LMFDB - Embedded newform 114.2.i.b.85.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,2,Mod(25,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("114.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	114.i (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:	$0.910294583043$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			85.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	114.85
Dual form			114.2.i.b.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{2} +(0.766044 - 0.642788i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.55303 + 0.565258i) q^{5} +(0.766044 + 0.642788i) q^{6} +(-0.0923963 + 0.160035i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{2} +(0.766044 - 0.642788i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.55303 + 0.565258i) q^{5} +(0.766044 + 0.642788i) q^{6} +(-0.0923963 + 0.160035i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.173648 - 0.984808i) q^{9} +(-0.286989 + 1.62760i) q^{10} +(2.17365 + 3.76487i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-4.96064 - 4.16247i) q^{13} +(-0.173648 - 0.0632028i) q^{14} +(1.55303 - 0.565258i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-0.368241 - 2.08840i) q^{17} +1.00000 q^{18} +(-4.11721 + 1.43128i) q^{19} -1.65270 q^{20} +(0.0320889 + 0.181985i) q^{21} +(-3.33022 + 2.79439i) q^{22} +(-0.0996702 + 0.0362770i) q^{23} +(-0.939693 - 0.342020i) q^{24} +(-1.73783 - 1.45821i) q^{25} +(3.23783 - 5.60808i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(0.0320889 - 0.181985i) q^{28} +(0.692066 - 3.92490i) q^{29} +(0.826352 + 1.43128i) q^{30} +(1.61334 - 2.79439i) q^{31} +(0.766044 + 0.642788i) q^{32} +(4.08512 + 1.48686i) q^{33} +(1.99273 - 0.725293i) q^{34} +(-0.233956 + 0.196312i) q^{35} +(0.173648 + 0.984808i) q^{36} +4.06418 q^{37} +(-2.12449 - 3.80612i) q^{38} -6.47565 q^{39} +(-0.286989 - 1.62760i) q^{40} +(-6.61721 + 5.55250i) q^{41} +(-0.173648 + 0.0632028i) q^{42} +(-0.0393628 - 0.0143269i) q^{43} +(-3.33022 - 2.79439i) q^{44} +(0.826352 - 1.43128i) q^{45} +(-0.0530334 - 0.0918566i) q^{46} +(-1.37551 + 7.80093i) q^{47} +(0.173648 - 0.984808i) q^{48} +(3.48293 + 6.03260i) q^{49} +(1.13429 - 1.96464i) q^{50} +(-1.62449 - 1.36310i) q^{51} +(6.08512 + 2.21480i) q^{52} +(8.65657 - 3.15074i) q^{53} +(0.766044 - 0.642788i) q^{54} +(1.24763 + 7.07564i) q^{55} +0.184793 q^{56} +(-2.23396 + 3.74292i) q^{57} +3.98545 q^{58} +(1.75237 + 9.93821i) q^{59} +(-1.26604 + 1.06234i) q^{60} +(-3.37939 + 1.23000i) q^{61} +(3.03209 + 1.10359i) q^{62} +(0.141559 + 0.118782i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-5.35117 - 9.26849i) q^{65} +(-0.754900 + 4.28125i) q^{66} +(-1.38666 + 7.86414i) q^{67} +(1.06031 + 1.83651i) q^{68} +(-0.0530334 + 0.0918566i) q^{69} +(-0.233956 - 0.196312i) q^{70} +(3.79813 + 1.38241i) q^{71} +(-0.939693 + 0.342020i) q^{72} +(11.6420 - 9.76882i) q^{73} +(0.705737 + 4.00243i) q^{74} -2.26857 q^{75} +(3.37939 - 2.75314i) q^{76} -0.803348 q^{77} +(-1.12449 - 6.37727i) q^{78} +(9.49660 - 7.96859i) q^{79} +(1.55303 - 0.565258i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(-6.61721 - 5.55250i) q^{82} +(-4.22803 + 7.32316i) q^{83} +(-0.0923963 - 0.160035i) q^{84} +(0.608593 - 3.45150i) q^{85} +(0.00727396 - 0.0412527i) q^{86} +(-1.99273 - 3.45150i) q^{87} +(2.17365 - 3.76487i) q^{88} +(-13.7404 - 11.5295i) q^{89} +(1.55303 + 0.565258i) q^{90} +(1.12449 - 0.409279i) q^{91} +(0.0812519 - 0.0681784i) q^{92} +(-0.560307 - 3.17766i) q^{93} -7.92127 q^{94} +(-7.20321 - 0.104455i) q^{95} +1.00000 q^{96} +(1.85591 + 10.5254i) q^{97} +(-5.33615 + 4.47756i) q^{98} +(4.08512 - 1.48686i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{5} + 3 q^{7} - 3 q^{8}+O(q^{10}) $ 6 * q - 3 * q^5 + 3 * q^7 - 3 * q^8	$ 6 q - 3 q^{5} + 3 q^{7} - 3 q^{8} + 6 q^{10} + 12 q^{11} - 3 q^{12} - 21 q^{13} - 3 q^{15} + 3 q^{17} + 6 q^{18} + 6 q^{19} - 12 q^{20} - 9 q^{21} + 3 q^{22} - 15 q^{23} + 9 q^{25} - 3 q^{27} - 9 q^{28} + 15 q^{29} + 6 q^{30} + 3 q^{31} + 3 q^{33} - 6 q^{34} - 6 q^{35} + 6 q^{37} + 6 q^{40} - 9 q^{41} - 9 q^{43} + 3 q^{44} + 6 q^{45} + 12 q^{46} - 21 q^{47} - 3 q^{50} + 3 q^{51} + 15 q^{52} + 30 q^{53} - 9 q^{55} - 6 q^{56} - 18 q^{57} - 12 q^{58} + 27 q^{59} - 3 q^{60} - 9 q^{61} + 9 q^{62} + 9 q^{63} - 3 q^{64} - 6 q^{65} - 6 q^{66} - 15 q^{67} + 12 q^{68} + 12 q^{69} - 6 q^{70} + 9 q^{71} + 12 q^{73} - 6 q^{74} + 6 q^{75} + 9 q^{76} + 42 q^{77} + 6 q^{78} + 15 q^{79} - 3 q^{80} - 9 q^{82} - 3 q^{83} + 3 q^{84} - 36 q^{85} + 18 q^{86} + 6 q^{87} + 12 q^{88} - 48 q^{89} - 3 q^{90} - 6 q^{91} + 3 q^{92} - 9 q^{93} - 30 q^{94} - 48 q^{95} + 6 q^{96} + 18 q^{97} - 36 q^{98} + 3 q^{99}+O(q^{100}) $ 6 * q - 3 * q^5 + 3 * q^7 - 3 * q^8 + 6 * q^10 + 12 * q^11 - 3 * q^12 - 21 * q^13 - 3 * q^15 + 3 * q^17 + 6 * q^18 + 6 * q^19 - 12 * q^20 - 9 * q^21 + 3 * q^22 - 15 * q^23 + 9 * q^25 - 3 * q^27 - 9 * q^28 + 15 * q^29 + 6 * q^30 + 3 * q^31 + 3 * q^33 - 6 * q^34 - 6 * q^35 + 6 * q^37 + 6 * q^40 - 9 * q^41 - 9 * q^43 + 3 * q^44 + 6 * q^45 + 12 * q^46 - 21 * q^47 - 3 * q^50 + 3 * q^51 + 15 * q^52 + 30 * q^53 - 9 * q^55 - 6 * q^56 - 18 * q^57 - 12 * q^58 + 27 * q^59 - 3 * q^60 - 9 * q^61 + 9 * q^62 + 9 * q^63 - 3 * q^64 - 6 * q^65 - 6 * q^66 - 15 * q^67 + 12 * q^68 + 12 * q^69 - 6 * q^70 + 9 * q^71 + 12 * q^73 - 6 * q^74 + 6 * q^75 + 9 * q^76 + 42 * q^77 + 6 * q^78 + 15 * q^79 - 3 * q^80 - 9 * q^82 - 3 * q^83 + 3 * q^84 - 36 * q^85 + 18 * q^86 + 6 * q^87 + 12 * q^88 - 48 * q^89 - 3 * q^90 - 6 * q^91 + 3 * q^92 - 9 * q^93 - 30 * q^94 - 48 * q^95 + 6 * q^96 + 18 * q^97 - 36 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	1.55303	+	0.565258i	0.694538	+	0.252791i	0.665077	−	0.746775i	$-0.268399\pi$
$5$	1.55303	+	0.565258i	0.694538	+	0.252791i	0.0294608	+	0.999566i	$0.490621\pi$
$6$	0.766044	+	0.642788i	0.312736	+	0.262417i
$7$	−0.0923963	+	0.160035i	−0.0349225	+	0.0604876i	−0.882958	−	0.469451i	$-0.844452\pi$
$7$	−0.0923963	+	0.160035i	−0.0349225	+	0.0604876i	0.848036	+	0.529939i	$0.177785\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$	−0.286989	+	1.62760i	−0.0907539	+	0.514691i
$11$	2.17365	+	3.76487i	0.655380	+	1.13515i	0.981798	+	0.189926i	$0.0608247\pi$
$11$	2.17365	+	3.76487i	0.655380	+	1.13515i	−0.326419	+	0.945225i	$0.605842\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−4.96064	−	4.16247i	−1.37583	−	1.15446i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−4.96064	−	4.16247i	−1.37583	−	1.15446i	−0.405108	−	0.914269i	$-0.632766\pi$
$14$	−0.173648	−	0.0632028i	−0.0464094	−	0.0168917i
$15$	1.55303	−	0.565258i	0.400992	−	0.145949i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−0.368241	−	2.08840i	−0.0893115	−	0.506511i	−0.996343	−	0.0854474i	$-0.972768\pi$
$17$	−0.368241	−	2.08840i	−0.0893115	−	0.506511i	0.907031	−	0.421064i	$-0.138343\pi$
$18$	1.00000			0.235702
$19$	−4.11721	+	1.43128i	−0.944553	+	0.328359i
$19$	−4.11721	+	1.43128i	−0.944553	+	0.328359i
$20$	−1.65270			−0.369556
$21$	0.0320889	+	0.181985i	0.00700237	+	0.0397124i
$22$	−3.33022	+	2.79439i	−0.710006	+	0.595766i
$23$	−0.0996702	+	0.0362770i	−0.0207827	+	0.00756428i	−0.352391	−	0.935853i	$-0.614631\pi$
$23$	−0.0996702	+	0.0362770i	−0.0207827	+	0.00756428i	0.331608	+	0.943417i	$0.392409\pi$
$24$	−0.939693	−	0.342020i	−0.191814	−	0.0698146i
$25$	−1.73783	−	1.45821i	−0.347565	−	0.291642i
$26$	3.23783	−	5.60808i	0.634990	−	1.09983i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	0.0320889	−	0.181985i	0.00606423	−	0.0343920i
$29$	0.692066	−	3.92490i	0.128514	−	0.728836i	−0.850645	−	0.525740i	$-0.823788\pi$
$29$	0.692066	−	3.92490i	0.128514	−	0.728836i	0.979159	−	0.203096i	$-0.0651004\pi$
$30$	0.826352	+	1.43128i	0.150871	+	0.261315i
$31$	1.61334	−	2.79439i	0.289765	−	0.501887i	−0.683989	−	0.729492i	$-0.739756\pi$
$31$	1.61334	−	2.79439i	0.289765	−	0.501887i	0.973753	+	0.227606i	$0.0730897\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	4.08512	+	1.48686i	0.711129	+	0.258830i
$34$	1.99273	−	0.725293i	0.341750	−	0.124387i
$35$	−0.233956	+	0.196312i	−0.0395457	+	0.0331828i
$36$	0.173648	+	0.984808i	0.0289414	+	0.164135i
$37$	4.06418			0.668147			0.334073	−	0.942547i	$-0.391577\pi$
$37$	4.06418			0.668147			0.334073	+	0.942547i	$0.391577\pi$
$38$	−2.12449	−	3.80612i	−0.344637	−	0.617434i
$39$	−6.47565			−1.03693
$40$	−0.286989	−	1.62760i	−0.0453769	−	0.257345i
$41$	−6.61721	+	5.55250i	−1.03343	+	0.867155i	−0.991256	−	0.131955i	$-0.957874\pi$
$41$	−6.61721	+	5.55250i	−1.03343	+	0.867155i	−0.0421791	+	0.999110i	$0.513430\pi$
$42$	−0.173648	+	0.0632028i	−0.0267945	+	0.00975240i
$43$	−0.0393628	−	0.0143269i	−0.00600278	−	0.00218483i	0.339017	−	0.940780i	$-0.389906\pi$
$43$	−0.0393628	−	0.0143269i	−0.00600278	−	0.00218483i	−0.345020	+	0.938595i	$0.612128\pi$
$44$	−3.33022	−	2.79439i	−0.502050	−	0.421270i
$45$	0.826352	−	1.43128i	0.123185	−	0.213363i
$46$	−0.0530334	−	0.0918566i	−0.00781935	−	0.0135435i
$47$	−1.37551	+	7.80093i	−0.200639	+	1.13788i	0.703516	+	0.710679i	$0.251612\pi$
$47$	−1.37551	+	7.80093i	−0.200639	+	1.13788i	−0.904155	+	0.427204i	$0.859499\pi$
$48$	0.173648	−	0.984808i	0.0250640	−	0.142145i
$49$	3.48293	+	6.03260i	0.497561	+	0.861801i
$50$	1.13429	−	1.96464i	0.160412	−	0.277842i
$51$	−1.62449	−	1.36310i	−0.227473	−	0.190873i
$52$	6.08512	+	2.21480i	0.843855	+	0.307138i
$53$	8.65657	−	3.15074i	1.18907	−	0.432787i	0.329674	−	0.944095i	$-0.393061\pi$
$53$	8.65657	−	3.15074i	1.18907	−	0.432787i	0.859398	+	0.511308i	$0.170839\pi$
$54$	0.766044	−	0.642788i	0.104245	−	0.0874723i
$55$	1.24763	+	7.07564i	0.168230	+	0.954079i
$56$	0.184793			0.0246939
$57$	−2.23396	+	3.74292i	−0.295895	+	0.495762i
$58$	3.98545			0.523315
$59$	1.75237	+	9.93821i	0.228140	+	1.29384i	0.856591	+	0.515996i	$0.172578\pi$
