0768844	−	0.0175919i
$904$	−4.63347	−	1.68645i	−0.154107	−	0.0560904i
$905$	−8.52547	−	3.10302i	−0.283396	−	0.103148i
$906$	−10.9731	+	11.8135i	−0.364558	+	0.392476i
$907$	−1.79393	+	10.1739i	−0.0595663	+	0.337817i	−0.999998	−	0.00216632i	$-0.999310\pi$
$907$	−1.79393	+	10.1739i	−0.0595663	+	0.337817i	0.940431	+	0.339984i	$0.110422\pi$
$908$	−0.127995	−	0.221693i	−0.00424765	−	0.00735715i
$909$	−6.12319	+	4.16507i	−0.203093	+	0.138147i
$910$	1.33109	−	2.30552i	0.0441253	−	0.0764273i
$911$	45.9420	+	38.5499i	1.52213	+	1.27721i	0.834251	+	0.551384i	$0.185900\pi$
$911$	45.9420	+	38.5499i	1.52213	+	1.27721i	0.687874	+	0.725830i	$0.258544\pi$
$912$	−0.213996	+	4.24193i	−0.00708612	+	0.140464i
$913$	0.268851	+	1.52473i	0.00889768	+	0.0504613i
$914$	−11.0213	+	9.24800i	−0.364553	+	0.305897i
$915$	−3.00134	+	0.374475i	−0.0992212	+	0.0123798i
$916$	−17.3377	+	6.31041i	−0.572854	+	0.208502i
$917$	21.3410			0.704741
$918$	−0.857031	−	0.289489i	−0.0282863	−	0.00955456i
$919$	−25.8803			−0.853714			−0.426857	−	0.904319i	$-0.640379\pi$
$919$	−25.8803			−0.853714			−0.426857	+	0.904319i	$0.640379\pi$
$920$	−0.0292527	+	0.0106471i	−0.000964432	+	0.000351025i
$921$	−10.1456	+	24.0321i	−0.334309	+	0.791884i
$922$	−5.07554	+	4.25888i	−0.167154	+	0.140259i
$923$	−3.16284	−	17.9373i	−0.104106	−	0.590415i
$924$	0.385677	−	0.197463i	0.0126878	−	0.00649605i
$925$	18.3455	+	15.3937i	0.603196	+	0.506141i
$926$	−1.89541	+	3.28294i	−0.0622869	+	0.107884i
$927$	32.5272	+	3.29023i	1.06833	+	0.108065i
$928$	0.338321	+	0.585990i	0.0111059	+	0.0192360i
$929$	5.39670	−	30.6062i	0.177060	−	1.00416i	−0.758679	−	0.651465i	$-0.774155\pi$
$929$	5.39670	−	30.6062i	0.177060	−	1.00416i	0.935739	−	0.352693i	$-0.114734\pi$
$930$	2.39223	+	7.77026i	0.0784442	+	0.254797i
$931$	2.30431	+	0.838700i	0.0755207	+	0.0274873i
$932$	−22.1547	−	8.06364i	−0.725701	−	0.264133i
$933$	15.9056	+	51.6635i	0.520727	+	1.69139i
$934$	2.34317	−	13.2888i	0.0766708	−	0.434822i
$935$	−0.0136529	−	0.0236475i	−0.000446497	−	0.000773356i
$936$	−5.22642	−	11.6163i	−0.170831	−	0.379690i
$937$	5.67749	−	9.83371i	0.185476	−	0.321253i	−0.758261	−	0.651951i	$-0.773951\pi$
$937$	5.67749	−	9.83371i	0.185476	−	0.321253i	0.943737	+	0.330698i	$0.107284\pi$
$938$	2.55910	+	2.14734i	0.0835575	+	0.0701130i
$939$	27.2394	−	13.9463i	0.888925	−	0.455121i
$940$	0.0483113	+	0.273987i	0.00157574	+	0.00893646i
$941$	2.25056	−	1.88844i	0.0733661	−	0.0615615i	−0.605367	−	0.795946i	$-0.706974\pi$
$941$	2.25056	−	1.88844i	0.0733661	−	0.0615615i	0.678733	+	0.734385i	$0.262529\pi$
$942$	4.77855	−	11.3190i	0.155693	−	0.368794i
$943$	0.564867	−	0.205595i	0.0183946	−	0.00669509i
$944$	4.88000			0.158830
$945$	−0.490776	+	3.22077i	−0.0159649	+	0.104772i
$946$	−0.342309			−0.0111294
$947$	17.7272	−	6.45217i	0.576057	−	0.209667i	−0.0375292	−	0.999296i	$-0.511949\pi$
$947$	17.7272	−	6.45217i	0.576057	−	0.209667i	0.613586	+	0.789628i	$0.289726\pi$
$948$	−9.36774	+	1.16881i	−0.304250	+	0.0379611i
$949$	−32.0921	+	26.9285i	−1.04175	+	0.874136i
$950$	1.96170	+	11.1253i	0.0636459	+	0.360954i
$951$	−2.03571	+	40.3528i	−0.0660124	+	1.30853i
$952$	−0.133361	−	0.111904i	−0.00432227	−	0.00362681i
$953$	16.8908	−	29.2558i	0.547148	−	0.947688i	−0.451320	−	0.892362i	$-0.649047\pi$
