LMFDB - Embedded newform 378.2.w.a.25.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(25,378)]

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([10, 12]))

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

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

chi := DirichletCharacter("378.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.w (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:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.12
Character	$\chi$	$=$	378.25
Dual form			378.2.w.a.121.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(1.71296 + 0.256429i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-3.35800 - 1.22221i) q^{5} +(-1.69736 + 0.344903i) q^{6} +(-2.15868 - 1.52974i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.86849 + 0.878508i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(1.71296 + 0.256429i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-3.35800 - 1.22221i) q^{5} +(-1.69736 + 0.344903i) q^{6} +(-2.15868 - 1.52974i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.86849 + 0.878508i) q^{9} +3.57351 q^{10} +(-3.98264 + 1.44956i) q^{11} +(1.47704 - 0.904635i) q^{12} +(-0.585610 - 3.32116i) q^{13} +(2.55170 + 0.699171i) q^{14} +(-5.43872 - 2.95469i) q^{15} +(0.173648 - 0.984808i) q^{16} -2.57160 q^{17} +(-2.99596 + 0.155553i) q^{18} -6.03842 q^{19} +(-3.35800 + 1.22221i) q^{20} +(-3.30547 - 3.17393i) q^{21} +(3.24668 - 2.72429i) q^{22} +(-0.397622 - 2.25502i) q^{23} +(-1.07856 + 1.35526i) q^{24} +(5.95212 + 4.99442i) q^{25} +(1.68620 + 2.92058i) q^{26} +(4.68834 + 2.24042i) q^{27} +(-2.63694 + 0.215726i) q^{28} +(-0.315874 + 1.79141i) q^{29} +(6.12129 + 0.916352i) q^{30} +(7.91342 - 6.64015i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-7.19382 + 1.46178i) q^{33} +(2.41652 - 0.879540i) q^{34} +(5.37918 + 7.77522i) q^{35} +(2.76208 - 1.17085i) q^{36} +(-3.58414 + 6.20792i) q^{37} +(5.67426 - 2.06526i) q^{38} +(-0.151486 - 5.83919i) q^{39} +(2.73746 - 2.29701i) q^{40} +(-1.32145 - 7.49429i) q^{41} +(4.19168 + 1.85198i) q^{42} +(-2.13929 - 1.79507i) q^{43} +(-2.11912 + 3.67042i) q^{44} +(-8.55865 - 6.45593i) q^{45} +(1.14491 + 1.98304i) q^{46} +(-2.42933 - 2.03845i) q^{47} +(0.549987 - 1.64241i) q^{48} +(2.31980 + 6.60443i) q^{49} +(-7.30136 - 2.65748i) q^{50} +(-4.40506 - 0.659435i) q^{51} +(-2.58340 - 2.16773i) q^{52} +(4.04351 - 7.00356i) q^{53} +(-5.17187 - 0.501796i) q^{54} +15.1454 q^{55} +(2.40413 - 1.10460i) q^{56} +(-10.3436 - 1.54843i) q^{57} +(-0.315874 - 1.79141i) q^{58} +(1.10586 + 6.27162i) q^{59} +(-6.06554 + 1.23251i) q^{60} +(3.99135 + 3.34914i) q^{61} +(-5.16512 + 8.94625i) q^{62} +(-4.84826 - 6.28445i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.09268 + 11.8682i) q^{65} +(6.26003 - 3.83406i) q^{66} +(1.75666 + 0.639372i) q^{67} +(-1.96996 + 1.65300i) q^{68} +(-0.102857 - 3.96474i) q^{69} +(-7.71406 - 5.46653i) q^{70} +(-3.31293 - 5.73817i) q^{71} +(-2.19505 + 2.04493i) q^{72} +(-6.08597 - 10.5412i) q^{73} +(1.24476 - 7.05938i) q^{74} +(8.91505 + 10.0816i) q^{75} +(-4.62570 + 3.88142i) q^{76} +(10.8147 + 2.96325i) q^{77} +(2.13947 + 5.43523i) q^{78} +(-3.25112 + 1.18331i) q^{79} +(-1.78675 + 3.09475i) q^{80} +(7.45645 + 5.03998i) q^{81} +(3.80495 + 6.59037i) q^{82} +(0.275388 - 1.56180i) q^{83} +(-4.57230 - 0.306658i) q^{84} +(8.63544 + 3.14304i) q^{85} +(2.62422 + 0.955139i) q^{86} +(-1.00045 + 2.98762i) q^{87} +(0.735962 - 4.17385i) q^{88} +5.16593 q^{89} +(10.2506 + 3.13935i) q^{90} +(-3.81636 + 8.06515i) q^{91} +(-1.75410 - 1.47186i) q^{92} +(15.2581 - 9.34510i) q^{93} +(2.98001 + 1.08464i) q^{94} +(20.2770 + 7.38022i) q^{95} +(0.0449194 + 1.73147i) q^{96} +(14.6758 + 12.3145i) q^{97} +(-4.43875 - 5.41272i) q^{98} +(-12.6976 + 0.659271i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9}+O(q^{10}) $ 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9	$ 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9} + 12 q^{10} - 6 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} + 36 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 30 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} + 9 q^{35} + 9 q^{36} + 3 q^{39} - 6 q^{41} + 3 q^{42} + 24 q^{43} - 30 q^{45} - 9 q^{47} - 6 q^{48} + 51 q^{49} + 6 q^{50} + 12 q^{51} + 6 q^{52} - 15 q^{53} - 27 q^{54} + 72 q^{55} + 6 q^{56} - 63 q^{57} + 3 q^{58} + 15 q^{59} - 3 q^{60} - 18 q^{61} - 24 q^{62} - 48 q^{63} - 36 q^{64} - 18 q^{65} - 36 q^{66} + 66 q^{67} - 18 q^{68} - 21 q^{69} - 6 q^{70} + 12 q^{71} - 12 q^{72} - 66 q^{73} + 9 q^{74} + 15 q^{75} - 15 q^{77} + 30 q^{78} + 9 q^{79} - 6 q^{80} - 33 q^{82} - 18 q^{83} - 12 q^{84} + 21 q^{85} - 12 q^{86} - 48 q^{87} + 12 q^{88} + 72 q^{89} + 69 q^{90} + 12 q^{91} + 30 q^{92} + 60 q^{93} - 36 q^{94} + 93 q^{95} - 48 q^{97} + 6 q^{98} - 54 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9 + 12 * q^10 - 6 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 + 36 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 30 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 + 9 * q^35 + 9 * q^36 + 3 * q^39 - 6 * q^41 + 3 * q^42 + 24 * q^43 - 30 * q^45 - 9 * q^47 - 6 * q^48 + 51 * q^49 + 6 * q^50 + 12 * q^51 + 6 * q^52 - 15 * q^53 - 27 * q^54 + 72 * q^55 + 6 * q^56 - 63 * q^57 + 3 * q^58 + 15 * q^59 - 3 * q^60 - 18 * q^61 - 24 * q^62 - 48 * q^63 - 36 * q^64 - 18 * q^65 - 36 * q^66 + 66 * q^67 - 18 * q^68 - 21 * q^69 - 6 * q^70 + 12 * q^71 - 12 * q^72 - 66 * q^73 + 9 * q^74 + 15 * q^75 - 15 * q^77 + 30 * q^78 + 9 * q^79 - 6 * q^80 - 33 * q^82 - 18 * q^83 - 12 * q^84 + 21 * q^85 - 12 * q^86 - 48 * q^87 + 12 * q^88 + 72 * q^89 + 69 * q^90 + 12 * q^91 + 30 * q^92 + 60 * q^93 - 36 * q^94 + 93 * q^95 - 48 * q^97 + 6 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	1.71296	+	0.256429i	0.988980	+	0.148050i
$3$	1.71296	+	0.256429i	0.988980	+	0.148050i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−3.35800	−	1.22221i	−1.50174	−	0.546589i	−0.545231	−	0.838286i	$-0.683558\pi$
$5$	−3.35800	−	1.22221i	−1.50174	−	0.546589i	−0.956511	+	0.291696i	$0.905780\pi$
$6$	−1.69736	+	0.344903i	−0.692946	+	0.140806i
$7$	−2.15868	−	1.52974i	−0.815905	−	0.578187i
$7$	−2.15868	−	1.52974i	−0.815905	−	0.578187i
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	2.86849	+	0.878508i	0.956163	+	0.292836i
$10$	3.57351			1.13004
$11$	−3.98264	+	1.44956i	−1.20081	+	0.437059i	−0.863507	−	0.504337i	$-0.831737\pi$
$11$	−3.98264	+	1.44956i	−1.20081	+	0.437059i	−0.337304	+	0.941396i	$0.609515\pi$
$12$	1.47704	−	0.904635i	0.426383	−	0.261146i
$13$	−0.585610	−	3.32116i	−0.162419	−	0.921123i	−0.951686	−	0.307073i	$-0.900650\pi$
$13$	−0.585610	−	3.32116i	−0.162419	−	0.921123i	0.789267	−	0.614050i	$-0.210461\pi$
$14$	2.55170	+	0.699171i	0.681970	+	0.186861i
$15$	−5.43872	−	2.95469i	−1.40427	−	0.762898i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−2.57160			−0.623706			−0.311853	−	0.950130i	$-0.600950\pi$
$17$	−2.57160			−0.623706			−0.311853	+	0.950130i	$0.600950\pi$
$18$	−2.99596	+	0.155553i	−0.706156	+	0.0366642i
$19$	−6.03842			−1.38531			−0.692654	−	0.721270i	$-0.743559\pi$
$19$	−6.03842			−1.38531			−0.692654	+	0.721270i	$0.743559\pi$
$20$	−3.35800	+	1.22221i	−0.750871	+	0.273295i
$21$	−3.30547	−	3.17393i	−0.721313	−	0.692609i
$22$	3.24668	−	2.72429i	0.692194	−	0.580820i
$23$	−0.397622	−	2.25502i	−0.0829099	−	0.470205i	−0.997788	−	0.0664752i	$-0.978825\pi$
$23$	−0.397622	−	2.25502i	−0.0829099	−	0.470205i	0.914878	−	0.403730i	$-0.132286\pi$
$24$	−1.07856	+	1.35526i	−0.220159	+	0.276640i
$25$	5.95212	+	4.99442i	1.19042	+	0.998885i
$26$	1.68620	+	2.92058i	0.330690	+	0.572772i
$27$	4.68834	+	2.24042i	0.902271	+	0.431168i
$28$	−2.63694	+	0.215726i	−0.498335	+	0.0407684i
$29$	−0.315874	+	1.79141i	−0.0586563	+	0.332657i	−0.999988	−	0.00482527i	$-0.998464\pi$
$29$	−0.315874	+	1.79141i	−0.0586563	+	0.332657i	0.941332	+	0.337482i	$0.109575\pi$
$30$	6.12129	+	0.916352i	1.11759	+	0.167302i
$31$	7.91342	−	6.64015i	1.42129	−	1.19261i	0.470649	−	0.882320i	$-0.344020\pi$
$31$	7.91342	−	6.64015i	1.42129	−	1.19261i	0.950643	−	0.310286i	$-0.100425\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	−7.19382	+	1.46178i	−1.25228	+	0.254463i
$34$	2.41652	−	0.879540i	0.414429	−	0.150840i
$35$	5.37918	+	7.77522i	0.909248	+	1.31425i
$36$	2.76208	−	1.17085i	0.460347	−	0.195142i
$37$	−3.58414	+	6.20792i	−0.589229	+	1.02058i	0.405104	+	0.914270i	$0.367235\pi$
$37$	−3.58414	+	6.20792i	−0.589229	+	1.02058i	−0.994334	+	0.106305i	$0.966098\pi$
$38$	5.67426	−	2.06526i	0.920486	−	0.335029i
$39$	−0.151486	−	5.83919i	−0.0242572	−	0.935019i
$40$	2.73746	−	2.29701i	0.432831	−	0.363188i
$41$	−1.32145	−	7.49429i	−0.206375	−	1.17041i	−0.895261	−	0.445542i	$-0.853011\pi$
$41$	−1.32145	−	7.49429i	−0.206375	−	1.17041i	0.688886	−	0.724870i	$-0.258100\pi$
$42$	4.19168	+	1.85198i	0.646790	+	0.285767i
$43$	−2.13929	−	1.79507i	−0.326238	−	0.273746i	0.464927	−	0.885349i	$-0.346081\pi$
$43$	−2.13929	−	1.79507i	−0.326238	−	0.273746i	−0.791165	+	0.611603i	$0.790525\pi$
$44$	−2.11912	+	3.67042i	−0.319469	+	0.553337i
$45$	−8.55865	−	6.45593i	−1.27585	−	0.962393i
$46$	1.14491	+	1.98304i	0.168807	+	0.292383i
$47$	−2.42933	−	2.03845i	−0.354354	−	0.297338i	0.448182	−	0.893943i	$-0.352072\pi$
$47$	−2.42933	−	2.03845i	−0.354354	−	0.297338i	−0.802536	+	0.596604i	$0.796516\pi$
$48$	0.549987	−	1.64241i	0.0793837	−	0.237062i
$49$	2.31980	+	6.60443i	0.331401	+	0.943490i
$50$	−7.30136	−	2.65748i	−1.03257	−	0.375824i
$51$	−4.40506	−	0.659435i	−0.616832	−	0.0923393i
$52$	−2.58340	−	2.16773i	−0.358253	−	0.300610i
$53$	4.04351	−	7.00356i	0.555418	−	0.962012i	−0.442453	−	0.896792i	$-0.645892\pi$
