LMFDB - Embedded newform 261.2.k.c.226.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,2,Mod(82,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("261.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.k (of order $7$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} + 18 x^{16} - 37 x^{15} + 71 x^{14} - 83 x^{13} + 225 x^{12} - 237 x^{11} + 485 x^{10} + \cdots + 64 $ x^18 - 6x^17 + 18x^16 - 37x^15 + 71x^14 - 83x^13 + 225x^12 - 237x^11 + 485x^10 - 319x^9 + 1092x^8 - 1080x^7 + 1833x^6 - 4032x^5 + 6004x^4 - 4480x^3 + 3200x^2 - 576*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 87)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			226.2
Root			$0.183119 + 0.802295i$ of defining polynomial
Character	$\chi$	$=$	261.226
Dual form			261.2.k.c.82.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.110403 + 0.138441i) q^{2} +(0.438065 + 1.91929i) q^{4} +(2.15193 - 2.69844i) q^{5} +(0.844514 - 3.70006i) q^{7} +(-0.633146 - 0.304907i) q^{8} +O(q^{10})$	\(q+(-0.110403 + 0.138441i) q^{2} +(0.438065 + 1.91929i) q^{4} +(2.15193 - 2.69844i) q^{5} +(0.844514 - 3.70006i) q^{7} +(-0.633146 - 0.304907i) q^{8} +(0.135995 + 0.595831i) q^{10} +(-3.84419 + 1.85126i) q^{11} +(4.18329 - 2.01457i) q^{13} +(0.419003 + 0.525413i) q^{14} +(-3.43526 + 1.65434i) q^{16} +3.07208 q^{17} +(0.799448 + 3.50261i) q^{19} +(6.12176 + 2.94808i) q^{20} +(0.168119 - 0.736579i) q^{22} +(0.270347 + 0.339005i) q^{23} +(-1.53815 - 6.73907i) q^{25} +(-0.182949 + 0.801554i) q^{26} +7.47142 q^{28} +(1.41466 + 5.19603i) q^{29} +(-2.81961 + 3.53568i) q^{31} +(0.462984 - 2.02846i) q^{32} +(-0.339167 + 0.425302i) q^{34} +(-8.16704 - 10.2411i) q^{35} +(-5.70128 - 2.74559i) q^{37} +(-0.573166 - 0.276022i) q^{38} +(-2.18526 + 1.05236i) q^{40} +1.97128 q^{41} +(-0.156607 - 0.196379i) q^{43} +(-5.23711 - 6.56713i) q^{44} -0.0767793 q^{46} +(-4.33933 + 2.08971i) q^{47} +(-6.67044 - 3.21231i) q^{49} +(1.10278 + 0.531070i) q^{50} +(5.69909 + 7.14643i) q^{52} +(-6.83931 + 8.57623i) q^{53} +(-3.27691 + 14.3571i) q^{55} +(-1.66287 + 2.08518i) q^{56} +(-0.875526 - 0.377811i) q^{58} +6.06991 q^{59} +(-0.843741 + 3.69667i) q^{61} +(-0.178190 - 0.780699i) q^{62} +(-4.52484 - 5.67398i) q^{64} +(3.56598 - 15.6236i) q^{65} +(4.74553 + 2.28533i) q^{67} +(1.34577 + 5.89620i) q^{68} +2.31946 q^{70} +(-5.25813 + 2.53218i) q^{71} +(-6.57753 - 8.24796i) q^{73} +(1.00954 - 0.486169i) q^{74} +(-6.37230 + 3.06874i) q^{76} +(3.60331 + 15.7871i) q^{77} +(-9.04273 - 4.35475i) q^{79} +(-2.92833 + 12.8299i) q^{80} +(-0.217635 + 0.272906i) q^{82} +(-1.57949 - 6.92019i) q^{83} +(6.61090 - 8.28981i) q^{85} +0.0444768 q^{86} +2.99840 q^{88} +(8.71402 - 10.9270i) q^{89} +(-3.92117 - 17.1798i) q^{91} +(-0.532218 + 0.667380i) q^{92} +(0.189773 - 0.831452i) q^{94} +(11.1719 + 5.38012i) q^{95} +(3.18704 + 13.9633i) q^{97} +(1.18115 - 0.568813i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{2} - 6 q^{4} + q^{5} - 4 q^{7} + 15 q^{8}+O(q^{10}) $ 18 * q + 4 * q^2 - 6 * q^4 + q^5 - 4 * q^7 + 15 * q^8	$ 18 q + 4 q^{2} - 6 q^{4} + q^{5} - 4 q^{7} + 15 q^{8} - 14 q^{10} - 26 q^{11} + 9 q^{13} + 10 q^{14} - 14 q^{16} - 4 q^{17} - 10 q^{19} + q^{20} - 8 q^{22} + 8 q^{23} + 16 q^{25} - 5 q^{26} + 80 q^{28} - 8 q^{29} - 12 q^{31} - 9 q^{32} - 22 q^{34} - 9 q^{35} - 16 q^{37} + 32 q^{38} + 33 q^{40} - 24 q^{41} - 31 q^{43} + 52 q^{44} - 44 q^{46} - 5 q^{47} - 47 q^{49} + 7 q^{50} + 80 q^{52} - 5 q^{53} - 17 q^{55} - 45 q^{56} + 54 q^{58} + 32 q^{59} - 28 q^{61} - 69 q^{62} - 75 q^{64} - 22 q^{65} + 6 q^{67} - 38 q^{68} - 12 q^{70} - 46 q^{71} - q^{73} + 35 q^{74} - 45 q^{76} + 36 q^{77} - 15 q^{79} + 86 q^{80} + 47 q^{82} + 16 q^{83} + 19 q^{85} - 116 q^{86} + 54 q^{88} + 72 q^{89} - 47 q^{91} + 121 q^{92} - 22 q^{94} + 72 q^{95} + 43 q^{97} - 31 q^{98}+O(q^{100}) $ 18 * q + 4 * q^2 - 6 * q^4 + q^5 - 4 * q^7 + 15 * q^8 - 14 * q^10 - 26 * q^11 + 9 * q^13 + 10 * q^14 - 14 * q^16 - 4 * q^17 - 10 * q^19 + q^20 - 8 * q^22 + 8 * q^23 + 16 * q^25 - 5 * q^26 + 80 * q^28 - 8 * q^29 - 12 * q^31 - 9 * q^32 - 22 * q^34 - 9 * q^35 - 16 * q^37 + 32 * q^38 + 33 * q^40 - 24 * q^41 - 31 * q^43 + 52 * q^44 - 44 * q^46 - 5 * q^47 - 47 * q^49 + 7 * q^50 + 80 * q^52 - 5 * q^53 - 17 * q^55 - 45 * q^56 + 54 * q^58 + 32 * q^59 - 28 * q^61 - 69 * q^62 - 75 * q^64 - 22 * q^65 + 6 * q^67 - 38 * q^68 - 12 * q^70 - 46 * q^71 - q^73 + 35 * q^74 - 45 * q^76 + 36 * q^77 - 15 * q^79 + 86 * q^80 + 47 * q^82 + 16 * q^83 + 19 * q^85 - 116 * q^86 + 54 * q^88 + 72 * q^89 - 47 * q^91 + 121 * q^92 - 22 * q^94 + 72 * q^95 + 43 * q^97 - 31 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{5}{7}\right)$	$1$

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 $

$2$	−0.110403	+	0.138441i	−0.0780667	+	0.0978926i	−0.819331	−	0.573320i	$-0.805655\pi$
$2$	−0.110403	+	0.138441i	−0.0780667	+	0.0978926i	0.741264	+	0.671213i	$0.234226\pi$
$3$		0			0
$3$		0			0
$4$	0.438065	+	1.91929i	0.219032	+	0.959644i
$5$	2.15193	−	2.69844i	0.962373	−	1.20678i	−0.0159877	−	0.999872i	$-0.505089\pi$
$5$	2.15193	−	2.69844i	0.962373	−	1.20678i	0.978361	−	0.206906i	$-0.0663393\pi$
$6$		0			0
$7$	0.844514	−	3.70006i	0.319196	−	1.39849i	−0.519770	−	0.854306i	$-0.673982\pi$
$7$	0.844514	−	3.70006i	0.319196	−	1.39849i	0.838966	−	0.544184i	$-0.183161\pi$
$8$	−0.633146	−	0.304907i	−0.223851	−	0.107801i
$9$		0			0
$10$	0.135995	+	0.595831i	0.0430053	+	0.188418i
$11$	−3.84419	+	1.85126i	−1.15907	+	0.558177i	−0.911745	−	0.410756i	$-0.865265\pi$
$11$	−3.84419	+	1.85126i	−1.15907	+	0.558177i	−0.247322	+	0.968933i	$0.579550\pi$
$12$		0			0
$13$	4.18329	−	2.01457i	1.16024	−	0.558741i	0.248144	−	0.968723i	$-0.420179\pi$
$13$	4.18329	−	2.01457i	1.16024	−	0.558741i	0.912093	+	0.409982i	$0.134465\pi$
$14$	0.419003	+	0.525413i	0.111983	+	0.140422i
$15$		0			0
$16$	−3.43526	+	1.65434i	−0.858816	+	0.413584i
$17$	3.07208			0.745088			0.372544	−	0.928014i	$-0.378486\pi$
$17$	3.07208			0.745088			0.372544	+	0.928014i	$0.378486\pi$
$18$		0			0
$19$	0.799448	+	3.50261i	0.183406	+	0.803554i	0.979993	+	0.199030i	$0.0637792\pi$
$19$	0.799448	+	3.50261i	0.183406	+	0.803554i	−0.796587	+	0.604523i	$0.793364\pi$
$20$	6.12176	+	2.94808i	1.36887	+	0.659212i
$21$		0			0
$22$	0.168119	−	0.736579i	0.0358432	−	0.157039i
$23$	0.270347	+	0.339005i	0.0563713	+	0.0706873i	0.809218	−	0.587509i	$-0.199891\pi$
$23$	0.270347	+	0.339005i	0.0563713	+	0.0706873i	−0.752847	+	0.658196i	$0.771320\pi$
$24$		0			0
$25$	−1.53815	−	6.73907i	−0.307630	−	1.34781i
$26$	−0.182949	+	0.801554i	−0.0358793	+	0.157198i
$27$		0			0
$28$	7.47142			1.41197
$29$	1.41466	+	5.19603i	0.262696	+	0.964879i
$29$	1.41466	+	5.19603i	0.262696	+	0.964879i
$30$		0			0
$31$	−2.81961	+	3.53568i	−0.506417	+	0.635027i	−0.967663	−	0.252245i	$-0.918831\pi$
$31$	−2.81961	+	3.53568i	−0.506417	+	0.635027i	0.461246	+	0.887272i	$0.347402\pi$
$32$	0.462984	−	2.02846i	0.0818447	−	0.358585i
$33$		0			0
$34$	−0.339167	+	0.425302i	−0.0581666	+	0.0729386i
$35$	−8.16704	−	10.2411i	−1.38048	−	1.73107i
$36$		0			0
$37$	−5.70128	−	2.74559i	−0.937284	−	0.451372i	−0.0980737	−	0.995179i	$-0.531268\pi$
$37$	−5.70128	−	2.74559i	−0.937284	−	0.451372i	−0.839210	+	0.543807i	$0.816982\pi$
$38$	−0.573166	−	0.276022i	−0.0929798	−	0.0447767i
$39$		0			0
$40$	−2.18526	+	1.05236i	−0.345520	+	0.166394i
$41$	1.97128			0.307862			0.153931	−	0.988082i	$-0.450807\pi$
$41$	1.97128			0.307862			0.153931	+	0.988082i	$0.450807\pi$
$42$		0			0
$43$	−0.156607	−	0.196379i	−0.0238823	−	0.0299475i	0.769747	−	0.638349i	$-0.220382\pi$
$43$	−0.156607	−	0.196379i	−0.0238823	−	0.0299475i	−0.793629	+	0.608402i	$0.791811\pi$
$44$	−5.23711	−	6.56713i	−0.789524	−	0.990032i
$45$		0			0
$46$	−0.0767793			−0.0113205
$47$	−4.33933	+	2.08971i	−0.632956	+	0.304816i	−0.722713	−	0.691148i	$-0.757105\pi$
$47$	−4.33933	+	2.08971i	−0.632956	+	0.304816i	0.0897569	+	0.995964i	$0.471391\pi$
$48$		0			0
$49$	−6.67044	−	3.21231i	−0.952919	−	0.458902i
