LMFDB - Embedded newform 378.2.u.e.211.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("378.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			211.2
Character	$\chi$	$=$	378.211
Dual form			378.2.u.e.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(-1.15570 + 1.29010i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-2.06967 + 0.753297i) q^{5} +(0.0560567 - 1.73114i) q^{6} +(0.173648 + 0.984808i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.328718 - 2.98194i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.15570 + 1.29010i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-2.06967 + 0.753297i) q^{5} +(0.0560567 - 1.73114i) q^{6} +(0.173648 + 0.984808i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.328718 - 2.98194i) q^{9} +(1.10125 - 1.90741i) q^{10} +(-5.37922 - 1.95788i) q^{11} +(1.06982 + 1.36217i) q^{12} +(2.61316 + 2.19270i) q^{13} +(-0.766044 - 0.642788i) q^{14} +(1.42008 - 3.54066i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.91274 - 3.31296i) q^{17} +(2.16856 + 2.07300i) q^{18} +(-0.761298 - 1.31861i) q^{19} +(0.382459 + 2.16903i) q^{20} +(-1.47119 - 0.914118i) q^{21} +(5.37922 - 1.95788i) q^{22} +(0.898594 - 5.09618i) q^{23} +(-1.69511 - 0.355815i) q^{24} +(-0.114163 + 0.0957945i) q^{25} -3.41124 q^{26} +(4.22690 + 3.02214i) q^{27} +1.00000 q^{28} +(-0.792586 + 0.665059i) q^{29} +(1.18805 + 3.62511i) q^{30} +(1.63955 - 9.29835i) q^{31} +(0.939693 - 0.342020i) q^{32} +(8.74262 - 4.67702i) q^{33} +(0.664288 + 3.76736i) q^{34} +(-1.10125 - 1.90741i) q^{35} +(-2.99372 - 0.194084i) q^{36} +(1.40410 - 2.43197i) q^{37} +(1.43077 + 0.520758i) q^{38} +(-5.84883 + 0.837135i) q^{39} +(-1.68721 - 1.41573i) q^{40} +(1.73883 + 1.45905i) q^{41} +(1.71458 - 0.245405i) q^{42} +(-6.53745 - 2.37944i) q^{43} +(-2.86222 + 4.95752i) q^{44} +(2.92662 + 5.92399i) q^{45} +(2.58740 + 4.48151i) q^{46} +(0.242556 + 1.37560i) q^{47} +(1.52724 - 0.817025i) q^{48} +(-0.939693 + 0.342020i) q^{49} +(0.0258788 - 0.146766i) q^{50} +(2.06350 + 6.29642i) q^{51} +(2.61316 - 2.19270i) q^{52} -7.06536 q^{53} +(-5.18059 + 0.401900i) q^{54} +12.6080 q^{55} +(-0.766044 + 0.642788i) q^{56} +(2.58097 + 0.541762i) q^{57} +(0.179665 - 1.01893i) q^{58} +(-4.62505 + 1.68338i) q^{59} +(-3.24027 - 2.01334i) q^{60} +(-0.390021 - 2.21192i) q^{61} +(4.72089 + 8.17683i) q^{62} +(2.87955 - 0.841531i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-7.06012 - 2.56967i) q^{65} +(-3.69091 + 9.20245i) q^{66} +(-9.77848 - 8.20512i) q^{67} +(-2.93049 - 2.45897i) q^{68} +(5.53608 + 7.04893i) q^{69} +(2.06967 + 0.753297i) q^{70} +(-2.19392 + 3.79999i) q^{71} +(2.41807 - 1.77565i) q^{72} +(0.0771978 + 0.133710i) q^{73} +(0.487638 + 2.76554i) q^{74} +(0.00835411 - 0.257992i) q^{75} +(-1.43077 + 0.520758i) q^{76} +(0.994040 - 5.63748i) q^{77} +(3.94237 - 4.40084i) q^{78} +(-8.88609 + 7.45631i) q^{79} +2.20249 q^{80} +(-8.78389 + 1.96043i) q^{81} -2.26988 q^{82} +(-2.52975 + 2.12271i) q^{83} +(-1.15570 + 1.29010i) q^{84} +(-1.46309 + 8.29759i) q^{85} +(6.53745 - 2.37944i) q^{86} +(0.0579989 - 1.79112i) q^{87} +(-0.994040 - 5.63748i) q^{88} +(-6.18042 - 10.7048i) q^{89} +(-6.04979 - 2.65684i) q^{90} +(-1.70562 + 2.95422i) q^{91} +(-4.86272 - 1.76988i) q^{92} +(10.1010 + 12.8613i) q^{93} +(-1.07003 - 0.897862i) q^{94} +(2.56893 + 2.15559i) q^{95} +(-0.644762 + 1.60757i) q^{96} +(-7.77738 - 2.83073i) q^{97} +(0.500000 - 0.866025i) q^{98} +(-4.07002 + 16.6841i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9}+O(q^{10}) $ 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9	$ 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{13} - 6 q^{15} + 6 q^{18} - 15 q^{19} - 6 q^{20} + 3 q^{21} - 3 q^{24} - 3 q^{25} - 18 q^{26} - 30 q^{27} + 36 q^{28} - 6 q^{29} - 9 q^{30} + 60 q^{33} + 9 q^{34} + 3 q^{35} - 27 q^{37} + 15 q^{38} + 6 q^{39} - 3 q^{40} - 9 q^{41} - 6 q^{43} + 9 q^{44} + 42 q^{45} - 9 q^{46} + 36 q^{47} + 3 q^{48} - 15 q^{50} - 36 q^{51} + 9 q^{52} - 42 q^{53} - 27 q^{54} + 30 q^{55} - 18 q^{57} - 21 q^{58} + 12 q^{59} + 24 q^{60} + 3 q^{61} + 18 q^{62} + 12 q^{63} - 18 q^{64} - 84 q^{65} + 18 q^{66} - 69 q^{67} + 9 q^{68} - 48 q^{69} - 3 q^{70} + 12 q^{71} + 6 q^{72} - 12 q^{73} + 9 q^{75} - 15 q^{76} + 9 q^{77} - 48 q^{78} - 51 q^{79} - 6 q^{80} - 69 q^{81} + 15 q^{83} + 3 q^{84} - 12 q^{85} + 6 q^{86} + 84 q^{87} - 9 q^{88} - 3 q^{89} + 6 q^{90} - 9 q^{91} + 18 q^{92} - 21 q^{93} + 9 q^{94} - 75 q^{95} - 42 q^{97} + 18 q^{98} + 39 q^{99}+O(q^{100}) $ 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9 - 3 * q^10 + 9 * q^13 - 6 * q^15 + 6 * q^18 - 15 * q^19 - 6 * q^20 + 3 * q^21 - 3 * q^24 - 3 * q^25 - 18 * q^26 - 30 * q^27 + 36 * q^28 - 6 * q^29 - 9 * q^30 + 60 * q^33 + 9 * q^34 + 3 * q^35 - 27 * q^37 + 15 * q^38 + 6 * q^39 - 3 * q^40 - 9 * q^41 - 6 * q^43 + 9 * q^44 + 42 * q^45 - 9 * q^46 + 36 * q^47 + 3 * q^48 - 15 * q^50 - 36 * q^51 + 9 * q^52 - 42 * q^53 - 27 * q^54 + 30 * q^55 - 18 * q^57 - 21 * q^58 + 12 * q^59 + 24 * q^60 + 3 * q^61 + 18 * q^62 + 12 * q^63 - 18 * q^64 - 84 * q^65 + 18 * q^66 - 69 * q^67 + 9 * q^68 - 48 * q^69 - 3 * q^70 + 12 * q^71 + 6 * q^72 - 12 * q^73 + 9 * q^75 - 15 * q^76 + 9 * q^77 - 48 * q^78 - 51 * q^79 - 6 * q^80 - 69 * q^81 + 15 * q^83 + 3 * q^84 - 12 * q^85 + 6 * q^86 + 84 * q^87 - 9 * q^88 - 3 * q^89 + 6 * q^90 - 9 * q^91 + 18 * q^92 - 21 * q^93 + 9 * q^94 - 75 * q^95 - 42 * q^97 + 18 * q^98 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	−1.15570	+	1.29010i	−0.667243	+	0.744840i
$3$	−1.15570	+	1.29010i	−0.667243	+	0.744840i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−2.06967	+	0.753297i	−0.925582	+	0.336884i	−0.760457	−	0.649388i	$-0.775025\pi$
$5$	−2.06967	+	0.753297i	−0.925582	+	0.336884i	−0.165125	+	0.986273i	$0.552803\pi$
$6$	0.0560567	−	1.73114i	0.0228850	−	0.706736i
$7$	0.173648	+	0.984808i	0.0656328	+	0.372222i
$7$	0.173648	+	0.984808i	0.0656328	+	0.372222i
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−0.328718	−	2.98194i	−0.109573	−	0.993979i
$10$	1.10125	−	1.90741i	0.348245	−	0.603177i
$11$	−5.37922	−	1.95788i	−1.62190	−	0.590322i	−0.638154	−	0.769909i	$-0.720302\pi$
$11$	−5.37922	−	1.95788i	−1.62190	−	0.590322i	−0.983742	+	0.179587i	$0.942524\pi$
$12$	1.06982	+	1.36217i	0.308829	+	0.393223i
$13$	2.61316	+	2.19270i	0.724760	+	0.608146i	0.928698	−	0.370838i	$-0.120929\pi$
$13$	2.61316	+	2.19270i	0.724760	+	0.608146i	−0.203937	+	0.978984i	$0.565374\pi$
$14$	−0.766044	−	0.642788i	−0.204734	−	0.171792i
$15$	1.42008	−	3.54066i	0.366664	−	0.914195i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	1.91274	−	3.31296i	0.463908	−	0.803512i	−0.535244	−	0.844698i	$-0.679780\pi$
$17$	1.91274	−	3.31296i	0.463908	−	0.803512i	0.999152	+	0.0411859i	$0.0131136\pi$
$18$	2.16856	+	2.07300i	0.511135	+	0.488611i
$19$	−0.761298	−	1.31861i	−0.174654	−	0.302509i	0.765388	−	0.643569i	$-0.222547\pi$
$19$	−0.761298	−	1.31861i	−0.174654	−	0.302509i	−0.940041	+	0.341060i	$0.889214\pi$
$20$	0.382459	+	2.16903i	0.0855204	+	0.485010i
$21$	−1.47119	−	0.914118i	−0.321039	−	0.199477i
$22$	5.37922	−	1.95788i	1.14685	−	0.417421i
$23$	0.898594	−	5.09618i	0.187370	−	1.06263i	−0.735503	−	0.677522i	$-0.763054\pi$
$23$	0.898594	−	5.09618i	0.187370	−	1.06263i	0.922873	−	0.385105i	$-0.125835\pi$
$24$	−1.69511	−	0.355815i	−0.346013	−	0.0726304i
$25$	−0.114163	+	0.0957945i	−0.0228327	+	0.0191589i
$26$	−3.41124			−0.668999
$27$	4.22690	+	3.02214i	0.813466	+	0.581612i
$28$	1.00000			0.188982
$29$	−0.792586	+	0.665059i	−0.147180	+	0.123498i	−0.713405	−	0.700752i	$-0.752848\pi$
$29$	−0.792586	+	0.665059i	−0.147180	+	0.123498i	0.566225	+	0.824251i	$0.308403\pi$
$30$	1.18805	+	3.62511i	0.216907	+	0.661852i
$31$	1.63955	−	9.29835i	0.294472	−	1.67003i	−0.374870	−	0.927077i	$-0.622313\pi$
$31$	1.63955	−	9.29835i	0.294472	−	1.67003i	0.669342	−	0.742955i	$-0.266576\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	8.74262	−	4.67702i	1.52189	−	0.814164i
$34$	0.664288	+	3.76736i	0.113924	+	0.646098i
$35$	−1.10125	−	1.90741i	−0.186145	−	0.322412i
$36$	−2.99372	−	0.194084i	−0.498953	−	0.0323474i
$37$	1.40410	−	2.43197i	0.230832	−	0.399814i	−0.727221	−	0.686404i	$-0.759188\pi$
$37$	1.40410	−	2.43197i	0.230832	−	0.399814i	0.958053	+	0.286590i	$0.0925217\pi$
$38$	1.43077	+	0.520758i	0.232102	+	0.0844782i
$39$	−5.84883	+	0.837135i	−0.936563	+	0.134049i
$40$	−1.68721	−	1.41573i	−0.266771	−	0.223847i
$41$	1.73883	+	1.45905i	0.271559	+	0.227865i	0.768390	−	0.639982i	$-0.221058\pi$
$41$	1.73883	+	1.45905i	0.271559	+	0.227865i	−0.496830	+	0.867848i	$0.665503\pi$
$42$	1.71458	−	0.245405i	0.264565	−	0.0378668i
$43$	−6.53745	−	2.37944i	−0.996952	−	0.362861i	−0.208544	−	0.978013i	$-0.566872\pi$
$43$	−6.53745	−	2.37944i	−0.996952	−	0.362861i	−0.788408	+	0.615152i	$0.789095\pi$
$44$	−2.86222	+	4.95752i	−0.431496	+	0.747374i
$45$	2.92662	+	5.92399i	0.436274	+	0.883096i
$46$	2.58740	+	4.48151i	0.381491	+	0.660762i
$47$	0.242556	+	1.37560i	0.0353804	+	0.200652i	0.997374	−	0.0724185i	$-0.0230717\pi$
$47$	0.242556	+	1.37560i	0.0353804	+	0.200652i	−0.961994	+	0.273071i	$0.911961\pi$
$48$	1.52724	−	0.817025i	0.220438	−	0.117927i
$49$	−0.939693	+	0.342020i	−0.134242	+	0.0488600i
$50$	0.0258788	−	0.146766i	0.00365981	−	0.0207558i
$51$	2.06350	+	6.29642i	0.288948	+	0.881675i
$52$	2.61316	−	2.19270i	0.362380	−	0.304073i
$53$	−7.06536			−0.970502			−0.485251	−	0.874375i	$-0.661272\pi$
$53$	−7.06536			−0.970502			−0.485251	+	0.874375i	$0.661272\pi$
$54$	−5.18059	+	0.401900i	−0.704989	+	0.0546916i
$55$	12.6080			1.70007
$56$	−0.766044	+	0.642788i	−0.102367	+	0.0858961i
$57$	2.58097	+	0.541762i	0.341857	+	0.0717582i
$58$	0.179665	−	1.01893i	0.0235911	−	0.133792i
