LMFDB - Embedded newform 169.2.g.a.27.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(14,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([18]))

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

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

chi := DirichletCharacter("169.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.g (of order $13$, degree $12$, 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:	$1.34947179416$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$13$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			27.7
Character	$\chi$	$=$	169.27
Dual form			169.2.g.a.144.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.000492135 - 0.00129765i) q^{2} +(-1.38011 + 1.99943i) q^{3} +(1.49702 - 1.32624i) q^{4} +(-0.444348 - 3.65953i) q^{5} +(0.00327377 + 0.000806912i) q^{6} +(3.94802 + 2.07208i) q^{7} +(-0.00491548 - 0.00257984i) q^{8} +(-1.02922 - 2.71382i) q^{9} +O(q^{10})$	\(q+(-0.000492135 - 0.00129765i) q^{2} +(-1.38011 + 1.99943i) q^{3} +(1.49702 - 1.32624i) q^{4} +(-0.444348 - 3.65953i) q^{5} +(0.00327377 + 0.000806912i) q^{6} +(3.94802 + 2.07208i) q^{7} +(-0.00491548 - 0.00257984i) q^{8} +(-1.02922 - 2.71382i) q^{9} +(-0.00453012 + 0.00237759i) q^{10} +(0.542210 - 1.42969i) q^{11} +(0.585685 + 4.82355i) q^{12} +(-1.24348 + 3.38434i) q^{13} +(0.000745884 - 0.00614291i) q^{14} +(7.93023 + 4.16211i) q^{15} +(0.482145 - 3.97082i) q^{16} +(1.41220 + 0.741181i) q^{17} +(-0.00301508 + 0.00267113i) q^{18} +4.73261 q^{19} +(-5.51863 - 4.88908i) q^{20} +(-9.59168 + 5.03410i) q^{21} -0.00212208 q^{22} -1.66155 q^{23} +(0.0119421 - 0.00626771i) q^{24} +(-8.34001 + 2.05563i) q^{25} +(0.00500366 - 5.19534e-5i) q^{26} +(-0.230156 - 0.0567285i) q^{27} +(8.65835 - 2.13409i) q^{28} +(-1.03007 - 2.71607i) q^{29} +(0.00149823 - 0.0123390i) q^{30} +(-7.97254 - 1.96505i) q^{31} +(-0.0161701 + 0.00398558i) q^{32} +(2.11026 + 3.05724i) q^{33} +(0.000266802 - 0.00219731i) q^{34} +(5.82855 - 15.3686i) q^{35} +(-5.13994 - 2.69765i) q^{36} +(-2.29530 - 0.565741i) q^{37} +(-0.00232909 - 0.00614129i) q^{38} +(-5.05063 - 7.15700i) q^{39} +(-0.00725684 + 0.0191347i) q^{40} +(-3.00968 + 4.36027i) q^{41} +(0.0112529 + 0.00996922i) q^{42} +(-4.53725 + 1.11833i) q^{43} +(-1.08442 - 2.85938i) q^{44} +(-9.47398 + 4.97233i) q^{45} +(0.000817706 + 0.00215611i) q^{46} +(9.37370 + 8.30437i) q^{47} +(7.27398 + 6.44419i) q^{48} +(7.31689 + 10.6004i) q^{49} +(0.00677191 + 0.00981080i) q^{50} +(-3.43093 + 1.80069i) q^{51} +(2.62696 + 6.71558i) q^{52} +(-8.08089 - 4.24118i) q^{53} +(3.96541e-5 + 0.000326581i) q^{54} +(-5.47292 - 1.34895i) q^{55} +(-0.0140608 - 0.0203706i) q^{56} +(-6.53152 + 9.46254i) q^{57} +(-0.00301759 + 0.00267335i) q^{58} +(1.58040 + 13.0158i) q^{59} +(17.3917 - 4.28667i) q^{60} +(0.874957 - 0.459213i) q^{61} +(0.00137361 + 0.0113127i) q^{62} +(1.55989 - 12.8468i) q^{63} +(-4.54449 - 6.58383i) q^{64} +(12.9376 + 3.04671i) q^{65} +(0.00292870 - 0.00424296i) q^{66} +(-5.03597 - 4.46148i) q^{67} +(3.09708 - 0.763362i) q^{68} +(2.29312 - 3.32216i) q^{69} -0.0228116 q^{70} +(0.462710 - 0.670351i) q^{71} +(-0.00194214 + 0.0159950i) q^{72} +(-0.658755 + 1.73699i) q^{73} +(0.000395463 + 0.00325693i) q^{74} +(7.40003 - 19.5123i) q^{75} +(7.08482 - 6.27660i) q^{76} +(5.10309 - 4.52094i) q^{77} +(-0.00680172 + 0.0100762i) q^{78} +(5.95782 + 5.27817i) q^{79} -14.7456 q^{80} +(6.94857 - 6.15589i) q^{81} +(0.00713929 + 0.00175968i) q^{82} +(-0.307363 - 0.445293i) q^{83} +(-7.68249 + 20.2571i) q^{84} +(2.08487 - 5.49734i) q^{85} +(0.00368414 + 0.00533740i) q^{86} +(6.85221 + 1.68892i) q^{87} +(-0.00635360 + 0.00562880i) q^{88} -14.2838 q^{89} +(0.0111148 + 0.00984688i) q^{90} +(-11.9219 + 10.7849i) q^{91} +(-2.48737 + 2.20362i) q^{92} +(14.9320 - 13.2286i) q^{93} +(0.00616307 - 0.0162507i) q^{94} +(-2.10293 - 17.3192i) q^{95} +(0.0143476 - 0.0378316i) q^{96} +(-0.263819 + 2.17274i) q^{97} +(0.0101547 - 0.0147116i) q^{98} -4.43797 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9}+O(q^{10}) $ 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9} + q^{10} - q^{11} + 11 q^{12} - 65 q^{13} + 9 q^{14} - 41 q^{15} + 3 q^{17} - 13 q^{18} - 6 q^{19} + 29 q^{20} + 19 q^{21} - 22 q^{22} - 82 q^{23} - 31 q^{24} + 2 q^{25} + 26 q^{26} + 21 q^{27} + 43 q^{28} + 13 q^{29} - 81 q^{30} - 33 q^{31} - 93 q^{32} + 35 q^{33} - 24 q^{34} + 27 q^{35} + 54 q^{36} + 25 q^{37} - 56 q^{38} - 13 q^{39} - 52 q^{40} + 29 q^{41} - 63 q^{42} + 21 q^{43} + 45 q^{44} + 33 q^{46} - 69 q^{47} + 54 q^{48} - 54 q^{49} + 80 q^{50} - 16 q^{51} + 13 q^{52} - 45 q^{53} + 29 q^{54} - 83 q^{55} + 91 q^{56} - 11 q^{57} + 25 q^{58} - 57 q^{59} + 51 q^{60} + 39 q^{61} + 4 q^{62} + 26 q^{63} + 86 q^{64} + 65 q^{65} - 138 q^{66} - 101 q^{67} + 36 q^{68} + 32 q^{69} - 90 q^{70} + 20 q^{71} + 13 q^{72} + 61 q^{73} - 4 q^{74} - 67 q^{75} - 107 q^{76} + 67 q^{77} + 13 q^{78} + 57 q^{79} + 160 q^{80} + 78 q^{81} - 31 q^{82} - 59 q^{83} - 36 q^{84} - 61 q^{85} + 41 q^{86} - 9 q^{87} - 45 q^{88} - 66 q^{89} + 191 q^{90} + 39 q^{91} + 79 q^{92} - 80 q^{93} - 21 q^{94} - 28 q^{95} + 70 q^{96} + 7 q^{97} + 158 q^{98} + 130 q^{99}+O(q^{100}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9 + q^10 - q^11 + 11 * q^12 - 65 * q^13 + 9 * q^14 - 41 * q^15 + 3 * q^17 - 13 * q^18 - 6 * q^19 + 29 * q^20 + 19 * q^21 - 22 * q^22 - 82 * q^23 - 31 * q^24 + 2 * q^25 + 26 * q^26 + 21 * q^27 + 43 * q^28 + 13 * q^29 - 81 * q^30 - 33 * q^31 - 93 * q^32 + 35 * q^33 - 24 * q^34 + 27 * q^35 + 54 * q^36 + 25 * q^37 - 56 * q^38 - 13 * q^39 - 52 * q^40 + 29 * q^41 - 63 * q^42 + 21 * q^43 + 45 * q^44 + 33 * q^46 - 69 * q^47 + 54 * q^48 - 54 * q^49 + 80 * q^50 - 16 * q^51 + 13 * q^52 - 45 * q^53 + 29 * q^54 - 83 * q^55 + 91 * q^56 - 11 * q^57 + 25 * q^58 - 57 * q^59 + 51 * q^60 + 39 * q^61 + 4 * q^62 + 26 * q^63 + 86 * q^64 + 65 * q^65 - 138 * q^66 - 101 * q^67 + 36 * q^68 + 32 * q^69 - 90 * q^70 + 20 * q^71 + 13 * q^72 + 61 * q^73 - 4 * q^74 - 67 * q^75 - 107 * q^76 + 67 * q^77 + 13 * q^78 + 57 * q^79 + 160 * q^80 + 78 * q^81 - 31 * q^82 - 59 * q^83 - 36 * q^84 - 61 * q^85 + 41 * q^86 - 9 * q^87 - 45 * q^88 - 66 * q^89 + 191 * q^90 + 39 * q^91 + 79 * q^92 - 80 * q^93 - 21 * q^94 - 28 * q^95 + 70 * q^96 + 7 * q^97 + 158 * q^98 + 130 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{13}\right)$

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 $

$2$	−0.000492135	−	0.00129765i	−0.000347992	−	0.000917579i	0.934842	−	0.355064i	$-0.115541\pi$
$2$	−0.000492135	−	0.00129765i	−0.000347992	−	0.000917579i	−0.935190	+	0.354146i	$0.884772\pi$
$3$	−1.38011	+	1.99943i	−0.796806	+	1.15437i	0.188247	+	0.982122i	$0.439719\pi$
$3$	−1.38011	+	1.99943i	−0.796806	+	1.15437i	−0.985053	+	0.172251i	$0.944896\pi$
$4$	1.49702	−	1.32624i	0.748510	−	0.663122i
$5$	−0.444348	−	3.65953i	−0.198718	−	1.63659i	−0.661376	−	0.750055i	$-0.730027\pi$
$5$	−0.444348	−	3.65953i	−0.198718	−	1.63659i	0.462657	−	0.886537i	$-0.346896\pi$
$6$	0.00327377		0.000806912i	0.00133651		0.000329420i
$7$	3.94802	+	2.07208i	1.49221	+	0.783173i	0.996361	−	0.0852348i	$-0.0271640\pi$
$7$	3.94802	+	2.07208i	1.49221	+	0.783173i	0.495851	+	0.868408i	$0.334856\pi$
$8$	−0.00491548	−	0.00257984i	−0.00173789	−	0.000912113i
$9$	−1.02922	−	2.71382i	−0.343072	−	0.904607i
$10$	−0.00453012	+	0.00237759i	−0.00143255	+	0.000751861i
$11$	0.542210	−	1.42969i	0.163482	−	0.431068i	−0.828094	−	0.560589i	$-0.810575\pi$
$11$	0.542210	−	1.42969i	0.163482	−	0.431068i	0.991577	+	0.129521i	$0.0413440\pi$
$12$	0.585685	+	4.82355i	0.169073	+	1.39244i
$13$	−1.24348	+	3.38434i	−0.344878	+	0.938648i
$13$	−1.24348	+	3.38434i	−0.344878	+	0.938648i
$14$	0.000745884	−	0.00614291i	0.000199346	−	0.00164176i
$15$	7.93023	+	4.16211i	2.04758	+	1.07465i
$16$	0.482145	−	3.97082i	0.120536	−	0.992706i
$17$	1.41220	+	0.741181i	0.342509	+	0.179763i	0.627203	−	0.778856i	$-0.284200\pi$
$17$	1.41220	+	0.741181i	0.342509	+	0.179763i	−0.284694	+	0.958619i	$0.591892\pi$
$18$	−0.00301508	+	0.00267113i	−0.000710662	+	0.000629592i
$19$	4.73261			1.08574			0.542868	−	0.839818i	$-0.317338\pi$
$19$	4.73261			1.08574			0.542868	+	0.839818i	$0.317338\pi$
$20$	−5.51863	−	4.88908i	−1.23400	−	1.09323i
$21$	−9.59168	+	5.03410i	−2.09308	+	1.09853i