$53$	4.04351	−	7.00356i	0.555418	−	0.962012i	0.997871	−	0.0652206i	$-0.0207751\pi$
$54$	−5.17187	−	0.501796i	−0.703802	−	0.0682858i
$55$	15.1454			2.04220
$56$	2.40413	−	1.10460i	0.321266	−	0.147609i
$57$	−10.3436	−	1.54843i	−1.37004	−	0.205094i
$58$	−0.315874	−	1.79141i	−0.0414763	−	0.235224i
$59$	1.10586	+	6.27162i	0.143970	+	0.816495i	0.968188	+	0.250223i	$0.0805039\pi$
$59$	1.10586	+	6.27162i	0.143970	+	0.816495i	−0.824218	+	0.566272i	$0.808385\pi$
$60$	−6.06554	+	1.23251i	−0.783058	+	0.159117i
$61$	3.99135	+	3.34914i	0.511040	+	0.428813i	0.861495	−	0.507766i	$-0.169529\pi$
$61$	3.99135	+	3.34914i	0.511040	+	0.428813i	−0.350455	+	0.936580i	$0.613973\pi$
$62$	−5.16512	+	8.94625i	−0.655971	+	1.13617i
$63$	−4.84826	−	6.28445i	−0.610824	−	0.791767i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−2.09268	+	11.8682i	−0.259565	+	1.47207i
$66$	6.26003	−	3.83406i	0.770556	−	0.471940i
$67$	1.75666	+	0.639372i	0.214610	+	0.0781117i	0.447088	−	0.894490i	$-0.352461\pi$
$67$	1.75666	+	0.639372i	0.214610	+	0.0781117i	−0.232478	+	0.972602i	$0.574683\pi$
$68$	−1.96996	+	1.65300i	−0.238893	+	0.200455i
$69$	−0.102857	−	3.96474i	−0.0123825	−	0.477298i
$70$	−7.71406	−	5.46653i	−0.922006	−	0.653375i
$71$	−3.31293	−	5.73817i	−0.393173	−	0.680996i	0.599693	−	0.800230i	$-0.295289\pi$
$71$	−3.31293	−	5.73817i	−0.393173	−	0.680996i	−0.992866	+	0.119234i	$0.961956\pi$
$72$	−2.19505	+	2.04493i	−0.258690	+	0.240997i
$73$	−6.08597	−	10.5412i	−0.712309	−	1.23376i	−0.963988	−	0.265945i	$-0.914316\pi$
$73$	−6.08597	−	10.5412i	−0.712309	−	1.23376i	0.251679	−	0.967811i	$-0.419017\pi$
$74$	1.24476	−	7.05938i	0.144700	−	0.820636i
$75$	8.91505	+	10.0816i	1.02942	+	1.16412i
$76$	−4.62570	+	3.88142i	−0.530604	+	0.445229i
$77$	10.8147	+	2.96325i	1.23245	+	0.337694i
$78$	2.13947	+	5.43523i	0.242247	+	0.615419i
$79$	−3.25112	+	1.18331i	−0.365780	+	0.133133i	−0.518370	−	0.855157i	$-0.673461\pi$
$79$	−3.25112	+	1.18331i	−0.365780	+	0.133133i	0.152590	+	0.988290i	$0.451239\pi$
$80$	−1.78675	+	3.09475i	−0.199765	+	0.346003i
$81$	7.45645	+	5.03998i	0.828494	+	0.559998i
$82$	3.80495	+	6.59037i	0.420187	+	0.727785i
$83$	0.275388	−	1.56180i	0.0302278	−	0.171430i	−0.965957	−	0.258704i	$-0.916704\pi$
$83$	0.275388	−	1.56180i	0.0302278	−	0.171430i	0.996184	+	0.0872741i	$0.0278156\pi$
$84$	−4.57230	−	0.306658i	−0.498879	−	0.0334592i
$85$	8.63544	+	3.14304i	0.936645	+	0.340911i
$86$	2.62422	+	0.955139i	0.282977	+	0.102995i
$87$	−1.00045	+	2.98762i	−0.107260	+	0.320307i
$88$	0.735962	−	4.17385i	0.0784538	−	0.444934i
$89$	5.16593			0.547588			0.273794	−	0.961788i	$-0.411721\pi$
$89$	5.16593			0.547588			0.273794	+	0.961788i	$0.411721\pi$
$90$	10.2506	+	3.13935i	1.08050	+	0.330917i
$91$	−3.81636	+	8.06515i	−0.400063	+	0.845457i
$92$	−1.75410	−	1.47186i	−0.182877	−	0.153452i
$93$	15.2581	−	9.34510i	1.58219	−	0.969042i
$94$	2.98001	+	1.08464i	0.307365	+	0.111872i
$95$	20.2770	+	7.38022i	2.08037	+	0.757195i
$96$	0.0449194	+	1.73147i	0.00458457	+	0.176717i
$97$	14.6758	+	12.3145i	1.49010	+	1.25034i	0.894504	+	0.447060i	$0.147529\pi$
$97$	14.6758	+	12.3145i	1.49010	+	1.25034i	0.595597	+	0.803284i	$0.296916\pi$
$98$	−4.43875	−	5.41272i	−0.448382	−	0.546767i
$99$	−12.6976	+	0.659271i	−1.27616	+	0.0662592i
$100$	7.76995			0.776995
$101$	−1.46588	+	8.31343i	−0.145861	+	0.827217i	0.820811	+	0.571199i	$0.193522\pi$
$101$	−1.46588	+	8.31343i	−0.145861	+	0.827217i	−0.966672	+	0.256018i	$0.917589\pi$
$102$	4.36495	−	0.886955i	0.432194	−	0.0878216i
$103$	−18.9437	−	6.89493i	−1.86658	−	0.679378i	−0.973152	−	0.230162i	$-0.926074\pi$
$103$	−18.9437	−	6.89493i	−1.86658	−	0.679378i	−0.893423	−	0.449216i	$-0.851704\pi$
$104$	3.16901	+	1.15343i	0.310747	+	0.113103i
$105$	7.22055	+	14.6980i	0.704653	+	1.43438i
$106$	−1.40429	+	7.96415i	−0.136397	+	0.773547i
$107$	3.04619	+	5.27616i	0.294487	+	0.510066i	0.974865	−	0.222795i	$-0.0715180\pi$
$107$	3.04619	+	5.27616i	0.294487	+	0.510066i	−0.680379	+	0.732861i	$0.738185\pi$
$108$	5.03159	−	1.29735i	0.484165	−	0.124837i
$109$	−5.46649	+	9.46824i	−0.523595	+	0.906893i	0.476028	+	0.879430i	$0.342076\pi$
$109$	−5.46649	+	9.46824i	−0.523595	+	0.906893i	−0.999623	+	0.0274630i	$0.991257\pi$
$110$	−14.2320	+	5.18002i	−1.35697	+	0.493895i
$111$	−7.73140	+	9.71485i	−0.733832	+	0.922093i
$112$	−1.88135	+	1.86025i	−0.177771	+	0.175777i
$113$	3.76639	−	3.16038i	0.354312	−	0.297303i	−0.448207	−	0.893930i	$-0.647937\pi$
$113$	3.76639	−	3.16038i	0.354312	−	0.297303i	0.802519	+	0.596627i	$0.203493\pi$
$114$	10.2494	−	2.08267i	0.959943	−	0.195060i
$115$	−1.42090	+	8.05834i	−0.132500	+	0.751445i
$116$	0.909523	+	1.57534i	0.0844471	+	0.146267i
$117$	1.23785	−	10.0412i	0.114439	−	0.928306i
$118$	−3.18418	−	5.51517i	−0.293128	−	0.507712i
$119$	5.55127	+	3.93388i	0.508884	+	0.360618i
$120$	5.27820	−	3.23272i	0.481831	−	0.295106i
$121$	5.33369	−	4.47550i	0.484881	−	0.406864i
$122$	−4.89612	−	1.78204i	−0.443273	−	0.161338i
$123$	−0.341833	−	13.1763i	−0.0308220	−	1.18807i
$124$	1.79383	−	10.1733i	0.161090	−	0.913589i
$125$	−4.94921	−	8.57228i	−0.442671	−	0.766728i
$126$	6.70529	+	4.24725i	0.597354	+	0.378375i
$127$	2.75557	−	4.77279i	0.244517	−	0.423517i	−0.717478	−	0.696581i	$-0.754704\pi$
$127$	2.75557	−	4.77279i	0.244517	−	0.423517i	0.961996	+	0.273064i	$0.0880371\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	−3.20421	−	3.62347i	−0.282115	−	0.319029i
$130$	−2.09268	−	11.8682i	−0.183540	−	1.04091i
$131$	0.509161	+	2.88760i	0.0444856	+	0.252290i	0.998938	−	0.0460725i	$-0.0146705\pi$
$131$	0.509161	+	2.88760i	0.0444856	+	0.252290i	−0.954452	+	0.298363i	$0.903559\pi$
$132$	−4.57117	+	5.74389i	−0.397870	+	0.499942i
$133$	13.0350	+	9.23719i	1.13028	+	0.800966i
$134$	−1.86940			−0.161491
$135$	−13.0052	−	13.2535i	−1.11931	−	1.14068i
$136$	1.28580	−	2.22707i	0.110257	−	0.190970i
$137$	−12.4103	−	10.4135i	−1.06029	−	0.889686i	−0.0661490	−	0.997810i	$-0.521071\pi$
$137$	−12.4103	−	10.4135i	−1.06029	−	0.889686i	−0.994137	+	0.108124i	$0.965516\pi$
$138$	1.45267	+	3.69045i	0.123660	+	0.314152i
$139$	−13.9917	−	5.09257i	−1.18676	−	0.431946i	−0.328176	−	0.944617i	$-0.606434\pi$
$139$	−13.9917	−	5.09257i	−1.18676	−	0.431946i	−0.858585	+	0.512671i	$0.828656\pi$
$140$	9.11851	+	2.49849i	0.770654	+	0.211161i
$141$	−3.63863	−	4.11474i	−0.306428	−	0.346523i
$142$	5.07571	+	4.25903i	0.425944	+	0.357410i
$143$	7.14650	+	12.3781i	0.597620	+	1.03511i
$144$	1.36327	−	2.67236i	0.113606	−	0.222696i
$145$	3.25019	−	5.62949i	0.269913	−	0.467504i
$146$	9.32425	+	7.82397i	0.771680	+	0.647517i
$147$	2.28017	+	11.9080i	0.188065	+	0.982157i
$148$	1.24476	+	7.05938i	0.102319	+	0.580278i
$149$	5.53187	−	4.64179i	0.453188	−	0.380270i	−0.387429	−	0.921899i	$-0.626637\pi$
$149$	5.53187	−	4.64179i	0.453188	−	0.380270i	0.840617	+	0.541629i	$0.182192\pi$
$150$	−11.8255	−	6.42445i	−0.965549	−	0.524554i
$151$	−7.67462	+	2.79333i	−0.624551	+	0.227318i	−0.634858	−	0.772629i	$-0.718941\pi$
$151$	−7.67462	+	2.79333i	−0.624551	+	0.227318i	0.0103067	+	0.999947i	$0.496719\pi$
$152$	3.01921	−	5.22942i	0.244890	−	0.424162i
$153$	−7.37662	−	2.25917i	−0.596364	−	0.182643i
$154$	−11.1760	+	0.914298i	−0.900586	+	0.0736762i
$155$	−34.6889	+	12.6257i	−2.78628	+	1.01412i
$156$	−3.86940	−	4.37571i	−0.309800	−	0.350337i
$157$	−2.98320	−	16.9185i	−0.238085	−	1.35025i	−0.836019	−	0.548701i	$-0.815123\pi$
$157$	−2.98320	−	16.9185i	−0.238085	−	1.35025i	0.597934	−	0.801546i	$-0.295989\pi$
$158$	2.65034	−	2.22390i	0.210850	−	0.176924i
$159$	8.72229	−	10.9600i	0.691723	−	0.869182i
$160$	0.620533	−	3.51922i	0.0490574	−	0.278218i
$161$	−2.59126	+	5.47614i	−0.204220	+	0.431580i
$162$	−8.73054	−	2.18578i	−0.685936	−	0.171731i
$163$	5.52476	+	9.56917i	0.432733	+	0.749515i	0.997108	−	0.0760035i	$-0.0242160\pi$
$163$	5.52476	+	9.56917i	0.432733	+	0.749515i	−0.564375	+	0.825519i	$0.690883\pi$
$164$	−5.82952	−	4.89155i	−0.455209	−	0.381966i
$165$	25.9435	+	3.88371i	2.01969	+	0.302347i
$166$	0.275388	+	1.56180i	0.0213743	+	0.121220i
$167$	15.1547	−	12.7163i	1.17270	−	0.984014i	0.172703	−	0.984974i	$-0.444750\pi$
$167$	15.1547	−	12.7163i	1.17270	−	0.984014i	1.00000		0.000959417i	$0.000305392\pi$
$168$	4.40144	−	1.27566i	0.339579	−	0.0984189i
$169$	1.52885	−	0.556457i	0.117604	−	0.0428044i
$170$	−9.18964			−0.704813
$171$	−17.3211	−	5.30480i	−1.32458	−	0.405668i
$172$	−2.79264			−0.212937
$173$	3.36453	−	19.0812i	0.255800	−	1.45072i	−0.538210	−	0.842811i	$-0.680899\pi$
$173$	3.36453	−	19.0812i	0.255800	−	1.45072i	0.794010	−	0.607904i	$-0.207990\pi$
$174$	−0.0817105	−	3.14962i	−0.00619446	−	0.238772i
$175$	−5.20857	−	19.8866i	−0.393731	−	1.50328i
$176$	0.735962	+	4.17385i	0.0554752	+	0.314616i
$177$	0.286063	+	11.0266i	0.0215018	+	0.828812i
$178$	−4.85439	+	1.76685i	−0.363852	+	0.132431i
$179$	−21.8562			−1.63361			−0.816805	−	0.576914i	$-0.804257\pi$
$179$	−21.8562			−1.63361			−0.816805	+	0.576914i	$0.804257\pi$
$180$	−10.7061	+	0.555870i	−0.797985	+	0.0414321i
$181$	2.48406	−	4.30251i	0.184638	−	0.319803i	−0.758816	−	0.651305i	$-0.774222\pi$
$181$	2.48406	−	4.30251i	0.184638	−	0.319803i	0.943455	+	0.331502i	$0.107555\pi$
$182$	0.827759	−	8.88403i	0.0613576	−	0.658528i
$183$	5.97822	+	6.76045i	0.441923	+	0.499747i
$184$	2.15172	+	0.783162i	0.158627	+	0.0577355i
$185$	19.6229	−	16.4656i	1.44271	−	1.21057i
$186$	−11.1417	+	14.0001i	−0.816952	+	1.02654i
$187$	10.2418	−	3.72770i	0.748952	−	0.272596i
$188$	−3.17126			−0.231288
$189$	−6.69338	−	12.0083i	−0.486872	−	0.873474i
$190$	−21.5783			−1.56546
$191$	−15.6167	+	5.68402i	−1.12999	+	0.411281i	−0.838287	−	0.545229i	$-0.816443\pi$
$191$	−15.6167	+	5.68402i	−1.12999	+	0.411281i	−0.291699	+	0.956510i	$0.594221\pi$
$192$	−0.634407	−	1.61168i	−0.0457844	−	0.116313i
