LMFDB - Embedded newform 231.2.y.b.4.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(4,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 6]))

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

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

chi := DirichletCharacter("231.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.y (of order $15$, degree $8$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			4.2
Character	$\chi$	$=$	231.4
Dual form			231.2.y.b.58.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.257299 + 2.44803i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-3.97037 - 0.843927i) q^{4} +(3.02928 + 1.34872i) q^{5} +(-1.99141 + 1.44684i) q^{6} +(2.02429 + 1.70360i) q^{7} +(1.56623 - 4.82036i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(-0.257299 + 2.44803i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-3.97037 - 0.843927i) q^{4} +(3.02928 + 1.34872i) q^{5} +(-1.99141 + 1.44684i) q^{6} +(2.02429 + 1.70360i) q^{7} +(1.56623 - 4.82036i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(-4.08115 + 7.06876i) q^{10} +(1.53584 - 2.93959i) q^{11} +(-2.02953 - 3.51525i) q^{12} +(-3.52247 - 2.55923i) q^{13} +(-4.69131 + 4.51719i) q^{14} +(1.02469 + 3.15367i) q^{15} +(3.98113 + 1.77251i) q^{16} +(-0.590445 - 5.61771i) q^{17} +(-2.40773 - 0.511778i) q^{18} +(-2.27984 + 0.484596i) q^{19} +(-10.8891 - 7.91142i) q^{20} +(0.0884929 + 2.64427i) q^{21} +(6.80104 + 4.51614i) q^{22} +(-0.699447 - 1.21148i) q^{23} +(4.63024 - 2.06152i) q^{24} +(4.01184 + 4.45560i) q^{25} +(7.17139 - 7.96464i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-6.59946 - 8.47227i) q^{28} +(-0.768970 - 2.36665i) q^{29} +(-7.98393 + 1.69704i) q^{30} +(1.27031 - 0.565577i) q^{31} +(-0.295082 + 0.511097i) q^{32} +(3.21222 - 0.825617i) q^{33} +13.9042 q^{34} +(3.83446 + 7.89089i) q^{35} +(1.25432 - 3.86040i) q^{36} +(1.03060 - 1.14460i) q^{37} +(-0.599705 - 5.70582i) q^{38} +(-0.455118 - 4.33016i) q^{39} +(11.2459 - 12.4898i) q^{40} +(-2.71653 + 8.36062i) q^{41} +(-6.49603 - 0.463734i) q^{42} -6.73424 q^{43} +(-8.57866 + 10.3751i) q^{44} +(-1.65798 + 2.87171i) q^{45} +(3.14571 - 1.40056i) q^{46} +(4.31884 - 0.917998i) q^{47} +(1.34666 + 4.14460i) q^{48} +(1.19550 + 6.89716i) q^{49} +(-11.9397 + 8.67469i) q^{50} +(3.77968 - 4.19776i) q^{51} +(11.8257 + 13.1338i) q^{52} +(-9.51955 + 4.23838i) q^{53} +(-1.23076 - 2.13174i) q^{54} +(8.61719 - 6.83342i) q^{55} +(11.3825 - 7.08958i) q^{56} +(-1.88564 - 1.37000i) q^{57} +(5.99148 - 1.27353i) q^{58} +(14.4997 + 3.08202i) q^{59} +(-1.40692 - 13.3860i) q^{60} +(-1.28144 - 0.570534i) q^{61} +(1.05770 + 3.25528i) q^{62} +(-1.90586 + 1.83513i) q^{63} +(5.87596 + 4.26913i) q^{64} +(-7.21887 - 12.5035i) q^{65} +(1.19464 + 8.07605i) q^{66} +(-7.57690 + 13.1236i) q^{67} +(-2.39665 + 22.8026i) q^{68} +(0.432282 - 1.33043i) q^{69} +(-20.3038 + 7.35657i) q^{70} +(9.30320 - 6.75917i) q^{71} +(4.63024 + 2.06152i) q^{72} +(-8.70766 - 1.85087i) q^{73} +(2.53684 + 2.81745i) q^{74} +(-0.626711 + 5.96275i) q^{75} +9.46078 q^{76} +(8.11687 - 3.33412i) q^{77} +10.7175 q^{78} +(-0.348373 + 3.31455i) q^{79} +(9.66933 + 10.7389i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-19.7681 - 8.80133i) q^{82} +(11.5379 - 8.38278i) q^{83} +(1.88022 - 10.5734i) q^{84} +(5.78811 - 17.8140i) q^{85} +(1.73271 - 16.4856i) q^{86} +(1.24422 - 2.15505i) q^{87} +(-11.7644 - 12.0074i) q^{88} +(-3.54340 - 6.13736i) q^{89} +(-6.60344 - 4.79768i) q^{90} +(-2.77061 - 11.1815i) q^{91} +(1.75466 + 5.40030i) q^{92} +(1.27031 + 0.565577i) q^{93} +(1.13606 + 10.8089i) q^{94} +(-7.55987 - 1.60690i) q^{95} +(-0.577267 + 0.122702i) q^{96} +(1.16912 + 0.849417i) q^{97} +(-17.1921 + 1.15199i) q^{98} +(2.76295 + 1.83470i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9} - 14 q^{10} + 11 q^{11} - 30 q^{12} - 8 q^{13} + 6 q^{14} - 12 q^{15} - 4 q^{17} - q^{18} - 2 q^{19} + 24 q^{20} - 2 q^{21} - 14 q^{22} + 16 q^{24} - 10 q^{25} + 4 q^{26} - 16 q^{27} + 29 q^{28} - 58 q^{29} + 11 q^{30} - 19 q^{31} - 64 q^{32} + 6 q^{33} - 88 q^{34} + 17 q^{35} - 20 q^{36} - 20 q^{37} + 29 q^{38} + 4 q^{39} + 51 q^{40} - 68 q^{41} - 11 q^{42} + 92 q^{43} - 21 q^{44} - 4 q^{45} - 5 q^{46} - 26 q^{47} - 10 q^{48} + 37 q^{49} - 10 q^{50} + 6 q^{51} - 14 q^{52} - 3 q^{53} - 6 q^{54} - 32 q^{55} + 24 q^{56} - 36 q^{57} + 52 q^{58} + 7 q^{59} - 12 q^{60} - 21 q^{61} + 92 q^{62} - 7 q^{63} - 72 q^{64} - 66 q^{65} - 23 q^{66} - 4 q^{67} - 17 q^{68} + 40 q^{69} - q^{70} + 58 q^{71} + 16 q^{72} - 3 q^{73} - 28 q^{74} + 20 q^{75} + 168 q^{76} - 34 q^{77} + 132 q^{78} + 9 q^{79} - 5 q^{80} + 8 q^{81} - 42 q^{82} + 60 q^{83} - 39 q^{84} + 110 q^{85} + 13 q^{86} - 46 q^{87} + 92 q^{88} - 10 q^{89} + 8 q^{90} + 10 q^{91} + 110 q^{92} - 19 q^{93} - 46 q^{94} + 43 q^{95} - 4 q^{96} + 64 q^{97} - 88 q^{98} + 28 q^{99}+O(q^{100}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9 - 14 * q^10 + 11 * q^11 - 30 * q^12 - 8 * q^13 + 6 * q^14 - 12 * q^15 - 4 * q^17 - q^18 - 2 * q^19 + 24 * q^20 - 2 * q^21 - 14 * q^22 + 16 * q^24 - 10 * q^25 + 4 * q^26 - 16 * q^27 + 29 * q^28 - 58 * q^29 + 11 * q^30 - 19 * q^31 - 64 * q^32 + 6 * q^33 - 88 * q^34 + 17 * q^35 - 20 * q^36 - 20 * q^37 + 29 * q^38 + 4 * q^39 + 51 * q^40 - 68 * q^41 - 11 * q^42 + 92 * q^43 - 21 * q^44 - 4 * q^45 - 5 * q^46 - 26 * q^47 - 10 * q^48 + 37 * q^49 - 10 * q^50 + 6 * q^51 - 14 * q^52 - 3 * q^53 - 6 * q^54 - 32 * q^55 + 24 * q^56 - 36 * q^57 + 52 * q^58 + 7 * q^59 - 12 * q^60 - 21 * q^61 + 92 * q^62 - 7 * q^63 - 72 * q^64 - 66 * q^65 - 23 * q^66 - 4 * q^67 - 17 * q^68 + 40 * q^69 - q^70 + 58 * q^71 + 16 * q^72 - 3 * q^73 - 28 * q^74 + 20 * q^75 + 168 * q^76 - 34 * q^77 + 132 * q^78 + 9 * q^79 - 5 * q^80 + 8 * q^81 - 42 * q^82 + 60 * q^83 - 39 * q^84 + 110 * q^85 + 13 * q^86 - 46 * q^87 + 92 * q^88 - 10 * q^89 + 8 * q^90 + 10 * q^91 + 110 * q^92 - 19 * q^93 - 46 * q^94 + 43 * q^95 - 4 * q^96 + 64 * q^97 - 88 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.257299	+	2.44803i	−0.181938	+	1.73102i	0.398894	+	0.916997i	$0.369394\pi$
$2$	−0.257299	+	2.44803i	−0.181938	+	1.73102i	−0.580832	+	0.814024i	$0.697273\pi$
$3$	0.669131	+	0.743145i	0.386323	+	0.429055i
$3$	0.669131	+	0.743145i	0.386323	+	0.429055i
$4$	−3.97037	−	0.843927i	−1.98518	−	0.421964i
$5$	3.02928	+	1.34872i	1.35474	+	0.603167i	0.950282	−	0.311391i	$-0.100795\pi$
$5$	3.02928	+	1.34872i	1.35474	+	0.603167i	0.404454	+	0.914558i	$0.367462\pi$
$6$	−1.99141	+	1.44684i	−0.812989	+	0.590671i
$7$	2.02429	+	1.70360i	0.765110	+	0.643900i
$7$	2.02429	+	1.70360i	0.765110	+	0.643900i
$8$	1.56623	−	4.82036i	0.553746	−	1.70426i
$9$	−0.104528	+	0.994522i	−0.0348428	+	0.331507i
$10$	−4.08115	+	7.06876i	−1.29057	+	2.23534i
$11$	1.53584	−	2.93959i	0.463074	−	0.886320i
$11$	1.53584	−	2.93959i	0.463074	−	0.886320i
$12$	−2.02953	−	3.51525i	−0.585876	−	1.01477i
$13$	−3.52247	−	2.55923i	−0.976958	−	0.709801i	−0.0199311	−	0.999801i	$-0.506345\pi$
$13$	−3.52247	−	2.55923i	−0.976958	−	0.709801i	−0.957027	+	0.290000i	$0.906345\pi$
$14$	−4.69131	+	4.51719i	−1.25381	+	1.20727i
$15$	1.02469	+	3.15367i	0.264573	+	0.814273i
$16$	3.98113	+	1.77251i	0.995283	+	0.443128i
$17$	−0.590445	−	5.61771i	−0.143204	−	1.36249i	−0.796155	−	0.605093i	$-0.793136\pi$
$17$	−0.590445	−	5.61771i	−0.143204	−	1.36249i	0.652951	−	0.757400i	$-0.273531\pi$
$18$	−2.40773	−	0.511778i	−0.567507	−	0.120627i
$19$	−2.27984	+	0.484596i	−0.523032	+	0.111174i	−0.461859	−	0.886953i	$-0.652817\pi$
$19$	−2.27984	+	0.484596i	−0.523032	+	0.111174i	−0.0611728	+	0.998127i	$0.519484\pi$
$20$	−10.8891	−	7.91142i	−2.43488	−	1.76905i
$21$	0.0884929	+	2.64427i	0.0193107	+	0.577027i
$22$	6.80104	+	4.51614i	1.44999	+	0.962845i
$23$	−0.699447	−	1.21148i	−0.145845	−	0.252611i	0.783843	−	0.620959i	$-0.213257\pi$
$23$	−0.699447	−	1.21148i	−0.145845	−	0.252611i	−0.929688	+	0.368348i	$0.879923\pi$
$24$	4.63024	−	2.06152i	0.945144	−	0.420805i
$25$	4.01184	+	4.45560i	0.802368	+	0.891120i
$26$	7.17139	−	7.96464i	1.40643	−	1.56199i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	−6.59946	−	8.47227i	−1.24718	−	1.60111i
$29$	−0.768970	−	2.36665i	−0.142794	−	0.439475i	0.853927	−	0.520393i	$-0.174215\pi$
$29$	−0.768970	−	2.36665i	−0.142794	−	0.439475i	−0.996721	+	0.0809183i	$0.974215\pi$
$30$	−7.98393	+	1.69704i	−1.45766	+	0.309835i
$31$	1.27031	−	0.565577i	0.228154	−	0.101581i	−0.289476	−	0.957185i	$-0.593481\pi$
$31$	1.27031	−	0.565577i	0.228154	−	0.101581i	0.517630	+	0.855605i	$0.326814\pi$
$32$	−0.295082	+	0.511097i	−0.0521636	+	0.0903500i
$33$	3.21222	−	0.825617i	0.559176	−	0.143721i
$34$	13.9042			2.38456
$35$	3.83446	+	7.89089i	0.648142	+	1.33380i
$36$	1.25432	−	3.86040i	0.209053	−	0.643400i
$37$	1.03060	−	1.14460i	0.169430	−	0.188171i	−0.652450	−	0.757832i	$-0.726259\pi$
$37$	1.03060	−	1.14460i	0.169430	−	0.188171i	0.821880	+	0.569661i	$0.192925\pi$
$38$	−0.599705	−	5.70582i	−0.0972851	−	0.925606i
$39$	−0.455118	−	4.33016i	−0.0728773	−	0.693381i
$40$	11.2459	−	12.4898i	1.77813	−	1.97481i
$41$	−2.71653	+	8.36062i	−0.424251	+	1.30571i	0.479459	+	0.877564i	$0.340833\pi$
$41$	−2.71653	+	8.36062i	−0.424251	+	1.30571i	−0.903710	+	0.428145i	$0.859167\pi$
$42$	−6.49603	−	0.463734i	−1.00236	−	0.0715557i
$43$	−6.73424			−1.02696			−0.513481	−	0.858101i	$-0.671644\pi$
$43$	−6.73424			−1.02696			−0.513481	+	0.858101i	$0.671644\pi$
$44$	−8.57866	+	10.3751i	−1.29328	+	1.56411i
$45$	−1.65798	+	2.87171i	−0.247157	+	0.428089i
$46$	3.14571	−	1.40056i	0.463809	−	0.206501i
$47$	4.31884	−	0.917998i	0.629968	−	0.133904i	0.118147	−	0.992996i	$-0.462305\pi$
$47$	4.31884	−	0.917998i	0.629968	−	0.133904i	0.511821	+	0.859092i	$0.328971\pi$
$48$	1.34666	+	4.14460i	0.194374	+	0.598221i
$49$	1.19550	+	6.89716i	0.170785	+	0.985308i
$50$	−11.9397	+	8.67469i	−1.68853	+	1.22679i
$51$	3.77968	−	4.19776i	0.529262	−	0.587805i