$59$	−4.62505	+	1.68338i	−0.602131	+	0.219158i	−0.625056	−	0.780580i	$-0.714924\pi$
$59$	−4.62505	+	1.68338i	−0.602131	+	0.219158i	0.0229258	+	0.999737i	$0.492702\pi$
$60$	−3.24027	−	2.01334i	−0.418318	−	0.259921i
$61$	−0.390021	−	2.21192i	−0.0499371	−	0.283207i	0.949606	−	0.313447i	$-0.101484\pi$
$61$	−0.390021	−	2.21192i	−0.0499371	−	0.283207i	−0.999543	+	0.0302402i	$0.990373\pi$
$62$	4.72089	+	8.17683i	0.599554	+	1.03846i
$63$	2.87955	−	0.841531i	0.362790	−	0.106023i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−7.06012	−	2.56967i	−0.875700	−	0.318729i
$66$	−3.69091	+	9.20245i	−0.454319	+	1.13274i
$67$	−9.77848	−	8.20512i	−1.19463	−	1.00242i	−0.999767	−	0.0215851i	$-0.993129\pi$
$67$	−9.77848	−	8.20512i	−1.19463	−	1.00242i	−0.194865	−	0.980830i	$-0.562427\pi$
$68$	−2.93049	−	2.45897i	−0.355374	−	0.298194i
$69$	5.53608	+	7.04893i	0.666465	+	0.848591i
$70$	2.06967	+	0.753297i	0.247372	+	0.0900362i
$71$	−2.19392	+	3.79999i	−0.260371	+	0.450975i	−0.966340	−	0.257267i	$-0.917178\pi$
$71$	−2.19392	+	3.79999i	−0.260371	+	0.450975i	0.705970	+	0.708242i	$0.250511\pi$
$72$	2.41807	−	1.77565i	0.284973	−	0.209262i
$73$	0.0771978	+	0.133710i	0.00903531	+	0.0156496i	0.870508	−	0.492155i	$-0.163791\pi$
$73$	0.0771978	+	0.133710i	0.00903531	+	0.0156496i	−0.861472	+	0.507804i	$0.830457\pi$
$74$	0.487638	+	2.76554i	0.0566868	+	0.321487i
$75$	0.00835411	−	0.257992i	0.000964650	−	0.0297903i
$76$	−1.43077	+	0.520758i	−0.164121	+	0.0597351i
$77$	0.994040	−	5.63748i	0.113281	−	0.642451i
$78$	3.94237	−	4.40084i	0.446385	−	0.498297i
$79$	−8.88609	+	7.45631i	−0.999763	+	0.838901i	−0.986952	−	0.161017i	$-0.948523\pi$
$79$	−8.88609	+	7.45631i	−0.999763	+	0.838901i	−0.0128116	+	0.999918i	$0.504078\pi$
$80$	2.20249			0.246246
$81$	−8.78389	+	1.96043i	−0.975988	+	0.217826i
$82$	−2.26988			−0.250666
$83$	−2.52975	+	2.12271i	−0.277676	+	0.232998i	−0.770980	−	0.636859i	$-0.780233\pi$
$83$	−2.52975	+	2.12271i	−0.277676	+	0.232998i	0.493304	+	0.869857i	$0.335789\pi$
$84$	−1.15570	+	1.29010i	−0.126097	+	0.140761i
$85$	−1.46309	+	8.29759i	−0.158694	+	0.900000i
$86$	6.53745	−	2.37944i	0.704952	−	0.256581i
$87$	0.0579989	−	1.79112i	0.00621813	−	0.192029i
$88$	−0.994040	−	5.63748i	−0.105965	−	0.600957i
$89$	−6.18042	−	10.7048i	−0.655123	−	1.13471i	−0.981863	−	0.189592i	$-0.939284\pi$
$89$	−6.18042	−	10.7048i	−0.655123	−	1.13471i	0.326740	−	0.945114i	$-0.394050\pi$
$90$	−6.04979	−	2.65684i	−0.637703	−	0.280056i
$91$	−1.70562	+	2.95422i	−0.178798	+	0.309686i
$92$	−4.86272	−	1.76988i	−0.506973	−	0.184523i
$93$	10.1010	+	12.8613i	1.04742	+	1.33365i
$94$	−1.07003	−	0.897862i	−0.110365	−	0.0926074i
$95$	2.56893	+	2.15559i	0.263567	+	0.221159i
$96$	−0.644762	+	1.60757i	−0.0658057	+	0.164072i
$97$	−7.77738	−	2.83073i	−0.789673	−	0.287417i	−0.0844728	−	0.996426i	$-0.526921\pi$
$97$	−7.77738	−	2.83073i	−0.789673	−	0.287417i	−0.705200	+	0.709008i	$0.749143\pi$
$98$	0.500000	−	0.866025i	0.0505076	−	0.0874818i
$99$	−4.07002	+	16.6841i	−0.409052	+	1.67681i
$100$	0.0745149	+	0.129064i	0.00745149	+	0.0129064i
$101$	2.75795	+	15.6411i	0.274427	+	1.55635i	0.740777	+	0.671751i	$0.234457\pi$
$101$	2.75795	+	15.6411i	0.274427	+	1.55635i	−0.466351	+	0.884600i	$0.654431\pi$
$102$	−5.62799	−	3.49694i	−0.557254	−	0.346249i
$103$	−15.6827	+	5.70804i	−1.54526	+	0.562430i	−0.967301	−	0.253632i	$-0.918375\pi$
$103$	−15.6827	+	5.70804i	−1.54526	+	0.562430i	−0.577964	+	0.816062i	$0.696153\pi$
$104$	−0.592355	+	3.35941i	−0.0580852	+	0.329418i
$105$	3.73346	+	0.783679i	0.364349	+	0.0764793i
$106$	5.41238	−	4.54153i	0.525697	−	0.441112i
$107$	−5.19185			−0.501915			−0.250958	−	0.967998i	$-0.580746\pi$
$107$	−5.19185			−0.501915			−0.250958	+	0.967998i	$0.580746\pi$
$108$	3.71022	−	3.63789i	0.357016	−	0.350056i
$109$	12.5134			1.19857			0.599284	−	0.800536i	$-0.295452\pi$
$109$	12.5134			1.19857			0.599284	+	0.800536i	$0.295452\pi$
$110$	−9.65833	+	8.10430i	−0.920885	+	0.772714i
$111$	1.51477	+	4.62206i	0.143776	+	0.438706i
$112$	0.173648	−	0.984808i	0.0164082	−	0.0930556i
$113$	19.7344	−	7.18273i	1.85646	−	0.675694i	0.874964	−	0.484189i	$-0.160885\pi$
$113$	19.7344	−	7.18273i	1.85646	−	0.675694i	0.981492	−	0.191506i	$-0.0613370\pi$
$114$	−2.32537	+	1.24400i	−0.217791	+	0.116511i
$115$	1.97915	+	11.2243i	0.184556	+	1.04667i
$116$	0.517324	+	0.896031i	0.0480323	+	0.0831944i
$117$	5.67951	−	8.51306i	0.525071	−	0.787033i
$118$	2.46094	−	4.26247i	0.226548	−	0.392392i
$119$	3.59478	+	1.30839i	0.329533	+	0.119940i
$120$	3.77634	−	0.540502i	0.344731	−	0.0493409i
$121$	16.6763	+	13.9930i	1.51602	+	1.27209i
$122$	1.72057	+	1.44373i	0.155773	+	0.130709i
$123$	−3.89188	+	0.557039i	−0.350919	+	0.0502265i
$124$	−8.87238	−	3.22928i	−0.796763	−	0.289998i
$125$	5.67035	−	9.82133i	0.507171	−	0.878447i
$126$	−1.66494	+	2.49559i	−0.148325	+	0.222325i
$127$	−4.02414	−	6.97001i	−0.357085	−	0.618489i	0.630388	−	0.776280i	$-0.282896\pi$
$127$	−4.02414	−	6.97001i	−0.357085	−	0.618489i	−0.987472	+	0.157792i	$0.949563\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	10.6250	−	5.68405i	0.935483	−	0.500453i
$130$	7.06012	−	2.56967i	0.619214	−	0.225375i
$131$	−3.45711	+	19.6063i	−0.302049	+	1.71301i	0.335028	+	0.942208i	$0.391254\pi$
$131$	−3.45711	+	19.6063i	−0.302049	+	1.71301i	−0.637078	+	0.770800i	$0.719857\pi$
$132$	−3.08782	−	9.42196i	−0.268761	−	0.820076i
$133$	1.16638	−	0.978706i	0.101138	−	0.0848645i
$134$	12.7649			1.10272
$135$	−11.0248	−	3.07072i	−0.948866	−	0.264285i
$136$	3.82548			0.328032
$137$	−1.25015	+	1.04900i	−0.106807	+	0.0896219i	−0.694627	−	0.719370i	$-0.744431\pi$
$137$	−1.25015	+	1.04900i	−0.106807	+	0.0896219i	0.587820	+	0.808992i	$0.299986\pi$
$138$	−8.77185	−	1.84127i	−0.746709	−	0.156739i
$139$	2.36390	−	13.4064i	0.200504	−	1.13711i	−0.703856	−	0.710342i	$-0.748540\pi$
$139$	2.36390	−	13.4064i	0.200504	−	1.13711i	0.904360	−	0.426771i	$-0.140349\pi$
$140$	−2.06967	+	0.753297i	−0.174919	+	0.0636652i
$141$	−2.05499	−	1.27686i	−0.173061	−	0.107531i
$142$	−0.761942	−	4.32119i	−0.0639407	−	0.362626i
$143$	−9.76373	−	16.9113i	−0.816484	−	1.41419i
$144$	−0.710989	+	2.91453i	−0.0592491	+	0.242878i
$145$	1.13940	−	1.97350i	0.0946221	−	0.163890i
$146$	−0.145084	−	0.0528064i	−0.0120073	−	0.00437029i
$147$	0.644762	−	1.60757i	0.0531791	−	0.132590i
$148$	−2.15120	−	1.80507i	−0.176828	−	0.148376i
$149$	−17.7456	−	14.8903i	−1.45377	−	1.21986i	−0.929767	−	0.368147i	$-0.879992\pi$
$149$	−17.7456	−	14.8903i	−1.45377	−	1.21986i	−0.524007	−	0.851714i	$-0.675563\pi$
$150$	0.159434	+	0.203003i	0.0130178	+	0.0165751i
$151$	−15.5807	−	5.67091i	−1.26794	−	0.461492i	−0.381513	−	0.924363i	$-0.624597\pi$
$151$	−15.5807	−	5.67091i	−1.26794	−	0.461492i	−0.886425	+	0.462872i	$0.846819\pi$
$152$	0.761298	−	1.31861i	0.0617494	−	0.106953i
$153$	−10.5078	−	4.61464i	−0.849505	−	0.373072i
$154$	2.86222	+	4.95752i	0.230645	+	0.399488i
$155$	3.61109	+	20.4795i	0.290050	+	1.64496i
$156$	−0.191223	+	5.90534i	−0.0153101	+	0.472806i
$157$	13.9480	−	5.07667i	1.11317	−	0.405163i	0.281018	−	0.959703i	$-0.409328\pi$
$157$	13.9480	−	5.07667i	1.11317	−	0.405163i	0.832157	+	0.554540i	$0.187106\pi$
$158$	2.01431	−	11.4237i	0.160250	−	0.908824i
$159$	8.16544	−	9.11503i	0.647561	−	0.722869i
$160$	−1.68721	+	1.41573i	−0.133385	+	0.111924i
$161$	5.17480			0.407831
$162$	5.46871	−	7.14795i	0.429662	−	0.561596i
$163$	16.4073			1.28512			0.642558	−	0.766237i	$-0.277873\pi$
$163$	16.4073			1.28512			0.642558	+	0.766237i	$0.277873\pi$
$164$	1.73883	−	1.45905i	0.135780	−	0.113933i
$165$	−14.5711	+	16.2656i	−1.13436	+	1.26628i
$166$	0.573447	−	3.25218i	0.0445081	−	0.252418i
$167$	16.3524	−	5.95179i	1.26539	−	0.460564i	0.379815	−	0.925063i	$-0.375988\pi$
$167$	16.3524	−	5.95179i	1.26539	−	0.460564i	0.885574	+	0.464499i	$0.153766\pi$
$168$	0.0560567	−	1.73114i	0.00432486	−	0.133561i
$169$	−0.236760	−	1.34273i	−0.0182123	−	0.103287i
$170$	−4.21280	−	7.29678i	−0.323107	−	0.559637i
$171$	−3.68175	+	2.70359i	−0.281550	+	0.206749i
$172$	−3.47851	+	6.02495i	−0.265234	+	0.459398i
$173$	9.02880	+	3.28621i	0.686447	+	0.249846i	0.661613	−	0.749845i	$-0.269872\pi$
$173$	9.02880	+	3.28621i	0.686447	+	0.249846i	0.0248337	+	0.999692i	$0.492094\pi$
$174$	1.10688	+	1.40936i	0.0839125	+	0.106843i
$175$	−0.114163	−	0.0957945i	−0.00862995	−	0.00724138i
$176$	4.38518	+	3.67960i	0.330545	+	0.277361i
$177$	3.17344	−	7.91227i	0.238530	−	0.594722i
$178$	11.6154	+	4.22765i	0.870610	+	0.316876i
$179$	8.03304	−	13.9136i	0.600418	−	1.03995i	−0.392340	−	0.919820i	$-0.628334\pi$
$179$	8.03304	−	13.9136i	0.600418	−	1.03995i	0.992758	−	0.120134i	$-0.0383324\pi$
$180$	6.34219	−	1.85347i	0.472719	−	0.138149i
$181$	−0.451806	−	0.782550i	−0.0335824	−	0.0581665i	0.848746	−	0.528801i	$-0.177358\pi$
$181$	−0.451806	−	0.782550i	−0.0335824	−	0.0581665i	−0.882328	+	0.470635i	$0.844025\pi$
$182$	−0.592355	−	3.35941i	−0.0439083	−	0.249016i
$183$	3.30434	+	2.05315i	0.244264	+	0.151773i
$184$	4.86272	−	1.76988i	0.358484	−	0.130478i
$185$	−1.07402	+	6.09107i	−0.0789635	+	0.447824i
$186$	−16.0049	−	3.35953i	−1.17353	−	0.246333i
$187$	−16.7754	+	14.0763i	−1.22674	+	1.02936i
$188$	1.39682			0.101874
$189$	−2.24224	+	4.68747i	−0.163099	+	0.340963i
$190$	−3.35350			−0.243289
$191$	14.9544	−	12.5483i	1.08207	−	0.907961i	0.0859750	−	0.996297i	$-0.472599\pi$
$191$	14.9544	−	12.5483i	1.08207	−	0.907961i	0.996091	+	0.0883364i	$0.0281550\pi$
$192$	−0.539410	−	1.64592i	−0.0389286	−	0.118784i
$193$	−4.05320	+	22.9868i	−0.291756	+	1.65463i	0.388347	+	0.921513i	$0.373046\pi$
$193$	−4.05320	+	22.9868i	−0.291756	+	1.65463i	−0.680103	+	0.733116i	$0.738065\pi$
$194$	7.77738	−	2.83073i	0.558383	−	0.203235i