$50$	1.10278	+	0.531070i	0.155957	+	0.0751047i
$51$		0			0
$52$	5.69909	+	7.14643i	0.790322	+	0.991032i
$53$	−6.83931	+	8.57623i	−0.939452	+	1.17804i	0.0443931	+	0.999014i	$0.485865\pi$
$53$	−6.83931	+	8.57623i	−0.939452	+	1.17804i	−0.983845	+	0.179021i	$0.942707\pi$
$54$		0			0
$55$	−3.27691	+	14.3571i	−0.441859	+	1.93591i
$56$	−1.66287	+	2.08518i	−0.222211	+	0.278644i
$57$		0			0
$58$	−0.875526	−	0.377811i	−0.114962	−	0.0496090i
$59$	6.06991			0.790234			0.395117	−	0.918631i	$-0.370704\pi$
$59$	6.06991			0.790234			0.395117	+	0.918631i	$0.370704\pi$
$60$		0			0
$61$	−0.843741	+	3.69667i	−0.108030	+	0.473310i	0.891754	+	0.452521i	$0.149475\pi$
$61$	−0.843741	+	3.69667i	−0.108030	+	0.473310i	−0.999784	+	0.0207897i	$0.993382\pi$
$62$	−0.178190	−	0.780699i	−0.0226301	−	0.0991489i
$63$		0			0
$64$	−4.52484	−	5.67398i	−0.565606	−	0.709247i
$65$	3.56598	−	15.6236i	0.442305	−	1.93787i
$66$		0			0
$67$	4.74553	+	2.28533i	0.579759	+	0.279197i	0.700693	−	0.713463i	$-0.252875\pi$
$67$	4.74553	+	2.28533i	0.579759	+	0.279197i	−0.120934	+	0.992661i	$0.538589\pi$
$68$	1.34577	+	5.89620i	0.163198	+	0.715019i
$69$		0			0
$70$	2.31946			0.277228
$71$	−5.25813	+	2.53218i	−0.624025	+	0.300515i	−0.719048	−	0.694960i	$-0.755422\pi$
$71$	−5.25813	+	2.53218i	−0.624025	+	0.300515i	0.0950227	+	0.995475i	$0.469708\pi$
$72$		0			0
$73$	−6.57753	−	8.24796i	−0.769841	−	0.965350i	0.230128	−	0.973160i	$-0.426085\pi$
$73$	−6.57753	−	8.24796i	−0.769841	−	0.965350i	−0.999970	+	0.00780984i	$0.997514\pi$
$74$	1.00954	−	0.486169i	0.117357	−	0.0565160i
$75$		0			0
$76$	−6.37230	+	3.06874i	−0.730953	+	0.352009i
$77$	3.60331	+	15.7871i	0.410636	+	1.79911i
$78$		0			0
$79$	−9.04273	−	4.35475i	−1.01739	−	0.489947i	−0.150583	−	0.988597i	$-0.548115\pi$
$79$	−9.04273	−	4.35475i	−1.01739	−	0.489947i	−0.866803	+	0.498650i	$0.833829\pi$
$80$	−2.92833	+	12.8299i	−0.327397	+	1.43442i
$81$		0			0
$82$	−0.217635	+	0.272906i	−0.0240338	+	0.0301374i
$83$	−1.57949	−	6.92019i	−0.173371	−	0.759590i	−0.984595	−	0.174853i	$-0.944055\pi$
$83$	−1.57949	−	6.92019i	−0.173371	−	0.759590i	0.811223	−	0.584737i	$-0.198802\pi$
$84$		0			0
$85$	6.61090	−	8.28981i	0.717053	−	0.899156i
$86$	0.0444768			0.00479606
$87$		0			0
$88$	2.99840			0.319630
$89$	8.71402	−	10.9270i	0.923684	−	1.15826i	−0.0633886	−	0.997989i	$-0.520191\pi$
$89$	8.71402	−	10.9270i	0.923684	−	1.15826i	0.987073	−	0.160274i	$-0.0512378\pi$
$90$		0			0
$91$	−3.92117	−	17.1798i	−0.411050	−	1.80093i
$92$	−0.532218	+	0.667380i	−0.0554875	+	0.0695792i
$93$		0			0
$94$	0.189773	−	0.831452i	0.0195736	−	0.0857577i
$95$	11.1719	+	5.38012i	1.14622	+	0.551988i
$96$		0			0
$97$	3.18704	+	13.9633i	0.323595	+	1.41776i	0.831105	+	0.556116i	$0.187709\pi$
$97$	3.18704	+	13.9633i	0.323595	+	1.41776i	−0.507510	+	0.861646i	$0.669434\pi$
$98$	1.18115	−	0.568813i	0.119314	−	0.0574588i
$99$		0			0
$100$	12.2604	−	5.90430i	1.22604	−	0.590430i
$101$	−0.509045	−	0.638322i	−0.0506519	−	0.0635154i	0.755860	−	0.654733i	$-0.227219\pi$
$101$	−0.509045	−	0.638322i	−0.0506519	−	0.0635154i	−0.806512	+	0.591218i	$0.798647\pi$
$102$		0			0
$103$	4.46695	−	2.15117i	0.440142	−	0.211961i	−0.200670	−	0.979659i	$-0.564312\pi$
$103$	4.46695	−	2.15117i	0.440142	−	0.211961i	0.640812	+	0.767698i	$0.278598\pi$
$104$	−3.26289			−0.319953
$105$		0			0
$106$	−0.432221	−	1.89368i	−0.0419810	−	0.183931i
$107$	−10.3935	−	5.00522i	−1.00477	−	0.483873i	−0.142218	−	0.989835i	$-0.545423\pi$
$107$	−10.3935	−	5.00522i	−1.00477	−	0.483873i	−0.862556	+	0.505962i	$0.831138\pi$
$108$		0			0
$109$	−1.92418	+	8.43038i	−0.184303	+	0.807484i	0.795247	+	0.606285i	$0.207341\pi$
$109$	−1.92418	+	8.43038i	−0.184303	+	0.807484i	−0.979550	+	0.201199i	$0.935516\pi$
$110$	−1.62583	−	2.03873i	−0.155017	−	0.194385i
$111$		0			0
$112$	3.22001	+	14.1078i	0.304262	+	1.33306i
$113$	1.68793	−	7.39532i	0.158787	−	0.695693i	−0.831368	−	0.555722i	$-0.812442\pi$
$113$	1.68793	−	7.39532i	0.158787	−	0.695693i	0.990156	−	0.139971i	$-0.0447010\pi$
$114$		0			0
$115$	1.49655			0.139554
$116$	−9.35296	+	4.99134i	−0.868401	+	0.463434i
$117$		0			0
$118$	−0.670136	+	0.840324i	−0.0616910	+	0.0773581i
$119$	2.59441	−	11.3669i	0.237829	−	1.04200i
$120$		0			0
$121$	4.49223	−	5.63308i	0.408385	−	0.512098i
$122$	−0.418620	−	0.524932i	−0.0379000	−	0.0475251i
$123$		0			0
$124$	−8.02116	−	3.86279i	−0.720321	−	0.346888i
$125$	−5.94678	−	2.86382i	−0.531896	−	0.256148i
$126$		0			0
$127$	−1.11242	+	0.535714i	−0.0987114	+	0.0475369i	−0.482588	−	0.875848i	$-0.660303\pi$
$127$	−1.11242	+	0.535714i	−0.0987114	+	0.0475369i	0.383877	+	0.923384i	$0.374589\pi$
$128$	5.44633			0.481392
$129$		0			0
$130$	1.76925	+	2.21857i	0.155173	+	0.194581i
$131$	2.49124	+	3.12392i	0.217661	+	0.272938i	0.878659	−	0.477449i	$-0.158439\pi$
$131$	2.49124	+	3.12392i	0.217661	+	0.272938i	−0.660999	+	0.750387i	$0.729867\pi$
$132$		0			0
$133$	13.6350			1.18230
$134$	−0.840304	+	0.404669i	−0.0725912	+	0.0349581i
$135$		0			0
$136$	−1.94507	−	0.936698i	−0.166789	−	0.0803212i
$137$	15.0046	+	7.22585i	1.28193	+	0.617346i	0.945886	−	0.324500i	$-0.105196\pi$
$137$	15.0046	+	7.22585i	1.28193	+	0.617346i	0.336046	+	0.941846i	$0.390910\pi$
$138$		0			0
$139$	5.15692	+	6.46658i	0.437405	+	0.548488i	0.950857	−	0.309630i	$-0.100205\pi$
$139$	5.15692	+	6.46658i	0.437405	+	0.548488i	−0.513452	+	0.858118i	$0.671634\pi$
$140$	16.0780	−	20.1612i	1.35884	−	1.70393i
$141$		0			0
$142$	0.229956	−	1.00750i	0.0192974	−	0.0845476i
$143$	−12.3519	+	15.4888i	−1.03292	+	1.29524i
$144$		0			0
$145$	17.0654	+	7.36414i	1.41721	+	0.611558i
$146$	1.86803			0.154600
$147$		0			0
$148$	2.77205	−	12.1451i	0.227861	−	0.998324i
$149$	−2.08913	−	9.15309i	−0.171149	−	0.749851i	−0.985527	−	0.169517i	$-0.945779\pi$
$149$	−2.08913	−	9.15309i	−0.171149	−	0.749851i	0.814379	−	0.580334i	$-0.197078\pi$
$150$		0			0
$151$	12.2599	+	15.3734i	0.997693	+	1.25107i	0.967854	+	0.251513i	$0.0809280\pi$
$151$	12.2599	+	15.3734i	0.997693	+	1.25107i	0.0298388	+	0.999555i	$0.490501\pi$
$152$	0.561803	−	2.46142i	0.0455682	−	0.199647i
$153$		0			0
$154$	−2.58340	−	1.24410i	−0.208177	−	0.100253i
$155$	3.47320	+	15.2171i	0.278974	+	1.22227i
$156$		0			0
$157$	−2.61457			−0.208665			−0.104333	−	0.994542i	$-0.533271\pi$
$157$	−2.61457			−0.208665			−0.104333	+	0.994542i	$0.533271\pi$
$158$	1.60122	−	0.771107i	0.127386	−	0.0613460i
$159$		0			0
$160$	−4.47737	−	5.61445i	−0.353967	−	0.443861i
$161$	1.48265	−	0.714006i	0.116849	−	0.0562715i
$162$		0			0
$163$	0.475531	−	0.229004i	0.0372465	−	0.0179370i	−0.415168	−	0.909745i	$-0.636277\pi$
$163$	0.475531	−	0.229004i	0.0372465	−	0.0179370i	0.452414	+	0.891808i	$0.350563\pi$
$164$	0.863547	+	3.78345i	0.0674317	+	0.295437i
$165$		0			0
$166$	1.13242	+	0.545344i	0.0878928	+	0.0423269i
$167$	−3.34870	+	14.6716i	−0.259131	+	1.13533i	0.663053	+	0.748573i	$0.269260\pi$
$167$	−3.34870	+	14.6716i	−0.259131	+	1.13533i	−0.922183	+	0.386753i	$0.873597\pi$
$168$		0			0
$169$	5.33610	−	6.69126i	0.410469	−	0.514712i
$170$	0.417786	+	1.83044i	0.0320427	+	0.140388i
$171$		0			0
$172$	0.308304	−	0.386601i	0.0235079	−	0.0294780i
$173$	−0.103233			−0.00784865			−0.00392433	−	0.999992i	$-0.501249\pi$
$173$	−0.103233			−0.00784865			−0.00392433	+	0.999992i	$0.501249\pi$
$174$		0			0
$175$	−26.2339			−1.98310
$176$	10.1432	−	12.7192i	0.764572	−	0.958743i
$177$		0			0
$178$	0.550695	+	2.41275i	0.0412764	+	0.180844i
$179$	2.52461	−	3.16576i	0.188698	−	0.236620i	−0.678479	−	0.734620i	$-0.737360\pi$
$179$	2.52461	−	3.16576i	0.188698	−	0.236620i	0.867177	+	0.498000i	$0.165932\pi$
$180$		0			0
$181$	2.56394	−	11.2334i	0.190576	−	0.834969i	−0.785729	−	0.618571i	$-0.787712\pi$
$181$	2.56394	−	11.2334i	0.190576	−	0.834969i	0.976305	−	0.216398i	$-0.0694309\pi$
$182$	2.81129	+	1.35385i	0.208387	+	0.100354i
$183$		0			0
$184$	−0.0678043	−	0.297070i	−0.00499860	−	0.0219003i
$185$	−19.6776	+	9.47621i	−1.44672	+	0.696705i
$186$		0			0