$22$	−0.00212208			−0.000452429
$23$	−1.66155			−0.346457			−0.173228	−	0.984882i	$-0.555420\pi$
$23$	−1.66155			−0.346457			−0.173228	+	0.984882i	$0.555420\pi$
$24$	0.0119421	−	0.00626771i	0.00243768	−	0.00127939i
$25$	−8.34001	+	2.05563i	−1.66800	+	0.411126i
$26$	0.00500366		5.19534e-5i	0.000981298		1.01889e-5i
$27$	−0.230156	−	0.0567285i	−0.0442936	−	0.0109174i
$28$	8.65835	−	2.13409i	1.63627	−	0.403305i
$29$	−1.03007	−	2.71607i	−0.191279	−	0.504362i	0.804727	−	0.593645i	$-0.202312\pi$
$29$	−1.03007	−	2.71607i	−0.191279	−	0.504362i	−0.996006	+	0.0892831i	$0.971542\pi$
$30$	0.00149823	−	0.0123390i	0.000273538	−	0.00225278i
$31$	−7.97254	−	1.96505i	−1.43191	−	0.352934i	−0.554303	−	0.832315i	$-0.687015\pi$
$31$	−7.97254	−	1.96505i	−1.43191	−	0.352934i	−0.877607	+	0.479381i	$0.840861\pi$
$32$	−0.0161701	+	0.00398558i	−0.00285850	+	0.000704557i
$33$	2.11026	+	3.05724i	0.367349	+	0.532197i
$34$	0.000266802	−	0.00219731i	4.57561e−5	−	0.000376835i
$35$	5.82855	−	15.3686i	0.985205	−	2.59777i
$36$	−5.13994	−	2.69765i	−0.856657	−	0.449608i
$37$	−2.29530	−	0.565741i	−0.377345	−	0.0930073i	0.0460812	−	0.998938i	$-0.485327\pi$
$37$	−2.29530	−	0.565741i	−0.377345	−	0.0930073i	−0.423427	+	0.905930i	$0.639173\pi$
$38$	−0.00232909	−	0.00614129i	−0.000377827	−	0.000996249i
$39$	−5.05063	−	7.15700i	−0.808748	−	1.14604i
$40$	−0.00725684	+	0.0191347i	−0.00114741	+	0.00302546i
$41$	−3.00968	+	4.36027i	−0.470033	+	0.680960i	−0.984267	−	0.176690i	$-0.943461\pi$
$41$	−3.00968	+	4.36027i	−0.470033	+	0.680960i	0.514234	+	0.857650i	$0.328076\pi$
$42$	0.0112529	+	0.00996922i	0.00173636	+	0.00153828i
$43$	−4.53725	+	1.11833i	−0.691923	+	0.170544i	−0.569570	−	0.821943i	$-0.692890\pi$
$43$	−4.53725	+	1.11833i	−0.691923	+	0.170544i	−0.122353	+	0.992487i	$0.539044\pi$
$44$	−1.08442	−	2.85938i	−0.163482	−	0.431067i
$45$	−9.47398	+	4.97233i	−1.41230	+	0.741231i
$46$	0.000817706		0.00215611i	0.000120564		0.000317902i
$47$	9.37370	+	8.30437i	1.36729	+	1.21132i	0.953665	+	0.300872i	$0.0972776\pi$
$47$	9.37370	+	8.30437i	1.36729	+	1.21132i	0.413630	+	0.910445i	$0.364261\pi$
$48$	7.27398	+	6.44419i	1.04991	+	0.930138i
$49$	7.31689	+	10.6004i	1.04527	+	1.51434i
$50$	0.00677191	+	0.00981080i	0.000957692	+	0.00138746i
$51$	−3.43093	+	1.80069i	−0.480427	+	0.252147i
$52$	2.62696	+	6.71558i	0.364293	+	0.931283i
$53$	−8.08089	−	4.24118i	−1.11000	−	0.582570i	−0.192892	−	0.981220i	$-0.561787\pi$
$53$	−8.08089	−	4.24118i	−1.11000	−	0.582570i	−0.917103	+	0.398650i	$0.869479\pi$
$54$	3.96541e−5	0	0.000326581i	5.39625e−6	0	4.44421e-5i
$55$	−5.47292	−	1.34895i	−0.737969	−	0.181893i
$56$	−0.0140608	−	0.0203706i	−0.00187895	−	0.00272213i
$57$	−6.53152	+	9.46254i	−0.865121	+	1.25334i
$58$	−0.00301759	+	0.00267335i	−0.000396228	+	0.000351028i
$59$	1.58040	+	13.0158i	0.205751	+	1.69451i	0.620206	+	0.784439i	$0.287049\pi$
$59$	1.58040	+	13.0158i	0.205751	+	1.69451i	−0.414456	+	0.910069i	$0.636028\pi$
$60$	17.3917	−	4.28667i	2.24526	−	0.553406i
$61$	0.874957	−	0.459213i	0.112027	−	0.0587962i	−0.407779	−	0.913081i	$-0.633697\pi$
$61$	0.874957	−	0.459213i	0.112027	−	0.0587962i	0.519806	+	0.854284i	$0.326004\pi$
$62$	0.00137361	+	0.0113127i	0.000174448	+	0.00143671i
$63$	1.55989	−	12.8468i	0.196527	−	1.61855i
$64$	−4.54449	−	6.58383i	−0.568061	−	0.822979i
$65$	12.9376	+	3.04671i	1.60472	+	0.377898i
$66$	0.00292870	−	0.00424296i	0.000360498	−	0.000522272i
$67$	−5.03597	−	4.46148i	−0.615242	−	0.545057i	0.296912	−	0.954905i	$-0.404043\pi$
$67$	−5.03597	−	4.46148i	−0.615242	−	0.545057i	−0.912154	+	0.409848i	$0.865582\pi$
$68$	3.09708	−	0.763362i	0.375576	−	0.0925712i
$69$	2.29312	−	3.32216i	0.276059	−	0.399941i
$70$	−0.0228116			−0.00272651
$71$	0.462710	−	0.670351i	0.0549136	−	0.0795560i	−0.794565	−	0.607179i	$-0.792301\pi$
$71$	0.462710	−	0.670351i	0.0549136	−	0.0795560i	0.849479	+	0.527623i	$0.176917\pi$
$72$	−0.00194214	+	0.0159950i	−0.000228883	+	0.00188502i
$73$	−0.658755	+	1.73699i	−0.0771015	+	0.203300i	−0.968025	−	0.250853i	$-0.919289\pi$
$73$	−0.658755	+	1.73699i	−0.0771015	+	0.203300i	0.890924	+	0.454153i	$0.150058\pi$
$74$	0.000395463		0.00325693i	4.59716e−5		0.000378610i
$75$	7.40003	−	19.5123i	0.854482	−	2.25308i
$76$	7.08482	−	6.27660i	0.812685	−	0.719976i
$77$	5.10309	−	4.52094i	0.581551	−	0.515209i
$78$	−0.00680172	+	0.0100762i	−0.000770143	+	0.00114090i
$79$	5.95782	+	5.27817i	0.670307	+	0.593841i	0.928087	−	0.372363i	$-0.121452\pi$
$79$	5.95782	+	5.27817i	0.670307	+	0.593841i	−0.257780	+	0.966204i	$0.582991\pi$
$80$	−14.7456			−1.64861
$81$	6.94857	−	6.15589i	0.772063	−	0.683988i
$82$	0.00713929	+	0.00175968i	0.000788402	+	0.000194324i
$83$	−0.307363	−	0.445293i	−0.0337375	−	0.0488772i	0.805752	−	0.592253i	$-0.201761\pi$
$83$	−0.307363	−	0.445293i	−0.0337375	−	0.0488772i	−0.839490	+	0.543376i	$0.817146\pi$
$84$	−7.68249	+	20.2571i	−0.838229	+	2.21023i
$85$	2.08487	−	5.49734i	0.226135	−	0.596270i
$86$	0.00368414	+	0.00533740i	0.000397271	+	0.000575547i
$87$	6.85221	+	1.68892i	0.734634	+	0.181071i
$88$	−0.00635360	+	0.00562880i	−0.000677296	+	0.000600032i
$89$	−14.2838			−1.51408			−0.757042	−	0.653366i	$-0.773356\pi$
$89$	−14.2838			−1.51408			−0.757042	+	0.653366i	$0.773356\pi$
$90$	0.0111148	+	0.00984688i	0.00117161	+	0.00103795i
$91$	−11.9219	+	10.7849i	−1.24975	+	1.13056i
$92$	−2.48737	+	2.20362i	−0.259327	+	0.229743i
$93$	14.9320	−	13.2286i	1.54837	−	1.37174i
$94$	0.00616307	−	0.0162507i	0.000635672	−	0.00167613i
$95$	−2.10293	−	17.3192i	−0.215756	−	1.77691i
$96$	0.0143476	−	0.0378316i	0.00146435	−	0.00386117i
$97$	−0.263819	+	2.17274i	−0.0267867	+	0.220609i	−0.999955	−	0.00948600i	$-0.996980\pi$
$97$	−0.263819	+	2.17274i	−0.0267867	+	0.220609i	0.973168	+	0.230095i	$0.0739035\pi$
$98$	0.0101547	−	0.0147116i	0.00102578	−	0.00148610i
$99$	−4.43797			−0.446033
$100$	−9.75890	+	14.1382i	−0.975890	+	1.41382i
$101$	−9.90116	+	2.44042i	−0.985203	+	0.242831i	−0.698830	−	0.715288i	$-0.746296\pi$
$101$	−9.90116	+	2.44042i	−0.985203	+	0.242831i	−0.286373	+	0.958118i	$0.592449\pi$
$102$	0.00402516	+	0.00356598i	0.000398550	+	0.000353084i
$103$	0.511941	−	0.741674i	0.0504430	−	0.0730793i	−0.796951	−	0.604044i	$-0.793555\pi$
$103$	0.511941	−	0.741674i	0.0504430	−	0.0730793i	0.847394	+	0.530965i	$0.178170\pi$
$104$	0.0148434	−	0.0134277i	0.00145551	−	0.00131669i
$105$	22.6845	+	32.8642i	2.21378	+	3.20722i
$106$	−0.00152669	+	0.0125734i	−0.000148285	+	0.00122124i
$107$	−1.46910	−	12.0991i	−0.142023	−	1.16966i	−0.873160	−	0.487434i	$-0.837933\pi$
$107$	−1.46910	−	12.0991i	−0.142023	−	1.16966i	0.731137	−	0.682231i	$-0.238990\pi$
$108$	−0.419785	+	0.220320i	−0.0403938	+	0.0212003i
$109$	10.2574	−	2.52823i	0.982483	−	0.242160i	0.284816	−	0.958582i	$-0.408068\pi$
$109$	10.2574	−	2.52823i	0.982483	−	0.242160i	0.697667	+	0.716422i	$0.254221\pi$
$110$	0.000942942		0.00776582i	8.99060e−5		0.000740442i
$111$	4.29893	−	3.80852i	0.408036	−	0.361489i
$112$	10.1314	−	14.6779i	0.957326	−	1.38693i
$113$	4.08945	+	5.92459i	0.384703	+	0.557339i	0.966720	−	0.255838i	$-0.0823514\pi$
$113$	4.08945	+	5.92459i	0.384703	+	0.557339i	−0.582016	+	0.813177i	$0.697736\pi$
$114$	0.0154935	+	0.00381880i	0.00145110	+	0.000357664i
$115$	0.738305	+	6.08049i	0.0688473	+	0.567009i
$116$	−5.14421	−	2.69989i	−0.477628	−	0.250678i
$117$	10.4643	−	0.108652i	0.967425	−	0.0100449i
$118$	0.0161122	−	0.00845632i	0.00148325	−	0.000778468i
$119$	4.03962	+	5.85239i	0.370311	+	0.536488i
$120$	−0.0282433	−	0.0409175i	−0.00257825	−	0.00373524i
$121$	6.48360	+	5.74397i	0.589418	+	0.522179i
$122$	−0.00102650		0.000909396i	−9.29345e−5		8.23328e-5i
$123$	−4.56439	−	12.0353i	−0.411557	−	1.08519i
$124$	−14.5412	+	7.63181i	−1.30584	+	0.685357i
$125$	4.69241	+	12.3729i	0.419702	+	1.10666i
$126$	−0.0174384	+	0.00429818i	−0.00155354	+	0.000382913i
$127$	1.76888	+	1.56709i	0.156963	+	0.139057i	0.737949	−	0.674856i	$-0.235794\pi$
$127$	1.76888	+	1.56709i	0.156963	+	0.139057i	−0.580986	+	0.813913i	$0.697333\pi$
$128$	−0.0252282	+	0.0365494i	−0.00222988	+	0.00323054i
$129$	4.02587	−	10.6153i	0.354458	−	0.934628i
$130$	−0.00241349	−	0.0182880i	−0.000211677	−	0.00160396i
$131$	−2.87299	−	7.57544i	−0.251014	−	0.661869i	0.748986	−	0.662586i	$-0.230541\pi$
$131$	−2.87299	−	7.57544i	−0.251014	−	0.661869i	−1.00000		0.000716780i	$0.999772\pi$