$59$	1.75237	+	9.93821i	0.228140	+	1.29384i	−0.628452	+	0.777849i	$0.716311\pi$
$60$	−1.26604	+	1.06234i	−0.163446	+	0.137147i
$61$	−3.37939	+	1.23000i	−0.432686	+	0.157485i	−0.549175	−	0.835707i	$-0.685058\pi$
$61$	−3.37939	+	1.23000i	−0.432686	+	0.157485i	0.116489	+	0.993192i	$0.462836\pi$
$62$	3.03209	+	1.10359i	0.385076	+	0.140156i
$63$	0.141559	+	0.118782i	0.0178348	+	0.0149652i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−5.35117	−	9.26849i	−0.663731	−	1.14962i
$66$	−0.754900	+	4.28125i	−0.0929218	+	0.526986i
$67$	−1.38666	+	7.86414i	−0.169407	+	0.960757i	0.774996	+	0.631967i	$0.217752\pi$
$67$	−1.38666	+	7.86414i	−0.169407	+	0.960757i	−0.944403	+	0.328790i	$0.893359\pi$
$68$	1.06031	+	1.83651i	0.128581	+	0.222709i
$69$	−0.0530334	+	0.0918566i	−0.00638447	+	0.0110582i
$70$	−0.233956	−	0.196312i	−0.0279630	−	0.0234638i
$71$	3.79813	+	1.38241i	0.450755	+	0.164062i	0.557415	−	0.830234i	$-0.311793\pi$
$71$	3.79813	+	1.38241i	0.450755	+	0.164062i	−0.106659	+	0.994296i	$0.534015\pi$
$72$	−0.939693	+	0.342020i	−0.110744	+	0.0403075i
$73$	11.6420	−	9.76882i	1.36260	−	1.14335i	0.387425	−	0.921901i	$-0.373365\pi$
$73$	11.6420	−	9.76882i	1.36260	−	1.14335i	0.975171	−	0.221453i	$-0.0710798\pi$
$74$	0.705737	+	4.00243i	0.0820403	+	0.465273i
$75$	−2.26857			−0.261952
$76$	3.37939	−	2.75314i	0.387642	−	0.315806i
$77$	−0.803348			−0.0915500
$78$	−1.12449	−	6.37727i	−0.127323	−	0.722084i
$79$	9.49660	−	7.96859i	1.06845	−	0.896536i	0.0735394	−	0.997292i	$-0.476571\pi$
$79$	9.49660	−	7.96859i	1.06845	−	0.896536i	0.994911	+	0.100756i	$0.0321261\pi$
$80$	1.55303	−	0.565258i	0.173634	−	0.0631978i
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$	−6.61721	−	5.55250i	−0.730749	−	0.613171i
$83$	−4.22803	+	7.32316i	−0.464086	+	0.803821i	−0.999160	−	0.0409847i	$-0.986951\pi$
$83$	−4.22803	+	7.32316i	−0.464086	+	0.803821i	0.535074	+	0.844805i	$0.320284\pi$
$84$	−0.0923963	−	0.160035i	−0.0100813	−	0.0174613i
$85$	0.608593	−	3.45150i	0.0660112	−	0.374368i
$86$	0.00727396	−	0.0412527i	0.000784371	−	0.00444839i
$87$	−1.99273	−	3.45150i	−0.213643	−	0.370040i
$88$	2.17365	−	3.76487i	0.231712	−	0.401336i
$89$	−13.7404	−	11.5295i	−1.45647	−	1.22213i	−0.927679	−	0.373378i	$-0.878200\pi$
$89$	−13.7404	−	11.5295i	−1.45647	−	1.22213i	−0.528795	−	0.848750i	$-0.677356\pi$
$90$	1.55303	+	0.565258i	0.163704	+	0.0595834i
$91$	1.12449	−	0.409279i	0.117878	−	0.0429041i
$92$	0.0812519	−	0.0681784i	0.00847110	−	0.00710809i
$93$	−0.560307	−	3.17766i	−0.0581012	−	0.329508i
$94$	−7.92127			−0.817017
$95$	−7.20321	−	0.104455i	−0.739034	−	0.0107169i
$96$	1.00000			0.102062
$97$	1.85591	+	10.5254i	0.188440	+	1.06869i	0.921456	+	0.388483i	$0.127001\pi$
$97$	1.85591	+	10.5254i	0.188440	+	1.06869i	−0.733016	+	0.680211i	$0.761888\pi$
$98$	−5.33615	+	4.47756i	−0.539033	+	0.452302i
$99$	4.08512	−	1.48686i	0.410570	−	0.149435i
$100$	2.13176	+	0.775897i	0.213176	+	0.0775897i
$101$	6.17752	+	5.18355i	0.614686	+	0.515783i	0.896128	−	0.443795i	$-0.146368\pi$
$101$	6.17752	+	5.18355i	0.614686	+	0.515783i	−0.281442	+	0.959578i	$0.590813\pi$
$102$	1.06031	−	1.83651i	0.104986	−	0.181841i
$103$	−8.96451	−	15.5270i	−0.883299	−	1.52992i	−0.847651	−	0.530555i	$-0.821984\pi$
$103$	−8.96451	−	15.5270i	−0.883299	−	1.52992i	−0.0356484	−	0.999364i	$-0.511350\pi$
$104$	−1.12449	+	6.37727i	−0.110265	+	0.625343i
$105$	−0.0530334	+	0.300767i	−0.00517553	+	0.0293519i
$106$	4.60607	+	7.97794i	0.447381	+	0.774886i
$107$	6.99407	−	12.1141i	0.676142	−	1.17111i	−0.299991	−	0.953942i	$-0.596984\pi$
$107$	6.99407	−	12.1141i	0.676142	−	1.17111i	0.976134	−	0.217171i	$-0.0696829\pi$
$108$	0.766044	+	0.642788i	0.0737127	+	0.0618523i
$109$	4.48545	+	1.63257i	0.429628	+	0.156372i	0.547778	−	0.836624i	$-0.315474\pi$
$109$	4.48545	+	1.63257i	0.429628	+	0.156372i	−0.118149	+	0.992996i	$0.537696\pi$
$110$	−6.75150	+	2.45734i	−0.643730	+	0.234299i
$111$	3.11334	−	2.61240i	0.295505	−	0.247958i
$112$	0.0320889	+	0.181985i	0.00303211	+	0.0171960i
$113$	−0.753718			−0.0709038			−0.0354519	−	0.999371i	$-0.511287\pi$
$113$	−0.753718			−0.0709038			−0.0354519	+	0.999371i	$0.511287\pi$
$114$	−4.07398	−	1.55007i	−0.381563	−	0.145177i
$115$	−0.175297			−0.0163465
$116$	0.692066	+	3.92490i	0.0642568	+	0.364418i
$117$	−4.96064	+	4.16247i	−0.458611	+	0.384820i
$118$	−9.48293	+	3.45150i	−0.872974	+	0.317737i
$119$	0.368241	+	0.134029i	0.0337566	+	0.0122864i
$120$	−1.26604	−	1.06234i	−0.115574	−	0.0969777i
$121$	−3.94949	+	6.84072i	−0.359045	+	0.621884i
$122$	−1.79813	−	3.11446i	−0.162795	−	0.281970i
$123$	−1.50000	+	8.50692i	−0.135250	+	0.767043i
$124$	−0.560307	+	3.17766i	−0.0503171	+	0.285362i
$125$	−6.00640	−	10.4034i	−0.537228	−	0.930507i
$126$	−0.0923963	+	0.160035i	−0.00823131	+	0.0142571i
$127$	−8.29086	−	6.95686i	−0.735695	−	0.617321i	0.195983	−	0.980607i	$-0.437210\pi$
$127$	−8.29086	−	6.95686i	−0.735695	−	0.617321i	−0.931678	+	0.363286i	$0.881655\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	−0.0393628	+	0.0143269i	−0.00346571	+	0.00126141i
$130$	8.19846	−	6.87933i	0.719053	−	0.603357i
$131$	1.88326	+	10.6805i	0.164541	+	0.933157i	0.949537	+	0.313656i	$0.101554\pi$
$131$	1.88326	+	10.6805i	0.164541	+	0.933157i	−0.784996	+	0.619501i	$0.787335\pi$
$132$	−4.34730			−0.378384
$133$	0.151359	−	0.791143i	0.0131245	−	0.0686008i
$134$	−7.98545			−0.689838
$135$	−0.286989	−	1.62760i	−0.0247001	−	0.140081i
$136$	−1.62449	+	1.36310i	−0.139298	+	0.116885i
$137$	13.1099	−	4.77163i	1.12006	−	0.407668i	0.285384	−	0.958413i	$-0.407879\pi$
$137$	13.1099	−	4.77163i	1.12006	−	0.407668i	0.834673	+	0.550746i	$0.185657\pi$
$138$	−0.0996702	−	0.0362770i	−0.00848449	−	0.00308810i
$139$	4.57011	+	3.83478i	0.387631	+	0.325261i	0.815690	−	0.578490i	$-0.196358\pi$
$139$	4.57011	+	3.83478i	0.387631	+	0.325261i	−0.428058	+	0.903751i	$0.640802\pi$
$140$	0.152704	−	0.264490i	0.0129058	−	0.0223535i
$141$	3.96064	+	6.86002i	0.333546	+	0.577718i
$142$	−0.701867	+	3.98048i	−0.0588993	+	0.334035i
$143$	4.88847	−	27.7239i	0.408794	−	2.31839i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	3.29339	−	5.70431i	0.273501	−	0.473717i
$146$	11.6420	+	9.76882i	0.963501	+	0.808473i
$147$	6.54576	+	2.38246i	0.539885	+	0.196502i
$148$	−3.81908	+	1.39003i	−0.313926	+	0.114260i
$149$	−10.8931	+	9.14036i	−0.892394	+	0.748807i	−0.968689	−	0.248278i	$-0.920135\pi$
$149$	−10.8931	+	9.14036i	−0.892394	+	0.748807i	0.0762949	+	0.997085i	$0.475691\pi$
$150$	−0.393933	−	2.23411i	−0.0321645	−	0.182414i
$151$	−15.2003			−1.23698			−0.618490	−	0.785792i	$-0.712255\pi$
$151$	−15.2003			−1.23698			−0.618490	+	0.785792i	$0.712255\pi$
$152$	3.29813	+	2.84997i	0.267514	+	0.231163i
$153$	−2.12061			−0.171442
$154$	−0.139500	−	0.791143i	−0.0112412	−	0.0637521i
$155$	4.08512	−	3.42782i	0.328125	−	0.275329i
$156$	6.08512	−	2.21480i	0.487200	−	0.177326i
$157$	−8.83662	−	3.21627i	−0.705239	−	0.256686i	−0.0355929	−	0.999366i	$-0.511332\pi$
$157$	−8.83662	−	3.21627i	−0.705239	−	0.256686i	−0.669646	+	0.742680i	$0.733554\pi$
$158$	9.49660	+	7.96859i	0.755509	+	0.633947i
$159$	4.60607	−	7.97794i	0.365285	−	0.632692i
$160$	0.826352	+	1.43128i	0.0653288	+	0.113153i
$161$	0.00340357	−	0.0193026i	0.000268239	−	0.00152126i
$162$	0.173648	−	0.984808i	0.0136431	−	0.0773738i
$163$	3.81180	+	6.60224i	0.298564	+	0.517127i	0.975808	−	0.218631i	$-0.0701592\pi$
$163$	3.81180	+	6.60224i	0.298564	+	0.517127i	−0.677244	+	0.735758i	$0.736826\pi$
$164$	4.31908	−	7.48086i	0.337263	−	0.584157i
$165$	5.50387	+	4.61830i	0.428476	+	0.359534i
$166$	−7.94609	−	2.89214i	−0.616736	−	0.224474i
$167$	16.1630	−	5.88284i	1.25073	−	0.455228i	0.370081	−	0.929000i	$-0.379330\pi$
$167$	16.1630	−	5.88284i	1.25073	−	0.455228i	0.880648	+	0.473772i	$0.157108\pi$
$168$	0.141559	−	0.118782i	0.0109215	−	0.00916426i
$169$	5.02435	+	28.4945i	0.386488	+	2.19188i
$170$	3.50475			0.268802
$171$	0.694593	+	4.30320i	0.0531168	+	0.329074i
$172$	0.0418891			0.00319401
$173$	−1.15018	−	6.52298i	−0.0874464	−	0.495933i	−0.996802	−	0.0799130i	$-0.974536\pi$
$173$	−1.15018	−	6.52298i	−0.0874464	−	0.495933i	0.909355	−	0.416020i	$-0.136575\pi$
$174$	3.05303	−	2.56180i	0.231450	−	0.194209i
$175$	0.393933	−	0.143380i	0.0297785	−	0.0108385i
$176$	4.08512	+	1.48686i	0.307928	+	0.112077i
$177$	7.73055	+	6.48670i	0.581064	+	0.487570i
$178$	8.96838	−	15.5337i	0.672208	−	1.16430i
$179$	10.7121	+	18.5540i	0.800662	+	1.38679i	0.919181	+	0.393836i	$0.128852\pi$
$179$	10.7121	+	18.5540i	0.800662	+	1.38679i	−0.118518	+	0.992952i	$0.537814\pi$
$180$	−0.286989	+	1.62760i	−0.0213909	+	0.121314i
$181$	−2.98411	+	16.9237i	−0.221807	+	1.25793i	0.646889	+	0.762584i	$0.276070\pi$
$181$	−2.98411	+	16.9237i	−0.221807	+	1.25793i	−0.868696	+	0.495346i	$0.835041\pi$
$182$	0.598326	+	1.03633i	0.0443509	+	0.0768180i
$183$	−1.79813	+	3.11446i	−0.132922	+	0.230227i
$184$	0.0812519	+	0.0681784i	0.00598997	+	0.00502618i
$185$	6.31180	+	2.29731i	0.464053	+	0.168901i
$186$	3.03209	−	1.10359i	0.222324	−	0.0809192i
$187$	7.06212	−	5.92582i	0.516433	−	0.433339i
$188$	−1.37551	−	7.80093i	−0.100320	−	0.568941i
$189$	0.184793			0.0134417
$190$	−1.14796	−	7.11192i	−0.0832815	−	0.515953i
$191$	−6.57398			−0.475676			−0.237838	−	0.971305i	$-0.576439\pi$
$191$	−6.57398			−0.475676			−0.237838	+	0.971305i	$0.576439\pi$
$192$	0.173648	+	0.984808i	0.0125320	+	0.0710724i
$193$	−8.69253	+	7.29390i	−0.625702	+	0.525027i	−0.899590	−	0.436735i	$-0.856135\pi$
$193$	−8.69253	+	7.29390i	−0.625702	+	0.525027i	0.273888	+	0.961762i	$0.411690\pi$
$194$	−10.0432	+	3.65544i	−0.721062	+	0.262445i
$195$	−10.0569	−	3.66041i	−0.720190	−	0.262128i
$196$	−5.33615	−	4.47756i	−0.381154	−	0.319826i
$197$	−3.22416	+	5.58440i	−0.229712	+	0.397872i	−0.957723	−	0.287693i	$-0.907112\pi$