$187$	−11.8097	+	5.68723i	−0.863607	+	0.415891i
$188$	−5.91166	−	7.41299i	−0.431152	−	0.540648i
$189$		0			0
$190$	−1.97824	+	0.952672i	−0.143517	+	0.0691141i
$191$	−1.55942			−0.112836			−0.0564179	−	0.998407i	$-0.517968\pi$
$191$	−1.55942			−0.112836			−0.0564179	+	0.998407i	$0.517968\pi$
$192$		0			0
$193$	−2.97677	−	13.0421i	−0.214273	−	0.938790i	−0.961626	−	0.274363i	$-0.911533\pi$
$193$	−2.97677	−	13.0421i	−0.214273	−	0.938790i	0.747354	−	0.664427i	$-0.231324\pi$
$194$	−2.28496	−	1.10038i	−0.164050	−	0.0790024i
$195$		0			0
$196$	3.24327	−	14.2097i	0.231662	−	1.01498i
$197$	7.96548	+	9.98840i	0.567517	+	0.711644i	0.979927	−	0.199354i	$-0.0638845\pi$
$197$	7.96548	+	9.98840i	0.567517	+	0.711644i	−0.412411	+	0.910998i	$0.635313\pi$
$198$		0			0
$199$	−1.96309	−	8.60088i	−0.139160	−	0.609700i	−0.995620	−	0.0934873i	$-0.970199\pi$
$199$	−1.96309	−	8.60088i	−0.139160	−	0.609700i	0.856460	−	0.516213i	$-0.172659\pi$
$200$	−1.08092	+	4.73580i	−0.0764323	+	0.334872i
$201$		0			0
$202$	0.144570			0.0101719
$203$	20.4203	−	0.846200i	1.43322	−	0.0593916i
$204$		0			0
$205$	4.24205	−	5.31937i	0.296278	−	0.371521i
$206$	−0.195355	+	0.855906i	−0.0136110	+	0.0596338i
$207$		0			0
$208$	−11.0379	+	13.8411i	−0.765344	+	0.959711i
$209$	−9.55749	−	11.9847i	−0.661105	−	0.829000i
$210$		0			0
$211$	13.5356	+	6.51841i	0.931830	+	0.448746i	0.837280	−	0.546774i	$-0.184144\pi$
$211$	13.5356	+	6.51841i	0.931830	+	0.448746i	0.0945500	+	0.995520i	$0.469859\pi$
$212$	−19.4563	−	9.36966i	−1.33626	−	0.643511i
$213$		0			0
$214$	1.84040	−	0.886289i	0.125807	−	0.0605854i
$215$	−0.866924			−0.0591237
$216$		0			0
$217$	10.7010	+	13.4186i	0.726432	+	0.910917i
$218$	−0.954675	−	1.19712i	−0.0646587	−	0.0810795i
$219$		0			0
$220$	−28.9909			−1.95457
$221$	12.8514	−	6.18891i	0.864479	−	0.416311i
$222$		0			0
$223$	−21.5743	−	10.3896i	−1.44472	−	0.695740i	−0.463050	−	0.886332i	$-0.653245\pi$
$223$	−21.5743	−	10.3896i	−1.44472	−	0.695740i	−0.981669	+	0.190592i	$0.938959\pi$
$224$	−7.11444	−	3.42613i	−0.475353	−	0.228918i
$225$		0			0
$226$	0.837463	+	1.05015i	0.0557072	+	0.0698546i
$227$	3.21628	−	4.03308i	0.213472	−	0.267685i	−0.663554	−	0.748128i	$-0.730953\pi$
$227$	3.21628	−	4.03308i	0.213472	−	0.267685i	0.877026	+	0.480443i	$0.159524\pi$
$228$		0			0
$229$	1.80280	−	7.89857i	0.119132	−	0.521952i	−0.879783	−	0.475376i	$-0.842312\pi$
$229$	1.80280	−	7.89857i	0.119132	−	0.521952i	0.998915	−	0.0465760i	$-0.0148310\pi$
$230$	−0.165224	+	0.207184i	−0.0108945	+	0.0136613i
$231$		0			0
$232$	0.688620	−	3.72118i	0.0452101	−	0.244308i
$233$	−24.5153			−1.60605			−0.803027	−	0.595943i	$-0.796778\pi$
$233$	−24.5153			−1.60605			−0.803027	+	0.595943i	$0.796778\pi$
$234$		0			0
$235$	−3.69899	+	16.2063i	−0.241295	+	1.05718i
$236$	2.65901	+	11.6499i	0.173087	+	0.758343i
$237$		0			0
$238$	1.28721	+	1.61411i	0.0834374	+	0.104627i
$239$	−6.21741	+	27.2402i	−0.402171	+	1.76202i	0.216410	+	0.976303i	$0.430565\pi$
$239$	−6.21741	+	27.2402i	−0.402171	+	1.76202i	−0.618580	+	0.785722i	$0.712292\pi$
$240$		0			0
$241$	−3.57537	−	1.72181i	−0.230310	−	0.110911i	0.315170	−	0.949035i	$-0.397938\pi$
$241$	−3.57537	−	1.72181i	−0.230310	−	0.110911i	−0.545480	+	0.838124i	$0.683653\pi$
$242$	0.283893	+	1.24382i	0.0182494	+	0.0799557i
$243$		0			0
$244$	−7.46459			−0.477871
$245$	−23.0225	+	11.0871i	−1.47086	+	0.708327i
$246$		0			0
$247$	10.4006	+	13.0419i	0.661773	+	0.829837i
$248$	2.86328	−	1.37888i	0.181818	−	0.0875591i
$249$		0			0
$250$	1.05301	−	0.507104i	0.0665983	−	0.0320721i
$251$	−7.03374	−	30.8168i	−0.443965	−	1.94514i	−0.289748	−	0.957103i	$-0.593571\pi$
$251$	−7.03374	−	30.8168i	−0.443965	−	1.94514i	−0.154218	−	0.988037i	$-0.549286\pi$
$252$		0			0
$253$	−1.66685	−	0.802714i	−0.104794	−	0.0504662i
$254$	0.0486499	−	0.213149i	0.00305256	−	0.0133742i
$255$		0			0
$256$	8.44840	−	10.5940i	0.528025	−	0.662122i
$257$	−0.901269	−	3.94872i	−0.0562196	−	0.246314i	0.939008	−	0.343895i	$-0.111747\pi$
$257$	−0.901269	−	3.94872i	−0.0562196	−	0.246314i	−0.995228	+	0.0975812i	$0.968889\pi$
$258$		0			0
$259$	−14.9736	+	18.7764i	−0.930417	+	1.16671i
$260$	31.5483			1.95654
$261$		0			0
$262$	−0.707518			−0.0437106
$263$	8.91597	−	11.1803i	0.549782	−	0.689405i	−0.426850	−	0.904322i	$-0.640377\pi$
$263$	8.91597	−	11.1803i	0.549782	−	0.689405i	0.976632	+	0.214917i	$0.0689482\pi$
$264$		0			0
$265$	8.42468	+	36.9109i	0.517524	+	2.26742i
$266$	−1.50534	+	1.88764i	−0.0922986	+	0.115739i
$267$		0			0
$268$	−2.30735	+	10.1092i	−0.140944	+	0.617515i
$269$	19.3865	+	9.33606i	1.18202	+	0.569230i	0.918498	−	0.395425i	$-0.129403\pi$
$269$	19.3865	+	9.33606i	1.18202	+	0.569230i	0.263519	+	0.964654i	$0.415117\pi$
$270$		0			0
$271$	4.40370	+	19.2939i	0.267506	+	1.17202i	0.912904	+	0.408174i	$0.133834\pi$
$271$	4.40370	+	19.2939i	0.267506	+	1.17202i	−0.645399	+	0.763846i	$0.723309\pi$
$272$	−10.5534	+	5.08225i	−0.639894	+	0.308157i
$273$		0			0
$274$	−2.65691	+	1.27950i	−0.160510	+	0.0772974i
$275$	18.3887	+	23.0587i	1.10888	+	1.39049i
$276$		0			0
$277$	−5.04862	+	2.43129i	−0.303342	+	0.146082i	−0.579363	−	0.815070i	$-0.696699\pi$
$277$	−5.04862	+	2.43129i	−0.303342	+	0.146082i	0.276020	+	0.961152i	$0.410984\pi$
$278$	−1.46458			−0.0878397
$279$		0			0
$280$	2.04833	+	8.97432i	0.122411	+	0.536318i
$281$	−9.74719	−	4.69400i	−0.581469	−	0.280021i	0.119939	−	0.992781i	$-0.461730\pi$
$281$	−9.74719	−	4.69400i	−0.581469	−	0.280021i	−0.701407	+	0.712761i	$0.747445\pi$
$282$		0			0
$283$	1.65442	−	7.24849i	0.0983451	−	0.430878i	−0.901654	−	0.432459i	$-0.857646\pi$
$283$	1.65442	−	7.24849i	0.0983451	−	0.430878i	0.999999	+	0.00158078i	$0.000503178\pi$
$284$	−7.16339	−	8.98260i	−0.425069	−	0.533019i
$285$		0			0
$286$	−0.780596	−	3.42001i	−0.0461576	−	0.202230i
$287$	1.66477	−	7.29384i	0.0982683	−	0.430542i
$288$		0			0
$289$	−7.56234			−0.444843
$290$	−2.90357	+	1.54953i	−0.170504	+	0.0909916i
$291$		0			0
$292$	12.9488	−	16.2373i	0.757772	−	0.950216i
$293$	2.76291	−	12.1051i	0.161411	−	0.707186i	−0.827841	−	0.560963i	$-0.810431\pi$
$293$	2.76291	−	12.1051i	0.161411	−	0.707186i	0.989252	−	0.146223i	$-0.0467118\pi$
$294$		0			0
$295$	13.0620	−	16.3793i	0.760500	−	0.953637i
$296$	2.77259	+	3.47672i	0.161153	+	0.202080i
$297$		0			0
$298$	1.49781	+	0.721307i	0.0867658	+	0.0417842i
$299$	1.81389	+	0.873523i	0.104900	+	0.0505172i
$300$		0			0
$301$	−0.858870	+	0.413610i	−0.0495045	+	0.0238401i
$302$	−3.48183			−0.200357
$303$		0			0
$304$	−8.54080	−	10.7098i	−0.489849	−	0.614251i
$305$	8.15957	+	10.2318i	0.467215	+	0.585870i
$306$		0			0
$307$	24.0387			1.37196			0.685981	−	0.727620i	$-0.259373\pi$
$307$	24.0387			1.37196			0.685981	+	0.727620i	$0.259373\pi$
$308$	−28.7216	+	13.8316i	−1.63656	+	0.788128i
$309$		0			0
$310$	−2.49012	−	1.19918i	−0.141429	−	0.0681088i
$311$	−28.1593	−	13.5608i	−1.59677	−	0.768963i	−0.597314	−	0.802007i	$-0.703766\pi$
$311$	−28.1593	−	13.5608i	−1.59677	−	0.768963i	−0.999454	+	0.0330440i	$0.989480\pi$
$312$		0			0
$313$	−13.1250	−	16.4582i	−0.741867	−	0.930272i	0.257484	−	0.966283i	$-0.417106\pi$
$313$	−13.1250	−	16.4582i	−0.741867	−	0.930272i	−0.999351	+	0.0360104i	$0.988535\pi$
$314$	0.288656	−	0.361964i	0.0162898	−	0.0204268i
$315$		0			0
$316$	4.39671	−	19.2633i	0.247334	−	1.08364i
$317$	9.75852	−	12.2368i	0.548093	−	0.687287i	−0.428214	−	0.903677i	$-0.640857\pi$
$317$	9.75852	−	12.2368i	0.548093	−	0.687287i	0.976307	+	0.216390i	$0.0694284\pi$
$318$		0			0
$319$	−15.0574	−	17.3556i	−0.843055	−	0.971728i
$320$	−25.0480			−1.40023
$321$		0			0
$322$	−0.0648412	+	0.284088i	−0.00361346	+	0.0158316i
$323$	2.45597	+	10.7603i	0.136654	+	0.598718i
$324$		0			0
$325$	−20.0108	−	25.0928i	−1.11000	−	1.39190i
$326$	−0.0207966	+	0.0911157i	−0.00115181	+	0.00504643i
$327$		0			0
$328$	−1.24811	−	0.601056i	−0.0689151	−	0.0331878i
$329$	4.06743	+	17.8206i	0.224244	+	0.982479i
$330$		0			0
$331$	−19.4595			−1.06959			−0.534796	−	0.844981i	$-0.679612\pi$
