LMFDB - Embedded newform 189.2.bd.a.185.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(47,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 15]))

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

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

chi := DirichletCharacter("189.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.bd (of order $18$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			185.19
Character	$\chi$	$=$	189.185
Dual form			189.2.bd.a.47.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.87320 - 0.330296i) q^{2} +(0.583821 - 1.63069i) q^{3} +(1.52040 - 0.553380i) q^{4} +(-0.848304 + 0.308757i) q^{5} +(0.555004 - 3.24744i) q^{6} +(2.48993 + 0.894564i) q^{7} +(-0.629295 + 0.363324i) q^{8} +(-2.31831 - 1.90406i) q^{9} +O(q^{10})$	\(q+(1.87320 - 0.330296i) q^{2} +(0.583821 - 1.63069i) q^{3} +(1.52040 - 0.553380i) q^{4} +(-0.848304 + 0.308757i) q^{5} +(0.555004 - 3.24744i) q^{6} +(2.48993 + 0.894564i) q^{7} +(-0.629295 + 0.363324i) q^{8} +(-2.31831 - 1.90406i) q^{9} +(-1.48706 + 0.858555i) q^{10} +(-1.19563 + 3.28497i) q^{11} +(-0.0147504 - 2.80238i) q^{12} +(-1.35464 - 3.72184i) q^{13} +(4.95961 + 0.853285i) q^{14} +(0.00822998 + 1.56358i) q^{15} +(-3.53767 + 2.96846i) q^{16} +(-0.233932 - 0.405183i) q^{17} +(-4.97156 - 2.80097i) q^{18} +(3.14258 + 1.81437i) q^{19} +(-1.11890 + 0.938869i) q^{20} +(2.91243 - 3.53804i) q^{21} +(-1.15465 + 6.54832i) q^{22} +(3.44344 + 0.607171i) q^{23} +(0.225073 + 1.23830i) q^{24} +(-3.20593 + 2.69010i) q^{25} +(-3.76682 - 6.52432i) q^{26} +(-4.45842 + 2.66881i) q^{27} +(4.28072 - 0.0177830i) q^{28} +(-1.79273 + 4.92550i) q^{29} +(0.531860 + 2.92618i) q^{30} +(-2.38270 - 6.54641i) q^{31} +(-4.71214 + 5.61571i) q^{32} +(4.65874 + 3.86754i) q^{33} +(-0.572032 - 0.681722i) q^{34} +(-2.38842 + 0.00992201i) q^{35} +(-4.57842 - 1.61203i) q^{36} +9.85377 q^{37} +(6.48596 + 2.36070i) q^{38} +(-6.86004 + 0.0361081i) q^{39} +(0.421655 - 0.502508i) q^{40} +(2.71326 - 0.987547i) q^{41} +(4.28697 - 7.58943i) q^{42} +(-1.54504 - 8.76238i) q^{43} +5.65611i q^{44} +(2.55452 + 0.899431i) q^{45} +6.65080 q^{46} +(-3.13508 - 1.14108i) q^{47} +(2.77527 + 7.50190i) q^{48} +(5.39951 + 4.45481i) q^{49} +(-5.11683 + 6.09800i) q^{50} +(-0.797302 + 0.144917i) q^{51} +(-4.11919 - 4.90906i) q^{52} +(-8.75304 - 5.05357i) q^{53} +(-7.47001 + 6.47181i) q^{54} -3.15581i q^{55} +(-1.89192 + 0.341706i) q^{56} +(4.79338 - 4.06531i) q^{57} +(-1.73128 + 9.81858i) q^{58} +(-2.48304 - 2.08352i) q^{59} +(0.877767 + 2.37271i) q^{60} +(0.0209011 - 0.0574254i) q^{61} +(-6.62553 - 11.4757i) q^{62} +(-4.06911 - 6.81486i) q^{63} +(-2.35384 + 4.07697i) q^{64} +(2.29829 + 2.73900i) q^{65} +(10.0042 + 5.70592i) q^{66} +(1.78024 - 10.0962i) q^{67} +(-0.579891 - 0.486586i) q^{68} +(3.00046 - 5.26070i) q^{69} +(-4.47071 + 0.807471i) q^{70} +(-2.19935 - 1.26979i) q^{71} +(2.15069 + 0.355923i) q^{72} -8.37008i q^{73} +(18.4581 - 3.25466i) q^{74} +(2.51503 + 6.79842i) q^{75} +(5.78202 + 1.01953i) q^{76} +(-5.91566 + 7.10978i) q^{77} +(-12.8383 + 2.33348i) q^{78} +(1.64089 + 9.30597i) q^{79} +(2.08449 - 3.61044i) q^{80} +(1.74908 + 8.82840i) q^{81} +(4.75630 - 2.74605i) q^{82} +(-10.6153 - 3.86367i) q^{83} +(2.47018 - 6.99092i) q^{84} +(0.323549 + 0.271490i) q^{85} +(-5.78836 - 15.9034i) q^{86} +(6.98533 + 5.79900i) q^{87} +(-0.441103 - 2.50162i) q^{88} +(-1.51868 + 2.63043i) q^{89} +(5.08221 + 0.841067i) q^{90} +(-0.0435318 - 10.4789i) q^{91} +(5.57140 - 0.982388i) q^{92} +(-12.0662 + 0.0635112i) q^{93} +(-6.24952 - 1.10196i) q^{94} +(-3.22606 - 0.568842i) q^{95} +(6.40644 + 10.9626i) q^{96} +(5.02929 - 0.886800i) q^{97} +(11.5858 + 6.56131i) q^{98} +(9.02664 - 5.33901i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.87320	−	0.330296i	1.32455	−	0.233554i	0.533759	−	0.845637i	$-0.320779\pi$
$2$	1.87320	−	0.330296i	1.32455	−	0.233554i	0.790794	+	0.612082i	$0.209668\pi$
$3$	0.583821	−	1.63069i	0.337069	−	0.941480i
$3$	0.583821	−	1.63069i	0.337069	−	0.941480i
$4$	1.52040	−	0.553380i	0.760200	−	0.276690i
$5$	−0.848304	+	0.308757i	−0.379373	+	0.138080i	−0.524666	−	0.851308i	$-0.675810\pi$
$5$	−0.848304	+	0.308757i	−0.379373	+	0.138080i	0.145293	+	0.989389i	$0.453588\pi$
$6$	0.555004	−	3.24744i	0.226579	−	1.32576i
$7$	2.48993	+	0.894564i	0.941105	+	0.338114i
$7$	2.48993	+	0.894564i	0.941105	+	0.338114i
$8$	−0.629295	+	0.363324i	−0.222489	+	0.128454i
$9$	−2.31831	−	1.90406i	−0.772768	−	0.634688i
$10$	−1.48706	+	0.858555i	−0.470250	+	0.271499i
$11$	−1.19563	+	3.28497i	−0.360497	+	0.990456i	0.618358	+	0.785897i	$0.287798\pi$
$11$	−1.19563	+	3.28497i	−0.360497	+	0.990456i	−0.978854	+	0.204559i	$0.934424\pi$
$12$	−0.0147504	−	2.80238i	−0.00425809	−	0.808977i
$13$	−1.35464	−	3.72184i	−0.375709	−	1.03225i	−0.973116	−	0.230315i	$-0.926024\pi$
$13$	−1.35464	−	3.72184i	−0.375709	−	1.03225i	0.597407	−	0.801938i	$-0.296198\pi$
$14$	4.95961	+	0.853285i	1.32551	+	0.228050i
$15$	0.00822998	+	1.56358i	0.00212497	+	0.403715i
$16$	−3.53767	+	2.96846i	−0.884419	+	0.742115i
$17$	−0.233932	−	0.405183i	−0.0567369	−	0.0982712i	0.836262	−	0.548330i	$-0.184736\pi$
$17$	−0.233932	−	0.405183i	−0.0567369	−	0.0982712i	−0.892999	+	0.450059i	$0.851403\pi$
$18$	−4.97156	−	2.80097i	−1.17181	−	0.660194i
$19$	3.14258	+	1.81437i	0.720958	+	0.416245i	0.815105	−	0.579313i	$-0.196679\pi$
$19$	3.14258	+	1.81437i	0.720958	+	0.416245i	−0.0941474	+	0.995558i	$0.530013\pi$
$20$	−1.11890	+	0.938869i	−0.250194	+	0.209938i
$21$	2.91243	−	3.53804i	0.635545	−	0.772064i
$22$	−1.15465	+	6.54832i	−0.246171	+	1.39611i
$23$	3.44344	+	0.607171i	0.718006	+	0.126604i	0.520702	−	0.853738i	$-0.325670\pi$
$23$	3.44344	+	0.607171i	0.718006	+	0.126604i	0.197304	+	0.980342i	$0.436781\pi$
$24$	0.225073	+	1.23830i	0.0459428	+	0.252767i
$25$	−3.20593	+	2.69010i	−0.641187	+	0.538020i
$26$	−3.76682	−	6.52432i	−0.738734	−	1.27953i
$27$	−4.45842	+	2.66881i	−0.858023	+	0.513612i
$28$	4.28072	−	0.0177830i	0.808981	−	0.00336068i
$29$	−1.79273	+	4.92550i	−0.332902	+	0.914642i	0.654451	+	0.756105i	$0.272900\pi$
$29$	−1.79273	+	4.92550i	−0.332902	+	0.914642i	−0.987353	+	0.158537i	$0.949322\pi$
$30$	0.531860	+	2.92618i	0.0971040	+	0.534245i
$31$	−2.38270	−	6.54641i	−0.427945	−	1.17577i	−0.947057	−	0.321064i	$-0.895959\pi$
$31$	−2.38270	−	6.54641i	−0.427945	−	1.17577i	0.519112	−	0.854706i	$-0.326263\pi$
$32$	−4.71214	+	5.61571i	−0.832997	+	0.992727i
$33$	4.65874	+	3.86754i	0.810982	+	0.673253i
$34$	−0.572032	−	0.681722i	−0.0981027	−	0.116914i
$35$	−2.38842	+	0.00992201i	−0.403717	+	0.00167713i
$36$	−4.57842	−	1.61203i	−0.763070	−	0.268672i
$37$	9.85377			1.61995			0.809975	−	0.586464i	$-0.199481\pi$
$37$	9.85377			1.61995			0.809975	+	0.586464i	$0.199481\pi$
$38$	6.48596	+	2.36070i	1.05216	+	0.382956i
$39$	−6.86004	+	0.0361081i	−1.09849	+	0.00578193i
$40$	0.421655	−	0.502508i	0.0666695	−	0.0794536i
$41$	2.71326	−	0.987547i	0.423741	−	0.154229i	−0.121343	−	0.992611i	$-0.538720\pi$
$41$	2.71326	−	0.987547i	0.423741	−	0.154229i	0.545084	+	0.838382i	$0.316498\pi$
$42$	4.28697	−	7.58943i	0.661494	−	1.17107i
$43$	−1.54504	−	8.76238i	−0.235617	−	1.33625i	−0.841310	−	0.540553i	$-0.818215\pi$
$43$	−1.54504	−	8.76238i	−0.235617	−	1.33625i	0.605693	−	0.795698i	$-0.292896\pi$
$44$			5.65611i			0.852690i
$45$	2.55452	+	0.899431i	0.380805	+	0.134079i
$46$	6.65080			0.980606
$47$	−3.13508	−	1.14108i	−0.457298	−	0.166443i	0.103092	−	0.994672i	$-0.467126\pi$
$47$	−3.13508	−	1.14108i	−0.457298	−	0.166443i	−0.560390	+	0.828229i	$0.689349\pi$
$48$	2.77527	+	7.50190i	0.400576	+	1.08281i
$49$	5.39951	+	4.45481i	0.771358	+	0.636401i
$50$	−5.11683	+	6.09800i	−0.723629	+	0.862387i
$51$	−0.797302	+	0.144917i	−0.111645	+	0.0202924i
$52$	−4.11919	−	4.90906i	−0.571228	−	0.680764i
$53$	−8.75304	−	5.05357i	−1.20232	−	0.694161i	−0.241251	−	0.970463i	$-0.577558\pi$
$53$	−8.75304	−	5.05357i	−1.20232	−	0.694161i	−0.961071	+	0.276302i	$0.910891\pi$
$54$	−7.47001	+	6.47181i	−1.01654	+	0.880701i
$55$		−	3.15581i		−	0.425530i
$56$	−1.89192	+	0.341706i	−0.252818	+	0.0456624i
$57$	4.79338	−	4.06531i	0.634899	−	0.538464i
$58$	−1.73128	+	9.81858i	−0.227328	+	1.28924i
$59$	−2.48304	−	2.08352i	−0.323265	−	0.271251i	0.466684	−	0.884424i	$-0.345449\pi$
$59$	−2.48304	−	2.08352i	−0.323265	−	0.271251i	−0.789949	+	0.613173i	$0.789893\pi$
$60$	0.877767	+	2.37271i	0.113319	+	0.306316i
$61$	0.0209011	−	0.0574254i	0.00267611	−	0.00735257i	−0.938347	−	0.345694i	$-0.887644\pi$
$61$	0.0209011	−	0.0574254i	0.00267611	−	0.00735257i	0.941023	+	0.338341i	$0.109866\pi$
$62$	−6.62553	−	11.4757i	−0.841443	−	1.45742i
$63$	−4.06911	−	6.81486i	−0.512660	−	0.858592i
$64$	−2.35384	+	4.07697i	−0.294230	+	0.509621i
$65$	2.29829	+	2.73900i	0.285068	+	0.339731i
$66$	10.0042	+	5.70592i	1.23143	+	0.702350i
$67$	1.78024	−	10.0962i	0.217491	−	1.23345i	−0.659041	−	0.752107i	$-0.729038\pi$
$67$	1.78024	−	10.0962i	0.217491	−	1.23345i	0.876532	−	0.481344i	$-0.159851\pi$
$68$	−0.579891	−	0.486586i	−0.0703221	−	0.0590072i
$69$	3.00046	−	5.26070i	0.361213	−	0.633314i
$70$	−4.47071	+	0.807471i	−0.534352	+	0.0965113i
$71$	−2.19935	−	1.26979i	−0.261014	−	0.150697i	0.363783	−	0.931484i	$-0.381485\pi$
$71$	−2.19935	−	1.26979i	−0.261014	−	0.150697i	−0.624797	+	0.780787i	$0.714818\pi$
$72$	2.15069	+	0.355923i	0.253461	+	0.0419459i