$132$	7.21375	+	1.77803i	0.627876	+	0.154758i
$133$	18.6845	+	9.80636i	1.62015	+	0.850319i
$134$	−0.00331108	+	0.00873060i	−0.000286034	+	0.000754209i
$135$	−0.105330	+	0.867472i	−0.00906537	+	0.0746601i
$136$	−0.00502953	−	0.00728652i	−0.000431278	−	0.000624814i
$137$	−5.27928	+	1.30123i	−0.451039	+	0.111171i	−0.458290	−	0.888803i	$-0.651538\pi$
$137$	−5.27928	+	1.30123i	−0.451039	+	0.111171i	0.00725119	+	0.999974i	$0.497692\pi$
$138$	−0.00543953	−	0.00134072i	−0.000463043	−	0.000114130i
$139$	0.0383126	−	0.315533i	0.00324964	−	0.0267632i	−0.990994	−	0.133907i	$-0.957248\pi$
$139$	0.0383126	−	0.315533i	0.00324964	−	0.0267632i	0.994243	+	0.107144i	$0.0341706\pi$
$140$	−11.6571	−	30.7372i	−0.985204	−	2.59777i
$141$	−29.5407	+	7.28114i	−2.48778	+	0.613183i
$142$	−0.00109760		0.000270534i	−9.21085e−5		2.27027e-5i
$143$	4.16433	+	3.61281i	0.348239	+	0.302118i
$144$	−11.2723	+	2.77838i	−0.939361	+	0.231532i
$145$	−9.48184	+	4.97645i	−0.787424	+	0.413272i
$146$	0.00257821			0.000213374
$147$	−31.2928			−2.58099
$148$	−4.18642	+	2.19721i	−0.344122	+	0.180609i
$149$	−2.27250	−	2.01326i	−0.186170	−	0.164932i	0.564890	−	0.825166i	$-0.308919\pi$
$149$	−2.27250	−	2.01326i	−0.186170	−	0.164932i	−0.751060	+	0.660234i	$0.770457\pi$
$150$	−0.0289620			−0.00236474
$151$	11.8624	−	10.5092i	0.965347	−	0.855223i	−0.0241597	−	0.999708i	$-0.507691\pi$
$151$	11.8624	−	10.5092i	0.965347	−	0.855223i	0.989507	+	0.144485i	$0.0461526\pi$
$152$	−0.0232631	−	0.0122094i	−0.00188689	−	0.000990314i
$153$	0.557970	−	4.59530i	0.0451092	−	0.371508i
$154$	−0.00837802	−	0.00439713i	−0.000675120	−	0.000354330i
$155$	−3.64860	+	30.0489i	−0.293063	+	2.41359i
$156$	−17.0528	−	4.01581i	−1.36532	−	0.321522i
$157$	−0.418361	−	3.44551i	−0.0333888	−	0.274982i	−0.999836	−	0.0181158i	$-0.994233\pi$
$157$	−0.418361	−	3.44551i	−0.0333888	−	0.274982i	0.966447	−	0.256866i	$-0.0826898\pi$
$158$	0.00391718	−	0.0103288i	0.000311634	−	0.000821712i
$159$	19.6324	−	10.3039i	1.55695	−	0.817153i
$160$	0.0217705	+	0.0574041i	0.00172111	+	0.00453819i
$161$	−6.55983	−	3.44286i	−0.516987	−	0.271336i
$162$	−0.0114078	−	0.00598730i	−0.000896285	−	0.000470407i
$163$	12.1872	+	3.00386i	0.954571	+	0.235281i	0.685691	−	0.727893i	$-0.259500\pi$
$163$	12.1872	+	3.00386i	0.954571	+	0.235281i	0.268881	+	0.963174i	$0.413346\pi$
$164$	1.27724	+	10.5190i	0.0997353	+	0.821394i
$165$	10.2504	−	9.08104i	0.797990	−	0.706958i
$166$	−0.000426571	0	0.000617995i	−3.31083e−5	0	4.79657e-5i
$167$	4.10366	+	10.8205i	0.317550	+	0.837312i	0.994827	+	0.101583i	$0.0323908\pi$
$167$	4.10366	+	10.8205i	0.317550	+	0.837312i	−0.677277	+	0.735729i	$0.736840\pi$
$168$	0.0601350			0.00463951
$169$	−9.90754	−	8.41669i	−0.762118	−	0.647438i
$170$	−0.00815968			−0.000625819
$171$	−4.87088	−	12.8435i	−0.372486	−	0.982164i
$172$	−5.30917	+	7.69166i	−0.404820	+	0.586483i
$173$	13.7356	−	12.1687i	1.04430	−	0.925170i	0.0470221	−	0.998894i	$-0.485027\pi$
$173$	13.7356	−	12.1687i	1.04430	−	0.925170i	0.997279	+	0.0737241i	$0.0234884\pi$
$174$	−0.00118058	−	0.00972297i	−8.94997e−5	−	0.000737096i
$175$	−37.1860	−	9.16552i	−2.81100	−	0.692848i
$176$	−5.41562	−	2.84234i	−0.408218	−	0.214249i
$177$	−28.2053	−	14.8033i	−2.12004	−	1.11268i
$178$	0.00702957	+	0.0185355i	0.000526889	+	0.00138929i
$179$	0.343774	−	0.180427i	0.0256949	−	0.0134857i	−0.451827	−	0.892106i	$-0.649228\pi$
$179$	0.343774	−	0.180427i	0.0256949	−	0.0134857i	0.477522	+	0.878620i	$0.341535\pi$
$180$	−7.58822	+	20.0085i	−0.565592	+	1.49134i
$181$	−0.896157	−	7.38052i	−0.0666109	−	0.548590i	−0.987367	−	0.158451i	$-0.949350\pi$
$181$	−0.896157	−	7.38052i	−0.0666109	−	0.548590i	0.920756	−	0.390139i	$-0.127573\pi$
$182$	0.0198622	+	0.0101629i	0.00147228	+	0.000753322i
$183$	−0.289370	+	2.38318i	−0.0213909	+	0.176170i
$184$	0.00816732	+	0.00428654i	0.000602103	+	0.000316008i
$185$	−1.05044	+	8.65112i	−0.0772296	+	0.636043i
$186$	−0.0245146	−	0.0128663i	−0.00179750	−	0.000943401i
$187$	1.82537	−	1.61714i	0.133484	−	0.118257i
$188$	25.0462			1.82668
$189$	−0.791116	−	0.700868i	−0.0575452	−	0.0509806i
$190$	−0.0214393	+	0.0112522i	−0.00155537	+	0.000816322i
$191$	−6.84984			−0.495637			−0.247819	−	0.968806i	$-0.579714\pi$
$191$	−6.84984			−0.495637			−0.247819	+	0.968806i	$0.579714\pi$
$192$	19.4358			1.40266
$193$	9.32249	−	4.89282i	0.671048	−	0.352193i	−0.0945432	−	0.995521i	$-0.530139\pi$
$193$	9.32249	−	4.89282i	0.671048	−	0.352193i	0.765591	+	0.643328i	$0.222447\pi$
$194$	0.00294930		0.000726937i	0.000211747		5.21910e-5i
$195$	−23.9470	+	21.6631i	−1.71488	+	1.55133i
$196$	25.0122	+	6.16495i	1.78658	+	0.440354i
$197$	3.42220	−	0.843497i	0.243822	−	0.0600967i	−0.115511	−	0.993306i	$-0.536850\pi$
$197$	3.42220	−	0.843497i	0.243822	−	0.0600967i	0.359333	+	0.933210i	$0.383004\pi$
$198$	0.00218408	+	0.00575895i	0.000155216	+	0.000409271i
$199$	2.78127	−	22.9058i	0.197159	−	1.62375i	−0.472672	−	0.881238i	$-0.656711\pi$
$199$	2.78127	−	22.9058i	0.197159	−	1.62375i	0.669831	−	0.742513i	$-0.266366\pi$
$200$	0.0462984	+	0.0114115i	0.00327379	+	0.000806917i
$201$	15.8706	−	3.91176i	1.11943	−	0.275914i
$202$	0.00803952	+	0.0116473i	0.000565659	+	0.000819498i
$203$	1.56118	−	12.8575i	0.109574	−	0.902419i
$204$	−2.74802	+	7.24593i	−0.192400	+	0.507316i
$205$	17.2939	+	9.07653i	1.20786	+	0.633933i
$206$	−0.00121438		0.000299318i	−8.46099e−5		2.08545e-5i
$207$	1.71009	+	4.50914i	0.118860	+	0.313407i
$208$	12.8391	+	6.56937i	0.890231	+	0.455504i
$209$	2.56607	−	6.76617i	0.177499	−	0.468026i
$210$	0.0314825	−	0.0456102i	0.00217250	−	0.00314740i
$211$	11.8143	+	10.4666i	0.813333	+	0.720550i	0.963383	−	0.268128i	$-0.0864051\pi$
$211$	11.8143	+	10.4666i	0.813333	+	0.720550i	−0.150050	+	0.988678i	$0.547944\pi$
$212$	−17.7221	+	4.36810i	−1.21716	+	0.300002i
$213$	0.701732	+	1.85031i	0.0480819	+	0.126781i
$214$	−0.0149774	+	0.00786077i	−0.00102384	+	0.000537351i
$215$	6.10868	+	16.1073i	0.416608	+	1.09851i
$216$	0.000984979	0	0.000872616i	6.70194e−5	0	5.93740e-5i
$217$	−27.4040	−	24.2778i	−1.86030	−	1.64809i
$218$	−0.00832880	−	0.0120664i	−0.000564098	−	0.000817236i
$219$	−2.56385	−	3.71438i	−0.173249	−	0.250994i
$220$	−9.98212	+	5.23902i	−0.672994	+	0.353215i
$221$	−4.26445	+	3.85773i	−0.286858	+	0.259499i
$222$	−0.00705779	−	0.00370421i	−0.000473688	−	0.000248611i
$223$	−0.419907	−	3.45825i	−0.0281191	−	0.231581i	0.971873	−	0.235505i	$-0.0756743\pi$
$223$	−0.419907	−	3.45825i	−0.0281191	−	0.231581i	−0.999992	+	0.00392323i	$0.998751\pi$
$224$	−0.0720984	−	0.0177707i	−0.00481728	−	0.00118735i
$225$	14.1623	+	20.5176i	0.944152	+	1.36784i
$226$	0.00567550	−	0.00822239i	0.000377529	−	0.000546945i
$227$	−4.87514	+	4.31899i	−0.323574	+	0.286662i	−0.809234	−	0.587486i	$-0.800118\pi$
$227$	−4.87514	+	4.31899i	−0.323574	+	0.286662i	0.485660	+	0.874148i	$0.338579\pi$
$228$	2.77182	+	22.8280i	0.183568	+	1.51182i
$229$	−1.47629	+	0.363872i	−0.0975558	+	0.0240453i	−0.287791	−	0.957693i	$-0.592921\pi$
$229$	−1.47629	+	0.363872i	−0.0975558	+	0.0240453i	0.190236	+	0.981738i	$0.439075\pi$
$230$	0.00752702	−	0.00395049i	0.000496317	−	0.000260487i
$231$	1.99650	+	16.4427i	0.131360	+	1.08185i
$232$	−0.00194375	+	0.0160082i	−0.000127613	+	0.00105099i
$233$	−7.86460	−	11.3938i	−0.515227	−	0.746435i	0.475879	−	0.879511i	$-0.342130\pi$
$233$	−7.86460	−	11.3938i	−0.515227	−	0.746435i	−0.991106	+	0.133076i	$0.957515\pi$
$234$	−0.00529084	−	0.0135256i	−0.000345873	−	0.000884193i
$235$	26.2249	−	37.9934i	1.71073	−	2.47841i
$236$	19.6280	+	17.3889i	1.27767	+	1.13192i
$237$	−18.7758	+	4.62782i	−1.21962	+	0.300609i
$238$	0.00560634	−	0.00812219i	0.000363405	−	0.000526483i
$239$	26.0080			1.68232			0.841159	−	0.540788i	$-0.181874\pi$
$239$	26.0080			1.68232			0.841159	+	0.540788i	$0.181874\pi$
$240$	20.3505	−	29.4828i	1.31362	−	1.90311i
$241$	−2.16732	+	17.8495i	−0.139610	+	1.14979i	0.739496	+	0.673161i	$0.235064\pi$
$241$	−2.16732	+	17.8495i	−0.139610	+	1.14979i	−0.879106	+	0.476627i	$0.841859\pi$
$242$	0.00426287	−	0.0112403i	0.000274028	−	0.000722552i
$243$	2.63280	+	21.6830i	0.168894	+	1.39097i
$244$	0.700800	−	1.84786i	0.0448641	−	0.118297i
$245$	35.5411	−	31.4866i	2.27064	−	2.01161i
$246$	−0.0133713	+	0.0118460i	−0.000852526	+	0.000755272i