$331$	−19.4595			−1.06959			−0.534796	+	0.844981i	$0.679612\pi$
$332$	12.5899	−	6.06299i	0.690962	−	0.332750i
$333$		0			0
$334$	−1.66145	−	2.08339i	−0.0909104	−	0.113998i
$335$	16.3789	−	7.88765i	0.894873	−	0.430948i
$336$		0			0
$337$	−18.1797	+	8.75489i	−0.990312	+	0.476909i	−0.857640	−	0.514251i	$-0.828070\pi$
$337$	−18.1797	+	8.75489i	−0.990312	+	0.476909i	−0.132672	+	0.991160i	$0.542356\pi$
$338$	0.337223	+	1.47747i	0.0183425	+	0.0803638i
$339$		0			0
$340$	18.8065	+	9.05675i	1.01993	+	0.491171i
$341$	4.29364	−	18.8117i	0.232514	−	1.01871i
$342$		0			0
$343$	−0.955090	+	1.19764i	−0.0515700	+	0.0646667i
$344$	0.0392777	+	0.172087i	0.00211771	+	0.00927831i
$345$		0			0
$346$	0.0113972	−	0.0142917i	0.000612719	−	0.000768325i
$347$	−0.788354			−0.0423211			−0.0211605	−	0.999776i	$-0.506736\pi$
$347$	−0.788354			−0.0423211			−0.0211605	+	0.999776i	$0.506736\pi$
$348$		0			0
$349$	20.9417			1.12098			0.560491	−	0.828161i	$-0.310613\pi$
$349$	20.9417			1.12098			0.560491	+	0.828161i	$0.310613\pi$
$350$	2.89630	−	3.63185i	0.154814	−	0.194131i
$351$		0			0
$352$	1.97543	+	8.65491i	0.105291	+	0.461308i
$353$	22.5006	−	28.2149i	1.19759	−	1.50173i	0.380929	−	0.924604i	$-0.375604\pi$
$353$	22.5006	−	28.2149i	1.19759	−	1.50173i	0.816658	−	0.577122i	$-0.195824\pi$
$354$		0			0
$355$	−4.48220	+	19.6378i	−0.237891	+	1.04227i
$356$	24.7894	+	11.9380i	1.31384	+	0.632710i
$357$		0			0
$358$	0.159547	+	0.699020i	0.00843230	+	0.0369443i
$359$	16.7787	−	8.08019i	0.885545	−	0.426456i	0.0648984	−	0.997892i	$-0.479328\pi$
$359$	16.7787	−	8.08019i	0.885545	−	0.426456i	0.820647	+	0.571436i	$0.193613\pi$
$360$		0			0
$361$	5.48925	−	2.64349i	0.288908	−	0.139131i
$362$	1.27209	+	1.59515i	0.0668596	+	0.0838393i
$363$		0			0
$364$	31.2552	−	15.0517i	1.63822	−	0.788923i
$365$	−36.4110			−1.90584
$366$		0			0
$367$	−3.58975	−	15.7277i	−0.187383	−	0.820981i	−0.977989	−	0.208655i	$-0.933091\pi$
$367$	−3.58975	−	15.7277i	−0.187383	−	0.820981i	0.790606	−	0.612325i	$-0.209766\pi$
$368$	−1.48954	−	0.717325i	−0.0776477	−	0.0373932i
$369$		0			0
$370$	0.860566	−	3.77038i	0.0447387	−	0.196013i
$371$	25.9566	+	32.5486i	1.34760	+	1.68984i
$372$		0			0
$373$	−0.252766	−	1.10744i	−0.0130877	−	0.0573410i	0.967962	−	0.251095i	$-0.0807907\pi$
$373$	−0.252766	−	1.10744i	−0.0130877	−	0.0573410i	−0.981050	+	0.193754i	$0.937934\pi$
$374$	0.516476	−	2.26283i	0.0267063	−	0.117008i
$375$		0			0
$376$	3.38460			0.174547
$377$	16.3857	+	18.8866i	0.843906	+	0.972709i
$378$		0			0
$379$	18.8590	−	23.6485i	0.968723	−	1.21474i	−0.00794116	−	0.999968i	$-0.502528\pi$
$379$	18.8590	−	23.6485i	0.968723	−	1.21474i	0.976664	−	0.214772i	$-0.0689008\pi$
$380$	−5.43196	+	23.7990i	−0.278654	+	1.22086i
$381$		0			0
$382$	0.172165	−	0.215888i	0.00880873	−	0.0110458i
$383$	10.9608	+	13.7443i	0.560068	+	0.702303i	0.978570	−	0.205912i	$-0.0660162\pi$
$383$	10.9608	+	13.7443i	0.560068	+	0.702303i	−0.418502	+	0.908216i	$0.637445\pi$
$384$		0			0
$385$	50.3547	+	24.2495i	2.56631	+	1.23587i
$386$	2.13420	+	1.02778i	0.108628	+	0.0523125i
$387$		0			0
$388$	−25.4035	+	12.2337i	−1.28967	+	0.621071i
$389$	−38.5442			−1.95427			−0.977134	−	0.212625i	$-0.931799\pi$
$389$	−38.5442			−1.95427			−0.977134	+	0.212625i	$0.931799\pi$
$390$		0			0
$391$	0.830527	+	1.04145i	0.0420016	+	0.0526683i
$392$	3.24390	+	4.06772i	0.163842	+	0.205451i
$393$		0			0
$394$	−2.26222			−0.113969
$395$	−31.2103	+	15.0301i	−1.57036	+	0.756247i
$396$		0			0
$397$	18.9872	+	9.14373i	0.952938	+	0.458911i	0.844715	−	0.535216i	$-0.179770\pi$
$397$	18.9872	+	9.14373i	0.952938	+	0.458911i	0.108223	+	0.994127i	$0.465484\pi$
$398$	1.40745	+	0.677790i	0.0705489	+	0.0339745i
$399$		0			0
$400$	16.4326	+	20.6059i	0.821631	+	1.03029i
$401$	21.6506	−	27.1490i	1.08118	−	1.35576i	0.151051	−	0.988526i	$-0.451734\pi$
$401$	21.6506	−	27.1490i	1.08118	−	1.35576i	0.930130	−	0.367231i	$-0.119694\pi$
$402$		0			0
$403$	−4.67239	+	20.4711i	−0.232748	+	1.01974i
$404$	1.00213	−	1.25663i	0.0498578	−	0.0625197i
$405$		0			0
$406$	−2.13732	+	2.92043i	−0.106073	+	0.144939i
$407$	26.9996			1.33832
$408$		0			0
$409$	0.697528	−	3.05607i	0.0344905	−	0.151113i	−0.954750	−	0.297408i	$-0.903878\pi$
$409$	0.697528	−	3.05607i	0.0344905	−	0.151113i	0.989241	+	0.146295i	$0.0467349\pi$
$410$	0.268083	+	1.17455i	0.0132397	+	0.0580068i
$411$		0			0
$412$	6.08553	+	7.63102i	0.299813	+	0.375953i
$413$	5.12612	−	22.4590i	0.252240	−	1.10514i
$414$		0			0
$415$	−22.0727	−	10.6296i	−1.08350	−	0.521788i
$416$	−2.14968	−	9.41838i	−0.105397	−	0.461774i
$417$		0			0
$418$	2.71435			0.132763
$419$	−7.82316	+	3.76744i	−0.382186	+	0.184051i	−0.615105	−	0.788445i	$-0.710887\pi$
$419$	−7.82316	+	3.76744i	−0.382186	+	0.184051i	0.232919	+	0.972496i	$0.425172\pi$
$420$		0			0
$421$	17.6965	+	22.1907i	0.862475	+	1.08151i	0.995901	+	0.0904508i	$0.0288308\pi$
$421$	17.6965	+	22.1907i	0.862475	+	1.08151i	−0.133426	+	0.991059i	$0.542598\pi$
$422$	−2.39679	+	1.15423i	−0.116674	+	0.0561871i
$423$		0			0
$424$	6.94523	−	3.34465i	0.337290	−	0.162430i
$425$	−4.72531	−	20.7029i	−0.229211	−	1.00424i
$426$		0			0
$427$	12.9653	+	6.24378i	0.627437	+	0.302158i
$428$	5.05346	−	22.1406i	0.244268	−	1.07021i
$429$		0			0
$430$	0.0957110	−	0.120018i	0.00461560	−	0.00578777i
$431$	0.0183247	+	0.0802859i	0.000882671	+	0.00386723i	0.975367	−	0.220587i	$-0.0707973\pi$
$431$	0.0183247	+	0.0802859i	0.000882671	+	0.00386723i	−0.974485	+	0.224454i	$0.927940\pi$
$432$		0			0
$433$	0.788400	−	0.988623i	0.0378881	−	0.0475102i	−0.762526	−	0.646957i	$-0.776041\pi$
$433$	0.788400	−	0.988623i	0.0378881	−	0.0475102i	0.800415	+	0.599447i	$0.204613\pi$
$434$	−3.03912			−0.145882
$435$		0			0
$436$	−17.0232			−0.815265
$437$	−0.971272	+	1.21794i	−0.0464623	+	0.0582618i
$438$		0			0
$439$	−6.49242	−	28.4451i	−0.309866	−	1.35761i	−0.854723	−	0.519084i	$-0.826273\pi$
$439$	−6.49242	−	28.4451i	−0.309866	−	1.35761i	0.544857	−	0.838529i	$-0.316584\pi$
$440$	6.45234	−	8.09098i	0.307603	−	0.385722i
$441$		0			0
$442$	−0.562035	+	2.46244i	−0.0267333	+	0.117126i
$443$	−16.4847	−	7.93860i	−0.783211	−	0.377174i	−0.000849826	−	1.00000i	$-0.500271\pi$
$443$	−16.4847	−	7.93860i	−0.783211	−	0.377174i	−0.782361	+	0.622825i	$0.785985\pi$
$444$		0			0
$445$	−10.7339	−	47.0285i	−0.508837	−	2.22936i
$446$	3.82021	−	1.83972i	0.180892	−	0.0871131i
$447$		0			0
$448$	−24.8153	+	11.9504i	−1.17241	+	0.564605i
$449$	6.63592	+	8.32119i	0.313169	+	0.392701i	0.913358	−	0.407157i	$-0.133480\pi$
$449$	6.63592	+	8.32119i	0.313169	+	0.392701i	−0.600190	+	0.799858i	$0.704908\pi$
$450$		0			0
$451$	−7.57796	+	3.64935i	−0.356832	+	0.171841i
$452$	14.9332			0.702397
$453$		0			0
$454$	0.203257	+	0.890529i	0.00953934	+	0.0417946i
$455$	−54.7966	−	26.3886i	−2.56890	−	1.23712i
$456$		0			0
$457$	−6.72070	+	29.4453i	−0.314381	+	1.37739i	0.532868	+	0.846199i	$0.321114\pi$
$457$	−6.72070	+	29.4453i	−0.314381	+	1.37739i	−0.847249	+	0.531196i	$0.821743\pi$
$458$	0.894452	+	1.12161i	0.0417950	+	0.0524093i
$459$		0			0
$460$	0.655586	+	2.87231i	0.0305669	+	0.133922i
$461$	−8.11297	+	35.5452i	−0.377859	+	1.65551i	0.326152	+	0.945317i	$0.394248\pi$
$461$	−8.11297	+	35.5452i	−0.377859	+	1.65551i	−0.704011	+	0.710189i	$0.748609\pi$
$462$		0			0
$463$	18.1919			0.845450			0.422725	−	0.906258i	$-0.361074\pi$
$463$	18.1919			0.845450			0.422725	+	0.906258i	$0.361074\pi$
$464$	−13.4557	−	15.5094i	−0.624666	−	0.720006i
$465$		0			0
$466$	2.70657	−	3.39393i	0.125379	−	0.157221i
$467$	2.20583	−	9.66436i	0.102074	−	0.447213i	−0.897902	−	0.440196i	$-0.854909\pi$
$467$	2.20583	−	9.66436i	0.102074	−	0.447213i	0.999975	−	0.00701766i	$-0.00223381\pi$
$468$		0			0
$469$	12.4635	−	15.6287i	0.575511	−	0.721669i
$470$	−1.83524	−	2.30132i	−0.0846533	−	0.106152i
$471$		0			0
$472$	−3.84313	−	1.85076i	−0.176895	−	0.0851880i
$473$	0.965577	+	0.464997i	0.0443973	+	0.0213806i
$474$		0			0
$475$	22.3746	−	10.7751i	1.02662	−	0.494394i
$476$	22.9528			1.05204
$477$		0			0