$73$		−	8.37008i		−	0.979643i	−0.871823	−	0.489822i	$-0.837062\pi$
$73$		−	8.37008i		−	0.979643i	0.871823	−	0.489822i	$-0.162938\pi$
$74$	18.4581	−	3.25466i	2.14571	−	0.378346i
$75$	2.51503	+	6.79842i	0.290410	+	0.785014i
$76$	5.78202	+	1.01953i	0.663243	+	0.116948i
$77$	−5.91566	+	7.10978i	−0.674152	+	0.810235i
$78$	−12.8383	+	2.33348i	−1.45365	+	0.264215i
$79$	1.64089	+	9.30597i	0.184615	+	1.04700i	0.926449	+	0.376420i	$0.122845\pi$
$79$	1.64089	+	9.30597i	0.184615	+	1.04700i	−0.741834	+	0.670583i	$0.766044\pi$
$80$	2.08449	−	3.61044i	0.233053	−	0.403659i
$81$	1.74908	+	8.82840i	0.194342	+	0.980934i
$82$	4.75630	−	2.74605i	0.525246	−	0.303251i
$83$	−10.6153	−	3.86367i	−1.16518	−	0.424092i	−0.314237	−	0.949344i	$-0.601749\pi$
$83$	−10.6153	−	3.86367i	−1.16518	−	0.424092i	−0.850947	+	0.525252i	$0.823971\pi$
$84$	2.47018	−	6.99092i	0.269519	−	0.762772i
$85$	0.323549	+	0.271490i	0.0350938	+	0.0294472i
$86$	−5.78836	−	15.9034i	−0.624175	−	1.71491i
$87$	6.98533	+	5.79900i	0.748906	+	0.621719i
$88$	−0.441103	−	2.50162i	−0.0470217	−	0.266673i
$89$	−1.51868	+	2.63043i	−0.160980	+	0.278825i	−0.935220	−	0.354066i	$-0.884799\pi$
$89$	−1.51868	+	2.63043i	−0.160980	+	0.278825i	0.774241	+	0.632891i	$0.218132\pi$
$90$	5.08221	+	0.841067i	0.535712	+	0.0886562i
$91$	−0.0435318	−	10.4789i	−0.00456337	−	1.09849i
$92$	5.57140	−	0.982388i	0.580858	−	0.102421i
$93$	−12.0662	+	0.0635112i	−1.25121	+	0.00658581i
$94$	−6.24952	−	1.10196i	−0.644589	−	0.113658i
$95$	−3.22606	−	0.568842i	−0.330987	−	0.0583620i
$96$	6.40644	+	10.9626i	0.653855	+	1.11887i
$97$	5.02929	−	0.886800i	0.510647	−	0.0900409i	0.0876131	−	0.996155i	$-0.472076\pi$
$97$	5.02929	−	0.886800i	0.510647	−	0.0900409i	0.423034	+	0.906114i	$0.360965\pi$
$98$	11.5858	+	6.56131i	1.17034	+	0.662792i
$99$	9.02664	−	5.33901i	0.907211	−	0.536590i
$100$	−3.38565	+	5.86413i	−0.338565	+	0.586413i
$101$	2.32953	+	13.2114i	0.231797	+	1.31459i	0.849255	+	0.527983i	$0.177052\pi$
$101$	2.32953	+	13.2114i	0.231797	+	1.31459i	−0.617457	+	0.786604i	$0.711837\pi$
$102$	−1.44564	+	0.534804i	−0.143140	+	0.0529535i
$103$	5.15600	+	14.1660i	0.508036	+	1.39582i	0.883260	+	0.468883i	$0.155343\pi$
$103$	5.15600	+	14.1660i	0.508036	+	1.39582i	−0.375225	+	0.926934i	$0.622434\pi$
$104$	2.20470	+	1.84996i	0.216189	+	0.181404i
$105$	−1.37823	+	3.90057i	−0.134502	+	0.380656i
$106$	−18.0654	−	6.57525i	−1.75466	−	0.638645i
$107$	12.8332	−	7.40924i	1.24063	−	0.716278i	0.271407	−	0.962465i	$-0.412511\pi$
$107$	12.8332	−	7.40924i	1.24063	−	0.716278i	0.969222	+	0.246187i	$0.0791777\pi$
$108$	−5.30171	+	6.52485i	−0.510157	+	0.627854i
$109$	−1.48332	+	2.56918i	−0.142076	+	0.246083i	−0.928278	−	0.371886i	$-0.878711\pi$
$109$	−1.48332	+	2.56918i	−0.142076	+	0.246083i	0.786202	+	0.617969i	$0.212044\pi$
$110$	−1.04235	−	5.91147i	−0.0993844	−	0.563637i
$111$	5.75284	−	16.0685i	0.546036	−	1.52515i
$112$	−11.4640	+	4.22659i	−1.08325	+	0.399375i
$113$	12.0005	+	2.11601i	1.12891	+	0.199058i	0.706751	−	0.707463i	$-0.250160\pi$
$113$	12.0005	+	2.11601i	1.12891	+	0.199058i	0.422162	+	0.906520i	$0.361271\pi$
$114$	7.63621	−	9.19838i	0.715197	−	0.861507i
$115$	−3.10855	+	0.548121i	−0.289874	+	0.0511126i
$116$			8.48079i			0.787421i
$117$	−3.94616	+	11.2077i	−0.364822	+	1.03615i
$118$	−5.33942	−	3.08271i	−0.491533	−	0.283787i
$119$	−0.220013	−	1.21814i	−0.0201686	−	0.111667i
$120$	−0.573265	−	0.980963i	−0.0523317	−	0.0895493i
$121$	−0.935012	−	0.784569i	−0.0850011	−	0.0713244i
$122$	0.0201846	−	0.114473i	0.00182743	−	0.0103639i
$123$	−0.0263232	−	5.00105i	−0.00237349	−	0.450929i
$124$	−7.24531	−	8.63463i	−0.650648	−	0.775412i
$125$	4.14588	−	7.18088i	0.370819	−	0.642277i
$126$	−9.87318	−	11.4216i	−0.879573	−	1.01752i
$127$	−4.12812	−	7.15011i	−0.366311	−	0.634469i	0.622675	−	0.782481i	$-0.286046\pi$
$127$	−4.12812	−	7.15011i	−0.366311	−	0.634469i	−0.988986	+	0.148012i	$0.952713\pi$
$128$	1.95195	−	5.36295i	0.172530	−	0.474022i
$129$	−15.1908	−	2.59618i	−1.33747	−	0.228581i
$130$	5.20984	+	4.37157i	0.456933	+	0.383412i
$131$	3.60230	−	20.4297i	0.314734	−	1.78495i	−0.258970	−	0.965885i	$-0.583383\pi$
$131$	3.60230	−	20.4297i	0.314734	−	1.78495i	0.573704	−	0.819062i	$-0.305506\pi$
$132$	9.22336	+	3.30216i	0.802791	+	0.287416i
$133$	6.20174	+	7.32890i	0.537759	+	0.635496i
$134$		−	19.5003i		−	1.68457i
$135$	2.95808	−	3.64053i	0.254591	−	0.313327i
$136$	0.294425	+	0.169986i	0.0252467	+	0.0145762i
$137$	7.84338	+	9.34738i	0.670105	+	0.798600i	0.988798	−	0.149258i	$-0.0476884\pi$
$137$	7.84338	+	9.34738i	0.670105	+	0.798600i	−0.318693	+	0.947858i	$0.603244\pi$
$138$	3.88288	−	10.8454i	0.330532	−	0.923221i
$139$	−11.5620	+	13.7791i	−0.980677	+	1.16873i	0.00498385	+	0.999988i	$0.498414\pi$
$139$	−11.5620	+	13.7791i	−0.980677	+	1.16873i	−0.985661	+	0.168738i	$0.946031\pi$
$140$	−3.62586	+	1.33679i	−0.306441	+	0.112979i
$141$	−3.69107	+	4.44616i	−0.310844	+	0.374434i
$142$	−4.53923	−	1.65214i	−0.380923	−	0.138645i
$143$	13.8458			1.15784
$144$	13.8536	−	0.145842i	1.15446	−	0.0121535i
$145$		−	4.73184i		−	0.392958i
$146$	−2.76460	−	15.6788i	−0.228800	−	1.29759i
$147$	10.4168	−	6.20412i	0.859160	−	0.511707i
$148$	14.9817	−	5.45288i	1.23149	−	0.448224i
$149$	−7.23973	+	8.62797i	−0.593102	+	0.706831i	−0.976199	−	0.216877i	$-0.930413\pi$
$149$	−7.23973	+	8.62797i	−0.593102	+	0.706831i	0.383097	+	0.923708i	$0.374857\pi$
$150$	6.95664	+	11.9041i	0.568007	+	0.971966i
$151$	5.72173	+	2.08254i	0.465628	+	0.169475i	0.564171	−	0.825658i	$-0.309196\pi$
$151$	5.72173	+	2.08254i	0.465628	+	0.169475i	−0.0985428	+	0.995133i	$0.531418\pi$
$152$	−2.63682			−0.213874
$153$	−0.229167	+	1.38476i	−0.0185271	+	0.111951i
$154$	−8.73288	+	15.2720i	−0.703716	+	1.23065i
$155$	4.04251	+	4.81767i	0.324702	+	0.386965i
$156$	−10.4100	+	3.85111i	−0.833469	+	0.308336i
$157$	3.07275	−	3.66196i	0.245232	−	0.292256i	−0.629362	−	0.777112i	$-0.716684\pi$
$157$	3.07275	−	3.66196i	0.245232	−	0.292256i	0.874594	+	0.484856i	$0.161128\pi$
$158$	6.14744	+	16.8900i	0.489064	+	1.34369i
$159$	−13.3510	+	11.3231i	−1.05880	+	0.897981i
$160$	2.26344	−	6.21874i	0.178940	−	0.491635i
$161$	8.03077	+	4.59219i	0.632913	+	0.361915i
$162$	6.19236	+	15.9597i	0.486518	+	1.25391i
$163$	3.98040	+	6.89426i	0.311769	+	0.540000i	0.978745	−	0.205079i	$-0.0657451\pi$
$163$	3.98040	+	6.89426i	0.311769	+	0.540000i	−0.666976	+	0.745079i	$0.732412\pi$
$164$	3.57876	−	3.00293i	0.279454	−	0.234490i
$165$	−5.14616	−	1.84243i	−0.400628	−	0.143433i
$166$	−21.1608	−	3.73122i	−1.64240	−	0.289599i
$167$	−3.90196	+	22.1291i	−0.301943	+	1.71240i	0.335613	+	0.942000i	$0.391057\pi$
$167$	−3.90196	+	22.1291i	−0.301943	+	1.71240i	−0.637556	+	0.770404i	$0.720055\pi$
$168$	−0.547325	+	3.28463i	−0.0422271	+	0.253415i
$169$	−2.05848	+	1.72727i	−0.158344	+	0.132867i
$170$	0.695744	+	0.401688i	0.0533611	+	0.0308080i
$171$	−3.83079	−	10.1899i	−0.292948	−	0.779244i
$172$	−7.19802	−	12.4673i	−0.548844	−	0.950625i
$173$	5.93288	−	4.97828i	0.451069	−	0.378491i	−0.388764	−	0.921338i	$-0.627098\pi$
$173$	5.93288	−	4.97828i	0.451069	−	0.378491i	0.839832	+	0.542846i	$0.182653\pi$
$174$	15.0003	+	8.55548i	1.13717	+	0.648589i
$175$	−10.3890	+	3.83024i	−0.785336	+	0.289539i
$176$	−5.52155	−	15.1703i	−0.416203	−	1.14351i
$177$	−4.84723	+	2.83267i	−0.364340	+	0.212917i
$178$	−1.97597	+	5.42893i	−0.148105	+	0.406916i
$179$	1.62040	−	0.935541i	0.121115	−	0.0699256i	−0.438219	−	0.898868i	$-0.644390\pi$
$179$	1.62040	−	0.935541i	0.121115	−	0.0699256i	0.559333	+	0.828943i	$0.311057\pi$
$180$	4.38162	−	0.0461270i	0.326587	−	0.00343810i
$181$	−18.1786	+	10.4954i	−1.35121	+	0.780121i	−0.988419	−	0.151751i	$-0.951509\pi$
$181$	−18.1786	+	10.4954i	−1.35121	+	0.780121i	−0.362790	+	0.931871i	$0.618176\pi$
$182$	−3.54269	−	19.6148i	−0.262602	−	1.45394i
$183$	−0.0814405	−	0.0676094i	−0.00602026	−	0.00499783i
$184$	−2.38754	+	0.868993i	−0.176012	+	0.0640630i
$185$	−8.35899	+	3.04242i	−0.614565	+	0.223683i
$186$	−22.5815	+	4.10440i	−1.65576	+	0.300949i
$187$	1.61071	−	0.284012i	0.117787	−	0.0207690i
$188$	−5.39802			−0.393691
$189$	−13.4886	+	2.65680i	−0.981149	+	0.193254i
$190$	−6.23095			−0.452041
$191$	10.0948	−	1.77999i	0.730436	−	0.128796i	0.203952	−	0.978981i	$-0.434621\pi$
$191$	10.0948	−	1.77999i	0.730436	−	0.128796i	0.526484	+	0.850185i	$0.323510\pi$
$192$	5.27405	+	6.21860i	0.380622	+	0.448789i
$193$	9.47459	−	3.44847i	0.681996	−	0.248226i	0.0222917	−	0.999752i	$-0.492904\pi$
$193$	9.47459	−	3.44847i	0.681996	−	0.248226i	0.659704	+	0.751525i	$0.270682\pi$
$194$	9.12797	−	3.32231i	0.655350	−	0.238528i
$195$	5.80825	−	2.14872i	0.415937	−	0.153873i
$196$	10.6746	+	3.78510i	0.762472	+	0.270365i
$197$	−23.0223	+	13.2919i	−1.64027	+	0.947010i	−0.659533	+	0.751676i	$0.729246\pi$
$197$	−23.0223	+	13.2919i	−1.64027	+	0.947010i	−0.980737	+	0.195334i	$0.937421\pi$
$198$	15.1452	−	12.9825i	1.07633	−	0.922626i
$199$	−16.8725	+	9.74135i	−1.19606	+	0.690546i	−0.959675	−	0.281113i	$-0.909297\pi$
$199$	−16.8725	+	9.74135i	−1.19606	+	0.690546i	−0.236387	+	0.971659i	$0.575963\pi$
$200$	1.04010	−	2.85766i	0.0735464	−	0.202067i
$201$	−15.4245	−	8.79742i	−1.08796	−	0.620522i
$202$	8.72737	+	23.9782i	0.614055	+	1.68710i
$203$	−8.86996	+	10.6604i	−0.622549	+	0.748215i
$204$	−1.13202	+	0.661543i	−0.0792575	+	0.0463173i
$205$	−1.99676	+	1.67548i	−0.139460	+	0.117021i
