LMFDB - Embedded newform 693.2.by.c.37.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(37,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 10, 6]))

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

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

chi := DirichletCharacter("693.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.by (of order $15$, degree $8$, 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:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			37.7
Character	$\chi$	$=$	693.37
Dual form			693.2.by.c.487.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.43967 - 0.640984i) q^{2} +(0.323537 - 0.359324i) q^{4} +(-0.433772 - 4.12706i) q^{5} +(-2.64557 - 0.0310171i) q^{7} +(-0.738505 + 2.27288i) q^{8} +O(q^{10})$	\(q+(1.43967 - 0.640984i) q^{2} +(0.323537 - 0.359324i) q^{4} +(-0.433772 - 4.12706i) q^{5} +(-2.64557 - 0.0310171i) q^{7} +(-0.738505 + 2.27288i) q^{8} +(-3.26987 - 5.66358i) q^{10} +(-2.14258 - 2.53167i) q^{11} +(-1.57878 - 1.14705i) q^{13} +(-3.82864 + 1.65111i) q^{14} +(0.494759 + 4.70732i) q^{16} +(4.15061 + 1.84797i) q^{17} +(-3.37641 - 3.74988i) q^{19} +(-1.62329 - 1.17939i) q^{20} +(-4.70737 - 2.27142i) q^{22} +(-0.495419 + 0.858091i) q^{23} +(-11.9537 + 2.54085i) q^{25} +(-3.00817 - 0.639406i) q^{26} +(-0.867085 + 0.940582i) q^{28} +(-0.853348 - 2.62634i) q^{29} +(0.485833 - 4.62239i) q^{31} +(1.33975 + 2.32052i) q^{32} +7.16004 q^{34} +(1.01956 + 10.9319i) q^{35} +(3.11960 + 0.663091i) q^{37} +(-7.26453 - 3.23438i) q^{38} +(9.70067 + 2.06194i) q^{40} +(3.23441 - 9.95449i) q^{41} +3.83062 q^{43} +(-1.60289 - 0.0492102i) q^{44} +(-0.163219 + 1.55293i) q^{46} +(4.00875 + 4.45217i) q^{47} +(6.99808 + 0.164116i) q^{49} +(-15.5808 + 11.3201i) q^{50} +(-0.922957 + 0.196181i) q^{52} +(1.01426 - 9.65000i) q^{53} +(-9.51898 + 9.94071i) q^{55} +(2.02426 - 5.99016i) q^{56} +(-2.91198 - 3.23408i) q^{58} +(4.39787 - 4.88433i) q^{59} +(0.790124 + 7.51753i) q^{61} +(-2.26344 - 6.96614i) q^{62} +(-4.24233 - 3.08223i) q^{64} +(-4.04912 + 7.01328i) q^{65} +(-0.922802 - 1.59834i) q^{67} +(2.00690 - 0.893529i) q^{68} +(8.47500 + 15.0848i) q^{70} +(-3.33445 + 2.42262i) q^{71} +(-3.15290 + 3.50165i) q^{73} +(4.91623 - 1.04498i) q^{74} -2.43982 q^{76} +(5.58981 + 6.76417i) q^{77} +(-1.18499 + 0.527591i) q^{79} +(19.2128 - 4.08380i) q^{80} +(-1.72417 - 16.4044i) q^{82} +(-1.10236 + 0.800908i) q^{83} +(5.82627 - 17.9314i) q^{85} +(5.51483 - 2.45536i) q^{86} +(7.33650 - 3.00017i) q^{88} +(7.79893 - 13.5081i) q^{89} +(4.14119 + 3.08357i) q^{91} +(0.148047 + 0.455640i) q^{92} +(8.62506 + 3.84013i) q^{94} +(-14.0114 + 15.5612i) q^{95} +(3.00835 + 2.18569i) q^{97} +(10.1801 - 4.24938i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{2} + 10 q^{4} + 4 q^{5} - q^{7} - 8 q^{8}+O(q^{10}) $ 64 * q - 4 * q^2 + 10 * q^4 + 4 * q^5 - q^7 - 8 * q^8	$ 64 q - 4 q^{2} + 10 q^{4} + 4 q^{5} - q^{7} - 8 q^{8} - 14 q^{10} - 11 q^{11} - 8 q^{13} - 6 q^{14} + 4 q^{17} - 2 q^{19} - 24 q^{20} - 14 q^{22} - 10 q^{25} - 4 q^{26} + 29 q^{28} + 58 q^{29} - 19 q^{31} + 64 q^{32} - 88 q^{34} - 17 q^{35} - 20 q^{37} - 29 q^{38} + 51 q^{40} + 68 q^{41} + 92 q^{43} + 21 q^{44} - 5 q^{46} + 26 q^{47} + 37 q^{49} + 10 q^{50} - 14 q^{52} + 3 q^{53} - 32 q^{55} - 24 q^{56} + 52 q^{58} - 7 q^{59} - 21 q^{61} - 92 q^{62} - 72 q^{64} + 66 q^{65} - 4 q^{67} + 17 q^{68} - q^{70} - 58 q^{71} - 3 q^{73} + 28 q^{74} + 168 q^{76} + 34 q^{77} + 9 q^{79} + 5 q^{80} - 42 q^{82} - 60 q^{83} + 110 q^{85} - 13 q^{86} + 92 q^{88} + 10 q^{89} + 10 q^{91} - 110 q^{92} - 46 q^{94} - 43 q^{95} + 64 q^{97} + 88 q^{98}+O(q^{100}) $ 64 * q - 4 * q^2 + 10 * q^4 + 4 * q^5 - q^7 - 8 * q^8 - 14 * q^10 - 11 * q^11 - 8 * q^13 - 6 * q^14 + 4 * q^17 - 2 * q^19 - 24 * q^20 - 14 * q^22 - 10 * q^25 - 4 * q^26 + 29 * q^28 + 58 * q^29 - 19 * q^31 + 64 * q^32 - 88 * q^34 - 17 * q^35 - 20 * q^37 - 29 * q^38 + 51 * q^40 + 68 * q^41 + 92 * q^43 + 21 * q^44 - 5 * q^46 + 26 * q^47 + 37 * q^49 + 10 * q^50 - 14 * q^52 + 3 * q^53 - 32 * q^55 - 24 * q^56 + 52 * q^58 - 7 * q^59 - 21 * q^61 - 92 * q^62 - 72 * q^64 + 66 * q^65 - 4 * q^67 + 17 * q^68 - q^70 - 58 * q^71 - 3 * q^73 + 28 * q^74 + 168 * q^76 + 34 * q^77 + 9 * q^79 + 5 * q^80 - 42 * q^82 - 60 * q^83 + 110 * q^85 - 13 * q^86 + 92 * q^88 + 10 * q^89 + 10 * q^91 - 110 * q^92 - 46 * q^94 - 43 * q^95 + 64 * q^97 + 88 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.43967	−	0.640984i	1.01800	−	0.453244i	0.171248	−	0.985228i	$-0.445220\pi$
$2$	1.43967	−	0.640984i	1.01800	−	0.453244i	0.846754	+	0.531984i	$0.178553\pi$
$3$		0			0
$3$		0			0
$4$	0.323537	−	0.359324i	0.161769	−	0.179662i
$5$	−0.433772	−	4.12706i	−0.193989	−	1.84568i	−0.467726	−	0.883873i	$-0.654927\pi$
$5$	−0.433772	−	4.12706i	−0.193989	−	1.84568i	0.273738	−	0.961804i	$-0.411740\pi$
$6$		0			0
$7$	−2.64557	−	0.0310171i	−0.999931	−	0.0117234i
$7$	−2.64557	−	0.0310171i	−0.999931	−	0.0117234i
$8$	−0.738505	+	2.27288i	−0.261101	+	0.803586i
$9$		0			0
$10$	−3.26987	−	5.66358i	−1.03402	−	1.79098i
$11$	−2.14258	−	2.53167i	−0.646011	−	0.763328i
$11$	−2.14258	−	2.53167i	−0.646011	−	0.763328i
$12$		0			0
$13$	−1.57878	−	1.14705i	−0.437875	−	0.318135i	0.346915	−	0.937897i	$-0.387229\pi$
$13$	−1.57878	−	1.14705i	−0.437875	−	0.318135i	−0.784790	+	0.619762i	$0.787229\pi$
$14$	−3.82864	+	1.65111i	−1.02325	+	0.441278i
$15$		0			0
$16$	0.494759	+	4.70732i	0.123690	+	1.17683i
$17$	4.15061	+	1.84797i	1.00667	+	0.448199i	0.842768	−	0.538277i	$-0.180925\pi$
$17$	4.15061	+	1.84797i	1.00667	+	0.448199i	0.163904	+	0.986476i	$0.447591\pi$
$18$		0			0
$19$	−3.37641	−	3.74988i	−0.774601	−	0.860281i	0.218705	−	0.975791i	$-0.429817\pi$
$19$	−3.37641	−	3.74988i	−0.774601	−	0.860281i	−0.993306	+	0.115509i	$0.963150\pi$
$20$	−1.62329	−	1.17939i	−0.362980	−	0.263720i
$21$		0			0
$22$	−4.70737	−	2.27142i	−1.00361	−	0.484269i
$23$	−0.495419	+	0.858091i	−0.103302	+	0.178924i	−0.913043	−	0.407863i	$-0.866274\pi$
$23$	−0.495419	+	0.858091i	−0.103302	+	0.178924i	0.809741	+	0.586787i	$0.199607\pi$
$24$		0			0
$25$	−11.9537	+	2.54085i	−2.39075	+	0.508169i
$26$	−3.00817	−	0.639406i	−0.589950	−	0.125398i
$27$		0			0
$28$	−0.867085	+	0.940582i	−0.163864	+	0.177753i
$29$	−0.853348	−	2.62634i	−0.158463	−	0.487698i	0.840032	−	0.542536i	$-0.182536\pi$
$29$	−0.853348	−	2.62634i	−0.158463	−	0.487698i	−0.998495	+	0.0548378i	$0.982536\pi$
$30$		0			0
$31$	0.485833	−	4.62239i	0.0872582	−	0.830206i	−0.860120	−	0.510091i	$-0.829612\pi$
$31$	0.485833	−	4.62239i	0.0872582	−	0.830206i	0.947379	−	0.320115i	$-0.103722\pi$
$32$	1.33975	+	2.32052i	0.236837	+	0.410214i
$33$		0			0
$34$	7.16004			1.22794
$35$	1.01956	+	10.9319i	0.172338	+	1.84783i
$36$		0			0
$37$	3.11960	+	0.663091i	0.512859	+	0.109011i	0.457069	−	0.889431i	$-0.348899\pi$
$37$	3.11960	+	0.663091i	0.512859	+	0.109011i	0.0557894	+	0.998443i	$0.482232\pi$
$38$	−7.26453	−	3.23438i	−1.17846	−	0.524686i
$39$		0			0
$40$	9.70067	+	2.06194i	1.53381	+	0.326022i
$41$	3.23441	−	9.95449i	0.505130	−	1.55463i	−0.295422	−	0.955367i	$-0.595460\pi$
$41$	3.23441	−	9.95449i	0.505130	−	1.55463i	0.800552	−	0.599263i	$-0.204540\pi$
$42$		0			0
$43$	3.83062			0.584163			0.292082	−	0.956393i	$-0.405652\pi$
$43$	3.83062			0.584163			0.292082	+	0.956393i	$0.405652\pi$
$44$	−1.60289	−	0.0492102i	−0.241645	−	0.00741871i
$45$		0			0
$46$	−0.163219	+	1.55293i	−0.0240653	+	0.228966i
$47$	4.00875	+	4.45217i	0.584737	+	0.649416i	0.960821	−	0.277169i	$-0.0893964\pi$
$47$	4.00875	+	4.45217i	0.584737	+	0.649416i	−0.376084	+	0.926585i	$0.622730\pi$
$48$		0			0
$49$	6.99808	+	0.164116i	0.999725	+	0.0234451i
$50$	−15.5808	+	11.3201i	−2.20346	+	1.60091i
$51$		0			0
$52$	−0.922957	+	0.196181i	−0.127991	+	0.0272054i
$53$	1.01426	−	9.65000i	0.139319	−	1.32553i	−0.671837	−	0.740699i	$-0.734494\pi$
$53$	1.01426	−	9.65000i	0.139319	−	1.32553i	0.811155	−	0.584831i	$-0.198839\pi$
$54$		0			0
$55$	−9.51898	+	9.94071i	−1.28354	+	1.34041i
$56$	2.02426	−	5.99016i	0.270504	−	0.800469i
$57$		0			0
$58$	−2.91198	−	3.23408i	−0.382362	−	0.424656i