$478$	−3.08475	−	3.86815i	−0.141093	−	0.176925i
$479$	−26.6415	−	33.4074i	−1.21728	−	1.52642i	−0.778255	−	0.627949i	$-0.783895\pi$
$479$	−26.6415	−	33.4074i	−1.21728	−	1.52642i	−0.439027	−	0.898474i	$-0.644677\pi$
$480$		0			0
$481$	−29.3813			−1.33967
$482$	0.633101	−	0.304885i	0.0288369	−	0.0138871i
$483$		0			0
$484$	12.7794	+	6.15423i	0.580881	+	0.279738i
$485$	44.5375	+	21.4481i	2.02234	+	0.973908i
$486$		0			0
$487$	−15.8593	−	19.8869i	−0.718654	−	0.901163i	0.279607	−	0.960115i	$-0.409796\pi$
$487$	−15.8593	−	19.8869i	−0.718654	−	0.901163i	−0.998261	+	0.0589511i	$0.981224\pi$
$488$	1.66135	−	2.08327i	0.0752059	−	0.0943052i
$489$		0			0
$490$	1.00685	−	4.41131i	0.0454850	−	0.199283i
$491$	−19.5910	+	24.5664i	−0.884131	+	1.10867i	0.109274	+	0.994012i	$0.465147\pi$
$491$	−19.5910	+	24.5664i	−0.884131	+	1.10867i	−0.993406	+	0.114654i	$0.963424\pi$
$492$		0			0
$493$	4.34594	+	15.9626i	0.195731	+	0.718920i
$494$	−2.95379			−0.132897
$495$		0			0
$496$	3.83690	−	16.8106i	0.172282	−	0.754817i
$497$	4.92865	+	21.5938i	0.221080	+	0.968616i
$498$		0			0
$499$	−4.33114	−	5.43107i	−0.193888	−	0.243128i	0.675379	−	0.737471i	$-0.263980\pi$
$499$	−4.33114	−	5.43107i	−0.193888	−	0.243128i	−0.869267	+	0.494343i	$0.835409\pi$
$500$	2.89141	−	12.6681i	0.129308	−	0.566535i
$501$		0			0
$502$	5.04286	+	2.42851i	0.225074	+	0.108390i
$503$	5.90822	+	25.8856i	0.263434	+	1.15418i	0.917497	+	0.397742i	$0.130206\pi$
$503$	5.90822	+	25.8856i	0.263434	+	1.15418i	−0.654063	+	0.756440i	$0.726937\pi$
$504$		0			0
$505$	−2.81790			−0.125395
$506$	0.295154	−	0.142139i	0.0131212	−	0.00631884i
$507$		0			0
$508$	−1.51550	−	1.90038i	−0.0672395	−	0.0843156i
$509$	−1.24379	+	0.598977i	−0.0551299	+	0.0265492i	−0.461246	−	0.887273i	$-0.652597\pi$
$509$	−1.24379	+	0.598977i	−0.0551299	+	0.0265492i	0.406116	+	0.913822i	$0.366883\pi$
$510$		0			0
$511$	−36.0727	+	17.3717i	−1.59576	+	0.768479i
$512$	2.95775	+	12.9588i	0.130715	+	0.572702i
$513$		0			0
$514$	0.646167	+	0.311178i	0.0285012	+	0.0137255i
$515$	3.80778	−	16.6830i	0.167791	−	0.735140i
$516$		0			0
$517$	12.8126	−	16.0665i	0.563498	−	0.706604i
$518$	−0.946282	−	4.14593i	−0.0415773	−	0.182162i
$519$		0			0
$520$	−7.02152	+	8.80471i	−0.307914	+	0.386112i
$521$	−8.46722			−0.370956			−0.185478	−	0.982648i	$-0.559383\pi$
$521$	−8.46722			−0.370956			−0.185478	+	0.982648i	$0.559383\pi$
$522$		0			0
$523$	4.74716			0.207579			0.103789	−	0.994599i	$-0.466903\pi$
$523$	4.74716			0.207579			0.103789	+	0.994599i	$0.466903\pi$
$524$	−4.90437	+	6.14988i	−0.214248	+	0.268659i
$525$		0			0
$526$	0.563458	+	2.46867i	0.0245679	+	0.107639i
$527$	−8.66206	+	10.8619i	−0.377325	+	0.473151i
$528$		0			0
$529$	5.07614	−	22.2400i	0.220702	−	0.966958i
$530$	−6.04009	−	2.90876i	−0.262365	−	0.126348i
$531$		0			0
$532$	5.97301	+	26.1695i	0.258963	+	1.13459i
$533$	8.24643	−	3.97127i	0.357193	−	0.172015i
$534$		0			0
$535$	−35.8723	+	17.2752i	−1.55089	+	0.746871i
$536$	−2.30780	−	2.89389i	−0.0996818	−	0.124997i
$537$		0			0
$538$	−3.43282	+	1.65316i	−0.148000	+	0.0712728i
$539$	31.5893			1.36065
$540$		0			0
$541$	−0.543856	−	2.38279i	−0.0233822	−	0.102444i	0.961890	−	0.273436i	$-0.0881601\pi$
$541$	−0.543856	−	2.38279i	−0.0233822	−	0.102444i	−0.985273	+	0.170992i	$0.945303\pi$
$542$	−3.15725	−	1.52045i	−0.135615	−	0.0653089i
$543$		0			0
$544$	1.42232	−	6.23160i	0.0609816	−	0.267178i
$545$	18.6081	+	23.3339i	0.797085	+	0.999513i
$546$		0			0
$547$	−1.37369	−	6.01855i	−0.0587350	−	0.257335i	0.937033	−	0.349242i	$-0.113561\pi$
$547$	−1.37369	−	6.01855i	−0.0587350	−	0.257335i	−0.995768	+	0.0919072i	$0.970704\pi$
$548$	−7.29548	+	31.9636i	−0.311647	+	1.36542i
$549$		0			0
$550$	−5.22245			−0.222686
$551$	−17.0687	+	9.10895i	−0.727152	+	0.388054i
$552$		0			0
$553$	−23.7495	+	29.7810i	−1.00993	+	1.26642i
$554$	0.220793	−	0.967358i	0.00938060	−	0.0410991i
$555$		0			0
$556$	−10.1522	+	12.7304i	−0.430547	+	0.539889i
$557$	7.76642	+	9.73879i	0.329074	+	0.412646i	0.918653	−	0.395065i	$-0.129278\pi$
$557$	7.76642	+	9.73879i	0.329074	+	0.412646i	−0.589579	+	0.807710i	$0.700706\pi$
$558$		0			0
$559$	−1.05075	−	0.506016i	−0.0444421	−	0.0214022i
$560$	44.9982	+	21.6700i	1.90152	+	0.915724i
$561$		0			0
$562$	1.72596	−	0.831179i	0.0728053	−	0.0350612i
$563$	3.58213			0.150969			0.0754843	−	0.997147i	$-0.475950\pi$
$563$	3.58213			0.150969			0.0754843	+	0.997147i	$0.475950\pi$
$564$		0			0
$565$	−16.3235	−	20.4690i	−0.686735	−	0.861138i
$566$	0.820836	+	1.02930i	0.0345023	+	0.0432645i
$567$		0			0
$568$	4.10124			0.172084
$569$	−24.2253	+	11.6663i	−1.01558	+	0.489076i	−0.866197	−	0.499703i	$-0.833442\pi$
$569$	−24.2253	+	11.6663i	−1.01558	+	0.489076i	−0.149381	+	0.988780i	$0.547728\pi$
$570$		0			0
$571$	27.0389	+	13.0212i	1.13154	+	0.544922i	0.903440	−	0.428715i	$-0.141033\pi$
$571$	27.0389	+	13.0212i	1.13154	+	0.544922i	0.228103	+	0.973637i	$0.426748\pi$
$572$	−35.1383	−	16.9217i	−1.46921	−	0.707533i
$573$		0			0
$574$	0.825970	+	1.03573i	0.0344753	+	0.0432307i
$575$	1.86874	−	2.34333i	0.0779319	−	0.0977235i
$576$		0			0
$577$	0.637724	−	2.79405i	0.0265488	−	0.116318i	−0.959917	−	0.280284i	$-0.909571\pi$
$577$	0.637724	−	2.79405i	0.0265488	−	0.116318i	0.986466	+	0.163966i	$0.0524286\pi$
$578$	0.834905	−	1.04694i	0.0347275	−	0.0435469i
$579$		0			0
$580$	−6.65813	+	35.9794i	−0.276464	+	1.49396i
$581$	−26.9390			−1.11762
$582$		0			0
$583$	10.4148	−	45.6300i	0.431335	−	1.88980i
$584$	1.64967	+	7.22769i	0.0682640	+	0.299084i
$585$		0			0
$586$	1.37081	+	1.71894i	0.0566275	+	0.0710086i
$587$	4.85992	−	21.2927i	0.200591	−	0.878844i	−0.769988	−	0.638059i	$-0.779738\pi$
$587$	4.85992	−	21.2927i	0.200591	−	0.878844i	0.970578	−	0.240786i	$-0.0774051\pi$
$588$		0			0
$589$	−14.6382	−	7.04940i	−0.603158	−	0.290466i
$590$	0.825474	+	3.61664i	0.0339842	+	0.148895i
$591$		0			0
$592$	24.1275			0.991635
$593$	17.9895	−	8.66330i	0.738741	−	0.355759i	−0.0263741	−	0.999652i	$-0.508396\pi$
$593$	17.9895	−	8.66330i	0.738741	−	0.355759i	0.765116	+	0.643893i	$0.222682\pi$
$594$		0			0
$595$	−25.0898	−	31.4616i	−1.02858	−	1.28980i
$596$	16.6522	−	8.01930i	0.682102	−	0.328483i
$597$		0			0
$598$	−0.321190	+	0.154677i	−0.0131345	+	0.00632522i
$599$	−5.76162	−	25.2433i	−0.235413	−	1.03141i	−0.945071	−	0.326866i	$-0.894007\pi$
$599$	−5.76162	−	25.2433i	−0.235413	−	1.03141i	0.709657	−	0.704547i	$-0.248850\pi$
$600$		0			0
$601$	−21.7322	−	10.4657i	−0.886473	−	0.426903i	−0.0654886	−	0.997853i	$-0.520861\pi$
$601$	−21.7322	−	10.4657i	−0.886473	−	0.426903i	−0.820985	+	0.570950i	$0.806575\pi$
$602$	0.0375613	−	0.164567i	0.00153088	−	0.00670724i
$603$		0			0
$604$	−24.1353	+	30.2647i	−0.982052	+	1.23145i
$605$	−5.53354	−	24.2440i	−0.224970	−	0.985659i
$606$		0			0
$607$	−3.54000	+	4.43901i	−0.143684	+	0.180174i	−0.848466	−	0.529250i	$-0.822473\pi$
$607$	−3.54000	+	4.43901i	−0.143684	+	0.180174i	0.704782	+	0.709424i	$0.251045\pi$
$608$	7.47505			0.303153
$609$		0			0
$610$	−2.31734			−0.0938262
$611$	−13.9428	+	17.4838i	−0.564067	+	0.707317i
$612$		0			0
$613$	9.97427	+	43.7001i	0.402857	+	1.76503i	0.615735	+	0.787953i	$0.288859\pi$
$613$	9.97427	+	43.7001i	0.402857	+	1.76503i	−0.212878	+	0.977079i	$0.568284\pi$
$614$	−2.65395	+	3.32794i	−0.107105	+	0.134305i
$615$		0			0
$616$	2.53219	−	11.0942i	0.102025	−	0.447000i
$617$	−26.1672	−	12.6015i	−1.05345	−	0.507316i	−0.174714	−	0.984619i	$-0.555900\pi$
$617$	−26.1672	−	12.6015i	−1.05345	−	0.507316i	−0.878739	+	0.477303i	$0.841614\pi$
$618$		0			0
$619$	1.69406	+	7.42218i	0.0680901	+	0.298322i	0.997495	−	0.0707399i	$-0.0225360\pi$
$619$	1.69406	+	7.42218i	0.0680901	+	0.298322i	−0.929405	+	0.369062i	$0.879679\pi$
$620$	−27.6845	+	13.3321i	−1.11183	+	0.535431i
$621$		0			0
$622$	4.98625	−	2.40125i	0.199930	−	0.0962813i
$623$	−33.0715	−	41.4704i	−1.32498	−	1.66148i
$624$		0			0
$625$	10.6143	−	5.11157i	0.424571	−	0.204463i
$626$	3.72753			0.148982
$627$		0			0
