LMFDB - Embedded newform 169.2.h.a.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(12,169)]

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([21]))

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

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

chi := DirichletCharacter("169.12");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.h (of order $26$, 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:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			25.2
Character	$\chi$	$=$	169.25
Dual form			169.2.h.a.142.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.16507 - 0.821103i) q^{2} +(1.73033 + 2.50681i) q^{3} +(2.51629 + 2.22924i) q^{4} +(3.34407 + 0.406044i) q^{5} +(-1.68793 - 6.84821i) q^{6} +(-0.858950 - 1.63659i) q^{7} +(-1.46534 - 2.79198i) q^{8} +(-2.22627 + 5.87018i) q^{9} +O(q^{10})$	\(q+(-2.16507 - 0.821103i) q^{2} +(1.73033 + 2.50681i) q^{3} +(2.51629 + 2.22924i) q^{4} +(3.34407 + 0.406044i) q^{5} +(-1.68793 - 6.84821i) q^{6} +(-0.858950 - 1.63659i) q^{7} +(-1.46534 - 2.79198i) q^{8} +(-2.22627 + 5.87018i) q^{9} +(-6.90674 - 3.62494i) q^{10} +(-1.93228 + 0.732816i) q^{11} +(-1.23428 + 10.1652i) q^{12} +(2.73847 - 2.34537i) q^{13} +(0.515876 + 4.24862i) q^{14} +(4.76847 + 9.08555i) q^{15} +(0.0696450 + 0.573578i) q^{16} +(-3.92016 + 2.05746i) q^{17} +(9.64004 - 10.8814i) q^{18} -4.57866i q^{19} +(7.50950 + 8.47647i) q^{20} +(2.61637 - 4.98507i) q^{21} +4.78523 q^{22} +1.39775 q^{23} +(4.46345 - 8.50439i) q^{24} +(6.16322 + 1.51910i) q^{25} +(-7.85477 + 2.82932i) q^{26} +(-9.69515 + 2.38964i) q^{27} +(1.48699 - 6.03296i) q^{28} +(-0.913692 + 2.40921i) q^{29} +(-2.86389 - 23.5863i) q^{30} +(2.22313 + 9.01957i) q^{31} +(-1.18902 + 4.82404i) q^{32} +(-5.18051 - 3.57585i) q^{33} +(10.1768 - 1.23569i) q^{34} +(-2.20786 - 5.82165i) q^{35} +(-18.6880 + 9.80822i) q^{36} +(-2.00301 - 8.12654i) q^{37} +(-3.75955 + 9.91313i) q^{38} +(10.6179 + 2.80658i) q^{39} +(-3.76655 - 9.93157i) q^{40} +(0.588837 - 0.406445i) q^{41} +(-9.75787 + 8.64472i) q^{42} +(-6.47343 - 1.59556i) q^{43} +(-6.49580 - 2.46353i) q^{44} +(-9.82834 + 18.7263i) q^{45} +(-3.02623 - 1.14770i) q^{46} +(-7.62554 - 8.60746i) q^{47} +(-1.31735 + 1.16707i) q^{48} +(2.03581 - 2.94939i) q^{49} +(-12.0965 - 8.34959i) q^{50} +(-11.9408 - 6.26703i) q^{51} +(12.1192 + 0.203076i) q^{52} +(7.19974 - 3.77871i) q^{53} +(22.9528 + 2.78698i) q^{54} +(-6.75923 + 1.66600i) q^{55} +(-3.31067 + 4.79634i) q^{56} +(11.4779 - 7.92260i) q^{57} +(3.95641 - 4.46587i) q^{58} +(1.45491 + 0.176659i) q^{59} +(-8.25504 + 33.4920i) q^{60} +(6.10284 + 3.20302i) q^{61} +(2.59277 - 21.3534i) q^{62} +(11.5193 - 1.39870i) q^{63} +(7.19178 - 10.4191i) q^{64} +(10.1100 - 6.73115i) q^{65} +(8.28003 + 11.9957i) q^{66} +(-7.61458 - 8.59508i) q^{67} +(-14.4508 - 3.56181i) q^{68} +(2.41857 + 3.50390i) q^{69} +14.4172i q^{70} +(-8.04194 + 5.55095i) q^{71} +(19.6517 - 2.38615i) q^{72} +(0.244764 - 0.0928266i) q^{73} +(-2.33606 + 19.2392i) q^{74} +(6.85631 + 18.0786i) q^{75} +(10.2070 - 11.5213i) q^{76} +(2.85905 + 2.53290i) q^{77} +(-20.6839 - 14.7948i) q^{78} +(1.19014 - 1.05437i) q^{79} +1.94636i q^{80} +(-8.66837 - 7.67951i) q^{81} +(-1.60861 + 0.396486i) q^{82} +(3.10268 + 2.14162i) q^{83} +(17.6965 - 6.71139i) q^{84} +(-13.9447 + 5.28853i) q^{85} +(12.7053 + 8.76984i) q^{86} +(-7.62043 + 1.87827i) q^{87} +(4.87746 + 4.32105i) q^{88} +6.14905i q^{89} +(36.6553 - 32.4738i) q^{90} +(-6.19063 - 2.46721i) q^{91} +(3.51715 + 3.11592i) q^{92} +(-18.7637 + 21.1798i) q^{93} +(9.44223 + 24.8971i) q^{94} +(1.85914 - 15.3114i) q^{95} +(-14.1504 + 5.36652i) q^{96} +(7.57566 - 0.919851i) q^{97} +(-6.82942 + 4.71401i) q^{98} -12.9743i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9}+O(q^{10}) $ 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9} - 9 q^{10} - 13 q^{11} - 9 q^{12} + 52 q^{13} - 15 q^{14} + 39 q^{15} - 31 q^{16} - 11 q^{17} + 26 q^{18} - 13 q^{20} - 13 q^{21} - 6 q^{22} - 102 q^{23} - 91 q^{24} + 3 q^{25} - 13 q^{26} - 19 q^{27} - 13 q^{28} - 17 q^{29} + 23 q^{30} + 39 q^{31} - 13 q^{33} + 52 q^{34} - 21 q^{35} + 11 q^{36} - 13 q^{37} - 40 q^{38} - 65 q^{39} + 53 q^{40} - 13 q^{41} + 101 q^{42} - 3 q^{43} - 39 q^{44} - 78 q^{45} - 39 q^{46} - 39 q^{47} + 8 q^{48} + 85 q^{49} - 13 q^{50} + 62 q^{51} - 78 q^{52} + 18 q^{53} + 65 q^{54} - 103 q^{55} + 3 q^{56} + 65 q^{57} + 39 q^{58} + 91 q^{59} - 117 q^{60} - 23 q^{61} - 64 q^{62} - 78 q^{63} + 15 q^{64} - 13 q^{65} + 134 q^{66} - 65 q^{67} + 40 q^{68} - 40 q^{69} + 26 q^{71} + 156 q^{72} - 13 q^{73} - 53 q^{74} + 35 q^{75} + 221 q^{76} + 3 q^{77} - 143 q^{78} - 23 q^{79} - 43 q^{81} - 129 q^{82} + 117 q^{83} + 234 q^{84} + 26 q^{85} - 91 q^{86} + 79 q^{87} + 95 q^{88} + 17 q^{90} + 39 q^{91} - 89 q^{92} + 52 q^{93} - 61 q^{94} + 122 q^{95} - 182 q^{96} - 91 q^{97} - 13 q^{98}+O(q^{100}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9 - 9 * q^10 - 13 * q^11 - 9 * q^12 + 52 * q^13 - 15 * q^14 + 39 * q^15 - 31 * q^16 - 11 * q^17 + 26 * q^18 - 13 * q^20 - 13 * q^21 - 6 * q^22 - 102 * q^23 - 91 * q^24 + 3 * q^25 - 13 * q^26 - 19 * q^27 - 13 * q^28 - 17 * q^29 + 23 * q^30 + 39 * q^31 - 13 * q^33 + 52 * q^34 - 21 * q^35 + 11 * q^36 - 13 * q^37 - 40 * q^38 - 65 * q^39 + 53 * q^40 - 13 * q^41 + 101 * q^42 - 3 * q^43 - 39 * q^44 - 78 * q^45 - 39 * q^46 - 39 * q^47 + 8 * q^48 + 85 * q^49 - 13 * q^50 + 62 * q^51 - 78 * q^52 + 18 * q^53 + 65 * q^54 - 103 * q^55 + 3 * q^56 + 65 * q^57 + 39 * q^58 + 91 * q^59 - 117 * q^60 - 23 * q^61 - 64 * q^62 - 78 * q^63 + 15 * q^64 - 13 * q^65 + 134 * q^66 - 65 * q^67 + 40 * q^68 - 40 * q^69 + 26 * q^71 + 156 * q^72 - 13 * q^73 - 53 * q^74 + 35 * q^75 + 221 * q^76 + 3 * q^77 - 143 * q^78 - 23 * q^79 - 43 * q^81 - 129 * q^82 + 117 * q^83 + 234 * q^84 + 26 * q^85 - 91 * q^86 + 79 * q^87 + 95 * q^88 + 17 * q^90 + 39 * q^91 - 89 * q^92 + 52 * q^93 - 61 * q^94 + 122 * q^95 - 182 * q^96 - 91 * q^97 - 13 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{26}\right)$

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 $

$2$	−2.16507	−	0.821103i	−1.53094	−	0.580607i	−0.561830	−	0.827253i	$-0.689902\pi$
$2$	−2.16507	−	0.821103i	−1.53094	−	0.580607i	−0.969106	+	0.246646i	$0.920672\pi$
$3$	1.73033	+	2.50681i	0.999006	+	1.44731i	0.891454	+	0.453111i	$0.149686\pi$
$3$	1.73033	+	2.50681i	0.999006	+	1.44731i	0.107552	+	0.994199i	$0.465699\pi$
$4$	2.51629	+	2.22924i	1.25815	+	1.11462i
$5$	3.34407	+	0.406044i	1.49551	+	0.181588i	0.827038	−	0.562146i	$-0.190024\pi$
$5$	3.34407	+	0.406044i	1.49551	+	0.181588i	0.668476	+	0.743734i	$0.266947\pi$
$6$	−1.68793	−	6.84821i	−0.689095	−	2.79577i
$7$	−0.858950	−	1.63659i	−0.324653	−	0.618574i	0.667357	−	0.744738i	$-0.267426\pi$
$7$	−0.858950	−	1.63659i	−0.324653	−	0.618574i	−0.992009	+	0.126164i	$0.959733\pi$
$8$	−1.46534	−	2.79198i	−0.518077	−	0.987114i
$9$	−2.22627	+	5.87018i	−0.742089	+	1.95673i
$10$	−6.90674	−	3.62494i	−2.18410	−	1.14631i
$11$	−1.93228	+	0.732816i	−0.582604	+	0.220952i	−0.628258	−	0.778005i	$-0.716232\pi$
$11$	−1.93228	+	0.732816i	−0.582604	+	0.220952i	0.0456547	+	0.998957i	$0.485463\pi$
$12$	−1.23428	+	10.1652i	−0.356306	+	2.93444i
$13$	2.73847	−	2.34537i	0.759516	−	0.650489i
$13$	2.73847	−	2.34537i	0.759516	−	0.650489i
$14$	0.515876	+	4.24862i	0.137874	+	1.13549i
$15$	4.76847	+	9.08555i	1.23121	+	2.34588i
$16$	0.0696450	+	0.573578i	0.0174112	+	0.143395i
$17$	−3.92016	+	2.05746i	−0.950778	+	0.499007i	−0.867455	−	0.497516i	$-0.834246\pi$
$17$	−3.92016	+	2.05746i	−0.950778	+	0.499007i	−0.0833228	+	0.996523i	$0.526553\pi$
$18$	9.64004	−	10.8814i	2.27218	−	2.56476i
$19$		−	4.57866i		−	1.05042i	−0.850973	−	0.525209i	$-0.823987\pi$
$19$		−	4.57866i		−	1.05042i	0.850973	−	0.525209i	$-0.176013\pi$
$20$	7.50950	+	8.47647i	1.67917	+	1.89540i
$21$	2.61637	−	4.98507i	0.570938	−	1.08783i
$22$	4.78523			1.02021