$197$	−3.22416	+	5.58440i	−0.229712	+	0.397872i	0.728011	+	0.685565i	$0.240445\pi$
$198$	2.17365	+	3.76487i	0.154474	+	0.267558i
$199$	2.90420	−	16.4705i	0.205873	−	1.16757i	−0.690186	−	0.723632i	$-0.742471\pi$
$199$	2.90420	−	16.4705i	0.205873	−	1.16757i	0.896060	−	0.443934i	$-0.146417\pi$
$200$	−0.393933	+	2.23411i	−0.0278553	+	0.157975i
$201$	3.99273	+	6.91560i	0.281625	+	0.487789i
$202$	−4.03209	+	6.98378i	−0.283697	+	0.491377i
$203$	0.564178	+	0.473401i	0.0395975	+	0.0332263i
$204$	1.99273	+	0.725293i	0.139519	+	0.0507807i
$205$	−13.4153	+	4.88279i	−0.936968	+	0.341029i
$206$	13.7344	−	11.5245i	0.956923	−	0.802953i
$207$	0.0184183	+	0.104455i	0.00128016	+	0.00726016i
$208$	−6.47565			−0.449006
$209$	−14.3380	−	12.3897i	−0.991778	−	0.857010i
$210$	−0.305407			−0.0210751
$211$	−0.847296	−	4.80526i	−0.0583303	−	0.330807i	0.941653	−	0.336585i	$-0.109272\pi$
$211$	−0.847296	−	4.80526i	−0.0583303	−	0.330807i	−0.999983	+	0.00577769i	$0.998161\pi$
$212$	−7.05690	+	5.92145i	−0.484670	+	0.406687i
$213$	3.79813	−	1.38241i	0.260244	−	0.0947210i
$214$	13.1446	+	4.78423i	0.898543	+	0.327043i
$215$	−0.0530334	−	0.0445003i	−0.00361685	−	0.00303490i
$216$	−0.500000	+	0.866025i	−0.0340207	+	0.0589256i
$217$	0.298133	+	0.516382i	0.0202386	+	0.0350543i
$218$	−0.828878	+	4.70080i	−0.0561387	+	0.318378i
$219$	2.63903	−	14.9667i	0.178329	−	1.01136i
$220$	−3.59240	−	6.22221i	−0.242199	−	0.419502i
$221$	−6.86618	+	11.8926i	−0.461869	+	0.799981i
$222$	3.11334	+	2.61240i	0.208954	+	0.175333i
$223$	−27.0453	−	9.84370i	−1.81109	−	0.659183i	−0.996908	−	0.0785736i	$-0.974963\pi$
$223$	−27.0453	−	9.84370i	−1.81109	−	0.659183i	−0.814182	−	0.580609i	$-0.802814\pi$
$224$	−0.173648	+	0.0632028i	−0.0116024	+	0.00422291i
$225$	−1.73783	+	1.45821i	−0.115855	+	0.0972139i
$226$	−0.130882	−	0.742267i	−0.00870613	−	0.0493749i
$227$	−3.75608			−0.249300			−0.124650	−	0.992201i	$-0.539781\pi$
$227$	−3.75608			−0.249300			−0.124650	+	0.992201i	$0.539781\pi$
$228$	0.819078	−	4.28125i	0.0542448	−	0.283533i
$229$	17.5175			1.15759			0.578796	−	0.815472i	$-0.303523\pi$
$229$	17.5175			1.15759			0.578796	+	0.815472i	$0.303523\pi$
$230$	−0.0304400	−	0.172634i	−0.00200716	−	0.0113831i
$231$	−0.615400	+	0.516382i	−0.0404904	+	0.0339754i
$232$	−3.74510	+	1.36310i	−0.245878	+	0.0894922i
$233$	6.58260	+	2.39587i	0.431240	+	0.156959i	0.548515	−	0.836141i	$-0.315193\pi$
$233$	6.58260	+	2.39587i	0.431240	+	0.156959i	−0.117274	+	0.993100i	$0.537416\pi$
$234$	−4.96064	−	4.16247i	−0.324287	−	0.272109i
$235$	−6.54576	+	11.3376i	−0.426998	+	0.739583i
$236$	−5.04576	−	8.73951i	−0.328451	−	0.568894i
$237$	2.15270	−	12.2086i	0.139833	−	0.793033i
$238$	−0.0680482	+	0.385920i	−0.00441091	+	0.0250155i
$239$	−0.467911	−	0.810446i	−0.0302667	−	0.0524234i	0.850495	−	0.525983i	$-0.176302\pi$
$239$	−0.467911	−	0.810446i	−0.0302667	−	0.0524234i	−0.880762	+	0.473559i	$0.842969\pi$
$240$	0.826352	−	1.43128i	0.0533408	−	0.0923889i
$241$	−22.0082	−	18.4671i	−1.41767	−	1.18957i	−0.952573	−	0.304311i	$-0.901574\pi$
$241$	−22.0082	−	18.4671i	−1.41767	−	1.18957i	−0.465101	−	0.885258i	$-0.653982\pi$
$242$	−7.42262	−	2.70161i	−0.477144	−	0.173666i
$243$	−0.939693	+	0.342020i	−0.0602813	+	0.0219406i
$244$	2.75490	−	2.31164i	0.176364	−	0.147987i
$245$	1.99912	+	11.3376i	0.127719	+	0.724332i
$246$	−8.63816			−0.550749
$247$	26.3817	+	10.0377i	1.67863	+	0.638683i
$248$	−3.22668			−0.204894
$249$	1.46838	+	8.32759i	0.0930547	+	0.527739i
$250$	9.20233	−	7.72167i	0.582007	−	0.488362i
$251$	−22.7271	+	8.27201i	−1.43452	+	0.522124i	−0.938225	−	0.346027i	$-0.887531\pi$
$251$	−22.7271	+	8.27201i	−1.43452	+	0.522124i	−0.496300	+	0.868151i	$0.665308\pi$
$252$	−0.173648	−	0.0632028i	−0.0109388	−	0.00398140i
$253$	−0.353226	−	0.296392i	−0.0222071	−	0.0186340i
$254$	5.41147	−	9.37295i	0.339546	−	0.588111i
$255$	−1.75237	−	3.03520i	−0.109738	−	0.190072i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	1.52822	−	8.66696i	0.0953277	−	0.540630i	−0.899319	−	0.437294i	$-0.855937\pi$
$257$	1.52822	−	8.66696i	0.0953277	−	0.540630i	0.994646	−	0.103336i	$-0.0329518\pi$
$258$	−0.0209445	−	0.0362770i	−0.00130395	−	0.00225851i
$259$	−0.375515	+	0.650411i	−0.0233334	+	0.0404146i
$260$	8.19846	+	6.87933i	0.508447	+	0.426638i
$261$	−3.74510	−	1.36310i	−0.231816	−	0.0843741i
$262$	−10.1912	+	3.70929i	−0.629614	+	0.229161i
$263$	1.00206	−	0.840828i	0.0617896	−	0.0518477i	−0.611370	−	0.791345i	$-0.709381\pi$
$263$	1.00206	−	0.840828i	0.0617896	−	0.0518477i	0.673159	+	0.739497i	$0.264937\pi$
$264$	−0.754900	−	4.28125i	−0.0464609	−	0.263493i
$265$	15.2249			0.935260
$266$	0.805407	+	0.0116794i	0.0493827	+	0.000716110i
$267$	−17.9368			−1.09771
$268$	−1.38666	−	7.86414i	−0.0847037	−	0.480379i
$269$	6.70368	−	5.62505i	0.408730	−	0.342966i	−0.415126	−	0.909764i	$-0.636263\pi$
$269$	6.70368	−	5.62505i	0.408730	−	0.342966i	0.823857	+	0.566798i	$0.191818\pi$
$270$	1.55303	−	0.565258i	0.0945146	−	0.0344005i
$271$	12.9179	+	4.70172i	0.784705	+	0.285609i	0.703133	−	0.711058i	$-0.251784\pi$
$271$	12.9179	+	4.70172i	0.784705	+	0.285609i	0.0815717	+	0.996667i	$0.474006\pi$
$272$	−1.62449	−	1.36310i	−0.0984989	−	0.0826504i
$273$	0.598326	−	1.03633i	0.0362123	−	0.0627216i
$274$	6.97565	+	12.0822i	0.421415	+	0.729911i
$275$	1.71254	−	9.71232i	0.103270	−	0.585675i
$276$	0.0184183	−	0.104455i	0.00110865	−	0.00628748i
$277$	−12.5039	−	21.6573i	−0.751285	−	1.30126i	−0.947200	−	0.320643i	$-0.896101\pi$
$277$	−12.5039	−	21.6573i	−0.751285	−	1.30126i	0.195915	−	0.980621i	$-0.437232\pi$
$278$	−2.98293	+	5.16658i	−0.178904	+	0.309871i
$279$	−2.47178	−	2.07407i	−0.147982	−	0.124171i
$280$	0.286989	+	0.104455i	0.0171509	+	0.00624241i
$281$	−11.4226	+	4.15749i	−0.681416	+	0.248015i	−0.659456	−	0.751744i	$-0.729213\pi$
$281$	−11.4226	+	4.15749i	−0.681416	+	0.248015i	−0.0219608	+	0.999759i	$0.506991\pi$
$282$	−6.06805	+	5.09170i	−0.361347	+	0.303206i
$283$	−1.85756	−	10.5348i	−0.110421	−	0.626227i	−0.988916	−	0.148476i	$-0.952563\pi$
$283$	−1.85756	−	10.5348i	−0.110421	−	0.626227i	0.878495	−	0.477751i	$-0.158548\pi$
$284$	−4.04189			−0.239842
$285$	−5.58512	+	4.55012i	−0.330834	+	0.269526i
$286$	28.1516			1.66464
$287$	−0.277189	−	1.57202i	−0.0163619	−	0.0927932i
$288$	0.766044	−	0.642788i	0.0451396	−	0.0378766i
$289$	11.7490	−	4.27628i	0.691116	−	0.251546i
$290$	6.18954	+	2.25281i	0.363462	+	0.132289i
$291$	8.18732	+	6.86998i	0.479949	+	0.402725i
$292$	−7.59879	+	13.1615i	−0.444686	+	0.770218i
$293$	6.67365	+	11.5591i	0.389879	+	0.675290i	0.992433	−	0.122788i	$-0.0391836\pi$
$293$	6.67365	+	11.5591i	0.389879	+	0.675290i	−0.602554	+	0.798078i	$0.705850\pi$
$294$	−1.20961	+	6.86002i	−0.0705457	+	0.400085i
$295$	−2.89615	+	16.4249i	−0.168621	+	0.956295i
$296$	−2.03209	−	3.51968i	−0.118113	−	0.204577i
$297$	2.17365	−	3.76487i	0.126128	−	0.218460i
$298$	−10.8931	−	9.14036i	−0.631018	−	0.529487i
$299$	0.645430	+	0.234917i	0.0373262	+	0.0135856i
$300$	2.13176	−	0.775897i	0.123077	−	0.0447964i
$301$	0.00592979	−	0.00497568i	0.000341787	−	0.000286794i
$302$	−2.63950	−	14.9693i	−0.151886	−	0.861389i
$303$	8.06418			0.463275
$304$	−2.23396	+	3.74292i	−0.128126	+	0.214671i
$305$	−5.94356			−0.340327
$306$	−0.368241	−	2.08840i	−0.0210509	−	0.119386i
$307$	11.9987	−	10.0681i	0.684799	−	0.574615i	−0.232605	−	0.972571i	$-0.574725\pi$
$307$	11.9987	−	10.0681i	0.684799	−	0.574615i	0.917404	+	0.397956i	$0.130280\pi$
$308$	0.754900	−	0.274761i	0.0430144	−	0.0156560i
$309$	−16.8478	−	6.13208i	−0.958436	−	0.348842i
$310$	4.08512	+	3.42782i	0.232019	+	0.194687i
$311$	−4.55303	+	7.88609i	−0.258179	+	0.447179i	−0.965754	−	0.259459i	$-0.916456\pi$
$311$	−4.55303	+	7.88609i	−0.258179	+	0.447179i	0.707575	+	0.706638i	$0.249789\pi$
$312$	3.23783	+	5.60808i	0.183306	+	0.317495i
$313$	3.08172	−	17.4773i	0.174189	−	0.987875i	−0.764887	−	0.644165i	$-0.777205\pi$
$313$	3.08172	−	17.4773i	0.174189	−	0.987875i	0.939076	−	0.343710i	$-0.111684\pi$
$314$	1.63294	−	9.26087i	0.0921522	−	0.522621i
$315$	0.152704	+	0.264490i	0.00860388	+	0.0149023i
$316$	−6.19846	+	10.7361i	−0.348691	+	0.603950i
$317$	23.7822	+	19.9557i	1.33574	+	1.12082i	0.982698	+	0.185216i	$0.0592985\pi$
$317$	23.7822	+	19.9557i	1.33574	+	1.12082i	0.353046	+	0.935606i	$0.385146\pi$
$318$	8.65657	+	3.15074i	0.485437	+	0.176684i
$319$	16.2811	−	5.92582i	0.911564	−	0.331782i
$320$	−1.26604	+	1.06234i	−0.0707740	+	0.0593865i
$321$	−2.42902	−	13.7756i	−0.135574	−	0.768881i
$322$	0.0196004			0.00109229
$323$	4.50521	+	8.07132i	0.250677	+	0.449100i
$324$	1.00000			0.0555556
$325$	2.55097	+	14.4673i	0.141503	+	0.802501i
$326$	−5.84002	+	4.90036i	−0.323449	+	0.271406i
$327$	4.48545	−	1.63257i	0.248046	−	0.0902814i
$328$	8.11721	+	2.95442i	0.448198	+	0.163131i
$329$	−1.12133	−	0.940908i	−0.0618209	−	0.0518739i
$330$	−3.59240	+	6.22221i	−0.197755	+	0.342522i
$331$	5.03983	+	8.72924i	0.277014	+	0.479802i	0.970641	−	0.240532i	$-0.0773218\pi$
$331$	5.03983	+	8.72924i	0.277014	+	0.479802i	−0.693627	+	0.720334i	$0.743988\pi$
$332$	1.46838	−	8.32759i	0.0805877	−	0.457036i
$333$	0.705737	−	4.00243i	0.0386742	−	0.219332i
$334$	8.60014	+	14.8959i	0.470579	+	0.815066i
$335$	−6.59879	+	11.4294i	−0.360531	+	0.624457i
$336$	0.141559	+	0.118782i	0.00772269	+	0.00648011i
$337$	7.87211	+	2.86521i	0.428821	+	0.156078i	0.547409	−	0.836865i	$-0.315614\pi$
$337$	7.87211	+	2.86521i	0.428821	+	0.156078i	−0.118587	+	0.992944i	$0.537837\pi$
$338$	−27.1891	+	9.89603i	−1.47889	+	0.538273i
$339$	−0.577382	+	0.484481i	−0.0313591	+	0.0263134i
$340$	0.608593	+	3.45150i	0.0330056	+	0.187184i
$341$	14.0273			0.759623
$342$	−4.11721	+	1.43128i	−0.222633	+	0.0773949i
$343$	−2.58079			−0.139349
