LMFDB - Embedded newform 114.2.i.c.55.1

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			55.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	114.55
Dual form			114.2.i.c.85.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 - 0.984808i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(2.20574 - 0.802823i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(-1.78699 - 3.09516i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +O(q^{10})$	\(q+(0.173648 - 0.984808i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(2.20574 - 0.802823i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(-1.78699 - 3.09516i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +(-0.407604 - 2.31164i) q^{10} +(-1.35844 + 2.35289i) q^{11} +(0.500000 + 0.866025i) q^{12} +(4.14543 - 3.47843i) q^{13} +(-3.35844 + 1.22237i) q^{14} +(-2.20574 - 0.802823i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-0.673648 + 3.82045i) q^{17} +1.00000 q^{18} +(1.01114 + 4.24000i) q^{19} -2.34730 q^{20} +(-0.620615 + 3.51968i) q^{21} +(2.08125 + 1.74638i) q^{22} +(7.73783 + 2.81634i) q^{23} +(0.939693 - 0.342020i) q^{24} +(0.390530 - 0.327693i) q^{25} +(-2.70574 - 4.68647i) q^{26} +(0.500000 - 0.866025i) q^{27} +(0.620615 + 3.51968i) q^{28} +(0.613341 + 3.47843i) q^{29} +(-1.17365 + 2.03282i) q^{30} +(-3.26604 - 5.65695i) q^{31} +(0.766044 - 0.642788i) q^{32} +(2.55303 - 0.929228i) q^{33} +(3.64543 + 1.32683i) q^{34} +(-6.42649 - 5.39246i) q^{35} +(0.173648 - 0.984808i) q^{36} +0.389185 q^{37} +(4.35117 - 0.259515i) q^{38} -5.41147 q^{39} +(-0.407604 + 2.31164i) q^{40} +(-1.48886 - 1.24930i) q^{41} +(3.35844 + 1.22237i) q^{42} +(-4.71941 + 1.71772i) q^{43} +(2.08125 - 1.74638i) q^{44} +(1.17365 + 2.03282i) q^{45} +(4.11721 - 7.13122i) q^{46} +(0.518418 + 2.94010i) q^{47} +(-0.173648 - 0.984808i) q^{48} +(-2.88666 + 4.99984i) q^{49} +(-0.254900 - 0.441500i) q^{50} +(2.97178 - 2.49362i) q^{51} +(-5.08512 + 1.85083i) q^{52} +(-7.80453 - 2.84062i) q^{53} +(-0.766044 - 0.642788i) q^{54} +(-1.10741 + 6.28044i) q^{55} +3.57398 q^{56} +(1.95084 - 3.89798i) q^{57} +3.53209 q^{58} +(0.474308 - 2.68993i) q^{59} +(1.79813 + 1.50881i) q^{60} +(-5.91147 - 2.15160i) q^{61} +(-6.13816 + 2.23411i) q^{62} +(2.73783 - 2.29731i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(6.35117 - 11.0005i) q^{65} +(-0.471782 - 2.67561i) q^{66} +(-2.59374 - 14.7098i) q^{67} +(1.93969 - 3.35965i) q^{68} +(-4.11721 - 7.13122i) q^{69} +(-6.42649 + 5.39246i) q^{70} +(-8.47818 + 3.08580i) q^{71} +(-0.939693 - 0.342020i) q^{72} +(7.88326 + 6.61484i) q^{73} +(0.0675813 - 0.383273i) q^{74} -0.509800 q^{75} +(0.500000 - 4.33013i) q^{76} +9.71007 q^{77} +(-0.939693 + 5.32926i) q^{78} +(9.96451 + 8.36121i) q^{79} +(2.20574 + 0.802823i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-1.48886 + 1.24930i) q^{82} +(4.08512 + 7.07564i) q^{83} +(1.78699 - 3.09516i) q^{84} +(1.58125 + 8.96773i) q^{85} +(0.872111 + 4.94599i) q^{86} +(1.76604 - 3.05888i) q^{87} +(-1.35844 - 2.35289i) q^{88} +(8.98158 - 7.53644i) q^{89} +(2.20574 - 0.802823i) q^{90} +(-18.1741 - 6.61484i) q^{91} +(-6.30793 - 5.29298i) q^{92} +(-1.13429 + 6.43285i) q^{93} +2.98545 q^{94} +(5.63429 + 8.54055i) q^{95} -1.00000 q^{96} +(-1.49407 + 8.47329i) q^{97} +(4.42262 + 3.71102i) q^{98} +(-2.55303 - 0.929228i) 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 $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$

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
$5$	2.20574	−	0.802823i	0.986436	−	0.359033i	0.202097	−	0.979366i	$-0.435225\pi$
$5$	2.20574	−	0.802823i	0.986436	−	0.359033i	0.784339	+	0.620332i	$0.213002\pi$
$6$	−0.766044	+	0.642788i	−0.312736	+	0.262417i
$7$	−1.78699	−	3.09516i	−0.675418	−	1.16986i	−0.976346	−	0.216212i	$-0.930630\pi$
$7$	−1.78699	−	3.09516i	−0.675418	−	1.16986i	0.300928	−	0.953647i	$-0.402704\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	0.173648	+	0.984808i	0.0578827	+	0.328269i
$10$	−0.407604	−	2.31164i	−0.128896	−	0.731003i
$11$	−1.35844	+	2.35289i	−0.409585	+	0.709423i	−0.994843	−	0.101425i	$-0.967660\pi$
$11$	−1.35844	+	2.35289i	−0.409585	+	0.709423i	0.585258	+	0.810847i	$0.300993\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	4.14543	−	3.47843i	1.14974	−	0.964742i	0.150022	−	0.988683i	$-0.452066\pi$
$13$	4.14543	−	3.47843i	1.14974	−	0.964742i	0.999713	+	0.0239402i	$0.00762112\pi$
$14$	−3.35844	+	1.22237i	−0.897581	+	0.326693i
$15$	−2.20574	−	0.802823i	−0.569519	−	0.207288i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−0.673648	+	3.82045i	−0.163384	+	0.926595i	0.787332	+	0.616530i	$0.211462\pi$
$17$	−0.673648	+	3.82045i	−0.163384	+	0.926595i	−0.950715	+	0.310065i	$0.899649\pi$
$18$	1.00000			0.235702
$19$	1.01114	+	4.24000i	0.231972	+	0.972722i
$19$	1.01114	+	4.24000i	0.231972	+	0.972722i
$20$	−2.34730			−0.524871
$21$	−0.620615	+	3.51968i	−0.135429	+	0.768057i
$22$	2.08125	+	1.74638i	0.443724	+	0.372329i
$23$	7.73783	+	2.81634i	1.61345	+	0.587247i	0.982118	−	0.188267i	$-0.0602870\pi$
$23$	7.73783	+	2.81634i	1.61345	+	0.587247i	0.631330	+	0.775514i	$0.282509\pi$
$24$	0.939693	−	0.342020i	0.191814	−	0.0698146i
$25$	0.390530	−	0.327693i	0.0781059	−	0.0655386i
$26$	−2.70574	−	4.68647i	−0.530639	−	0.919093i
$27$	0.500000	−	0.866025i	0.0962250	−	0.166667i
$28$	0.620615	+	3.51968i	0.117285	+	0.665157i
$29$	0.613341	+	3.47843i	0.113895	+	0.645928i	0.987292	+	0.158919i	$0.0508009\pi$
$29$	0.613341	+	3.47843i	0.113895	+	0.645928i	−0.873397	+	0.487009i	$0.838088\pi$
$30$	−1.17365	+	2.03282i	−0.214278	+	0.371140i
$31$	−3.26604	−	5.65695i	−0.586599	−	1.01602i	−0.994674	−	0.103071i	$-0.967133\pi$
$31$	−3.26604	−	5.65695i	−0.586599	−	1.01602i	0.408075	−	0.912948i	$-0.366200\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$	2.55303	−	0.929228i	0.444426	−	0.161758i
$34$	3.64543	+	1.32683i	0.625186	+	0.227549i
$35$	−6.42649	−	5.39246i	−1.08627	−	0.911493i
$36$	0.173648	−	0.984808i	0.0289414	−	0.164135i
$37$	0.389185			0.0639817			0.0319908	−	0.999488i	$-0.489815\pi$
$37$	0.389185			0.0639817			0.0319908	+	0.999488i	$0.489815\pi$
$38$	4.35117	−	0.259515i	0.705852	−	0.0420989i
$39$	−5.41147			−0.866529
$40$	−0.407604	+	2.31164i	−0.0644478	+	0.365502i
$41$	−1.48886	−	1.24930i	−0.232520	−	0.195108i	0.519082	−	0.854725i	$-0.326274\pi$
$41$	−1.48886	−	1.24930i	−0.232520	−	0.195108i	−0.751602	+	0.659617i	$0.770718\pi$
$42$	3.35844	+	1.22237i	0.518219	+	0.188616i
$43$	−4.71941	+	1.71772i	−0.719703	+	0.261950i	−0.675800	−	0.737085i	$-0.736202\pi$
$43$	−4.71941	+	1.71772i	−0.719703	+	0.261950i	−0.0439033	+	0.999036i	$0.513979\pi$
$44$	2.08125	−	1.74638i	0.313761	−	0.263276i
$45$	1.17365	+	2.03282i	0.174957	+	0.303035i
$46$	4.11721	−	7.13122i	0.607050	−	1.05144i
$47$	0.518418	+	2.94010i	0.0756191	+	0.428857i	0.998989	+	0.0449466i	$0.0143118\pi$
$47$	0.518418	+	2.94010i	0.0756191	+	0.428857i	−0.923370	+	0.383911i	$0.874577\pi$
$48$	−0.173648	−	0.984808i	−0.0250640	−	0.142145i
$49$	−2.88666	+	4.99984i	−0.412380	+	0.714263i
$50$	−0.254900	−	0.441500i	−0.0360483	−	0.0624375i
$51$	2.97178	−	2.49362i	0.416133	−	0.349177i
$52$	−5.08512	+	1.85083i	−0.705180	+	0.256664i
