LMFDB - Embedded newform 37.2.f.a.12.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,2,Mod(7,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("37.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	37.f (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.295446487479$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			12.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	37.12
Dual form			37.2.f.a.34.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17365 + 0.984808i) q^{2} +(0.673648 + 0.565258i) q^{3} +(0.0603074 - 0.342020i) q^{4} +(-0.652704 + 0.237565i) q^{5} -1.34730 q^{6} +(2.20574 - 0.802823i) q^{7} +(-1.26604 - 2.19285i) q^{8} +(-0.386659 - 2.19285i) q^{9} +O(q^{10})$	\(q+(-1.17365 + 0.984808i) q^{2} +(0.673648 + 0.565258i) q^{3} +(0.0603074 - 0.342020i) q^{4} +(-0.652704 + 0.237565i) q^{5} -1.34730 q^{6} +(2.20574 - 0.802823i) q^{7} +(-1.26604 - 2.19285i) q^{8} +(-0.386659 - 2.19285i) q^{9} +(0.532089 - 0.921605i) q^{10} +(-0.939693 - 1.62760i) q^{11} +(0.233956 - 0.196312i) q^{12} +(-0.213011 + 1.20805i) q^{13} +(-1.79813 + 3.11446i) q^{14} +(-0.573978 - 0.208911i) q^{15} +(4.29813 + 1.56439i) q^{16} +(1.33750 + 7.58532i) q^{17} +(2.61334 + 2.19285i) q^{18} +(-5.03596 - 4.22567i) q^{19} +(0.0418891 + 0.237565i) q^{20} +(1.93969 + 0.705990i) q^{21} +(2.70574 + 0.984808i) q^{22} +(-0.326352 + 0.565258i) q^{23} +(0.386659 - 2.19285i) q^{24} +(-3.46064 + 2.90382i) q^{25} +(-0.939693 - 1.62760i) q^{26} +(2.29813 - 3.98048i) q^{27} +(-0.141559 - 0.802823i) q^{28} +(-2.84730 - 4.93166i) q^{29} +(0.879385 - 0.320070i) q^{30} +4.06418 q^{31} +(-1.82635 + 0.664738i) q^{32} +(0.286989 - 1.62760i) q^{33} +(-9.03983 - 7.58532i) q^{34} +(-1.24897 + 1.04801i) q^{35} -0.773318 q^{36} +(1.81908 + 5.80439i) q^{37} +10.0719 q^{38} +(-0.826352 + 0.693392i) q^{39} +(1.34730 + 1.13052i) q^{40} +(-0.592396 + 3.35965i) q^{41} +(-2.97178 + 1.08164i) q^{42} -8.86484 q^{43} +(-0.613341 + 0.223238i) q^{44} +(0.773318 + 1.33943i) q^{45} +(-0.173648 - 0.984808i) q^{46} +(4.03209 - 6.98378i) q^{47} +(2.01114 + 3.48340i) q^{48} +(-1.14156 + 0.957882i) q^{49} +(1.20187 - 6.81612i) q^{50} +(-3.38666 + 5.86587i) q^{51} +(0.400330 + 0.145708i) q^{52} +(8.00387 + 2.91317i) q^{53} +(1.22281 + 6.93491i) q^{54} +(1.00000 + 0.839100i) q^{55} +(-4.55303 - 3.82045i) q^{56} +(-1.00387 - 5.69323i) q^{57} +(8.19846 + 2.98400i) q^{58} +(6.81180 + 2.47929i) q^{59} +(-0.106067 + 0.183713i) q^{60} +(0.790859 - 4.48519i) q^{61} +(-4.76991 + 4.00243i) q^{62} +(-2.61334 - 4.52644i) q^{63} +(-3.08512 + 5.34359i) q^{64} +(-0.147956 - 0.839100i) q^{65} +(1.26604 + 2.19285i) q^{66} +(-4.35844 + 1.58634i) q^{67} +2.67499 q^{68} +(-0.539363 + 0.196312i) q^{69} +(0.433763 - 2.45999i) q^{70} +(5.18345 + 4.34943i) q^{71} +(-4.31908 + 3.62414i) q^{72} +1.85710 q^{73} +(-7.85117 - 5.02087i) q^{74} -3.97266 q^{75} +(-1.74897 + 1.46756i) q^{76} +(-3.37939 - 2.83564i) q^{77} +(0.286989 - 1.62760i) q^{78} +(7.86959 - 2.86429i) q^{79} -3.17705 q^{80} +(-2.47906 + 0.902302i) q^{81} +(-2.61334 - 4.52644i) q^{82} +(-1.30066 - 7.37641i) q^{83} +(0.358441 - 0.620838i) q^{84} +(-2.67499 - 4.63322i) q^{85} +(10.4042 - 8.73016i) q^{86} +(0.869585 - 4.93166i) q^{87} +(-2.37939 + 4.12122i) q^{88} +(-0.992726 - 0.361323i) q^{89} +(-2.22668 - 0.810446i) q^{90} +(0.500000 + 2.83564i) q^{91} +(0.173648 + 0.145708i) q^{92} +(2.73783 + 2.29731i) q^{93} +(2.14543 + 12.1673i) q^{94} +(4.29086 + 1.56175i) q^{95} +(-1.60607 - 0.584561i) q^{96} +(6.58512 - 11.4058i) q^{97} +(0.396459 - 2.24843i) q^{98} +(-3.20574 + 2.68993i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 6 q^{5} - 6 q^{6} + 3 q^{7} - 3 q^{8} - 9 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 6 * q^5 - 6 * q^6 + 3 * q^7 - 3 * q^8 - 9 * q^9	\( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 6 q^{5} - 6 q^{6} + 3 q^{7} - 3 q^{8} - 9 q^{9} - 6 q^{10} + 6 q^{12} - 9 q^{13} + 3 q^{14} + 12 q^{15} + 12 q^{16} + 3 q^{17} + 9 q^{18} + 3 q^{19} - 6 q^{20} + 6 q^{21} + 6 q^{22} - 3 q^{23} + 9 q^{24} - 12 q^{25} - 9 q^{28} - 15 q^{29} - 6 q^{30} + 6 q^{31} - 12 q^{32} - 6 q^{33} + 3 q^{34} + 18 q^{35} - 18 q^{36} - 6 q^{37} - 6 q^{38} - 6 q^{39} + 6 q^{40} - 3 q^{42} - 6 q^{43} + 3 q^{44} + 18 q^{45} + 15 q^{47} + 6 q^{48} - 15 q^{49} + 21 q^{50} - 27 q^{51} - 12 q^{52} + 24 q^{53} + 18 q^{54} + 6 q^{55} - 15 q^{56} + 18 q^{57} + 21 q^{58} + 6 q^{59} + 24 q^{60} - 27 q^{61} - 9 q^{63} + 3 q^{64} + 30 q^{65} + 3 q^{66} - 18 q^{67} + 6 q^{68} - 12 q^{69} - 30 q^{70} + 33 q^{71} - 9 q^{72} + 12 q^{73} - 21 q^{74} - 66 q^{75} + 15 q^{76} - 9 q^{77} - 6 q^{78} + 33 q^{79} - 60 q^{80} - 18 q^{81} - 9 q^{82} + 21 q^{83} - 6 q^{84} - 6 q^{85} + 24 q^{86} - 9 q^{87} - 3 q^{88} + 12 q^{89} + 3 q^{91} - 3 q^{93} - 3 q^{94} - 6 q^{95} + 15 q^{96} + 18 q^{97} + 12 q^{98} - 9 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 6 * q^5 - 6 * q^6 + 3 * q^7 - 3 * q^8 - 9 * q^9 - 6 * q^10 + 6 * q^12 - 9 * q^13 + 3 * q^14 + 12 * q^15 + 12 * q^16 + 3 * q^17 + 9 * q^18 + 3 * q^19 - 6 * q^20 + 6 * q^21 + 6 * q^22 - 3 * q^23 + 9 * q^24 - 12 * q^25 - 9 * q^28 - 15 * q^29 - 6 * q^30 + 6 * q^31 - 12 * q^32 - 6 * q^33 + 3 * q^34 + 18 * q^35 - 18 * q^36 - 6 * q^37 - 6 * q^38 - 6 * q^39 + 6 * q^40 - 3 * q^42 - 6 * q^43 + 3 * q^44 + 18 * q^45 + 15 * q^47 + 6 * q^48 - 15 * q^49 + 21 * q^50 - 27 * q^51 - 12 * q^52 + 24 * q^53 + 18 * q^54 + 6 * q^55 - 15 * q^56 + 18 * q^57 + 21 * q^58 + 6 * q^59 + 24 * q^60 - 27 * q^61 - 9 * q^63 + 3 * q^64 + 30 * q^65 + 3 * q^66 - 18 * q^67 + 6 * q^68 - 12 * q^69 - 30 * q^70 + 33 * q^71 - 9 * q^72 + 12 * q^73 - 21 * q^74 - 66 * q^75 + 15 * q^76 - 9 * q^77 - 6 * q^78 + 33 * q^79 - 60 * q^80 - 18 * q^81 - 9 * q^82 + 21 * q^83 - 6 * q^84 - 6 * q^85 + 24 * q^86 - 9 * q^87 - 3 * q^88 + 12 * q^89 + 3 * q^91 - 3 * q^93 - 3 * q^94 - 6 * q^95 + 15 * q^96 + 18 * q^97 + 12 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.17365	+	0.984808i	−0.829895	+	0.696364i	−0.955267	−	0.295746i	$-0.904432\pi$
$2$	−1.17365	+	0.984808i	−0.829895	+	0.696364i	0.125372	+	0.992110i	$0.459988\pi$
$3$	0.673648	+	0.565258i	0.388931	+	0.326352i	0.816197	−	0.577774i	$-0.196079\pi$
$3$	0.673648	+	0.565258i	0.388931	+	0.326352i	−0.427266	+	0.904126i	$0.640523\pi$
$4$	0.0603074	−	0.342020i	0.0301537	−	0.171010i
$5$	−0.652704	+	0.237565i	−0.291898	+	0.106242i	−0.483819	−	0.875168i	$-0.660751\pi$
$5$	−0.652704	+	0.237565i	−0.291898	+	0.106242i	0.191921	+	0.981410i	$0.438528\pi$
$6$	−1.34730			−0.550031
$7$	2.20574	−	0.802823i	0.833690	−	0.303438i	0.110318	−	0.993896i	$-0.464813\pi$
$7$	2.20574	−	0.802823i	0.833690	−	0.303438i	0.723373	+	0.690458i	$0.242591\pi$
$8$	−1.26604	−	2.19285i	−0.447614	−	0.775291i
$9$	−0.386659	−	2.19285i	−0.128886	−	0.730951i
$10$	0.532089	−	0.921605i	0.168261	−	0.291437i
$11$	−0.939693	−	1.62760i	−0.283328	−	0.490738i	0.688874	−	0.724881i	$-0.258105\pi$
$11$	−0.939693	−	1.62760i	−0.283328	−	0.490738i	−0.972202	+	0.234142i	$0.924772\pi$
$12$	0.233956	−	0.196312i	0.0675372	−	0.0566704i
$13$	−0.213011	+	1.20805i	−0.0590786	+	0.335052i	−0.999994	−	0.00359149i	$-0.998857\pi$
$13$	−0.213011	+	1.20805i	−0.0590786	+	0.335052i	0.940915	+	0.338643i	$0.109968\pi$
$14$	−1.79813	+	3.11446i	−0.480571	+	0.832374i
$15$	−0.573978	−	0.208911i	−0.148200	−	0.0539406i
$16$	4.29813	+	1.56439i	1.07453	+	0.391098i
$17$	1.33750	+	7.58532i	0.324390	+	1.83971i	0.513924	+	0.857836i	$0.328191\pi$
$17$	1.33750	+	7.58532i	0.324390	+	1.83971i	−0.189534	+	0.981874i	$0.560698\pi$
$18$	2.61334	+	2.19285i	0.615970	+	0.516860i
$19$	−5.03596	−	4.22567i	−1.15533	−	0.969436i	−0.155498	−	0.987836i	$-0.549698\pi$
$19$	−5.03596	−	4.22567i	−1.15533	−	0.969436i	−0.999831	+	0.0184007i	$0.994143\pi$
$20$	0.0418891	+	0.237565i	0.00936668	+	0.0531211i
$21$	1.93969	+	0.705990i	0.423276	+	0.154060i
$22$	2.70574	+	0.984808i	0.576865	+	0.209962i
$23$	−0.326352	+	0.565258i	−0.0680491	+	0.117864i	−0.898042	−	0.439909i	$-0.855011\pi$
$23$	−0.326352	+	0.565258i	−0.0680491	+	0.117864i	0.829993	+	0.557773i	$0.188344\pi$
$24$	0.386659	−	2.19285i	0.0789265	−	0.447614i
$25$	−3.46064	+	2.90382i	−0.692127	+	0.580764i
$26$	−0.939693	−	1.62760i	−0.184289	−	0.319198i
$27$	2.29813	−	3.98048i	0.442276	−	0.766044i
$28$	−0.141559	−	0.802823i	−0.0267522	−	0.151719i
$29$	−2.84730	−	4.93166i	−0.528730	−	0.915787i	−0.999439	−	0.0334982i	$-0.989335\pi$
$29$	−2.84730	−	4.93166i	−0.528730	−	0.915787i	0.470709	−	0.882288i	$-0.343998\pi$
$30$	0.879385	−	0.320070i	0.160553	−	0.0584365i
$31$	4.06418			0.729948			0.364974	−	0.931018i	$-0.381078\pi$
$31$	4.06418			0.729948			0.364974	+	0.931018i	$0.381078\pi$
$32$	−1.82635	+	0.664738i	−0.322856	+	0.117510i
$33$	0.286989	−	1.62760i	0.0499584	−	0.283328i
$34$	−9.03983	−	7.58532i	−1.55032	−	1.30087i
$35$	−1.24897	+	1.04801i	−0.211115	+	0.177146i
$36$	−0.773318			−0.128886
$37$	1.81908	+	5.80439i	0.299055	+	0.954236i
$37$	1.81908	+	5.80439i	0.299055	+	0.954236i
$38$	10.0719			1.63388
$39$	−0.826352	+	0.693392i	−0.132322	+	0.111032i
$40$	1.34730	+	1.13052i	0.213026	+	0.178750i
$41$	−0.592396	+	3.35965i	−0.0925168	+	0.524689i	0.902963	+	0.429718i	$0.141387\pi$
$41$	−0.592396	+	3.35965i	−0.0925168	+	0.524689i	−0.995480	+	0.0949709i	$0.969724\pi$
$42$	−2.97178	+	1.08164i	−0.458556	+	0.166901i
$43$	−8.86484			−1.35188			−0.675938	−	0.736959i	$-0.736261\pi$
$43$	−8.86484			−1.35188			−0.675938	+	0.736959i	$0.736261\pi$
$44$	−0.613341	+	0.223238i	−0.0924646	+	0.0336544i
$45$	0.773318	+	1.33943i	0.115280	+	0.199670i
$46$	−0.173648	−	0.984808i	−0.0256030	−	0.145202i
$47$	4.03209	−	6.98378i	0.588141	−	1.01869i	−0.406335	−	0.913724i	$-0.633193\pi$
$47$	4.03209	−	6.98378i	0.588141	−	1.01869i	0.994476	−	0.104965i	$-0.0334732\pi$
$48$	2.01114	+	3.48340i	0.290284	+	0.502786i
$49$	−1.14156	+	0.957882i	−0.163080	+	0.136840i
