LMFDB - Embedded newform 207.2.o.a.11.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(5,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("207.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.o (of order $66$, degree $20$, 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:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			11.14
Character	$\chi$	$=$	207.11
Dual form			207.2.o.a.113.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.435484 - 0.0207447i) q^{2} +(0.849649 - 1.50934i) q^{3} +(-1.80173 + 0.172044i) q^{4} +(-0.978477 - 0.932976i) q^{5} +(0.338698 - 0.674918i) q^{6} +(-0.518116 - 2.68824i) q^{7} +(-1.64413 + 0.236391i) q^{8} +(-1.55619 - 2.56481i) q^{9} +O(q^{10})$	\(q+(0.435484 - 0.0207447i) q^{2} +(0.849649 - 1.50934i) q^{3} +(-1.80173 + 0.172044i) q^{4} +(-0.978477 - 0.932976i) q^{5} +(0.338698 - 0.674918i) q^{6} +(-0.518116 - 2.68824i) q^{7} +(-1.64413 + 0.236391i) q^{8} +(-1.55619 - 2.56481i) q^{9} +(-0.445465 - 0.385998i) q^{10} +(2.26641 - 1.16842i) q^{11} +(-1.27116 + 2.86559i) q^{12} +(1.92317 + 0.370661i) q^{13} +(-0.281398 - 1.15994i) q^{14} +(-2.23954 + 0.684149i) q^{15} +(2.84334 - 0.548009i) q^{16} +(1.01838 + 2.22994i) q^{17} +(-0.730904 - 1.08465i) q^{18} +(-0.894779 - 0.408632i) q^{19} +(1.92346 + 1.51263i) q^{20} +(-4.49767 - 1.50205i) q^{21} +(0.962749 - 0.555843i) q^{22} +(1.58713 + 4.52560i) q^{23} +(-1.04014 + 2.68240i) q^{24} +(-0.150937 - 3.16855i) q^{25} +(0.845200 + 0.121521i) q^{26} +(-5.19338 + 0.169631i) q^{27} +(1.39600 + 4.75434i) q^{28} +(-0.476107 + 4.98601i) q^{29} +(-0.961089 + 0.344394i) q^{30} +(6.18643 - 4.86506i) q^{31} +(4.45530 - 1.08084i) q^{32} +(0.162120 - 4.41353i) q^{33} +(0.489746 + 0.949975i) q^{34} +(-2.00110 + 3.11377i) q^{35} +(3.24510 + 4.35336i) q^{36} +(-1.37276 + 4.67521i) q^{37} +(-0.398139 - 0.159391i) q^{38} +(2.19347 - 2.58778i) q^{39} +(1.82929 + 1.30263i) q^{40} +(-1.77786 + 1.86457i) q^{41} +(-1.98982 - 0.560815i) q^{42} +(7.09317 - 9.01971i) q^{43} +(-3.88244 + 2.49509i) q^{44} +(-0.870207 + 3.96150i) q^{45} +(0.785050 + 1.93790i) q^{46} +(-0.317168 - 0.183117i) q^{47} +(1.58871 - 4.75717i) q^{48} +(-0.459608 + 0.183999i) q^{49} +(-0.131461 - 1.37672i) q^{50} +(4.23099 + 0.357588i) q^{51} +(-3.52880 - 0.336960i) q^{52} +(-2.70059 - 3.11665i) q^{53} +(-2.25812 + 0.181607i) q^{54} +(-3.30774 - 0.971240i) q^{55} +(1.48733 + 4.29735i) q^{56} +(-1.37701 + 1.00333i) q^{57} +(-0.103904 + 2.18121i) q^{58} +(-1.79834 + 9.33067i) q^{59} +(3.91733 - 1.61795i) q^{60} +(1.63147 - 4.07522i) q^{61} +(2.59317 - 2.24699i) q^{62} +(-6.08854 + 5.51229i) q^{63} +(-3.63896 + 1.06849i) q^{64} +(-1.53596 - 2.15696i) q^{65} +(-0.0209563 - 1.92538i) q^{66} +(0.0594220 - 0.115263i) q^{67} +(-2.21849 - 3.84253i) q^{68} +(8.17915 + 1.44966i) q^{69} +(-0.806852 + 1.39751i) q^{70} +(8.28371 + 12.8897i) q^{71} +(3.16489 + 3.84903i) q^{72} +(-2.19371 + 4.80356i) q^{73} +(-0.500831 + 2.06446i) q^{74} +(-4.91065 - 2.46434i) q^{75} +(1.68245 + 0.582302i) q^{76} +(-4.31525 - 5.48729i) q^{77} +(0.901540 - 1.17244i) q^{78} +(-13.9483 + 4.82754i) q^{79} +(-3.29342 - 2.11655i) q^{80} +(-4.15652 + 7.98269i) q^{81} +(-0.735550 + 0.848870i) q^{82} +(5.56093 - 5.30234i) q^{83} +(8.36200 + 1.93248i) q^{84} +(1.08402 - 3.13206i) q^{85} +(2.90185 - 4.07508i) q^{86} +(7.12105 + 4.95497i) q^{87} +(-3.45009 + 2.45680i) q^{88} +(2.57173 - 17.8868i) q^{89} +(-0.296781 + 1.74322i) q^{90} -5.36199i q^{91} +(-3.63817 - 7.88084i) q^{92} +(-2.08673 - 13.4710i) q^{93} +(-0.141920 - 0.0731651i) q^{94} +(0.494277 + 1.23464i) q^{95} +(2.15408 - 7.64289i) q^{96} +(-9.09184 - 2.20566i) q^{97} +(-0.196335 + 0.0896631i) q^{98} +(-6.52375 - 3.99464i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.435484	−	0.0207447i	0.307934	−	0.0146687i	0.106954	−	0.994264i	$-0.465890\pi$
$2$	0.435484	−	0.0207447i	0.307934	−	0.0146687i	0.200980	+	0.979595i	$0.435587\pi$
$3$	0.849649	−	1.50934i	0.490545	−	0.871416i
$3$	0.849649	−	1.50934i	0.490545	−	0.871416i
$4$	−1.80173	+	0.172044i	−0.900864	+	0.0860221i
$5$	−0.978477	−	0.932976i	−0.437588	−	0.417239i	0.438995	−	0.898489i	$-0.355334\pi$
$5$	−0.978477	−	0.932976i	−0.437588	−	0.417239i	−0.876583	+	0.481250i	$0.840183\pi$
$6$	0.338698	−	0.674918i	0.138273	−	0.275534i
$7$	−0.518116	−	2.68824i	−0.195829	−	1.01606i	−0.938206	−	0.346076i	$-0.887514\pi$
$7$	−0.518116	−	2.68824i	−0.195829	−	1.01606i	0.742377	−	0.669982i	$-0.233698\pi$
$8$	−1.64413	+	0.236391i	−0.581289	+	0.0835768i
$9$	−1.55619	−	2.56481i	−0.518731	−	0.854937i
$10$	−0.445465	−	0.385998i	−0.140868	−	0.122063i
$11$	2.26641	−	1.16842i	0.683350	−	0.352291i	−0.0813431	−	0.996686i	$-0.525921\pi$
$11$	2.26641	−	1.16842i	0.683350	−	0.352291i	0.764693	+	0.644395i	$0.222891\pi$
$12$	−1.27116	+	2.86559i	−0.366953	+	0.827225i
$13$	1.92317	+	0.370661i	0.533392	+	0.102803i	0.448833	−	0.893616i	$-0.351840\pi$
$13$	1.92317	+	0.370661i	0.533392	+	0.102803i	0.0845590	+	0.996418i	$0.473052\pi$
$14$	−0.281398	−	1.15994i	−0.0752067	−	0.310006i
$15$	−2.23954	+	0.684149i	−0.578246	+	0.176647i
$16$	2.84334	−	0.548009i	0.710835	−	0.137002i
$17$	1.01838	+	2.22994i	0.246993	+	0.540839i	0.992003	−	0.126214i	$-0.0402827\pi$
$17$	1.01838	+	2.22994i	0.246993	+	0.540839i	−0.745010	+	0.667053i	$0.767555\pi$
$18$	−0.730904	−	1.08465i	−0.172276	−	0.255655i
$19$	−0.894779	−	0.408632i	−0.205276	−	0.0937466i	0.310124	−	0.950696i	$-0.399629\pi$
$19$	−0.894779	−	0.408632i	−0.205276	−	0.0937466i	−0.515400	+	0.856950i	$0.672357\pi$
$20$	1.92346	+	1.51263i	0.430099	+	0.338234i
$21$	−4.49767	−	1.50205i	−0.981473	−	0.327774i
$22$	0.962749	−	0.555843i	0.205259	−	0.118506i
$23$	1.58713	+	4.52560i	0.330939	+	0.943652i
$23$	1.58713	+	4.52560i	0.330939	+	0.943652i
$24$	−1.04014	+	2.68240i	−0.212318	+	0.547543i
$25$	−0.150937	−	3.16855i	−0.0301873	−	0.633709i
$26$	0.845200	+	0.121521i	0.165757	+	0.0238323i
$27$	−5.19338	+	0.169631i	−0.999467	+	0.0326456i
$28$	1.39600	+	4.75434i	0.263819	+	0.898485i
$29$	−0.476107	+	4.98601i	−0.0884108	+	0.925880i	0.837073	+	0.547092i	$0.184265\pi$
$29$	−0.476107	+	4.98601i	−0.0884108	+	0.925880i	−0.925483	+	0.378788i	$0.876341\pi$
$30$	−0.961089	+	0.344394i	−0.175470	+	0.0628775i
$31$	6.18643	−	4.86506i	1.11112	−	0.873791i	0.118245	−	0.992984i	$-0.462273\pi$
$31$	6.18643	−	4.86506i	1.11112	−	0.873791i	0.992871	+	0.119193i	$0.0380307\pi$
$32$	4.45530	−	1.08084i	0.787593	−	0.191068i
$33$	0.162120	−	4.41353i	0.0282215	−	0.768297i
$34$	0.489746	+	0.949975i	0.0839908	+	0.162919i
$35$	−2.00110	+	3.11377i	−0.338247	+	0.526323i
$36$	3.24510	+	4.35336i	0.540850	+	0.725560i
$37$	−1.37276	+	4.67521i	−0.225681	+	0.768599i	0.766330	+	0.642447i	$0.222081\pi$
$37$	−1.37276	+	4.67521i	−0.225681	+	0.768599i	−0.992011	+	0.126152i	$0.959737\pi$
$38$	−0.398139	−	0.159391i	−0.0645867	−	0.0258566i
$39$	2.19347	−	2.58778i	0.351237	−	0.414377i
$40$	1.82929	+	1.30263i	0.289237	+	0.205965i
$41$	−1.77786	+	1.86457i	−0.277655	+	0.291196i	−0.847765	−	0.530372i	$-0.822052\pi$
$41$	−1.77786	+	1.86457i	−0.277655	+	0.291196i	0.570110	+	0.821569i	$0.306901\pi$
$42$	−1.98982	−	0.560815i	−0.307037	−	0.0865356i
$43$	7.09317	−	9.01971i	1.08170	−	1.37549i	0.160212	−	0.987083i	$-0.448782\pi$
$43$	7.09317	−	9.01971i	1.08170	−	1.37549i	0.921487	−	0.388410i	$-0.126975\pi$
$44$	−3.88244	+	2.49509i	−0.585300	+	0.376150i
$45$	−0.870207	+	3.96150i	−0.129723	+	0.590545i
$46$	0.785050	+	1.93790i	0.115749	+	0.285728i
$47$	−0.317168	−	0.183117i	−0.0462638	−	0.0267104i	0.476690	−	0.879072i	$-0.341837\pi$
$47$	−0.317168	−	0.183117i	−0.0462638	−	0.0267104i	−0.522953	+	0.852361i	$0.675170\pi$
$48$	1.58871	−	4.75717i	0.229311	−	0.686639i
$49$	−0.459608	+	0.183999i	−0.0656582	+	0.0262856i
$50$	−0.131461	−	1.37672i	−0.0185914	−	0.194698i
$51$	4.23099	+	0.357588i	0.592457	+	0.0500723i
$52$	−3.52880	−	0.336960i	−0.489357	−	0.0467279i
$53$	−2.70059	−	3.11665i	−0.370954	−	0.428104i	0.539326	−	0.842097i	$-0.318679\pi$
$53$	−2.70059	−	3.11665i	−0.370954	−	0.428104i	−0.910280	+	0.413993i	$0.864134\pi$
$54$	−2.25812	+	0.181607i	−0.307291	+	0.0247135i
$55$	−3.30774	−	0.971240i	−0.446016	−	0.130962i
$56$	1.48733	+	4.29735i	0.198752	+	0.574257i
$57$	−1.37701	+	1.00333i	−0.182390	+	0.132894i
$58$	−0.103904	+	2.18121i	−0.0136432	+	0.286406i
$59$	−1.79834	+	9.33067i	−0.234124	+	1.21475i	0.654482	+	0.756078i	$0.272887\pi$
$59$	−1.79834	+	9.33067i	−0.234124	+	1.21475i	−0.888605	+	0.458672i	$0.848325\pi$
$60$	3.91733	−	1.61795i	0.505725	−	0.208876i
$61$	1.63147	−	4.07522i	0.208888	−	0.521778i	−0.786513	−	0.617574i	$-0.788116\pi$
$61$	1.63147	−	4.07522i	0.208888	−	0.521778i	0.995401	+	0.0957963i	$0.0305397\pi$
$62$	2.59317	−	2.24699i	0.329333	−	0.285368i
$63$	−6.08854	+	5.51229i	−0.767084	+	0.694483i
$64$	−3.63896	+	1.06849i	−0.454870	+	0.133562i
$65$	−1.53596	−	2.15696i	−0.190513	−	0.267538i
$66$	−0.0209563	−	1.92538i	−0.00257954	−	0.236998i
$67$	0.0594220	−	0.115263i	0.00725955	−	0.0140816i	−0.885178	−	0.465253i	$-0.845963\pi$
$67$	0.0594220	−	0.115263i	0.00725955	−	0.0140816i	0.892437	+	0.451171i	$0.148994\pi$
$68$	−2.21849	−	3.84253i	−0.269031	−	0.465975i
$69$	8.17915	+	1.44966i	0.984654	+	0.174518i
$70$	−0.806852	+	1.39751i	−0.0964372	+	0.167034i
$71$	8.28371	+	12.8897i	0.983096	+	1.52973i	0.841821	+	0.539757i	$0.181484\pi$
$71$	8.28371	+	12.8897i	0.983096	+	1.52973i	0.141275	+	0.989970i	$0.454880\pi$
$72$	3.16489	+	3.84903i	0.372986	+	0.453612i
$73$	−2.19371	+	4.80356i	−0.256755	+	0.562215i	−0.993484	−	0.113973i	$-0.963642\pi$