$23$	1.39775			0.291451			0.145726	−	0.989325i	$-0.453448\pi$
$23$	1.39775			0.291451			0.145726	+	0.989325i	$0.453448\pi$
$24$	4.46345	−	8.50439i	0.911097	−	1.73595i
$25$	6.16322	+	1.51910i	1.23264	+	0.303820i
$26$	−7.85477	+	2.82932i	−1.54045	+	0.554876i
$27$	−9.69515	+	2.38964i	−1.86583	+	0.459886i
$28$	1.48699	−	6.03296i	0.281015	−	1.14012i
$29$	−0.913692	+	2.40921i	−0.169668	+	0.447379i	−0.992699	−	0.120618i	$-0.961512\pi$
$29$	−0.913692	+	2.40921i	−0.169668	+	0.447379i	0.823031	+	0.567997i	$0.192282\pi$
$30$	−2.86389	−	23.5863i	−0.522872	−	4.30624i
$31$	2.22313	+	9.01957i	0.399285	+	1.61996i	0.735047	+	0.678016i	$0.237160\pi$
$31$	2.22313	+	9.01957i	0.399285	+	1.61996i	−0.335762	+	0.941947i	$0.608994\pi$
$32$	−1.18902	+	4.82404i	−0.210191	+	0.852777i
$33$	−5.18051	−	3.57585i	−0.901811	−	0.622475i
$34$	10.1768	−	1.23569i	1.74531	−	0.211918i
$35$	−2.20786	−	5.82165i	−0.373197	−	0.984039i
$36$	−18.6880	+	9.80822i	−3.11467	+	1.63470i
$37$	−2.00301	−	8.12654i	−0.329293	−	1.33600i	−0.869279	−	0.494321i	$-0.835417\pi$
$37$	−2.00301	−	8.12654i	−0.329293	−	1.33600i	0.539986	−	0.841674i	$-0.318429\pi$
$38$	−3.75955	+	9.91313i	−0.609880	+	1.60812i
$39$	10.6179	+	2.80658i	1.70022	+	0.449413i
$40$	−3.76655	−	9.93157i	−0.595543	−	1.57032i
$41$	0.588837	−	0.406445i	0.0919609	−	0.0634760i	−0.521197	−	0.853436i	$-0.674514\pi$
$41$	0.588837	−	0.406445i	0.0919609	−	0.0634760i	0.613158	+	0.789960i	$0.289899\pi$
$42$	−9.75787	+	8.64472i	−1.50567	+	1.33391i
$43$	−6.47343	−	1.59556i	−0.987189	−	0.243320i	−0.287510	−	0.957778i	$-0.592827\pi$
$43$	−6.47343	−	1.59556i	−0.987189	−	0.243320i	−0.699679	+	0.714458i	$0.746674\pi$
$44$	−6.49580	−	2.46353i	−0.979279	−	0.371392i
$45$	−9.82834	+	18.7263i	−1.46512	+	2.79156i
$46$	−3.02623	−	1.14770i	−0.446193	−	0.169219i
$47$	−7.62554	−	8.60746i	−1.11230	−	1.25553i	−0.963803	−	0.266614i	$-0.914095\pi$
$47$	−7.62554	−	8.60746i	−1.11230	−	1.25553i	−0.148497	−	0.988913i	$-0.547443\pi$
$48$	−1.31735	+	1.16707i	−0.190142	+	0.168451i
$49$	2.03581	−	2.94939i	0.290830	−	0.421341i
$50$	−12.0965	−	8.34959i	−1.71070	−	1.18081i
$51$	−11.9408	−	6.26703i	−1.67205	−	0.877560i
$52$	12.1192	+	0.203076i	1.68063	+	0.0281616i
$53$	7.19974	−	3.77871i	0.988960	−	0.519046i	0.108973	−	0.994045i	$-0.465244\pi$
$53$	7.19974	−	3.77871i	0.988960	−	0.519046i	0.879987	+	0.474999i	$0.157551\pi$
$54$	22.9528	+	2.78698i	3.12348	+	0.379259i
$55$	−6.75923	+	1.66600i	−0.911414	+	0.224643i
$56$	−3.31067	+	4.79634i	−0.442408	+	0.640938i
$57$	11.4779	−	7.92260i	1.52028	−	1.04937i
$58$	3.95641	−	4.46587i	0.519503	−	0.586397i
$59$	1.45491	+	0.176659i	0.189414	+	0.0229990i	0.214694	−	0.976681i	$-0.431125\pi$
$59$	1.45491	+	0.176659i	0.189414	+	0.0229990i	−0.0252800	+	0.999680i	$0.508048\pi$
$60$	−8.25504	+	33.4920i	−1.06572	+	4.32380i
$61$	6.10284	+	3.20302i	0.781388	+	0.410104i	0.807733	−	0.589549i	$-0.200694\pi$
$61$	6.10284	+	3.20302i	0.781388	+	0.410104i	−0.0263445	+	0.999653i	$0.508387\pi$
$62$	2.59277	−	21.3534i	0.329283	−	2.71189i
$63$	11.5193	−	1.39870i	1.45130	−	0.176220i
$64$	7.19178	−	10.4191i	0.898972	−	1.30239i
$65$	10.1100	−	6.73115i	1.25399	−	0.834896i
$66$	8.28003	+	11.9957i	1.01920	+	1.47657i
$67$	−7.61458	−	8.59508i	−0.930269	−	1.05006i	−0.998626	−	0.0523958i	$-0.983314\pi$
$67$	−7.61458	−	8.59508i	−0.930269	−	1.05006i	0.0683574	−	0.997661i	$-0.478224\pi$
$68$	−14.4508	−	3.56181i	−1.75242	−	0.431933i
$69$	2.41857	+	3.50390i	0.291161	+	0.421820i
$70$			14.4172i			1.72318i
$71$	−8.04194	+	5.55095i	−0.954403	+	0.658777i	−0.940020	−	0.341120i	$-0.889194\pi$
$71$	−8.04194	+	5.55095i	−0.954403	+	0.658777i	−0.0143832	+	0.999897i	$0.504578\pi$
$72$	19.6517	−	2.38615i	2.31597	−	0.281210i
$73$	0.244764	−	0.0928266i	0.0286474	−	0.0108645i	−0.340240	−	0.940339i	$-0.610508\pi$
$73$	0.244764	−	0.0928266i	0.0286474	−	0.0108645i	0.368887	+	0.929474i	$0.379739\pi$
$74$	−2.33606	+	19.2392i	−0.271562	+	2.23651i
$75$	6.85631	+	18.0786i	0.791698	+	2.08754i
$76$	10.2070	−	11.5213i	1.17082	−	1.32158i
$77$	2.85905	+	2.53290i	0.325819	+	0.288651i
$78$	−20.6839	−	14.7948i	−2.34199	−	1.67518i
$79$	1.19014	−	1.05437i	0.133901	−	0.118626i	−0.593514	−	0.804824i	$-0.702260\pi$
$79$	1.19014	−	1.05437i	0.133901	−	0.118626i	0.727415	+	0.686197i	$0.240721\pi$
$80$			1.94636i			0.217610i
$81$	−8.66837	−	7.67951i	−0.963152	−	0.853278i
$82$	−1.60861	+	0.396486i	−0.177641	+	0.0437845i
$83$	3.10268	+	2.14162i	0.340563	+	0.235074i	0.726054	−	0.687638i	$-0.241352\pi$
$83$	3.10268	+	2.14162i	0.340563	+	0.235074i	−0.385491	+	0.922712i	$0.625968\pi$
$84$	17.6965	−	6.71139i	1.93085	−	0.732273i
$85$	−13.9447	+	5.28853i	−1.51251	+	0.573621i
$86$	12.7053	+	8.76984i	1.37005	+	0.945676i
$87$	−7.62043	+	1.87827i	−0.816996	+	0.201371i
$88$	4.87746	+	4.32105i	0.519939	+	0.460626i
$89$			6.14905i			0.651798i	0.945405	+	0.325899i	$0.105667\pi$
$89$			6.14905i			0.651798i	−0.945405	+	0.325899i	$0.894333\pi$
$90$	36.6553	−	32.4738i	3.86381	−	3.42303i
$91$	−6.19063	−	2.46721i	−0.648954	−	0.258634i
$92$	3.51715	+	3.11592i	0.366688	+	0.324858i
$93$	−18.7637	+	21.1798i	−1.94570	+	2.19624i
$94$	9.44223	+	24.8971i	0.973891	+	2.56794i
$95$	1.85914	−	15.3114i	0.190743	−	1.57091i
$96$	−14.1504	+	5.36652i	−1.44421	+	0.547718i
$97$	7.57566	−	0.919851i	0.769191	−	0.0933968i	0.273473	−	0.961880i	$-0.411828\pi$
$97$	7.57566	−	0.919851i	0.769191	−	0.0933968i	0.495719	+	0.868483i	$0.334905\pi$
$98$	−6.82942	+	4.71401i	−0.689876	+	0.476187i
$99$		−	12.9743i		−	1.30396i
$100$	12.1220	+	17.5618i	1.21220	+	1.75618i
$101$	9.42729	+	2.32362i	0.938051	+	0.231209i	0.678567	−	0.734539i	$-0.262601\pi$
$101$	9.42729	+	2.32362i	0.938051	+	0.231209i	0.259484	+	0.965747i	$0.416448\pi$
$102$	20.7068	+	23.3732i	2.05028	+	2.31429i
$103$	−3.12891	−	4.53301i	−0.308300	−	0.446650i	0.637954	−	0.770075i	$-0.279781\pi$
$103$	−3.12891	−	4.53301i	−0.308300	−	0.446650i	−0.946254	+	0.323425i	$0.895166\pi$
$104$	−10.5610	−	4.20898i	−1.03559	−	0.412725i
$105$	10.7735	−	15.6081i	1.05138	−	1.52319i
$106$	−18.6906	+	2.26945i	−1.81540	+	0.220429i
$107$	0.516489	−	4.25367i	0.0499309	−	0.411218i	−0.946217	−	0.323532i	$-0.895130\pi$
$107$	0.516489	−	4.25367i	0.0499309	−	0.411218i	0.996148	−	0.0876860i	$-0.0279472\pi$
$108$	−29.7229	−	15.5998i	−2.86009	−	1.50109i
$109$	1.93414	−	7.84710i	0.185257	−	0.751616i	−0.802635	−	0.596471i	$-0.796569\pi$
$109$	1.93414	−	7.84710i	0.185257	−	0.751616i	0.987892	−	0.155146i	$-0.0495846\pi$
$110$	16.0022	+	1.94301i	1.52575	+	0.185259i
$111$	16.9059	−	19.0828i	1.60463	−	1.81126i
$112$	0.878892	−	0.606655i	0.0830475	−	0.0573235i
$113$	7.09717	−	10.2820i	0.667646	−	0.967252i	−0.332066	−	0.943256i	$-0.607746\pi$
$113$	7.09717	−	10.2820i	0.667646	−	0.967252i	0.999712	−	0.0239957i	$-0.00763879\pi$
$114$	−31.3556	+	7.72847i	−2.93672	+	0.723838i
$115$	4.67418	+	0.567548i	0.435869	+	0.0529241i
$116$	−7.66983	+	4.02544i	−0.712126	+	0.373752i
$117$	7.67119	+	21.2968i	0.709201	+	1.96889i
$118$	−3.00494	−	1.57711i	−0.276627	−	0.145185i
$119$	6.73444	+	4.64845i	0.617345	+	0.426122i
$120$	18.3792	−	26.6269i	1.67779	−	2.43069i
$121$	−5.03694	+	4.46234i	−0.457904	+	0.405667i
$122$	−10.5831	−	11.9458i	−0.958146	−	1.08152i
$123$	2.03776	+	0.772822i	0.183739	+	0.0696830i
$124$	−14.5128	+	27.6518i	−1.30329	+	2.48320i
$125$	4.24481	+	1.60984i	0.379667	+	0.143989i
$126$	−26.0887	−	6.43028i	−2.32416	−	0.572855i
$127$	−8.48458	+	7.51668i	−0.752884	+	0.666997i	−0.949600	−	0.313463i	$-0.898511\pi$
$127$	−8.48458	+	7.51668i	−0.752884	+	0.666997i	0.196716	+	0.980461i	$0.436972\pi$
$128$	−15.9480	+	11.0081i	−1.40962	+	0.972989i
$129$	−7.20140	−	18.9885i	−0.634048	−	1.67185i
$130$	−27.4157	+	6.27208i	−2.40452	+	0.550097i
$131$	−2.16429	+	5.70676i	−0.189095	+	0.498602i	−0.995716	−	0.0924671i	$-0.970525\pi$
$131$	−2.16429	+	5.70676i	−0.189095	+	0.498602i	0.806621	+	0.591069i	$0.201294\pi$