$52$	11.8257	+	13.1338i	1.63993	+	1.82133i
$53$	−9.51955	+	4.23838i	−1.30761	+	0.582186i	−0.937882	−	0.346954i	$-0.887216\pi$
$53$	−9.51955	+	4.23838i	−1.30761	+	0.582186i	−0.369729	+	0.929140i	$0.620549\pi$
$54$	−1.23076	−	2.13174i	−0.167485	−	0.290093i
$55$	8.61719	−	6.83342i	1.16194	−	0.921418i
$56$	11.3825	−	7.08958i	1.52105	−	0.947385i
$57$	−1.88564	−	1.37000i	−0.249759	−	0.181460i
$58$	5.99148	−	1.27353i	0.786720	−	0.167223i
$59$	14.4997	+	3.08202i	1.88771	+	0.401244i	0.998424	−	0.0561159i	$-0.0178716\pi$
$59$	14.4997	+	3.08202i	1.88771	+	0.401244i	0.889282	+	0.457360i	$0.151205\pi$
$60$	−1.40692	−	13.3860i	−0.181633	−	1.72812i
$61$	−1.28144	−	0.570534i	−0.164072	−	0.0730493i	0.323058	−	0.946379i	$-0.395289\pi$
$61$	−1.28144	−	0.570534i	−0.164072	−	0.0730493i	−0.487129	+	0.873330i	$0.661956\pi$
$62$	1.05770	+	3.25528i	0.134329	+	0.413421i
$63$	−1.90586	+	1.83513i	−0.240116	+	0.231204i
$64$	5.87596	+	4.26913i	0.734495	+	0.533642i
$65$	−7.21887	−	12.5035i	−0.895391	−	1.55086i
$66$	1.19464	+	8.07605i	0.147050	+	0.994093i
$67$	−7.57690	+	13.1236i	−0.925665	+	1.60330i	−0.135178	+	0.990821i	$0.543161\pi$
$67$	−7.57690	+	13.1236i	−0.925665	+	1.60330i	−0.790487	+	0.612478i	$0.790173\pi$
$68$	−2.39665	+	22.8026i	−0.290637	+	2.76523i
$69$	0.432282	−	1.33043i	0.0520407	−	0.160165i
$70$	−20.3038	+	7.35657i	−2.42676	+	0.879278i
$71$	9.30320	−	6.75917i	1.10409	−	0.802166i	0.122365	−	0.992485i	$-0.460952\pi$
$71$	9.30320	−	6.75917i	1.10409	−	0.802166i	0.981722	+	0.190319i	$0.0609522\pi$
$72$	4.63024	+	2.06152i	0.545679	+	0.242952i
$73$	−8.70766	−	1.85087i	−1.01915	−	0.216628i	−0.332108	−	0.943241i	$-0.607760\pi$
$73$	−8.70766	−	1.85087i	−1.01915	−	0.216628i	−0.687047	+	0.726613i	$0.741093\pi$
$74$	2.53684	+	2.81745i	0.294902	+	0.327522i
$75$	−0.626711	+	5.96275i	−0.0723663	+	0.688520i
$76$	9.46078			1.08523
$77$	8.11687	−	3.33412i	0.925004	−	0.379958i
$78$	10.7175			1.21352
$79$	−0.348373	+	3.31455i	−0.0391950	+	0.372916i	0.957289	+	0.289133i	$0.0933669\pi$
$79$	−0.348373	+	3.31455i	−0.0391950	+	0.372916i	−0.996484	+	0.0837829i	$0.973300\pi$
$80$	9.66933	+	10.7389i	1.08106	+	1.20064i
$81$	−0.978148	−	0.207912i	−0.108683	−	0.0231013i
$82$	−19.7681	−	8.80133i	−2.18302	−	0.971944i
$83$	11.5379	−	8.38278i	1.26645	−	0.920130i	0.267395	−	0.963587i	$-0.413837\pi$
$83$	11.5379	−	8.38278i	1.26645	−	0.920130i	0.999055	+	0.0434573i	$0.0138373\pi$
$84$	1.88022	−	10.5734i	0.205149	−	1.15365i
$85$	5.78811	−	17.8140i	0.627808	−	1.93219i
$86$	1.73271	−	16.4856i	0.186843	−	1.77769i
$87$	1.24422	−	2.15505i	0.133394	−	0.231046i
$88$	−11.7644	−	12.0074i	−1.25409	−	1.27999i
$89$	−3.54340	−	6.13736i	−0.375600	−	0.650559i	0.614817	−	0.788670i	$-0.289230\pi$
$89$	−3.54340	−	6.13736i	−0.375600	−	0.650559i	−0.990417	+	0.138112i	$0.955897\pi$
$90$	−6.60344	−	4.79768i	−0.696063	−	0.505720i
$91$	−2.77061	−	11.1815i	−0.290439	−	1.17214i
$92$	1.75466	+	5.40030i	0.182936	+	0.563020i
$93$	1.27031	+	0.565577i	0.131725	+	0.0586476i
$94$	1.13606	+	10.8089i	0.117175	+	1.11485i
$95$	−7.55987	−	1.60690i	−0.775626	−	0.164864i
$96$	−0.577267	+	0.122702i	−0.0589171	+	0.0125232i
$97$	1.16912	+	0.849417i	0.118706	+	0.0862452i	0.645554	−	0.763714i	$-0.276626\pi$
$97$	1.16912	+	0.849417i	0.118706	+	0.0862452i	−0.526848	+	0.849959i	$0.676626\pi$
$98$	−17.1921	+	1.15199i	−1.73666	+	0.116368i
$99$	2.76295	+	1.83470i	0.277687	+	0.184394i
$100$	−12.1683	−	21.0761i	−1.21683	−	2.10761i
$101$	1.35768	−	0.604476i	0.135094	−	0.0601476i	−0.338076	−	0.941119i	$-0.609776\pi$
$101$	1.35768	−	0.604476i	0.135094	−	0.0601476i	0.473170	+	0.880971i	$0.343110\pi$
$102$	9.30376	+	10.3329i	0.921209	+	1.02311i
$103$	2.93422	−	3.25879i	0.289118	−	0.321098i	−0.581036	−	0.813878i	$-0.697353\pi$
$103$	2.93422	−	3.25879i	0.289118	−	0.321098i	0.870154	+	0.492780i	$0.164019\pi$
$104$	−17.8534	+	12.9712i	−1.75067	+	1.27194i
$105$	−3.29832	+	8.12959i	−0.321883	+	0.793367i
$106$	−7.92632	−	24.3947i	−0.769872	−	2.36942i
$107$	−7.56628	+	1.60826i	−0.731460	+	0.155477i	−0.558562	−	0.829463i	$-0.688647\pi$
$107$	−7.56628	+	1.60826i	−0.731460	+	0.155477i	−0.172898	+	0.984940i	$0.555313\pi$
$108$	3.70814	−	1.65097i	0.356816	−	0.158865i
$109$	−3.73990	+	6.47769i	−0.358217	+	0.620450i	−0.987663	−	0.156594i	$-0.949949\pi$
$109$	−3.73990	+	6.47769i	−0.358217	+	0.620450i	0.629446	+	0.777044i	$0.283282\pi$
$110$	14.5112	+	22.8534i	1.38359	+	2.17899i
$111$	1.54021			0.146190
$112$	5.03931	+	10.3703i	0.476170	+	0.979904i
$113$	−2.40868	+	7.41315i	−0.226590	+	0.697371i	0.771537	+	0.636185i	$0.219488\pi$
$113$	−2.40868	+	7.41315i	−0.226590	+	0.697371i	−0.998126	+	0.0611863i	$0.980512\pi$
$114$	3.83897	−	4.26360i	0.359552	−	0.399323i
$115$	−0.484874	−	4.61327i	−0.0452148	−	0.430190i
$116$	1.05581	+	10.0454i	0.0980300	+	0.932693i
$117$	2.91340	−	3.23566i	0.269344	−	0.299137i
$118$	−11.2756	+	34.7028i	−1.03801	+	3.19466i
$119$	8.37509	−	12.3777i	0.767743	−	1.13467i
$120$	16.8067			1.53424
$121$	−6.28238	−	9.02949i	−0.571125	−	0.820863i
$122$	1.72640	−	2.99021i	0.156301	−	0.270721i
$123$	−8.03086	+	3.57557i	−0.724118	+	0.322398i
$124$	−5.52089	+	1.17350i	−0.495791	+	0.105384i
$125$	1.02018	+	3.13979i	0.0912476	+	0.280831i
$126$	−4.00207	−	5.13779i	−0.356533	−	0.457711i
$127$	−10.3486	+	7.51870i	−0.918290	+	0.667177i	−0.943098	−	0.332516i	$-0.892103\pi$
$127$	−10.3486	+	7.51870i	−0.918290	+	0.667177i	0.0248079	+	0.999692i	$0.492103\pi$
$128$	−12.7526	+	14.1632i	−1.12719	+	1.25187i
$129$	−4.50609	−	5.00452i	−0.396739	−	0.440623i
$130$	32.4663	−	14.4549i	2.84748	−	1.26778i
$131$	8.36576	+	14.4899i	0.730920	+	1.26599i	0.956490	+	0.291764i	$0.0942421\pi$
$131$	8.36576	+	14.4899i	0.730920	+	1.26599i	−0.225570	+	0.974227i	$0.572425\pi$
$132$	−13.4505	+	0.567120i	−1.17071	+	0.0493615i
$133$	−5.44062	−	2.90298i	−0.471762	−	0.251720i
$134$	−30.1774	−	21.9252i	−2.60693	−	1.89405i
$135$	−3.24350	+	0.689427i	−0.279156	+	0.0593364i
$136$	−28.0041	−	5.95246i	−2.40134	−	0.510420i
$137$	0.295379	+	2.81034i	0.0252359	+	0.240104i	0.999867	+	0.0162878i	$0.00518480\pi$
$137$	0.295379	+	2.81034i	0.0252359	+	0.240104i	−0.974631	+	0.223816i	$0.928149\pi$
$138$	3.14571	+	1.40056i	0.267780	+	0.119223i
$139$	−0.954810	−	2.93860i	−0.0809859	−	0.249249i	0.902363	−	0.430977i	$-0.141831\pi$
$139$	−0.954810	−	2.93860i	−0.0809859	−	0.249249i	−0.983349	+	0.181728i	$0.941831\pi$
$140$	−8.56487	−	34.5657i	−0.723864	−	2.92134i
$141$	3.57207	+	2.59526i	0.300823	+	0.218561i
$142$	14.1530	+	24.5137i	1.18769	+	2.05714i
$143$	−12.9330	+	6.42406i	−1.08151	+	0.537207i
$144$	−2.17894	+	3.77404i	−0.181579	+	0.314504i
$145$	0.862524	−	8.20637i	0.0716287	−	0.681502i
$146$	6.77146	−	20.8404i	0.560410	−	1.72477i
$147$	−4.32564	+	5.50353i	−0.356773	+	0.453923i
$148$	−5.05782	+	3.67472i	−0.415750	+	0.302060i
$149$	−14.2834	−	6.35938i	−1.17014	−	0.520981i	−0.272694	−	0.962101i	$-0.587915\pi$
$149$	−14.2834	−	6.35938i	−1.17014	−	0.520981i	−0.897448	+	0.441120i	$0.854581\pi$
$150$	−14.4358	−	3.06842i	−1.17868	−	0.250535i
$151$	11.5070	+	12.7798i	0.936424	+	1.04000i	0.999119	+	0.0419716i	$0.0133639\pi$
$151$	11.5070	+	12.7798i	0.936424	+	1.04000i	−0.0626947	+	0.998033i	$0.519969\pi$
$152$	−1.23483	+	11.7487i	−0.100158	+	0.952942i
$153$	5.64865			0.456666
$154$	6.07358	+	20.7282i	0.489423	+	1.67033i
$155$	4.61093			0.370359
$156$	−1.84736	+	17.5764i	−0.147907	+	1.40724i
$157$	−7.64514	−	8.49079i	−0.610148	−	0.677638i	0.356338	−	0.934357i	$-0.384025\pi$
$157$	−7.64514	−	8.49079i	−0.610148	−	0.677638i	−0.966486	+	0.256719i	$0.917359\pi$
$158$	−8.02448	−	1.70566i	−0.638394	−	0.135695i
$159$	−9.51955	−	4.23838i	−0.754949	−	0.336125i
$160$	−1.58321	+	1.15027i	−0.125164	+	0.0909370i
$161$	0.647990	−	3.64396i	0.0510688	−	0.287184i
$162$	0.760651	−	2.34104i	0.0597624	−	0.183930i
$163$	1.64887	−	15.6880i	0.129150	−	1.22878i	−0.717475	−	0.696585i	$-0.754702\pi$
$163$	1.64887	−	15.6880i	0.129150	−	1.22878i	0.846624	−	0.532191i	$-0.178631\pi$
$164$	17.8414	−	30.9022i	1.39318	−	2.41305i
$165$	10.8442	+	1.83137i	0.844223	+	0.142572i
$166$	17.5526	+	30.4021i	1.36235	+	2.35966i
$167$	6.29585	+	4.57421i	0.487188	+	0.353963i	0.804102	−	0.594492i	$-0.202647\pi$
$167$	6.29585	+	4.57421i	0.487188	+	0.353963i	−0.316914	+	0.948454i	$0.602647\pi$
$168$	12.8849	+	3.71497i	0.994095	+	0.286616i
$169$	1.84095	+	5.66586i	0.141612	+	0.435835i
$170$	42.1199	+	18.7530i	3.23045	+	1.43829i
$171$	−0.243632	−	2.31801i	−0.0186310	−	0.177262i
$172$	26.7374	+	5.68321i	2.03871	+	0.433341i
$173$	13.1594	−	2.79712i	1.00049	−	0.212661i	0.321582	−	0.946882i	$-0.395785\pi$
$173$	13.1594	−	2.79712i	1.00049	−	0.212661i	0.678911	+	0.734220i	$0.262452\pi$
$174$	4.95550	+	3.60038i	0.375676	+	0.272944i
$175$	0.530568	+	15.8540i	0.0401072	+	1.19845i
$176$	11.3248	−	8.98059i	0.853643	−	0.676937i
$177$	7.41184	+	12.8377i	0.557108	+	0.964939i
$178$	15.9362	−	7.09524i	1.19447	−	0.531810i
$179$	2.10844	+	2.34166i	0.157592	+	0.175024i	0.816770	−	0.576963i	$-0.195762\pi$
$179$	2.10844	+	2.34166i	0.157592	+	0.175024i	−0.659178	+	0.751987i	$0.729096\pi$
$180$	9.00630	−	10.0025i	0.671290	−	0.745543i
$181$	−6.80104	+	4.94124i	−0.505517	+	0.367280i	−0.811120	−	0.584879i	$-0.801142\pi$
$181$	−6.80104	+	4.94124i	−0.505517	+	0.367280i	0.305603	+	0.952159i	$0.401142\pi$
$182$	28.0855	−	3.90555i	2.08184	−	0.289499i
$183$	−0.433461	−	1.33406i	−0.0320424	−	0.0986163i
$184$	−6.93526	+	1.47414i	−0.511274	+	0.108675i
$185$	4.66573	−	2.07731i	0.343031	−	0.152727i
$186$	−1.71140	+	2.96423i	−0.125486	+	0.217348i
$187$	−17.4206	−	6.89224i	−1.27392	−	0.504011i
$188$	−17.9221			−1.30710
$189$	−2.63904	−	0.188393i	−0.191962	−	0.0137036i
$190$	5.87889	−	18.0934i	0.426499	−	1.31263i
$191$	−12.6994	+	14.1041i	−0.918896	+	1.02054i	0.0808202	+	0.996729i	$0.474246\pi$
$191$	−12.6994	+	14.1041i	−0.918896	+	1.02054i	−0.999717	+	0.0238090i	$0.992421\pi$