$195$	11.4745	−	6.13850i	0.821707	−	0.439587i
$196$	0.173648	+	0.984808i	0.0124034	+	0.0703434i
$197$	−7.99997	−	13.8563i	−0.569974	−	0.987224i	−0.996568	−	0.0827806i	$-0.973620\pi$
$197$	−7.99997	−	13.8563i	−0.569974	−	0.987224i	0.426594	−	0.904443i	$-0.359713\pi$
$198$	−7.60651	−	15.3969i	−0.540571	−	1.09421i
$199$	−7.80857	+	13.5248i	−0.553535	+	0.958751i	0.444481	+	0.895788i	$0.353388\pi$
$199$	−7.80857	+	13.5248i	−0.553535	+	0.958751i	−0.998016	+	0.0629625i	$0.979945\pi$
$200$	−0.140042	−	0.0509712i	−0.00990248	−	0.00360421i
$201$	21.8864	−	3.13257i	1.54375	−	0.220954i
$202$	−12.1666	−	10.2090i	−0.856042	−	0.718304i
$203$	−0.792586	−	0.665059i	−0.0556286	−	0.0466780i
$204$	6.55908	−	0.938792i	0.459228	−	0.0657286i
$205$	−4.69789	−	1.70989i	−0.328115	−	0.119424i
$206$	8.34460	−	14.4533i	0.581396	−	1.00701i
$207$	−15.4919	−	1.00435i	−1.07676	−	0.0698069i
$208$	−1.70562	−	2.95422i	−0.118263	−	0.204838i
$209$	1.51352	+	8.58360i	0.104692	+	0.593740i
$210$	−3.36374	+	1.79949i	−0.232120	+	0.124177i
$211$	−13.2530	+	4.82370i	−0.912375	+	0.332077i	−0.755201	−	0.655494i	$-0.772461\pi$
$211$	−13.2530	+	4.82370i	−0.912375	+	0.332077i	−0.157174	+	0.987571i	$0.550238\pi$
$212$	−1.22689	+	6.95802i	−0.0842630	+	0.477879i
$213$	−2.36685	−	7.22202i	−0.162174	−	0.494845i
$214$	3.97719	−	3.33726i	0.271875	−	0.228130i
$215$	15.3228			1.04500
$216$	−0.503805	+	5.17167i	−0.0342796	+	0.351888i
$217$	9.44179			0.640950
$218$	−9.58583	+	8.04347i	−0.649235	+	0.544773i
$219$	−0.261717	−	0.0549362i	−0.0176852	−	0.00371225i
$220$	2.18936	−	12.4165i	0.147607	−	0.837121i
$221$	12.2626	−	4.46324i	0.824875	−	0.300230i
$222$	−4.13138	−	2.56702i	−0.277280	−	0.172287i
$223$	−2.99386	−	16.9790i	−0.200484	−	1.13700i	−0.904390	−	0.426707i	$-0.859674\pi$
$223$	−2.99386	−	16.9790i	−0.200484	−	1.13700i	0.703906	−	0.710293i	$-0.251438\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$	0.323181	+	0.308939i	0.0215454	+	0.0205959i
$226$	−10.5004	+	18.1873i	−0.698479	+	1.20980i
$227$	1.14996	+	0.418552i	0.0763256	+	0.0277802i	0.379901	−	0.925027i	$-0.375958\pi$
$227$	1.14996	+	0.418552i	0.0763256	+	0.0277802i	−0.303575	+	0.952807i	$0.598180\pi$
$228$	0.981712	−	2.44768i	0.0650154	−	0.162102i
$229$	−17.2782	−	14.4982i	−1.14178	−	0.958066i	−0.142283	−	0.989826i	$-0.545444\pi$
$229$	−17.2782	−	14.4982i	−1.14178	−	0.958066i	−0.999496	+	0.0317606i	$0.989889\pi$
$230$	−8.73095	−	7.32614i	−0.575702	−	0.483071i
$231$	6.12410	+	7.79764i	0.402936	+	0.513047i
$232$	−0.972251	−	0.353870i	−0.0638314	−	0.0232327i
$233$	−1.70758	+	2.95761i	−0.111867	+	0.193760i	−0.916523	−	0.399982i	$-0.869016\pi$
$233$	−1.70758	+	2.95761i	−0.111867	+	0.193760i	0.804656	+	0.593741i	$0.202350\pi$
$234$	1.12133	+	10.1721i	0.0733039	+	0.664971i
$235$	−1.53825	−	2.66432i	−0.100344	−	0.173801i
$236$	0.854675	+	4.84710i	0.0556346	+	0.315520i
$237$	0.650255	−	20.0812i	0.0422386	−	1.30441i
$238$	−3.59478	+	1.30839i	−0.233015	+	0.0848104i
$239$	−0.690830	+	3.91789i	−0.0446861	+	0.253428i	−0.998965	−	0.0454910i	$-0.985515\pi$
$239$	−0.690830	+	3.91789i	−0.0446861	+	0.253428i	0.954279	+	0.298919i	$0.0966259\pi$
$240$	−2.54542	+	2.84144i	−0.164306	+	0.183414i
$241$	−7.34887	+	6.16643i	−0.473382	+	0.397215i	−0.848027	−	0.529954i	$-0.822209\pi$
$241$	−7.34887	+	6.16643i	−0.473382	+	0.397215i	0.374644	+	0.927169i	$0.377765\pi$
$242$	−21.7693			−1.39938
$243$	7.62239	−	13.5978i	0.488976	−	0.872297i
$244$	−2.24604			−0.143788
$245$	1.68721	−	1.41573i	0.107792	−	0.0904480i
$246$	2.62330	−	2.92837i	0.167255	−	0.186706i
$247$	0.901918	−	5.11503i	0.0573877	−	0.325462i
$248$	8.87238	−	3.22928i	0.563397	−	0.205060i
$249$	0.185119	−	5.71684i	0.0117314	−	0.362290i
$250$	1.96929	+	11.1684i	0.124549	+	0.706352i
$251$	13.3738	+	23.1640i	0.844144	+	1.46210i	0.886362	+	0.462992i	$0.153224\pi$
$251$	13.3738	+	23.1640i	0.844144	+	1.46210i	−0.0422182	+	0.999108i	$0.513442\pi$
$252$	−0.328718	−	2.98194i	−0.0207073	−	0.187844i
$253$	−14.8114	+	25.6541i	−0.931186	+	1.61286i
$254$	7.56291	+	2.75267i	0.474539	+	0.172718i
$255$	−9.01383	−	11.4770i	−0.564468	−	0.718721i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	11.0634	+	9.28332i	0.690118	+	0.579078i	0.918943	−	0.394390i	$-0.129044\pi$
$257$	11.0634	+	9.28332i	0.690118	+	0.579078i	−0.228825	+	0.973467i	$0.573488\pi$
$258$	−4.48562	+	11.1839i	−0.279262	+	0.696278i
$259$	2.63884	+	0.960460i	0.163970	+	0.0596801i
$260$	−3.75661	+	6.50664i	−0.232975	+	0.403525i
$261$	2.24370	+	2.14482i	0.138882	+	0.132761i
$262$	−9.95436	−	17.2415i	−0.614983	−	1.06518i
$263$	−3.48490	−	19.7638i	−0.214888	−	1.21869i	−0.881101	−	0.472928i	$-0.843197\pi$
$263$	−3.48490	−	19.7638i	−0.214888	−	1.21869i	0.666213	−	0.745762i	$-0.267914\pi$
$264$	8.42173	+	5.23282i	0.518321	+	0.322058i
$265$	14.6229	−	5.32231i	0.898280	−	0.326947i
$266$	−0.264396	+	1.49946i	−0.0162112	+	0.0919380i
$267$	20.9530	+	4.39817i	1.28230	+	0.269164i
$268$	−9.77848	+	8.20512i	−0.597316	+	0.501208i
$269$	−23.3876			−1.42596			−0.712982	−	0.701182i	$-0.752656\pi$
$269$	−23.3876			−1.42596			−0.712982	+	0.701182i	$0.752656\pi$
$270$	10.4193	−	4.73432i	0.634100	−	0.288121i
$271$	9.27590			0.563471			0.281735	−	0.959492i	$-0.409090\pi$
$271$	9.27590			0.563471			0.281735	+	0.959492i	$0.409090\pi$
$272$	−2.93049	+	2.45897i	−0.177687	+	0.149097i
$273$	−1.84006	−	5.61461i	−0.111365	−	0.339812i
$274$	0.283385	−	1.60716i	0.0171199	−	0.0970919i
$275$	0.801664	−	0.291782i	0.0483422	−	0.0175951i
$276$	7.90317	−	4.22794i	0.475715	−	0.254492i
$277$	2.18748	+	12.4058i	0.131433	+	0.745392i	0.977278	+	0.211963i	$0.0679856\pi$
$277$	2.18748	+	12.4058i	0.131433	+	0.745392i	−0.845845	+	0.533429i	$0.820903\pi$
$278$	6.80659	+	11.7894i	0.408232	+	0.707079i
$279$	−28.2660	−	1.83250i	−1.69224	−	0.109709i
$280$	1.10125	−	1.90741i	0.0658120	−	0.113990i
$281$	−16.5288	−	6.01598i	−0.986024	−	0.358883i	−0.201845	−	0.979418i	$-0.564694\pi$
$281$	−16.5288	−	6.01598i	−0.986024	−	0.358883i	−0.784179	+	0.620534i	$0.786916\pi$
$282$	2.39496	−	0.342788i	0.142618	−	0.0204127i
$283$	22.7005	+	19.0480i	1.34941	+	1.13229i	0.979101	+	0.203376i	$0.0651914\pi$
$283$	22.7005	+	19.0480i	1.34941	+	1.13229i	0.370305	+	0.928910i	$0.379253\pi$
$284$	3.36129	+	2.82045i	0.199456	+	0.167363i
$285$	−5.74984	+	0.822966i	−0.340591	+	0.0487483i
$286$	18.3498	+	6.67878i	1.08505	+	0.394925i
$287$	−1.13494	+	1.96577i	−0.0669934	+	0.116036i
$288$	−1.32878	−	2.68968i	−0.0782989	−	0.158491i
$289$	1.18285	+	2.04875i	0.0695792	+	0.120515i
$290$	0.395710	+	2.24418i	0.0232369	+	0.131783i
$291$	12.6402	−	6.76212i	0.740984	−	0.396402i
$292$	0.145084	−	0.0528064i	0.00849042	−	0.00309026i
$293$	−2.41714	+	13.7083i	−0.141211	+	0.800846i	0.829121	+	0.559069i	$0.188841\pi$
$293$	−2.41714	+	13.7083i	−0.141211	+	0.800846i	−0.970332	+	0.241777i	$0.922270\pi$
$294$	0.539410	+	1.64592i	0.0314590	+	0.0959917i
$295$	8.30423	−	6.96807i	0.483491	−	0.405697i
$296$	2.80820			0.163223
$297$	−16.8204	−	24.5325i	−0.976020	−	1.42352i
$298$	23.1652			1.34192
$299$	13.5226	−	11.3468i	0.782031	−	0.656202i
$300$	−0.252622	−	0.0530270i	−0.0145851	−	0.00306152i
$301$	1.20807	−	6.85132i	0.0696321	−	0.394903i
$302$	15.5807	−	5.67091i	0.896568	−	0.326324i
$303$	−23.3660	−	14.5184i	−1.34234	−	0.834061i
$304$	0.264396	+	1.49946i	0.0151641	+	0.0860002i
$305$	2.47344	+	4.28413i	0.141629	+	0.245309i
$306$	11.0157	−	3.21926i	0.629724	−	0.184033i
$307$	−8.67963	+	15.0336i	−0.495373	+	0.858011i	−0.999986	−	0.00533473i	$-0.998302\pi$
$307$	−8.67963	+	15.0336i	−0.495373	+	0.858011i	0.504613	+	0.863346i	$0.331635\pi$
$308$	−5.37922	−	1.95788i	−0.306510	−	0.111560i
$309$	10.7606	−	26.8291i	0.612147	−	1.52625i
$310$	−15.9302	−	13.3671i	−0.904777	−	0.759198i
$311$	15.0087	+	12.5938i	0.851064	+	0.714128i	0.960024	−	0.279918i	$-0.0903074\pi$
$311$	15.0087	+	12.5938i	0.851064	+	0.714128i	−0.108959	+	0.994046i	$0.534752\pi$
$312$	−3.64940	−	4.64667i	−0.206606	−	0.263066i
$313$	0.394174	+	0.143467i	0.0222800	+	0.00810926i	0.353136	−	0.935572i	$-0.385115\pi$
$313$	0.394174	+	0.143467i	0.0222800	+	0.00810926i	−0.330856	+	0.943681i	$0.607337\pi$
$314$	−7.42160	+	12.8546i	−0.418825	+	0.725426i
$315$	−5.32579	+	3.91085i	−0.300074	+	0.220351i
$316$	5.79998	+	10.0459i	0.326275	+	0.565124i
$317$	−2.46164	−	13.9606i	−0.138259	−	0.784107i	−0.972534	−	0.232759i	$-0.925225\pi$
$317$	−2.46164	−	13.9606i	−0.138259	−	0.784107i	0.834275	−	0.551348i	$-0.185886\pi$
$318$	−0.396061	+	12.2312i	−0.0222100	+	0.685889i
$319$	5.56560	−	2.02571i	0.311614	−	0.113418i
$320$	0.382459	−	2.16903i	0.0213801	−	0.121253i
$321$	6.00022	−	6.69801i	0.334900	−	0.373847i
$322$	−3.96412	+	3.32629i	−0.220912	+	0.185367i
$323$	−5.82466			−0.324093
$324$	0.405340	+	8.99087i	0.0225189	+	0.499493i
$325$	−0.508376			−0.0281996
$326$	−12.5687	+	10.5464i	−0.696115	+	0.584110i
$327$	−14.4618	+	16.1436i	−0.799737	+	0.892741i
$328$	−0.394160	+	2.23539i	−0.0217639	+	0.123429i
$329$	−1.31259	+	0.477742i	−0.0723652	+	0.0263388i
$330$	0.706765	−	21.8263i	0.0389061	−	1.20150i
$331$	1.97663	+	11.2100i	0.108645	+	0.616158i	0.989701	+	0.143147i	$0.0457221\pi$
$331$	1.97663	+	11.2100i	0.108645	+	0.616158i	−0.881056	+	0.473012i	$0.843167\pi$
$332$	1.65117	+	2.85992i	0.0906200	+	0.156958i
$333$	−7.71353	−	3.38750i	−0.422699	−	0.185634i
$334$	−8.70094	+	15.0705i	−0.476094	+	0.824620i
$335$	26.4191	+	9.61576i	1.44343	+	0.525365i
$336$	1.06982	+	1.36217i	0.0583632	+	0.0743122i
$337$	9.02729	+	7.57480i	0.491748	+	0.412625i	0.854652	−	0.519201i	$-0.173770\pi$
$337$	9.02729	+	7.57480i	0.491748	+	0.412625i	−0.362904	+	0.931826i	$0.618215\pi$
$338$	1.04446	+	0.876408i	0.0568113	+	0.0476703i
$339$	−13.5406	+	33.7604i	−0.735423	+	1.83361i