$132$	−5.06426	−	20.5465i	−0.440787	−	1.78834i
$133$	−7.49341	+	3.93284i	−0.649761	+	0.341021i
$134$	9.42865	+	24.8613i	0.814511	+	2.14769i
$135$	−33.3916	+	4.05447i	−2.87389	+	0.348953i
$136$	11.4888	+	7.93011i	0.985152	+	0.680002i
$137$	−0.243891	+	0.989504i	−0.0208370	+	0.0845390i	−0.980440	−	0.196819i	$-0.936939\pi$
$137$	−0.243891	+	0.989504i	−0.0208370	+	0.0845390i	0.959603	+	0.281358i	$0.0907849\pi$
$138$	−2.35931	−	9.57208i	−0.200838	−	0.814830i
$139$	1.18734	+	9.77861i	0.100709	+	0.829411i	0.952291	+	0.305190i	$0.0987201\pi$
$139$	1.18734	+	9.77861i	0.100709	+	0.829411i	−0.851583	+	0.524220i	$0.824357\pi$
$140$	7.42224	−	19.5708i	0.627294	−	1.65404i
$141$	8.38261	−	34.0096i	0.705943	−	2.86412i
$142$	21.9693	−	5.41494i	1.84362	−	0.454411i
$143$	−3.57276	+	6.53870i	−0.298770	+	0.546794i
$144$	−3.52206	−	0.868109i	−0.293505	−	0.0723424i
$145$	−4.03369	+	7.68556i	−0.334980	+	0.638251i
$146$	−0.606151			−0.0501654
$147$	10.9162			0.900352
$148$	13.0759	−	24.9140i	1.07483	−	2.04792i
$149$	−4.50145	−	5.08109i	−0.368773	−	0.416259i	0.534606	−	0.845101i	$-0.320460\pi$
$149$	−4.50145	−	5.08109i	−0.368773	−	0.416259i	−0.903379	+	0.428843i	$0.858922\pi$
$150$		−	44.7712i		−	3.65555i
$151$	−0.747919	+	0.844227i	−0.0608648	+	0.0687022i	−0.778155	−	0.628073i	$-0.783844\pi$
$151$	−0.747919	+	0.844227i	−0.0608648	+	0.0687022i	0.717290	+	0.696775i	$0.245382\pi$
$152$	−12.7835	+	6.70932i	−1.03688	+	0.544197i
$153$	−3.35033	−	27.5925i	−0.270858	−	2.23072i
$154$	−4.11027	−	7.83147i	−0.331215	−	0.631078i
$155$	3.77195	+	31.0648i	0.302970	+	2.49518i
$156$	20.4611	+	30.7320i	1.63820	+	2.46053i
$157$	−1.62352	+	13.3709i	−0.129571	+	1.06712i	0.772345	+	0.635204i	$0.219084\pi$
$157$	−1.62352	+	13.3709i	−0.129571	+	1.06712i	−0.901916	+	0.431912i	$0.857839\pi$
$158$	−3.44248	+	1.30556i	−0.273869	+	0.103865i
$159$	21.9304	+	11.5100i	1.73920	+	0.912801i
$160$	−5.93493	+	15.6491i	−0.469197	+	1.23717i
$161$	−1.20060	−	2.28755i	−0.0946204	−	0.180284i
$162$	12.4620	+	23.7443i	0.979104	+	1.86553i
$163$	3.11100	+	12.6218i	0.243672	+	0.988617i	0.957532	+	0.288328i	$0.0930993\pi$
$163$	3.11100	+	12.6218i	0.243672	+	0.988617i	−0.713860	+	0.700289i	$0.753055\pi$
$164$	2.38775	+	0.289925i	0.186452	+	0.0226394i
$165$	−15.8720	−	14.0614i	−1.23564	−	1.09468i
$166$	−4.95902	−	7.18438i	−0.384894	−	0.557616i
$167$	−13.8833	−	5.26524i	−1.07432	−	0.407437i	−0.246914	−	0.969037i	$-0.579417\pi$
$167$	−13.8833	−	5.26524i	−1.07432	−	0.407437i	−0.827409	+	0.561600i	$0.810186\pi$
$168$	−17.7521			−1.36960
$169$	1.99847	−	12.8455i	0.153728	−	0.988113i
$170$	34.5337			2.64861
$171$	26.8776	+	10.1933i	2.05538	+	0.779503i
$172$	−12.7322	−	18.4457i	−0.970819	−	1.40647i
$173$	−0.277251	−	0.245623i	−0.0210790	−	0.0186744i	0.652517	−	0.757774i	$-0.273713\pi$
$173$	−0.277251	−	0.245623i	−0.0210790	−	0.0186744i	−0.673596	+	0.739099i	$0.735251\pi$
$174$	18.0410	+	2.19057i	1.36769	+	0.166067i
$175$	−2.80776	−	11.3915i	−0.212246	−	0.861118i
$176$	−0.554901	−	1.05727i	−0.0418272	−	0.0796951i
$177$	2.07463	+	3.95288i	0.155939	+	0.297117i
$178$	5.04900	−	13.3131i	0.378438	−	0.997860i
$179$	−7.99509	−	4.19615i	−0.597581	−	0.313635i	0.138675	−	0.990338i	$-0.455716\pi$
$179$	−7.99509	−	4.19615i	−0.597581	−	0.313635i	−0.736256	+	0.676703i	$0.763408\pi$
$180$	−66.4766	+	25.2112i	−4.95487	+	1.87913i
$181$	−0.683663	+	5.63047i	−0.0508163	+	0.418510i	0.944996	+	0.327083i	$0.106066\pi$
$181$	−0.683663	+	5.63047i	−0.0508163	+	0.418510i	−0.995812	+	0.0914265i	$0.970857\pi$
$182$	11.3773	+	10.4248i	0.843342	+	0.772739i
$183$	2.53055	+	20.8410i	0.187064	+	1.54061i
$184$	−2.04818	−	3.90249i	−0.150994	−	0.287695i
$185$	−3.39848	−	27.9890i	−0.249862	−	2.05779i
$186$	58.0154	−	30.4488i	4.25390	−	2.23262i
$187$	6.06709	−	6.84833i	0.443670	−	0.500800i
$188$		−	38.6581i		−	2.81943i
$189$	12.2385	+	13.8144i	0.890221	+	1.00485i
$190$	−16.5974	+	31.6236i	−1.20410	+	2.29422i
$191$	13.3904			0.968892			0.484446	−	0.874821i	$-0.339021\pi$
$191$	13.3904			0.968892			0.484446	+	0.874821i	$0.339021\pi$
$192$	38.5629			2.78304
$193$	−9.10029	+	17.3392i	−0.655053	+	1.24810i	0.300640	+	0.953738i	$0.402800\pi$
$193$	−9.10029	+	17.3392i	−0.655053	+	1.24810i	−0.955694	+	0.294362i	$0.904893\pi$
$194$	−17.1571	−	4.22885i	−1.23181	−	0.303614i
$195$	34.3673	+	13.6967i	2.46109	+	0.980843i
$196$	11.6976	−	2.88320i	0.835543	−	0.205943i
$197$	0.959595	−	3.89323i	0.0683683	−	0.277381i	−0.926801	−	0.375552i	$-0.877453\pi$
$197$	0.959595	−	3.89323i	0.0683683	−	0.277381i	0.995170	+	0.0981711i	$0.0312992\pi$
$198$	−10.6532	+	28.0902i	−0.757090	+	1.99628i
$199$	2.03290	+	16.7424i	0.144108	+	1.18684i	0.867871	+	0.496789i	$0.165488\pi$
$199$	2.03290	+	16.7424i	0.144108	+	1.18684i	−0.723763	+	0.690049i	$0.757589\pi$
$200$	−4.78995	−	19.4336i	−0.338701	−	1.37416i
$201$	8.37055	−	33.9607i	0.590413	−	2.39540i
$202$	−18.5028	−	12.7716i	−1.30185	−	0.898605i
$203$	4.72771	−	0.574048i	0.331820	−	0.0402903i
$204$	−16.0759	−	42.3887i	−1.12554	−	2.96780i
$205$	2.13415	−	1.12009i	0.149055	−	0.0782302i
$206$	3.05224	+	12.3834i	0.212660	+	0.862794i
$207$	−3.11177	+	8.20505i	−0.216283	+	0.570290i
$208$	1.53597	+	1.40738i	0.106501	+	0.0975846i
$209$	3.35532	+	8.84725i	0.232092	+	0.611977i
$210$	−36.1411	+	24.9464i	−2.49398	+	1.72147i
$211$	5.00731	−	4.43609i	0.344717	−	0.305393i	−0.472944	−	0.881093i	$-0.656809\pi$
$211$	5.00731	−	4.43609i	0.344717	−	0.305393i	0.817661	+	0.575700i	$0.195270\pi$
$212$	26.5403	+	6.54160i	1.82280	+	0.449279i
$213$	−27.8304	−	10.5547i	−1.90691	−	0.723195i
$214$	−4.61093	+	8.78540i	−0.315197	+	0.600558i
$215$	−20.9997	−	7.96415i	−1.43217	−	0.543150i
$216$	20.8785	+	23.5670i	1.42061	+	1.60353i
$217$	12.8518	−	11.3857i	0.872438	−	0.772913i
$218$	−10.6308	+	15.4014i	−0.720010	+	1.04311i
$219$	0.656221	+	0.452957i	0.0443433	+	0.0306080i
$220$	−20.7221	−	10.8758i	−1.39709	−	0.733247i
$221$	−5.90974	+	14.8285i	−0.397532	+	0.997474i
$222$	−52.2713	+	27.4341i	−3.50822	+	1.84126i
$223$	16.2096	+	1.96820i	1.08548	+	0.131801i	0.643665	−	0.765307i	$-0.277413\pi$
$223$	16.2096	+	1.96820i	1.08548	+	0.131801i	0.441811	+	0.897108i	$0.354336\pi$
$224$	8.91629	−	2.19767i	0.595745	−	0.146838i
$225$	−22.6384	+	32.7973i	−1.50922	+	2.18649i
$226$	−23.8085	+	16.4338i	−1.58372	+	1.09316i
$227$	−8.25925	+	9.32277i	−0.548186	+	0.618774i	−0.955671	−	0.294438i	$-0.904867\pi$
$227$	−8.25925	+	9.32277i	−0.548186	+	0.618774i	0.407485	+	0.913212i	$0.366406\pi$
$228$	46.5431	+	5.65135i	3.08239	+	0.374270i
$229$	−3.55544	+	14.4250i	−0.234950	+	0.953231i	0.728436	+	0.685114i	$0.240248\pi$
$229$	−3.55544	+	14.4250i	−0.234950	+	0.953231i	−0.963386	+	0.268117i	$0.913599\pi$
$230$	−9.65390	−	5.06676i	−0.636559	−	0.334092i
$231$	−1.40241	+	11.5499i	−0.0922716	+	0.759925i
$232$	8.06533	−	0.979309i	0.529515	−	0.0642948i
$233$	−0.359362	+	0.520626i	−0.0235426	+	0.0341073i	−0.834578	−	0.550889i	$-0.814289\pi$
$233$	−0.359362	+	0.520626i	−0.0235426	+	0.0341073i	0.811036	+	0.584996i	$0.198904\pi$
$234$	0.878174	−	52.4078i	0.0574080	−	3.42600i
$235$	−22.0054	−	31.8803i	−1.43547	−	2.07964i
$236$	3.26718	+	3.68788i	0.212675	+	0.240061i
$237$	4.70245	+	1.15905i	0.305457	+	0.0752884i
$238$	−10.7637	−	15.5939i	−0.697705	−	1.01080i
$239$			0.277805i			0.0179697i	0.999960	+	0.00898487i	$0.00286001\pi$
$239$			0.277805i			0.0179697i	−0.999960	+	0.00898487i	$0.997140\pi$
$240$	−4.87917	+	3.36785i	−0.314949	+	0.217394i
$241$	13.0651	−	1.58639i	0.841599	−	0.102189i	0.311628	−	0.950204i	$-0.399126\pi$
$241$	13.0651	−	1.58639i	0.841599	−	0.102189i	0.529971	+	0.848016i	$0.322203\pi$
$242$	14.5694	−	5.52543i	0.936554	−	0.355188i
$243$	0.641179	−	5.28058i	0.0411316	−	0.338749i
$244$	8.21624	+	21.6644i	0.525991	+	1.38692i
$245$	8.00548	−	9.03632i	0.511451	−	0.577309i
$246$	−3.77733	−	3.34643i	−0.240834	−	0.213360i
$247$	−10.7387	−	12.5385i	−0.683285	−	0.797809i
