LMFDB - Embedded newform 261.2.k.c.199.2

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			199.2
Root			$1.03105 + 0.496527i$ of defining polynomial
Character	$\chi$	$=$	261.199
Dual form			261.2.k.c.181.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0321271 + 0.140758i) q^{2} +(1.78316 + 0.858723i) q^{4} +(0.345850 - 1.51527i) q^{5} +(1.37625 - 0.662766i) q^{7} +(-0.358196 + 0.449164i) q^{8} +O(q^{10})$	\(q+(-0.0321271 + 0.140758i) q^{2} +(1.78316 + 0.858723i) q^{4} +(0.345850 - 1.51527i) q^{5} +(1.37625 - 0.662766i) q^{7} +(-0.358196 + 0.449164i) q^{8} +(0.202175 + 0.0973624i) q^{10} +(0.478737 + 0.600317i) q^{11} +(-1.63237 - 2.04693i) q^{13} +(0.0490748 + 0.215011i) q^{14} +(2.41625 + 3.02988i) q^{16} +3.51434 q^{17} +(-4.72829 - 2.27702i) q^{19} +(1.91790 - 2.40497i) q^{20} +(-0.0998798 + 0.0480996i) q^{22} +(1.89083 + 8.28425i) q^{23} +(2.32842 + 1.12131i) q^{25} +(0.340565 - 0.164008i) q^{26} +3.02320 q^{28} +(-3.40207 - 4.17443i) q^{29} +(0.315006 - 1.38013i) q^{31} +(-1.53932 + 0.741300i) q^{32} +(-0.112906 + 0.494672i) q^{34} +(-0.528293 - 2.31460i) q^{35} +(-1.87409 + 2.35004i) q^{37} +(0.472416 - 0.592391i) q^{38} +(0.556722 + 0.698107i) q^{40} -5.79055 q^{41} +(-0.955986 - 4.18845i) q^{43} +(0.338157 + 1.48156i) q^{44} -1.22682 q^{46} +(-1.10631 - 1.38727i) q^{47} +(-2.90963 + 3.64856i) q^{49} +(-0.232638 + 0.291719i) q^{50} +(-1.15303 - 5.05176i) q^{52} +(1.50686 - 6.60199i) q^{53} +(1.07521 - 0.517795i) q^{55} +(-0.195276 + 0.855561i) q^{56} +(0.696884 - 0.344757i) q^{58} -14.9605 q^{59} +(-12.3585 + 5.95153i) q^{61} +(0.184144 + 0.0886793i) q^{62} +(1.66981 + 7.31591i) q^{64} +(-3.66621 + 1.76555i) q^{65} +(-4.54833 + 5.70342i) q^{67} +(6.26662 + 3.01785i) q^{68} +0.342772 q^{70} +(2.99945 + 3.76119i) q^{71} +(-2.04705 - 8.96872i) q^{73} +(-0.270578 - 0.339294i) q^{74} +(-6.47595 - 8.12058i) q^{76} +(1.05673 + 0.508894i) q^{77} +(0.340352 - 0.426788i) q^{79} +(5.42674 - 2.61338i) q^{80} +(0.186034 - 0.815067i) q^{82} +(10.4943 + 5.05376i) q^{83} +(1.21543 - 5.32517i) q^{85} +0.620271 q^{86} -0.441122 q^{88} +(3.06588 - 13.4325i) q^{89} +(-3.60319 - 1.73520i) q^{91} +(-3.74224 + 16.3958i) q^{92} +(0.230813 - 0.111154i) q^{94} +(-5.08558 + 6.37712i) q^{95} +(1.60034 + 0.770683i) q^{97} +(-0.420086 - 0.526771i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{4}{7}\right)$	$1$

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 $

$2$	−0.0321271	+	0.140758i	−0.0227173	+	0.0995310i	−0.985016	−	0.172465i	$-0.944827\pi$
$2$	−0.0321271	+	0.140758i	−0.0227173	+	0.0995310i	0.962298	+	0.271996i	$0.0876839\pi$
$3$		0			0
$3$		0			0
$4$	1.78316	+	0.858723i	0.891579	+	0.429362i
$5$	0.345850	−	1.51527i	0.154669	−	0.677649i	−0.836822	−	0.547475i	$-0.815589\pi$
$5$	0.345850	−	1.51527i	0.154669	−	0.677649i	0.991491	−	0.130174i	$-0.0415536\pi$
$6$		0			0
$7$	1.37625	−	0.662766i	0.520173	−	0.250502i	−0.155326	−	0.987863i	$-0.549643\pi$
$7$	1.37625	−	0.662766i	0.520173	−	0.250502i	0.675499	+	0.737361i	$0.263928\pi$
$8$	−0.358196	+	0.449164i	−0.126641	+	0.158803i
$9$		0			0
$10$	0.202175	+	0.0973624i	0.0639334	+	0.0307887i
$11$	0.478737	+	0.600317i	0.144345	+	0.181002i	0.848748	−	0.528797i	$-0.177357\pi$
$11$	0.478737	+	0.600317i	0.144345	+	0.181002i	−0.704404	+	0.709800i	$0.748785\pi$
$12$		0			0
$13$	−1.63237	−	2.04693i	−0.452739	−	0.567716i	0.502112	−	0.864803i	$-0.332557\pi$
$13$	−1.63237	−	2.04693i	−0.452739	−	0.567716i	−0.954851	+	0.297086i	$0.903985\pi$
$14$	0.0490748	+	0.215011i	0.0131158	+	0.0574641i
$15$		0			0
$16$	2.41625	+	3.02988i	0.604063	+	0.757471i
$17$	3.51434			0.852353			0.426176	−	0.904640i	$-0.359860\pi$
$17$	3.51434			0.852353			0.426176	+	0.904640i	$0.359860\pi$
$18$		0			0
$19$	−4.72829	−	2.27702i	−1.08474	−	0.522385i	−0.195913	−	0.980621i	$-0.562767\pi$
$19$	−4.72829	−	2.27702i	−1.08474	−	0.522385i	−0.888831	+	0.458236i	$0.848481\pi$
$20$	1.91790	−	2.40497i	0.428856	−	0.537768i
$21$		0			0
$22$	−0.0998798	+	0.0480996i	−0.0212945	+	0.0102549i
$23$	1.89083	+	8.28425i	0.394264	+	1.72739i	0.649371	+	0.760472i	$0.275032\pi$
$23$	1.89083	+	8.28425i	0.394264	+	1.72739i	−0.255106	+	0.966913i	$0.582110\pi$
$24$		0			0
$25$	2.32842	+	1.12131i	0.465684	+	0.224261i
$26$	0.340565	−	0.164008i	0.0667904	−	0.0321645i
$27$		0			0
$28$	3.02320			0.571331
$29$	−3.40207	−	4.17443i	−0.631749	−	0.775173i
$29$	−3.40207	−	4.17443i	−0.631749	−	0.775173i
$30$		0			0
$31$	0.315006	−	1.38013i	0.0565768	−	0.247879i	−0.938729	−	0.344655i	$-0.887996\pi$
$31$	0.315006	−	1.38013i	0.0565768	−	0.247879i	0.995306	+	0.0967760i	$0.0308531\pi$
$32$	−1.53932	+	0.741300i	−0.272117	+	0.131044i
$33$		0			0
$34$	−0.112906	+	0.494672i	−0.0193631	+	0.0848355i
$35$	−0.528293	−	2.31460i	−0.0892978	−	0.391239i
$36$		0			0
$37$	−1.87409	+	2.35004i	−0.308099	+	0.386344i	−0.911641	−	0.410987i	$-0.865184\pi$
$37$	−1.87409	+	2.35004i	−0.308099	+	0.386344i	0.603542	+	0.797331i	$0.293756\pi$
$38$	0.472416	−	0.592391i	0.0766360	−	0.0960984i
$39$		0			0
$40$	0.556722	+	0.698107i	0.0880254	+	0.110380i
$41$	−5.79055			−0.904332			−0.452166	−	0.891934i	$-0.649349\pi$
$41$	−5.79055			−0.904332			−0.452166	+	0.891934i	$0.649349\pi$
$42$		0			0
$43$	−0.955986	−	4.18845i	−0.145787	−	0.638733i	−0.994028	−	0.109123i	$-0.965196\pi$
$43$	−0.955986	−	4.18845i	−0.145787	−	0.638733i	0.848242	−	0.529609i	$-0.177661\pi$
$44$	0.338157	+	1.48156i	0.0509790	+	0.223354i
$45$		0			0
$46$	−1.22682			−0.180885
$47$	−1.10631	−	1.38727i	−0.161372	−	0.202355i	0.694571	−	0.719424i	$-0.255594\pi$
$47$	−1.10631	−	1.38727i	−0.161372	−	0.202355i	−0.855943	+	0.517070i	$0.827023\pi$
$48$		0			0
$49$	−2.90963	+	3.64856i	−0.415661	+	0.521223i
$50$	−0.232638	+	0.291719i	−0.0329000	+	0.0412553i
$51$		0			0
$52$	−1.15303	−	5.05176i	−0.159897	−	0.700552i
$53$	1.50686	−	6.60199i	0.206983	−	0.906853i	−0.759578	−	0.650417i	$-0.774594\pi$
$53$	1.50686	−	6.60199i	0.206983	−	0.906853i	0.966561	−	0.256437i	$-0.0825485\pi$
$54$		0			0
$55$	1.07521	−	0.517795i	0.144982	−	0.0698194i
$56$	−0.195276	+	0.855561i	−0.0260949	+	0.114329i
$57$		0			0
$58$	0.696884	−	0.344757i	0.0915054	−	0.0452688i
$59$	−14.9605			−1.94769			−0.973845	−	0.227213i	$-0.927039\pi$
$59$	−14.9605			−1.94769			−0.973845	+	0.227213i	$0.927039\pi$
$60$		0			0
$61$	−12.3585	+	5.95153i	−1.58234	+	0.762016i	−0.998748	−	0.0500301i	$-0.984068\pi$
$61$	−12.3585	+	5.95153i	−1.58234	+	0.762016i	−0.583594	+	0.812046i	$0.698354\pi$
$62$	0.184144	+	0.0886793i	0.0233864	+	0.0112623i
$63$		0			0
$64$	1.66981	+	7.31591i	0.208726	+	0.914489i
$65$	−3.66621	+	1.76555i	−0.454737	+	0.218990i
$66$		0			0
$67$	−4.54833	+	5.70342i	−0.555666	+	0.696784i	−0.977750	−	0.209773i	$-0.932727\pi$
$67$	−4.54833	+	5.70342i	−0.555666	+	0.696784i	0.422084	+	0.906557i	$0.361299\pi$
$68$	6.26662	+	3.01785i	0.759939	+	0.365968i
$69$		0			0
$70$	0.342772			0.0409690
$71$	2.99945	+	3.76119i	0.355969	+	0.446371i	0.927283	−	0.374360i	$-0.122138\pi$
$71$	2.99945	+	3.76119i	0.355969	+	0.446371i	−0.571314	+	0.820731i	$0.693566\pi$
$72$		0			0
$73$	−2.04705	−	8.96872i	−0.239589	−	1.04971i	−0.941386	−	0.337332i	$-0.890476\pi$
$73$	−2.04705	−	8.96872i	−0.239589	−	1.04971i	0.701796	−	0.712378i	$-0.252382\pi$
$74$	−0.270578	−	0.339294i	−0.0314540	−	0.0394421i
$75$		0			0
$76$	−6.47595	−	8.12058i	−0.742842	−	0.931495i
$77$	1.05673	+	0.508894i	0.120426	+	0.0579939i
$78$		0			0
$79$	0.340352	−	0.426788i	0.0382926	−	0.0480174i	−0.762316	−	0.647204i	$-0.775938\pi$