$340$	7.91747	+	2.88172i	0.429385	+	0.156283i
$341$	−27.0245	+	46.8078i	−1.46346	+	2.53479i
$342$	1.08255	−	4.43765i	0.0585375	−	0.239961i
$343$	−0.500000	−	0.866025i	−0.0269975	−	0.0467610i
$344$	−1.20807	−	6.85132i	−0.0651349	−	0.369398i
$345$	−16.7678	−	10.4186i	−0.902746	−	0.560919i
$346$	−9.02880	+	3.28621i	−0.485391	+	0.176668i
$347$	−1.58496	+	8.98875i	−0.0850850	+	0.482541i	0.912253	+	0.409627i	$0.134341\pi$
$347$	−1.58496	+	8.98875i	−0.0850850	+	0.482541i	−0.997338	+	0.0729144i	$0.976770\pi$
$348$	−1.75384	−	0.368143i	−0.0940157	−	0.0197345i
$349$	−10.0449	+	8.42863i	−0.537689	+	0.451174i	−0.870747	−	0.491732i	$-0.836364\pi$
$349$	−10.0449	+	8.42863i	−0.537689	+	0.451174i	0.333058	+	0.942906i	$0.391920\pi$
$350$	0.149030			0.00796598
$351$	4.41890	+	17.1657i	0.235863	+	0.916236i
$352$	−5.72445			−0.305114
$353$	−1.31702	+	1.10511i	−0.0700978	+	0.0588190i	−0.677163	−	0.735833i	$-0.736791\pi$
$353$	−1.31702	+	1.10511i	−0.0700978	+	0.0588190i	0.607066	+	0.794652i	$0.292347\pi$
$354$	2.65491	+	8.10100i	0.141107	+	0.430563i
$355$	1.67817	−	9.51738i	0.0890680	−	0.505130i
$356$	−11.6154	+	4.22765i	−0.615614	+	0.224065i
$357$	−5.84244	+	3.12551i	−0.309215	+	0.165420i
$358$	2.78985	+	15.8220i	0.147448	+	0.836219i
$359$	−10.2364	−	17.7300i	−0.540259	−	0.935756i	−0.998889	−	0.0471285i	$-0.984993\pi$
$359$	−10.2364	−	17.7300i	−0.540259	−	0.935756i	0.458630	−	0.888627i	$-0.348340\pi$
$360$	−3.66702	+	5.49652i	−0.193269	+	0.289692i
$361$	8.34085	−	14.4468i	0.438992	−	0.760357i
$362$	0.849117	+	0.309053i	0.0446286	+	0.0162435i
$363$	−37.3252	+	5.34229i	−1.95906	+	0.280398i
$364$	2.61316	+	2.19270i	0.136967	+	0.114929i
$365$	−0.260497	−	0.218583i	−0.0136350	−	0.0114412i
$366$	−3.85101	+	0.551189i	−0.201296	+	0.0288111i
$367$	17.8390	+	6.49287i	0.931189	+	0.338925i	0.762681	−	0.646775i	$-0.223883\pi$
$367$	17.8390	+	6.49287i	0.931189	+	0.338925i	0.168508	+	0.985700i	$0.446105\pi$
$368$	−2.58740	+	4.48151i	−0.134877	+	0.233615i
$369$	3.77921	−	5.66469i	0.196738	−	0.294892i
$370$	−3.09252	−	5.35640i	−0.160772	−	0.278466i
$371$	−1.22689	−	6.95802i	−0.0636968	−	0.361243i
$372$	14.4199	−	7.71418i	0.747637	−	0.399962i
$373$	−1.32974	+	0.483986i	−0.0688513	+	0.0250598i	−0.376216	−	0.926532i	$-0.622775\pi$
$373$	−1.32974	+	0.483986i	−0.0688513	+	0.0250598i	0.307365	+	0.951592i	$0.400553\pi$
$374$	3.80268	−	21.5661i	0.196632	−	1.11516i
$375$	6.11728	+	18.6658i	0.315895	+	0.963899i
$376$	−1.07003	+	0.897862i	−0.0551826	+	0.0463037i
$377$	−3.52943			−0.181775
$378$	−1.29539	−	5.03209i	−0.0666279	−	0.258823i
$379$	−25.4616			−1.30788			−0.653938	−	0.756548i	$-0.726884\pi$
$379$	−25.4616			−1.30788			−0.653938	+	0.756548i	$0.726884\pi$
$380$	2.56893	−	2.15559i	0.131783	−	0.110579i
$381$	13.6427	+	2.86370i	0.698937	+	0.146712i
$382$	−3.38990	+	19.2251i	−0.173442	+	0.983640i
$383$	−12.4630	+	4.53618i	−0.636832	+	0.231788i	−0.640202	−	0.768206i	$-0.721149\pi$
$383$	−12.4630	+	4.53618i	−0.636832	+	0.231788i	0.00337032	+	0.999994i	$0.498927\pi$
$384$	1.47119	+	0.914118i	0.0750761	+	0.0466484i
$385$	2.18936	+	12.4165i	0.111580	+	0.632804i
$386$	−11.6707	−	20.2143i	−0.594024	−	1.02888i
$387$	−4.94636	+	20.2764i	−0.251437	+	1.03071i
$388$	−4.13826	+	7.16767i	−0.210088	+	0.363883i
$389$	−5.90876	−	2.15061i	−0.299586	−	0.109040i	0.187854	−	0.982197i	$-0.439847\pi$
$389$	−5.90876	−	2.15061i	−0.299586	−	0.109040i	−0.487440	+	0.873157i	$0.662069\pi$
$390$	−4.84424	+	12.0780i	−0.245298	+	0.611595i
$391$	−15.1647	−	12.7247i	−0.766911	−	0.643515i
$392$	−0.766044	−	0.642788i	−0.0386911	−	0.0324657i
$393$	−21.2987	−	27.1190i	−1.07438	−	1.36797i
$394$	15.0350	+	5.47230i	0.757453	+	0.275690i
$395$	12.7744	−	22.1259i	0.642751	−	1.11328i
$396$	15.7239	+	6.90535i	0.790154	+	0.347007i
$397$	−7.38723	−	12.7951i	−0.370754	−	0.642165i	0.618927	−	0.785448i	$-0.287568\pi$
$397$	−7.38723	−	12.7951i	−0.370754	−	0.642165i	−0.989682	+	0.143283i	$0.954234\pi$
$398$	−2.71189	−	15.3799i	−0.135935	−	0.770924i
$399$	−0.0853516	+	2.63583i	−0.00427293	+	0.131957i
$400$	0.140042	−	0.0509712i	0.00700211	−	0.00254856i
$401$	−4.38149	+	24.8487i	−0.218801	+	1.24088i	0.655386	+	0.755294i	$0.272506\pi$
$401$	−4.38149	+	24.8487i	−0.218801	+	1.24088i	−0.874187	+	0.485589i	$0.838605\pi$
$402$	−14.7524	+	16.4680i	−0.735782	+	0.821349i
$403$	24.6729	−	20.7030i	1.22905	−	1.03129i
$404$	15.8824			0.790180
$405$	16.7029	−	10.6743i	0.829975	−	0.530411i
$406$	1.03465			0.0513487
$407$	−12.3145	+	10.3331i	−0.610405	+	0.512191i
$408$	−4.42111	+	4.93525i	−0.218877	+	0.244332i
$409$	−1.69079	+	9.58893i	−0.0836040	+	0.474142i	0.914045	+	0.405613i	$0.132942\pi$
$409$	−1.69079	+	9.58893i	−0.0836040	+	0.474142i	−0.997649	+	0.0685294i	$0.978169\pi$
$410$	4.69789	−	1.70989i	0.232012	−	0.0844455i
$411$	0.0914817	−	2.82514i	0.00451246	−	0.139354i
$412$	2.89805	+	16.4357i	0.142777	+	0.809727i
$413$	−2.46094	−	4.26247i	−0.121095	−	0.209743i
$414$	12.5130	−	9.18861i	0.614982	−	0.451595i
$415$	3.63670	−	6.29895i	0.178519	−	0.309203i
$416$	3.20552	+	1.16671i	0.157163	+	0.0572028i
$417$	14.5636	+	18.5434i	0.713182	+	0.908074i
$418$	−6.67686	−	5.60255i	−0.326576	−	0.274030i
$419$	−24.5012	−	20.5589i	−1.19696	−	1.00437i	−0.999712	−	0.0240171i	$-0.992354\pi$
$419$	−24.5012	−	20.5589i	−1.19696	−	1.00437i	−0.197250	−	0.980353i	$-0.563201\pi$
$420$	1.42008	−	3.54066i	0.0692930	−	0.172767i
$421$	−23.0145	−	8.37660i	−1.12166	−	0.408251i	−0.286402	−	0.958110i	$-0.592459\pi$
$421$	−23.0145	−	8.37660i	−1.12166	−	0.408251i	−0.835258	+	0.549859i	$0.814681\pi$
$422$	7.05178	−	12.2140i	0.343275	−	0.594570i
$423$	4.02223	−	1.17547i	0.195568	−	0.0571534i
$424$	−3.53268	−	6.11878i	−0.171562	−	0.297154i
$425$	0.0989987	+	0.561449i	0.00480214	+	0.0272343i
$426$	6.45534	+	4.01101i	0.312762	+	0.194334i
$427$	2.11059	−	0.768191i	0.102139	−	0.0371754i
$428$	−0.901556	+	5.11298i	−0.0435783	+	0.247145i
$429$	33.1012	+	6.94816i	1.59814	+	0.335460i
$430$	−11.7379	+	9.84928i	−0.566052	+	0.474974i
$431$	−22.1390			−1.06640			−0.533198	−	0.845990i	$-0.679010\pi$
$431$	−22.1390			−1.06640			−0.533198	+	0.845990i	$0.679010\pi$
$432$	−2.93835	−	4.28557i	−0.141371	−	0.206190i
$433$	−4.91292			−0.236100			−0.118050	−	0.993008i	$-0.537664\pi$
$433$	−4.91292			−0.236100			−0.118050	+	0.993008i	$0.537664\pi$
$434$	−7.23283	+	6.06906i	−0.347187	+	0.291324i
$435$	1.22921	+	3.75072i	0.0589361	+	0.179833i
$436$	2.17293	−	12.3233i	0.104065	−	0.590180i
$437$	−7.40395	+	2.69482i	−0.354179	+	0.128911i
$438$	0.235799	−	0.126145i	0.0112669	−	0.00602744i
$439$	−3.51463	−	19.9324i	−0.167744	−	0.951324i	−0.946190	−	0.323612i	$-0.895103\pi$
$439$	−3.51463	−	19.9324i	−0.167744	−	0.951324i	0.778446	−	0.627712i	$-0.216008\pi$
$440$	6.30402	+	10.9189i	0.300533	+	0.520538i
$441$	1.32878	+	2.68968i	0.0632750	+	0.128080i
$442$	−6.52482	+	11.3013i	−0.310354	+	0.537549i
$443$	25.8616	+	9.41287i	1.22872	+	0.447219i	0.873160	−	0.487433i	$-0.162067\pi$
$443$	25.8616	+	9.41287i	1.22872	+	0.447219i	0.355564	+	0.934652i	$0.384289\pi$
$444$	4.81487	−	0.689145i	0.228504	−	0.0327054i
$445$	20.8553	+	17.4997i	0.988635	+	0.829563i
$446$	13.2073	+	11.0823i	0.625386	+	0.524761i
$447$	39.7185	−	5.68485i	1.87862	−	0.268884i
$448$	−0.939693	−	0.342020i	−0.0443963	−	0.0161589i
$449$	3.70377	−	6.41511i	0.174792	−	0.302748i	−0.765298	−	0.643677i	$-0.777408\pi$
$449$	3.70377	−	6.41511i	0.174792	−	0.302748i	0.940089	+	0.340929i	$0.110742\pi$
$450$	−0.446153	−	0.0289243i	−0.0210318	−	0.00136351i
$451$	−6.49690	−	11.2530i	−0.305927	−	0.529881i
$452$	−3.64677	−	20.6818i	−0.171530	−	0.972792i
$453$	25.3226	−	13.5468i	1.18976	−	0.636484i
$454$	−1.14996	+	0.418552i	−0.0539704	+	0.0196436i
$455$	1.30466	−	7.39908i	0.0611633	−	0.346874i
$456$	0.821303	+	2.50606i	0.0384610	+	0.117357i
$457$	20.0224	−	16.8008i	0.936608	−	0.785908i	−0.0403835	−	0.999184i	$-0.512858\pi$
$457$	20.0224	−	16.8008i	0.936608	−	0.785908i	0.976992	+	0.213277i	$0.0684135\pi$
$458$	22.5551			1.05393
$459$	18.0972	−	8.22298i	0.844705	−	0.383816i
$460$	11.3974			0.531409
$461$	4.14636	−	3.47921i	0.193115	−	0.162043i	−0.541103	−	0.840956i	$-0.681993\pi$
$461$	4.14636	−	3.47921i	0.193115	−	0.162043i	0.734219	+	0.678913i	$0.237549\pi$
$462$	−9.70356	−	2.03684i	−0.451451	−	0.0947626i
$463$	3.02652	−	17.1642i	0.140654	−	0.797689i	−0.830100	−	0.557614i	$-0.811717\pi$
$463$	3.02652	−	17.1642i	0.140654	−	0.797689i	0.970754	−	0.240075i	$-0.0771720\pi$
$464$	0.972251	−	0.353870i	0.0451356	−	0.0164280i
$465$	−30.5940	−	19.0095i	−1.41876	−	0.881545i
$466$	−0.593036	−	3.36327i	−0.0274719	−	0.155801i
$467$	9.54160	+	16.5265i	0.441533	+	0.764757i	0.997803	−	0.0662439i	$-0.0211015\pi$
$467$	9.54160	+	16.5265i	0.441533	+	0.764757i	−0.556271	+	0.831001i	$0.687768\pi$
$468$	−7.39749	−	7.07150i	−0.341949	−	0.326880i
$469$	6.38245	−	11.0547i	0.294714	−	0.510460i
$470$	2.89096	+	1.05222i	0.133350	+	0.0485354i
$471$	−9.57033	+	23.8615i	−0.440977	+	1.09948i
$472$	−3.77038	−	3.16372i	−0.173546	−	0.145622i
$473$	30.5078	+	25.5990i	1.40275	+	1.17705i
$474$	12.4098	+	15.8011i	0.570002	+	0.725767i
$475$	0.213228	+	0.0776085i	0.00978356	+	0.00356092i
$476$	1.91274	−	3.31296i	0.0876703	−	0.151849i
$477$	2.32251	+	21.0685i	0.106340	+	0.964659i
$478$	−1.98917	−	3.44534i	−0.0909824	−	0.157586i
$479$	0.323335	+	1.83372i	0.0147735	+	0.0837849i	0.991303	−	0.131599i	$-0.0420110\pi$
$479$	0.323335	+	1.83372i	0.0147735	+	0.0837849i	−0.976530	+	0.215383i	$0.930900\pi$
$480$	0.123464	−	3.81283i	0.00563535	−	0.174031i
$481$	9.00172	−	3.27636i	0.410443	−	0.149389i
$482$	1.66585	−	9.44753i	0.0758776	−	0.430323i
$483$	−5.98051	+	6.67601i	−0.272123	+	0.303769i
$484$	16.6763	−	13.9930i	0.758012	−	0.636047i