$247$	−5.88489	+	16.0168i	−0.374447	+	1.01912i
$248$	0.0341194	+	0.0302271i	0.00216658	+	0.00191942i
$249$	1.31453			0.0833048
$250$	0.0137464	−	0.0121782i	0.000869398	−	0.000770219i
$251$	−8.73968	−	2.15414i	−0.551643	−	0.135968i	−0.0463655	−	0.998925i	$-0.514764\pi$
$251$	−8.73968	−	2.15414i	−0.551643	−	0.135968i	−0.505278	+	0.862957i	$0.668610\pi$
$252$	−14.7029	−	21.3008i	−0.926193	−	1.34182i
$253$	−0.900908	+	2.37550i	−0.0566396	+	0.149346i
$254$	0.00116301	−	0.00306662i	7.29740e−5	−	0.000192417i
$255$	8.11422	+	11.7555i	0.508132	+	0.736156i
$256$	−15.5349	−	3.82901i	−0.970932	−	0.239313i
$257$	0.358033	−	0.317189i	0.0223335	−	0.0197857i	−0.651882	−	0.758320i	$-0.726020\pi$
$257$	0.358033	−	0.317189i	0.0223335	−	0.0197857i	0.674216	+	0.738535i	$0.264482\pi$
$258$	−0.0157563			−0.000980944
$259$	−7.88964	−	6.98961i	−0.490238	−	0.434313i
$260$	23.4086	−	12.5975i	1.45174	−	0.781262i
$261$	−6.31076	+	5.59085i	−0.390626	+	0.346065i
$262$	−0.00841640	+	0.00745628i	−0.000519967	+	0.000460650i
$263$	−1.98464	+	5.23308i	−0.122378	+	0.322685i	−0.982180	−	0.187943i	$-0.939818\pi$
$263$	−1.98464	+	5.23308i	−0.122378	+	0.322685i	0.859802	+	0.510628i	$0.170587\pi$
$264$	−0.00248574	−	0.0204720i	−0.000152987	−	0.00125996i
$265$	−11.9300	+	31.4568i	−0.732854	+	1.93238i
$266$	0.00352998	−	0.0290720i	0.000216437	−	0.00178252i
$267$	19.7132	−	28.5596i	1.20643	−	1.74782i
$268$	−13.4560			−0.821954
$269$	4.27575	−	6.19450i	0.260697	−	0.377685i	−0.670676	−	0.741750i	$-0.733996\pi$
$269$	4.27575	−	6.19450i	0.260697	−	0.377685i	0.931374	+	0.364065i	$0.118611\pi$
$270$	0.00117751		0.000290231i	7.16612e−5		1.76629e-5i
$271$	−6.92775	−	6.13745i	−0.420831	−	0.372823i	0.425967	−	0.904739i	$-0.359934\pi$
$271$	−6.92775	−	6.13745i	−0.420831	−	0.372823i	−0.846798	+	0.531915i	$0.821472\pi$
$272$	3.62399	−	5.25025i	0.219736	−	0.318343i
$273$	−5.11011	−	38.7213i	−0.309278	−	2.34352i
$274$	0.00428666	+	0.00621029i	0.000258966	+	0.000375178i
$275$	−1.58313	+	13.0382i	−0.0954661	+	0.786234i
$276$	−0.973145	−	8.01457i	−0.0585764	−	0.482420i
$277$	−16.6019	+	8.71333i	−0.997510	+	0.523534i	−0.882742	−	0.469859i	$-0.844305\pi$
$277$	−16.6019	+	8.71333i	−0.997510	+	0.523534i	−0.114768	+	0.993392i	$0.536613\pi$
$278$	−0.000428307	0	0.000105568i	−2.56882e−5	0	6.33156e-6i
$279$	2.87266	+	23.6585i	0.171982	+	1.41640i
$280$	−0.0682988	+	0.0605075i	−0.00408164	+	0.00361601i
$281$	−16.3908	+	23.7462i	−0.977793	+	1.41658i	−0.0698149	+	0.997560i	$0.522241\pi$
$281$	−16.3908	+	23.7462i	−0.977793	+	1.41658i	−0.907978	+	0.419018i	$0.862375\pi$
$282$	0.0239864	+	0.0347503i	0.00142837	+	0.00206935i
$283$	−27.5003	−	6.77821i	−1.63472	−	0.402923i	−0.688190	−	0.725530i	$-0.741595\pi$
$283$	−27.5003	−	6.77821i	−1.63472	−	0.402923i	−0.946533	+	0.322607i	$0.895441\pi$
$284$	−0.196363	−	1.61720i	−0.0116520	−	0.0959629i
$285$	37.5307	+	19.6977i	2.22313	+	1.16679i
$286$	0.00263876	−	0.00718185i	0.000156033	−	0.000424672i
$287$	−20.9171	+	10.9781i	−1.23470	+	0.648019i
$288$	0.0274587	+	0.0397808i	0.00161802	+	0.00234410i
$289$	−8.21213	−	11.8973i	−0.483067	−	0.699843i
$290$	0.0111241	+	0.00985505i	0.000653227	+	0.000578709i
$291$	−3.98015	−	3.52611i	−0.233321	−	0.206704i
$292$	1.31751	+	3.47399i	0.0771014	+	0.203300i
$293$	7.10061	−	3.72669i	0.414822	−	0.217715i	−0.244383	−	0.969679i	$-0.578585\pi$
$293$	7.10061	−	3.72669i	0.414822	−	0.217715i	0.659205	+	0.751963i	$0.270893\pi$
$294$	0.0154003	+	0.0406072i	0.000898162	+	0.00236826i
$295$	46.9293	−	11.5670i	2.73233	−	0.673459i
$296$	0.00982300	+	0.00870242i	0.000570950	+	0.000505818i
$297$	−0.205897	+	0.298294i	−0.0119474	+	0.0173087i
$298$	−0.00149413	+	0.00393971i	−8.65528e−5	+	0.000228221i
$299$	2.06610	−	5.62325i	0.119485	−	0.325201i
$300$	−14.8001	−	39.0245i	−0.854482	−	2.25308i
$301$	−20.2304	−	4.98635i	−1.16606	−	0.287408i
$302$	−0.0194751	−	0.0102213i	−0.00112067	−	0.000588172i
$303$	8.78523	−	23.1648i	0.504698	−	1.33078i
$304$	2.28181	−	18.7924i	0.130871	−	1.07782i
$305$	−2.06929	−	2.99788i	−0.118487	−	0.171658i
$306$	−0.00623770	+	0.00153745i	−0.000356585	+	8.78904e-5i
$307$	29.4307	+	7.25401i	1.67970	+	0.414008i	0.959937	−	0.280215i	$-0.0904057\pi$
$307$	29.4307	+	7.25401i	1.67970	+	0.414008i	0.719760	+	0.694223i	$0.244252\pi$
$308$	1.64355	−	13.5359i	0.0936502	−	0.771278i
$309$	0.776394	+	2.04718i	0.0441675	+	0.116460i
$310$	0.0407887	−	0.0100535i	0.00231664	−	0.000571001i
$311$	28.2867	+	6.97206i	1.60399	+	0.395349i	0.936892	−	0.349618i	$-0.113689\pi$
$311$	28.2867	+	6.97206i	1.60399	+	0.395349i	0.667102	+	0.744967i	$0.267535\pi$
$312$	0.00636234	+	0.0482100i	0.000360197	+	0.00272935i
$313$	−29.9396	+	7.37946i	−1.69229	+	0.417112i	−0.963517	−	0.267646i	$-0.913754\pi$
$313$	−29.9396	+	7.37946i	−1.69229	+	0.417112i	−0.728771	+	0.684758i	$0.759908\pi$
$314$	−0.00426519	+	0.00223854i	−0.000240698	+	0.000126328i
$315$	−47.7065			−2.68796
$316$	15.9191			0.895521
$317$	1.94214	−	1.01931i	0.109081	−	0.0572504i	−0.409300	−	0.912400i	$-0.634227\pi$
$317$	1.94214	−	1.01931i	0.109081	−	0.0572504i	0.518381	+	0.855149i	$0.326535\pi$
$318$	−0.0230327	−	0.0204052i	−0.00129161	−	0.00114427i
$319$	−4.44165			−0.248685
$320$	−22.0744	+	19.5562i	−1.23400	+	1.09323i
$321$	26.2189	+	13.7607i	1.46339	+	0.768048i
$322$	−0.00123932	+	0.0102067i	−6.90647e−5	+	0.000568799i
$323$	6.68341	+	3.50772i	0.371875	+	0.195175i
$324$	2.23793	−	18.4310i	0.124329	−	1.02394i
$325$	3.41365	−	30.7816i	0.189355	−	1.70745i
$326$	−0.00209975	−	0.0172930i	−0.000116294	−	0.000957771i
$327$	−9.10134	+	23.9983i	−0.503305	+	1.32711i
$328$	0.0260428	−	0.0136683i	0.00143798	−	0.000754708i
$329$	19.8002	+	52.2089i	1.09162	+	2.87837i
$330$	−0.0168286	−	0.00883233i	−0.000926384	−	0.000486204i
$331$	22.5026	+	11.8103i	1.23685	+	0.649150i	0.951020	−	0.309129i	$-0.100038\pi$
$331$	22.5026	+	11.8103i	1.23685	+	0.649150i	0.285833	+	0.958280i	$0.407730\pi$
$332$	−1.05070	−	0.258973i	−0.0576644	−	0.0142130i
$333$	0.827042	+	6.81131i	0.0453216	+	0.373257i
$334$	0.0120216	−	0.0106502i	0.000657795	−	0.000582756i
$335$	−14.0892	+	20.4118i	−0.769776	+	1.11521i
$336$	15.3650	+	40.5141i	0.838227	+	2.21022i
$337$	−4.88186			−0.265932			−0.132966	−	0.991121i	$-0.542450\pi$
$337$	−4.88186			−0.265932			−0.132966	+	0.991121i	$0.542450\pi$
$338$	−0.00604610	+	0.0169987i	−0.000328864	+	0.000924607i
$339$	−17.4897			−0.949911
$340$	−4.16973	−	10.9947i	−0.226135	−	0.596270i
$341$	−7.13221	+	10.3328i	−0.386231	+	0.559552i
$342$	−0.0142692	+	0.0126414i	−0.000771592	+	0.000683570i
$343$	3.16037	+	26.0280i	0.170644	+	1.40538i
$344$	0.0251879	+	0.00620825i	0.00135804	+	0.000334727i
$345$	−13.1765	−	6.91555i	−0.709397	−	0.372321i
$346$	−0.0225505	−	0.0118354i	−0.00121232	−	0.000636277i
$347$	−7.01378	−	18.4938i	−0.376520	−	0.992801i	−0.980625	−	0.195896i	$-0.937238\pi$
$347$	−7.01378	−	18.4938i	−0.376520	−	0.992801i	0.604105	−	0.796905i	$-0.293531\pi$
$348$	12.4978	−	6.55936i	0.669953	−	0.351619i
$349$	8.85512	−	23.3490i	0.474004	−	1.24984i	−0.458503	−	0.888693i	$-0.651614\pi$
$349$	8.85512	−	23.3490i	0.474004	−	1.24984i	0.932507	−	0.361152i	$-0.117616\pi$
$350$	0.00640685	+	0.0527652i	0.000342461	+	0.00282042i
$351$	0.478182	−	0.708388i	0.0255235	−	0.0378109i
$352$	−0.00306946	+	0.0252793i	−0.000163603	+	0.00134739i
$353$	9.23401	+	4.84638i	0.491477	+	0.257947i	0.692206	−	0.721700i	$-0.256639\pi$
$353$	9.23401	+	4.84638i	0.491477	+	0.257947i	−0.200729	+	0.979647i	$0.564331\pi$
$354$	−0.00532871	+	0.0438859i	−0.000283218	+	0.00233251i
$355$	−2.65877	−	1.39543i	−0.141113	−	0.0740619i
$356$	−21.3832	+	18.9439i	−1.13331	+	1.00402i
$357$	−17.2766			−0.914373
$358$	−0.000403314	0	0.000357305i	−2.13158e−5	0	1.88842e-5i
$359$	−4.13758	+	2.17157i	−0.218373	+	0.114611i	−0.570363	−	0.821393i	$-0.693197\pi$
$359$	−4.13758	+	2.17157i	−0.218373	+	0.114611i	0.351990	+	0.936004i	$0.385505\pi$
$360$	0.0593970			0.00313050
$361$	3.39764			0.178823
$362$	−0.00913633	+	0.00479511i	−0.000480195	+	0.000252026i
$363$	−20.4327	+	5.03622i	−1.07244	+	0.264333i
$364$	−3.54395	+	31.9565i	−0.185753	+	1.67498i
$365$	6.64930	+	1.63891i	0.348040	+	0.0857843i
$366$	0.00323495		0.000797344i	0.000169094		4.16778e-5i
$367$	−1.74183	−	4.59282i	−0.0909226	−	0.239743i	0.881839	−	0.471550i	$-0.156305\pi$