$193$	−1.40689	+	1.18052i	−0.101270	+	0.0849756i	−0.692017	−	0.721881i	$-0.743278\pi$
$193$	−1.40689	+	1.18052i	−0.101270	+	0.0849756i	0.590747	+	0.806857i	$0.298833\pi$
$194$	−18.0025	−	6.55238i	−1.29251	−	0.470434i
$195$	−6.62803	+	19.7931i	−0.474643	+	1.41742i
$196$	6.02232	+	3.56815i	0.430166	+	0.254868i
$197$	5.53938	−	9.59449i	0.394665	−	0.683579i	−0.598394	−	0.801202i	$-0.704194\pi$
$197$	5.53938	−	9.59449i	0.394665	−	0.683579i	0.993058	+	0.117623i	$0.0375274\pi$
$198$	11.7064	−	4.96235i	0.831935	−	0.352659i
$199$	−9.99777			−0.708723			−0.354362	−	0.935108i	$-0.615302\pi$
$199$	−9.99777			−0.708723			−0.354362	+	0.935108i	$0.615302\pi$
$200$	−7.30136	+	2.65748i	−0.516284	+	0.187912i
$201$	2.84514	+	1.54568i	0.200681	+	0.109024i
$202$	−1.46588	−	8.31343i	−0.103139	−	0.584931i
$203$	3.42226	−	3.38388i	0.240196	−	0.237502i
$204$	−3.79835	+	2.32636i	−0.265938	+	0.162878i
$205$	−4.72219	+	26.7809i	−0.329812	+	1.87046i
$206$	20.1594			1.40457
$207$	0.840484	−	6.81783i	0.0584177	−	0.473872i
$208$	−3.37239			−0.233833
$209$	24.0488	−	8.75306i	1.66349	−	0.605462i
$210$	−11.8121	−	11.3421i	−0.815114	−	0.782677i
$211$	−15.4658	+	12.9774i	−1.06471	+	0.893398i	−0.994563	−	0.104139i	$-0.966791\pi$
$211$	−15.4658	+	12.9774i	−1.06471	+	0.893398i	−0.0701473	+	0.997537i	$0.522347\pi$
$212$	−1.40429	−	7.96415i	−0.0964474	−	0.546980i
$213$	−4.20350	−	10.6788i	−0.288019	−	0.731700i
$214$	−4.66704	−	3.91611i	−0.319032	−	0.267700i
$215$	4.98976	+	8.64251i	0.340299	+	0.589415i
$216$	−4.28443	+	2.94001i	−0.291518	+	0.200043i
$217$	−27.2402	+	2.22850i	−1.84919	+	0.151281i
$218$	1.89849	−	10.7669i	0.128582	−	0.729226i
$219$	−7.72197	−	19.6173i	−0.521802	−	1.32562i
$220$	11.6020	−	9.73525i	0.782208	−	0.656350i
$221$	1.50596	+	8.54070i	0.101302	+	0.574510i
$222$	3.94246	−	11.7733i	0.264601	−	0.790170i
$223$	−23.0056	+	8.37336i	−1.54057	+	0.560722i	−0.966182	−	0.257861i	$-0.916982\pi$
$223$	−23.0056	+	8.37336i	−1.54057	+	0.560722i	−0.574388	+	0.818583i	$0.694760\pi$
$224$	1.13165	−	2.39152i	0.0756113	−	0.159790i
$225$	12.6860	+	19.5554i	0.845730	+	1.30370i
$226$	−2.45834	+	4.25796i	−0.163526	+	0.283236i
$227$	13.3859	−	4.87208i	0.888456	−	0.323372i	0.142839	−	0.989746i	$-0.454377\pi$
$227$	13.3859	−	4.87208i	0.888456	−	0.323372i	0.745617	+	0.666374i	$0.232155\pi$
$228$	−8.91896	+	5.46257i	−0.590672	+	0.361767i
$229$	14.8283	−	12.4424i	0.979881	−	0.822217i	−0.00419079	−	0.999991i	$-0.501334\pi$
$229$	14.8283	−	12.4424i	0.979881	−	0.822217i	0.984071	+	0.177774i	$0.0568895\pi$
$230$	−1.42090	−	8.05834i	−0.0936916	−	0.531352i
$231$	17.7653	+	7.84915i	1.16887	+	0.516436i
$232$	−1.39347	−	1.16926i	−0.0914858	−	0.0767657i
$233$	7.22886	−	12.5208i	0.473579	−	0.820262i	−0.525964	−	0.850507i	$-0.676295\pi$
$233$	7.22886	−	12.5208i	0.473579	−	0.820262i	0.999543	+	0.0302447i	$0.00962866\pi$
$234$	2.27108	+	9.85898i	0.148465	+	0.644502i
$235$	5.66626	+	9.81426i	0.369626	+	0.640211i
$236$	4.87845	+	4.09351i	0.317560	+	0.266465i
$237$	−5.87249	+	1.19329i	−0.381459	+	0.0775124i
$238$	−6.56196	−	1.79799i	−0.425348	−	0.116546i
$239$	4.16230	+	1.51495i	0.269237	+	0.0979941i	0.473111	−	0.881003i	$-0.343131\pi$
$239$	4.16230	+	1.51495i	0.269237	+	0.0979941i	−0.203874	+	0.978997i	$0.565353\pi$
$240$	−3.85423	+	4.84301i	−0.248789	+	0.312615i
$241$	5.68259	+	4.76826i	0.366048	+	0.307151i	0.807196	−	0.590284i	$-0.200984\pi$
$241$	5.68259	+	4.76826i	0.366048	+	0.307151i	−0.441148	+	0.897434i	$0.645429\pi$
$242$	−3.48132	+	6.02982i	−0.223788	+	0.387612i
$243$	11.4802	+	10.5454i	0.736457	+	0.676485i
$244$	5.21034			0.333558
$245$	0.282112	−	25.0130i	0.0180235	−	1.59802i
$246$	4.82778	+	12.2648i	0.307808	+	0.781973i
$247$	3.53616	+	20.0545i	0.225000	+	1.27604i
$248$	1.79383	+	10.1733i	0.113908	+	0.646005i
$249$	0.872222	−	2.60470i	0.0552748	−	0.165066i
$250$	7.58263	+	6.36258i	0.479568	+	0.402405i
$251$	7.82057	−	13.5456i	0.493630	−	0.854993i	−0.506343	−	0.862332i	$-0.669003\pi$
$251$	7.82057	−	13.5456i	0.493630	−	0.854993i	0.999973	+	0.00733960i	$0.00233629\pi$
$252$	−7.75355	−	1.69777i	−0.488428	−	0.106949i
$253$	4.85238	+	8.40457i	0.305067	+	0.528391i
$254$	−0.957000	+	5.42742i	−0.0600475	+	0.340546i
$255$	13.9862	+	7.59830i	0.875851	+	0.475824i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−2.63354	+	2.20980i	−0.164276	+	0.137844i	−0.721220	−	0.692706i	$-0.756418\pi$
$257$	−2.63354	+	2.20980i	−0.164276	+	0.137844i	0.556944	+	0.830550i	$0.311974\pi$
$258$	4.25027	+	2.30905i	0.264610	+	0.143755i
$259$	17.2335	−	7.91811i	1.07084	−	0.492007i
$260$	6.02563	+	10.4367i	0.373694	+	0.647257i
$261$	−2.47985	+	4.86114i	−0.153499	+	0.300897i
$262$	−1.46607	−	2.53931i	−0.0905742	−	0.156879i
$263$	3.20019	−	18.1492i	0.197332	−	1.11913i	−0.711725	−	0.702458i	$-0.752086\pi$
$263$	3.20019	−	18.1492i	0.197332	−	1.11913i	0.909058	−	0.416670i	$-0.136803\pi$
$264$	2.33097	−	6.96093i	0.143461	−	0.428415i
$265$	−22.1379	+	18.5759i	−1.35992	+	1.14111i
$266$	−15.4082	−	4.22189i	−0.944738	−	0.258860i
$267$	8.84905	+	1.32470i	0.541553	+	0.0810701i
$268$	1.75666	−	0.639372i	0.107305	−	0.0390558i
$269$	2.60573	−	4.51325i	0.158874	−	0.275178i	−0.775589	−	0.631238i	$-0.782547\pi$
$269$	2.60573	−	4.51325i	0.158874	−	0.275178i	0.934463	+	0.356060i	$0.115880\pi$
$270$	16.7538	+	8.00614i	1.01960	+	0.487238i
$271$	−7.42537	−	12.8611i	−0.451059	−	0.781257i	0.547393	−	0.836876i	$-0.315620\pi$
$271$	−7.42537	−	12.8611i	−0.451059	−	0.781257i	−0.998452	+	0.0556184i	$0.982287\pi$
$272$	−0.446554	+	2.53254i	−0.0270763	+	0.153558i
$273$	−8.60542	+	12.8367i	−0.520824	+	0.776911i
$274$	15.2235	+	5.54091i	0.919687	+	0.334739i
$275$	−30.9449	−	11.2630i	−1.86605	−	0.679186i
$276$	−2.62728	−	2.97105i	−0.158143	−	0.178836i
$277$	−1.10140	+	6.24637i	−0.0661769	+	0.375308i	0.933675	+	0.358120i	$0.116582\pi$
$277$	−1.10140	+	6.24637i	−0.0661769	+	0.375308i	−0.999852	+	0.0171874i	$0.994529\pi$
$278$	14.8897			0.893023
$279$	28.5330	−	12.0952i	1.70823	−	0.724120i
$280$	−9.42313	+	0.770898i	−0.563140	+	0.0460700i
$281$	6.51650	+	5.46799i	0.388742	+	0.326193i	0.816123	−	0.577879i	$-0.196119\pi$
$281$	6.51650	+	5.46799i	0.388742	+	0.326193i	−0.427381	+	0.904072i	$0.640564\pi$
$282$	4.82652	+	2.62210i	0.287415	+	0.156144i
$283$	−4.95705	−	1.80422i	−0.294666	−	0.107250i	0.190457	−	0.981696i	$-0.439003\pi$
$283$	−4.95705	−	1.80422i	−0.294666	−	0.107250i	−0.485123	+	0.874446i	$0.661225\pi$
$284$	−6.22628	−	2.26618i	−0.369462	−	0.134473i
$285$	32.8412	+	17.8417i	1.94535	+	1.05685i
$286$	−10.9491	−	9.18736i	−0.647432	−	0.543260i
$287$	−8.61172	+	18.1992i	−0.508334	+	1.07427i
$288$	−0.367054	+	2.97746i	−0.0216289	+	0.175449i
$289$	−10.3869			−0.610991
$290$	−1.12878	+	6.40162i	−0.0662841	+	0.375916i
$291$	21.9813	+	24.8575i	1.28857	+	1.45717i
$292$	−11.4379	−	4.16305i	−0.669351	−	0.243624i
$293$	−24.2167	−	8.81416i	−1.41476	−	0.514929i	−0.482234	−	0.876043i	$-0.660174\pi$
$293$	−24.2167	−	8.81416i	−1.41476	−	0.514929i	−0.932522	+	0.361114i	$0.882397\pi$
$294$	−6.21544	−	10.4100i	−0.362492	−	0.607124i
$295$	3.95178	−	22.4117i	0.230082	−	1.30486i
$296$	−3.58414	−	6.20792i	−0.208324	−	0.360828i
$297$	−21.9196	−	2.12673i	−1.27190	−	0.123405i
$298$	−3.61067	+	6.25386i	−0.209161	+	0.362277i
$299$	−7.25644	+	2.64113i	−0.419651	+	0.152740i
$300$	13.3096	+	1.99244i	0.768432	+	0.115034i
$301$	1.87204	+	7.14754i	0.107903	+	0.411977i
$302$	6.25640	−	5.24975i	0.360016	−	0.302089i
$303$	−4.64281	+	13.8647i	−0.266722	+	0.796507i
$304$	−1.04856	+	5.94668i	−0.0601390	+	0.341065i
$305$	−9.30959	−	16.1247i	−0.533065	−	0.923296i
$306$	7.70443	−	0.400021i	0.440433	−	0.0228677i
$307$	−12.7518	−	22.0867i	−0.727783	−	1.26056i	−0.957818	−	0.287374i	$-0.907218\pi$
$307$	−12.7518	−	22.0867i	−0.727783	−	1.26056i	0.230036	−	0.973182i	$-0.426116\pi$
$308$	10.1893	−	4.68157i	0.580588	−	0.266757i
$309$	−30.6818	−	16.6685i	−1.74542	−	0.948237i
$310$	28.2787	−	23.7286i	1.60612	−	1.34769i
$311$	−6.19697	−	2.25551i	−0.351398	−	0.127898i	0.160290	−	0.987070i	$-0.448757\pi$
$311$	−6.19697	−	2.25551i	−0.351398	−	0.127898i	−0.511687	+	0.859172i	$0.670979\pi$
$312$	5.13263	+	2.78840i	0.290578	+	0.157862i
$313$	4.12899	−	23.4167i	0.233384	−	1.32359i	−0.612606	−	0.790389i	$-0.709879\pi$
$313$	4.12899	−	23.4167i	0.233384	−	1.32359i	0.845990	−	0.533199i	$-0.179010\pi$
$314$	8.58977	+	14.8779i	0.484749	+	0.839609i
$315$	8.59952	+	27.0288i	0.484528	+	1.52290i
$316$	−1.72989	+	2.99625i	−0.0973138	+	0.168552i
$317$	20.2470	+	16.9892i	1.13718	+	0.954210i	0.999343	−	0.0362441i	$-0.0115394\pi$
$317$	20.2470	+	16.9892i	1.13718	+	0.954210i	0.137841	+	0.990454i	$0.455984\pi$
$318$	−4.44775	+	13.2822i	−0.249417	+	0.744829i
$319$	−1.33875	−	7.59242i	−0.0749555	−	0.425094i
$320$	0.620533	+	3.51922i	0.0346888	+	0.196730i
$321$	3.86506	+	9.81901i	0.215726	+	0.548044i
$322$	0.562038	−	6.03215i	0.0313211	−	0.336158i
$323$	15.5284			0.864024
$324$	8.95161	−	0.932063i	0.497311	−	0.0517813i
$325$	13.1017	−	22.6927i	0.726749	−	1.25877i
$326$	−8.46443	−	7.10250i	−0.468801	−	0.393371i
$327$	−11.7918	+	14.8170i	−0.652090	+	0.819381i
$328$	7.15097	+	2.60274i	0.394846	+	0.143712i
$329$	2.12585	+	8.11659i	0.117202	+	0.447482i
$330$	−25.7072	+	5.22369i	−1.41513	+	0.287554i
$331$	6.04210	+	5.06993i	0.332104	+	0.278668i	0.793556	−	0.608497i	$-0.208227\pi$
$331$	6.04210	+	5.06993i	0.332104	+	0.278668i	−0.461453	+	0.887165i	$0.652672\pi$
$332$	−0.792949	−	1.37343i	−0.0435187	−	0.0753766i
$333$	−15.7348	+	14.6586i	−0.862260	+	0.803288i
$334$	−9.89150	+	17.1326i	−0.541239	+	0.937453i
$335$	−5.11741	−	4.29402i	−0.279594	−	0.234607i
$336$	−3.69970	+	2.70411i	−0.201835	+	0.147521i
$337$	−0.904111	−	5.12747i	−0.0492501	−	0.279311i	0.950230	−	0.311549i	$-0.100848\pi$