$79$	0.340352	−	0.426788i	0.0382926	−	0.0480174i	0.800609	+	0.599187i	$0.204509\pi$
$80$	5.42674	−	2.61338i	0.606728	−	0.292185i
$81$		0			0
$82$	0.186034	−	0.815067i	0.0205440	−	0.0900090i
$83$	10.4943	+	5.05376i	1.15189	+	0.554723i	0.909602	−	0.415481i	$-0.136387\pi$
$83$	10.4943	+	5.05376i	1.15189	+	0.554723i	0.242292	+	0.970203i	$0.422101\pi$
$84$		0			0
$85$	1.21543	−	5.32517i	0.131832	−	0.577596i
$86$	0.620271			0.0668856
$87$		0			0
$88$	−0.441122			−0.0470238
$89$	3.06588	−	13.4325i	0.324982	−	1.42384i	−0.503583	−	0.863947i	$-0.667985\pi$
$89$	3.06588	−	13.4325i	0.324982	−	1.42384i	0.828565	−	0.559893i	$-0.189158\pi$
$90$		0			0
$91$	−3.60319	−	1.73520i	−0.377717	−	0.181899i
$92$	−3.74224	+	16.3958i	−0.390155	+	1.70938i
$93$		0			0
$94$	0.230813	−	0.111154i	0.0238065	−	0.0114646i
$95$	−5.08558	+	6.37712i	−0.521770	+	0.654278i
$96$		0			0
$97$	1.60034	+	0.770683i	0.162490	+	0.0782510i	0.513361	−	0.858173i	$-0.328400\pi$
$97$	1.60034	+	0.770683i	0.162490	+	0.0782510i	−0.350871	+	0.936424i	$0.614114\pi$
$98$	−0.420086	−	0.526771i	−0.0424351	−	0.0532119i
$99$		0			0
$100$	3.18904	+	3.99893i	0.318904	+	0.399893i
$101$	−0.993780	−	4.35404i	−0.0988848	−	0.433243i	0.901115	−	0.433580i	$-0.142750\pi$
$101$	−0.993780	−	4.35404i	−0.0988848	−	0.433243i	−1.00000		0.000337172i	$0.999893\pi$
$102$		0			0
$103$	6.43434	+	8.06841i	0.633995	+	0.795004i	0.990238	−	0.139389i	$-0.0445139\pi$
$103$	6.43434	+	8.06841i	0.633995	+	0.795004i	−0.356243	+	0.934393i	$0.615942\pi$
$104$	1.50412			0.147491
$105$		0			0
$106$	0.880873	+	0.424206i	0.0855579	+	0.0412025i
$107$	9.78294	−	12.2674i	0.945753	−	1.18594i	−0.0366812	−	0.999327i	$-0.511679\pi$
$107$	9.78294	−	12.2674i	0.945753	−	1.18594i	0.982434	−	0.186610i	$-0.0597500\pi$
$108$		0			0
$109$	8.86268	−	4.26804i	0.848891	−	0.408804i	0.0417249	−	0.999129i	$-0.486715\pi$
$109$	8.86268	−	4.26804i	0.848891	−	0.408804i	0.807166	+	0.590325i	$0.201000\pi$
$110$	0.0383403	+	0.167980i	0.00365561	+	0.0160163i
$111$		0			0
$112$	5.33346	+	2.56846i	0.503965	+	0.242697i
$113$	−11.4046	+	5.49216i	−1.07285	+	0.516659i	−0.885026	−	0.465542i	$-0.845859\pi$
$113$	−11.4046	+	5.49216i	−1.07285	+	0.516659i	−0.187829	+	0.982202i	$0.560145\pi$
$114$		0			0
$115$	13.2068			1.23154
$116$	−2.48175	−	10.3651i	−0.230424	−	0.962376i
$117$		0			0
$118$	0.480637	−	2.10581i	0.0442463	−	0.193856i
$119$	4.83661	−	2.32919i	0.443371	−	0.213516i
$120$		0			0
$121$	2.31654	−	10.1494i	0.210594	−	0.922675i
$122$	−0.440684	−	1.93076i	−0.0398976	−	0.174803i
$123$		0			0
$124$	1.74686	−	2.19049i	0.156872	−	0.196712i
$125$	7.34962	−	9.21613i	0.657370	−	0.824316i
$126$		0			0
$127$	12.0574	+	15.1195i	1.06992	+	1.34164i	0.936534	+	0.350578i	$0.114015\pi$
$127$	12.0574	+	15.1195i	1.06992	+	1.34164i	0.133390	+	0.991064i	$0.457414\pi$
$128$	−4.50046			−0.397788
$129$		0			0
$130$	−0.130731	−	0.572770i	−0.0114659	−	0.0502353i
$131$	3.74018	+	16.3868i	0.326781	+	1.43172i	0.825227	+	0.564801i	$0.191047\pi$
$131$	3.74018	+	16.3868i	0.326781	+	1.43172i	−0.498446	+	0.866921i	$0.666096\pi$
$132$		0			0
$133$	−8.01644			−0.695113
$134$	−0.656678	−	0.823448i	−0.0567283	−	0.0711351i
$135$		0			0
$136$	−1.25882	+	1.57851i	−0.107943	+	0.135357i
$137$	−11.3794	+	14.2693i	−0.972210	+	1.21911i	0.00348811	+	0.999994i	$0.498890\pi$
$137$	−11.3794	+	14.2693i	−0.972210	+	1.21911i	−0.975698	+	0.219119i	$0.929682\pi$
$138$		0			0
$139$	1.52781	+	6.69377i	0.129587	+	0.567758i	0.997476	+	0.0710004i	$0.0226192\pi$
$139$	1.52781	+	6.69377i	0.129587	+	0.567758i	−0.867889	+	0.496758i	$0.834524\pi$
$140$	1.04557	−	4.58096i	0.0883671	−	0.387162i
$141$		0			0
$142$	−0.625781	+	0.301360i	−0.0525144	+	0.0252896i
$143$	0.447330	−	1.95988i	0.0374076	−	0.163893i
$144$		0			0
$145$	−7.50199	+	3.71132i	−0.623007	+	0.308209i
$146$	1.32819			0.109921
$147$		0			0
$148$	−5.35983	+	2.58116i	−0.440576	+	0.212170i
$149$	−1.64542	−	0.792394i	−0.134798	−	0.0649154i	0.365269	−	0.930902i	$-0.380977\pi$
$149$	−1.64542	−	0.792394i	−0.134798	−	0.0649154i	−0.500067	+	0.865987i	$0.666691\pi$
$150$		0			0
$151$	−1.46012	−	6.39722i	−0.118823	−	0.520599i	−0.998948	−	0.0458562i	$-0.985398\pi$
$151$	−1.46012	−	6.39722i	−0.118823	−	0.520599i	0.880125	−	0.474742i	$-0.157459\pi$
$152$	2.71641	−	1.30816i	0.220330	−	0.106105i
$153$		0			0
$154$	−0.105581	+	0.132394i	−0.00850793	+	0.0106686i
$155$	−1.98232	−	0.954637i	−0.159224	−	0.0766783i
$156$		0			0
$157$	20.8825			1.66661			0.833304	−	0.552815i	$-0.186447\pi$
$157$	20.8825			1.66661			0.833304	+	0.552815i	$0.186447\pi$
$158$	0.0491393	+	0.0616187i	0.00390931	+	0.00490212i
$159$		0			0
$160$	0.590892	+	2.58887i	0.0467141	+	0.204668i
$161$	8.09277	+	10.1480i	0.637799	+	0.799775i
$162$		0			0
$163$	−0.155754	−	0.195310i	−0.0121996	−	0.0152979i	0.775694	−	0.631109i	$-0.217400\pi$
$163$	−0.155754	−	0.195310i	−0.0121996	−	0.0152979i	−0.787894	+	0.615811i	$0.788828\pi$
$164$	−10.3255	−	4.97248i	−0.806283	−	0.388285i
$165$		0			0
$166$	−1.04851	+	1.31479i	−0.0813800	+	0.102047i
$167$	12.0865	−	5.82055i	0.935281	−	0.450408i	0.0967789	−	0.995306i	$-0.469146\pi$
$167$	12.0865	−	5.82055i	0.935281	−	0.450408i	0.838502	+	0.544898i	$0.183432\pi$
$168$		0			0
$169$	1.36749	−	5.99135i	0.105191	−	0.460873i
$170$	0.710512	+	0.342165i	0.0544938	+	0.0262428i
$171$		0			0
$172$	1.89204	−	8.28959i	0.144267	−	0.632075i
$173$	3.51856			0.267511			0.133755	−	0.991014i	$-0.457296\pi$
$173$	3.51856			0.267511			0.133755	+	0.991014i	$0.457296\pi$
$174$		0			0
$175$	3.94765			0.298414
$176$	−0.662141	+	2.90103i	−0.0499108	+	0.218673i
$177$		0			0
$178$	1.79223	+	0.863094i	0.134333	+	0.0646916i
$179$	−0.543093	+	2.37945i	−0.0405927	+	0.177848i	−0.991160	−	0.132669i	$-0.957645\pi$
$179$	−0.543093	+	2.37945i	−0.0405927	+	0.177848i	0.950568	+	0.310517i	$0.100502\pi$
$180$		0			0
$181$	0.583248	−	0.280877i	0.0433525	−	0.0208775i	−0.412082	−	0.911147i	$-0.635198\pi$
$181$	0.583248	−	0.280877i	0.0433525	−	0.0208775i	0.455434	+	0.890269i	$0.349484\pi$
$182$	0.360004	−	0.451431i	0.0266853	−	0.0334623i
$183$		0			0
$184$	−4.39827	−	2.11810i	−0.324245	−	0.156148i
$185$	2.91278	+	3.65251i	0.214152	+	0.268538i
$186$		0			0
$187$	1.68244	+	2.10972i	0.123032	+	0.154278i
$188$	−0.781447	−	3.42374i	−0.0569929	−	0.249702i
$189$		0			0
$190$	−0.734246	−	0.920715i	−0.0532678	−	0.0667957i
$191$	20.7888			1.50422			0.752112	−	0.659035i	$-0.229035\pi$
$191$	20.7888			1.50422			0.752112	+	0.659035i	$0.229035\pi$
$192$		0			0
$193$	−18.2385	−	8.78319i	−1.31284	−	0.632228i	−0.359219	−	0.933253i	$-0.616957\pi$
$193$	−18.2385	−	8.78319i	−1.31284	−	0.632228i	−0.953616	+	0.301025i	$0.902671\pi$
$194$	−0.159894	+	0.200501i	−0.0114797	+	0.0143951i
$195$		0			0
$196$	−8.32143	+	4.00739i	−0.594388	+	0.286242i
$197$	0.766446	+	3.35802i	0.0546070	+	0.239249i	0.994865	−	0.101215i	$-0.0322730\pi$
$197$	0.766446	+	3.35802i	0.0546070	+	0.239249i	−0.940258	+	0.340464i	$0.889416\pi$
$198$		0			0
$199$	−10.8360	−	5.21833i	−0.768142	−	0.369918i	0.00841481	−	0.999965i	$-0.497321\pi$
$199$	−10.8360	−	5.21833i	−0.768142	−	0.369918i	−0.776557	+	0.630047i	$0.783036\pi$
$200$	−1.33768	+	0.644194i	−0.0945884	+	0.0455514i
$201$		0			0
$202$	0.644793			0.0453675
$203$	−7.44877	−	3.49028i	−0.522801	−	0.244970i
$204$		0			0
$205$	−2.00266	+	8.77424i	−0.139872	+	0.612819i
$206$	−1.34241	+	0.646471i	−0.0935302	+	0.0450418i
$207$		0			0
$208$	2.25774	−	9.89179i	0.156546	−	0.685873i
$209$	−0.896669	−	3.92857i	−0.0620239	−	0.271745i
$210$		0			0
$211$	2.59412	−	3.25292i	0.178586	−	0.223940i	−0.684479	−	0.729033i	$-0.739970\pi$