$206$	14.3372	+	24.8327i	0.998919	+	1.73018i
$207$	−6.82685	−	7.96413i	−0.474499	−	0.553546i
$208$	15.8404	+	9.14547i	1.09834	+	0.634124i
$209$	−9.71752	+	8.15397i	−0.672175	+	0.564022i
$210$	−1.29336	+	7.76177i	−0.0892504	+	0.535613i
$211$	−0.926175	+	5.25260i	−0.0637605	+	0.361604i	0.936188	+	0.351499i	$0.114328\pi$
$211$	−0.926175	+	5.25260i	−0.0637605	+	0.361604i	−0.999949	+	0.0101053i	$0.996783\pi$
$212$	−16.1047	−	2.83969i	−1.10607	−	0.195030i
$213$	−3.35467	+	2.84512i	−0.229858	+	0.194945i
$214$	21.5919	−	18.1177i	1.47599	−	1.23850i
$215$	4.01612	+	6.95612i	0.273897	+	0.474403i
$216$	1.83602	−	3.29932i	0.124925	−	0.224490i
$217$	−0.0765688	−	18.4316i	−0.00519783	−	1.25122i
$218$	−1.92996	+	5.30253i	−0.130713	+	0.359132i
$219$	−13.6490	−	4.88663i	−0.922314	−	0.330208i
$220$	−1.74636	−	4.79810i	−0.117740	−	0.323488i
$221$	−1.19113	+	1.41954i	−0.0801242	+	0.0954883i
$222$	5.46888	−	31.9996i	0.367047	−	2.14767i
$223$	5.44697	+	6.49144i	0.364756	+	0.434699i	0.916941	−	0.399022i	$-0.130650\pi$
$223$	5.44697	+	6.49144i	0.364756	+	0.434699i	−0.552185	+	0.833721i	$0.686206\pi$
$224$	−16.7565	+	9.76742i	−1.11959	+	0.652613i
$225$	12.5545	−	0.132166i	0.836964	−	0.00881104i
$226$	23.1783			1.54180
$227$	−21.1352	−	7.69258i	−1.40279	−	0.510575i	−0.473787	−	0.880640i	$-0.657113\pi$
$227$	−21.1352	−	7.69258i	−1.40279	−	0.510575i	−0.929006	+	0.370065i	$0.879335\pi$
$228$	5.03820	−	8.83346i	0.333663	−	0.585010i
$229$	0.509720	−	0.607461i	0.0336833	−	0.0401421i	−0.748940	−	0.662638i	$-0.769437\pi$
$229$	0.509720	−	0.607461i	0.0336833	−	0.0401421i	0.782623	+	0.622496i	$0.213881\pi$
$230$	−5.64189	+	2.05348i	−0.372015	+	0.135403i
$231$	8.14017	+	13.7975i	0.535584	+	0.907806i
$232$	−0.661391	−	3.75093i	−0.0434224	−	0.246261i
$233$			8.67731i			0.568470i	0.958755	+	0.284235i	$0.0917395\pi$
$233$			8.67731i			0.568470i	−0.958755	+	0.284235i	$0.908260\pi$
$234$	−3.69009	+	22.2976i	−0.241229	+	1.45764i
$235$	3.01181			0.196469
$236$	−4.92820	−	1.79372i	−0.320798	−	0.116761i
$237$	16.1331	+	2.75723i	1.04796	+	0.179101i
$238$	−0.814477	−	2.20916i	−0.0527947	−	0.143199i
$239$	14.4054	−	17.1677i	0.931810	−	1.11049i	−0.0618527	−	0.998085i	$-0.519701\pi$
$239$	14.4054	−	17.1677i	0.931810	−	1.11049i	0.993663	−	0.112403i	$-0.0358546\pi$
$240$	−4.67054	−	5.50701i	−0.301482	−	0.355476i
$241$	6.75864	+	8.05464i	0.435362	+	0.518845i	0.938461	−	0.345384i	$-0.112251\pi$
$241$	6.75864	+	8.05464i	0.435362	+	0.518845i	−0.503099	+	0.864229i	$0.667807\pi$
$242$	−2.01061	−	1.16082i	−0.129247	−	0.0746206i
$243$	15.4175	+	2.30200i	0.989036	+	0.147673i
$244$		−	0.0988758i		−	0.00632987i
$245$	−5.95588	−	2.11189i	−0.380507	−	0.134924i
$246$	−1.70113	−	9.35927i	−0.108460	−	0.596725i
$247$	2.49573	−	14.1540i	0.158800	−	0.900598i
$248$	3.87789	+	3.25394i	0.246246	+	0.206625i
$249$	−12.4979	+	15.0546i	−0.792022	+	0.954049i
$250$	5.39426	−	14.8206i	0.341163	−	0.937337i
$251$	−4.71175	−	8.16098i	−0.297403	−	0.515117i	0.678138	−	0.734934i	$-0.262787\pi$
$251$	−4.71175	−	8.16098i	−0.297403	−	0.515117i	−0.975541	+	0.219818i	$0.929454\pi$
$252$	−9.95789	−	8.10955i	−0.627288	−	0.510853i
$253$	−6.11162	+	10.5856i	−0.384234	+	0.665514i
$254$	−10.0944	−	12.0301i	−0.633381	−	0.754835i
$255$	0.631610	−	0.369107i	0.0395530	−	0.0231144i
$256$	3.52000	−	19.9629i	0.220000	−	1.24768i
$257$	9.03217	+	7.57889i	0.563411	+	0.472758i	0.879452	−	0.475987i	$-0.157909\pi$
$257$	9.03217	+	7.57889i	0.563411	+	0.472758i	−0.316041	+	0.948746i	$0.602354\pi$
$258$	−29.3129	+	0.154290i	−1.82494	+	0.00960565i
$259$	24.5352	+	8.81483i	1.52454	+	0.547727i
$260$	5.01003	+	2.89254i	0.310709	+	0.179388i
$261$	13.5346	−	8.00533i	0.837769	−	0.495517i
$262$		−	39.4587i		−	2.43777i
$263$	−4.57306	+	0.806354i	−0.281987	+	0.0497219i	−0.312853	−	0.949802i	$-0.601285\pi$
$263$	−4.57306	+	0.806354i	−0.281987	+	0.0497219i	0.0308658	+	0.999524i	$0.490174\pi$
$264$	−4.33689	−	0.741196i	−0.266917	−	0.0456174i
$265$	8.98556	+	1.58440i	0.551978	+	0.0973287i
$266$	14.0378	+	11.6801i	0.860713	+	0.716152i
$267$	3.40278	+	4.01220i	0.208247	+	0.245542i
$268$	−2.88038	−	16.3355i	−0.175947	−	0.997847i
$269$	13.5452	−	23.4609i	0.825864	−	1.43044i	−0.0753937	−	0.997154i	$-0.524021\pi$
$269$	13.5452	−	23.4609i	0.825864	−	1.43044i	0.901257	−	0.433284i	$-0.142645\pi$
$270$	4.33862	−	7.79648i	0.264040	−	0.474479i
$271$	−3.93162	+	2.26992i	−0.238829	+	0.137888i	−0.614638	−	0.788809i	$-0.710698\pi$
$271$	−3.93162	+	2.26992i	−0.238829	+	0.137888i	0.375810	+	0.926697i	$0.377365\pi$
$272$	2.03035	+	0.738985i	0.123108	+	0.0448076i
$273$	−17.1133	−	6.04684i	−1.03575	−	0.365971i
$274$	17.7796	+	14.9189i	1.07411	+	0.901282i
$275$	−5.00378	−	13.7478i	−0.301739	−	0.829022i
$276$	1.65073	−	9.65877i	0.0993623	−	0.581389i
$277$	1.38431	+	7.85082i	0.0831752	+	0.471710i	0.997735	+	0.0672603i	$0.0214258\pi$
$277$	1.38431	+	7.85082i	0.0831752	+	0.471710i	−0.914560	+	0.404450i	$0.867463\pi$
$278$	−17.1068	+	29.6298i	−1.02600	+	1.77708i
$279$	−6.94096	+	19.7134i	−0.415545	+	1.18021i
$280$	1.49942	−	0.874014i	0.0896073	−	0.0522323i
$281$	6.05459	−	1.06759i	0.361187	−	0.0636870i	0.00988990	−	0.999951i	$-0.496852\pi$
$281$	6.05459	−	1.06759i	0.361187	−	0.0636870i	0.351297	+	0.936264i	$0.385741\pi$
$282$	−5.44556	+	9.54769i	−0.324278	+	0.568557i
$283$	−11.2989	−	1.99229i	−0.671647	−	0.118430i	−0.172584	−	0.984995i	$-0.555212\pi$
$283$	−11.2989	−	1.99229i	−0.671647	−	0.118430i	−0.499064	+	0.866565i	$0.666323\pi$
$284$	−4.04657	−	0.713519i	−0.240119	−	0.0423395i
$285$	−2.81105	+	4.92861i	−0.166512	+	0.291946i
$286$	25.9359	−	4.57321i	1.53362	−	0.270419i
$287$	7.63926	−	0.0317351i	0.450931	−	0.00187327i
$288$	21.6169	−	4.04672i	1.27379	−	0.238455i
$289$	8.39055	−	14.5329i	0.493562	−	0.854874i
$290$	−1.56291	−	8.86368i	−0.0917770	−	0.520493i
$291$	1.49011	−	8.71896i	0.0873519	−	0.511114i
$292$	−4.63183	−	12.7259i	−0.271058	−	0.744725i
$293$	−0.840836	−	0.705545i	−0.0491222	−	0.0412184i	0.617896	−	0.786260i	$-0.287985\pi$
$293$	−0.840836	−	0.705545i	−0.0491222	−	0.0412184i	−0.667018	+	0.745041i	$0.732430\pi$
$294$	17.4635	−	15.0622i	1.01849	−	0.878444i
$295$	2.74968	+	1.00080i	0.160092	+	0.0582689i
$296$	−6.20093	+	3.58011i	−0.360422	+	0.208090i
$297$	−3.43633	−	17.8367i	−0.199396	−	1.03499i
$298$	−10.7117	+	18.5532i	−0.620511	+	1.07476i
$299$	−2.40482	−	13.6384i	−0.139074	−	0.788730i
$300$	7.58596	+	8.94456i	0.437976	+	0.516414i
$301$	3.99146	−	23.1999i	0.230064	−	1.33722i
$302$	11.4058	+	2.01115i	0.656331	+	0.115729i
$303$	22.9038	+	3.91437i	1.31579	+	0.224875i
$304$	−16.5033	+	2.90998i	−0.946530	+	0.166899i
$305$			0.0551675i			0.00315888i
$306$	0.0281042	+	2.66962i	0.00160661	+	0.152612i
$307$	−5.93612	−	3.42722i	−0.338792	−	0.195602i	0.320945	−	0.947098i	$-0.395999\pi$
$307$	−5.93612	−	3.42722i	−0.338792	−	0.195602i	−0.659738	+	0.751496i	$0.729333\pi$
$308$	−5.05975	+	14.0833i	−0.288306	+	0.802472i
$309$	26.1105	−	0.137434i	1.48538	−	0.00781835i
$310$	9.16368	+	7.68924i	0.520462	+	0.436720i
$311$	3.87680	−	21.9864i	0.219833	−	1.24674i	−0.652487	−	0.757800i	$-0.726274\pi$
$311$	3.87680	−	21.9864i	0.219833	−	1.24674i	0.872320	−	0.488935i	$-0.162615\pi$
$312$	4.30387	−	2.51514i	0.243659	−	0.142392i
$313$	0.650065	+	0.774717i	0.0367439	+	0.0437896i	0.784103	−	0.620630i	$-0.213123\pi$
$313$	0.650065	+	0.774717i	0.0367439	+	0.0437896i	−0.747360	+	0.664420i	$0.768679\pi$
$314$	4.54635	−	7.87450i	0.256565	−	0.444384i
$315$	5.55598	+	4.52470i	0.313044	+	0.254938i
$316$	7.64455	+	13.2408i	0.430040	+	0.744850i
$317$	−8.50091	+	23.3561i	−0.477459	+	1.31181i	0.434184	+	0.900824i	$0.357037\pi$
$317$	−8.50091	+	23.3561i	−0.477459	+	1.31181i	−0.911643	+	0.410983i	$0.865186\pi$
$318$	−21.2692	+	25.6203i	−1.19271	+	1.43671i
$319$	−14.0367	−	11.7782i	−0.785902	−	0.659450i
$320$	0.737976	−	4.18527i	0.0412541	−	0.233964i
$321$	−4.58989	−	25.2526i	−0.256183	−	1.40946i
$322$	16.5600	+	5.94956i	0.922854	+	0.331556i
$323$		−	1.69776i		−	0.0944659i
$324$	7.54477	+	12.4548i	0.419154	+	0.691933i
$325$	14.3550	+	8.28786i	0.796272	+	0.459728i
$326$	9.73324	+	11.5996i	0.539074	+	0.642444i
$327$	3.32355	+	3.91877i	0.183793	+	0.216709i
$328$	−1.34864	+	1.60725i	−0.0744664	+	0.0887457i
$329$	−6.78536	−	5.64573i	−0.374089	−	0.311259i
$330$	−10.2483	−	1.75149i	−0.564152	−	0.0964163i
$331$	−24.9441	−	9.07889i	−1.37105	−	0.499021i	−0.451597	−	0.892222i	$-0.649145\pi$
$331$	−24.9441	−	9.07889i	−1.37105	−	0.499021i	−0.919453	+	0.393201i	$0.871368\pi$
$332$	−18.2776			−1.00312
$333$	−22.8441	−	18.7622i	−1.25185	−	1.02816i
$334$			42.7411i			2.33869i
$335$	1.60710	+	9.11434i	0.0878054	+	0.497969i
$336$	0.199302	+	21.1619i	0.0108728	+	1.15448i
$337$	23.2967	−	8.47930i	1.26905	−	0.461897i	0.382254	−	0.924057i	$-0.375148\pi$
$337$	23.2967	−	8.47930i	1.26905	−	0.461897i	0.886796	+	0.462161i	$0.152926\pi$
$338$	−3.28543	+	3.91542i	−0.178704	+	0.212971i
$339$	10.4567	−	18.3337i	0.567931	−	0.995752i
$340$	0.642160	+	0.233727i	0.0348260	+	0.0126756i
$341$	24.3536			1.31882
$342$	−10.5415	−	17.8225i	−0.570020	−	0.963731i
$343$	9.45929	+	15.9224i	0.510754	+	0.859727i
$344$	4.15587	+	4.95278i	0.224070	+	0.267036i
$345$	−0.921021	+	5.38909i	−0.0495861	+	0.290139i
$346$	9.46917	−	11.2849i	0.509066	−	0.606681i
$347$	−6.40998	−	17.6113i	−0.344106	−	0.945423i	−0.984190	−	0.177118i	$-0.943323\pi$