$337$	−0.904111	−	5.12747i	−0.0492501	−	0.279311i	−0.999480	+	0.0322377i	$0.989737\pi$
$338$	−1.24633	+	1.04580i	−0.0677916	+	0.0568839i
$339$	7.26210	−	4.44780i	0.394423	−	0.241571i
$340$	8.63544	−	3.14304i	0.468322	−	0.170455i
$341$	−21.8910	+	37.9163i	−1.18546	+	2.05328i
$342$	18.0909	−	0.939295i	0.978243	−	0.0507912i
$343$	5.09533	−	17.8055i	0.275122	−	0.961409i
$344$	2.62422	−	0.955139i	0.141489	−	0.0514976i
$345$	−4.50035	+	13.4393i	−0.242291	+	0.723547i
$346$	3.36453	+	19.0812i	0.180878	+	1.02581i
$347$	−2.68207	+	2.25052i	−0.143981	+	0.120814i	−0.711933	−	0.702247i	$-0.752180\pi$
$347$	−2.68207	+	2.25052i	−0.143981	+	0.120814i	0.567952	+	0.823061i	$0.307736\pi$
$348$	1.15402	+	2.93173i	0.0618618	+	0.157157i
$349$	−0.112862	+	0.640070i	−0.00604134	+	0.0342622i	−0.987679	−	0.156491i	$-0.949982\pi$
$349$	−0.112862	+	0.640070i	−0.00604134	+	0.0342622i	0.981638	+	0.190753i	$0.0610929\pi$
$350$	11.6961	+	16.9058i	0.625181	+	0.903654i
$351$	4.69524	−	16.8827i	0.250613	−	0.901133i
$352$	−2.11912	−	3.67042i	−0.112949	−	0.195634i
$353$	6.53926	+	5.48709i	0.348050	+	0.292049i	0.800006	−	0.599991i	$-0.204829\pi$
$353$	6.53926	+	5.48709i	0.348050	+	0.292049i	−0.451957	+	0.892040i	$0.649274\pi$
$354$	−4.04014	−	10.2638i	−0.214731	−	0.545515i
$355$	4.11157	+	23.3179i	0.218219	+	1.23758i
$356$	3.95733	−	3.32060i	0.209738	−	0.175991i
$357$	8.50036	+	8.16210i	0.449887	+	0.431984i
$358$	20.5381	−	7.47527i	1.08547	−	0.395080i
$359$	−18.6289			−0.983198			−0.491599	−	0.870822i	$-0.663587\pi$
$359$	−18.6289			−0.983198			−0.491599	+	0.870822i	$0.663587\pi$
$360$	9.87032	−	4.18405i	0.520212	−	0.220519i
$361$	17.4625			0.919078
$362$	−0.862704	+	4.89264i	−0.0453427	+	0.257151i
$363$	10.2841	−	6.29865i	0.539774	−	0.330593i
$364$	2.26068	+	8.63137i	0.118492	+	0.452407i
$365$	7.55309	+	42.8357i	0.395347	+	2.24212i
$366$	−7.92990	−	4.30808i	−0.414502	−	0.225187i
$367$	10.7969	−	3.92975i	0.563594	−	0.205131i	−0.0444820	−	0.999010i	$-0.514164\pi$
$367$	10.7969	−	3.92975i	0.563594	−	0.205131i	0.608076	+	0.793879i	$0.291942\pi$
$368$	−2.28981			−0.119365
$369$	2.79324	−	22.6582i	0.145410	−	1.17954i
$370$	−12.8080	+	22.1840i	−0.665854	+	1.15329i
$371$	−19.4422	+	8.93294i	−1.00939	+	0.463775i
$372$	5.68149	−	16.9665i	0.294572	−	0.879672i
$373$	8.62672	+	3.13987i	0.446674	+	0.162576i	0.555557	−	0.831478i	$-0.312505\pi$
$373$	8.62672	+	3.13987i	0.446674	+	0.162576i	−0.108883	+	0.994055i	$0.534727\pi$
$374$	−8.34917	+	7.00578i	−0.431725	+	0.362260i
$375$	−6.27963	−	15.9531i	−0.324279	−	0.823816i
$376$	2.98001	−	1.08464i	0.153682	−	0.0559358i
$377$	6.13454			0.315945
$378$	10.3968	+	8.99482i	0.534753	+	0.462643i
$379$	29.4786			1.51421			0.757107	−	0.653291i	$-0.226612\pi$
$379$	29.4786			1.51421			0.757107	+	0.653291i	$0.226612\pi$
$380$	20.2770	−	7.38022i	1.04019	−	0.378597i
$381$	5.94408	−	7.46900i	0.304524	−	0.382649i
$382$	12.7309	−	10.6825i	0.651368	−	0.546562i
$383$	−7.78787	−	2.83455i	−0.397941	−	0.144839i	0.135294	−	0.990805i	$-0.456802\pi$
$383$	−7.78787	−	2.83455i	−0.397941	−	0.144839i	−0.533236	+	0.845967i	$0.679024\pi$
$384$	1.14738	+	1.29751i	0.0585518	+	0.0662132i
$385$	−32.6940	−	23.1684i	−1.66624	−	1.18077i
$386$	0.918281	−	1.59051i	0.0467393	−	0.0809548i
$387$	−4.55953	−	7.02853i	−0.231774	−	0.357280i
$388$	19.1579			0.972594
$389$	−20.7025	+	7.53509i	−1.04966	+	0.382044i	−0.808534	−	0.588450i	$-0.799738\pi$
$389$	−20.7025	+	7.53509i	−1.04966	+	0.382044i	−0.241125	+	0.970494i	$0.577516\pi$
$390$	−0.541336	−	20.8664i	−0.0274116	−	1.05661i
$391$	1.02253	+	5.79903i	0.0517113	+	0.293270i
$392$	−6.87951	−	1.29321i	−0.347468	−	0.0653168i
$393$	0.131710	+	5.07691i	0.00664390	+	0.256096i
$394$	−1.92381	+	10.9105i	−0.0969200	+	0.549661i
$395$	12.3635			0.622076
$396$	−9.30316	+	8.66689i	−0.467501	+	0.435528i
$397$	−18.5493			−0.930962			−0.465481	−	0.885058i	$-0.654119\pi$
$397$	−18.5493			−0.930962			−0.465481	+	0.885058i	$0.654119\pi$
$398$	9.39483	−	3.41944i	0.470920	−	0.171401i
$399$	19.9598	+	19.1655i	0.999241	+	0.959477i
$400$	5.95212	−	4.99442i	0.297606	−	0.249721i
$401$	0.0696996	+	0.395286i	0.00348063	+	0.0197397i	0.986499	−	0.163770i	$-0.0523654\pi$
$401$	0.0696996	+	0.395286i	0.00348063	+	0.0197397i	−0.983018	+	0.183509i	$0.941254\pi$
$402$	−3.20221	−	0.479368i	−0.159712	−	0.0239087i
$403$	−26.6872	−	22.3932i	−1.32938	−	1.11548i
$404$	4.22084	+	7.31071i	0.209995	+	0.363721i
$405$	−18.8788	−	26.0376i	−0.938096	−	1.29382i
$406$	−2.05852	+	4.35029i	−0.102163	+	0.215901i
$407$	5.27558	−	29.9193i	0.261501	−	1.48305i
$408$	2.77362	−	3.48518i	0.137315	−	0.172542i
$409$	−13.7220	+	11.5142i	−0.678511	+	0.569338i	−0.915571	−	0.402157i	$-0.868261\pi$
$409$	−13.7220	+	11.5142i	−0.678511	+	0.569338i	0.237060	+	0.971495i	$0.423816\pi$
$410$	−4.72219	−	26.7809i	−0.233213	−	1.32261i
$411$	−18.5881	−	21.0203i	−0.916884	−	1.03686i
$412$	−18.9437	+	6.89493i	−0.933288	+	0.339689i
$413$	7.20674	−	15.2301i	0.354621	−	0.749424i
$414$	1.54204	+	6.69412i	0.0757870	+	0.328998i
$415$	−2.83361	+	4.90795i	−0.139096	+	0.240922i
$416$	3.16901	−	1.15343i	0.155374	−	0.0565514i
$417$	−22.6614	−	12.3113i	−1.10973	−	0.602885i
$418$	−19.6048	+	16.4504i	−0.958901	+	0.804614i
$419$	−3.74670	−	21.2486i	−0.183038	−	1.03806i	−0.928450	−	0.371457i	$-0.878858\pi$
$419$	−3.74670	−	21.2486i	−0.183038	−	1.03806i	0.745412	−	0.666604i	$-0.232253\pi$
$420$	14.9790	+	6.61808i	0.730899	+	0.322929i
$421$	8.86652	+	7.43990i	0.432128	+	0.362598i	0.832754	−	0.553643i	$-0.186763\pi$
$421$	8.86652	+	7.43990i	0.432128	+	0.362598i	−0.400626	+	0.916242i	$0.631207\pi$
$422$	10.0946	−	17.4843i	0.491397	−	0.851124i
$423$	−5.17771	−	7.98145i	−0.251749	−	0.388071i
$424$	4.04351	+	7.00356i	0.196370	+	0.340123i
$425$	−15.3065	−	12.8437i	−0.742475	−	0.623010i
$426$	7.60237	+	8.59712i	0.368336	+	0.416532i
$427$	−3.49274	−	13.3354i	−0.169026	−	0.645347i
$428$	5.72497	+	2.08372i	0.276727	+	0.100720i
$429$	9.06758	+	23.0358i	0.437787	+	1.11218i
$430$	−7.64475	−	6.41471i	−0.368663	−	0.309345i
$431$	−12.2662	+	21.2456i	−0.590840	+	1.02336i	0.403280	+	0.915077i	$0.367870\pi$
$431$	−12.2662	+	21.2456i	−0.590840	+	1.02336i	−0.994120	+	0.108288i	$0.965463\pi$
$432$	3.02050	−	4.22807i	0.145324	−	0.203423i
$433$	16.3713			0.786753			0.393377	−	0.919377i	$-0.371307\pi$
$433$	16.3713			0.786753			0.393377	+	0.919377i	$0.371307\pi$
$434$	24.8353	−	11.4108i	1.19213	−	0.547737i
$435$	7.01102	−	8.80966i	0.336152	−	0.422391i
$436$	1.89849	+	10.7669i	0.0909213	+	0.515640i
$437$	2.40101	+	13.6168i	0.114856	+	0.651379i
$438$	13.9658	+	15.7932i	0.667312	+	0.754628i
$439$	16.1405	+	13.5435i	0.770346	+	0.646397i	0.940798	−	0.338969i	$-0.110078\pi$
$439$	16.1405	+	13.5435i	0.770346	+	0.646397i	−0.170451	+	0.985366i	$0.554523\pi$
$440$	−7.57268	+	13.1163i	−0.361013	+	0.625294i
$441$	0.852285	+	20.9827i	0.0405850	+	0.999176i
$442$	−4.33623	−	7.51057i	−0.206253	−	0.357241i
$443$	3.49317	−	19.8107i	0.165965	−	0.941236i	−0.782098	−	0.623155i	$-0.785851\pi$
$443$	3.49317	−	19.8107i	0.165965	−	0.941236i	0.948064	−	0.318081i	$-0.103038\pi$
$444$	0.321995	+	12.4117i	0.0152812	+	0.589031i
$445$	−17.3472	−	6.31386i	−0.822335	−	0.299306i
$446$	18.7544	−	15.7368i	0.888044	−	0.745158i
$447$	10.6662	−	6.53268i	0.504493	−	0.308985i
$448$	−0.245452	+	2.63434i	−0.0115965	+	0.124461i
$449$	6.10832	+	10.5799i	0.288270	+	0.499298i	0.973397	−	0.229126i	$-0.0735867\pi$
$449$	6.10832	+	10.5799i	0.288270	+	0.499298i	−0.685127	+	0.728423i	$0.740253\pi$
$450$	−18.6093	−	14.0372i	−0.877248	−	0.661722i
$451$	16.1263	+	27.9315i	0.759357	+	1.31524i
$452$	0.853771	−	4.84198i	0.0401580	−	0.227747i
$453$	−13.8626	+	2.81688i	−0.651323	+	0.132349i
$454$	−10.9123	+	9.15652i	−0.512141	+	0.429737i
$455$	22.6726	−	22.4184i	1.06291	−	1.05099i
$456$	6.51277	−	8.18360i	0.304988	−	0.383232i
$457$	18.1281	−	6.59810i	0.847999	−	0.308646i	0.118775	−	0.992921i	$-0.462103\pi$
$457$	18.1281	−	6.59810i	0.847999	−	0.308646i	0.729224	+	0.684275i	$0.239881\pi$
$458$	−9.67848	+	16.7636i	−0.452245	+	0.783312i
$459$	−12.0566	−	5.76146i	−0.562752	−	0.268922i
$460$	4.09133	+	7.08639i	0.190759	+	0.330405i
$461$	−2.70552	+	15.3438i	−0.126009	+	0.714630i	0.854695	+	0.519130i	$0.173744\pi$
$461$	−2.70552	+	15.3438i	−0.126009	+	0.714630i	−0.980704	+	0.195500i	$0.937367\pi$
$462$	−19.3785	−	1.29969i	−0.901569	−	0.0604671i
$463$	11.9099	+	4.33484i	0.553499	+	0.201457i	0.603600	−	0.797287i	$-0.293732\pi$
$463$	11.9099	+	4.33484i	0.553499	+	0.201457i	−0.0501015	+	0.998744i	$0.515954\pi$
$464$	1.70934	+	0.622150i	0.0793543	+	0.0288826i
$465$	−62.6585	+	12.7322i	−2.90572	+	0.590440i
$466$	−2.51056	+	14.2381i	−0.116299	+	0.659566i
$467$	−2.44253			−0.113027			−0.0565135	−	0.998402i	$-0.517998\pi$
$467$	−2.44253			−0.113027			−0.0565135	+	0.998402i	$0.517998\pi$
$468$	−5.50609	−	8.48765i	−0.254519	−	0.392342i
$469$	−2.81400	−	4.06743i	−0.129938	−	0.187816i
$470$	−8.68122	−	7.28441i	−0.400435	−	0.336005i
$471$	−0.771695	−	29.7458i	−0.0355578	−	1.37062i
$472$	−5.98431	−	2.17811i	−0.275450	−	0.100256i
$473$	11.1221	+	4.04810i	0.511394	+	0.186132i
$474$	5.11021	−	3.12983i	0.234720	−	0.143758i
$475$	−35.9414	−	30.1584i	−1.64910	−	1.38376i
$476$	6.78117	−	0.554762i	0.310814	−	0.0254275i
$477$	17.7514	−	16.5374i	0.812782	−	0.757194i
$478$	−4.42942			−0.202597
$479$	−6.30771	+	35.7728i	−0.288206	+	1.63450i	0.405396	+	0.914141i	$0.367134\pi$
$479$	−6.30771	+	35.7728i	−0.288206	+	1.63450i	−0.693602	+	0.720358i	$0.743977\pi$
$480$	1.96538	−	5.86917i	0.0897069	−	0.267890i
$481$	22.7164	+	8.26809i	1.03578	+	0.376992i
$482$	−6.97073	−	2.53714i	−0.317508	−	0.115563i
$483$	−5.84297	+	8.71595i	−0.265864	+	0.396589i
$484$	1.20905	−	6.85686i	0.0549568	−	0.311676i