$248$	21.9248	−	19.4237i	1.39223	−	1.23341i
$249$			11.4835i			0.727740i
$250$	−7.86846	−	6.97085i	−0.497645	−	0.440875i
$251$	−3.79803	+	0.936131i	−0.239730	+	0.0590881i	−0.357350	−	0.933971i	$-0.616320\pi$
$251$	−3.79803	+	0.936131i	−0.239730	+	0.0590881i	0.117620	+	0.993059i	$0.462473\pi$
$252$	32.1041	+	22.1599i	2.02237	+	1.39594i
$253$	−2.70084	+	1.02429i	−0.169800	+	0.0643968i
$254$	24.5417	−	9.30742i	1.53988	−	0.584000i
$255$	−37.3863	−	25.8059i	−2.34122	−	1.61603i
$256$	18.9828	−	4.67884i	1.18643	−	0.292428i
$257$	−6.01646	−	5.33012i	−0.375296	−	0.332484i	0.454298	−	0.890850i	$-0.349890\pi$
$257$	−6.01646	−	5.33012i	−0.375296	−	0.332484i	−0.829595	+	0.558366i	$0.811428\pi$
$258$			47.0246i			2.92762i
$259$	−11.5793	+	10.2584i	−0.719506	+	0.637426i
$260$	40.4450	+	5.60003i	2.50829	+	0.347299i
$261$	−12.1084	−	10.7271i	−0.749489	−	0.663990i
$262$	9.37167	−	10.5784i	0.578984	−	0.653538i
$263$	−0.542947	−	1.43163i	−0.0334796	−	0.0882784i	0.917234	−	0.398349i	$-0.130417\pi$
$263$	−0.542947	−	1.43163i	−0.0334796	−	0.0882784i	−0.950714	+	0.310070i	$0.899647\pi$
$264$	−2.39247	+	19.7037i	−0.147246	+	1.21268i
$265$	25.6107	−	9.71287i	1.57326	−	0.596657i
$266$	19.4530	−	2.36202i	1.19274	−	0.144825i
$267$	−15.4145	+	10.6399i	−0.943354	+	0.651150i
$268$		−	38.6025i		−	2.35802i
$269$	−16.4421	−	23.8204i	−1.00249	−	1.45236i	−0.888501	−	0.458875i	$-0.848253\pi$
$269$	−16.4421	−	23.8204i	−1.00249	−	1.45236i	−0.113989	−	0.993482i	$-0.536363\pi$
$270$	75.6242	+	18.6397i	4.60234	+	1.13437i
$271$	8.66506	+	9.78083i	0.526365	+	0.594143i	0.950217	−	0.311588i	$-0.100861\pi$
$271$	8.66506	+	9.78083i	0.526365	+	0.594143i	−0.423852	+	0.905731i	$0.639322\pi$
$272$	−1.45313	−	2.10522i	−0.0881090	−	0.127648i
$273$	−4.52699	−	19.7878i	−0.273986	−	1.19761i
$274$	1.34052	−	1.94209i	0.0809841	−	0.117326i
$275$	−13.0223	+	1.58119i	−0.785273	+	0.0953494i
$276$	−1.72522	+	14.2084i	−0.103846	+	0.855247i
$277$	−3.72267	−	1.95381i	−0.223674	−	0.117393i	0.349165	−	0.937061i	$-0.386465\pi$
$277$	−3.72267	−	1.95381i	−0.223674	−	0.117393i	−0.572838	+	0.819668i	$0.694158\pi$
$278$	5.45857	−	22.1463i	0.327383	−	1.32825i
$279$	−57.8958	−	7.02982i	−3.46613	−	0.420865i
$280$	−13.0187	+	14.6950i	−0.778013	+	0.878195i
$281$	−24.1010	+	16.6357i	−1.43774	+	0.992403i	−0.442320	+	0.896857i	$0.645844\pi$
$281$	−24.1010	+	16.6357i	−1.43774	+	0.992403i	−0.995425	+	0.0955460i	$0.969540\pi$
$282$	−46.0743	+	66.7501i	−2.74368	+	3.97491i
$283$	17.5908	−	4.33573i	1.04566	−	0.257732i	0.321174	−	0.947020i	$-0.395923\pi$
$283$	17.5908	−	4.33573i	1.04566	−	0.257732i	0.724488	+	0.689288i	$0.242076\pi$
$284$	−32.6103	−	3.95961i	−1.93507	−	0.234960i
$285$	41.5997	−	21.8332i	2.46415	−	1.29329i
$286$	13.1042	−	11.2231i	0.774869	−	0.663638i
$287$	−1.17097	−	0.614570i	−0.0691199	−	0.0362769i
$288$	−25.6709	−	17.7193i	−1.51267	−	1.04412i
$289$	1.47740	−	2.14038i	0.0869057	−	0.125905i
$290$	15.0439	−	13.3277i	0.883406	−	0.782630i
$291$	15.4143	+	17.3991i	0.903601	+	1.01995i
$292$	0.822831	+	0.312058i	0.0481525	+	0.0182618i
$293$	−5.07770	+	9.67474i	−0.296642	+	0.565205i	−0.987468	−	0.157816i	$-0.949555\pi$
$293$	−5.07770	+	9.67474i	−0.296642	+	0.565205i	0.690826	+	0.723021i	$0.257247\pi$
$294$	−23.6343	−	8.96331i	−1.37838	−	0.522751i
$295$	4.79360	+	1.18152i	0.279094	+	0.0687906i
$296$	−19.7540	+	17.5005i	−1.14818	+	1.01720i
$297$	16.9825	−	11.7222i	0.985427	−	0.680191i
$298$	5.57386	+	14.6971i	0.322885	+	0.851378i
$299$	3.82770	−	3.27824i	0.221362	−	0.189586i
$300$	−23.0491	+	60.7755i	−1.33074	+	3.50887i
$301$	2.94908	+	11.9649i	0.169982	+	0.689644i
$302$	2.31249	−	1.21369i	0.133069	−	0.0698400i
$303$	10.4874	+	27.6531i	0.602488	+	1.58863i
$304$	2.62622	−	0.318881i	0.150624	−	0.0182891i
$305$	19.1078	+	13.1891i	1.09411	+	0.755207i
$306$	−15.4025	+	62.4906i	−0.880505	+	3.57235i
$307$	0.266609	+	1.08168i	0.0152162	+	0.0617346i	0.978059	−	0.208327i	$-0.0668020\pi$
$307$	0.266609	+	1.08168i	0.0152162	+	0.0617346i	−0.962843	+	0.270062i	$0.912956\pi$
$308$	1.54777	+	12.7470i	0.0881924	+	0.726330i
$309$	5.94936	−	15.6872i	0.338448	−	0.892413i
$310$	17.3408	−	70.3545i	0.984893	−	3.99587i
$311$	2.66411	−	0.656644i	0.151068	−	0.0372348i	−0.163057	−	0.986617i	$-0.552135\pi$
$311$	2.66411	−	0.656644i	0.151068	−	0.0372348i	0.314124	+	0.949382i	$0.398289\pi$
$312$	−7.72292	−	33.7575i	−0.437224	−	1.91114i
$313$	−11.1607	−	2.75086i	−0.630839	−	0.155488i	−0.0890840	−	0.996024i	$-0.528394\pi$
$313$	−11.1607	−	2.75086i	−0.630839	−	0.155488i	−0.541755	+	0.840536i	$0.682240\pi$
$314$	14.4939	−	27.6159i	0.817940	−	1.55845i
$315$	39.0894			2.20244
$316$	5.34519			0.300691
$317$	−13.7688	+	26.2343i	−0.773335	+	1.47347i	0.104512	+	0.994524i	$0.466672\pi$
$317$	−13.7688	+	26.2343i	−0.773335	+	1.47347i	−0.877846	+	0.478943i	$0.841020\pi$
$318$	−38.0301	−	42.9271i	−2.13262	−	2.40723i
$319$		−	5.32483i		−	0.298133i
$320$	28.2804	−	31.9220i	1.58092	−	1.78449i
$321$	11.5569	−	6.06551i	0.645041	−	0.338544i
$322$	0.721066	+	5.93851i	0.0401834	+	0.330940i
$323$	9.42040	+	17.9491i	0.524165	+	0.998713i
$324$	−4.69269	−	38.6478i	−0.260705	−	2.14710i
$325$	20.4407	−	10.2950i	1.13384	−	0.571066i
$326$	3.62828	−	29.8815i	0.200952	−	1.65499i
$327$	23.0179	−	8.72955i	1.27289	−	0.482745i
$328$	−1.99763	−	1.04844i	−0.110301	−	0.0578904i
$329$	−7.53694	+	19.8733i	−0.415525	+	1.09565i
$330$	22.8182	+	43.4765i	1.25610	+	2.39330i
$331$	−8.14000	−	15.5095i	−0.447415	−	0.852478i	−0.999821	−	0.0189028i	$-0.993983\pi$
$331$	−8.14000	−	15.5095i	−0.447415	−	0.852478i	0.552407	−	0.833575i	$-0.313710\pi$
$332$	3.03305	+	12.3056i	0.166460	+	0.675356i
$333$	52.1635	+	6.33380i	2.85854	+	0.347090i
$334$	25.7350	+	22.7992i	1.40816	+	1.24752i
$335$	−21.9737	−	31.8344i	−1.20055	−	1.73930i
$336$	3.04155	+	1.15351i	0.165930	+	0.0629289i
$337$	22.1846			1.20847			0.604235	−	0.796806i	$-0.293479\pi$
$337$	22.1846			1.20847			0.604235	+	0.796806i	$0.293479\pi$
$338$	−14.8743	+	26.1704i	−0.809054	+	1.42348i
$339$	38.0556			2.06690
$340$	−46.8784	−	17.7786i	−2.54234	−	0.964181i
$341$	−10.9054	−	15.7992i	−0.590560	−	0.855573i
$342$	−49.8221	−	44.1385i	−2.69407	−	2.38674i
$343$	−19.4194	−	2.35794i	−1.04855	−	0.127317i
$344$	5.03104	+	20.4117i	0.271255	+	1.10053i
$345$	6.66513	+	12.6993i	0.358838	+	0.683709i
$346$	0.398586	+	0.759443i	0.0214281	+	0.0408279i
$347$	7.45499	−	19.6572i	0.400205	−	1.05525i	−0.571821	−	0.820379i	$-0.693763\pi$
$347$	7.45499	−	19.6572i	0.400205	−	1.05525i	0.972026	−	0.234875i	$-0.0754681\pi$
$348$	−23.3624	−	12.2615i	−1.25235	−	0.657286i
$349$	11.2056	−	4.24974i	0.599824	−	0.227483i	−0.0359563	−	0.999353i	$-0.511448\pi$
$349$	11.2056	−	4.24974i	0.599824	−	0.227483i	0.635780	+	0.771870i	$0.280678\pi$
$350$	−3.27461	+	26.9689i	−0.175036	+	1.44155i
$351$	−20.9453	+	29.2827i	−1.11798	+	1.56299i
$352$	−1.23762	−	10.1927i	−0.0659653	−	0.543273i
$353$	8.25458	+	15.7278i	0.439347	+	0.837105i	0.999959	+	0.00902714i	$0.00287347\pi$
$353$	8.25458	+	15.7278i	0.439347	+	0.837105i	−0.560612	+	0.828078i	$0.689434\pi$
$354$	−1.24600	−	10.2617i	−0.0662242	−	0.545405i
$355$	−29.1468	+	15.2974i	−1.54695	+	0.811901i
$356$	−13.7077	+	15.4728i	−0.726508	+	0.820058i
$357$			24.9253i			1.31919i
$358$	13.8645	+	15.6497i	0.732759	+	0.827114i
$359$	−10.8059	+	20.5889i	−0.570313	+	1.08664i	0.414011	+	0.910272i	$0.364128\pi$
$359$	−10.8059	+	20.5889i	−0.570313	+	1.08664i	−0.984324	+	0.176369i	$0.943565\pi$
$360$	66.6855			3.51463
$361$	−1.96417			−0.103377
$362$	6.10337	−	11.6290i	0.320786	−	0.611207i
$363$	−19.9018	−	4.90536i	−1.04458	−	0.257465i
$364$	−10.0774	−	20.0086i	−0.528201	−	1.04874i
$365$	0.856199	−	0.211034i	0.0448155	−	0.0110460i
$366$	11.6337	−	47.2000i	0.608106	−	2.46718i
$367$	−5.87707	+	15.4966i	−0.306780	+	0.808913i	0.689622	+	0.724169i	$0.257777\pi$