$347$	−6.40998	−	17.6113i	−0.344106	−	0.945423i	0.640084	−	0.768305i	$-0.278900\pi$
$348$	13.8295	+	4.95126i	0.741341	+	0.265416i
$349$	−8.31455	+	22.8440i	−0.445067	+	1.22281i	0.491052	+	0.871130i	$0.336613\pi$
$349$	−8.31455	+	22.8440i	−0.445067	+	1.22281i	−0.936119	+	0.351682i	$0.885610\pi$
$350$	−18.1956	+	10.6063i	−0.972596	+	0.566929i
$351$	15.9724	+	12.9782i	0.852545	+	0.692727i
$352$	−12.8135	−	22.1936i	−0.682960	−	1.18292i
$353$	17.5265	−	14.7065i	0.932841	−	0.782747i	−0.0434839	−	0.999054i	$-0.513846\pi$
$353$	17.5265	−	14.7065i	0.932841	−	0.782747i	0.976325	+	0.216307i	$0.0694013\pi$
$354$	−8.14422	+	6.90719i	−0.432860	+	0.367113i
$355$	2.25777	+	0.398106i	0.119830	+	0.0211293i
$356$	−0.853371	+	4.83971i	−0.0452286	+	0.256504i
$357$	−2.11487	−	0.352405i	−0.111931	−	0.0186512i
$358$	2.72634	−	2.28767i	0.144091	−	0.120907i
$359$	7.23348	+	4.17625i	0.381768	+	0.220414i	0.678587	−	0.734520i	$-0.262592\pi$
$359$	7.23348	+	4.17625i	0.381768	+	0.220414i	−0.296819	+	0.954934i	$0.595926\pi$
$360$	−1.93433	+	0.362111i	−0.101948	+	0.0190849i
$361$	−2.91612	−	5.05087i	−0.153480	−	0.265835i
$362$	−30.5857	+	25.6644i	−1.60755	+	1.34889i
$363$	−1.82527	+	1.06667i	−0.0958018	+	0.0559856i
$364$	−5.86502	−	15.9081i	−0.307411	−	0.833810i
$365$	2.58432	+	7.10037i	0.135270	+	0.371650i
$366$	−0.174886	−	0.0997466i	−0.00914141	−	0.00521384i
$367$	3.33853	−	9.17253i	0.174270	−	0.478802i	−0.821551	−	0.570136i	$-0.806891\pi$
$367$	3.33853	−	9.17253i	0.174270	−	0.478802i	0.995820	+	0.0913333i	$0.0291129\pi$
$368$	−13.9841	+	8.07374i	−0.728973	+	0.420873i
$369$	−8.17053	−	2.87679i	−0.425341	−	0.149760i
$370$	−14.6532	+	8.46001i	−0.761782	+	0.439815i
$371$	−17.2737	−	20.4132i	−0.896806	−	1.05980i
$372$	−18.3104	+	6.77379i	−0.949349	+	0.351204i
$373$	−9.95905	+	3.62480i	−0.515660	+	0.187685i	−0.586724	−	0.809787i	$-0.699583\pi$
$373$	−9.95905	+	3.62480i	−0.515660	+	0.187685i	0.0710640	+	0.997472i	$0.477361\pi$
$374$	2.92338	−	1.06402i	0.151164	−	0.0550193i
$375$	−9.28934	−	10.9530i	−0.479700	−	0.565611i
$376$	2.38747	−	0.420975i	0.123124	−	0.0217102i
$377$	20.7604			1.06922
$378$	−24.3893	+	9.43194i	−1.25445	+	0.485127i
$379$	−6.26462			−0.321792			−0.160896	−	0.986971i	$-0.551438\pi$
$379$	−6.26462			−0.321792			−0.160896	+	0.986971i	$0.551438\pi$
$380$	−5.21969	+	0.920373i	−0.267765	+	0.0472141i
$381$	−14.0697	+	2.55730i	−0.720812	+	0.131014i
$382$	18.3217	−	6.66856i	0.937420	−	0.341193i
$383$	7.86054	−	2.86100i	0.401655	−	0.146190i	−0.133291	−	0.991077i	$-0.542554\pi$
$383$	7.86054	−	2.86100i	0.401655	−	0.146190i	0.534945	+	0.844887i	$0.320332\pi$
$384$	−7.60572	−	6.31404i	−0.388128	−	0.322212i
$385$	2.82308	−	7.85776i	0.143877	−	0.400468i
$386$	16.6088	−	9.58909i	0.845365	−	0.488072i
$387$	−13.1023	+	23.2557i	−0.666025	+	1.18216i
$388$	7.15580	−	4.13140i	0.363281	−	0.209740i
$389$	−6.64622	+	18.2603i	−0.336977	+	0.925835i	0.649270	+	0.760558i	$0.275074\pi$
$389$	−6.64622	+	18.2603i	−0.336977	+	0.925835i	−0.986247	+	0.165278i	$0.947148\pi$
$390$	10.1703	−	5.94342i	0.514993	−	0.300957i
$391$	−0.559516	−	1.53726i	−0.0282960	−	0.0777425i
$392$	−5.01642	−	0.841618i	−0.253368	−	0.0425081i
$393$	−31.2114	−	17.8015i	−1.57441	−	0.897967i
$394$	−38.7351	+	32.5026i	−1.95145	+	1.63746i
$395$	−4.26526	−	7.38765i	−0.214609	−	0.371713i
$396$	10.7696	−	13.1126i	0.541192	−	0.658932i
$397$	−24.5677	−	14.1842i	−1.23302	−	0.711882i	−0.265359	−	0.964150i	$-0.585490\pi$
$397$	−24.5677	−	14.1842i	−1.23302	−	0.711882i	−0.967658	+	0.252267i	$0.918824\pi$
$398$	−28.3881	+	23.8204i	−1.42297	+	1.19401i
$399$	15.5719	−	5.83435i	0.779569	−	0.292083i
$400$	3.35610	−	19.0334i	0.167805	−	0.951669i
$401$	−19.2271	−	3.39026i	−0.960157	−	0.169302i	−0.328461	−	0.944518i	$-0.606530\pi$
$401$	−19.2271	−	3.39026i	−0.960157	−	0.169302i	−0.631696	+	0.775216i	$0.717641\pi$
$402$	−31.7989	−	11.3847i	−1.58599	−	0.567816i
$403$	−21.1370	+	17.7361i	−1.05291	+	0.883496i
$404$	10.8528	+	18.7976i	0.539946	+	0.935213i
$405$	−4.20959	−	6.94913i	−0.209176	−	0.345305i
$406$	−13.0941	+	22.8988i	−0.649850	+	1.13645i
$407$	−11.7815	+	32.3694i	−0.583986	+	1.60449i
$408$	0.449087	−	0.380875i	0.0222331	−	0.0188561i
$409$	11.9596	+	32.8586i	0.591362	+	1.62475i	0.767980	+	0.640474i	$0.221262\pi$
$409$	11.9596	+	32.8586i	0.591362	+	1.62475i	−0.176618	+	0.984279i	$0.556516\pi$
$410$	−3.18693	+	3.79803i	−0.157391	+	0.187571i
$411$	19.8218	−	7.33293i	0.977738	−	0.361707i
$412$	15.6784	+	18.6847i	0.772418	+	0.920531i
$413$	−4.31876	−	7.40907i	−0.212512	−	0.364576i
$414$	−15.4186	−	12.6635i	−0.757782	−	0.622379i
$415$	10.1980			0.500598
$416$	27.2840	+	9.93058i	1.33771	+	0.486887i
$417$	15.7193	+	26.8986i	0.769775	+	1.31723i
$418$	−15.5096	+	18.4837i	−0.758602	+	0.904066i
$419$	38.1160	−	13.8731i	1.86209	−	0.677745i	0.884748	−	0.466070i	$-0.154331\pi$
$419$	38.1160	−	13.8731i	1.86209	−	0.677745i	0.977340	−	0.211674i	$-0.0678916\pi$
$420$	0.0630355	+	6.69311i	0.00307582	+	0.326590i
$421$	2.74861	+	15.5881i	0.133959	+	0.759718i	0.975579	+	0.219649i	$0.0704911\pi$
$421$	2.74861	+	15.5881i	0.133959	+	0.759718i	−0.841620	+	0.540070i	$0.818398\pi$
$422$			10.1451i			0.493855i
$423$	5.09539	+	8.61475i	0.247746	+	0.418864i
$424$	7.34433			0.356672
$425$	1.83995	+	0.669688i	0.0892508	+	0.0324846i
$426$	−5.34423	+	6.43752i	−0.258929	+	0.311899i
$427$	0.103413	−	0.124288i	0.00500451	−	0.00601471i
$428$	15.4114	−	18.3666i	0.744939	−	0.887784i
$429$	8.08347	−	22.5782i	0.390273	−	1.09009i
$430$	9.82057	+	11.7037i	0.473590	+	0.564403i
$431$	−6.88208	−	3.97337i	−0.331498	−	0.191391i	0.325008	−	0.945711i	$-0.394633\pi$
$431$	−6.88208	−	3.97337i	−0.331498	−	0.191391i	−0.656506	+	0.754321i	$0.727966\pi$
$432$	7.85017	−	22.6760i	0.377692	−	1.09100i
$433$		−	16.4757i		−	0.791770i	−0.918300	−	0.395885i	$-0.870438\pi$
$433$		−	16.4757i		−	0.791770i	0.918300	−	0.395885i	$-0.129562\pi$
$434$	−6.23131	−	34.5008i	−0.299112	−	1.65609i
$435$	−7.71616	−	2.76255i	−0.369962	−	0.132454i
$436$	−0.833501	+	4.72702i	−0.0399175	+	0.226383i
$437$	9.71965	+	8.15575i	0.464954	+	0.390143i
$438$	−27.1814	−	4.64542i	−1.29878	−	0.221967i
$439$	2.08683	−	5.73351i	0.0995988	−	0.273646i	−0.879879	−	0.475198i	$-0.842376\pi$
$439$	2.08683	−	5.73351i	0.0995988	−	0.273646i	0.979478	+	0.201552i	$0.0645986\pi$
$440$	1.14658	+	1.98594i	0.0546612	+	0.0946759i
$441$	−4.03548	−	20.6086i	−0.192166	−	0.981363i
$442$	−1.76236	+	3.05250i	−0.0838270	+	0.145193i
$443$	12.7961	+	15.2497i	0.607959	+	0.724537i	0.978950	−	0.204099i	$-0.0654265\pi$
$443$	12.7961	+	15.2497i	0.607959	+	0.724537i	−0.370991	+	0.928636i	$0.620982\pi$
$444$	−0.145347	−	27.6140i	−0.00689789	−	1.31050i
$445$	0.476137	−	2.70031i	0.0225710	−	0.128007i
$446$	12.3474	+	10.3607i	0.584664	+	0.490592i
$447$	9.84285	+	16.8430i	0.465551	+	0.796645i
$448$	−9.50800	+	8.04570i	−0.449211	+	0.380124i
$449$	−0.412263	−	0.238020i	−0.0194559	−	0.0112329i	0.490241	−	0.871587i	$-0.336909\pi$
$449$	−0.412263	−	0.238020i	−0.0194559	−	0.0112329i	−0.509696	+	0.860354i	$0.670242\pi$
$450$	23.4734	−	4.39426i	1.10654	−	0.207147i
$451$			10.0937i			0.475295i
$452$	19.4165	−	3.42366i	0.913277	−	0.161035i
$453$	6.73645	−	8.11455i	0.316506	−	0.381255i
$454$	−42.1313	−	7.42888i	−1.97732	−	0.348655i
$455$	3.27238	+	8.87588i	0.153411	+	0.416108i
$456$	−1.53943	+	4.29983i	−0.0720904	+	0.201358i
$457$	2.00670	+	11.3806i	0.0938695	+	0.532360i	0.995088	+	0.0989952i	$0.0315628\pi$
$457$	2.00670	+	11.3806i	0.0938695	+	0.532360i	−0.901218	+	0.433365i	$0.857326\pi$
$458$	0.754166	−	1.30625i	0.0352399	−	0.0610373i
$459$	2.12432	+	1.18215i	0.0991548	+	0.0551782i
$460$	−4.42292	+	2.55357i	−0.206220	+	0.119061i
$461$	19.0273	+	6.92536i	0.886189	+	0.322546i	0.744705	−	0.667394i	$-0.232590\pi$
$461$	19.0273	+	6.92536i	0.886189	+	0.322546i	0.141484	+	0.989941i	$0.454813\pi$
$462$	19.8054	+	23.1567i	0.921431	+	1.07735i
$463$	−4.74389	−	3.98059i	−0.220467	−	0.184994i	0.525864	−	0.850569i	$-0.323742\pi$
$463$	−4.74389	−	3.98059i	−0.220467	−	0.184994i	−0.746331	+	0.665575i	$0.768186\pi$
$464$	−8.27904	−	22.7465i	−0.384345	−	1.05598i
$465$	10.2162	−	3.77942i	0.473766	−	0.175266i
$466$	2.86608	+	16.2543i	0.132769	+	0.752968i
$467$	1.90348	−	3.29692i	0.0880826	−	0.152563i	−0.818618	−	0.574338i	$-0.805259\pi$
$467$	1.90348	−	3.29692i	0.0880826	−	0.152563i	0.906701	+	0.421775i	$0.138593\pi$
$468$	0.202377	+	19.2239i	0.00935489	+	0.888624i
$469$	13.4644	−	23.5464i	0.621728	−	1.08727i
$470$	5.64173	−	0.994790i	0.260234	−	0.0458862i
$471$	−4.17759	−	7.14863i	−0.192493	−	0.329392i
$472$	2.31956	+	0.409001i	0.106766	+	0.0188258i
$473$	30.6315	+	5.40116i	1.40844	+	0.248346i
$474$	31.1313	−	0.163861i	1.42991	−	0.00752639i
$475$	−14.9557	+	2.63710i	−0.686217	+	0.120998i
$476$	−1.00861	−	1.73032i	−0.0462293	−	0.0793089i
$477$	10.6699	+	28.3821i	0.488541	+	1.29952i
$478$	21.3138	−	36.9166i	0.974872	−	1.68853i
$479$	−5.21941	−	29.6008i	−0.238481	−	1.35249i	−0.835157	−	0.550011i	$-0.814623\pi$
$479$	−5.21941	−	29.6008i	−0.238481	−	1.35249i	0.596676	−	0.802482i	$-0.296488\pi$
$480$	−8.81940	−	7.32160i	−0.402549	−	0.334184i
$481$	−13.3483	−	36.6742i	−0.608630	−	1.67220i
$482$	15.3207	+	12.8556i	0.697839	+	0.585556i
$483$	12.1770	−	10.4147i	0.554072	−	0.473884i
$484$	−1.85576	−	0.675440i	−0.0843526	−	0.0307018i