$485$	18.2289			0.827734
$486$	2.90139	+	15.3161i	0.131610	+	0.694751i
$487$	18.7130			0.847967			0.423983	−	0.905670i	$-0.360632\pi$
$487$	18.7130			0.847967			0.423983	+	0.905670i	$0.360632\pi$
$488$	1.72057	−	1.44373i	0.0778864	−	0.0653545i
$489$	−18.9619	+	21.1670i	−0.857485	+	0.957205i
$490$	−0.382459	+	2.16903i	−0.0172777	+	0.0979868i
$491$	−31.8048	+	11.5760i	−1.43533	+	0.522417i	−0.938454	−	0.345405i	$-0.887741\pi$
$491$	−31.8048	+	11.5760i	−1.43533	+	0.522417i	−0.496875	+	0.867822i	$0.665519\pi$
$492$	−0.127242	+	3.92949i	−0.00573650	+	0.177155i
$493$	0.687304	+	3.89789i	0.0309546	+	0.175552i
$494$	2.59697	+	4.49808i	0.116843	+	0.202378i
$495$	−4.14449	−	37.5964i	−0.186281	−	1.68983i
$496$	−4.72089	+	8.17683i	−0.211974	+	0.367150i
$497$	−4.12323	−	1.50073i	−0.184952	−	0.0673170i
$498$	3.53291	+	4.49835i	0.158313	+	0.201576i
$499$	−11.3795	−	9.54852i	−0.509416	−	0.427451i	0.351508	−	0.936185i	$-0.385669\pi$
$499$	−11.3795	−	9.54852i	−0.509416	−	0.427451i	−0.860924	+	0.508734i	$0.830114\pi$
$500$	−8.68748	−	7.28966i	−0.388516	−	0.326003i
$501$	−11.2201	+	27.9747i	−0.501276	+	1.24982i
$502$	−25.1344	−	9.14819i	−1.12181	−	0.408304i
$503$	6.60956	−	11.4481i	0.294706	−	0.510445i	−0.680211	−	0.733017i	$-0.738112\pi$
$503$	6.60956	−	11.4481i	0.294706	−	0.510445i	0.974916	+	0.222571i	$0.0714450\pi$
$504$	2.16856	+	2.07300i	0.0965955	+	0.0923388i
$505$	−17.4905	−	30.2944i	−0.778315	−	1.34808i
$506$	−5.14395	−	29.1728i	−0.228677	−	1.29689i
$507$	2.00589	+	1.24635i	0.0890845	+	0.0553525i
$508$	−7.56291	+	2.75267i	−0.335550	+	0.122130i
$509$	2.56215	−	14.5307i	0.113565	−	0.644060i	−0.873885	−	0.486132i	$-0.838407\pi$
$509$	2.56215	−	14.5307i	0.113565	−	0.644060i	0.987451	−	0.157928i	$-0.0504814\pi$
$510$	14.2823	+	2.99795i	0.632431	+	0.132752i
$511$	−0.118274	+	0.0992435i	−0.00523213	+	0.00439027i
$512$	−1.00000			−0.0441942
$513$	0.767092	−	7.87436i	0.0338679	−	0.347662i
$514$	−14.4423			−0.637022
$515$	28.1581	−	23.6275i	1.24080	−	1.04115i
$516$	−3.75268	−	11.4506i	−0.165203	−	0.504087i
$517$	1.38850	−	7.87457i	0.0610662	−	0.346323i
$518$	−2.63884	+	0.960460i	−0.115944	+	0.0422002i
$519$	−14.6741	+	7.85018i	−0.644122	+	0.344585i
$520$	−1.30466	−	7.39908i	−0.0572130	−	0.324471i
$521$	−0.373969	−	0.647733i	−0.0163839	−	0.0283777i	0.857717	−	0.514122i	$-0.171882\pi$
$521$	−0.373969	−	0.647733i	−0.0163839	−	0.0283777i	−0.874101	+	0.485744i	$0.838549\pi$
$522$	−3.09744	−	0.200809i	−0.135571	−	0.00878916i
$523$	14.5109	−	25.1337i	0.634519	−	1.09902i	−0.352097	−	0.935963i	$-0.614531\pi$
$523$	14.5109	−	25.1337i	0.634519	−	1.09902i	0.986617	−	0.163056i	$-0.0521353\pi$
$524$	18.7081	+	6.80919i	0.817267	+	0.297461i
$525$	0.255523	−	0.0365726i	0.0111519	−	0.00159616i
$526$	15.3735	+	12.8999i	0.670318	+	0.562463i
$527$	−27.6691	−	23.2171i	−1.20528	−	1.01135i
$528$	−9.81501	+	1.40481i	−0.427143	+	0.0611364i
$529$	−3.55064	−	1.29233i	−0.154376	−	0.0561882i
$530$	−7.78070	+	13.4766i	−0.337972	+	0.585385i
$531$	6.54007	+	13.2383i	0.283815	+	0.574491i
$532$	−0.761298	−	1.31861i	−0.0330064	−	0.0571688i
$533$	1.34458	+	7.62546i	0.0582400	+	0.330296i
$534$	−18.8780	+	10.0991i	−0.816931	+	0.437031i
$535$	10.7454	−	3.91101i	0.464564	−	0.169088i
$536$	2.21660	−	12.5710i	0.0957426	−	0.542983i
$537$	8.66621	+	26.4434i	0.373974	+	1.14112i
$538$	17.9159	−	15.0332i	0.772409	−	0.648129i
$539$	5.72445			0.246569
$540$	−4.93851	+	10.3241i	−0.212520	+	0.444279i
$541$	35.1934			1.51308			0.756542	−	0.653945i	$-0.226887\pi$
$541$	35.1934			1.51308			0.756542	+	0.653945i	$0.226887\pi$
$542$	−7.10575	+	5.96243i	−0.305218	+	0.256108i
$543$	1.53172	+	0.321518i	0.0657324	+	0.0137977i
$544$	0.664288	−	3.76736i	0.0284811	−	0.161524i
$545$	−25.8986	+	9.42631i	−1.10937	+	0.403779i
$546$	5.01857	+	3.11828i	0.214775	+	0.133450i
$547$	−6.58914	−	37.3689i	−0.281731	−	1.59778i	−0.716733	−	0.697348i	$-0.754363\pi$
$547$	−6.58914	−	37.3689i	−0.281731	−	1.59778i	0.435001	−	0.900430i	$-0.356748\pi$
$548$	0.815975	+	1.41331i	0.0348567	+	0.0603736i
$549$	−6.46759	+	1.89011i	−0.276030	+	0.0806681i
$550$	−0.426557	+	0.738818i	−0.0181884	+	0.0315033i
$551$	1.48034	+	0.538801i	0.0630648	+	0.0229537i
$552$	−3.33651	+	8.31885i	−0.142011	+	0.354074i
$553$	−8.88609	−	7.45631i	−0.377875	−	0.317075i
$554$	−9.64999	−	8.09731i	−0.409989	−	0.344022i
$555$	−6.61685	−	8.42504i	−0.280869	−	0.357623i
$556$	−12.7922	−	4.65598i	−0.542510	−	0.197458i
$557$	−1.01902	+	1.76500i	−0.0431773	+	0.0747853i	−0.886806	−	0.462141i	$-0.847081\pi$
$557$	−1.01902	+	1.76500i	−0.0431773	+	0.0747853i	0.843629	+	0.536926i	$0.180415\pi$
$558$	22.8309	−	16.7653i	0.966511	−	0.709731i
$559$	−11.8660	−	20.5525i	−0.501879	−	0.869280i
$560$	0.382459	+	2.16903i	0.0161618	+	0.0916583i
$561$	1.22757	−	37.9099i	0.0518281	−	1.60056i
$562$	16.5288	−	6.01598i	0.697224	−	0.253769i
$563$	−0.0476308	+	0.270128i	−0.00200740	+	0.0113845i	−0.985795	−	0.167953i	$-0.946284\pi$
$563$	−0.0476308	+	0.270128i	−0.00200740	+	0.0113845i	0.983788	+	0.179338i	$0.0573954\pi$
$564$	−1.61431	+	1.80204i	−0.0679747	+	0.0758798i
$565$	−35.4329	+	29.7317i	−1.49067	+	1.25082i
$566$	−29.6334			−1.24559
$567$	−3.45595	−	8.31002i	−0.145136	−	0.348988i
$568$	−4.38785			−0.184110
$569$	2.24467	−	1.88351i	0.0941016	−	0.0789607i	−0.594523	−	0.804078i	$-0.702659\pi$
$569$	2.24467	−	1.88351i	0.0941016	−	0.0789607i	0.688625	+	0.725118i	$0.258215\pi$
$570$	3.87564	−	4.32636i	0.162333	−	0.181211i
$571$	−0.539460	+	3.05943i	−0.0225757	+	0.128033i	−0.994013	−	0.109264i	$-0.965151\pi$
$571$	−0.539460	+	3.05943i	−0.0225757	+	0.128033i	0.971437	+	0.237297i	$0.0762616\pi$
$572$	−18.3498	+	6.67878i	−0.767244	+	0.279254i
$573$	−1.09432	+	33.7948i	−0.0457158	+	1.41180i
$574$	−0.394160	−	2.23539i	−0.0164519	−	0.0933036i
$575$	0.385599	+	0.667878i	0.0160806	+	0.0278524i
$576$	2.74679	+	1.20629i	0.114450	+	0.0502621i
$577$	−2.86870	+	4.96873i	−0.119425	+	0.206851i	−0.919540	−	0.392996i	$-0.871439\pi$
$577$	−2.86870	+	4.96873i	−0.119425	+	0.206851i	0.800115	+	0.599847i	$0.204772\pi$
$578$	−2.22302	−	0.809114i	−0.0924656	−	0.0336547i
$579$	−24.9711	−	31.7949i	−1.03776	−	1.32135i
$580$	−1.74566	−	1.46479i	−0.0724848	−	0.0608219i
$581$	−2.52975	−	2.12271i	−0.104952	−	0.0880648i
$582$	−5.33638	+	13.3051i	−0.221200	+	0.551513i
$583$	38.0062	+	13.8331i	1.57405	+	0.572909i
$584$	−0.0771978	+	0.133710i	−0.00319447	+	0.00553298i
$585$	−5.34182	+	21.8975i	−0.220857	+	0.905352i
$586$	−6.95988	−	12.0549i	−0.287510	−	0.497982i
$587$	2.91280	+	16.5193i	0.120224	+	0.681826i	0.984030	+	0.178001i	$0.0569631\pi$
$587$	2.91280	+	16.5193i	0.120224	+	0.681826i	−0.863806	+	0.503825i	$0.831926\pi$
$588$	−1.47119	−	0.914118i	−0.0606707	−	0.0376976i
$589$	−13.5090	+	4.91689i	−0.556630	+	0.202597i
$590$	−1.88242	+	10.6757i	−0.0774978	+	0.439512i
$591$	27.1216	+	5.69301i	1.11564	+	0.234179i
$592$	−2.15120	+	1.80507i	−0.0884140	+	0.0741881i
$593$	−10.1970			−0.418741			−0.209371	−	0.977836i	$-0.567142\pi$
$593$	−10.1970			−0.418741			−0.209371	+	0.977836i	$0.567142\pi$
$594$	28.6544	+	7.98104i	1.17570	+	0.327466i
$595$	−8.42559			−0.345416
$596$	−17.7456	+	14.8903i	−0.726887	+	0.609931i
$597$	−8.42404	−	25.7045i	−0.344773	−	1.05202i
$598$	−3.06532	+	17.3843i	−0.125350	+	0.710896i
$599$	20.0777	−	7.30768i	0.820352	−	0.298584i	0.102459	−	0.994737i	$-0.467329\pi$
$599$	20.0777	−	7.30768i	0.820352	−	0.298584i	0.717893	+	0.696154i	$0.245107\pi$
$600$	0.227605	−	0.121761i	0.00929192	−	0.00497088i
$601$	2.32847	+	13.2054i	0.0949801	+	0.538659i	0.994753	+	0.102301i	$0.0326206\pi$
$601$	2.32847	+	13.2054i	0.0949801	+	0.538659i	−0.899773	+	0.436358i	$0.856268\pi$
$602$	3.47851	+	6.02495i	0.141773	+	0.245559i
$603$	−21.2528	+	31.8560i	−0.865481	+	1.29728i
$604$	−8.29031	+	14.3592i	−0.337328	+	0.584269i
$605$	−45.0552	−	16.3987i	−1.83175	−	0.666704i
$606$	27.2316	−	3.89762i	1.10621	−	0.158330i
$607$	−16.7272	−	14.0358i	−0.678935	−	0.569694i	0.236760	−	0.971568i	$-0.423914\pi$
$607$	−16.7272	−	14.0358i	−0.678935	−	0.569694i	−0.915695	+	0.401874i	$0.868359\pi$
$608$	−1.16638	−	0.978706i	−0.0473028	−	0.0396918i
$609$	1.77398	−	0.253908i	0.0718855	−	0.0102889i
$610$	−4.64855	−	1.69193i	−0.188214	−	0.0685044i
$611$	−2.38245	+	4.12653i	−0.0963837	+	0.166941i
$612$	−6.36920	+	9.54684i	−0.257459	+	0.385908i
$613$	5.49679	+	9.52072i	0.222013	+	0.384538i	0.955419	−	0.295253i	$-0.0954038\pi$
$613$	5.49679	+	9.52072i	0.222013	+	0.384538i	−0.733406	+	0.679791i	$0.762070\pi$
$614$	−3.01441	−	17.0955i	−0.121651	−	0.689920i
$615$	7.63528	−	4.08463i	0.307884	−	0.164708i
$616$	5.37922	−	1.95788i	0.216735	−	0.0788851i
$617$	−0.862361	+	4.89069i	−0.0347174	+	0.196892i	−0.997234	−	0.0743324i	$-0.976317\pi$
$617$	−0.862361	+	4.89069i	−0.0347174	+	0.196892i	0.962516	+	0.271224i	$0.0874285\pi$
$618$	9.00232	+	27.4690i	0.362127	+	1.10497i
$619$	18.7660	−	15.7466i	0.754271	−	0.632908i	−0.182358	−	0.983232i	$-0.558373\pi$
$619$	18.7660	−	15.7466i	0.754271	−	0.632908i	0.936629	+	0.350324i	$0.113929\pi$
$620$	20.7955			0.835166
$621$	19.1996	−	18.8253i	0.770455	−	0.755435i
$622$	−19.5924			−0.785586
$623$	9.46895	−	7.94539i	0.379365	−	0.318325i
$624$	5.78242	+	1.21377i	0.231482	+	0.0485897i
$625$	−4.20795	+	23.8645i	−0.168318	+	0.954580i
$626$	−0.394174	+	0.143467i	−0.0157544	+	0.00573411i
$627$	−12.8229	−	7.96747i	−0.512097	−	0.318190i
$628$	−2.57749	−	14.6177i	−0.102853	−	0.583310i
$629$	−5.37135	−	9.30346i	−0.214170	−	0.370953i
$630$	1.56595	−	6.41923i	0.0623888	−	0.255748i
$631$	−1.08966	+	1.88734i	−0.0433786	+	0.0751339i	−0.886900	−	0.461962i	$-0.847145\pi$
$631$	−1.08966	+	1.88734i	−0.0433786	+	0.0751339i	0.843521	+	0.537096i	$0.180479\pi$
$632$	−10.9004	−	3.96742i	−0.433595	−	0.157816i
