LMFDB - Embedded newform 693.2.m.g.64.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (of order $5$, degree $4$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			64.1
Root			$1.43801 + 1.04478i$ of defining polynomial
Character	$\chi$	$=$	693.64
Dual form			693.2.m.g.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.549273 + 1.69049i) q^{2} +(-0.938015 - 0.681508i) q^{4} +(0.858290 + 2.64154i) q^{5} +(0.809017 + 0.587785i) q^{7} +(-1.20872 + 0.878189i) q^{8} +O(q^{10})$	\(q+(-0.549273 + 1.69049i) q^{2} +(-0.938015 - 0.681508i) q^{4} +(0.858290 + 2.64154i) q^{5} +(0.809017 + 0.587785i) q^{7} +(-1.20872 + 0.878189i) q^{8} -4.93693 q^{10} +(-1.14849 - 3.11143i) q^{11} +(-1.32676 + 4.08334i) q^{13} +(-1.43801 + 1.04478i) q^{14} +(-1.53723 - 4.73110i) q^{16} +(0.851514 + 2.62069i) q^{17} +(-1.56876 + 1.13977i) q^{19} +(0.995144 - 3.06274i) q^{20} +(5.89066 - 0.232480i) q^{22} -4.37009 q^{23} +(-2.19601 + 1.59550i) q^{25} +(-6.17408 - 4.48573i) q^{26} +(-0.358290 - 1.10270i) q^{28} +(6.98027 + 5.07146i) q^{29} +(-0.0619850 + 0.190770i) q^{31} +5.85410 q^{32} -4.89796 q^{34} +(-0.858290 + 2.64154i) q^{35} +(-0.837721 - 0.608640i) q^{37} +(-1.06509 - 3.27802i) q^{38} +(-3.35721 - 2.43916i) q^{40} +(7.77155 - 5.64636i) q^{41} -4.70820 q^{43} +(-1.04316 + 3.70127i) q^{44} +(2.40037 - 7.38759i) q^{46} +(-10.5541 + 7.66797i) q^{47} +(0.309017 + 0.951057i) q^{49} +(-1.49096 - 4.58869i) q^{50} +(4.02734 - 2.92604i) q^{52} +(1.20520 - 3.70923i) q^{53} +(7.23324 - 5.70428i) q^{55} -1.49406 q^{56} +(-12.4073 + 9.01445i) q^{58} +(-6.92286 - 5.02975i) q^{59} +(-0.305497 - 0.940223i) q^{61} +(-0.288448 - 0.209570i) q^{62} +(-0.141042 + 0.434084i) q^{64} -11.9251 q^{65} -5.41745 q^{67} +(0.987288 - 3.03856i) q^{68} +(-3.99406 - 2.90186i) q^{70} +(0.623302 + 1.91833i) q^{71} +(8.06677 + 5.86085i) q^{73} +(1.48904 - 1.08185i) q^{74} +2.24828 q^{76} +(0.899706 - 3.19226i) q^{77} +(1.94479 - 5.98545i) q^{79} +(11.1780 - 8.12131i) q^{80} +(5.27640 + 16.2391i) q^{82} +(0.531960 + 1.63720i) q^{83} +(-6.19182 + 4.49862i) q^{85} +(2.58609 - 7.95916i) q^{86} +(4.12062 + 2.75227i) q^{88} +15.3035 q^{89} +(-3.47350 + 2.52364i) q^{91} +(4.09921 + 2.97825i) q^{92} +(-7.16556 - 22.0533i) q^{94} +(-4.35721 - 3.16570i) q^{95} +(3.58961 - 11.0477i) q^{97} -1.77748 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 3 q^{4} - 3 q^{5} + 2 q^{7} - 3 q^{8}+O(q^{10}) $ 8 * q + q^2 + 3 * q^4 - 3 * q^5 + 2 * q^7 - 3 * q^8	$ 8 q + q^{2} + 3 q^{4} - 3 q^{5} + 2 q^{7} - 3 q^{8} - 28 q^{10} - 5 q^{11} + 5 q^{13} - q^{14} - 3 q^{16} + 11 q^{17} - 9 q^{19} - 21 q^{20} - q^{22} + 16 q^{23} + 5 q^{25} - 21 q^{26} + 7 q^{28} + 9 q^{29} - 11 q^{31} + 20 q^{32} - 24 q^{34} + 3 q^{35} + 6 q^{37} - 35 q^{38} - 16 q^{40} + 22 q^{41} + 16 q^{43} - 29 q^{44} + 29 q^{46} - 7 q^{47} - 2 q^{49} + 34 q^{50} + 21 q^{52} - 2 q^{53} + 26 q^{55} + 18 q^{56} - 39 q^{58} - 25 q^{59} + 7 q^{61} + 5 q^{62} + q^{64} - 24 q^{65} - 30 q^{67} - 8 q^{68} - 2 q^{70} + 14 q^{71} + 3 q^{73} + 9 q^{74} - 52 q^{76} + 5 q^{77} - 9 q^{79} + 33 q^{80} + 31 q^{82} - 23 q^{83} - 10 q^{85} + 17 q^{86} - 7 q^{88} + 34 q^{89} + 5 q^{91} + 34 q^{92} - 30 q^{94} - 24 q^{95} + 30 q^{97} - 4 q^{98}+O(q^{100}) $ 8 * q + q^2 + 3 * q^4 - 3 * q^5 + 2 * q^7 - 3 * q^8 - 28 * q^10 - 5 * q^11 + 5 * q^13 - q^14 - 3 * q^16 + 11 * q^17 - 9 * q^19 - 21 * q^20 - q^22 + 16 * q^23 + 5 * q^25 - 21 * q^26 + 7 * q^28 + 9 * q^29 - 11 * q^31 + 20 * q^32 - 24 * q^34 + 3 * q^35 + 6 * q^37 - 35 * q^38 - 16 * q^40 + 22 * q^41 + 16 * q^43 - 29 * q^44 + 29 * q^46 - 7 * q^47 - 2 * q^49 + 34 * q^50 + 21 * q^52 - 2 * q^53 + 26 * q^55 + 18 * q^56 - 39 * q^58 - 25 * q^59 + 7 * q^61 + 5 * q^62 + q^64 - 24 * q^65 - 30 * q^67 - 8 * q^68 - 2 * q^70 + 14 * q^71 + 3 * q^73 + 9 * q^74 - 52 * q^76 + 5 * q^77 - 9 * q^79 + 33 * q^80 + 31 * q^82 - 23 * q^83 - 10 * q^85 + 17 * q^86 - 7 * q^88 + 34 * q^89 + 5 * q^91 + 34 * q^92 - 30 * q^94 - 24 * q^95 + 30 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.549273	+	1.69049i	−0.388395	+	1.19536i	0.545593	+	0.838050i	$0.316304\pi$
$2$	−0.549273	+	1.69049i	−0.388395	+	1.19536i	−0.933988	+	0.357305i	$0.883696\pi$
$3$		0			0
$3$		0			0
$4$	−0.938015	−	0.681508i	−0.469007	−	0.340754i
$5$	0.858290	+	2.64154i	0.383839	+	1.18133i	0.937319	+	0.348472i	$0.113299\pi$
$5$	0.858290	+	2.64154i	0.383839	+	1.18133i	−0.553480	+	0.832862i	$0.686701\pi$
$6$		0			0
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$8$	−1.20872	+	0.878189i	−0.427348	+	0.310487i
$9$		0			0
$10$	−4.93693			−1.56120
$11$	−1.14849	−	3.11143i	−0.346282	−	0.938131i
$11$	−1.14849	−	3.11143i	−0.346282	−	0.938131i
$12$		0			0
$13$	−1.32676	+	4.08334i	−0.367976	+	1.13251i	0.580120	+	0.814531i	$0.303006\pi$
$13$	−1.32676	+	4.08334i	−0.367976	+	1.13251i	−0.948096	+	0.317983i	$0.896994\pi$
$14$	−1.43801	+	1.04478i	−0.384326	+	0.279229i
$15$		0			0
$16$	−1.53723	−	4.73110i	−0.384307	−	1.18278i
$17$	0.851514	+	2.62069i	0.206522	+	0.635611i	0.999647	+	0.0265518i	$0.00845268\pi$
$17$	0.851514	+	2.62069i	0.206522	+	0.635611i	−0.793125	+	0.609059i	$0.791547\pi$
$18$		0			0
$19$	−1.56876	+	1.13977i	−0.359898	+	0.261482i	−0.753010	−	0.658009i	$-0.771399\pi$
$19$	−1.56876	+	1.13977i	−0.359898	+	0.261482i	0.393111	+	0.919491i	$0.371399\pi$
$20$	0.995144	−	3.06274i	0.222521	−	0.684849i
$21$		0			0
$22$	5.89066	−	0.232480i	1.25589	−	0.0495649i
$23$	−4.37009			−0.911228			−0.455614	−	0.890178i	$-0.650580\pi$
$23$	−4.37009			−0.911228			−0.455614	+	0.890178i	$0.650580\pi$
$24$		0			0
$25$	−2.19601	+	1.59550i	−0.439202	+	0.319099i
$26$	−6.17408	−	4.48573i	−1.21084	−	0.879725i
$27$		0			0
$28$	−0.358290	−	1.10270i	−0.0677104	−	0.208391i
$29$	6.98027	+	5.07146i	1.29620	+	0.941747i	0.999911	−	0.0133499i	$-0.00424953\pi$
$29$	6.98027	+	5.07146i	1.29620	+	0.941747i	0.296293	+	0.955097i	$0.404250\pi$
$30$		0			0
$31$	−0.0619850	+	0.190770i	−0.0111328	+	0.0342634i	−0.956469	−	0.291835i	$-0.905734\pi$
$31$	−0.0619850	+	0.190770i	−0.0111328	+	0.0342634i	0.945336	+	0.326099i	$0.105734\pi$
$32$	5.85410			1.03487
$33$		0			0
$34$	−4.89796			−0.839993
$35$	−0.858290	+	2.64154i	−0.145077	+	0.446503i
$36$		0			0
$37$	−0.837721	−	0.608640i	−0.137720	−	0.100060i	0.516792	−	0.856111i	$-0.327126\pi$
$37$	−0.837721	−	0.608640i	−0.137720	−	0.100060i	−0.654512	+	0.756051i	$0.727126\pi$
$38$	−1.06509	−	3.27802i	−0.172781	−	0.531765i
$39$		0			0
$40$	−3.35721	−	2.43916i	−0.530821	−	0.385664i
$41$	7.77155	−	5.64636i	1.21371	−	0.881813i	0.218149	−	0.975915i	$-0.429998\pi$
$41$	7.77155	−	5.64636i	1.21371	−	0.881813i	0.995563	+	0.0941021i	$0.0299980\pi$
$42$		0			0
$43$	−4.70820			−0.717994			−0.358997	−	0.933339i	$-0.616881\pi$
$43$	−4.70820			−0.717994			−0.358997	+	0.933339i	$0.616881\pi$
$44$	−1.04316	+	3.70127i	−0.157263	+	0.557987i
$45$		0			0
$46$	2.40037	−	7.38759i	0.353916	−	1.08924i
$47$	−10.5541	+	7.66797i	−1.53947	+	1.11849i	−0.588800	+	0.808279i	$0.700399\pi$
$47$	−10.5541	+	7.66797i	−1.53947	+	1.11849i	−0.950668	+	0.310210i	$0.899601\pi$
$48$		0			0
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	−1.49096	−	4.58869i	−0.210853	−	0.648939i
$51$		0			0
$52$	4.02734	−	2.92604i	0.558492	−	0.405768i
$53$	1.20520	−	3.70923i	0.165547	−	0.509502i	−0.833529	−	0.552476i	$-0.813683\pi$
$53$	1.20520	−	3.70923i	0.165547	−	0.509502i	0.999076	+	0.0429735i	$0.0136831\pi$
$54$		0			0
$55$	7.23324	−	5.70428i	0.975330	−	0.769165i
$56$	−1.49406			−0.199653
$57$		0			0
$58$	−12.4073	+	9.01445i	−1.62916	+	1.18365i
$59$	−6.92286	−	5.02975i	−0.901280	−	0.654818i	0.0375144	−	0.999296i	$-0.488056\pi$
$59$	−6.92286	−	5.02975i	−0.901280	−	0.654818i	−0.938794	+	0.344478i	$0.888056\pi$
$60$		0			0
$61$	−0.305497	−	0.940223i	−0.0391149	−	0.120383i	0.929592	−	0.368589i	$-0.120159\pi$
$61$	−0.305497	−	0.940223i	−0.0391149	−	0.120383i	−0.968707	+	0.248206i	$0.920159\pi$