$50$	1.20187	−	6.81612i	0.169970	−	0.963946i
$51$	−3.38666	+	5.86587i	−0.474227	+	0.821386i
$52$	0.400330	+	0.145708i	0.0555158	+	0.0202061i
$53$	8.00387	+	2.91317i	1.09942	+	0.400155i	0.827101	−	0.562053i	$-0.189988\pi$
$53$	8.00387	+	2.91317i	1.09942	+	0.400155i	0.272315	+	0.962208i	$0.412211\pi$
$54$	1.22281	+	6.93491i	0.166404	+	0.943721i
$55$	1.00000	+	0.839100i	0.134840	+	0.113144i
$56$	−4.55303	−	3.82045i	−0.608425	−	0.510529i
$57$	−1.00387	−	5.69323i	−0.132966	−	0.754087i
$58$	8.19846	+	2.98400i	1.07651	+	0.391818i
$59$	6.81180	+	2.47929i	0.886821	+	0.322777i	0.744959	−	0.667110i	$-0.232469\pi$
$59$	6.81180	+	2.47929i	0.886821	+	0.322777i	0.141862	+	0.989886i	$0.454691\pi$
$60$	−0.106067	+	0.183713i	−0.0136932	+	0.0237173i
$61$	0.790859	−	4.48519i	0.101259	−	0.574269i	−0.891390	−	0.453238i	$-0.850269\pi$
$61$	0.790859	−	4.48519i	0.101259	−	0.574269i	0.992649	−	0.121031i	$-0.0386201\pi$
$62$	−4.76991	+	4.00243i	−0.605780	+	0.508310i
$63$	−2.61334	−	4.52644i	−0.329250	−	0.570278i
$64$	−3.08512	+	5.34359i	−0.385640	+	0.667949i
$65$	−0.147956	−	0.839100i	−0.0183517	−	0.104078i
$66$	1.26604	+	2.19285i	0.155839	+	0.269922i
$67$	−4.35844	+	1.58634i	−0.532468	+	0.193803i	−0.594240	−	0.804288i	$-0.702547\pi$
$67$	−4.35844	+	1.58634i	−0.532468	+	0.193803i	0.0617718	+	0.998090i	$0.480325\pi$
$68$	2.67499			0.324390
$69$	−0.539363	+	0.196312i	−0.0649317	+	0.0236332i
$70$	0.433763	−	2.45999i	0.0518446	−	0.294025i
$71$	5.18345	+	4.34943i	0.615162	+	0.516182i	0.896279	−	0.443491i	$-0.146260\pi$
$71$	5.18345	+	4.34943i	0.615162	+	0.516182i	−0.281117	+	0.959674i	$0.590705\pi$
$72$	−4.31908	+	3.62414i	−0.509008	+	0.427109i
$73$	1.85710			0.217357			0.108678	−	0.994077i	$-0.465338\pi$
$73$	1.85710			0.217357			0.108678	+	0.994077i	$0.465338\pi$
$74$	−7.85117	−	5.02087i	−0.912680	−	0.583664i
$75$	−3.97266			−0.458723
$76$	−1.74897	+	1.46756i	−0.200621	+	0.168341i
$77$	−3.37939	−	2.83564i	−0.385117	−	0.323151i
$78$	0.286989	−	1.62760i	0.0324951	−	0.184289i
$79$	7.86959	−	2.86429i	0.885397	−	0.322258i	0.141012	−	0.990008i	$-0.454965\pi$
$79$	7.86959	−	2.86429i	0.885397	−	0.322258i	0.744386	+	0.667750i	$0.232742\pi$
$80$	−3.17705			−0.355205
$81$	−2.47906	+	0.902302i	−0.275451	+	0.100256i
$82$	−2.61334	−	4.52644i	−0.288595	−	0.499862i
$83$	−1.30066	−	7.37641i	−0.142766	−	0.809666i	−0.969134	−	0.246535i	$-0.920708\pi$
$83$	−1.30066	−	7.37641i	−0.142766	−	0.809666i	0.826368	−	0.563131i	$-0.190403\pi$
$84$	0.358441	−	0.620838i	0.0391091	−	0.0677389i
$85$	−2.67499	−	4.63322i	−0.290144	−	0.502544i
$86$	10.4042	−	8.73016i	1.12191	−	0.941397i
$87$	0.869585	−	4.93166i	0.0932293	−	0.528730i
$88$	−2.37939	+	4.12122i	−0.253643	+	0.439323i
$89$	−0.992726	−	0.361323i	−0.105229	−	0.0383001i	0.288869	−	0.957369i	$-0.406721\pi$
$89$	−0.992726	−	0.361323i	−0.105229	−	0.0383001i	−0.394098	+	0.919068i	$0.628943\pi$
$90$	−2.22668	−	0.810446i	−0.234713	−	0.0854285i
$91$	0.500000	+	2.83564i	0.0524142	+	0.297256i
$92$	0.173648	+	0.145708i	0.0181041	+	0.0151911i
$93$	2.73783	+	2.29731i	0.283899	+	0.238220i
$94$	2.14543	+	12.1673i	0.221284	+	1.25496i
$95$	4.29086	+	1.56175i	0.440233	+	0.160232i
$96$	−1.60607	−	0.584561i	−0.163919	−	0.0596615i
$97$	6.58512	−	11.4058i	0.668618	−	1.15808i	−0.309673	−	0.950843i	$-0.600220\pi$
$97$	6.58512	−	11.4058i	0.668618	−	1.15808i	0.978291	−	0.207237i	$-0.0664471\pi$
$98$	0.396459	−	2.24843i	0.0400484	−	0.227126i
$99$	−3.20574	+	2.68993i	−0.322189	+	0.270348i
$100$	0.784463	+	1.35873i	0.0784463	+	0.135873i
$101$	−3.64543	+	6.31407i	−0.362734	+	0.628273i	−0.988410	−	0.151810i	$-0.951490\pi$
$101$	−3.64543	+	6.31407i	−0.362734	+	0.628273i	0.625676	+	0.780083i	$0.284823\pi$
$102$	−1.80200	−	10.2197i	−0.178425	−	1.01190i
$103$	8.55690	+	14.8210i	0.843137	+	1.46036i	0.887230	+	0.461328i	$0.152627\pi$
$103$	8.55690	+	14.8210i	0.843137	+	1.46036i	−0.0440927	+	0.999027i	$0.514040\pi$
$104$	2.91875	−	1.06234i	0.286207	−	0.104171i
$105$	−1.43376			−0.139921
$106$	−12.2626	+	4.46324i	−1.19105	+	0.433508i
$107$	−1.15018	+	6.52298i	−0.111192	+	0.630600i	0.877374	+	0.479808i	$0.159294\pi$
$107$	−1.15018	+	6.52298i	−0.111192	+	0.630600i	−0.988565	+	0.150792i	$0.951817\pi$
$108$	−1.22281	−	1.02606i	−0.117665	−	0.0987327i
$109$	5.20574	−	4.36813i	0.498619	−	0.418391i	−0.358484	−	0.933536i	$-0.616706\pi$
$109$	5.20574	−	4.36813i	0.498619	−	0.418391i	0.857103	+	0.515145i	$0.172262\pi$
$110$	−2.00000			−0.190693
$111$	−2.05556	+	4.93837i	−0.195105	+	0.468729i
$112$	10.7365			1.01450
$113$	−9.10607	+	7.64090i	−0.856627	+	0.718795i	−0.961239	−	0.275718i	$-0.911084\pi$
$113$	−9.10607	+	7.64090i	−0.856627	+	0.718795i	0.104612	+	0.994513i	$0.466640\pi$
$114$	6.78493	+	5.69323i	0.635467	+	0.533220i
$115$	0.0787257	−	0.446476i	0.00734121	−	0.0416341i
$116$	−1.85844	+	0.676417i	−0.172552	+	0.0628038i
$117$	2.73143			0.252521
$118$	−10.4363	+	3.79850i	−0.960738	+	0.349680i
$119$	9.03983	+	15.6574i	0.828680	+	1.43532i
$120$	0.268571	+	1.52314i	0.0245170	+	0.139043i
$121$	3.73396	−	6.46740i	0.339451	−	0.587946i
$122$	3.48886	+	6.04288i	0.315866	+	0.547096i
$123$	−2.29813	+	1.92836i	−0.207216	+	0.173875i
$124$	0.245100	−	1.39003i	0.0220106	−	0.124828i
$125$	3.30541	−	5.72513i	0.295645	−	0.512071i
$126$	7.52481	+	2.73881i	0.670364	+	0.243992i
$127$	−6.49020	−	2.36224i	−0.575912	−	0.209615i	0.0376099	−	0.999292i	$-0.488026\pi$
$127$	−6.49020	−	2.36224i	−0.575912	−	0.209615i	−0.613522	+	0.789678i	$0.710248\pi$
$128$	−2.31655	−	13.1378i	−0.204756	−	1.16123i
$129$	−5.97178	−	5.01092i	−0.525786	−	0.441187i
$130$	1.00000	+	0.839100i	0.0877058	+	0.0735939i
$131$	−1.27584	−	7.23567i	−0.111471	−	0.632184i	−0.988437	−	0.151631i	$-0.951547\pi$
$131$	−1.27584	−	7.23567i	−0.111471	−	0.632184i	0.876966	−	0.480552i	$-0.159564\pi$
$132$	−0.539363	−	0.196312i	−0.0469455	−	0.0170868i
$133$	−14.5005	−	5.27774i	−1.25735	−	0.457638i
$134$	3.55303	−	6.15403i	0.306935	−	0.531628i
$135$	−0.554378	+	3.14403i	−0.0477132	+	0.270595i
$136$	14.9402	−	12.5363i	1.28111	−	1.07498i
$137$	−4.13176	−	7.15642i	−0.353000	−	0.611414i	0.633774	−	0.773519i	$-0.281505\pi$
$137$	−4.13176	−	7.15642i	−0.353000	−	0.611414i	−0.986774	+	0.162105i	$0.948172\pi$
$138$	0.439693	−	0.761570i	0.0374291	−	0.0648291i
$139$	0.581719	+	3.29909i	0.0493407	+	0.279825i	0.999489	−	0.0319742i	$-0.0101794\pi$
$139$	0.581719	+	3.29909i	0.0493407	+	0.279825i	−0.950148	+	0.311799i	$0.899068\pi$
$140$	0.283119	+	0.490376i	0.0239279	+	0.0414443i
$141$	6.66385	−	2.42544i	0.561197	−	0.204259i
$142$	−10.3669			−0.869971
$143$	2.16637	−	0.788496i	0.181161	−	0.0659373i
$144$	1.76857	−	10.0301i	0.147381	−	0.835839i
$145$	3.03003	+	2.54250i	0.251630	+	0.211143i
$146$	−2.17958	+	1.82888i	−0.180383	+	0.151359i
$147$	−1.31046			−0.108085
$148$	2.09492	−	0.272114i	0.172202	−	0.0223676i
$149$	−21.4466			−1.75697			−0.878485	−	0.477770i	$-0.841445\pi$
$149$	−21.4466			−1.75697			−0.878485	+	0.477770i	$0.841445\pi$
$150$	4.66250	−	3.91231i	0.380692	−	0.319438i
$151$	−17.6420	−	14.8034i	−1.43569	−	1.20469i	−0.942253	−	0.334902i	$-0.891297\pi$
$151$	−17.6420	−	14.8034i	−1.43569	−	1.20469i	−0.493435	−	0.869783i	$-0.664259\pi$
$152$	−2.89053	+	16.3930i	−0.234453	+	1.32965i
$153$	16.1163	−	5.86587i	1.30293	−	0.474227i
$154$	6.75877			0.544637
$155$	−2.65270	+	0.965505i	−0.213070	+	0.0775512i
$156$	0.187319	+	0.324446i	0.0149975	+	0.0259764i
$157$	0.538019	+	3.05126i	0.0429386	+	0.243517i	0.998721	−	0.0505575i	$-0.0160998\pi$
$157$	0.538019	+	3.05126i	0.0429386	+	0.243517i	−0.955783	+	0.294074i	$0.904989\pi$
$158$	−6.41534	+	11.1117i	−0.510377	+	0.884000i
$159$	3.74510	+	6.48670i	0.297006	+	0.514429i
$160$	1.03415	−	0.867753i	0.0817566	−	0.0686019i
$161$	−0.266044	+	1.50881i	−0.0209672	+	0.118911i
$162$	2.02094	−	3.50038i	0.158780	−	0.275016i
$163$	−16.6027	−	6.04288i	−1.30042	−	0.473315i	−0.403287	−	0.915073i	$-0.632132\pi$
$163$	−16.6027	−	6.04288i	−1.30042	−	0.473315i	−0.897134	+	0.441759i	$0.854355\pi$
$164$	1.11334	+	0.405223i	0.0869373	+	0.0316426i
$165$	0.199340	+	1.13052i	0.0155186	+	0.0880105i
$166$	8.79086	+	7.37641i	0.682303	+	0.572520i
$167$	5.59034	+	4.69085i	0.432593	+	0.362989i	0.832929	−	0.553380i	$-0.186662\pi$
$167$	5.59034	+	4.69085i	0.432593	+	0.362989i	−0.400336	+	0.916368i	$0.631107\pi$
$168$	−0.907604	−	5.14728i	−0.0700231	−	0.397121i
$169$	10.8020	+	3.93161i	0.830923	+	0.302431i
$170$	7.70233	+	2.80342i	0.590742	+	0.215013i
$171$	−7.31908	+	12.6770i	−0.559704	+	0.969436i
$172$	−0.534615	+	3.03195i	−0.0407640	+	0.231184i
$173$	0.300193	−	0.251892i	0.0228232	−	0.0191510i	−0.631305	−	0.775535i	$-0.717480\pi$
$173$	0.300193	−	0.251892i	0.0228232	−	0.0191510i	0.654128	+	0.756384i	$0.273036\pi$
$174$	3.83615	+	6.64441i	0.290818	+	0.503711i
$175$	−5.30200	+	9.18334i	−0.400794	+	0.694195i
$176$	−1.49273	−	8.46567i	−0.112518	−	0.638124i
$177$	3.18732	+	5.52060i	0.239574	+	0.414954i
$178$	1.52094	−	0.553579i	0.114000	−	0.0414925i
$179$	7.77837			0.581383			0.290691	−	0.956817i	$-0.406115\pi$
$179$	7.77837			0.581383			0.290691	+	0.956817i	$0.406115\pi$
$180$	0.504748	−	0.183713i	0.0376217	−	0.0136932i
$181$	−1.89558	+	10.7504i	−0.140898	+	0.799069i	0.829673	+	0.558250i	$0.188527\pi$
$181$	−1.89558	+	10.7504i	−0.140898	+	0.799069i	−0.970570	+	0.240819i	$0.922584\pi$
$182$	−3.37939	−	2.83564i	−0.250497	−	0.210192i
$183$	3.06805	−	2.57440i	0.226797	−	0.190305i
$184$	1.65270			0.121839
$185$	−2.56624	−	3.35640i	−0.188674	−	0.246767i
$186$	−5.47565			−0.401494
$187$	11.0890	−	9.30477i	0.810907	−	0.680432i
$188$	−2.14543	−	1.80023i	−0.156472	−	0.131295i
$189$	1.87346	−	10.6249i	0.136274	−	0.772847i
$190$	−6.57398	+	2.39273i	−0.476926	+	0.173587i
$191$	13.3523			0.966142			0.483071	−	0.875581i	$-0.339521\pi$
$191$	13.3523			0.966142			0.483071	+	0.875581i	$0.339521\pi$
$192$	−5.09879	+	1.85581i	−0.367974	+	0.133931i