$485$	−34.2304	−	59.2888i	−1.55432	−	2.69217i
$486$	−14.3946	−	5.98292i	−0.652953	−	0.271391i
$487$	−14.0709	+	24.3714i	−0.637611	+	1.10437i	0.348344	+	0.937367i	$0.386744\pi$
$487$	−14.0709	+	24.3714i	−0.637611	+	1.10437i	−0.985955	+	0.167008i	$0.946589\pi$
$488$	−4.89612	+	1.78204i	−0.221637	+	0.0806692i
$489$	7.00990	+	17.8083i	0.316999	+	0.805321i
$490$	8.28983	+	23.6010i	0.374497	+	1.06618i
$491$	−20.3127	+	17.0443i	−0.916698	+	0.769201i	−0.973381	−	0.229192i	$-0.926392\pi$
$491$	−20.3127	+	17.0443i	−0.916698	+	0.769201i	0.0566838	+	0.998392i	$0.481947\pi$
$492$	−8.73142	−	9.87391i	−0.393643	−	0.445150i
$493$	0.812303	−	4.60680i	0.0365843	−	0.207480i
$494$	−10.1820	−	17.6357i	−0.458108	−	0.793466i
$495$	43.4443	+	13.3053i	1.95268	+	0.598030i
$496$	−5.16512	−	8.94625i	−0.231921	−	0.401698i
$497$	−1.62633	+	17.4548i	−0.0729509	+	0.782955i
$498$	0.0712376	+	2.74593i	0.00319223	+	0.123048i
$499$	12.4637	−	10.4583i	0.557952	−	0.468177i	−0.319671	−	0.947529i	$-0.603572\pi$
$499$	12.4637	−	10.4583i	0.557952	−	0.468177i	0.877623	+	0.479351i	$0.159128\pi$
$500$	−9.30147	−	3.38546i	−0.415974	−	0.151402i
$501$	29.2202	−	17.8964i	1.30546	−	0.799553i
$502$	−2.71606	+	15.4035i	−0.121224	+	0.687493i
$503$	12.7106	+	22.0155i	0.566739	+	0.981621i	0.996886	+	0.0788616i	$0.0251285\pi$
$503$	12.7106	+	22.0155i	0.566739	+	0.981621i	−0.430147	+	0.902759i	$0.641538\pi$
$504$	7.86663	−	1.05649i	0.350407	−	0.0470599i
$505$	15.0832	−	26.1249i	0.671193	−	1.16254i
$506$	−7.43428	−	6.23810i	−0.330494	−	0.277317i
$507$	2.76156	−	0.561148i	0.122645	−	0.0249215i
$508$	−0.957000	−	5.42742i	−0.0424600	−	0.240803i
$509$	5.07800	+	28.7988i	0.225079	+	1.27648i	0.862535	+	0.505998i	$0.168876\pi$
$509$	5.07800	+	28.7988i	0.225079	+	1.27648i	−0.637456	+	0.770487i	$0.720013\pi$
$510$	−15.7415	−	2.35649i	−0.697046	−	0.104347i
$511$	−2.98762	+	32.0650i	−0.132165	+	1.41847i
$512$	1.00000			0.0441942
$513$	−28.3102	−	13.5286i	−1.24992	−	0.597301i
$514$	1.71892	−	2.97726i	0.0758184	−	0.131321i
$515$	55.1857	+	46.3063i	2.43177	+	2.04050i
$516$	−4.78369	−	0.716115i	−0.210590	−	0.0315252i
$517$	12.6300	+	4.59694i	0.555466	+	0.202173i
$518$	−13.4860	+	13.3348i	−0.592543	+	0.585897i
$519$	10.6563	−	31.8226i	0.467759	−	1.39686i
$520$	−9.23180	−	7.74640i	−0.404841	−	0.339702i
$521$	16.0092	+	27.7287i	0.701375	+	1.21482i	0.967984	+	0.251012i	$0.0807633\pi$
$521$	16.0092	+	27.7287i	0.701375	+	1.21482i	−0.266609	+	0.963805i	$0.585903\pi$
$522$	0.667688	−	5.41614i	0.0292239	−	0.237058i
$523$	5.70819	−	9.88687i	0.249602	−	0.432323i	−0.713814	−	0.700336i	$-0.753034\pi$
$523$	5.70819	−	9.88687i	0.249602	−	0.432323i	0.963415	+	0.268013i	$0.0863670\pi$
$524$	2.24615	+	1.88474i	0.0981236	+	0.0823354i
$525$	−3.82260	−	35.4006i	−0.166832	−	1.54501i
$526$	3.20019	+	18.1492i	0.139535	+	0.791343i
$527$	−20.3502	+	17.0758i	−0.886468	+	0.743835i
$528$	0.190379	+	7.33837i	0.00828519	+	0.319362i
$529$	16.6859	−	6.07317i	0.725474	−	0.264051i
$530$	14.4495	−	25.0273i	0.627646	−	1.08711i
$531$	−2.33753	+	18.9616i	−0.101440	+	0.822862i
$532$	15.9230	−	1.30264i	0.690348	−	0.0564768i
$533$	−24.1159	+	8.77746i	−1.04457	+	0.380194i
$534$	−8.76846	+	1.78175i	−0.379448	+	0.0771037i
$535$	−3.78053	−	21.4404i	−0.163446	−	0.926951i
$536$	−1.43204	+	1.20163i	−0.0618548	+	0.0519023i
$537$	−37.4389	−	5.60457i	−1.61561	−	0.241855i
$538$	−0.904960	+	5.13228i	−0.0390156	+	0.221268i
$539$	−18.8125	−	22.9404i	−0.810311	−	0.988111i
$540$	−18.4817	−	1.79317i	−0.795326	−	0.0771658i
$541$	−8.61153	−	14.9156i	−0.370239	−	0.641272i	0.619363	−	0.785104i	$-0.287391\pi$
$541$	−8.61153	−	14.9156i	−0.370239	−	0.641272i	−0.989602	+	0.143832i	$0.954057\pi$
$542$	11.3763	+	9.54587i	0.488655	+	0.410030i
$543$	5.35839	−	6.73306i	0.229950	−	0.288943i
$544$	−0.446554	−	2.53254i	−0.0191459	−	0.108582i
$545$	29.9287	−	25.1131i	1.28200	−	1.07573i
$546$	3.69605	−	15.0058i	0.158176	−	0.642187i
$547$	17.2209	−	6.26790i	0.736313	−	0.267996i	0.0534785	−	0.998569i	$-0.482969\pi$
$547$	17.2209	−	6.26790i	0.736313	−	0.267996i	0.682835	+	0.730573i	$0.260747\pi$
$548$	−16.2005			−0.692053
$549$	8.50689	+	13.1134i	0.363065	+	0.559666i
$550$	32.9309			1.40418
$551$	1.90738	−	10.8173i	0.0812571	−	0.460832i
$552$	3.48499	+	1.89329i	0.148331	+	0.0805838i
$553$	8.82830	+	2.41897i	0.375417	+	0.102865i
$554$	−1.10140	−	6.24637i	−0.0467941	−	0.265383i
$555$	37.8356	−	23.1731i	1.60603	−	0.983642i
$556$	−13.9917	+	5.09257i	−0.593381	+	0.215973i
$557$	32.9370			1.39558			0.697792	−	0.716301i	$-0.254166\pi$
$557$	32.9370			1.39558			0.697792	+	0.716301i	$0.254166\pi$
$558$	−22.6754	+	21.1246i	−0.959928	+	0.894276i
$559$	−4.70894	+	8.15612i	−0.199167	+	0.344967i
$560$	8.59118	−	3.94731i	0.363044	−	0.166804i
$561$	18.4997	−	3.75912i	0.781057	−	0.158710i
$562$	−7.99367	−	2.90946i	−0.337192	−	0.122728i
$563$	−12.4522	+	10.4487i	−0.524799	+	0.440358i	−0.866301	−	0.499523i	$-0.833509\pi$
$563$	−12.4522	+	10.4487i	−0.524799	+	0.440358i	0.341502	+	0.939881i	$0.389064\pi$
$564$	−5.43226	−	0.813205i	−0.228739	−	0.0342421i
$565$	−16.5102	+	6.00921i	−0.694588	+	0.252809i
$566$	5.27518			0.221732
$567$	−8.38624	−	22.2861i	−0.352189	−	0.935929i
$568$	6.62587			0.278015
$569$	13.2341	−	4.81682i	0.554802	−	0.201932i	−0.0493766	−	0.998780i	$-0.515723\pi$
$569$	13.2341	−	4.81682i	0.554802	−	0.201932i	0.604179	+	0.796849i	$0.293501\pi$
$570$	−36.9629	−	5.53331i	−1.54820	−	0.231765i
$571$	−4.87222	+	4.08827i	−0.203896	+	0.171089i	−0.739018	−	0.673686i	$-0.764710\pi$
$571$	−4.87222	+	4.08827i	−0.203896	+	0.171089i	0.535122	+	0.844775i	$0.320266\pi$
$572$	13.4310	+	4.88849i	0.561579	+	0.204398i
$573$	−28.2084	+	5.73194i	−1.17842	+	0.239455i
$574$	1.86786	−	20.0471i	0.0779631	−	0.836749i
$575$	8.89586	−	15.4081i	0.370983	−	0.642561i
$576$	−0.673434	−	2.92344i	−0.0280597	−	0.121810i
$577$	8.81850			0.367119			0.183559	−	0.983009i	$-0.441238\pi$
$577$	8.81850			0.367119			0.183559	+	0.983009i	$0.441238\pi$
$578$	9.76045	−	3.55251i	0.405981	−	0.147765i
$579$	−2.71267	+	1.66142i	−0.112735	+	0.0690462i
$580$	−1.12878	−	6.40162i	−0.0468699	−	0.265813i
$581$	−2.98363	+	2.95016i	−0.123782	+	0.122393i
$582$	−29.1574	−	15.8404i	−1.20861	−	0.656604i
$583$	−5.95173	+	33.7539i	−0.246496	+	1.39795i
$584$	12.1719			0.503679
$585$	−16.4291	+	32.2053i	−0.679260	+	1.33152i
$586$	25.7709			1.06459
$587$	−35.6777	+	12.9856i	−1.47258	+	0.535974i	−0.948799	−	0.315882i	$-0.897700\pi$
$587$	−35.6777	+	12.9856i	−1.47258	+	0.535974i	−0.523777	+	0.851855i	$0.675478\pi$
$588$	9.40104	+	7.65640i	0.387692	+	0.315745i
$589$	−47.7845	+	40.0960i	−1.96893	+	1.65213i
$590$	3.95178	+	22.4117i	0.162692	+	0.922674i
$591$	11.9491	−	15.0146i	0.491519	−	0.617616i
$592$	5.49122	+	4.60768i	0.225688	+	0.189375i
$593$	−10.9811	−	19.0198i	−0.450939	−	0.781049i	0.547506	−	0.836802i	$-0.315578\pi$
$593$	−10.9811	−	19.0198i	−0.450939	−	0.781049i	−0.998445	+	0.0557527i	$0.982244\pi$
$594$	21.3251	−	5.49847i	0.874978	−	0.225605i
$595$	−13.8331	−	19.9948i	−0.567103	−	0.819706i
$596$	1.25397	−	7.11163i	0.0513647	−	0.291304i
$597$	−17.1258	−	2.56372i	−0.700913	−	0.104926i
$598$	5.91551	−	4.96370i	0.241903	−	0.202981i
$599$	6.74569	+	38.2567i	0.275621	+	1.56313i	0.736981	+	0.675913i	$0.236250\pi$
$599$	6.74569	+	38.2567i	0.275621	+	1.56313i	−0.461360	+	0.887213i	$0.652638\pi$
$600$	−13.1884	+	2.67988i	−0.538415	+	0.109406i
$601$	35.2616	−	12.8342i	1.43835	−	0.523516i	0.499037	−	0.866581i	$-0.333687\pi$
$601$	35.2616	−	12.8342i	1.43835	−	0.523516i	0.939312	+	0.343064i	$0.111465\pi$
$602$	−4.20375	−	6.07621i	−0.171332	−	0.247648i
$603$	4.47726	+	3.37727i	0.182328	+	0.137533i
$604$	−4.08358	+	7.07296i	−0.166158	+	0.287795i
$605$	−23.3805	+	8.50982i	−0.950554	+	0.345973i
$606$	−0.379195	−	14.6165i	−0.0154038	−	0.593755i
$607$	6.46845	−	5.42767i	0.262546	−	0.220302i	−0.502006	−	0.864864i	$-0.667405\pi$
$607$	6.46845	−	5.42767i	0.262546	−	0.220302i	0.764552	+	0.644562i	$0.222960\pi$
$608$	−1.04856	−	5.94668i	−0.0425247	−	0.241170i
$609$	6.72993	−	4.91889i	0.272711	−	0.199324i
$610$	14.2631	+	11.9682i	0.577497	+	0.484577i
$611$	−5.34737	+	9.26192i	−0.216331	+	0.374697i
$612$	−7.10298	+	3.01097i	−0.287121	+	0.121711i
$613$	−15.5330	−	26.9039i	−0.627370	−	1.08664i	−0.988077	−	0.153958i	$-0.950798\pi$
$613$	−15.5330	−	26.9039i	−0.627370	−	1.08664i	0.360707	−	0.932679i	$-0.382535\pi$
$614$	19.5369	+	16.3934i	0.788444	+	0.661583i
$615$	−14.9564	+	44.6638i	−0.603098	+	1.80102i
$616$	−7.97360	+	7.88417i	−0.321265	+	0.317662i
$617$	−1.58599	−	0.577253i	−0.0638495	−	0.0232393i	0.309898	−	0.950770i	$-0.399705\pi$
$617$	−1.58599	−	0.577253i	−0.0638495	−	0.0232393i	−0.373747	+	0.927531i	$0.621927\pi$
$618$	34.5324	+	5.16947i	1.38910	+	0.207947i
$619$	8.85436	+	7.42969i	0.355887	+	0.298624i	0.803149	−	0.595779i	$-0.203156\pi$
$619$	8.85436	+	7.42969i	0.355887	+	0.298624i	−0.447262	+	0.894403i	$0.647601\pi$
$620$	−18.4576	+	31.9695i	−0.741275	+	1.28393i
$621$	3.18801	−	11.4632i	0.127930	−	0.460001i
$622$	6.59468			0.264422
$623$	−11.1516	−	7.90252i	−0.446779	−	0.316608i
$624$	−5.77678	−	0.864780i	−0.231256	−	0.0346189i
$625$	−0.603891	−	3.42484i	−0.0241556	−	0.136993i
$626$	4.12899	+	23.4167i	0.165028	+	0.935918i
$627$	43.4393	−	8.82685i	1.73480	−	0.352510i
$628$	−13.1603	−	11.0428i	−0.525153	−	0.440655i
$629$	9.21699	−	15.9643i	0.367506	−	0.636538i
$630$	−17.3253	−	22.4575i	−0.690256	−	0.894729i
$631$	−20.7060	−	35.8638i	−0.824291	−	1.42771i	−0.902460	−	0.430774i	$-0.858241\pi$
$631$	−20.7060	−	35.8638i	−0.824291	−	1.42771i	0.0781684	−	0.996940i	$-0.475093\pi$
$632$	0.600783	−	3.40721i	0.0238979	−	0.135532i
$633$	−29.8201	+	18.2638i	−1.18524	+	0.725923i