$192$	0.759199	+	7.22329i	0.0547905	+	0.521296i
$193$	−1.50397	−	14.3093i	−0.108258	−	1.03001i	−0.904920	−	0.425581i	$-0.860070\pi$
$193$	−1.50397	−	14.3093i	−0.108258	−	1.03001i	0.796662	−	0.604425i	$-0.206597\pi$
$194$	−2.38021	+	2.64350i	−0.170889	+	0.189792i
$195$	4.46151	−	13.7311i	0.319495	−	0.983305i
$196$	1.07414	−	28.3932i	0.0767244	−	2.02808i
$197$	1.36271			0.0970894			0.0485447	−	0.998821i	$-0.484542\pi$
$197$	1.36271			0.0970894			0.0485447	+	0.998821i	$0.484542\pi$
$198$	−5.20231	+	6.29172i	−0.369712	+	0.447133i
$199$	5.51137	−	9.54597i	0.390691	−	0.676696i	−0.601850	−	0.798609i	$-0.705570\pi$
$199$	5.51137	−	9.54597i	0.390691	−	0.676696i	0.992541	+	0.121913i	$0.0389029\pi$
$200$	27.7611	−	12.3600i	1.96300	−	0.873985i
$201$	−14.8226	+	3.15065i	−1.04551	+	0.222230i
$202$	1.13045	+	3.47916i	0.0795381	+	0.244793i
$203$	2.47520	−	6.10079i	0.173725	−	0.428192i
$204$	−18.5493	+	13.4769i	−1.29871	+	0.943571i
$205$	−19.5053	+	21.6628i	−1.36231	+	1.51300i
$206$	7.22264	+	8.02156i	0.503225	+	0.558889i
$207$	1.27795	−	0.568982i	0.0888239	−	0.0395470i
$208$	−9.48716	−	16.4322i	−0.657816	−	1.13937i
$209$	−2.07697	+	7.44607i	−0.143667	+	0.515055i
$210$	−19.0529	−	10.1661i	−1.31477	−	0.701529i
$211$	9.52042	+	6.91699i	0.655413	+	0.476185i	0.865111	−	0.501581i	$-0.167248\pi$
$211$	9.52042	+	6.91699i	0.655413	+	0.476185i	−0.209698	+	0.977766i	$0.567248\pi$
$212$	41.3730	−	8.79410i	2.84151	−	0.603981i
$213$	11.2481	+	2.39086i	0.770707	+	0.163819i
$214$	−1.99029	−	18.9363i	−0.136053	−	1.29446i
$215$	−20.3999	−	9.08263i	−1.39126	−	0.619430i
$216$	1.56623	+	4.82036i	0.106568	+	0.327984i
$217$	3.53499	+	1.01920i	0.239971	+	0.0691880i
$218$	−14.8953	−	10.8221i	−1.00884	−	0.732964i
$219$	−4.45110	−	7.70953i	−0.300777	−	0.520962i
$220$	−39.9803	+	19.8589i	−2.69547	+	1.33889i
$221$	−12.2971	+	21.2993i	−0.827196	+	1.43275i
$222$	−0.396294	+	3.77048i	−0.0265975	+	0.253058i
$223$	−0.430616	+	1.32530i	−0.0288362	+	0.0887486i	−0.964439	−	0.264306i	$-0.914857\pi$
$223$	−0.430616	+	1.32530i	−0.0288362	+	0.0887486i	0.935603	+	0.353055i	$0.114857\pi$
$224$	−1.46803	+	0.531906i	−0.0980872	+	0.0355395i
$225$	−4.85054	+	3.52412i	−0.323369	+	0.234942i
$226$	−17.5279	−	7.80392i	−1.16594	−	0.519109i
$227$	0.583838	+	0.124099i	0.0387507	+	0.00823672i	0.227246	−	0.973837i	$-0.427028\pi$
$227$	0.583838	+	0.124099i	0.0387507	+	0.00823672i	−0.188496	+	0.982074i	$0.560361\pi$
$228$	6.33049	+	7.03073i	0.419247	+	0.465621i
$229$	0.00960223	−	0.0913591i	0.000634533	−	0.00603718i	−0.994200	−	0.107547i	$-0.965701\pi$
$229$	0.00960223	−	0.0913591i	0.000634533	−	0.00603718i	0.994835	+	0.101509i	$0.0323672\pi$
$230$	11.4182			0.752893
$231$	7.90898	+	3.80105i	0.520373	+	0.250091i
$232$	−12.6125			−0.828050
$233$	−1.12703	+	10.7230i	−0.0738343	+	0.702487i	0.893514	+	0.449036i	$0.148232\pi$
$233$	−1.12703	+	10.7230i	−0.0738343	+	0.702487i	−0.967348	+	0.253451i	$0.918434\pi$
$234$	7.17139	+	7.96464i	0.468809	+	0.520665i
$235$	14.3211	+	3.04405i	0.934206	+	0.198572i
$236$	−54.9683	−	24.4735i	−3.57813	−	1.59309i
$237$	−2.69630	+	1.95897i	−0.175143	+	0.127249i
$238$	28.1462	+	23.6873i	1.82445	+	1.53542i
$239$	4.61373	−	14.1996i	0.298438	−	0.918497i	−0.683607	−	0.729850i	$-0.739590\pi$
$239$	4.61373	−	14.1996i	0.298438	−	0.918497i	0.982045	−	0.188647i	$-0.0604101\pi$
$240$	−1.51050	+	14.3714i	−0.0975022	+	0.927672i
$241$	−4.47518	+	7.75123i	−0.288271	+	0.499301i	−0.973397	−	0.229124i	$-0.926414\pi$
$241$	−4.47518	+	7.75123i	−0.288271	+	0.499301i	0.685126	+	0.728425i	$0.259747\pi$
$242$	23.7209	−	13.0562i	1.52484	−	0.839284i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	4.60630	+	3.34667i	0.294888	+	0.214249i
$245$	−5.68086	+	22.5058i	−0.362937	+	1.43784i
$246$	−6.68678	−	20.5798i	−0.426334	−	1.31212i
$247$	9.27087	+	4.12766i	0.589891	+	0.262637i
$248$	−0.736693	−	7.00917i	−0.0467801	−	0.445083i
$249$	13.9500	+	2.96516i	0.884045	+	0.187909i
$250$	−7.94879	+	1.68957i	−0.502726	+	0.106858i
$251$	6.00307	+	4.36148i	0.378910	+	0.275294i	0.760896	−	0.648874i	$-0.224760\pi$
$251$	6.00307	+	4.36148i	0.378910	+	0.275294i	−0.381986	+	0.924168i	$0.624760\pi$
$252$	9.11569	−	5.67771i	0.574234	−	0.357662i
$253$	−4.63549	+	0.195449i	−0.291431	+	0.0122878i
$254$	−15.7433	−	27.2683i	−0.987825	−	1.71096i
$255$	17.1113	−	7.61846i	1.07155	−	0.477087i
$256$	−21.6710	−	24.0680i	−1.35443	−	1.50425i
$257$	1.40662	−	1.56221i	0.0877424	−	0.0974478i	−0.697675	−	0.716415i	$-0.745782\pi$
$257$	1.40662	−	1.56221i	0.0877424	−	0.0974478i	0.785417	+	0.618967i	$0.212449\pi$
$258$	13.4106	−	9.74340i	0.834910	−	0.606597i
$259$	4.03617	−	0.561267i	0.250795	−	0.0348754i
$260$	18.1096	+	55.7355i	1.12311	+	3.45657i
$261$	2.43406	−	0.517376i	0.150665	−	0.0320247i
$262$	−37.6243	+	16.7514i	−2.32444	+	1.03491i
$263$	−7.58416	+	13.1362i	−0.467660	+	0.810010i	−0.999317	−	0.0369493i	$-0.988236\pi$
$263$	−7.58416	+	13.1362i	−0.467660	+	0.810010i	0.531658	+	0.846959i	$0.321569\pi$
$264$	1.05131	−	16.7772i	0.0647034	−	1.03256i
$265$	−34.5538			−2.12262
$266$	8.50645	−	12.5719i	0.521564	−	0.770832i
$267$	2.18994	−	6.73996i	0.134022	−	0.412479i
$268$	41.1584	−	45.7110i	2.51415	−	2.79225i
$269$	−0.946354	−	9.00396i	−0.0577002	−	0.548981i	−0.984742	−	0.174022i	$-0.944324\pi$
$269$	−0.946354	−	9.00396i	−0.0577002	−	0.548981i	0.927041	−	0.374959i	$-0.122343\pi$
$270$	−0.853192	−	8.11758i	−0.0519236	−	0.494020i
$271$	−0.333117	+	0.369964i	−0.0202354	+	0.0224737i	−0.753178	−	0.657817i	$-0.771480\pi$
$271$	−0.333117	+	0.369964i	−0.0202354	+	0.0224737i	0.732942	+	0.680291i	$0.238147\pi$
$272$	7.60682	−	23.4114i	0.461231	−	1.41952i
$273$	6.45557	−	9.54084i	0.390709	−	0.577438i
$274$	−6.95581			−0.420216
$275$	19.2592	−	4.95007i	1.16137	−	0.298500i
$276$	−2.83910	+	4.91747i	−0.170894	+	0.295997i
$277$	3.91640	−	1.74369i	0.235314	−	0.104768i	−0.285692	−	0.958321i	$-0.592224\pi$
$277$	3.91640	−	1.74369i	0.235314	−	0.104768i	0.521006	+	0.853553i	$0.325557\pi$
$278$	7.43946	−	1.58131i	0.446189	−	0.0948405i
$279$	0.429696	+	1.32247i	0.0257252	+	0.0791741i
$280$	44.0426	−	6.12453i	2.63205	−	0.366011i
$281$	15.3087	−	11.1225i	0.913243	−	0.663510i	−0.0285901	−	0.999591i	$-0.509102\pi$
$281$	15.3087	−	11.1225i	0.913243	−	0.663510i	0.941833	+	0.336081i	$0.109102\pi$
$282$	−7.27238	+	8.07680i	−0.433064	+	0.480966i
$283$	−0.140887	−	0.156471i	−0.00837485	−	0.00930122i	0.738943	−	0.673768i	$-0.235325\pi$
$283$	−0.140887	−	0.156471i	−0.00837485	−	0.00930122i	−0.747318	+	0.664467i	$0.768659\pi$
$284$	−42.6414	+	18.9852i	−2.53030	+	1.12656i
$285$	−3.86438	−	6.69331i	−0.228906	−	0.396477i
$286$	−12.3986	−	33.3134i	−0.733147	−	1.96986i
$287$	−19.7422	+	12.2964i	−1.16534	+	0.725835i
$288$	−0.477452	−	0.346889i	−0.0281341	−	0.0204407i
$289$	−14.5815	+	3.09939i	−0.857734	+	0.182317i
$290$	19.8675	+	4.22297i	1.16666	+	0.247981i
$291$	0.151056	+	1.43720i	0.00885504	+	0.0842500i
$292$	33.0106	+	14.6973i	1.93180	+	0.860093i
$293$	−3.29812	−	10.1506i	−0.192678	−	0.593003i	−0.999996	−	0.00288587i	$-0.999081\pi$
$293$	−3.29812	−	10.1506i	−0.192678	−	0.593003i	0.807317	−	0.590118i	$-0.200919\pi$
$294$	−12.3598	−	12.0054i	−0.720840	−	0.700167i
$295$	39.7670	+	28.8924i	2.31533	+	1.68218i
$296$	−3.90322	−	6.76057i	−0.226870	−	0.392950i
$297$	0.485325	+	3.28092i	0.0281614	+	0.190378i
$298$	19.2431	−	33.3300i	1.11472	−	1.93075i
$299$	−0.636663	+	6.05744i	−0.0368192	+	0.350311i
$300$	7.52040	−	23.1454i	0.434191	−	1.33630i
$301$	−13.6321	−	11.4725i	−0.785739	−	0.661261i
$302$	−34.2461	+	24.8812i	−1.97064	+	1.43175i
$303$	1.35768	+	0.604476i	0.0779964	+	0.0347262i
$304$	−9.93530	−	2.11181i	−0.569829	−	0.121121i
$305$	−3.11235	−	3.45661i	−0.178213	−	0.197925i
$306$	−1.45339	+	13.8281i	−0.0830848	+	0.790499i
$307$	23.3838			1.33458			0.667292	−	0.744796i	$-0.267453\pi$
$307$	23.3838			1.33458			0.667292	+	0.744796i	$0.267453\pi$
$308$	−35.0407	+	6.38763i	−1.99663	+	0.363969i
$309$	4.38513			0.249461
$310$	−1.18639	+	11.2877i	−0.0673821	+	0.641098i
$311$	−7.63540	−	8.47997i	−0.432964	−	0.480855i	0.486696	−	0.873571i	$-0.338202\pi$
$311$	−7.63540	−	8.47997i	−0.432964	−	0.480855i	−0.919660	+	0.392717i	$0.871535\pi$
$312$	−21.5858	−	4.58820i	−1.22205	−	0.259755i
$313$	21.9134	+	9.75647i	1.23862	+	0.551468i	0.918316	−	0.395847i	$-0.129549\pi$
$313$	21.9134	+	9.75647i	1.23862	+	0.551468i	0.320302	+	0.947316i	$0.396216\pi$
$314$	22.7528	−	16.5309i	1.28402	−	0.932892i
$315$	−8.24847	+	2.98863i	−0.464749	+	0.168390i
$316$	4.18040	−	12.8660i	0.235166	−	0.723767i
$317$	−1.55194	+	14.7657i	−0.0871658	+	0.829327i	0.860368	+	0.509673i	$0.170233\pi$
$317$	−1.55194	+	14.7657i	−0.0871658	+	0.829327i	−0.947534	+	0.319654i	$0.896433\pi$
$318$	12.8251	−	22.2136i	0.719193	−	1.24568i
$319$	−8.13799	−	1.37434i	−0.455640	−	0.0769482i
$320$	12.0420	+	20.8574i	0.673171	+	1.16597i
$321$	−6.25800	−	4.54671i	−0.349288	−	0.253772i
$322$	8.75381	+	2.52389i	0.487831	+	0.140651i
$323$	4.06844	+	12.5214i	0.226374	+	0.696707i
$324$	3.70814	+	1.65097i	0.206008	+	0.0917206i
$325$	−2.72871	−	25.9619i	−0.151361	−	1.44011i
$326$	37.9804	+	8.07298i	2.10354	+	0.447121i
$327$	−7.31634	+	1.55514i	−0.404595	+	0.0859992i
$328$	36.0465	+	26.1893i	1.99033	+	1.44606i
$329$	10.3065	+	5.49928i	0.568215	+	0.303185i
$330$	−7.27346	+	26.0759i	−0.400391	+	1.43543i
$331$	−10.9431	−	18.9540i	−0.601486	−	1.04180i	−0.992596	−	0.121461i	$-0.961242\pi$
$331$	−10.9431	−	18.9540i	−0.601486	−	1.04180i	0.391110	−	0.920344i	$-0.372091\pi$
$332$	−52.8842	+	23.5456i	−2.90240	+	1.29223i
$333$	1.03060	+	1.14460i	0.0564766	+	0.0627236i
$334$	−12.8177	+	14.2355i	−0.701355	+	0.778933i
$335$	−40.6526	+	29.5359i	−2.22109	+	1.61372i
$336$	−4.33470	+	10.6840i	−0.236477	+	0.582862i
$337$	1.27060	+	3.91051i	0.0692140	+	0.213019i	0.979681	−	0.200564i	$-0.0642773\pi$