$193$	−1.78106	−	3.08489i	−0.128203	−	0.222055i	0.794777	−	0.606901i	$-0.207588\pi$
$193$	−1.78106	−	3.08489i	−0.128203	−	0.222055i	−0.922981	+	0.384847i	$0.874254\pi$
$194$	3.50387	+	19.8714i	0.251563	+	1.42669i
$195$	0.374638	−	0.648891i	0.0268283	−	0.0464681i
$196$	0.258770	+	0.448204i	0.0184836	+	0.0320145i
$197$	−4.15136	+	3.48340i	−0.295772	+	0.248182i	−0.778582	−	0.627543i	$-0.784061\pi$
$197$	−4.15136	+	3.48340i	−0.295772	+	0.248182i	0.482810	+	0.875725i	$0.339616\pi$
$198$	1.11334	−	6.31407i	0.0791217	−	0.448721i
$199$	9.33409	−	16.1671i	0.661676	−	1.14606i	−0.318499	−	0.947923i	$-0.603179\pi$
$199$	9.33409	−	16.1671i	0.661676	−	1.14606i	0.980175	−	0.198134i	$-0.0634880\pi$
$200$	10.7490	+	3.91231i	0.760067	+	0.276642i
$201$	−3.83275	−	1.39501i	−0.270341	−	0.0983962i
$202$	−1.93969	−	11.0005i	−0.136476	−	0.773996i
$203$	−10.2396	−	8.59208i	−0.718682	−	0.603045i
$204$	1.80200	+	1.51206i	0.126165	+	0.105865i
$205$	−0.411474	−	2.33359i	−0.0287386	−	0.162985i
$206$	−24.6386	−	8.96773i	−1.71665	−	0.624811i
$207$	1.36571	+	0.497079i	0.0949237	+	0.0345494i
$208$	−2.80541	+	4.85911i	−0.194520	+	0.336919i
$209$	−2.14543	+	12.1673i	−0.148402	+	0.841632i
$210$	1.68273	−	1.41198i	0.116120	−	0.0974359i
$211$	10.4855	+	18.1613i	0.721848	+	1.25028i	0.960258	+	0.279113i	$0.0900405\pi$
$211$	10.4855	+	18.1613i	0.721848	+	1.25028i	−0.238410	+	0.971165i	$0.576626\pi$
$212$	1.47906	−	2.56180i	0.101582	−	0.175945i
$213$	1.03327	+	5.85997i	0.0707986	+	0.401519i
$214$	−5.07398	−	8.78839i	−0.346850	−	0.600762i
$215$	5.78611	−	2.10597i	0.394610	−	0.143626i
$216$	−11.6382			−0.791876
$217$	8.96451	−	3.26281i	0.608550	−	0.221494i
$218$	−1.80793	+	10.2533i	−0.122449	+	0.694441i
$219$	1.25103	+	1.04974i	0.0845368	+	0.0709348i
$220$	0.347296	−	0.291416i	0.0234147	−	0.0196473i
$221$	−9.44831			−0.635562
$222$	−2.45084	−	7.82023i	−0.164489	−	0.524860i
$223$	0.101014			0.00676442			0.00338221	−	0.999994i	$-0.498923\pi$
$223$	0.101014			0.00676442			0.00338221	+	0.999994i	$0.498923\pi$
$224$	−3.49479	+	2.93247i	−0.233505	+	0.195934i
$225$	7.70574	+	6.46588i	0.513716	+	0.431059i
$226$	3.16250	−	17.9355i	0.210367	−	1.19305i
$227$	−2.70574	+	0.984808i	−0.179586	+	0.0653640i	−0.430248	−	0.902711i	$-0.641574\pi$
$227$	−2.70574	+	0.984808i	−0.179586	+	0.0653640i	0.250662	+	0.968075i	$0.419352\pi$
$228$	−2.00774			−0.132966
$229$	17.5398	−	6.38398i	1.15906	−	0.421865i	0.310301	−	0.950638i	$-0.399570\pi$
$229$	17.5398	−	6.38398i	1.15906	−	0.421865i	0.848763	+	0.528773i	$0.177348\pi$
$230$	0.347296	+	0.601535i	0.0229000	+	0.0396640i
$231$	−0.673648	−	3.82045i	−0.0443228	−	0.251367i
$232$	−7.20961	+	12.4874i	−0.473334	+	0.819838i
$233$	−5.23648	−	9.06985i	−0.343053	−	0.594186i	0.641945	−	0.766751i	$-0.278128\pi$
$233$	−5.23648	−	9.06985i	−0.343053	−	0.594186i	−0.984998	+	0.172565i	$0.944794\pi$
$234$	−3.20574	+	2.68993i	−0.209566	+	0.175846i
$235$	−0.972659	+	5.51622i	−0.0634493	+	0.359839i
$236$	1.25877	−	2.18025i	0.0819390	−	0.141922i
$237$	6.92040	+	2.51882i	0.449528	+	0.163615i
$238$	−26.0292	−	9.47384i	−1.68722	−	0.614098i
$239$	−2.32635	−	13.1934i	−0.150479	−	0.853410i	−0.962803	−	0.270204i	$-0.912909\pi$
$239$	−2.32635	−	13.1934i	−0.150479	−	0.853410i	0.812324	−	0.583206i	$-0.198202\pi$
$240$	−2.14022	−	1.79585i	−0.138150	−	0.115922i
$241$	13.8387	+	11.6120i	0.891428	+	0.747997i	0.968496	−	0.249029i	$-0.0801115\pi$
$241$	13.8387	+	11.6120i	0.891428	+	0.747997i	−0.0770683	+	0.997026i	$0.524556\pi$
$242$	1.98680	+	11.2677i	0.127716	+	0.724314i
$243$	−15.1373	−	5.50952i	−0.971057	−	0.353436i
$244$	−1.48633	−	0.540980i	−0.0951525	−	0.0346327i
$245$	0.517541	−	0.896407i	0.0330645	−	0.0572694i
$246$	0.798133	−	4.52644i	0.0508871	−	0.288595i
$247$	6.17752	−	5.18355i	0.393066	−	0.329822i
$248$	−5.14543	−	8.91215i	−0.326735	−	0.565922i
$249$	3.29339	−	5.70431i	0.208710	−	0.361496i
$250$	1.75877	+	9.97448i	0.111234	+	0.630842i
$251$	−10.5633	−	18.2962i	−0.666750	−	1.15484i	−0.978808	−	0.204781i	$-0.934352\pi$
$251$	−10.5633	−	18.2962i	−0.666750	−	1.15484i	0.312058	−	0.950063i	$-0.398982\pi$
$252$	−1.70574	+	0.620838i	−0.107451	+	0.0391091i
$253$	1.22668			0.0771208
$254$	9.94356	−	3.61916i	0.623915	−	0.227086i
$255$	0.816962	−	4.63322i	0.0511602	−	0.290144i
$256$	6.20368	+	5.20550i	0.387730	+	0.325344i
$257$	−0.577382	+	0.484481i	−0.0360161	+	0.0302211i	−0.660618	−	0.750722i	$-0.729706\pi$
$257$	−0.577382	+	0.484481i	−0.0360161	+	0.0302211i	0.624602	+	0.780943i	$0.285261\pi$
$258$	11.9436			0.743574
$259$	8.67230	+	11.3426i	0.538871	+	0.704793i
$260$	−0.295912			−0.0183517
$261$	−9.71348	+	8.15058i	−0.601249	+	0.504508i
$262$	8.62314	+	7.23567i	0.532739	+	0.447021i
$263$	−0.849823	+	4.81958i	−0.0524023	+	0.297188i	−0.999734	−	0.0230660i	$-0.992657\pi$
$263$	−0.849823	+	4.81958i	−0.0524023	+	0.297188i	0.947332	+	0.320254i	$0.103768\pi$
$264$	−3.93242	+	1.43128i	−0.242024	+	0.0880894i
$265$	−5.91622			−0.363431
$266$	22.2160	−	8.08596i	1.36215	−	0.495782i
$267$	−0.464508	−	0.804551i	−0.0284274	−	0.0492377i
$268$	0.279715	+	1.58634i	0.0170863	+	0.0969013i
$269$	7.97313	−	13.8099i	0.486130	−	0.842002i	−0.513743	−	0.857944i	$-0.671741\pi$
$269$	7.97313	−	13.8099i	0.486130	−	0.842002i	0.999873	+	0.0159423i	$0.00507479\pi$
$270$	−2.44562	−	4.23594i	−0.148836	−	0.257791i
$271$	−8.19459	+	6.87608i	−0.497786	+	0.417692i	−0.856807	−	0.515637i	$-0.827555\pi$
$271$	−8.19459	+	6.87608i	−0.497786	+	0.417692i	0.359021	+	0.933330i	$0.383111\pi$
$272$	−6.11768	+	34.6951i	−0.370939	+	2.10370i
$273$	−1.26604	+	2.19285i	−0.0766245	+	0.132718i
$274$	11.8969	+	4.33013i	0.718720	+	0.261593i
$275$	7.97818	+	2.90382i	0.481102	+	0.175107i
$276$	0.0346151	+	0.196312i	0.00208358	+	0.0118166i
$277$	7.73577	+	6.49108i	0.464797	+	0.390011i	0.844892	−	0.534936i	$-0.179664\pi$
$277$	7.73577	+	6.49108i	0.464797	+	0.390011i	−0.380095	+	0.924947i	$0.624109\pi$
$278$	−3.93170	−	3.29909i	−0.235808	−	0.197866i
$279$	−1.57145	−	8.91215i	−0.0940804	−	0.533556i
$280$	3.87939	+	1.41198i	0.231838	+	0.0843820i
$281$	−5.83750	−	2.12467i	−0.348236	−	0.126747i	0.161980	−	0.986794i	$-0.448212\pi$
$281$	−5.83750	−	2.12467i	−0.348236	−	0.126747i	−0.510215	+	0.860047i	$0.670434\pi$
$282$	−5.43242	+	9.40923i	−0.323496	+	0.560311i
$283$	−0.582434	+	3.30315i	−0.0346221	+	0.196352i	−0.997213	−	0.0746073i	$-0.976230\pi$
$283$	−0.582434	+	3.30315i	−0.0346221	+	0.196352i	0.962591	+	0.270959i	$0.0873408\pi$
$284$	1.80019	−	1.51054i	0.106822	−	0.0896341i
$285$	2.00774	+	3.47751i	0.118928	+	0.205990i
$286$	−1.76604	+	3.05888i	−0.104428	+	0.180875i
$287$	1.39053	+	7.88609i	0.0820804	+	0.465501i
$288$	2.16385	+	3.74789i	0.127506	+	0.220847i
$289$	−39.7734	+	14.4763i	−2.33961	+	0.851549i
$290$	−6.06006			−0.355859
$291$	10.8833	−	3.96118i	0.637988	−	0.232209i
$292$	0.111997	−	0.635164i	0.00655411	−	0.0371702i
$293$	23.7422	+	19.9220i	1.38703	+	1.16386i	0.966526	+	0.256568i	$0.0825918\pi$
$293$	23.7422	+	19.9220i	1.38703	+	1.16386i	0.420506	+	0.907290i	$0.361853\pi$
$294$	1.53802	−	1.29055i	0.0896991	−	0.0752665i
$295$	−5.03508			−0.293154
$296$	10.4251	−	11.3376i	0.605949	−	0.658984i
$297$	−8.63816			−0.501237
$298$	25.1707	−	21.1207i	1.45810	−	1.22349i
$299$	−0.613341	−	0.514654i	−0.0354704	−	0.0297632i
$300$	−0.239581	+	1.35873i	−0.0138322	+	0.0784463i
$301$	−19.5535	+	7.11689i	−1.12705	+	0.410211i
$302$	35.2841			2.03037
$303$	−6.02481	+	2.19285i	−0.346117	+	0.125976i
$304$	−15.0346	−	26.0407i	−0.862294	−	1.49354i
$305$	0.549325	+	3.11538i	0.0314543	+	0.178386i
$306$	−13.1382	+	22.7560i	−0.751058	+	1.30087i
$307$	−8.00640	−	13.8675i	−0.456949	−	0.791459i	0.541849	−	0.840476i	$-0.317725\pi$
$307$	−8.00640	−	13.8675i	−0.456949	−	0.791459i	−0.998798	+	0.0490168i	$0.984391\pi$
$308$	−1.17365	+	0.984808i	−0.0668748	+	0.0561146i
$309$	−2.61334	+	14.8210i	−0.148668	+	0.843137i
$310$	2.16250	−	3.74557i	0.122822	−	0.212734i
$311$	−24.9907	−	9.09586i	−1.41709	−	0.515779i	−0.483888	−	0.875130i	$-0.660776\pi$
$311$	−24.9907	−	9.09586i	−1.41709	−	0.515779i	−0.933202	+	0.359351i	$0.882998\pi$
$312$	2.56670	+	0.934204i	0.145311	+	0.0528889i
$313$	0.699807	+	3.96880i	0.0395554	+	0.224330i	0.998177	−	0.0603532i	$-0.0192227\pi$
$313$	0.699807	+	3.96880i	0.0395554	+	0.224330i	−0.958622	+	0.284683i	$0.908112\pi$
$314$	−3.63634	−	3.05126i	−0.205211	−	0.172192i
$315$	2.78106	+	2.33359i	0.156695	+	0.131483i
$316$	−0.505052	−	2.86429i	−0.0284114	−	0.161129i
$317$	−20.8726	−	7.59700i	−1.17232	−	0.426690i	−0.318837	−	0.947810i	$-0.603292\pi$
$317$	−20.8726	−	7.59700i	−1.17232	−	0.426690i	−0.853484	+	0.521120i	$0.825515\pi$
$318$	−10.7836	−	3.92490i	−0.604713	−	0.220098i
$319$	−5.35117	+	9.26849i	−0.299608	+	0.518936i
$320$	0.744223	−	4.22070i	0.0416033	−	0.235944i
$321$	−4.46198	+	3.74405i	−0.249044	+	0.208972i
$322$	−1.17365	−	2.03282i	−0.0654049	−	0.113285i
$323$	25.3175	−	43.8512i	1.40870	−	2.43994i
$324$	0.159100	+	0.902302i	0.00883890	+	0.0501279i
$325$	−2.77079	−	4.79915i	−0.153696	−	0.266209i
$326$	25.4368	−	9.25822i	1.40881	−	0.512765i
$327$	5.97596			0.330471
$328$	8.11721	−	2.95442i	0.448198	−	0.163131i
$329$	3.28699	−	18.6414i	0.181218	−	1.02774i
$330$	−1.34730	−	1.13052i	−0.0741662	−	0.0622329i
$331$	8.75356	−	7.34511i	0.481139	−	0.403724i	−0.369699	−	0.929152i	$-0.620539\pi$
$331$	8.75356	−	7.34511i	0.481139	−	0.403724i	0.850838	+	0.525428i	$0.176095\pi$
$332$	−2.60132			−0.142766
$333$	12.0248	−	6.23329i	0.658956	−	0.341582i
$334$	−11.1807			−0.611779
$335$	2.46791	−	2.07082i	0.134836	−	0.113141i
$336$	7.23261	+	6.06888i	0.394571	+	0.331085i
$337$	3.98411	−	22.5950i	0.217028	−	1.23083i	−0.660324	−	0.750981i	$-0.729581\pi$
$337$	3.98411	−	22.5950i	0.217028	−	1.23083i	0.877352	−	0.479847i	$-0.159308\pi$
$338$	−16.5496	+	6.02357i	−0.900181	+	0.327639i
$339$	−10.4534			−0.567749
$340$	−1.74598	+	0.635484i	−0.0946889	+	0.0344639i
