LMFDB - Embedded newform 114.2.i.c.25.1

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			25.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	114.25
Dual form			114.2.i.c.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(0.939693 + 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.613341 - 3.47843i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-1.85844 + 3.21891i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(0.939693 + 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.613341 - 3.47843i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-1.85844 + 3.21891i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +(-2.70574 - 2.27038i) q^{10} +(2.64543 + 4.58202i) q^{11} +(0.500000 - 0.866025i) q^{12} +(0.213011 - 0.0775297i) q^{13} +(0.645430 + 3.66041i) q^{14} +(0.613341 - 3.47843i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-1.26604 + 1.06234i) q^{17} +1.00000 q^{18} +(-4.17752 + 1.24432i) q^{19} -3.53209 q^{20} +(-2.84730 + 2.38917i) q^{21} +(4.97178 + 1.80958i) q^{22} +(1.50727 - 8.54818i) q^{23} +(-0.173648 - 0.984808i) q^{24} +(-7.02481 + 2.55682i) q^{25} +(0.113341 - 0.196312i) q^{26} +(0.500000 + 0.866025i) q^{27} +(2.84730 + 2.38917i) q^{28} +(0.0923963 + 0.0775297i) q^{29} +(-1.76604 - 3.05888i) q^{30} +(-1.56031 + 2.70253i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.918748 + 5.21048i) q^{33} +(-0.286989 + 1.62760i) q^{34} +(12.3366 + 4.49016i) q^{35} +(0.766044 - 0.642788i) q^{36} +5.12836 q^{37} +(-2.40033 + 3.63846i) q^{38} +0.226682 q^{39} +(-2.70574 + 2.27038i) q^{40} +(-6.67752 - 2.43042i) q^{41} +(-0.645430 + 3.66041i) q^{42} +(-0.929892 - 5.27368i) q^{43} +(4.97178 - 1.80958i) q^{44} +(1.76604 - 3.05888i) q^{45} +(-4.34002 - 7.51714i) q^{46} +(-1.92262 - 1.61327i) q^{47} +(-0.766044 - 0.642788i) q^{48} +(-3.40760 - 5.90214i) q^{49} +(-3.73783 + 6.47410i) q^{50} +(-1.55303 + 0.565258i) q^{51} +(-0.0393628 - 0.223238i) q^{52} +(1.03074 - 5.84564i) q^{53} +(0.939693 + 0.342020i) q^{54} +(14.3157 - 12.0123i) q^{55} +3.71688 q^{56} +(-4.35117 - 0.259515i) q^{57} +0.120615 q^{58} +(0.167718 - 0.140732i) q^{59} +(-3.31908 - 1.20805i) q^{60} +(-0.273318 + 1.55007i) q^{61} +(0.541889 + 3.07321i) q^{62} +(-3.49273 + 1.27125i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.400330 - 0.693392i) q^{65} +(4.05303 + 3.40090i) q^{66} +(11.8589 + 9.95080i) q^{67} +(0.826352 + 1.43128i) q^{68} +(4.34002 - 7.51714i) q^{69} +(12.3366 - 4.49016i) q^{70} +(-0.235300 - 1.33445i) q^{71} +(0.173648 - 0.984808i) q^{72} +(-2.27972 - 0.829748i) q^{73} +(3.92855 - 3.29644i) q^{74} -7.47565 q^{75} +(0.500000 + 4.33013i) q^{76} -19.6655 q^{77} +(0.173648 - 0.145708i) q^{78} +(2.69207 + 0.979832i) q^{79} +(-0.613341 + 3.47843i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-6.67752 + 2.43042i) q^{82} +(-0.960637 + 1.66387i) q^{83} +(1.85844 + 3.21891i) q^{84} +(4.47178 + 3.75227i) q^{85} +(-4.10220 - 3.44215i) q^{86} +(0.0603074 + 0.104455i) q^{87} +(2.64543 - 4.58202i) q^{88} +(11.4226 - 4.15749i) q^{89} +(-0.613341 - 3.47843i) q^{90} +(-0.146307 + 0.829748i) q^{91} +(-8.15657 - 2.96875i) q^{92} +(-2.39053 + 2.00589i) q^{93} -2.50980 q^{94} +(6.89053 + 13.7680i) q^{95} -1.00000 q^{96} +(13.4081 - 11.2507i) q^{97} +(-6.40420 - 2.33094i) q^{98} +(-0.918748 + 5.21048i) 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} + 3 q^{12} + 9 q^{13} - 12 q^{14} - 3 q^{15} - 3 q^{17} + 6 q^{18} - 12 q^{20} - 15 q^{21} + 15 q^{22} + 27 q^{23} - 15 q^{25} - 6 q^{26} + 3 q^{27} + 15 q^{28} - 3 q^{29} - 6 q^{30} - 15 q^{31} + 3 q^{33} + 6 q^{34} + 12 q^{35} - 6 q^{37} - 12 q^{39} - 6 q^{40} - 15 q^{41} + 12 q^{42} + 3 q^{43} + 15 q^{44} + 6 q^{45} - 6 q^{46} + 15 q^{47} - 24 q^{49} - 3 q^{50} + 3 q^{51} - 9 q^{52} + 6 q^{53} + 27 q^{55} + 6 q^{56} + 12 q^{58} - 27 q^{59} - 3 q^{60} - 15 q^{61} - 3 q^{62} - 3 q^{63} - 3 q^{64} + 12 q^{65} + 12 q^{66} - 3 q^{67} + 6 q^{68} + 6 q^{69} + 12 q^{70} + 3 q^{71} + 12 q^{73} + 24 q^{74} - 6 q^{75} + 3 q^{76} - 42 q^{77} + 27 q^{79} + 3 q^{80} - 15 q^{82} + 3 q^{83} + 3 q^{84} + 12 q^{85} - 24 q^{86} + 6 q^{87} + 42 q^{89} + 3 q^{90} - 42 q^{91} - 27 q^{92} + 3 q^{93} - 18 q^{94} + 24 q^{95} - 6 q^{96} + 18 q^{97} - 3 q^{99}+O(q^{100}) $ 6 * q + 3 * q^5 - 3 * q^7 - 3 * q^8 - 6 * q^10 + 3 * q^12 + 9 * q^13 - 12 * q^14 - 3 * q^15 - 3 * q^17 + 6 * q^18 - 12 * q^20 - 15 * q^21 + 15 * q^22 + 27 * q^23 - 15 * q^25 - 6 * q^26 + 3 * q^27 + 15 * q^28 - 3 * q^29 - 6 * q^30 - 15 * q^31 + 3 * q^33 + 6 * q^34 + 12 * q^35 - 6 * q^37 - 12 * q^39 - 6 * q^40 - 15 * q^41 + 12 * q^42 + 3 * q^43 + 15 * q^44 + 6 * q^45 - 6 * q^46 + 15 * q^47 - 24 * q^49 - 3 * q^50 + 3 * q^51 - 9 * q^52 + 6 * q^53 + 27 * q^55 + 6 * q^56 + 12 * q^58 - 27 * q^59 - 3 * q^60 - 15 * q^61 - 3 * q^62 - 3 * q^63 - 3 * q^64 + 12 * q^65 + 12 * q^66 - 3 * q^67 + 6 * q^68 + 6 * q^69 + 12 * q^70 + 3 * q^71 + 12 * q^73 + 24 * q^74 - 6 * q^75 + 3 * q^76 - 42 * q^77 + 27 * q^79 + 3 * q^80 - 15 * q^82 + 3 * q^83 + 3 * q^84 + 12 * q^85 - 24 * q^86 + 6 * q^87 + 42 * q^89 + 3 * q^90 - 42 * q^91 - 27 * q^92 + 3 * q^93 - 18 * q^94 + 24 * q^95 - 6 * q^96 + 18 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$97$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$	0.939693	+	0.342020i	0.542532	+	0.197465i
$3$	0.939693	+	0.342020i	0.542532	+	0.197465i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−0.613341	−	3.47843i	−0.274294	−	1.55560i	−0.741194	−	0.671290i	$-0.765740\pi$
$5$	−0.613341	−	3.47843i	−0.274294	−	1.55560i	0.466900	−	0.884310i	$-0.345371\pi$
$6$	0.939693	−	0.342020i	0.383628	−	0.139629i
$7$	−1.85844	+	3.21891i	−0.702425	+	1.21664i	0.265188	+	0.964197i	$0.414566\pi$
$7$	−1.85844	+	3.21891i	−0.702425	+	1.21664i	−0.967613	+	0.252438i	$0.918767\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	0.766044	+	0.642788i	0.255348	+	0.214263i
$10$	−2.70574	−	2.27038i	−0.855629	−	0.717958i
$11$	2.64543	+	4.58202i	0.797627	+	1.38153i	0.921158	+	0.389190i	$0.127245\pi$
$11$	2.64543	+	4.58202i	0.797627	+	1.38153i	−0.123531	+	0.992341i	$0.539422\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	0.213011	−	0.0775297i	0.0590786	−	0.0215029i	−0.312312	−	0.949980i	$-0.601103\pi$
$13$	0.213011	−	0.0775297i	0.0590786	−	0.0215029i	0.371390	+	0.928477i	$0.378881\pi$
$14$	0.645430	+	3.66041i	0.172498	+	0.978287i
$15$	0.613341	−	3.47843i	0.158364	−	0.898126i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−1.26604	+	1.06234i	−0.307061	+	0.257655i	−0.783276	−	0.621674i	$-0.786453\pi$
$17$	−1.26604	+	1.06234i	−0.307061	+	0.257655i	0.476215	+	0.879329i	$0.342008\pi$
$18$	1.00000			0.235702
$19$	−4.17752	+	1.24432i	−0.958388	+	0.285467i
$19$	−4.17752	+	1.24432i	−0.958388	+	0.285467i
$20$	−3.53209			−0.789799
$21$	−2.84730	+	2.38917i	−0.621331	+	0.521359i
$22$	4.97178	+	1.80958i	1.05999	+	0.385804i
$23$	1.50727	−	8.54818i	0.314288	−	1.78242i	−0.261894	−	0.965097i	$-0.584347\pi$
$23$	1.50727	−	8.54818i	0.314288	−	1.78242i	0.576182	−	0.817321i	$-0.304542\pi$
$24$	−0.173648	−	0.984808i	−0.0354458	−	0.201023i
$25$	−7.02481	+	2.55682i	−1.40496	+	0.511365i
$26$	0.113341	−	0.196312i	0.0222280	−	0.0385000i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	2.84730	+	2.38917i	0.538088	+	0.451510i
$29$	0.0923963	+	0.0775297i	0.0171576	+	0.0143969i	0.651326	−	0.758798i	$-0.274213\pi$
$29$	0.0923963	+	0.0775297i	0.0171576	+	0.0143969i	−0.634169	+	0.773195i	$0.718657\pi$
$30$	−1.76604	−	3.05888i	−0.322434	−	0.558472i
$31$	−1.56031	+	2.70253i	−0.280239	+	0.485389i	−0.971444	−	0.237271i	$-0.923747\pi$
$31$	−1.56031	+	2.70253i	−0.280239	+	0.485389i	0.691204	+	0.722660i	$0.257081\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	0.918748	+	5.21048i	0.159934	+	0.907028i
$34$	−0.286989	+	1.62760i	−0.0492182	+	0.279130i
$35$	12.3366	+	4.49016i	2.08527	+	0.758976i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$	5.12836			0.843096			0.421548	−	0.906806i	$-0.361487\pi$
$37$	5.12836			0.843096			0.421548	+	0.906806i	$0.361487\pi$
$38$	−2.40033	+	3.63846i	−0.389385	+	0.590237i
$39$	0.226682			0.0362981
$40$	−2.70574	+	2.27038i	−0.427815	+	0.358979i
$41$	−6.67752	−	2.43042i	−1.04285	−	0.379568i	−0.236892	−	0.971536i	$-0.576129\pi$
$41$	−6.67752	−	2.43042i	−1.04285	−	0.379568i	−0.805961	+	0.591968i	$0.798351\pi$
$42$	−0.645430	+	3.66041i	−0.0995920	+	0.564814i
$43$	−0.929892	−	5.27368i	−0.141807	−	0.804229i	−0.969875	−	0.243602i	$-0.921671\pi$
$43$	−0.929892	−	5.27368i	−0.141807	−	0.804229i	0.828068	−	0.560627i	$-0.189440\pi$
$44$	4.97178	−	1.80958i	0.749524	−	0.272805i
$45$	1.76604	−	3.05888i	0.263266	−	0.455991i
$46$	−4.34002	−	7.51714i	−0.639901	−	1.10834i
$47$	−1.92262	−	1.61327i	−0.280443	−	0.235319i	0.491706	−	0.870761i	$-0.336374\pi$
$47$	−1.92262	−	1.61327i	−0.280443	−	0.235319i	−0.772149	+	0.635442i	$0.780818\pi$
$48$	−0.766044	−	0.642788i	−0.110569	−	0.0927784i
$49$	−3.40760	−	5.90214i	−0.486801	−	0.843163i
$50$	−3.73783	+	6.47410i	−0.528608	+	0.915577i
$51$	−1.55303	+	0.565258i	−0.217468	+	0.0791519i
$52$	−0.0393628	−	0.223238i	−0.00545864	−	0.0309575i
$53$	1.03074	−	5.84564i	0.141584	−	0.802961i	−0.828463	−	0.560043i	$-0.810784\pi$
$53$	1.03074	−	5.84564i	0.141584	−	0.802961i	0.970047	−	0.242918i	$-0.0781044\pi$
$54$	0.939693	+	0.342020i	0.127876	+	0.0465430i
$55$	14.3157	−	12.0123i	1.93033	−	1.61974i
$56$	3.71688			0.496689
$57$	−4.35117	−	0.259515i	−0.576326	−	0.0343736i
$58$	0.120615			0.0158375
$59$	0.167718	−	0.140732i	0.0218351	−	0.0183218i	−0.631805	−	0.775128i	$-0.717686\pi$
$59$	0.167718	−	0.140732i	0.0218351	−	0.0183218i	0.653640	+	0.756806i	$0.273241\pi$
$60$	−3.31908	−	1.20805i	−0.428491	−	0.155958i