$367$	−1.74183	−	4.59282i	−0.0909226	−	0.239743i	−0.972762	+	0.231807i	$0.925536\pi$
$368$	−0.801108	+	6.59772i	−0.0417607	+	0.343930i
$369$	14.9306	+	3.68006i	0.777256	+	0.191576i
$370$	0.0117431	−	0.00289442i	0.000610495	−	0.000150473i
$371$	−23.1154	−	33.4885i	−1.20009	−	1.73864i
$372$	4.80914	−	39.6069i	0.249342	−	2.05352i
$373$	−6.61976	+	17.4549i	−0.342758	+	0.903779i	0.647187	+	0.762331i	$0.275945\pi$
$373$	−6.61976	+	17.4549i	−0.342758	+	0.903779i	−0.989946	+	0.141448i	$0.954824\pi$
$374$	−0.00299681	−	0.00157285i	−0.000154961	−	8.13300e-5i
$375$	−31.2147	−	7.69374i	−1.61192	−	0.397303i
$376$	−0.0246523	−	0.0650027i	−0.00127134	−	0.00335226i
$377$	10.4730	−	0.108742i	0.539386	−	0.00560049i
$378$	−0.000520147		0.00137152i	−2.67535e−5		7.05432e-5i
$379$	16.0510	−	23.2538i	0.824483	−	1.19447i	−0.153985	−	0.988073i	$-0.549211\pi$
$379$	16.0510	−	23.2538i	0.824483	−	1.19447i	0.978468	−	0.206397i	$-0.0661738\pi$
$380$	−26.1175	−	23.1381i	−1.33980	−	1.18696i
$381$	−5.57455	+	1.37400i	−0.285593	+	0.0703923i
$382$	0.00337105	+	0.00888872i	0.000172478	+	0.000454787i
$383$	−15.1506	+	7.95163i	−0.774157	+	0.406309i	−0.805045	−	0.593214i	$-0.797859\pi$
$383$	−15.1506	+	7.95163i	−0.774157	+	0.406309i	0.0308876	+	0.999523i	$0.490167\pi$
$384$	−0.0382603	−	0.100884i	−0.00195246	−	0.00514822i
$385$	−18.8121	−	16.6660i	−0.958752	−	0.849380i
$386$	−0.0109371	−	0.00968943i	−0.000556684	−	0.000493179i
$387$	7.70475	+	11.1623i	0.391655	+	0.567410i
$388$	2.48664	+	3.60253i	0.126240	+	0.182891i
$389$	−1.24873	+	0.655385i	−0.0633132	+	0.0332294i	−0.496083	−	0.868275i	$-0.665229\pi$
$389$	−1.24873	+	0.655385i	−0.0633132	+	0.0332294i	0.432769	+	0.901505i	$0.357536\pi$
$390$	0.0398964	+	0.0204138i	0.00202023	+	0.00103369i
$391$	−2.34644	−	1.23151i	−0.118665	−	0.0622801i
$392$	−0.00861881	−	0.0709823i	−0.000435316	−	0.00358515i
$393$	19.1116	+	4.71059i	0.964053	+	0.237618i
$394$	−0.00277875	−	0.00402572i	−0.000139992	−	0.000202813i
$395$	16.6683	−	24.1482i	0.838672	−	1.21503i
$396$	−6.64373	+	5.88583i	−0.333860	+	0.295774i
$397$	−2.93542	−	24.1753i	−0.147324	−	1.21332i	−0.859430	−	0.511253i	$-0.829182\pi$
$397$	−2.93542	−	24.1753i	−0.147324	−	1.21332i	0.712106	−	0.702072i	$-0.247742\pi$
$398$	−0.0310926	+	0.00766363i	−0.00155853	+	0.000384143i
$399$	−45.3937	+	23.8245i	−2.27253	+	1.19272i
$400$	4.14144	+	34.1078i	0.207072	+	1.70539i
$401$	2.85134	−	23.4829i	0.142389	−	1.17268i	−0.729853	−	0.683605i	$-0.760411\pi$
$401$	2.85134	−	23.4829i	0.142389	−	1.17268i	0.872242	−	0.489075i	$-0.162666\pi$
$402$	−0.0128866	−	0.0186695i	−0.000642725	−	0.000931148i
$403$	16.5641	−	24.5383i	0.825115	−	1.22234i
$404$	−11.5857	+	16.7847i	−0.576408	+	0.835071i
$405$	−25.6153	−	22.6931i	−1.27283	−	1.12763i
$406$	−0.0174529	+	0.00430175i	−0.000866172	+	0.000213492i
$407$	−2.05337	+	2.97482i	−0.101782	+	0.147456i
$408$	0.0215102			0.00106491
$409$	3.74228	−	5.42163i	0.185044	−	0.268082i	−0.719473	−	0.694521i	$-0.755617\pi$
$409$	3.74228	−	5.42163i	0.185044	−	0.268082i	0.904517	+	0.426438i	$0.140232\pi$
$410$	0.00326727	−	0.0269083i	0.000161359	−	0.00132891i
$411$	4.68427	−	12.3514i	0.231058	−	0.609249i
$412$	−0.217255	−	1.78926i	−0.0107034	−	0.0881505i
$413$	−20.7303	+	54.6612i	−1.02007	+	2.68970i
$414$	0.00500971	−	0.00443822i	0.000246214	−	0.000218126i
$415$	−1.49299	+	1.32267i	−0.0732878	+	0.0649273i
$416$	0.00661859	−	0.0596812i	0.000324503	−	0.00292611i
$417$	0.578011	+	0.512073i	0.0283053	+	0.0250763i
$418$	−0.0100430			−0.000491219
$419$	15.7151	−	13.9224i	0.767733	−	0.680152i	−0.185414	−	0.982661i	$-0.559363\pi$
$419$	15.7151	−	13.9224i	0.767733	−	0.680152i	0.953147	+	0.302509i	$0.0978241\pi$
$420$	77.5451	+	19.1131i	3.78381	+	0.932626i
$421$	−14.5090	−	21.0199i	−0.707124	−	1.02445i	−0.997713	−	0.0675983i	$-0.978466\pi$
$421$	−14.5090	−	21.0199i	−0.707124	−	1.02445i	0.290588	−	0.956848i	$-0.406149\pi$
$422$	0.00776776	−	0.0204819i	0.000378129	−	0.000997043i
$423$	12.8890	−	33.9855i	0.626685	−	1.65243i
$424$	0.0287799	+	0.0416949i	0.00139767	+	0.00202488i
$425$	−13.3014	−	3.27850i	−0.645212	−	0.159030i
$426$	0.00205572	−	0.00182121i	9.96000e−5	−	8.82379e-5i
$427$	4.40587			0.213215
$428$	−18.2456	−	16.1642i	−0.881936	−	0.781327i
$429$	−12.9708	+	3.34024i	−0.626236	+	0.161268i
$430$	0.0178953	−	0.0158539i	0.000862990	−	0.000764543i
$431$	−8.74005	+	7.74301i	−0.420994	+	0.372968i	−0.846858	−	0.531819i	$-0.821509\pi$
$431$	−8.74005	+	7.74301i	−0.420994	+	0.372968i	0.425864	+	0.904787i	$0.359970\pi$
$432$	−0.336228	+	0.886559i	−0.0161768	+	0.0426546i
$433$	0.859716	+	7.08040i	0.0413153	+	0.340262i	0.998679	+	0.0513777i	$0.0163612\pi$
$433$	0.859716	+	7.08040i	0.0413153	+	0.340262i	−0.957364	+	0.288884i	$0.906716\pi$
$434$	−0.0180177	+	0.0475089i	−0.000864879	+	0.00228050i
$435$	3.13589	−	25.8263i	0.150354	−	1.23828i
$436$	12.0025	−	17.3887i	0.574817	−	0.832766i
$437$	−7.86347			−0.376161
$438$	−0.00355821	+	0.00515496i	−0.000170018	+	0.000246314i
$439$	−14.2016	+	3.50037i	−0.677803	+	0.167064i	−0.563166	−	0.826344i	$-0.690417\pi$
$439$	−14.2016	+	3.50037i	−0.677803	+	0.167064i	−0.114637	+	0.993407i	$0.536571\pi$
$440$	0.0234220	+	0.0207501i	0.00111660	+	0.000989220i
$441$	21.2368	−	30.7668i	1.01128	−	1.46508i
$442$	0.00710469	+	0.00363525i	0.000337935	+	0.000172911i
$443$	21.2588	+	30.7988i	1.01004	+	1.46329i	0.881842	+	0.471544i	$0.156303\pi$
$443$	21.2588	+	30.7988i	1.01004	+	1.46329i	0.128196	+	0.991749i	$0.459081\pi$
$444$	1.38456	−	11.4029i	0.0657082	−	0.541156i
$445$	6.34699	+	52.2721i	0.300876	+	2.47794i
$446$	−0.00428095	+	0.00224682i	−0.000202709	+	0.000106390i
$447$	7.16166	−	1.76519i	0.338735	−	0.0834907i
$448$	−4.29951	−	35.4097i	−0.203133	−	1.67295i
$449$	21.7092	−	19.2327i	1.02452	−	0.907648i	0.0287580	−	0.999586i	$-0.490845\pi$
$449$	21.7092	−	19.2327i	1.02452	−	0.907648i	0.995765	+	0.0919385i	$0.0293063\pi$
$450$	0.0196550	−	0.0284752i	0.000926545	−	0.00134233i
$451$	4.60196	+	6.66709i	0.216698	+	0.313941i
$452$	13.9794	+	3.44562i	0.657538	+	0.162069i
$453$	4.64097	+	38.2218i	0.218052	+	1.79582i
$454$	0.00800378	+	0.00420071i	0.000375636	+	0.000197149i
$455$	44.7650	+	38.8363i	2.09862	+	1.82067i
$456$	0.0565175	−	0.0296627i	0.00264667	−	0.00138908i
$457$	5.28366	+	7.65470i	0.247159	+	0.358072i	0.926853	−	0.375424i	$-0.122503\pi$
$457$	5.28366	+	7.65470i	0.247159	+	0.358072i	−0.679694	+	0.733496i	$0.737888\pi$
$458$	0.00119871	+	0.00173663i	5.60121e−5	+	8.11476e-5i
$459$	−0.282981	−	0.250700i	−0.0132084	−	0.0117017i
$460$	9.16947	+	8.12344i	0.427529	+	0.378758i
$461$	14.2389	+	37.5450i	0.663173	+	1.74864i	0.662972	+	0.748644i	$0.269295\pi$
$461$	14.2389	+	37.5450i	0.663173	+	1.74864i	0.000201327		1.00000i	$0.499936\pi$
$462$	0.0203543	−	0.0106828i	0.000946969	−	0.000497008i
$463$	−3.33342	−	8.78950i	−0.154917	−	0.408483i	0.834978	−	0.550283i	$-0.185480\pi$
$463$	−3.33342	−	8.78950i	−0.154917	−	0.408483i	−0.989895	+	0.141800i	$0.954711\pi$
$464$	−11.2817	+	2.78069i	−0.523739	+	0.129090i
$465$	−55.0453	−	48.7659i	−2.55267	−	2.26146i
$466$	−0.0109148	+	0.0158128i	−0.000505619	+	0.000732515i
$467$	−13.5318	+	35.6804i	−0.626177	+	1.65109i	0.125921	+	0.992040i	$0.459811\pi$
$467$	−13.5318	+	35.6804i	−0.626177	+	1.65109i	−0.752098	+	0.659052i	$0.770958\pi$
$468$	15.5212	−	14.0409i	0.717466	−	0.649039i
$469$	−10.6376	−	28.0490i	−0.491198	−	1.29518i
$470$	−0.0622084	−	0.0153330i	−0.00286946	−	0.000707258i
$471$	7.46645	+	3.91869i	0.344036	+	0.180564i
$472$	0.0258102	−	0.0680560i	0.00118801	−	0.00313253i
$473$	−0.861273	+	7.09322i	−0.0396014	+	0.326147i
$474$	0.0152455	+	0.0220870i	0.000700250	+	0.00101449i
$475$	−39.4701	+	9.72850i	−1.81101	+	0.446374i
$476$	13.8091	+	3.40364i	0.632939	+	0.156005i
$477$	−3.19281	+	26.2952i	−0.146189	+	1.20397i
$478$	−0.0127994	−	0.0337494i	−0.000585433	−	0.00154366i
$479$	16.1690	−	3.98529i	0.738779	−	0.182093i	0.148069	−	0.988977i	$-0.452694\pi$
$479$	16.1690	−	3.98529i	0.738779	−	0.182093i	0.590709	+	0.806884i	$0.298848\pi$
$480$	−0.144821	−	0.0356952i	−0.00661016	−	0.00162926i
$481$	4.76881	−	7.06460i	0.217439	−	0.322118i
$482$	0.0242291	−	0.00597193i	0.00110360	−	0.000272014i
$483$	15.9371	−	8.36441i	0.725161	−	0.380594i
$484$	17.3240			0.787453
$485$	8.06844			0.366369
