LMFDB - Embedded newform 342.2.x.c.281.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(29,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([3, 17]))

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

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

chi := DirichletCharacter("342.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.x (of order $18$, 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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			281.9
Character	$\chi$	$=$	342.281
Dual form			342.2.x.c.185.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(1.60646 - 0.647527i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-1.41442 + 3.88608i) q^{5} +(0.814396 - 1.52865i) q^{6} +(2.04763 + 3.54660i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.16142 - 2.08045i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(1.60646 - 0.647527i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-1.41442 + 3.88608i) q^{5} +(0.814396 - 1.52865i) q^{6} +(2.04763 + 3.54660i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.16142 - 2.08045i) q^{9} +(1.41442 + 3.88608i) q^{10} -4.97998i q^{11} +(-0.358731 - 1.69449i) q^{12} +(0.452603 + 1.24352i) q^{13} +(3.84828 + 1.40066i) q^{14} +(0.244139 + 7.15870i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.10469 - 3.03510i) q^{17} +(0.318454 - 2.98305i) q^{18} +(-1.63432 + 4.04092i) q^{19} +(3.58143 + 2.06774i) q^{20} +(5.58595 + 4.37157i) q^{21} +(-3.20107 - 3.81489i) q^{22} +(-3.60155 - 0.635050i) q^{23} +(-1.36400 - 1.06747i) q^{24} +(-9.27084 - 7.77916i) q^{25} +(1.14603 + 0.661661i) q^{26} +(2.12508 - 4.74173i) q^{27} +(3.84828 - 1.40066i) q^{28} +(1.14546 - 6.49624i) q^{29} +(4.78855 + 5.32696i) q^{30} +1.67808i q^{31} +(-0.939693 + 0.342020i) q^{32} +(-3.22467 - 8.00013i) q^{33} +(-1.10469 - 3.03510i) q^{34} +(-16.6786 + 2.94088i) q^{35} +(-1.67352 - 2.48985i) q^{36} -0.879116i q^{37} +(1.34549 + 4.14604i) q^{38} +(1.53230 + 1.70459i) q^{39} +(4.07266 - 0.718119i) q^{40} +(0.319184 - 0.267827i) q^{41} +(7.08907 - 0.241764i) q^{42} +(-0.381958 - 2.16619i) q^{43} +(-4.90432 - 0.864764i) q^{44} +(5.02765 + 11.3421i) q^{45} +(-3.16715 + 1.82855i) q^{46} +(-8.12523 - 1.43270i) q^{47} +(-1.73104 + 0.0590351i) q^{48} +(-4.88556 + 8.46204i) q^{49} -12.1022 q^{50} +(-0.190677 - 5.59109i) q^{51} +(1.30322 - 0.229793i) q^{52} +(1.78669 + 1.49921i) q^{53} +(-1.42002 - 4.99835i) q^{54} +(19.3526 + 7.04378i) q^{55} +(2.04763 - 3.54660i) q^{56} +(-0.00886369 + 7.54983i) q^{57} +(-3.29823 - 5.71270i) q^{58} +(1.22642 + 6.95540i) q^{59} +(7.09234 + 1.00267i) q^{60} +(5.46876 - 1.99047i) q^{61} +(1.07865 + 1.28548i) q^{62} +(11.8043 + 3.40569i) q^{63} +(-0.500000 + 0.866025i) q^{64} -5.47258 q^{65} +(-7.61263 - 4.05568i) q^{66} +(4.68587 - 5.58440i) q^{67} +(-2.79717 - 1.61495i) q^{68} +(-6.19695 + 1.31192i) q^{69} +(-10.8862 + 12.9736i) q^{70} +(-5.35879 + 4.49656i) q^{71} +(-2.88243 - 0.831618i) q^{72} +(-0.522366 - 2.96249i) q^{73} +(-0.565085 - 0.673442i) q^{74} +(-19.9304 - 6.49377i) q^{75} +(3.69573 + 2.31119i) q^{76} +(17.6620 - 10.1971i) q^{77} +(2.26950 + 0.320846i) q^{78} +(-3.63432 + 9.98520i) q^{79} +(2.65824 - 3.16796i) q^{80} +(0.343453 - 8.99344i) q^{81} +(0.0723531 - 0.410335i) q^{82} +(7.01966 - 4.05280i) q^{83} +(5.27514 - 4.74197i) q^{84} +(10.2322 + 8.58582i) q^{85} +(-1.68500 - 1.41388i) q^{86} +(-2.36635 - 11.1777i) q^{87} +(-4.31279 + 2.48999i) q^{88} +(-1.49181 + 8.46047i) q^{89} +(11.1420 + 5.45682i) q^{90} +(-3.48349 + 4.15146i) q^{91} +(-1.25080 + 3.43656i) q^{92} +(1.08660 + 2.69576i) q^{93} +(-7.14521 + 4.12529i) q^{94} +(-13.3917 - 12.0666i) q^{95} +(-1.28811 + 1.15792i) q^{96} +(5.33788 + 6.36144i) q^{97} +(1.69674 + 9.62268i) q^{98} +(-10.3606 - 10.7638i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 6 q^{3} - 30 q^{8} + 6 q^{9}+O(q^{10}) $ 60 * q - 6 * q^3 - 30 * q^8 + 6 * q^9	$ 60 q - 6 q^{3} - 30 q^{8} + 6 q^{9} + 3 q^{13} + 3 q^{14} + 27 q^{15} - 27 q^{17} - 18 q^{18} + 3 q^{19} + 18 q^{23} + 3 q^{24} - 6 q^{27} + 3 q^{28} + 57 q^{33} + 27 q^{34} + 9 q^{38} - 30 q^{39} + 9 q^{41} - 3 q^{43} - 9 q^{44} + 27 q^{45} - 30 q^{49} - 132 q^{50} - 66 q^{51} + 6 q^{52} + 27 q^{54} + 102 q^{57} - 54 q^{59} + 6 q^{60} - 24 q^{61} - 3 q^{62} - 30 q^{64} + 36 q^{65} - 63 q^{66} + 51 q^{67} - 18 q^{68} + 3 q^{69} - 18 q^{71} - 3 q^{72} - 66 q^{73} - 6 q^{74} + 3 q^{78} - 51 q^{79} - 30 q^{81} - 36 q^{83} + 60 q^{84} - 3 q^{86} + 54 q^{87} - 27 q^{89} + 36 q^{90} - 69 q^{91} + 69 q^{93} + 18 q^{94} - 27 q^{95} + 81 q^{97} + 60 q^{98} + 51 q^{99}+O(q^{100}) $ 60 * q - 6 * q^3 - 30 * q^8 + 6 * q^9 + 3 * q^13 + 3 * q^14 + 27 * q^15 - 27 * q^17 - 18 * q^18 + 3 * q^19 + 18 * q^23 + 3 * q^24 - 6 * q^27 + 3 * q^28 + 57 * q^33 + 27 * q^34 + 9 * q^38 - 30 * q^39 + 9 * q^41 - 3 * q^43 - 9 * q^44 + 27 * q^45 - 30 * q^49 - 132 * q^50 - 66 * q^51 + 6 * q^52 + 27 * q^54 + 102 * q^57 - 54 * q^59 + 6 * q^60 - 24 * q^61 - 3 * q^62 - 30 * q^64 + 36 * q^65 - 63 * q^66 + 51 * q^67 - 18 * q^68 + 3 * q^69 - 18 * q^71 - 3 * q^72 - 66 * q^73 - 6 * q^74 + 3 * q^78 - 51 * q^79 - 30 * q^81 - 36 * q^83 + 60 * q^84 - 3 * q^86 + 54 * q^87 - 27 * q^89 + 36 * q^90 - 69 * q^91 + 69 * q^93 + 18 * q^94 - 27 * q^95 + 81 * q^97 + 60 * q^98 + 51 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$	1.60646	−	0.647527i	0.927489	−	0.373850i
$3$	1.60646	−	0.647527i	0.927489	−	0.373850i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−1.41442	+	3.88608i	−0.632547	+	1.73791i	0.0414138	+	0.999142i	$0.486814\pi$
$5$	−1.41442	+	3.88608i	−0.632547	+	1.73791i	−0.673961	+	0.738767i	$0.735408\pi$
$6$	0.814396	−	1.52865i	0.332476	−	0.624067i
$7$	2.04763	+	3.54660i	0.773931	+	1.34049i	0.935394	+	0.353609i	$0.115045\pi$
$7$	2.04763	+	3.54660i	0.773931	+	1.34049i	−0.161463	+	0.986879i	$0.551621\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	2.16142	−	2.08045i	0.720473	−	0.693483i
$10$	1.41442	+	3.88608i	0.447278	+	1.22889i
$11$		−	4.97998i		−	1.50152i	−0.660575	−	0.750760i	$-0.729687\pi$
$11$		−	4.97998i		−	1.50152i	0.660575	−	0.750760i	$-0.270313\pi$
$12$	−0.358731	−	1.69449i	−0.103557	−	0.489158i
$13$	0.452603	+	1.24352i	0.125530	+	0.344889i	0.986499	−	0.163767i	$-0.0523645\pi$
$13$	0.452603	+	1.24352i	0.125530	+	0.344889i	−0.860970	+	0.508657i	$0.830142\pi$
$14$	3.84828	+	1.40066i	1.02850	+	0.374342i
$15$	0.244139	+	7.15870i	0.0630363	+	1.84837i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	1.10469	−	3.03510i	0.267926	−	0.736121i	−0.730649	−	0.682754i	$-0.760782\pi$
$17$	1.10469	−	3.03510i	0.267926	−	0.736121i	0.998575	−	0.0533675i	$-0.0169955\pi$
$18$	0.318454	−	2.98305i	0.0750604	−	0.703112i
$19$	−1.63432	+	4.04092i	−0.374938	+	0.927050i
$19$	−1.63432	+	4.04092i	−0.374938	+	0.927050i
$20$	3.58143	+	2.06774i	0.800833	+	0.462361i
$21$	5.58595	+	4.37157i	1.21895	+	0.953954i
$22$	−3.20107	−	3.81489i	−0.682470	−	0.813336i
$23$	−3.60155	−	0.635050i	−0.750975	−	0.132417i	−0.214957	−	0.976624i	$-0.568961\pi$
$23$	−3.60155	−	0.635050i	−0.750975	−	0.132417i	−0.536018	+	0.844207i	$0.680072\pi$
$24$	−1.36400	−	1.06747i	−0.278426	−	0.217896i
$25$	−9.27084	−	7.77916i	−1.85417	−	1.55583i
$26$	1.14603	+	0.661661i	0.224755	+	0.129762i
$27$	2.12508	−	4.74173i	0.408972	−	0.912547i
$28$	3.84828	−	1.40066i	0.727257	−	0.264700i
$29$	1.14546	−	6.49624i	0.212707	−	1.20632i	−0.672134	−	0.740429i	$-0.734622\pi$
$29$	1.14546	−	6.49624i	0.212707	−	1.20632i	0.884841	−	0.465892i	$-0.154267\pi$
$30$	4.78855	+	5.32696i	0.874265	+	0.972565i
$31$			1.67808i			0.301391i	0.988580	+	0.150696i	$0.0481514\pi$
$31$			1.67808i			0.301391i	−0.988580	+	0.150696i	$0.951849\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	−3.22467	−	8.00013i	−0.561343	−	1.39264i
$34$	−1.10469	−	3.03510i	−0.189452	−	0.520516i
$35$	−16.6786	+	2.94088i	−2.81919	+	0.497100i
$36$	−1.67352	−	2.48985i	−0.278920	−	0.414975i
$37$		−	0.879116i		−	0.144526i	−0.997386	−	0.0722629i	$-0.976978\pi$
$37$		−	0.879116i		−	0.144526i	0.997386	−	0.0722629i	$-0.0230221\pi$
$38$	1.34549	+	4.14604i	0.218267	+	0.672577i
$39$	1.53230	+	1.70459i	0.245364	+	0.272952i
$40$	4.07266	−	0.718119i	0.643943	−	0.113545i
$41$	0.319184	−	0.267827i	0.0498481	−	0.0418276i	−0.617523	−	0.786553i	$-0.711864\pi$
$41$	0.319184	−	0.267827i	0.0498481	−	0.0418276i	0.667371	+	0.744725i	$0.267419\pi$
$42$	7.08907	−	0.241764i	1.09387	−	0.0373050i
$43$	−0.381958	−	2.16619i	−0.0582480	−	0.330341i	0.941734	−	0.336359i	$-0.109195\pi$
$43$	−0.381958	−	2.16619i	−0.0582480	−	0.330341i	−0.999982	+	0.00601807i	$0.998084\pi$
$44$	−4.90432	−	0.864764i	−0.739354	−	0.130368i
$45$	5.02765	+	11.3421i	0.749478	+	1.69078i
$46$	−3.16715	+	1.82855i	−0.466971	+	0.269606i
$47$	−8.12523	−	1.43270i	−1.18519	−	0.208980i	−0.453901	−	0.891052i	$-0.649968\pi$
$47$	−8.12523	−	1.43270i	−1.18519	−	0.208980i	−0.731285	+	0.682072i	$0.761079\pi$
$48$	−1.73104	+	0.0590351i	−0.249855	+	0.00852098i
$49$	−4.88556	+	8.46204i	−0.697938	+	1.20886i
$50$	−12.1022			−1.71151
$51$	−0.190677	−	5.59109i	−0.0267001	−	0.782909i
$52$	1.30322	−	0.229793i	0.180724	−	0.0318665i
$53$	1.78669	+	1.49921i	0.245421	+	0.205933i	0.757198	−	0.653186i	$-0.226568\pi$
$53$	1.78669	+	1.49921i	0.245421	+	0.205933i	−0.511777	+	0.859119i	$0.671012\pi$
$54$	−1.42002	−	4.99835i	−0.193240	−	0.680190i
$55$	19.3526	+	7.04378i	2.60951	+	0.949783i
$56$	2.04763	−	3.54660i	0.273626	−	0.473934i
$57$	−0.00886369	+	7.54983i	−0.00117402	+	0.999999i
$58$	−3.29823	−	5.71270i	−0.433079	−	0.750114i
$59$	1.22642	+	6.95540i	0.159667	+	0.905515i	0.954394	+	0.298549i	$0.0965026\pi$