$53$	−7.80453	−	2.84062i	−1.07203	−	0.390189i	−0.255097	−	0.966915i	$-0.582108\pi$
$53$	−7.80453	−	2.84062i	−1.07203	−	0.390189i	−0.816937	+	0.576727i	$0.804330\pi$
$54$	−0.766044	−	0.642788i	−0.104245	−	0.0874723i
$55$	−1.10741	+	6.28044i	−0.149323	+	0.846854i
$56$	3.57398			0.477593
$57$	1.95084	−	3.89798i	0.258395	−	0.516300i
$58$	3.53209			0.463786
$59$	0.474308	−	2.68993i	0.0617496	−	0.350199i	−0.938241	−	0.345981i	$-0.887546\pi$
$59$	0.474308	−	2.68993i	0.0617496	−	0.350199i	0.999991	−	0.00421836i	$-0.00134275\pi$
$60$	1.79813	+	1.50881i	0.232138	+	0.194787i
$61$	−5.91147	−	2.15160i	−0.756887	−	0.275484i	−0.0653860	−	0.997860i	$-0.520828\pi$
$61$	−5.91147	−	2.15160i	−0.756887	−	0.275484i	−0.691501	+	0.722376i	$0.743050\pi$
$62$	−6.13816	+	2.23411i	−0.779547	+	0.283732i
$63$	2.73783	−	2.29731i	0.344934	−	0.289434i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	6.35117	−	11.0005i	0.787765	−	1.36445i
$66$	−0.471782	−	2.67561i	−0.0580723	−	0.329344i
$67$	−2.59374	−	14.7098i	−0.316876	−	1.79709i	−0.561503	−	0.827475i	$-0.689777\pi$
$67$	−2.59374	−	14.7098i	−0.316876	−	1.79709i	0.244627	−	0.969617i	$-0.421335\pi$
$68$	1.93969	−	3.35965i	0.235222	−	0.407417i
$69$	−4.11721	−	7.13122i	−0.495654	−	0.858498i
$70$	−6.42649	+	5.39246i	−0.768112	+	0.644523i
$71$	−8.47818	+	3.08580i	−1.00617	+	0.366218i	−0.791963	−	0.610570i	$-0.790941\pi$
$71$	−8.47818	+	3.08580i	−1.00617	+	0.366218i	−0.214212	+	0.976787i	$0.568718\pi$
$72$	−0.939693	−	0.342020i	−0.110744	−	0.0403075i
$73$	7.88326	+	6.61484i	0.922665	+	0.774208i	0.974486	−	0.224448i	$-0.0720580\pi$
$73$	7.88326	+	6.61484i	0.922665	+	0.774208i	−0.0518207	+	0.998656i	$0.516502\pi$
$74$	0.0675813	−	0.383273i	0.00785617	−	0.0445546i
$75$	−0.509800			−0.0588667
$76$	0.500000	−	4.33013i	0.0573539	−	0.496700i
$77$	9.71007			1.10657
$78$	−0.939693	+	5.32926i	−0.106399	+	0.603420i
$79$	9.96451	+	8.36121i	1.12109	+	0.940710i	0.998659	−	0.0517663i	$-0.0164851\pi$
$79$	9.96451	+	8.36121i	1.12109	+	0.940710i	0.122435	+	0.992476i	$0.460930\pi$
$80$	2.20574	+	0.802823i	0.246609	+	0.0897583i
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$	−1.48886	+	1.24930i	−0.164417	+	0.137962i
$83$	4.08512	+	7.07564i	0.448400	+	0.776652i	0.998282	−	0.0585902i	$-0.0186605\pi$
$83$	4.08512	+	7.07564i	0.448400	+	0.776652i	−0.549882	+	0.835243i	$0.685327\pi$
$84$	1.78699	−	3.09516i	0.194976	−	0.337709i
$85$	1.58125	+	8.96773i	0.171511	+	0.972686i
$86$	0.872111	+	4.94599i	0.0940422	+	0.533340i
$87$	1.76604	−	3.05888i	0.189340	−	0.327946i
$88$	−1.35844	−	2.35289i	−0.144810	−	0.250819i
$89$	8.98158	−	7.53644i	0.952046	−	0.798861i	−0.0275951	−	0.999619i	$-0.508785\pi$
$89$	8.98158	−	7.53644i	0.952046	−	0.798861i	0.979641	+	0.200758i	$0.0643405\pi$
$90$	2.20574	−	0.802823i	0.232505	−	0.0846249i
$91$	−18.1741	−	6.61484i	−1.90516	−	0.693423i
$92$	−6.30793	−	5.29298i	−0.657648	−	0.551832i
$93$	−1.13429	+	6.43285i	−0.117620	+	0.667056i
$94$	2.98545			0.307926
$95$	5.63429	+	8.54055i	0.578065	+	0.876242i
$96$	−1.00000			−0.102062
$97$	−1.49407	+	8.47329i	−0.151700	+	0.860333i	0.810041	+	0.586373i	$0.199445\pi$
$97$	−1.49407	+	8.47329i	−0.151700	+	0.860333i	−0.961741	+	0.273960i	$0.911666\pi$
$98$	4.42262	+	3.71102i	0.446752	+	0.374869i
$99$	−2.55303	−	0.929228i	−0.256590	−	0.0933909i
$100$	−0.479055	+	0.174362i	−0.0479055	+	0.0174362i
$101$	−0.984985	+	0.826501i	−0.0980097	+	0.0822399i	−0.690476	−	0.723355i	$-0.742599\pi$
$101$	−0.984985	+	0.826501i	−0.0980097	+	0.0822399i	0.592466	+	0.805595i	$0.298154\pi$
$102$	−1.93969	−	3.35965i	−0.192058	−	0.332655i
$103$	−0.368241	+	0.637812i	−0.0362839	+	0.0628455i	−0.883597	−	0.468248i	$-0.844885\pi$
$103$	−0.368241	+	0.637812i	−0.0362839	+	0.0628455i	0.847313	+	0.531094i	$0.178219\pi$
$104$	0.939693	+	5.32926i	0.0921444	+	0.522577i
$105$	1.45677	+	8.26173i	0.142166	+	0.806263i
$106$	−4.15270	+	7.19269i	−0.403346	+	0.698616i
$107$	−5.01367	−	8.68393i	−0.484690	−	0.839507i	0.515155	−	0.857097i	$-0.327734\pi$
$107$	−5.01367	−	8.68393i	−0.484690	−	0.839507i	−0.999845	+	0.0175893i	$0.994401\pi$
$108$	−0.766044	+	0.642788i	−0.0737127	+	0.0618523i
$109$	−13.0817	+	4.76136i	−1.25300	+	0.456055i	−0.881415	−	0.472343i	$-0.843408\pi$
$109$	−13.0817	+	4.76136i	−1.25300	+	0.456055i	−0.371587	+	0.928398i	$0.621186\pi$
$110$	5.99273	+	2.18117i	0.571384	+	0.207967i
$111$	−0.298133	−	0.250164i	−0.0282976	−	0.0237445i
$112$	0.620615	−	3.51968i	0.0586426	−	0.332579i
$113$	−0.226682			−0.0213244			−0.0106622	−	0.999943i	$-0.503394\pi$
$113$	−0.226682			−0.0213244			−0.0106622	+	0.999943i	$0.503394\pi$
$114$	−3.50000	−	2.59808i	−0.327805	−	0.243332i
$115$	19.3286			1.80240
$116$	0.613341	−	3.47843i	0.0569473	−	0.322964i
$117$	4.14543	+	3.47843i	0.383245	+	0.321581i
$118$	−2.56670	−	0.934204i	−0.236284	−	0.0860004i
$119$	13.0287	−	4.74205i	1.19434	−	0.434703i
$120$	1.79813	−	1.50881i	0.164146	−	0.137735i
$121$	1.80928	+	3.13376i	0.164480	+	0.284887i
$122$	−3.14543	+	5.44804i	−0.284774	+	0.493243i
$123$	0.337496	+	1.91404i	0.0304310	+	0.172583i
$124$	1.13429	+	6.43285i	0.101862	+	0.577687i
$125$	−5.26991	+	9.12776i	−0.471356	+	0.816412i
$126$	−1.78699	−	3.09516i	−0.159198	−	0.275738i
$127$	6.66044	−	5.58878i	0.591019	−	0.495924i	−0.297526	−	0.954714i	$-0.596161\pi$
$127$	6.66044	−	5.58878i	0.591019	−	0.495924i	0.888545	+	0.458790i	$0.151717\pi$
$128$	−0.939693	+	0.342020i	−0.0830579	+	0.0302306i
$129$	4.71941	+	1.71772i	0.415521	+	0.151237i
$130$	−9.73055	−	8.16490i	−0.853426	−	0.716109i
$131$	−2.19547	+	12.4511i	−0.191819	+	1.08786i	0.725057	+	0.688689i	$0.241813\pi$
$131$	−2.19547	+	12.4511i	−0.191819	+	1.08786i	−0.916876	+	0.399172i	$0.869298\pi$
$132$	−2.71688			−0.236474
$133$	11.3166	−	10.7065i	0.981269	−	0.928370i
$134$	−14.9368			−1.29034
$135$	0.407604	−	2.31164i	0.0350809	−	0.198954i
$136$	−2.97178	−	2.49362i	−0.254828	−	0.213826i
$137$	−20.4795	−	7.45394i	−1.74968	−	0.636833i	−0.749987	−	0.661453i	$-0.769940\pi$
$137$	−20.4795	−	7.45394i	−1.74968	−	0.636833i	−0.999697	+	0.0246200i	$0.992162\pi$
$138$	−7.73783	+	2.81634i	−0.658687	+	0.239743i
$139$	−8.60014	+	7.21637i	−0.729454	+	0.612085i	−0.929983	−	0.367603i	$-0.880178\pi$
$139$	−8.60014	+	7.21637i	−0.729454	+	0.612085i	0.200529	+	0.979688i	$0.435734\pi$
$140$	4.19459	+	7.26525i	0.354508	+	0.614025i
$141$	1.49273	−	2.58548i	0.125710	−	0.217736i
$142$	1.56670	+	8.88522i	0.131475	+	0.745631i
$143$	2.55303	+	14.4790i	0.213495	+	1.21079i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	4.14543	+	7.18009i	0.344259	+	0.596274i
$146$	7.88326	−	6.61484i	0.652423	−	0.547448i
$147$	5.42514	−	1.97459i	0.447458	−	0.162862i
$148$	−0.365715	−	0.133109i	−0.0300616	−	0.0109415i
$149$	−16.8366	−	14.1276i	−1.37931	−	1.15738i	−0.969467	−	0.245222i	$-0.921139\pi$
$149$	−16.8366	−	14.1276i	−1.37931	−	1.15738i	−0.409843	−	0.912156i	$-0.634416\pi$
$150$	−0.0885259	+	0.502055i	−0.00722811	+	0.0409926i
$151$	2.36184			0.192204			0.0961021	−	0.995371i	$-0.469362\pi$
$151$	2.36184			0.192204			0.0961021	+	0.995371i	$0.469362\pi$
$152$	−4.17752	−	1.24432i	−0.338841	−	0.100928i
$153$	−3.87939			−0.313630
$154$	1.68614	−	9.56256i	0.135873	−	0.770573i
$155$	−11.7456	−	9.85570i	−0.943427	−	0.791629i
$156$	5.08512	+	1.85083i	0.407136	+	0.148185i