$485$	−3.99256	+	2.30511i	−0.181293	+	0.104670i
$486$	29.6405	−	0.780244i	1.34452	−	0.0353926i
$487$	−18.9944	+	32.8993i	−0.860720	+	1.49081i	0.0105150	+	0.999945i	$0.496653\pi$
$487$	−18.9944	+	32.8993i	−0.860720	+	1.49081i	−0.871235	+	0.490866i	$0.836680\pi$
$488$	0.00771102	+	0.0437314i	0.000349062	+	0.00197963i
$489$	13.5663	−	2.46579i	0.613487	−	0.111507i
$490$	−11.8541	−	1.98879i	−0.535514	−	0.0898445i
$491$	−31.0131	−	5.46844i	−1.39960	−	0.246787i	−0.577622	−	0.816305i	$-0.696019\pi$
$491$	−31.0131	−	5.46844i	−1.39960	−	0.246787i	−0.821979	+	0.569517i	$0.807130\pi$
$492$	−2.80750	−	7.58902i	−0.126572	−	0.342140i
$493$	2.41510	−	0.425848i	0.108771	−	0.0191792i
$494$		−	27.3376i		−	1.22998i
$495$	−6.00887	+	7.31614i	−0.270079	+	0.328836i
$496$	27.8620	+	16.0861i	1.25104	+	0.722288i
$497$	−4.34031	−	5.12916i	−0.194689	−	0.230074i
$498$	−18.4386	+	32.3284i	−0.826253	+	1.44867i
$499$	−14.4091	−	12.0907i	−0.645039	−	0.541252i	0.260522	−	0.965468i	$-0.416105\pi$
$499$	−14.4091	−	12.0907i	−0.645039	−	0.541252i	−0.905561	+	0.424216i	$0.860550\pi$
$500$	2.32964	−	13.2121i	0.104185	−	0.590861i
$501$	33.8077	+	19.2824i	1.51042	+	0.861472i
$502$	−11.5216	−	13.7309i	−0.514233	−	0.612839i
$503$	3.04934	−	5.28161i	0.135963	−	0.235495i	−0.790002	−	0.613105i	$-0.789920\pi$
$503$	3.04934	−	5.28161i	0.135963	−	0.235495i	0.925965	+	0.377609i	$0.123254\pi$
$504$	5.03667	+	2.81015i	0.224351	+	0.125174i
$505$	−6.05528	−	10.4881i	−0.269456	−	0.466712i
$506$	−7.95190	+	21.8477i	−0.353505	+	0.971247i
$507$	1.61486	+	4.36515i	0.0717182	+	0.193863i
$508$	−10.2331	−	8.58660i	−0.454021	−	0.380969i
$509$	7.51248	−	42.6054i	0.332985	−	1.88845i	−0.113303	−	0.993560i	$-0.536143\pi$
$509$	7.51248	−	42.6054i	0.332985	−	1.88845i	0.446288	−	0.894889i	$-0.352746\pi$
$510$	1.06122	−	0.900029i	0.0469915	−	0.0398539i
$511$	7.48757	−	20.8409i	0.331231	−	0.921947i
$512$		−	27.1429i		−	1.19956i
$513$	−18.8531	+	0.297725i	−0.832386	+	0.0131449i
$514$	19.4223	+	11.2135i	0.856683	+	0.494606i
$515$	−8.74771	−	10.4251i	−0.385470	−	0.459385i
$516$	−24.5327	+	4.45905i	−1.07999	+	0.196299i
$517$	7.49680	−	8.93434i	0.329709	−	0.392932i
$518$	48.8709	+	8.40807i	2.14726	+	0.369430i
$519$	−4.65429	−	12.5811i	−0.204301	−	0.552250i
$520$	−2.44145	−	0.888614i	−0.107065	−	0.0389683i
$521$	−20.0431			−0.878105			−0.439053	−	0.898461i	$-0.644686\pi$
$521$	−20.0431			−0.878105			−0.439053	+	0.898461i	$0.644686\pi$
$522$	22.7088	−	19.4660i	0.993939	−	0.852003i
$523$			26.6736i			1.16635i	0.812345	+	0.583177i	$0.198191\pi$
$523$			26.6736i			1.16635i	−0.812345	+	0.583177i	$0.801809\pi$
$524$	−5.82843	−	33.0547i	−0.254616	−	1.44400i
$525$	0.180613	+	19.1775i	0.00788258	+	0.836973i
$526$	−8.29992	+	3.02093i	−0.361894	+	0.131719i
$527$	−2.09510	+	2.49685i	−0.0912641	+	0.108764i
$528$	−27.9617	+	0.147178i	−1.21688	+	0.00640510i
$529$	−10.1243	−	3.68495i	−0.440188	−	0.160215i
$530$	17.3551			0.753856
$531$	1.78930	+	9.55811i	0.0776489	+	0.414787i
$532$	13.4848	+	7.71093i	0.584640	+	0.334311i
$533$	−7.35099	−	8.76057i	−0.318407	−	0.379462i
$534$	7.69930	+	6.39172i	0.333181	+	0.276597i
$535$	−8.59877	+	10.2476i	−0.371757	+	0.443043i
$536$	2.54791	+	7.00032i	0.110053	+	0.302368i
$537$	−0.579552	−	3.18857i	−0.0250095	−	0.137597i
$538$	17.6238	−	48.4209i	0.759815	−	2.08757i
$539$	−21.0897	+	12.4109i	−0.908399	+	0.534576i
$540$	2.48286	−	7.17200i	0.106845	−	0.308634i
$541$	−5.16825	−	8.95167i	−0.222200	−	0.384862i	0.733275	−	0.679932i	$-0.237991\pi$
$541$	−5.16825	−	8.95167i	−0.222200	−	0.384862i	−0.955476	+	0.295069i	$0.904657\pi$
$542$	−6.61497	+	5.55061i	−0.284137	+	0.238419i
$543$	6.50175	+	35.7712i	0.279017	+	1.53509i
$544$	3.37771	+	0.595582i	0.144818	+	0.0255354i
$545$	0.465050	−	2.63743i	0.0199206	−	0.112975i
$546$	−34.0539	−	5.67449i	−1.45737	−	0.242846i
$547$	2.39360	−	2.00847i	0.102343	−	0.0858758i	−0.590181	−	0.807271i	$-0.700943\pi$
$547$	2.39360	−	2.00847i	0.102343	−	0.0858758i	0.692523	+	0.721396i	$0.256499\pi$
$548$	17.0977	+	9.87138i	0.730379	+	0.421684i
$549$	−0.157797	+	0.0933325i	−0.00673460	+	0.00398333i
$550$	−13.9139	−	24.0996i	−0.593291	−	1.02761i
$551$	−14.5705	+	12.2261i	−0.620724	+	0.520849i
$552$	0.0231632	+	4.40067i	0.000985889	+	0.187305i
$553$	−4.23908	+	24.6391i	−0.180264	+	1.04776i
$554$	5.18618	+	14.2489i	0.220340	+	0.605379i
$555$	0.0810963	+	15.4072i	0.00344235	+	0.653998i
$556$	−9.95382	+	27.3479i	−0.422136	+	1.15981i
$557$	12.2609	−	7.07881i	0.519509	−	0.299939i	−0.217225	−	0.976122i	$-0.569700\pi$
$557$	12.2609	−	7.07881i	0.519509	−	0.299939i	0.736734	+	0.676183i	$0.236367\pi$
$558$	−6.49057	+	39.2197i	−0.274768	+	1.66030i
$559$	−30.5192	+	17.6203i	−1.29083	+	0.745259i
$560$	8.42000	−	7.12504i	0.355810	−	0.301088i
$561$	0.477232	−	2.79238i	0.0201487	−	0.117894i
$562$	10.9888	−	3.99961i	0.463537	−	0.168714i
$563$	−21.1089	+	7.68303i	−0.889636	+	0.323801i	−0.746092	−	0.665843i	$-0.768072\pi$
$563$	−21.1089	+	7.68303i	−0.889636	+	0.323801i	−0.143544	+	0.989644i	$0.545850\pi$
$564$	−3.15148	+	8.80251i	−0.132701	+	0.370652i
$565$	−10.8334	+	1.91022i	−0.455765	+	0.0803637i
$566$	−21.8231			−0.917292
$567$	−3.54249	+	23.5468i	−0.148770	+	0.988872i
$568$	1.84539			0.0774306
$569$	−18.4001	+	3.24444i	−0.771373	+	0.136014i	−0.545464	−	0.838135i	$-0.683646\pi$
$569$	−18.4001	+	3.24444i	−0.771373	+	0.136014i	−0.225909	+	0.974148i	$0.572535\pi$
$570$	−3.63776	+	10.1608i	−0.152369	+	0.425587i
$571$	34.2455	−	12.4643i	1.43313	−	0.521616i	0.495303	−	0.868720i	$-0.335057\pi$
$571$	34.2455	−	12.4643i	1.43313	−	0.521616i	0.937827	+	0.347104i	$0.112835\pi$
$572$	21.0511	−	7.66199i	0.880192	−	0.320364i
$573$	2.99096	−	17.5007i	0.124949	−	0.731104i
$574$	14.2994	−	2.58266i	0.596845	−	0.107798i
$575$	−12.6728	+	7.31663i	−0.528492	+	0.305125i
$576$	13.2197	−	4.96979i	0.550821	−	0.207075i
$577$	−25.0637	+	14.4705i	−1.04341	+	0.602416i	−0.920799	−	0.390039i	$-0.872462\pi$
$577$	−25.0637	+	14.4705i	−1.04341	+	0.602416i	−0.122616	+	0.992454i	$0.539128\pi$
$578$	10.9170	−	29.9943i	0.454089	−	1.24760i
$579$	−0.0919195	−	17.4634i	−0.00382004	−	0.725755i
$580$	−2.61850	−	7.19428i	−0.108728	−	0.298726i
$581$	−22.9751	−	19.1164i	−0.953170	−	0.793080i
$582$	−0.0885567	−	16.8245i	−0.00367079	−	0.697399i
$583$	27.0662	−	22.7113i	1.12097	−	0.940605i
$584$	3.04105	+	5.26725i	0.125839	+	0.217960i
$585$	−0.112916	−	10.7259i	−0.00466850	−	0.443462i
$586$	−1.80809	−	1.04390i	−0.0746916	−	0.0431232i
$587$	24.4251	−	20.4951i	1.00813	−	0.845924i	0.0200431	−	0.999799i	$-0.493620\pi$
$587$	24.4251	−	20.4951i	1.00813	−	0.845924i	0.988090	+	0.153875i	$0.0491752\pi$
$588$	12.4044	−	15.1972i	0.511549	−	0.626721i
$589$	4.38979	−	24.8957i	0.180878	−	1.02581i
$590$	5.48126	+	0.966494i	0.225660	+	0.0397899i
$591$	8.23411	+	45.3023i	0.338706	+	1.86349i
$592$	−34.8594	+	29.2505i	−1.43271	+	1.20219i
$593$	2.99491	+	5.18734i	0.122986	+	0.213018i	0.920944	−	0.389695i	$-0.127420\pi$
$593$	2.99491	+	5.18734i	0.122986	+	0.213018i	−0.797958	+	0.602713i	$0.794086\pi$
$594$	−12.3283	−	32.2767i	−0.505837	−	1.32433i
$595$	0.562749	+	0.965426i	0.0230705	+	0.0395786i
$596$	−6.23273	+	17.1243i	−0.255303	+	0.701438i
$597$	6.03460	+	33.2011i	0.246980	+	1.35883i
$598$	−9.00943	−	24.7532i	−0.368423	−	1.01223i
$599$	5.26383	−	6.27319i	0.215074	−	0.256316i	−0.647711	−	0.761886i	$-0.724274\pi$
$599$	5.26383	−	6.27319i	0.215074	−	0.256316i	0.862785	+	0.505570i	$0.168718\pi$
$600$	−4.05272	−	3.36445i	−0.165452	−	0.137353i
$601$	−11.1245	−	13.2576i	−0.453777	−	0.540791i	0.489847	−	0.871808i	$-0.337052\pi$
$601$	−11.1245	−	13.2576i	−0.453777	−	0.540791i	−0.943625	+	0.331018i	$0.892608\pi$
$602$	−0.186011	−	44.7764i	−0.00758123	−	1.82495i
$603$	−23.3510	+	20.0165i	−0.950927	+	0.815134i
$604$	9.85176			0.400862
$605$	1.03542	+	0.376860i	0.0420956	+	0.0153216i
$606$	44.1963	−	0.232629i	1.79535	−	0.00944992i
$607$	−12.6088	+	15.0266i	−0.511776	+	0.609911i	−0.958616	−	0.284703i	$-0.908105\pi$
$607$	−12.6088	+	15.0266i	−0.511776	+	0.609911i	0.446839	+	0.894614i	$0.352550\pi$
$608$	−24.9973	+	9.09826i	−1.01377	+	0.368983i
$609$	12.2054	+	20.6879i	0.494588	+	0.838318i
$610$	0.0182216	+	0.103340i	0.000737771	+	0.00418411i
$611$			13.2140i			0.534582i
$612$	0.417873	+	2.23220i	0.0168915	+	0.0902315i
$613$	27.8234			1.12378			0.561889	−	0.827213i	$-0.310075\pi$
$613$	27.8234			1.12378			0.561889	+	0.827213i	$0.310075\pi$
$614$	−12.2515	−	4.45920i	−0.494432	−	0.179959i
$615$	1.56644	+	4.23428i	0.0631649	+	0.170743i
$616$	1.13954	−	6.62345i	0.0459135	−	0.266866i
$617$	−18.1901	+	21.6782i	−0.732308	+	0.872730i	−0.995764	−	0.0919408i	$-0.970693\pi$
$617$	−18.1901	+	21.6782i	−0.732308	+	0.872730i	0.263457	+	0.964671i	$0.415137\pi$
$618$	48.8649	−	8.88164i	1.96563	−	0.357272i
$619$	−18.7035	−	22.2899i	−0.751755	−	0.895907i	0.245542	−	0.969386i	$-0.421034\pi$
$619$	−18.7035	−	22.2899i	−0.751755	−	0.895907i	−0.997297	+	0.0734791i	$0.976590\pi$
$620$	8.81223	+	5.08774i	0.353908	+	0.204329i
$621$	−16.9727	+	6.48285i	−0.681091	+	0.260148i
$622$		−	42.4655i		−	1.70271i
$623$	−6.13449	+	5.19103i	−0.245773	+	0.207974i
$624$	24.1614	−	20.4915i	0.967230	−	0.820317i
$625$	2.33381	−	13.2357i	0.0933525	−	0.529428i
$626$	1.47359	+	1.23649i	0.0588964	+	0.0494200i
$627$	7.62331	+	20.6067i	0.304446	+	0.822954i