$59$	1.22642	+	6.95540i	0.159667	+	0.905515i	−0.794728	+	0.606966i	$0.792386\pi$
$60$	7.09234	+	1.00267i	0.915617	+	0.129444i
$61$	5.46876	−	1.99047i	0.700204	−	0.254853i	0.0327057	−	0.999465i	$-0.489588\pi$
$61$	5.46876	−	1.99047i	0.700204	−	0.254853i	0.667498	+	0.744612i	$0.267365\pi$
$62$	1.07865	+	1.28548i	0.136988	+	0.163256i
$63$	11.8043	+	3.40569i	1.48720	+	0.429076i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−5.47258			−0.678790
$66$	−7.61263	−	4.05568i	−0.937050	−	0.499219i
$67$	4.68587	−	5.58440i	0.572470	−	0.682243i	−0.399666	−	0.916661i	$-0.630874\pi$
$67$	4.68587	−	5.58440i	0.572470	−	0.682243i	0.972136	+	0.234418i	$0.0753184\pi$
$68$	−2.79717	−	1.61495i	−0.339206	−	0.195841i
$69$	−6.19695	+	1.31192i	−0.746025	+	0.157936i
$70$	−10.8862	+	12.9736i	−1.30115	+	1.55064i
$71$	−5.35879	+	4.49656i	−0.635972	+	0.533644i	−0.902778	−	0.430107i	$-0.858476\pi$
$71$	−5.35879	+	4.49656i	−0.635972	+	0.533644i	0.266806	+	0.963750i	$0.414032\pi$
$72$	−2.88243	−	0.831618i	−0.339698	−	0.0980071i
$73$	−0.522366	−	2.96249i	−0.0611383	−	0.346733i	−0.999997	−	0.00243011i	$-0.999226\pi$
$73$	−0.522366	−	2.96249i	−0.0611383	−	0.346733i	0.938859	−	0.344303i	$-0.111885\pi$
$74$	−0.565085	−	0.673442i	−0.0656898	−	0.0782860i
$75$	−19.9304	−	6.49377i	−2.30137	−	0.749837i
$76$	3.69573	+	2.31119i	0.423929	+	0.265111i
$77$	17.6620	−	10.1971i	2.01277	−	1.16207i
$78$	2.26950	+	0.320846i	0.256970	+	0.0363286i
$79$	−3.63432	+	9.98520i	−0.408892	+	1.12342i	0.548882	+	0.835900i	$0.315054\pi$
$79$	−3.63432	+	9.98520i	−0.408892	+	1.12342i	−0.957774	+	0.287522i	$0.907168\pi$
$80$	2.65824	−	3.16796i	0.297200	−	0.354189i
$81$	0.343453	−	8.99344i	0.0381615	−	0.999272i
$82$	0.0723531	−	0.410335i	0.00799006	−	0.0453139i
$83$	7.01966	−	4.05280i	0.770508	−	0.444853i	−0.0625479	−	0.998042i	$-0.519923\pi$
$83$	7.01966	−	4.05280i	0.770508	−	0.444853i	0.833056	+	0.553189i	$0.186589\pi$
$84$	5.27514	−	4.74197i	0.575565	−	0.517391i
$85$	10.2322	+	8.58582i	1.10984	+	0.931263i
$86$	−1.68500	−	1.41388i	−0.181698	−	0.152463i
$87$	−2.36635	−	11.1777i	−0.253700	−	1.19837i
$88$	−4.31279	+	2.48999i	−0.459745	+	0.265434i
$89$	−1.49181	+	8.46047i	−0.158132	+	0.896808i	0.797735	+	0.603008i	$0.206031\pi$
$89$	−1.49181	+	8.46047i	−0.158132	+	0.896808i	−0.955867	+	0.293800i	$0.905080\pi$
$90$	11.1420	+	5.45682i	1.17446	+	0.575199i
$91$	−3.48349	+	4.15146i	−0.365169	+	0.435191i
$92$	−1.25080	+	3.43656i	−0.130405	+	0.358286i
$93$	1.08660	+	2.69576i	0.112675	+	0.279537i
$94$	−7.14521	+	4.12529i	−0.736972	+	0.425491i
$95$	−13.3917	−	12.0666i	−1.37396	−	1.23801i
$96$	−1.28811	+	1.15792i	−0.131467	+	0.118179i
$97$	5.33788	+	6.36144i	0.541980	+	0.645907i	0.965630	−	0.259919i	$-0.0836959\pi$
$97$	5.33788	+	6.36144i	0.541980	+	0.645907i	−0.423650	+	0.905826i	$0.639251\pi$
$98$	1.69674	+	9.62268i	0.171396	+	0.972037i
$99$	−10.3606	−	10.7638i	−1.04128	−	1.08180i
$100$	−9.27084	+	7.77916i	−0.927084	+	0.777916i
$101$	−5.38453	+	6.41703i	−0.535780	+	0.638518i	−0.964236	−	0.265045i	$-0.914613\pi$
$101$	−5.38453	+	6.41703i	−0.535780	+	0.638518i	0.428456	+	0.903563i	$0.359058\pi$
$102$	−3.73995	−	4.16045i	−0.370310	−	0.411946i
$103$	−13.5768	−	7.83856i	−1.33776	−	0.772356i	−0.351285	−	0.936269i	$-0.614255\pi$
$103$	−13.5768	−	7.83856i	−1.33776	−	0.772356i	−0.986475	+	0.163913i	$0.947588\pi$
$104$	0.850616	−	1.01372i	0.0834097	−	0.0994038i
$105$	−24.8891	+	15.5242i	−2.42893	+	1.51501i
$106$	2.33236			0.226539
$107$	5.59234	−	9.68621i	0.540631	−	0.936401i	−0.458236	−	0.888830i	$-0.651519\pi$
$107$	5.59234	−	9.68621i	0.540631	−	0.936401i	0.998868	−	0.0475708i	$-0.0151480\pi$
$108$	−4.30068	−	2.91619i	−0.413833	−	0.280610i
$109$	−1.78819	−	2.13108i	−0.171277	−	0.204120i	0.673577	−	0.739117i	$-0.264757\pi$
$109$	−1.78819	−	2.13108i	−0.171277	−	0.204120i	−0.844854	+	0.534997i	$0.820313\pi$
$110$	19.3526	−	7.04378i	1.84520	−	0.671598i
$111$	−0.569251	−	1.41226i	−0.0540309	−	0.134046i
$112$	−0.711134	−	4.03304i	−0.0671958	−	0.381086i
$113$	−0.600734	−	1.04050i	−0.0565123	−	0.0978821i	0.836385	−	0.548142i	$-0.184665\pi$
$113$	−0.600734	−	1.04050i	−0.0565123	−	0.0978821i	−0.892898	+	0.450260i	$0.851331\pi$
$114$	4.84615	+	5.78920i	0.453883	+	0.542208i
$115$	7.56195	−	13.0977i	0.705156	−	1.22137i
$116$	−6.19864	−	2.25612i	−0.575529	−	0.209476i
$117$	3.56534	+	1.74614i	0.329616	+	0.161431i
$118$	5.41034	+	4.53981i	0.498062	+	0.417924i
$119$	13.0263	−	2.29688i	1.19412	−	0.210555i
$120$	6.07755	−	3.79078i	0.554802	−	0.346050i
$121$	−13.8002			−1.25456
$122$	2.90987	−	5.04004i	0.263447	−	0.456304i
$123$	0.339330	−	0.636933i	0.0305964	−	0.0574303i
$124$	1.65258	+	0.291395i	0.148406	+	0.0261680i
$125$	25.4361	−	14.6856i	2.27508	−	1.31352i
$126$	11.2317	−	4.97875i	1.00060	−	0.443542i
$127$	−11.7244	−	2.06732i	−1.04037	−	0.183445i	−0.372738	−	0.927937i	$-0.621581\pi$
$127$	−11.7244	−	2.06732i	−1.04037	−	0.183445i	−0.667632	+	0.744492i	$0.732692\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	−2.01626	−	3.23257i	−0.177522	−	0.284611i
$130$	−4.19224	+	3.51771i	−0.367684	+	0.308523i
$131$	−13.5707	+	2.39288i	−1.18568	+	0.209067i	−0.731498	−	0.681843i	$-0.761179\pi$
$131$	−13.5707	+	2.39288i	−1.18568	+	0.209067i	−0.454180	+	0.890910i	$0.650068\pi$
$132$	−8.43855	+	1.78647i	−0.734481	+	0.155493i
$133$	−17.6780	+	2.47802i	−1.53287	+	0.214872i
$134$		−	7.28992i		−	0.629753i
$135$	15.4210	+	14.9650i	1.32723	+	1.28798i
$136$	−3.18082	+	0.560865i	−0.272753	+	0.0480938i
$137$	5.09235	+	13.9911i	0.435069	+	1.19534i	0.942663	+	0.333745i	$0.108313\pi$
$137$	5.09235	+	13.9911i	0.435069	+	1.19534i	−0.507595	+	0.861596i	$0.669465\pi$
$138$	−3.90385	+	4.98831i	−0.332318	+	0.424633i
$139$	18.8493	−	6.86058i	1.59878	−	0.581907i	0.619600	−	0.784918i	$-0.287295\pi$
$139$	18.8493	−	6.86058i	1.59878	−	0.581907i	0.979176	+	0.203011i	$0.0650728\pi$
$140$			16.9359i			1.43134i
$141$	−13.9806	+	2.95974i	−1.17738	+	0.249255i
$142$	−1.21474	+	6.88913i	−0.101939	+	0.578123i
$143$	6.19269	−	2.25395i	0.517859	−	0.188485i
$144$	−2.74262	+	1.21574i	−0.228552	+	0.101311i
$145$	23.6248	+	13.6398i	1.96193	+	1.13272i
$146$	−2.30441	−	1.93363i	−0.190714	−	0.160028i
$147$	−2.36905	+	16.7575i	−0.195396	+	1.38213i
$148$	−0.865760	−	0.152657i	−0.0711650	−	0.0125483i
$149$	2.49554	+	2.97407i	0.204443	+	0.243646i	0.858517	−	0.512785i	$-0.171386\pi$
$149$	2.49554	+	2.97407i	0.204443	+	0.243646i	−0.654074	+	0.756430i	$0.726942\pi$
$150$	−19.4417	+	7.83651i	−1.58741	+	0.639849i
$151$	2.15650	+	1.24505i	0.175493	+	0.101321i	0.585173	−	0.810908i	$-0.301026\pi$
$151$	2.15650	+	1.24505i	0.175493	+	0.101321i	−0.409680	+	0.912229i	$0.634360\pi$
$152$	4.31670	−	0.605096i	0.350130	−	0.0490798i
$153$	−3.92669	−	8.85838i	−0.317454	−	0.716157i
$154$	6.97526	−	19.1644i	0.562082	−	1.54431i
$155$	−6.52114	−	2.37350i	−0.523791	−	0.190644i
$156$	1.94477	−	1.21302i	0.155706	−	0.0971194i
$157$	19.0890	+	6.94782i	1.52347	+	0.554496i	0.962011	−	0.273010i	$-0.0880194\pi$
$157$	19.0890	+	6.94782i	1.52347	+	0.554496i	0.561455	+	0.827507i	$0.310242\pi$
$158$	3.63432	+	9.98520i	0.289131	+	0.794380i
$159$	3.84103	+	1.25149i	0.304613	+	0.0992498i
$160$		−	4.13548i		−	0.326939i
$161$	−5.12237	−	14.0736i	−0.403699	−	1.10915i
$162$	−5.51777	−	7.11015i	−0.433517	−	0.558626i
$163$	1.22244	+	2.11733i	0.0957492	+	0.165842i	0.909921	−	0.414782i	$-0.136142\pi$
$163$	1.22244	+	2.11733i	0.0957492	+	0.165842i	−0.814172	+	0.580624i	$0.802809\pi$
$164$	−0.208332	−	0.360842i	−0.0162680	−	0.0281771i
$165$	35.6502	−	1.21581i	2.77536	−	0.0946504i
$166$	2.77228	−	7.61678i	0.215171	−	0.591177i
$167$	2.24797	−	12.7489i	0.173953	−	0.986539i	−0.765392	−	0.643565i	$-0.777455\pi$
$167$	2.24797	−	12.7489i	0.173953	−	0.986539i	0.939345	−	0.342974i	$-0.111434\pi$
$168$	0.992913	−	7.02335i	0.0766049	−	0.541864i
$169$	8.61709	−	7.23060i	0.662853	−	0.556200i
$170$	13.3572			1.02445
$171$	4.87448	+	12.1342i	0.372761	+	0.927928i
$172$	−2.19961			−0.167718
$173$	−19.3644	+	16.2486i	−1.47225	+	1.23536i	−0.558230	+	0.829686i	$0.688519\pi$
$173$	−19.3644	+	16.2486i	−1.47225	+	1.23536i	−0.914017	+	0.405675i	$0.867036\pi$
$174$	−8.99759	−	7.04152i	−0.682106	−	0.533816i
$175$	8.60630	−	48.8087i	0.650575	−	3.68959i
$176$	−1.70325	+	4.67965i	−0.128388	+	0.352742i
$177$	6.47401	+	10.3794i	0.486616	+	0.780164i
$178$	4.29549	+	7.44001i	0.321961	+	0.557653i
$179$	6.01092	+	10.4112i	0.449277	+	0.778171i	0.998339	−	0.0576109i	$-0.0183483\pi$
$179$	6.01092	+	10.4112i	0.449277	+	0.778171i	−0.549062	+	0.835782i	$0.685015\pi$
$180$	12.0428	−	2.98174i	0.897618	−	0.222246i
$181$	−2.38138	−	6.54280i	−0.177007	−	0.486322i	0.819183	−	0.573532i	$-0.194427\pi$
$181$	−2.38138	−	6.54280i	−0.177007	−	0.486322i	−0.996190	+	0.0872098i	$0.972205\pi$
$182$			5.41935i			0.401709i
$183$	7.49646	−	6.73878i	0.554154	−	0.498145i
$184$	1.25080	+	3.43656i	0.0922105	+	0.253346i
$185$	3.41632	+	1.24344i	0.251173	+	0.0914194i
$186$	2.56518	+	1.36662i	0.188088	+	0.100205i
$187$	−15.1148	−	5.50132i	−1.10530	−	0.402297i
$188$	−2.82186	+	7.75301i	−0.205806	+	0.565446i
$189$	21.1684	−	2.17250i	1.53977	−	0.158026i
$190$	−18.0149	−	0.635553i	−1.30694	−	0.0461078i
$191$	−18.8151	−	10.8629i	−1.36141	−	0.786011i	−0.371599	−	0.928393i	$-0.621190\pi$
$191$	−18.8151	−	10.8629i	−1.36141	−	0.786011i	−0.989812	+	0.142382i	$0.954524\pi$
$192$	−0.242454	+	1.71500i	−0.0174976	+	0.123769i
$193$	−4.41877	−	5.26609i	−0.318070	−	0.379061i	0.583193	−	0.812334i	$-0.301803\pi$
$193$	−4.41877	−	5.26609i	−0.318070	−	0.379061i	−0.901263	+	0.433273i	$0.857359\pi$
$194$	8.17811	+	1.44202i	0.587154	+	0.103531i