$634$	−24.8366	−	9.03978i	−0.986387	−	0.359016i
$635$	−15.0866	+	12.6591i	−0.598692	+	0.502362i
$636$	−0.363264	−	14.0024i	−0.0144044	−	0.555231i
$637$	20.5759	−	11.5721i	0.815245	−	0.458502i
$638$	3.85477	+	6.67666i	0.152612	+	0.264332i
$639$	−4.46208	−	19.3703i	−0.176517	−	0.766278i
$640$	−1.78675	−	3.09475i	−0.0706276	−	0.122331i
$641$	8.41641	−	47.7318i	0.332428	−	1.88529i	−0.118854	−	0.992912i	$-0.537922\pi$
$641$	8.41641	−	47.7318i	0.332428	−	1.88529i	0.451282	−	0.892381i	$-0.350967\pi$
$642$	−6.99026	−	7.90492i	−0.275884	−	0.311982i
$643$	−14.2836	+	11.9854i	−0.563291	+	0.472658i	−0.879412	−	0.476061i	$-0.842064\pi$
$643$	−14.2836	+	11.9854i	−0.563291	+	0.472658i	0.316121	+	0.948719i	$0.397620\pi$
$644$	1.53497	+	5.86059i	0.0604864	+	0.230940i
$645$	6.33108	+	16.0838i	0.249286	+	0.633300i
$646$	−14.5919	+	5.31103i	−0.574112	+	0.208960i
$647$	−7.77304	+	13.4633i	−0.305590	+	0.529297i	−0.977392	−	0.211433i	$-0.932187\pi$
$647$	−7.77304	+	13.4633i	−0.305590	+	0.529297i	0.671803	+	0.740730i	$0.265520\pi$
$648$	−8.09297	+	3.93748i	−0.317922	+	0.154679i
$649$	−13.4953	−	23.3746i	−0.529738	−	0.917533i
$650$	−4.55016	+	25.8052i	−0.178472	+	1.01216i
$651$	−47.2330	−	3.16785i	−1.85121	−	0.124158i
$652$	10.3832	+	3.77916i	0.406636	+	0.148003i
$653$	1.28862	+	0.469020i	0.0504277	+	0.0183542i	0.367111	−	0.930177i	$-0.380347\pi$
$653$	1.28862	+	0.469020i	0.0504277	+	0.0183542i	−0.316683	+	0.948531i	$0.602569\pi$
$654$	6.01300	−	17.9565i	0.235127	−	0.702153i
$655$	1.81949	−	10.3188i	0.0710934	−	0.403191i
$656$	−7.60990			−0.297117
$657$	−8.19700	−	35.5839i	−0.319795	−	1.38826i
$658$	−4.77369	−	6.90002i	−0.186098	−	0.268991i
$659$	21.0943	+	17.7002i	0.821718	+	0.689503i	0.953374	−	0.301792i	$-0.0975850\pi$
$659$	21.0943	+	17.7002i	0.821718	+	0.689503i	−0.131656	+	0.991295i	$0.542029\pi$
$660$	22.3702	−	13.7010i	0.870760	−	0.533312i
$661$	6.90642	+	2.51373i	0.268629	+	0.0977729i	0.472823	−	0.881158i	$-0.343235\pi$
$661$	6.90642	+	2.51373i	0.268629	+	0.0977729i	−0.204194	+	0.978930i	$0.565457\pi$
$662$	−7.41174	−	2.69765i	−0.288065	−	0.104847i
$663$	0.389562	+	15.0161i	0.0151293	+	0.583176i
$664$	1.21487	+	1.01940i	0.0471460	+	0.0395602i
$665$	−32.4817	−	46.9500i	−1.25959	−	1.82064i
$666$	9.77230	−	19.1562i	0.378669	−	0.742288i
$667$	4.16527			0.161280
$668$	3.43528	−	19.4825i	0.132915	−	0.753799i
$669$	−41.5550	+	8.44395i	−1.60661	+	0.326462i
$670$	6.27743	+	2.28480i	0.242518	+	0.0882695i
$671$	−20.7509	−	7.55271i	−0.801079	−	0.291569i
$672$	2.55173	−	3.80640i	0.0984350	−	0.146835i
$673$	−3.58323	+	20.3215i	−0.138123	+	0.783336i	0.834510	+	0.550992i	$0.185751\pi$
$673$	−3.58323	+	20.3215i	−0.138123	+	0.783336i	−0.972634	+	0.232344i	$0.925361\pi$
$674$	2.60328	+	4.50902i	0.100275	+	0.173681i
$675$	16.7160	+	36.7508i	0.643399	+	1.41454i
$676$	0.813486	−	1.40900i	0.0312879	−	0.0541923i
$677$	−30.3450	+	11.0447i	−1.16625	+	0.424482i	−0.851328	−	0.524634i	$-0.824202\pi$
$677$	−30.3450	+	11.0447i	−1.16625	+	0.424482i	−0.314927	+	0.949116i	$0.601980\pi$
$678$	−5.30291	+	6.66335i	−0.203657	+	0.255904i
$679$	−12.8425	−	49.0331i	−0.492849	−	1.88172i
$680$	−7.03967	+	5.90699i	−0.269959	+	0.226523i
$681$	24.1790	−	4.91315i	0.926540	−	0.188273i
$682$	7.60266	−	43.1168i	0.291121	−	1.65103i
$683$	11.1500	+	19.3124i	0.426643	+	0.738968i	0.996572	−	0.0827262i	$-0.0263627\pi$
$683$	11.1500	+	19.3124i	0.426643	+	0.738968i	−0.569929	+	0.821694i	$0.693029\pi$
$684$	−16.6786	+	7.07009i	−0.637723	+	0.270332i
$685$	28.9464	+	50.1366i	1.10598	+	1.91562i
$686$	1.30181	+	18.4744i	0.0497034	+	0.705358i
$687$	28.5909	−	17.5110i	1.09081	−	0.668086i
$688$	−2.13929	+	1.79507i	−0.0815595	+	0.0684366i
$689$	−25.6278	−	9.32777i	−0.976343	−	0.355360i
$690$	−0.367560	−	14.1680i	−0.0139928	−	0.539367i
$691$	−2.95689	+	16.7693i	−0.112485	+	0.637936i	0.875479	+	0.483256i	$0.160546\pi$
$691$	−2.95689	+	16.7693i	−0.112485	+	0.637936i	−0.987965	+	0.154680i	$0.950565\pi$
$692$	−9.68777	−	16.7797i	−0.368274	−	0.637869i
$693$	28.4186	+	18.0008i	1.07953	+	0.683796i
$694$	1.75060	−	3.03212i	0.0664517	−	0.115098i
$695$	40.7599	+	34.2016i	1.54611	+	1.29734i
$696$	−2.08713	−	2.36023i	−0.0791125	−	0.0894642i
$697$	3.39824	+	19.2723i	0.128717	+	0.729992i
$698$	−0.112862	−	0.640070i	−0.00427188	−	0.0242270i
$699$	15.5935	−	19.5939i	0.589799	−	0.741110i
$700$	−16.7728	−	11.8860i	−0.633953	−	0.449248i
$701$	−4.91861			−0.185773			−0.0928867	−	0.995677i	$-0.529609\pi$
$701$	−4.91861			−0.185773			−0.0928867	+	0.995677i	$0.529609\pi$
$702$	1.36215	+	17.4704i	0.0514111	+	0.659379i
$703$	21.6425	−	37.4860i	0.816264	−	1.41381i
$704$	3.24668	+	2.72429i	0.122364	+	0.102675i
$705$	7.18944	+	18.2645i	0.270770	+	0.687879i
$706$	−8.02159	−	2.91962i	−0.301897	−	0.109881i
$707$	15.8817	−	15.7036i	0.597294	−	0.590596i
$708$	7.30692	+	8.26301i	0.274611	+	0.310543i
$709$	−11.9617	−	10.0370i	−0.449230	−	0.376949i	0.389920	−	0.920849i	$-0.372503\pi$
$709$	−11.9617	−	10.0370i	−0.449230	−	0.376949i	−0.839150	+	0.543900i	$0.816947\pi$
$710$	−11.8388	−	20.5054i	−0.444302	−	0.769554i
$711$	−10.3654	+	0.538179i	−0.388731	+	0.0201833i
$712$	−2.58297	+	4.47383i	−0.0968007	+	0.167664i
$713$	−18.1203	−	15.2047i	−0.678609	−	0.569420i
$714$	−10.7793	−	4.76257i	−0.403406	−	0.178235i
$715$	−8.86927	−	50.3001i	−0.331692	−	1.88112i
$716$	−16.7428	+	14.0489i	−0.625709	+	0.525032i
$717$	6.74138	+	3.66239i	0.251762	+	0.136775i
$718$	17.5055	−	6.37147i	0.653299	−	0.237781i
$719$	9.95128	−	17.2361i	0.371120	−	0.642799i	−0.618618	−	0.785692i	$-0.712307\pi$
$719$	9.95128	−	17.2361i	0.371120	−	0.642799i	0.989738	+	0.142893i	$0.0456405\pi$
$720$	−7.84404	+	7.30757i	−0.292330	+	0.272337i
$721$	30.3459	+	43.8628i	1.13014	+	1.63354i
$722$	−16.4094	+	5.97252i	−0.610693	+	0.222274i
$723$	8.51135	+	9.62504i	0.316540	+	0.357959i
$724$	−0.862704	−	4.89264i	−0.0320621	−	0.181833i
$725$	−10.8272	+	9.08509i	−0.402112	+	0.337412i
$726$	−7.50960	+	9.43616i	−0.278707	+	0.350209i
$727$	0.456609	−	2.58956i	0.0169347	−	0.0960414i	−0.975169	−	0.221462i	$-0.928917\pi$
$727$	0.456609	−	2.58956i	0.0169347	−	0.0960414i	0.992104	+	0.125421i	$0.0400281\pi$
$728$	−5.07645	−	7.33764i	−0.188146	−	0.271951i
$729$	16.9611	+	21.0077i	0.628188	+	0.778062i
$730$	−21.7483	−	37.6691i	−0.804939	−	1.39420i
$731$	5.50140	+	4.61622i	0.203477	+	0.170737i
$732$	8.92512	+	1.33608i	0.329882	+	0.0493830i
$733$	7.36370	+	41.7616i	0.271984	+	1.54250i	0.748381	+	0.663269i	$0.230832\pi$
$733$	7.36370	+	41.7616i	0.271984	+	1.54250i	−0.476397	+	0.879231i	$0.658057\pi$
$734$	−8.80172	+	7.38552i	−0.324877	+	0.272605i
$735$	6.89730	−	42.7739i	0.254411	−	1.57774i
$736$	2.15172	−	0.783162i	0.0793134	−	0.0288677i
$737$	−7.92295			−0.291846
$738$	5.12477	+	22.2471i	0.188645	+	0.818926i
$739$	0.422006			0.0155237			0.00776186	−	0.999970i	$-0.497529\pi$
$739$	0.422006			0.0155237			0.00776186	+	0.999970i	$0.497529\pi$
$740$	4.44816	−	25.2267i	0.163517	−	0.927354i
$741$	0.914735	+	35.2595i	0.0336036	+	1.29529i
$742$	15.2145	−	15.0439i	0.558541	−	0.552277i
$743$	−7.01750	−	39.7982i	−0.257447	−	1.46006i	−0.789712	−	0.613477i	$-0.789770\pi$
$743$	−7.01750	−	39.7982i	−0.257447	−	1.46006i	0.532265	−	0.846578i	$-0.321341\pi$
$744$	0.464029	+	17.8865i	0.0170121	+	0.655750i
$745$	−24.2492	+	8.82600i	−0.888424	+	0.323360i
$746$	−9.18036			−0.336117
$747$	2.16201	−	4.23809i	0.0791036	−	0.155063i
$748$	5.44953	−	9.43887i	0.199255	−	0.345119i
$749$	1.49539	−	16.0494i	0.0546402	−	0.586433i
$750$	11.3572	+	12.8433i	0.414707	+	0.468970i
$751$	21.2544	+	7.73597i	0.775585	+	0.282290i	0.699330	−	0.714799i	$-0.253482\pi$
$751$	21.2544	+	7.73597i	0.775585	+	0.282290i	0.0762543	+	0.997088i	$0.475704\pi$
$752$	−2.42933	+	2.03845i	−0.0885885	+	0.0743346i
$753$	16.8699	−	21.1977i	0.614772	−	0.772489i
$754$	−5.76458	+	2.09814i	−0.209934	+	0.0764096i
$755$	29.1854			1.06216
$756$	−12.8462	−	4.89645i	−0.467212	−	0.178082i
$757$	−2.49660			−0.0907406			−0.0453703	−	0.998970i	$-0.514447\pi$
$757$	−2.49660			−0.0907406			−0.0453703	+	0.998970i	$0.514447\pi$
$758$	−27.7008	+	10.0823i	−1.00614	+	0.366205i
$759$	6.15677	+	15.6410i	0.223477	+	0.567733i
$760$	−16.5300	+	13.8703i	−0.599604	+	0.503128i
$761$	−4.52944	−	1.64858i	−0.164192	−	0.0597610i	0.258616	−	0.965980i	$-0.416733\pi$
$761$	−4.52944	−	1.64858i	−0.164192	−	0.0597610i	−0.422808	+	0.906219i	$0.638956\pi$
$762$	−3.03105	+	9.05156i	−0.109803	+	0.327903i
$763$	26.2843	−	12.0766i	0.951557	−	0.437203i
$764$	−8.30948	+	14.3924i	−0.300627	+	0.520700i
$765$	22.0095	+	16.6021i	0.795754	+	0.600250i
$766$	8.28767			0.299446
$767$	20.1814	−	7.34544i	0.728709	−	0.265229i
$768$	−1.52196	−	0.826833i	−0.0549188	−	0.0298358i
$769$	0.959984	+	5.44434i	0.0346179	+	0.196328i	0.997212	−	0.0746194i	$-0.0237742\pi$
$769$	0.959984	+	5.44434i	0.0346179	+	0.196328i	−0.962594	+	0.270947i	$0.912663\pi$
$770$	38.6464	+	10.5892i	1.39272	+	0.381608i
$771$	−5.07782	+	3.11000i	−0.182873	+	0.112004i
$772$	−0.318916	+	1.80866i	−0.0114780	+	0.0650951i
$773$	6.60760			0.237659			0.118829	−	0.992915i	$-0.462086\pi$
$773$	6.60760			0.237659			0.118829	+	0.992915i	$0.462086\pi$
$774$	6.68845	+	5.04521i	0.240412	+	0.181346i
$775$	80.2654			2.88322
$776$	−18.0025	+	6.55238i	−0.646253	+	0.235217i
$777$	31.5508	−	9.14426i	1.13188	−	0.328048i
$778$	16.8768	−	14.1613i	0.605064	−	0.507709i
$779$	7.97944	+	45.2537i	0.285893	+	1.62138i
$780$	7.64541	+	19.4228i	0.273750	+	0.695449i
$781$	21.5121	+	18.0508i	0.769762	+	0.645907i
$782$	−2.94425	−	5.09958i	−0.105286	−	0.182361i
$783$	−5.49443	+	7.69105i	−0.196355	+	0.274856i
$784$	6.90692	−	1.13771i	0.246676	−	0.0406326i
$785$	−10.6605	+	60.4585i	−0.380488	+	2.15786i
$786$	−1.86017	−	4.72569i	−0.0663502	−	0.168560i