$341$	−3.81908	−	6.61484i	−0.206815	−	0.358214i
$342$	−3.89440	−	22.0862i	−0.210585	−	1.19429i
$343$	−9.96451	+	17.2590i	−0.538033	+	0.931900i
$344$	11.2233	+	19.4393i	0.605119	+	1.04810i
$345$	0.305407	−	0.256267i	0.0164426	−	0.0137970i
$346$	−0.104256	+	0.591264i	−0.00560483	+	0.0317866i
$347$	−5.19119	+	8.99140i	−0.278678	+	0.482684i	−0.971056	−	0.238850i	$-0.923229\pi$
$347$	−5.19119	+	8.99140i	−0.278678	+	0.482684i	0.692379	+	0.721534i	$0.256563\pi$
$348$	−1.63429	−	0.594831i	−0.0876069	−	0.0318863i
$349$	6.38326	+	2.32332i	0.341688	+	0.124364i	0.507164	−	0.861850i	$-0.330694\pi$
$349$	6.38326	+	2.32332i	0.341688	+	0.124364i	−0.165476	+	0.986214i	$0.552916\pi$
$350$	−2.82114	−	15.9995i	−0.150796	−	0.855207i
$351$	4.31908	+	3.62414i	0.230535	+	0.193442i
$352$	2.79813	+	2.34791i	0.149141	+	0.125144i
$353$	5.42767	+	30.7819i	0.288886	+	1.63835i	0.691066	+	0.722792i	$0.257142\pi$
$353$	5.42767	+	30.7819i	0.288886	+	1.63835i	−0.402180	+	0.915561i	$0.631747\pi$
$354$	−9.17752	−	3.34034i	−0.487780	−	0.177537i
$355$	−4.41653	−	1.60748i	−0.234405	−	0.0853164i
$356$	−0.183448	+	0.317742i	−0.00972274	+	0.0168403i
$357$	−2.76083	+	15.6574i	−0.146119	+	0.828680i
$358$	−9.12907	+	7.66020i	−0.482486	+	0.404854i
$359$	3.82976	+	6.63333i	0.202127	+	0.350094i	0.949213	−	0.314633i	$-0.101881\pi$
$359$	3.82976	+	6.63333i	0.202127	+	0.350094i	−0.747087	+	0.664727i	$0.768548\pi$
$360$	1.95811	−	3.39155i	0.103202	−	0.178750i
$361$	4.20527	+	23.8493i	0.221330	+	1.25522i
$362$	−8.36231	−	14.4839i	−0.439513	−	0.761259i
$363$	6.17112	−	2.24610i	0.323900	−	0.117890i
$364$	1.00000			0.0524142
$365$	−1.21213	+	0.441181i	−0.0634460	+	0.0230924i
$366$	−1.06552	+	6.04288i	−0.0556957	+	0.315866i
$367$	−18.9834	−	15.9290i	−0.990925	−	0.831485i	−0.00522364	−	0.999986i	$-0.501663\pi$
$367$	−18.9834	−	15.9290i	−0.990925	−	0.831485i	−0.985701	+	0.168502i	$0.946107\pi$
$368$	−2.28699	+	1.91901i	−0.119218	+	0.100035i
$369$	7.59627			0.395446
$370$	6.31727	+	1.41198i	0.328419	+	0.0734054i
$371$	19.9932			1.03799
$372$	0.950837	−	0.797847i	0.0492986	−	0.0413664i
$373$	11.0778	+	9.29542i	0.573589	+	0.481299i	0.882835	−	0.469684i	$-0.155632\pi$
$373$	11.0778	+	9.29542i	0.573589	+	0.481299i	−0.309246	+	0.950982i	$0.600076\pi$
$374$	−3.85117	+	21.8411i	−0.199139	+	1.12937i
$375$	5.46286	−	1.98832i	0.282101	−	0.102676i
$376$	−20.4192			−1.05304
$377$	6.56418	−	2.38917i	0.338072	−	0.123048i
$378$	8.26470	+	14.3149i	0.425090	+	0.736278i
$379$	4.10014	+	23.2530i	0.210610	+	1.19443i	0.888364	+	0.459140i	$0.151842\pi$
$379$	4.10014	+	23.2530i	0.210610	+	1.19443i	−0.677754	+	0.735288i	$0.737047\pi$
$380$	0.792919	−	1.37338i	0.0406759	−	0.0704527i
$381$	−3.03684	−	5.25996i	−0.155582	−	0.269476i
$382$	−15.6710	+	13.1495i	−0.801796	+	0.672787i
$383$	2.63681	−	14.9541i	0.134735	−	0.764119i	−0.840309	−	0.542107i	$-0.817627\pi$
$383$	2.63681	−	14.9541i	0.134735	−	0.764119i	0.975044	−	0.222012i	$-0.0712623\pi$
$384$	5.86571	−	10.1597i	0.299333	−	0.518461i
$385$	2.87939	+	1.04801i	0.146747	+	0.0534116i
$386$	5.12836	+	1.86657i	0.261026	+	0.0950058i
$387$	3.42767	+	19.4393i	0.174238	+	0.988155i
$388$	−3.50387	−	2.94010i	−0.177882	−	0.149261i
$389$	−3.88326	−	3.25844i	−0.196889	−	0.165209i	0.539013	−	0.842297i	$-0.318797\pi$
$389$	−3.88326	−	3.25844i	−0.196889	−	0.165209i	−0.735902	+	0.677088i	$0.763242\pi$
$390$	0.199340	+	1.13052i	0.0100940	+	0.0572459i
$391$	−4.72416	−	1.71945i	−0.238911	−	0.0869564i
$392$	3.54576	+	1.29055i	0.179088	+	0.0651827i
$393$	3.23055	−	5.59548i	0.162960	−	0.282255i
$394$	1.44175	−	8.17658i	0.0726344	−	0.411930i
$395$	−4.45605	+	3.73907i	−0.224208	+	0.188133i
$396$	0.726682	+	1.25865i	0.0365171	+	0.0632495i
$397$	2.80659	−	4.86116i	0.140859	−	0.243974i	−0.786962	−	0.617002i	$-0.788347\pi$
$397$	2.80659	−	4.86116i	0.140859	−	0.243974i	0.927820	+	0.373028i	$0.121680\pi$
$398$	4.96657	+	28.1668i	0.248952	+	1.41187i
$399$	−6.78493	−	11.7518i	−0.339671	−	0.588328i
$400$	−19.4170	+	7.06721i	−0.970850	+	0.353360i
$401$	3.64765			0.182155			0.0910775	−	0.995844i	$-0.470969\pi$
$401$	3.64765			0.182155			0.0910775	+	0.995844i	$0.470969\pi$
$402$	5.87211	−	2.13727i	0.292874	−	0.106598i
$403$	−0.865715	+	4.90971i	−0.0431243	+	0.244570i
$404$	1.93969	+	1.62760i	0.0965033	+	0.0809759i
$405$	1.40373	−	1.17787i	0.0697521	−	0.0585289i
$406$	20.4793			1.01637
$407$	7.73783	−	8.41507i	0.383550	−	0.417119i
$408$	17.1506			0.849083
$409$	12.3923	−	10.3984i	0.612762	−	0.514168i	−0.282757	−	0.959192i	$-0.591249\pi$
$409$	12.3923	−	10.3984i	0.612762	−	0.514168i	0.895519	+	0.445023i	$0.146805\pi$
$410$	2.78106	+	2.33359i	0.137347	+	0.115248i
$411$	1.26187	−	7.15642i	0.0622434	−	0.353000i
$412$	5.58512	−	2.03282i	0.275159	−	0.100150i
$413$	17.0155			0.837277
$414$	−2.09240	+	0.761570i	−0.102836	+	0.0374291i
$415$	2.60132	+	4.50562i	0.127694	+	0.221172i
$416$	−0.414000	−	2.34791i	−0.0202980	−	0.115116i
$417$	−1.47296	+	2.55125i	−0.0721313	+	0.124935i
$418$	−9.46451	−	16.3930i	−0.462924	−	0.801808i
$419$	−5.52616	+	4.63700i	−0.269971	+	0.226532i	−0.767715	−	0.640792i	$-0.778606\pi$
$419$	−5.52616	+	4.63700i	−0.269971	+	0.226532i	0.497744	+	0.867324i	$0.334162\pi$
$420$	−0.0864665	+	0.490376i	−0.00421913	+	0.0239279i
$421$	1.92649	−	3.33678i	0.0938913	−	0.162625i	−0.815254	−	0.579103i	$-0.803403\pi$
$421$	1.92649	−	3.33678i	0.0938913	−	0.162625i	0.909145	+	0.416479i	$0.136736\pi$
$422$	−30.1917	−	10.9889i	−1.46971	−	0.534930i
$423$	−16.8735	−	6.14144i	−0.820415	−	0.298607i
$424$	−3.74510	−	21.2395i	−0.181878	−	1.03148i
$425$	−26.6550	−	22.3662i	−1.29296	−	1.08492i
$426$	−6.98364	−	5.85997i	−0.338359	−	0.283917i
$427$	−1.85638	−	10.5281i	−0.0898366	−	0.509489i
$428$	2.16163	+	0.786768i	0.104486	+	0.0380299i
$429$	1.90508	+	0.693392i	0.0919780	+	0.0334773i
$430$	−4.71688	+	8.16988i	−0.227468	+	0.393987i
$431$	−1.07573	+	6.10078i	−0.0518162	+	0.293864i	−0.999693	−	0.0247724i	$-0.992114\pi$
$431$	−1.07573	+	6.10078i	−0.0518162	+	0.293864i	0.947877	+	0.318637i	$0.103225\pi$
$432$	16.1047	−	13.5135i	0.774839	−	0.650167i
$433$	5.59492	+	9.69069i	0.268875	+	0.465705i	0.968572	−	0.248735i	$-0.0800149\pi$
$433$	5.59492	+	9.69069i	0.268875	+	0.465705i	−0.699697	+	0.714440i	$0.746682\pi$
$434$	−7.30793	+	12.6577i	−0.350792	+	0.607590i
$435$	0.604007	+	3.42550i	0.0289599	+	0.164240i
$436$	−1.18004	−	2.04390i	−0.0565139	−	0.0978849i
$437$	4.03209	−	1.46756i	0.192881	−	0.0702029i
$438$	−2.50206			−0.119553
$439$	0.0457595	−	0.0166551i	0.00218398	−	0.000794904i	−0.340928	−	0.940089i	$-0.610741\pi$
$439$	0.0457595	−	0.0166551i	0.00218398	−	0.000794904i	0.343112	+	0.939295i	$0.388519\pi$
$440$	0.573978	−	3.25519i	0.0273633	−	0.155185i
$441$	2.54189	+	2.13290i	0.121042	+	0.101567i
$442$	11.0890	−	9.30477i	0.527450	−	0.442583i
$443$	1.85298			0.0880376			0.0440188	−	0.999031i	$-0.485984\pi$
$443$	1.85298			0.0880376			0.0440188	+	0.999031i	$0.485984\pi$
$444$	1.56506	+	1.00086i	0.0742742	+	0.0474988i
$445$	0.733793			0.0347851
$446$	−0.118555	+	0.0994798i	−0.00561376	+	0.00471050i
$447$	−14.4474	−	12.1228i	−0.683340	−	0.573390i
$448$	−2.51501	+	14.2634i	−0.118823	+	0.673880i
$449$	−21.0300	+	7.65430i	−0.992468	+	0.361229i	−0.786676	−	0.617367i	$-0.788200\pi$
$449$	−21.0300	+	7.65430i	−0.992468	+	0.361229i	−0.205793	+	0.978596i	$0.565977\pi$
$450$	−15.4115			−0.726504
$451$	6.02481	−	2.19285i	0.283697	−	0.103257i
$452$	2.06418	+	3.57526i	0.0970908	+	0.168166i
$453$	−3.51677	−	19.9446i	−0.165232	−	0.937079i
$454$	2.20574	−	3.82045i	0.103520	−	0.179303i
$455$	−1.00000	−	1.73205i	−0.0468807	−	0.0811998i
$456$	−11.2135	+	9.40923i	−0.525119	+	0.440627i
$457$	0.775540	−	4.39831i	0.0362782	−	0.205744i	−0.961281	−	0.275570i	$-0.911133\pi$
$457$	0.775540	−	4.39831i	0.0362782	−	0.205744i	0.997559	+	0.0698262i	$0.0222445\pi$
$458$	−14.2986	+	24.7659i	−0.668130	+	1.15723i
$459$	33.2670	+	12.1082i	1.55277	+	0.565162i
$460$	−0.147956	−	0.0538515i	−0.00689848	−	0.00251084i
$461$	0.642026	+	3.64111i	0.0299021	+	0.169583i	0.996102	−	0.0882116i	$-0.0281152\pi$
$461$	0.642026	+	3.64111i	0.0299021	+	0.169583i	−0.966200	+	0.257795i	$0.917004\pi$
$462$	4.55303	+	3.82045i	0.211826	+	0.177743i
$463$	−1.78312	−	1.49621i	−0.0828685	−	0.0695350i	0.600412	−	0.799691i	$-0.295003\pi$
$463$	−1.78312	−	1.49621i	−0.0828685	−	0.0695350i	−0.683281	+	0.730156i	$0.739448\pi$
$464$	−4.52300	−	25.6512i	−0.209975	−	1.19083i
$465$	−2.33275	−	0.849051i	−0.108179	−	0.0393738i
$466$	15.0778	+	5.48789i	0.698468	+	0.254222i
$467$	0.329755	−	0.571153i	0.0152593	−	0.0264298i	−0.858295	−	0.513157i	$-0.828476\pi$
$467$	0.329755	−	0.571153i	0.0152593	−	0.0264298i	0.873554	+	0.486727i	$0.161809\pi$
$468$	0.164725	−	0.934204i	0.00761443	−	0.0431836i
$469$	−8.34002	+	6.99811i	−0.385106	+	0.323143i
$470$	−4.29086	−	7.43199i	−0.197923	−	0.342812i
$471$	−1.36231	+	2.35959i	−0.0627720	+	0.108724i
$472$	−3.18732	−	18.0762i	−0.146708	−	0.832024i
$473$	8.33022	+	14.4284i	0.383024	+	0.663417i
$474$	−10.6027	+	3.85905i	−0.486996	+	0.177252i
$475$	29.6982			1.36265
$476$	5.90033	−	2.14754i	0.270441	−	0.0984325i
$477$	3.29339	−	18.6777i	0.150794	−	0.855194i
$478$	15.7233	+	13.1934i	0.719166	+	0.603452i
$479$	−32.9197	+	27.6229i	−1.50414	+	1.26212i	−0.629849	+	0.776718i	$0.716883\pi$
$479$	−32.9197	+	27.6229i	−1.50414	+	1.26212i	−0.874290	+	0.485405i	$0.838672\pi$
$480$	1.18716			0.0541860
$481$	−7.39945	+	0.961130i	−0.337386	+	0.0438237i
$482$	−27.6774			−1.26067
$483$	−1.03209	+	0.866025i	−0.0469617	+	0.0394055i
$484$	−1.98680	−	1.66712i	−0.0903089	−	0.0757782i
$485$	−1.58853	+	9.00898i	−0.0721312	+	0.409077i
$486$	23.1917	−	8.44107i	1.05199	−	0.382895i
$487$	−8.61175			−0.390236			−0.195118	−	0.980780i	$-0.562509\pi$
$487$	−8.61175			−0.390236			−0.195118	+	0.980780i	$0.562509\pi$
$488$	−10.8366	+	3.94421i	−0.490551	+	0.178546i
$489$	−7.76857	−	13.4556i	−0.351307	−	0.608481i