$62$	−0.288448	−	0.209570i	−0.0366330	−	0.0266154i
$63$		0			0
$64$	−0.141042	+	0.434084i	−0.0176303	+	0.0542605i
$65$	−11.9251			−1.47912
$66$		0			0
$67$	−5.41745			−0.661846			−0.330923	−	0.943658i	$-0.607360\pi$
$67$	−5.41745			−0.661846			−0.330923	+	0.943658i	$0.607360\pi$
$68$	0.987288	−	3.03856i	0.119726	−	0.368479i
$69$		0			0
$70$	−3.99406	−	2.90186i	−0.477382	−	0.346838i
$71$	0.623302	+	1.91833i	0.0739724	+	0.227664i	0.981206	−	0.192964i	$-0.0618100\pi$
$71$	0.623302	+	1.91833i	0.0739724	+	0.227664i	−0.907234	+	0.420627i	$0.861810\pi$
$72$		0			0
$73$	8.06677	+	5.86085i	0.944144	+	0.685961i	0.949415	−	0.314025i	$-0.101678\pi$
$73$	8.06677	+	5.86085i	0.944144	+	0.685961i	−0.00527037	+	0.999986i	$0.501678\pi$
$74$	1.48904	−	1.08185i	0.173097	−	0.125762i
$75$		0			0
$76$	2.24828			0.257896
$77$	0.899706	−	3.19226i	0.102531	−	0.363792i
$78$		0			0
$79$	1.94479	−	5.98545i	0.218806	−	0.673416i	−0.780055	−	0.625711i	$-0.784809\pi$
$79$	1.94479	−	5.98545i	0.218806	−	0.673416i	0.998861	−	0.0477054i	$-0.0151909\pi$
$80$	11.1780	−	8.12131i	1.24974	−	0.907991i
$81$		0			0
$82$	5.27640	+	16.2391i	0.582681	+	1.79331i
$83$	0.531960	+	1.63720i	0.0583902	+	0.179707i	0.975998	−	0.217781i	$-0.0698820\pi$
$83$	0.531960	+	1.63720i	0.0583902	+	0.179707i	−0.917607	+	0.397488i	$0.869882\pi$
$84$		0			0
$85$	−6.19182	+	4.49862i	−0.671598	+	0.487944i
$86$	2.58609	−	7.95916i	0.278865	−	0.858259i
$87$		0			0
$88$	4.12062	+	2.75227i	0.439260	+	0.293393i
$89$	15.3035			1.62217			0.811086	−	0.584928i	$-0.198877\pi$
$89$	15.3035			1.62217			0.811086	+	0.584928i	$0.198877\pi$
$90$		0			0
$91$	−3.47350	+	2.52364i	−0.364121	+	0.264550i
$92$	4.09921	+	2.97825i	0.427373	+	0.310504i
$93$		0			0
$94$	−7.16556	−	22.0533i	−0.739071	−	2.27463i
$95$	−4.35721	−	3.16570i	−0.447040	−	0.324794i
$96$		0			0
$97$	3.58961	−	11.0477i	0.364470	−	1.12172i	−0.585843	−	0.810425i	$-0.699236\pi$
$97$	3.58961	−	11.0477i	0.364470	−	1.12172i	0.950313	−	0.311297i	$-0.100764\pi$
$98$	−1.77748			−0.179553
$99$		0			0
$100$	3.14723			0.314723
$101$	−1.05430	+	3.24480i	−0.104907	+	0.322870i	−0.989709	−	0.143098i	$-0.954294\pi$
$101$	−1.05430	+	3.24480i	−0.104907	+	0.322870i	0.884802	+	0.465968i	$0.154294\pi$
$102$		0			0
$103$	14.7100	+	10.6875i	1.44942	+	1.05307i	0.985966	+	0.166945i	$0.0533903\pi$
$103$	14.7100	+	10.6875i	1.44942	+	1.05307i	0.463455	+	0.886121i	$0.346610\pi$
$104$	−1.98226	−	6.10077i	−0.194377	−	0.598230i
$105$		0			0
$106$	5.60843	+	4.07476i	0.544739	+	0.395776i
$107$	2.62725	−	1.90881i	0.253986	−	0.184532i	−0.453506	−	0.891253i	$-0.649827\pi$
$107$	2.62725	−	1.90881i	0.253986	−	0.184532i	0.707491	+	0.706722i	$0.249827\pi$
$108$		0			0
$109$	12.6912			1.21559			0.607796	−	0.794093i	$-0.292054\pi$
$109$	12.6912			1.21559			0.607796	+	0.794093i	$0.292054\pi$
$110$	5.67000	+	15.3609i	0.540613	+	1.46461i
$111$		0			0
$112$	1.53723	−	4.73110i	0.145254	−	0.447047i
$113$	−14.9248	+	10.8435i	−1.40401	+	1.02007i	−0.409845	+	0.912155i	$0.634417\pi$
$113$	−14.9248	+	10.8435i	−1.40401	+	1.02007i	−0.994160	+	0.107915i	$0.965583\pi$
$114$		0			0
$115$	−3.75081	−	11.5438i	−0.349765	−	1.07646i
$116$	−3.09136	−	9.51422i	−0.287025	−	0.883373i
$117$		0			0
$118$	12.3053	−	8.94031i	1.13279	−	0.823022i
$119$	−0.851514	+	2.62069i	−0.0780581	+	0.240238i
$120$		0			0
$121$	−8.36196	+	7.14686i	−0.760178	+	0.649715i
$122$	1.75724			0.159093
$123$		0			0
$124$	0.188154	−	0.136702i	0.0168968	−	0.0122762i
$125$	5.13577	+	3.73136i	0.459358	+	0.333743i
$126$		0			0
$127$	6.02870	+	18.5544i	0.534961	+	1.64644i	0.743733	+	0.668476i	$0.233053\pi$
$127$	6.02870	+	18.5544i	0.534961	+	1.64644i	−0.208772	+	0.977964i	$0.566947\pi$
$128$	8.81579	+	6.40505i	0.779213	+	0.566132i
$129$		0			0
$130$	6.55011	−	20.1592i	0.574483	−	1.76808i
$131$	6.89796			0.602677			0.301339	−	0.953517i	$-0.402567\pi$
$131$	6.89796			0.602677			0.301339	+	0.953517i	$0.402567\pi$
$132$		0			0
$133$	−1.93910			−0.168141
$134$	2.97566	−	9.15813i	0.257058	−	0.791142i
$135$		0			0
$136$	−3.33070	−	2.41990i	−0.285606	−	0.207505i
$137$	0.806750	+	2.48292i	0.0689253	+	0.212130i	0.979586	−	0.201024i	$-0.0644270\pi$
$137$	0.806750	+	2.48292i	0.0689253	+	0.212130i	−0.910661	+	0.413154i	$0.864427\pi$
$138$		0			0
$139$	0.810097	+	0.588570i	0.0687116	+	0.0499219i	0.621611	−	0.783326i	$-0.286479\pi$
$139$	0.810097	+	0.588570i	0.0687116	+	0.0499219i	−0.552899	+	0.833248i	$0.686479\pi$
$140$	2.60532	−	1.89288i	0.220190	−	0.159977i
$141$		0			0
$142$	−3.58527			−0.300869
$143$	14.2288	−	0.561550i	1.18987	−	0.0469592i
$144$		0			0
$145$	−7.40540	+	22.7915i	−0.614985	+	1.89273i
$146$	−14.3386	+	10.4176i	−1.18667	+	0.862165i
$147$		0			0
$148$	0.371002	+	1.14183i	0.0304962	+	0.0938576i
$149$	4.60273	+	14.1658i	0.377071	+	1.16050i	0.942071	+	0.335413i	$0.108876\pi$
$149$	4.60273	+	14.1658i	0.377071	+	1.16050i	−0.565000	+	0.825091i	$0.691124\pi$
$150$		0			0
$151$	−12.7862	+	9.28970i	−1.04052	+	0.755985i	−0.970388	−	0.241552i	$-0.922344\pi$
$151$	−12.7862	+	9.28970i	−1.04052	+	0.755985i	−0.0701368	+	0.997537i	$0.522344\pi$
$152$	0.895263	−	2.75534i	0.0726154	−	0.223487i
$153$		0			0
$154$	4.90229	+	3.27436i	0.395038	+	0.263856i
$155$	−0.557129			−0.0447497
$156$		0			0
$157$	−3.71438	+	2.69866i	−0.296440	+	0.215376i	−0.726056	−	0.687635i	$-0.758649\pi$
$157$	−3.71438	+	2.69866i	−0.296440	+	0.215376i	0.429616	+	0.903011i	$0.358649\pi$
$158$	9.05011	+	6.57529i	0.719988	+	0.523102i
$159$		0			0
$160$	5.02452	+	15.4639i	0.397223	+	1.22253i
$161$	−3.53548	−	2.56868i	−0.278635	−	0.202440i
$162$		0			0
$163$	2.48377	−	7.64425i	0.194544	−	0.598744i	−0.805438	−	0.592680i	$-0.798070\pi$
$163$	2.48377	−	7.64425i	0.194544	−	0.598744i	0.999982	−	0.00606379i	$-0.00193018\pi$
$164$	−11.1379			−0.869721
$165$		0			0
$166$	−3.05987			−0.237492
$167$	4.14296	−	12.7507i	0.320592	−	0.986681i	−0.652799	−	0.757531i	$-0.726405\pi$
$167$	4.14296	−	12.7507i	0.320592	−	0.986681i	0.973391	−	0.229150i	$-0.0735946\pi$
$168$		0			0
$169$	−4.39615	−	3.19399i	−0.338165	−	0.245691i
$170$	−4.20387	−	12.9382i	−0.322422	−	0.992313i
$171$		0			0
$172$	4.41637	+	3.20868i	0.336745	+	0.244659i
$173$	−16.6512	+	12.0978i	−1.26597	+	0.919782i	−0.999035	−	0.0439325i	$-0.986011\pi$
$173$	−16.6512	+	12.0978i	−1.26597	+	0.919782i	−0.266936	+	0.963714i	$0.586011\pi$
$174$		0			0
$175$	−2.71442			−0.205191
$176$	−12.9550	+	10.2166i	−0.976520	+	0.770104i
$177$		0			0
$178$	−8.40581	+	25.8704i	−0.630042	+	1.93907i
$179$	−3.00566	+	2.18374i	−0.224653	+	0.163220i	−0.694419	−	0.719571i	$-0.744338\pi$
$179$	−3.00566	+	2.18374i	−0.224653	+	0.163220i	0.469765	+	0.882791i	$0.344338\pi$
$180$		0			0
$181$	1.47458	+	4.53828i	0.109604	+	0.337327i	0.990783	−	0.135455i	$-0.0432496\pi$
$181$	1.47458	+	4.53828i	0.109604	+	0.337327i	−0.881179	+	0.472783i	$0.843250\pi$
$182$	−2.35829	−	7.25807i	−0.174808	−	0.538004i
$183$		0			0
$184$	5.28223	−	3.83777i	0.389411	−	0.282924i
$185$	0.888742	−	2.73527i	0.0653416	−	0.201101i
$186$		0			0
$187$	7.17613	−	5.65925i	0.524771	−	0.413845i
$188$	15.1257			1.10315
$189$		0			0
$190$	7.74487	−	5.62698i	0.561872	−	0.408224i
$191$	−0.670803	−	0.487367i	−0.0485376	−	0.0352646i	0.563252	−	0.826285i	$-0.309550\pi$
$191$	−0.670803	−	0.487367i	−0.0485376	−	0.0352646i	−0.611790	+	0.791021i	$0.709550\pi$
$192$		0			0
$193$	−2.08216	−	6.40824i	−0.149878	−	0.461276i	0.847728	−	0.530430i	$-0.177970\pi$
$193$	−2.08216	−	6.40824i	−0.149878	−	0.461276i	−0.997606	+	0.0691550i	$0.977970\pi$
$194$	16.7043	+	12.1364i	1.19930	+	0.871341i
$195$		0			0
$196$	0.358290	−	1.10270i	0.0255921	−	0.0787645i
$197$	10.9216			0.778129			0.389065	−	0.921210i	$-0.372798\pi$
$197$	10.9216			0.778129			0.389065	+	0.921210i	$0.372798\pi$
$198$		0			0
$199$	20.9746			1.48685			0.743424	−	0.668820i	$-0.233200\pi$