$59$	4.39787	−	4.88433i	0.572554	−	0.635886i	−0.385420	−	0.922741i	$-0.625943\pi$
$59$	4.39787	−	4.88433i	0.572554	−	0.635886i	0.957974	+	0.286856i	$0.0926100\pi$
$60$		0			0
$61$	0.790124	+	7.51753i	0.101165	+	0.962521i	0.920906	+	0.389786i	$0.127451\pi$
$61$	0.790124	+	7.51753i	0.101165	+	0.962521i	−0.819741	+	0.572735i	$0.805882\pi$
$62$	−2.26344	−	6.96614i	−0.287457	−	0.884701i
$63$		0			0
$64$	−4.24233	−	3.08223i	−0.530291	−	0.385279i
$65$	−4.04912	+	7.01328i	−0.502231	+	0.869890i
$66$		0			0
$67$	−0.922802	−	1.59834i	−0.112738	−	0.195268i	0.804135	−	0.594446i	$-0.202629\pi$
$67$	−0.922802	−	1.59834i	−0.112738	−	0.195268i	−0.916873	+	0.399178i	$0.869295\pi$
$68$	2.00690	−	0.893529i	0.243372	−	0.108356i
$69$		0			0
$70$	8.47500	+	15.0848i	1.01296	+	1.80298i
$71$	−3.33445	+	2.42262i	−0.395726	+	0.287512i	−0.767798	−	0.640692i	$-0.778648\pi$
$71$	−3.33445	+	2.42262i	−0.395726	+	0.287512i	0.372072	+	0.928204i	$0.378648\pi$
$72$		0			0
$73$	−3.15290	+	3.50165i	−0.369019	+	0.409837i	−0.898843	−	0.438270i	$-0.855591\pi$
$73$	−3.15290	+	3.50165i	−0.369019	+	0.409837i	0.529824	+	0.848108i	$0.322258\pi$
$74$	4.91623	−	1.04498i	0.571500	−	0.121476i
$75$		0			0
$76$	−2.43982			−0.279866
$77$	5.58981	+	6.76417i	0.637018	+	0.770849i
$78$		0			0
$79$	−1.18499	+	0.527591i	−0.133322	+	0.0593587i	−0.472313	−	0.881431i	$-0.656581\pi$
$79$	−1.18499	+	0.527591i	−0.133322	+	0.0593587i	0.338991	+	0.940789i	$0.389914\pi$
$80$	19.2128	−	4.08380i	2.14805	−	0.456583i
$81$		0			0
$82$	−1.72417	−	16.4044i	−0.190403	−	1.81156i
$83$	−1.10236	+	0.800908i	−0.120999	+	0.0879111i	−0.646639	−	0.762796i	$-0.723826\pi$
$83$	−1.10236	+	0.800908i	−0.120999	+	0.0879111i	0.525640	+	0.850707i	$0.323826\pi$
$84$		0			0
$85$	5.82627	−	17.9314i	0.631948	−	1.94494i
$86$	5.51483	−	2.45536i	0.594680	−	0.264769i
$87$		0			0
$88$	7.33650	−	3.00017i	0.782073	−	0.319820i
$89$	7.79893	−	13.5081i	0.826685	−	1.43186i	−0.0739396	−	0.997263i	$-0.523557\pi$
$89$	7.79893	−	13.5081i	0.826685	−	1.43186i	0.900625	−	0.434598i	$-0.143109\pi$
$90$		0			0
$91$	4.14119	+	3.08357i	0.434115	+	0.323246i
$92$	0.148047	+	0.455640i	0.0154349	+	0.0475038i
$93$		0			0
$94$	8.62506	+	3.84013i	0.889607	+	0.396079i
$95$	−14.0114	+	15.5612i	−1.43754	+	1.59655i
$96$		0			0
$97$	3.00835	+	2.18569i	0.305451	+	0.221923i	0.729942	−	0.683509i	$-0.239547\pi$
$97$	3.00835	+	2.18569i	0.305451	+	0.221923i	−0.424491	+	0.905432i	$0.639547\pi$
$98$	10.1801	−	4.24938i	1.02835	−	0.429252i
$99$		0			0
$100$	−2.95449	+	5.11733i	−0.295449	+	0.511733i
$101$	−1.19986	+	11.4159i	−0.119391	+	1.13592i	0.756695	+	0.653768i	$0.226813\pi$
$101$	−1.19986	+	11.4159i	−0.119391	+	1.13592i	−0.876085	+	0.482156i	$0.839854\pi$
$102$		0			0
$103$	−5.84111	−	1.24157i	−0.575542	−	0.122335i	−0.0890605	−	0.996026i	$-0.528386\pi$
$103$	−5.84111	−	1.24157i	−0.575542	−	0.122335i	−0.486481	+	0.873691i	$0.661720\pi$
$104$	3.77305	−	2.74128i	0.369978	−	0.268805i
$105$		0			0
$106$	−4.72530	−	14.5430i	−0.458962	−	1.41254i
$107$	2.55515	+	2.83778i	0.247016	+	0.274339i	0.853884	−	0.520464i	$-0.174241\pi$
$107$	2.55515	+	2.83778i	0.247016	+	0.274339i	−0.606868	+	0.794803i	$0.707574\pi$
$108$		0			0
$109$	−2.52250	−	4.36909i	−0.241611	−	0.418483i	0.719562	−	0.694428i	$-0.244343\pi$
$109$	−2.52250	−	4.36909i	−0.241611	−	0.418483i	−0.961173	+	0.275945i	$0.911009\pi$
$110$	−7.33238	+	20.4129i	−0.699115	+	1.94629i
$111$		0			0
$112$	−1.16291	−	12.4689i	−0.109885	−	1.17820i
$113$	4.75887	−	14.6463i	0.447677	−	1.37781i	−0.431844	−	0.901949i	$-0.642137\pi$
$113$	4.75887	−	14.6463i	0.447677	−	1.37781i	0.879521	−	0.475860i	$-0.157863\pi$
$114$		0			0
$115$	3.75629	+	1.67241i	0.350276	+	0.155953i
$116$	−1.21980	−	0.543088i	−0.113255	−	0.0504245i
$117$		0			0
$118$	3.20072	−	9.85080i	0.294650	−	0.906840i
$119$	−10.9234	−	5.01768i	−1.00135	−	0.459970i
$120$		0			0
$121$	−1.81873	+	10.8486i	−0.165339	+	0.986237i
$122$	5.95613	+	10.3163i	0.539243	+	0.933996i
$123$		0			0
$124$	−1.50375	−	1.67009i	−0.135041	−	0.149978i
$125$	9.25963	+	28.4982i	0.828206	+	2.54896i
$126$		0			0
$127$	−12.6872	+	9.21782i	−1.12581	+	0.817949i	−0.985080	−	0.172099i	$-0.944945\pi$
$127$	−12.6872	+	9.21782i	−1.12581	+	0.817949i	−0.140731	+	0.990048i	$0.544945\pi$
$128$	−13.3251	−	2.83235i	−1.17779	−	0.250346i
$129$		0			0
$130$	−1.33401	+	12.6922i	−0.117000	+	1.11318i
$131$	5.39188	−	9.33900i	0.471090	−	0.815952i	−0.528363	−	0.849019i	$-0.677194\pi$
$131$	5.39188	−	9.33900i	0.471090	−	0.815952i	0.999453	+	0.0330662i	$0.0105272\pi$
$132$		0			0
$133$	8.81621	+	10.0253i	0.764462	+	0.869303i
$134$	−2.35304	−	1.70958i	−0.203272	−	0.147686i
$135$		0			0
$136$	−7.26547	+	8.06912i	−0.623009	+	0.691922i
$137$	14.2311	+	6.33611i	1.21585	+	0.541330i	0.911527	−	0.411240i	$-0.134904\pi$
$137$	14.2311	+	6.33611i	1.21585	+	0.541330i	0.304320	+	0.952570i	$0.401571\pi$
$138$		0			0
$139$	5.54456	+	17.0644i	0.470284	+	1.44738i	0.852214	+	0.523193i	$0.175259\pi$
$139$	5.54456	+	17.0644i	0.470284	+	1.44738i	−0.381930	+	0.924191i	$0.624741\pi$
$140$	4.25796	+	3.17051i	0.359863	+	0.267957i
$141$		0			0
$142$	−3.24766	+	5.62511i	−0.272537	+	0.472048i
$143$	0.478700	+	6.45460i	0.0400309	+	0.539761i
$144$		0			0
$145$	−10.4689	+	4.66105i	−0.869394	+	0.387079i
$146$	−2.29465	+	7.06219i	−0.189906	+	0.584471i
$147$		0			0
$148$	1.24757	−	0.906413i	0.102550	−	0.0745067i
$149$	0.406831	+	3.87074i	0.0333289	+	0.317103i	0.998466	+	0.0553600i	$0.0176306\pi$
$149$	0.406831	+	3.87074i	0.0333289	+	0.317103i	−0.965138	+	0.261743i	$0.915703\pi$
$150$		0			0
$151$	−1.58865	+	0.337678i	−0.129282	+	0.0274798i	−0.272098	−	0.962269i	$-0.587718\pi$
$151$	−1.58865	+	0.337678i	−0.129282	+	0.0274798i	0.142816	+	0.989749i	$0.454384\pi$
$152$	11.0165	−	4.90488i	0.893559	−	0.397838i
$153$		0			0
$154$	12.3832	+	6.15522i	0.997869	+	0.496002i
$155$	−19.2876			−1.54922
$156$		0			0
$157$	8.10823	−	1.72346i	0.647107	−	0.137547i	0.127346	−	0.991858i	$-0.459354\pi$
$157$	8.10823	−	1.72346i	0.647107	−	0.137547i	0.519761	+	0.854312i	$0.326021\pi$
$158$	−1.36782	+	1.51912i	−0.108818	+	0.120855i
$159$		0			0
$160$	8.99579	−	6.53582i	0.711180	−	0.516702i
$161$	1.33728	−	2.25477i	0.105393	−	0.177701i
$162$		0			0
$163$	−2.35298	+	1.04762i	−0.184300	+	0.0820556i	−0.496812	−	0.867858i	$-0.665496\pi$
$163$	−2.35298	+	1.04762i	−0.184300	+	0.0820556i	0.312512	+	0.949914i	$0.398830\pi$
$164$	−2.53044	−	4.38285i	−0.197594	−	0.342243i
$165$		0			0
$166$	−1.07366	+	1.85964i	−0.0833324	+	0.144336i
$167$	−10.9144	−	7.92980i	−0.844584	−	0.613626i	0.0790634	−	0.996870i	$-0.474807\pi$
$167$	−10.9144	−	7.92980i	−0.844584	−	0.613626i	−0.923647	+	0.383243i	$0.874807\pi$
$168$		0			0
$169$	−2.84040	−	8.74185i	−0.218492	−	0.672450i
$170$	−3.10582	−	29.5499i	−0.238206	−	2.26638i
$171$		0			0
$172$	1.23935	−	1.37643i	0.0944992	−	0.104952i
$173$	−0.339703	−	0.377278i	−0.0258271	−	0.0286839i	0.730093	−	0.683348i	$-0.239477\pi$
$173$	−0.339703	−	0.377278i	−0.0258271	−	0.0286839i	−0.755920	+	0.654664i	$0.772810\pi$
$174$		0			0
$175$	31.7033	−	6.35121i	2.39654	−	0.480107i
$176$	10.8573	−	11.3384i	0.818402	−	0.854661i
$177$		0			0
$178$	2.56941	−	24.4463i	0.192585	−	1.83233i
$179$	−15.0606	+	3.20122i	−1.12568	+	0.239270i	−0.732882	−	0.680355i	$-0.761825\pi$
$179$	−15.0606	+	3.20122i	−1.12568	+	0.239270i	−0.392796	+	0.919626i	$0.628492\pi$
$180$		0			0
$181$	18.9457	−	13.7649i	1.40822	−	1.02313i	0.414646	−	0.909983i	$-0.363905\pi$
$181$	18.9457	−	13.7649i	1.40822	−	1.02313i	0.993578	−	0.113152i	$-0.0360946\pi$
$182$	7.93849	+	1.78490i	0.588440	+	0.132305i
$183$		0			0
$184$	−1.58447	−	1.75973i	−0.116809	−	0.129729i
$185$	1.38342	−	13.1624i	0.101711	−	0.967719i
$186$		0			0
$187$	−4.21454	−	14.4674i	−0.308198	−	1.05796i
$188$	2.89675			0.211267
$189$		0			0
$190$	−10.1973	+	31.3842i	−0.739792	+	2.27685i
$191$	−23.0020	−	4.88923i	−1.66437	−	0.353772i	−0.722921	−	0.690931i	$-0.757201\pi$
$191$	−23.0020	−	4.88923i	−1.66437	−	0.353772i	−0.941448	+	0.337158i	$0.890534\pi$
$192$		0			0