$211$	2.59412	−	3.25292i	0.178586	−	0.223940i	0.863065	+	0.505092i	$0.168542\pi$
$212$	8.35626	−	10.4784i	0.573910	−	0.719660i
$213$		0			0
$214$	1.41244	+	1.77115i	0.0965525	+	0.121073i
$215$	−6.67725			−0.455385
$216$		0			0
$217$	−0.481178	−	2.10818i	−0.0326645	−	0.143113i
$218$	0.316029	+	1.38461i	0.0214042	+	0.0937778i
$219$		0			0
$220$	2.36191			0.159240
$221$	−5.73671	−	7.19361i	−0.385893	−	0.483895i
$222$		0			0
$223$	−2.93272	+	3.67751i	−0.196389	+	0.246264i	−0.870269	−	0.492577i	$-0.836055\pi$
$223$	−2.93272	+	3.67751i	−0.196389	+	0.246264i	0.673880	+	0.738841i	$0.264627\pi$
$224$	−1.62718	+	2.04042i	−0.108721	+	0.136332i
$225$		0			0
$226$	−0.406670	−	1.78174i	−0.0270513	−	0.118519i
$227$	−3.04552	+	13.3433i	−0.202138	+	0.885625i	0.767494	+	0.641056i	$0.221503\pi$
$227$	−3.04552	+	13.3433i	−0.202138	+	0.885625i	−0.969632	+	0.244568i	$0.921354\pi$
$228$		0			0
$229$	−18.1945	+	8.76201i	−1.20233	+	0.579010i	−0.924338	−	0.381575i	$-0.875382\pi$
$229$	−18.1945	+	8.76201i	−1.20233	+	0.579010i	−0.277988	+	0.960584i	$0.589668\pi$
$230$	−0.424296	+	1.85896i	−0.0279773	+	0.122576i
$231$		0			0
$232$	3.09361	−	0.0328216i	0.203106	−	0.00215484i
$233$	7.28500			0.477257			0.238628	−	0.971111i	$-0.423302\pi$
$233$	7.28500			0.477257			0.238628	+	0.971111i	$0.423302\pi$
$234$		0			0
$235$	−2.48471	+	1.19657i	−0.162085	+	0.0780559i
$236$	−26.6769	−	12.8469i	−1.73652	−	0.836263i
$237$		0			0
$238$	0.172466	+	0.755621i	0.0111793	+	0.0489796i
$239$	−21.0551	+	10.1396i	−1.36194	+	0.655878i	−0.965069	−	0.261995i	$-0.915619\pi$
$239$	−21.0551	+	10.1396i	−1.36194	+	0.655878i	−0.396875	+	0.917873i	$0.629905\pi$
$240$		0			0
$241$	15.8736	−	19.9049i	1.02251	−	1.28219i	0.0637504	−	0.997966i	$-0.479694\pi$
$241$	15.8736	−	19.9049i	1.02251	−	1.28219i	0.958759	−	0.284220i	$-0.0917347\pi$
$242$	1.35419	+	0.652143i	0.0870506	+	0.0419213i
$243$		0			0
$244$	−27.1478			−1.73796
$245$	4.52225	+	5.67072i	0.288916	+	0.362289i
$246$		0			0
$247$	3.05742	+	13.3954i	0.194539	+	0.852331i
$248$	0.507071	+	0.635847i	0.0321991	+	0.0403763i
$249$		0			0
$250$	1.06112	+	1.33061i	0.0671113	+	0.0841549i
$251$	−11.7619	−	5.66425i	−0.742406	−	0.357524i	0.0241437	−	0.999708i	$-0.492314\pi$
$251$	−11.7619	−	5.66425i	−0.742406	−	0.357524i	−0.766550	+	0.642184i	$0.778028\pi$
$252$		0			0
$253$	−4.06796	+	5.10107i	−0.255751	+	0.320701i
$254$	−2.51557	+	1.21143i	−0.157841	+	0.0760121i
$255$		0			0
$256$	−3.19503	+	13.9984i	−0.199690	+	0.874897i
$257$	1.23614	+	0.595293i	0.0771082	+	0.0371333i	0.472040	−	0.881577i	$-0.343518\pi$
$257$	1.23614	+	0.595293i	0.0771082	+	0.0371333i	−0.394932	+	0.918710i	$0.629232\pi$
$258$		0			0
$259$	−1.02169	+	4.47632i	−0.0634848	+	0.278145i
$260$	−8.05354			−0.499459
$261$		0			0
$262$	−2.42674			−0.149924
$263$	4.61815	−	20.2334i	0.284767	−	1.24765i	−0.606836	−	0.794827i	$-0.707561\pi$
$263$	4.61815	−	20.2334i	0.284767	−	1.24765i	0.891603	−	0.452819i	$-0.149582\pi$
$264$		0			0
$265$	−9.48264	−	4.56660i	−0.582514	−	0.280524i
$266$	0.257545	−	1.12838i	0.0157911	−	0.0691853i
$267$		0			0
$268$	−13.0080	+	6.26434i	−0.794592	+	0.382656i
$269$	−0.597581	+	0.749343i	−0.0364352	+	0.0456883i	−0.799715	−	0.600379i	$-0.795016\pi$
$269$	−0.597581	+	0.749343i	−0.0364352	+	0.0456883i	0.763280	+	0.646068i	$0.223588\pi$
$270$		0			0
$271$	19.0251	+	9.16200i	1.15569	+	0.556552i	0.910739	−	0.412983i	$-0.135513\pi$
$271$	19.0251	+	9.16200i	1.15569	+	0.556552i	0.244953	+	0.969535i	$0.421227\pi$
$272$	8.49153	+	10.6480i	0.514874	+	0.645632i
$273$		0			0
$274$	−1.64294	−	2.06018i	−0.0992535	−	0.124460i
$275$	0.441560	+	1.93460i	0.0266271	+	0.116661i
$276$		0			0
$277$	6.49558	+	8.14520i	0.390282	+	0.489398i	0.937693	−	0.347466i	$-0.112958\pi$
$277$	6.49558	+	8.14520i	0.390282	+	0.489398i	−0.547411	+	0.836864i	$0.684386\pi$
$278$	−0.991286			−0.0594534
$279$		0			0
$280$	1.22887	+	0.591792i	0.0734390	+	0.0353663i
$281$	−2.08541	+	2.61502i	−0.124405	+	0.155999i	−0.840133	−	0.542380i	$-0.817523\pi$
$281$	−2.08541	+	2.61502i	−0.124405	+	0.155999i	0.715728	+	0.698379i	$0.246095\pi$
$282$		0			0
$283$	14.2126	−	6.84442i	0.844850	−	0.406858i	0.0391866	−	0.999232i	$-0.487523\pi$
$283$	14.2126	−	6.84442i	0.844850	−	0.406858i	0.805663	+	0.592374i	$0.201809\pi$
$284$	2.11867	+	9.28249i	0.125720	+	0.550814i
$285$		0			0
$286$	0.261498	+	0.125931i	0.0154627	+	0.00744643i
$287$	−7.96923	+	3.83778i	−0.470409	+	0.226537i
$288$		0			0
$289$	−4.64941			−0.273495
$290$	−0.281381	−	1.17520i	−0.0165233	−	0.0690101i
$291$		0			0
$292$	4.05143	−	17.7505i	0.237092	−	1.03877i
$293$	−14.2429	+	6.85902i	−0.832079	+	0.400708i	−0.800894	−	0.598806i	$-0.795642\pi$
$293$	−14.2429	+	6.85902i	−0.832079	+	0.400708i	−0.0311843	+	0.999514i	$0.509928\pi$
$294$		0			0
$295$	−5.17409	+	22.6692i	−0.301247	+	1.31985i
$296$	−0.384259	−	1.68355i	−0.0223346	−	0.0978543i
$297$		0			0
$298$	0.164398	−	0.206149i	0.00952335	−	0.0119419i
$299$	13.8707	−	17.3934i	0.802166	−	1.00588i
$300$		0			0
$301$	−4.09164	−	5.13075i	−0.235838	−	0.295732i
$302$	0.947370			0.0545150
$303$		0			0
$304$	−4.52562	−	19.8280i	−0.259562	−	1.13721i
$305$	4.74398	+	20.7848i	0.271640	+	1.19013i
$306$		0			0
$307$	8.83474			0.504225			0.252113	−	0.967698i	$-0.418875\pi$
$307$	8.83474			0.504225			0.252113	+	0.967698i	$0.418875\pi$
$308$	1.44732	+	1.81488i	0.0824685	+	0.103412i
$309$		0			0
$310$	0.198059	−	0.248358i	0.0112490	−	0.0141058i
$311$	8.09774	−	10.1542i	0.459181	−	0.575795i	−0.497304	−	0.867576i	$-0.665677\pi$
$311$	8.09774	−	10.1542i	0.459181	−	0.575795i	0.956485	+	0.291782i	$0.0942481\pi$
$312$		0			0
$313$	−4.25967	−	18.6628i	−0.240771	−	1.05489i	−0.940317	−	0.340299i	$-0.889472\pi$
$313$	−4.25967	−	18.6628i	−0.240771	−	1.05489i	0.699546	−	0.714587i	$-0.253385\pi$
$314$	−0.670895	+	2.93938i	−0.0378608	+	0.165879i
$315$		0			0
$316$	0.973393	−	0.468762i	0.0547577	−	0.0263699i
$317$	5.92875	−	25.9755i	0.332992	−	1.45893i	−0.480315	−	0.877096i	$-0.659478\pi$
$317$	5.92875	−	25.9755i	0.332992	−	1.45893i	0.813307	−	0.581835i	$-0.197665\pi$
$318$		0			0
$319$	0.877286	−	4.04078i	0.0491186	−	0.226240i
$320$	11.6631			0.651986
$321$		0			0
$322$	−1.68841	+	0.813096i	−0.0940915	+	0.0453121i
$323$	−16.6168	−	8.00224i	−0.924584	−	0.445256i
$324$		0			0
$325$	−1.50561	−	6.59650i	−0.0835162	−	0.365908i
$326$	0.0324954	−	0.0156490i	0.00179975	−	0.000866715i
$327$		0			0
$328$	2.07415	−	2.60091i	0.114526	−	0.143611i
$329$	−2.44200	−	1.17601i	−0.134632	−	0.0648353i
$330$		0			0
$331$	−2.21519			−0.121758			−0.0608789	−	0.998145i	$-0.519390\pi$
$331$	−2.21519			−0.121758			−0.0608789	+	0.998145i	$0.519390\pi$
$332$	14.3731	+	18.0233i	0.788827	+	0.989158i
$333$		0			0
$334$	0.430985	+	1.88827i	0.0235825	+	0.103321i
$335$	7.06917	+	8.86446i	0.386230	+	0.484317i
$336$		0			0
$337$	4.99853	+	6.26796i	0.272288	+	0.341438i	0.899109	−	0.437725i	$-0.144216\pi$
$337$	4.99853	+	6.26796i	0.272288	+	0.341438i	−0.626821	+	0.779163i	$0.715644\pi$
$338$	0.799398	+	0.384970i	0.0434815	+	0.0209396i
$339$		0			0
$340$	6.74016	−	8.45189i	0.365536	−	0.458368i
$341$	0.979321	−	0.471616i	0.0530332	−	0.0255394i
$342$		0			0
$343$	−3.96557	+	17.3743i	−0.214120	+	0.938123i
$344$	2.22373	+	1.07089i	0.119896	+	0.0577386i
$345$		0			0
$346$	−0.113041	+	0.495265i	−0.00607713	+	0.0266256i
$347$	26.2715			1.41033			0.705165	−	0.709044i	$-0.250873\pi$
$347$	26.2715			1.41033			0.705165	+	0.709044i	$0.250873\pi$
$348$		0			0