$73$	−2.19371	+	4.80356i	−0.256755	+	0.562215i	0.736729	+	0.676188i	$0.236369\pi$
$74$	−0.500831	+	2.06446i	−0.0582205	+	0.239988i
$75$	−4.91065	−	2.46434i	−0.567033	−	0.284557i
$76$	1.68245	+	0.582302i	0.192990	+	0.0667946i
$77$	−4.31525	−	5.48729i	−0.491769	−	0.625335i
$78$	0.901540	−	1.17244i	0.102079	−	0.132753i
$79$	−13.9483	+	4.82754i	−1.56930	+	0.543140i	−0.966923	−	0.255070i	$-0.917902\pi$
$79$	−13.9483	+	4.82754i	−1.56930	+	0.543140i	−0.602379	+	0.798210i	$0.705780\pi$
$80$	−3.29342	−	2.11655i	−0.368216	−	0.236638i
$81$	−4.15652	+	7.98269i	−0.461836	+	0.886966i
$82$	−0.735550	+	0.848870i	−0.0812279	+	0.0937420i
$83$	5.56093	−	5.30234i	0.610391	−	0.582007i	−0.320525	−	0.947240i	$-0.603859\pi$
$83$	5.56093	−	5.30234i	0.610391	−	0.582007i	0.930916	+	0.365233i	$0.119011\pi$
$84$	8.36200	+	1.93248i	0.912369	+	0.210851i
$85$	1.08402	−	3.13206i	0.117578	−	0.339720i
$86$	2.90185	−	4.07508i	0.312915	−	0.439427i
$87$	7.12105	+	4.95497i	0.763457	+	0.531228i
$88$	−3.45009	+	2.45680i	−0.367781	+	0.261895i
$89$	2.57173	−	17.8868i	0.272603	−	1.89599i	−0.148387	−	0.988929i	$-0.547408\pi$
$89$	2.57173	−	17.8868i	0.272603	−	1.89599i	0.420989	−	0.907066i	$-0.361683\pi$
$90$	−0.296781	+	1.74322i	−0.0312835	+	0.183752i
$91$		−	5.36199i		−	0.562090i
$92$	−3.63817	−	7.88084i	−0.379306	−	0.821634i
$93$	−2.08673	−	13.4710i	−0.216383	−	1.39688i
$94$	−0.141920	−	0.0731651i	−0.0146380	−	0.00754640i
$95$	0.494277	+	1.23464i	0.0507117	+	0.126672i
$96$	2.15408	−	7.64289i	0.219850	−	0.780049i
$97$	−9.09184	−	2.20566i	−0.923137	−	0.223951i	−0.254098	−	0.967178i	$-0.581779\pi$
$97$	−9.09184	−	2.20566i	−0.923137	−	0.223951i	−0.669038	+	0.743228i	$0.733294\pi$
$98$	−0.196335	+	0.0896631i	−0.0198328	+	0.00905734i
$99$	−6.52375	−	3.99464i	−0.655662	−	0.401477i
$100$	0.817077	+	5.68289i	0.0817077	+	0.568289i
$101$	1.69146	+	1.77395i	0.168306	+	0.176515i	0.802486	−	0.596671i	$-0.203510\pi$
$101$	1.69146	+	1.77395i	0.168306	+	0.176515i	−0.634179	+	0.773186i	$0.718662\pi$
$102$	1.84995	+	0.0679533i	0.183172	+	0.00672838i
$103$	10.4510	+	0.497841i	1.02976	+	0.0490537i	0.555655	−	0.831413i	$-0.312467\pi$
$103$	10.4510	+	0.497841i	1.02976	+	0.0490537i	0.474109	+	0.880466i	$0.342770\pi$
$104$	−3.24958	−	0.154796i	−0.318647	−	0.0151790i
$105$	2.99949	+	5.66594i	0.292721	+	0.552939i
$106$	−1.24072	−	1.30123i	−0.120509	−	0.126386i
$107$	−1.27356	−	8.85781i	−0.123120	−	0.856316i	−0.953987	−	0.299847i	$-0.903065\pi$
$107$	−1.27356	−	8.85781i	−0.123120	−	0.856316i	0.830868	−	0.556470i	$-0.187845\pi$
$108$	9.32788	−	1.19912i	0.897576	−	0.115385i
$109$	10.8197	−	4.94119i	1.03634	−	0.473280i	0.176744	−	0.984257i	$-0.443443\pi$
$109$	10.8197	−	4.94119i	1.03634	−	0.473280i	0.859595	+	0.510977i	$0.170716\pi$
$110$	−1.46062	−	0.354341i	−0.139264	−	0.0337851i
$111$	5.89009	+	6.04425i	0.559063	+	0.573695i
$112$	−2.94636	−	7.35965i	−0.278405	−	0.695421i
$113$	−6.65600	−	3.43141i	−0.626144	−	0.322800i	0.115789	−	0.993274i	$-0.463060\pi$
$113$	−6.65600	−	3.43141i	−0.626144	−	0.322800i	−0.741933	+	0.670474i	$0.766091\pi$
$114$	−0.578852	+	0.465499i	−0.0542145	+	0.0435980i
$115$	2.66930	−	5.90894i	0.248914	−	0.551012i
$116$		−	9.06535i		−	0.841697i
$117$	−2.04215	−	5.50940i	−0.188797	−	0.509344i
$118$	−0.589587	+	4.10066i	−0.0542758	+	0.377497i
$119$	5.46696	−	3.89301i	0.501156	−	0.356871i
$120$	3.52037	−	1.65424i	0.321365	−	0.151011i
$121$	−2.60919	+	3.66410i	−0.237199	+	0.333100i
$122$	0.625940	−	1.80854i	0.0566700	−	0.163737i
$123$	1.30370	+	4.26762i	0.117551	+	0.384798i
$124$	−10.3093	+	9.82986i	−0.925799	+	0.882748i
$125$	−7.23529	+	8.34997i	−0.647144	+	0.746844i
$126$	−2.53711	+	2.52682i	−0.226024	+	0.225107i
$127$	−5.94349	−	3.81965i	−0.527399	−	0.338939i	0.249694	−	0.968325i	$-0.419670\pi$
$127$	−5.94349	−	3.81965i	−0.527399	−	0.338939i	−0.777093	+	0.629386i	$0.783306\pi$
$128$	−10.2273	+	3.53971i	−0.903975	+	0.312869i
$129$	−7.58706	−	18.3696i	−0.668004	−	1.61735i
$130$	−0.713632	−	0.907457i	−0.0625897	−	0.0795892i
$131$	−0.0361202	−	0.0125013i	−0.00315584	−	0.00109225i	0.325490	−	0.945546i	$-0.394471\pi$
$131$	−0.0361202	−	0.0125013i	−0.00315584	−	0.00109225i	−0.328645	+	0.944453i	$0.606592\pi$
$132$	0.467225	+	7.97987i	0.0406667	+	0.694558i
$133$	−0.634901	+	2.61710i	−0.0550529	+	0.226931i
$134$	0.0234862	−	0.0514277i	0.00202890	−	0.00444267i
$135$	5.23987	+	4.67932i	0.450976	+	0.402732i
$136$	−2.20149	−	3.42558i	−0.188776	−	0.293741i
$137$	−0.366398	+	0.634620i	−0.0313035	+	0.0542192i	−0.881253	−	0.472645i	$-0.843299\pi$
$137$	−0.366398	+	0.634620i	−0.0313035	+	0.0542192i	0.849949	+	0.526865i	$0.176633\pi$
$138$	3.59196	+	0.461629i	0.305768	+	0.0392965i
$139$	8.37752	+	14.5103i	0.710572	+	1.23075i	0.964643	+	0.263561i	$0.0848970\pi$
$139$	8.37752	+	14.5103i	0.710572	+	1.23075i	−0.254071	+	0.967186i	$0.581770\pi$
$140$	3.06973	−	5.95444i	0.259439	−	0.503242i
$141$	−0.545867	+	0.323129i	−0.0459703	+	0.0272123i
$142$	3.87482	+	5.44142i	0.325167	+	0.456634i
$143$	4.79179	−	1.40700i	0.400710	−	0.117659i
$144$	−5.83033	−	6.43983i	−0.485861	−	0.536652i
$145$	5.11769	−	4.43450i	0.425001	−	0.368265i
$146$	−0.855679	+	2.13738i	−0.0708165	+	0.176891i
$147$	−0.112788	+	0.850037i	−0.00930263	+	0.0701099i
$148$	1.66901	−	8.65963i	0.137191	−	0.711817i
$149$	−0.336594	+	7.06599i	−0.0275749	+	0.578868i	0.942227	+	0.334975i	$0.108728\pi$
$149$	−0.336594	+	7.06599i	−0.0275749	+	0.578868i	−0.969802	+	0.243893i	$0.921575\pi$
$150$	−2.18963	−	0.971310i	−0.178783	−	0.0793071i
$151$	5.02031	+	14.5052i	0.408547	+	1.18042i	0.942297	+	0.334777i	$0.108661\pi$
$151$	5.02031	+	14.5052i	0.408547	+	1.18042i	−0.533750	+	0.845642i	$0.679218\pi$
$152$	1.56773	+	0.460328i	0.127160	+	0.0373376i
$153$	4.13457	−	6.08216i	0.334260	−	0.491714i
$154$	−1.99305	−	2.30011i	−0.160605	−	0.185348i
$155$	−10.5923	−	1.01144i	−0.850791	−	0.0812407i
$156$	−3.50683	+	5.03986i	−0.280771	+	0.403511i
$157$	0.847770	+	8.87825i	0.0676594	+	0.708561i	0.964125	+	0.265448i	$0.0855199\pi$
$157$	0.847770	+	8.87825i	0.0676594	+	0.708561i	−0.896466	+	0.443113i	$0.853874\pi$
$158$	−5.97410	+	2.39167i	−0.475274	+	0.190271i
$159$	−6.99862	+	1.42804i	−0.555027	+	0.113251i
$160$	−5.36781	−	3.09911i	−0.424363	−	0.245006i
$161$	11.3436	−	6.61136i	0.893998	−	0.521048i
$162$	−1.64450	+	3.56256i	−0.129204	+	0.279901i
$163$	−10.8330	+	6.96192i	−0.848503	+	0.545300i	−0.891108	−	0.453792i	$-0.850071\pi$
$163$	−10.8330	+	6.96192i	−0.848503	+	0.545300i	0.0426042	+	0.999092i	$0.486435\pi$
$164$	2.88243	−	3.66531i	0.225080	−	0.286213i
$165$	−4.27634	+	4.16728i	−0.332913	+	0.324422i
$166$	2.31170	−	2.42444i	0.179423	−	0.188173i
$167$	17.6578	+	12.5741i	1.36640	+	0.973012i	0.999079	+	0.0429197i	$0.0136659\pi$
$167$	17.6578	+	12.5741i	1.36640	+	0.973012i	0.367326	+	0.930092i	$0.380273\pi$
$168$	7.74985	+	1.40636i	0.597914	+	0.108503i
$169$	−8.50758	−	3.40592i	−0.654429	−	0.261994i
$170$	0.407098	−	1.38645i	0.0312230	−	0.106336i
$171$	0.344386	+	2.93085i	0.0263358	+	0.224128i
$172$	−11.2282	+	17.4714i	−0.856141	+	1.33218i
$173$	−9.04667	−	17.5481i	−0.687806	−	1.33416i	−0.931299	−	0.364254i	$-0.881324\pi$
$173$	−9.04667	−	17.5481i	−0.687806	−	1.33416i	0.243494	−	0.969902i	$-0.421706\pi$
$174$	3.20389	+	2.01008i	0.242886	+	0.152384i
$175$	−8.43961	+	2.04743i	−0.637974	+	0.154771i
$176$	5.80389	−	4.56423i	0.437484	−	0.344042i
$177$	12.5552	+	10.6421i	0.943704	+	0.799909i
$178$	0.748892	−	7.84276i	0.0561319	−	0.587839i
$179$	4.45121	+	15.1594i	0.332699	+	1.13307i	0.940730	+	0.339156i	$0.110141\pi$
$179$	4.45121	+	15.1594i	0.332699	+	1.13307i	−0.608031	+	0.793913i	$0.708040\pi$
$180$	0.886324	−	7.28726i	0.0660627	−	0.543160i
$181$	9.86500	+	1.41837i	0.733260	+	0.105427i	0.498822	−	0.866704i	$-0.333766\pi$
$181$	9.86500	+	1.41837i	0.733260	+	0.105427i	0.234438	+	0.972131i	$0.424675\pi$
$182$	−0.111233	−	2.33506i	−0.00824512	−	0.173086i
$183$	−4.76470	−	5.92494i	−0.352216	−	0.437984i
$184$	−3.67926	−	7.06551i	−0.271239	−	0.520876i
$185$	5.70507	−	3.29383i	0.419445	−	0.242167i
$186$	−1.18819	−	5.82312i	−0.0871221	−	0.426972i
$187$	4.91356	+	3.86407i	0.359315	+	0.282569i
$188$	0.602956	+	0.275361i	0.0439751	+	0.0200827i
$189$	3.14678	+	13.8732i	0.228895	+	1.00912i
$190$	0.240862	+	0.527414i	0.0174740	+	0.0382626i
$191$	−18.5052	+	3.56658i	−1.33899	+	0.258069i	−0.807936	−	0.589271i	$-0.799415\pi$
$191$	−18.5052	+	3.56658i	−1.33899	+	0.258069i	−0.531052	+	0.847340i	$0.678203\pi$
$192$	−1.47912	+	6.40026i	−0.106746	+	0.461899i
$193$	1.54840	+	6.38261i	0.111457	+	0.459430i	1.00000		0.000637309i	$0.000202862\pi$
$193$	1.54840	+	6.38261i	0.111457	+	0.459430i	−0.888543	+	0.458793i	$0.848282\pi$
$194$	−4.00511	−	0.771921i	−0.287550	−	0.0554207i
$195$	−4.56060	+	0.485628i	−0.326591	+	0.0347765i
$196$	0.796432	−	0.410589i	0.0568880	−	0.0293278i
$197$	3.37228	+	2.92210i	0.240265	+	0.208191i	0.766667	−	0.642045i	$-0.221914\pi$
$197$	3.37228	+	2.92210i	0.240265	+	0.208191i	−0.526402	+	0.850236i	$0.676459\pi$
$198$	−2.92386	−	1.60427i	−0.207790	−	0.114010i
$199$	7.91094	−	1.13742i	0.560792	−	0.0806297i	0.143911	−	0.989591i	$-0.454032\pi$
$199$	7.91094	−	1.13742i	0.560792	−	0.0806297i	0.416881	+	0.908961i	$0.363123\pi$
$200$	0.997176	+	5.17384i	0.0705110	+	0.365846i
$201$	−0.123482	−	0.187620i	−0.00870976	−	0.0132337i
$202$	0.773402	+	0.737438i	0.0544164	+	0.0518859i
$203$	13.6503	−	1.30344i	0.958061	−	0.0914838i
$204$	−7.68461	+	0.0836410i	−0.538030	+	0.00585604i
$205$	3.47919	−	0.165734i	0.242997	−	0.0115754i
$206$	4.56155			0.317819
$207$	9.13743	−	11.1134i	0.635095	−	0.772434i