$193$	19.7783	+	8.80585i	1.42367	+	0.633859i	0.966767	−	0.255657i	$-0.0822919\pi$
$193$	19.7783	+	8.80585i	1.42367	+	0.633859i	0.456903	+	0.889516i	$0.348959\pi$
$194$	5.73203	+	1.21838i	0.411536	+	0.0874746i
$195$		0			0
$196$	2.32311	−	2.46148i	0.165936	−	0.175820i
$197$	15.2088			1.08358			0.541790	−	0.840514i	$-0.317747\pi$
$197$	15.2088			1.08358			0.541790	+	0.840514i	$0.317747\pi$
$198$		0			0
$199$	−6.60469	−	11.4397i	−0.468194	−	0.810936i	0.531145	−	0.847281i	$-0.321762\pi$
$199$	−6.60469	−	11.4397i	−0.468194	−	0.810936i	−0.999339	+	0.0363450i	$0.988428\pi$
$200$	3.05284	−	29.0459i	0.215869	−	2.05385i
$201$		0			0
$202$	5.59000	+	17.2043i	0.393311	+	1.21049i
$203$	2.17613	+	6.97462i	0.152734	+	0.489522i
$204$		0			0
$205$	−42.4858	−	9.03063i	−2.96733	−	0.630727i
$206$	−9.20511	+	1.95661i	−0.641351	+	0.136323i
$207$		0			0
$208$	4.61842	−	7.99933i	0.320230	−	0.554654i
$209$	−2.25926	+	16.5824i	−0.156276	+	1.14703i
$210$		0			0
$211$	9.82946	+	7.14152i	0.676688	+	0.491643i	0.872257	−	0.489047i	$-0.162655\pi$
$211$	9.82946	+	7.14152i	0.676688	+	0.491643i	−0.195569	+	0.980690i	$0.562655\pi$
$212$	−3.13933	−	3.48658i	−0.215610	−	0.239459i
$213$		0			0
$214$	5.49756	+	2.44767i	0.375805	+	0.167319i
$215$	−1.66161	−	15.8092i	−0.113321	−	1.07818i
$216$		0			0
$217$	−1.42868	+	12.2138i	−0.0969850	+	0.829126i
$218$	−6.43209	−	4.67319i	−0.435636	−	0.316508i
$219$		0			0
$220$	0.492197	+	6.63659i	0.0331839	+	0.447439i
$221$	−4.43319	−	7.67851i	−0.298208	−	0.516512i
$222$		0			0
$223$	−3.00327	+	9.24310i	−0.201114	+	0.618964i	0.798737	+	0.601680i	$0.205502\pi$
$223$	−3.00327	+	9.24310i	−0.201114	+	0.618964i	−0.999851	+	0.0172836i	$0.994498\pi$
$224$	−3.47244	−	6.18066i	−0.232012	−	0.412963i
$225$		0			0
$226$	−2.53682	−	24.1363i	−0.168747	−	1.60552i
$227$	13.1067	−	14.5565i	0.869925	−	0.966149i	−0.129753	−	0.991546i	$-0.541418\pi$
$227$	13.1067	−	14.5565i	0.869925	−	0.966149i	0.999677	+	0.0253973i	$0.00808508\pi$
$228$		0			0
$229$	−2.97206	+	1.32325i	−0.196399	+	0.0874426i	−0.502580	−	0.864531i	$-0.667616\pi$
$229$	−2.97206	+	1.32325i	−0.196399	+	0.0874426i	0.306180	+	0.951974i	$0.400949\pi$
$230$	6.47982			0.427267
$231$		0			0
$232$	6.59956			0.433282
$233$	−26.0359	+	11.5919i	−1.70567	+	0.759414i	−0.707036	+	0.707178i	$0.749968\pi$
$233$	−26.0359	+	11.5919i	−1.70567	+	0.759414i	−0.998635	+	0.0522360i	$0.983365\pi$
$234$		0			0
$235$	16.6355	−	18.4756i	1.08518	−	1.20521i
$236$	−0.332184	−	3.16052i	−0.0216234	−	0.205733i
$237$		0			0
$238$	−18.9424	−	0.222084i	−1.22785	−	0.0143956i
$239$	−0.503891	+	1.55082i	−0.0325940	+	0.100314i	−0.966030	−	0.258430i	$-0.916795\pi$
$239$	−0.503891	+	1.55082i	−0.0325940	+	0.100314i	0.933436	+	0.358744i	$0.116795\pi$
$240$		0			0
$241$	−2.73011	−	4.72869i	−0.175862	−	0.304602i	0.764597	−	0.644508i	$-0.222938\pi$
$241$	−2.73011	−	4.72869i	−0.175862	−	0.304602i	−0.940459	+	0.339907i	$0.889605\pi$
$242$	4.33540	+	16.7842i	0.278690	+	1.07893i
$243$		0			0
$244$	2.95686	+	2.14829i	0.189294	+	0.137530i
$245$	−2.35825	−	28.9527i	−0.150663	−	1.84972i
$246$		0			0
$247$	1.02930	+	9.79315i	0.0654929	+	0.623123i
$248$	10.1474	+	4.51790i	0.644358	+	0.286887i
$249$		0			0
$250$	31.5977	+	35.0928i	1.99842	+	2.21947i
$251$	15.8982	+	11.5507i	1.00348	+	0.729073i	0.962832	−	0.270100i	$-0.0870568\pi$
$251$	15.8982	+	11.5507i	1.00348	+	0.729073i	0.0406509	+	0.999173i	$0.487057\pi$
$252$		0			0
$253$	3.23388	−	0.584287i	0.203312	−	0.0367338i
$254$	−12.3570	+	21.4030i	−0.775347	+	1.34294i
$255$		0			0
$256$	−10.7409	+	2.28305i	−0.671306	+	0.142690i
$257$	−9.78629	−	2.08014i	−0.610452	−	0.129756i	−0.107696	−	0.994184i	$-0.534347\pi$
$257$	−9.78629	−	2.08014i	−0.610452	−	0.129756i	−0.502756	+	0.864428i	$0.667681\pi$
$258$		0			0
$259$	−8.23255	−	1.85101i	−0.511546	−	0.115016i
$260$	1.21000	+	3.72400i	0.0750411	+	0.230953i
$261$		0			0
$262$	1.77639	−	16.9012i	0.109746	−	1.04416i
$263$	−3.33921	−	5.78367i	−0.205904	−	0.356637i	0.744516	−	0.667604i	$-0.232680\pi$
$263$	−3.33921	−	5.78367i	−0.205904	−	0.356637i	−0.950420	+	0.310968i	$0.899347\pi$
$264$		0			0
$265$	−40.2661			−2.47353
$266$	19.1185	+	8.78210i	1.17223	+	0.538465i
$267$		0			0
$268$	−0.872883	−	0.185537i	−0.0533198	−	0.0113335i
$269$	−25.1952	−	11.2176i	−1.53618	−	0.683951i	−0.547891	−	0.836550i	$-0.684569\pi$
$269$	−25.1952	−	11.2176i	−1.53618	−	0.683951i	−0.988288	+	0.152599i	$0.951236\pi$
$270$		0			0
$271$	−4.24166	−	0.901594i	−0.257663	−	0.0547679i	0.0772690	−	0.997010i	$-0.475380\pi$
$271$	−4.24166	−	0.901594i	−0.257663	−	0.0547679i	−0.334932	+	0.942242i	$0.608713\pi$
$272$	−6.64544	+	20.4526i	−0.402939	+	1.24012i
$273$		0			0
$274$	24.5495			1.48309
$275$	32.0444	+	24.8190i	1.93235	+	1.49664i
$276$		0			0
$277$	0.799494	−	7.60667i	0.0480369	−	0.457041i	−0.943893	−	0.330252i	$-0.892866\pi$
$277$	0.799494	−	7.60667i	0.0480369	−	0.457041i	0.991930	−	0.126789i	$-0.0404671\pi$
$278$	18.9204	+	21.0132i	1.13477	+	1.26029i
$279$		0			0
$280$	−25.5998	−	5.75590i	−1.52988	−	0.343981i
$281$	−9.49612	+	6.89934i	−0.566491	+	0.411580i	−0.833829	−	0.552023i	$-0.813856\pi$
$281$	−9.49612	+	6.89934i	−0.566491	+	0.411580i	0.267338	+	0.963603i	$0.413856\pi$
$282$		0			0
$283$	7.39881	−	1.57267i	0.439813	−	0.0934852i	0.0173175	−	0.999850i	$-0.494487\pi$
$283$	7.39881	−	1.57267i	0.439813	−	0.0934852i	0.422496	+	0.906365i	$0.361154\pi$
$284$	−0.208312	+	1.98196i	−0.0123610	+	0.117607i
$285$		0			0
$286$	4.82646	+	8.98567i	0.285395	+	0.531334i
$287$	−8.86561	+	26.2350i	−0.523321	+	1.54860i
$288$		0			0
$289$	2.43736	+	2.70697i	0.143374	+	0.159233i
$290$	−12.0841	+	13.4208i	−0.709604	+	0.788095i
$291$		0			0
$292$	0.238148	+	2.26583i	0.0139366	+	0.132598i
$293$	−4.69184	−	14.4400i	−0.274100	−	0.843594i	−0.989456	−	0.144834i	$-0.953735\pi$
$293$	−4.69184	−	14.4400i	−0.274100	−	0.843594i	0.715356	−	0.698760i	$-0.246265\pi$
$294$		0			0
$295$	−22.0656	−	16.0316i	−1.28471	−	0.933396i
$296$	−3.81097	+	6.60079i	−0.221508	+	0.383663i
$297$		0			0
$298$	3.06678	+	5.31182i	0.177654	+	0.307706i
$299$	1.76643	−	0.786466i	0.102155	−	0.0454825i
$300$		0			0
$301$	−10.1342	−	0.118815i	−0.584123	−	0.00684836i
$302$	−2.07069	+	1.50444i	−0.119155	+	0.0865711i
$303$		0			0
$304$	15.9814	−	17.7491i	0.916594	−	1.01798i
$305$	30.6826	−	6.52178i	1.75688	−	0.373436i
$306$		0			0
$307$	−11.8851			−0.678321			−0.339161	−	0.940729i	$-0.610143\pi$
$307$	−11.8851			−0.678321			−0.339161	+	0.940729i	$0.610143\pi$
$308$	4.23904	+	0.179906i	0.241542	+	0.0102511i
$309$		0			0
$310$	−27.7679	+	12.3631i	−1.57711	+	0.702175i
$311$	−17.3291	+	3.68340i	−0.982641	+	0.208867i	−0.671101	−	0.741366i	$-0.734178\pi$
$311$	−17.3291	+	3.68340i	−0.982641	+	0.208867i	−0.311540	+	0.950233i	$0.600845\pi$
$312$		0			0
$313$	−1.36213	−	12.9598i	−0.0769924	−	0.732534i	−0.963116	−	0.269085i	$-0.913279\pi$
$313$	−1.36213	−	12.9598i	−0.0769924	−	0.732534i	0.886124	−	0.463448i	$-0.153388\pi$
$314$	10.5685	−	7.67846i	0.596414	−	0.433320i
$315$		0			0
$316$	−0.193812	+	0.596491i	−0.0109028	+	0.0335552i
$317$	14.9625	−	6.66174i	0.840379	−	0.374161i	0.0590307	−	0.998256i	$-0.481199\pi$
$317$	14.9625	−	6.66174i	0.840379	−	0.374161i	0.781348	+	0.624095i	$0.214532\pi$
$318$		0			0
$319$	−4.82066	+	7.78752i	−0.269905	+	0.436018i
$320$	−10.8804	+	18.8453i	−0.608231	+	1.05349i
$321$		0			0
$322$	0.479975	−	4.10331i	0.0267480	−	0.228669i
$323$	−7.08449	−	21.8038i	−0.394191	−	1.21320i
$324$		0			0
$325$	21.7868	+	9.70011i	1.20851	+	0.538065i
$326$	−2.71602	+	3.01645i	−0.150427	+	0.167066i
$327$		0			0
$328$	20.2368	+	14.7029i	1.11739	+	0.811830i
$329$	−10.4673	−	11.9029i	−0.577083	−	0.656226i
$330$		0			0
$331$	1.64859	−	2.85543i	0.0906145	−	0.156949i	−0.817155	−	0.576417i	$-0.804450\pi$
$331$	1.64859	−	2.85543i	0.0906145	−	0.156949i	0.907770	+	0.419469i	$0.137784\pi$
$332$	−0.0688671	+	0.655227i	−0.00377957	+	0.0359602i
$333$		0			0
$334$	−20.7961	−	4.42034i	−1.13791	−	0.241870i
$335$	−6.19616	+	4.50177i	−0.338532	+	0.245958i
$336$		0			0
$337$	9.76850	+	30.0644i	0.532124	+	1.63771i	0.749782	+	0.661685i	$0.230158\pi$