$490$	0.275378	+	1.56175i	0.0124403	+	0.0705525i
$491$	3.70692	−	6.42057i	0.167291	−	0.289756i	−0.770176	−	0.637832i	$-0.779831\pi$
$491$	3.70692	−	6.42057i	0.167291	−	0.289756i	0.937466	+	0.348076i	$0.113165\pi$
$492$	0.520945	+	0.902302i	0.0234860	+	0.0406789i
$493$	33.6000	−	28.1937i	1.51327	−	1.26978i
$494$	−2.14543	+	12.1673i	−0.0965274	+	0.547434i
$495$	1.45336	−	2.51730i	0.0653238	−	0.113144i
$496$	17.4684	+	6.35797i	0.784353	+	0.285481i
$497$	14.9251	+	5.43231i	0.669484	+	0.243672i
$498$	1.75237	+	9.93821i	0.0785258	+	0.445342i
$499$	2.27513	+	1.90906i	0.101849	+	0.0854613i	0.692290	−	0.721619i	$-0.256602\pi$
$499$	2.27513	+	1.90906i	0.101849	+	0.0854613i	−0.590441	+	0.807081i	$0.701046\pi$
$500$	−1.75877	−	1.47578i	−0.0786546	−	0.0659991i
$501$	1.11438	+	6.31996i	0.0497868	+	0.282355i
$502$	30.4158	+	11.0704i	1.35752	+	0.494098i
$503$	4.93882	+	1.79758i	0.220211	+	0.0801502i	0.449770	−	0.893145i	$-0.351506\pi$
$503$	4.93882	+	1.79758i	0.220211	+	0.0801502i	−0.229559	+	0.973295i	$0.573728\pi$
$504$	−6.61721	+	11.4613i	−0.294754	+	0.510529i
$505$	0.879385	−	4.98724i	0.0391321	−	0.221929i
$506$	−1.43969	+	1.20805i	−0.0640021	+	0.0537042i
$507$	5.05438	+	8.75444i	0.224473	+	0.388798i
$508$	−1.19934	+	2.07732i	−0.0532121	+	0.0921661i
$509$	−5.57785	−	31.6335i	−0.247234	−	1.40213i	−0.815247	−	0.579113i	$-0.803399\pi$
$509$	−5.57785	−	31.6335i	−0.247234	−	1.40213i	0.568013	−	0.823019i	$-0.307712\pi$
$510$	3.60401	+	6.24232i	0.159588	+	0.276415i
$511$	4.09627	−	1.49092i	0.181208	−	0.0659544i
$512$	14.2736			0.630811
$513$	−28.3935	+	10.3344i	−1.25360	+	0.456275i
$514$	0.200522	−	1.13722i	0.00884467	−	0.0501606i
$515$	−9.10607	−	7.64090i	−0.401261	−	0.336698i
$516$	−2.07398	+	1.74027i	−0.0913018	+	0.0766113i
$517$	−15.1557			−0.666547
$518$	−21.3485	−	4.77163i	−0.937998	−	0.209653i
$519$	0.344608			0.0151266
$520$	−1.65270	+	1.38678i	−0.0724758	+	0.0608145i
$521$	5.22668	+	4.38571i	0.228985	+	0.192141i	0.750060	−	0.661369i	$-0.230024\pi$
$521$	5.22668	+	4.38571i	0.228985	+	0.192141i	−0.521075	+	0.853511i	$0.674469\pi$
$522$	3.37346	−	19.1318i	0.147652	−	0.837377i
$523$	9.80200	−	3.56764i	0.428612	−	0.156002i	−0.118701	−	0.992930i	$-0.537873\pi$
$523$	9.80200	−	3.56764i	0.428612	−	0.156002i	0.547313	+	0.836928i	$0.315651\pi$
$524$	−2.55169			−0.111471
$525$	−8.76264	+	3.18934i	−0.382433	+	0.139194i
$526$	−3.74897	−	6.49341i	−0.163463	−	0.283126i
$527$	5.43582	+	30.8281i	0.236788	+	1.34289i
$528$	3.77972	−	6.54666i	0.164491	−	0.284907i
$529$	11.2870	+	19.5496i	0.490739	+	0.849984i
$530$	6.94356	−	5.82634i	0.301609	−	0.253080i
$531$	2.80288	−	15.8959i	0.121635	−	0.689825i
$532$	−2.67958	+	4.64117i	−0.116174	+	0.201220i
$533$	−3.93242	−	1.43128i	−0.170332	−	0.0619958i
$534$	1.33750	+	0.486809i	0.0578791	+	0.0210663i
$535$	−0.798905	−	4.53081i	−0.0345397	−	0.195884i
$536$	8.99660	+	7.54904i	0.388594	+	0.326069i
$537$	5.23989	+	4.39679i	0.226118	+	0.189735i
$538$	4.24241	+	24.0599i	0.182903	+	1.03730i
$539$	2.63176	+	0.957882i	0.113358	+	0.0412589i
$540$	1.04189	+	0.379217i	0.0448358	+	0.0163189i
$541$	2.31861	−	4.01595i	0.0996849	−	0.172659i	−0.811869	−	0.583839i	$-0.801550\pi$
$541$	2.31861	−	4.01595i	0.0996849	−	0.172659i	0.911554	+	0.411180i	$0.134883\pi$
$542$	2.84595	−	16.1402i	0.122244	−	0.693281i
$543$	−7.35369	+	6.17048i	−0.315577	+	0.264801i
$544$	−7.48499	−	12.9644i	−0.320916	−	0.555843i
$545$	−2.36009	+	4.08780i	−0.101095	+	0.175102i
$546$	−0.673648	−	3.82045i	−0.0288295	−	0.163500i
$547$	16.3692	+	28.3522i	0.699895	+	1.21225i	0.968502	+	0.249004i	$0.0801034\pi$
$547$	16.3692	+	28.3522i	0.699895	+	1.21225i	−0.268607	+	0.963250i	$0.586563\pi$
$548$	−2.69681	+	0.981560i	−0.115202	+	0.0419302i
$549$	−10.1411			−0.432814
$550$	−12.2233	+	4.44891i	−0.521202	+	0.189702i
$551$	−6.50072	+	36.8674i	−0.276940	+	1.57060i
$552$	1.11334	+	0.934204i	0.0473869	+	0.0397624i
$553$	15.0587	−	12.6358i	0.640362	−	0.537327i
$554$	−15.4715			−0.657322
$555$	0.168490	−	3.71162i	0.00715200	−	0.157549i
$556$	1.16344			0.0493407
$557$	−34.6875	+	29.1063i	−1.46976	+	1.23327i	−0.553399	+	0.832916i	$0.686669\pi$
$557$	−34.6875	+	29.1063i	−1.46976	+	1.23327i	−0.916359	+	0.400357i	$0.868886\pi$
$558$	10.6211	+	8.91215i	0.449626	+	0.377281i
$559$	1.88831	−	10.7091i	0.0798669	−	0.452948i
$560$	−7.00774	+	2.55061i	−0.296131	+	0.107783i
$561$	12.7297			0.537447
$562$	8.94356	−	3.25519i	0.377261	−	0.137312i
$563$	12.4017	+	21.4803i	0.522668	+	0.905288i	0.999652	+	0.0263759i	$0.00839668\pi$
$563$	12.4017	+	21.4803i	0.522668	+	0.905288i	−0.476984	+	0.878912i	$0.658270\pi$
$564$	−0.427671	−	2.42544i	−0.0180082	−	0.102130i
$565$	4.12836	−	7.15052i	0.173681	−	0.300825i
$566$	−2.56939	−	4.45032i	−0.108000	−	0.187061i
$567$	−4.74376	+	3.98048i	−0.199219	+	0.167165i
$568$	2.97519	−	16.8731i	0.124836	−	0.707980i
$569$	16.6591	−	28.8544i	0.698386	−	1.20964i	−0.270640	−	0.962681i	$-0.587235\pi$
$569$	16.6591	−	28.8544i	0.698386	−	1.20964i	0.969026	−	0.246959i	$-0.0794313\pi$
$570$	−5.78106	−	2.10413i	−0.242142	−	0.0881325i
$571$	−17.2271	−	6.27017i	−0.720934	−	0.262398i	−0.0446116	−	0.999004i	$-0.514205\pi$
$571$	−17.2271	−	6.27017i	−0.720934	−	0.262398i	−0.676322	+	0.736606i	$0.736427\pi$
$572$	−0.139033	−	0.788496i	−0.00581326	−	0.0329687i
$573$	8.99479	+	7.54752i	0.375763	+	0.315302i
$574$	−9.39827	−	7.88609i	−0.392276	−	0.329159i
$575$	−0.512022	−	2.90382i	−0.0213528	−	0.121098i
$576$	12.9106	+	4.69907i	0.537942	+	0.195795i
$577$	−29.7679	−	10.8346i	−1.23925	−	0.451051i	−0.362496	−	0.931985i	$-0.618075\pi$
$577$	−29.7679	−	10.8346i	−1.23925	−	0.451051i	−0.876756	+	0.480935i	$0.840297\pi$
$578$	32.4236	−	56.1592i	1.34864	−	2.33592i
$579$	0.543948	−	3.08489i	0.0226057	−	0.128203i
$580$	1.05232	−	0.883000i	0.0436951	−	0.0366646i
$581$	−8.79086	−	15.2262i	−0.364706	−	0.631690i
$582$	−8.87211	+	15.3669i	−0.367761	+	0.636980i
$583$	−2.77972	−	15.7645i	−0.115124	−	0.652901i
$584$	−2.35117	−	4.07234i	−0.0972920	−	0.168515i
$585$	−1.78281	+	0.648891i	−0.0737103	+	0.0268283i
$586$	−47.4843			−1.96156
$587$	−2.00640	+	0.730269i	−0.0828129	+	0.0301414i	−0.383094	−	0.923709i	$-0.625142\pi$
$587$	−2.00640	+	0.730269i	−0.0828129	+	0.0301414i	0.300282	+	0.953851i	$0.402919\pi$
$588$	−0.0790304	+	0.448204i	−0.00325916	+	0.0184836i
$589$	−20.4670	−	17.1739i	−0.843329	−	0.707637i
$590$	5.90941	−	4.95859i	0.243287	−	0.204142i
$591$	−4.76558			−0.196030
$592$	−1.26171	+	27.7938i	−0.0518558	+	1.14232i
$593$	15.1807			0.623396			0.311698	−	0.950181i	$-0.399102\pi$
$593$	15.1807			0.623396			0.311698	+	0.950181i	$0.399102\pi$
$594$	10.1382	−	8.50692i	0.415974	−	0.349043i
$595$	−9.61999	−	8.07213i	−0.394381	−	0.330925i
$596$	−1.29339	+	7.33515i	−0.0529791	+	0.300460i
$597$	15.4265	−	5.61478i	0.631364	−	0.229798i
$598$	1.22668			0.0501627
$599$	−13.5915	+	4.94691i	−0.555334	+	0.202125i	−0.604415	−	0.796670i	$-0.706593\pi$
$599$	−13.5915	+	4.94691i	−0.555334	+	0.202125i	0.0490806	+	0.998795i	$0.484371\pi$
$600$	5.02956	+	8.71146i	0.205331	+	0.355644i
$601$	−5.98973	−	33.9695i	−0.244326	−	1.38564i	−0.822052	−	0.569412i	$-0.807171\pi$
$601$	−5.98973	−	33.9695i	−0.244326	−	1.38564i	0.577726	−	0.816231i	$-0.303940\pi$
$602$	15.9402	−	27.6092i	0.649672	−	1.12527i
$603$	5.16385	+	8.94405i	0.210288	+	0.364230i
$604$	−6.12701	+	5.14117i	−0.249305	+	0.209191i
$605$	−0.900740	+	5.10835i	−0.0366203	+	0.207684i
$606$	4.91147	−	8.50692i	0.199515	−	0.345570i
$607$	−5.62361	−	2.04683i	−0.228255	−	0.0830781i	0.225361	−	0.974275i	$-0.427644\pi$
$607$	−5.62361	−	2.04683i	−0.228255	−	0.0830781i	−0.453616	+	0.891197i	$0.649866\pi$
$608$	12.0064	+	4.36997i	0.486924	+	0.177226i
$609$	−2.04117	−	11.5761i	−0.0827125	−	0.469086i
$610$	−3.71276	−	3.11538i	−0.150325	−	0.126138i
$611$	7.57785	+	6.35857i	0.306567	+	0.257240i
$612$	−1.03431	−	5.86587i	−0.0418095	−	0.237114i
$613$	14.3782	+	5.23324i	0.580730	+	0.211368i	0.615647	−	0.788022i	$-0.288895\pi$
$613$	14.3782	+	5.23324i	0.580730	+	0.211368i	−0.0349173	+	0.999390i	$0.511117\pi$
$614$	23.0535	+	8.39079i	0.930364	+	0.338625i
$615$	1.04189	−	1.80460i	0.0420130	−	0.0727687i
$616$	−1.93969	+	11.0005i	−0.0781524	+	0.443225i
$617$	0.131759	−	0.110559i	0.00530442	−	0.00445094i	−0.640132	−	0.768265i	$-0.721120\pi$
$617$	0.131759	−	0.110559i	0.00530442	−	0.00445094i	0.645436	+	0.763814i	$0.276676\pi$
$618$	−11.5287	−	19.9683i	−0.463752	−	0.803242i
$619$	−15.5621	+	26.9544i	−0.625494	+	1.08339i	0.362951	+	0.931808i	$0.381769\pi$
$619$	−15.5621	+	26.9544i	−0.625494	+	1.08339i	−0.988445	+	0.151580i	$0.951564\pi$
$620$	0.170245	+	0.965505i	0.00683719	+	0.0387756i
$621$	1.50000	+	2.59808i	0.0601929	+	0.104257i
$622$	38.2879	−	13.9357i	1.53521	−	0.558769i
$623$	−2.47977			−0.0993499
$624$	−4.63651	+	1.68755i	−0.185609	+	0.0675561i
$625$	3.12495	−	17.7225i	0.124998	−	0.708899i
$626$	−4.72984	−	3.96880i	−0.189042	−	0.158625i
$627$	−8.32295	+	6.98378i	−0.332387	+	0.278905i
$628$	1.07604			0.0429386
$629$	−41.5951	+	21.5616i	−1.65851	+	0.859719i
$630$	−5.56212			−0.221600
$631$	−23.1630	+	19.4360i	−0.922103	+	0.773737i	−0.974383	−	0.224896i	$-0.927796\pi$
$631$	−23.1630	+	19.4360i	−0.922103	+	0.773737i	0.0522795	+	0.998632i	$0.483351\pi$
$632$	−16.2442	−	13.6305i	−0.646160	−	0.542193i
$633$	−3.20233	+	18.1613i	−0.127281	+	0.721848i
$634$	31.9786	−	11.6393i	1.27003	−	0.462255i
$635$	4.79736			0.190377
$636$	2.44444	−	0.889704i	0.0969284	−	0.0352790i
$637$	−0.914000	−	1.58310i	−0.0362140	−	0.0627245i
$638$	−2.84730	−	16.1478i	−0.112726	−	0.639298i
$639$	7.53343	−	13.0483i	0.298018	−	0.516182i
$640$	4.63310	+	8.02477i	0.183139	+	0.317207i
$641$	26.9636	−	22.6252i	1.06500	−	0.893641i	0.0704093	−	0.997518i	$-0.477569\pi$
$641$	26.9636	−	22.6252i	1.06500	−	0.893641i	0.994590	+	0.103878i	$0.0331250\pi$
$642$	1.54963	−	8.78839i	0.0611590	−	0.346850i