$486$	0.0268414	−	0.0140874i	0.00121755	−	0.000639019i
$487$	−0.976539	−	0.865138i	−0.0442512	−	0.0392032i	0.640707	−	0.767785i	$-0.278641\pi$
$487$	−0.976539	−	0.865138i	−0.0442512	−	0.0392032i	−0.684958	+	0.728582i	$0.740180\pi$
$488$	−0.00548553			−0.000248318
$489$	−22.8256	+	20.2217i	−1.03221	+	0.914458i
$490$	−0.0583497	−	0.0306243i	−0.00263597	−	0.00138347i
$491$	−3.00281	+	24.7304i	−0.135515	+	1.11607i	0.753260	+	0.657723i	$0.228480\pi$
$491$	−3.00281	+	24.7304i	−0.135515	+	1.11607i	−0.888775	+	0.458343i	$0.848443\pi$
$492$	−22.7947	−	11.9636i	−1.02767	−	0.539360i
$493$	0.558433	−	4.59911i	0.0251506	−	0.207134i
$494$	0.0236804		0.000245876i	0.00106543		1.10625e-5i
$495$	1.97200	+	16.2409i	0.0886349	+	0.729974i
$496$	−11.6468	+	30.7101i	−0.522957	+	1.37892i
$497$	3.21581	−	1.68779i	0.144249	−	0.0757076i
$498$	−0.000646925	−	0.00170580i	−2.89894e−5	−	7.64388e-5i
$499$	20.8059	+	10.9198i	0.931402	+	0.488837i	0.860957	−	0.508678i	$-0.169866\pi$
$499$	20.8059	+	10.9198i	0.931402	+	0.488837i	0.0704452	+	0.997516i	$0.477558\pi$
$500$	23.4341	+	12.2991i	1.04800	+	0.550035i
$501$	−27.2983	−	6.72842i	−1.21960	−	0.300603i
$502$	0.00150578	+	0.0124012i	6.72061e−5	+	0.000553492i
$503$	15.8550	−	14.0463i	0.706938	−	0.626293i	−0.231057	−	0.972940i	$-0.574218\pi$
$503$	15.8550	−	14.0463i	0.706938	−	0.626293i	0.937995	+	0.346648i	$0.112680\pi$
$504$	−0.0408104	+	0.0591241i	−0.00181784	+	0.00263360i
$505$	13.3303	+	35.1492i	0.593192	+	1.56412i
$506$	0.00352594			0.000156747
$507$	30.5021	−	8.19351i	1.35465	−	0.363887i
$508$	4.72640			0.209700
$509$	−4.27859	−	11.2817i	−0.189645	−	0.500054i	0.806145	−	0.591719i	$-0.201550\pi$
$509$	−4.27859	−	11.2817i	−0.189645	−	0.500054i	−0.995790	+	0.0916649i	$0.970781\pi$
$510$	0.0112612	−	0.0163147i	0.000498656	−	0.000722428i
$511$	−6.19997	+	5.49270i	−0.274271	+	0.242983i
$512$	0.0133828	+	0.110217i	0.000591442	+	0.00487096i
$513$	−1.08924	−	0.268474i	−0.0480912	−	0.0118534i
$514$	−0.000587802	0	0.000308502i	−2.59268e−5	0	1.36075e-5i
$515$	−2.94166	−	1.54390i	−0.129625	−	0.0680325i
$516$	−8.05172	−	21.2306i	−0.354457	−	0.934627i
$517$	16.9552	−	8.89877i	0.745688	−	0.391367i
$518$	−0.00518732	+	0.0136778i	−0.000227918	+	0.000600970i
$519$	5.37385	+	44.2576i	0.235886	+	1.94269i
$520$	−0.0557347	−	0.0483532i	−0.00244413	−	0.00212043i
$521$	3.27140	−	26.9424i	0.143323	−	1.18037i	−0.726558	−	0.687105i	$-0.758881\pi$
$521$	3.27140	−	26.9424i	0.143323	−	1.18037i	0.869880	−	0.493263i	$-0.164196\pi$
$522$	0.0103607	+	0.00543773i	0.000453477	+	0.000238003i
$523$	2.09291	−	17.2367i	0.0915165	−	0.753707i	−0.872638	−	0.488367i	$-0.837593\pi$
$523$	2.09291	−	17.2367i	0.0915165	−	0.753707i	0.964155	−	0.265340i	$-0.0854841\pi$
$524$	−14.3478	−	7.53030i	−0.626786	−	0.328963i
$525$	69.6465	−	61.7014i	3.03962	−	2.69287i
$526$	0.00776743			0.000338676
$527$	−9.80238	−	8.68415i	−0.426998	−	0.378287i
$528$	13.1572	−	6.90544i	0.572594	−	0.300521i
$529$	−20.2393			−0.879968
$530$	0.0466912			0.00202814
$531$	33.6959	−	17.6850i	1.46228	−	0.767462i
$532$	40.9766	−	10.0998i	1.77656	−	0.437883i
$533$	−11.0142	−	15.6077i	−0.477077	−	0.676043i
$534$	−0.0467620	−	0.0115258i	−0.00202359	−	0.000498770i
$535$	−43.6243	+	10.7524i	−1.88604	+	0.464867i
$536$	0.0132443	+	0.0349224i	0.000572067	+	0.00150842i
$537$	−0.113695	+	0.936361i	−0.00490630	+	0.0404070i
$538$	−0.0101426	−	0.00249991i	−0.000437276	−	0.000107779i
$539$	19.1225	−	4.71327i	0.823665	−	0.203015i
$540$	0.992798	+	1.43832i	0.0427232	+	0.0618953i
$541$	0.620950	−	5.11398i	0.0266967	−	0.219867i	−0.973255	−	0.229729i	$-0.926216\pi$
$541$	0.620950	−	5.11398i	0.0266967	−	0.219867i	0.999951	+	0.00986170i	$0.00313913\pi$
$542$	−0.00455489	+	0.0120103i	−0.000195649	+	0.000515885i
$543$	15.9936	+	8.39411i	0.686353	+	0.360226i
$544$	−0.0257895	−	0.00635655i	−0.00110572	−	0.000272535i
$545$	−13.8100	−	36.4140i	−0.591555	−	1.55980i
$546$	−0.0477320	+	0.0256873i	−0.00204274	+	0.00109931i
$547$	−14.6331	+	38.5842i	−0.625664	+	1.64974i	0.127445	+	0.991846i	$0.459323\pi$
$547$	−14.6331	+	38.5842i	−0.625664	+	1.64974i	−0.753109	+	0.657896i	$0.771447\pi$
$548$	−6.17744	+	8.94957i	−0.263887	+	0.382307i
$549$	−2.14674	−	1.90185i	−0.0916206	−	0.0811688i
$550$	0.0176982	−	0.00436221i	0.000754653	−	0.000186005i
$551$	−4.87493	−	12.8541i	−0.207679	−	0.547604i
$552$	−0.0198424	+	0.0104141i	−0.000844550	+	0.000443254i
$553$	12.5848	+	33.1834i	0.535161	+	1.41110i
$554$	0.0194772	+	0.0172553i	0.000827509	+	0.000733109i
$555$	−15.8476	−	14.0398i	−0.672694	−	0.595954i
$556$	−0.361119	−	0.523171i	−0.0153149	−	0.0221874i
$557$	14.7662	+	21.3926i	0.625666	+	0.906434i	0.999781	−	0.0209489i	$-0.00666874\pi$
$557$	14.7662	+	21.3926i	0.625666	+	0.906434i	−0.374115	+	0.927382i	$0.622053\pi$
$558$	0.0292868	−	0.0153709i	0.00123981	−	0.000650702i
$559$	1.85714	−	16.7462i	0.0785486	−	0.708289i
$560$	−58.2159	−	30.5541i	−2.46007	−	1.29114i
$561$	0.714146	+	5.88152i	0.0301513	+	0.248318i
$562$	0.0388808	+	0.00958325i	0.00164009	+	0.000404245i
$563$	−14.5246	−	21.0424i	−0.612137	−	0.886833i	0.387245	−	0.921977i	$-0.373427\pi$
$563$	−14.5246	−	21.0424i	−0.612137	−	0.886833i	−0.999382	+	0.0351432i	$0.988811\pi$
$564$	−34.5665	+	50.0783i	−1.45551	+	2.10867i
$565$	19.8641	−	17.5981i	0.835689	−	0.740356i
$566$	0.00473809	+	0.0390216i	0.000199157	+	0.00164020i
$567$	40.1886	−	9.90560i	1.68776	−	0.415996i
$568$	−0.00400385	+	0.00210138i	−0.000167998	+	8.81720e-5i
$569$	−3.80603	−	31.3455i	−0.159557	−	1.31407i	−0.823939	−	0.566678i	$-0.808228\pi$
$569$	−3.80603	−	31.3455i	−0.159557	−	1.31407i	0.664382	−	0.747393i	$-0.268695\pi$
$570$	0.00709053	−	0.0583958i	0.000296990	−	0.00244593i
$571$	0.221253	+	0.320541i	0.00925917	+	0.0134142i	0.827586	−	0.561339i	$-0.189714\pi$
$571$	0.221253	+	0.320541i	0.00925917	+	0.0134142i	−0.818327	+	0.574753i	$0.805098\pi$
$572$	11.0256	−	0.114479i	0.461002	−	0.00478662i
$573$	9.45353	−	13.6958i	0.394927	−	0.572150i
$574$	0.0245399	+	0.0217404i	0.00102427	+	0.000907428i
$575$	13.8573	−	3.41553i	0.577891	−	0.142437i
$576$	−13.1901	+	19.1091i	−0.549586	+	0.796213i
$577$	34.4533			1.43431			0.717154	−	0.696914i	$-0.245444\pi$
$577$	34.4533			1.43431			0.717154	+	0.696914i	$0.245444\pi$
$578$	−0.0113971	+	0.0165116i	−0.000474058	+	0.000686792i
$579$	−3.08319	+	25.3923i	−0.128133	+	1.05527i
$580$	−7.59451	+	20.0251i	−0.315345	+	0.831496i
$581$	−0.290794	−	2.39491i	−0.0120642	−	0.0993575i
$582$	−0.00261689	+	0.00690018i	−0.000108474	+	0.000286022i
$583$	−10.4451	+	9.25355i	−0.432592	+	0.383243i
$584$	0.00771928	−	0.00683868i	0.000319426	−	0.000282987i
$585$	−5.04740	−	38.2461i	−0.208684	−	1.58128i
$586$	−0.00833041	−	0.00738010i	−0.000344126	−	0.000304869i
$587$	−9.34500			−0.385709			−0.192855	−	0.981227i	$-0.561775\pi$
$587$	−9.34500			−0.385709			−0.192855	+	0.981227i	$0.561775\pi$
$588$	−46.8459	+	41.5019i	−1.93189	+	1.71151i
$589$	−37.7310	−	9.29985i	−1.55468	−	0.383193i
$590$	−0.0381056	−	0.0552055i	−0.00156878	−	0.00227277i
$591$	−3.03650	+	8.00658i	−0.124905	+	0.329347i
$592$	−3.35313	+	8.84147i	−0.137813	+	0.363382i
$593$	−4.85486	−	7.03348i	−0.199365	−	0.288830i	0.710531	−	0.703665i	$-0.248455\pi$
$593$	−4.85486	−	7.03348i	−0.199365	−	0.288830i	−0.909897	+	0.414835i	$0.863839\pi$
$594$	0.000488411	0	0.000120382i	2.00397e−5	0	4.93935e-6i
$595$	19.6220	−	17.3836i	0.804425	−	0.712658i
$596$	−6.07204			−0.248721
$597$	41.9602	+	37.1735i	1.71732	+	1.52141i
$598$	−0.00831383		8.63232e-5i	−0.000339978		3.53002e-6i
$599$	−0.521196	+	0.461739i	−0.0212955	+	0.0188662i	−0.673703	−	0.739002i	$-0.735297\pi$
$599$	−0.521196	+	0.461739i	−0.0212955	+	0.0188662i	0.652408	+	0.757868i	$0.273759\pi$
$600$	−0.0867134	+	0.0768214i	−0.00354006	+	0.00313622i
$601$	−1.11082	+	2.92899i	−0.0453113	+	0.119476i	−0.955762	−	0.294142i	$-0.904966\pi$
$601$	−1.11082	+	2.92899i	−0.0453113	+	0.119476i	0.910450	+	0.413618i	$0.135735\pi$
$602$	0.00348554	+	0.0287060i	0.000142060	+	0.00116997i
$603$	−6.92456	+	18.2586i	−0.281990	+	0.743546i
$604$	3.82052	−	31.4648i	0.155455	−	1.28029i
$605$	18.1393	−	26.2792i	0.737465	−	1.06840i
$606$	−0.0343833			−0.00139673
$607$	−10.8181	+	15.6727i	−0.439092	+	0.636134i	−0.978582	−	0.205858i	$-0.934002\pi$
$607$	−10.8181	+	15.6727i	−0.439092	+	0.636134i	0.539490	+	0.841992i	$0.318617\pi$