$157$	13.4893	−	4.90971i	1.07657	−	0.391838i	0.257937	−	0.966162i	$-0.416957\pi$
$157$	13.4893	−	4.90971i	1.07657	−	0.391838i	0.818628	+	0.574324i	$0.194735\pi$
$158$	9.96451	−	8.36121i	0.792734	−	0.665183i
$159$	4.15270	+	7.19269i	0.329331	+	0.570418i
$160$	1.17365	−	2.03282i	0.0927850	−	0.160708i
$161$	−5.11040	−	28.9825i	−0.402756	−	2.28414i
$162$	0.173648	+	0.984808i	0.0136431	+	0.0773738i
$163$	8.57057	−	14.8447i	0.671299	−	1.16272i	−0.306237	−	0.951955i	$-0.599070\pi$
$163$	8.57057	−	14.8447i	0.671299	−	1.16272i	0.977536	−	0.210769i	$-0.0675968\pi$
$164$	0.971782	+	1.68317i	0.0758834	+	0.131434i
$165$	4.88532	−	4.09927i	0.380321	−	0.319127i
$166$	7.67752	−	2.79439i	0.595891	−	0.216887i
$167$	13.7369	+	4.99984i	1.06300	+	0.386899i	0.813553	−	0.581490i	$-0.197530\pi$
$167$	13.7369	+	4.99984i	1.06300	+	0.386899i	0.249444	+	0.968389i	$0.419752\pi$
$168$	−2.73783	−	2.29731i	−0.211228	−	0.177241i
$169$	2.82770	−	16.0367i	0.217515	−	1.23359i
$170$	9.10607			0.698403
$171$	−4.00000	+	1.73205i	−0.305888	+	0.132453i
$172$	5.02229			0.382946
$173$	−3.58899	+	20.3542i	−0.272866	+	1.54750i	0.472794	+	0.881173i	$0.343246\pi$
$173$	−3.58899	+	20.3542i	−0.272866	+	1.54750i	−0.745660	+	0.666327i	$0.767865\pi$
$174$	−2.70574	−	2.27038i	−0.205121	−	0.172117i
$175$	−1.71213	−	0.623166i	−0.129425	−	0.0471069i
$176$	−2.55303	+	0.929228i	−0.192442	+	0.0700432i
$177$	−2.09240	+	1.75573i	−0.157274	+	0.131969i
$178$	−5.86231	−	10.1538i	−0.439399	−	0.761061i
$179$	−2.84730	+	4.93166i	−0.212817	+	0.368610i	−0.952595	−	0.304241i	$-0.901597\pi$
$179$	−2.84730	+	4.93166i	−0.212817	+	0.368610i	0.739778	+	0.672851i	$0.234930\pi$
$180$	−0.407604	−	2.31164i	−0.0303810	−	0.172299i
$181$	−3.85844	−	21.8823i	−0.286796	−	1.62650i	−0.698800	−	0.715317i	$-0.746282\pi$
$181$	−3.85844	−	21.8823i	−0.286796	−	1.62650i	0.412004	−	0.911182i	$-0.364829\pi$
$182$	−9.67024	+	16.7494i	−0.716806	+	1.24154i
$183$	3.14543	+	5.44804i	0.232517	+	0.402731i
$184$	−6.30793	+	5.29298i	−0.465027	+	0.390204i
$185$	0.858441	−	0.312447i	0.0631138	−	0.0229716i
$186$	6.13816	+	2.23411i	0.450071	+	0.163813i
$187$	−8.07398	−	6.77487i	−0.590428	−	0.495428i
$188$	0.518418	−	2.94010i	0.0378095	−	0.214429i
$189$	−3.57398			−0.259969
$190$	9.38919	−	4.06564i	0.681163	−	0.294952i
$191$	6.04694			0.437541			0.218771	−	0.975776i	$-0.429795\pi$
$191$	6.04694			0.437541			0.218771	+	0.975776i	$0.429795\pi$
$192$	−0.173648	+	0.984808i	−0.0125320	+	0.0710724i
$193$	4.82501	+	4.04866i	0.347312	+	0.291429i	0.799709	−	0.600387i	$-0.204987\pi$
$193$	4.82501	+	4.04866i	0.347312	+	0.291429i	−0.452398	+	0.891816i	$0.649431\pi$
$194$	8.08512	+	2.94274i	0.580478	+	0.211277i
$195$	−11.9363	+	4.34445i	−0.854775	+	0.311113i
$196$	4.42262	−	3.71102i	0.315901	−	0.265073i
$197$	−9.96838	−	17.2657i	−0.710218	−	1.23013i	−0.964775	−	0.263075i	$-0.915263\pi$
$197$	−9.96838	−	17.2657i	−0.710218	−	1.23013i	0.254558	−	0.967058i	$-0.418070\pi$
$198$	−1.35844	+	2.35289i	−0.0965402	+	0.167212i
$199$	2.23695	+	12.6864i	0.158573	+	0.899313i	0.955446	+	0.295166i	$0.0953749\pi$
$199$	2.23695	+	12.6864i	0.158573	+	0.899313i	−0.796873	+	0.604147i	$0.793514\pi$
$200$	0.0885259	+	0.502055i	0.00625972	+	0.0355007i
$201$	−7.46838	+	12.9356i	−0.526779	+	0.912408i
$202$	0.642903	+	1.11354i	0.0452345	+	0.0783485i
$203$	9.67024	−	8.11430i	0.678718	−	0.569512i
$204$	−3.64543	+	1.32683i	−0.255231	+	0.0928965i
$205$	−4.28699	−	1.56034i	−0.299416	−	0.108979i
$206$	0.564178	+	0.473401i	0.0393081	+	0.0329834i
$207$	−1.42989	+	8.10932i	−0.0993844	+	0.563637i
$208$	5.41147			0.375218
$209$	−11.3498	−	3.38068i	−0.785084	−	0.233846i
$210$	8.38919			0.578909
$211$	0.401674	−	2.27801i	0.0276524	−	0.156824i	−0.967855	−	0.251509i	$-0.919073\pi$
$211$	0.401674	−	2.27801i	0.0276524	−	0.156824i	0.995507	+	0.0946847i	$0.0301843\pi$
$212$	6.36231	+	5.33861i	0.436965	+	0.366657i
$213$	8.47818	+	3.08580i	0.580915	+	0.211436i
$214$	−9.42262	+	3.42955i	−0.644117	+	0.234439i
$215$	−9.03074	+	7.57769i	−0.615892	+	0.516794i
$216$	0.500000	+	0.866025i	0.0340207	+	0.0589256i
$217$	−11.6728	+	20.2178i	−0.792399	+	1.37248i
$218$	2.41740	+	13.7098i	0.163727	+	0.928543i
$219$	−1.78699	−	10.1345i	−0.120754	−	0.684827i
$220$	3.18866	−	5.52293i	0.214980	−	0.372356i
$221$	10.4966	+	18.1806i	0.706077	+	1.22296i
$222$	−0.298133	+	0.250164i	−0.0200094	+	0.0167899i
$223$	−3.82547	+	1.39236i	−0.256173	+	0.0932392i	−0.466914	−	0.884303i	$-0.654634\pi$
$223$	−3.82547	+	1.39236i	−0.256173	+	0.0932392i	0.210742	+	0.977542i	$0.432412\pi$
$224$	−3.35844	−	1.22237i	−0.224395	−	0.0816732i
$225$	0.390530	+	0.327693i	0.0260353	+	0.0218462i
$226$	−0.0393628	+	0.223238i	−0.00261838	+	0.0148496i
$227$	−0.440570			−0.0292417			−0.0146208	−	0.999893i	$-0.504654\pi$
$227$	−0.440570			−0.0292417			−0.0146208	+	0.999893i	$0.504654\pi$
$228$	−3.16637	+	2.99568i	−0.209698	+	0.198393i
$229$	−3.38919			−0.223964			−0.111982	−	0.993710i	$-0.535720\pi$
$229$	−3.38919			−0.223964			−0.111982	+	0.993710i	$0.535720\pi$
$230$	3.35638	−	19.0350i	0.221313	−	1.25513i
$231$	−7.43835	−	6.24152i	−0.489407	−	0.410662i
$232$	−3.31908	−	1.20805i	−0.217908	−	0.0793121i
$233$	−1.98633	+	0.722965i	−0.130129	+	0.0473630i	−0.406264	−	0.913756i	$-0.633169\pi$
$233$	−1.98633	+	0.722965i	−0.130129	+	0.0473630i	0.276135	+	0.961119i	$0.410946\pi$
$234$	4.14543	−	3.47843i	0.270995	−	0.227392i
$235$	3.50387	+	6.06888i	0.228567	+	0.395890i
$236$	−1.36571	+	2.36549i	−0.0889005	+	0.153980i
$237$	−2.25877	−	12.8101i	−0.146723	−	0.832107i
$238$	−2.40760	−	13.6542i	−0.156062	−	0.885070i
$239$	2.01455	−	3.48930i	0.130310	−	0.225704i	−0.793486	−	0.608589i	$-0.791736\pi$
$239$	2.01455	−	3.48930i	0.130310	−	0.225704i	0.923796	+	0.382885i	$0.125069\pi$
$240$	−1.17365	−	2.03282i	−0.0757587	−	0.131218i
$241$	−7.79607	+	6.54168i	−0.502189	+	0.421387i	−0.858371	−	0.513030i	$-0.828523\pi$
$241$	−7.79607	+	6.54168i	−0.502189	+	0.421387i	0.356181	+	0.934417i	$0.384079\pi$
$242$	3.40033	−	1.23762i	0.218581	−	0.0795572i
$243$	0.939693	+	0.342020i	0.0602813	+	0.0219406i
$244$	4.81908	+	4.04369i	0.308510	+	0.258870i
$245$	−2.35323	+	13.3458i	−0.150342	+	0.852632i
$246$	1.94356			0.123917
$247$	18.9402	+	14.0594i	1.20513	+	0.894580i
$248$	6.53209			0.414788
$249$	1.41875	−	8.04612i	0.0899095	−	0.509902i
$250$	8.07398	+	6.77487i	0.510643	+	0.428481i
$251$	−2.73396	−	0.995078i	−0.172566	−	0.0628088i	0.254292	−	0.967127i	$-0.418157\pi$
$251$	−2.73396	−	0.995078i	−0.172566	−	0.0628088i	−0.426858	+	0.904319i	$0.640380\pi$
$252$	−3.35844	+	1.22237i	−0.211562	+	0.0770022i
$253$	−17.1379	+	14.3804i	−1.07745	+	0.904089i
$254$	−4.34730	−	7.52974i	−0.272774	−	0.472458i
$255$	4.55303	−	7.88609i	0.285122	−	0.493846i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−0.444440	−	2.52055i	−0.0277234	−	0.157227i	0.967803	−	0.251708i	$-0.0809922\pi$
$257$	−0.444440	−	2.52055i	−0.0277234	−	0.157227i	−0.995527	+	0.0944803i	$0.969881\pi$
$258$	2.51114	−	4.34943i	0.156337	−	0.270784i
$259$	−0.695470	−	1.20459i	−0.0432144	−	0.0748495i
$260$	−9.73055	+	8.16490i	−0.603463	+	0.506366i
$261$	−3.31908	+	1.20805i	−0.205446	+	0.0747761i
$262$	11.8807	+	4.32423i	0.733994	+	0.267152i