$337$	1.27060	+	3.91051i	0.0692140	+	0.213019i	−0.910467	+	0.413582i	$0.864277\pi$
$338$	−14.3439	+	3.04889i	−0.780205	+	0.165838i
$339$	−7.12077	+	3.17037i	−0.386747	+	0.172191i
$340$	−38.0146	+	65.8432i	−2.06163	+	3.57085i
$341$	0.288426	−	4.60282i	0.0156191	−	0.249257i
$342$	5.73725			0.310235
$343$	−9.32996	+	15.9985i	−0.503771	+	0.863837i
$344$	−10.5474	+	32.4615i	−0.568676	+	1.75021i
$345$	3.10388	−	3.44721i	0.167107	−	0.185592i
$346$	3.46155	+	32.9344i	0.186094	+	1.77057i
$347$	−1.29266	−	12.2988i	−0.0693935	−	0.660235i	−0.972831	−	0.231515i	$-0.925632\pi$
$347$	−1.29266	−	12.2988i	−0.0693935	−	0.660235i	0.903438	−	0.428719i	$-0.141035\pi$
$348$	−6.75871	+	7.50631i	−0.362305	+	0.402381i
$349$	7.14677	−	21.9955i	0.382558	−	1.17739i	−0.555679	−	0.831397i	$-0.687542\pi$
$349$	7.14677	−	21.9955i	0.382558	−	1.17739i	0.938237	−	0.345995i	$-0.112458\pi$
$350$	−38.9476	−	2.78036i	−2.08184	−	0.148617i
$351$	4.35401			0.232400
$352$	1.04922	+	1.65238i	0.0559234	+	0.0880723i
$353$	−12.3003	+	21.3048i	−0.654681	+	1.13394i	0.327293	+	0.944923i	$0.393864\pi$
$353$	−12.3003	+	21.3048i	−0.654681	+	1.13394i	−0.981974	+	0.189017i	$0.939470\pi$
$354$	−33.3341	+	14.8413i	−1.77169	+	0.788806i
$355$	37.2983	−	7.92799i	1.97959	−	0.420774i
$356$	8.88913	+	27.3579i	0.471123	+	1.44997i
$357$	14.8025	−	2.05842i	0.783431	−	0.108943i
$358$	−6.27495	+	4.55902i	−0.331642	+	0.240952i
$359$	5.84037	−	6.48639i	0.308243	−	0.342339i	−0.569042	−	0.822309i	$-0.692686\pi$
$359$	5.84037	−	6.48639i	0.308243	−	0.342339i	0.877285	+	0.479970i	$0.159352\pi$
$360$	11.2459	+	12.4898i	0.592710	+	0.658271i
$361$	−12.3945	+	5.51839i	−0.652343	+	0.290442i
$362$	−10.3464	−	17.9205i	−0.543796	−	0.941883i
$363$	2.50649	−	10.7106i	0.131556	−	0.562162i
$364$	1.56396	+	46.7328i	0.0819735	+	2.44947i
$365$	−23.8817	−	17.3510i	−1.25002	−	0.908195i
$366$	3.37734	−	0.717876i	0.176537	−	0.0375240i
$367$	24.2054	+	5.14501i	1.26351	+	0.268567i	0.790485	−	0.612482i	$-0.209829\pi$
$367$	24.2054	+	5.14501i	1.26351	+	0.268567i	0.473025	+	0.881049i	$0.343162\pi$
$368$	−0.637229	−	6.06283i	−0.0332179	−	0.316047i
$369$	−8.03086	−	3.57557i	−0.418070	−	0.186137i
$370$	3.88485	+	11.9563i	0.201964	+	0.621580i
$371$	−26.4908	−	7.63780i	−1.37533	−	0.396535i
$372$	−4.56628	−	3.31760i	−0.236751	−	0.172009i
$373$	−17.2647	−	29.9033i	−0.893930	−	1.54833i	−0.835123	−	0.550063i	$-0.814604\pi$
$373$	−17.2647	−	29.9033i	−0.893930	−	1.54833i	−0.0588067	−	0.998269i	$-0.518730\pi$
$374$	21.3547	−	40.8728i	1.10423	−	2.11348i
$375$	−1.65068	+	2.85907i	−0.0852410	+	0.147642i
$376$	2.33922	−	22.2562i	0.120636	−	1.14777i
$377$	−3.34811	+	10.3044i	−0.172436	+	0.530704i
$378$	1.14021	−	6.41197i	0.0586463	−	0.329796i
$379$	−12.2429	+	8.89502i	−0.628878	+	0.456906i	−0.856011	−	0.516957i	$-0.827065\pi$
$379$	−12.2429	+	8.89502i	−0.628878	+	0.456906i	0.227134	+	0.973864i	$0.427065\pi$
$380$	28.6594	+	12.7600i	1.47019	+	0.654572i
$381$	−12.5120	−	2.65952i	−0.641012	−	0.136251i
$382$	−31.2598	−	34.7175i	−1.59939	−	1.77630i
$383$	2.49796	−	23.7665i	0.127640	−	1.21441i	−0.723818	−	0.689991i	$-0.757615\pi$
$383$	2.49796	−	23.7665i	0.127640	−	1.21441i	0.851458	−	0.524422i	$-0.175719\pi$
$384$	−19.0585			−0.972576
$385$	29.0851	+	0.847420i	1.48231	+	0.0431885i
$386$	35.4166			1.80266
$387$	0.703920	−	6.69735i	0.0357823	−	0.340446i
$388$	−3.92500	−	4.35915i	−0.199262	−	0.221302i
$389$	−27.6829	−	5.88419i	−1.40358	−	0.298340i	−0.556961	−	0.830538i	$-0.688033\pi$
$389$	−27.6829	−	5.88419i	−1.40358	−	0.298340i	−0.846620	+	0.532198i	$0.821366\pi$
$390$	32.4663	+	14.4549i	1.64399	+	0.731953i
$391$	−6.39274	+	4.64460i	−0.323295	+	0.234888i
$392$	35.1192	+	5.03981i	1.77379	+	0.254549i
$393$	−5.17033	+	15.9126i	−0.260808	+	0.802686i
$394$	−0.350625	+	3.33597i	−0.0176642	+	0.168064i
$395$	−5.52572	+	9.57084i	−0.278029	+	0.481561i
$396$	−9.42156	−	9.61616i	−0.473451	−	0.483230i
$397$	−0.231645	−	0.401222i	−0.0116259	−	0.0201367i	0.860154	−	0.510035i	$-0.170367\pi$
$397$	−0.231645	−	0.401222i	−0.0116259	−	0.0201367i	−0.871780	+	0.489898i	$0.837034\pi$
$398$	21.9508	+	15.9482i	1.10029	+	0.799410i
$399$	−1.48315	−	5.98564i	−0.0742505	−	0.299657i
$400$	8.07405	+	24.8494i	0.403702	+	1.24247i
$401$	5.82845	+	2.59499i	0.291059	+	0.129588i	0.547072	−	0.837086i	$-0.315742\pi$
$401$	5.82845	+	2.59499i	0.291059	+	0.129588i	−0.256013	+	0.966673i	$0.582409\pi$
$402$	−3.89905	−	37.0970i	−0.194467	−	1.85023i
$403$	−5.92206	−	1.25877i	−0.294999	−	0.0627040i
$404$	−5.90060	+	1.25421i	−0.293566	+	0.0623994i
$405$	−2.68267	−	1.94907i	−0.133303	−	0.0968502i
$406$	14.2981	+	7.62910i	0.709602	+	0.378626i
$407$	−1.78181	−	4.78747i	−0.0883210	−	0.237306i
$408$	−14.3149	−	24.7941i	−0.708693	−	1.22749i
$409$	19.0782	−	8.49414i	0.943354	−	0.420008i	0.123348	−	0.992363i	$-0.460637\pi$
$409$	19.0782	−	8.49414i	0.943354	−	0.420008i	0.820006	+	0.572355i	$0.193970\pi$
$410$	−48.0126	−	53.3234i	−2.37117	−	2.63345i
$411$	−1.89084	+	2.10000i	−0.0932685	+	0.103585i
$412$	−14.4001	+	10.4623i	−0.709443	+	0.515441i
$413$	24.1012	+	30.9406i	1.18594	+	1.52249i
$414$	1.06407	+	3.27487i	0.0522962	+	0.160951i
$415$	46.2576	−	9.83236i	2.27070	−	0.482652i
$416$	2.34743	−	1.04514i	0.115092	−	0.0512423i
$417$	1.54491	−	2.67587i	0.0756548	−	0.131038i
$418$	−17.6938	−	7.00034i	−0.865433	−	0.342398i
$419$	35.1738			1.71835			0.859176	−	0.511680i	$-0.170976\pi$
$419$	35.1738			1.71835			0.859176	+	0.511680i	$0.170976\pi$
$420$	19.9563	−	29.4939i	0.973769	−	1.43916i
$421$	−1.27954	+	3.93803i	−0.0623612	+	0.191928i	−0.977383	−	0.211476i	$-0.932173\pi$
$421$	−1.27954	+	3.93803i	−0.0623612	+	0.191928i	0.915022	+	0.403404i	$0.132173\pi$
$422$	−19.3826	+	21.5266i	−0.943531	+	1.04790i
$423$	0.461527	+	4.39114i	0.0224402	+	0.213504i
$424$	5.52070	+	52.5259i	0.268109	+	2.55089i
$425$	22.6615	−	25.1681i	1.09924	−	1.22083i
$426$	−8.74702	+	26.9206i	−0.423794	+	1.30431i
$427$	−1.62204	−	3.33799i	−0.0784962	−	0.161536i
$428$	31.3982			1.51769
$429$	−13.4279	−	5.31258i	−0.648305	−	0.256494i
$430$	27.4834	−	47.6027i	1.32537	−	2.29561i
$431$	18.2753	−	8.13668i	0.880289	−	0.391930i	0.0837286	−	0.996489i	$-0.473317\pi$
$431$	18.2753	−	8.13668i	0.880289	−	0.391930i	0.796561	+	0.604559i	$0.206650\pi$
$432$	−4.26266	+	0.906056i	−0.205087	+	0.0435926i
$433$	−4.88254	−	15.0269i	−0.234640	−	0.722147i	−0.997169	−	0.0751932i	$-0.976043\pi$
$433$	−4.88254	−	15.0269i	−0.234640	−	0.722147i	0.762529	−	0.646954i	$-0.223957\pi$
$434$	−3.40459	+	8.39153i	−0.163426	+	0.402806i
$435$	6.67566	−	4.85015i	0.320073	−	0.232547i
$436$	20.3155	−	22.5626i	0.972934	−	1.08055i
$437$	2.18171	+	2.42303i	0.104365	+	0.115909i
$438$	20.0184	−	8.91278i	0.956518	−	0.425869i
$439$	0.344549	+	0.596777i	0.0164444	+	0.0284826i	0.874131	−	0.485691i	$-0.161432\pi$
$439$	0.344549	+	0.596777i	0.0164444	+	0.0284826i	−0.857686	+	0.514174i	$0.828099\pi$
$440$	−19.4431	−	52.2407i	−0.926911	−	2.49048i
$441$	−6.98434	+	0.467998i	−0.332588	+	0.0222856i
$442$	−48.9773	−	35.5841i	−2.32961	−	1.69256i
$443$	−1.62885	+	0.346224i	−0.0773892	+	0.0164496i	−0.246444	−	0.969157i	$-0.579262\pi$
$443$	−1.62885	+	0.346224i	−0.0773892	+	0.0164496i	0.169054	+	0.985607i	$0.445929\pi$
$444$	−6.11519	−	1.29982i	−0.290214	−	0.0616869i
$445$	−2.45638	−	23.3709i	−0.116443	−	1.10788i
$446$	−3.13358	−	1.39516i	−0.148379	−	0.0660627i
$447$	−4.83152	−	14.8699i	−0.228523	−	0.703322i
$448$	4.62175	+	18.6522i	0.218357	+	0.881235i
$449$	17.2487	+	12.5319i	0.814016	+	0.591418i	0.914992	−	0.403471i	$-0.132196\pi$
$449$	17.2487	+	12.5319i	0.814016	+	0.591418i	−0.100976	+	0.994889i	$0.532196\pi$
$450$	−7.37914	−	12.7810i	−0.347856	−	0.602504i
$451$	20.4046	+	20.8261i	0.960816	+	0.980661i
$452$	15.8195	−	27.4002i	0.744087	−	1.28880i
$453$	−1.79757	+	17.1027i	−0.0844570	+	0.803555i
$454$	−0.454018	+	1.39732i	−0.0213081	+	0.0655797i
$455$	6.68779	−	37.6087i	0.313528	−	1.76312i
$456$	−9.55722	+	6.94373i	−0.447558	+	0.325170i
$457$	37.4043	+	16.6535i	1.74970	+	0.779016i	0.991974	+	0.126443i	$0.0403562\pi$
$457$	37.4043	+	16.6535i	1.74970	+	0.779016i	0.757726	+	0.652573i	$0.226310\pi$
$458$	0.221179	+	0.0470131i	0.0103350	+	0.00219678i
$459$	3.77968	+	4.19776i	0.176421	+	0.195935i
$460$	−1.96814	+	18.7256i	−0.0917649	+	0.873084i
$461$	−1.66969			−0.0777650			−0.0388825	−	0.999244i	$-0.512380\pi$
$461$	−1.66969			−0.0777650			−0.0388825	+	0.999244i	$0.512380\pi$
$462$	−11.3401	+	18.3834i	−0.527588	+	0.855275i
$463$	−36.7528			−1.70805			−0.854023	−	0.520235i	$-0.825844\pi$
$463$	−36.7528			−1.70805			−0.854023	+	0.520235i	$0.825844\pi$
$464$	1.13354	−	10.7849i	0.0526234	−	0.500678i
$465$	3.08531	+	3.42659i	0.143078	+	0.158904i
$466$	−25.9603	−	5.51802i	−1.20259	−	0.255617i
$467$	−23.1649	−	10.3137i	−1.07194	−	0.477260i	−0.206593	−	0.978427i	$-0.566237\pi$
$467$	−23.1649	−	10.3137i	−1.07194	−	0.477260i	−0.865350	+	0.501167i	$0.832904\pi$
$468$	−14.2979	+	10.3881i	−0.660923	+	0.480189i
$469$	−37.6951	+	13.6579i	−1.74060	+	0.630664i
$470$	−11.1367	+	34.2753i	−0.513699	+	1.58100i
$471$	1.19429	−	11.3629i	0.0550299	−	0.523574i
$472$	37.5664	−	65.0669i	1.72913	−	2.99495i
$473$	−10.3427	+	19.7959i	−0.475559	+	0.910217i
$474$	−4.10188	−	7.10466i	−0.188405	−	0.326328i
$475$	−11.3055	−	8.21395i	−0.518733	−	0.376882i
$476$	−43.6981	+	42.0762i	−2.00290	+	1.92856i
$477$	−3.22009	−	9.91043i	−0.147438	−	0.453767i
$478$	33.5740	+	14.9481i	1.53564	+	0.683711i
$479$	−0.321897	−	3.06265i	−0.0147079	−	0.139936i	0.984704	−	0.174237i	$-0.0557460\pi$
$479$	−0.321897	−	3.06265i	−0.0147079	−	0.139936i	−0.999412	+	0.0343015i	$0.989079\pi$
$480$	−1.91419	−	0.406875i	−0.0873706	−	0.0185712i
$481$	−6.55955	+	1.39427i	−0.299090	+	0.0635734i
$482$	−17.8238	−	12.9498i	−0.811852	−	0.589845i
$483$	3.14158	−	1.95674i	0.142947	−	0.0890346i
$484$	17.3231	+	41.1523i	0.787414	+	1.87056i
$485$	2.39597	+	4.14994i	0.108795	+	0.188439i