$608$	−0.0765270	+	0.0188622i	−0.00310358	+	0.000764963i
$609$	23.5531	+	20.8662i	0.954420	+	0.845542i
$610$	−0.00287184	+	0.00416058i	−0.000116277	+	0.000168457i
$611$	−39.7608	+	21.3975i	−1.60855	+	0.865651i
$612$	−5.25919	−	7.61926i	−0.212590	−	0.307990i
$613$	−0.316339	+	2.60529i	−0.0127768	+	0.105227i	−0.997702	−	0.0677539i	$-0.978417\pi$
$613$	−0.316339	+	2.60529i	−0.0127768	+	0.105227i	0.984925	+	0.172981i	$0.0553398\pi$
$614$	−0.00507067	−	0.0417608i	−0.000204636	−	0.00168533i
$615$	−42.0154	+	22.0514i	−1.69422	+	0.889197i
$616$	−0.0367475	+	0.00905744i	−0.00148060	+	0.000364935i
$617$	−2.84915	−	23.4648i	−0.114702	−	0.944659i	−0.930492	−	0.366311i	$-0.880621\pi$
$617$	−2.84915	−	23.4648i	−0.114702	−	0.944659i	0.815790	−	0.578348i	$-0.196302\pi$
$618$	0.00227444	−	0.00201498i	9.14915e−5	−	8.10544e-5i
$619$	−11.6160	+	16.8287i	−0.466887	+	0.676403i	−0.983725	−	0.179680i	$-0.942494\pi$
$619$	−11.6160	+	16.8287i	−0.466887	+	0.676403i	0.516838	+	0.856083i	$0.327109\pi$
$620$	34.3902	+	49.8228i	1.38114	+	2.00093i
$621$	0.382416	+	0.0942571i	0.0153458	+	0.00378241i
$622$	−0.00487358	−	0.0401376i	−0.000195413	−	0.00160937i
$623$	−56.3929	−	29.5973i	−2.25933	−	1.18579i
$624$	−30.8543	+	16.6045i	−1.23516	+	0.664710i
$625$	5.16521	−	2.71091i	0.206608	−	0.108436i
$626$	0.0243103	+	0.0352196i	0.000971636	+	0.00140766i
$627$	9.98705	+	14.4687i	0.398844	+	0.577826i
$628$	−5.19588	−	4.60315i	−0.207338	−	0.183686i
$629$	−2.82211	−	2.50018i	−0.112525	−	0.0996885i
$630$	0.0234780	+	0.0619065i	0.000935388	+	0.00246641i
$631$	13.3489	−	7.00603i	0.531410	−	0.278906i	−0.177601	−	0.984103i	$-0.556834\pi$
$631$	13.3489	−	7.00603i	0.531410	−	0.278906i	0.709011	+	0.705197i	$0.249141\pi$
$632$	−0.0156687	−	0.0413150i	−0.000623268	−	0.00164342i
$633$	−37.2323	+	9.17695i	−1.47985	+	0.364751i
$634$	−0.00227851	−	0.00201858i	−9.04912e−5	−	8.01682e-5i
$635$	4.94883	−	7.16961i	0.196388	−	0.284517i
$636$	15.7247	−	41.4626i	0.623524	−	1.64410i
$637$	−44.9736	+	11.5816i	−1.78192	+	0.458880i
$638$	0.00218589	+	0.00576373i	8.65403e−5	+	0.000228188i
$639$	−2.29544	−	0.565775i	−0.0908062	−	0.0223817i
$640$	0.144964	+	0.0760828i	0.00573019	+	0.00300744i
$641$	2.51779	−	6.63885i	0.0994465	−	0.262219i	−0.876055	−	0.482211i	$-0.839834\pi$
$641$	2.51779	−	6.63885i	0.0994465	−	0.262219i	0.975502	+	0.219992i	$0.0706031\pi$
$642$	0.00495342	−	0.0407951i	0.000195496	−	0.00161005i
$643$	−2.58066	−	3.73873i	−0.101771	−	0.147441i	0.768790	−	0.639502i	$-0.220859\pi$
$643$	−2.58066	−	3.73873i	−0.101771	−	0.147441i	−0.870561	+	0.492060i	$0.836244\pi$
$644$	−14.3863	+	3.54590i	−0.566899	+	0.139728i
$645$	−40.6360	−	10.0159i	−1.60004	−	0.394375i
$646$	0.00126267	−	0.0103990i	4.96791e−5	−	0.000409144i
$647$	9.61896	+	25.3631i	0.378160	+	0.997127i	0.980086	+	0.198574i	$0.0636312\pi$
$647$	9.61896	+	25.3631i	0.378160	+	0.997127i	−0.601926	+	0.798552i	$0.705600\pi$
$648$	−0.0500368	+	0.0123330i	−0.00196563	+	0.000484485i
$649$	19.4654	+	4.79779i	0.764084	+	0.188330i
$650$	−0.0416238	+	0.0107190i	−0.00163262	+	0.000420432i
$651$	86.3624	−	21.2864i	3.38481	−	0.834280i
$652$	22.2283	−	11.6663i	0.870526	−	0.456887i
$653$	−14.5463			−0.569239			−0.284620	−	0.958641i	$-0.591867\pi$
$653$	−14.5463			−0.569239			−0.284620	+	0.958641i	$0.591867\pi$
$654$	0.0356205			0.00139287
$655$	−26.4460	+	13.8799i	−1.03333	+	0.542333i
$656$	15.8628	+	14.0532i	0.619337	+	0.548685i
$657$	5.39189			0.210358
$658$	0.0580046	−	0.0513876i	0.00226126	−	0.00200330i
$659$	−12.0419	−	6.32009i	−0.469087	−	0.246196i	0.213580	−	0.976926i	$-0.431488\pi$
$659$	−12.0419	−	6.32009i	−0.469087	−	0.246196i	−0.682667	+	0.730730i	$0.739180\pi$
$660$	3.30134	−	27.1890i	0.128505	−	1.05833i
$661$	−9.90960	−	5.20096i	−0.385439	−	0.202294i	0.260863	−	0.965376i	$-0.415993\pi$
$661$	−9.90960	−	5.20096i	−0.385439	−	0.202294i	−0.646302	+	0.763082i	$0.723685\pi$
$662$	0.00425132	−	0.0350128i	0.000165232	−	0.00136081i
$663$	−1.82788	−	13.8506i	−0.0709890	−	0.537912i
$664$	0.000362053		0.00298178i	1.40504e−5		0.000115715i
$665$	27.5843	−	72.7338i	1.06967	−	2.82050i
$666$	0.00843170	−	0.00442530i	0.000326722	−	0.000171477i
$667$	1.71151	+	4.51289i	0.0662700	+	0.174740i
$668$	20.4938	+	10.7560i	0.792930	+	0.416162i
$669$	7.49405	+	3.93318i	0.289737	+	0.152066i
$670$	0.0334212	+	0.00823758i	0.00129117	+	0.000318245i
$671$	−0.182122	−	1.49991i	−0.00703072	−	0.0579032i
$672$	0.135035	−	0.119630i	0.00520908	−	0.00461485i
$673$	14.6070	−	21.1619i	0.563060	−	0.815733i	−0.433276	−	0.901261i	$-0.642643\pi$
$673$	14.6070	−	21.1619i	0.563060	−	0.815733i	0.996336	+	0.0855287i	$0.0272579\pi$
$674$	0.00240253	+	0.00633496i	9.25422e−5	+	0.000244014i
$675$	2.03612			0.0783703
$676$	−25.9944	+	0.539862i	−0.999783	+	0.0207639i
$677$	35.8276			1.37697			0.688484	−	0.725251i	$-0.258276\pi$
$677$	35.8276			1.37697			0.688484	+	0.725251i	$0.258276\pi$
$678$	0.00860730	+	0.0226956i	0.000330561	+	0.000871618i
$679$	−5.54366	+	8.03138i	−0.212746	+	0.308216i
$680$	−0.0244304	+	0.0216435i	−0.000936863	+	0.000829989i
$681$	−1.90732	−	15.7082i	−0.0730886	−	0.601939i
$682$	0.0169184	+	0.00417001i	0.000647838	+	0.000159678i
$683$	−0.0995596	−	0.0522529i	−0.00380954	−	0.00199940i	0.462817	−	0.886454i	$-0.346839\pi$
$683$	−0.0995596	−	0.0522529i	−0.00380954	−	0.00199940i	−0.466627	+	0.884454i	$0.654531\pi$
$684$	−24.3254	−	12.7669i	−0.930104	−	0.488156i
$685$	7.10771	+	18.7415i	0.271572	+	0.716075i
$686$	0.0322199	−	0.0169103i	0.00123016	−	0.000645640i
$687$	1.30990	−	3.45392i	0.0499758	−	0.131775i
$688$	2.25308	+	18.5558i	0.0858980	+	0.707433i
$689$	24.4020	−	22.0747i	0.929641	−	0.840978i
$690$	−0.00248938	+	0.0205019i	−9.47690e−5	+	0.000780493i
$691$	−21.5758	−	11.3238i	−0.820782	−	0.430780i	0.00140377	−	0.999999i	$-0.499553\pi$
$691$	−21.5758	−	11.3238i	−0.820782	−	0.430780i	−0.822186	+	0.569219i	$0.807245\pi$
$692$	4.42384	−	36.4336i	0.168169	−	1.38500i
$693$	−17.5212	−	9.19584i	−0.665575	−	0.349321i
$694$	−0.0205468	+	0.0182029i	−0.000779948	+	0.000690973i
$695$	−1.17173			−0.0444461
$696$	−0.0293248	−	0.0259795i	−0.00111155	−	0.000984750i
$697$	−7.48202	+	3.92687i	−0.283402	+	0.148741i
$698$	−0.0346568			−0.00131178
$699$	33.6352			1.27220
$700$	−67.8239	+	35.5967i	−2.56350	+	1.34543i
$701$	−22.7779	+	5.61424i	−0.860308	+	0.212047i	−0.644703	−	0.764434i	$-0.723019\pi$
$701$	−22.7779	+	5.61424i	−0.860308	+	0.212047i	−0.215606	+	0.976480i	$0.569173\pi$
$702$	−0.00115457		0.000271892i	−4.35765e−5		1.02619e-5i
$703$	−10.8628	−	2.67744i	−0.409698	−	0.100981i
$704$	−11.8769	+	2.92739i	−0.447628	+	0.110330i
$705$	39.7719	+	104.870i	1.49790	+	3.94963i
$706$	0.00174454	−	0.0143676i	6.56568e−5	−	0.000540732i
$707$	−44.1467	−	10.8812i	−1.66031	−	0.409229i
$708$	−61.8566	+	15.2463i	−2.32471	+	0.572990i
$709$	20.3217	+	29.4411i	0.763199	+	1.10569i	0.991245	+	0.132035i	$0.0421510\pi$
$709$	20.3217	+	29.4411i	0.763199	+	1.10569i	−0.228046	+	0.973650i	$0.573234\pi$
$710$	−0.000502312		0.00413691i	−1.88514e−5		0.000155255i
$711$	8.19212	−	21.6008i	0.307228	−	0.810095i
$712$	0.0702120	+	0.0368501i	0.00263130	+	0.00138102i
$713$	13.2468	+	3.26503i	0.496095	+	0.122277i
$714$	0.00850241	+	0.0224190i	0.000318195	+	0.000839010i
$715$	11.3708	−	16.8449i	0.425243	−	0.629962i
$716$	0.275347	−	0.726031i	0.0102902	−	0.0271330i
$717$	−35.8939	+	52.0012i	−1.34048	+	1.94202i
$718$	0.00485419	+	0.00430044i	0.000181157	+	0.000160491i
$719$	23.9950	−	5.91423i	0.894862	−	0.220564i	0.235040	−	0.971986i	$-0.424478\pi$
$719$	23.9950	−	5.91423i	0.894862	−	0.220564i	0.659822	+	0.751422i	$0.270632\pi$
$720$	15.1764	+	40.0169i	0.565591	+	1.49134i
$721$	3.55796	−	1.86736i	0.132505	−	0.0695442i
$722$	−0.00167210	−	0.00440896i	−6.22291e−5	−	0.000164085i
$723$	−32.6977	−	28.9677i	−1.21604	−	1.07732i
$724$	−11.1299	−	9.86026i	−0.413641	−	0.366454i
$725$	14.1740	+	20.5346i	0.526410	+	0.762637i
$726$	0.0165909	+	0.0240361i	0.000615747	+	0.000892064i
$727$	24.1489	−	12.6743i	0.895634	−	0.470065i	0.0469090	−	0.998899i	$-0.485063\pi$
$727$	24.1489	−	12.6743i	0.895634	−	0.470065i	0.848725	+	0.528834i	$0.177371\pi$
$728$	0.0864252	−	0.0222562i	0.00320313	−	0.000824870i
$729$	−22.3278	−	11.7185i	−0.826954	−	0.434019i