$199$	20.9746			1.48685			0.743424	+	0.668820i	$0.233200\pi$
$200$	1.25322	−	3.85702i	0.0886163	−	0.272733i
$201$		0			0
$202$	−4.90620	−	3.56457i	−0.345199	−	0.250802i
$203$	2.66623	+	8.20580i	0.187132	+	0.575934i
$204$		0			0
$205$	21.5854	+	15.6827i	1.50759	+	1.09533i
$206$	−26.1468	+	18.9968i	−1.82174	+	1.32357i
$207$		0			0
$208$	21.3582			1.48093
$209$	5.34802	+	3.57207i	0.369930	+	0.247086i
$210$		0			0
$211$	−1.86140	+	5.72879i	−0.128144	+	0.394386i	−0.994461	−	0.105109i	$-0.966481\pi$
$211$	−1.86140	+	5.72879i	−0.128144	+	0.394386i	0.866317	+	0.499495i	$0.166481\pi$
$212$	−3.65837	+	2.65796i	−0.251258	+	0.182550i
$213$		0			0
$214$	1.78374	+	5.48979i	0.121934	+	0.375274i
$215$	−4.04100	−	12.4369i	−0.275594	−	0.848192i
$216$		0			0
$217$	−0.162279	+	0.117903i	−0.0110162	+	0.00800375i
$218$	−6.97091	+	21.4542i	−0.472129	+	1.45306i
$219$		0			0
$220$	−10.6724	+	0.421195i	−0.719533	+	0.0283970i
$221$	−11.8309			−0.795833
$222$		0			0
$223$	3.74176	−	2.71855i	0.250567	−	0.182048i	−0.455411	−	0.890281i	$-0.650508\pi$
$223$	3.74176	−	2.71855i	0.250567	−	0.182048i	0.705978	+	0.708234i	$0.250508\pi$
$224$	4.73607	+	3.44095i	0.316442	+	0.229908i
$225$		0			0
$226$	−10.1330	−	31.1862i	−0.674038	−	2.07448i
$227$	13.9963	+	10.1689i	0.928965	+	0.674932i	0.945739	−	0.324927i	$-0.105340\pi$
$227$	13.9963	+	10.1689i	0.928965	+	0.674932i	−0.0167745	+	0.999859i	$0.505340\pi$
$228$		0			0
$229$	−1.36775	+	4.20949i	−0.0903832	+	0.278171i	−0.986023	−	0.166609i	$-0.946718\pi$
$229$	−1.36775	+	4.20949i	−0.0903832	+	0.278171i	0.895640	+	0.444780i	$0.146718\pi$
$230$	21.5749			1.42260
$231$		0			0
$232$	−12.8909			−0.846330
$233$	3.25489	−	10.0175i	0.213235	−	0.656269i	−0.786039	−	0.618176i	$-0.787872\pi$
$233$	3.25489	−	10.0175i	0.213235	−	0.656269i	0.999274	−	0.0380929i	$-0.0121283\pi$
$234$		0			0
$235$	−29.3137	−	21.2977i	−1.91222	−	1.38931i
$236$	3.06593	+	9.43597i	0.199575	+	0.614229i
$237$		0			0
$238$	−3.96253	−	2.87895i	−0.256853	−	0.186614i
$239$	−7.89314	+	5.73470i	−0.510565	+	0.370947i	−0.813038	−	0.582211i	$-0.802188\pi$
$239$	−7.89314	+	5.73470i	−0.510565	+	0.370947i	0.302473	+	0.953158i	$0.402188\pi$
$240$		0			0
$241$	12.5501			0.808422			0.404211	−	0.914666i	$-0.367546\pi$
$241$	12.5501			0.808422			0.404211	+	0.914666i	$0.367546\pi$
$242$	−7.48869	−	18.0614i	−0.481391	−	1.16103i
$243$		0			0
$244$	−0.354208	+	1.09014i	−0.0226759	+	0.0697892i
$245$	−2.24703	+	1.63256i	−0.143558	+	0.104301i
$246$		0			0
$247$	−2.57271	−	7.91798i	−0.163698	−	0.503809i
$248$	−0.0926096	−	0.285023i	−0.00588072	−	0.0180990i
$249$		0			0
$250$	−9.12876	+	6.63243i	−0.577353	+	0.419472i
$251$	3.39646	−	10.4532i	0.214383	−	0.659803i	−0.784814	−	0.619732i	$-0.787241\pi$
$251$	3.39646	−	10.4532i	0.214383	−	0.659803i	0.999197	−	0.0400713i	$-0.0127585\pi$
$252$		0			0
$253$	5.01899	+	13.5972i	0.315541	+	0.854850i
$254$	−34.6775			−2.17586
$255$		0			0
$256$	−16.4084	+	11.9214i	−1.02553	+	0.745089i
$257$	4.31432	+	3.13454i	0.269120	+	0.195527i	0.714158	−	0.699985i	$-0.246810\pi$
$257$	4.31432	+	3.13454i	0.269120	+	0.195527i	−0.445038	+	0.895512i	$0.646810\pi$
$258$		0			0
$259$	−0.319981	−	0.984800i	−0.0198827	−	0.0611925i
$260$	11.1859	+	8.12702i	0.693719	+	0.504017i
$261$		0			0
$262$	−3.78886	+	11.6609i	−0.234077	+	0.720414i
$263$	8.18034			0.504421			0.252211	−	0.967672i	$-0.418842\pi$
$263$	8.18034			0.504421			0.252211	+	0.967672i	$0.418842\pi$
$264$		0			0
$265$	10.8325			0.665436
$266$	1.06509	−	3.27802i	0.0653050	−	0.200988i
$267$		0			0
$268$	5.08165	+	3.69203i	0.310411	+	0.225527i
$269$	−3.96899	−	12.2153i	−0.241993	−	0.744779i	−0.996116	−	0.0880459i	$-0.971938\pi$
$269$	−3.96899	−	12.2153i	−0.241993	−	0.744779i	0.754123	−	0.656733i	$-0.228062\pi$
$270$		0			0
$271$	17.8366	+	12.9590i	1.08349	+	0.787205i	0.978289	−	0.207246i	$-0.0664499\pi$
$271$	17.8366	+	12.9590i	1.08349	+	0.787205i	0.105206	+	0.994450i	$0.466450\pi$
$272$	11.0898	−	8.05720i	0.672417	−	0.488539i
$273$		0			0
$274$	−4.64047			−0.280341
$275$	7.48636	+	5.00032i	0.451444	+	0.301531i
$276$		0			0
$277$	7.44019	−	22.8986i	0.447038	−	1.37584i	−0.433196	−	0.901300i	$-0.642614\pi$
$277$	7.44019	−	22.8986i	0.447038	−	1.37584i	0.880234	−	0.474541i	$-0.157386\pi$
$278$	−1.43994	+	1.04617i	−0.0863616	+	0.0627454i
$279$		0			0
$280$	−1.28234	−	3.94664i	−0.0766345	−	0.235857i
$281$	−4.77179	−	14.6861i	−0.284661	−	0.876097i	−0.986500	−	0.163761i	$-0.947637\pi$
$281$	−4.77179	−	14.6861i	−0.284661	−	0.876097i	0.701839	−	0.712336i	$-0.252363\pi$
$282$		0			0
$283$	2.71613	−	1.97338i	0.161457	−	0.117305i	−0.504123	−	0.863632i	$-0.668184\pi$
$283$	2.71613	−	1.97338i	0.161457	−	0.117305i	0.665580	+	0.746326i	$0.268184\pi$
$284$	0.722688	−	2.22421i	0.0428836	−	0.131982i
$285$		0			0
$286$	−6.86618	+	24.3620i	−0.406006	+	1.44056i
$287$	9.60616			0.567034
$288$		0			0
$289$	7.61035	−	5.52924i	0.447668	−	0.325250i
$290$	−34.4611	−	25.0375i	−2.02363	−	1.47025i
$291$		0			0
$292$	−3.57254	−	10.9951i	−0.209067	−	0.643442i
$293$	5.53129	+	4.01872i	0.323142	+	0.234776i	0.737515	−	0.675331i	$-0.235999\pi$
$293$	5.53129	+	4.01872i	0.323142	+	0.234776i	−0.414373	+	0.910107i	$0.635999\pi$
$294$		0			0
$295$	7.34450	−	22.6040i	0.427613	−	1.31606i
$296$	1.54707			0.0899218
$297$		0			0
$298$	−26.4752			−1.53367
$299$	5.79805	−	17.8446i	0.335310	−	1.03198i
$300$		0			0
$301$	−3.80902	−	2.76741i	−0.219548	−	0.159511i
$302$	−8.68103	−	26.7175i	−0.499537	−	1.53742i
$303$		0			0
$304$	7.80392	+	5.66988i	0.447586	+	0.325190i
$305$	2.22144	−	1.61397i	0.127199	−	0.0924155i
$306$		0			0
$307$	−11.7970			−0.673293			−0.336646	−	0.941631i	$-0.609293\pi$
$307$	−11.7970			−0.673293			−0.336646	+	0.941631i	$0.609293\pi$
$308$	−3.01949	+	2.38123i	−0.172051	+	0.135683i
$309$		0			0
$310$	0.306016	−	0.941821i	0.0173805	−	0.0534918i
$311$	20.4794	−	14.8791i	1.16128	−	0.843718i	0.171339	−	0.985212i	$-0.445191\pi$
$311$	20.4794	−	14.8791i	1.16128	−	0.843718i	0.989939	+	0.141494i	$0.0451906\pi$
$312$		0			0
$313$	−6.07352	−	18.6924i	−0.343296	−	1.05656i	−0.962490	−	0.271318i	$-0.912540\pi$
$313$	−6.07352	−	18.6924i	−0.343296	−	1.05656i	0.619194	−	0.785238i	$-0.287460\pi$
$314$	−2.52184	−	7.76141i	−0.142315	−	0.438002i
$315$		0			0
$316$	−5.90337	+	4.28905i	−0.332091	+	0.241278i
$317$	−1.11572	+	3.43385i	−0.0626653	+	0.192864i	−0.977488	−	0.210992i	$-0.932330\pi$
$317$	−1.11572	+	3.43385i	−0.0626653	+	0.192864i	0.914822	+	0.403856i	$0.132330\pi$
$318$		0			0
$319$	7.76275	−	27.5431i	0.434630	−	1.54212i
$320$	−1.26771			−0.0708670
$321$		0			0
$322$	6.28426	−	4.56578i	0.350208	−	0.254441i
$323$	−4.32281	−	3.14071i	−0.240528	−	0.174754i
$324$		0			0
$325$	−3.60137	−	11.0839i	−0.199768	−	0.614824i
$326$	11.5582	+	8.39756i	0.640152	+	0.465098i
$327$		0			0
$328$	−4.43508	+	13.6498i	−0.244886	+	0.753683i
$329$	−13.0455			−0.719224
$330$		0			0
$331$	−26.5335			−1.45841			−0.729205	−	0.684295i	$-0.760110\pi$
$331$	−26.5335			−1.45841			−0.729205	+	0.684295i	$0.760110\pi$
$332$	0.616781	−	1.89826i	0.0338503	−	0.104180i
$333$		0			0
$334$	19.2793	+	14.0073i	1.05492	+	0.766443i
$335$	−4.64974	−	14.3104i	−0.254042	−	0.781862i
$336$		0			0
$337$	0.554969	+	0.403208i	0.0302311	+	0.0219642i	0.602798	−	0.797894i	$-0.294052\pi$
$337$	0.554969	+	0.403208i	0.0302311	+	0.0219642i	−0.572567	+	0.819858i	$0.694052\pi$
$338$	7.81408	−	5.67726i	0.425030	−	0.308802i
$339$		0			0
$340$	8.87387			0.481253
$341$	0.664757	−	0.0262352i	0.0359986	−	0.00142071i
$342$		0			0
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$	5.69091	−	4.13469i	0.306834	−	0.222928i
$345$		0			0
$346$	−11.3052	−	34.7937i	−0.607770	−	1.87052i
$347$	−6.64555	−	20.4529i	−0.356752	−	1.09797i	−0.954987	−	0.296649i	$-0.904131\pi$
$347$	−6.64555	−	20.4529i	−0.356752	−	1.09797i	0.598235	−	0.801321i	$-0.295869\pi$
$348$		0			0