$337$	9.76850	+	30.0644i	0.532124	+	1.63771i	−0.217658	+	0.976025i	$0.569842\pi$
$338$	−9.69263	−	10.7648i	−0.527210	−	0.585526i
$339$		0			0
$340$	−4.55818	−	7.89500i	−0.247202	−	0.428167i
$341$	−12.7433	+	8.67386i	−0.690089	+	0.469716i
$342$		0			0
$343$	−18.5088	−	0.651240i	−0.999382	−	0.0351636i
$344$	−2.82893	+	8.70654i	−0.152526	+	0.469425i
$345$		0			0
$346$	−0.730890	−	0.325413i	−0.0392929	−	0.0174943i
$347$	30.6627	+	13.6519i	1.64606	+	0.732873i	0.999549	−	0.0300308i	$-0.00956053\pi$
$347$	30.6627	+	13.6519i	1.64606	+	0.732873i	0.646512	+	0.762904i	$0.276227\pi$
$348$		0			0
$349$	3.38656	−	10.4228i	0.181279	−	0.557918i	−0.818586	−	0.574384i	$-0.805242\pi$
$349$	3.38656	−	10.4228i	0.181279	−	0.557918i	0.999864	+	0.0164660i	$0.00524152\pi$
$350$	41.5713	−	29.4649i	2.22208	−	1.57497i
$351$		0			0
$352$	3.00428	−	8.36372i	0.160129	−	0.445788i
$353$	−15.1279	−	26.2023i	−0.805177	−	1.39461i	−0.916172	−	0.400786i	$-0.868737\pi$
$353$	−15.1279	−	26.2023i	−0.805177	−	1.39461i	0.110995	−	0.993821i	$-0.464596\pi$
$354$		0			0
$355$	11.4447	+	12.7106i	0.607421	+	0.674609i
$356$	−2.33056	−	7.17273i	−0.123520	−	0.380154i
$357$		0			0
$358$	−19.6303	+	14.2623i	−1.03750	+	0.753785i
$359$	19.7846	+	4.20534i	1.04419	+	0.221949i	0.697913	−	0.716183i	$-0.254112\pi$
$359$	19.7846	+	4.20534i	1.04419	+	0.221949i	0.346277	+	0.938132i	$0.387446\pi$
$360$		0			0
$361$	−0.675434	+	6.42633i	−0.0355492	+	0.338228i
$362$	18.4526	−	31.9608i	0.969846	−	1.67982i
$363$		0			0
$364$	2.44783	−	0.490382i	0.128301	−	0.0257030i
$365$	15.8192	+	11.4933i	0.828013	+	0.601587i
$366$		0			0
$367$	1.57767	−	1.75218i	0.0823537	−	0.0914631i	−0.700560	−	0.713594i	$-0.747066\pi$
$367$	1.57767	−	1.75218i	0.0823537	−	0.0914631i	0.782913	+	0.622131i	$0.213733\pi$
$368$	−4.28442	−	1.90755i	−0.223341	−	0.0994378i
$369$		0			0
$370$	−6.44521	−	19.8363i	−0.335070	−	1.03124i
$371$	−2.98260	+	25.4983i	−0.154849	+	1.32381i
$372$		0			0
$373$	8.05587	−	13.9532i	0.417117	−	0.722468i	−0.578531	−	0.815660i	$-0.696374\pi$
$373$	8.05587	−	13.9532i	0.417117	−	0.722468i	0.995648	+	0.0931924i	$0.0297072\pi$
$374$	−15.3409	−	18.1269i	−0.793261	−	0.937319i
$375$		0			0
$376$	−13.0797	+	5.82348i	−0.674537	+	0.300323i
$377$	−1.66529	+	5.12524i	−0.0857669	+	0.263963i
$378$		0			0
$379$	−22.4027	+	16.2765i	−1.15075	+	0.836069i	−0.988581	−	0.150694i	$-0.951849\pi$
$379$	−22.4027	+	16.2765i	−1.15075	+	0.836069i	−0.162170	+	0.986763i	$0.551849\pi$
$380$	1.05832	+	10.0693i	0.0542908	+	0.516543i
$381$		0			0
$382$	−36.2493	+	7.70503i	−1.85468	+	0.394224i
$383$	−13.9016	+	6.18940i	−0.710340	+	0.316264i	−0.729908	−	0.683545i	$-0.760437\pi$
$383$	−13.9016	+	6.18940i	−0.710340	+	0.316264i	0.0195688	+	0.999809i	$0.493771\pi$
$384$		0			0
$385$	25.4915	−	26.0036i	1.29916	−	1.32527i
$386$	34.1186			1.73659
$387$		0			0
$388$	1.75868	−	0.373820i	0.0892836	−	0.0189778i
$389$	3.88654	−	4.31644i	0.197055	−	0.218852i	−0.636517	−	0.771263i	$-0.719625\pi$
$389$	3.88654	−	4.31644i	0.197055	−	0.218852i	0.833572	+	0.552411i	$0.186292\pi$
$390$		0			0
$391$	−3.64202	+	2.64608i	−0.184185	+	0.133818i
$392$	−5.54113	+	15.7846i	−0.279869	+	0.797243i
$393$		0			0
$394$	21.8957	−	9.74858i	1.10309	−	0.491126i
$395$	2.69142	+	4.66167i	0.135420	+	0.234554i
$396$		0			0
$397$	10.5158	−	18.2139i	0.527772	−	0.914127i	−0.471704	−	0.881757i	$-0.656361\pi$
$397$	10.5158	−	18.2139i	0.527772	−	0.914127i	0.999476	−	0.0323706i	$-0.0103057\pi$
$398$	−16.8412	−	12.2359i	−0.844174	−	0.613329i
$399$		0			0
$400$	−17.8748	−	55.0129i	−0.893739	−	2.75065i
$401$	−0.0334066	−	0.317843i	−0.00166825	−	0.0158723i	0.993656	−	0.112461i	$-0.0358734\pi$
$401$	−0.0334066	−	0.317843i	−0.00166825	−	0.0158723i	−0.995324	+	0.0965890i	$0.969207\pi$
$402$		0			0
$403$	−6.06914	+	6.74047i	−0.302326	+	0.335767i
$404$	3.71381	+	4.12461i	0.184769	+	0.205207i
$405$		0			0
$406$	7.60354	+	8.64631i	0.377357	+	0.429109i
$407$	−5.00525	−	9.31852i	−0.248101	−	0.461902i
$408$		0			0
$409$	1.02405	−	9.74319i	0.0506360	−	0.481770i	−0.939590	−	0.342301i	$-0.888794\pi$
$409$	1.02405	−	9.74319i	0.0506360	−	0.481770i	0.990226	−	0.139469i	$-0.0445395\pi$
$410$	−66.9541	+	14.2315i	−3.30663	+	0.702845i
$411$		0			0
$412$	−2.33594	+	1.69716i	−0.115084	+	0.0836131i
$413$	−11.7864	+	12.7854i	−0.579969	+	0.629130i
$414$		0			0
$415$	3.78357	+	4.20208i	0.185728	+	0.206272i
$416$	0.546580	−	5.20036i	0.0267983	−	0.254969i
$417$		0			0
$418$	7.37643	+	25.3213i	0.360793	+	1.23851i
$419$	24.4796			1.19591			0.597953	−	0.801531i	$-0.295981\pi$
$419$	24.4796			1.19591			0.597953	+	0.801531i	$0.295981\pi$
$420$		0			0
$421$	−2.19524	+	6.75624i	−0.106989	+	0.329279i	−0.990192	−	0.139712i	$-0.955382\pi$
$421$	−2.19524	+	6.75624i	−0.106989	+	0.329279i	0.883203	+	0.468991i	$0.155382\pi$
$422$	18.7288	+	3.98093i	0.911704	+	0.193789i
$423$		0			0
$424$	21.1843	+	9.43186i	1.02880	+	0.458052i
$425$	−54.3107	−	11.5441i	−2.63446	−	0.559971i
$426$		0			0
$427$	−1.85716	−	19.9126i	−0.0898741	−	0.963640i
$428$	1.84637			0.0892477
$429$		0			0
$430$	−12.5256	−	21.6950i	−0.604038	−	1.04623i
$431$	−0.802324	+	7.63360i	−0.0386466	+	0.367698i	0.958058	+	0.286576i	$0.0925170\pi$
$431$	−0.802324	+	7.63360i	−0.0386466	+	0.367698i	−0.996704	+	0.0811220i	$0.974150\pi$
$432$		0			0
$433$	1.06654	+	3.28247i	0.0512547	+	0.157746i	0.973408	−	0.229080i	$-0.0735716\pi$
$433$	1.06654	+	3.28247i	0.0512547	+	0.157746i	−0.922153	+	0.386825i	$0.873572\pi$
$434$	5.77201	+	18.4996i	0.277065	+	0.888010i
$435$		0			0
$436$	−2.38604	−	0.507169i	−0.114271	−	0.0242890i
$437$	4.89048	−	1.03950i	0.233943	−	0.0497262i
$438$		0			0
$439$	−15.7554	+	27.2892i	−0.751965	+	1.30244i	0.194905	+	0.980822i	$0.437560\pi$
$439$	−15.7554	+	27.2892i	−0.751965	+	1.30244i	−0.946869	+	0.321619i	$0.895773\pi$
$440$	−15.5643	−	28.9768i	−0.741997	−	1.38141i
$441$		0			0
$442$	−11.3041	−	8.21294i	−0.537683	−	0.390650i
$443$	6.53109	+	7.25351i	0.310301	+	0.344625i	0.878043	−	0.478582i	$-0.158849\pi$
$443$	6.53109	+	7.25351i	0.310301	+	0.344625i	−0.567741	+	0.823207i	$0.692183\pi$
$444$		0			0
$445$	−59.1319	−	26.3272i	−2.80312	−	1.24803i
$446$	1.60096	+	15.2321i	0.0758075	+	0.721260i
$447$		0			0
$448$	11.1278	+	8.28584i	0.525738	+	0.391469i
$449$	13.4686	+	9.78552i	0.635623	+	0.461807i	0.858344	−	0.513075i	$-0.171494\pi$
$449$	13.4686	+	9.78552i	0.635623	+	0.461807i	−0.222720	+	0.974882i	$0.571494\pi$
$450$		0			0
$451$	−32.1315	+	13.1398i	−1.51301	+	0.618728i
$452$	−3.72310	−	6.44860i	−0.175120	−	0.303317i
$453$		0			0
$454$	9.53893	−	29.3578i	0.447684	−	1.37783i
$455$	10.9298	−	18.4285i	0.512395	−	0.863943i
$456$		0			0
$457$	1.33196	+	12.6728i	0.0623067	+	0.592809i	0.980479	+	0.196626i	$0.0629985\pi$
$457$	1.33196	+	12.6728i	0.0623067	+	0.592809i	−0.918172	+	0.396182i	$0.870335\pi$
$458$	−3.43062	+	3.81009i	−0.160302	+	0.178034i
$459$		0			0
$460$	1.81624	−	0.808641i	0.0846825	−	0.0377031i
$461$	−5.21592			−0.242929			−0.121465	−	0.992596i	$-0.538759\pi$
$461$	−5.21592			−0.242929			−0.121465	+	0.992596i	$0.538759\pi$
$462$		0			0
$463$	−10.6551			−0.495186			−0.247593	−	0.968864i	$-0.579640\pi$
$463$	−10.6551			−0.495186			−0.247593	+	0.968864i	$0.579640\pi$
$464$	11.9408	−	5.31638i	0.554337	−	0.246807i
$465$		0			0
$466$	−30.0530	+	33.3772i	−1.39218	+	1.54617i
$467$	−3.10324	−	29.5253i	−0.143601	−	1.36627i	−0.794573	−	0.607169i	$-0.792305\pi$
$467$	−3.10324	−	29.5253i	−0.143601	−	1.36627i	0.650972	−	0.759102i	$-0.274361\pi$
$468$		0			0
$469$	2.39176	+	4.25714i	0.110441	+	0.196576i
$470$	12.1071	−	37.2619i	0.558460	−	1.71876i
$471$		0			0
$472$	7.85367	+	13.6029i	0.361494	+	0.626126i
$473$	−8.20739	−	9.69786i	−0.377376	−	0.445908i
$474$		0			0
$475$	49.8885	+	36.2461i	2.28904	+	1.66309i
$476$	−5.33710	+	2.30164i	−0.244626	+	0.105496i
$477$		0			0
$478$	0.268610	+	2.55566i	0.0122859	+	0.116893i
$479$	20.1742	+	8.98211i	0.921780	+	0.410403i	0.812070	−	0.583560i	$-0.198341\pi$
$479$	20.1742	+	8.98211i	0.921780	+	0.410403i	0.109711	+	0.993964i	$0.465008\pi$