$208$	5.67136			0.393238
$209$	−2.50539	+	0.119347i	−0.173302	+	0.00825538i
$210$	1.42377	+	2.40520i	0.0982494	+	0.165975i
$211$	−1.64012	+	0.156612i	−0.112910	+	0.0107816i	−0.151358	−	0.988479i	$-0.548365\pi$
$211$	−1.64012	+	0.156612i	−0.112910	+	0.0107816i	0.0384478	+	0.999261i	$0.487759\pi$
$212$	5.40193	+	5.15073i	0.371006	+	0.353753i
$213$	26.4932	−	1.55119i	1.81528	−	0.106286i
$214$	−0.738367	−	3.83101i	−0.0504737	−	0.261883i
$215$	−15.3557	+	2.20781i	−1.04725	+	0.150572i
$216$	8.49852	−	1.50657i	0.578251	−	0.102509i
$217$	−16.2837	−	14.1099i	−1.10541	−	0.957845i
$218$	4.60930	−	2.37626i	0.312181	−	0.160941i
$219$	5.38631	+	7.39240i	0.363973	+	0.499532i
$220$	6.12674	+	1.18083i	0.413065	+	0.0796117i
$221$	1.13197	+	4.66602i	0.0761442	+	0.313871i
$222$	2.69043	+	2.50999i	0.180570	+	0.168459i
$223$	11.1823	−	2.15522i	0.748824	−	0.144324i	0.199459	−	0.979906i	$-0.436082\pi$
$223$	11.1823	−	2.15522i	0.748824	−	0.144324i	0.549365	+	0.835582i	$0.314870\pi$
$224$	−5.21393	−	11.4169i	−0.348370	−	0.762824i
$225$	−7.89184	+	5.31800i	−0.526123	+	0.354533i
$226$	−2.96976	−	1.35625i	−0.197546	−	0.0902162i
$227$	20.9681	+	16.4895i	1.39170	+	1.09445i	0.983370	+	0.181614i	$0.0581322\pi$
$227$	20.9681	+	16.4895i	1.39170	+	1.09445i	0.408333	+	0.912833i	$0.366110\pi$
$228$	2.30838	−	2.04463i	0.152876	−	0.135409i
$229$	−15.6536	+	9.03759i	−1.03442	+	0.597221i	−0.918247	−	0.396008i	$-0.870395\pi$
$229$	−15.6536	+	9.03759i	−1.03442	+	0.597221i	−0.116170	+	0.993229i	$0.537062\pi$
$230$	1.03986	−	2.62862i	0.0685663	−	0.173326i
$231$	−11.9486	+	1.85090i	−0.786161	+	0.121780i
$232$	−0.395865	−	8.31023i	−0.0259898	−	0.545593i
$233$	5.87150	+	0.844194i	0.384655	+	0.0553050i	0.331930	−	0.943304i	$-0.392300\pi$
$233$	5.87150	+	0.844194i	0.384655	+	0.0553050i	0.0527249	+	0.998609i	$0.483209\pi$
$234$	−1.00362	−	2.35689i	−0.0656084	−	0.154075i
$235$	0.139498	+	0.475086i	0.00909984	+	0.0309912i
$236$	1.63483	−	17.1207i	0.106418	−	1.11446i
$237$	−4.56474	+	25.1543i	−0.296512	+	1.63395i
$238$	2.30002	−	1.80875i	0.149088	−	0.117244i
$239$	−22.9348	+	5.56392i	−1.48353	+	0.359900i	−0.894080	−	0.447907i	$-0.852170\pi$
$239$	−22.9348	+	5.56392i	−1.48353	+	0.359900i	−0.589448	+	0.807807i	$0.700655\pi$
$240$	−5.99284	+	3.17255i	−0.386836	+	0.204788i
$241$	−0.00222490	−	0.00431571i	−0.000143319	−	0.000277999i	0.888764	−	0.458366i	$-0.151565\pi$
$241$	−0.00222490	−	0.00431571i	−0.000143319	−	0.000277999i	−0.888907	+	0.458088i	$0.848535\pi$
$242$	−1.06025	+	1.64978i	−0.0681555	+	0.106052i
$243$	8.51698	+	13.0561i	0.546365	+	0.837547i
$244$	−2.23835	+	7.62312i	−0.143296	+	0.488020i
$245$	0.621382	+	0.248764i	0.0396986	+	0.0158929i
$246$	0.656272	+	1.83143i	0.0418423	+	0.116768i
$247$	−1.56935	−	1.11753i	−0.0998554	−	0.0711067i
$248$	−9.02127	+	9.46124i	−0.572851	+	0.600789i
$249$	−3.27817	−	12.8984i	−0.207746	−	0.817405i
$250$	−2.97764	+	3.78637i	−0.188322	+	0.239471i
$251$	−9.80270	+	6.29981i	−0.618741	+	0.397641i	−0.812126	−	0.583482i	$-0.801690\pi$
$251$	−9.80270	+	6.29981i	−0.618741	+	0.397641i	0.193385	+	0.981123i	$0.438053\pi$
$252$	10.0215	−	10.9791i	0.631297	−	0.691621i
$253$	8.88488	+	8.40245i	0.558588	+	0.528258i
$254$	−2.66753	−	1.54010i	−0.167376	−	0.0966344i
$255$	−3.80630	−	4.29730i	−0.238360	−	0.269107i
$256$	2.66143	−	1.06547i	0.166339	−	0.0665922i
$257$	−1.83598	−	19.2272i	−0.114525	−	1.19936i	−0.851836	−	0.523809i	$-0.824511\pi$
$257$	−1.83598	−	19.2272i	−0.114525	−	1.19936i	0.737311	−	0.675554i	$-0.236095\pi$
$258$	−3.68512	−	7.84226i	−0.229425	−	0.488238i
$259$	13.2793	+	1.26802i	0.825137	+	0.0787910i
$260$	3.13848	+	3.62200i	0.194640	+	0.224627i
$261$	13.5291	−	6.53808i	0.837430	−	0.404697i
$262$	−0.0159891	−	0.00469483i	−0.000987811	−	0.000290048i
$263$	6.09501	+	17.6104i	0.375835	+	1.08590i	0.961371	+	0.275256i	$0.0887627\pi$
$263$	6.09501	+	17.6104i	0.375835	+	1.08590i	−0.585536	+	0.810646i	$0.699116\pi$
$264$	0.776770	+	7.29476i	0.0478069	+	0.448961i
$265$	−0.265291	+	5.56915i	−0.0162967	+	0.342110i
$266$	−0.222198	+	1.15288i	−0.0136239	+	0.0706873i
$267$	−24.8121	−	19.0791i	−1.51848	−	1.16762i
$268$	−0.0872320	+	0.217895i	−0.00532854	+	0.0133100i
$269$	−17.1967	+	14.9010i	−1.04850	+	0.908533i	−0.995934	−	0.0900845i	$-0.971286\pi$
$269$	−17.1967	+	14.9010i	−1.04850	+	0.908533i	−0.0525686	+	0.998617i	$0.516741\pi$
$270$	2.37895	+	1.92907i	0.144778	+	0.117399i
$271$	−15.0529	+	4.41992i	−0.914397	+	0.268491i	−0.704891	−	0.709316i	$-0.749004\pi$
$271$	−15.0529	+	4.41992i	−0.914397	+	0.268491i	−0.209507	+	0.977807i	$0.567186\pi$
$272$	4.11762	+	5.78239i	0.249667	+	0.350609i
$273$	−8.09305	−	4.55581i	−0.489814	−	0.275730i
$274$	−0.146395	+	0.283968i	−0.00884407	+	0.0171551i
$275$	−4.04427	−	7.00489i	−0.243879	−	0.422410i
$276$	−14.9860	−	1.20471i	−0.902052	−	0.0725153i
$277$	6.50354	−	11.2645i	0.390760	−	0.676816i	−0.601790	−	0.798654i	$-0.705546\pi$
$277$	6.50354	−	11.2645i	0.390760	−	0.676816i	0.992550	+	0.121838i	$0.0388790\pi$
$278$	3.94929	+	6.14521i	0.236862	+	0.368565i
$279$	−22.1053	−	8.29605i	−1.32341	−	0.496672i
$280$	2.55401	−	5.59250i	0.152631	−	0.334216i
$281$	3.57724	−	14.7456i	0.213401	−	0.879649i	−0.759886	−	0.650056i	$-0.774745\pi$
$281$	3.57724	−	14.7456i	0.213401	−	0.879649i	0.973287	−	0.229593i	$-0.0737395\pi$
$282$	−0.231013	+	0.152041i	−0.0137566	+	0.00905392i
$283$	26.5103	+	9.17530i	1.57587	+	0.545415i	0.968502	−	0.249004i	$-0.0801033\pi$
$283$	26.5103	+	9.17530i	1.57587	+	0.545415i	0.607370	+	0.794419i	$0.292225\pi$
$284$	−17.1426	−	21.7986i	−1.01723	−	1.29351i
$285$	2.28345	+	0.302983i	0.135260	+	0.0179472i
$286$	2.05756	−	0.712129i	0.121666	−	0.0421091i
$287$	5.93354	+	3.81325i	0.350246	+	0.225089i
$288$	−9.70547	−	9.74500i	−0.571901	−	0.574230i
$289$	7.19711	−	8.30591i	0.423359	−	0.488583i
$290$	2.13668	−	2.03732i	0.125470	−	0.119636i
$291$	−11.0540	+	11.8486i	−0.647994	+	0.694578i
$292$	3.12605	−	9.03213i	0.182938	−	0.528566i
$293$	0.779937	−	1.09527i	0.0455644	−	0.0639862i	−0.791165	−	0.611602i	$-0.790525\pi$
$293$	0.779937	−	1.09527i	0.0455644	−	0.0639862i	0.836730	+	0.547616i	$0.184465\pi$
$294$	−0.0314838	+	0.372517i	−0.00183617	+	0.0217257i
$295$	10.4649	−	7.45204i	0.609291	−	0.433874i
$296$	1.15183	−	8.01118i	0.0669490	−	0.465640i
$297$	−11.5722	+	6.45250i	−0.671485	+	0.374412i
$298$			3.08411i			0.178657i
$299$	1.37486	+	9.29179i	0.0795100	+	0.537358i
$300$	9.27163	+	3.59522i	0.535298	+	0.207570i
$301$	−27.9222	−	14.3949i	−1.60941	−	0.829708i
$302$	2.48717	+	6.21265i	0.143121	+	0.357498i
$303$	4.11463	−	1.04574i	0.236379	−	0.0600764i
$304$	−2.76810	−	0.671533i	−0.158761	−	0.0385150i
$305$	−5.39843	+	2.46538i	−0.309113	+	0.141167i
$306$	1.67437	−	2.73445i	0.0957172	−	0.156318i
$307$	−3.37744	−	23.4906i	−0.192761	−	1.34068i	−0.824659	−	0.565630i	$-0.808633\pi$
$307$	−3.37744	−	23.4906i	−0.192761	−	1.34068i	0.631899	−	0.775051i	$-0.282276\pi$
$308$	8.71896	+	9.14419i	0.496809	+	0.521038i
$309$	9.63106	−	15.3510i	0.547892	−	0.873290i
$310$	−4.63374	−	0.220732i	−0.263179	−	0.0125368i
$311$	19.5020	+	0.928995i	1.10586	+	0.0526785i	0.592556	−	0.805529i	$-0.298119\pi$
$311$	19.5020	+	0.928995i	1.10586	+	0.0526785i	0.513302	+	0.858208i	$0.328422\pi$
$312$	−2.99464	+	4.77318i	−0.169538	+	0.270228i
$313$	−2.21259	−	2.32050i	−0.125063	−	0.131162i	0.658225	−	0.752821i	$-0.271307\pi$
$313$	−2.21259	−	2.32050i	−0.125063	−	0.131162i	−0.783288	+	0.621659i	$0.786459\pi$
$314$	0.553366	+	3.84875i	0.0312283	+	0.217197i
$315$	11.1003	+	0.286811i	0.625432	+	0.0161600i
$316$	24.3004	−	11.0976i	1.36700	−	0.624290i
$317$	15.4465	+	3.74727i	0.867560	+	0.210468i	0.644749	−	0.764394i	$-0.276962\pi$
$317$	15.4465	+	3.74727i	0.867560	+	0.210468i	0.222810	+	0.974862i	$0.428477\pi$
$318$	−3.01816	+	0.767074i	−0.169250	+	0.0430154i
$319$	4.74669	+	11.8567i	0.265764	+	0.663846i
$320$	4.55752	+	2.34956i	0.254773	+	0.131345i
$321$	−14.4515	−	5.60379i	−0.806604	−	0.312773i
$322$	4.80279	−	3.11446i	0.267649	−	0.173562i
$323$		−	2.41144i		−	0.134176i
$324$	6.11554	−	15.0977i	0.339752	−	0.838763i
$325$	0.884180	−	6.14961i	0.0490455	−	0.341119i
$326$	−4.57316	+	3.25653i	−0.253284	+	0.180363i
$327$	1.73502	−	20.5288i	0.0959470	−	1.13525i
$328$	2.48228	−	3.48587i	0.137061	−	0.192475i
$329$	−0.327933	+	0.947500i	−0.0180795	+	0.0522374i
$330$	−1.77583	+	1.90349i	−0.0977563	+	0.104784i
$331$	13.2349	−	12.6195i	0.727458	−	0.693630i	−0.232868	−	0.972508i	$-0.574811\pi$
$331$	13.2349	−	12.6195i	0.727458	−	0.693630i	0.960326	+	0.278878i	$0.0899626\pi$
$332$	−9.10705	+	10.5101i	−0.499814	+	0.576816i
$333$	14.1273	−	3.75465i	0.774172	−	0.205753i
$334$	7.95055	+	5.10951i	0.435035	+	0.279580i
$335$	−0.165680	+	0.0573424i	−0.00905207	+	0.00313295i
$336$	−13.6116	−	1.80607i	−0.742571	−	0.0985291i
$337$	−21.9142	−	27.8662i	−1.19374	−	1.51797i	−0.801381	−	0.598155i	$-0.795901\pi$
$337$	−21.9142	−	27.8662i	−1.19374	−	1.51797i	−0.392361	−	0.919811i	$-0.628342\pi$
$338$	−3.77557	−	1.30674i	−0.205364	−	0.0710771i
$339$	−10.8344	+	7.13066i	−0.588444	+	0.387284i
$340$	−1.41425	+	5.82962i	−0.0766985	+	0.316156i
$341$	8.33659	−	18.2546i	0.451452	−	0.988542i
$342$	0.210774	+	1.26919i	0.0113974	+	0.0686302i
$343$	−9.62807	−	14.9816i	−0.519867	−	0.808929i
$344$	−9.52996	+	16.5064i	−0.513821	+	0.889964i
$345$	−6.65061	−	9.04940i	−0.358057	−	0.487204i
$346$	−4.30371	−	7.45424i	−0.231369	−	0.400743i
$347$	13.0739	−	25.3598i	0.701842	−	1.36138i	−0.220644	−	0.975354i	$-0.570816\pi$
$347$	13.0739	−	25.3598i	0.701842	−	1.36138i	0.922486	−	0.386030i	$-0.126154\pi$