$628$	−1.14535	−	5.01811i	−0.0457045	−	0.200244i
$629$	−17.5148	−	8.43467i	−0.698359	−	0.336312i
$630$		0			0
$631$	−9.73830	+	42.6663i	−0.387676	+	1.69852i	0.284957	+	0.958540i	$0.408021\pi$
$631$	−9.73830	+	42.6663i	−0.387676	+	1.69852i	−0.672632	+	0.739977i	$0.734836\pi$
$632$	4.39757	+	5.51438i	0.174926	+	0.219350i
$633$		0			0
$634$	0.616705	+	2.70196i	0.0244925	+	0.107309i
$635$	−0.948264	+	4.15462i	−0.0376307	+	0.164871i
$636$		0			0
$637$	−34.3758			−1.36202
$638$	4.06512	−	0.168455i	0.160940	−	0.00666920i
$639$		0			0
$640$	11.7201	−	14.6966i	0.463279	−	0.580933i
$641$	3.41266	−	14.9519i	0.134792	−	0.590563i	−0.861740	−	0.507351i	$-0.830625\pi$
$641$	3.41266	−	14.9519i	0.134792	−	0.590563i	0.996532	−	0.0832123i	$-0.0265180\pi$
$642$		0			0
$643$	17.0010	−	21.3185i	0.670453	−	0.840721i	−0.323984	−	0.946063i	$-0.605022\pi$
$643$	17.0010	−	21.3185i	0.670453	−	0.840721i	0.994436	+	0.105342i	$0.0335937\pi$
$644$	2.01988	+	2.53285i	0.0795943	+	0.0998082i
$645$		0			0
$646$	−1.76081	−	0.847962i	−0.0692782	−	0.0333626i
$647$	−21.7872	−	10.4921i	−0.856542	−	0.412489i	−0.0465402	−	0.998916i	$-0.514820\pi$
$647$	−21.7872	−	10.4921i	−0.856542	−	0.412489i	−0.810002	+	0.586428i	$0.800534\pi$
$648$		0			0
$649$	−23.3339	+	11.2370i	−0.915935	+	0.441091i
$650$	5.68313			0.222911
$651$		0			0
$652$	0.647837	+	0.812362i	0.0253713	+	0.0318146i
$653$	15.6696	+	19.6491i	0.613200	+	0.768929i	0.987370	−	0.158432i	$-0.0506437\pi$
$653$	15.6696	+	19.6491i	0.613200	+	0.768929i	−0.374170	+	0.927360i	$0.622072\pi$
$654$		0			0
$655$	13.7907			0.538846
$656$	−6.77185	+	3.26115i	−0.264396	+	0.127327i
$657$		0			0
$658$	−2.91615	−	1.40434i	−0.113683	−	0.0547471i
$659$	8.69220	+	4.18594i	0.338600	+	0.163061i	0.595455	−	0.803389i	$-0.296972\pi$
$659$	8.69220	+	4.18594i	0.338600	+	0.163061i	−0.256855	+	0.966450i	$0.582686\pi$
$660$		0			0
$661$	9.84536	+	12.3457i	0.382940	+	0.480192i	0.935523	−	0.353266i	$-0.114929\pi$
$661$	9.84536	+	12.3457i	0.382940	+	0.480192i	−0.552583	+	0.833458i	$0.686358\pi$
$662$	2.14839	−	2.69400i	0.0834996	−	0.104705i
$663$		0			0
$664$	−1.10997	+	4.86309i	−0.0430751	+	0.188724i
$665$	29.3416	−	36.7932i	1.13782	−	1.42678i
$666$		0			0
$667$	−1.37903	+	1.88431i	−0.0533962	+	0.0729607i
$668$	−29.6260			−1.14627
$669$		0			0
$670$	−0.716303	+	3.13833i	−0.0276732	+	0.121244i
$671$	−3.60002	−	15.7727i	−0.138977	−	0.608898i
$672$		0			0
$673$	−10.1812	−	12.7668i	−0.392456	−	0.492124i	0.545873	−	0.837868i	$-0.316198\pi$
$673$	−10.1812	−	12.7668i	−0.392456	−	0.492124i	−0.938329	+	0.345744i	$0.887627\pi$
$674$	0.795060	−	3.48338i	0.0306246	−	0.134175i
$675$		0			0
$676$	15.1800	+	7.31031i	0.583846	+	0.281166i
$677$	2.52618	+	11.0679i	0.0970889	+	0.425374i	0.999990	−	0.00447406i	$-0.00142414\pi$
$677$	2.52618	+	11.0679i	0.0970889	+	0.425374i	−0.902901	+	0.429848i	$0.858567\pi$
$678$		0			0
$679$	54.3566			2.08602
$680$	−6.71328	+	3.23295i	−0.257443	+	0.123978i
$681$		0			0
$682$	2.13028	+	2.67128i	0.0815725	+	0.102289i
$683$	18.9882	−	9.14425i	0.726565	−	0.349895i	−0.0337673	−	0.999430i	$-0.510750\pi$
$683$	18.9882	−	9.14425i	0.726565	−	0.349895i	0.760332	+	0.649535i	$0.225036\pi$
$684$		0			0
$685$	51.7874	−	24.9395i	1.97870	−	0.952890i
$686$	−0.0603583	−	0.264447i	−0.00230449	−	0.0100966i
$687$		0			0
$688$	0.862863	+	0.415533i	0.0328963	+	0.0158420i
$689$	−11.3335	+	49.6552i	−0.431771	+	1.89171i
$690$		0			0
$691$	3.48847	−	4.37440i	0.132708	−	0.166410i	−0.711038	−	0.703154i	$-0.751774\pi$
$691$	3.48847	−	4.37440i	0.132708	−	0.166410i	0.843745	+	0.536744i	$0.180346\pi$
$692$	−0.0452227	−	0.198134i	−0.00171911	−	0.00753191i
$693$		0			0
$694$	0.0870367	−	0.109141i	0.00330387	−	0.00414292i
$695$	28.5470			1.08285
$696$		0			0
$697$	6.05592			0.229384
$698$	−2.31202	+	2.89918i	−0.0875113	+	0.109736i
$699$		0			0
$700$	−11.4922	−	50.3504i	−0.434363	−	1.90307i
$701$	10.7892	−	13.5292i	0.407502	−	0.510991i	−0.535155	−	0.844754i	$-0.679747\pi$
$701$	10.7892	−	13.5292i	0.407502	−	0.510991i	0.942657	+	0.333762i	$0.108318\pi$
$702$		0			0
$703$	5.05886	−	22.1643i	0.190798	−	0.835942i
$704$	27.8984	+	13.4352i	1.05146	+	0.506357i
$705$		0			0
$706$	1.42196	+	6.23002i	0.0535162	+	0.234470i
$707$	−2.79172	+	1.34442i	−0.104994	+	0.0505623i
$708$		0			0
$709$	−16.8452	+	8.11221i	−0.632634	+	0.304660i	−0.722581	−	0.691286i	$-0.757044\pi$
$709$	−16.8452	+	8.11221i	−0.632634	+	0.304660i	0.0899473	+	0.995947i	$0.471330\pi$
$710$	−2.22383	−	2.78860i	−0.0834589	−	0.104654i
$711$		0			0
$712$	−8.84897	+	4.26144i	−0.331629	+	0.159704i
$713$	−1.96089			−0.0734357
$714$		0			0
$715$	15.2151	+	66.6616i	0.569011	+	2.49300i
$716$	7.18195	+	3.45865i	0.268402	+	0.129256i
$717$		0			0
$718$	−0.733788	+	3.21494i	−0.0273847	+	0.119980i
$719$	10.7768	+	13.5137i	0.401908	+	0.503977i	0.941064	−	0.338229i	$-0.109828\pi$
$719$	10.7768	+	13.5137i	0.401908	+	0.503977i	−0.539156	+	0.842206i	$0.681257\pi$
$720$		0			0
$721$	−4.18705	−	18.3447i	−0.155934	−	0.683192i
$722$	−0.240063	+	1.05179i	−0.00893424	+	0.0391434i
$723$		0			0
$724$	22.6832			0.843015
$725$	32.8404	−	17.5257i	1.21966	−	0.650890i
$726$		0			0
$727$	1.79057	−	2.24531i	0.0664086	−	0.0832738i	−0.747518	−	0.664242i	$-0.768754\pi$
$727$	1.79057	−	2.24531i	0.0664086	−	0.0832738i	0.813926	+	0.580968i	$0.197326\pi$
$728$	−2.75556	+	12.0729i	−0.102128	+	0.447451i
$729$		0			0
$730$	4.01988	−	5.04077i	0.148783	−	0.186567i
$731$	−0.481109	−	0.603292i	−0.0177945	−	0.0223135i
$732$		0			0
$733$	−42.1829	−	20.3142i	−1.55806	−	0.750323i	−0.561065	−	0.827771i	$-0.689608\pi$
$733$	−42.1829	−	20.3142i	−1.55806	−	0.750323i	−0.996996	+	0.0774484i	$0.975323\pi$
$734$	2.57368	+	1.23942i	0.0949963	+	0.0457478i
$735$		0			0
$736$	0.812825	−	0.391436i	0.0299611	−	0.0144285i
$737$	−22.4735			−0.827821
$738$		0			0
$739$	15.6343	+	19.6048i	0.575116	+	0.721173i	0.981271	−	0.192631i	$-0.0617021\pi$
$739$	15.6343	+	19.6048i	0.575116	+	0.721173i	−0.406155	+	0.913804i	$0.633131\pi$
$740$	−26.8076	−	33.6157i	−0.985468	−	1.23574i
$741$		0			0
$742$	−7.37175			−0.270626
$743$	25.3667	−	12.2160i	0.930616	−	0.448161i	0.0937664	−	0.995594i	$-0.470109\pi$
$743$	25.3667	−	12.2160i	0.930616	−	0.448161i	0.836849	+	0.547433i	$0.184395\pi$
$744$		0			0
$745$	−29.1947	−	14.0594i	−1.06961	−	0.515098i
$746$	0.181221	+	0.0872714i	0.00663497	+	0.00319523i
$747$		0			0
$748$	−16.0888	−	20.1747i	−0.588265	−	0.737662i
$749$	−27.2970	+	34.2294i	−0.997412	+	1.25071i
$750$		0			0
$751$	9.07997	−	39.7820i	0.331333	−	1.45166i	−0.485219	−	0.874393i	$-0.661260\pi$
$751$	9.07997	−	39.7820i	0.331333	−	1.45166i	0.816552	−	0.577272i	$-0.195883\pi$
$752$	11.4497	−	14.3574i	0.417526	−	0.523561i
$753$		0			0
$754$	−4.42371	+	0.183315i	−0.161102	+	0.00667593i
$755$	67.8664			2.46991
$756$		0			0
$757$	−9.07919	+	39.7785i	−0.329989	+	1.44578i	0.489160	+	0.872194i	$0.337303\pi$
$757$	−9.07919	+	39.7785i	−0.329989	+	1.44578i	−0.819149	+	0.573581i	$0.805554\pi$
$758$	1.19182	+	5.22172i	0.0432890	+	0.189662i
$759$		0			0
$760$	−5.43302	−	6.81280i	−0.197076	−	0.247126i
$761$	−9.26200	+	40.5795i	−0.335747	+	1.47100i	0.472064	+	0.881564i	$0.343509\pi$
$761$	−9.26200	+	40.5795i	−0.335747	+	1.47100i	−0.807812	+	0.589441i	$0.799348\pi$
$762$		0			0
$763$	29.5679	+	14.2391i	1.07043	+	0.515492i
$764$	−0.683128	−	2.99298i	−0.0247147	−	0.108282i
$765$		0			0
$766$	−3.11288			−0.112473
$767$	25.3922	−	12.2282i	0.916859	−	0.441536i
$768$		0			0
$769$	−5.80053	−	7.27364i	−0.209173	−	0.262294i	0.666167	−	0.745802i	$-0.267934\pi$
$769$	−5.80053	−	7.27364i	−0.209173	−	0.262294i	−0.875340	+	0.483508i	$0.839362\pi$
$770$	−8.91644	+	4.29393i	−0.321326	+	0.154743i
$771$		0			0
$772$	23.7275	−	11.4266i	0.853971	−	0.411251i
$773$	3.20648	+	14.0485i	0.115329	+	0.505289i	0.999288	+	0.0377251i	$0.0120111\pi$
$773$	3.20648	+	14.0485i	0.115329	+	0.505289i	−0.883959	+	0.467564i	$0.845132\pi$
$774$		0			0
$775$	28.1642	+	13.5631i	1.01169	+	0.487202i