$367$	−5.87707	+	15.4966i	−0.306780	+	0.808913i	−0.996403	+	0.0847442i	$0.972993\pi$
$368$	0.0973463	+	0.801719i	0.00507453	+	0.0417925i
$369$	1.07500	+	4.36143i	0.0559621	+	0.227047i
$370$	−15.6239	+	63.3887i	−0.812249	+	3.29542i
$371$	−12.3684	−	8.53731i	−0.642137	−	0.443235i
$372$	−94.4298	+	11.4659i	−4.89596	+	0.594477i
$373$	12.7459	+	33.6082i	0.659958	+	1.74017i	0.672339	+	0.740243i	$0.265290\pi$
$373$	12.7459	+	33.6082i	0.659958	+	1.74017i	−0.0123812	+	0.999923i	$0.503941\pi$
$374$	−18.7589	+	9.84541i	−0.969997	+	0.509094i
$375$	3.30934	+	13.4265i	0.170893	+	0.693342i
$376$	−12.8578	+	33.9032i	−0.663091	+	1.74843i
$377$	3.14837	+	8.74050i	0.162149	+	0.450159i
$378$	−15.1542	−	39.9583i	−0.779446	−	2.05523i
$379$	6.95767	−	4.80253i	0.357392	−	0.246690i	−0.375816	−	0.926694i	$-0.622638\pi$
$379$	6.95767	−	4.80253i	0.357392	−	0.246690i	0.733208	+	0.680005i	$0.238022\pi$
$380$	38.8109	−	34.3835i	1.99096	−	1.76383i
$381$	−33.5240	−	8.26293i	−1.71749	−	0.423323i
$382$	−28.9911	−	10.9949i	−1.48331	−	0.562546i
$383$	14.7831	−	28.1668i	0.755379	−	1.43926i	−0.138226	−	0.990401i	$-0.544140\pi$
$383$	14.7831	−	28.1668i	0.755379	−	1.43926i	0.893605	−	0.448854i	$-0.148168\pi$
$384$	−55.1906	−	20.9310i	−2.81643	−	1.06813i
$385$	8.53240	+	9.63109i	0.434851	+	0.490846i
$386$	33.9400	−	30.0682i	1.72750	−	1.53043i
$387$	23.7778	−	34.4481i	1.20869	−	1.75109i
$388$	21.1132	+	14.5734i	1.07186	+	0.739850i
$389$	−33.1525	−	17.3998i	−1.68090	−	0.882204i	−0.986726	−	0.162396i	$-0.948078\pi$
$389$	−33.1525	−	17.3998i	−1.68090	−	0.882204i	−0.694174	−	0.719808i	$-0.744230\pi$
$390$	−63.1612	−	57.8734i	−3.19829	−	2.93054i
$391$	−5.47940	+	2.87581i	−0.277105	+	0.145436i
$392$	−11.2178	−	1.36209i	−0.566584	−	0.0687957i
$393$	−18.0507	+	4.44910i	−0.910539	+	0.224428i
$394$	−5.27433	+	7.64119i	−0.265717	+	0.384957i
$395$	4.40803	−	3.04265i	0.221792	−	0.153092i
$396$	28.9228	−	32.6471i	1.45342	−	1.64058i
$397$	22.2104	+	2.69683i	1.11471	+	0.135350i	0.657100	−	0.753803i	$-0.271783\pi$
$397$	22.2104	+	2.69683i	1.11471	+	0.135350i	0.457609	+	0.889153i	$0.348706\pi$
$398$	9.34587	−	37.9177i	0.468466	−	1.90064i
$399$	−22.8250	−	11.9795i	−1.14268	−	0.599724i
$400$	−0.442084	+	3.64089i	−0.0221042	+	0.182044i
$401$	15.9900	−	1.94154i	0.798505	−	0.0969560i	0.288894	−	0.957361i	$-0.406713\pi$
$401$	15.9900	−	1.94154i	0.798505	−	0.0969560i	0.509611	+	0.860405i	$0.329789\pi$
$402$	−46.0080	+	66.6541i	−2.29467	+	3.32441i
$403$	27.2422	+	19.4858i	1.35703	+	0.970657i
$404$	18.5419	+	26.8626i	0.922496	+	1.33647i
$405$	−25.8694	−	29.2005i	−1.28546	−	1.45099i
$406$	−10.7072	−	2.63908i	−0.531388	−	0.130975i
$407$	9.82564	+	14.2349i	0.487039	+	0.705597i
$408$			42.5219i			2.10515i
$409$	−12.1667	+	8.39809i	−0.601606	+	0.415259i	−0.829564	−	0.558412i	$-0.811411\pi$
$409$	−12.1667	+	8.39809i	−0.601606	+	0.415259i	0.227957	+	0.973671i	$0.426795\pi$
$410$	−5.54028	+	0.672712i	−0.273615	+	0.0332229i
$411$	−2.90251	+	1.10078i	−0.143171	+	0.0542974i
$412$	2.23191	−	18.3815i	0.109959	−	0.905590i
$413$	−0.960580	−	2.53284i	−0.0472671	−	0.124633i
$414$	13.4744	−	15.2094i	0.662229	−	0.747502i
$415$	9.50597	+	8.42156i	0.466630	+	0.413398i
$416$	8.05806	+	15.9992i	0.395079	+	0.784424i
$417$	−22.4587	+	19.8966i	−1.09981	+	0.974343i
$418$		−	21.9100i		−	1.07165i
$419$	4.56830	+	4.04716i	0.223176	+	0.197717i	0.767300	−	0.641288i	$-0.221600\pi$
$419$	4.56830	+	4.04716i	0.223176	+	0.197717i	−0.544124	+	0.839005i	$0.683138\pi$
$420$	61.9034	−	15.2578i	3.02058	−	0.744505i
$421$	−29.1945	−	20.1515i	−1.42285	−	0.982123i	−0.997006	−	0.0773269i	$-0.975361\pi$
$421$	−29.1945	−	20.1515i	−1.42285	−	0.982123i	−0.425845	−	0.904796i	$-0.640023\pi$
$422$	−14.4837	+	5.49293i	−0.705053	+	0.267391i
$423$	67.5039	−	25.6008i	3.28215	−	1.24476i
$424$	−21.1002	−	14.5644i	−1.02472	−	0.707310i
$425$	−27.2863	+	6.72546i	−1.32358	+	0.326233i
$426$	51.5883	+	45.7033i	2.49946	+	2.21433i
$427$		−	12.7391i		−	0.616488i
$428$	10.7821	−	9.55211i	0.521172	−	0.461719i
$429$	−22.5734	+	2.35786i	−1.08985	+	0.113838i
$430$	38.9265	+	34.4859i	1.87720	+	1.66306i
$431$	8.46212	−	9.55176i	0.407606	−	0.460092i	−0.508480	−	0.861074i	$-0.669792\pi$
$431$	8.46212	−	9.55176i	0.407606	−	0.460092i	0.916086	+	0.400982i	$0.131331\pi$
$432$	−2.04586	−	5.39450i	−0.0984316	−	0.259543i
$433$	0.458235	−	3.77390i	0.0220214	−	0.181362i	−0.977548	−	0.210714i	$-0.932421\pi$
$433$	0.458235	−	3.77390i	0.0220214	−	0.181362i	0.999569	+	0.0293516i	$0.00934424\pi$
$434$	−37.1739	+	14.0982i	−1.78440	+	0.676735i
$435$	−26.2459	+	3.18683i	−1.25839	+	0.152797i
$436$	22.3600	−	15.4340i	1.07085	−	0.739153i
$437$		−	6.39983i		−	0.306145i
$438$	−1.04884	−	1.51951i	−0.0501155	−	0.0726049i
$439$	−18.5950	−	4.58325i	−0.887489	−	0.218746i	−0.230884	−	0.972981i	$-0.574162\pi$
$439$	−18.5950	−	4.58325i	−0.887489	−	0.218746i	−0.656605	+	0.754235i	$0.728008\pi$
$440$	14.5560	+	16.4304i	0.693931	+	0.783286i
$441$	12.7812	+	18.5167i	0.608627	+	0.881748i
$442$	24.9707	−	27.2522i	1.18774	−	1.29626i
$443$	2.91397	−	4.22162i	0.138447	−	0.200575i	−0.747627	−	0.664119i	$-0.768807\pi$
$443$	2.91397	−	4.22162i	0.138447	−	0.200575i	0.886074	+	0.463544i	$0.153422\pi$
$444$	85.0803	−	10.3306i	4.03773	−	0.490269i
$445$	−2.49678	+	20.5628i	−0.118359	+	0.974772i
$446$	−33.4789	−	17.5711i	−1.58527	−	0.832014i
$447$	4.94835	−	20.0763i	0.234049	−	0.949574i
$448$	−23.2292	−	2.82053i	−1.09748	−	0.133258i
$449$	−8.35101	+	9.42634i	−0.394108	+	0.444856i	−0.911753	−	0.410739i	$-0.865271\pi$
$449$	−8.35101	+	9.42634i	−0.394108	+	0.444856i	0.517644	+	0.855596i	$0.326809\pi$
$450$	75.9436	−	52.4201i	3.58002	−	2.47111i
$451$	−0.839947	+	1.21687i	−0.0395516	+	0.0573003i
$452$	40.7797	−	10.0513i	1.91812	−	0.472773i
$453$	−3.41047	−	0.414106i	−0.160238	−	0.0194564i
$454$	25.5368	−	13.4027i	1.19850	−	0.629022i
$455$	−19.7001	−	10.7642i	−0.923555	−	0.504633i
$456$	−38.9387	−	20.4366i	−1.82347	−	0.957033i
$457$	−22.0844	−	15.2438i	−1.03307	−	0.713074i	−0.0742900	−	0.997237i	$-0.523669\pi$
$457$	−22.0844	−	15.2438i	−1.03307	−	0.713074i	−0.958776	+	0.284163i	$0.908284\pi$
$458$	19.5422	−	28.3118i	0.913147	−	1.32292i
$459$	33.0899	−	29.3151i	1.54451	−	1.36831i
$460$	10.4964	+	11.8480i	0.489397	+	0.552415i
$461$	29.7565	+	11.2852i	1.38590	+	0.525603i	0.931026	−	0.364953i	$-0.118915\pi$
$461$	29.7565	+	11.2852i	1.38590	+	0.525603i	0.454874	+	0.890556i	$0.349684\pi$
$462$	12.5199	−	23.8547i	0.582480	−	1.10982i
$463$	15.1736	+	5.75459i	0.705178	+	0.267439i	0.681015	−	0.732269i	$-0.261539\pi$
$463$	15.1736	+	5.75459i	0.705178	+	0.267439i	0.0241627	+	0.999708i	$0.492308\pi$
$464$	−1.44550	−	0.356285i	−0.0671058	−	0.0165401i
$465$	−71.3469	+	63.2079i	−3.30863	+	2.93119i
$466$	1.20553	−	0.832118i	0.0558451	−	0.0385471i
$467$	−6.46120	−	17.0368i	−0.298989	−	0.788368i	−0.997359	−	0.0726316i	$-0.976860\pi$
$467$	−6.46120	−	17.0368i	−0.298989	−	0.788368i	0.698370	−	0.715737i	$-0.253909\pi$
$468$	−28.1727	+	70.6898i	−1.30228	+	3.26764i
$469$	−7.52611	+	19.8447i	−0.347523	+	0.916344i
$470$	21.4662	+	87.0916i	0.990160	+	4.01724i
$471$	−36.3276	+	19.0662i	−1.67389	+	0.878525i
$472$	−1.63872	−	4.32096i	−0.0754283	−	0.198888i
$473$	13.6777	−	1.66077i	0.628902	−	0.0763625i
$474$	−9.22943	−	6.37062i	−0.423922	−	0.292612i
$475$	6.95544	−	28.2193i	0.319138	−	1.29479i
$476$	6.58331	+	26.7095i	0.301746	+	1.22423i
$477$	6.15320	+	50.6762i	0.281736	+	2.32030i
$478$	0.228107	−	0.601468i	0.0104334	−	0.0275105i
$479$	−7.16464	+	29.0681i	−0.327361	+	1.32816i	0.544648	+	0.838665i	$0.316663\pi$
$479$	−7.16464	+	29.0681i	−0.327361	+	1.32816i	−0.872009	+	0.489490i	$0.837183\pi$
$480$	−49.4988	+	12.2004i	−2.25930	+	0.556868i
$481$	−24.5450	−	17.5565i	−1.11915	−	0.800508i
$482$	−29.5895	−	7.29316i	−1.34777	−	0.332194i
$483$	3.65703	−	6.96789i	0.166401	−	0.317050i
$484$	−22.6221			−1.02828
$485$	25.7070			1.16730
$486$	−5.72409	+	10.9064i	−0.259650	+	0.494722i