$195$	−8.79147	+	3.54364i	−0.629570	+	0.253765i
$196$	7.48512	+	6.28076i	0.534651	+	0.448626i
$197$	−10.2773	−	5.93357i	−0.732224	−	0.422750i	0.0870114	−	0.996207i	$-0.472268\pi$
$197$	−10.2773	−	5.93357i	−0.732224	−	0.422750i	−0.819235	+	0.573458i	$0.805602\pi$
$198$	−14.8555	−	1.58590i	−1.05574	−	0.112705i
$199$	5.62586	−	2.04765i	0.398807	−	0.145154i	−0.134828	−	0.990869i	$-0.543048\pi$
$199$	5.62586	−	2.04765i	0.398807	−	0.145154i	0.533634	+	0.845715i	$0.320826\pi$
$200$	−2.10153	+	11.9184i	−0.148600	+	0.842755i
$201$	3.91160	−	12.0053i	0.275903	−	0.846791i
$202$			8.37683i			0.589392i
$203$	25.3850	−	9.23939i	1.78168	−	0.648478i
$204$	−5.53925	−	0.783102i	−0.387825	−	0.0548281i
$205$	0.589339	+	1.61919i	0.0411612	+	0.113089i
$206$	−15.4389	+	2.72230i	−1.07568	+	0.189672i
$207$	−9.10564	+	6.12023i	−0.632886	+	0.425386i
$208$		−	1.32332i		−	0.0917559i
$209$	20.1237	+	8.13888i	1.39198	+	0.562978i
$210$	−9.08740	+	27.8907i	−0.627090	+	1.92464i
$211$	10.7424	−	1.89417i	0.739534	−	0.130400i	0.208824	−	0.977953i	$-0.433036\pi$
$211$	10.7424	−	1.89417i	0.739534	−	0.130400i	0.530710	+	0.847553i	$0.321925\pi$
$212$	1.78669	−	1.49921i	0.122711	−	0.102966i
$213$	−5.69703	+	10.6935i	−0.390354	+	0.732707i
$214$	−1.94220	−	11.0148i	−0.132766	−	0.752953i
$215$	8.95824	+	1.57958i	0.610947	+	0.107726i
$216$	−5.16900	+	0.530493i	−0.351706	+	0.0360955i
$217$	−5.95146	+	3.43608i	−0.404011	+	0.233256i
$218$	−2.73966	−	0.483076i	−0.185553	−	0.0327181i
$219$	−2.75745	−	4.42087i	−0.186331	−	0.298734i
$220$	10.2973	−	17.8355i	0.694245	−	1.20247i
$221$	4.27419			0.287513
$222$	−1.34386	−	0.715949i	−0.0901938	−	0.0480513i
$223$	−20.6486	+	3.64091i	−1.38273	+	0.243813i	−0.815029	−	0.579420i	$-0.803279\pi$
$223$	−20.6486	+	3.64091i	−1.38273	+	0.243813i	−0.567704	+	0.823233i	$0.692168\pi$
$224$	−3.13715	−	2.63238i	−0.209610	−	0.175883i
$225$	−36.2223	+	2.47351i	−2.41482	+	0.164901i
$226$	−1.12901	−	0.410926i	−0.0751006	−	0.0273344i
$227$	−10.2109	+	17.6858i	−0.677721	+	1.17385i	0.297945	+	0.954583i	$0.403699\pi$
$227$	−10.2109	+	17.6858i	−0.677721	+	1.17385i	−0.975666	+	0.219264i	$0.929634\pi$
$228$	7.43359	+	1.31974i	0.492302	+	0.0874021i
$229$	7.06699	+	12.2404i	0.467000	+	0.808867i	0.999289	−	0.0376952i	$-0.0120016\pi$
$229$	7.06699	+	12.2404i	0.467000	+	0.808867i	−0.532290	+	0.846562i	$0.678668\pi$
$230$	−2.62624	−	14.8941i	−0.173169	−	0.982091i
$231$	21.7703	−	27.8179i	1.43238	−	1.83028i
$232$	−6.19864	+	2.25612i	−0.406961	+	0.148122i
$233$	5.36301	+	6.39138i	0.351342	+	0.418713i	0.912552	−	0.408960i	$-0.134108\pi$
$233$	5.36301	+	6.39138i	0.351342	+	0.418713i	−0.561210	+	0.827673i	$0.689664\pi$
$234$	3.85361	−	0.954134i	0.251918	−	0.0623737i
$235$	17.0601	−	29.5489i	1.11288	−	1.92756i
$236$	7.06269			0.459742
$237$	0.627309	+	18.3941i	0.0407481	+	1.19483i
$238$	8.50230	−	10.1326i	0.551122	−	0.656802i
$239$	22.9373	+	13.2428i	1.48369	+	0.856608i	0.999828	−	0.0185366i	$-0.00590072\pi$
$239$	22.9373	+	13.2428i	1.48369	+	0.856608i	0.483861	+	0.875145i	$0.339234\pi$
$240$	2.21901	−	6.81048i	0.143236	−	0.439615i
$241$	−6.22554	+	7.41932i	−0.401023	+	0.477920i	−0.928331	−	0.371754i	$-0.878757\pi$
$241$	−6.22554	+	7.41932i	−0.401023	+	0.477920i	0.527309	+	0.849674i	$0.323201\pi$
$242$	−10.5716	+	8.87060i	−0.679566	+	0.570224i
$243$	−5.27175	−	14.6700i	−0.338183	−	0.941080i
$244$	−1.01059	−	5.73132i	−0.0646962	−	0.366910i
$245$	−25.9740	−	30.9546i	−1.65942	−	1.97761i
$246$	−0.149471	−	0.706037i	−0.00952990	−	0.0450152i
$247$	−5.76464	−	0.203372i	−0.366796	−	0.0129402i
$248$	1.45326	−	0.839038i	0.0922819	−	0.0532790i
$249$	8.65249	−	11.0561i	0.548330	−	0.700651i
$250$	10.0455	−	27.5998i	0.635334	−	1.74557i
$251$	−6.05647	+	7.21782i	−0.382281	+	0.455585i	−0.922533	−	0.385919i	$-0.873885\pi$
$251$	−6.05647	+	7.21782i	−0.382281	+	0.455585i	0.540252	+	0.841503i	$0.318329\pi$
$252$	5.40374	−	11.0336i	0.340404	−	0.695050i
$253$	−3.16254	+	17.9356i	−0.198827	+	1.12760i
$254$	−10.3102	+	5.95262i	−0.646922	+	0.373500i
$255$	21.9971	+	7.16715i	1.37751	+	0.448824i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	17.5306	+	14.7099i	1.09353	+	0.917577i	0.996973	−	0.0777505i	$-0.0247737\pi$
$257$	17.5306	+	14.7099i	1.09353	+	0.917577i	0.0965533	+	0.995328i	$0.469218\pi$
$258$	−3.62240	−	1.18026i	−0.225521	−	0.0734797i
$259$	3.11787	−	1.80010i	0.193735	−	0.111853i
$260$	−0.950303	+	5.38944i	−0.0589353	+	0.334239i
$261$	−11.0393	−	16.4242i	−0.683315	−	1.01663i
$262$	−8.85765	+	10.5561i	−0.547227	+	0.652160i
$263$	−0.563920	+	1.54936i	−0.0347728	+	0.0955375i	−0.955864	−	0.293809i	$-0.905077\pi$
$263$	−0.563920	+	1.54936i	−0.0347728	+	0.0955375i	0.921091	+	0.389347i	$0.127299\pi$
$264$	−5.31598	+	6.79271i	−0.327176	+	0.418063i
$265$	−8.35320	+	4.82272i	−0.513133	+	0.296257i
$266$	−11.9493	+	13.2615i	−0.732657	+	0.813112i
$267$	3.08185	+	14.5574i	0.188606	+	0.890898i
$268$	−4.68587	−	5.58440i	−0.286235	−	0.341121i
$269$	1.92584	+	10.9220i	0.117421	+	0.665926i	0.985523	+	0.169541i	$0.0542286\pi$
$269$	1.92584	+	10.9220i	0.117421	+	0.665926i	−0.868102	+	0.496385i	$0.834660\pi$
$270$	21.4325	+	1.55144i	1.30434	+	0.0944178i
$271$	−8.25637	+	6.92792i	−0.501539	+	0.420841i	−0.858140	−	0.513416i	$-0.828380\pi$
$271$	−8.25637	+	6.92792i	−0.501539	+	0.420841i	0.356601	+	0.934257i	$0.383935\pi$
$272$	−2.07613	+	2.47424i	−0.125884	+	0.150023i
$273$	−2.90790	+	8.92480i	−0.175994	+	0.540154i
$274$	12.8943	+	7.44452i	0.778972	+	0.449740i
$275$	−38.7400	+	46.1686i	−2.33611	+	2.78407i
$276$	0.215898	+	6.33062i	0.0129955	+	0.381058i
$277$	22.3386			1.34220			0.671099	−	0.741368i	$-0.265822\pi$
$277$	22.3386			1.34220			0.671099	+	0.741368i	$0.265822\pi$
$278$	10.0295	−	17.3716i	0.601529	−	1.04188i
$279$	3.49115	+	3.62702i	0.209010	+	0.217144i
$280$	10.8862	+	12.9736i	0.650573	+	0.775322i
$281$	16.1181	−	5.86652i	0.961527	−	0.349967i	0.186895	−	0.982380i	$-0.440157\pi$
$281$	16.1181	−	5.86652i	0.961527	−	0.349967i	0.774632	+	0.632413i	$0.217935\pi$
$282$	−8.80725	+	11.2538i	−0.524464	+	0.670155i
$283$	1.24019	+	7.03344i	0.0737214	+	0.418095i	0.999225	+	0.0393564i	$0.0125308\pi$
$283$	1.24019	+	7.03344i	0.0737214	+	0.418095i	−0.925504	+	0.378738i	$0.876358\pi$
$284$	3.49770	+	6.05820i	0.207551	+	0.359488i
$285$	−29.3267	−	10.7131i	−1.73717	−	0.634587i
$286$	3.29506	−	5.70721i	0.194841	−	0.337475i
$287$	1.60344	+	0.583606i	0.0946483	+	0.0344492i
$288$	−1.31951	+	2.69423i	−0.0777530	+	0.158759i
$289$	5.03123	+	4.22170i	0.295955	+	0.248335i
$290$	26.8651	−	4.73704i	1.57757	−	0.278169i
$291$	12.6943	+	6.76297i	0.744153	+	0.396452i
$292$	−3.00819			−0.176041
$293$	9.17820	−	15.8971i	0.536196	−	0.928719i	−0.462908	−	0.886406i	$-0.653194\pi$
$293$	9.17820	−	15.8971i	0.536196	−	0.928719i	0.999104	−	0.0423130i	$-0.0134727\pi$
$294$	8.95668	+	14.3598i	0.522364	+	0.837478i
$295$	−28.7639	−	5.07186i	−1.67470	−	0.295295i
$296$	−0.761337	+	0.439558i	−0.0442518	+	0.0255488i
$297$	−23.6137	−	10.5829i	−1.37021	−	0.614080i
$298$	3.82340	+	0.674168i	0.221483	+	0.0390535i
$299$	−0.840376	−	4.76601i	−0.0486002	−	0.275626i
$300$	−9.85600	+	18.5000i	−0.569037	+	1.06810i
$301$	6.90049	−	5.79020i	0.397738	−	0.333742i
$302$	2.45228	−	0.432403i	0.141113	−	0.0248820i
$303$	−4.49482	+	13.7953i	−0.258221	+	0.792520i
$304$	2.91783	−	3.23825i	0.167349	−	0.185726i
$305$			24.0674i			1.37810i
$306$	−8.70208	−	4.26188i	−0.497465	−	0.243636i
$307$	−22.1625	+	3.90785i	−1.26488	+	0.223033i	−0.765549	−	0.643378i	$-0.777532\pi$
$307$	−22.1625	+	3.90785i	−1.26488	+	0.223033i	−0.499332	+	0.866411i	$0.666421\pi$
$308$	−6.97526	−	19.1644i	−0.397452	−	1.09199i
$309$	−26.8862	−	3.80099i	−1.52950	−	0.216231i
$310$	−6.52114	+	2.37350i	−0.370376	+	0.134806i
$311$		−	16.3173i		−	0.925272i	−0.886548	−	0.462636i	$-0.846904\pi$
$311$		−	16.3173i		−	0.925272i	0.886548	−	0.462636i	$-0.153096\pi$
$312$	0.710065	−	2.17930i	0.0401995	−	0.123379i
$313$	0.946559	−	5.36821i	0.0535027	−	0.303429i	−0.946300	−	0.323290i	$-0.895211\pi$
$313$	0.946559	−	5.36821i	0.0535027	−	0.303429i	0.999803	+	0.0198608i	$0.00632229\pi$
$314$	19.0890	−	6.94782i	1.07725	−	0.392088i
$315$	−29.9310	+	41.0554i	−1.68642	+	2.31321i
$316$	9.20241	+	5.31301i	0.517676	+	0.298880i
$317$	−5.69439	−	4.77816i	−0.319829	−	0.268368i	0.468711	−	0.883351i	$-0.344718\pi$
$317$	−5.69439	−	4.77816i	−0.319829	−	0.268368i	−0.788540	+	0.614983i	$0.789163\pi$
$318$	3.74684	−	1.51027i	0.210112	−	0.0846916i
$319$	−32.3512	−	5.70438i	−1.81132	−	0.319384i
$320$	−2.65824	−	3.16796i	−0.148600	−	0.177095i
$321$	2.71177	−	19.1817i	0.151356	−	1.07062i
$322$	−12.9703	−	7.48840i	−0.722806	−	0.417312i
$323$	10.4592	+	9.42428i	0.581965	+	0.524381i
$324$	−8.79717	−	1.89993i	−0.488732	−	0.105552i
$325$	5.47750	−	15.0493i	0.303837	−	0.834786i
$326$	2.29744	+	0.836201i	0.127244	+	0.0463129i
$327$	−4.25258	−	2.26559i	−0.235168	−	0.125287i
$328$	−0.391537	−	0.142508i	−0.0216190	−	0.00786868i
$329$	−11.5563	−	31.7505i	−0.637117	−	1.75046i
$330$	26.5281	−	23.8469i	1.46033	−	1.31273i
$331$			10.3588i			0.569372i	0.958621	+	0.284686i	$0.0918893\pi$
$331$			10.3588i			0.569372i	−0.958621	+	0.284686i	$0.908111\pi$
$332$	−2.77228	−	7.61678i	−0.152149	−	0.418025i
$333$	−1.82896	−	1.90014i	−0.100226	−	0.104127i
$334$	−6.47278	−	11.2112i	−0.354175	−	0.613449i
$335$	15.0737	+	26.1083i	0.823562	+	1.42645i
$336$	−3.75391	−	6.01843i	−0.204793	−	0.328332i
$337$	−10.1284	+	27.8276i	−0.551730	+	1.51587i	0.279617	+	0.960112i	$0.409792\pi$
$337$	−10.1284	+	27.8276i	−0.551730	+	1.51587i	−0.831347	+	0.555754i	$0.812430\pi$
$338$	1.95334	−	11.0779i	0.106248	−	0.602560i