$61$	−0.273318	+	1.55007i	−0.0349948	+	0.198466i	−0.997293	−	0.0735316i	$-0.976573\pi$
$61$	−0.273318	+	1.55007i	−0.0349948	+	0.198466i	0.962298	+	0.271997i	$0.0876841\pi$
$62$	0.541889	+	3.07321i	0.0688200	+	0.390298i
$63$	−3.49273	+	1.27125i	−0.440042	+	0.160162i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−0.400330	−	0.693392i	−0.0496548	−	0.0860046i
$66$	4.05303	+	3.40090i	0.498894	+	0.418622i
$67$	11.8589	+	9.95080i	1.44880	+	1.21568i	0.933453	+	0.358701i	$0.116780\pi$
$67$	11.8589	+	9.95080i	1.44880	+	1.21568i	0.515343	+	0.856984i	$0.327664\pi$
$68$	0.826352	+	1.43128i	0.100210	+	0.173569i
$69$	4.34002	−	7.51714i	0.522477	−	0.904957i
$70$	12.3366	−	4.49016i	1.47451	−	0.536677i
$71$	−0.235300	−	1.33445i	−0.0279249	−	0.158370i	0.967657	−	0.252271i	$-0.0811775\pi$
$71$	−0.235300	−	1.33445i	−0.0279249	−	0.158370i	−0.995582	+	0.0939008i	$0.970066\pi$
$72$	0.173648	−	0.984808i	0.0204646	−	0.116061i
$73$	−2.27972	−	0.829748i	−0.266820	−	0.0971147i	0.205145	−	0.978731i	$-0.434233\pi$
$73$	−2.27972	−	0.829748i	−0.266820	−	0.0971147i	−0.471966	+	0.881617i	$0.656455\pi$
$74$	3.92855	−	3.29644i	0.456684	−	0.383204i
$75$	−7.47565			−0.863214
$76$	0.500000	+	4.33013i	0.0573539	+	0.496700i
$77$	−19.6655			−2.24109
$78$	0.173648	−	0.145708i	0.0196618	−	0.0164982i
$79$	2.69207	+	0.979832i	0.302881	+	0.110240i	0.488990	−	0.872289i	$-0.337365\pi$
$79$	2.69207	+	0.979832i	0.302881	+	0.110240i	−0.186109	+	0.982529i	$0.559588\pi$
$80$	−0.613341	+	3.47843i	−0.0685736	+	0.388900i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	−6.67752	+	2.43042i	−0.737409	+	0.268395i
$83$	−0.960637	+	1.66387i	−0.105444	+	0.182634i	−0.913919	−	0.405896i	$-0.866960\pi$
$83$	−0.960637	+	1.66387i	−0.105444	+	0.182634i	0.808476	+	0.588530i	$0.200293\pi$
$84$	1.85844	+	3.21891i	0.202773	+	0.351212i
$85$	4.47178	+	3.75227i	0.485033	+	0.406991i
$86$	−4.10220	−	3.44215i	−0.442351	−	0.371177i
$87$	0.0603074	+	0.104455i	0.00646563	+	0.0111988i
$88$	2.64543	−	4.58202i	0.282004	−	0.488445i
$89$	11.4226	−	4.15749i	1.21080	−	0.440693i	0.343816	−	0.939037i	$-0.388280\pi$
$89$	11.4226	−	4.15749i	1.21080	−	0.440693i	0.866980	+	0.498344i	$0.166058\pi$
$90$	−0.613341	−	3.47843i	−0.0646518	−	0.366659i
$91$	−0.146307	+	0.829748i	−0.0153371	+	0.0869813i
$92$	−8.15657	−	2.96875i	−0.850382	−	0.309514i
$93$	−2.39053	+	2.00589i	−0.247886	+	0.208001i
$94$	−2.50980			−0.258866
$95$	6.89053	+	13.7680i	0.706953	+	1.41257i
$96$	−1.00000			−0.102062
$97$	13.4081	−	11.2507i	1.36138	−	1.14234i	0.385831	−	0.922570i	$-0.373915\pi$
$97$	13.4081	−	11.2507i	1.36138	−	1.14234i	0.975552	−	0.219767i	$-0.0705296\pi$
$98$	−6.40420	−	2.33094i	−0.646922	−	0.235460i
$99$	−0.918748	+	5.21048i	−0.0923377	+	0.523673i
$100$	1.29813	+	7.36208i	0.129813	+	0.736208i
$101$	−14.1099	+	5.13560i	−1.40399	+	0.511011i	−0.929360	−	0.369174i	$-0.879641\pi$
$101$	−14.1099	+	5.13560i	−1.40399	+	0.511011i	−0.474631	+	0.880185i	$0.657418\pi$
$102$	−0.826352	+	1.43128i	−0.0818210	+	0.141718i
$103$	−3.33022	−	5.76811i	−0.328137	−	0.568349i	0.654006	−	0.756490i	$-0.273087\pi$
$103$	−3.33022	−	5.76811i	−0.328137	−	0.568349i	−0.982142	+	0.188141i	$0.939754\pi$
$104$	−0.173648	−	0.145708i	−0.0170276	−	0.0142879i
$105$	10.0569	+	8.43874i	0.981453	+	0.823537i
$106$	−2.96791	−	5.14057i	−0.288269	−	0.499297i
$107$	−4.04323	+	7.00309i	−0.390874	+	0.677014i	−0.992565	−	0.121715i	$-0.961161\pi$
$107$	−4.04323	+	7.00309i	−0.390874	+	0.677014i	0.601691	+	0.798729i	$0.294494\pi$
$108$	0.939693	−	0.342020i	0.0904220	−	0.0329109i
$109$	2.64796	+	15.0173i	0.253628	+	1.43840i	0.799570	+	0.600573i	$0.205061\pi$
$109$	2.64796	+	15.0173i	0.253628	+	1.43840i	−0.545941	+	0.837823i	$0.683828\pi$
$110$	3.24510	−	18.4039i	0.309408	−	1.75474i
$111$	4.81908	+	1.75400i	0.457407	+	0.166482i
$112$	2.84730	−	2.38917i	0.269044	−	0.225755i
$113$	0.815207			0.0766883			0.0383441	−	0.999265i	$-0.487792\pi$
$113$	0.815207			0.0766883			0.0383441	+	0.999265i	$0.487792\pi$
$114$	−3.50000	+	2.59808i	−0.327805	+	0.243332i
$115$	−30.6587			−2.85894
$116$	0.0923963	−	0.0775297i	0.00857878	−	0.00719845i
$117$	0.213011	+	0.0775297i	0.0196929	+	0.00716762i
$118$	0.0380187	−	0.215615i	0.00349990	−	0.0198489i
$119$	−1.06670	−	6.04958i	−0.0977846	−	0.554564i
$120$	−3.31908	+	1.20805i	−0.302989	+	0.110279i
$121$	−8.49660	+	14.7165i	−0.772418	+	1.33787i
$122$	0.786989	+	1.36310i	0.0712506	+	0.123410i
$123$	−5.44356	−	4.56769i	−0.490830	−	0.411855i
$124$	2.39053	+	2.00589i	0.214676	+	0.180134i
$125$	4.37211	+	7.57272i	0.391054	+	0.677325i
$126$	−1.85844	+	3.21891i	−0.165563	+	0.286764i
$127$	−10.3969	+	3.78417i	−0.922578	+	0.335791i	−0.759264	−	0.650783i	$-0.774441\pi$
$127$	−10.3969	+	3.78417i	−0.922578	+	0.335791i	−0.163314	+	0.986574i	$0.552218\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	0.929892	−	5.27368i	0.0818725	−	0.464322i
$130$	−0.752374	−	0.273842i	−0.0659876	−	0.0240175i
$131$	−11.0307	+	9.25589i	−0.963761	+	0.808691i	−0.981561	−	0.191150i	$-0.938778\pi$
$131$	−11.0307	+	9.25589i	−0.963761	+	0.808691i	0.0178001	+	0.999842i	$0.494334\pi$
$132$	5.29086			0.460510
$133$	3.75830	−	15.7596i	0.325886	−	1.36653i
$134$	15.4807			1.33733
$135$	2.70574	−	2.27038i	0.232873	−	0.195403i
$136$	1.55303	+	0.565258i	0.133172	+	0.0484705i
$137$	−0.0821293	+	0.465778i	−0.00701678	+	0.0397941i	−0.988115	−	0.153716i	$-0.950876\pi$
$137$	−0.0821293	+	0.465778i	−0.00701678	+	0.0397941i	0.981098	+	0.193510i	$0.0619871\pi$
$138$	−1.50727	−	8.54818i	−0.128308	−	0.727669i
$139$	9.57057	−	3.48340i	0.811766	−	0.295458i	0.0974126	−	0.995244i	$-0.468943\pi$
$139$	9.57057	−	3.48340i	0.811766	−	0.295458i	0.714353	+	0.699786i	$0.246721\pi$
$140$	6.56418	−	11.3695i	0.554774	−	0.960897i
$141$	−1.25490	−	2.17355i	−0.105682	−	0.183046i
$142$	−1.03802	−	0.871001i	−0.0871086	−	0.0730928i
$143$	0.918748	+	0.770921i	0.0768296	+	0.0644677i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	0.213011	−	0.368946i	0.0176896	−	0.0306393i
$146$	−2.27972	+	0.829748i	−0.188671	+	0.0686705i
$147$	−1.18345	−	6.71167i	−0.0976092	−	0.553569i
$148$	0.890530	−	5.05044i	0.0732011	−	0.415144i
$149$	−4.58987	−	1.67058i	−0.376017	−	0.136859i	0.147096	−	0.989122i	$-0.453007\pi$
$149$	−4.58987	−	1.67058i	−0.376017	−	0.136859i	−0.523113	+	0.852263i	$0.675229\pi$
$150$	−5.72668	+	4.80526i	−0.467582	+	0.392348i
$151$	9.04189			0.735818			0.367909	−	0.929862i	$-0.380074\pi$
$151$	9.04189			0.735818			0.367909	+	0.929862i	$0.380074\pi$
$152$	3.16637	+	2.99568i	0.256827	+	0.242981i
$153$	−1.65270			−0.133613
$154$	−15.0646	+	12.6407i	−1.21394	+	1.01862i
$155$	10.3576	+	3.76984i	0.831940	+	0.302801i
$156$	0.0393628	−	0.223238i	0.00315155	−	0.0178733i
$157$	0.0577812	+	0.327693i	0.00461144	+	0.0261528i	0.987027	−	0.160556i	$-0.0513289\pi$
$157$	0.0577812	+	0.327693i	0.00461144	+	0.0261528i	−0.982415	+	0.186709i	$0.940218\pi$
$158$	2.69207	−	0.979832i	0.214169	−	0.0779513i
$159$	2.96791	−	5.14057i	0.235371	−	0.407674i
$160$	1.76604	+	3.05888i	0.139618	+	0.241826i
$161$	24.7147	+	20.7381i	1.94779	+	1.63439i
$162$	0.766044	+	0.642788i	0.0601861	+	0.0505022i
$163$	−1.97044	−	3.41290i	−0.154337	−	0.267319i	0.778481	−	0.627669i	$-0.215991\pi$
$163$	−1.97044	−	3.41290i	−0.154337	−	0.267319i	−0.932817	+	0.360350i	$0.882657\pi$
$164$	−3.55303	+	6.15403i	−0.277445	+	0.480549i
$165$	17.5608	−	6.39160i	1.36710	−	0.497585i
$166$	0.333626	+	1.89209i	0.0258944	+	0.146854i
$167$	1.04071	−	5.90214i	0.0805323	−	0.456722i	−0.917699	−	0.397276i	$-0.869956\pi$
$167$	1.04071	−	5.90214i	0.0805323	−	0.456722i	0.998232	−	0.0594456i	$-0.0189333\pi$
$168$	3.49273	+	1.27125i	0.269470	+	0.0980789i
$169$	−9.91921	+	8.32321i	−0.763017	+	0.640247i
$170$	5.83750			0.447716
$171$	−4.00000	−	1.73205i	−0.305888	−	0.132453i
$172$	−5.35504			−0.408318
$173$	9.39306	−	7.88171i	0.714141	−	0.599235i	−0.211617	−	0.977353i	$-0.567873\pi$
$173$	9.39306	−	7.88171i	0.714141	−	0.599235i	0.925758	+	0.378117i	$0.123428\pi$
$174$	0.113341	+	0.0412527i	0.00859234	+	0.00312736i
$175$	4.82501	−	27.3640i	0.364736	−	2.06852i
$176$	−0.918748	−	5.21048i	−0.0692532	−	0.392755i
$177$	0.205737	−	0.0748822i	0.0154641	−	0.00562849i
$178$	6.07785	−	10.5271i	0.455554	−	0.789043i
$179$	−4.03209	−	6.98378i	−0.301372	−	0.521992i	0.675075	−	0.737749i	$-0.264111\pi$
$179$	−4.03209	−	6.98378i	−0.301372	−	0.521992i	−0.976447	+	0.215757i	$0.930778\pi$
$180$	−2.70574	−	2.27038i	−0.201674	−	0.169224i
$181$	0.145430	+	0.122030i	0.0108097	+	0.00907042i	0.648176	−	0.761490i	$-0.275532\pi$
$181$	0.145430	+	0.122030i	0.0108097	+	0.00907042i	−0.637367	+	0.770561i	$0.719976\pi$
$182$	0.421274	+	0.729669i	0.0312269	+	0.0540866i
$183$	−0.786989	+	1.36310i	−0.0581759	+	0.100764i
$184$	−8.15657	+	2.96875i	−0.601311	+	0.218859i
$185$	−3.14543	−	17.8386i	−0.231257	−	1.31152i
$186$	−0.541889	+	3.07321i	−0.0397332	+	0.225338i
$187$	−8.21688	−	2.99070i	−0.600878	−	0.218702i
$188$	−1.92262	+	1.61327i	−0.140221	+	0.117660i
$189$	−3.71688			−0.270363
$190$	14.1284	+	6.11776i	1.02498	+	0.443829i
$191$	18.0378			1.30517			0.652584	−	0.757717i	$-0.273685\pi$
$191$	18.0378			1.30517			0.652584	+	0.757717i	$0.273685\pi$
$192$	−0.766044	+	0.642788i	−0.0552845	+	0.0463892i
$193$	16.3871	+	5.96443i	1.17957	+	0.429329i	0.856050	−	0.516892i	$-0.172911\pi$
$193$	16.3871	+	5.96443i	1.17957	+	0.429329i	0.323521	+	0.946221i	$0.395133\pi$
$194$	3.03936	−	17.2371i	0.218214	−	1.23755i
$195$	−0.139033	−	0.788496i	−0.00995637	−	0.0564654i
$196$	−6.40420	+	2.33094i	−0.457443	+	0.166496i
$197$	5.24035	−	9.07656i	0.373360	−	0.646678i	−0.616720	−	0.787182i	$-0.711539\pi$