$480$		0			0
$481$	−4.16456	−	4.62521i	−0.189888	−	0.210892i
$482$	−6.96148	−	5.05781i	−0.317087	−	0.230377i
$483$		0			0
$484$	3.30974	+	4.16344i	0.150443	+	0.189247i
$485$	7.71555	−	13.3637i	0.350345	−	0.606815i
$486$		0			0
$487$	31.7266	−	6.74370i	1.43767	−	0.305586i	0.577833	−	0.816155i	$-0.303898\pi$
$487$	31.7266	−	6.74370i	1.43767	−	0.305586i	0.859837	+	0.510569i	$0.170565\pi$
$488$	−17.6700	−	3.75587i	−0.799882	−	0.170020i
$489$		0			0
$490$	−21.9533	−	40.1708i	−0.991749	−	1.81473i
$491$	1.64832	+	5.07301i	0.0743877	+	0.228942i	0.981336	−	0.192300i	$-0.0615945\pi$
$491$	1.64832	+	5.07301i	0.0743877	+	0.228942i	−0.906949	+	0.421241i	$0.861595\pi$
$492$		0			0
$493$	1.31148	−	12.4779i	0.0590659	−	0.561975i
$494$	7.75911	+	13.4392i	0.349099	+	0.604657i
$495$		0			0
$496$	21.9994			0.987804
$497$	8.89666	−	6.30578i	0.399070	−	0.282853i
$498$		0			0
$499$	36.5148	+	7.76145i	1.63462	+	0.347450i	0.931535	−	0.363651i	$-0.118470\pi$
$499$	36.5148	+	7.76145i	1.63462	+	0.347450i	0.703090	+	0.711101i	$0.251803\pi$
$500$	13.2359	+	5.89302i	0.591929	+	0.263544i
$501$		0			0
$502$	30.2920	+	6.43876i	1.35200	+	0.287376i
$503$	1.78265	−	5.48642i	0.0794843	−	0.244627i	−0.903416	−	0.428764i	$-0.858949\pi$
$503$	1.78265	−	5.48642i	0.0794843	−	0.244627i	0.982901	+	0.184137i	$0.0589490\pi$
$504$		0			0
$505$	47.6346			2.11971
$506$	4.28121	−	2.91405i	0.190323	−	0.129545i
$507$		0			0
$508$	−0.792606	+	7.54114i	−0.0351662	+	0.334584i
$509$	−2.23691	−	2.48434i	−0.0991494	−	0.110117i	0.691528	−	0.722350i	$-0.256938\pi$
$509$	−2.23691	−	2.48434i	−0.0991494	−	0.110117i	−0.790677	+	0.612233i	$0.790271\pi$
$510$		0			0
$511$	8.44983	−	9.16607i	0.373799	−	0.405483i
$512$	8.04222	−	5.84302i	0.355419	−	0.258227i
$513$		0			0
$514$	−15.4224	+	3.27813i	−0.680253	+	0.144592i
$515$	−2.59031	+	24.6452i	−0.114143	+	1.08600i
$516$		0			0
$517$	2.68238	−	19.6880i	0.117971	−	0.865876i
$518$	−13.0386	+	2.61207i	−0.572885	+	0.114768i
$519$		0			0
$520$	−12.9501	−	14.3825i	−0.567898	−	0.630715i
$521$	−6.50638	+	7.22607i	−0.285050	+	0.316580i	−0.868616	−	0.495486i	$-0.834990\pi$
$521$	−6.50638	+	7.22607i	−0.285050	+	0.316580i	0.583566	+	0.812065i	$0.301657\pi$
$522$		0			0
$523$	−1.19187	−	11.3399i	−0.0521169	−	0.495859i	−0.989181	−	0.146701i	$-0.953134\pi$
$523$	−1.19187	−	11.3399i	−0.0521169	−	0.495859i	0.937064	−	0.349158i	$-0.113532\pi$
$524$	−1.61126	−	4.95895i	−0.0703882	−	0.216633i
$525$		0			0
$526$	−8.51461	−	6.18622i	−0.371254	−	0.269732i
$527$	10.5586	−	18.2880i	0.459938	−	0.796636i
$528$		0			0
$529$	11.0091	+	19.0684i	0.478657	+	0.829059i
$530$	−57.9700	+	25.8099i	−2.51806	+	1.12111i
$531$		0			0
$532$	6.45470	+	0.0756760i	0.279847	+	0.00328097i
$533$	−16.5247	+	12.0059i	−0.715765	+	0.520034i
$534$		0			0
$535$	10.6034	−	11.7762i	0.458423	−	0.509130i
$536$	4.31433	−	0.917039i	0.186351	−	0.0396101i
$537$		0			0
$538$	−43.4632			−1.87383
$539$	−14.5784	−	18.0685i	−0.627937	−	0.778264i
$540$		0			0
$541$	10.9349	−	4.86851i	0.470126	−	0.209314i	−0.157979	−	0.987443i	$-0.550498\pi$
$541$	10.9349	−	4.86851i	0.470126	−	0.209314i	0.628105	+	0.778129i	$0.283831\pi$
$542$	−6.68452	+	1.42084i	−0.287125	+	0.0610302i
$543$		0			0
$544$	1.27254	+	12.1074i	0.0545597	+	0.519101i
$545$	−16.9373	+	12.3057i	−0.725515	+	0.527118i
$546$		0			0
$547$	0.385883	−	1.18762i	0.0164991	−	0.0507791i	−0.942468	−	0.334296i	$-0.891501\pi$
$547$	0.385883	−	1.18762i	0.0164991	−	0.0507791i	0.958967	+	0.283517i	$0.0915013\pi$
$548$	6.88101	−	3.06363i	0.293942	−	0.130872i
$549$		0			0
$550$	62.0420	+	15.1913i	2.64548	+	0.647760i
$551$	−6.96719	+	12.0675i	−0.296812	+	0.514094i
$552$		0			0
$553$	3.15134	−	1.35902i	0.134008	−	0.0577916i
$554$	−3.72475	−	11.4636i	−0.158249	−	0.487041i
$555$		0			0
$556$	7.92553	+	3.52867i	0.336117	+	0.149649i
$557$	−0.905939	+	1.00615i	−0.0383859	+	0.0426318i	−0.762032	−	0.647539i	$-0.775798\pi$
$557$	−0.905939	+	1.00615i	−0.0383859	+	0.0426318i	0.723646	+	0.690171i	$0.242465\pi$
$558$		0			0
$559$	−6.04770	−	4.39391i	−0.255790	−	0.185843i
$560$	−50.9554	+	10.2081i	−2.15326	+	0.431369i
$561$		0			0
$562$	−9.24895	+	16.0197i	−0.390143	+	0.675748i
$563$	2.73488	−	26.0207i	0.115262	−	1.09664i	−0.772079	−	0.635526i	$-0.780783\pi$
$563$	2.73488	−	26.0207i	0.115262	−	1.09664i	0.887341	−	0.461114i	$-0.152550\pi$
$564$		0			0
$565$	−62.5105	−	13.2870i	−2.62984	−	0.558989i
$566$	9.64381	−	7.00664i	0.405360	−	0.294511i
$567$		0			0
$568$	−3.04382	−	9.36793i	−0.127716	−	0.393070i
$569$	−7.16986	−	7.96294i	−0.300576	−	0.333824i	0.573870	−	0.818947i	$-0.305442\pi$
$569$	−7.16986	−	7.96294i	−0.300576	−	0.333824i	−0.874446	+	0.485123i	$0.838775\pi$
$570$		0			0
$571$	−0.748830	−	1.29701i	−0.0313376	−	0.0542783i	0.849931	−	0.526894i	$-0.176643\pi$
$571$	−0.748830	−	1.29701i	−0.0313376	−	0.0542783i	−0.881269	+	0.472615i	$0.843310\pi$
$572$	2.47417	+	1.91629i	0.103450	+	0.0801243i
$573$		0			0
$574$	4.05260	+	43.4525i	0.169152	+	1.81367i
$575$	3.74183	−	11.5162i	0.156045	−	0.480258i
$576$		0			0
$577$	23.8569	+	10.6218i	0.993177	+	0.442191i	0.837985	−	0.545694i	$-0.183734\pi$
$577$	23.8569	+	10.6218i	0.993177	+	0.442191i	0.155192	+	0.987884i	$0.450400\pi$
$578$	5.24413	+	2.33484i	0.218127	+	0.0971164i
$579$		0			0
$580$	−1.71225	+	5.26975i	−0.0710971	+	0.218814i
$581$	2.94120	−	2.08467i	0.122022	−	0.0864866i
$582$		0			0
$583$	−26.6038	+	18.1081i	−1.10182	+	0.749961i
$584$	−5.63041	−	9.75216i	−0.232988	−	0.403547i
$585$		0			0
$586$	−16.0105	−	17.7815i	−0.661389	−	0.734547i
$587$	6.81855	+	20.9853i	0.281432	+	0.866158i	0.987446	+	0.157960i	$0.0504916\pi$
$587$	6.81855	+	20.9853i	0.281432	+	0.866158i	−0.706014	+	0.708198i	$0.749508\pi$
$588$		0			0
$589$	−18.9738	+	13.7853i	−0.781801	+	0.568012i
$590$	−42.0432	−	8.93657i	−1.73089	−	0.367913i
$591$		0			0
$592$	−1.57793	+	15.0130i	−0.0648526	+	0.617031i
$593$	5.52727	−	9.57352i	0.226978	−	0.393137i	−0.729933	−	0.683519i	$-0.760449\pi$
$593$	5.52727	−	9.57352i	0.226978	−	0.393137i	0.956911	+	0.290381i	$0.0937821\pi$
$594$		0			0
$595$	−15.9700	+	47.2581i	−0.654706	+	1.93739i
$596$	1.52247	+	1.10614i	0.0623630	+	0.0453094i
$597$		0			0
$598$	2.03897	−	2.26451i	0.0833798	−	0.0926026i
$599$	2.18297	+	0.971919i	0.0891936	+	0.0397115i	0.450848	−	0.892600i	$-0.351121\pi$
$599$	2.18297	+	0.971919i	0.0891936	+	0.0397115i	−0.361655	+	0.932312i	$0.617788\pi$
$600$		0			0
$601$	5.39235	+	16.5959i	0.219959	+	0.676963i	0.998764	+	0.0496976i	$0.0158257\pi$
$601$	5.39235	+	16.5959i	0.219959	+	0.676963i	−0.778806	+	0.627265i	$0.784174\pi$
$602$	−14.6660	+	6.32478i	−0.597743	+	0.257779i
$603$		0			0
$604$	−0.392651	+	0.680092i	−0.0159768	+	0.0276725i
$605$	45.5618	+	2.80021i	1.85235	+	0.113845i
$606$		0			0
$607$	44.2709	−	19.7107i	1.79690	−	0.800031i	0.824812	−	0.565406i	$-0.191281\pi$
$607$	44.2709	−	19.7107i	1.79690	−	0.800031i	0.972086	−	0.234624i	$-0.0753860\pi$
$608$	4.17813	−	12.8589i	0.169445	−	0.521499i
$609$		0			0
$610$	39.9925	−	29.0562i	1.61925	−	1.17645i
$611$	−1.22207	−	11.6272i	−0.0494398	−	0.470388i
$612$		0			0
$613$	−4.85729	+	1.03245i	−0.196184	+	0.0417002i	−0.304956	−	0.952367i	$-0.598642\pi$
$613$	−4.85729	+	1.03245i	−0.196184	+	0.0417002i	0.108772	+	0.994067i	$0.465308\pi$
$614$	−17.1107	+	7.61818i	−0.690533	+	0.307445i
$615$		0			0
$616$	−19.5023	+	7.70961i	−0.785769	+	0.310629i
$617$	22.2393			0.895322			0.447661	−	0.894203i	$-0.352257\pi$
$617$	22.2393			0.895322			0.447661	+	0.894203i	$0.352257\pi$
$618$		0			0
$619$	28.6331	−	6.08616i	1.15086	−	0.244623i	0.407303	−	0.913293i	$-0.366469\pi$
$619$	28.6331	−	6.08616i	1.15086	−	0.244623i	0.743560	+	0.668670i	$0.233136\pi$
$620$	−6.24026	+	6.93052i	−0.250615	+	0.278336i
$621$		0			0
$622$	−22.5872	+	16.4105i	−0.905663	+	0.658003i
$623$	−21.0516	+	35.4948i	−0.843414	+	1.42207i
$624$		0			0
$625$	57.7760	−	25.7236i	2.31104	−	1.02894i
$626$	−10.2681	−	17.7848i	−0.410395	−	0.710825i
$627$		0			0
$628$	2.00403	−	3.47109i	0.0799696	−	0.138511i
$629$	11.7229	+	8.51716i	0.467421	+	0.339602i
$630$		0			0