$487$	16.0548	+	18.1221i	0.727511	+	0.821190i	0.989599	−	0.143854i	$-0.0459495\pi$
$487$	16.0548	+	18.1221i	0.727511	+	0.821190i	−0.262088	+	0.965044i	$0.584411\pi$
$488$		−	21.7325i		−	0.983785i
$489$	−26.2575	+	29.6386i	−1.18740	+	1.34030i
$490$	−24.7522	+	12.9909i	−1.11819	+	0.586871i
$491$	2.80642	+	23.1130i	0.126652	+	1.04307i	0.907998	+	0.418975i	$0.137611\pi$
$491$	2.80642	+	23.1130i	0.126652	+	1.04307i	−0.781345	+	0.624099i	$0.785466\pi$
$492$	3.40481	+	6.48732i	0.153501	+	0.292471i
$493$	−1.37503	−	11.3244i	−0.0619280	−	0.510023i
$494$	12.9545	+	35.9644i	0.582852	+	1.61811i
$495$	5.26812	−	43.3869i	0.236784	−	1.95009i
$496$	−5.01860	+	1.90330i	−0.225342	+	0.0854609i
$497$	15.9923	+	8.39339i	0.717352	+	0.376495i
$498$	9.42917	−	24.8627i	0.422531	−	1.11412i
$499$	8.63303	+	16.4489i	0.386468	+	0.736353i	0.998516	−	0.0544681i	$-0.0173463\pi$
$499$	8.63303	+	16.4489i	0.386468	+	0.736353i	−0.612048	+	0.790821i	$0.709654\pi$
$500$	7.09246	+	13.5136i	0.317184	+	0.604344i
$501$	−10.8237	−	43.9135i	−0.483567	−	1.96191i
$502$	8.99166	+	1.09179i	0.401318	+	0.0487288i
$503$	−0.486660	−	0.431143i	−0.0216991	−	0.0192237i	0.652203	−	0.758044i	$-0.273845\pi$
$503$	−0.486660	−	0.431143i	−0.0216991	−	0.0192237i	−0.673903	+	0.738820i	$0.735383\pi$
$504$	−20.7850	−	30.1122i	−0.925835	−	1.34130i
$505$	30.5820	+	11.5982i	1.36088	+	0.516115i
$506$	6.68856			0.297343
$507$	35.6592	−	17.2171i	1.58368	−	0.764638i
$508$	−38.1062			−1.69069
$509$	4.54629	+	1.72418i	0.201511	+	0.0764229i	0.453295	−	0.891360i	$-0.350248\pi$
$509$	4.54629	+	1.72418i	0.201511	+	0.0764229i	−0.251785	+	0.967783i	$0.581018\pi$
$510$	59.7546	+	86.5695i	2.64598	+	3.83336i
$511$	−0.362159	−	0.320845i	−0.0160210	−	0.0141933i
$512$	−6.46693	−	0.785227i	−0.285801	−	0.0347025i
$513$	10.9414	+	44.3908i	0.483073	+	1.95990i
$514$	8.64948	+	16.4802i	0.381512	+	0.726911i
$515$	−8.62269	−	16.4292i	−0.379961	−	0.723955i
$516$	24.2092	−	63.8344i	1.06575	−	2.81015i
$517$	21.0424	+	11.0439i	0.925442	+	0.485709i
$518$	33.4933	−	12.7023i	1.47161	−	0.558108i
$519$	0.135996	−	1.12003i	0.00596955	−	0.0491637i
$520$	−33.6078	−	18.3634i	−1.47380	−	0.805287i
$521$	2.99478	+	24.6643i	0.131204	+	1.08056i	0.898409	+	0.439159i	$0.144724\pi$
$521$	2.99478	+	24.6643i	0.131204	+	1.08056i	−0.767205	+	0.641402i	$0.778353\pi$
$522$	17.4074	+	33.1671i	0.761903	+	1.45168i
$523$	−1.07738	−	8.87306i	−0.0471107	−	0.387992i	−0.997124	−	0.0757831i	$-0.975854\pi$
$523$	−1.07738	−	8.87306i	−0.0471107	−	0.387992i	0.950014	−	0.312208i	$-0.101069\pi$
$524$	−18.1677	+	9.53517i	−0.793661	+	0.416546i
$525$	23.6981	−	26.7496i	1.03427	−	1.16745i
$526$			3.54540i			0.154587i
$527$	−27.2724	−	30.7842i	−1.18800	−	1.34098i
$528$	1.69023	−	3.22047i	0.0735579	−	0.140153i
$529$	−21.0463			−0.915056
$530$	−63.4243			−2.75498
$531$	−4.27605	+	8.14732i	−0.185565	+	0.353564i
$532$	−27.6229	−	6.80843i	−1.19760	−	0.295183i
$533$	0.659250	−	2.49408i	0.0285553	−	0.108031i
$534$	42.1099	−	10.3792i	1.82228	−	0.449151i
$535$	3.45435	−	14.0149i	0.149345	−	0.605915i
$536$	−12.8393	+	33.8545i	−0.554574	+	1.46229i
$537$	−3.31517	−	27.3029i	−0.143060	−	1.17821i
$538$	16.0392	+	65.0735i	0.691498	+	2.80552i
$539$	−1.77240	+	7.19091i	−0.0763426	+	0.309734i
$540$	−93.0614	−	64.2356i	−4.00472	−	2.76426i
$541$	−17.7415	+	2.15420i	−0.762765	+	0.0926164i	−0.492669	−	0.870217i	$-0.663979\pi$
$541$	−17.7415	+	2.15420i	−0.762765	+	0.0926164i	−0.270096	+	0.962833i	$0.587055\pi$
$542$	−10.7294	−	28.2911i	−0.460867	−	1.21521i
$543$	−15.2975	+	8.02875i	−0.656479	+	0.344547i
$544$	−5.26411	−	21.3573i	−0.225697	−	0.915688i
$545$	9.65416	−	25.4559i	0.413539	−	1.09041i
$546$	−6.44659	+	46.5592i	−0.275889	+	1.99255i
$547$	−16.1000	−	42.4523i	−0.688387	−	1.81513i	−0.569100	−	0.822268i	$-0.692708\pi$
$547$	−16.1000	−	42.4523i	−0.688387	−	1.81513i	−0.119287	−	0.992860i	$-0.538061\pi$
$548$	−2.81955	+	1.94619i	−0.120445	+	0.0831372i
$549$	−32.3888	+	28.6940i	−1.38232	+	1.22463i
$550$	29.4925	+	7.26924i	1.25756	+	0.309961i
$551$	11.0310	+	4.18349i	0.469935	+	0.178223i
$552$	6.23879	−	11.8870i	0.265540	−	0.505945i
$553$	−2.74785	−	1.04212i	−0.116850	−	0.0443155i
$554$	6.45556	+	7.28682i	0.274271	+	0.309587i
$555$	64.2828	−	56.9496i	2.72865	−	2.41738i
$556$	−18.8112	+	27.2527i	−0.797772	+	1.15577i
$557$	25.3051	+	17.4668i	1.07221	+	0.740094i	0.967108	−	0.254367i	$-0.0818672\pi$
$557$	25.3051	+	17.4668i	1.07221	+	0.740094i	0.105103	+	0.994461i	$0.466483\pi$
$558$	119.576	+	62.7585i	5.06207	+	2.65678i
$559$	−21.4695	+	10.8132i	−0.908062	+	0.457350i
$560$	3.18540	−	1.67183i	0.134608	−	0.0706477i
$561$	27.6656	+	3.35921i	1.16804	+	0.141826i
$562$	65.8399	−	16.2281i	2.77729	−	0.684541i
$563$	9.77971	−	14.1683i	0.412165	−	0.597125i	−0.560835	−	0.827928i	$-0.689520\pi$
$563$	9.77971	−	14.1683i	0.412165	−	0.597125i	0.973001	+	0.230803i	$0.0741352\pi$
$564$	96.9087	−	66.8912i	4.08059	−	2.81663i
$565$	27.9084	−	31.5021i	1.17411	−	1.32530i
$566$	−41.6453	−	5.05665i	−1.75048	−	0.212547i
$567$	−5.12253	+	20.7829i	−0.215126	+	0.872800i
$568$	27.2824	+	14.3189i	1.14474	+	0.600807i
$569$	3.13526	−	25.8212i	0.131437	−	1.08248i	−0.766466	−	0.642285i	$-0.777986\pi$
$569$	3.13526	−	25.8212i	0.131437	−	1.08248i	0.897902	−	0.440195i	$-0.145091\pi$
$570$	−107.994	+	13.1128i	−4.52335	+	0.549234i
$571$	24.4519	−	35.4248i	1.02328	−	1.48248i	0.154057	−	0.988062i	$-0.450766\pi$
$571$	24.4519	−	35.4248i	1.02328	−	1.48248i	0.869224	−	0.494418i	$-0.164619\pi$
$572$	−23.5665	+	8.48875i	−0.985364	+	0.354932i
$573$	23.1697	+	33.5671i	0.967929	+	1.40229i
$574$	2.03060	+	2.29207i	0.0847555	+	0.0956692i
$575$	8.61465	+	2.12332i	0.359256	+	0.0885486i
$576$	45.1512	+	65.4127i	1.88130	+	2.72553i
$577$		−	22.5192i		−	0.937485i	−0.883335	−	0.468742i	$-0.844707\pi$
$577$		−	22.5192i		−	0.937485i	0.883335	−	0.468742i	$-0.155293\pi$
$578$	−4.95613	+	3.42097i	−0.206148	+	0.142294i
$579$	−59.2126	+	7.18971i	−2.46079	+	0.298794i
$580$	−27.2829	+	10.3471i	−1.13286	+	0.429638i
$581$	0.839920	−	6.91736i	0.0348458	−	0.286981i
$582$	−19.0865	−	50.3270i	−0.791162	−	2.08612i
$583$	−11.1428	+	12.5776i	−0.461487	+	0.520911i
$584$	−0.617833	−	0.547352i	−0.0255661	−	0.0226496i
$585$	17.0056	+	74.3327i	0.703094	+	3.07328i
$586$	18.9375	−	16.7772i	0.782302	−	0.693059i
$587$			29.3340i			1.21075i	0.795942	+	0.605373i	$0.206976\pi$
$587$			29.3340i			1.21075i	−0.795942	+	0.605373i	$0.793024\pi$
$588$	27.4684	+	24.3348i	1.13278	+	1.00355i
$589$	41.2976	−	10.1789i	1.70164	−	0.419416i
$590$	−9.40834	−	6.49411i	−0.387335	−	0.267358i
$591$	11.4200	−	4.33104i	0.469757	−	0.178155i
$592$	4.52171	−	1.71486i	0.185841	−	0.0704802i
$593$	−4.44503	−	3.06818i	−0.182535	−	0.125995i	0.473293	−	0.880905i	$-0.343065\pi$
$593$	−4.44503	−	3.06818i	−0.182535	−	0.125995i	−0.655829	+	0.754910i	$0.727681\pi$
$594$	−46.3935	+	11.4350i	−1.90355	+	0.469183i
$595$	20.6330	+	18.2792i	0.845869	+	0.749374i
$596$		−	22.8203i		−	0.934757i
$597$	−38.4525	+	34.0660i	−1.57376	+	1.39423i
$598$	−10.9790	+	3.95469i	−0.448965	+	0.161719i
$599$	−34.3595	−	30.4398i	−1.40389	−	1.24374i	−0.932185	−	0.361982i	$-0.882100\pi$
$599$	−34.3595	−	30.4398i	−1.40389	−	1.24374i	−0.471705	−	0.881756i	$-0.656361\pi$
$600$	40.4282	−	45.6340i	1.65048	−	1.86300i
$601$	−8.27891	−	21.8297i	−0.337704	−	0.890452i	−0.991062	−	0.133403i	$-0.957410\pi$
$601$	−8.27891	−	21.8297i	−0.337704	−	0.890452i	0.653358	−	0.757049i	$-0.273360\pi$
$602$	3.43943	−	28.3263i	0.140181	−	1.15449i
$603$	67.4068	−	25.5640i	2.74502	−	1.04105i
$604$	−3.76397	+	0.457029i	−0.153154	+	0.0185962i
$605$	−18.6558	+	12.8772i	−0.758466	+	0.523531i
$606$		−	68.4822i		−	2.78190i
$607$	21.2810	+	30.8308i	0.863768	+	1.25138i	0.966498	+	0.256674i	$0.0826268\pi$
$607$	21.2810	+	30.8308i	0.863768	+	1.25138i	−0.102730	+	0.994709i	$0.532758\pi$
$608$	22.0876	+	5.44411i	0.895772	+	0.220788i