$197$	5.24035	−	9.07656i	0.373360	−	0.646678i	0.990080	+	0.140504i	$0.0448724\pi$
$198$	2.64543	+	4.58202i	0.188003	+	0.325630i
$199$	−10.4593	−	8.77639i	−0.741440	−	0.622142i	0.191784	−	0.981437i	$-0.438573\pi$
$199$	−10.4593	−	8.77639i	−0.741440	−	0.622142i	−0.933224	+	0.359295i	$0.883017\pi$
$200$	5.72668	+	4.80526i	0.404938	+	0.339783i
$201$	7.74035	+	13.4067i	0.545962	+	0.945635i
$202$	−7.50774	+	13.0038i	−0.528243	+	0.914943i
$203$	−0.421274	+	0.153331i	−0.0295677	+	0.0107617i
$204$	0.286989	+	1.62760i	0.0200932	+	0.113954i
$205$	−4.35844	+	24.7179i	−0.304407	+	1.72638i
$206$	−6.25877	−	2.27801i	−0.436069	−	0.158716i
$207$	6.64930	−	5.57943i	0.462158	−	0.387797i
$208$	−0.226682			−0.0157175
$209$	−16.7528	−	15.8497i	−1.15882	−	1.09635i
$210$	13.1284			0.905943
$211$	−12.2023	+	10.2390i	−0.840043	+	0.704880i	−0.957573	−	0.288189i	$-0.906947\pi$
$211$	−12.2023	+	10.2390i	−0.840043	+	0.704880i	0.117530	+	0.993069i	$0.462502\pi$
$212$	−5.57785	−	2.03017i	−0.383088	−	0.139433i
$213$	0.235300	−	1.33445i	0.0161225	−	0.0914351i
$214$	1.40420	+	7.96361i	0.0959891	+	0.544382i
$215$	−17.7738	+	6.46913i	−1.21216	+	0.441191i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	−5.79948	−	10.0450i	−0.393694	−	0.681898i
$218$	11.6814	+	9.80185i	0.791163	+	0.663865i
$219$	−1.85844	−	1.55942i	−0.125582	−	0.105376i
$220$	−9.34389	−	16.1841i	−0.629965	−	1.09113i
$221$	−0.187319	+	0.324446i	−0.0126004	+	0.0218246i
$222$	4.81908	−	1.75400i	0.323435	−	0.117721i
$223$	3.23261	+	18.3331i	0.216472	+	1.22767i	0.878334	+	0.478047i	$0.158655\pi$
$223$	3.23261	+	18.3331i	0.216472	+	1.22767i	−0.661863	+	0.749625i	$0.730234\pi$
$224$	0.645430	−	3.66041i	0.0431246	−	0.244572i
$225$	−7.02481	−	2.55682i	−0.468321	−	0.170455i
$226$	0.624485	−	0.524005i	0.0415401	−	0.0348563i
$227$	−5.79292			−0.384490			−0.192245	−	0.981347i	$-0.561577\pi$
$227$	−5.79292			−0.384490			−0.192245	+	0.981347i	$0.561577\pi$
$228$	−1.01114	+	4.24000i	−0.0669647	+	0.280801i
$229$	−8.12836			−0.537137			−0.268568	−	0.963261i	$-0.586551\pi$
$229$	−8.12836			−0.537137			−0.268568	+	0.963261i	$0.586551\pi$
$230$	−23.4859	+	19.7070i	−1.54862	+	1.29944i
$231$	−18.4795	−	6.72600i	−1.21586	−	0.442538i
$232$	0.0209445	−	0.118782i	0.00137508	−	0.00779844i
$233$	−2.95677	−	16.7687i	−0.193704	−	1.09855i	−0.914252	−	0.405146i	$-0.867221\pi$
$233$	−2.95677	−	16.7687i	−0.193704	−	1.09855i	0.720548	−	0.693405i	$-0.243890\pi$
$234$	0.213011	−	0.0775297i	0.0139250	−	0.00506827i
$235$	−4.43242	+	7.67717i	−0.289139	+	0.500804i
$236$	−0.109470	−	0.189608i	−0.00712592	−	0.0123424i
$237$	2.19459	+	1.84148i	0.142554	+	0.119617i
$238$	−4.70574	−	3.94858i	−0.305028	−	0.255949i
$239$	7.50980	+	13.0074i	0.485769	+	0.841376i	0.999866	−	0.0163558i	$-0.00520644\pi$
$239$	7.50980	+	13.0074i	0.485769	+	0.841376i	−0.514098	+	0.857732i	$0.671873\pi$
$240$	−1.76604	+	3.05888i	−0.113998	+	0.197450i
$241$	20.1596	−	7.33748i	1.29859	−	0.472649i	0.402054	−	0.915616i	$-0.368296\pi$
$241$	20.1596	−	7.33748i	1.29859	−	0.472649i	0.896538	+	0.442967i	$0.146074\pi$
$242$	2.95084	+	16.7350i	0.189687	+	1.07577i
$243$	−0.173648	+	0.984808i	−0.0111395	+	0.0631754i
$244$	1.47906	+	0.538332i	0.0946868	+	0.0344632i
$245$	−18.4402	+	15.4731i	−1.17810	+	0.988542i
$246$	−7.10607			−0.453066
$247$	−0.793386	+	0.588936i	−0.0504819	+	0.0374731i
$248$	3.12061			0.198159
$249$	−1.47178	+	1.23497i	−0.0932704	+	0.0782631i
$250$	8.21688	+	2.99070i	0.519681	+	0.189148i
$251$	−4.43969	+	25.1787i	−0.280231	+	1.58927i	0.441608	+	0.897208i	$0.354408\pi$
$251$	−4.43969	+	25.1787i	−0.280231	+	1.58927i	−0.721839	+	0.692061i	$0.756703\pi$
$252$	0.645430	+	3.66041i	0.0406582	+	0.230584i
$253$	43.1553	−	15.7072i	2.71315	−	0.987506i
$254$	−5.53209	+	9.58186i	−0.347114	+	0.601219i
$255$	2.91875	+	5.05542i	0.182779	+	0.316583i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	2.13950	+	1.79525i	0.133458	+	0.111985i	0.707073	−	0.707140i	$-0.250015\pi$
$257$	2.13950	+	1.79525i	0.133458	+	0.111985i	−0.573615	+	0.819125i	$0.694459\pi$
$258$	−2.67752	−	4.63760i	−0.166695	−	0.288724i
$259$	−9.53074	+	16.5077i	−0.592212	+	1.02574i
$260$	−0.752374	+	0.273842i	−0.0466602	+	0.0169829i
$261$	0.0209445	+	0.118782i	0.00129643	+	0.00735244i
$262$	−2.50047	+	14.1809i	−0.154479	+	0.876096i
$263$	−1.30066	−	0.473401i	−0.0802021	−	0.0291912i	0.301608	−	0.953432i	$-0.402477\pi$
$263$	−1.30066	−	0.473401i	−0.0802021	−	0.0291912i	−0.381810	+	0.924241i	$0.624699\pi$
$264$	4.05303	−	3.40090i	0.249447	−	0.209311i
$265$	−20.9659			−1.28792
$266$	−7.25103	−	14.4883i	−0.444589	−	0.888336i
$267$	12.1557			0.743917
$268$	11.8589	−	9.95080i	0.724398	−	0.607842i
$269$	16.0471	+	5.84067i	0.978409	+	0.356112i	0.781221	−	0.624254i	$-0.214597\pi$
$269$	16.0471	+	5.84067i	0.978409	+	0.356112i	0.197188	+	0.980366i	$0.436819\pi$
$270$	0.613341	−	3.47843i	0.0373267	−	0.211690i
$271$	−4.46064	−	25.2975i	−0.270964	−	1.53672i	−0.751496	−	0.659738i	$-0.770667\pi$
$271$	−4.46064	−	25.2975i	−0.270964	−	1.53672i	0.480531	−	0.876978i	$-0.340444\pi$
$272$	1.55303	−	0.565258i	0.0941665	−	0.0342738i
$273$	−0.421274	+	0.729669i	−0.0254967	+	0.0441615i
$274$	0.236482	+	0.409598i	0.0142864	+	0.0247447i
$275$	−30.2991	−	25.4239i	−1.82710	−	1.53312i
$276$	−6.64930	−	5.57943i	−0.400241	−	0.335842i
$277$	−11.1125	−	19.2474i	−0.667683	−	1.15646i	−0.978550	−	0.206008i	$-0.933953\pi$
$277$	−11.1125	−	19.2474i	−0.667683	−	1.15646i	0.310867	−	0.950453i	$-0.399381\pi$
$278$	5.09240	−	8.82029i	0.305422	−	0.529006i
$279$	−2.93242	+	1.06731i	−0.175559	+	0.0638984i
$280$	−2.27972	−	12.9289i	−0.136239	−	0.772650i
$281$	0.268104	−	1.52049i	0.0159937	−	0.0907050i	−0.975766	−	0.218816i	$-0.929780\pi$
$281$	0.268104	−	1.52049i	0.0159937	−	0.0907050i	0.991760	+	0.128111i	$0.0408915\pi$
$282$	−2.35844	−	0.858402i	−0.140443	−	0.0511171i
$283$	7.88326	−	6.61484i	0.468611	−	0.393211i	−0.377677	−	0.925938i	$-0.623277\pi$
$283$	7.88326	−	6.61484i	0.468611	−	0.393211i	0.846288	+	0.532726i	$0.178832\pi$
$284$	−1.35504			−0.0804067
$285$	1.76604	+	15.2944i	0.104611	+	0.905962i
$286$	1.19934			0.0709185
$287$	20.2331	−	16.9776i	1.19432	−	1.00215i
$288$	−0.939693	−	0.342020i	−0.0553719	−	0.0201537i
$289$	−2.47771	+	14.0518i	−0.145748	+	0.826576i
$290$	−0.0739780	−	0.419550i	−0.00434413	−	0.0246368i
$291$	16.4474	−	5.98638i	0.964166	−	0.350928i
$292$	−1.21301	+	2.10100i	−0.0709861	+	0.122952i
$293$	14.2515	+	24.6843i	0.832581	+	1.44207i	0.895985	+	0.444085i	$0.146471\pi$
$293$	14.2515	+	24.6843i	0.832581	+	1.44207i	−0.0634033	+	0.997988i	$0.520195\pi$
$294$	−5.22075	−	4.38073i	−0.304480	−	0.255489i
$295$	−0.592396	−	0.497079i	−0.0344906	−	0.0289411i
$296$	−2.56418	−	4.44129i	−0.149040	−	0.258145i
$297$	−2.64543	+	4.58202i	−0.153503	+	0.265876i
$298$	−4.58987	+	1.67058i	−0.265884	+	0.0967739i
$299$	−0.341671	−	1.93771i	−0.0197594	−	0.112061i
$300$	−1.29813	+	7.36208i	−0.0749478	+	0.425050i
$301$	18.7037	+	6.80758i	1.07806	+	0.392382i
$302$	6.92649	−	5.81201i	0.398575	−	0.334444i
$303$	−15.0155			−0.862617
$304$	4.35117	+	0.259515i	0.249557	+	0.0148842i
$305$	5.55943			0.318332
$306$	−1.26604	+	1.06234i	−0.0723749	+	0.0607298i
$307$	24.0180	+	8.74184i	1.37078	+	0.498923i	0.919370	−	0.393394i	$-0.128699\pi$
$307$	24.0180	+	8.74184i	1.37078	+	0.498923i	0.451410	+	0.892317i	$0.350921\pi$
$308$	−3.41488	+	19.3667i	−0.194581	+	1.10352i
$309$	−1.15657	−	6.55926i	−0.0657952	−	0.373143i
$310$	10.3576	−	3.76984i	0.588270	−	0.214113i
$311$	−5.18732	+	8.98470i	−0.294146	+	0.509476i	−0.974786	−	0.223142i	$-0.928368\pi$
$311$	−5.18732	+	8.98470i	−0.294146	+	0.509476i	0.680640	+	0.732618i	$0.261702\pi$
$312$	−0.113341	−	0.196312i	−0.00641666	−	0.0111140i
$313$	−11.8250	−	9.92236i	−0.668389	−	0.560845i	0.244199	−	0.969725i	$-0.421475\pi$
$313$	−11.8250	−	9.92236i	−0.668389	−	0.560845i	−0.912588	+	0.408880i	$0.865919\pi$
$314$	0.254900	+	0.213887i	0.0143848	+	0.0120703i
$315$	6.56418	+	11.3695i	0.369850	+	0.640598i
$316$	1.43242	−	2.48102i	0.0805798	−	0.139568i
$317$	−26.6844	+	9.71232i	−1.49874	+	0.545498i	−0.955735	−	0.294229i	$-0.904937\pi$
$317$	−26.6844	+	9.71232i	−1.49874	+	0.545498i	−0.543009	+	0.839727i	$0.682715\pi$
$318$	−1.03074	−	5.84564i	−0.0578013	−	0.327807i
$319$	−0.110815	+	0.628461i	−0.00620443	+	0.0351870i
$320$	3.31908	+	1.20805i	0.185542	+	0.0675318i
$321$	−6.19459	+	5.19788i	−0.345748	+	0.290117i
$322$	32.2627			1.79793
$323$	3.96703	−	6.01330i	0.220732	−	0.334589i
$324$	1.00000			0.0555556
$325$	−1.29813	+	1.08926i	−0.0720075	+	0.0604215i
$326$	−3.70321	−	1.34786i	−0.205102	−	0.0746510i
$327$	−2.64796	+	15.0173i	−0.146432	+	0.830459i
$328$	1.23396	+	6.99811i	0.0681338	+	0.386406i
$329$	8.76604	−	3.19058i	0.483288	−	0.175902i
$330$	9.34389	−	16.1841i	0.514364	−	0.890905i
$331$	12.9611	+	22.4493i	0.712407	+	1.23392i	0.963951	+	0.266079i	$0.0857282\pi$
$331$	12.9611	+	22.4493i	0.712407	+	1.23392i	−0.251545	+	0.967846i	$0.580938\pi$
$332$	1.47178	+	1.23497i	0.0807745	+	0.0677779i
$333$	3.92855	+	3.29644i	0.215283	+	0.180644i
$334$	−2.99660	−	5.19026i	−0.163966	−	0.283998i
$335$	27.3396	−	47.3536i	1.49372	−	2.58720i
$336$	3.49273	−	1.27125i	0.190544	−	0.0693523i
$337$	−4.08260	−	23.1536i	−0.222393	−	1.26125i	−0.867606	−	0.497252i	$-0.834343\pi$
$337$	−4.08260	−	23.1536i	−0.222393	−	1.26125i	0.645213	−	0.764003i	$-0.276769\pi$
$338$	−2.24850	+	12.7519i	−0.122302	+	0.693612i
$339$	0.766044	+	0.278817i	0.0416058	+	0.0151433i
$340$	4.47178	−	3.75227i	0.242516	−	0.203495i
$341$	−16.5107			−0.894106
$342$	−4.17752	+	1.24432i	−0.225894	+	0.0672853i
$343$	−0.686852			−0.0370865
$344$	−4.10220	+	3.44215i	−0.221176	+	0.185588i
$345$	−28.8097	−	10.4859i	−1.55106	−	0.564541i