$633$	9.09344	−	22.6725i	0.361432	−	0.901149i
$634$	10.8594	+	9.11216i	0.431284	+	0.361890i
$635$	13.5791	+	11.3942i	0.538871	+	0.452166i
$636$	−7.55864	−	9.62419i	−0.299719	−	0.381624i
$637$	−3.20552	−	1.16671i	−0.127007	−	0.0462268i
$638$	−2.96139	+	5.12928i	−0.117243	+	0.203070i
$639$	12.0525	+	5.29302i	0.476790	+	0.209389i
$640$	1.10125	+	1.90741i	0.0435306	+	0.0753972i
$641$	−1.04497	−	5.92634i	−0.0412740	−	0.234077i	0.957191	−	0.289456i	$-0.0934743\pi$
$641$	−1.04497	−	5.92634i	−0.0412740	−	0.234077i	−0.998465	+	0.0553793i	$0.982363\pi$
$642$	−0.291038	+	8.98784i	−0.0114864	+	0.354722i
$643$	−10.7943	+	3.92879i	−0.425685	+	0.154936i	−0.545974	−	0.837802i	$-0.683840\pi$
$643$	−10.7943	+	3.92879i	−0.425685	+	0.154936i	0.120289	+	0.992739i	$0.461618\pi$
$644$	0.898594	−	5.09618i	0.0354096	−	0.200818i
$645$	−17.7085	+	19.7679i	−0.697272	+	0.778360i
$646$	4.46195	−	3.74402i	0.175553	−	0.147306i
$647$	−21.8637			−0.859552			−0.429776	−	0.902936i	$-0.641407\pi$
$647$	−21.8637			−0.859552			−0.429776	+	0.902936i	$0.641407\pi$
$648$	−6.08973	−	6.62686i	−0.239227	−	0.260328i
$649$	28.1750			1.10597
$650$	0.389439	−	0.326778i	0.0152750	−	0.0128173i
$651$	−10.9119	+	12.1809i	−0.427670	+	0.477405i
$652$	2.84909	−	16.1580i	0.111579	−	0.632796i
$653$	−6.83898	+	2.48919i	−0.267630	+	0.0974094i	−0.472350	−	0.881411i	$-0.656594\pi$
$653$	−6.83898	+	2.48919i	−0.267630	+	0.0974094i	0.204720	+	0.978821i	$0.434372\pi$
$654$	0.701460	−	21.6625i	0.0274293	−	0.847072i
$655$	−7.61427	−	43.1827i	−0.297514	−	1.68729i
$656$	−1.13494	−	1.96577i	−0.0443119	−	0.0767505i
$657$	0.373340	−	0.274152i	0.0145654	−	0.0106957i
$658$	0.698412	−	1.20969i	0.0272270	−	0.0471585i
$659$	42.5625	+	15.4915i	1.65800	+	0.603463i	0.990047	−	0.140739i	$-0.0449480\pi$
$659$	42.5625	+	15.4915i	1.65800	+	0.603463i	0.667954	+	0.744202i	$0.267170\pi$
$660$	13.4883	+	17.1742i	0.525031	+	0.668507i
$661$	0.788042	+	0.661246i	0.0306513	+	0.0257195i	0.657985	−	0.753031i	$-0.271409\pi$
$661$	0.788042	+	0.661246i	0.0306513	+	0.0257195i	−0.627333	+	0.778751i	$0.715854\pi$
$662$	−8.71985	−	7.31682i	−0.338907	−	0.284376i
$663$	−8.41391	+	20.9782i	−0.326769	+	0.814726i
$664$	−3.10319	−	1.12947i	−0.120427	−	0.0438319i
$665$	−1.67675	+	2.90422i	−0.0650217	+	0.112621i
$666$	8.08635	−	2.36319i	0.313340	−	0.0915716i
$667$	2.67705	+	4.63678i	0.103656	+	0.179537i
$668$	−3.02181	−	17.1375i	−0.116917	−	0.663070i
$669$	25.3647	+	15.7603i	0.980654	+	0.609327i
$670$	−26.4191	+	9.61576i	−1.02066	+	0.371489i
$671$	−2.23265	+	12.6620i	−0.0861907	+	0.488812i
$672$	−1.69511	−	0.355815i	−0.0653903	−	0.0137259i
$673$	20.9240	−	17.5573i	0.806561	−	0.676785i	−0.143223	−	0.989690i	$-0.545747\pi$
$673$	20.9240	−	17.5573i	0.806561	−	0.676785i	0.949784	+	0.312905i	$0.101302\pi$
$674$	−11.7843			−0.453914
$675$	−0.772062	+	0.0598951i	−0.0297167	+	0.00230536i
$676$	−1.36345			−0.0524403
$677$	23.2032	−	19.4698i	0.891771	−	0.748285i	−0.0767937	−	0.997047i	$-0.524468\pi$
$677$	23.2032	−	19.4698i	0.891771	−	0.748285i	0.968565	+	0.248762i	$0.0800239\pi$
$678$	−11.3281	−	34.5657i	−0.435053	−	1.32749i
$679$	1.43720	−	8.15077i	0.0551547	−	0.312798i
$680$	−7.91747	+	2.88172i	−0.303621	+	0.110509i
$681$	−1.86898	+	0.999845i	−0.0716196	+	0.0383142i
$682$	−9.38551	−	53.2279i	−0.359390	−	2.03820i
$683$	−5.86057	−	10.1508i	−0.224248	−	0.388410i	0.731845	−	0.681471i	$-0.238659\pi$
$683$	−5.86057	−	10.1508i	−0.224248	−	0.388410i	−0.956094	+	0.293061i	$0.905326\pi$
$684$	2.02319	+	4.09529i	0.0773585	+	0.156587i
$685$	1.79718	−	3.11280i	0.0686667	−	0.118934i
$686$	0.939693	+	0.342020i	0.0358776	+	0.0130584i
$687$	38.6725	−	5.53514i	1.47545	−	0.211179i
$688$	5.32938	+	4.47188i	0.203181	+	0.170489i
$689$	−18.4629	−	15.4922i	−0.703382	−	0.590207i
$690$	19.5418	−	2.79699i	0.743944	−	0.106480i
$691$	47.7050	+	17.3632i	1.81478	+	0.660528i	0.996294	+	0.0860077i	$0.0274110\pi$
$691$	47.7050	+	17.3632i	1.81478	+	0.660528i	0.818491	+	0.574520i	$0.194811\pi$
$692$	4.80412	−	8.32099i	0.182625	−	0.316316i
$693$	−17.1374	−	1.11102i	−0.650995	−	0.0422043i
$694$	−4.56371	−	7.90457i	−0.173236	−	0.300053i
$695$	5.20648	+	29.5274i	0.197493	+	1.12004i
$696$	1.58016	−	0.845333i	0.0598957	−	0.0320423i
$697$	8.15971	−	2.96989i	0.309071	−	0.112493i
$698$	2.27698	−	12.9134i	0.0861851	−	0.488780i
$699$	−1.84217	−	5.62106i	−0.0696773	−	0.212608i
$700$	−0.114163	+	0.0957945i	−0.00431497	+	0.00362069i
$701$	38.4852			1.45357			0.726783	−	0.686868i	$-0.241015\pi$
$701$	38.4852			1.45357			0.726783	+	0.686868i	$0.241015\pi$
$702$	−14.4190	−	10.3093i	−0.544208	−	0.389098i
$703$	−4.27575			−0.161263
$704$	4.38518	−	3.67960i	0.165273	−	0.138680i
$705$	5.21500	+	1.09466i	0.196408	+	0.0412274i
$706$	0.298544	−	1.69313i	0.0112358	−	0.0637216i
$707$	−14.9246	+	5.43211i	−0.561297	+	0.204295i
$708$	−7.24100	−	4.49918i	−0.272133	−	0.169089i
$709$	−3.77437	−	21.4055i	−0.141749	−	0.803901i	−0.969920	−	0.243425i	$-0.921729\pi$
$709$	−3.77437	−	21.4055i	−0.141749	−	0.803901i	0.828170	−	0.560476i	$-0.189382\pi$
$710$	4.83210	+	8.36944i	0.181345	+	0.314099i
$711$	25.1553	+	24.0467i	0.943396	+	0.901823i
$712$	6.18042	−	10.7048i	0.231621	−	0.401179i
$713$	−45.9127	−	16.7109i	−1.71945	−	0.625827i
$714$	2.46652	−	6.14973i	0.0923074	−	0.230148i
$715$	32.9469	+	27.6457i	1.23214	+	1.03389i
$716$	−12.3073	−	10.3271i	−0.459947	−	0.385941i
$717$	−4.25608	−	5.41915i	−0.158946	−	0.202382i
$718$	19.2382	+	7.00214i	0.717964	+	0.261318i
$719$	−13.4274	+	23.2569i	−0.500756	+	0.867335i	0.499243	+	0.866462i	$0.333611\pi$
$719$	−13.4274	+	23.2569i	−0.500756	+	0.867335i	−1.00000		0.000873332i	$0.999722\pi$
$720$	−0.723998	−	6.56769i	−0.0269818	−	0.244763i
$721$	−8.34460	−	14.4533i	−0.310769	−	0.538268i
$722$	2.89675	+	16.4283i	0.107806	+	0.611397i
$723$	0.537767	−	16.6073i	0.0199998	−	0.617633i
$724$	−0.849117	+	0.309053i	−0.0315572	+	0.0114859i
$725$	0.0267754	−	0.151851i	0.000994413	−	0.00563960i
$726$	25.1588	−	28.0846i	0.933730	−	1.04232i
$727$	−14.0375	+	11.7788i	−0.520622	+	0.436853i	−0.864848	−	0.502033i	$-0.832586\pi$
$727$	−14.0375	+	11.7788i	−0.520622	+	0.436853i	0.344227	+	0.938887i	$0.388141\pi$
$728$	−3.41124			−0.126429
$729$	8.73330	+	25.5486i	0.323455	+	0.946243i
$730$	0.340055			0.0125860
$731$	−20.3874	+	17.1071i	−0.754057	+	0.632729i
$732$	2.59575	−	2.89762i	0.0959416	−	0.107099i
$733$	−5.93254	+	33.6451i	−0.219123	+	1.24271i	0.654483	+	0.756077i	$0.272887\pi$
$733$	−5.93254	+	33.6451i	−0.219123	+	1.24271i	−0.873606	+	0.486634i	$0.838225\pi$
$734$	−17.8390	+	6.49287i	−0.658450	+	0.239656i
$735$	−0.123464	+	3.81283i	−0.00455405	+	0.140638i
$736$	−0.898594	−	5.09618i	−0.0331226	−	0.187848i
$737$	36.5360	+	63.2822i	1.34582	+	2.33103i
$738$	0.746149	+	6.76863i	0.0274661	+	0.249157i
$739$	−13.8116	+	23.9224i	−0.508068	+	0.879999i	0.491889	+	0.870658i	$0.336307\pi$
$739$	−13.8116	+	23.9224i	−0.508068	+	0.879999i	−0.999956	+	0.00934113i	$0.997027\pi$
$740$	5.81203	+	2.11541i	0.213654	+	0.0777639i
$741$	5.55656	+	7.07500i	0.204125	+	0.259907i
$742$	5.41238	+	4.54153i	0.198695	+	0.166725i
$743$	40.1091	+	33.6555i	1.47146	+	1.23470i	0.914767	+	0.403981i	$0.132374\pi$
$743$	40.1091	+	33.6555i	1.47146	+	1.23470i	0.556691	+	0.830719i	$0.312071\pi$
$744$	−6.08771	+	15.1783i	−0.223186	+	0.556465i
$745$	47.9442	+	17.4503i	1.75654	+	0.639328i
$746$	0.707540	−	1.22550i	0.0259049	−	0.0448686i
$747$	7.16136	+	6.84577i	0.262020	+	0.250474i
$748$	10.9494	+	18.9649i	0.400349	+	0.693425i
$749$	−0.901556	−	5.11298i	−0.0329421	−	0.186824i
$750$	−16.6843	−	10.3667i	−0.609223	−	0.378540i
$751$	−30.2877	+	11.0238i	−1.10521	+	0.402264i	−0.829235	−	0.558900i	$-0.811224\pi$
$751$	−30.2877	+	11.0238i	−1.10521	+	0.402264i	−0.275977	+	0.961164i	$0.589001\pi$
$752$	0.242556	−	1.37560i	0.00884511	−	0.0501631i
$753$	−45.3400	−	9.51717i	−1.65228	−	0.346825i
$754$	2.70370	−	2.26867i	0.0984630	−	0.0826202i
$755$	36.5187			1.32905
$756$	4.22690	+	3.02214i	0.153731	+	0.109914i
$757$	−13.8766			−0.504355			−0.252177	−	0.967681i	$-0.581147\pi$
$757$	−13.8766			−0.504355			−0.252177	+	0.967681i	$0.581147\pi$
$758$	19.5047	−	16.3664i	0.708444	−	0.594455i
$759$	−15.9789	−	48.7567i	−0.579996	−	1.76976i
$760$	−0.582330	+	3.30256i	−0.0211233	+	0.119796i
$761$	−29.3613	+	10.6866i	−1.06434	+	0.387390i	−0.814059	−	0.580782i	$-0.802747\pi$
$761$	−29.3613	+	10.6866i	−1.06434	+	0.387390i	−0.250286	+	0.968172i	$0.580525\pi$
$762$	−12.2917	+	6.57565i	−0.445280	+	0.238211i
$763$	2.17293	+	12.3233i	0.0786654	+	0.446134i
$764$	−9.76082	−	16.9062i	−0.353134	−	0.611646i
$765$	25.2238	+	1.63527i	0.911969	+	0.0591235i
$766$	6.63145	−	11.4860i	0.239604	−	0.415006i
$767$	−15.7772	−	5.74242i	−0.569680	−	0.207347i
$768$	−1.71458	+	0.245405i	−0.0618695	+	0.00885529i
$769$	−19.6837	−	16.5165i	−0.709811	−	0.595602i	0.214735	−	0.976672i	$-0.431111\pi$
$769$	−19.6837	−	16.5165i	−0.709811	−	0.595602i	−0.924546	+	0.381070i	$0.875556\pi$
$770$	−9.65833	−	8.10430i	−0.348062	−	0.292059i
$771$	−24.7624	+	3.54421i	−0.891797	+	0.127641i
$772$	21.9338	+	7.98325i	0.789414	+	0.287323i
$773$	−0.160253	+	0.277567i	−0.00576392	+	0.00998339i	−0.868893	−	0.495000i	$-0.835168\pi$
$773$	−0.160253	+	0.277567i	−0.00576392	+	0.00998339i	0.863129	+	0.504983i	$0.168501\pi$
$774$	−9.24431	−	18.7121i	−0.332280	−	0.672593i
$775$	0.703554	+	1.21859i	0.0252724	+	0.0437731i
$776$	−1.43720	−	8.15077i	−0.0515925	−	0.292596i
$777$	−4.28880	+	2.29437i	−0.153860	+	0.0823100i
$778$	5.90876	−	2.15061i	0.211839	−	0.0771032i
$779$	0.600147	−	3.40360i	0.0215025	−	0.121947i
$780$	−4.05271	−	12.3661i	−0.145110	−	0.442779i
$781$	19.2415	−	16.1455i	0.688515	−	0.577733i
$782$	19.7961			0.707907