$349$	−15.7296	+	11.4282i	−0.841987	+	0.611739i	−0.922925	−	0.384980i	$-0.874208\pi$
$349$	−15.7296	+	11.4282i	−0.841987	+	0.611739i	0.0809381	+	0.996719i	$0.474208\pi$
$350$	1.49096	−	4.58869i	0.0796950	−	0.245276i
$351$		0			0
$352$	−6.72336	−	18.2146i	−0.358356	−	0.970842i
$353$	20.9307			1.11403			0.557015	−	0.830502i	$-0.311947\pi$
$353$	20.9307			1.11403			0.557015	+	0.830502i	$0.311947\pi$
$354$		0			0
$355$	−4.53237	+	3.29296i	−0.240553	+	0.174772i
$356$	−14.3549	−	10.4295i	−0.760810	−	0.552761i
$357$		0			0
$358$	−2.04066	−	6.28050i	−0.107852	−	0.331935i
$359$	7.90512	+	5.74341i	0.417216	+	0.303125i	0.776517	−	0.630096i	$-0.216985\pi$
$359$	7.90512	+	5.74341i	0.417216	+	0.303125i	−0.359300	+	0.933222i	$0.616985\pi$
$360$		0			0
$361$	−4.70939	+	14.4940i	−0.247863	+	0.762843i
$362$	−8.48185			−0.445796
$363$		0			0
$364$	4.97807			0.260922
$365$	−8.55808	+	26.3390i	−0.447950	+	1.37865i
$366$		0			0
$367$	−8.00901	−	5.81889i	−0.418067	−	0.303744i	0.358793	−	0.933417i	$-0.383189\pi$
$367$	−8.00901	−	5.81889i	−0.418067	−	0.303744i	−0.776860	+	0.629674i	$0.783189\pi$
$368$	6.71783	+	20.6754i	0.350191	+	1.07778i
$369$		0			0
$370$	4.13577	+	3.00482i	0.215009	+	0.156213i
$371$	3.15526	−	2.29243i	0.163813	−	0.119017i
$372$		0			0
$373$	−4.27475			−0.221338			−0.110669	−	0.993857i	$-0.535299\pi$
$373$	−4.27475			−0.221338			−0.110669	+	0.993857i	$0.535299\pi$
$374$	5.62524	+	15.2396i	0.290874	+	0.788023i
$375$		0			0
$376$	6.02301	−	18.5369i	0.310613	−	0.955968i
$377$	−29.9696	+	21.7742i	−1.54351	+	1.12143i
$378$		0			0
$379$	1.33679	+	4.11421i	0.0686662	+	0.211333i	0.979501	−	0.201437i	$-0.0645612\pi$
$379$	1.33679	+	4.11421i	0.0686662	+	0.211333i	−0.910835	+	0.412770i	$0.864561\pi$
$380$	1.92968	+	5.93894i	0.0989905	+	0.304661i
$381$		0			0
$382$	1.19234	−	0.866287i	0.0610055	−	0.0443231i
$383$	0.408551	−	1.25739i	0.0208760	−	0.0642497i	−0.940076	−	0.340966i	$-0.889246\pi$
$383$	0.408551	−	1.25739i	0.0208760	−	0.0642497i	0.960952	+	0.276716i	$0.0892461\pi$
$384$		0			0
$385$	9.20471	−	0.363271i	0.469115	−	0.0185140i
$386$	11.9767			0.609600
$387$		0			0
$388$	−10.8962	+	7.91654i	−0.553170	+	0.401902i
$389$	−31.1546	−	22.6351i	−1.57960	−	1.14765i	−0.917152	−	0.398537i	$-0.869518\pi$
$389$	−31.1546	−	22.6351i	−1.57960	−	1.14765i	−0.662447	−	0.749109i	$-0.730482\pi$
$390$		0			0
$391$	−3.72119	−	11.4527i	−0.188189	−	0.579186i
$392$	−1.20872	−	0.878189i	−0.0610497	−	0.0443552i
$393$		0			0
$394$	−5.99892	+	18.4628i	−0.302221	+	0.930141i
$395$	17.4800			0.879516
$396$		0			0
$397$	−0.410109			−0.0205828			−0.0102914	−	0.999947i	$-0.503276\pi$
$397$	−0.410109			−0.0205828			−0.0102914	+	0.999947i	$0.503276\pi$
$398$	−11.5208	+	35.4573i	−0.577484	+	1.77731i
$399$		0			0
$400$	10.9242	+	7.93691i	0.546211	+	0.396846i
$401$	0.484180	+	1.49015i	0.0241788	+	0.0744147i	0.962418	−	0.271573i	$-0.0875439\pi$
$401$	0.484180	+	1.49015i	0.0241788	+	0.0744147i	−0.938239	+	0.345988i	$0.887544\pi$
$402$		0			0
$403$	−0.696741	−	0.506212i	−0.0347071	−	0.0252162i
$404$	3.20031	−	2.32516i	0.159221	−	0.115681i
$405$		0			0
$406$	−15.3363			−0.761127
$407$	−0.931628	+	3.30552i	−0.0461791	+	0.163849i
$408$		0			0
$409$	−2.09468	+	6.44676i	−0.103575	+	0.318772i	−0.989393	−	0.145261i	$-0.953598\pi$
$409$	−2.09468	+	6.44676i	−0.103575	+	0.318772i	0.885818	+	0.464032i	$0.153598\pi$
$410$	−38.3676	+	27.8757i	−1.89484	+	1.37668i
$411$		0			0
$412$	−6.51463	−	20.0500i	−0.320953	−	0.987792i
$413$	−2.64430	−	8.13831i	−0.130117	−	0.400460i
$414$		0			0
$415$	−3.86817	+	2.81039i	−0.189881	+	0.137957i
$416$	−7.76697	+	23.9043i	−0.380807	+	1.17200i
$417$		0			0
$418$	−8.97607	+	7.07872i	−0.439034	+	0.346231i
$419$	−28.7218			−1.40315			−0.701577	−	0.712594i	$-0.747520\pi$
$419$	−28.7218			−1.40315			−0.701577	+	0.712594i	$0.747520\pi$
$420$		0			0
$421$	−9.89070	+	7.18601i	−0.482043	+	0.350225i	−0.802116	−	0.597168i	$-0.796293\pi$
$421$	−9.89070	+	7.18601i	−0.482043	+	0.350225i	0.320073	+	0.947393i	$0.396293\pi$
$422$	−8.66204	−	6.29334i	−0.421661	−	0.306355i
$423$		0			0
$424$	1.80065	+	5.54183i	0.0874473	+	0.269135i
$425$	−6.05123	−	4.39648i	−0.293528	−	0.213260i
$426$		0			0
$427$	0.305497	−	0.940223i	0.0147840	−	0.0455006i
$428$	−3.76527			−0.182001
$429$		0			0
$430$	23.2441			1.12093
$431$	−1.14067	+	3.51063i	−0.0549442	+	0.169101i	−0.974763	−	0.223243i	$-0.928336\pi$
$431$	−1.14067	+	3.51063i	−0.0549442	+	0.169101i	0.919819	+	0.392344i	$0.128336\pi$
$432$		0			0
$433$	−23.5221	−	17.0898i	−1.13040	−	0.821283i	−0.144646	−	0.989483i	$-0.546204\pi$
$433$	−23.5221	−	17.0898i	−1.13040	−	0.821283i	−0.985753	+	0.168201i	$0.946204\pi$
$434$	−0.110177	−	0.339091i	−0.00528869	−	0.0162769i
$435$		0			0
$436$	−11.9045	−	8.64912i	−0.570122	−	0.414218i
$437$	6.85563	−	4.98091i	0.327949	−	0.238269i
$438$		0			0
$439$	−14.2017			−0.677811			−0.338905	−	0.940820i	$-0.610057\pi$
$439$	−14.2017			−0.677811			−0.338905	+	0.940820i	$0.610057\pi$
$440$	−3.73355	+	13.2470i	−0.177990	+	0.631528i
$441$		0			0
$442$	6.49840	−	20.0000i	0.309097	−	0.951304i
$443$	22.0341	−	16.0087i	1.04687	−	0.760595i	0.0752548	−	0.997164i	$-0.476023\pi$
$443$	22.0341	−	16.0087i	1.04687	−	0.760595i	0.971615	+	0.236569i	$0.0760230\pi$
$444$		0			0
$445$	13.1349	+	40.4250i	0.622652	+	1.91633i
$446$	2.54043	+	7.81863i	0.120293	+	0.370223i
$447$		0			0
$448$	−0.369254	+	0.268279i	−0.0174456	+	0.0126750i
$449$	12.9527	−	39.8644i	0.611277	−	1.88132i	0.165389	−	0.986228i	$-0.447112\pi$
$449$	12.9527	−	39.8644i	0.611277	−	1.88132i	0.445888	−	0.895089i	$-0.352888\pi$
$450$		0			0
$451$	−26.4938	−	17.6958i	−1.24754	−	0.833265i
$452$	21.3896			1.00608
$453$		0			0
$454$	−24.8781	+	18.0750i	−1.16759	+	0.848303i
$455$	−9.64758	−	7.00938i	−0.452285	−	0.328605i
$456$		0			0
$457$	6.02512	+	18.5434i	0.281843	+	0.867424i	0.987327	+	0.158698i	$0.0507296\pi$
$457$	6.02512	+	18.5434i	0.281843	+	0.867424i	−0.705484	+	0.708726i	$0.749270\pi$
$458$	−6.36483	−	4.62432i	−0.297409	−	0.216080i
$459$		0			0
$460$	−4.34887	+	13.3845i	−0.202767	+	0.624054i
$461$	−12.2251			−0.569380			−0.284690	−	0.958620i	$-0.591891\pi$
$461$	−12.2251			−0.569380			−0.284690	+	0.958620i	$0.591891\pi$
$462$		0			0
$463$	13.8550			0.643894			0.321947	−	0.946758i	$-0.395663\pi$
$463$	13.8550			0.643894			0.321947	+	0.946758i	$0.395663\pi$
$464$	13.2633	−	40.8204i	0.615735	−	1.89504i
$465$		0			0
$466$	15.1467	+	11.0047i	0.701656	+	0.509783i
$467$	5.07428	+	15.6170i	0.234810	+	0.722671i	0.997147	+	0.0754899i	$0.0240521\pi$
$467$	5.07428	+	15.6170i	0.234810	+	0.722671i	−0.762337	+	0.647181i	$0.775948\pi$
$468$		0			0
$469$	−4.38281	−	3.18429i	−0.202379	−	0.147037i
$470$	52.1047	−	37.8563i	2.40341	−	1.74618i
$471$		0			0
$472$	12.7849			0.588473
$473$	5.40731	+	14.6492i	0.248628	+	0.673572i
$474$		0			0
$475$	1.62652	−	5.00590i	0.0746297	−	0.229687i
$476$	2.58475	−	1.87793i	0.118472	−	0.0860749i
$477$		0			0
$478$	−5.35896	−	16.4932i	−0.245113	−	0.754380i
$479$	7.66096	+	23.5780i	0.350038	+	1.07731i	0.958831	+	0.283977i	$0.0916540\pi$
$479$	7.66096	+	23.5780i	0.350038	+	1.07731i	−0.608793	+	0.793329i	$0.708346\pi$
$480$		0			0
$481$	3.59674	−	2.61318i	0.163997	−	0.119151i
$482$	−6.89342	+	21.2158i	−0.313987	+	0.966352i
$483$		0			0
$484$	12.7143	−	1.00512i	0.577922	−	0.0456875i
$485$	32.2639			1.46503
$486$		0			0
$487$	11.5966	−	8.42542i	0.525492	−	0.381792i	−0.293177	−	0.956058i	$-0.594712\pi$
$487$	11.5966	−	8.42542i	0.525492	−	0.381792i	0.818669	+	0.574266i	$0.194712\pi$
$488$	1.19495	+	0.868185i	0.0540930	+	0.0393009i
$489$		0			0
$490$	−1.52560	−	4.69530i	−0.0689194	−	0.212112i
$491$	−17.8140	−	12.9426i	−0.803935	−	0.584093i	0.108131	−	0.994137i	$-0.465514\pi$
$491$	−17.8140	−	12.9426i	−0.803935	−	0.584093i	−0.912066	+	0.410044i	$0.865514\pi$
$492$		0			0
$493$	−7.34694	+	22.6115i	−0.330889	+	1.01837i
$494$	14.7984			0.665810