$346$	2.12923	−	12.0755i	0.114468	−	0.649182i
$347$	−0.417566	−	2.36813i	−0.0224161	−	0.127128i	0.971546	−	0.236850i	$-0.0761150\pi$
$347$	−0.417566	−	2.36813i	−0.0224161	−	0.127128i	−0.993962	+	0.109722i	$0.965004\pi$
$348$	0.113341	−	0.0412527i	0.00607570	−	0.00221138i
$349$	−2.59879	+	4.50124i	−0.139110	+	0.240946i	−0.927160	−	0.374665i	$-0.877758\pi$
$349$	−2.59879	+	4.50124i	−0.139110	+	0.240946i	0.788050	+	0.615611i	$0.211091\pi$
$350$	−13.8931	−	24.0635i	−0.742615	−	1.28625i
$351$	0.173648	+	0.145708i	0.00926865	+	0.00777732i
$352$	−4.05303	−	3.40090i	−0.216027	−	0.181269i
$353$	−4.13816	−	7.16750i	−0.220252	−	0.381487i	0.734633	−	0.678465i	$-0.237355\pi$
$353$	−4.13816	−	7.16750i	−0.220252	−	0.381487i	−0.954884	+	0.296978i	$0.904021\pi$
$354$	0.109470	−	0.189608i	0.00581829	−	0.0100776i
$355$	−4.49747	+	1.63695i	−0.238701	+	0.0868801i
$356$	−2.11081	−	11.9710i	−0.111873	−	0.634463i
$357$	1.06670	−	6.04958i	0.0564560	−	0.320178i
$358$	−7.57785	−	2.75811i	−0.400502	−	0.145771i
$359$	−1.75877	+	1.47578i	−0.0928244	+	0.0778889i	−0.688019	−	0.725693i	$-0.741519\pi$
$359$	−1.75877	+	1.47578i	−0.0928244	+	0.0778889i	0.595195	+	0.803582i	$0.297075\pi$
$360$	−3.53209			−0.186157
$361$	15.9033	−	10.3964i	0.837017	−	0.547177i
$362$	0.189845			0.00997803
$363$	−13.0175	+	10.9230i	−0.683244	+	0.573310i
$364$	0.791737	+	0.288169i	0.0414983	+	0.0151041i
$365$	−1.48798	+	8.43874i	−0.0778843	+	0.441704i
$366$	0.273318	+	1.55007i	0.0142866	+	0.0810232i
$367$	−28.0638	+	10.2144i	−1.46492	+	0.533186i	−0.946715	−	0.322072i	$-0.895621\pi$
$367$	−28.0638	+	10.2144i	−1.46492	+	0.533186i	−0.518202	+	0.855258i	$0.673398\pi$
$368$	−4.34002	+	7.51714i	−0.226239	+	0.391858i
$369$	−3.55303	−	6.15403i	−0.184964	−	0.320366i
$370$	−13.8760	−	11.6433i	−0.721378	−	0.605308i
$371$	16.9010	+	14.1817i	0.877459	+	0.736275i
$372$	1.56031	+	2.70253i	0.0808982	+	0.140120i
$373$	9.92649	−	17.1932i	0.513974	−	0.890229i	−0.485894	−	0.874017i	$-0.661506\pi$
$373$	9.92649	−	17.1932i	0.513974	−	0.890229i	0.999869	−	0.0162118i	$-0.00516060\pi$
$374$	−8.21688	+	2.99070i	−0.424885	+	0.154645i
$375$	1.51842	+	8.61138i	0.0784108	+	0.444690i
$376$	−0.435822	+	2.47167i	−0.0224758	+	0.127467i
$377$	0.0256923	+	0.00935122i	0.00132322	+	0.000481612i
$378$	−2.84730	+	2.38917i	−0.146449	+	0.122885i
$379$	25.8256			1.32657			0.663287	−	0.748365i	$-0.269161\pi$
$379$	25.8256			1.32657			0.663287	+	0.748365i	$0.269161\pi$
$380$	14.7554	−	4.39506i	0.756934	−	0.225462i
$381$	−11.0642			−0.566835
$382$	13.8177	−	11.5945i	0.706977	−	0.593224i
$383$	−18.9201	−	6.88635i	−0.966772	−	0.351876i	−0.190088	−	0.981767i	$-0.560877\pi$
$383$	−18.9201	−	6.88635i	−0.966772	−	0.351876i	−0.776684	+	0.629891i	$0.783100\pi$
$384$	−0.173648	+	0.984808i	−0.00886145	+	0.0502558i
$385$	12.0617	+	68.4050i	0.614719	+	3.48624i
$386$	16.3871	−	5.96443i	0.834083	−	0.303581i
$387$	2.67752	−	4.63760i	0.136106	−	0.235742i
$388$	−8.75150	−	15.1580i	−0.444290	−	0.769533i
$389$	8.68139	+	7.28455i	0.440164	+	0.369341i	0.835771	−	0.549079i	$-0.185021\pi$
$389$	8.68139	+	7.28455i	0.440164	+	0.369341i	−0.395607	+	0.918420i	$0.629466\pi$
$390$	−0.613341	−	0.514654i	−0.0310577	−	0.0260605i
$391$	7.17277	+	12.4236i	0.362743	+	0.628289i
$392$	−3.40760	+	5.90214i	−0.172110	+	0.298103i
$393$	−13.5312	+	4.92496i	−0.682559	+	0.248431i
$394$	−1.81996	−	10.3215i	−0.0916880	−	0.519989i
$395$	1.75712	−	9.96513i	0.0884104	−	0.501400i
$396$	4.97178	+	1.80958i	0.249841	+	0.0909348i
$397$	10.0307	−	8.41679i	0.503429	−	0.422427i	−0.355381	−	0.934722i	$-0.615649\pi$
$397$	10.0307	−	8.41679i	0.503429	−	0.422427i	0.858810	+	0.512295i	$0.171204\pi$
$398$	−13.6536			−0.684395
$399$	8.92174	−	13.5237i	0.446646	−	0.677034i
$400$	7.47565			0.373783
$401$	16.2554	−	13.6399i	0.811754	−	0.681143i	−0.139272	−	0.990254i	$-0.544476\pi$
$401$	16.2554	−	13.6399i	0.811754	−	0.681143i	0.951026	+	0.309112i	$0.100032\pi$
$402$	14.5471	+	5.29471i	0.725544	+	0.264076i
$403$	−0.122836	+	0.696639i	−0.00611891	+	0.0347021i
$404$	2.60741	+	14.7874i	0.129724	+	0.735699i
$405$	3.31908	−	1.20805i	0.164926	−	0.0600283i
$406$	−0.224155	+	0.388249i	−0.0111246	+	0.0192684i
$407$	13.5667	+	23.4982i	0.672477	+	1.16476i
$408$	1.26604	+	1.06234i	0.0626785	+	0.0525935i
$409$	−22.2763	−	18.6920i	−1.10149	−	0.924262i	−0.103968	−	0.994581i	$-0.533154\pi$
$409$	−22.2763	−	18.6920i	−1.10149	−	0.924262i	−0.997525	+	0.0703185i	$0.977598\pi$
$410$	12.5496	+	21.7366i	0.619782	+	1.07349i
$411$	−0.236482	+	0.409598i	−0.0116648	+	0.0202040i
$412$	−6.25877	+	2.27801i	−0.308347	+	0.112229i
$413$	0.141311	+	0.801414i	0.00695345	+	0.0394350i
$414$	1.50727	−	8.54818i	0.0740785	−	0.420120i
$415$	6.37686	+	2.32099i	0.313028	+	0.113933i
$416$	−0.173648	+	0.145708i	−0.00851380	+	0.00714393i
$417$	10.1848			0.498751
$418$	−23.0214	−	1.37306i	−1.12601	−	0.0671584i
$419$	40.4962			1.97837			0.989184	−	0.146679i	$-0.0468586\pi$
$419$	40.4962			1.97837			0.989184	+	0.146679i	$0.0468586\pi$
$420$	10.0569	−	8.43874i	0.490727	−	0.411769i
$421$	−29.3491	−	10.6822i	−1.43039	−	0.520619i	−0.493345	−	0.869834i	$-0.664226\pi$
$421$	−29.3491	−	10.6822i	−1.43039	−	0.520619i	−0.937043	+	0.349215i	$0.886448\pi$
$422$	−2.76604	+	15.6870i	−0.134649	+	0.763632i
$423$	−0.435822	−	2.47167i	−0.0211904	−	0.120177i
$424$	−5.57785	+	2.03017i	−0.270884	+	0.0985938i
$425$	6.17752	−	10.6998i	0.299654	−	0.519015i
$426$	−0.677519	−	1.17350i	−0.0328259	−	0.0568561i
$427$	−4.48158	−	3.76049i	−0.216879	−	0.181983i
$428$	6.19459	+	5.19788i	0.299427	+	0.251249i
$429$	0.599670	+	1.03866i	0.0289524	+	0.0501469i
$430$	−9.45723	+	16.3804i	−0.456068	+	0.789933i
$431$	−24.4513	+	8.89955i	−1.17778	+	0.428676i	−0.855417	−	0.517941i	$-0.826699\pi$
$431$	−24.4513	+	8.89955i	−1.17778	+	0.428676i	−0.322361	+	0.946617i	$0.604477\pi$
$432$	−0.173648	−	0.984808i	−0.00835465	−	0.0473816i
$433$	−4.69965	+	26.6530i	−0.225851	+	1.28086i	0.635202	+	0.772346i	$0.280917\pi$
$433$	−4.69965	+	26.6530i	−0.225851	+	1.28086i	−0.861053	+	0.508516i	$0.830194\pi$
$434$	−10.8995	−	3.96708i	−0.523190	−	0.190426i
$435$	0.326352	−	0.273842i	0.0156474	−	0.0131297i
$436$	15.2490			0.730293
$437$	4.34002	+	37.5857i	0.207611	+	1.79797i
$438$	−2.42602			−0.115920
$439$	−2.25284	+	1.89036i	−0.107522	+	0.0902219i	−0.694964	−	0.719045i	$-0.744580\pi$
$439$	−2.25284	+	1.89036i	−0.107522	+	0.0902219i	0.587442	+	0.809267i	$0.300135\pi$
$440$	−17.5608	−	6.39160i	−0.837177	−	0.304708i
$441$	1.18345	−	6.71167i	0.0563547	−	0.319603i
$442$	0.0650551	+	0.368946i	0.00309436	+	0.0175490i
$443$	−25.9402	+	9.44145i	−1.23245	+	0.448577i	−0.874437	−	0.485138i	$-0.838769\pi$
$443$	−25.9402	+	9.44145i	−1.23245	+	0.448577i	−0.358017	+	0.933715i	$0.616547\pi$
$444$	2.56418	−	4.44129i	0.121690	−	0.210774i
$445$	−21.4675	−	37.1828i	−1.01766	−	1.76263i
$446$	14.2606	+	11.9660i	0.675258	+	0.566609i
$447$	−3.74170	−	3.13966i	−0.176976	−	0.148501i
$448$	−1.85844	−	3.21891i	−0.0878031	−	0.152079i
$449$	−8.46110	+	14.6551i	−0.399304	+	0.691615i	−0.993640	−	0.112602i	$-0.964082\pi$
$449$	−8.46110	+	14.6551i	−0.399304	+	0.691615i	0.594336	+	0.804217i	$0.297415\pi$
$450$	−7.02481	+	2.55682i	−0.331153	+	0.120530i
$451$	−6.52869	−	37.0260i	−0.307424	−	1.74349i
$452$	0.141559	−	0.802823i	0.00665839	−	0.0377616i
$453$	8.49660	+	3.09251i	0.399205	+	0.145299i
$454$	−4.43763	+	3.72362i	−0.208268	+	0.174758i
$455$	2.97596			0.139515
$456$	1.95084	+	3.89798i	0.0913563	+	0.182540i
$457$	9.19160			0.429965			0.214982	−	0.976618i	$-0.431031\pi$
$457$	9.19160			0.429965			0.214982	+	0.976618i	$0.431031\pi$
$458$	−6.22668	+	5.22481i	−0.290954	+	0.244139i
$459$	−1.55303	−	0.565258i	−0.0724894	−	0.0263840i
$460$	−5.32383	+	30.1929i	−0.248225	+	1.40775i
$461$	−2.68210	−	15.2110i	−0.124918	−	0.708445i	−0.981357	−	0.192196i	$-0.938439\pi$
$461$	−2.68210	−	15.2110i	−0.124918	−	0.708445i	0.856438	−	0.516249i	$-0.172672\pi$
$462$	−18.4795	+	6.72600i	−0.859745	+	0.312922i
$463$	−14.9907	+	25.9646i	−0.696675	+	1.20668i	0.272937	+	0.962032i	$0.412005\pi$
$463$	−14.9907	+	25.9646i	−0.696675	+	1.20668i	−0.969613	+	0.244645i	$0.921328\pi$
$464$	−0.0603074	−	0.104455i	−0.00279970	−	0.00484922i
$465$	8.44356	+	7.08499i	0.391561	+	0.328559i
$466$	−13.0437	−	10.9450i	−0.604238	−	0.507016i
$467$	−14.4427	−	25.0155i	−0.668328	−	1.15758i	−0.978372	−	0.206855i	$-0.933677\pi$
$467$	−14.4427	−	25.0155i	−0.668328	−	1.15758i	0.310044	−	0.950722i	$-0.399656\pi$
$468$	0.113341	−	0.196312i	0.00523918	−	0.00907453i
$469$	−54.0699	+	19.6798i	−2.49671	+	0.908730i
$470$	1.53936	+	8.73016i	0.0710055	+	0.402692i
$471$	−0.0577812	+	0.327693i	−0.00266242	+	0.0150993i
$472$	−0.205737	−	0.0748822i	−0.00946982	−	0.00344673i
$473$	21.7041	−	18.2119i	0.997958	−	0.837386i
$474$	2.86484			0.131586
$475$	26.1648	−	19.4223i	1.20052	−	0.891157i
$476$	−6.14290			−0.281560
$477$	4.54710	−	3.81547i	0.208198	−	0.174699i
$478$	14.1138	+	5.13701i	0.645551	+	0.234961i
$479$	2.37211	−	13.4529i	0.108385	−	0.614679i	−0.881430	−	0.472315i	$-0.843418\pi$
$479$	2.37211	−	13.4529i	0.108385	−	0.614679i	0.989814	−	0.142364i	$-0.0454704\pi$
$480$	0.613341	+	3.47843i	0.0279950	+	0.158768i
$481$	1.09240	−	0.397600i	0.0498090	−	0.0181290i
$482$	10.7267	−	18.5792i	0.488587	−	0.846257i
$483$	16.1313	+	27.9403i	0.734002	+	1.27133i
$484$	13.0175	+	10.9230i	0.591706	+	0.496501i
$485$	−47.3585	−	39.7385i	−2.15044	−	1.80443i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	3.08899	−	5.35029i	0.139976	−	0.242445i	−0.787512	−	0.616300i	$-0.788631\pi$
$487$	3.08899	−	5.35029i	0.139976	−	0.242445i	0.927487	+	0.373855i	$0.121964\pi$