$349$	−3.86308			−0.206786			−0.103393	−	0.994641i	$-0.532970\pi$
$349$	−3.86308			−0.206786			−0.103393	+	0.994641i	$0.532970\pi$
$350$	−0.126827	+	0.555663i	−0.00677916	+	0.0297015i
$351$		0			0
$352$	−1.18195	−	0.569195i	−0.0629979	−	0.0303382i
$353$	4.46526	−	19.5636i	0.237662	−	1.04126i	−0.705442	−	0.708767i	$-0.749252\pi$
$353$	4.46526	−	19.5636i	0.237662	−	1.04126i	0.943104	−	0.332497i	$-0.107891\pi$
$354$		0			0
$355$	6.73657	−	3.24416i	0.357540	−	0.172182i
$356$	17.0017	−	21.3195i	0.901089	−	1.12993i
$357$		0			0
$358$	−0.317478	−	0.152889i	−0.0167792	−	0.00808046i
$359$	13.2185	+	16.5755i	0.697645	+	0.874819i	0.996845	−	0.0793713i	$-0.0252913\pi$
$359$	13.2185	+	16.5755i	0.697645	+	0.874819i	−0.299200	+	0.954190i	$0.596720\pi$
$360$		0			0
$361$	5.32557	+	6.67806i	0.280293	+	0.351477i
$362$	0.0207977	+	0.0911206i	0.00109310	+	0.00478919i
$363$		0			0
$364$	−4.93499	−	6.18828i	−0.258664	−	0.324354i
$365$	−14.2980			−0.748391
$366$		0			0
$367$	17.6518	+	8.50065i	0.921416	+	0.443730i	0.833576	−	0.552404i	$-0.186289\pi$
$367$	17.6518	+	8.50065i	0.921416	+	0.443730i	0.0878394	+	0.996135i	$0.472004\pi$
$368$	−20.5316	+	25.7458i	−1.07028	+	1.34209i
$369$		0			0
$370$	−0.607700	+	0.292653i	−0.0315928	+	0.0152143i
$371$	−2.30176	−	10.0847i	−0.119502	−	0.523570i
$372$		0			0
$373$	−0.177910	−	0.0856769i	−0.00921182	−	0.00443618i	0.429272	−	0.903175i	$-0.358770\pi$
$373$	−0.177910	−	0.0856769i	−0.00921182	−	0.00443618i	−0.438484	+	0.898739i	$0.644484\pi$
$374$	−0.351012	+	0.169038i	−0.0181504	+	0.00874076i
$375$		0			0
$376$	1.01939			0.0525711
$377$	−2.99133	+	13.7780i	−0.154061	+	0.709605i
$378$		0			0
$379$	5.00474	−	21.9272i	0.257076	−	1.12632i	−0.667284	−	0.744804i	$-0.732543\pi$
$379$	5.00474	−	21.9272i	0.257076	−	1.12632i	0.924360	−	0.381521i	$-0.124600\pi$
$380$	−14.5446	+	7.00429i	−0.746121	+	0.359313i
$381$		0			0
$382$	−0.667884	+	2.92619i	−0.0341719	+	0.149717i
$383$	−0.134254	−	0.588207i	−0.00686008	−	0.0300560i	0.971382	−	0.237522i	$-0.0763353\pi$
$383$	−0.134254	−	0.588207i	−0.00686008	−	0.0300560i	−0.978242	+	0.207467i	$0.933478\pi$
$384$		0			0
$385$	1.13658	−	1.42523i	0.0579256	−	0.0726364i
$386$	1.82226	−	2.28504i	0.0927503	−	0.116305i
$387$		0			0
$388$	2.19185	+	2.74850i	0.111275	+	0.139534i
$389$	21.8263			1.10664			0.553318	−	0.832970i	$-0.313362\pi$
$389$	21.8263			1.10664			0.553318	+	0.832970i	$0.313362\pi$
$390$		0			0
$391$	6.64500	+	29.1137i	0.336052	+	1.47234i
$392$	−0.596583	−	2.61380i	−0.0301320	−	0.132017i
$393$		0			0
$394$	−0.497292			−0.0250532
$395$	−0.528987	−	0.663329i	−0.0266162	−	0.0333757i
$396$		0			0
$397$	9.00827	−	11.2960i	0.452112	−	0.566931i	−0.502578	−	0.864532i	$-0.667615\pi$
$397$	9.00827	−	11.2960i	0.452112	−	0.566931i	0.954690	+	0.297601i	$0.0961865\pi$
$398$	1.08265	−	1.35760i	0.0542684	−	0.0680504i
$399$		0			0
$400$	2.22861	+	9.76419i	0.111431	+	0.488210i
$401$	−5.86987	+	25.7176i	−0.293128	+	1.28428i	0.587019	+	0.809573i	$0.300301\pi$
$401$	−5.86987	+	25.7176i	−0.293128	+	1.28428i	−0.880146	+	0.474702i	$0.842556\pi$
$402$		0			0
$403$	−3.33924	+	1.60809i	−0.166339	+	0.0801049i
$404$	1.96685	−	8.61731i	0.0978542	−	0.428727i
$405$		0			0
$406$	0.730592	−	0.936342i	0.0362587	−	0.0464699i
$407$	−2.30796			−0.114402
$408$		0			0
$409$	28.0056	−	13.4868i	1.38479	−	0.666878i	0.414772	−	0.909925i	$-0.363861\pi$
$409$	28.0056	−	13.4868i	1.38479	−	0.666878i	0.970014	+	0.243048i	$0.0781471\pi$
$410$	−1.17070	−	0.563782i	−0.0578170	−	0.0278432i
$411$		0			0
$412$	4.54491	+	19.9126i	0.223912	+	0.981022i
$413$	−20.5894	+	9.91531i	−1.01314	+	0.487901i
$414$		0			0
$415$	11.2872	−	14.1538i	0.554069	−	0.694781i
$416$	4.03014	+	1.94081i	0.197594	+	0.0951562i
$417$		0			0
$418$	0.581785			0.0284560
$419$	−12.6866	−	15.9085i	−0.619782	−	0.777182i	0.368532	−	0.929615i	$-0.379861\pi$
$419$	−12.6866	−	15.9085i	−0.619782	−	0.777182i	−0.988314	+	0.152433i	$0.951289\pi$
$420$		0			0
$421$	1.89714	+	8.31193i	0.0924611	+	0.405099i	0.999886	−	0.0151163i	$-0.00481185\pi$
$421$	1.89714	+	8.31193i	0.0924611	+	0.405099i	−0.907425	+	0.420215i	$0.861955\pi$
$422$	0.374533	+	0.469650i	0.0182320	+	0.0228622i
$423$		0			0
$424$	2.42562	+	3.04164i	0.117799	+	0.147715i
$425$	8.18286	+	3.94066i	0.396927	+	0.191150i
$426$		0			0
$427$	−13.0639	+	16.3816i	−0.632205	+	0.792760i
$428$	27.9788	−	13.4739i	1.35241	−	0.651286i
$429$		0			0
$430$	0.214521	−	0.939877i	0.0103451	−	0.0453249i
$431$	−4.29075	−	2.06632i	−0.206678	−	0.0995309i	0.327681	−	0.944788i	$-0.393733\pi$
$431$	−4.29075	−	2.06632i	−0.206678	−	0.0995309i	−0.534359	+	0.845257i	$0.679447\pi$
$432$		0			0
$433$	−0.940217	+	4.11936i	−0.0451839	+	0.197964i	−0.992482	−	0.122389i	$-0.960944\pi$
$433$	−0.940217	+	4.11936i	−0.0451839	+	0.197964i	0.947298	+	0.320353i	$0.103802\pi$
$434$	0.312202			0.0149862
$435$		0			0
$436$	19.4686			0.932377
$437$	9.92306	−	43.4758i	0.474684	−	2.07973i
$438$		0			0
$439$	−24.6771	−	11.8839i	−1.17777	−	0.567186i	−0.260512	−	0.965471i	$-0.583891\pi$
$439$	−24.6771	−	11.8839i	−1.17777	−	0.567186i	−0.917262	+	0.398285i	$0.869606\pi$
$440$	−0.152562	+	0.668418i	−0.00727311	+	0.0318656i
$441$		0			0
$442$	1.19686	−	0.576379i	0.0569290	−	0.0274155i
$443$	−0.484554	+	0.607611i	−0.0230219	+	0.0288685i	−0.793209	−	0.608949i	$-0.791591\pi$
$443$	−0.484554	+	0.607611i	−0.0230219	+	0.0288685i	0.770187	+	0.637818i	$0.220163\pi$
$444$		0			0
$445$	−19.2935	−	9.29125i	−0.914598	−	0.440447i
$446$	−0.423420	−	0.530952i	−0.0200495	−	0.0251413i
$447$		0			0
$448$	7.14681	+	8.96182i	0.337655	+	0.423406i
$449$	−0.695827	−	3.04862i	−0.0328381	−	0.143873i	0.955851	−	0.293851i	$-0.0949369\pi$
$449$	−0.695827	−	3.04862i	−0.0328381	−	0.143873i	−0.988689	+	0.149978i	$0.952080\pi$
$450$		0			0
$451$	−2.77215	−	3.47616i	−0.130535	−	0.163686i
$452$	−25.0524			−1.17837
$453$		0			0
$454$	−1.78033	−	0.857362i	−0.0835551	−	0.0402380i
$455$	−3.87546	+	4.85967i	−0.181684	+	0.227825i
$456$		0			0
$457$	25.7939	−	12.4217i	1.20659	−	0.581061i	0.281039	−	0.959696i	$-0.409321\pi$
$457$	25.7939	−	12.4217i	1.20659	−	0.581061i	0.925546	+	0.378635i	$0.123607\pi$
$458$	−0.648787	−	2.84252i	−0.0303158	−	0.132822i
$459$		0			0
$460$	23.5498	+	11.3410i	1.09801	+	0.528776i
$461$	−25.1273	+	12.1007i	−1.17029	+	0.563584i	−0.915069	−	0.403297i	$-0.867864\pi$
$461$	−25.1273	+	12.1007i	−1.17029	+	0.563584i	−0.255226	+	0.966882i	$0.582150\pi$
$462$		0			0
$463$	−18.3196			−0.851382			−0.425691	−	0.904869i	$-0.639969\pi$
$463$	−18.3196			−0.851382			−0.425691	+	0.904869i	$0.639969\pi$
$464$	4.42778	−	20.3944i	0.205555	−	0.946784i
$465$		0			0
$466$	−0.234046	+	1.02542i	−0.0108420	+	0.0475018i
$467$	−19.7132	+	9.49337i	−0.912218	+	0.439301i	−0.830286	−	0.557337i	$-0.811823\pi$
$467$	−19.7132	+	9.49337i	−0.912218	+	0.439301i	−0.0819314	+	0.996638i	$0.526109\pi$
$468$		0			0
$469$	−2.47959	+	10.8638i	−0.114497	+	0.501644i
$470$	−0.0886008	−	0.388186i	−0.00408685	−	0.0179057i
$471$		0			0
$472$	5.35879	−	6.71971i	0.246658	−	0.309300i
$473$	2.05673	−	2.57906i	0.0945686	−	0.118585i
$474$		0			0
$475$	−8.45619	−	10.6037i	−0.387997	−	0.486533i
$476$	10.6246			0.486976
$477$		0			0
$478$	−0.750793	−	3.28944i	−0.0343405	−	0.150455i
$479$	5.21867	+	22.8645i	0.238447	+	1.04471i	0.942408	+	0.334467i	$0.108556\pi$
$479$	5.21867	+	22.8645i	0.238447	+	1.04471i	−0.703960	+	0.710239i	$0.748587\pi$
$480$		0			0
$481$	7.86958			0.358822
$482$	2.29180	+	2.87383i	0.104389	+	0.130899i
$483$		0			0
$484$	12.8463	−	16.1087i	0.583922	−	0.732216i