$339$	−1.63881	−	1.28253i	−0.0890078	−	0.0696575i
$340$	10.2322	−	8.58582i	0.554918	−	0.465631i
$341$	8.35678			0.452545
$342$	11.5338	+	6.16210i	0.623676	+	0.333208i
$343$	−11.3485			−0.612760
$344$	−1.68500	+	1.41388i	−0.0908489	+	0.0762313i
$345$	3.66686	−	25.9375i	0.197417	−	1.39643i
$346$	−4.38955	+	24.8944i	−0.235984	+	1.33833i
$347$	−2.96189	+	8.13771i	−0.159002	+	0.436855i	−0.993455	−	0.114224i	$-0.963562\pi$
$347$	−2.96189	+	8.13771i	−0.159002	+	0.436855i	0.834453	+	0.551080i	$0.185784\pi$
$348$	−11.4188	+	0.389423i	−0.612110	+	0.0208752i
$349$	−3.44347	−	5.96427i	−0.184325	−	0.319260i	0.759024	−	0.651063i	$-0.225676\pi$
$349$	−3.44347	−	5.96427i	−0.184325	−	0.319260i	−0.943349	+	0.331803i	$0.892343\pi$
$350$	−24.7808	−	42.9217i	−1.32459	−	2.29426i
$351$	6.85824	+	0.496450i	0.366066	+	0.0264985i
$352$	1.70325	+	4.67965i	0.0907837	+	0.249426i
$353$		−	16.2884i		−	0.866943i	−0.901167	−	0.433472i	$-0.857288\pi$
$353$		−	16.2884i		−	0.866943i	0.901167	−	0.433472i	$-0.142712\pi$
$354$	11.6311	+	3.78968i	0.618188	+	0.201419i
$355$	−9.89443	−	27.1847i	−0.525142	−	1.44282i
$356$	8.07289	+	2.93829i	0.427862	+	0.155729i
$357$	19.4389	−	12.1247i	1.02881	−	0.641708i
$358$	11.2968	+	4.11171i	0.597056	+	0.217311i
$359$	−4.65951	+	12.8019i	−0.245919	+	0.675658i	0.753906	+	0.656982i	$0.228167\pi$
$359$	−4.65951	+	12.8019i	−0.245919	+	0.675658i	−0.999826	+	0.0186760i	$0.994055\pi$
$360$	7.30870	−	10.0251i	0.385202	−	0.528370i
$361$	−13.6580	−	13.2083i	−0.718842	−	0.695173i
$362$	−6.02987	−	3.48135i	−0.316923	−	0.182976i
$363$	−22.1694	+	8.93600i	−1.16359	+	0.469018i
$364$	3.48349	+	4.15146i	0.182584	+	0.217596i
$365$	12.2513	+	2.16024i	0.641263	+	0.113072i
$366$	1.41102	−	9.98083i	0.0737553	−	0.521707i
$367$	−16.8114	−	14.1065i	−0.877549	−	0.736351i	0.0881246	−	0.996109i	$-0.471913\pi$
$367$	−16.8114	−	14.1065i	−0.877549	−	0.736351i	−0.965674	+	0.259758i	$0.916357\pi$
$368$	3.16715	+	1.82855i	0.165099	+	0.0953200i
$369$	0.132689	−	1.24293i	0.00690750	−	0.0647045i
$370$	3.41632	−	1.24344i	0.177606	−	0.0646433i
$371$	−1.65862	+	9.40651i	−0.0861113	+	0.488362i
$372$	2.84349	−	0.601978i	0.147428	−	0.0312111i
$373$		−	35.2139i		−	1.82331i	−0.410960	−	0.911653i	$-0.634806\pi$
$373$		−	35.2139i		−	1.82331i	0.410960	−	0.911653i	$-0.365194\pi$
$374$	−15.1148	+	5.50132i	−0.781566	+	0.284467i
$375$	31.3528	−	40.0623i	1.61905	−	2.06881i
$376$	2.82186	+	7.75301i	0.145526	+	0.399831i
$377$	8.59662	−	1.51582i	0.442749	−	0.0780685i
$378$	14.8195	−	15.2710i	0.762231	−	0.785456i
$379$		−	13.9968i		−	0.718969i	−0.933151	−	0.359484i	$-0.882953\pi$
$379$		−	13.9968i		−	0.718969i	0.933151	−	0.359484i	$-0.117047\pi$
$380$	−14.2088	+	11.0929i	−0.728895	+	0.569055i
$381$	−20.1734	+	4.27078i	−1.03351	+	0.218799i
$382$	−21.3957	+	3.77264i	−1.09470	+	0.193025i
$383$	4.80578	−	4.03252i	0.245564	−	0.206052i	−0.511696	−	0.859167i	$-0.670982\pi$
$383$	4.80578	−	4.03252i	0.245564	−	0.206052i	0.757259	+	0.653114i	$0.226538\pi$
$384$	0.916648	+	1.46961i	0.0467775	+	0.0749958i
$385$	14.6455	+	83.0589i	0.746405	+	4.23308i
$386$	−6.76995	−	1.19372i	−0.344581	−	0.0607590i
$387$	−5.33222	−	3.88740i	−0.271052	−	0.197607i
$388$	7.19171	−	4.15214i	0.365104	−	0.210793i
$389$	37.0450	+	6.53202i	1.87825	+	0.331187i	0.991400	−	0.130864i	$-0.0417752\pi$
$389$	37.0450	+	6.53202i	1.87825	+	0.331187i	0.886853	+	0.462051i	$0.152886\pi$
$390$	−4.45685	+	8.36564i	−0.225681	+	0.423610i
$391$	−5.90603	+	10.2295i	−0.298681	+	0.517330i
$392$	9.77113			0.493516
$393$	−20.2513	+	12.6315i	−1.02154	+	0.637173i
$394$	−11.6869	+	2.06071i	−0.588775	+	0.103817i
$395$	−33.6629	−	28.2465i	−1.69376	−	1.42124i
$396$	−12.3994	+	8.33408i	−0.623093	+	0.418803i
$397$	7.45506	+	2.71342i	0.374159	+	0.136183i	0.522253	−	0.852791i	$-0.325092\pi$
$397$	7.45506	+	2.71342i	0.374159	+	0.136183i	−0.148094	+	0.988973i	$0.547314\pi$
$398$	2.99346	−	5.18482i	0.150048	−	0.259892i
$399$	−26.7943	+	15.4278i	−1.34140	+	0.772356i
$400$	6.05111	+	10.4808i	0.302555	+	0.524041i
$401$	−0.824491	−	4.67592i	−0.0411731	−	0.233504i	0.957276	−	0.289176i	$-0.0933812\pi$
$401$	−0.824491	−	4.67592i	−0.0411731	−	0.233504i	−0.998449	+	0.0556713i	$0.982270\pi$
$402$	−4.72042	−	11.7109i	−0.235433	−	0.584089i
$403$	−2.08672	+	0.759502i	−0.103947	+	0.0378335i
$404$	5.38453	+	6.41703i	0.267890	+	0.319259i
$405$	34.4635	+	14.0552i	1.71250	+	0.698408i
$406$	13.5071	−	23.3950i	0.670346	−	1.16107i
$407$	−4.37798			−0.217008
$408$	−4.74668	+	2.96067i	−0.234996	+	0.146575i
$409$	0.410989	−	0.489797i	0.0203221	−	0.0242189i	−0.755788	−	0.654817i	$-0.772746\pi$
$409$	0.410989	−	0.489797i	0.0203221	−	0.0242189i	0.776110	+	0.630598i	$0.217190\pi$
$410$	1.49226	+	0.861555i	0.0736974	+	0.0425492i
$411$	17.2403	+	19.1787i	0.850400	+	0.946016i
$412$	−10.0771	+	12.0094i	−0.496461	+	0.591659i
$413$	−22.1567	+	18.5917i	−1.09026	+	0.914837i
$414$	−3.04131	+	10.5414i	−0.149472	+	0.518080i
$415$	5.82079	+	33.0113i	0.285731	+	1.62046i
$416$	−0.850616	−	1.01372i	−0.0417049	−	0.0497019i
$417$	25.8382	−	23.2267i	1.26530	−	1.13741i
$418$	20.6472	−	6.70051i	1.00989	−	0.327733i
$419$	−13.9358	+	8.04582i	−0.680807	+	0.393064i	−0.800159	−	0.599788i	$-0.795252\pi$
$419$	−13.9358	+	8.04582i	−0.680807	+	0.393064i	0.119352	+	0.992852i	$0.461918\pi$
$420$	10.9664	+	27.2068i	0.535107	+	1.32755i
$421$	6.51581	−	17.9020i	0.317561	−	0.872492i	−0.673513	−	0.739176i	$-0.735215\pi$
$421$	6.51581	−	17.9020i	0.317561	−	0.872492i	0.991074	−	0.133316i	$-0.0425625\pi$
$422$	7.01157	−	8.35607i	0.341318	−	0.406767i
$423$	−20.5427	+	13.8075i	−0.998819	+	0.671343i
$424$	0.405010	−	2.29693i	0.0196690	−	0.111549i
$425$	−33.8519	+	19.5444i	−1.64206	+	0.948044i
$426$	2.50947	+	11.8537i	0.121584	+	0.574313i
$427$	18.2574	+	15.3198i	0.883537	+	0.741375i
$428$	−8.56795	−	7.18937i	−0.414148	−	0.347511i
$429$	8.48880	−	7.63082i	0.409843	−	0.368419i
$430$	7.87774	−	4.54822i	0.379898	−	0.219334i
$431$	−6.52811	+	37.0227i	−0.314448	+	1.78332i	0.260851	+	0.965379i	$0.415997\pi$
$431$	−6.52811	+	37.0227i	−0.314448	+	1.78332i	−0.575299	+	0.817943i	$0.695114\pi$
$432$	−3.61869	+	3.72895i	−0.174104	+	0.179409i
$433$	−6.41000	+	7.63914i	−0.308045	+	0.367114i	−0.897750	−	0.440505i	$-0.854799\pi$
$433$	−6.41000	+	7.63914i	−0.308045	+	0.367114i	0.589705	+	0.807619i	$0.299244\pi$
$434$	−2.35041	+	6.45771i	−0.112823	+	0.309980i
$435$	46.7843	+	6.61405i	2.24314	+	0.317119i
$436$	−2.40922	+	1.39096i	−0.115381	+	0.0666150i
$437$	8.45226	−	13.5157i	0.404327	−	0.646543i
$438$	−4.95401	−	1.61412i	−0.236712	−	0.0771259i
$439$	19.0716	+	22.7287i	0.910239	+	1.08478i	0.996079	+	0.0884714i	$0.0281982\pi$
$439$	19.0716	+	22.7287i	0.910239	+	1.08478i	−0.0858400	+	0.996309i	$0.527357\pi$
$440$	−3.57622	−	20.2817i	−0.170490	−	0.966894i
$441$	7.04512	+	28.4542i	0.335482	+	1.35496i
$442$	3.27422	−	2.74740i	0.155739	−	0.130680i
$443$	8.58984	−	10.2370i	0.408115	−	0.486373i	−0.522361	−	0.852724i	$-0.674949\pi$
$443$	8.58984	−	10.2370i	0.408115	−	0.486373i	0.930477	+	0.366351i	$0.119393\pi$
$444$	−1.48966	+	0.315366i	−0.0706960	+	0.0149666i
$445$	−30.7681	−	17.7639i	−1.45855	−	0.842092i
$446$	−13.4774	+	16.0618i	−0.638175	+	0.760547i
$447$	5.93478	+	3.16179i	0.280705	+	0.149548i
$448$	−4.09526			−0.193483
$449$	0.117777	−	0.203995i	0.00555822	−	0.00962712i	−0.863233	−	0.504806i	$-0.831564\pi$
$449$	0.117777	−	0.203995i	0.00555822	−	0.00962712i	0.868791	+	0.495179i	$0.164897\pi$
$450$	−26.1580	+	25.1781i	−1.23310	+	1.18691i
$451$	−1.33377	−	1.58953i	−0.0628049	−	0.0748480i
$452$	−1.12901	+	0.410926i	−0.0531042	+	0.0193283i
$453$	4.27053	+	0.603738i	0.200647	+	0.0283661i
$454$	3.54621	+	20.1115i	0.166432	+	0.943881i
$455$	−11.2058	−	19.4090i	−0.525336	−	0.909909i
$456$	6.54278	−	3.76724i	0.306394	−	0.176417i
$457$	3.41599	−	5.91667i	0.159793	−	0.276770i	−0.775001	−	0.631960i	$-0.782251\pi$
$457$	3.41599	−	5.91667i	0.159793	−	0.276770i	0.934794	+	0.355190i	$0.115584\pi$
$458$	13.2816	+	4.83410i	0.620608	+	0.225883i
$459$	−12.0441	−	11.6880i	−0.562171	−	0.545548i
$460$	−11.5856	−	9.72146i	−0.540181	−	0.453265i
$461$	−21.4989	+	3.79084i	−1.00130	+	0.176557i	−0.650187	−	0.759774i	$-0.725309\pi$
$461$	−21.4989	+	3.79084i	−1.00130	+	0.176557i	−0.351117	+	0.936331i	$0.614198\pi$
$462$	−1.20398	−	35.3034i	−0.0560142	−	1.64246i
$463$	15.5364			0.722039			0.361019	−	0.932558i	$-0.382429\pi$
$463$	15.5364			0.722039			0.361019	+	0.932558i	$0.382429\pi$
$464$	−3.29823	+	5.71270i	−0.153116	+	0.265205i
$465$	−12.0129	+	0.409683i	−0.557083	+	0.0189986i
$466$	8.21660	+	1.44881i	0.380627	+	0.0671148i
$467$	21.2660	−	12.2779i	0.984072	−	0.568154i	0.0805749	−	0.996749i	$-0.474324\pi$
$467$	21.2660	−	12.2779i	0.984072	−	0.568154i	0.903497	+	0.428594i	$0.140991\pi$
$468$	2.33873	−	3.20796i	0.108108	−	0.148288i
$469$	29.4005	+	5.18411i	1.35759	+	0.239380i
$470$	−5.92490	−	33.6018i	−0.273295	−	1.54993i
$471$	35.1646	−	1.19924i	1.62030	−	0.0552582i
$472$	5.41034	−	4.53981i	0.249031	−	0.208962i
$473$	−10.7876	+	1.90214i	−0.496013	+	0.0874605i
$474$	12.3041	+	13.6875i	0.565144	+	0.628687i
$475$	46.5864	−	24.7491i	2.13753	−	1.13556i
$476$		−	13.2272i		−	0.606269i
$477$	6.98083	−	0.476699i	0.319630	−	0.0218266i
$478$	26.0833	−	4.59919i	1.19302	−	0.210362i
$479$	−0.375462	−	1.03157i	−0.0171553	−	0.0471338i	0.930819	−	0.365479i	$-0.119095\pi$
$479$	−0.375462	−	1.03157i	−0.0171553	−	0.0471338i	−0.947975	+	0.318346i	$0.896873\pi$
$480$	−2.67784	−	6.64348i	−0.122226	−	0.303232i
$481$	1.09320	−	0.397891i	0.0498454	−	0.0181422i
$482$			9.68523i			0.441150i
$483$	−17.3419	−	19.2918i	−0.789083	−	0.877805i