$486$	2.24871	−	1.00119i	0.102003	−	0.0454149i
$487$	−7.15359	−	7.94486i	−0.324160	−	0.360016i	0.558934	−	0.829212i	$-0.311210\pi$
$487$	−7.15359	−	7.94486i	−0.324160	−	0.360016i	−0.883094	+	0.469196i	$0.844544\pi$
$488$	−4.75721	+	5.28341i	−0.215349	+	0.239169i
$489$	12.7617	−	9.27194i	0.577106	−	0.419292i
$490$	−53.6333	−	19.6976i	−2.42291	−	0.889849i
$491$	−5.95208	−	18.3186i	−0.268614	−	0.826708i	−0.990839	−	0.135050i	$-0.956881\pi$
$491$	−5.95208	−	18.3186i	−0.268614	−	0.826708i	0.722225	−	0.691658i	$-0.243119\pi$
$492$	34.9030	−	7.41886i	1.57355	−	0.334468i
$493$	−12.8411	+	5.71722i	−0.578334	+	0.257491i
$494$	−12.4900	+	21.6334i	−0.561953	+	0.973331i
$495$	5.89524	+	9.28427i	0.264972	+	0.417297i
$496$	6.05975			0.272091
$497$	30.3473	+	2.16641i	1.36126	+	0.0971768i
$498$	−10.8481	+	33.3871i	−0.486116	+	1.49611i
$499$	10.7214	−	11.9073i	0.479955	−	0.533044i	−0.453730	−	0.891139i	$-0.649907\pi$
$499$	10.7214	−	11.9073i	0.479955	−	0.533044i	0.933685	+	0.358095i	$0.116574\pi$
$500$	−1.40073	−	13.3271i	−0.0626426	−	0.596005i
$501$	0.813451	+	7.73947i	0.0363423	+	0.345774i
$502$	−12.2216	+	13.5735i	−0.545478	+	0.605815i
$503$	4.97226	−	15.3031i	0.221702	−	0.682329i	−0.776907	−	0.629615i	$-0.783213\pi$
$503$	4.97226	−	15.3031i	0.221702	−	0.682329i	0.998610	−	0.0527145i	$-0.0167873\pi$
$504$	5.86095	+	12.0612i	0.261067	+	0.537248i
$505$	4.92805			0.219295
$506$	0.714239	−	11.3981i	0.0317518	−	0.506708i
$507$	−2.97872	+	5.15929i	−0.132290	+	0.229132i
$508$	47.4330	−	21.1185i	2.10450	−	0.936983i
$509$	7.51513	−	1.59739i	0.333102	−	0.0708030i	−0.0383245	−	0.999265i	$-0.512202\pi$
$509$	7.51513	−	1.59739i	0.333102	−	0.0708030i	0.371427	+	0.928462i	$0.378869\pi$
$510$	14.2475	+	43.8494i	0.630891	+	1.94168i
$511$	−14.4737	−	18.5811i	−0.640278	−	0.821978i
$512$	33.6579	−	24.4539i	1.48748	−	1.08072i
$513$	1.55959	−	1.73210i	0.0688577	−	0.0764743i
$514$	3.46241	+	3.84540i	0.152721	+	0.169613i
$515$	13.2838	−	5.91433i	0.585354	−	0.260616i
$516$	13.6674	+	23.6726i	0.601672	+	1.04213i
$517$	3.93452	−	14.1055i	0.173040	−	0.620360i
$518$	0.335499	+	10.0251i	0.0147410	+	0.440477i
$519$	10.8840	+	7.90772i	0.477757	+	0.347111i
$520$	−71.5776	+	15.2143i	−3.13888	+	0.667190i
$521$	28.9197	+	6.14707i	1.26699	+	0.269308i	0.791913	−	0.610634i	$-0.209085\pi$
$521$	28.9197	+	6.14707i	1.26699	+	0.269308i	0.475081	+	0.879942i	$0.342419\pi$
$522$	0.640272	+	6.09178i	0.0280239	+	0.266630i
$523$	−7.43765	−	3.31146i	−0.325226	−	0.144800i	0.237628	−	0.971356i	$-0.423630\pi$
$523$	−7.43765	−	3.31146i	−0.325226	−	0.144800i	−0.562854	+	0.826556i	$0.690297\pi$
$524$	−20.9867	−	64.5904i	−0.916808	−	2.82165i
$525$	−11.4268	+	11.0027i	−0.498706	+	0.480196i
$526$	−30.2063	−	21.9462i	−1.31706	−	0.956900i
$527$	−3.92729	−	6.80227i	−0.171076	−	0.296312i
$528$	14.2517	+	2.40682i	0.620225	+	0.104743i
$529$	10.5215	−	18.2239i	0.457459	−	0.792341i
$530$	8.89064	−	84.5888i	0.386185	−	3.67430i
$531$	−4.58077	+	14.0982i	−0.198788	+	0.611808i
$532$	19.1513	+	16.1174i	0.830316	+	0.698777i
$533$	30.9656	−	22.4978i	1.34127	−	0.974489i
$534$	15.9362	+	7.09524i	0.689625	+	0.307041i
$535$	−25.0895	−	5.33294i	−1.08471	−	0.230563i
$536$	51.3932	+	57.0779i	2.21985	+	2.46539i
$537$	−0.329370	+	3.13375i	−0.0142134	+	0.135231i
$538$	22.2855			0.960795
$539$	22.1109	+	7.07867i	0.952384	+	0.304900i
$540$	13.4597			0.579214
$541$	−3.93958	+	37.4826i	−0.169376	+	1.61150i	0.498270	+	0.867022i	$0.333969\pi$
$541$	−3.93958	+	37.4826i	−0.169376	+	1.61150i	−0.667646	+	0.744479i	$0.732698\pi$
$542$	−0.819974	−	0.910673i	−0.0352209	−	0.0391168i
$543$	−8.22284	−	1.74782i	−0.352876	−	0.0750061i
$544$	3.04542	+	1.35591i	0.130571	+	0.0581341i
$545$	−20.0658	+	14.5787i	−0.859525	+	0.624481i
$546$	21.6953	+	18.2583i	0.928472	+	0.781383i
$547$	−2.44111	+	7.51296i	−0.104374	+	0.321231i	−0.989583	−	0.143963i	$-0.954015\pi$
$547$	−2.44111	+	7.51296i	−0.104374	+	0.321231i	0.885209	+	0.465194i	$0.154015\pi$
$548$	1.19896	−	11.4074i	0.0512172	−	0.487299i
$549$	0.701355	−	1.21478i	0.0299331	−	0.0518457i
$550$	7.16256	+	48.4208i	0.305413	+	2.06467i
$551$	2.90000	+	5.02294i	0.123544	+	0.213985i
$552$	−5.73609	−	4.16751i	−0.244144	−	0.177381i
$553$	−6.35187	+	6.11611i	−0.270109	+	0.260084i
$554$	3.26094	+	10.0361i	0.138544	+	0.426394i
$555$	4.66573	+	2.07731i	0.198049	+	0.0881771i
$556$	1.31098	+	12.4731i	0.0555978	+	0.528978i
$557$	−19.0245	−	4.04379i	−0.806095	−	0.171341i	−0.213606	−	0.976920i	$-0.568521\pi$
$557$	−19.0245	−	4.04379i	−0.806095	−	0.171341i	−0.592488	+	0.805579i	$0.701854\pi$
$558$	−3.34800	+	0.711640i	−0.141732	+	0.0301261i
$559$	23.7212	+	17.2344i	1.00330	+	0.728939i
$560$	1.27877	+	38.2113i	0.0540381	+	1.61472i
$561$	−6.53471	−	17.5578i	−0.275896	−	0.741292i
$562$	23.2892	+	40.3381i	0.982396	+	1.70156i
$563$	−40.7381	+	18.1378i	−1.71691	+	0.764416i	−0.719344	+	0.694654i	$0.755557\pi$
$563$	−40.7381	+	18.1378i	−1.71691	+	0.764416i	−0.997564	+	0.0697622i	$0.977776\pi$
$564$	−11.9922	−	13.3187i	−0.504964	−	0.560819i
$565$	−17.2949	+	19.2079i	−0.727600	+	0.808082i
$566$	0.419295	−	0.304636i	0.0176243	−	0.0128048i
$567$	−1.62586	−	2.08725i	−0.0682795	−	0.0876561i
$568$	−18.0107	−	55.4312i	−0.755712	−	2.32584i
$569$	37.2557	−	7.91894i	1.56184	−	0.331979i	0.655721	−	0.755003i	$-0.272365\pi$
$569$	37.2557	−	7.91894i	1.56184	−	0.331979i	0.906119	+	0.423024i	$0.139031\pi$
$570$	17.3797	−	7.73795i	0.727957	−	0.324107i
$571$	−12.3237	+	21.3453i	−0.515731	+	0.893271i	0.484103	+	0.875011i	$0.339146\pi$
$571$	−12.3237	+	21.3453i	−0.515731	+	0.893271i	−0.999833	+	0.0182603i	$0.994187\pi$
$572$	56.7703	−	14.5913i	2.37369	−	0.610094i
$573$	−18.9790			−0.792857
$574$	−25.0224	−	51.4934i	−1.04442	−	2.14929i
$575$	2.59179	−	7.97671i	0.108085	−	0.332652i
$576$	−4.85995	+	5.39752i	−0.202498	+	0.224897i
$577$	0.814413	+	7.74862i	0.0339044	+	0.322579i	0.998308	+	0.0581450i	$0.0185186\pi$
$577$	0.814413	+	7.74862i	0.0339044	+	0.322579i	−0.964404	+	0.264434i	$0.914815\pi$
$578$	−3.83561	−	36.4934i	−0.159540	−	1.51793i
$579$	9.62753	−	10.6925i	0.400107	−	0.444363i
$580$	−10.3501	+	31.8544i	−0.429765	+	1.32268i
$581$	37.6370	+	2.68680i	1.56144	+	0.111467i
$582$	−3.55717			−0.147450
$583$	−2.16143	+	34.4930i	−0.0895174	+	1.42856i
$584$	−22.5601	+	39.0752i	−0.933543	+	1.61694i
$585$	13.1895	−	5.87236i	0.545320	−	0.242792i
$586$	25.6976	−	5.46219i	1.06156	−	0.225641i
$587$	0.354180	+	1.09005i	0.0146186	+	0.0449913i	0.958100	−	0.286435i	$-0.0924702\pi$
$587$	0.354180	+	1.09005i	0.0146186	+	0.0449913i	−0.943481	+	0.331426i	$0.892470\pi$
$588$	21.8190	−	18.2005i	0.899799	−	0.750575i
$589$	−2.62203	+	1.90501i	−0.108039	+	0.0784947i
$590$	−80.9616	+	89.9170i	−3.33314	+	3.70182i
$591$	0.911834	+	1.01269i	0.0375078	+	0.0416567i
$592$	6.13177	−	2.73004i	0.252014	−	0.112204i
$593$	−15.4085	−	26.6882i	−0.632749	−	1.09595i	−0.986987	−	0.160799i	$-0.948593\pi$
$593$	−15.4085	−	26.6882i	−0.632749	−	1.09595i	0.354238	−	0.935155i	$-0.384740\pi$
$594$	−8.15668	+	0.343916i	−0.334673	+	0.0141110i
$595$	42.0647	−	26.2000i	1.72448	−	1.07410i
$596$	51.3435	+	37.3032i	2.10311	+	1.52800i
$597$	10.7819	−	2.29176i	0.441272	−	0.0937953i
$598$	−14.6650	−	3.11714i	−0.599697	−	0.127469i
$599$	−1.97566	−	18.7972i	−0.0807234	−	0.768031i	−0.957752	−	0.287594i	$-0.907145\pi$
$599$	−1.97566	−	18.7972i	−0.0807234	−	0.768031i	0.877029	−	0.480437i	$-0.159522\pi$
$600$	27.7611	+	12.3600i	1.13334	+	0.504596i
$601$	3.29026	+	10.1264i	0.134212	+	0.413063i	0.995467	−	0.0951109i	$-0.0303206\pi$
$601$	3.29026	+	10.1264i	0.134212	+	0.413063i	−0.861254	+	0.508174i	$0.830321\pi$
$602$	31.5925	−	30.4199i	1.28761	−	1.23982i
$603$	−12.2597	−	8.90718i	−0.499253	−	0.362728i
$604$	−34.9017	−	60.4515i	−1.42013	−	2.45974i
$605$	−6.85281	−	35.8261i	−0.278606	−	1.45654i
$606$	−1.82911	+	3.16810i	−0.0743023	+	0.128695i
$607$	−2.48790	+	23.6708i	−0.100981	+	0.960769i	0.820316	+	0.571910i	$0.193797\pi$
$607$	−2.48790	+	23.6708i	−0.100981	+	0.960769i	−0.921297	+	0.388859i	$0.872869\pi$
$608$	0.425065	−	1.30822i	0.0172387	−	0.0530551i
$609$	6.19001	−	2.24280i	0.250832	−	0.0908827i
$610$	9.26271	−	6.72975i	0.375036	−	0.272480i
$611$	−17.5624	−	7.81927i	−0.710497	−	0.316334i
$612$	−22.4272	−	4.76705i	−0.906566	−	0.192697i
$613$	19.4646	+	21.6177i	0.786169	+	0.873129i	0.994479	−	0.104933i	$-0.0334629\pi$
$613$	19.4646	+	21.6177i	0.786169	+	0.873129i	−0.208310	+	0.978063i	$0.566796\pi$
$614$	−6.01662	+	57.2443i	−0.242811	+	2.31019i
$615$	−29.1502			−1.17545
$616$	−3.35878	−	44.3483i	−0.135329	−	1.78684i
$617$	−4.31770			−0.173824			−0.0869121	−	0.996216i	$-0.527700\pi$
$617$	−4.31770			−0.173824			−0.0869121	+	0.996216i	$0.527700\pi$
$618$	−1.12829	+	10.7349i	−0.0453864	+	0.431823i
$619$	12.1402	+	13.4830i	0.487955	+	0.541929i	0.935962	−	0.352101i	$-0.114533\pi$
$619$	12.1402	+	13.4830i	0.487955	+	0.541929i	−0.448007	+	0.894030i	$0.647866\pi$
$620$	−18.3071	−	3.89129i	−0.735230	−	0.156278i
$621$	1.27795	+	0.568982i	0.0512825	+	0.0228325i
$622$	22.7238	−	16.5098i	0.911142	−	0.661983i
$623$	3.28272	−	18.4603i	0.131519	−	0.739597i
$624$	5.86338	−	18.0456i	0.234723	−	0.722404i
$625$	1.98926	−	18.9265i	0.0795704	−	0.757061i
$626$	−29.5224	+	51.1344i	−1.17995	+	2.04374i
$627$	−6.92327	+	3.43890i	−0.276489	+	0.137337i
$628$	23.1884	+	40.1635i	0.925318	+	1.60270i
$629$	−7.03853	−	5.11379i	−0.280644	−	0.203900i
$630$	−5.19395	−	20.9615i	−0.206932	−	0.835126i
$631$	5.40040	+	16.6207i	0.214986	+	0.661660i	0.999155	+	0.0411118i	$0.0130900\pi$
$631$	5.40040	+	16.6207i	0.214986	+	0.661660i	−0.784168	+	0.620548i	$0.786910\pi$
$632$	15.4317	+	6.87063i	0.613839	+	0.273299i
$633$	1.23008	+	11.7034i	0.0488913	+	0.465169i
$634$	−35.7477	−	7.59841i	−1.41972	−	0.301772i
$635$	−41.4895	+	8.81886i	−1.64646	+	0.349966i
$636$	34.2192	+	24.8617i	1.35688	+	0.985831i