$628$	2.64535	−	7.26804i	0.105561	−	0.290026i
$629$	−2.30512	−	3.99258i	−0.0919110	−	0.159194i
$630$	11.9020	+	6.64056i	0.474185	+	0.264566i
$631$	3.11061	−	5.38773i	0.123831	−	0.214482i	−0.797444	−	0.603393i	$-0.793815\pi$
$631$	3.11061	−	5.38773i	0.123831	−	0.214482i	0.921275	+	0.388911i	$0.127149\pi$
$632$	−4.41368	−	5.26002i	−0.175567	−	0.209233i
$633$	8.02464	+	4.57688i	0.318951	+	0.181915i
$634$	−8.20950	+	46.5584i	−0.326041	+	1.84907i
$635$	5.70954	+	4.79088i	0.226576	+	0.190120i
$636$	−14.0329	+	24.6039i	−0.556440	+	0.975606i
$637$	9.26569	−	26.1308i	0.367120	−	1.03534i
$638$	−30.1838	−	17.4266i	−1.19499	−	0.689926i
$639$	2.68099	+	7.13147i	0.106058	+	0.282116i
$640$			5.15209i			0.203654i
$641$	6.29675	−	1.11029i	0.248707	−	0.0438537i	−0.0479049	−	0.998852i	$-0.515254\pi$
$641$	6.29675	−	1.11029i	0.248707	−	0.0438537i	0.296612	+	0.954998i	$0.404143\pi$
$642$	−16.9386	−	45.7872i	−0.668514	−	1.80708i
$643$	2.20568	+	0.388920i	0.0869834	+	0.0153375i	0.216970	−	0.976178i	$-0.430382\pi$
$643$	2.20568	+	0.388920i	0.0869834	+	0.0153375i	−0.129987	+	0.991516i	$0.541494\pi$
$644$	14.7512	+	2.53790i	0.581279	+	0.100007i
$645$	13.6880	−	2.48792i	0.538964	−	0.0979616i
$646$	−0.560763	−	3.18024i	−0.0220629	−	0.125125i
$647$	−13.4891	+	23.3638i	−0.530311	+	0.918525i	0.469064	+	0.883164i	$0.344591\pi$
$647$	−13.4891	+	23.3638i	−0.530311	+	0.918525i	−0.999375	+	0.0353609i	$0.988742\pi$
$648$	−4.30826	−	4.92019i	−0.169244	−	0.193283i
$649$	9.81311	−	5.66560i	0.385198	−	0.222394i
$650$	29.6272	+	10.7834i	1.16208	+	0.422961i
$651$	−30.1009	−	10.6359i	−1.17975	−	0.416854i
$652$	9.86695	+	8.27936i	0.386420	+	0.324245i
$653$	−7.80301	−	21.4386i	−0.305355	−	0.838957i	−0.993546	−	0.113427i	$-0.963817\pi$
$653$	−7.80301	−	21.4386i	−0.305355	−	0.838957i	0.688191	−	0.725529i	$-0.258405\pi$
$654$	7.52003	+	6.24290i	0.294056	+	0.244117i
$655$	3.25196	+	18.4428i	0.127065	+	0.720620i
$656$	−6.66715	+	11.5478i	−0.260308	+	0.450867i
$657$	−15.9372	+	19.4044i	−0.621768	+	0.757037i
$658$	−14.5751	−	8.33441i	−0.568197	−	0.324909i
$659$	21.2918	−	3.75431i	0.829409	−	0.146247i	0.257203	−	0.966357i	$-0.417199\pi$
$659$	21.2918	−	3.75431i	0.829409	−	0.146247i	0.572206	+	0.820110i	$0.306088\pi$
$660$	−8.84378	+	0.0465496i	−0.344244	+	0.00181194i
$661$	28.7597	+	5.07112i	1.11862	+	0.197244i	0.702237	−	0.711944i	$-0.252185\pi$
$661$	28.7597	+	5.07112i	1.11862	+	0.197244i	0.416387	+	0.909187i	$0.363296\pi$
$662$	−49.7239	−	8.76767i	−1.93258	−	0.340765i
$663$	1.61942	+	2.77112i	0.0628929	+	0.107621i
$664$	8.08394	−	1.42542i	0.313718	−	0.0553169i
$665$	−7.52381	−	4.30230i	−0.291761	−	0.166836i
$666$	−48.9886	−	27.6001i	−1.89827	−	1.06948i
$667$	−9.16379	+	15.8721i	−0.354823	+	0.614572i
$668$	6.31328	+	35.8044i	0.244268	+	1.38531i
$669$	13.7656	−	5.09248i	0.532208	−	0.196887i
$670$	6.02085	+	16.5422i	0.232606	+	0.639079i
$671$	0.163651	+	0.137319i	0.00631766	+	0.00530115i
$672$	6.14483	+	33.0271i	0.237042	+	1.27405i
$673$	22.4647	+	8.17648i	0.865950	+	0.315180i	0.736526	−	0.676409i	$-0.236465\pi$
$673$	22.4647	+	8.17648i	0.865950	+	0.315180i	0.129424	+	0.991589i	$0.458687\pi$
$674$	40.8387	−	23.5782i	1.57305	−	0.908199i
$675$	7.11404	−	20.5496i	0.273819	−	0.790954i
$676$	−2.17387	+	3.76525i	−0.0836104	+	0.144817i
$677$	−5.37818	−	30.5012i	−0.206700	−	1.17225i	−0.894742	−	0.446584i	$-0.852641\pi$
$677$	−5.37818	−	30.5012i	−0.206700	−	1.17225i	0.688042	−	0.725671i	$-0.258471\pi$
$678$	13.5320	−	37.7966i	0.519692	−	1.45157i
$679$	13.3159	+	2.29096i	0.511017	+	0.0879188i
$680$	−0.302246	−	0.0532942i	−0.0115906	−	0.00204374i
$681$	−24.8834	+	29.9739i	−0.953534	+	1.14860i
$682$	45.6192	−	8.04390i	1.74685	−	0.308017i
$683$			3.83140i			0.146604i	0.997310	+	0.0733022i	$0.0233538\pi$
$683$			3.83140i			0.146604i	−0.997310	+	0.0733022i	$0.976646\pi$
$684$	−11.4632	−	13.3729i	−0.438308	−	0.511326i
$685$	−9.53964	−	5.50771i	−0.364491	−	0.210439i
$686$	22.9782	+	26.7014i	0.877313	+	1.01947i
$687$	−0.692995	−	1.18584i	−0.0264394	−	0.0452428i
$688$	31.4767	+	26.4121i	1.20004	+	1.00695i
$689$	−6.95137	+	39.4232i	−0.264826	+	1.50190i
$690$	0.0547359	+	10.3991i	0.00208376	+	0.395885i
$691$	−5.31576	−	6.33507i	−0.202221	−	0.240998i	0.655397	−	0.755284i	$-0.272501\pi$
$691$	−5.31576	−	6.33507i	−0.202221	−	0.240998i	−0.857618	+	0.514287i	$0.828057\pi$
$692$	6.26547	−	10.8521i	0.238177	−	0.412535i
$693$	27.2518	−	5.21885i	1.03521	−	0.198248i
$694$	−17.8241	−	30.8723i	−0.676594	−	1.17190i
$695$	5.55371	−	15.2587i	0.210664	−	0.578795i
$696$	−6.50275	−	1.11135i	−0.246486	−	0.0421257i
$697$	−1.03486	−	0.868348i	−0.0391980	−	0.0328910i
$698$	−8.02953	+	45.5377i	−0.303922	+	1.72363i
$699$	14.1500	+	5.06600i	0.535203	+	0.191614i
$700$	−13.6759	+	11.5726i	−0.516900	+	0.437402i
$701$			19.8898i			0.751226i	0.926777	+	0.375613i	$0.122568\pi$
$701$			19.8898i			0.751226i	−0.926777	+	0.375613i	$0.877432\pi$
$702$	34.2062	+	19.0352i	1.29103	+	0.718439i
$703$	30.9663	+	17.8784i	1.16792	+	0.674296i
$704$	−10.5784	−	12.6068i	−0.398688	−	0.475138i
$705$	1.75836	−	4.91134i	0.0662237	−	0.184972i
$706$	27.9732	−	33.3371i	1.05278	−	1.25466i
$707$	−6.01811	+	34.9795i	−0.226334	+	1.31554i
$708$	−5.80219	+	6.98916i	−0.218060	+	0.262669i
$709$	−13.1341	−	4.78042i	−0.493262	−	0.179533i	0.0833991	−	0.996516i	$-0.473422\pi$
$709$	−13.1341	−	4.78042i	−0.493262	−	0.179533i	−0.576661	+	0.816984i	$0.695645\pi$
$710$	4.36075			0.163656
$711$	13.9151	−	24.6984i	0.521856	−	0.926264i
$712$		−	2.20709i		−	0.0827141i
$713$	−4.22989	−	23.9889i	−0.158410	−	0.898390i
$714$	−4.07796	+	0.0384061i	−0.152614	+	0.00143731i
$715$	−11.7454	+	4.27499i	−0.439254	+	0.159876i
$716$	1.94595	−	2.31910i	0.0727237	−	0.0866687i
$717$	−19.5851	−	33.5137i	−0.731417	−	1.25159i
$718$	14.9292	+	5.43377i	0.557151	+	0.202786i
$719$	−31.4331			−1.17226			−0.586128	−	0.810218i	$-0.699348\pi$
$719$	−31.4331			−1.17226			−0.586128	+	0.810218i	$0.699348\pi$
$720$	−11.7070	+	4.40110i	−0.436294	+	0.164019i
$721$	0.165690	+	39.8847i	0.00617061	+	1.48538i
$722$	−7.13076	−	8.49811i	−0.265380	−	0.316267i
$723$	17.0805	−	6.31879i	0.635229	−	0.234998i
$724$	−21.8308	+	26.0170i	−0.811337	+	0.966914i
$725$	−7.50268	−	20.6134i	−0.278643	−	0.765564i
$726$	−3.06678	+	2.60096i	−0.113819	+	0.0965308i
$727$	−9.57818	+	26.3158i	−0.355235	+	0.976000i	0.625426	+	0.780284i	$0.284925\pi$
$727$	−9.57818	+	26.3158i	−0.355235	+	0.976000i	−0.980661	+	0.195716i	$0.937297\pi$
$728$	3.83464	+	6.57853i	0.142121	+	0.243817i
$729$	12.7549	−	23.7973i	0.472405	−	0.881381i
$730$	7.18617	+	12.4468i	0.265972	+	0.460677i
$731$	−3.18893	+	2.67583i	−0.117947	+	0.0989692i
$732$	−0.161236	−	0.0577258i	−0.00595945	−	0.00213361i
$733$	−24.5292	−	4.32516i	−0.906006	−	0.159753i	−0.298817	−	0.954311i	$-0.596592\pi$
$733$	−24.5292	−	4.32516i	−0.906006	−	0.159753i	−0.607189	+	0.794557i	$0.707703\pi$
$734$	3.22409	−	18.2847i	0.119003	−	0.674900i
$735$	−6.92101	+	8.47923i	−0.255285	+	0.312761i
$736$	−19.6357	+	16.4763i	−0.723780	+	0.607324i
$737$	31.0373	+	17.9194i	1.14327	+	0.660070i
$738$	−16.2552	−	2.69012i	−0.598363	−	0.0990246i
$739$	−23.2659	−	40.2978i	−0.855851	−	1.48238i	−0.875853	−	0.482578i	$-0.839701\pi$
$739$	−23.2659	−	40.2978i	−0.855851	−	1.48238i	0.0200017	−	0.999800i	$-0.493633\pi$
$740$	−11.0254	+	9.25140i	−0.405301	+	0.340088i
$741$	−21.6237	−	12.3332i	−0.794368	−	0.453071i
$742$	−39.0995	−	32.5326i	−1.43539	−	1.19431i
$743$	−11.9890	−	32.9395i	−0.439834	−	1.20843i	−0.939600	−	0.342273i	$-0.888803\pi$
$743$	−11.9890	−	32.9395i	−0.439834	−	1.20843i	0.499767	−	0.866160i	$-0.333419\pi$
$744$	7.57016	−	4.42392i	0.277535	−	0.162189i
$745$	3.47754	−	9.55446i	0.127407	−	0.350048i
$746$	−17.4580	+	10.0794i	−0.639185	+	0.369033i
$747$	17.2529	+	29.1694i	0.631251	+	1.06725i
$748$	2.29176	−	1.32315i	0.0837949	−	0.0483790i
$749$	38.5817	−	6.96838i	1.40975	−	0.254619i
$750$	−21.0185	−	17.4489i	−0.767488	−	0.637145i
$751$	−3.85948	+	1.40474i	−0.140834	+	0.0512595i	−0.411476	−	0.911421i	$-0.634986\pi$
$751$	−3.85948	+	1.40474i	−0.140834	+	0.0512595i	0.270641	+	0.962680i	$0.412764\pi$
$752$	14.4781	−	5.26961i	0.527963	−	0.192163i
$753$	−16.0589	+	2.91885i	−0.585217	+	0.106369i
$754$	38.8884	−	6.85708i	1.41623	−	0.249720i
$755$	−5.49677			−0.200048
$756$	−19.0378	+	11.5037i	−0.692398	+	0.418386i
$757$	−15.6872			−0.570161			−0.285081	−	0.958504i	$-0.592020\pi$
$757$	−15.6872			−0.570161			−0.285081	+	0.958504i	$0.592020\pi$
$758$	−11.7349	+	2.06918i	−0.426231	+	0.0751560i
$759$	13.6938	+	16.1463i	0.497054	+	0.586073i
$760$	2.23682	−	0.814136i	0.0811380	−	0.0295318i
$761$	−26.4207	+	9.61636i	−0.957751	+	0.348593i	−0.773152	−	0.634221i	$-0.781321\pi$
$761$	−26.4207	+	9.61636i	−0.957751	+	0.348593i	−0.184599	+	0.982814i	$0.559099\pi$
$762$	−25.5107	+	9.43749i	−0.924155	+	0.341884i
$763$	−5.99166	+	5.07016i	−0.216912	+	0.183552i
$764$	14.3632	−	8.29258i	0.519641	−	0.300015i
$765$	−0.233151	−	1.24545i	−0.00842960	−	0.0450295i
$766$	13.7794	−	7.95553i	0.497869	−	0.287445i
$767$	−4.39091	+	12.0639i	−0.158546	+	0.435603i
$768$	−30.4983	−	17.3948i	−1.10051	−	0.627681i
$769$	9.49574	+	26.0893i	0.342425	+	0.940806i	0.984689	+	0.174322i	$0.0557733\pi$
$769$	9.49574	+	26.0893i	0.342425	+	0.940806i	−0.642263	+	0.766484i	$0.722004\pi$
$770$	2.69281	−	15.6516i	0.0970420	−	0.564045i