$348$	−13.6827	−	7.70237i	−0.733468	−	0.412890i
$349$	10.0967	+	14.1789i	0.540465	+	0.758977i	0.991012	−	0.133776i	$-0.0427103\pi$
$349$	10.0967	+	14.1789i	0.540465	+	0.758977i	−0.450547	+	0.892753i	$0.648771\pi$
$350$	−3.63284	+	1.06670i	−0.194184	+	0.0570174i
$351$	−10.0506	−	1.59875i	−0.536464	−	0.0853352i
$352$	8.83468	−	7.65530i	0.470890	−	0.408029i
$353$	−2.53392	+	6.32944i	−0.134867	+	0.336882i	−0.980393	−	0.197053i	$-0.936863\pi$
$353$	−2.53392	+	6.32944i	−0.134867	+	0.336882i	0.845526	+	0.533935i	$0.179287\pi$
$354$	5.68834	+	4.37401i	0.302332	+	0.232476i
$355$	3.92037	−	20.3408i	0.208071	−	1.07958i
$356$	−1.55624	+	32.6696i	−0.0824807	+	1.73148i
$357$	−1.23086	−	11.5592i	−0.0651440	−	0.611776i
$358$	2.25291	+	6.50935i	0.119070	+	0.344030i
$359$	−3.72931	−	1.09502i	−0.196825	−	0.0577931i	0.181834	−	0.983329i	$-0.441797\pi$
$359$	−3.72931	−	1.09502i	−0.196825	−	0.0577931i	−0.378659	+	0.925536i	$0.623615\pi$
$360$	0.494276	−	6.71895i	0.0260506	−	0.354120i
$361$	−11.8087	−	13.6280i	−0.621511	−	0.717262i
$362$	4.32547	+	0.413033i	0.227342	+	0.0217085i
$363$	3.31346	+	7.05134i	0.173911	+	0.370099i
$364$	0.922499	+	9.66085i	0.0483521	+	0.506366i
$365$	6.62811	−	2.65349i	0.346931	−	0.138890i
$366$	−2.19786	−	2.48137i	−0.114884	−	0.129704i
$367$	−1.28450	−	0.741608i	−0.0670505	−	0.0387116i	0.466100	−	0.884732i	$-0.345659\pi$
$367$	−1.28450	−	0.741608i	−0.0670505	−	0.0387116i	−0.533150	+	0.846020i	$0.678992\pi$
$368$	6.99281	+	11.9981i	0.364526	+	0.625442i
$369$	7.54896	+	1.65825i	0.392983	+	0.0863251i
$370$	2.41614	−	1.55276i	0.125609	−	0.0807240i
$371$	−6.97907	+	8.87461i	−0.362335	+	0.460747i
$372$	6.07732	+	23.9121i	0.315094	+	1.23978i
$373$	−3.12431	+	3.27669i	−0.161771	+	0.169660i	−0.799631	−	0.600492i	$-0.794971\pi$
$373$	−3.12431	+	3.27669i	−0.161771	+	0.169660i	0.637860	+	0.770152i	$0.279820\pi$
$374$	2.21994	+	1.58081i	0.114790	+	0.0817417i
$375$	6.45546	+	18.0150i	0.333359	+	0.930293i
$376$	0.564755	+	0.226094i	0.0291250	+	0.0116599i
$377$	−2.76376	+	9.41249i	−0.142341	+	0.484768i
$378$	1.65817	+	5.97626i	0.0852869	+	0.307386i
$379$	9.67600	−	15.0561i	0.497023	−	0.773382i	−0.498602	−	0.866831i	$-0.666153\pi$
$379$	9.67600	−	15.0561i	0.497023	−	0.773382i	0.995624	+	0.0934491i	$0.0297893\pi$
$380$	−1.10297	−	2.13945i	−0.0565809	−	0.109752i
$381$	−10.8150	+	5.72536i	−0.554070	+	0.293319i
$382$	−7.98472	+	1.93707i	−0.408534	+	0.0991092i
$383$	−19.1401	+	15.0520i	−0.978015	+	0.769120i	−0.972985	−	0.230868i	$-0.925844\pi$
$383$	−19.1401	+	15.0520i	−0.978015	+	0.769120i	−0.00503021	+	0.999987i	$0.501601\pi$
$384$	−3.34701	+	18.4440i	−0.170802	+	0.941215i
$385$	−0.897134	+	9.39521i	−0.0457222	+	0.478824i
$386$	0.806710	+	2.74740i	0.0410605	+	0.139839i
$387$	−34.1722	−	4.15625i	−1.73707	−	0.211274i
$388$	16.7605	+	2.40980i	0.850886	+	0.122339i
$389$	−0.0955095	−	2.00499i	−0.00484253	−	0.101657i	−0.999995	−	0.00330828i	$-0.998947\pi$
$389$	−0.0955095	−	2.00499i	−0.00484253	−	0.101657i	0.995152	−	0.0983488i	$-0.0313561\pi$
$390$	−1.97599	+	0.306091i	−0.100058	+	0.0154995i
$391$	−8.47550	+	8.14796i	−0.428624	+	0.412060i
$392$	0.712161	−	0.411167i	0.0359696	−	0.0207670i
$393$	−0.0495583	+	0.0438959i	−0.00249988	+	0.00221425i
$394$	1.52919	+	1.20257i	0.0770396	+	0.0605846i
$395$	18.1520	+	8.28975i	0.913327	+	0.417103i
$396$	12.4413	+	6.07489i	0.625198	+	0.305274i
$397$	14.4489	+	31.6388i	0.725171	+	1.58790i	0.806512	+	0.591217i	$0.201352\pi$
$397$	14.4489	+	31.6388i	0.725171	+	1.58790i	−0.0813410	+	0.996686i	$0.525920\pi$
$398$	3.42149	−	0.659439i	0.171504	−	0.0330547i
$399$	3.41064	+	3.18189i	0.170746	+	0.159294i
$400$	−2.16556	−	8.92655i	−0.108278	−	0.446327i
$401$	−30.5919	−	5.89610i	−1.52768	−	0.294437i	−0.644919	−	0.764251i	$-0.723109\pi$
$401$	−30.5919	−	5.89610i	−1.52768	−	0.294437i	−0.882765	+	0.469814i	$0.844321\pi$
$402$	−0.0576666	−	0.0791441i	−0.00287615	−	0.00394735i
$403$	13.7009	−	7.06329i	0.682489	−	0.351848i
$404$	−3.35274	−	2.90517i	−0.166805	−	0.144538i
$405$	11.5147	−	3.93294i	0.572171	−	0.195430i
$406$	5.91744	−	0.850799i	0.293677	−	0.0422244i
$407$	2.35134	+	12.1999i	0.116552	+	0.604728i
$408$	−7.04084	+	0.412245i	−0.348574	+	0.0204091i
$409$	−5.36308	−	5.11369i	−0.265187	−	0.252855i	0.545805	−	0.837912i	$-0.316224\pi$
$409$	−5.36308	−	5.11369i	−0.265187	−	0.252855i	−0.810992	+	0.585057i	$0.801072\pi$
$410$	1.51169	−	0.144349i	0.0746572	−	0.00712890i
$411$	0.646545	+	1.09222i	0.0318917	+	0.0538753i
$412$	−18.9154	+	0.901054i	−0.931897	+	0.0443917i
$413$	26.0148			1.28011
$414$	3.74866	−	5.02926i	0.184237	−	0.247174i
$415$	−10.3882			−0.509936
$416$	8.96894	−	0.427243i	0.439738	−	0.0209473i
$417$	29.0189	−	0.315848i	1.42106	−	0.0154671i
$418$	−1.08858	+	0.103947i	−0.0532443	+	0.00508422i
$419$	5.38418	+	5.13380i	0.263034	+	0.250803i	0.810107	−	0.586283i	$-0.199409\pi$
$419$	5.38418	+	5.13380i	0.263034	+	0.250803i	−0.547072	+	0.837085i	$0.684258\pi$
$420$	−6.37906	−	9.69243i	−0.311266	−	0.472942i
$421$	7.09791	+	36.8275i	0.345931	+	1.79486i	0.571465	+	0.820626i	$0.306375\pi$
$421$	7.09791	+	36.8275i	0.345931	+	1.79486i	−0.225534	+	0.974235i	$0.572413\pi$
$422$	−0.710997	+	0.102226i	−0.0346108	+	0.00497628i
$423$	0.0239142	+	1.09844i	0.00116275	+	0.0534081i
$424$	5.17688	+	4.48579i	0.251412	+	0.217849i
$425$	6.91195	−	3.56336i	0.335279	−	0.172848i
$426$	11.5052	−	1.22511i	0.557427	−	0.0593567i
$427$	−11.8004	−	2.27435i	−0.571063	−	0.110063i
$428$	3.81854	+	15.7402i	0.184576	+	0.760834i
$429$	1.94771	−	8.42788i	0.0940363	−	0.406902i
$430$	−6.64135	+	1.28001i	−0.320274	+	0.0617278i
$431$	−14.6755	−	32.1349i	−0.706895	−	1.54788i	−0.831406	−	0.555665i	$-0.812464\pi$
$431$	−14.6755	−	32.1349i	−0.706895	−	1.54788i	0.124511	−	0.992218i	$-0.460264\pi$
$432$	−14.6736	+	3.32834i	−0.705984	+	0.160135i
$433$	24.8474	+	11.3474i	1.19409	+	0.545323i	0.910454	−	0.413609i	$-0.135732\pi$
$433$	24.8474	+	11.3474i	1.19409	+	0.545323i	0.283636	+	0.958932i	$0.408459\pi$
$434$	−7.38401	−	5.80685i	−0.354444	−	0.278738i
$435$	−2.34492	−	11.4921i	−0.112430	−	0.551003i
$436$	−18.6440	+	10.7641i	−0.892888	+	0.515509i
$437$	0.429175	−	4.69796i	0.0205302	−	0.224734i
$438$	2.49900	+	3.10753i	0.119407	+	0.148484i
$439$	1.32594	+	27.8350i	0.0632839	+	1.32849i	0.777640	+	0.628710i	$0.216417\pi$
$439$	1.32594	+	27.8350i	0.0632839	+	1.32849i	−0.714356	+	0.699782i	$0.753280\pi$
$440$	5.66796	+	0.814930i	0.270209	+	0.0388503i
$441$	1.18716	+	0.892469i	0.0565315	+	0.0424985i
$442$	0.589748	+	2.00850i	0.0280514	+	0.0955344i
$443$	1.02281	−	10.7114i	0.0485953	−	0.508913i	−0.938104	−	0.346355i	$-0.887419\pi$
$443$	1.02281	−	10.7114i	0.0485953	−	0.508913i	0.986699	−	0.162559i	$-0.0519746\pi$
$444$	−11.6522	−	9.87674i	−0.552990	−	0.468729i
$445$	−19.2043	+	15.1024i	−0.910371	+	0.715924i
$446$	4.82501	−	1.17054i	0.228471	−	0.0554265i
$447$	10.3790	+	6.51164i	0.490908	+	0.307990i
$448$	4.75777	+	9.22879i	0.224783	+	0.436019i
$449$	−9.10546	+	14.1684i	−0.429713	+	0.668647i	−0.986825	−	0.161791i	$-0.948273\pi$
$449$	−9.10546	+	14.1684i	−0.429713	+	0.668647i	0.557112	+	0.830437i	$0.311909\pi$
$450$	−3.32645	+	2.47962i	−0.156810	+	0.116890i
$451$	−1.85078	+	6.30317i	−0.0871497	+	0.296805i
$452$	12.5827	+	5.03734i	0.591838	+	0.236936i
$453$	26.1588	+	4.74702i	1.22905	+	0.223034i
$454$	9.47335	+	6.74594i	0.444606	+	0.316603i
$455$	−5.00261	+	5.24658i	−0.234526	+	0.245964i
$456$	2.02681	−	1.97512i	0.0949143	−	0.0924935i
$457$	−0.819490	+	1.04207i	−0.0383341	+	0.0487458i	−0.804842	−	0.593489i	$-0.797750\pi$
$457$	−0.819490	+	1.04207i	−0.0383341	+	0.0487458i	0.766508	+	0.642235i	$0.221993\pi$
$458$	−6.62940	+	4.26045i	−0.309771	+	0.199078i
$459$	−5.66709	−	11.4082i	−0.264517	−	0.532487i
$460$	−3.79276	+	11.1055i	−0.176838	+	0.517799i
$461$	−19.3746	−	11.1859i	−0.902367	−	0.520982i	−0.0243994	−	0.999702i	$-0.507767\pi$
$461$	−19.3746	−	11.1859i	−0.902367	−	0.520982i	−0.877967	+	0.478721i	$0.841101\pi$
$462$	−5.16503	+	1.05391i	−0.240299	+	0.0490322i
$463$	−10.6377	+	4.25870i	−0.494376	+	0.197918i	−0.605434	−	0.795896i	$-0.707000\pi$
$463$	−10.6377	+	4.25870i	−0.494376	+	0.197918i	0.111058	+	0.993814i	$0.464576\pi$
$464$	1.37865	+	14.4378i	0.0640021	+	0.670260i
$465$	−10.5263	+	15.1279i	−0.488146	+	0.701541i
$466$	2.57446	+	0.245831i	0.119259	+	0.0113879i
$467$	−24.8219	−	28.6460i	−1.14862	−	1.32558i	−0.937447	−	0.348128i	$-0.886817\pi$
$467$	−24.8219	−	28.6460i	−1.14862	−	1.32558i	−0.211172	−	0.977449i	$-0.567728\pi$
$468$	4.62726	+	9.57509i	0.213895	+	0.442609i
$469$	−0.340641	−	0.100021i	−0.0157293	−	0.00461855i
$470$	0.0706046	+	0.203999i	0.00325675	+	0.00940976i
$471$	14.1206	+	6.26382i	0.650642	+	0.288622i
$472$	0.751027	−	15.7660i	0.0345688	−	0.725689i
$473$	5.53729	−	28.7302i	0.254605	−	1.32102i
$474$	−1.46605	+	11.0490i	−0.0673380	+	0.507497i
$475$	−1.15971	+	2.89683i	−0.0532114	+	0.132916i
$476$	−9.18021	+	7.95470i	−0.420774	+	0.364603i
$477$	−3.79097	+	11.7766i	−0.173577	+	0.539214i
$478$	−9.87231	+	2.89877i	−0.451549	+	0.132587i
$479$	−16.9516	−	23.8052i	−0.774539	−	1.08769i	−0.993708	−	0.112001i	$-0.964274\pi$
$479$	−16.9516	−	23.8052i	−0.774539	−	1.08769i	0.219169	−	0.975687i	$-0.429665\pi$
$480$	−9.23835	+	5.46868i	−0.421671	+	0.249610i
$481$	−4.37298	+	8.48240i	−0.199391	+	0.386764i
$482$	−0.00105844	−	0.00183327i	−4.82105e−5	−	8.35031e-5i
$483$	−0.340717	−	22.7386i	−0.0155032	−	1.03464i
$484$	4.07066	−	7.05060i	0.185030	−	0.320482i
$485$	6.83833	+	10.6407i	0.310513	+	0.483167i
$486$	3.97985	+	5.50903i	0.180530	+	0.249895i