$488$	1.47906	−	0.538332i	0.0669537	−	0.0243692i
$489$	−0.684326	−	3.88100i	−0.0309463	−	0.175505i
$490$	−4.18004	+	23.7062i	−0.188835	+	1.07094i
$491$	−3.85591	−	1.40344i	−0.174015	−	0.0633363i	0.253543	−	0.967324i	$-0.418404\pi$
$491$	−3.85591	−	1.40344i	−0.174015	−	0.0633363i	−0.427558	+	0.903988i	$0.640626\pi$
$492$	−5.44356	+	4.56769i	−0.245415	+	0.205927i
$493$	−0.199340			−0.00897784
$494$	−0.229208	+	0.961130i	−0.0103125	+	0.0432433i
$495$	18.6878			0.839953
$496$	2.39053	−	2.00589i	0.107338	−	0.0900672i
$497$	4.73277	+	1.72259i	0.212294	+	0.0772687i
$498$	−0.333626	+	1.89209i	−0.0149501	+	0.0847864i
$499$	4.61540	+	26.1752i	0.206614	+	1.17176i	0.894880	+	0.446306i	$0.147261\pi$
$499$	4.61540	+	26.1752i	0.206614	+	1.17176i	−0.688266	+	0.725458i	$0.741628\pi$
$500$	8.21688	−	2.99070i	0.367470	−	0.133748i
$501$	2.99660	−	5.19026i	0.133878	−	0.231884i
$502$	12.7836	+	22.1418i	0.570559	+	0.988238i
$503$	−19.8746	−	16.6768i	−0.886166	−	0.743582i	0.0812712	−	0.996692i	$-0.474102\pi$
$503$	−19.8746	−	16.6768i	−0.886166	−	0.743582i	−0.967437	+	0.253110i	$0.918546\pi$
$504$	2.84730	+	2.38917i	0.126829	+	0.106422i
$505$	26.5180	+	45.9305i	1.18004	+	2.04388i
$506$	22.9624	−	39.7721i	1.02081	−	1.76809i
$507$	−12.1677	+	4.42869i	−0.540387	+	0.196685i
$508$	1.92127	+	10.8961i	0.0852428	+	0.483436i
$509$	−4.37551	+	24.8148i	−0.193941	+	1.09990i	0.719977	+	0.693998i	$0.244152\pi$
$509$	−4.37551	+	24.8148i	−0.193941	+	1.09990i	−0.913918	+	0.405898i	$0.866959\pi$
$510$	5.48545	+	1.99654i	0.242900	+	0.0884083i
$511$	6.90760	−	5.79617i	0.305574	−	0.256407i
$512$	1.00000			0.0441942
$513$	−3.16637	−	2.99568i	−0.139799	−	0.132262i
$514$	2.79292			0.123190
$515$	−18.0214	+	15.1218i	−0.794118	+	0.666344i
$516$	−5.03209	−	1.83153i	−0.221525	−	0.0806286i
$517$	2.30587	−	13.0773i	0.101412	−	0.575137i
$518$	3.30999	+	18.7719i	0.145433	+	0.824790i
$519$	11.5223	−	4.19377i	0.505772	−	0.184086i
$520$	−0.400330	+	0.693392i	−0.0175556	+	0.0304072i
$521$	1.38800	+	2.40409i	0.0608095	+	0.105325i	0.894827	−	0.446412i	$-0.147298\pi$
$521$	1.38800	+	2.40409i	0.0608095	+	0.105325i	−0.834018	+	0.551737i	$0.813965\pi$
$522$	0.0923963	+	0.0775297i	0.00404407	+	0.00339338i
$523$	8.60678	+	7.22195i	0.376348	+	0.315794i	0.811267	−	0.584676i	$-0.198778\pi$
$523$	8.60678	+	7.22195i	0.376348	+	0.315794i	−0.434919	+	0.900470i	$0.643223\pi$
$524$	7.19981	+	12.4704i	0.314525	+	0.544773i
$525$	13.8931	−	24.0635i	0.606343	−	1.05022i
$526$	−1.30066	+	0.473401i	−0.0567115	+	0.0206413i
$527$	−0.895582	−	5.07910i	−0.0390122	−	0.221249i
$528$	0.918748	−	5.21048i	0.0399834	−	0.226757i
$529$	−49.1865	−	17.9024i	−2.13854	−	0.778366i
$530$	−16.0608	+	13.4766i	−0.697635	+	0.585386i
$531$	0.218941			0.00950122
$532$	−14.8675	−	6.43783i	−0.644589	−	0.279115i
$533$	−1.61081			−0.0697721
$534$	9.31180	−	7.81353i	0.402961	−	0.338125i
$535$	26.8396	+	9.76882i	1.16038	+	0.422343i
$536$	2.68820	−	15.2455i	0.116112	−	0.658506i
$537$	−1.40033	−	7.94166i	−0.0604287	−	0.342708i
$538$	16.0471	−	5.84067i	0.691840	−	0.251809i
$539$	18.0292	−	31.2274i	0.776571	−	1.34506i
$540$	−1.76604	−	3.05888i	−0.0759985	−	0.131633i
$541$	−16.8628	−	14.1496i	−0.724987	−	0.608337i	0.203773	−	0.979018i	$-0.434680\pi$
$541$	−16.8628	−	14.1496i	−0.724987	−	0.608337i	−0.928760	+	0.370682i	$0.879124\pi$
$542$	−19.6780	−	16.5118i	−0.845242	−	0.709242i
$543$	0.0949225	+	0.164411i	0.00407351	+	0.00705553i
$544$	0.826352	−	1.43128i	0.0354295	−	0.0613658i
$545$	50.6125	−	18.4215i	2.16800	−	0.789088i
$546$	0.146307	+	0.829748i	0.00626136	+	0.0355100i
$547$	5.93107	−	33.6368i	0.253594	−	1.43821i	−0.546061	−	0.837746i	$-0.683873\pi$
$547$	5.93107	−	33.6368i	0.253594	−	1.43821i	0.799655	−	0.600460i	$-0.205016\pi$
$548$	0.444440	+	0.161763i	0.0189856	+	0.00691018i
$549$	−1.20574	+	1.01173i	−0.0514596	+	0.0431797i
$550$	−39.5526			−1.68653
$551$	−0.482459	−	0.208911i	−0.0205534	−	0.00889990i
$552$	−8.68004			−0.369447
$553$	−8.15704	+	6.84457i	−0.346873	+	0.291061i
$554$	−20.8846	−	7.60137i	−0.887302	−	0.322951i
$555$	3.14543	−	17.8386i	0.133516	−	0.757207i
$556$	−1.76857	−	10.0301i	−0.0750041	−	0.425369i
$557$	35.5774	−	12.9491i	1.50746	−	0.548672i	0.549484	−	0.835504i	$-0.314824\pi$
$557$	35.5774	−	12.9491i	1.50746	−	0.548672i	0.957981	+	0.286832i	$0.0926023\pi$
$558$	−1.56031	+	2.70253i	−0.0660531	+	0.114407i
$559$	−0.606944	−	1.05126i	−0.0256710	−	0.0444635i
$560$	−10.0569	−	8.43874i	−0.424982	−	0.356602i
$561$	−6.69846	−	5.62068i	−0.282809	−	0.237305i
$562$	−0.771974	−	1.33710i	−0.0325638	−	0.0564021i
$563$	−5.86231	+	10.1538i	−0.247067	+	0.427933i	−0.962711	−	0.270533i	$-0.912800\pi$
$563$	−5.86231	+	10.1538i	−0.247067	+	0.427933i	0.715644	+	0.698465i	$0.246133\pi$
$564$	−2.35844	+	0.858402i	−0.0993083	+	0.0361453i
$565$	−0.500000	−	2.83564i	−0.0210352	−	0.119296i
$566$	1.78699	−	10.1345i	0.0751127	−	0.425986i
$567$	−3.49273	−	1.27125i	−0.146681	−	0.0533874i
$568$	−1.03802	+	0.871001i	−0.0435543	+	0.0365464i
$569$	14.8972			0.624524			0.312262	−	0.949996i	$-0.398913\pi$
$569$	14.8972			0.624524			0.312262	+	0.949996i	$0.398913\pi$
$570$	11.1839	+	10.5810i	0.468443	+	0.443189i
$571$	12.9409			0.541559			0.270779	−	0.962641i	$-0.412719\pi$
$571$	12.9409			0.541559			0.270779	+	0.962641i	$0.412719\pi$
$572$	0.918748	−	0.770921i	0.0384148	−	0.0322338i
$573$	16.9500	+	6.16928i	0.708095	+	0.257725i
$574$	4.58647	−	26.0111i	0.191435	−	1.08568i
$575$	11.2679	+	63.9032i	0.469902	+	2.66495i
$576$	−0.939693	+	0.342020i	−0.0391539	+	0.0142508i
$577$	−11.3657	+	19.6860i	−0.473161	+	0.819539i	−0.999528	−	0.0307187i	$-0.990220\pi$
$577$	−11.3657	+	19.6860i	−0.473161	+	0.819539i	0.526367	+	0.850257i	$0.323554\pi$
$578$	7.13429	+	12.3569i	0.296747	+	0.513981i
$579$	13.3589	+	11.2095i	0.555177	+	0.465849i
$580$	−0.326352	−	0.273842i	−0.0135510	−	0.0113707i
$581$	−3.57057	−	6.18442i	−0.148132	−	0.256573i
$582$	8.75150	−	15.1580i	0.362761	−	0.628321i
$583$	29.5116	−	10.7413i	1.22225	−	0.444861i
$584$	0.421274	+	2.38917i	0.0174325	+	0.0988644i
$585$	0.139033	−	0.788496i	0.00574831	−	0.0326003i
$586$	26.7841	+	9.74860i	1.10644	+	0.402711i
$587$	−8.08899	+	6.78747i	−0.333868	+	0.280149i	−0.794274	−	0.607560i	$-0.792148\pi$
$587$	−8.08899	+	6.78747i	−0.333868	+	0.280149i	0.460405	+	0.887709i	$0.347704\pi$
$588$	−6.81521			−0.281054
$589$	3.15539	−	13.2314i	0.130016	−	0.545190i
$590$	−0.773318			−0.0318370
$591$	8.02869	−	6.73687i	0.330256	−	0.277118i
$592$	−4.81908	−	1.75400i	−0.198063	−	0.0720890i
$593$	−1.86808	+	10.5944i	−0.0767128	+	0.435060i	0.922126	+	0.386889i	$0.126450\pi$
$593$	−1.86808	+	10.5944i	−0.0767128	+	0.435060i	−0.998839	+	0.0481709i	$0.984661\pi$
$594$	0.918748	+	5.21048i	0.0376967	+	0.213789i
$595$	−20.3888	+	7.42091i	−0.835858	+	0.304228i
$596$	−2.44222	+	4.23005i	−0.100037	+	0.173269i
$597$	−6.82682	−	11.8244i	−0.279403	−	0.483940i
$598$	−1.50727	−	1.26475i	−0.0616370	−	0.0517196i
$599$	−18.7153	−	15.7040i	−0.764686	−	0.641648i	0.174656	−	0.984630i	$-0.444119\pi$
$599$	−18.7153	−	15.7040i	−0.764686	−	0.641648i	−0.939342	+	0.342982i	$0.888563\pi$
$600$	3.73783	+	6.47410i	0.152596	+	0.264304i
$601$	13.2057	−	22.8730i	0.538673	−	0.933009i	−0.460303	−	0.887762i	$-0.652259\pi$
$601$	13.2057	−	22.8730i	0.538673	−	0.933009i	0.998976	−	0.0452473i	$-0.0144076\pi$
$602$	18.7037	−	6.80758i	0.762305	−	0.277456i
$603$	2.68820	+	15.2455i	0.109472	+	0.620845i
$604$	1.57011	−	8.90452i	0.0638868	−	0.362320i
$605$	56.4017	+	20.5286i	2.29306	+	0.834604i
$606$	−11.5025	+	9.65177i	−0.467258	+	0.392076i
$607$	−16.3618			−0.664107			−0.332053	−	0.943261i	$-0.607741\pi$
$607$	−16.3618			−0.664107			−0.332053	+	0.943261i	$0.607741\pi$
$608$	3.50000	−	2.59808i	0.141944	−	0.105366i
$609$	−0.448311			−0.0181665
$610$	4.25877	−	3.57353i	0.172433	−	0.144688i
$611$	−0.534615	−	0.194584i	−0.0216282	−	0.00787203i
$612$	−0.286989	+	1.62760i	−0.0116008	+	0.0657916i
$613$	1.03162	+	5.85062i	0.0416668	+	0.236304i	0.998528	−	0.0542418i	$-0.0172742\pi$
$613$	1.03162	+	5.85062i	0.0416668	+	0.236304i	−0.956861	+	0.290546i	$0.906163\pi$
$614$	24.0180	−	8.74184i	0.969288	−	0.352792i
$615$	−12.5496	+	21.7366i	−0.506050	+	0.876504i
$616$	9.83275	+	17.0308i	0.396173	+	0.686191i
$617$	−26.1438	−	21.9373i	−1.05251	−	0.883162i	−0.0591558	−	0.998249i	$-0.518841\pi$
$617$	−26.1438	−	21.9373i	−1.05251	−	0.883162i	−0.993355	+	0.115087i	$0.963285\pi$
$618$	−5.10220	−	4.28125i	−0.205240	−	0.172217i
$619$	−16.1506	−	27.9737i	−0.649149	−	1.12436i	−0.983326	−	0.181849i	$-0.941792\pi$
$619$	−16.1506	−	27.9737i	−0.649149	−	1.12436i	0.334177	−	0.942510i	$-0.391542\pi$
$620$	5.51114	−	9.54558i	0.221333	−	0.383360i
$621$	8.15657	−	2.96875i	0.327312	−	0.119132i
$622$	1.80154	+	10.2170i	0.0722350	+	0.409665i
$623$	−7.84565	+	44.4949i	−0.314329	+	1.78265i
$624$	−0.213011	−	0.0775297i	−0.00852727	−	0.00310367i
$625$	−4.97384	+	4.17355i	−0.198954	+	0.166942i
$626$	−15.4365			−0.616965
$627$	−10.3216	−	20.6237i	−0.412205	−	0.823629i
$628$	0.332748			0.0132781
$629$	−6.49273	+	5.44804i	−0.258882	+	0.217228i
$630$	12.3366	+	4.49016i	0.491503	+	0.178892i
$631$	3.13058	−	17.7544i	0.124626	−	0.706791i	−0.856903	−	0.515478i	$-0.827614\pi$
$631$	3.13058	−	17.7544i	0.124626	−	0.706791i	0.981529	−	0.191313i	$-0.0612745\pi$
$632$	−0.497474	−	2.82131i	−0.0197884	−	0.112226i
$633$	−14.9684	+	5.44804i	−0.594940	+	0.216540i
$634$	−14.1985	+	24.5925i	−0.563893	+	0.976691i
$635$	19.5398	+	33.8440i	0.775414	+	1.34306i
$636$	−4.54710	−	3.81547i	−0.180304	−	0.151293i
$637$	−1.18345	−	0.993031i	−0.0468899	−	0.0393453i
$638$	0.319078	+	0.552659i	0.0126324	+	0.0218800i
$639$	0.677519	−	1.17350i	0.0268022	−	0.0464228i