$484$	−2.39638	+	13.5905i	−0.108926	+	0.617752i
$485$	−32.2711	+	11.7457i	−1.46535	+	0.533346i
$486$	−13.4681	−	7.84925i	−0.610925	−	0.356049i
$487$	−15.3483	−	8.86135i	−0.695498	−	0.401546i	0.110170	−	0.993913i	$-0.464860\pi$
$487$	−15.3483	−	8.86135i	−0.695498	−	0.401546i	−0.805668	+	0.592367i	$0.798194\pi$
$488$	−4.45818	−	3.74086i	−0.201812	−	0.169341i
$489$	3.33484	+	2.60985i	0.150807	+	0.118021i
$490$	−39.7944	−	7.01683i	−1.79773	−	0.316988i
$491$	−3.06400	−	3.65153i	−0.138276	−	0.164791i	0.692462	−	0.721454i	$-0.256526\pi$
$491$	−3.06400	−	3.65153i	−0.138276	−	0.164791i	−0.830738	+	0.556663i	$0.812081\pi$
$492$	−0.568333	−	0.444777i	−0.0256224	−	0.0200521i
$493$	−18.4514	−	10.6529i	−0.831009	−	0.479783i
$494$	−4.54670	+	3.54965i	−0.204566	+	0.159706i
$495$	56.4833	−	25.0376i	2.53874	−	1.12536i
$496$	0.573936	−	1.57688i	0.0257705	−	0.0708038i
$497$	−26.9203	−	9.79819i	−1.20754	−	0.439509i
$498$	−0.478515	−	14.0312i	−0.0214428	−	0.628752i
$499$	29.0554	+	10.5753i	1.30070	+	0.473415i	0.897224	−	0.441576i	$-0.145580\pi$
$499$	29.0554	+	10.5753i	1.30070	+	0.473415i	0.403474	+	0.914991i	$0.367803\pi$
$500$	−10.0455	−	27.5998i	−0.449249	−	1.23430i
$501$	−4.64397	−	21.9362i	−0.207477	−	0.980036i
$502$			9.42219i			0.420533i
$503$	−7.38162	−	20.2808i	−0.329130	−	0.904278i	−0.988332	−	0.152312i	$-0.951328\pi$
$503$	−7.38162	−	20.2808i	−0.329130	−	0.904278i	0.659202	−	0.751966i	$-0.270894\pi$
$504$	−2.95274	−	11.9257i	−0.131525	−	0.531211i
$505$	−17.3211	−	30.0011i	−0.770780	−	1.33503i
$506$	9.10616	+	15.7723i	0.404818	+	0.701166i
$507$	9.16099	−	17.1955i	0.406854	−	0.763677i
$508$	−4.07183	+	11.1873i	−0.180658	+	0.496355i
$509$	4.08212	−	23.1508i	0.180937	−	1.02614i	−0.750129	−	0.661291i	$-0.770009\pi$
$509$	4.08212	−	23.1508i	0.180937	−	1.02614i	0.931066	−	0.364851i	$-0.118880\pi$
$510$	21.4577	−	8.64912i	0.950164	−	0.382989i
$511$	9.43713	−	7.91869i	0.417474	−	0.350302i
$512$	1.00000			0.0441942
$513$	15.6879	+	16.3368i	0.692637	+	0.721286i
$514$	22.8845			1.00939
$515$	49.6645	−	41.6735i	2.18848	−	1.83635i
$516$	−3.53358	+	1.42430i	−0.155557	+	0.0627015i
$517$	−7.13480	+	40.4635i	−0.313788	+	1.77958i
$518$	1.23134	−	3.38309i	0.0541021	−	0.148644i
$519$	−20.5866	+	38.6417i	−0.903653	+	1.69618i
$520$	2.73629	+	4.73939i	0.119994	+	0.207836i
$521$	11.1314	+	19.2802i	0.487677	+	0.844682i	0.999900	−	0.0141712i	$-0.00451099\pi$
$521$	11.1314	+	19.2802i	0.487677	+	0.844682i	−0.512222	+	0.858853i	$0.671178\pi$
$522$	−19.0138	−	5.48573i	−0.832213	−	0.240104i
$523$	−5.41103	−	14.8667i	−0.236608	−	0.650075i	−0.999991	−	0.00412951i	$-0.998686\pi$
$523$	−5.41103	−	14.8667i	−0.236608	−	0.650075i	0.763384	−	0.645946i	$-0.223537\pi$
$524$			13.7801i			0.601985i
$525$	−17.7793	−	83.9820i	−0.775953	−	3.66528i
$526$	0.563920	+	1.54936i	0.0245881	+	0.0675552i
$527$	5.09314	+	1.85375i	0.221861	+	0.0807506i
$528$	0.293994	+	8.62057i	0.0127944	+	0.375162i
$529$	−9.04507	−	3.29214i	−0.393264	−	0.143136i
$530$	−3.29894	+	9.06375i	−0.143297	+	0.393704i
$531$	17.1212	+	12.4820i	0.742995	+	0.541673i
$532$	−0.629371	+	17.8397i	−0.0272867	+	0.773450i
$533$	0.477511	+	0.275691i	0.0206833	+	0.0119415i
$534$	11.7181	+	9.17063i	0.507094	+	0.396852i
$535$	29.7315	+	35.4326i	1.28541	+	1.53189i
$536$	−7.17916	−	1.26588i	−0.310093	−	0.0546777i
$537$	16.3978	+	12.8330i	0.707619	+	0.553783i
$538$	8.49581	+	7.12883i	0.366280	+	0.307346i
$539$	42.1408	+	24.3300i	1.81513	+	1.04797i
$540$	17.4155	−	12.5881i	0.749444	−	0.541705i
$541$	−7.38088	+	2.68642i	−0.317329	+	0.115498i	−0.495774	−	0.868452i	$-0.665116\pi$
$541$	−7.38088	+	2.68642i	−0.317329	+	0.115498i	0.178445	+	0.983950i	$0.442893\pi$
$542$	−1.87157	+	10.6142i	−0.0803907	+	0.455918i
$543$	−8.06223	−	8.96872i	−0.345983	−	0.384885i
$544$			3.22989i			0.138480i
$545$	10.8108	−	3.93481i	0.463083	−	0.168549i
$546$	3.50917	+	8.70595i	0.150179	+	0.372580i
$547$	15.0284	+	41.2903i	0.642570	+	1.76545i	0.643499	+	0.765447i	$0.277482\pi$
$547$	15.0284	+	41.2903i	0.642570	+	1.76545i	−0.000929226		1.00000i	$0.500296\pi$
$548$	14.6628	−	2.58545i	0.626365	−	0.110445i
$549$	7.67922	−	15.6797i	0.327741	−	0.669194i
$550$			60.2688i			2.56987i
$551$	24.3787	+	15.2456i	1.03857	+	0.649486i
$552$	4.23463	+	4.71076i	0.180238	+	0.200503i
$553$	−42.8552	+	7.55653i	−1.82239	+	0.321336i
$554$	17.1124	−	14.3590i	0.727036	−	0.610055i
$555$	6.29333	−	0.214626i	0.267137	−	0.00911038i
$556$	−3.48321	−	19.7543i	−0.147721	−	0.837767i
$557$	34.4976	+	6.08286i	1.46171	+	0.257739i	0.847244	−	0.531204i	$-0.178260\pi$
$557$	34.4976	+	6.08286i	1.46171	+	0.257739i	0.614467	+	0.788943i	$0.289371\pi$
$558$	5.00578	+	0.534391i	0.211912	+	0.0226226i
$559$	2.52082	−	1.45539i	0.106619	−	0.0615566i
$560$	16.6786	+	2.94088i	0.704798	+	0.124275i
$561$	−27.8435	+	0.949568i	−1.17555	+	0.0400908i
$562$	8.57628	−	14.8546i	0.361768	−	0.626601i
$563$	−29.3396			−1.23652			−0.618258	−	0.785976i	$-0.712161\pi$
$563$	−29.3396			−1.23652			−0.618258	+	0.785976i	$0.712161\pi$
$564$	0.487074	+	14.2821i	0.0205095	+	0.601385i
$565$	4.89316	−	0.862797i	0.205857	−	0.0362981i
$566$	5.47104	+	4.59075i	0.229965	+	0.192964i
$567$	32.5994	−	17.1971i	1.36905	−	0.722212i
$568$	6.57353	+	2.39257i	0.275819	+	0.100390i
$569$	−3.72965	+	6.45994i	−0.156355	+	0.270815i	−0.933552	−	0.358443i	$-0.883308\pi$
$569$	−3.72965	+	6.45994i	−0.156355	+	0.270815i	0.777197	+	0.629258i	$0.216641\pi$
$570$	−29.3518	+	10.6442i	−1.22941	+	0.445835i
$571$	−15.5243	−	26.8888i	−0.649671	−	1.12526i	−0.983201	−	0.182524i	$-0.941573\pi$
$571$	−15.5243	−	26.8888i	−0.649671	−	1.12526i	0.333530	−	0.942739i	$-0.391760\pi$
$572$	−1.14436	−	6.49000i	−0.0478482	−	0.271361i
$573$	−37.2596	−	5.26751i	−1.55654	−	0.220053i
$574$	1.60344	−	0.583606i	0.0669265	−	0.0243592i
$575$	28.4492	+	33.9045i	1.18641	+	1.41391i
$576$	0.721014	+	2.91207i	0.0300422	+	0.121336i
$577$	−19.0367	+	32.9725i	−0.792507	+	1.37266i	0.131902	+	0.991263i	$0.457891\pi$
$577$	−19.0367	+	32.9725i	−0.792507	+	1.37266i	−0.924410	+	0.381400i	$0.875442\pi$
$578$	6.56780			0.273185
$579$	−10.5085	−	5.59848i	−0.436719	−	0.232665i
$580$	17.5349	−	20.8973i	0.728099	−	0.867715i
$581$	28.7473	+	16.5973i	1.19264	+	0.688571i
$582$	14.0715	−	2.97900i	0.583284	−	0.123484i
$583$	7.46605	−	8.89769i	0.309212	−	0.368505i
$584$	−2.30441	+	1.93363i	−0.0953570	+	0.0800140i
$585$	−11.8285	+	11.3854i	−0.489049	+	0.470730i
$586$	−3.18756	−	18.0775i	−0.131677	−	0.746776i
$587$	−5.25700	−	6.26504i	−0.216979	−	0.258586i	0.646565	−	0.762859i	$-0.276205\pi$
$587$	−5.25700	−	6.26504i	−0.216979	−	0.258586i	−0.863544	+	0.504273i	$0.831761\pi$
$588$	16.0915	+	5.24296i	0.663602	+	0.216216i
$589$	−6.78096	−	2.74251i	−0.279405	−	0.113003i
$590$	−25.2946	+	14.6038i	−1.04136	+	0.601230i
$591$	−20.3521	−	2.87724i	−0.837175	−	0.118354i
$592$	−0.300675	+	0.826099i	−0.0123577	+	0.0339525i
$593$	−7.47150	+	8.90418i	−0.306818	+	0.365651i	−0.897317	−	0.441387i	$-0.854486\pi$
$593$	−7.47150	+	8.90418i	−0.306818	+	0.365651i	0.590499	+	0.807038i	$0.298931\pi$
$594$	−24.8917	+	7.07168i	−1.02132	+	0.290154i
$595$	−9.49873	+	53.8700i	−0.389410	+	2.20845i
$596$	3.36224	−	1.94119i	0.137723	−	0.0795142i
$597$	7.71180	−	6.93235i	0.315623	−	0.283722i
$598$	−3.70730	−	3.11079i	−0.151603	−	0.127210i
$599$	−21.9152	−	18.3890i	−0.895431	−	0.751355i	0.0738613	−	0.997269i	$-0.476468\pi$
$599$	−21.9152	−	18.3890i	−0.895431	−	0.751355i	−0.969292	+	0.245913i	$0.920912\pi$
$600$	4.34144	+	20.5071i	0.177239	+	0.837201i
$601$	−6.83917	+	3.94859i	−0.278975	+	0.161067i	−0.632959	−	0.774185i	$-0.718160\pi$
$601$	−6.83917	+	3.94859i	−0.278975	+	0.161067i	0.353984	+	0.935251i	$0.384827\pi$
$602$	1.56421	−	8.87110i	0.0637526	−	0.361559i
$603$	−1.48995	−	21.8189i	−0.0606754	−	0.888536i
$604$	1.60061	−	1.90753i	0.0651279	−	0.0776164i
$605$	19.5193	−	53.6287i	0.793571	−	2.18032i
$606$	5.42423	+	13.4570i	0.220344	+	0.546655i
$607$	−21.7612	+	12.5639i	−0.883261	+	0.509951i	−0.871732	−	0.489982i	$-0.837003\pi$
$607$	−21.7612	+	12.5639i	−0.883261	+	0.509951i	−0.0115289	+	0.999934i	$0.503670\pi$
$608$	0.153683	−	4.35619i	0.00623266	−	0.176667i
$609$	34.7972	−	31.2802i	1.41006	−	1.26754i
$610$	15.4702	+	18.4367i	0.626372	+	0.746481i
$611$	−1.89592	−	10.7523i	−0.0767008	−	0.434992i
$612$	−9.40566	+	2.32880i	−0.380201	+	0.0941360i
$613$	−4.94225	+	4.14704i	−0.199615	+	0.167497i	−0.737116	−	0.675766i	$-0.763813\pi$
$613$	−4.94225	+	4.14704i	−0.199615	+	0.167497i	0.537501	+	0.843263i	$0.319369\pi$
$614$	−14.4655	+	17.2394i	−0.583782	+	0.695724i
$615$	1.99522	+	2.21956i	0.0804550	+	0.0895011i
$616$	−17.6620	−	10.1971i	−0.711621	−	0.410855i
$617$	4.05009	−	4.82671i	0.163051	−	0.194316i	−0.678333	−	0.734755i	$-0.737297\pi$
$617$	4.05009	−	4.82671i	0.163051	−	0.194316i	0.841383	+	0.540439i	$0.181742\pi$
$618$	−23.0393	+	14.3704i	−0.926775	+	0.578062i
$619$	22.5813			0.907617			0.453809	−	0.891099i	$-0.350065\pi$
$619$	22.5813			0.907617			0.453809	+	0.891099i	$0.350065\pi$
$620$	−3.46983	+	6.00992i	−0.139352	+	0.241364i
$621$	−10.6648	+	15.7280i	−0.427964	+	0.631145i
$622$	−10.4886	−	12.4998i	−0.420554	−	0.501197i
$623$	−33.0606	+	12.0331i	−1.32454	+	0.482094i
$624$	−0.856887	−	2.12586i	−0.0343029	−	0.0851026i
$625$	10.5843	+	60.0266i	0.423372	+	2.40106i
$626$	−2.72551	−	4.72072i	−0.108933	−	0.188678i
$627$	37.5980	+	0.0441410i	1.50152	+	0.00176282i
$628$	10.1570	−	17.5925i	0.405310	−	0.702017i
$629$	−2.66821	−	0.971149i	−0.106388	−	0.0387222i
$630$	3.46143	+	50.6895i	0.137907	+	2.01952i
$631$	−0.585574	−	0.491355i	−0.0233113	−	0.0195605i	0.631058	−	0.775736i	$-0.282621\pi$