$495$		0			0
$496$	0.997839			0.0448043
$497$	−0.623302	+	1.91833i	−0.0279589	+	0.0860487i
$498$		0			0
$499$	20.4776	+	14.8779i	0.916704	+	0.666024i	0.942701	−	0.333638i	$-0.108276\pi$
$499$	20.4776	+	14.8779i	0.916704	+	0.666024i	−0.0259975	+	0.999662i	$0.508276\pi$
$500$	−2.27448	−	7.00014i	−0.101718	−	0.313056i
$501$		0			0
$502$	15.8055	+	11.4834i	0.705434	+	0.512528i
$503$	−21.0518	+	15.2950i	−0.938653	+	0.681971i	−0.948096	−	0.317984i	$-0.896994\pi$
$503$	−21.0518	+	15.2950i	−0.938653	+	0.681971i	0.00944301	+	0.999955i	$0.496994\pi$
$504$		0			0
$505$	−9.47619			−0.421685
$506$	−25.7427	+	1.01596i	−1.14440	+	0.0451649i
$507$		0			0
$508$	6.98998	−	21.5130i	0.310130	−	0.954483i
$509$	30.8453	−	22.4104i	1.36719	−	0.993325i	0.369244	−	0.929333i	$-0.379617\pi$
$509$	30.8453	−	22.4104i	1.36719	−	0.993325i	0.997950	−	0.0639922i	$-0.0203833\pi$
$510$		0			0
$511$	3.08123	+	9.48306i	0.136306	+	0.419506i
$512$	−4.40566	−	13.5592i	−0.194704	−	0.599238i
$513$		0			0
$514$	−7.66864	+	5.57159i	−0.338249	+	0.245753i
$515$	−15.6059	+	48.0301i	−0.687679	+	2.11646i
$516$		0			0
$517$	35.9795	+	24.0316i	1.58238	+	1.05691i
$518$	1.84055			0.0808691
$519$		0			0
$520$	14.4141	−	10.4725i	0.632100	−	0.459248i
$521$	−21.0684	−	15.3071i	−0.923024	−	0.670616i	0.0212509	−	0.999774i	$-0.493235\pi$
$521$	−21.0684	−	15.3071i	−0.923024	−	0.670616i	−0.944275	+	0.329158i	$0.893235\pi$
$522$		0			0
$523$	5.90933	+	18.1870i	0.258397	+	0.795263i	0.993141	+	0.116920i	$0.0373020\pi$
$523$	5.90933	+	18.1870i	0.258397	+	0.795263i	−0.734745	+	0.678344i	$0.762698\pi$
$524$	−6.47039	−	4.70101i	−0.282660	−	0.205365i
$525$		0			0
$526$	−4.49324	+	13.8288i	−0.195915	+	0.602963i
$527$	−0.552731			−0.0240773
$528$		0			0
$529$	−3.90228			−0.169664
$530$	−5.95001	+	18.3122i	−0.258452	+	0.795433i
$531$		0			0
$532$	1.81890	+	1.32151i	0.0788593	+	0.0572947i
$533$	12.7450	+	39.2252i	0.552049	+	1.69903i
$534$		0			0
$535$	7.29714	+	5.30169i	0.315483	+	0.229212i
$536$	6.54819	−	4.75754i	0.282839	−	0.205494i
$537$		0			0
$538$	22.8298			0.984265
$539$	2.60424	−	2.05376i	0.112173	−	0.0884617i
$540$		0			0
$541$	3.36397	−	10.3532i	0.144628	−	0.445120i	−0.852335	−	0.522997i	$-0.824814\pi$
$541$	3.36397	−	10.3532i	0.144628	−	0.445120i	0.996963	+	0.0778764i	$0.0248139\pi$
$542$	−31.7042	+	23.0345i	−1.36181	+	0.989415i
$543$		0			0
$544$	4.98485	+	15.3418i	0.213724	+	0.657774i
$545$	10.8927	+	33.5243i	0.466592	+	1.43602i
$546$		0			0
$547$	10.4436	−	7.58775i	0.446538	−	0.324429i	−0.341689	−	0.939813i	$-0.610999\pi$
$547$	10.4436	−	7.58775i	0.446538	−	0.324429i	0.788227	+	0.615384i	$0.210999\pi$
$548$	0.935386	−	2.87882i	0.0399577	−	0.122977i
$549$		0			0
$550$	−12.5650	+	9.90905i	−0.535775	+	0.422523i
$551$	−16.7307			−0.712751
$552$		0			0
$553$	5.09153	−	3.69921i	0.216514	−	0.157307i
$554$	34.6230	+	25.1551i	1.47099	+	1.06874i
$555$		0			0
$556$	−0.358768	−	1.10418i	−0.0152152	−	0.0468275i
$557$	−0.616977	−	0.448260i	−0.0261422	−	0.0189934i	0.574637	−	0.818408i	$-0.305143\pi$
$557$	−0.616977	−	0.448260i	−0.0261422	−	0.0189934i	−0.600780	+	0.799415i	$0.705143\pi$
$558$		0			0
$559$	6.24664	−	19.2252i	0.264205	−	0.813139i
$560$	13.8168			0.583867
$561$		0			0
$562$	27.4476			1.15781
$563$	6.86886	−	21.1402i	0.289488	−	0.890953i	−0.695529	−	0.718498i	$-0.744830\pi$
$563$	6.86886	−	21.1402i	0.289488	−	0.890953i	0.985017	−	0.172455i	$-0.0551700\pi$
$564$		0			0
$565$	−41.4534	−	30.1176i	−1.74396	−	1.26706i
$566$	1.84408	+	5.67551i	0.0775127	+	0.238559i
$567$		0			0
$568$	−2.43805	−	1.77135i	−0.102298	−	0.0743242i
$569$	−16.5955	+	12.0573i	−0.695719	+	0.505469i	−0.878535	−	0.477678i	$-0.841479\pi$
$569$	−16.5955	+	12.0573i	−0.695719	+	0.505469i	0.182816	+	0.983147i	$0.441479\pi$
$570$		0			0
$571$	−19.5654			−0.818785			−0.409393	−	0.912358i	$-0.634259\pi$
$571$	−19.5654			−0.818785			−0.409393	+	0.912358i	$0.634259\pi$
$572$	−13.7295	−	9.17028i	−0.574059	−	0.383429i
$573$		0			0
$574$	−5.27640	+	16.2391i	−0.220233	+	0.677807i
$575$	9.59677	−	6.97246i	0.400213	−	0.290772i
$576$		0			0
$577$	−6.04795	−	18.6137i	−0.251780	−	0.774898i	−0.994447	−	0.105237i	$-0.966440\pi$
$577$	−6.04795	−	18.6137i	−0.251780	−	0.774898i	0.742668	−	0.669660i	$-0.233560\pi$
$578$	5.16696	+	15.9023i	0.214917	+	0.661447i
$579$		0			0
$580$	22.4790	−	16.3319i	0.933388	−	0.678146i
$581$	−0.531960	+	1.63720i	−0.0220694	+	0.0679227i
$582$		0			0
$583$	−12.9252	+	0.510102i	−0.535306	+	0.0211263i
$584$	−14.8974			−0.616460
$585$		0			0
$586$	−9.83178	+	7.14321i	−0.406147	+	0.295083i
$587$	1.27071	+	0.923224i	0.0524477	+	0.0381055i	0.613700	−	0.789539i	$-0.289680\pi$
$587$	1.27071	+	0.923224i	0.0524477	+	0.0381055i	−0.561253	+	0.827645i	$0.689680\pi$
$588$		0			0
$589$	−0.120195	−	0.369922i	−0.00495254	−	0.0152424i
$590$	34.1777	+	24.8316i	1.40707	+	1.02230i
$591$		0			0
$592$	−1.59177	+	4.89896i	−0.0654213	+	0.201346i
$593$	30.1230			1.23700			0.618502	−	0.785783i	$-0.287740\pi$
$593$	30.1230			1.23700			0.618502	+	0.785783i	$0.287740\pi$
$594$		0			0
$595$	−7.65351			−0.313763
$596$	5.33664	−	16.4245i	0.218597	−	0.672773i
$597$		0			0
$598$	26.9813	+	19.6031i	1.10335	+	0.801629i
$599$	−1.78547	−	5.49513i	−0.0729525	−	0.224525i	0.907931	−	0.419119i	$-0.137661\pi$
$599$	−1.78547	−	5.49513i	−0.0729525	−	0.224525i	−0.980884	+	0.194594i	$0.937661\pi$
$600$		0			0
$601$	−36.8625	−	26.7822i	−1.50365	−	1.09247i	−0.968898	−	0.247460i	$-0.920404\pi$
$601$	−36.8625	−	26.7822i	−1.50365	−	1.09247i	−0.534754	−	0.845008i	$-0.679596\pi$
$602$	6.77047	−	4.91903i	0.275944	−	0.200485i
$603$		0			0
$604$	18.3246			0.745619
$605$	−26.0557	−	15.9544i	−1.05932	−	0.648639i
$606$		0			0
$607$	10.7294	−	33.0217i	0.435493	−	1.34031i	−0.457088	−	0.889421i	$-0.651108\pi$
$607$	10.7294	−	33.0217i	0.435493	−	1.34031i	0.892581	−	0.450887i	$-0.148892\pi$
$608$	−9.18369	+	6.67234i	−0.372448	+	0.270599i
$609$		0			0
$610$	1.50822	+	4.64182i	0.0610660	+	0.187942i
$611$	−17.3083	−	53.2693i	−0.700217	−	2.15505i
$612$		0			0
$613$	19.5315	−	14.1905i	0.788870	−	0.573148i	−0.118758	−	0.992923i	$-0.537891\pi$
$613$	19.5315	−	14.1905i	0.788870	−	0.573148i	0.907628	+	0.419776i	$0.137891\pi$
$614$	6.47979	−	19.9428i	0.261503	−	0.804824i
$615$		0			0
$616$	1.71591	+	4.64867i	0.0691361	+	0.187300i
$617$	13.4967			0.543358			0.271679	−	0.962388i	$-0.412421\pi$
$617$	13.4967			0.543358			0.271679	+	0.962388i	$0.412421\pi$
$618$		0			0
$619$	35.1806	−	25.5602i	1.41403	−	1.02735i	0.421307	−	0.906918i	$-0.361572\pi$
$619$	35.1806	−	25.5602i	1.41403	−	1.02735i	0.992721	−	0.120433i	$-0.0384284\pi$
$620$	0.522596	+	0.379688i	0.0209879	+	0.0152486i
$621$		0			0
$622$	13.9042	+	42.7928i	0.557509	+	1.71584i
$623$	12.3808	+	8.99519i	0.496027	+	0.360385i
$624$		0			0
$625$	−9.64257	+	29.6768i	−0.385703	+	1.18707i
$626$	34.9353			1.39629
$627$		0			0
$628$	5.32330			0.212423
$629$	0.881726	−	2.71367i	0.0351567	−	0.108201i
$630$		0			0
$631$	−5.19398	−	3.77365i	−0.206769	−	0.150227i	0.479581	−	0.877497i	$-0.340788\pi$
$631$	−5.19398	−	3.77365i	−0.206769	−	0.150227i	−0.686351	+	0.727271i	$0.740788\pi$
$632$	2.90564	+	8.94265i	0.115580	+	0.355719i
$633$		0			0
$634$	−5.19204	−	3.77224i	−0.206202	−	0.149815i
$635$	−43.8380	+	31.8502i	−1.73966	+	1.26394i
$636$		0			0
$637$	−4.29348			−0.170114
$638$	42.2974	+	28.2515i	1.67457	+	1.11849i
$639$		0			0
$640$	−9.35272	+	28.7847i	−0.369699	+	1.13782i
$641$	−5.17447	+	3.75947i	−0.204379	+	0.148490i	−0.685267	−	0.728292i	$-0.740314\pi$
$641$	−5.17447	+	3.75947i	−0.204379	+	0.148490i	0.480888	+	0.876782i	$0.340314\pi$
$642$		0			0
$643$	0.201683	+	0.620716i	0.00795360	+	0.0244787i	0.954955	−	0.296752i	$-0.0959035\pi$
$643$	0.201683	+	0.620716i	0.00795360	+	0.0244787i	−0.947001	+	0.321231i	$0.895903\pi$
$644$	1.56576	+	4.81891i	0.0616996	+	0.189892i
$645$		0			0