$783$	−5.36008	+	0.415825i	−0.191554	+	0.0148604i
$784$	1.00000			0.0357143
$785$	−25.0435	+	21.0140i	−0.893842	+	0.750023i
$786$	33.7475	+	7.08382i	1.20373	+	0.252672i
$787$	−7.59471	+	43.0717i	−0.270722	+	1.53534i	0.481508	+	0.876441i	$0.340089\pi$
$787$	−7.59471	+	43.0717i	−0.270722	+	1.53534i	−0.752231	+	0.658900i	$0.771022\pi$
$788$	−15.0350	+	5.47230i	−0.535600	+	0.194943i
$789$	29.5248	+	18.3452i	1.05111	+	0.653106i
$790$	4.43651	+	25.1607i	0.157844	+	0.895177i
$791$	10.5004	+	18.1873i	0.373353	+	0.646666i
$792$	−16.4839	+	4.81730i	−0.585728	+	0.171175i
$793$	3.83089	−	6.63530i	0.136039	−	0.235626i
$794$	13.8834	+	5.05316i	0.492705	+	0.179330i
$795$	−10.0334	+	25.0160i	−0.355848	+	0.887228i
$796$	11.9634	+	10.0385i	0.424032	+	0.355806i
$797$	−33.5655	−	28.1648i	−1.18895	−	0.997648i	−0.999877	−	0.0156855i	$-0.995007\pi$
$797$	−33.5655	−	28.1648i	−1.18895	−	0.997648i	−0.189074	−	0.981963i	$-0.560549\pi$
$798$	−1.62890	−	2.07403i	−0.0576623	−	0.0734198i
$799$	5.02127	+	1.82759i	0.177640	+	0.0646556i
$800$	−0.0745149	+	0.129064i	−0.00263450	+	0.00456309i
$801$	−29.8894	+	21.9485i	−1.05609	+	0.775511i
$802$	−12.6160	−	21.8515i	−0.445486	−	0.771605i
$803$	−0.153475	−	0.870402i	−0.00541603	−	0.0307158i
$804$	0.715558	−	22.0979i	0.0252358	−	0.779332i
$805$	−10.7101	+	3.89816i	−0.377481	+	0.137392i
$806$	−5.59289	+	31.7189i	−0.197001	+	1.11725i
$807$	27.0290	−	30.1723i	0.951465	−	1.06211i
$808$	−12.1666	+	10.2090i	−0.428021	+	0.359152i
$809$	−7.57639			−0.266372			−0.133186	−	0.991091i	$-0.542521\pi$
$809$	−7.57639			−0.266372			−0.133186	+	0.991091i	$0.542521\pi$
$810$	−5.93387	+	18.9134i	−0.208495	+	0.664550i
$811$	36.8841			1.29518			0.647588	−	0.761990i	$-0.275778\pi$
$811$	36.8841			1.29518			0.647588	+	0.761990i	$0.275778\pi$
$812$	−0.792586	+	0.665059i	−0.0278143	+	0.0233390i
$813$	−10.7201	+	11.9668i	−0.375972	+	0.419695i
$814$	2.79146	−	15.8312i	0.0978407	−	0.554882i
$815$	−33.9575	+	12.3595i	−1.18948	+	0.432935i
$816$	0.214444	−	6.62246i	0.00750703	−	0.231832i
$817$	1.83941	+	10.4318i	0.0643526	+	0.364962i
$818$	−4.86843	−	8.43236i	−0.170221	−	0.294831i
$819$	9.36996	+	4.11495i	0.327413	+	0.143788i
$820$	−2.49969	+	4.32960i	−0.0872931	+	0.151196i
$821$	−32.9530	−	11.9939i	−1.15007	−	0.418590i	−0.304527	−	0.952504i	$-0.598498\pi$
$821$	−32.9530	−	11.9939i	−1.15007	−	0.418590i	−0.845539	+	0.533914i	$0.820721\pi$
$822$	1.74589	+	2.22299i	0.0608948	+	0.0775355i
$823$	14.8926	+	12.4964i	0.519124	+	0.435597i	0.864326	−	0.502931i	$-0.167745\pi$
$823$	14.8926	+	12.4964i	0.519124	+	0.435597i	−0.345202	+	0.938528i	$0.612190\pi$
$824$	−12.7847	−	10.7276i	−0.445375	−	0.373714i
$825$	−0.550055	+	1.37144i	−0.0191505	+	0.0477474i
$826$	4.62505	+	1.68338i	0.160926	+	0.0585723i
$827$	19.2795	−	33.3931i	0.670414	−	1.16119i	−0.307373	−	0.951589i	$-0.599450\pi$
$827$	19.2795	−	33.3931i	0.670414	−	1.16119i	0.977787	−	0.209602i	$-0.0672168\pi$
$828$	−3.67922	+	15.0821i	−0.127862	+	0.524139i
$829$	−5.24895	−	9.09146i	−0.182304	−	0.315759i	0.760361	−	0.649501i	$-0.225022\pi$
$829$	−5.24895	−	9.09146i	−0.182304	−	0.315759i	−0.942665	+	0.333741i	$0.891689\pi$
$830$	1.26301	+	7.16290i	0.0438398	+	0.248628i
$831$	−18.5328	−	11.5153i	−0.642895	−	0.399461i
$832$	−3.20552	+	1.16671i	−0.111131	+	0.0404485i
$833$	−0.664288	+	3.76736i	−0.0230162	+	0.130531i
$834$	−23.0758	−	4.84377i	−0.799051	−	0.167726i
$835$	−29.3606	+	24.6364i	−1.01606	+	0.852579i
$836$	8.71602			0.301450
$837$	35.0311	−	34.3482i	1.21085	−	1.18725i
$838$	31.9840			1.10487
$839$	24.7797	−	20.7926i	0.855489	−	0.717840i	−0.105503	−	0.994419i	$-0.533645\pi$
$839$	24.7797	−	20.7926i	0.855489	−	0.717840i	0.960991	+	0.276579i	$0.0892007\pi$
$840$	1.18805	+	3.62511i	0.0409915	+	0.125078i
$841$	−4.84991	+	27.5052i	−0.167238	+	0.948455i
$842$	23.0145	−	8.37660i	0.793133	−	0.288677i
$843$	26.8635	−	14.3711i	0.925229	−	0.494967i
$844$	2.44906	+	13.8893i	0.0843000	+	0.478089i
$845$	1.50149	+	2.60066i	0.0516529	+	0.0894654i
$846$	−2.32563	+	3.48590i	−0.0799568	+	0.119848i
$847$	−10.8847	+	18.8528i	−0.374001	+	0.647789i
$848$	6.63927	+	2.41650i	0.227993	+	0.0829828i
$849$	−50.8088	+	7.27219i	−1.74375	+	0.249581i
$850$	−0.436730	−	0.366460i	−0.0149797	−	0.0125695i
$851$	−11.1320	−	9.34089i	−0.381602	−	0.320202i
$852$	−7.52330	+	1.07680i	−0.257744	+	0.0368905i
$853$	−32.4445	−	11.8088i	−1.11088	−	0.404327i	−0.279564	−	0.960127i	$-0.590190\pi$
$853$	−32.4445	−	11.8088i	−1.11088	−	0.404327i	−0.831316	+	0.555800i	$0.812412\pi$
$854$	−1.12302	+	1.94513i	−0.0384290	+	0.0665609i
$855$	5.58338	−	8.36898i	0.190948	−	0.286213i
$856$	−2.59593	−	4.49628i	−0.0887269	−	0.153680i
$857$	1.68543	+	9.55854i	0.0575731	+	0.326513i	0.999968	−	0.00798881i	$-0.00254294\pi$
$857$	1.68543	+	9.55854i	0.0575731	+	0.326513i	−0.942395	+	0.334502i	$0.891432\pi$
$858$	−29.8232	+	15.9544i	−1.01815	+	0.544675i
$859$	9.99320	−	3.63723i	0.340964	−	0.124101i	−0.165863	−	0.986149i	$-0.553041\pi$
$859$	9.99320	−	3.63723i	0.340964	−	0.124101i	0.506826	+	0.862048i	$0.330819\pi$
$860$	2.66077	−	15.0900i	0.0907315	−	0.514564i
$861$	−1.22440	−	3.73603i	−0.0417273	−	0.127323i
$862$	16.9594	−	14.2306i	0.577640	−	0.484698i
$863$	−4.77498			−0.162542			−0.0812711	−	0.996692i	$-0.525898\pi$
$863$	−4.77498			−0.162542			−0.0812711	+	0.996692i	$0.525898\pi$
$864$	5.00562	+	1.39420i	0.170295	+	0.0474317i
$865$	−21.1621			−0.719532
$866$	3.76351	−	3.15796i	0.127889	−	0.107312i
$867$	−4.01011	−	0.841749i	−0.136190	−	0.0285873i
$868$	1.63955	−	9.29835i	0.0556499	−	0.315606i
$869$	62.3988	−	22.7113i	2.11673	−	0.770428i
$870$	−3.35254	−	2.08310i	−0.113662	−	0.0706235i
$871$	−7.56136	−	42.8826i	−0.256207	−	1.45302i
$872$	6.25671	+	10.8369i	0.211879	+	0.366985i
$873$	−5.88451	+	24.1222i	−0.199160	+	0.816411i
$874$	3.93956	−	6.82352i	0.133258	−	0.230809i
$875$	10.6568	+	3.87875i	0.360265	+	0.131126i
$876$	−0.0995483	+	0.248202i	−0.00336343	+	0.00838596i
$877$	38.4539	+	32.2666i	1.29849	+	1.08957i	0.990403	+	0.138210i	$0.0441347\pi$
$877$	38.4539	+	32.2666i	1.29849	+	1.08957i	0.308091	+	0.951357i	$0.400310\pi$
$878$	15.5047	+	13.0100i	0.523258	+	0.439065i
$879$	−14.8916	−	18.9610i	−0.502280	−	0.639539i
$880$	−11.8477	−	4.31221i	−0.399386	−	0.145364i
$881$	−13.0520	+	22.6067i	−0.439732	+	0.761639i	−0.997669	−	0.0682451i	$-0.978260\pi$
$881$	−13.0520	+	22.6067i	−0.439732	+	0.761639i	0.557936	+	0.829884i	$0.311593\pi$
$882$	−2.74679	−	1.20629i	−0.0924893	−	0.0406179i
$883$	−26.0206	−	45.0691i	−0.875664	−	1.51670i	−0.856053	−	0.516888i	$-0.827091\pi$
$883$	−26.0206	−	45.0691i	−0.875664	−	1.51670i	−0.0196111	−	0.999808i	$-0.506243\pi$
$884$	−2.26604	−	12.8514i	−0.0762153	−	0.432239i
$885$	−0.607676	+	18.7663i	−0.0204268	+	0.630822i
$886$	−25.8616	+	9.41287i	−0.868839	+	0.316232i
$887$	0.821141	−	4.65692i	0.0275712	−	0.156364i	−0.967914	−	0.251282i	$-0.919148\pi$
$887$	0.821141	−	4.65692i	0.0275712	−	0.156364i	0.995485	+	0.0949180i	$0.0302589\pi$
$888$	−3.24543	+	3.62286i	−0.108910	+	0.121575i
$889$	6.16534	−	5.17333i	0.206779	−	0.173508i
$890$	−27.2246			−0.912572
$891$	51.0888	+	6.65218i	1.71154	+	0.222857i
$892$	−17.2410			−0.577270
$893$	1.62922	−	1.36708i	0.0545199	−	0.0457476i
$894$	−26.7720	+	29.8854i	−0.895390	+	0.999519i
$895$	−6.14461	+	34.8478i	−0.205392	+	1.16483i
$896$	0.939693	−	0.342020i	0.0313929	−	0.0114261i
$897$	−0.989538	+	30.5590i	−0.0330397	+	1.02033i
$898$	1.28630	+	7.29500i	0.0429245	+	0.243437i
$899$	4.88446	+	8.46014i	0.162906	+	0.282161i
$900$	0.360365	−	0.264624i	0.0120122	−	0.00882081i
$901$	−13.5142	+	23.4073i	−0.450224	+	0.779810i
$902$	12.2102	+	4.44414i	0.406555	+	0.147974i
$903$	7.44272	+	9.47660i	0.247678	+	0.315361i
$904$	16.0876	+	13.4991i	0.535066	+	0.448974i
$905$	1.52458	+	1.27927i	0.0506787	+	0.0425245i
$906$	−10.6906	+	26.6545i	−0.355170	+	0.885537i
$907$	−43.0525	−	15.6698i	−1.42954	−	0.520308i	−0.492737	−	0.870178i	$-0.664004\pi$
$907$	−43.0525	−	15.6698i	−1.42954	−	0.520308i	−0.936798	+	0.349870i	$0.886226\pi$
$908$	0.611882	−	1.05981i	0.0203060	−	0.0351710i
$909$	45.7343	−	13.3656i	1.51691	−	0.443308i
$910$	3.75661	+	6.50664i	0.124531	+	0.215693i
$911$	4.88713	+	27.7163i	0.161918	+	0.918282i	0.952186	+	0.305520i	$0.0988304\pi$
$911$	4.88713	+	27.7163i	0.161918	+	0.918282i	−0.790268	+	0.612762i	$0.790058\pi$
$912$	−2.24002	−	1.39183i	−0.0741745	−	0.0460882i
$913$	17.7641	−	6.46559i	0.587905	−	0.213980i
$914$	−4.53871	+	25.7403i	−0.150127	+	0.851413i
$915$	−8.38551	−	1.76018i	−0.277217	−	0.0581896i
$916$	−17.2782	+	14.4982i	−0.570889	+	0.479033i
$917$	−19.9087			−0.657444
$918$	−8.57764	+	17.9318i	−0.283104	+	0.591838i
$919$	1.59582			0.0526414			0.0263207	−	0.999654i	$-0.491621\pi$
$919$	1.59582			0.0526414			0.0263207	+	0.999654i	$0.491621\pi$
$920$	−8.73095	+	7.32614i	−0.287851	+	0.241536i
$921$	−9.36376	−	28.5719i	−0.308546	−	0.941476i
$922$	−0.939904	+	5.33046i	−0.0309541	+	0.175549i
$923$	−14.0653	+	5.11936i	−0.462965	+	0.168506i
$924$	8.74262	−	4.67702i	0.287611	−	0.153863i
$925$	0.0726727	+	0.412147i	0.00238946	+	0.0135513i
$926$	8.71450	+	15.0940i	0.286376	+	0.496018i
$927$	22.1762	+	44.8886i	0.728362	+	1.47433i
$928$	−0.517324	+	0.896031i	−0.0169820	+	0.0294137i
$929$	−12.3750	−	4.50413i	−0.406011	−	0.147776i	0.130938	−	0.991391i	$-0.458201\pi$
$929$	−12.3750	−	4.50413i	−0.406011	−	0.147776i	−0.536949	+	0.843615i	$0.680423\pi$
$930$	35.6554	−	5.10331i	1.16919	−	0.167344i
$931$	1.16638	+	0.978706i	0.0382264	+	0.0320758i
$932$	2.61616	+	2.19522i	0.0856952	+	0.0719069i
$933$	−33.5928	+	4.80808i	−1.09978	+	0.157410i
$934$	−17.9324	−	6.52684i	−0.586764	−	0.213565i
$935$	24.1159	−	41.7700i	0.788675	−	1.36603i
$936$	10.2123	+	0.662068i	0.333799	+	0.0216404i