$487$	−1.19488	+	2.61642i	−0.0541451	+	0.118561i	−0.934771	−	0.355251i	$-0.884395\pi$
$487$	−1.19488	+	2.61642i	−0.0541451	+	0.118561i	0.880626	+	0.473813i	$0.157123\pi$
$488$	−1.71901	+	7.08587i	−0.0778161	+	0.320762i
$489$	1.30367	+	22.2658i	0.0589541	+	1.00689i
$490$	0.275762	+	0.0954423i	0.0124577	+	0.00431164i
$491$	2.09820	+	2.66807i	0.0946903	+	0.120408i	0.831089	−	0.556139i	$-0.187718\pi$
$491$	2.09820	+	2.66807i	0.0946903	+	0.120408i	−0.736399	+	0.676547i	$0.763475\pi$
$492$	−3.08313	−	7.46479i	−0.138998	−	0.336539i
$493$	−11.6033	+	4.01596i	−0.522589	+	0.180870i
$494$	−0.706610	−	0.454111i	−0.0317919	−	0.0204314i
$495$	2.65644	+	9.99517i	0.119398	+	0.449249i
$496$	14.9240	−	17.2233i	0.670109	−	0.773347i
$497$	30.3587	−	28.9470i	1.36177	−	1.29845i
$498$	−1.69517	−	5.54906i	−0.0759622	−	0.248659i
$499$	11.4324	−	33.0319i	0.511786	−	1.47871i	−0.332648	−	0.943051i	$-0.607942\pi$
$499$	11.4324	−	33.0319i	0.511786	−	1.47871i	0.844435	−	0.535659i	$-0.179937\pi$
$500$	11.5995	−	16.2892i	0.518744	−	0.728474i
$501$	33.9815	−	15.9681i	1.51818	−	0.713400i
$502$	−4.13823	+	2.94682i	−0.184698	+	0.131523i
$503$	5.17787	−	36.0129i	0.230870	−	1.60574i	−0.463486	−	0.886104i	$-0.653402\pi$
$503$	5.17787	−	36.0129i	0.230870	−	1.60574i	0.694356	−	0.719632i	$-0.255689\pi$
$504$	8.70732	−	10.5022i	0.387855	−	0.467806i
$505$		−	3.31386i		−	0.147465i
$506$	4.04353	+	3.47482i	0.179757	+	0.154475i
$507$	−12.3691	+	9.94696i	−0.549333	+	0.441760i
$508$	11.3657	+	5.85942i	0.504271	+	0.259970i
$509$	6.35187	+	15.8662i	0.281542	+	0.703257i	0.999971	+	0.00765692i	$0.00243730\pi$
$509$	6.35187	+	15.8662i	0.281542	+	0.703257i	−0.718429	+	0.695600i	$0.755138\pi$
$510$	−1.74673	−	1.79244i	−0.0773465	−	0.0793708i
$511$	14.0497	+	3.40843i	0.621523	+	0.150780i
$512$	20.8260	−	9.51090i	0.920387	−	0.420327i
$513$	4.71625	+	1.97040i	0.208227	+	0.0869953i
$514$	−1.19840	−	8.33507i	−0.0528592	−	0.367644i
$515$	−9.76155	−	10.2376i	−0.430145	−	0.451123i
$516$	16.8302	+	31.7917i	0.740908	+	1.39955i
$517$	−0.932793	−	0.0444344i	−0.0410242	−	0.00195422i
$518$	5.80924	+	0.276728i	0.255243	+	0.0121587i
$519$	−34.1725	−	1.25524i	−1.50001	−	0.0550991i
$520$	3.03521	+	3.18324i	0.133103	+	0.139594i
$521$	0.986728	+	6.86285i	0.0432294	+	0.300667i	0.999953	+	0.00966953i	$0.00307796\pi$
$521$	0.986728	+	6.86285i	0.0432294	+	0.300667i	−0.956724	+	0.290997i	$0.906013\pi$
$522$	5.75608	−	3.12789i	0.251937	−	0.136904i
$523$	−11.6936	+	5.34027i	−0.511324	+	0.233514i	−0.654332	−	0.756208i	$-0.727050\pi$
$523$	−11.6936	+	5.34027i	−0.511324	+	0.233514i	0.143008	+	0.989722i	$0.454323\pi$
$524$	0.0672296	+	0.0163097i	0.00293694	+	0.000712494i
$525$	−4.08045	+	14.4778i	−0.178085	+	0.631863i
$526$	3.01960	+	7.54260i	0.131661	+	0.328873i
$527$	17.1489	+	8.84088i	0.747018	+	0.385115i
$528$	−1.95769	−	12.6380i	−0.0851975	−	0.549999i
$529$	−17.9621	+	14.3654i	−0.780959	+	0.624583i
$530$			2.43078i			0.105586i
$531$	26.7300	−	9.90794i	1.15998	−	0.429968i
$532$	0.693663	−	4.82453i	0.0300741	−	0.209170i
$533$	−4.11026	+	2.92690i	−0.178035	+	0.126778i
$534$	−11.2011	−	7.79392i	−0.484717	−	0.337276i
$535$	−7.01797	+	9.85536i	−0.303413	+	0.426084i
$536$	−0.0704507	+	0.203554i	−0.00304301	+	0.00879219i
$537$	26.6626	+	6.16182i	1.15058	+	0.265902i
$538$	−7.17978	+	6.84591i	−0.309542	+	0.295148i
$539$	−0.826674	+	0.954032i	−0.0356074	+	0.0410931i
$540$	−10.2459	−	7.52937i	−0.440912	−	0.324013i
$541$	−21.9951	−	14.1354i	−0.945644	−	0.607728i	−0.0256542	−	0.999671i	$-0.508167\pi$
$541$	−21.9951	−	14.1354i	−0.945644	−	0.607728i	−0.919990	+	0.391942i	$0.871803\pi$
$542$	−6.46360	+	2.23707i	−0.277635	+	0.0960905i
$543$	10.5226	−	13.6845i	0.451567	−	0.587258i
$544$	6.94739	+	8.83433i	0.297867	+	0.378769i
$545$	−15.1968	−	5.25967i	−0.650961	−	0.225300i
$546$	−3.61890	−	1.81609i	−0.154875	−	0.0777217i
$547$	5.31227	−	21.8975i	0.227136	−	0.936269i	−0.738058	−	0.674737i	$-0.764257\pi$
$547$	5.31227	−	21.8975i	0.227136	−	0.936269i	0.965195	−	0.261532i	$-0.0842278\pi$
$548$	0.550967	−	1.20645i	0.0235361	−	0.0515369i
$549$	−12.9910	+	2.15741i	−0.554444	+	0.0920761i
$550$	−1.90653	−	2.96662i	−0.0812947	−	0.126497i
$551$	2.46345	−	4.26683i	0.104947	−	0.181773i
$552$	−13.7903	−	0.449957i	−0.586955	−	0.0191514i
$553$	20.2044	+	34.9950i	0.859178	+	1.48814i
$554$	2.59851	−	5.04041i	0.110400	−	0.214146i
$555$	−0.124183	−	11.4095i	−0.00527128	−	0.484305i
$556$	−17.5904	−	24.7023i	−0.746000	−	1.04761i
$557$	−10.1124	+	2.96927i	−0.428476	+	0.125812i	−0.488858	−	0.872364i	$-0.662586\pi$
$557$	−10.1124	+	2.96927i	−0.428476	+	0.125812i	0.0603820	+	0.998175i	$0.480768\pi$
$558$	−9.79859	−	3.15423i	−0.414807	−	0.133529i
$559$	16.9847	−	14.7173i	0.718374	−	0.622475i
$560$	−3.98343	+	9.95012i	−0.168331	+	0.420469i
$561$	10.0070	−	4.13312i	0.422495	−	0.174500i
$562$	1.25194	−	6.49568i	0.0528099	−	0.274004i
$563$	−0.897103	+	18.8325i	−0.0378084	+	0.793695i	0.897746	+	0.440513i	$0.145203\pi$
$563$	−0.897103	+	18.8325i	−0.0378084	+	0.793695i	−0.935555	+	0.353182i	$0.885100\pi$
$564$	0.927912	−	0.676103i	0.0390722	−	0.0284691i
$565$	3.31132	+	9.56744i	0.139308	+	0.402505i
$566$	11.7351	+	3.44575i	0.493265	+	0.144836i
$567$	23.6129	+	7.03776i	0.991650	+	0.295558i
$568$	−16.6666	−	19.2342i	−0.699313	−	0.807050i
$569$	−36.4721	−	3.48267i	−1.52899	−	0.146001i	−0.703614	−	0.710582i	$-0.748432\pi$
$569$	−36.4721	−	3.48267i	−1.52899	−	0.146001i	−0.825377	+	0.564581i	$0.809038\pi$
$570$	1.00069	+	0.0845749i	0.0419144	+	0.00354245i
$571$	2.19694	+	23.0074i	0.0919389	+	0.962828i	0.917293	+	0.398213i	$0.130369\pi$
$571$	2.19694	+	23.0074i	0.0919389	+	0.962828i	−0.825354	+	0.564615i	$0.809025\pi$
$572$	−8.39144	+	3.35943i	−0.350864	+	0.140465i
$573$	−10.3397	+	30.9609i	−0.431948	+	1.29341i
$574$	2.66307	+	1.53752i	0.111154	+	0.0641749i
$575$	14.1000	−	5.71197i	0.588011	−	0.238205i
$576$	8.40341	+	7.67046i	0.350142	+	0.319603i
$577$	−10.2451	+	6.58412i	−0.426509	+	0.274100i	−0.736236	−	0.676725i	$-0.763399\pi$
$577$	−10.2451	+	6.58412i	−0.426509	+	0.274100i	0.309727	+	0.950825i	$0.399762\pi$
$578$	2.96192	−	3.76639i	0.123200	−	0.156661i
$579$	10.9491	+	3.08591i	0.455029	+	0.128246i
$580$	−8.45775	+	8.87024i	−0.351189	+	0.368316i
$581$	−17.1352	−	12.2019i	−0.710886	−	0.506220i
$582$	−4.56802	+	5.38919i	−0.189351	+	0.223389i
$583$	−9.76220	−	3.90820i	−0.404309	−	0.161861i
$584$	2.47124	−	8.41628i	0.102261	−	0.348268i
$585$	−3.14193	+	7.29610i	−0.129903	+	0.301656i
$586$	0.316929	−	0.493151i	0.0130922	−	0.0203719i
$587$	9.45446	+	18.3391i	0.390227	+	0.756935i	0.999347	−	0.0361432i	$-0.0115072\pi$
$587$	9.45446	+	18.3391i	0.390227	+	0.756935i	−0.609119	+	0.793079i	$0.708477\pi$
$588$	0.0569701	−	1.55094i	0.00234941	−	0.0639597i
$589$	−7.52351	+	1.82518i	−0.310001	+	0.0752054i
$590$	4.40272	−	3.46233i	0.181257	−	0.142542i
$591$	7.27569	−	2.60715i	0.299282	−	0.107244i
$592$	−1.34118	+	14.0455i	−0.0551223	+	0.577266i
$593$	−5.52792	−	18.8264i	−0.227005	−	0.773106i	−0.991684	−	0.128696i	$-0.958921\pi$
$593$	−5.52792	−	18.8264i	−0.227005	−	0.773106i	0.764680	−	0.644411i	$-0.222897\pi$
$594$	−4.90564	+	3.05002i	−0.201281	+	0.125144i
$595$	−8.98138	−	1.29133i	−0.368200	−	0.0529392i
$596$	−0.609210	−	12.7889i	−0.0249542	−	0.523853i
$597$	5.00477	−	12.9067i	0.204832	−	0.528236i
$598$	0.791483	+	4.01790i	0.0323662	+	0.164304i
$599$	11.5561	−	6.67194i	0.472171	−	0.272608i	−0.244977	−	0.969529i	$-0.578780\pi$
$599$	11.5561	−	6.67194i	0.472171	−	0.272608i	0.717148	+	0.696921i	$0.245447\pi$
$600$	8.65631	+	2.89087i	0.353393	+	0.118019i
$601$	−4.12717	−	3.24564i	−0.168351	−	0.132393i	0.530429	−	0.847729i	$-0.322031\pi$
$601$	−4.12717	−	3.24564i	−0.168351	−	0.132393i	−0.698780	+	0.715337i	$0.746273\pi$
$602$	−12.4583	−	5.68951i	−0.507762	−	0.231887i
$603$	−0.388099	+	0.0269647i	−0.0158046	+	0.00109809i
$604$	−11.5408	−	25.2708i	−0.469588	−	1.02825i
$605$	5.97154	−	1.15092i	0.242778	−	0.0467916i
$606$	1.77016	−	0.540761i	0.0719079	−	0.0219669i
$607$	−10.1058	−	41.6567i	−0.410182	−	1.69079i	−0.684384	−	0.729122i	$-0.739929\pi$
$607$	−10.1058	−	41.6567i	−0.410182	−	1.69079i	0.274202	−	0.961672i	$-0.411586\pi$
$608$	−4.42818	−	0.853461i	−0.179586	−	0.0346124i
$609$	9.63060	−	21.7103i	0.390252	−	0.879747i
$610$	−2.29979	+	1.18562i	−0.0931157	+	0.0480045i
$611$	−0.542095	−	0.469728i	−0.0219308	−	0.0190032i
$612$	−6.40298	+	11.6697i	−0.258825	+	0.471721i
$613$	−36.5534	+	5.25558i	−1.47638	+	0.212271i	−0.832998	−	0.553277i	$-0.813377\pi$
$613$	−36.5534	+	5.25558i	−1.47638	+	0.212271i	−0.643379	+	0.765547i	$0.722468\pi$
$614$	−1.95813	−	10.1597i	−0.0790236	−	0.410013i
$615$	2.70594	−	5.39209i	0.109114	−	0.217430i
$616$	8.39200	+	8.00176i	0.338123	+	0.322400i
$617$	6.47414	−	0.618205i	0.260639	−	0.0248880i	0.0360815	−	0.999349i	$-0.488512\pi$
$617$	6.47414	−	0.618205i	0.260639	−	0.0248880i	0.224557	+	0.974461i	$0.427906\pi$
$618$	3.87572	−	6.88492i	0.155904	−	0.276952i
$619$	0.141736	−	0.00675172i	0.00569686	−	0.000271375i	−0.0447333	−	0.998999i	$-0.514244\pi$
$619$	0.141736	−	0.00675172i	0.00569686	−	0.000271375i	0.0504302	+	0.998728i	$0.483941\pi$
$620$	19.2584			0.773436
$621$	−9.01024	−	23.2339i	−0.361569	−	0.932346i
$622$	8.51209			0.341304
$623$	−49.4164	+	2.35399i	−1.97983	+	0.0943107i
$624$	4.81866	−	8.55999i	0.192901	−	0.342674i
$625$	−0.918994	+	0.0877532i	−0.0367597	+	0.00351013i
$626$	−1.01169	−	0.964640i	−0.0404351	−	0.0385548i
$627$	−1.94857	+	3.88288i	−0.0778184	+	0.155067i
$628$	−3.05490	−	15.8503i	−0.121904	−	0.632497i