$953$	16.8908	−	29.2558i	0.547148	−	0.947688i	0.998468	−	0.0553263i	$-0.0176199\pi$
$954$	2.67288	+	36.1901i	0.0865376	+	1.17170i
$955$	2.21374	+	3.83431i	0.0716350	+	0.124076i
$956$	−1.61209	+	9.14259i	−0.0521386	+	0.295693i
$957$	0.199529	−	0.214809i	0.00644987	−	0.00694380i
$958$	12.9131	+	4.69999i	0.417204	+	0.151850i
$959$	−5.21790	−	1.89916i	−0.168495	−	0.0613271i
$960$	−1.05862	−	0.242224i	−0.0341670	−	0.00781775i
$961$	4.34939	−	24.6666i	0.140303	−	0.795697i
$962$	−11.0361	−	19.1150i	−0.355817	−	0.616293i
$963$	13.4140	−	47.4801i	0.432261	−	1.53002i
$964$	7.92754	−	13.7309i	0.255329	−	0.442243i
$965$	−5.70567	−	4.78763i	−0.183672	−	0.154119i
$966$	0.0722137	+	0.0466957i	0.00232344	+	0.00150241i
$967$	−5.41447	−	30.7070i	−0.174118	−	0.987470i	−0.939157	−	0.343487i	$-0.888392\pi$
$967$	−5.41447	−	30.7070i	−0.174118	−	0.987470i	0.765040	−	0.643983i	$-0.222719\pi$
$968$	−8.37855	+	7.03044i	−0.269297	+	0.225967i
$969$	−0.446148	−	0.589657i	−0.0143323	−	0.0189425i
$970$	8.97936	−	3.26822i	0.288310	−	0.104936i
$971$	−17.9773			−0.576919			−0.288459	−	0.957492i	$-0.593143\pi$
$971$	−17.9773			−0.576919			−0.288459	+	0.957492i	$0.593143\pi$
$972$	11.1299	+	10.9144i	0.356992	+	0.350081i
$973$	−0.885459			−0.0283865
$974$	−22.0038	+	8.00871i	−0.705046	+	0.256616i
$975$	−20.4424	−	27.0179i	−0.654679	−	0.865264i
$976$	−2.13354	+	1.79025i	−0.0682929	+	0.0573045i
$977$	−0.424980	−	2.41018i	−0.0135963	−	0.0771085i	0.977255	−	0.212069i	$-0.0680203\pi$
$977$	−0.424980	−	2.41018i	−0.0135963	−	0.0771085i	−0.990851	+	0.134961i	$0.956909\pi$
$978$	0.0959887	+	0.0620693i	0.00306938	+	0.00198476i
$979$	1.35485	+	1.13685i	0.0433011	+	0.0363340i
$980$	−0.313496	+	0.542992i	−0.0100143	+	0.0173452i
$981$	11.6306	−	41.1674i	0.371335	−	1.31437i
$982$	−4.29358	−	7.43670i	−0.137014	−	0.237315i
$983$	0.620277	−	3.51776i	0.0197838	−	0.112199i	−0.973317	−	0.229466i	$-0.926302\pi$
$983$	0.620277	−	3.51776i	0.0197838	−	0.112199i	0.993100	+	0.117267i	$0.0374132\pi$
$984$	20.4420	+	4.67733i	0.651666	+	0.149108i
$985$	14.8350	+	5.39949i	0.472681	+	0.172042i
$986$	−0.110693	−	0.0402891i	−0.00352519	−	0.00128307i
$987$	0.523055	−	0.563111i	0.0166490	−	0.0179240i
$988$	1.80801	−	10.2537i	0.0575205	−	0.326215i
$989$	−0.0339695	−	0.0588370i	−0.00108017	−	0.00187091i
$990$	0.0346584	+	0.469265i	0.00110152	+	0.0149142i
$991$	−24.6671	+	42.7247i	−0.783577	+	1.35720i	0.146269	+	0.989245i	$0.453274\pi$
$991$	−24.6671	+	42.7247i	−0.783577	+	1.35720i	−0.929846	+	0.367950i	$0.880060\pi$
$992$	5.73496	+	4.81221i	0.182085	+	0.152788i
$993$	−1.16458	+	23.0849i	−0.0369569	+	0.732577i
$994$	0.744905	+	4.22457i	0.0236270	+	0.133995i
$995$	−3.70107	+	3.10557i	−0.117332	+	0.0984531i
$996$	−10.6373	+	1.32721i	−0.337057	+	0.0420543i
$997$	15.8756	−	5.77823i	0.502784	−	0.182998i	−0.0781618	−	0.996941i	$-0.524905\pi$
$997$	15.8756	−	5.77823i	0.502784	−	0.182998i	0.580946	+	0.813942i	$0.302683\pi$
$998$	−33.0714			−1.04686
$999$	21.0913	+	16.8755i	0.667298	+	0.533918i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.b.169.1	yes	12
27.4	even	9	inner	378.2.u.b.85.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.b.85.1	✓	12	27.4	even	9	inner