$776$	2.23966	−	9.81257i	0.0803989	−	0.352251i
$777$		0			0
$778$	4.25539	−	5.33610i	0.152563	−	0.191308i
$779$	1.57593	+	6.90461i	0.0564636	+	0.247383i
$780$		0			0
$781$	15.5255	−	19.4684i	0.555547	−	0.696634i
$782$	−0.235872			−0.00843476
$783$		0			0
$784$	28.2289			1.00818
$785$	−5.62637	+	7.05525i	−0.200814	+	0.251813i
$786$		0			0
$787$	−6.90993	−	30.2744i	−0.246312	−	1.07916i	−0.935151	−	0.354250i	$-0.884736\pi$
$787$	−6.90993	−	30.2744i	−0.246312	−	1.07916i	0.688839	−	0.724915i	$-0.258121\pi$
$788$	−15.6812	+	19.6636i	−0.558620	+	0.700487i
$789$		0			0
$790$	1.36493	−	5.98016i	0.0485621	−	0.212765i
$791$	−25.9376	−	12.4909i	−0.922236	−	0.444125i
$792$		0			0
$793$	3.91758	+	17.1640i	0.139117	+	0.609513i
$794$	−3.36211	+	1.61911i	−0.119317	+	0.0574599i
$795$		0			0
$796$	15.6476	−	7.53548i	0.554614	−	0.267088i
$797$	20.8826	+	26.1860i	0.739700	+	0.927555i	0.999271	−	0.0381694i	$-0.0121527\pi$
$797$	20.8826	+	26.1860i	0.739700	+	0.927555i	−0.259571	+	0.965724i	$0.583581\pi$
$798$		0			0
$799$	−13.3308	+	6.41976i	−0.471608	+	0.227115i
$800$	−14.3821			−0.508484
$801$		0			0
$802$	1.36824	+	5.99467i	0.0483144	+	0.211679i
$803$	40.5544	+	19.5300i	1.43113	+	0.689198i
$804$		0			0
$805$	1.26386	−	5.53732i	0.0445452	−	0.195165i
$806$	−2.31819	−	2.90692i	−0.0816548	−	0.102392i
$807$		0			0
$808$	0.127671	+	0.559362i	0.00449144	+	0.0196783i
$809$	3.99369	−	17.4975i	0.140411	−	0.615180i	−0.854929	−	0.518746i	$-0.826399\pi$
$809$	3.99369	−	17.4975i	0.140411	−	0.615180i	0.995339	−	0.0964341i	$-0.0307437\pi$
$810$		0			0
$811$	6.11810			0.214836			0.107418	−	0.994214i	$-0.465742\pi$
$811$	6.11810			0.214836			0.107418	+	0.994214i	$0.465742\pi$
$812$	10.5695	+	38.8218i	0.370917	+	1.36238i
$813$		0			0
$814$	−2.98084	+	3.73785i	−0.104478	+	0.131012i
$815$	0.405358	−	1.77599i	0.0141991	−	0.0622102i
$816$		0			0
$817$	0.562640	−	0.705528i	0.0196843	−	0.0246833i
$818$	0.346076	+	0.433966i	0.0121003	+	0.0151733i
$819$		0			0
$820$	12.0677	+	5.81149i	0.421422	+	0.202946i
$821$	−34.7342	−	16.7271i	−1.21223	−	0.583780i	−0.285094	−	0.958500i	$-0.592025\pi$
$821$	−34.7342	−	16.7271i	−1.21223	−	0.583780i	−0.927138	+	0.374719i	$0.877739\pi$
$822$		0			0
$823$	13.5341	−	6.51769i	0.471770	−	0.227192i	−0.182864	−	0.983138i	$-0.558537\pi$
$823$	13.5341	−	6.51769i	0.471770	−	0.227192i	0.654634	+	0.755946i	$0.272823\pi$
$824$	−3.48414			−0.121376
$825$		0			0
$826$	2.54331	+	3.18921i	0.0884930	+	0.110967i
$827$	−10.9633	−	13.7476i	−0.381232	−	0.478050i	0.553782	−	0.832662i	$-0.313184\pi$
$827$	−10.9633	−	13.7476i	−0.381232	−	0.478050i	−0.935013	+	0.354612i	$0.884613\pi$
$828$		0			0
$829$	−27.9182			−0.969640			−0.484820	−	0.874614i	$-0.661115\pi$
$829$	−27.9182			−0.969640			−0.484820	+	0.874614i	$0.661115\pi$
$830$	3.90847	−	1.88222i	0.135665	−	0.0653327i
$831$		0			0
$832$	−30.3594	−	14.6203i	−1.05252	−	0.506868i
$833$	−20.4921	−	9.86848i	−0.710009	−	0.341922i
$834$		0			0
$835$	32.3843	+	40.6086i	1.12070	+	1.40532i
$836$	18.8153	−	23.5936i	0.650741	−	0.816003i
$837$		0			0
$838$	0.342133	−	1.49898i	0.0118188	−	0.0517815i
$839$	13.8407	−	17.3556i	0.477832	−	0.599183i	−0.483237	−	0.875489i	$-0.660539\pi$
$839$	13.8407	−	17.3556i	0.477832	−	0.599183i	0.961070	+	0.276307i	$0.0891105\pi$
$840$		0			0
$841$	−24.9975	+	14.7012i	−0.861982	+	0.506939i
$842$	−5.02585			−0.173202
$843$		0			0
$844$	−6.58122	+	28.8342i	−0.226535	+	0.992515i
$845$	−6.57302	−	28.7983i	−0.226119	−	0.990691i
$846$		0			0
$847$	−17.0490	−	21.3787i	−0.585810	−	0.734582i
$848$	9.30688	−	40.7761i	0.319600	−	1.40026i
$849$		0			0
$850$	3.38782	+	1.63149i	0.116201	+	0.0559596i
$851$	−0.610556	−	2.67502i	−0.0209296	−	0.0916986i
$852$		0			0
$853$	26.4548			0.905794			0.452897	−	0.891563i	$-0.350391\pi$
$853$	26.4548			0.905794			0.452897	+	0.891563i	$0.350391\pi$
$854$	−2.29581	+	1.10560i	−0.0785610	+	0.0378330i
$855$		0			0
$856$	5.05444	+	6.33807i	0.172757	+	0.216631i
$857$	−41.3020	+	19.8900i	−1.41085	+	0.679429i	−0.975330	−	0.220750i	$-0.929149\pi$
$857$	−41.3020	+	19.8900i	−1.41085	+	0.679429i	−0.435519	+	0.900180i	$0.643435\pi$
$858$		0			0
$859$	−7.47303	+	3.59882i	−0.254977	+	0.122790i	−0.557006	−	0.830508i	$-0.688050\pi$
$859$	−7.47303	+	3.59882i	−0.254977	+	0.122790i	0.302030	+	0.953299i	$0.402336\pi$
$860$	−0.379769	−	1.66388i	−0.0129500	−	0.0567377i
$861$		0			0
$862$	−0.0131380	−	0.00632691i	−0.000447481	−	0.000215495i
$863$	−1.72339	+	7.55067i	−0.0586649	+	0.257028i	−0.995753	−	0.0920653i	$-0.970653\pi$
$863$	−1.72339	+	7.55067i	−0.0586649	+	0.257028i	0.937088	+	0.349093i	$0.113510\pi$
$864$		0			0
$865$	−0.222150	+	0.278568i	−0.00755333	+	0.00947158i
$866$	0.0498242	+	0.218294i	0.00169309	+	0.00741793i
$867$		0			0
$868$	−21.0665	+	26.4166i	−0.715044	+	0.896636i
$869$	42.8238			1.45270
$870$		0			0
$871$	24.4559			0.828657
$872$	3.78877	−	4.75096i	0.128304	−	0.160888i
$873$		0			0
$874$	−0.0613810	−	0.268928i	−0.00207624	−	0.00909662i
$875$	−15.6184	+	19.5849i	−0.527999	+	0.662090i
$876$		0			0
$877$	−8.29427	+	36.3396i	−0.280078	+	1.22710i	0.617616	+	0.786480i	$0.288099\pi$
$877$	−8.29427	+	36.3396i	−0.280078	+	1.22710i	−0.897694	+	0.440620i	$0.854759\pi$
$878$	4.65476	+	2.24161i	0.157090	+	0.0756508i
$879$		0			0
$880$	−12.4944	−	54.7415i	−0.421186	−	1.84534i
$881$	−13.7290	+	6.61153i	−0.462542	+	0.222748i	−0.650617	−	0.759406i	$-0.725489\pi$
$881$	−13.7290	+	6.61153i	−0.462542	+	0.222748i	0.188075	+	0.982155i	$0.439775\pi$
$882$		0			0
$883$	43.8849	−	21.1338i	1.47684	−	0.711210i	0.489826	−	0.871820i	$-0.337060\pi$
$883$	43.8849	−	21.1338i	1.47684	−	0.711210i	0.987018	+	0.160610i	$0.0513461\pi$
$884$	17.5080	+	21.9544i	0.588859	+	0.738406i
$885$		0			0
$886$	2.91899	−	1.40571i	0.0980653	−	0.0472258i
$887$	8.21801			0.275934			0.137967	−	0.990437i	$-0.455943\pi$
$887$	8.21801			0.275934			0.137967	+	0.990437i	$0.455943\pi$
$888$		0			0
$889$	1.04272	+	4.56844i	0.0349716	+	0.153220i
$890$	7.69573	+	3.70607i	0.257961	+	0.124228i
$891$		0			0
$892$	10.4897	−	45.9585i	0.351222	−	1.53881i
$893$	−10.7885	−	13.5284i	−0.361024	−	0.452709i
$894$		0			0
$895$	−3.10982	−	13.6250i	−0.103950	−	0.455434i
$896$	4.59950	−	20.1517i	0.153658	−	0.673222i
$897$		0			0
$898$	−1.88462			−0.0628906
$899$	−22.3603	−	9.64900i	−0.745757	−	0.321812i
$900$		0			0
$901$	−21.0109	+	26.3468i	−0.699975	+	0.877741i
$902$	0.331410	−	1.45200i	0.0110347	−	0.0483463i
$903$		0			0
$904$	−3.32359	+	4.16765i	−0.110541	+	0.138614i
$905$	−24.7951	−	31.0921i	−0.824217	−	1.03354i
$906$		0			0
$907$	3.78527	+	1.82289i	0.125688	+	0.0605280i	0.495671	−	0.868510i	$-0.334922\pi$
$907$	3.78527	+	1.82289i	0.125688	+	0.0605280i	−0.369983	+	0.929038i	$0.620637\pi$
$908$	9.14958	+	4.40621i	0.303640	+	0.146225i
$909$		0			0
$910$	9.70298	−	4.67271i	0.321651	−	0.154899i
$911$	13.0361			0.431906			0.215953	−	0.976404i	$-0.430714\pi$
$911$	13.0361			0.431906			0.215953	+	0.976404i	$0.430714\pi$
$912$		0			0
$913$	18.8830	+	23.6785i	0.624935	+	0.783644i
$914$	−3.33446	−	4.18127i	−0.110294	−	0.138304i
$915$		0			0
$916$	15.9494			0.526982
$917$	13.6626	−	6.57954i	0.451177	−	0.217275i
$918$		0			0
$919$	−1.94603	−	0.937160i	−0.0641937	−	0.0309141i	0.401511	−	0.915854i	$-0.368485\pi$
$919$	−1.94603	−	0.937160i	−0.0641937	−	0.0309141i	−0.465705	+	0.884940i	$0.654199\pi$
$920$	−0.947535	−	0.456309i	−0.0312393	−	0.0150441i
$921$		0			0
$922$	−4.02522	−	5.04747i	−0.132564	−	0.166230i
$923$	−16.8951	+	21.1857i	−0.556108	+	0.697337i
$924$		0			0
$925$	−9.73331	+	42.6444i	−0.320029	+	1.40214i
$926$	−2.00844	+	2.51851i	−0.0660015	+	0.0827632i
$927$		0			0
$928$	11.1949	−	0.463908i	0.367491	−	0.0152285i
$929$	−5.52224			−0.181179			−0.0905894	−	0.995888i	$-0.528875\pi$
$929$	−5.52224			−0.181179			−0.0905894	+	0.995888i	$0.528875\pi$
$930$		0			0
$931$	5.91881	−	25.9320i	0.193981	−	0.849887i
$932$	−10.7393	−	47.0520i	−0.351778	−	1.54124i
$933$		0			0
$934$	1.09441	+	1.37235i	0.0358103	+	0.0449047i