$771$	17.6320	−	10.3040i	0.635001	−	0.371088i
$772$	12.4969	−	10.4861i	0.449772	−	0.377403i
$773$	−6.54808	−	11.3416i	−0.235518	−	0.407929i	0.723905	−	0.689900i	$-0.242345\pi$
$773$	−6.54808	−	11.3416i	−0.235518	−	0.407929i	−0.959423	+	0.281970i	$0.909012\pi$
$774$	−16.8619	+	47.8903i	−0.606088	+	1.72138i
$775$	25.2493	+	14.5777i	0.906981	+	0.523646i
$776$	−2.84272	+	2.38532i	−0.102048	+	0.0856280i
$777$	28.6984	−	34.8631i	1.02955	−	1.25071i
$778$	−6.41839	+	36.4005i	−0.230110	+	1.30502i
$779$	10.3184	+	1.81942i	0.369696	+	0.0651874i
$780$	7.64180	−	6.48108i	0.273620	−	0.232060i
$781$	6.80084	−	5.70659i	0.243353	−	0.204198i
$782$	−1.55584	−	2.69479i	−0.0556366	−	0.0963654i
$783$	−5.15244	−	26.7444i	−0.184133	−	0.955766i
$784$	−32.3256	+	0.268580i	−1.15449	+	0.00959214i
$785$	−1.47597	+	4.05519i	−0.0526796	+	0.144736i
$786$	−64.3449	−	23.0368i	−2.29511	−	0.821696i
$787$	16.1148	+	44.2749i	0.574429	+	1.57823i	0.797430	+	0.603412i	$0.206193\pi$
$787$	16.1148	+	44.2749i	0.574429	+	1.57823i	−0.223001	+	0.974818i	$0.571585\pi$
$788$	−27.6476	+	32.9491i	−0.984904	+	1.17376i
$789$	−1.35494	+	7.92802i	−0.0482370	+	0.282245i
$790$	−10.4298	−	12.4297i	−0.371076	−	0.442231i
$791$	27.9875	+	16.0040i	0.995122	+	0.569035i
$792$	−3.74063	+	6.63940i	−0.132918	+	0.235921i
$793$	−0.242042			−0.00859515
$794$	−50.7052	−	18.4552i	−1.79946	−	0.654949i
$795$	7.82962	−	13.7277i	0.277688	−	0.486870i
$796$	−20.2623	+	24.1477i	−0.718178	+	0.855892i
$797$	−35.7462	+	13.0105i	−1.26619	+	0.460857i	−0.885843	−	0.463985i	$-0.846419\pi$
$797$	−35.7462	+	13.0105i	−1.26619	+	0.460857i	−0.380352	+	0.924842i	$0.624197\pi$
$798$	27.2422	−	16.0722i	0.964363	−	0.568951i
$799$	0.271052	+	1.53721i	0.00958914	+	0.0543827i
$800$		−	30.6797i		−	1.08469i
$801$	8.52927	−	3.20648i	0.301367	−	0.113295i
$802$	−37.1361			−1.31132
$803$	27.4955	+	10.0075i	0.970294	+	0.353158i
$804$	−28.3197	−	4.83998i	−0.998760	−	0.170693i
$805$	−8.23040	−	1.41601i	−0.290084	−	0.0499079i
$806$	−33.7357	+	40.2047i	−1.18829	+	1.41615i
$807$	−30.3496	−	35.7850i	−1.06836	−	1.25969i
$808$	−6.26600	−	7.46752i	−0.220437	−	0.262707i
$809$	−7.26934	−	4.19695i	−0.255576	−	0.147557i	0.366739	−	0.930324i	$-0.380474\pi$
$809$	−7.26934	−	4.19695i	−0.255576	−	0.147557i	−0.622315	+	0.782767i	$0.713808\pi$
$810$	−10.1807	−	11.6267i	−0.357712	−	0.408521i
$811$		−	36.2880i		−	1.27425i	−0.770762	−	0.637123i	$-0.780124\pi$
$811$		−	36.2880i		−	1.27425i	0.770762	−	0.637123i	$-0.219876\pi$
$812$	−7.58661	+	21.1166i	−0.266238	+	0.741046i
$813$	1.40618	+	7.73648i	0.0493168	+	0.271330i
$814$	−11.3776	+	64.5257i	−0.398785	+	2.26162i
$815$	−5.50524	−	4.61945i	−0.192840	−	0.161812i
$816$	2.39042	−	2.87943i	0.0836813	−	0.100800i
$817$	11.0428	−	30.3398i	0.386338	−	1.06145i
$818$	33.2557	+	57.6006i	1.16276	+	2.01396i
$819$	−19.8516	+	24.3763i	−0.693673	+	0.851776i
$820$	−2.10869	+	3.65237i	−0.0736388	+	0.127546i
$821$	32.8795	+	39.1842i	1.14750	+	1.36754i	0.919125	+	0.393967i	$0.128897\pi$
$821$	32.8795	+	39.1842i	1.14750	+	1.36754i	0.228377	+	0.973573i	$0.426658\pi$
$822$	34.7082	−	20.2831i	1.21059	−	0.707455i
$823$	0.738462	−	4.18802i	0.0257412	−	0.145985i	−0.969228	−	0.246163i	$-0.920830\pi$
$823$	0.738462	−	4.18802i	0.0257412	−	0.145985i	0.994970	+	0.100178i	$0.0319412\pi$
$824$	−8.39149	−	7.04130i	−0.292331	−	0.245295i
$825$	−25.3397	+	0.133377i	−0.882214	+	0.00464357i
$826$	−10.5371	−	12.4522i	−0.366632	−	0.433267i
$827$	15.9647	+	9.21722i	0.555147	+	0.320514i	0.751195	−	0.660080i	$-0.229478\pi$
$827$	15.9647	+	9.21722i	0.555147	+	0.320514i	−0.196048	+	0.980594i	$0.562811\pi$
$828$	−14.7867	−	8.33082i	−0.513874	−	0.289516i
$829$			2.47231i			0.0858670i	0.999078	+	0.0429335i	$0.0136704\pi$
$829$			2.47231i			0.0858670i	−0.999078	+	0.0429335i	$0.986330\pi$
$830$	19.1028	−	3.36834i	0.663069	−	0.116917i
$831$	13.6104	+	2.32609i	0.472141	+	0.0806912i
$832$	18.3624	+	3.23779i	0.636602	+	0.112250i
$833$	0.541891	−	3.22991i	0.0187754	−	0.111910i
$834$	38.3298	+	45.1944i	1.32725	+	1.56496i
$835$	−3.52248	−	19.9770i	−0.121901	−	0.691332i
$836$	−10.2623	+	17.7748i	−0.354928	+	0.614754i
$837$	28.0942	+	22.8277i	0.971077	+	0.789040i
$838$	66.8167	−	38.5766i	2.30814	−	1.33261i
$839$	11.0811	+	4.03321i	0.382563	+	0.139242i	0.526141	−	0.850397i	$-0.323638\pi$
$839$	11.0811	+	4.03321i	0.382563	+	0.139242i	−0.143578	+	0.989639i	$0.545861\pi$
$840$	−0.549855	−	2.95535i	−0.0189718	−	0.101969i
$841$	1.16867	+	0.980630i	0.0402989	+	0.0338148i
$842$	10.2974	+	28.2918i	0.354871	+	0.975001i
$843$	1.79389	−	10.4965i	0.0617850	−	0.361517i
$844$	1.49853	+	8.49858i	0.0515815	+	0.292533i
$845$	1.21291	−	2.10082i	0.0417252	−	0.0722702i
$846$	12.3901	+	14.4542i	0.425981	+	0.496945i
$847$	−1.62627	−	2.78995i	−0.0558793	−	0.0958638i
$848$	45.9667	−	8.10517i	1.57850	−	0.278333i
$849$	−9.84533	+	17.2618i	−0.337891	+	0.592423i
$850$	3.66780	+	0.646731i	0.125804	+	0.0221827i
$851$	33.9308	+	5.98292i	1.16313	+	0.205092i
$852$	−3.52600	+	6.18213i	−0.120799	+	0.211796i
$853$	14.3072	−	2.52275i	0.489869	−	0.0863772i	0.0767431	−	0.997051i	$-0.475548\pi$
$853$	14.3072	−	2.52275i	0.489869	−	0.0863772i	0.413126	+	0.910674i	$0.364437\pi$
$854$	0.152662	−	0.266973i	0.00522397	−	0.00913562i
$855$	6.39589	+	7.46138i	0.218735	+	0.255174i
$856$	−5.38390	+	9.32519i	−0.184018	+	0.318729i
$857$	2.88185	+	16.3438i	0.0984422	+	0.558293i	0.993638	+	0.112621i	$0.0359244\pi$
$857$	2.88185	+	16.3438i	0.0984422	+	0.558293i	−0.895196	+	0.445673i	$0.852964\pi$
$858$	7.68447	−	44.9634i	0.262343	−	1.53503i
$859$	7.49548	+	20.5937i	0.255742	+	0.702647i	0.999418	+	0.0341061i	$0.0108584\pi$
$859$	7.49548	+	20.5937i	0.255742	+	0.702647i	−0.743676	+	0.668540i	$0.766919\pi$
$860$	9.95548	+	8.35364i	0.339479	+	0.284857i
$861$	4.40821	−	12.4758i	0.150232	−	0.425174i
$862$	−14.2039	−	5.16980i	−0.483787	−	0.176084i
$863$	6.94716	−	4.01095i	0.236484	−	0.136534i	−0.377076	−	0.926182i	$-0.623070\pi$
$863$	6.94716	−	4.01095i	0.236484	−	0.136534i	0.613560	+	0.789648i	$0.289737\pi$
$864$	6.02144	−	37.6130i	0.204854	−	1.27962i
$865$	−3.49580	+	6.05491i	−0.118861	+	0.205873i
$866$	−5.44185	−	30.8622i	−0.184921	−	1.04874i
$867$	−18.8000	−	22.1670i	−0.638482	−	0.752830i
$868$	−10.3161	−	27.9810i	−0.350151	−	0.949738i
$869$	−32.5317	−	5.73622i	−1.10356	−	0.194588i
$870$	−15.3664	−	2.62619i	−0.520969	−	0.0890361i
$871$	−39.9882	+	7.05099i	−1.35495	+	0.238914i
$872$		−	2.15570i		−	0.0730012i
$873$	−13.3480	−	7.52022i	−0.451760	−	0.254521i
$874$	20.9007	+	12.0670i	0.706976	+	0.408173i
$875$	16.7467	−	14.1711i	0.566142	−	0.479072i
$876$	−23.4561	+	0.123462i	−0.792508	+	0.00417140i
$877$	27.6050	+	23.1634i	0.932155	+	0.782171i	0.976203	−	0.216858i	$-0.0695810\pi$
$877$	27.6050	+	23.1634i	0.932155	+	0.782171i	−0.0440478	+	0.999029i	$0.514025\pi$
$878$	2.01529	−	11.4293i	0.0680128	−	0.385720i
$879$	−1.64142	+	0.959231i	−0.0553639	+	0.0323541i
$880$	9.36791	+	11.1642i	0.315792	+	0.376346i
$881$	−21.1819	+	36.6881i	−0.713636	+	1.23605i	0.249847	+	0.968285i	$0.419620\pi$
$881$	−21.1819	+	36.6881i	−0.713636	+	1.23605i	−0.963483	+	0.267769i	$0.913714\pi$
$882$	−14.3662	−	37.2712i	−0.483735	−	1.25499i
$883$	−3.68137	−	6.37633i	−0.123888	−	0.214580i	0.797410	−	0.603438i	$-0.206203\pi$
$883$	−3.68137	−	6.37633i	−0.123888	−	0.214580i	−0.921298	+	0.388858i	$0.872870\pi$
$884$	−1.02545	+	2.81741i	−0.0344897	+	0.0947598i
$885$	3.23732	−	3.89959i	0.108821	−	0.131083i
$886$	29.0065	+	24.3393i	0.974493	+	0.817696i
$887$	0.0845808	−	0.479682i	0.00283995	−	0.0161061i	−0.983355	−	0.181695i	$-0.941842\pi$
$887$	0.0845808	−	0.479682i	0.00283995	−	0.0161061i	0.986195	+	0.165589i	$0.0529526\pi$
$888$	2.21782	+	12.2019i	0.0744250	+	0.409471i
$889$	−3.88249	−	21.4961i	−0.130215	−	0.720957i
$890$		−	5.21548i		−	0.174823i
$891$	−31.0923	−	4.80984i	−1.04163	−	0.161136i
$892$	11.8738	+	6.85534i	0.397564	+	0.229534i
$893$	−7.78191	−	9.27412i	−0.260412	−	0.310346i
$894$	24.0008	+	28.2992i	0.802707	+	0.946466i
$895$	−1.08574	+	1.29393i	−0.0362923	+	0.0432515i
$896$	9.65773	−	11.6072i	0.322642	−	0.387770i
$897$	−23.6440	−	4.04088i	−0.789452	−	0.134921i
$898$	−0.850867	−	0.309690i	−0.0283938	−	0.0103345i
$899$	36.5159			1.21787
$900$	19.0147	−	7.14833i	0.633822	−	0.238278i
$901$			4.72877i			0.157538i
$902$	3.33392	+	18.9076i	0.111007	+	0.629554i
$903$	−35.5015	−	20.0534i	−1.18142	−	0.667336i
$904$	−8.32066	+	3.02847i	−0.276741	+	0.100726i
$905$	12.1805	−	14.5161i	0.404892	−	0.482532i
$906$	9.93852	−	17.4252i	0.330185	−	0.578913i
$907$	2.19110	+	0.797495i	0.0727542	+	0.0264804i	0.378141	−	0.925748i	$-0.376563\pi$
$907$	2.19110	+	0.797495i	0.0727542	+	0.0264804i	−0.305387	+	0.952228i	$0.598786\pi$
$908$	−36.3909			−1.20767
$909$	19.7549	−	35.0637i	0.655227	−	1.16299i
$910$	9.06148	+	15.5455i	0.300385	+	0.515327i
$911$	−17.0700	−	20.3432i	−0.565553	−	0.674000i	0.405159	−	0.914246i	$-0.367216\pi$
$911$	−17.0700	−	20.3432i	−0.565553	−	0.674000i	−0.970712	+	0.240246i	$0.922772\pi$
$912$	−4.88971	+	28.6107i	−0.161914	+	0.947396i
$913$	25.3841	−	30.2515i	0.840090	−	1.00118i
$914$	7.51791	+	20.6553i	0.248670	+	0.683216i
$915$	0.0899612	+	0.0322080i	0.00297403	+	0.00106476i
$916$	0.438822	−	1.20565i	0.0144991	−	0.0398359i
$917$	27.2451	−	47.6460i	0.899713	−	1.57341i
$918$	4.36974	+	1.51275i	0.144223	+	0.0499283i