378.2.u.b.169.1	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)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-1.04508 - 1.38124i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.108876 + 0.617467i) q^{5} +(1.45446 + 0.940501i) q^{6} +(0.766044 + 0.642788i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.815631 + 2.88700i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-1.04508 - 1.38124i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.108876 + 0.617467i) q^{5} +(1.45446 + 0.940501i) q^{6} +(0.766044 + 0.642788i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.815631 + 2.88700i) q^{9} +(-0.313496 - 0.542992i) q^{10} +(-0.0434396 + 0.246358i) q^{11} +(-1.68842 - 0.386327i) q^{12} +(3.98990 + 1.45220i) q^{13} +(-0.939693 - 0.342020i) q^{14} +(0.739085 - 0.795684i) q^{15} +(0.173648 - 0.984808i) q^{16} +(0.0870455 + 0.150767i) q^{17} +(-0.220968 - 2.99185i) q^{18} +(1.22610 - 2.12366i) q^{19} +(0.480304 + 0.403023i) q^{20} +(0.0872671 - 1.72985i) q^{21} +(-0.0434396 - 0.246358i) q^{22} +(0.0380340 - 0.0319143i) q^{23} +(1.71872 - 0.214444i) q^{24} +(4.32905 - 1.57565i) q^{25} -4.24596 q^{26} +(4.84002 - 1.89055i) q^{27} +1.00000 q^{28} +(0.635836 - 0.231425i) q^{29} +(-0.422372 + 1.00048i) q^{30} +(5.73496 - 4.81221i) q^{31} +(0.173648 + 0.984808i) q^{32} +(0.385677 - 0.197463i) q^{33} +(-0.133361 - 0.111904i) q^{34} +(-0.313496 + 0.542992i) q^{35} +(1.23092 + 2.73584i) q^{36} +(2.59919 + 4.50193i) q^{37} +(-0.425819 + 2.41494i) q^{38} +(-2.16391 - 7.02866i) q^{39} +(-0.589180 - 0.214444i) q^{40} +(11.3770 + 4.14090i) q^{41} +(0.509640 + 1.65538i) q^{42} +(0.237614 - 1.34758i) q^{43} +(0.125079 + 0.216644i) q^{44} +(-1.87143 - 0.189301i) q^{45} +(-0.0248249 + 0.0429980i) q^{46} +(0.339914 + 0.285222i) q^{47} +(-1.54173 + 0.789350i) q^{48} +(0.173648 + 0.984808i) q^{49} +(-3.52908 + 2.96125i) q^{50} +(0.117276 - 0.277794i) q^{51} +(3.98990 - 1.45220i) q^{52} -12.0962 q^{53} +(-3.90153 + 3.43192i) q^{54} -0.156848 q^{55} +(-0.939693 + 0.342020i) q^{56} +(-4.21465 + 0.525859i) q^{57} +(-0.518338 + 0.434937i) q^{58} +(0.847403 + 4.80586i) q^{59} +(0.0547159 - 1.08460i) q^{60} +(-2.13354 - 1.79025i) q^{61} +(-3.74323 + 6.48347i) q^{62} +(-2.48053 + 1.68729i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.462284 + 2.62174i) q^{65} +(-0.294882 + 0.317464i) q^{66} +(-3.13920 - 1.14257i) q^{67} +(0.163592 + 0.0595426i) q^{68} +(-0.0838296 - 0.0191810i) q^{69} +(0.108876 - 0.617467i) q^{70} +(-2.14487 - 3.71502i) q^{71} +(-2.09240 - 2.14986i) q^{72} +(-4.93331 + 8.54475i) q^{73} +(-3.98219 - 3.34146i) q^{74} +(-6.70053 - 4.33278i) q^{75} +(-0.425819 - 2.41494i) q^{76} +(-0.191633 + 0.160799i) q^{77} +(4.43735 + 5.86468i) q^{78} +(5.12170 - 1.86415i) q^{79} +0.626993 q^{80} +(-7.66949 - 4.70945i) q^{81} -12.1072 q^{82} +(5.81583 - 2.11679i) q^{83} +(-1.04508 - 1.38124i) q^{84} +(-0.0836166 + 0.0701627i) q^{85} +(0.237614 + 1.34758i) q^{86} +(-0.984150 - 0.636383i) q^{87} +(-0.191633 - 0.160799i) q^{88} +(3.53501 - 6.12282i) q^{89} +(1.82331 - 0.462182i) q^{90} +(2.12298 + 3.67711i) q^{91} +(0.00862160 - 0.0488955i) q^{92} +(-12.6403 - 2.89222i) q^{93} +(-0.416967 - 0.151763i) q^{94} +(1.44478 + 0.525859i) q^{95} +(1.17878 - 1.26905i) q^{96} +(-2.64647 + 15.0089i) q^{97} +(-0.500000 - 0.866025i) q^{98} +(-0.675805 - 0.326348i) 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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