$485$	1.72127	−	2.15840i	0.0781588	−	0.0980081i
$486$		0			0
$487$	7.92727	+	34.7316i	0.359219	+	1.57384i	0.755145	+	0.655558i	$0.227567\pi$
$487$	7.92727	+	34.7316i	0.359219	+	1.57384i	−0.395926	+	0.918282i	$0.629576\pi$
$488$	1.75355	−	7.68280i	0.0793794	−	0.347784i
$489$		0			0
$490$	−0.943486	+	0.454359i	−0.0426224	+	0.0205259i
$491$	0.624505	−	2.73613i	0.0281835	−	0.123480i	−0.958879	−	0.283814i	$-0.908400\pi$
$491$	0.624505	−	2.73613i	0.0281835	−	0.123480i	0.987063	+	0.160334i	$0.0512572\pi$
$492$		0			0
$493$	−11.9560	−	14.6704i	−0.538473	−	0.660721i
$494$	−1.98374			−0.0892527
$495$		0			0
$496$	4.94277	−	2.38031i	0.221937	−	0.106879i
$497$	6.62078	+	3.18840i	0.296982	+	0.143019i
$498$		0			0
$499$	−9.04769	−	39.6405i	−0.405030	−	1.77455i	−0.606527	−	0.795063i	$-0.707438\pi$
$499$	−9.04769	−	39.6405i	−0.405030	−	1.77455i	0.201497	−	0.979489i	$-0.435420\pi$
$500$	21.0196	−	10.1225i	0.940026	−	0.452693i
$501$		0			0
$502$	1.17517	−	1.47361i	0.0524502	−	0.0657705i
$503$	−16.7015	−	8.04304i	−0.744685	−	0.358621i	0.0227560	−	0.999741i	$-0.492756\pi$
$503$	−16.7015	−	8.04304i	−0.744685	−	0.358621i	−0.767441	+	0.641120i	$0.778470\pi$
$504$		0			0
$505$	−6.94123			−0.308881
$506$	−0.587324	−	0.736481i	−0.0261097	−	0.0327406i
$507$		0			0
$508$	8.51679	+	37.3145i	0.377871	+	1.65556i
$509$	26.5311	+	33.2689i	1.17597	+	1.47462i	0.848053	+	0.529911i	$0.177775\pi$
$509$	26.5311	+	33.2689i	1.17597	+	1.47462i	0.327916	+	0.944707i	$0.393654\pi$
$510$		0			0
$511$	−8.76142	−	10.9865i	−0.387582	−	0.486013i
$512$	−9.97729	−	4.80481i	−0.440938	−	0.212345i
$513$		0			0
$514$	−0.123506	+	0.154871i	−0.00544761	+	0.00683108i
$515$	14.4511	−	6.95929i	0.636793	−	0.306663i
$516$		0			0
$517$	0.303171	−	1.32828i	0.0133334	−	0.0584176i
$518$	−0.597254	−	0.287623i	−0.0262419	−	0.0126374i
$519$		0			0
$520$	0.520199	−	2.27914i	0.0228122	−	0.0999469i
$521$	27.6372			1.21081			0.605404	−	0.795919i	$-0.293012\pi$
$521$	27.6372			1.21081			0.605404	+	0.795919i	$0.293012\pi$
$522$		0			0
$523$	−21.3122			−0.931919			−0.465959	−	0.884806i	$-0.654291\pi$
$523$	−21.3122			−0.931919			−0.465959	+	0.884806i	$0.654291\pi$
$524$	−7.40240	+	32.4320i	−0.323375	+	1.41680i
$525$		0			0
$526$	2.69965	+	1.30008i	0.117710	+	0.0566863i
$527$	1.10704	−	4.85025i	0.0482233	−	0.211280i
$528$		0			0
$529$	−44.3313	+	21.3488i	−1.92745	+	0.928209i
$530$	0.947436	−	1.18805i	0.0411540	−	0.0516054i
$531$		0			0
$532$	−14.2946	−	6.88390i	−0.619748	−	0.298455i
$533$	9.45234	+	11.8529i	0.409426	+	0.513404i
$534$		0			0
$535$	−15.2050	−	19.0665i	−0.657370	−	0.824316i
$536$	−0.932577	−	4.08589i	−0.0402812	−	0.176483i
$537$		0			0
$538$	−0.0862775	−	0.108189i	−0.00371969	−	0.00466434i
$539$	−3.58324			−0.154341
$540$		0			0
$541$	−19.9182	−	9.59210i	−0.856350	−	0.412397i	−0.0464196	−	0.998922i	$-0.514781\pi$
$541$	−19.9182	−	9.59210i	−0.856350	−	0.412397i	−0.809931	+	0.586525i	$0.800495\pi$
$542$	−1.90085	+	2.38359i	−0.0816484	+	0.102384i
$543$		0			0
$544$	−5.40971	+	2.60518i	−0.231939	+	0.111696i
$545$	−3.40207	−	14.9054i	−0.145729	−	0.638479i
$546$		0			0
$547$	−14.8690	−	7.16051i	−0.635751	−	0.306161i	0.0881066	−	0.996111i	$-0.471918\pi$
$547$	−14.8690	−	7.16051i	−0.635751	−	0.306161i	−0.723857	+	0.689950i	$0.757633\pi$
$548$	−32.5447	+	15.6727i	−1.39024	+	0.669505i
$549$		0			0
$550$	−0.286497			−0.0122163
$551$	6.58070	+	27.4845i	0.280347	+	1.17088i
$552$		0			0
$553$	0.185548	−	0.812940i	0.00789031	−	0.0345697i
$554$	−1.35519	+	0.652624i	−0.0575764	+	0.0277273i
$555$		0			0
$556$	−3.02377	+	13.2480i	−0.128236	+	0.561841i
$557$	1.21930	+	5.34211i	0.0516635	+	0.226353i	0.994168	−	0.107840i	$-0.0343935\pi$
$557$	1.21930	+	5.34211i	0.0516635	+	0.226353i	−0.942505	+	0.334193i	$0.891536\pi$
$558$		0			0
$559$	−7.01294	+	8.79395i	−0.296616	+	0.371944i
$560$	5.73649	−	7.19333i	0.242411	−	0.303974i
$561$		0			0
$562$	−0.301087	−	0.377551i	−0.0127006	−	0.0159260i
$563$	−13.7797			−0.580744			−0.290372	−	0.956914i	$-0.593779\pi$
$563$	−13.7797			−0.580744			−0.290372	+	0.956914i	$0.593779\pi$
$564$		0			0
$565$	4.37782	+	19.1805i	0.184176	+	0.806929i
$566$	0.506798	+	2.22043i	0.0213023	+	0.0933315i
$567$		0			0
$568$	−2.76378			−0.115966
$569$	−22.4007	−	28.0895i	−0.939085	−	1.17758i	−0.983925	−	0.178581i	$-0.942849\pi$
$569$	−22.4007	−	28.0895i	−0.939085	−	1.17758i	0.0448404	−	0.998994i	$-0.485722\pi$
$570$		0			0
$571$	−4.09271	+	5.13210i	−0.171275	+	0.214772i	−0.860059	−	0.510195i	$-0.829573\pi$
$571$	−4.09271	+	5.13210i	−0.171275	+	0.214772i	0.688784	+	0.724966i	$0.258145\pi$
$572$	2.48066	−	3.11064i	0.103721	−	0.130063i
$573$		0			0
$574$	−0.284170	−	1.24503i	−0.0118610	−	0.0519666i
$575$	−4.88656	+	21.4094i	−0.203783	+	0.892834i
$576$		0			0
$577$	7.26885	−	3.50050i	0.302606	−	0.145728i	−0.276419	−	0.961037i	$-0.589148\pi$
$577$	7.26885	−	3.50050i	0.302606	−	0.145728i	0.579025	+	0.815310i	$0.303433\pi$
$578$	0.149372	−	0.654442i	0.00621307	−	0.0272212i
$579$		0			0
$580$	−16.5642	+	0.175738i	−0.687792	+	0.00729710i
$581$	17.7922			0.738143
$582$		0			0
$583$	4.68468	−	2.25602i	0.194019	−	0.0934348i
$584$	4.76167	+	2.29310i	0.197039	+	0.0948892i
$585$		0			0
$586$	−0.507879	−	2.22516i	−0.0209803	−	0.0919206i
$587$	−7.25462	+	3.49364i	−0.299430	+	0.144198i	−0.577567	−	0.816344i	$-0.695998\pi$
$587$	−7.25462	+	3.49364i	−0.299430	+	0.144198i	0.278136	+	0.960542i	$0.410283\pi$
$588$		0			0
$589$	−4.63203	+	5.80838i	−0.190860	+	0.239330i
$590$	−3.02464	−	1.45659i	−0.124522	−	0.0599668i
$591$		0			0
$592$	−11.6486			−0.478755
$593$	−21.4831	−	26.9390i	−0.882206	−	1.10625i	−0.993654	−	0.112481i	$-0.964120\pi$
$593$	−21.4831	−	26.9390i	−0.882206	−	1.10625i	0.111448	−	0.993770i	$-0.464451\pi$
$594$		0			0
$595$	−1.85660	−	8.13430i	−0.0761132	−	0.333474i
$596$	−2.25360	−	2.82592i	−0.0923110	−	0.115754i
$597$		0			0
$598$	2.00263	+	2.51122i	0.0818936	+	0.102691i
$599$	−28.5373	−	13.7428i	−1.16600	−	0.561517i	−0.252199	−	0.967675i	$-0.581154\pi$
$599$	−28.5373	−	13.7428i	−1.16600	−	0.561517i	−0.913802	+	0.406159i	$0.866868\pi$
$600$		0			0
$601$	2.41007	−	3.02214i	0.0983089	−	0.123275i	−0.730244	−	0.683187i	$-0.760593\pi$
$601$	2.41007	−	3.02214i	0.0983089	−	0.123275i	0.828552	+	0.559911i	$0.189165\pi$
$602$	0.853647	−	0.411095i	0.0347921	−	0.0167550i
$603$		0			0
$604$	2.88981	−	12.6611i	0.117585	−	0.515173i
$605$	−14.5779	−	7.02036i	−0.592677	−	0.285418i
$606$		0			0
$607$	−0.295851	+	1.29621i	−0.0120082	+	0.0526115i	−0.980577	−	0.196134i	$-0.937161\pi$
$607$	−0.295851	+	1.29621i	−0.0120082	+	0.0526115i	0.968569	+	0.248746i	$0.0800183\pi$
$608$	8.96633			0.363633
$609$		0			0
$610$	−3.07803			−0.124626
$611$	−1.03374	+	4.52910i	−0.0418205	+	0.183228i
$612$		0			0
$613$	−2.72323	−	1.31144i	−0.109990	−	0.0529684i	0.378080	−	0.925773i	$-0.376585\pi$
$613$	−2.72323	−	1.31144i	−0.109990	−	0.0529684i	−0.488070	+	0.872805i	$0.662299\pi$
$614$	−0.283835	+	1.24356i	−0.0114546	+	0.0501860i
$615$		0			0
$616$	−0.607094	+	0.292361i	−0.0244605	+	0.0117796i
$617$	−1.20090	+	1.50588i	−0.0483464	+	0.0606244i	−0.805417	−	0.592709i	$-0.798058\pi$
$617$	−1.20090	+	1.50588i	−0.0483464	+	0.0606244i	0.757070	+	0.653333i	$0.226630\pi$
$618$		0			0
$619$	−0.266348	−	0.128266i	−0.0107054	−	0.00515546i	0.428523	−	0.903531i	$-0.359034\pi$
$619$	−0.266348	−	0.128266i	−0.0107054	−	0.00515546i	−0.439229	+	0.898375i	$0.644748\pi$
$620$	−2.71503	−	3.40454i	−0.109038	−	0.136729i
$621$		0			0
$622$	1.16914	+	1.46605i	0.0468781	+	0.0587832i