$643$	−17.6297	+	30.5355i	−0.695247	+	1.20420i	0.274850	+	0.961487i	$0.411372\pi$
$643$	−17.6297	+	30.5355i	−0.695247	+	1.20420i	−0.970097	+	0.242717i	$0.921961\pi$
$644$	0.500000	+	0.181985i	0.0197028	+	0.00717122i
$645$	5.08822	+	1.85196i	0.200349	+	0.0729209i
$646$	13.4712	+	76.3987i	0.530015	+	3.00587i
$647$	19.8496	+	16.6558i	0.780367	+	0.654806i	0.943341	−	0.331824i	$-0.107664\pi$
$647$	19.8496	+	16.6558i	0.780367	+	0.654806i	−0.162974	+	0.986630i	$0.552109\pi$
$648$	5.11721	+	4.29385i	0.201023	+	0.168678i
$649$	−2.36571	−	13.4166i	−0.0928624	−	0.526649i
$650$	7.97818	+	2.90382i	0.312930	+	0.113897i
$651$	7.88326	+	2.86927i	0.308969	+	0.112456i
$652$	−3.06805	+	5.31402i	−0.120154	+	0.208113i
$653$	2.06118	−	11.6896i	0.0806604	−	0.457448i	−0.917549	−	0.397624i	$-0.869835\pi$
$653$	2.06118	−	11.6896i	0.0806604	−	0.457448i	0.998209	−	0.0598240i	$-0.0190540\pi$
$654$	−7.01367	+	5.88517i	−0.274256	+	0.230128i
$655$	2.55169	+	4.41966i	0.0997027	+	0.172690i
$656$	−7.80200	+	13.5135i	−0.304617	+	0.527612i
$657$	−0.718063	−	4.07234i	−0.0280143	−	0.158877i
$658$	14.5005	+	25.1155i	0.565287	+	0.979106i
$659$	26.1018	−	9.50027i	1.01678	−	0.370078i	0.220748	−	0.975331i	$-0.429150\pi$
$659$	26.1018	−	9.50027i	1.01678	−	0.370078i	0.796033	+	0.605253i	$0.206928\pi$
$660$	0.398681			0.0155186
$661$	−10.1429	+	3.69171i	−0.394513	+	0.143591i	−0.531656	−	0.846960i	$-0.678430\pi$
$661$	−10.1429	+	3.69171i	−0.394513	+	0.143591i	0.137143	+	0.990551i	$0.456208\pi$
$662$	−3.04008	+	17.2411i	−0.118156	+	0.670096i
$663$	−6.36484	−	5.34073i	−0.247190	−	0.207417i
$664$	−14.5287	+	12.1910i	−0.563822	+	0.473103i
$665$	10.7183			0.415638
$666$	−7.97431	+	19.1578i	−0.308998	+	0.742351i
$667$	3.71688			0.143918
$668$	1.94150	−	1.62911i	0.0751190	−	0.0630324i
$669$	0.0680482	+	0.0570992i	0.00263089	+	0.00220758i
$670$	−0.857097	+	4.86084i	−0.0331125	+	0.187790i
$671$	−8.04323	+	2.92750i	−0.310506	+	0.113015i
$672$	−4.01186			−0.154761
$673$	−41.5531	+	15.1241i	−1.60175	+	0.582991i	−0.979785	−	0.200052i	$-0.935889\pi$
$673$	−41.5531	+	15.1241i	−1.60175	+	0.582991i	−0.621969	+	0.783042i	$0.713667\pi$
$674$	17.5758	+	30.4422i	0.676994	+	1.17259i
$675$	3.60560	+	20.4484i	0.138780	+	0.787058i
$676$	1.99613	−	3.45740i	0.0767742	−	0.132977i
$677$	13.1245	+	22.7323i	0.504415	+	0.873672i	0.999987	+	0.00510546i	$0.00162512\pi$
$677$	13.1245	+	22.7323i	0.504415	+	0.873672i	−0.495572	+	0.868567i	$0.665042\pi$
$678$	12.2686	−	10.2946i	0.471172	−	0.395360i
$679$	5.36824	−	30.4448i	0.206014	−	1.16836i
$680$	−6.77332	+	11.7317i	−0.259745	+	0.449891i
$681$	−2.37939	−	0.866025i	−0.0911782	−	0.0331862i
$682$	10.9966	+	4.00243i	0.421081	+	0.153261i
$683$	−2.84049	−	16.1092i	−0.108688	−	0.616402i	−0.989683	−	0.143276i	$-0.954236\pi$
$683$	−2.84049	−	16.1092i	−0.108688	−	0.616402i	0.880995	−	0.473126i	$-0.156875\pi$
$684$	3.89440	+	3.26779i	0.148906	+	0.124947i
$685$	4.39693	+	3.68946i	0.167998	+	0.140967i
$686$	−5.30200	−	30.0692i	−0.202431	−	1.14805i
$687$	15.4243	+	5.61397i	0.588473	+	0.214186i
$688$	−38.1023	−	13.8681i	−1.45263	−	0.528716i
$689$	−5.22416	+	9.04850i	−0.199024	+	0.344720i
$690$	−0.106067	+	0.601535i	−0.00403790	+	0.0229000i
$691$	29.6753	−	24.9005i	1.12890	−	0.947261i	0.129882	−	0.991529i	$-0.458540\pi$
$691$	29.6753	−	24.9005i	1.12890	−	0.947261i	0.999020	+	0.0442686i	$0.0140958\pi$
$692$	−0.0680482	−	0.117863i	−0.00258680	−	0.00448047i
$693$	−4.91147	+	8.50692i	−0.186571	+	0.323151i
$694$	−2.76217	−	15.6651i	−0.104851	−	0.594638i
$695$	−1.16344	−	2.01513i	−0.0441317	−	0.0764383i
$696$	−11.9153	+	4.33683i	−0.451650	+	0.164387i
$697$	−26.2763			−0.995286
$698$	−9.77972	+	3.55953i	−0.370168	+	0.134730i
$699$	1.59926	−	9.06985i	0.0604896	−	0.343053i
$700$	2.82114	+	2.36722i	0.106629	+	0.0894723i
$701$	33.4347	−	28.0550i	1.26281	−	1.05962i	0.267434	−	0.963576i	$-0.413824\pi$
$701$	33.4347	−	28.0550i	1.26281	−	1.05962i	0.995377	−	0.0960482i	$-0.0306203\pi$
$702$	−8.63816			−0.326026
$703$	15.3666	−	36.9175i	0.579564	−	1.39237i
$704$	11.5963			0.437051
$705$	−3.77332	+	3.16619i	−0.142111	+	0.119246i
$706$	−36.6844	−	30.7819i	−1.38063	−	1.15849i
$707$	−2.97178	+	16.8538i	−0.111765	+	0.633853i
$708$	2.08037	−	0.757194i	0.0781853	−	0.0284571i
$709$	−6.67911			−0.250839			−0.125420	−	0.992104i	$-0.540028\pi$
$709$	−6.67911			−0.250839			−0.125420	+	0.992104i	$0.540028\pi$
$710$	6.76651	−	2.46281i	0.253943	−	0.0924276i
$711$	−9.32383	−	16.1493i	−0.349671	−	0.605648i
$712$	0.464508	+	2.63435i	0.0174082	+	0.0987266i
$713$	−1.32635	+	2.29731i	−0.0496723	+	0.0860349i
$714$	−12.1793	−	21.0952i	−0.455800	−	0.789469i
$715$	−1.22668	+	1.02931i	−0.0458753	+	0.0384939i
$716$	0.469093	−	2.66036i	0.0175308	−	0.0994223i
$717$	5.89053	−	10.2027i	0.219986	−	0.381027i
$718$	−11.0273	−	4.01362i	−0.411537	−	0.149787i
$719$	22.9457	+	8.35154i	0.855729	+	0.311460i	0.732374	−	0.680903i	$-0.238412\pi$
$719$	22.9457	+	8.35154i	0.855729	+	0.311460i	0.123355	+	0.992363i	$0.460634\pi$
$720$	1.22844	+	6.96681i	0.0457811	+	0.259638i
$721$	30.7729	+	25.8215i	1.14604	+	0.961644i
$722$	−28.4225	−	23.8493i	−1.05777	−	0.887578i
$723$	2.75861	+	15.6448i	0.102594	+	0.581838i
$724$	3.56253	+	1.29665i	0.132400	+	0.0481898i
$725$	24.1741	+	8.79866i	0.897804	+	0.326774i
$726$	−5.03074	+	8.71351i	−0.186708	+	0.323389i
$727$	−0.259237	+	1.47021i	−0.00961458	+	0.0545270i	−0.989238	−	0.146318i	$-0.953258\pi$
$727$	−0.259237	+	1.47021i	−0.00961458	+	0.0545270i	0.979623	+	0.200845i	$0.0643688\pi$
$728$	5.58512	−	4.68647i	0.206998	−	0.173692i
$729$	−3.12567	−	5.41381i	−0.115765	−	0.200512i
$730$	0.988140	−	1.71151i	0.0365727	−	0.0633458i
$731$	−11.8567	−	67.2426i	−0.438535	−	2.48706i
$732$	−0.695470	−	1.20459i	−0.0257053	−	0.0445229i
$733$	−4.47906	+	1.63024i	−0.165438	+	0.0602144i	−0.423411	−	0.905938i	$-0.639167\pi$
$733$	−4.47906	+	1.63024i	−0.165438	+	0.0602144i	0.257974	+	0.966152i	$0.416945\pi$
$734$	37.9668			1.40138
$735$	0.855342	−	0.311319i	0.0315498	−	0.0114832i
$736$	0.220285	−	1.24930i	0.00811981	−	0.0460497i
$737$	6.67752	+	5.60310i	0.245970	+	0.206393i
$738$	−8.91534	+	7.48086i	−0.328178	+	0.275374i
$739$	−12.6408			−0.465001			−0.232500	−	0.972596i	$-0.574691\pi$
$739$	−12.6408			−0.465001			−0.232500	+	0.972596i	$0.574691\pi$
$740$	−1.30272	+	0.675289i	−0.0478889	+	0.0248241i
$741$	7.09152			0.260513
$742$	−23.4650	+	19.6895i	−0.861426	+	0.722822i
$743$	−25.9629	−	21.7855i	−0.952487	−	0.799231i	0.0272276	−	0.999629i	$-0.491332\pi$
$743$	−25.9629	−	21.7855i	−0.952487	−	0.799231i	−0.979715	+	0.200398i	$0.935777\pi$
$744$	1.57145	−	8.91215i	0.0576122	−	0.326735i
$745$	13.9982	−	5.09494i	0.512856	−	0.186664i
$746$	−22.1557			−0.811178
$747$	−15.6725	+	5.70431i	−0.573426	+	0.208710i
$748$	−2.51367	−	4.35381i	−0.0919089	−	0.159191i
$749$	2.69981	+	15.3114i	0.0986488	+	0.559465i
$750$	−4.45336	+	7.71345i	−0.162614	+	0.281655i
$751$	2.42514	+	4.20047i	0.0884948	+	0.153277i	0.906875	−	0.421400i	$-0.138461\pi$
$751$	2.42514	+	4.20047i	0.0884948	+	0.153277i	−0.818380	+	0.574677i	$0.805128\pi$
$752$	28.2558	−	23.7095i	1.03038	−	0.864595i
$753$	3.22611	−	18.2962i	0.117566	−	0.666750i
$754$	−5.35117	+	9.26849i	−0.194878	+	0.337539i
$755$	15.0318	+	5.47112i	0.547063	+	0.199115i
$756$	−3.52094	−	1.28152i	−0.128056	−	0.0466084i
$757$	2.02987	+	11.5119i	0.0737768	+	0.418409i	0.999219	+	0.0395197i	$0.0125828\pi$
$757$	2.02987	+	11.5119i	0.0737768	+	0.418409i	−0.925442	+	0.378889i	$0.876306\pi$
$758$	−27.7119	−	23.2530i	−1.00654	−	0.844588i
$759$	0.826352	+	0.693392i	0.0299947	+	0.0251685i
$760$	−2.00774	−	11.3865i	−0.0728284	−	0.413030i
$761$	9.93154	+	3.61479i	0.360018	+	0.131036i	0.515695	−	0.856772i	$-0.327534\pi$
$761$	9.93154	+	3.61479i	0.360018	+	0.131036i	−0.155677	+	0.987808i	$0.549756\pi$
$762$	8.74422	+	3.18264i	0.316770	+	0.115295i
$763$	7.97565	−	13.8142i	0.288738	−	0.500109i
$764$	0.805245	−	4.56677i	0.0291327	−	0.165220i
$765$	−9.12567	+	7.65734i	−0.329939	+	0.276852i
$766$	11.6322	+	20.1476i	0.420289	+	0.727963i
$767$	−4.44609	+	7.70085i	−0.160539	+	0.278062i
$768$	1.23664	+	7.01336i	0.0446235	+	0.253073i
$769$	5.23396	+	9.06548i	0.188741	+	0.326909i	0.944831	−	0.327559i	$-0.106226\pi$
$769$	5.23396	+	9.06548i	0.188741	+	0.326909i	−0.756090	+	0.654468i	$0.772893\pi$
$770$	−4.41147	+	1.60565i	−0.158978	+	0.0578634i
$771$	−0.662809			−0.0238705
$772$	−1.16250	+	0.423117i	−0.0418394	+	0.0152283i
$773$	−3.70368	+	21.0046i	−0.133212	+	0.755483i	0.842876	+	0.538108i	$0.180861\pi$
$773$	−3.70368	+	21.0046i	−0.133212	+	0.755483i	−0.976088	+	0.217375i	$0.930250\pi$
$774$	−23.1668	−	19.4393i	−0.832715	−	0.698731i
$775$	−14.0646	+	11.8016i	−0.505217	+	0.423927i
$776$	−33.3482			−1.19713
$777$	−0.569392	+	12.5430i	−0.0204268	+	0.449977i
$778$	7.76651			0.278443
$779$	17.1800	−	14.4158i	0.615539	−	0.516499i
$780$	−0.199340	−	0.167266i	−0.00713753	−	0.00598910i
$781$	2.20826	−	12.5237i	0.0790179	−	0.448133i
$782$	7.23783	−	2.63435i	0.258824	−	0.0942043i
$783$	−26.1739			−0.935378
$784$	−6.40508	+	2.33126i	−0.228753	+	0.0832592i
$785$	−1.07604	−	1.86375i	−0.0384054	−	0.0665201i
$786$	1.71894	+	9.74860i	0.0613126	+	0.347721i
$787$	−4.53730	+	7.85884i	−0.161737	+	0.280137i	−0.935492	−	0.353348i	$-0.885043\pi$
$787$	−4.53730	+	7.85884i	−0.161737	+	0.280137i	0.773754	+	0.633486i	$0.218376\pi$
$788$	0.941037	+	1.62992i	0.0335230	+	0.0580636i
$789$	−3.29679	+	2.76633i	−0.117369	+	0.0984841i
$790$	1.54757	−	8.77671i	0.0550601	−	0.312261i
$791$	−13.9513	+	24.1644i	−0.496051	+	0.859186i
$792$	9.95723	+	3.62414i	0.353815	+	0.128778i
$793$	5.24985	+	1.91079i	0.186428	+	0.0678541i
$794$	1.49335	+	8.46924i	0.0529972	+	0.300562i
$795$	−3.98545	−	3.34419i	−0.141349	−	0.118606i
$796$	−4.96657	−	4.16744i	−0.176035	−	0.147711i
$797$	5.11974	+	29.0355i	0.181350	+	1.02849i	0.930555	+	0.366151i	$0.119325\pi$