$263$	12.2023	+	10.2390i	0.752428	+	0.631362i	0.936144	−	0.351617i	$-0.114368\pi$
$263$	12.2023	+	10.2390i	0.752428	+	0.631362i	−0.183716	+	0.982979i	$0.558813\pi$
$264$	−0.471782	+	2.67561i	−0.0290361	+	0.164672i
$265$	−19.4953			−1.19758
$266$	−8.57873	−	13.0038i	−0.525995	−	0.797313i
$267$	−11.7246			−0.717535
$268$	−2.59374	+	14.7098i	−0.158438	+	0.898546i
$269$	12.9422	+	10.8598i	0.789101	+	0.662134i	0.945523	−	0.325556i	$-0.105551\pi$
$269$	12.9422	+	10.8598i	0.789101	+	0.662134i	−0.156422	+	0.987690i	$0.549996\pi$
$270$	−2.20574	−	0.802823i	−0.134237	−	0.0488582i
$271$	0.585122	−	0.212967i	0.0355436	−	0.0129368i	−0.324187	−	0.945993i	$-0.605091\pi$
$271$	0.585122	−	0.212967i	0.0355436	−	0.0129368i	0.359731	+	0.933056i	$0.382869\pi$
$272$	−2.97178	+	2.49362i	−0.180191	+	0.151198i
$273$	9.67024	+	16.7494i	0.585270	+	1.01372i
$274$	−10.8969	+	18.8740i	−0.658307	+	1.14022i
$275$	0.240514	+	1.36402i	0.0145036	+	0.0822538i
$276$	1.42989	+	8.10932i	0.0860694	+	0.488124i
$277$	13.7383	−	23.7954i	0.825454	−	1.42973i	−0.0761178	−	0.997099i	$-0.524253\pi$
$277$	13.7383	−	23.7954i	0.825454	−	1.42973i	0.901572	−	0.432629i	$-0.142414\pi$
$278$	5.61334	+	9.72259i	0.336666	+	0.583122i
$279$	5.00387	−	4.19875i	0.299574	−	0.251372i
$280$	7.88326	−	2.86927i	0.471115	−	0.171472i
$281$	2.33110	+	0.848451i	0.139062	+	0.0506143i	0.410613	−	0.911810i	$-0.365315\pi$
$281$	2.33110	+	0.848451i	0.139062	+	0.0506143i	−0.271552	+	0.962424i	$0.587537\pi$
$282$	−2.28699	−	1.91901i	−0.136188	−	0.114275i
$283$	0.396459	−	2.24843i	0.0235671	−	0.133655i	−0.970754	−	0.240076i	$-0.922828\pi$
$283$	0.396459	−	2.24843i	0.0235671	−	0.133655i	0.994321	+	0.106420i	$0.0339389\pi$
$284$	9.02229			0.535374
$285$	1.17365	−	10.1641i	0.0695209	−	0.602069i
$286$	14.7023			0.869367
$287$	−1.20620	+	6.84072i	−0.0712000	+	0.403795i
$288$	0.766044	+	0.642788i	0.0451396	+	0.0378766i
$289$	1.83275	+	0.667066i	0.107809	+	0.0392392i
$290$	7.79086	−	2.83564i	0.457495	−	0.166515i
$291$	6.59105	−	5.53055i	0.386374	−	0.324207i
$292$	−5.14543	−	8.91215i	−0.301113	−	0.521544i
$293$	1.19800	−	2.07499i	0.0699877	−	0.121222i	−0.828908	−	0.559385i	$-0.811037\pi$
$293$	1.19800	−	2.07499i	0.0699877	−	0.121222i	0.898896	+	0.438163i	$0.144371\pi$
$294$	−1.00253	−	5.68561i	−0.0584685	−	0.331591i
$295$	−1.11334	−	6.31407i	−0.0648212	−	0.367619i
$296$	−0.194593	+	0.337044i	−0.0113105	+	0.0195903i
$297$	1.35844	+	2.35289i	0.0788247	+	0.136528i
$298$	−16.8366	+	14.1276i	−0.975319	+	0.818390i
$299$	41.8730	−	15.2405i	2.42158	−	0.881383i
$300$	0.479055	+	0.174362i	0.0276583	+	0.0100668i
$301$	13.7502	+	11.5377i	0.792546	+	0.665025i
$302$	0.410130	−	2.32596i	0.0236003	−	0.133844i
$303$	1.28581			0.0738677
$304$	−1.95084	+	3.89798i	−0.111888	+	0.223564i
$305$	−14.7665			−0.845528
$306$	−0.673648	+	3.82045i	−0.0385099	+	0.218401i
$307$	−4.00908	−	3.36402i	−0.228811	−	0.191995i	0.521174	−	0.853451i	$-0.325494\pi$
$307$	−4.00908	−	3.36402i	−0.228811	−	0.191995i	−0.749984	+	0.661456i	$0.769939\pi$
$308$	−9.12449	−	3.32104i	−0.519916	−	0.189234i
$309$	0.692066	−	0.251892i	0.0393703	−	0.0143296i
$310$	−11.7456	+	9.85570i	−0.667103	+	0.559766i
$311$	5.49660	+	9.52038i	0.311683	+	0.539851i	0.978727	−	0.205167i	$-0.0657738\pi$
$311$	5.49660	+	9.52038i	0.311683	+	0.539851i	−0.667044	+	0.745019i	$0.732441\pi$
$312$	2.70574	−	4.68647i	0.153182	−	0.265319i
$313$	−5.28787	−	29.9890i	−0.298888	−	1.69508i	−0.650966	−	0.759107i	$-0.725636\pi$
$313$	−5.28787	−	29.9890i	−0.298888	−	1.69508i	0.352078	−	0.935971i	$-0.385475\pi$
$314$	−2.49273	−	14.1370i	−0.140673	−	0.797794i
$315$	4.19459	−	7.26525i	0.236339	−	0.409350i
$316$	−6.50387	−	11.2650i	−0.365871	−	0.633708i
$317$	8.68660	−	7.28893i	0.487888	−	0.409387i	−0.365381	−	0.930858i	$-0.619061\pi$
$317$	8.68660	−	7.28893i	0.487888	−	0.409387i	0.853269	+	0.521471i	$0.174617\pi$
$318$	7.80453	−	2.84062i	0.437656	−	0.159294i
$319$	−9.01754	−	3.28212i	−0.504885	−	0.183763i
$320$	−1.79813	−	1.50881i	−0.100519	−	0.0843452i
$321$	−1.74123	+	9.87500i	−0.0971860	+	0.551169i
$322$	−29.4296			−1.64005
$323$	−16.8799	+	1.00676i	−0.939220	+	0.0560175i
$324$	1.00000			0.0555556
$325$	0.479055	−	2.71686i	0.0265732	−	0.150704i
$326$	−13.1309	−	11.0181i	−0.727252	−	0.610237i
$327$	13.0817	+	4.76136i	0.723421	+	0.263304i
$328$	1.82635	−	0.664738i	0.100843	−	0.0367040i
$329$	8.17365	−	6.85851i	0.450628	−	0.378122i
$330$	−3.18866	−	5.52293i	−0.175530	−	0.304027i
$331$	−6.46585	+	11.1992i	−0.355395	+	0.615563i	−0.987186	−	0.159577i	$-0.948987\pi$
$331$	−6.46585	+	11.1992i	−0.355395	+	0.615563i	0.631790	+	0.775139i	$0.282320\pi$
$332$	−1.41875	−	8.04612i	−0.0778639	−	0.441588i
$333$	0.0675813	+	0.383273i	0.00370343	+	0.0210032i
$334$	7.30928	−	12.6600i	0.399946	−	0.692727i
$335$	−17.5305	−	30.3637i	−0.957793	−	1.65895i
$336$	−2.73783	+	2.29731i	−0.149361	+	0.125328i
$337$	−10.0988	+	3.67566i	−0.550116	+	0.200226i	−0.602098	−	0.798422i	$-0.705668\pi$
$337$	−10.0988	+	3.67566i	−0.550116	+	0.200226i	0.0519819	+	0.998648i	$0.483446\pi$
$338$	−15.3020	−	5.56947i	−0.832319	−	0.302939i
$339$	0.173648	+	0.145708i	0.00943127	+	0.00791378i
$340$	1.58125	−	8.96773i	0.0857554	−	0.486343i
$341$	17.7469			0.961049
$342$	1.01114	+	4.24000i	0.0546764	+	0.229273i
$343$	−4.38413			−0.236721
$344$	0.872111	−	4.94599i	0.0470211	−	0.266670i
$345$	−14.8066	−	12.4242i	−0.797160	−	0.668897i
$346$	19.4217	+	7.06894i	1.04412	+	0.380028i
$347$	−21.4281	+	7.79920i	−1.15032	+	0.418683i	−0.845631	−	0.533768i	$-0.820776\pi$
$347$	−21.4281	+	7.79920i	−1.15032	+	0.418683i	−0.304692	+	0.952451i	$0.598553\pi$
$348$	−2.70574	+	2.27038i	−0.145043	+	0.121705i
$349$	12.6814	+	21.9648i	0.678819	+	1.17575i	0.975337	+	0.220722i	$0.0708413\pi$
$349$	12.6814	+	21.9648i	0.678819	+	1.17575i	−0.296518	+	0.955027i	$0.595825\pi$
$350$	−0.911007	+	1.57791i	−0.0486954	+	0.0843429i
$351$	−0.939693	−	5.32926i	−0.0501571	−	0.284455i
$352$	0.471782	+	2.67561i	0.0251460	+	0.142610i
$353$	6.09627	−	10.5590i	0.324472	−	0.562001i	−0.656934	−	0.753948i	$-0.728147\pi$
$353$	6.09627	−	10.5590i	0.324472	−	0.562001i	0.981405	+	0.191947i	$0.0614802\pi$
$354$	1.36571	+	2.36549i	0.0725869	+	0.125724i
$355$	−16.2233	+	13.6129i	−0.861042	+	0.722500i
$356$	−11.0175	+	4.01006i	−0.583929	+	0.212533i
$357$	−13.0287	−	4.74205i	−0.689551	−	0.250976i
$358$	4.36231	+	3.66041i	0.230555	+	0.193459i
$359$	5.06418	−	28.7204i	0.267277	−	1.51580i	−0.495195	−	0.868782i	$-0.664903\pi$
$359$	5.06418	−	28.7204i	0.267277	−	1.51580i	0.762472	−	0.647022i	$-0.223986\pi$
$360$	−2.34730			−0.123713
$361$	−16.9552	+	8.57450i	−0.892378	+	0.451290i
$362$	−22.2199			−1.16785
$363$	0.628356	−	3.56358i	0.0329801	−	0.187040i
$364$	14.8157	+	12.4318i	0.776552	+	0.651605i
$365$	22.6989	+	8.26173i	1.18812	+	0.432439i
$366$	5.91147	−	2.15160i	0.308998	−	0.112466i
$367$	10.7187	−	8.99405i	0.559511	−	0.469486i	−0.318635	−	0.947877i	$-0.603225\pi$
$367$	10.7187	−	8.99405i	0.559511	−	0.469486i	0.878147	+	0.478392i	$0.158780\pi$
$368$	4.11721	+	7.13122i	0.214624	+	0.371740i
$369$	0.971782	−	1.68317i	0.0505889	−	0.0876226i
$370$	−0.158633	−	0.899655i	−0.00824696	−	0.0467708i
$371$	5.15446	+	29.2324i	0.267606	+	1.51767i