$623$	−4.68319	−	20.5184i	−0.187628	−	0.822052i
$624$		0			0
$625$	−3.36646	−	4.22141i	−0.134658	−	0.168856i
$626$	2.76380			0.110464
$627$		0			0
$628$	37.2368	+	17.9323i	1.48591	+	0.715577i
$629$	−6.58620	+	8.25883i	−0.262609	+	0.329301i
$630$		0			0
$631$	−29.7396	+	14.3219i	−1.18392	+	0.570144i	−0.919050	−	0.394141i	$-0.871042\pi$
$631$	−29.7396	+	14.3219i	−1.18392	+	0.570144i	−0.264867	+	0.964285i	$0.585328\pi$
$632$	0.0697849	+	0.305748i	0.00277589	+	0.0121620i
$633$		0			0
$634$	3.46579	+	1.66904i	0.137644	+	0.0662860i
$635$	27.0802	−	13.0411i	1.07465	−	0.517522i
$636$		0			0
$637$	12.2179			0.484093
$638$	0.540587	+	0.253303i	0.0214020	+	0.0100284i
$639$		0			0
$640$	−1.55649	+	6.81941i	−0.0615255	+	0.269561i
$641$	−19.3740	+	9.33001i	−0.765226	+	0.368513i	−0.775429	−	0.631435i	$-0.782466\pi$
$641$	−19.3740	+	9.33001i	−0.765226	+	0.368513i	0.0102034	+	0.999948i	$0.496752\pi$
$642$		0			0
$643$	3.70655	−	16.2394i	0.146172	−	0.640421i	−0.847756	−	0.530387i	$-0.822047\pi$
$643$	3.70655	−	16.2394i	0.146172	−	0.640421i	0.993928	−	0.110034i	$-0.0350961\pi$
$644$	5.71634	+	25.0449i	0.225255	+	0.986909i
$645$		0			0
$646$	1.66023	−	2.08186i	0.0653209	−	0.0819098i
$647$	0.400169	−	0.501796i	0.0157323	−	0.0197276i	−0.773903	−	0.633304i	$-0.781698\pi$
$647$	0.400169	−	0.501796i	0.0157323	−	0.0197276i	0.789635	+	0.613576i	$0.210270\pi$
$648$		0			0
$649$	−7.16213	−	8.98103i	−0.281138	−	0.352536i
$650$	0.976882			0.0383165
$651$		0			0
$652$	−0.110018	−	0.482018i	−0.00430862	−	0.0188773i
$653$	−9.30253	−	40.7570i	−0.364036	−	1.59495i	−0.742840	−	0.669469i	$-0.766522\pi$
$653$	−9.30253	−	40.7570i	−0.364036	−	1.59495i	0.378804	−	0.925477i	$-0.376336\pi$
$654$		0			0
$655$	26.1239			1.02075
$656$	−13.9914	−	17.5447i	−0.546273	−	0.685005i
$657$		0			0
$658$	0.243987	−	0.305950i	0.00951159	−	0.0119272i
$659$	3.91860	−	4.91377i	0.152647	−	0.191413i	−0.699628	−	0.714507i	$-0.746651\pi$
$659$	3.91860	−	4.91377i	0.152647	−	0.191413i	0.852275	+	0.523094i	$0.175222\pi$
$660$		0			0
$661$	4.51078	+	19.7630i	0.175449	+	0.768693i	0.983695	+	0.179847i	$0.0575603\pi$
$661$	4.51078	+	19.7630i	0.175449	+	0.768693i	−0.808245	+	0.588846i	$0.799583\pi$
$662$	0.0711676	−	0.311805i	0.00276601	−	0.0121187i
$663$		0			0
$664$	−6.02897	+	2.90340i	−0.233969	+	0.112674i
$665$	−2.77248	+	12.1470i	−0.107512	+	0.471042i
$666$		0			0
$667$	28.1493	−	36.0767i	1.08995	−	1.39690i
$668$	26.5504			1.02726
$669$		0			0
$670$	−1.47486	+	0.710253i	−0.0569787	+	0.0274395i
$671$	−9.48926	−	4.56979i	−0.366329	−	0.176415i
$672$		0			0
$673$	4.83575	+	21.1868i	0.186405	+	0.816692i	0.978492	+	0.206284i	$0.0661371\pi$
$673$	4.83575	+	21.1868i	0.186405	+	0.816692i	−0.792088	+	0.610407i	$0.791006\pi$
$674$	−1.04286	+	0.502213i	−0.0401693	+	0.0193445i
$675$		0			0
$676$	7.58336	−	9.50923i	0.291668	−	0.365740i
$677$	14.2342	+	6.85484i	0.547066	+	0.263453i	0.686937	−	0.726717i	$-0.258955\pi$
$677$	14.2342	+	6.85484i	0.547066	+	0.263453i	−0.139872	+	0.990170i	$0.544669\pi$
$678$		0			0
$679$	2.71325			0.104125
$680$	1.95651	+	2.45338i	0.0750287	+	0.0940830i
$681$		0			0
$682$	0.0349210	+	0.152999i	0.00133719	+	0.00585863i
$683$	21.3231	+	26.7383i	0.815907	+	1.02311i	0.999197	+	0.0400557i	$0.0127535\pi$
$683$	21.3231	+	26.7383i	0.815907	+	1.02311i	−0.183291	+	0.983059i	$0.558675\pi$
$684$		0			0
$685$	17.6863	+	22.1779i	0.675759	+	0.847376i
$686$	−2.31817	−	1.11637i	−0.0885081	−	0.0426232i
$687$		0			0
$688$	10.3806	−	13.0169i	0.395757	−	0.496263i
$689$	−15.9736	+	7.69247i	−0.608545	+	0.293060i
$690$		0			0
$691$	7.64507	−	33.4953i	0.290832	−	1.27422i	−0.592537	−	0.805543i	$-0.701874\pi$
$691$	7.64507	−	33.4953i	0.290832	−	1.27422i	0.883370	−	0.468677i	$-0.155269\pi$
$692$	6.27414	+	3.02147i	0.238507	+	0.114859i
$693$		0			0
$694$	−0.844028	+	3.69793i	−0.0320389	+	0.140371i
$695$	10.6713			0.404784
$696$		0			0
$697$	−20.3500			−0.770810
$698$	0.124109	−	0.543759i	0.00469761	−	0.0205816i
$699$		0			0
$700$	7.03928	+	3.38994i	0.266060	+	0.128128i
$701$	0.382708	−	1.67675i	0.0144547	−	0.0633301i	−0.967186	−	0.254069i	$-0.918231\pi$
$701$	0.382708	−	1.67675i	0.0144547	−	0.0633301i	0.981641	+	0.190738i	$0.0610882\pi$
$702$		0			0
$703$	14.2123	−	6.84430i	0.536029	−	0.258138i
$704$	−3.59247	+	4.50481i	−0.135396	+	0.169781i
$705$		0			0
$706$	2.61028	+	1.25704i	0.0982391	+	0.0473094i
$707$	−4.25340	−	5.33359i	−0.159965	−	0.200590i
$708$		0			0
$709$	26.2297	+	32.8910i	0.985077	+	1.23525i	0.971915	+	0.235334i	$0.0756184\pi$
$709$	26.2297	+	32.8910i	0.985077	+	1.23525i	0.0131625	+	0.999913i	$0.495810\pi$
$710$	0.240215	+	1.05245i	0.00901512	+	0.0394978i
$711$		0			0
$712$	4.93520	+	6.18854i	0.184954	+	0.231925i
$713$	12.0290			0.450489
$714$		0			0
$715$	−2.81504	−	1.35565i	−0.105276	−	0.0506984i
$716$	−3.01171	+	3.77656i	−0.112553	+	0.141137i
$717$		0			0
$718$	−2.75780	+	1.32809i	−0.102920	+	0.0495638i
$719$	0.447704	+	1.96152i	0.0166965	+	0.0731523i	0.982590	−	0.185788i	$-0.0594838\pi$
$719$	0.447704	+	1.96152i	0.0166965	+	0.0731523i	−0.965893	+	0.258940i	$0.916627\pi$
$720$		0			0
$721$	14.2027	+	6.83967i	0.528937	+	0.254723i
$722$	−1.11109	+	0.535071i	−0.0413503	+	0.0199133i
$723$		0			0
$724$	1.28122			0.0476161
$725$	−3.24063	−	13.5346i	−0.120354	−	0.502662i
$726$		0			0
$727$	−1.63010	+	7.14193i	−0.0604570	+	0.264880i	−0.996119	−	0.0880183i	$-0.971947\pi$
$727$	−1.63010	+	7.14193i	−0.0604570	+	0.264880i	0.935662	+	0.352898i	$0.114804\pi$
$728$	2.07004	−	0.996878i	0.0767207	−	0.0369468i
$729$		0			0
$730$	0.459353	−	2.01256i	0.0170014	−	0.0744881i
$731$	−3.35966	−	14.7196i	−0.124262	−	0.544425i
$732$		0			0
$733$	3.27009	−	4.10056i	0.120783	−	0.151458i	−0.717764	−	0.696287i	$-0.754834\pi$
$733$	3.27009	−	4.10056i	0.120783	−	0.151458i	0.838547	+	0.544829i	$0.183406\pi$
$734$	−1.76364	+	2.21153i	−0.0650970	+	0.0816291i
$735$		0			0
$736$	−9.05170	−	11.3505i	−0.333650	−	0.418384i
$737$	−5.60131			−0.206327
$738$		0			0
$739$	−5.24580	−	22.9833i	−0.192970	−	0.845456i	−0.974998	−	0.222213i	$-0.928672\pi$
$739$	−5.24580	−	22.9833i	−0.192970	−	0.845456i	0.782028	−	0.623243i	$-0.214185\pi$
$740$	2.05745	+	9.01428i	0.0756334	+	0.331372i
$741$		0			0
$742$	1.49345			0.0548262
$743$	12.1730	+	15.2644i	0.446582	+	0.559997i	0.953265	−	0.302136i	$-0.0976997\pi$
$743$	12.1730	+	15.2644i	0.446582	+	0.559997i	−0.506682	+	0.862133i	$0.669128\pi$
$744$		0			0
$745$	−1.76976	+	2.21921i	−0.0648389	+	0.0813054i
$746$	0.0177754	−	0.0222897i	0.000650805	−	0.000816084i
$747$		0			0
$748$	1.18840	+	5.20671i	0.0434521	+	0.190376i
$749$	5.33333	−	23.3668i	0.194876	−	0.853805i
$750$		0			0
$751$	−1.27601	+	0.614494i	−0.0465622	+	0.0224232i	−0.457020	−	0.889456i	$-0.651083\pi$
$751$	−1.27601	+	0.614494i	−0.0465622	+	0.0224232i	0.410458	+	0.911880i	$0.365369\pi$
$752$	1.53014	−	6.70400i	0.0557986	−	0.244470i
$753$		0			0
$754$	−1.84327	−	0.863702i	−0.0671278	−	0.0314542i
$755$	−10.1985			−0.371161
$756$		0			0
$757$	−39.0305	+	18.7961i	−1.41859	+	0.683156i	−0.976838	−	0.213982i	$-0.931357\pi$
$757$	−39.0305	+	18.7961i	−1.41859	+	0.683156i	−0.441751	+	0.897138i	$0.645642\pi$
$758$	2.92564	+	1.40892i	0.106264	+	0.0511741i
$759$		0			0
$760$	−1.04273	−	4.56852i	−0.0378240	−	0.165718i
$761$	0.433634	−	0.208827i	0.0157192	−	0.00756998i	−0.426008	−	0.904720i	$-0.640080\pi$
$761$	0.433634	−	0.208827i	0.0157192	−	0.00756998i	0.441727	+	0.897150i	$0.354366\pi$
$762$		0			0
$763$	9.36853	−	11.7478i	0.339164	−	0.425298i
$764$	37.0697	+	17.8518i	1.34113	+	0.645856i