$629$	−11.8234	+	1.69995i	−0.471430	+	0.0677814i
$630$	4.83996	−	0.105371i	0.192829	−	0.00419808i
$631$	−7.68879	−	6.66238i	−0.306086	−	0.265225i	0.488250	−	0.872704i	$-0.337635\pi$
$631$	−7.68879	−	6.66238i	−0.306086	−	0.265225i	−0.794336	+	0.607479i	$0.792181\pi$
$632$	21.7916	−	11.2344i	0.866824	−	0.446879i
$633$	−1.15714	+	2.60856i	−0.0459924	+	0.103681i
$634$	6.80442	+	1.31145i	0.270238	+	0.0520841i
$635$	2.25193	+	9.28256i	0.0893649	+	0.368367i
$636$	12.3639	−	3.77702i	0.490261	−	0.149769i
$637$	−0.952106	+	0.183503i	−0.0377238	+	0.00727067i
$638$	2.31307	+	5.06492i	0.0915754	+	0.200522i
$639$	20.1686	−	41.3051i	0.797858	−	1.63400i
$640$	13.3096	+	6.07831i	0.526110	+	0.240266i
$641$	1.47068	+	1.15656i	0.0580886	+	0.0456813i	0.646781	−	0.762676i	$-0.276115\pi$
$641$	1.47068	+	1.15656i	0.0580886	+	0.0456813i	−0.588693	+	0.808357i	$0.700357\pi$
$642$	−6.40964	−	2.14057i	−0.252968	−	0.0844816i
$643$	3.84585	−	2.22040i	0.151665	−	0.0875641i	−0.422247	−	0.906481i	$-0.638758\pi$
$643$	3.84585	−	2.22040i	0.151665	−	0.0875641i	0.573912	+	0.818917i	$0.305425\pi$
$644$	−19.3006	+	13.8635i	−0.760549	+	0.546297i
$645$	−9.71459	+	25.0527i	−0.382512	+	0.986451i
$646$	−0.0500245	−	1.05014i	−0.00196819	−	0.0413174i
$647$	−6.43376	−	0.925035i	−0.252937	−	0.0363669i	0.0146798	−	0.999892i	$-0.495327\pi$
$647$	−6.43376	−	0.925035i	−0.252937	−	0.0363669i	−0.267617	+	0.963525i	$0.586236\pi$
$648$	4.94684	−	14.1072i	0.194330	−	0.554182i
$649$	6.82634	+	23.2484i	0.267957	+	0.912579i
$650$	0.257475	−	2.69640i	0.0100990	−	0.105761i
$651$	−35.1321	+	12.5892i	−1.37694	+	0.493408i
$652$	18.3203	−	14.4072i	0.717478	−	0.564231i
$653$	−7.00368	+	1.69907i	−0.274075	+	0.0664899i	−0.370441	−	0.928856i	$-0.620793\pi$
$653$	−7.00368	+	1.69907i	−0.274075	+	0.0664899i	0.0963657	+	0.995346i	$0.469278\pi$
$654$	0.329711	−	8.97597i	0.0128927	−	0.350988i
$655$	0.0236794	+	0.0459316i	0.000925230	+	0.00179470i
$656$	−4.03327	+	6.27588i	−0.157473	+	0.245032i
$657$	15.7341	−	1.84881i	0.613845	−	0.0721291i
$658$	−0.123154	+	0.419424i	−0.00480104	+	0.0163509i
$659$	33.3067	+	13.3340i	1.29745	+	0.519419i	0.914587	−	0.404388i	$-0.132515\pi$
$659$	33.3067	+	13.3340i	1.29745	+	0.519419i	0.382858	+	0.923807i	$0.374940\pi$
$660$	6.98785	−	8.24402i	0.272002	−	0.320898i
$661$	28.0015	+	19.9398i	1.08913	+	0.775569i	0.975948	−	0.218005i	$-0.0699550\pi$
$661$	28.0015	+	19.9398i	1.08913	+	0.775569i	0.113186	+	0.993574i	$0.463894\pi$
$662$	5.50182	−	5.77014i	0.213834	−	0.224263i
$663$	8.00438	+	2.25597i	0.310864	+	0.0876144i
$664$	−7.88950	+	10.0323i	−0.306172	+	0.389329i
$665$	3.06292	−	1.96842i	0.118775	−	0.0763321i
$666$	6.07433	−	1.92815i	0.235376	−	0.0747145i
$667$	−23.3203	+	5.75877i	−0.902967	+	0.222981i
$668$	−33.9779	−	19.6172i	−1.31464	−	0.759011i
$669$	6.24810	−	18.7091i	0.241566	−	0.723334i
$670$	−0.0709615	+	0.0284087i	−0.00274148	+	0.00109752i
$671$	−1.06397	−	11.1424i	−0.0410740	−	0.430146i
$672$	−21.6620	−	1.83079i	−0.835628	−	0.0706243i
$673$	−18.5330	−	1.76969i	−0.714395	−	0.0682164i	−0.268472	−	0.963288i	$-0.586519\pi$
$673$	−18.5330	−	1.76969i	−0.714395	−	0.0682164i	−0.445923	+	0.895071i	$0.647125\pi$
$674$	−10.1213	−	11.6807i	−0.389860	−	0.449922i
$675$	1.32136	+	16.4299i	0.0508590	+	0.632386i
$676$	15.9143	+	4.67286i	0.612089	+	0.179726i
$677$	0.499320	+	1.44269i	0.0191904	+	0.0554471i	0.954189	−	0.299204i	$-0.0967210\pi$
$677$	0.499320	+	1.44269i	0.0191904	+	0.0554471i	−0.934999	+	0.354651i	$0.884600\pi$
$678$	−4.57029	+	3.33004i	−0.175521	+	0.127889i
$679$	−1.21871	+	25.5838i	−0.0467697	+	0.981817i
$680$	−1.04188	+	5.40578i	−0.0399543	+	0.207302i
$681$	42.7038	−	17.6377i	1.63641	−	0.675876i
$682$	3.25177	−	8.12252i	0.124517	−	0.311027i
$683$	−35.5066	+	30.7666i	−1.35862	+	1.17725i	−0.392323	+	0.919827i	$0.628329\pi$
$683$	−35.5066	+	30.7666i	−1.35862	+	1.17725i	−0.966298	+	0.257425i	$0.917126\pi$
$684$	−1.12473	−	5.22135i	−0.0430049	−	0.199643i
$685$	0.950597	−	0.279120i	0.0363204	−	0.0106646i
$686$	−4.50366	−	6.32450i	−0.171950	−	0.241471i
$687$	0.340734	+	31.3053i	0.0129998	+	1.19437i
$688$	15.2254	−	29.5332i	0.580464	−	1.12594i
$689$	−4.03848	−	6.99485i	−0.153854	−	0.266483i
$690$	−3.08396	−	3.80291i	−0.117404	−	0.144774i
$691$	2.37066	−	4.10610i	0.0901840	−	0.156203i	−0.817404	−	0.576064i	$-0.804588\pi$
$691$	2.37066	−	4.10610i	0.0901840	−	0.156203i	0.907588	+	0.419861i	$0.137921\pi$
$692$	19.3187	+	30.0605i	0.734386	+	1.14273i
$693$	−7.35849	+	19.6071i	−0.279526	+	0.744812i
$694$	5.16738	−	11.3150i	0.196151	−	0.429511i
$695$	5.34054	−	22.0140i	0.202578	−	0.835039i
$696$	−12.8793	−	6.46328i	−0.488188	−	0.244990i
$697$	−5.96840	−	2.06568i	−0.226069	−	0.0782433i
$698$	4.69109	+	5.96521i	0.177561	+	0.225787i
$699$	6.26289	−	8.14480i	0.236884	−	0.308065i
$700$	14.8536	−	5.14089i	0.561414	−	0.194307i
$701$	−30.7509	−	19.7624i	−1.16144	−	0.746415i	−0.189559	−	0.981869i	$-0.560706\pi$
$701$	−30.7509	−	19.7624i	−1.16144	−	0.746415i	−0.971885	+	0.235454i	$0.924342\pi$
$702$	−4.41006	−	0.487735i	−0.166447	−	0.0184084i
$703$	3.13876	−	3.62232i	0.118381	−	0.136618i
$704$	−6.99894	+	6.67348i	−0.263783	+	0.251516i
$705$	0.835590	+	0.193107i	0.0314701	+	0.00727284i
$706$	−0.972181	+	2.80893i	−0.0365885	+	0.105716i
$707$	3.89243	−	5.46615i	0.146390	−	0.205576i
$708$	−24.4519	−	17.0141i	−0.918959	−	0.639430i
$709$	−7.42448	+	5.28695i	−0.278832	+	0.198555i	−0.710914	−	0.703279i	$-0.751719\pi$
$709$	−7.42448	+	5.28695i	−0.278832	+	0.198555i	0.432082	+	0.901834i	$0.357779\pi$
$710$	1.28529	−	8.93941i	0.0482362	−	0.335490i
$711$	34.0879	+	28.2621i	1.27840	+	1.05991i
$712$			30.0162i			1.12491i
$713$	31.8360	+	20.2758i	1.19227	+	0.759336i
$714$	−0.775811	−	5.00830i	−0.0290340	−	0.187431i
$715$	−6.00135	−	3.09391i	−0.224438	−	0.115706i
$716$	−10.6280	−	26.5474i	−0.397186	−	0.992122i
$717$	−11.0887	+	39.3437i	−0.414115	+	1.46932i
$718$	−1.64677	−	0.399502i	−0.0614569	−	0.0149093i
$719$	29.0098	−	13.2483i	1.08188	−	0.494079i	0.206963	−	0.978349i	$-0.433642\pi$
$719$	29.0098	−	13.2483i	1.08188	−	0.494079i	0.874919	+	0.484270i	$0.160915\pi$
$720$	−0.303359	+	11.7408i	−0.0113055	+	0.437553i
$721$	−4.07649	−	28.3526i	−0.151816	−	1.05591i
$722$	−5.42521	−	5.68980i	−0.201905	−	0.211752i
$723$	−0.00840425		0.000308710i	−0.000312557		1.14810e-5i
$724$	−18.0181	−	0.858306i	−0.669636	−	0.0318987i
$725$	15.8703	+	0.755995i	0.589408	+	0.0280769i
$726$	1.58924	+	3.00201i	0.0589821	+	0.111415i
$727$	−7.55075	−	7.91900i	−0.280042	−	0.293700i	0.568658	−	0.822574i	$-0.307463\pi$
$727$	−7.55075	−	7.91900i	−0.280042	−	0.293700i	−0.848700	+	0.528874i	$0.822614\pi$
$728$	1.26753	+	8.81584i	0.0469776	+	0.326737i
$729$	26.9425	−	1.76192i	0.997869	−	0.0652563i
$730$	2.83139	−	1.29305i	0.104794	−	0.0478580i
$731$	27.3369	+	6.63186i	1.01109	+	0.245288i
$732$	9.60404	+	9.85539i	0.354975	+	0.364266i
$733$	0.799117	+	1.99610i	0.0295161	+	0.0737275i	0.942394	−	0.334506i	$-0.108569\pi$
$733$	0.799117	+	1.99610i	0.0295161	+	0.0737275i	−0.912878	+	0.408233i	$0.866145\pi$
$734$	−0.574765	−	0.296312i	−0.0212150	−	0.0109371i
$735$	0.903425	−	0.726513i	0.0333233	−	0.0267978i
$736$	11.9626	+	18.4475i	0.440947	+	0.679982i
$737$		−	0.330662i		−	0.0121801i
$738$	3.32185	+	0.565541i	0.122279	+	0.0208179i
$739$	−4.84988	+	33.7317i	−0.178406	+	1.24084i	0.682047	+	0.731308i	$0.261090\pi$
$739$	−4.84988	+	33.7317i	−0.178406	+	1.24084i	−0.860453	+	0.509531i	$0.829819\pi$
$740$	−9.71231	+	6.91610i	−0.357031	+	0.254241i
$741$	−3.02013	+	1.41917i	−0.110947	+	0.0521345i
$742$	−2.85517	+	4.00953i	−0.104817	+	0.147194i
$743$	13.8188	−	39.9269i	0.506963	−	1.46477i	−0.343708	−	0.939077i	$-0.611683\pi$
$743$	13.8188	−	39.9269i	0.506963	−	1.46477i	0.850671	−	0.525698i	$-0.176196\pi$
$744$	6.61528	+	21.6549i	0.242528	+	0.793906i
$745$	6.92174	−	6.59987i	0.253593	−	0.241800i
$746$	−1.29261	+	1.49176i	−0.0473260	+	0.0546171i
$747$	−22.2534	−	6.01128i	−0.814209	−	0.219941i
$748$	−9.51770	−	6.11665i	−0.348001	−	0.223647i
$749$	−23.1520	+	8.01300i	−0.845957	+	0.292789i
$750$	3.18497	+	7.71134i	0.116299	+	0.281578i
$751$	16.2729	+	20.6927i	0.593806	+	0.755086i	0.986353	−	0.164646i	$-0.0526483\pi$
$751$	16.2729	+	20.6927i	0.593806	+	0.755086i	−0.392547	+	0.919732i	$0.628406\pi$
$752$	−1.00217	−	0.346854i	−0.0365453	−	0.0126485i
$753$	1.17969	+	20.1482i	0.0429902	+	0.734241i
$754$	−1.00831	+	4.15632i	−0.0367206	+	0.151364i
$755$	8.62077	−	18.8769i	0.313742	−	0.686999i
$756$	−8.05644	−	24.4543i	−0.293010	−	0.889394i
$757$	20.0637	+	31.2197i	0.729226	+	1.13470i	0.985759	+	0.168162i	$0.0537833\pi$
$757$	20.0637	+	31.2197i	0.729226	+	1.13470i	−0.256533	+	0.966535i	$0.582580\pi$
$758$	3.90141	−	6.75743i	0.141705	−	0.245441i
$759$	20.2312	−	6.27114i	0.734344	−	0.227628i
$760$	−1.10452	−	1.91308i	−0.0400650	−	0.0693946i
$761$	−20.1421	+	39.0703i	−0.730151	+	1.41630i	0.172098	+	0.985080i	$0.444946\pi$
$761$	−20.1421	+	39.0703i	−0.730151	+	1.41630i	−0.902249	+	0.431216i	$0.858085\pi$
$762$	−4.59099	+	2.71766i	−0.166314	+	0.0984504i
$763$	−18.8890	−	26.5258i	−0.683826	−	0.960299i
$764$	32.7277	−	9.60971i	1.18405	−	0.347667i
$765$	−9.72009	+	2.09380i	−0.351431	+	0.0757013i
$766$	−8.02298	+	6.95195i	−0.289882	+	0.251184i
$767$	−6.91704	+	17.2779i	−0.249760	+	0.623870i
$768$	0.653118	−	4.92227i	0.0235674	−	0.177617i
$769$	1.30539	−	6.77301i	0.0470736	−	0.244241i	−0.950768	−	0.309902i	$-0.899704\pi$
$769$	1.30539	−	6.77301i	0.0470736	−	0.244241i	0.997842	+	0.0656615i	$0.0209157\pi$
$770$	−0.195787	+	4.11007i	−0.00705567	+	0.148117i