$646$	7.68373	−	5.58255i	0.302312	−	0.219643i
$647$	−5.55061	+	17.0830i	−0.218217	+	0.671603i	0.780693	+	0.624915i	$0.214866\pi$
$647$	−5.55061	+	17.0830i	−0.218217	+	0.671603i	−0.998910	+	0.0466874i	$0.985134\pi$
$648$		0			0
$649$	−7.69890	+	27.3166i	−0.302208	+	1.07227i
$650$	20.7153			0.812522
$651$		0			0
$652$	−7.53943	+	5.47771i	−0.295267	+	0.214524i
$653$	−13.6870	−	9.94419i	−0.535614	−	0.389146i	0.286840	−	0.957979i	$-0.407395\pi$
$653$	−13.6870	−	9.94419i	−0.535614	−	0.389146i	−0.822454	+	0.568832i	$0.807395\pi$
$654$		0			0
$655$	5.92045	+	18.2213i	0.231331	+	0.711964i
$656$	−38.6602	−	28.0882i	−1.50943	−	1.09666i
$657$		0			0
$658$	7.16556	−	22.0533i	0.279343	−	0.859728i
$659$	−23.6249			−0.920297			−0.460148	−	0.887842i	$-0.652204\pi$
$659$	−23.6249			−0.920297			−0.460148	+	0.887842i	$0.652204\pi$
$660$		0			0
$661$	−20.9819			−0.816103			−0.408051	−	0.912959i	$-0.633792\pi$
$661$	−20.9819			−0.816103			−0.408051	+	0.912959i	$0.633792\pi$
$662$	14.5741	−	44.8545i	0.566439	−	1.74332i
$663$		0			0
$664$	−2.08077	−	1.51177i	−0.0807494	−	0.0586679i
$665$	−1.66431	−	5.12221i	−0.0645390	−	0.198631i
$666$		0			0
$667$	−30.5044	−	22.1628i	−1.18114	−	0.858146i
$668$	−12.5759	+	9.13691i	−0.486575	+	0.353518i
$669$		0			0
$670$	26.7456			1.03327
$671$	−2.57458	+	2.03036i	−0.0993904	+	0.0783813i
$672$		0			0
$673$	3.73868	−	11.5065i	0.144116	−	0.443542i	−0.852781	−	0.522269i	$-0.825086\pi$
$673$	3.73868	−	11.5065i	0.144116	−	0.443542i	0.996896	+	0.0787272i	$0.0250856\pi$
$674$	−0.986448	+	0.716696i	−0.0379965	+	0.0276061i
$675$		0			0
$676$	1.94692	+	5.99202i	0.0748817	+	0.230462i
$677$	2.91399	+	8.96834i	0.111994	+	0.344681i	0.991308	−	0.131560i	$-0.0419987\pi$
$677$	2.91399	+	8.96834i	0.111994	+	0.344681i	−0.879314	+	0.476242i	$0.841999\pi$
$678$		0			0
$679$	9.39772	−	6.82784i	0.360651	−	0.262029i
$680$	3.53356	−	10.8752i	0.135506	−	0.417044i
$681$		0			0
$682$	−0.320783	+	1.13817i	−0.0122834	+	0.0435829i
$683$	15.2986			0.585385			0.292692	−	0.956207i	$-0.405449\pi$
$683$	15.2986			0.585385			0.292692	+	0.956207i	$0.405449\pi$
$684$		0			0
$685$	−5.86632	+	4.26213i	−0.224141	+	0.162848i
$686$	−1.43801	−	1.04478i	−0.0549037	−	0.0398898i
$687$		0			0
$688$	7.23758	+	22.2750i	0.275930	+	0.849226i
$689$	13.5470	+	9.84250i	0.516101	+	0.374970i
$690$		0			0
$691$	7.05154	−	21.7024i	0.268253	−	0.825599i	−0.722673	−	0.691190i	$-0.757087\pi$
$691$	7.05154	−	21.7024i	0.268253	−	0.825599i	0.990926	−	0.134408i	$-0.0429134\pi$
$692$	23.8639			0.907169
$693$		0			0
$694$	38.2256			1.45102
$695$	−0.859436	+	2.64507i	−0.0326003	+	0.100333i
$696$		0			0
$697$	21.4149	+	15.5589i	0.811149	+	0.589334i
$698$	−10.6794	−	32.8679i	−0.404223	−	1.24407i
$699$		0			0
$700$	2.54617	+	1.84990i	0.0962360	+	0.0699196i
$701$	−26.1508	+	18.9997i	−0.987702	+	0.717607i	−0.959417	−	0.281992i	$-0.909005\pi$
$701$	−26.1508	+	18.9997i	−0.987702	+	0.717607i	−0.0282853	+	0.999600i	$0.509005\pi$
$702$		0			0
$703$	2.00789			0.0757292
$704$	1.51261	−	0.0596962i	0.0570085	−	0.00224989i
$705$		0			0
$706$	−11.4967	+	35.3831i	−0.432683	+	1.33166i
$707$	−2.76020	+	2.00540i	−0.103808	+	0.0754208i
$708$		0			0
$709$	4.49922	+	13.8472i	0.168972	+	0.520041i	0.999307	−	0.0372228i	$-0.0118511\pi$
$709$	4.49922	+	13.8472i	0.168972	+	0.520041i	−0.830335	+	0.557264i	$0.811851\pi$
$710$	−3.07720	−	9.47066i	−0.115485	−	0.355427i
$711$		0			0
$712$	−18.4977	+	13.4394i	−0.693232	+	0.503662i
$713$	0.270880	−	0.833684i	0.0101446	−	0.0312217i
$714$		0			0
$715$	13.6958	+	37.1040i	0.512193	+	1.38761i
$716$	4.30759			0.160982
$717$		0			0
$718$	−14.0512	+	10.2088i	−0.524387	+	0.380990i
$719$	36.2926	+	26.3682i	1.35349	+	0.983366i	0.998829	+	0.0483700i	$0.0154027\pi$
$719$	36.2926	+	26.3682i	1.35349	+	0.983366i	0.354658	+	0.934996i	$0.384597\pi$
$720$		0			0
$721$	5.61873	+	17.2927i	0.209252	+	0.644012i
$722$	−21.9152	−	15.9223i	−0.815600	−	0.592568i
$723$		0			0
$724$	1.70970	−	5.26191i	0.0635404	−	0.195557i
$725$	−23.4202			−0.869806
$726$		0			0
$727$	28.3582			1.05175			0.525874	−	0.850562i	$-0.323738\pi$
$727$	28.3582			1.05175			0.525874	+	0.850562i	$0.323738\pi$
$728$	1.98226	−	6.10077i	0.0734674	−	0.226110i
$729$		0			0
$730$	−39.8251	−	28.9346i	−1.47399	−	1.07092i
$731$	−4.00910	−	12.3387i	−0.148282	−	0.456365i
$732$		0			0
$733$	−5.06199	−	3.67775i	−0.186969	−	0.135841i	0.490364	−	0.871518i	$-0.336864\pi$
$733$	−5.06199	−	3.67775i	−0.186969	−	0.135841i	−0.677332	+	0.735677i	$0.736864\pi$
$734$	14.2359	−	10.3430i	0.525456	−	0.381766i
$735$		0			0
$736$	−25.5830			−0.943001
$737$	6.22186	+	16.8560i	0.229185	+	0.620898i
$738$		0			0
$739$	2.88993	−	8.89429i	0.106308	−	0.327182i	−0.883727	−	0.468002i	$-0.844974\pi$
$739$	2.88993	−	8.89429i	0.106308	−	0.327182i	0.990035	+	0.140820i	$0.0449740\pi$
$740$	−2.69776	+	1.96004i	−0.0991716	+	0.0720524i
$741$		0			0
$742$	2.14223	+	6.59310i	0.0786437	+	0.242040i
$743$	−7.78926	−	23.9729i	−0.285760	−	0.879480i	−0.986170	−	0.165739i	$-0.946999\pi$
$743$	−7.78926	−	23.9729i	−0.285760	−	0.879480i	0.700409	−	0.713741i	$-0.253001\pi$
$744$		0			0
$745$	−33.4690	+	24.3167i	−1.22621	+	0.890893i
$746$	2.34800	−	7.22641i	0.0859665	−	0.264578i
$747$		0			0
$748$	−10.5881	+	0.417870i	−0.387141	+	0.0152788i
$749$	3.24746			0.118660
$750$		0			0
$751$	28.1128	−	20.4251i	1.02585	−	0.745323i	0.0583755	−	0.998295i	$-0.481408\pi$
$751$	28.1128	−	20.4251i	1.02585	−	0.745323i	0.967474	+	0.252972i	$0.0814079\pi$
$752$	52.5020	+	38.1449i	1.91455	+	1.39100i
$753$		0			0
$754$	−20.3475	−	62.6233i	−0.741014	−	2.28061i
$755$	−35.5134	−	25.8020i	−1.29247	−	0.939031i
$756$		0			0
$757$	10.7526	−	33.0930i	0.390808	−	1.20278i	−0.541370	−	0.840784i	$-0.682094\pi$
$757$	10.7526	−	33.0930i	0.390808	−	1.20278i	0.932178	−	0.362000i	$-0.117906\pi$
$758$	−7.68929			−0.279288
$759$		0			0
$760$	8.04674			0.291886
$761$	3.77787	−	11.6271i	0.136948	−	0.421482i	−0.858940	−	0.512076i	$-0.828877\pi$
$761$	3.77787	−	11.6271i	0.136948	−	0.421482i	0.995888	+	0.0905941i	$0.0288766\pi$
$762$		0			0
$763$	10.2674	+	7.45967i	0.371703	+	0.270058i
$764$	0.297079	+	0.914315i	0.0107479	+	0.0330788i
$765$		0			0
$766$	1.90120	+	1.38130i	0.0686931	+	0.0499085i
$767$	29.7231	−	21.5951i	1.07324	−	0.779755i
$768$		0			0
$769$	−2.61946			−0.0944603			−0.0472301	−	0.998884i	$-0.515039\pi$
$769$	−2.61946			−0.0944603			−0.0472301	+	0.998884i	$0.515039\pi$
$770$	−4.44179	+	15.7600i	−0.160071	+	0.567950i
$771$		0			0
$772$	−2.41417	+	7.43004i	−0.0868878	+	0.267413i
$773$	−0.172162	+	0.125083i	−0.00619225	+	0.00449894i	−0.590877	−	0.806762i	$-0.701218\pi$
$773$	−0.172162	+	0.125083i	−0.00619225	+	0.00449894i	0.584685	+	0.811261i	$0.301218\pi$
$774$		0			0
$775$	−0.168253	−	0.517831i	−0.00604384	−	0.0186010i
$776$	5.36310	+	16.5059i	0.192524	+	0.592529i
$777$		0			0
$778$	55.3767	−	40.2336i	1.98535	−	1.44244i
$779$	−5.75614	+	17.7156i	−0.206235	+	0.634727i
$780$		0			0
$781$	5.25288	−	4.14253i	0.187963	−	0.148231i
$782$	21.4045			0.765425
$783$		0			0
$784$	4.02452	−	2.92398i	0.143733	−	0.104428i
$785$	−10.3166	−	7.49547i	−0.368216	−	0.267525i
$786$		0			0
$787$	9.00399	+	27.7114i	0.320958	+	0.987806i	0.973232	+	0.229823i	$0.0738148\pi$
$787$	9.00399	+	27.7114i	0.320958	+	0.987806i	−0.652275	+	0.757983i	$0.726185\pi$
$788$	−10.2446	−	7.44313i	−0.364948	−	0.265151i
$789$		0			0
$790$	−9.60131	+	29.5498i	−0.341599	+	1.05133i
$791$	−18.4480			−0.655937
$792$		0			0
$793$	4.24457			0.150729
$794$	0.225262	−	0.693284i	0.00799424	−	0.0246037i
$795$		0			0
$796$	−19.6745	−	14.2943i	−0.697343	−	0.506649i
$797$	−9.95913	−	30.6510i	−0.352770	−	1.08572i	−0.957291	−	0.289126i	$-0.906635\pi$
$797$	−9.95913	−	30.6510i	−0.352770	−	1.08572i	0.604521	−	0.796589i	$-0.293365\pi$
$798$		0			0
$799$	−29.0823	−	21.1295i	−1.02886	−	0.747509i
$800$	−12.8557	+	9.34019i	−0.454517	+	0.330226i