$372$	3.26604	−	5.65695i	0.169337	−	0.293299i
$373$	3.41013	+	5.90652i	0.176570	+	0.305828i	0.940703	−	0.339230i	$-0.110167\pi$
$373$	3.41013	+	5.90652i	0.176570	+	0.305828i	−0.764134	+	0.645058i	$0.776833\pi$
$374$	−8.07398	+	6.77487i	−0.417495	+	0.350320i
$375$	9.90420	−	3.60483i	0.511451	−	0.186153i
$376$	−2.80541	−	1.02108i	−0.144678	−	0.0526584i
$377$	14.6420	+	12.2861i	0.754103	+	0.632767i
$378$	−0.620615	+	3.51968i	−0.0319210	+	0.181033i
$379$	31.9341			1.64034			0.820171	−	0.572118i	$-0.193878\pi$
$379$	31.9341			1.64034			0.820171	+	0.572118i	$0.193878\pi$
$380$	−2.37346	−	9.95253i	−0.121756	−	0.510554i
$381$	−8.69459			−0.445437
$382$	1.05004	−	5.95507i	0.0537247	−	0.304688i
$383$	−28.2049	−	23.6667i	−1.44120	−	1.20931i	−0.938700	−	0.344734i	$-0.887969\pi$
$383$	−28.2049	−	23.6667i	−1.44120	−	1.20931i	−0.502501	−	0.864577i	$-0.667587\pi$
$384$	0.939693	+	0.342020i	0.0479535	+	0.0174536i
$385$	21.4179	−	7.79547i	1.09156	−	0.397294i
$386$	4.82501	−	4.04866i	0.245586	−	0.206071i
$387$	−2.51114	−	4.34943i	−0.127649	−	0.221094i
$388$	4.30200	−	7.45129i	0.218401	−	0.378282i
$389$	−0.582596	−	3.30407i	−0.0295388	−	0.167523i	0.966470	−	0.256780i	$-0.0826617\pi$
$389$	−0.582596	−	3.30407i	−0.0295388	−	0.167523i	−0.996009	+	0.0892575i	$0.971551\pi$
$390$	2.20574	+	12.5094i	0.111692	+	0.633436i
$391$	−15.9722	+	27.6647i	−0.807751	+	1.39907i
$392$	−2.88666	−	4.99984i	−0.145798	−	0.252530i
$393$	9.68526	−	8.12690i	0.488557	−	0.409948i
$394$	−18.7344	+	6.81877i	−0.943827	+	0.343525i
$395$	28.6917	+	10.4429i	1.44363	+	0.525440i
$396$	2.08125	+	1.74638i	0.104587	+	0.0877588i
$397$	1.19547	−	6.77985i	0.0599989	−	0.340271i	−0.940001	−	0.341173i	$-0.889176\pi$
$397$	1.19547	−	6.77985i	0.0599989	−	0.340271i	1.00000		0.000901796i	$0.000287051\pi$
$398$	12.8821			0.645720
$399$	−15.5510	+	0.927500i	−0.778522	+	0.0464331i
$400$	0.509800			0.0254900
$401$	−0.873455	+	4.95361i	−0.0436183	+	0.247372i	−0.998819	−	0.0485874i	$-0.984528\pi$
$401$	−0.873455	+	4.95361i	−0.0436183	+	0.247372i	0.955201	+	0.295959i	$0.0956392\pi$
$402$	11.4422	+	9.60116i	0.570686	+	0.478862i
$403$	−33.2165	−	12.0898i	−1.65463	−	0.602236i
$404$	1.20826	−	0.439772i	0.0601133	−	0.0218795i
$405$	−1.79813	+	1.50881i	−0.0893500	+	0.0749735i
$406$	−6.31180	−	10.9324i	−0.313250	−	0.542564i
$407$	−0.528685	+	0.915710i	−0.0262060	+	0.0453901i
$408$	0.673648	+	3.82045i	0.0333506	+	0.189140i
$409$	−1.80747	−	10.2507i	−0.0893735	−	0.506862i	−0.996327	−	0.0856312i	$-0.972709\pi$
$409$	−1.80747	−	10.2507i	−0.0893735	−	0.506862i	0.906953	−	0.421231i	$-0.138402\pi$
$410$	−2.28106	+	3.95091i	−0.112653	+	0.195122i
$411$	10.8969	+	18.8740i	0.537506	+	0.930987i
$412$	0.564178	−	0.473401i	0.0277950	−	0.0233228i
$413$	−9.17334	+	3.33882i	−0.451391	+	0.164293i
$414$	7.73783	+	2.81634i	0.380293	+	0.138415i
$415$	14.6912	+	12.3274i	0.721162	+	0.605127i
$416$	0.939693	−	5.32926i	0.0460722	−	0.261289i
$417$	11.2267			0.549773
$418$	−5.30019	+	10.5903i	−0.259241	+	0.517991i
$419$	−6.22256			−0.303992			−0.151996	−	0.988381i	$-0.548570\pi$
$419$	−6.22256			−0.303992			−0.151996	+	0.988381i	$0.548570\pi$
$420$	1.45677	−	8.26173i	0.0710829	−	0.403131i
$421$	−20.3917	−	17.1107i	−0.993831	−	0.833923i	−0.00771335	−	0.999970i	$-0.502455\pi$
$421$	−20.3917	−	17.1107i	−0.993831	−	0.833923i	−0.986118	+	0.166047i	$0.946900\pi$
$422$	−2.17365	−	0.791143i	−0.105812	−	0.0385123i
$423$	−2.80541	+	1.02108i	−0.136404	+	0.0496468i
$424$	6.36231	−	5.33861i	0.308981	−	0.259266i
$425$	0.988856	+	1.71275i	0.0479665	+	0.0830805i
$426$	4.51114	−	7.81353i	0.218566	−	0.378567i
$427$	3.90420	+	22.1418i	0.188937	+	1.07152i
$428$	1.74123	+	9.87500i	0.0841655	+	0.477326i
$429$	7.35117	−	12.7326i	0.354918	−	0.614735i
$430$	5.89440	+	10.2094i	0.284253	+	0.492341i
$431$	−10.5196	+	8.82699i	−0.506711	+	0.425181i	−0.859970	−	0.510344i	$-0.829518\pi$
$431$	−10.5196	+	8.82699i	−0.506711	+	0.425181i	0.353259	+	0.935526i	$0.385074\pi$
$432$	0.939693	−	0.342020i	0.0452110	−	0.0164555i
$433$	23.2053	+	8.44605i	1.11518	+	0.405891i	0.832890	−	0.553439i	$-0.186685\pi$
$433$	23.2053	+	8.44605i	1.11518	+	0.405891i	0.282287	+	0.959330i	$0.408907\pi$
$434$	17.8837	+	15.0062i	0.858446	+	0.720322i
$435$	1.43969	−	8.16490i	0.0690280	−	0.391477i
$436$	13.9213			0.666708
$437$	−4.11721	+	35.6561i	−0.196953	+	1.70566i
$438$	−10.2909			−0.491716
$439$	3.15018	−	17.8655i	0.150350	−	0.852676i	−0.812565	−	0.582870i	$-0.801930\pi$
$439$	3.15018	−	17.8655i	0.150350	−	0.852676i	0.962915	−	0.269805i	$-0.0869594\pi$
$440$	−4.88532	−	4.09927i	−0.232898	−	0.195425i
$441$	−5.42514	−	1.97459i	−0.258340	−	0.0940282i
$442$	19.7271	−	7.18009i	0.938325	−	0.341522i
$443$	−9.85323	+	8.26784i	−0.468141	+	0.392817i	−0.846116	−	0.532999i	$-0.821065\pi$
$443$	−9.85323	+	8.26784i	−0.468141	+	0.392817i	0.377975	+	0.925816i	$0.376621\pi$
$444$	0.194593	+	0.337044i	0.00923496	+	0.0159954i
$445$	13.7606	−	23.8340i	0.652314	−	1.12984i
$446$	0.706919	+	4.00914i	0.0334736	+	0.189838i
$447$	3.81655	+	21.6447i	0.180517	+	1.02376i
$448$	−1.78699	+	3.09516i	−0.0844273	+	0.146232i
$449$	10.9659	+	18.9934i	0.517511	+	0.896355i	0.999793	+	0.0203389i	$0.00647451\pi$
$449$	10.9659	+	18.9934i	0.517511	+	0.896355i	−0.482283	+	0.876016i	$0.660192\pi$
$450$	0.390530	−	0.327693i	0.0184097	−	0.0154476i
$451$	4.96198	−	1.80601i	0.233651	−	0.0850419i
$452$	0.213011	+	0.0775297i	0.0100192	+	0.00364669i
$453$	−1.80928	−	1.51816i	−0.0850073	−	0.0713296i
$454$	−0.0765042	+	0.433877i	−0.00359052	+	0.0203628i
$455$	−45.3979			−2.12828
$456$	2.40033	+	3.63846i	0.112406	+	0.170387i
$457$	30.8452			1.44288			0.721440	−	0.692477i	$-0.243481\pi$
$457$	30.8452			1.44288			0.721440	+	0.692477i	$0.243481\pi$
$458$	−0.588526	+	3.33770i	−0.0275000	+	0.155960i
$459$	2.97178	+	2.49362i	0.138711	+	0.116392i
$460$	−18.1630	−	6.61078i	−0.846853	−	0.308229i
$461$	11.5770	−	4.21367i	0.539193	−	0.196250i	−0.0580453	−	0.998314i	$-0.518487\pi$
$461$	11.5770	−	4.21367i	0.539193	−	0.196250i	0.597239	+	0.802064i	$0.296265\pi$
$462$	−7.43835	+	6.24152i	−0.346063	+	0.290382i
$463$	−6.10472	−	10.5737i	−0.283711	−	0.491401i	0.688585	−	0.725156i	$-0.258232\pi$
$463$	−6.10472	−	10.5737i	−0.283711	−	0.491401i	−0.972296	+	0.233754i	$0.924899\pi$
$464$	−1.76604	+	3.05888i	−0.0819866	+	0.142005i
$465$	2.66250	+	15.0998i	0.123471	+	0.700237i
$466$	0.367059	+	2.08169i	0.0170037	+	0.0964326i
$467$	13.3701	−	23.1576i	0.618692	−	1.07161i	−0.371032	−	0.928620i	$-0.620996\pi$
$467$	13.3701	−	23.1576i	0.618692	−	1.07161i	0.989725	−	0.142986i	$-0.0456705\pi$
$468$	−2.70574	−	4.68647i	−0.125073	−	0.216632i
$469$	−40.8942	+	34.3143i	−1.88832	+	1.58449i
$470$	6.58512	−	2.39679i	0.303749	−	0.110556i
$471$	−13.4893	−	4.90971i	−0.621555	−	0.226228i
$472$	2.09240	+	1.75573i	0.0963103	+	0.0808140i
$473$	2.36942	−	13.4377i	0.108946	−	0.617865i
$474$	−13.0077			−0.597465
$475$	1.78430	+	1.32450i	0.0818693	+	0.0607722i
$476$	−13.8648			−0.635494
$477$	1.44222	−	8.17923i	0.0660347	−	0.374501i
$478$	−3.08647	−	2.58985i	−0.141172	−	0.118457i
$479$	−7.26991	−	2.64603i	−0.332171	−	0.120900i	0.170550	−	0.985349i	$-0.445445\pi$
$479$	−7.26991	−	2.64603i	−0.332171	−	0.120900i	−0.502721	+	0.864449i	$0.667668\pi$