$935$	−10.0669	+	44.1061i	−0.329224	+	1.44242i
$936$		0			0
$937$	−50.2070	−	24.1784i	−1.64019	−	0.789874i	−0.999761	−	0.0218560i	$-0.993042\pi$
$937$	−50.2070	−	24.1784i	−1.64019	−	0.789874i	−0.640429	−	0.768018i	$-0.721243\pi$
$938$	0.787650	+	3.45092i	0.0257177	+	0.112677i
$939$		0			0
$940$	−32.7250			−1.06737
$941$	47.5433	−	22.8957i	1.54987	−	0.746377i	0.553608	−	0.832778i	$-0.313251\pi$
$941$	47.5433	−	22.8957i	1.54987	−	0.746377i	0.996260	+	0.0864004i	$0.0275364\pi$
$942$		0			0
$943$	0.532929	+	0.668272i	0.0173546	+	0.0217619i
$944$	−20.8517	+	10.0417i	−0.678666	+	0.326828i
$945$		0			0
$946$	−0.170977	+	0.0823383i	−0.00555895	+	0.00267705i
$947$	9.42788	+	41.3062i	0.306365	+	1.34227i	0.860332	+	0.509734i	$0.170256\pi$
$947$	9.42788	+	41.3062i	0.306365	+	1.34227i	−0.553967	+	0.832539i	$0.686887\pi$
$948$		0			0
$949$	−44.1318	−	21.2528i	−1.43258	−	0.689894i
$950$	−0.978518	+	4.28717i	−0.0317473	+	0.139094i
$951$		0			0
$952$	−5.10848	+	6.40583i	−0.165567	+	0.207614i
$953$	0.319167	+	1.39836i	0.0103388	+	0.0452974i	0.979834	−	0.199812i	$-0.0640332\pi$
$953$	0.319167	+	1.39836i	0.0103388	+	0.0452974i	−0.969495	+	0.245110i	$0.921176\pi$
$954$		0			0
$955$	−3.35577	+	4.20801i	−0.108590	+	0.136168i
$956$	−55.0055			−1.77900
$957$		0			0
$958$	7.56626			0.244455
$959$	39.4077	−	49.4156i	1.27254	−	1.59571i
$960$		0			0
$961$	2.34732	+	10.2843i	0.0757201	+	0.331751i
$962$	3.24378	−	4.06758i	0.104584	−	0.131144i
$963$		0			0
$964$	1.73840	−	7.61643i	0.0559901	−	0.245309i
$965$	−41.5990	−	20.0330i	−1.33912	−	0.644887i
$966$		0			0
$967$	2.31872	+	10.1590i	0.0745650	+	0.326691i	0.998429	−	0.0560300i	$-0.0178443\pi$
$967$	2.31872	+	10.1590i	0.0745650	+	0.326691i	−0.923864	+	0.382721i	$0.874987\pi$
$968$	−4.56180	+	2.19685i	−0.146622	+	0.0706094i
$969$		0			0
$970$	−7.88637	+	3.79787i	−0.253216	+	0.121942i
$971$	24.6053	+	30.8541i	0.789623	+	0.990155i	0.999922	+	0.0125184i	$0.00398483\pi$
$971$	24.6053	+	30.8541i	0.789623	+	0.990155i	−0.210299	+	0.977637i	$0.567444\pi$
$972$		0			0
$973$	28.2818	−	13.6198i	0.906673	−	0.436631i
$974$	4.50408			0.144320
$975$		0			0
$976$	−3.21706	−	14.0949i	−0.102976	−	0.451166i
$977$	6.58708	+	3.17217i	0.210739	+	0.101487i	0.536276	−	0.844043i	$-0.319831\pi$
$977$	6.58708	+	3.17217i	0.210739	+	0.101487i	−0.325537	+	0.945529i	$0.605545\pi$
$978$		0			0
$979$	−13.2695	+	58.1375i	−0.424096	+	1.85808i
$980$	−31.3646	−	39.3300i	−1.00191	−	1.25635i
$981$		0			0
$982$	−1.23809	−	5.42441i	−0.0395089	−	0.173100i
$983$	−8.71704	+	38.1918i	−0.278030	+	1.21813i	0.622250	+	0.782819i	$0.286219\pi$
$983$	−8.71704	+	38.1918i	−0.278030	+	1.21813i	−0.900280	+	0.435311i	$0.856638\pi$
$984$		0			0
$985$	44.0942			1.40496
$986$	−2.68969	−	1.16066i	−0.0856570	−	0.0369631i
$987$		0			0
$988$	−20.4750	+	25.6749i	−0.651398	+	0.816827i
$989$	0.0242351	−	0.106181i	0.000770632	−	0.00337636i
$990$		0			0
$991$	−29.8332	+	37.4097i	−0.947684	+	1.18836i	0.0343035	+	0.999411i	$0.489079\pi$
$991$	−29.8332	+	37.4097i	−0.947684	+	1.18836i	−0.981987	+	0.188947i	$0.939493\pi$
$992$	5.86657	+	7.35644i	0.186264	+	0.233567i
$993$		0			0
$994$	−3.53361	−	1.70170i	−0.112079	−	0.0539746i
$995$	−27.4334	−	13.2112i	−0.869696	−	0.418824i
$996$		0			0
$997$	−46.2944	+	22.2942i	−1.46616	+	0.706064i	−0.985316	−	0.170743i	$-0.945383\pi$
$997$	−46.2944	+	22.2942i	−1.46616	+	0.706064i	−0.480842	+	0.876807i	$0.659669\pi$
$998$	1.23005			0.0389367
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.k.c.226.2		18
3.2	odd	2		87.2.g.a.52.2	✓	18
29.13	even	14		7569.2.a.bm.1.5		9
29.16	even	7		7569.2.a.bj.1.5		9
29.24	even	7	inner	261.2.k.c.82.2		18
87.53	odd	14		87.2.g.a.82.2	yes	18
87.71	odd	14		2523.2.a.o.1.5		9
87.74	odd	14		2523.2.a.r.1.5		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.g.a.52.2	✓	18	3.2	odd	2
87.2.g.a.82.2	yes	18	87.53	odd	14
261.2.k.c.82.2		18	29.24	even	7	inner
261.2.k.c.226.2		18	1.1	even	1	trivial
2523.2.a.o.1.5		9	87.71	odd	14
2523.2.a.r.1.5		9	87.74	odd	14
7569.2.a.bj.1.5		9	29.16	even	7
7569.2.a.bm.1.5		9	29.13	even	14

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.110403 + 0.138441i) q^{2} +(0.438065 + 1.91929i) q^{4} +(2.15193 - 2.69844i) q^{5} +(0.844514 - 3.70006i) q^{7} +(-0.633146 - 0.304907i) q^{8} +O(q^{10})\)	\(q+(-0.110403 + 0.138441i) q^{2} +(0.438065 + 1.91929i) q^{4} +(2.15193 - 2.69844i) q^{5} +(0.844514 - 3.70006i) q^{7} +(-0.633146 - 0.304907i) q^{8} +(0.135995 + 0.595831i) q^{10} +(-3.84419 + 1.85126i) q^{11} +(4.18329 - 2.01457i) q^{13} +(0.419003 + 0.525413i) q^{14} +(-3.43526 + 1.65434i) q^{16} +3.07208 q^{17} +(0.799448 + 3.50261i) q^{19} +(6.12176 + 2.94808i) q^{20} +(0.168119 - 0.736579i) q^{22} +(0.270347 + 0.339005i) q^{23} +(-1.53815 - 6.73907i) q^{25} +(-0.182949 + 0.801554i) q^{26} +7.47142 q^{28} +(1.41466 + 5.19603i) q^{29} +(-2.81961 + 3.53568i) q^{31} +(0.462984 - 2.02846i) q^{32} +(-0.339167 + 0.425302i) q^{34} +(-8.16704 - 10.2411i) q^{35} +(-5.70128 - 2.74559i) q^{37} +(-0.573166 - 0.276022i) q^{38} +(-2.18526 + 1.05236i) q^{40} +1.97128 q^{41} +(-0.156607 - 0.196379i) q^{43} +(-5.23711 - 6.56713i) q^{44} -0.0767793 q^{46} +(-4.33933 + 2.08971i) q^{47} +(-6.67044 - 3.21231i) q^{49} +(1.10278 + 0.531070i) q^{50} +(5.69909 + 7.14643i) q^{52} +(-6.83931 + 8.57623i) q^{53} +(-3.27691 + 14.3571i) q^{55} +(-1.66287 + 2.08518i) q^{56} +(-0.875526 - 0.377811i) q^{58} +6.06991 q^{59} +(-0.843741 + 3.69667i) q^{61} +(-0.178190 - 0.780699i) q^{62} +(-4.52484 - 5.67398i) q^{64} +(3.56598 - 15.6236i) q^{65} +(4.74553 + 2.28533i) q^{67} +(1.34577 + 5.89620i) q^{68} +2.31946 q^{70} +(-5.25813 + 2.53218i) q^{71} +(-6.57753 - 8.24796i) q^{73} +(1.00954 - 0.486169i) q^{74} +(-6.37230 + 3.06874i) q^{76} +(3.60331 + 15.7871i) q^{77} +(-9.04273 - 4.35475i) q^{79} +(-2.92833 + 12.8299i) q^{80} +(-0.217635 + 0.272906i) q^{82} +(-1.57949 - 6.92019i) q^{83} +(6.61090 - 8.28981i) q^{85} +0.0444768 q^{86} +2.99840 q^{88} +(8.71402 - 10.9270i) q^{89} +(-3.92117 - 17.1798i) q^{91} +(-0.532218 + 0.667380i) q^{92} +(0.189773 - 0.831452i) q^{94} +(11.1719 + 5.38012i) q^{95} +(3.18704 + 13.9633i) q^{97} +(1.18115 - 0.568813i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{2} - 6 q^{4} + q^{5} - 4 q^{7} + 15 q^{8}+O(q^{10}) \) 18 * q + 4 * q^2 - 6 * q^4 + q^5 - 4 * q^7 + 15 * q^8	\( 18 q + 4 q^{2} - 6 q^{4} + q^{5} - 4 q^{7} + 15 q^{8} - 14 q^{10} - 26 q^{11} + 9 q^{13} + 10 q^{14} - 14 q^{16} - 4 q^{17} - 10 q^{19} + q^{20} - 8 q^{22} + 8 q^{23} + 16 q^{25} - 5 q^{26} + 80 q^{28} - 8 q^{29} - 12 q^{31} - 9 q^{32} - 22 q^{34} - 9 q^{35} - 16 q^{37} + 32 q^{38} + 33 q^{40} - 24 q^{41} - 31 q^{43} + 52 q^{44} - 44 q^{46} - 5 q^{47} - 47 q^{49} + 7 q^{50} + 80 q^{52} - 5 q^{53} - 17 q^{55} - 45 q^{56} + 54 q^{58} + 32 q^{59} - 28 q^{61} - 69 q^{62} - 75 q^{64} - 22 q^{65} + 6 q^{67} - 38 q^{68} - 12 q^{70} - 46 q^{71} - q^{73} + 35 q^{74} - 45 q^{76} + 36 q^{77} - 15 q^{79} + 86 q^{80} + 47 q^{82} + 16 q^{83} + 19 q^{85} - 116 q^{86} + 54 q^{88} + 72 q^{89} - 47 q^{91} + 121 q^{92} - 22 q^{94} + 72 q^{95} + 43 q^{97} - 31 q^{98}+O(q^{100}) \) 18 * q + 4 * q^2 - 6 * q^4 + q^5 - 4 * q^7 + 15 * q^8 - 14 * q^10 - 26 * q^11 + 9 * q^13 + 10 * q^14 - 14 * q^16 - 4 * q^17 - 10 * q^19 + q^20 - 8 * q^22 + 8 * q^23 + 16 * q^25 - 5 * q^26 + 80 * q^28 - 8 * q^29 - 12 * q^31 - 9 * q^32 - 22 * q^34 - 9 * q^35 - 16 * q^37 + 32 * q^38 + 33 * q^40 - 24 * q^41 - 31 * q^43 + 52 * q^44 - 44 * q^46 - 5 * q^47 - 47 * q^49 + 7 * q^50 + 80 * q^52 - 5 * q^53 - 17 * q^55 - 45 * q^56 + 54 * q^58 + 32 * q^59 - 28 * q^61 - 69 * q^62 - 75 * q^64 - 22 * q^65 + 6 * q^67 - 38 * q^68 - 12 * q^70 - 46 * q^71 - q^73 + 35 * q^74 - 45 * q^76 + 36 * q^77 - 15 * q^79 + 86 * q^80 + 47 * q^82 + 16 * q^83 + 19 * q^85 - 116 * q^86 + 54 * q^88 + 72 * q^89 - 47 * q^91 + 121 * q^92 - 22 * q^94 + 72 * q^95 + 43 * q^97 - 31 * q^98

Introduction

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