$801$		0			0
$802$	−2.78503			−0.0983430
$803$	8.97104	−	31.8303i	0.316581	−	1.12327i
$804$		0			0
$805$	3.75081	−	11.5438i	0.132199	−	0.406865i
$806$	1.23845	−	0.899783i	0.0436224	−	0.0316935i
$807$		0			0
$808$	−1.57519	−	4.84794i	−0.0554151	−	0.170550i
$809$	9.06844	+	27.9098i	0.318829	+	0.981256i	0.974149	+	0.225905i	$0.0725338\pi$
$809$	9.06844	+	27.9098i	0.318829	+	0.981256i	−0.655320	+	0.755351i	$0.727466\pi$
$810$		0			0
$811$	−0.840891	+	0.610943i	−0.0295277	+	0.0214531i	−0.602451	−	0.798156i	$-0.705809\pi$
$811$	−0.840891	+	0.610943i	−0.0295277	+	0.0214531i	0.572924	+	0.819609i	$0.305809\pi$
$812$	3.09136	−	9.51422i	0.108485	−	0.333884i
$813$		0			0
$814$	−5.07623	−	3.39054i	−0.177922	−	0.118838i
$815$	22.3244			0.781990
$816$		0			0
$817$	7.38605	−	5.36628i	0.258405	−	0.187742i
$818$	−9.74762	−	7.08206i	−0.340817	−	0.247618i
$819$		0			0
$820$	−9.55952	−	29.4212i	−0.333833	−	1.02743i
$821$	23.0831	+	16.7709i	0.805607	+	0.585308i	0.912554	−	0.408957i	$-0.134107\pi$
$821$	23.0831	+	16.7709i	0.805607	+	0.585308i	−0.106946	+	0.994265i	$0.534107\pi$
$822$		0			0
$823$	8.23767	−	25.3529i	0.287147	−	0.883748i	−0.698600	−	0.715513i	$-0.746193\pi$
$823$	8.23767	−	25.3529i	0.287147	−	0.883748i	0.985747	−	0.168235i	$-0.0538068\pi$
$824$	−27.1659			−0.946370
$825$		0			0
$826$	15.2102			0.529229
$827$	−0.531399	+	1.63548i	−0.0184785	+	0.0568711i	−0.959871	−	0.280443i	$-0.909519\pi$
$827$	−0.531399	+	1.63548i	−0.0184785	+	0.0568711i	0.941392	+	0.337314i	$0.109519\pi$
$828$		0			0
$829$	−22.6205	−	16.4347i	−0.785642	−	0.570802i	0.121025	−	0.992649i	$-0.461382\pi$
$829$	−22.6205	−	16.4347i	−0.785642	−	0.570802i	−0.906667	+	0.421847i	$0.861382\pi$
$830$	−2.62625	−	8.08277i	−0.0911585	−	0.280557i
$831$		0			0
$832$	−1.58538	−	1.15185i	−0.0549632	−	0.0399331i
$833$	−2.22929	+	1.61968i	−0.0772404	+	0.0561184i
$834$		0			0
$835$	37.2375			1.28866
$836$	−2.58212	−	6.99537i	−0.0893046	−	0.241940i
$837$		0			0
$838$	15.7761	−	48.5539i	0.544977	−	1.67727i
$839$	29.0133	−	21.0794i	1.00165	−	0.727742i	0.0392091	−	0.999231i	$-0.487516\pi$
$839$	29.0133	−	21.0794i	1.00165	−	0.727742i	0.962441	+	0.271489i	$0.0875162\pi$
$840$		0			0
$841$	14.0429	+	43.2197i	0.484240	+	1.49034i
$842$	−6.71518	−	20.6672i	−0.231420	−	0.712239i
$843$		0			0
$844$	5.65023	−	4.10514i	0.194489	−	0.141305i
$845$	4.66389	−	14.3540i	0.160443	−	0.493792i
$846$		0			0
$847$	−10.9658	+	0.866898i	−0.376789	+	0.0297870i
$848$	−19.4014			−0.666248
$849$		0			0
$850$	10.7560	−	7.81467i	0.368927	−	0.268041i
$851$	3.66092	+	2.65981i	0.125495	+	0.0911772i
$852$		0			0
$853$	−4.67937	−	14.4016i	−0.160218	−	0.493102i	0.838434	−	0.545004i	$-0.183472\pi$
$853$	−4.67937	−	14.4016i	−0.160218	−	0.493102i	−0.998652	+	0.0519019i	$0.983472\pi$
$854$	1.42163	+	1.03288i	0.0486473	+	0.0353443i
$855$		0			0
$856$	−1.49932	+	4.61444i	−0.0512458	+	0.157718i
$857$	−25.3267			−0.865142			−0.432571	−	0.901600i	$-0.642394\pi$
$857$	−25.3267			−0.865142			−0.432571	+	0.901600i	$0.642394\pi$
$858$		0			0
$859$	41.5291			1.41696			0.708478	−	0.705733i	$-0.249382\pi$
$859$	41.5291			1.41696			0.708478	+	0.705733i	$0.249382\pi$
$860$	−4.68534	+	14.4200i	−0.159769	+	0.491718i
$861$		0			0
$862$	−5.30813	−	3.85658i	−0.180796	−	0.131356i
$863$	7.43197	+	22.8733i	0.252987	+	0.778615i	0.994220	+	0.107366i	$0.0342417\pi$
$863$	7.43197	+	22.8733i	0.252987	+	0.778615i	−0.741232	+	0.671249i	$0.765758\pi$
$864$		0			0
$865$	−46.2486	−	33.6016i	−1.57250	−	1.14249i
$866$	41.8101	−	30.3768i	1.42077	−	1.03225i
$867$		0			0
$868$	0.232572			0.00789399
$869$	−20.8569	+	0.823133i	−0.707521	+	0.0279229i
$870$		0			0
$871$	7.18764	−	22.1213i	0.243544	−	0.749551i
$872$	−15.3401	+	11.1452i	−0.519481	+	0.377425i
$873$		0			0
$874$	4.65455	+	14.3252i	0.157443	+	0.484559i
$875$	1.96169	+	6.03746i	0.0663173	+	0.204104i
$876$		0			0
$877$	−27.3490	+	19.8702i	−0.923509	+	0.670969i	−0.944395	−	0.328813i	$-0.893351\pi$
$877$	−27.3490	+	19.8702i	−0.923509	+	0.670969i	0.0208857	+	0.999782i	$0.493351\pi$
$878$	7.80061	−	24.0078i	0.263258	−	0.810225i
$879$		0			0
$880$	−38.1067	−	25.4524i	−1.28458	−	0.858001i
$881$	36.8296			1.24082			0.620410	−	0.784278i	$-0.286966\pi$
$881$	36.8296			1.24082			0.620410	+	0.784278i	$0.286966\pi$
$882$		0			0
$883$	−43.2099	+	31.3938i	−1.45413	+	1.05649i	−0.469283	+	0.883048i	$0.655488\pi$
$883$	−43.2099	+	31.3938i	−1.45413	+	1.05649i	−0.984845	+	0.173438i	$0.944512\pi$
$884$	11.0976	+	8.06286i	0.373252	+	0.271183i
$885$		0			0
$886$	14.9598	+	46.0414i	0.502583	+	1.54679i
$887$	9.27263	+	6.73696i	0.311344	+	0.226205i	0.732473	−	0.680796i	$-0.238366\pi$
$887$	9.27263	+	6.73696i	0.311344	+	0.226205i	−0.421129	+	0.907001i	$0.638366\pi$
$888$		0			0
$889$	−6.02870	+	18.5544i	−0.202196	+	0.622296i
$890$	−75.5525			−2.53253
$891$		0			0
$892$	−5.36254			−0.179551
$893$	7.81706	−	24.0584i	0.261588	−	0.805085i
$894$		0			0
$895$	−8.34817	−	6.06530i	−0.279048	−	0.202741i
$896$	3.36733	+	10.3636i	0.112495	+	0.346223i
$897$		0			0
$898$	60.2757	+	43.7929i	2.01143	+	1.46139i
$899$	−1.40016	+	1.01727i	−0.0466979	+	0.0339280i
$900$		0			0
$901$	10.7470			0.358034
$902$	44.4669	−	35.0675i	1.48059	−	1.16762i
$903$		0			0
$904$	8.51730	−	26.2136i	0.283281	−	0.871850i
$905$	−10.7224	+	7.79031i	−0.356426	+	0.258959i
$906$		0			0
$907$	17.6319	+	54.2655i	0.585459	+	1.80186i	0.597419	+	0.801929i	$0.296193\pi$
$907$	17.6319	+	54.2655i	0.585459	+	1.80186i	−0.0119596	+	0.999928i	$0.503807\pi$
$908$	−6.19853	−	19.0771i	−0.205706	−	0.633097i
$909$		0			0
$910$	17.1484	−	12.4591i	0.568465	−	0.413014i
$911$	−2.06289	+	6.34893i	−0.0683467	+	0.210350i	−0.979396	−	0.201947i	$-0.935273\pi$
$911$	−2.06289	+	6.34893i	−0.0683467	+	0.210350i	0.911050	+	0.412296i	$0.135273\pi$
$912$		0			0
$913$	4.48309	−	3.53546i	0.148369	−	0.117007i
$914$	−34.6568			−1.14635
$915$		0			0
$916$	4.15177	−	3.01643i	0.137178	−	0.0996658i
$917$	5.58057	+	4.05452i	0.184286	+	0.133892i
$918$		0			0
$919$	−9.00287	−	27.7080i	−0.296977	−	0.914002i	−0.982550	−	0.185998i	$-0.940448\pi$
$919$	−9.00287	−	27.7080i	−0.296977	−	0.914002i	0.685573	−	0.728004i	$-0.259552\pi$
$920$	14.6713	+	10.6593i	0.483699	+	0.351428i
$921$		0			0
$922$	6.71491	−	20.6664i	0.221144	−	0.680611i
$923$	−8.66015			−0.285052
$924$		0			0
$925$	2.81073			0.0924161
$926$	−7.61015	+	23.4216i	−0.250085	+	0.769683i
$927$		0			0
$928$	40.8632	+	29.6889i	1.34140	+	0.974585i
$929$	−0.724557	−	2.22996i	−0.0237720	−	0.0731626i	0.938467	−	0.345370i	$-0.112246\pi$
$929$	−0.724557	−	2.22996i	−0.0237720	−	0.0731626i	−0.962239	+	0.272207i	$0.912246\pi$
$930$		0			0
$931$	−1.56876	−	1.13977i	−0.0514141	−	0.0373545i
$932$	−9.88015	+	7.17835i	−0.323635	+	0.235135i
$933$		0			0
$934$	−29.1876			−0.955047
$935$	21.1084	+	14.0988i	0.690317	+	0.461080i
$936$		0			0
$937$	2.71558	−	8.35769i	0.0887141	−	0.273034i	−0.896850	−	0.442334i	$-0.854151\pi$
$937$	2.71558	−	8.35769i	0.0887141	−	0.273034i	0.985565	+	0.169300i	$0.0541506\pi$
$938$	7.79037	−	5.66003i	0.254365	−	0.184807i
$939$		0			0
$940$	12.9822	+	39.9551i	0.423432	+	1.30319i
$941$	−2.74676	−	8.45366i	−0.0895419	−	0.275582i	0.896251	−	0.443547i	$-0.146280\pi$
$941$	−2.74676	−	8.45366i	−0.0895419	−	0.275582i	−0.985793	+	0.167966i	$0.946280\pi$
$942$		0			0
$943$	−33.9624	+	24.6751i	−1.10597	+	0.803533i
$944$	−13.1543	+	40.4847i	−0.428135	+	1.31766i
$945$		0			0
$946$	−27.7344	+	1.09456i	−0.901724	+	0.0355873i
$947$	7.86275			0.255505			0.127752	−	0.991806i	$-0.459224\pi$
$947$	7.86275			0.255505			0.127752	+	0.991806i	$0.459224\pi$
$948$		0			0
$949$	−34.6345	+	25.1634i	−1.12428	+	0.816840i
$950$	7.56902	+	5.49921i	0.245571	+	0.178418i
$951$		0			0
$952$	−1.27222	−	3.91548i	−0.0412328	−	0.126901i
$953$	−14.1290	−	10.2653i	−0.457683	−	0.332526i	0.334939	−	0.942240i	$-0.391284\pi$