$480$	−2.20574	+	0.802823i	−0.100678	+	0.0366437i
$481$	1.61334	−	1.35375i	0.0735620	−	0.0617259i
$482$	5.08853	+	8.81359i	0.231776	+	0.401448i
$483$	−14.7148	+	25.4868i	−0.669548	+	1.15969i
$484$	−0.628356	−	3.56358i	−0.0285616	−	0.161981i
$485$	3.50703	+	19.8893i	0.159246	+	0.903128i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−6.69594	−	11.5977i	−0.303422	−	0.525542i	0.673487	−	0.739199i	$-0.264796\pi$
$487$	−6.69594	−	11.5977i	−0.303422	−	0.525542i	−0.976909	+	0.213657i	$0.931462\pi$
$488$	4.81908	−	4.04369i	0.218149	−	0.183049i
$489$	−16.1074	+	5.86262i	−0.728402	+	0.265117i
$490$	12.7344	+	4.63495i	0.575283	+	0.209386i
$491$	−15.5103	−	13.0147i	−0.699969	−	0.587343i	0.221796	−	0.975093i	$-0.428808\pi$
$491$	−15.5103	−	13.0147i	−0.699969	−	0.587343i	−0.921765	+	0.387750i	$0.873252\pi$
$492$	0.337496	−	1.91404i	0.0152155	−	0.0862914i
$493$	−13.7023			−0.617122
$494$	17.1348	−	16.2110i	0.770929	−	0.729368i
$495$	−6.37733			−0.286639
$496$	1.13429	−	6.43285i	0.0509309	−	0.288844i
$497$	24.7015	+	20.7270i	1.10801	+	0.929732i
$498$	−7.67752	−	2.79439i	−0.344038	−	0.125220i
$499$	4.45171	−	1.62029i	0.199286	−	0.0725342i	−0.240449	−	0.970662i	$-0.577295\pi$
$499$	4.45171	−	1.62029i	0.199286	−	0.0725342i	0.439735	+	0.898128i	$0.355072\pi$
$500$	8.07398	−	6.77487i	0.361079	−	0.302981i
$501$	−7.30928	−	12.6600i	−0.326554	−	0.565609i
$502$	−1.45471	+	2.51963i	−0.0649268	+	0.112456i
$503$	1.49319	+	8.46832i	0.0665782	+	0.377584i	0.999831	+	0.0183643i	$0.00584588\pi$
$503$	1.49319	+	8.46832i	0.0665782	+	0.377584i	−0.933253	+	0.359219i	$0.883043\pi$
$504$	0.620615	+	3.51968i	0.0276444	+	0.156779i
$505$	−1.50908	+	2.61381i	−0.0671534	+	0.116313i
$506$	11.1860	+	19.3747i	0.497277	+	0.861309i
$507$	−12.4743	+	10.4672i	−0.554003	+	0.464864i
$508$	−8.17024	+	2.97373i	−0.362496	+	0.131938i
$509$	−5.03936	−	1.83418i	−0.223366	−	0.0812985i	0.227913	−	0.973681i	$-0.426810\pi$
$509$	−5.03936	−	1.83418i	−0.223366	−	0.0812985i	−0.451279	+	0.892383i	$0.649032\pi$
$510$	−6.97565	−	5.85327i	−0.308887	−	0.259187i
$511$	6.38666	−	36.2205i	0.282529	−	1.60230i
$512$	1.00000			0.0441942
$513$	4.17752	+	1.24432i	0.184442	+	0.0549382i
$514$	−2.55943			−0.112892
$515$	−0.300193	+	1.70248i	−0.0132281	+	0.0750201i
$516$	−3.84730	−	3.22826i	−0.169368	−	0.142116i
$517$	−7.62196	−	2.77417i	−0.335213	−	0.122008i
$518$	−1.30706	+	0.475730i	−0.0574288	+	0.0209024i
$519$	15.8327	−	13.2853i	0.694981	−	0.583158i
$520$	6.35117	+	11.0005i	0.278517	+	0.482406i
$521$	11.8576	−	20.5379i	0.519489	−	0.899782i	−0.480254	−	0.877129i	$-0.659456\pi$
$521$	11.8576	−	20.5379i	0.519489	−	0.899782i	0.999743	−	0.0226524i	$-0.00721111\pi$
$522$	0.613341	+	3.47843i	0.0268452	+	0.152247i
$523$	−5.43794	−	30.8401i	−0.237784	−	1.34854i	−0.836670	−	0.547708i	$-0.815501\pi$
$523$	−5.43794	−	30.8401i	−0.237784	−	1.34854i	0.598885	−	0.800835i	$-0.295611\pi$
$524$	6.32160	−	10.9493i	0.276161	−	0.478324i
$525$	0.911007	+	1.57791i	0.0397596	+	0.0688657i
$526$	12.2023	−	10.2390i	0.532047	−	0.446440i
$527$	23.8123	−	8.66696i	1.03728	−	0.377539i
$528$	2.55303	+	0.929228i	0.111107	+	0.0404395i
$529$	34.3232	+	28.8006i	1.49231	+	1.25220i
$530$	−3.38532	+	19.1991i	−0.147049	+	0.833955i
$531$	2.73143			0.118534
$532$	−14.2959	+	6.19031i	−0.619806	+	0.268384i
$533$	−10.5175			−0.455565
$534$	−2.03596	+	11.5465i	−0.0881046	+	0.499666i
$535$	−18.0305	−	15.1294i	−0.779526	−	0.654100i
$536$	14.0360	+	5.10867i	0.606261	+	0.220661i
$537$	5.35117	−	1.94767i	0.230920	−	0.0840480i
$538$	12.9422	−	10.8598i	0.557979	−	0.468200i
$539$	−7.84271	−	13.5840i	−0.337809	−	0.585103i
$540$	−1.17365	+	2.03282i	−0.0505058	+	0.0874786i
$541$	1.66519	+	9.44377i	0.0715922	+	0.406020i	0.999452	+	0.0330912i	$0.0105352\pi$
$541$	1.66519	+	9.44377i	0.0715922	+	0.406020i	−0.927860	+	0.372928i	$0.878354\pi$
$542$	−0.108126	−	0.613214i	−0.00464442	−	0.0263398i
$543$	−11.1099	+	19.2430i	−0.476773	+	0.825795i
$544$	1.93969	+	3.35965i	0.0831636	+	0.144044i
$545$	−25.0323	+	21.0046i	−1.07227	+	0.899738i
$546$	18.1741	−	6.61484i	0.777780	−	0.283089i
$547$	−9.65570	−	3.51439i	−0.412848	−	0.150264i	0.127242	−	0.991872i	$-0.459388\pi$
$547$	−9.65570	−	3.51439i	−0.412848	−	0.150264i	−0.540090	+	0.841607i	$0.681610\pi$
$548$	16.6951	+	14.0088i	0.713178	+	0.598427i
$549$	1.09240	−	6.19529i	0.0466223	−	0.264408i
$550$	1.38507			0.0590594
$551$	−14.1284	+	6.11776i	−0.601888	+	0.260625i
$552$	8.23442			0.350480
$553$	8.07280	−	45.7831i	0.343290	−	1.94690i
$554$	−21.0483	−	17.6616i	−0.894256	−	0.750370i
$555$	−0.858441	−	0.312447i	−0.0364388	−	0.0132626i
$556$	10.5496	−	3.83975i	0.447404	−	0.162842i
$557$	−12.7756	+	10.7200i	−0.541319	+	0.454221i	−0.871989	−	0.489526i	$-0.837170\pi$
$557$	−12.7756	+	10.7200i	−0.541319	+	0.454221i	0.330669	+	0.943747i	$0.392725\pi$
$558$	−3.26604	−	5.65695i	−0.138263	−	0.239478i
$559$	−13.5890	+	23.5368i	−0.574753	+	0.995502i
$560$	−1.45677	−	8.26173i	−0.0615596	−	0.349122i
$561$	1.83022	+	10.3797i	0.0772720	+	0.438232i
$562$	1.24035	−	2.14835i	0.0523211	−	0.0906228i
$563$	−1.71554	−	2.97140i	−0.0723013	−	0.125229i	0.827608	−	0.561306i	$-0.189701\pi$
$563$	−1.71554	−	2.97140i	−0.0723013	−	0.125229i	−0.899910	+	0.436077i	$0.856368\pi$
$564$	−2.28699	+	1.91901i	−0.0962996	+	0.0808050i
$565$	−0.500000	+	0.181985i	−0.0210352	+	0.00765617i
$566$	−2.14543	−	0.780873i	−0.0901791	−	0.0328225i
$567$	2.73783	+	2.29731i	0.114978	+	0.0964779i
$568$	1.56670	−	8.88522i	0.0657374	−	0.372816i
$569$	−43.5681			−1.82647			−0.913235	−	0.407433i	$-0.866424\pi$
$569$	−43.5681			−1.82647			−0.913235	+	0.407433i	$0.866424\pi$
$570$	−9.80587	−	2.92079i	−0.410723	−	0.122339i
$571$	−8.14115			−0.340696			−0.170348	−	0.985384i	$-0.554489\pi$
$571$	−8.14115			−0.340696			−0.170348	+	0.985384i	$0.554489\pi$
$572$	2.55303	−	14.4790i	0.106748	−	0.605396i
$573$	−4.63223	−	3.88690i	−0.193514	−	0.162378i
$574$	6.52734	+	2.37576i	0.272446	+	0.0991622i
$575$	3.94475	−	1.43577i	0.164507	−	0.0598757i
$576$	0.766044	−	0.642788i	0.0319185	−	0.0267828i
$577$	−17.5248	−	30.3539i	−0.729568	−	1.26365i	−0.957066	−	0.289870i	$-0.906388\pi$
$577$	−17.5248	−	30.3539i	−0.729568	−	1.26365i	0.227499	−	0.973778i	$-0.426945\pi$
$578$	0.975185	−	1.68907i	0.0405624	−	0.0702561i
$579$	−1.09374	−	6.20291i	−0.0454543	−	0.257784i
$580$	−1.43969	−	8.16490i	−0.0597800	−	0.339029i
$581$	14.6001	−	25.2882i	0.605716	−	1.04913i
$582$	−4.30200	−	7.45129i	−0.178324	−	0.308866i
$583$	17.2856	−	14.5044i	0.715898	−	0.600710i
$584$	−9.67024	+	3.51968i	−0.400158	+	0.145645i
$585$	11.9363	+	4.34445i	0.493505	+	0.179621i
$586$	−1.83544	−	1.54011i	−0.0758212	−	0.0636215i
$587$	1.69594	−	9.61814i	0.0699988	−	0.396983i	−0.929598	−	0.368576i	$-0.879845\pi$
$587$	1.69594	−	9.61814i	0.0699988	−	0.396983i	0.999596	−	0.0284070i	$-0.00904344\pi$
$588$	−5.77332			−0.238088
$589$	20.6830	−	19.5680i	0.852230	−	0.806286i
$590$	−6.41147			−0.263956
$591$	−3.46198	+	19.6339i	−0.142407	+	0.807630i
$592$	0.298133	+	0.250164i	0.0122532	+	0.0102817i
$593$	30.7254	+	11.1831i	1.26174	+	0.459236i	0.884353	−	0.466819i	$-0.154600\pi$
$593$	30.7254	+	11.1831i	1.26174	+	0.459236i	0.377388	+	0.926055i	$0.376822\pi$