$797$	5.11974	+	29.0355i	0.181350	+	1.02849i	−0.749205	+	0.662338i	$0.769564\pi$
$798$	19.5364	+	7.11068i	0.691582	+	0.251715i
$799$	58.3671	+	21.2439i	2.06488	+	0.751555i
$800$	4.39006	−	7.60381i	0.155212	−	0.268835i
$801$	−0.408481	+	2.31661i	−0.0144330	+	0.0818534i
$802$	−4.28106	+	3.59224i	−0.151169	+	0.126846i
$803$	−1.74510	−	3.02260i	−0.0615832	−	0.106665i
$804$	−0.708263	+	1.22675i	−0.0249785	+	0.0432641i
$805$	−0.184793	−	1.04801i	−0.00651308	−	0.0369375i
$806$	−3.81908	−	6.61484i	−0.134521	−	0.232998i
$807$	13.1772	−	4.79611i	0.463860	−	0.168831i
$808$	18.4611			0.649459
$809$	−30.3105	+	11.0321i	−1.06566	+	0.387869i	−0.814552	−	0.580090i	$-0.803017\pi$
$809$	−30.3105	+	11.0321i	−1.06566	+	0.387869i	−0.251109	+	0.967959i	$0.580795\pi$
$810$	−0.487511	+	2.76481i	−0.0171294	+	0.0971457i
$811$	−27.6013	−	23.1603i	−0.969213	−	0.813267i	0.0132138	−	0.999913i	$-0.495794\pi$
$811$	−27.6013	−	23.1603i	−0.969213	−	0.813267i	−0.982427	+	0.186646i	$0.940238\pi$
$812$	−3.55619	+	2.98400i	−0.124798	+	0.104718i
$813$	−9.40703			−0.329919
$814$	−0.794263	+	17.4966i	−0.0278389	+	0.613255i
$815$	12.2722			0.429876
$816$	−23.7328	+	19.9142i	−0.830815	+	0.697137i
$817$	44.6430	+	37.4599i	1.56186	+	1.31056i
$818$	−4.30381	+	24.4081i	−0.150479	+	0.853411i
$819$	6.02481	−	2.19285i	0.210524	−	0.0766245i
$820$	−0.822948			−0.0287386
$821$	45.9029	−	16.7073i	1.60202	−	0.583089i	0.622183	−	0.782872i	$-0.286246\pi$
$821$	45.9029	−	16.7073i	1.60202	−	0.583089i	0.979840	+	0.199784i	$0.0640239\pi$
$822$	5.56670	+	9.64181i	0.194161	+	0.336297i
$823$	−8.95012	−	50.7587i	−0.311982	−	1.76934i	−0.588667	−	0.808375i	$-0.700347\pi$
$823$	−8.95012	−	50.7587i	−0.311982	−	1.76934i	0.276686	−	0.960960i	$-0.410764\pi$
$824$	21.6668	−	37.5281i	0.754800	−	1.30735i
$825$	3.73308	+	6.46588i	0.129969	+	0.225113i
$826$	−19.9702	+	16.7570i	−0.694852	+	0.583050i
$827$	2.82542	−	16.0237i	0.0982494	−	0.557200i	−0.895454	−	0.445155i	$-0.853149\pi$
$827$	2.82542	−	16.0237i	0.0982494	−	0.557200i	0.993703	−	0.112045i	$-0.0357402\pi$
$828$	0.252374	−	0.437124i	0.00877060	−	0.0151911i
$829$	5.15270	+	1.87543i	0.178961	+	0.0651364i	0.429946	−	0.902854i	$-0.358532\pi$
$829$	5.15270	+	1.87543i	0.178961	+	0.0651364i	−0.250986	+	0.967991i	$0.580755\pi$
$830$	−7.49020	−	2.72621i	−0.259989	−	0.0946281i
$831$	1.54205	+	8.74541i	0.0534932	+	0.303375i
$832$	−5.79813	−	4.86521i	−0.201014	−	0.168671i
$833$	−8.79267	−	7.37793i	−0.304648	−	0.255630i
$834$	−0.783748	−	4.44485i	−0.0271390	−	0.153913i
$835$	−4.76321	−	1.73367i	−0.164838	−	0.0599961i
$836$	4.03209	+	1.46756i	0.139453	+	0.0507566i
$837$	9.34002	−	16.1774i	0.322838	−	0.559173i
$838$	1.91921	−	10.8844i	0.0662982	−	0.375996i
$839$	−19.8558	+	16.6610i	−0.685497	+	0.575200i	−0.917607	−	0.397490i	$-0.869882\pi$
$839$	−19.8558	+	16.6610i	−0.685497	+	0.575200i	0.232110	+	0.972690i	$0.425437\pi$
$840$	1.81521	+	3.14403i	0.0626306	+	0.108479i
$841$	−1.71419	+	2.96907i	−0.0591101	+	0.102382i
$842$	1.02506	+	5.81342i	0.0353260	+	0.200344i
$843$	−2.73143	−	4.73097i	−0.0940754	−	0.162943i
$844$	6.84389	−	2.49097i	0.235577	−	0.0857428i
$845$	−7.98452			−0.274676
$846$	25.8516	−	9.40923i	0.888797	−	0.323496i
$847$	3.04395	−	17.2631i	0.104591	−	0.593167i
$848$	29.8444	+	25.0424i	1.02486	+	0.859959i
$849$	−2.25949	+	1.89593i	−0.0775453	+	0.0650683i
$850$	53.3100			1.82852
$851$	−3.87464	−	0.866025i	−0.132821	−	0.0296870i
$852$	2.06654			0.0707986
$853$	−2.22803	+	1.86954i	−0.0762861	+	0.0640117i	−0.680133	−	0.733088i	$-0.738078\pi$
$853$	−2.22803	+	1.86954i	−0.0762861	+	0.0640117i	0.603847	+	0.797100i	$0.293634\pi$
$854$	12.5469	+	10.5281i	0.429345	+	0.360263i
$855$	1.76558	−	10.0131i	0.0603815	−	0.342440i
$856$	15.7601	−	5.73621i	0.538670	−	0.196060i
$857$	−19.5054			−0.666290			−0.333145	−	0.942876i	$-0.608110\pi$
$857$	−19.5054			−0.666290			−0.333145	+	0.942876i	$0.608110\pi$
$858$	−2.91875	+	1.06234i	−0.0996444	+	0.0362676i
$859$	20.4187	+	35.3663i	0.696679	+	1.20668i	0.969612	+	0.244650i	$0.0786730\pi$
$859$	20.4187	+	35.3663i	0.696679	+	1.20668i	−0.272933	+	0.962033i	$0.587994\pi$
$860$	−0.371340	−	2.10597i	−0.0126626	−	0.0718131i
$861$	−3.52094	+	6.09845i	−0.119993	+	0.207835i
$862$	−4.74557	−	8.21956i	−0.161635	−	0.279959i
$863$	−33.4491	+	28.0671i	−1.13862	+	0.955416i	−0.999393	−	0.0348448i	$-0.988906\pi$
$863$	−33.4491	+	28.0671i	−1.13862	+	0.955416i	−0.139227	+	0.990260i	$0.544462\pi$
$864$	−1.55122	+	8.79742i	−0.0527737	+	0.299294i
$865$	−0.136096	+	0.235726i	−0.00462741	+	0.00801492i
$866$	−16.1099	−	5.86354i	−0.547438	−	0.199251i
$867$	−34.9761	−	12.7303i	−1.18785	−	0.432343i
$868$	−0.575322	−	3.26281i	−0.0195277	−	0.110747i
$869$	−12.0569	−	10.1169i	−0.409002	−	0.343194i
$870$	−4.08235	−	3.42550i	−0.138405	−	0.116135i
$871$	−0.987978	−	5.60310i	−0.0334764	−	0.189854i
$872$	−16.1694	−	5.88517i	−0.547564	−	0.199297i
$873$	−27.5574	−	10.0301i	−0.932676	−	0.339466i
$874$	−3.28699	+	5.69323i	−0.111184	+	0.192576i
$875$	2.69459	−	15.2818i	0.0910939	−	0.516619i
$876$	0.434478	−	0.364570i	0.0146797	−	0.0123177i
$877$	−10.5405	−	18.2568i	−0.355929	−	0.616487i	0.631348	−	0.775500i	$-0.282502\pi$
$877$	−10.5405	−	18.2568i	−0.355929	−	0.616487i	−0.987276	+	0.159013i	$0.949169\pi$
$878$	−0.0373035	+	0.0646115i	−0.00125893	+	0.00218053i
$879$	4.73277	+	26.8409i	0.159632	+	0.905321i
$880$	2.98545	+	5.17095i	0.100640	+	0.174313i
$881$	7.25537	−	2.64074i	0.244440	−	0.0889687i	−0.216895	−	0.976195i	$-0.569593\pi$
$881$	7.25537	−	2.64074i	0.244440	−	0.0889687i	0.461335	+	0.887226i	$0.347371\pi$
$882$	−5.08378			−0.171180
$883$	11.2297	−	4.08727i	0.377909	−	0.137547i	−0.146080	−	0.989273i	$-0.546666\pi$
$883$	11.2297	−	4.08727i	0.377909	−	0.137547i	0.523989	+	0.851725i	$0.324443\pi$
$884$	−0.569803	+	3.23151i	−0.0191645	+	0.108688i
$885$	−3.39187	−	2.84612i	−0.114017	−	0.0956713i
$886$	−2.17474	+	1.82483i	−0.0730620	+	0.0613063i
$887$	30.8667			1.03640			0.518201	−	0.855259i	$-0.326602\pi$
$887$	30.8667			1.03640			0.518201	+	0.855259i	$0.326602\pi$
$888$	13.4315	−	1.74465i	0.450733	−	0.0585466i
$889$	−16.2121			−0.543738
$890$	−0.861215	+	0.722645i	−0.0288680	+	0.0242231i
$891$	3.79813	+	3.18701i	0.127242	+	0.106769i
$892$	0.00609191	−	0.0345490i	0.000203972	−	0.00115678i
$893$	−49.8166	+	18.1318i	−1.66705	+	0.606756i
$894$	28.8949			0.966389
$895$	−5.07697	+	1.84787i	−0.169704	+	0.0617674i
$896$	−15.6570	−	27.1188i	−0.523065	−	0.905975i
$897$	−0.122264	−	0.693392i	−0.00408226	−	0.0231517i
$898$	17.1438	−	29.6940i	0.572097	−	0.990902i
$899$	−11.5719	−	20.0432i	−0.385945	−	0.668477i
$900$	2.67617	−	2.24558i	0.0892058	−	0.0748526i
$901$	−11.3922	+	64.6083i	−0.379528	+	2.15241i
$902$	−4.91147	+	8.50692i	−0.163534	+	0.283250i
$903$	−17.1951	−	6.25849i	−0.572216	−	0.208270i
$904$	28.2841	+	10.2946i	0.940714	+	0.342392i
$905$	−1.31666	−	7.46714i	−0.0437672	−	0.248216i
$906$	23.7690	+	19.9446i	0.789673	+	0.662615i
$907$	−38.7493	−	32.5145i	−1.28665	−	1.07963i	−0.992291	−	0.123931i	$-0.960450\pi$
$907$	−38.7493	−	32.5145i	−1.28665	−	1.07963i	−0.294358	−	0.955695i	$-0.595106\pi$
$908$	0.173648	+	0.984808i	0.00576272	+	0.0326820i
$909$	15.2554	+	5.55250i	0.505989	+	0.184165i
$910$	2.87939	+	1.04801i	0.0954507	+	0.0347412i
$911$	−9.76904	+	16.9205i	−0.323663	+	0.560600i	−0.981241	−	0.192786i	$-0.938248\pi$
$911$	−9.76904	+	16.9205i	−0.323663	+	0.560600i	0.657578	+	0.753386i	$0.271581\pi$
$912$	4.59168	−	26.0407i	0.152046	−	0.862294i
$913$	−10.7836	+	9.04850i	−0.356885	+	0.299462i
$914$	3.42127	+	5.92582i	0.113166	+	0.196009i
$915$	−1.39094	+	2.40918i	−0.0459831	+	0.0796450i
$916$	−1.12567	−	6.38398i	−0.0371931	−	0.210933i
$917$	−8.62314	−	14.9357i	−0.284761	−	0.493221i
$918$	−50.9680	+	18.5508i	−1.68219	+	0.612268i
$919$	38.5695			1.27229			0.636146	−	0.771569i	$-0.280528\pi$
$919$	38.5695			1.27229			0.636146	+	0.771569i	$0.280528\pi$
$920$	−1.07873	+	0.392624i	−0.0355645	+	0.0129444i
$921$	2.44521	−	13.8675i	0.0805725	−	0.456949i
$922$	−4.33931	−	3.64111i	−0.142907	−	0.119914i
$923$	−6.35844	+	5.33537i	−0.209291	+	0.175616i
$924$	−1.34730			−0.0443228
$925$	−23.1501	−	14.8046i	−0.761170	−	0.486773i
$926$	3.56624			0.117194
$927$	29.1917	−	24.4947i	0.958780	−	0.804512i
$928$	8.47843	+	7.11424i	0.278318	+	0.233537i
$929$	6.78271	−	38.4666i	0.222533	−	1.26205i	−0.644811	−	0.764342i	$-0.723064\pi$
$929$	6.78271	−	38.4666i	0.222533	−	1.26205i	0.867345	−	0.497708i	$-0.165825\pi$
$930$	3.57398	−	1.30082i	0.117195	−	0.0426556i
$931$	9.79654			0.321069
$932$	−3.41787	+	1.24400i	−0.111956	+	0.0407487i
$933$	−11.6934	−	20.2536i	−0.382825	−	0.663072i
$934$	0.175459	+	0.995078i	0.00574120	+	0.0325600i
$935$	−5.02734	+	8.70761i	−0.164412	+	0.284769i
$936$	−3.45811	−	5.98962i	−0.113032	−	0.195777i
$937$	7.96522	−	6.68362i	0.260212	−	0.218344i	−0.503343	−	0.864087i	$-0.667897\pi$
$937$	7.96522	−	6.68362i	0.260212	−	0.218344i	0.763555	+	0.645743i	$0.223452\pi$
$938$	2.89646	−	16.4266i	0.0945728	−	0.536349i
$939$	−1.77197	+	3.06915i	−0.0578262	+	0.100158i
$940$	1.82800	+	0.665338i	0.0596228	+	0.0217009i
$941$	34.4971	+	12.5559i	1.12457	+	0.409311i	0.836319	−	0.548243i	$-0.184703\pi$
$941$	34.4971	+	12.5559i	1.12457	+	0.409311i	0.288253	+	0.957554i	$0.406925\pi$
$942$	−0.724871	−	4.11095i	−0.0236176	−	0.133942i
$943$	−1.70574	−	1.43128i	−0.0555464	−	0.0466090i
$944$	25.3995	+	21.3127i	0.826682	+	0.693668i
$945$	1.30129	+	7.37997i	0.0423309	+	0.240071i
$946$	−23.9859	−	8.73016i	−0.779849	−	0.283842i
$947$	−23.1853	−	8.43874i	−0.753420	−	0.274222i	−0.0633757	−	0.997990i	$-0.520187\pi$
$947$	−23.1853	−	8.43874i	−0.753420	−	0.274222i	−0.690044	+	0.723767i	$0.742409\pi$
$948$	1.27884	−	2.21501i	0.0415347	−	0.0719402i
$949$	−0.395582	+	2.24346i	−0.0128411	+	0.0728257i
$950$	−34.8553	+	29.2470i	−1.13085	+	0.948899i
$951$	−9.76651	−	16.9161i	−0.316701	−	0.548542i