$953$	−14.1290	−	10.2653i	−0.457683	−	0.332526i	−0.792622	+	0.609714i	$0.791284\pi$
$954$		0			0
$955$	0.711658	−	2.19026i	0.0230287	−	0.0708751i
$956$	11.3121			0.365860
$957$		0			0
$958$	−44.0663			−1.42372
$959$	−0.806750	+	2.48292i	−0.0260513	+	0.0801777i
$960$		0			0
$961$	25.0470	+	18.1977i	0.807967	+	0.587022i
$962$	2.44196	+	7.51559i	0.0787320	+	0.242312i
$963$		0			0
$964$	−11.7722	−	8.55298i	−0.379156	−	0.275473i
$965$	15.1406	−	11.0003i	0.487392	−	0.354111i
$966$		0			0
$967$	−45.6122			−1.46679			−0.733395	−	0.679802i	$-0.762066\pi$
$967$	−45.6122			−1.46679			−0.733395	+	0.679802i	$0.762066\pi$
$968$	3.83100	−	15.9820i	0.123133	−	0.513680i
$969$		0			0
$970$	−17.7217	+	54.5417i	−0.569008	+	1.75123i
$971$	1.92852	−	1.40115i	0.0618892	−	0.0449651i	−0.556411	−	0.830908i	$-0.687822\pi$
$971$	1.92852	−	1.40115i	0.0618892	−	0.0449651i	0.618300	+	0.785942i	$0.287822\pi$
$972$		0			0
$973$	0.309430	+	0.952327i	0.00991986	+	0.0305302i
$974$	7.87338	+	24.2318i	0.252279	+	0.776436i
$975$		0			0
$976$	−3.97867	+	2.89067i	−0.127354	+	0.0925282i
$977$	5.95358	−	18.3232i	0.190472	−	0.586212i	−0.809528	−	0.587082i	$-0.800277\pi$
$977$	5.95358	−	18.3232i	0.190472	−	0.586212i	1.00000		0.000869450i	$0.000276755\pi$
$978$		0			0
$979$	−17.5759	−	47.6158i	−0.561728	−	1.52181i
$980$	3.22035			0.102870
$981$		0			0
$982$	31.6641	−	23.0053i	1.01044	−	0.734130i
$983$	−13.1268	−	9.53718i	−0.418680	−	0.304189i	0.358426	−	0.933558i	$-0.383313\pi$
$983$	−13.1268	−	9.53718i	−0.418680	−	0.304189i	−0.777107	+	0.629369i	$0.783313\pi$
$984$		0			0
$985$	9.37387	+	28.8498i	0.298676	+	0.919231i
$986$	−34.1891	−	24.8398i	−1.08880	−	0.791061i
$987$		0			0
$988$	−2.98293	+	9.18051i	−0.0948996	+	0.292071i
$989$	20.5753			0.654256
$990$		0			0
$991$	−50.5214			−1.60487			−0.802433	−	0.596743i	$-0.796461\pi$
$991$	−50.5214			−1.60487			−0.802433	+	0.596743i	$0.796461\pi$
$992$	−0.362867	+	1.11679i	−0.0115210	+	0.0354581i
$993$		0			0
$994$	−2.90055	−	2.10737i	−0.0919997	−	0.0668417i
$995$	18.0023	+	55.4053i	0.570710	+	1.75647i
$996$		0			0
$997$	36.4224	+	26.4625i	1.15351	+	0.838074i	0.988944	−	0.148292i	$-0.0473774\pi$
$997$	36.4224	+	26.4625i	1.15351	+	0.838074i	0.164567	+	0.986366i	$0.447377\pi$
$998$	−36.3986	+	26.4452i	−1.15218	+	0.837107i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.g.64.1		8
3.2	odd	2		77.2.f.a.64.2	✓	8
11.4	even	5		7623.2.a.ch.1.2		4
11.5	even	5	inner	693.2.m.g.379.1		8
11.7	odd	10		7623.2.a.co.1.3		4
21.2	odd	6		539.2.q.c.361.1		16
21.5	even	6		539.2.q.b.361.1		16
21.11	odd	6		539.2.q.c.471.2		16
21.17	even	6		539.2.q.b.471.2		16
21.20	even	2		539.2.f.d.295.2		8
33.2	even	10		847.2.f.s.729.2		8
33.5	odd	10		77.2.f.a.71.2	yes	8
33.8	even	10		847.2.f.s.323.2		8
33.14	odd	10		847.2.f.p.323.1		8
33.17	even	10		847.2.f.q.148.1		8
33.20	odd	10		847.2.f.p.729.1		8
33.26	odd	10		847.2.a.l.1.3		4
33.29	even	10		847.2.a.k.1.2		4
33.32	even	2		847.2.f.q.372.1		8
231.5	even	30		539.2.q.b.214.2		16
231.38	even	30		539.2.q.b.324.1		16
231.62	odd	10		5929.2.a.bb.1.2		4
231.104	even	10		539.2.f.d.148.2		8
231.125	even	10		5929.2.a.bi.1.3		4
231.137	odd	30		539.2.q.c.324.1		16
231.170	odd	30		539.2.q.c.214.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.64.2	✓	8	3.2	odd	2
77.2.f.a.71.2	yes	8	33.5	odd	10
539.2.f.d.148.2		8	231.104	even	10
539.2.f.d.295.2		8	21.20	even	2
539.2.q.b.214.2		16	231.5	even	30
539.2.q.b.324.1		16	231.38	even	30
539.2.q.b.361.1		16	21.5	even	6
539.2.q.b.471.2		16	21.17	even	6
539.2.q.c.214.2		16	231.170	odd	30
539.2.q.c.324.1		16	231.137	odd	30
539.2.q.c.361.1		16	21.2	odd	6
539.2.q.c.471.2		16	21.11	odd	6
693.2.m.g.64.1		8	1.1	even	1	trivial
693.2.m.g.379.1		8	11.5	even	5	inner
847.2.a.k.1.2		4	33.29	even	10
847.2.a.l.1.3		4	33.26	odd	10
847.2.f.p.323.1		8	33.14	odd	10
847.2.f.p.729.1		8	33.20	odd	10
847.2.f.q.148.1		8	33.17	even	10
847.2.f.q.372.1		8	33.32	even	2
847.2.f.s.323.2		8	33.8	even	10
847.2.f.s.729.2		8	33.2	even	10
5929.2.a.bb.1.2		4	231.62	odd	10
5929.2.a.bi.1.3		4	231.125	even	10
7623.2.a.ch.1.2		4	11.4	even	5
7623.2.a.co.1.3		4	11.7	odd	10

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.549273 + 1.69049i) q^{2} +(-0.938015 - 0.681508i) q^{4} +(0.858290 + 2.64154i) q^{5} +(0.809017 + 0.587785i) q^{7} +(-1.20872 + 0.878189i) q^{8} +O(q^{10})\)	\(q+(-0.549273 + 1.69049i) q^{2} +(-0.938015 - 0.681508i) q^{4} +(0.858290 + 2.64154i) q^{5} +(0.809017 + 0.587785i) q^{7} +(-1.20872 + 0.878189i) q^{8} -4.93693 q^{10} +(-1.14849 - 3.11143i) q^{11} +(-1.32676 + 4.08334i) q^{13} +(-1.43801 + 1.04478i) q^{14} +(-1.53723 - 4.73110i) q^{16} +(0.851514 + 2.62069i) q^{17} +(-1.56876 + 1.13977i) q^{19} +(0.995144 - 3.06274i) q^{20} +(5.89066 - 0.232480i) q^{22} -4.37009 q^{23} +(-2.19601 + 1.59550i) q^{25} +(-6.17408 - 4.48573i) q^{26} +(-0.358290 - 1.10270i) q^{28} +(6.98027 + 5.07146i) q^{29} +(-0.0619850 + 0.190770i) q^{31} +5.85410 q^{32} -4.89796 q^{34} +(-0.858290 + 2.64154i) q^{35} +(-0.837721 - 0.608640i) q^{37} +(-1.06509 - 3.27802i) q^{38} +(-3.35721 - 2.43916i) q^{40} +(7.77155 - 5.64636i) q^{41} -4.70820 q^{43} +(-1.04316 + 3.70127i) q^{44} +(2.40037 - 7.38759i) q^{46} +(-10.5541 + 7.66797i) q^{47} +(0.309017 + 0.951057i) q^{49} +(-1.49096 - 4.58869i) q^{50} +(4.02734 - 2.92604i) q^{52} +(1.20520 - 3.70923i) q^{53} +(7.23324 - 5.70428i) q^{55} -1.49406 q^{56} +(-12.4073 + 9.01445i) q^{58} +(-6.92286 - 5.02975i) q^{59} +(-0.305497 - 0.940223i) q^{61} +(-0.288448 - 0.209570i) q^{62} +(-0.141042 + 0.434084i) q^{64} -11.9251 q^{65} -5.41745 q^{67} +(0.987288 - 3.03856i) q^{68} +(-3.99406 - 2.90186i) q^{70} +(0.623302 + 1.91833i) q^{71} +(8.06677 + 5.86085i) q^{73} +(1.48904 - 1.08185i) q^{74} +2.24828 q^{76} +(0.899706 - 3.19226i) q^{77} +(1.94479 - 5.98545i) q^{79} +(11.1780 - 8.12131i) q^{80} +(5.27640 + 16.2391i) q^{82} +(0.531960 + 1.63720i) q^{83} +(-6.19182 + 4.49862i) q^{85} +(2.58609 - 7.95916i) q^{86} +(4.12062 + 2.75227i) q^{88} +15.3035 q^{89} +(-3.47350 + 2.52364i) q^{91} +(4.09921 + 2.97825i) q^{92} +(-7.16556 - 22.0533i) q^{94} +(-4.35721 - 3.16570i) q^{95} +(3.58961 - 11.0477i) q^{97} -1.77748 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 3 q^{4} - 3 q^{5} + 2 q^{7} - 3 q^{8}+O(q^{10}) \) 8 * q + q^2 + 3 * q^4 - 3 * q^5 + 2 * q^7 - 3 * q^8	\( 8 q + q^{2} + 3 q^{4} - 3 q^{5} + 2 q^{7} - 3 q^{8} - 28 q^{10} - 5 q^{11} + 5 q^{13} - q^{14} - 3 q^{16} + 11 q^{17} - 9 q^{19} - 21 q^{20} - q^{22} + 16 q^{23} + 5 q^{25} - 21 q^{26} + 7 q^{28} + 9 q^{29} - 11 q^{31} + 20 q^{32} - 24 q^{34} + 3 q^{35} + 6 q^{37} - 35 q^{38} - 16 q^{40} + 22 q^{41} + 16 q^{43} - 29 q^{44} + 29 q^{46} - 7 q^{47} - 2 q^{49} + 34 q^{50} + 21 q^{52} - 2 q^{53} + 26 q^{55} + 18 q^{56} - 39 q^{58} - 25 q^{59} + 7 q^{61} + 5 q^{62} + q^{64} - 24 q^{65} - 30 q^{67} - 8 q^{68} - 2 q^{70} + 14 q^{71} + 3 q^{73} + 9 q^{74} - 52 q^{76} + 5 q^{77} - 9 q^{79} + 33 q^{80} + 31 q^{82} - 23 q^{83} - 10 q^{85} + 17 q^{86} - 7 q^{88} + 34 q^{89} + 5 q^{91} + 34 q^{92} - 30 q^{94} - 24 q^{95} + 30 q^{97} - 4 q^{98}+O(q^{100}) \) 8 * q + q^2 + 3 * q^4 - 3 * q^5 + 2 * q^7 - 3 * q^8 - 28 * q^10 - 5 * q^11 + 5 * q^13 - q^14 - 3 * q^16 + 11 * q^17 - 9 * q^19 - 21 * q^20 - q^22 + 16 * q^23 + 5 * q^25 - 21 * q^26 + 7 * q^28 + 9 * q^29 - 11 * q^31 + 20 * q^32 - 24 * q^34 + 3 * q^35 + 6 * q^37 - 35 * q^38 - 16 * q^40 + 22 * q^41 + 16 * q^43 - 29 * q^44 + 29 * q^46 - 7 * q^47 - 2 * q^49 + 34 * q^50 + 21 * q^52 - 2 * q^53 + 26 * q^55 + 18 * q^56 - 39 * q^58 - 25 * q^59 + 7 * q^61 + 5 * q^62 + q^64 - 24 * q^65 - 30 * q^67 - 8 * q^68 - 2 * q^70 + 14 * q^71 + 3 * q^73 + 9 * q^74 - 52 * q^76 + 5 * q^77 - 9 * q^79 + 33 * q^80 + 31 * q^82 - 23 * q^83 - 10 * q^85 + 17 * q^86 - 7 * q^88 + 34 * q^89 + 5 * q^91 + 34 * q^92 - 30 * q^94 - 24 * q^95 + 30 * q^97 - 4 * q^98

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