$787$	−18.3793	+	15.4220i	−0.655150	+	0.549736i	−0.908629	−	0.417605i	$-0.862870\pi$
$787$	−18.3793	+	15.4220i	−0.655150	+	0.549736i	0.253479	+	0.967341i	$0.418425\pi$
$788$	−1.92381	−	10.9105i	−0.0685328	−	0.388669i
$789$	10.1358	−	30.2683i	0.360844	−	1.07758i
$790$	−11.6179	+	4.22857i	−0.413347	+	0.150446i
$791$	−12.9650	+	1.06065i	−0.460982	+	0.0377125i
$792$	5.77786	−	11.3261i	0.205307	−	0.402455i
$793$	8.78565	−	15.2172i	0.311988	−	0.540378i
$794$	17.4306	−	6.34423i	0.618590	−	0.225148i
$795$	−42.6848	+	26.1430i	−1.51387	+	0.927198i
$796$	−7.65874	+	6.42644i	−0.271457	+	0.227779i
$797$	5.25048	+	29.7770i	0.185982	+	1.05475i	0.924688	+	0.380726i	$0.124326\pi$
$797$	5.25048	+	29.7770i	0.185982	+	1.05475i	−0.738706	+	0.674028i	$0.764563\pi$
$798$	−25.3111	−	11.1831i	−0.896003	−	0.395876i
$799$	6.24727	+	5.24208i	0.221013	+	0.185452i
$800$	−3.88497	+	6.72897i	−0.137355	+	0.237905i
$801$	14.8184	+	4.53831i	0.523583	+	0.160353i
$802$	−0.200692	−	0.347609i	−0.00708668	−	0.0122745i
$803$	39.5184	+	33.1598i	1.39457	+	1.17019i
$804$	3.17305	−	0.644762i	0.111905	−	0.0227390i
$805$	15.3944	−	15.2218i	0.542582	−	0.536497i
$806$	32.7367	+	11.9152i	1.15310	+	0.419694i
$807$	5.62085	−	7.06286i	0.197863	−	0.248624i
$808$	−6.46670	−	5.42621i	−0.227498	−	0.190893i
$809$	19.0848	−	33.0558i	0.670984	−	1.16218i	−0.306641	−	0.951825i	$-0.599205\pi$
$809$	19.0848	−	33.0558i	0.670984	−	1.16218i	0.977625	−	0.210354i	$-0.0674615\pi$
$810$	26.6457	+	18.0104i	0.936233	+	0.632821i
$811$	39.4404			1.38494			0.692470	−	0.721447i	$-0.256522\pi$
$811$	39.4404			1.38494			0.692470	+	0.721447i	$0.256522\pi$
$812$	0.446488	−	4.79199i	0.0156686	−	0.168166i
$813$	−9.42142	−	23.9347i	−0.330424	−	0.839427i
$814$	5.27558	+	29.9193i	0.184909	+	1.04867i
$815$	−6.85659	−	38.8857i	−0.240176	−	1.36211i
$816$	−1.41435	+	4.22363i	−0.0495121	+	0.147857i
$817$	12.9179	+	10.8394i	0.451940	+	0.379223i
$818$	8.95642	−	15.5130i	0.313154	−	0.542399i
$819$	−18.0325	+	19.7821i	−0.630106	+	0.691242i
$820$	13.5970	+	23.5507i	0.474828	+	0.822427i
$821$	−5.18533	+	29.4075i	−0.180969	+	1.02633i	0.750057	+	0.661374i	$0.230026\pi$
$821$	−5.18533	+	29.4075i	−0.180969	+	1.02633i	−0.931026	+	0.364954i	$0.881085\pi$
$822$	24.6565	+	13.3951i	0.859994	+	0.467209i
$823$	−0.191642	−	0.0697520i	−0.00668022	−	0.00243140i	0.338678	−	0.940902i	$-0.390020\pi$
$823$	−0.191642	−	0.0697520i	−0.00668022	−	0.00243140i	−0.345358	+	0.938471i	$0.612243\pi$
$824$	15.4430	−	12.9582i	0.537983	−	0.451422i
$825$	−50.1193	−	27.2283i	−1.74493	−	0.947968i
$826$	−1.56313	+	16.7765i	−0.0543881	+	0.583728i
$827$	−10.1906	−	17.6506i	−0.354362	−	0.613773i	0.632647	−	0.774441i	$-0.281969\pi$
$827$	−10.1906	−	17.6506i	−0.354362	−	0.613773i	−0.987009	+	0.160668i	$0.948635\pi$
$828$	−3.73857	−	5.76301i	−0.129924	−	0.200278i
$829$	−11.6789	−	20.2284i	−0.405624	−	0.702561i	0.588770	−	0.808301i	$-0.299612\pi$
$829$	−11.6789	−	20.2284i	−0.405624	−	0.702561i	−0.994394	+	0.105740i	$0.966279\pi$
$830$	0.984101	−	5.58112i	0.0341587	−	0.193723i
$831$	−3.48841	+	10.4174i	−0.121012	+	0.361374i
$832$	−2.58340	+	2.16773i	−0.0895634	+	0.0751526i
$833$	−5.96562	−	16.9840i	−0.206696	−	0.588460i
$834$	25.5055	+	3.81815i	0.883182	+	0.132212i
$835$	−66.4313	+	24.1790i	−2.29895	+	0.836749i
$836$	12.7961	−	22.1635i	0.442563	−	0.766541i
$837$	51.9775	−	13.4019i	1.79661	−	0.463238i
$838$	10.7882	+	18.6857i	0.372672	+	0.645486i
$839$	2.87441	−	16.3016i	0.0992358	−	0.562794i	−0.894131	−	0.447806i	$-0.852206\pi$
$839$	2.87441	−	16.3016i	0.0992358	−	0.562794i	0.993367	−	0.114989i	$-0.0366832\pi$
$840$	−16.3392	−	1.09585i	−0.563754	−	0.0378103i
$841$	24.1417	+	8.78686i	0.832473	+	0.302995i
$842$	−10.8764	−	3.95869i	−0.374826	−	0.136425i
$843$	9.76037	+	11.0375i	0.336165	+	0.380151i
$844$	−3.50581	+	19.8825i	−0.120675	+	0.684382i
$845$	−5.81399			−0.200007
$846$	7.59527	+	5.72923i	0.261131	+	0.196975i
$847$	−18.3601	+	1.50202i	−0.630860	+	0.0516101i
$848$	−6.19501	−	5.19823i	−0.212737	−	0.178508i
$849$	−8.02859	−	4.36169i	−0.275540	−	0.149693i
$850$	18.7762	+	6.83398i	0.644019	+	0.234404i
$851$	15.4241	+	5.61393i	0.528733	+	0.192443i
$852$	−10.0843	−	5.47849i	−0.345482	−	0.187690i
$853$	−32.9561	−	27.6534i	−1.12839	−	0.946836i	−0.129397	−	0.991593i	$-0.541304\pi$
$853$	−32.9561	−	27.6534i	−1.12839	−	0.946836i	−0.998998	+	0.0447572i	$0.985749\pi$
$854$	7.84309	+	11.3366i	0.268385	+	0.387931i
$855$	51.6807	+	38.9836i	1.76744	+	1.33321i
$856$	−6.09239			−0.208234
$857$	−2.78442	+	15.7912i	−0.0951139	+	0.539418i	0.899598	+	0.436718i	$0.143859\pi$
$857$	−2.78442	+	15.7912i	−0.0951139	+	0.539418i	−0.994712	+	0.102700i	$0.967252\pi$
$858$	−16.3994	−	18.5453i	−0.559868	−	0.633125i
$859$	−34.8923	−	12.6997i	−1.19051	−	0.433310i	−0.330607	−	0.943769i	$-0.607253\pi$
$859$	−34.8923	−	12.6997i	−1.19051	−	0.433310i	−0.859902	+	0.510459i	$0.829476\pi$
$860$	9.37768	+	3.41320i	0.319776	+	0.116389i
$861$	−19.4184	+	28.9663i	−0.661777	+	0.987171i
$862$	4.25999	−	24.1596i	0.145096	−	0.822879i
$863$	−8.50835	−	14.7369i	−0.289627	−	0.501650i	0.684093	−	0.729394i	$-0.260198\pi$
$863$	−8.50835	−	14.7369i	−0.289627	−	0.501650i	−0.973721	+	0.227745i	$0.926865\pi$
$864$	−1.39226	+	5.00616i	−0.0473656	+	0.170313i
$865$	−34.6193	+	59.9624i	−1.17709	+	2.03878i
$866$	−15.3840	+	5.59931i	−0.522768	+	0.190272i
$867$	−17.7923	−	2.66349i	−0.604258	−	0.0904570i
$868$	−19.4348	+	19.2168i	−0.659660	+	0.652261i
$869$	11.2328	−	9.42541i	0.381046	−	0.319735i
$870$	−3.57512	+	10.6763i	−0.121208	+	0.361960i
$871$	1.09474	−	6.20857i	0.0370938	−	0.210369i
$872$	−5.46649	−	9.46824i	−0.185119	−	0.320635i
$873$	31.2790	+	48.2167i	1.05863	+	1.63189i
$874$	−6.91342	−	11.9744i	−0.233850	−	0.405040i
$875$	−2.42958	+	26.0758i	−0.0821349	+	0.881523i
$876$	−18.5251	−	10.0642i	−0.625907	−	0.340036i
$877$	33.3671	−	27.9983i	1.12673	−	0.945436i	0.127802	−	0.991800i	$-0.459208\pi$
$877$	33.3671	−	27.9983i	1.12673	−	0.945436i	0.998925	+	0.0463638i	$0.0147633\pi$
$878$	−19.7993	−	7.20636i	−0.668194	−	0.243203i
$879$	−39.2221	−	21.3082i	−1.32293	−	0.718708i
$880$	2.62996	−	14.9153i	0.0886561	−	0.502794i
$881$	−5.49845	−	9.52359i	−0.185247	−	0.320858i	0.758412	−	0.651775i	$-0.225975\pi$
$881$	−5.49845	−	9.52359i	−0.185247	−	0.320858i	−0.943660	+	0.330917i	$0.892642\pi$
$882$	−7.97739	−	19.4258i	−0.268613	−	0.654100i
$883$	−17.2558	+	29.8879i	−0.580703	+	1.00581i	0.414693	+	0.909961i	$0.363889\pi$
$883$	−17.2558	+	29.8879i	−0.580703	+	1.00581i	−0.995396	+	0.0958457i	$0.969444\pi$
$884$	6.64349	+	5.57455i	0.223445	+	0.187492i
$885$	12.5163	−	37.3770i	0.420730	−	1.25641i
$886$	3.49317	+	19.8107i	0.117355	+	0.665554i
$887$	−2.29613	−	13.0220i	−0.0770966	−	0.437237i	−0.998784	−	0.0493029i	$-0.984300\pi$
$887$	−2.29613	−	13.0220i	−0.0770966	−	0.437237i	0.921687	−	0.387934i	$-0.126811\pi$
$888$	−4.54761	−	11.5530i	−0.152608	−	0.387694i
$889$	−13.2495	+	6.08763i	−0.444374	+	0.204172i
$890$	18.4605			0.618797
$891$	−37.0021	−	9.26384i	−1.23962	−	0.310350i
$892$	−12.2410	+	21.2021i	−0.409860	+	0.709899i
$893$	14.6693	+	12.3090i	0.490889	+	0.411905i
$894$	−7.78862	+	9.78676i	−0.260490	+	0.327318i
$895$	73.3931	+	26.7129i	2.45326	+	0.892914i
$896$	−0.670349	−	2.55942i	−0.0223948	−	0.0855042i
$897$	−13.1073	+	2.66339i	−0.437639	+	0.0889281i
$898$	−9.35849	−	7.85271i	−0.312297	−	0.262048i
$899$	9.39559	+	16.2736i	0.313361	+	0.542756i
$900$	22.2880	+	6.82596i	0.742933	+	0.227532i
$901$	−10.3983	+	18.0104i	−0.346417	+	0.600013i
$902$	−24.7069	−	20.7315i	−0.822650	−	0.690285i
$903$	1.37390	+	12.7235i	0.0457206	+	0.423412i
$904$	0.853771	+	4.84198i	0.0283960	+	0.161042i
$905$	−13.6000	+	11.4118i	−0.452080	+	0.379341i
$906$	12.0632	−	7.38830i	0.400772	−	0.245460i
$907$	4.98234	−	1.81342i	0.165436	−	0.0602138i	−0.257974	−	0.966152i	$-0.583055\pi$
$907$	4.98234	−	1.81342i	0.165436	−	0.0602138i	0.423410	+	0.905938i	$0.360833\pi$
$908$	7.12251	−	12.3365i	0.236369	−	0.409403i
$909$	−11.5083	+	22.5592i	−0.381706	+	0.748241i
$910$	−13.6378	+	28.8209i	−0.452088	+	0.955402i
$911$	39.5736	−	14.4036i	1.31113	−	0.477213i	0.410525	−	0.911849i	$-0.365345\pi$
$911$	39.5736	−	14.4036i	1.31113	−	0.477213i	0.900606	+	0.434636i	$0.143123\pi$
$912$	−3.32105	+	9.91756i	−0.109971	+	0.328403i
$913$	1.16716	+	6.61929i	0.0386274	+	0.219067i
$914$	−14.7782	+	12.4004i	−0.488819	+	0.410168i
$915$	−11.8121	−	30.0082i	−0.390497	−	0.992041i
$916$	3.36130	−	19.0629i	0.111060	−	0.629855i
$917$	3.31815	−	7.01228i	0.109575	−	0.231566i
$918$	13.3000	+	1.29042i	0.438965	+	0.0425902i
$919$	−1.88056	−	3.25723i	−0.0620340	−	0.107446i	0.833340	−	0.552760i	$-0.186425\pi$
$919$	−1.88056	−	3.25723i	−0.0620340	−	0.107446i	−0.895374	+	0.445314i	$0.853092\pi$
$920$	−6.26828	−	5.25971i	−0.206659	−	0.173408i
$921$	−16.1797	−	41.1037i	−0.533138	−	1.35441i
$922$	−2.70552	−	15.3438i	−0.0891015	−	0.505320i
$923$	−17.1173	+	14.3631i	−0.563422	+	0.472767i
$924$	18.6544	−	5.40653i	0.613683	−	0.177862i
$925$	−52.3382	+	19.0496i	−1.72087	+	0.626346i
$926$	−12.6742			−0.416501
$927$	−48.2824	−	36.4202i	−1.58580	−	1.19620i
$928$	−1.81905			−0.0597131
$929$	7.27235	−	41.2436i	0.238598	−	1.35316i	−0.596304	−	0.802759i	$-0.703365\pi$
$929$	7.27235	−	41.2436i	0.238598	−	1.35316i	0.834902	−	0.550399i	$-0.185524\pi$
$930$	54.5250	−	33.3948i	1.78795	−	1.09506i
$931$	−14.0079	−	39.8803i	−0.459092	−	1.30702i
$932$	−2.51056	−	14.2381i	−0.0822361	−	0.466384i
$933$	−10.0368	−	5.45269i	−0.328590	−	0.178513i
$934$	2.29523	−	0.835395i	0.0751022	−	0.0273350i
$935$	−38.9479			−1.27373
$936$	8.07698	+	6.09259i	0.264004	+	0.199143i
$937$	−3.70662	+	6.42005i	−0.121090	+	0.209734i	−0.920198	−	0.391454i	$-0.871972\pi$