$344$	0.00727396	+	0.0412527i	0.000392186	+	0.00222420i
$345$	−0.134285	+	0.112679i	−0.00722968	+	0.00606642i
$346$	6.22416	−	2.26541i	0.334613	−	0.121789i
$347$	−12.2306	−	4.45156i	−0.656570	−	0.238972i	−0.00781546	−	0.999969i	$-0.502488\pi$
$347$	−12.2306	−	4.45156i	−0.656570	−	0.238972i	−0.648755	+	0.760997i	$0.724710\pi$
$348$	3.05303	+	2.56180i	0.163660	+	0.137327i
$349$	3.35369	−	5.80877i	0.179519	−	0.310936i	−0.762197	−	0.647345i	$-0.775879\pi$
$349$	3.35369	−	5.80877i	0.179519	−	0.310936i	0.941716	+	0.336409i	$0.109213\pi$
$350$	0.209607	+	0.363051i	0.0112040	+	0.0194059i
$351$	−1.12449	+	6.37727i	−0.0600206	+	0.340394i
$352$	−0.754900	+	4.28125i	−0.0402363	+	0.228191i
$353$	−5.32295	−	9.21962i	−0.283312	−	0.490711i	0.688886	−	0.724869i	$-0.258100\pi$
$353$	−5.32295	−	9.21962i	−0.283312	−	0.490711i	−0.972198	+	0.234159i	$0.924767\pi$
$354$	−5.04576	+	8.73951i	−0.268179	+	0.464500i
$355$	5.11721	+	4.29385i	0.271593	+	0.227894i
$356$	16.8550	+	6.13473i	0.893315	+	0.325140i
$357$	0.368241	−	0.134029i	0.0194894	−	0.00709355i
$358$	−16.4119	+	13.7713i	−0.867398	+	0.727833i
$359$	−5.06418	−	28.7204i	−0.267277	−	1.51580i	−0.762472	−	0.647022i	$-0.776014\pi$
$359$	−5.06418	−	28.7204i	−0.267277	−	1.51580i	0.495195	−	0.868782i	$-0.335097\pi$
$360$	−1.65270			−0.0871051
$361$	14.9029	−	11.7858i	0.784361	−	0.620305i
$362$	−17.1848			−0.903213
$363$	1.37164	+	7.77898i	0.0719927	+	0.408291i
$364$	−0.916689	+	0.769193i	−0.0480475	+	0.0403167i
$365$	23.6024	−	8.59056i	1.23540	−	0.449650i
$366$	−3.37939	−	1.23000i	−0.176643	−	0.0642929i
$367$	−2.71095	−	2.27476i	−0.141511	−	0.118741i	0.569285	−	0.822141i	$-0.307220\pi$
$367$	−2.71095	−	2.27476i	−0.141511	−	0.118741i	−0.710795	+	0.703399i	$0.751665\pi$
$368$	−0.0530334	+	0.0918566i	−0.00276456	+	0.00478836i
$369$	4.31908	+	7.48086i	0.224842	+	0.389438i
$370$	−1.16637	+	6.61484i	−0.0606369	+	0.343889i
$371$	−0.295607	+	1.67647i	−0.0153472	+	0.0870380i
$372$	1.61334	+	2.79439i	0.0836478	+	0.144882i
$373$	−5.10472	+	8.84164i	−0.264313	+	0.457803i	−0.967383	−	0.253317i	$-0.918478\pi$
$373$	−5.10472	+	8.84164i	−0.264313	+	0.457803i	0.703071	+	0.711120i	$0.251812\pi$
$374$	7.06212	+	5.92582i	0.365173	+	0.306417i
$375$	−11.2883	−	4.10862i	−0.582927	−	0.212168i
$376$	7.44356	−	2.70924i	0.383872	−	0.139718i
$377$	−19.7704	+	16.5893i	−1.01823	+	0.854393i
$378$	0.0320889	+	0.181985i	0.00165047	+	0.00936030i
$379$	12.6287			0.648691			0.324345	−	0.945939i	$-0.394856\pi$
$379$	12.6287			0.648691			0.324345	+	0.945939i	$0.394856\pi$
$380$	6.80453	−	2.36549i	0.349065	−	0.121347i
$381$	−10.8229			−0.554476
$382$	−1.14156	−	6.47410i	−0.0584073	−	0.331244i
$383$	−6.67546	+	5.60138i	−0.341100	+	0.286217i	−0.797205	−	0.603709i	$-0.793689\pi$
$383$	−6.67546	+	5.60138i	−0.341100	+	0.286217i	0.456105	+	0.889926i	$0.349244\pi$
$384$	−0.939693	+	0.342020i	−0.0479535	+	0.0174536i
$385$	−1.24763	−	0.454099i	−0.0635849	−	0.0231430i
$386$	−8.69253	−	7.29390i	−0.442438	−	0.371250i
$387$	−0.0209445	+	0.0362770i	−0.00106467	+	0.00184406i
$388$	−5.34389	−	9.25589i	−0.271295	−	0.469897i
$389$	−1.50118	+	8.51363i	−0.0761130	+	0.431658i	0.922810	+	0.385256i	$0.125887\pi$
$389$	−1.50118	+	8.51363i	−0.0761130	+	0.431658i	−0.998923	+	0.0464023i	$0.985224\pi$
$390$	1.85844	−	10.5397i	0.0941058	−	0.533701i
$391$	0.112463	+	0.194792i	0.00568752	+	0.00985108i
$392$	3.48293	−	6.03260i	0.175914	−	0.304693i
$393$	8.30793	+	6.97118i	0.419080	+	0.351650i
$394$	−6.05943	−	2.20545i	−0.305270	−	0.111109i
$395$	19.2528	−	7.00746i	0.968716	−	0.352584i
$396$	−3.33022	+	2.79439i	−0.167350	+	0.140423i
$397$	−1.19372	−	6.76990i	−0.0599109	−	0.339771i	0.940088	−	0.340931i	$-0.110742\pi$
$397$	−1.19372	−	6.76990i	−0.0599109	−	0.339771i	−0.999999	+	0.00115924i	$0.999631\pi$
$398$	16.7246			0.838330
$399$	−0.392589	−	0.703343i	−0.0196540	−	0.0352112i
$400$	−2.26857			−0.113429
$401$	−5.11200	−	28.9916i	−0.255281	−	1.44777i	−0.795351	−	0.606150i	$-0.792713\pi$
$401$	−5.11200	−	28.9916i	−0.255281	−	1.44777i	0.540070	−	0.841620i	$-0.318398\pi$
$402$	−6.11721	+	5.13295i	−0.305099	+	0.256008i
$403$	−19.6348	+	7.14647i	−0.978077	+	0.355991i
$404$	−7.57785	−	2.75811i	−0.377012	−	0.137221i
$405$	−1.26604	−	1.06234i	−0.0629103	−	0.0527880i
$406$	−0.368241	+	0.637812i	−0.0182755	+	0.0316541i
$407$	8.83409	+	15.3011i	0.437890	+	0.758447i
$408$	−0.368241	+	2.08840i	−0.0182306	+	0.103391i
$409$	−3.69459	+	20.9531i	−0.182686	+	1.03606i	0.746207	+	0.665714i	$0.231873\pi$
$409$	−3.69459	+	20.9531i	−0.182686	+	1.03606i	−0.928893	+	0.370349i	$0.879238\pi$
$410$	−7.13816	−	12.3636i	−0.352528	−	0.610597i
$411$	6.97565	−	12.0822i	0.344084	−	0.595970i
$412$	13.7344	+	11.5245i	0.676646	+	0.567774i
$413$	−1.75237	−	0.637812i	−0.0862287	−	0.0313847i
$414$	−0.0996702	+	0.0362770i	−0.00489852	+	0.00178292i
$415$	−10.7057	+	8.98318i	−0.525524	+	0.440967i
$416$	−1.12449	−	6.37727i	−0.0551324	−	0.312671i
$417$	5.96585			0.292149
$418$	9.71167	−	16.2716i	0.475013	−	0.795869i
$419$	15.8922			0.776384			0.388192	−	0.921579i	$-0.373100\pi$
$419$	15.8922			0.776384			0.388192	+	0.921579i	$0.373100\pi$
$420$	−0.0530334	−	0.300767i	−0.00258777	−	0.0146759i
$421$	15.0103	−	12.5951i	0.731556	−	0.613848i	−0.199000	−	0.980000i	$-0.563769\pi$
$421$	15.0103	−	12.5951i	0.731556	−	0.613848i	0.930555	+	0.366151i	$0.119325\pi$
$422$	4.58512	−	1.66885i	0.223200	−	0.0812383i
$423$	7.44356	+	2.70924i	0.361918	+	0.131728i
$424$	−7.05690	−	5.92145i	−0.342714	−	0.287571i
$425$	−2.40538	+	4.16624i	−0.116678	+	0.202093i
$426$	2.02094	+	3.50038i	0.0979151	+	0.169594i
$427$	0.115400	−	0.654467i	0.00558461	−	0.0316719i
$428$	−2.42902	+	13.7756i	−0.117411	+	0.665870i
$429$	−14.0758	−	24.3800i	−0.679585	−	1.17708i
$430$	0.0346151	−	0.0599551i	0.00166929	−	0.00289129i
$431$	−3.18273	−	2.67063i	−0.153307	−	0.128640i	0.562908	−	0.826520i	$-0.309683\pi$
$431$	−3.18273	−	2.67063i	−0.153307	−	0.128640i	−0.716215	+	0.697880i	$0.754127\pi$
$432$	−0.939693	−	0.342020i	−0.0452110	−	0.0164555i
$433$	3.34730	−	1.21832i	0.160861	−	0.0585485i	−0.260335	−	0.965518i	$-0.583833\pi$
$433$	3.34730	−	1.21832i	0.160861	−	0.0585485i	0.421195	+	0.906970i	$0.361611\pi$
$434$	−0.456767	+	0.383273i	−0.0219255	+	0.0183977i
$435$	−1.14378	−	6.48670i	−0.0548401	−	0.311014i
$436$	−4.77332			−0.228600
$437$	0.358441	−	0.292016i	0.0171465	−	0.0139690i
$438$	15.1976			0.726169
$439$	−1.42649	−	8.09002i	−0.0680826	−	0.386116i	−0.999741	−	0.0227790i	$-0.992749\pi$
$439$	−1.42649	−	8.09002i	−0.0680826	−	0.386116i	0.931658	−	0.363337i	$-0.118363\pi$
$440$	5.50387	−	4.61830i	0.262387	−	0.220169i
$441$	6.54576	−	2.38246i	0.311703	−	0.113451i
$442$	−12.9042	−	4.69674i	−0.613790	−	0.223401i
$443$	−14.5137	−	12.1784i	−0.689565	−	0.578614i	0.229219	−	0.973375i	$-0.426383\pi$
$443$	−14.5137	−	12.1784i	−0.689565	−	0.578614i	−0.918784	+	0.394761i	$0.870827\pi$
$444$	−2.03209	+	3.51968i	−0.0964387	+	0.167037i
$445$	−14.8221	−	25.6726i	−0.702634	−	1.21700i
$446$	4.99778	−	28.3438i	0.236652	−	1.34212i
$447$	−2.46926	+	14.0038i	−0.116792	+	0.662359i
$448$	−0.0923963	−	0.160035i	−0.00436531	−	0.00756094i
$449$	−5.24628	+	9.08683i	−0.247587	+	0.428834i	−0.962856	−	0.270016i	$-0.912971\pi$
$449$	−5.24628	+	9.08683i	−0.247587	+	0.428834i	0.715269	+	0.698850i	$0.246304\pi$
$450$	−1.73783	−	1.45821i	−0.0819219	−	0.0687406i
$451$	−35.2879	−	12.8438i	−1.66164	−	0.604789i
$452$	0.708263	−	0.257787i	0.0333139	−	0.0121253i
$453$	−11.6441	+	9.77055i	−0.547087	+	0.459060i
$454$	−0.652237	−	3.69902i	−0.0306110	−	0.173604i
$455$	1.97771			0.0927165
$456$	4.35844	+	0.0632028i	0.204103	+	0.00295974i
$457$	−0.415593			−0.0194406			−0.00972031	−	0.999953i	$-0.503094\pi$
$457$	−0.415593			−0.0194406			−0.00972031	+	0.999953i	$0.503094\pi$
$458$	3.04189	+	17.2514i	0.142138	+	0.806105i
$459$	−1.62449	+	1.36310i	−0.0758245	+	0.0636243i
$460$	0.164725	−	0.0599551i	0.00768036	−	0.00279542i
$461$	−23.7344	−	8.63862i	−1.10542	−	0.402341i	−0.276110	−	0.961126i	$-0.589045\pi$
$461$	−23.7344	−	8.63862i	−1.10542	−	0.402341i	−0.829312	+	0.558785i	$0.811268\pi$
$462$	−0.615400	−	0.516382i	−0.0286310	−	0.0240243i
$463$	−9.39558	+	16.2736i	−0.436650	+	0.756300i	−0.997429	−	0.0716660i	$-0.977168\pi$
$463$	−9.39558	+	16.2736i	−0.436650	+	0.756300i	0.560779	+	0.827966i	$0.310502\pi$
$464$	−1.99273	−	3.45150i	−0.0925100	−	0.160232i
$465$	0.926022	−	5.25173i	0.0429432	−	0.243543i
$466$	−1.21641	+	6.89863i	−0.0563493	+	0.319573i
$467$	8.56670	+	14.8380i	0.396420	+	0.686619i	0.993281	−	0.115725i	$-0.0369192\pi$
$467$	8.56670	+	14.8380i	0.396420	+	0.686619i	−0.596861	+	0.802344i	$0.703586\pi$
$468$	3.23783	−	5.60808i	0.149669	−	0.259234i
$469$	−1.13041	−	0.948531i	−0.0521977	−	0.0437991i
$470$	−12.3020	−	4.47756i	−0.567449	−	0.206535i
$471$	−8.83662	+	3.21627i	−0.407170	+	0.148198i
$472$	7.73055	−	6.48670i	0.355827	−	0.298575i
$473$	−0.0316221	−	0.179338i	−0.00145398	−	0.00824595i
$474$	12.3969			0.569410
$475$	9.24211	+	3.51643i	0.424057	+	0.161345i
$476$	−0.391874			−0.0179615
$477$	−1.59967	−	9.07218i	−0.0732439	−	0.415387i
$478$	0.716881	−	0.601535i	0.0327894	−	0.0275136i
$479$	10.2973	−	3.74789i	0.470494	−	0.171246i	−0.0958823	−	0.995393i	$-0.530567\pi$
$479$	10.2973	−	3.74789i	0.470494	−	0.171246i	0.566376	+	0.824147i	$0.308345\pi$
$480$	1.55303	+	0.565258i	0.0708860	+	0.0258004i
$481$	−20.1609	−	16.9170i	−0.919258	−	0.771349i
$482$	14.3648	−	24.8806i	0.654300	−	1.13328i
$483$	−0.00980018	−	0.0169744i	−0.000445924	−	0.000772362i
$484$	1.37164	−	7.77898i	0.0623475	−	0.353590i
$485$	−3.06728	+	17.3954i	−0.139278	+	0.789884i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−8.44016	+	14.6188i	−0.382460	+	0.662440i	−0.991413	−	0.130766i	$-0.958256\pi$