$919$	−4.06315	−	7.03758i	−0.134031	−	0.232148i	0.791196	−	0.611563i	$-0.209459\pi$
$919$	−4.06315	−	7.03758i	−0.134031	−	0.232148i	−0.925227	+	0.379414i	$0.876125\pi$
$920$	1.75705	−	1.47434i	0.0579282	−	0.0486075i
$921$	−9.05437	+	7.67910i	−0.298352	+	0.253035i
$922$	37.9293	+	6.68796i	1.24914	+	0.220256i
$923$	−1.74665	+	9.90573i	−0.0574916	+	0.326051i
$924$	20.0115	+	16.4730i	0.658332	+	0.541923i
$925$	−31.5905	+	26.5076i	−1.03869	+	0.871565i
$926$	−10.2010	−	5.88956i	−0.335226	−	0.193543i
$927$	15.0198	−	42.6585i	0.493314	−	1.40109i
$928$	−19.2126	−	33.2771i	−0.630683	−	1.09238i
$929$	15.6525	−	13.1340i	0.513541	−	0.430912i	−0.348832	−	0.937185i	$-0.613422\pi$
$929$	15.6525	−	13.1340i	0.513541	−	0.430912i	0.862373	+	0.506273i	$0.168977\pi$
$930$	17.8887	−	10.4540i	0.586594	−	0.342800i
$931$	8.88573	+	23.7963i	0.291218	+	0.779892i
$932$	4.80185	+	13.1930i	0.157290	+	0.432150i
$933$	−33.5897	−	19.1580i	−1.09968	−	0.627205i
$934$	2.47664	−	6.80451i	0.0810381	−	0.222650i
$935$	−1.27868	+	0.738247i	−0.0418173	+	0.0241433i
$936$	−1.58872	−	8.48668i	−0.0519290	−	0.277396i
$937$	29.2827	−	16.9064i	0.956625	−	0.552308i	0.0614921	−	0.998108i	$-0.480414\pi$
$937$	29.2827	−	16.9064i	0.956625	−	0.552308i	0.895133	+	0.445800i	$0.147081\pi$
$938$	17.4443	−	48.5543i	0.569575	−	1.58536i
$939$	1.64285	−	0.607759i	0.0536123	−	0.0198335i
$940$	4.57916	−	1.66668i	0.149356	−	0.0543611i
$941$	−42.3099	+	15.3995i	−1.37926	+	0.502011i	−0.921955	−	0.387297i	$-0.873409\pi$
$941$	−42.3099	+	15.3995i	−1.37926	+	0.502011i	−0.457309	+	0.889308i	$0.651186\pi$
$942$	−10.1866	−	12.0110i	−0.331898	−	0.391339i
$943$	9.94256	−	1.75314i	0.323774	−	0.0570902i
$944$	14.9691			0.487201
$945$	10.6221	−	6.41847i	0.345537	−	0.208793i
$946$	59.1629			1.92355
$947$	−1.23405	+	0.217597i	−0.0401014	+	0.00707095i	−0.193663	−	0.981068i	$-0.562037\pi$
$947$	−1.23405	+	0.217597i	−0.0401014	+	0.00707095i	0.153562	+	0.988139i	$0.450926\pi$
$948$	26.0546	−	4.73567i	0.846215	−	0.153807i
$949$	−31.1521	+	11.3384i	−1.01124	+	0.368061i
$950$	−27.1441	+	9.87964i	−0.880670	+	0.320538i
$951$	33.1235	+	27.4981i	1.07410	+	0.891688i
$952$	0.581034	+	0.686636i	0.0188314	+	0.0222540i
$953$	41.3947	−	23.8992i	1.34091	−	0.774172i	0.353965	−	0.935259i	$-0.384833\pi$
$953$	41.3947	−	23.8992i	1.34091	−	0.774172i	0.986940	+	0.161086i	$0.0514997\pi$
$954$	29.3613	+	49.6411i	0.950608	+	1.60719i
$955$	−8.01390	+	4.62682i	−0.259324	+	0.149721i
$956$	12.4017	−	34.0735i	0.401101	−	1.10202i
$957$	−27.4014	+	16.0131i	−0.885763	+	0.517631i
$958$	−19.5540	−	53.7242i	−0.631762	−	1.73575i
$959$	11.1676	+	30.2907i	0.360622	+	0.978139i
$960$	−6.39403	−	3.64686i	−0.206367	−	0.117702i
$961$	−13.4309	+	11.2699i	−0.433255	+	0.363544i
$962$	−37.1174	−	64.2892i	−1.19671	−	2.07277i
$963$	−43.8589	−	7.25831i	−1.41333	−	0.233896i
$964$	14.7331	+	8.50617i	0.474522	+	0.273965i
$965$	−6.97259	+	5.85070i	−0.224456	+	0.188341i
$966$	19.3700	−	23.5308i	0.623219	−	0.757091i
$967$	−3.01993	+	17.1269i	−0.0971143	+	0.550763i	0.896965	+	0.442102i	$0.145767\pi$
$967$	−3.01993	+	17.1269i	−0.0971143	+	0.550763i	−0.994079	+	0.108660i	$0.965344\pi$
$968$	0.873451	+	0.154013i	0.0280738	+	0.00495017i
$969$	−2.76852	−	0.991188i	−0.0889377	−	0.0318415i
$970$	−6.71750	+	5.63665i	−0.215686	+	0.180982i
$971$	13.6117	+	23.5762i	0.436821	+	0.756596i	0.997442	−	0.0714765i	$-0.0227711\pi$
$971$	13.6117	+	23.5762i	0.436821	+	0.756596i	−0.560622	+	0.828072i	$0.689438\pi$
$972$	24.7147	−	5.03181i	0.792725	−	0.161395i
$973$	−41.1149	+	23.9660i	−1.31808	+	0.768314i
$974$	−24.7139	+	67.9008i	−0.791884	+	2.17568i
$975$	21.8957	−	18.5699i	0.701224	−	0.594714i
$976$	0.0965236	+	0.265196i	0.00308965	+	0.00848873i
$977$	−14.5399	+	17.3280i	−0.465173	+	0.554372i	−0.946724	−	0.322046i	$-0.895629\pi$
$977$	−14.5399	+	17.3280i	−0.465173	+	0.554372i	0.481550	+	0.876418i	$0.340074\pi$
$978$	24.5979	−	9.09980i	0.786553	−	0.290979i
$979$	−6.82510	−	8.13384i	−0.218131	−	0.259959i
$980$	−10.2240	+	0.0849468i	−0.326593	+	0.00271353i
$981$	8.33067	−	3.13182i	0.265978	−	0.0999912i
$982$	−59.8999			−1.91148
$983$	−20.7495	−	7.55220i	−0.661806	−	0.240878i	−0.0107901	−	0.999942i	$-0.503435\pi$
$983$	−20.7495	−	7.55220i	−0.661806	−	0.240878i	−0.651016	+	0.759064i	$0.725657\pi$
$984$	1.83356	+	3.13757i	0.0584519	+	0.100022i
$985$	15.4259	−	18.3839i	0.491510	−	0.585759i
$986$	4.38332	−	1.59540i	0.139593	−	0.0508078i
$987$	−13.1679	+	7.76873i	−0.419138	+	0.247282i
$988$	−4.03804	−	22.9008i	−0.128467	−	0.728573i
$989$		−	31.1108i		−	0.989267i
$990$	−8.83933	+	15.6893i	−0.280932	+	0.498639i
$991$	10.8816			0.345665			0.172832	−	0.984951i	$-0.444708\pi$
$991$	10.8816			0.345665			0.172832	+	0.984951i	$0.444708\pi$
$992$	47.9904	+	17.4671i	1.52370	+	0.554580i
$993$	−29.3677	+	35.3756i	−0.931957	+	1.12261i
$994$	−9.82441	−	8.17435i	−0.311611	−	0.259275i
$995$	11.3053	−	13.4731i	0.358402	−	0.427127i
$996$	−10.6709	+	29.8052i	−0.338119	+	0.944413i
$997$	3.84409	+	4.58120i	0.121743	+	0.145088i	0.823473	−	0.567355i	$-0.192033\pi$
$997$	3.84409	+	4.58120i	0.121743	+	0.145088i	−0.701730	+	0.712443i	$0.747589\pi$
$998$	−30.9846	−	17.8890i	−0.980801	−	0.566266i
$999$	−43.9322	+	26.2978i	−1.38995	+	0.832026i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.bd.a.185.19	yes	132
3.2	odd	2		567.2.bd.a.17.4		132
7.5	odd	6		189.2.ba.a.131.4	yes	132
21.5	even	6		567.2.ba.a.341.19		132
27.7	even	9		567.2.ba.a.143.19		132
27.20	odd	18		189.2.ba.a.101.4	✓	132
189.47	even	18	inner	189.2.bd.a.47.19	yes	132
189.61	odd	18		567.2.bd.a.467.4		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.4	✓	132	27.20	odd	18
189.2.ba.a.131.4	yes	132	7.5	odd	6
189.2.bd.a.47.19	yes	132	189.47	even	18	inner
189.2.bd.a.185.19	yes	132	1.1	even	1	trivial
567.2.ba.a.143.19		132	27.7	even	9
567.2.ba.a.341.19		132	21.5	even	6
567.2.bd.a.17.4		132	3.2	odd	2
567.2.bd.a.467.4		132	189.61	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.bd (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.87320 - 0.330296i) q^{2} +(0.583821 - 1.63069i) q^{3} +(1.52040 - 0.553380i) q^{4} +(-0.848304 + 0.308757i) q^{5} +(0.555004 - 3.24744i) q^{6} +(2.48993 + 0.894564i) q^{7} +(-0.629295 + 0.363324i) q^{8} +(-2.31831 - 1.90406i) q^{9} +O(q^{10})\)	\(q+(1.87320 - 0.330296i) q^{2} +(0.583821 - 1.63069i) q^{3} +(1.52040 - 0.553380i) q^{4} +(-0.848304 + 0.308757i) q^{5} +(0.555004 - 3.24744i) q^{6} +(2.48993 + 0.894564i) q^{7} +(-0.629295 + 0.363324i) q^{8} +(-2.31831 - 1.90406i) q^{9} +(-1.48706 + 0.858555i) q^{10} +(-1.19563 + 3.28497i) q^{11} +(-0.0147504 - 2.80238i) q^{12} +(-1.35464 - 3.72184i) q^{13} +(4.95961 + 0.853285i) q^{14} +(0.00822998 + 1.56358i) q^{15} +(-3.53767 + 2.96846i) q^{16} +(-0.233932 - 0.405183i) q^{17} +(-4.97156 - 2.80097i) q^{18} +(3.14258 + 1.81437i) q^{19} +(-1.11890 + 0.938869i) q^{20} +(2.91243 - 3.53804i) q^{21} +(-1.15465 + 6.54832i) q^{22} +(3.44344 + 0.607171i) q^{23} +(0.225073 + 1.23830i) q^{24} +(-3.20593 + 2.69010i) q^{25} +(-3.76682 - 6.52432i) q^{26} +(-4.45842 + 2.66881i) q^{27} +(4.28072 - 0.0177830i) q^{28} +(-1.79273 + 4.92550i) q^{29} +(0.531860 + 2.92618i) q^{30} +(-2.38270 - 6.54641i) q^{31} +(-4.71214 + 5.61571i) q^{32} +(4.65874 + 3.86754i) q^{33} +(-0.572032 - 0.681722i) q^{34} +(-2.38842 + 0.00992201i) q^{35} +(-4.57842 - 1.61203i) q^{36} +9.85377 q^{37} +(6.48596 + 2.36070i) q^{38} +(-6.86004 + 0.0361081i) q^{39} +(0.421655 - 0.502508i) q^{40} +(2.71326 - 0.987547i) q^{41} +(4.28697 - 7.58943i) q^{42} +(-1.54504 - 8.76238i) q^{43} +5.65611i q^{44} +(2.55452 + 0.899431i) q^{45} +6.65080 q^{46} +(-3.13508 - 1.14108i) q^{47} +(2.77527 + 7.50190i) q^{48} +(5.39951 + 4.45481i) q^{49} +(-5.11683 + 6.09800i) q^{50} +(-0.797302 + 0.144917i) q^{51} +(-4.11919 - 4.90906i) q^{52} +(-8.75304 - 5.05357i) q^{53} +(-7.47001 + 6.47181i) q^{54} -3.15581i q^{55} +(-1.89192 + 0.341706i) q^{56} +(4.79338 - 4.06531i) q^{57} +(-1.73128 + 9.81858i) q^{58} +(-2.48304 - 2.08352i) q^{59} +(0.877767 + 2.37271i) q^{60} +(0.0209011 - 0.0574254i) q^{61} +(-6.62553 - 11.4757i) q^{62} +(-4.06911 - 6.81486i) q^{63} +(-2.35384 + 4.07697i) q^{64} +(2.29829 + 2.73900i) q^{65} +(10.0042 + 5.70592i) q^{66} +(1.78024 - 10.0962i) q^{67} +(-0.579891 - 0.486586i) q^{68} +(3.00046 - 5.26070i) q^{69} +(-4.47071 + 0.807471i) q^{70} +(-2.19935 - 1.26979i) q^{71} +(2.15069 + 0.355923i) q^{72} -8.37008i q^{73} +(18.4581 - 3.25466i) q^{74} +(2.51503 + 6.79842i) q^{75} +(5.78202 + 1.01953i) q^{76} +(-5.91566 + 7.10978i) q^{77} +(-12.8383 + 2.33348i) q^{78} +(1.64089 + 9.30597i) q^{79} +(2.08449 - 3.61044i) q^{80} +(1.74908 + 8.82840i) q^{81} +(4.75630 - 2.74605i) q^{82} +(-10.6153 - 3.86367i) q^{83} +(2.47018 - 6.99092i) q^{84} +(0.323549 + 0.271490i) q^{85} +(-5.78836 - 15.9034i) q^{86} +(6.98533 + 5.79900i) q^{87} +(-0.441103 - 2.50162i) q^{88} +(-1.51868 + 2.63043i) q^{89} +(5.08221 + 0.841067i) q^{90} +(-0.0435318 - 10.4789i) q^{91} +(5.57140 - 0.982388i) q^{92} +(-12.0662 + 0.0635112i) q^{93} +(-6.24952 - 1.10196i) q^{94} +(-3.22606 - 0.568842i) q^{95} +(6.40644 + 10.9626i) q^{96} +(5.02929 - 0.886800i) q^{97} +(11.5858 + 6.56131i) q^{98} +(9.02664 - 5.33901i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Introduction

L-functions

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