$730$	−0.00114562	−	0.00943505i	−4.24014e−5	−	0.000349207i
$731$	−7.23639	−	1.78361i	−0.267648	−	0.0659692i
$732$	2.72748	+	3.95144i	0.100811	+	0.146050i
$733$	6.07225	−	8.79717i	0.224284	−	0.324931i	−0.694647	−	0.719351i	$-0.744439\pi$
$733$	6.07225	−	8.79717i	0.224284	−	0.324931i	0.918930	+	0.394420i	$0.129055\pi$
$734$	−0.00510267	+	0.00452057i	−0.000188343	+	0.000166857i
$735$	13.9049	+	114.517i	0.512889	+	4.22402i
$736$	0.0268675	−	0.00662223i	0.000990348	−	0.000244099i
$737$	−9.10909	+	4.78082i	−0.335538	+	0.176104i
$738$	−0.00257242	−	0.0211858i	−9.46923e−5	−	0.000779861i
$739$	−1.73696	+	14.3051i	−0.0638950	+	0.526223i	0.925258	+	0.379337i	$0.123848\pi$
$739$	−1.73696	+	14.3051i	−0.0638950	+	0.526223i	−0.989153	+	0.146886i	$0.953075\pi$
$740$	9.90097	+	14.3440i	0.363967	+	0.527297i
$741$	−23.9027	−	33.8713i	−0.878088	−	1.24429i
$742$	−0.0320805	+	0.0464767i	−0.00117771	+	0.00170621i
$743$	28.5301	+	25.2754i	1.04667	+	0.927266i	0.997439	−	0.0715215i	$-0.0227854\pi$
$743$	28.5301	+	25.2754i	1.04667	+	0.927266i	0.0492280	+	0.998788i	$0.484324\pi$
$744$	−0.107525	+	0.0265027i	−0.00394208	+	0.000971634i
$745$	−6.35779	+	9.21086i	−0.232932	+	0.337460i
$746$	0.0259082			0.000948566
$747$	−0.892101	+	1.29243i	−0.0326403	+	0.0472876i
$748$	0.587897	−	4.84177i	0.0214956	−	0.177033i
$749$	19.2703	−	50.8116i	0.704121	−	1.85662i
$750$	0.00537806	+	0.0442923i	0.000196379	+	0.00161733i
$751$	7.03850	−	18.5590i	0.256839	−	0.677228i	−0.743129	−	0.669148i	$-0.766659\pi$
$751$	7.03850	−	18.5590i	0.256839	−	0.677228i	0.999967	−	0.00807934i	$-0.00257176\pi$
$752$	37.4947	−	33.2174i	1.36729	−	1.21131i
$753$	16.3688	−	14.5014i	0.596510	−	0.528462i
$754$	−0.00529523	−	0.0135368i	−0.000192841	−	0.000492981i
$755$	−43.7296	−	38.7411i	−1.59148	−	1.40993i
$756$	−2.11384			−0.0768796
$757$	9.64031	−	8.54057i	0.350383	−	0.310412i	−0.469512	−	0.882926i	$-0.655570\pi$
$757$	9.64031	−	8.54057i	0.350383	−	0.310412i	0.819895	+	0.572514i	$0.194032\pi$
$758$	−0.0380747	−	0.00938456i	−0.00138293	−	0.000340863i
$759$	−3.50630	−	5.07975i	−0.127271	−	0.184383i
$760$	−0.0343438	+	0.0905572i	−0.00124578	+	0.00328486i
$761$	6.88989	−	18.1672i	0.249758	−	0.658559i	−0.750238	−	0.661168i	$-0.770061\pi$
$761$	6.88989	−	18.1672i	0.249758	−	0.658559i	0.999997	+	0.00260879i	$0.000830404\pi$
$762$	0.00452641	+	0.00655763i	0.000163974	+	0.000237558i
$763$	45.7352	+	11.2727i	1.65573	+	0.408100i
$764$	−10.2544	+	9.08456i	−0.370989	+	0.328668i
$765$	−17.0646			−0.616971

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	169.g (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.000492135 - 0.00129765i) q^{2} +(-1.38011 + 1.99943i) q^{3} +(1.49702 - 1.32624i) q^{4} +(-0.444348 - 3.65953i) q^{5} +(0.00327377 + 0.000806912i) q^{6} +(3.94802 + 2.07208i) q^{7} +(-0.00491548 - 0.00257984i) q^{8} +(-1.02922 - 2.71382i) q^{9} +O(q^{10})\)	\(q+(-0.000492135 - 0.00129765i) q^{2} +(-1.38011 + 1.99943i) q^{3} +(1.49702 - 1.32624i) q^{4} +(-0.444348 - 3.65953i) q^{5} +(0.00327377 + 0.000806912i) q^{6} +(3.94802 + 2.07208i) q^{7} +(-0.00491548 - 0.00257984i) q^{8} +(-1.02922 - 2.71382i) q^{9} +(-0.00453012 + 0.00237759i) q^{10} +(0.542210 - 1.42969i) q^{11} +(0.585685 + 4.82355i) q^{12} +(-1.24348 + 3.38434i) q^{13} +(0.000745884 - 0.00614291i) q^{14} +(7.93023 + 4.16211i) q^{15} +(0.482145 - 3.97082i) q^{16} +(1.41220 + 0.741181i) q^{17} +(-0.00301508 + 0.00267113i) q^{18} +4.73261 q^{19} +(-5.51863 - 4.88908i) q^{20} +(-9.59168 + 5.03410i) q^{21} -0.00212208 q^{22} -1.66155 q^{23} +(0.0119421 - 0.00626771i) q^{24} +(-8.34001 + 2.05563i) q^{25} +(0.00500366 - 5.19534e-5i) q^{26} +(-0.230156 - 0.0567285i) q^{27} +(8.65835 - 2.13409i) q^{28} +(-1.03007 - 2.71607i) q^{29} +(0.00149823 - 0.0123390i) q^{30} +(-7.97254 - 1.96505i) q^{31} +(-0.0161701 + 0.00398558i) q^{32} +(2.11026 + 3.05724i) q^{33} +(0.000266802 - 0.00219731i) q^{34} +(5.82855 - 15.3686i) q^{35} +(-5.13994 - 2.69765i) q^{36} +(-2.29530 - 0.565741i) q^{37} +(-0.00232909 - 0.00614129i) q^{38} +(-5.05063 - 7.15700i) q^{39} +(-0.00725684 + 0.0191347i) q^{40} +(-3.00968 + 4.36027i) q^{41} +(0.0112529 + 0.00996922i) q^{42} +(-4.53725 + 1.11833i) q^{43} +(-1.08442 - 2.85938i) q^{44} +(-9.47398 + 4.97233i) q^{45} +(0.000817706 + 0.00215611i) q^{46} +(9.37370 + 8.30437i) q^{47} +(7.27398 + 6.44419i) q^{48} +(7.31689 + 10.6004i) q^{49} +(0.00677191 + 0.00981080i) q^{50} +(-3.43093 + 1.80069i) q^{51} +(2.62696 + 6.71558i) q^{52} +(-8.08089 - 4.24118i) q^{53} +(3.96541e-5 + 0.000326581i) q^{54} +(-5.47292 - 1.34895i) q^{55} +(-0.0140608 - 0.0203706i) q^{56} +(-6.53152 + 9.46254i) q^{57} +(-0.00301759 + 0.00267335i) q^{58} +(1.58040 + 13.0158i) q^{59} +(17.3917 - 4.28667i) q^{60} +(0.874957 - 0.459213i) q^{61} +(0.00137361 + 0.0113127i) q^{62} +(1.55989 - 12.8468i) q^{63} +(-4.54449 - 6.58383i) q^{64} +(12.9376 + 3.04671i) q^{65} +(0.00292870 - 0.00424296i) q^{66} +(-5.03597 - 4.46148i) q^{67} +(3.09708 - 0.763362i) q^{68} +(2.29312 - 3.32216i) q^{69} -0.0228116 q^{70} +(0.462710 - 0.670351i) q^{71} +(-0.00194214 + 0.0159950i) q^{72} +(-0.658755 + 1.73699i) q^{73} +(0.000395463 + 0.00325693i) q^{74} +(7.40003 - 19.5123i) q^{75} +(7.08482 - 6.27660i) q^{76} +(5.10309 - 4.52094i) q^{77} +(-0.00680172 + 0.0100762i) q^{78} +(5.95782 + 5.27817i) q^{79} -14.7456 q^{80} +(6.94857 - 6.15589i) q^{81} +(0.00713929 + 0.00175968i) q^{82} +(-0.307363 - 0.445293i) q^{83} +(-7.68249 + 20.2571i) q^{84} +(2.08487 - 5.49734i) q^{85} +(0.00368414 + 0.00533740i) q^{86} +(6.85221 + 1.68892i) q^{87} +(-0.00635360 + 0.00562880i) q^{88} -14.2838 q^{89} +(0.0111148 + 0.00984688i) q^{90} +(-11.9219 + 10.7849i) q^{91} +(-2.48737 + 2.20362i) q^{92} +(14.9320 - 13.2286i) q^{93} +(0.00616307 - 0.0162507i) q^{94} +(-2.10293 - 17.3192i) q^{95} +(0.0143476 - 0.0378316i) q^{96} +(-0.263819 + 2.17274i) q^{97} +(0.0101547 - 0.0147116i) q^{98} -4.43797 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9}+O(q^{10}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9} + q^{10} - q^{11} + 11 q^{12} - 65 q^{13} + 9 q^{14} - 41 q^{15} + 3 q^{17} - 13 q^{18} - 6 q^{19} + 29 q^{20} + 19 q^{21} - 22 q^{22} - 82 q^{23} - 31 q^{24} + 2 q^{25} + 26 q^{26} + 21 q^{27} + 43 q^{28} + 13 q^{29} - 81 q^{30} - 33 q^{31} - 93 q^{32} + 35 q^{33} - 24 q^{34} + 27 q^{35} + 54 q^{36} + 25 q^{37} - 56 q^{38} - 13 q^{39} - 52 q^{40} + 29 q^{41} - 63 q^{42} + 21 q^{43} + 45 q^{44} + 33 q^{46} - 69 q^{47} + 54 q^{48} - 54 q^{49} + 80 q^{50} - 16 q^{51} + 13 q^{52} - 45 q^{53} + 29 q^{54} - 83 q^{55} + 91 q^{56} - 11 q^{57} + 25 q^{58} - 57 q^{59} + 51 q^{60} + 39 q^{61} + 4 q^{62} + 26 q^{63} + 86 q^{64} + 65 q^{65} - 138 q^{66} - 101 q^{67} + 36 q^{68} + 32 q^{69} - 90 q^{70} + 20 q^{71} + 13 q^{72} + 61 q^{73} - 4 q^{74} - 67 q^{75} - 107 q^{76} + 67 q^{77} + 13 q^{78} + 57 q^{79} + 160 q^{80} + 78 q^{81} - 31 q^{82} - 59 q^{83} - 36 q^{84} - 61 q^{85} + 41 q^{86} - 9 q^{87} - 45 q^{88} - 66 q^{89} + 191 q^{90} + 39 q^{91} + 79 q^{92} - 80 q^{93} - 21 q^{94} - 28 q^{95} + 70 q^{96} + 7 q^{97} + 158 q^{98} + 130 q^{99}+O(q^{100}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9 + q^10 - q^11 + 11 * q^12 - 65 * q^13 + 9 * q^14 - 41 * q^15 + 3 * q^17 - 13 * q^18 - 6 * q^19 + 29 * q^20 + 19 * q^21 - 22 * q^22 - 82 * q^23 - 31 * q^24 + 2 * q^25 + 26 * q^26 + 21 * q^27 + 43 * q^28 + 13 * q^29 - 81 * q^30 - 33 * q^31 - 93 * q^32 + 35 * q^33 - 24 * q^34 + 27 * q^35 + 54 * q^36 + 25 * q^37 - 56 * q^38 - 13 * q^39 - 52 * q^40 + 29 * q^41 - 63 * q^42 + 21 * q^43 + 45 * q^44 + 33 * q^46 - 69 * q^47 + 54 * q^48 - 54 * q^49 + 80 * q^50 - 16 * q^51 + 13 * q^52 - 45 * q^53 + 29 * q^54 - 83 * q^55 + 91 * q^56 - 11 * q^57 + 25 * q^58 - 57 * q^59 + 51 * q^60 + 39 * q^61 + 4 * q^62 + 26 * q^63 + 86 * q^64 + 65 * q^65 - 138 * q^66 - 101 * q^67 + 36 * q^68 + 32 * q^69 - 90 * q^70 + 20 * q^71 + 13 * q^72 + 61 * q^73 - 4 * q^74 - 67 * q^75 - 107 * q^76 + 67 * q^77 + 13 * q^78 + 57 * q^79 + 160 * q^80 + 78 * q^81 - 31 * q^82 - 59 * q^83 - 36 * q^84 - 61 * q^85 + 41 * q^86 - 9 * q^87 - 45 * q^88 - 66 * q^89 + 191 * q^90 + 39 * q^91 + 79 * q^92 - 80 * q^93 - 21 * q^94 - 28 * q^95 + 70 * q^96 + 7 * q^97 + 158 * q^98 + 130 * q^99

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