$637$	13.4403	−	27.3546i	0.532523	−	1.08383i
$638$	5.45832	−	19.5684i	0.216097	−	0.774722i
$639$	5.74970	+	9.95877i	0.227454	+	0.393963i
$640$	−57.7336	+	25.7047i	−2.28212	+	1.01607i
$641$	23.0665	+	25.6179i	0.911070	+	1.01185i	0.999875	+	0.0157972i	$0.00502860\pi$
$641$	23.0665	+	25.6179i	0.911070	+	1.01185i	−0.0888048	+	0.996049i	$0.528305\pi$
$642$	12.7407	−	14.1499i	0.502834	−	0.558453i
$643$	−1.54859	+	1.12512i	−0.0610706	+	0.0443704i	−0.617902	−	0.786255i	$-0.712017\pi$
$643$	−1.54859	+	1.12512i	−0.0610706	+	0.0443704i	0.556831	+	0.830626i	$0.312017\pi$
$644$	−5.64800	+	13.9210i	−0.222562	+	0.548565i
$645$	−6.90050	−	21.2376i	−0.271707	−	0.836228i
$646$	−31.6995	+	6.73794i	−1.24720	+	0.265101i
$647$	0.837855	−	0.373037i	0.0329395	−	0.0146656i	−0.390201	−	0.920730i	$-0.627594\pi$
$647$	0.837855	−	0.373037i	0.0329395	−	0.0146656i	0.423140	+	0.906064i	$0.360928\pi$
$648$	−2.53421	+	4.38939i	−0.0995533	+	0.172431i
$649$	31.3292	−	37.8898i	1.22978	−	1.48731i
$650$	64.2577			2.52040
$651$	1.60795	+	3.30899i	0.0630207	+	0.129689i
$652$	−19.7861	+	60.8954i	−0.774884	+	2.38485i
$653$	−19.1120	+	21.2260i	−0.747909	+	0.830637i	−0.990213	−	0.139563i	$-0.955430\pi$
$653$	−19.1120	+	21.2260i	−0.747909	+	0.830637i	0.242304	+	0.970200i	$0.422097\pi$
$654$	−1.92454	−	18.3108i	−0.0752555	−	0.716008i
$655$	5.79935	+	55.1772i	0.226599	+	2.15595i
$656$	−25.6342	+	28.4696i	−1.00085	+	1.11155i
$657$	2.75093	−	8.46649i	0.107324	−	0.330309i
$658$	−16.1143	+	23.8157i	−0.628200	+	0.928431i
$659$	10.3651			0.403767			0.201884	−	0.979410i	$-0.435294\pi$
$659$	10.3651			0.403767			0.201884	+	0.979410i	$0.435294\pi$
$660$	−41.5101	−	16.4230i	−1.61578	−	0.639263i
$661$	−6.59237	+	11.4183i	−0.256413	+	0.444121i	−0.965278	−	0.261223i	$-0.915874\pi$
$661$	−6.59237	+	11.4183i	−0.256413	+	0.444121i	0.708865	+	0.705344i	$0.249207\pi$
$662$	49.2156	−	21.9122i	1.91282	−	0.851641i
$663$	−24.0569	+	5.11344i	−0.934291	+	0.198590i
$664$	−22.3370	−	68.7463i	−0.866844	−	2.66787i
$665$	−12.5659	−	16.1318i	−0.487283	−	0.625565i
$666$	−3.06719	+	2.22844i	−0.118851	+	0.0863503i
$667$	−2.32929	+	2.58694i	−0.0901904	+	0.100167i
$668$	−21.1366	−	23.4745i	−0.817798	−	0.908256i
$669$	−1.27303	+	0.566788i	−0.0492181	+	0.0219133i
$670$	−61.8449	−	107.118i	−2.38928	−	4.13835i
$671$	−3.64522	+	2.89066i	−0.140722	+	0.111593i
$672$	−1.37759	−	0.735048i	−0.0531417	−	0.0283551i
$673$	28.9769	+	21.0530i	1.11698	+	0.811532i	0.983748	−	0.179554i	$-0.0574653\pi$
$673$	28.9769	+	21.0530i	1.11698	+	0.811532i	0.133229	+	0.991085i	$0.457465\pi$
$674$	−9.89997	+	2.10430i	−0.381333	+	0.0810547i
$675$	−5.86458	−	1.24656i	−0.225728	−	0.0479799i
$676$	−2.52767	−	24.0492i	−0.0972181	−	0.924968i
$677$	−8.66786	−	3.85918i	−0.333133	−	0.148320i	0.233352	−	0.972392i	$-0.425030\pi$
$677$	−8.66786	−	3.85918i	−0.333133	−	0.148320i	−0.566485	+	0.824072i	$0.691697\pi$
$678$	−5.92901	−	18.2476i	−0.227702	−	0.700795i
$679$	0.919575	+	3.71118i	0.0352901	+	0.142422i
$680$	−76.8042	−	55.8015i	−2.94531	−	2.13989i
$681$	0.298441	+	0.516915i	0.0114363	+	0.0198082i
$682$	11.1936	+	1.89038i	0.428627	+	0.0723862i
$683$	4.48670	−	7.77119i	0.171679	−	0.297356i	−0.767328	−	0.641255i	$-0.778414\pi$
$683$	4.48670	−	7.77119i	0.171679	−	0.297356i	0.939007	+	0.343898i	$0.111748\pi$
$684$	−0.988920	+	9.40895i	−0.0378123	+	0.359760i
$685$	−2.89559	+	8.91170i	−0.110635	+	0.340499i
$686$	−36.7642	−	26.9564i	−1.40367	−	1.02920i
$687$	0.0743182	−	0.0539953i	0.00283542	−	0.00206005i
$688$	−26.8099	−	11.9365i	−1.02212	−	0.455076i
$689$	44.3793	+	9.43311i	1.69072	+	0.359373i
$690$	7.64026	+	8.48537i	0.290860	+	0.323033i
$691$	−1.24330	+	11.8292i	−0.0472972	+	0.450003i	0.945087	+	0.326820i	$0.105977\pi$
$691$	−1.24330	+	11.8292i	−0.0472972	+	0.450003i	−0.992384	+	0.123183i	$0.960690\pi$
$692$	−54.6083			−2.07590
$693$	2.46741	+	8.42092i	0.0937293	+	0.319884i
$694$	30.4405			1.15550
$695$	1.07097	−	10.1896i	0.0406243	−	0.386514i
$696$	−8.43939	−	9.37290i	−0.319894	−	0.355279i
$697$	48.5714	+	10.3242i	1.83977	+	0.391056i
$698$	52.0068	+	23.1549i	1.96849	+	0.876427i
$699$	−8.72287	+	6.33754i	−0.329929	+	0.239708i
$700$	11.2731	−	63.3939i	0.426082	−	2.39606i
$701$	−14.5270	+	44.7094i	−0.548676	+	1.68865i	0.163408	+	0.986559i	$0.447751\pi$
$701$	−14.5270	+	44.7094i	−0.548676	+	1.68865i	−0.712084	+	0.702094i	$0.752249\pi$
$702$	−1.12028	+	10.6588i	−0.0422823	+	0.402289i
$703$	−1.79494	+	3.10893i	−0.0676975	+	0.117255i
$704$	21.5740	−	10.7162i	0.813102	−	0.403882i
$705$	7.32053	+	12.6795i	0.275707	+	0.477538i
$706$	−48.9900	−	35.5933i	−1.84376	−	1.33957i
$707$	3.77811	+	1.08930i	0.142091	+	0.0409674i
$708$	−18.5936	−	57.2253i	−0.698792	−	2.15066i
$709$	−15.9881	−	7.11837i	−0.600447	−	0.267336i	0.0839218	−	0.996472i	$-0.473255\pi$
$709$	−15.9881	−	7.11837i	−0.600447	−	0.267336i	−0.684369	+	0.729136i	$0.739922\pi$
$710$	9.81119	+	93.3473i	0.368207	+	3.50326i
$711$	−3.25997	−	0.692929i	−0.122259	−	0.0259869i
$712$	−35.1341	+	7.46798i	−1.31670	+	0.279874i
$713$	−1.57370	−	1.14336i	−0.0589355	−	0.0428191i
$714$	1.23043	+	36.7666i	0.0460476	+	1.37596i
$715$	−47.8421	+	2.01720i	−1.78919	+	0.0754389i
$716$	−6.39508	−	11.0766i	−0.238995	−	0.413952i
$717$	13.6396	−	6.07272i	0.509379	−	0.226790i
$718$	14.3762	+	15.9664i	0.536514	+	0.595860i
$719$	−2.93093	+	3.25513i	−0.109305	+	0.121396i	−0.795314	−	0.606197i	$-0.792694\pi$
$719$	−2.93093	+	3.25513i	−0.109305	+	0.121396i	0.686009	+	0.727593i	$0.259361\pi$
$720$	−11.6908	+	8.49385i	−0.435689	+	0.316547i
$721$	11.4914	−	1.59798i	0.427962	−	0.0595120i
$722$	−10.3201	−	31.7620i	−0.384075	−	1.18206i
$723$	−8.75477	+	1.86088i	−0.325593	+	0.0692070i
$724$	31.1727	−	13.8790i	1.15852	−	0.515808i
$725$	7.45984	−	12.9208i	0.277052	−	0.479867i
$726$	25.5750	+	8.89179i	0.949179	+	0.330005i
$727$	−34.7553			−1.28900			−0.644502	−	0.764603i	$-0.722935\pi$
$727$	−34.7553			−1.28900			−0.644502	+	0.764603i	$0.722935\pi$
$728$	−58.2383	−	4.15747i	−2.15845	−	0.154086i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	48.6206	−	53.9987i	1.79953	−	1.99858i
$731$	3.97620	+	37.8310i	0.147065	+	1.39923i
$732$	0.595153	+	5.66250i	0.0219975	+	0.209292i
$733$	−25.6546	+	28.4923i	−0.947573	+	1.05239i	0.0509845	+	0.998699i	$0.483764\pi$
$733$	−25.6546	+	28.4923i	−0.947573	+	1.05239i	−0.998558	+	0.0536874i	$0.982903\pi$
$734$	−18.8232	+	57.9317i	−0.694775	+	2.13830i
$735$	−20.5263	+	10.8376i	−0.757125	+	0.399752i
$736$	0.825577			0.0304312
$737$	26.9410	+	42.4287i	0.992385	+	1.56288i
$738$	10.8194	−	18.7398i	0.398269	−	0.689822i
$739$	9.97735	−	4.44220i	0.367023	−	0.163409i	−0.214934	−	0.976628i	$-0.568954\pi$
$739$	9.97735	−	4.44220i	0.367023	−	0.163409i	0.581957	+	0.813219i	$0.302287\pi$
$740$	−20.2777	+	4.31017i	−0.745425	+	0.158445i
$741$	3.13598	+	9.65154i	0.115203	+	0.354558i
$742$	25.5136	−	62.8852i	0.936635	−	2.30859i
$743$	−33.9925	+	24.6970i	−1.24707	+	0.906046i	−0.998048	−	0.0624527i	$-0.980108\pi$
$743$	−33.9925	+	24.6970i	−1.24707	+	0.906046i	−0.249018	+	0.968499i	$0.580108\pi$
$744$	4.71588	−	5.23752i	0.172893	−	0.192017i
$745$	−34.6914	−	38.5287i	−1.27099	−	1.41158i
$746$	77.6463	−	34.5704i	2.84283	−	1.26571i
$747$	7.13082	+	12.3509i	0.260903	+	0.451897i
$748$	63.3495	+	42.0664i	2.31629	+	1.53810i
$749$	−18.0562	−	9.63432i	−0.659759	−	0.352031i
$750$	−6.57438	−	4.77656i	−0.240062	−	0.174415i
$751$	−6.09626	+	1.29580i	−0.222456	+	0.0472844i	−0.317791	−	0.948161i	$-0.602941\pi$
$751$	−6.09626	+	1.29580i	−0.222456	+	0.0472844i	0.0953353	+	0.995445i	$0.469608\pi$
$752$	18.8210	+	4.00053i	0.686332	+	0.145884i
$753$	0.775622	+	7.37955i	0.0282652	+	0.268926i
$754$	−24.3641	−	10.8476i	−0.887287	−	0.395046i
$755$	17.6215	+	54.2333i	0.641311	+	1.97375i
$756$	10.3189	+	2.97515i	0.375296	+	0.108205i
$757$	−9.81904	−	7.13395i	−0.356879	−	0.259288i	0.394870	−	0.918737i	$-0.370790\pi$
$757$	−9.81904	−	7.13395i	−0.356879	−	0.259288i	−0.751749	+	0.659449i	$0.770790\pi$
$758$	−18.6252	−	32.2598i	−0.676498	−	1.17173i
$759$	−3.24700	−	3.31406i	−0.117858	−	0.120293i
$760$	−19.5863	+	33.9245i	−0.710471	+	1.23057i
$761$	0.463487	−	4.40978i	0.0168014	−	0.159855i	−0.982904	−	0.184118i	$-0.941057\pi$
$761$	0.463487	−	4.40978i	0.0168014	−	0.159855i	0.999706	+	0.0242631i	$0.00772393\pi$
$762$	9.72992	−	29.9456i	0.352478	−	1.08482i
$763$	−18.6060	+	6.74144i	−0.673583	+	0.244056i
$764$	62.3241	−	45.2811i	2.25481	−	1.63821i
$765$	17.1113	+	7.61846i	0.618662	+	0.275446i
$766$	57.5385	+	12.2302i	2.07895	+	0.441895i
$767$	−43.1874	−	47.9644i	−1.55941	−	1.73189i
$768$	3.38533	−	32.2093i	0.122158	−	1.16225i
$769$	46.7321			1.68520			0.842602	−	0.538537i	$-0.181023\pi$
$769$	46.7321			1.68520			0.842602	+	0.538537i	$0.181023\pi$
$770$	−9.55807	+	70.9832i	−0.344449	+	2.55806i
$771$	2.10216			0.0757074
$772$	−6.10471	+	58.0824i	−0.219713	+	2.09043i
$773$	−21.6906	−	24.0899i	−0.780157	−	0.866452i	0.213726	−	0.976894i	$-0.431440\pi$
$773$	−21.6906	−	24.0899i	−0.780157	−	0.866452i	−0.993883	+	0.110442i	$0.964773\pi$
$774$	16.2142	+	3.44644i	0.582808	+	0.123880i
$775$	7.61626	+	3.39098i	0.273584	+	0.121807i
$776$	5.92561	−	4.30521i	0.212717	−	0.154548i
$777$	3.11783	+	2.62390i	0.111851	+	0.0941318i
$778$	21.5275	−	66.2548i	0.771798	−	2.37535i
$779$	2.14174	−	20.3773i	0.0767359	−	0.730093i
$780$	−29.3019	+	50.7523i	−1.04918	+	1.81723i
$781$	−5.58095	−	37.7286i	−0.199702	−	1.35004i
$782$	−9.72529	−	16.8447i	−0.347776	−	0.602365i
$783$	2.01319	+	1.46267i	0.0719455	+	0.0522715i
$784$	−7.46588	+	29.5775i	−0.266638	+	1.05634i
$785$	−11.7076	−	36.0322i	−0.417861	−	1.28604i
$786$	−37.6243	−	16.7514i	−1.34201	−	0.597503i
$787$	3.56321	+	33.9017i	0.127015	+	1.20846i	0.853430	+	0.521208i	$0.174519\pi$
$787$	3.56321	+	33.9017i	0.127015	+	1.20846i	−0.726415	+	0.687257i	$0.758815\pi$
$788$	−5.41048	−	1.15003i	−0.192740	−	0.0409682i
$789$	−14.8369	+	3.15367i	−0.528206	+	0.112274i