$487$	−8.44016	+	14.6188i	−0.382460	+	0.662440i	0.608953	+	0.793206i	$0.291590\pi$
$488$	2.75490	+	2.31164i	0.124708	+	0.104643i
$489$	7.16385	+	2.60743i	0.323960	+	0.117912i
$490$	−10.8182	+	3.93750i	−0.488716	+	0.177878i
$491$	−8.62314	+	7.23567i	−0.389157	+	0.326541i	−0.816285	−	0.577650i	$-0.803970\pi$
$491$	−8.62314	+	7.23567i	−0.389157	+	0.326541i	0.427128	+	0.904191i	$0.359525\pi$
$492$	−1.50000	−	8.50692i	−0.0676252	−	0.383522i
$493$	−8.45161			−0.380641
$494$	−5.30406	+	27.7239i	−0.238641	+	1.24736i
$495$	7.18479			0.322932
$496$	−0.560307	−	3.17766i	−0.0251585	−	0.142681i
$497$	−0.572167	+	0.480105i	−0.0256652	+	0.0215357i
$498$	−7.94609	+	2.89214i	−0.356073	+	0.129600i
$499$	9.18139	+	3.34175i	0.411015	+	0.149597i	0.539249	−	0.842147i	$-0.318708\pi$
$499$	9.18139	+	3.34175i	0.411015	+	0.149597i	−0.128233	+	0.991744i	$0.540931\pi$
$500$	9.20233	+	7.72167i	0.411541	+	0.345324i
$501$	8.60014	−	14.8959i	0.384226	−	0.665499i
$502$	−12.0929	−	20.9455i	−0.539731	−	0.934841i
$503$	−6.50093	+	36.8686i	−0.289862	+	1.64389i	0.397519	+	0.917594i	$0.369871\pi$
$503$	−6.50093	+	36.8686i	−0.289862	+	1.64389i	−0.687381	+	0.726297i	$0.741240\pi$
$504$	0.0320889	−	0.181985i	0.00142935	−	0.00810626i
$505$	6.66385	+	11.5421i	0.296537	+	0.513618i
$506$	0.230552	−	0.399328i	0.0102493	−	0.0177523i
$507$	22.1648	+	18.5985i	0.984373	+	0.825987i
$508$	10.1702	+	3.70167i	0.451232	+	0.164235i
$509$	3.49273	−	1.27125i	0.154812	−	0.0563471i	−0.263452	−	0.964673i	$-0.584861\pi$
$509$	3.49273	−	1.27125i	0.154812	−	0.0563471i	0.418264	+	0.908326i	$0.362639\pi$
$510$	2.68479	−	2.25281i	0.118885	−	0.0997560i
$511$	0.487674	+	2.76573i	0.0215734	+	0.122349i
$512$	1.00000			0.0441942
$513$	3.29813	+	2.84997i	0.145616	+	0.125829i
$514$	8.80066			0.388180
$515$	−5.14543	−	29.1812i	−0.226735	−	1.28588i
$516$	0.0320889	−	0.0269258i	0.00141263	−	0.00118534i
$517$	−32.3594	+	11.7778i	−1.42316	+	0.517989i
$518$	−0.705737	−	0.256867i	−0.0310083	−	0.0112861i
$519$	−5.07398	−	4.25757i	−0.222723	−	0.186887i
$520$	−5.35117	+	9.26849i	−0.234664	+	0.406450i
$521$	0.446089	+	0.772649i	0.0195435	+	0.0338504i	0.875632	−	0.482979i	$-0.160445\pi$
$521$	0.446089	+	0.772649i	0.0195435	+	0.0338504i	−0.856088	+	0.516830i	$0.827112\pi$
$522$	0.692066	−	3.92490i	0.0302909	−	0.171788i
$523$	−2.44238	+	13.8514i	−0.106798	+	0.605681i	0.883689	+	0.468074i	$0.155052\pi$
$523$	−2.44238	+	13.8514i	−0.106798	+	0.605681i	−0.990487	+	0.137606i	$0.956059\pi$
$524$	−5.42262	−	9.39225i	−0.236888	−	0.410302i
$525$	0.209607	−	0.363051i	0.00914802	−	0.0158448i
$526$	1.00206	+	0.840828i	0.0436919	+	0.0366618i
$527$	−6.42989	−	2.34029i	−0.280091	−	0.101945i
$528$	4.08512	−	1.48686i	0.177782	−	0.0647074i
$529$	−17.6104	+	14.7769i	−0.765670	+	0.642473i
$530$	2.64378	+	14.9936i	0.114839	+	0.651281i
$531$	10.0915			0.437935
$532$	0.128356	+	0.795199i	0.00556492	+	0.0344763i
$533$	55.9377			2.42293
$534$	−3.11468	−	17.6643i	−0.134786	−	0.764407i
$535$	17.7096	−	14.8601i	0.765653	−	0.642459i
$536$	7.50387	−	2.73119i	0.324118	−	0.117969i
$537$	20.1322	+	7.32753i	0.868770	+	0.316206i
$538$	6.70368	+	5.62505i	0.289016	+	0.242513i
$539$	−15.1413	+	26.2255i	−0.652182	+	1.12961i
$540$	0.826352	+	1.43128i	0.0355605	+	0.0615926i
$541$	4.44862	−	25.2294i	0.191261	−	1.08469i	−0.726383	−	0.687290i	$-0.758800\pi$
$541$	4.44862	−	25.2294i	0.191261	−	1.08469i	0.917644	−	0.397404i	$-0.130089\pi$
$542$	−2.38713	+	13.5381i	−0.102536	+	0.581510i
$543$	8.59240	+	14.8825i	0.368735	+	0.638668i
$544$	1.06031	−	1.83651i	0.0454603	−	0.0787396i
$545$	6.04323	+	5.07087i	0.258864	+	0.217212i
$546$	1.12449	+	0.409279i	0.0481235	+	0.0175155i
$547$	−34.1263	+	12.4210i	−1.45914	+	0.531082i	−0.945127	−	0.326704i	$-0.894062\pi$
$547$	−34.1263	+	12.4210i	−1.45914	+	0.531082i	−0.514008	+	0.857785i	$0.671840\pi$
$548$	−10.6873	+	8.96773i	−0.456540	+	0.383082i
$549$	0.624485	+	3.54163i	0.0266524	+	0.151153i
$550$	9.86215			0.420523
$551$	2.76827	+	17.1502i	0.117932	+	0.730623i
$552$	0.106067			0.00451450
$553$	0.397804	+	2.25606i	0.0169163	+	0.0959373i
$554$	19.1570	−	16.0747i	0.813905	−	0.682947i
$555$	6.31180	−	2.29731i	0.267921	−	0.0975153i
$556$	−5.60607	−	2.04044i	−0.237750	−	0.0865340i
$557$	17.8635	+	14.9893i	0.756900	+	0.635115i	0.937318	−	0.348475i	$-0.113300\pi$
$557$	17.8635	+	14.9893i	0.756900	+	0.635115i	−0.180418	+	0.983590i	$0.557745\pi$
$558$	1.61334	−	2.79439i	0.0682982	−	0.118296i
$559$	0.135630	+	0.234917i	0.00573652	+	0.00993594i
$560$	−0.0530334	+	0.300767i	−0.00224107	+	0.0127097i
$561$	1.60085	−	9.07888i	0.0675880	−	0.383311i
$562$	−6.07785	−	10.5271i	−0.256379	−	0.444061i
$563$	−2.26991	+	3.93161i	−0.0956655	+	0.165698i	−0.909886	−	0.414858i	$-0.863831\pi$
$563$	−2.26991	+	3.93161i	−0.0956655	+	0.165698i	0.814221	+	0.580556i	$0.197165\pi$
$564$	−6.06805	−	5.09170i	−0.255511	−	0.214399i
$565$	−1.17055	−	0.426045i	−0.0492454	−	0.0179239i
$566$	10.0522	−	3.65869i	0.422524	−	0.153786i
$567$	0.141559	−	0.118782i	0.00594493	−	0.00498839i
$568$	−0.701867	−	3.98048i	−0.0294497	−	0.167017i
$569$	−6.26621			−0.262693			−0.131347	−	0.991337i	$-0.541930\pi$
$569$	−6.26621			−0.262693			−0.131347	+	0.991337i	$0.541930\pi$
$570$	−5.45084	−	4.71015i	−0.228310	−	0.197287i
$571$	1.03777			0.0434293			0.0217147	−	0.999764i	$-0.493087\pi$
$571$	1.03777			0.0434293			0.0217147	+	0.999764i	$0.493087\pi$
$572$	4.88847	+	27.7239i	0.204397	+	1.15919i
$573$	−5.03596	+	4.22567i	−0.210380	+	0.176530i
$574$	1.50000	−	0.545955i	0.0626088	−	0.0227877i
$575$	0.226109	+	0.0822969i	0.00942940	+	0.00343202i
$576$	0.766044	+	0.642788i	0.0319185	+	0.0267828i
$577$	20.1211	−	34.8507i	0.837652	−	1.45086i	−0.0542015	−	0.998530i	$-0.517261\pi$
$577$	20.1211	−	34.8507i	0.837652	−	1.45086i	0.891853	−	0.452325i	$-0.149405\pi$
$578$	6.25150	+	10.8279i	0.260028	+	0.450382i
$579$	−1.97044	+	11.1749i	−0.0818886	+	0.464413i
$580$	−1.14378	+	6.48670i	−0.0474929	+	0.269346i
$581$	−0.781308	−	1.35326i	−0.0324141	−	0.0561429i
$582$	−5.34389	+	9.25589i	−0.221511	+	0.383669i
$583$	30.6785	+	25.7423i	1.27057	+	1.06614i
$584$	−14.2811	−	5.19788i	−0.590954	−	0.215090i
$585$	−10.0569	+	3.66041i	−0.415802	+	0.151339i
$586$	−10.2246	+	8.57948i	−0.422375	+	0.354415i
$587$	−8.37598	−	47.5026i	−0.345714	−	1.96064i	−0.266766	−	0.963761i	$-0.585955\pi$
$587$	−8.37598	−	47.5026i	−0.345714	−	1.96064i	−0.0789482	−	0.996879i	$-0.525156\pi$
$588$	−6.96585			−0.287267
$589$	−2.64290	+	13.8142i	−0.108899	+	0.569206i
$590$	−16.6783			−0.686634
$591$	1.11974	+	6.35035i	0.0460598	+	0.261218i
$592$	3.11334	−	2.61240i	0.127958	−	0.107369i
$593$	16.4217	−	5.97702i	0.674360	−	0.245447i	0.0179361	−	0.999839i	$-0.494290\pi$
$593$	16.4217	−	5.97702i	0.674360	−	0.245447i	0.656424	+	0.754392i	$0.272068\pi$
$594$	4.08512	+	1.48686i	0.167615	+	0.0610067i
$595$	0.496130	+	0.416302i	0.0203393	+	0.0170667i
$596$	7.10994	−	12.3148i	0.291234	−	0.504433i
$597$	−8.36231	−	14.4839i	−0.342247	−	0.592789i
$598$	−0.119271	+	0.676417i	−0.00487734	+	0.0276608i
$599$	3.80376	−	21.5722i	0.155417	−	0.881416i	−0.802986	−	0.595998i	$-0.796757\pi$
$599$	3.80376	−	21.5722i	0.155417	−	0.881416i	0.958403	−	0.285418i	$-0.0921323\pi$
$600$	1.13429	+	1.96464i	0.0463070	+	0.0802061i
$601$	−4.63903	+	8.03504i	−0.189230	+	0.327756i	−0.944994	−	0.327088i	$-0.893933\pi$
$601$	−4.63903	+	8.03504i	−0.189230	+	0.327756i	0.755764	+	0.654844i	$0.227266\pi$
$602$	0.00592979	+	0.00497568i	0.000241680	+	0.000202794i
$603$	7.50387	+	2.73119i	0.305581	+	0.111222i
$604$	14.2836	−	5.19880i	0.581191	−	0.211536i
$605$	−10.0005	+	8.39139i	−0.406577	+	0.341158i
$606$	1.40033	+	7.94166i	0.0568845	+	0.322608i
$607$	29.3354			1.19069			0.595344	−	0.803471i	$-0.297016\pi$
$607$	29.3354			1.19069			0.595344	+	0.803471i	$0.297016\pi$
$608$	−4.07398	−	1.55007i	−0.165222	−	0.0628635i
$609$	0.736482			0.0298437
$610$	−1.03209	−	5.85327i	−0.0417881	−	0.236992i
$611$	39.2946	−	32.9721i	1.58969	−	1.33391i
$612$	1.99273	−	0.725293i	0.0805512	−	0.0293182i
$613$	22.7875	+	8.29396i	0.920377	+	0.334990i	0.758388	−	0.651803i	$-0.225987\pi$
$613$	22.7875	+	8.29396i	0.920377	+	0.334990i	0.161988	+	0.986793i	$0.448209\pi$
$614$	11.9987	+	10.0681i	0.484226	+	0.406314i
$615$	−7.13816	+	12.3636i	−0.287838	+	0.498550i
$616$	0.401674	+	0.695720i	0.0161839	+	0.0280313i
$617$	3.47834	−	19.7266i	0.140033	−	0.794165i	−0.831189	−	0.555989i	$-0.812340\pi$
$617$	3.47834	−	19.7266i	0.140033	−	0.794165i	0.971222	−	0.238176i	$-0.0765494\pi$
$618$	3.11334	−	17.6566i	0.125237	−	0.710254i
$619$	4.00774	+	6.94161i	0.161085	+	0.279007i	0.935258	−	0.353967i	$-0.115167\pi$
$619$	4.00774	+	6.94161i	0.161085	+	0.279007i	−0.774173	+	0.632974i	$0.781834\pi$
$620$	−2.66637	+	4.61830i	−0.107084	+	0.185475i
$621$	0.0812519	+	0.0681784i	0.00326053	+	0.00273591i
$622$	−8.55690	−	3.11446i	−0.343101	−	0.124878i
$623$	3.11468	−	1.13365i	0.124787	−	0.0454188i
$624$	−4.96064	+	4.16247i	−0.198584	+	0.166632i
$625$	−1.47787	−	8.38144i	−0.0591149	−	0.335257i
$626$	17.7469			0.709309
$627$	−18.9474	−	0.274761i	−0.756688	−	0.0109729i
$628$	9.40373			0.375250
$629$	−1.49660	−	8.48762i	−0.0596732	−	0.338424i
$630$	−0.233956	+	0.196312i	−0.00932101	+	0.00782126i
$631$	−3.74763	+	1.36402i	−0.149191	+	0.0543010i	−0.415536	−	0.909577i	$-0.636406\pi$
$631$	−3.74763	+	1.36402i	−0.149191	+	0.0543010i	0.266345	+	0.963878i	$0.414184\pi$
$632$	−11.6493	−	4.24000i	−0.463384	−	0.168658i
$633$	−3.73783	−	3.13641i	−0.148565	−	0.124661i
$634$	−15.5228	+	26.8862i	−0.616487	+	1.06779i
$635$	−8.94356	−	15.4907i	−0.354914	−	0.614730i
$636$	−1.59967	+	9.07218i	−0.0634311	+	0.359735i
$637$	7.83300	−	44.4231i	0.310355	−	1.76011i
$638$	8.66297	+	15.0047i	0.342970	+	0.594042i
$639$	2.02094	−	3.50038i	0.0799473	−	0.138473i