$952$	22.8897	−	39.6460i	0.741858	−	1.28494i
$953$	8.42292	+	47.7688i	0.272845	+	1.54738i	0.745724	+	0.666255i	$0.232104\pi$
$953$	8.42292	+	47.7688i	0.272845	+	1.54738i	−0.472879	+	0.881127i	$0.656785\pi$
$954$	14.5287	+	25.1644i	0.470384	+	0.814728i
$955$	−8.71513	+	3.17205i	−0.282015	+	0.102645i
$956$	−4.65270			−0.150479
$957$	−8.84389	+	3.21891i	−0.285882	+	0.104053i
$958$	11.4329	−	64.8391i	0.369380	−	2.09486i
$959$	−14.8589	−	12.4681i	−0.479819	−	0.402616i
$960$	2.88713	−	2.42259i	0.0931816	−	0.0781886i
$961$	−14.4825			−0.467176
$962$	7.73783	−	8.41507i	0.249478	−	0.271313i
$963$	14.7487			0.475269
$964$	4.80612	−	4.03282i	0.154795	−	0.129888i
$965$	1.89536	+	1.59040i	0.0610139	+	0.0511968i
$966$	0.358441	−	2.03282i	0.0115326	−	0.0654049i
$967$	−28.6908	+	10.4426i	−0.922633	+	0.335811i	−0.759286	−	0.650758i	$-0.774451\pi$
$967$	−28.6908	+	10.4426i	−0.922633	+	0.335811i	−0.163348	+	0.986569i	$0.552229\pi$
$968$	−18.9094			−0.607772
$969$	41.8423	−	15.2294i	1.34417	−	0.489237i
$970$	−7.00774	−	12.1378i	−0.225005	−	0.389720i
$971$	3.39363	+	19.2462i	0.108907	+	0.617641i	0.989588	+	0.143931i	$0.0459743\pi$
$971$	3.39363	+	19.2462i	0.108907	+	0.617641i	−0.880681	+	0.473710i	$0.842915\pi$
$972$	−2.79726	+	4.84499i	−0.0897220	+	0.155403i
$973$	3.93170	+	6.80991i	0.126045	+	0.218316i
$974$	10.1072	−	8.48092i	0.323854	−	0.271746i
$975$	0.846220	−	4.79915i	0.0271007	−	0.153696i
$976$	10.4158	−	18.0407i	0.333402	−	0.577469i
$977$	30.0355	+	10.9320i	0.960922	+	0.349747i	0.774395	−	0.632703i	$-0.218054\pi$
$977$	30.0355	+	10.9320i	0.960922	+	0.349747i	0.186527	+	0.982450i	$0.440277\pi$
$978$	22.3687	+	8.14154i	0.715272	+	0.260338i
$979$	0.344770	+	1.95529i	0.0110189	+	0.0624913i
$980$	−0.275378	−	0.231069i	−0.00879662	−	0.00738124i
$981$	−11.5915	−	9.72644i	−0.370089	−	0.310541i
$982$	1.97241	+	11.1861i	0.0629421	+	0.356963i
$983$	39.5984	+	14.4126i	1.26299	+	0.459692i	0.884772	−	0.466024i	$-0.154314\pi$
$983$	39.5984	+	14.4126i	1.26299	+	0.459692i	0.378220	+	0.925716i	$0.376536\pi$
$984$	7.13816	+	2.59808i	0.227556	+	0.0828236i
$985$	1.88207	−	3.25985i	0.0599679	−	0.103867i
$986$	−11.6691	+	66.1790i	−0.371621	+	2.10757i
$987$	12.7515	−	10.6998i	0.405885	−	0.340578i
$988$	−1.40033	−	2.42544i	−0.0445504	−	0.0771636i
$989$	2.89306	−	5.01092i	0.0919938	−	0.159338i
$990$	0.773318	+	4.38571i	0.0245777	+	0.139387i
$991$	−22.2822	−	38.5940i	−0.707819	−	1.22598i	−0.965665	−	0.259792i	$-0.916346\pi$
$991$	−22.2822	−	38.5940i	−0.707819	−	1.22598i	0.257846	−	0.966186i	$-0.416987\pi$
$992$	−7.42262	+	2.70161i	−0.235668	+	0.0857763i
$993$	10.0487			0.318886
$994$	−22.8666	+	8.32278i	−0.725286	+	0.263983i
$995$	−2.25166	+	12.7698i	−0.0713824	+	0.404830i
$996$	−1.75237	−	1.47042i	−0.0555261	−	0.0465919i
$997$	−23.1634	+	19.4364i	−0.733593	+	0.615558i	−0.931109	−	0.364742i	$-0.881157\pi$
$997$	−23.1634	+	19.4364i	−0.733593	+	0.615558i	0.197515	+	0.980300i	$0.436713\pi$
$998$	−4.55026			−0.144036
$999$	27.2848	+	6.09845i	0.863252	+	0.192947i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.2.f.a.12.1	✓	6
3.2	odd	2		333.2.x.c.271.1		6
4.3	odd	2		592.2.bc.a.49.1		6
5.2	odd	4		925.2.bc.a.49.1		12
5.3	odd	4		925.2.bc.a.49.2		12
5.4	even	2		925.2.p.b.826.1		6
37.15	odd	36		1369.2.b.f.1368.2		6
37.16	even	9		1369.2.a.j.1.1		3
37.21	even	18		1369.2.a.k.1.3		3
37.22	odd	36		1369.2.b.f.1368.5		6
37.34	even	9	inner	37.2.f.a.34.1	yes	6
111.71	odd	18		333.2.x.c.145.1		6
148.71	odd	18		592.2.bc.a.145.1		6
185.34	even	18		925.2.p.b.626.1		6
185.108	odd	36		925.2.bc.a.774.1		12
185.182	odd	36		925.2.bc.a.774.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.2.f.a.12.1	✓	6	1.1	even	1	trivial
37.2.f.a.34.1	yes	6	37.34	even	9	inner
333.2.x.c.145.1		6	111.71	odd	18
333.2.x.c.271.1		6	3.2	odd	2
592.2.bc.a.49.1		6	4.3	odd	2
592.2.bc.a.145.1		6	148.71	odd	18
925.2.p.b.626.1		6	185.34	even	18
925.2.p.b.826.1		6	5.4	even	2
925.2.bc.a.49.1		12	5.2	odd	4
925.2.bc.a.49.2		12	5.3	odd	4
925.2.bc.a.774.1		12	185.108	odd	36
925.2.bc.a.774.2		12	185.182	odd	36
1369.2.a.j.1.1		3	37.16	even	9
1369.2.a.k.1.3		3	37.21	even	18
1369.2.b.f.1368.2		6	37.15	odd	36
1369.2.b.f.1368.5		6	37.22	odd	36

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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	37.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17365 + 0.984808i) q^{2} +(0.673648 + 0.565258i) q^{3} +(0.0603074 - 0.342020i) q^{4} +(-0.652704 + 0.237565i) q^{5} -1.34730 q^{6} +(2.20574 - 0.802823i) q^{7} +(-1.26604 - 2.19285i) q^{8} +(-0.386659 - 2.19285i) q^{9} +O(q^{10})\)	\(q+(-1.17365 + 0.984808i) q^{2} +(0.673648 + 0.565258i) q^{3} +(0.0603074 - 0.342020i) q^{4} +(-0.652704 + 0.237565i) q^{5} -1.34730 q^{6} +(2.20574 - 0.802823i) q^{7} +(-1.26604 - 2.19285i) q^{8} +(-0.386659 - 2.19285i) q^{9} +(0.532089 - 0.921605i) q^{10} +(-0.939693 - 1.62760i) q^{11} +(0.233956 - 0.196312i) q^{12} +(-0.213011 + 1.20805i) q^{13} +(-1.79813 + 3.11446i) q^{14} +(-0.573978 - 0.208911i) q^{15} +(4.29813 + 1.56439i) q^{16} +(1.33750 + 7.58532i) q^{17} +(2.61334 + 2.19285i) q^{18} +(-5.03596 - 4.22567i) q^{19} +(0.0418891 + 0.237565i) q^{20} +(1.93969 + 0.705990i) q^{21} +(2.70574 + 0.984808i) q^{22} +(-0.326352 + 0.565258i) q^{23} +(0.386659 - 2.19285i) q^{24} +(-3.46064 + 2.90382i) q^{25} +(-0.939693 - 1.62760i) q^{26} +(2.29813 - 3.98048i) q^{27} +(-0.141559 - 0.802823i) q^{28} +(-2.84730 - 4.93166i) q^{29} +(0.879385 - 0.320070i) q^{30} +4.06418 q^{31} +(-1.82635 + 0.664738i) q^{32} +(0.286989 - 1.62760i) q^{33} +(-9.03983 - 7.58532i) q^{34} +(-1.24897 + 1.04801i) q^{35} -0.773318 q^{36} +(1.81908 + 5.80439i) q^{37} +10.0719 q^{38} +(-0.826352 + 0.693392i) q^{39} +(1.34730 + 1.13052i) q^{40} +(-0.592396 + 3.35965i) q^{41} +(-2.97178 + 1.08164i) q^{42} -8.86484 q^{43} +(-0.613341 + 0.223238i) q^{44} +(0.773318 + 1.33943i) q^{45} +(-0.173648 - 0.984808i) q^{46} +(4.03209 - 6.98378i) q^{47} +(2.01114 + 3.48340i) q^{48} +(-1.14156 + 0.957882i) q^{49} +(1.20187 - 6.81612i) q^{50} +(-3.38666 + 5.86587i) q^{51} +(0.400330 + 0.145708i) q^{52} +(8.00387 + 2.91317i) q^{53} +(1.22281 + 6.93491i) q^{54} +(1.00000 + 0.839100i) q^{55} +(-4.55303 - 3.82045i) q^{56} +(-1.00387 - 5.69323i) q^{57} +(8.19846 + 2.98400i) q^{58} +(6.81180 + 2.47929i) q^{59} +(-0.106067 + 0.183713i) q^{60} +(0.790859 - 4.48519i) q^{61} +(-4.76991 + 4.00243i) q^{62} +(-2.61334 - 4.52644i) q^{63} +(-3.08512 + 5.34359i) q^{64} +(-0.147956 - 0.839100i) q^{65} +(1.26604 + 2.19285i) q^{66} +(-4.35844 + 1.58634i) q^{67} +2.67499 q^{68} +(-0.539363 + 0.196312i) q^{69} +(0.433763 - 2.45999i) q^{70} +(5.18345 + 4.34943i) q^{71} +(-4.31908 + 3.62414i) q^{72} +1.85710 q^{73} +(-7.85117 - 5.02087i) q^{74} -3.97266 q^{75} +(-1.74897 + 1.46756i) q^{76} +(-3.37939 - 2.83564i) q^{77} +(0.286989 - 1.62760i) q^{78} +(7.86959 - 2.86429i) q^{79} -3.17705 q^{80} +(-2.47906 + 0.902302i) q^{81} +(-2.61334 - 4.52644i) q^{82} +(-1.30066 - 7.37641i) q^{83} +(0.358441 - 0.620838i) q^{84} +(-2.67499 - 4.63322i) q^{85} +(10.4042 - 8.73016i) q^{86} +(0.869585 - 4.93166i) q^{87} +(-2.37939 + 4.12122i) q^{88} +(-0.992726 - 0.361323i) q^{89} +(-2.22668 - 0.810446i) q^{90} +(0.500000 + 2.83564i) q^{91} +(0.173648 + 0.145708i) q^{92} +(2.73783 + 2.29731i) q^{93} +(2.14543 + 12.1673i) q^{94} +(4.29086 + 1.56175i) q^{95} +(-1.60607 - 0.584561i) q^{96} +(6.58512 - 11.4058i) q^{97} +(0.396459 - 2.24843i) q^{98} +(-3.20574 + 2.68993i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 6 q^{5} - 6 q^{6} + 3 q^{7} - 3 q^{8} - 9 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 6 * q^5 - 6 * q^6 + 3 * q^7 - 3 * q^8 - 9 * q^9	\( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 6 q^{5} - 6 q^{6} + 3 q^{7} - 3 q^{8} - 9 q^{9} - 6 q^{10} + 6 q^{12} - 9 q^{13} + 3 q^{14} + 12 q^{15} + 12 q^{16} + 3 q^{17} + 9 q^{18} + 3 q^{19} - 6 q^{20} + 6 q^{21} + 6 q^{22} - 3 q^{23} + 9 q^{24} - 12 q^{25} - 9 q^{28} - 15 q^{29} - 6 q^{30} + 6 q^{31} - 12 q^{32} - 6 q^{33} + 3 q^{34} + 18 q^{35} - 18 q^{36} - 6 q^{37} - 6 q^{38} - 6 q^{39} + 6 q^{40} - 3 q^{42} - 6 q^{43} + 3 q^{44} + 18 q^{45} + 15 q^{47} + 6 q^{48} - 15 q^{49} + 21 q^{50} - 27 q^{51} - 12 q^{52} + 24 q^{53} + 18 q^{54} + 6 q^{55} - 15 q^{56} + 18 q^{57} + 21 q^{58} + 6 q^{59} + 24 q^{60} - 27 q^{61} - 9 q^{63} + 3 q^{64} + 30 q^{65} + 3 q^{66} - 18 q^{67} + 6 q^{68} - 12 q^{69} - 30 q^{70} + 33 q^{71} - 9 q^{72} + 12 q^{73} - 21 q^{74} - 66 q^{75} + 15 q^{76} - 9 q^{77} - 6 q^{78} + 33 q^{79} - 60 q^{80} - 18 q^{81} - 9 q^{82} + 21 q^{83} - 6 q^{84} - 6 q^{85} + 24 q^{86} - 9 q^{87} - 3 q^{88} + 12 q^{89} + 3 q^{91} - 3 q^{93} - 3 q^{94} - 6 q^{95} + 15 q^{96} + 18 q^{97} + 12 q^{98} - 9 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 6 * q^5 - 6 * q^6 + 3 * q^7 - 3 * q^8 - 9 * q^9 - 6 * q^10 + 6 * q^12 - 9 * q^13 + 3 * q^14 + 12 * q^15 + 12 * q^16 + 3 * q^17 + 9 * q^18 + 3 * q^19 - 6 * q^20 + 6 * q^21 + 6 * q^22 - 3 * q^23 + 9 * q^24 - 12 * q^25 - 9 * q^28 - 15 * q^29 - 6 * q^30 + 6 * q^31 - 12 * q^32 - 6 * q^33 + 3 * q^34 + 18 * q^35 - 18 * q^36 - 6 * q^37 - 6 * q^38 - 6 * q^39 + 6 * q^40 - 3 * q^42 - 6 * q^43 + 3 * q^44 + 18 * q^45 + 15 * q^47 + 6 * q^48 - 15 * q^49 + 21 * q^50 - 27 * q^51 - 12 * q^52 + 24 * q^53 + 18 * q^54 + 6 * q^55 - 15 * q^56 + 18 * q^57 + 21 * q^58 + 6 * q^59 + 24 * q^60 - 27 * q^61 - 9 * q^63 + 3 * q^64 + 30 * q^65 + 3 * q^66 - 18 * q^67 + 6 * q^68 - 12 * q^69 - 30 * q^70 + 33 * q^71 - 9 * q^72 + 12 * q^73 - 21 * q^74 - 66 * q^75 + 15 * q^76 - 9 * q^77 - 6 * q^78 + 33 * q^79 - 60 * q^80 - 18 * q^81 - 9 * q^82 + 21 * q^83 - 6 * q^84 - 6 * q^85 + 24 * q^86 - 9 * q^87 - 3 * q^88 + 12 * q^89 + 3 * q^91 - 3 * q^93 - 3 * q^94 - 6 * q^95 + 15 * q^96 + 18 * q^97 + 12 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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