$594$	2.55303	−	0.929228i	0.104752	−	0.0381267i
$595$	24.9308	−	20.9194i	1.02206	−	0.857614i
$596$	10.9893	+	19.0341i	0.450140	+	0.779666i
$597$	6.44104	−	11.1562i	0.263614	−	0.456593i
$598$	−7.73783	−	43.8834i	−0.316423	−	1.79453i
$599$	−1.53580	−	8.70994i	−0.0627510	−	0.355878i	−0.999974	−	0.00714909i	$-0.997724\pi$
$599$	−1.53580	−	8.70994i	−0.0627510	−	0.355878i	0.937223	−	0.348729i	$-0.113387\pi$
$600$	0.254900	−	0.441500i	0.0104063	−	0.0180242i
$601$	10.9076	+	18.8925i	0.444930	+	0.770642i	0.998047	−	0.0624615i	$-0.0198951\pi$
$601$	10.9076	+	18.8925i	0.444930	+	0.770642i	−0.553117	+	0.833104i	$0.686562\pi$
$602$	13.7502	−	11.5377i	0.560414	−	0.470243i
$603$	14.0360	−	5.10867i	0.571588	−	0.208041i
$604$	−2.21941	−	0.807798i	−0.0903064	−	0.0328688i
$605$	6.50665	+	5.45972i	0.264533	+	0.221969i
$606$	0.223278	−	1.26627i	0.00907005	−	0.0514388i
$607$	−26.5963			−1.07951			−0.539755	−	0.841822i	$-0.681483\pi$
$607$	−26.5963			−1.07951			−0.539755	+	0.841822i	$0.681483\pi$
$608$	3.50000	+	2.59808i	0.141944	+	0.105366i
$609$	−12.6236			−0.511534
$610$	−2.56418	+	14.5422i	−0.103821	+	0.588795i
$611$	12.3760	+	10.3847i	0.500679	+	0.420119i
$612$	3.64543	+	1.32683i	0.147358	+	0.0536338i
$613$	14.2280	−	5.17858i	0.574665	−	0.209161i	−0.0383067	−	0.999266i	$-0.512196\pi$
$613$	14.2280	−	5.17858i	0.574665	−	0.209161i	0.612971	+	0.790105i	$0.289974\pi$
$614$	−4.00908	+	3.36402i	−0.161794	+	0.135761i
$615$	2.28106	+	3.95091i	0.0919812	+	0.159316i
$616$	−4.85504	+	8.40917i	−0.195615	+	0.338815i
$617$	−5.10338	−	28.9427i	−0.205454	−	1.16519i	−0.896723	−	0.442592i	$-0.854059\pi$
$617$	−5.10338	−	28.9427i	−0.205454	−	1.16519i	0.691269	−	0.722598i	$-0.257052\pi$
$618$	−0.127889	−	0.725293i	−0.00514444	−	0.0291756i
$619$	−15.7219	+	27.2312i	−0.631918	+	1.09451i	0.355241	+	0.934775i	$0.384399\pi$
$619$	−15.7219	+	27.2312i	−0.631918	+	1.09451i	−0.987159	+	0.159739i	$0.948935\pi$
$620$	7.66637	+	13.2785i	0.307889	+	0.533279i
$621$	6.30793	−	5.29298i	0.253129	−	0.212400i
$622$	10.3302	−	3.75989i	0.414204	−	0.150758i
$623$	−39.3764	−	14.3319i	−1.57758	−	0.574194i
$624$	−4.14543	−	3.47843i	−0.165950	−	0.139249i
$625$	−4.73870	+	26.8745i	−0.189548	+	1.07498i
$626$	−30.4516			−1.21709
$627$	6.52141	+	9.88527i	0.260440	+	0.394780i
$628$	−14.3550			−0.572828
$629$	−0.262174	+	1.48686i	−0.0104536	+	0.0592851i
$630$	−6.42649	−	5.39246i	−0.256037	−	0.214841i
$631$	28.0736	+	10.2179i	1.11759	+	0.406770i	0.833773	−	0.552108i	$-0.186176\pi$
$631$	28.0736	+	10.2179i	1.11759	+	0.406770i	0.283819	+	0.958878i	$0.408399\pi$
$632$	−12.2233	+	4.44891i	−0.486216	+	0.176968i
$633$	−1.77197	+	1.48686i	−0.0704297	+	0.0590975i
$634$	−5.66978	−	9.82034i	−0.225176	−	0.390016i
$635$	10.2044	−	17.6745i	0.404949	−	0.701392i
$636$	−1.44222	−	8.17923i	−0.0571877	−	0.324328i
$637$	5.42514	+	30.7675i	0.214952	+	1.21905i
$638$	−4.79813	+	8.31061i	−0.189960	+	0.329020i
$639$	−4.51114	−	7.81353i	−0.178458	−	0.309099i
$640$	−1.79813	+	1.50881i	−0.0710775	+	0.0596411i
$641$	−6.75150	+	2.45734i	−0.266668	+	0.0970592i	−0.471894	−	0.881655i	$-0.656429\pi$
$641$	−6.75150	+	2.45734i	−0.266668	+	0.0970592i	0.205226	+	0.978715i	$0.434207\pi$
$642$	9.42262	+	3.42955i	0.371881	+	0.135354i
$643$	6.95858	+	5.83894i	0.274420	+	0.230265i	0.769602	−	0.638523i	$-0.220454\pi$
$643$	6.95858	+	5.83894i	0.274420	+	0.230265i	−0.495183	+	0.868789i	$0.664899\pi$
$644$	−5.11040	+	28.9825i	−0.201378	+	1.14207i
$645$	11.7888			0.464184
$646$	−1.93969	+	16.7982i	−0.0763162	+	0.660918i
$647$	37.5749			1.47722			0.738611	−	0.674132i	$-0.235482\pi$
$647$	37.5749			1.47722			0.738611	+	0.674132i	$0.235482\pi$
$648$	0.173648	−	0.984808i	0.00682154	−	0.0386869i
$649$	5.68479	+	4.77011i	0.223148	+	0.187243i
$650$	−2.59240	−	0.943555i	−0.101682	−	0.0370093i
$651$	21.9376	−	7.98465i	0.859804	−	0.312943i
$652$	−13.1309	+	11.0181i	−0.514245	+	0.431503i
$653$	−0.870767	−	1.50821i	−0.0340758	−	0.0590209i	0.848485	−	0.529220i	$-0.177515\pi$
$653$	−0.870767	−	1.50821i	−0.0340758	−	0.0590209i	−0.882560	+	0.470199i	$0.844182\pi$
$654$	6.96064	−	12.0562i	0.272182	−	0.471434i
$655$	5.15342	+	29.2265i	0.201361	+	1.14197i
$656$	−0.337496	−	1.91404i	−0.0131770	−	0.0747305i
$657$	−5.14543	+	8.91215i	−0.200742	+	0.347696i
$658$	−5.33497	−	9.24044i	−0.207979	−	0.360230i
$659$	−3.98680	+	3.34532i	−0.155304	+	0.130315i	−0.717128	−	0.696941i	$-0.754544\pi$
$659$	−3.98680	+	3.34532i	−0.155304	+	0.130315i	0.561825	+	0.827256i	$0.310099\pi$
$660$	−5.99273	+	2.18117i	−0.233267	+	0.0849021i
$661$	23.3427	+	8.49605i	0.907926	+	0.330458i	0.753425	−	0.657534i	$-0.228401\pi$
$661$	23.3427	+	8.49605i	0.907926	+	0.330458i	0.154502	+	0.987993i	$0.450623\pi$
$662$	9.90626	+	8.31234i	0.385018	+	0.323068i
$663$	3.64543	−	20.6743i	0.141577	−	0.802922i
$664$	−8.17024			−0.317067
$665$	16.3659	−	32.7009i	0.634644	−	1.26809i
$666$	0.389185			0.0150806
$667$	−5.05051	+	28.6428i	−0.195556	+	1.10906i
$668$	−11.1985	−	9.39663i	−0.433282	−	0.363566i
$669$	3.82547	+	1.39236i	0.147901	+	0.0538317i
$670$	−32.9466	+	11.9916i	−1.27284	+	0.463275i
$671$	13.0929	−	10.9862i	0.505444	−	0.424118i
$672$	1.78699	+	3.09516i	0.0689346	+	0.119398i
$673$	−4.49613	+	7.78752i	−0.173313	+	0.300187i	−0.939576	−	0.342340i	$-0.888781\pi$
$673$	−4.49613	+	7.78752i	−0.173313	+	0.300187i	0.766263	+	0.642527i	$0.222114\pi$
$674$	1.86618	+	10.5836i	0.0718826	+	0.407667i
$675$	−0.0885259	−	0.502055i	−0.00340736	−	0.0193241i
$676$	−8.14203	+	14.1024i	−0.313155	+	0.542400i
$677$	−3.20780	−	5.55607i	−0.123286	−	0.213537i	0.797776	−	0.602954i	$-0.206010\pi$
$677$	−3.20780	−	5.55607i	−0.123286	−	0.213537i	−0.921062	+	0.389417i	$0.872676\pi$
$678$	0.173648	−	0.145708i	0.00666892	−	0.00559589i
$679$	28.8960	−	10.5173i	1.10893	−	0.403617i
$680$	−8.55690	−	3.11446i	−0.328142	−	0.119434i
$681$	0.337496	+	0.283193i	0.0129329	+	0.0108520i
$682$	3.08172	−	17.4773i	0.118005	−	0.669240i
$683$	−26.0000			−0.994862			−0.497431	−	0.867503i	$-0.665723\pi$
$683$	−26.0000			−0.994862			−0.497431	+	0.867503i	$0.665723\pi$
$684$	4.35117	−	0.259515i	0.166371	−	0.00992280i
$685$	−51.1566			−1.95459
$686$	−0.761297	+	4.31753i	−0.0290664	+	0.164844i
$687$	2.59627	+	2.17853i	0.0990538	+	0.0831160i
$688$	−4.71941	−	1.71772i	−0.179926	−	0.0654876i
$689$	−42.2340	+	15.3719i	−1.60899	+	0.585624i
$690$	−14.8066	+	12.4242i	−0.563677	+	0.472981i
$691$	22.1509	+	38.3666i	0.842662	+	1.45953i	0.887636	+	0.460545i	$0.152346\pi$
$691$	22.1509	+	38.3666i	0.842662	+	1.45953i	−0.0449746	+	0.998988i	$0.514321\pi$
$692$	10.3341	−	17.8992i	0.392843	−	0.680424i
$693$	1.68614	+	9.56256i	0.0640510	+	0.363251i
$694$	3.95976	+	22.4569i	0.150310	+	0.852453i
$695$	−13.1762	+	22.8218i	−0.499801	+	0.865680i
$696$	1.76604	+	3.05888i	0.0669417	+	0.115946i
$697$	5.77584	−	4.84651i	0.218776	−	0.183575i
$698$	23.8332	−	8.67458i	0.902101	−	0.328338i
$699$	1.98633	+	0.722965i	0.0751299	+	0.0273450i
$700$	1.39574	+	1.17117i	0.0527542	+	0.0442660i
$701$	−8.11334	+	46.0130i	−0.306437	+	1.73789i	0.310228	+	0.950662i	$0.399595\pi$
$701$	−8.11334	+	46.0130i	−0.306437	+	1.73789i	−0.616664	+	0.787226i	$0.711516\pi$
$702$	−5.41147			−0.204243
$703$	0.393523	+	1.65015i	0.0148420	+	0.0622364i