$631$	−0.585574	−	0.491355i	−0.0233113	−	0.0195605i	−0.654369	+	0.756175i	$0.727066\pi$
$632$	10.4646	−	1.84519i	0.416259	−	0.0733977i
$633$	16.0306	−	9.99886i	0.637160	−	0.397419i
$634$	−7.43350			−0.295222
$635$	24.6170	−	42.6378i	0.976894	−	1.69203i
$636$	1.89947	−	3.56535i	0.0753187	−	0.141376i
$637$	−12.7339	−	2.24533i	−0.504536	−	0.0889633i
$638$	−28.4491	+	16.4251i	−1.12631	+	0.650276i
$639$	−2.22772	+	20.8676i	−0.0881272	+	0.825511i
$640$	−4.07266	−	0.718119i	−0.160986	−	0.0283861i
$641$	−3.01521	−	17.1001i	−0.119094	−	0.675413i	−0.984642	−	0.174587i	$-0.944141\pi$
$641$	−3.01521	−	17.1001i	−0.119094	−	0.675413i	0.865548	−	0.500826i	$-0.166970\pi$
$642$	−10.2524	−	16.4371i	−0.404630	−	0.648721i
$643$	−14.5183	+	12.1823i	−0.572547	+	0.480424i	−0.882490	−	0.470331i	$-0.844135\pi$
$643$	−14.5183	+	12.1823i	−0.572547	+	0.480424i	0.309943	+	0.950755i	$0.399690\pi$
$644$	−14.7493	+	2.60069i	−0.581202	+	0.102482i
$645$	15.4139	−	3.26317i	0.606920	−	0.128487i
$646$	14.0700	+	0.496379i	0.553577	+	0.0195298i
$647$		−	44.2632i		−	1.74017i	−0.492904	−	0.870084i	$-0.664065\pi$
$647$		−	44.2632i		−	1.74017i	0.492904	−	0.870084i	$-0.335935\pi$
$648$	−7.96028	+	4.19928i	−0.312709	+	0.164963i
$649$	34.6377	−	6.10757i	1.35965	−	0.239743i
$650$	−5.47750	−	15.0493i	−0.214845	−	0.590283i
$651$	−7.33582	+	9.37364i	−0.287513	+	0.367382i
$652$	2.29744	−	0.836201i	0.0899748	−	0.0327482i
$653$			37.9070i			1.48342i	0.670723	+	0.741708i	$0.265984\pi$
$653$			37.9070i			1.48342i	−0.670723	+	0.741708i	$0.734016\pi$
$654$	−4.71396	+	0.997963i	−0.184330	+	0.0390234i
$655$	9.89572	−	56.1214i	0.386658	−	2.19285i
$656$	−0.391537	+	0.142508i	−0.0152870	+	0.00556399i
$657$	−7.29236	−	5.31641i	−0.284502	−	0.207413i
$658$	−29.2615	−	16.8941i	−1.14073	−	0.658601i
$659$	5.20861	+	4.37054i	0.202899	+	0.170252i	0.738575	−	0.674171i	$-0.235499\pi$
$659$	5.20861	+	4.37054i	0.202899	+	0.170252i	−0.535677	+	0.844423i	$0.679943\pi$
$660$	4.99326	−	35.3197i	0.194362	−	1.37482i
$661$	29.2596	+	5.15926i	1.13807	+	0.200672i	0.710761	−	0.703434i	$-0.248351\pi$
$661$	29.2596	+	5.15926i	1.13807	+	0.200672i	0.427308	+	0.904106i	$0.359462\pi$
$662$	6.65852	+	7.93531i	0.258791	+	0.308415i
$663$	6.86631	−	2.76765i	0.266665	−	0.107487i
$664$	−7.01966	−	4.05280i	−0.272416	−	0.157279i
$665$	15.3742	−	72.2030i	0.596188	−	2.79991i
$666$	−2.62245	−	0.279958i	−0.101618	−	0.0108482i
$667$	−8.25088	+	22.6691i	−0.319475	+	0.877751i
$668$	−12.1648	−	4.42764i	−0.470672	−	0.171311i
$669$	−30.8136	+	19.2195i	−1.19132	+	0.743069i
$670$	28.3292	+	10.3110i	1.09445	+	0.398348i
$671$	−9.91249	−	27.2343i	−0.382667	−	1.05137i
$672$	−6.74424	−	2.19742i	−0.260165	−	0.0847674i
$673$		−	27.6168i		−	1.06455i	−0.846571	−	0.532275i	$-0.821337\pi$
$673$		−	27.6168i		−	1.06455i	0.846571	−	0.532275i	$-0.178663\pi$
$674$	10.1284	+	27.8276i	0.390132	+	1.07188i
$675$	−56.5880	+	27.4285i	−2.17807	+	1.05572i
$676$	−5.62441	−	9.74176i	−0.216323	−	0.374683i
$677$	−8.84456	−	15.3192i	−0.339924	−	0.588766i	0.644494	−	0.764609i	$-0.277068\pi$
$677$	−8.84456	−	15.3192i	−0.339924	−	0.588766i	−0.984418	+	0.175844i	$0.943735\pi$
$678$	−2.07979	+	0.0709288i	−0.0798740	+	0.00272400i
$679$	−11.6315	+	31.9572i	−0.446375	+	1.22640i
$680$	2.31945	−	13.1542i	0.0889467	−	0.504442i
$681$	−4.95136	+	35.0233i	−0.189736	+	1.34210i
$682$	6.40167	−	5.37164i	0.245133	−	0.205691i
$683$	−39.1236			−1.49702			−0.748511	−	0.663122i	$-0.769231\pi$
$683$	−39.1236			−1.49702			−0.748511	+	0.663122i	$0.769231\pi$
$684$	12.7963	−	2.69334i	0.489280	−	0.102982i
$685$	−61.5733			−2.35260
$686$	−8.69343	+	7.29466i	−0.331917	+	0.278511i
$687$	19.2788	+	15.0876i	0.735532	+	0.575628i
$688$	−0.381958	+	2.16619i	−0.0145620	+	0.0825852i
$689$	−1.05563	+	2.90033i	−0.0402164	+	0.110494i
$690$	−13.8633	−	22.2263i	−0.527767	−	0.846139i
$691$	−6.29658	−	10.9060i	−0.239533	−	0.414884i	0.721047	−	0.692886i	$-0.243661\pi$
$691$	−6.29658	−	10.9060i	−0.239533	−	0.414884i	−0.960580	+	0.278002i	$0.910328\pi$
$692$	12.6392	+	21.8917i	0.480470	+	0.832199i
$693$	16.9603	−	58.7852i	0.644267	−	2.23306i
$694$	2.96189	+	8.13771i	0.112432	+	0.308903i
$695$			82.9536i			3.14661i
$696$	−8.49696	+	7.63815i	−0.322076	+	0.289523i
$697$	−0.460285	−	1.26462i	−0.0174345	−	0.0479010i
$698$	−6.47161	−	2.35547i	−0.244954	−	0.0891560i
$699$	12.7540	+	6.79480i	0.482402	+	0.257003i
$700$	−46.5728	−	16.9511i	−1.76028	−	0.640691i
$701$	−6.22452	+	17.1017i	−0.235097	+	0.645923i	0.764902	+	0.644147i	$0.222788\pi$
$701$	−6.22452	+	17.1017i	−0.235097	+	0.645923i	−0.999998	+	0.00177611i	$0.999435\pi$
$702$	5.57283	−	4.02809i	0.210333	−	0.152030i
$703$	3.55243	+	1.43676i	0.133983	+	0.0541883i
$704$	4.31279	+	2.48999i	0.162544	+	0.0938450i
$705$	8.27257	−	58.5159i	0.311563	−	2.20384i
$706$	−10.4700	−	12.4776i	−0.394043	−	0.469602i
$707$	−33.7841	−	5.95705i	−1.27058	−	0.224038i
$708$	11.3459	−	4.57328i	0.426406	−	0.171875i
$709$	−12.3542	−	10.3664i	−0.463971	−	0.389318i	0.380619	−	0.924732i	$-0.375711\pi$
$709$	−12.3542	−	10.3664i	−0.463971	−	0.389318i	−0.844590	+	0.535414i	$0.820155\pi$
$710$	−25.0536	−	14.4647i	−0.940244	−	0.542850i
$711$	12.9184	+	29.1432i	0.484479	+	1.09296i
$712$	8.07289	−	2.93829i	0.302544	−	0.110117i
$713$	1.06566	−	6.04367i	0.0399094	−	0.226337i
$714$	7.09743	−	21.7831i	0.265615	−	0.815214i
$715$			27.2533i			1.01922i
$716$	11.2968	−	4.11171i	0.422182	−	0.153662i
$717$	45.4229	+	6.42157i	1.69635	+	0.239818i
$718$	4.65951	+	12.8019i	0.173891	+	0.477762i
$719$	−21.9242	+	3.86583i	−0.817636	+	0.144171i	−0.566797	−	0.823858i	$-0.691818\pi$
$719$	−21.9242	+	3.86583i	−0.817636	+	0.144171i	−0.250839	+	0.968029i	$0.580706\pi$
$720$	−0.845230	−	12.3776i	−0.0314999	−	0.461287i
$721$		−	64.2018i		−	2.39100i
$722$	−18.9528	−	1.33894i	−0.705349	−	0.0498303i
$723$	−5.19687	+	15.9500i	−0.193274	+	0.593188i
$724$	−6.85692	+	1.20906i	−0.254835	+	0.0449344i
$725$	−61.1547	+	51.3149i	−2.27123	+	1.90579i
$726$	−11.2388	+	21.0956i	−0.417112	+	0.782932i
$727$	−6.76571	−	38.3703i	−0.250926	−	1.42307i	−0.806317	−	0.591484i	$-0.798542\pi$
$727$	−6.76571	−	38.3703i	−0.250926	−	1.42307i	0.555390	−	0.831590i	$-0.312569\pi$
$728$	5.33701	+	0.941060i	0.197803	+	0.0348780i
$729$	−17.9681	−	20.1531i	−0.665484	−	0.746412i
$730$	10.7736	−	6.22015i	0.398750	−	0.230218i
$731$	−6.99656	−	1.23368i	−0.258777	−	0.0456294i
$732$	−5.33465	−	8.55275i	−0.197174	−	0.316119i
$733$	2.21308	−	3.83317i	0.0817420	−	0.141581i	−0.822256	−	0.569117i	$-0.807285\pi$
$733$	2.21308	−	3.83317i	0.0817420	−	0.141581i	0.903998	+	0.427536i	$0.140618\pi$
$734$	−21.9458			−0.810033
$735$	−61.7700	−	32.9084i	−2.27842	−	1.21384i
$736$	3.60155	−	0.635050i	0.132755	−	0.0234083i
$737$	−27.8102	−	23.3355i	−1.02440	−	0.859575i
$738$	−0.697296	−	1.03743i	−0.0256678	−	0.0381884i
$739$	−24.6255	−	8.96294i	−0.905862	−	0.329707i	−0.153263	−	0.988185i	$-0.548978\pi$
$739$	−24.6255	−	8.96294i	−0.905862	−	0.329707i	−0.752600	+	0.658478i	$0.771200\pi$
$740$	1.81778	−	3.14850i	0.0668231	−	0.115741i
$741$	−9.39235	+	3.40605i	−0.345037	+	0.125125i
$742$	4.77581	+	8.27194i	0.175325	+	0.303673i
$743$	7.74828	+	43.9427i	0.284257	+	1.61210i	0.707928	+	0.706284i	$0.249630\pi$
$743$	7.74828	+	43.9427i	0.284257	+	1.61210i	−0.423672	+	0.905816i	$0.639259\pi$
$744$	1.79130	−	2.28890i	0.0656721	−	0.0839152i
$745$	−15.0872	+	5.49131i	−0.552754	+	0.201186i
$746$	−22.6351	−	26.9754i	−0.828728	−	0.987640i
$747$	6.74076	−	23.3639i	0.246632	−	0.854839i
$748$	−8.04240	+	13.9298i	−0.294059	+	0.509325i
$749$	45.8041			1.67365
$750$	−1.73393	−	50.8427i	−0.0633140	−	1.85651i
$751$	18.3938	−	21.9208i	0.671198	−	0.799903i	−0.317748	−	0.948175i	$-0.602927\pi$
$751$	18.3938	−	21.9208i	0.671198	−	0.799903i	0.988947	+	0.148272i	$0.0473711\pi$
$752$	7.14521	+	4.12529i	0.260559	+	0.150434i
$753$	−5.05573	+	15.5169i	−0.184241	+	0.565466i
$754$	5.61105	−	6.68699i	0.204342	−	0.243526i
$755$	−7.88857	+	6.61930i	−0.287094	+	0.240901i
$756$	1.53635	−	21.2240i	0.0558766	−	0.771911i
$757$	−4.44866	−	25.2296i	−0.161689	−	0.916985i	−0.952413	−	0.304811i	$-0.901407\pi$
$757$	−4.44866	−	25.2296i	−0.161689	−	0.916985i	0.790724	−	0.612173i	$-0.209705\pi$
$758$	−8.99699	−	10.7222i	−0.326785	−	0.389448i
$759$	6.53332	+	30.8607i	0.237145	+	1.12017i
$760$	−3.75416	+	17.6309i	−0.136178	+	0.639540i
$761$	23.8853	−	13.7902i	0.865841	−	0.499894i	−0.000122725	−	1.00000i	$-0.500039\pi$
$761$	23.8853	−	13.7902i	0.865841	−	0.499894i	0.865964	+	0.500106i	$0.166706\pi$
$762$	−12.7085	+	16.2388i	−0.460380	+	0.588269i
$763$	3.89653	−	10.7056i	0.141064	−	0.387570i
$764$	−13.9651	+	16.6429i	−0.505238	+	0.602119i
$765$	39.9784	−	2.73000i	1.44542	−	0.0987034i
$766$	1.08938	−	6.17819i	0.0393609	−	0.223227i
$767$	−8.09407	+	4.67311i	−0.292260	+	0.168736i
$768$	1.64684	+	0.536577i	0.0594253	+	0.0193621i
$769$	−3.43683	−	2.88384i	−0.123935	−	0.103994i	0.578713	−	0.815531i	$-0.303555\pi$
$769$	−3.43683	−	2.88384i	−0.123935	−	0.103994i	−0.702649	+	0.711537i	$0.747999\pi$
$770$	64.6084	+	54.2129i	2.32832	+	1.95370i
$771$	37.6872	+	12.2793i	1.35727	+	0.442229i
$772$	−5.95339	+	3.43719i	−0.214267	+	0.123707i
$773$	6.73042	−	38.1701i	0.242076	−	1.37288i	−0.585109	−	0.810955i	$-0.698948\pi$
$773$	6.73042	−	38.1701i	0.242076	−	1.37288i	0.827185	−	0.561929i	$-0.189941\pi$
$774$	−6.58349	+	0.449566i	−0.236639	+	0.0161593i
$775$	13.0540	−	15.5572i	0.468914	−	0.558830i
$776$	2.84023	−	7.80346i	0.101958	−	0.280128i
$777$	3.84311	−	4.91069i	0.137871	−	0.176170i
$778$	32.5768	−	18.8082i	1.16793	−	0.674307i
$779$	0.560618	+	1.72751i	0.0200862	+	0.0618945i
$780$	1.96318	+	9.27326i	0.0702932	+	0.332036i