$790$	−22.0080	−	15.9897i	−0.783008	−	0.568889i
$791$	−17.5049	+	10.9029i	−0.622403	+	0.387664i
$792$	13.1713	−	10.4448i	0.468023	−	0.371141i
$793$	3.05371	+	5.28918i	0.108440	+	0.187824i
$794$	1.04181	−	0.463842i	0.0369723	−	0.0164611i
$795$	−23.1210	−	25.6785i	−0.820017	−	0.910721i
$796$	−29.9383	+	33.2498i	−1.06113	+	1.17851i
$797$	5.96563	−	4.33428i	0.211313	−	0.153528i	−0.477094	−	0.878852i	$-0.658310\pi$
$797$	5.96563	−	4.33428i	0.211313	−	0.153528i	0.688408	+	0.725324i	$0.258310\pi$
$798$	15.0347	−	2.09071i	0.532221	−	0.0740103i
$799$	−7.70708	−	23.7200i	−0.272657	−	0.839152i
$800$	−3.46106	+	0.735671i	−0.122367	+	0.0260099i
$801$	6.47412	−	2.88246i	0.228752	−	0.101847i
$802$	−7.85228	+	13.6005i	−0.277274	+	0.480252i
$803$	−18.8144	+	22.7543i	−0.663946	+	0.802982i
$804$	61.5103			2.16930
$805$	6.87764	−	10.1646i	0.242405	−	0.358256i
$806$	4.60526	−	14.1735i	0.162213	−	0.499241i
$807$	6.05801	−	6.72810i	0.213252	−	0.236840i
$808$	−0.787361	−	7.49124i	−0.0276992	−	0.263541i
$809$	−3.26387	−	31.0536i	−0.114751	−	1.09179i	−0.888684	−	0.458519i	$-0.848380\pi$
$809$	−3.26387	−	31.0536i	−0.114751	−	1.09179i	0.773933	−	0.633267i	$-0.218287\pi$
$810$	5.46164	−	6.06577i	0.191903	−	0.213129i
$811$	−10.3174	+	31.7538i	−0.362294	+	1.11503i	0.589364	+	0.807868i	$0.299378\pi$
$811$	−10.3174	+	31.7538i	−0.362294	+	1.11503i	−0.951658	+	0.307159i	$0.900622\pi$
$812$	−14.9761	+	22.1335i	−0.525557	+	0.776734i
$813$	−0.497836			−0.0174599
$814$	12.1783	−	3.13012i	0.426850	−	0.109711i
$815$	26.1536	−	45.2994i	0.916121	−	1.58677i
$816$	22.4880	−	10.0123i	0.787238	−	0.350501i
$817$	15.3530	−	3.26338i	0.537134	−	0.114171i
$818$	15.8852	+	48.8895i	0.555412	+	1.70938i
$819$	11.4098	−	1.58664i	0.398692	−	0.0554419i
$820$	95.7250	−	69.5483i	3.34286	−	2.42873i
$821$	15.7373	−	17.4780i	0.549236	−	0.609988i	−0.403057	−	0.915175i	$-0.632052\pi$
$821$	15.7373	−	17.4780i	0.549236	−	0.609988i	0.952292	+	0.305187i	$0.0987190\pi$
$822$	−4.65435	−	5.16918i	−0.162339	−	0.180296i
$823$	−41.8109	+	18.6154i	−1.45744	+	0.648893i	−0.974013	−	0.226493i	$-0.927274\pi$
$823$	−41.8109	+	18.6154i	−1.45744	+	0.648893i	−0.483424	+	0.875386i	$0.660607\pi$
$824$	−11.1129	−	19.2480i	−0.387135	−	0.670537i
$825$	16.5655	+	11.0001i	0.576738	+	0.382975i
$826$	−81.9449	+	51.0394i	−2.85123	+	1.77589i
$827$	−17.7914	−	12.9262i	−0.618667	−	0.449488i	0.233789	−	0.972287i	$-0.424888\pi$
$827$	−17.7914	−	12.9262i	−0.618667	−	0.449488i	−0.852456	+	0.522800i	$0.824888\pi$
$828$	−5.55413	+	1.18057i	−0.193019	+	0.0410275i
$829$	−37.4775	−	7.96608i	−1.30165	−	0.276673i	−0.495613	−	0.868544i	$-0.665056\pi$
$829$	−37.4775	−	7.96608i	−1.30165	−	0.276673i	−0.806033	+	0.591870i	$0.798390\pi$
$830$	12.1679	+	115.770i	0.422355	+	4.01844i
$831$	3.91640	+	1.74369i	0.135858	+	0.0604881i
$832$	−9.77222	−	30.0758i	−0.338791	−	1.04269i
$833$	38.0403	−	10.7883i	1.31802	−	0.373794i
$834$	6.15311	+	4.47050i	0.213065	+	0.154801i
$835$	12.9026	+	22.3479i	0.446512	+	0.773382i
$836$	14.5303	−	27.8108i	0.502539	−	0.961857i
$837$	−0.695262	+	1.20423i	−0.0240318	+	0.0416243i
$838$	−9.05017	+	86.1066i	−0.312633	+	2.97450i
$839$	−12.1261	+	37.3204i	−0.418641	+	1.28844i	0.490312	+	0.871547i	$0.336883\pi$
$839$	−12.1261	+	37.3204i	−0.418641	+	1.28844i	−0.908953	+	0.416898i	$0.863117\pi$
$840$	34.0217	+	28.6319i	1.17386	+	0.987895i
$841$	18.4518	−	13.4060i	0.636269	−	0.462276i
$842$	−9.31121	−	4.14562i	−0.320885	−	0.142867i
$843$	18.5091	+	3.93424i	0.637489	+	0.135502i
$844$	−31.9621	−	35.4975i	−1.10018	−	1.22188i
$845$	−2.06492	+	19.6464i	−0.0710355	+	0.675857i
$846$	−10.8684			−0.373663
$847$	2.66528	−	28.9810i	0.0915802	−	0.995798i
$848$	−45.4111			−1.55943
$849$	0.0220087	−	0.209399i	0.000755336	−	0.00718654i
$850$	55.7816	+	61.9517i	1.91329	+	2.12493i
$851$	−2.10751	−	0.447964i	−0.0722444	−	0.0153560i
$852$	−42.6414	−	18.9852i	−1.46087	−	0.650421i
$853$	2.28660	−	1.66131i	0.0782917	−	0.0568823i	−0.547951	−	0.836511i	$-0.684592\pi$
$853$	2.28660	−	1.66131i	0.0782917	−	0.0568823i	0.626243	+	0.779628i	$0.284592\pi$
$854$	8.58885	−	3.11196i	0.293904	−	0.106489i
$855$	2.38832	−	7.35049i	0.0816788	−	0.251381i
$856$	−4.09813	+	38.9911i	−0.140071	+	1.33269i
$857$	0.176398	−	0.305530i	0.00602563	−	0.0104367i	−0.862997	−	0.505209i	$-0.831415\pi$
$857$	0.176398	−	0.305530i	0.00602563	−	0.0104367i	0.869022	+	0.494773i	$0.164749\pi$
$858$	16.4604	−	31.5050i	0.561947	−	1.07556i
$859$	−26.5797	−	46.0374i	−0.906888	−	1.57078i	−0.818363	−	0.574702i	$-0.805118\pi$
$859$	−26.5797	−	46.0374i	−0.906888	−	1.57078i	−0.0885253	−	0.996074i	$-0.528215\pi$
$860$	73.3301	+	53.2774i	2.50053	+	1.81674i
$861$	−22.3481	−	6.44338i	−0.761622	−	0.219590i
$862$	15.2167	+	46.8320i	0.518281	+	1.59511i
$863$	29.7100	+	13.2278i	1.01134	+	0.450278i	0.844414	−	0.535691i	$-0.179949\pi$
$863$	29.7100	+	13.2278i	1.01134	+	0.450278i	0.166927	+	0.985969i	$0.446615\pi$
$864$	−0.0616889	−	0.586930i	−0.00209870	−	0.0199678i
$865$	43.6362	+	9.27515i	1.48367	+	0.315365i
$866$	38.0426	−	8.08621i	1.29274	−	0.274781i
$867$	−12.0602	−	8.76226i	−0.409586	−	0.297582i
$868$	−13.1751	−	7.02988i	−0.447191	−	0.238610i
$869$	9.20836	+	6.11469i	0.312372	+	0.207427i
$870$	10.1557	+	17.5902i	0.344310	+	0.596363i
$871$	60.2756	−	26.8364i	2.04236	−	0.909317i
$872$	25.3673	+	28.1732i	0.859044	+	0.954065i
$873$	−0.966970	+	1.07393i	−0.0327270	+	0.0363470i
$874$	−6.49301	+	4.71745i	−0.219629	+	0.159570i
$875$	−3.28380	+	8.09382i	−0.111013	+	0.273621i
$876$	11.1662	+	34.3661i	0.377271	+	1.16112i
$877$	−19.8841	+	4.22649i	−0.671437	+	0.142718i	−0.531001	−	0.847371i	$-0.678184\pi$
$877$	−19.8841	+	4.22649i	−0.671437	+	0.142718i	−0.140436	+	0.990090i	$0.544850\pi$
$878$	−1.54958	+	0.689918i	−0.0522958	+	0.0232836i
$879$	5.33648	−	9.24305i	0.179995	−	0.311760i
$880$	46.4185	−	11.9307i	1.56477	−	0.402182i
$881$	34.7025			1.16916			0.584578	−	0.811338i	$-0.301260\pi$
$881$	34.7025			1.16916			0.584578	+	0.811338i	$0.301260\pi$
$882$	0.651385	−	17.2183i	0.0219333	−	0.579770i
$883$	−4.10389	+	12.6305i	−0.138107	+	0.425049i	−0.996060	−	0.0886784i	$-0.971736\pi$
$883$	−4.10389	+	12.6305i	−0.138107	+	0.425049i	0.857954	+	0.513727i	$0.171736\pi$
$884$	66.7992	−	74.1881i	2.24670	−	2.49522i
$885$	5.13807	+	48.8855i	0.172714	+	1.64327i
$886$	−0.428465	−	4.07657i	−0.0143946	−	0.136955i
$887$	−4.91100	+	5.45422i	−0.164895	+	0.183135i	−0.819930	−	0.572464i	$-0.805988\pi$
$887$	−4.91100	+	5.45422i	−0.164895	+	0.183135i	0.655034	+	0.755599i	$0.272654\pi$
$888$	2.41232	−	7.42436i	0.0809522	−	0.249145i
$889$	−33.7574	−	2.40985i	−1.13219	−	0.0808237i
$890$	57.8446			1.93896
$891$	−2.11346	+	2.55603i	−0.0708034	+	0.0856303i
$892$	2.82816	−	4.89851i	0.0946937	−	0.164014i
$893$	−9.40142	+	4.18578i	−0.314607	+	0.140072i
$894$	37.6451	−	8.00172i	1.25904	−	0.267618i
$895$	3.22880	+	9.93724i	0.107927	+	0.332165i
$896$	−49.9435	+	6.94511i	−1.66850	+	0.232020i
$897$	−4.92757	+	3.58009i	−0.164527	+	0.119536i
$898$	−35.1166	+	39.0009i	−1.17186	+	1.30148i
$899$	−2.31535	−	2.57146i	−0.0772213	−	0.0857629i
$900$	22.2325	−	9.89856i	0.741084	−	0.329952i
$901$	29.4307	+	50.9755i	0.980479	+	1.69824i
$902$	−56.2330	+	44.5927i	−1.87235	+	1.48477i
$903$	−0.595933	−	17.8072i	−0.0198314	−	0.592585i
$904$	31.9615	+	23.2214i	1.06302	+	0.772333i
$905$	−27.2666	+	5.79570i	−0.906374	+	0.192656i
$906$	−41.4054	−	8.80100i	−1.37560	−	0.292394i
$907$	−2.37943	−	22.6388i	−0.0790078	−	0.751709i	−0.960268	−	0.279078i	$-0.909971\pi$
$907$	−2.37943	−	22.6388i	−0.0790078	−	0.751709i	0.881260	−	0.472631i	$-0.156696\pi$
$908$	−2.21332	−	0.985434i	−0.0734517	−	0.0327028i
$909$	0.459249	+	1.41342i	0.0152323	+	0.0468803i
$910$	90.3465	+	26.0486i	2.99496	+	0.863502i
$911$	−11.9326	−	8.66957i	−0.395346	−	0.287236i	0.372297	−	0.928114i	$-0.378570\pi$
$911$	−11.9326	−	8.66957i	−0.395346	−	0.287236i	−0.767643	+	0.640878i	$0.778570\pi$
$912$	−5.07863	−	8.79645i	−0.168170	−	0.291280i
$913$	−6.92154	−	46.7913i	−0.229069	−	1.54857i
$914$	−50.3923	+	87.2820i	−1.66683	+	2.88703i
$915$	0.486197	−	4.62585i	0.0160732	−	0.152926i
$916$	−0.115225	+	0.354625i	−0.00380713	+	0.0117172i
$917$	−7.75031	+	43.5837i	−0.255938	+	1.43926i
$918$	−11.2488	+	8.17271i	−0.371265	+	0.269740i
$919$	−12.5400	−	5.58316i	−0.413656	−	0.184172i	0.189347	−	0.981910i	$-0.439363\pi$
$919$	−12.5400	−	5.58316i	−0.413656	−	0.184172i	−0.603003	+	0.797739i	$0.706029\pi$
$920$	−22.9971	−	4.88818i	−0.758190	−	0.161158i
$921$	15.6468	+	17.3776i	0.515580	+	0.572610i
$922$	0.429608	−	4.08745i	0.0141484	−	0.134613i
$923$	−50.0685			−1.64803
$924$	−28.1938	−	21.7662i	−0.927506	−	0.716054i
$925$	9.23447			0.303628
$926$	9.45644	−	89.9720i	0.310758	−	2.95666i
$927$	2.93422	+	3.25879i	0.0963726	+	0.107033i
$928$	1.43649	+	0.305336i	0.0471552	+	0.0100232i
$929$	16.0994	+	7.16790i	0.528203	+	0.235171i	0.653471	−	0.756952i	$-0.273312\pi$
$929$	16.0994	+	7.16790i	0.528203	+	0.235171i	−0.125268	+	0.992123i	$0.539979\pi$
$930$	−9.18224	+	6.67129i	−0.301098	+	0.218760i
$931$	−6.06788	−	15.1451i	−0.198867	−	0.496361i
$932$	13.5242	−	41.6231i	0.442999	−	1.36341i
$933$	1.19277	−	11.3484i	0.0390494	−	0.371530i
$934$	31.2085	−	54.0547i	1.02117	−	1.76872i
$935$	−43.4761	−	44.3741i	−1.42182	−	1.45119i
$936$	−11.0340	−	19.1115i	−0.360658	−	0.624677i
$937$	−35.4523	−	25.7576i	−1.15818	−	0.841464i	−0.168629	−	0.985680i	$-0.553934\pi$
$937$	−35.4523	−	25.7576i	−1.15818	−	0.841464i	−0.989546	+	0.144216i	$0.953934\pi$
$938$	−23.7361	−	95.7931i	−0.775011	−	3.12776i
$939$	7.41245	+	22.8132i	0.241896	+	0.744480i
$940$	−54.2911	−	24.1720i	−1.77078	−	0.788402i
$941$	−2.14376	−	20.3965i	−0.0698847	−	0.664908i	−0.972251	−	0.233939i	$-0.924838\pi$
$941$	−2.14376	−	20.3965i	−0.0698847	−	0.664908i	0.902367	−	0.430969i	$-0.141828\pi$
$942$	27.5094	+	5.84731i	0.896306	+	0.190516i