$640$	3.31908	−	1.20805i	0.131198	−	0.0477522i
$641$	0.449493	+	2.54920i	0.0177539	+	0.100687i	0.992397	−	0.123077i	$-0.0392764\pi$
$641$	0.449493	+	2.54920i	0.0177539	+	0.100687i	−0.974643	+	0.223765i	$0.928165\pi$
$642$	−1.40420	+	7.96361i	−0.0554194	+	0.314299i
$643$	−15.2160	−	5.53817i	−0.600061	−	0.218404i	0.0240880	−	0.999710i	$-0.492332\pi$
$643$	−15.2160	−	5.53817i	−0.600061	−	0.218404i	−0.624149	+	0.781306i	$0.714554\pi$
$644$	24.7147	−	20.7381i	0.973894	−	0.817194i
$645$	−18.9145			−0.744756
$646$	−0.826352	−	7.15642i	−0.0325124	−	0.281565i
$647$	0.477407			0.0187688			0.00938439	−	0.999956i	$-0.497013\pi$
$647$	0.477407			0.0187688			0.00938439	+	0.999956i	$0.497013\pi$
$648$	0.766044	−	0.642788i	0.0300931	−	0.0252511i
$649$	1.08853	+	0.396191i	0.0427284	+	0.0155519i
$650$	−0.294263	+	1.66885i	−0.0115419	+	0.0654576i
$651$	−2.01414	−	11.4227i	−0.0789403	−	0.447693i
$652$	−3.70321	+	1.34786i	−0.145029	+	0.0527862i
$653$	−8.05097	+	13.9447i	−0.315059	+	0.545698i	−0.979450	−	0.201687i	$-0.935358\pi$
$653$	−8.05097	+	13.9447i	−0.315059	+	0.545698i	0.664391	+	0.747385i	$0.268691\pi$
$654$	7.62449	+	13.2060i	0.298141	+	0.516395i
$655$	38.9616	+	32.6926i	1.52235	+	1.27741i
$656$	5.44356	+	4.56769i	0.212535	+	0.178338i
$657$	−1.21301	−	2.10100i	−0.0473241	−	0.0819677i
$658$	4.66431	−	8.07883i	0.181834	−	0.314946i
$659$	13.6630	−	4.97291i	0.532234	−	0.193717i	−0.0619017	−	0.998082i	$-0.519717\pi$
$659$	13.6630	−	4.97291i	0.532234	−	0.193717i	0.594135	+	0.804365i	$0.297494\pi$
$660$	−3.24510	−	18.4039i	−0.126315	−	0.716370i
$661$	−2.52915	+	14.3435i	−0.0983726	+	0.557899i	0.895289	+	0.445486i	$0.146969\pi$
$661$	−2.52915	+	14.3435i	−0.0983726	+	0.557899i	−0.993662	+	0.112413i	$0.964142\pi$
$662$	24.3589	+	8.86592i	0.946736	+	0.344584i
$663$	−0.286989	+	0.240812i	−0.0111457	+	0.00935238i
$664$	1.92127			0.0745599
$665$	−57.1237	−	3.40700i	−2.21516	−	0.132118i
$666$	5.12836			0.198720
$667$	0.802004	−	0.672961i	0.0310537	−	0.0260572i
$668$	−5.63176	−	2.04979i	−0.217899	−	0.0793089i
$669$	−3.23261	+	18.3331i	−0.124980	+	0.708797i
$670$	−9.49495	−	53.8485i	−0.366822	−	2.08035i
$671$	−7.82547	+	2.84824i	−0.302099	+	0.109955i
$672$	1.85844	−	3.21891i	0.0716909	−	0.124172i
$673$	−12.4324	−	21.5336i	−0.479235	−	0.830059i	0.520482	−	0.853873i	$-0.325752\pi$
$673$	−12.4324	−	21.5336i	−0.479235	−	0.830059i	−0.999716	+	0.0238142i	$0.992419\pi$
$674$	−18.0103	−	15.1124i	−0.693730	−	0.582108i
$675$	−5.72668	−	4.80526i	−0.220420	−	0.184954i
$676$	6.47431	+	11.2138i	0.249012	+	0.431301i
$677$	−23.2271	+	40.2306i	−0.892692	+	1.54619i	−0.0560563	+	0.998428i	$0.517853\pi$
$677$	−23.2271	+	40.2306i	−0.892692	+	1.54619i	−0.836636	+	0.547760i	$0.815481\pi$
$678$	0.766044	−	0.278817i	0.0294198	−	0.0107079i
$679$	11.2970	+	64.0682i	0.433537	+	2.45871i
$680$	1.01367	−	5.74881i	0.0388725	−	0.220457i
$681$	−5.44356	−	1.98129i	−0.208598	−	0.0759234i
$682$	−12.6480	+	10.6129i	−0.484315	+	0.406389i
$683$	−26.0000			−0.994862			−0.497431	−	0.867503i	$-0.665723\pi$
$683$	−26.0000			−0.994862			−0.497431	+	0.867503i	$0.665723\pi$
$684$	−2.40033	+	3.63846i	−0.0917789	+	0.139120i
$685$	1.67055			0.0638284
$686$	−0.526159	+	0.441500i	−0.0200888	+	0.0168565i
$687$	−7.63816	−	2.78006i	−0.291414	−	0.106066i
$688$	−0.929892	+	5.27368i	−0.0354518	+	0.201057i
$689$	−0.233651	−	1.32510i	−0.00890139	−	0.0504823i
$690$	−28.8097	+	10.4859i	−1.09677	+	0.399191i
$691$	8.03478	−	13.9166i	0.305657	−	0.529414i	−0.671750	−	0.740778i	$-0.734457\pi$
$691$	8.03478	−	13.9166i	0.305657	−	0.529414i	0.977407	+	0.211364i	$0.0677905\pi$
$692$	−6.13088	−	10.6190i	−0.233061	−	0.403674i
$693$	−15.0646	−	12.6407i	−0.572259	−	0.480182i
$694$	−1.84208	−	1.54569i	−0.0699245	−	0.0586736i
$695$	−17.9868	−	31.1540i	−0.682278	−	1.18174i
$696$	0.0603074	−	0.104455i	0.00228595	−	0.00395937i
$697$	11.0360	−	4.01676i	0.418017	−	0.152146i
$698$	0.902551	+	5.11862i	0.0341621	+	0.193743i
$699$	2.95677	−	16.7687i	0.111835	−	0.634249i
$700$	−26.1104	−	9.50341i	−0.986881	−	0.359195i
$701$	−7.59240	+	6.37078i	−0.286761	+	0.240621i	−0.774808	−	0.632196i	$-0.782154\pi$
$701$	−7.59240	+	6.37078i	−0.286761	+	0.240621i	0.488048	+	0.872817i	$0.337709\pi$
$702$	0.226682			0.00855555
$703$	−21.4238	+	6.38133i	−0.808014	+	0.240676i
$704$	−5.29086			−0.199407
$705$	−6.79086	+	5.69821i	−0.255759	+	0.214607i
$706$	−7.77719	−	2.83067i	−0.292698	−	0.106533i
$707$	9.69144	−	54.9629i	0.364484	−	2.06709i
$708$	−0.0380187	−	0.215615i	−0.00142883	−	0.00810329i
$709$	25.8148	−	9.39582i	0.969495	−	0.352867i	0.191748	−	0.981444i	$-0.438584\pi$
$709$	25.8148	−	9.39582i	0.969495	−	0.352867i	0.777747	+	0.628577i	$0.216362\pi$
$710$	−2.39306	+	4.14489i	−0.0898098	+	0.155555i
$711$	1.43242	+	2.48102i	0.0537199	+	0.0930456i
$712$	−9.31180	−	7.81353i	−0.348975	−	0.292824i
$713$	20.7499	+	17.4112i	0.777090	+	0.652056i
$714$	−3.07145	−	5.31991i	−0.114946	−	0.199093i
$715$	2.11809	−	3.66864i	0.0792120	−	0.137199i
$716$	−7.57785	+	2.75811i	−0.283197	+	0.103075i
$717$	2.60813	+	14.7914i	0.0974023	+	0.552396i
$718$	−0.398681	+	2.26103i	−0.0148786	+	0.0843810i
$719$	−11.5239	−	4.19437i	−0.429770	−	0.156424i	0.118072	−	0.993005i	$-0.462329\pi$
$719$	−11.5239	−	4.19437i	−0.429770	−	0.156424i	−0.547843	+	0.836581i	$0.684551\pi$
$720$	−2.70574	+	2.27038i	−0.100837	+	0.0846122i
$721$	24.7561			0.921965
$722$	5.50000	−	18.1865i	0.204689	−	0.676833i
$723$	21.4534			0.797859
$724$	0.145430	−	0.122030i	0.00540485	−	0.00453521i
$725$	−0.847296	−	0.308391i	−0.0314678	−	0.0114533i
$726$	−2.95084	+	16.7350i	−0.109516	+	0.621095i
$727$	4.90719	+	27.8301i	0.181998	+	1.03216i	0.929752	+	0.368185i	$0.120021\pi$
$727$	4.90719	+	27.8301i	0.181998	+	1.03216i	−0.747755	+	0.663975i	$0.768868\pi$
$728$	0.791737	−	0.288169i	0.0293437	−	0.0106802i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	4.28446	+	7.42091i	0.158575	+	0.274660i
$731$	6.77972	+	5.68886i	0.250757	+	0.210410i
$732$	1.20574	+	1.01173i	0.0445653	+	0.0373947i
$733$	11.2883	+	19.5520i	0.416944	+	0.722168i	0.995630	−	0.0933819i	$-0.0297677\pi$
$733$	11.2883	+	19.5520i	0.416944	+	0.722168i	−0.578686	+	0.815550i	$0.696434\pi$
$734$	−14.9324	+	25.8637i	−0.551166	+	0.954647i
$735$	−22.6202	+	8.23308i	−0.834359	+	0.303682i
$736$	1.50727	+	8.54818i	0.0555589	+	0.315090i
$737$	−14.2229	+	80.6619i	−0.523906	+	2.97122i
$738$	−6.67752	−	2.43042i	−0.245803	−	0.0894649i
$739$	20.2986	−	17.0325i	0.746696	−	0.626552i	−0.187931	−	0.982182i	$-0.560178\pi$
$739$	20.2986	−	17.0325i	0.746696	−	0.626552i	0.934627	+	0.355630i	$0.115734\pi$
$740$	−18.1138			−0.665877
$741$	−0.946967	+	0.282065i	−0.0347877	+	0.0103619i
$742$	22.0627			0.809949
$743$	−21.1536	+	17.7500i	−0.776052	+	0.651185i	−0.942251	−	0.334907i	$-0.891295\pi$
$743$	−21.1536	+	17.7500i	−0.776052	+	0.651185i	0.166199	+	0.986092i	$0.446850\pi$
$744$	2.93242	+	1.06731i	0.107508	+	0.0391296i
$745$	−2.99582	+	16.9902i	−0.109759	+	0.622472i
$746$	−3.44743	−	19.5514i	−0.126220	−	0.715826i
$747$	−1.80541	+	0.657115i	−0.0660564	+	0.0240426i
$748$	−4.37211	+	7.57272i	−0.159860	+	0.276886i
$749$	−15.0282	−	26.0296i	−0.549119	−	0.951102i
$750$	6.69846	+	5.62068i	0.244593	+	0.205238i
$751$	0.988140	+	0.829148i	0.0360578	+	0.0302561i	0.660638	−	0.750704i	$-0.270286\pi$
$751$	0.988140	+	0.829148i	0.0360578	+	0.0302561i	−0.624581	+	0.780960i	$0.714730\pi$
$752$	1.25490	+	2.17355i	0.0457615	+	0.0792612i
$753$	−12.7836	+	22.1418i	−0.465860	+	0.806893i
$754$	0.0256923	−	0.00935122i	0.000935657	−	0.000340551i
$755$	−5.54576	−	31.4516i	−0.201831	−	1.14464i
$756$	−0.645430	+	3.66041i	−0.0234741	+	0.133128i
$757$	24.3259	+	8.85392i	0.884141	+	0.321801i	0.743880	−	0.668313i	$-0.232983\pi$
$757$	24.3259	+	8.85392i	0.884141	+	0.321801i	0.140262	+	0.990114i	$0.455206\pi$
$758$	19.7836	−	16.6004i	0.718572	−	0.602954i
$759$	45.9249			1.66697
$760$	8.47818	−	12.8514i	0.307536	−	0.466168i
$761$	11.3396			0.411059			0.205529	−	0.978651i	$-0.434108\pi$
$761$	11.3396			0.411059			0.205529	+	0.978651i	$0.434108\pi$
$762$	−8.47565	+	7.11192i	−0.307040	+	0.257638i
$763$	−53.2605	−	19.3852i	−1.92816	−	0.701792i
$764$	3.13223	−	17.7637i	0.113320	−	0.642669i
$765$	1.01367	+	5.74881i	0.0366493	+	0.207849i
$766$	−18.9201	+	6.88635i	−0.683611	+	0.248814i
$767$	0.0248149	−	0.0429807i	0.000896015	−	0.00155194i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	16.4283	+	13.7850i	0.592420	+	0.497099i	0.888999	−	0.457909i	$-0.151401\pi$
$769$	16.4283	+	13.7850i	0.592420	+	0.497099i	−0.296579	+	0.955008i	$0.595846\pi$
$770$	53.2097	+	44.6482i	1.91754	+	1.60901i
$771$	1.39646	+	2.41874i	0.0502923	+	0.0871087i
$772$	8.71941	−	15.1025i	0.313818	−	0.543549i
$773$	−3.99108	+	1.45263i	−0.143549	+	0.0522476i	−0.412796	−	0.910824i	$-0.635448\pi$
$773$	−3.99108	+	1.45263i	−0.143549	+	0.0522476i	0.269246	+	0.963071i	$0.413225\pi$
$774$	−0.929892	−	5.27368i	−0.0334243	−	0.189559i
$775$	4.05097	−	22.9742i	0.145515	−	0.825258i
$776$	−16.4474	−	5.98638i	−0.590428	−	0.214898i
$777$	−14.6019	+	12.2525i	−0.523842	+	0.439556i
$778$	11.3327			0.406299
$779$	30.9197	+	1.84413i	1.10781	+	0.0660728i
$780$	−0.800660			−0.0286682
$781$	5.49201	−	4.60834i	0.196520	−	0.164900i
$782$	13.4804	+	4.90646i	0.482058	+	0.175455i
$783$	−0.0209445	+	0.118782i	−0.000748497	+	0.00424493i
$784$	1.18345	+	6.71167i	0.0422660	+	0.239702i
$785$	1.10442	−	0.401975i	0.0394184	−	0.0143471i
$786$	−7.19981	+	12.4704i	−0.256809	+	0.444806i
$787$	5.41013	+	9.37062i	0.192850	+	0.334027i	0.946194	−	0.323601i	$-0.104893\pi$
$787$	5.41013	+	9.37062i	0.192850	+	0.334027i	−0.753343	+	0.657627i	$0.771560\pi$
$788$	−8.02869	−	6.73687i	−0.286010	−	0.239991i