$640$	−1.26604	−	1.06234i	−0.0500448	−	0.0419926i
$641$	26.2221	+	9.54406i	1.03571	+	0.376968i	0.803253	−	0.595639i	$-0.203101\pi$
$641$	26.2221	+	9.54406i	1.03571	+	0.376968i	0.232458	+	0.972606i	$0.425323\pi$
$642$	13.1446	−	4.78423i	0.518774	−	0.188818i
$643$	−8.27584	+	6.94426i	−0.326367	+	0.273855i	−0.791218	−	0.611534i	$-0.790553\pi$
$643$	−8.27584	+	6.94426i	−0.326367	+	0.273855i	0.464850	+	0.885389i	$0.346108\pi$
$644$	0.00340357	+	0.0193026i	0.000134119	+	0.000760628i
$645$	−0.0692302			−0.00272594
$646$	−7.16637	+	5.83834i	−0.281957	+	0.229706i
$647$	−34.4662			−1.35500			−0.677502	−	0.735521i	$-0.736938\pi$
$647$	−34.4662			−1.35500			−0.677502	+	0.735521i	$0.736938\pi$
$648$	0.173648	+	0.984808i	0.00682154	+	0.0386869i
$649$	−33.6070	+	28.1996i	−1.31919	+	1.10693i
$650$	−13.8045	+	5.02444i	−0.541458	+	0.197075i
$651$	0.560307	+	0.203935i	0.0219602	+	0.00799285i
$652$	−5.84002	−	4.90036i	−0.228713	−	0.191913i
$653$	11.4971	−	19.9135i	0.449915	−	0.779275i	−0.548465	−	0.836173i	$-0.684788\pi$
$653$	11.4971	−	19.9135i	0.449915	−	0.779275i	0.998380	+	0.0568980i	$0.0181210\pi$
$654$	2.38666	+	4.13381i	0.0933258	+	0.161645i
$655$	−3.11246	+	17.6517i	−0.121614	+	0.689707i
$656$	−1.50000	+	8.50692i	−0.0585652	+	0.332140i
$657$	−7.59879	−	13.1615i	−0.296457	−	0.513479i
$658$	0.731896	−	1.26768i	0.0285323	−	0.0494194i
$659$	−26.0742	−	21.8788i	−1.01571	−	0.852279i	−0.0266245	−	0.999646i	$-0.508476\pi$
$659$	−26.0742	−	21.8788i	−1.01571	−	0.852279i	−0.989082	+	0.147367i	$0.952920\pi$
$660$	−6.75150	−	2.45734i	−0.262802	−	0.0956520i
$661$	−8.04411	+	2.92782i	−0.312880	+	0.113879i	−0.493687	−	0.869640i	$-0.664351\pi$
$661$	−8.04411	+	2.92782i	−0.312880	+	0.113879i	0.180807	+	0.983519i	$0.442129\pi$
$662$	−7.72147	+	6.47908i	−0.300103	+	0.251817i
$663$	2.38460	+	13.5237i	0.0926102	+	0.525218i
$664$	8.45605			0.328158
$665$	0.682266	−	1.14311i	0.0264572	−	0.0443281i
$666$	4.06418			0.157484
$667$	0.0734053	+	0.416302i	0.00284226	+	0.0161193i
$668$	−13.1762	+	11.0561i	−0.509801	+	0.427774i
$669$	−27.0453	+	9.84370i	−1.04563	+	0.380580i
$670$	−12.4017	−	4.51384i	−0.479118	−	0.174385i
$671$	−11.9764	−	10.0494i	−0.462343	−	0.387951i
$672$	−0.0923963	+	0.160035i	−0.00356426	+	0.00617349i
$673$	6.07011	+	10.5137i	0.233985	+	0.405275i	0.958977	−	0.283483i	$-0.0914899\pi$
$673$	6.07011	+	10.5137i	0.233985	+	0.405275i	−0.724992	+	0.688757i	$0.758157\pi$
$674$	−1.45471	+	8.25006i	−0.0560332	+	0.317780i
$675$	−0.393933	+	2.23411i	−0.0151625	+	0.0859908i
$676$	−14.4670	−	25.0576i	−0.556424	−	0.963755i
$677$	−0.776722	+	1.34532i	−0.0298519	+	0.0517049i	−0.880565	−	0.473925i	$-0.842837\pi$
$677$	−0.776722	+	1.34532i	−0.0298519	+	0.0517049i	0.850714	+	0.525630i	$0.176170\pi$
$678$	−0.577382	−	0.484481i	−0.0221742	−	0.0186064i
$679$	−1.85591	−	0.675498i	−0.0712235	−	0.0259232i
$680$	−3.29339	+	1.19869i	−0.126296	+	0.0459678i
$681$	−2.87733	+	2.41436i	−0.110259	+	0.0925186i
$682$	2.43582	+	13.8142i	0.0932725	+	0.528974i
$683$	−35.3892			−1.35413			−0.677065	−	0.735923i	$-0.736748\pi$
$683$	−35.3892			−1.35413			−0.677065	+	0.735923i	$0.736748\pi$
$684$	−2.12449	−	3.80612i	−0.0812317	−	0.145531i
$685$	23.0574			0.880977
$686$	−0.448149	−	2.54158i	−0.0171104	−	0.0970379i
$687$	13.4192	−	11.2601i	0.511975	−	0.429598i
$688$	−0.0393628	+	0.0143269i	−0.00150069	+	0.000546208i
$689$	−56.0570	−	20.4031i	−2.13560	−	0.777295i
$690$	−0.134285	−	0.112679i	−0.00511216	−	0.00428961i
$691$	19.6411	−	34.0195i	0.747185	−	1.29416i	−0.201983	−	0.979389i	$-0.564738\pi$
$691$	19.6411	−	34.0195i	0.747185	−	1.29416i	0.949167	−	0.314772i	$-0.101928\pi$
$692$	3.31180	+	5.73621i	0.125896	+	0.218058i
$693$	−0.139500	+	0.791143i	−0.00529916	+	0.0300530i
$694$	2.26011	−	12.8177i	0.0857928	−	0.486555i
$695$	4.92989	+	8.53882i	0.187001	+	0.323896i
$696$	−1.99273	+	3.45150i	−0.0755341	+	0.130829i
$697$	14.0326	+	11.7747i	0.531521	+	0.445999i
$698$	6.30288	+	2.29406i	0.238568	+	0.0868315i
$699$	6.58260	−	2.39587i	0.248977	−	0.0906201i
$700$	−0.321137	+	0.269466i	−0.0121378	+	0.0101849i
$701$	2.89171	+	16.3997i	0.109218	+	0.619409i	0.989451	+	0.144866i	$0.0462752\pi$
$701$	2.89171	+	16.3997i	0.109218	+	0.619409i	−0.880233	+	0.474542i	$0.842614\pi$
$702$	−6.47565			−0.244408
$703$	−16.7331	+	5.81699i	−0.631100	+	0.219392i
$704$	−4.34730			−0.163845
$705$	2.27332	+	12.8926i	0.0856181	+	0.485565i
$706$	8.15523	−	6.84305i	0.306926	−	0.257542i
$707$	−1.40033	+	0.509678i	−0.0526648	+	0.0191684i
$708$	−9.48293	−	3.45150i	−0.356390	−	0.129715i
$709$	33.3723	+	28.0027i	1.25332	+	1.05166i	0.996360	+	0.0852428i	$0.0271666\pi$
$709$	33.3723	+	28.0027i	1.25332	+	1.05166i	0.256964	+	0.966421i	$0.417278\pi$
$710$	−3.34002	+	5.78509i	−0.125349	+	0.217111i
$711$	−6.19846	−	10.7361i	−0.232461	−	0.402633i
$712$	−3.11468	+	17.6643i	−0.116728	+	0.661996i
$713$	−0.0594300	+	0.337044i	−0.00222567	+	0.0126224i
$714$	0.195937	+	0.339373i	0.00733275	+	0.0127007i
$715$	23.2631	−	40.2929i	0.869991	−	1.50687i
$716$	−16.4119	−	13.7713i	−0.613343	−	0.514656i
$717$	−0.879385	−	0.320070i	−0.0328412	−	0.0119532i
$718$	27.4047	−	9.97448i	1.02273	−	0.372244i
$719$	4.94949	−	4.15312i	0.184585	−	0.154885i	−0.545813	−	0.837907i	$-0.683779\pi$
$719$	4.94949	−	4.15312i	0.184585	−	0.154885i	0.730398	+	0.683022i	$0.239335\pi$
$720$	−0.286989	−	1.62760i	−0.0106954	−	0.0606569i
$721$	3.31315			0.123388
$722$	14.1946	+	12.6299i	0.528268	+	0.470035i
$723$	−28.7297			−1.06847
$724$	−2.98411	−	16.9237i	−0.110903	−	0.628965i
$725$	−6.92602	+	5.81162i	−0.257226	+	0.215838i
$726$	−7.42262	+	2.70161i	−0.275479	+	0.100266i
$727$	−1.73308	−	0.630789i	−0.0642763	−	0.0233947i	0.309682	−	0.950840i	$-0.399777\pi$
$727$	−1.73308	−	0.630789i	−0.0642763	−	0.0233947i	−0.373958	+	0.927446i	$0.622000\pi$
$728$	−0.916689	−	0.769193i	−0.0339747	−	0.0285082i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	12.5586	+	21.7521i	0.464813	+	0.805080i
$731$	−0.0154253	+	0.0874810i	−0.000570524	+	0.00323560i
$732$	0.624485	−	3.54163i	0.0230816	−	0.130902i
$733$	−16.1793	−	28.0234i	−0.597597	−	1.03507i	−0.993175	−	0.116636i	$-0.962789\pi$
$733$	−16.1793	−	28.0234i	−0.597597	−	1.03507i	0.395578	−	0.918433i	$-0.370544\pi$
$734$	1.76945	−	3.06477i	0.0653115	−	0.113123i
$735$	8.81908	+	7.40008i	0.325297	+	0.272956i
$736$	−0.0996702	−	0.0362770i	−0.00367389	−	0.00133719i
$737$	−32.6215	+	11.8733i	−1.20163	+	0.437358i
$738$	−6.61721	+	5.55250i	−0.243583	+	0.204390i
$739$	−1.89899	−	10.7697i	−0.0698553	−	0.396169i	−0.999608	−	0.0279854i	$-0.991091\pi$
$739$	−1.89899	−	10.7697i	−0.0698553	−	0.396169i	0.929753	−	0.368184i	$-0.120020\pi$
$740$	−6.71688			−0.246917
$741$	26.6616	−	9.26849i	0.979439	−	0.340487i
$742$	−1.70233			−0.0624946
$743$	−1.81820	−	10.3115i	−0.0667033	−	0.378293i	−0.999825	−	0.0187314i	$-0.994037\pi$
$743$	−1.81820	−	10.3115i	−0.0667033	−	0.378293i	0.933121	−	0.359562i	$-0.117074\pi$
$744$	−2.47178	+	2.07407i	−0.0906199	+	0.0760391i
$745$	−22.0839	+	8.03790i	−0.809093	+	0.294486i
$746$	−9.59374	−	3.49184i	−0.351252	−	0.127845i
$747$	6.47771	+	5.43545i	0.237007	+	0.198873i
$748$	−4.60947	+	7.98384i	−0.168539	+	0.291918i
$749$	1.29245	+	2.23859i	0.0472252	+	0.0817964i
$750$	2.08600	−	11.8303i	0.0761699	−	0.431981i
$751$	−4.58079	+	25.9789i	−0.167155	+	0.947984i	0.779659	+	0.626204i	$0.215392\pi$
$751$	−4.58079	+	25.9789i	−0.167155	+	0.947984i	−0.946814	+	0.321780i	$0.895719\pi$
$752$	3.96064	+	6.86002i	0.144430	+	0.250159i
$753$	−12.0929	+	20.9455i	−0.440688	+	0.763295i
$754$	−19.7704	−	16.5893i	−0.719995	−	0.604147i
$755$	−23.6065	−	8.59208i	−0.859130	−	0.312698i
$756$	−0.173648	+	0.0632028i	−0.00631552	+	0.00229866i
$757$	17.4715	−	14.6604i	0.635014	−	0.532840i	−0.267469	−	0.963567i	$-0.586187\pi$
$757$	17.4715	−	14.6604i	0.635014	−	0.532840i	0.902482	+	0.430727i	$0.141743\pi$
$758$	2.19294	+	12.4368i	0.0796513	+	0.451725i
$759$	−0.461104			−0.0167370
$760$	3.51114	+	6.29039i	0.127363	+	0.228176i
$761$	41.5012			1.50442			0.752209	−	0.658924i	$-0.228988\pi$
$761$	41.5012			1.50442			0.752209	+	0.658924i	$0.228988\pi$
$762$	−1.87939	−	10.6585i	−0.0680829	−	0.386118i
$763$	−0.675708	+	0.566986i	−0.0244623	+	0.0205263i
$764$	6.17752	−	2.24843i	0.223495	−	0.0813454i
$765$	−3.29339	−	1.19869i	−0.119073	−	0.0433389i
$766$	−6.67546	−	5.60138i	−0.241194	−	0.202386i
$767$	32.6746	−	56.5940i	1.17981	−	2.04349i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	3.29948	−	18.7123i	0.118982	−	0.674782i	−0.865719	−	0.500530i	$-0.833138\pi$
$769$	3.29948	−	18.7123i	0.118982	−	0.674782i	0.984701	−	0.174251i	$-0.0557505\pi$
$770$	0.230552	−	1.30753i	0.00830852	−	0.0471199i
$771$	−4.40033	−	7.62159i	−0.158474	−	0.274485i
$772$	5.67365	−	9.82705i	0.204199	−	0.353683i
$773$	13.1329	+	11.0198i	0.472359	+	0.396356i	0.847654	−	0.530549i	$-0.178014\pi$
$773$	13.1329	+	11.0198i	0.472359	+	0.396356i	−0.375295	+	0.926905i	$0.622459\pi$
$774$	−0.0393628	−	0.0143269i	−0.00141487	−	0.000514970i
$775$	−6.87851	+	2.50357i	−0.247083	+	0.0899310i
$776$	8.18732	−	6.86998i	0.293908	−	0.246618i
$777$	0.130415	+	0.739620i	0.00467861	+	0.0265337i
$778$	−8.64496			−0.309937
$779$	19.2973	−	32.3319i	0.691396	−	1.15841i
$780$	10.7023			0.383205
$781$	3.05122	+	17.3043i	0.109181	+	0.619198i
$782$	−0.172304	+	0.144580i	−0.00616158	+	0.00517018i
$783$	−3.74510	+	1.36310i	−0.133839	+	0.0487134i
$784$	6.54576	+	2.38246i	0.233777	+	0.0850879i
$785$	−11.9055	−	9.98994i	−0.424927	−	0.356556i
$786$	−5.42262	+	9.39225i	−0.193418	+	0.335010i
$787$	9.10014	+	15.7619i	0.324385	+	0.561851i	0.981388	−	0.192037i	$-0.0615094\pi$
$787$	9.10014	+	15.7619i	0.324385	+	0.561851i	−0.657003	+	0.753888i	$0.728176\pi$
$788$	1.11974	−	6.35035i	0.0398890	−	0.226222i
$789$	0.227148	−	1.28822i	0.00808670	−	0.0458619i