$781$	22.3928	+	26.6867i	0.801277	+	0.954924i
$782$	2.05114	+	11.6326i	0.0733487	+	0.415981i
$783$	−28.3692	−	19.2365i	−1.01383	−	0.687457i
$784$	7.48512	−	6.28076i	0.267326	−	0.224313i
$785$	−53.9996	+	64.3542i	−1.92733	+	2.29690i
$786$	−7.39406	+	22.6936i	−0.263738	+	0.809452i
$787$	−3.62632	−	2.09366i	−0.129265	−	0.0746309i	0.433973	−	0.900926i	$-0.357111\pi$
$787$	−3.62632	−	2.09366i	−0.129265	−	0.0746309i	−0.563238	+	0.826295i	$0.690445\pi$
$788$	−7.62806	+	9.09076i	−0.271738	+	0.323845i
$789$	0.0973366	+	2.85413i	0.00346528	+	0.101610i
$790$	−43.9438			−1.56345
$791$	2.46016	−	4.26112i	0.0874732	−	0.151508i
$792$	−4.14144	+	14.3545i	−0.147160	+	0.510063i
$793$	4.95036	+	5.89961i	0.175792	+	0.209501i
$794$	7.45506	−	2.71342i	0.264570	−	0.0962957i
$795$	−10.2962	+	13.1564i	−0.365169	+	0.466610i
$796$	−1.03962	−	5.89596i	−0.0368482	−	0.208977i
$797$	−0.924494	−	1.60127i	−0.0327473	−	0.0567199i	0.849187	−	0.528092i	$-0.177092\pi$
$797$	−0.924494	−	1.60127i	−0.0327473	−	0.0567199i	−0.881935	+	0.471372i	$0.843759\pi$
$798$	−10.6089	+	29.0415i	−0.375549	+	1.02806i
$799$	−13.3242	+	23.0782i	−0.471377	+	0.816450i
$800$	11.3724	+	4.13920i	0.402074	+	0.146343i
$801$	14.3772	+	21.3903i	0.507992	+	0.755787i
$802$	−3.63722	−	3.05199i	−0.128435	−	0.107770i
$803$	−14.7531	+	2.60137i	−0.520626	+	0.0918005i
$804$	−11.1437	−	5.93688i	−0.393008	−	0.209378i
$805$	61.9363			2.18297
$806$	−1.11032	+	1.92313i	−0.0391093	+	0.0677393i
$807$	10.1661	+	16.2987i	0.357863	+	0.573742i
$808$	8.24957	+	1.45462i	0.290219	+	0.0511734i
$809$	−33.5259	+	19.3562i	−1.17871	+	0.680527i	−0.955715	−	0.294293i	$-0.904916\pi$
$809$	−33.5259	+	19.3562i	−1.17871	+	0.680527i	−0.222992	+	0.974820i	$0.571582\pi$
$810$	35.4351	−	11.3858i	1.24506	−	0.400056i
$811$	8.23971	+	1.45288i	0.289335	+	0.0510176i	0.316432	−	0.948615i	$-0.397515\pi$
$811$	8.23971	+	1.45288i	0.289335	+	0.0510176i	−0.0270967	+	0.999633i	$0.508626\pi$
$812$	−4.69096	−	26.6038i	−0.164621	−	0.933610i
$813$	−8.77750	+	16.4756i	−0.307840	+	0.577826i
$814$	−3.35373	+	2.81411i	−0.117548	+	0.0986345i
$815$	−9.95719	+	1.75572i	−0.348785	+	0.0615002i
$816$	−1.73309	+	5.31912i	−0.0606701	+	0.186206i
$817$	9.37763	+	1.99679i	0.328082	+	0.0698587i
$818$		−	0.639385i		−	0.0223556i
$819$	1.10763	+	16.2203i	0.0387038	+	0.566782i
$820$	1.69693	−	0.299215i	0.0592595	−	0.0104490i
$821$	−12.0007	−	32.9717i	−0.418827	−	1.15072i	−0.952370	−	0.304945i	$-0.901362\pi$
$821$	−12.0007	−	32.9717i	−0.418827	−	1.15072i	0.533543	−	0.845773i	$-0.320860\pi$
$822$	25.5346	+	3.60991i	0.890623	+	0.125910i
$823$	−35.0983	+	12.7747i	−1.22345	+	0.445299i	−0.871349	−	0.490663i	$-0.836754\pi$
$823$	−35.0983	+	12.7747i	−1.22345	+	0.445299i	−0.352100	+	0.935962i	$0.614532\pi$
$824$			15.6771i			0.546138i
$825$	−32.3389	+	99.2531i	−1.12589	+	3.45555i
$826$	−5.02252	+	28.4841i	−0.174756	+	0.991090i
$827$	−1.87462	+	0.682307i	−0.0651870	+	0.0237261i	−0.374408	−	0.927264i	$-0.622154\pi$
$827$	−1.87462	+	0.682307i	−0.0651870	+	0.0237261i	0.309221	+	0.950990i	$0.399932\pi$
$828$	4.44607	+	10.0301i	0.154512	+	0.348569i
$829$	28.9016	+	16.6864i	1.00379	+	0.579541i	0.909369	−	0.415991i	$-0.136565\pi$
$829$	28.9016	+	16.6864i	1.00379	+	0.579541i	0.0944261	+	0.995532i	$0.469898\pi$
$830$	25.6783	+	21.5466i	0.891306	+	0.747894i
$831$	35.8861	−	14.4649i	1.24487	−	0.501781i
$832$	−1.30322	−	0.229793i	−0.0451810	−	0.00796662i
$833$	20.2862	+	24.1761i	0.702874	+	0.837653i
$834$	4.86339	−	34.4011i	0.168406	−	1.19121i
$835$	46.3637	+	26.7681i	1.60448	+	0.926347i
$836$	11.5097	−	18.4047i	0.398070	−	0.636538i
$837$	7.95699	+	3.56605i	0.275034	+	0.123261i
$838$	−5.50366	+	15.1212i	−0.190121	+	0.522353i
$839$	−17.9424	−	6.53049i	−0.619440	−	0.225458i	0.0131888	−	0.999913i	$-0.495802\pi$
$839$	−17.9424	−	6.53049i	−0.619440	−	0.225458i	−0.632628	+	0.774455i	$0.718024\pi$
$840$	25.8889	+	13.7925i	0.893253	+	0.475887i
$841$	−13.6380	−	4.96382i	−0.470275	−	0.171166i
$842$	−6.51581	−	17.9020i	−0.224550	−	0.616945i
$843$	22.0944	−	19.8612i	0.760971	−	0.684058i
$844$		−	10.9081i		−	0.375471i
$845$	15.9105	+	43.7138i	0.547339	+	1.50380i
$846$	−6.86132	+	23.7817i	−0.235897	+	0.817632i
$847$	−28.2577	−	48.9437i	−0.970945	−	1.68173i
$848$	−1.16618	−	2.01988i	−0.0400468	−	0.0693631i
$849$	6.54665	+	10.4959i	0.224680	+	0.360217i
$850$	−13.3692	+	36.7315i	−0.458559	+	1.25988i
$851$	−0.558283	+	3.16618i	−0.0191377	+	0.108535i
$852$	9.54176	+	7.46739i	0.326895	+	0.255829i
$853$	9.92692	−	8.32968i	0.339891	−	0.285203i	−0.456824	−	0.889557i	$-0.651013\pi$
$853$	9.92692	−	8.32968i	0.339891	−	0.285203i	0.796716	+	0.604354i	$0.206569\pi$
$854$	23.8333			0.815559
$855$	−54.0492	+	1.77975i	−1.84844	+	0.0608663i
$856$	−11.1847			−0.382284
$857$	41.7211	−	35.0081i	1.42516	−	1.19585i	0.476661	−	0.879087i	$-0.341847\pi$
$857$	41.7211	−	35.0081i	1.42516	−	1.19585i	0.948503	−	0.316767i	$-0.102597\pi$
$858$	1.59780	−	11.3020i	0.0545481	−	0.385845i
$859$	7.35697	−	41.7235i	0.251017	−	1.42359i	−0.555077	−	0.831799i	$-0.687311\pi$
$859$	7.35697	−	41.7235i	0.251017	−	1.42359i	0.806094	−	0.591788i	$-0.201578\pi$
$860$	3.11116	−	8.54785i	0.106090	−	0.291479i
$861$	2.95377	−	0.100735i	0.100664	−	0.00343302i
$862$	18.7969	+	32.5572i	0.640226	+	1.10890i
$863$	−10.9221	−	18.9176i	−0.371792	−	0.643962i	0.618049	−	0.786139i	$-0.287923\pi$
$863$	−10.9221	−	18.9176i	−0.371792	−	0.643962i	−0.989841	+	0.142177i	$0.954590\pi$
$864$	−0.375154	+	5.18259i	−0.0127630	+	0.176315i
$865$	−35.7542	−	98.2340i	−1.21568	−	3.34006i
$866$			9.97219i			0.338869i
$867$	10.8161	+	3.52413i	0.367335	+	0.119686i
$868$	2.35041	+	6.45771i	0.0797783	+	0.219189i
$869$	49.7261	+	18.0988i	1.68684	+	0.613960i
$870$	40.0903	−	25.0057i	1.35919	−	0.847774i
$871$	9.06513	+	3.29944i	0.307160	+	0.111797i
$872$	−0.951475	+	2.61415i	−0.0322210	+	0.0885265i
$873$	24.7721	+	2.64453i	0.838407	+	0.0895039i
$874$	−2.21290	−	15.7866i	−0.0748525	−	0.533990i
$875$	104.167	+	60.1411i	3.52150	+	2.03314i
$876$	−4.83253	+	1.94788i	−0.163276	+	0.0658128i
$877$	1.31753	+	1.57018i	0.0444900	+	0.0530211i	0.787831	−	0.615892i	$-0.211204\pi$
$877$	1.31753	+	1.57018i	0.0444900	+	0.0530211i	−0.743341	+	0.668913i	$0.766760\pi$
$878$	29.2194	+	5.15217i	0.986108	+	0.173877i
$879$	4.45059	−	31.4812i	0.150115	−	1.06183i
$880$	−15.7764	−	13.2380i	−0.531822	−	0.446252i
$881$	4.12027	+	2.37884i	0.138815	+	0.0801450i	0.567799	−	0.823167i	$-0.307795\pi$
$881$	4.12027	+	2.37884i	0.138815	+	0.0801450i	−0.428984	+	0.903312i	$0.641128\pi$
$882$	23.6869	+	17.2687i	0.797578	+	0.581466i
$883$	24.7207	−	8.99762i	0.831919	−	0.302794i	0.109273	−	0.994012i	$-0.465148\pi$
$883$	24.7207	−	8.99762i	0.831919	−	0.302794i	0.722646	+	0.691218i	$0.242926\pi$
$884$	0.742205	−	4.20925i	0.0249631	−	0.141573i
$885$	−49.4922	+	10.4777i	−1.66366	+	0.352204i
$886$		−	13.3634i		−	0.448953i
$887$	−3.11771	+	1.13475i	−0.104682	+	0.0381013i	−0.393830	−	0.919183i	$-0.628850\pi$
$887$	−3.11771	+	1.13475i	−0.104682	+	0.0381013i	0.289148	+	0.957284i	$0.406628\pi$
$888$	−0.938430	+	1.19912i	−0.0314917	+	0.0402398i
$889$	−16.6752	−	45.8147i	−0.559268	−	1.53658i
$890$	−34.9881	+	6.16935i	−1.17281	+	0.206797i
$891$	−44.7872	−	1.71039i	−1.50043	−	0.0573003i
$892$			20.9672i			0.702032i
$893$	19.0686	−	30.4919i	0.638107	−	1.02037i
$894$	6.57867	−	1.39273i	0.220024	−	0.0465798i
$895$	−48.9608	+	8.63311i	−1.63658	+	0.288573i
$896$	−3.13715	+	2.63238i	−0.104805	+	0.0879416i
$897$	−4.43615	−	7.11223i	−0.148119	−	0.237471i
$898$	−0.0409034	−	0.231975i	−0.00136496	−	0.00774109i
$899$	10.9012	+	1.92217i	0.363575	+	0.0641081i
$900$	−3.85401	+	36.1015i	−0.128467	+	1.20338i
$901$	6.52401	−	3.76664i	0.217346	−	0.125485i
$902$	−2.04346	−	0.360317i	−0.0680398	−	0.0119972i
$903$	7.33604	−	13.7700i	0.244128	−	0.458236i
$904$	−0.600734	+	1.04050i	−0.0199801	+	0.0346066i
$905$	28.7941			0.957149
$906$	3.65949	−	2.28255i	0.121578	−	0.0758327i
$907$	32.3015	−	5.69563i	1.07255	−	0.189120i	0.390633	−	0.920546i	$-0.372256\pi$
$907$	32.3015	−	5.69563i	1.07255	−	0.189120i	0.681921	+	0.731426i	$0.261145\pi$
$908$	15.6440	+	13.1269i	0.519164	+	0.435631i
$909$	1.71210	+	25.0721i	0.0567867	+	0.831590i
$910$	−21.0600	−	7.66522i	−0.698133	−	0.254100i
$911$	−13.2907	+	23.0202i	−0.440341	+	0.762694i	−0.997715	−	0.0675683i	$-0.978476\pi$
$911$	−13.2907	+	23.0202i	−0.440341	+	0.762694i	0.557373	+	0.830262i	$0.311809\pi$
$912$	2.59052	−	7.09149i	0.0857808	−	0.234823i
$913$	−20.1829	−	34.9578i	−0.667956	−	1.15693i
$914$	−1.18636	−	6.72819i	−0.0392413	−	0.222549i
$915$	15.5843	+	38.6633i	0.515201	+	1.27817i
$916$	13.2816	−	4.83410i	0.438836	−	0.159723i
$917$	−36.2743	−	43.2301i	−1.19788	−	1.42758i
$918$	−16.7392	−	1.21171i	−0.552476	−	0.0399923i
$919$	5.25188	−	9.09653i	0.173244	−	0.300067i	−0.766308	−	0.642473i	$-0.777909\pi$
$919$	5.25188	−	9.09653i	0.173244	−	0.300067i	0.939552	+	0.342406i	$0.111242\pi$
$920$	−15.1239			−0.498620
$921$	−33.0727	+	20.6286i	−1.08978	+	0.679736i
$922$	−14.0324	+	16.7232i	−0.462133	+	0.550749i
$923$	−8.01695	−	4.62859i	−0.263881	−	0.152352i
$924$	−23.6149	−	26.2701i	−0.776873	−	0.864223i
$925$	−6.83878	+	8.15014i	−0.224858	+	0.267975i
$926$	11.9016	−	9.98662i	0.391111	−	0.328181i
$927$	−45.6528	+	11.3034i	−1.49944	+	0.371253i
$928$	1.14546	+	6.49624i	0.0376017	+	0.213250i
$929$	−18.2654	−	21.7678i	−0.599268	−	0.714180i	0.378091	−	0.925769i	$-0.376581\pi$
$929$	−18.2654	−	21.7678i	−0.599268	−	0.714180i	−0.977359	+	0.211589i	$0.932136\pi$
$930$	−8.93904	+	8.03555i	−0.293123	+	0.263496i
$931$	−26.2098	−	33.5718i	−0.858993	−	1.10027i