$704$	2.71688			0.102396
$705$	1.21688	−	6.90128i	0.0458304	−	0.259917i
$706$	−9.34002	−	7.83721i	−0.351516	−	0.294957i
$707$	4.31831	+	1.57173i	0.162407	+	0.0591112i
$708$	2.56670	−	0.934204i	0.0964626	−	0.0351095i
$709$	−11.6400	+	9.76709i	−0.437148	+	0.366811i	−0.834641	−	0.550794i	$-0.814325\pi$
$709$	−11.6400	+	9.76709i	−0.437148	+	0.366811i	0.397493	+	0.917605i	$0.369880\pi$
$710$	10.5890	+	18.3407i	0.397398	+	0.688313i
$711$	−6.50387	+	11.2650i	−0.243914	+	0.422472i
$712$	2.03596	+	11.5465i	0.0763008	+	0.432723i
$713$	−9.34018	−	52.9708i	−0.349793	−	1.98377i
$714$	−6.93242	+	12.0073i	−0.259439	+	0.449362i
$715$	17.2554	+	29.8872i	0.645314	+	1.11772i
$716$	4.36231	−	3.66041i	0.163027	−	0.136796i
$717$	−3.78611	+	1.37803i	−0.141395	+	0.0514635i
$718$	−27.4047	−	9.97448i	−1.02273	−	0.372244i
$719$	17.9231	+	15.0393i	0.668418	+	0.560870i	0.912597	−	0.408861i	$-0.134074\pi$
$719$	17.9231	+	15.0393i	0.668418	+	0.560870i	−0.244178	+	0.969730i	$0.578518\pi$
$720$	−0.407604	+	2.31164i	−0.0151905	+	0.0861496i
$721$	2.63217			0.0980271
$722$	5.50000	+	18.1865i	0.204689	+	0.676833i
$723$	10.1771			0.378489
$724$	−3.85844	+	21.8823i	−0.143398	+	0.813249i
$725$	1.37939	+	1.15744i	0.0512291	+	0.0429863i
$726$	−3.40033	−	1.23762i	−0.126198	−	0.0459323i
$727$	−32.0266	+	11.6567i	−1.18780	+	0.432325i	−0.858951	−	0.512057i	$-0.828883\pi$
$727$	−32.0266	+	11.6567i	−1.18780	+	0.432325i	−0.328851	+	0.944382i	$0.606661\pi$
$728$	14.8157	−	12.4318i	0.549105	−	0.460754i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	12.0778	−	20.9194i	0.447021	−	0.774263i
$731$	−3.38326	−	19.1874i	−0.125134	−	0.709671i
$732$	−1.09240	−	6.19529i	−0.0403761	−	0.228984i
$733$	15.0064	−	25.9918i	0.554274	−	0.960031i	−0.443686	−	0.896182i	$-0.646329\pi$
$733$	15.0064	−	25.9918i	0.554274	−	0.960031i	0.997960	−	0.0638481i	$-0.0203373\pi$
$734$	−6.99613	−	12.1177i	−0.258232	−	0.447271i
$735$	10.3812	−	8.71086i	0.382916	−	0.321305i
$736$	7.73783	−	2.81634i	0.285220	−	0.103812i
$737$	38.1340	+	13.8797i	1.40469	+	0.511264i
$738$	−1.48886	−	1.24930i	−0.0548055	−	0.0459873i
$739$	4.14022	−	23.4803i	0.152300	−	0.863738i	−0.808912	−	0.587929i	$-0.799943\pi$
$739$	4.14022	−	23.4803i	0.152300	−	0.863738i	0.961213	−	0.275808i	$-0.0889456\pi$
$740$	−0.913534			−0.0335822
$741$	−5.47178	−	22.9446i	−0.201011	−	0.842892i
$742$	29.6833			1.08971
$743$	5.38207	−	30.5233i	0.197449	−	1.11979i	−0.711438	−	0.702748i	$-0.751956\pi$
$743$	5.38207	−	30.5233i	0.197449	−	1.11979i	0.908888	−	0.417041i	$-0.136933\pi$
$744$	−5.00387	−	4.19875i	−0.183451	−	0.153933i
$745$	−48.4791	−	17.6450i	−1.77614	−	0.646461i
$746$	6.40895	−	2.33267i	0.234648	−	0.0854050i
$747$	−6.25877	+	5.25173i	−0.228996	+	0.192151i
$748$	5.26991	+	9.12776i	0.192687	+	0.333744i
$749$	−17.9187	+	31.0362i	−0.654737	+	1.13404i
$750$	−1.83022	−	10.3797i	−0.0668303	−	0.379013i
$751$	3.82800	+	21.7097i	0.139686	+	0.792197i	0.971482	+	0.237115i	$0.0762019\pi$
$751$	3.82800	+	21.7097i	0.139686	+	0.792197i	−0.831796	+	0.555082i	$0.812687\pi$
$752$	−1.49273	+	2.58548i	−0.0544341	+	0.0942827i
$753$	1.45471	+	2.51963i	0.0530125	+	0.0918203i
$754$	14.6420	−	12.2861i	0.533231	−	0.447434i
$755$	5.20961	−	1.89614i	0.189597	−	0.0690077i
$756$	3.35844	+	1.22237i	0.122145	+	0.0444573i
$757$	−10.9736	−	9.20794i	−0.398842	−	0.334668i	0.421204	−	0.906966i	$-0.361608\pi$
$757$	−10.9736	−	9.20794i	−0.398842	−	0.334668i	−0.820046	+	0.572298i	$0.806052\pi$
$758$	5.54529	−	31.4489i	0.201414	−	1.14228i
$759$	22.3719			0.812050
$760$	−10.2135	+	0.609158i	−0.370482	+	0.0220965i
$761$	17.2635			0.625802			0.312901	−	0.949786i	$-0.398699\pi$
$761$	17.2635			0.625802			0.312901	+	0.949786i	$0.398699\pi$
$762$	−1.50980	+	8.56250i	−0.0546943	+	0.310187i
$763$	38.1140	+	31.9815i	1.37982	+	1.15781i
$764$	−5.68227	−	2.06818i	−0.205577	−	0.0748240i
$765$	−8.55690	+	3.11446i	−0.309376	+	0.112603i
$766$	−28.2049	+	23.6667i	−1.01908	+	0.855112i

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)

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(2.20574 - 0.802823i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(-1.78699 - 3.09516i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +O(q^{10})\)	\(q+(0.173648 - 0.984808i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(2.20574 - 0.802823i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(-1.78699 - 3.09516i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +(-0.407604 - 2.31164i) q^{10} +(-1.35844 + 2.35289i) q^{11} +(0.500000 + 0.866025i) q^{12} +(4.14543 - 3.47843i) q^{13} +(-3.35844 + 1.22237i) q^{14} +(-2.20574 - 0.802823i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-0.673648 + 3.82045i) q^{17} +1.00000 q^{18} +(1.01114 + 4.24000i) q^{19} -2.34730 q^{20} +(-0.620615 + 3.51968i) q^{21} +(2.08125 + 1.74638i) q^{22} +(7.73783 + 2.81634i) q^{23} +(0.939693 - 0.342020i) q^{24} +(0.390530 - 0.327693i) q^{25} +(-2.70574 - 4.68647i) q^{26} +(0.500000 - 0.866025i) q^{27} +(0.620615 + 3.51968i) q^{28} +(0.613341 + 3.47843i) q^{29} +(-1.17365 + 2.03282i) q^{30} +(-3.26604 - 5.65695i) q^{31} +(0.766044 - 0.642788i) q^{32} +(2.55303 - 0.929228i) q^{33} +(3.64543 + 1.32683i) q^{34} +(-6.42649 - 5.39246i) q^{35} +(0.173648 - 0.984808i) q^{36} +0.389185 q^{37} +(4.35117 - 0.259515i) q^{38} -5.41147 q^{39} +(-0.407604 + 2.31164i) q^{40} +(-1.48886 - 1.24930i) q^{41} +(3.35844 + 1.22237i) q^{42} +(-4.71941 + 1.71772i) q^{43} +(2.08125 - 1.74638i) q^{44} +(1.17365 + 2.03282i) q^{45} +(4.11721 - 7.13122i) q^{46} +(0.518418 + 2.94010i) q^{47} +(-0.173648 - 0.984808i) q^{48} +(-2.88666 + 4.99984i) q^{49} +(-0.254900 - 0.441500i) q^{50} +(2.97178 - 2.49362i) q^{51} +(-5.08512 + 1.85083i) q^{52} +(-7.80453 - 2.84062i) q^{53} +(-0.766044 - 0.642788i) q^{54} +(-1.10741 + 6.28044i) q^{55} +3.57398 q^{56} +(1.95084 - 3.89798i) q^{57} +3.53209 q^{58} +(0.474308 - 2.68993i) q^{59} +(1.79813 + 1.50881i) q^{60} +(-5.91147 - 2.15160i) q^{61} +(-6.13816 + 2.23411i) q^{62} +(2.73783 - 2.29731i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(6.35117 - 11.0005i) q^{65} +(-0.471782 - 2.67561i) q^{66} +(-2.59374 - 14.7098i) q^{67} +(1.93969 - 3.35965i) q^{68} +(-4.11721 - 7.13122i) q^{69} +(-6.42649 + 5.39246i) q^{70} +(-8.47818 + 3.08580i) q^{71} +(-0.939693 - 0.342020i) q^{72} +(7.88326 + 6.61484i) q^{73} +(0.0675813 - 0.383273i) q^{74} -0.509800 q^{75} +(0.500000 - 4.33013i) q^{76} +9.71007 q^{77} +(-0.939693 + 5.32926i) q^{78} +(9.96451 + 8.36121i) q^{79} +(2.20574 + 0.802823i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-1.48886 + 1.24930i) q^{82} +(4.08512 + 7.07564i) q^{83} +(1.78699 - 3.09516i) q^{84} +(1.58125 + 8.96773i) q^{85} +(0.872111 + 4.94599i) q^{86} +(1.76604 - 3.05888i) q^{87} +(-1.35844 - 2.35289i) q^{88} +(8.98158 - 7.53644i) q^{89} +(2.20574 - 0.802823i) q^{90} +(-18.1741 - 6.61484i) q^{91} +(-6.30793 - 5.29298i) q^{92} +(-1.13429 + 6.43285i) q^{93} +2.98545 q^{94} +(5.63429 + 8.54055i) q^{95} -1.00000 q^{96} +(-1.49407 + 8.47329i) q^{97} +(4.42262 + 3.71102i) q^{98} +(-2.55303 - 0.929228i) 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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