$765$		0			0
$766$	0.0871081			0.00314734
$767$	24.4211	+	30.6231i	0.881795	+	1.10574i
$768$		0			0
$769$	3.62260	+	15.8716i	0.130634	+	0.572346i	0.997299	+	0.0734542i	$0.0234023\pi$
$769$	3.62260	+	15.8716i	0.130634	+	0.572346i	−0.866664	+	0.498892i	$0.833741\pi$
$770$	0.164097	+	0.205772i	0.00591366	+	0.00741549i
$771$		0			0
$772$	−24.9798	−	31.3236i	−0.899041	−	1.12736i
$773$	15.6051	+	7.51500i	0.561275	+	0.270296i	0.692936	−	0.720999i	$-0.256317\pi$
$773$	15.6051	+	7.51500i	0.561275	+	0.270296i	−0.131661	+	0.991295i	$0.542031\pi$
$774$		0			0
$775$	2.28102	−	2.86031i	0.0819366	−	0.102745i
$776$	−0.919399	+	0.442759i	−0.0330045	+	0.0158941i
$777$		0			0
$778$	−0.701215	+	3.07222i	−0.0251398	+	0.110145i
$779$	27.3794	+	13.1852i	0.980968	+	0.472410i
$780$		0			0
$781$	−0.821959	+	3.60124i	−0.0294120	+	0.128862i
$782$	−4.31147			−0.154178
$783$		0			0
$784$	−18.0851			−0.645896
$785$	7.22222	−	31.6426i	0.257772	−	1.12937i
$786$		0			0
$787$	−0.612998	−	0.295204i	−0.0218510	−	0.0105229i	0.422926	−	0.906164i	$-0.361003\pi$
$787$	−0.612998	−	0.295204i	−0.0218510	−	0.0105229i	−0.444777	+	0.895641i	$0.646717\pi$
$788$	−1.51691	+	6.64604i	−0.0540378	+	0.236755i
$789$		0			0
$790$	0.110364	−	0.0531484i	0.00392657	−	0.00189093i
$791$	−12.0555	+	15.1172i	−0.428646	+	0.537505i
$792$		0			0
$793$	32.3560	+	15.5818i	1.14900	+	0.553327i
$794$	1.30060	+	1.63090i	0.0461564	+	0.0578783i
$795$		0			0
$796$	−14.8412	−	18.6102i	−0.526031	−	0.659622i
$797$	9.98074	+	43.7285i	0.353536	+	1.54894i	0.768950	+	0.639309i	$0.220780\pi$
$797$	9.98074	+	43.7285i	0.353536	+	1.54894i	−0.415414	+	0.909633i	$0.636363\pi$
$798$		0			0
$799$	−3.88796	−	4.87535i	−0.137546	−	0.172478i
$800$	−4.41542			−0.156109
$801$		0			0
$802$	−3.43138	−	1.65246i	−0.121166	−	0.0583505i
$803$	4.40407	−	5.52254i	0.155416	−	0.194886i
$804$		0			0
$805$	18.1758	−	8.75302i	0.640614	−	0.308503i
$806$	−0.119072	−	0.521689i	−0.00419413	−	0.0183757i
$807$		0			0
$808$	2.31164	+	1.11323i	0.0813233	+	0.0391633i
$809$	26.5024	−	12.7629i	0.931774	−	0.448719i	0.0945137	−	0.995524i	$-0.469870\pi$
$809$	26.5024	−	12.7629i	0.931774	−	0.448719i	0.837260	+	0.546805i	$0.184156\pi$
$810$		0			0
$811$	−20.6973			−0.726781			−0.363391	−	0.931637i	$-0.618381\pi$
$811$	−20.6973			−0.726781			−0.363391	+	0.931637i	$0.618381\pi$
$812$	−10.2851	−	12.6201i	−0.360938	−	0.442880i
$813$		0			0
$814$	0.0741482	−	0.324865i	0.00259889	−	0.0113865i
$815$	−0.349815	+	0.168462i	−0.0122535	+	0.00590096i
$816$		0			0
$817$	−5.01702	+	21.9810i	−0.175523	+	0.769018i
$818$	0.998634	+	4.37530i	0.0349164	+	0.152979i
$819$		0			0
$820$	−11.1057	+	13.9261i	−0.387828	+	0.486321i
$821$	−17.1872	+	21.5520i	−0.599836	+	0.752171i	−0.985352	−	0.170530i	$-0.945452\pi$
$821$	−17.1872	+	21.5520i	−0.599836	+	0.752171i	0.385516	+	0.922701i	$0.374023\pi$
$822$		0			0
$823$	14.3719	+	18.0218i	0.500974	+	0.628201i	0.966449	−	0.256860i	$-0.0826879\pi$
$823$	14.3719	+	18.0218i	0.500974	+	0.628201i	−0.465475	+	0.885061i	$0.654116\pi$
$824$	−5.92880			−0.206539
$825$		0			0
$826$	−0.734183	−	3.21667i	−0.0255455	−	0.111922i
$827$	−9.91752	−	43.4515i	−0.344866	−	1.51096i	−0.788661	−	0.614828i	$-0.789225\pi$
$827$	−9.91752	−	43.4515i	−0.344866	−	1.51096i	0.443795	−	0.896128i	$-0.353632\pi$
$828$		0			0
$829$	44.8796			1.55873			0.779367	−	0.626568i	$-0.215541\pi$
$829$	44.8796			1.55873			0.779367	+	0.626568i	$0.215541\pi$
$830$	1.62963	+	2.04349i	0.0565653	+	0.0709306i
$831$		0			0
$832$	12.2494	−	15.3603i	0.424672	−	0.532522i
$833$	−10.2254	+	12.8223i	−0.354290	+	0.444265i
$834$		0			0
$835$	−4.63958	−	20.3273i	−0.160559	−	0.703456i
$836$	1.77465	−	7.77524i	0.0613775	−	0.268912i
$837$		0			0
$838$	2.64684	−	1.27465i	0.0914334	−	0.0440320i
$839$	2.89501	−	12.6839i	0.0999469	−	0.437896i	−0.900051	−	0.435785i	$-0.856471\pi$
$839$	2.89501	−	12.6839i	0.0999469	−	0.437896i	0.999998	−	0.00211105i	$-0.000671967\pi$
$840$		0			0
$841$	−5.85180	+	28.4035i	−0.201786	+	0.979430i
$842$	−1.23092			−0.0424203
$843$		0			0
$844$	7.41908	−	3.57284i	0.255375	−	0.122982i
$845$	−8.60556	−	4.14422i	−0.296040	−	0.142566i
$846$		0			0
$847$	−3.53856	−	15.5034i	−0.121586	−	0.532705i
$848$	23.6442	−	11.3865i	0.811946	−	0.391012i
$849$		0			0
$850$	−0.817571	+	1.02520i	−0.0280424	+	0.0351641i
$851$	−23.0119	−	11.0819i	−0.788837	−	0.379884i
$852$		0			0
$853$	27.7373			0.949706			0.474853	−	0.880065i	$-0.342501\pi$
$853$	27.7373			0.949706			0.474853	+	0.880065i	$0.342501\pi$
$854$	−1.88613	−	2.36514i	−0.0645422	−	0.0809333i
$855$		0			0
$856$	2.00587	+	8.78829i	0.0685592	+	0.300378i
$857$	−11.6553	−	14.6153i	−0.398137	−	0.499249i	0.541842	−	0.840481i	$-0.317727\pi$
$857$	−11.6553	−	14.6153i	−0.398137	−	0.499249i	−0.939979	+	0.341232i	$0.889156\pi$
$858$		0			0
$859$	14.5498	+	18.2448i	0.496431	+	0.622505i	0.965420	−	0.260699i	$-0.0839530\pi$
$859$	14.5498	+	18.2448i	0.496431	+	0.622505i	−0.468989	+	0.883204i	$0.655382\pi$
$860$	−11.9066	−	5.73391i	−0.406011	−	0.195525i
$861$		0			0
$862$	0.428700	−	0.537573i	0.0146016	−	0.0183098i
$863$	−9.70141	+	4.67195i	−0.330240	+	0.159035i	−0.591655	−	0.806191i	$-0.701525\pi$
$863$	−9.70141	+	4.67195i	−0.330240	+	0.159035i	0.261415	+	0.965226i	$0.415811\pi$
$864$		0			0
$865$	1.21689	−	5.33156i	0.0413756	−	0.181278i
$866$	−0.549626	−	0.264686i	−0.0186771	−	0.00899440i
$867$		0			0
$868$	0.952326	−	4.17241i	0.0323241	−	0.141621i
$869$	0.419147			0.0142186
$870$		0			0
$871$	19.0991			0.647147
$872$	−1.25753	+	5.50959i	−0.0425853	+	0.186578i
$873$		0			0
$874$	5.80077	+	2.79350i	0.196214	+	0.0944916i
$875$	4.00676	−	17.5548i	0.135453	−	0.593459i
$876$		0			0
$877$	38.4422	−	18.5128i	1.29810	−	0.625133i	0.348124	−	0.937448i	$-0.386819\pi$
$877$	38.4422	−	18.5128i	1.29810	−	0.625133i	0.949979	+	0.312315i	$0.101105\pi$
$878$	2.46555	−	3.09171i	0.0832084	−	0.104340i
$879$		0			0
$880$	4.16684	+	2.00664i	0.140464	+	0.0676439i
$881$	14.9468	+	18.7427i	0.503570	+	0.631457i	0.967031	−	0.254660i	$-0.0819637\pi$
$881$	14.9468	+	18.7427i	0.503570	+	0.631457i	−0.463460	+	0.886118i	$0.653392\pi$
$882$		0			0
$883$	−19.3865	−	24.3099i	−0.652408	−	0.818094i	0.340085	−	0.940395i	$-0.389544\pi$
$883$	−19.3865	−	24.3099i	−0.652408	−	0.818094i	−0.992493	+	0.122301i	$0.960973\pi$
$884$	−4.05214	−	17.7536i	−0.136288	−	0.597118i
$885$		0			0
$886$	−0.0699589	−	0.0877257i	−0.00235032	−	0.00294720i
$887$	−10.1518			−0.340864			−0.170432	−	0.985369i	$-0.554516\pi$
$887$	−10.1518			−0.340864			−0.170432	+	0.985369i	$0.554516\pi$
$888$		0			0
$889$	26.6147	+	12.8170i	0.892629	+	0.429868i
$890$	1.92766	−	2.41721i	0.0646154	−	0.0810251i
$891$		0			0
$892$	−8.38746	+	4.03919i	−0.280833	+	0.135242i
$893$	2.07212	+	9.07854i	0.0693407	+	0.303802i
$894$		0			0
$895$	3.41767	+	1.64586i	0.114240	+	0.0550151i
$896$	−6.19376	+	2.98276i	−0.206919	+	0.0996469i
$897$		0			0
$898$	0.451472			0.0150658
$899$	−6.83294	+	3.38034i	−0.227891	+	0.112741i
$900$		0			0
$901$	5.29562	−	23.2016i	0.176423	−	0.772959i
$902$	0.578359	−	0.278523i	0.0192573	−	0.00927380i
$903$		0			0
$904$	1.61820	−	7.08981i	0.0538206	−	0.235803i
$905$	−0.223888	−	0.980918i	−0.00744230	−	0.0326068i
$906$		0			0
$907$	−30.0145	+	37.6371i	−0.996617	+	1.24972i	−0.0284022	+	0.999597i	$0.509042\pi$
$907$	−30.0145	+	37.6371i	−0.996617	+	1.24972i	−0.968215	+	0.250121i	$0.919530\pi$
$908$	−16.8888	+	21.1779i	−0.560475	+	0.702814i
$909$		0			0
$910$	−0.559531	−	0.701630i	−0.0185483	−	0.0232588i
$911$	18.1251			0.600510			0.300255	−	0.953859i	$-0.402928\pi$