$937$	−3.70662	+	6.42005i	−0.121090	+	0.209734i	0.799108	+	0.601188i	$0.205306\pi$
$938$	4.03543	+	2.85969i	0.131762	+	0.0933721i
$939$	13.0775	−	39.0531i	0.426769	−	1.27445i
$940$	10.6491	+	3.87595i	0.347335	+	0.126420i
$941$	−24.0059	+	20.1434i	−0.782572	+	0.656656i	−0.943895	−	0.330246i	$-0.892868\pi$
$941$	−24.0059	+	20.1434i	−0.782572	+	0.656656i	0.161323	+	0.986902i	$0.448424\pi$
$942$	10.8988	+	27.6880i	0.355103	+	0.902124i
$943$	−16.3744	+	5.95979i	−0.533223	+	0.194077i
$944$	6.36837			0.207273
$945$	7.79970	+	48.5045i	0.253724	+	1.57785i
$946$	−11.8359			−0.384817
$947$	27.0803	−	9.85643i	0.879992	−	0.320291i	0.137786	−	0.990462i	$-0.456001\pi$
$947$	27.0803	−	9.85643i	0.879992	−	0.320291i	0.742207	+	0.670171i	$0.233779\pi$
$948$	−3.73156	+	4.68888i	−0.121195	+	0.152288i
$949$	−31.4450	+	26.3855i	−1.02075	+	0.856510i
$950$	44.0887	+	16.0470i	1.43042	+	0.520632i
$951$	30.3258	+	34.2939i	0.983381	+	1.11205i
$952$	−6.18248	+	2.84060i	−0.200375	+	0.0920645i
$953$	−10.4605	+	18.1180i	−0.338848	+	0.586901i	−0.984216	−	0.176970i	$-0.943370\pi$
$953$	−10.4605	+	18.1180i	−0.338848	+	0.586901i	0.645369	+	0.763871i	$0.276704\pi$
$954$	−11.0248	+	21.6114i	−0.356940	+	0.699694i
$955$	59.3880			1.92175
$956$	4.16230	−	1.51495i	0.134618	−	0.0489971i
$957$	−0.346308	−	13.3488i	−0.0111946	−	0.431507i
$958$	−6.30771	−	35.7728i	−0.203793	−	1.15577i
$959$	10.8600	+	41.4640i	0.350688	+	1.33894i
$960$	0.160520	+	6.18741i	0.00518076	+	0.199698i
$961$	13.1476	−	74.5636i	0.424115	−	2.40528i
$962$	−24.1743			−0.779410
$963$	4.10282	+	17.8107i	0.132212	+	0.573942i
$964$	7.41810			0.238921
$965$	6.16717	−	2.24467i	0.198528	−	0.0722584i
$966$	2.50957	−	10.1887i	0.0807441	−	0.327817i
$967$	2.48476	−	2.08496i	0.0799045	−	0.0670478i	−0.601961	−	0.798526i	$-0.705614\pi$
$967$	2.48476	−	2.08496i	0.0799045	−	0.0670478i	0.681865	+	0.731478i	$0.261169\pi$
$968$	1.20905	+	6.85686i	0.0388603	+	0.220388i
$969$	26.5996	+	3.98194i	0.854503	+	0.127918i
$970$	52.4440	+	44.0058i	1.68388	+	1.41294i
$971$	−6.98231	−	12.0937i	−0.224073	−	0.388106i	0.731968	−	0.681339i	$-0.238602\pi$
$971$	−6.98231	−	12.0937i	−0.224073	−	0.388106i	−0.956041	+	0.293233i	$0.905269\pi$
$972$	15.5728	+	0.698864i	0.499497	+	0.0224161i
$973$	22.4133	+	32.3969i	0.718539	+	1.03860i
$974$	4.88676	−	27.7142i	0.156582	−	0.888019i
$975$	28.2617	−	35.5122i	0.905100	−	1.13730i
$976$	3.99135	−	3.34914i	0.127760	−	0.107203i
$977$	−4.67345	−	26.5044i	−0.149517	−	0.847952i	−0.963629	−	0.267244i	$-0.913887\pi$
$977$	−4.67345	−	26.5044i	−0.149517	−	0.847952i	0.814112	−	0.580708i	$-0.197224\pi$
$978$	−12.6780	−	14.3368i	−0.405397	−	0.458442i
$979$	−20.5740	+	7.48834i	−0.657549	+	0.239328i
$980$	−15.8619	−	19.3424i	−0.506690	−	0.617869i
$981$	−23.9985	+	22.3572i	−0.766213	+	0.713810i
$982$	13.2581	−	22.9638i	0.423084	−	0.732804i
$983$	34.9484	−	12.7202i	1.11468	−	0.405710i	0.281972	−	0.959423i	$-0.409012\pi$
$983$	34.9484	−	12.7202i	1.11468	−	0.405710i	0.832708	+	0.553712i	$0.186789\pi$
$984$	11.5819	+	6.29212i	0.369218	+	0.200585i
$985$	−30.3277	+	25.4480i	−0.966322	+	0.810840i
$986$	0.812303	+	4.60680i	0.0258690	+	0.146710i
$987$	1.56017	+	14.4486i	0.0496609	+	0.459903i
$988$	15.5997	+	13.0897i	0.496291	+	0.416438i
$989$	−3.19731	+	5.53790i	−0.101669	+	0.176095i
$990$	−45.3750	+	2.35591i	−1.44211	+	0.0748757i
$991$	−10.6984	−	18.5302i	−0.339847	−	0.588632i	0.644557	−	0.764557i	$-0.277042\pi$
$991$	−10.6984	−	18.5302i	−0.339847	−	0.588632i	−0.984404	+	0.175924i	$0.943709\pi$
$992$	7.91342	+	6.64015i	0.251251	+	0.210825i
$993$	9.04982	+	10.2340i	0.287187	+	0.324765i
$994$	−4.44164	−	16.9584i	−0.140880	−	0.537887i
$995$	33.5725	+	12.2194i	1.06432	+	0.387381i
$996$	−1.00611	−	2.55597i	−0.0318797	−	0.0809889i
$997$	−21.9068	−	18.3820i	−0.693795	−	0.582163i	0.226206	−	0.974080i	$-0.427368\pi$
$997$	−21.9068	−	18.3820i	−0.693795	−	0.582163i	−0.920001	+	0.391916i	$0.871812\pi$
$998$	−8.13510	+	14.0904i	−0.257512	+	0.446024i
$999$	−30.7120	+	21.0749i	−0.971685	+	0.666779i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.w.a.25.12	yes	72
7.2	even	3		378.2.v.b.79.4	yes	72
27.13	even	9		378.2.v.b.67.4	✓	72
189.121	even	9	inner	378.2.w.a.121.12	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.b.67.4	✓	72	27.13	even	9
378.2.v.b.79.4	yes	72	7.2	even	3
378.2.w.a.25.12	yes	72	1.1	even	1	trivial
378.2.w.a.121.12	yes	72	189.121	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.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(1.71296 + 0.256429i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-3.35800 - 1.22221i) q^{5} +(-1.69736 + 0.344903i) q^{6} +(-2.15868 - 1.52974i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.86849 + 0.878508i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(1.71296 + 0.256429i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-3.35800 - 1.22221i) q^{5} +(-1.69736 + 0.344903i) q^{6} +(-2.15868 - 1.52974i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.86849 + 0.878508i) q^{9} +3.57351 q^{10} +(-3.98264 + 1.44956i) q^{11} +(1.47704 - 0.904635i) q^{12} +(-0.585610 - 3.32116i) q^{13} +(2.55170 + 0.699171i) q^{14} +(-5.43872 - 2.95469i) q^{15} +(0.173648 - 0.984808i) q^{16} -2.57160 q^{17} +(-2.99596 + 0.155553i) q^{18} -6.03842 q^{19} +(-3.35800 + 1.22221i) q^{20} +(-3.30547 - 3.17393i) q^{21} +(3.24668 - 2.72429i) q^{22} +(-0.397622 - 2.25502i) q^{23} +(-1.07856 + 1.35526i) q^{24} +(5.95212 + 4.99442i) q^{25} +(1.68620 + 2.92058i) q^{26} +(4.68834 + 2.24042i) q^{27} +(-2.63694 + 0.215726i) q^{28} +(-0.315874 + 1.79141i) q^{29} +(6.12129 + 0.916352i) q^{30} +(7.91342 - 6.64015i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-7.19382 + 1.46178i) q^{33} +(2.41652 - 0.879540i) q^{34} +(5.37918 + 7.77522i) q^{35} +(2.76208 - 1.17085i) q^{36} +(-3.58414 + 6.20792i) q^{37} +(5.67426 - 2.06526i) q^{38} +(-0.151486 - 5.83919i) q^{39} +(2.73746 - 2.29701i) q^{40} +(-1.32145 - 7.49429i) q^{41} +(4.19168 + 1.85198i) q^{42} +(-2.13929 - 1.79507i) q^{43} +(-2.11912 + 3.67042i) q^{44} +(-8.55865 - 6.45593i) q^{45} +(1.14491 + 1.98304i) q^{46} +(-2.42933 - 2.03845i) q^{47} +(0.549987 - 1.64241i) q^{48} +(2.31980 + 6.60443i) q^{49} +(-7.30136 - 2.65748i) q^{50} +(-4.40506 - 0.659435i) q^{51} +(-2.58340 - 2.16773i) q^{52} +(4.04351 - 7.00356i) q^{53} +(-5.17187 - 0.501796i) q^{54} +15.1454 q^{55} +(2.40413 - 1.10460i) q^{56} +(-10.3436 - 1.54843i) q^{57} +(-0.315874 - 1.79141i) q^{58} +(1.10586 + 6.27162i) q^{59} +(-6.06554 + 1.23251i) q^{60} +(3.99135 + 3.34914i) q^{61} +(-5.16512 + 8.94625i) q^{62} +(-4.84826 - 6.28445i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.09268 + 11.8682i) q^{65} +(6.26003 - 3.83406i) q^{66} +(1.75666 + 0.639372i) q^{67} +(-1.96996 + 1.65300i) q^{68} +(-0.102857 - 3.96474i) q^{69} +(-7.71406 - 5.46653i) q^{70} +(-3.31293 - 5.73817i) q^{71} +(-2.19505 + 2.04493i) q^{72} +(-6.08597 - 10.5412i) q^{73} +(1.24476 - 7.05938i) q^{74} +(8.91505 + 10.0816i) q^{75} +(-4.62570 + 3.88142i) q^{76} +(10.8147 + 2.96325i) q^{77} +(2.13947 + 5.43523i) q^{78} +(-3.25112 + 1.18331i) q^{79} +(-1.78675 + 3.09475i) q^{80} +(7.45645 + 5.03998i) q^{81} +(3.80495 + 6.59037i) q^{82} +(0.275388 - 1.56180i) q^{83} +(-4.57230 - 0.306658i) q^{84} +(8.63544 + 3.14304i) q^{85} +(2.62422 + 0.955139i) q^{86} +(-1.00045 + 2.98762i) q^{87} +(0.735962 - 4.17385i) q^{88} +5.16593 q^{89} +(10.2506 + 3.13935i) q^{90} +(-3.81636 + 8.06515i) q^{91} +(-1.75410 - 1.47186i) q^{92} +(15.2581 - 9.34510i) q^{93} +(2.98001 + 1.08464i) q^{94} +(20.2770 + 7.38022i) q^{95} +(0.0449194 + 1.73147i) q^{96} +(14.6758 + 12.3145i) q^{97} +(-4.43875 - 5.41272i) q^{98} +(-12.6976 + 0.659271i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9}+O(q^{10}) \) 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9	\( 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9} + 12 q^{10} - 6 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} + 36 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 30 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} + 9 q^{35} + 9 q^{36} + 3 q^{39} - 6 q^{41} + 3 q^{42} + 24 q^{43} - 30 q^{45} - 9 q^{47} - 6 q^{48} + 51 q^{49} + 6 q^{50} + 12 q^{51} + 6 q^{52} - 15 q^{53} - 27 q^{54} + 72 q^{55} + 6 q^{56} - 63 q^{57} + 3 q^{58} + 15 q^{59} - 3 q^{60} - 18 q^{61} - 24 q^{62} - 48 q^{63} - 36 q^{64} - 18 q^{65} - 36 q^{66} + 66 q^{67} - 18 q^{68} - 21 q^{69} - 6 q^{70} + 12 q^{71} - 12 q^{72} - 66 q^{73} + 9 q^{74} + 15 q^{75} - 15 q^{77} + 30 q^{78} + 9 q^{79} - 6 q^{80} - 33 q^{82} - 18 q^{83} - 12 q^{84} + 21 q^{85} - 12 q^{86} - 48 q^{87} + 12 q^{88} + 72 q^{89} + 69 q^{90} + 12 q^{91} + 30 q^{92} + 60 q^{93} - 36 q^{94} + 93 q^{95} - 48 q^{97} + 6 q^{98} - 54 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9 + 12 * q^10 - 6 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 + 36 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 30 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 + 9 * q^35 + 9 * q^36 + 3 * q^39 - 6 * q^41 + 3 * q^42 + 24 * q^43 - 30 * q^45 - 9 * q^47 - 6 * q^48 + 51 * q^49 + 6 * q^50 + 12 * q^51 + 6 * q^52 - 15 * q^53 - 27 * q^54 + 72 * q^55 + 6 * q^56 - 63 * q^57 + 3 * q^58 + 15 * q^59 - 3 * q^60 - 18 * q^61 - 24 * q^62 - 48 * q^63 - 36 * q^64 - 18 * q^65 - 36 * q^66 + 66 * q^67 - 18 * q^68 - 21 * q^69 - 6 * q^70 + 12 * q^71 - 12 * q^72 - 66 * q^73 + 9 * q^74 + 15 * q^75 - 15 * q^77 + 30 * q^78 + 9 * q^79 - 6 * q^80 - 33 * q^82 - 18 * q^83 - 12 * q^84 + 21 * q^85 - 12 * q^86 - 48 * q^87 + 12 * q^88 + 72 * q^89 + 69 * q^90 + 12 * q^91 + 30 * q^92 + 60 * q^93 - 36 * q^94 + 93 * q^95 - 48 * q^97 + 6 * q^98 - 54 * q^99

Introduction

L-functions

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