$789$	−1.06031	−	0.889704i	−0.0377479	−	0.0316743i
$790$	−5.05943	−	8.76319i	−0.180006	−	0.311780i
$791$	−1.51501	+	2.62408i	−0.0538677	+	0.0933016i
$792$	4.97178	−	1.80958i	0.176665	−	0.0643006i
$793$	0.0619563	+	0.351371i	0.00220013	+	0.0124776i
$794$	2.27379	−	12.8953i	0.0806936	−	0.457636i
$795$	−19.7015	−	7.17074i	−0.698739	−	0.254320i
$796$	−10.4593	+	8.77639i	−0.370720	+	0.311071i
$797$	22.0327			0.780439			0.390219	−	0.920722i	$-0.372399\pi$
$797$	22.0327			0.780439			0.390219	+	0.920722i	$0.372399\pi$
$798$	−1.85844	−	16.0946i	−0.0657881	−	0.569742i
$799$	4.14796			0.146744
$800$	5.72668	−	4.80526i	0.202469	−	0.169891i
$801$	11.4226	+	4.15749i	0.403598	+	0.146898i
$802$	3.68479	−	20.8975i	0.130115	−	0.737916i
$803$	−2.22890	−	12.6407i	−0.0786563	−	0.446082i
$804$	14.5471	−	5.29471i	0.513037	−	0.186730i
$805$	56.9774	−	98.6877i	2.00819	−	3.47828i
$806$	0.353693	+	0.612614i	0.0124583	+	0.0215784i
$807$	13.0817	+	10.9769i	0.460498	+	0.386404i
$808$	11.5025	+	9.65177i	0.404657	+	0.339548i
$809$	−3.34343	−	5.79098i	−0.117549	−	0.203600i	0.801247	−	0.598334i	$-0.204170\pi$
$809$	−3.34343	−	5.79098i	−0.117549	−	0.203600i	−0.918796	+	0.394733i	$0.870837\pi$
$810$	1.76604	−	3.05888i	0.0620525	−	0.107478i
$811$	−23.9530	+	8.71816i	−0.841102	+	0.306136i	−0.726407	−	0.687265i	$-0.758811\pi$
$811$	−23.9530	+	8.71816i	−0.841102	+	0.306136i	−0.114695	+	0.993401i	$0.536589\pi$
$812$	0.0778483	+	0.441500i	0.00273194	+	0.0154936i
$813$	4.46064	−	25.2975i	0.156441	−	0.887223i
$814$	25.4971	+	9.28017i	0.893672	+	0.325270i
$815$	−10.6630	+	8.94729i	−0.373508	+	0.313410i
$816$	1.65270			0.0578562
$817$	10.4468	+	20.8738i	0.365487	+	0.730282i
$818$	−29.0797			−1.01675
$819$	−0.645430	+	0.541580i	−0.0225531	+	0.0189243i
$820$	23.5856	+	8.58445i	0.823644	+	0.299782i
$821$	−7.34348	+	41.6470i	−0.256289	+	1.45349i	0.536452	+	0.843931i	$0.319764\pi$
$821$	−7.34348	+	41.6470i	−0.256289	+	1.45349i	−0.792741	+	0.609558i	$0.791347\pi$
$822$	0.0821293	+	0.465778i	0.00286459	+	0.0162459i
$823$	0.506397	−	0.184313i	0.0176519	−	0.00642476i	−0.333179	−	0.942864i	$-0.608121\pi$
$823$	0.506397	−	0.184313i	0.0176519	−	0.00642476i	0.350831	+	0.936439i	$0.385899\pi$
$824$	−3.33022	+	5.76811i	−0.116014	+	0.200942i
$825$	−19.7763	−	34.2536i	−0.688523	−	1.19256i
$826$	0.623389	+	0.523086i	0.0216905	+	0.0182005i
$827$	−12.2745	−	10.2995i	−0.426826	−	0.358150i	0.403926	−	0.914791i	$-0.367645\pi$
$827$	−12.2745	−	10.2995i	−0.426826	−	0.358150i	−0.830753	+	0.556642i	$0.812090\pi$
$828$	−4.34002	−	7.51714i	−0.150826	−	0.261239i
$829$	10.0517	−	17.4100i	0.349110	−	0.604676i	−0.636982	−	0.770879i	$-0.719817\pi$
$829$	10.0517	−	17.4100i	0.349110	−	0.604676i	0.986092	+	0.166203i	$0.0531508\pi$
$830$	6.37686	−	2.32099i	0.221344	−	0.0805626i
$831$	−3.85932	−	21.8873i	−0.133878	−	0.759261i
$832$	−0.0393628	+	0.223238i	−0.00136466	+	0.00773938i
$833$	10.5842	+	3.85235i	0.366722	+	0.133476i
$834$	7.80200	−	6.54666i	0.270161	−	0.226692i
$835$	−21.1685			−0.732566
$836$	−18.5180	+	13.7461i	−0.640459	+	0.475417i
$837$	−3.12061			−0.107864
$838$	31.0219	−	26.0304i	1.07163	−	0.899207i
$839$	−29.1031	−	10.5927i	−1.00475	−	0.365700i	−0.213337	−	0.976979i	$-0.568433\pi$
$839$	−29.1031	−	10.5927i	−1.00475	−	0.365700i	−0.791415	+	0.611279i	$0.790655\pi$
$840$	2.27972	−	12.9289i	0.0786576	−	0.446090i
$841$	−5.03327	−	28.5451i	−0.173561	−	0.984314i
$842$	−29.3491	+	10.6822i	−1.01144	+	0.368133i
$843$	0.771974	−	1.33710i	0.0265882	−	0.0460521i
$844$	7.96451	+	13.7949i	0.274150	+	0.474841i
$845$	35.0355	+	29.3983i	1.20526	+	1.01133i
$846$	−1.92262	−	1.61327i	−0.0661010	−	0.0554653i
$847$	−31.5808	−	54.6996i	−1.08513	−	1.87950i
$848$	−2.96791	+	5.14057i	−0.101918	+	0.176528i
$849$	9.67024	−	3.51968i	0.331882	−	0.120795i
$850$	−2.14543	−	12.1673i	−0.0735876	−	0.417336i
$851$	7.72984	−	43.8381i	0.264975	−	1.50275i
$852$	−1.27332	−	0.463450i	−0.0436232	−	0.0158775i
$853$	−16.3209	+	13.6949i	−0.558817	+	0.468903i	−0.877913	−	0.478819i	$-0.841065\pi$
$853$	−16.3209	+	13.6949i	−0.558817	+	0.468903i	0.319097	+	0.947722i	$0.396620\pi$
$854$	−5.85029			−0.200193
$855$	−3.57145	+	14.9761i	−0.122141	+	0.512170i
$856$	8.08647			0.276390
$857$	42.5551	−	35.7080i	1.45366	−	1.21976i	0.523799	−	0.851842i	$-0.324514\pi$
$857$	42.5551	−	35.7080i	1.45366	−	1.21976i	0.929857	−	0.367920i	$-0.119930\pi$
$858$	1.12701	+	0.410199i	0.0384755	+	0.0140039i
$859$	−4.11902	+	23.3601i	−0.140539	+	0.797038i	0.830302	+	0.557314i	$0.188168\pi$
$859$	−4.11902	+	23.3601i	−0.140539	+	0.797038i	−0.970841	+	0.239724i	$0.922943\pi$
$860$	3.28446	+	18.6271i	0.111999	+	0.635179i
$861$	24.8195	−	9.03358i	0.845848	−	0.307863i
$862$	−13.0103	+	22.5344i	−0.443131	+	0.767526i
$863$	−10.5410	−	18.2576i	−0.358820	−	0.621495i	0.628944	−	0.777451i	$-0.283488\pi$
$863$	−10.5410	−	18.2576i	−0.358820	−	0.621495i	−0.987764	+	0.155956i	$0.950154\pi$
$864$	−0.766044	−	0.642788i	−0.0260614	−	0.0218681i
$865$	−33.1771	−	27.8389i	−1.12806	−	0.946551i
$866$	13.5321	+	23.4383i	0.459839	+	0.796465i
$867$	−7.13429	+	12.3569i	−0.242293	+	0.419664i
$868$	−10.8995	+	3.96708i	−0.369952	+	0.134651i
$869$	2.63206	+	14.9272i	0.0892866	+	0.506370i
$870$	0.0739780	−	0.419550i	0.00250809	−	0.0142241i
$871$	3.29756	+	1.20021i	0.111734	+	0.0406677i
$872$	11.6814	−	9.80185i	0.395582	−	0.331932i
$873$	17.5030			0.592387
$874$	27.4843	+	26.0026i	0.929669	+	0.879551i
$875$	−32.5012			−1.09874
$876$	−1.85844	+	1.55942i	−0.0627909	+	0.0526878i
$877$	48.1134	+	17.5118i	1.62467	+	0.591333i	0.984265	−	0.176701i	$-0.0565425\pi$
$877$	48.1134	+	17.5118i	1.62467	+	0.591333i	0.640409	+	0.768034i	$0.278765\pi$
$878$	−0.510678	+	2.89620i	−0.0172345	+	0.0977419i
$879$	4.94949	+	28.0700i	0.166942	+	0.946777i
$880$	−17.5608	+	6.39160i	−0.591974	+	0.215461i
$881$	17.0804	−	29.5841i	0.575452	−	0.996713i	−0.420540	−	0.907274i	$-0.638159\pi$
$881$	17.0804	−	29.5841i	0.575452	−	0.996713i	0.995992	−	0.0894388i	$-0.0285074\pi$
$882$	−3.40760	−	5.90214i	−0.114740	−	0.198735i
$883$	21.5403	+	18.0745i	0.724889	+	0.608254i	0.928733	−	0.370750i	$-0.120899\pi$
$883$	21.5403	+	18.0745i	0.724889	+	0.608254i	−0.203844	+	0.979003i	$0.565344\pi$
$884$	0.286989	+	0.240812i	0.00965248	+	0.00809940i
$885$	−0.386659	−	0.669713i	−0.0129974	−	0.0225122i
$886$	−13.8025	+	23.9066i	−0.463703	+	0.803157i
$887$	33.4298	−	12.1674i	1.12246	−	0.408543i	0.286912	−	0.957957i	$-0.407371\pi$
$887$	33.4298	−	12.1674i	1.12246	−	0.408543i	0.835550	+	0.549414i	$0.185149\pi$
$888$	−0.890530	−	5.05044i	−0.0298842	−	0.169482i
$889$	7.14115	−	40.4995i	0.239506	−	1.35831i
$890$	−40.3457	−	14.6846i	−1.35239	−	0.492230i
$891$	−4.05303	+	3.40090i	−0.135782	+	0.113934i
$892$	18.6159			0.623305
$893$	10.0392	+	4.34710i	0.335949	+	0.145470i
$894$	−4.88444			−0.163360
$895$	−21.8195	+	18.3088i	−0.729347	+	0.611995i
$896$	−3.49273	−	1.27125i	−0.116684	−	0.0424694i
$897$	0.341671	−	1.93771i	0.0114081	−	0.0646984i
$898$	2.93851	+	16.6651i	0.0980594	+	0.556122i
$899$	−0.353693	+	0.128734i	−0.0117963	+	0.00429351i
$900$	−3.73783	+	6.47410i	−0.124594	+	0.215803i
$901$	4.90508	+	8.49584i	0.163412	+	0.283038i
$902$	−28.8011	−	24.1670i	−0.958973	−	0.804674i
$903$	15.2474	+	12.7941i	0.507401	+	0.425760i
$904$	−0.407604	−	0.705990i	−0.0135567	−	0.0234809i
$905$	0.335275	−	0.580713i	0.0111449	−	0.0193035i
$906$	8.49660	−	3.09251i	0.282281	−	0.102742i
$907$	−1.61422	−	9.15469i	−0.0535992	−	0.303976i	0.946209	−	0.323556i	$-0.104878\pi$
$907$	−1.61422	−	9.15469i	−0.0535992	−	0.303976i	−0.999808	+	0.0195795i	$0.993767\pi$
$908$	−1.00593	+	5.70491i	−0.0333830	+	0.189324i
$909$	−14.1099	−	5.13560i	−0.467997	−	0.170337i
$910$	2.27972	−	1.91291i	0.0755718	−	0.0634123i
$911$	3.79055			0.125587			0.0627933	−	0.998027i	$-0.479999\pi$
$911$	3.79055			0.125587			0.0627933	+	0.998027i	$0.479999\pi$
$912$	4.00000	+	1.73205i	0.132453	+	0.0573539i
$913$	−10.1652			−0.336419
$914$	7.04117	−	5.90825i	0.232901	−	0.195427i
$915$	5.22416	+	1.90144i	0.172705	+	0.0628596i
$916$	−1.41147	+	8.00487i	−0.0466364	+	0.264488i
$917$	−9.29394	−	52.7085i	−0.306913	−	1.74059i
$918$	−1.55303	+	0.565258i	−0.0512577	+	0.0186563i
$919$	2.21554	−	3.83742i	0.0730838	−	0.126585i	−0.827168	−	0.561955i	$-0.810049\pi$
$919$	2.21554	−	3.83742i	0.0730838	−	0.126585i	0.900251	+	0.435370i	$0.143383\pi$
$920$	15.3293	+	26.5512i	0.505394	+	0.875367i
$921$	19.5797	+	16.4293i	0.645172	+	0.541363i
$922$	−11.8320	−	9.92825i	−0.389667	−	0.326970i
$923$	−0.153581	−	0.266010i	−0.00505518	−	0.00875583i
$924$	−9.83275	+	17.0308i	−0.323474	+	0.560273i
$925$	−36.0257	+	13.1123i	−1.18452	+	0.431130i
$926$	5.20620	+	29.5258i	0.171086	+	0.970280i
$927$	1.15657	−	6.55926i	0.0379869	−	0.215434i
$928$	−0.113341	−	0.0412527i	−0.00372059	−	0.00135419i
$929$	23.3384	−	19.5833i	0.765709	−	0.642506i	−0.173897	−	0.984764i	$-0.555636\pi$
$929$	23.3384	−	19.5833i	0.765709	−	0.642506i	0.939606	+	0.342258i	$0.111192\pi$
$930$	11.0223			0.361435
$931$	21.5795	+	20.4162i	0.707239	+	0.669112i
$932$	−17.0273			−0.557749
$933$	−7.94743	+	6.66869i	−0.260187	+	0.218323i
$934$	−27.1434	−	9.87938i	−0.888158	−	0.323263i
$935$	−5.36319	+	30.4162i	−0.175395	+	0.994715i
$936$	−0.0393628	−	0.223238i	−0.00128661	−	0.00729676i
$937$	1.34477	−	0.489456i	0.0439317	−	0.0159898i	−0.319961	−	0.947431i	$-0.603670\pi$
$937$	1.34477	−	0.489456i	0.0439317	−	0.0159898i	0.363893	+	0.931441i	$0.381448\pi$
$938$	−28.7700	+	49.8311i	−0.939373	+	1.62704i
$939$	−7.71823	−	13.3684i	−0.251875	−	0.436260i
$940$	6.79086	+	5.69821i	0.221493	+	0.185855i
$941$	3.47384	+	2.91490i	0.113244	+	0.0950230i	0.697651	−	0.716437i	$-0.254229\pi$