$911$	18.1251			0.600510			0.300255	+	0.953859i	$0.402928\pi$
$912$		0			0
$913$	1.99012	+	8.71930i	0.0658634	+	0.288567i
$914$	0.919768	+	4.02976i	0.0304232	+	0.133293i
$915$		0			0
$916$	−39.9678			−1.32057
$917$	16.0080	+	20.0735i	0.528632	+	0.662884i
$918$		0			0
$919$	−22.9890	+	28.8273i	−0.758337	+	0.950925i	−0.999810	−	0.0194827i	$-0.993798\pi$
$919$	−22.9890	+	28.8273i	−0.758337	+	0.950925i	0.241473	+	0.970408i	$0.422370\pi$
$920$	−4.73063	+	5.93202i	−0.155964	+	0.195573i
$921$		0			0
$922$	−0.895999	−	3.92563i	−0.0295082	−	0.129284i
$923$	2.80268	−	12.2793i	0.0922512	−	0.404179i
$924$		0			0
$925$	−6.99879	+	3.37044i	−0.230119	+	0.110819i
$926$	0.588554	−	2.57862i	0.0193411	−	0.0847389i
$927$		0			0
$928$	8.33140	+	3.90385i	0.273492	+	0.128150i
$929$	−25.3154			−0.830571			−0.415285	−	0.909691i	$-0.636318\pi$
$929$	−25.3154			−0.830571			−0.415285	+	0.909691i	$0.636318\pi$
$930$		0			0
$931$	22.0654	−	10.6261i	0.723165	−	0.348258i
$932$	12.9903	+	6.25580i	0.425512	+	0.204916i
$933$		0			0
$934$	−0.702941	−	3.07979i	−0.0230009	−	0.100774i
$935$	3.77866	−	1.81971i	0.123575	−	0.0595108i
$936$		0			0
$937$	−31.6136	+	39.6422i	−1.03277	+	1.29506i	−0.0782446	+	0.996934i	$0.524932\pi$
$937$	−31.6136	+	39.6422i	−1.03277	+	1.29506i	−0.954528	+	0.298122i	$0.903640\pi$
$938$	−1.44951	−	0.698045i	−0.0473280	−	0.0227920i
$939$		0			0
$940$	−5.45816			−0.178025
$941$	−1.10773	−	1.38905i	−0.0361109	−	0.0452817i	0.763448	−	0.645869i	$-0.223505\pi$
$941$	−1.10773	−	1.38905i	−0.0361109	−	0.0452817i	−0.799559	+	0.600587i	$0.794933\pi$
$942$		0			0
$943$	−10.9489	−	47.9703i	−0.356546	−	1.56213i
$944$	−36.1483	−	45.3285i	−1.17653	−	1.47532i
$945$		0			0
$946$	0.296946	+	0.372359i	0.00965456	+	0.0121064i
$947$	−12.2985	−	5.92264i	−0.399647	−	0.192460i	0.223254	−	0.974760i	$-0.428332\pi$
$947$	−12.2985	−	5.92264i	−0.399647	−	0.192460i	−0.622901	+	0.782300i	$0.714046\pi$
$948$		0			0
$949$	−15.0168	+	18.8305i	−0.487466	+	0.611263i
$950$	1.76423	−	0.849610i	0.0572393	−	0.0275650i
$951$		0			0
$952$	−0.686267	+	3.00673i	−0.0222421	+	0.0974488i
$953$	25.5209	+	12.2902i	0.826703	+	0.398119i	0.798877	−	0.601494i	$-0.205428\pi$
$953$	25.5209	+	12.2902i	0.826703	+	0.398119i	0.0278251	+	0.999613i	$0.491142\pi$
$954$		0			0
$955$	7.18981	−	31.5006i	0.232657	−	1.01934i
$956$	−46.2517			−1.49589
$957$		0			0
$958$	−3.38602			−0.109397
$959$	−6.20367	+	27.1801i	−0.200327	+	0.877690i
$960$		0			0
$961$	26.1245	+	12.5809i	0.842726	+	0.405835i
$962$	−0.252827	+	1.10771i	−0.00815147	+	0.0357139i
$963$		0			0
$964$	45.3979	−	21.8625i	1.46217	−	0.704143i
$965$	−19.6167	+	24.5985i	−0.631483	+	0.791855i
$966$		0			0
$967$	−10.5952	−	5.10238i	−0.340719	−	0.164082i	0.255697	−	0.966757i	$-0.417695\pi$
$967$	−10.5952	−	5.10238i	−0.340719	−	0.164082i	−0.596416	+	0.802675i	$0.703409\pi$
$968$	3.72898	+	4.67599i	0.119854	+	0.150292i
$969$		0			0
$970$	0.248513	+	0.311626i	0.00797928	+	0.0100057i
$971$	−8.50069	−	37.2440i	−0.272800	−	1.19522i	−0.906692	−	0.421794i	$-0.861401\pi$
$971$	−8.50069	−	37.2440i	−0.272800	−	1.19522i	0.633892	−	0.773422i	$-0.281456\pi$
$972$		0			0
$973$	6.53905	+	8.19971i	0.209632	+	0.262871i
$974$	−5.14344			−0.164806
$975$		0			0
$976$	−47.8936	−	23.0644i	−1.53304	−	0.738272i
$977$	20.0225	−	25.1074i	0.640575	−	0.803256i	−0.350500	−	0.936563i	$-0.613988\pi$
$977$	20.0225	−	25.1074i	0.640575	−	0.803256i	0.991075	+	0.133307i	$0.0425597\pi$
$978$		0			0
$979$	9.53149	−	4.59012i	0.304628	−	0.146701i
$980$	3.19430	+	13.9951i	0.102038	+	0.447059i
$981$		0			0
$982$	0.365069	+	0.175808i	0.0116498	+	0.00561027i
$983$	40.6408	−	19.5716i	1.29624	−	0.624237i	0.346728	−	0.937966i	$-0.387293\pi$
$983$	40.6408	−	19.5716i	1.29624	−	0.624237i	0.949513	+	0.313729i	$0.101578\pi$
$984$		0			0
$985$	5.35337			0.170573
$986$	2.44909	−	1.21159i	0.0779948	−	0.0385850i
$987$		0			0
$988$	−6.05111	+	26.5116i	−0.192511	+	0.843447i
$989$	32.8906	−	15.8393i	1.04586	−	0.503659i
$990$		0			0
$991$	−1.36309	+	5.97209i	−0.0433000	+	0.189710i	−0.991953	−	0.126610i	$-0.959590\pi$
$991$	−1.36309	+	5.97209i	−0.0433000	+	0.189710i	0.948653	+	0.316320i	$0.102447\pi$
$992$	0.538195	+	2.35798i	0.0170877	+	0.0748661i
$993$		0			0
$994$	−0.661499	+	0.829494i	−0.0209815	+	0.0263099i
$995$	−11.6548	+	14.6147i	−0.369482	+	0.463316i
$996$		0			0
$997$	−21.3367	−	26.7554i	−0.675741	−	0.847353i	0.319213	−	0.947683i	$-0.396582\pi$
$997$	−21.3367	−	26.7554i	−0.675741	−	0.847353i	−0.994954	+	0.100330i	$0.968010\pi$
$998$	5.87040			0.185824
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.k.c.199.2		18
3.2	odd	2		87.2.g.a.25.2	yes	18
29.6	even	14		7569.2.a.bm.1.4		9
29.7	even	7	inner	261.2.k.c.181.2		18
29.23	even	7		7569.2.a.bj.1.6		9
87.23	odd	14		2523.2.a.r.1.4		9
87.35	odd	14		2523.2.a.o.1.6		9
87.65	odd	14		87.2.g.a.7.2	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.g.a.7.2	✓	18	87.65	odd	14
87.2.g.a.25.2	yes	18	3.2	odd	2
261.2.k.c.181.2		18	29.7	even	7	inner
261.2.k.c.199.2		18	1.1	even	1	trivial
2523.2.a.o.1.6		9	87.35	odd	14
2523.2.a.r.1.4		9	87.23	odd	14
7569.2.a.bj.1.6		9	29.23	even	7
7569.2.a.bm.1.4		9	29.6	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)

\(f(q)\)	\(=\)	\(q+(-0.0321271 + 0.140758i) q^{2} +(1.78316 + 0.858723i) q^{4} +(0.345850 - 1.51527i) q^{5} +(1.37625 - 0.662766i) q^{7} +(-0.358196 + 0.449164i) q^{8} +O(q^{10})\)	\(q+(-0.0321271 + 0.140758i) q^{2} +(1.78316 + 0.858723i) q^{4} +(0.345850 - 1.51527i) q^{5} +(1.37625 - 0.662766i) q^{7} +(-0.358196 + 0.449164i) q^{8} +(0.202175 + 0.0973624i) q^{10} +(0.478737 + 0.600317i) q^{11} +(-1.63237 - 2.04693i) q^{13} +(0.0490748 + 0.215011i) q^{14} +(2.41625 + 3.02988i) q^{16} +3.51434 q^{17} +(-4.72829 - 2.27702i) q^{19} +(1.91790 - 2.40497i) q^{20} +(-0.0998798 + 0.0480996i) q^{22} +(1.89083 + 8.28425i) q^{23} +(2.32842 + 1.12131i) q^{25} +(0.340565 - 0.164008i) q^{26} +3.02320 q^{28} +(-3.40207 - 4.17443i) q^{29} +(0.315006 - 1.38013i) q^{31} +(-1.53932 + 0.741300i) q^{32} +(-0.112906 + 0.494672i) q^{34} +(-0.528293 - 2.31460i) q^{35} +(-1.87409 + 2.35004i) q^{37} +(0.472416 - 0.592391i) q^{38} +(0.556722 + 0.698107i) q^{40} -5.79055 q^{41} +(-0.955986 - 4.18845i) q^{43} +(0.338157 + 1.48156i) q^{44} -1.22682 q^{46} +(-1.10631 - 1.38727i) q^{47} +(-2.90963 + 3.64856i) q^{49} +(-0.232638 + 0.291719i) q^{50} +(-1.15303 - 5.05176i) q^{52} +(1.50686 - 6.60199i) q^{53} +(1.07521 - 0.517795i) q^{55} +(-0.195276 + 0.855561i) q^{56} +(0.696884 - 0.344757i) q^{58} -14.9605 q^{59} +(-12.3585 + 5.95153i) q^{61} +(0.184144 + 0.0886793i) q^{62} +(1.66981 + 7.31591i) q^{64} +(-3.66621 + 1.76555i) q^{65} +(-4.54833 + 5.70342i) q^{67} +(6.26662 + 3.01785i) q^{68} +0.342772 q^{70} +(2.99945 + 3.76119i) q^{71} +(-2.04705 - 8.96872i) q^{73} +(-0.270578 - 0.339294i) q^{74} +(-6.47595 - 8.12058i) q^{76} +(1.05673 + 0.508894i) q^{77} +(0.340352 - 0.426788i) q^{79} +(5.42674 - 2.61338i) q^{80} +(0.186034 - 0.815067i) q^{82} +(10.4943 + 5.05376i) q^{83} +(1.21543 - 5.32517i) q^{85} +0.620271 q^{86} -0.441122 q^{88} +(3.06588 - 13.4325i) q^{89} +(-3.60319 - 1.73520i) q^{91} +(-3.74224 + 16.3958i) q^{92} +(0.230813 - 0.111154i) q^{94} +(-5.08558 + 6.37712i) q^{95} +(1.60034 + 0.770683i) q^{97} +(-0.420086 - 0.526771i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{2} - 6 q^{4} + q^{5} - 4 q^{7} + 15 q^{8}+O(q^{10}) \) 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

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