$631$	10.5313	+	32.4119i	0.419243	+	1.29030i	0.908401	+	0.418101i	$0.137304\pi$
$631$	10.5313	+	32.4119i	0.419243	+	1.29030i	−0.489158	+	0.872195i	$0.662696\pi$
$632$	−0.324033	−	3.08297i	−0.0128894	−	0.122634i
$633$		0			0
$634$	17.2711	−	19.1815i	0.685922	−	0.761793i
$635$	43.5459	+	48.3626i	1.72806	+	1.91921i
$636$		0			0
$637$	−10.8602	−	8.28625i	−0.430296	−	0.328313i
$638$	−1.94850	+	14.3015i	−0.0771417	+	0.566200i
$639$		0			0
$640$	−5.90920	+	56.2222i	−0.233581	+	2.22238i
$641$	27.6062	−	5.86788i	1.09038	−	0.231767i	0.372568	−	0.928005i	$-0.378477\pi$
$641$	27.6062	−	5.86788i	1.09038	−	0.231767i	0.717812	+	0.696237i	$0.245144\pi$
$642$		0			0
$643$	−4.28751	+	3.11506i	−0.169083	+	0.122846i	−0.669109	−	0.743165i	$-0.733324\pi$
$643$	−4.28751	+	3.11506i	−0.169083	+	0.122846i	0.500026	+	0.866011i	$0.333324\pi$
$644$	−0.377535	−	1.21002i	−0.0148770	−	0.0476815i
$645$		0			0
$646$	−24.1752	−	26.8493i	−0.951162	−	1.05637i
$647$	2.41816	−	23.0072i	0.0950675	−	0.904507i	−0.838209	−	0.545349i	$-0.816397\pi$
$647$	2.41816	−	23.0072i	0.0950675	−	0.904507i	0.933277	−	0.359158i	$-0.116936\pi$
$648$		0			0
$649$	−21.7883	−	0.668918i	−0.855266	−	0.0262573i
$650$	37.5835			1.47415
$651$		0			0
$652$	−0.384844	+	1.18443i	−0.0150716	+	0.0463857i
$653$	−5.03855	−	1.07098i	−0.197174	−	0.0419106i	0.108266	−	0.994122i	$-0.465470\pi$
$653$	−5.03855	−	1.07098i	−0.197174	−	0.0419106i	−0.305440	+	0.952211i	$0.598803\pi$
$654$		0			0
$655$	−40.8815	−	18.2016i	−1.59737	−	0.711196i
$656$	48.4592	+	10.3003i	1.89201	+	0.402160i
$657$		0			0
$658$	−22.6991	−	10.4268i	−0.884903	−	0.406481i
$659$	3.97856			0.154983			0.0774913	−	0.996993i	$-0.475309\pi$
$659$	3.97856			0.154983			0.0774913	+	0.996993i	$0.475309\pi$
$660$		0			0
$661$	−9.08125	−	15.7292i	−0.353220	−	0.611794i	0.633592	−	0.773667i	$-0.281580\pi$
$661$	−9.08125	−	15.7292i	−0.353220	−	0.611794i	−0.986812	+	0.161873i	$0.948246\pi$
$662$	0.543138	−	5.16761i	0.0211096	−	0.200845i
$663$		0			0
$664$	−1.00628	−	3.09700i	−0.0390511	−	0.120187i
$665$	37.5508	−	40.7337i	1.45616	−	1.57959i
$666$		0			0
$667$	2.67640	+	0.568886i	0.103631	+	0.0220274i
$668$	−6.38059	+	1.35624i	−0.246872	+	0.0524744i
$669$		0			0
$670$	−6.03488	+	10.4527i	−0.233148	+	0.403824i
$671$	17.3390	−	18.1072i	0.669365	−	0.699021i
$672$		0			0
$673$	−8.98748	−	6.52978i	−0.346442	−	0.251705i	0.400933	−	0.916107i	$-0.368686\pi$
$673$	−8.98748	−	6.52978i	−0.346442	−	0.251705i	−0.747375	+	0.664403i	$0.768686\pi$
$674$	33.3342	+	37.0214i	1.28399	+	1.42601i
$675$		0			0
$676$	−4.06013	−	1.80769i	−0.156159	−	0.0695265i
$677$	2.15837	+	20.5355i	0.0829529	+	0.789244i	0.954355	+	0.298675i	$0.0965446\pi$
$677$	2.15837	+	20.5355i	0.0829529	+	0.789244i	−0.871402	+	0.490570i	$0.836789\pi$
$678$		0			0
$679$	−7.89099	−	5.87571i	−0.302829	−	0.225489i
$680$	36.4533	+	26.4849i	1.39792	+	1.01565i
$681$		0			0
$682$	−12.7864	+	20.6558i	−0.489617	+	0.790951i
$683$	−11.4215	−	19.7826i	−0.437032	−	0.756961i	0.560427	−	0.828204i	$-0.310637\pi$
$683$	−11.4215	−	19.7826i	−0.437032	−	0.756961i	−0.997459	+	0.0712425i	$0.977304\pi$
$684$		0			0
$685$	19.9764	−	61.4812i	0.763261	−	2.34907i
$686$	−27.0641	+	10.9263i	−1.03331	+	0.417167i
$687$		0			0
$688$	1.89523	+	18.0319i	0.0722550	+	0.687461i
$689$	−12.6703	+	14.0718i	−0.482701	+	0.536094i
$690$		0			0
$691$	16.2753	−	7.24623i	0.619142	−	0.275660i	−0.0731008	−	0.997325i	$-0.523289\pi$
$691$	16.2753	−	7.24623i	0.619142	−	0.275660i	0.692243	+	0.721665i	$0.256623\pi$
$692$	−0.245472			−0.00933143
$693$		0			0
$694$	52.8949			2.00786
$695$	68.0208	−	30.2848i	2.58018	−	1.14877i
$696$		0			0
$697$	31.8204	−	35.3401i	1.20528	−	1.33860i
$698$	−1.80528	−	17.1761i	−0.0683310	−	0.650126i
$699$		0			0
$700$	7.97503	−	13.4466i	0.301428	−	0.508234i
$701$	−11.2347	+	34.5768i	−0.424328	+	1.30595i	0.479308	+	0.877647i	$0.340888\pi$
$701$	−11.2347	+	34.5768i	−0.424328	+	1.30595i	−0.903636	+	0.428301i	$0.859112\pi$
$702$		0			0
$703$	−8.04652	−	13.9370i	−0.303480	−	0.525643i
$704$	1.28631	+	17.3441i	0.0484796	+	0.653681i
$705$		0			0
$706$	−38.5745	−	28.0260i	−1.45177	−	1.05477i
$707$	3.52840	−	30.1644i	0.132699	−	1.13445i
$708$		0			0
$709$	2.05233	+	19.5266i	0.0770770	+	0.733338i	0.962999	+	0.269504i	$0.0868599\pi$
$709$	2.05233	+	19.5266i	0.0770770	+	0.733338i	−0.885922	+	0.463834i	$0.846473\pi$
$710$	24.6239	+	10.9633i	0.924118	+	0.411444i
$711$		0			0
$712$	24.9429	+	27.7019i	0.934774	+	1.03817i
$713$	3.72574	+	2.70691i	0.139530	+	0.101375i
$714$		0			0
$715$	26.4309	−	4.77544i	0.988459	−	0.178591i
$716$	−3.72237	+	6.44733i	−0.139112	+	0.240948i
$717$		0			0
$718$	31.1789	−	6.62727i	1.16359	−	0.247328i
$719$	28.1362	+	5.98053i	1.04930	+	0.223036i	0.700125	−	0.714021i	$-0.253128\pi$
$719$	28.1362	+	5.98053i	1.04930	+	0.223036i	0.349178	+	0.937057i	$0.386461\pi$
$720$		0			0
$721$	15.4146	+	3.46582i	0.574068	+	0.129074i
$722$	3.14677	+	9.68475i	0.117111	+	0.360429i
$723$		0			0
$724$	1.18359	−	11.2611i	0.0439878	−	0.418515i
$725$	16.8738	+	29.2263i	0.626678	+	1.08544i
$726$		0			0
$727$	37.1335			1.37721			0.688603	−	0.725139i	$-0.258224\pi$
$727$	37.1335			1.37721			0.688603	+	0.725139i	$0.258224\pi$
$728$	−10.0669	+	7.13522i	−0.373104	+	0.264449i
$729$		0			0
$730$	30.1415	+	6.40676i	1.11559	+	0.237125i
$731$	15.8994	+	7.07887i	0.588061	+	0.261821i
$732$		0			0
$733$	−27.5778	−	5.86183i	−1.01861	−	0.216512i	−0.331799	−	0.943350i	$-0.607656\pi$
$733$	−27.5778	−	5.86183i	−1.01861	−	0.216512i	−0.686809	+	0.726838i	$0.740989\pi$
$734$	1.14821	−	3.53383i	0.0423812	−	0.130436i
$735$		0			0
$736$	−2.65496			−0.0978631
$737$	−2.06930	+	5.76080i	−0.0762236	+	0.212202i
$738$		0			0
$739$	0.853356	−	8.11914i	0.0313912	−	0.298667i	−0.967551	−	0.252677i	$-0.918689\pi$
$739$	0.853356	−	8.11914i	0.0313912	−	0.298667i	0.998942	−	0.0459904i	$-0.0146443\pi$
$740$	−4.28198	−	4.75562i	−0.157409	−	0.174820i
$741$		0			0
$742$	12.0500	+	38.6210i	0.442370	+	1.41782i
$743$	−19.2134	+	13.9593i	−0.704871	+	0.512119i	−0.881515	−	0.472156i	$-0.843476\pi$
$743$	−19.2134	+	13.9593i	−0.704871	+	0.512119i	0.176644	+	0.984275i	$0.443476\pi$
$744$		0			0
$745$	15.7983	−	3.35803i	0.578805	−	0.123029i
$746$	2.65406	−	25.2517i	0.0971720	−	0.924530i
$747$		0			0
$748$	−6.56205	−	3.16636i	−0.239932	−	0.115773i
$749$	−6.67181	−	7.58681i	−0.243783	−	0.277216i
$750$		0			0
$751$	−28.9990	−	32.2067i	−1.05819	−	1.17524i	−0.984032	−	0.177992i	$-0.943040\pi$
$751$	−28.9990	−	32.2067i	−1.05819	−	1.17524i	−0.0741578	−	0.997247i	$-0.523627\pi$
$752$	−18.9744	+	21.0732i	−0.691926	+	0.768462i
$753$		0			0
$754$	0.887720	+	8.44610i	0.0323289	+	0.307589i
$755$	2.08273	+	6.40998i	0.0757983	+	0.233283i
$756$		0			0
$757$	23.5693	+	17.1241i	0.856643	+	0.622387i	0.926969	−	0.375137i	$-0.122404\pi$
$757$	23.5693	+	17.1241i	0.856643	+	0.622387i	−0.0703269	+	0.997524i	$0.522404\pi$
$758$	−21.8196	+	37.7927i	−0.792524	+	1.37269i
$759$		0			0
$760$	−25.0214	−	43.3383i	−0.907621	−	1.57205i
$761$	22.6054	−	10.0646i	0.819446	−	0.364841i	0.0461883	−	0.998933i	$-0.485293\pi$
$761$	22.6054	−	10.0646i	0.819446	−	0.364841i	0.773258	+	0.634092i	$0.218626\pi$
$762$		0			0
$763$	6.53792	+	11.6370i	0.236689	+	0.421287i
$764$	−9.19883	+	6.68334i	−0.332802	+	0.241795i
$765$		0			0
$766$	−16.0465	+	17.8214i	−0.579783	+	0.643914i
$767$	−12.5458	+	2.66670i	−0.453004	+	0.0962890i
$768$		0			0
$769$	−38.7769			−1.39833			−0.699165	−	0.714960i	$-0.746445\pi$
$769$	−38.7769			−1.39833			−0.699165	+	0.714960i	$0.746445\pi$
$770$	20.0315	−	53.7763i	0.721884	−	1.93796i
$771$		0			0
$772$	9.56316	−	4.25779i	0.344186	−	0.153241i
$773$	13.6281	−	2.89674i	0.490169	−	0.104189i	0.0438049	−	0.999040i	$-0.486052\pi$
$773$	13.6281	−	2.89674i	0.490169	−	0.104189i	0.446364	+	0.894852i	$0.352719\pi$
$774$		0			0
$775$	5.93726	+	56.4893i	0.213273	+	2.02915i
$776$	−7.18950	+	5.22348i	−0.258088	+	0.187512i
$777$		0			0
$778$	2.82858	−	8.70547i	0.101409	−	0.312106i
$779$	−48.2488	+	21.4818i	−1.72869	+	0.769664i
$780$		0			0
$781$	13.2776	+	3.25109i	0.475109	+	0.116333i