$771$	−30.5803	−	13.5653i	−1.10132	−	0.488542i
$772$	−3.88789	−	11.2333i	−0.139928	−	0.404296i
$773$	32.1216	+	9.43175i	1.15533	+	0.339237i	0.802618	−	0.596494i	$-0.203440\pi$
$773$	32.1216	+	9.43175i	1.15533	+	0.339237i	0.352716	+	0.935730i	$0.385258\pi$
$774$	−14.9677	−	1.10109i	−0.538002	−	0.0395778i
$775$	−16.3489	−	18.8677i	−0.587271	−	0.677747i
$776$	15.4696	+	1.47717i	0.555327	+	0.0530273i
$777$	13.1966	−	18.9656i	0.473427	−	0.680387i
$778$	−0.0831857	−	0.871160i	−0.00298235	−	0.0312326i
$779$	2.35271	−	0.941885i	0.0842947	−	0.0337465i
$780$	8.13341	−	1.65959i	0.291223	−	0.0594230i
$781$	33.8349	+	19.5346i	1.21071	+	0.699003i
$782$	−3.52192	+	3.72413i	−0.125943	+	0.133174i
$783$	1.62682	−	25.9750i	0.0581378	−	0.928272i
$784$	−1.20599	+	0.775042i	−0.0430710	+	0.0276801i
$785$	7.45367	−	9.47811i	0.266033	−	0.338288i
$786$	−0.0206712	+	0.0201440i	−0.000737318	+	0.000718513i
$787$	7.40492	−	7.76605i	0.263957	−	0.276830i	−0.578396	−	0.815756i	$-0.696321\pi$
$787$	7.40492	−	7.76605i	0.263957	−	0.276830i	0.842353	+	0.538926i	$0.181170\pi$
$788$	−6.57867	−	4.68465i	−0.234355	−	0.166884i
$789$	31.7586	+	5.76321i	1.13064	+	0.205176i
$790$	8.07688	+	3.23350i	0.287362	+	0.115043i
$791$	−5.77586	+	19.6708i	−0.205366	+	0.699413i
$792$	11.6702	+	5.02558i	0.414684	+	0.178576i
$793$	4.64812	−	7.23262i	0.165060	−	0.256838i
$794$	6.94861	+	13.4784i	0.246597	+	0.478332i
$795$	8.18032	+	5.13223i	0.290126	+	0.182022i
$796$	−14.0577	+	3.41036i	−0.498261	+	0.120877i
$797$	−7.79011	+	6.12621i	−0.275940	+	0.217002i	−0.746532	−	0.665349i	$-0.768283\pi$
$797$	−7.79011	+	6.12621i	−0.275940	+	0.217002i	0.470592	+	0.882351i	$0.344040\pi$
$798$	1.55129	+	1.31491i	0.0549149	+	0.0465474i
$799$	0.0853426	−	0.893748i	0.00301920	−	0.0316185i
$800$	−4.09717	−	13.9537i	−0.144857	−	0.493337i
$801$	−49.8783	+	21.2393i	−1.76236	+	0.750454i
$802$	−13.4446	−	1.93304i	−0.474744	−	0.0682579i
$803$	0.640705	+	13.4500i	0.0226100	+	0.474642i
$804$	0.254760	+	0.316796i	0.00898470	+	0.0111726i
$805$	−17.2677	−	4.11421i	−0.608605	−	0.145007i
$806$	5.81998	−	3.36017i	0.205000	−	0.118357i
$807$	7.87952	+	38.6163i	0.277372	+	1.35936i
$808$	−3.20033	−	2.51677i	−0.112587	−	0.0885395i
$809$	−36.8621	−	16.8343i	−1.29600	−	0.591864i	−0.356463	−	0.934309i	$-0.616018\pi$
$809$	−36.8621	−	16.8343i	−1.29600	−	0.591864i	−0.939538	+	0.342445i	$0.888745\pi$
$810$	4.93288	−	1.95160i	0.173324	−	0.0685723i
$811$	9.77239	+	21.3986i	0.343155	+	0.751405i	0.999997	−	0.00262392i	$-0.000835220\pi$
$811$	9.77239	+	21.3986i	0.343155	+	0.751405i	−0.656842	+	0.754029i	$0.728108\pi$
$812$	−24.3698	+	4.69690i	−0.855213	+	0.164829i
$813$	−6.11851	+	26.4752i	−0.214585	+	0.928527i
$814$	1.27706	+	5.26409i	0.0447608	+	0.184506i
$815$	17.0951	+	3.29481i	0.598816	+	0.115412i
$816$	12.2261	−	1.30188i	0.427999	−	0.0455748i
$817$	−10.0326	+	5.17215i	−0.350995	+	0.180950i
$818$	−2.44162	−	2.11567i	−0.0853691	−	0.0739728i
$819$	−13.7525	+	8.34430i	−0.480551	+	0.291573i
$820$	−6.24004	+	0.897183i	−0.217912	+	0.0313310i
$821$	1.34507	+	6.97891i	0.0469434	+	0.243566i	0.997819	−	0.0660073i	$-0.0210261\pi$
$821$	1.34507	+	6.97891i	0.0469434	+	0.243566i	−0.950876	+	0.309573i	$0.899814\pi$
$822$	0.304218	+	0.462233i	0.0106108	+	0.0161222i
$823$	−19.1424	−	18.2523i	−0.667263	−	0.636234i	0.278750	−	0.960364i	$-0.410080\pi$
$823$	−19.1424	−	18.2523i	−0.667263	−	0.636234i	−0.946013	+	0.324130i	$0.894929\pi$
$824$	−17.3005	+	1.65200i	−0.602691	+	0.0575500i
$825$	−14.0089	+	0.152476i	−0.487729	+	0.00530855i
$826$	11.3290	−	0.539669i	0.394188	−	0.0187775i
$827$	35.7098			1.24175			0.620876	−	0.783908i	$-0.286777\pi$
$827$	35.7098			1.24175			0.620876	+	0.783908i	$0.286777\pi$
$828$	−14.5512	+	21.5953i	−0.505688	+	0.750490i
$829$	29.4105			1.02147			0.510734	−	0.859739i	$-0.329374\pi$
$829$	29.4105			1.02147			0.510734	+	0.859739i	$0.329374\pi$
$830$	−4.52389	+	0.215499i	−0.157027	+	0.00748010i
$831$	−11.4761	−	19.3869i	−0.398103	−	0.672523i
$832$	−7.39440	+	0.706079i	−0.256355	+	0.0244789i
$833$	−0.878361	−	0.837515i	−0.0304334	−	0.0290182i
$834$	12.6307	−	0.739533i	0.437365	−	0.0256079i
$835$	−5.54646	−	28.7778i	−0.191943	−	0.995896i
$836$	4.49350	−	0.646068i	0.155411	−	0.0223447i
$837$	−31.3032	+	26.3156i	−1.08200	+	0.909599i
$838$	2.45122	+	2.12400i	0.0846761	+	0.0733722i
$839$	8.26163	−	4.25917i	0.285223	−	0.147043i	−0.309678	−	0.950841i	$-0.600221\pi$
$839$	8.26163	−	4.25917i	0.285223	−	0.147043i	0.594902	+	0.803799i	$0.297191\pi$
$840$	−6.27095	−	8.60651i	−0.216368	−	0.296953i
$841$	3.84227	+	0.740537i	0.132492	+	0.0255358i
$842$	3.85500	+	15.8905i	0.132852	+	0.547624i
$843$	−19.2167	−	17.9279i	−0.661858	−	0.617468i
$844$	2.92811	−	0.564346i	0.100790	−	0.0194256i
$845$	5.14683	+	11.2700i	0.177056	+	0.387699i
$846$	0.0332011	+	0.477858i	0.00114148	+	0.0164291i
$847$	11.2018	+	5.11570i	0.384899	+	0.175778i
$848$	−9.38665	−	7.38174i	−0.322339	−	0.253490i
$849$	36.3730	−	32.2172i	1.24832	−	1.10569i
$850$	2.93612	−	1.69517i	0.100708	−	0.0581439i
$851$	−23.3369	+	1.20757i	−0.799977	+	0.0413950i
$852$	−47.4666	+	7.35281i	−1.62618	+	0.251903i
$853$	−0.654281	−	13.7350i	−0.0224021	−	0.470279i	−0.981997	−	0.188895i	$-0.939510\pi$
$853$	−0.654281	−	13.7350i	−0.0224021	−	0.470279i	0.959595	−	0.281384i	$-0.0907935\pi$
$854$	−5.18608	−	0.745646i	−0.177464	−	0.0255155i
$855$	2.39744	−	3.18907i	0.0819907	−	0.109064i
$856$	4.18781	+	14.2624i	0.143136	+	0.487478i
$857$	−2.18685	+	22.9018i	−0.0747015	+	0.782309i	0.878052	+	0.478565i	$0.158843\pi$
$857$	−2.18685	+	22.9018i	−0.0747015	+	0.782309i	−0.952754	+	0.303744i	$0.901763\pi$
$858$	0.673362	−	3.71061i	0.0229882	−	0.126678i
$859$	37.5404	−	29.5221i	1.28086	−	1.00728i	0.282010	−	0.959411i	$-0.408999\pi$
$859$	37.5404	−	29.5221i	1.28086	−	1.00728i	0.998854	−	0.0478706i	$-0.0152435\pi$
$860$	27.2869	−	6.61973i	0.930476	−	0.225731i
$861$	10.7969	−	5.71578i	0.367958	−	0.194793i
$862$	−7.05758	−	13.6898i	−0.240382	−	0.466276i
$863$	−12.6011	+	19.6077i	−0.428946	+	0.667452i	−0.986700	−	0.162554i	$-0.948027\pi$
$863$	−12.6011	+	19.6077i	−0.428946	+	0.667452i	0.557754	+	0.830006i	$0.311663\pi$
$864$	−22.9547	+	6.36900i	−0.780936	+	0.216678i
$865$	−7.51999	+	25.6107i	−0.255687	+	0.870791i
$866$	11.0560	+	4.42617i	0.375700	+	0.150407i
$867$	−6.42140	−	17.9200i	−0.218082	−	0.608594i
$868$	31.7664	+	22.6208i	1.07822	+	0.767798i
$869$	−25.9720	+	27.2386i	−0.881038	+	0.924006i
$870$	−1.25957	−	4.95597i	−0.0427036	−	0.168023i
$871$	0.157002	−	0.199644i	0.00531981	−	0.00676469i
$872$	−16.6210	+	10.6817i	−0.562858	+	0.361727i
$873$	8.49158	+	26.7513i	0.287396	+	0.905394i
$874$	0.0894412	−	2.05479i	0.00302539	−	0.0695043i
$875$	26.1954	+	15.1239i	0.885568	+	0.511283i
$876$	−10.9765	−	12.3924i	−0.370861	−	0.418701i
$877$	−4.21544	+	1.68761i	−0.142345	+	0.0569864i	−0.441741	−	0.897143i	$-0.645639\pi$
$877$	−4.21544	+	1.68761i	−0.142345	+	0.0569864i	0.299396	+	0.954129i	$0.403215\pi$
$878$	1.15485	+	12.0942i	0.0389745	+	0.408159i
$879$	−0.990456	−	2.10778i	−0.0334072	−	0.0710937i
$880$	−9.93728	−	0.948895i	−0.334986	−	0.0319872i
$881$	25.4503	+	29.3713i	0.857444	+	0.989543i	1.00000		0.000243744i	$-7.75863e-5\pi$
$881$	25.4503	+	29.3713i	0.857444	+	0.989543i	−0.142556	+	0.989787i	$0.545532\pi$
$882$	0.535504	+	0.364029i	0.0180314	+	0.0122575i
$883$	−3.13390	−	0.920197i	−0.105464	−	0.0309671i	0.228575	−	0.973526i	$-0.426594\pi$
$883$	−3.13390	−	0.920197i	−0.105464	−	0.0309671i	−0.334039	+	0.942559i	$0.608412\pi$
$884$	−2.84226	−	8.21216i	−0.0955954	−	0.276205i
$885$	−2.35613	−	22.1267i	−0.0792003	−	0.743781i
$886$	0.223215	−	4.68586i	0.00749905	−	0.157424i
$887$	8.76327	−	45.4682i	0.294242	−	1.52667i	−0.470537	−	0.882380i	$-0.655940\pi$
$887$	8.76327	−	45.4682i	0.294242	−	1.52667i	0.764779	−	0.644292i	$-0.222848\pi$
$888$	−11.1129	−	8.54520i	−0.372925	−	0.286758i
$889$	−7.18871	+	17.9565i	−0.241102	+	0.602243i
$890$	−8.04987	+	6.97525i	−0.269832	+	0.233811i
$891$	−0.0932806	+	22.9486i	−0.00312502	+	0.768808i
$892$	−19.7767	+	5.80697i	−0.662173	+	0.194432i
$893$	0.208968	+	0.293455i	0.00699285	+	0.00982009i
$894$	4.65495	+	2.62041i	0.155685	+	0.0876395i
$895$	9.78797	−	18.9860i	0.327176	−	0.634633i
$896$	14.8145	+	25.6595i	0.494918	+	0.857223i
$897$	15.1926	+	5.81964i	0.507266	+	0.194312i
$898$	−3.67136	+	6.35899i	−0.122515	+	0.212202i
$899$	21.3119	+	33.1619i	0.710791	+	1.10601i
$900$	13.3040	−	10.9393i	0.443467	−	0.364644i
$901$	4.19970	−	9.19606i	0.139912	−	0.306365i
$902$	−0.675227	+	2.78332i	−0.0224826	+	0.0926745i
$903$	−45.4508	+	29.9134i	−1.51251	+	0.995456i
$904$	11.7545	+	4.06828i	0.390949	+	0.135309i
$905$	−8.32936	−	10.5916i	−0.276877	−	0.352078i
$906$	11.4902	+	1.52459i	0.381737	+	0.0506513i
$907$	49.4188	−	17.1040i	1.64093	−	0.567930i	0.658175	−	0.752865i	$-0.271329\pi$
$907$	49.4188	−	17.1040i	1.64093	−	0.567930i	0.982751	+	0.184935i	$0.0592076\pi$
$908$	−40.6158	−	26.1022i	−1.34788	−	0.866231i
$909$	1.91761	−	7.09888i	0.0636031	−	0.235455i
$910$	−2.06972	+	2.38858i	−0.0686104	+	0.0791807i
$911$	−19.2806	+	18.3840i	−0.638795	+	0.609090i	−0.938640	−	0.344898i	$-0.887914\pi$
$911$	−19.2806	+	18.3840i	−0.638795	+	0.609090i	0.299845	+	0.953988i	$0.403065\pi$
$912$	−3.36548	+	3.60742i	−0.111442	+	0.119454i
$913$	6.40803	−	18.5148i	0.212075	−	0.612750i
$914$	−0.335257	+	0.470803i	−0.0110893	+	0.0155728i
$915$	−0.865681	+	10.2428i	−0.0286185	+	0.338615i
$916$	26.6486	−	18.9764i	0.880495	−	0.626997i
$917$	−0.0148921	+	0.103577i	−0.000491781	+	0.00342041i