$941$	3.47384	+	2.91490i	0.113244	+	0.0950230i	−0.584407	+	0.811460i	$0.698673\pi$
$942$	0.166374	+	0.288169i	0.00542076	+	0.00938904i
$943$	−30.8405	+	53.4173i	−1.00430	+	1.73951i
$944$	−0.205737	+	0.0748822i	−0.00669617	+	0.00243721i
$945$	2.27972	+	12.9289i	0.0741591	+	0.420577i
$946$	4.91993	−	27.9023i	0.159961	−	0.907182i
$947$	−0.388881	−	0.141541i	−0.0126369	−	0.00459946i	0.335694	−	0.941971i	$-0.391029\pi$
$947$	−0.388881	−	0.141541i	−0.0126369	−	0.00459946i	−0.348331	+	0.937372i	$0.613251\pi$
$948$	2.19459	−	1.84148i	0.0712771	−	0.0598086i
$949$	−0.549935			−0.0178516
$950$	7.55896	−	31.6968i	0.245245	−	1.02838i
$951$	−28.3969			−0.920833
$952$	−4.70574	+	3.94858i	−0.152514	+	0.127974i
$953$	−13.3678	−	4.86549i	−0.433027	−	0.157609i	0.116304	−	0.993214i	$-0.462895\pi$
$953$	−13.3678	−	4.86549i	−0.433027	−	0.157609i	−0.549331	+	0.835605i	$0.685117\pi$
$954$	1.03074	−	5.84564i	0.0333716	−	0.189260i
$955$	−11.0633	−	62.7431i	−0.358000	−	2.03032i
$956$	14.1138	−	5.13701i	0.456473	−	0.166143i
$957$	−0.319078	+	0.552659i	−0.0103143	+	0.0178649i
$958$	−6.83022	−	11.8303i	−0.220674	−	0.382219i
$959$	−1.34667	−	1.12999i	−0.0434862	−	0.0364892i
$960$	2.70574	+	2.27038i	0.0873273	+	0.0732763i
$961$	10.6309	+	18.4132i	0.342932	+	0.593975i
$962$	0.581252	−	1.00676i	0.0187403	−	0.0324592i
$963$	−7.59879	+	2.76573i	−0.244868	+	0.0891245i
$964$	−3.72534	−	21.1274i	−0.119985	−	0.680469i
$965$	10.6959	−	60.6597i	0.344314	−	1.95270i
$966$	30.3170	+	11.0345i	0.975434	+	0.355029i
$967$	−43.5376	+	36.5324i	−1.40008	+	1.17480i	−0.439009	+	0.898482i	$0.644671\pi$
$967$	−43.5376	+	36.5324i	−1.40008	+	1.17480i	−0.961066	+	0.276320i	$0.910885\pi$
$968$	16.9932			0.546182
$969$	5.78446	−	4.29385i	0.185824	−	0.137938i
$970$	−61.8221			−1.98499
$971$	−6.94356	+	5.82634i	−0.222830	+	0.186976i	−0.747368	−	0.664411i	$-0.768683\pi$
$971$	−6.94356	+	5.82634i	−0.222830	+	0.186976i	0.524538	+	0.851387i	$0.324238\pi$
$972$	0.939693	+	0.342020i	0.0301407	+	0.0109703i
$973$	−6.57357	+	37.2806i	−0.210739	+	1.19516i
$974$	−1.07280	−	6.08413i	−0.0343746	−	0.194948i
$975$	−1.59240	+	0.579585i	−0.0509975	+	0.0185616i
$976$	0.786989	−	1.36310i	0.0251909	−	0.0436319i
$977$	1.32635	+	2.29731i	0.0424338	+	0.0734974i	0.886462	−	0.462801i	$-0.153156\pi$
$977$	1.32635	+	2.29731i	0.0424338	+	0.0734974i	−0.844028	+	0.536298i	$0.819822\pi$
$978$	−3.01889	−	2.53315i	−0.0965333	−	0.0810011i
$979$	49.2674	+	41.3403i	1.57459	+	1.32124i
$980$	12.0360	+	20.8469i	0.384475	+	0.665930i
$981$	−7.62449	+	13.2060i	−0.243431	+	0.421635i
$982$	−3.85591	+	1.40344i	−0.123047	+	0.0447855i
$983$	−9.34183	−	52.9802i	−0.297958	−	1.68980i	−0.654930	−	0.755690i	$-0.727302\pi$
$983$	−9.34183	−	52.9802i	−0.297958	−	1.68980i	0.356972	−	0.934115i	$-0.383809\pi$
$984$	−1.23396	+	6.99811i	−0.0393371	+	0.223092i
$985$	−34.7863	−	12.6612i	−1.10838	−	0.403418i
$986$	−0.152704	+	0.128134i	−0.00486307	+	0.00408060i
$987$	9.32863			0.296934
$988$	0.442219	+	0.883600i	0.0140689	+	0.0281111i
$989$	−46.4820			−1.47804
$990$	14.3157	−	12.0123i	0.454982	−	0.381775i
$991$	−50.3598	−	18.3295i	−1.59973	−	0.582255i	−0.620360	−	0.784317i	$-0.713014\pi$
$991$	−50.3598	−	18.3295i	−1.59973	−	0.582255i	−0.979373	+	0.202062i	$0.935236\pi$
$992$	0.541889	−	3.07321i	0.0172050	−	0.0975744i
$993$	4.50134	+	25.5284i	0.142846	+	0.810119i
$994$	4.73277	−	1.72259i	0.150114	−	0.0546372i
$995$	−24.1129	+	41.7648i	−0.764431	+	1.32403i
$996$	0.960637	+	1.66387i	0.0304390	+	0.0527218i
$997$	13.8938	+	11.6583i	0.440020	+	0.369221i	0.835717	−	0.549160i	$-0.185052\pi$
$997$	13.8938	+	11.6583i	0.440020	+	0.369221i	−0.395697	+	0.918381i	$0.629497\pi$
$998$	20.3607	+	17.0847i	0.644507	+	0.540806i
$999$	2.56418	+	4.44129i	0.0811270	+	0.140516i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.i.c.25.1	✓	6
3.2	odd	2		342.2.u.b.253.1		6
4.3	odd	2		912.2.bo.d.481.1		6
19.4	even	9		2166.2.a.r.1.1		3
19.15	odd	18		2166.2.a.p.1.1		3
19.16	even	9	inner	114.2.i.c.73.1	yes	6
57.23	odd	18		6498.2.a.bp.1.3		3
57.35	odd	18		342.2.u.b.73.1		6
57.53	even	18		6498.2.a.bu.1.3		3
76.35	odd	18		912.2.bo.d.529.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.c.25.1	✓	6	1.1	even	1	trivial
114.2.i.c.73.1	yes	6	19.16	even	9	inner
342.2.u.b.73.1		6	57.35	odd	18
342.2.u.b.253.1		6	3.2	odd	2
912.2.bo.d.481.1		6	4.3	odd	2
912.2.bo.d.529.1		6	76.35	odd	18
2166.2.a.p.1.1		3	19.15	odd	18
2166.2.a.r.1.1		3	19.4	even	9
6498.2.a.bp.1.3		3	57.23	odd	18
6498.2.a.bu.1.3		3	57.53	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)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(0.939693 + 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.613341 - 3.47843i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-1.85844 + 3.21891i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(0.939693 + 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.613341 - 3.47843i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-1.85844 + 3.21891i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +(-2.70574 - 2.27038i) q^{10} +(2.64543 + 4.58202i) q^{11} +(0.500000 - 0.866025i) q^{12} +(0.213011 - 0.0775297i) q^{13} +(0.645430 + 3.66041i) q^{14} +(0.613341 - 3.47843i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-1.26604 + 1.06234i) q^{17} +1.00000 q^{18} +(-4.17752 + 1.24432i) q^{19} -3.53209 q^{20} +(-2.84730 + 2.38917i) q^{21} +(4.97178 + 1.80958i) q^{22} +(1.50727 - 8.54818i) q^{23} +(-0.173648 - 0.984808i) q^{24} +(-7.02481 + 2.55682i) q^{25} +(0.113341 - 0.196312i) q^{26} +(0.500000 + 0.866025i) q^{27} +(2.84730 + 2.38917i) q^{28} +(0.0923963 + 0.0775297i) q^{29} +(-1.76604 - 3.05888i) q^{30} +(-1.56031 + 2.70253i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.918748 + 5.21048i) q^{33} +(-0.286989 + 1.62760i) q^{34} +(12.3366 + 4.49016i) q^{35} +(0.766044 - 0.642788i) q^{36} +5.12836 q^{37} +(-2.40033 + 3.63846i) q^{38} +0.226682 q^{39} +(-2.70574 + 2.27038i) q^{40} +(-6.67752 - 2.43042i) q^{41} +(-0.645430 + 3.66041i) q^{42} +(-0.929892 - 5.27368i) q^{43} +(4.97178 - 1.80958i) q^{44} +(1.76604 - 3.05888i) q^{45} +(-4.34002 - 7.51714i) q^{46} +(-1.92262 - 1.61327i) q^{47} +(-0.766044 - 0.642788i) q^{48} +(-3.40760 - 5.90214i) q^{49} +(-3.73783 + 6.47410i) q^{50} +(-1.55303 + 0.565258i) q^{51} +(-0.0393628 - 0.223238i) q^{52} +(1.03074 - 5.84564i) q^{53} +(0.939693 + 0.342020i) q^{54} +(14.3157 - 12.0123i) q^{55} +3.71688 q^{56} +(-4.35117 - 0.259515i) q^{57} +0.120615 q^{58} +(0.167718 - 0.140732i) q^{59} +(-3.31908 - 1.20805i) q^{60} +(-0.273318 + 1.55007i) q^{61} +(0.541889 + 3.07321i) q^{62} +(-3.49273 + 1.27125i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.400330 - 0.693392i) q^{65} +(4.05303 + 3.40090i) q^{66} +(11.8589 + 9.95080i) q^{67} +(0.826352 + 1.43128i) q^{68} +(4.34002 - 7.51714i) q^{69} +(12.3366 - 4.49016i) q^{70} +(-0.235300 - 1.33445i) q^{71} +(0.173648 - 0.984808i) q^{72} +(-2.27972 - 0.829748i) q^{73} +(3.92855 - 3.29644i) q^{74} -7.47565 q^{75} +(0.500000 + 4.33013i) q^{76} -19.6655 q^{77} +(0.173648 - 0.145708i) q^{78} +(2.69207 + 0.979832i) q^{79} +(-0.613341 + 3.47843i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-6.67752 + 2.43042i) q^{82} +(-0.960637 + 1.66387i) q^{83} +(1.85844 + 3.21891i) q^{84} +(4.47178 + 3.75227i) q^{85} +(-4.10220 - 3.44215i) q^{86} +(0.0603074 + 0.104455i) q^{87} +(2.64543 - 4.58202i) q^{88} +(11.4226 - 4.15749i) q^{89} +(-0.613341 - 3.47843i) q^{90} +(-0.146307 + 0.829748i) q^{91} +(-8.15657 - 2.96875i) q^{92} +(-2.39053 + 2.00589i) q^{93} -2.50980 q^{94} +(6.89053 + 13.7680i) q^{95} -1.00000 q^{96} +(13.4081 - 11.2507i) q^{97} +(-6.40420 - 2.33094i) q^{98} +(-0.918748 + 5.21048i) 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	\( 6 q + 3 q^{5} - 3 q^{7} - 3 q^{8} - 6 q^{10} + 3 q^{12} + 9 q^{13} - 12 q^{14} - 3 q^{15} - 3 q^{17} + 6 q^{18} - 12 q^{20} - 15 q^{21} + 15 q^{22} + 27 q^{23} - 15 q^{25} - 6 q^{26} + 3 q^{27} + 15 q^{28} - 3 q^{29} - 6 q^{30} - 15 q^{31} + 3 q^{33} + 6 q^{34} + 12 q^{35} - 6 q^{37} - 12 q^{39} - 6 q^{40} - 15 q^{41} + 12 q^{42} + 3 q^{43} + 15 q^{44} + 6 q^{45} - 6 q^{46} + 15 q^{47} - 24 q^{49} - 3 q^{50} + 3 q^{51} - 9 q^{52} + 6 q^{53} + 27 q^{55} + 6 q^{56} + 12 q^{58} - 27 q^{59} - 3 q^{60} - 15 q^{61} - 3 q^{62} - 3 q^{63} - 3 q^{64} + 12 q^{65} + 12 q^{66} - 3 q^{67} + 6 q^{68} + 6 q^{69} + 12 q^{70} + 3 q^{71} + 12 q^{73} + 24 q^{74} - 6 q^{75} + 3 q^{76} - 42 q^{77} + 27 q^{79} + 3 q^{80} - 15 q^{82} + 3 q^{83} + 3 q^{84} + 12 q^{85} - 24 q^{86} + 6 q^{87} + 42 q^{89} + 3 q^{90} - 42 q^{91} - 27 q^{92} + 3 q^{93} - 18 q^{94} + 24 q^{95} - 6 q^{96} + 18 q^{97} - 3 q^{99}+O(q^{100}) \) 6 * q + 3 * q^5 - 3 * q^7 - 3 * q^8 - 6 * q^10 + 3 * q^12 + 9 * q^13 - 12 * q^14 - 3 * q^15 - 3 * q^17 + 6 * q^18 - 12 * q^20 - 15 * q^21 + 15 * q^22 + 27 * q^23 - 15 * q^25 - 6 * q^26 + 3 * q^27 + 15 * q^28 - 3 * q^29 - 6 * q^30 - 15 * q^31 + 3 * q^33 + 6 * q^34 + 12 * q^35 - 6 * q^37 - 12 * q^39 - 6 * q^40 - 15 * q^41 + 12 * q^42 + 3 * q^43 + 15 * q^44 + 6 * q^45 - 6 * q^46 + 15 * q^47 - 24 * q^49 - 3 * q^50 + 3 * q^51 - 9 * q^52 + 6 * q^53 + 27 * q^55 + 6 * q^56 + 12 * q^58 - 27 * q^59 - 3 * q^60 - 15 * q^61 - 3 * q^62 - 3 * q^63 - 3 * q^64 + 12 * q^65 + 12 * q^66 - 3 * q^67 + 6 * q^68 + 6 * q^69 + 12 * q^70 + 3 * q^71 + 12 * q^73 + 24 * q^74 - 6 * q^75 + 3 * q^76 - 42 * q^77 + 27 * q^79 + 3 * q^80 - 15 * q^82 + 3 * q^83 + 3 * q^84 + 12 * q^85 - 24 * q^86 + 6 * q^87 + 42 * q^89 + 3 * q^90 - 42 * q^91 - 27 * q^92 + 3 * q^93 - 18 * q^94 + 24 * q^95 - 6 * q^96 + 18 * q^97 - 3 * q^99

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