$932$	7.22556	−	4.17168i	0.236681	−	0.136648i
$933$	−10.5659	−	26.2131i	−0.345913	−	0.858180i
$934$	8.39859	−	23.0749i	0.274810	−	0.755035i
$935$	42.7572	−	50.9560i	1.39831	−	1.66644i
$936$	−0.270467	−	3.96074i	−0.00884049	−	0.129461i
$937$	−2.27288	+	12.8901i	−0.0742517	+	0.421103i	0.924911	+	0.380184i	$0.124139\pi$
$937$	−2.27288	+	12.8901i	−0.0742517	+	0.421103i	−0.999162	+	0.0409183i	$0.986972\pi$
$938$	25.8544	−	14.9270i	0.844176	−	0.487385i
$939$	−1.95545	−	9.23672i	−0.0638137	−	0.301429i
$940$	−26.1375	−	21.9320i	−0.852512	−	0.715343i
$941$	28.4209	+	23.8479i	0.926494	+	0.777421i	0.975185	−	0.221393i	$-0.0710603\pi$
$941$	28.4209	+	23.8479i	0.926494	+	0.777421i	−0.0486905	+	0.998814i	$0.515505\pi$
$942$	26.1668	−	23.5220i	0.852559	−	0.766389i
$943$	−1.31964	+	0.761894i	−0.0429734	+	0.0248107i
$944$	1.22642	−	6.95540i	0.0399167	−	0.226379i
$945$	−21.4984	+	85.3349i	−0.699344	+	2.77595i
$946$	−7.04109	+	8.39125i	−0.228926	+	0.272823i
$947$	2.41560	−	6.63682i	0.0784966	−	0.215668i	−0.894237	−	0.447595i	$-0.852281\pi$
$947$	2.41560	−	6.63682i	0.0784966	−	0.215668i	0.972733	+	0.231927i	$0.0745030\pi$
$948$	18.2236	+	2.57633i	0.591875	+	0.0836752i
$949$	3.44748	−	1.99040i	0.111910	−	0.0646112i
$950$	19.7789	−	48.9041i	0.641712	−	1.58666i
$951$	−12.2418	−	3.98865i	−0.396967	−	0.129341i
$952$	−8.50230	−	10.1326i	−0.275561	−	0.328401i
$953$	2.36910	+	13.4359i	0.0767428	+	0.435230i	0.998835	+	0.0482594i	$0.0153674\pi$
$953$	2.36910	+	13.4359i	0.0767428	+	0.435230i	−0.922092	+	0.386971i	$0.873521\pi$
$954$	5.04121	−	4.85236i	0.163215	−	0.157101i
$955$	68.8265	−	57.7523i	2.22717	−	1.86882i
$956$	17.0247	−	20.2892i	0.550617	−	0.656200i
$957$	−55.6645	+	11.7844i	−1.79938	+	0.380935i
$958$	−0.950704	−	0.548889i	−0.0307159	−	0.0177338i
$959$	−39.1936	+	46.7091i	−1.26563	+	1.50832i
$960$	−6.32169	−	3.36792i	−0.204032	−	0.108699i
$961$	28.1841			0.909163
$962$	0.581677	−	1.00749i	0.0187540	−	0.0324829i
$963$	−8.06430	−	32.5705i	−0.259869	−	1.04957i
$964$	6.22554	+	7.41932i	0.200511	+	0.238960i
$965$	26.7144	−	9.72326i	0.859968	−	0.313003i
$966$	−25.6852	−	3.63119i	−0.826406	−	0.116832i
$967$	−0.584359	−	3.31406i	−0.0187917	−	0.106573i	0.973969	−	0.226680i	$-0.0727873\pi$
$967$	−0.584359	−	3.31406i	−0.0187917	−	0.106573i	−0.992761	+	0.120107i	$0.961676\pi$
$968$	6.90010	+	11.9513i	0.221778	+	0.384130i
$969$	22.9047	+	8.36711i	0.735806	+	0.268790i
$970$	−17.1711	+	29.7412i	−0.551330	+	0.954932i
$971$	−11.5688	−	4.21070i	−0.371260	−	0.135128i	0.149650	−	0.988739i	$-0.452185\pi$
$971$	−11.5688	−	4.21070i	−0.371260	−	0.135128i	−0.520910	+	0.853611i	$0.674407\pi$
$972$	−15.3626	+	2.64425i	−0.492754	+	0.0848143i
$973$	62.9280	+	52.8029i	2.01738	+	1.69278i
$974$	−17.4534	+	3.07751i	−0.559244	+	0.0986099i
$975$	−0.945456	−	27.7229i	−0.0302788	−	0.887844i
$976$	−5.81974			−0.186285
$977$	−7.74983	+	13.4231i	−0.247939	+	0.429443i	−0.962954	−	0.269666i	$-0.913087\pi$
$977$	−7.74983	+	13.4231i	−0.247939	+	0.429443i	0.715015	+	0.699109i	$0.246420\pi$
$978$	4.23221	−	0.144334i	0.135331	−	0.00461530i
$979$	42.1330	+	7.42918i	1.34658	+	0.237438i
$980$	−34.9946	+	20.2042i	−1.11786	+	0.645398i
$981$	−8.29862	−	0.885916i	−0.264955	−	0.0282851i
$982$	−4.69431	−	0.827734i	−0.149802	−	0.0264141i
$983$	0.730023	+	4.14017i	0.0232841	+	0.132051i	0.994234	−	0.107232i	$-0.0341988\pi$
$983$	0.730023	+	4.14017i	0.0232841	+	0.132051i	−0.970950	+	0.239283i	$0.923088\pi$
$984$	−0.721266	+	0.0245979i	−0.0229931	+	0.000784151i
$985$	37.5947	−	31.5457i	1.19787	−	1.00513i
$986$	−20.9822	+	3.69972i	−0.668208	+	0.117823i
$987$	−39.1240	−	43.5229i	−1.24533	−	1.38535i
$988$	−1.20130	+	5.64175i	−0.0382185	+	0.179488i
$989$			8.04420i			0.255791i
$990$	27.1749	−	55.4867i	0.863674	−	1.76348i
$991$	2.52415	−	0.445076i	0.0801824	−	0.0141383i	−0.133413	−	0.991061i	$-0.542594\pi$
$991$	2.52415	−	0.445076i	0.0801824	−	0.0141383i	0.213595	+	0.976922i	$0.431483\pi$
$992$	−0.573936	−	1.57688i	−0.0182225	−	0.0500659i
$993$	6.70761	+	16.6410i	0.212860	+	0.528086i
$994$	−26.9203	+	9.79819i	−0.853860	+	0.310780i
$995$			24.7588i			0.784906i
$996$	−9.38562	−	10.4409i	−0.297395	−	0.330833i
$997$	−9.33939	+	52.9663i	−0.295781	+	1.67746i	0.368228	+	0.929736i	$0.379965\pi$
$997$	−9.33939	+	52.9663i	−0.295781	+	1.67746i	−0.664009	+	0.747724i	$0.731146\pi$
$998$	29.0554	−	10.5753i	0.919732	−	0.334755i
$999$	−4.16853	−	1.86819i	−0.131887	−	0.0591070i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.x.c.281.9	yes	60
9.5	odd	6		342.2.bf.c.167.10	yes	60
19.14	odd	18		342.2.bf.c.299.10	yes	60
171.14	even	18	inner	342.2.x.c.185.9	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.x.c.185.9	✓	60	171.14	even	18	inner
342.2.x.c.281.9	yes	60	1.1	even	1	trivial
342.2.bf.c.167.10	yes	60	9.5	odd	6
342.2.bf.c.299.10	yes	60	19.14	odd	18

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(1.60646 - 0.647527i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-1.41442 + 3.88608i) q^{5} +(0.814396 - 1.52865i) q^{6} +(2.04763 + 3.54660i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.16142 - 2.08045i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(1.60646 - 0.647527i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-1.41442 + 3.88608i) q^{5} +(0.814396 - 1.52865i) q^{6} +(2.04763 + 3.54660i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.16142 - 2.08045i) q^{9} +(1.41442 + 3.88608i) q^{10} -4.97998i q^{11} +(-0.358731 - 1.69449i) q^{12} +(0.452603 + 1.24352i) q^{13} +(3.84828 + 1.40066i) q^{14} +(0.244139 + 7.15870i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.10469 - 3.03510i) q^{17} +(0.318454 - 2.98305i) q^{18} +(-1.63432 + 4.04092i) q^{19} +(3.58143 + 2.06774i) q^{20} +(5.58595 + 4.37157i) q^{21} +(-3.20107 - 3.81489i) q^{22} +(-3.60155 - 0.635050i) q^{23} +(-1.36400 - 1.06747i) q^{24} +(-9.27084 - 7.77916i) q^{25} +(1.14603 + 0.661661i) q^{26} +(2.12508 - 4.74173i) q^{27} +(3.84828 - 1.40066i) q^{28} +(1.14546 - 6.49624i) q^{29} +(4.78855 + 5.32696i) q^{30} +1.67808i q^{31} +(-0.939693 + 0.342020i) q^{32} +(-3.22467 - 8.00013i) q^{33} +(-1.10469 - 3.03510i) q^{34} +(-16.6786 + 2.94088i) q^{35} +(-1.67352 - 2.48985i) q^{36} -0.879116i q^{37} +(1.34549 + 4.14604i) q^{38} +(1.53230 + 1.70459i) q^{39} +(4.07266 - 0.718119i) q^{40} +(0.319184 - 0.267827i) q^{41} +(7.08907 - 0.241764i) q^{42} +(-0.381958 - 2.16619i) q^{43} +(-4.90432 - 0.864764i) q^{44} +(5.02765 + 11.3421i) q^{45} +(-3.16715 + 1.82855i) q^{46} +(-8.12523 - 1.43270i) q^{47} +(-1.73104 + 0.0590351i) q^{48} +(-4.88556 + 8.46204i) q^{49} -12.1022 q^{50} +(-0.190677 - 5.59109i) q^{51} +(1.30322 - 0.229793i) q^{52} +(1.78669 + 1.49921i) q^{53} +(-1.42002 - 4.99835i) q^{54} +(19.3526 + 7.04378i) q^{55} +(2.04763 - 3.54660i) q^{56} +(-0.00886369 + 7.54983i) q^{57} +(-3.29823 - 5.71270i) q^{58} +(1.22642 + 6.95540i) q^{59} +(7.09234 + 1.00267i) q^{60} +(5.46876 - 1.99047i) q^{61} +(1.07865 + 1.28548i) q^{62} +(11.8043 + 3.40569i) q^{63} +(-0.500000 + 0.866025i) q^{64} -5.47258 q^{65} +(-7.61263 - 4.05568i) q^{66} +(4.68587 - 5.58440i) q^{67} +(-2.79717 - 1.61495i) q^{68} +(-6.19695 + 1.31192i) q^{69} +(-10.8862 + 12.9736i) q^{70} +(-5.35879 + 4.49656i) q^{71} +(-2.88243 - 0.831618i) q^{72} +(-0.522366 - 2.96249i) q^{73} +(-0.565085 - 0.673442i) q^{74} +(-19.9304 - 6.49377i) q^{75} +(3.69573 + 2.31119i) q^{76} +(17.6620 - 10.1971i) q^{77} +(2.26950 + 0.320846i) q^{78} +(-3.63432 + 9.98520i) q^{79} +(2.65824 - 3.16796i) q^{80} +(0.343453 - 8.99344i) q^{81} +(0.0723531 - 0.410335i) q^{82} +(7.01966 - 4.05280i) q^{83} +(5.27514 - 4.74197i) q^{84} +(10.2322 + 8.58582i) q^{85} +(-1.68500 - 1.41388i) q^{86} +(-2.36635 - 11.1777i) q^{87} +(-4.31279 + 2.48999i) q^{88} +(-1.49181 + 8.46047i) q^{89} +(11.1420 + 5.45682i) q^{90} +(-3.48349 + 4.15146i) q^{91} +(-1.25080 + 3.43656i) q^{92} +(1.08660 + 2.69576i) q^{93} +(-7.14521 + 4.12529i) q^{94} +(-13.3917 - 12.0666i) q^{95} +(-1.28811 + 1.15792i) q^{96} +(5.33788 + 6.36144i) q^{97} +(1.69674 + 9.62268i) q^{98} +(-10.3606 - 10.7638i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 6 q^{3} - 30 q^{8} + 6 q^{9}+O(q^{10}) \) 60 * q - 6 * q^3 - 30 * q^8 + 6 * q^9	\( 60 q - 6 q^{3} - 30 q^{8} + 6 q^{9} + 3 q^{13} + 3 q^{14} + 27 q^{15} - 27 q^{17} - 18 q^{18} + 3 q^{19} + 18 q^{23} + 3 q^{24} - 6 q^{27} + 3 q^{28} + 57 q^{33} + 27 q^{34} + 9 q^{38} - 30 q^{39} + 9 q^{41} - 3 q^{43} - 9 q^{44} + 27 q^{45} - 30 q^{49} - 132 q^{50} - 66 q^{51} + 6 q^{52} + 27 q^{54} + 102 q^{57} - 54 q^{59} + 6 q^{60} - 24 q^{61} - 3 q^{62} - 30 q^{64} + 36 q^{65} - 63 q^{66} + 51 q^{67} - 18 q^{68} + 3 q^{69} - 18 q^{71} - 3 q^{72} - 66 q^{73} - 6 q^{74} + 3 q^{78} - 51 q^{79} - 30 q^{81} - 36 q^{83} + 60 q^{84} - 3 q^{86} + 54 q^{87} - 27 q^{89} + 36 q^{90} - 69 q^{91} + 69 q^{93} + 18 q^{94} - 27 q^{95} + 81 q^{97} + 60 q^{98} + 51 q^{99}+O(q^{100}) \) 60 * q - 6 * q^3 - 30 * q^8 + 6 * q^9 + 3 * q^13 + 3 * q^14 + 27 * q^15 - 27 * q^17 - 18 * q^18 + 3 * q^19 + 18 * q^23 + 3 * q^24 - 6 * q^27 + 3 * q^28 + 57 * q^33 + 27 * q^34 + 9 * q^38 - 30 * q^39 + 9 * q^41 - 3 * q^43 - 9 * q^44 + 27 * q^45 - 30 * q^49 - 132 * q^50 - 66 * q^51 + 6 * q^52 + 27 * q^54 + 102 * q^57 - 54 * q^59 + 6 * q^60 - 24 * q^61 - 3 * q^62 - 30 * q^64 + 36 * q^65 - 63 * q^66 + 51 * q^67 - 18 * q^68 + 3 * q^69 - 18 * q^71 - 3 * q^72 - 66 * q^73 - 6 * q^74 + 3 * q^78 - 51 * q^79 - 30 * q^81 - 36 * q^83 + 60 * q^84 - 3 * q^86 + 54 * q^87 - 27 * q^89 + 36 * q^90 - 69 * q^91 + 69 * q^93 + 18 * q^94 - 27 * q^95 + 81 * q^97 + 60 * q^98 + 51 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more