$918$	−2.70459	−	4.85051i	−0.0892646	−	0.160091i
$919$			38.9593i			1.28515i	0.766223	+	0.642575i	$0.222134\pi$
$919$			38.9593i			1.28515i	−0.766223	+	0.642575i	$0.777866\pi$
$920$	−2.99188	+	10.3461i	−0.0986392	+	0.341101i
$921$	−38.3249	−	14.8611i	−1.26285	−	0.489689i
$922$	−8.66939	−	4.46938i	−0.285511	−	0.147191i
$923$	11.1533	+	27.8596i	0.367115	+	0.917010i
$924$	21.2097	−	5.39051i	0.697748	−	0.177335i
$925$	15.0208	+	3.64401i	0.493881	+	0.119814i
$926$	−4.54421	+	2.07527i	−0.149332	+	0.0681976i
$927$	−14.9869	−	27.5795i	−0.492233	−	0.905829i
$928$	3.26791	+	22.7288i	0.107274	+	0.746109i
$929$	7.02891	+	7.37171i	0.230611	+	0.241858i	0.828865	−	0.559449i	$-0.188987\pi$
$929$	7.02891	+	7.37171i	0.230611	+	0.241858i	−0.598254	+	0.801307i	$0.704139\pi$
$930$	−4.27021	+	6.80633i	−0.140026	+	0.223189i
$931$	0.486435	+	0.0231718i	0.0159423	+	0.000759424i
$932$	−10.7241	−	0.510851i	−0.351279	−	0.0167335i
$933$	17.9720	−	28.6458i	0.588378	−	0.937821i
$934$	−11.4038	−	11.9599i	−0.373143	−	0.391341i
$935$	−1.20273	−	8.36514i	−0.0393333	−	0.273569i
$936$	4.65995	+	8.57544i	0.152315	+	0.280297i
$937$	12.4042	−	5.66481i	0.405227	−	0.185061i	−0.202365	−	0.979310i	$-0.564863\pi$
$937$	12.4042	−	5.66481i	0.405227	−	0.185061i	0.607592	+	0.794249i	$0.292135\pi$
$938$	−0.150418	−	0.0364911i	−0.00491134	−	0.00119148i
$939$	−5.38233	+	1.36793i	−0.175646	+	0.0446409i
$940$	−0.333073	−	0.831977i	−0.0108636	−	0.0271361i
$941$	32.6463	+	16.8303i	1.06424	+	0.548653i	0.899157	−	0.437626i	$-0.144181\pi$
$941$	32.6463	+	16.8303i	1.06424	+	0.548653i	0.165082	+	0.986280i	$0.447211\pi$
$942$	6.27922	+	2.43487i	0.204588	+	0.0793323i
$943$	−11.2600	−	5.08658i	−0.366675	−	0.165642i
$944$			27.5158i			0.895563i
$945$	9.86427	−	16.5104i	0.320885	−	0.537085i
$946$	1.81540	−	12.6264i	0.0590238	−	0.410520i
$947$	4.10650	−	2.92422i	0.133443	−	0.0950245i	−0.511386	−	0.859351i	$-0.670868\pi$
$947$	4.10650	−	2.92422i	0.133443	−	0.0950245i	0.644829	+	0.764327i	$0.276928\pi$
$948$	3.89676	−	46.1066i	0.126561	−	1.49747i
$949$	−5.99939	+	8.42496i	−0.194748	+	0.273486i
$950$	−0.444943	+	1.28558i	−0.0144359	+	0.0417097i
$951$	18.7800	−	20.1300i	0.608982	−	0.652762i
$952$	−8.06815	+	7.69297i	−0.261490	+	0.249331i
$953$	−1.03662	+	1.19633i	−0.0335795	+	0.0387528i	−0.772291	−	0.635269i	$-0.780889\pi$
$953$	−1.03662	+	1.19633i	−0.0335795	+	0.0387528i	0.738711	+	0.674022i	$0.235435\pi$
$954$	−1.40661	+	5.20717i	−0.0455405	+	0.168588i
$955$	21.4344	+	13.7751i	0.693601	+	0.445750i
$956$	40.3650	−	13.9705i	1.30550	−	0.451837i
$957$	21.9287	+	2.90964i	0.708855	+	0.0940555i
$958$	−7.87598	−	10.0151i	−0.254461	−	0.323574i
$959$	1.89585	+	0.656159i	0.0612201	+	0.0211885i
$960$	7.41857	−	4.88252i	0.239433	−	0.157583i
$961$	7.29457	−	30.0686i	0.235309	−	0.969956i
$962$	−1.72840	+	3.78467i	−0.0557258	+	0.122023i
$963$	−20.7367	+	17.0509i	−0.668231	+	0.549458i
$964$	0.00475116	+	0.00739295i	0.000153025	+	0.000238111i
$965$	4.43974	−	7.68986i	0.142920	−	0.247545i
$966$	−0.620081	−	9.89523i	−0.0199508	−	0.318374i
$967$	16.0051	+	27.7217i	0.514690	+	0.891469i	0.999855	+	0.0170460i	$0.00542618\pi$
$967$	16.0051	+	27.7217i	0.514690	+	0.891469i	−0.485165	+	0.874423i	$0.661240\pi$
$968$	3.42370	−	6.64106i	0.110042	−	0.213452i
$969$	−3.63968	−	2.04888i	−0.116923	−	0.0658195i
$970$	3.19872	+	4.49197i	0.102705	+	0.144229i
$971$	−53.1509	+	15.6065i	−1.70569	+	0.500837i	−0.981935	−	0.189217i	$-0.939405\pi$
$971$	−53.1509	+	15.6065i	−1.70569	+	0.500837i	−0.723758	+	0.690054i	$0.757587\pi$
$972$	−17.5915	−	22.0582i	−0.564248	−	0.707517i
$973$	34.6666	−	30.0388i	1.11136	−	0.962999i
$974$	−0.466073	+	1.16420i	−0.0149340	+	0.0373032i
$975$	−8.53059	−	6.55953i	−0.273197	−	0.210073i
$976$	2.40557	−	12.4813i	0.0770005	−	0.399516i
$977$	2.47661	−	51.9904i	0.0792337	−	1.66332i	−0.513626	−	0.858014i	$-0.671698\pi$
$977$	2.47661	−	51.9904i	0.0792337	−	1.66332i	0.592860	−	0.805306i	$-0.297999\pi$
$978$	1.02962	+	9.66935i	0.0329237	+	0.309192i
$979$	−15.0706	−	43.5437i	−0.481659	−	1.39166i
$980$	−1.16236	−	0.341300i	−0.0371302	−	0.0109024i
$981$	−29.5108	−	20.0610i	−0.942207	−	0.640500i
$982$	0.969079	+	1.11838i	0.0309246	+	0.0356888i
$983$	−13.9624	−	1.33325i	−0.445331	−	0.0425240i	−0.130018	−	0.991512i	$-0.541504\pi$
$983$	−13.9624	−	1.33325i	−0.445331	−	0.0425240i	−0.315313	+	0.948988i	$0.602110\pi$
$984$	−3.15229	−	6.70836i	−0.100491	−	0.213855i
$985$	−0.573452	−	6.00546i	−0.0182717	−	0.191350i
$986$	−4.96976	+	1.98959i	−0.158269	+	0.0633615i
$987$	1.15147	+	1.30000i	0.0366517	+	0.0413796i
$988$	3.01981	+	1.74349i	0.0960729	+	0.0554677i
$989$	52.0773	+	17.7854i	1.65596	+	0.565544i
$990$	1.36418	+	4.29763i	0.0433565	+	0.136588i
$991$	−17.0456	+	10.9545i	−0.541470	+	0.347982i	−0.782614	−	0.622508i	$-0.786114\pi$
$991$	−17.0456	+	10.9545i	−0.541470	+	0.347982i	0.241144	+	0.970489i	$0.422478\pi$
$992$	22.3040	−	28.3619i	0.708154	−	0.900491i
$993$	−7.80201	−	30.6981i	−0.247589	−	0.974175i
$994$	12.6202	−	13.2357i	0.400289	−	0.419811i
$995$	−8.80186	−	6.26778i	−0.279038	−	0.198702i
$996$	8.12548	+	22.6755i	0.257466	+	0.718500i
$997$	3.54605	+	1.41962i	0.112304	+	0.0449599i	0.427134	−	0.904188i	$-0.359523\pi$
$997$	3.54605	+	1.41962i	0.112304	+	0.0449599i	−0.314830	+	0.949148i	$0.601947\pi$
$998$	4.29341	−	14.6220i	0.135906	−	0.462852i
$999$	6.33623	−	24.5130i	0.200470	−	0.775557i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.o.a.11.14	✓	440
3.2	odd	2		621.2.s.a.494.9		440
9.4	even	3		621.2.s.a.287.9		440
9.5	odd	6	inner	207.2.o.a.149.14	yes	440
23.21	odd	22	inner	207.2.o.a.182.14	yes	440
69.44	even	22		621.2.s.a.251.9		440
207.67	odd	66		621.2.s.a.44.9		440
207.113	even	66	inner	207.2.o.a.113.14	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.14	✓	440	1.1	even	1	trivial
207.2.o.a.113.14	yes	440	207.113	even	66	inner
207.2.o.a.149.14	yes	440	9.5	odd	6	inner
207.2.o.a.182.14	yes	440	23.21	odd	22	inner
621.2.s.a.44.9		440	207.67	odd	66
621.2.s.a.251.9		440	69.44	even	22
621.2.s.a.287.9		440	9.4	even	3
621.2.s.a.494.9		440	3.2	odd	2

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.o (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.435484 - 0.0207447i) q^{2} +(0.849649 - 1.50934i) q^{3} +(-1.80173 + 0.172044i) q^{4} +(-0.978477 - 0.932976i) q^{5} +(0.338698 - 0.674918i) q^{6} +(-0.518116 - 2.68824i) q^{7} +(-1.64413 + 0.236391i) q^{8} +(-1.55619 - 2.56481i) q^{9} +O(q^{10})\)	\(q+(0.435484 - 0.0207447i) q^{2} +(0.849649 - 1.50934i) q^{3} +(-1.80173 + 0.172044i) q^{4} +(-0.978477 - 0.932976i) q^{5} +(0.338698 - 0.674918i) q^{6} +(-0.518116 - 2.68824i) q^{7} +(-1.64413 + 0.236391i) q^{8} +(-1.55619 - 2.56481i) q^{9} +(-0.445465 - 0.385998i) q^{10} +(2.26641 - 1.16842i) q^{11} +(-1.27116 + 2.86559i) q^{12} +(1.92317 + 0.370661i) q^{13} +(-0.281398 - 1.15994i) q^{14} +(-2.23954 + 0.684149i) q^{15} +(2.84334 - 0.548009i) q^{16} +(1.01838 + 2.22994i) q^{17} +(-0.730904 - 1.08465i) q^{18} +(-0.894779 - 0.408632i) q^{19} +(1.92346 + 1.51263i) q^{20} +(-4.49767 - 1.50205i) q^{21} +(0.962749 - 0.555843i) q^{22} +(1.58713 + 4.52560i) q^{23} +(-1.04014 + 2.68240i) q^{24} +(-0.150937 - 3.16855i) q^{25} +(0.845200 + 0.121521i) q^{26} +(-5.19338 + 0.169631i) q^{27} +(1.39600 + 4.75434i) q^{28} +(-0.476107 + 4.98601i) q^{29} +(-0.961089 + 0.344394i) q^{30} +(6.18643 - 4.86506i) q^{31} +(4.45530 - 1.08084i) q^{32} +(0.162120 - 4.41353i) q^{33} +(0.489746 + 0.949975i) q^{34} +(-2.00110 + 3.11377i) q^{35} +(3.24510 + 4.35336i) q^{36} +(-1.37276 + 4.67521i) q^{37} +(-0.398139 - 0.159391i) q^{38} +(2.19347 - 2.58778i) q^{39} +(1.82929 + 1.30263i) q^{40} +(-1.77786 + 1.86457i) q^{41} +(-1.98982 - 0.560815i) q^{42} +(7.09317 - 9.01971i) q^{43} +(-3.88244 + 2.49509i) q^{44} +(-0.870207 + 3.96150i) q^{45} +(0.785050 + 1.93790i) q^{46} +(-0.317168 - 0.183117i) q^{47} +(1.58871 - 4.75717i) q^{48} +(-0.459608 + 0.183999i) q^{49} +(-0.131461 - 1.37672i) q^{50} +(4.23099 + 0.357588i) q^{51} +(-3.52880 - 0.336960i) q^{52} +(-2.70059 - 3.11665i) q^{53} +(-2.25812 + 0.181607i) q^{54} +(-3.30774 - 0.971240i) q^{55} +(1.48733 + 4.29735i) q^{56} +(-1.37701 + 1.00333i) q^{57} +(-0.103904 + 2.18121i) q^{58} +(-1.79834 + 9.33067i) q^{59} +(3.91733 - 1.61795i) q^{60} +(1.63147 - 4.07522i) q^{61} +(2.59317 - 2.24699i) q^{62} +(-6.08854 + 5.51229i) q^{63} +(-3.63896 + 1.06849i) q^{64} +(-1.53596 - 2.15696i) q^{65} +(-0.0209563 - 1.92538i) q^{66} +(0.0594220 - 0.115263i) q^{67} +(-2.21849 - 3.84253i) q^{68} +(8.17915 + 1.44966i) q^{69} +(-0.806852 + 1.39751i) q^{70} +(8.28371 + 12.8897i) q^{71} +(3.16489 + 3.84903i) q^{72} +(-2.19371 + 4.80356i) q^{73} +(-0.500831 + 2.06446i) q^{74} +(-4.91065 - 2.46434i) q^{75} +(1.68245 + 0.582302i) q^{76} +(-4.31525 - 5.48729i) q^{77} +(0.901540 - 1.17244i) q^{78} +(-13.9483 + 4.82754i) q^{79} +(-3.29342 - 2.11655i) q^{80} +(-4.15652 + 7.98269i) q^{81} +(-0.735550 + 0.848870i) q^{82} +(5.56093 - 5.30234i) q^{83} +(8.36200 + 1.93248i) q^{84} +(1.08402 - 3.13206i) q^{85} +(2.90185 - 4.07508i) q^{86} +(7.12105 + 4.95497i) q^{87} +(-3.45009 + 2.45680i) q^{88} +(2.57173 - 17.8868i) q^{89} +(-0.296781 + 1.74322i) q^{90} -5.36199i q^{91} +(-3.63817 - 7.88084i) q^{92} +(-2.08673 - 13.4710i) q^{93} +(-0.141920 - 0.0731651i) q^{94} +(0.494277 + 1.23464i) q^{95} +(2.15408 - 7.64289i) q^{96} +(-9.09184 - 2.20566i) q^{97} +(-0.196335 + 0.0896631i) q^{98} +(-6.52375 - 3.99464i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Introduction

L-functions

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