$782$	−3.54722	+	6.14397i	−0.126848	+	0.219708i
$783$		0			0
$784$	2.68982	+	33.0234i	0.0960649	+	1.17941i
$785$	−10.6299	−	32.7156i	−0.379398	−	1.16767i
$786$		0			0
$787$	24.4386	+	10.8807i	0.871140	+	0.387857i	0.793099	−	0.609093i	$-0.208467\pi$
$787$	24.4386	+	10.8807i	0.871140	+	0.387857i	0.0780419	+	0.996950i	$0.475133\pi$
$788$	4.92060	−	5.46488i	0.175289	−	0.194678i
$789$		0			0
$790$	6.86281	+	4.98613i	0.244168	+	0.177398i
$791$	−13.0442	+	38.6002i	−0.463799	+	1.37247i
$792$		0			0
$793$	7.37555	−	12.7748i	0.261914	−	0.453648i
$794$	3.46449	−	32.9624i	0.122950	−	1.16979i
$795$		0			0
$796$	−6.24741	−	1.32793i	−0.221433	−	0.0470671i
$797$	−11.9802	+	8.70412i	−0.424360	+	0.308316i	−0.779390	−	0.626539i	$-0.784471\pi$
$797$	−11.9802	+	8.70412i	−0.424360	+	0.308316i	0.355029	+	0.934855i	$0.384471\pi$
$798$		0			0
$799$	8.41129	+	25.8873i	0.297570	+	0.915827i
$800$	−21.9112	−	24.3348i	−0.774676	−	0.860365i
$801$		0			0
$802$	−0.251827	−	0.436177i	−0.00889231	−	0.0154019i
$803$	15.6204	+	0.479558i	0.551231	+	0.0169232i
$804$		0			0
$805$	−9.88566	−	4.54098i	−0.348424	−	0.160049i
$806$	−4.41705	+	13.5943i	−0.155584	+	0.478838i
$807$		0			0
$808$	−25.0609	−	11.1578i	−0.881640	−	0.392531i
$809$	3.75781	+	1.67309i	0.132118	+	0.0588226i	0.471731	−	0.881743i	$-0.343629\pi$
$809$	3.75781	+	1.67309i	0.132118	+	0.0588226i	−0.339613	+	0.940565i	$0.610296\pi$
$810$		0			0
$811$	8.54601	−	26.3019i	0.300091	−	0.923585i	−0.681373	−	0.731936i	$-0.738617\pi$
$811$	8.54601	−	26.3019i	0.300091	−	0.923585i	0.981464	−	0.191648i	$-0.0613832\pi$
$812$	3.21021	+	1.47461i	0.112656	+	0.0517487i
$813$		0			0
$814$	−13.1789	−	10.2073i	−0.461922	−	0.357767i
$815$	5.34423	+	9.25648i	0.187200	+	0.324241i
$816$		0			0
$817$	−12.9337	−	14.3643i	−0.452493	−	0.502545i
$818$	−4.77093	−	14.6834i	−0.166812	−	0.513393i
$819$		0			0
$820$	−16.9906	+	12.3444i	−0.593339	+	0.431086i
$821$	22.0625	+	4.68954i	0.769988	+	0.163666i	0.576124	−	0.817362i	$-0.304565\pi$
$821$	22.0625	+	4.68954i	0.769988	+	0.163666i	0.193864	+	0.981028i	$0.437898\pi$
$822$		0			0
$823$	−4.73887	+	45.0873i	−0.165187	+	1.57164i	0.526962	+	0.849889i	$0.323331\pi$
$823$	−4.73887	+	45.0873i	−0.165187	+	1.57164i	−0.692148	+	0.721756i	$0.743335\pi$
$824$	7.13562	−	12.3593i	0.248581	−	0.430555i
$825$		0			0
$826$	−8.77327	+	25.9617i	−0.305261	+	0.903323i
$827$	−22.1062	−	16.0611i	−0.768708	−	0.558499i	0.132861	−	0.991135i	$-0.457584\pi$
$827$	−22.1062	−	16.0611i	−0.768708	−	0.558499i	−0.901569	+	0.432636i	$0.857584\pi$
$828$		0			0
$829$	−14.6719	+	16.2948i	−0.509576	+	0.565942i	−0.941950	−	0.335753i	$-0.891009\pi$
$829$	−14.6719	+	16.2948i	−0.509576	+	0.565942i	0.432374	+	0.901694i	$0.357676\pi$
$830$	8.14057	+	3.62441i	0.282563	+	0.125805i
$831$		0			0
$832$	3.16223	+	9.73234i	0.109631	+	0.337408i
$833$	28.7430	+	13.6134i	0.995887	+	0.471677i
$834$		0			0
$835$	−27.9924	+	48.4842i	−0.968717	+	1.67787i
$836$	5.22749	+	6.17681i	0.180797	+	0.213630i
$837$		0			0
$838$	35.2426	−	15.6910i	1.21744	−	0.542037i
$839$	−6.51321	+	20.0456i	−0.224861	+	0.692051i	0.773445	+	0.633864i	$0.218532\pi$
$839$	−6.51321	+	20.0456i	−0.224861	+	0.692051i	−0.998306	+	0.0581871i	$0.981468\pi$
$840$		0			0
$841$	17.2921	−	12.5634i	0.596278	−	0.433221i
$842$	1.17022	+	11.1339i	0.0403284	+	0.383699i
$843$		0			0
$844$	5.74632	−	1.22142i	0.197796	−	0.0420429i
$845$	−34.8461	+	15.5145i	−1.19874	+	0.533714i
$846$		0			0
$847$	5.14808	−	28.6443i	0.176890	−	0.984231i
$848$	45.9274			1.57715
$849$		0			0
$850$	−85.5893	+	18.1926i	−2.93569	+	0.624000i
$851$	−2.11450	+	2.34839i	−0.0724842	+	0.0805018i
$852$		0			0
$853$	−6.49921	+	4.72195i	−0.222529	+	0.161677i	−0.693464	−	0.720491i	$-0.743916\pi$
$853$	−6.49921	+	4.72195i	−0.222529	+	0.161677i	0.470935	+	0.882168i	$0.343916\pi$
$854$	−15.4374	−	27.4773i	−0.528256	−	0.940253i
$855$		0			0
$856$	−8.33694	+	3.71185i	−0.284951	+	0.126868i
$857$	−1.46402	−	2.53576i	−0.0500099	−	0.0866198i	0.839937	−	0.542684i	$-0.182592\pi$
$857$	−1.46402	−	2.53576i	−0.0500099	−	0.0866198i	−0.889947	+	0.456064i	$0.849259\pi$
$858$		0			0
$859$	−12.8540	+	22.2638i	−0.438572	+	0.759629i	−0.997580	−	0.0695333i	$-0.977849\pi$
$859$	−12.8540	+	22.2638i	−0.438572	+	0.759629i	0.559007	+	0.829163i	$0.311182\pi$
$860$	−6.21822	−	4.51780i	−0.212039	−	0.154056i
$861$		0			0
$862$	3.73793	+	11.5042i	0.127314	+	0.391834i
$863$	0.163461	+	1.55523i	0.00556427	+	0.0529405i	0.996952	−	0.0780212i	$-0.0248602\pi$
$863$	0.163461	+	1.55523i	0.00556427	+	0.0529405i	−0.991387	+	0.130962i	$0.958194\pi$
$864$		0			0
$865$	−1.40970	+	1.56563i	−0.0479311	+	0.0532329i
$866$	3.63948	+	4.04205i	0.123675	+	0.137355i
$867$		0			0
$868$	3.92648	+	4.46497i	0.133273	+	0.151551i
$869$	3.87462	+	1.86960i	0.131437	+	0.0634219i
$870$		0			0
$871$	−0.376476	+	3.58193i	−0.0127564	+	0.121369i
$872$	11.7933	−	2.50675i	0.399372	−	0.0848891i
$873$		0			0
$874$	6.37438	−	4.63126i	0.215617	−	0.156655i
$875$	−23.6131	−	75.6812i	−0.798267	−	2.55849i
$876$		0			0
$877$	36.3060	+	40.3219i	1.22597	+	1.36157i	0.910965	+	0.412483i	$0.135338\pi$
$877$	36.3060	+	40.3219i	1.22597	+	1.36157i	0.315001	+	0.949091i	$0.397995\pi$
$878$	−5.19072	+	49.3864i	−0.175178	+	1.66671i
$879$		0			0
$880$	−51.5037	−	39.8906i	−1.73619	−	1.34471i
$881$	−44.2360			−1.49035			−0.745174	−	0.666870i	$-0.767634\pi$
$881$	−44.2360			−1.49035			−0.745174	+	0.666870i	$0.767634\pi$
$882$		0			0
$883$	11.4908	−	35.3652i	0.386698	−	1.19013i	−0.548543	−	0.836122i	$-0.684817\pi$
$883$	11.4908	−	35.3652i	0.386698	−	1.19013i	0.935241	−	0.354011i	$-0.115183\pi$
$884$	−4.19337	−	0.891329i	−0.141038	−	0.0299786i
$885$		0			0
$886$	14.0520	+	6.25636i	0.472087	+	0.210187i
$887$	−13.0342	−	2.77051i	−0.437646	−	0.0930245i	−0.0161806	−	0.999869i	$-0.505151\pi$
$887$	−13.0342	−	2.77051i	−0.437646	−	0.0930245i	−0.421465	+	0.906845i	$0.638484\pi$
$888$		0			0
$889$	33.8509	−	23.9929i	1.13532	−	0.804695i
$890$	−102.006			−3.41925
$891$		0			0
$892$	2.34960	+	4.06963i	0.0786705	+	0.136261i
$893$	3.15993	−	30.0647i	0.105743	−	1.00608i
$894$		0			0
$895$	19.7445	+	60.7672i	0.659985	+	2.03122i
$896$	35.1647	+	7.90647i	1.17477	+	0.264137i
$897$		0			0
$898$	25.6628	+	5.45479i	0.856378	+	0.182029i
$899$	−12.5545	+	2.66855i	−0.418717	+	0.0890011i
$900$		0			0
$901$	22.0427	−	38.1791i	0.734349	−	1.27193i
$902$	−37.8364	+	39.5127i	−1.25982	+	1.31563i
$903$		0			0
$904$	29.7749	+	21.6327i	0.990299	+	0.719494i
$905$	−65.0266	−	72.2193i	−2.16156	−	2.40065i
$906$		0			0
$907$	1.36948	+	0.609732i	0.0454728	+	0.0202458i	0.429347	−	0.903140i	$-0.358744\pi$
$907$	1.36948	+	0.609732i	0.0454728	+	0.0202458i	−0.383874	+	0.923385i	$0.625410\pi$
$908$	−0.989991	−	9.41914i	−0.0328540	−	0.312585i
$909$		0			0
$910$	3.92289	−	33.5369i	0.130043	−	1.11174i
$911$	16.7328	+	12.1571i	0.554384	+	0.402784i	0.829399	−	0.558656i	$-0.188683\pi$
$911$	16.7328	+	12.1571i	0.554384	+	0.402784i	−0.275015	+	0.961440i	$0.588683\pi$
$912$		0			0
$913$	4.38952	+	1.07480i	0.145272	+	0.0355706i
$914$	10.0407	+	17.3909i	0.332115	+	0.575241i
$915$		0			0
$916$	−0.486097	+	1.49605i	−0.0160611	+	0.0494310i
$917$	−14.5543	+	24.5397i	−0.480624	+	0.810374i
$918$		0			0
$919$	−1.22941	−	11.6970i	−0.0405544	−	0.385849i	−0.995907	−	0.0903817i	$-0.971191\pi$
$919$	−1.22941	−	11.6970i	−0.0405544	−	0.385849i	0.955353	−	0.295467i	$-0.0954754\pi$
$920$	−6.57523	+	7.30253i	−0.216779	+	0.240757i
$921$		0			0
$922$	−7.50921	+	3.34332i	−0.247303	+	0.110106i
$923$	8.04323			0.264746
$924$		0			0
$925$	−38.9757			−1.28151
$926$	−15.3399	+	6.82976i	−0.504100	+	0.224440i
$927$		0			0
$928$	4.95119	−	5.49886i	0.162531	−	0.180509i
$929$	2.94637	+	28.0329i	0.0966673	+	0.919728i	0.930149	+	0.367182i	$0.119677\pi$
$929$	2.94637	+	28.0329i	0.0966673	+	0.919728i	−0.833482	+	0.552547i	$0.813656\pi$
$930$		0			0
$931$	−23.0129	−	26.7961i	−0.754219	−	0.878206i
$932$	−4.25832	+	13.1058i	−0.139486	+	0.429294i
$933$		0			0
$934$	−23.3929	−	40.5177i	−0.765440	−	1.32578i
$935$	−57.8797	+	23.6692i	−1.89287	+	0.774067i