$790$	10.2442	+	17.7435i	0.364473	+	0.631286i
$791$	0.0696407	−	0.120621i	0.00247614	−	0.00428880i
$792$	−3.33022	−	2.79439i	−0.118334	−	0.0992943i
$793$	21.8837	+	7.96502i	0.777114	+	0.282846i
$794$	6.45976	−	2.35116i	0.229248	−	0.0834396i
$795$	11.6630	−	9.78639i	0.413643	−	0.347088i
$796$	2.90420	+	16.4705i	0.102937	+	0.583783i
$797$	−26.4584			−0.937205			−0.468603	−	0.883409i	$-0.655242\pi$
$797$	−26.4584			−0.937205			−0.468603	+	0.883409i	$0.655242\pi$
$798$	0.624485	−	0.508759i	0.0221065	−	0.0180099i
$799$	16.7980			0.594270
$800$	−0.393933	−	2.23411i	−0.0139276	−	0.0789876i
$801$	−13.7404	+	11.5295i	−0.485491	+	0.407376i
$802$	27.6634	−	10.0687i	0.976830	−	0.355537i
$803$	62.0840	+	22.5967i	2.19090	+	0.797421i
$804$	−6.11721	−	5.13295i	−0.215737	−	0.181025i
$805$	0.0161968	−	0.0280537i	0.000570862	−	0.000988762i
$806$	−10.4474	−	18.0955i	−0.367995	−	0.637386i
$807$	1.51960	−	8.61808i	0.0534925	−	0.303371i
$808$	1.40033	−	7.94166i	0.0492634	−	0.279387i
$809$	15.2836	+	26.4719i	0.537342	+	0.930704i	0.999046	+	0.0436699i	$0.0139050\pi$
$809$	15.2836	+	26.4719i	0.537342	+	0.930704i	−0.461704	+	0.887034i	$0.652762\pi$
$810$	0.826352	−	1.43128i	0.0290350	−	0.0502902i
$811$	−5.25284	−	4.40766i	−0.184452	−	0.154774i	0.545886	−	0.837859i	$-0.316193\pi$
$811$	−5.25284	−	4.40766i	−0.184452	−	0.154774i	−0.730338	+	0.683086i	$0.760638\pi$
$812$	−0.692066	−	0.251892i	−0.0242868	−	0.00883966i
$813$	12.9179	−	4.70172i	0.453050	−	0.164897i
$814$	−13.5346	+	11.3569i	−0.474388	+	0.398059i
$815$	2.18789	+	12.4081i	0.0766385	+	0.434638i
$816$	−2.12061			−0.0742364
$817$	0.182571	+	0.00264750i	0.00638735	+	9.26245e-5i
$818$	−21.2763			−0.743909
$819$	−0.207796	−	1.17847i	−0.00726100	−	0.0411792i
$820$	10.9363	−	9.17664i	0.381912	−	0.320462i
$821$	−37.2870	+	13.5714i	−1.30133	+	0.473644i	−0.897429	−	0.441160i	$-0.854567\pi$
$821$	−37.2870	+	13.5714i	−1.30133	+	0.473644i	−0.403898	+	0.914804i	$0.632345\pi$
$822$	13.1099	+	4.77163i	0.457262	+	0.166430i
$823$	−35.7900	−	30.0314i	−1.24756	−	1.04683i	−0.996894	−	0.0787539i	$-0.974906\pi$
$823$	−35.7900	−	30.0314i	−1.24756	−	1.04683i	−0.250666	−	0.968074i	$-0.580650\pi$
$824$	−8.96451	+	15.5270i	−0.312293	+	0.540908i
$825$	−4.93107	−	8.54087i	−0.171678	−	0.297355i
$826$	0.323826	−	1.83651i	0.0112673	−	0.0639002i
$827$	−7.27884	+	41.2803i	−0.253110	+	1.43546i	0.547768	+	0.836630i	$0.315478\pi$
$827$	−7.27884	+	41.2803i	−0.253110	+	1.43546i	−0.800878	+	0.598828i	$0.795633\pi$
$828$	−0.0530334	−	0.0918566i	−0.00184304	−	0.00319224i
$829$	0.251030	−	0.434796i	0.00871862	−	0.0151011i	−0.861633	−	0.507532i	$-0.830558\pi$
$829$	0.251030	−	0.434796i	0.00871862	−	0.0151011i	0.870352	+	0.492430i	$0.163891\pi$
$830$	−10.7057	−	8.98318i	−0.371602	−	0.311811i
$831$	−23.4996	−	8.55315i	−0.815192	−	0.296706i
$832$	6.08512	−	2.21480i	0.210964	−	0.0767845i
$833$	11.3159	−	9.49519i	0.392073	−	0.328989i
$834$	1.03596	+	5.87522i	0.0358723	+	0.203442i
$835$	28.4270			0.983755
$836$	17.7108	+	6.73859i	0.612540	+	0.233059i
$837$	−3.22668			−0.111530
$838$	2.75965	+	15.6507i	0.0953305	+	0.540646i
$839$	−24.0646	+	20.1926i	−0.830804	+	0.697127i	−0.955475	−	0.295071i	$-0.904657\pi$
$839$	−24.0646	+	20.1926i	−0.830804	+	0.697127i	0.124672	+	0.992198i	$0.460212\pi$
$840$	0.286989	−	0.104455i	0.00990206	−	0.00360406i
$841$	12.3252	+	4.48599i	0.425006	+	0.154689i
$842$	15.0103	+	12.5951i	0.517288	+	0.434056i
$843$	−6.07785	+	10.5271i	−0.209332	+	0.362574i
$844$	2.43969	+	4.22567i	0.0839777	+	0.145454i
$845$	−8.30376	+	47.0930i	−0.285658	+	1.62005i
$846$	−1.37551	+	7.80093i	−0.0472912	+	0.268202i
$847$	−0.729837	−	1.26411i	−0.0250775	−	0.0434355i
$848$	4.60607	−	7.97794i	0.158173	−	0.273964i
$849$	−8.19459	−	6.87608i	−0.281238	−	0.235986i
$850$	−4.52064	−	1.64538i	−0.155057	−	0.0564360i
$851$	−0.405078	+	0.147436i	−0.0138859	+	0.00505405i
$852$	−3.09627	+	2.59808i	−0.106076	+	0.0890086i
$853$	3.26682	+	18.5270i	0.111854	+	0.634354i	0.988260	+	0.152781i	$0.0488230\pi$
$853$	3.26682	+	18.5270i	0.111854	+	0.634354i	−0.876406	+	0.481572i	$0.840066\pi$
$854$	0.664563			0.0227409
$855$	−1.35369	+	7.07564i	−0.0462953	+	0.241982i
$856$	−13.9881			−0.478105
$857$	5.20305	+	29.5080i	0.177733	+	1.00797i	0.934942	+	0.354800i	$0.115451\pi$
$857$	5.20305	+	29.5080i	0.177733	+	1.00797i	−0.757209	+	0.653172i	$0.773438\pi$
$858$	21.5654	−	18.0955i	0.736229	−	0.617770i
$859$	31.1698	−	11.3449i	1.06350	−	0.387083i	0.249758	−	0.968308i	$-0.419649\pi$
$859$	31.1698	−	11.3449i	1.06350	−	0.387083i	0.813743	+	0.581225i	$0.197427\pi$
$860$	0.0650551	+	0.0236781i	0.00221836	+	0.000807417i
$861$	−1.22281	−	1.02606i	−0.0416733	−	0.0349680i
$862$	2.07738	−	3.59813i	0.0707559	−	0.122553i
$863$	19.1238	+	33.1233i	0.650981	+	1.12753i	0.982885	+	0.184219i	$0.0589755\pi$
$863$	19.1238	+	33.1233i	0.650981	+	1.12753i	−0.331905	+	0.943313i	$0.607691\pi$
$864$	0.173648	−	0.984808i	0.00590763	−	0.0335038i
$865$	1.90090	−	10.7806i	0.0646326	−	0.366550i
$866$	1.78106	+	3.08489i	0.0605229	+	0.104829i
$867$	6.25150	−	10.8279i	0.212312	−	0.367735i
$868$	−0.456767	−	0.383273i	−0.0155037	−	0.0130091i
$869$	50.6430	+	18.4325i	1.71794	+	0.625281i
$870$	6.18954	−	2.25281i	0.209845	−	0.0763774i
$871$	39.6129	−	33.2392i	1.34223	−	1.12627i
$872$	−0.828878	−	4.70080i	−0.0280694	−	0.159189i
$873$	10.6878			0.361727
$874$	0.349823	+	0.302287i	0.0118329	+	0.0102250i
$875$	2.21987			0.0750455
$876$	2.63903	+	14.9667i	0.0891647	+	0.505678i
$877$	−36.8981	+	30.9612i	−1.24596	+	1.04549i	−0.248927	+	0.968522i	$0.580078\pi$
$877$	−36.8981	+	30.9612i	−1.24596	+	1.04549i	−0.997034	+	0.0769627i	$0.975478\pi$
$878$	7.71941	−	2.80963i	0.260517	−	0.0948206i
$879$	12.5424	+	4.56504i	0.423043	+	0.153975i
$880$	5.50387	+	4.61830i	0.185535	+	0.155683i
$881$	−18.8542	+	32.6564i	−0.635213	+	1.10022i	0.351257	+	0.936279i	$0.385754\pi$
$881$	−18.8542	+	32.6564i	−0.635213	+	1.10022i	−0.986470	+	0.163942i	$0.947579\pi$
$882$	3.48293	+	6.03260i	0.117276	+	0.203128i
$883$	−5.27022	+	29.8889i	−0.177357	+	1.00584i	0.758031	+	0.652219i	$0.226162\pi$
$883$	−5.27022	+	29.8889i	−0.177357	+	1.00584i	−0.935388	+	0.353623i	$0.884950\pi$
$884$	2.38460	−	13.5237i	0.0802028	−	0.454853i
$885$	8.33915	+	14.4438i	0.280317	+	0.485524i
$886$	9.47313	−	16.4079i	0.318256	−	0.551235i
$887$	−0.709856	−	0.595640i	−0.0238346	−	0.0199996i	0.630793	−	0.775952i	$-0.282730\pi$
$887$	−0.709856	−	0.595640i	−0.0238346	−	0.0199996i	−0.654627	+	0.755952i	$0.727174\pi$
$888$	−3.81908	−	1.39003i	−0.128160	−	0.0466464i
$889$	1.87939	−	0.684040i	0.0630326	−	0.0229420i
$890$	22.7087	−	19.0549i	0.761198	−	0.638721i
$891$	−0.754900	−	4.28125i	−0.0252901	−	0.143427i
$892$	28.7811			0.963661
$893$	−5.50206	−	34.0868i	−0.184119	−	1.14067i
$894$	−14.2199			−0.475584
$895$	6.14853	+	34.8700i	0.205523	+	1.16558i
$896$	0.141559	−	0.118782i	0.00472916	−	0.00396824i
$897$	0.645430	−	0.234917i	0.0215503	−	0.00784366i
$898$	−9.85978	−	3.58867i	−0.329025	−	0.119755i
$899$	−9.85117	−	8.26611i	−0.328555	−	0.275690i
$900$	1.13429	−	1.96464i	0.0378095	−	0.0654880i
$901$	−9.76769	−	16.9181i	−0.325409	−	0.563625i
$902$	6.52094	−	36.9821i	0.217124	−	1.23137i
$903$	0.00134417	−	0.00762319i	4.47313e−5	−	0.000253684i
$904$	0.376859	+	0.652739i	0.0125341	+	0.0217098i
$905$	−14.2007	+	24.5963i	−0.472047	+	0.817609i
$906$	−11.6441	−	9.77055i	−0.386849	−	0.324605i
$907$	3.98932	+	1.45199i	0.132463	+	0.0482127i	0.407401	−	0.913249i	$-0.366435\pi$
$907$	3.98932	+	1.45199i	0.132463	+	0.0482127i	−0.274938	+	0.961462i	$0.588657\pi$
$908$	3.52956	−	1.28466i	0.117133	−	0.0426328i
$909$	6.17752	−	5.18355i	0.204895	−	0.171928i
$910$	0.343426	+	1.94767i	0.0113845	+	0.0645645i
$911$	−56.5509			−1.87361			−0.936807	−	0.349847i	$-0.886234\pi$
$911$	−56.5509			−1.87361			−0.936807	+	0.349847i	$0.886234\pi$
$912$	0.694593	+	4.30320i	0.0230003	+	0.142493i
$913$	−36.7610			−1.21661
$914$	−0.0721670	−	0.409279i	−0.00238707	−	0.0135378i
$915$	−4.55303	+	3.82045i	−0.150519	+	0.126300i
$916$	−16.4611	+	5.99135i	−0.543890	+	0.197960i
$917$	−1.88326	−	0.685449i	−0.0621906	−	0.0226355i
$918$	−1.62449	−	1.36310i	−0.0536160	−	0.0449892i
$919$	−29.4778	+	51.0570i	−0.972382	+	1.68421i	−0.284064	+	0.958805i	$0.591683\pi$
$919$	−29.4778	+	51.0570i	−0.972382	+	1.68421i	−0.688318	+	0.725409i	$0.741650\pi$
$920$	0.0876485	+	0.151812i	0.00288969	+	0.00500508i
$921$	2.71987	−	15.4252i	0.0896229	−	0.508277i
$922$	4.38594	−	24.8739i	0.144443	−	0.819179i
$923$	−13.0869	−	22.6672i	−0.430762	−	0.746101i
$924$	0.401674	−	0.695720i	0.0132141	−	0.0228875i
$925$	−7.06283	−	5.92642i	−0.232225	−	0.194860i
$926$	−17.6579	−	6.42696i	−0.580275	−	0.211203i
$927$	−16.8478	+	6.13208i	−0.553353	+	0.201404i
$928$	3.05303	−	2.56180i	0.100221	−	0.0840952i
$929$	−2.15446	−	12.2185i	−0.0706855	−	0.400877i	−0.999537	−	0.0304252i	$-0.990314\pi$
$929$	−2.15446	−	12.2185i	−0.0706855	−	0.400877i	0.928852	−	0.370452i	$-0.120797\pi$
$930$	5.33275			0.174868
$931$	−22.9743	−	19.8525i	−0.752953	−	0.650638i
$932$	−7.00505			−0.229458
$933$	1.58125	+	8.96773i	0.0517679	+	0.293590i
$934$	−13.1250	+	11.0131i	−0.429462	+	0.360361i
$935$	14.3173	−	5.21108i	0.468227	−	0.170421i
$936$	6.08512	+	2.21480i	0.198898	+	0.0723931i
$937$	21.2973	+	17.8705i	0.695751	+	0.583804i	0.920561	−	0.390598i	$-0.127732\pi$
$937$	21.2973	+	17.8705i	0.695751	+	0.583804i	−0.224810	+	0.974403i	$0.572176\pi$
$938$	0.737826	−	1.27795i	0.0240909	−	0.0417266i
$939$	−8.87346	−	15.3693i	−0.289574	−	0.501557i
$940$	2.27332	−	12.8926i	0.0741475	−	0.420511i
$941$	−3.46632	+	19.6585i	−0.112999	+	0.640848i	0.874723	+	0.484623i	$0.161043\pi$
$941$	−3.46632	+	19.6585i	−0.112999	+	0.640848i	−0.987722	+	0.156224i	$0.950068\pi$