$937$	−13.3286	−	23.0858i	−0.435427	−	0.754182i	0.561903	−	0.827203i	$-0.310069\pi$
$937$	−13.3286	−	23.0858i	−0.435427	−	0.754182i	−0.997330	+	0.0730211i	$0.976736\pi$
$938$	2.21660	+	12.5710i	0.0723746	+	0.410457i
$939$	−0.640634	+	0.342718i	−0.0209063	+	0.0111842i
$940$	−2.89096	+	1.05222i	−0.0942927	+	0.0343197i
$941$	5.57232	−	31.6022i	0.181652	−	1.03020i	−0.748529	−	0.663102i	$-0.769239\pi$
$941$	5.57232	−	31.6022i	0.181652	−	1.03020i	0.930181	−	0.367100i	$-0.119649\pi$
$942$	−8.00657	−	24.4306i	−0.260868	−	0.795993i
$943$	8.99808	−	7.55029i	0.293018	−	0.245871i
$944$	4.92188			0.160194
$945$	1.10963	−	11.3906i	0.0360962	−	0.370535i
$946$	−39.8250			−1.29482
$947$	−14.7698	+	12.3934i	−0.479956	+	0.402731i	−0.850410	−	0.526120i	$-0.823646\pi$
$947$	−14.7698	+	12.3934i	−0.479956	+	0.402731i	0.370455	+	0.928850i	$0.379202\pi$
$948$	−19.6632	−	4.12744i	−0.638631	−	0.134053i
$949$	−0.0914570	+	0.518679i	−0.00296882	+	0.0168370i
$950$	−0.213228	+	0.0776085i	−0.00691802	+	0.00251795i
$951$	20.8555	+	12.9585i	0.676287	+	0.420209i
$952$	0.664288	+	3.76736i	0.0215297	+	0.122101i
$953$	−5.90855	−	10.2339i	−0.191397	−	0.331509i	0.754317	−	0.656511i	$-0.227968\pi$
$953$	−5.90855	−	10.2339i	−0.191397	−	0.331509i	−0.945713	+	0.325002i	$0.894635\pi$
$954$	−15.3217	−	14.6465i	−0.496058	−	0.474198i
$955$	−21.4981	+	37.2358i	−0.695663	+	1.20492i
$956$	3.73841	+	1.36067i	0.120909	+	0.0440072i
$957$	−3.81879	+	9.52130i	−0.123444	+	0.307780i
$958$	−1.42638	−	1.19688i	−0.0460843	−	0.0386694i
$959$	−1.25015	−	1.04900i	−0.0403693	−	0.0338739i
$960$	2.35626	+	3.00016i	0.0760480	+	0.0968297i
$961$	−54.6406	−	19.8876i	−1.76260	−	0.641534i
$962$	−4.78972	+	8.29603i	−0.154427	+	0.267475i
$963$	1.70665	+	15.4818i	0.0549961	+	0.498893i
$964$	4.79663	+	8.30801i	0.154489	+	0.267583i
$965$	−8.92714	−	50.6283i	−0.287375	−	1.62978i
$966$	0.290082	−	8.95831i	0.00933323	−	0.288229i
$967$	25.4574	−	9.26572i	0.818654	−	0.297966i	0.101460	−	0.994840i	$-0.467649\pi$
$967$	25.4574	−	9.26572i	0.818654	−	0.297966i	0.717193	+	0.696874i	$0.245426\pi$
$968$	−3.78020	+	21.4386i	−0.121500	+	0.689062i
$969$	6.73156	−	7.51440i	0.216249	−	0.241397i
$970$	−13.9642	+	11.7173i	−0.448363	+	0.376221i
$971$	39.2114			1.25835			0.629177	−	0.777262i	$-0.283392\pi$
$971$	39.2114			1.25835			0.629177	+	0.777262i	$0.283392\pi$
$972$	−12.0676	−	9.86781i	−0.387068	−	0.316510i
$973$	13.6132			0.436418
$974$	−14.3350	+	12.0285i	−0.459322	+	0.385417i
$975$	0.587530	−	0.655856i	0.0188160	−	0.0210042i
$976$	−0.390021	+	2.21192i	−0.0124843	+	0.0708018i
$977$	−4.15720	+	1.51310i	−0.133001	+	0.0484083i	−0.407663	−	0.913132i	$-0.633656\pi$
$977$	−4.15720	+	1.51310i	−0.133001	+	0.0484083i	0.274662	+	0.961541i	$0.411434\pi$
$978$	0.919736	−	28.4033i	0.0294099	−	0.908238i
$979$	12.2872	+	69.6840i	0.392699	+	2.22711i
$980$	−1.10125	−	1.90741i	−0.0351780	−	0.0609301i
$981$	−4.11338	−	37.3142i	−0.131330	−	1.19135i
$982$	16.9230	−	29.3114i	0.540033	−	0.935365i
$983$	−19.5054	−	7.09940i	−0.622127	−	0.226436i	0.0116741	−	0.999932i	$-0.496284\pi$
$983$	−19.5054	−	7.09940i	−0.622127	−	0.226436i	−0.633801	+	0.773496i	$0.718506\pi$
$984$	−2.42835	−	3.09195i	−0.0774130	−	0.0985678i
$985$	26.9952	+	22.6517i	0.860138	+	0.721742i
$986$	−3.03202	−	2.54417i	−0.0965593	−	0.0810229i
$987$	0.900620	−	2.24549i	0.0286670	−	0.0714749i
$988$	−4.88070	−	1.77643i	−0.155276	−	0.0565158i
$989$	−18.0006	+	31.1779i	−0.572384	+	0.991399i
$990$	27.3414	+	26.1365i	0.868966	+	0.830672i
$991$	1.51981	+	2.63238i	0.0482783	+	0.0836204i	0.889155	−	0.457607i	$-0.151293\pi$
$991$	1.51981	+	2.63238i	0.0482783	+	0.0836204i	−0.840876	+	0.541227i	$0.817960\pi$
$992$	−1.63955	−	9.29835i	−0.0520557	−	0.295223i
$993$	−16.7464	−	10.4054i	−0.531432	−	0.330204i
$994$	4.12323	−	1.50073i	0.130781	−	0.0476003i
$995$	5.97291	−	33.8741i	0.189354	−	1.07388i
$996$	−5.59784	−	1.17503i	−0.177374	−	0.0372321i
$997$	9.93668	−	8.33786i	0.314698	−	0.264063i	−0.471733	−	0.881742i	$-0.656371\pi$
$997$	9.93668	−	8.33786i	0.314698	−	0.264063i	0.786430	+	0.617679i	$0.211927\pi$
$998$	14.8549			0.470223
$999$	13.2847	−	6.03630i	0.420311	−	0.190980i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.e.211.2	yes	36
27.16	even	9	inner	378.2.u.e.43.2	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.e.43.2	✓	36	27.16	even	9	inner
378.2.u.e.211.2	yes	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.15570 + 1.29010i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-2.06967 + 0.753297i) q^{5} +(0.0560567 - 1.73114i) q^{6} +(0.173648 + 0.984808i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.328718 - 2.98194i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.15570 + 1.29010i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-2.06967 + 0.753297i) q^{5} +(0.0560567 - 1.73114i) q^{6} +(0.173648 + 0.984808i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.328718 - 2.98194i) q^{9} +(1.10125 - 1.90741i) q^{10} +(-5.37922 - 1.95788i) q^{11} +(1.06982 + 1.36217i) q^{12} +(2.61316 + 2.19270i) q^{13} +(-0.766044 - 0.642788i) q^{14} +(1.42008 - 3.54066i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.91274 - 3.31296i) q^{17} +(2.16856 + 2.07300i) q^{18} +(-0.761298 - 1.31861i) q^{19} +(0.382459 + 2.16903i) q^{20} +(-1.47119 - 0.914118i) q^{21} +(5.37922 - 1.95788i) q^{22} +(0.898594 - 5.09618i) q^{23} +(-1.69511 - 0.355815i) q^{24} +(-0.114163 + 0.0957945i) q^{25} -3.41124 q^{26} +(4.22690 + 3.02214i) q^{27} +1.00000 q^{28} +(-0.792586 + 0.665059i) q^{29} +(1.18805 + 3.62511i) q^{30} +(1.63955 - 9.29835i) q^{31} +(0.939693 - 0.342020i) q^{32} +(8.74262 - 4.67702i) q^{33} +(0.664288 + 3.76736i) q^{34} +(-1.10125 - 1.90741i) q^{35} +(-2.99372 - 0.194084i) q^{36} +(1.40410 - 2.43197i) q^{37} +(1.43077 + 0.520758i) q^{38} +(-5.84883 + 0.837135i) q^{39} +(-1.68721 - 1.41573i) q^{40} +(1.73883 + 1.45905i) q^{41} +(1.71458 - 0.245405i) q^{42} +(-6.53745 - 2.37944i) q^{43} +(-2.86222 + 4.95752i) q^{44} +(2.92662 + 5.92399i) q^{45} +(2.58740 + 4.48151i) q^{46} +(0.242556 + 1.37560i) q^{47} +(1.52724 - 0.817025i) q^{48} +(-0.939693 + 0.342020i) q^{49} +(0.0258788 - 0.146766i) q^{50} +(2.06350 + 6.29642i) q^{51} +(2.61316 - 2.19270i) q^{52} -7.06536 q^{53} +(-5.18059 + 0.401900i) q^{54} +12.6080 q^{55} +(-0.766044 + 0.642788i) q^{56} +(2.58097 + 0.541762i) q^{57} +(0.179665 - 1.01893i) q^{58} +(-4.62505 + 1.68338i) q^{59} +(-3.24027 - 2.01334i) q^{60} +(-0.390021 - 2.21192i) q^{61} +(4.72089 + 8.17683i) q^{62} +(2.87955 - 0.841531i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-7.06012 - 2.56967i) q^{65} +(-3.69091 + 9.20245i) q^{66} +(-9.77848 - 8.20512i) q^{67} +(-2.93049 - 2.45897i) q^{68} +(5.53608 + 7.04893i) q^{69} +(2.06967 + 0.753297i) q^{70} +(-2.19392 + 3.79999i) q^{71} +(2.41807 - 1.77565i) q^{72} +(0.0771978 + 0.133710i) q^{73} +(0.487638 + 2.76554i) q^{74} +(0.00835411 - 0.257992i) q^{75} +(-1.43077 + 0.520758i) q^{76} +(0.994040 - 5.63748i) q^{77} +(3.94237 - 4.40084i) q^{78} +(-8.88609 + 7.45631i) q^{79} +2.20249 q^{80} +(-8.78389 + 1.96043i) q^{81} -2.26988 q^{82} +(-2.52975 + 2.12271i) q^{83} +(-1.15570 + 1.29010i) q^{84} +(-1.46309 + 8.29759i) q^{85} +(6.53745 - 2.37944i) q^{86} +(0.0579989 - 1.79112i) q^{87} +(-0.994040 - 5.63748i) q^{88} +(-6.18042 - 10.7048i) q^{89} +(-6.04979 - 2.65684i) q^{90} +(-1.70562 + 2.95422i) q^{91} +(-4.86272 - 1.76988i) q^{92} +(10.1010 + 12.8613i) q^{93} +(-1.07003 - 0.897862i) q^{94} +(2.56893 + 2.15559i) q^{95} +(-0.644762 + 1.60757i) q^{96} +(-7.77738 - 2.83073i) q^{97} +(0.500000 - 0.866025i) q^{98} +(-4.07002 + 16.6841i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9}+O(q^{10}) \) 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9	\( 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{13} - 6 q^{15} + 6 q^{18} - 15 q^{19} - 6 q^{20} + 3 q^{21} - 3 q^{24} - 3 q^{25} - 18 q^{26} - 30 q^{27} + 36 q^{28} - 6 q^{29} - 9 q^{30} + 60 q^{33} + 9 q^{34} + 3 q^{35} - 27 q^{37} + 15 q^{38} + 6 q^{39} - 3 q^{40} - 9 q^{41} - 6 q^{43} + 9 q^{44} + 42 q^{45} - 9 q^{46} + 36 q^{47} + 3 q^{48} - 15 q^{50} - 36 q^{51} + 9 q^{52} - 42 q^{53} - 27 q^{54} + 30 q^{55} - 18 q^{57} - 21 q^{58} + 12 q^{59} + 24 q^{60} + 3 q^{61} + 18 q^{62} + 12 q^{63} - 18 q^{64} - 84 q^{65} + 18 q^{66} - 69 q^{67} + 9 q^{68} - 48 q^{69} - 3 q^{70} + 12 q^{71} + 6 q^{72} - 12 q^{73} + 9 q^{75} - 15 q^{76} + 9 q^{77} - 48 q^{78} - 51 q^{79} - 6 q^{80} - 69 q^{81} + 15 q^{83} + 3 q^{84} - 12 q^{85} + 6 q^{86} + 84 q^{87} - 9 q^{88} - 3 q^{89} + 6 q^{90} - 9 q^{91} + 18 q^{92} - 21 q^{93} + 9 q^{94} - 75 q^{95} - 42 q^{97} + 18 q^{98} + 39 q^{99}+O(q^{100}) \) 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9 - 3 * q^10 + 9 * q^13 - 6 * q^15 + 6 * q^18 - 15 * q^19 - 6 * q^20 + 3 * q^21 - 3 * q^24 - 3 * q^25 - 18 * q^26 - 30 * q^27 + 36 * q^28 - 6 * q^29 - 9 * q^30 + 60 * q^33 + 9 * q^34 + 3 * q^35 - 27 * q^37 + 15 * q^38 + 6 * q^39 - 3 * q^40 - 9 * q^41 - 6 * q^43 + 9 * q^44 + 42 * q^45 - 9 * q^46 + 36 * q^47 + 3 * q^48 - 15 * q^50 - 36 * q^51 + 9 * q^52 - 42 * q^53 - 27 * q^54 + 30 * q^55 - 18 * q^57 - 21 * q^58 + 12 * q^59 + 24 * q^60 + 3 * q^61 + 18 * q^62 + 12 * q^63 - 18 * q^64 - 84 * q^65 + 18 * q^66 - 69 * q^67 + 9 * q^68 - 48 * q^69 - 3 * q^70 + 12 * q^71 + 6 * q^72 - 12 * q^73 + 9 * q^75 - 15 * q^76 + 9 * q^77 - 48 * q^78 - 51 * q^79 - 6 * q^80 - 69 * q^81 + 15 * q^83 + 3 * q^84 - 12 * q^85 + 6 * q^86 + 84 * q^87 - 9 * q^88 - 3 * q^89 + 6 * q^90 - 9 * q^91 + 18 * q^92 - 21 * q^93 + 9 * q^94 - 75 * q^95 - 42 * q^97 + 18 * q^98 + 39 * q^99

Introduction

L-functions

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