$609$	9.61952	+	10.8582i	0.389803	+	0.439996i
$610$	−30.5400	−	44.2448i	−1.23653	−	1.79142i
$611$	−41.0700	−	5.68657i	−1.66152	−	0.230054i
$612$	53.0799	−	76.8995i	2.14563	−	3.10848i
$613$	−32.4927	+	3.94533i	−1.31237	+	0.159350i	−0.746632	−	0.665237i	$-0.768331\pi$
$613$	−32.4927	+	3.94533i	−1.31237	+	0.159350i	−0.565735	+	0.824587i	$0.691407\pi$
$614$	0.310940	−	2.56082i	0.0125485	−	0.103346i
$615$	6.50063	+	3.41179i	0.262131	+	0.137577i
$616$	2.88231	−	11.6940i	0.116131	−	0.471164i
$617$	15.7933	+	1.91765i	0.635813	+	0.0772016i	0.432095	−	0.901828i	$-0.357774\pi$
$617$	15.7933	+	1.91765i	0.635813	+	0.0772016i	0.203718	+	0.979030i	$0.434698\pi$
$618$	−25.7616	+	29.0788i	−1.03628	+	1.16972i
$619$	32.1818	−	22.2135i	1.29350	−	0.892836i	0.295453	−	0.955357i	$-0.404529\pi$
$619$	32.1818	−	22.2135i	1.29350	−	0.892836i	0.998044	+	0.0625210i	$0.0199140\pi$
$620$	−59.7596	+	86.5767i	−2.40000	+	3.47700i
$621$	−13.5514	+	3.34012i	−0.543799	+	0.134034i
$622$	−6.30715	−	0.765827i	−0.252894	−	0.0307069i
$623$	10.0635	−	5.28172i	0.403185	−	0.211608i
$624$	−0.870312	+	6.28564i	−0.0348403	+	0.251627i
$625$	−14.5617	−	7.64255i	−0.582467	−	0.305702i
$626$	21.9049	+	15.1199i	0.875497	+	0.604312i
$627$	−16.3726	+	23.7198i	−0.653859	+	0.947278i
$628$	−33.8923	+	30.0259i	−1.35245	+	1.19817i
$629$	24.5721	+	27.7362i	0.979755	+	1.10591i
$630$	−84.6314	−	32.0964i	−3.37179	−	1.27875i
$631$	4.51343	−	8.59962i	0.179677	−	0.342346i	−0.778915	−	0.627130i	$-0.784230\pi$
$631$	4.51343	−	8.59962i	0.179677	−	0.342346i	0.958592	+	0.284784i	$0.0919219\pi$
$632$	−4.68775	−	1.77783i	−0.186469	−	0.0707182i
$633$	19.7847	+	4.87650i	0.786373	+	0.193824i
$634$	51.3515	−	45.4935i	2.03943	−	1.80678i
$635$	−31.4251	+	21.6912i	−1.24707	+	0.860789i
$636$	29.5249	+	77.8508i	1.17074	+	3.08699i
$637$	−1.34238	−	12.8515i	−0.0531871	−	0.509197i
$638$	−4.37223	+	11.5286i	−0.173098	+	0.456422i
$639$	−14.6816	−	59.5656i	−0.580795	−	2.35638i
$640$	−57.8010	+	30.3363i	−2.28479	+	1.19915i
$641$	−10.5061	−	27.7024i	−0.414967	−	1.09418i	−0.965738	−	0.259521i	$-0.916435\pi$
$641$	−10.5061	−	27.7024i	−0.414967	−	1.09418i	0.550771	−	0.834657i	$-0.314334\pi$
$642$	−30.0018	+	3.64288i	−1.18408	+	0.143773i
$643$	−20.6930	−	14.2833i	−0.816051	−	0.563279i	0.0853067	−	0.996355i	$-0.472813\pi$
$643$	−20.6930	−	14.2833i	−0.816051	−	0.563279i	−0.901358	+	0.433075i	$0.857428\pi$
$644$	2.07844	−	8.43257i	0.0819021	−	0.332290i
$645$	−16.3718	−	66.4231i	−0.644639	−	2.61541i
$646$	−5.65779	−	46.5961i	−0.222603	−	1.83330i
$647$	−0.715508	+	1.88664i	−0.0281295	+	0.0741715i	−0.948345	−	0.317240i	$-0.897244\pi$
$647$	−0.715508	+	1.88664i	−0.0281295	+	0.0741715i	0.920216	+	0.391412i	$0.128013\pi$
$648$	−8.73888	+	35.4550i	−0.343296	+	1.39280i
$649$	−2.94076	+	0.724831i	−0.115435	+	0.0284521i
$650$	−52.7088	+	5.50558i	−2.06741	+	0.215947i
$651$	50.7797	+	12.5161i	1.99022	+	0.490544i
$652$	−20.3089	+	38.6954i	−0.795358	+	1.51543i
$653$	−9.72617			−0.380614			−0.190307	−	0.981725i	$-0.560948\pi$
$653$	−9.72617			−0.380614			−0.190307	+	0.981725i	$0.560948\pi$
$654$	−57.0033			−2.22900
$655$	−9.55473	+	18.2050i	−0.373334	+	0.711329i
$656$	0.274137	+	0.309437i	0.0107033	+	0.0120815i
$657$			1.64346i			0.0641176i
$658$	32.6360	−	36.8384i	1.27228	−	1.43611i
$659$	21.5325	−	11.3011i	0.838785	−	0.440229i	0.0101039	−	0.999949i	$-0.496784\pi$
$659$	21.5325	−	11.3011i	0.838785	−	0.440229i	0.828682	+	0.559720i	$0.189091\pi$
$660$	−8.59246	−	70.7653i	−0.334461	−	2.75453i
$661$	−9.28679	−	17.6945i	−0.361214	−	0.688236i	0.635245	−	0.772310i	$-0.280899\pi$
$661$	−9.28679	−	17.6945i	−0.361214	−	0.688236i	−0.996459	+	0.0840743i	$0.973207\pi$
$662$	4.88880	+	40.2629i	0.190008	+	1.56486i
$663$	−47.3981	+	10.8436i	−1.84079	+	0.421130i
$664$	1.43288	−	11.8008i	0.0556065	−	0.457961i
$665$	−26.6554	+	10.1091i	−1.03365	+	0.392012i
$666$	−107.737	−	56.5447i	−4.17472	−	2.19106i
$667$	−1.27711	+	3.36747i	−0.0494500	+	0.130389i
$668$	−23.1970	−	44.1982i	−0.897518	−	1.71008i
$669$	23.1141	+	44.0402i	0.893641	+	1.70269i
$670$	21.4353	+	86.9664i	0.828117	+	3.35980i
$671$	−14.1396	−	1.71686i	−0.545853	−	0.0662786i
$672$	20.9373	+	18.5488i	0.807672	+	0.715535i
$673$	−20.3233	−	29.4434i	−0.783405	−	1.13496i	−0.987748	−	0.156058i	$-0.950121\pi$
$673$	−20.3233	−	29.4434i	−0.783405	−	1.13496i	0.204343	−	0.978899i	$-0.434494\pi$
$674$	−48.0311	−	18.2158i	−1.85009	−	0.701646i
$675$	−63.3835			−2.43963
$676$	33.6644	−	27.8679i	1.29478	−	1.07184i
$677$	31.9603			1.22833			0.614167	−	0.789176i	$-0.289492\pi$
$677$	31.9603			1.22833			0.614167	+	0.789176i	$0.289492\pi$
$678$	−82.3930	−	31.2475i	−3.16428	−	1.20005i
$679$	−8.01253	−	11.6082i	−0.307493	−	0.445480i
$680$	35.1992	+	31.1838i	1.34983	+	1.19584i
$681$	−37.6617	−	4.57296i	−1.44320	−	0.175236i
$682$	10.6382	+	43.1608i	0.407357	+	1.65271i
$683$	−20.6747	−	39.3924i	−0.791096	−	1.50731i	−0.860347	−	0.509709i	$-0.829753\pi$
$683$	−20.6747	−	39.3924i	−0.791096	−	1.50731i	0.0692509	−	0.997599i	$-0.477939\pi$
$684$	44.9085	+	85.5661i	1.71712	+	3.27170i
$685$	−1.21737	+	3.20994i	−0.0465133	+	0.122646i
$686$	40.1082	+	21.0504i	1.53134	+	0.803709i
$687$	−42.3129	+	16.0472i	−1.61434	+	0.612238i
$688$	0.464335	−	3.82414i	0.0177026	−	0.145794i
$689$	10.8538	−	27.2340i	0.413497	−	1.03753i
$690$	−4.00300	−	32.9677i	−0.152392	−	1.25506i
$691$	17.9646	+	34.2286i	0.683404	+	1.30212i	0.941831	+	0.336087i	$0.109104\pi$
$691$	17.9646	+	34.2286i	0.683404	+	1.30212i	−0.258427	+	0.966031i	$0.583204\pi$
$692$	−0.150092	−	1.23612i	−0.00570565	−	0.0469902i
$693$	−21.2336	+	11.1442i	−0.806597	+	0.423335i
$694$	−32.2811	+	36.4379i	−1.22538	+	1.38316i
$695$			33.1825i			1.25868i
$696$	16.4106	+	18.5238i	0.622043	+	0.702142i
$697$	−1.47209	+	2.80483i	−0.0557594	+	0.106241i
$698$	−27.7504			−1.05037
$699$	−1.92693			−0.0728831
$700$	18.3293	−	34.9236i	0.692783	−	1.31999i
$701$	19.3782	+	4.77629i	0.731903	+	0.180398i	0.587618	−	0.809138i	$-0.300066\pi$
$701$	19.3782	+	4.77629i	0.731903	+	0.180398i	0.144285	+	0.989536i	$0.453912\pi$
$702$	69.3921	−	46.2008i	2.61904	−	1.74374i
$703$	−37.2087	+	9.17112i	−1.40335	+	0.345895i
$704$	−6.26123	+	25.4028i	−0.235979	+	0.957405i
$705$	41.8414	−	110.327i	1.57584	−	4.15514i
$706$	−4.95761	−	40.8296i	−0.186582	−	1.53664i
$707$	−4.29476	−	17.4245i	−0.161521	−	0.655316i
$708$	−3.59154	+	14.5715i	−0.134978	+	0.547629i
$709$	34.8508	+	24.0558i	1.30885	+	0.903433i	0.998880	−	0.0473136i	$-0.0150660\pi$
$709$	34.8508	+	24.0558i	1.30885	+	0.903433i	0.309969	+	0.950747i	$0.399681\pi$
$710$	75.6655	−	9.18745i	2.83967	−	0.344799i
$711$	3.53979	+	9.33365i	0.132752	+	0.350039i
$712$	17.1680	−	9.01047i	0.643399	−	0.337682i
$713$	3.10737	+	12.6071i	0.116372	+	0.472140i
$714$	20.4662	−	53.9651i	0.765930	−	2.01959i
$715$	−14.6026	+	20.4152i	−0.546105	+	0.763485i
$716$	−10.7638	−	28.3817i	−0.402261	−	1.06067i
$717$	−0.696407	+	0.480695i	−0.0260078	+	0.0179519i
$718$	40.3011	−	35.7037i	1.50402	−	1.33245i
$719$	30.3642	+	7.48411i	1.13239	+	0.279110i	0.760610	−	0.649209i	$-0.224900\pi$
$719$	30.3642	+	7.48411i	1.13239	+	0.279110i	0.371784	+	0.928319i	$0.378746\pi$
$720$	−11.4255	−	4.33313i	−0.425804	−	0.161486i
$721$	−4.73111	+	9.01437i	−0.176196	+	0.335713i
$722$	4.25255	+	1.61278i	0.158264	+	0.0600215i
$723$	26.5838	+	30.0069i	0.988662	+	1.11597i
$724$	−14.2720	+	12.6439i	−0.530414	+	0.469906i
$725$	−9.29112	+	13.4605i	−0.345063	+	0.499911i
$726$	39.0610	+	26.9619i	1.44969	+	1.00065i
$727$	35.0735	+	18.4080i	1.30080	+	0.682714i	0.965747	−	0.259484i	$-0.0835524\pi$
$727$	35.0735	+	18.4080i	1.30080	+	0.682714i	0.335056	+	0.942198i	$0.391245\pi$
$728$	2.18300	+	20.8994i	0.0809075	+	0.774584i
$729$	−16.4160	+	8.61580i	−0.608001	+	0.319104i
$730$	−2.02701	−	0.246124i	−0.0750230	−	0.00910944i
$731$	28.6596	−	7.06397i	1.06002	−	0.261270i