$943$	12.0288	−	2.55680i	0.391711	−	0.0832607i
$944$	52.2625	+	37.9709i	1.70100	+	1.23585i
$945$	−7.74029	−	4.13002i	−0.251792	−	0.134350i
$946$	−45.7999	−	30.4128i	−1.48908	−	0.988806i
$947$	−3.00545	−	5.20559i	−0.0976639	−	0.169159i	0.813053	−	0.582189i	$-0.197804\pi$
$947$	−3.00545	−	5.20559i	−0.0976639	−	0.169159i	−0.910717	+	0.413030i	$0.864470\pi$
$948$	12.3585	−	5.50236i	0.401386	−	0.178708i
$949$	25.9357	+	28.8045i	0.841908	+	0.935034i
$950$	23.0169	−	25.5629i	0.746767	−	0.829369i
$951$	−12.0115	+	8.72690i	−0.389501	+	0.282989i
$952$	−46.5479	−	59.7574i	−1.50863	−	1.93675i
$953$	3.45588	+	10.6361i	0.111947	+	0.344537i	0.991298	−	0.131637i	$-0.0420232\pi$
$953$	3.45588	+	10.6361i	0.111947	+	0.344537i	−0.879351	+	0.476174i	$0.842023\pi$
$954$	25.0896	−	5.33296i	0.812305	−	0.172661i
$955$	−57.4926	+	25.5974i	−1.86042	+	0.828311i
$956$	−30.3017	+	52.4840i	−0.980026	+	1.69745i
$957$	−4.42404	−	6.96731i	−0.143009	−	0.225221i
$958$	7.58029			0.244908
$959$	−4.18977	+	6.19215i	−0.135295	+	0.199955i
$960$	−7.44240	+	22.9053i	−0.240202	+	0.739267i
$961$	−19.4492	+	21.6006i	−0.627395	+	0.696793i
$962$	−1.72547	−	16.4167i	−0.0556313	−	0.529297i
$963$	−0.808561	−	7.69294i	−0.0260555	−	0.247902i
$964$	24.3096	−	26.9985i	0.782958	−	0.869563i
$965$	14.7433	−	45.3753i	0.474605	−	1.46068i
$966$	3.98183	+	8.19416i	0.128113	+	0.263643i
$967$	38.8394			1.24899			0.624496	−	0.781028i	$-0.285305\pi$
$967$	38.8394			1.24899			0.624496	+	0.781028i	$0.285305\pi$
$968$	−53.3651	+	16.1411i	−1.71522	+	0.518794i
$969$	−6.58287	+	11.4019i	−0.211472	+	0.366281i
$970$	−10.7757	+	4.79764i	−0.345986	+	0.154043i
$971$	10.2382	−	2.17621i	0.328561	−	0.0698378i	−0.0406779	−	0.999172i	$-0.512952\pi$
$971$	10.2382	−	2.17621i	0.328561	−	0.0698378i	0.369239	+	0.929335i	$0.379618\pi$
$972$	1.25432	+	3.86040i	0.0402324	+	0.123822i
$973$	3.07339	−	7.57519i	0.0985283	−	0.242850i
$974$	21.2899	−	15.4680i	0.682172	−	0.495627i
$975$	17.4676	−	19.3997i	0.559411	−	0.621289i
$976$	−4.09030	−	4.54274i	−0.130927	−	0.145409i
$977$	20.4860	−	9.12096i	0.655405	−	0.291805i	−0.0519644	−	0.998649i	$-0.516548\pi$
$977$	20.4860	−	9.12096i	0.655405	−	0.291805i	0.707370	+	0.706844i	$0.249882\pi$
$978$	19.4144	+	33.6268i	0.620806	+	1.07527i
$979$	−23.4834	+	0.990147i	−0.750533	+	0.0316452i
$980$	41.5484	−	84.5621i	1.32721	−	2.70124i
$981$	−6.05128	−	4.39651i	−0.193202	−	0.140370i
$982$	46.3760	−	9.85753i	1.47992	−	0.314566i
$983$	35.5366	+	7.55354i	1.13344	+	0.240921i	0.736181	−	0.676785i	$-0.236627\pi$
$983$	35.5366	+	7.55354i	1.13344	+	0.240921i	0.397262	+	0.917705i	$0.369961\pi$
$984$	4.65736	+	44.3118i	0.148471	+	1.41261i
$985$	4.12805	+	1.83792i	0.131530	+	0.0585611i
$986$	−10.6919	−	32.9064i	−0.340501	−	1.04795i
$987$	2.80962	+	11.3390i	0.0894313	+	0.360923i
$988$	−33.3253	−	24.2123i	−1.06022	−	0.770294i
$989$	4.71025	+	8.15839i	0.149777	+	0.259422i
$990$	−24.2450	+	12.0429i	−0.770558	+	0.382749i
$991$	6.32841	−	10.9611i	0.201029	−	0.348192i	−0.747831	−	0.663889i	$-0.768905\pi$
$991$	6.32841	−	10.9611i	0.201029	−	0.348192i	0.948860	+	0.315697i	$0.102238\pi$
$992$	−0.0857799	+	0.816141i	−0.00272352	+	0.0259125i
$993$	6.76320	−	20.8150i	0.214624	−	0.660543i
$994$	−13.1118	+	73.7338i	−0.415880	+	2.33869i
$995$	29.5704	−	21.4841i	0.937443	−	0.681092i
$996$	−52.8842	−	23.5456i	−1.67570	−	0.746069i
$997$	48.5343	+	10.3163i	1.53710	+	0.326720i	0.897159	−	0.441707i	$-0.145627\pi$
$997$	48.5343	+	10.3163i	1.53710	+	0.326720i	0.639937	+	0.768427i	$0.278960\pi$
$998$	26.3909	+	29.3100i	0.835389	+	0.927793i
$999$	−0.160996	+	1.53177i	−0.00509368	+	0.0484631i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.y.b.4.2	✓	64
3.2	odd	2		693.2.by.c.235.7		64
7.2	even	3	inner	231.2.y.b.37.7	yes	64
11.3	even	5	inner	231.2.y.b.25.7	yes	64
21.2	odd	6		693.2.by.c.37.2		64
33.14	odd	10		693.2.by.c.487.2		64
77.58	even	15	inner	231.2.y.b.58.2	yes	64
231.212	odd	30		693.2.by.c.289.7		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.y.b.4.2	✓	64	1.1	even	1	trivial
231.2.y.b.25.7	yes	64	11.3	even	5	inner
231.2.y.b.37.7	yes	64	7.2	even	3	inner
231.2.y.b.58.2	yes	64	77.58	even	15	inner
693.2.by.c.37.2		64	21.2	odd	6
693.2.by.c.235.7		64	3.2	odd	2
693.2.by.c.289.7		64	231.212	odd	30
693.2.by.c.487.2		64	33.14	odd	10

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.257299 + 2.44803i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-3.97037 - 0.843927i) q^{4} +(3.02928 + 1.34872i) q^{5} +(-1.99141 + 1.44684i) q^{6} +(2.02429 + 1.70360i) q^{7} +(1.56623 - 4.82036i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(-0.257299 + 2.44803i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-3.97037 - 0.843927i) q^{4} +(3.02928 + 1.34872i) q^{5} +(-1.99141 + 1.44684i) q^{6} +(2.02429 + 1.70360i) q^{7} +(1.56623 - 4.82036i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(-4.08115 + 7.06876i) q^{10} +(1.53584 - 2.93959i) q^{11} +(-2.02953 - 3.51525i) q^{12} +(-3.52247 - 2.55923i) q^{13} +(-4.69131 + 4.51719i) q^{14} +(1.02469 + 3.15367i) q^{15} +(3.98113 + 1.77251i) q^{16} +(-0.590445 - 5.61771i) q^{17} +(-2.40773 - 0.511778i) q^{18} +(-2.27984 + 0.484596i) q^{19} +(-10.8891 - 7.91142i) q^{20} +(0.0884929 + 2.64427i) q^{21} +(6.80104 + 4.51614i) q^{22} +(-0.699447 - 1.21148i) q^{23} +(4.63024 - 2.06152i) q^{24} +(4.01184 + 4.45560i) q^{25} +(7.17139 - 7.96464i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-6.59946 - 8.47227i) q^{28} +(-0.768970 - 2.36665i) q^{29} +(-7.98393 + 1.69704i) q^{30} +(1.27031 - 0.565577i) q^{31} +(-0.295082 + 0.511097i) q^{32} +(3.21222 - 0.825617i) q^{33} +13.9042 q^{34} +(3.83446 + 7.89089i) q^{35} +(1.25432 - 3.86040i) q^{36} +(1.03060 - 1.14460i) q^{37} +(-0.599705 - 5.70582i) q^{38} +(-0.455118 - 4.33016i) q^{39} +(11.2459 - 12.4898i) q^{40} +(-2.71653 + 8.36062i) q^{41} +(-6.49603 - 0.463734i) q^{42} -6.73424 q^{43} +(-8.57866 + 10.3751i) q^{44} +(-1.65798 + 2.87171i) q^{45} +(3.14571 - 1.40056i) q^{46} +(4.31884 - 0.917998i) q^{47} +(1.34666 + 4.14460i) q^{48} +(1.19550 + 6.89716i) q^{49} +(-11.9397 + 8.67469i) q^{50} +(3.77968 - 4.19776i) q^{51} +(11.8257 + 13.1338i) q^{52} +(-9.51955 + 4.23838i) q^{53} +(-1.23076 - 2.13174i) q^{54} +(8.61719 - 6.83342i) q^{55} +(11.3825 - 7.08958i) q^{56} +(-1.88564 - 1.37000i) q^{57} +(5.99148 - 1.27353i) q^{58} +(14.4997 + 3.08202i) q^{59} +(-1.40692 - 13.3860i) q^{60} +(-1.28144 - 0.570534i) q^{61} +(1.05770 + 3.25528i) q^{62} +(-1.90586 + 1.83513i) q^{63} +(5.87596 + 4.26913i) q^{64} +(-7.21887 - 12.5035i) q^{65} +(1.19464 + 8.07605i) q^{66} +(-7.57690 + 13.1236i) q^{67} +(-2.39665 + 22.8026i) q^{68} +(0.432282 - 1.33043i) q^{69} +(-20.3038 + 7.35657i) q^{70} +(9.30320 - 6.75917i) q^{71} +(4.63024 + 2.06152i) q^{72} +(-8.70766 - 1.85087i) q^{73} +(2.53684 + 2.81745i) q^{74} +(-0.626711 + 5.96275i) q^{75} +9.46078 q^{76} +(8.11687 - 3.33412i) q^{77} +10.7175 q^{78} +(-0.348373 + 3.31455i) q^{79} +(9.66933 + 10.7389i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-19.7681 - 8.80133i) q^{82} +(11.5379 - 8.38278i) q^{83} +(1.88022 - 10.5734i) q^{84} +(5.78811 - 17.8140i) q^{85} +(1.73271 - 16.4856i) q^{86} +(1.24422 - 2.15505i) q^{87} +(-11.7644 - 12.0074i) q^{88} +(-3.54340 - 6.13736i) q^{89} +(-6.60344 - 4.79768i) q^{90} +(-2.77061 - 11.1815i) q^{91} +(1.75466 + 5.40030i) q^{92} +(1.27031 + 0.565577i) q^{93} +(1.13606 + 10.8089i) q^{94} +(-7.55987 - 1.60690i) q^{95} +(-0.577267 + 0.122702i) q^{96} +(1.16912 + 0.849417i) q^{97} +(-17.1921 + 1.15199i) q^{98} +(2.76295 + 1.83470i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9} - 14 q^{10} + 11 q^{11} - 30 q^{12} - 8 q^{13} + 6 q^{14} - 12 q^{15} - 4 q^{17} - q^{18} - 2 q^{19} + 24 q^{20} - 2 q^{21} - 14 q^{22} + 16 q^{24} - 10 q^{25} + 4 q^{26} - 16 q^{27} + 29 q^{28} - 58 q^{29} + 11 q^{30} - 19 q^{31} - 64 q^{32} + 6 q^{33} - 88 q^{34} + 17 q^{35} - 20 q^{36} - 20 q^{37} + 29 q^{38} + 4 q^{39} + 51 q^{40} - 68 q^{41} - 11 q^{42} + 92 q^{43} - 21 q^{44} - 4 q^{45} - 5 q^{46} - 26 q^{47} - 10 q^{48} + 37 q^{49} - 10 q^{50} + 6 q^{51} - 14 q^{52} - 3 q^{53} - 6 q^{54} - 32 q^{55} + 24 q^{56} - 36 q^{57} + 52 q^{58} + 7 q^{59} - 12 q^{60} - 21 q^{61} + 92 q^{62} - 7 q^{63} - 72 q^{64} - 66 q^{65} - 23 q^{66} - 4 q^{67} - 17 q^{68} + 40 q^{69} - q^{70} + 58 q^{71} + 16 q^{72} - 3 q^{73} - 28 q^{74} + 20 q^{75} + 168 q^{76} - 34 q^{77} + 132 q^{78} + 9 q^{79} - 5 q^{80} + 8 q^{81} - 42 q^{82} + 60 q^{83} - 39 q^{84} + 110 q^{85} + 13 q^{86} - 46 q^{87} + 92 q^{88} - 10 q^{89} + 8 q^{90} + 10 q^{91} + 110 q^{92} - 19 q^{93} - 46 q^{94} + 43 q^{95} - 4 q^{96} + 64 q^{97} - 88 q^{98} + 28 q^{99}+O(q^{100}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9 - 14 * q^10 + 11 * q^11 - 30 * q^12 - 8 * q^13 + 6 * q^14 - 12 * q^15 - 4 * q^17 - q^18 - 2 * q^19 + 24 * q^20 - 2 * q^21 - 14 * q^22 + 16 * q^24 - 10 * q^25 + 4 * q^26 - 16 * q^27 + 29 * q^28 - 58 * q^29 + 11 * q^30 - 19 * q^31 - 64 * q^32 + 6 * q^33 - 88 * q^34 + 17 * q^35 - 20 * q^36 - 20 * q^37 + 29 * q^38 + 4 * q^39 + 51 * q^40 - 68 * q^41 - 11 * q^42 + 92 * q^43 - 21 * q^44 - 4 * q^45 - 5 * q^46 - 26 * q^47 - 10 * q^48 + 37 * q^49 - 10 * q^50 + 6 * q^51 - 14 * q^52 - 3 * q^53 - 6 * q^54 - 32 * q^55 + 24 * q^56 - 36 * q^57 + 52 * q^58 + 7 * q^59 - 12 * q^60 - 21 * q^61 + 92 * q^62 - 7 * q^63 - 72 * q^64 - 66 * q^65 - 23 * q^66 - 4 * q^67 - 17 * q^68 + 40 * q^69 - q^70 + 58 * q^71 + 16 * q^72 - 3 * q^73 - 28 * q^74 + 20 * q^75 + 168 * q^76 - 34 * q^77 + 132 * q^78 + 9 * q^79 - 5 * q^80 + 8 * q^81 - 42 * q^82 + 60 * q^83 - 39 * q^84 + 110 * q^85 + 13 * q^86 - 46 * q^87 + 92 * q^88 - 10 * q^89 + 8 * q^90 + 10 * q^91 + 110 * q^92 - 19 * q^93 - 46 * q^94 + 43 * q^95 - 4 * q^96 + 64 * q^97 - 88 * q^98 + 28 * q^99

Introduction

L-functions

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