$942$	−4.70187	−	8.14387i	−0.153195	−	0.265342i
$943$	0.458111	−	0.793471i	0.0149181	−	0.0258390i
$944$	7.73055	+	6.48670i	0.251608	+	0.211124i
$945$	0.286989	+	0.104455i	0.00933575	+	0.00339794i
$946$	0.171122	−	0.0622833i	0.00556365	−	0.00202500i
$947$	22.9807	−	19.2831i	0.746773	−	0.626617i	−0.187875	−	0.982193i	$-0.560160\pi$
$947$	22.9807	−	19.2831i	0.746773	−	0.626617i	0.934647	+	0.355576i	$0.115715\pi$
$948$	2.15270	+	12.2086i	0.0699166	+	0.396517i
$949$	−98.4143			−3.19466
$950$	−1.85814	+	9.71232i	−0.0602859	+	0.315109i
$951$	31.0455			1.00672
$952$	−0.0680482	−	0.385920i	−0.00220545	−	0.0125077i
$953$	17.5713	−	14.7441i	0.569190	−	0.477607i	−0.312187	−	0.950021i	$-0.601062\pi$
$953$	17.5713	−	14.7441i	0.569190	−	0.477607i	0.881377	+	0.472414i	$0.156617\pi$
$954$	8.65657	−	3.15074i	0.280267	−	0.102009i
$955$	−10.2096	−	3.71599i	−0.330375	−	0.120247i
$956$	0.716881	+	0.601535i	0.0231856	+	0.0194550i
$957$	8.66297	−	15.0047i	0.280034	−	0.485033i
$958$	5.47906	+	9.49000i	0.177020	+	0.306608i
$959$	−0.447682	+	2.53893i	−0.0144564	+	0.0819863i
$960$	−0.286989	+	1.62760i	−0.00926253	+	0.0525304i
$961$	10.2943	+	17.8302i	0.332073	+	0.575167i
$962$	13.1591	−	22.7922i	0.424266	−	0.734851i
$963$	−10.7155	−	8.99140i	−0.345303	−	0.289744i
$964$	26.9971	+	9.82613i	0.869517	+	0.316478i
$965$	−17.6227	+	6.41415i	−0.567296	+	0.206479i
$966$	0.0150147	−	0.0125989i	0.000483092	−	0.000405362i
$967$	−6.57233	−	37.2735i	−0.211352	−	1.19864i	−0.887126	−	0.461527i	$-0.847302\pi$
$967$	−6.57233	−	37.2735i	−0.211352	−	1.19864i	0.675774	−	0.737109i	$-0.263809\pi$
$968$	7.89899			0.253883
$969$	8.63934	+	3.28709i	0.277536	+	0.105597i
$970$	−17.6637			−0.567149
$971$	−5.09421	−	28.8907i	−0.163481	−	0.927146i	−0.950617	−	0.310367i	$-0.899548\pi$
$971$	−5.09421	−	28.8907i	−0.163481	−	0.927146i	0.787136	−	0.616779i	$-0.211563\pi$
$972$	0.766044	−	0.642788i	0.0245709	−	0.0206174i
$973$	−1.03596	+	0.377058i	−0.0332113	+	0.0120879i
$974$	−15.8623	−	5.77341i	−0.508261	−	0.184992i
$975$	11.2536	+	9.44285i	0.360402	+	0.302413i
$976$	−1.79813	+	3.11446i	−0.0575568	+	0.0996914i
$977$	−7.08054	−	12.2638i	−0.226526	−	0.392355i	0.730250	−	0.683180i	$-0.239404\pi$
$977$	−7.08054	−	12.2638i	−0.226526	−	0.392355i	−0.956776	+	0.290825i	$0.906070\pi$
$978$	−1.32383	+	7.50779i	−0.0423313	+	0.240073i
$979$	13.5405	−	76.7918i	0.432755	−	2.45428i
$980$	−5.75624	−	9.97011i	−0.183876	−	0.318483i
$981$	2.38666	−	4.13381i	0.0762002	−	0.131983i
$982$	−8.62314	−	7.23567i	−0.275175	−	0.230900i
$983$	32.6724	+	11.8918i	1.04209	+	0.379288i	0.805671	−	0.592364i	$-0.201805\pi$
$983$	32.6724	+	11.8918i	1.04209	+	0.379288i	0.236416	+	0.971652i	$0.424027\pi$
$984$	8.11721	−	2.95442i	0.258767	−	0.0941836i
$985$	−8.16385	+	6.85028i	−0.260122	+	0.218268i
$986$	−1.46761	−	8.32321i	−0.0467381	−	0.265065i
$987$	−1.46379			−0.0465930
$988$	−28.2237	−	0.409279i	−0.897917	−	0.0130209i
$989$	0.00444304			0.000141280
$990$	1.24763	+	7.07564i	0.0396522	+	0.224879i
$991$	−4.20393	+	3.52751i	−0.133542	+	0.112055i	−0.707112	−	0.707101i	$-0.750002\pi$
$991$	−4.20393	+	3.52751i	−0.133542	+	0.112055i	0.573570	+	0.819156i	$0.305558\pi$
$992$	3.03209	−	1.10359i	0.0962689	−	0.0350390i
$993$	9.47178	+	3.44745i	0.300578	+	0.109401i
$994$	−0.572167	−	0.480105i	−0.0181480	−	0.0152280i
$995$	13.8204	−	23.9377i	0.438137	−	0.758875i
$996$	−4.22803	−	7.32316i	−0.133970	−	0.232043i
$997$	−1.67128	+	9.47832i	−0.0529301	+	0.300182i	−0.999768	−	0.0215289i	$-0.993147\pi$
$997$	−1.67128	+	9.47832i	−0.0529301	+	0.300182i	0.946838	+	0.321710i	$0.104258\pi$
$998$	−1.69665	+	9.62219i	−0.0537066	+	0.304585i
$999$	−2.03209	−	3.51968i	−0.0642924	−	0.111358i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.i.b.85.1	yes	6
3.2	odd	2		342.2.u.d.199.1		6
4.3	odd	2		912.2.bo.c.769.1		6
19.6	even	9		2166.2.a.t.1.2		3
19.13	odd	18		2166.2.a.n.1.2		3
19.17	even	9	inner	114.2.i.b.55.1	✓	6
57.17	odd	18		342.2.u.d.55.1		6
57.32	even	18		6498.2.a.bt.1.2		3
57.44	odd	18		6498.2.a.bo.1.2		3
76.55	odd	18		912.2.bo.c.625.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.b.55.1	✓	6	19.17	even	9	inner
114.2.i.b.85.1	yes	6	1.1	even	1	trivial
342.2.u.d.55.1		6	57.17	odd	18
342.2.u.d.199.1		6	3.2	odd	2
912.2.bo.c.625.1		6	76.55	odd	18
912.2.bo.c.769.1		6	4.3	odd	2
2166.2.a.n.1.2		3	19.13	odd	18
2166.2.a.t.1.2		3	19.6	even	9
6498.2.a.bo.1.2		3	57.44	odd	18
6498.2.a.bt.1.2		3	57.32	even	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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(0.766044 - 0.642788i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.55303 + 0.565258i) q^{5} +(0.766044 + 0.642788i) q^{6} +(-0.0923963 + 0.160035i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{2} +(0.766044 - 0.642788i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.55303 + 0.565258i) q^{5} +(0.766044 + 0.642788i) q^{6} +(-0.0923963 + 0.160035i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.173648 - 0.984808i) q^{9} +(-0.286989 + 1.62760i) q^{10} +(2.17365 + 3.76487i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-4.96064 - 4.16247i) q^{13} +(-0.173648 - 0.0632028i) q^{14} +(1.55303 - 0.565258i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-0.368241 - 2.08840i) q^{17} +1.00000 q^{18} +(-4.11721 + 1.43128i) q^{19} -1.65270 q^{20} +(0.0320889 + 0.181985i) q^{21} +(-3.33022 + 2.79439i) q^{22} +(-0.0996702 + 0.0362770i) q^{23} +(-0.939693 - 0.342020i) q^{24} +(-1.73783 - 1.45821i) q^{25} +(3.23783 - 5.60808i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(0.0320889 - 0.181985i) q^{28} +(0.692066 - 3.92490i) q^{29} +(0.826352 + 1.43128i) q^{30} +(1.61334 - 2.79439i) q^{31} +(0.766044 + 0.642788i) q^{32} +(4.08512 + 1.48686i) q^{33} +(1.99273 - 0.725293i) q^{34} +(-0.233956 + 0.196312i) q^{35} +(0.173648 + 0.984808i) q^{36} +4.06418 q^{37} +(-2.12449 - 3.80612i) q^{38} -6.47565 q^{39} +(-0.286989 - 1.62760i) q^{40} +(-6.61721 + 5.55250i) q^{41} +(-0.173648 + 0.0632028i) q^{42} +(-0.0393628 - 0.0143269i) q^{43} +(-3.33022 - 2.79439i) q^{44} +(0.826352 - 1.43128i) q^{45} +(-0.0530334 - 0.0918566i) q^{46} +(-1.37551 + 7.80093i) q^{47} +(0.173648 - 0.984808i) q^{48} +(3.48293 + 6.03260i) q^{49} +(1.13429 - 1.96464i) q^{50} +(-1.62449 - 1.36310i) q^{51} +(6.08512 + 2.21480i) q^{52} +(8.65657 - 3.15074i) q^{53} +(0.766044 - 0.642788i) q^{54} +(1.24763 + 7.07564i) q^{55} +0.184793 q^{56} +(-2.23396 + 3.74292i) q^{57} +3.98545 q^{58} +(1.75237 + 9.93821i) q^{59} +(-1.26604 + 1.06234i) q^{60} +(-3.37939 + 1.23000i) q^{61} +(3.03209 + 1.10359i) q^{62} +(0.141559 + 0.118782i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-5.35117 - 9.26849i) q^{65} +(-0.754900 + 4.28125i) q^{66} +(-1.38666 + 7.86414i) q^{67} +(1.06031 + 1.83651i) q^{68} +(-0.0530334 + 0.0918566i) q^{69} +(-0.233956 - 0.196312i) q^{70} +(3.79813 + 1.38241i) q^{71} +(-0.939693 + 0.342020i) q^{72} +(11.6420 - 9.76882i) q^{73} +(0.705737 + 4.00243i) q^{74} -2.26857 q^{75} +(3.37939 - 2.75314i) q^{76} -0.803348 q^{77} +(-1.12449 - 6.37727i) q^{78} +(9.49660 - 7.96859i) q^{79} +(1.55303 - 0.565258i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(-6.61721 - 5.55250i) q^{82} +(-4.22803 + 7.32316i) q^{83} +(-0.0923963 - 0.160035i) q^{84} +(0.608593 - 3.45150i) q^{85} +(0.00727396 - 0.0412527i) q^{86} +(-1.99273 - 3.45150i) q^{87} +(2.17365 - 3.76487i) q^{88} +(-13.7404 - 11.5295i) q^{89} +(1.55303 + 0.565258i) q^{90} +(1.12449 - 0.409279i) q^{91} +(0.0812519 - 0.0681784i) q^{92} +(-0.560307 - 3.17766i) q^{93} -7.92127 q^{94} +(-7.20321 - 0.104455i) q^{95} +1.00000 q^{96} +(1.85591 + 10.5254i) q^{97} +(-5.33615 + 4.47756i) q^{98} +(4.08512 - 1.48686i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{5} + 3 q^{7} - 3 q^{8}+O(q^{10}) \) 6 * q - 3 * q^5 + 3 * q^7 - 3 * q^8	\( 6 q - 3 q^{5} + 3 q^{7} - 3 q^{8} + 6 q^{10} + 12 q^{11} - 3 q^{12} - 21 q^{13} - 3 q^{15} + 3 q^{17} + 6 q^{18} + 6 q^{19} - 12 q^{20} - 9 q^{21} + 3 q^{22} - 15 q^{23} + 9 q^{25} - 3 q^{27} - 9 q^{28} + 15 q^{29} + 6 q^{30} + 3 q^{31} + 3 q^{33} - 6 q^{34} - 6 q^{35} + 6 q^{37} + 6 q^{40} - 9 q^{41} - 9 q^{43} + 3 q^{44} + 6 q^{45} + 12 q^{46} - 21 q^{47} - 3 q^{50} + 3 q^{51} + 15 q^{52} + 30 q^{53} - 9 q^{55} - 6 q^{56} - 18 q^{57} - 12 q^{58} + 27 q^{59} - 3 q^{60} - 9 q^{61} + 9 q^{62} + 9 q^{63} - 3 q^{64} - 6 q^{65} - 6 q^{66} - 15 q^{67} + 12 q^{68} + 12 q^{69} - 6 q^{70} + 9 q^{71} + 12 q^{73} - 6 q^{74} + 6 q^{75} + 9 q^{76} + 42 q^{77} + 6 q^{78} + 15 q^{79} - 3 q^{80} - 9 q^{82} - 3 q^{83} + 3 q^{84} - 36 q^{85} + 18 q^{86} + 6 q^{87} + 12 q^{88} - 48 q^{89} - 3 q^{90} - 6 q^{91} + 3 q^{92} - 9 q^{93} - 30 q^{94} - 48 q^{95} + 6 q^{96} + 18 q^{97} - 36 q^{98} + 3 q^{99}+O(q^{100}) \) 6 * q - 3 * q^5 + 3 * q^7 - 3 * q^8 + 6 * q^10 + 12 * q^11 - 3 * q^12 - 21 * q^13 - 3 * q^15 + 3 * q^17 + 6 * q^18 + 6 * q^19 - 12 * q^20 - 9 * q^21 + 3 * q^22 - 15 * q^23 + 9 * q^25 - 3 * q^27 - 9 * q^28 + 15 * q^29 + 6 * q^30 + 3 * q^31 + 3 * q^33 - 6 * q^34 - 6 * q^35 + 6 * q^37 + 6 * q^40 - 9 * q^41 - 9 * q^43 + 3 * q^44 + 6 * q^45 + 12 * q^46 - 21 * q^47 - 3 * q^50 + 3 * q^51 + 15 * q^52 + 30 * q^53 - 9 * q^55 - 6 * q^56 - 18 * q^57 - 12 * q^58 + 27 * q^59 - 3 * q^60 - 9 * q^61 + 9 * q^62 + 9 * q^63 - 3 * q^64 - 6 * q^65 - 6 * q^66 - 15 * q^67 + 12 * q^68 + 12 * q^69 - 6 * q^70 + 9 * q^71 + 12 * q^73 - 6 * q^74 + 6 * q^75 + 9 * q^76 + 42 * q^77 + 6 * q^78 + 15 * q^79 - 3 * q^80 - 9 * q^82 - 3 * q^83 + 3 * q^84 - 36 * q^85 + 18 * q^86 + 6 * q^87 + 12 * q^88 - 48 * q^89 - 3 * q^90 - 6 * q^91 + 3 * q^92 - 9 * q^93 - 30 * q^94 - 48 * q^95 + 6 * q^96 + 18 * q^97 - 36 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

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