$936$		0			0
$937$	21.6468	+	15.7273i	0.707170	+	0.513789i	0.882259	−	0.470763i	$-0.156021\pi$
$937$	21.6468	+	15.7273i	0.707170	+	0.513789i	−0.175090	+	0.984553i	$0.556021\pi$
$938$	6.17211	+	4.59581i	0.201527	+	0.150059i
$939$		0			0
$940$	−1.25653	−	11.9551i	−0.0409835	−	0.389932i
$941$	15.7183	+	6.99822i	0.512401	+	0.228136i	0.646615	−	0.762817i	$-0.276184\pi$
$941$	15.7183	+	6.99822i	0.512401	+	0.228136i	−0.134214	+	0.990952i	$0.542851\pi$
$942$		0			0
$943$	6.93947	+	7.70706i	0.225980	+	0.250976i
$944$	25.1680	+	18.2856i	0.819148	+	0.595146i
$945$		0			0
$946$	−18.0321	−	8.70095i	−0.586275	−	0.282892i
$947$	19.2943	−	33.4187i	0.626980	−	1.08596i	−0.361174	−	0.932498i	$-0.617624\pi$
$947$	19.2943	−	33.4187i	0.626980	−	1.08596i	0.988154	−	0.153463i	$-0.0490427\pi$
$948$		0			0
$949$	8.99431	−	1.91180i	0.291968	−	0.0620597i
$950$	95.0564	+	20.2049i	3.08404	+	0.655532i
$951$		0			0
$952$	19.4716	−	21.1221i	0.631078	−	0.684570i
$953$	6.61448	+	20.3573i	0.214264	+	0.659437i	0.999205	+	0.0398663i	$0.0126932\pi$
$953$	6.61448	+	20.3573i	0.214264	+	0.659437i	−0.784941	+	0.619571i	$0.787307\pi$
$954$		0			0
$955$	−10.2005	+	97.0516i	−0.330082	+	3.14052i
$956$	0.394219	+	0.682807i	0.0127500	+	0.0220836i
$957$		0			0
$958$	34.8016			1.12439
$959$	−37.4529	−	17.2040i	−1.20942	−	0.555547i
$960$		0			0
$961$	9.19210	+	1.95384i	0.296519	+	0.0630271i
$962$	−8.96029	−	3.98938i	−0.288891	−	0.128623i
$963$		0			0
$964$	−2.58242	−	0.548911i	−0.0831743	−	0.0176792i
$965$	27.7630	−	85.4458i	0.893724	−	2.75060i
$966$		0			0
$967$	−54.9040			−1.76559			−0.882796	−	0.469756i	$-0.844342\pi$
$967$	−54.9040			−1.76559			−0.882796	+	0.469756i	$0.844342\pi$
$968$	−23.3145	−	12.1455i	−0.749355	−	0.390372i
$969$		0			0
$970$	2.54194	−	24.1849i	0.0816167	−	0.776531i
$971$	−35.0096	−	38.8821i	−1.12351	−	1.24779i	−0.965515	−	0.260347i	$-0.916163\pi$
$971$	−35.0096	−	38.8821i	−1.12351	−	1.24779i	−0.157997	−	0.987440i	$-0.550504\pi$
$972$		0			0
$973$	−14.1392	−	45.3171i	−0.453283	−	1.45280i
$974$	41.3533	−	30.0450i	1.32505	−	0.962703i
$975$		0			0
$976$	−34.9965	+	7.43873i	−1.12021	+	0.238108i
$977$	6.44842	−	61.3526i	0.206303	−	1.96284i	−0.0577332	−	0.998332i	$-0.518387\pi$
$977$	6.44842	−	61.3526i	0.206303	−	1.96284i	0.264036	−	0.964513i	$-0.414946\pi$
$978$		0			0
$979$	−50.9080	+	9.19789i	−1.62703	+	0.293966i
$980$	−11.1664	−	8.51989i	−0.356697	−	0.272158i
$981$		0			0
$982$	5.62476	+	6.24693i	0.179493	+	0.199348i
$983$	−6.94838	+	7.71695i	−0.221619	+	0.246133i	−0.843693	−	0.536825i	$-0.819623\pi$
$983$	−6.94838	+	7.71695i	−0.221619	+	0.246133i	0.622075	+	0.782958i	$0.286290\pi$
$984$		0			0
$985$	−6.59714	−	62.7676i	−0.210202	−	1.99994i
$986$	−6.11001	−	18.8047i	−0.194582	−	0.598863i
$987$		0			0
$988$	3.85193	+	2.79859i	0.122546	+	0.0890351i
$989$	−1.89776	+	3.28702i	−0.0603453	+	0.104521i
$990$		0			0
$991$	−21.8063	−	37.7696i	−0.692699	−	1.19979i	−0.970950	−	0.239282i	$-0.923088\pi$
$991$	−21.8063	−	37.7696i	−0.692699	−	1.19979i	0.278251	−	0.960508i	$-0.410245\pi$
$992$	11.3773	−	5.06548i	0.361228	−	0.160829i
$993$		0			0
$994$	8.76638	−	14.7809i	0.278053	−	0.468821i
$995$	−44.3472	+	32.2201i	−1.40590	+	1.02145i
$996$		0			0
$997$	18.4452	−	20.4855i	0.584165	−	0.648781i	−0.376524	−	0.926407i	$-0.622881\pi$
$997$	18.4452	−	20.4855i	0.584165	−	0.648781i	0.960689	+	0.277626i	$0.0895475\pi$
$998$	57.5443	−	12.2314i	1.82153	−	0.387179i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.by.c.37.7		64
3.2	odd	2		231.2.y.b.37.2	yes	64
7.4	even	3	inner	693.2.by.c.235.2		64
11.3	even	5	inner	693.2.by.c.289.2		64
21.11	odd	6		231.2.y.b.4.7	✓	64
33.14	odd	10		231.2.y.b.58.7	yes	64
77.25	even	15	inner	693.2.by.c.487.7		64
231.179	odd	30		231.2.y.b.25.2	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.y.b.4.7	✓	64	21.11	odd	6
231.2.y.b.25.2	yes	64	231.179	odd	30
231.2.y.b.37.2	yes	64	3.2	odd	2
231.2.y.b.58.7	yes	64	33.14	odd	10
693.2.by.c.37.7		64	1.1	even	1	trivial
693.2.by.c.235.2		64	7.4	even	3	inner
693.2.by.c.289.2		64	11.3	even	5	inner
693.2.by.c.487.7		64	77.25	even	15	inner

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.by (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.43967 - 0.640984i) q^{2} +(0.323537 - 0.359324i) q^{4} +(-0.433772 - 4.12706i) q^{5} +(-2.64557 - 0.0310171i) q^{7} +(-0.738505 + 2.27288i) q^{8} +O(q^{10})\)	\(q+(1.43967 - 0.640984i) q^{2} +(0.323537 - 0.359324i) q^{4} +(-0.433772 - 4.12706i) q^{5} +(-2.64557 - 0.0310171i) q^{7} +(-0.738505 + 2.27288i) q^{8} +(-3.26987 - 5.66358i) q^{10} +(-2.14258 - 2.53167i) q^{11} +(-1.57878 - 1.14705i) q^{13} +(-3.82864 + 1.65111i) q^{14} +(0.494759 + 4.70732i) q^{16} +(4.15061 + 1.84797i) q^{17} +(-3.37641 - 3.74988i) q^{19} +(-1.62329 - 1.17939i) q^{20} +(-4.70737 - 2.27142i) q^{22} +(-0.495419 + 0.858091i) q^{23} +(-11.9537 + 2.54085i) q^{25} +(-3.00817 - 0.639406i) q^{26} +(-0.867085 + 0.940582i) q^{28} +(-0.853348 - 2.62634i) q^{29} +(0.485833 - 4.62239i) q^{31} +(1.33975 + 2.32052i) q^{32} +7.16004 q^{34} +(1.01956 + 10.9319i) q^{35} +(3.11960 + 0.663091i) q^{37} +(-7.26453 - 3.23438i) q^{38} +(9.70067 + 2.06194i) q^{40} +(3.23441 - 9.95449i) q^{41} +3.83062 q^{43} +(-1.60289 - 0.0492102i) q^{44} +(-0.163219 + 1.55293i) q^{46} +(4.00875 + 4.45217i) q^{47} +(6.99808 + 0.164116i) q^{49} +(-15.5808 + 11.3201i) q^{50} +(-0.922957 + 0.196181i) q^{52} +(1.01426 - 9.65000i) q^{53} +(-9.51898 + 9.94071i) q^{55} +(2.02426 - 5.99016i) q^{56} +(-2.91198 - 3.23408i) q^{58} +(4.39787 - 4.88433i) q^{59} +(0.790124 + 7.51753i) q^{61} +(-2.26344 - 6.96614i) q^{62} +(-4.24233 - 3.08223i) q^{64} +(-4.04912 + 7.01328i) q^{65} +(-0.922802 - 1.59834i) q^{67} +(2.00690 - 0.893529i) q^{68} +(8.47500 + 15.0848i) q^{70} +(-3.33445 + 2.42262i) q^{71} +(-3.15290 + 3.50165i) q^{73} +(4.91623 - 1.04498i) q^{74} -2.43982 q^{76} +(5.58981 + 6.76417i) q^{77} +(-1.18499 + 0.527591i) q^{79} +(19.2128 - 4.08380i) q^{80} +(-1.72417 - 16.4044i) q^{82} +(-1.10236 + 0.800908i) q^{83} +(5.82627 - 17.9314i) q^{85} +(5.51483 - 2.45536i) q^{86} +(7.33650 - 3.00017i) q^{88} +(7.79893 - 13.5081i) q^{89} +(4.14119 + 3.08357i) q^{91} +(0.148047 + 0.455640i) q^{92} +(8.62506 + 3.84013i) q^{94} +(-14.0114 + 15.5612i) q^{95} +(3.00835 + 2.18569i) q^{97} +(10.1801 - 4.24938i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{2} + 10 q^{4} + 4 q^{5} - q^{7} - 8 q^{8}+O(q^{10}) \) 64 * q - 4 * q^2 + 10 * q^4 + 4 * q^5 - q^7 - 8 * q^8	\( 64 q - 4 q^{2} + 10 q^{4} + 4 q^{5} - q^{7} - 8 q^{8} - 14 q^{10} - 11 q^{11} - 8 q^{13} - 6 q^{14} + 4 q^{17} - 2 q^{19} - 24 q^{20} - 14 q^{22} - 10 q^{25} - 4 q^{26} + 29 q^{28} + 58 q^{29} - 19 q^{31} + 64 q^{32} - 88 q^{34} - 17 q^{35} - 20 q^{37} - 29 q^{38} + 51 q^{40} + 68 q^{41} + 92 q^{43} + 21 q^{44} - 5 q^{46} + 26 q^{47} + 37 q^{49} + 10 q^{50} - 14 q^{52} + 3 q^{53} - 32 q^{55} - 24 q^{56} + 52 q^{58} - 7 q^{59} - 21 q^{61} - 92 q^{62} - 72 q^{64} + 66 q^{65} - 4 q^{67} + 17 q^{68} - q^{70} - 58 q^{71} - 3 q^{73} + 28 q^{74} + 168 q^{76} + 34 q^{77} + 9 q^{79} + 5 q^{80} - 42 q^{82} - 60 q^{83} + 110 q^{85} - 13 q^{86} + 92 q^{88} + 10 q^{89} + 10 q^{91} - 110 q^{92} - 46 q^{94} - 43 q^{95} + 64 q^{97} + 88 q^{98}+O(q^{100}) \) 64 * q - 4 * q^2 + 10 * q^4 + 4 * q^5 - q^7 - 8 * q^8 - 14 * q^10 - 11 * q^11 - 8 * q^13 - 6 * q^14 + 4 * q^17 - 2 * q^19 - 24 * q^20 - 14 * q^22 - 10 * q^25 - 4 * q^26 + 29 * q^28 + 58 * q^29 - 19 * q^31 + 64 * q^32 - 88 * q^34 - 17 * q^35 - 20 * q^37 - 29 * q^38 + 51 * q^40 + 68 * q^41 + 92 * q^43 + 21 * q^44 - 5 * q^46 + 26 * q^47 + 37 * q^49 + 10 * q^50 - 14 * q^52 + 3 * q^53 - 32 * q^55 - 24 * q^56 + 52 * q^58 - 7 * q^59 - 21 * q^61 - 92 * q^62 - 72 * q^64 + 66 * q^65 - 4 * q^67 + 17 * q^68 - q^70 - 58 * q^71 - 3 * q^73 + 28 * q^74 + 168 * q^76 + 34 * q^77 + 9 * q^79 + 5 * q^80 - 42 * q^82 - 60 * q^83 + 110 * q^85 - 13 * q^86 + 92 * q^88 + 10 * q^89 + 10 * q^91 - 110 * q^92 - 46 * q^94 - 43 * q^95 + 64 * q^97 + 88 * q^98

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