$732$	−40.0919	+	58.0832i	−1.48184	+	2.14682i
$733$	−34.3868	+	23.7355i	−1.27011	+	0.876691i	−0.996371	−	0.0851136i	$-0.972875\pi$
$733$	−34.3868	+	23.7355i	−1.27011	+	0.876691i	−0.273736	+	0.961805i	$0.588259\pi$
$734$	25.4485	−	28.7254i	0.939322	−	1.06028i
$735$	36.5045	+	4.43245i	1.34649	+	0.163493i
$736$	−1.66195	+	6.74280i	−0.0612603	+	0.248543i
$737$	21.0121	+	11.0280i	0.773991	+	0.406222i
$738$	1.25374	−	10.3255i	0.0461509	−	0.380087i
$739$	45.6033	−	5.53724i	1.67754	−	0.203691i	0.774300	−	0.632819i	$-0.218102\pi$
$739$	45.6033	−	5.53724i	1.67754	−	0.203691i	0.903244	+	0.429128i	$0.141179\pi$
$740$	53.8428	−	78.0047i	1.97930	−	2.86751i
$741$	12.8504	−	48.6157i	0.472071	−	1.78594i
$742$	19.7685	+	28.6396i	0.725724	+	1.05139i
$743$	−16.8186	−	18.9843i	−0.617015	−	0.696466i	0.354065	−	0.935221i	$-0.384799\pi$
$743$	−16.8186	−	18.9843i	−0.617015	−	0.696466i	−0.971080	+	0.238755i	$0.923261\pi$
$744$	86.6288	+	21.3521i	3.17596	+	0.782805i
$745$	−12.9900	−	18.8193i	−0.475917	−	0.689486i
$746$		−	83.2298i		−	3.04726i
$747$	−19.4791	+	13.4455i	−0.712703	+	0.491943i
$748$	30.5332	−	3.70740i	1.11640	−	0.135556i
$749$	−7.40516	+	2.80841i	−0.270579	+	0.102617i
$750$	3.85960	−	31.7866i	0.140933	−	1.16068i
$751$	9.42080	+	24.8406i	0.343770	+	0.906447i	0.989714	+	0.143062i	$0.0456948\pi$
$751$	9.42080	+	24.8406i	0.343770	+	0.906447i	−0.645944	+	0.763385i	$0.723536\pi$
$752$	4.40597	−	4.97331i	0.160669	−	0.181358i
$753$	−8.91855	−	7.90115i	−0.325010	−	0.287934i
$754$	0.360415	−	21.5089i	0.0131255	−	0.783309i
$755$	−2.84389	+	2.51946i	−0.103500	+	0.0916927i
$756$			62.0438i			2.25651i
$757$	9.13049	+	8.08891i	0.331853	+	0.293996i	0.812551	−	0.582890i	$-0.198078\pi$
$757$	9.13049	+	8.08891i	0.331853	+	0.293996i	−0.480698	+	0.876886i	$0.659617\pi$
$758$	−19.0072	+	4.68486i	−0.690373	+	0.170162i
$759$	−7.24106	−	4.99814i	−0.262834	−	0.181421i
$760$	−45.4733	+	17.2458i	−1.64949	+	0.625569i
$761$	35.8941	−	13.6128i	1.30116	−	0.493464i	0.395888	−	0.918299i	$-0.370437\pi$
$761$	35.8941	−	13.6128i	1.30116	−	0.493464i	0.905271	+	0.424835i	$0.139668\pi$
$762$	65.7972	+	45.4165i	2.38358	+	1.64527i
$763$	−14.5038	+	3.57487i	−0.525074	+	0.129419i
$764$	33.6941	+	29.8504i	1.21901	+	1.07995i
$765$		−	93.6316i		−	3.38526i
$766$	−55.1342	+	48.8446i	−1.99208	+	1.76483i
$767$	4.39857	−	2.92854i	0.158823	−	0.105743i
$768$

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.h (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.16507 - 0.821103i) q^{2} +(1.73033 + 2.50681i) q^{3} +(2.51629 + 2.22924i) q^{4} +(3.34407 + 0.406044i) q^{5} +(-1.68793 - 6.84821i) q^{6} +(-0.858950 - 1.63659i) q^{7} +(-1.46534 - 2.79198i) q^{8} +(-2.22627 + 5.87018i) q^{9} +O(q^{10})\)	\(q+(-2.16507 - 0.821103i) q^{2} +(1.73033 + 2.50681i) q^{3} +(2.51629 + 2.22924i) q^{4} +(3.34407 + 0.406044i) q^{5} +(-1.68793 - 6.84821i) q^{6} +(-0.858950 - 1.63659i) q^{7} +(-1.46534 - 2.79198i) q^{8} +(-2.22627 + 5.87018i) q^{9} +(-6.90674 - 3.62494i) q^{10} +(-1.93228 + 0.732816i) q^{11} +(-1.23428 + 10.1652i) q^{12} +(2.73847 - 2.34537i) q^{13} +(0.515876 + 4.24862i) q^{14} +(4.76847 + 9.08555i) q^{15} +(0.0696450 + 0.573578i) q^{16} +(-3.92016 + 2.05746i) q^{17} +(9.64004 - 10.8814i) q^{18} -4.57866i q^{19} +(7.50950 + 8.47647i) q^{20} +(2.61637 - 4.98507i) q^{21} +4.78523 q^{22} +1.39775 q^{23} +(4.46345 - 8.50439i) q^{24} +(6.16322 + 1.51910i) q^{25} +(-7.85477 + 2.82932i) q^{26} +(-9.69515 + 2.38964i) q^{27} +(1.48699 - 6.03296i) q^{28} +(-0.913692 + 2.40921i) q^{29} +(-2.86389 - 23.5863i) q^{30} +(2.22313 + 9.01957i) q^{31} +(-1.18902 + 4.82404i) q^{32} +(-5.18051 - 3.57585i) q^{33} +(10.1768 - 1.23569i) q^{34} +(-2.20786 - 5.82165i) q^{35} +(-18.6880 + 9.80822i) q^{36} +(-2.00301 - 8.12654i) q^{37} +(-3.75955 + 9.91313i) q^{38} +(10.6179 + 2.80658i) q^{39} +(-3.76655 - 9.93157i) q^{40} +(0.588837 - 0.406445i) q^{41} +(-9.75787 + 8.64472i) q^{42} +(-6.47343 - 1.59556i) q^{43} +(-6.49580 - 2.46353i) q^{44} +(-9.82834 + 18.7263i) q^{45} +(-3.02623 - 1.14770i) q^{46} +(-7.62554 - 8.60746i) q^{47} +(-1.31735 + 1.16707i) q^{48} +(2.03581 - 2.94939i) q^{49} +(-12.0965 - 8.34959i) q^{50} +(-11.9408 - 6.26703i) q^{51} +(12.1192 + 0.203076i) q^{52} +(7.19974 - 3.77871i) q^{53} +(22.9528 + 2.78698i) q^{54} +(-6.75923 + 1.66600i) q^{55} +(-3.31067 + 4.79634i) q^{56} +(11.4779 - 7.92260i) q^{57} +(3.95641 - 4.46587i) q^{58} +(1.45491 + 0.176659i) q^{59} +(-8.25504 + 33.4920i) q^{60} +(6.10284 + 3.20302i) q^{61} +(2.59277 - 21.3534i) q^{62} +(11.5193 - 1.39870i) q^{63} +(7.19178 - 10.4191i) q^{64} +(10.1100 - 6.73115i) q^{65} +(8.28003 + 11.9957i) q^{66} +(-7.61458 - 8.59508i) q^{67} +(-14.4508 - 3.56181i) q^{68} +(2.41857 + 3.50390i) q^{69} +14.4172i q^{70} +(-8.04194 + 5.55095i) q^{71} +(19.6517 - 2.38615i) q^{72} +(0.244764 - 0.0928266i) q^{73} +(-2.33606 + 19.2392i) q^{74} +(6.85631 + 18.0786i) q^{75} +(10.2070 - 11.5213i) q^{76} +(2.85905 + 2.53290i) q^{77} +(-20.6839 - 14.7948i) q^{78} +(1.19014 - 1.05437i) q^{79} +1.94636i q^{80} +(-8.66837 - 7.67951i) q^{81} +(-1.60861 + 0.396486i) q^{82} +(3.10268 + 2.14162i) q^{83} +(17.6965 - 6.71139i) q^{84} +(-13.9447 + 5.28853i) q^{85} +(12.7053 + 8.76984i) q^{86} +(-7.62043 + 1.87827i) q^{87} +(4.87746 + 4.32105i) q^{88} +6.14905i q^{89} +(36.6553 - 32.4738i) q^{90} +(-6.19063 - 2.46721i) q^{91} +(3.51715 + 3.11592i) q^{92} +(-18.7637 + 21.1798i) q^{93} +(9.44223 + 24.8971i) q^{94} +(1.85914 - 15.3114i) q^{95} +(-14.1504 + 5.36652i) q^{96} +(7.57566 - 0.919851i) q^{97} +(-6.82942 + 4.71401i) q^{98} -12.9743i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9}+O(q^{10}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9} - 9 q^{10} - 13 q^{11} - 9 q^{12} + 52 q^{13} - 15 q^{14} + 39 q^{15} - 31 q^{16} - 11 q^{17} + 26 q^{18} - 13 q^{20} - 13 q^{21} - 6 q^{22} - 102 q^{23} - 91 q^{24} + 3 q^{25} - 13 q^{26} - 19 q^{27} - 13 q^{28} - 17 q^{29} + 23 q^{30} + 39 q^{31} - 13 q^{33} + 52 q^{34} - 21 q^{35} + 11 q^{36} - 13 q^{37} - 40 q^{38} - 65 q^{39} + 53 q^{40} - 13 q^{41} + 101 q^{42} - 3 q^{43} - 39 q^{44} - 78 q^{45} - 39 q^{46} - 39 q^{47} + 8 q^{48} + 85 q^{49} - 13 q^{50} + 62 q^{51} - 78 q^{52} + 18 q^{53} + 65 q^{54} - 103 q^{55} + 3 q^{56} + 65 q^{57} + 39 q^{58} + 91 q^{59} - 117 q^{60} - 23 q^{61} - 64 q^{62} - 78 q^{63} + 15 q^{64} - 13 q^{65} + 134 q^{66} - 65 q^{67} + 40 q^{68} - 40 q^{69} + 26 q^{71} + 156 q^{72} - 13 q^{73} - 53 q^{74} + 35 q^{75} + 221 q^{76} + 3 q^{77} - 143 q^{78} - 23 q^{79} - 43 q^{81} - 129 q^{82} + 117 q^{83} + 234 q^{84} + 26 q^{85} - 91 q^{86} + 79 q^{87} + 95 q^{88} + 17 q^{90} + 39 q^{91} - 89 q^{92} + 52 q^{93} - 61 q^{94} + 122 q^{95} - 182 q^{96} - 91 q^{97} - 13 q^{98}+O(q^{100}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9 - 9 * q^10 - 13 * q^11 - 9 * q^12 + 52 * q^13 - 15 * q^14 + 39 * q^15 - 31 * q^16 - 11 * q^17 + 26 * q^18 - 13 * q^20 - 13 * q^21 - 6 * q^22 - 102 * q^23 - 91 * q^24 + 3 * q^25 - 13 * q^26 - 19 * q^27 - 13 * q^28 - 17 * q^29 + 23 * q^30 + 39 * q^31 - 13 * q^33 + 52 * q^34 - 21 * q^35 + 11 * q^36 - 13 * q^37 - 40 * q^38 - 65 * q^39 + 53 * q^40 - 13 * q^41 + 101 * q^42 - 3 * q^43 - 39 * q^44 - 78 * q^45 - 39 * q^46 - 39 * q^47 + 8 * q^48 + 85 * q^49 - 13 * q^50 + 62 * q^51 - 78 * q^52 + 18 * q^53 + 65 * q^54 - 103 * q^55 + 3 * q^56 + 65 * q^57 + 39 * q^58 + 91 * q^59 - 117 * q^60 - 23 * q^61 - 64 * q^62 - 78 * q^63 + 15 * q^64 - 13 * q^65 + 134 * q^66 - 65 * q^67 + 40 * q^68 - 40 * q^69 + 26 * q^71 + 156 * q^72 - 13 * q^73 - 53 * q^74 + 35 * q^75 + 221 * q^76 + 3 * q^77 - 143 * q^78 - 23 * q^79 - 43 * q^81 - 129 * q^82 + 117 * q^83 + 234 * q^84 + 26 * q^85 - 91 * q^86 + 79 * q^87 + 95 * q^88 + 17 * q^90 + 39 * q^91 - 89 * q^92 + 52 * q^93 - 61 * q^94 + 122 * q^95 - 182 * q^96 - 91 * q^97 - 13 * q^98

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